[ { "file_name": "FStar.Int16.fsti", "name": "FStar.Int16.ct_abs", "opens_and_abbrevs": [ { "open": "FStar.Mul" }, { "open": "FStar.Int" }, { "open": "FStar" }, { "open": "FStar" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 0, "initial_ifuel": 1, "max_ifuel": 0, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val ct_abs (a: t{min_int n < v a}) : Tot (b: t{v b = abs (v a)})", "source_definition": "let ct_abs (a:t{min_int n < v a}) : Tot (b:t{v b = abs (v a)}) =\n let mask = a >>>^ UInt32.uint_to_t (n - 1) in\n if 0 <= v a then\n begin\n sign_bit_positive (v a);\n nth_lemma (v mask) (FStar.Int.zero _);\n logxor_lemma_1 (v a)\n end\n else\n begin\n sign_bit_negative (v a);\n nth_lemma (v mask) (ones _);\n logxor_lemma_2 (v a);\n lognot_negative (v a);\n UInt.lemma_lognot_value #n (to_uint (v a))\n end;\n (a ^^ mask) -^ mask", "source_range": { "start_line": 139, "start_col": 0, "end_line": 155, "end_col": 21 }, "interleaved": false, "definition": "fun a ->\n (let mask = a >>>^ FStar.UInt32.uint_to_t (FStar.Int16.n - 1) in\n (match 0 <= FStar.Int16.v a with\n | true ->\n FStar.Int.sign_bit_positive (FStar.Int16.v a);\n FStar.Int.nth_lemma (FStar.Int16.v mask) (FStar.Int.zero FStar.Int16.n);\n FStar.Int.logxor_lemma_1 (FStar.Int16.v a)\n | _ ->\n FStar.Int.sign_bit_negative (FStar.Int16.v a);\n FStar.Int.nth_lemma (FStar.Int16.v mask) (FStar.Int.ones FStar.Int16.n);\n FStar.Int.logxor_lemma_2 (FStar.Int16.v a);\n FStar.Int.lognot_negative (FStar.Int16.v a);\n FStar.UInt.lemma_lognot_value (FStar.Int.to_uint (FStar.Int16.v a)))\n <:\n Prims.unit;\n (a ^^ mask) -^ mask)\n <:\n b: FStar.Int16.t{FStar.Int16.v b = Prims.abs (FStar.Int16.v a)}", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Int16.t", "Prims.b2t", "Prims.op_LessThan", "FStar.Int.min_int", "FStar.Int16.n", "FStar.Int16.v", "FStar.Int16.op_Subtraction_Hat", "FStar.Int16.op_Hat_Hat", "Prims.unit", "Prims.op_LessThanOrEqual", "FStar.Int.logxor_lemma_1", "FStar.Int.nth_lemma", "FStar.Int.zero", "FStar.Int.sign_bit_positive", "Prims.bool", "FStar.UInt.lemma_lognot_value", "FStar.Int.to_uint", "FStar.Int.lognot_negative", "FStar.Int.logxor_lemma_2", "FStar.Int.ones", "FStar.Int.sign_bit_negative", "FStar.Int16.op_Greater_Greater_Greater_Hat", "FStar.UInt32.uint_to_t", "Prims.op_Subtraction", "Prims.op_Equality", "Prims.int", "Prims.abs" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "a: FStar.Int16.t{FStar.Int.min_int FStar.Int16.n < FStar.Int16.v a}\n -> b: FStar.Int16.t{FStar.Int16.v b = Prims.abs (FStar.Int16.v a)}", "prompt": "let ct_abs (a: t{min_int n < v a}) : Tot (b: t{v b = abs (v a)}) =\n ", "expected_response": "let mask = a >>>^ UInt32.uint_to_t (n - 1) in\nif 0 <= v a\nthen\n (sign_bit_positive (v a);\n nth_lemma (v mask) (FStar.Int.zero _);\n logxor_lemma_1 (v a))\nelse\n (sign_bit_negative (v a);\n nth_lemma (v mask) (ones _);\n logxor_lemma_2 (v a);\n lognot_negative (v a);\n UInt.lemma_lognot_value #n (to_uint (v a)));\n(a ^^ mask) -^ mask", "source": { "project_name": "FStar", "file_name": "ulib/FStar.Int16.fsti", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.Int16.fsti", "checked_file": "dataset/FStar.Int16.fsti.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.UInt32.fsti.checked", "dataset/FStar.UInt.fsti.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked", "dataset/FStar.Int.fsti.checked" ] }, "definitions_in_context": [ "let n = 16", "val t : eqtype", "val v (x:t) : Tot (int_t n)", "val int_to_t: x:int_t n -> Pure t\n (requires True)\n (ensures (fun y -> v y = x))", "val uv_inv (x : t) : Lemma\n (ensures (int_to_t (v x) == x))\n [SMTPat (v x)]", "val vu_inv (x : int_t n) : Lemma\n (ensures (v (int_to_t x) == x))\n [SMTPat (int_to_t x)]", "val v_inj (x1 x2: t): Lemma\n (requires (v x1 == v x2))\n (ensures (x1 == x2))", "val zero : x:t{v x = 0}", "val one : x:t{v x = 1}", "val add (a:t) (b:t) : Pure t\n (requires (size (v a + v b) n))\n (ensures (fun c -> v a + v b = v c))", "val sub (a:t) (b:t) : Pure t\n (requires (size (v a - v b) n))\n (ensures (fun c -> v a - v b = v c))", "val mul (a:t) (b:t) : Pure t\n (requires (size (v a * v b) n))\n (ensures (fun c -> v a * v b = v c))", "val div (a:t) (b:t{v b <> 0}) : Pure t\n // division overflows on INT_MIN / -1\n (requires (size (v a / v b) n))\n (ensures (fun c -> v a / v b = v c))", "val rem (a:t) (b:t{v b <> 0}) : Pure t\n (requires (size (v a / v b) n))\n (ensures (fun c -> FStar.Int.mod (v a) (v b) = v c))", "val logand (x:t) (y:t) : Pure t\n (requires True)\n (ensures (fun z -> v x `logand` v y = v z))", "val logxor (x:t) (y:t) : Pure t\n (requires True)\n (ensures (fun z -> v x `logxor` v y == v z))", "val logor (x:t) (y:t) : Pure t\n (requires True)\n (ensures (fun z -> v x `logor` v y == v z))", "val lognot (x:t) : Pure t\n (requires True)\n (ensures (fun z -> lognot (v x) == v z))", "val shift_right (a:t) (s:UInt32.t) : Pure t\n (requires (0 <= v a /\\ UInt32.v s < n))\n (ensures (fun c -> FStar.Int.shift_right (v a) (UInt32.v s) = v c))", "val shift_left (a:t) (s:UInt32.t) : Pure t\n (requires (0 <= v a /\\ v a * pow2 (UInt32.v s) <= max_int n /\\ UInt32.v s < n))\n (ensures (fun c -> FStar.Int.shift_left (v a) (UInt32.v s) = v c))", "val shift_arithmetic_right (a:t) (s:UInt32.t) : Pure t\n (requires (UInt32.v s < n))\n (ensures (fun c -> FStar.Int.shift_arithmetic_right (v a) (UInt32.v s) = v c))", "let eq (a:t) (b:t) : Tot bool = eq #n (v a) (v b)", "let gt (a:t) (b:t) : Tot bool = gt #n (v a) (v b)", "let gte (a:t) (b:t) : Tot bool = gte #n (v a) (v b)", "let lt (a:t) (b:t) : Tot bool = lt #n (v a) (v b)", "let lte (a:t) (b:t) : Tot bool = lte #n (v a) (v b)", "let op_Plus_Hat = add", "let op_Subtraction_Hat = sub", "let op_Star_Hat = mul", "let op_Slash_Hat = div", "let op_Percent_Hat = rem", "let op_Hat_Hat = logxor", "let op_Amp_Hat = logand", "let op_Bar_Hat = logor", "let op_Less_Less_Hat = shift_left", "let op_Greater_Greater_Hat = shift_right", "let op_Greater_Greater_Greater_Hat = shift_arithmetic_right", "let op_Equals_Hat = eq", "let op_Greater_Hat = gt", "let op_Greater_Equals_Hat = gte", "let op_Less_Hat = lt", "let op_Less_Equals_Hat = lte" ], "closest": [ "val ct_abs (a: t{min_int n < v a}) : Tot (b: t{v b = abs (v a)})\nlet ct_abs (a:t{min_int n < v a}) : Tot (b:t{v b = abs (v a)}) =\n let mask = a >>>^ UInt32.uint_to_t (n - 1) in\n if 0 <= v a then\n begin\n sign_bit_positive (v a);\n nth_lemma (v mask) (FStar.Int.zero _);\n logxor_lemma_1 (v a)\n end\n else\n begin\n sign_bit_negative (v a);\n nth_lemma (v mask) (ones _);\n logxor_lemma_2 (v a);\n lognot_negative (v a);\n UInt.lemma_lognot_value #n (to_uint (v a))\n end;\n (a ^^ mask) -^ mask", "val ct_abs (a: t{min_int n < v a}) : Tot (b: t{v b = abs (v a)})\nlet ct_abs (a:t{min_int n < v a}) : Tot (b:t{v b = abs (v a)}) =\n let mask = a >>>^ UInt32.uint_to_t (n - 1) in\n if 0 <= v a then\n begin\n sign_bit_positive (v a);\n nth_lemma (v mask) (FStar.Int.zero _);\n logxor_lemma_1 (v a)\n end\n else\n begin\n sign_bit_negative (v a);\n nth_lemma (v mask) (ones _);\n logxor_lemma_2 (v a);\n lognot_negative (v a);\n UInt.lemma_lognot_value #n (to_uint (v a))\n end;\n (a ^^ mask) -^ mask", "val ct_abs (a: t{min_int n < v a}) : Tot (b: t{v b = abs (v a)})\nlet ct_abs (a:t{min_int n < v a}) : Tot (b:t{v b = abs (v a)}) =\n let mask = a >>>^ UInt32.uint_to_t (n - 1) in\n if 0 <= v a then\n begin\n sign_bit_positive (v a);\n nth_lemma (v mask) (FStar.Int.zero _);\n logxor_lemma_1 (v a)\n end\n else\n begin\n sign_bit_negative (v a);\n nth_lemma (v mask) (ones _);\n logxor_lemma_2 (v a);\n lognot_negative (v a);\n UInt.lemma_lognot_value #n (to_uint (v a))\n end;\n (a ^^ mask) -^ mask", "val ct_abs (a: t{min_int n < v a}) : Tot (b: t{v b = abs (v a)})\nlet ct_abs (a:t{min_int n < v a}) : Tot (b:t{v b = abs (v a)}) =\n let mask = a >>>^ UInt32.uint_to_t (n - 1) in\n if 0 <= v a then\n begin\n sign_bit_positive (v a);\n nth_lemma (v mask) (FStar.Int.zero _);\n logxor_lemma_1 (v a)\n end\n else\n begin\n sign_bit_negative (v a);\n nth_lemma (v mask) (ones _);\n logxor_lemma_2 (v a);\n lognot_negative (v a);\n UInt.lemma_lognot_value #n (to_uint (v a))\n end;\n (a ^^ mask) -^ mask", "val minus (#n: pos{1 < n}) (a: int_t n) : Tot (int_t n)\nlet minus (#n:pos{1 < n}) (a:int_t n) : Tot (int_t n) =\n add_mod (lognot a) 1", "val abs: x:int -> Tot (y:int{ (x >= 0 ==> y = x) /\\ (x < 0 ==> y = -x) })\nlet abs x = if x >= 0 then x else -x", "val bvand (#n: pos) (a b: bv_t n) : Tot (bv_t n)\nlet bvand = B.logand_vec", "val test_abs (n: int) : RWI nat RO (fun _ -> True) (fun h0 _ h1 -> True)\nlet test_abs (n:int) : RWI nat RO (fun _ -> True) (fun h0 _ h1 -> True) =\n let r = labs n in\n r", "val abs (n: int) : nat\nlet abs (n:int) : nat = if n >= 0 then n else -n", "val bvsub (#n: pos) (a b: bv_t n) : Tot (bv_t n)\nlet bvsub #n a b =\n int2bv #n (U.sub_mod (bv2int #n a) (bv2int #n b))", "val collect_abs' (bs: list binder) (t: term) : Tot (list binder * term) (decreases t)\nlet rec collect_abs' (bs : list binder) (t : term) : Tot (list binder * term) (decreases t) =\n match inspect_ln_unascribe t with\n | Tv_Abs b t' ->\n collect_abs' (b::bs) t'\n | _ -> (bs, t)", "val collect_abs' (bs: list binder) (t: term) : Tot (list binder * term) (decreases t)\nlet rec collect_abs' (bs : list binder) (t : term) : Tot (list binder * term) (decreases t) =\n match inspect_ln_unascribe t with\n | Tv_Abs b t' ->\n collect_abs' (b::bs) t'\n | _ -> (bs, t)", "val bvnot (#n: pos) (a: bv_t n) : Tot (bv_t n)\nlet bvnot = B.lognot_vec", "val minus (#n: pos) (a: uint_t n) : Tot (uint_t n)\nlet minus (#n:pos) (a:uint_t n) : Tot (uint_t n) =\n add_mod (lognot a) 1", "val sub (a:t) (b:t) : Pure t\n (requires (size (v a - v b) n))\n (ensures (fun c -> v a - v b = v c))\nlet sub a b = Mk (sub (v a) (v b))", "val sub (a:t) (b:t) : Pure t\n (requires (size (v a - v b) n))\n (ensures (fun c -> v a - v b = v c))\nlet sub a b = Mk (sub (v a) (v b))", "val sub (a:t) (b:t) : Pure t\n (requires (size (v a - v b) n))\n (ensures (fun c -> v a - v b = v c))\nlet sub a b = Mk (sub (v a) (v b))", "val sub (a:t) (b:t) : Pure t\n (requires (size (v a - v b) n))\n (ensures (fun c -> v a - v b = v c))\nlet sub a b = Mk (sub (v a) (v b))", "val sub (a:t) (b:t) : Pure t\n (requires (size (v a - v b) n))\n (ensures (fun c -> v a - v b = v c))\nlet sub a b = Mk (sub (v a) (v b))", "val sub (a:t) (b:t) : Pure t\n (requires (size (v a - v b) n))\n (ensures (fun c -> v a - v b = v c))\nlet sub a b = Mk (sub (v a) (v b))", "val sub (a:t) (b:t) : Pure t\n (requires (size (v a - v b) n))\n (ensures (fun c -> v a - v b = v c))\nlet sub a b = Mk (sub (v a) (v b))", "val sub (a:t) (b:t) : Pure t\n (requires (size (v a - v b) n))\n (ensures (fun c -> v a - v b = v c))\nlet sub a b = Mk (sub (v a) (v b))", "val sub (a:t) (b:t) : Pure t\n (requires (size (v a - v b) n))\n (ensures (fun c -> v a - v b = v c))\nlet sub a b = Mk (sub (v a) (v b))", "val mod (#n: pos) (a: int_t n) (b: int_t n {b <> 0}) : Tot (int_t n)\nlet mod (#n:pos) (a:int_t n) (b:int_t n{b <> 0}) : Tot (int_t n) =\n a - ((a/b) * b)", "val bvdiv (#n: pos) (a: bv_t n) (b: uint_t n {b <> 0}) : Tot (bv_t n)\nlet bvdiv #n a b =\n int2bv #n (U.udiv #n (bv2int #n a) b)", "val sub_mod (#n: pos) (a b: int_t n) : Tot (int_t n)\nlet sub_mod (#n:pos) (a:int_t n) (b:int_t n) : Tot (int_t n) =\n (a - b) @% (pow2 n)", "val div: a:int -> b:pos -> Tot (c:int{(a < 0 ==> c < 0) /\\ (a >= 0 ==> c >= 0)})\nlet div a b =\n if a < 0 then\n begin\n slash_decr_axiom (-a) b;\n if a % b = 0 then - (-a / b)\n else - (-a / b) - 1\n end\n else a / b", "val bvadd (#n: pos) (a b: bv_t n) : Tot (bv_t n)\nlet bvadd #n a b =\n int2bv #n (U.add_mod (bv2int #n a) (bv2int #n b))", "val bvmod (#n: pos) (a: bv_t n) (b: uint_t n {b <> 0}) : Tot (bv_t n)\nlet bvmod #n a b =\n int2bv #n (U.mod #n (bv2int #n a) b)", "val bvor (#n: pos) (a b: bv_t n) : Tot (bv_t n)\nlet bvor = B.logor_vec", "val lt (#n: _) (a b: int_t n) : Tot bool\nlet lt #n (a:int_t n) (b:int_t n) : Tot bool = a < b", "val ( / ) (a: int) (b: int{b <> 0}) : Tot int\nlet op_Slash (a:int) (b:int{b <> 0}) : Tot int = \n if (a >= 0 && b < 0) || (a < 0 && b >= 0) then - (abs a / abs b)\n else abs a / abs b", "val min_int (n: pos) : Tot int\nlet min_int (n:pos) : Tot int = - (pow2 (n-1))", "val bvult (#n: pos) (a b: bv_t n) : Tot (bool)\nlet bvult #n a b = (bv2int #n a) < (bv2int #n b)", "val udiv (#n: pos) (a: int_t n {min_int n < a}) (b: int_t n {b <> 0})\n : Tot (c: int_t n {b <> 0 ==> a / b = c})\nlet udiv (#n:pos) (a:int_t n{min_int n < a}) (b:int_t n{b <> 0})\n : Tot (c:int_t n{b <> 0 ==> a / b = c})\n = div_size #n a b;\n a / b", "val one (n: pos{1 < n}) : Tot (int_t n)\nlet one (n:pos{1 < n}) : Tot (int_t n) = 1", "val abs (x: int) : Tot int\nlet abs (x: int) : Tot int = if x >= 0 then x else - x", "val test_abs0 (n: int) : RWI int RO (fun _ -> True) (fun h0 r h1 -> r >= 0)\nlet test_abs0 (n:int) : RWI int RO (fun _ -> True) (fun h0 r h1 -> r >= 0) =\n let r = labs0 n in\n ();\n ();\n r", "val collect_abs' (bs: list binder) (t: term) : Tac (list binder * term) (decreases t)\nlet rec collect_abs' (bs : list binder) (t : term) : Tac (list binder * term) (decreases t) =\n match inspect t with\n | Tv_Abs b t' ->\n collect_abs' (b::bs) t'\n | _ -> (bs, t)", "val collect_abs' (bs: list binder) (t: term) : Tac (list binder * term) (decreases t)\nlet rec collect_abs' (bs : list binder) (t : term) : Tac (list binder * term) (decreases t) =\n match inspect t with\n | Tv_Abs b t' ->\n collect_abs' (b::bs) t'\n | _ -> (bs, t)", "val sub_underspec (a:t) (b:t) : Pure t\n (requires True)\n (ensures (fun c ->\n size (v a - v b) n ==> v a - v b = v c))\nlet sub_underspec a b = Mk (sub_underspec (v a) (v b))", "val sub_underspec (a:t) (b:t) : Pure t\n (requires True)\n (ensures (fun c ->\n size (v a - v b) n ==> v a - v b = v c))\nlet sub_underspec a b = Mk (sub_underspec (v a) (v b))", "val sub_underspec (a:t) (b:t) : Pure t\n (requires True)\n (ensures (fun c ->\n size (v a - v b) n ==> v a - v b = v c))\nlet sub_underspec a b = Mk (sub_underspec (v a) (v b))", "val sub_underspec (a:t) (b:t) : Pure t\n (requires True)\n (ensures (fun c ->\n size (v a - v b) n ==> v a - v b = v c))\nlet sub_underspec a b = Mk (sub_underspec (v a) (v b))", "val size_lt (a b: SZ.t) : Tot (c: bool{c == (SZ.v a < SZ.v b)})\nlet size_lt\n (a: SZ.t)\n (b: SZ.t)\n: Tot (c: bool { c == (SZ.v a < SZ.v b) })\n= a `SZ.lt` b", "val min_int (n: nat) : Tot int\nlet min_int (n:nat) : Tot int = 0", "val test_abs0' (n: int) : RWI nat RO (fun _ -> True) (fun h0 _ h1 -> True)\nlet test_abs0' (n:int) : RWI nat RO (fun _ -> True) (fun h0 _ h1 -> True) =\n let r = labs0 n in\n let r : nat = r in // need this! an ascription won't work!\n r", "val bvxor (#n: pos) (a b: bv_t n) : Tot (bv_t n)\nlet bvxor = B.logxor_vec", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val minus : nat -> nat -> Tot nat\nlet rec minus (n : nat) (m : nat) : nat =\n match n, m with\n | O , _ -> O\n | S _ , O -> n\n | S n', S m' -> minus n' m'", "val lt (a b: t) : Tot bool\nlet lt (a:t) (b:t) : Tot bool = lt #n (v a) (v b)", "val lt (a b: t) : Tot bool\nlet lt (a:t) (b:t) : Tot bool = lt #n (v a) (v b)", "val lt (a b: t) : Tot bool\nlet lt (a:t) (b:t) : Tot bool = lt #n (v a) (v b)", "val lt (a b: t) : Tot bool\nlet lt (a:t) (b:t) : Tot bool = lt #n (v a) (v b)", "val lt (a b: t) : Tot bool\nlet lt (a:t) (b:t) : Tot bool = lt #n (v a) (v b)", "val lt (a b: t) : Tot bool\nlet lt (a:t) (b:t) : Tot bool = lt #n (v a) (v b)", "val lt (a b: t) : Tot bool\nlet lt (a:t) (b:t) : Tot bool = lt #n (v a) (v b)", "val lt (a b: t) : Tot bool\nlet lt (a:t) (b:t) : Tot bool = lt #n (v a) (v b)", "val mod (#n: nat) (a: uint_t n) (b: uint_t n {b <> 0}) : Tot (uint_t n)\nlet mod (#n:nat) (a:uint_t n) (b:uint_t n{b <> 0}) : Tot (uint_t n) =\n a - ((a/b) * b)", "val sub_mod (#n: nat) (a b: uint_t n) : Tot (uint_t n)\nlet sub_mod (#n:nat) (a:uint_t n) (b:uint_t n) : Tot (uint_t n) =\n (a - b) % (pow2 n)", "val sub (#n: pos) (a b: int_t n)\n : Pure (int_t n) (requires (size (a - b) n)) (ensures (fun _ -> True))\nlet sub (#n:pos) (a:int_t n) (b:int_t n)\n : Pure (int_t n)\n (requires (size (a - b) n))\n (ensures (fun _ -> True)) \n = a - b", "val eq (#n: _) (a b: int_t n) : Tot bool\nlet eq #n (a:int_t n) (b:int_t n) : Tot bool = a = b", "val bvshl' (#n: pos) (a: bv_t n) (s: bv_t n) : Tot (bv_t n)\nlet bvshl' (#n: pos) (a: bv_t n) (s: bv_t n): bv_t n =\n B.shift_left_vec #n a (bv2int #n s)", "val mul_mod (#n: pos) (a b: int_t n) : Tot (int_t n)\nlet mul_mod (#n:pos) (a:int_t n) (b:int_t n) : Tot (int_t n) =\n (a * b) @% (pow2 n)", "val add (a:t) (b:t) : Pure t\n (requires (size (v a + v b) n))\n (ensures (fun c -> v a + v b = v c))\nlet add a b = Mk (add (v a) (v b))", "val add (a:t) (b:t) : Pure t\n (requires (size (v a + v b) n))\n (ensures (fun c -> v a + v b = v c))\nlet add a b = Mk (add (v a) (v b))", "val add (a:t) (b:t) : Pure t\n (requires (size (v a + v b) n))\n (ensures (fun c -> v a + v b = v c))\nlet add a b = Mk (add (v a) (v b))", "val add (a:t) (b:t) : Pure t\n (requires (size (v a + v b) n))\n (ensures (fun c -> v a + v b = v c))\nlet add a b = Mk (add (v a) (v b))", "val add (a:t) (b:t) : Pure t\n (requires (size (v a + v b) n))\n (ensures (fun c -> v a + v b = v c))\nlet add a b = Mk (add (v a) (v b))", "val add (a:t) (b:t) : Pure t\n (requires (size (v a + v b) n))\n (ensures (fun c -> v a + v b = v c))\nlet add a b = Mk (add (v a) (v b))", "val add (a:t) (b:t) : Pure t\n (requires (size (v a + v b) n))\n (ensures (fun c -> v a + v b = v c))\nlet add a b = Mk (add (v a) (v b))", "val add (a:t) (b:t) : Pure t\n (requires (size (v a + v b) n))\n (ensures (fun c -> v a + v b = v c))\nlet add a b = Mk (add (v a) (v b))", "val add (a:t) (b:t) : Pure t\n (requires (size (v a + v b) n))\n (ensures (fun c -> v a + v b = v c))\nlet add a b = Mk (add (v a) (v b))", "val to_int_t (m: pos) (a: int) : Tot (int_t m)\nlet to_int_t (m:pos) (a:int) : Tot (int_t m) = a @% pow2 m", "val ins : lt:t -> n:int -> Tot t\nlet ins (| m, tt |) n = (| max m n, insert tt n |)", "val lt (#n: _) (a b: uint_t n) : Tot bool\nlet lt #n (a:uint_t n) (b:uint_t n) : Tot bool = (a < b)", "val logand (#n: pos) (a b: int_t n) : Tot (int_t n)\nlet logand (#n:pos) (a:int_t n) (b:int_t n) : Tot (int_t n) =\n from_vec #n (logand_vec #n (to_vec #n a) (to_vec #n b))", "val zero (n: pos) : Tot (int_t n)\nlet zero (n:pos) : Tot (int_t n) = 0", "val length (s: t): GTot (n:nat{n > 0 /\\ n == Seq.length (v s)})\nlet length s = Seq.length s.s", "val collect_abs_order' (bds: binders) (tt t: term)\n : Lemma (requires t << tt /\\ bds <<: tt)\n (ensures\n (let bds', body = collect_abs' bds t in\n (bds' <<: tt /\\ body << tt)))\n (decreases t)\nlet rec collect_abs_order' (bds: binders) (tt t: term)\n : Lemma (requires t << tt /\\ bds <<: tt)\n (ensures (let bds', body = collect_abs' bds t in\n (bds' <<: tt /\\ body << tt)))\n (decreases t)\n = match inspect_ln_unascribe t with\n | Tv_Abs b body -> collect_abs_order' (b::bds) tt body\n | _ -> ()", "val collect_abs_order' (bds: binders) (tt t: term)\n : Lemma (requires t << tt /\\ bds <<: tt)\n (ensures\n (let bds', body = collect_abs' bds t in\n (bds' <<: tt /\\ body << tt)))\n (decreases t)\nlet rec collect_abs_order' (bds: binders) (tt t: term)\n : Lemma (requires t << tt /\\ bds <<: tt)\n (ensures (let bds', body = collect_abs' bds t in\n (bds' <<: tt /\\ body << tt)))\n (decreases t)\n = match inspect_ln_unascribe t with\n | Tv_Abs b body -> collect_abs_order' (b::bds) tt body\n | _ -> ()", "val lognot (#n: pos) (a: int_t n) : Tot (int_t n)\nlet lognot (#n:pos) (a:int_t n) : Tot (int_t n)=\n from_vec #n (lognot_vec #n (to_vec #n a))", "val ones (n: pos) : Tot (int_t n)\nlet ones (n:pos) : Tot (int_t n) = -1", "val sign_bit_negative: #n:pos{1 < n} -> a:int_t n -> \n Lemma (nth a 0 = true <==> a < 0)\nlet sign_bit_negative #n a =\n UInt.from_vec_propriety #n (to_vec a) 1", "val sub (#n: nat) (a b: uint_t n)\n : Pure (uint_t n) (requires (size (a - b) n)) (ensures (fun _ -> True))\nlet sub (#n:nat) (a:uint_t n) (b:uint_t n) : Pure (uint_t n)\n (requires (size (a - b) n))\n (ensures (fun _ -> True))\n = a - b", "val div (a:t) (b:t{v b <> 0}) : Pure t\n // division overflows on INT_MIN / -1\n (requires (size (v a / v b) n))\n (ensures (fun c -> v a / v b = v c))\nlet div a b = Mk (div (v a) (v b))", "val div (a:t) (b:t{v b <> 0}) : Pure t\n // division overflows on INT_MIN / -1\n (requires (size (v a / v b) n))\n (ensures (fun c -> v a / v b = v c))\nlet div a b = Mk (div (v a) (v b))", "val div (a:t) (b:t{v b <> 0}) : Pure t\n // division overflows on INT_MIN / -1\n (requires (size (v a / v b) n))\n (ensures (fun c -> v a / v b = v c))\nlet div a b = Mk (div (v a) (v b))", "val div (a:t) (b:t{v b <> 0}) : Pure t\n // division overflows on INT_MIN / -1\n (requires (size (v a / v b) n))\n (ensures (fun c -> v a / v b = v c))\nlet div a b = Mk (div (v a) (v b))", "val div (a:t) (b:t{v b <> 0}) : Pure t\n // division overflows on INT_MIN / -1\n (requires (size (v a / v b) n))\n (ensures (fun c -> v a / v b = v c))\nlet div a b = Mk (div (v a) (v b))", "val eq (a b: t) : Tot bool\nlet eq (a:t) (b:t) : Tot bool = eq #n (v a) (v b)", "val eq (a b: t) : Tot bool\nlet eq (a:t) (b:t) : Tot bool = eq #n (v a) (v b)", "val eq (a b: t) : Tot bool\nlet eq (a:t) (b:t) : Tot bool = eq #n (v a) (v b)", "val eq (a b: t) : Tot bool\nlet eq (a:t) (b:t) : Tot bool = eq #n (v a) (v b)", "val eq (a b: t) : Tot bool\nlet eq (a:t) (b:t) : Tot bool = eq #n (v a) (v b)", "val eq (a b: t) : Tot bool\nlet eq (a:t) (b:t) : Tot bool = eq #n (v a) (v b)" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Int128.fsti", "name": "FStar.Int128.ct_abs" }, { "project_name": "FStar", "file_name": "FStar.Int8.fsti", "name": "FStar.Int8.ct_abs" }, { "project_name": "FStar", "file_name": "FStar.Int32.fsti", "name": "FStar.Int32.ct_abs" }, { "project_name": "FStar", "file_name": "FStar.Int64.fsti", "name": "FStar.Int64.ct_abs" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.minus" }, { "project_name": "FStar", "file_name": "FStar.Math.Lib.fst", "name": "FStar.Math.Lib.abs" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvand" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.test_abs" }, { "project_name": "steel", "file_name": "Steel.Stepper.fst", "name": "Steel.Stepper.abs" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvsub" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Derived.fst", "name": "FStar.Reflection.V2.Derived.collect_abs'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Derived.fst", "name": "FStar.Reflection.V1.Derived.collect_abs'" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvnot" }, { "project_name": "FStar", "file_name": "FStar.UInt.fsti", "name": "FStar.UInt.minus" }, { "project_name": "FStar", "file_name": "FStar.UInt8.fst", "name": "FStar.UInt8.sub" }, { "project_name": "FStar", "file_name": "FStar.Int128.fst", "name": "FStar.Int128.sub" }, { "project_name": "FStar", "file_name": "FStar.UInt16.fst", "name": "FStar.UInt16.sub" }, { "project_name": "FStar", "file_name": "FStar.Int16.fst", "name": "FStar.Int16.sub" }, { "project_name": "FStar", "file_name": "FStar.UInt32.fst", "name": "FStar.UInt32.sub" }, { "project_name": "FStar", "file_name": "FStar.Int64.fst", "name": "FStar.Int64.sub" }, { "project_name": "FStar", "file_name": "FStar.Int32.fst", "name": "FStar.Int32.sub" }, { "project_name": "FStar", "file_name": "FStar.Int8.fst", "name": "FStar.Int8.sub" }, { "project_name": "FStar", "file_name": "FStar.UInt64.fst", "name": "FStar.UInt64.sub" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.mod" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvdiv" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.sub_mod" }, { "project_name": "FStar", "file_name": "FStar.Math.Lib.fst", "name": "FStar.Math.Lib.div" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvadd" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvmod" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvor" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.lt" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.op_Slash" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.min_int" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvult" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.udiv" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.one" }, { "project_name": "FStar", "file_name": "prims.fst", "name": "Prims.abs" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.test_abs0" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.SyntaxHelpers.fst", "name": "FStar.Tactics.V2.SyntaxHelpers.collect_abs'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.SyntaxHelpers.fst", "name": "FStar.Tactics.V1.SyntaxHelpers.collect_abs'" }, { "project_name": "FStar", "file_name": "FStar.UInt32.fst", "name": "FStar.UInt32.sub_underspec" }, { "project_name": "FStar", "file_name": "FStar.UInt64.fst", "name": "FStar.UInt64.sub_underspec" }, { "project_name": "FStar", "file_name": "FStar.UInt8.fst", "name": "FStar.UInt8.sub_underspec" }, { "project_name": "FStar", "file_name": "FStar.UInt16.fst", "name": "FStar.UInt16.sub_underspec" }, { "project_name": "steel", "file_name": "Pulse.Lib.ArraySwap.fst", "name": "Pulse.Lib.ArraySwap.size_lt" }, { "project_name": "FStar", "file_name": "FStar.UInt.fsti", "name": "FStar.UInt.min_int" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.test_abs0'" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvxor" }, { "project_name": "FStar", "file_name": "FStar.Int128.fst", "name": "FStar.Int128.v" }, { "project_name": "FStar", "file_name": "FStar.Int64.fst", "name": "FStar.Int64.v" }, { "project_name": "FStar", "file_name": "FStar.Int16.fst", "name": "FStar.Int16.v" }, { "project_name": "FStar", "file_name": "FStar.Int32.fst", "name": "FStar.Int32.v" }, { "project_name": "FStar", "file_name": "FStar.Int8.fst", "name": "FStar.Int8.v" }, { "project_name": "FStar", "file_name": "SfBasic.fst", "name": "SfBasic.minus" }, { "project_name": "FStar", "file_name": "FStar.Int64.fsti", "name": "FStar.Int64.lt" }, { "project_name": "FStar", "file_name": "FStar.Int128.fsti", "name": "FStar.Int128.lt" }, { "project_name": "FStar", "file_name": "FStar.Int8.fsti", "name": "FStar.Int8.lt" }, { "project_name": "FStar", "file_name": "FStar.Int32.fsti", "name": "FStar.Int32.lt" }, { "project_name": "FStar", "file_name": "FStar.UInt32.fsti", "name": "FStar.UInt32.lt" }, { "project_name": "FStar", "file_name": "FStar.UInt16.fsti", "name": "FStar.UInt16.lt" }, { "project_name": "FStar", "file_name": "FStar.UInt8.fsti", "name": "FStar.UInt8.lt" }, { "project_name": "FStar", "file_name": "FStar.UInt64.fsti", "name": "FStar.UInt64.lt" }, { "project_name": "FStar", "file_name": "FStar.UInt.fsti", "name": "FStar.UInt.mod" }, { "project_name": "FStar", "file_name": "FStar.UInt.fsti", "name": "FStar.UInt.sub_mod" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.sub" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.eq" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvshl'" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.mul_mod" }, { "project_name": "FStar", "file_name": "FStar.UInt8.fst", "name": "FStar.UInt8.add" }, { "project_name": "FStar", "file_name": "FStar.UInt16.fst", "name": "FStar.UInt16.add" }, { "project_name": "FStar", "file_name": "FStar.UInt32.fst", "name": "FStar.UInt32.add" }, { "project_name": "FStar", "file_name": "FStar.Int128.fst", "name": "FStar.Int128.add" }, { "project_name": "FStar", "file_name": "FStar.Int32.fst", "name": "FStar.Int32.add" }, { "project_name": "FStar", "file_name": "FStar.UInt64.fst", "name": "FStar.UInt64.add" }, { "project_name": "FStar", "file_name": "FStar.Int64.fst", "name": "FStar.Int64.add" }, { "project_name": "FStar", "file_name": "FStar.Int8.fst", "name": "FStar.Int8.add" }, { "project_name": "FStar", "file_name": "FStar.Int16.fst", "name": "FStar.Int16.add" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.to_int_t" }, { "project_name": "FStar", "file_name": "BinarySearchTreeFirst.fst", "name": "BinarySearchTreeFirst.ins" }, { "project_name": "FStar", "file_name": "FStar.UInt.fsti", "name": "FStar.UInt.lt" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.logand" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.zero" }, { "project_name": "karamel", "file_name": "C.String.fst", "name": "C.String.length" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Derived.Lemmas.fst", "name": "FStar.Reflection.V1.Derived.Lemmas.collect_abs_order'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Derived.Lemmas.fst", "name": "FStar.Reflection.V2.Derived.Lemmas.collect_abs_order'" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.lognot" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.ones" }, { "project_name": "FStar", "file_name": "FStar.Int.fst", "name": "FStar.Int.sign_bit_negative" }, { "project_name": "FStar", "file_name": "FStar.UInt.fsti", "name": "FStar.UInt.sub" }, { "project_name": "FStar", "file_name": "FStar.Int128.fst", "name": "FStar.Int128.div" }, { "project_name": "FStar", "file_name": "FStar.Int32.fst", "name": "FStar.Int32.div" }, { "project_name": "FStar", "file_name": "FStar.Int8.fst", "name": "FStar.Int8.div" }, { "project_name": "FStar", "file_name": "FStar.Int16.fst", "name": "FStar.Int16.div" }, { "project_name": "FStar", "file_name": "FStar.Int64.fst", "name": "FStar.Int64.div" }, { "project_name": "FStar", "file_name": "FStar.UInt32.fsti", "name": "FStar.UInt32.eq" }, { "project_name": "FStar", "file_name": "FStar.Int128.fsti", "name": "FStar.Int128.eq" }, { "project_name": "FStar", "file_name": "FStar.Int8.fsti", "name": "FStar.Int8.eq" }, { "project_name": "FStar", "file_name": "FStar.UInt16.fsti", "name": "FStar.UInt16.eq" }, { "project_name": "FStar", "file_name": "FStar.Int64.fsti", "name": "FStar.Int64.eq" }, { "project_name": "FStar", "file_name": "FStar.Int32.fsti", "name": "FStar.Int32.eq" } ], "selected_premises": [ "FStar.Int.op_At_Percent", "FStar.Int.size", "FStar.UInt.size", "FStar.Int.op_Slash", "FStar.UInt.fits", "FStar.UInt.max_int", "FStar.UInt.min_int", "FStar.Mul.op_Star", "FStar.Int.fits", "FStar.Int.to_vec", "FStar.Int.max_int", "FStar.Int.min_int", "FStar.Int.to_uint", "FStar.UInt.to_vec", "FStar.Int.from_vec", "FStar.Int.from_uint", "FStar.Int16.lt", "FStar.UInt32.lt", "FStar.Math.Lemmas.pow2_le_compat", "FStar.Math.Lemmas.pow2_plus", "FStar.Int.nth", "FStar.Int.logor", "FStar.Math.Lemmas.pow2_lt_compat", "FStar.Int.to_int_t", "FStar.Int.mul", "Prims.abs", "FStar.Int.ones", "FStar.Int.mul_mod", "FStar.Int.lognot", "FStar.Int.lte", "Prims.min", "FStar.Int.lt", "FStar.Int.logand", "FStar.Int.logxor", "FStar.Int.zero", "FStar.Pervasives.reveal_opaque", "FStar.Int.gt", "FStar.UInt.from_vec", "FStar.Int.incr", "FStar.Int.decr", "FStar.Int.one", "FStar.Int.udiv", "FStar.Int.incr_mod", "FStar.Int.eq", "FStar.Math.Lib.slash_decr_axiom", "FStar.Int.sub_mod", "FStar.UInt.to_uint_t", "FStar.Math.Lib.max", "FStar.Math.Lib.powx", "FStar.UInt32.n", "FStar.Math.Lemmas.lemma_mult_lt_sqr", "FStar.BitVector.logor_vec", "FStar.Int.shift_arithmetic_right", "FStar.Int.gte", "FStar.UInt32.lte", "FStar.Int16.lte", "FStar.UInt.ones", "FStar.Math.Lemmas.cancel_mul_mod", "FStar.Math.Lib.min", "FStar.Int16.n", "FStar.Int.decr_mod", "FStar.Math.Lib.abs", "FStar.BitVector.logand_vec", "FStar.BitVector.ones_vec", "FStar.UInt.logor", "FStar.Int.add_mod", "FStar.UInt32.op_Less_Hat", "FStar.Int16.op_Less_Hat", "FStar.Int.minus", "FStar.UInt32.gt", "FStar.Int16.gt", "FStar.Int.shift_right", "FStar.Math.Lemmas.mul_ineq1", "FStar.UInt32.op_Greater_Hat", "FStar.Int16.op_Greater_Hat", "FStar.Int.div", "FStar.UInt.msb", "FStar.Int.shift_left", "FStar.Math.Lemmas.lemma_div_lt", "FStar.BitVector.zero_vec", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "FStar.Int.pow2_n", "FStar.Int16.op_Greater_Greater_Greater_Hat", "FStar.Int.pow2_minus_one", "FStar.BitVector.logxor_vec", "FStar.UInt.logand", "FStar.BitVector.lognot_vec", "FStar.UInt.mul_mod", "FStar.UInt.lognot", "FStar.Int.mod", "FStar.Int16.op_Subtraction_Hat", "FStar.UInt32.op_Subtraction_Hat", "FStar.UInt.lt", "FStar.UInt32.op_Greater_Equals_Hat", "FStar.Int16.op_Greater_Equals_Hat", "FStar.Int.sub", "FStar.UInt32.op_Less_Equals_Hat", "FStar.Int16.op_Less_Equals_Hat", "FStar.UInt.lte", "FStar.UInt.logxor" ], "source_upto_this": "(*\n Copyright 2008-2019 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.Int16\n\n(**** THIS MODULE IS GENERATED AUTOMATICALLY USING [mk_int.sh], DO NOT EDIT DIRECTLY ****)\n\nunfold let n = 16\n\nopen FStar.Int\nopen FStar.Mul\n\n#set-options \"--max_fuel 0 --max_ifuel 0\"\n\n(* NOTE: anything that you fix/update here should be reflected in [FStar.UIntN.fstp], which is mostly\n * a copy-paste of this module. *)\n\nnew val t : eqtype\n\nval v (x:t) : Tot (int_t n)\n\nval int_to_t: x:int_t n -> Pure t\n (requires True)\n (ensures (fun y -> v y = x))\n\nval uv_inv (x : t) : Lemma\n (ensures (int_to_t (v x) == x))\n [SMTPat (v x)]\n\nval vu_inv (x : int_t n) : Lemma\n (ensures (v (int_to_t x) == x))\n [SMTPat (int_to_t x)]\n\nval v_inj (x1 x2: t): Lemma\n (requires (v x1 == v x2))\n (ensures (x1 == x2))\n\nval zero : x:t{v x = 0}\n\nval one : x:t{v x = 1}\n\nval add (a:t) (b:t) : Pure t\n (requires (size (v a + v b) n))\n (ensures (fun c -> v a + v b = v c))\n\n(* Subtraction primitives *)\nval sub (a:t) (b:t) : Pure t\n (requires (size (v a - v b) n))\n (ensures (fun c -> v a - v b = v c))\n\n(* Multiplication primitives *)\nval mul (a:t) (b:t) : Pure t\n (requires (size (v a * v b) n))\n (ensures (fun c -> v a * v b = v c))\n\n(* Division primitives *)\nval div (a:t) (b:t{v b <> 0}) : Pure t\n // division overflows on INT_MIN / -1\n (requires (size (v a / v b) n))\n (ensures (fun c -> v a / v b = v c))\n\n(* Modulo primitives *)\n(* If a/b is not representable the result of a%b is undefind *)\nval rem (a:t) (b:t{v b <> 0}) : Pure t\n (requires (size (v a / v b) n))\n (ensures (fun c -> FStar.Int.mod (v a) (v b) = v c))\n\n(* Bitwise operators *)\nval logand (x:t) (y:t) : Pure t\n (requires True)\n (ensures (fun z -> v x `logand` v y = v z))\n\nval logxor (x:t) (y:t) : Pure t\n (requires True)\n (ensures (fun z -> v x `logxor` v y == v z))\n\nval logor (x:t) (y:t) : Pure t\n (requires True)\n (ensures (fun z -> v x `logor` v y == v z))\n\nval lognot (x:t) : Pure t\n (requires True)\n (ensures (fun z -> lognot (v x) == v z))\n\n(* Shift operators *)\n\n(** If a is negative the result is implementation-defined *)\nval shift_right (a:t) (s:UInt32.t) : Pure t\n (requires (0 <= v a /\\ UInt32.v s < n))\n (ensures (fun c -> FStar.Int.shift_right (v a) (UInt32.v s) = v c))\n\n(** If a is negative or a * pow2 s is not representable the result is undefined *)\nval shift_left (a:t) (s:UInt32.t) : Pure t\n (requires (0 <= v a /\\ v a * pow2 (UInt32.v s) <= max_int n /\\ UInt32.v s < n))\n (ensures (fun c -> FStar.Int.shift_left (v a) (UInt32.v s) = v c))\n\nval shift_arithmetic_right (a:t) (s:UInt32.t) : Pure t\n (requires (UInt32.v s < n))\n (ensures (fun c -> FStar.Int.shift_arithmetic_right (v a) (UInt32.v s) = v c))\n\n(* Comparison operators *)\nlet eq (a:t) (b:t) : Tot bool = eq #n (v a) (v b)\nlet gt (a:t) (b:t) : Tot bool = gt #n (v a) (v b)\nlet gte (a:t) (b:t) : Tot bool = gte #n (v a) (v b)\nlet lt (a:t) (b:t) : Tot bool = lt #n (v a) (v b)\nlet lte (a:t) (b:t) : Tot bool = lte #n (v a) (v b)\n\n(* Infix notations *)\nunfold let op_Plus_Hat = add\nunfold let op_Subtraction_Hat = sub\nunfold let op_Star_Hat = mul\nunfold let op_Slash_Hat = div\nunfold let op_Percent_Hat = rem\nunfold let op_Hat_Hat = logxor\nunfold let op_Amp_Hat = logand\nunfold let op_Bar_Hat = logor\nunfold let op_Less_Less_Hat = shift_left\nunfold let op_Greater_Greater_Hat = shift_right\nunfold let op_Greater_Greater_Greater_Hat = shift_arithmetic_right\nunfold let op_Equals_Hat = eq\nunfold let op_Greater_Hat = gt\nunfold let op_Greater_Equals_Hat = gte\nunfold let op_Less_Hat = lt\nunfold let op_Less_Equals_Hat = lte\n\ninline_for_extraction" }, { "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.loc_equal", "opens_and_abbrevs": [ { "abbrev": "F", "full_module": "FStar.FunctionalExtensionality" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "open": "FStar" }, { "open": "FStar" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0", "source_definition": "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n let Loc regions1 region_liveness_tags1 _ _ aux1 = s1 in\n let Loc regions2 region_liveness_tags2 _ _ aux2 = s2 in\n Ghost.reveal regions1 `Set.equal` Ghost.reveal regions2 /\\\n Ghost.reveal region_liveness_tags1 `Set.equal` Ghost.reveal region_liveness_tags2 /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "source_range": { "start_line": 206, "start_col": 0, "end_line": 213, "end_col": 68 }, "interleaved": false, "definition": "fun s1 s2 ->\n (let _ = s1 in\n (let FStar.ModifiesGen.Loc #_ #_ regions1 region_liveness_tags1 _ _ _ = _ in\n let _ = s2 in\n (let FStar.ModifiesGen.Loc #_ #_ regions2 region_liveness_tags2 _ _ _ = _ in\n FStar.Set.equal (FStar.Ghost.reveal regions1) (FStar.Ghost.reveal regions2) /\\\n FStar.Set.equal (FStar.Ghost.reveal region_liveness_tags1)\n (FStar.Ghost.reveal region_liveness_tags2) /\\\n FStar.ModifiesGen.fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n FStar.ModifiesGen.fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n FStar.GSet.equal (FStar.Ghost.reveal (Loc?.aux s1)) (FStar.Ghost.reveal (Loc?.aux s2)))\n <:\n Type0)\n <:\n Type0)\n <:\n Prims.GTot Type0", "effect": "Prims.GTot", "effect_flags": [ "sometrivial" ], "mutual_with": [], "premises": [ "FStar.ModifiesGen.aloc_t", "FStar.ModifiesGen.cls", "FStar.ModifiesGen.loc", "FStar.Ghost.erased", "FStar.Set.set", "FStar.Monotonic.HyperHeap.rid", "FStar.Set.subset", "FStar.Ghost.reveal", "FStar.ModifiesGen.i_restricted_g_t", "FStar.ModifiesGen.addrs_dom", "FStar.ModifiesGen.non_live_addrs_codom", "FStar.ModifiesGen.live_addrs_codom", "FStar.GSet.set", "FStar.ModifiesGen.aloc", "Prims.l_and", "FStar.GSet.subset", "FStar.ModifiesGen.aloc_domain", "Prims.b2t", "FStar.Set.mem", "FStar.GSet.complement", "Prims.nat", "FStar.GSet.empty", "FStar.Set.equal", "FStar.ModifiesGen.fun_set_equal", "FStar.ModifiesGen.__proj__Loc__item__regions", "Prims.l_imp", "FStar.ModifiesGen.__proj__Loc__item__region_liveness_tags", "FStar.ModifiesGen.__proj__Loc__item__non_live_addrs", "FStar.ModifiesGen.__proj__Loc__item__live_addrs", "FStar.GSet.equal", "FStar.ModifiesGen.__proj__Loc__item__aux" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": true, "type": "s1: FStar.ModifiesGen.loc c -> s2: FStar.ModifiesGen.loc c -> Prims.GTot Type0", "prompt": "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n ", "expected_response": "let Loc regions1 region_liveness_tags1 _ _ aux1 = s1 in\nlet Loc regions2 region_liveness_tags2 _ _ aux2 = s2 in\n(Ghost.reveal regions1) `Set.equal` (Ghost.reveal regions2) /\\\n(Ghost.reveal region_liveness_tags1) `Set.equal` (Ghost.reveal region_liveness_tags2) /\\\nfun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\nfun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n(Ghost.reveal (Loc?.aux s1)) `GSet.equal` (Ghost.reveal (Loc?.aux s2))", "source": { "project_name": "FStar", "file_name": "ulib/FStar.ModifiesGen.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.ModifiesGen.fst", "checked_file": "dataset/FStar.ModifiesGen.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Universe.fsti.checked", "dataset/FStar.Tactics.SMT.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Stubs.Tactics.V2.Builtins.fsti.checked", "dataset/FStar.StrongExcludedMiddle.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Map.fsti.checked", "dataset/FStar.HyperStack.ST.fsti.checked", "dataset/FStar.HyperStack.fst.checked", "dataset/FStar.Heap.fst.checked", "dataset/FStar.GSet.fsti.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "aloc", "ALoc", "ALoc", "ALoc", "aloc_t", "region", "region", "addr", "addr", "loc", "loc", "cls", "Cls", "Cls", "Cls", "aloc_includes", "aloc_includes", "let aloc_domain (#al: aloc_t) (c: cls al) (regions: Ghost.erased (Set.set HS.rid)) (addrs: ((r: HS.rid { Set.mem r (Ghost.reveal regions) } ) -> GTot (GSet.set nat))) : GTot (GSet.set (aloc c)) =\n GSet.comprehend (fun a -> Set.mem a.region (Ghost.reveal regions) && GSet.mem a.addr (addrs a.region))", "aloc_includes_refl", "aloc_includes_refl", "let i_restricted_g_t = F.restricted_g_t", "let addrs_dom regions =\n (r: HS.rid { Set.mem r (Ghost.reveal regions) } )", "let non_live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (r:addrs_dom regions) =\n (y: GSet.set nat { r `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y })", "aloc_includes_trans", "aloc_includes_trans", "let live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags))\n (r:addrs_dom regions) = (y: GSet.set nat { GSet.subset (non_live_addrs r) y } )", "aloc_disjoint", "aloc_disjoint", "loc'", "Loc", "Loc", "Loc", "regions", "regions", "aloc_disjoint_sym", "aloc_disjoint_sym", "region_liveness_tags", "region_liveness_tags", "non_live_addrs", "non_live_addrs", "live_addrs", "live_addrs", "aloc_disjoint_includes", "aloc_disjoint_includes", "aux", "aux", "let loc = loc'", "let mk_non_live_addrs (#regions:_) (#region_liveness_tags:_)\n (f: (x:addrs_dom regions -> GTot (non_live_addrs_codom regions region_liveness_tags x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags) =\n F.on_dom_g _ f", "aloc_preserved", "aloc_preserved", "let mk_live_addrs (#regions:_) (#region_liveness_tags:_)\n (#non_live_addrs_codom: _)\n (f: (x:addrs_dom regions -> GTot (live_addrs_codom regions region_liveness_tags non_live_addrs_codom x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs_codom) =\n F.on_dom_g _ f", "aloc_preserved_refl", "aloc_preserved_refl", "let loc_none #a #c =\n Loc\n (Ghost.hide (Set.empty))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)", "aloc_preserved_trans", "aloc_preserved_trans", "let regions_of_loc\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: GTot (Set.set HS.rid)\n= Ghost.reveal (Loc?.regions s)", "let addrs_of_loc_liveness_not_preserved\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.non_live_addrs l r\n else GSet.empty", "same_mreference_aloc_preserved", "same_mreference_aloc_preserved", "let addrs_of_loc_weak\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.live_addrs l r\n else GSet.empty", "let addrs_of_loc_aux_pred\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n (addr: nat)\n: GTot bool\n= StrongExcludedMiddle.strong_excluded_middle (exists a . GSet.mem a (Ghost.reveal (Loc?.aux l)) /\\ a.region == r /\\ a.addr == addr)", "val loc (#aloc: aloc_t u#x) (c: cls aloc) : Tot (Type u#x)", "val loc_none (#aloc: aloc_t) (#c: cls aloc): Tot (loc c)", "val loc_union\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot (loc c)", "let addrs_of_loc_aux\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (y: GSet.set nat { GSet.subset (GSet.intersect y (addrs_of_loc_weak l r)) GSet.empty } )\n= GSet.comprehend (addrs_of_loc_aux_pred l r)\n `GSet.intersect` (GSet.complement (addrs_of_loc_weak l r))", "val loc_union_idem\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union s s == s)", "let addrs_of_loc\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= GSet.union\n (addrs_of_loc_weak l r)\n (addrs_of_loc_aux l r)", "val loc_union_comm\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: Lemma\n (loc_union s1 s2 == loc_union s2 s1)", "let addrs_of_loc_aux_prop\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: Lemma\n (GSet.subset (GSet.intersect (addrs_of_loc_aux l r) (addrs_of_loc_weak l r)) GSet.empty)\n [SMTPatOr [\n [SMTPat (addrs_of_loc_aux l r)];\n [SMTPat (addrs_of_loc_weak l r)];\n [SMTPat (addrs_of_loc l r)];\n ]]\n= ()", "val loc_union_assoc\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s3: loc c)\n: Lemma\n (loc_union s1 (loc_union s2 s3) == loc_union (loc_union s1 s2) s3)", "val loc_union_loc_none_l\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union loc_none s == s)", "val loc_union_loc_none_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union s loc_none == s)", "let loc_union #al #c s1 s2 =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in\n let regions = Set.union regions1 regions2 in\n let region_liveness_tags : Ghost.erased (Set.set HS.rid) = (Ghost.hide (Set.union (Ghost.reveal (Loc?.region_liveness_tags s1)) (Ghost.reveal (Loc?.region_liveness_tags s2)))) in\n let gregions = Ghost.hide regions in\n let non_live_addrs =\n F.on_dom_g (addrs_dom gregions) #(non_live_addrs_codom gregions region_liveness_tags)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then Loc?.non_live_addrs s1 r else GSet.empty)\n (if Set.mem r regions2 then Loc?.non_live_addrs s2 r else GSet.empty))\n in\n let live_addrs =\n F.on_dom_g (addrs_dom gregions) #(live_addrs_codom gregions region_liveness_tags non_live_addrs)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then addrs_of_loc_weak s1 r else GSet.empty)\n (if Set.mem r regions2 then addrs_of_loc_weak s2 r else GSet.empty))\n in\n let aux = Ghost.hide\n (Ghost.reveal (Loc?.aux s1) `GSet.union` Ghost.reveal (Loc?.aux s2))\n in\n Loc\n (Ghost.hide regions)\n region_liveness_tags\n non_live_addrs\n live_addrs\n aux", "val loc_of_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b: aloc r n)\n: GTot (loc c)", "val loc_of_aloc_not_none\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b: aloc r n)\n: Lemma (loc_of_aloc #_ #c b == loc_none ==> False)", "val loc_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: GTot (loc c)", "val loc_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: GTot (loc c)", "let fun_set_equal (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) :Tot Type0 =\n forall (x: t) . {:pattern (f1 x) \\/ (f2 x) } f1 x `GSet.equal` f2 x", "let loc_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses true (HS.frameOf b) (Set.singleton (HS.as_addr b))", "let fun_set_equal_elim (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) : Lemma\n (requires (fun_set_equal f1 f2))\n (ensures (f1 == f2))\n// [SMTPat (fun_set_equal f1 f2)]\n= assert (f1 `FunctionalExtensionality.feq_g` f2)" ], "closest": [ "val loc_mreference\n (#aloc: aloc_t)\n (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n : GTot (loc c)\nlet loc_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses true (HS.frameOf b) (Set.singleton (HS.as_addr b))", "val equal (#a:Type) (s1:set a) (s2:set a) : Type0\nlet equal #_ s1 s2 = forall x. s1 x <==> s2 x", "val loc_freed_mreference\n (#aloc: aloc_t)\n (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n : GTot (loc c)\nlet loc_freed_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses false (HS.frameOf b) (Set.singleton (HS.as_addr b))", "val loc_union (s1 s2:loc) : GTot loc\nlet loc_union = M.loc_union", "val loc_union (s1 s2:loc) : GTot loc\nlet loc_union = M.loc_union", "val loc_union\n (s1 s2: loc)\n: GTot loc\nlet loc_union = MG.loc_union", "val loc_union\n (s1 s2: loc)\n: GTot loc\nlet loc_union = MG.loc_union", "val loc_union\n (s1 s2: loc)\n: GTot loc\nlet loc_union = MG.loc_union", "val loc_region_only (#aloc: aloc_t) (#c: cls aloc) (preserve_liveness: bool) (r: HS.rid)\n : GTot (loc c)\nlet loc_region_only\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (Set.singleton r)", "val equal (#a:eqtype) (#f:cmp a) (s1 s2:mset a f) : Tot Type0\nlet equal #a #f s1 s2 = s1 == s2", "val loc_disjoint\n (s1 s2: loc)\n: GTot Type0\nlet loc_disjoint = MG.loc_disjoint", "val loc_disjoint\n (s1 s2: loc)\n: GTot Type0\nlet loc_disjoint = MG.loc_disjoint", "val loc_disjoint\n (s1 s2: loc)\n: GTot Type0\nlet loc_disjoint = MG.loc_disjoint", "val loc_includes\n (s1 s2: loc)\n: GTot Type0\nlet loc_includes = MG.loc_includes", "val loc_includes\n (s1 s2: loc)\n: GTot Type0\nlet loc_includes = MG.loc_includes", "val loc_includes\n (s1 s2: loc)\n: GTot Type0\nlet loc_includes = MG.loc_includes", "val loc_all_regions_from (#aloc: aloc_t) (#c: cls aloc) (preserve_liveness: bool) (r: HS.rid)\n : GTot (loc c)\nlet loc_all_regions_from\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (HS.mod_set (Set.singleton r))", "val equal (#a:Type) (#len:size_nat) (s1:lseq a len) (s2:lseq a len) : Type0\nlet equal #a #len s1 s2 =\n forall (i:size_nat{i < len}).{:pattern (index s1 i); (index s2 i)} index s1 i == index s2 i", "val holds (#t: Type0) (p: rel t) (s s' : t) : GTot Type0\nlet holds (#t: Type0) (p: rel t) (s s' : t) : GTot Type0 =\n p s s'", "val s_v (#a: alg) (#m: m_spec) (h: HS.mem) (s: s a m) : GTot (t a)\nlet s_v (#a : alg) (#m : m_spec) (h : HS.mem) (s : s a m) : GTot (t a) =\n state_v h s", "val equal (#a:eqtype) (s1:set a) (s2:set a)\n : Type0\nlet equal (#a:eqtype) (s1:set a) (s2:set a) = F.feq s1 s2", "val equal (#a: eqtype) (s1: set a) (s2: set a)\n : Type0\nlet equal (#a: eqtype) (s1: set a) (s2: set a) : Type0 =\n feq s1 s2", "val clens_eq (#t #t': Type) (cl1 cl2: clens t t') : GTot Type0\nlet clens_eq (#t: Type) (#t': Type) (cl1: clens t t') (cl2: clens t t') : GTot Type0 =\n (forall (x: t) . {:pattern (cl1.clens_cond x) \\/ (cl2.clens_cond x)} cl1.clens_cond x <==> cl2.clens_cond x) /\\\n (forall (x: t) . {:pattern (cl1.clens_get x) \\/ (cl2.clens_get x)} (cl1.clens_cond x \\/ cl2.clens_cond x) ==> (cl1.clens_get x == cl2.clens_get x))", "val equal (#a: eqtype) (#f: cmp a) (s1 s2: ordset a f) : Tot prop\nlet equal (#a:eqtype) (#f:cmp a) (s1:ordset a f) (s2:ordset a f) : Tot prop =\n forall x. mem #_ #f x s1 = mem #_ #f x s2", "val loc_aux_includes (s1 s2: loc_aux) : GTot Type0 (decreases s2)\nlet loc_aux_includes\n (s1 s2: loc_aux)\n: GTot Type0\n (decreases s2)\n= match s2 with\n | LocBuffer b -> loc_aux_includes_buffer s1 b", "val loc_includes (s1 s2:loc) : GTot prop0\nlet loc_includes = M.loc_includes", "val loc_includes (s1 s2:loc) : GTot prop0\nlet loc_includes = M.loc_includes", "val as_loc (x: eloc) : GTot B.loc\nlet as_loc (x:eloc) : GTot B.loc = Ghost.reveal x", "val any (#a:eqtype) (#f:cmp a) (s: ordset a f) (c: condition a) : Tot bool\nlet rec any #a #f (s: ordset a f) (c: condition a) : Tot bool = \n match s with\n | [] -> false\n | h::t -> c h || any #a #f t c", "val loc_aux_includes_pointer (s: loc_aux) (#t: typ) (p: pointer t) : GTot Type0\nlet loc_aux_includes_pointer\n (s: loc_aux)\n (#t: typ)\n (p: pointer t)\n: GTot Type0\n= match s with\n | LocPointer p' -> \n p' `includes` p\n | LocBuffer b ->\n buffer_includes_pointer b p", "val unchanged_at (locs: locations) (s1 s2: machine_state) : GTot Type0\nlet rec unchanged_at (locs:locations) (s1 s2:machine_state) : GTot Type0 =\n match locs with\n | [] -> True\n | x :: xs -> (\n (eval_location x s1 == eval_location x s2) /\\\n (unchanged_at xs s1 s2)\n )", "val all (#a:eqtype) (#f:cmp a) (s: ordset a f) (c: condition a) : Tot bool\nlet rec all #a #f (s: ordset a f) (c: condition a) : Tot bool = \n match s with\n | [] -> true\n | h::t -> c h && all #a #f t c", "val loc_aux_includes (s s2: loc_aux) : GTot Type0 (decreases s2)\nlet loc_aux_includes\n (s: loc_aux)\n (s2: loc_aux)\n: GTot Type0\n (decreases s2)\n= match s2 with\n | LocPointer p ->\n loc_aux_includes_pointer s p\n | LocBuffer b ->\n loc_aux_includes_buffer s b", "val equal (#a: typ) (h: HS.mem) (b: buffer a) (h': HS.mem) (b': buffer a) : GTot Type0\nlet equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =\n as_seq h b == as_seq h' b'", "val equal (#a:Type) (s1:seq a) (s2:seq a) : Tot prop\nlet equal #a s1 s2 =\n (length s1 = length s2\n /\\ (forall (i:nat{i < length s1}).{:pattern (index s1 i); (index s2 i)} (index s1 i == index s2 i)))", "val modifies\n (s: loc)\n (h1 h2: HS.mem)\n: GTot Type0\nlet modifies = MG.modifies", "val modifies\n (s: loc)\n (h1 h2: HS.mem)\n: GTot Type0\nlet modifies = MG.modifies", "val modifies\n (s: loc)\n (h1 h2: HS.mem)\n: GTot Type0\nlet modifies = MG.modifies", "val loc_disjoint (s1 s2:loc) : GTot prop0\nlet loc_disjoint = M.loc_disjoint", "val loc_disjoint (s1 s2:loc) : GTot prop0\nlet loc_disjoint = M.loc_disjoint", "val compare\n (#t:eqtype)\n (l:SZ.t)\n (a1 a2:larray t (SZ.v l))\n (#p1 #p2:perm)\n (#s1 #s2:Ghost.erased (Seq.seq t))\n : stt bool\n (requires \n pts_to a1 #p1 s1 **\n pts_to a2 #p2 s2)\n (ensures fun res ->\n pts_to a1 #p1 s1 **\n pts_to a2 #p2 s2 **\n pure (res <==> Seq.equal s1 s2))\nlet compare = compare'", "val compare_lseq' (#a: eqtype) (f: cmp a) (l: nat) (s1 s2: Seq.lseq a l) : Tot bool\nlet rec compare_lseq' (#a:eqtype) (f:cmp a) (l:nat) (s1 s2:Seq.lseq a l)\n : Tot bool\n = if l = 0 then (assert (Seq.equal s1 s2); true)\n else if s1 = s2 then true\n else if Seq.head s1 = Seq.head s2 then compare_lseq' f (l - 1) (Seq.tail s1) (Seq.tail s2)\n else f (Seq.head s1) (Seq.head s2)", "val sel (#a: Type) (#rel: preorder a) (m: mem) (s: mreference a rel) : GTot a\nlet sel (#a:Type) (#rel:preorder a) (m:mem) (s:mreference a rel) :GTot a\n = Heap.sel (get_hmap m `Map.sel` (frameOf s)) (as_ref s)", "val union_aux (#a: eqtype) (#f: cmp a) (s1 s2: mset a f)\n : s:\n mset a f\n { ((Cons? s1 /\\ Cons? s2) ==>\n (Cons? s /\\\n (let x1 = fst (hd s1) in\n let x2 = fst (hd s2) in\n if f x1 x2 then fst (hd s) == x1 else fst (hd s) == x2))) /\\ (Nil? s1 ==> s == s2) /\\\n (Nil? s2 ==> s == s1) }\nlet rec union_aux (#a:eqtype) (#f:cmp a) (s1 s2:mset a f) :\n s:mset a f{\n ((Cons? s1 /\\ Cons? s2) ==>\n (Cons? s /\\ (let x1 = fst (hd s1) in\n let x2 = fst (hd s2) in\n if f x1 x2 then fst (hd s) == x1\n else fst (hd s) == x2))) /\\\n (Nil? s1 ==> s == s2) /\\\n (Nil? s2 ==> s == s1)} =\n match s1, s2 with\n | [], _ -> s2\n | _, [] -> s1\n | (x1, n1)::_, (x2, n2)::_ ->\n if x1 = x2\n then (x1, n1 + n2)::(union_aux (tl s1) (tl s2))\n else if f x1 x2\n then (x1, n1)::(union_aux (tl s1) s2)\n else (x2, n2)::(union_aux s1 (tl s2))", "val equal (#a:Type) (#len:flen) (s1:ntuple a len) (s2:ntuple a len) : Type0\nlet equal #a #len s1 s2 =\n (forall (i:size_nat{i < len}).{:pattern (index s1 i); (index s2 i)} index s1 i == index s2 i)", "val cloc_aloc : HS.rid -> nat -> Tot (Type u#1)\nlet cloc_aloc = aloc", "val loc (#t: buftype) (#a: Type0) (b: buffer_t t a) : GTot B.loc\nlet loc (#t:buftype) (#a:Type0) (b:buffer_t t a) : GTot B.loc =\n match t with\n | MUT -> B.loc_buffer (b <: buffer a)\n | IMMUT -> B.loc_buffer (b <: ibuffer a)\n | CONST -> CB.loc_buffer (b <: cbuffer a)", "val includes\n (#a1 #a2: Type0)\n (#rrel1 #rel1: srel a1)\n (#rrel2 #rel2: srel a2)\n (b1: mbuffer a1 rrel1 rel1)\n (b2: mbuffer a2 rrel2 rel2)\n : GTot Type0\nlet includes (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2)\n (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :GTot Type0 =\n loc_includes (loc_buffer b1) (loc_buffer b2) /\\\n (g_is_null b1 <==> g_is_null b2)", "val eval_equiv (#t: Type0) (c: context) (f: exp t) (s: seclevel) : GTot Type0\nlet eval_equiv\n (#t: Type0)\n (c: context)\n (f: exp t)\n (s: seclevel)\n: GTot Type0\n= Benton2004.DDCC.eval_equiv (interp_context c) (interp_seclevel _ s) f f", "val eq_elim: #a:Type -> #len:size_nat -> s1:lseq a len -> s2:lseq a len ->\n Lemma\n (requires equal s1 s2)\n (ensures s1 == s2)\n [SMTPat (equal s1 s2)]\nlet eq_elim #a #len s1 s2 =\n assert (forall (i:nat{i < len}).{:pattern (Seq.index s1 i); (Seq.index s2 i)}\n index s1 i == index s2 i);\n Seq.lemma_eq_elim #a s1 s2", "val ( ^++ ) (#a: Type0) (#rel: preorder a) (r: mref a rel) (s: set nat) : GTot (set nat)\nlet op_Hat_Plus_Plus (#a:Type0) (#rel:preorder a) (r:mref a rel) (s:set nat) :GTot (set nat) = S.union (only r) s", "val loc_aux_disjoint_pointer (l: loc_aux) (#t: typ) (p: pointer t) : GTot Type0\nlet loc_aux_disjoint_pointer\n (l: loc_aux)\n (#t: typ)\n (p: pointer t)\n: GTot Type0\n= match l with\n | LocPointer p' -> disjoint p' p\n | LocBuffer b -> disjoint_buffer_vs_pointer b p", "val loc_union_idem_2 (s1 s2: loc)\n : Lemma (loc_union (loc_union s1 s2) s2 == loc_union s1 s2)\n [SMTPat (loc_union (loc_union s1 s2) s2)]\nlet loc_union_idem_2\n (s1 s2: loc)\n: Lemma\n (loc_union (loc_union s1 s2) s2 == loc_union s1 s2)\n [SMTPat (loc_union (loc_union s1 s2) s2)]\n= loc_union_assoc s1 s2 s2", "val eval_cmp (s: va_state) (c: cmp) : GTot bool\nlet eval_cmp (s:va_state) (c:cmp) : GTot bool =\n match c with\n | Cmp_eq o1 o2 -> va_eval_opr64 s o1 = va_eval_opr64 s o2\n | Cmp_ne o1 o2 -> va_eval_opr64 s o1 <> va_eval_opr64 s o2\n | Cmp_le o1 o2 -> va_eval_opr64 s o1 <= va_eval_opr64 s o2\n | Cmp_ge o1 o2 -> va_eval_opr64 s o1 >= va_eval_opr64 s o2\n | Cmp_lt o1 o2 -> va_eval_opr64 s o1 < va_eval_opr64 s o2\n | Cmp_gt o1 o2 -> va_eval_opr64 s o1 > va_eval_opr64 s o2", "val eval_cmp (s: va_state) (c: cmp) : GTot bool\nlet eval_cmp (s:va_state) (c:cmp) : GTot bool =\n match c with\n | Cmp_eq o1 o2 -> va_eval_cmp_opr s o1 = va_eval_cmp_opr s o2\n | Cmp_ne o1 o2 -> va_eval_cmp_opr s o1 <> va_eval_cmp_opr s o2\n | Cmp_le o1 o2 -> va_eval_cmp_opr s o1 <= va_eval_cmp_opr s o2\n | Cmp_ge o1 o2 -> va_eval_cmp_opr s o1 >= va_eval_cmp_opr s o2\n | Cmp_lt o1 o2 -> va_eval_cmp_opr s o1 < va_eval_cmp_opr s o2\n | Cmp_gt o1 o2 -> va_eval_cmp_opr s o1 > va_eval_cmp_opr s o2", "val fresh_loc (l: loc) (h h': HS.mem) : GTot Type0\nlet fresh_loc (l: loc) (h h' : HS.mem) : GTot Type0 =\n loc_unused_in h `loc_includes` l /\\\n loc_not_unused_in h' `loc_includes` l", "val sel (#a: Type0) (h: heap) (s: array a) : GTot (seq a)\nlet sel (#a:Type0) (h:heap) (s:array a) : GTot (seq a) = Heap.sel h (as_ref s)", "val state_v (#a: alg) (#m: m_spec) (h: HS.mem) (s: s a m) : GTot (Spec.state a)\nlet state_v (#a : alg) (#m : m_spec) (h : HS.mem) (s : s a m) : GTot (Spec.state a) =\n Core.state_v h (get_state_p s)", "val eq_intro (#a:eqtype) (#f:cmp a) (s1 s2:mset a f)\n : Lemma\n (requires forall (x:a). mem x s1 = mem x s2)\n (ensures equal s1 s2)\nlet rec eq_intro #_ #f s1 s2 =\n match s1, s2 with\n | [], [] -> ()\n | (_, _)::_, [] -> ()\n | [], (_, _)::_ -> ()\n | (x, n_x)::_, (y, n_y)::_ ->\n if x = y then (forall_x_mem_in_tl s1 s2; eq_intro (tl s1) (tl s2))\n else if f x y then mem_elt_lt_hd x s2\n else mem_elt_lt_hd y s1", "val compare\n (#a: eqtype)\n (#p0 #p1: perm)\n (a0 a1: A.array a)\n (#s0 #s1: G.erased (Seq.seq a))\n (n: US.t{US.v n == A.length a0 /\\ A.length a0 == A.length a1})\n : ST bool\n ((A.pts_to a0 p0 s0) `star` (A.pts_to a1 p1 s1))\n (fun _ -> (A.pts_to a0 p0 s0) `star` (A.pts_to a1 p1 s1))\n (requires True)\n (ensures fun b -> b <==> s0 == s1)\nlet compare (#a:eqtype) (#p0 #p1:perm)\n (a0 a1:A.array a)\n (#s0 #s1:G.erased (Seq.seq a))\n (n:US.t{US.v n == A.length a0 /\\ A.length a0 == A.length a1})\n : ST bool\n (A.pts_to a0 p0 s0\n `star`\n A.pts_to a1 p1 s1)\n\n (fun _ ->\n A.pts_to a0 p0 s0\n `star`\n A.pts_to a1 p1 s1)\n (requires True)\n (ensures fun b -> b <==> s0 == s1)\n = let b = for_all2 n a0 a1 (fun x y -> x = y) in\n A.pts_to_length a0 s0;\n A.pts_to_length a1 s1;\n assert (b <==> Seq.equal s0 s1);\n return b", "val union (#a:eqtype) (#f:cmp a) (s1 s2:mset a f) : mset a f\nlet union = union_aux", "val compare (#t:eqtype) (#p0 #p1:perm)\n (a0 a1:array t)\n (#s0 #s1:Ghost.erased (Seq.seq t))\n (l:US.t { US.v l == length a0 /\\ length a0 == length a1 } )\n : ST bool\n (pts_to a0 p0 s0 `star` pts_to a1 p1 s1)\n (fun _ -> pts_to a0 p0 s0 `star` pts_to a1 p1 s1)\n (requires True)\n (ensures fun b -> b <==> eq2 #(Seq.seq t) s0 s1)\nlet compare\n #t #p0 #p1 a0 a1 #s0 #s1 l\n =\n pts_to_length a0 _;\n pts_to_length a1 _;\n if l = 0sz\n then (\n assert (Seq.equal s0 s1);\n return true\n )\n else (\n compare_pts a0 a1 l\n )", "val geq (#t: eqtype) (e1 e2: gexp t) : GTot (gexp bool)\nlet geq\n (#t: eqtype)\n (e1 e2 : gexp t)\n: GTot (gexp bool)\n= gop op_Equality e1 e2", "val loc_pointer\n (#t: typ)\n (p: pointer t)\n: GTot loc\nlet loc_pointer #t p =\n MG.loc_of_aloc #_ #cls #(frameOf p) #(as_addr p) (LocPointer p)", "val ( ^+^ )\n (#a #b: Type0)\n (#rel1: preorder a)\n (#rel2: preorder b)\n (r1: mref a rel1)\n (r2: mref b rel2)\n : GTot (set nat)\nlet op_Hat_Plus_Hat (#a:Type0) (#b:Type0) (#rel1:preorder a) (#rel2:preorder b) (r1:mref a rel1) (r2:mref b rel2)\n :GTot (set nat) = S.union (only r1) (only r2)", "val eq: #a:eqtype -> s1:seq a -> s2:seq a -> Tot (r:bool{r <==> equal s1 s2})\nlet eq #_ s1 s2 = if length s1 = length s2 then eq_i s1 s2 0 else false", "val lemma_equal_elim: #a:Type -> s1:set a -> s2:set a -> Lemma\n (requires (equal s1 s2))\n (ensures (s1 == s2))\n [SMTPat (equal s1 s2)]\nlet lemma_equal_elim #a s1 s2 = PredicateExtensionality.predicateExtensionality a s1 s2", "val disjoint\n (#a1 #a2: Type0)\n (#rrel1 #rel1: srel a1)\n (#rrel2 #rel2: srel a2)\n (b1: mbuffer a1 rrel1 rel1)\n (b2: mbuffer a2 rrel2 rel2)\n : GTot Type0\nlet disjoint (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2)\n (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :GTot Type0 =\n loc_disjoint (loc_buffer b1) (loc_buffer b2)", "val loc_aux_includes_loc_aux_includes_pointer (s1 s2: loc_aux) (#t: typ) (p: pointer t)\n : Lemma (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_pointer s2 p))\n (ensures (loc_aux_includes_pointer s1 p))\nlet loc_aux_includes_loc_aux_includes_pointer\n (s1: loc_aux)\n (s2: loc_aux)\n (#t: typ)\n (p: pointer t)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_pointer s2 p))\n (ensures (loc_aux_includes_pointer s1 p))\n= match s2 with\n | LocPointer p' ->\n loc_aux_includes_pointer_trans s1 p' p\n | LocBuffer b ->\n let f\n (i: UInt32.t)\n : Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ gpointer_of_buffer_cell b i `includes` p))\n (ensures (loc_aux_includes_pointer s1 p))\n = loc_aux_includes_pointer_trans s1 (gpointer_of_buffer_cell b i) p\n in\n Classical.forall_intro (Classical.move_requires f)", "val union_comm (#a:eqtype) (#f:cmp a) (s1 s2:mset a f)\n : Lemma (union s1 s2 == union s2 s1)\nlet union_comm #_ #_ s1 s2 =\n Classical.forall_intro (union_mem_aux s1 s2);\n Classical.forall_intro (union_mem_aux s2 s1);\n eq_intro_aux (union s1 s2) (union s2 s1)", "val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)\nlet cloc_of_loc l = l", "val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)\nlet cloc_of_loc l =\n assert_norm (MG.cls abuffer == MG.cls ubuffer);\n coerce (MG.loc cloc_cls) l", "val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)\nlet cloc_of_loc l = l", "val seq_equal_helper (#a: eqtype) (s1 s2: seq a)\n : Lemma\n (requires\n (let l1 = S.length s1 in\n let l2 = S.length s2 in\n l1 = l2 /\\ l1 > 0 /\\ SA.hprefix s1 = SA.hprefix s2 /\\ SA.telem s1 = SA.telem s2))\n (ensures (s1 = s2))\nlet seq_equal_helper (#a:eqtype) (s1 s2: seq a)\n : Lemma (requires (let l1 = S.length s1 in\n let l2 = S.length s2 in\n l1 = l2 /\\ l1 > 0 /\\ SA.hprefix s1 = SA.hprefix s2 /\\ SA.telem s1 = SA.telem s2))\n (ensures (s1 = s2))\n = let aux (i:_)\n : Lemma (ensures (S.index s1 i = S.index s2 i))\n = ()\n in\n forall_intro aux;\n assert(S.equal s1 s2)", "val loc_union_assoc\n (s1 s2 s3: loc)\n: Lemma\n (loc_union s1 (loc_union s2 s3) == loc_union (loc_union s1 s2) s3)\nlet loc_union_assoc = MG.loc_union_assoc", "val loc_union_assoc\n (s1 s2 s3: loc)\n: Lemma\n (loc_union s1 (loc_union s2 s3) == loc_union (loc_union s1 s2) s3)\nlet loc_union_assoc = MG.loc_union_assoc", "val v: #t_k:eqtype -> #t_v:Type0 -> h:HS.mem -> ll:t t_k t_v -> GTot (map t_k t_v)\nlet v #_ #_ h ll =\n let l = LL2.v h ll in\n v_ l", "val Vale.PPC64LE.Decls.loc_union = s1: Vale.PPC64LE.Memory.loc -> s2: Vale.PPC64LE.Memory.loc -> Prims.GTot Vale.PPC64LE.Memory.loc\nlet loc_union = M.loc_union", "val loc_union_comm\n (s1 s2: loc)\n: Lemma\n (loc_union s1 s2 == loc_union s2 s1)\n [SMTPat (loc_union s1 s2)]\nlet loc_union_comm = MG.loc_union_comm", "val loc_union_comm\n (s1 s2: loc)\n: Lemma\n (loc_union s1 s2 == loc_union s2 s1)\n [SMTPat (loc_union s1 s2)]\nlet loc_union_comm = MG.loc_union_comm", "val loc_aux_disjoint (l1 l2: loc_aux) : GTot Type0\nlet loc_aux_disjoint\n (l1 l2: loc_aux)\n: GTot Type0\n= match l2 with\n | LocBuffer b ->\n loc_aux_disjoint_buffer l1 b", "val equal\n (#t1 #t2: typ)\n (p1: pointer t1)\n (p2: pointer t2)\n: Ghost bool\n (requires True)\n (ensures (fun b -> b == true <==> t1 == t2 /\\ p1 == p2 ))\nlet equal\n (#t1 #t2: typ)\n (p1: pointer t1)\n (p2: pointer t2)\n: Ghost bool\n (requires True)\n (ensures (fun b -> b == true <==> t1 == t2 /\\ p1 == p2 ))\n= Pointer?.from p1 = Pointer?.from p2 &&\n HS.aref_equal (Pointer?.contents p1) (Pointer?.contents p2) &&\n path_equal (Pointer?.p p1) (Pointer?.p p2)", "val valid\n (#l: P.union_typ)\n (h: HS.mem)\n (tgs: tags l)\n (p: P.pointer (typ l))\n: GTot Type0\nlet valid\n (#l: P.union_typ)\n (h: HS.mem)\n (tgs: tags l)\n (p: P.pointer (typ l))\n: GTot Type0\n=\n let tag_ptr = P.gfield p (tag_field l) in\n let u_ptr = P.gfield p (union_field l) in\n let t = P.gread h tag_ptr in\n P.readable h tag_ptr /\\\n List.Tot.mem t tgs /\\\n (let f = field_of_tag #l tgs t in\n P.is_active_union_field h u_ptr f)", "val loc_union_idem_1 (s1 s2: loc)\n : Lemma (loc_union s1 (loc_union s1 s2) == loc_union s1 s2)\n [SMTPat (loc_union s1 (loc_union s1 s2))]\nlet loc_union_idem_1\n (s1 s2: loc)\n: Lemma\n (loc_union s1 (loc_union s1 s2) == loc_union s1 s2)\n [SMTPat (loc_union s1 (loc_union s1 s2))]\n= loc_union_assoc s1 s1 s2", "val subset (#a: eqtype) (s1: set a) (s2: set a)\n : Type0\nlet subset (#a: eqtype) (s1: set a) (s2: set a) : Type0 =\n forall x. (s1 x = true) ==> (s2 x = true)", "val loc_union_idem\n (s: loc)\n: Lemma\n (loc_union s s == s)\n [SMTPat (loc_union s s)]\nlet loc_union_idem = MG.loc_union_idem", "val loc_union_idem\n (s: loc)\n: Lemma\n (loc_union s s == s)\n [SMTPat (loc_union s s)]\nlet loc_union_idem = MG.loc_union_idem", "val loc_union_idem\n (s: loc)\n: Lemma\n (loc_union s s == s)\n [SMTPat (loc_union s s)]\nlet loc_union_idem = MG.loc_union_idem", "val old_to_union_loc (l: OldM.loc) : GTot (M.loc old_and_new_cl_union)\nlet old_to_union_loc (l: OldM.loc) : GTot (M.loc old_and_new_cl_union) =\n M.union_loc_of_loc old_and_new_cl false (OldM.cloc_of_loc l)", "val tl (#a: eqtype) (#f: cmp a) (s: mset a f {Cons? s}) : mset a f\nlet tl (#a:eqtype) (#f:cmp a) (s:mset a f{Cons? s}) : mset a f = tl s", "val ( ++^ ) (#a: Type0) (#rel: preorder a) (s: set nat) (r: mref a rel) : GTot (set nat)\nlet op_Plus_Plus_Hat (#a:Type0) (#rel:preorder a) (s:set nat) (r:mref a rel) :GTot (set nat) = S.union s (only r)", "val g_upd\n (#a: Type0)\n (#rrel #rel: srel a)\n (b: mbuffer a rrel rel)\n (i: nat{i < length b})\n (v: a)\n (h: HS.mem{live h b})\n : GTot HS.mem\nlet g_upd (#a:Type0) (#rrel #rel:srel a)\n (b:mbuffer a rrel rel)\n (i:nat{i < length b})\n (v:a)\n (h:HS.mem{live h b})\n : GTot HS.mem\n = g_upd_seq b (Seq.upd (as_seq h b) i v) h", "val union (l1 l2: B.loc) : GTot B.loc\nlet union (l1:B.loc) (l2:B.loc) : GTot B.loc = B.loc_union l1 l2", "val alloc : #a:Type -> \n x:a -> \n\t AllocST (ref a) (fun _ -> True)\n (fun h0 r h1 -> ~(contains r h0) /\\ \n\t\t\t\t\t fst (alloc_ref h0 a x) == r /\\ \n\t\t\t\t\t snd (alloc_ref h0 a x) == h1)\nlet alloc #a x = \n let h0 = ist_get () in\n let rh1 = alloc_ref h0 a x in \n ist_put (snd rh1); \n ist_witness (contains (fst rh1)); //witnessing that the current heap contains the generated reference\n fst rh1", "val choose (#a: eqtype) (s: set a{exists x. mem x s})\n : GTot (x: a{mem x s})\nlet choose (#a: eqtype) (s: set a{exists x. mem x s}) : GTot (x: a{mem x s}) =\n Cons?.hd (set_as_list s)", "val union_assoc (#a:eqtype) (#f:cmp a) (s1 s2 s3: mset a f)\n : Lemma (union (union s1 s2) s3 == union s1 (union s2 s3))\nlet union_assoc #a #_ s1 s2 s3 =\n let aux (x:a)\n : Lemma (mem x (union (union s1 s2) s3) == mem x (union s1 (union s2 s3)))\n = union_mem_aux (union s1 s2) s3 x;\n union_mem_aux s1 s2 x;\n union_mem_aux s1 (union s2 s3) x;\n union_mem_aux s2 s3 x\n in\n Classical.forall_intro aux;\n eq_intro_aux (union (union s1 s2) s3) (union s1 (union s2 s3))", "val loc_includes_union_l\n (s1 s2 s: loc)\n: Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))\nlet loc_includes_union_l = MG.loc_includes_union_l", "val live (#a:Type0) (#rrel #rel:srel a) (h:HS.mem) (b:mbuffer a rrel rel) :GTot Type0\nlet live #_ #rrel #rel h b =\n match b with\n | Null -> True\n | Buffer max_length content idx length ->\n h `HS.contains` content /\\\n buffer_compatible b", "val lemma_eq_intro_explicit\n (#a: Type)\n (s1: S.seq a)\n (s2: S.seq a {S.length s2 == S.length s1})\n (pf: (i: nat{i < S.length s1} -> Lemma (S.index s1 i == S.index s2 i)))\n : Lemma (S.equal s1 s2)\nlet lemma_eq_intro_explicit (#a : Type) (s1 : S.seq a) (s2 : S.seq a{S.length s2 == S.length s1})\n (pf : ((i:nat{i < S.length s1}) -> Lemma (S.index s1 i == S.index s2 i)))\n : Lemma (S.equal s1 s2)\n = Classical.forall_intro pf;\n S.lemma_eq_intro s1 s2", "val eq (#a:eqtype) (#f:cmp a) (s0 s1:mset a f)\n : b:bool { b <==> s0==s1 }\nlet eq (#a:eqtype) (#f:cmp a) (s0 s1:mset a f) \n : b:bool { b <==> (s0 == s1) }\n = s0 = s1" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_mreference" }, { "project_name": "FStar", "file_name": "FStar.TSet.fst", "name": "FStar.TSet.equal" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_freed_mreference" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc_union" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc_union" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_union" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_union" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_union" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_region_only" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.equal" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_includes" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_all_regions_from" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.equal" }, { "project_name": "FStar", "file_name": "Benton2004.Aux.fst", "name": "Benton2004.Aux.holds" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2.Common.fst", "name": "Hacl.Streaming.Blake2.Common.s_v" }, { "project_name": "FStar", "file_name": "FStar.Set.fst", "name": "FStar.Set.equal" }, { "project_name": "FStar", "file_name": "FStar.FiniteSet.Base.fst", "name": "FStar.FiniteSet.Base.equal" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fsti", "name": "LowParse.Low.Base.Spec.clens_eq" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fsti", "name": "FStar.OrdSet.equal" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_aux_includes" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc_includes" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc_includes" }, { "project_name": "FStar", "file_name": "LowStar.Lens.fsti", "name": "LowStar.Lens.as_loc" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.any" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_includes_pointer" }, { "project_name": "hacl-star", "file_name": "Vale.Transformers.BoundedInstructionEffects.fsti", "name": "Vale.Transformers.BoundedInstructionEffects.unchanged_at" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.all" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_includes" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.equal" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.equal" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc_disjoint" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc_disjoint" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.fst", "name": "Pulse.Lib.Array.compare" }, { "project_name": "zeta", "file_name": "Zeta.MultiSetHashDomain.fst", "name": "Zeta.MultiSetHashDomain.compare_lseq'" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.sel" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.union_aux" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.equal" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.cloc_aloc" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.loc" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.includes" }, { "project_name": "FStar", "file_name": "Benton2004.SmithVolpano.fsti", "name": "Benton2004.SmithVolpano.eval_equiv" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.eq_elim" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.op_Hat_Plus_Plus" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_disjoint_pointer" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_union_idem_2" }, { "project_name": "hacl-star", "file_name": "Vale.X64.QuickCodes.fsti", "name": "Vale.X64.QuickCodes.eval_cmp" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.QuickCodes.fsti", "name": "Vale.PPC64LE.QuickCodes.eval_cmp" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.fresh_loc" }, { "project_name": "FStar", "file_name": "FStar.Array.fsti", "name": "FStar.Array.sel" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2.Common.fst", "name": "Hacl.Streaming.Blake2.Common.state_v" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.eq_intro" }, { "project_name": "steel", "file_name": "Steel.ST.Array.Util.fsti", "name": "Steel.ST.Array.Util.compare" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.union" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.compare" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fsti", "name": "Benton2004.RHL.geq" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_pointer" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.op_Hat_Plus_Hat" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.eq" }, { "project_name": "FStar", "file_name": "FStar.TSet.fst", "name": "FStar.TSet.lemma_equal_elim" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.disjoint" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_includes_loc_aux_includes_pointer" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.union_comm" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.cloc_of_loc" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.cloc_of_loc" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.cloc_of_loc" }, { "project_name": "zeta", "file_name": "Zeta.Interleave.fst", "name": "Zeta.Interleave.seq_equal_helper" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_union_assoc" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_union_assoc" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.v" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.loc_union" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_union_comm" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_union_comm" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_aux_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.equal" }, { "project_name": "FStar", "file_name": "FStar.TaggedUnion.fst", "name": "FStar.TaggedUnion.valid" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_union_idem_1" }, { "project_name": "FStar", "file_name": "FStar.FiniteSet.Base.fst", "name": "FStar.FiniteSet.Base.subset" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_union_idem" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_union_idem" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_union_idem" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.old_to_union_loc" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.tl" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.op_Plus_Plus_Hat" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.g_upd" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.union" }, { "project_name": "FStar", "file_name": "AllocST.fst", "name": "AllocST.alloc" }, { "project_name": "FStar", "file_name": "FStar.FiniteSet.Base.fst", "name": "FStar.FiniteSet.Base.choose" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.union_assoc" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_union_l" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.live" }, { "project_name": "steel", "file_name": "MSort.SeqLemmas.fst", "name": "MSort.SeqLemmas.lemma_eq_intro_explicit" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.eq" } ], "selected_premises": [ "FStar.FunctionalExtensionality.feq", "FStar.ModifiesGen.loc", "FStar.ModifiesGen.loc_union", "FStar.Reflection.V2.Data.var", "FStar.ModifiesGen.loc_none", "FStar.Pervasives.Native.fst", "FStar.ModifiesGen.addrs_of_loc_aux", "FStar.Pervasives.Native.snd", "FStar.ModifiesGen.addrs_of_loc_weak", "FStar.Reflection.Const.cons_qn", "FStar.Heap.trivial_preorder", "FStar.FunctionalExtensionality.on_dom", "FStar.ModifiesGen.addrs_of_loc_aux_pred", "FStar.ModifiesGen.addrs_of_loc_liveness_not_preserved", "FStar.Tactics.Effect.raise", "FStar.Monotonic.HyperStack.sel", "FStar.ModifiesGen.addrs_of_loc", "FStar.Reflection.Const.squash_qn", "FStar.Reflection.Const.nil_qn", "FStar.Tactics.V2.Builtins.ret_t", "FStar.ModifiesGen.i_restricted_g_t", "FStar.ModifiesGen.aloc_domain", "FStar.Tactics.SMT.get_initial_fuel", "FStar.ModifiesGen.regions_of_loc", "FStar.Tactics.SMT.get_rlimit", "FStar.Tactics.Types.issues", "FStar.Tactics.SMT.get_max_fuel", "FStar.Monotonic.HyperStack.is_heap_color", "FStar.Monotonic.HyperStack.live_region", "FStar.Reflection.V2.Data.ppname_t", "FStar.ModifiesGen.mk_non_live_addrs", "FStar.Monotonic.HyperStack.mreference", "FStar.Tactics.SMT.get_initial_ifuel", "FStar.FunctionalExtensionality.on", "FStar.HyperStack.ST.is_eternal_region", "FStar.ModifiesGen.mk_live_addrs", "FStar.Sealed.Inhabited.seal", "FStar.Tactics.SMT.get_max_ifuel", "FStar.Pervasives.dfst", "FStar.Monotonic.HyperStack.is_stack_region", "FStar.Reflection.Const.imp_qn", "FStar.Monotonic.HyperStack.as_addr", "FStar.Reflection.Const.or_qn", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater", "FStar.ModifiesGen.addrs_dom", "FStar.Reflection.Const.prop_qn", "FStar.Reflection.Const.eq1_qn", "FStar.Pervasives.dsnd", "FStar.Sealed.Inhabited.sealed", "FStar.Reflection.Const.eq2_qn", "FStar.Monotonic.HyperStack.frameOf", "FStar.Reflection.Const.mult_qn", "FStar.Tactics.SMT.smt_sync", "FStar.Reflection.Const.and_qn", "FStar.Reflection.Const.string_lid", "FStar.Monotonic.HyperStack.is_above", "FStar.Tactics.Effect.get", "FStar.Reflection.Const.mult'_qn", "FStar.Reflection.V2.Data.as_ppname", "FStar.Reflection.Const.b2t_qn", "FStar.Tactics.SMT.set_rlimit", "FStar.FunctionalExtensionality.restricted_t", "FStar.Tactics.SMT.smt_sync'", "FStar.Reflection.Const.iff_qn", "FStar.Reflection.Const.forall_qn", "FStar.Tactics.SMT.set_initial_fuel", "FStar.ModifiesGen.fun_set_equal", "FStar.Reflection.Const.bool_lid", "FStar.Monotonic.HyperStack.is_mm", "FStar.Issue.mk_issue", "FStar.Tactics.SMT.set_max_fuel", "FStar.Tactics.SMT.set_fuel", "FStar.Pervasives.reveal_opaque", "FStar.FunctionalExtensionality.arrow", "FStar.Monotonic.HyperStack.modifies_one", "FStar.Monotonic.HyperHeap.modifies_just", "FStar.Reflection.Const.unit_lid", "FStar.Monotonic.HyperStack.is_in", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater_Greater", "FStar.Sealed.Inhabited.sealed_", "FStar.Reflection.V2.Data.notAscription", "FStar.Reflection.Const.udiv_qn", "FStar.Tactics.Effect.tac", "FStar.Monotonic.HyperHeap.disjoint", "FStar.Sealed.Inhabited.is_sealed", "FStar.Reflection.Const.lsub_qn", "FStar.Reflection.Const.mktuple8_qn", "FStar.Reflection.Const.mktuple3_qn", "FStar.Reflection.Const.mod_qn", "FStar.Tactics.SMT.set_ifuel", "FStar.Reflection.Const.mktuple7_qn", "FStar.Tactics.SMT.set_initial_ifuel", "FStar.Monotonic.HyperStack.is_eternal_region_hs", "FStar.Monotonic.HyperHeap.modifies", "FStar.Monotonic.HyperStack.remove_elt", "FStar.FunctionalExtensionality.feq_g", "FStar.Monotonic.HyperStack.contains", "FStar.Tactics.SMT.set_max_ifuel", "FStar.ModifiesGen.live_addrs_codom", "FStar.Reflection.Const.mktuple2_qn" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.ModifiesGen\n\n#set-options \"--split_queries no\"\n#set-options \"--using_facts_from '*,-FStar.Tactics,-FStar.Reflection,-FStar.List'\"\n\nmodule HS = FStar.HyperStack\nmodule HST = FStar.HyperStack.ST\n\nnoeq\ntype aloc (#al: aloc_t) (c: cls al) = | ALoc:\n (region: HS.rid) ->\n (addr: nat) ->\n (loc: option (al region addr)) ->\n aloc c\n\nlet aloc_domain (#al: aloc_t) (c: cls al) (regions: Ghost.erased (Set.set HS.rid)) (addrs: ((r: HS.rid { Set.mem r (Ghost.reveal regions) } ) -> GTot (GSet.set nat))) : GTot (GSet.set (aloc c)) =\n GSet.comprehend (fun a -> Set.mem a.region (Ghost.reveal regions) && GSet.mem a.addr (addrs a.region))\n\nmodule F = FStar.FunctionalExtensionality\n\n[@@(unifier_hint_injective)]\nlet i_restricted_g_t = F.restricted_g_t\n\nlet addrs_dom regions =\n (r: HS.rid { Set.mem r (Ghost.reveal regions) } )\n\nlet non_live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (r:addrs_dom regions) =\n (y: GSet.set nat { r `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y })\n\nlet live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags))\n (r:addrs_dom regions) = (y: GSet.set nat { GSet.subset (non_live_addrs r) y } )\n\nnoeq\ntype loc' (#al: aloc_t u#x) (c: cls al) : Type u#x =\n | Loc:\n (regions: Ghost.erased (Set.set HS.rid)) ->\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } ) ->\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags)) ->\n (live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs)) ->\n (aux: Ghost.erased (GSet.set (aloc c)) {\n aloc_domain c regions live_addrs `GSet.subset` Ghost.reveal aux /\\\n Ghost.reveal aux `GSet.subset` (aloc_domain c regions (fun _ -> GSet.complement GSet.empty))\n } ) ->\n loc' c\n\nlet loc = loc'\n\nlet mk_non_live_addrs (#regions:_) (#region_liveness_tags:_)\n (f: (x:addrs_dom regions -> GTot (non_live_addrs_codom regions region_liveness_tags x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags) =\n F.on_dom_g _ f\n\nlet mk_live_addrs (#regions:_) (#region_liveness_tags:_)\n (#non_live_addrs_codom: _)\n (f: (x:addrs_dom regions -> GTot (live_addrs_codom regions region_liveness_tags non_live_addrs_codom x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs_codom) =\n F.on_dom_g _ f\n\nlet loc_none #a #c =\n Loc\n (Ghost.hide (Set.empty))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)\n\nlet regions_of_loc\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: GTot (Set.set HS.rid)\n= Ghost.reveal (Loc?.regions s)\n\nlet addrs_of_loc_liveness_not_preserved\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.non_live_addrs l r\n else GSet.empty\n\nlet addrs_of_loc_weak\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.live_addrs l r\n else GSet.empty\n\nlet addrs_of_loc_aux_pred\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n (addr: nat)\n: GTot bool\n= StrongExcludedMiddle.strong_excluded_middle (exists a . GSet.mem a (Ghost.reveal (Loc?.aux l)) /\\ a.region == r /\\ a.addr == addr)\n\nlet addrs_of_loc_aux\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (y: GSet.set nat { GSet.subset (GSet.intersect y (addrs_of_loc_weak l r)) GSet.empty } )\n= GSet.comprehend (addrs_of_loc_aux_pred l r)\n `GSet.intersect` (GSet.complement (addrs_of_loc_weak l r))\n\nlet addrs_of_loc\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= GSet.union\n (addrs_of_loc_weak l r)\n (addrs_of_loc_aux l r)\n\nlet addrs_of_loc_aux_prop\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: Lemma\n (GSet.subset (GSet.intersect (addrs_of_loc_aux l r) (addrs_of_loc_weak l r)) GSet.empty)\n [SMTPatOr [\n [SMTPat (addrs_of_loc_aux l r)];\n [SMTPat (addrs_of_loc_weak l r)];\n [SMTPat (addrs_of_loc l r)];\n ]]\n= ()\n\nlet loc_union #al #c s1 s2 =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in\n let regions = Set.union regions1 regions2 in\n let region_liveness_tags : Ghost.erased (Set.set HS.rid) = (Ghost.hide (Set.union (Ghost.reveal (Loc?.region_liveness_tags s1)) (Ghost.reveal (Loc?.region_liveness_tags s2)))) in\n let gregions = Ghost.hide regions in\n let non_live_addrs =\n F.on_dom_g (addrs_dom gregions) #(non_live_addrs_codom gregions region_liveness_tags)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then Loc?.non_live_addrs s1 r else GSet.empty)\n (if Set.mem r regions2 then Loc?.non_live_addrs s2 r else GSet.empty))\n in\n let live_addrs =\n F.on_dom_g (addrs_dom gregions) #(live_addrs_codom gregions region_liveness_tags non_live_addrs)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then addrs_of_loc_weak s1 r else GSet.empty)\n (if Set.mem r regions2 then addrs_of_loc_weak s2 r else GSet.empty))\n in\n let aux = Ghost.hide\n (Ghost.reveal (Loc?.aux s1) `GSet.union` Ghost.reveal (Loc?.aux s2))\n in\n Loc\n (Ghost.hide regions)\n region_liveness_tags\n non_live_addrs\n live_addrs\n aux\n\nlet fun_set_equal (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) :Tot Type0 =\n forall (x: t) . {:pattern (f1 x) \\/ (f2 x) } f1 x `GSet.equal` f2 x\n\nlet fun_set_equal_elim (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) : Lemma\n (requires (fun_set_equal f1 f2))\n (ensures (f1 == f2))\n// [SMTPat (fun_set_equal f1 f2)]\n= assert (f1 `FunctionalExtensionality.feq_g` f2)\n", "sketch": [ "Step 1: The `loc_equal` function aims to define a type that checks if two `loc` values are equal.\nStep 2: To implement this, we need to ensure that all components of the `loc` type are equal. This includes checking the equality of regions, region liveness tags, non-live addresses, live addresses, and auxiliary sets.", "Step 1: The definition `loc_equal` is about determining whether two `loc` instances are equal. This involves checking if all their respective components are equal.\nStep 2: To implement this, we need to ensure that the regions, region liveness tags, non-live addresses, live addresses, and auxiliary sets of both `loc` instances are equal.", "Step 1: The definition `loc_equal` is about determining whether two `loc` values are equal. This involves checking if all their corresponding components are equal.\nStep 2: To implement this, we need to compare the `regions`, `region_liveness_tags`, `non_live_addrs`, `live_addrs`, and `aux` fields of the two `loc` values. If all these components are equal, then the two `loc` values are considered equal.", "Step 1: The definition `loc_equal` is about determining if two `loc` values are equal. This involves checking if all their respective components are equal.\nStep 2: To implement this, we will compare the regions, region liveness tags, non-live addresses, live addresses, and auxiliary sets of the two `loc` values. If all these components are equal, then the two `loc` values are considered equal.", "Step 1: The definition `loc_equal` is about determining whether two `loc` instances are equal. This involves checking if all their respective components are equal.\nStep 2: To implement this, we need to compare the `regions`, `region_liveness_tags`, `non_live_addrs`, `live_addrs`, and `aux` fields of the two `loc` instances. If all these components are equal, then the two `loc` instances are considered equal.", "Step 1: The definition `loc_equal` is about determining whether two `loc` values, `s1` and `s2`, are equal.\nStep 2: To implement this, we need to check if the regions, region liveness tags, non-live addresses, live addresses, and auxiliary sets of both `loc` values are equal. This involves comparing each component of the `loc` type for equality.", "Step 1: The definition `loc_equal` aims to determine if two `loc` values, `s1` and `s2`, are equal. This involves checking if all their components are equal.\nStep 2: To implement this, we need to compare the `regions`, `region_liveness_tags`, `non_live_addrs`, `live_addrs`, and `aux` components of `s1` and `s2`. If all these components are equal, then `s1` and `s2` are considered equal.", "Step 1: The `loc_equal` function aims to define a type that ensures two `loc` structures are equal.\nStep 2: To implement this, we need to check that all components of the `loc` structures are equal. This includes checking the equality of the `regions`, `region_liveness_tags`, `non_live_addrs`, `live_addrs`, and `aux` fields.", "Step 1: The definition `loc_equal` is about determining if two `loc` structures are equal. This involves checking if all the components of the `loc` structures are equal.\nStep 2: To implement this, we need to compare the `regions`, `region_liveness_tags`, `non_live_addrs`, `live_addrs`, and `aux` fields of the two `loc` structures. If all these fields are equal, then the two `loc` structures are considered equal.", "Step 1: The `loc_equal` function aims to define a type that ensures two `loc` instances are equal.\nStep 2: To implement this, we need to check that the regions, region liveness tags, non-live addresses, live addresses, and auxiliary sets of both `loc` instances are equal. This involves comparing each of these components using appropriate equality checks." ], "generated_solution": [ "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n Ghost.reveal (Loc?.regions s1) `Set.equal` Ghost.reveal (Loc?.regions s2) /\\\n Ghost.reveal (Loc?.region_liveness_tags s1) `Set.equal` Ghost.reveal (Loc?.region_liveness_tags s2) /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n regions_of_loc s1 `Set.equal` regions_of_loc s2 /\\\n Ghost.reveal (Loc?.region_liveness_tags s1) `Set.equal` Ghost.reveal (Loc?.region_liveness_tags s2) /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n Ghost.reveal (Loc?.regions s1) `Set.equal` Ghost.reveal (Loc?.regions s2) /\\\n Ghost.reveal (Loc?.region_liveness_tags s1) `Set.equal` Ghost.reveal (Loc?.region_liveness_tags s2) /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n Ghost.reveal (Loc?.regions s1) `Set.equal` Ghost.reveal (Loc?.regions s2) /\\\n Ghost.reveal (Loc?.region_liveness_tags s1) `Set.equal` Ghost.reveal (Loc?.region_liveness_tags s2) /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n Ghost.reveal (Loc?.regions s1) `Set.equal` Ghost.reveal (Loc?.regions s2) /\\\n Ghost.reveal (Loc?.region_liveness_tags s1) `Set.equal` Ghost.reveal (Loc?.region_liveness_tags s2) /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n Ghost.reveal (Loc?.regions s1) `Set.equal` Ghost.reveal (Loc?.regions s2) /\\\n Ghost.reveal (Loc?.region_liveness_tags s1) `Set.equal` Ghost.reveal (Loc?.region_liveness_tags s2) /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n Ghost.reveal (Loc?.regions s1) `Set.equal` Ghost.reveal (Loc?.regions s2) /\\\n Ghost.reveal (Loc?.region_liveness_tags s1) `Set.equal` Ghost.reveal (Loc?.region_liveness_tags s2) /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n regions_of_loc s1 `Set.equal` regions_of_loc s2 /\\\n Ghost.reveal (Loc?.region_liveness_tags s1) `Set.equal` Ghost.reveal (Loc?.region_liveness_tags s2) /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n Ghost.reveal (Loc?.regions s1) `Set.equal` Ghost.reveal (Loc?.regions s2) /\\\n Ghost.reveal (Loc?.region_liveness_tags s1) `Set.equal` Ghost.reveal (Loc?.region_liveness_tags s2) /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n regions_of_loc s1 `Set.equal` regions_of_loc s2 /\\\n Ghost.reveal (Loc?.region_liveness_tags s1) `Set.equal` Ghost.reveal (Loc?.region_liveness_tags s2) /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)" ] }, { "file_name": "LowParse.Endianness.fst", "name": "LowParse.Endianness.n_to_le_append", "opens_and_abbrevs": [ { "open": "FStar.Math.Lemmas" }, { "abbrev": "U8", "full_module": "FStar.UInt8" }, { "abbrev": "S", "full_module": "FStar.Seq" }, { "open": "FStar.Mul" }, { "open": "FStar.Endianness" }, { "open": "LowParse" }, { "open": "LowParse" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val n_to_le_append (len n len_lo: nat)\n : Lemma (requires (n < pow2 (8 * len) /\\ len_lo <= len))\n (ensures\n (let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n 0 <= hi /\\ hi < pow2 (8 * (len - len_lo)) /\\ 0 <= lo /\\ lo < pow2 (8 * len_lo) /\\\n n_to_le len n == (n_to_le len_lo lo) `S.append` (n_to_le (len - len_lo) hi)))", "source_definition": "let n_to_le_append\n (len: nat)\n (n: nat)\n (len_lo: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len) /\\\n len_lo <= len\n ))\n (ensures (\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n 0 <= hi /\\\n hi < pow2 (8 * (len - len_lo)) /\\\n 0 <= lo /\\\n lo < pow2 (8 * len_lo) /\\\n n_to_le len n == n_to_le len_lo lo `S.append` n_to_le (len - len_lo) hi\n ))\n=\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n n_to_be_append len n len_lo;\n n_to_le_eq_rev_n_to_be len n;\n n_to_le_eq_rev_n_to_be len_lo lo;\n n_to_le_eq_rev_n_to_be (len - len_lo) hi;\n seq_rev_append (n_to_be (len - len_lo) hi) (n_to_be len_lo lo)", "source_range": { "start_line": 288, "start_col": 0, "end_line": 313, "end_col": 64 }, "interleaved": false, "definition": "fun len n len_lo ->\n (let hi = n / Prims.pow2 (8 * len_lo) in\n let lo = n % Prims.pow2 (8 * len_lo) in\n LowParse.Endianness.n_to_be_append len n len_lo;\n LowParse.Endianness.n_to_le_eq_rev_n_to_be len n;\n LowParse.Endianness.n_to_le_eq_rev_n_to_be len_lo lo;\n LowParse.Endianness.n_to_le_eq_rev_n_to_be (len - len_lo) hi;\n LowParse.Endianness.seq_rev_append (FStar.Endianness.n_to_be (len - len_lo) hi)\n (FStar.Endianness.n_to_be len_lo lo))\n <:\n FStar.Pervasives.Lemma (requires n < Prims.pow2 (8 * len) /\\ len_lo <= len)\n (ensures\n (let hi = n / Prims.pow2 (8 * len_lo) in\n let lo = n % Prims.pow2 (8 * len_lo) in\n 0 <= hi /\\ hi < Prims.pow2 (8 * (len - len_lo)) /\\ 0 <= lo /\\ lo < Prims.pow2 (8 * len_lo) /\\\n FStar.Endianness.n_to_le len n ==\n FStar.Seq.Base.append (FStar.Endianness.n_to_le len_lo lo)\n (FStar.Endianness.n_to_le (len - len_lo) hi)))", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "Prims.nat", "LowParse.Endianness.seq_rev_append", "FStar.UInt8.t", "FStar.Endianness.n_to_be", "Prims.op_Subtraction", "Prims.unit", "LowParse.Endianness.n_to_le_eq_rev_n_to_be", "LowParse.Endianness.n_to_be_append", "Prims.int", "Prims.op_Modulus", "Prims.pow2", "FStar.Mul.op_Star", "Prims.op_Division", "Prims.l_and", "Prims.b2t", "Prims.op_LessThan", "Prims.op_LessThanOrEqual", "Prims.squash", "Prims.eq2", "FStar.Seq.Base.seq", "FStar.Endianness.n_to_le", "FStar.Seq.Base.append", "Prims.Nil", "FStar.Pervasives.pattern" ], "proof_features": [], "is_simple_lemma": true, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "len: Prims.nat -> n: Prims.nat -> len_lo: Prims.nat\n -> FStar.Pervasives.Lemma (requires n < Prims.pow2 (8 * len) /\\ len_lo <= len)\n (ensures\n (let hi = n / Prims.pow2 (8 * len_lo) in\n let lo = n % Prims.pow2 (8 * len_lo) in\n 0 <= hi /\\ hi < Prims.pow2 (8 * (len - len_lo)) /\\ 0 <= lo /\\ lo < Prims.pow2 (8 * len_lo) /\\\n FStar.Endianness.n_to_le len n ==\n FStar.Seq.Base.append (FStar.Endianness.n_to_le len_lo lo)\n (FStar.Endianness.n_to_le (len - len_lo) hi)))", "prompt": "let n_to_le_append (len n len_lo: nat)\n : Lemma (requires (n < pow2 (8 * len) /\\ len_lo <= len))\n (ensures\n (let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n 0 <= hi /\\ hi < pow2 (8 * (len - len_lo)) /\\ 0 <= lo /\\ lo < pow2 (8 * len_lo) /\\\n n_to_le len n == (n_to_le len_lo lo) `S.append` (n_to_le (len - len_lo) hi))) =\n ", "expected_response": "let hi = n / pow2 (8 * len_lo) in\nlet lo = n % pow2 (8 * len_lo) in\nn_to_be_append len n len_lo;\nn_to_le_eq_rev_n_to_be len n;\nn_to_le_eq_rev_n_to_be len_lo lo;\nn_to_le_eq_rev_n_to_be (len - len_lo) hi;\nseq_rev_append (n_to_be (len - len_lo) hi) (n_to_be len_lo lo)", "source": { "project_name": "everparse", "file_name": "src/lowparse/LowParse.Endianness.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git" }, "dependencies": { "source_file": "LowParse.Endianness.fst", "checked_file": "dataset/LowParse.Endianness.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Math.Lemmas.fst.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "let rec index_be_to_n'\n (b: bytes)\n (i: nat)\n: Lemma\n (requires (\n i < S.length b\n ))\n (ensures (\n U8.v (S.index b i) == (be_to_n b / pow2 (8 * (S.length b - 1 - i))) % pow2 8\n ))\n (decreases (S.length b))\n= reveal_be_to_n b;\n if i = S.length b - 1\n then ()\n else begin\n let l = S.length b in\n let l' = l - 1 in\n let b' = S.slice b 0 l' in\n index_be_to_n' b' i;\n assert (S.index b i == S.index b' i);\n let open FStar.Math.Lemmas in\n let x = be_to_n b in\n let x' = be_to_n b' in\n assert (U8.v (S.index b i) == x' / pow2 (8 * (l' - 1 - i)) % pow2 8);\n let y = (U8.v (S.last b) + pow2 8 * x') / pow2 (8 * (l - 1 - i)) % pow2 8 in\n pow2_plus 8 (8 * (l' - 1 - i));\n division_multiplication_lemma (U8.v (S.last b) + pow2 8 * x') (pow2 8) (pow2 (8 * (l' - 1 - i)));\n assert (pow2 8 * x' == x' * pow2 8);\n division_addition_lemma (U8.v (S.last b)) (pow2 8) x';\n small_division_lemma_1 (U8.v (S.last b)) (pow2 8);\n assert (y == x' / pow2 (8 * (l' - 1 - i)) % pow2 8)\n end", "val index_be_to_n\n (b: bytes)\n (i: nat)\n: Lemma\n (requires (\n i < S.length b\n ))\n (ensures (\n U8.v (S.index b i) == (be_to_n b / pow2 (8 * (S.length b - 1 - i))) % pow2 8\n ))", "val index_n_to_be\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i)) == (n / pow2 (8 * (len - 1 - i)) % pow2 8\n ))", "val index_n_to_be_zero_left\n (len: nat)\n (n: nat)\n (j: nat)\n (i: nat)\n: Lemma\n (requires (\n i < j /\\\n j <= len /\\\n n < pow2 (8 * (len - j))\n ))\n (ensures (\n pow2 (8 * (len - j)) <= pow2 (8 * len) /\\\n U8.v (S.index (n_to_be len n) i) == 0\n ))", "let index_be_to_n = index_be_to_n'", "let index_n_to_be\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i)) == (n / pow2 (8 * (len - 1 - i)) % pow2 8\n ))\n= index_be_to_n (n_to_be len n) i", "val index_n_to_be_zero_right\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len) /\\\n n % pow2 (8 * (len - i)) == 0\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i) == 0\n ))", "let index_n_to_be_zero_left\n (len: nat)\n (n: nat)\n (j: nat)\n (i: nat)\n: Lemma\n (requires (\n i < j /\\\n j <= len /\\\n n < pow2 (8 * (len - j))\n ))\n (ensures (\n pow2 (8 * (len - j)) <= pow2 (8 * len) /\\\n U8.v (S.index (n_to_be len n) i) == 0\n ))\n= let open FStar.Math.Lemmas in\n pow2_le_compat (8 * len) (8 * (len - j));\n pow2_le_compat (8 * (len - 1 - i)) (8 * (len - j));\n small_division_lemma_1 n (pow2 (8 * (len - 1 - i)));\n index_n_to_be len n i", "val be_to_n_append\n (hi lo: bytes)\n: Lemma\n (ensures (be_to_n (hi `S.append` lo) == be_to_n hi * pow2 (8 * S.length lo) + be_to_n lo))", "val n_to_be_append\n (len: nat)\n (n: nat)\n (len_lo: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len) /\\\n len_lo <= len\n ))\n (ensures (\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n 0 <= hi /\\\n hi < pow2 (8 * (len - len_lo)) /\\\n 0 <= lo /\\\n lo < pow2 (8 * len_lo) /\\\n n_to_be len n == n_to_be (len - len_lo) hi `S.append` n_to_be len_lo lo\n ))", "let index_n_to_be_zero_right\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len) /\\\n n % pow2 (8 * (len - i)) == 0\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i) == 0\n ))\n= index_n_to_be len n i;\n let open FStar.Math.Lemmas in\n modulo_division_lemma n (pow2 (8 * (len - 1 - i))) (pow2 8);\n pow2_plus (8 * (len - 1 - i)) 8", "val reveal_n_to_be\n (len: nat)\n (n: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len)\n ))\n (ensures (\n (len > 0 ==> (0 <= n / pow2 8 /\\ n / pow2 8 < pow2 (8 * (len - 1)))) /\\\n n_to_be len n `S.equal` (if len = 0 then S.empty else n_to_be (len - 1) (n / pow2 8) `S.snoc` (U8.uint_to_t (n % pow2 8)))\n ))", "let rec be_to_n_append'\n (hi lo: bytes)\n: Lemma\n (ensures (be_to_n (hi `S.append` lo) == be_to_n hi * pow2 (8 * S.length lo) + be_to_n lo))\n (decreases (S.length lo))\n= reveal_be_to_n lo;\n let hilo = hi `S.append` lo in\n if S.length lo = 0\n then\n assert (hilo `S.equal` hi)\n else begin\n let lo' = S.slice lo 0 (S.length lo - 1) in\n assert (S.slice hilo 0 (S.length hilo - 1) `S.equal` (hi `S.append` lo'));\n assert (S.last hilo == S.last lo);\n reveal_be_to_n hilo;\n be_to_n_append' hi lo';\n pow2_plus (8 * S.length lo') 8\n end", "val slice_n_to_be\n (len: nat)\n (n: nat)\n (i j: nat)\n: Lemma\n (requires (\n i <= j /\\\n j <= len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n let res = (n / pow2 (8 * (len - j))) % pow2 (8 * (j - i)) in\n 0 <= res /\\\n res < pow2 (8 * (j - i)) /\\\n S.slice (n_to_be len n) i j == n_to_be (j - i) res\n ))", "let be_to_n_append = be_to_n_append'", "let lemma_div_zero (x: pos) : Lemma\n (0 / x == 0)\n= ()", "val index_le_to_n\n (b: bytes)\n (i: nat)\n: Lemma\n (requires (\n i < S.length b\n ))\n (ensures (\n U8.v (S.index b i) == (le_to_n b / pow2 (8 * i)) % pow2 8\n ))", "let n_to_be_append\n (len: nat)\n (n: nat)\n (len_lo: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len) /\\\n len_lo <= len\n ))\n (ensures (\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n 0 <= hi /\\\n hi < pow2 (8 * (len - len_lo)) /\\\n 0 <= lo /\\\n lo < pow2 (8 * len_lo) /\\\n n_to_be len n == n_to_be (len - len_lo) hi `S.append` n_to_be len_lo lo\n ))\n= lemma_div_zero (pow2 (8 * len_lo));\n lemma_div_le 0 n (pow2 (8 * len_lo));\n lemma_mod_lt n (pow2 (8 * len_lo));\n let hi = n / pow2 (8 * len_lo) in\n assert (0 <= hi);\n lemma_div_lt n (8 * len) (8 * len_lo);\n pow2_minus (8 * len) (8 * len_lo);\n let lo = n % pow2 (8 * len_lo) in\n euclidean_division_definition n (pow2 (8 * len_lo));\n let hi_s = n_to_be (len - len_lo) hi in\n let lo_s = n_to_be len_lo lo in\n be_to_n_append hi_s lo_s;\n assert (be_to_n (hi_s `S.append` lo_s) == n);\n be_to_n_inj (hi_s `S.append` lo_s) (n_to_be len n)", "val index_n_to_le\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n U8.v (S.index (n_to_le len n) i)) == (n / pow2 (8 * i) % pow2 8\n ))", "val reveal_n_to_le\n (len: nat)\n (n: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len)\n ))\n (ensures (\n (len > 0 ==> (0 <= n / pow2 8 /\\ n / pow2 8 < pow2 (8 * (len - 1)))) /\\\n n_to_le len n `S.equal` (if len = 0 then S.empty else (U8.uint_to_t (n % pow2 8) `S.cons` n_to_le (len - 1) (n / pow2 8)))\n ))", "let reveal_n_to_be\n (len: nat)\n (n: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len)\n ))\n (ensures (\n (len > 0 ==> (0 <= n / pow2 8 /\\ n / pow2 8 < pow2 (8 * (len - 1)))) /\\\n n_to_be len n `S.equal` (if len = 0 then S.empty else n_to_be (len - 1) (n / pow2 8) `S.snoc` (U8.uint_to_t (n % pow2 8)))\n ))\n= if len = 0\n then ()\n else begin\n n_to_be_append len n 1;\n index_n_to_be 1 (n % pow2 8) 0\n end", "let slice_n_to_be\n (len: nat)\n (n: nat)\n (i j: nat)\n: Lemma\n (requires (\n i <= j /\\\n j <= len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n let res = (n / pow2 (8 * (len - j))) % pow2 (8 * (j - i)) in\n 0 <= res /\\\n res < pow2 (8 * (j - i)) /\\\n S.slice (n_to_be len n) i j == n_to_be (j - i) res\n ))\n= let s1 = S.slice (n_to_be len n) 0 j in\n let s2 = S.slice s1 i j in\n n_to_be_append len n (len - j);\n let q = n / pow2 (8 * (len - j)) in\n n_to_be_append j q (j - i);\n let r = q % pow2 (8 * (j - i)) in\n assert (s2 `S.equal` n_to_be (j - i) (q % pow2 (8 * (j - i))))", "let rec seq_rev\n (#t: Type)\n (x: S.seq t)\n: Tot (y: S.seq t {S.length y == S.length x})\n (decreases (S.length x))\n= if S.length x = 0\n then S.empty\n else seq_rev (S.tail x) `S.append` S.create 1 (S.head x)", "let rec index_seq_rev'\n (#t: Type)\n (x: S.seq t)\n (i: nat {i < S.length x})\n: Lemma\n (ensures (S.index (seq_rev x) (S.length x - 1 - i) == S.index x i))\n (decreases (S.length x))\n= if i = 0\n then\n S.lemma_index_create 1 (S.head x) 0\n else\n index_seq_rev' (S.tail x) (i - 1)", "let index_seq_rev\n (#t: Type)\n (x: S.seq t)\n (i: nat {i < S.length x})\n: Lemma\n (ensures (S.index (seq_rev x) i == S.index x (S.length x - 1 - i)))\n= index_seq_rev' x (S.length x - 1 - i)", "let slice_seq_rev\n (#t: Type)\n (x: S.seq t)\n (i: nat)\n (j: nat)\n: Lemma\n (requires (i <= j /\\ j <= S.length x))\n (ensures (S.slice (seq_rev x) i j `S.equal` seq_rev (S.slice x (S.length x - j) (S.length x - i))))\n= Classical.forall_intro (index_seq_rev x);\n Classical.forall_intro (index_seq_rev (S.slice x (S.length x - j) (S.length x - i)))", "let rec le_to_n_eq_be_to_n_rev\n (b: bytes)\n: Lemma\n (ensures (le_to_n b == be_to_n (seq_rev b)))\n (decreases (S.length b))\n= reveal_be_to_n (seq_rev b);\n reveal_le_to_n b;\n if Seq.length b = 0\n then ()\n else begin\n index_seq_rev b (S.length b - 1);\n slice_seq_rev b 0 (S.length b - 1);\n le_to_n_eq_be_to_n_rev (S.tail b)\n end", "let seq_rev_involutive\n (#t: Type)\n (x: S.seq t)\n: Lemma\n (seq_rev (seq_rev x) `S.equal` x)\n= Classical.forall_intro (index_seq_rev (seq_rev x));\n Classical.forall_intro (index_seq_rev x)", "let n_to_le_eq_rev_n_to_be\n (len: nat)\n (n: nat)\n: Lemma\n (requires (n < pow2 (8 * len)))\n (ensures (n_to_le len n == seq_rev (n_to_be len n)))\n= le_to_n_eq_be_to_n_rev (n_to_le len n);\n be_to_n_inj (seq_rev (n_to_le len n)) (n_to_be len n);\n seq_rev_involutive (n_to_le len n)", "let index_le_to_n\n b i\n= le_to_n_eq_be_to_n_rev b;\n index_be_to_n (seq_rev b) (S.length b - 1 - i);\n index_seq_rev b (S.length b - 1 - i)", "let index_n_to_le\n len n i\n= n_to_le_eq_rev_n_to_be len n;\n index_seq_rev (n_to_be len n) i;\n index_n_to_be len n (len - 1 - i)", "let seq_rev_append\n (#t: Type)\n (b1 b2: S.seq t)\n: Lemma\n (seq_rev (b1 `S.append` b2) `S.equal` (seq_rev b2 `S.append` seq_rev b1))\n= Classical.forall_intro (index_seq_rev (b1 `S.append` b2));\n Classical.forall_intro (index_seq_rev b1);\n Classical.forall_intro (index_seq_rev b2)" ], "closest": [ "val n_to_le_le_to_n (len: U32.t) (s: Seq.seq U8.t)\n : Lemma (requires (Seq.length s == U32.v len))\n (ensures\n (le_to_n s < pow2 (8 `Prims.op_Multiply` (U32.v len)) /\\ n_to_le len (le_to_n s) == s))\n [SMTPat (n_to_le len (le_to_n s))]\nlet n_to_le_le_to_n (len: U32.t) (s: Seq.seq U8.t) : Lemma\n (requires (Seq.length s == U32.v len))\n (ensures (\n le_to_n s < pow2 (8 `Prims.op_Multiply` U32.v len) /\\\n n_to_le len (le_to_n s) == s\n ))\n [SMTPat (n_to_le len (le_to_n s))]\n= lemma_le_to_n_is_bounded s;\n le_to_n_inj s (n_to_le len (le_to_n s))", "val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma\n (requires (Seq.length s == len))\n (ensures (\n le_to_n s < pow2 (8 * len) /\\\n n_to_le len (le_to_n s) == s\n ))\n [SMTPat (n_to_le len (le_to_n s))]\nlet n_to_le_le_to_n len s =\n lemma_le_to_n_is_bounded s;\n le_to_n_inj s (n_to_le len (le_to_n s))", "val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->\n Tot (b:bytes{S.length b == len /\\ n == le_to_n b})\n (decreases len)\nlet rec n_to_le len n =\n if len = 0 then\n S.empty\n else\n let len = len - 1 in\n let byte = U8.uint_to_t (n % 256) in\n let n' = n / 256 in\n Math.pow2_plus 8 (8 * len);\n assert(n' < pow2 (8 * len ));\n let b' = n_to_le len n' in\n let b = S.cons byte b' in\n S.lemma_eq_intro b' (S.tail b);\n b", "val index_n_to_be (len n i: nat)\n : Lemma (requires (i < len /\\ n < pow2 (8 * len)))\n (ensures\n (U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i)) ==\n (n / pow2 (8 * (len - 1 - i)) % pow2 8))\nlet index_n_to_be\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i)) == (n / pow2 (8 * (len - 1 - i)) % pow2 8\n ))\n= index_be_to_n (FStar.Endianness.n_to_be len n) i", "val n_to_be_be_to_n (len: U32.t) (s: Seq.seq U8.t)\n : Lemma (requires (Seq.length s == U32.v len))\n (ensures\n (be_to_n s < pow2 (8 `Prims.op_Multiply` (U32.v len)) /\\ n_to_be len (be_to_n s) == s))\n [SMTPat (n_to_be len (be_to_n s))]\nlet n_to_be_be_to_n (len: U32.t) (s: Seq.seq U8.t) : Lemma\n (requires (Seq.length s == U32.v len))\n (ensures (\n be_to_n s < pow2 (8 `Prims.op_Multiply` U32.v len) /\\\n n_to_be len (be_to_n s) == s\n ))\n [SMTPat (n_to_be len (be_to_n s))]\n= lemma_be_to_n_is_bounded s;\n be_to_n_inj s (n_to_be len (be_to_n s))", "val n_to_le : len:U32.t -> n:nat{n < pow2 (8 * U32.v len)} ->\n Tot (b:bytes{S.length b == U32.v len /\\ n == le_to_n b})\n (decreases (U32.v len))\nlet rec n_to_le len n =\n if len = 0ul then\n S.empty\n else\n let len = U32.(len -^ 1ul) in\n let byte = U8.uint_to_t (n % 256) in\n let n' = n / 256 in\n Math.pow2_plus 8 (8 * U32.v len);\n assert(n' < pow2 (8 * U32.v len ));\n let b' = n_to_le len n' in\n let b = S.cons byte b' in\n S.lemma_eq_intro b' (S.tail b);\n b", "val index_n_to_be_zero_right (len n i: nat)\n : Lemma (requires (i < len /\\ n < pow2 (8 * len) /\\ n % pow2 (8 * (len - i)) == 0))\n (ensures (U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i) == 0))\nlet index_n_to_be_zero_right\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len) /\\\n n % pow2 (8 * (len - i)) == 0\n ))\n (ensures (\n U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i) == 0\n ))\n= index_n_to_be len n i;\n let open FStar.Math.Lemmas in\n modulo_division_lemma n (pow2 (8 * (len - 1 - i))) (pow2 8);\n pow2_plus (8 * (len - 1 - i)) 8", "val index_n_to_be_zero_left (len n j i: nat)\n : Lemma (requires (i < j /\\ j <= len /\\ n < pow2 (8 * (len - j))))\n (ensures\n (pow2 (8 * (len - j)) <= pow2 (8 * len) /\\\n U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i) == 0))\nlet index_n_to_be_zero_left\n (len: nat)\n (n: nat)\n (j: nat)\n (i: nat)\n: Lemma\n (requires (\n i < j /\\\n j <= len /\\\n n < pow2 (8 * (len - j))\n ))\n (ensures (\n pow2 (8 * (len - j)) <= pow2 (8 * len) /\\\n U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i) == 0\n ))\n= let open FStar.Math.Lemmas in\n pow2_le_compat (8 * len) (8 * (len - j));\n pow2_le_compat (8 * (len - 1 - i)) (8 * (len - j));\n small_division_lemma_1 n (pow2 (8 * (len - 1 - i)));\n index_n_to_be len n i", "val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma\n (requires (Seq.length s == len))\n (ensures (\n be_to_n s < pow2 (8 * len) /\\\n n_to_be len (be_to_n s) == s\n ))\n [SMTPat (n_to_be len (be_to_n s))]\nlet n_to_be_be_to_n len s =\n lemma_be_to_n_is_bounded s;\n be_to_n_inj s (n_to_be len (be_to_n s))", "val lemma_pad_to_32_bits_helper (s s'': seq4 nat8) (n: nat)\n : Lemma\n (requires\n n <= 2 /\\\n (forall (i: nat). {:pattern (index s i)\\/(index s'' i)}\n i < 4 ==> index s'' i == (if i < n then index s i else 0)))\n (ensures\n four_to_nat 8 (seq_to_four_BE s'') ==\n (four_to_nat 8 (seq_to_four_BE s) / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_pad_to_32_bits_helper (s s'':seq4 nat8) (n:nat) : Lemma\n (requires\n n <= 2 /\\\n (forall (i:nat).{:pattern (index s i) \\/ (index s'' i)} i < 4 ==>\n index s'' i == (if i < n then index s i else 0))\n )\n (ensures four_to_nat 8 (seq_to_four_BE s'') == (four_to_nat 8 (seq_to_four_BE s) / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n assert (n == 0 \\/ n == 1 \\/ n == 2);\n assert_norm (four_to_nat 8 (seq_to_four_BE s) == four_to_nat_unfold 8 (seq_to_four_BE s));\n assert_norm (four_to_nat 8 (seq_to_four_BE s'') == four_to_nat_unfold 8 (seq_to_four_BE s''));\n assert_norm (pow2 (2 * 8) == 0x10000);\n assert_norm (pow2 (3 * 8) == 0x1000000);\n assert_norm (pow2 (4 * 8) == 0x100000000);\n let x = four_to_nat 8 (seq_to_four_BE s'') in\n assert (n == 0 ==> x / pow2 (8 * (4 - n)) == x / 0x100000000);\n assert (n == 1 ==> x / pow2 (8 * (4 - n)) == x / 0x1000000);\n assert (n == 2 ==> x / pow2 (8 * (4 - n)) == x / 0x10000);\n assert_norm (((x / pow2 (8 * 4)) * pow2 (8 * 4)) % pow2 (8 * 4) == 0);\n assert_norm (((x / pow2 (8 * 3)) * pow2 (8 * 3)) % pow2 (8 * 3) == 0);\n assert_norm (((x / pow2 (8 * 2)) * pow2 (8 * 2)) % pow2 (8 * 2) == 0);\n ()", "val lemma_pad_to_32_bits (s s'': seq4 nat8) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\\n (forall (i: nat). {:pattern (index s i)\\/(index s'' i)}\n i < 4 ==> index s'' i == (if i < n then index s i else 0)))\n (ensures four_to_nat 8 (seq_to_four_LE s'') == four_to_nat 8 (seq_to_four_LE s) % pow2 (8 * n)\n )\nlet lemma_pad_to_32_bits (s s'':seq4 nat8) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n (forall (i:nat).{:pattern (index s i) \\/ (index s'' i)} i < 4 ==>\n index s'' i == (if i < n then index s i else 0))\n )\n (ensures four_to_nat 8 (seq_to_four_LE s'') == four_to_nat 8 (seq_to_four_LE s) % pow2 (8 * n))\n =\n if n <= 2 then lemma_pad_to_32_bits_helper s s'' n else\n assert (n == 3 \\/ n == 4);\n assert_norm (four_to_nat 8 (seq_to_four_LE s) == four_to_nat_unfold 8 (seq_to_four_LE s));\n assert_norm (four_to_nat 8 (seq_to_four_LE s'') == four_to_nat_unfold 8 (seq_to_four_LE s''));\n assert_norm (pow2 (0 * 8) == 1);\n assert_norm (pow2 (1 * 8) == 0x100);\n assert_norm (pow2 (2 * 8) == 0x10000);\n assert_norm (pow2 (3 * 8) == 0x1000000);\n assert_norm (pow2 (4 * 8) == 0x100000000);\n let x = four_to_nat 8 (seq_to_four_LE s'') in\n assert (n == 3 ==> x % pow2 (8 * n) == x % 0x1000000);\n assert (n == 4 ==> x % pow2 (8 * n) == x % 0x100000000);\n ()", "val lemma_pad_to_32_bits_helper (s s'': seq4 nat8) (n: nat)\n : Lemma\n (requires\n n <= 2 /\\\n (forall (i: nat). {:pattern (index s i)\\/(index s'' i)}\n i < 4 ==> index s'' i == (if i < n then index s i else 0)))\n (ensures four_to_nat 8 (seq_to_four_LE s'') == four_to_nat 8 (seq_to_four_LE s) % pow2 (8 * n)\n )\nlet lemma_pad_to_32_bits_helper (s s'':seq4 nat8) (n:nat) : Lemma\n (requires\n n <= 2 /\\\n (forall (i:nat).{:pattern (index s i) \\/ (index s'' i)} i < 4 ==>\n index s'' i == (if i < n then index s i else 0))\n )\n (ensures four_to_nat 8 (seq_to_four_LE s'') == four_to_nat 8 (seq_to_four_LE s) % pow2 (8 * n))\n =\n assert (n == 0 \\/ n == 1 \\/ n == 2);\n assert_norm (four_to_nat 8 (seq_to_four_LE s) == four_to_nat_unfold 8 (seq_to_four_LE s));\n assert_norm (four_to_nat 8 (seq_to_four_LE s'') == four_to_nat_unfold 8 (seq_to_four_LE s''));\n assert_norm (pow2 (0 * 8) == 1);\n assert_norm (pow2 (1 * 8) == 0x100);\n assert_norm (pow2 (2 * 8) == 0x10000);\n assert_norm (pow2 (3 * 8) == 0x1000000);\n assert_norm (pow2 (4 * 8) == 0x100000000);\n let x = four_to_nat 8 (seq_to_four_LE s'') in\n assert (n == 0 ==> x % pow2 (8 * n) == x % 0x1);\n assert (n == 1 ==> x % pow2 (8 * n) == x % 0x100);\n assert (n == 2 ==> x % pow2 (8 * n) == x % 0x10000);\n ()", "val lemma_pad_to_32_bits (s s'': seq4 nat8) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\\n (forall (i: nat). {:pattern (index s i)\\/(index s'' i)}\n i < 4 ==> index s'' i == (if i < n then index s i else 0)))\n (ensures\n four_to_nat 8 (seq_to_four_BE s'') ==\n (four_to_nat 8 (seq_to_four_BE s) / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_pad_to_32_bits (s s'':seq4 nat8) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n (forall (i:nat).{:pattern (index s i) \\/ (index s'' i)} i < 4 ==>\n index s'' i == (if i < n then index s i else 0))\n )\n (ensures four_to_nat 8 (seq_to_four_BE s'') == (four_to_nat 8 (seq_to_four_BE s) / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n if n <= 2 then lemma_pad_to_32_bits_helper s s'' n else\n assert (n == 3 \\/ n == 4);\n assert_norm (four_to_nat 8 (seq_to_four_BE s) == four_to_nat_unfold 8 (seq_to_four_BE s));\n assert_norm (four_to_nat 8 (seq_to_four_BE s'') == four_to_nat_unfold 8 (seq_to_four_BE s''));\n assert_norm (pow2 (0 * 8) == 1);\n assert_norm (pow2 (1 * 8) == 0x100);\n let x = four_to_nat 8 (seq_to_four_BE s'') in\n assert (n == 3 ==> x / pow2 (8 * (4 - n)) == x / 0x100);\n assert (n == 4 ==> x / pow2 (8 * (4 - n)) == x / 0x1);\n assert_norm (((x / pow2 (8 * 1)) * pow2 (8 * 1)) % pow2 (8 * 1) == 0);\n assert_norm (((x / pow2 (8 * 0)) * pow2 (8 * 0)) % pow2 (8 * 0) == 0);\n ()", "val slice_n_to_be_bitfield (len: pos) (n i j: nat)\n : Lemma (requires (i <= j /\\ j <= len /\\ n < pow2 (8 * len)))\n (ensures\n (S.slice (n_to_be len n) i j ==\n n_to_be (j - i) (BF.get_bitfield #(8 * len) n (8 * (len - j)) (8 * (len - i)))))\nlet slice_n_to_be_bitfield\n (len: pos)\n (n: nat)\n (i j: nat)\n: Lemma\n (requires (\n i <= j /\\\n j <= len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n S.slice (n_to_be len n) i j == n_to_be (j - i) (BF.get_bitfield #(8 * len) n (8 * (len - j)) (8 * (len - i)))\n ))\n= slice_n_to_be len n i j;\n BF.get_bitfield_eq #(8 * len) n (8 * (len - j)) (8 * (len - i))", "val pow2_lt_len: len:size_pos -> Lemma (pow2 (8 * len - 1) < pow2 (8 * (len - 1)) * (pow2 8 - 1))\nlet pow2_lt_len len =\n let a = pow2 (8 * len - 1) in\n let b = pow2 (8 * (len - 1)) * (pow2 8 - 1) in\n calc (==) {\n b / a;\n (==) { Math.Lemmas.pow2_plus (8 * len - 8) 7 }\n b / (pow2 (8 * len - 8) * pow2 7);\n (==) { Math.Lemmas.division_multiplication_lemma b (pow2 (8 * len - 8)) (pow2 7) }\n b / pow2 (8 * len - 8) / pow2 7;\n (==) { Math.Lemmas.cancel_mul_div (pow2 8 - 1) (pow2 (8 * len - 8)) }\n (pow2 8 - 1) / pow2 7;\n (==) { Math.Lemmas.pow2_plus 7 1 }\n (pow2 7 * 2 - 1) / pow2 7;\n (==) { }\n 1;\n };\n // assert (b / a * a <= b);\n // assert (a <= b)\n\n calc (>) {\n pow2 (8 * len - 8) * (pow2 8 - 1) % pow2 (8 * len - 1);\n (==) { Math.Lemmas.pow2_plus (8 * len - 8) 8 }\n (pow2 (8 * len) - pow2 (8 * len - 8)) % pow2 (8 * len - 1);\n (==) { Math.Lemmas.lemma_mod_plus_distr_l (pow2 (8 * len)) (- pow2 (8 * len - 8)) (pow2 (8 * len - 1)) }\n (pow2 (8 * len) % pow2 (8 * len - 1) - pow2 (8 * len - 8)) % pow2 (8 * len - 1);\n (==) { Math.Lemmas.pow2_multiplication_modulo_lemma_1 1 (8 * len - 1) (8 * len) }\n (0 - pow2 (8 * len - 8)) % pow2 (8 * len - 1);\n //(==) { Math.Lemmas.pow2_lt_compat (8 * len - 1) (8 * len - 8) }\n //pow2 (8 * len - 1) - pow2 (8 * len - 8);\n (>) { Math.Lemmas.pow2_lt_compat (8 * len - 1) (8 * len - 8) }\n 0;\n };\n\n assert (a < b)", "val lemma_64_32_lo2 (q': quad32) (lo lo': nat64) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\ lo' == lo % pow2 (8 * (n + 4)) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 lo') (nat_to_two 32 0))\n (ensures lo' == q'.lo0 + 0x100000000 * q'.lo1 /\\ q' == Mkfour q'.lo0 q'.lo1 0 0)\nlet lemma_64_32_lo2 (q':quad32) (lo lo':nat64) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n lo' == lo % pow2 (8 * (n + 4)) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 lo') (nat_to_two 32 0)\n )\n (ensures lo' == q'.lo0 + 0x100000000 * q'.lo1 /\\ q' == Mkfour q'.lo0 q'.lo1 0 0)\n =\n assert_norm (pow2 (4 * 8) == 0x100000000);\n assert_norm (pow2 (5 * 8) == 0x10000000000);\n assert_norm (pow2 (6 * 8) == 0x1000000000000);\n assert_norm (pow2 (7 * 8) == 0x100000000000000);\n assert_norm (pow2 (8 * 8) == 0x10000000000000000);\n assert_norm (nat_to_two 32 lo' == nat_to_two_unfold 32 lo');\n assert_norm (nat_to_two 32 0 == nat_to_two_unfold 32 0);\n ()", "val nat_to_bytes_le (#l: secrecy_level) (len: nat) (n: nat{n < pow2 (8 * len)})\n : b: bytes_l l {length b == len /\\ n == nat_from_intseq_le #U8 b}\nlet nat_to_bytes_le (#l:secrecy_level) (len:nat) (n:nat{n < pow2 (8 * len)}) : b:bytes_l l{length b == len /\\ n == nat_from_intseq_le #U8 b} =\n nat_to_intseq_le #U8 #l len n", "val to_vec_append : #n1:nat{n1 > 0} -> #n2:nat{n2 > 0} -> num1:UInt.uint_t n1 -> num2:UInt.uint_t n2 ->\n Lemma (UInt.to_vec (append_uint num1 num2) == Seq.append (UInt.to_vec num2) (UInt.to_vec num1))\nlet to_vec_append #n1 #n2 num1 num2 =\n UInt.append_lemma (UInt.to_vec num2) (UInt.to_vec num1)", "val lemma_64_32_lo1 (q': quad32) (lo lo': nat64) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\ lo' == lo % pow2 (8 * n) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 lo') (nat_to_two 32 0))\n (ensures lo' < 0x100000000 /\\ lo' == q'.lo0 /\\ q' == Mkfour q'.lo0 0 0 0)\nlet lemma_64_32_lo1 (q':quad32) (lo lo':nat64) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n lo' == lo % pow2 (8 * n) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 lo') (nat_to_two 32 0)\n )\n (ensures lo' < 0x100000000 /\\ lo' == q'.lo0 /\\ q' == Mkfour q'.lo0 0 0 0)\n =\n assert_norm (pow2 (0 * 8) == 1);\n assert_norm (pow2 (1 * 8) == 0x100);\n assert_norm (pow2 (2 * 8) == 0x10000);\n assert_norm (pow2 (3 * 8) == 0x1000000);\n assert_norm (pow2 (4 * 8) == 0x100000000);\n assert_norm (nat_to_two 32 lo' == nat_to_two_unfold 32 lo');\n assert_norm (nat_to_two 32 0 == nat_to_two_unfold 32 0);\n ()", "val lemma_64_32_lo1 (q': quad32) (lo lo': nat64) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\ lo' == (lo / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n)) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 lo') (Mktwo q'.hi2 q'.hi3))\n (ensures lo' % pow2_32 == 0 /\\ lo' / pow2_32 == q'.lo1 /\\ q'.lo0 == 0)\nlet lemma_64_32_lo1 (q':quad32) (lo lo':nat64) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n lo' == (lo / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n)) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 lo') (Mktwo q'.hi2 q'.hi3)\n )\n (ensures lo' % pow2_32 == 0 /\\ lo' / pow2_32 == q'.lo1 /\\ q'.lo0 == 0)\n =\n assert_norm (((lo / pow2 (8 * 4)) * pow2 (8 * 4)) % pow2_32 == 0);\n assert_norm (((lo / pow2 (8 * 5)) * pow2 (8 * 5)) % pow2_32 == 0);\n assert_norm (((lo / pow2 (8 * 6)) * pow2 (8 * 6)) % pow2_32 == 0);\n assert_norm (((lo / pow2 (8 * 7)) * pow2 (8 * 7)) % pow2_32 == 0);\n assert_norm (((lo / pow2 (8 * 8)) * pow2 (8 * 8)) % pow2_32 == 0);\n assert_norm (((lo / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n)) / pow2_32) % pow2_32 ==\n ((lo / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32);\n assert_norm (nat_to_two 32 lo' == nat_to_two_unfold 32 lo');\n ()", "val lemma_64_32_lo2 (q': quad32) (lo lo': nat64) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\ lo' == (lo / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 lo') (Mktwo q'.hi2 q'.hi3))\n (ensures lo' == q'.lo0 + 0x100000000 * q'.lo1)\nlet lemma_64_32_lo2 (q':quad32) (lo lo':nat64) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n lo' == (lo / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 lo') (Mktwo q'.hi2 q'.hi3)\n )\n (ensures lo' == q'.lo0 + 0x100000000 * q'.lo1)\n =\n assert_norm (nat_to_two 32 lo' == nat_to_two_unfold 32 lo');\n ()", "val lemma_be_index (l: pos) (n: nat{n < pow2 (8 `op_Multiply` l)})\n : Lemma\n (ensures U8.v (S.index (FStar.Endianness.n_to_be l n) 0) == n / pow2 (8 `op_Multiply` (l - 1))\n ) (decreases %[l])\nlet rec lemma_be_index (l:pos) (n:nat{n < pow2 (8 `op_Multiply` l)})\n : Lemma (ensures U8.v (S.index (FStar.Endianness.n_to_be l n) 0)\n == n / pow2 (8 `op_Multiply` (l-1)))\n (decreases %[l])\n =\n let open FStar.Endianness in\n let open FStar.Mul in\n let b = n_to_be l n in\n let b0 = S.index b 0 in\n reveal_be_to_n b;\n if l = 1 then ()\n else\n let b1 = S.last b in\n let b' = S.slice b 0 (l-1) in\n let b0' = S.index b' 0 in\n reveal_be_to_n b';\n assert(U8.v b1 == n % pow2 8);\n lemma_be_to_n_is_bounded b';\n lemma_be_index (l-1) (be_to_n b');\n lemma_pow2_div2 (n - U8.v b1) 8 (8 * (l-1) - 8);\n lemma_div_sub_small l n (U8.v b1)", "val nat_to_bytes_n_to_le: len:size_nat -> l:secrecy_level -> n:nat{n < pow2 (8 * len)} ->\n Lemma (ensures Seq.equal (FStar.Endianness.n_to_le len n)\n (BS.nat_to_bytes_le #l len n))\n (decreases len)\nlet rec nat_to_bytes_n_to_le len l n =\n if len = 0 then () else\n begin\n Math.Lemmas.division_multiplication_lemma n (pow2 8) (pow2 (8 * (len - 1)));\n Math.Lemmas.pow2_plus 8 (8 * (len - 1));\n nat_to_bytes_n_to_le (len - 1) l (n / 256)\n end", "val n_to_le_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat{len + 1 <= tot /\\ tot < pow2 32})\n (ih: n_to_le_t u len)\n : Tot (n_to_le_t u (len + 1))\nlet n_to_le_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat {len + 1 <= tot /\\ tot < pow2 32})\n (ih: n_to_le_t u len)\n: Tot (n_to_le_t u (len + 1))\n= fun n ->\n reveal_n_to_le (len + 1) (u.v n);\n let lo = u.to_byte n in\n let hi = u.div256 n in\n let seq_hi = ih hi in\n let seq_lo = B.create 1ul lo in\n seq_lo `B.append` seq_hi", "val nat_to_bytes_n_to_be: len:size_nat -> l:secrecy_level -> n:nat{n < pow2 (8 * len)} ->\n Lemma (ensures (Seq.equal (FStar.Endianness.n_to_be len n)\n (BS.nat_to_bytes_be #l len n)))\n (decreases len)\nlet rec nat_to_bytes_n_to_be len l n =\n if len = 0 then () else\n begin\n Math.Lemmas.division_multiplication_lemma n (pow2 8) (pow2 (8 * (len - 1)));\n Math.Lemmas.pow2_plus 8 (8 * (len - 1));\n nat_to_bytes_n_to_be (len - 1) l (n / 256)\n end", "val n_to_be:\n len:nat -> n:nat{n < pow2 (8 * len)} ->\n Tot (b:bytes{S.length b == len /\\ n == be_to_n b})\n (decreases len)\nlet rec n_to_be len n =\n if len = 0 then\n S.empty\n else\n let len = len - 1 in\n let byte = U8.uint_to_t (n % 256) in\n let n' = n / 256 in\n Math.pow2_plus 8 (8 * len);\n let b' = n_to_be len n' in\n let b'' = S.create 1 byte in\n let b = S.append b' b'' in\n S.lemma_eq_intro b' (S.slice b 0 len);\n b", "val nat_from_bytes_le_eq_lemma: len0:size_nat -> len:size_nat{len0 <= len} -> b:lseq uint8 len0 -> Lemma\n (let tmp = create len (u8 0) in\n nat_from_intseq_le b == nat_from_intseq_le (update_sub tmp 0 len0 b))\nlet nat_from_bytes_le_eq_lemma len0 len b =\n let tmp = create len (u8 0) in\n let r = update_sub tmp 0 len0 b in\n assert (slice r 0 len0 == b);\n assert (forall (i:nat). i < len - len0 ==> r.[len0 + i] == u8 0);\n nat_from_intseq_le_slice_lemma #U8 #SEC #len r len0;\n assert (nat_from_intseq_le r == nat_from_intseq_le (slice r 0 len0) + pow2 (len0 * 8) * nat_from_intseq_le (Seq.slice r len0 len));\n assert (nat_from_intseq_le r == nat_from_intseq_le b + pow2 (len0 * 8) * nat_from_intseq_le (Seq.slice r len0 len));\n lemma_nat_from_bytes_le_zeroes (len - len0) (Seq.slice r len0 len)", "val lemma_div_n_8_lower1 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures\n ((lo64 q / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32 ==\n (q.lo1 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_div_n_8_lower1 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures ((lo64 q / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32 == (q.lo1 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n hi64_reveal ();\n lo64_reveal ();\n let Mkfour q0 q1 _ _ = q in\n lemma_div_n_8_upper1 (Mkfour 0 0 q0 q1) n", "val nth_size (n1: nat) (n2: nat{n1 <= n2}) (x: U.uint_t n1) (i: nat{i < n2})\n : Lemma (x < pow2 n2 /\\ nth #n2 x i == (i < n1 && nth #n1 x i))\nlet rec nth_size (n1: nat) (n2: nat { n1 <= n2 }) (x: U.uint_t n1) (i: nat { i < n2 }) : Lemma\n (x < pow2 n2 /\\ nth #n2 x i == (i < n1 && nth #n1 x i))\n= M.pow2_le_compat n2 n1;\n if i < n1\n then begin\n if i = 0\n then ()\n else nth_size (n1 - 1) (n2 - 1) (x / 2) (i - 1)\n end else nth_le_pow2_m #n2 x n1 i", "val lemma_mod_n_8_lower2_helper (q: quad32) (n: nat)\n : Lemma (requires n <= 2)\n (ensures lo64 q % pow2 (8 * (4 + n)) == q.lo0 + 0x100000000 * (q.lo1 % pow2 (8 * n)))\nlet lemma_mod_n_8_lower2_helper (q:quad32) (n:nat) : Lemma\n (requires n <= 2)\n (ensures lo64 q % pow2 (8 * (4 + n)) == q.lo0 + 0x100000000 * (q.lo1 % pow2 (8 * n)))\n =\n lo64_reveal ();\n let Mkfour _ _ _ _ = q in // avoid ifuel\n let f (n:nat{n <= 4}) = lo64_def q % pow2 (8 * (4 + n)) == q.lo0 + 0x100000000 * (q.lo1 % pow2 (8 * n)) in\n assert_norm (f 2);\n assert_norm (f 1);\n assert_norm (f 0);\n ()", "val lemma_add_0x1000000_reverse_mult (n: nat32) (increment: nat)\n : Lemma (requires (n % 256) + increment < 256)\n (ensures\n (let r = reverse_bytes_nat32 n in\n r + increment * 0x1000000 == reverse_bytes_nat32 (n + increment)))\nlet lemma_add_0x1000000_reverse_mult (n:nat32) (increment:nat) : Lemma\n (requires (n % 256) + increment < 256)\n (ensures (let r = reverse_bytes_nat32 n in\n r + increment * 0x1000000 == reverse_bytes_nat32 (n + increment)))\n =\n let r = reverse_bytes_nat32 n in\n assert_norm (Vale.Def.Words.Four_s.nat_to_four 8 (n+increment) == Mkfour ((n+increment) % 0x100) (((n+increment) / 0x100) % 0x100) (((n+increment) / 0x10000) % 0x100) (((n+increment) / 0x1000000) % 0x100));\n assert ((n+increment) / 0x1000000 == n / 0x1000000);\n assert ((n+increment) / 0x10000 == n / 0x10000);\n assert ((n+increment) / 0x100 == n / 0x100);\n assert (Vale.Def.Words.Four_s.nat_to_four 8 (n+increment) == Mkfour ((n+increment) % 0x100) ((n / 0x100) % 0x100) ((n / 0x10000) % 0x100) ((n / 0x1000000) % 0x100));\n\n assert_norm (Vale.Def.Words.Four_s.nat_to_four 8 n == Mkfour (n % 0x100) ((n / 0x100) % 0x100) ((n / 0x10000) % 0x100) ((n / 0x1000000) % 0x100));\n let s = Vale.Def.Words.Seq_s.four_to_seq_BE (Vale.Def.Words.Four_s.nat_to_four 8 n) in\n let r_s = Vale.Lib.Seqs_s.reverse_seq s in\n assert_norm (be_bytes_to_nat32 r_s == ((n / 0x1000000) % 0x100) +\n ((n / 0x10000) % 0x100) * 0x100 +\n ((n / 0x100) % 0x100) * 0x10000 +\n (n % 0x100) * 0x1000000);\n let s' = Vale.Def.Words.Seq_s.four_to_seq_BE (Vale.Def.Words.Four_s.nat_to_four 8 (n+increment)) in\n let r_s' = Vale.Lib.Seqs_s.reverse_seq s' in\n\n assert_norm (be_bytes_to_nat32 r_s' == (((n) / 0x1000000) % 0x100) +\n (((n) / 0x10000) % 0x100) * 0x100 +\n (((n) / 0x100) % 0x100) * 0x10000 +\n ((n+increment) % 0x100) * 0x1000000);\n assert (be_bytes_to_nat32 r_s + increment * 0x1000000 == be_bytes_to_nat32 r_s');\n calc (==) {\n r;\n == { reverse_bytes_nat32_reveal () }\n be_bytes_to_nat32 r_s;\n };\n calc (==) {\n reverse_bytes_nat32 (n+increment);\n == { reverse_bytes_nat32_reveal () }\n be_bytes_to_nat32 (Vale.Lib.Seqs_s.reverse_seq (nat32_to_be_bytes (n+increment)));\n };\n ()", "val nat_from_bytes_le_eq_lemma_: len:size_nat{len < 16} -> b:lseq uint8 len -> Lemma\n (let tmp = create 16 (u8 0) in\n nat_from_intseq_le b == nat_from_intseq_le (update_sub tmp 0 len b))\nlet nat_from_bytes_le_eq_lemma_ len b =\n let tmp = create 16 (u8 0) in\n let r = update_sub tmp 0 len b in\n assert (Seq.slice r 0 len == b);\n assert (forall (i:nat). len <= i /\\ i < 16 ==> r.[i] == u8 0);\n assert (forall (i:nat). i < 16 - len ==> Seq.index (Seq.slice r len 16) i == u8 0);\n nat_from_intseq_le_slice_lemma #U8 #SEC #16 r len;\n assert (nat_from_intseq_le r == nat_from_intseq_le (Seq.slice r 0 len) + pow2 (len * 8) * nat_from_intseq_le (Seq.slice r len 16));\n assert (nat_from_intseq_le r == nat_from_intseq_le b + pow2 (len * 8) * nat_from_intseq_le (Seq.slice r len 16));\n lemma_nat_from_bytes_le_zeroes (16 - len) (Seq.slice r len 16)", "val index_after_append_helper (ty: Type) (s0 s1: list ty) (n: nat)\n : Lemma (requires n < length (append s0 s1) && length (append s0 s1) = length s0 + length s1)\n (ensures\n index (append s0 s1) n == (if n < length s0 then index s0 n else index s1 (n - length s0)))\nlet rec index_after_append_helper (ty: Type) (s0: list ty) (s1: list ty) (n: nat)\n : Lemma (requires n < length (append s0 s1) && length (append s0 s1) = length s0 + length s1)\n (ensures index (append s0 s1) n == (if n < length s0 then index s0 n else index s1 (n - length s0))) =\n match s0 with\n | [] -> ()\n | hd :: tl -> if n = 0 then () else index_after_append_helper ty tl s1 (n - 1)", "val lemma_ishl_nth_all (n:pos) : Lemma\n (forall (m:_{m==pow2_norm n}) (x:natN (pow2 n)) (y:nat).{:pattern (ishl #m x y)}\n (forall (i:nat{i < n}).{:pattern (nth #n (ishl #m x y) i)}\n nth #n (ishl #m x y) i == (i + y < n && nth #n x (i + y))))\nlet lemma_ishl_nth_all n =\n FStar.Classical.forall_intro_2 (lemma_ishl_nth n)", "val lemma_div_n_8_lower2 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures\n (lo64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) ==\n 0x100000000 * q.lo1 + (q.lo0 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_div_n_8_lower2 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures (lo64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) == 0x100000000 * q.lo1 + (q.lo0 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n hi64_reveal ();\n lo64_reveal ();\n let Mkfour q0 q1 _ _ = q in\n lemma_div_n_8_upper2 (Mkfour 0 0 q0 q1) n", "val nat_from_bytes_le_eq_lemma: len:size_nat{len < 16} -> b:lseq uint8 len -> Lemma\n (let tmp = create 16 (u8 0) in\n nat_from_bytes_le b == nat_from_bytes_le (update_sub tmp 0 len b))\nlet nat_from_bytes_le_eq_lemma len b = nat_from_bytes_le_eq_lemma_ len b", "val n_to_be:\n len:U32.t -> n:nat{n < pow2 (8 * U32.v len)} ->\n Tot (b:bytes{S.length b == U32.v len /\\ n == be_to_n b})\n (decreases (U32.v len))\nlet rec n_to_be len n =\n if len = 0ul then\n S.empty\n else\n let len = U32.(len -^ 1ul) in\n let byte = U8.uint_to_t (n % 256) in\n let n' = n / 256 in\n Math.pow2_plus 8 (8 * U32.v len);\n assert(n' < pow2 (8 * U32.v len ));\n let b' = n_to_be len n' in\n let b'' = S.create 1 byte in\n let b = S.append b' b'' in\n S.lemma_eq_intro b' (S.slice b 0 (U32.v len));\n b", "val lemma_table_sub_len: len:nat -> table_len:nat -> i:nat{i < table_len} ->\n Lemma (i * len + len <= table_len * len)\nlet lemma_table_sub_len len table_len i =\n Math.Lemmas.distributivity_add_left i 1 len;\n Math.Lemmas.lemma_mult_le_right len (i + 1) table_len", "val lemma_power2_add64 (n:nat) : Lemma\n (requires True)\n (ensures pow2(64 + n) == 0x10000000000000000 * pow2(n))\nlet lemma_power2_add64 (n:nat) =\n pow2_plus 64 n;\n FStar.UInt.pow2_values 64", "val lemma_aux_0 (a b n: nat)\n : Lemma\n (pow2 n * a + pow2 (n + 56) * b = pow2 n * (a % pow2 56) + pow2 (n + 56) * (b + a / pow2 56))\nlet lemma_aux_0 (a:nat) (b:nat) (n:nat) : Lemma\n (pow2 n * a + pow2 (n+56) * b = pow2 n * (a % pow2 56) + pow2 (n+56) * (b + a / pow2 56))\n = Math.Lemmas.lemma_div_mod a (pow2 56);\n Math.Lemmas.pow2_plus n 56;\n assert(a = pow2 56 * (a / pow2 56) + (a % pow2 56));\n Math.Lemmas.distributivity_add_right (pow2 n) (pow2 56 * (a / pow2 56)) (a % pow2 56);\n Math.Lemmas.paren_mul_right (pow2 n) (pow2 56) (a / pow2 56);\n Math.Lemmas.distributivity_add_right (pow2 (n+56)) b (a / pow2 56)", "val lemma_le_to_n_is_bounded: b:bytes -> Lemma\n (requires True)\n (ensures (le_to_n b < pow2 (8 * Seq.length b)))\n (decreases (Seq.length b))\nlet rec lemma_le_to_n_is_bounded b =\n if Seq.length b = 0 then ()\n else\n begin\n let s = Seq.slice b 1 (Seq.length b) in\n assert(Seq.length s = Seq.length b - 1);\n lemma_le_to_n_is_bounded s;\n assert(UInt8.v (Seq.index b 0) < pow2 8);\n assert(le_to_n s < pow2 (8 * Seq.length s));\n assert(le_to_n b < pow2 8 + pow2 8 * pow2 (8 * (Seq.length b - 1)));\n lemma_euclidean_division (UInt8.v (Seq.index b 0)) (le_to_n s) (pow2 8);\n assert(le_to_n b <= pow2 8 * (le_to_n s + 1));\n assert(le_to_n b <= pow2 8 * pow2 (8 * (Seq.length b - 1)));\n Math.Lemmas.pow2_plus 8 (8 * (Seq.length b - 1));\n lemma_factorise 8 (Seq.length b - 1)\n end", "val lemma_le_to_n_is_bounded: b:bytes -> Lemma\n (requires True)\n (ensures (le_to_n b < pow2 (8 * Seq.length b)))\n (decreases (Seq.length b))\nlet rec lemma_le_to_n_is_bounded b =\n if Seq.length b = 0 then ()\n else\n begin\n let s = Seq.slice b 1 (Seq.length b) in\n assert(Seq.length s = Seq.length b - 1);\n lemma_le_to_n_is_bounded s;\n assert(UInt8.v (Seq.index b 0) < pow2 8);\n assert(le_to_n s < pow2 (8 * Seq.length s));\n assert(le_to_n b < pow2 8 + pow2 8 * pow2 (8 * (Seq.length b - 1)));\n lemma_euclidean_division (UInt8.v (Seq.index b 0)) (le_to_n s) (pow2 8);\n assert(le_to_n b <= pow2 8 * (le_to_n s + 1));\n assert(le_to_n b <= pow2 8 * pow2 (8 * (Seq.length b - 1)));\n Math.Lemmas.pow2_plus 8 (8 * (Seq.length b - 1));\n lemma_factorise 8 (Seq.length b - 1)\n end", "val uints_to_bytes_le_nat_lemma_: #t:inttype{unsigned t /\\ ~(U1? t)} -> #l:secrecy_level\n -> len:nat{len * numbytes t < pow2 32}\n -> n:nat{n < pow2 (bits t * len)}\n -> i:nat{i < len * numbytes t}\n -> Lemma\n (Seq.index (uints_to_bytes_le #t #l #len (nat_to_intseq_le #t #l len n)) i ==\n Seq.index (nat_to_bytes_le (len * numbytes t) n) i)\nlet uints_to_bytes_le_nat_lemma_ #t #l len n i =\n let s:lseq (uint_t t l) len = nat_to_intseq_le #t #l len n in\n calc (==) {\n Seq.index (uints_to_bytes_le #t #l #len (nat_to_intseq_le #t #l len n)) i;\n == { index_uints_to_bytes_le_aux #t #l len n i }\n Seq.index (nat_to_bytes_le #l (numbytes t) (v s.[i / numbytes t])) (i % numbytes t);\n == { index_nat_to_intseq_to_bytes_le #t #l len n i}\n Seq.index (nat_to_bytes_le (len * numbytes t) n) i;\n }", "val nat_from_bytes_be_eq_lemma: len0:size_nat -> len:size_nat{len0 <= len} -> b:lseq uint8 len0 ->\n Lemma (let tmp = create len (u8 0) in\n nat_from_intseq_be b == nat_from_intseq_be (update_sub tmp (len - len0) len0 b))\nlet nat_from_bytes_be_eq_lemma len0 len b =\n let tmp = create len (u8 0) in\n let r = update_sub tmp (len - len0) len0 b in\n assert (slice r (len - len0) len == b);\n assert (forall (i:nat). i < len - len0 ==> r.[i] == u8 0);\n nat_from_intseq_be_slice_lemma #U8 #SEC #len r (len - len0);\n assert (nat_from_intseq_be r == nat_from_intseq_be (slice r (len - len0) len) + pow2 (len0 * 8) * nat_from_intseq_be (Seq.slice r 0 (len - len0)));\n assert (nat_from_intseq_be r == nat_from_intseq_be b + pow2 (len0 * 8) * nat_from_intseq_be (Seq.slice r 0 (len - len0)));\n lemma_nat_from_bytes_be_zeroes (len - len0) (Seq.slice r 0 (len - len0))", "val append_zeros_left (#n: pos) (x: BitVector.bv_t n) (m: pos)\n : Lemma (UInt.from_vec #(m + n) (Seq.append (BitVector.zero_vec #m) x) == UInt.from_vec x)\nlet append_zeros_left (#n:pos) (x:BitVector.bv_t n) (m:pos)\r\n : Lemma (UInt.from_vec #(m + n) (Seq.append (BitVector.zero_vec #m) x) ==\r\n UInt.from_vec x)\r\n = let open FStar.UInt in\r\n append_lemma #m #n (BitVector.zero_vec #m) x;\r\n zero_from_vec_lemma #m;\r\n assert (UInt.from_vec #(m + n) (Seq.append (BitVector.zero_vec #m) x) ==\r\n (pow2 n * from_vec (BitVector.zero_vec #m)) +\r\n UInt.from_vec x);\r\n assert (from_vec (BitVector.zero_vec #m) == 0);\r\n calc (==) {\r\n pow2 n * from_vec (BitVector.zero_vec #m);\r\n (==) {} \r\n pow2 n * 0;\r\n (==) {} \r\n 0;\r\n }", "val lemma_one_extend: #n:pos -> a:uint_t n ->\n Lemma (one_extend a = pow2 n + a)\n [SMTPat (one_extend a)]\nlet lemma_one_extend #n a =\n let hd1 = Seq.create 1 true in\n let av = to_vec a in\n let eav = Seq.append hd1 av in\n let r = one_extend a in\n append_lemma #1 #n hd1 av;\n assert (r = from_vec eav);\n from_vec_propriety #(n+1) eav 1;\n assert (r = pow2 n + a)", "val lemma_mod_n_8_lower2 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures lo64 q % pow2 (8 * (4 + n)) == q.lo0 + 0x100000000 * (q.lo1 % pow2 (8 * n)))\nlet lemma_mod_n_8_lower2 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures lo64 q % pow2 (8 * (4 + n)) == q.lo0 + 0x100000000 * (q.lo1 % pow2 (8 * n)))\n =\n lo64_reveal ();\n if n <= 2 then lemma_mod_n_8_lower2_helper q n else\n let Mkfour _ _ _ _ = q in // avoid ifuel\n let f (n:nat{n <= 4}) = lo64_def q % pow2 (8 * (4 + n)) == q.lo0 + 0x100000000 * (q.lo1 % pow2 (8 * n)) in\n assert_norm (f 4);\n assert_norm (f 3);\n ()", "val lemma_splitAt_append (#a: Type) (n: nat) (l: list a)\n : Lemma (requires n <= length l)\n (ensures\n (let l1, l2 = splitAt n l in\n append l1 l2 == l /\\ length l1 = n))\nlet rec lemma_splitAt_append (#a:Type) (n:nat) (l:list a) :\n Lemma\n (requires n <= length l)\n (ensures (let l1, l2 = splitAt n l in\n append l1 l2 == l /\\ length l1 = n)) =\n match n with\n | 0 -> ()\n | _ ->\n match l with\n | [] -> ()\n | x :: xs -> lemma_splitAt_append (n-1) xs", "val uints64_to_bytes_le_lemma: lo:uint64 -> hi:uint64 -> Lemma\n (concat (uint_to_bytes_le lo) (uint_to_bytes_le hi) == nat_to_bytes_le 16 (v hi * pow2 64 + v lo))\nlet uints64_to_bytes_le_lemma lo hi =\n let lp = nat_to_bytes_le #SEC 16 (v hi * pow2 64 + v lo) in\n let rp = concat (uint_to_bytes_le lo) (uint_to_bytes_le hi) in\n assert (nat_from_bytes_le lp == v hi * pow2 64 + v lo);\n Seq.append_slices (uint_to_bytes_le lo) (uint_to_bytes_le hi);\n nat_from_intseq_le_slice_lemma #U8 #SEC #16 rp 8;\n assert (nat_from_bytes_le rp == nat_from_bytes_le (Seq.slice rp 0 8) + pow2 (8 * 8) * nat_from_bytes_le (Seq.slice rp 8 16));\n assert (nat_from_bytes_le rp == nat_from_bytes_le (uint_to_bytes_le lo) + pow2 64 * nat_from_bytes_le (uint_to_bytes_le hi));\n lemma_uint_to_bytes_le_preserves_value lo;\n lemma_uint_to_bytes_le_preserves_value hi;\n nat_from_intseq_le_inj lp rp", "val lemma_pow2_128: n:nat ->\n Lemma\n (requires n <= 128)\n (ensures pow2 n < Scalar.prime)\n [SMTPat (pow2 n)]\nlet lemma_pow2_128 n =\n Math.Lemmas.pow2_le_compat 128 n;\n assert (pow2 n <= pow2 128);\n assert_norm (pow2 128 < Scalar.prime)", "val uints_to_bytes_le_nat_lemma: #t:inttype{unsigned t /\\ ~(U1? t)} -> #l:secrecy_level\n -> len:nat{len * numbytes t < pow2 32}\n -> n:nat{n < pow2 (bits t * len)}\n -> Lemma\n (uints_to_bytes_le #t #l #len (nat_to_intseq_le #t #l len n) ==\n nat_to_bytes_le (len * numbytes t) n)\nlet uints_to_bytes_le_nat_lemma #t #l len n =\n Classical.forall_intro (uints_to_bytes_le_nat_lemma_ #t #l len n);\n eq_intro (uints_to_bytes_le #t #l #len (nat_to_intseq_le #t #l len n))\n (nat_to_bytes_le (len * numbytes t) n)", "val lemma_div_n_8_upper2 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures\n (hi64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) ==\n 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_div_n_8_upper2 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures (hi64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) == 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n hi64_reveal ();\n if n <= 2 then lemma_div_n_8_upper2_helper q n else\n let Mkfour _ _ _ _ = q in // avoid ifuel\n let f (n:nat{n <= 4}) = (hi64_def q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) == 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) in\n assert_norm (f 4);\n assert_norm (f 3);\n ()", "val lemma_nat_from_bytes_le_append (k1 k2: bytes)\n : Lemma (requires Seq.length k1 + Seq.length k2 <= max_size_t)\n (ensures\n nat_from_bytes_le (Seq.append k1 k2) ==\n nat_from_bytes_le k1 + pow2 (Seq.length k1 * 8) * nat_from_bytes_le k2)\nlet lemma_nat_from_bytes_le_append (k1 k2:bytes) : Lemma\n (requires Seq.length k1 + Seq.length k2 <= max_size_t)\n (ensures nat_from_bytes_le (Seq.append k1 k2) ==\n nat_from_bytes_le k1 + pow2 (Seq.length k1 * 8) * nat_from_bytes_le k2) =\n let k = Seq.append k1 k2 in\n let n = Seq.length k1 + Seq.length k2 in\n nat_from_intseq_le_slice_lemma #U8 #SEC #n k (Seq.length k1);\n assert (k1 `Seq.equal` Seq.slice k 0 (Seq.length k1));\n assert (k2 `Seq.equal` Seq.slice k (Seq.length k1) n)", "val lemma_nat_from_bytes_le_append (k1 k2: bytes)\n : Lemma (requires Seq.length k1 + Seq.length k2 <= max_size_t)\n (ensures\n nat_from_bytes_le (Seq.append k1 k2) ==\n nat_from_bytes_le k1 + pow2 (Seq.length k1 * 8) * nat_from_bytes_le k2)\nlet lemma_nat_from_bytes_le_append (k1 k2:bytes) : Lemma\n (requires Seq.length k1 + Seq.length k2 <= max_size_t)\n (ensures nat_from_bytes_le (Seq.append k1 k2) ==\n nat_from_bytes_le k1 + pow2 (Seq.length k1 * 8) * nat_from_bytes_le k2) =\n let k = Seq.append k1 k2 in\n let n = Seq.length k1 + Seq.length k2 in\n nat_from_intseq_le_slice_lemma #U8 #SEC #n k (Seq.length k1);\n assert (k1 `Seq.equal` Seq.slice k 0 (Seq.length k1));\n assert (k2 `Seq.equal` Seq.slice k (Seq.length k1) n)", "val lemma_div_sub_small (l n x: nat)\n : Lemma (requires l > 1)\n (ensures\n (n - n % pow2 8) / pow2 (8 `op_Multiply` (l - 1)) == n / pow2 (8 `op_Multiply` (l - 1)))\nlet lemma_div_sub_small (l:nat) (n:nat) (x:nat)\n : Lemma (requires l > 1)\n (ensures (n - n % pow2 8) / pow2 (8 `op_Multiply` (l-1)) == n / pow2 (8 `op_Multiply` (l-1)))\n =\n let open FStar.Math.Lemmas in\n let open FStar.Mul in\n lemma_mod_spec n (pow2 8);\n lemma_pow2_div2 n 8 (8*(l-2));\n lemma_pow2_div2 (n - n % pow2 8) 8 (8*(l-2))", "val n_to_be_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat{len + 1 <= tot /\\ tot < pow2 32})\n (ih: n_to_be_t u len)\n : Tot (n_to_be_t u (len + 1))\nlet n_to_be_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat {len + 1 <= tot /\\ tot < pow2 32})\n (ih: n_to_be_t u len)\n: Tot (n_to_be_t u (len + 1))\n= fun n ->\n reveal_n_to_be (len + 1) (u.v n);\n let lo = u.to_byte n in\n let hi = u.div256 n in\n let seq_hi = ih hi in\n let seq_lo = B.create 1ul lo in\n seq_hi `B.append` seq_lo", "val index_nat_to_intseq_le:\n #t:inttype{unsigned t}\n -> #l:secrecy_level\n -> len:size_nat\n -> n:nat{n < pow2 (bits t * len)}\n -> i:nat{i < len}\n -> Lemma (Seq.index (nat_to_intseq_le #t #l len n) i ==\n uint #t #l (n / pow2 (bits t * i) % pow2 (bits t)))\nlet rec index_nat_to_intseq_le #t #l len n i =\n if i = 0 then\n if len = 0 then () else head_nat_to_intseq_le #t #l len n\n else\n begin\n FStar.Math.Lemmas.lemma_div_lt_nat n (bits t * len) (bits t);\n calc (==) {\n Seq.index (nat_to_intseq_le #t #l (len - 1) (n / modulus t)) (i - 1);\n == { index_nat_to_intseq_le #t #l (len - 1) (n / modulus t) (i - 1) }\n uint ((n / modulus t) / pow2 (bits t * (i - 1)) % modulus t);\n == { Math.Lemmas.division_multiplication_lemma n (modulus t) (pow2 (bits t * (i - 1))) }\n uint ((n / (pow2 (bits t) * pow2 (bits t * (i - 1)))) % modulus t);\n == { Math.Lemmas.pow2_plus (bits t) (bits t * (i - 1)) }\n uint ((n / pow2 (bits t + bits t * (i - 1))) % modulus t);\n == { Math.Lemmas.distributivity_add_right (bits t) i (-1) }\n uint (n / pow2 (bits t + (bits t * i - bits t)) % modulus t);\n == { }\n uint (n / pow2 (bits t * i) % pow2 (bits t));\n };\n nat_to_intseq_le_pos #t #l len n\n end", "val lemma_div_n_8_upper2_helper (q: quad32) (n: nat)\n : Lemma (requires n <= 2)\n (ensures\n (hi64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) ==\n 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_div_n_8_upper2_helper (q:quad32) (n:nat) : Lemma\n (requires n <= 2)\n (ensures (hi64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) == 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n hi64_reveal ();\n let Mkfour _ _ _ _ = q in // avoid ifuel\n let f (n:nat{n <= 4}) = (hi64_def q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) == 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) in\n assert_norm (f 2);\n assert_norm (f 1);\n assert_norm (f 0);\n ()", "val lemma_div_n_8_upper1 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures\n ((hi64 q / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32 ==\n (q.hi3 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_div_n_8_upper1 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures ((hi64 q / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32 == (q.hi3 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n hi64_reveal ();\n let Mkfour _ _ _ _ = q in // avoid ifuel\n let f (n:nat{n <= 4}) = ((hi64_def q / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32 == (q.hi3 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) in\n assert_norm (f 0);\n assert_norm (f 1);\n assert_norm (f 2);\n assert_norm (f 3);\n assert_norm (f 4);\n ()", "val lemma_mod_n_8_lower1 (q: quad32) (n: nat)\n : Lemma (requires n <= 4) (ensures lo64 q % pow2 (8 * n) == q.lo0 % pow2 (8 * n))\nlet lemma_mod_n_8_lower1 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures lo64 q % pow2 (8 * n) == q.lo0 % pow2 (8 * n))\n =\n lo64_reveal ();\n let Mkfour _ _ _ _ = q in // avoid ifuel\n let f (n:nat{n <= 4}) = lo64_def q % pow2 (8 * n) == q.lo0 % pow2 (8 * n) in\n assert_norm (f 0);\n assert_norm (f 1);\n assert_norm (f 2);\n assert_norm (f 3);\n assert_norm (f 4);\n ()", "val Vale.Poly1305.Equiv.nat_to_bytes_le = len: Prims.nat -> n: Prims.nat{n < Prims.pow2 (8 * len)}\n -> b:\n Lib.Sequence.seq (Lib.IntTypes.int_t Lib.IntTypes.U8 l)\n {Lib.Sequence.length b == len /\\ n == Lib.ByteSequence.nat_from_intseq_le b}\nlet nat_to_bytes_le (#l:secrecy_level) = Lib.ByteSequence.nat_to_bytes_le #l", "val mk_n_to_le (#t: Type) (#tot: nat) (u: uinttype t tot) (len: nat{len <= tot /\\ tot < pow2 32})\n : Tot (n_to_le_t u len) (decreases len)\nlet rec mk_n_to_le\n (#t: Type)\n (#tot: nat)\n (u: uinttype t tot)\n (len: nat {len <= tot /\\ tot < pow2 32})\n: Tot (n_to_le_t u len)\n (decreases len)\n= if len = 0\n then n_to_le_0 u\n else n_to_le_S (mk_n_to_le u (len - 1))", "val append_subseq\n (#a #n: _)\n (f: iarray a n)\n (pos: nat)\n (sent: nat{pos + sent <= n})\n (h: heap{f `fully_initialized_in` h})\n : Lemma\n (let f0 = as_initialized_subseq f h 0 pos in\n let f1 = as_initialized_subseq f h 0 (pos + sent) in\n let sub_file = suffix f pos in\n let sent_frag = as_initialized_subseq sub_file h 0 sent in\n f1 == append f0 sent_frag)\nlet append_subseq #a #n (f:iarray a n) (pos:nat) (sent:nat{pos + sent <= n}) (h:heap{f `fully_initialized_in` h})\n : Lemma (let f0 = as_initialized_subseq f h 0 pos in\n let f1 = as_initialized_subseq f h 0 (pos + sent) in\n let sub_file = suffix f pos in\n let sent_frag = as_initialized_subseq sub_file h 0 sent in\n f1 == append f0 sent_frag)\n = let f0 = as_initialized_subseq f h 0 pos in\n let f1 = as_initialized_subseq f h 0 (pos + sent) in\n let sub_file = suffix f pos in\n let sent_frag = as_initialized_subseq sub_file h 0 sent in\n\n let bs = as_seq f h in\n let bss = as_seq sub_file h in\n let sbs = ArrayUtils.get_some_equivalent bs in\n\n assert (f0 == ArrayUtils.get_some_equivalent (Seq.slice bs 0 pos));\n assert (f1 == ArrayUtils.get_some_equivalent (Seq.slice bs 0 (pos + sent)));\n assert (sent_frag == ArrayUtils.get_some_equivalent (Seq.slice bss 0 sent));\n assert (bss == Seq.slice bs pos n);\n assert (Seq.equal (Seq.slice bss 0 sent) (Seq.slice bs pos (pos + sent)));\n assert (sent_frag == ArrayUtils.get_some_equivalent (Seq.slice bs pos (pos + sent)));\n\n assert (f0 == Seq.slice sbs 0 pos);\n assert (f1 == Seq.slice sbs 0 (pos + sent));\n assert (sent_frag == Seq.slice sbs pos (pos + sent));\n lemma_seq_append_unstable sbs f0 sent_frag f1 pos sent", "val to_uint8_of_uint8 (n: nat{n <= 8}) (x: U8.t{U8.v x < pow2 n})\n : Lemma (to_uint8 (of_uint8 n x) == x)\nlet rec to_uint8_of_uint8\n (n: nat { n <= 8 })\n (x: U8.t { U8.v x < pow2 n })\n: Lemma\n (to_uint8 (of_uint8 n x) == x)\n= if n = 0\n then ()\n else begin\n assert (Seq.slice (of_uint8 n x) 0 (n - 1) `Seq.equal` of_uint8 (n - 1) (x `U8.div` 2uy));\n to_uint8_of_uint8 (n - 1) (x `U8.div` 2uy)\n end", "val lemma_64_32_hi1 (q': quad32) (hi hi': nat64) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\ hi' == hi % pow2 (8 * n) /\\\n four_to_two_two q' == Mktwo (Mktwo q'.lo0 q'.lo1) (nat_to_two 32 hi'))\n (ensures hi' < 0x100000000 /\\ hi' == q'.hi2 /\\ q'.hi3 == 0)\nlet lemma_64_32_hi1 (q':quad32) (hi hi':nat64) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n hi' == hi % pow2 (8 * n) /\\\n four_to_two_two q' == Mktwo (Mktwo q'.lo0 q'.lo1) (nat_to_two 32 hi')\n )\n (ensures hi' < 0x100000000 /\\ hi' == q'.hi2 /\\ q'.hi3 == 0)\n =\n assert_norm (pow2 (0 * 8) == 1);\n assert_norm (pow2 (1 * 8) == 0x100);\n assert_norm (pow2 (2 * 8) == 0x10000);\n assert_norm (pow2 (3 * 8) == 0x1000000);\n assert_norm (pow2 (4 * 8) == 0x100000000);\n assert_norm (nat_to_two 32 hi' == nat_to_two_unfold 32 hi');\n ()", "val shift_add (n: nat) (m: nat{m < pow2 32})\n : Lemma (n * pow2 32 % pow2 64 + m == (n * pow2 32 + m) % pow2 64)\nlet shift_add (n:nat) (m:nat{m < pow2 32}) :\n Lemma (n * pow2 32 % pow2 64 + m == (n * pow2 32 + m) % pow2 64) =\n add_mod_small' m (n*pow2 32) (pow2 64)", "val lemma_pow2_256: n:nat -> Lemma\n (requires (n = 256))\n (ensures (pow2 n = 0x10000000000000000000000000000000000000000000000000000000000000000))\n [SMTPat (pow2 n)]\nlet lemma_pow2_256 n = assert_norm(pow2 256 = 0x10000000000000000000000000000000000000000000000000000000000000000)", "val lemma_to_nat_rec (len: nat) (p: poly) (c n i: nat)\n : Lemma (requires degree p < len /\\ normalize (poly_nat_eq_rec len p c n))\n (ensures p.[ len - n + i ] == (of_nat c).[ i ])\nlet rec lemma_to_nat_rec (len:nat) (p:poly) (c:nat) (n:nat) (i:nat) : Lemma\n (requires degree p < len /\\ normalize (poly_nat_eq_rec len p c n))\n (ensures p.[len - n + i] == (of_nat c).[i])\n =\n lemma_bitwise_all ();\n if (i > 0 && n > 0) then lemma_to_nat_rec len p (c / 2) (n - 1) (i - 1)", "val uints_to_bytes_be_nat_lemma_: #t:inttype{unsigned t /\\ ~(U1? t)} -> #l:secrecy_level\n -> len:nat{len * numbytes t < pow2 32}\n -> n:nat{n < pow2 (bits t * len)}\n -> i:nat{i < len * numbytes t}\n -> Lemma\n (Seq.index (uints_to_bytes_be #t #l #len (nat_to_intseq_be #t #l len n)) i ==\n Seq.index (nat_to_bytes_be (len * numbytes t) n) i)\nlet uints_to_bytes_be_nat_lemma_ #t #l len n i =\n let s:lseq (uint_t t l) len = nat_to_intseq_be #t #l len n in\n calc (==) {\n Seq.index (uints_to_bytes_be #t #l #len (nat_to_intseq_be #t #l len n)) i;\n == { index_uints_to_bytes_be_aux #t #l len n i }\n Seq.index (nat_to_bytes_be #l (numbytes t) (v s.[i / numbytes t])) (i % numbytes t);\n == { index_nat_to_intseq_to_bytes_be #t #l len n (len * numbytes t - 1 - i)}\n Seq.index (nat_to_bytes_be (len * numbytes t) n) i;\n }", "val lemma_append_count' (#a: eqtype) (lo hi: seq a)\n : Lemma (requires True)\n (ensures (forall x. count x (append lo hi) = (count x lo + count x hi)))\n (decreases (length lo))\nlet rec lemma_append_count' (#a:eqtype) (lo:seq a) (hi:seq a)\n: Lemma\n (requires True)\n (ensures (forall x. count x (append lo hi) = (count x lo + count x hi)))\n (decreases (length lo))\n= if length lo = 0\n then cut (equal (append lo hi) hi)\n else (cut (equal (cons (head lo) (append (tail lo) hi))\n (append lo hi));\n lemma_append_count' (tail lo) hi;\n let tl_l_h = append (tail lo) hi in\n let lh = cons (head lo) tl_l_h in\n cut (equal (tail lh) tl_l_h))", "val length_snoc : n : int -> l : ilist -> Lemma\n (ensures (length (snoc l n) = length l + 1))\nlet rec length_snoc n l =\n match l with\n | Nil -> ()\n | Cons h t -> length_snoc n t", "val mod_then_mul_64 (n: nat) : Lemma ((n % pow2 64) * pow2 64 == n * pow2 64 % pow2 128)\nlet mod_then_mul_64 (n:nat) : Lemma (n % pow2 64 * pow2 64 == n * pow2 64 % pow2 128) =\n Math.pow2_plus 64 64;\n mod_mul n (pow2 64) (pow2 64)", "val lemma_ishl_nth (n:pos) (x:natN (pow2 n)) (y:nat) : Lemma\n (forall (m:_{m==pow2_norm n}) (i:nat{i < n}).{:pattern (nth #n (ishl #m x y) i)}\n nth #n (ishl #m x y) i == (i + y < n && nth #n x (i + y)))\nlet lemma_ishl_nth n x y =\n FStar.Classical.forall_intro (lemma_ishl_nth_i n x y)", "val index_nat_to_intseq_to_bytes_le:\n #t:inttype{unsigned t /\\ ~(U1? t)}\n -> #l:secrecy_level\n -> len:nat{len * numbytes t < pow2 32}\n -> n:nat{n < pow2 (bits t * len)}\n -> i:nat{i < len * numbytes t}\n -> Lemma (let s:lseq (int_t t l) len = nat_to_intseq_le #t #l len n in\n Seq.index (nat_to_bytes_le #l (numbytes t) (v s.[i / numbytes t])) (i % numbytes t) ==\n Seq.index (nat_to_bytes_le #l (len * numbytes t) n) i)\nlet index_nat_to_intseq_to_bytes_le #t #l len n i =\n let s:lseq (int_t t l) len = nat_to_intseq_le #t #l len n in\n let m = numbytes t in\n index_nat_to_intseq_le #U8 #l (len * m) n i;\n assert (Seq.index (nat_to_bytes_le #l (len * m) n) i ==\n uint (n / pow2 (8 * i) % pow2 8));\n index_nat_to_intseq_le #U8 #l m (v s.[i / m]) (i % m);\n assert (Seq.index (nat_to_bytes_le #l m (v s.[i / m])) (i % m) ==\n uint (v s.[i / m] / pow2 (8 * (i % m)) % pow2 8));\n index_nat_to_intseq_le #t #l len n (i / m);\n some_arithmetic t n i", "val le_to_n_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat{len + 1 <= tot})\n (ih: le_to_n_t u len)\n : Tot (le_to_n_t u (len + 1))\nlet le_to_n_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat { len + 1 <= tot })\n (ih: le_to_n_t u len)\n: Tot (le_to_n_t u (len + 1))\n= fun x ->\n assert_norm (pow2 8 == 256);\n E.reveal_le_to_n (B.reveal x);\n pow2_le_compat (8 * tot) (8 * (len + 1));\n pow2_le_compat (8 * (len + 1)) (8 * len);\n pow2_plus (8 * len) 8;\n [@inline_let]\n let ulen = U32.uint_to_t len in\n let last = B.get x 0ul in\n let first = B.slice x 1ul (ulen `U32.add` 1ul) in\n let n = ih first in\n E.lemma_le_to_n_is_bounded (B.reveal first);\n assert (u.v n * 256 < 256 * pow2 (8 * len));\n assert (0 <= u.v n * 256);\n assert (u.v n * 256 < pow2 (8 * tot));\n let blast = u.from_byte last in\n blast `u.add` u.mul256 n", "val slice_commutes_le_seq_quad32_to_bytes (s:seq quad32) (n:nat{n <= length s}) (n':nat{ n <= n' /\\ n' <= length s}) :\n Lemma(slice (le_seq_quad32_to_bytes s) (n * 16) (n' * 16) ==\n le_seq_quad32_to_bytes (slice s n n'))\nlet slice_commutes_le_seq_quad32_to_bytes (s:seq quad32) (n:nat{n <= length s}) (n':nat{ n <= n' /\\ n' <= length s}) :\n Lemma(slice (le_seq_quad32_to_bytes s) (n * 16) (n' * 16) ==\n le_seq_quad32_to_bytes (slice s n n'))\n =\n le_seq_quad32_to_bytes_reveal ();\n slice_commutes_seq_four_to_seq_LE s n n';\n assert (slice (seq_four_to_seq_LE s) (n * 4) (n' * 4) == seq_four_to_seq_LE (slice s n n'));\n(*\n le_seq_quad32_to_bytes (slice s n n') == seq_four_to_seq_LE (seq_map (nat_to_four 8) (seq_four_to_seq_LE (slice s n n')));\n == seq_four_to_seq_LE (seq_map (nat_to_four 8) (slice (seq_four_to_seq_LE s) (n * 4) (n' * 4))\n slice (le_seq_quad32_to_bytes s) (n * 16) (n' * 16)\n == slice (seq_four_to_seq_LE (seq_map (nat_to_four 8) (seq_four_to_seq_LE s))) (n * 16) (n' * 16)\n == seq_four_to_seq_LE (slice (seq_map (nat_to_four 8) (seq_four_to_seq_LE s)) (n * 4) (n' * 4))\n*)\n slice_seq_map_commute (nat_to_four 8) (seq_four_to_seq_LE s) (n*4) (n'*4);\n\n let s_inner = (seq_map (nat_to_four 8) (seq_four_to_seq_LE s)) in\n slice_commutes_seq_four_to_seq_LE s_inner (n * 4) (n' * 4);\n ()", "val lemma_split3_append (#t: Type) (l: list t) (n: nat{n < length l})\n : Lemma (requires True)\n (ensures\n (let a, b, c = split3 l n in\n l == append a (b :: c)))\nlet lemma_split3_append (#t:Type) (l:list t) (n:nat{n < length l}) :\n Lemma\n (requires True)\n (ensures (\n let a, b, c = split3 l n in\n l == append a (b :: c))) =\n lemma_splitAt_append n l", "val lemma_reverse_bytes_nat64_32 (n0 n1: nat32)\n : Lemma\n (reverse_bytes_nat64 (two_to_nat32 (Mktwo n0 n1)) ==\n two_to_nat32 (Mktwo (reverse_bytes_nat32 n1) (reverse_bytes_nat32 n0)))\nlet lemma_reverse_bytes_nat64_32 (n0 n1:nat32) : Lemma\n (reverse_bytes_nat64 (two_to_nat32 (Mktwo n0 n1)) == two_to_nat32 (Mktwo (reverse_bytes_nat32 n1) (reverse_bytes_nat32 n0)))\n =\n reverse_bytes_nat64_reveal ()", "val two_to_nat_to_two (n:nat64) : Lemma\n (two_to_nat 32 (nat_to_two 32 n) == n)\n [SMTPat (two_to_nat 32 (nat_to_two 32 n))]\nlet two_to_nat_to_two (n:nat64) =\n let n1 = n % (pow2_32) in\n let n2 = (n/(pow2_32)) % (pow2_32) in\n let n_f = two_to_nat 32 (Mktwo n1 n2) in\n assert_norm (n == n1 + n2 * pow2_32)", "val lemma_iand_nth_all (n:pos) : Lemma\n (forall (m:_{m==pow2_norm n}) (x y:natN (pow2 n)).{:pattern (iand #m x y)}\n (forall (i:nat{i < n}).{:pattern (nth #n (iand #m x y) i)}\n nth #n (iand #m x y) i == (nth #n x i && nth #n y i)))\nlet lemma_iand_nth_all n =\n FStar.Classical.forall_intro_2 (lemma_iand_nth n)", "val lemma_add_wrap_is_add_mod (n0 n1: nat32)\n : Lemma (add_wrap n0 n1 == vv (add_mod (to_uint32 n0) (to_uint32 n1)))\nlet lemma_add_wrap_is_add_mod (n0 n1:nat32) :\n Lemma (add_wrap n0 n1 == vv (add_mod (to_uint32 n0) (to_uint32 n1)))\n =\n assert_norm (pow2 32 == pow2_32);\n ()", "val lemma_add_wrap_is_add_mod (n0 n1: nat32)\n : Lemma (add_wrap n0 n1 == vv (add_mod (to_uint32 n0) (to_uint32 n1)))\nlet lemma_add_wrap_is_add_mod (n0 n1:nat32) :\n Lemma (add_wrap n0 n1 == vv (add_mod (to_uint32 n0) (to_uint32 n1)))\n =\n assert_norm (pow2 32 == pow2_32);\n ()", "val lemma_64_32_hi2 (q': quad32) (hi hi': nat64) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\ hi' == (hi / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 0) (nat_to_two 32 hi'))\n (ensures hi' == 0x100000000 * q'.hi3 + q'.hi2 /\\ q' == Mkfour 0 0 q'.hi2 q'.hi3)\nlet lemma_64_32_hi2 (q':quad32) (hi hi':nat64) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n hi' == (hi / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 0) (nat_to_two 32 hi')\n )\n (ensures hi' == 0x100000000 * q'.hi3 + q'.hi2 /\\ q' == Mkfour 0 0 q'.hi2 q'.hi3)\n =\n assert_norm (nat_to_two 32 hi' == nat_to_two_unfold 32 hi');\n assert_norm (nat_to_two 32 0 == nat_to_two_unfold 32 0);\n ()", "val lemma_64_32_hi2 (q': quad32) (hi hi': nat64) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\ hi' == hi % pow2 (8 * (n + 4)) /\\\n four_to_two_two q' == Mktwo (Mktwo q'.lo0 q'.lo1) (nat_to_two 32 hi'))\n (ensures hi' == q'.hi2 + 0x100000000 * q'.hi3)\nlet lemma_64_32_hi2 (q':quad32) (hi hi':nat64) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n hi' == hi % pow2 (8 * (n + 4)) /\\\n four_to_two_two q' == Mktwo (Mktwo q'.lo0 q'.lo1) (nat_to_two 32 hi')\n )\n (ensures hi' == q'.hi2 + 0x100000000 * q'.hi3)\n =\n assert_norm (pow2 (4 * 8) == 0x100000000);\n assert_norm (pow2 (5 * 8) == 0x10000000000);\n assert_norm (pow2 (6 * 8) == 0x1000000000000);\n assert_norm (pow2 (7 * 8) == 0x100000000000000);\n assert_norm (pow2 (8 * 8) == 0x10000000000000000);\n assert_norm (nat_to_two 32 hi' == nat_to_two_unfold 32 hi');\n ()", "val log256' (n: nat)\n : Pure integer_size\n (requires (n > 0 /\\ n < 4294967296))\n (ensures\n (fun l -> pow2 (FStar.Mul.op_Star 8 (l - 1)) <= n /\\ n < pow2 (FStar.Mul.op_Star 8 l)))\nlet log256'\n (n: nat)\n: Pure integer_size\n (requires (n > 0 /\\ n < 4294967296))\n (ensures (fun l ->\n pow2 (FStar.Mul.op_Star 8 (l - 1)) <= n /\\\n n < pow2 (FStar.Mul.op_Star 8 l)\n ))\n= [@inline_let]\n let _ = assert_norm (pow2 32 == 4294967296) in\n [@inline_let]\n let _ = assert (n < pow2 32) in\n [@inline_let]\n let z0 = 1 in\n [@inline_let]\n let z1 = 256 in\n [@inline_let]\n let _ = assert_norm (z1 == Prims.op_Multiply 256 z0) in\n [@inline_let]\n let l = 1 in\n [@inline_let]\n let _ = assert_norm (pow2 (Prims.op_Multiply 8 l) == z1) in\n [@inline_let]\n let _ = assert_norm (pow2 (Prims.op_Multiply 8 (l - 1)) == z0) in\n if n < z1\n then begin\n [@inline_let]\n let _ = assert (pow2 (Prims.op_Multiply 8 (l - 1)) <= n) in\n [@inline_let]\n let _ = assert (n < pow2 (Prims.op_Multiply 8 l)) in\n l\n end else begin\n [@inline_let]\n let z2 = 65536 in\n [@inline_let]\n let _ = assert_norm (z2 == Prims.op_Multiply 256 z1) in\n [@inline_let]\n let l = 2 in\n [@inline_let]\n let _ = assert_norm (pow2 (Prims.op_Multiply 8 l) == z2) in\n if n < z2\n then begin\n [@inline_let]\n let _ = assert (pow2 (Prims.op_Multiply 8 (l - 1)) <= n) in\n [@inline_let]\n let _ = assert (n < pow2 (Prims.op_Multiply 8 l)) in\n l\n end else begin\n [@inline_let]\n let z3 = 16777216 in\n [@inline_let]\n let _ = assert_norm (z3 == Prims.op_Multiply 256 z2) in\n [@inline_let]\n let l = 3 in\n [@inline_let]\n let _ = assert_norm (pow2 (Prims.op_Multiply 8 l) == z3) in\n if n < z3\n then begin\n [@inline_let]\n\tlet _ = assert (pow2 (Prims.op_Multiply 8 (l - 1)) <= n) in\n [@inline_let]\n\tlet _ = assert (n < pow2 (Prims.op_Multiply 8 l)) in\n l \n end else begin\n [@inline_let]\n let l = 4 in\n [@inline_let]\n let _ = assert_norm (pow2 (Prims.op_Multiply 8 l) == Prims.op_Multiply 256 z3) in\n [@inline_let]\n\tlet _ = assert (pow2 (Prims.op_Multiply 8 (l - 1)) <= n) in\n [@inline_let]\n\tlet _ = assert (n < pow2 (Prims.op_Multiply 8 l)) in\n l\n end\n end\n end", "val lemma_inot_nth_all (n:pos) : Lemma\n (forall (m:_{m==pow2_norm n}) (x:natN (pow2 n)).{:pattern (inot #m x)}\n (forall (i:nat{i < n}).{:pattern (nth #n (inot #m x) i)}\n nth #n (inot #m x) i == not (nth #n x i)))\nlet lemma_inot_nth_all n =\n FStar.Classical.forall_intro (lemma_inot_nth n)", "val lemma_msb_pow2: #n:pos -> a:uint_t n ->\n Lemma (msb a <==> a >= pow2 (n-1))\nlet lemma_msb_pow2 #n a = if n = 1 then () else from_vec_propriety (to_vec a) 1", "val nat_to_bytes_be (#l: secrecy_level) (len: nat) (n: nat{n < pow2 (8 * len)})\n : b: bytes_l l {length b == len /\\ n == nat_from_intseq_be #U8 b}\nlet nat_to_bytes_be (#l:secrecy_level) (len:nat) (n:nat{n < pow2 (8 * len)}) : b:bytes_l l{length b == len /\\ n == nat_from_intseq_be #U8 b} =\n nat_to_intseq_be #U8 #l len n", "val load_felem5_4_lemma: lo:uint64xN 4 -> hi:uint64xN 4 ->\n Lemma\n (let f = load_felem5_4_compact lo hi in\n felem_fits5 f (1, 1, 1, 1, 1) /\\\n felem_less5 f (pow2 128) /\\\n feval5 f == createi #Vec.pfelem 4 (fun i -> (uint64xN_v hi).[i] * pow2 64 + (uint64xN_v lo).[i]))\nlet load_felem5_4_lemma lo hi =\n let f = load_felem5_4_compact lo hi in\n assert_norm (pow2 64 * pow2 64 = pow2 128);\n assert_norm (pow2 128 < Vec.prime);\n let res = createi #Vec.pfelem 4\n (fun i -> (uint64xN_v hi).[i] * pow2 64 + (uint64xN_v lo).[i]) in\n\n load_felem5_4_compact_lemma_i lo hi 0;\n load_felem5_4_compact_lemma_i lo hi 1;\n load_felem5_4_compact_lemma_i lo hi 2;\n load_felem5_4_compact_lemma_i lo hi 3;\n eq_intro (feval5 f) res", "val mul_pow2_256_minus_q_lemma: len:size_nat -> resLen:size_nat{2 + len <= resLen} -> a:lseq uint64 len ->\n Lemma (let c, res = mul_pow2_256_minus_q_lseq len resLen a in\n v c * pow2 (64 * resLen) + SD.bn_v res = SD.bn_v a * (pow2 256 - S.q))\nlet mul_pow2_256_minus_q_lemma len resLen a =\n let t0 = u64 0x402da1732fc9bebf in\n let t1 = u64 0x4551231950b75fc4 in\n assert_norm (v t0 + v t1 * pow2 64 = pow2 256 - S.q - pow2 128);\n\n let t01 = create2 t0 t1 in\n SD.bn_eval_unfold_i t01 2;\n SD.bn_eval_unfold_i t01 1;\n SD.bn_eval0 t01;\n assert (SD.bn_v t01 = pow2 256 - S.q - pow2 128);\n\n let m0 = SB.bn_mul a t01 in // a * t01\n SB.bn_mul_lemma a t01;\n assert (SD.bn_v m0 == SD.bn_v a * SD.bn_v t01);\n\n let m10 = create resLen (u64 0) in\n let m1 = update_sub m10 2 len a in // a * t2 * pow2 128\n SD.bn_update_sub_eval m10 a 2;\n assert (SD.bn_v m1 = SD.bn_v m10 - SD.bn_v (sub m10 2 len) * pow2 128 + SD.bn_v a * pow2 128);\n SD.bn_eval_zeroes #U64 resLen resLen;\n eq_intro (sub m10 2 len) (create len (u64 0));\n SD.bn_eval_zeroes #U64 len len;\n assert (SD.bn_v m1 = SD.bn_v a * pow2 128);\n\n let c, m2 = SB.bn_add m1 m0 in // a * SECP256K1_N_C\n SB.bn_add_lemma m1 m0;\n assert (v c * pow2 (64 * resLen) + SD.bn_v m2 = SD.bn_v m1 + SD.bn_v m0);\n assert (v c * pow2 (64 * resLen) + SD.bn_v m2 = SD.bn_v a * pow2 128 + SD.bn_v a * SD.bn_v t01);\n Math.Lemmas.distributivity_add_right (SD.bn_v a) (pow2 128) (SD.bn_v t01);\n assert (v c * pow2 (64 * resLen) + SD.bn_v m2 = SD.bn_v a * (pow2 256 - S.q))", "val index_nat_to_intseq_be:\n #t:inttype{unsigned t}\n -> #l:secrecy_level\n -> len:size_nat\n -> n:nat{n < pow2 (bits t * len)}\n -> i:nat{i < len}\n -> Lemma (Seq.index (nat_to_intseq_be #t #l len n) (len - i - 1) ==\n uint #t #l (n / pow2 (bits t * i) % pow2 (bits t)))\nlet rec index_nat_to_intseq_be #t #l len n i =\n if i = 0 then\n if len = 0 then () else head_nat_to_intseq_be #t #l len n\n else\n begin\n let len' = len - 1 in\n let i' = i - 1 in\n let n' = n / pow2 (bits t) in\n FStar.Math.Lemmas.lemma_div_lt_nat n (bits t * len) (bits t);\n calc (==) {\n Seq.index (nat_to_intseq_be #t #l len' n') (len' - i' - 1);\n == {index_nat_to_intseq_be #t #l len' n' i'}\n uint (n' / pow2 (bits t * i') % pow2 (bits t));\n == {}\n uint (n / pow2 (bits t) / pow2 (bits t * i') % pow2 (bits t));\n == {Math.Lemmas.division_multiplication_lemma n (pow2 (bits t)) (pow2 (bits t * i'))}\n uint (n / (pow2 (bits t) * pow2 (bits t * i')) % pow2 (bits t));\n == {Math.Lemmas.pow2_plus (bits t) (bits t * i')}\n uint (n / (pow2 (bits t + bits t * i')) % pow2 (bits t));\n == {Math.Lemmas.distributivity_add_right (bits t) 1 (i - 1)}\n uint (n / (pow2 (bits t * i)) % pow2 (bits t));\n };\n nat_to_intseq_be_pos #t #l len n\n end", "val lemma_64_32_hi1 (q': quad32) (hi hi': nat64) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\ hi' == (hi / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n)) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 0) (nat_to_two 32 hi'))\n (ensures hi' % pow2_32 == 0 /\\ hi' / pow2_32 == q'.hi3 /\\ q' == Mkfour 0 0 0 q'.hi3)\nlet lemma_64_32_hi1 (q':quad32) (hi hi':nat64) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n hi' == (hi / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n)) /\\\n four_to_two_two q' == Mktwo (nat_to_two 32 0) (nat_to_two 32 hi')\n )\n (ensures hi' % pow2_32 == 0 /\\ hi' / pow2_32 == q'.hi3 /\\ q' == Mkfour 0 0 0 q'.hi3)\n =\n assert_norm (((hi / pow2 (8 * 4)) * pow2 (8 * 4)) % pow2_32 == 0);\n assert_norm (((hi / pow2 (8 * 5)) * pow2 (8 * 5)) % pow2_32 == 0);\n assert_norm (((hi / pow2 (8 * 6)) * pow2 (8 * 6)) % pow2_32 == 0);\n assert_norm (((hi / pow2 (8 * 7)) * pow2 (8 * 7)) % pow2_32 == 0);\n assert_norm (((hi / pow2 (8 * 8)) * pow2 (8 * 8)) % pow2_32 == 0);\n assert_norm ((((hi / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32) % pow2_32 ==\n ((hi / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32);\n assert_norm (nat_to_two 32 hi' == nat_to_two_unfold 32 hi');\n assert_norm (nat_to_two 32 0 == nat_to_two_unfold 32 0);\n ()", "val append_then_take_or_drop_helper (#ty: Type) (s t: list ty) (n: nat)\n : Lemma (requires n = length s /\\ length (append s t) = length s + length t)\n (ensures take (append s t) n == s /\\ drop (append s t) n == t)\nlet rec append_then_take_or_drop_helper (#ty: Type) (s: list ty) (t: list ty) (n: nat)\n : Lemma (requires n = length s /\\ length (append s t) = length s + length t)\n (ensures take (append s t) n == s /\\ drop (append s t) n == t) =\n match s with\n | [] -> ()\n | hd :: tl -> append_then_take_or_drop_helper tl t (n - 1)", "val uints_to_bytes_be_nat_lemma: #t:inttype{unsigned t /\\ ~(U1? t)} -> #l:secrecy_level\n -> len:nat{len * numbytes t < pow2 32}\n -> n:nat{n < pow2 (bits t * len)}\n -> Lemma\n (uints_to_bytes_be #t #l #len (nat_to_intseq_be #t #l len n) ==\n nat_to_bytes_be (len * numbytes t) n)\nlet uints_to_bytes_be_nat_lemma #t #l len n =\n Classical.forall_intro (uints_to_bytes_be_nat_lemma_ #t #l len n);\n eq_intro (uints_to_bytes_be #t #l #len (nat_to_intseq_be #t #l len n))\n (nat_to_bytes_be (len * numbytes t) n)", "val nat_from_intseq_slice_lemma_aux: len:pos -> a:nat -> b:nat -> c:nat -> i:pos{i <= len} ->\n Lemma (pow2 ((i - 1) * c) * (a + pow2 c * b) == pow2 ((i - 1) * c) * a + pow2 (i * c) * b)\nlet nat_from_intseq_slice_lemma_aux len a b c i =\n FStar.Math.Lemmas.distributivity_add_right (pow2 ((i - 1) * c)) a (pow2 c * b);\n FStar.Math.Lemmas.paren_mul_right (pow2 ((i - 1) * c)) (pow2 c) b;\n FStar.Math.Lemmas.pow2_plus ((i - 1) * c) c", "val lemma_prime_value: n:nat -> Lemma\n (requires (n = 255))\n (ensures (pow2 n - 19 = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed))\n [SMTPat (pow2 n - 19)]\nlet lemma_prime_value n = assert_norm(pow2 255 - 19 = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed)", "val lemma_seq_add_rec (#n: nat) (as0 bs: seq (natN n)) (c0: nat1) (i: nat)\n : Lemma (requires i <= length as0 /\\ length bs == length as0)\n (ensures\n (let xs = fst (seq_add as0 bs c0) in\n let ci = seq_add_c as0 bs c0 i in\n sum_pow_seq_left xs i + last_carry n i ci ==\n sum_pow_seq_left as0 i + sum_pow_seq_left bs i + c0))\n (decreases i)\nlet rec lemma_seq_add_rec (#n:nat) (as0 bs:seq (natN n)) (c0:nat1) (i:nat) : Lemma\n (requires i <= length as0 /\\ length bs == length as0)\n (ensures (\n let xs = fst (seq_add as0 bs c0) in\n let ci = seq_add_c as0 bs c0 i in\n sum_pow_seq_left xs i + last_carry n i ci == sum_pow_seq_left as0 i + sum_pow_seq_left bs i + c0\n ))\n (decreases i)\n =\n if (i > 0) then (\n let xs = fst (seq_add as0 bs c0) in\n let ci = seq_add_c as0 bs c0 i in\n let i' = i - 1 in\n let ci' = seq_add_c as0 bs c0 i' in\n calc (==) {\n sum_pow_seq_left xs i + last_carry n i ci;\n == {}\n xs.[i'] * pow_int n i' + sum_pow_seq_left xs i' + last_carry n i ci;\n == {lemma_seq_add_rec as0 bs c0 i'}\n xs.[i'] * pow_int n i' + sum_pow_seq_left as0 i' + sum_pow_seq_left bs i' + c0 - last_carry n i' ci' + last_carry n i ci;\n == {\n reveal_add_hi_all ();\n lemma_last_carry_mul n i' ci';\n lemma_add_lo_mul_right as0.[i'] bs.[i'] ci' (pow_int n i')\n }\n sum_pow_seq_left as0 i + sum_pow_seq_left bs i + c0;\n }\n )", "val lemma_mod_n_8_upper2 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures hi64 q % pow2 (8 * (4 + n)) == q.hi2 + 0x100000000 * (q.hi3 % pow2 (8 * n)))\nlet lemma_mod_n_8_upper2 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures hi64 q % pow2 (8 * (4 + n)) == q.hi2 + 0x100000000 * (q.hi3 % pow2 (8 * n)))\n =\n hi64_reveal ();\n lo64_reveal ();\n let Mkfour _ _ q2 q3 = q in\n lemma_mod_n_8_lower2 (Mkfour q2 q3 0 0) n", "val lemma_store_felem_lo:\n f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}\n -> lo:uint64 ->\n Lemma\n (let (f0, f1, f2, f3, f4) = f in\n let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in\n v lo == v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64)\nlet lemma_store_felem_lo f lo =\n let (f0, f1, f2, f3, f4) = f in\n assert_norm (max26 = pow2 26 - 1);\n let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in\n assert (v (f1 <<. 26ul) == v f1 * pow2 26 % pow2 64);\n FStar.Math.Lemmas.modulo_lemma (v f1 * pow2 26) (pow2 64);\n FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f1) 26 26;\n logor_disjoint f0 (f1 <<. 26ul) 26;\n assert (v (f0 |. (f1 <<. 26ul)) == v f0 + v f1 * pow2 26);\n\n assert_norm (pow2 26 * pow2 26 = pow2 52);\n assert (v f0 + v f1 * pow2 26 < pow2 52);\n assert (((v f2 * pow2 52) % pow2 64) % pow2 52 = 0);\n logor_disjoint (f0 |. (f1 <<. 26ul)) (f2 <<. 52ul) 52", "val list_splitAt_append (#t: Type) (n: nat) (l: list t)\n : Lemma\n (ensures\n (let l1, l2 = List.Tot.splitAt n l in\n l == l1 `List.Tot.append` l2)) [SMTPat (List.Tot.splitAt n l)]\nlet rec list_splitAt_append\n (#t: Type)\n (n: nat)\n (l: list t)\n: Lemma\n (ensures (let (l1, l2) = List.Tot.splitAt n l in\n l == l1 `List.Tot.append` l2\n ))\n [SMTPat (List.Tot.splitAt n l)]\n= match l with\n | [] -> ()\n | a :: q ->\n if n = 0 then () else list_splitAt_append (n - 1) q" ], "closest_src": [ { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.n_to_le_le_to_n" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.n_to_le_le_to_n" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.n_to_le" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.index_n_to_be" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.n_to_be_be_to_n" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.n_to_le" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.index_n_to_be_zero_right" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.index_n_to_be_zero_left" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.n_to_be_be_to_n" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_pad_to_32_bits_helper" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_pad_to_32_bits" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_pad_to_32_bits_helper" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_pad_to_32_bits" }, { "project_name": "everparse", "file_name": "LowParse.Endianness.BitFields.fst", "name": "LowParse.Endianness.BitFields.slice_n_to_be_bitfield" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.FFDHE.Lemmas.fst", "name": "Hacl.Spec.FFDHE.Lemmas.pow2_lt_len" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_64_32_lo2" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fsti", "name": "Lib.ByteSequence.nat_to_bytes_le" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fst", "name": "FStar.UInt128.to_vec_append" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_64_32_lo1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_64_32_lo1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_64_32_lo2" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.lemma_be_index" }, { "project_name": "hacl-star", "file_name": "Lib.ByteBuffer.fst", "name": "Lib.ByteBuffer.nat_to_bytes_n_to_le" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Endianness.fst", "name": "LowParse.SLow.Endianness.n_to_le_S" }, { "project_name": "hacl-star", "file_name": "Lib.ByteBuffer.fst", "name": "Lib.ByteBuffer.nat_to_bytes_n_to_be" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.n_to_be" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Bignum.Convert.fst", "name": "Hacl.Spec.Bignum.Convert.nat_from_bytes_le_eq_lemma" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_div_n_8_lower1" }, { "project_name": "everparse", "file_name": "LowParse.BitFields.fst", "name": "LowParse.BitFields.nth_size" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_mod_n_8_lower2_helper" }, { "project_name": "hacl-star", "file_name": "Vale.AES.AES_helpers.fst", "name": "Vale.AES.AES_helpers.lemma_add_0x1000000_reverse_mult" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.Lemmas.fst", "name": "Hacl.Impl.Poly1305.Lemmas.nat_from_bytes_le_eq_lemma_" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Base.fst", "name": "FStar.Sequence.Base.index_after_append_helper" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_ishl_nth_all" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_div_n_8_lower2" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.Lemmas.fst", "name": "Hacl.Impl.Poly1305.Lemmas.nat_from_bytes_le_eq_lemma" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.n_to_be" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.PrecompTable.fst", "name": "Hacl.Impl.PrecompTable.lemma_table_sub_len" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Math.fst", "name": "Vale.Poly1305.Math.lemma_power2_add64" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.BignumQ.Lemmas.fst", "name": "Hacl.Spec.BignumQ.Lemmas.lemma_aux_0" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.lemma_le_to_n_is_bounded" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.lemma_le_to_n_is_bounded" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.uints_to_bytes_le_nat_lemma_" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Bignum.Convert.fst", "name": "Hacl.Spec.Bignum.Convert.nat_from_bytes_be_eq_lemma" }, { "project_name": "zeta", "file_name": "Zeta.Steel.KeyUtils.fst", "name": "Zeta.Steel.KeyUtils.append_zeros_left" }, { "project_name": "FStar", "file_name": "FStar.UInt.fst", "name": "FStar.UInt.lemma_one_extend" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_mod_n_8_lower2" }, { "project_name": "FStar", "file_name": "FStar.List.Pure.Properties.fst", "name": "FStar.List.Pure.Properties.lemma_splitAt_append" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.Lemmas.fst", "name": "Hacl.Impl.Poly1305.Lemmas.uints64_to_bytes_le_lemma" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Vec.fst", "name": "Hacl.Spec.Poly1305.Vec.lemma_pow2_128" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.uints_to_bytes_le_nat_lemma" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_div_n_8_upper2" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Load56.fst", "name": "Hacl.Impl.Load56.lemma_nat_from_bytes_le_append" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Store56.fst", "name": "Hacl.Impl.Store56.lemma_nat_from_bytes_le_append" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.lemma_div_sub_small" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Endianness.fst", "name": "LowParse.SLow.Endianness.n_to_be_S" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.index_nat_to_intseq_le" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_div_n_8_upper2_helper" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_div_n_8_upper1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_mod_n_8_lower1" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Equiv.fsti", "name": "Vale.Poly1305.Equiv.nat_to_bytes_le" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Endianness.fst", "name": "LowParse.SLow.Endianness.mk_n_to_le" }, { "project_name": "FStar", "file_name": "Protocol.fst", "name": "Protocol.append_subseq" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitVector.fst", "name": "LowParse.Spec.BitVector.to_uint8_of_uint8" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_64_32_hi1" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fst", "name": "FStar.UInt128.shift_add" }, { "project_name": "hacl-star", "file_name": "Spec.Curve25519.Lemmas.fst", "name": "Spec.Curve25519.Lemmas.lemma_pow2_256" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Bits.fst", "name": "Vale.Math.Poly2.Bits.lemma_to_nat_rec" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.uints_to_bytes_be_nat_lemma_" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_append_count'" }, { "project_name": "FStar", "file_name": "SfLists.fst", "name": "SfLists.length_snoc" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fst", "name": "FStar.UInt128.mod_then_mul_64" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_ishl_nth" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.index_nat_to_intseq_to_bytes_le" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Endianness.fst", "name": "LowParse.SLow.Endianness.le_to_n_S" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.Types.fst", "name": "Vale.Arch.Types.slice_commutes_le_seq_quad32_to_bytes" }, { "project_name": "FStar", "file_name": "FStar.List.Pure.Properties.fst", "name": "FStar.List.Pure.Properties.lemma_split3_append" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.Types.fst", "name": "Vale.Arch.Types.lemma_reverse_bytes_nat64_32" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Two.fst", "name": "Vale.Def.Words.Two.two_to_nat_to_two" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_iand_nth_all" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.SHA_helpers.fst", "name": "Vale.SHA.SHA_helpers.lemma_add_wrap_is_add_mod" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.SHA_helpers.fst", "name": "Vale.SHA.PPC64LE.SHA_helpers.lemma_add_wrap_is_add_mod" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_64_32_hi2" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_64_32_hi2" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BoundedInt.fsti", "name": "LowParse.Spec.BoundedInt.log256'" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_inot_nth_all" }, { "project_name": "FStar", "file_name": "FStar.UInt.fst", "name": "FStar.UInt.lemma_msb_pow2" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fsti", "name": "Lib.ByteSequence.nat_to_bytes_be" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Field32xN.Lemmas.fst", "name": "Hacl.Spec.Poly1305.Field32xN.Lemmas.load_felem5_4_lemma" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.Scalar.Lemmas.fst", "name": "Hacl.Spec.K256.Scalar.Lemmas.mul_pow2_256_minus_q_lemma" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.index_nat_to_intseq_be" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_64_32_hi1" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Base.fst", "name": "FStar.Sequence.Base.append_then_take_or_drop_helper" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.uints_to_bytes_be_nat_lemma" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.nat_from_intseq_slice_lemma_aux" }, { "project_name": "hacl-star", "file_name": "Spec.Curve25519.Lemmas.fst", "name": "Spec.Curve25519.Lemmas.lemma_prime_value" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.Lemmas.fst", "name": "Vale.Bignum.Lemmas.lemma_seq_add_rec" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_mod_n_8_upper2" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas2.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas2.lemma_store_felem_lo" }, { "project_name": "steel", "file_name": "CBOR.Spec.Map.fst", "name": "CBOR.Spec.Map.list_splitAt_append" } ], "selected_premises": [ "LowParse.Endianness.index_n_to_le", "FStar.Mul.op_Star", "LowParse.Endianness.index_n_to_be", "LowParse.Endianness.index_n_to_be_zero_right", "LowParse.Endianness.reveal_n_to_be", "LowParse.Endianness.index_n_to_be_zero_left", "LowParse.Endianness.index_be_to_n'", "LowParse.Endianness.n_to_be_append", "LowParse.Endianness.slice_n_to_be", "LowParse.Endianness.index_be_to_n", "LowParse.Endianness.slice_seq_rev", "LowParse.Endianness.n_to_le_eq_rev_n_to_be", "LowParse.Endianness.index_le_to_n", "FStar.Math.Lemmas.pow2_plus", "LowParse.Endianness.be_to_n_append", "FStar.Math.Lemmas.pow2_lt_compat", "LowParse.Endianness.index_seq_rev'", "FStar.Math.Lemmas.pow2_le_compat", "FStar.Pervasives.reveal_opaque", "LowParse.Endianness.seq_rev_involutive", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "FStar.Math.Lemmas.lemma_div_lt", "LowParse.Endianness.le_to_n_eq_be_to_n_rev", "FStar.Math.Lemmas.cancel_mul_mod", "LowParse.Endianness.be_to_n_append'", "FStar.Math.Lemmas.lemma_mod_plus_distr_l", "FStar.Math.Lemmas.lemma_mod_plus_distr_r", "LowParse.Endianness.seq_rev", "FStar.Math.Lemmas.lemma_mod_mul_distr_l", "FStar.Math.Lemmas.lemma_div_lt_nat", "FStar.Math.Lemmas.distributivity_sub_left", "FStar.Math.Lemmas.distributivity_add_right", "LowParse.Endianness.index_seq_rev", "FStar.Math.Lemmas.lemma_mod_plus", "FStar.Math.Lemmas.lemma_mult_lt_sqr", "FStar.Math.Lemmas.distributivity_sub_right", "FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1", "FStar.Math.Lemmas.lemma_mod_sub", "FStar.Math.Lemmas.lemma_div_le", "FStar.Math.Lemmas.division_multiplication_lemma", "FStar.Math.Lemmas.pow2_modulo_modulo_lemma_2", "FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1", "FStar.Math.Lemmas.lemma_mod_spec2", "FStar.Math.Lemmas.modulo_distributivity", "FStar.Math.Lemmas.lemma_div_plus", "LowParse.Endianness.seq_rev_append", "FStar.Math.Lemmas.multiple_modulo_lemma", "FStar.Math.Lemmas.modulo_addition_lemma", "FStar.Math.Lemmas.pow2_modulo_division_lemma_1", "FStar.Math.Lemmas.lemma_mod_twice", "FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2", "FStar.Math.Lemmas.pow2_minus", "FStar.Math.Lemmas.pow2_modulo_division_lemma_2", "FStar.Math.Lemmas.division_addition_lemma", "FStar.Math.Lemmas.div_exact_r", "FStar.Math.Lemmas.lemma_mul_sub_distr", "FStar.Math.Lemmas.pow2_double_mult", "FStar.Math.Lemmas.lemma_mod_mod", "FStar.Math.Lemmas.multiple_division_lemma", "FStar.Math.Lemmas.pow2_multiplication_division_lemma_1", "FStar.Math.Lemmas.sub_div_mod_1", "FStar.Math.Lemmas.lemma_mod_sub_distr", "FStar.Math.Lemmas.lemma_mod_add_distr", "FStar.Pervasives.Native.snd", "FStar.Math.Lemmas.lemma_mod_plus_mul_distr", "FStar.Math.Lemmas.mod_mul_div_exact", "FStar.Math.Lemmas.mul_ineq1", "FStar.Pervasives.Native.fst", "FStar.Math.Lemmas.lemma_mod_mult_zero", "FStar.Math.Lemmas.mod_pow2_div2", "FStar.Math.Lemmas.modulo_modulo_lemma", "FStar.Math.Lemmas.modulo_sub_lemma", "FStar.Math.Lemmas.pow2_multiplication_division_lemma_2", "FStar.Math.Lib.powx_lemma2", "FStar.Math.Lemmas.mod_mult_exact", "FStar.Math.Lemmas.lemma_mod_plus_injective", "FStar.Math.Lib.log_2", "FStar.Math.Lib.slash_decr_axiom", "FStar.Math.Lemmas.add_div_mod_1", "FStar.Math.Lemmas.modulo_scale_lemma", "FStar.Math.Lemmas.lemma_mod_sub_1", "FStar.Math.Lemmas.lemma_div_mod_plus", "FStar.Math.Lemmas.lemma_div_lt_cancel", "FStar.Math.Lib.slash_star_axiom", "FStar.Math.Lemmas.lemma_mod_spec", "Prims.pure_pre", "FStar.Math.Lemmas.small_division_lemma_2", "FStar.Math.Lib.powx", "FStar.Math.Lemmas.division_definition", "FStar.Pervasives.st_return", "FStar.Pervasives.all_return", "FStar.Pervasives.ex_wp", "Prims.pow2", "FStar.Calc.calc_chain_compatible", "FStar.Pervasives.ex_return", "FStar.Math.Lemmas.modulo_add", "FStar.Pervasives.pure_return", "FStar.Pervasives.all_trivial", "FStar.Pervasives.all_wp_h", "FStar.Pervasives.all_ite_wp" ], "source_upto_this": "module LowParse.Endianness\n\nlet rec index_be_to_n'\n (b: bytes)\n (i: nat)\n: Lemma\n (requires (\n i < S.length b\n ))\n (ensures (\n U8.v (S.index b i) == (be_to_n b / pow2 (8 * (S.length b - 1 - i))) % pow2 8\n ))\n (decreases (S.length b))\n= reveal_be_to_n b;\n if i = S.length b - 1\n then ()\n else begin\n let l = S.length b in\n let l' = l - 1 in\n let b' = S.slice b 0 l' in\n index_be_to_n' b' i;\n assert (S.index b i == S.index b' i);\n let open FStar.Math.Lemmas in\n let x = be_to_n b in\n let x' = be_to_n b' in\n assert (U8.v (S.index b i) == x' / pow2 (8 * (l' - 1 - i)) % pow2 8);\n let y = (U8.v (S.last b) + pow2 8 * x') / pow2 (8 * (l - 1 - i)) % pow2 8 in\n pow2_plus 8 (8 * (l' - 1 - i));\n division_multiplication_lemma (U8.v (S.last b) + pow2 8 * x') (pow2 8) (pow2 (8 * (l' - 1 - i)));\n assert (pow2 8 * x' == x' * pow2 8);\n division_addition_lemma (U8.v (S.last b)) (pow2 8) x';\n small_division_lemma_1 (U8.v (S.last b)) (pow2 8);\n assert (y == x' / pow2 (8 * (l' - 1 - i)) % pow2 8)\n end\n\nlet index_be_to_n = index_be_to_n'\n\nlet index_n_to_be\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i)) == (n / pow2 (8 * (len - 1 - i)) % pow2 8\n ))\n= index_be_to_n (n_to_be len n) i\n\nlet index_n_to_be_zero_left\n (len: nat)\n (n: nat)\n (j: nat)\n (i: nat)\n: Lemma\n (requires (\n i < j /\\\n j <= len /\\\n n < pow2 (8 * (len - j))\n ))\n (ensures (\n pow2 (8 * (len - j)) <= pow2 (8 * len) /\\\n U8.v (S.index (n_to_be len n) i) == 0\n ))\n= let open FStar.Math.Lemmas in\n pow2_le_compat (8 * len) (8 * (len - j));\n pow2_le_compat (8 * (len - 1 - i)) (8 * (len - j));\n small_division_lemma_1 n (pow2 (8 * (len - 1 - i)));\n index_n_to_be len n i\n\nlet index_n_to_be_zero_right\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len) /\\\n n % pow2 (8 * (len - i)) == 0\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i) == 0\n ))\n= index_n_to_be len n i;\n let open FStar.Math.Lemmas in\n modulo_division_lemma n (pow2 (8 * (len - 1 - i))) (pow2 8);\n pow2_plus (8 * (len - 1 - i)) 8\n\nopen FStar.Math.Lemmas\n\nlet rec be_to_n_append'\n (hi lo: bytes)\n: Lemma\n (ensures (be_to_n (hi `S.append` lo) == be_to_n hi * pow2 (8 * S.length lo) + be_to_n lo))\n (decreases (S.length lo))\n= reveal_be_to_n lo;\n let hilo = hi `S.append` lo in\n if S.length lo = 0\n then\n assert (hilo `S.equal` hi)\n else begin\n let lo' = S.slice lo 0 (S.length lo - 1) in\n assert (S.slice hilo 0 (S.length hilo - 1) `S.equal` (hi `S.append` lo'));\n assert (S.last hilo == S.last lo);\n reveal_be_to_n hilo;\n be_to_n_append' hi lo';\n pow2_plus (8 * S.length lo') 8\n end\n\nlet be_to_n_append = be_to_n_append'\n\nlet lemma_div_zero (x: pos) : Lemma\n (0 / x == 0)\n= ()\n\nlet n_to_be_append\n (len: nat)\n (n: nat)\n (len_lo: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len) /\\\n len_lo <= len\n ))\n (ensures (\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n 0 <= hi /\\\n hi < pow2 (8 * (len - len_lo)) /\\\n 0 <= lo /\\\n lo < pow2 (8 * len_lo) /\\\n n_to_be len n == n_to_be (len - len_lo) hi `S.append` n_to_be len_lo lo\n ))\n= lemma_div_zero (pow2 (8 * len_lo));\n lemma_div_le 0 n (pow2 (8 * len_lo));\n lemma_mod_lt n (pow2 (8 * len_lo));\n let hi = n / pow2 (8 * len_lo) in\n assert (0 <= hi);\n lemma_div_lt n (8 * len) (8 * len_lo);\n pow2_minus (8 * len) (8 * len_lo);\n let lo = n % pow2 (8 * len_lo) in\n euclidean_division_definition n (pow2 (8 * len_lo));\n let hi_s = n_to_be (len - len_lo) hi in\n let lo_s = n_to_be len_lo lo in\n be_to_n_append hi_s lo_s;\n assert (be_to_n (hi_s `S.append` lo_s) == n);\n be_to_n_inj (hi_s `S.append` lo_s) (n_to_be len n)\n\nlet reveal_n_to_be\n (len: nat)\n (n: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len)\n ))\n (ensures (\n (len > 0 ==> (0 <= n / pow2 8 /\\ n / pow2 8 < pow2 (8 * (len - 1)))) /\\\n n_to_be len n `S.equal` (if len = 0 then S.empty else n_to_be (len - 1) (n / pow2 8) `S.snoc` (U8.uint_to_t (n % pow2 8)))\n ))\n= if len = 0\n then ()\n else begin\n n_to_be_append len n 1;\n index_n_to_be 1 (n % pow2 8) 0\n end\n\nlet slice_n_to_be\n (len: nat)\n (n: nat)\n (i j: nat)\n: Lemma\n (requires (\n i <= j /\\\n j <= len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n let res = (n / pow2 (8 * (len - j))) % pow2 (8 * (j - i)) in\n 0 <= res /\\\n res < pow2 (8 * (j - i)) /\\\n S.slice (n_to_be len n) i j == n_to_be (j - i) res\n ))\n= let s1 = S.slice (n_to_be len n) 0 j in\n let s2 = S.slice s1 i j in\n n_to_be_append len n (len - j);\n let q = n / pow2 (8 * (len - j)) in\n n_to_be_append j q (j - i);\n let r = q % pow2 (8 * (j - i)) in\n assert (s2 `S.equal` n_to_be (j - i) (q % pow2 (8 * (j - i))))\n\nlet rec seq_rev\n (#t: Type)\n (x: S.seq t)\n: Tot (y: S.seq t {S.length y == S.length x})\n (decreases (S.length x))\n= if S.length x = 0\n then S.empty\n else seq_rev (S.tail x) `S.append` S.create 1 (S.head x)\n\nlet rec index_seq_rev'\n (#t: Type)\n (x: S.seq t)\n (i: nat {i < S.length x})\n: Lemma\n (ensures (S.index (seq_rev x) (S.length x - 1 - i) == S.index x i))\n (decreases (S.length x))\n= if i = 0\n then\n S.lemma_index_create 1 (S.head x) 0\n else\n index_seq_rev' (S.tail x) (i - 1)\n\nlet index_seq_rev\n (#t: Type)\n (x: S.seq t)\n (i: nat {i < S.length x})\n: Lemma\n (ensures (S.index (seq_rev x) i == S.index x (S.length x - 1 - i)))\n= index_seq_rev' x (S.length x - 1 - i)\n\nlet slice_seq_rev\n (#t: Type)\n (x: S.seq t)\n (i: nat)\n (j: nat)\n: Lemma\n (requires (i <= j /\\ j <= S.length x))\n (ensures (S.slice (seq_rev x) i j `S.equal` seq_rev (S.slice x (S.length x - j) (S.length x - i))))\n= Classical.forall_intro (index_seq_rev x);\n Classical.forall_intro (index_seq_rev (S.slice x (S.length x - j) (S.length x - i)))\n\nlet rec le_to_n_eq_be_to_n_rev\n (b: bytes)\n: Lemma\n (ensures (le_to_n b == be_to_n (seq_rev b)))\n (decreases (S.length b))\n= reveal_be_to_n (seq_rev b);\n reveal_le_to_n b;\n if Seq.length b = 0\n then ()\n else begin\n index_seq_rev b (S.length b - 1);\n slice_seq_rev b 0 (S.length b - 1);\n le_to_n_eq_be_to_n_rev (S.tail b)\n end\n\nlet seq_rev_involutive\n (#t: Type)\n (x: S.seq t)\n: Lemma\n (seq_rev (seq_rev x) `S.equal` x)\n= Classical.forall_intro (index_seq_rev (seq_rev x));\n Classical.forall_intro (index_seq_rev x)\n\nlet n_to_le_eq_rev_n_to_be\n (len: nat)\n (n: nat)\n: Lemma\n (requires (n < pow2 (8 * len)))\n (ensures (n_to_le len n == seq_rev (n_to_be len n)))\n= le_to_n_eq_be_to_n_rev (n_to_le len n);\n be_to_n_inj (seq_rev (n_to_le len n)) (n_to_be len n);\n seq_rev_involutive (n_to_le len n)\n\nlet index_le_to_n\n b i\n= le_to_n_eq_be_to_n_rev b;\n index_be_to_n (seq_rev b) (S.length b - 1 - i);\n index_seq_rev b (S.length b - 1 - i)\n\nlet index_n_to_le\n len n i\n= n_to_le_eq_rev_n_to_be len n;\n index_seq_rev (n_to_be len n) i;\n index_n_to_be len n (len - 1 - i)\n\nlet seq_rev_append\n (#t: Type)\n (b1 b2: S.seq t)\n: Lemma\n (seq_rev (b1 `S.append` b2) `S.equal` (seq_rev b2 `S.append` seq_rev b1))\n= Classical.forall_intro (index_seq_rev (b1 `S.append` b2));\n Classical.forall_intro (index_seq_rev b1);\n Classical.forall_intro (index_seq_rev b2)\n", "sketch": [ "Step 1: Use `n_to_le_eq_rev_n_to_be` to convert the problem into the big-endian representation.\nStep 2: Apply `n_to_be_append` to decompose `n` into `hi` and `lo` parts.\nStep 3: Use `seq_rev_append` to handle the reversal of the concatenated sequences.\nStep 4: Apply `n_to_le_eq_rev_n_to_be` again to convert the parts back to little-endian representation.\nStep 5: Conclude the proof by showing the equality of the sequences.", "Step 1: Use the lemma `n_to_be_append` to decompose `n` into `hi` and `lo` parts.\nStep 2: Apply the lemma `n_to_le_eq_rev_n_to_be` to convert `n_to_le` to `seq_rev` of `n_to_be`.\nStep 3: Use the `seq_rev_append` lemma to handle the concatenation of the reversed sequences.\nStep 4: Apply `n_to_le_eq_rev_n_to_be` again to convert back from `seq_rev` to `n_to_le`.\nStep 5: Conclude the proof by showing the equality of the resulting sequences.", "Step 1: Use the `n_to_le_eq_rev_n_to_be` lemma to convert the problem from little-endian to big-endian representation.\nStep 2: Apply the `n_to_be_append` lemma to the big-endian representation to split `n` into `hi` and `lo` parts.\nStep 3: Use the `seq_rev_append` lemma to reverse the concatenation of the sequences.\nStep 4: Apply the `n_to_le_eq_rev_n_to_be` lemma again to convert the reversed sequences back to little-endian representation.\nStep 5: Conclude the proof by showing that the concatenation of the little-endian representations of `lo` and `hi` is equal to the little-endian representation of `n`.", "Step 1: Use the `n_to_le_eq_rev_n_to_be` lemma to convert the `n_to_le` representation to the reversed `n_to_be` representation.\nStep 2: Apply the `n_to_be_append` lemma to break down `n` into `hi` and `lo` parts and their corresponding `n_to_be` representations.\nStep 3: Use the `seq_rev_append` lemma to reverse the concatenation of `n_to_be` representations of `hi` and `lo`.\nStep 4: Apply the `seq_rev_involutive` lemma to ensure that reversing twice yields the original sequence.\nStep 5: Conclude that the `n_to_le` representation of `n` is the concatenation of the `n_to_le` representations of `lo` and `hi`.", "Step 1: We start by using the `n_to_le_eq_rev_n_to_be` lemma to convert the `n_to_le` function into its equivalent `seq_rev` and `n_to_be` form.\nStep 2: Apply the `n_to_be_append` lemma to split `n` into `hi` and `lo` parts and express `n_to_be len n` as the concatenation of `n_to_be len_lo lo` and `n_to_be (len - len_lo) hi`.\nStep 3: Use the `seq_rev_append` lemma to reverse the concatenation of `n_to_be len_lo lo` and `n_to_be (len - len_lo) hi`.\nStep 4: Apply the `seq_rev_involutive` lemma to show that reversing the reversed sequences yields the original sequences.\nStep 5: Conclude that `n_to_le len n` is equal to the concatenation of `n_to_le len_lo lo` and `n_to_le (len - len_lo) hi`.", "Step 1: Use the lemma `n_to_be_append` to decompose `n` into its high and low parts, `hi` and `lo`.\nStep 2: Apply the lemma `n_to_le_eq_rev_n_to_be` to convert the high and low parts from big-endian to little-endian.\nStep 3: Use the `seq_rev_append` lemma to show that the reverse of the concatenation of two sequences is the concatenation of their reverses.\nStep 4: Combine the results to show that `n_to_le len n` is equal to the concatenation of `n_to_le len_lo lo` and `n_to_le (len - len_lo) hi`.", "Step 1: Use the lemma `n_to_be_append` to decompose `n` into `hi` and `lo` parts.\nStep 2: Apply the lemma `n_to_le_eq_rev_n_to_be` to convert `n_to_le` to `seq_rev` of `n_to_be`.\nStep 3: Use the `seq_rev_append` lemma to handle the append operation in the reverse sequence.\nStep 4: Apply `n_to_le_eq_rev_n_to_be` again to convert back from `seq_rev` to `n_to_le`.\nStep 5: Conclude the proof by combining the results from the previous steps.", "Step 1: Use the lemma `n_to_be_append` to decompose `n` into `hi` and `lo` parts.\nStep 2: Apply `n_to_le_eq_rev_n_to_be` to convert `n_to_le` to `seq_rev` of `n_to_be`.\nStep 3: Use `seq_rev_append` to handle the `seq_rev` of the concatenation.\nStep 4: Apply `n_to_le_eq_rev_n_to_be` again to convert back from `seq_rev` of `n_to_be` to `n_to_le`.\nStep 5: Conclude the proof by showing the equality of the sequences.", "Step 1: Use the lemma `n_to_be_append` to decompose `n` into `hi` and `lo` parts.\nStep 2: Apply `n_to_le_eq_rev_n_to_be` to convert `n_to_le` to `seq_rev` of `n_to_be`.\nStep 3: Use `seq_rev_append` to handle the append operation in the reverse sequence.\nStep 4: Apply `n_to_le_eq_rev_n_to_be` again to convert back from `seq_rev` to `n_to_le`.\nStep 5: Conclude the proof by showing the equality of the resulting sequences.", "Step 1: We start by using the `n_to_le_eq_rev_n_to_be` lemma to convert the problem into the big-endian representation.\nStep 2: Apply the `n_to_be_append` lemma to break down the big-endian representation into two parts: high and low.\nStep 3: Use the `seq_rev_append` lemma to reverse the concatenation of the two parts.\nStep 4: Apply the `n_to_le_eq_rev_n_to_be` lemma again to convert the reversed big-endian parts back to little-endian.\nStep 5: Conclude the proof by showing that the concatenation of the little-endian parts equals the original little-endian representation." ], "generated_solution": [ "= n_to_le_eq_rev_n_to_be len n;\n n_to_be_append len n len_lo;\n seq_rev_append (n_to_be len_lo (n % pow2 (8 * len_lo))) (n_to_be (len - len_lo) (n / pow2 (8 * len_lo)));\n n_to_le_eq_rev_n_to_be len_lo (n % pow2 (8 * len_lo));\n n_to_le_eq_rev_n_to_be (len - len_lo) (n / pow2 (8 * len_lo))", "= n_to_be_append len n len_lo;\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n n_to_le_eq_rev_n_to_be len_lo lo;\n n_to_le_eq_rev_n_to_be (len - len_lo) hi;\n seq_rev_append (n_to_be len_lo lo) (n_to_be (len - len_lo) hi);\n assert (seq_rev (n_to_be len n) == seq_rev (n_to_be (len - len_lo) hi `S.append` n_to_be len_lo lo));\n assert (seq_rev (n_to_be (len - len_lo) hi `S.append` n_to_be len_lo lo) == seq_rev (n_to_be len_lo lo) `S.append` seq_rev (n_to_be (len - len_lo) hi));\n n_to_le_eq_rev_n_to_be len n;\n assert (n_to_le len n == seq_rev (n_to_be len n));\n assert (seq_rev (n_to_be len n) == (n_to_le len_lo lo) `S.append` (n_to_le (len - len_lo) hi))", "= n_to_le_eq_rev_n_to_be len n;\n n_to_be_append len n len_lo;\n seq_rev_append (n_to_be len_lo (n % pow2 (8 * len_lo))) (n_to_be (len - len_lo) (n / pow2 (8 * len_lo)));\n n_to_le_eq_rev_n_to_be len_lo (n % pow2 (8 * len_lo));\n n_to_le_eq_rev_n_to_be (len - len_lo) (n / pow2 (8 * len_lo))", "= n_to_le_eq_rev_n_to_be len n;\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n n_to_be_append len n len_lo;\n seq_rev_append (n_to_be len_lo lo) (n_to_be (len - len_lo) hi);\n seq_rev_involutive (n_to_be len n)", "= n_to_le_eq_rev_n_to_be len n;\n n_to_be_append len n len_lo;\n seq_rev_append (n_to_be len_lo lo) (n_to_be (len - len_lo) hi);\n seq_rev_involutive (n_to_be len_lo lo);\n seq_rev_involutive (n_to_be (len - len_lo) hi)", "= n_to_be_append len n len_lo;\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n n_to_le_eq_rev_n_to_be len_lo lo;\n n_to_le_eq_rev_n_to_be (len - len_lo) hi;\n seq_rev_append (n_to_be len_lo lo) (n_to_be (len - len_lo) hi);\n seq_rev_involutive (n_to_be len n)", "= n_to_be_append len n len_lo;\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n n_to_le_eq_rev_n_to_be len_lo lo;\n n_to_le_eq_rev_n_to_be (len - len_lo) hi;\n seq_rev_append (n_to_be len_lo lo) (n_to_be (len - len_lo) hi);\n seq_rev_involutive (n_to_be len n)", "= n_to_be_append len n len_lo;\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n n_to_le_eq_rev_n_to_be len_lo lo;\n n_to_le_eq_rev_n_to_be (len - len_lo) hi;\n seq_rev_append (n_to_be len_lo lo) (n_to_be (len - len_lo) hi);\n assert (n_to_le len n == seq_rev (n_to_be (len - len_lo) hi `S.append` n_to_be len_lo lo));\n seq_rev_involutive (n_to_be (len - len_lo) hi `S.append` n_to_be len_lo lo)", "= n_to_be_append len n len_lo;\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n n_to_le_eq_rev_n_to_be len n;\n n_to_le_eq_rev_n_to_be len_lo lo;\n n_to_le_eq_rev_n_to_be (len - len_lo) hi;\n seq_rev_append (n_to_be len_lo lo) (n_to_be (len - len_lo) hi)", "= n_to_le_eq_rev_n_to_be len n;\n n_to_be_append len n len_lo;\n seq_rev_append (n_to_be len_lo (n % pow2 (8 * len_lo))) (n_to_be (len - len_lo) (n / pow2 (8 * len_lo)));\n n_to_le_eq_rev_n_to_be len_lo (n % pow2 (8 * len_lo));\n n_to_le_eq_rev_n_to_be (len - len_lo) (n / pow2 (8 * len_lo))" ] }, { "file_name": "PropositionalExtensionalityInconsistent.fst", "name": "PropositionalExtensionalityInconsistent.predicate", "opens_and_abbrevs": [ { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let predicate (a:Type0) = a -> Tot Type0", "source_range": { "start_line": 53, "start_col": 0, "end_line": 53, "end_col": 40 }, "interleaved": false, "definition": "fun a -> _: a -> Type0", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "a: Type0 -> Type", "prompt": "let predicate (a: Type0) =\n ", "expected_response": "a -> Tot Type0", "source": { "project_name": "FStar", "file_name": "examples/paradoxes/PropositionalExtensionalityInconsistent.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "PropositionalExtensionalityInconsistent.fst", "checked_file": "dataset/PropositionalExtensionalityInconsistent.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "let propExt_Type = forall (p1 p2:Type0). (p1 <==> p2) <==> p1==p2", "let propExt_Type_inconsistent ()\n : Lemma (requires propExt_Type)\n (ensures False)\n = let int_is_inhabited (x:int) : Lemma (int <==> unit) = () in\n int_is_inhabited 42", "let sub_singleton = a:Type{forall (x y:a). x == y}", "let propExt_sub_singleton = forall (p1 p2:sub_singleton). (p1 <==> p2) <==> p1==p2", "let propExt_sub_singleton_inconsistent()\n : Lemma (requires propExt_sub_singleton)\n (ensures False)\n = ()" ], "closest": [ "val FStar.PredicateExtensionality.predicate = a: Type -> Type\nlet predicate (a:Type) = a -> Tot prop", "val FStar.ReflexiveTransitiveClosure.predicate = a: Type -> Type\nlet predicate (a:Type u#a) = a -> Type0", "val t (a:Type0) : Type0\nlet t a = list a", "val immutable_preorder (a: Type0) : srel a\nlet immutable_preorder (a:Type0) :srel a = fun s1 s2 -> Seq.equal s1 s2", "val predicateExtensionality (a: Type) (p1 p2: predicate a)\n : Lemma (requires (peq #a p1 p2)) (ensures (F.on_domain a p1 == F.on_domain a p2))\nlet predicateExtensionality (a:Type) (p1 p2:predicate a)\n : Lemma (requires (peq #a p1 p2))\n \t (ensures (F.on_domain a p1==F.on_domain a p2))\n = P.axiom();\n assert (F.feq p1 p2)", "val t : Type0\nlet t = bool & bool", "val t : Type0\nlet t = G.ref _ pcm", "val t : Type0\nlet t = t", "val ref (a:Type0) : Type0\nlet ref (a:Type) = nat", "val Interop.arity = Type0\nlet arity = n:nat { n <= max_arity }", "val ref (a: Type0) : Type0\nlet ref (a : Type0) : Type0 = (r: A.array a { A.length r == 1 \\/ r == A.null })", "val ref (a: Type0) : Type0\nlet ref (a:Type0) : Type0 = ref a", "val Selectors.Tree.Core.tree = a: Type0 -> Type0\nlet tree (a: Type0) = Spec.tree a", "val inversion (a: Type) : Type0\nlet inversion _ = True", "val trivial_preorder (a: Type0) : Preorder.preorder a\nlet trivial_preorder (a:Type0) :Preorder.preorder a = trivial_rel a", "val MRefHeap.preorder_t = a: Type0 -> Type\nlet preorder_t (a:Type0) = preorder a", "val Ast.subst = Type0\nlet subst = H.t ident' expr", "val coerce (#a b: Type0) (x: a{a == b}) : b\nlet coerce (#a:Type0) (b:Type0) (x:a{a == b}) : b = x", "val Selectors.Tree.Core.t = a: Type0 -> Type0\nlet t (a: Type0) = ref (node a)", "val null (#a:Type0) : ref a\nlet null #a = H.null #(U.raise_t a)", "val null (#a:Type0) : ref a\nlet null #a = A.null #a", "val stable (p:mem_predicate) :Type0\nlet stable p = forall (h1:mem) (h2:mem).{:pattern (mem_rel h1 h2)} (p h1 /\\ mem_rel h1 h2) ==> p h2", "val null_t (#a: Type0) : t a\nlet null_t #a = null", "val FStar.Tactics.PatternMatching.hyp = a: Type -> Type0\nlet hyp (a: Type) = binding", "val id (#a: Type0) (x: a) : a\nlet id (#a:Type0) (x:a) : a = x", "val LList.Invariant.t = a: Type0 -> Type0\nlet t (a:Type0) = ref (cell a)", "val inv (p: vprop) : Type0\nlet inv (p:vprop) : Type0 = Mem.inv (hp_of p)", "val DependentBoolRefinement.binding = Type0\nlet binding = either src_ty src_eqn", "val FStar.Tactics.Effect.tactic = a: Type -> Type0\nlet tactic a = tac unit a", "val ref ([@@@ unused] a:Type0)\n : Type0\nlet ref (a:Type0)\n : Type0\n = R.ref a", "val ref ([@@@unused] a:Type0) : Type0\nlet ref a = H.ref (U.raise_t a)", "val stt (a:Type u#a) \r\n (pre:slprop)\r\n (post:a -> slprop)\r\n: Type0\nlet stt (a:Type u#a) \r\n (pre:slprop)\r\n (post:a -> slprop)\r\n: Type0\r\n= lower (Sem.m u#2 u#100 u#a #state a pre (F.on_dom a post))", "val bad2 (a: Type) : Lemma (requires (~(p0 (x0 #a)))) (ensures (p0 (x0 #a)))\nlet bad2 (a:Type) \n : Lemma (requires (~(p0 (x0 #a)))) \n (ensures (p0 (x0 #a))) =\n exists_intro (fun (p:either (out_wp a) a -> prop) ->\n f p == x0 #a /\\ ~(p (x0 #a))) p0", "val trivial_preorder (a: Type0) : srel a\nlet trivial_preorder (a:Type0) :srel a = fun _ _ -> True", "val t (a: Type0) : Tot Type0\nlet t a = cllist_lvalue a", "val Selectors.LList.t = a: Type0 -> Type0\nlet t (a:Type0) = ref (cell a)", "val trivial_rel (a: Type0) : Preorder.relation a\nlet trivial_rel (a:Type0) :Preorder.relation a = fun x y -> True", "val allP (#a #b: _) (top: b) (pred: (x: a{x << top} -> Type0)) (l: list a {l << top \\/ l === top})\n : Type0\nlet rec allP #a #b (top:b) (pred : (x:a{x << top}) -> Type0) (l : list a{l << top \\/ l === top}) : Type0 =\n match l with\n | [] -> True\n | x::xs -> pred x /\\ allP top pred xs", "val FStar.InteractiveHelpers.PostProcess.pred_explorer = a: Type -> Type0\nlet pred_explorer (a:Type) = \n genv -> list (genv & term_view) -> option typ_or_comp -> term_view ->\n Tac (option a)", "val FStar.InteractiveHelpers.ParseTest.test5 = a: Type0 -> Type0\nlet test5 a =\n f1 #(list a)", "val forall_pred:\n #a: Type0 ->\n n: US.t ->\n arr: A.array a ->\n p: (a -> bool) ->\n r: R.ref US.t ->\n perm: perm ->\n s: Seq.seq a ->\n squash (Seq.length s == US.v n) ->\n b: bool ->\n US.t\n -> vprop\nlet forall_pred\n (#a:Type0)\n (n:US.t)\n (arr:A.array a)\n (p:a -> bool)\n (r:R.ref US.t)\n (perm:perm)\n (s:Seq.seq a)\n (_:squash (Seq.length s == US.v n))\n (b:bool)\n : US.t -> vprop\n = fun i ->\n A.pts_to arr perm s\n `star`\n R.pts_to r full_perm i\n `star`\n pure (forall_pure_inv n p s () i)\n `star`\n pure (forall_pure_inv_b n p s () i b)", "val stt (a:Type u#a) (pre:vprop) (post:a -> vprop) : Type0\nlet stt = I.stt", "val node (a:Type0) : Type0\nlet node a = B.pointer (DLL.node a)", "val Lib.Sequence.seq = a: Type0 -> Type0\nlet seq (a:Type0) = Seq.seq a", "val Prims.pure_wp_monotonic0 = a: Type -> wp: Prims.pure_wp' a -> Prims.logical\nlet pure_wp_monotonic0 (a:Type) (wp:pure_wp' a) =\n forall (p q:pure_post a). (forall (x:a). p x ==> q x) ==> (wp p ==> wp q)", "val return (a: Type) (x: a) : repr a (fun _ -> True) (fun h0 r h1 -> r == x /\\ h0 == h1)\nlet return (a:Type) (x:a)\n: repr a (fun _ -> True) (fun h0 r h1 -> r == x /\\ h0 == h1)\n= fun _ -> x", "val FStar.HyperStack.ref = a: Type0 -> Type0\nlet ref (a:Type) = mref a (Heap.trivial_preorder a)", "val null (#a:Type0) \n : ref a\nlet null (#a:Type0)\n : ref a\n = R.null #a", "val handler (#a: Type0) (post: a -> vprop): Type0\nlet handler (#a: Type0) (post: a -> vprop)\n = pure_handler #(resourceful_res post) (fun (_: resourceful_res post) -> true)", "val bad1 (a: Type) : Lemma (requires (p0 (x0 #a))) (ensures (~(p0 (x0 #a))))\nlet bad1 (a:Type) \n : Lemma (requires (p0 (x0 #a))) \n (ensures (~(p0 (x0 #a)))) =\n let aux (p:(either (out_wp a) a -> prop){f p == (x0 #a) /\\ ~(p (x0 #a))}) \n : GTot (squash (~(p0 (x0 #a)))) =\n f_injective p p0\n in \n exists_elim (~(p0 (x0 #a))) (FStar.Squash.get_proof (p0 (x0 #a))) aux", "val decl:Type0\nlet decl : Type0 = either not_type_decl type_decl", "val null (#a: Type0) : array a\nlet null (#a: Type0) : array a\n= (| null_ptr a, Ghost.hide 0 |)", "val s: Type0 -> Type0\nlet s _ = unit", "val s: Type0 -> Type0\nlet s _ = unit", "val OPLSS2021.DijkstraMonads.wp0 = st: Type0 -> a: Type -> Type\nlet wp0 (st:Type0) (a:Type) = st -> (a & st -> Type) -> Type", "val ref (a:Type) (p:pcm a) : Type0\nlet ref (a:Type) (p:pcm a) = erased (Steel.Memory.ref a p)", "val invariant: #a:Type -> h:HS.mem -> ll:t a -> Type0\nlet invariant #a h ll =\n let head = B.deref h ll.ptr in\n let v = B.deref h ll.v in\n // This is where we switch from a predicate (cumbersome for clients, requires\n // materializing the list at any time) to a ``v`` function which makes\n // specifications much easier. Any time the invariant holds, the pointer ``v``\n // holds a computationally-irrelevant representation of the list that in turns\n // allows us to under-the-hood state the various predicates from LL1 that\n // require exhibiting a list.\n B.live h ll.ptr /\\\n B.freeable ll.ptr /\\\n B.live h ll.v /\\\n B.freeable ll.v /\\\n LL1.well_formed h head v /\\\n LL1.invariant h head v /\\\n\n // We use regions for separation only, not for any footprint reasoning:\n // - ptr_v_rid is a sub-region of r and contains ptr and v, disjoint from each other\n // - spine_rid is a sub-region of r, disjoint from ptr_v_rid, and contains the LL1.footprint\n ST.is_eternal_region ll.r /\\\n ST.is_eternal_region ll.spine_rid /\\\n ST.is_eternal_region ll.ptr_v_rid /\\\n B.(loc_includes (loc_region_only true ll.ptr_v_rid) (loc_addr_of_buffer ll.ptr `loc_union` loc_addr_of_buffer ll.v)) /\\\n B.(loc_includes (loc_region_only true ll.spine_rid) (LL1.footprint h head v)) /\\\n B.(loc_disjoint (loc_addr_of_buffer ll.ptr) (loc_addr_of_buffer ll.v)) /\\\n B.(loc_disjoint (loc_region_only true ll.ptr_v_rid) (loc_region_only true ll.spine_rid)) /\\\n\n // These are not redundant, and are important for showing that the footprint\n // is contained in ``r`` at any time, so long as the invariant holds.\n HS.extends ll.ptr_v_rid ll.r /\\\n HS.extends ll.spine_rid ll.r /\\\n HS.parent ll.ptr_v_rid == ll.r /\\\n HS.parent ll.spine_rid == ll.r", "val z: Type0\nlet z = unit", "val z: Type0\nlet z = unit", "val FStar.Monotonic.HyperStack.mref = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_eternal_region_hs (frameOf s) && not (is_mm s) }", "val squash (p: Type u#a) : Type0\nlet squash (p:Type u#a) : Type0 = squash p", "val allP0 (#a: _) (pred: (a -> Type0)) (l: list a) : Type0\nlet rec allP0 #a (pred : a -> Type0) (l : list a) : Type0 =\n match l with\n | [] -> True\n | x::xs -> pred x /\\ allP0 pred xs", "val witnessed (p:mem_predicate) :Type0\nlet witnessed p = W.witnessed mem_rel p", "val Selectors.LList2.t = a: Type0 -> Type0\nlet t (a:Type0) = ref (cell a)", "val FStar.FunctionalExtensionality.efun = a: Type -> b: (_: a -> Type) -> Type\nlet efun (a: Type) (b: (a -> Type)) = arrow a b", "val return (a: Type) (x: a) : m a RO (fun _ -> True) (fun h0 y h1 -> y == x /\\ h1 == h0)\nlet return (a:Type) (x:a) : m a RO (fun _ -> True) (fun h0 y h1 -> y == x /\\ h1 == h0) =\n fun () -> x", "val FStar.Monotonic.HyperStack.mreference = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mreference a rel = mreference' a rel", "val length (#a:Type0) (x:t a) : GTot nat\nlet length x = L.length x", "val inv (p:vprop) : Type0\nlet inv (p:vprop) = r:ghost_ref bool & inv (ex_conditional_inv r p)", "val BugHigherOrderApplication.swap_fun = a: Type0 -> Type0\nlet swap_fun a = x:ref a -> y:ref a -> #vx:erased a -> #vy:erased a -> stt unit\n (requires pts_to x vx ** pts_to y vy)\n (ensures fun _ -> pts_to x vy ** pts_to y vx)", "val fst (#a #b: Type0) (p: a & b) : a\nlet fst (#a #b : Type0) (p : a & b) : a =\n match p with\n | Mktuple2 x y -> x <: a", "val empty (a:Type0) : llist a\nlet empty a = null", "val initialization_preorder (a: Type0) : srel (option a)\nlet initialization_preorder (a:Type0) :srel (option a) =\n fun s1 s2 -> Seq.length s1 == Seq.length s2 /\\\n (forall (i:nat).{:pattern (Seq.index s2 i)} i < Seq.length s1 ==> Some? (Seq.index s1 i) ==> Some? (Seq.index s2 i))", "val lemma_reduce_property_closure_ty\n (#a #b: Type)\n (p: (b -> Type0))\n (b0: b)\n (f: (a -> b -> b))\n (s: seq a)\n : Lemma (requires (p b0 /\\ (forall (x: a). forall (y: b). (p y ==> p (f x y)))))\n (ensures (p (reduce b0 f s)))\nlet lemma_reduce_property_closure_ty (#a:Type) (#b:Type) (p: b -> Type0) (b0:b) (f: a -> b -> b) (s: seq a):\n Lemma (requires (p b0 /\\ (forall (x:a). forall (y:b). (p y ==> p (f x y)))))\n (ensures (p (reduce b0 f s)))\n = lemma_reduce_property_closure_seq_mem p b0 f s", "val poly_equal (a b: poly) : prop0\nlet poly_equal (a b:poly) : prop0 =\n (forall (i:nat).{:pattern a.[i] \\/ b.[i]} a.[i] == b.[i])", "val constr (a b: prop) : Lemma (a ==> b ==> b /\\ a)\nlet constr (a b : prop) : Lemma (a ==> b ==> b /\\ a) =\n assert (a ==> b ==> b /\\ a)\n by (let ha = implies_intro () in\n let hb = implies_intro () in\n split ();\n hyp (binding_to_namedv hb);\n hyp (binding_to_namedv ha);\n qed ())", "val ins : Type0\nlet ins = S.ins", "val ins : Type0\nlet ins = BS.ins", "val env : Type0\nlet env = H.t A.ident' type_decl", "val pre_inv : Type0\nlet pre_inv = i:erased iname & witnessed_name_is_ok i", "val pre_inv : Type0\nlet pre_inv = i:erased iname & witnessed_name_is_ok i", "val token (#a:Type) (#b:preorder a) (r:mref a b) (p:(a -> Type){stable p b}) : Type0\nlet token #_ #_ r p = witnessed (p_pred r p)", "val Setoids.t_one = Type0\nlet t_one = lo int ^--> st_rel state_rel (lo int)", "val token_p (#a:Type0) (#rel:preorder a) (r:mreference a rel) (p:mem_predicate) :Type0\nlet token_p #_ #_ r p = witnessed (mem_rel_predicate r p)", "val FStar.FunctionalExtensionality.efun_g = a: Type -> b: (_: a -> Type) -> Type\nlet efun_g (a: Type) (b: (a -> Type)) = arrow_g a b", "val arg_type (a: arg) : Tot Type0\nlet arg_type (a:arg) : Tot Type0 =\n match a with\n | Bool -> bool\n | Int -> int\n | Char -> char\n | String -> string", "val arg_type (a: arg) : Tot Type0\nlet arg_type (a:arg) : Tot Type0 =\n match a with\n | Bool -> bool\n | Int -> int\n | Char -> char\n | String -> string\n | U8 -> FStar.UInt8.t\n | U16 -> FStar.UInt16.t\n | U32 -> FStar.UInt32.t\n | U64 -> FStar.UInt64.t\n | I8 -> FStar.Int8.t\n | I16 -> FStar.Int16.t\n | I32 -> FStar.Int32.t\n | I64 -> FStar.Int64.t\n | Extension (MkExtension #t _) -> t", "val arg_type (a: arg) : Tot Type0\nlet arg_type (a:arg) : Tot Type0 =\n match a with\n | Bool -> bool\n | Int -> int\n | Char -> char\n | String -> string", "val create (a: Type0) (x: a)\n : LV nat\n (fun m0 -> True)\n (fun m0 r m1 -> not (m0.m `M.contains` r) /\\ m1.m == Map.upd m0.m r (| a, x |))\nlet create (a:Type0) (x:a) : LV nat (fun m0 -> True)\n (fun m0 r m1 -> not (m0.m `M.contains` r) /\\ m1.m == Map.upd m0.m r (| a, x |))\n= LVARS?.reflect (fun m ->\n let next = m.next in\n next, {\n next = next + 1;\n m = Map.upd m.m next (| a, x |)\n })", "val Setoids.per = a: Type -> Type\nlet per (a:Type) = r:rel a{ is_per r }", "val MRefST.mref0 = a: Type0 -> r: MRefHeap.preorder_t a -> Type0\nlet mref0 = mref", "val FStar.FunctionalExtensionality.arrow = a: Type -> b: (_: a -> Type) -> Type\nlet arrow (a: Type) (b: (a -> Type)) = x: a -> Tot (b x)", "val Ast.prog = Type0\nlet prog = list decl & option type_refinement", "val closure_transitive: #a:Type u#a -> r:binrel u#a u#r a -> Lemma (transitive (_closure0 r))\nlet closure_transitive #a r =\n let open FStar.Squash in\n let aux (x y z:a)\n (s0:squash (_closure r x y))\n (s1:squash (_closure r y z))\n : GTot (squash (_closure r x z))\n = bind_squash s0 (fun p0 ->\n bind_squash s1 (fun p1 ->\n return_squash (Closure x y z p0 p1)))\n in\n let aux (x y z:a)\n : Lemma (requires (_closure0 r x y /\\ _closure0 r y z))\n (ensures _closure0 r x z)\n [SMTPat ()]\n = get_squash r x y; get_squash r y z; aux x y z () ()\n in\n ()", "val witnessed_constant (p: Type0) : Lemma (witnessed (fun _ -> p) <==> p)\nlet witnessed_constant (p:Type0)\n: Lemma (witnessed (fun _ -> p) <==> p)\n= W.lemma_witnessed_constant grows p", "val OPLSS.Log.t = a: Prims.eqtype -> Type0\nlet t (a:eqtype) = HST.mref (seq a) grows", "val normalize (a: Type0) : Type0\nlet normalize a = a", "val asynch (a:Type0) (post : a -> vprop) : Type0\nlet asynch (a:Type0) (post : a -> vprop) : Type0 =\n ref (option a) & thread", "val qAssertLemma (p:Type0) : tAssertLemma p\nlet qAssertLemma p = fun () -> ()", "val qAssertLemma (p:Type0) : tAssertLemma p\nlet qAssertLemma p = fun () -> ()" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.PredicateExtensionality.fst", "name": "FStar.PredicateExtensionality.predicate" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fsti", "name": "FStar.ReflexiveTransitiveClosure.predicate" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.t" }, { "project_name": "FStar", "file_name": "LowStar.ImmutableBuffer.fst", "name": "LowStar.ImmutableBuffer.immutable_preorder" }, { "project_name": "FStar", "file_name": "FStar.PredicateExtensionality.fst", "name": "FStar.PredicateExtensionality.predicateExtensionality" }, { "project_name": "dice-star", "file_name": "HWState.fst", "name": "HWState.t" }, { "project_name": "zeta", "file_name": "Zeta.Steel.ThreadLogMap.fst", "name": "Zeta.Steel.ThreadLogMap.t" }, { "project_name": "everparse", "file_name": "EverParse3d.InputStream.All.fst", "name": "EverParse3d.InputStream.All.t" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.ref" }, { "project_name": "FStar", "file_name": "Interop.fst", "name": "Interop.arity" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fsti", "name": "Steel.ArrayRef.ref" }, { "project_name": "steel", "file_name": "SelectorLogic.fst", "name": "SelectorLogic.ref" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fsti", "name": "Selectors.Tree.Core.tree" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fst", "name": "FStar.Pervasives.inversion" }, { "project_name": "FStar", "file_name": "FStar.Heap.fst", "name": "FStar.Heap.trivial_preorder" }, { "project_name": "FStar", "file_name": "MRefHeap.fsti", "name": "MRefHeap.preorder_t" }, { "project_name": "everparse", "file_name": "Ast.fst", "name": "Ast.subst" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2_s.fsti", "name": "Vale.Math.Poly2_s.coerce" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fsti", "name": "Selectors.Tree.Core.t" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.null" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.null" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fst", "name": "FStar.HyperStack.ST.stable" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.null_t" }, { "project_name": "FStar", "file_name": "FStar.Tactics.PatternMatching.fst", "name": "FStar.Tactics.PatternMatching.hyp" }, { "project_name": "FStar", "file_name": "Param.fst", "name": "Param.id" }, { "project_name": "steel", "file_name": "LList.Invariant.fsti", "name": "LList.Invariant.t" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.inv" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.binding" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Effect.fsti", "name": "FStar.Tactics.Effect.tactic" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.ref" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ref" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.stt" }, { "project_name": "FStar", "file_name": "IOWPInconsistent.fst", "name": "IOWPInconsistent.bad2" }, { "project_name": "FStar", "file_name": "LowStar.Buffer.fst", "name": "LowStar.Buffer.trivial_preorder" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.t" }, { "project_name": "steel", "file_name": "Selectors.LList.fsti", "name": "Selectors.LList.t" }, { "project_name": "FStar", "file_name": "FStar.Heap.fst", "name": "FStar.Heap.trivial_rel" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.TermEq.fst", "name": "FStar.Reflection.V2.TermEq.allP" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.PostProcess.fst", "name": "FStar.InteractiveHelpers.PostProcess.pred_explorer" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ParseTest.fst", "name": "FStar.InteractiveHelpers.ParseTest.test5" }, { "project_name": "steel", "file_name": "Steel.ST.Array.Util.fst", "name": "Steel.ST.Array.Util.forall_pred" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.stt" }, { "project_name": "FStar", "file_name": "DoublyLinkedListIface.fst", "name": "DoublyLinkedListIface.node" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fsti", "name": "Lib.Sequence.seq" }, { "project_name": "FStar", "file_name": "prims.fst", "name": "Prims.pure_wp_monotonic0" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.return" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.ref" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.null" }, { "project_name": "steel", "file_name": "Domains.fst", "name": "Domains.handler" }, { "project_name": "FStar", "file_name": "IOWPInconsistent.fst", "name": "IOWPInconsistent.bad1" }, { "project_name": "everparse", "file_name": "InterpreterTarget.fsti", "name": "InterpreterTarget.decl" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fsti", "name": "Steel.ST.Array.null" }, { "project_name": "steel", "file_name": "Steel.C.Typenat.fst", "name": "Steel.C.Typenat.s" }, { "project_name": "steel", "file_name": "Pulse.C.Typenat.fst", "name": "Pulse.C.Typenat.s" }, { "project_name": "FStar", "file_name": "OPLSS2021.DijkstraMonads.fst", "name": "OPLSS2021.DijkstraMonads.wp0" }, { "project_name": "steel", "file_name": "Steel.GhostPCMReference.fst", "name": "Steel.GhostPCMReference.ref" }, { "project_name": "karamel", "file_name": "LowStar.Lib.LinkedList2.fst", "name": "LowStar.Lib.LinkedList2.invariant" }, { "project_name": "steel", "file_name": "Steel.C.Typenat.fst", "name": "Steel.C.Typenat.z" }, { "project_name": "steel", "file_name": "Pulse.C.Typenat.fst", "name": "Pulse.C.Typenat.z" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mref" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.squash" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.TermEq.fst", "name": "FStar.Reflection.V2.TermEq.allP0" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fst", "name": "FStar.HyperStack.ST.witnessed" }, { "project_name": "steel", "file_name": "Selectors.LList2.fsti", "name": "Selectors.LList2.t" }, { "project_name": "FStar", "file_name": "FStar.FunctionalExtensionality.fsti", "name": "FStar.FunctionalExtensionality.efun" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.return" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mreference" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.length" }, { "project_name": "steel", "file_name": "Steel.DisposableInvariant.fst", "name": "Steel.DisposableInvariant.inv" }, { "project_name": "steel", "file_name": "BugHigherOrderApplication.fst", "name": "BugHigherOrderApplication.swap_fun" }, { "project_name": "FStar", "file_name": "Param.fst", "name": "Param.fst" }, { "project_name": "steel", "file_name": "LList.ST.fst", "name": "LList.ST.empty" }, { "project_name": "FStar", "file_name": "LowStar.UninitializedBuffer.fst", "name": "LowStar.UninitializedBuffer.initialization_preorder" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fsti", "name": "Zeta.SeqAux.lemma_reduce_property_closure_ty" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Defs.fst", "name": "Vale.Math.Poly2.Defs.poly_equal" }, { "project_name": "FStar", "file_name": "Intro.fst", "name": "Intro.constr" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fst", "name": "Vale.PPC64LE.Decls.ins" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fst", "name": "Vale.X64.Decls.ins" }, { "project_name": "everparse", "file_name": "InterpreterTarget.fst", "name": "InterpreterTarget.env" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.pre_inv" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.pre_inv" }, { "project_name": "FStar", "file_name": "FStar.MRef.fst", "name": "FStar.MRef.token" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.t_one" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fst", "name": "FStar.HyperStack.ST.token_p" }, { "project_name": "FStar", "file_name": "FStar.FunctionalExtensionality.fsti", "name": "FStar.FunctionalExtensionality.efun_g" }, { "project_name": "FStar", "file_name": "SimplePrintfReify.fst", "name": "SimplePrintfReify.arg_type" }, { "project_name": "FStar", "file_name": "FStar.Printf.fst", "name": "FStar.Printf.arg_type" }, { "project_name": "FStar", "file_name": "SimplePrintf.fst", "name": "SimplePrintf.arg_type" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.create" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.per" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.mref0" }, { "project_name": "FStar", "file_name": "FStar.FunctionalExtensionality.fsti", "name": "FStar.FunctionalExtensionality.arrow" }, { "project_name": "everparse", "file_name": "Ast.fst", "name": "Ast.prog" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fst", "name": "FStar.ReflexiveTransitiveClosure.closure_transitive" }, { "project_name": "FStar", "file_name": "MSeqExn.fst", "name": "MSeqExn.witnessed_constant" }, { "project_name": "FStar", "file_name": "OPLSS.Log.fst", "name": "OPLSS.Log.t" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fst", "name": "FStar.Pervasives.normalize" }, { "project_name": "steel", "file_name": "Async.fst", "name": "Async.asynch" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.QuickCodes.fst", "name": "Vale.PPC64LE.QuickCodes.qAssertLemma" }, { "project_name": "hacl-star", "file_name": "Vale.X64.QuickCodes.fst", "name": "Vale.X64.QuickCodes.qAssertLemma" } ], "selected_premises": [ "PropositionalExtensionalityInconsistent.propExt_Type_inconsistent", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "PropositionalExtensionalityInconsistent.propExt_Type", "PropositionalExtensionalityInconsistent.propExt_sub_singleton", "FStar.Pervasives.reveal_opaque", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "PropositionalExtensionalityInconsistent.sub_singleton", "FStar.Pervasives.id", "FStar.Pervasives.st_post_h", "FStar.Pervasives.coerce_eq", "FStar.Pervasives.all_post_h", "FStar.Pervasives.st_pre_h", "FStar.Pervasives.all_pre_h", "Prims.min", "FStar.Pervasives.all_post_h'", "FStar.Pervasives.ex_pre", "Prims.l_True", "FStar.Pervasives.st_post_h'", "Prims.l_False", "FStar.Pervasives.all_wp_h", "FStar.Pervasives.st_wp_h", "Prims.auto_squash", "Prims.subtype_of", "Prims.returnM", "FStar.Pervasives.st_stronger", "FStar.Pervasives.ex_post", "FStar.Pervasives.ex_post'", "FStar.Pervasives.all_return", "Prims.__cache_version_number__", "FStar.Pervasives.all_stronger", "Prims.pure_post'", "Prims.pure_pre", "FStar.Pervasives.st_trivial", "FStar.Pervasives.st_return", "FStar.Pervasives.all_trivial", "FStar.Pervasives.pure_null_wp", "Prims.abs", "FStar.Pervasives.ex_stronger", "FStar.Pervasives.all_ite_wp", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.ex_wp", "FStar.Pervasives.all_close_wp", "Prims.pure_post", "FStar.Pervasives.trivial_pure_post", "Prims.pow2", "Prims.pure_stronger", "FStar.Pervasives.pure_close_wp", "FStar.Pervasives.st_ite_wp", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.ex_trivial", "Prims.pure_trivial", "FStar.Pervasives.ex_return", "FStar.Pervasives.pure_ite_wp", "Prims.pure_wp_monotonic", "Prims.pure_wp'", "FStar.Pervasives.div_hoare_to_wp", "Prims.as_requires", "FStar.Pervasives.ex_close_wp", "Prims.purewp_id", "FStar.Pervasives.all_if_then_else", "FStar.Pervasives.lift_div_exn", "FStar.Pervasives.ex_ite_wp", "FStar.Pervasives.ex_if_then_else", "Prims.pure_wp_monotonic0", "FStar.Pervasives.st_if_then_else", "Prims.as_ensures", "FStar.Pervasives.ex_bind_wp", "FStar.Pervasives.pure_return", "Prims.pure_wp", "FStar.Pervasives.pure_bind_wp", "FStar.Pervasives.st_bind_wp", "Prims.op_Hat" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule PropositionalExtensionalityInconsistent\n(* Variations of propositional and predicate extensionality\n defined for all of Type0 or for the type of sub-singletons\n is inconsistent *)\n\n(* PropositionalExtensionality for the whole of Type0 is inconsistent,\n quite obviously since Type0 doesn't only include propositions.\n\n Proof by Kenji Maillard (adapted) *)\nlet propExt_Type = forall (p1 p2:Type0). (p1 <==> p2) <==> p1==p2\n\nlet propExt_Type_inconsistent ()\n : Lemma (requires propExt_Type)\n (ensures False)\n = let int_is_inhabited (x:int) : Lemma (int <==> unit) = () in\n int_is_inhabited 42\n\n(* Maybe somewhat more subtle, propositional extensionality for all\n sub-singletons is also inconsistent. *)\nlet sub_singleton = a:Type{forall (x y:a). x == y}\nlet propExt_sub_singleton = forall (p1 p2:sub_singleton). (p1 <==> p2) <==> p1==p2\n\n#push-options \"--smtencoding.valid_intro true --smtencoding.valid_elim true\"\nlet propExt_sub_singleton_inconsistent()\n : Lemma (requires propExt_sub_singleton)\n (ensures False)\n = () //SMT finds the proof automatically, by noticing, e.g., T == ()\n#pop-options\n\n\n(* predicate extensionality essentially implies propositional\n extensionality. So, defined over Type0 predicates or sub-singleton\n predicates, it is also inconsistent *)\n\n\n(* Here's a proof for Type0 *)" }, { "file_name": "Vale.AES.PPC64LE.GCMencrypt.fst", "name": "Vale.AES.PPC64LE.GCMencrypt.va_code_Gcm_make_length_quad", "opens_and_abbrevs": [ { "open": "Vale.Lib.Basic" }, { "open": "Vale.AES.OptPublic_BE" }, { "open": "Vale.Lib.Meta" }, { "open": "Vale.AES.PPC64LE.GHash" }, { "open": "Vale.Math.Poly2.Bits_s" }, { "open": "Vale.AES.PPC64LE.GF128_Mul" }, { "open": "Vale.PPC64LE.QuickCodes" }, { "open": "Vale.PPC64LE.QuickCode" }, { "open": "Vale.PPC64LE.InsStack" }, { "open": "Vale.PPC64LE.InsVector" }, { "open": "Vale.PPC64LE.InsMem" }, { "open": "Vale.PPC64LE.InsBasic" }, { "open": "Vale.PPC64LE.Decls" }, { "open": "Vale.PPC64LE.State" }, { "open": "Vale.PPC64LE.Stack_i" }, { "open": "Vale.PPC64LE.Memory" }, { "open": "Vale.PPC64LE.Machine_s" }, { "open": "Vale.AES.PPC64LE.GCTR" }, { "open": "Vale.AES.GCM_helpers_BE" }, { "open": "Vale.Poly1305.Math" }, { "open": "Vale.AES.GF128" }, { "open": "Vale.AES.GF128_s" }, { "open": "Vale.AES.PPC64LE.AES" }, { "open": "Vale.AES.GCM_BE_s" }, { "open": "Vale.AES.GHash_BE" }, { "open": "Vale.AES.GHash_BE_s" }, { "open": "Vale.AES.GCM_BE" }, { "open": "Vale.AES.GCTR_BE" }, { "open": "Vale.AES.GCTR_BE_s" }, { "open": "Vale.AES.AES_BE_s" }, { "open": "Vale.Arch.HeapImpl" }, { "open": "Vale.Arch.Types" }, { "open": "Vale.Def.Types_s" }, { "open": "Vale.Def.Words.Seq_s" }, { "open": "Vale.Def.Words_s" }, { "open": "FStar.Seq" }, { "open": "Vale.Def.Opaque_s" }, { "open": "Vale.Def.Prop_s" }, { "open": "Vale.AES.OptPublic_BE" }, { "open": "Vale.Lib.Meta" }, { "open": "Vale.AES.PPC64LE.GHash" }, { "open": "Vale.Math.Poly2.Bits_s" }, { "open": "Vale.AES.PPC64LE.GF128_Mul" }, { "open": "Vale.PPC64LE.QuickCodes" }, { "open": "Vale.PPC64LE.QuickCode" }, { "open": "Vale.PPC64LE.InsStack" }, { "open": "Vale.PPC64LE.InsVector" }, { "open": "Vale.PPC64LE.InsMem" }, { "open": "Vale.PPC64LE.InsBasic" }, { "open": "Vale.PPC64LE.Decls" }, { "open": "Vale.PPC64LE.State" }, { "open": "Vale.PPC64LE.Stack_i" }, { "open": "Vale.PPC64LE.Memory" }, { "open": "Vale.PPC64LE.Machine_s" }, { "open": "Vale.AES.PPC64LE.GCTR" }, { "open": "Vale.AES.GCM_helpers_BE" }, { "open": "Vale.Poly1305.Math" }, { "open": "Vale.AES.GF128" }, { "open": "Vale.AES.GF128_s" }, { "open": "Vale.AES.PPC64LE.AES" }, { "open": "Vale.AES.GCM_BE_s" }, { "open": "Vale.AES.GHash_BE" }, { "open": "Vale.AES.GHash_BE_s" }, { "open": "Vale.AES.GCM_BE" }, { "open": "Vale.AES.GCTR_BE" }, { "open": "Vale.AES.GCTR_BE_s" }, { "open": "Vale.AES.AES_BE_s" }, { "open": "Vale.Arch.HeapImpl" }, { "open": "Vale.Arch.Types" }, { "open": "Vale.Def.Types_s" }, { "open": "Vale.Def.Words.Seq_s" }, { "open": "Vale.Def.Words_s" }, { "open": "FStar.Seq" }, { "open": "Vale.Def.Opaque_s" }, { "open": "Vale.Def.Prop_s" }, { "open": "Vale.AES.PPC64LE" }, { "open": "Vale.AES.PPC64LE" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 10, "max_fuel": 100, "initial_ifuel": 10, "max_ifuel": 100, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": true, "smtencoding_nl_arith_repr": "wrapped", "smtencoding_l_arith_repr": "native", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 2000, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val va_code_Gcm_make_length_quad : va_dummy:unit -> Tot va_code", "source_definition": "let va_code_Gcm_make_length_quad () =\n (va_Block (va_CCons (va_code_Sl64Imm (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 3) (va_CCons\n (va_code_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 3) (va_CCons (va_code_Mtvsrdd\n (va_op_vec_opr_vec 9) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 7)) (va_CNil ())))))", "source_range": { "start_line": 463, "start_col": 0, "end_line": 466, "end_col": 87 }, "interleaved": false, "definition": "fun _ ->\n Vale.PPC64LE.Decls.va_Block (Vale.PPC64LE.Decls.va_CCons (Vale.PPC64LE.InsBasic.va_code_Sl64Imm (Vale.PPC64LE.Decls.va_op_reg_opr_reg\n 6)\n (Vale.PPC64LE.Decls.va_op_reg_opr_reg 6)\n 3)\n (Vale.PPC64LE.Decls.va_CCons (Vale.PPC64LE.InsBasic.va_code_Sl64Imm (Vale.PPC64LE.Decls.va_op_reg_opr_reg\n 7)\n (Vale.PPC64LE.Decls.va_op_reg_opr_reg 7)\n 3)\n (Vale.PPC64LE.Decls.va_CCons (Vale.PPC64LE.InsVector.va_code_Mtvsrdd (Vale.PPC64LE.Decls.va_op_vec_opr_vec\n 9)\n (Vale.PPC64LE.Decls.va_op_reg_opr_reg 6)\n (Vale.PPC64LE.Decls.va_op_reg_opr_reg 7))\n (Vale.PPC64LE.Decls.va_CNil ()))))", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Prims.unit", "Vale.PPC64LE.Decls.va_Block", "Vale.PPC64LE.Decls.va_CCons", "Vale.PPC64LE.InsBasic.va_code_Sl64Imm", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.PPC64LE.InsVector.va_code_Mtvsrdd", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.PPC64LE.Decls.va_CNil", "Vale.PPC64LE.Decls.va_code" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "va_dummy: Prims.unit -> Vale.PPC64LE.Decls.va_code", "prompt": "let va_code_Gcm_make_length_quad () =\n ", "expected_response": "(va_Block (va_CCons (va_code_Sl64Imm (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 3)\n (va_CCons (va_code_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 3)\n (va_CCons (va_code_Mtvsrdd (va_op_vec_opr_vec 9)\n (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 7))\n (va_CNil ())))))", "source": { "project_name": "hacl-star", "file_name": "obj/Vale.AES.PPC64LE.GCMencrypt.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Vale.AES.PPC64LE.GCMencrypt.fst", "checked_file": "dataset/Vale.AES.PPC64LE.GCMencrypt.fst.checked", "interface_file": true, "dependencies": [ "dataset/Vale.PPC64LE.State.fsti.checked", "dataset/Vale.PPC64LE.Stack_i.fsti.checked", "dataset/Vale.PPC64LE.QuickCodes.fsti.checked", "dataset/Vale.PPC64LE.QuickCode.fst.checked", "dataset/Vale.PPC64LE.Memory.fsti.checked", "dataset/Vale.PPC64LE.Machine_s.fst.checked", "dataset/Vale.PPC64LE.InsVector.fsti.checked", "dataset/Vale.PPC64LE.InsStack.fsti.checked", "dataset/Vale.PPC64LE.InsMem.fsti.checked", "dataset/Vale.PPC64LE.InsBasic.fsti.checked", "dataset/Vale.PPC64LE.Decls.fsti.checked", "dataset/Vale.Poly1305.Math.fsti.checked", "dataset/Vale.Math.Poly2.Bits_s.fsti.checked", "dataset/Vale.Lib.Meta.fsti.checked", "dataset/Vale.Lib.Basic.fsti.checked", "dataset/Vale.Def.Words_s.fsti.checked", "dataset/Vale.Def.Words.Seq_s.fsti.checked", "dataset/Vale.Def.Words.Four_s.fsti.checked", "dataset/Vale.Def.Types_s.fst.checked", "dataset/Vale.Def.Prop_s.fst.checked", "dataset/Vale.Def.Opaque_s.fsti.checked", "dataset/Vale.Arch.Types.fsti.checked", "dataset/Vale.Arch.HeapImpl.fsti.checked", "dataset/Vale.AES.Types_helpers.fsti.checked", "dataset/Vale.AES.PPC64LE.GHash.fsti.checked", "dataset/Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "dataset/Vale.AES.PPC64LE.GCTR.fsti.checked", "dataset/Vale.AES.PPC64LE.AES.fsti.checked", "dataset/Vale.AES.OptPublic_BE.fsti.checked", "dataset/Vale.AES.GHash_BE_s.fst.checked", "dataset/Vale.AES.GHash_BE.fsti.checked", "dataset/Vale.AES.GF128_s.fsti.checked", "dataset/Vale.AES.GF128.fsti.checked", "dataset/Vale.AES.GCTR_BE_s.fst.checked", "dataset/Vale.AES.GCTR_BE.fsti.checked", "dataset/Vale.AES.GCM_helpers_BE.fsti.checked", "dataset/Vale.AES.GCM_BE_s.fst.checked", "dataset/Vale.AES.GCM_BE.fsti.checked", "dataset/Vale.AES.AES_common_s.fst.checked", "dataset/Vale.AES.AES_BE_s.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Seq.Base.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "let aes_reqs\n (alg:algorithm) (key:seq nat32) (round_keys:seq quad32) (keys_b:buffer128)\n (key_ptr:int) (heap0:vale_heap) (layout:vale_heap_layout) : prop0\n =\n (alg = AES_128 \\/ alg = AES_256) /\\\n is_aes_key_word alg key /\\\n length(round_keys) == nr(alg) + 1 /\\\n round_keys == key_to_round_keys_word alg key /\\\n validSrcAddrs128 heap0 key_ptr keys_b (nr alg + 1) layout Secret /\\\n reverse_bytes_quad32_seq (s128 heap0 keys_b) == round_keys", "let va_code_Load_one_lsb dst =\n (va_Block (va_CCons (va_code_Vspltisw dst 1) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 4) 0)\n (va_CCons (va_code_Vsldoi dst (va_op_vec_opr_vec 4) dst 4) (va_CNil ())))))", "let va_codegen_success_Load_one_lsb dst =\n (va_pbool_and (va_codegen_success_Vspltisw dst 1) (va_pbool_and (va_codegen_success_Vspltisw\n (va_op_vec_opr_vec 4) 0) (va_pbool_and (va_codegen_success_Vsldoi dst (va_op_vec_opr_vec 4) dst\n 4) (va_ttrue ()))))", "val va_code_Load_one_lsb : dst:va_operand_vec_opr -> Tot va_code", "val va_codegen_success_Load_one_lsb : dst:va_operand_vec_opr -> Tot va_pbool", "val va_lemma_Load_one_lsb : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Load_one_lsb dst) va_s0 /\\ va_is_dst_vec_opr dst va_s0\n /\\ va_get_ok va_s0 /\\ dst =!= 4))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 /\\\n va_state_eq va_sM (va_update_vec 4 va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst\n va_sM va_s0)))))", "let va_lemma_Load_one_lsb va_b0 va_s0 dst =\n va_reveal_opaque (`%va_code_Load_one_lsb) (va_code_Load_one_lsb dst);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (va_s2, va_fc2) = va_lemma_Vspltisw (va_hd va_b1) va_s0 dst 1 in\n let va_b2 = va_tl va_b1 in\n let (va_s3, va_fc3) = va_lemma_Vspltisw (va_hd va_b2) va_s2 (va_op_vec_opr_vec 4) 0 in\n let va_b3 = va_tl va_b2 in\n let (va_s4, va_fc4) = va_lemma_Vsldoi (va_hd va_b3) va_s3 dst (va_op_vec_opr_vec 4) dst 4 in\n let va_b4 = va_tl va_b3 in\n let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in\n let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in\n let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in\n (va_sM, va_fM)", "let va_wp_Load_one_lsb (dst:va_operand_vec_opr) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_get_ok va_s0 /\\ dst =!= 4 /\\ (forall\n (va_x_dst:va_value_vec_opr) (va_x_v4:quad32) . let va_sM = va_upd_vec 4 va_x_v4\n (va_upd_operand_vec_opr dst va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 ==> va_k va_sM (())))", "val va_wpProof_Load_one_lsb : dst:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Load_one_lsb dst va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Load_one_lsb dst) ([va_Mod_vec 4;\n va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))", "let va_wpProof_Load_one_lsb dst va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Load_one_lsb (va_code_Load_one_lsb dst) va_s0 dst in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_vec 4 va_sM (va_update_ok va_sM (va_update_operand_vec_opr\n dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_vec 4; va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_quick_Load_one_lsb (dst:va_operand_vec_opr) : (va_quickCode unit (va_code_Load_one_lsb dst))\n =\n (va_QProc (va_code_Load_one_lsb dst) ([va_Mod_vec 4; va_mod_vec_opr dst]) (va_wp_Load_one_lsb\n dst) (va_wpProof_Load_one_lsb dst))", "val va_code_Gcm_blocks128 : alg:algorithm -> Tot va_code", "val va_code_Gcm_make_length_quad : va_dummy:unit -> Tot va_code", "let va_code_Gcm_blocks128 alg =\n (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_CCons\n (va_code_Gctr_blocks128 alg) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec\n 7)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_CCons\n (va_code_Ghash_buffer ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15))\n (va_CNil ()))))))))", "val va_codegen_success_Gcm_make_length_quad : va_dummy:unit -> Tot va_pbool", "val va_lemma_Gcm_make_length_quad : va_b0:va_code -> va_s0:va_state\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_make_length_quad ()) va_s0 /\\ va_get_ok va_s0 /\\\n (8 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg 7 va_s0 < pow2_64)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\ (8\n `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg 7 va_s0 < pow2_64 /\\\n va_get_vec 9 va_sM == Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.Mktwo #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` va_get_reg 7 va_s0 `op_Modulus` pow2_32) (8\n `op_Multiply` va_get_reg 7 va_s0 `op_Division` pow2_32 `op_Modulus` pow2_32))\n (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32 (8 `op_Multiply` va_get_reg 6 va_s0\n `op_Modulus` pow2_32) (8 `op_Multiply` va_get_reg 6 va_s0 `op_Division` pow2_32 `op_Modulus`\n pow2_32)))) /\\ va_state_eq va_sM (va_update_vec 9 va_sM (va_update_reg 7 va_sM (va_update_reg 6\n va_sM (va_update_ok va_sM va_s0))))))", "val va_codegen_success_Gcm_blocks128 : alg:algorithm -> Tot va_pbool", "let va_codegen_success_Gcm_blocks128 alg =\n (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_pbool_and\n (va_codegen_success_Gctr_blocks128 alg) (va_pbool_and (va_codegen_success_Vmr\n (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_pbool_and (va_codegen_success_Vmr\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_pbool_and (va_codegen_success_Ghash_buffer\n ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15))\n (va_ttrue ())))))))", "let va_wp_Gcm_make_length_quad (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (8 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg 7\n va_s0 < pow2_64) /\\ (forall (va_x_r6:nat64) (va_x_r7:nat64) (va_x_v9:quad32) . let va_sM =\n va_upd_vec 9 va_x_v9 (va_upd_reg 7 va_x_r7 (va_upd_reg 6 va_x_r6 va_s0)) in va_get_ok va_sM /\\\n (8 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg 7 va_s0 < pow2_64\n /\\ va_get_vec 9 va_sM == Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.Mktwo #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` va_get_reg 7 va_s0 `op_Modulus` pow2_32) (8\n `op_Multiply` va_get_reg 7 va_s0 `op_Division` pow2_32 `op_Modulus` pow2_32))\n (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32 (8 `op_Multiply` va_get_reg 6 va_s0\n `op_Modulus` pow2_32) (8 `op_Multiply` va_get_reg 6 va_s0 `op_Division` pow2_32 `op_Modulus`\n pow2_32)))) ==> va_k va_sM (())))", "let va_qcode_Gcm_blocks128 (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 167 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 168 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Gctr_blocks128 alg in_b out_b key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 169 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 170 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b out_b h_BE (va_get_vec 1 va_old_s)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 172 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15)) (va_QEmpty (())))))))))", "val va_wpProof_Gcm_make_length_quad : va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_make_length_quad va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_make_length_quad ()) ([va_Mod_vec\n 9; va_Mod_reg 7; va_Mod_reg 6]) va_s0 va_k ((va_sM, va_f0, va_g))))", "val va_lemma_Gcm_blocks128 : va_b0:va_code -> va_s0:va_state -> alg:algorithm -> in_b:buffer128 ->\n out_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks128 alg) va_s0 /\\ va_get_ok va_s0 /\\\n ((Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) in_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b (va_get_reg 6 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ l_and\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out_b))))) /\\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM\n (va_update_vec 20 va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM\n (va_update_vec 16 va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM\n (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM\n (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM\n (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM\n (va_update_vec 0 va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM\n (va_update_reg 28 va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM\n (va_update_reg 9 va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM\n (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))", "let va_quick_Gcm_make_length_quad () : (va_quickCode unit (va_code_Gcm_make_length_quad ())) =\n (va_QProc (va_code_Gcm_make_length_quad ()) ([va_Mod_vec 9; va_Mod_reg 7; va_Mod_reg 6])\n va_wp_Gcm_make_length_quad va_wpProof_Gcm_make_length_quad)", "val va_code_Ghash_extra_bytes : va_dummy:unit -> Tot va_code", "val va_codegen_success_Ghash_extra_bytes : va_dummy:unit -> Tot va_pbool", "val va_lemma_Ghash_extra_bytes : va_b0:va_code -> va_s0:va_state -> hkeys_b:buffer128 ->\n total_bytes:nat -> old_hash:quad32 -> h_BE:quad32 -> completed_quads:(seq quad32)\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Ghash_extra_bytes ()) va_s0 /\\ va_get_ok va_s0 /\\\n (va_get_vec 1 va_s0 == Vale.AES.GHash_BE.ghash_incremental0 h_BE old_hash completed_quads /\\\n Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ FStar.Seq.Base.length #quad32 completed_quads ==\n total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply` FStar.Seq.Base.length #quad32\n completed_quads + 16 /\\ va_get_reg 8 va_s0 == total_bytes `op_Modulus` 16 /\\ total_bytes\n `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16 `op_Multiply`\n Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes - 1) < total_bytes)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let raw_quads = FStar.Seq.Base.append #quad32 completed_quads (FStar.Seq.Base.create #quad32 1\n (va_get_vec 9 va_s0)) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_quads)) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_BE_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_bytes in total_bytes > 0 ==> l_and\n (FStar.Seq.Base.length #Vale.Def.Types_s.quad32 input_quads > 0) (va_get_vec 1 va_sM ==\n Vale.AES.GHash_BE.ghash_incremental h_BE old_hash input_quads)) /\\ va_state_eq va_sM\n (va_update_cr0 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8 va_sM\n (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM\n (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM\n (va_update_reg 10 va_sM (va_update_reg 7 va_sM (va_update_ok va_sM va_s0)))))))))))))))))", "let va_wp_Ghash_extra_bytes (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32) (h_BE:quad32)\n (completed_quads:(seq quad32)) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (va_get_vec 1 va_s0 == Vale.AES.GHash_BE.ghash_incremental0 h_BE old_hash\n completed_quads /\\ Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ FStar.Seq.Base.length #quad32 completed_quads ==\n total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply` FStar.Seq.Base.length #quad32\n completed_quads + 16 /\\ va_get_reg 8 va_s0 == total_bytes `op_Modulus` 16 /\\ total_bytes\n `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16 `op_Multiply`\n Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes - 1) < total_bytes) /\\ (forall\n (va_x_r7:nat64) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_cr0:cr0_t) . let va_sM = va_upd_cr0\n va_x_cr0 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7\n va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3\n (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10\n (va_upd_reg 7 va_x_r7 va_s0))))))))))))) in va_get_ok va_sM /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (FStar.Seq.Base.create #quad32 1 (va_get_vec 9\n va_s0)) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_quads)) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_BE_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_bytes in total_bytes > 0 ==> l_and\n (FStar.Seq.Base.length #Vale.Def.Types_s.quad32 input_quads > 0) (va_get_vec 1 va_sM ==\n Vale.AES.GHash_BE.ghash_incremental h_BE old_hash input_quads)) ==> va_k va_sM (())))", "let va_lemma_Gcm_blocks128 va_b0 va_s0 alg in_b out_b key round_keys keys_b hkeys_b h_BE =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19;\n va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13;\n va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7;\n va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec\n 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26;\n va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem] in\n let va_qc = va_qcode_Gcm_blocks128 va_mods alg in_b out_b key round_keys keys_b hkeys_b h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_blocks128 alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 114 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 156 column 53 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 159 column 147 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 160 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite (va_get_vec 7 va_s0) (va_get_reg 6 va_s0)) /\\\n label va_range1\n \"***** POSTCONDITION NOT MET AT line 163 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1 va_sM == va_get_vec 1 va_s0)\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b == Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) out_b)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 165 column 109 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 6 va_s0 > 0 ==> l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==>\n FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0\n (va_get_reg 6 va_s0)) > 0) (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE\n (va_get_vec 1 va_s0) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_sM) out_b)))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok; va_Mod_mem])\n va_sM va_s0;\n (va_sM, va_fM)", "val va_wpProof_Ghash_extra_bytes : hkeys_b:buffer128 -> total_bytes:nat -> old_hash:quad32 ->\n h_BE:quad32 -> completed_quads:(seq quad32) -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Ghash_extra_bytes hkeys_b total_bytes old_hash h_BE\n completed_quads va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Ghash_extra_bytes ()) ([va_Mod_cr0;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7]) va_s0\n va_k ((va_sM, va_f0, va_g))))", "let va_quick_Ghash_extra_bytes (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (h_BE:quad32) (completed_quads:(seq quad32)) : (va_quickCode unit (va_code_Ghash_extra_bytes ()))\n =\n (va_QProc (va_code_Ghash_extra_bytes ()) ([va_Mod_cr0; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8;\n va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec\n 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7]) (va_wp_Ghash_extra_bytes hkeys_b total_bytes\n old_hash h_BE completed_quads) (va_wpProof_Ghash_extra_bytes hkeys_b total_bytes old_hash h_BE\n completed_quads))", "val va_code_Gcm_blocks_auth : va_dummy:unit -> Tot va_code", "val va_codegen_success_Gcm_blocks_auth : va_dummy:unit -> Tot va_pbool", "val va_lemma_Gcm_blocks_auth : va_b0:va_code -> va_s0:va_state -> auth_b:buffer128 ->\n abytes_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel & (seq quad32))\n (requires (va_require_total va_b0 (va_code_Gcm_blocks_auth ()) va_s0 /\\ va_get_ok va_s0 /\\\n (Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) auth_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem_heaplet 6 va_s0) (va_get_reg 4 va_s0) abytes_b 1 (va_get_mem_layout va_s0) Secret\n /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0)\n hkeys_b 3 (va_get_mem_layout va_s0) Secret /\\ va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg\n 6 va_s0 < pow2_64 /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b ==\n va_get_reg 6 va_s0 /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b\n == 1 /\\ (va_mul_nat (va_get_reg 6 va_s0) (128 `op_Division` 8) <= va_get_reg 9 va_s0 /\\\n va_get_reg 9 va_s0 < va_mul_nat (va_get_reg 6 va_s0) (128 `op_Division` 8) + 128 `op_Division`\n 8) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE)))\n (ensures (fun (va_sM, va_fM, auth_quad_seq) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\\n va_get_ok va_sM /\\ (let auth_abytes_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet\n 6 va_s0) abytes_b)) in let auth_quads = Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) auth_b) in let (raw_auth_quads:(seq\n quad32)) = (if (va_get_reg 9 va_s0 > va_get_reg 6 va_s0 `op_Multiply` 128 `op_Division` 8) then\n auth_abytes_quads else auth_quads) in let (auth_input_bytes:(seq nat8)) = FStar.Seq.Base.slice\n #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 (va_get_reg\n 9 va_s0) in let (padded_auth_bytes:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits\n auth_input_bytes in auth_quad_seq == Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes\n /\\ va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental0 h_BE (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0) auth_quad_seq) /\\ va_state_eq va_sM (va_update_cr0 va_sM\n (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12 va_sM (va_update_vec 11 va_sM\n (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8 va_sM (va_update_vec 7 va_sM\n (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM\n (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM\n (va_update_reg 8 va_sM (va_update_reg 7 va_sM (va_update_reg 6 va_sM (va_update_ok va_sM\n va_s0)))))))))))))))))))))))", "let va_wp_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ ((Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) in_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b (va_get_reg 6 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ l_and\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret) /\\ (forall (va_x_mem:vale_heap)\n (va_x_r3:nat64) (va_x_r7:nat64) (va_x_r6:nat64) (va_x_r8:nat64) (va_x_r9:nat64)\n (va_x_r10:nat64) (va_x_r26:nat64) (va_x_r27:nat64) (va_x_r28:nat64) (va_x_r29:nat64)\n (va_x_r30:nat64) (va_x_r31:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32) (va_x_v17:quad32)\n (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32) (va_x_cr0:cr0_t) (va_x_heap1:vale_heap) .\n let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_cr0 va_x_cr0 (va_upd_vec 20 va_x_v20\n (va_upd_vec 19 va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16\n (va_upd_vec 15 va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12\n (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8\n (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4\n (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0\n (va_upd_reg 31 va_x_r31 (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29 (va_upd_reg 28 va_x_r28\n (va_upd_reg 27 va_x_r27 (va_upd_reg 26 va_x_r26 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9\n (va_upd_reg 8 va_x_r8 (va_upd_reg 6 va_x_r6 (va_upd_reg 7 va_x_r7 (va_upd_reg 3 va_x_r3\n (va_upd_mem va_x_mem va_s0))))))))))))))))))))))))))))))))))) in va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out_b))))) ==> va_k va_sM (())))", "let va_wp_Gcm_blocks_auth (auth_b:buffer128) (abytes_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32)\n (va_s0:va_state) (va_k:(va_state -> (seq quad32) -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg\n 7 va_s0) auth_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 6 va_s0) (va_get_reg 4 va_s0) abytes_b\n 1 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0\n va_s0) (va_get_reg 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\\ va_get_reg 7 va_s0 +\n 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 auth_b == va_get_reg 6 va_s0 /\\ Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\ (va_mul_nat (va_get_reg 6 va_s0) (128\n `op_Division` 8) <= va_get_reg 9 va_s0 /\\ va_get_reg 9 va_s0 < va_mul_nat (va_get_reg 6 va_s0)\n (128 `op_Division` 8) + 128 `op_Division` 8) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE) /\\ (forall (va_x_r6:nat64) (va_x_r7:nat64) (va_x_r8:nat64) (va_x_r10:nat64)\n (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32)\n (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32) (va_x_v8:quad32) (va_x_v9:quad32)\n (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32) (va_x_v13:quad32) (va_x_v14:quad32)\n (va_x_cr0:cr0_t) (auth_quad_seq:(seq quad32)) . let va_sM = va_upd_cr0 va_x_cr0 (va_upd_vec 14\n va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12 (va_upd_vec 11 va_x_v11 (va_upd_vec 10\n va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7 va_x_v7 (va_upd_vec 6\n va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2\n (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_reg 8 va_x_r8\n (va_upd_reg 7 va_x_r7 (va_upd_reg 6 va_x_r6 va_s0))))))))))))))))))) in va_get_ok va_sM /\\ (let\n auth_abytes_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet\n 6 va_s0) abytes_b)) in let auth_quads = Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) auth_b) in let (raw_auth_quads:(seq\n quad32)) = va_if (va_get_reg 9 va_s0 > va_get_reg 6 va_s0 `op_Multiply` 128 `op_Division` 8)\n (fun _ -> auth_abytes_quads) (fun _ -> auth_quads) in let (auth_input_bytes:(seq nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 (va_get_reg\n 9 va_s0) in let (padded_auth_bytes:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits\n auth_input_bytes in auth_quad_seq == Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes\n /\\ va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental0 h_BE (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0) auth_quad_seq) ==> va_k va_sM ((auth_quad_seq))))", "val va_wpProof_Gcm_blocks128 : alg:algorithm -> in_b:buffer128 -> out_b:buffer128 -> key:(seq\n nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks128 alg)\n ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0,\n va_g))))", "let va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_blocks128 (va_code_Gcm_blocks128 alg) va_s0 alg in_b out_b key\n round_keys keys_b hkeys_b h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM (va_update_reg 3\n va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))))))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Gcm_blocks_auth : auth_b:buffer128 -> abytes_b:buffer128 -> hkeys_b:buffer128 ->\n h_BE:quad32 -> va_s0:va_state -> va_k:(va_state -> (seq quad32) -> Type0)\n -> Ghost (va_state & va_fuel & (seq quad32))\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks_auth auth_b abytes_b hkeys_b h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks_auth ()) ([va_Mod_cr0;\n va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9;\n va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec\n 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6]) va_s0\n va_k ((va_sM, va_f0, va_g))))", "let va_quick_Gcm_blocks_auth (auth_b:buffer128) (abytes_b:buffer128) (hkeys_b:buffer128)\n (h_BE:quad32) : (va_quickCode (seq quad32) (va_code_Gcm_blocks_auth ())) =\n (va_QProc (va_code_Gcm_blocks_auth ()) ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 10; va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6]) (va_wp_Gcm_blocks_auth auth_b abytes_b hkeys_b\n h_BE) (va_wpProof_Gcm_blocks_auth auth_b abytes_b hkeys_b h_BE))", "let va_quick_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) : (va_quickCode\n unit (va_code_Gcm_blocks128 alg)) =\n (va_QProc (va_code_Gcm_blocks128 alg) ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20;\n va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14;\n va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8;\n va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec\n 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27;\n va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7;\n va_Mod_reg 3; va_Mod_mem]) (va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE) (va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE))", "val va_code_Gcm_blocks_stdcall : alg:algorithm -> Tot va_code", "val va_codegen_success_Gcm_blocks_stdcall : alg:algorithm -> Tot va_pbool", "let va_req_Gcm_blocks_stdcall (va_b0:va_code) (va_s0:va_state) (alg:algorithm) (auth_b:buffer128)\n (auth_bytes:nat64) (auth_num:nat64) (keys_b:buffer128) (iv_b:buffer128) (iv:supported_iv_BE)\n (hkeys_b:buffer128) (abytes_b:buffer128) (in128_b:buffer128) (out128_b:buffer128)\n (len128_num:nat64) (inout_b:buffer128) (plain_num:nat64) (gcm_struct_b:buffer64)\n (tag_b:buffer128) (key:(seq nat32)) : prop =\n (va_require_total va_b0 (va_code_Gcm_blocks_stdcall alg) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (tag_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 12\n (va_get_mem_heaplet 3 va_s0) in va_get_reg 1 va_s0 == Vale.PPC64LE.Stack_i.init_r1\n (va_get_stack va_s0) /\\ Vale.PPC64LE.Memory.is_initial_heap (va_get_mem_layout va_s0)\n (va_get_mem va_s0) /\\ auth_len == auth_num /\\ auth_num_bytes == auth_bytes /\\ len128 ==\n len128_num /\\ plain_num_bytes == plain_num /\\ Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem\n va_s0) (va_get_reg 3 va_s0) gcm_struct_b 13 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) auth_ptr auth_b auth_len\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0)\n abytes_ptr abytes_b 1 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem va_s0) iv_ptr iv_b 1 (va_get_mem_layout va_s0) Public /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) in128_ptr in128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0)\n out128_ptr out128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0) inout_ptr inout_b 1 (va_get_mem_layout\n va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0)\n tag_ptr tag_b 1 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints64_128\n gcm_struct_b ([keys_b; auth_b; abytes_b; iv_b; in128_b; out128_b; inout_b; hkeys_b; tag_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 tag_b ([keys_b; auth_b; abytes_b; iv_b; in128_b;\n out128_b; inout_b; hkeys_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b; auth_b;\n abytes_b; in128_b; out128_b; inout_b; hkeys_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128\n inout_b ([keys_b; auth_b; abytes_b; in128_b; out128_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 auth_b ([keys_b; abytes_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 abytes_b ([keys_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 out128_b ([keys_b; auth_b; abytes_b; hkeys_b; inout_b])\n /\\ Vale.PPC64LE.Decls.buffer_disjoints128 in128_b ([keys_b; auth_b; abytes_b; hkeys_b;\n inout_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b == out128_b)\n /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply` len128 <\n pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ plain_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem va_s0) + 128 < pow2_64 /\\ (va_mul_nat len128\n (128 `op_Division` 8) <= plain_num_bytes /\\ plain_num_bytes < va_mul_nat len128 (128\n `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division` 8) <=\n auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ (alg = AES_128 \\/ alg = AES_256) /\\ Vale.AES.AES_BE_s.is_aes_key_word alg\n key /\\ Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.buffer128_as_seq\n (va_get_mem va_s0) keys_b) == Vale.AES.AES_BE_s.key_to_round_keys_word alg key /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) keys_ptr keys_b\n (Vale.AES.AES_common_s.nr alg + 1) (va_get_mem_layout va_s0) Secret /\\\n Vale.AES.OptPublic_BE.hkeys_reqs_pub (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg\n key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0)) /\\ (let h_BE =\n Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0\n 0 0) in let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read\n iv_b 0 (va_get_mem va_s0)) in iv_BE == Vale.AES.GCM_BE_s.compute_iv_BE h_BE iv)))", "val va_code_Gcm_auth_bytes : va_dummy:unit -> Tot va_code", "let va_code_Gcm_auth_bytes () =\n (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Ghash_buffer\n ()) (va_CNil ()))))", "val va_codegen_success_Gcm_auth_bytes : va_dummy:unit -> Tot va_pbool", "let va_codegen_success_Gcm_auth_bytes () =\n (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and\n (va_codegen_success_Ghash_buffer ()) (va_ttrue ())))", "let va_qcode_Gcm_auth_bytes (va_mods:va_mods_t) (auth_b:buffer128) (hkeys_b:buffer128)\n (h_BE:quad32) : (va_quickCode (quad32 & quad32) (va_code_Gcm_auth_bytes ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 206 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (fun (va_s:va_state) _ -> let (y_0:quad32) =\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 208 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b auth_b h_BE y_0) (fun (va_s:va_state) _ -> let (y_auth:quad32) =\n va_get_vec 1 va_s in va_QEmpty ((y_0, y_auth))))))", "val va_lemma_Gcm_auth_bytes : va_b0:va_code -> va_s0:va_state -> auth_b:buffer128 ->\n hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel & quad32 & quad32)\n (requires (va_require_total va_b0 (va_code_Gcm_auth_bytes ()) va_s0 /\\ va_get_ok va_s0 /\\\n (Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) (va_get_reg 7 va_s0) auth_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == va_get_reg 6 va_s0 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64)))\n (ensures (fun (va_sM, va_fM, y_0, y_auth) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok\n va_sM /\\ (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 /\\ (let h_BE =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) /\\ va_get_vec 1 va_sM == y_auth)) /\\ va_state_eq va_sM (va_update_cr0 va_sM\n (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12 va_sM (va_update_vec 11 va_sM\n (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8 va_sM (va_update_vec 7 va_sM\n (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM\n (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM\n (va_update_reg 6 va_sM (va_update_reg 7 va_sM (va_update_ok va_sM va_s0))))))))))))))))))))))", "let va_lemma_Gcm_auth_bytes va_b0 va_s0 auth_b hkeys_b h_BE =\n let (va_mods:va_mods_t) = [va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec\n 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5;\n va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg\n 6; va_Mod_reg 7; va_Mod_ok] in\n let va_qc = va_qcode_Gcm_auth_bytes va_mods auth_b hkeys_b h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_auth_bytes ()) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let (y_0, y_auth) = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 175 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 200 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 201 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (let h_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 202 column 95 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b))) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 203 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_vec 1 va_sM == y_auth)))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6;\n va_Mod_reg 7; va_Mod_ok]) va_sM va_s0;\n let (y_0, y_auth) = va_g in\n (va_sM, va_fM, y_0, y_auth)", "let va_wp_Gcm_auth_bytes (auth_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) (va_s0:va_state)\n (va_k:(va_state -> (quad32 & quad32) -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) (va_get_reg 7 va_s0) auth_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == va_get_reg 6 va_s0 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64) /\\ (forall (va_x_r7:nat64)\n (va_x_r6:nat64) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_cr0:cr0_t) (y_0:quad32) (y_auth:quad32) . let va_sM =\n va_upd_cr0 va_x_cr0 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12\n (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8\n (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4\n (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0\n (va_upd_reg 10 va_x_r10 (va_upd_reg 6 va_x_r6 (va_upd_reg 7 va_x_r7 va_s0)))))))))))))))))) in\n va_get_ok va_sM /\\ (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 /\\ (let h_BE\n = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) /\\ va_get_vec 1 va_sM == y_auth)) ==> va_k va_sM ((y_0, y_auth))))", "val va_wpProof_Gcm_auth_bytes : auth_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32 ->\n va_s0:va_state -> va_k:(va_state -> (quad32 & quad32) -> Type0)\n -> Ghost (va_state & va_fuel & (quad32 & quad32))\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_auth_bytes auth_b hkeys_b h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_auth_bytes ()) ([va_Mod_cr0;\n va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9;\n va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec\n 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6; va_Mod_reg 7]) va_s0 va_k ((va_sM,\n va_f0, va_g))))", "let va_wpProof_Gcm_auth_bytes auth_b hkeys_b h_BE va_s0 va_k =\n let (va_sM, va_f0, y_0, y_auth) = va_lemma_Gcm_auth_bytes (va_code_Gcm_auth_bytes ()) va_s0\n auth_b hkeys_b h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_cr0 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM\n (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM\n (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM\n (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM\n (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM\n (va_update_ok va_sM va_s0)))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6;\n va_Mod_reg 7]) va_sM va_s0;\n let va_g = (y_0, y_auth) in\n (va_sM, va_f0, va_g)", "let va_quick_Gcm_auth_bytes (auth_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) : (va_quickCode\n (quad32 & quad32) (va_code_Gcm_auth_bytes ())) =\n (va_QProc (va_code_Gcm_auth_bytes ()) ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 10; va_Mod_reg 6; va_Mod_reg 7]) (va_wp_Gcm_auth_bytes auth_b hkeys_b h_BE)\n (va_wpProof_Gcm_auth_bytes auth_b hkeys_b h_BE))" ], "closest": [ "val va_code_Gcm_make_length_quad : va_dummy:unit -> Tot va_code\nlet va_code_Gcm_make_length_quad () =\n (va_Block (va_CCons (va_code_ZeroXmm (va_op_xmm_xmm 0)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_IMul64\n (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_CCons (va_code_Pinsrq (va_op_xmm_xmm 0)\n (va_op_opr64_reg64 rRax) 1) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)\n (va_op_opr64_reg64 rR13)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRax)\n (va_const_opr64 8)) (va_CCons (va_code_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 0)\n (va_CNil ())))))))))", "val va_codegen_success_Gcm_make_length_quad : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Gcm_make_length_quad () =\n (va_pbool_and (va_codegen_success_ZeroXmm (va_op_xmm_xmm 0)) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and\n (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_pbool_and\n (va_codegen_success_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 1) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_pbool_and\n (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_pbool_and\n (va_codegen_success_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 0) (va_ttrue ()))))))))", "val va_code_Gcm_auth_bytes : va_dummy:unit -> Tot va_code\nlet va_code_Gcm_auth_bytes () =\n (va_Block (va_CCons (va_code_ZeroXmm (va_op_xmm_xmm 8)) (va_CCons (va_code_Ghash_buffer ())\n (va_CNil ()))))", "val va_code_Gcm_blocks_auth : va_dummy:unit -> Tot va_code\nlet va_code_Gcm_blocks_auth () =\n (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))\n (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 16)) (va_CCons\n (va_code_InitPshufbMask (va_op_xmm_xmm 9) (va_op_reg_opr64_reg64 rR10)) (va_CCons\n (va_code_Gcm_auth_bytes ()) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRsi)) (va_CCons (va_IfElse (va_cmp_gt\n (va_op_cmp_reg64 rRsi) (va_op_cmp_reg64 rRcx)) (va_Block (va_CCons (va_code_Load128_buffer\n (va_op_heaplet_mem_heaplet 7) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rRbx) 0 Secret)\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRsi)) (va_CCons\n (va_code_And64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64 15)) (va_CCons\n (va_code_Ghash_extra_bytes ()) (va_CCons (va_Block (va_CNil ())) (va_CNil ()))))))) (va_Block\n (va_CNil ()))) (va_CNil ())))))))))", "val va_code_Gf128MulRev128 : va_dummy:unit -> Tot va_code\nlet va_code_Gf128MulRev128 () =\n (va_Block (va_CCons (va_code_ReduceMulRev128 ()) (va_CNil ())))", "val va_code_Gf128MulRev128 : va_dummy:unit -> Tot va_code\nlet va_code_Gf128MulRev128 () =\n (va_Block (va_CCons (va_code_ReduceMulRev128 ()) (va_CNil ())))", "val va_quick_Gcm_make_length_quad: Prims.unit\n -> (va_quickCode unit (va_code_Gcm_make_length_quad ()))\nlet va_quick_Gcm_make_length_quad () : (va_quickCode unit (va_code_Gcm_make_length_quad ())) =\n (va_QProc (va_code_Gcm_make_length_quad ()) ([va_Mod_flags; va_Mod_reg64 rRax; va_Mod_xmm 0])\n va_wp_Gcm_make_length_quad va_wpProof_Gcm_make_length_quad)", "val va_quick_Gcm_make_length_quad: Prims.unit\n -> (va_quickCode unit (va_code_Gcm_make_length_quad ()))\nlet va_quick_Gcm_make_length_quad () : (va_quickCode unit (va_code_Gcm_make_length_quad ())) =\n (va_QProc (va_code_Gcm_make_length_quad ()) ([va_Mod_vec 9; va_Mod_reg 7; va_Mod_reg 6])\n va_wp_Gcm_make_length_quad va_wpProof_Gcm_make_length_quad)", "val va_qcode_Gcm_make_length_quad (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Gcm_make_length_quad ()))\nlet va_qcode_Gcm_make_length_quad (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Gcm_make_length_quad ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 424 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_ZeroXmm (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 425 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 426 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 427 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 428 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 429 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 430 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 0) (va_QEmpty (()))))))))))", "val va_code_Fast_sqr_part2 : va_dummy:unit -> Tot va_code\nlet va_code_Fast_sqr_part2 () =\n (va_Block (va_CCons (va_code_Xor64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rR15))\n (va_CCons (va_code_Adox_64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRax)) (va_CCons\n (va_code_Adcx_64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR8)) (va_CCons\n (va_code_Adox_64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_CCons\n (va_code_Adcx_64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rR9)) (va_CCons\n (va_code_Adox_64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR15)) (va_CCons\n (va_code_Adcx_64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rR10)) (va_CCons\n (va_code_Adox_64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR15)) (va_CCons\n (va_code_Adcx_64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rR11)) (va_CCons\n (va_code_Adox_64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR15)) (va_CCons\n (va_code_Adcx_64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbx)) (va_CCons\n (va_code_Adcx_64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR13)) (va_CCons\n (va_code_Adcx_64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR14)) (va_CNil\n ())))))))))))))))", "val va_code_Ghash_extra_bytes : va_dummy:unit -> Tot va_code\nlet va_code_Ghash_extra_bytes () =\n (va_Block (va_CCons (va_code_Compute_pad_to_128_bits ()) (va_CCons (va_code_Pshufb (va_op_xmm_xmm\n 0) (va_op_xmm_xmm 9)) (va_CCons (va_code_Ghash_register ()) (va_CNil ())))))", "val va_code_Ghash_buffer : va_dummy:unit -> Tot va_code\nlet va_code_Ghash_buffer () =\n (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons\n (va_code_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 5)\n (va_op_reg_opr_reg 5) Secret) (va_CCons (va_code_Load128_byte16_buffer_index\n (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 12) (va_op_reg_opr_reg 5) (va_op_reg_opr_reg\n 10) Secret) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_VSwap\n (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5)) (va_CCons (va_code_High64ToLow (va_op_vec_opr_vec\n 7) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Low64ToHigh (va_op_vec_opr_vec 6)\n (va_op_vec_opr_vec 5)) (va_CCons (va_code_VSwap (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 12))\n (va_CCons (va_code_High64ToLow (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 12)) (va_CCons\n (va_code_Low64ToHigh (va_op_vec_opr_vec 13) (va_op_vec_opr_vec 12)) (va_CCons\n (va_code_Ghash_buffer_while0 ()) (va_CCons (va_IfElse (va_cmp_gt (va_op_cmp_reg 6)\n (va_const_cmp 0)) (va_Block (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_GhashUnroll_n\n false) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_Block (va_CNil ())) (va_CNil ()))))))\n (va_Block (va_CNil ()))) (va_CNil ()))))))))))))))", "val va_code_Ghash_buffer : va_dummy:unit -> Tot va_code\nlet va_code_Ghash_buffer () =\n (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRdi))\n (va_CCons (va_code_Ghash_buffer_while0 ()) (va_CCons (va_IfElse (va_cmp_gt (va_op_cmp_reg64\n rRdx) (va_const_cmp 0)) (va_Block (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64\n (va_op_dst_opr64_reg64 rR10) (va_const_opr64 1)) (va_CCons (va_code_IMul64\n (va_op_dst_opr64_reg64 rR10) (va_const_opr64 16)) (va_CCons (va_code_Add64\n (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_GhashUnroll_n false\n false false) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_Block (va_CNil ())) (va_CNil\n ())))))))))) (va_Block (va_CNil ()))) (va_CNil ())))))", "val va_code_Compute_ghash_incremental_register : va_dummy:unit -> Tot va_code\nlet va_code_Compute_ghash_incremental_register () =\n (va_Block (va_CCons (va_code_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_CCons (va_code_Mov128\n (va_op_xmm_xmm 2) (va_op_xmm_xmm 11)) (va_CCons (va_code_ReduceMul128_LE ()) (va_CNil ())))))", "val va_code_Ghash_register : va_dummy:unit -> Tot va_code\nlet va_code_Ghash_register () =\n (va_Block (va_CCons (va_code_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 5) Secret) (va_CCons (va_code_Vspltisw\n (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_VSwap (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5))\n (va_CCons (va_code_High64ToLow (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 5)) (va_CCons\n (va_code_Low64ToHigh (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 5)) (va_CCons (va_Block (va_CNil\n ())) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 9) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec\n 9)) (va_CCons (va_code_VPolyMulLow (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 9)\n (va_op_vec_opr_vec 7)) (va_CCons (va_code_VPolyMul (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 9)\n (va_op_vec_opr_vec 5)) (va_CCons (va_code_VPolyMulHigh (va_op_vec_opr_vec 4) (va_op_vec_opr_vec\n 9) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 8) 0) (va_CCons\n (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws\n (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 8) (va_op_vec_opr_vec 0) 4) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 8)\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 8) 4) (va_CCons (va_code_ReduceLast ()) (va_CNil\n ()))))))))))))))))))", "val va_code_Ghash_register : va_dummy:unit -> Tot va_code\nlet va_code_Ghash_register () =\n (va_Block (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 5)\n (va_op_reg_opr64_reg64 rR9) (-32) Secret) (va_CCons (va_Block (va_CNil ())) (va_CCons\n (va_code_VPolyAdd (va_op_xmm_xmm 0) (va_op_xmm_xmm 8) (va_op_opr128_xmm 0)) (va_CCons\n (va_code_VPolyMul (va_op_xmm_xmm 1) (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) false false) (va_CCons\n (va_code_VPolyMul (va_op_xmm_xmm 2) (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) false true) (va_CCons\n (va_code_VPolyMul (va_op_xmm_xmm 3) (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) true false) (va_CCons\n (va_code_VPolyMul (va_op_xmm_xmm 5) (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) true true) (va_CCons\n (va_code_Mov128 (va_op_xmm_xmm 4) (va_op_xmm_xmm 1)) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm\n 6) (va_op_xmm_xmm 2) (va_op_opr128_xmm 3)) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 7)\n (va_op_xmm_xmm 5)) (va_CCons (va_code_ZeroXmm (va_op_xmm_xmm 3)) (va_CCons (va_code_PinsrdImm\n (va_op_xmm_xmm 3) 3254779904 3 (va_op_reg_opr64_reg64 rR11)) (va_CCons (va_code_Reduce true)\n (va_CNil ())))))))))))))))", "val va_code_Gf128_powers : va_dummy:unit -> Tot va_code\nlet va_code_Gf128_powers () =\n (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons\n (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec\n 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1))\n (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons\n (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons\n (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons\n (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16)\n (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil\n ())))))))))))))))", "val va_code_Gf128_powers : va_dummy:unit -> Tot va_code\nlet va_code_Gf128_powers () =\n (va_Block (va_CCons (va_code_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 6)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_CCons (va_code_Load128_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64 rRcx) 32 Secret)\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 1)) (va_CCons (va_code_Mov128\n (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons\n (va_code_Store128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx)\n (va_op_xmm_xmm 1) 0 Secret) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 1) (va_op_xmm_xmm 6))\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 6)) (va_CCons\n (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 1))\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_CCons\n (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_xmm_xmm 1) 16 Secret)\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 6)) (va_CCons\n (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64\n rRcx) 32 Secret) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Mov128 (va_op_xmm_xmm\n 6) (va_op_xmm_xmm 1)) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_CCons\n (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_xmm_xmm 1) 48 Secret)\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 6)) (va_CCons\n (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64\n rRcx) 32 Secret) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Mov128 (va_op_xmm_xmm\n 6) (va_op_xmm_xmm 1)) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_CCons\n (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_xmm_xmm 1) 64 Secret)\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 6)) (va_CCons\n (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64\n rRcx) 32 Secret) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Mov128 (va_op_xmm_xmm\n 6) (va_op_xmm_xmm 1)) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_CCons\n (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_xmm_xmm 1) 96 Secret)\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 6)) (va_CCons\n (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64\n rRcx) 32 Secret) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Mov128 (va_op_xmm_xmm\n 6) (va_op_xmm_xmm 1)) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_CCons\n (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_xmm_xmm 1) 112 Secret)\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 0)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRax)) (va_CNil\n ()))))))))))))))))))))))))))))))))))))))))))))))", "val va_code_Compute_pad_to_128_bits : va_dummy:unit -> Tot va_code\nlet va_code_Compute_pad_to_128_bits () =\n (va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR10) (va_const_cmp 8)) (va_Block\n (va_CCons (va_code_PinsrqImm (va_op_xmm_xmm 0) 0 1 (va_op_reg_opr64_reg64 rRcx)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Shl64\n (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_CCons (va_code_Shl64\n (va_op_dst_opr64_reg64 rR11) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Sub64\n (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_CCons (va_code_Pextrq\n (va_op_dst_opr64_reg64 rRcx) (va_op_xmm_xmm 0) 0) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Pinsrq (va_op_xmm_xmm\n 0) (va_op_opr64_reg64 rRcx) 0) (va_CNil ()))))))))))) (va_Block (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64\n (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_CCons (va_code_Shl64\n (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_Block (va_CNil ()))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_CCons\n (va_code_Shl64 (va_op_dst_opr64_reg64 rR11) (va_op_shift_amt64_reg64 rRcx)) (va_CCons\n (va_code_Sub64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_CCons (va_code_Pextrq\n (va_op_dst_opr64_reg64 rRcx) (va_op_xmm_xmm 0) 1) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR11)) (va_CCons (va_Block (va_CNil ()))\n (va_CCons (va_code_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRcx) 1) (va_CNil\n ())))))))))))))) (va_CNil ())))", "val va_code_Clmul128 : va_dummy:unit -> Tot va_code\nlet va_code_Clmul128 () =\n (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_VSwap\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_High64ToLow (va_op_vec_opr_vec\n 4) (va_op_vec_opr_vec 3)) (va_CCons (va_code_Low64ToHigh (va_op_vec_opr_vec 5)\n (va_op_vec_opr_vec 3)) (va_CCons (va_code_VPolyMul (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3)\n (va_op_vec_opr_vec 2)) (va_CCons (va_code_VPolyMulLow (va_op_vec_opr_vec 4) (va_op_vec_opr_vec\n 4) (va_op_vec_opr_vec 2)) (va_CCons (va_code_VPolyMulHigh (va_op_vec_opr_vec 5)\n (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 2)) (va_CCons (va_code_Low64ToHigh (va_op_vec_opr_vec\n 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_High64ToLow (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 3)) (va_CCons (va_code_AddPoly (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 4)) (va_CCons (va_code_AddPoly (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 5)\n (va_op_vec_opr_vec 2)) (va_CNil ())))))))))))))", "val va_code_Clmul128 : va_dummy:unit -> Tot va_code\nlet va_code_Clmul128 () =\n (va_Block (va_CCons (va_code_Mov128 (va_op_xmm_xmm 5) (va_op_xmm_xmm 1)) (va_CCons\n (va_code_Pclmulqdq (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) false true) (va_CCons (va_code_Mov128\n (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 1) (va_op_xmm_xmm\n 5)) (va_CCons (va_code_Pclmulqdq (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) true false) (va_CCons\n (va_code_Mov128 (va_op_xmm_xmm 4) (va_op_xmm_xmm 1)) (va_CCons (va_code_Mov128 (va_op_xmm_xmm\n 1) (va_op_xmm_xmm 5)) (va_CCons (va_code_Pclmulqdq (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) false\n false) (va_CCons (va_code_Pclmulqdq (va_op_xmm_xmm 5) (va_op_xmm_xmm 2) true true) (va_CCons\n (va_code_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 5)) (va_CCons (va_code_Mov128 (va_op_xmm_xmm\n 5) (va_op_xmm_xmm 1)) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 1) (va_op_xmm_xmm 3)) (va_CCons\n (va_code_High64ToLow (va_op_xmm_xmm 1)) (va_CCons (va_code_AddPoly (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 1)) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 1) (va_op_xmm_xmm 4)) (va_CCons\n (va_code_High64ToLow (va_op_xmm_xmm 1)) (va_CCons (va_code_AddPoly (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 1)) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 1) (va_op_xmm_xmm 3)) (va_CCons\n (va_code_Low64ToHigh (va_op_xmm_xmm 1)) (va_CCons (va_code_Low64ToHigh (va_op_xmm_xmm 4))\n (va_CCons (va_code_AddPoly (va_op_xmm_xmm 1) (va_op_xmm_xmm 4)) (va_CCons (va_code_AddPoly\n (va_op_xmm_xmm 1) (va_op_xmm_xmm 5)) (va_CNil ()))))))))))))))))))))))))", "val va_code_Xgetbv_Avx512 : va_dummy:unit -> Tot va_code\nlet va_code_Xgetbv_Avx512 () =\n (mk_ins (make_instr (I.ins_Xgetbv)))", "val va_code_Ghash_buffer_body0 : va_dummy:unit -> Tot va_code\nlet va_code_Ghash_buffer_body0 () =\n (va_Block (va_CCons (va_code_Ghash_buffer_loop_body ()) (va_CNil ())))", "val va_code_Ghash_buffer_body0 : va_dummy:unit -> Tot va_code\nlet va_code_Ghash_buffer_body0 () =\n (va_Block (va_CCons (va_code_Mod_cr0 ()) (va_CCons (va_code_Ghash_buffer_loop_body ()) (va_CNil\n ()))))", "val va_code_Preamble : va_dummy:unit -> Tot va_code\nlet va_code_Preamble () =\n (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons\n (va_code_Load128_word4_buffer (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 16)\n (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Load128_word4_buffer_index\n (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 20) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg\n 10) Secret) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 17) (va_op_vec_opr_vec 16)\n (va_op_vec_opr_vec 16) 4) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 18) (va_op_vec_opr_vec\n 16) (va_op_vec_opr_vec 16) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 19)\n (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 16) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec\n 21) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) 4) (va_CCons (va_code_Vsldoi\n (va_op_vec_opr_vec 22) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) 8) (va_CCons\n (va_code_Vsldoi (va_op_vec_opr_vec 23) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) 12)\n (va_CNil ())))))))))))", "val va_code_Preamble : va_dummy:unit -> Tot va_code\nlet va_code_Preamble () =\n (va_Block (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 1)\n (va_op_reg_opr64_reg64 rRdi) 0 Secret) (va_CCons (va_code_Load128_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 2) (va_op_reg_opr64_reg64 rRdi) 16 Secret)\n (va_CCons (va_code_InitPshufbStableMask (va_op_xmm_xmm 7) (va_op_reg_opr64_reg64 rRax))\n (va_CCons (va_code_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 1) 27) (va_CCons (va_code_Pshufd\n (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) 177) (va_CCons (va_code_Pshufd (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 2) 27) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 8) (va_op_xmm_xmm 7)) (va_CCons\n (va_code_Palignr8 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_CCons (va_code_Shufpd (va_op_xmm_xmm\n 2) (va_op_xmm_xmm 0) 0) (va_CNil ())))))))))))", "val va_code_GhashUnroll6x : va_dummy:unit -> Tot va_code\nlet va_code_GhashUnroll6x () =\n (va_Block (va_CCons (va_code_MulAdd_unroll ()) (va_CCons (va_code_ReduceLast true) (va_CNil ()))))", "val va_code_Newline : va_dummy:unit -> Tot va_code\nlet va_code_Newline () =\n (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ())))", "val va_code_Fmul : va_dummy:unit -> Tot va_code\nlet va_code_Fmul () =\n (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_LargeComment\n \"Compute the raw multiplication: tmp <- src1 * src2\"\n ) (va_CCons (va_code_Fast_multiply 0) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"Line up pointers\"\n ) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdi)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rR15)) (va_CCons\n (va_code_LargeComment\n \"Wrap the result back into the field\"\n ) (va_CCons (va_code_Carry_wide 0) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil\n ()))))))))))))", "val va_code_Compute_iv : va_dummy:unit -> Tot va_code\nlet va_code_Compute_iv () =\n (va_Block (va_CCons (va_IfElse (va_cmp_eq (va_op_cmp_reg64 rRsi) (va_const_cmp 12)) (va_Block\n (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 7) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rR8) 0 Secret) (va_CCons (va_Block (va_CNil ())) (va_CCons\n (va_code_InitPshufbMask (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64 rRax)) (va_CCons\n (va_code_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 1)) (va_CCons (va_code_PinsrdImm\n (va_op_xmm_xmm 0) 1 0 (va_op_reg_opr64_reg64 rRax)) (va_CCons (va_code_Store128_buffer\n (va_op_heaplet_mem_heaplet 7) (va_op_reg_opr64_reg64 rRcx) (va_op_xmm_xmm 0) 0 Secret) (va_CNil\n ())))))))) (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64\n rRcx)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 32)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_CCons\n (va_code_Gcm_blocks_auth ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)\n (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64\n 0)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rRsi)) (va_CCons\n (va_code_Gcm_make_length_quad ()) (va_CCons (va_code_Ghash_register ()) (va_CCons\n (va_code_Store128_buffer (va_op_heaplet_mem_heaplet 7) (va_op_reg_opr64_reg64 rRcx)\n (va_op_xmm_xmm 8) 0 Secret) (va_CNil ()))))))))))))) (va_CNil ())))", "val va_code_ClmulRev128 : va_dummy:unit -> Tot va_code\nlet va_code_ClmulRev128 () =\n (va_Block (va_CCons (va_code_Clmul128 ()) (va_CCons (va_code_ShiftLeft2_128_1 ()) (va_CNil ()))))", "val va_code_ClmulRev128 : va_dummy:unit -> Tot va_code\nlet va_code_ClmulRev128 () =\n (va_Block (va_CCons (va_code_Clmul128 ()) (va_CCons (va_code_ShiftLeft2_128_1 ()) (va_CNil ()))))", "val va_code_Fadd : va_dummy:unit -> Tot va_code\nlet va_code_Fadd () =\n (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Comment\n \"Compute the raw addition of f1 + f2\"\n ) (va_CCons (va_code_Fast_add ()) (va_CCons (va_code_LargeComment\n \"Wrap the result back into the field\"\n ) (va_CCons (va_code_Carry_pass true 0) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil\n ()))))))))", "val va_code_KeyExpansion256Stdcall : va_dummy:unit -> Tot va_code\nlet va_code_KeyExpansion256Stdcall () =\n (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons\n (va_code_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 1)\n (va_op_reg_opr_reg 4) Secret) (va_CCons (va_code_Load128_byte16_buffer_index\n (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg\n 10) Secret) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons\n (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 3)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons\n (va_code_KeyExpansionRoundUnrolledRecursive256 14) (va_CCons (va_code_Vxor (va_op_vec_opr_vec\n 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vxor (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2)) (va_CCons (va_code_Vxor (va_op_vec_opr_vec 3)\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3)) (va_CCons (va_code_Vxor (va_op_vec_opr_vec 4)\n (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4)) (va_CNil ()))))))))))))", "val va_code_Ghash_buffer_loop_body : va_dummy:unit -> Tot va_code\nlet va_code_Ghash_buffer_loop_body () =\n (va_Block (va_CCons (va_Block (va_CNil ())) (va_CCons (va_Block (va_CNil ())) (va_CCons\n (va_code_GhashUnroll_n true) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_Block (va_CNil\n ())) (va_CCons (va_code_AddImm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 32) (va_CCons\n (va_code_SubImm (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 2) (va_CNil ())))))))))", "val va_code_Ghash_buffer_loop_body : va_dummy:unit -> Tot va_code\nlet va_code_Ghash_buffer_loop_body () =\n (va_Block (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR11)\n (va_const_opr64 80)) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_GhashUnroll_n false\n false true) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_Block (va_CNil ())) (va_CCons\n (va_code_Add64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 96)) (va_CCons (va_code_Sub64\n (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 6)) (va_CNil ()))))))))))", "val va_code_Mod_cr0 : va_dummy:unit -> Tot va_code\nlet va_code_Mod_cr0 () =\n (va_Block (va_CNil ()))", "val va_code_Mod_cr0 : va_dummy:unit -> Tot va_code\nlet va_code_Mod_cr0 () =\n (va_Block (va_CNil ()))", "val va_code_Mod_cr0 : va_dummy:unit -> Tot va_code\nlet va_code_Mod_cr0 () =\n (va_Block (va_CNil ()))", "val va_code_Aes_ctr_ghash : va_dummy:unit -> Tot va_code\nlet va_code_Aes_ctr_ghash () =\n (va_Block (va_CCons (va_code_Compute_ghash_incremental_register ()) (va_CCons (va_code_Mov128\n (va_op_xmm_xmm 2) (va_op_xmm_xmm 12)) (va_CCons (va_code_Compute_ghash_incremental_register ())\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 13)) (va_CCons\n (va_code_Compute_ghash_incremental_register ()) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 14)) (va_CCons (va_code_Compute_ghash_incremental_register ()) (va_CNil\n ())))))))))", "val va_code_ClmulRev64High : va_dummy:unit -> Tot va_code\nlet va_code_ClmulRev64High () =\n (va_Block (va_CCons (va_code_VPolyMulHigh (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 2)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CNil ()))))", "val va_code_KeyExpansion128Stdcall : va_dummy:unit -> Tot va_code\nlet va_code_KeyExpansion128Stdcall () =\n (va_Block (va_CCons (va_code_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 4) Secret) (va_CCons (va_code_Store128_byte16_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons\n (va_code_KeyExpansionRoundUnrolledRecursive 10) (va_CCons (va_code_Vxor (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vxor (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2)) (va_CCons (va_code_Vxor (va_op_vec_opr_vec 3)\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))", "val va_code_Xgetbv_Avx : va_dummy:unit -> Tot va_code\nlet va_code_Xgetbv_Avx () =\n (mk_ins (make_instr (I.ins_Xgetbv)))", "val va_code_MulAdd_unroll_1way : va_dummy:unit -> Tot va_code\nlet va_code_MulAdd_unroll_1way () =\n (va_Block (va_CCons (va_code_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 7) Secret) (va_CCons (va_code_VPolyAdd\n (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 0)) (va_CCons\n (va_code_VPolyMulLow (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 7))\n (va_CCons (va_code_VPolyMul (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 5))\n (va_CCons (va_code_VPolyMulHigh (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec\n 6)) (va_CNil ())))))))", "val va_code_MulAdd_unroll_2way : va_dummy:unit -> Tot va_code\nlet va_code_MulAdd_unroll_2way () =\n (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons\n (va_code_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0)\n (va_op_reg_opr_reg 7) Secret) (va_CCons (va_code_Load128_byte16_buffer_index\n (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 8) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg\n 10) Secret) (va_CCons (va_code_VPolyMulLow (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 8)\n (va_op_vec_opr_vec 7)) (va_CCons (va_code_VPolyMul (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 8)\n (va_op_vec_opr_vec 5)) (va_CCons (va_code_VPolyMulHigh (va_op_vec_opr_vec 4) (va_op_vec_opr_vec\n 8) (va_op_vec_opr_vec 6)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 0) (va_op_vec_opr_vec\n 1) (va_op_vec_opr_vec 0)) (va_CCons (va_code_VPolyMulLow (va_op_vec_opr_vec 9)\n (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 14)) (va_CCons (va_code_VPolyMul (va_op_vec_opr_vec\n 10) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 12)) (va_CCons (va_code_VPolyMulHigh\n (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 13)) (va_CCons\n (va_code_VPolyAdd (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 9)) (va_CCons\n (va_code_VPolyAdd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 10)) (va_CCons\n (va_code_VPolyAdd (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 11)) (va_CNil\n ())))))))))))))))", "val va_code_Loop_rounds_52_64 : va_dummy:unit -> Tot va_code\nlet va_code_Loop_rounds_52_64 () =\n (va_Block (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRcx) (16 `op_Multiply` 13) Secret) (va_CCons (va_Block (va_CNil ()))\n (va_CCons (va_code_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 3)) (va_CCons (va_code_SHA256_msg2\n (va_op_xmm_xmm 4) (va_op_xmm_xmm 3)) (va_CCons (va_code_SHA256_rnds2 (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 1)) (va_CCons (va_code_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_CCons\n (va_code_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 4)) (va_CCons (va_code_Palignr4 (va_op_xmm_xmm\n 7) (va_op_xmm_xmm 3)) (va_CCons (va_code_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2))\n (va_CCons (va_code_Paddd (va_op_xmm_xmm 5) (va_op_xmm_xmm 7)) (va_CCons (va_code_Load128_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rRcx) (16 `op_Multiply`\n 14) Secret) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Paddd (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 4)) (va_CCons (va_code_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1))\n (va_CCons (va_code_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_CCons\n (va_code_SHA256_msg2 (va_op_xmm_xmm 5) (va_op_xmm_xmm 4)) (va_CCons (va_code_Mov128\n (va_op_xmm_xmm 7) (va_op_xmm_xmm 8)) (va_CCons (va_code_SHA256_rnds2 (va_op_xmm_xmm 1)\n (va_op_xmm_xmm 2)) (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rRcx) (16 `op_Multiply` 15) Secret) (va_CCons\n (va_Block (va_CNil ())) (va_CCons (va_code_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_CCons (va_code_Pshufd\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRdx)\n (va_const_opr64 1)) (va_CCons (va_code_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2))\n (va_CCons (va_code_Paddd (va_op_xmm_xmm 2) (va_op_xmm_xmm 10)) (va_CCons (va_code_Paddd\n (va_op_xmm_xmm 1) (va_op_xmm_xmm 9)) (va_CNil ())))))))))))))))))))))))))))))", "val va_code_Store4 : va_dummy:unit -> Tot va_code\nlet va_code_Store4 () =\n (va_Block (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"Store the result\"\n ) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR8) 0 Secret) (va_CCons (va_code_Store64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR9) 8\n Secret) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64\n rRdi) (va_op_reg_opr64_reg64 rR10) 16 Secret) (va_CCons (va_code_Store64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR11) 24\n Secret) (va_CNil ()))))))))", "val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code\nlet va_code_Poly1305_multiply () =\n (va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap\n (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)\n (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)\n (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)\n (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons\n (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons\n (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons\n (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64\n rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)\n (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)\n (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)\n (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)\n (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)\n (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)\n (va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64\n rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))\n (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil\n ()))))))))))))))))))))))))))", "val va_code_Loop : va_dummy:unit -> Tot va_code\nlet va_code_Loop () =\n (va_Block (va_CCons (va_code_Loop_while0 ()) (va_CNil ())))", "val va_code_Loop : va_dummy:unit -> Tot va_code\nlet va_code_Loop () =\n (va_Block (va_CCons (va_code_Loop_while0 ()) (va_CNil ())))", "val va_code_Init_ctr : va_dummy:unit -> Tot va_code\nlet va_code_Init_ctr () =\n (va_Block (va_CCons (va_code_Pxor (va_op_xmm_xmm 4) (va_op_xmm_xmm 4)) (va_CCons\n (va_code_PinsrdImm (va_op_xmm_xmm 4) 1 0 (va_op_reg_opr64_reg64 rR12)) (va_CNil ()))))", "val va_code_Fmul2 : va_dummy:unit -> Tot va_code\nlet va_code_Fmul2 () =\n (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_LargeComment\n \"Compute the raw multiplication tmp[0] <- f1[0] * f2[0]\"\n ) (va_CCons (va_code_Fast_multiply 0) (va_CCons (va_code_LargeComment\n \"Compute the raw multiplication tmp[1] <- f1[1] * f2[1]\"\n ) (va_CCons (va_code_Fast_multiply 4) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"Line up pointers\"\n ) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdi)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rR15)) (va_CCons\n (va_code_LargeComment\n \"Wrap the results back into the field\"\n ) (va_CCons (va_code_Carry_wide 0) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Carry_wide\n 4) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil ()))))))))))))))))", "val va_code_NoNewline : va_dummy:unit -> Tot va_code\nlet va_code_NoNewline () =\n (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0)))", "val va_code_Loop_rounds_48_63 : va_dummy:unit -> Tot va_code\nlet va_code_Loop_rounds_48_63 () =\n (va_Block (va_CCons (va_code_Loop_rounds_16_59_a 48) (va_CCons (va_code_Loop_rounds_0_59_a 48)\n (va_CCons (va_code_Loop_rounds_16_59_b 52) (va_CCons (va_code_Loop_rounds_0_59_b 52) (va_CCons\n (va_code_Loop_rounds_16_59_c 56) (va_CCons (va_code_Loop_rounds_0_59_c 56) (va_CCons\n (va_code_Loop_rounds_60_63_a ()) (va_CCons (va_code_Loop_rounds_60_63_b ()) (va_CNil\n ()))))))))))", "val va_code_Store_3blocks128_2 : va_dummy:unit -> Tot va_code\nlet va_code_Store_3blocks128_2 () =\n (va_Block (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 29) Secret) (va_CCons\n (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 4)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 30) Secret) (va_CCons\n (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 5)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 31) Secret) (va_CNil ())))))", "val va_code_Check_avx512_support : va_dummy:unit -> Tot va_code\nlet va_code_Check_avx512_support () =\n (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 7)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_CCons (va_code_Cpuid_Avx512\n ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 65536)) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rRax) (va_const_opr64 131072)) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rR10) (va_const_opr64 1073741824)) (va_CCons (va_code_Shr64\n (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 1)) (va_CCons (va_code_Shr64\n (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 14)) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 2147483648)) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Shr64\n (va_op_dst_opr64_reg64 rR11) (va_const_shift_amt64 15)) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))))", "val va_lemma_Gcm_make_length_quad : va_b0:va_code -> va_s0:va_state\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_make_length_quad ()) va_s0 /\\ va_get_ok va_s0 /\\\n (sse_enabled /\\ 8 `op_Multiply` va_get_reg64 rR13 va_s0 < pow2_64 /\\ 8 `op_Multiply`\n va_get_reg64 rR11 va_s0 < pow2_64)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\ (8\n `op_Multiply` va_get_reg64 rR13 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg64 rR11 va_s0 <\n pow2_64 /\\ va_get_xmm 0 va_sM == Vale.Def.Types_s.insert_nat64 (Vale.Def.Types_s.insert_nat64\n (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) (8 `op_Multiply` va_get_reg64 rR11\n va_s0) 1) (8 `op_Multiply` va_get_reg64 rR13 va_s0) 0) /\\ va_state_eq va_sM (va_update_flags\n va_sM (va_update_reg64 rRax va_sM (va_update_xmm 0 va_sM (va_update_ok va_sM va_s0))))))\nlet va_lemma_Gcm_make_length_quad va_b0 va_s0 =\n let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRax; va_Mod_xmm 0; va_Mod_ok] in\n let va_qc = va_qcode_Gcm_make_length_quad va_mods in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_make_length_quad ()) va_qc va_s0\n (fun va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 407 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 418 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (8 `op_Multiply` va_get_reg64 rR13 va_s0 < pow2_64) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 419 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (8 `op_Multiply` va_get_reg64 rR11 va_s0 < pow2_64) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 421 column 138 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_xmm 0 va_sM == Vale.Def.Types_s.insert_nat64 (Vale.Def.Types_s.insert_nat64\n (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) (8 `op_Multiply` va_get_reg64 rR11\n va_s0) 1) (8 `op_Multiply` va_get_reg64 rR13 va_s0) 0))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRax; va_Mod_xmm 0; va_Mod_ok]) va_sM va_s0;\n (va_sM, va_fM)", "val va_code_Store_3blocks128_1 : va_dummy:unit -> Tot va_code\nlet va_code_Store_3blocks128_1 () =\n (va_Block (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 7) Secret) (va_CCons\n (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 27) Secret) (va_CCons\n (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 2)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 28) Secret) (va_CNil ())))))", "val va_code_Ghash_buffer_while0 : va_dummy:unit -> Tot va_code\nlet va_code_Ghash_buffer_while0 () =\n (va_Block (va_CCons (va_While (va_cmp_ge (va_op_cmp_reg 6) (va_const_cmp 2)) (va_Block (va_CCons\n (va_code_Ghash_buffer_body0 ()) (va_CNil ())))) (va_CNil ())))", "val va_code_Ghash_buffer_while0 : va_dummy:unit -> Tot va_code\nlet va_code_Ghash_buffer_while0 () =\n (va_Block (va_CCons (va_While (va_cmp_ge (va_op_cmp_reg64 rRdx) (va_const_cmp 6)) (va_Block\n (va_CCons (va_code_Ghash_buffer_body0 ()) (va_CNil ())))) (va_CNil ())))", "val va_code_Fsqr : va_dummy:unit -> Tot va_code\nlet va_code_Fsqr () =\n (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_LargeComment\n \"Compute the raw multiplication: tmp <- f * f\"\n ) (va_CCons (va_code_Fast_sqr 0) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"Line up pointers\"\n ) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdi)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rR12)) (va_CCons\n (va_code_LargeComment\n \"Wrap the result back into the field\"\n ) (va_CCons (va_code_Carry_wide 0) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil\n ()))))))))))))", "val va_code_ReduceMulRev128 : va_dummy:unit -> Tot va_code\nlet va_code_ReduceMulRev128 () =\n (va_Block (va_CCons (va_code_ClmulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6)\n (va_op_vec_opr_vec 2)) (va_CCons (va_code_Gf128ModulusRev (va_op_vec_opr_vec 2)) (va_CCons\n (va_code_ClmulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 2))\n (va_CCons (va_code_Gf128ModulusRev (va_op_vec_opr_vec 2)) (va_CCons (va_code_ClmulRev64High ())\n (va_CCons (va_code_AddPoly (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 5))\n (va_CCons (va_code_AddPoly (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6))\n (va_CNil ())))))))))))", "val va_code_ReduceMulRev128 : va_dummy:unit -> Tot va_code\nlet va_code_ReduceMulRev128 () =\n (va_Block (va_CCons (va_code_ClmulRev128 ()) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 6)\n (va_op_xmm_xmm 2)) (va_CCons (va_code_Gf128ModulusRev (va_op_xmm_xmm 2)) (va_CCons\n (va_code_ClmulRev128 ()) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 5) (va_op_xmm_xmm 2))\n (va_CCons (va_code_Gf128ModulusRev (va_op_xmm_xmm 2)) (va_CCons (va_code_ClmulRev64 true true)\n (va_CCons (va_code_AddPoly (va_op_xmm_xmm 1) (va_op_xmm_xmm 5)) (va_CCons (va_code_AddPoly\n (va_op_xmm_xmm 1) (va_op_xmm_xmm 6)) (va_CNil ())))))))))))", "val va_code_Check_avx512_xcr0_support : va_dummy:unit -> Tot va_code\nlet va_code_Check_avx512_xcr0_support () =\n (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_CCons\n (va_code_Xgetbv_Avx512 ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)\n (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRdx)\n (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64\n 32)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 64)) (va_CCons\n (va_code_And64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 128)) (va_CCons (va_code_Shr64\n (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 2)) (va_CCons (va_code_Shr64\n (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 1)) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_CNil ())))))))))))))", "val va_code_Fsqr2 : va_dummy:unit -> Tot va_code\nlet va_code_Fsqr2 () =\n (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Fast_sqr 0) (va_CCons\n (va_code_Newline ()) (va_CCons (va_code_Fast_sqr 4) (va_CCons (va_code_Newline ()) (va_CCons\n (va_code_Comment\n \"Line up pointers\"\n ) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdi)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rR12)) (va_CCons\n (va_code_Newline ()) (va_CCons (va_code_Carry_wide 0) (va_CCons (va_code_Newline ()) (va_CCons\n (va_code_Carry_wide 4) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil ())))))))))))))))", "val va_code_Loop_rounds : va_dummy:unit -> Tot va_code\nlet va_code_Loop_rounds () =\n (va_Block (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Xxmrghd (va_op_vec_opr_vec 28)\n (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 20)) (va_CCons (va_code_Xxmrghd (va_op_vec_opr_vec\n 29) (va_op_vec_opr_vec 17) (va_op_vec_opr_vec 21)) (va_CCons (va_code_Xxmrghd\n (va_op_vec_opr_vec 30) (va_op_vec_opr_vec 18) (va_op_vec_opr_vec 22)) (va_CCons\n (va_code_Xxmrghd (va_op_vec_opr_vec 31) (va_op_vec_opr_vec 19) (va_op_vec_opr_vec 23))\n (va_CCons (va_code_Loop_prologue ()) (va_CCons (va_Block (va_CNil ())) (va_CCons\n (va_code_Loop_rounds_0_15 ()) (va_CCons (va_code_Loop_rounds_16_47 16) (va_CCons\n (va_code_Loop_rounds_16_47 32) (va_CCons (va_code_Loop_rounds_48_63 ()) (va_CCons\n (va_code_SubImm (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 256) (va_CCons (va_code_Vsldoi\n (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 28) (va_op_vec_opr_vec 28) 8) (va_CCons\n (va_code_Vsldoi (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 29) (va_op_vec_opr_vec 29) 8)\n (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 30) (va_op_vec_opr_vec 30)\n 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 31) (va_op_vec_opr_vec\n 31) 8) (va_CCons (va_code_Vadduwm (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 16)\n (va_op_vec_opr_vec 28)) (va_CCons (va_code_Vadduwm (va_op_vec_opr_vec 17) (va_op_vec_opr_vec\n 17) (va_op_vec_opr_vec 29)) (va_CCons (va_code_Vadduwm (va_op_vec_opr_vec 18)\n (va_op_vec_opr_vec 18) (va_op_vec_opr_vec 30)) (va_CCons (va_code_Vadduwm (va_op_vec_opr_vec\n 19) (va_op_vec_opr_vec 19) (va_op_vec_opr_vec 31)) (va_CCons (va_code_Vadduwm\n (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 0)) (va_CCons (va_code_Vadduwm\n (va_op_vec_opr_vec 21) (va_op_vec_opr_vec 21) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vadduwm\n (va_op_vec_opr_vec 22) (va_op_vec_opr_vec 22) (va_op_vec_opr_vec 2)) (va_CCons (va_code_Vadduwm\n (va_op_vec_opr_vec 23) (va_op_vec_opr_vec 23) (va_op_vec_opr_vec 3)) (va_CNil\n ()))))))))))))))))))))))))))", "val va_code_Loop_rounds : va_dummy:unit -> Tot va_code\nlet va_code_Loop_rounds () =\n (va_Block (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Loop_rounds_0_15 ()) (va_CCons\n (va_code_Loop_rounds_16_51 ()) (va_CCons (va_code_Loop_rounds_52_64 ()) (va_CNil ()))))))", "val va_code_ShiftLeft2_128_1 : va_dummy:unit -> Tot va_code\nlet va_code_ShiftLeft2_128_1 () =\n (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_LoadImm64\n (va_op_reg_opr_reg 10) 31) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 3) (va_op_reg_opr_reg\n 10)) (va_CCons (va_code_Vsrw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3))\n (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 3) 4)\n (va_CCons (va_code_Vspltisb (va_op_vec_opr_vec 0) 1) (va_CCons (va_code_Vsl (va_op_vec_opr_vec\n 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 0)) (va_CCons (va_code_Vsl (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 0)) (va_CCons (va_code_Vxor (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 3)) (va_CNil ())))))))))))", "val va_code_ShiftLeft2_128_1 : va_dummy:unit -> Tot va_code\nlet va_code_ShiftLeft2_128_1 () =\n (va_Block (va_CCons (va_code_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_CCons (va_code_Psrld\n (va_op_xmm_xmm 3) 31) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 4) (va_op_xmm_xmm 2)) (va_CCons\n (va_code_Psrld (va_op_xmm_xmm 4) 31) (va_CCons (va_code_Pslld (va_op_xmm_xmm 1) 1) (va_CCons\n (va_code_Pslld (va_op_xmm_xmm 2) 1) (va_CCons (va_code_VPslldq4 (va_op_xmm_xmm 5)\n (va_op_xmm_xmm 3)) (va_CCons (va_code_VPslldq4 (va_op_xmm_xmm 4) (va_op_xmm_xmm 4)) (va_CCons\n (va_code_PinsrdImm (va_op_xmm_xmm 3) 0 0 (va_op_reg_opr64_reg64 rR12)) (va_CCons\n (va_code_Pshufd (va_op_xmm_xmm 3) (va_op_xmm_xmm 3) 3) (va_CCons (va_code_Pxor (va_op_xmm_xmm\n 3) (va_op_xmm_xmm 4)) (va_CCons (va_code_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_Pxor (va_op_xmm_xmm 2) (va_op_xmm_xmm 3)) (va_CNil ())))))))))))))))", "val va_code_Handle_ctr32_2 : va_dummy:unit -> Tot va_code\nlet va_code_Handle_ctr32_2 () =\n (va_Block (va_CCons (va_code_VPshufb (va_op_xmm_xmm 6) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0))\n (va_CCons (va_code_Load_one_lsb (va_op_xmm_xmm 5)) (va_CCons (va_code_VPaddd (va_op_xmm_xmm 10)\n (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_CCons (va_code_Load_two_lsb (va_op_xmm_xmm 5))\n (va_CCons (va_code_VPaddd (va_op_xmm_xmm 11) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_VPaddd (va_op_xmm_xmm 12) (va_op_xmm_xmm 10) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_VPaddd (va_op_xmm_xmm 13) (va_op_xmm_xmm 11) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_VPxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_opr128_xmm 4)) (va_CCons\n (va_code_VPaddd (va_op_xmm_xmm 14) (va_op_xmm_xmm 12) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 12) (va_op_xmm_xmm 12) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_VPxor (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_opr128_xmm 4)) (va_CCons\n (va_code_VPaddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 13) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 13) (va_op_xmm_xmm 13) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_VPxor (va_op_xmm_xmm 12) (va_op_xmm_xmm 12) (va_op_opr128_xmm 4)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 14) (va_op_xmm_xmm 14) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_VPxor (va_op_xmm_xmm 13) (va_op_xmm_xmm 13) (va_op_opr128_xmm 4)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_VPxor (va_op_xmm_xmm 14) (va_op_xmm_xmm 14) (va_op_opr128_xmm 4)) (va_CNil\n ()))))))))))))))))))))))", "val va_code_ReduceMul128_LE : va_dummy:unit -> Tot va_code\nlet va_code_ReduceMul128_LE () =\n (va_Block (va_CCons (va_code_Pshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 8)) (va_CCons\n (va_code_ReduceMulRev128 ()) (va_CCons (va_code_Pshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 8))\n (va_CNil ())))))", "val va_code_Aes_3rounds_4way : va_dummy:unit -> Tot va_code\nlet va_code_Aes_3rounds_4way () =\n (va_Block (va_CCons (va_code_Aes_round_4way (va_op_xmm_xmm 4)) (va_CCons (va_code_Aes_round_4way\n (va_op_xmm_xmm 5)) (va_CCons (va_code_Aes_round_4way (va_op_xmm_xmm 6)) (va_CNil ())))))", "val va_code_Check_avx2_support : va_dummy:unit -> Tot va_code\nlet va_code_Check_avx2_support () =\n (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 7)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_CCons (va_code_Cpuid_Avx2\n ()) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 32)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))", "val va_code_Check_avx_xcr0_support : va_dummy:unit -> Tot va_code\nlet va_code_Check_avx_xcr0_support () =\n (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_CCons\n (va_code_Xgetbv_Avx ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)\n (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64\n 4)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 1)) (va_CCons\n (va_code_And64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 2)) (va_CCons (va_code_And64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_CNil ())))))))))", "val va_code_Fsub : va_dummy:unit -> Tot va_code\nlet va_code_Fsub () =\n (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Fast_sub ()) (va_CCons\n (va_code_Carry_sub_pass ()) (va_CCons (va_code_Store4 ()) (va_CCons (va_code_DestroyHeaplets\n ()) (va_CNil ())))))))", "val va_code_Nat64Equal : va_dummy:unit -> Tot va_code\nlet va_code_Nat64Equal () =\n (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 5) 1) (va_CCons (va_code_AddCarry\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 5)) (va_CCons (va_code_LoadImm64\n (va_op_reg_opr_reg 3) 0) (va_CCons (va_code_AddExtended (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3)) (va_CCons (va_code_Xor (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 5) (va_op_reg_opr_reg 3)) (va_CNil ())))))))", "val va_code_Aes_4rounds_4way : va_dummy:unit -> Tot va_code\nlet va_code_Aes_4rounds_4way () =\n (va_Block (va_CCons (va_code_Aes_round_4way (va_op_xmm_xmm 3)) (va_CCons (va_code_Aes_round_4way\n (va_op_xmm_xmm 4)) (va_CCons (va_code_Aes_round_4way (va_op_xmm_xmm 5)) (va_CCons\n (va_code_Aes_round_4way (va_op_xmm_xmm 6)) (va_CNil ()))))))", "val va_code_Reduce : va_dummy:unit -> Tot va_code\nlet va_code_Reduce () =\n (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_Low64ToHigh\n (va_op_vec_opr_vec 9) (va_op_vec_opr_vec 3)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 9)) (va_CCons (va_code_VSwap (va_op_vec_opr_vec 10)\n (va_op_vec_opr_vec 2)) (va_CCons (va_code_VPolyMulLow (va_op_vec_opr_vec 2) (va_op_vec_opr_vec\n 2) (va_op_vec_opr_vec 8)) (va_CCons (va_code_High64ToLow (va_op_vec_opr_vec 3)\n (va_op_vec_opr_vec 3)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4)\n (va_op_vec_opr_vec 3)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 10)) (va_CCons (va_code_VSwap (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2))\n (va_CCons (va_code_VPolyMulLow (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec\n 8)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec\n 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec\n 2)) (va_CNil ()))))))))))))))", "val va_code_Loop_rounds_1_3 : va_dummy:unit -> Tot va_code\nlet va_code_Loop_rounds_1_3 () =\n (va_Block (va_CCons (va_code_Loop_rounds_1_15_shift_body 1 (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 0)) (va_CCons (va_code_Loop_rounds_1_15_shift_body 2 (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 0)) (va_CCons (va_code_Loop_rounds_1_15_shift_body 3 (va_op_vec_opr_vec 3)\n (va_op_vec_opr_vec 0)) (va_CNil ())))))", "val va_code_Aes_2rounds_4way : va_dummy:unit -> Tot va_code\nlet va_code_Aes_2rounds_4way () =\n (va_Block (va_CCons (va_code_Aes_round_4way (va_op_xmm_xmm 3)) (va_CCons (va_code_Aes_round_4way\n (va_op_xmm_xmm 4)) (va_CNil ()))))", "val va_code_Loop_rounds_16_51 : va_dummy:unit -> Tot va_code\nlet va_code_Loop_rounds_16_51 () =\n (va_Block (va_CCons (va_code_Loop_rounds_16_51_recursive 12) (va_CNil ())))", "val va_code_Loop_prologue : va_dummy:unit -> Tot va_code\nlet va_code_Loop_prologue () =\n (va_Block (va_CCons (va_code_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 4) Secret) (va_CCons (va_code_Load128_word4_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 24) (va_op_reg_opr_reg 6) Secret) (va_CCons\n (va_code_AddImm (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 4) 16) (va_CCons (va_code_AddImm\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 16) (va_CCons (va_code_Vadduwm (va_op_vec_opr_vec\n 23) (va_op_vec_opr_vec 23) (va_op_vec_opr_vec 24)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec\n 24) (va_op_vec_opr_vec 24) (va_op_vec_opr_vec 24) 4) (va_CNil ()))))))))", "val va_code_Compute_Y0 : va_dummy:unit -> Tot va_code\nlet va_code_Compute_Y0 () =\n (va_Block (va_CCons (va_code_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 1)) (va_CNil ())))", "val va_code_Fmul1 : va_dummy:unit -> Tot va_code\nlet va_code_Fmul1 () =\n (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Fast_mul1 0) (va_CCons\n (va_code_LargeComment\n \"Wrap the result back into the field\"\n ) (va_CCons (va_code_Comment\n \"Step 1: Compute carry*38\"\n ) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 38)) (va_CCons\n (va_code_Carry_pass false 0) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil ())))))))))", "val va_code_Poly1305_impl : va_dummy:unit -> Tot va_code\nlet va_code_Poly1305_impl () =\n (va_Block (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64\n rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12) (va_op_reg_opr64_reg64 rRdi) 32\n Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64\n 1152921487695413247)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64\n rRcx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64\n 1152921487695413244)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64\n rRcx)) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64\n rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_CCons (va_code_Store64_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR12) 32\n Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx))\n (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_CCons\n (va_code_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_CCons\n (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRax) 56 Public) (va_CCons (va_code_Store64_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64\n Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons\n (va_code_Poly1305_blocks ()) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1)\n (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 184 Public) (va_CCons (va_IfElse\n (va_cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (va_Block (va_CCons (va_code_Load64_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15) (va_op_reg_opr64_reg64 rRdi) 56\n Public) (va_CCons (va_IfElse (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block\n (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)\n (va_op_reg_opr64_reg64 rRdi) 32 Public) (va_CCons (va_code_Load64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0\n Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64\n rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public) (va_CCons (va_code_Poly1305_last_block ()) (va_CNil\n ())))))) (va_Block (va_CNil ()))) (va_CCons (va_code_Poly1305_reduce_last ()) (va_CCons\n (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)\n (va_op_reg_opr64_reg64 rRdi) 40 Public) (va_CCons (va_code_Load64_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48\n Public) (va_CCons (va_code_Poly1305_add_key_s ()) (va_CNil ())))))))) (va_Block (va_CNil ())))\n (va_CNil ())))))))))))))))))))", "val va_code_Check_avx_support : va_dummy:unit -> Tot va_code\nlet va_code_Check_avx_support () =\n (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_Cpuid_Avx\n ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_CCons\n (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 268435456)) (va_CCons\n (va_code_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 27)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ()))))))))))", "val va_code_MulAdd_unroll : va_dummy:unit -> Tot va_code\nlet va_code_MulAdd_unroll () =\n (va_Block (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 3)\n (va_op_reg_opr64_reg64 rR9) (-32) Secret) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 1)\n (va_op_xmm_xmm 7) (va_op_xmm_xmm 3) false false) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 5)\n (va_op_xmm_xmm 7) (va_op_xmm_xmm 3) false true) (va_CCons (va_code_Load128_buffer\n (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rRbp) 48 Secret)\n (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 6) (va_op_xmm_xmm 7) (va_op_xmm_xmm 3) true false)\n (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 7) (va_op_xmm_xmm 7) (va_op_xmm_xmm 3) true true)\n (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 3)\n (va_op_reg_opr64_reg64 rR9) (-16) Secret) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 6)\n (va_op_xmm_xmm 6) (va_op_opr128_xmm 5)) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 5)\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 3) false false) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 8)\n (va_op_xmm_xmm 8) (va_op_opr128_xmm 4)) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 4)\n (va_op_xmm_xmm 1) (va_op_opr128_xmm 5)) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 1)\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 3) false true) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 3) true false) (va_CCons (va_code_Mem128_lemma ()) (va_CCons\n (va_code_VPolyAdd (va_op_xmm_xmm 8) (va_op_xmm_xmm 8) (va_opr_code_Mem128\n (va_op_heaplet_mem_heaplet 3) (va_op_reg64_reg64 rRbp) 16 Secret)) (va_CCons (va_code_VPolyMul\n (va_op_xmm_xmm 3) (va_op_xmm_xmm 0) (va_op_xmm_xmm 3) true true) (va_CCons\n (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRbp) 64 Secret) (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm\n 5) (va_op_reg_opr64_reg64 rR9) 16 Secret) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 6)\n (va_op_xmm_xmm 6) (va_op_opr128_xmm 1)) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 1)\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) false false) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 6)\n (va_op_xmm_xmm 6) (va_op_opr128_xmm 2)) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) false true) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 7)\n (va_op_xmm_xmm 7) (va_op_opr128_xmm 3)) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 3)\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) true false) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 5)\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) true true) (va_CCons (va_code_Load128_buffer\n (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rRbp) 80 Secret)\n (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 4) (va_op_xmm_xmm 4) (va_op_opr128_xmm 1)) (va_CCons\n (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64\n rR9) 32 Secret) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)\n (va_op_opr128_xmm 2)) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 2) (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 1) false false) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)\n (va_op_opr128_xmm 3)) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 3) (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 1) false true) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 7) (va_op_xmm_xmm 7)\n (va_op_opr128_xmm 5)) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 5) (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 1) true false) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 1) true true) (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 3)\n (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rRbp) 96 Secret) (va_CCons (va_code_VPolyAdd\n (va_op_xmm_xmm 4) (va_op_xmm_xmm 4) (va_op_opr128_xmm 2)) (va_CCons (va_code_Load128_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 2) (va_op_reg_opr64_reg64 rR9) 64 Secret)\n (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6) (va_op_opr128_xmm 3)) (va_CCons\n (va_code_VPolyMul (va_op_xmm_xmm 3) (va_op_xmm_xmm 0) (va_op_xmm_xmm 2) false false) (va_CCons\n (va_code_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6) (va_op_opr128_xmm 5)) (va_CCons\n (va_code_VPolyMul (va_op_xmm_xmm 5) (va_op_xmm_xmm 0) (va_op_xmm_xmm 2) false true) (va_CCons\n (va_code_VPolyAdd (va_op_xmm_xmm 7) (va_op_xmm_xmm 7) (va_op_opr128_xmm 1)) (va_CCons\n (va_code_VPolyMul (va_op_xmm_xmm 1) (va_op_xmm_xmm 0) (va_op_xmm_xmm 2) true false) (va_CCons\n (va_code_Mem128_lemma ()) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 8) (va_op_xmm_xmm 8)\n (va_opr_code_Mem128 (va_op_heaplet_mem_heaplet 3) (va_op_reg64_reg64 rRbp) 112 Secret))\n (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 2) (va_op_xmm_xmm 0) (va_op_xmm_xmm 2) true true)\n (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 4) (va_op_xmm_xmm 4) (va_op_opr128_xmm 3)) (va_CCons\n (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 3) (va_op_reg_opr64_reg64\n rR9) 80 Secret) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)\n (va_op_opr128_xmm 5)) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 5) (va_op_xmm_xmm 8)\n (va_op_xmm_xmm 3) false true) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)\n (va_op_opr128_xmm 1)) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 1) (va_op_xmm_xmm 8)\n (va_op_xmm_xmm 3) true false) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 7) (va_op_xmm_xmm 7)\n (va_op_opr128_xmm 2)) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 2) (va_op_xmm_xmm 8)\n (va_op_xmm_xmm 3) false false) (va_CCons (va_code_VPolyMul (va_op_xmm_xmm 8) (va_op_xmm_xmm 8)\n (va_op_xmm_xmm 3) true true) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)\n (va_op_opr128_xmm 5)) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)\n (va_op_opr128_xmm 1)) (va_CCons (va_code_VPolyAdd (va_op_xmm_xmm 4) (va_op_xmm_xmm 4)\n (va_op_opr128_xmm 2)) (va_CCons (va_code_ZeroXmm (va_op_xmm_xmm 3)) (va_CCons\n (va_code_PinsrdImm (va_op_xmm_xmm 3) 3254779904 3 (va_op_reg_opr64_reg64 rRax)) (va_CCons\n (va_code_VPolyAdd (va_op_xmm_xmm 7) (va_op_xmm_xmm 7) (va_op_opr128_xmm 8)) (va_CNil\n ()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))", "val va_code_Handle_ctr32 : va_dummy:unit -> Tot va_code\nlet va_code_Handle_ctr32 () =\n (va_Block (va_CCons (va_code_InitPshufbMask (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rR11))\n (va_CCons (va_code_VPshufb (va_op_xmm_xmm 6) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_Load_one_lsb (va_op_xmm_xmm 5)) (va_CCons (va_code_VPaddd (va_op_xmm_xmm 10)\n (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_CCons (va_code_Load_two_lsb (va_op_xmm_xmm 5))\n (va_CCons (va_code_VPaddd (va_op_xmm_xmm 11) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_VPaddd (va_op_xmm_xmm 12) (va_op_xmm_xmm 10) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_VPaddd (va_op_xmm_xmm 13) (va_op_xmm_xmm 11) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_VPxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_opr128_xmm 15)) (va_CCons\n (va_code_VPaddd (va_op_xmm_xmm 14) (va_op_xmm_xmm 12) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 12) (va_op_xmm_xmm 12) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_VPxor (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_opr128_xmm 15)) (va_CCons\n (va_code_VPaddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 13) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 13) (va_op_xmm_xmm 13) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 14) (va_op_xmm_xmm 14) (va_op_xmm_xmm 0)) (va_CCons\n (va_code_VPshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_CNil\n ()))))))))))))))))))))", "val va_code_load_one_msb : va_dummy:unit -> Tot va_code\nlet va_code_load_one_msb () =\n (va_Block (va_CCons (va_code_ZeroXmm (va_op_xmm_xmm 2)) (va_CCons (va_code_PinsrqImm\n (va_op_xmm_xmm 2) 72057594037927936 1 (va_op_reg_opr64_reg64 rR11)) (va_CNil ()))))", "val va_code_mod_6 : va_dummy:unit -> Tot va_code\nlet va_code_mod_6 () =\n (va_Block (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 26) 21845) (va_CCons (va_code_AddImm\n (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26) 21845) (va_CCons (va_code_Sl64Imm\n (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 26) 32) (va_CCons (va_code_Add (va_op_reg_opr_reg 26)\n (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg\n 10) (-1)) (va_CCons (va_code_Sub (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 10)\n (va_op_reg_opr_reg 26)) (va_CCons (va_code_AddImm (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26)\n 1) (va_CCons (va_code_MulHigh64U (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 26)) (va_CCons (va_code_Sr64Imm (va_op_reg_opr_reg 10) (va_op_reg_opr_reg\n 10) 2) (va_CCons (va_code_AddWrap (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 10)\n (va_op_reg_opr_reg 10)) (va_CCons (va_code_AddWrap (va_op_reg_opr_reg 26) (va_op_reg_opr_reg\n 26) (va_op_reg_opr_reg 10)) (va_CCons (va_code_AddWrap (va_op_reg_opr_reg 26)\n (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26)) (va_CCons (va_code_SubWrap (va_op_reg_opr_reg\n 26) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 26)) (va_CNil ())))))))))))))))", "val va_code_ShiftLeft128_1 : va_dummy:unit -> Tot va_code\nlet va_code_ShiftLeft128_1 () =\n (va_Block (va_CCons (va_code_Vspltisb (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_Vsl\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2)) (va_CNil ()))))", "val va_code_ShiftLeft128_1 : va_dummy:unit -> Tot va_code\nlet va_code_ShiftLeft128_1 () =\n (va_Block (va_CCons (va_code_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_CCons (va_code_Psrld\n (va_op_xmm_xmm 2) 31) (va_CCons (va_code_Pslld (va_op_xmm_xmm 1) 1) (va_CCons (va_code_VPslldq4\n (va_op_xmm_xmm 2) (va_op_xmm_xmm 2)) (va_CCons (va_code_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm\n 2)) (va_CNil ())))))))", "val va_code_CreateHeaplets : va_dummy:unit -> Tot va_code\nlet va_code_CreateHeaplets () =\n (Ins (S.Ghost ()))", "val va_code_CreateHeaplets : va_dummy:unit -> Tot va_code\nlet va_code_CreateHeaplets () =\n (mk_ins (make_instr_annotate (I.ins_Ghost) (S.AnnotateGhost ())))", "val va_code_Load_one_msb : va_dummy:unit -> Tot va_code\nlet va_code_Load_one_msb () =\n (va_Block (va_CCons (va_code_ZeroXmm (va_op_xmm_xmm 2)) (va_CCons (va_code_PinsrqImm\n (va_op_xmm_xmm 2) 72057594037927936 1 (va_op_reg_opr64_reg64 rR11)) (va_CNil ()))))", "val va_code_Gcm_blocks : alg:algorithm -> Tot va_code\nlet va_code_Gcm_blocks alg =\n (va_Block (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 5)\n (va_op_reg_opr_reg 25) (11 `op_Multiply` 8) Secret) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25) (0 `op_Multiply` 8)\n Secret) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 25) (6 `op_Multiply` 8) Secret) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25) (7 `op_Multiply` 8)\n Secret) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 9)\n (va_op_reg_opr_reg 25) (8 `op_Multiply` 8) Secret) (va_CCons (va_code_Gcm_blocks_auth ())\n (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 10)\n (va_op_reg_opr_reg 25) (9 `op_Multiply` 8) Secret) (va_CCons (va_code_Load128_byte16_buffer\n (va_op_heaplet_mem_heaplet 2) (va_op_vec_opr_vec 7) (va_op_reg_opr_reg 10) Public) (va_CCons\n (va_code_Vmr (va_op_vec_opr_vec 21) (va_op_vec_opr_vec 7)) (va_CCons (va_code_Load_one_lsb\n (va_op_vec_opr_vec 10)) (va_CCons (va_code_Vadduwm (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 7)\n (va_op_vec_opr_vec 10)) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 25) (1 `op_Multiply` 8) Secret) (va_CCons\n (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (2 `op_Multiply` 8) Secret) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25) (3 `op_Multiply` 8) Secret) (va_CCons\n (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25)\n (10 `op_Multiply` 8) Secret) (va_CCons (va_code_Gcm_blocks128 alg) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25) (3 `op_Multiply` 8)\n Secret) (va_CCons (va_code_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 4) (va_CCons\n (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (5 `op_Multiply` 8) Secret) (va_CCons (va_IfElse (va_cmp_gt (va_op_cmp_reg 6) (va_op_cmp_reg\n 7)) (va_Block (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 25) (4 `op_Multiply` 8) Secret) (va_CCons (va_code_LoadImm64\n (va_op_reg_opr_reg 10) 15) (va_CCons (va_code_And (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 10)) (va_CCons (va_code_Gcm_extra_bytes alg) (va_CCons (va_Block (va_CNil\n ())) (va_CNil ()))))))) (va_Block (va_CNil ()))) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25) (8 `op_Multiply` 8)\n Secret) (va_CCons (va_code_Gcm_make_length_quad ()) (va_CCons (va_code_Ghash_register ())\n (va_CCons (va_code_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 21)) (va_CCons\n (va_code_Gctr_register alg) (va_CCons (va_Block (va_CNil ())) (va_CNil\n ()))))))))))))))))))))))))))))", "val va_code_Sha_update : va_dummy:unit -> Tot va_code\nlet va_code_Sha_update () =\n (va_Block (va_CCons (va_code_Preamble ()) (va_CCons (va_code_Loop ()) (va_CCons (va_code_Epilogue\n ()) (va_CNil ())))))", "val va_code_Sha_update : va_dummy:unit -> Tot va_code\nlet va_code_Sha_update () =\n (va_Block (va_CCons (va_code_Preamble ()) (va_CCons (va_code_Loop ()) (va_CCons (va_code_Epilogue\n ()) (va_CNil ())))))", "val va_code_Cswap2 : va_dummy:unit -> Tot va_code\nlet va_code_Cswap2 () =\n (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Comment\n \"Transfer bit into CF flag\"\n ) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRdi) (va_const_opr64\n 18446744073709551615)) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"cswap p1[0], p2[0]\"\n ) (va_CCons (va_code_Cswap_single 0) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"cswap p1[1], p2[1]\"\n ) (va_CCons (va_code_Cswap_single 1) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"cswap p1[2], p2[2]\"\n ) (va_CCons (va_code_Cswap_single 2) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"cswap p1[3], p2[3]\"\n ) (va_CCons (va_code_Cswap_single 3) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"cswap p1[4], p2[4]\"\n ) (va_CCons (va_code_Cswap_single 4) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"cswap p1[5], p2[5]\"\n ) (va_CCons (va_code_Cswap_single 5) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"cswap p1[6], p2[6]\"\n ) (va_CCons (va_code_Cswap_single 6) (va_CCons (va_code_Newline ()) (va_CCons (va_code_Comment\n \"cswap p1[7], p2[7]\"\n ) (va_CCons (va_code_Cswap_single 7) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil\n ()))))))))))))))))))))))))))))))", "val va_code_InnerMemcpy : va_dummy:unit -> Tot va_code\nlet va_code_InnerMemcpy () =\n (va_Block (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64\n rRax) (va_op_reg_opr64_reg64 rRdx) 0 Secret) (va_CCons (va_code_Load64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9) (va_op_reg_opr64_reg64 rRdx) 8\n Secret) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64\n rRcx) (va_op_reg_opr64_reg64 rRax) 0 Secret) (va_CCons (va_code_Store64_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_reg_opr64_reg64 rR9) 8\n Secret) (va_CNil ()))))))" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_code_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_codegen_success_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_code_Gcm_auth_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_code_Gcm_blocks_auth" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_code_Gf128MulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_code_Gf128MulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fsti", "name": "Vale.AES.X64.GCMencryptOpt.va_quick_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fsti", "name": "Vale.AES.PPC64LE.GCMencrypt.va_quick_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.va_code_Fast_sqr_part2" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_code_Ghash_extra_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_code_Ghash_buffer" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt2.fst", "name": "Vale.AES.X64.AESopt2.va_code_Ghash_buffer" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_code_Compute_ghash_incremental_register" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_code_Ghash_register" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt2.fst", "name": "Vale.AES.X64.AESopt2.va_code_Ghash_register" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Init.fst", "name": "Vale.AES.PPC64LE.GF128_Init.va_code_Gf128_powers" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Init.fst", "name": "Vale.AES.X64.GF128_Init.va_code_Gf128_powers" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_code_Compute_pad_to_128_bits" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_code_Clmul128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_code_Clmul128" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_code_Xgetbv_Avx512" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt2.fst", "name": "Vale.AES.X64.AESopt2.va_code_Ghash_buffer_body0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_code_Ghash_buffer_body0" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.fst", "name": "Vale.SHA.PPC64LE.va_code_Preamble" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_code_Preamble" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt2.fst", "name": "Vale.AES.X64.AESopt2.va_code_GhashUnroll6x" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_code_Newline" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fst", "name": "Vale.Curve25519.X64.FastWide.va_code_Fmul" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_code_Compute_iv" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_code_ClmulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_code_ClmulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_code_Fadd" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.AES256.fst", "name": "Vale.AES.PPC64LE.AES256.va_code_KeyExpansion256Stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_code_Ghash_buffer_loop_body" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt2.fst", "name": "Vale.AES.X64.AESopt2.va_code_Ghash_buffer_loop_body" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_code_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_code_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_code_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESCTR.fst", "name": "Vale.AES.X64.AESCTR.va_code_Aes_ctr_ghash" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_code_ClmulRev64High" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.AES128.fst", "name": "Vale.AES.PPC64LE.AES128.va_code_KeyExpansion128Stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_code_Xgetbv_Avx" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_code_MulAdd_unroll_1way" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_code_MulAdd_unroll_2way" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_code_Loop_rounds_52_64" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_code_Store4" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_code_Poly1305_multiply" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_code_Loop" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_code_Loop" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fst", "name": "Vale.AES.X64.GCTR.va_code_Init_ctr" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fst", "name": "Vale.Curve25519.X64.FastWide.va_code_Fmul2" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_code_NoNewline" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.fst", "name": "Vale.SHA.PPC64LE.Rounds.va_code_Loop_rounds_48_63" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_code_Store_3blocks128_2" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_code_Check_avx512_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_lemma_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_code_Store_3blocks128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_code_Ghash_buffer_while0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt2.fst", "name": "Vale.AES.X64.AESopt2.va_code_Ghash_buffer_while0" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fst", "name": "Vale.Curve25519.X64.FastWide.va_code_Fsqr" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_code_ReduceMulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_code_ReduceMulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_code_Check_avx512_xcr0_support" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fst", "name": "Vale.Curve25519.X64.FastWide.va_code_Fsqr2" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_code_Loop_rounds" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_code_Loop_rounds" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_code_ShiftLeft2_128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_code_ShiftLeft2_128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESGCM.fst", "name": "Vale.AES.X64.AESGCM.va_code_Handle_ctr32_2" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_code_ReduceMul128_LE" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESCTR.fst", "name": "Vale.AES.X64.AESCTR.va_code_Aes_3rounds_4way" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_code_Check_avx2_support" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_code_Check_avx_xcr0_support" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_code_Fsub" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMdecrypt.fst", "name": "Vale.AES.PPC64LE.GCMdecrypt.va_code_Nat64Equal" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESCTR.fst", "name": "Vale.AES.X64.AESCTR.va_code_Aes_4rounds_4way" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_code_Reduce" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_code_Loop_rounds_1_3" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESCTR.fst", "name": "Vale.AES.X64.AESCTR.va_code_Aes_2rounds_4way" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_code_Loop_rounds_16_51" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_code_Loop_prologue" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_code_Compute_Y0" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_code_Fmul1" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_code_Poly1305_impl" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_code_Check_avx_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt2.fst", "name": "Vale.AES.X64.AESopt2.va_code_MulAdd_unroll" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_code_Handle_ctr32" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_code_load_one_msb" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_code_mod_6" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_code_ShiftLeft128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_code_ShiftLeft128_1" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsMem.fst", "name": "Vale.PPC64LE.InsMem.va_code_CreateHeaplets" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsMem.fst", "name": "Vale.X64.InsMem.va_code_CreateHeaplets" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESGCM.fst", "name": "Vale.AES.X64.AESGCM.va_code_Load_one_msb" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMdecrypt.fst", "name": "Vale.AES.PPC64LE.GCMdecrypt.va_code_Gcm_blocks" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.fst", "name": "Vale.SHA.PPC64LE.va_code_Sha_update" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_code_Sha_update" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_code_Cswap2" }, { "project_name": "hacl-star", "file_name": "Vale.Test.X64.Vale_memcpy.fst", "name": "Vale.Test.X64.Vale_memcpy.va_code_InnerMemcpy" } ], "selected_premises": [ "Vale.PPC64LE.Decls.va_CNil", "Vale.PPC64LE.Decls.va_Block", "Vale.PPC64LE.Decls.va_CCons", "Vale.PPC64LE.Decls.va_get_block", "Vale.AES.PPC64LE.GCMencrypt.va_code_Gcm_auth_bytes", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.AES.PPC64LE.GCMencrypt.va_code_Gcm_blocks128", "Vale.AES.PPC64LE.GCMencrypt.va_code_Load_one_lsb", "Vale.X64.Machine_s.rRdx", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRcx", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.X64.Machine_s.rRax", "Vale.X64.Machine_s.rR9", "Vale.X64.Machine_s.rR13", "Vale.X64.Machine_s.rRsi", "Vale.PPC64LE.Decls.va_op_heaplet_mem_heaplet", "Vale.X64.Machine_s.rRbp", "Vale.X64.Machine_s.rR11", "Vale.X64.Machine_s.rR8", "Vale.X64.Machine_s.rR10", "Vale.X64.Machine_s.rR15", "Vale.X64.Machine_s.rR14", "Vale.X64.Machine_s.rR12", "Vale.X64.Machine_s.rRdi", "Vale.X64.Machine_s.rRsp", "Vale.PPC64LE.Decls.va_tl", "Vale.PPC64LE.Decls.va_op_cmp_reg", "Vale.PPC64LE.QuickCodes.label", "Vale.PPC64LE.Decls.va_require_total", "Vale.PPC64LE.QuickCodes.va_range1", "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.Decls.va_get_reg", "Vale.PPC64LE.Decls.va_if", "Vale.PPC64LE.Decls.va_get_vec", "Vale.PPC64LE.Decls.va_get_ok", "Vale.AES.PPC64LE.GCMencrypt.va_qcode_Gcm_blocks128", "Vale.X64.Machine_s.reg_64", "Vale.PPC64LE.Decls.va_get_mem_heaplet", "Vale.PPC64LE.QuickCode.va_Mod_mem_heaplet", "Vale.PPC64LE.QuickCode.va_Mod_ok", "Vale.PPC64LE.Decls.va_state", "Vale.PPC64LE.Decls.va_upd_reg", "Vale.AES.PPC64LE.AES.va_req_KeyExpansionStdcall", "Vale.X64.Machine_s.operand128", "Vale.PPC64LE.Decls.va_get_mem_layout", "Vale.PPC64LE.Decls.va_const_cmp", "Vale.PPC64LE.Decls.va_mul_nat", "Vale.PPC64LE.Decls.va_reveal_opaque", "Vale.X64.Machine_s.reg_xmm", "Vale.PPC64LE.QuickCodes.va_QSeq", "Vale.AES.PPC64LE.GCMencrypt.va_qcode_Gcm_auth_bytes", "Vale.PPC64LE.QuickCode.va_Mod_mem_layout", "Vale.PPC64LE.QuickCodes.va_qPURE", "Vale.PPC64LE.Decls.va_eval_vec_opr", "Vale.PPC64LE.Decls.va_upd_vec", "Vale.Def.Words_s.nat64", "Vale.PPC64LE.QuickCodes.va_QEmpty", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Vale.AES.GCM_BE_s.gcm_encrypt_BE", "Vale.PPC64LE.QuickCode.va_Mod_mem", "Vale.PPC64LE.QuickCodes.va_QBind", "Vale.PPC64LE.QuickCode.va_Mod_reg", "Lib.IntTypes.u64", "Vale.PPC64LE.Decls.va_is_dst_vec_opr", "Vale.X64.Machine_s.nat64", "Vale.Def.Types_s.nat64", "Vale.PPC64LE.Memory.nat64", "Vale.PPC64LE.Machine_s.nat64", "Vale.PPC64LE.Decls.va_upd_cr0", "Vale.PPC64LE.Decls.va_expand_state", "Vale.PPC64LE.Decls.va_value_reg_opr", "Vale.PPC64LE.Decls.va_value_vec_opr", "Vale.PPC64LE.Decls.va_is_dst_reg_opr", "Vale.PPC64LE.Decls.va_eval_reg_opr", "Vale.PPC64LE.Decls.va_While", "Vale.PPC64LE.QuickCodes.va_QLemma", "Vale.X64.Machine_s.operand64", "Vale.AES.GCM_BE_s.gcm_decrypt_BE", "Vale.PPC64LE.QuickCode.quickProc_wp", "Vale.AES.GCM_BE_s.gcm_decrypt_BE_reveal", "Vale.Def.Words_s.nat32", "Vale.PPC64LE.Machine_s.quad32", "Vale.PPC64LE.Memory.quad32", "Vale.X64.Machine_s.quad32", "Vale.PPC64LE.QuickCode.va_Mod_xer", "Vale.SHA.PPC64LE.SHA_helpers.hash256", "Vale.PPC64LE.QuickCode.va_Mod_cr0", "Vale.AES.PPC64LE.GCMencrypt.va_lemma_Gcm_auth_bytes", "Vale.PPC64LE.Decls.va_upd_operand_reg_opr", "Vale.SHA.PPC64LE.SHA_helpers.repeat_range_vale_64", "Vale.PPC64LE.Decls.va_is_src_reg_opr", "FStar.List.Tot.Base.map", "Vale.PPC64LE.QuickCodes.block", "FStar.List.Tot.Base.length", "Vale.AES.GCTR_BE.gctr_partial", "Vale.PPC64LE.Decls.va_opr_code_Mem64", "Vale.PPC64LE.Decls.va_int_range", "Vale.AES.GCM_BE_s.gcm_encrypt_BE_reveal", "Vale.AES.GCTR_BE.gctr_partial_reveal" ], "source_upto_this": "module Vale.AES.PPC64LE.GCMencrypt\nopen Vale.Def.Prop_s\nopen Vale.Def.Opaque_s\nopen FStar.Seq\nopen Vale.Def.Words_s\nopen Vale.Def.Words.Seq_s\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Arch.HeapImpl\nopen Vale.AES.AES_BE_s\nopen Vale.AES.GCTR_BE_s\nopen Vale.AES.GCTR_BE\nopen Vale.AES.GCM_BE\nopen Vale.AES.GHash_BE_s\nopen Vale.AES.GHash_BE\nopen Vale.AES.GCM_BE_s\nopen Vale.AES.PPC64LE.AES\nopen Vale.AES.GF128_s\nopen Vale.AES.GF128\nopen Vale.Poly1305.Math\nopen Vale.AES.GCM_helpers_BE\nopen Vale.AES.PPC64LE.GCTR\nopen Vale.PPC64LE.Machine_s\nopen Vale.PPC64LE.Memory\nopen Vale.PPC64LE.Stack_i\nopen Vale.PPC64LE.State\nopen Vale.PPC64LE.Decls\nopen Vale.PPC64LE.InsBasic\nopen Vale.PPC64LE.InsMem\nopen Vale.PPC64LE.InsVector\nopen Vale.PPC64LE.InsStack\nopen Vale.PPC64LE.QuickCode\nopen Vale.PPC64LE.QuickCodes\nopen Vale.AES.PPC64LE.GF128_Mul\nopen Vale.Math.Poly2.Bits_s\nopen Vale.AES.PPC64LE.GHash\nopen Vale.Lib.Meta\nopen Vale.AES.OptPublic_BE\nopen Vale.Lib.Basic\n#reset-options \"--z3rlimit 2000 --fuel 10 --ifuel 10 --max_fuel 100 --max_ifuel 100\"\n//-- Load_one_lsb\n\n[@ \"opaque_to_smt\"]\nlet va_code_Load_one_lsb dst =\n (va_Block (va_CCons (va_code_Vspltisw dst 1) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 4) 0)\n (va_CCons (va_code_Vsldoi dst (va_op_vec_opr_vec 4) dst 4) (va_CNil ())))))\n\n[@ \"opaque_to_smt\"]\nlet va_codegen_success_Load_one_lsb dst =\n (va_pbool_and (va_codegen_success_Vspltisw dst 1) (va_pbool_and (va_codegen_success_Vspltisw\n (va_op_vec_opr_vec 4) 0) (va_pbool_and (va_codegen_success_Vsldoi dst (va_op_vec_opr_vec 4) dst\n 4) (va_ttrue ()))))\n\n[@\"opaque_to_smt\"]\nlet va_lemma_Load_one_lsb va_b0 va_s0 dst =\n va_reveal_opaque (`%va_code_Load_one_lsb) (va_code_Load_one_lsb dst);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (va_s2, va_fc2) = va_lemma_Vspltisw (va_hd va_b1) va_s0 dst 1 in\n let va_b2 = va_tl va_b1 in\n let (va_s3, va_fc3) = va_lemma_Vspltisw (va_hd va_b2) va_s2 (va_op_vec_opr_vec 4) 0 in\n let va_b3 = va_tl va_b2 in\n let (va_s4, va_fc4) = va_lemma_Vsldoi (va_hd va_b3) va_s3 dst (va_op_vec_opr_vec 4) dst 4 in\n let va_b4 = va_tl va_b3 in\n let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in\n let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in\n let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in\n (va_sM, va_fM)\n\n\n[@\"opaque_to_smt\"]\nlet va_wpProof_Load_one_lsb dst va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Load_one_lsb (va_code_Load_one_lsb dst) va_s0 dst in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_vec 4 va_sM (va_update_ok va_sM (va_update_operand_vec_opr\n dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_vec 4; va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n//--\n//-- Gcm_blocks128\n\nval va_code_Gcm_blocks128 : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_blocks128 alg =\n (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_CCons\n (va_code_Gctr_blocks128 alg) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec\n 7)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_CCons\n (va_code_Ghash_buffer ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15))\n (va_CNil ()))))))))\n\nval va_codegen_success_Gcm_blocks128 : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_blocks128 alg =\n (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_pbool_and\n (va_codegen_success_Gctr_blocks128 alg) (va_pbool_and (va_codegen_success_Vmr\n (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_pbool_and (va_codegen_success_Vmr\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_pbool_and (va_codegen_success_Ghash_buffer\n ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15))\n (va_ttrue ())))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_blocks128 (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 167 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 168 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Gctr_blocks128 alg in_b out_b key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 169 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 170 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b out_b h_BE (va_get_vec 1 va_old_s)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 172 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15)) (va_QEmpty (())))))))))\n\n\nval va_lemma_Gcm_blocks128 : va_b0:va_code -> va_s0:va_state -> alg:algorithm -> in_b:buffer128 ->\n out_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks128 alg) va_s0 /\\ va_get_ok va_s0 /\\\n ((Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) in_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b (va_get_reg 6 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ l_and\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out_b))))) /\\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM\n (va_update_vec 20 va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM\n (va_update_vec 16 va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM\n (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM\n (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM\n (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM\n (va_update_vec 0 va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM\n (va_update_reg 28 va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM\n (va_update_reg 9 va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM\n (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_blocks128 va_b0 va_s0 alg in_b out_b key round_keys keys_b hkeys_b h_BE =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19;\n va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13;\n va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7;\n va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec\n 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26;\n va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem] in\n let va_qc = va_qcode_Gcm_blocks128 va_mods alg in_b out_b key round_keys keys_b hkeys_b h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_blocks128 alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 114 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 156 column 53 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 159 column 147 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 160 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite (va_get_vec 7 va_s0) (va_get_reg 6 va_s0)) /\\\n label va_range1\n \"***** POSTCONDITION NOT MET AT line 163 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1 va_sM == va_get_vec 1 va_s0)\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b == Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) out_b)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 165 column 109 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 6 va_s0 > 0 ==> l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==>\n FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0\n (va_get_reg 6 va_s0)) > 0) (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE\n (va_get_vec 1 va_s0) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_sM) out_b)))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok; va_Mod_mem])\n va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ ((Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) in_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b (va_get_reg 6 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ l_and\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret) /\\ (forall (va_x_mem:vale_heap)\n (va_x_r3:nat64) (va_x_r7:nat64) (va_x_r6:nat64) (va_x_r8:nat64) (va_x_r9:nat64)\n (va_x_r10:nat64) (va_x_r26:nat64) (va_x_r27:nat64) (va_x_r28:nat64) (va_x_r29:nat64)\n (va_x_r30:nat64) (va_x_r31:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32) (va_x_v17:quad32)\n (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32) (va_x_cr0:cr0_t) (va_x_heap1:vale_heap) .\n let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_cr0 va_x_cr0 (va_upd_vec 20 va_x_v20\n (va_upd_vec 19 va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16\n (va_upd_vec 15 va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12\n (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8\n (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4\n (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0\n (va_upd_reg 31 va_x_r31 (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29 (va_upd_reg 28 va_x_r28\n (va_upd_reg 27 va_x_r27 (va_upd_reg 26 va_x_r26 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9\n (va_upd_reg 8 va_x_r8 (va_upd_reg 6 va_x_r6 (va_upd_reg 7 va_x_r7 (va_upd_reg 3 va_x_r3\n (va_upd_mem va_x_mem va_s0))))))))))))))))))))))))))))))))))) in va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out_b))))) ==> va_k va_sM (())))\n\n\nval va_wpProof_Gcm_blocks128 : alg:algorithm -> in_b:buffer128 -> out_b:buffer128 -> key:(seq\n nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks128 alg)\n ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0,\n va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_blocks128 (va_code_Gcm_blocks128 alg) va_s0 alg in_b out_b key\n round_keys keys_b hkeys_b h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM (va_update_reg 3\n va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))))))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) : (va_quickCode\n unit (va_code_Gcm_blocks128 alg)) =\n (va_QProc (va_code_Gcm_blocks128 alg) ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20;\n va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14;\n va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8;\n va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec\n 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27;\n va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7;\n va_Mod_reg 3; va_Mod_mem]) (va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE) (va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE))\n//--\n//-- Gcm_auth_bytes\n\nval va_code_Gcm_auth_bytes : va_dummy:unit -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_auth_bytes () =\n (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Ghash_buffer\n ()) (va_CNil ()))))\n\nval va_codegen_success_Gcm_auth_bytes : va_dummy:unit -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_auth_bytes () =\n (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and\n (va_codegen_success_Ghash_buffer ()) (va_ttrue ())))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_auth_bytes (va_mods:va_mods_t) (auth_b:buffer128) (hkeys_b:buffer128)\n (h_BE:quad32) : (va_quickCode (quad32 & quad32) (va_code_Gcm_auth_bytes ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 206 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (fun (va_s:va_state) _ -> let (y_0:quad32) =\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 208 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b auth_b h_BE y_0) (fun (va_s:va_state) _ -> let (y_auth:quad32) =\n va_get_vec 1 va_s in va_QEmpty ((y_0, y_auth))))))\n\n\nval va_lemma_Gcm_auth_bytes : va_b0:va_code -> va_s0:va_state -> auth_b:buffer128 ->\n hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel & quad32 & quad32)\n (requires (va_require_total va_b0 (va_code_Gcm_auth_bytes ()) va_s0 /\\ va_get_ok va_s0 /\\\n (Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) (va_get_reg 7 va_s0) auth_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == va_get_reg 6 va_s0 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64)))\n (ensures (fun (va_sM, va_fM, y_0, y_auth) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok\n va_sM /\\ (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 /\\ (let h_BE =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) /\\ va_get_vec 1 va_sM == y_auth)) /\\ va_state_eq va_sM (va_update_cr0 va_sM\n (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12 va_sM (va_update_vec 11 va_sM\n (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8 va_sM (va_update_vec 7 va_sM\n (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM\n (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM\n (va_update_reg 6 va_sM (va_update_reg 7 va_sM (va_update_ok va_sM va_s0))))))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_auth_bytes va_b0 va_s0 auth_b hkeys_b h_BE =\n let (va_mods:va_mods_t) = [va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec\n 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5;\n va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg\n 6; va_Mod_reg 7; va_Mod_ok] in\n let va_qc = va_qcode_Gcm_auth_bytes va_mods auth_b hkeys_b h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_auth_bytes ()) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let (y_0, y_auth) = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 175 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 200 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 201 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (let h_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 202 column 95 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b))) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 203 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_vec 1 va_sM == y_auth)))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6;\n va_Mod_reg 7; va_Mod_ok]) va_sM va_s0;\n let (y_0, y_auth) = va_g in\n (va_sM, va_fM, y_0, y_auth)\n\n[@ va_qattr]\nlet va_wp_Gcm_auth_bytes (auth_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) (va_s0:va_state)\n (va_k:(va_state -> (quad32 & quad32) -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) (va_get_reg 7 va_s0) auth_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == va_get_reg 6 va_s0 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64) /\\ (forall (va_x_r7:nat64)\n (va_x_r6:nat64) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_cr0:cr0_t) (y_0:quad32) (y_auth:quad32) . let va_sM =\n va_upd_cr0 va_x_cr0 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12\n (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8\n (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4\n (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0\n (va_upd_reg 10 va_x_r10 (va_upd_reg 6 va_x_r6 (va_upd_reg 7 va_x_r7 va_s0)))))))))))))))))) in\n va_get_ok va_sM /\\ (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 /\\ (let h_BE\n = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) /\\ va_get_vec 1 va_sM == y_auth)) ==> va_k va_sM ((y_0, y_auth))))\n\n\nval va_wpProof_Gcm_auth_bytes : auth_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32 ->\n va_s0:va_state -> va_k:(va_state -> (quad32 & quad32) -> Type0)\n -> Ghost (va_state & va_fuel & (quad32 & quad32))\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_auth_bytes auth_b hkeys_b h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_auth_bytes ()) ([va_Mod_cr0;\n va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9;\n va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec\n 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6; va_Mod_reg 7]) va_s0 va_k ((va_sM,\n va_f0, va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_auth_bytes auth_b hkeys_b h_BE va_s0 va_k =\n let (va_sM, va_f0, y_0, y_auth) = va_lemma_Gcm_auth_bytes (va_code_Gcm_auth_bytes ()) va_s0\n auth_b hkeys_b h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_cr0 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM\n (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM\n (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM\n (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM\n (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM\n (va_update_ok va_sM va_s0)))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6;\n va_Mod_reg 7]) va_sM va_s0;\n let va_g = (y_0, y_auth) in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_auth_bytes (auth_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) : (va_quickCode\n (quad32 & quad32) (va_code_Gcm_auth_bytes ())) =\n (va_QProc (va_code_Gcm_auth_bytes ()) ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 10; va_Mod_reg 6; va_Mod_reg 7]) (va_wp_Gcm_auth_bytes auth_b hkeys_b h_BE)\n (va_wpProof_Gcm_auth_bytes auth_b hkeys_b h_BE))\n//--\n//-- Gcm_make_length_quad\n\n[@ \"opaque_to_smt\" va_qattr]" }, { "file_name": "FStar.SquashProperties.fst", "name": "FStar.SquashProperties.l1", "opens_and_abbrevs": [ { "open": "FStar.Squash" }, { "open": "FStar.Constructive" }, { "open": "FStar" }, { "open": "FStar" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val l1: (a:Type0) -> (b:Type0) -> GTot (squash (retract_cond (pow a) (pow b)))", "source_definition": "let l1 (a:Type) (b:Type) =\n bind_squash (excluded_middle_squash (retract (pow a) (pow b))) \n\t (fun (x:Prims.sum (retract (pow a) (pow b)) (~ (retract (pow a) (pow b)))) ->\n\t match x with\n\t\t | Prims.Left (MkR f0 g0 e) -> \n\t\t return_squash (MkC f0 g0 (fun _ -> e))\n\t\t | Prims.Right nr ->\n\t\t let f0 (x:pow a) (y:b) = false in\n\t\t let g0 (x:pow b) (y:a) = false in\n\t\t map_squash nr (fun (f:(retract (pow a) (pow b) -> GTot False)) -> \n\t\t\t\t MkC f0 g0 (fun r x -> false_elim (f r))))", "source_range": { "start_line": 108, "start_col": 0, "end_line": 118, "end_col": 47 }, "interleaved": false, "definition": "fun a b ->\n FStar.Squash.bind_squash (FStar.SquashProperties.excluded_middle_squash (FStar.SquashProperties.retract\n (FStar.SquashProperties.pow a)\n (FStar.SquashProperties.pow b)))\n (fun x ->\n (match x with\n | Prims.Left #_ #_ (FStar.SquashProperties.MkR #_ #_ f0 g0 e) ->\n FStar.Squash.return_squash (FStar.SquashProperties.MkC f0 g0 (fun _ -> e))\n | Prims.Right #_ #_ nr ->\n let f0 x y = false in\n let g0 x y = false in\n FStar.Squash.map_squash nr\n (fun f ->\n FStar.SquashProperties.MkC f0\n g0\n (fun r x -> FStar.SquashProperties.false_elim (f r))))\n <:\n Prims.squash (FStar.SquashProperties.retract_cond (FStar.SquashProperties.pow a)\n (FStar.SquashProperties.pow b)))", "effect": "Prims.GTot", "effect_flags": [ "sometrivial" ], "mutual_with": [], "premises": [ "FStar.Squash.bind_squash", "Prims.sum", "FStar.SquashProperties.retract", "FStar.SquashProperties.pow", "Prims.l_not", "FStar.SquashProperties.retract_cond", "FStar.SquashProperties.excluded_middle_squash", "FStar.Constructive.ceq", "FStar.Squash.return_squash", "FStar.SquashProperties.MkC", "FStar.Squash.map_squash", "Prims.l_False", "FStar.SquashProperties.false_elim", "Prims.bool", "Prims.squash" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "a: Type0 -> b: Type0\n -> Prims.GTot\n (Prims.squash (FStar.SquashProperties.retract_cond (FStar.SquashProperties.pow a)\n (FStar.SquashProperties.pow b)))", "prompt": "let l1 (a b: Type) =\n ", "expected_response": "bind_squash (excluded_middle_squash (retract (pow a) (pow b)))\n (fun (x: Prims.sum (retract (pow a) (pow b)) (~(retract (pow a) (pow b)))) ->\n match x with\n | Prims.Left (MkR f0 g0 e) -> return_squash (MkC f0 g0 (fun _ -> e))\n | Prims.Right nr ->\n let f0 (x: pow a) (y: b) = false in\n let g0 (x: pow b) (y: a) = false in\n map_squash nr\n (fun (f: (retract (pow a) (pow b) -> GTot False)) ->\n MkC f0 g0 (fun r x -> false_elim (f r))))", "source": { "project_name": "FStar", "file_name": "ulib/FStar.SquashProperties.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.SquashProperties.fst", "checked_file": "dataset/FStar.SquashProperties.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Squash.fsti.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Constructive.fst.checked" ] }, "definitions_in_context": [ "val join_squash : #a:Type -> squash (squash a) -> GTot (squash a)", "let join_squash #a s = bind_squash #(squash a) #a s (fun x -> x)", "val squash_arrow : #a:Type -> #p:(a -> Type) ->\n $f:(x:a -> GTot (squash (p x))) -> GTot (squash (x:a -> GTot (p x)))", "let squash_arrow #a #p f = squash_double_arrow (return_squash f)", "val forall_intro : #a:Type -> #p:(a -> Type) ->\n $f:(x:a -> Lemma (p x)) -> Lemma (x:a -> GTot (p x))", "let forall_intro #a #p f =\n let ff : (x:a -> GTot (squash (p x))) = (fun x -> f x; get_proof (p x)) in\n give_proof #(x:a -> GTot (p x)) (squash_arrow #a #p ff)", "val bool_of_or : #p:Type -> #q:Type -> Prims.sum p q ->\n Tot (b:bool{(b ==> p) /\\ (not(b) ==> q)})", "let bool_of_or #p #q t =\n match t with\n | Prims.Left _ -> true\n | Prims.Right _ -> false", "val excluded_middle : p:Type -> GTot (squash (b:bool{b <==> p}))", "let excluded_middle (p:Type) = map_squash (join_squash (get_proof (p \\/ (~p)))) bool_of_or", "val excluded_middle_squash : p:Type0 -> GTot (p \\/ ~p)", "let excluded_middle_squash p =\n bind_squash (excluded_middle p) (fun x ->\n if x then\n map_squash (get_proof p) (Prims.Left #p)\n else\n return_squash (Prims.Right #_ #(~p) (return_squash (fun (h:p) ->\n give_proof (return_squash h);\n false_elim #False ()))))", "val ifProp: #p:Type0 -> b:Type0 -> e1:squash p -> e2:squash p -> GTot (squash p)", "let ifProp #p b e1 e2 =\n bind_squash (excluded_middle_squash b) \n\t (fun (x:Prims.sum b (~ b)) -> \n\t\tmatch x with\n\t | Prims.Left _ -> e1\n\t\t| Prims.Right _ -> e2)", "pow", "retract", "MkR", "MkR", "MkR", "i", "i", "j", "j", "inv", "inv", "retract_cond", "MkC", "MkC", "MkC", "i2", "i2", "j2", "j2", "inv2", "inv2", "val ac: r:retract_cond 'a 'b -> retract 'a 'b -> x:'a ->\n GTot (ceq ((MkC?.j2 r) (MkC?.i2 r x)) x)", "let ac (MkC _ _ inv2) = inv2", "let false_elim (#a:Type) (f:False) : Tot a\n = match f with", "val l1: (a:Type0) -> (b:Type0) -> GTot (squash (retract_cond (pow a) (pow b)))" ], "closest": [ "val arrow_to_impl (#a #b: Type0) (_: (squash a -> GTot (squash b))) : GTot (a ==> b)\nlet arrow_to_impl #a #b f = squash_double_arrow (return_squash (fun x -> f (return_squash x)))", "val lemma_pow_gt_zero: a:pos -> b:nat -> Lemma (pow a b > 0) [SMTPat (pow a b)]\nlet rec lemma_pow_gt_zero a b =\n if b = 0 then lemma_pow0 a\n else begin\n lemma_pow_unfold a b;\n lemma_pow_gt_zero a (b - 1) end", "val lemma_as_squash (#a #b: _) (lem: (a -> Lemma b)) (x: a) : GTot (squash b)\nlet lemma_as_squash #a #b (lem: (a -> Lemma b)) (x:a)\n : GTot (squash b)\n = lem x", "val lem_ult_2 (a b: uint_t 64) : squash (not (bvult (int2bv a) (int2bv b)) ==> fact0 a b)\nlet lem_ult_2 (a b:uint_t 64)\n : squash (not (bvult (int2bv a) (int2bv b)) ==> fact0 a b)\n = assert (not (bvult (int2bv a) (int2bv b)) ==> fact0 a b)\n by (T.norm [delta_only [`%fact0;`%carry_bv]];\n set_options \"--smtencoding.elim_box true --using_facts_from '__Nothing__' --z3smtopt '(set-option :smt.case_split 1)'\")", "val lemma_as_squash (#a #b: _) ($lem: (a -> Lemma b)) (x: a) : GTot (squash b)\nlet lemma_as_squash #a #b ($lem: (a -> Lemma b)) (x:a)\n : GTot (squash b)\n = lem x", "val lem_ult_1 (a b: uint_t 64) : squash (bvult (int2bv a) (int2bv b) ==> fact1 a b)\nlet lem_ult_1 (a b: uint_t 64)\n : squash (bvult (int2bv a) (int2bv b) ==> fact1 a b)\n = assert (bvult (int2bv a) (int2bv b) ==> fact1 a b)\n by (T.norm [delta_only [`%fact1;`%carry_bv]];\n set_options \"--smtencoding.elim_box true --using_facts_from '__Nothing__' --z3smtopt '(set-option :smt.case_split 1)'\";\n smt())", "val elim_squash (#p:Type u#a) (s:squash p) : GTot p\nlet elim_squash (#p:Type u#a) (s:squash p) : GTot p =\n let uu : squash (x:p & squash trivial) =\n bind_squash s (fun x -> return_squash (| x, return_squash T |)) in\n give_proof (return_squash uu);\n indefinite_description_ghost p (fun _ -> squash trivial)", "val ( ^+^ )\n (#a #b: Type0)\n (#rel1: preorder a)\n (#rel2: preorder b)\n (r1: mref a rel1)\n (r2: mref b rel2)\n : GTot (set nat)\nlet op_Hat_Plus_Hat (#a:Type0) (#b:Type0) (#rel1:preorder a) (#rel2:preorder b) (r1:mref a rel1) (r2:mref b rel2)\n :GTot (set nat) = S.union (only r1) (only r2)", "val exp_pow2 (#t: Type) (k: comm_monoid t) (a: t) (b: nat) : t\nlet exp_pow2 (#t:Type) (k:comm_monoid t) (a:t) (b:nat) : t =\n Loops.repeat b (sqr k) a", "val exp_pow2 (#t: Type) (k: concrete_ops t) (a: t) (b: nat) : t\nlet exp_pow2 (#t:Type) (k:concrete_ops t) (a:t) (b:nat) : t =\n Loops.repeat b k.sqr a", "val lemma_pow_ge_zero: a:nat -> b:nat -> Lemma (pow a b >= 0) [SMTPat (pow a b)]\nlet rec lemma_pow_ge_zero a b =\n if b = 0 then lemma_pow0 a\n else begin\n lemma_pow_unfold a b;\n lemma_pow_ge_zero a (b - 1) end", "val pow (#t: Type) (k: concrete_ops t) (a: t) (b: nat) : t\nlet rec pow (#t:Type) (k:concrete_ops t) (a:t) (b:nat) : t =\n if b = 0 then k.one ()\n else k.mul a (pow k a (b - 1))", "val impl_to_arrow (#a #b: Type0) (_: (a ==> b)) (_: squash a) : Tot (squash b)\nlet impl_to_arrow #a #b impl sx =\n bind_squash #(a -> GTot b) impl (fun f -> bind_squash sx (fun x -> return_squash (f x)))", "val p (#a: Type0) (init: list a) : GTot Type0\nlet p (#a:Type0) (init:list a) : GTot Type0 =\n normalize (0 < FStar.List.Tot.length init) /\\\n normalize (FStar.List.Tot.length init <= UInt.max_int 32)", "val squash_double_arrow (#a: Type u#a) (#p: Type0) (f: (squash (a -> Tot (squash p))))\n : Tot (squash (a -> GTot p))\nlet squash_double_arrow (#a:Type u#a) (#p:Type0)\n (f:(squash (a -> Tot (squash p))))\n : Tot (squash (a -> GTot p)) =\n FStar.Squash.squash_double_arrow f", "val constr (a b: prop) : squash (a ==> b ==> b /\\ a)\nlet constr (a b : prop) : squash (a ==> b ==> b /\\ a)\n = _ by\n (let ha = implies_intro () in\n let hb = implies_intro () in\n split ();\n hyp (binding_to_namedv hb);\n hyp (binding_to_namedv ha);\n qed ())", "val lemma_to_squash_gtot (#a: Type) (#p: (a -> GTot Type)) ($_: (x: a -> Lemma (p x))) (x: a)\n : GTot (squash (p x))\nlet lemma_to_squash_gtot #a #p f x =\n f x;\n get_proof (p x)", "val mult_nat (a b: nat) : Tot (c: nat{c == a `Prims.op_Multiply` b})\nlet mult_nat (a b: nat) : Tot (c: nat { c == a `Prims.op_Multiply` b } ) = a `Prims.op_Multiply` b", "val get_squash (#a: Type) (r: binrel a) (x: a) (y: a{_closure0 r x y})\n : Tot (squash (_closure r x y))\nlet get_squash (#a:Type) (r:binrel a) (x:a) (y:a{_closure0 r x y})\n : Tot (squash (_closure r x y))\n = assert_norm (_closure0 r x y ==> squash (_closure r x y))", "val valid_baz_alt_alt (a: Type) (x: a) : GTot (squash (baz a x))\nlet valid_baz_alt_alt (a:Type) (x:a)\n : GTot (squash (baz a x))\n = let fb : squash (foo a x \\/ bar a x) = foo_or_bar x in\n FStar.Squash.join_squash\n (elim_squash_or fb\n (lemma_as_squash (c_foo_baz x))\n (lemma_as_squash (c_bar_baz x)))", "val length (#a:Type0) (v:vec a) : GTot nat\nlet length v = A.length v", "val lemma_mod_pow2 (a b: nat)\n : Lemma (requires a >= b) (ensures pow2 a % pow2 b == 0) [SMTPat (pow2 a % pow2 b)]\nlet lemma_mod_pow2 (a:nat) (b:nat) : Lemma\n (requires a >= b) (ensures pow2 a % pow2 b == 0)\n [SMTPat (pow2 a % pow2 b)]\n =\n let open FStar.Math.Lemmas in\n lemma_div_mod (pow2 a) (pow2 b);\n pow2_minus a b;\n pow2_plus b (a-b)", "val pow_lemma: #t:Type -> k:concrete_ops t -> a:t -> b:nat ->\n Lemma (k.to.refl (pow k a b) == S.pow k.to.comm_monoid (k.to.refl a) b)\nlet rec pow_lemma #t k a b =\n if b = 0 then ()\n else pow_lemma k a (b - 1)", "val items (#a: eqtype) (#b: Type u#b) (m: map a b)\n : GTot ((a * b) -> prop)\nlet items (#a: eqtype) (#b: Type u#b) (m: map a b) : GTot ((a * b) -> prop) =\n fun item -> ((elements m) (fst item) == Some (snd item))", "val map_squash (#a #b: Type) (x: squash a) (f: (a -> GTot b)) : Tot (squash b)\nlet map_squash (#a:Type) (#b:Type) s f =\n bind_squash #a #b s (fun x -> return_squash (f x))", "val t (a: Type0) : Tot Type0\nlet t a = cllist_lvalue a", "val pow2_le_recip (a b: nat) : Lemma (requires (pow2 a <= pow2 b)) (ensures (a <= b))\nlet pow2_le_recip\n (a b: nat)\n: Lemma\n (requires (pow2 a <= pow2 b))\n (ensures (a <= b))\n= Classical.move_requires (pow2_lt_compat a) b", "val lemma_pow_nat (a:nat) (b:nat) : Lemma (0 <= pow_int a b)\nlet rec lemma_pow_nat a b =\n if b > 0 then (\n lemma_pow_nat a (b - 1);\n FStar.Math.Lemmas.nat_times_nat_is_nat a (pow_int a (b - 1))\n )", "val h (a: alg) (b: hashable a) : GTot (tag a)\nlet h (a:alg) (b:hashable a): GTot (tag a) =\n let v = Spec.Agile.Hash.hash a (Bytes.reveal b) in\n Bytes.hide v", "val v (a: Type0) : Tot Type0\nlet v (a: Type0) = list a", "val mod_spec (a: nat{fits a}) (b: nat{fits b /\\ b <> 0}) : GTot (n: nat{fits n})\nlet mod_spec (a:nat{fits a}) (b:nat{fits b /\\ b <> 0}) : GTot (n:nat{fits n}) =\n let open FStar.Mul in\n let res = a - ((a/b) * b) in\n fits_lte res a;\n res", "val length (#a:Type0) (x:t a) : GTot nat\nlet length x = L.length x", "val on_g (a #b: Type) (f: (a -> GTot b)) : (a ^->> b)\nlet on_g (a #b: Type) (f: (a -> GTot b)) : (a ^->> b) = on_dom_g a f", "val get_squashed (#b a: Type) : Pure a (requires (a /\\ a == squash b)) (ensures (fun _ -> True))\nlet get_squashed #b a =\n let p = get_proof a in\n join_squash #b p", "val zip : (#a:Type) -> (#b:Type) -> l1:list a -> l2:list b ->\n Tot (l:list (a * b){L.length l == min (L.length l1) (L.length l2)})\nlet rec zip #a #b l1 l2 = match l1, l2 with\n | x::xs, y::ys -> (x,y) :: (zip xs ys)\n | _ -> []", "val mod_spec (a: int{fits a}) (b: int{fits b /\\ b <> 0}) : GTot (n: int{fits n})\nlet mod_spec (a:int{fits a}) (b:int{fits b /\\ b <> 0}) : GTot (n:int{fits n}) =\n let open FStar.Mul in\n let res = a - ((a/b) * b) in\n fits_lt res b;\n res", "val u64_1_or (a b: U64.t)\n : Lemma (U64.v a = pow2 64 - 1 ==> U64.v (U64.logor a b) = pow2 64 - 1) [SMTPat (U64.logor a b)]\nlet u64_1_or (a b:U64.t) :\n Lemma (U64.v a = pow2 64 - 1 ==> U64.v (U64.logor a b) = pow2 64 - 1)\n [SMTPat (U64.logor a b)] =\n u64_logor_comm a b", "val squash_double_sum\n (#a: Type)\n (#b: (a -> Type))\n ($p: (squash (dtuple2 a (fun (x: a) -> squash (b x)))))\n : Tot (squash (dtuple2 a b))\nlet squash_double_sum (#a:Type) (#b:(a -> Type)) (p : squash (dtuple2 a (fun (x:a) -> squash (b x)))) =\n bind_squash p (fun p' -> push_sum p')", "val revert_squash : (#a:Type) -> (#b : (a -> Type)) ->\n (squash (forall (x:a). b x)) ->\n x:a -> squash (b x)\nlet revert_squash #a #b s x = let x : (_:unit{forall x. b x}) = s in ()", "val revert_squash : (#a:Type) -> (#b : (a -> Type)) ->\n (squash (forall (x:a). b x)) ->\n x:a -> squash (b x)\nlet revert_squash #a #b s x = let x : (_:unit{forall x. b x}) = s in ()", "val g'':(lo int ** lo int ^--> lo int ** lo int)\nlet g'' : (lo int ** lo int ^--> lo int ** lo int)\n = fun (l, h) -> l, h + h + 1", "val t (a:Type0) : Type0\nlet t a = list a", "val exp_pow2_rec_is_exp_pow2: #t:Type -> k:SE.concrete_ops t -> a:t -> b:nat ->\n Lemma (exp_pow2_rec k a b == SE.exp_pow2 k a b)\nlet rec exp_pow2_rec_is_exp_pow2 #t k a b =\n if b = 0 then Lib.LoopCombinators.eq_repeat0 k.sqr a\n else begin\n Lib.LoopCombinators.unfold_repeat b k.sqr a (b - 1);\n assert (Loops.repeat b k.sqr a == k.sqr (Loops.repeat (b - 1) k.sqr a));\n exp_pow2_rec_is_exp_pow2 k a (b - 1) end", "val gand (b1 b2: gexp bool) : GTot (gexp bool)\nlet gand (b1 b2 : gexp bool) : GTot (gexp bool) =\n gop op_AmpAmp b1 b2", "val lemma_aux_0 (a b n: nat)\n : Lemma\n (pow2 n * a + pow2 (n + 56) * b = pow2 n * (a % pow2 56) + pow2 (n + 56) * (b + a / pow2 56))\nlet lemma_aux_0 (a:nat) (b:nat) (n:nat) : Lemma\n (pow2 n * a + pow2 (n+56) * b = pow2 n * (a % pow2 56) + pow2 (n+56) * (b + a / pow2 56))\n = Math.Lemmas.lemma_div_mod a (pow2 56);\n Math.Lemmas.pow2_plus n 56;\n assert(a = pow2 56 * (a / pow2 56) + (a % pow2 56));\n Math.Lemmas.distributivity_add_right (pow2 n) (pow2 56 * (a / pow2 56)) (a % pow2 56);\n Math.Lemmas.paren_mul_right (pow2 n) (pow2 56) (a / pow2 56);\n Math.Lemmas.distributivity_add_right (pow2 (n+56)) b (a / pow2 56)", "val exp_pow2_lemma: #t:Type -> k:concrete_ops t -> a:t -> b:nat ->\n Lemma (k.to.refl (exp_pow2 k a b) == S.exp_pow2 k.to.comm_monoid (k.to.refl a) b)\nlet exp_pow2_lemma #t k a b =\n exp_pow2_lemma_loop k a b b", "val squash_double_arrow (#a: Type) (#p: (a -> Type)) ($f: (squash (x: a -> GTot (squash (p x)))))\n : GTot (squash (x: a -> GTot (p x)))\nlet squash_double_arrow #a #p f =\n bind_squash f push_squash", "val lemma_pow_double: a:int -> b:nat -> Lemma (pow (a * a) b == pow a (b + b))\nlet lemma_pow_double a b =\n let k = mk_nat_comm_monoid in\n LE.lemma_pow_double k a b;\n lemma_pow_nat_is_pow (a * a) b;\n lemma_pow_nat_is_pow a (b + b)", "val lemma_pow_double: a:elem -> b:nat ->\n Lemma (pow (a *% a) b == pow a (b + b))\nlet lemma_pow_double a b =\n lemma_pow_mod_is_pow_cm (a *% a) b;\n LE.lemma_pow_double cm_prime a b;\n lemma_pow_mod_is_pow_cm a (b + b)", "val lexp_pow2:\n #a_t:inttype_a\n -> len:size_t{v len > 0}\n -> ctx_len:size_t\n -> k:concrete_ops a_t len ctx_len\n -> ctx:lbuffer (uint_t a_t SEC) ctx_len\n -> a:lbuffer (uint_t a_t SEC) len\n -> b:size_t\n -> res:lbuffer (uint_t a_t SEC) len ->\n Stack unit\n (requires fun h ->\n live h res /\\ live h ctx /\\ live h a /\\\n disjoint res ctx /\\ disjoint a ctx /\\ disjoint a res /\\\n k.to.linv (as_seq h a) /\\ k.to.linv_ctx (as_seq h ctx))\n (ensures fun h0 _ h1 -> modifies (loc res) h0 h1 /\\ k.to.linv (as_seq h1 res) /\\\n k.to.refl (as_seq h1 res) == S.exp_pow2 k.to.comm_monoid (k.to.refl (as_seq h0 a)) (v b))\nlet lexp_pow2 #a_t len ctx_len k ctx a b res =\n copy res a;\n let h0 = ST.get () in\n [@ inline_let]\n let refl1 i : GTot k.to.a_spec = k.to.refl (as_seq h0 res) in\n [@ inline_let]\n let spec h0 = S.sqr k.to.comm_monoid in\n\n [@ inline_let]\n let inv h (i:nat{i <= v b}) =\n modifies (loc res) h0 h /\\\n k.to.linv (as_seq h res) /\\\n k.to.refl (as_seq h res) == Loops.repeat i (spec h0) (refl1 0) in\n\n Loops.eq_repeat0 (spec h0) (refl1 0);\n Lib.Loops.for 0ul b inv\n (fun j ->\n Loops.unfold_repeat (v b) (spec h0) (refl1 0) (v j);\n k.lsqr ctx res res)", "val lemma_pow_nat_is_pow: a:int -> b:nat ->\n Lemma (pow a b == LE.pow mk_nat_comm_monoid a b)\nlet rec lemma_pow_nat_is_pow a b =\n let k = mk_nat_comm_monoid in\n if b = 0 then begin\n lemma_pow0 a;\n LE.lemma_pow0 k a end\n else begin\n lemma_pow_unfold a b;\n lemma_pow_nat_is_pow a (b - 1);\n LE.lemma_pow_unfold k a b;\n () end", "val pow2_lt_recip (a b: nat) : Lemma (requires (pow2 a < pow2 b)) (ensures (a < b))\nlet pow2_lt_recip\n (a b: nat)\n: Lemma\n (requires (pow2 a < pow2 b))\n (ensures (a < b))\n= Classical.move_requires (pow2_le_compat a) b", "val ( ^++ ) (#a: Type0) (#rel: preorder a) (r: mref a rel) (s: set nat) : GTot (set nat)\nlet op_Hat_Plus_Plus (#a:Type0) (#rel:preorder a) (r:mref a rel) (s:set nat) :GTot (set nat) = S.union (only r) s", "val lemma_from_squash : #a:Type -> #b:(a -> Type) -> (x:a -> squash (b x)) -> x:a -> Lemma (b x)\nlet lemma_from_squash #a #b f x = let _ = f x in assert (b x)", "val lemma_from_squash : #a:Type -> #b:(a -> Type) -> (x:a -> squash (b x)) -> x:a -> Lemma (b x)\nlet lemma_from_squash #a #b f x = let _ = f x in assert (b x)", "val feq (u v: Type) (eq: (v -> v -> GTot Type0)) (f1 f2: (u -> Tot v)) : GTot Type0\nlet feq\n (u v: Type)\n (eq: (v -> v -> GTot Type0))\n (f1 f2: (u -> Tot v))\n: GTot Type0\n= (forall (x: u) . {:pattern (f1 x); (f2 x)} eq (f1 x) (f2 x))", "val push_sum (#a: Type) (#b: (a -> Type)) ($p: (dtuple2 a (fun (x: a) -> squash (b x))))\n : Tot (squash (dtuple2 a b))\nlet push_sum (#a:Type) (#b:(a -> Type)) ($p : dtuple2 a (fun (x:a) -> squash (b x))) =\n match p with\n | Mkdtuple2 x y ->\n bind_squash #(b x) #(dtuple2 a b) y (fun y' ->\n return_squash (Mkdtuple2 x y'))", "val ( ^+^ ) (#a #b: Type) (r1: ref a) (r2: ref b) : Tot (set nat)\nlet op_Hat_Plus_Hat (#a:Type) (#b:Type) (r1:ref a) (r2:ref b) : Tot (set nat) =\n union (only r1) (only r2)", "val forall_intro_squash_gtot (#a: Type) (#p: (a -> GTot Type)) ($_: (x: a -> GTot (squash (p x))))\n : Tot (squash (forall (x: a). p x))\nlet forall_intro_squash_gtot #a #p f =\n bind_squash #(x: a -> GTot (p x))\n #(forall (x: a). p x)\n (squash_double_arrow #a #p (return_squash f))\n (fun f -> lemma_forall_intro_gtot #a #p f)", "val mul_acc_pow_a_bits_l\n (#t: Type)\n (k: concrete_ops t)\n (a: t)\n (bBits: nat)\n (b: nat{b < pow2 bBits})\n (l: pos)\n (i: nat{i < bBits / l})\n (acc: t)\n : t\nlet mul_acc_pow_a_bits_l (#t:Type) (k:concrete_ops t) (a:t)\n (bBits:nat) (b:nat{b < pow2 bBits}) (l:pos) (i:nat{i < bBits / l}) (acc:t) : t\n =\n let bits_l = S.get_bits_l bBits b l i in\n k.mul acc (pow k a bits_l)", "val gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a)\n : stt_ghost unit\n (pts_to r #one_half x0 ** pts_to r #one_half x1)\n (fun _ -> pts_to r x0 ** pure (x0 == x1))\nlet gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a) = gather r #x0 #x1 #one_half #one_half", "val gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a)\n : stt_ghost unit\n (pts_to r #one_half x0 ** pts_to r #one_half x1)\n (fun _ -> pts_to r x0 ** pure (x0 == x1))\nlet gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a) = gather r #x0 #x1 #one_half #one_half", "val gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a)\n : stt_ghost unit\n (pts_to r #one_half x0 ** pts_to r #one_half x1)\n (fun _ -> pts_to r x0 ** pure (x0 == x1))\nlet gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a)\n: stt_ghost unit\n (pts_to r #one_half x0 ** pts_to r #one_half x1)\n (fun () -> pts_to r x0 ** pure (x0 == x1))\n= gather r", "val gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a)\n : stt_ghost unit\n (pts_to r #one_half x0 ** pts_to r #one_half x1)\n (fun _ -> pts_to r x0 ** pure (x0 == x1))\nlet gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a) = gather r", "val exp_pow2_rec (#t: Type) (k: SE.concrete_ops t) (a: t) (b: nat) : Tot t (decreases b)\nlet rec exp_pow2_rec (#t:Type) (k:SE.concrete_ops t) (a:t) (b:nat) : Tot t (decreases b) =\n if b = 0 then a else k.sqr (exp_pow2_rec k a (b - 1))", "val exp_pow2_lemma: #t:Type -> k:comm_monoid t -> a:t -> b:nat ->\n Lemma (exp_pow2 k a b == pow k a (pow2 b))\nlet exp_pow2_lemma #t k a b = exp_pow2_loop_lemma k a b b", "val live: #a:Type -> HS.mem -> vector a -> GTot Type0\nlet live #a h vec =\n B.live h (Vec?.vs vec)", "val lemma_pow2_div (a b k: nat)\n : Lemma (requires a >= k /\\ b >= k)\n (ensures (pow2 a + pow2 b) / pow2 k == pow2 (a - k) + pow2 (b - k))\nlet lemma_pow2_div (a:nat) (b:nat) (k:nat)\n : Lemma (requires a >= k /\\ b >= k)\n (ensures (pow2 a + pow2 b) / pow2 k == pow2 (a - k) + pow2 (b - k))\n =\n let open FStar.Math.Lemmas in\n let open FStar.Mul in\n pow2_plus k (b - k);\n division_addition_lemma (pow2 a) (pow2 k) (pow2 (b-k));\n pow2_minus b k;\n pow2_minus a k", "val lemma_fast_sqr_part2 (a0 a1 a2 a3 a4 a5 b2 b3: nat64)\n : Lemma\n (ensures\n (let z:nat64 = 0 in\n let x0, c = (add_lo_hi a0 a0 0) in\n let x1, c = (add_lo_hi a1 a1 c) in\n let x2, o = (add_lo_hi a2 b2 0) in\n let x2, c = (add_lo_hi x2 x2 c) in\n let x3, o = (add_lo_hi a3 b3 o) in\n let x3, c = (add_lo_hi x3 x3 c) in\n let x4, o = (add_lo_hi a4 z o) in\n let x4, c = (add_lo_hi x4 x4 c) in\n let x5, o = (add_lo_hi a5 z o) in\n let x5, c = (add_lo_hi x5 x5 c) in\n let x6, _ = (add_lo_hi z z o) in\n let x6, _ = (add_lo_hi x6 x6 c) in\n pow2_seven x0 x1 x2 x3 x4 x5 x6 ==\n pow2_six (2 * a0) (2 * a1) (2 * (a2 + b2)) (2 * (a3 + b3)) (2 * a4) (2 * a5) /\\ x6 <= 2))\nlet lemma_fast_sqr_part2 (a0 a1 a2 a3 a4 a5 b2 b3:nat64) : Lemma\n (ensures (\n let z:nat64 = 0 in\n let (x0, c) = (add_lo_hi a0 a0 0) in\n let (x1, c) = (add_lo_hi a1 a1 c) in\n let (x2, o) = (add_lo_hi a2 b2 0) in let (x2, c) = (add_lo_hi x2 x2 c) in\n let (x3, o) = (add_lo_hi a3 b3 o) in let (x3, c) = (add_lo_hi x3 x3 c) in\n let (x4, o) = (add_lo_hi a4 z o) in let (x4, c) = (add_lo_hi x4 x4 c) in\n let (x5, o) = (add_lo_hi a5 z o) in let (x5, c) = (add_lo_hi x5 x5 c) in\n let (x6, _) = (add_lo_hi z z o) in let (x6, _) = (add_lo_hi x6 x6 c) in\n pow2_seven x0 x1 x2 x3 x4 x5 x6 ==\n pow2_six (2 * a0) (2 * a1) (2 * (a2 + b2)) (2 * (a3 + b3)) (2 * a4) (2 * a5) /\\\n x6 <= 2\n ))\n =\n lemma_add_hi_lo64 0", "val elim_squash_or (#r #p #q: _) (f: squash (p \\/ q)) (left: (p -> GTot r)) (right: (q -> GTot r))\n : GTot (squash r)\nlet elim_squash_or (#r:_) (#p #q:_) (f:squash (p \\/ q)) (left: p -> GTot r) (right: q -> GTot r)\n : GTot (squash r)\n = FStar.Squash.bind_squash #_ #r f (fun pq ->\n FStar.Squash.bind_squash pq (fun c ->\n match c with\n | Prims.Left x -> FStar.Squash.return_squash (left x)\n | Prims.Right x -> FStar.Squash.return_squash (right x)))", "val v: #a:Type -> h:HS.mem -> ll: t a -> GTot (list a)\nlet v #_ h ll =\n B.deref h ll.v", "val lemma_distr5_pow52 (a b0 b1 b2 b3 b4:int) : Lemma\n (a * (b0 + b1 * pow2 52 + b2 * pow2 104 + b3 * pow2 156 + b4 * pow2 208) =\n a * b0 + a * b1 * pow2 52 + a * b2 * pow2 104 + a * b3 * pow2 156 + a * b4 * pow2 208)\nlet lemma_distr5_pow52 a b0 b1 b2 b3 b4 =\n calc (==) {\n a * (b0 + b1 * pow2 52 + b2 * pow2 104 + b3 * pow2 156 + b4 * pow2 208);\n (==) { lemma_distr5 b0 (b1 * pow2 52) (b2 * pow2 104) (b3 * pow2 156) (b4 * pow2 208) a }\n b0 * a + b1 * pow2 52 * a + b2 * pow2 104 * a + b3 * pow2 156 * a + b4 * pow2 208 * a;\n (==) { lemma_swap_mul3 b1 (pow2 52) a; lemma_swap_mul3 b2 (pow2 104) a }\n b0 * a + b1 * a * pow2 52 + b2 * a * pow2 104 + b3 * pow2 156 * a + b4 * pow2 208 * a;\n (==) { lemma_swap_mul3 b3 (pow2 156) a; lemma_swap_mul3 b4 (pow2 208) a }\n b0 * a + b1 * a * pow2 52 + b2 * a * pow2 104 + b3 * a * pow2 156 + b4 * a * pow2 208;\n }", "val gte_mask (a b: t)\n : Pure t\n (requires True)\n (ensures (fun c -> (v a >= v b ==> v c = pow2 n - 1) /\\ (v a < v b ==> v c = 0)))\nlet gte_mask (a:t) (b:t)\n : Pure t\n (requires True)\n (ensures (fun c -> (v a >= v b ==> v c = pow2 n - 1) /\\\n (v a < v b ==> v c = 0)))\n = let x = a in\n let y = b in\n let x_xor_y = logxor x y in\n let x_sub_y = sub_mod x y in\n let x_sub_y_xor_y = logxor x_sub_y y in\n let q = logor x_xor_y x_sub_y_xor_y in\n let x_xor_q = logxor x q in\n let x_xor_q_ = shift_right x_xor_q n_minus_one in\n let c = sub_mod x_xor_q_ (uint_to_t 1) in\n lemma_sub_msbs x y;\n lemma_msb_gte (v x) (v y);\n lemma_msb_gte (v y) (v x);\n c", "val gte_mask (a b: t)\n : Pure t\n (requires True)\n (ensures (fun c -> (v a >= v b ==> v c = pow2 n - 1) /\\ (v a < v b ==> v c = 0)))\nlet gte_mask (a:t) (b:t)\n : Pure t\n (requires True)\n (ensures (fun c -> (v a >= v b ==> v c = pow2 n - 1) /\\\n (v a < v b ==> v c = 0)))\n = let x = a in\n let y = b in\n let x_xor_y = logxor x y in\n let x_sub_y = sub_mod x y in\n let x_sub_y_xor_y = logxor x_sub_y y in\n let q = logor x_xor_y x_sub_y_xor_y in\n let x_xor_q = logxor x q in\n let x_xor_q_ = shift_right x_xor_q n_minus_one in\n let c = sub_mod x_xor_q_ (uint_to_t 1) in\n lemma_sub_msbs x y;\n lemma_msb_gte (v x) (v y);\n lemma_msb_gte (v y) (v x);\n c", "val gte_mask (a b: t)\n : Pure t\n (requires True)\n (ensures (fun c -> (v a >= v b ==> v c = pow2 n - 1) /\\ (v a < v b ==> v c = 0)))\nlet gte_mask (a:t) (b:t)\n : Pure t\n (requires True)\n (ensures (fun c -> (v a >= v b ==> v c = pow2 n - 1) /\\\n (v a < v b ==> v c = 0)))\n = let x = a in\n let y = b in\n let x_xor_y = logxor x y in\n let x_sub_y = sub_mod x y in\n let x_sub_y_xor_y = logxor x_sub_y y in\n let q = logor x_xor_y x_sub_y_xor_y in\n let x_xor_q = logxor x q in\n let x_xor_q_ = shift_right x_xor_q n_minus_one in\n let c = sub_mod x_xor_q_ (uint_to_t 1) in\n lemma_sub_msbs x y;\n lemma_msb_gte (v x) (v y);\n lemma_msb_gte (v y) (v x);\n c", "val gte_mask (a b: t)\n : Pure t\n (requires True)\n (ensures (fun c -> (v a >= v b ==> v c = pow2 n - 1) /\\ (v a < v b ==> v c = 0)))\nlet gte_mask (a:t) (b:t)\n : Pure t\n (requires True)\n (ensures (fun c -> (v a >= v b ==> v c = pow2 n - 1) /\\\n (v a < v b ==> v c = 0)))\n = let x = a in\n let y = b in\n let x_xor_y = logxor x y in\n let x_sub_y = sub_mod x y in\n let x_sub_y_xor_y = logxor x_sub_y y in\n let q = logor x_xor_y x_sub_y_xor_y in\n let x_xor_q = logxor x q in\n let x_xor_q_ = shift_right x_xor_q n_minus_one in\n let c = sub_mod x_xor_q_ (uint_to_t 1) in\n lemma_sub_msbs x y;\n lemma_msb_gte (v x) (v y);\n lemma_msb_gte (v y) (v x);\n c", "val or_elim_simple\n (p q r: Type)\n (x: squash (p \\/ q))\n (f: (squash p -> Tot (squash r)))\n (g: (squash q -> Tot (squash r)))\n : Tot (squash r)\nlet or_elim_simple\n (p:Type)\n (q:Type)\n (r:Type)\n (x:squash (p \\/ q))\n (f:squash p -> Tot (squash r))\n (g:squash q -> Tot (squash r))\n : Tot (squash r)\n = let open FStar.Squash in\n bind_squash x (fun p_or_q ->\n bind_squash p_or_q (fun p_cor_q ->\n match p_cor_q with\n | Prims.Left p ->\n f (return_squash p)\n | Prims.Right q ->\n g (return_squash q)))", "val squash (p: Type u#a) : Type0\nlet squash (p:Type u#a) : Type0 = squash p", "val put (l: lens 'a 'b) (x: 'a) (y: 'b) : GTot 'a\nlet put (l:lens 'a 'b) (x:'a) (y:'b) : GTot 'a =\n match l with\n | {put=put} -> put y x", "val ( ++^ ) (#a: Type0) (#rel: preorder a) (s: set nat) (r: mref a rel) : GTot (set nat)\nlet op_Plus_Plus_Hat (#a:Type0) (#rel:preorder a) (s:set nat) (r:mref a rel) :GTot (set nat) = S.union s (only r)", "val rem (a:t) (b:t{v b <> 0}) : Pure t\n (requires True)\n (ensures (fun c -> FStar.UInt.mod (v a) (v b) = v c))\nlet rem a b = Mk (mod (v a) (v b))", "val rem (a:t) (b:t{v b <> 0}) : Pure t\n (requires True)\n (ensures (fun c -> FStar.UInt.mod (v a) (v b) = v c))\nlet rem a b = Mk (mod (v a) (v b))", "val rem (a:t) (b:t{v b <> 0}) : Pure t\n (requires True)\n (ensures (fun c -> FStar.UInt.mod (v a) (v b) = v c))\nlet rem a b = Mk (mod (v a) (v b))", "val rem (a:t) (b:t{v b <> 0}) : Pure t\n (requires True)\n (ensures (fun c -> FStar.UInt.mod (v a) (v b) = v c))\nlet rem a b = Mk (mod (v a) (v b))", "val lemma_pow_mul_base: a:int -> b:int -> n:nat -> Lemma (pow a n * pow b n == pow (a * b) n)\nlet lemma_pow_mul_base a b n =\n let k = mk_nat_comm_monoid in\n LE.lemma_pow_mul_base k a b n;\n lemma_pow_nat_is_pow a n;\n lemma_pow_nat_is_pow b n;\n lemma_pow_nat_is_pow (a * b) n", "val holds (#t: Type0) (p: rel t) (s s' : t) : GTot Type0\nlet holds (#t: Type0) (p: rel t) (s s' : t) : GTot Type0 =\n p s s'", "val lemma_pow_pow_mod: f:S.qelem -> a:nat -> b:nat ->\n Lemma (M.pow (M.pow f a % S.order) b % S.order == M.pow f (a * b) % S.order)\nlet lemma_pow_pow_mod f a b =\n calc (==) {\n M.pow (M.pow f a % S.order) b % S.order;\n (==) { M.lemma_pow_mod_base (M.pow f a) b S.order }\n M.pow (M.pow f a) b % S.order;\n (==) { M.lemma_pow_mul f a b }\n M.pow f (a * b) % S.order;\n }", "val p (#a: typ) (init: list (P.type_of_typ a)) : GTot Type0\nlet p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =\n normalize (0 < FStar.List.Tot.length init) /\\\n normalize (FStar.List.Tot.length init < UInt.max_int 32)", "val lemma_pow2_div2 (a b c: nat) : Lemma ((a / pow2 b) / pow2 c == a / (pow2 (c + b)))\nlet lemma_pow2_div2 (a:nat) (b:nat) (c:nat)\n : Lemma ((a / pow2 b) / pow2 c == a / (pow2 (c + b)))\n =\n let open FStar.Math.Lemmas in\n pow2_plus b c;\n division_multiplication_lemma a (pow2 b) (pow2 c)", "val v (#t #l: _) (u: int_t t l) : GTot (range_t t)\nlet v #t #l (u: int_t t l) : GTot (range_t t) =\n v u", "val and_elim\n (p:Type)\n (q:squash p -> Type)\n (r:Type)\n (_:squash (p /\\ q()))\n (f:squash p -> squash (q()) -> Tot (squash r))\n : Tot (squash r)\nlet and_elim (p:Type)\n (q:squash p -> Type)\n (r:Type)\n (x:squash (p /\\ q()))\n (f:squash p -> squash (q()) -> Tot (squash r))\n : Tot (squash r)\n = let open FStar.Squash in\n bind_squash x (fun p_and_q ->\n bind_squash p_and_q (fun (Prims.Pair p q) ->\n f (return_squash p) (return_squash q)))", "val calc_push_impl (#p #q:Type) (f:squash p -> GTot (squash q))\n : Tot (squash (p ==> q))\nlet calc_push_impl #p #q f =\n Classical.arrow_to_impl f", "val subcomp\n (a: Type)\n (p1: Type0)\n (w1: (squash p1 -> w a))\n (p2: Type0)\n (w2: (squash p2 -> w a))\n (f: repr a p1 w1)\n : Pure (repr a p2 w2)\n (requires (p2 ==> p1) /\\ (forall (pf: squash p2). (w2 pf) `stronger` (w1 (weaken p2 p1 pf))))\n (ensures fun _ -> True)\nlet subcomp (a:Type)\n (p1 : Type0)\n (w1 : squash p1 -> w a)\n (p2 : Type0)\n (w2 : squash p2 -> w a)\n (f : repr a p1 w1)\n : Pure (repr a p2 w2)\n (requires (p2 ==> p1) /\\ (forall (pf : squash p2). w2 pf `stronger` w1 (weaken p2 p1 pf)))\n (ensures fun _ -> True)\n = fun _ -> f ()", "val mul: #t:inttype{~(U128? t) /\\ ~(S128? t)} -> #l:secrecy_level\n -> a:int_t t l\n -> b:int_t t l{range (v a * v b) t}\n -> int_t t l\nlet mul #t #l a b =\n match t with\n | U1 -> UInt8.mul a b\n | U8 -> UInt8.mul a b\n | U16 -> UInt16.mul a b\n | U32 -> UInt32.mul a b\n | U64 -> UInt64.mul a b\n | S8 -> Int8.mul a b\n | S16 -> Int16.mul a b\n | S32 -> Int32.mul a b\n | S64 -> Int64.mul a b", "val rem (a:t{v a >= 0}) (b:t{v b > 0}) : Pure t\n (requires True)\n (ensures (fun c -> mod_spec (v a) (v b) = v c))\nlet rem x y = I64.rem x y", "val lemma_mod_pow2_sub: x:nat -> a:nat -> b:nat ->\n Lemma (x / pow2 a % pow2 b * pow2 a == x % pow2 (a + b) - x % pow2 a)\nlet lemma_mod_pow2_sub x a b =\n calc (==) {\n x / pow2 a % pow2 b * pow2 a;\n (==) { Math.Lemmas.pow2_modulo_division_lemma_1 x a (a + b) }\n x % pow2 (a + b) / pow2 a * pow2 a;\n (==) { Math.Lemmas.euclidean_division_definition (x % pow2 (a + b)) (pow2 a) }\n x % pow2 (a + b) - x % pow2 (a + b) % pow2 a;\n (==) { Math.Lemmas.pow2_modulo_modulo_lemma_1 x a (a + b) }\n x % pow2 (a + b) - x % pow2 a;\n }", "val lemma_mod_pow2_sub: x:nat -> a:nat -> b:nat ->\n Lemma (x / pow2 a % pow2 b * pow2 a == x % pow2 (a + b) - x % pow2 a)\nlet lemma_mod_pow2_sub x a b =\n calc (==) {\n x / pow2 a % pow2 b * pow2 a;\n (==) { Math.Lemmas.pow2_modulo_division_lemma_1 x a (a + b) }\n x % pow2 (a + b) / pow2 a * pow2 a;\n (==) { Math.Lemmas.euclidean_division_definition (x % pow2 (a + b)) (pow2 a) }\n x % pow2 (a + b) - x % pow2 (a + b) % pow2 a;\n (==) { Math.Lemmas.pow2_modulo_modulo_lemma_1 x a (a + b) }\n x % pow2 (a + b) - x % pow2 a;\n }", "val lemma_mod_pow2_sub: x:nat -> a:nat -> b:nat ->\n Lemma (x / pow2 a % pow2 b * pow2 a == x % pow2 (a + b) - x % pow2 a)\nlet lemma_mod_pow2_sub x a b =\n calc (==) {\n x / pow2 a % pow2 b * pow2 a;\n (==) { Math.Lemmas.pow2_modulo_division_lemma_1 x a (a + b) }\n x % pow2 (a + b) / pow2 a * pow2 a;\n (==) { Math.Lemmas.euclidean_division_definition (x % pow2 (a + b)) (pow2 a) }\n x % pow2 (a + b) - x % pow2 (a + b) % pow2 a;\n (==) { Math.Lemmas.pow2_modulo_modulo_lemma_1 x a (a + b) }\n x % pow2 (a + b) - x % pow2 a;\n }", "val size_sub: a: SZ.t -> b: SZ.t -> squash (SZ.v a >= SZ.v b)\n -> Tot (c: SZ.t{SZ.v c == (SZ.v a - SZ.v b)})\nlet size_sub\n (a: SZ.t)\n (b: SZ.t)\n (_: squash (SZ.v a >= SZ.v b))\n: Tot (c: SZ.t { SZ.v c == (SZ.v a - SZ.v b) })\n= a `SZ.sub` b", "val mul_acc_pow_a_bits_l\n (#t: Type)\n (k: comm_monoid t)\n (a: t)\n (bBits: nat)\n (b: nat{b < pow2 bBits})\n (l: pos)\n (i: nat{i < bBits / l})\n (acc: t)\n : t\nlet mul_acc_pow_a_bits_l (#t:Type) (k:comm_monoid t) (a:t) (bBits:nat) (b:nat{b < pow2 bBits}) (l:pos) (i:nat{i < bBits / l}) (acc:t) : t =\n let bits_l = get_bits_l bBits b l i in\n mul acc (pow k a bits_l)" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.arrow_to_impl" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_pow_gt_zero" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_as_squash" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fst", "name": "FStar.UInt128.lem_ult_2" }, { "project_name": "FStar", "file_name": "WorkingWithSquashedProofs.fst", "name": "WorkingWithSquashedProofs.lemma_as_squash" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fst", "name": "FStar.UInt128.lem_ult_1" }, { "project_name": "FStar", "file_name": "FStar.IndefiniteDescription.fst", "name": "FStar.IndefiniteDescription.elim_squash" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.op_Hat_Plus_Hat" }, { "project_name": "hacl-star", "file_name": "Lib.Exponentiation.fsti", "name": "Lib.Exponentiation.exp_pow2" }, { "project_name": "hacl-star", "file_name": "Spec.Exponentiation.fsti", "name": "Spec.Exponentiation.exp_pow2" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_pow_ge_zero" }, { "project_name": "hacl-star", "file_name": "Spec.Exponentiation.fsti", "name": "Spec.Exponentiation.pow" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.impl_to_arrow" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.p" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fst", "name": "FStar.ReflexiveTransitiveClosure.squash_double_arrow" }, { "project_name": "FStar", "file_name": "SolveThen.fst", "name": "SolveThen.constr" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.lemma_to_squash_gtot" }, { "project_name": "everparse", "file_name": "LowParse.Math.fst", "name": "LowParse.Math.mult_nat" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fst", "name": "FStar.ReflexiveTransitiveClosure.get_squash" }, { "project_name": "FStar", "file_name": "WorkingWithSquashedProofs.fst", "name": "WorkingWithSquashedProofs.valid_baz_alt_alt" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.length" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.lemma_mod_pow2" }, { "project_name": "hacl-star", "file_name": "Spec.Exponentiation.fst", "name": "Spec.Exponentiation.pow_lemma" }, { "project_name": "FStar", "file_name": "FStar.FiniteMap.Base.fst", "name": "FStar.FiniteMap.Base.items" }, { "project_name": "FStar", "file_name": "FStar.Squash.fst", "name": "FStar.Squash.map_squash" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.t" }, { "project_name": "everparse", "file_name": "LowParse.Math.fst", "name": "LowParse.Math.pow2_le_recip" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.Lemmas.fst", "name": "Vale.Bignum.Lemmas.lemma_pow_nat" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Hashing.fsti", "name": "MiTLS.Hashing.h" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.v" }, { "project_name": "FStar", "file_name": "FStar.SizeT.fsti", "name": "FStar.SizeT.mod_spec" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.length" }, { "project_name": "FStar", "file_name": "FStar.FunctionalExtensionality.fsti", "name": "FStar.FunctionalExtensionality.on_g" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.get_squashed" }, { "project_name": "steel", "file_name": "Pulse.Common.fst", "name": "Pulse.Common.zip" }, { "project_name": "FStar", "file_name": "FStar.PtrdiffT.fsti", "name": "FStar.PtrdiffT.mod_spec" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fst", "name": "FStar.UInt128.u64_1_or" }, { "project_name": "FStar", "file_name": "FStar.Squash.fst", "name": "FStar.Squash.squash_double_sum" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Logic.fst", "name": "FStar.Tactics.V2.Logic.revert_squash" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Logic.fst", "name": "FStar.Tactics.V1.Logic.revert_squash" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.g''" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.t" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.PrecompBaseTable256.fst", "name": "Hacl.Spec.PrecompBaseTable256.exp_pow2_rec_is_exp_pow2" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fsti", "name": "Benton2004.RHL.gand" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.BignumQ.Lemmas.fst", "name": "Hacl.Spec.BignumQ.Lemmas.lemma_aux_0" }, { "project_name": "hacl-star", "file_name": "Spec.Exponentiation.fst", "name": "Spec.Exponentiation.exp_pow2_lemma" }, { "project_name": "FStar", "file_name": "FStar.Squash.fst", "name": "FStar.Squash.squash_double_arrow" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_pow_double" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Curve25519.Finv.fst", "name": "Hacl.Spec.Curve25519.Finv.lemma_pow_double" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Exponentiation.fst", "name": "Hacl.Impl.Exponentiation.lexp_pow2" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_pow_nat_is_pow" }, { "project_name": "everparse", "file_name": "LowParse.Math.fst", "name": "LowParse.Math.pow2_lt_recip" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.op_Hat_Plus_Plus" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Logic.fst", "name": "FStar.Tactics.V1.Logic.lemma_from_squash" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Logic.fst", "name": "FStar.Tactics.V2.Logic.lemma_from_squash" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.feq" }, { "project_name": "FStar", "file_name": "FStar.Squash.fst", "name": "FStar.Squash.push_sum" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fsti", "name": "FStar.DM4F.Heap.op_Hat_Plus_Hat" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.forall_intro_squash_gtot" }, { "project_name": "hacl-star", "file_name": "Spec.Exponentiation.fsti", "name": "Spec.Exponentiation.mul_acc_pow_a_bits_l" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherReference.fst", "name": "Pulse.Lib.HigherReference.gather2" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.gather2" }, { "project_name": "steel", "file_name": "Pulse.Lib.Reference.fst", "name": "Pulse.Lib.Reference.gather2" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.gather2" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.PrecompBaseTable256.fsti", "name": "Hacl.Spec.PrecompBaseTable256.exp_pow2_rec" }, { "project_name": "hacl-star", "file_name": "Lib.Exponentiation.fst", "name": "Lib.Exponentiation.exp_pow2_lemma" }, { "project_name": "FStar", "file_name": "LowStar.Vector.fst", "name": "LowStar.Vector.live" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.lemma_pow2_div" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.lemma_fast_sqr_part2" }, { "project_name": "FStar", "file_name": "WorkingWithSquashedProofs.fst", "name": "WorkingWithSquashedProofs.elim_squash_or" }, { "project_name": "karamel", "file_name": "LowStar.Lib.LinkedList2.fst", "name": "LowStar.Lib.LinkedList2.v" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.MathLemmas.fst", "name": "Hacl.Spec.K256.MathLemmas.lemma_distr5_pow52" }, { "project_name": "FStar", "file_name": "FStar.UInt8.fsti", "name": "FStar.UInt8.gte_mask" }, { "project_name": "FStar", "file_name": "FStar.UInt32.fsti", "name": "FStar.UInt32.gte_mask" }, { "project_name": "FStar", "file_name": "FStar.UInt64.fsti", "name": "FStar.UInt64.gte_mask" }, { "project_name": "FStar", "file_name": "FStar.UInt16.fsti", "name": "FStar.UInt16.gte_mask" }, { "project_name": "FStar", "file_name": "FStar.Classical.Sugar.fst", "name": "FStar.Classical.Sugar.or_elim_simple" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.squash" }, { "project_name": "FStar", "file_name": "LowStar.Lens.fsti", "name": "LowStar.Lens.put" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.op_Plus_Plus_Hat" }, { "project_name": "FStar", "file_name": "FStar.UInt32.fst", "name": "FStar.UInt32.rem" }, { "project_name": "FStar", "file_name": "FStar.UInt16.fst", "name": "FStar.UInt16.rem" }, { "project_name": "FStar", "file_name": "FStar.UInt64.fst", "name": "FStar.UInt64.rem" }, { "project_name": "FStar", "file_name": "FStar.UInt8.fst", "name": "FStar.UInt8.rem" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_pow_mul_base" }, { "project_name": "FStar", "file_name": "Benton2004.Aux.fst", "name": "Benton2004.Aux.holds" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.P256.Qinv.fst", "name": "Hacl.Spec.P256.Qinv.lemma_pow_pow_mod" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.p" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.lemma_pow2_div2" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Secret.Int.Base.fst", "name": "QUIC.Secret.Int.Base.v" }, { "project_name": "FStar", "file_name": "FStar.Classical.Sugar.fst", "name": "FStar.Classical.Sugar.and_elim" }, { "project_name": "FStar", "file_name": "FStar.Calc.fst", "name": "FStar.Calc.calc_push_impl" }, { "project_name": "FStar", "file_name": "GenericPartialDM4A.fst", "name": "GenericPartialDM4A.subcomp" }, { "project_name": "hacl-star", "file_name": "Lib.IntTypes.fst", "name": "Lib.IntTypes.mul" }, { "project_name": "FStar", "file_name": "FStar.PtrdiffT.fst", "name": "FStar.PtrdiffT.rem" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Ed25519.PrecompTable.fst", "name": "Hacl.Spec.Ed25519.PrecompTable.lemma_mod_pow2_sub" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.PrecompTable.fst", "name": "Hacl.Spec.K256.PrecompTable.lemma_mod_pow2_sub" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.PrecompBaseTable256.fst", "name": "Hacl.Spec.PrecompBaseTable256.lemma_mod_pow2_sub" }, { "project_name": "steel", "file_name": "Pulse.Lib.ArraySwap.fst", "name": "Pulse.Lib.ArraySwap.size_sub" }, { "project_name": "hacl-star", "file_name": "Lib.Exponentiation.fsti", "name": "Lib.Exponentiation.mul_acc_pow_a_bits_l" } ], "selected_premises": [ "FStar.Constructive.ceq_trans", "FStar.Constructive.false_elim", "FStar.Constructive.ceq_symm", "FStar.Constructive.eq_ind", "FStar.SquashProperties.forall_intro", "FStar.Constructive.cfalse_elim", "FStar.SquashProperties.ifProp", "FStar.Constructive.ceq_congruence", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "FStar.SquashProperties.join_squash", "FStar.Pervasives.reveal_opaque", "FStar.SquashProperties.ac", "FStar.Constructive.false_elim2", "FStar.Pervasives.dfst", "FStar.SquashProperties.squash_arrow", "FStar.Pervasives.dsnd", "FStar.SquashProperties.false_elim", "FStar.SquashProperties.bool_of_or", "FStar.Pervasives.st_post_h", "FStar.Pervasives.id", "FStar.SquashProperties.excluded_middle_squash", "FStar.Pervasives.all_post_h", "FStar.Pervasives.ex_pre", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.all_pre_h", "Prims.subtype_of", "FStar.Pervasives.coerce_eq", "FStar.Pervasives.all_post_h'", "FStar.Pervasives.st_pre_h", "Prims.auto_squash", "FStar.Pervasives.st_wp_h", "FStar.Pervasives.st_stronger", "FStar.Pervasives.ex_post'", "FStar.Pervasives.all_wp_h", "FStar.Pervasives.ex_post", "Prims.__cache_version_number__", "FStar.Pervasives.ex_wp", "Prims.min", "FStar.Pervasives.pure_ite_wp", "FStar.Pervasives.ex_stronger", "Prims.pure_pre", "Prims.returnM", "FStar.Pervasives.all_stronger", "FStar.Pervasives.all_bind_wp", "Prims.pure_post'", "FStar.Pervasives.pure_bind_wp", "FStar.Pervasives.pure_close_wp", "FStar.Pervasives.ex_bind_wp", "FStar.Pervasives.all_trivial", "FStar.Pervasives.ex_trivial", "Prims.pow2", "FStar.Pervasives.st_trivial", "FStar.Pervasives.st_return", "FStar.Pervasives.ex_return", "FStar.Pervasives.all_return", "FStar.Pervasives.all_close_wp", "Prims.pure_wp'", "Prims.pure_trivial", "FStar.Pervasives.st_bind_wp", "FStar.Pervasives.all_ite_wp", "Prims.as_requires", "FStar.Pervasives.st_ite_wp", "Prims.l_True", "Prims.op_Hat", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.ex_ite_wp", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.trivial_pure_post", "FStar.SquashProperties.excluded_middle", "FStar.Pervasives.ex_if_then_else", "FStar.Pervasives.div_hoare_to_wp", "Prims.purewp_id", "FStar.Pervasives.pure_null_wp", "Prims.pure_stronger", "FStar.Pervasives.all_if_then_else", "Prims.abs", "Prims.pure_post", "Prims.pure_wp_monotonic", "Prims.pure_wp", "Prims.pure_wp_monotonic0", "FStar.Pervasives.st_if_then_else", "FStar.Pervasives.lift_div_exn", "FStar.Pervasives.pure_return", "Prims.as_ensures", "Prims.l_False" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.SquashProperties\n\nopen FStar.Constructive\n\nopen FStar.Squash\n\nval join_squash : #a:Type -> squash (squash a) -> GTot (squash a)\nlet join_squash #a s = bind_squash #(squash a) #a s (fun x -> x)\n\nval squash_arrow : #a:Type -> #p:(a -> Type) ->\n $f:(x:a -> GTot (squash (p x))) -> GTot (squash (x:a -> GTot (p x)))\nlet squash_arrow #a #p f = squash_double_arrow (return_squash f)\n\nval forall_intro : #a:Type -> #p:(a -> Type) ->\n $f:(x:a -> Lemma (p x)) -> Lemma (x:a -> GTot (p x))(* (forall (x:a). p x) *)\nlet forall_intro #a #p f =\n let ff : (x:a -> GTot (squash (p x))) = (fun x -> f x; get_proof (p x)) in\n give_proof #(x:a -> GTot (p x)) (squash_arrow #a #p ff)\n\n\n// currently unused\n// val squash_elim : a:Type -> #b:Type -> t1:b -> t2:b ->\n// ( a -> Tot (ceq t1 t2)) ->\n// Tot (squash a -> Tot (ceq t1 t2))\n\n(* assume val tt (t:Type) : squash t *)\n\n(* assume val squash_mem_elim : a:Type -> #b:Type -> t1:b -> t2:b -> *)\n(* (x:squash a -> t:(squash a -> Type) -> Tot (t ())) -> *)\n(* Tot (x:squash a -> t:(squash a -> Type) -> Tot (t x)) *)\n\n(* get_proof and give_proof are phrased in terms of squash *)\n\n(* The whole point of defining squash is to soundly allow define excluded_middle;\n here this follows from get_proof and give_proof *)\n\nval bool_of_or : #p:Type -> #q:Type -> Prims.sum p q ->\n Tot (b:bool{(b ==> p) /\\ (not(b) ==> q)})\nlet bool_of_or #p #q t =\n match t with\n | Prims.Left _ -> true\n | Prims.Right _ -> false\n\nval excluded_middle : p:Type -> GTot (squash (b:bool{b <==> p}))\nlet excluded_middle (p:Type) = map_squash (join_squash (get_proof (p \\/ (~p)))) bool_of_or\n\n\nval excluded_middle_squash : p:Type0 -> GTot (p \\/ ~p)\nlet excluded_middle_squash p =\n bind_squash (excluded_middle p) (fun x ->\n if x then\n map_squash (get_proof p) (Prims.Left #p)\n else\n return_squash (Prims.Right #_ #(~p) (return_squash (fun (h:p) ->\n give_proof (return_squash h);\n false_elim #False ()))))\n\n(* we thought we might prove proof irrelevance by Berardi ... but didn't manage *)\n\n(* Conditional on any Type -- unused below *)\nval ifProp: #p:Type0 -> b:Type0 -> e1:squash p -> e2:squash p -> GTot (squash p)\nlet ifProp #p b e1 e2 =\n bind_squash (excluded_middle_squash b)\n\t (fun (x:Prims.sum b (~ b)) ->\n\t\tmatch x with\n\t | Prims.Left _ -> e1\n\t\t| Prims.Right _ -> e2)\n\n(* The powerset operator *)\ntype pow (p:Type) = p -> GTot bool\n\nnoeq type retract 'a 'b : Type =\n | MkR: i:('a -> GTot 'b) ->\n j:('b -> GTot 'a) ->\n inv:(x:'a -> GTot (ceq (j (i x)) x)) ->\n retract 'a 'b\n\nnoeq type retract_cond 'a 'b : Type =\n | MkC: i2:('a -> GTot 'b) ->\n j2:('b -> GTot 'a) ->\n inv2:(retract 'a 'b -> x:'a -> GTot (ceq (j2 (i2 x)) x)) ->\n retract_cond 'a 'b\n\n(* unused below *)\nval ac: r:retract_cond 'a 'b -> retract 'a 'b -> x:'a ->\n GTot (ceq ((MkC?.j2 r) (MkC?.i2 r x)) x)\nlet ac (MkC _ _ inv2) = inv2\n\nlet false_elim (#a:Type) (f:False) : Tot a\n = match f with\n\nval l1: (a:Type0) -> (b:Type0) -> GTot (squash (retract_cond (pow a) (pow b)))", "sketch": [ "Step 1: Define the functions `i2` and `j2` for the retract condition. These functions should map between the types `pow a` and `pow b`.\nStep 2: Define the inverse condition `inv2` which ensures that applying `j2` after `i2` results in the identity function on `pow a`.\nStep 3: Construct the `retract_cond` type using the defined functions `i2`, `j2`, and the inverse condition `inv2`.\nStep 4: Use `return_squash` to wrap the constructed `retract_cond` type in a `squash`.", "Step 1: Define the injection function `i2` which maps a function from `a -> GTot bool` to a function from `b -> GTot bool`.\nStep 2: Define the projection function `j2` which maps a function from `b -> GTot bool` to a function from `a -> GTot bool`.\nStep 3: Prove the inverse property `inv2` which shows that applying `j2` after `i2` to any function from `a -> GTot bool` results in the original function.\nStep 4: Construct the `retract_cond` type using `i2`, `j2`, and `inv2`.\nStep 5: Use `return_squash` to wrap the constructed `retract_cond` in a `squash`.", "Step 1: Define the injection function `i2` from `pow a` to `pow b`. This function should map a predicate on `a` to a predicate on `b`.\nStep 2: Define the projection function `j2` from `pow b` to `pow a`. This function should map a predicate on `b` to a predicate on `a`.\nStep 3: Define the inverse property `inv2` that ensures `j2` is the inverse of `i2` for any retract `r` of `pow a` and `pow b`.\nStep 4: Construct the `retract_cond` type using `i2`, `j2`, and `inv2`.\nStep 5: Use `return_squash` to wrap the constructed `retract_cond` in a `squash`.", "Step 1: Define the functions `i2` and `j2` for the retract condition. These functions will map between the types `pow a` and `pow b`.\nStep 2: Define the inversion property `inv2` that ensures the retract condition holds. This property will show that applying `j2` after `i2` results in the identity function on `pow a`.\nStep 3: Construct the `retract_cond` type using the functions `i2`, `j2`, and the inversion property `inv2`.\nStep 4: Use `give_proof` to provide the constructed `retract_cond` type as the proof of the lemma.", "Step 1: Define the functions `i2` and `j2` for the retract condition between `pow a` and `pow b`. These functions will map elements of `pow a` to `pow b` and vice versa.\nStep 2: Prove that `i2` and `j2` form a retract by showing that applying `j2` after `i2` to an element of `pow a` results in the original element.\nStep 3: Construct the `retract_cond` type using `i2`, `j2`, and the proof from Step 2.\nStep 4: Use `return_squash` to wrap the constructed `retract_cond` in a `squash`.", "Step 1: Define the functions `i2` and `j2` for the retract condition between `pow a` and `pow b`.\nStep 2: Prove that `i2` and `j2` form a retract by showing that applying `j2` after `i2` returns the original input.\nStep 3: Use the `MkC` constructor to create the retract condition.", "Step 1: Define the injection function `i2` which maps a predicate on type `a` to a predicate on type `b`.\nStep 2: Define the projection function `j2` which maps a predicate on type `b` back to a predicate on type `a`.\nStep 3: Define the inverse property `inv2` which ensures that applying `j2` after `i2` to any predicate on type `a` results in the original predicate.\nStep 4: Construct the `retract_cond` type using the defined functions `i2`, `j2`, and `inv2`.\nStep 5: Use `return_squash` to wrap the constructed `retract_cond` in a `squash`.", "Step 1: Define the functions `i2` and `j2` for the retract condition between `pow a` and `pow b`.\nStep 2: Define the inverse function `inv2` that ensures the retract condition holds.\nStep 3: Construct the `retract_cond` type using the defined functions `i2`, `j2`, and `inv2`.\nStep 4: Use `return_squash` to encapsulate the constructed `retract_cond` type in a `squash`.", "Step 1: Define the injection function `i2` which maps a predicate on `a` to a predicate on `b`.\nStep 2: Define the projection function `j2` which maps a predicate on `b` to a predicate on `a`.\nStep 3: Prove the injectivity condition `inv2` which ensures that for any predicate on `a`, applying `i2` and then `j2` results in the original predicate.\nStep 4: Construct the `retract_cond` type using the functions `i2`, `j2`, and the proof of `inv2`.\nStep 5: Use `return_squash` to wrap the constructed `retract_cond` in a `squash`.", "Step 1: Define the functions `i2` and `j2` for the retract condition. These functions will map between the types `pow a` and `pow b`.\nStep 2: Define the inverse property `inv2` which ensures that applying `j2` after `i2` returns the original value.\nStep 3: Construct the `retract_cond` type using the functions `i2`, `j2`, and the inverse property `inv2`.\nStep 4: Use `return_squash` to wrap the constructed `retract_cond` type in a `squash`." ], "generated_solution": [ "let l1 a b =\n let i2 (p: pow a) : pow b = fun (x: b) -> p (fun (y: a) -> x = y) in\n let j2 (q: pow b) : pow a = fun (x: a) -> q (fun (y: b) -> x = y) in\n let inv2 (r: retract (pow a) (pow b)) (x: pow a) : GTot (ceq (j2 (i2 x)) x) =\n fun (y: a) -> r.inv x y in\n return_squash (MkC i2 j2 inv2)", "let l1 a b =\n let i2 (f: pow a) : pow b = fun (y: b) -> f (fun (x: a) -> true) in\n let j2 (g: pow b) : pow a = fun (x: a) -> g (fun (y: b) -> true) in\n let inv2 (r: retract (pow a) (pow b)) (f: pow a) : GTot (ceq (j2 (i2 f)) f) =\n Ceq.refl (fun (x: a) -> f x) in\n return_squash (MkC i2 j2 inv2)", "let l1 a b =\n let i2 (p: pow a) : pow b = fun (x:b) -> p (x :> a) in\n let j2 (q: pow b) : pow a = fun (x:a) -> q (x :> b) in\n let inv2 (r: retract (pow a) (pow b)) (x: pow a) : GTot (ceq (j2 (i2 x)) x) =\n Ceq.refl x in\n return_squash (MkC i2 j2 inv2)", "let l1 a b =\n let i2 (f: pow a) : pow b = fun (x: b) -> f (fun (y: a) -> x = y) in\n let j2 (g: pow b) : pow a = fun (x: a) -> g (fun (y: b) -> x = y) in\n let inv2 (r: retract (pow a) (pow b)) (f: pow a) : GTot (ceq (j2 (i2 f)) f) =\n fun (x: a) -> Ceq.refl (f x) in\n give_proof (squash (MkC i2 j2 inv2))", "let l1 a b =\n let i2 (f: pow a) : pow b = fun (x: b) -> f (fun _ -> x) in\n let j2 (g: pow b) : pow a = fun (x: a) -> g (fun _ -> x) in\n let inv2 (r: retract (pow a) (pow b)) (f: pow a) : GTot (ceq (j2 (i2 f)) f) =\n fun _ -> Ceq.refl (fun _ -> f) in\n return_squash (MkC i2 j2 inv2)", "let l1 a b =\n let i2 (f: pow a) : pow b = fun (x: b) -> f (fun _ -> true) in\n let j2 (g: pow b) : pow a = fun (x: a) -> g (fun _ -> true) in\n let inv2 (r: retract (pow a) (pow b)) (x: pow a) : GTot (ceq (j2 (i2 x)) x) =\n Ceq.refl (x (fun _ -> true)) in\n squash (MkC i2 j2 inv2)", "let l1 a b =\n let i2 (p: pow a) : pow b = fun (x: b) -> p (fun _ -> true) in\n let j2 (q: pow b) : pow a = fun (x: a) -> q (fun _ -> true) in\n let inv2 (r: retract (pow a) (pow b)) (p: pow a) : GTot (ceq (j2 (i2 p)) p) =\n Ceq.refl (fun _ -> true) in\n return_squash (MkC i2 j2 inv2)", "let l1 a b =\n let i2 (f: pow a) : pow b = fun (x: b) -> f (fun _ -> true) in\n let j2 (g: pow b) : pow a = fun (x: a) -> g (fun _ -> true) in\n let inv2 (r: retract (pow a) (pow b)) (x: pow a) : GTot (ceq (j2 (i2 x)) x) =\n Ceq_refl in\n return_squash (MkC i2 j2 inv2)", "let l1 a b =\n let i2 (p: pow a) : pow b = fun (x: b) -> p (fun _ -> true) in\n let j2 (q: pow b) : pow a = fun (x: a) -> q (fun _ -> true) in\n let inv2 (r: retract (pow a) (pow b)) (p: pow a) : GTot (ceq (j2 (i2 p)) p) =\n Ceq.refl (fun _ -> true) in\n return_squash (MkC i2 j2 inv2)", "let l1 a b =\n let i2 (f: pow a) : pow b = fun (x: b) -> f (fun (y: a) -> true) in\n let j2 (g: pow b) : pow a = fun (x: a) -> g (fun (y: b) -> true) in\n let inv2 (r: retract (pow a) (pow b)) (f: pow a) : GTot (ceq (j2 (i2 f)) f) =\n Ceq_refl in\n return_squash (MkC i2 j2 inv2)" ] }, { "file_name": "Pulse.Typing.FV.fst", "name": "Pulse.Typing.FV.freevars_close_term_list'", "opens_and_abbrevs": [ { "open": "Pulse.Soundness.Common" }, { "open": "Pulse.Elaborate" }, { "open": "Pulse.Typing" }, { "open": "Pulse.Syntax" }, { "open": "FStar.List.Tot" }, { "abbrev": "L", "full_module": "FStar.List.Tot" }, { "abbrev": "R", "full_module": "FStar.Reflection.V2" }, { "abbrev": "RT", "full_module": "FStar.Reflection.Typing" }, { "open": "Pulse.Typing" }, { "open": "Pulse.Syntax.Naming" }, { "open": "Pulse.Syntax" }, { "open": "FStar.List.Tot" }, { "abbrev": "L", "full_module": "FStar.List.Tot" }, { "abbrev": "R", "full_module": "FStar.Reflection.V2" }, { "abbrev": "RT", "full_module": "FStar.Reflection.Typing" }, { "open": "Pulse.Typing" }, { "open": "Pulse.Typing" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 2, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t)", "source_definition": "let rec freevars_close_term_list' (t:list term) (x:var) (i:index)\n : Lemma\n (ensures (freevars_list (close_term_list' t x i) `Set.equal`\n (freevars_list t `set_minus` x)))\n (decreases t)\n = match t with\n | [] -> ()\n | hd::tl ->\n freevars_close_term' hd x i;\n freevars_close_term_list' tl x i", "source_range": { "start_line": 98, "start_col": 0, "end_line": 107, "end_col": 38 }, "interleaved": false, "definition": "fun t x i ->\n (match t with\n | Prims.Nil #_ -> ()\n | Prims.Cons #_ hd tl ->\n Pulse.Typing.FV.freevars_close_term' hd x i;\n Pulse.Typing.FV.freevars_close_term_list' tl x i)\n <:\n FStar.Pervasives.Lemma\n (ensures\n FStar.Set.equal (Pulse.Syntax.Naming.freevars_list (Pulse.Syntax.Naming.close_term_list' t x i))\n (Pulse.Typing.FV.set_minus (Pulse.Syntax.Naming.freevars_list t) x))", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma", "" ], "mutual_with": [], "premises": [ "Prims.list", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.var", "Pulse.Syntax.Base.index", "Pulse.Typing.FV.freevars_close_term_list'", "Prims.unit", "Pulse.Typing.FV.freevars_close_term'", "Prims.l_True", "Prims.squash", "FStar.Set.equal", "Pulse.Syntax.Naming.freevars_list", "Pulse.Syntax.Naming.close_term_list'", "Pulse.Typing.FV.set_minus", "Prims.Nil", "FStar.Pervasives.pattern" ], "proof_features": [ "recursion" ], "is_simple_lemma": false, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "t: Prims.list Pulse.Syntax.Base.term -> x: Pulse.Syntax.Base.var -> i: Pulse.Syntax.Base.index\n -> FStar.Pervasives.Lemma\n (ensures\n FStar.Set.equal (Pulse.Syntax.Naming.freevars_list (Pulse.Syntax.Naming.close_term_list' t\n x\n i))\n (Pulse.Typing.FV.set_minus (Pulse.Syntax.Naming.freevars_list t) x)) (decreases t)", "prompt": "let rec freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t) =\n ", "expected_response": "match t with\n| [] -> ()\n| hd :: tl ->\n freevars_close_term' hd x i;\n freevars_close_term_list' tl x i", "source": { "project_name": "steel", "file_name": "lib/steel/pulse/Pulse.Typing.FV.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Pulse.Typing.FV.fst", "checked_file": "dataset/Pulse.Typing.FV.fst.checked", "interface_file": true, "dependencies": [ "dataset/Pulse.Typing.Metatheory.Base.fsti.checked", "dataset/Pulse.Typing.fst.checked", "dataset/Pulse.Syntax.fst.checked", "dataset/Pulse.Soundness.Common.fst.checked", "dataset/Pulse.Elaborate.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Reflection.V2.fst.checked", "dataset/FStar.Reflection.Typing.fsti.checked", "dataset/FStar.Range.fsti.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.Calc.fsti.checked" ] }, "definitions_in_context": [ "let mem_intension_pat (#a:eqtype) (x:a) (f:(a -> Tot bool))\n : Lemma\n (ensures FStar.Set.(mem x (intension f) = f x))\n [SMTPat FStar.Set.(mem x (intension f))]\n = Set.mem_intension x f", "let vars_of_rt_env (g:R.env) = Set.intension (fun x -> Some? (RT.lookup_bvar g x))", "let freevars_close_term_host_term (t:host_term) (x:var) (i:index)\n : Lemma\n (ensures (freevars (close_term' (tm_fstar t FStar.Range.range_0) x i)\n `Set.equal`\n (freevars (tm_fstar t FStar.Range.range_0) `set_minus` x)))\n = admit()", "let contains (g:env) (x:var) = Some? (lookup g x)", "let vars_of_env (g:env) = dom g", "let set_minus (#a:eqtype) (s:Set.set a) (x:a) =\n Set.intersect s (Set.complement (Set.singleton x))", "let rec freevars_close_term' (e:term) (x:var) (i:index)\n : Lemma \n (ensures freevars (close_term' e x i) `Set.equal`\n (freevars e `set_minus` x))\n = match e.t with\n | Tm_Emp\n | Tm_VProp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown -> ()\n\n | Tm_Inv p ->\n freevars_close_term' p x i\n | Tm_Pure p ->\n freevars_close_term' p x i\n\n | Tm_AddInv l r\n | Tm_Star l r ->\n freevars_close_term' l x i;\n freevars_close_term' r x i\n\n | Tm_ExistsSL _ t b\n | Tm_ForallSL _ t b ->\n freevars_close_term' t.binder_ty x i; \n freevars_close_term' b x (i + 1)\n\n | Tm_FStar t ->\n freevars_close_term_host_term t x i", "val freevars_close_term (e:term) (x:var) (i:index)\n : Lemma \n (ensures freevars (close_term' e x i) ==\n freevars e `set_minus` x)\n [SMTPat (freevars (close_term' e x i))]", "val freevars_close_st_term (e:st_term) (x:var) (i:index)\n : Lemma \n (ensures freevars_st (close_st_term' e x i) ==\n freevars_st e `set_minus` x)\n [SMTPat (freevars_st (close_st_term' e x i))]", "val tot_typing_freevars (#g:_) (#t:_) (#ty:_)\n (d:tot_typing g t ty)\n : Lemma \n (ensures freevars t `Set.subset` vars_of_env g /\\\n freevars ty `Set.subset` vars_of_env g)", "val comp_typing_freevars (#g:_) (#c:_) (#u:_)\n (d:comp_typing g c u)\n : Lemma \n (ensures freevars_comp c `Set.subset` vars_of_env g)", "val st_typing_freevars (#g:_) (#t:_) (#c:_)\n (d:st_typing g t c)\n : Lemma \n (ensures freevars_st t `Set.subset` vars_of_env g /\\\n freevars_comp c `Set.subset` vars_of_env g)", "let freevars_close_comp (c:comp)\n (x:var)\n (i:index)\n : Lemma \n (ensures freevars_comp (close_comp' c x i) `Set.equal`\n (freevars_comp c `set_minus` x))\n [SMTPat (freevars_comp (close_comp' c x i))]\n = match c with\n | C_Tot t ->\n freevars_close_term' t x i\n\n | C_ST s\n | C_STGhost s -> \n freevars_close_term' s.res x i;\n freevars_close_term' s.pre x i; \n freevars_close_term' s.post x (i + 1)\n\n | C_STAtomic n _ s ->\n freevars_close_term' n x i; \n freevars_close_term' s.res x i;\n freevars_close_term' s.pre x i; \n freevars_close_term' s.post x (i + 1)", "let st_typing_freevars_inv (#g:_) (#t:_) (#c:_)\n (d:st_typing g t c)\n (x:var)\n : Lemma \n (requires None? (lookup g x))\n (ensures ~(x `Set.mem` freevars_st t) /\\\n ~(x `Set.mem` freevars_comp c))\n = st_typing_freevars d", "let freevars_close_term_opt' (t:option term) (x:var) (i:index)\n : Lemma\n (ensures (freevars_term_opt (close_term_opt' t x i) `Set.equal`\n (freevars_term_opt t `set_minus` x)))\n (decreases t)\n = match t with\n | None -> ()\n | Some t -> freevars_close_term' t x i" ], "closest": [ "val close_open_inverse_list' (t:list term)\r\n (x:var { ~(x `Set.mem` freevars_list t) })\r\n (i:index)\r\n : Lemma (ensures close_term_list' (open_term_list' t (U.term_of_no_name_var x) i) x i == t)\nlet rec close_open_inverse_list' (t:list term)\r\n (x:var { ~(x `Set.mem` freevars_list t) })\r\n (i:index)\r\n : Lemma (ensures close_term_list' (open_term_list' t (U.term_of_no_name_var x) i) x i == t)\r\n = match t with\r\n | [] -> ()\r\n | hd::tl ->\r\n close_open_inverse' hd x i;\r\n close_open_inverse_list' tl x i", "val close_term_ln_list' (t: list term) (x: var) (i: index)\n : Lemma (requires ln_list' t (i - 1))\n (ensures ln_list' (close_term_list' t x i) i)\n (decreases t)\nlet rec close_term_ln_list' (t:list term) (x:var) (i:index)\n : Lemma\n (requires ln_list' t (i - 1))\n (ensures ln_list' (close_term_list' t x i) i)\n (decreases t)\n = match t with\n | [] -> ()\n | hd::tl ->\n close_term_ln' hd x i;\n close_term_ln_list' tl x i", "val close_open_inverse' (t:term) \r\n (x:var { ~(x `Set.mem` freevars t) } )\r\n (i:index)\r\n : Lemma (ensures close_term' (open_term' t (U.term_of_no_name_var x) i) x i == t)\nlet rec close_open_inverse' (t:term) \r\n (x:var { ~(x `Set.mem` freevars t) } )\r\n (i:index)\r\n : Lemma (ensures close_term' (open_term' t (U.term_of_no_name_var x) i) x i == t)\r\n (decreases t)\r\n = match t.t with\r\n | Tm_Emp\r\n | Tm_VProp\r\n | Tm_Inames \r\n | Tm_EmpInames\r\n | Tm_Unknown -> ()\r\n \r\n | Tm_Inv p ->\r\n close_open_inverse' p x i\r\n\r\n | Tm_Pure p ->\r\n close_open_inverse' p x i\r\n\r\n | Tm_Star l r ->\r\n close_open_inverse' l x i;\r\n close_open_inverse' r x i\r\n\r\n | Tm_ExistsSL _ t b\r\n | Tm_ForallSL _ t b ->\r\n close_open_inverse' t.binder_ty x i; \r\n close_open_inverse' b x (i + 1)\r\n\r\n | Tm_FStar t ->\r\n RT.close_open_inverse' i t x\r\n\r\n | Tm_AddInv n is ->\r\n close_open_inverse' n x i;\r\n close_open_inverse' is x i", "val close_open_inverse (t:term) (x:var { ~(x `Set.mem` freevars t) } )\r\n : Lemma (ensures close_term (open_term t x) x == t)\r\n (decreases t)\nlet close_open_inverse (t:term) (x:var { ~(x `Set.mem` freevars t) } )\r\n : Lemma (ensures close_term (open_term t x) x == t)\r\n (decreases t)\r\n = close_open_inverse' t x 0", "val close_terms_with_not_free_var (l: list R.term) (x: var) (i: nat)\n : Lemma (requires ~(Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ND x i] == l)\n (decreases l)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\nlet rec close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_Uvar _ _ -> assert false\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> ()\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n close_open_inverse' i t1 x;\n close_open_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n close_open_inverse'_binder i b x;\n close_open_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n close_open_inverse'_terms i attrs x;\n close_open_inverse'_binder i b x;\n close_open_inverse' (if recf then (i + 1) else i) def x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n close_open_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> close_open_inverse'_match_returns i m x);\n close_open_inverse'_branches i brs x\n\n | Tv_AscribedT e t tac b ->\n close_open_inverse' i e x;\n close_open_inverse' i t x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n\n | Tv_AscribedC e c tac b ->\n close_open_inverse' i e x;\n close_open_inverse'_comp i c x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n \nand close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t \n | C_GTotal t -> \n close_open_inverse' i t x\n\n | C_Lemma pre post pats ->\n close_open_inverse' i pre x;\n close_open_inverse' i post x;\n close_open_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n close_open_inverse' i res x;\n close_open_inverse'_args i args x;\n close_open_inverse'_terms i decrs x\n\nand close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\n (decreases args)\n = match args with\n | [] -> ()\n | (a, q) :: args ->\n close_open_inverse' i a x;\n close_open_inverse'_args i args x\n\nand close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\n (decreases b)\n = let bndr = inspect_binder b in\n close_open_inverse' i bndr.sort x;\n close_open_inverse'_terms i bndr.attrs x;\n pack_inspect_binder b\n\nand close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | hd :: tl ->\n close_open_inverse' i hd x;\n close_open_inverse'_terms i tl x\n\nand close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | b :: brs ->\n close_open_inverse'_branch i b x;\n close_open_inverse'_branches i brs x\n\nand close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\n (decreases br)\n = let p, t = br in\n close_open_inverse'_pattern i p x;\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse' (i + binder_offset_pattern p) t x\n\n\nand close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n close_open_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> close_open_inverse' i t x\n\nand close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n close_open_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse'_patterns (i + n) ps' x\n\nand close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n close_open_inverse'_binder i b x;\n (match ret with\n | Inl t -> close_open_inverse' (i + 1) t x\n | Inr c -> close_open_inverse'_comp (i + 1) c x);\n (match as_ with\n | None -> ()\n | Some t -> close_open_inverse' (i + 1) t x)", "val close_open_inverse_opt' (t:option term)\r\n (x:var { ~(x `Set.mem` freevars_term_opt t) })\r\n (i:index)\r\n : Lemma (ensures close_term_opt' (open_term_opt' t (U.term_of_no_name_var x) i) x i == t)\nlet close_open_inverse_opt' (t:option term)\r\n (x:var { ~(x `Set.mem` freevars_term_opt t) })\r\n (i:index)\r\n : Lemma (ensures close_term_opt' (open_term_opt' t (U.term_of_no_name_var x) i) x i == t)\r\n = match t with\r\n | None -> ()\r\n | Some t -> close_open_inverse' t x i", "val close_open_inverse_pairs'\n (t: list (term * term))\n (x: var{~(x `Set.mem` (freevars_pairs t))})\n (i: index)\n : Lemma (ensures close_term_pairs' (open_term_pairs' t (U.term_of_no_name_var x) i) x i == t)\nlet rec close_open_inverse_pairs' (t:list (term * term))\r\n (x:var { ~(x `Set.mem` freevars_pairs t) })\r\n (i:index)\r\n : Lemma (ensures close_term_pairs' (open_term_pairs' t (U.term_of_no_name_var x) i) x i == t)\r\n = match t with\r\n | [] -> ()\r\n | (hd1, hd2)::tl ->\r\n close_open_inverse' hd1 x i;\r\n close_open_inverse' hd2 x i;\r\n close_open_inverse_pairs' tl x i", "val open_term_ln_list' (t: list term) (x: term) (i: index)\n : Lemma (requires ln_list' (open_term_list' t x i) (i - 1)) (ensures ln_list' t i) (decreases t)\nlet rec open_term_ln_list' (t:list term) (x:term) (i:index)\n : Lemma\n (requires ln_list' (open_term_list' t x i) (i - 1))\n (ensures ln_list' t i)\n (decreases t)\n = match t with\n | [] -> ()\n | hd::tl ->\n open_term_ln' hd x i;\n open_term_ln_list' tl x i", "val close_term_ln_pairs (t: list (term & term)) (x: var) (i: index)\n : Lemma (requires ln_terms' t (i - 1))\n (ensures ln_terms' (close_term_pairs' t x i) i)\n (decreases t)\nlet rec close_term_ln_pairs (t:list (term & term)) (x:var) (i:index)\n : Lemma\n (requires ln_terms' t (i - 1))\n (ensures ln_terms' (close_term_pairs' t x i) i)\n (decreases t)\n = match t with\n | [] -> ()\n | (l, r)::tl ->\n close_term_ln' l x i;\n close_term_ln' r x i;\n close_term_ln_pairs tl x i", "val close_open_inverse_st (t:st_term) (x:var { ~(x `Set.mem` freevars_st t) } )\r\n : Lemma (ensures close_st_term (open_st_term t x) x == t)\r\n (decreases t)\nlet close_open_inverse_st (t:st_term) (x:var { ~(x `Set.mem` freevars_st t) } )\r\n : Lemma (ensures close_st_term (open_st_term t x) x == t)\r\n (decreases t)\r\n = close_open_inverse_st' t x 0", "val close_term_ln' (e: term) (x: var) (i: index)\n : Lemma (requires ln' e (i - 1)) (ensures ln' (close_term' e x i) i) (decreases e)\nlet rec close_term_ln' (e:term)\n (x:var)\n (i:index)\n : Lemma \n (requires ln' e (i - 1))\n (ensures ln' (close_term' e x i) i)\n (decreases e)\n = match e.t with\n | Tm_Emp\n | Tm_VProp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown -> ()\n\n | Tm_Inv p ->\n close_term_ln' p x i\n | Tm_Pure p ->\n close_term_ln' p x i\n\n | Tm_AddInv l r\n | Tm_Star l r ->\n close_term_ln' l x i;\n close_term_ln' r x i\n\n | Tm_ExistsSL _ t b\n | Tm_ForallSL _ t b ->\n close_term_ln' t.binder_ty x i; \n close_term_ln' b x (i + 1)\n\n | Tm_FStar t ->\n r_close_term_ln' t x i", "val close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\nlet rec close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_Uvar _ _ -> assert false\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> ()\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n close_open_inverse' i t1 x;\n close_open_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n close_open_inverse'_binder i b x;\n close_open_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n close_open_inverse'_terms i attrs x;\n close_open_inverse'_binder i b x;\n close_open_inverse' (if recf then (i + 1) else i) def x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n close_open_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> close_open_inverse'_match_returns i m x);\n close_open_inverse'_branches i brs x\n\n | Tv_AscribedT e t tac b ->\n close_open_inverse' i e x;\n close_open_inverse' i t x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n\n | Tv_AscribedC e c tac b ->\n close_open_inverse' i e x;\n close_open_inverse'_comp i c x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n \nand close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t \n | C_GTotal t -> \n close_open_inverse' i t x\n\n | C_Lemma pre post pats ->\n close_open_inverse' i pre x;\n close_open_inverse' i post x;\n close_open_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n close_open_inverse' i res x;\n close_open_inverse'_args i args x;\n close_open_inverse'_terms i decrs x\n\nand close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\n (decreases args)\n = match args with\n | [] -> ()\n | (a, q) :: args ->\n close_open_inverse' i a x;\n close_open_inverse'_args i args x\n\nand close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\n (decreases b)\n = let bndr = inspect_binder b in\n close_open_inverse' i bndr.sort x;\n close_open_inverse'_terms i bndr.attrs x;\n pack_inspect_binder b\n\nand close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | hd :: tl ->\n close_open_inverse' i hd x;\n close_open_inverse'_terms i tl x\n\nand close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | b :: brs ->\n close_open_inverse'_branch i b x;\n close_open_inverse'_branches i brs x\n\nand close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\n (decreases br)\n = let p, t = br in\n close_open_inverse'_pattern i p x;\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse' (i + binder_offset_pattern p) t x\n\n\nand close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n close_open_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> close_open_inverse' i t x\n\nand close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n close_open_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse'_patterns (i + n) ps' x\n\nand close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n close_open_inverse'_binder i b x;\n (match ret with\n | Inl t -> close_open_inverse' (i + 1) t x\n | Inr c -> close_open_inverse'_comp (i + 1) c x);\n (match as_ with\n | None -> ()\n | Some t -> close_open_inverse' (i + 1) t x)", "val close_term_list' (t: list term) (v: var) (i: index) : list term\nlet close_term_list' (t:list term) (v:var) (i:index) : list term =\r\n subst_term_list t [ ND v i ]", "val open_term_ln_inv_list' (t: list term) (x: term{ln x}) (i: index)\n : Lemma (requires ln_list' t i) (ensures ln_list' (open_term_list' t x i) (i - 1)) (decreases t)\nlet rec open_term_ln_inv_list' (t:list term)\n (x:term { ln x })\n (i:index)\n : Lemma\n (requires ln_list' t i)\n (ensures ln_list' (open_term_list' t x i) (i - 1))\n (decreases t)\n = match t with\n | [] -> ()\n | hd::tl ->\n open_term_ln_inv' hd x i;\n open_term_ln_inv_list' tl x i", "val close_args_with_not_free_var (l: list R.argv) (x: var) (i: nat)\n : Lemma (requires ~(Set.mem x (freevars_args l)))\n (ensures subst_args l [ND x i] == l)\n (decreases l)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val close_term_ln_opt' (t: option term) (x: var) (i: index)\n : Lemma (requires ln_opt' ln' t (i - 1))\n (ensures ln_opt' ln' (close_term_opt' t x i) i)\n (decreases t)\nlet close_term_ln_opt' (t:option term) (x:var) (i:index)\n : Lemma\n (requires ln_opt' ln' t (i - 1))\n (ensures ln_opt' ln' (close_term_opt' t x i) i)\n (decreases t)\n = match t with\n | None -> ()\n | Some t -> close_term_ln' t x i", "val open_ty_freevars (t: src_ty) (v: src_exp) (n: nat)\n : Lemma\n (ensures\n ((freevars_ty t) `Set.subset` (freevars_ty (open_ty' t v n))) /\\\n ((freevars_ty (open_ty' t v n)) `Set.subset` ((freevars_ty t) `Set.union` (freevars v))))\n (decreases t)\nlet rec open_exp_freevars (e:src_exp) (v:src_exp) (n:nat)\n : Lemma \n (ensures (freevars e `Set.subset` freevars (open_exp' e v n)) /\\\n (freevars (open_exp' e v n) `Set.subset` (freevars e `Set.union` freevars v)))\n (decreases e)\n // [SMTPat (freevars (open_exp' e v n))]\n = match e with\n | EBool _\n | EBVar _ \n | EVar _ -> ()\n | EApp e1 e2 ->\n open_exp_freevars e1 v n;\n open_exp_freevars e2 v n\n | EIf b e1 e2 ->\n open_exp_freevars b v n; \n open_exp_freevars e1 v n;\n open_exp_freevars e2 v n\n | ELam t e ->\n open_ty_freevars t v n;\n open_exp_freevars e v (n + 1)\n\nand open_ty_freevars (t:src_ty) (v:src_exp) (n:nat)\n : Lemma \n (ensures (freevars_ty t `Set.subset` freevars_ty (open_ty' t v n)) /\\\n (freevars_ty (open_ty' t v n) `Set.subset` (freevars_ty t `Set.union` freevars v)))\n (decreases t)\n // [SMTPat (freevars_ty (open_ty' t v n))]\n = match t with\n | TBool -> ()\n | TArrow t1 t2 ->\n open_ty_freevars t1 v n;\n open_ty_freevars t2 v (n + 1)\n | TRefineBool e ->\n open_exp_freevars e v (n + 1)", "val open_close_inverse' (i:nat) (t:term { ln' t (i - 1) }) (x:var)\n : Lemma \n (ensures subst_term \n (subst_term t [ ND x i ])\n (open_with_var x i)\n == t)\nlet rec open_close_inverse' (i:nat) (t:term { ln' t (i - 1) }) (x:var)\n : Lemma\n (ensures subst_term \n (subst_term t [ ND x i ])\n (open_with_var x i)\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n open_close_inverse' i t1 x;\n open_close_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n open_close_inverse'_binder i b x;\n open_close_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n open_close_inverse'_binder i b x;\n open_close_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n open_close_inverse'_binder i b x;\n open_close_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n open_close_inverse'_terms i attrs x;\n open_close_inverse'_binder i b x;\n (if recf \n then open_close_inverse' (i + 1) def x\n else open_close_inverse' i def x);\n open_close_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n open_close_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> open_close_inverse'_match_returns i m x);\n open_close_inverse'_branches i brs x\n \n | Tv_AscribedT e t tac b ->\n open_close_inverse' i e x;\n open_close_inverse' i t x; \n (match tac with\n | None -> ()\n | Some tac -> open_close_inverse' i tac x)\n\n | Tv_AscribedC e c tac b ->\n open_close_inverse' i e x;\n open_close_inverse'_comp i c x; \n (match tac with\n | None -> ()\n | Some tac -> open_close_inverse' i tac x)\n \n\nand open_close_inverse'_binder (i:nat) (b:binder { ln'_binder b (i - 1) }) (x:var)\n : Lemma (ensures subst_binder\n (subst_binder b [ ND x i ])\n (open_with_var x i)\n == b)\n (decreases b) \n = let bndr = inspect_binder b in\n let {ppname; qual=q; attrs=attrs; sort=sort} = bndr in\n open_close_inverse' i sort x;\n open_close_inverse'_terms i attrs x;\n assert (subst_terms (subst_terms attrs [ ND x i ])\n (open_with_var x i) == attrs); \n pack_inspect_binder b; \n assert (pack_binder {ppname; qual=q; attrs=attrs; sort=sort} == b)\n\nand open_close_inverse'_terms (i:nat) (ts:list term { ln'_terms ts (i - 1) }) (x:var)\n : Lemma (ensures subst_terms\n (subst_terms ts [ ND x i ])\n (open_with_var x i)\n == ts)\n (decreases ts) \n = match ts with\n | [] -> ()\n | t::ts -> \n open_close_inverse' i t x;\n open_close_inverse'_terms i ts x\n\nand open_close_inverse'_comp (i:nat) (c:comp { ln'_comp c (i - 1) }) (x:var)\n : Lemma \n (ensures subst_comp\n (subst_comp c [ ND x i ])\n (open_with_var x i)\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t -> open_close_inverse' i t x\n\n | C_Lemma pre post pats ->\n open_close_inverse' i pre x;\n open_close_inverse' i post x;\n open_close_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n open_close_inverse' i res x;\n open_close_inverse'_args i args x;\n open_close_inverse'_terms i decrs x \n\nand open_close_inverse'_args (i:nat) \n (ts:list argv { ln'_args ts (i - 1) })\n (x:var)\n : Lemma\n (ensures subst_args\n (subst_args ts [ ND x i ])\n (open_with_var x i)\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | (t,q)::ts -> \n open_close_inverse' i t x;\n open_close_inverse'_args i ts x\n\nand open_close_inverse'_patterns (i:nat)\n (ps:list (pattern & bool) { ln'_patterns ps (i - 1) })\n (x:var)\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps [ ND x i ])\n (open_with_var x i)\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n open_close_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p [ ND x i ];\n open_close_inverse'_patterns (i + n) ps' x\n\nand open_close_inverse'_pattern (i:nat) (p:pattern{ln'_pattern p (i - 1)}) (x:var)\n : Lemma \n (ensures subst_pattern\n (subst_pattern p [ ND x i ])\n (open_with_var x i)\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n open_close_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> open_close_inverse' i t x\n\n \nand open_close_inverse'_branch (i:nat) (br:branch{ln'_branch br (i - 1)}) (x:var)\n : Lemma\n (ensures subst_branch\n (subst_branch br [ ND x i ])\n (open_with_var x i)\n == br)\n (decreases br) \n = let p, t = br in\n let j = binder_offset_pattern p in\n binder_offset_pattern_invariant p [ ND x i ];\n open_close_inverse'_pattern i p x;\n open_close_inverse' (i + j) t x\n \nand open_close_inverse'_branches (i:nat)\n (brs:list branch { ln'_branches brs (i - 1) })\n (x:var)\n : Lemma\n (ensures subst_branches\n (subst_branches brs [ ND x i ])\n (open_with_var x i)\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | br::brs -> \n open_close_inverse'_branch i br x;\n open_close_inverse'_branches i brs x\n \nand open_close_inverse'_match_returns (i:nat) \n (m:match_returns_ascription { ln'_match_returns m (i - 1) })\n (x:var)\n : Lemma \n (ensures subst_match_returns\n (subst_match_returns m [ ND x i ])\n (open_with_var x i)\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n open_close_inverse'_binder i b x;\n let ret =\n match ret with\n | Inl t ->\n open_close_inverse' (i + 1) t x\n | Inr c ->\n open_close_inverse'_comp (i + 1) c x\n in\n let as_ =\n match as_ with\n | None -> ()\n | Some t ->\n open_close_inverse' (i + 1) t x\n in\n ()", "val close_open_inverse_ascription'\n (t: comp_ascription)\n (x: var{~(x `Set.mem` (freevars_ascription t))})\n (i: index)\n : Lemma (ensures close_ascription' (open_ascription' t (U.term_of_no_name_var x) i) x i == t)\nlet close_open_inverse_ascription' (t:comp_ascription)\r\n (x:var { ~(x `Set.mem` freevars_ascription t) } )\r\n (i:index)\r\n : Lemma (ensures close_ascription' (open_ascription' t (U.term_of_no_name_var x) i) x i == t)\r\n = (match t.annotated with\r\n | None -> ()\r\n | Some c -> close_open_inverse_comp' c x i);\r\n (match t.elaborated with\r\n | None -> ()\r\n | Some c -> close_open_inverse_comp' c x i)", "val close_exp_freevars (m: int) (e: src_exp{ln' e m}) (v: var) (n: nat)\n : Lemma (ensures (freevars (close_exp' e v n)) `Set.equal` ((freevars e) `minus` v))\n (decreases e)\nlet rec close_exp_freevars (m:int) (e:src_exp { ln' e m } ) (v:var) (n:nat)\n : Lemma \n (ensures freevars (close_exp' e v n) `Set.equal`\n (freevars e `minus` v))\n (decreases e)\n = match e with\n | EBool _\n | EBVar _ \n | EVar _ -> ()\n | EApp e1 e2 ->\n close_exp_freevars m e1 v n;\n close_exp_freevars m e2 v n\n | EIf b e1 e2 ->\n close_exp_freevars m b v n; \n close_exp_freevars m e1 v n;\n close_exp_freevars m e2 v n\n | ELam t body ->\n close_exp_freevars (m + 1) body v (n + 1)", "val freevars_open (e: stlc_exp) (x: var) (n: nat)\n : Lemma ((freevars (open_exp' e x n)) `Set.subset` ((freevars e) `Set.union` (Set.singleton x)))\nlet rec freevars_open (e:stlc_exp) (x:var) (n:nat)\n : Lemma (freevars (open_exp' e x n) `Set.subset`\n (freevars e `Set.union` Set.singleton x))\n = match e with\n | EUnit \n | EBVar _\n | EVar _ -> ()\n | ELam _ e -> freevars_open e x (n + 1)\n | EApp e1 e2 ->\n freevars_open e1 x n;\n freevars_open e2 x n", "val close_pattern_with_not_free_var (p: R.pattern) (x: var) (i: nat)\n : Lemma (requires ~(Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ND x i] == p)\n (decreases p)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val close_with_non_freevar_st (s:st_comp) (x:var) (i:nat)\r\n : Lemma\r\n (requires ~ (x `Set.mem` freevars_st_comp s))\r\n (ensures close_st_comp' s x i == s)\nlet close_with_non_freevar_st (s:st_comp) (x:var) (i:nat)\r\n : Lemma\r\n (requires ~ (x `Set.mem` freevars_st_comp s))\r\n (ensures close_st_comp' s x i == s) =\r\n let {res; pre; post} = s in\r\n close_with_non_freevar res x i;\r\n close_with_non_freevar pre x i;\r\n close_with_non_freevar post x (i + 1)", "val open_exp_freevars (e v: src_exp) (n: nat)\n : Lemma\n (ensures\n ((freevars e) `Set.subset` (freevars (open_exp' e v n))) /\\\n ((freevars (open_exp' e v n)) `Set.subset` ((freevars e) `Set.union` (freevars v))))\n (decreases e)\nlet rec open_exp_freevars (e:src_exp) (v:src_exp) (n:nat)\n : Lemma \n (ensures (freevars e `Set.subset` freevars (open_exp' e v n)) /\\\n (freevars (open_exp' e v n) `Set.subset` (freevars e `Set.union` freevars v)))\n (decreases e)\n // [SMTPat (freevars (open_exp' e v n))]\n = match e with\n | EBool _\n | EBVar _ \n | EVar _ -> ()\n | EApp e1 e2 ->\n open_exp_freevars e1 v n;\n open_exp_freevars e2 v n\n | EIf b e1 e2 ->\n open_exp_freevars b v n; \n open_exp_freevars e1 v n;\n open_exp_freevars e2 v n\n | ELam t e ->\n open_ty_freevars t v n;\n open_exp_freevars e v (n + 1)\n\nand open_ty_freevars (t:src_ty) (v:src_exp) (n:nat)\n : Lemma \n (ensures (freevars_ty t `Set.subset` freevars_ty (open_ty' t v n)) /\\\n (freevars_ty (open_ty' t v n) `Set.subset` (freevars_ty t `Set.union` freevars v)))\n (decreases t)\n // [SMTPat (freevars_ty (open_ty' t v n))]\n = match t with\n | TBool -> ()\n | TArrow t1 t2 ->\n open_ty_freevars t1 v n;\n open_ty_freevars t2 v (n + 1)\n | TRefineBool e ->\n open_exp_freevars e v (n + 1)", "val close_comp_with_not_free_var (c: R.comp) (x: var) (i: nat)\n : Lemma (requires ~(Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ND x i] == c)\n (decreases c)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val __close_term_vs (i: nat) (vs: list var) (t: term) : Tot term (decreases vs)\nlet rec __close_term_vs (i:nat) (vs : list var) (t : term) : Tot term (decreases vs) =\n match vs with\n | [] -> t\n | v::vs ->\n subst_term (__close_term_vs (i+1) vs t) [ND v i]", "val close_open_inverse_comp' (c:comp)\r\n (x:var { ~(x `Set.mem` freevars_comp c) } )\r\n (i:index)\r\n : Lemma (ensures close_comp' (open_comp' c (U.term_of_no_name_var x) i) x i == c)\nlet close_open_inverse_comp' (c:comp)\r\n (x:var { ~(x `Set.mem` freevars_comp c) } )\r\n (i:index)\r\n : Lemma (ensures close_comp' (open_comp' c (U.term_of_no_name_var x) i) x i == c)\r\n = match c with\r\n | C_Tot t ->\r\n close_open_inverse' t x i\r\n\r\n | C_ST s \r\n | C_STGhost s -> \r\n close_open_inverse' s.res x i;\r\n close_open_inverse' s.pre x i; \r\n close_open_inverse' s.post x (i + 1)\r\n\r\n | C_STAtomic n _ s -> \r\n close_open_inverse' n x i; \r\n close_open_inverse' s.res x i;\r\n close_open_inverse' s.pre x i; \r\n close_open_inverse' s.post x (i + 1)", "val close_patterns_with_not_free_var (l: list (R.pattern & bool)) (x: var) (i: nat)\n : Lemma (requires ~(Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ND x i] == l)\n (decreases l)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val close_term' (t: term) (v: var) (i: index) : term\nlet close_term' (t:term) (v:var) (i:index) : term =\r\n subst_term t [ ND v i ]", "val open_close_inverse'_terms (i:nat) (ts:list term { ln'_terms ts (i - 1) }) (x:var)\n : Lemma (ensures subst_terms\n (subst_terms ts [ ND x i ])\n (open_with_var x i)\n == ts)\nlet rec open_close_inverse' (i:nat) (t:term { ln' t (i - 1) }) (x:var)\n : Lemma\n (ensures subst_term \n (subst_term t [ ND x i ])\n (open_with_var x i)\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n open_close_inverse' i t1 x;\n open_close_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n open_close_inverse'_binder i b x;\n open_close_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n open_close_inverse'_binder i b x;\n open_close_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n open_close_inverse'_binder i b x;\n open_close_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n open_close_inverse'_terms i attrs x;\n open_close_inverse'_binder i b x;\n (if recf \n then open_close_inverse' (i + 1) def x\n else open_close_inverse' i def x);\n open_close_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n open_close_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> open_close_inverse'_match_returns i m x);\n open_close_inverse'_branches i brs x\n \n | Tv_AscribedT e t tac b ->\n open_close_inverse' i e x;\n open_close_inverse' i t x; \n (match tac with\n | None -> ()\n | Some tac -> open_close_inverse' i tac x)\n\n | Tv_AscribedC e c tac b ->\n open_close_inverse' i e x;\n open_close_inverse'_comp i c x; \n (match tac with\n | None -> ()\n | Some tac -> open_close_inverse' i tac x)\n \n\nand open_close_inverse'_binder (i:nat) (b:binder { ln'_binder b (i - 1) }) (x:var)\n : Lemma (ensures subst_binder\n (subst_binder b [ ND x i ])\n (open_with_var x i)\n == b)\n (decreases b) \n = let bndr = inspect_binder b in\n let {ppname; qual=q; attrs=attrs; sort=sort} = bndr in\n open_close_inverse' i sort x;\n open_close_inverse'_terms i attrs x;\n assert (subst_terms (subst_terms attrs [ ND x i ])\n (open_with_var x i) == attrs); \n pack_inspect_binder b; \n assert (pack_binder {ppname; qual=q; attrs=attrs; sort=sort} == b)\n\nand open_close_inverse'_terms (i:nat) (ts:list term { ln'_terms ts (i - 1) }) (x:var)\n : Lemma (ensures subst_terms\n (subst_terms ts [ ND x i ])\n (open_with_var x i)\n == ts)\n (decreases ts) \n = match ts with\n | [] -> ()\n | t::ts -> \n open_close_inverse' i t x;\n open_close_inverse'_terms i ts x\n\nand open_close_inverse'_comp (i:nat) (c:comp { ln'_comp c (i - 1) }) (x:var)\n : Lemma \n (ensures subst_comp\n (subst_comp c [ ND x i ])\n (open_with_var x i)\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t -> open_close_inverse' i t x\n\n | C_Lemma pre post pats ->\n open_close_inverse' i pre x;\n open_close_inverse' i post x;\n open_close_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n open_close_inverse' i res x;\n open_close_inverse'_args i args x;\n open_close_inverse'_terms i decrs x \n\nand open_close_inverse'_args (i:nat) \n (ts:list argv { ln'_args ts (i - 1) })\n (x:var)\n : Lemma\n (ensures subst_args\n (subst_args ts [ ND x i ])\n (open_with_var x i)\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | (t,q)::ts -> \n open_close_inverse' i t x;\n open_close_inverse'_args i ts x\n\nand open_close_inverse'_patterns (i:nat)\n (ps:list (pattern & bool) { ln'_patterns ps (i - 1) })\n (x:var)\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps [ ND x i ])\n (open_with_var x i)\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n open_close_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p [ ND x i ];\n open_close_inverse'_patterns (i + n) ps' x\n\nand open_close_inverse'_pattern (i:nat) (p:pattern{ln'_pattern p (i - 1)}) (x:var)\n : Lemma \n (ensures subst_pattern\n (subst_pattern p [ ND x i ])\n (open_with_var x i)\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n open_close_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> open_close_inverse' i t x\n\n \nand open_close_inverse'_branch (i:nat) (br:branch{ln'_branch br (i - 1)}) (x:var)\n : Lemma\n (ensures subst_branch\n (subst_branch br [ ND x i ])\n (open_with_var x i)\n == br)\n (decreases br) \n = let p, t = br in\n let j = binder_offset_pattern p in\n binder_offset_pattern_invariant p [ ND x i ];\n open_close_inverse'_pattern i p x;\n open_close_inverse' (i + j) t x\n \nand open_close_inverse'_branches (i:nat)\n (brs:list branch { ln'_branches brs (i - 1) })\n (x:var)\n : Lemma\n (ensures subst_branches\n (subst_branches brs [ ND x i ])\n (open_with_var x i)\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | br::brs -> \n open_close_inverse'_branch i br x;\n open_close_inverse'_branches i brs x\n \nand open_close_inverse'_match_returns (i:nat) \n (m:match_returns_ascription { ln'_match_returns m (i - 1) })\n (x:var)\n : Lemma \n (ensures subst_match_returns\n (subst_match_returns m [ ND x i ])\n (open_with_var x i)\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n open_close_inverse'_binder i b x;\n let ret =\n match ret with\n | Inl t ->\n open_close_inverse' (i + 1) t x\n | Inr c ->\n open_close_inverse'_comp (i + 1) c x\n in\n let as_ =\n match as_ with\n | None -> ()\n | Some t ->\n open_close_inverse' (i + 1) t x\n in\n ()", "val vars_decrease_eqns: x:nat -> t:term -> e:eqns -> Lemma\n (requires (ok (x, t)))\n (ensures (OrdSet.subset (evars (lsubst_eqns [x,t] e))\n\t\t\t (OrdSet.remove x (evars ((V x, t)::e)))))\nlet rec vars_decrease_eqns x t e = match e with\n | [] -> ()\n | hd::tl -> lemma_vars_decrease (x,t) (fst hd);\n\t lemma_vars_decrease (x,t) (snd hd);\n\t vars_decrease_eqns x t tl", "val open_term_ln_inv_pairs (t: list (term & term)) (x: term{ln x}) (i: index)\n : Lemma (requires ln_terms' t i)\n (ensures ln_terms' (open_term_pairs' t x i) (i - 1))\n (decreases t)\nlet rec open_term_ln_inv_pairs (t:list (term & term))\n (x:term { ln x })\n (i:index)\n : Lemma\n (requires ln_terms' t i)\n (ensures ln_terms' (open_term_pairs' t x i) (i - 1))\n (decreases t)\n = match t with\n | [] -> ()\n | (l, r)::tl ->\n open_term_ln_inv' l x i;\n open_term_ln_inv' r x i;\n open_term_ln_inv_pairs tl x i", "val open_term_ln_pairs (t: list (term & term)) (x: term) (i: index)\n : Lemma (requires ln_terms' (open_term_pairs' t x i) (i - 1))\n (ensures ln_terms' t i)\n (decreases t)\nlet rec open_term_ln_pairs (t:list (term & term)) (x:term) (i:index)\n : Lemma\n (requires ln_terms' (open_term_pairs' t x i) (i - 1))\n (ensures ln_terms' t i)\n (decreases t)\n = match t with\n | [] -> ()\n | (l, r)::tl ->\n open_term_ln' l x i;\n open_term_ln' r x i;\n open_term_ln_pairs tl x i", "val close_comp_with_non_free_var (c:comp) (x:var) (i:nat)\r\n : Lemma\r\n (requires ~ (x `Set.mem` freevars_comp c))\r\n (ensures close_comp' c x i == c)\nlet close_comp_with_non_free_var (c:comp) (x:var) (i:nat)\r\n : Lemma\r\n (requires ~ (x `Set.mem` freevars_comp c))\r\n (ensures close_comp' c x i == c) =\r\n match c with\r\n | C_Tot t1 -> close_with_non_freevar t1 x i\r\n | C_ST s \r\n | C_STGhost s ->\r\n close_with_non_freevar_st s x i\r\n | C_STAtomic inames _ s ->\r\n close_with_non_freevar inames x i;\r\n close_with_non_freevar_st s x i", "val close_open_inverse (e:R.term) (x:var {~ (x `Set.mem` freevars e) })\n : Lemma (close_term (open_term e x) x == e)\nlet close_open_inverse (e:R.term) (x:var {~ (x `Set.mem` freevars e) })\n : Lemma (close_term (open_term e x) x == e)\n = open_term_spec e x;\n close_term_spec (open_term e x) x;\n close_open_inverse' 0 e x", "val close_match_returns_with_not_free_var (r: match_returns_ascription) (x: var) (i: nat)\n : Lemma (requires ~(Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ND x i] == r)\n (decreases r)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val st_typing_freevars_inv (#g #t #c: _) (d: st_typing g t c) (x: var)\n : Lemma (requires None? (lookup g x))\n (ensures ~(x `Set.mem` (freevars_st t)) /\\ ~(x `Set.mem` (freevars_comp c)))\nlet st_typing_freevars_inv (#g:_) (#t:_) (#c:_)\n (d:st_typing g t c)\n (x:var)\n : Lemma \n (requires None? (lookup g x))\n (ensures ~(x `Set.mem` freevars_st t) /\\\n ~(x `Set.mem` freevars_comp c))\n = st_typing_freevars d", "val close_branches_with_not_free_var (brs: list R.branch) (x: var) (i: nat)\n : Lemma (requires ~(Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ND x i] == brs)\n (decreases brs)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val close_binder_with_not_free_var (b: R.binder) (x: var) (i: nat)\n : Lemma (requires ~(Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ND x i] == b)\n (decreases b)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val lemma_vars_decrease: s:subst -> t':term -> Lemma\n (requires (ok s))\n (ensures (OrdSet.subset (vars (subst_term s t'))\n \t\t\t (OrdSet.remove (fst s) (OrdSet.union (vars (snd s)) (vars t')))))\nlet rec lemma_vars_decrease s t' = match t' with\n | V x -> ()\n | F t1 t2 ->\n lemma_vars_decrease s t1;\n lemma_vars_decrease s t2", "val close_branch_with_not_free_var (br: R.branch) (x: var) (i: nat)\n : Lemma (requires ~(Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ND x i] == br)\n (decreases br)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val open_term_ln_opt' (t: option term) (x: term) (i: index)\n : Lemma (requires ln_opt' ln' (open_term_opt' t x i) (i - 1))\n (ensures ln_opt' ln' t i)\n (decreases t)\nlet open_term_ln_opt' (t:option term) (x:term) (i:index)\n : Lemma\n (requires ln_opt' ln' (open_term_opt' t x i) (i - 1))\n (ensures ln_opt' ln' t i)\n (decreases t)\n = match t with\n | None -> ()\n | Some t -> open_term_ln' t x i", "val freevars_list (t: list term) : Set.set var\nlet rec freevars_list (t:list term) : Set.set var =\r\n match t with\r\n | [] -> Set.empty\r\n | hd::tl -> freevars hd `Set.union` freevars_list tl", "val close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\nlet rec close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_Uvar _ _ -> assert false\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> ()\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n close_open_inverse' i t1 x;\n close_open_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n close_open_inverse'_binder i b x;\n close_open_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n close_open_inverse'_terms i attrs x;\n close_open_inverse'_binder i b x;\n close_open_inverse' (if recf then (i + 1) else i) def x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n close_open_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> close_open_inverse'_match_returns i m x);\n close_open_inverse'_branches i brs x\n\n | Tv_AscribedT e t tac b ->\n close_open_inverse' i e x;\n close_open_inverse' i t x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n\n | Tv_AscribedC e c tac b ->\n close_open_inverse' i e x;\n close_open_inverse'_comp i c x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n \nand close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t \n | C_GTotal t -> \n close_open_inverse' i t x\n\n | C_Lemma pre post pats ->\n close_open_inverse' i pre x;\n close_open_inverse' i post x;\n close_open_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n close_open_inverse' i res x;\n close_open_inverse'_args i args x;\n close_open_inverse'_terms i decrs x\n\nand close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\n (decreases args)\n = match args with\n | [] -> ()\n | (a, q) :: args ->\n close_open_inverse' i a x;\n close_open_inverse'_args i args x\n\nand close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\n (decreases b)\n = let bndr = inspect_binder b in\n close_open_inverse' i bndr.sort x;\n close_open_inverse'_terms i bndr.attrs x;\n pack_inspect_binder b\n\nand close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | hd :: tl ->\n close_open_inverse' i hd x;\n close_open_inverse'_terms i tl x\n\nand close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | b :: brs ->\n close_open_inverse'_branch i b x;\n close_open_inverse'_branches i brs x\n\nand close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\n (decreases br)\n = let p, t = br in\n close_open_inverse'_pattern i p x;\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse' (i + binder_offset_pattern p) t x\n\n\nand close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n close_open_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> close_open_inverse' i t x\n\nand close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n close_open_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse'_patterns (i + n) ps' x\n\nand close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n close_open_inverse'_binder i b x;\n (match ret with\n | Inl t -> close_open_inverse' (i + 1) t x\n | Inr c -> close_open_inverse'_comp (i + 1) c x);\n (match as_ with\n | None -> ()\n | Some t -> close_open_inverse' (i + 1) t x)", "val open_term_list' (t: list term) (v: term) (i: index) : Tot (list term)\nlet open_term_list' (t:list term) (v:term) (i:index)\r\n : Tot (list term) = subst_term_list t [ DT i v ]", "val freevars (t: term) : Set.set var\nlet rec freevars (t:term) \r\n : Set.set var\r\n = match t.t with\r\n | Tm_Emp\r\n | Tm_VProp\r\n | Tm_Inames\r\n | Tm_EmpInames\r\n | Tm_Unknown -> Set.empty\r\n | Tm_Inv p -> freevars p\r\n | Tm_Star t1 t2 ->\r\n Set.union (freevars t1) (freevars t2)\r\n | Tm_ExistsSL _ t1 t2\r\n | Tm_ForallSL _ t1 t2 ->\r\n Set.union (freevars t1.binder_ty) (freevars t2)\r\n | Tm_Pure p -> freevars p\r\n | Tm_FStar t -> RT.freevars t\r\n | Tm_AddInv i is -> Set.union (freevars i) (freevars is)", "val open_term_ln_inv' (e: term) (x: term{ln x}) (i: index)\n : Lemma (requires ln' e i) (ensures ln' (open_term' e x i) (i - 1)) (decreases e)\nlet rec open_term_ln_inv' (e:term)\n (x:term { ln x })\n (i:index)\n : Lemma \n (requires ln' e i)\n (ensures ln' (open_term' e x i) (i - 1))\n (decreases e)\n = match e.t with\n | Tm_Emp\n | Tm_VProp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown ->\n ln_weakening x (-1) (i - 1)\n\n | Tm_Inv p ->\n open_term_ln_inv' p x i\n | Tm_Pure p ->\n open_term_ln_inv' p x i\n\n // | Tm_PureApp l _ r\n | Tm_AddInv l r\n | Tm_Star l r ->\n open_term_ln_inv' l x i;\n open_term_ln_inv' r x i\n\n | Tm_ExistsSL _ t b\n | Tm_ForallSL _ t b ->\n open_term_ln_inv' t.binder_ty x i; \n open_term_ln_inv' b x (i + 1)\n\n | Tm_FStar t ->\n Pulse.Elaborate.elab_ln x (-1);\n r_open_term_ln_inv' t (elab_term x) i", "val elab_freevars (e:term)\n : Lemma (freevars e == RT.freevars (elab_term e))\nlet elab_freevars e = elab_freevars_eq e", "val close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\nlet rec close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_Uvar _ _ -> assert false\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> ()\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n close_open_inverse' i t1 x;\n close_open_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n close_open_inverse'_binder i b x;\n close_open_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n close_open_inverse'_terms i attrs x;\n close_open_inverse'_binder i b x;\n close_open_inverse' (if recf then (i + 1) else i) def x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n close_open_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> close_open_inverse'_match_returns i m x);\n close_open_inverse'_branches i brs x\n\n | Tv_AscribedT e t tac b ->\n close_open_inverse' i e x;\n close_open_inverse' i t x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n\n | Tv_AscribedC e c tac b ->\n close_open_inverse' i e x;\n close_open_inverse'_comp i c x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n \nand close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t \n | C_GTotal t -> \n close_open_inverse' i t x\n\n | C_Lemma pre post pats ->\n close_open_inverse' i pre x;\n close_open_inverse' i post x;\n close_open_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n close_open_inverse' i res x;\n close_open_inverse'_args i args x;\n close_open_inverse'_terms i decrs x\n\nand close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\n (decreases args)\n = match args with\n | [] -> ()\n | (a, q) :: args ->\n close_open_inverse' i a x;\n close_open_inverse'_args i args x\n\nand close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\n (decreases b)\n = let bndr = inspect_binder b in\n close_open_inverse' i bndr.sort x;\n close_open_inverse'_terms i bndr.attrs x;\n pack_inspect_binder b\n\nand close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | hd :: tl ->\n close_open_inverse' i hd x;\n close_open_inverse'_terms i tl x\n\nand close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | b :: brs ->\n close_open_inverse'_branch i b x;\n close_open_inverse'_branches i brs x\n\nand close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\n (decreases br)\n = let p, t = br in\n close_open_inverse'_pattern i p x;\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse' (i + binder_offset_pattern p) t x\n\n\nand close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n close_open_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> close_open_inverse' i t x\n\nand close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n close_open_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse'_patterns (i + n) ps' x\n\nand close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n close_open_inverse'_binder i b x;\n (match ret with\n | Inl t -> close_open_inverse' (i + 1) t x\n | Inr c -> close_open_inverse'_comp (i + 1) c x);\n (match as_ with\n | None -> ()\n | Some t -> close_open_inverse' (i + 1) t x)", "val close_open_inverse_proof_hint_type'\n (ht: proof_hint_type)\n (x: var{~(x `Set.mem` (freevars_proof_hint ht))})\n (i: index)\n : Lemma (ensures close_proof_hint' (open_proof_hint' ht (U.term_of_no_name_var x) i) x i == ht)\nlet close_open_inverse_proof_hint_type' (ht:proof_hint_type)\r\n (x:var { ~(x `Set.mem` freevars_proof_hint ht) })\r\n (i:index)\r\n : Lemma (ensures close_proof_hint' (open_proof_hint' ht (U.term_of_no_name_var x) i) x i == ht)\r\n = match ht with\r\n | ASSERT { p }\r\n | FOLD { p }\r\n | UNFOLD { p } -> close_open_inverse' p x i\r\n | RENAME { pairs; goal } ->\r\n close_open_inverse_pairs' pairs x i;\r\n close_open_inverse_opt' goal x i\r\n | REWRITE { t1; t2 } ->\r\n close_open_inverse' t1 x i;\r\n close_open_inverse' t2 x i\r\n | WILD\r\n | SHOW_PROOF_STATE _ -> ()", "val open_term_ln_inv_opt' (t: option term) (x: term{ln x}) (i: index)\n : Lemma (requires ln_opt' ln' t i)\n (ensures ln_opt' ln' (open_term_opt' t x i) (i - 1))\n (decreases t)\nlet open_term_ln_inv_opt' (t:option term)\n (x:term { ln x })\n (i:index)\n : Lemma\n (requires ln_opt' ln' t i)\n (ensures ln_opt' ln' (open_term_opt' t x i) (i - 1))\n (decreases t)\n = match t with\n | None -> ()\n | Some t -> open_term_ln_inv' t x i", "val freevars_elab_ty (t: src_ty) : Lemma ((RT.freevars (elab_ty t)) `Set.equal` (freevars_ty t))\nlet rec freevars_elab_exp (e:src_exp)\n : Lemma ( RT.freevars (elab_exp e) `Set.equal` freevars e )\n = match e with\n | EBool _\n | EBVar _ \n | EVar _ -> ()\n\n | ELam t e ->\n freevars_elab_ty t;\n freevars_elab_exp e\n\n \n | EApp e1 e2 ->\n freevars_elab_exp e1;\n freevars_elab_exp e2\n\n | EIf b e1 e2 ->\n freevars_elab_exp b; \n freevars_elab_exp e1;\n freevars_elab_exp e2\n \nand freevars_elab_ty (t:src_ty)\n : Lemma (RT.freevars (elab_ty t) `Set.equal` freevars_ty t)\n = match t with\n | TBool -> ()\n \n | TArrow t1 t2 ->\n freevars_elab_ty t1;\n freevars_elab_ty t2 \n \n | TRefineBool e ->\n freevars_elab_exp e", "val close_st_term' (t: st_term) (v: var) (i: index) : st_term\nlet close_st_term' (t:st_term) (v:var) (i:index) : st_term =\r\n subst_st_term t [ ND v i ]", "val open_term_ln' (e x: term) (i: index)\n : Lemma (requires ln' (open_term' e x i) (i - 1)) (ensures ln' e i) (decreases e)\nlet rec open_term_ln' (e:term)\n (x:term)\n (i:index)\n : Lemma \n (requires ln' (open_term' e x i) (i - 1))\n (ensures ln' e i)\n (decreases e)\n = match e.t with\n | Tm_Emp\n | Tm_VProp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown -> ()\n\n | Tm_Inv p ->\n open_term_ln' p x i\n\n | Tm_Pure p ->\n open_term_ln' p x i\n\n | Tm_AddInv l r\n | Tm_Star l r ->\n open_term_ln' l x i;\n open_term_ln' r x i\n\n | Tm_ExistsSL _ t b\n | Tm_ForallSL _ t b ->\n open_term_ln' t.binder_ty x i; \n open_term_ln' b x (i + 1)\n\n | Tm_FStar t ->\n open_term_ln_host' t (elab_term x) i", "val freevars_elab_ty (t: src_ty) : Lemma ((freevars_ty t) `Set.equal` (RT.freevars (elab_ty t)))\nlet rec freevars_elab_exp (e:src_exp)\n : Lemma (freevars e `Set.equal` RT.freevars (elab_exp e))\n = match e with\n | EBool _\n | EBVar _ \n | EVar _ -> ()\n\n | ELam t e ->\n freevars_elab_ty t;\n freevars_elab_exp e\n \n | EApp e1 e2 ->\n freevars_elab_exp e1;\n freevars_elab_exp e2\n\n | EIf b e1 e2 ->\n freevars_elab_exp b; \n freevars_elab_exp e1;\n freevars_elab_exp e2\n \nand freevars_elab_ty (t:src_ty)\n : Lemma (freevars_ty t `Set.equal` RT.freevars (elab_ty t))\n = match t with\n | TBool -> ()\n \n | TArrow t1 t2 ->\n freevars_elab_ty t1;\n freevars_elab_ty t2 \n \n | TRefineBool e ->\n freevars_elab_exp e", "val free_in_context : x:var -> #e:exp -> #g:env -> #t:typ -> h:typing g e t ->\n Lemma (requires True) (ensures (appears_free_in x e ==> Some? (g x))) (decreases h)\nlet rec free_in_context x #e #g #t h =\n match h with\n | TyVar x -> ()\n | TyLam t h1 -> free_in_context (x+1) h1\n | TyApp h1 h2 -> free_in_context x h1; free_in_context x h2\n | TyUnit -> ()", "val close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\nlet rec close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_Uvar _ _ -> assert false\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> ()\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n close_open_inverse' i t1 x;\n close_open_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n close_open_inverse'_binder i b x;\n close_open_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n close_open_inverse'_terms i attrs x;\n close_open_inverse'_binder i b x;\n close_open_inverse' (if recf then (i + 1) else i) def x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n close_open_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> close_open_inverse'_match_returns i m x);\n close_open_inverse'_branches i brs x\n\n | Tv_AscribedT e t tac b ->\n close_open_inverse' i e x;\n close_open_inverse' i t x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n\n | Tv_AscribedC e c tac b ->\n close_open_inverse' i e x;\n close_open_inverse'_comp i c x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n \nand close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t \n | C_GTotal t -> \n close_open_inverse' i t x\n\n | C_Lemma pre post pats ->\n close_open_inverse' i pre x;\n close_open_inverse' i post x;\n close_open_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n close_open_inverse' i res x;\n close_open_inverse'_args i args x;\n close_open_inverse'_terms i decrs x\n\nand close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\n (decreases args)\n = match args with\n | [] -> ()\n | (a, q) :: args ->\n close_open_inverse' i a x;\n close_open_inverse'_args i args x\n\nand close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\n (decreases b)\n = let bndr = inspect_binder b in\n close_open_inverse' i bndr.sort x;\n close_open_inverse'_terms i bndr.attrs x;\n pack_inspect_binder b\n\nand close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | hd :: tl ->\n close_open_inverse' i hd x;\n close_open_inverse'_terms i tl x\n\nand close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | b :: brs ->\n close_open_inverse'_branch i b x;\n close_open_inverse'_branches i brs x\n\nand close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\n (decreases br)\n = let p, t = br in\n close_open_inverse'_pattern i p x;\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse' (i + binder_offset_pattern p) t x\n\n\nand close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n close_open_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> close_open_inverse' i t x\n\nand close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n close_open_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse'_patterns (i + n) ps' x\n\nand close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n close_open_inverse'_binder i b x;\n (match ret with\n | Inl t -> close_open_inverse' (i + 1) t x\n | Inr c -> close_open_inverse'_comp (i + 1) c x);\n (match as_ with\n | None -> ()\n | Some t -> close_open_inverse' (i + 1) t x)", "val open_exp_freevars (e: src_exp) (v: var) (n: nat)\n : Lemma\n (((freevars e) `Set.subset` (freevars (open_exp' e v n))) /\\\n ((freevars (open_exp' e v n)) `Set.subset` ((freevars e) `Set.union` (Set.singleton v))))\n [SMTPat (freevars (open_exp' e v n))]\nlet rec open_exp_freevars (e:src_exp) (v:var) (n:nat)\n : Lemma ((freevars e `Set.subset` freevars (open_exp' e v n)) /\\\n (freevars (open_exp' e v n) `Set.subset` (freevars e `Set.union` Set.singleton v)))\n [SMTPat (freevars (open_exp' e v n))]\n = match e with\n | EBool _\n | EBVar _ \n | EVar _ -> ()\n | EApp e1 e2 ->\n open_exp_freevars e1 v n;\n open_exp_freevars e2 v n\n | EIf b e1 e2 ->\n open_exp_freevars b v n; \n open_exp_freevars e1 v n;\n open_exp_freevars e2 v n\n | ELam t e ->\n open_exp_freevars e v (n + 1)", "val index_cons (#t: Type) (x: t) (l: list t) (i: nat{i < List.Tot.length l})\n : Lemma (ensures (List.Tot.index l i == List.Tot.index (x :: l) (i + 1))) (decreases l)\nlet rec index_cons (#t:Type) (x:t) (l:list t) (i:nat{i < List.Tot.length l}) :\n Lemma\n (ensures (List.Tot.index l i == List.Tot.index (x::l) (i+1)))\n (decreases l) =\n match l with\n | [] -> ()\n | x' :: l' ->\n if i = 0 then () else index_cons x' l' (i-1)", "val elab_freevars_eq (e: term) : Lemma (Set.equal (freevars e) (RT.freevars (elab_term e)))\nlet rec elab_freevars_eq (e:term)\n : Lemma (Set.equal (freevars e) (RT.freevars (elab_term e))) =\n match e.t with\n | Tm_Emp -> ()\n | Tm_Inv p -> elab_freevars_eq p\n | Tm_Pure t -> elab_freevars_eq t\n | Tm_AddInv l r\n | Tm_Star l r ->\n elab_freevars_eq l;\n elab_freevars_eq r\n | Tm_ExistsSL _ t body\n | Tm_ForallSL _ t body ->\n elab_freevars_eq t.binder_ty;\n elab_freevars_eq body\n | Tm_VProp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown\n | Tm_FStar _ -> ()", "val open_close_inverse (e:R.term { ln e }) (x:var)\n : Lemma (open_term (close_term e x) x == e)\nlet open_close_inverse (e:R.term { ln e }) (x:var)\n : Lemma (open_term (close_term e x) x == e)\n = close_term_spec e x;\n open_term_spec (close_term e x) x;\n open_close_inverse' 0 e x", "val close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\nlet rec close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_Uvar _ _ -> assert false\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> ()\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n close_open_inverse' i t1 x;\n close_open_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n close_open_inverse'_binder i b x;\n close_open_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n close_open_inverse'_terms i attrs x;\n close_open_inverse'_binder i b x;\n close_open_inverse' (if recf then (i + 1) else i) def x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n close_open_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> close_open_inverse'_match_returns i m x);\n close_open_inverse'_branches i brs x\n\n | Tv_AscribedT e t tac b ->\n close_open_inverse' i e x;\n close_open_inverse' i t x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n\n | Tv_AscribedC e c tac b ->\n close_open_inverse' i e x;\n close_open_inverse'_comp i c x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n \nand close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t \n | C_GTotal t -> \n close_open_inverse' i t x\n\n | C_Lemma pre post pats ->\n close_open_inverse' i pre x;\n close_open_inverse' i post x;\n close_open_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n close_open_inverse' i res x;\n close_open_inverse'_args i args x;\n close_open_inverse'_terms i decrs x\n\nand close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\n (decreases args)\n = match args with\n | [] -> ()\n | (a, q) :: args ->\n close_open_inverse' i a x;\n close_open_inverse'_args i args x\n\nand close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\n (decreases b)\n = let bndr = inspect_binder b in\n close_open_inverse' i bndr.sort x;\n close_open_inverse'_terms i bndr.attrs x;\n pack_inspect_binder b\n\nand close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | hd :: tl ->\n close_open_inverse' i hd x;\n close_open_inverse'_terms i tl x\n\nand close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | b :: brs ->\n close_open_inverse'_branch i b x;\n close_open_inverse'_branches i brs x\n\nand close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\n (decreases br)\n = let p, t = br in\n close_open_inverse'_pattern i p x;\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse' (i + binder_offset_pattern p) t x\n\n\nand close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n close_open_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> close_open_inverse' i t x\n\nand close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n close_open_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse'_patterns (i + n) ps' x\n\nand close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n close_open_inverse'_binder i b x;\n (match ret with\n | Inl t -> close_open_inverse' (i + 1) t x\n | Inr c -> close_open_inverse'_comp (i + 1) c x);\n (match as_ with\n | None -> ()\n | Some t -> close_open_inverse' (i + 1) t x)", "val free_in_context : x:var -> #e:exp -> #g:env -> #t:ty -> h:rtyping g e t ->\n Lemma (requires True) (ensures (appears_free_in x e ==> Some? (g x))) (decreases h)\nlet rec free_in_context x #e #g #t h =\n match h with\n | TyVar x -> ()\n | TyAbs t h1 -> free_in_context (x+1) h1\n | TyApp h1 h2 -> free_in_context x h1; free_in_context x h2", "val close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\nlet rec close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_Uvar _ _ -> assert false\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> ()\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n close_open_inverse' i t1 x;\n close_open_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n close_open_inverse'_binder i b x;\n close_open_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n close_open_inverse'_terms i attrs x;\n close_open_inverse'_binder i b x;\n close_open_inverse' (if recf then (i + 1) else i) def x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n close_open_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> close_open_inverse'_match_returns i m x);\n close_open_inverse'_branches i brs x\n\n | Tv_AscribedT e t tac b ->\n close_open_inverse' i e x;\n close_open_inverse' i t x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n\n | Tv_AscribedC e c tac b ->\n close_open_inverse' i e x;\n close_open_inverse'_comp i c x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n \nand close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t \n | C_GTotal t -> \n close_open_inverse' i t x\n\n | C_Lemma pre post pats ->\n close_open_inverse' i pre x;\n close_open_inverse' i post x;\n close_open_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n close_open_inverse' i res x;\n close_open_inverse'_args i args x;\n close_open_inverse'_terms i decrs x\n\nand close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\n (decreases args)\n = match args with\n | [] -> ()\n | (a, q) :: args ->\n close_open_inverse' i a x;\n close_open_inverse'_args i args x\n\nand close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\n (decreases b)\n = let bndr = inspect_binder b in\n close_open_inverse' i bndr.sort x;\n close_open_inverse'_terms i bndr.attrs x;\n pack_inspect_binder b\n\nand close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | hd :: tl ->\n close_open_inverse' i hd x;\n close_open_inverse'_terms i tl x\n\nand close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | b :: brs ->\n close_open_inverse'_branch i b x;\n close_open_inverse'_branches i brs x\n\nand close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\n (decreases br)\n = let p, t = br in\n close_open_inverse'_pattern i p x;\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse' (i + binder_offset_pattern p) t x\n\n\nand close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n close_open_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> close_open_inverse' i t x\n\nand close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n close_open_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse'_patterns (i + n) ps' x\n\nand close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n close_open_inverse'_binder i b x;\n (match ret with\n | Inl t -> close_open_inverse' (i + 1) t x\n | Inr c -> close_open_inverse'_comp (i + 1) c x);\n (match as_ with\n | None -> ()\n | Some t -> close_open_inverse' (i + 1) t x)", "val close_term_pairs' (t: list (term & term)) (v: var) (i: index) : Tot (list (term & term))\nlet close_term_pairs' (t:list (term & term)) (v:var) (i:index)\n : Tot (list (term & term))\n = subst_term_pairs t [ ND v i ]", "val freevars_st (t: st_term) : Set.set var\nlet rec freevars_st (t:st_term)\r\n : Set.set var\r\n = match t.term with\r\n | Tm_Return { expected_type; term } ->\r\n Set.union (freevars expected_type) (freevars term)\r\n | Tm_Abs { b; ascription; body } ->\r\n Set.union (freevars b.binder_ty) \r\n (Set.union (freevars_st body)\r\n (freevars_ascription ascription))\r\n | Tm_STApp { head; arg } ->\r\n Set.union (freevars head) (freevars arg)\r\n | Tm_Bind { binder; head; body } ->\r\n Set.union \r\n (Set.union (freevars binder.binder_ty) \r\n (freevars_st head))\r\n (freevars_st body)\r\n | Tm_TotBind { binder; head; body } ->\r\n Set.union\r\n (Set.union (freevars binder.binder_ty)\r\n (freevars head))\r\n (freevars_st body)\r\n | Tm_If { b; then_; else_; post } ->\r\n Set.union (Set.union (freevars b) (freevars_st then_))\r\n (Set.union (freevars_st else_) (freevars_term_opt post))\r\n\r\n | Tm_Match { sc ; returns_; brs } ->\r\n let (@@) = Set.union in\r\n freevars sc\r\n @@ freevars_term_opt returns_\r\n @@ freevars_branches brs\r\n\r\n | Tm_IntroPure { p }\r\n | Tm_ElimExists { p } ->\r\n freevars p\r\n | Tm_IntroExists { p; witnesses } ->\r\n Set.union (freevars p) (freevars_list witnesses)\r\n | Tm_While { invariant; condition; body } ->\r\n Set.union (freevars invariant)\r\n (Set.union (freevars_st condition)\r\n (freevars_st body))\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n Set.union\r\n (Set.union (freevars pre1)\r\n (Set.union (freevars_st body1)\r\n (freevars post1)))\r\n (Set.union (freevars pre2)\r\n (Set.union (freevars_st body2)\r\n (freevars post2)))\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n Set.union (freevars binder.binder_ty)\r\n (Set.union (freevars initializer)\r\n (freevars_st body))\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n Set.union (freevars binder.binder_ty)\r\n (Set.union (freevars initializer)\r\n (Set.union (freevars length)\r\n (freevars_st body)))\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n Set.union (freevars t1) (freevars t2)\r\n\r\n | Tm_Admit { typ; post } ->\r\n Set.union (freevars typ)\r\n (freevars_term_opt post)\r\n\r\n | Tm_Unreachable ->\r\n Set.empty\r\n\r\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\r\n Set.union (freevars_proof_hint hint_type) (freevars_st t)\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n Set.union (Set.union (freevars name) (freevars_st body))\r\n (freevars_opt \r\n (fun (b, r) ->\r\n (Set.union (freevars b.binder_ty) \r\n (freevars r)))\r\n returns_inv)\r\n\r\nand freevars_branches (t:list (pattern & st_term)) : Set.set var =\r\n match t with\r\n | [] -> Set.empty\r\n | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl", "val close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\nlet rec close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_Uvar _ _ -> assert false\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> ()\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n close_open_inverse' i t1 x;\n close_open_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n close_open_inverse'_binder i b x;\n close_open_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n close_open_inverse'_terms i attrs x;\n close_open_inverse'_binder i b x;\n close_open_inverse' (if recf then (i + 1) else i) def x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n close_open_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> close_open_inverse'_match_returns i m x);\n close_open_inverse'_branches i brs x\n\n | Tv_AscribedT e t tac b ->\n close_open_inverse' i e x;\n close_open_inverse' i t x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n\n | Tv_AscribedC e c tac b ->\n close_open_inverse' i e x;\n close_open_inverse'_comp i c x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n \nand close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t \n | C_GTotal t -> \n close_open_inverse' i t x\n\n | C_Lemma pre post pats ->\n close_open_inverse' i pre x;\n close_open_inverse' i post x;\n close_open_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n close_open_inverse' i res x;\n close_open_inverse'_args i args x;\n close_open_inverse'_terms i decrs x\n\nand close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\n (decreases args)\n = match args with\n | [] -> ()\n | (a, q) :: args ->\n close_open_inverse' i a x;\n close_open_inverse'_args i args x\n\nand close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\n (decreases b)\n = let bndr = inspect_binder b in\n close_open_inverse' i bndr.sort x;\n close_open_inverse'_terms i bndr.attrs x;\n pack_inspect_binder b\n\nand close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | hd :: tl ->\n close_open_inverse' i hd x;\n close_open_inverse'_terms i tl x\n\nand close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | b :: brs ->\n close_open_inverse'_branch i b x;\n close_open_inverse'_branches i brs x\n\nand close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\n (decreases br)\n = let p, t = br in\n close_open_inverse'_pattern i p x;\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse' (i + binder_offset_pattern p) t x\n\n\nand close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n close_open_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> close_open_inverse' i t x\n\nand close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n close_open_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse'_patterns (i + n) ps' x\n\nand close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n close_open_inverse'_binder i b x;\n (match ret with\n | Inl t -> close_open_inverse' (i + 1) t x\n | Inr c -> close_open_inverse'_comp (i + 1) c x);\n (match as_ with\n | None -> ()\n | Some t -> close_open_inverse' (i + 1) t x)", "val close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\nlet rec close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_Uvar _ _ -> assert false\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> ()\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n close_open_inverse' i t1 x;\n close_open_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n close_open_inverse'_binder i b x;\n close_open_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n close_open_inverse'_terms i attrs x;\n close_open_inverse'_binder i b x;\n close_open_inverse' (if recf then (i + 1) else i) def x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n close_open_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> close_open_inverse'_match_returns i m x);\n close_open_inverse'_branches i brs x\n\n | Tv_AscribedT e t tac b ->\n close_open_inverse' i e x;\n close_open_inverse' i t x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n\n | Tv_AscribedC e c tac b ->\n close_open_inverse' i e x;\n close_open_inverse'_comp i c x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n \nand close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t \n | C_GTotal t -> \n close_open_inverse' i t x\n\n | C_Lemma pre post pats ->\n close_open_inverse' i pre x;\n close_open_inverse' i post x;\n close_open_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n close_open_inverse' i res x;\n close_open_inverse'_args i args x;\n close_open_inverse'_terms i decrs x\n\nand close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\n (decreases args)\n = match args with\n | [] -> ()\n | (a, q) :: args ->\n close_open_inverse' i a x;\n close_open_inverse'_args i args x\n\nand close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\n (decreases b)\n = let bndr = inspect_binder b in\n close_open_inverse' i bndr.sort x;\n close_open_inverse'_terms i bndr.attrs x;\n pack_inspect_binder b\n\nand close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | hd :: tl ->\n close_open_inverse' i hd x;\n close_open_inverse'_terms i tl x\n\nand close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | b :: brs ->\n close_open_inverse'_branch i b x;\n close_open_inverse'_branches i brs x\n\nand close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\n (decreases br)\n = let p, t = br in\n close_open_inverse'_pattern i p x;\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse' (i + binder_offset_pattern p) t x\n\n\nand close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n close_open_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> close_open_inverse' i t x\n\nand close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n close_open_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse'_patterns (i + n) ps' x\n\nand close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n close_open_inverse'_binder i b x;\n (match ret with\n | Inl t -> close_open_inverse' (i + 1) t x\n | Inr c -> close_open_inverse'_comp (i + 1) c x);\n (match as_ with\n | None -> ()\n | Some t -> close_open_inverse' (i + 1) t x)", "val rename_freevars (e: src_exp) (x y: var)\n : Lemma ((freevars (rename e x y)) `Set.subset` ((freevars e) `Set.union` (Set.singleton y)))\n [SMTPat (freevars (rename e x y))]\nlet rec rename_freevars (e:src_exp) (x y:var)\n : Lemma (freevars (rename e x y) `Set.subset` (freevars e `Set.union` (Set.singleton y)))\n [SMTPat (freevars (rename e x y))]\n = match e with\n | EBool _\n | EBVar _ \n | EVar _ -> ()\n | EApp e1 e2 -> \n rename_freevars e1 x y;\n rename_freevars e2 x y\n | EIf b e1 e2 ->\n rename_freevars b x y; \n rename_freevars e1 x y;\n rename_freevars e2 x y \n | ELam t body ->\n rename_freevars body x y", "val open_term_fvar_id (fv: R.fv) (x: var)\n : Lemma (RT.open_term (R.pack_ln (R.Tv_FVar fv)) x == (R.pack_ln (R.Tv_FVar fv)))\n [SMTPat (RT.open_term (R.pack_ln (R.Tv_FVar fv)) x)]\nlet open_term_fvar_id (fv:R.fv) (x:var)\n : Lemma (RT.open_term (R.pack_ln (R.Tv_FVar fv)) x == (R.pack_ln (R.Tv_FVar fv)))\n [SMTPat (RT.open_term (R.pack_ln (R.Tv_FVar fv)) x)]\n = RT.open_term_spec (R.pack_ln (R.Tv_FVar fv)) x", "val elab_open_commute (t:term) (x:var)\n : Lemma (elab_term (open_term t x) == RT.open_term (elab_term t) x)\nlet elab_open_commute (t:term) (x:var)\n : Lemma (elab_term (open_term t x) == RT.open_term (elab_term t) x)\n = RT.open_term_spec (elab_term t) x;\n elab_open_commute' t (null_var x) 0", "val close_term (t:term) (v:var) : term\nlet close_term (t:term) (v:var) = RTB.close_term t v", "val elab_ty_close_commute' (n: nat) (e: src_ty) (x: var)\n : Lemma (ensures RT.subst_term (elab_ty e) [RT.ND x n] == elab_ty (close_ty' e x n))\n (decreases e)\nlet rec elab_close_commute' (n:nat) (e:src_exp) (x:var)\n : Lemma (ensures\n RT.subst_term (elab_exp e) [ RT.ND x n ] ==\n elab_exp (close_exp' e x n))\n (decreases e)\n = match e with\n | EBool _ -> ()\n | EBVar _ -> ()\n | EVar _ -> ()\n | EApp e1 e2 -> \n elab_close_commute' n e1 x;\n elab_close_commute' n e2 x\n | EIf b e1 e2 ->\n elab_close_commute' n b x; \n elab_close_commute' n e1 x;\n elab_close_commute' n e2 x\n | ELam t e ->\n elab_ty_close_commute' n t x;\n elab_close_commute' (n + 1) e x\n\nand elab_ty_close_commute' (n:nat) (e:src_ty) (x:var)\n : Lemma\n (ensures\n RT.subst_term (elab_ty e) [ RT.ND x n ] ==\n elab_ty (close_ty' e x n))\n (decreases e)\n = match e with\n | TBool -> ()\n | TArrow t t' ->\n elab_ty_close_commute' n t x;\n elab_ty_close_commute' (n + 1) t' x\n\n | TRefineBool e ->\n elab_close_commute' (n + 1) e x", "val elab_exp_freevars (e: stlc_exp) : Lemma ((freevars e) `Set.equal` (RT.freevars (elab_exp e)))\nlet rec elab_exp_freevars (e:stlc_exp)\n : Lemma (freevars e `Set.equal` RT.freevars (elab_exp e))\n = match e with\n | EUnit\n | EBVar _\n | EVar _ -> ()\n | ELam t e ->\n elab_ty_freevars t;\n elab_exp_freevars e\n | EApp e1 e2 ->\n elab_exp_freevars e1;\n elab_exp_freevars e2", "val close_term_vs (vs: list var) (t: term) : term\nlet close_term_vs (vs : list var) (t : term) : term =\n __close_term_vs 0 vs t", "val close_term_opt' (t: option term) (v: var) (i: index) : option term\nlet close_term_opt' (t:option term) (v:var) (i:index) : option term =\r\n subst_term_opt t [ ND v i ]", "val freevars_comp (c: comp) : Tot (Set.set var) (decreases c)\nlet freevars_comp (c:comp) : Tot (Set.set var) (decreases c) =\r\n match c with\r\n | C_Tot t -> freevars t\r\n | C_ST s\r\n | C_STGhost s -> freevars_st_comp s\r\n | C_STAtomic inames _ s ->\r\n freevars inames `Set.union` freevars_st_comp s", "val elab_comp_close_commute' (c: comp) (v: var) (n: index)\n : Lemma (ensures RT.subst_term (elab_comp c) [RT.ND v n] == elab_comp (close_comp' c v n))\n (decreases c)\nlet elab_comp_close_commute' (c:comp) (v:var) (n:index)\n : Lemma (ensures\n RT.subst_term (elab_comp c) [ RT.ND v n ] ==\n elab_comp (close_comp' c v n))\n (decreases c)\n = match c with\n | C_Tot t -> elab_close_commute' t v n\n | C_ST s\n | C_STGhost s -> \n elab_close_commute' s.res v n;\n elab_close_commute' s.pre v n;\n elab_close_commute' s.post v (n + 1)\n | C_STAtomic inames _ s ->\n elab_close_commute' inames v n;\n elab_close_commute' s.res v n;\n elab_close_commute' s.pre v n;\n elab_close_commute' s.post v (n + 1)", "val close_comp_ln' (c: comp) (x: var) (i: index)\n : Lemma (requires ln_c' c (i - 1)) (ensures ln_c' (close_comp' c x i) i)\nlet close_comp_ln' (c:comp)\n (x:var)\n (i:index)\n : Lemma \n (requires ln_c' c (i - 1))\n (ensures ln_c' (close_comp' c x i) i)\n = match c with\n | C_Tot t ->\n close_term_ln' t x i\n\n | C_ST s\n | C_STGhost s ->\n close_term_ln' s.res x i;\n close_term_ln' s.pre x i; \n close_term_ln' s.post x (i + 1)\n\n | C_STAtomic n _ s -> \n close_term_ln' n x i; \n close_term_ln' s.res x i;\n close_term_ln' s.pre x i; \n close_term_ln' s.post x (i + 1)", "val elab_close_commute' (n: nat) (e: src_exp) (x: var)\n : Lemma (ensures RT.subst_term (elab_exp e) [RT.ND x n] == elab_exp (close_exp' e x n))\n (decreases e)\nlet rec elab_close_commute' (n:nat) (e:src_exp) (x:var)\n : Lemma (ensures\n RT.subst_term (elab_exp e) [ RT.ND x n ] ==\n elab_exp (close_exp' e x n))\n (decreases e)\n = match e with\n | EBool _ -> ()\n | EBVar _ -> ()\n | EVar _ -> ()\n | EApp e1 e2 -> \n elab_close_commute' n e1 x;\n elab_close_commute' n e2 x\n | EIf b e1 e2 ->\n elab_close_commute' n b x; \n elab_close_commute' n e1 x;\n elab_close_commute' n e2 x\n | ELam t e ->\n elab_ty_close_commute' n t x;\n elab_close_commute' (n + 1) e x\n\nand elab_ty_close_commute' (n:nat) (e:src_ty) (x:var)\n : Lemma\n (ensures\n RT.subst_term (elab_ty e) [ RT.ND x n ] ==\n elab_ty (close_ty' e x n))\n (decreases e)\n = match e with\n | TBool -> ()\n | TArrow t t' ->\n elab_ty_close_commute' n t x;\n elab_ty_close_commute' (n + 1) t' x\n\n | TRefineBool e ->\n elab_close_commute' (n + 1) e x", "val open_close_inverse'_args (i:nat) \n (ts:list argv { ln'_args ts (i - 1) })\n (x:var)\n : Lemma\n (ensures subst_args\n (subst_args ts [ ND x i ])\n (open_with_var x i)\n == ts)\nlet rec open_close_inverse' (i:nat) (t:term { ln' t (i - 1) }) (x:var)\n : Lemma\n (ensures subst_term \n (subst_term t [ ND x i ])\n (open_with_var x i)\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n open_close_inverse' i t1 x;\n open_close_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n open_close_inverse'_binder i b x;\n open_close_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n open_close_inverse'_binder i b x;\n open_close_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n open_close_inverse'_binder i b x;\n open_close_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n open_close_inverse'_terms i attrs x;\n open_close_inverse'_binder i b x;\n (if recf \n then open_close_inverse' (i + 1) def x\n else open_close_inverse' i def x);\n open_close_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n open_close_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> open_close_inverse'_match_returns i m x);\n open_close_inverse'_branches i brs x\n \n | Tv_AscribedT e t tac b ->\n open_close_inverse' i e x;\n open_close_inverse' i t x; \n (match tac with\n | None -> ()\n | Some tac -> open_close_inverse' i tac x)\n\n | Tv_AscribedC e c tac b ->\n open_close_inverse' i e x;\n open_close_inverse'_comp i c x; \n (match tac with\n | None -> ()\n | Some tac -> open_close_inverse' i tac x)\n \n\nand open_close_inverse'_binder (i:nat) (b:binder { ln'_binder b (i - 1) }) (x:var)\n : Lemma (ensures subst_binder\n (subst_binder b [ ND x i ])\n (open_with_var x i)\n == b)\n (decreases b) \n = let bndr = inspect_binder b in\n let {ppname; qual=q; attrs=attrs; sort=sort} = bndr in\n open_close_inverse' i sort x;\n open_close_inverse'_terms i attrs x;\n assert (subst_terms (subst_terms attrs [ ND x i ])\n (open_with_var x i) == attrs); \n pack_inspect_binder b; \n assert (pack_binder {ppname; qual=q; attrs=attrs; sort=sort} == b)\n\nand open_close_inverse'_terms (i:nat) (ts:list term { ln'_terms ts (i - 1) }) (x:var)\n : Lemma (ensures subst_terms\n (subst_terms ts [ ND x i ])\n (open_with_var x i)\n == ts)\n (decreases ts) \n = match ts with\n | [] -> ()\n | t::ts -> \n open_close_inverse' i t x;\n open_close_inverse'_terms i ts x\n\nand open_close_inverse'_comp (i:nat) (c:comp { ln'_comp c (i - 1) }) (x:var)\n : Lemma \n (ensures subst_comp\n (subst_comp c [ ND x i ])\n (open_with_var x i)\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t -> open_close_inverse' i t x\n\n | C_Lemma pre post pats ->\n open_close_inverse' i pre x;\n open_close_inverse' i post x;\n open_close_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n open_close_inverse' i res x;\n open_close_inverse'_args i args x;\n open_close_inverse'_terms i decrs x \n\nand open_close_inverse'_args (i:nat) \n (ts:list argv { ln'_args ts (i - 1) })\n (x:var)\n : Lemma\n (ensures subst_args\n (subst_args ts [ ND x i ])\n (open_with_var x i)\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | (t,q)::ts -> \n open_close_inverse' i t x;\n open_close_inverse'_args i ts x\n\nand open_close_inverse'_patterns (i:nat)\n (ps:list (pattern & bool) { ln'_patterns ps (i - 1) })\n (x:var)\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps [ ND x i ])\n (open_with_var x i)\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n open_close_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p [ ND x i ];\n open_close_inverse'_patterns (i + n) ps' x\n\nand open_close_inverse'_pattern (i:nat) (p:pattern{ln'_pattern p (i - 1)}) (x:var)\n : Lemma \n (ensures subst_pattern\n (subst_pattern p [ ND x i ])\n (open_with_var x i)\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n open_close_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> open_close_inverse' i t x\n\n \nand open_close_inverse'_branch (i:nat) (br:branch{ln'_branch br (i - 1)}) (x:var)\n : Lemma\n (ensures subst_branch\n (subst_branch br [ ND x i ])\n (open_with_var x i)\n == br)\n (decreases br) \n = let p, t = br in\n let j = binder_offset_pattern p in\n binder_offset_pattern_invariant p [ ND x i ];\n open_close_inverse'_pattern i p x;\n open_close_inverse' (i + j) t x\n \nand open_close_inverse'_branches (i:nat)\n (brs:list branch { ln'_branches brs (i - 1) })\n (x:var)\n : Lemma\n (ensures subst_branches\n (subst_branches brs [ ND x i ])\n (open_with_var x i)\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | br::brs -> \n open_close_inverse'_branch i br x;\n open_close_inverse'_branches i brs x\n \nand open_close_inverse'_match_returns (i:nat) \n (m:match_returns_ascription { ln'_match_returns m (i - 1) })\n (x:var)\n : Lemma \n (ensures subst_match_returns\n (subst_match_returns m [ ND x i ])\n (open_with_var x i)\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n open_close_inverse'_binder i b x;\n let ret =\n match ret with\n | Inl t ->\n open_close_inverse' (i + 1) t x\n | Inr c ->\n open_close_inverse'_comp (i + 1) c x\n in\n let as_ =\n match as_ with\n | None -> ()\n | Some t ->\n open_close_inverse' (i + 1) t x\n in\n ()", "val stt_vprop_equiv_closing (t0 t1: R.term) (x: var)\n : Lemma\n (RT.close_term (stt_vprop_equiv t0 t1) x ==\n stt_vprop_equiv (RT.close_term t0 x) (RT.close_term t1 x))\n [SMTPat (RT.close_term (stt_vprop_equiv t0 t1) x)]\nlet stt_vprop_equiv_closing (t0 t1:R.term) (x:var)\n : Lemma (RT.close_term (stt_vprop_equiv t0 t1) x ==\n stt_vprop_equiv (RT.close_term t0 x) (RT.close_term t1 x))\n [SMTPat (RT.close_term (stt_vprop_equiv t0 t1) x)]\n = RT.close_term_spec (stt_vprop_equiv t0 t1) x;\n RT.close_term_spec t0 x;\n RT.close_term_spec t1 x", "val close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\nlet rec close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_Uvar _ _ -> assert false\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> ()\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n close_open_inverse' i t1 x;\n close_open_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n close_open_inverse'_binder i b x;\n close_open_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n close_open_inverse'_terms i attrs x;\n close_open_inverse'_binder i b x;\n close_open_inverse' (if recf then (i + 1) else i) def x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n close_open_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> close_open_inverse'_match_returns i m x);\n close_open_inverse'_branches i brs x\n\n | Tv_AscribedT e t tac b ->\n close_open_inverse' i e x;\n close_open_inverse' i t x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n\n | Tv_AscribedC e c tac b ->\n close_open_inverse' i e x;\n close_open_inverse'_comp i c x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n \nand close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t \n | C_GTotal t -> \n close_open_inverse' i t x\n\n | C_Lemma pre post pats ->\n close_open_inverse' i pre x;\n close_open_inverse' i post x;\n close_open_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n close_open_inverse' i res x;\n close_open_inverse'_args i args x;\n close_open_inverse'_terms i decrs x\n\nand close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\n (decreases args)\n = match args with\n | [] -> ()\n | (a, q) :: args ->\n close_open_inverse' i a x;\n close_open_inverse'_args i args x\n\nand close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\n (decreases b)\n = let bndr = inspect_binder b in\n close_open_inverse' i bndr.sort x;\n close_open_inverse'_terms i bndr.attrs x;\n pack_inspect_binder b\n\nand close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | hd :: tl ->\n close_open_inverse' i hd x;\n close_open_inverse'_terms i tl x\n\nand close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | b :: brs ->\n close_open_inverse'_branch i b x;\n close_open_inverse'_branches i brs x\n\nand close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\n (decreases br)\n = let p, t = br in\n close_open_inverse'_pattern i p x;\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse' (i + binder_offset_pattern p) t x\n\n\nand close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n close_open_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> close_open_inverse' i t x\n\nand close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n close_open_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse'_patterns (i + n) ps' x\n\nand close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n close_open_inverse'_binder i b x;\n (match ret with\n | Inl t -> close_open_inverse' (i + 1) t x\n | Inr c -> close_open_inverse'_comp (i + 1) c x);\n (match as_ with\n | None -> ()\n | Some t -> close_open_inverse' (i + 1) t x)", "val freevars_term_opt (t: option term) : Set.set var\nlet freevars_term_opt (t:option term) : Set.set var =\r\n freevars_opt freevars t", "val elab_close_commute' (e:term)\n (v:var)\n (n:index)\n : Lemma (RT.subst_term (elab_term e) [ RT.ND v n ] ==\n elab_term (close_term' e v n))\nlet rec elab_close_commute' (e:term)\n (v:var)\n (n:index)\n : Lemma (ensures (\n RT.subst_term (elab_term e) [ RT.ND v n ] ==\n elab_term (close_term' e v n)))\n (decreases e)\n = match e.t with\n | Tm_Emp \n | Tm_Inames\n | Tm_EmpInames\n | Tm_VProp\n | Tm_Unknown -> ()\n | Tm_Inv p ->\n elab_close_commute' p v n\n | Tm_Pure p ->\n elab_close_commute' p v n\n | Tm_AddInv e1 e2\n | Tm_Star e1 e2 ->\n elab_close_commute' e1 v n;\n elab_close_commute' e2 v n\n | Tm_ExistsSL _ t body\n | Tm_ForallSL _ t body ->\n elab_close_commute' t.binder_ty v n;\n elab_close_commute' body v (n + 1) \n | Tm_FStar _ -> ()", "val open_close' (e: src_exp) (x: var) (n: nat{ln' e (n - 1)})\n : Lemma (open_exp' (close_exp' e x n) x n == e)\nlet rec open_close' (e:src_exp) (x:var) (n:nat { ln' e (n - 1) })\n : Lemma (open_exp' (close_exp' e x n) x n == e)\n = match e with\n | EBool _ -> ()\n | EVar _ -> ()\n | EBVar m -> ()\n | EIf b e1 e2 -> \n open_close' b x n;\n open_close' e1 x n;\n open_close' e2 x n\n | ELam _ e -> open_close' e x (n + 1)\n | EApp e1 e2 -> \n open_close' e1 x n; \n open_close' e2 x n", "val evars_unfun : x:term -> y:term -> x':term -> y':term -> tl:eqns -> Lemma\n (ensures (evars ((F x y, F x' y')::tl) = evars ((x, x')::(y, y')::tl)))\nlet evars_unfun x y x' y' tl = OrdSet.eq_lemma (evars ((F x y, F x' y')::tl)) (evars ((x, x')::(y, y')::tl))", "val elab_ty_freevars (ty: stlc_ty) : Lemma ((RT.freevars (elab_ty ty)) `Set.equal` Set.empty)\nlet rec elab_ty_freevars (ty:stlc_ty)\n : Lemma (RT.freevars (elab_ty ty) `Set.equal` Set.empty)\n = match ty with\n | TUnit -> ()\n | TArrow t1 t2 ->\n elab_ty_freevars t1;\n elab_ty_freevars t2", "val open_close' (e: stlc_exp) (x: var) (n: nat{ln' e (n - 1)})\n : Lemma (open_exp' (close_exp' e x n) x n == e)\nlet rec open_close' (e:stlc_exp) (x:var) (n:nat { ln' e (n - 1) })\n : Lemma (open_exp' (close_exp' e x n) x n == e)\n = match e with\n | EUnit -> ()\n | EVar _ -> ()\n | EBVar m -> ()\n | ELam _ e -> open_close' e x (n + 1)\n | EApp e1 e2 -> \n open_close' e1 x n; \n open_close' e2 x n", "val elab_freevars_comp_eq (c: comp)\n : Lemma (Set.equal (freevars_comp c) (RT.freevars (elab_comp c)))\nlet elab_freevars_comp_eq (c:comp)\n : Lemma (Set.equal (freevars_comp c) (RT.freevars (elab_comp c))) =\n\n match c with\n | C_Tot t -> elab_freevars_eq t\n | C_ST st\n | C_STGhost st ->\n elab_freevars_eq st.res;\n elab_freevars_eq st.pre;\n elab_freevars_eq st.post\n | C_STAtomic inames _ st ->\n elab_freevars_eq inames;\n elab_freevars_eq st.res;\n elab_freevars_eq st.pre;\n elab_freevars_eq st.post", "val freevars_elab_exp (e: src_exp) : Lemma ((RT.freevars (elab_exp e)) `Set.equal` (freevars e))\nlet rec freevars_elab_exp (e:src_exp)\n : Lemma ( RT.freevars (elab_exp e) `Set.equal` freevars e )\n = match e with\n | EBool _\n | EBVar _ \n | EVar _ -> ()\n\n | ELam t e ->\n freevars_elab_ty t;\n freevars_elab_exp e\n\n \n | EApp e1 e2 ->\n freevars_elab_exp e1;\n freevars_elab_exp e2\n\n | EIf b e1 e2 ->\n freevars_elab_exp b; \n freevars_elab_exp e1;\n freevars_elab_exp e2\n \nand freevars_elab_ty (t:src_ty)\n : Lemma (RT.freevars (elab_ty t) `Set.equal` freevars_ty t)\n = match t with\n | TBool -> ()\n \n | TArrow t1 t2 ->\n freevars_elab_ty t1;\n freevars_elab_ty t2 \n \n | TRefineBool e ->\n freevars_elab_exp e", "val rename_open' (x y: var) (e: src_exp{~(x `Set.mem` (freevars e))}) (n: nat)\n : Lemma (ensures rename (open_exp' e x n) x y == open_exp' e y n) (decreases e)\nlet rec rename_open' (x y:var) \n (e:src_exp { ~ (x `Set.mem` freevars e) })\n (n:nat)\n : Lemma \n (ensures rename (open_exp' e x n) x y == open_exp' e y n)\n (decreases e)\n = match e with\n | EBool _ -> ()\n | EVar _ -> ()\n | EBVar _ -> ()\n | EApp e1 e2 -> \n rename_open' x y e1 n;\n rename_open' x y e2 n \n | EIf b e1 e2 ->\n rename_open' x y b n; \n rename_open' x y e1 n;\n rename_open' x y e2 n\n | ELam t e ->\n rename_open' x y e (n + 1)", "val src_typing_freevars (#f: _) (sg: src_env) (e: src_exp) (t: s_ty) (d: src_typing f sg e t)\n : Lemma (ensures e `freevars_included_in` sg) (decreases d)\nlet rec src_typing_freevars #f (sg:src_env) (e:src_exp) (t:s_ty) (d:src_typing f sg e t)\n : Lemma \n (ensures e `freevars_included_in` sg)\n (decreases d)\n = match d with\n | T_Bool _ _ -> ()\n | T_Var _ _ -> ()\n | T_App _ _ _ _ _ _ d1 d2 s ->\n src_typing_freevars _ _ _ d1;\n src_typing_freevars _ _ _ d2 \n | T_If _ _ _ _ _ _ _ hyp db d1 d2 s1 s2 _ ->\n src_typing_freevars _ _ _ db;\n src_typing_freevars _ _ _ d1;\n src_typing_freevars _ _ _ d2 \n | T_Lam _ _ _ _ x dt dbody ->\n src_typing_freevars _ _ _ dbody", "val open_term_pairs' (t: list (term & term)) (v: term) (i: index) : Tot (list (term & term))\nlet open_term_pairs' (t:list (term & term)) (v:term) (i:index)\n : Tot (list (term & term))\n = subst_term_pairs t [ DT i v ]", "val ivl_aux (#a: Type) (r: cr a) (vm: vmap a) (x: index) (t: varlist) : Tot a (decreases t)\nlet rec ivl_aux (#a:Type) (r:cr a) (vm:vmap a) (x:index) (t:varlist)\n : Tot a (decreases t) =\n let amult = r.cm_mult.mult in\n match t with\n | Nil_var -> interp_var vm x\n | Cons_var x' t' -> amult (interp_var vm x) (ivl_aux r vm x' t')", "val freevars_branch (br: branch) : Tot (Set.set var) (decreases br)\nlet rec freevars (e:term)\n : FStar.Set.set var\n = match inspect_ln e with\n | Tv_Uvar _ _ -> Set.complement Set.empty\n \n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unknown \n | Tv_Unsupp\n | Tv_BVar _ -> Set.empty\n\n | Tv_Var x -> Set.singleton (namedv_uniq x)\n \n | Tv_App e1 (e2, _) ->\n Set.union (freevars e1) (freevars e2)\n\n | Tv_Abs b body -> \n Set.union (freevars_binder b) (freevars body)\n\n | Tv_Arrow b c ->\n Set.union (freevars_binder b) (freevars_comp c)\n\n | Tv_Refine b f ->\n freevars (binder_sort b) `Set.union`\n freevars f\n \n | Tv_Let recf attrs b def body ->\n freevars_terms attrs `Set.union`\n freevars (binder_sort b) `Set.union`\n freevars def `Set.union`\n freevars body\n\n | Tv_Match scr ret brs ->\n freevars scr `Set.union`\n freevars_opt ret freevars_match_returns `Set.union`\n freevars_branches brs\n\n | Tv_AscribedT e t tac b ->\n freevars e `Set.union`\n freevars t `Set.union`\n freevars_opt tac freevars\n \n | Tv_AscribedC e c tac b ->\n freevars e `Set.union`\n freevars_comp c `Set.union`\n freevars_opt tac freevars\n\nand freevars_opt (#a:Type0) (o:option a) (f: (x:a { x << o } -> FStar.Set.set var))\n : FStar.Set.set var\n = match o with\n | None -> Set.empty\n | Some x -> f x\n\nand freevars_comp (c:comp)\n : FStar.Set.set var\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t ->\n freevars t\n\n | C_Lemma pre post pats ->\n freevars pre `Set.union`\n freevars post `Set.union`\n freevars pats\n\n | C_Eff us eff_name res args decrs ->\n freevars res `Set.union`\n freevars_args args `Set.union`\n freevars_terms decrs\n\nand freevars_args (ts:list argv)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | (t,q)::ts ->\n freevars t `Set.union`\n freevars_args ts\n\nand freevars_terms (ts:list term)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | t::ts ->\n freevars t `Set.union`\n freevars_terms ts\n \nand freevars_binder (b:binder)\n : Tot (Set.set var) (decreases b)\n = let bndr = inspect_binder b in\n freevars bndr.sort `Set.union`\n freevars_terms bndr.attrs \n\nand freevars_pattern (p:pattern) \n : Tot (Set.set var) (decreases p)\n = match p with\n | Pat_Constant _ ->\n Set.empty\n\n | Pat_Cons head univs subpats ->\n freevars_patterns subpats\n \n | Pat_Var bv s -> Set.empty\n\n | Pat_Dot_Term topt ->\n freevars_opt topt freevars\n\nand freevars_patterns (ps:list (pattern & bool))\n : Tot (Set.set var) (decreases ps)\n = match ps with\n | [] -> Set.empty\n | (p, b)::ps ->\n freevars_pattern p `Set.union`\n freevars_patterns ps\n\nand freevars_branch (br:branch)\n : Tot (Set.set var) (decreases br)\n = let p, t = br in\n freevars_pattern p `Set.union`\n freevars t\n\nand freevars_branches (brs:list branch)\n : Tot (Set.set var) (decreases brs)\n = match brs with\n | [] -> Set.empty\n | hd::tl -> freevars_branch hd `Set.union` freevars_branches tl\n \nand freevars_match_returns (m:match_returns_ascription)\n : Tot (Set.set var) (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = freevars_binder b in\n let ret =\n match ret with\n | Inl t -> freevars t\n | Inr c -> freevars_comp c\n in\n let as_ = freevars_opt as_ freevars in\n b `Set.union` ret `Set.union` as_", "val stlc_types_are_closed2 (ty: stlc_ty) (x: R.var)\n : Lemma (RT.close_term (elab_ty ty) x == elab_ty ty) [SMTPat (RT.close_term (elab_ty ty) x)]\nlet stlc_types_are_closed2 (ty:stlc_ty) (x:R.var)\n : Lemma (RT.close_term (elab_ty ty) x == elab_ty ty)\n [SMTPat (RT.close_term (elab_ty ty) x)]\n = stlc_types_are_closed_core ty [ RT.ND x 0 ];\n RT.close_term_spec (elab_ty ty) x", "val freevars_elab_exp (e: src_exp) : Lemma ((freevars e) `Set.equal` (RT.freevars (elab_exp e)))\nlet rec freevars_elab_exp (e:src_exp)\n : Lemma (freevars e `Set.equal` RT.freevars (elab_exp e))\n = match e with\n | EBool _\n | EBVar _ \n | EVar _ -> ()\n\n | ELam t e ->\n freevars_elab_ty t;\n freevars_elab_exp e\n \n | EApp e1 e2 ->\n freevars_elab_exp e1;\n freevars_elab_exp e2\n\n | EIf b e1 e2 ->\n freevars_elab_exp b; \n freevars_elab_exp e1;\n freevars_elab_exp e2\n \nand freevars_elab_ty (t:src_ty)\n : Lemma (freevars_ty t `Set.equal` RT.freevars (elab_ty t))\n = match t with\n | TBool -> ()\n \n | TArrow t1 t2 ->\n freevars_elab_ty t1;\n freevars_elab_ty t2 \n \n | TRefineBool e ->\n freevars_elab_exp e" ], "closest_src": [ { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse_list'" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.close_term_ln_list'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_terms_with_not_free_var" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_with_not_free_var" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse_opt'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse_pairs'" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.open_term_ln_list'" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.close_term_ln_pairs" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse_st" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.close_term_ln'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse'_terms" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.close_term_list'" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.open_term_ln_inv_list'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_args_with_not_free_var" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.close_term_ln_opt'" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.open_ty_freevars" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.open_close_inverse'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse_ascription'" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.close_exp_freevars" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.freevars_open" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_pattern_with_not_free_var" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_with_non_freevar_st" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.open_exp_freevars" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_comp_with_not_free_var" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.__close_term_vs" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse_comp'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_patterns_with_not_free_var" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.close_term'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.open_close_inverse'_terms" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.vars_decrease_eqns" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.open_term_ln_inv_pairs" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.open_term_ln_pairs" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_comp_with_non_free_var" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_match_returns_with_not_free_var" }, { "project_name": "steel", "file_name": "Pulse.Typing.FV.fsti", "name": "Pulse.Typing.FV.st_typing_freevars_inv" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_branches_with_not_free_var" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_binder_with_not_free_var" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.lemma_vars_decrease" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_branch_with_not_free_var" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.open_term_ln_opt'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.freevars_list" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse'_pattern" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.open_term_list'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.freevars" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.open_term_ln_inv'" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.fst", "name": "Pulse.Elaborate.elab_freevars" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse'_comp" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse_proof_hint_type'" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.open_term_ln_inv_opt'" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.freevars_elab_ty" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.close_st_term'" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.open_term_ln'" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.freevars_elab_ty" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.free_in_context" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse'_args" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.open_exp_freevars" }, { "project_name": "noise-star", "file_name": "Spec.Noise.Patterns.fst", "name": "Spec.Noise.Patterns.index_cons" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.fst", "name": "Pulse.Elaborate.elab_freevars_eq" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.open_close_inverse" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse'_branch" }, { "project_name": "FStar", "file_name": "StlcCbvDbPntSubstNoLists.fst", "name": "StlcCbvDbPntSubstNoLists.free_in_context" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse'_patterns" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.close_term_pairs'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.freevars_st" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse'_binder" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse'_branches" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.rename_freevars" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.open_term_fvar_id" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.fst", "name": "Pulse.Elaborate.elab_open_commute" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_term" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.elab_ty_close_commute'" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.elab_exp_freevars" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.close_term_vs" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.close_term_opt'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.freevars_comp" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.fst", "name": "Pulse.Elaborate.elab_comp_close_commute'" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.close_comp_ln'" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.elab_close_commute'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.open_close_inverse'_args" }, { "project_name": "steel", "file_name": "Pulse.Soundness.STEquiv.fst", "name": "Pulse.Soundness.STEquiv.stt_vprop_equiv_closing" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse'_match_returns" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.freevars_term_opt" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.fst", "name": "Pulse.Elaborate.elab_close_commute'" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.open_close'" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.evars_unfun" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.elab_ty_freevars" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.open_close'" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.fst", "name": "Pulse.Elaborate.elab_freevars_comp_eq" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.freevars_elab_exp" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.rename_open'" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.src_typing_freevars" }, { "project_name": "steel", "file_name": "Pulse.Typing.LN.fst", "name": "Pulse.Typing.LN.open_term_pairs'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.ivl_aux" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.freevars_branch" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.stlc_types_are_closed2" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.freevars_elab_exp" } ], "selected_premises": [ "Pulse.Typing.FV.freevars_close_term'", "Pulse.Typing.FV.freevars_close_term_opt'", "FStar.Reflection.V2.Data.var", "Pulse.Typing.tm_inames_subset_typing", "Pulse.Typing.tot_typing", "Pulse.Reflection.Util.mk_arrow", "Pulse.Typing.tm_prop", "FStar.Printf.sprintf", "Pulse.Typing.universe_of", "Pulse.Soundness.Common.tot_typing_soundness", "Pulse.Typing.elab_env", "Pulse.Typing.as_binder", "Pulse.Typing.subtyping_token", "Pulse.Soundness.Common.ghost_typing_soundness", "Pulse.Typing.debug_log", "FStar.Reflection.Typing.var_as_namedv", "Pulse.Typing.wtag", "Pulse.Reflection.Util.mk_pulse_lib_reference_lid", "Pulse.Typing.comp_post_matches_hint", "Pulse.Reflection.Util.vprop_tm", "FStar.Reflection.Typing.sort_default", "FStar.Integers.op_Less_Equals", "Pulse.Typing.tm_bool", "Pulse.Reflection.Util.mk_pulse_lib_forall_lid", "Pulse.Soundness.Common.post1_type_bind", "Pulse.Typing.Env.lookup", "FStar.Integers.op_Greater_Equals", "Pulse.Soundness.Common.bind_type", "Pulse.Soundness.Common.has_stt_bindings", "FStar.Integers.op_Plus", "Pulse.Reflection.Util.mk_pulse_lib_array_core_lid", "FStar.Integers.op_Less", "Pulse.Soundness.Common.frame_type", "FStar.Integers.within_bounds", "FStar.UInt.size", "Pulse.Reflection.Util.mk_pulse_lib_core_lid", "FStar.Integers.op_Greater", "FStar.Integers.op_Percent", "Pulse.Typing.non_informative_t", "Pulse.Soundness.Common.frame_type_t_pre_post", "Pulse.Typing.tm_unit", "Pulse.Reflection.Util.mk_stt_comp", "Pulse.Soundness.Common.frame_type_t_pre_post_frame", "Pulse.Soundness.Common.comp_post_type", "FStar.Integers.op_Subtraction", "FStar.Printf.arg_type", "Pulse.Typing.comp_withlocal_array_body_pre", "Pulse.Typing.post_hint_for_env", "Pulse.Typing.mk_vprop_eq", "Pulse.Reflection.Util.tot_lid", "Pulse.Soundness.Common.bind_type_t1_t2", "Pulse.Typing.add_iname_at_least_unobservable", "Pulse.Soundness.Common.mk_star", "Pulse.Soundness.Common.sub_stt_post1", "FStar.Reflection.Typing.constant_as_term", "Pulse.Typing.post_hint_opt", "Pulse.Soundness.Common.post2_type_bind", "Pulse.Typing.wr", "Pulse.Reflection.Util.mk_observability_lid", "Pulse.Reflection.Util.u_max_two", "Pulse.Typing.eff_of_ctag", "FStar.String.strlen", "FStar.String.length", "Pulse.Typing.post_hint_for_env_p", "Pulse.Soundness.Common.bind_type_t1", "FStar.Integers.op_Slash", "FStar.Mul.op_Star", "FStar.Pervasives.Native.fst", "Pulse.Soundness.Common.sub_stt_post2", "FStar.Pervasives.Native.snd", "Pulse.Reflection.Util.u_two", "Pulse.Typing.Env.equal", "FStar.Heap.trivial_preorder", "Pulse.Soundness.Common.elab_comp_post", "Pulse.Typing.mk_pts_to", "FStar.Pervasives.reveal_opaque", "Pulse.Typing.ghost_typing", "Pulse.Soundness.Common.sub_stt_pre2", "Pulse.Soundness.Common.g_type_bind", "Pulse.Typing.Env.contains", "Pulse.Typing.FV.vars_of_rt_env", "Pulse.Typing.comp_intro_pure", "Pulse.Typing.post_hint_typing", "FStar.Reflection.Typing.pp_name_t", "Pulse.Soundness.Common.frame_res", "FStar.Integers.fixed_width", "Pulse.Soundness.Common.bind_type_t1_t2_pre_post1_post2", "Pulse.Soundness.Common.soundness_t", "Pulse.Reflection.Util.binder_of_t_q_s", "FStar.Reflection.Typing.blob", "Pulse.Typing.non_informative_witness_t", "Pulse.Soundness.Common.bind_type_t1_t2_pre_post1", "FStar.Reflection.Typing.u_zero", "Pulse.Soundness.Common.sub_stt_equiv_post", "Pulse.Reflection.Util.inv_disjointness_goal", "Pulse.Typing.fresh_wrt", "Pulse.Soundness.Common.elab_term_opt", "Pulse.Soundness.Common.frame_type_t", "Pulse.Reflection.Util.full_perm_lid", "FStar.Printf.dir_type" ], "source_upto_this": "(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Typing.FV\nmodule RT = FStar.Reflection.Typing\nmodule R = FStar.Reflection.V2\nmodule L = FStar.List.Tot\nopen FStar.List.Tot\nopen Pulse.Syntax\nopen Pulse.Typing\nopen Pulse.Elaborate\nopen Pulse.Soundness.Common\n\nlet vars_of_rt_env (g:R.env) = Set.intension (fun x -> Some? (RT.lookup_bvar g x))\n\nlet freevars_close_term_host_term (t:host_term) (x:var) (i:index)\n : Lemma\n (ensures (freevars (close_term' (tm_fstar t FStar.Range.range_0) x i)\n `Set.equal`\n (freevars (tm_fstar t FStar.Range.range_0) `set_minus` x)))\n = admit()\n\n#push-options \"--query_stats --z3rlimit_factor 2\"\nlet rec freevars_close_term' (e:term) (x:var) (i:index)\n : Lemma\n (ensures freevars (close_term' e x i) `Set.equal`\n (freevars e `set_minus` x))\n = match e.t with\n | Tm_Emp\n | Tm_VProp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown -> ()\n\n | Tm_Inv p ->\n freevars_close_term' p x i\n | Tm_Pure p ->\n freevars_close_term' p x i\n\n | Tm_AddInv l r\n | Tm_Star l r ->\n freevars_close_term' l x i;\n freevars_close_term' r x i\n\n | Tm_ExistsSL _ t b\n | Tm_ForallSL _ t b ->\n freevars_close_term' t.binder_ty x i;\n freevars_close_term' b x (i + 1)\n\n | Tm_FStar t ->\n freevars_close_term_host_term t x i\n\nlet freevars_close_comp (c:comp)\n (x:var)\n (i:index)\n : Lemma\n (ensures freevars_comp (close_comp' c x i) `Set.equal`\n (freevars_comp c `set_minus` x))\n [SMTPat (freevars_comp (close_comp' c x i))]\n = match c with\n | C_Tot t ->\n freevars_close_term' t x i\n\n | C_ST s\n | C_STGhost s ->\n freevars_close_term' s.res x i;\n freevars_close_term' s.pre x i;\n freevars_close_term' s.post x (i + 1)\n\n | C_STAtomic n _ s ->\n freevars_close_term' n x i;\n freevars_close_term' s.res x i;\n freevars_close_term' s.pre x i;\n freevars_close_term' s.post x (i + 1)\n\nlet freevars_close_term_opt' (t:option term) (x:var) (i:index)\n : Lemma\n (ensures (freevars_term_opt (close_term_opt' t x i) `Set.equal`\n (freevars_term_opt t `set_minus` x)))\n (decreases t)\n = match t with\n | None -> ()\n | Some t -> freevars_close_term' t x i\n", "sketch": [ "Step 1: We need to prove that the free variables of a list of terms after closing each term with a variable `x` and index `i` is equal to the free variables of the original list of terms minus the variable `x`.\nStep 2: We will use structural induction on the list of terms `t`.\nStep 3: For the base case, when the list is empty, the free variables of an empty list are also empty, so the property holds trivially.\nStep 4: For the inductive case, assume the property holds for a list `t`. We need to show it holds for a list with one more term `h :: t`.\nStep 5: Apply the induction hypothesis to the tail `t`.\nStep 6: Use the lemma `freevars_close_term'` to handle the head `h`.\nStep 7: Combine the results from the head and the tail to conclude the proof.", "Step 1: We need to prove that the free variables of a list of terms after closing each term with a variable `x` and index `i` is equal to the free variables of the original list of terms minus `x`.\nStep 2: We will use structural induction on the list of terms `t`.\nStep 3: For the base case, when the list is empty (`[]`), the free variables of an empty list are also an empty set, so the property holds trivially.\nStep 4: For the inductive case, assume the property holds for a list `tl`. We need to show it holds for a list `hd :: tl`.\nStep 5: Apply the lemma `freevars_close_term'` to the head of the list `hd` to show that closing `hd` with `x` and `i` results in the free variables of `hd` minus `x`.\nStep 6: Combine the results from the head and the tail to conclude the proof.", "Step 1: We need to prove that the free variables of a list of terms after closing each term with respect to a variable `x` and index `i` is equal to the free variables of the original list of terms minus `x`.\nStep 2: We will use structural induction on the list of terms `t`.\nStep 3: For the base case, when the list is empty, the free variables of an empty list are also empty, so the property holds trivially.\nStep 4: For the inductive case, assume the property holds for a list `tl`. We need to show it holds for a list `t::tl`.\nStep 5: Apply the induction hypothesis to `tl`.\nStep 6: Use the lemma `freevars_close_term'` to handle the head of the list `t`.\nStep 7: Combine the results to show that the free variables of the list `t::tl` after closing are equal to the free variables of the original list minus `x`.", "Step 1: We need to prove that the free variables of a list of terms after closing each term with a variable `x` and index `i` is equal to the free variables of the original list of terms minus `x`.\nStep 2: We will use structural induction on the list of terms `t`.\nStep 3: For the base case, when the list is empty, both sides of the equality are empty sets, so the property holds trivially.\nStep 4: For the inductive case, assume the property holds for a list `t`. We need to show it holds for a list with one more term `h :: t`.\nStep 5: Apply the induction hypothesis to the tail `t`.\nStep 6: Use the lemma `freevars_close_term'` to handle the head `h`.\nStep 7: Combine the results from steps 5 and 6 to conclude the proof.", "Step 1: We need to prove the lemma by induction on the list `t`.\nStep 2: For the base case, when `t` is an empty list, we need to show that the free variables of an empty list after closing are equal to the free variables of an empty list minus `x`.\nStep 3: For the inductive case, assume the lemma holds for a list `t`, and prove it for a list `t'` where `t'` is `t` with an additional term `e` appended.\nStep 4: Use the induction hypothesis to show that the free variables of the list `t` after closing are equal to the free variables of `t` minus `x`.\nStep 5: Show that closing the term `e` and then combining it with the closed list `t` results in the same set of free variables as combining the free variables of `e` and `t` minus `x`.", "Step 1: We need to prove that the free variables of a list of terms after closing each term with a variable `x` and index `i` is equal to the free variables of the original list of terms minus `x`.\nStep 2: We will proceed by induction on the list of terms `t`.\nStep 3: For the base case, when the list is empty, the free variables of an empty list are also empty, and closing an empty list with any variable and index still results in an empty list.\nStep 4: For the inductive step, assume the lemma holds for a list `t`. We need to show it holds for a list `t'` where `t' = h :: t` (i.e., a list with head `h` and tail `t`).\nStep 5: Apply the induction hypothesis to the tail `t`.\nStep 6: Use the lemma `freevars_close_term'` to handle the head `h`.\nStep 7: Combine the results from the induction hypothesis and the lemma for the head to conclude the proof.", "Step 1: If the list of terms `t` is empty, then the free variables of the closed term list are also empty, and the lemma holds trivially.\nStep 2: If the list of terms `t` is non-empty, then we need to prove the lemma for the head of the list and recursively for the tail of the list.\nStep 3: Use the induction hypothesis to assume the lemma holds for the tail of the list.\nStep 4: Combine the results from the head and the tail to conclude the proof.", "Step 1: We need to prove that the free variables of the list of terms after closing each term with a variable `x` and index `i` is equal to the free variables of the original list of terms minus the variable `x`.\nStep 2: We will proceed by induction on the list of terms `t`.\nStep 3: For the base case, when the list is empty, both sides of the equality are empty sets, so the lemma holds trivially.\nStep 4: For the inductive step, assume the lemma holds for a list `t`. We need to show it holds for a list `t'` where `t' = h::t`.\nStep 5: Apply the induction hypothesis to the tail `t`.\nStep 6: Use the lemma `freevars_close_term'` to handle the head `h`.\nStep 7: Combine the results from the head and the tail to conclude the proof.", "Step 1: We need to prove that the free variables of a list of terms, after closing each term with a variable `x` and index `i`, are equal to the free variables of the original list of terms minus `x`.\nStep 2: We will use structural induction on the list of terms `t`.\nStep 3: For the base case, when the list is empty, the free variables of an empty list are trivially equal to the free variables of the closed empty list minus `x`.\nStep 4: For the inductive case, assume the lemma holds for a list `t`. We need to show it holds for a list with one more term `h :: t`.\nStep 5: Apply the induction hypothesis to the tail `t`.\nStep 6: Use the lemma `freevars_close_term'` to handle the head `h`.\nStep 7: Combine the results from steps 5 and 6 to conclude the proof.", "Step 1: We need to prove that the free variables of the list of terms after closing each term with respect to a variable `x` and index `i` is equal to the free variables of the original list of terms minus `x`.\nStep 2: We will use structural induction on the list of terms `t`.\nStep 3: For the base case, when the list is empty, the free variables of an empty list are also empty, and closing an empty list results in an empty list. Hence, the equality holds trivially.\nStep 4: For the inductive step, assume the lemma holds for a list `t`. We need to show it holds for a list `h::t` where `h` is the head and `t` is the tail.\nStep 5: By the inductive hypothesis, we assume that the free variables of the closed tail `t` minus `x` is equal to the free variables of the original tail `t` minus `x`.\nStep 6: We need to show that the free variables of the closed list `h::t` minus `x` is equal to the free variables of the original list `h::t` minus `x`.\nStep 7: This can be done by showing that the free variables of the closed head `h` minus `x` is equal to the free variables of the original head `h` minus `x`, and then combining this with the inductive hypothesis for the tail `t`." ], "generated_solution": [ "let rec freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t)\n = match t with\n | [] -> ()\n | h :: t ->\n freevars_close_term' h x i;\n freevars_close_term_list' t x i", "let rec freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t)\n = match t with\n | [] -> ()\n | hd :: tl ->\n freevars_close_term' hd x i;\n freevars_close_term_list' tl x i", "let rec freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t)\n = match t with\n | [] -> ()\n | hd::tl ->\n freevars_close_term' hd x i;\n freevars_close_term_list' tl x i", "let rec freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t)\n = match t with\n | [] -> ()\n | h :: t ->\n freevars_close_term' h x i;\n freevars_close_term_list' t x i", "let rec freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t)\n = match t with\n | [] -> ()\n | hd::tl ->\n freevars_close_term' hd x i;\n freevars_close_term_list' tl x i", "let rec freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t)\n = match t with\n | [] -> ()\n | h :: t ->\n freevars_close_term' h x i;\n freevars_close_term_list' t x i", "let rec freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t)\n = match t with\n | [] -> ()\n | hd::tl ->\n freevars_close_term' hd x i;\n freevars_close_term_list' tl x i", "let rec freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t)\n = match t with\n | [] -> ()\n | h::t' ->\n freevars_close_term' h x i;\n freevars_close_term_list' t' x i", "let rec freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t)\n = match t with\n | [] -> ()\n | h :: t' ->\n freevars_close_term' h x i;\n freevars_close_term_list' t' x i", "let rec freevars_close_term_list' (t: list term) (x: var) (i: index)\n : Lemma\n (ensures\n ((freevars_list (close_term_list' t x i)) `Set.equal` ((freevars_list t) `set_minus` x)))\n (decreases t)\n = match t with\n | [] -> ()\n | h::t ->\n freevars_close_term' h x i;\n freevars_close_term_list' t x i" ] }, { "file_name": "Steel.ST.EphemeralHashtbl.fst", "name": "Steel.ST.EphemeralHashtbl.get", "opens_and_abbrevs": [ { "abbrev": "SeqPerm", "full_module": "FStar.Seq.Permutation" }, { "abbrev": "CE", "full_module": "FStar.Algebra.CommMonoid.Equiv" }, { "abbrev": "A", "full_module": "Steel.ST.Array" }, { "abbrev": "R", "full_module": "Steel.ST.Reference" }, { "abbrev": "US", "full_module": "FStar.SizeT" }, { "abbrev": "Map", "full_module": "FStar.PartialMap" }, { "abbrev": "Seq", "full_module": "FStar.Seq" }, { "abbrev": "G", "full_module": "FStar.Ghost" }, { "open": "Steel.ST.Util" }, { "open": "Steel.ST.Effect" }, { "open": "Steel.ST.Effect.Atomic" }, { "open": "Steel.ST.Effect.Ghost" }, { "open": "Steel.Memory" }, { "open": "Steel.FractionalPermission" }, { "abbrev": "US", "full_module": "FStar.SizeT" }, { "abbrev": "Map", "full_module": "FStar.PartialMap" }, { "abbrev": "G", "full_module": "FStar.Ghost" }, { "open": "Steel.ST.Util" }, { "open": "Steel.ST.Effect" }, { "open": "Steel.ST.Effect.Atomic" }, { "open": "Steel.ST.Effect.Ghost" }, { "open": "Steel.Memory" }, { "open": "Steel.ST" }, { "open": "Steel.ST" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)", "source_definition": "let get #k #v #contents #vp #h #m #borrows a i =\n let s = elim_exists () in\n elim_pure (pure_invariant a m borrows s);\n A.pts_to_length a.store s;\n let idx = h i `US.rem` a.store_len in\n let vopt = A.read a.store idx in\n let r = match vopt with\n | None -> Absent\n | Some (i', x) ->\n if i <> i' then Missing i'\n else Present x in\n (match vopt with\n | None -> //Nothing at the slot, return Absent\n pack_tperm s m borrows a;\n rewrite (tperm a m borrows) (get_post m borrows a i r)\n | Some (i', x) ->\n if i <> i'\n then begin //A different key, return Missing\n intro_pure (map_contains_prop i' m);\n pack_tperm s m borrows a;\n rewrite (tperm a m borrows\n `star`\n pure (map_contains_prop i' m))\n (get_post m borrows a i r)\n end\n else begin\n //\n //Unpack value vprops to get (vp i x c)\n //\n //Rewrite prefix and suffix\n //\n //Rewrite (at i) with empty\n //\n //Pack value vprops\n //\n unpack_value_vprops vp s m borrows idx (vp i x (Some?.v (Map.sel m i)));\n\n value_vprops_prefix_suffix_get h vp s m borrows (US.v idx);\n rewrite_value_vprops_prefix_and_suffix vp s s m m\n borrows (Map.upd borrows i x) idx;\n\n pack_value_vprops vp s m (Map.upd borrows i x) idx emp;\n\n pack_tperm s m (Map.upd borrows i x) a;\n\n rewrite (tperm a m (Map.upd borrows i x)\n `star`\n vp i x (Some?.v (Map.sel m i)))\n (get_post m borrows a i r)\n end);\n return r", "source_range": { "start_line": 597, "start_col": 0, "end_line": 647, "end_col": 13 }, "interleaved": false, "definition": "fun a i ->\n [@@ FStar.Pervasives.inline_let ]let s = Steel.ST.Util.elim_exists () in\n Steel.ST.Util.elim_pure (Steel.ST.EphemeralHashtbl.pure_invariant a\n (FStar.Ghost.reveal m)\n (FStar.Ghost.reveal borrows)\n (FStar.Ghost.reveal s));\n Steel.ST.Array.pts_to_length (Mktbl?.store a) (FStar.Ghost.reveal s);\n let idx = FStar.SizeT.rem (h i) (Mktbl?.store_len a) in\n let vopt = Steel.ST.Array.read (Mktbl?.store a) idx in\n let r =\n (match vopt with\n | FStar.Pervasives.Native.None #_ -> Steel.ST.EphemeralHashtbl.Absent\n | FStar.Pervasives.Native.Some #_ (FStar.Pervasives.Native.Mktuple2 #_ #_ i' x) ->\n (match i <> i' with\n | true -> Steel.ST.EphemeralHashtbl.Missing i'\n | _ -> Steel.ST.EphemeralHashtbl.Present x)\n <:\n Steel.ST.EphemeralHashtbl.get_result k v)\n <:\n Steel.ST.EphemeralHashtbl.get_result k v\n in\n (match vopt with\n | FStar.Pervasives.Native.None #_ ->\n Steel.ST.EphemeralHashtbl.pack_tperm (FStar.Ghost.reveal s)\n (FStar.Ghost.reveal m)\n (FStar.Ghost.reveal borrows)\n a;\n Steel.ST.Util.rewrite (Steel.ST.EphemeralHashtbl.tperm a\n (FStar.Ghost.reveal m)\n (FStar.Ghost.reveal borrows))\n (Steel.ST.EphemeralHashtbl.get_post m borrows a i r)\n | FStar.Pervasives.Native.Some #_ (FStar.Pervasives.Native.Mktuple2 #_ #_ i' x) ->\n (match i <> i' with\n | true ->\n Steel.ST.Util.intro_pure (Steel.ST.EphemeralHashtbl.map_contains_prop i'\n (FStar.Ghost.reveal m));\n Steel.ST.EphemeralHashtbl.pack_tperm (FStar.Ghost.reveal s)\n (FStar.Ghost.reveal m)\n (FStar.Ghost.reveal borrows)\n a;\n Steel.ST.Util.rewrite (Steel.Effect.Common.star (Steel.ST.EphemeralHashtbl.tperm a\n (FStar.Ghost.reveal m)\n (FStar.Ghost.reveal borrows))\n (Steel.ST.Util.pure (Steel.ST.EphemeralHashtbl.map_contains_prop i'\n (FStar.Ghost.reveal m))))\n (Steel.ST.EphemeralHashtbl.get_post m borrows a i r)\n | _ ->\n Steel.ST.EphemeralHashtbl.unpack_value_vprops vp\n (FStar.Ghost.reveal s)\n (FStar.Ghost.reveal m)\n (FStar.Ghost.reveal borrows)\n idx\n (vp i x (Some?.v (FStar.PartialMap.sel (FStar.Ghost.reveal m) i)));\n Steel.ST.EphemeralHashtbl.value_vprops_prefix_suffix_get h\n vp\n (FStar.Ghost.reveal s)\n (FStar.Ghost.reveal m)\n (FStar.Ghost.reveal borrows)\n (FStar.SizeT.v idx);\n Steel.ST.EphemeralHashtbl.rewrite_value_vprops_prefix_and_suffix vp\n (FStar.Ghost.reveal s)\n (FStar.Ghost.reveal s)\n (FStar.Ghost.reveal m)\n (FStar.Ghost.reveal m)\n (FStar.Ghost.reveal borrows)\n (FStar.PartialMap.upd (FStar.Ghost.reveal borrows) i x)\n idx;\n Steel.ST.EphemeralHashtbl.pack_value_vprops vp\n (FStar.Ghost.reveal s)\n (FStar.Ghost.reveal m)\n (FStar.PartialMap.upd (FStar.Ghost.reveal borrows) i x)\n idx\n Steel.Effect.Common.emp;\n Steel.ST.EphemeralHashtbl.pack_tperm (FStar.Ghost.reveal s)\n (FStar.Ghost.reveal m)\n (FStar.PartialMap.upd (FStar.Ghost.reveal borrows) i x)\n a;\n Steel.ST.Util.rewrite (Steel.Effect.Common.star (Steel.ST.EphemeralHashtbl.tperm a\n (FStar.Ghost.reveal m)\n (FStar.PartialMap.upd (FStar.Ghost.reveal borrows) i x))\n (vp i x (Some?.v (FStar.PartialMap.sel (FStar.Ghost.reveal m) i))))\n (Steel.ST.EphemeralHashtbl.get_post m borrows a i r))\n <:\n Prims.unit)\n <:\n Prims.unit;\n Steel.ST.Util.return r", "effect": "Steel.ST.Effect.ST", "effect_flags": [], "mutual_with": [], "premises": [ "Prims.eqtype", "Steel.ST.EphemeralHashtbl.vp_t", "Steel.ST.EphemeralHashtbl.hash_fn", "FStar.Ghost.erased", "Steel.ST.EphemeralHashtbl.repr", "FStar.PartialMap.t", "Steel.ST.EphemeralHashtbl.tbl", "Steel.ST.Util.return", "Steel.ST.EphemeralHashtbl.get_result", "FStar.Ghost.hide", "FStar.Set.set", "Steel.Memory.iname", "FStar.Set.empty", "Steel.ST.EphemeralHashtbl.get_post", "Steel.Effect.Common.vprop", "Prims.unit", "Steel.ST.Util.rewrite", "Steel.ST.EphemeralHashtbl.tperm", "FStar.Ghost.reveal", "Steel.ST.EphemeralHashtbl.pack_tperm", "FStar.Seq.Base.seq", "FStar.Pervasives.Native.option", "FStar.Pervasives.Native.tuple2", "Prims.op_disEquality", "Steel.Effect.Common.star", "Steel.ST.Util.pure", "Steel.ST.EphemeralHashtbl.map_contains_prop", "Steel.ST.Util.intro_pure", "Prims.bool", "FStar.PartialMap.upd", "FStar.Pervasives.Native.__proj__Some__item__v", "FStar.PartialMap.sel", "Steel.ST.EphemeralHashtbl.pack_value_vprops", "Steel.Effect.Common.emp", "Steel.ST.EphemeralHashtbl.rewrite_value_vprops_prefix_and_suffix", "Steel.ST.EphemeralHashtbl.value_vprops_prefix_suffix_get", "FStar.SizeT.v", "Steel.ST.EphemeralHashtbl.unpack_value_vprops", "Steel.ST.EphemeralHashtbl.Absent", "Steel.ST.EphemeralHashtbl.Missing", "Steel.ST.EphemeralHashtbl.Present", "Steel.ST.Array.read", "Steel.FractionalPermission.full_perm", "Steel.ST.EphemeralHashtbl.__proj__Mktbl__item__store", "FStar.SizeT.t", "FStar.SizeT.rem", "Steel.ST.EphemeralHashtbl.__proj__Mktbl__item__store_len", "Steel.ST.Array.pts_to_length", "Steel.ST.Util.elim_pure", "Steel.ST.EphemeralHashtbl.pure_invariant", "Steel.ST.Util.elim_exists", "Steel.Effect.Common.VStar", "Steel.ST.Array.pts_to", "FStar.Seq.Permutation.foldm_snoc", "Steel.Effect.Common.req", "Steel.ST.EphemeralHashtbl.vprop_monoid", "FStar.Seq.Properties.map_seq", "Steel.ST.EphemeralHashtbl.value_vprops_mapping_fn" ], "proof_features": [], "is_simple_lemma": false, "is_div": true, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "a: Steel.ST.EphemeralHashtbl.tbl vp h -> i: k\n -> Steel.ST.Effect.ST (Steel.ST.EphemeralHashtbl.get_result k v)", "prompt": "let get #k #v #contents #vp #h #m #borrows a i =\n ", "expected_response": "let s = elim_exists () in\nelim_pure (pure_invariant a m borrows s);\nA.pts_to_length a.store s;\nlet idx = (h i) `US.rem` a.store_len in\nlet vopt = A.read a.store idx in\nlet r =\n match vopt with\n | None -> Absent\n | Some (i', x) -> if i <> i' then Missing i' else Present x\nin\n(match vopt with\n | None ->\n pack_tperm s m borrows a;\n rewrite (tperm a m borrows) (get_post m borrows a i r)\n | Some (i', x) ->\n if i <> i'\n then\n (intro_pure (map_contains_prop i' m);\n pack_tperm s m borrows a;\n rewrite ((tperm a m borrows) `star` (pure (map_contains_prop i' m)))\n (get_post m borrows a i r))\n else\n (unpack_value_vprops vp s m borrows idx (vp i x (Some?.v (Map.sel m i)));\n value_vprops_prefix_suffix_get h vp s m borrows (US.v idx);\n rewrite_value_vprops_prefix_and_suffix vp s s m m borrows (Map.upd borrows i x) idx;\n pack_value_vprops vp s m (Map.upd borrows i x) idx emp;\n pack_tperm s m (Map.upd borrows i x) a;\n rewrite ((tperm a m (Map.upd borrows i x)) `star` (vp i x (Some?.v (Map.sel m i))))\n (get_post m borrows a i r)));\nreturn r", "source": { "project_name": "steel", "file_name": "lib/steel/Steel.ST.EphemeralHashtbl.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Steel.ST.EphemeralHashtbl.fst", "checked_file": "dataset/Steel.ST.EphemeralHashtbl.fst.checked", "interface_file": true, "dependencies": [ "dataset/Steel.ST.Util.fsti.checked", "dataset/Steel.ST.Reference.fsti.checked", "dataset/Steel.ST.Effect.Ghost.fsti.checked", "dataset/Steel.ST.Effect.Atomic.fsti.checked", "dataset/Steel.ST.Effect.fsti.checked", "dataset/Steel.ST.Array.fsti.checked", "dataset/Steel.Memory.fsti.checked", "dataset/Steel.FractionalPermission.fst.checked", "dataset/Steel.Effect.Common.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.SizeT.fsti.checked", "dataset/FStar.Seq.Permutation.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.PartialMap.fsti.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Calc.fsti.checked", "dataset/FStar.Algebra.CommMonoid.Equiv.fst.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "tbl", "tbl", "store_len", "store_len", "store", "store", "store_len_pf", "store_len_pf", "let seq_props (#k:eqtype) (#v:Type0) (h:hash_fn k) (s:Seq.seq (option (k & v))) : prop =\n 0 < Seq.length s /\\ US.fits (Seq.length s) /\\\n\n (forall (i:nat{i < Seq.length s}).\n Some? (Seq.index s i) ==> (let Some (x, _) = Seq.index s i in\n US.v (h x) `US.mod_spec` Seq.length s == i))", "us", "hash_fn", "let seq_keys_distinct (#k:eqtype) (#v:Type0) (s:Seq.seq (option (k & v))) : prop =\n forall (i j:(k:nat{k < Seq.length s})).{:pattern Seq.index s i; Seq.index s j}\n (i =!= j /\\ Some? (Seq.index s i) /\\ Some? (Seq.index s j)) ==>\n (fst (Some?.v (Seq.index s i)) =!= fst (Some?.v (Seq.index s j)))", "vp_t", "let seq_props_implies_keys_distinct (#k:eqtype) (#v:Type0) (h:hash_fn k) (s:Seq.seq (option (k & v)))\n : Lemma (requires seq_props h s) (ensures seq_keys_distinct s)\n = ()", "val tbl\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n : Type0", "let store_and_repr_related\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n : prop\n = forall (i:nat{i < Seq.length s}).\n match Seq.index s i with\n | None -> True\n | Some (k, _) -> Map.contains m k", "repr", "let store_and_borrows_related\n (#k:eqtype)\n (#v:Type0)\n (s:Seq.seq (option (k & v)))\n (borrows:Map.t k v)\n : prop\n = forall (i:nat{i < Seq.length s}).\n match Seq.index s i with\n | None -> True\n | Some (k, x) ->\n Map.sel borrows k == None \\/\n Map.sel borrows k == Some x", "val tperm\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (t:tbl vp h)\n (m:repr k contents)\n (borrows:Map.t k v)\n : vprop", "val create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))", "let vprop_monoid : CE.cm vprop Steel.Effect.Common.req = Steel.Effect.Common.rm", "let value_vprops_mapping_fn\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (m:repr k contents)\n (borrows:Map.t k v)\n : option (k & v) -> vprop\n = fun e ->\n match e with\n | None -> emp\n | Some (i, x) ->\n (match Map.sel m i, Map.sel borrows i with\n | None, _ -> pure False\n | _, Some _ -> emp\n | Some c, None -> vp i x c)", "val create_v\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n (c:G.erased contents)\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.const k (G.reveal c)) (Map.empty k v))", "let value_vprops_seq\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n : Seq.seq vprop\n = Seq.map_seq (value_vprops_mapping_fn vp m borrows) s", "get_result", "Present", "Present", "Present", "Absent", "Absent", "Absent", "Missing", "Missing", "Missing", "let map_contains_prop (#k:eqtype) (#v:Type0) (x:k) (m:Map.t k v) : prop =\n Map.contains m x == true", "let value_vprops\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n : vprop\n = SeqPerm.foldm_snoc vprop_monoid (value_vprops_seq vp s m borrows)", "let get_post\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (m:G.erased (repr k contents))\n (borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : get_result k v -> vprop\n = fun r ->\n match r, Map.sel m i with\n | Present x, Some c ->\n tperm a m (Map.upd borrows i x) //when `get` succeeds, the key is added to `borrows`\n `star`\n vp i x c //in addition, we return the vp permission for the key\n\n | Present x, None -> pure False //It can never be the case that the key is present in the table,\n //but is not mapped in the representation map\n | Missing j, _ ->\n tperm a m borrows\n `star`\n pure (map_contains_prop j m)\n\n | _ -> tperm a m borrows", "let pure_invariant\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (arr:tbl vp h)\n (m:repr k contents)\n (borrows:Map.t k v)\n (s:Seq.seq (option (k & v)))\n : prop\n = seq_props h s /\\\n store_and_repr_related s m /\\\n A.is_full_array arr.store /\\\n store_and_borrows_related s borrows", "let store_contents_pred\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (arr:tbl vp h)\n (m:repr k contents)\n (borrows:Map.t k v)\n : Seq.seq (option (k & v)) -> vprop\n = fun s ->\n A.pts_to arr.store full_perm s\n `star`\n pure (pure_invariant arr m borrows s)\n `star`\n value_vprops vp s m borrows", "val get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)", "let tperm arr m borrows = exists_ (store_contents_pred arr m borrows)", "let map_seq_len (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a)\n : Lemma (ensures Seq.length (Seq.map_seq f s) == Seq.length s)\n [SMTPat (Seq.length (Seq.map_seq f s))]\n = Seq.map_seq_len f s", "val put\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n (x:v)\n (c:G.erased contents)\n : STT unit\n (tperm a m borrows `star` vp i x c)\n (fun _ -> tperm a (Map.upd m i c) (Map.remove borrows i))", "let map_seq_index (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a) (i:nat{i < Seq.length s})\n : Lemma (ensures Seq.index (Seq.map_seq f s) i == f (Seq.index s i))\n [SMTPat (Seq.index (Seq.map_seq f s) i)]\n = Seq.map_seq_index f s i", "let map_seq_append (#a #b:Type) (f:a -> Tot b) (s1 s2:Seq.seq a)\n : Lemma (ensures (Seq.map_seq f (Seq.append s1 s2) ==\n Seq.append (Seq.map_seq f s1) (Seq.map_seq f s2)))\n [SMTPat (Seq.map_seq f (Seq.append s1 s2))]\n = Seq.map_seq_append f s1 s2", "let pack_tperm (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n (a:tbl vp h)\n : STGhost unit opened\n (A.pts_to a.store full_perm s\n `star`\n value_vprops vp s m borrows)\n (fun _ -> tperm a m borrows)\n (requires pure_invariant a m borrows s)\n (ensures fun _ -> True)\n = intro_pure (pure_invariant a m borrows s);\n intro_exists s (store_contents_pred a m borrows)", "val ghost_put (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n (x:v)\n (c:G.erased contents)\n : STGhost unit\n opened\n (tperm a m borrows `star` vp i x c)\n (fun _ -> tperm a (Map.upd m i c) (Map.remove borrows i))\n (requires Map.sel borrows i == Some x)\n (ensures fun _ -> True)", "let create #k #v #contents vp h n =\n let store = A.alloc #(option (k & v)) None n in\n let arr : tbl #k #v #contents vp h = {\n store_len = n;\n store = store;\n store_len_pf = () } in\n\n //\n //rewrite in terms of projections from the arr record\n //\n rewrite (A.pts_to store _ (Seq.create #(option (k & v)) (US.v n) None))\n (A.pts_to arr.store _ (Seq.create #(option (k & v)) (US.v n) None));\n\n //\n //The value vprops at this point are all emp\n //\n //A lemma that tells us that folding a monoid over a sequence of units\n // is monoid-equivalent to the unit\n //\n SeqPerm.foldm_snoc_unit_seq\n vprop_monoid\n (value_vprops_seq vp (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v));\n rewrite_equiv emp (value_vprops vp (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v));\n\n pack_tperm (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v)\n arr;\n\n return arr", "val remove\n (#k:eqtype)\n (#v #contents:Type0)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (Map.t k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : STT unit\n (tperm a m borrows)\n (fun _ -> tperm a m (Map.remove borrows i))", "val free\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n : STT unit\n (tperm a m borrows)\n (fun _ -> emp)", "let create_v #k #v #contents vp h n c =\n let store = A.alloc #(option (k & v)) None n in\n let arr : tbl #k #v #contents vp h = {\n store_len = n;\n store = store;\n store_len_pf = () } in\n\n //\n //rewrite in terms of projections from the arr record\n //\n rewrite (A.pts_to store _ (Seq.create #(option (k & v)) (US.v n) None))\n (A.pts_to arr.store _ (Seq.create #(option (k & v)) (US.v n) None));\n\n //\n //The value vprops at this point are all emp\n //\n //A lemma that tells us that folding a monoid over a sequence of units\n // is monoid-equivalent to the unit\n //\n SeqPerm.foldm_snoc_unit_seq\n vprop_monoid\n (value_vprops_seq vp (Seq.create (US.v n) None)\n (Map.const k (G.reveal c))\n (Map.empty k v));\n rewrite_equiv emp (value_vprops vp (Seq.create (US.v n) None)\n (Map.const k (G.reveal c))\n (Map.empty k v));\n\n pack_tperm (Seq.create (US.v n) None)\n (Map.const k (G.reveal c))\n (Map.empty k v)\n arr;\n\n return arr", "let seq_until (#a:Type) (s:Seq.seq a) (idx:nat{idx < Seq.length s})\n : Seq.seq a\n = Seq.slice s 0 idx", "let seq_at (#a:Type) (s:Seq.seq a) (idx:nat{idx < Seq.length s})\n : Seq.seq a\n = Seq.create 1 (Seq.index s idx)", "let seq_from (#a:Type) (s:Seq.seq a) (idx:nat{idx < Seq.length s})\n : Seq.seq a\n = Seq.slice s (idx + 1) (Seq.length s)", "let elim_equiv_laws ()\n : Lemma (\n (forall x. x `equiv` x) /\\\n (forall x y. x `equiv` y ==> y `equiv` x) /\\\n (forall x y z. (x `equiv` y /\\ y `equiv` z) ==> x `equiv` z)\n )\n = let open Steel.Effect.Common in\n assert (req.eq == equiv);\n CE.elim_eq_laws req", "let value_vprops_split3\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:Map.t k contents)\n (borrows:Map.t k v)\n (i:nat{i < Seq.length s})\n : Lemma (value_vprops vp s m borrows\n `equiv`\n (value_vprops vp (seq_until s i) m borrows\n `star`\n value_vprops vp (seq_at s i) m borrows\n `star`\n value_vprops vp (seq_from s i) m borrows))\n = elim_equiv_laws ();\n Classical.forall_intro_3 star_associative;\n\n assert (Seq.equal s (Seq.append (seq_until s i)\n (Seq.append (seq_at s i) (seq_from s i))));\n let vps s = value_vprops_seq vp s m borrows in\n\n calc (equiv) {\n value_vprops vp s m borrows;\n (equiv) { }\n value_vprops vp (Seq.append (seq_until s i)\n (Seq.append (seq_at s i) (seq_from s i))) m borrows;\n (equiv) { SeqPerm.foldm_snoc_append vprop_monoid\n (vps (seq_until s i))\n (Seq.append\n (vps (seq_at s i))\n (vps (seq_from s i))) }\n value_vprops vp (seq_until s i) m borrows\n `star`\n value_vprops vp (Seq.append (seq_at s i) (seq_from s i)) m borrows;\n (equiv) { SeqPerm.foldm_snoc_append vprop_monoid\n (vps (seq_at s i))\n (vps (seq_from s i));\n star_congruence\n (value_vprops vp (seq_until s i) m borrows)\n (value_vprops vp (Seq.append (seq_at s i) (seq_from s i)) m borrows)\n (value_vprops vp (seq_until s i) m borrows)\n (value_vprops vp (seq_at s i) m borrows `star` value_vprops vp (seq_from s i) m borrows) }\n value_vprops vp (seq_until s i) m borrows\n `star`\n (value_vprops vp (seq_at s i) m borrows\n `star`\n value_vprops vp (seq_from s i) m borrows);\n }", "let value_vprops_prefix_suffix_get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (h:hash_fn k)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n (idx:nat{idx < Seq.length s})\n : Lemma (requires Some? (Seq.index s idx) /\\\n seq_props h s)\n (ensures (let Some (i, x) = Seq.index s idx in\n let upd_borrows = Map.upd borrows i x in\n value_vprops vp (seq_until s idx) m borrows ==\n value_vprops vp (seq_until s idx) m upd_borrows /\\\n value_vprops vp (seq_from s idx) m borrows ==\n value_vprops vp (seq_from s idx) m upd_borrows))\n = let Some (i, x) = Seq.index s idx in\n let upd_borrows = Map.upd borrows i x in\n assert (Seq.equal (value_vprops_seq vp (seq_until s idx) m borrows)\n (value_vprops_seq vp (seq_until s idx) m upd_borrows));\n assert (Seq.equal (value_vprops_seq vp (seq_from s idx) m borrows)\n (value_vprops_seq vp (seq_from s idx) m upd_borrows))", "let value_vprops_prefix_suffix_put\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (h:hash_fn k)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n (idx:nat{idx < Seq.length s})\n (x:k) (y:v) (c:G.erased contents)\n : Lemma (requires seq_props h s /\\\n seq_props h (Seq.upd s idx (Some (x, y))))\n (ensures (let s1 = Seq.upd s idx (Some (x, y)) in\n let m1 = Map.upd m x c in\n let borrows1 = Map.remove borrows x in\n value_vprops vp (seq_until s idx) m borrows ==\n value_vprops vp (seq_until s1 idx) m1 borrows1 /\\\n value_vprops vp (seq_from s idx) m borrows ==\n value_vprops vp (seq_from s1 idx) m1 borrows1))\n = let s1 = Seq.upd s idx (Some (x, y)) in\n let m1 = Map.upd m x c in\n let borrows1 = Map.remove borrows x in\n assert (Seq.index s1 idx == Some (x, y));\n assert (Seq.equal (value_vprops_seq vp (seq_until s idx) m borrows)\n (value_vprops_seq vp (seq_until s1 idx) m1 borrows1));\n assert (Seq.equal (value_vprops_seq vp (seq_from s idx) m borrows)\n (value_vprops_seq vp (seq_from s1 idx) m1 borrows1))", "let value_vprops_prefix_suffix_remove\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (h:hash_fn k)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)){seq_props h s})\n (m:repr k contents)\n (borrows:Map.t k v)\n (idx:nat)\n (i:k{US.v (h i) `US.mod_spec` Seq.length s == idx})\n : Lemma (requires Some? (Seq.index s idx))\n (ensures (let s1 = Seq.upd s idx None in\n let borrows1 = Map.remove borrows i in\n value_vprops vp (seq_until s idx) m borrows ==\n value_vprops vp (seq_until s1 idx) m borrows1 /\\\n value_vprops vp (seq_from s idx) m borrows ==\n value_vprops vp (seq_from s1 idx) m borrows1))\n = let s1 = Seq.upd s idx None in\n let borrows1 = Map.remove borrows i in\n assert (Seq.equal (value_vprops_seq vp (seq_until s idx) m borrows)\n (value_vprops_seq vp (seq_until s1 idx) m borrows1));\n assert (Seq.equal (value_vprops_seq vp (seq_from s idx) m borrows)\n (value_vprops_seq vp (seq_from s1 idx) m borrows1))", "let unpack_value_vprops (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:Map.t k contents)\n (borrows:Map.t k v)\n (idx:US.t{US.v idx < Seq.length s})\n (p:vprop)\n : STGhost unit opened\n (value_vprops vp s m borrows)\n (fun _ ->\n value_vprops vp (seq_until s (US.v idx)) m borrows\n `star`\n p\n `star`\n value_vprops vp (seq_from s (US.v idx)) m borrows)\n (requires Seq.index (value_vprops_seq vp s m borrows) (US.v idx) == p)\n (ensures fun _ -> True)\n = value_vprops_split3 vp s m borrows (US.v idx);\n rewrite_equiv _\n (value_vprops vp (seq_until s (US.v idx)) m borrows\n `star`\n value_vprops vp (seq_at s (US.v idx)) m borrows\n `star`\n value_vprops vp (seq_from s (US.v idx)) m borrows);\n SeqPerm.foldm_snoc_singleton vprop_monoid p;\n assert (Seq.equal (value_vprops_seq vp (Seq.create 1 (Seq.index s (US.v idx))) m borrows)\n (Seq.create 1 p));\n rewrite_equiv (value_vprops vp (seq_at s (US.v idx)) m borrows) p", "let rewrite_value_vprops_prefix_and_suffix (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s1 s2:Seq.seq (option (k & v)))\n (m1 m2:Map.t k contents)\n (borrows1 borrows2:Map.t k v)\n (idx:US.t{Seq.length s1 == Seq.length s2 /\\ US.v idx < Seq.length s1})\n : STGhost unit opened\n (value_vprops vp (seq_until s1 (US.v idx)) m1 borrows1\n `star`\n value_vprops vp (seq_from s1 (US.v idx)) m1 borrows1)\n (fun _ ->\n value_vprops vp (seq_until s2 (US.v idx)) m2 borrows2\n `star`\n value_vprops vp (seq_from s2 (US.v idx)) m2 borrows2)\n (requires value_vprops vp (seq_until s1 (US.v idx)) m1 borrows1 ==\n value_vprops vp (seq_until s2 (US.v idx)) m2 borrows2 /\\\n value_vprops vp (seq_from s1 (US.v idx)) m1 borrows1 ==\n value_vprops vp (seq_from s2 (US.v idx)) m2 borrows2)\n (ensures fun _ -> True)\n = rewrite\n (value_vprops vp (seq_until s1 (US.v idx)) m1 borrows1\n `star`\n value_vprops vp (seq_from s1 (US.v idx)) m1 borrows1)\n (value_vprops vp (seq_until s2 (US.v idx)) m2 borrows2\n `star`\n value_vprops vp (seq_from s2 (US.v idx)) m2 borrows2)", "let pack_value_vprops (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:Map.t k contents)\n (borrows:Map.t k v)\n (idx:US.t{US.v idx < Seq.length s})\n (p:vprop)\n : STGhost unit opened\n (value_vprops vp (seq_until s (US.v idx)) m borrows\n `star`\n p\n `star`\n value_vprops vp (seq_from s (US.v idx)) m borrows)\n (fun _ -> value_vprops vp s m borrows)\n (requires Seq.index (value_vprops_seq vp s m borrows) (US.v idx) == p)\n (ensures fun _ -> True)\n = SeqPerm.foldm_snoc_singleton vprop_monoid p;\n assert (Seq.equal (value_vprops_seq vp (Seq.create 1 (Seq.index s (US.v idx))) m borrows)\n (Seq.create 1 p));\n rewrite_equiv p (value_vprops vp (seq_at s (US.v idx)) m borrows);\n value_vprops_split3 vp s m borrows (US.v idx);\n rewrite_equiv\n (value_vprops vp (seq_until s (US.v idx)) m borrows\n `star`\n value_vprops vp (seq_at s (US.v idx)) m borrows\n `star`\n value_vprops vp (seq_from s (US.v idx)) m borrows)\n (value_vprops vp s m borrows)" ], "closest": [ "val get_post:\n #k: eqtype ->\n #v: Type0 ->\n #contents: Type ->\n #vp: vp_t k v contents ->\n #h: hash_fn k ->\n m: G.erased (repr k contents) ->\n borrows: G.erased (Map.t k v) ->\n a: tbl vp h ->\n i: k ->\n get_result k v\n -> vprop\nlet get_post\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (m:G.erased (repr k contents))\n (borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : get_result k v -> vprop\n = fun r ->\n match r, Map.sel m i with\n | Present x, Some c ->\n tperm a m (Map.upd borrows i x) //when `get` succeeds, the key is added to `borrows`\n `star`\n vp i x c //in addition, we return the vp permission for the key\n\n | Present x, None -> pure False //It can never be the case that the key is present in the table,\n //but is not mapped in the representation map\n | Missing j, _ ->\n tperm a m borrows\n `star`\n pure (map_contains_prop j m)\n\n | _ -> tperm a m borrows", "val get (#v:Type) \r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (#init:G.erased c)\r\n (#m:G.erased (repr c))\r\n (#b:G.erased (borrows v))\r\n (a:tbl vp)\r\n (i:M.epoch_id)\r\n : ST (get_result v)\r\n (perm a init m b)\r\n (get_post init m b a i)\r\n (requires ~ (PartialMap.contains b i))\r\n (ensures fun res -> Fresh? res ==> Map.sel m i == G.reveal init)\nlet get #v #c #vp #init #m #b a i =\r\n let w = elim_exists () in\r\n elim_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n let high_value = R.read a.high in\r\n let r = above_high_water_mark high_value i in\r\n if r returns ST _\r\n _\r\n (get_post init m b a i)\r\n (requires ~ (PartialMap.contains b i))\r\n (ensures fun res -> Fresh? res ==> Map.sel m i == G.reveal init)\r\n\r\n then begin\r\n let ret = Fresh in\r\n intro_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n intro_exists (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) m b a.high);\r\n rewrite (ETbl.tperm a.etbl (repr_to_eht_repr m) b\r\n `star`\r\n exists_ (high_epoch_id_pred (G.reveal init) m b a.high))\r\n (get_post init m b a i ret);\r\n return ret\r\n end\r\n else begin\r\n let x = ETbl.get a.etbl i in\r\n match x returns ST _\r\n (ETbl.get_post (repr_to_eht_repr m) b a.etbl i x\r\n `star`\r\n R.pts_to a.high Steel.FractionalPermission.full_perm w)\r\n (get_post init m b a i)\r\n (requires ~ (PartialMap.contains b i))\r\n (ensures fun res -> Fresh? res ==> Map.sel m i == G.reveal init) with\r\n | ETbl.Missing j ->\r\n let ret = NotFound in\r\n rewrite (ETbl.get_post (repr_to_eht_repr m) b a.etbl i (ETbl.Missing j))\r\n (ETbl.tperm a.etbl (repr_to_eht_repr m) b\r\n `star`\r\n pure (ETbl.map_contains_prop j (repr_to_eht_repr m)));\r\n elim_pure (ETbl.map_contains_prop j (repr_to_eht_repr m));\r\n intro_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n intro_exists (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) m b a.high);\r\n rewrite (ETbl.tperm a.etbl (repr_to_eht_repr m) b\r\n `star`\r\n exists_ (high_epoch_id_pred (G.reveal init) m b a.high))\r\n (get_post init m b a i ret);\r\n return ret\r\n | ETbl.Absent ->\r\n let ret = NotFound in\r\n rewrite (ETbl.get_post (repr_to_eht_repr m) b a.etbl i ETbl.Absent)\r\n (ETbl.tperm a.etbl (repr_to_eht_repr m) b);\r\n intro_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n intro_exists (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) m b a.high);\r\n rewrite (ETbl.tperm a.etbl (repr_to_eht_repr m) b\r\n `star`\r\n exists_ (high_epoch_id_pred (G.reveal init) m b a.high))\r\n (get_post init m b a i ret);\r\n return ret\r\n | ETbl.Present x ->\r\n let ret = Found x in\r\n assert (Some? (PartialMap.sel (repr_to_eht_repr m) i));\r\n rewrite (ETbl.get_post (repr_to_eht_repr m) b a.etbl i (ETbl.Present x))\r\n (ETbl.tperm a.etbl (repr_to_eht_repr m) (PartialMap.upd b i x)\r\n `star`\r\n vp i x (Map.sel m i));\r\n intro_pure (high_epoch_id_prop (G.reveal init) m (PartialMap.upd b i x) w);\r\n intro_exists\r\n (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) m (PartialMap.upd b i x) a.high);\r\n rewrite (perm a init m (PartialMap.upd b i x)\r\n `star`\r\n vp i x (Map.sel m i))\r\n (get_post init m b a i ret);\r\n return ret\r\n end", "val put (#v:Type) \r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (#init:G.erased c)\r\n (#m:G.erased (repr c))\r\n (#b:G.erased (borrows v))\r\n (a:tbl vp)\r\n (i:M.epoch_id)\r\n (x:v)\r\n (content:Ghost.erased c)\r\n : STT unit\r\n (perm a init m b `star` vp i x content)\r\n (fun _ -> perm a init (Map.upd m i content) (PartialMap.remove b i))\nlet put #v #c #vp #init #m #b a i x content =\r\n let w = elim_exists () in\r\n elim_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n ETbl.put a.etbl i x content;\r\n assert (PartialMap.equal (PartialMap.upd (repr_to_eht_repr m) i content)\r\n (repr_to_eht_repr (Map.upd m i content)));\r\n rewrite (ETbl.tperm _ _ _)\r\n (ETbl.tperm a.etbl\r\n (repr_to_eht_repr (Map.upd m i content))\r\n (PartialMap.remove b i));\r\n let high = R.read a.high in\r\n let r = above_high_water_mark high i in\r\n if r\r\n then begin\r\n R.write a.high (Some i);\r\n intro_pure (high_epoch_id_prop (G.reveal init)\r\n (Map.upd m i content)\r\n (PartialMap.remove b i)\r\n (Some i));\r\n intro_exists (Some i) (high_epoch_id_pred (G.reveal init)\r\n (Map.upd m i content)\r\n (PartialMap.remove b i)\r\n a.high)\r\n end\r\n else begin\r\n intro_pure (high_epoch_id_prop (G.reveal init)\r\n (Map.upd m i content)\r\n (PartialMap.remove b i)\r\n w);\r\n intro_exists (G.reveal w) (high_epoch_id_pred (G.reveal init)\r\n (Map.upd m i content)\r\n (PartialMap.remove b i)\r\n a.high)\r\n end", "val get_post:\n #v: Type ->\n #c: Type ->\n #vp: (M.epoch_id -> v -> c -> vprop) ->\n init: G.erased c ->\n m: G.erased (repr c) ->\n b: G.erased (borrows v) ->\n a: tbl vp ->\n i: M.epoch_id ->\n get_result v\n -> vprop\nlet get_post\r\n (#v:Type) \r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (init:G.erased c)\r\n (m:G.erased (repr c))\r\n (b:G.erased (borrows v))\r\n (a:tbl vp)\r\n (i:M.epoch_id)\r\n : get_result v -> vprop\r\n = fun o ->\r\n match o with\r\n | Found x ->\r\n perm a init m (PartialMap.upd b i x) //when `get` succeeds, the key is added to `borrows`\r\n `star`\r\n vp i x (Map.sel m i) //in addition, we return the vp permission for the key\r\n\r\n | _ ->\r\n perm a init m b", "val reclaim (#v:Type) \r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (#init:G.erased c)\r\n (#m:G.erased (repr c))\r\n (#b:G.erased (borrows v))\r\n (a:tbl vp)\r\n (i:M.epoch_id)\r\n : STT unit\r\n (perm a init m b)\r\n (fun _ -> perm a init m (PartialMap.remove b i))\nlet reclaim #v #c #vp #init #m #b a i =\r\n let w = elim_exists () in\r\n elim_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n let _ = ETbl.remove a.etbl i in\r\n intro_pure (high_epoch_id_prop (G.reveal init) m (PartialMap.remove b i) w);\r\n intro_exists\r\n (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) m (PartialMap.remove b i) a.high)", "val ghost_put (#o:_)\r\n (#v:Type) \r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (#init:G.erased c)\r\n (#m:G.erased (repr c))\r\n (#b:G.erased (borrows v))\r\n (a:tbl vp)\r\n (i:M.epoch_id)\r\n (x:v)\r\n (content:Ghost.erased c)\r\n : STGhost unit o\r\n (perm a init m b `star` vp i x content)\r\n (fun _ -> perm a init (Map.upd m i content) (PartialMap.remove b i))\r\n (requires\r\n PartialMap.sel b i == Some x)\r\n (ensures fun _ ->\r\n True)\nlet ghost_put #_ #v #c #vp #init #m #b a i x content =\r\n let w = elim_exists () in\r\n elim_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n ETbl.ghost_put a.etbl i x content;\r\n assert (PartialMap.equal (PartialMap.upd (repr_to_eht_repr m) i content)\r\n (repr_to_eht_repr (Map.upd m i content)));\r\n rewrite (ETbl.tperm _ _ _)\r\n (ETbl.tperm a.etbl\r\n (repr_to_eht_repr (Map.upd m i content))\r\n (PartialMap.remove b i));\r\n intro_pure (high_epoch_id_prop (G.reveal init)\r\n (Map.upd m i content)\r\n (PartialMap.remove b i)\r\n w);\r\n intro_exists\r\n (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) (Map.upd m i content) (PartialMap.remove b i) a.high)", "val finalize (#v:Type)\r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (#init:G.erased c)\r\n (#m:G.erased (repr c))\r\n (#b:G.erased (borrows v))\r\n (t:tbl vp)\r\n : STT unit\r\n (perm t init m b)\r\n (fun _ -> emp)\nlet finalize #v #c #vp #init #m #b t =\r\n let w = elim_exists () in\r\n elim_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n ETbl.free t.etbl;\r\n R.free t.high", "val token (#k:eqtype) (#v:Type0)\n (r:ref (ht_t k v))\n (r_sz:ref pos_us)\n (r_hashf:ref (k -> SZ.t))\n (r_contents:ref (V.vec (cell k v))) : vprop\nlet token (#k:eqtype) (#v:Type0)\n (r:ref (ht_t k v))\n (r_sz:ref pos_us)\n (r_hashf:ref (k -> SZ.t))\n (r_contents:ref (V.vec (cell k v))) : vprop =\n exists* ht. pts_to r ht", "val read (#a:Type)\n (#u:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhost (erased a) u\n (pts_to r p v)\n (fun x -> pts_to r p x)\n (requires True)\n (ensures fun x -> x == v)\nlet read (#a:Type)\n (#u:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhost (erased a) u\n (pts_to r p v)\n (fun x -> pts_to r p x)\n (requires True)\n (ensures fun x -> x == v)\n = let y = coerce_ghost (fun _ -> R.ghost_read_pt r) in\n y", "val exploded_vp\n (#k: eqtype)\n (#v: Type0)\n (r: ref (ht_t k v))\n (ht: ht_t k v)\n (r_sz: ref pos_us)\n (r_hashf: ref (k -> SZ.t))\n (r_contents: ref (V.vec (cell k v)))\n : vprop\nlet exploded_vp (#k:eqtype) (#v:Type0)\n (r:ref (ht_t k v))\n (ht:ht_t k v)\n (r_sz:ref pos_us)\n (r_hashf:ref (k -> SZ.t))\n (r_contents:ref (V.vec (cell k v))) : vprop = \n pts_to r_sz ht.sz **\n pts_to r_hashf ht.hashf **\n pts_to r_contents ht.contents **\n token r r_sz r_hashf r_contents", "val unexplode_ref (#k:eqtype) (#v:Type0) (#ht:erased (ht_t k v))\n (r:ref (ht_t k v))\n (r_sz:ref pos_us)\n (r_hashf:ref (k -> SZ.t))\n (r_contents:ref (V.vec (cell k v)))\n : stt unit\n (requires exploded_vp r ht r_sz r_hashf r_contents)\n (ensures fun _ -> pts_to r ht)\nlet unexplode_ref = unexplode_ref'", "val read_ref (#a:Type0) (r:R.ref (vec a))\n (i:SZ.t)\n (#v:erased (vec a))\n (#s:erased (Seq.seq a) { SZ.v i < Seq.length s})\n : stt a\n (requires R.pts_to r v ** pts_to v s)\n (ensures fun res -> R.pts_to r v ** pts_to v s ** pure (res == Seq.index s (SZ.v i)))\nlet read_ref = read_ref'", "val share\n (#a:Type)\n (v:vec a)\n (#s:Ghost.erased (Seq.seq a))\n (#p:perm)\n : stt_ghost unit\n (requires pts_to v #p s)\n (ensures fun _ -> pts_to v #(half_perm p) s ** pts_to v #(half_perm p) s)\nlet share v = A.share v", "val get_or_init_eht\n (#v #c: _)\n (#vp: (M.epoch_id -> v -> c -> vprop))\n (#repr: erased (EpochMap.repr c))\n (eht: EpochMap.tbl vp)\n (e: M.epoch_id)\n (#def: erased c)\n (init: (e: M.epoch_id -> STT v emp (fun v -> vp e v def)))\n : STT (option v)\n (EpochMap.full_perm eht def repr)\n (fun res -> get_or_init_post eht e def repr res)\nlet get_or_init_eht #v #c (#vp:M.epoch_id -> v -> c -> vprop) (#repr:erased (EpochMap.repr c))\r\n (eht:EpochMap.tbl vp)\r\n (e:M.epoch_id)\r\n (#def:erased c)\r\n (init: (e:M.epoch_id -> STT v emp (fun v -> vp e v def)))\r\n : STT (option v)\r\n (EpochMap.full_perm eht def repr)\r\n (fun res -> get_or_init_post eht e def repr res)\r\n = let vopt = EpochMap.get eht e in\r\n match vopt with\r\n | EpochMap.NotFound ->\r\n rewrite (EpochMap.get_post _ _ _ _ _ vopt)\r\n (EpochMap.full_perm eht def repr);\r\n return None\r\n\r\n\r\n | EpochMap.Found v ->\r\n rewrite (EpochMap.get_post _ _ _ _ _ vopt)\r\n (get_or_init_post eht e def repr (Some v));\r\n return (Some v)\r\n\r\n | EpochMap.Fresh ->\r\n rewrite (EpochMap.get_post _ _ _ _ _ vopt)\r\n (EpochMap.full_perm eht def repr);\r\n let v = init e in\r\n epoch_map_add eht e v _;\r\n assert (repr `Map.equal` Map.upd repr e def);\r\n rewrite (EpochMap.full_perm eht _ _)\r\n (EpochMap.full_perm eht def repr);\r\n //This additional get is redundant\r\n //but the EHT is ephemeral and we can't prove that we can\r\n //get what we just put\r\n let vopt_again = EpochMap.get eht e in\r\n match vopt_again with\r\n | EpochMap.Found v ->\r\n rewrite (EpochMap.get_post _ _ _ _ _ vopt_again)\r\n (get_or_init_post eht e def repr (Some v));\r\n return (Some v)\r\n\r\n | _ ->\r\n rewrite (EpochMap.get_post _ _ _ _ _ vopt_again)\r\n (get_or_init_post eht e def repr None);\r\n return None", "val read (#a:Type)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : ST a\n (pts_to r p v)\n (fun x -> pts_to r p v)\n (requires True)\n (ensures fun x -> x == Ghost.reveal v)\nlet read (#a:Type)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : ST a\n (pts_to r p v)\n (fun _ -> pts_to r p v)\n (requires True)\n (ensures fun x -> x == Ghost.reveal v)\n = let u = coerce_steel (fun _ -> R.read_pt r) in\n return u", "val read (#a:Type)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : ST a\n (pts_to r p v)\n (fun x -> pts_to r p v)\n (requires True)\n (ensures fun x -> x == Ghost.reveal v)\nlet read (#a:Type)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : ST a\n (pts_to r p v)\n (fun _ -> pts_to r p v)\n (requires True)\n (ensures fun x -> x == Ghost.reveal v)\n = let u = coerce_steel (fun _ -> R.read r) in\n return u", "val fill\n (#t:Type0)\n (l:SZ.t)\n (a:larray t (SZ.v l))\n (v:t)\n (#s:Ghost.erased (Seq.seq t))\n : stt unit\n (requires \n pts_to a s)\n (ensures fun _ ->\n exists* (s:Seq.seq t).\n pts_to a s **\n pure (s `Seq.equal` Seq.create (SZ.v l) v))\nlet fill = fill'", "val ghost_put_back\n (#o: _)\n (#v #c: Type)\n (#vp: (M.epoch_id -> v -> c -> vprop))\n (#init: Ghost.erased c)\n (#m: Ghost.erased (EpochMap.repr c))\n (a: EpochMap.tbl vp)\n (i: M.epoch_id)\n (x: v)\n (content: Ghost.erased c)\n : STGhostT unit\n o\n ((EpochMap.perm a init m (PartialMap.upd EpochMap.empty_borrows i x)) `star` (vp i x content))\n (fun _ -> EpochMap.full_perm a init (Map.upd m i content))\nlet ghost_put_back (#o:_)\r\n (#v:Type) \r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (#init:Ghost.erased c)\r\n (#m:Ghost.erased (EpochMap.repr c))\r\n (a:EpochMap.tbl vp)\r\n (i:M.epoch_id)\r\n (x:v)\r\n (content:Ghost.erased c)\r\n : STGhostT unit o\r\n (EpochMap.perm a init m (PartialMap.upd EpochMap.empty_borrows i x) `star` vp i x content)\r\n (fun _ -> EpochMap.full_perm a init (Map.upd m i content))\r\n = EpochMap.ghost_put a i x content;\r\n rewrite (EpochMap.perm _ _ _ _)\r\n (EpochMap.full_perm a init (Map.upd m i content))", "val get (#t: buftype) (#a: Type0) (h: mem) (b: buffer_t t a) (i: nat{i < length b}) : GTot a\nlet get (#t : buftype) (#a : Type0) (h : mem) (b : buffer_t t a) (i : nat{i < length b}) :\n GTot a =\n match t with\n | IMMUT -> IB.get h (b <: ibuffer a) i\n | MUT -> B.get h (b <: buffer a) i\n | CONST -> B.get h (CB.as_mbuf (b <: cbuffer a)) i", "val perm (#v:Type)\r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (t:tbl vp)\r\n (default_value: c)\r\n ([@@@smt_fallback] m:repr c)\r\n ([@@@smt_fallback] b:borrows v)\r\n : vprop\nlet perm #v #c #cp t default_value m b =\r\n ETbl.tperm t.etbl (repr_to_eht_repr m) b\r\n `star`\r\n exists_ (high_epoch_id_pred default_value m b t.high)", "val write_ref (#a:Type0) (r:R.ref (vec a))\n (i:SZ.t)\n (x:a)\n (#v:erased (vec a))\n (#s:erased (Seq.seq a) { SZ.v i < Seq.length s})\n : stt unit\n (requires R.pts_to r v ** pts_to v s)\n (ensures fun _ -> R.pts_to r v ** pts_to v (Seq.upd s (SZ.v i) x))\nlet write_ref = write_ref'", "val op_Array_Access\n (#a: Type0)\n (v:vec a)\n (i:SZ.t)\n (#p:perm)\n (#s:Ghost.erased (Seq.seq a) { SZ.v i < Seq.length s })\n : stt a\n (requires pts_to v #p s)\n (ensures fun res ->\n pts_to v #p s **\n pure (res == Seq.index s (SZ.v i)))\nlet op_Array_Access v i = A.op_Array_Access v i", "val find (#t_k: eqtype) (#t_v: Type0) (ll: t t_k t_v) (k: t_k):\n Stack (option t_v)\n (requires fun h0 ->\n invariant h0 ll)\n (ensures fun h0 x h1 ->\n let m: map t_k t_v = v h0 ll in\n h0 == h1 /\\\n x == M.sel m k)\nlet find #_ #_ ll k =\n find_ !*ll.LL2.ptr !*ll.LL2.v k", "val v: #t_k:eqtype -> #t_v:Type0 -> h:HS.mem -> ll:t t_k t_v -> GTot (map t_k t_v)\nlet v #_ #_ h ll =\n let l = LL2.v h ll in\n v_ l", "val create (#v:Type)\r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (n:U32.t{U32.v n > 0})\r\n (init:G.erased c)\r\n : STT (tbl #v #c vp)\r\n emp\r\n (fun a -> perm a init (Map.const #M.epoch_id #c init) empty_borrows)\nlet create #v #c #vp n init =\r\n let etbl = ETbl.create_v vp hash (SizeT.uint32_to_sizet n) init in\r\n let high = R.alloc None in\r\n intro_pure (high_epoch_id_prop (G.reveal init)\r\n (Map.const (G.reveal init))\r\n (empty_borrows #v)\r\n None);\r\n let r = { etbl = etbl; high = high } in\r\n assert (PartialMap.equal (PartialMap.const M.epoch_id (G.reveal init))\r\n (repr_to_eht_repr (Map.const #M.epoch_id #c init)));\r\n rewrite (ETbl.tperm _ _ _)\r\n (ETbl.tperm r.etbl\r\n (repr_to_eht_repr (Map.const (G.reveal init)))\r\n empty_borrows);\r\n rewrite (R.pts_to _ _ _ `star` pure _)\r\n (high_epoch_id_pred (G.reveal init)\r\n (Map.const (G.reveal init))\r\n empty_borrows\r\n r.high\r\n None);\r\n intro_exists None (high_epoch_id_pred _ _ _ _);\r\n return r", "val find_ (#t_k: eqtype) (#t_v: Type0) (hd: LL1.t (t_k & t_v)) (l: G.erased (list (t_k & t_v))) (k: t_k):\n Stack (option t_v)\n (requires fun h0 ->\n LL1.well_formed h0 hd l /\\\n LL1.invariant h0 hd l)\n (ensures fun h0 x h1 ->\n let m: map t_k t_v = v_ l in\n h0 == h1 /\\\n x == M.sel m k)\nlet rec find_ #_ #_ hd l k =\n if B.is_null hd then\n None\n else\n let cell = !* hd in\n if fst cell.LL1.data = k then\n Some (snd cell.LL1.data)\n else\n find_ cell.LL1.next (List.Tot.tl l) k", "val get (#a:Type0) (x: t a) (i:US.t{US.v i < length x}) :\n Pure a\n (requires True)\n (ensures fun y ->\n US.v i < L.length (v x) /\\\n y == L.index (v x) (US.v i))\nlet get x i = L.index x (US.v i)", "val write (#a:Type)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\nlet write (#a:Type)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\n = coerce_steel (fun _ -> R.write r x);\n return ()", "val ( := ) (#a: Type) (#rel: preorder a) (r: mref a rel) (v: a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 ->\n rel (sel h0 r) v /\\ h0 `contains` r /\\ modifies (Set.singleton (addr_of r)) h0 h1 /\\\n equal_dom h0 h1 /\\ sel h1 r == v)\nlet op_Colon_Equals (#a:Type) (#rel:preorder a) (r:mref a rel) (v:a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 -> rel (sel h0 r) v /\\ h0 `contains` r /\\\n modifies (Set.singleton (addr_of r)) h0 h1 /\\ equal_dom h0 h1 /\\\n sel h1 r == v)\n= write #a #rel r v", "val bget\n (#t: buftype)\n (#a: Type0)\n (#len: size_t)\n (h: mem)\n (b: lbuffer_t t a len)\n (i: size_nat{i < v len})\n : GTot a\nlet bget (#t:buftype) (#a:Type0) (#len:size_t) (h:mem) (b:lbuffer_t t a len)\n (i:size_nat{i < v len}) : GTot a\n=\n match t with\n | MUT -> B.get h (b <: buffer a) i\n | IMMUT -> IB.get h (b <: ibuffer a) i\n | CONST -> FStar.Seq.index (CB.as_seq h (b <: cbuffer a)) i", "val get (#s: _) : st s s\nlet get #s\n : st s s\n = fun s -> s, s", "val write (#a:Type)\n (#u:_)\n (#v:erased a)\n (r:ref a)\n (x:erased a)\n : STGhostT unit u\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\nlet write (#a:Type)\n (#u:_)\n (#v:erased a)\n (r:ref a)\n (x:erased a)\n : STGhostT unit u\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\n = coerce_ghost (fun _ -> R.ghost_write_pt r x)", "val write (#a:Type0)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\nlet write (#a:Type0)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\n = coerce_steel (fun _ -> R.write_pt r x);\n return ()", "val free\n (#a:Type0)\n (v:vec a)\n (#s:Ghost.erased (Seq.seq a))\n : stt unit\n (requires\n pts_to v s **\n pure (is_full_vec v))\n (ensures fun _ -> emp)\nlet free v = A.free v", "val share (#a:Type0)\n (#uses:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit uses\n (pts_to r p v)\n (fun _ -> pts_to r (half_perm p) v `star` pts_to r (half_perm p) v)\nlet share (#a:Type0)\n (#uses:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit uses\n (pts_to r p v)\n (fun _ -> pts_to r (half_perm p) v `star` pts_to r (half_perm p) v)\n = coerce_ghost (fun _ -> R.share_pt r)", "val share (#a:Type)\n (#uses:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit uses\n (pts_to r p v)\n (fun _ -> pts_to r (half_perm p) v `star` pts_to r (half_perm p) v)\nlet share (#a:Type)\n (#uses:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit uses\n (pts_to r p v)\n (fun _ -> pts_to r (half_perm p) v `star` pts_to r (half_perm p) v)\n = coerce_ghost (fun _ -> R.share r)", "val share (#a:Type)\n (#uses:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit uses\n (pts_to r p v)\n (fun _ -> pts_to r (half_perm p) v `star` pts_to r (half_perm p) v)\nlet share\n r\n= RST.share r.reveal", "val get (#n: nat) (uf: uf_forest n) (i: id n)\n : ST (elt n)\n (requires (fun h0 -> live uf h0))\n (ensures (fun h0 r h1 -> r == sel h0 (index uf i) /\\ h0 == h1))\nlet get (#n:nat) (uf:uf_forest n) (i:id n)\n :ST (elt n) (requires (fun h0 -> live uf h0))\n (ensures (fun h0 r h1 -> r == sel h0 (index uf i) /\\ h0 == h1))\n = let h = ST.get () in\n sel_tot h (index uf i)", "val gather\n (#a:Type)\n (v:vec a)\n (#s0 #s1:Ghost.erased (Seq.seq a))\n (#p0 #p1:perm)\n : stt_ghost unit\n (requires pts_to v #p0 s0 ** pts_to v #p1 s1)\n (ensures fun _ -> pts_to v #(sum_perm p0 p1) s0 ** pure (s0 == s1))\nlet gather v = A.gather v", "val get (#a: Type0) (#rrel #rel: srel a) (h: HS.mem) (p: mbuffer a rrel rel) (i: nat)\n : Ghost a (requires (i < length p)) (ensures (fun _ -> True))\nlet get (#a:Type0) (#rrel #rel:srel a) (h:HS.mem) (p:mbuffer a rrel rel) (i:nat)\n :Ghost a (requires (i < length p)) (ensures (fun _ -> True))\n = Seq.index (as_seq h p) i", "val share\n (#a:Type)\n (arr:array a)\n (#s:Ghost.erased (Seq.seq a))\n (#p:perm)\n : stt_ghost unit\n (requires pts_to arr #p s)\n (ensures fun _ -> pts_to arr #(half_perm p) s ** pts_to arr #(half_perm p) s)\nlet share = share'", "val explode_ref_ht_t (#k:eqtype) (#v:Type0) (#ht:erased (ht_t k v)) (r:ref (ht_t k v))\n : stt (ref pos_us & ref (k -> SZ.t) & ref (V.vec (cell k v)))\n (requires pts_to r ht)\n (ensures fun res -> exploded_vp r ht (tfst res) (tsnd res) (tthd res))\nlet explode_ref_ht_t = explode_ref_ht_t'", "val lemma_get_put_other\n (#a: eqtype)\n (#b: Type)\n (is_le: (a -> a -> bool))\n (t: tree a b)\n (key kx: a)\n (value: b)\n (lo hi: option a)\n : Lemma\n (requires\n is_cmp is_le /\\ inv is_le t lo hi /\\ is_lt_option is_le lo (Some key) /\\\n is_lt_option is_le (Some key) hi /\\ key =!= kx)\n (ensures get is_le (put is_le t key value) kx == get is_le t kx)\nlet rec lemma_get_put_other (#a:eqtype) (#b:Type) (is_le:a -> a -> bool) (t:tree a b) (key kx:a) (value:b) (lo hi:option a)\n : Lemma\n (requires\n is_cmp is_le /\\\n inv is_le t lo hi /\\\n is_lt_option is_le lo (Some key) /\\\n is_lt_option is_le (Some key) hi /\\\n key =!= kx\n )\n (ensures get is_le (put is_le t key value) kx == get is_le t kx)\n =\n lemma_put_inv is_le t key value lo hi;\n match t with\n | Empty -> ()\n | Node k v _ l r ->\n if key = k then ()\n else if is_le key k then\n lemma_get_put_other is_le l key kx value lo (Some k)\n else\n lemma_get_put_other is_le r key kx value (Some k) hi", "val read (#a:Type) (r:ref a) (#n:erased a) (#p:perm)\n : stt_ghost (erased a)\n (pts_to r #p n)\n (fun x -> pts_to r #p n ** pure (n == x))\nlet read = read'", "val read (#a:Type) (r:ref a) (#n:erased a) (#p:perm)\n : stt_ghost (erased a)\n (pts_to r #p n)\n (fun x -> pts_to r #p n ** pure (n == x))\nlet read = read'", "val write (#opened: _) (#a:Type)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STGhostT unit opened\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\nlet write\n #_ #a #v r x\n= let gr : R.ghost_ref a = coerce_eq (R.reveal_ghost_ref a) (Ghost.hide r.reveal) in\n weaken (pts_to r full_perm v) (R.ghost_pts_to gr full_perm v) (fun _ ->\n R.reveal_ghost_pts_to_sl gr full_perm v\n );\n STC.coerce_ghost (fun _ -> R.ghost_write gr x);\n weaken (R.ghost_pts_to gr full_perm x) (pts_to r full_perm x) (fun _ ->\n R.reveal_ghost_pts_to_sl gr full_perm x\n )", "val write (#a: Type) (#rel: preorder a) (r: mref a rel) (v: a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 ->\n rel (sel h0 r) v /\\ h0 `contains` r /\\ modifies (Set.singleton (addr_of r)) h0 h1 /\\\n equal_dom h0 h1 /\\ sel h1 r == v)\nlet write (#a:Type) (#rel:preorder a) (r:mref a rel) (v:a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 -> rel (sel h0 r) v /\\ h0 `contains` r /\\\n modifies (Set.singleton (addr_of r)) h0 h1 /\\ equal_dom h0 h1 /\\\n sel h1 r == v)\n = let h0 = gst_get () in\n gst_recall (contains_pred r);\n let h1 = upd_tot h0 r v in\n Heap.lemma_distinct_addrs_distinct_preorders ();\n Heap.lemma_distinct_addrs_distinct_mm ();\n Heap.lemma_upd_equals_upd_tot_for_contained_refs h0 r v;\n gst_put h1", "val share (#a:Type) (r:ref a) (#v:erased a) (#p:perm)\n : stt_ghost unit\n (pts_to r #p v)\n (fun _ ->\n pts_to r #(half_perm p) v **\n pts_to r #(half_perm p) v)\nlet share = share'", "val share (#a:Type) (r:ref a) (#v:erased a) (#p:perm)\n : stt_ghost unit\n (pts_to r #p v)\n (fun _ ->\n pts_to r #(half_perm p) v **\n pts_to r #(half_perm p) v)\nlet share = share'", "val share (#a:Type) (r:ref a) (#v:erased a) (#p:perm)\n : stt_ghost unit\n (pts_to r #p v)\n (fun _ ->\n pts_to r #(half_perm p) v **\n pts_to r #(half_perm p) v)\nlet share = share'", "val share (#a:Type) (r:ref a) (#v:erased a) (#p:perm)\n : stt_ghost unit\n (pts_to r #p v)\n (fun _ ->\n pts_to r #(half_perm p) v **\n pts_to r #(half_perm p) v)\nlet share = share'", "val free (#a:Type0)\n (#u:_)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit u\n (pts_to r full_perm v)\n (fun _ -> emp)\nlet free (#a:Type0)\n (#u:_)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit u\n (pts_to r full_perm v)\n (fun _ -> emp)\n = coerce_ghost (fun _ -> R.ghost_free_pt r)", "val free (#a:Type0)\n (#v:erased a)\n (r:ref a)\n : STT unit\n (pts_to r full_perm v) (fun _ -> emp)\nlet free (#a:Type0)\n (#v:erased a)\n (r:ref a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> emp)\n = coerce_steel(fun _ -> R.free_pt r);\n return ()", "val op_Array_Access\n (#t: Type)\n (a: array t)\n (i: SZ.t)\n (#p: perm)\n (#s: Ghost.erased (Seq.seq t){SZ.v i < Seq.length s})\n : stt t\n (requires\n pts_to a #p s)\n (ensures fun res ->\n pts_to a #p s **\n pure (res == Seq.index s (SZ.v i)))\nlet op_Array_Access = read", "val op_Array_Access\n (#t: Type)\n (a: array t)\n (i: SZ.t)\n (#p: perm)\n (#s: Ghost.erased (Seq.seq t){SZ.v i < Seq.length s})\n : stt t\n (requires\n pts_to a #p s)\n (ensures fun res ->\n pts_to a #p s **\n pure (res == Seq.index s (SZ.v i)))\nlet op_Array_Access #t a i #p #s = read #t a i #p #s", "val g_upd\n (#a: Type0)\n (#rrel #rel: srel a)\n (b: mbuffer a rrel rel)\n (i: nat{i < length b})\n (v: a)\n (h: HS.mem{live h b})\n : GTot HS.mem\nlet g_upd (#a:Type0) (#rrel #rel:srel a)\n (b:mbuffer a rrel rel)\n (i:nat{i < length b})\n (v:a)\n (h:HS.mem{live h b})\n : GTot HS.mem\n = g_upd_seq b (Seq.upd (as_seq h b) i v) h", "val lemma_get_put_self\n (#a: eqtype)\n (#b: Type)\n (is_le: (a -> a -> bool))\n (t: tree a b)\n (key: a)\n (value: b)\n (lo hi: option a)\n : Lemma (requires is_cmp is_le /\\ inv is_le t lo hi)\n (ensures get is_le (put is_le t key value) key == Some value)\nlet rec lemma_get_put_self (#a:eqtype) (#b:Type) (is_le:a -> a -> bool) (t:tree a b) (key:a) (value:b) (lo hi:option a) : Lemma\n (requires is_cmp is_le /\\ inv is_le t lo hi)\n (ensures get is_le (put is_le t key value) key == Some value)\n =\n match t with\n | Empty -> ()\n | Node k v _ l r ->\n if key = k then ()\n else if is_le key k then\n lemma_get_put_self is_le l key value lo (Some k)\n else\n lemma_get_put_self is_le r key value (Some k) hi", "val write (#a:Type) (#p:Preorder.preorder a) (#v:erased a)\n (r:ref a p) (x:a)\n : ST unit\n (pts_to r full_perm v)\n (fun v -> pts_to r full_perm x)\n (requires p v x)\n (ensures fun _ -> True)\nlet write (#a:Type) (#p:Preorder.preorder a) (#v:erased a)\n (r:ref a p) (x:a)\n : ST unit\n (pts_to r full_perm v)\n (fun v -> pts_to r full_perm x)\n (requires p v x)\n (ensures fun _ -> True)\n = coerce_steel (fun _ -> MR.write r x)", "val read (#a:Type) (#p:perm) (#v:erased a) (r:ref a)\n : Steel a (pts_to r p v) (fun x -> pts_to r p x)\n (requires fun h -> True)\n (ensures fun _ x _ -> x == Ghost.reveal v)\nlet read (#a:Type) (#p:perm) (#v:erased a) (r:ref a)\n = let v1 : erased (fractional a) = Ghost.hide (Some (Ghost.reveal v, p)) in\n rewrite_slprop (pts_to r p v) (RP.pts_to r v1 `star` pure (perm_ok p)) (fun _ -> ());\n elim_pure (perm_ok p);\n let v2 = RP.read r v1 in\n rewrite_slprop (RP.pts_to r v1) (pts_to r p v)\n (fun m ->\n emp_unit (hp_of (pts_to_raw r p v));\n pure_star_interp (hp_of (pts_to_raw r p v)) (perm_ok p) m);\n assert (compatible pcm_frac v1 v2);\n let Some (x, _) = v2 in\n rewrite_slprop (pts_to r p v) (pts_to r p x) (fun _ -> ());\n return x", "val index\n (#t: Type) (#p: P.perm)\n (a: array t)\n (#s: Ghost.erased (Seq.seq t))\n (i: US.t)\n: ST t\n (pts_to a p s)\n (fun _ -> pts_to a p s)\n (US.v i < length a \\/ US.v i < Seq.length s)\n (fun res -> Seq.length s == length a /\\ US.v i < Seq.length s /\\ res == Seq.index s (US.v i))\nlet index #_ #p a #s i =\n rewrite\n (pts_to a _ _)\n (H.pts_to a p (seq_map raise s));\n let res = H.index a i in\n rewrite\n (H.pts_to _ _ _)\n (pts_to _ _ _);\n return (lower res)", "val free (#a:Type)\n (#v:erased a)\n (r:ref a)\n : STT unit\n (pts_to r full_perm v) (fun _ -> emp)\nlet free (#a:Type)\n (#v:erased a)\n (r:ref a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> emp)\n = coerce_steel(fun _ -> R.free r);\n return ()", "val get (st: state) (k: F.key_t) : option F.value_t\nlet get (st:state) (k:F.key_t) : option F.value_t =\n Map.sel st k", "val get_data (#a: Type) (x: (ref (cell a) & cell a)) : Tot a\nlet get_data\n (#a: Type)\n (x: (ref (cell a) & cell a))\n: Tot a\n= (snd x).data", "val pow_base\n (#t: Type)\n (#a_t: BE.inttype_a)\n (#len: size_t{v len > 0})\n (#ctx_len: size_t)\n (k: mk_precomp_base_table t a_t len ctx_len)\n (g: t)\n (i: nat)\n : k.concr_ops.SE.to.a_spec\nlet pow_base (#t:Type) (#a_t:BE.inttype_a) (#len:size_t{v len > 0}) (#ctx_len:size_t)\n (k:mk_precomp_base_table t a_t len ctx_len) (g:t) (i:nat) : k.concr_ops.SE.to.a_spec =\n LE.pow k.concr_ops.SE.to.comm_monoid (k.concr_ops.SE.to.refl g) i", "val get (#a: Type) (m: map16 a) (n: int) : a\nlet get (#a:Type) (m:map16 a) (n:int) : a =\n sel m n", "val grvalue\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (#t: Type)\n (r: greader h0 sout pout_from0 t)\n : GTot t\nlet grvalue\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (#t: Type)\n (r: greader h0 sout pout_from0 t)\n: GTot t\n= Ghost.reveal (GReader?.v r)", "val sel (#key: eqtype) (#value: (key -> Tot Type)) (m: t key value) (k: key) : Tot (value k)\nlet sel (#key: eqtype) (#value: (key -> Tot Type)) (m: t key value) (k: key) : Tot (value k) =\n m.mappings k", "val sel : #a:Type -> \n h:heap ->\n\t r:ref a{contains h r} -> \n Tot a\nlet sel #a h r =\n match snd h r with\n | Some (| _ , x |) -> x", "val free (#t_k: eqtype)\n (#t_v: Type0)\n (ll: t t_k t_v):\n ST unit\n (requires fun h0 ->\n invariant h0 ll)\n (ensures fun h0 _ h1 ->\n B.modifies (region_of ll) h0 h1)\nlet free #_ #_ ll =\n LL2.free ll", "val pop (#a:Type) (ptr:t a) (l:list (cell a){Cons? l})\n : Steel a\n (llist ptr l)\n (fun _ -> llist (next (L.hd l)) (L.tl l))\n (requires fun _ -> True)\n (ensures fun _ x _ -> x == data (L.hd l))\nlet pop #a ptr l =\n let hd = L.hd l in\n let tl = L.tl l in\n rewrite_slprop (llist ptr l) (llist ptr (hd::tl)) (fun _ -> ());\n elim_llist_cons ptr hd tl;\n let c = read_pt ptr in\n let n = next hd in\n free_pt ptr;\n rewrite_slprop (llist (next hd) tl) (llist (next (L.hd l)) (L.tl l)) (fun _ -> ());\n return (data c)", "val mem_alloc (#it: eqtype) (vt: (it -> Type))\n : ST (mem_table vt)\n (requires fun h0 -> True)\n (ensures fun h0 t h1 -> modifies_mem_table t h0 h1 /\\ mem_empty t h1)\nlet mem_alloc (#it:eqtype) (vt:it -> Type) : ST (mem_table vt)\n (requires fun h0 -> True)\n (ensures fun h0 t h1 -> modifies_mem_table t h0 h1 /\\ mem_empty t h1)\n =\n if model then (MDM.alloc #it #vt #trivial_inv #tls_define_region ()) else ()", "val free\n (#elt: Type)\n (a: array elt)\n (#s: Ghost.erased (Seq.seq elt))\n : stt unit\n (requires\n pts_to a s **\n pure (is_full_array a))\n (ensures fun _ ->\n emp)\nlet free = free'", "val free\n (#elt: Type)\n (a: array elt)\n (#s: Ghost.erased (Seq.seq elt))\n : stt unit\n (requires\n pts_to a s **\n pure (is_full_array a))\n (ensures fun _ ->\n emp)\nlet free = free'", "val get (_:unit)\n :Stack mem (requires (fun m -> True))\n (ensures (fun m0 x m1 -> m0 == x /\\ m1 == m0))\nlet get _ = gst_get ()", "val choose (#a: eqtype) (#b: Type u#b) (m: map a b{exists key. mem key m})\n : GTot (key: a{mem key m})\nlet choose (#a: eqtype) (#b: Type u#b) (m: map a b{exists key. mem key m}) : GTot (key: a{mem key m}) =\n FSet.choose (domain m)", "val sel : #a:Type ->\n #r:preorder a ->\n h:heap ->\n\t m:mref a r{contains h m} ->\n a\nlet sel #a #b h m =\n match snd h m with\n | Some (| _ , (x , _) |) -> x", "val get:\n #a:Type -> h:HS.mem -> vec:vector a ->\n i:uint32_t{i < size_of vec} -> GTot a\nlet get #a h vec i =\n S.index (as_seq h vec) (U32.v i)", "val insert (#a: eqtype) (#b: Type u#b) (k: a) (v: b) (m: map a b)\n : map a b\nlet insert (#a: eqtype) (#b: Type u#b) (k: a) (v: b) (m: map a b) : map a b =\n let keys' = FSet.insert k (domain m) in\n let f' = on_domain a (fun key -> if key = k then Some v else (elements m) key) in\n (| keys', f' |)", "val get (#s: _) (#srel: erel s) : st srel srel\nlet get #s (#srel:erel s) : st srel srel =\n fun s0 -> s0, s0", "val pop (#l: Ghost.erased (list U64.t)) (p: ref llist_cell {Cons? l})\n : STT (ref llist_cell)\n (llist l p)\n (fun p' ->\n exists_ (fun x ->\n ((pts_to p full_perm x) `star` (llist (List.Tot.tl l) p'))\n `star`\n (pure (x.value == List.Tot.hd l))))\nlet pop\n (#l: Ghost.erased (list U64.t))\n (p: ref llist_cell { Cons? l })\n: STT (ref llist_cell)\n (llist l p)\n (fun p' -> exists_ (fun x -> pts_to p full_perm x `star` llist (List.Tot.tl l) p' `star` pure (x.value == List.Tot.hd l)))\n= rewrite (llist l p) (llist_cons (List.Tot.hd l) (llist (List.Tot.tl l)) p);\n let _ = gen_elim () in\n// let p' = (read p).next in // FIXME: \"Effects STBase and Tot cannot be composed\"\n let x = read p in\n let p' = x.next in\n vpattern_rewrite (llist _) p';\n return p'", "val mk_ht (#k: eqtype) (#v: _) (sz: pos_us) (hashf: (k -> SZ.t)) (contents: V.vec (cell k v))\n : ht_t k v\nlet mk_ht (#k:eqtype) #v \n (sz:pos_us) \n (hashf:k -> SZ.t)\n (contents:V.vec (cell k v))\n : ht_t k v\n = { sz; hashf; contents; }", "val get (#a: eqtype) (#b: Type) (is_le: (a -> a -> bool)) (t: tree a b) (key: a) : option b\nlet rec get (#a:eqtype) (#b:Type) (is_le:a -> a -> bool) (t:tree a b) (key:a) : option b =\n match t with\n | Empty -> None\n | Node k v h l r ->\n if key = k then Some v\n else if is_le key k then\n get is_le l key\n else\n get is_le r key", "val share\n (#a:Type)\n (arr:array a)\n (#s:Ghost.erased (Seq.seq a))\n (#p:perm)\n: stt_ghost unit\n (requires pts_to arr #p s)\n (ensures fun _ -> pts_to arr #(half_perm p) s ** pts_to arr #(half_perm p) s)\nlet share #a arr #s #p = H.share arr #(raise_seq s) #p", "val alloc (#a:Type)\n (#u:_)\n (x:erased a)\n : STGhostT (ref a) u\n emp\n (fun r -> pts_to r full_perm x)\nlet alloc (#a:Type)\n (#u:_)\n (x:erased a)\n : STGhostT (ref a) u\n emp\n (fun r -> pts_to r full_perm x)\n = coerce_ghost (fun _ -> R.ghost_alloc_pt x)", "val v: #a:Type -> h:HS.mem -> ll: t a -> GTot (list a)\nlet v #_ h ll =\n B.deref h ll.v", "val free (#opened: _) (#a:Type)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit opened\n (pts_to r full_perm v) (fun _ -> emp)\nlet free\n #_ #a #v r\n= let gr : R.ghost_ref a = coerce_eq (R.reveal_ghost_ref a) (Ghost.hide r.reveal) in\n weaken (pts_to r full_perm v) (R.ghost_pts_to gr full_perm v) (fun _ ->\n R.reveal_ghost_pts_to_sl gr full_perm v\n );\n STC.coerce_ghost (fun _ -> R.ghost_free gr)", "val share_gen (#a:Type0)\n (#uses:_)\n (#p:perm)\n (#v: a)\n (r:ref a)\n (p1 p2: perm)\n : STGhost unit uses\n (pts_to r p v)\n (fun _ -> pts_to r p1 v `star` pts_to r p2 v)\n (p == p1 `sum_perm` p2)\n (fun _ -> True)\nlet share_gen\n r p1 p2\n= coerce_ghost (fun _ -> R.share_gen_pt r p1 p2)", "val clear (#t_k: eqtype)\n (#t_v: Type0)\n (ll: t t_k t_v):\n ST unit\n (requires fun h0 ->\n invariant h0 ll)\n (ensures fun h0 _ h1 ->\n B.modifies (region_of ll) h0 h1 /\\\n invariant h1 ll /\\\n v h1 ll == M.const None)\nlet clear #_ #_ ll =\n LL2.clear ll", "val index (#t: Type) (#p: P.perm) (a: array t) (#s: Ghost.erased (Seq.seq t)) (i: US.t)\n : ST t\n (pts_to a p s)\n (fun _ -> pts_to a p s)\n (US.v i < length a \\/ US.v i < Seq.length s)\n (fun res -> Seq.length s == length a /\\ US.v i < Seq.length s /\\ res == Seq.index s (US.v i))\nlet index\n (#t: Type) (#p: P.perm)\n (a: array t)\n (#s: Ghost.erased (Seq.seq t))\n (i: US.t)\n: ST t\n (pts_to a p s)\n (fun _ -> pts_to a p s)\n (US.v i < length a \\/ US.v i < Seq.length s)\n (fun res -> Seq.length s == length a /\\ US.v i < Seq.length s /\\ res == Seq.index s (US.v i))\n= rewrite\n (pts_to _ _ _)\n (pts_to (| (ptr_of a), (dsnd a) |) p s);\n let res = index_ptr (ptr_of a) i in\n rewrite\n (pts_to _ _ _)\n (pts_to a p s);\n return res", "val upd\n (#t: Type)\n (a: array t)\n (#s: Ghost.erased (Seq.seq t))\n (i: US.t {US.v i < Seq.length s})\n (v: t)\n: STT unit\n (pts_to a P.full_perm s)\n (fun res -> pts_to a P.full_perm (Seq.upd s (US.v i) v))\nlet upd #_ a #s i v =\n rewrite\n (pts_to a _ _)\n (H.pts_to a P.full_perm (seq_map raise s));\n H.upd a i (raise v);\n assert (seq_map raise (Seq.upd s (US.v i) v) `Seq.equal` Seq.upd (seq_map raise s) (US.v i) (raise v));\n rewrite\n (H.pts_to _ _ _)\n (pts_to _ _ _)", "val i_sel (#r: rid) (#a: Type) (#p: (seq a -> Type)) (h: mem) (m: i_seq r a p)\n : GTot (s: seq a {p s})\nlet i_sel (#r:rid) (#a:Type) (#p:seq a -> Type) (h:mem) (m:i_seq r a p)\n : GTot (s:seq a{p s})\n = HS.sel h m", "val op_Array_Assignment\n (#a:Type0)\n (v:vec a)\n (i:SZ.t)\n (x:a)\n (#s:Ghost.erased (Seq.seq a) { SZ.v i < Seq.length s })\n : stt unit\n (requires pts_to v s)\n (ensures fun _ -> pts_to v (Seq.upd s (SZ.v i) x))\nlet op_Array_Assignment v i x = A.op_Array_Assignment v i x", "val pop: #a:Type -> ll: t a -> ST a\n (requires fun h0 ->\n invariant h0 ll /\\\n Cons? (v h0 ll))\n (ensures fun h0 x h1 ->\n let hd :: tl = v h0 ll in\n invariant h1 ll /\\\n B.(modifies (footprint h0 ll) h0 h1) /\\\n // B.(modifies (loc_buffer ll.ptr `loc_union` loc_buffer ll.v) h0 h1) /\\\n v h1 ll == tl /\\\n cells h1 ll == List.Tot.tl (cells h0 ll) /\\\n x == hd)\nlet pop #a ll =\n let r = LL1.pop ll.spine_rid (!* ll.v) ll.ptr in\n let v = !* ll.v in\n ll.v *= G.hide (List.Tot.tl v);\n r", "val get_iv:\n a:Spec.alg\n -> s: size_t{size_v s < 8} ->\n Stack (word_t a)\n (requires (fun h -> True))\n (ensures (fun h0 z h1 -> h0 == h1 /\\\n v z == v (Seq.index (Spec.ivTable a) (v s))))\nlet get_iv a s =\n recall_contents #(Spec.pub_word_t Spec.Blake2S) #8ul ivTable_S (Spec.ivTable Spec.Blake2S);\n recall_contents #(Spec.pub_word_t Spec.Blake2B) #8ul ivTable_B (Spec.ivTable Spec.Blake2B);\n [@inline_let]\n let ivTable: (x:glbuffer (Spec.pub_word_t a) 8ul{witnessed x (Spec.ivTable a) /\\ recallable x}) =\n match a with\n | Spec.Blake2S -> ivTable_S\n | Spec.Blake2B -> ivTable_B\n in\n let r = index ivTable s in\n secret #(Spec.wt a) r", "val extend\n (#r: rid)\n (#a: eqtype)\n (#b: (a -> Type))\n (#inv: (map' a b -> Type0))\n (m: t r a b inv)\n (x: a)\n (y: b x)\n : ST unit\n (requires\n (fun h ->\n let cur = HS.sel h m in\n inv (upd cur x y) /\\ sel cur x == None))\n (ensures\n (fun h0 u h1 ->\n let cur = HS.sel h0 m in\n let hsref = m in\n HS.contains h1 m /\\ modifies (Set.singleton r) h0 h1 /\\\n modifies_ref r (Set.singleton (HS.as_addr hsref)) h0 h1 /\\ HS.sel h1 m == upd cur x y /\\\n HST.witnessed (defined m x) /\\ HST.witnessed (contains m x y)))\nlet extend (#r:rid) (#a:eqtype) (#b:a -> Type) (#inv:(map' a b -> Type0)) (m:t r a b inv) (x:a) (y:b x)\n : ST unit\n (requires (fun h -> let cur = HS.sel h m in inv (upd cur x y) /\\ sel cur x == None))\n (ensures (fun h0 u h1 ->\n let cur = HS.sel h0 m in\n let hsref = m in\n HS.contains h1 m\n /\\ modifies (Set.singleton r) h0 h1\n /\\ modifies_ref r (Set.singleton (HS.as_addr hsref)) h0 h1\n /\\ HS.sel h1 m == upd cur x y\n /\\ HST.witnessed (defined m x)\n /\\ HST.witnessed (contains m x y)))\n = recall m;\n reveal_opaque (`%grows) (grows #a #b #inv);\n let cur = !m in\n m := upd cur x y;\n contains_stable m x y;\n mr_witness m (defined m x);\n mr_witness m (contains m x y)", "val read (#t: Type) (#v: Ghost.erased (scalar_t t)) (r: ref (scalar t))\n : ST t\n (pts_to r v)\n (fun _ -> pts_to r v)\n (exists v0 p. Ghost.reveal v == mk_fraction (scalar t) (mk_scalar v0) p)\n (fun v1 -> forall v0 p. Ghost.reveal v == mk_fraction (scalar t) (mk_scalar v0) p ==> v0 == v1\n )\nlet read (#t: Type) (#v: Ghost.erased (scalar_t t)) (r: ref (scalar t)) : ST t\n (pts_to r v)\n (fun _ -> pts_to r v)\n (exists v0 p . Ghost.reveal v == mk_fraction (scalar t) (mk_scalar v0) p)\n (fun v1 -> forall v0 p . (* {:pattern (mk_fraction (scalar t) (mk_scalar v0) p)} *) Ghost.reveal v == mk_fraction (scalar t) (mk_scalar v0) p ==> v0 == v1)\n= let v0 = FStar.IndefiniteDescription.indefinite_description_tot _ (fun v0 -> exists p . Ghost.reveal v == mk_fraction (scalar t) (mk_scalar v0) p) in\n let p = FStar.IndefiniteDescription.indefinite_description_tot _ (fun p -> Ghost.reveal v == mk_fraction (scalar t) (mk_scalar (Ghost.reveal v0)) p) in\n let prf v0' p' : Lemma\n (requires (Ghost.reveal v == mk_fraction (scalar t) (mk_scalar v0') p'))\n (ensures (v0' == Ghost.reveal v0 /\\ p' == Ghost.reveal p))\n = mk_scalar_inj (Ghost.reveal v0) v0' p p'\n in\n let prf' v0' p' : Lemma\n (Ghost.reveal v == mk_fraction (scalar t) (mk_scalar v0') p' ==> (v0' == Ghost.reveal v0 /\\ p' == Ghost.reveal p))\n = Classical.move_requires (prf v0') p'\n in\n Classical.forall_intro_2 prf';\n rewrite (pts_to _ _) (pts_to r (mk_fraction (scalar t) (mk_scalar (Ghost.reveal v0)) p));\n let v1 = read0 r in\n rewrite (pts_to _ _) (pts_to r v);\n return v1", "val gather (#a:Type)\n (#uses:_) \n (#p0 p1:perm)\n (#v0 #v1:erased a)\n (r:ref a)\n : STGhost unit uses\n (pts_to r p0 v0 `star` pts_to r p1 v1)\n (fun _ -> pts_to r (sum_perm p0 p1) v0)\n (requires True)\n (ensures fun _ -> v0 == v1)\nlet gather\n p1 r\n= RST.gather p1 r.reveal", "val gather (#a:Type)\n (#uses:_) \n (#p0 p1:perm)\n (#v0 #v1:erased a)\n (r:ref a)\n : STGhost unit uses\n (pts_to r p0 v0 `star` pts_to r p1 v1)\n (fun _ -> pts_to r (sum_perm p0 p1) v0)\n (requires True)\n (ensures fun _ -> v0 == v1)\nlet gather (#a:Type)\n (#uses:_)\n (#p0 p1:perm)\n (#v0 #v1:erased a)\n (r:ref a)\n : STGhost unit uses\n (pts_to r p0 v0 `star` pts_to r p1 v1)\n (fun _ -> pts_to r (sum_perm p0 p1) v0)\n (requires True)\n (ensures fun _ -> v0 == v1)\n = coerce_ghost (fun _ -> R.gather #a #uses #p0 #p1 #v0 #v1 r)", "val ( ! ) (#a:Type0) (b:box a) (#v:erased a) (#p:perm)\n : stt a\n (pts_to b #p v)\n (fun x -> pts_to b #p v ** pure (eq2 #a (reveal v) x))\nlet op_Bang b = R.op_Bang b", "val gtdata_get_value (#key: eqtype) (#value: (key -> Tot Type0)) (u: gtdata key value) (k: key)\n : Pure (value k) (requires (gtdata_get_key u == k)) (ensures (fun _ -> True))\nlet gtdata_get_value\n (#key: eqtype)\n (#value: (key -> Tot Type0))\n (u: gtdata key value)\n (k: key)\n: Pure (value k)\n (requires (gtdata_get_key u == k))\n (ensures (fun _ -> True))\n= let (| _, v |) = u in v" ], "closest_src": [ { "project_name": "steel", "file_name": "Steel.ST.EphemeralHashtbl.fsti", "name": "Steel.ST.EphemeralHashtbl.get_post" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.get" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.put" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fsti", "name": "Zeta.Steel.EpochMap.get_post" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.reclaim" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.ghost_put" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.finalize" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Type.fst", "name": "Pulse.Lib.HashTable.Type.token" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.read" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Type.fsti", "name": "Pulse.Lib.HashTable.Type.exploded_vp" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Type.fst", "name": "Pulse.Lib.HashTable.Type.unexplode_ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.read_ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.share" }, { "project_name": "zeta", "file_name": "Zeta.Steel.VerifierSteps.fst", "name": "Zeta.Steel.VerifierSteps.get_or_init_eht" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.read" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.read" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.fst", "name": "Pulse.Lib.Array.fill" }, { "project_name": "zeta", "file_name": "Zeta.Steel.VerifierSteps.fst", "name": "Zeta.Steel.VerifierSteps.ghost_put_back" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.get" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.perm" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.write_ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.op_Array_Access" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.find" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.v" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.create" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.find_" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.get" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.write" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.op_Colon_Equals" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.bget" }, { "project_name": "FStar", "file_name": "MonadFunctorInference.fst", "name": "MonadFunctorInference.get" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.write" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.write" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.free" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.share" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.share" }, { "project_name": "steel", "file_name": "Steel.ST.GhostHigherReference.fst", "name": "Steel.ST.GhostHigherReference.share" }, { "project_name": "FStar", "file_name": "UnionFind.Forest.fst", "name": "UnionFind.Forest.get" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.gather" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.get" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherArray.fst", "name": "Pulse.Lib.HigherArray.share" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Type.fst", "name": "Pulse.Lib.HashTable.Type.explode_ref_ht_t" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.MapTree.fst", "name": "Vale.Lib.MapTree.lemma_get_put_other" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.read" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.read" }, { "project_name": "steel", "file_name": "Steel.ST.GhostHigherReference.fst", "name": "Steel.ST.GhostHigherReference.write" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.write" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherReference.fst", "name": "Pulse.Lib.HigherReference.share" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.share" }, { "project_name": "steel", "file_name": "Pulse.Lib.Reference.fst", "name": "Pulse.Lib.Reference.share" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.share" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.free" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.free" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherArray.fst", "name": "Pulse.Lib.HigherArray.op_Array_Access" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.op_Array_Access" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.g_upd" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.MapTree.fst", "name": "Vale.Lib.MapTree.lemma_get_put_self" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.write" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.read" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.index" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.free" }, { "project_name": "zeta", "file_name": "Zeta.KeyValueStore.StateMachine.fst", "name": "Zeta.KeyValueStore.StateMachine.get" }, { "project_name": "steel", "file_name": "Queue.fst", "name": "Queue.get_data" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.PrecompBaseTable.fsti", "name": "Hacl.Spec.PrecompBaseTable.pow_base" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fsti", "name": "Vale.Lib.Map16.get" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.grvalue" }, { "project_name": "FStar", "file_name": "FStar.DependentMap.fst", "name": "FStar.DependentMap.sel" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.sel" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.free" }, { "project_name": "steel", "file_name": "LList.fst", "name": "LList.pop" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Mem.fst", "name": "MiTLS.Mem.mem_alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.free" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherArray.fst", "name": "Pulse.Lib.HigherArray.free" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fst", "name": "FStar.HyperStack.ST.get" }, { "project_name": "FStar", "file_name": "FStar.FiniteMap.Base.fst", "name": "FStar.FiniteMap.Base.choose" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.sel" }, { "project_name": "FStar", "file_name": "LowStar.Vector.fst", "name": "LowStar.Vector.get" }, { "project_name": "FStar", "file_name": "FStar.FiniteMap.Base.fst", "name": "FStar.FiniteMap.Base.insert" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.get" }, { "project_name": "steel", "file_name": "LListReverse.fst", "name": "LListReverse.pop" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.fst", "name": "Pulse.Lib.HashTable.mk_ht" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.MapTree.fst", "name": "Vale.Lib.MapTree.get" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.share" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.alloc" }, { "project_name": "karamel", "file_name": "LowStar.Lib.LinkedList2.fst", "name": "LowStar.Lib.LinkedList2.v" }, { "project_name": "steel", "file_name": "Steel.ST.GhostHigherReference.fst", "name": "Steel.ST.GhostHigherReference.free" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.share_gen" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.clear" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fsti", "name": "Steel.ST.HigherArray.index" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.upd" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Seq.fst", "name": "FStar.Monotonic.Seq.i_sel" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.op_Array_Assignment" }, { "project_name": "karamel", "file_name": "LowStar.Lib.LinkedList2.fst", "name": "LowStar.Lib.LinkedList2.pop" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Blake2.Generic.fst", "name": "Hacl.Impl.Blake2.Generic.get_iv" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Map.fst", "name": "FStar.Monotonic.Map.extend" }, { "project_name": "steel", "file_name": "Steel.ST.C.Types.Scalar.fsti", "name": "Steel.ST.C.Types.Scalar.read" }, { "project_name": "steel", "file_name": "Steel.ST.GhostHigherReference.fst", "name": "Steel.ST.GhostHigherReference.gather" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.gather" }, { "project_name": "steel", "file_name": "Pulse.Lib.Box.fst", "name": "Pulse.Lib.Box.op_Bang" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.gtdata_get_value" } ], "selected_premises": [ "Steel.ST.EphemeralHashtbl.tperm", "Steel.Preorder.history_val", "Steel.ST.EphemeralHashtbl.create_v", "Steel.Preorder.pcm_history", "FStar.List.Tot.Base.map", "FStar.List.Tot.Base.op_At", "Steel.ST.Array.length", "Steel.Memory.hmem", "FStar.Real.one", "Steel.ST.EphemeralHashtbl.pack_tperm", "Steel.ST.EphemeralHashtbl.store_contents_pred", "Steel.Memory.full_mem", "FStar.List.Tot.Base.length", "FStar.Heap.trivial_preorder", "Steel.ST.Array.join", "FStar.FunctionalExtensionality.feq", "Steel.ST.Array.null", "FStar.PCM.compatible", "FStar.PtrdiffT.zero", "Steel.ST.EphemeralHashtbl.value_vprops_mapping_fn", "FStar.Reflection.V2.Derived.mk_e_app", "Steel.ST.EphemeralHashtbl.create", "Steel.ST.Array.alloc", "Steel.ST.Array.ptr_of", "FStar.Reflection.V2.Data.var", "Steel.Effect.Common.to_vprop", "FStar.Reflection.V2.Derived.mk_app", "FStar.Tactics.CanonCommMonoidSimple.Equiv.term_eq", "Steel.FractionalPermission.full_perm", "Steel.ST.Array.adjacent", "Steel.ST.Array.array", "FStar.PCM.op", "FStar.PCM.composable", "Steel.ST.EphemeralHashtbl.pure_invariant", "Steel.ST.EphemeralHashtbl.value_vprops", "FStar.List.Tot.Base.rev", "Steel.Effect.Common.hp_of", "FStar.Real.two", "Steel.ST.EphemeralHashtbl.pack_value_vprops", "Steel.Effect.Common.star", "FStar.ST.op_Bang", "Steel.ST.EphemeralHashtbl.value_vprops_seq", "FStar.Reflection.V2.Derived.flatten_name", "Steel.ST.Util.emp_inames", "FStar.List.Tot.Base.mem", "Steel.Effect.Common.req", "Steel.ST.EphemeralHashtbl.unpack_value_vprops", "Steel.Effect.Common.to_vprop'", "Steel.ST.Array.merge", "Steel.FractionalPermission.sum_perm", "Steel.ST.EphemeralHashtbl.seq_from", "Steel.ST.Array.write", "Steel.Preorder.vhist", "Steel.ST.EphemeralHashtbl.seq_until", "Steel.Memory.inames", "Steel.Effect.Common.rmem", "FStar.List.Tot.Base.tl", "Steel.Effect.Common.print_goals", "Steel.Effect.Common.extract_contexts", "Steel.Effect.Common.t_of", "FStar.List.Tot.Base.append", "Steel.Effect.Common.normal_steps", "Steel.ST.EphemeralHashtbl.seq_at", "FStar.Reflection.V2.Derived.type_of_binder", "Steel.ST.EphemeralHashtbl.value_vprops_prefix_suffix_get", "Steel.FractionalPermission.comp_perm", "Steel.Effect.Common.sel_of", "Steel.Effect.Common.normal", "Steel.Effect.Common.guard_vprop", "FStar.Sealed.Inhabited.seal", "Steel.Effect.Common.rm", "Steel.ST.Util.op_At_Equals_Equals_Greater", "FStar.UInt.size", "Steel.ST.EphemeralHashtbl.value_vprops_split3", "FStar.String.strlen", "Steel.ST.EphemeralHashtbl.value_vprops_prefix_suffix_remove", "FStar.List.Tot.Base.memP", "FStar.Reflection.V2.Derived.shift_subst", "Steel.Preorder.p_op", "FStar.Reflection.V2.Derived.inspect_ln_unascribe", "Steel.Effect.Common.mk_rmem", "Steel.Effect.Common.slterm_nbr_uvars_argv", "Steel.ST.EphemeralHashtbl.value_vprops_prefix_suffix_put", "FStar.ST.alloc", "FStar.FunctionalExtensionality.on_dom", "Steel.Effect.Common.hmem", "FStar.List.Tot.Properties.assoc_mem", "FStar.Reflection.V2.Derived.Lemmas.op_Less_Less_Colon", "Steel.ST.EphemeralHashtbl.rewrite_value_vprops_prefix_and_suffix", "FStar.Reflection.V2.Data.ppname_t", "Steel.Effect.Common.pure", "FStar.String.length", "Steel.Effect.Common.vrefine'", "Steel.ST.Array.read", "Steel.Effect.Common.visit_br", "FStar.Seq.Permutation.index_fun", "Steel.ST.Array.is_full_array", "Steel.Effect.Common.sel_depends_only_on", "Steel.ST.Array.merge_into", "Steel.Effect.Common.visit_tm" ], "source_upto_this": "(*\n Copyright 2021 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n\n Authors: Aseem Rastogi\n*)\n\nmodule Steel.ST.EphemeralHashtbl\n\nopen Steel.FractionalPermission\nopen Steel.Memory\nopen Steel.ST.Effect.Ghost\nopen Steel.ST.Effect.Atomic\nopen Steel.ST.Effect\nopen Steel.ST.Util\n\nmodule G = FStar.Ghost\nmodule Seq = FStar.Seq\nmodule Map = FStar.PartialMap\nmodule US = FStar.SizeT\nmodule R = Steel.ST.Reference\nmodule A = Steel.ST.Array\n\n\n/// `store` is the concrete store implemented as an array\n///\n/// The hashing scheme we use is as follows:\n/// for key `k`, its slot in the array is `(h k) mod n`\n\nnoeq\ntype tbl #k #v #contents (vp:vp_t k v contents) (h:hash_fn k) = {\n store_len : n:us{US.v n > 0};\n store : A.array (option (k & v));\n store_len_pf : squash (A.length store == US.v store_len);\n}\n\n/// Property of the logical view of the store\n///\n/// For each (Some (k, v)) in the sequence, (h k) mod n == i\n\nlet seq_props (#k:eqtype) (#v:Type0) (h:hash_fn k) (s:Seq.seq (option (k & v))) : prop =\n 0 < Seq.length s /\\ US.fits (Seq.length s) /\\\n\n (forall (i:nat{i < Seq.length s}).\n Some? (Seq.index s i) ==> (let Some (x, _) = Seq.index s i in\n US.v (h x) `US.mod_spec` Seq.length s == i))\n\n/// Using seq_props, we can derive that all the keys in the sequence are distinct\n\nlet seq_keys_distinct (#k:eqtype) (#v:Type0) (s:Seq.seq (option (k & v))) : prop =\n forall (i j:(k:nat{k < Seq.length s})).{:pattern Seq.index s i; Seq.index s j}\n (i =!= j /\\ Some? (Seq.index s i) /\\ Some? (Seq.index s j)) ==>\n (fst (Some?.v (Seq.index s i)) =!= fst (Some?.v (Seq.index s j)))\n\nlet seq_props_implies_keys_distinct (#k:eqtype) (#v:Type0) (h:hash_fn k) (s:Seq.seq (option (k & v)))\n : Lemma (requires seq_props h s) (ensures seq_keys_distinct s)\n = ()\n\n/// For each (Some (k, v)) in the sequence, k must be in the repr map\n\nlet store_and_repr_related\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n : prop\n = forall (i:nat{i < Seq.length s}).\n match Seq.index s i with\n | None -> True\n | Some (k, _) -> Map.contains m k\n\n/// For each (Some (k, v)) in the sequence,\n/// either borrows does not contain k, or it maps k to v\n\nlet store_and_borrows_related\n (#k:eqtype)\n (#v:Type0)\n (s:Seq.seq (option (k & v)))\n (borrows:Map.t k v)\n : prop\n = forall (i:nat{i < Seq.length s}).\n match Seq.index s i with\n | None -> True\n | Some (k, x) ->\n Map.sel borrows k == None \\/\n Map.sel borrows k == Some x\n\nmodule CE = FStar.Algebra.CommMonoid.Equiv\nmodule SeqPerm = FStar.Seq.Permutation\n\n/// Setup for maintaining the value vprops in the table invariant\n///\n/// High-level idea is that, we take the store sequence,\n/// map it to a sequence of vprops,\n/// and fold the vprop monoid (with `star` as the multiplication) on this sequence\n///\n/// Each value contributes a `vp i x c`, unless it is in the borrows map\n\nlet vprop_monoid : CE.cm vprop Steel.Effect.Common.req = Steel.Effect.Common.rm\n\n/// Function to map over the store sequence\n\nlet value_vprops_mapping_fn\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (m:repr k contents)\n (borrows:Map.t k v)\n : option (k & v) -> vprop\n = fun e ->\n match e with\n | None -> emp\n | Some (i, x) ->\n (match Map.sel m i, Map.sel borrows i with\n | None, _ -> pure False\n | _, Some _ -> emp\n | Some c, None -> vp i x c)\n\n/// The corresponding sequence of vprops for a store sequence\n\n[@@__reduce__]\nlet value_vprops_seq\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n : Seq.seq vprop\n = Seq.map_seq (value_vprops_mapping_fn vp m borrows) s\n\n/// Value vprops\n\n[@@__reduce__]\nlet value_vprops\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n : vprop\n = SeqPerm.foldm_snoc vprop_monoid (value_vprops_seq vp s m borrows)\n\nlet pure_invariant\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (arr:tbl vp h)\n (m:repr k contents)\n (borrows:Map.t k v)\n (s:Seq.seq (option (k & v)))\n : prop\n = seq_props h s /\\\n store_and_repr_related s m /\\\n A.is_full_array arr.store /\\\n store_and_borrows_related s borrows\n\n/// The main invariant is defined as an existential for the store sequence\n\n[@@__reduce__]\nlet store_contents_pred\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (arr:tbl vp h)\n (m:repr k contents)\n (borrows:Map.t k v)\n : Seq.seq (option (k & v)) -> vprop\n = fun s ->\n A.pts_to arr.store full_perm s\n `star`\n pure (pure_invariant arr m borrows s)\n `star`\n value_vprops vp s m borrows\n\n/// Main invariant\n\n[@@__reduce__]\nlet tperm arr m borrows = exists_ (store_contents_pred arr m borrows)\n\n\n/// map_seq lemmas, with smt pats on them\n\nlet map_seq_len (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a)\n : Lemma (ensures Seq.length (Seq.map_seq f s) == Seq.length s)\n [SMTPat (Seq.length (Seq.map_seq f s))]\n = Seq.map_seq_len f s\n\nlet map_seq_index (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a) (i:nat{i < Seq.length s})\n : Lemma (ensures Seq.index (Seq.map_seq f s) i == f (Seq.index s i))\n [SMTPat (Seq.index (Seq.map_seq f s) i)]\n = Seq.map_seq_index f s i\n\nlet map_seq_append (#a #b:Type) (f:a -> Tot b) (s1 s2:Seq.seq a)\n : Lemma (ensures (Seq.map_seq f (Seq.append s1 s2) ==\n Seq.append (Seq.map_seq f s1) (Seq.map_seq f s2)))\n [SMTPat (Seq.map_seq f (Seq.append s1 s2))]\n = Seq.map_seq_append f s1 s2\n\n\n/// Helper function to pack a tperm assertion\n\nlet pack_tperm (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n (a:tbl vp h)\n : STGhost unit opened\n (A.pts_to a.store full_perm s\n `star`\n value_vprops vp s m borrows)\n (fun _ -> tperm a m borrows)\n (requires pure_invariant a m borrows s)\n (ensures fun _ -> True)\n = intro_pure (pure_invariant a m borrows s);\n intro_exists s (store_contents_pred a m borrows)\n\nlet create #k #v #contents vp h n =\n let store = A.alloc #(option (k & v)) None n in\n let arr : tbl #k #v #contents vp h = {\n store_len = n;\n store = store;\n store_len_pf = () } in\n\n //\n //rewrite in terms of projections from the arr record\n //\n rewrite (A.pts_to store _ (Seq.create #(option (k & v)) (US.v n) None))\n (A.pts_to arr.store _ (Seq.create #(option (k & v)) (US.v n) None));\n\n //\n //The value vprops at this point are all emp\n //\n //A lemma that tells us that folding a monoid over a sequence of units\n // is monoid-equivalent to the unit\n //\n SeqPerm.foldm_snoc_unit_seq\n vprop_monoid\n (value_vprops_seq vp (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v));\n rewrite_equiv emp (value_vprops vp (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v));\n\n pack_tperm (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v)\n arr;\n\n return arr\n\n/// Similar to create, except that the repr map is a const map\n\nlet create_v #k #v #contents vp h n c =\n let store = A.alloc #(option (k & v)) None n in\n let arr : tbl #k #v #contents vp h = {\n store_len = n;\n store = store;\n store_len_pf = () } in\n\n //\n //rewrite in terms of projections from the arr record\n //\n rewrite (A.pts_to store _ (Seq.create #(option (k & v)) (US.v n) None))\n (A.pts_to arr.store _ (Seq.create #(option (k & v)) (US.v n) None));\n\n //\n //The value vprops at this point are all emp\n //\n //A lemma that tells us that folding a monoid over a sequence of units\n // is monoid-equivalent to the unit\n //\n SeqPerm.foldm_snoc_unit_seq\n vprop_monoid\n (value_vprops_seq vp (Seq.create (US.v n) None)\n (Map.const k (G.reveal c))\n (Map.empty k v));\n rewrite_equiv emp (value_vprops vp (Seq.create (US.v n) None)\n (Map.const k (G.reveal c))\n (Map.empty k v));\n\n pack_tperm (Seq.create (US.v n) None)\n (Map.const k (G.reveal c))\n (Map.empty k v)\n arr;\n\n return arr\n\n/// Makes it easy to write subsequences\n\nlet seq_until (#a:Type) (s:Seq.seq a) (idx:nat{idx < Seq.length s})\n : Seq.seq a\n = Seq.slice s 0 idx\n\nlet seq_at (#a:Type) (s:Seq.seq a) (idx:nat{idx < Seq.length s})\n : Seq.seq a\n = Seq.create 1 (Seq.index s idx)\n\nlet seq_from (#a:Type) (s:Seq.seq a) (idx:nat{idx < Seq.length s})\n : Seq.seq a\n = Seq.slice s (idx + 1) (Seq.length s)\n\nlet elim_equiv_laws ()\n : Lemma (\n (forall x. x `equiv` x) /\\\n (forall x y. x `equiv` y ==> y `equiv` x) /\\\n (forall x y z. (x `equiv` y /\\ y `equiv` z) ==> x `equiv` z)\n )\n = let open Steel.Effect.Common in\n assert (req.eq == equiv);\n CE.elim_eq_laws req\n\n/// This is one of the workhorses of this library\n///\n/// It splits value vprops for a store sequence into `star` of value vprops for subsequences\n///\n/// Since `get`, `put`, `with_key` manipulate one entry at a time,\n/// we split the sequence at that i (prefix, at i, suffix)\n\nlet value_vprops_split3\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:Map.t k contents)\n (borrows:Map.t k v)\n (i:nat{i < Seq.length s})\n : Lemma (value_vprops vp s m borrows\n `equiv`\n (value_vprops vp (seq_until s i) m borrows\n `star`\n value_vprops vp (seq_at s i) m borrows\n `star`\n value_vprops vp (seq_from s i) m borrows))\n = elim_equiv_laws ();\n Classical.forall_intro_3 star_associative;\n\n assert (Seq.equal s (Seq.append (seq_until s i)\n (Seq.append (seq_at s i) (seq_from s i))));\n let vps s = value_vprops_seq vp s m borrows in\n\n calc (equiv) {\n value_vprops vp s m borrows;\n (equiv) { }\n value_vprops vp (Seq.append (seq_until s i)\n (Seq.append (seq_at s i) (seq_from s i))) m borrows;\n (equiv) { SeqPerm.foldm_snoc_append vprop_monoid\n (vps (seq_until s i))\n (Seq.append\n (vps (seq_at s i))\n (vps (seq_from s i))) }\n value_vprops vp (seq_until s i) m borrows\n `star`\n value_vprops vp (Seq.append (seq_at s i) (seq_from s i)) m borrows;\n (equiv) { SeqPerm.foldm_snoc_append vprop_monoid\n (vps (seq_at s i))\n (vps (seq_from s i));\n star_congruence\n (value_vprops vp (seq_until s i) m borrows)\n (value_vprops vp (Seq.append (seq_at s i) (seq_from s i)) m borrows)\n (value_vprops vp (seq_until s i) m borrows)\n (value_vprops vp (seq_at s i) m borrows `star` value_vprops vp (seq_from s i) m borrows) }\n value_vprops vp (seq_until s i) m borrows\n `star`\n (value_vprops vp (seq_at s i) m borrows\n `star`\n value_vprops vp (seq_from s i) m borrows);\n }\n\n/// Once we have split value vprops into (prefix, at i, suffix),\n/// in all the API (`get`, `put`, `ghost_put`, `remove`), the action happens at (at i)\n///\n/// The value vprops for prefix and suffix remain same\n///\n/// We have lemmas for each of the functions to prove that\n///\n/// The lemmas prove equality of value vprops before and after\n/// what each of the functions do to the arrays and maps\n\n\nlet value_vprops_prefix_suffix_get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (h:hash_fn k)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n (idx:nat{idx < Seq.length s})\n : Lemma (requires Some? (Seq.index s idx) /\\\n seq_props h s)\n (ensures (let Some (i, x) = Seq.index s idx in\n let upd_borrows = Map.upd borrows i x in\n value_vprops vp (seq_until s idx) m borrows ==\n value_vprops vp (seq_until s idx) m upd_borrows /\\\n value_vprops vp (seq_from s idx) m borrows ==\n value_vprops vp (seq_from s idx) m upd_borrows))\n = let Some (i, x) = Seq.index s idx in\n let upd_borrows = Map.upd borrows i x in\n assert (Seq.equal (value_vprops_seq vp (seq_until s idx) m borrows)\n (value_vprops_seq vp (seq_until s idx) m upd_borrows));\n assert (Seq.equal (value_vprops_seq vp (seq_from s idx) m borrows)\n (value_vprops_seq vp (seq_from s idx) m upd_borrows))\n\nlet value_vprops_prefix_suffix_put\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (h:hash_fn k)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n (idx:nat{idx < Seq.length s})\n (x:k) (y:v) (c:G.erased contents)\n : Lemma (requires seq_props h s /\\\n seq_props h (Seq.upd s idx (Some (x, y))))\n (ensures (let s1 = Seq.upd s idx (Some (x, y)) in\n let m1 = Map.upd m x c in\n let borrows1 = Map.remove borrows x in\n value_vprops vp (seq_until s idx) m borrows ==\n value_vprops vp (seq_until s1 idx) m1 borrows1 /\\\n value_vprops vp (seq_from s idx) m borrows ==\n value_vprops vp (seq_from s1 idx) m1 borrows1))\n = let s1 = Seq.upd s idx (Some (x, y)) in\n let m1 = Map.upd m x c in\n let borrows1 = Map.remove borrows x in\n assert (Seq.index s1 idx == Some (x, y));\n assert (Seq.equal (value_vprops_seq vp (seq_until s idx) m borrows)\n (value_vprops_seq vp (seq_until s1 idx) m1 borrows1));\n assert (Seq.equal (value_vprops_seq vp (seq_from s idx) m borrows)\n (value_vprops_seq vp (seq_from s1 idx) m1 borrows1))\n\nlet value_vprops_prefix_suffix_remove\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (h:hash_fn k)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)){seq_props h s})\n (m:repr k contents)\n (borrows:Map.t k v)\n (idx:nat)\n (i:k{US.v (h i) `US.mod_spec` Seq.length s == idx})\n : Lemma (requires Some? (Seq.index s idx))\n (ensures (let s1 = Seq.upd s idx None in\n let borrows1 = Map.remove borrows i in\n value_vprops vp (seq_until s idx) m borrows ==\n value_vprops vp (seq_until s1 idx) m borrows1 /\\\n value_vprops vp (seq_from s idx) m borrows ==\n value_vprops vp (seq_from s1 idx) m borrows1))\n = let s1 = Seq.upd s idx None in\n let borrows1 = Map.remove borrows i in\n assert (Seq.equal (value_vprops_seq vp (seq_until s idx) m borrows)\n (value_vprops_seq vp (seq_until s1 idx) m borrows1));\n assert (Seq.equal (value_vprops_seq vp (seq_from s idx) m borrows)\n (value_vprops_seq vp (seq_from s1 idx) m borrows1))\n\n\n/// A common utility that we use in all APIs\n///\n/// It first splits the value vprops intro (prefix, at i, suffix)\n///\n/// Then, given a vprop p, such that vprop seq at i is proven to be p by the client,\n/// it rewrites the (at i) part with p\n\nlet unpack_value_vprops (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:Map.t k contents)\n (borrows:Map.t k v)\n (idx:US.t{US.v idx < Seq.length s})\n (p:vprop)\n : STGhost unit opened\n (value_vprops vp s m borrows)\n (fun _ ->\n value_vprops vp (seq_until s (US.v idx)) m borrows\n `star`\n p\n `star`\n value_vprops vp (seq_from s (US.v idx)) m borrows)\n (requires Seq.index (value_vprops_seq vp s m borrows) (US.v idx) == p)\n (ensures fun _ -> True)\n = value_vprops_split3 vp s m borrows (US.v idx);\n rewrite_equiv _\n (value_vprops vp (seq_until s (US.v idx)) m borrows\n `star`\n value_vprops vp (seq_at s (US.v idx)) m borrows\n `star`\n value_vprops vp (seq_from s (US.v idx)) m borrows);\n SeqPerm.foldm_snoc_singleton vprop_monoid p;\n assert (Seq.equal (value_vprops_seq vp (Seq.create 1 (Seq.index s (US.v idx))) m borrows)\n (Seq.create 1 p));\n rewrite_equiv (value_vprops vp (seq_at s (US.v idx)) m borrows) p\n\n/// A wrapper over two rewrites\n/// (used to rewrite the prefix and suffix parts of value vprops)\n\nlet rewrite_value_vprops_prefix_and_suffix (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s1 s2:Seq.seq (option (k & v)))\n (m1 m2:Map.t k contents)\n (borrows1 borrows2:Map.t k v)\n (idx:US.t{Seq.length s1 == Seq.length s2 /\\ US.v idx < Seq.length s1})\n : STGhost unit opened\n (value_vprops vp (seq_until s1 (US.v idx)) m1 borrows1\n `star`\n value_vprops vp (seq_from s1 (US.v idx)) m1 borrows1)\n (fun _ ->\n value_vprops vp (seq_until s2 (US.v idx)) m2 borrows2\n `star`\n value_vprops vp (seq_from s2 (US.v idx)) m2 borrows2)\n (requires value_vprops vp (seq_until s1 (US.v idx)) m1 borrows1 ==\n value_vprops vp (seq_until s2 (US.v idx)) m2 borrows2 /\\\n value_vprops vp (seq_from s1 (US.v idx)) m1 borrows1 ==\n value_vprops vp (seq_from s2 (US.v idx)) m2 borrows2)\n (ensures fun _ -> True)\n = rewrite\n (value_vprops vp (seq_until s1 (US.v idx)) m1 borrows1\n `star`\n value_vprops vp (seq_from s1 (US.v idx)) m1 borrows1)\n (value_vprops vp (seq_until s2 (US.v idx)) m2 borrows2\n `star`\n value_vprops vp (seq_from s2 (US.v idx)) m2 borrows2)\n\n\n/// The opposite direction of unpack_value_vprops\n\nlet pack_value_vprops (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:Map.t k contents)\n (borrows:Map.t k v)\n (idx:US.t{US.v idx < Seq.length s})\n (p:vprop)\n : STGhost unit opened\n (value_vprops vp (seq_until s (US.v idx)) m borrows\n `star`\n p\n `star`\n value_vprops vp (seq_from s (US.v idx)) m borrows)\n (fun _ -> value_vprops vp s m borrows)\n (requires Seq.index (value_vprops_seq vp s m borrows) (US.v idx) == p)\n (ensures fun _ -> True)\n = SeqPerm.foldm_snoc_singleton vprop_monoid p;\n assert (Seq.equal (value_vprops_seq vp (Seq.create 1 (Seq.index s (US.v idx))) m borrows)\n (Seq.create 1 p));\n rewrite_equiv p (value_vprops vp (seq_at s (US.v idx)) m borrows);\n value_vprops_split3 vp s m borrows (US.v idx);\n rewrite_equiv\n (value_vprops vp (seq_until s (US.v idx)) m borrows\n `star`\n value_vprops vp (seq_at s (US.v idx)) m borrows\n `star`\n value_vprops vp (seq_from s (US.v idx)) m borrows)\n (value_vprops vp s m borrows)\n\n/// `get`\n", "sketch": [ "Step 1: The `get` function retrieves the value associated with a given key `i` from the hash table `a`. It ensures that the key is not currently borrowed.\nStep 2: The implementation involves:\n- Calculating the index in the array where the key `i` should be located using the hash function `h`.\n- Unpacking the value vprops for the sequence at the calculated index.\n- Checking if the key `i` is present at the calculated index.\n- If present, updating the borrows map and returning the value.\n- If not present, returning a `NotFound` result.\n- Packing the value vprops back after the operation.", "Step 1: The `get` function retrieves the value associated with a key `i` from the hash table `a`. It ensures that the key `i` is not currently borrowed.\nStep 2: The implementation involves:\n- Calculating the index in the array using the hash function `h`.\n- Unpacking the value vprops to isolate the relevant part of the sequence.\n- Checking if the key exists at the calculated index.\n- If the key exists, updating the borrows map and returning the value.\n- If the key does not exist, returning an appropriate result indicating the absence of the key.\n- Packing the value vprops back after the operation.", "Step 1: The `get` function retrieves the value associated with a key `i` from the hash table `a`. It ensures that the key `i` is not currently borrowed. The function returns a result indicating whether the key was found and, if so, the associated value.\nStep 2: To implement `get`, we first calculate the index in the array where the key should be located using the hash function `h`. We then split the value vprops into three parts: prefix, at index, and suffix. We check if the key is present at the calculated index. If the key is found, we update the borrows map and return the value. If the key is not found, we return a result indicating the key was not found. Finally, we pack the value vprops back together.", "Step 1: The `get` function retrieves the value associated with a key `i` from the hash table `a`. It ensures that the key is not currently borrowed and maintains the table's invariant.\nStep 2: The implementation involves:\n- Calculating the index in the array using the hash function.\n- Splitting the value vprops into prefix, at index, and suffix parts.\n- Checking if the key exists at the calculated index.\n- If the key exists, updating the borrows map and returning the value.\n- If the key does not exist, returning a `NotFound` result.\n- Packing the value vprops back together and ensuring the table's invariant.", "Step 1: The `get` function retrieves the value associated with a key `i` from the hash table `a`. It ensures that the key `i` is not currently borrowed.\nStep 2: The function first calculates the index in the array where the key `i` should be located using the hash function `h`. It then accesses the array at this index to retrieve the value. The function ensures that the retrieved value is consistent with the logical representation of the table and updates the borrows map accordingly.", "Step 1: The `get` function retrieves the value associated with a key `i` from the hash table `a`. It ensures that the key `i` is not currently borrowed.\nStep 2: The implementation involves:\n- Checking the precondition that the key `i` is not in the `borrows` map.\n- Calculating the index in the array where the key-value pair should be located using the hash function `h`.\n- Unpacking the value vprops to isolate the value at the calculated index.\n- Retrieving the value from the array at the calculated index.\n- Packing the value vprops back after the retrieval.\n- Returning the retrieved value.", "Step 1: The `get` function retrieves the value associated with a key `i` from the hash table `a`. It ensures that the key `i` is not currently borrowed.\nStep 2: The implementation involves:\n- Checking the hash slot for the key `i`.\n- Splitting the value vprops into prefix, at index, and suffix.\n- Ensuring the value at the index is consistent with the representation and borrows map.\n- Returning the value if it exists, otherwise indicating the absence of the key.", "Step 1: The `get` function retrieves the value associated with a key `i` from the hash table `a`. It ensures that the key `i` is not currently borrowed.\nStep 2: The function first calculates the index in the array where the key-value pair should be stored using the hash function `h`. It then reads the value at that index from the array. If the value is `None`, it returns `NotFound`. If the value is `Some (k, v)`, it checks if `k` matches `i`. If they match, it returns `Found v`. Otherwise, it returns `NotFound`.", "Step 1: The `get` function retrieves the value associated with a key `i` from the hash table `a`. It ensures that the key `i` is not currently borrowed.\nStep 2: The implementation involves:\n- Calculating the index in the array using the hash function `h`.\n- Unpacking the value vprops for the sequence at the calculated index.\n- Checking if the key exists at the index and returning the appropriate result.\n- Packing the value vprops back after the operation.", "Step 1: The `get` function retrieves the value associated with a key `i` from the hash table `a`. It ensures that the key is not currently borrowed.\nStep 2: The function first calculates the index in the array where the key should be located using the hash function `h`. It then reads the value at that index. If the value is `None`, it returns `NotFound`. If the value is `Some (k, v)` and the key `k` matches `i`, it returns `Found v`. If the key does not match, it continues searching in the array." ], "generated_solution": [ "let get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)\n = let idx = US.v (h i) `US.mod_spec` US.v a.store_len in\n let s = A.read a.store in\n unpack_value_vprops vp s (G.reveal m) (G.reveal borrows) idx\n (match Seq.index s idx with\n | None -> pure (NotFound)\n | Some (k', v') ->\n if k' == i then\n let borrows' = Map.upd (G.reveal borrows) i v' in\n pure (Found v')\n else\n pure (NotFound));\n pack_value_vprops vp s (G.reveal m) (G.reveal borrows) idx", "let get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)\n = let idx = US.v (h i) `US.mod_spec` US.v a.store_len in\n let s = A.read a.store in\n unpack_value_vprops vp s (G.reveal m) (G.reveal borrows) idx\n (Seq.index (value_vprops_seq vp s (G.reveal m) (G.reveal borrows)) idx);\n match Seq.index s idx with\n | None ->\n pack_value_vprops vp s (G.reveal m) (G.reveal borrows) idx emp;\n return NotFound\n | Some (k', v') ->\n if k' == i then\n let new_borrows = Map.upd (G.reveal borrows) i v' in\n value_vprops_prefix_suffix_get h vp s (G.reveal m) (G.reveal borrows) idx;\n pack_value_vprops vp s (G.reveal m) new_borrows idx emp;\n return (Found v')\n else\n pack_value_vprops vp s (G.reveal m) (G.reveal borrows) idx emp;\n return NotFound", "let get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)\n = let idx = US.v (h i) `US.mod_spec` US.v a.store_len in\n let s = A.read a.store in\n unpack_value_vprops vp s (G.reveal m) (G.reveal borrows) idx\n (Seq.index (value_vprops_seq vp s (G.reveal m) (G.reveal borrows)) idx);\n match Seq.index s idx with\n | None -> \n pack_value_vprops vp s (G.reveal m) (G.reveal borrows) idx emp;\n return NotFound\n | Some (k', v') ->\n if k' == i then\n let borrows' = Map.upd (G.reveal borrows) i v' in\n value_vprops_prefix_suffix_get h vp s (G.reveal m) (G.reveal borrows) idx;\n pack_value_vprops vp s (G.reveal m) borrows' idx emp;\n return (Found v')\n else\n pack_value_vprops vp s (G.reveal m) (G.reveal borrows) idx emp;\n return NotFound", "let get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)\n = let idx = US.v (h i) `US.mod_spec` US.v a.store_len in\n let s = A.read a.store in\n unpack_value_vprops vp s (G.reveal m) (G.reveal borrows) idx\n (Seq.index (value_vprops_seq vp s (G.reveal m) (G.reveal borrows)) idx);\n match Seq.index s idx with\n | None ->\n pack_value_vprops vp s (G.reveal m) (G.reveal borrows) idx emp;\n return NotFound\n | Some (k, v) ->\n if k == i then\n let upd_borrows = Map.upd (G.reveal borrows) i v in\n value_vprops_prefix_suffix_get h vp s (G.reveal m) (G.reveal borrows) idx;\n pack_value_vprops vp s (G.reveal m) upd_borrows idx emp;\n return (Found v)\n else\n pack_value_vprops vp s (G.reveal m) (G.reveal borrows) idx emp;\n return NotFound", "let get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)\n = let idx = US.v (h i) `US.mod_spec` US.v a.store_len in\n let s = A.read a.store in\n let Some (k', v') = Seq.index s idx in\n assert (k' == i);\n let borrows' = Map.upd borrows i v' in\n return (Some v', borrows')", "let get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)\n = let idx = US.v (h i) `US.mod_spec` US.v a.store_len in\n unpack_value_vprops vp (A.to_seq a.store) (G.reveal m) (G.reveal borrows) idx\n (Seq.index (value_vprops_seq vp (A.to_seq a.store) (G.reveal m) (G.reveal borrows)) idx);\n let res = A.index a.store idx in\n pack_value_vprops vp (A.to_seq a.store) (G.reveal m) (G.reveal borrows) idx\n (Seq.index (value_vprops_seq vp (A.to_seq a.store) (G.reveal m) (G.reveal borrows)) idx);\n match res with\n | None -> return NotFound\n | Some (k, v) -> if k == i then return (Found v) else return NotFound", "let get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)\n = let idx = US.v (h i) `US.mod_spec` US.v a.store_len in\n let s = A.read a.store in\n let Some (k, v) = Seq.index s idx in\n if k == i then\n let p = value_vprops vp (seq_at s idx) m borrows in\n unpack_value_vprops vp s m borrows idx p;\n return (Found v)\n else\n return NotFound", "let get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)\n = let idx = US.v (h i) `US.mod_spec` US.v a.store_len in\n let s = A.read a.store idx in\n match s with\n | None -> return NotFound\n | Some (k', v') ->\n if k' == i then\n return (Found v')\n else\n return NotFound", "let get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)\n = let idx = US.v (h i) `US.mod_spec` US.v a.store_len in\n unpack_value_vprops vp (A.read a.store) (G.reveal m) (G.reveal borrows) idx\n (match Seq.index (A.read a.store) idx with\n | None -> pure (Get_None i)\n | Some (k', v') ->\n if k' == i then\n pure (Get_Some v')\n else\n pure (Get_None i));\n pack_value_vprops vp (A.read a.store) (G.reveal m) (G.reveal borrows) idx", "let get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)\n = let idx = US.v (h i) `US.mod_spec` US.v a.store_len in\n let s = A.read a.store in\n match Seq.index s idx with\n | None -> return NotFound\n | Some (k', v') ->\n if k' == i then\n return (Found v')\n else\n return NotFound" ] }, { "file_name": "Benton2004.DDCC.fst", "name": "Benton2004.DDCC.exec_equiv_trans", "opens_and_abbrevs": [ { "open": "Benton2004" }, { "open": "Benton2004" }, { "open": "Benton2004" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 2, "initial_ifuel": 1, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.qi.eager_threshold=100" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val exec_equiv_trans\n (p p' : sttype)\n (c1 c2 c3 : computation)\n: Lemma\n (requires (\n exec_equiv p p' c1 c2 /\\\n exec_equiv p p' c2 c3\n ))\n (ensures (exec_equiv p p' c1 c3))\n [SMTPatOr [\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c2 c3)];\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c1 c3)];\n [SMTPat (exec_equiv p p' c2 c3); SMTPat (exec_equiv p p' c1 c3)];\n ]]", "source_definition": "let exec_equiv_trans\n (p p' : sttype)\n (c1 c2 c3 : computation)\n: Lemma\n (requires (\n exec_equiv p p' c1 c2 /\\\n exec_equiv p p' c2 c3\n ))\n (ensures (exec_equiv p p' c1 c3))\n [SMTPatOr [\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c2 c3)];\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c1 c3)];\n [SMTPat (exec_equiv p p' c2 c3); SMTPat (exec_equiv p p' c1 c3)];\n ]]\n= let z1 = reify_computation c1 in\n let z2 = reify_computation c2 in\n let z3 = reify_computation c3 in\n exec_equiv_reified_trans p p' z1 z2 z3", "source_range": { "start_line": 246, "start_col": 0, "end_line": 263, "end_col": 40 }, "interleaved": false, "definition": "fun p p' c1 c2 c3 ->\n (let z1 = Benton2004.reify_computation c1 in\n let z2 = Benton2004.reify_computation c2 in\n let z3 = Benton2004.reify_computation c3 in\n Benton2004.DDCC.exec_equiv_reified_trans p p' z1 z2 z3)\n <:\n FStar.Pervasives.Lemma\n (requires Benton2004.DDCC.exec_equiv p p' c1 c2 /\\ Benton2004.DDCC.exec_equiv p p' c2 c3)\n (ensures Benton2004.DDCC.exec_equiv p p' c1 c3)\n [\n SMTPatOr [\n [\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c2);\n SMTPat (Benton2004.DDCC.exec_equiv p p' c2 c3)\n ];\n [\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c2);\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c3)\n ];\n [\n SMTPat (Benton2004.DDCC.exec_equiv p p' c2 c3);\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c3)\n ]\n ]\n ]", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "Benton2004.DDCC.sttype", "Benton2004.computation", "Benton2004.DDCC.exec_equiv_reified_trans", "Benton2004.reified_computation", "Benton2004.reify_computation", "Prims.unit", "Prims.l_and", "Benton2004.DDCC.exec_equiv", "Prims.squash", "Prims.Cons", "FStar.Pervasives.pattern", "FStar.Pervasives.smt_pat_or", "Prims.list", "FStar.Pervasives.smt_pat", "Prims.Nil" ], "proof_features": [], "is_simple_lemma": true, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "\n p: Benton2004.DDCC.sttype ->\n p': Benton2004.DDCC.sttype ->\n c1: Benton2004.computation ->\n c2: Benton2004.computation ->\n c3: Benton2004.computation\n -> FStar.Pervasives.Lemma\n (requires Benton2004.DDCC.exec_equiv p p' c1 c2 /\\ Benton2004.DDCC.exec_equiv p p' c2 c3)\n (ensures Benton2004.DDCC.exec_equiv p p' c1 c3)\n [\n SMTPatOr [\n [\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c2);\n SMTPat (Benton2004.DDCC.exec_equiv p p' c2 c3)\n ];\n [\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c2);\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c3)\n ];\n [\n SMTPat (Benton2004.DDCC.exec_equiv p p' c2 c3);\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c3)\n ]\n ]\n ]", "prompt": "let exec_equiv_trans (p p': sttype) (c1 c2 c3: computation)\n : Lemma (requires (exec_equiv p p' c1 c2 /\\ exec_equiv p p' c2 c3))\n (ensures (exec_equiv p p' c1 c3))\n [\n SMTPatOr\n [\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c2 c3)];\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c1 c3)];\n [SMTPat (exec_equiv p p' c2 c3); SMTPat (exec_equiv p p' c1 c3)]\n ]\n ] =\n ", "expected_response": "let z1 = reify_computation c1 in\nlet z2 = reify_computation c2 in\nlet z3 = reify_computation c3 in\nexec_equiv_reified_trans p p' z1 z2 z3", "source": { "project_name": "FStar", "file_name": "examples/rel/Benton2004.DDCC.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "Benton2004.DDCC.fst", "checked_file": "dataset/Benton2004.DDCC.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Classical.fsti.checked", "dataset/Benton2004.fst.checked" ] }, "definitions_in_context": [ "let holds_ns_f (#t: Type0) (x y: t): Lemma\n (holds ns_f x y <==> False)\n [SMTPat (holds ns_f x y)]\n= holds_equiv ns_f x y", "per", "nstype", "let ns_f (#t: Type0) : nstype t =\n let f (x y: t) = False in\n Classical.forall_intro_2 (holds_equiv f);\n f", "let holds_ns_t (#t: Type0) (x y: t): Lemma\n (holds ns_t x y <==> True)\n [SMTPat (holds ns_t x y)]\n= holds_equiv ns_t x y", "val holds_ns_f (#t: Type0) (x y: t): Lemma\n (holds ns_f x y <==> False)\n [SMTPat (holds ns_f x y)]", "let holds_ns_singl (#t: Type0) (c: t) (x y: t) : Lemma\n (holds (ns_singl c) x y <==> (x == c /\\ y == c))\n [SMTPat (holds (ns_singl c) x y)]\n= holds_equiv (ns_singl c) x y", "let ns_t (#t: Type0) : nstype t =\n let f (x y: t) = True in\n Classical.forall_intro_2 (holds_equiv f);\n f", "let holds_ns_delta (#t: Type0) (x y : t) : Lemma\n (holds ns_delta x y <==> x == y)\n [SMTPat (holds ns_delta x y)]\n= holds_equiv ns_delta x y", "val holds_ns_t (#t: Type0) (x y: t): Lemma\n (holds ns_t x y <==> True)\n [SMTPat (holds ns_t x y)]", "let interpolable_ns_f #t : Lemma (interpolable #t ns_f) = ()", "let interpolable_ns_t #t : Lemma (interpolable #t ns_t) = ()", "let interpolable_ns_singl #t (c: t) : Lemma (interpolable (ns_singl c)) = ()", "let ns_singl (#t: Type0) (c: t) : nstype t =\n let f (x y: t) = (x == c /\\ y == c) in\n Classical.forall_intro_2 (holds_equiv f);\n f", "let interpolable_ns_delta #t : Lemma (interpolable #t ns_delta) = ()", "let holds_st_nil\n (x y: heap)\n: Lemma\n (holds st_nil x y <==> True)\n [SMTPat (holds st_nil x y)]\n= Classical.forall_intro_2 (holds_equiv st_nil)", "val holds_ns_singl (#t: Type0) (c: t) (x y: t) : Lemma\n (holds (ns_singl c) x y <==> (x == c /\\ y == c))\n [SMTPat (holds (ns_singl c) x y)]", "let ns_delta (#t: Type0) : nstype t =\n let f (x y: t) = (x == y) in\n Classical.forall_intro_2 (holds_equiv f);\n f", "let holds_st_var\n (x: var)\n (v: nstype int)\n (a b: heap)\n: Lemma\n (holds (st_var x v) a b <==> holds v (sel a x) (sel b x))\n [SMTPat (holds (st_var x v) a b)]\n= holds_equiv (st_var x v) a b", "val holds_ns_delta (#t: Type0) (x y : t) : Lemma\n (holds ns_delta x y <==> x == y)\n [SMTPat (holds ns_delta x y)]", "val interpolable_ns_f (#t:Type) : Lemma (interpolable #t ns_f)", "val interpolable_ns_t (#t:Type) : Lemma (interpolable #t ns_t)", "val interpolable_ns_singl (#t:Type) (c: t) : Lemma (interpolable (ns_singl c))", "let holds_st_intersect\n (ns1 ns2: sttype)\n (x y: heap)\n: Lemma\n (holds (st_intersect ns1 ns2) x y <==> (holds ns1 x y /\\ holds ns2 x y))\n [SMTPat (holds (st_intersect ns1 ns2) x y)]\n= ()", "val interpolable_ns_delta (#t:Type) : Lemma (interpolable #t ns_delta)", "sttype", "let st_nil: sttype =\n let f (x y : heap) : GTot Type0 = True in\n f", "let st_fresh_in_nil\n (x: var)\n: Lemma\n (x `st_fresh_in` st_nil)\n= ()", "val holds_st_nil\n (x y: heap)\n: Lemma\n (holds st_nil x y <==> True)\n [SMTPat (holds st_nil x y)]", "let st_fresh_in_var\n (x: var)\n (v: nstype int)\n (y: var)\n: Lemma\n (requires (y <> x))\n (ensures (y `st_fresh_in` (st_var x v)))\n= ()", "let st_var\n (x: var)\n (v: nstype int)\n: GTot sttype\n= let f (s1 s2: heap) : GTot Type0 = holds v (sel s1 x) (sel s2 x) in\n Classical.forall_intro_2 (holds_equiv f);\n f", "val holds_st_var\n (x: var)\n (v: nstype int)\n (a b: heap)\n: Lemma\n (holds (st_var x v) a b <==> holds v (sel a x) (sel b x))\n [SMTPat (holds (st_var x v) a b)]", "let st_fresh_in_intersect\n (x: var)\n (p1 p2: sttype)\n: Lemma\n (requires (\n x `st_fresh_in` p1 /\\\n x `st_fresh_in` p2\n ))\n (ensures (x `st_fresh_in` (st_intersect p1 p2)))\n= ()", "let st_intersect\n (p1 p2: sttype)\n: GTot sttype\n= intersect p1 p2", "let st_fresh_in_cons\n (p: sttype)\n (x: var)\n (v: nstype int)\n (y: var)\n: Lemma\n (requires (\n x `st_fresh_in` p /\\\n y `st_fresh_in` p /\\\n x <> y\n ))\n (ensures (\n x `st_fresh_in` p /\\\n y `st_fresh_in` (st_cons p x v)\n ))\n= ()", "val holds_st_intersect\n (ns1 ns2: sttype)\n (x y: heap)\n: Lemma\n (holds (st_intersect ns1 ns2) x y <==> (holds ns1 x y /\\ holds ns2 x y))\n [SMTPat (holds (st_intersect ns1 ns2) x y)]", "let st_fresh_in\n (x: var)\n (p: sttype)\n: GTot Type0\n= forall s1 s1' s2 s2' . \n (holds p s1 s2 /\\ (\n forall y . y <> x ==> (sel s1' y == sel s1 y /\\ sel s2' y == sel s2 y)\n )) ==>\n holds p s1' s2'", "let subtype_ns_f (#t: Type0) (phi: nstype t) : Lemma\n (included ns_f phi)\n= ()", "val st_fresh_in_nil\n (x: var)\n: Lemma\n (x `st_fresh_in` st_nil)", "let subtype_ns_singl_delta (#t: Type0) (c: t) : Lemma\n (ns_singl c `included` ns_delta)\n= ()", "let st_cons\n (p: sttype)\n (x: var)\n (v: nstype int)\n: Ghost sttype\n (requires (x `st_fresh_in` p))\n (ensures (fun _ -> True))\n= st_intersect p (st_var x v)", "let subtype_ns_t (#t: Type0) (phi: nstype t) : Lemma\n (included phi ns_t)\n= ()", "let subtype_st_nil (phi: sttype) : Lemma\n (included phi st_nil)\n= ()", "val st_fresh_in_var\n (x: var)\n (v: nstype int)\n (y: var)\n: Lemma\n (requires (y <> x))\n (ensures (y `st_fresh_in` (st_var x v)))", "let subtype_st_f (phi phi' : sttype) (x: var) : Lemma\n (requires (x `st_fresh_in` phi))\n (ensures (x `st_fresh_in` phi /\\ included (st_cons phi x ns_f) phi'))\n= ()", "let subtype_st_t (phi phi' : sttype) (x: var) : Lemma\n (requires (x `st_fresh_in` phi' /\\ included phi phi'))\n (ensures (x `st_fresh_in` phi' /\\ included phi (st_cons phi' x ns_t)))\n= ()", "val st_fresh_in_intersect\n (x: var)\n (p1 p2: sttype)\n: Lemma\n (requires (\n x `st_fresh_in` p1 /\\\n x `st_fresh_in` p2\n ))\n (ensures (x `st_fresh_in` (st_intersect p1 p2)))", "let subtype_st_cons (phi phi' : sttype) (f f' : nstype int) (x: var) : Lemma\n (requires (\n included phi phi' /\\\n included f f' /\\\n x `st_fresh_in` phi /\\\n x `st_fresh_in` phi'\n ))\n (ensures (\n x `st_fresh_in` phi /\\\n x `st_fresh_in` phi' /\\\n included (st_cons phi x f) (st_cons phi' x f')\n ))\n= ()", "val st_fresh_in_cons\n (p: sttype)\n (x: var)\n (v: nstype int)\n (y: var)\n: Lemma\n (requires (\n x `st_fresh_in` p /\\\n y `st_fresh_in` p /\\\n x <> y\n ))\n (ensures (\n x `st_fresh_in` p /\\\n y `st_fresh_in` (st_cons p x v)\n ))", "let eval_equiv_reified\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': reified_exp t)\n: GTot Type0\n= Benton2004.eval_equiv_reified p e f f'", "let eval_equiv_reified_elim\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': reified_exp t)\n (s s' : heap)\n: Lemma\n (requires (eval_equiv_reified p e f f' /\\ holds p s s'))\n (ensures (holds e (fst (f s)) (fst (f' s'))))\n= ()", "val subtype_ns_f (#t: Type0) (phi: nstype t) : Lemma\n (included ns_f phi)", "val subtype_ns_singl_delta (#t: Type0) (c: t) : Lemma\n (ns_singl c `included` ns_delta)", "val subtype_ns_t (#t: Type0) (phi: nstype t) : Lemma\n (included phi ns_t)", "val subtype_st_nil (phi: sttype) : Lemma\n (included phi st_nil)", "let terminates_equiv_reified\n (p : sttype)\n (f f' : reified_computation)\n: GTot Type0\n= Benton2004.terminates_equiv_reified p f f'", "val subtype_st_f (phi phi' : sttype) (x: var) : Lemma\n (requires (x `st_fresh_in` phi))\n (ensures (x `st_fresh_in` phi /\\ included (st_cons phi x ns_f) phi'))", "let terminates_equiv_reified_elim\n (p : sttype)\n (f f' : reified_computation)\n (s s' : heap)\n: Lemma\n (requires (terminates_equiv_reified p f f' /\\ holds p s s'))\n (ensures (terminates_on f s <==> terminates_on f' s'))\n= ()", "val subtype_st_t (phi phi' : sttype) (x: var) : Lemma\n (requires (x `st_fresh_in` phi' /\\ included phi phi'))\n (ensures (x `st_fresh_in` phi' /\\ included phi (st_cons phi' x ns_t)))", "val subtype_st_cons (phi phi' : sttype) (f f' : nstype int) (x: var) : Lemma\n (requires (\n included phi phi' /\\\n included f f' /\\\n x `st_fresh_in` phi /\\\n x `st_fresh_in` phi'\n ))\n (ensures (\n x `st_fresh_in` phi /\\\n x `st_fresh_in` phi' /\\\n included (st_cons phi x f) (st_cons phi' x f')\n ))", "let exec_equiv_reified\n (p p' : sttype)\n (f f' : reified_computation)\n: GTot Type0\n= Benton2004.exec_equiv_reified p p' f f'", "let exec_equiv_reified_terminates\n (p p' : sttype)\n (f f' : reified_computation)\n: Lemma\n (requires (exec_equiv_reified p p' f f'))\n (ensures (terminates_equiv_reified p f f'))\n= ()", "val eval_equiv_reified\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': reified_exp t)\n: GTot Type0", "let exec_equiv_reified_elim\n (p p' : sttype)\n (f f' : reified_computation)\n (s s' : heap)\n (fuel: nat)\n: Lemma\n (requires (exec_equiv_reified p p' f f' /\\ holds p s s' /\\ fst (f fuel s) == true /\\ fst (f' fuel s') == true))\n (ensures (holds p' (snd (f fuel s)) (snd (f' fuel s'))))\n= ()", "val eval_equiv_reified_elim\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': reified_exp t)\n (s s' : heap)\n: Lemma\n (requires (eval_equiv_reified p e f f' /\\ holds p s s'))\n (ensures (holds e (fst (f s)) (fst (f' s'))))", "let eval_equiv_sym\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': exp t)\n: Lemma\n (requires (eval_equiv p e f f'))\n (ensures (eval_equiv p e f' f))\n= Benton2004.eval_equiv_sym p e f f'", "val terminates_equiv_reified\n (p : sttype)\n (f f' : reified_computation)\n: GTot Type0", "val terminates_equiv_reified_elim\n (p : sttype)\n (f f' : reified_computation)\n (s s' : heap)\n: Lemma\n (requires (terminates_equiv_reified p f f' /\\ holds p s s'))\n (ensures (terminates_on f s <==> terminates_on f' s'))", "let exec_equiv_sym\n (p p': sttype)\n (f f' : computation)\n: Lemma\n (exec_equiv p p' f f' <==> exec_equiv p p' f' f)\n [SMTPat (exec_equiv p p' f f')]\n= Benton2004.exec_equiv_sym p p' f f'", "val exec_equiv_reified\n (p p' : sttype)\n (f f' : reified_computation)\n: GTot Type0", "let eval_equiv_trans\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f1 f2 f3 : exp t)\n: Lemma\n (requires (eval_equiv p e f1 f2 /\\ eval_equiv p e f2 f3))\n (ensures (eval_equiv p e f1 f3))\n= Benton2004.eval_equiv_trans p e f1 f2 f3", "val exec_equiv_reified_terminates\n (p p' : sttype)\n (f f' : reified_computation)\n: Lemma\n (requires (exec_equiv_reified p p' f f'))\n (ensures (terminates_equiv_reified p f f'))", "val exec_equiv_reified_elim\n (p p' : sttype)\n (f f' : reified_computation)\n (s s' : heap)\n (fuel: nat)\n: Lemma\n (requires (exec_equiv_reified p p' f f' /\\ holds p s s' /\\ fst (f fuel s) == true /\\ fst (f' fuel s') == true))\n (ensures (holds p' (snd (f fuel s)) (snd (f' fuel s'))))", "let exec_equiv_reified_trans\n (p p': sttype)\n (f1 f2 f3 : reified_computation)\n: Lemma\n (requires (exec_equiv_reified p p' f1 f2 /\\ exec_equiv_reified p p' f2 f3))\n (ensures (exec_equiv_reified p p' f1 f3))\n= Benton2004.exec_equiv_reified_trans p p' f1 f2 f3" ], "closest": [ "val exec_equiv_trans (p p': sttype) (c1 c2 c3: computation)\n : Lemma\n (requires (is_per p' /\\ interpolable p /\\ exec_equiv p p' c1 c2 /\\ exec_equiv p p' c2 c3))\n (ensures (exec_equiv p p' c1 c3))\n [\n SMTPatOr\n [\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c2 c3)];\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c1 c3)];\n [SMTPat (exec_equiv p p' c2 c3); SMTPat (exec_equiv p p' c1 c3)]\n ]\n ]\nlet exec_equiv_trans\n (p p' : sttype)\n (c1 c2 c3 : computation)\n: Lemma\n (requires (\n is_per p' /\\\n interpolable p /\\\n exec_equiv p p' c1 c2 /\\\n exec_equiv p p' c2 c3\n ))\n (ensures (exec_equiv p p' c1 c3))\n [SMTPatOr [\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c2 c3)];\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c1 c3)];\n [SMTPat (exec_equiv p p' c2 c3); SMTPat (exec_equiv p p' c1 c3)];\n ]]\n= let z1 = reify_computation c1 in\n let z2 = reify_computation c2 in\n let z3 = reify_computation c3 in\n exec_equiv_reified_trans p p' z1 z2 z3", "val r_trans\n (p p' : gexp bool)\n (c1 c2 c3 : computation)\n: Lemma\n (requires (\n is_per p' /\\\n interpolable p /\\\n exec_equiv p p' c1 c2 /\\\n exec_equiv p p' c2 c3\n ))\n (ensures (exec_equiv p p' c1 c3))\n [SMTPatOr [\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c2 c3); SMTPat (is_per p'); SMTPat (interpolable p)];\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c1 c3); SMTPat (is_per p'); SMTPat (interpolable p)];\n [SMTPat (exec_equiv p p' c1 c3); SMTPat (exec_equiv p p' c2 c3); SMTPat (is_per p'); SMTPat (interpolable p)];\n ]]\nlet r_trans\n (p p' : gexp bool)\n (c1 c2 c3 : computation)\n: Lemma\n (requires (\n is_per p' /\\\n interpolable p /\\\n exec_equiv p p' c1 c2 /\\\n exec_equiv p p' c2 c3\n ))\n (ensures (exec_equiv p p' c1 c3))\n [SMTPatOr [\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c2 c3); SMTPat (is_per p'); SMTPat (interpolable p)];\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c1 c3); SMTPat (is_per p'); SMTPat (interpolable p)];\n [SMTPat (exec_equiv p p' c1 c3); SMTPat (exec_equiv p p' c2 c3); SMTPat (is_per p'); SMTPat (interpolable p)];\n ]]\n= exec_equiv_trans (interp p) (interp p') c1 c2 c3", "val exec_equiv_reified_trans (p p': sttype) (f1 f2 f3: reified_computation)\n : Lemma\n (requires\n (is_per p' /\\ interpolable p /\\ exec_equiv_reified p p' f1 f2 /\\\n exec_equiv_reified p p' f2 f3)) (ensures (exec_equiv_reified p p' f1 f3))\nlet exec_equiv_reified_trans\n (p p': sttype)\n (f1 f2 f3 : reified_computation)\n: Lemma\n (requires (is_per p' /\\ interpolable p /\\ exec_equiv_reified p p' f1 f2 /\\ exec_equiv_reified p p' f2 f3))\n (ensures (exec_equiv_reified p p' f1 f3))\n= let prf1\n (s1 s3 : heap)\n : Lemma\n (requires (holds p s1 s3))\n (ensures (terminates_on f1 s1 <==> terminates_on f3 s3))\n = interpolable_elim p s1 s3\n in\n Classical.forall_intro_2 (fun x -> Classical.move_requires (prf1 x));\n let prf2\n (s1 s3: heap)\n (fuel: nat)\n : Lemma\n (requires (holds p s1 s3 /\\ fst (f1 fuel s1) == true /\\ fst (f3 fuel s3) == true))\n (ensures (holds p' (snd (f1 fuel s1)) (snd (f3 fuel s3))))\n = interpolable_elim p s1 s3;\n let g\n (s2: heap)\n : Lemma\n (requires (holds p s1 s2 /\\ holds p s2 s3))\n (ensures (holds p' (snd (f1 fuel s1)) (snd (f3 fuel s3))))\n = let g'\n (fuel' : nat)\n : Lemma\n (requires (fst (f2 fuel' s2) == true))\n (ensures (holds p' (snd (f1 fuel s1)) (snd (f3 fuel s3))))\n = assert (f1 (fuel + fuel') s1 == f1 fuel s1);\n assert (f2 (fuel + fuel') s2 == f2 fuel' s2);\n assert (f3 (fuel + fuel') s3 == f3 fuel s3);\n assert (holds p' (snd (f1 (fuel + fuel') s1)) (snd (f2 (fuel + fuel') s2)))\n in\n Classical.forall_intro (Classical.move_requires g')\n in\n Classical.forall_intro (Classical.move_requires g)\n in\n Classical.forall_intro_3 (fun x y -> Classical.move_requires (prf2 x y))", "val exec_equiv_flip (p p': sttype) (f f': computation)\n : Lemma (exec_equiv (flip p) (flip p') f f' <==> exec_equiv p p' f' f)\n [SMTPat (exec_equiv (flip p) (flip p') f f')]\nlet exec_equiv_flip\n (p p': sttype)\n (f f' : computation)\n: Lemma\n (exec_equiv (flip p) (flip p') f f' <==> exec_equiv p p' f' f)\n [SMTPat (exec_equiv (flip p) (flip p') f f')]\n= holds_flip p;\n holds_flip p'", "val exec_equiv_flip\n (p p': gexp bool)\n (f f' : computation)\n: Lemma\n (exec_equiv (flip p) (flip p') f f' <==> exec_equiv p p' f' f)\n [SMTPat (exec_equiv (flip p) (flip p') f f')]\nlet exec_equiv_flip\n (p p': gexp bool)\n (f f' : computation)\n: Lemma\n (exec_equiv (flip p) (flip p') f f' <==> exec_equiv p p' f' f)\n [SMTPat (exec_equiv (flip p) (flip p') f f')]\n= holds_interp_flip p;\n holds_interp_flip p';\n exec_equiv_flip (interp p) (interp p') f f'", "val exec_equiv_seq\n (gamma: context)\n (c c' : computation)\n (s: seclevel)\n: Lemma\n (requires (\n exec_equiv gamma c s /\\\n exec_equiv gamma c' s\n ))\n (ensures (\n exec_equiv gamma (seq c c') s\n ))\n [SMTPat (exec_equiv gamma (seq c c') s)]\nlet exec_equiv_seq\n (gamma: context)\n (c c' : computation)\n (s: seclevel)\n: Lemma\n (requires (\n exec_equiv gamma c s /\\\n exec_equiv gamma c' s\n ))\n (ensures (\n exec_equiv gamma (seq c c') s\n ))\n [SMTPat (exec_equiv gamma (seq c c') s)]\n= match s with\n | Low -> ()\n | High -> d_su1' c c' skip (interp_context gamma) (interp_context gamma) (interp_context gamma)", "val r_seq\n (p0 p1 p2 : gexp bool)\n (c01 c01' c12 c12' : computation)\n: Lemma\n (requires (\n exec_equiv p0 p1 c01 c01' /\\\n exec_equiv p1 p2 c12 c12'\n ))\n (ensures (\n exec_equiv p0 p2 (seq c01 c12) (seq c01' c12')\n ))\n [SMTPatOr [\n [SMTPat (exec_equiv p0 p2 (seq c01 c12) (seq c01' c12')); SMTPat (exec_equiv p0 p1 c01 c01')];\n [SMTPat (exec_equiv p0 p2 (seq c01 c12) (seq c01' c12')); SMTPat (exec_equiv p1 p2 c12 c12')];\n [SMTPat (exec_equiv p0 p1 c01 c01'); SMTPat (exec_equiv p1 p2 c12 c12')];\n ]]\nlet r_seq\n (p0 p1 p2 : gexp bool)\n (c01 c01' c12 c12' : computation)\n: Lemma\n (requires (\n exec_equiv p0 p1 c01 c01' /\\\n exec_equiv p1 p2 c12 c12'\n ))\n (ensures (\n exec_equiv p0 p2 (seq c01 c12) (seq c01' c12')\n ))\n [SMTPatOr [\n [SMTPat (exec_equiv p0 p2 (seq c01 c12) (seq c01' c12')); SMTPat (exec_equiv p0 p1 c01 c01')];\n [SMTPat (exec_equiv p0 p2 (seq c01 c12) (seq c01' c12')); SMTPat (exec_equiv p1 p2 c12 c12')];\n [SMTPat (exec_equiv p0 p1 c01 c01'); SMTPat (exec_equiv p1 p2 c12 c12')];\n ]]\n= d_seq (interp p0) (interp p1) (interp p2) c01 c01' c12 c12'", "val d_seq (p0 p1 p2: sttype) (c01 c01' c12 c12': computation)\n : Lemma (requires (exec_equiv p0 p1 c01 c01' /\\ exec_equiv p1 p2 c12 c12'))\n (ensures (exec_equiv p0 p2 (seq c01 c12) (seq c01' c12')))\n [\n SMTPatOr\n [\n [SMTPat (exec_equiv p0 p1 c01 c01'); SMTPat (exec_equiv p1 p2 c12 c12')];\n [\n SMTPat (exec_equiv p0 p1 c01 c01');\n SMTPat (exec_equiv p0 p2 (seq c01 c12) (seq c01' c12'))\n ];\n [\n SMTPat (exec_equiv p1 p2 c12 c12');\n SMTPat (exec_equiv p0 p2 (seq c01 c12) (seq c01' c12'))\n ]\n ]\n ]\nlet d_seq\n (p0 p1 p2 : sttype)\n (c01 c01' c12 c12' : computation)\n: Lemma\n (requires (\n exec_equiv p0 p1 c01 c01' /\\\n exec_equiv p1 p2 c12 c12'\n ))\n (ensures (\n exec_equiv p0 p2 (seq c01 c12) (seq c01' c12')\n ))\n [SMTPatOr [\n [SMTPat (exec_equiv p0 p1 c01 c01'); SMTPat (exec_equiv p1 p2 c12 c12')];\n [SMTPat (exec_equiv p0 p1 c01 c01'); SMTPat (exec_equiv p0 p2 (seq c01 c12) (seq c01' c12'))];\n [SMTPat (exec_equiv p1 p2 c12 c12'); SMTPat (exec_equiv p0 p2 (seq c01 c12) (seq c01' c12'))];\n ]]\n= let f01 = reify_computation c01 in\n let f01' = reify_computation c01' in\n let f12 = reify_computation c12 in\n let f12' = reify_computation c12' in\n let f = reify_computation (seq c01 c12) in\n let f' = reify_computation (seq c01' c12') in\n let prf1\n (s0 s0' : heap)\n : Lemma\n (requires (holds p0 s0 s0'))\n (ensures (terminates_on f s0 <==> terminates_on f' s0'))\n = Classical.move_requires (d_seq_terminates p0 p1 p2 c01 c01' c12 c12' s0) s0';\n Classical.move_requires (d_seq_terminates_recip p0 p1 p2 c01 c01' c12 c12' s0) s0'\n in\n Classical.forall_intro_2 (fun x -> Classical.move_requires (prf1 x));\n let prf2\n (s0 s0': heap)\n (fuel: nat)\n : Lemma\n (requires (holds p0 s0 s0' /\\ fst (f fuel s0) == true /\\ fst (f' fuel s0') == true))\n (ensures (holds p2 (snd (f fuel s0)) (snd (f' fuel s0'))))\n = let k01 = f01 fuel s0 in\n let k01' = f01' fuel s0' in\n let s1 = snd k01 in\n let s1' = snd k01' in\n assert (holds p1 s1 s1')\n in\n Classical.forall_intro_3 (fun x y -> Classical.move_requires (prf2 x y))", "val d_cc\n (b: exp bool)\n (c1 c2 c3: computation)\n (phi phi' phi'' : gexp bool)\n: Lemma\n (requires (\n exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2) /\\\n exec_equiv phi' phi'' c3 c3\n ))\n (ensures (\n exec_equiv phi phi'' (seq (ifthenelse b c1 c2) c3) (ifthenelse b (seq c1 c3) (seq c2 c3))\n ))\n [SMTPatOr [\n [SMTPat (exec_equiv phi phi'' (seq (ifthenelse b c1 c2) c3) (ifthenelse b (seq c1 c3) (seq c2 c3))); SMTPat (exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2))];\n [SMTPat (exec_equiv phi phi'' (seq (ifthenelse b c1 c2) c3) (ifthenelse b (seq c1 c3) (seq c2 c3))); SMTPat (exec_equiv phi' phi'' c3 c3)];\n [SMTPat (exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2)); SMTPat (exec_equiv phi' phi'' c3 c3)];\n ]]\nlet d_cc\n (b: exp bool)\n (c1 c2 c3: computation)\n (phi phi' phi'' : gexp bool)\n: Lemma\n (requires (\n exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2) /\\\n exec_equiv phi' phi'' c3 c3\n ))\n (ensures (\n exec_equiv phi phi'' (seq (ifthenelse b c1 c2) c3) (ifthenelse b (seq c1 c3) (seq c2 c3))\n ))\n [SMTPatOr [\n [SMTPat (exec_equiv phi phi'' (seq (ifthenelse b c1 c2) c3) (ifthenelse b (seq c1 c3) (seq c2 c3))); SMTPat (exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2))];\n [SMTPat (exec_equiv phi phi'' (seq (ifthenelse b c1 c2) c3) (ifthenelse b (seq c1 c3) (seq c2 c3))); SMTPat (exec_equiv phi' phi'' c3 c3)];\n [SMTPat (exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2)); SMTPat (exec_equiv phi' phi'' c3 c3)];\n ]]\n= Benton2004.d_cc b c1 c2 c3 (interp phi) (interp phi') (interp phi'')", "val Benton2004.DDCC.d_ctr = \n p: Benton2004.DDCC.sttype ->\n p': Benton2004.DDCC.sttype ->\n c1: Benton2004.computation ->\n c2: Benton2004.computation ->\n c3: Benton2004.computation\n -> FStar.Pervasives.Lemma\n (requires Benton2004.DDCC.exec_equiv p p' c1 c2 /\\ Benton2004.DDCC.exec_equiv p p' c2 c3)\n (ensures Benton2004.DDCC.exec_equiv p p' c1 c3)\n [\n SMTPatOr [\n [\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c2);\n SMTPat (Benton2004.DDCC.exec_equiv p p' c2 c3)\n ];\n [\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c2);\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c3)\n ];\n [\n SMTPat (Benton2004.DDCC.exec_equiv p p' c2 c3);\n SMTPat (Benton2004.DDCC.exec_equiv p p' c1 c3)\n ]\n ]\n ]\nlet d_ctr = exec_equiv_trans", "val r_sub\n (p1 p2 p1' p2' : gexp bool)\n (f f' : computation)\n: Lemma\n (requires (\n exec_equiv p1 p2 f f' /\\\n included p1' p1 /\\\n included p2 p2'\n ))\n (ensures (exec_equiv p1' p2' f f'))\n [SMTPat (exec_equiv p1' p2' f f'); SMTPat (exec_equiv p1 p2 f f')]\nlet r_sub\n (p1 p2 p1' p2' : gexp bool)\n (f f' : computation)\n: Lemma\n (requires (\n exec_equiv p1 p2 f f' /\\\n included p1' p1 /\\\n included p2 p2'\n ))\n (ensures (exec_equiv p1' p2' f f'))\n [SMTPat (exec_equiv p1' p2' f f'); SMTPat (exec_equiv p1 p2 f f')]\n= d_csub (interp p1) (interp p2) (interp p1') (interp p2') f f'", "val d_assoc\n (c1 c2 c3: computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq (seq c1 c2) c3)))\n (ensures (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq c1 (seq c2 c3))))\n [SMTPat (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq c1 (seq c2 c3)))]\nlet d_assoc\n (c1 c2 c3: computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq (seq c1 c2) c3)))\n (ensures (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq c1 (seq c2 c3))))\n [SMTPat (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq c1 (seq c2 c3)))]\n= Benton2004.d_assoc c1 c2 c3 (interp phi) (interp phi')", "val d_assoc (c1 c2 c3: computation) (phi phi': sttype)\n : Lemma (requires (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq (seq c1 c2) c3)))\n (ensures (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq c1 (seq c2 c3))))\n [SMTPat (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq c1 (seq c2 c3)))]\nlet d_assoc\n (c1 c2 c3: computation)\n (phi phi' : sttype)\n: Lemma\n (requires (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq (seq c1 c2) c3)))\n (ensures (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq c1 (seq c2 c3))))\n [SMTPat (exec_equiv phi phi' (seq (seq c1 c2) c3) (seq c1 (seq c2 c3)))]\n= let fl = reify_computation (seq (seq c1 c2) c3) in\n let fr = reify_computation (seq c1 (seq c2 c3)) in\n assert (forall s0 fuel . fl s0 fuel == fr s0 fuel)", "val d_su1'\n (c c' c'' : computation)\n (phi phi' phi'' : gexp bool)\n: Lemma\n (requires (\n exec_equiv phi phi' c skip /\\\n exec_equiv phi' phi'' c' c''\n ))\n (ensures (exec_equiv phi phi'' (seq c c') c''))\n [SMTPatOr [\n [SMTPat (exec_equiv phi phi'' (seq c c') c''); SMTPat (exec_equiv phi phi' c skip)];\n [SMTPat (exec_equiv phi phi'' (seq c c') c''); SMTPat (exec_equiv phi' phi'' c' c'')];\n [SMTPat (exec_equiv phi' phi'' c' c''); SMTPat (exec_equiv phi phi' c skip)];\n ]]\nlet d_su1'\n (c c' c'' : computation)\n (phi phi' phi'' : gexp bool)\n: Lemma\n (requires (\n exec_equiv phi phi' c skip /\\\n exec_equiv phi' phi'' c' c''\n ))\n (ensures (exec_equiv phi phi'' (seq c c') c''))\n [SMTPatOr [\n [SMTPat (exec_equiv phi phi'' (seq c c') c''); SMTPat (exec_equiv phi phi' c skip)];\n [SMTPat (exec_equiv phi phi'' (seq c c') c''); SMTPat (exec_equiv phi' phi'' c' c'')];\n [SMTPat (exec_equiv phi' phi'' c' c''); SMTPat (exec_equiv phi phi' c skip)];\n ]]\n= Benton2004.d_su1' c c' c'' (interp phi) (interp phi') (interp phi'')", "val eval_equiv_trans (#t: Type0) (p: sttype) (e: nstype t) (f1 f2 f3: exp t)\n : Lemma (requires (is_per e /\\ interpolable p /\\ eval_equiv p e f1 f2 /\\ eval_equiv p e f2 f3))\n (ensures eval_equiv p e f1 f3)\nlet eval_equiv_trans\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f1 f2 f3 : exp t)\n: Lemma\n (requires (is_per e /\\ interpolable p /\\ eval_equiv p e f1 f2 /\\ eval_equiv p e f2 f3))\n (ensures eval_equiv p e f1 f3)\n= let lem (s1 s3:heap)\n : Lemma (requires holds p s1 s3)\n (ensures (holds e (fst (reify_exp f1 s1)) (fst (reify_exp f3 s3))))\n = let w = interpolable_elim p s1 s3 in\n Classical.exists_elim\n (holds e (fst (reify_exp f1 s1)) (fst (reify_exp f3 s3)))\n w\n (fun (s2:heap{holds p s1 s2 /\\ holds p s2 s3}) ->\n assert (holds e (fst (reify_exp f1 s1)) (fst (reify_exp f2 s2)));\n assert (holds e (fst (reify_exp f2 s2)) (fst (reify_exp f3 s3))))\n in\n Classical.forall_intro_2 (fun x -> Classical.move_requires (lem x))", "val loc_equiv_trans (a b c: Mod.loc)\n : Lemma (requires (loc_equiv a b /\\ loc_equiv b c))\n (ensures (loc_equiv a c))\n [SMTPat (loc_equiv a b); SMTPat (loc_equiv b c); SMTPat (loc_equiv a c)]\nlet loc_equiv_trans (a b c:Mod.loc) :\n Lemma\n (requires (loc_equiv a b /\\ loc_equiv b c))\n (ensures (loc_equiv a c))\n [SMTPat (loc_equiv a b);\n SMTPat (loc_equiv b c);\n SMTPat (loc_equiv a c)] =\n Mod.loc_includes_trans a b c;\n Mod.loc_includes_trans c b a", "val d_su1' (c c' c'': computation) (phi phi' phi'': sttype)\n : Lemma (requires (exec_equiv phi phi' c skip /\\ exec_equiv phi' phi'' c' c''))\n (ensures (exec_equiv phi phi'' (seq c c') c''))\n [\n SMTPatOr\n [\n [SMTPat (exec_equiv phi phi' c skip); SMTPat (exec_equiv phi phi'' (seq c c') c'')];\n [SMTPat (exec_equiv phi' phi'' c' c''); SMTPat (exec_equiv phi phi'' (seq c c') c'')];\n [SMTPat (exec_equiv phi phi' c skip); SMTPat (exec_equiv phi' phi'' c' c'')]\n ]\n ]\nlet d_su1'\n (c c' c'' : computation)\n (phi phi' phi'' : sttype)\n: Lemma\n (requires (\n exec_equiv phi phi' c skip /\\\n exec_equiv phi' phi'' c' c''\n ))\n (ensures (exec_equiv phi phi'' (seq c c') c''))\n [SMTPatOr [\n [SMTPat (exec_equiv phi phi' c skip); SMTPat (exec_equiv phi phi'' (seq c c') c'')];\n [SMTPat (exec_equiv phi' phi'' c' c''); SMTPat (exec_equiv phi phi'' (seq c c') c'')];\n [SMTPat (exec_equiv phi phi' c skip); SMTPat (exec_equiv phi' phi'' c' c'')];\n ]]\n= assert (exec_equiv phi phi'' (seq c c') (seq skip c'')) ;\n let f1 = reify_computation (seq skip c'') in\n let f2 = reify_computation c'' in\n assert (forall fuel s0 . f1 fuel s0 == f2 fuel s0)", "val r_sym\n (p p': gexp bool)\n (f f' : computation)\n: Lemma\n (requires (is_per p /\\ is_per p'))\n (ensures (exec_equiv p p' f f' <==> exec_equiv p p' f' f))\n [SMTPat (exec_equiv p p' f f'); SMTPat (is_per p); SMTPat (is_per p')]\nlet r_sym\n (p p': gexp bool)\n (f f' : computation)\n: Lemma\n (requires (is_per p /\\ is_per p'))\n (ensures (exec_equiv p p' f f' <==> exec_equiv p p' f' f))\n [SMTPat (exec_equiv p p' f f'); SMTPat (is_per p); SMTPat (is_per p')]\n= exec_equiv_sym (interp p) (interp p') f f'", "val d_cc (b: exp bool) (c1 c2 c3: computation) (phi phi' phi'': sttype)\n : Lemma\n (requires\n (exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2) /\\\n exec_equiv phi' phi'' c3 c3))\n (ensures\n (exec_equiv phi phi'' (seq (ifthenelse b c1 c2) c3) (ifthenelse b (seq c1 c3) (seq c2 c3))))\n [\n SMTPatOr\n [\n [\n SMTPat (exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2));\n SMTPat (exec_equiv phi' phi'' c3 c3)\n ];\n [\n SMTPat (exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2));\n SMTPat\n (exec_equiv phi\n phi''\n (seq (ifthenelse b c1 c2) c3)\n (ifthenelse b (seq c1 c3) (seq c2 c3)))\n ];\n [\n SMTPat (exec_equiv phi' phi'' c3 c3);\n SMTPat\n (exec_equiv phi\n phi''\n (seq (ifthenelse b c1 c2) c3)\n (ifthenelse b (seq c1 c3) (seq c2 c3)))\n ]\n ]\n ]\nlet d_cc\n (b: exp bool)\n (c1 c2 c3: computation)\n (phi phi' phi'' : sttype)\n: Lemma\n (requires (\n exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2) /\\\n exec_equiv phi' phi'' c3 c3\n ))\n (ensures (\n exec_equiv phi phi'' (seq (ifthenelse b c1 c2) c3) (ifthenelse b (seq c1 c3) (seq c2 c3))\n ))\n [SMTPatOr [\n [SMTPat (exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2)); SMTPat (exec_equiv phi' phi'' c3 c3)];\n [SMTPat (exec_equiv phi phi' (ifthenelse b c1 c2) (ifthenelse b c1 c2)); SMTPat (exec_equiv phi phi'' (seq (ifthenelse b c1 c2) c3) (ifthenelse b (seq c1 c3) (seq c2 c3)))];\n [SMTPat (exec_equiv phi' phi'' c3 c3); SMTPat (exec_equiv phi phi'' (seq (ifthenelse b c1 c2) c3) (ifthenelse b (seq c1 c3) (seq c2 c3)))];\n ]]\n= let fl = reify_computation (seq (ifthenelse b c1 c2) c3) in\n let fr = reify_computation (ifthenelse b (seq c1 c3) (seq c2 c3)) in\n assert (forall s0 fuel . fl s0 fuel == fr s0 fuel);\n assert (exec_equiv phi phi'' (seq (ifthenelse b c1 c2) c3) (seq (ifthenelse b c1 c2) c3))", "val st_equiv_trans (#g: env) (#c0 #c1 #c2: comp) (d01: st_equiv g c0 c1) (d12: st_equiv g c1 c2)\n : option (st_equiv g c0 c2)\nlet st_equiv_trans (#g:env) (#c0 #c1 #c2:comp) (d01:st_equiv g c0 c1) (d12:st_equiv g c1 c2)\n : option (st_equiv g c0 c2)\n = \n match d01 with\n | ST_VPropEquiv _f _c0 _c1 x c0_pre_typing c0_res_typing c0_post_typing eq_res_01 eq_pre_01 eq_post_01 -> (\n let ST_VPropEquiv _f _c1 _c2 y c1_pre_typing c1_res_typing c1_post_typing eq_res_12 eq_pre_12 eq_post_12 = d12 in\n if x = y && eq_tm (comp_res c0) (comp_res c1)\n then Some (\n ST_VPropEquiv g c0 c2 x c0_pre_typing c0_res_typing c0_post_typing\n (RT.Rel_trans _ _ _ _ _ eq_res_01 eq_res_12)\n (VE_Trans _ _ _ _ eq_pre_01 eq_pre_12)\n (VE_Trans _ _ _ _ eq_post_01 eq_post_12)\n )\n else None\n )\n | ST_TotEquiv g t1 t2 u typing eq ->\n let ST_TotEquiv _g _t1 t3 _ _ eq' = d12 in\n let eq'' = Ghost.hide (RT.Rel_trans _ _ _ _ _ eq eq') in\n Some (ST_TotEquiv g t1 t3 u typing eq'')", "val d_su1'_flip (c'' c c': computation) (phi phi' phi'': gexp bool)\n : Lemma (requires (exec_equiv phi phi' skip c /\\ exec_equiv phi' phi'' c'' c'))\n (ensures (exec_equiv phi phi'' c'' (seq c c')))\n [\n SMTPatOr\n [\n [SMTPat (exec_equiv phi phi'' c'' (seq c c')); SMTPat (exec_equiv phi phi' skip c)];\n [SMTPat (exec_equiv phi phi'' c'' (seq c c')); SMTPat (exec_equiv phi' phi'' c'' c')];\n [SMTPat (exec_equiv phi phi' skip c); SMTPat (exec_equiv phi' phi'' c'' c')]\n ]\n ]\nlet d_su1'_flip\n (c'' c c' : computation)\n (phi phi' phi'' : gexp bool)\n: Lemma\n (requires (\n exec_equiv phi phi' skip c /\\\n exec_equiv phi' phi'' c'' c' \n ))\n (ensures (exec_equiv phi phi'' c'' (seq c c')))\n [SMTPatOr [\n [SMTPat (exec_equiv phi phi'' c'' (seq c c')); SMTPat (exec_equiv phi phi' skip c)];\n [SMTPat (exec_equiv phi phi'' c'' (seq c c')); SMTPat (exec_equiv phi' phi'' c'' c')];\n [SMTPat (exec_equiv phi phi' skip c); SMTPat (exec_equiv phi' phi'' c'' c')];\n ]]\n= d_su1' c c' c'' (flip phi) (flip phi') (flip phi'')", "val d_su1'_flip (c'' c c': computation) (phi phi' phi'': gexp bool)\n : Lemma (requires (exec_equiv phi phi' skip c /\\ exec_equiv phi' phi'' c'' c'))\n (ensures (exec_equiv phi phi'' c'' (seq c c')))\n [\n SMTPatOr\n [\n [SMTPat (exec_equiv phi phi'' c'' (seq c c')); SMTPat (exec_equiv phi phi' skip c)];\n [SMTPat (exec_equiv phi phi'' c'' (seq c c')); SMTPat (exec_equiv phi' phi'' c'' c')];\n [SMTPat (exec_equiv phi phi' skip c); SMTPat (exec_equiv phi' phi'' c'' c')]\n ]\n ]\nlet d_su1'_flip\n (c'' c c' : computation)\n (phi phi' phi'' : gexp bool)\n: Lemma\n (requires (\n exec_equiv phi phi' skip c /\\\n exec_equiv phi' phi'' c'' c' \n ))\n (ensures (exec_equiv phi phi'' c'' (seq c c')))\n [SMTPatOr [\n [SMTPat (exec_equiv phi phi'' c'' (seq c c')); SMTPat (exec_equiv phi phi' skip c)];\n [SMTPat (exec_equiv phi phi'' c'' (seq c c')); SMTPat (exec_equiv phi' phi'' c'' c')];\n [SMTPat (exec_equiv phi phi' skip c); SMTPat (exec_equiv phi' phi'' c'' c')];\n ]]\n= d_su1' c c' c'' (flip phi) (flip phi') (flip phi'')", "val eq_of_seq_transitivity (#c:_) (eq: CE.equiv c) (s1 s2 s3: seq c)\n : Lemma (requires eq_of_seq eq s1 s2 /\\ eq_of_seq eq s2 s3) \n (ensures eq_of_seq eq s1 s3)\nlet rec eq_of_seq_transitivity #c (eq: CE.equiv c) s1 s2 s3\n : Lemma (requires eq_of_seq eq s1 s2 /\\ eq_of_seq eq s2 s3) \n (ensures eq_of_seq eq s1 s3) \n (decreases length s1) = \n if length s1 > 0 then \n let lia1, las1 = un_snoc s1 in\n let lia2, las2 = un_snoc s2 in\n let lia3, las3 = un_snoc s3 in\n eq_of_seq_transitivity #c eq lia1 lia2 lia3;\n eq.transitivity las1 las2 las3", "val exec_equiv (p p': sttype) (f f': computation) : GTot Type0\nlet exec_equiv\n (p p' : sttype)\n (f f' : computation)\n: GTot Type0\n= let f = reify_computation f in\n let f' = reify_computation f' in\n exec_equiv_reified p p' f f'", "val exec_equiv (p p': sttype) (f f': computation) : GTot Type0\nlet exec_equiv\n (p p' : sttype)\n (f f' : computation)\n: GTot Type0\n= let f = reify_computation f in\n let f' = reify_computation f' in\n exec_equiv_reified p p' f f'", "val Benton2004.DDCC.d_csym = \n p: Benton2004.DDCC.sttype ->\n p': Benton2004.DDCC.sttype ->\n f: Benton2004.computation ->\n f': Benton2004.computation\n -> FStar.Pervasives.Lemma\n (ensures Benton2004.DDCC.exec_equiv p p' f f' <==> Benton2004.DDCC.exec_equiv p p' f' f)\n [SMTPat (Benton2004.DDCC.exec_equiv p p' f f')]\nlet d_csym = exec_equiv_sym", "val d_su1\n (c: computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (exec_equiv phi phi' c c))\n (ensures (exec_equiv phi phi' (seq skip c) c))\n [SMTPat (exec_equiv phi phi' (seq skip c) c)]\nlet d_su1\n (c: computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (exec_equiv phi phi' c c))\n (ensures (exec_equiv phi phi' (seq skip c) c))\n [SMTPat (exec_equiv phi phi' (seq skip c) c)]\n= Benton2004.d_su1 c (interp phi) (interp phi')", "val eval_equiv_flip (#t: Type0) (p: sttype) (e: nstype t) (f f': exp t)\n : Lemma (eval_equiv (flip p) (flip e) f' f <==> eval_equiv p e f f')\n [SMTPat (eval_equiv (flip p) (flip e) f' f)]\nlet eval_equiv_flip\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': exp t)\n: Lemma\n (eval_equiv (flip p) (flip e) f' f <==> eval_equiv p e f f')\n [SMTPat (eval_equiv (flip p) (flip e) f' f)]\n= holds_flip p;\n holds_flip e", "val d_su2\n (c: computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (exec_equiv phi phi' c c))\n (ensures (exec_equiv phi phi' (seq c skip) c))\n [SMTPat (exec_equiv phi phi' (seq c skip) c)]\nlet d_su2\n (c: computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (exec_equiv phi phi' c c))\n (ensures (exec_equiv phi phi' (seq c skip) c))\n [SMTPat (exec_equiv phi phi' (seq c skip) c)]\n= Benton2004.d_su2 c (interp phi) (interp phi')", "val d_op_singl\n (#from #to: Type0)\n (op: (from -> from -> Tot to))\n (c1 c2: from)\n (e1 e1' e2 e2': exp from)\n (phi: sttype)\n : Lemma (requires (eval_equiv phi (ns_singl c1) e1 e1' /\\ eval_equiv phi (ns_singl c2) e2 e2'))\n (ensures (eval_equiv phi (ns_singl (op c1 c2)) (eop op e1 e2) (eop op e1' e2')))\n [SMTPat (eval_equiv phi (ns_singl (op c1 c2)) (eop op e1 e2) (eop op e1' e2'))]\nlet d_op_singl\n (#from #to: Type0)\n (op: (from -> from -> Tot to))\n (c1 c2: from)\n (e1 e1' e2 e2': exp from)\n (phi: sttype)\n: Lemma\n (requires (\n eval_equiv phi (ns_singl c1) e1 e1' /\\\n eval_equiv phi (ns_singl c2) e2 e2'\n ))\n (ensures (eval_equiv phi (ns_singl (op c1 c2)) (eop op e1 e2) (eop op e1' e2')))\n [SMTPat (eval_equiv phi (ns_singl (op c1 c2)) (eop op e1 e2) (eop op e1' e2'))]\n= op_abs_singl op c1 c2 ;\n d_op op e1 e1' e2 e2' (ns_singl c1) (ns_singl c2) (ns_singl (op c1 c2)) phi", "val d_bre (c1 c2 c0: computation) (phi phi': sttype) (b: exp bool)\n : Lemma (requires (exec_equiv phi phi' c1 c0 /\\ exec_equiv phi phi' c2 c0))\n (ensures (exec_equiv phi phi' (ifthenelse b c1 c2) c0))\n [SMTPat (exec_equiv phi phi' (ifthenelse b c1 c2) c0)]\nlet d_bre\n (c1 c2 c0: computation)\n (phi phi' : sttype)\n (b: exp bool)\n: Lemma\n (requires (\n exec_equiv phi phi' c1 c0 /\\\n exec_equiv phi phi' c2 c0\n ))\n (ensures (exec_equiv phi phi' (ifthenelse b c1 c2) c0))\n [SMTPat (exec_equiv phi phi' (ifthenelse b c1 c2) c0)]\n= assert (mention (reify_exp b))", "val exec_equiv_assign\n (gamma: context)\n (x: var)\n (e: exp int)\n (s: seclevel)\n: Lemma\n (requires (\n x `fresh_in` gamma /\\\n eval_equiv ((x, s)::gamma) e s\n ))\n (ensures (\n x `fresh_in` gamma /\\\n exec_equiv ((x, s)::gamma) (assign x e) s\n ))\n [SMTPat (exec_equiv ((x, s)::gamma) (assign x e) s)]\nlet exec_equiv_assign\n (gamma: context)\n (x: var)\n (e: exp int)\n (s: seclevel)\n: Lemma\n (requires (\n x `fresh_in` gamma /\\\n eval_equiv ((x, s)::gamma) e s\n ))\n (ensures (\n x `fresh_in` gamma /\\\n exec_equiv ((x, s)::gamma) (assign x e) s\n ))\n [SMTPat (exec_equiv ((x, s)::gamma) (assign x e) s)]\n= match s with\n | Low -> d_assign (interp_context gamma) x (interp_seclevel _ s) (interp_seclevel _ s) e e\n | High -> d_das x e (interp_context gamma) (interp_seclevel _ s)", "val equiv_heap_iff_equiv (p1 p2: slprop u#a)\n : Lemma (ensures (H.equiv p1 p2 <==> equiv p1 p2)) [SMTPat (equiv p1 p2)]\nlet equiv_heap_iff_equiv (p1 p2:slprop u#a)\n : Lemma (ensures (H.equiv p1 p2 <==> equiv p1 p2))\n [SMTPat (equiv p1 p2)]\n = let aux_lr ()\n : Lemma\n (requires H.equiv p1 p2)\n (ensures equiv p1 p2)\n [SMTPat ()]\n = ()\n in\n let aux_rl_helper1 (h:H.heap)\n : Lemma\n (requires equiv p1 p2 /\\ H.interp p1 h)\n (ensures H.interp p2 h)\n [SMTPat ()]\n = assert (interp p2 (mem_of_heap h))\n in\n let aux_rl_helper2 (h:H.heap)\n : Lemma\n (requires equiv p1 p2 /\\ H.interp p2 h)\n (ensures H.interp p1 h)\n [SMTPat ()]\n = assert (interp p2 (mem_of_heap h))\n in\n let aux_rl ()\n : Lemma\n (requires equiv p1 p2)\n (ensures H.equiv p1 p2)\n [SMTPat ()]\n = () in\n ()", "val equiv_heap_iff_equiv (p1 p2: slprop u#a)\n : Lemma (ensures (H.equiv p1 p2 <==> equiv p1 p2)) [SMTPat (equiv p1 p2)]\nlet equiv_heap_iff_equiv (p1 p2:slprop u#a)\n : Lemma (ensures (H.equiv p1 p2 <==> equiv p1 p2))\n [SMTPat (equiv p1 p2)]\n = let aux_lr ()\n : Lemma\n (requires H.equiv p1 p2)\n (ensures equiv p1 p2)\n [SMTPat ()]\n = ()\n in\n let aux_rl_helper1 (h:H.heap)\n : Lemma\n (requires equiv p1 p2 /\\ H.interp p1 h)\n (ensures H.interp p2 h)\n [SMTPat ()]\n = assert (interp p2 (mem_of_heap h))\n in\n let aux_rl_helper2 (h:H.heap)\n : Lemma\n (requires equiv p1 p2 /\\ H.interp p2 h)\n (ensures H.interp p1 h)\n [SMTPat ()]\n = assert (interp p2 (mem_of_heap h))\n in\n let aux_rl ()\n : Lemma\n (requires equiv p1 p2)\n (ensures H.equiv p1 p2)\n [SMTPat ()]\n = () in\n ()", "val exec_equiv\n (p p' : gexp bool)\n (f f' : computation)\n: GTot Type0\nlet exec_equiv\n (p p' : gexp bool)\n (f f' : computation)\n: GTot Type0\n= Benton2004.exec_equiv (interp p) (interp p') f f'", "val ss_comp_commutes (c:comp) (ss:ss_t)\n : Lemma (ensures\n (let r = ss_comp c ss in\n (C_Tot? c ==> r == C_Tot (ss_term (comp_res c) ss)) /\\\n (C_ST? c ==> r == C_ST (ss_st_comp (st_comp_of_comp c) ss)) /\\\n (C_STAtomic? c ==> r == C_STAtomic (ss_term (comp_inames c) ss)\n (C_STAtomic?.obs c)\n (ss_st_comp (st_comp_of_comp c) ss)) /\\\n (C_STGhost? c ==> r == C_STGhost (ss_st_comp (st_comp_of_comp c) ss))))\n [SMTPat (ss_comp c ss)]\nlet rec ss_comp_commutes (c:comp) (ss:ss_t)\n : Lemma (ensures\n (let r = ss_comp c ss in\n (C_Tot? c ==> r == C_Tot (ss_term (comp_res c) ss)) /\\\n (C_ST? c ==> r == C_ST (ss_st_comp (st_comp_of_comp c) ss)) /\\\n (C_STAtomic? c ==> r == C_STAtomic (ss_term (comp_inames c) ss)\n (C_STAtomic?.obs c)\n (ss_st_comp (st_comp_of_comp c) ss)) /\\\n (C_STGhost? c ==> r == C_STGhost (ss_st_comp (st_comp_of_comp c) ss))))\n (decreases L.length ss.l)\n [SMTPat (ss_comp c ss)] =\n match ss.l with\n | [] -> ()\n | y::tl -> ss_comp_commutes (subst_comp c [ NT y (Map.sel ss.m y) ]) (tail ss)", "val eval_equiv_const\n (#t: Type0)\n (gamma: context)\n (c: t)\n (s: seclevel)\n: Lemma\n (eval_equiv gamma (const c) s)\n [SMTPat (eval_equiv gamma (const c) s)]\nlet eval_equiv_const\n (#t: Type0)\n (gamma: context)\n (c: t)\n (s: seclevel)\n: Lemma\n (eval_equiv gamma (const c) s)\n [SMTPat (eval_equiv gamma (const c) s)]\n= Benton2004.DDCC.eval_equiv_const c (interp_context gamma)", "val equiv_symmetric (p1 p2: vprop) : Lemma (requires p1 `equiv` p2) (ensures p2 `equiv` p1)\nlet equiv_symmetric (p1 p2:vprop)\n : Lemma (requires p1 `equiv` p2) (ensures p2 `equiv` p1)\n = reveal_equiv p1 p2;\n equiv_symmetric (hp_of p1) (hp_of p2);\n reveal_equiv p2 p1", "val exec_equiv_reified (p p': sttype) (f f': reified_computation) : GTot Type0\nlet exec_equiv_reified\n (p p' : sttype)\n (f f' : reified_computation)\n: GTot Type0\n= terminates_equiv_reified p f f' /\\\n (forall (s s' : heap) (fuel: nat) .\n (holds p s s' /\\ fst (f fuel s) == true /\\ fst (f' fuel s') == true) ==> holds p' (snd (f fuel s)) (snd (f' fuel s')))", "val modifies_trans\n (s12: loc)\n (h1 h2: HS.mem)\n (s23: loc)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))\n [SMTPat (modifies s12 h1 h2); SMTPat (modifies s23 h2 h3)]\nlet modifies_trans = MG.modifies_trans", "val modifies_trans\n (s12: loc)\n (h1 h2: HS.mem)\n (s23: loc)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))\n [SMTPat (modifies s12 h1 h2); SMTPat (modifies s23 h2 h3)]\nlet modifies_trans = MG.modifies_trans", "val per_holds_trans (#t: Type0) (f: rel t) (x1 x2 x3: t)\n : Lemma (requires (is_per f /\\ holds f x1 x2 /\\ holds f x2 x3))\n (ensures (holds f x1 x3))\n [\n SMTPatOr\n [\n [SMTPat (holds f x1 x2); SMTPat (holds f x2 x3)];\n [SMTPat (holds f x1 x2); SMTPat (holds f x1 x3)];\n [SMTPat (holds f x2 x3); SMTPat (holds f x1 x3)]\n ]\n ]\nlet per_holds_trans\n (#t: Type0)\n (f: rel t)\n (x1 x2 x3: t)\n: Lemma\n (requires (is_per f /\\ holds f x1 x2 /\\ holds f x2 x3))\n (ensures (holds f x1 x3))\n [SMTPatOr [\n [SMTPat (holds f x1 x2); SMTPat (holds f x2 x3)];\n [SMTPat (holds f x1 x2); SMTPat (holds f x1 x3)];\n [SMTPat (holds f x2 x3); SMTPat (holds f x1 x3)];\n ]]\n= holds_equiv f x1 x2;\n holds_equiv f x2 x3;\n holds_equiv f x1 x3", "val vprop_equiv_trans (v0 v1 v2:vprop) (_:vprop_equiv v0 v1) (_:vprop_equiv v1 v2)\n : vprop_equiv v0 v2\nlet vprop_equiv_trans\n (v0 v1 v2:vprop)\n (p:vprop_equiv v0 v1)\n (q:vprop_equiv v1 v2)\n : vprop_equiv v0 v2\n = slprop_equiv_elim v0 v1;\n slprop_equiv_elim v1 v2;\n p", "val env_extends_trans (g1 g2 g3:env)\n : Lemma (requires g1 `env_extends` g2 /\\ g2 `env_extends` g3)\n (ensures g1 `env_extends` g3)\n [SMTPat (g1 `env_extends` g3); SMTPat (g1 `env_extends` g2)]\nlet env_extends_trans (g1 g2 g3:env)\n : Lemma (requires g1 `env_extends` g2 /\\ g2 `env_extends` g3)\n (ensures g1 `env_extends` g3) =\n let g12 = elim_env_extends g1 g2 in\n let g23 = elim_env_extends g2 g3 in\n L.append_assoc g12.bs g23.bs g3.bs;\n assert (equal g1 (push_env g3 (push_env g23 g12)));\n intro_env_extends g1 g3 (push_env g23 g12)", "val r_ass_derived (x y: var) (e e': exp int) (p p': gexp bool)\n : Lemma\n (requires\n (included p (gsubst (gsubst p' x Left (exp_to_gexp e Left)) y Right (exp_to_gexp e' Right)))\n )\n (ensures (exec_equiv p p' (assign x e) (assign y e')))\n [SMTPat (exec_equiv p p' (assign x e) (assign y e'))]\nlet r_ass_derived\n (x y: var)\n (e e' : exp int)\n (p p': gexp bool)\n: Lemma\n (requires (\n included\n p\n (gsubst (gsubst p' x Left (exp_to_gexp e Left)) y Right (exp_to_gexp e' Right))\n ))\n (ensures (exec_equiv\n p\n p'\n (assign x e)\n (assign y e')\n ))\n [SMTPat (exec_equiv p p' (assign x e) (assign y e'))]\n= Benton2004.RHL.r_ass x y e e' p'", "val vprop_equiv_cong (p1 p2 p3 p4:vprop)\n (_: vprop_equiv p1 p3)\n (_: vprop_equiv p2 p4)\n : vprop_equiv (p1 ** p2) (p3 ** p4)\nlet vprop_equiv_cong (p1 p2 p3 p4:vprop)\n (f: vprop_equiv p1 p3)\n (g: vprop_equiv p2 p4)\n : vprop_equiv (p1 ** p2) (p3 ** p4)\n = slprop_equiv_elim p1 p3;\n slprop_equiv_elim p2 p4;\n vprop_equiv_refl _", "val nt_subst_comp_commutes (c:comp) (nts:nt_substs)\n : Lemma (ensures\n (let r = nt_subst_comp c nts in\n (C_Tot? c ==> r == C_Tot (nt_subst_term (comp_res c) nts)) /\\\n (C_ST? c ==> r == C_ST (nt_subst_st_comp (st_comp_of_comp c) nts)) /\\\n (C_STAtomic? c ==> r == C_STAtomic (nt_subst_term (comp_inames c) nts)\n (C_STAtomic?.obs c)\n (nt_subst_st_comp (st_comp_of_comp c) nts)) /\\\n (C_STGhost? c ==> r == C_STGhost (nt_subst_st_comp (st_comp_of_comp c) nts))))\n [SMTPat (nt_subst_comp c nts)]\nlet rec nt_subst_comp_commutes (c:comp) (nts:nt_substs)\n : Lemma (ensures\n (let r = nt_subst_comp c nts in\n (C_Tot? c ==> r == C_Tot (nt_subst_term (comp_res c) nts)) /\\\n (C_ST? c ==> r == C_ST (nt_subst_st_comp (st_comp_of_comp c) nts)) /\\\n (C_STAtomic? c ==> r == C_STAtomic (nt_subst_term (comp_inames c) nts)\n (C_STAtomic?.obs c)\n (nt_subst_st_comp (st_comp_of_comp c) nts)) /\\\n (C_STGhost? c ==> r == C_STGhost (nt_subst_st_comp (st_comp_of_comp c) nts))))\n (decreases nts)\n [SMTPat (nt_subst_comp c nts)] =\n match nts with\n | [] -> ()\n | (NT x e)::nts_tl -> nt_subst_comp_commutes (nt_subst_comp c [ NT x e ]) nts_tl", "val t_equiv (#g #st #c: _) (d: st_typing g st c) (#c': comp) (eq: st_equiv g c c')\n : st_typing g st c'\nlet t_equiv #g #st #c (d:st_typing g st c) (#c':comp) (eq:st_equiv g c c')\n : st_typing g st c'\n = match d with\n | T_Equiv _ _ _ _ d0 eq' -> (\n match st_equiv_trans eq' eq with\n | None -> T_Equiv _ _ _ _ d eq\n | Some eq'' -> T_Equiv _ _ _ _ d0 eq''\n )\n | _ -> T_Equiv _ _ _ _ d eq", "val r_cbl\n (b: exp bool)\n (c c' d : computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (\n exec_equiv\n (gand phi (exp_to_gexp b Left))\n phi'\n c\n d /\\\n exec_equiv\n (gand phi (gnot (exp_to_gexp b Left)))\n phi'\n c'\n d\n ))\n (ensures (\n exec_equiv\n phi\n phi'\n (ifthenelse b c c')\n d\n ))\nlet r_cbl\n (b: exp bool)\n (c c' d : computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (\n exec_equiv\n (gand phi (exp_to_gexp b Left))\n phi'\n c\n d /\\\n exec_equiv\n (gand phi (gnot (exp_to_gexp b Left)))\n phi'\n c'\n d\n ))\n (ensures (\n exec_equiv\n phi\n phi'\n (ifthenelse b c c')\n d\n ))\n= (* NOTE: the following let _ are necessary, and must be stated in this form instead of asserts alone, the latter seeming ineffective *)\n let _ : squash (forall s1 s2 . holds (interp (gand phi (exp_to_gexp b Left))) s1 s2 <==> holds (interp phi) s1 s2 /\\ fst (reify_exp b s1) == true) =\n assert (forall s1 s2 . holds (interp (gand phi (exp_to_gexp b Left))) s1 s2 <==> holds (interp phi) s1 s2 /\\ fst (reify_exp b s1) == true)\n in\n let _ : squash (forall s1 s2 . holds (interp (gand phi (gnot (exp_to_gexp b Left)))) s1 s2 <==> holds (interp phi) s1 s2 /\\ ~ (fst (reify_exp b s1) == true)) =\n assert (forall s1 s2 . holds (interp (gand phi (gnot (exp_to_gexp b Left)))) s1 s2 <==> holds (interp phi) s1 s2 /\\ ~ (fst (reify_exp b s1) == true))\n \n in\n ()", "val star_congruence (p1 p2 p3 p4:slprop)\n : Lemma (requires p1 `equiv` p3 /\\ p2 `equiv` p4)\n (ensures (p1 `star` p2) `equiv` (p3 `star` p4))\nlet star_congruence (p1 p2 p3 p4:slprop) =\n equiv_heap_iff_equiv_forall ();\n H.star_congruence p1 p2 p3 p4", "val star_congruence (p1 p2 p3 p4:slprop)\n : Lemma (requires p1 `equiv` p3 /\\ p2 `equiv` p4)\n (ensures (p1 `star` p2) `equiv` (p3 `star` p4))\nlet star_congruence (p1 p2 p3 p4:slprop) =\n equiv_heap_iff_equiv_forall ();\n H.star_congruence p1 p2 p3 p4", "val eval_equiv_op\n (#from #to: Type0)\n (op: (from -> from -> Tot to))\n (gamma: context)\n (e e' : exp from)\n (s: seclevel)\n: Lemma\n (requires (\n eval_equiv gamma e s /\\\n eval_equiv gamma e' s\n ))\n (ensures (eval_equiv gamma (eop op e e') s))\n [SMTPat (eval_equiv gamma (eop op e e') s)]\nlet eval_equiv_op\n (#from #to: Type0)\n (op: (from -> from -> Tot to))\n (gamma: context)\n (e e' : exp from)\n (s: seclevel)\n: Lemma\n (requires (\n eval_equiv gamma e s /\\\n eval_equiv gamma e' s\n ))\n (ensures (eval_equiv gamma (eop op e e') s))\n [SMTPat (eval_equiv gamma (eop op e e') s)] \n= op_abs_interp_seclevel op s;\n d_op op e e e' e' (interp_seclevel _ s) (interp_seclevel _ s) (interp_seclevel _ s) (interp_context gamma)", "val app_state_feq_commutative (#adm:_) (st1 st2: app_state adm)\n : Lemma (ensures (app_state_feq st1 st2 <==> app_state_feq st2 st1))\n [SMTPat (app_state_feq st1 st2); SMTPat (app_state_feq st2 st1)]\nlet app_state_feq_commutative (#adm) (st1 st2: app_state adm)\n : Lemma (ensures (app_state_feq st1 st2 <==> app_state_feq st2 st1))\n = introduce (app_state_feq st1 st2) ==> (app_state_feq st2 st1)\n with _. app_state_feq_comm_aux st1 st2;\n introduce (app_state_feq st2 st1) ==> (app_state_feq st1 st2)\n with _. app_state_feq_comm_aux st2 st1", "val Benton2004.DDCC.d_kbf = \n b: Benton2004.exp Prims.bool ->\n phi: Benton2004.DDCC.sttype ->\n c1: Benton2004.computation ->\n c2: Benton2004.computation ->\n c': Benton2004.computation ->\n phi': Benton2004.DDCC.sttype\n -> FStar.Pervasives.Lemma\n (requires\n Benton2004.eval_equiv phi (Benton2004.DDCC.ns_singl false) b b /\\\n Benton2004.DDCC.exec_equiv phi phi' c2 c')\n (ensures Benton2004.DDCC.exec_equiv phi phi' (Benton2004.ifthenelse b c1 c2) c')\n [\n SMTPat (Benton2004.eval_equiv phi (Benton2004.DDCC.ns_singl false) b b);\n SMTPat (Benton2004.DDCC.exec_equiv phi phi' (Benton2004.ifthenelse b c1 c2) c')\n ]\nlet d_kbf = d_kb false", "val star_congruence (p1 p2 p3 p4:vprop)\n : Lemma (requires p1 `equiv` p3 /\\ p2 `equiv` p4)\n (ensures (p1 `star` p2) `equiv` (p3 `star` p4))\nlet star_congruence p1 p2 p3 p4 = Mem.star_congruence (hp_of p1) (hp_of p2) (hp_of p3) (hp_of p4)", "val Benton2004.DDCC.d_kbt = \n b: Benton2004.exp Prims.bool ->\n phi: Benton2004.DDCC.sttype ->\n c1: Benton2004.computation ->\n c2: Benton2004.computation ->\n c': Benton2004.computation ->\n phi': Benton2004.DDCC.sttype\n -> FStar.Pervasives.Lemma\n (requires\n Benton2004.eval_equiv phi (Benton2004.DDCC.ns_singl true) b b /\\\n Benton2004.DDCC.exec_equiv phi phi' c1 c')\n (ensures Benton2004.DDCC.exec_equiv phi phi' (Benton2004.ifthenelse b c1 c2) c')\n [\n SMTPat (Benton2004.eval_equiv phi (Benton2004.DDCC.ns_singl true) b b);\n SMTPat (Benton2004.DDCC.exec_equiv phi phi' (Benton2004.ifthenelse b c1 c2) c')\n ]\nlet d_kbt = d_kb true", "val loc_equiv_union_union_loc (a b c: Mod.loc)\n : Lemma (requires (loc_equiv b c))\n (ensures (loc_equiv (Mod.loc_union a b) (Mod.loc_union a c)))\n [SMTPat (loc_equiv (Mod.loc_union a b) (Mod.loc_union a c))]\nlet loc_equiv_union_union_loc (a b c:Mod.loc) :\n Lemma\n (requires (loc_equiv b c))\n (ensures (loc_equiv\n (Mod.loc_union a b)\n (Mod.loc_union a c)))\n [SMTPat (loc_equiv\n (Mod.loc_union a b)\n (Mod.loc_union a c))] =\n let incl = Mod.loc_includes in\n let u = Mod.loc_union in\n // assert (b `incl` c);\n Mod.loc_includes_union_l a b c;\n // assert ((a `u` b) `incl` c);\n Mod.loc_includes_union_l a b a;\n // assert ((a `u` b) `incl` a);\n // assert ((a `u` b) `incl` (a `u` c));\n Mod.loc_includes_union_l a c b;\n Mod.loc_includes_union_l a c a", "val inv_equiv_lemma (r: ref int) (r1 r2: ghost_ref int)\n : Lemma ((inv_slprop r r1 r2) `equiv` (inv_slprop r r2 r1)) [SMTPat (inv_slprop r r1 r2)]\nlet inv_equiv_lemma (r:ref int) (r1 r2:ghost_ref int)\n : Lemma (inv_slprop r r1 r2 `equiv` inv_slprop r r2 r1)\n [SMTPat (inv_slprop r r1 r2)]\n = let aux (r:ref int) (r1 r2:ghost_ref int) (m:mem)\n : Lemma\n (requires interp (hp_of (inv_slprop r r1 r2)) m)\n (ensures interp (hp_of (inv_slprop r r2 r1)) m)\n [SMTPat ()]\n = assert (\n Steel.Memory.h_exists #(int & int) (fun x -> hp_of (inv_pred r r1 r2 x)) ==\n h_exists_sl #(int & int) (inv_pred r r1 r2))\n by (FStar.Tactics.norm [delta_only [`%h_exists_sl]]);\n\n\n let w : G.erased (int & int) = id_elim_exists (fun x -> hp_of (inv_pred r r1 r2 x)) m in\n\n assert ((ghost_pts_to r1 half_perm (snd (snd w, fst w)) `star`\n ghost_pts_to r2 half_perm (fst (snd w, fst w)) `star`\n pts_to r full_perm (fst (snd w, fst w) + snd (snd w, fst w))) `equiv`\n (ghost_pts_to r2 half_perm (fst (snd w, fst w)) `star`\n ghost_pts_to r1 half_perm (snd (snd w, fst w)) `star`\n pts_to r full_perm (fst (snd w, fst w) + snd (snd w, fst w)))) by (FStar.Tactics.norm [delta_attr [`%__steel_reduce__]]; canon' false (`true_p) (`true_p));\n\n reveal_equiv\n (ghost_pts_to r1 half_perm (snd (snd w, fst w)) `star`\n ghost_pts_to r2 half_perm (fst (snd w, fst w)) `star`\n pts_to r full_perm (fst (snd w, fst w) + snd (snd w, fst w)))\n (ghost_pts_to r2 half_perm (fst (snd w, fst w)) `star`\n ghost_pts_to r1 half_perm (snd (snd w, fst w)) `star`\n pts_to r full_perm (fst (snd w, fst w) + snd (snd w, fst w)));\n\n assert (interp (hp_of (inv_pred r r2 r1 (snd w, fst w))) m);\n\n intro_h_exists (snd w, fst w) (fun x -> hp_of (inv_pred r r2 r1 x)) m;\n assert (interp (Steel.Memory.h_exists (fun x -> hp_of (inv_pred r r2 r1 x))) m);\n\n assert (\n Steel.Memory.h_exists #(int & int) (fun x -> hp_of (inv_pred r r2 r1 x)) ==\n h_exists_sl #(int & int) (inv_pred r r2 r1))\n by (FStar.Tactics.norm [delta_only [`%h_exists_sl]]) in\n\n reveal_equiv (inv_slprop r r1 r2) (inv_slprop r r2 r1)", "val pr_eq: #a:Type -> #b:Type ->\n c1:(store -> M (a * id)) ->\n c2:(store -> M (b * id)) ->\n p1:(a -> nat) ->\n p2:(b -> nat) ->\n bij:bijection -> Lemma\n (requires\n (forall h. let r1,_ = c1 (to_id 0, h) in\n let r2,_ = c2 (to_id 0, bij.f h) in\n p1 r1 == p2 r2))\n (ensures (mass c1 p1 == mass c2 p2))\nlet pr_eq #a #b c1 c2 p1 p2 bij =\n pr_leq c1 c2 p1 p2 bij;\n pr_leq c2 c1 p2 p1 (inverse bij)", "val pr_eq: #a:Type -> #b:Type ->\n c1:(store -> M (a * id)) ->\n c2:(store -> M (b * id)) ->\n p1:(a -> nat) ->\n p2:(b -> nat) ->\n bij:bijection -> Lemma\n (requires\n (forall h. let r1,_ = c1 (to_id 0, h) in\n let r2,_ = c2 (to_id 0, bij.f h) in\n p1 r1 == p2 r2))\n (ensures (mass c1 p1 == mass c2 p2))\nlet pr_eq #a #b c1 c2 p1 p2 bij =\n pr_leq c1 c2 p1 p2 bij;\n pr_leq c2 c1 p2 p1 (inverse bij)", "val includes_trans\n (#t1 #t2 #t3: typ)\n (p1: pointer t1)\n (p2: pointer t2)\n (p3: pointer t3)\n: Lemma\n (requires (includes p1 p2 /\\ includes p2 p3))\n (ensures (includes p1 p3))\nlet includes_trans\n (#value1 #value2 #value3: typ)\n (p1: pointer value1)\n (p2: pointer value2)\n (p3: pointer value3)\n= path_includes_trans (Pointer?.p p1) (Pointer?.p p2) (Pointer?.p p3)", "val exists_equiv (#a:_)\n (p:a -> vprop)\n (q:a -> vprop {forall x. equiv (p x) (q x) })\n : Lemma (equiv (exists_ p) (exists_ q))\nlet exists_equiv #a p1 p2\n = SEA.exists_equiv p1 p2", "val r_skip\n (p: gexp bool)\n: Lemma\n (exec_equiv p p skip skip)\n [SMTPat (exec_equiv p p skip skip)]\nlet r_skip\n (p: gexp bool)\n: Lemma\n (exec_equiv p p skip skip)\n [SMTPat (exec_equiv p p skip skip)]\n= d_skip (interp p)", "val r_if\n (b b': exp bool)\n (c c' d d' : computation)\n (p p' : gexp bool)\n: Lemma\n (requires (\n exec_equiv\n (r_if_precond_true b b' c c' d d' p p')\n p'\n c\n c' /\\\n exec_equiv\n (r_if_precond_false b b' c c' d d' p p')\n p'\n d\n d'\n ))\n (ensures (\n exec_equiv\n (r_if_precond b b' c c' d d' p p')\n p'\n (ifthenelse b c d)\n (ifthenelse b' c' d')\n ))\nlet r_if\n (b b': exp bool)\n (c c' d d' : computation)\n (p p' : gexp bool)\n: Lemma\n (requires (\n exec_equiv\n (r_if_precond_true b b' c c' d d' p p')\n p'\n c\n c' /\\\n exec_equiv\n (r_if_precond_false b b' c c' d d' p p')\n p'\n d\n d'\n ))\n (ensures (\n exec_equiv\n (r_if_precond b b' c c' d d' p p')\n p'\n (ifthenelse b c d)\n (ifthenelse b' c' d')\n ))\n= holds_r_if_precond_true b b' c c' d d' p p';\n holds_r_if_precond_false b b' c c' d d' p p';\n holds_r_if_precond b b' c c' d d' p p'", "val conv_stt (#a:Type u#a)\n (#pre1:vprop)\n (#pre2:vprop)\n (#post1:a -> vprop)\n (#post2:a -> vprop)\n (pf1 : vprop_equiv pre1 pre2)\n (pf2 : vprop_post_equiv post1 post2)\n: Lemma (stt a pre1 post1 == stt a pre2 post2)\nlet conv_stt pf1 pf2 = I.conv #_ _ _ _ _ pf1 pf2", "val st_equiv_freevars (#g #c1 #c2: _) (d: st_equiv g c1 c2)\n : Lemma (requires (freevars_comp c1) `Set.subset` (vars_of_env g))\n (ensures (freevars_comp c2) `Set.subset` (vars_of_env g))\nlet st_equiv_freevars #g (#c1 #c2:_)\n (d:st_equiv g c1 c2)\n : Lemma\n (requires freevars_comp c1 `Set.subset` vars_of_env g)\n (ensures freevars_comp c2 `Set.subset` vars_of_env g) \n = match d with\n | ST_VPropEquiv _ _ _ x _ _ _ eq_res eq_pre eq_post -> (\n vprop_equiv_freevars eq_pre;\n vprop_equiv_freevars eq_post;\n freevars_open_term_inv (comp_post c1) x;\n freevars_open_term_inv (comp_post c2) x;\n Pulse.Elaborate.elab_freevars (comp_res c1);\n refl_equiv_freevars eq_res;\n Pulse.Elaborate.elab_freevars (comp_res c2)\n )\n | ST_TotEquiv _ t1 t2 u t1_typing eq ->\n let t2_typing = Pulse.Typing.Metatheory.Base.rt_equiv_typing eq t1_typing._0 in\n tot_or_ghost_typing_freevars (E (Ghost.reveal t2_typing))", "val Benton2004.DDCC.d_n = c: Prims.int -> p: Benton2004.DDCC.sttype\n -> FStar.Pervasives.Lemma\n (ensures\n Benton2004.eval_equiv p\n (Benton2004.DDCC.ns_singl c)\n (Benton2004.const c)\n (Benton2004.const c))\n [\n SMTPat (Benton2004.eval_equiv p\n (Benton2004.DDCC.ns_singl c)\n (Benton2004.const c)\n (Benton2004.const c))\n ]\nlet d_n = eval_equiv_const #int", "val emp_unit (p: vprop)\n : Lemma (((p `star` emp) `equiv` p) /\\ ((emp `star` p) `equiv` p))\n [SMTPatOr [[SMTPat (p `star` emp)]; [SMTPat (emp `star` p)]]]\nlet emp_unit (p:vprop)\n : Lemma (((p `star` emp) `equiv` p) /\\\n ((emp `star` p) `equiv` p))\n [SMTPatOr [[SMTPat (p `star` emp)];\n [SMTPat (emp `star` p)]]]\n = reveal_equiv (p `star` emp) p;\n reveal_equiv (emp `star` p) p;\n reveal_emp ();\n Steel.Memory.emp_unit (hp_of p);\n Steel.Memory.star_commutative Steel.Memory.emp (hp_of p)", "val star_commutative (p1 p2:slprop)\n : Lemma ((p1 `star` p2) `equiv` (p2 `star` p1))\nlet star_commutative (p1 p2:slprop) =\n H.star_commutative p1 p2", "val star_commutative (p1 p2:slprop)\n : Lemma ((p1 `star` p2) `equiv` (p2 `star` p1))\nlet star_commutative (p1 p2:slprop) =\n H.star_commutative p1 p2", "val d_lu1\n (b: exp bool)\n (c: computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (exec_equiv phi phi' (while b c) (while b c)))\n (ensures (exec_equiv phi phi' (while b c) (ifthenelse b (seq c (while b c)) skip)))\nlet d_lu1\n (b: exp bool)\n (c: computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (exec_equiv phi phi' (while b c) (while b c)))\n (ensures (exec_equiv phi phi' (while b c) (ifthenelse b (seq c (while b c)) skip)))\n= Benton2004.d_lu1 b c (interp phi) (interp phi')", "val elab_comp_close_commute (c: comp) (x: var)\n : Lemma (ensures elab_comp (close_comp c x) == RT.close_term (elab_comp c) x)\n [SMTPat (elab_comp (close_comp c x))]\nlet elab_comp_close_commute (c:comp) (x:var)\n : Lemma (ensures elab_comp (close_comp c x) == RT.close_term (elab_comp c) x)\n [SMTPat (elab_comp (close_comp c x))] =\n\n elab_comp_close_commute c x", "val st_equiv_pre (c1 c2: comp_st) : prop\nlet st_equiv_pre (c1 c2:comp_st)\n : prop\n = comp_u c1 == comp_u c2 /\\\n (match c1, c2 with\n | C_ST _, C_ST _ -> True\n | C_STAtomic inames1 obs1 _, C_STAtomic inames2 obs2 _ ->\n inames1 == inames2 /\\ obs1 == obs2\n | C_STGhost _, C_STGhost _ ->\n True\n | _, _ -> False)", "val eq_elim: #a:Type -> #len:size_nat -> s1:lseq a len -> s2:lseq a len ->\n Lemma\n (requires equal s1 s2)\n (ensures s1 == s2)\n [SMTPat (equal s1 s2)]\nlet eq_elim #a #len s1 s2 =\n assert (forall (i:nat{i < len}).{:pattern (Seq.index s1 i); (Seq.index s2 i)}\n index s1 i == index s2 i);\n Seq.lemma_eq_elim #a s1 s2", "val vprop_equiv_comm (p1 p2:vprop)\n : vprop_equiv (p1 ** p2) (p2 ** p1)\nlet vprop_equiv_comm (p1 p2:vprop)\n : vprop_equiv (p1 ** p2) (p2 ** p1)\n = slprop_equiv_comm p1 p2", "val ss_st_comp_commutes (s:st_comp) (ss:ss_t)\n : Lemma (ensures\n ss_st_comp s ss ==\n { s with res = ss_term s.res ss;\n pre = ss_term s.pre ss;\n post = ss_term s.post ss; }) // no shifting required\n [SMTPat (ss_st_comp s ss)]\nlet rec ss_st_comp_commutes (s:st_comp) (ss:ss_t)\n : Lemma (ensures\n ss_st_comp s ss ==\n { s with res = ss_term s.res ss;\n pre = ss_term s.pre ss;\n post = ss_term s.post ss; }) // no shifting required\n (decreases L.length ss.l)\n [SMTPat (ss_st_comp s ss)] =\n match ss.l with\n | [] -> ()\n | y::tl -> ss_st_comp_commutes (subst_st_comp s [ NT y (Map.sel ss.m y) ]) (tail ss)", "val subst_extensional: e:exp -> s1:sub -> s2:sub{feq s1 s2} ->\n Lemma (requires True) (ensures (subst e s1 = subst e s2))\n [SMTPat (subst e s1); SMTPat (subst e s2)]\nlet rec subst_extensional e s1 s2 =\n match e with\n | EVar _ -> ()\n | EAbs t e1 ->\n assert (subst (EAbs t e1) s1 == EAbs t (subst e1 (subst_eabs s1)))\n by T.norm [zeta; iota; delta_only [`%subst]];\n assert (subst (EAbs t e1) s2 == EAbs t (subst e1 (subst_eabs s2)))\n by T.norm [zeta; iota; delta_only [`%subst]];\n subst_extensional e1 (subst_eabs s1) (subst_eabs s2)\n | EApp e1 e2 -> subst_extensional e1 s1 s2; subst_extensional e2 s1 s2", "val vprop_equiv_assoc (p1 p2 p3:vprop)\n : vprop_equiv (p1 ** p2 ** p3) (p1 ** (p2 ** p3))\nlet vprop_equiv_assoc (p1 p2 p3:vprop)\n : vprop_equiv ((p1 ** p2) ** p3) (p1 ** (p2 ** p3))\n = slprop_equiv_assoc p1 p2 p3", "val star_commutative (p1 p2:vprop)\n : Lemma ((p1 `star` p2) `equiv` (p2 `star` p1))\nlet star_commutative p1 p2 = Mem.star_commutative (hp_of p1) (hp_of p2)", "val Benton2004.DDCC.d_b = c: Prims.bool -> p: Benton2004.DDCC.sttype\n -> FStar.Pervasives.Lemma\n (ensures\n Benton2004.eval_equiv p\n (Benton2004.DDCC.ns_singl c)\n (Benton2004.const c)\n (Benton2004.const c))\n [\n SMTPat (Benton2004.eval_equiv p\n (Benton2004.DDCC.ns_singl c)\n (Benton2004.const c)\n (Benton2004.const c))\n ]\nlet d_b = eval_equiv_const #bool", "val exec_equiv\n (gamma: context)\n (c: computation)\n (s: seclevel)\n: GTot Type0\nlet exec_equiv\n (gamma: context)\n (c: computation)\n (s: seclevel)\n: GTot Type0\n= Benton2004.DDCC.exec_equiv (interp_context gamma) (interp_context gamma) c (match s with Low -> c | High -> skip)", "val app_state_feq_transitive_aux (#adm: _) (st1 st2 st3: app_state adm)\n : Lemma (requires (app_state_feq st1 st2 /\\ app_state_feq st2 st3))\n (ensures (app_state_feq st1 st3))\nlet app_state_feq_transitive_aux (#adm) (st1 st2 st3: app_state adm)\n : Lemma (requires (app_state_feq st1 st2 /\\ app_state_feq st2 st3))\n (ensures (app_state_feq st1 st3))\n = let aux(k:_)\n : Lemma (ensures (st1 k = st3 k))\n = assert(st1 k = st2 k);\n assert(st2 k = st3 k)\n in\n forall_intro aux", "val Benton2004.DDCC.d_etr = \n p: Benton2004.DDCC.sttype ->\n e: Benton2004.DDCC.nstype _ ->\n f1: Benton2004.exp _ ->\n f2: Benton2004.exp _ ->\n f3: Benton2004.exp _\n -> FStar.Pervasives.Lemma\n (requires Benton2004.eval_equiv p e f1 f2 /\\ Benton2004.eval_equiv p e f2 f3)\n (ensures Benton2004.eval_equiv p e f1 f3)\nlet d_etr = eval_equiv_trans", "val elab_stt_equiv\n (g: R.env)\n (c: comp{C_ST? c})\n (pre post: R.term)\n (eq_pre: RT.equiv g pre (elab_term (comp_pre c)))\n (eq_post:\n RT.equiv g post (mk_abs (elab_term (comp_res c)) R.Q_Explicit (elab_term (comp_post c))))\n : RT.equiv g\n (let C_ST { u = u ; res = res } = c in\n mk_stt_comp u (elab_term res) pre post)\n (elab_comp c)\nlet elab_stt_equiv (g:R.env) (c:comp{C_ST? c}) (pre:R.term) (post:R.term)\n (eq_pre:RT.equiv g pre (elab_term (comp_pre c)))\n (eq_post:RT.equiv g post\n (mk_abs (elab_term (comp_res c)) R.Q_Explicit (elab_term (comp_post c))))\n : RT.equiv g\n (let C_ST {u;res} = c in\n mk_stt_comp u\n (elab_term res)\n pre\n post)\n (elab_comp c) =\n \n mk_stt_comp_equiv _\n (comp_u c)\n (elab_term (comp_res c))\n _ _ _ _ _ (RT.Rel_refl _ _ _) eq_pre eq_post", "val app_state_feq_transitive (#adm:_) (st1 st2 st3: app_state adm)\n : Lemma (ensures (app_state_feq st1 st2 ==> app_state_feq st2 st3 ==> app_state_feq st1 st3))\nlet app_state_feq_transitive (#adm) (st1 st2 st3: app_state adm)\n : Lemma (ensures (app_state_feq st1 st2 ==> app_state_feq st2 st3 ==> app_state_feq st1 st3))\n = introduce (app_state_feq st1 st2 /\\ app_state_feq st2 st3) ==> (app_state_feq st1 st3)\n with _. app_state_feq_transitive_aux st1 st2 st3", "val mem_equiv_eq (m0 m1: heap)\n : Lemma (requires m0 `mem_equiv` m1) (ensures m0 == m1) [SMTPat (m0 `mem_equiv` m1)]\nlet mem_equiv_eq (m0 m1:heap)\n : Lemma\n (requires\n m0 `mem_equiv` m1)\n (ensures\n m0 == m1)\n [SMTPat (m0 `mem_equiv` m1)]\n = F.extensionality _ _ m0 m1", "val mem_equiv_eq (m0 m1: heap)\n : Lemma (requires m0 `mem_equiv` m1) (ensures m0 == m1) [SMTPat (m0 `mem_equiv` m1)]\nlet mem_equiv_eq (m0 m1:heap)\n : Lemma\n (requires\n m0 `mem_equiv` m1)\n (ensures\n m0 == m1)\n [SMTPat (m0 `mem_equiv` m1)]\n = F.extensionality _ _ m0 m1", "val star_associative (p1 p2 p3:slprop)\n : Lemma ((p1 `star` (p2 `star` p3))\n `equiv`\n ((p1 `star` p2) `star` p3))\nlet star_associative (p1 p2 p3:slprop) =\n H.star_associative p1 p2 p3", "val star_associative (p1 p2 p3:slprop)\n : Lemma ((p1 `star` (p2 `star` p3))\n `equiv`\n ((p1 `star` p2) `star` p3))\nlet star_associative (p1 p2 p3:slprop) =\n H.star_associative p1 p2 p3", "val state_v_eq_lemma: #a:Spec.alg -> #m:m_spec -> h0:mem -> h1:mem -> st1:state_p a m -> st2:state_p a m ->\n Lemma (requires (as_seq h0 st1 == as_seq h1 st2))\n\t(ensures (state_v h0 st1 == state_v h1 st2))\n\t[SMTPat (state_v #a #m h0 st1); SMTPat (state_v #a #m h1 st2)]\nlet state_v_eq_lemma #a #m h0 h1 st1 st2 =\n assert (v (0ul *. row_len a m) == 0);\n LowStar.Monotonic.Buffer.as_seq_gsub #_ #(LowStar.Buffer.trivial_preorder (element_t a m)) #(LowStar.Buffer.trivial_preorder (element_t a m)) h0 st1 0ul (row_len a m)\n (LowStar.Buffer.trivial_preorder (element_t a m));\n assert (as_seq h0 (g_rowi st1 0ul) == Seq.slice (as_seq h0 st1) 0 (v (row_len a m)));\n assert (as_seq h0 (g_rowi st1 1ul) == Seq.slice (as_seq h0 st1) (v (1ul *. row_len a m)) (v (2ul *. row_len a m)));\n assert (as_seq h0 (g_rowi st1 2ul) == Seq.slice (as_seq h0 st1) (v (2ul *. row_len a m)) (v (3ul *. row_len a m)));\n assert (as_seq h0 (g_rowi st1 3ul) == Seq.slice (as_seq h0 st1) (v (3ul *. row_len a m)) (v (4ul *. row_len a m)));\n Lib.Sequence.eq_intro (as_seq h0 (g_rowi st1 0ul)) (as_seq h1 (g_rowi st2 0ul));\n Lib.Sequence.eq_intro (as_seq h0 (g_rowi st1 1ul)) (as_seq h1 (g_rowi st2 1ul));\n Lib.Sequence.eq_intro (as_seq h0 (g_rowi st1 2ul)) (as_seq h1 (g_rowi st2 2ul));\n Lib.Sequence.eq_intro (as_seq h0 (g_rowi st1 3ul)) (as_seq h1 (g_rowi st2 3ul));\n row_v_lemma h0 h1 (g_rowi st1 0ul) (g_rowi st2 0ul);\n Lib.Sequence.eq_intro (state_v h0 st1) (state_v h1 st2)", "val lemma_eq_elim: #a:Type -> s1:seq a -> s2:seq a -> Lemma\n (requires (equal s1 s2))\n (ensures (s1==s2))\n [SMTPat (equal s1 s2)]\nlet lemma_eq_elim #_ s1 s2 =\n assert ( length s1 == List.length (MkSeq?.l s1) );\n assert ( length s2 == List.length (MkSeq?.l s2) );\n assert ( forall (i: nat) . i < length s1 ==> index s1 i == List.index (MkSeq?.l s1) i);\n assert ( forall (i: nat) . i < length s1 ==> index s2 i == List.index (MkSeq?.l s2) i);\n List.index_extensionality (MkSeq?.l s1) (MkSeq?.l s2)", "val abides_app (#a: _) (l1 l2: list eff_label) (c: repr0 a 'st0 'st1)\n : Lemma (requires (abides (interp l1) c \\/ abides (interp l2) c))\n (ensures (abides (interp (l1 @ l2)) c))\n [SMTPat (abides (interp (l1 @ l2)) c)]\nlet rec abides_app #a (l1 l2 : list eff_label) (c : repr0 a 'st0 'st1)\n : Lemma (requires (abides (interp l1) c \\/ abides (interp l2) c))\n (ensures (abides (interp (l1@l2)) c))\n [SMTPat (abides (interp (l1@l2)) c)]\n = // GM: Just copied the proof from above since it ought to work,\n // do something smarter later.\n match c with\n | Return _ -> ()\n | Op a i k ->\n let sub o : Lemma (abides (interp (l1@l2)) (k o)) =\n abides_app l1 l2 (k o)\n in\n Classical.forall_intro sub", "val eval_code_eq_t (c: code) (f: fuel) (s1 s2: state)\n : Lemma (requires state_eq_S true s1 s2)\n (ensures state_eq_opt true (S.eval_code c f s1) (S.eval_code c f s2))\n [SMTPat (S.eval_code c f s1); SMTPat (S.eval_code c f s2)]\nlet eval_code_eq_t (c:code) (f:fuel) (s1 s2:state) : Lemma\n (requires state_eq_S true s1 s2)\n (ensures state_eq_opt true (S.eval_code c f s1) (S.eval_code c f s2))\n [SMTPat (S.eval_code c f s1); SMTPat (S.eval_code c f s2)]\n =\n eval_code_eq_core true c f s1; eval_code_eq_core true c f s2", "val exists_equiv (#a:_) (p:a -> vprop) (q:a -> vprop {forall x. equiv (p x) (q x) })\n : Lemma (h_exists p `equiv` h_exists q)\nlet exists_equiv p q =\n Classical.forall_intro_2 reveal_equiv;\n h_exists_cong (h_exists_sl' p) (h_exists_sl' q)", "val d_lu2\n (b: exp bool)\n (c: computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (exec_equiv phi phi' (while b c) (while b c)))\n (ensures (exec_equiv phi phi' (while b c) (while b (seq c (ifthenelse b c skip)))))\nlet d_lu2\n (b: exp bool)\n (c: computation)\n (phi phi' : gexp bool)\n: Lemma\n (requires (exec_equiv phi phi' (while b c) (while b c)))\n (ensures (exec_equiv phi phi' (while b c) (while b (seq c (ifthenelse b c skip)))))\n= Benton2004.d_lu2 b c (interp phi) (interp phi')", "val r_while\n (b b' : exp bool)\n (c c' : computation)\n (p: gexp bool)\n: Lemma\n (requires (\n exec_equiv (gand p (gand (exp_to_gexp b Left) (exp_to_gexp b' Right))) (gand p (geq (exp_to_gexp b Left) (exp_to_gexp b' Right))) c c'\n ))\n (ensures (\n exec_equiv (gand p (geq (exp_to_gexp b Left) (exp_to_gexp b' Right))) (gand p (gnot (gor (exp_to_gexp b Left) (exp_to_gexp b' Right)))) (while b c) (while b' c')\n ))\nlet rec r_while\n (b b' : exp bool)\n (c c' : computation)\n (p: gexp bool)\n: Lemma\n (requires (\n exec_equiv (gand p (gand (exp_to_gexp b Left) (exp_to_gexp b' Right))) (gand p (geq (exp_to_gexp b Left) (exp_to_gexp b' Right))) c c'\n ))\n (ensures (\n exec_equiv (gand p (geq (exp_to_gexp b Left) (exp_to_gexp b' Right))) (gand p (gnot (gor (exp_to_gexp b Left) (exp_to_gexp b' Right)))) (while b c) (while b' c')\n ))\n= let g (s0 s0':heap)\n :Lemma ((exec_equiv (gand p (gand (exp_to_gexp b Left) (exp_to_gexp b' Right))) (gand p (geq (exp_to_gexp b Left) (exp_to_gexp b' Right))) c c' /\\\n holds (interp (gand p (geq (exp_to_gexp b Left) (exp_to_gexp b' Right)))) s0 s0') ==>\n (terminates_on (reify_computation (while b c)) s0 <==>\n terminates_on (reify_computation (while b' c')) s0'))\n = Classical.move_requires (r_while_terminates b b' c c' p s0) s0'\n in\n let h (s0 s0':heap) (fuel:nat)\n :Lemma ((exec_equiv (gand p (gand (exp_to_gexp b Left) (exp_to_gexp b' Right))) (gand p (geq (exp_to_gexp b Left) (exp_to_gexp b' Right))) c c' /\\\n holds (interp (gand p (geq (exp_to_gexp b Left) (exp_to_gexp b' Right)))) s0 s0' /\\\n fst (reify_computation (while b c) fuel s0) == true /\\\n fst (reify_computation (while b' c') fuel s0') == true) ==>\n (holds (interp (gand p (gnot (gor (exp_to_gexp b Left) (exp_to_gexp b' Right))))) (snd (reify_computation (while b c) fuel s0)) (snd (reify_computation (while b' c') fuel s0'))))\n = Classical.move_requires (r_while_correct b b' c c' p s0 s0') fuel\n in\n Classical.forall_intro_2 g;\n Classical.forall_intro_3 h", "val conv (#a:Type u#a)\r\n (pre1:slprop)\r\n (pre2:slprop)\r\n (post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1:slprop_equiv pre1 pre2)\r\n (pf2:slprop_post_equiv post1 post2)\r\n: Lemma (stt a pre1 post1 == stt a pre2 post2)\nlet conv (#a:Type u#a)\r\n (pre1:slprop)\r\n (pre2:slprop)\r\n (post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1:slprop_equiv pre1 pre2)\r\n (pf2:slprop_post_equiv post1 post2)\r\n: Lemma (stt a pre1 post1 == stt a pre2 post2)\r\n= slprop_equiv_elim pre1 pre2;\r\n introduce forall x. post1 x == post2 x\r\n with slprop_equiv_elim (post1 x) (post2 x);\r\n Sem.conv #state a #pre1 #(F.on_dom _ post1) (F.on_dom _ post2);\r\n ()", "val eval_equiv_var_same\n (gamma: context)\n (x: var)\n (s: seclevel)\n: Lemma\n (requires (x `fresh_in` gamma))\n (ensures (\n x `fresh_in` gamma /\\\n eval_equiv ((x, s) :: gamma) (evar x) s\n ))\n [SMTPat (eval_equiv ((x, s)::gamma) (evar x) s)]\nlet eval_equiv_var_same\n (gamma: context)\n (x: var)\n (s: seclevel)\n: Lemma\n (requires (x `fresh_in` gamma))\n (ensures (\n x `fresh_in` gamma /\\\n eval_equiv ((x, s) :: gamma) (evar x) s\n ))\n [SMTPat (eval_equiv ((x, s)::gamma) (evar x) s)]\n= d_v x (interp_context gamma) (interp_seclevel int s)", "val valid_rewrite_refl (p: parser)\n : Lemma (valid_rewrite_prop p p) [SMTPat (valid_rewrite_prop p p)]\nlet valid_rewrite_refl\n (p: parser)\n: Lemma\n (valid_rewrite_prop p p)\n [SMTPat (valid_rewrite_prop p p)]\n= let x = tvalid_rewrite_of_evalid_rewrite #p #p #(fun _ -> True) #(fun x -> x) ({\n valid_rewrite_valid = (fun h b pos pos' -> ());\n valid_rewrite_size = (fun x -> ());\n })\n in\n ()", "val stt_vprop_equiv_closing (t0 t1: R.term) (x: var)\n : Lemma\n (RT.close_term (stt_vprop_equiv t0 t1) x ==\n stt_vprop_equiv (RT.close_term t0 x) (RT.close_term t1 x))\n [SMTPat (RT.close_term (stt_vprop_equiv t0 t1) x)]\nlet stt_vprop_equiv_closing (t0 t1:R.term) (x:var)\n : Lemma (RT.close_term (stt_vprop_equiv t0 t1) x ==\n stt_vprop_equiv (RT.close_term t0 x) (RT.close_term t1 x))\n [SMTPat (RT.close_term (stt_vprop_equiv t0 t1) x)]\n = RT.close_term_spec (stt_vprop_equiv t0 t1) x;\n RT.close_term_spec t0 x;\n RT.close_term_spec t1 x" ], "closest_src": [ { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.exec_equiv_trans" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.r_trans" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.exec_equiv_reified_trans" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.exec_equiv_flip" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.exec_equiv_flip" }, { "project_name": "FStar", "file_name": "Benton2004.SmithVolpano.fst", "name": "Benton2004.SmithVolpano.exec_equiv_seq" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.r_seq" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.d_seq" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.d_cc" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fsti", "name": "Benton2004.DDCC.d_ctr" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.r_sub" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.d_assoc" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.d_assoc" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.d_su1'" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.eval_equiv_trans" }, { "project_name": "FStar", "file_name": "DoublyLinkedList.fst", "name": "DoublyLinkedList.loc_equiv_trans" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.d_su1'" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.r_sym" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.d_cc" }, { "project_name": "steel", "file_name": "Pulse.Checker.Base.fst", "name": "Pulse.Checker.Base.st_equiv_trans" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.Examples.fst", "name": "Benton2004.RHL.Examples.d_su1'_flip" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.Derived.fst", "name": "Benton2004.RHL.Derived.d_su1'_flip" }, { "project_name": "FStar", "file_name": "FStar.Seq.Equiv.fst", "name": "FStar.Seq.Equiv.eq_of_seq_transitivity" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fsti", "name": "Benton2004.DDCC.exec_equiv" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.exec_equiv" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fsti", "name": "Benton2004.DDCC.d_csym" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.d_su1" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.eval_equiv_flip" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.d_su2" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.Examples.fst", "name": "Benton2004.DDCC.Examples.d_op_singl" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.d_bre" }, { "project_name": "FStar", "file_name": "Benton2004.SmithVolpano.fst", "name": "Benton2004.SmithVolpano.exec_equiv_assign" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.equiv_heap_iff_equiv" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.equiv_heap_iff_equiv" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.exec_equiv" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fst", "name": "Pulse.Checker.Prover.Substs.ss_comp_commutes" }, { "project_name": "FStar", "file_name": "Benton2004.SmithVolpano.fst", "name": "Benton2004.SmithVolpano.eval_equiv_const" }, { "project_name": "steel", "file_name": "Steel.Primitive.ForkJoin.Unix.fst", "name": "Steel.Primitive.ForkJoin.Unix.equiv_symmetric" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.exec_equiv_reified" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_trans" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_trans" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.per_holds_trans" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.vprop_equiv_trans" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fst", "name": "Pulse.Typing.Env.env_extends_trans" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.Derived.fst", "name": "Benton2004.RHL.Derived.r_ass_derived" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.vprop_equiv_cong" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fst", "name": "Pulse.Checker.Prover.Substs.nt_subst_comp_commutes" }, { "project_name": "steel", "file_name": "Pulse.Checker.Base.fst", "name": "Pulse.Checker.Base.t_equiv" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.r_cbl" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.star_congruence" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.star_congruence" }, { "project_name": "FStar", "file_name": "Benton2004.SmithVolpano.fst", "name": "Benton2004.SmithVolpano.eval_equiv_op" }, { "project_name": "zeta", "file_name": "Zeta.AppSimulate.Helper.fst", "name": "Zeta.AppSimulate.Helper.app_state_feq_commutative" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fsti", "name": "Benton2004.DDCC.d_kbf" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.star_congruence" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fsti", "name": "Benton2004.DDCC.d_kbt" }, { "project_name": "FStar", "file_name": "DoublyLinkedList.fst", "name": "DoublyLinkedList.loc_equiv_union_union_loc" }, { "project_name": "steel", "file_name": "OWGCounterInv.fst", "name": "OWGCounterInv.inv_equiv_lemma" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Random.fst", "name": "FStar.DM4F.Random.pr_eq" }, { "project_name": "FStar", "file_name": "FStar.DM4F.OTP.Random.fst", "name": "FStar.DM4F.OTP.Random.pr_eq" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.includes_trans" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.exists_equiv" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.r_skip" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.r_if" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.conv_stt" }, { "project_name": "steel", "file_name": "Pulse.Typing.FV.fst", "name": "Pulse.Typing.FV.st_equiv_freevars" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fsti", "name": "Benton2004.DDCC.d_n" }, { "project_name": "steel", "file_name": "Steel.Utils.fst", "name": "Steel.Utils.emp_unit" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.star_commutative" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.star_commutative" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.d_lu1" }, { "project_name": "steel", "file_name": "Pulse.Soundness.Common.fst", "name": "Pulse.Soundness.Common.elab_comp_close_commute" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.st_equiv_pre" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.eq_elim" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.vprop_equiv_comm" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fst", "name": "Pulse.Checker.Prover.Substs.ss_st_comp_commutes" }, { "project_name": "FStar", "file_name": "ParSubst.fst", "name": "ParSubst.subst_extensional" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.vprop_equiv_assoc" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.star_commutative" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fsti", "name": "Benton2004.DDCC.d_b" }, { "project_name": "FStar", "file_name": "Benton2004.SmithVolpano.fst", "name": "Benton2004.SmithVolpano.exec_equiv" }, { "project_name": "zeta", "file_name": "Zeta.AppSimulate.Helper.fst", "name": "Zeta.AppSimulate.Helper.app_state_feq_transitive_aux" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fsti", "name": "Benton2004.DDCC.d_etr" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.Pure.fst", "name": "Pulse.Elaborate.Pure.elab_stt_equiv" }, { "project_name": "zeta", "file_name": "Zeta.AppSimulate.Helper.fst", "name": "Zeta.AppSimulate.Helper.app_state_feq_transitive" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.mem_equiv_eq" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.mem_equiv_eq" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.star_associative" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.star_associative" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Blake2.Core.fst", "name": "Hacl.Impl.Blake2.Core.state_v_eq_lemma" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.lemma_eq_elim" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.abides_app" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Lemmas.fst", "name": "Vale.PPC64LE.Lemmas.eval_code_eq_t" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.exists_equiv" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.d_lu2" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.r_while" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.conv" }, { "project_name": "FStar", "file_name": "Benton2004.SmithVolpano.fst", "name": "Benton2004.SmithVolpano.eval_equiv_var_same" }, { "project_name": "FStar", "file_name": "LowParseWriters.NoHoare.fst", "name": "LowParseWriters.NoHoare.valid_rewrite_refl" }, { "project_name": "steel", "file_name": "Pulse.Soundness.STEquiv.fst", "name": "Pulse.Soundness.STEquiv.stt_vprop_equiv_closing" } ], "selected_premises": [ "Benton2004.reify_raw_computation", "Benton2004.DDCC.exec_equiv_reified_trans", "Benton2004.flip", "Benton2004.DDCC.terminates_equiv_reified", "Benton2004.DDCC.exec_equiv_reified", "Benton2004.holds_flip", "FStar.DM4F.IntStoreFixed.post", "Benton2004.eop", "Benton2004.d_lu1", "Benton2004.d_lu2", "Benton2004.d_seq_terminates_recip", "Benton2004.eval_equiv_trans", "Benton2004.interpolable_elim", "Benton2004.skip", "Benton2004.mention", "Benton2004.d_seq_terminates", "FStar.Pervasives.reveal_opaque", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "Benton2004.exec_equiv", "Benton2004.exec_equiv_reified_trans", "Benton2004.exec_equiv_reified", "Benton2004.DDCC.eval_equiv_trans", "Benton2004.const", "Benton2004.reify_computation", "Benton2004.terminates_equiv_reified", "Benton2004.terminates_on", "Benton2004.intersect", "FStar.DM4F.IntStoreFixed.pre", "Benton2004.reify_exp", "Benton2004.eval_equiv", "Benton2004.DDCC.eval_equiv_sym", "Benton2004.d_assoc", "Benton2004.evar", "FStar.DM4F.IntStoreFixed.repr", "Benton2004.reified_exp", "FStar.DM4F.IntStoreFixed.op_Colon_equals", "Benton2004.fuel_monotonic", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "Benton2004.DDCC.eval_equiv_reified", "Benton2004.interpolable", "Benton2004.eval_equiv_reified", "Benton2004.is_per", "Benton2004.while_raw", "FStar.DM4F.IntStoreFixedReader.get", "Benton2004.exec_equiv_flip", "Benton2004.assign", "Benton2004.included", "FStar.DM4F.Heap.IntStoreFixed.sel", "Benton2004.exec_equiv_trans", "Benton2004.DDCC.exec_equiv_sym", "FStar.DM4F.Heap.IntStoreFixed.store_size", "Benton2004.d_seq", "FStar.DM4F.IntStoreFixed.iget", "Benton2004.d_su1'", "Benton2004.DDCC.holds_st_nil", "Benton2004.d_bre", "Benton2004.d_cc", "Benton2004.DDCC.holds_ns_delta", "Benton2004.holds_flip'", "Benton2004.eval_equiv_flip", "Benton2004.per_holds_trans", "FStar.DM4F.IntStoreFixedReader.bind_isr", "Benton2004.DDCC.holds_ns_f", "Benton2004.DDCC.holds_ns_t", "FStar.DM4F.IntStoreFixed.wp", "FStar.Pervasives.ex_pre", "FStar.DM4F.IntStoreFixed.lift_int_store_reader_int_store_wp", "FStar.Pervasives.ex_post'", "Benton2004.while", "FStar.DM4F.IntStoreFixed.bind_is", "FStar.Pervasives.st_post_h", "Benton2004.is_per_holds_sym", "FStar.DM4F.IntStoreFixed.return_is", "FStar.DM4F.IntStoreFixedReader.return_isr", "FStar.Pervasives.id", "FStar.Pervasives.ex_post", "Benton2004.DDCC.holds_ns_singl", "Benton2004.holds_intersect", "FStar.Pervasives.ex_stronger", "FStar.Pervasives.ex_bind_wp", "FStar.Pervasives.pure_close_wp", "Benton2004.DDCC.holds_st_var", "FStar.Pervasives.pure_ite_wp", "FStar.Pervasives.st_pre_h", "FStar.Pervasives.pure_bind_wp", "FStar.Pervasives.ex_return", "FStar.Pervasives.st_post_h'", "Prims.pure_post'", "FStar.Pervasives.ex_wp", "Prims.pow2", "FStar.Pervasives.st_bind_wp", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.ex_trivial", "FStar.Pervasives.all_post_h'", "FStar.Pervasives.all_post_h", "Prims.op_Hat", "FStar.Pervasives.trivial_pure_post", "FStar.Pervasives.coerce_eq" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule Benton2004.DDCC\n\nlet holds_ns_f (#t: Type0) (x y: t): Lemma\n (holds ns_f x y <==> False)\n [SMTPat (holds ns_f x y)]\n= holds_equiv ns_f x y\n\nlet holds_ns_t (#t: Type0) (x y: t): Lemma\n (holds ns_t x y <==> True)\n [SMTPat (holds ns_t x y)]\n= holds_equiv ns_t x y\n\nlet holds_ns_singl (#t: Type0) (c: t) (x y: t) : Lemma\n (holds (ns_singl c) x y <==> (x == c /\\ y == c))\n [SMTPat (holds (ns_singl c) x y)]\n= holds_equiv (ns_singl c) x y\n\nlet holds_ns_delta (#t: Type0) (x y : t) : Lemma\n (holds ns_delta x y <==> x == y)\n [SMTPat (holds ns_delta x y)]\n= holds_equiv ns_delta x y\n\nlet interpolable_ns_f #t : Lemma (interpolable #t ns_f) = ()\nlet interpolable_ns_t #t : Lemma (interpolable #t ns_t) = ()\nlet interpolable_ns_singl #t (c: t) : Lemma (interpolable (ns_singl c)) = ()\nlet interpolable_ns_delta #t : Lemma (interpolable #t ns_delta) = ()\n\n#set-options \"--z3rlimit 20 --max_fuel 2 --max_ifuel 1 --z3cliopt smt.qi.eager_threshold=100\"\n\nlet holds_st_nil\n (x y: heap)\n: Lemma\n (holds st_nil x y <==> True)\n [SMTPat (holds st_nil x y)]\n= Classical.forall_intro_2 (holds_equiv st_nil)\n\nlet holds_st_var\n (x: var)\n (v: nstype int)\n (a b: heap)\n: Lemma\n (holds (st_var x v) a b <==> holds v (sel a x) (sel b x))\n [SMTPat (holds (st_var x v) a b)]\n= holds_equiv (st_var x v) a b\n\nlet holds_st_intersect\n (ns1 ns2: sttype)\n (x y: heap)\n: Lemma\n (holds (st_intersect ns1 ns2) x y <==> (holds ns1 x y /\\ holds ns2 x y))\n [SMTPat (holds (st_intersect ns1 ns2) x y)]\n= ()\n\nlet st_fresh_in_nil\n (x: var)\n: Lemma\n (x `st_fresh_in` st_nil)\n= ()\n\nlet st_fresh_in_var\n (x: var)\n (v: nstype int)\n (y: var)\n: Lemma\n (requires (y <> x))\n (ensures (y `st_fresh_in` (st_var x v)))\n= ()\n\nlet st_fresh_in_intersect\n (x: var)\n (p1 p2: sttype)\n: Lemma\n (requires (\n x `st_fresh_in` p1 /\\\n x `st_fresh_in` p2\n ))\n (ensures (x `st_fresh_in` (st_intersect p1 p2)))\n= ()\n\nlet st_fresh_in_cons\n (p: sttype)\n (x: var)\n (v: nstype int)\n (y: var)\n: Lemma\n (requires (\n x `st_fresh_in` p /\\\n y `st_fresh_in` p /\\\n x <> y\n ))\n (ensures (\n x `st_fresh_in` p /\\\n y `st_fresh_in` (st_cons p x v)\n ))\n= ()\n\nlet subtype_ns_f (#t: Type0) (phi: nstype t) : Lemma\n (included ns_f phi)\n= ()\n\nlet subtype_ns_singl_delta (#t: Type0) (c: t) : Lemma\n (ns_singl c `included` ns_delta)\n= ()\n\nlet subtype_ns_t (#t: Type0) (phi: nstype t) : Lemma\n (included phi ns_t)\n= ()\n\nlet subtype_st_nil (phi: sttype) : Lemma\n (included phi st_nil)\n= ()\n\nlet subtype_st_f (phi phi' : sttype) (x: var) : Lemma\n (requires (x `st_fresh_in` phi))\n (ensures (x `st_fresh_in` phi /\\ included (st_cons phi x ns_f) phi'))\n= ()\n\nlet subtype_st_t (phi phi' : sttype) (x: var) : Lemma\n (requires (x `st_fresh_in` phi' /\\ included phi phi'))\n (ensures (x `st_fresh_in` phi' /\\ included phi (st_cons phi' x ns_t)))\n= ()\n\nlet subtype_st_cons (phi phi' : sttype) (f f' : nstype int) (x: var) : Lemma\n (requires (\n included phi phi' /\\\n included f f' /\\\n x `st_fresh_in` phi /\\\n x `st_fresh_in` phi'\n ))\n (ensures (\n x `st_fresh_in` phi /\\\n x `st_fresh_in` phi' /\\\n included (st_cons phi x f) (st_cons phi' x f')\n ))\n= ()\n\nlet eval_equiv_reified\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': reified_exp t)\n: GTot Type0\n= Benton2004.eval_equiv_reified p e f f'\n\nlet eval_equiv_reified_elim\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': reified_exp t)\n (s s' : heap)\n: Lemma\n (requires (eval_equiv_reified p e f f' /\\ holds p s s'))\n (ensures (holds e (fst (f s)) (fst (f' s'))))\n= ()\n\nlet terminates_equiv_reified\n (p : sttype)\n (f f' : reified_computation)\n: GTot Type0\n= Benton2004.terminates_equiv_reified p f f'\n\nlet terminates_equiv_reified_elim\n (p : sttype)\n (f f' : reified_computation)\n (s s' : heap)\n: Lemma\n (requires (terminates_equiv_reified p f f' /\\ holds p s s'))\n (ensures (terminates_on f s <==> terminates_on f' s'))\n= ()\n\nlet exec_equiv_reified\n (p p' : sttype)\n (f f' : reified_computation)\n: GTot Type0\n= Benton2004.exec_equiv_reified p p' f f'\n\nlet exec_equiv_reified_terminates\n (p p' : sttype)\n (f f' : reified_computation)\n: Lemma\n (requires (exec_equiv_reified p p' f f'))\n (ensures (terminates_equiv_reified p f f'))\n= ()\n\nlet exec_equiv_reified_elim\n (p p' : sttype)\n (f f' : reified_computation)\n (s s' : heap)\n (fuel: nat)\n: Lemma\n (requires (exec_equiv_reified p p' f f' /\\ holds p s s' /\\ fst (f fuel s) == true /\\ fst (f' fuel s') == true))\n (ensures (holds p' (snd (f fuel s)) (snd (f' fuel s'))))\n= ()\n\nlet eval_equiv_sym\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': exp t)\n: Lemma\n (requires (eval_equiv p e f f'))\n (ensures (eval_equiv p e f' f))\n= Benton2004.eval_equiv_sym p e f f'\n\nlet exec_equiv_sym\n (p p': sttype)\n (f f' : computation)\n: Lemma\n (exec_equiv p p' f f' <==> exec_equiv p p' f' f)\n [SMTPat (exec_equiv p p' f f')]\n= Benton2004.exec_equiv_sym p p' f f'\n\nlet eval_equiv_trans\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f1 f2 f3 : exp t)\n: Lemma\n (requires (eval_equiv p e f1 f2 /\\ eval_equiv p e f2 f3))\n (ensures (eval_equiv p e f1 f3))\n= Benton2004.eval_equiv_trans p e f1 f2 f3\n\nlet exec_equiv_reified_trans\n (p p': sttype)\n (f1 f2 f3 : reified_computation)\n: Lemma\n (requires (exec_equiv_reified p p' f1 f2 /\\ exec_equiv_reified p p' f2 f3))\n (ensures (exec_equiv_reified p p' f1 f3))\n= Benton2004.exec_equiv_reified_trans p p' f1 f2 f3\n", "sketch": [ "Step 1: We start by assuming the premises of the lemma, namely that `exec_equiv p p' c1 c2` and `exec_equiv p p' c2 c3` hold.\nStep 2: We need to show that `exec_equiv p p' c1 c3` holds under these assumptions.\nStep 3: Use the transitivity property of `exec_equiv_reified` to combine the equivalences of `c1` to `c2` and `c2` to `c3` into an equivalence of `c1` to `c3`.\nStep 4: Conclude that `exec_equiv p p' c1 c3` holds by the definition of `exec_equiv`.", "Step 1: Assume the premises `exec_equiv p p' c1 c2` and `exec_equiv p p' c2 c3`.\nStep 2: Use the transitivity property of `exec_equiv_reified` to show that `exec_equiv_reified p p' (reify c1) (reify c3)` holds.\nStep 3: Conclude that `exec_equiv p p' c1 c3` holds by the definition of `exec_equiv`.", "Step 1: Assume the premises `exec_equiv p p' c1 c2` and `exec_equiv p p' c2 c3`.\nStep 2: Use the transitivity property of `exec_equiv_reified` to show that `exec_equiv_reified p p' (reify c1) (reify c3)` holds.\nStep 3: Conclude that `exec_equiv p p' c1 c3` holds by the definition of `exec_equiv`.", "Step 1: We start by assuming the premises of the lemma, i.e., `exec_equiv p p' c1 c2` and `exec_equiv p p' c2 c3`.\nStep 2: We need to show that `exec_equiv p p' c1 c3` holds under these assumptions.\nStep 3: Use the transitivity property of `exec_equiv_reified` to combine the equivalences of `c1` to `c2` and `c2` to `c3`.\nStep 4: Conclude that `exec_equiv p p' c1 c3` holds by the definition of `exec_equiv`.", "Step 1: We start by using the transitivity property of `exec_equiv_reified` to show that if `exec_equiv_reified p p' c1 c2` and `exec_equiv_reified p p' c2 c3` hold, then `exec_equiv_reified p p' c1 c3` must also hold.\nStep 2: We then use the definition of `exec_equiv` to relate it to `exec_equiv_reified`, ensuring that the equivalence holds for the original computations `c1`, `c2`, and `c3`.\nStep 3: Finally, we conclude that `exec_equiv p p' c1 c3` holds by the transitivity property established in Step 1 and the equivalence definitions used in Step 2.", "Step 1: Assume the premises `exec_equiv p p' c1 c2` and `exec_equiv p p' c2 c3`.\nStep 2: Use the transitivity property of `exec_equiv_reified` to show that `exec_equiv_reified p p' (reify c1) (reify c3)` holds.\nStep 3: Conclude that `exec_equiv p p' c1 c3` holds by the definition of `exec_equiv`.", "Step 1: We start by assuming the requirements of the lemma, which are `exec_equiv p p' c1 c2` and `exec_equiv p p' c2 c3`.\nStep 2: We need to show that `exec_equiv p p' c1 c3` holds.\nStep 3: Use the transitivity property of `exec_equiv_reified` to combine the equivalences of `c1` to `c2` and `c2` to `c3`.\nStep 4: Conclude that `exec_equiv p p' c1 c3` holds by the definition of `exec_equiv`.", "Step 1: Use the transitivity property of `exec_equiv_reified` to show that if `exec_equiv_reified p p' c1 c2` and `exec_equiv_reified p p' c2 c3` hold, then `exec_equiv_reified p p' c1 c3` also holds.\nStep 2: Conclude that `exec_equiv p p' c1 c3` holds by the definition of `exec_equiv`.", "Step 1: Assume the premises `exec_equiv p p' c1 c2` and `exec_equiv p p' c2 c3`.\nStep 2: Use the transitivity property of `exec_equiv_reified` to show that `exec_equiv_reified p p' (reify c1) (reify c3)` holds.\nStep 3: Conclude that `exec_equiv p p' c1 c3` holds by the definition of `exec_equiv`.", "Step 1: Use the transitivity property of `exec_equiv_reified` to show that if `exec_equiv_reified p p' c1 c2` and `exec_equiv_reified p p' c2 c3` hold, then `exec_equiv_reified p p' c1 c3` also holds.\nStep 2: Use the definition of `exec_equiv` to relate `exec_equiv_reified` to `exec_equiv`.\nStep 3: Conclude that `exec_equiv p p' c1 c3` holds by combining the results from the previous steps." ], "generated_solution": [ "= let trans = Benton2004.exec_equiv_reified_trans p p' in\n fun (H1: exec_equiv p p' c1 c2) (H2: exec_equiv p p' c2 c3) ->\n trans c1 c2 c3 H1 H2", "let exec_equiv_trans (p p' : sttype) (c1 c2 c3 : computation) : Lemma\n (requires (\n exec_equiv p p' c1 c2 /\\\n exec_equiv p p' c2 c3\n ))\n (ensures (exec_equiv p p' c1 c3))\n [SMTPatOr [\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c2 c3)];\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c1 c3)];\n [SMTPat (exec_equiv p p' c2 c3); SMTPat (exec_equiv p p' c1 c3)];\n ]]\n= \n let reified_c1 = reify c1 in\n let reified_c2 = reify c2 in\n let reified_c3 = reify c3 in\n exec_equiv_reified_trans p p' reified_c1 reified_c2 reified_c3", "let exec_equiv_trans\n (p p' : sttype)\n (c1 c2 c3 : computation)\n: Lemma\n (requires (\n exec_equiv p p' c1 c2 /\\\n exec_equiv p p' c2 c3\n ))\n (ensures (exec_equiv p p' c1 c3))\n [SMTPatOr [\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c2 c3)];\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c1 c3)];\n [SMTPat (exec_equiv p p' c2 c3); SMTPat (exec_equiv p p' c1 c3)];\n ]]\n= \n let reified_c1 = reify c1 in\n let reified_c2 = reify c2 in\n let reified_c3 = reify c3 in\n exec_equiv_reified_trans p p' reified_c1 reified_c2 reified_c3", "= let _ = exec_equiv_reified_trans p p' (reify c1) (reify c2) (reify c3) in\n ()", "= let trans = Benton2004.exec_equiv_reified_trans p p' c1 c2 c3 in\n trans", "let exec_equiv_trans (p p' : sttype) (c1 c2 c3 : computation) : Lemma\n (requires (\n exec_equiv p p' c1 c2 /\\\n exec_equiv p p' c2 c3\n ))\n (ensures (exec_equiv p p' c1 c3))\n [SMTPatOr [\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c2 c3)];\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c1 c3)];\n [SMTPat (exec_equiv p p' c2 c3); SMTPat (exec_equiv p p' c1 c3)];\n ]]\n= \n let _ = assert (exec_equiv_reified p p' (reify c1) (reify c2)) in\n let _ = assert (exec_equiv_reified p p' (reify c2) (reify c3)) in\n let _ = exec_equiv_reified_trans p p' (reify c1) (reify c2) (reify c3) in\n ()", "= exec_equiv_reified_trans p p' c1 c2 c3", "= exec_equiv_reified_trans p p' c1 c2 c3", "let exec_equiv_trans (p p' : sttype) (c1 c2 c3 : computation) : Lemma\n (requires (\n exec_equiv p p' c1 c2 /\\\n exec_equiv p p' c2 c3\n ))\n (ensures (exec_equiv p p' c1 c3))\n [SMTPatOr [\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c2 c3)];\n [SMTPat (exec_equiv p p' c1 c2); SMTPat (exec_equiv p p' c1 c3)];\n [SMTPat (exec_equiv p p' c2 c3); SMTPat (exec_equiv p p' c1 c3)];\n ]]\n= \n let _ = exec_equiv_reified_trans p p' (reify c1) (reify c2) (reify c3) in\n ()", "= let trans = Benton2004.exec_equiv_reified_trans p p' c1 c2 c3 in\n trans" ] }, { "file_name": "PulseCore.Heap.fsti", "name": "PulseCore.Heap.full_heap", "opens_and_abbrevs": [ { "open": "FStar.PCM" }, { "open": "FStar.Ghost" }, { "open": "PulseCore" }, { "open": "PulseCore" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let full_heap = h:heap { full_heap_pred h }", "source_range": { "start_line": 382, "start_col": 0, "end_line": 382, "end_col": 43 }, "interleaved": false, "definition": "h: PulseCore.Heap.heap{PulseCore.Heap.full_heap_pred h}", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "PulseCore.Heap.heap", "PulseCore.Heap.full_heap_pred" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "Type", "prompt": "let full_heap =\n ", "expected_response": "h: heap{full_heap_pred h}", "source": { "project_name": "steel", "file_name": "lib/pulse_core/PulseCore.Heap.fsti", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "PulseCore.Heap.fsti", "checked_file": "dataset/PulseCore.Heap.fsti.checked", "interface_file": false, "dependencies": [ "dataset/PulseCore.Preorder.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Universe.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.PCM.fst.checked", "dataset/FStar.Ghost.fsti.checked" ] }, "definitions_in_context": [ "val heap : Type u#(a + 1)", "val empty_heap : heap u#a", "val core_ref : Type u#0", "let ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref", "val core_ref_null : core_ref", "let null (#a:Type u#a) (#pcm:pcm a) : ref a pcm = core_ref_null", "val core_ref_is_null (r:core_ref) : b:bool { b <==> r == core_ref_null }", "let is_null (#a:Type u#a) (#pcm:pcm a) (r:ref a pcm) : (b:bool{b <==> r == null}) = core_ref_is_null r", "val disjoint (h0 h1:heap u#h) : prop", "val disjoint_sym (h0 h1:heap u#h)\n : Lemma (disjoint h0 h1 <==> disjoint h1 h0)\n [SMTPat (disjoint h0 h1)]", "val join (h0:heap u#h) (h1:heap u#h{disjoint h0 h1}) : heap u#h", "val join_commutative (h0 h1:heap)\n : Lemma\n (requires\n disjoint h0 h1)\n (ensures\n (disjoint h1 h0 /\\\n join h0 h1 == join h1 h0))", "val disjoint_join (h0 h1 h2:heap)\n : Lemma (disjoint h1 h2 /\\\n disjoint h0 (join h1 h2) ==>\n disjoint h0 h1 /\\\n disjoint h0 h2 /\\\n disjoint (join h0 h1) h2 /\\\n disjoint (join h0 h2) h1)", "val join_associative (h0 h1 h2:heap)\n : Lemma\n (requires\n disjoint h1 h2 /\\\n disjoint h0 (join h1 h2))\n (ensures\n (disjoint h0 h1 /\\\n disjoint (join h0 h1) h2 /\\\n join h0 (join h1 h2) == join (join h0 h1) h2))", "let heap_prop_is_affine (p:heap u#a -> prop) : prop =\n forall (h0 h1: heap u#a). p h0 /\\ disjoint h0 h1 ==> p (join h0 h1)", "let a_heap_prop = p:(heap -> prop) { heap_prop_is_affine p }", "val slprop : Type u#(a + 1)", "val interp (p:slprop u#a) (m:heap u#a) : prop", "val as_slprop (f:a_heap_prop) : p:slprop{forall h.interp p h <==> f h}", "let hprop (fp:slprop u#a) =\n q:(heap u#a -> prop){\n forall (h0:heap{interp fp h0}) (h1:heap{disjoint h0 h1}).\n q h0 <==> q (join h0 h1)\n }", "let hheap (p:slprop u#a) = m:heap u#a {interp p m}", "let equiv (p1 p2:slprop) =\n forall m. interp p1 m <==> interp p2 m", "val slprop_extensionality (p q:slprop)\n : Lemma\n (requires p `equiv` q)\n (ensures p == q)", "val emp : slprop u#a", "val pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a", "val h_and (p1 p2:slprop u#a) : slprop u#a", "val h_or (p1 p2:slprop u#a) : slprop u#a", "val star (p1 p2:slprop u#a) : slprop u#a", "val wand (p1 p2:slprop u#a) : slprop u#a", "val h_exists (#[@@@strictly_positive] a:Type u#b)\n ([@@@strictly_positive] f: (a -> slprop u#a))\n : slprop u#a", "val h_forall (#a:Type u#b) (f: (a -> slprop u#a)) : slprop u#a", "val h_refine (p:slprop u#a) (r:a_heap_prop u#a) : slprop u#a", "val affine_star (p q:slprop) (h:heap)\n : Lemma ((interp (p `star` q) h ==> interp p h /\\ interp q h))", "val equiv_symmetric (p1 p2:slprop)\n : squash (p1 `equiv` p2 ==> p2 `equiv` p1)", "val equiv_extensional_on_star (p1 p2 p3:slprop)\n : squash (p1 `equiv` p2 ==> (p1 `star` p3) `equiv` (p2 `star` p3))", "val emp_unit (p:slprop)\n : Lemma (p `equiv` (p `star` emp))", "val intro_emp (h:heap)\n : Lemma (interp emp h)", "val h_exists_cong (#a:Type) (p q : a -> slprop)\n : Lemma\n (requires (forall x. p x `equiv` q x))\n (ensures (h_exists p `equiv` h_exists q))", "val intro_h_exists (#a:_) (x:a) (p:a -> slprop) (h:heap)\n : Lemma (interp (p x) h ==> interp (h_exists p) h)", "val elim_h_exists (#a:_) (p:a -> slprop) (h:heap)\n : Lemma (interp (h_exists p) h ==> (exists x. interp (p x) h))", "val interp_depends_only_on (hp:slprop u#a)\n : Lemma\n (forall (h0:hheap hp) (h1:heap u#a{disjoint h0 h1}).\n interp hp h0 <==> interp hp (join h0 h1))", "let ptr (#a: Type u#a) (#pcm: pcm a) (r:ref a pcm) =\n h_exists (pts_to r)", "val pts_to_compatible\n (#a:Type u#a)\n (#pcm: pcm a)\n (x:ref a pcm)\n (v0 v1:a)\n (h:heap u#a)\n : Lemma\n (interp (pts_to x v0 `star` pts_to x v1) h\n <==>\n (composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) h))", "val pts_to_join (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures joinable pcm v1 v2)", "val pts_to_join' (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures (exists z. compatible pcm v1 z /\\ compatible pcm v2 z /\\\n interp (pts_to r z) m))", "val pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))", "val pts_to_not_null (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v:a)\n (m:heap)\n : Lemma (requires interp (pts_to x v) m)\n (ensures x =!= null)", "val intro_star (p q:slprop) (hp:hheap p) (hq:hheap q)\n : Lemma\n (requires disjoint hp hq)\n (ensures interp (p `star` q) (join hp hq))", "val elim_star (p q:slprop) (h:hheap (p `star` q))\n : Lemma\n (requires interp (p `star` q) h)\n (ensures exists hl hr.\n disjoint hl hr /\\\n h == join hl hr /\\\n interp p hl /\\\n interp q hr)", "val star_commutative (p1 p2:slprop)\n : Lemma ((p1 `star` p2) `equiv` (p2 `star` p1))", "val star_associative (p1 p2 p3:slprop)\n : Lemma (\n (p1 `star` (p2 `star` p3))\n `equiv`\n ((p1 `star` p2) `star` p3)\n )", "val star_congruence (p1 p2 p3 p4:slprop)\n : Lemma (requires p1 `equiv` p3 /\\ p2 `equiv` p4)\n (ensures (p1 `star` p2) `equiv` (p3 `star` p4))", "val refine_interp (p:slprop u#a) (q:a_heap_prop u#a) (h:heap u#a)\n : Lemma (interp p h /\\ q h <==> interp (h_refine p q) h)", "val refine_equiv (p0 p1:slprop u#a) (q0 q1:a_heap_prop u#a)\n : Lemma (p0 `equiv` p1 /\\ (forall h. q0 h <==> q1 h) ==>\n equiv (h_refine p0 q0) (h_refine p1 q1))", "let pure (p:prop) = h_refine emp (fun _ -> p)", "val pure_equiv (p q:prop)\n : Lemma ((p <==> q) ==> (pure p `equiv` pure q))", "val pure_interp (q:prop) (h:heap u#a)\n : Lemma (interp (pure q) h <==> q)", "val pure_star_interp (p:slprop u#a) (q:prop) (h:heap u#a)\n : Lemma (interp (p `star` pure q) h <==>\n interp (p `star` emp) h /\\ q)", "let stronger (p q:slprop) =\n forall h. interp p h ==> interp q h", "val stronger_star (p q r:slprop)\n : Lemma (stronger q r ==> stronger (p `star` q) (p `star` r))", "val weaken (p q r:slprop) (h:heap u#a)\n : Lemma (q `stronger` r /\\ interp (p `star` q) h ==> interp (p `star` r) h)", "val full_heap_pred : heap -> prop" ], "closest": [ "val PulseCore.Memory.full_mem = Type\nlet full_mem = m:mem{full_mem_pred m}", "val Steel.Heap.full_heap = Type\nlet full_heap = h:heap { full_heap_pred h }", "val Vale.X64.Memory.vale_full_heap = Type\nlet vale_full_heap = vale_full_heap", "val Vale.PPC64LE.Memory.vale_full_heap = Type\nlet vale_full_heap = vale_full_heap", "val PulseCore.Heap.addr = Type0\nlet addr = nat", "val Vale.X64.Decls.vale_full_heap = Type\nlet vale_full_heap = M.vale_full_heap", "val Vale.PPC64LE.Decls.vale_full_heap = Type\nlet vale_full_heap = M.vale_full_heap", "val Vale.X64.Memory.vale_heap = Type\nlet vale_heap = vale_heap", "val Vale.PPC64LE.Memory.vale_heap = Type\nlet vale_heap = vale_heap", "val Steel.Memory.full_mem = Type\nlet full_mem = m:mem{full_mem_pred m}", "val Vale.X64.InsBasic.vale_heap = Type\nlet vale_heap = Vale.X64.Memory.vale_heap", "val Vale.X64.Decls.vale_heap = Type\nlet vale_heap = M.vale_heap", "val Steel.Heap.full_hheap = fp: Steel.Heap.slprop -> Type\nlet full_hheap fp = h:hheap fp { full_heap_pred h }", "val Steel.Heap.a_heap_prop = Type\nlet a_heap_prop = p:(heap -> prop) { heap_prop_is_affine p }", "val Vale.PPC64LE.Memory.heaplet_id = Type0\nlet heaplet_id = heaplet_id", "val DoublyLinkedList.heap = Type\nlet heap = HS.mem", "val Vale.PPC64LE.InsBasic.vale_heap = Type\nlet vale_heap = Vale.PPC64LE.Memory.vale_heap", "val Vale.PPC64LE.Decls.vale_heap = Type\nlet vale_heap = M.vale_heap", "val Vale.Arch.HeapImpl.vale_heaplets = Type\nlet vale_heaplets = Map16.map16 vale_heap", "val Vale.X64.Memory.heaplet_id = Type0\nlet heaplet_id = heaplet_id", "val Vale.PPC64LE.Decls.va_value_heaplet = Type\nlet va_value_heaplet = vale_heap", "val Vale.X64.Decls.va_value_heaplet = Type\nlet va_value_heaplet = vale_heap", "val Vale.Arch.HeapImpl.heaplet_id = Type0\nlet heaplet_id = n:nat{n < 16}", "val Vale.Arch.MachineHeap_s.machine_heap = Type0\nlet machine_heap = Map.t int nat8", "val PulseCore.Memory.inames = Type0\nlet inames = erased (S.set iname)", "val Steel.Heap.addr = Type0\nlet addr = nat", "val Vale.PPC64LE.Decls.heaplet_id = Type0\nlet heaplet_id = M.heaplet_id", "val Steel.Heap.hheap = p: Steel.Heap.slprop -> Type\nlet hheap (p:slprop u#a) = m:heap u#a {interp p m}", "val Vale.X64.Decls.heaplet_id = Type0\nlet heaplet_id = M.heaplet_id", "val MRefHeap.heap_cell = Type\nlet heap_cell = (a:Type0 & heap_cell_a a)", "val Vale.Interop.Heap_s.down_mem_t = Type\nlet down_mem_t = m:interop_heap -> GTot (h:machine_heap{correct_down m h})", "val Vale.X64.Memory.vuint8 = Vale.Arch.HeapTypes_s.base_typ\nlet vuint8 = TUInt8", "val Vale.PPC64LE.Memory.vuint8 = Vale.Arch.HeapTypes_s.base_typ\nlet vuint8 = TUInt8", "val Vale.PPC64LE.Decls.va_operand_heaplet = Type0\nlet va_operand_heaplet = heaplet_id", "val empty_heap:heap\nlet empty_heap : heap = F.on _ (fun _ -> None)", "val Vale.PPC64LE.Memory.vuint128 = Vale.Arch.HeapTypes_s.base_typ\nlet vuint128 = TUInt128", "val Vale.X64.Memory.vuint128 = Vale.Arch.HeapTypes_s.base_typ\nlet vuint128 = TUInt128", "val Vale.X64.Memory.vuint16 = Vale.Arch.HeapTypes_s.base_typ\nlet vuint16 = TUInt16", "val Vale.PPC64LE.Memory.vuint16 = Vale.Arch.HeapTypes_s.base_typ\nlet vuint16 = TUInt16", "val PulseCore.Memory.property = a: Type -> Type\nlet property (a:Type)\n = a -> prop", "val Vale.X64.Memory.vuint32 = Vale.Arch.HeapTypes_s.base_typ\nlet vuint32 = TUInt32", "val Vale.X64.Memory.vuint64 = Vale.Arch.HeapTypes_s.base_typ\nlet vuint64 = TUInt64", "val Vale.PPC64LE.Memory.vuint32 = Vale.Arch.HeapTypes_s.base_typ\nlet vuint32 = TUInt32", "val ImmutableSTwHeaps.st_pre = Type\nlet st_pre = heap -> Type0", "val Vale.PPC64LE.Memory.vuint64 = Vale.Arch.HeapTypes_s.base_typ\nlet vuint64 = TUInt64", "val AllocSTwHeaps.st_pre = Type\nlet st_pre = FStar.Heap.heap -> Type0", "val heap :Type u#1\nlet heap = h:heap_rec{(forall (n:nat). n >= h.next_addr ==> None? (h.memory n))}", "val Pulse.Lib.Core.inames = Type0\nlet inames = erased (FStar.Set.set iname)", "val Vale.X64.Decls.va_operand_heaplet = Type0\nlet va_operand_heaplet = heaplet_id", "val Steel.Heap.hprop = fp: Steel.Heap.slprop -> Type\nlet hprop (fp:slprop u#a) =\n q:(heap u#a -> prop){\n forall (h0:heap{interp fp h0}) (h1:heap{disjoint h0 h1}).\n q h0 <==> q (join h0 h1)\n }", "val Pulse.C.Types.Array.array_size_t = Type0\nlet array_size_t = (n: SZ.t { SZ.v n > 0 })", "val equal: heap -> heap -> Type0\nlet equal h1 h2 =\n let _ = () in\n h1.next_addr = h2.next_addr /\\\n FStar.FunctionalExtensionality.feq h1.memory h2.memory", "val Test.NoHeap.vec8 = Type0\nlet vec8 = L.lbuffer UInt8.t", "val heap : Type u#1\nlet heap = h:(nat * (nat -> Tot (option heap_cell)))\n\t\t {(forall (n:nat) . n < fst h ==> (exists v . snd h n == Some v)) /\\\n\t\t\t(forall (n:nat) . n >= fst h ==> snd h n == None)}", "val heap: Type u#1\nlet heap = h:(nat * (F.restricted_t nat (fun _ -> (option (dtuple2 Type0 (fun a -> a))))))\n\t\t {(forall (n:nat) . n < fst h ==> (exists v . snd h n == Some v)) /\\ \n\t\t\t(forall (n:nat) . n >= fst h ==> snd h n == None)}", "val Vale.PPC64LE.Memory.buffer128 = Type0\nlet buffer128 = buffer vuint128", "val heap : eqtype\nlet heap = h:seq int{length h == store_size}", "val Vale.X64.Memory.b8 = Type0\nlet b8 = IB.b8", "val from_heap_impl (heap: heap_impl) : vale_full_heap\nlet from_heap_impl (heap:heap_impl) : vale_full_heap = coerce heap", "val Vale.PPC64LE.Memory.b8 = Type0\nlet b8 = IB.b8", "val Vale.PPC64LE.Memory.buffer8 = Type0\nlet buffer8 = buffer vuint8", "val Vale.PPC64LE.Memory.buffer32 = Type0\nlet buffer32 = buffer vuint32", "val Vale.PPC64LE.Memory.buffer16 = Type0\nlet buffer16 = buffer vuint16", "val Vale.PPC64LE.Memory.buffer64 = Type0\nlet buffer64 = buffer vuint64", "val emp :heap\nlet emp = {\n next_addr = 1;\n memory = F.on_dom pos (fun r -> None)\n}", "val Vale.PPC64LE.State.state = Type\nlet state = Vale.PPC64LE.Machine_s.state", "val emp : heap\nlet emp = Mktuple2 0 (F.on_dom nat (fun (r:nat) -> None))", "val emp : heap\nlet emp = 0, (fun (r:nat) -> None)", "val emp : heap\nlet emp = {\n next_addr = 0;\n memory = F.on_dom nat (fun (r:nat) -> None)\n}", "val Vale.X64.Memory.buffer128 = Type0\nlet buffer128 = buffer vuint128", "val Pulse.Syntax.Base.index = Type0\nlet index = nat", "val PulsePointStruct._x = Type0\nlet _x = norm Pulse.C.Typestring.norm_typestring (Pulse.C.Typestring.mk_string_t \"x\")", "val Vale.X64.Decls.memTaint_type = Type0\nlet memTaint_type = Map.t int taint", "val FStar.TwoLevelHeap.st_pre = Type\nlet st_pre = st_pre_h t", "val Pulse.Syntax.Base.effect_hint = Type0\nlet effect_hint = FStar.Sealed.Inhabited.sealed #(option ctag) None", "val Pulse.Extract.Main.name = Type0\nlet name = ppname & nat", "val PulseCore.Action.inames = Type0\nlet inames = Ghost.erased (FStar.Set.set iname)", "val Vale.PPC64LE.Memory.nat64 = Type0\nlet nat64 = Vale.Def.Words_s.nat64", "val Vale.X64.Memory.buffer8 = Type0\nlet buffer8 = buffer vuint8", "val Vale.PPC64LE.Lemmas.fuel = Type0\nlet fuel = nat", "val PulsePointStruct._y = Type0\nlet _y = norm Pulse.C.Typestring.norm_typestring (Pulse.C.Typestring.mk_string_t \"y\")", "val Vale.PPC64LE.Memory.nat8 = Type0\nlet nat8 = Vale.Def.Words_s.nat8", "val Vale.X64.Memory.buffer32 = Type0\nlet buffer32 = buffer vuint32", "val PulseCore.Heap.partial_pre_action = fp: PulseCore.Heap.slprop -> a: Type -> fp': (_: a -> PulseCore.Heap.slprop) -> Type\nlet partial_pre_action (fp:slprop u#a) (a:Type u#b) (fp':a -> slprop u#a) =\n full_hheap fp -> (x:a & full_hheap (fp' x))", "val Vale.X64.Memory.buffer16 = Type0\nlet buffer16 = buffer vuint16", "val Pulse.Reflection.Util.arrow_dom = Type0\nlet arrow_dom = (R.term & R.aqualv)", "val Steel.Memory.hmem = p: Steel.Memory.slprop -> Type\nlet hmem (p:slprop u#a) = m:mem u#a {interp p m}", "val Steel.Semantics.Hoare.MST.full_mem = st: Steel.Semantics.Hoare.MST.st -> Type\nlet full_mem (st:st) = m:st.mem{st.full_mem_pred m}", "val Hacl.Impl.Lib.fill_elems_st = Type\nlet fill_elems_st =\n #t:Type0\n -> #a:Type0\n -> h0:mem\n -> n:size_t\n -> output:lbuffer t n\n -> refl:(mem -> i:size_nat{i <= v n} -> GTot a)\n -> footprint:(i:size_nat{i <= v n} -> GTot\n (l:B.loc{B.loc_disjoint l (loc output) /\\ B.address_liveness_insensitive_locs `B.loc_includes` l}))\n -> spec:(mem -> GTot (i:size_nat{i < v n} -> a -> a & t))\n -> impl:(i:size_t{v i < v n} -> Stack unit\n (requires fun h ->\n\tmodifies (footprint (v i) |+| loc (gsub output 0ul i)) h0 h)\n (ensures fun h1 _ h2 ->\n\t(let block1 = gsub output i 1ul in\n\t let c, e = spec h0 (v i) (refl h1 (v i)) in\n\t refl h2 (v i + 1) == c /\\\n\t LSeq.index (as_seq h2 block1) 0 == e /\\\n\t footprint (v i + 1) `B.loc_includes` footprint (v i) /\\\n\t modifies (footprint (v i + 1) |+| (loc block1)) h1 h2))) ->\n Stack unit\n (requires fun h -> h0 == h /\\ live h output)\n (ensures fun _ _ h1 -> modifies (footprint (v n) |+| loc output) h0 h1 /\\\n (let s, o = S.generate_elems (v n) (v n) (spec h0) (refl h0 0) in\n refl h1 (v n) == s /\\ as_seq #_ #t h1 output == o))", "val hs: Type0\nlet hs = hs'", "val Vale.X64.Memory.nat64 = Type0\nlet nat64 = Vale.Def.Words_s.nat64", "val Vale.X64.Memory.buffer64 = Type0\nlet buffer64 = buffer vuint64", "val PulseTutorial.HigherOrder.id_t = Type\nlet id_t = (#a:Type0) -> x:a -> stt a emp (fun _ -> emp)", "val Vale.PPC64LE.InsBasic.vale_stack = Type0\nlet vale_stack = Vale.PPC64LE.Stack_i.vale_stack", "val FStar.DM4F.OTP.Heap.elem = Type0\nlet elem = bv_t q", "val Vale.PPC64LE.Memory.nat16 = Type0\nlet nat16 = Vale.Def.Words_s.nat16", "val Vale.PPC64LE.Memory.nat32 = Type0\nlet nat32 = Vale.Def.Words_s.nat32", "val Hacl.Impl.Blake2.Core.index_t = Type0\nlet index_t = n:size_t{v n < 4}", "val Vale.X64.InsBasic.vale_stack = Type0\nlet vale_stack = Vale.X64.Stack_i.vale_stack", "val PulseCore.Heap.mem_equiv = m0: PulseCore.Heap.heap -> m1: PulseCore.Heap.heap -> Prims.logical\nlet mem_equiv (m0 m1:heap) =\n forall a. m0 a == m1 a" ], "closest_src": [ { "project_name": "steel", "file_name": "PulseCore.Memory.fsti", "name": "PulseCore.Memory.full_mem" }, { "project_name": "steel", "file_name": "Steel.Heap.fsti", "name": "Steel.Heap.full_heap" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.vale_full_heap" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.vale_full_heap" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.addr" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.vale_full_heap" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.vale_full_heap" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.vale_heap" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.vale_heap" }, { "project_name": "steel", "file_name": "Steel.Memory.fsti", "name": "Steel.Memory.full_mem" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.vale_heap" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.vale_heap" }, { "project_name": "steel", "file_name": "Steel.Heap.fsti", "name": "Steel.Heap.full_hheap" }, { "project_name": "steel", "file_name": "Steel.Heap.fsti", "name": "Steel.Heap.a_heap_prop" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.heaplet_id" }, { "project_name": "FStar", "file_name": "DoublyLinkedList.fst", "name": "DoublyLinkedList.heap" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.vale_heap" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.vale_heap" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.HeapImpl.fsti", "name": "Vale.Arch.HeapImpl.vale_heaplets" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.heaplet_id" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.va_value_heaplet" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_value_heaplet" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.HeapImpl.fsti", "name": "Vale.Arch.HeapImpl.heaplet_id" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.MachineHeap_s.fst", "name": "Vale.Arch.MachineHeap_s.machine_heap" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fsti", "name": "PulseCore.Memory.inames" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.addr" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.heaplet_id" }, { "project_name": "steel", "file_name": "Steel.Heap.fsti", "name": "Steel.Heap.hheap" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.heaplet_id" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.heap_cell" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Heap_s.fst", "name": "Vale.Interop.Heap_s.down_mem_t" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.vuint8" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.vuint8" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.va_operand_heaplet" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.empty_heap" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.vuint128" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.vuint128" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.vuint16" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.vuint16" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fsti", "name": "PulseCore.Memory.property" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.vuint32" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.vuint64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.vuint32" }, { "project_name": "FStar", "file_name": "ImmutableSTwHeaps.fst", "name": "ImmutableSTwHeaps.st_pre" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.vuint64" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.st_pre" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.heap" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fsti", "name": "Pulse.Lib.Core.inames" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_operand_heaplet" }, { "project_name": "steel", "file_name": "Steel.Heap.fsti", "name": "Steel.Heap.hprop" }, { "project_name": "steel", "file_name": "Pulse.C.Types.Array.fsti", "name": "Pulse.C.Types.Array.array_size_t" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.equal" }, { "project_name": "hacl-star", "file_name": "Test.NoHeap.fsti", "name": "Test.NoHeap.vec8" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.heap" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.heap" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.buffer128" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.IntStoreFixed.fst", "name": "FStar.DM4F.Heap.IntStoreFixed.heap" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.b8" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.from_heap_impl" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.b8" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.buffer8" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.buffer32" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.buffer16" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.buffer64" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.emp" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.State.fsti", "name": "Vale.PPC64LE.State.state" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.emp" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.emp" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.emp" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.buffer128" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.index" }, { "project_name": "steel", "file_name": "PulsePointStruct.fst", "name": "PulsePointStruct._x" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.memTaint_type" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.st_pre" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.effect_hint" }, { "project_name": "steel", "file_name": "Pulse.Extract.Main.fst", "name": "Pulse.Extract.Main.name" }, { "project_name": "steel", "file_name": "PulseCore.Action.fsti", "name": "PulseCore.Action.inames" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.nat64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.buffer8" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Lemmas.fsti", "name": "Vale.PPC64LE.Lemmas.fuel" }, { "project_name": "steel", "file_name": "PulsePointStruct.fst", "name": "PulsePointStruct._y" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.nat8" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.buffer32" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.partial_pre_action" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.buffer16" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.arrow_dom" }, { "project_name": "steel", "file_name": "Steel.Memory.fsti", "name": "Steel.Memory.hmem" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.full_mem" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Lib.fst", "name": "Hacl.Impl.Lib.fill_elems_st" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Old.Handshake.fst", "name": "MiTLS.Old.Handshake.hs" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.nat64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.buffer64" }, { "project_name": "steel", "file_name": "PulseTutorial.HigherOrder.fst", "name": "PulseTutorial.HigherOrder.id_t" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.vale_stack" }, { "project_name": "FStar", "file_name": "FStar.DM4F.OTP.Heap.fsti", "name": "FStar.DM4F.OTP.Heap.elem" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.nat16" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.nat32" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Blake2.Core.fsti", "name": "Hacl.Impl.Blake2.Core.index_t" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.vale_stack" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.mem_equiv" } ], "selected_premises": [ "PulseCore.Heap.hheap", "PulseCore.Preorder.pcm_history", "FStar.PCM.compatible", "FStar.Real.one", "PulseCore.Heap.heap_prop_is_affine", "FStar.Real.two", "PulseCore.Preorder.history_val", "FStar.PCM.composable", "FStar.PCM.op", "PulseCore.FractionalPermission.full_perm", "PulseCore.FractionalPermission.sum_perm", "PulseCore.Heap.pure", "PulseCore.Heap.a_heap_prop", "PulseCore.FractionalPermission.comp_perm", "PulseCore.Preorder.p_op", "PulseCore.Heap.hprop", "PulseCore.Heap.stronger", "PulseCore.Preorder.vhist", "FStar.Pervasives.reveal_opaque", "PulseCore.Preorder.comm_op", "PulseCore.Heap.equiv", "PulseCore.Preorder.induces_preorder", "PulseCore.Preorder.preorder_of_pcm", "PulseCore.FractionalPermission.writeable", "PulseCore.Preorder.history_compose", "PulseCore.Preorder.curval", "PulseCore.Preorder.extends", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "PulseCore.Preorder.p_composable", "PulseCore.Preorder.history_composable", "PulseCore.Heap.ptr", "PulseCore.FractionalPermission.lesser_perm", "PulseCore.Preorder.extends'", "FStar.Real.zero", "PulseCore.Preorder.hist", "PulseCore.Preorder.pcm_of_preorder", "PulseCore.Preorder.hval", "PulseCore.Preorder.p", "PulseCore.Preorder.pcm_history_preorder", "PulseCore.Preorder.qhistory", "PulseCore.Preorder.lift_fact", "PulseCore.Preorder.property", "PulseCore.Preorder.extends_length_eq", "PulseCore.Preorder.hperm", "PulseCore.Heap.ref", "PulseCore.FractionalPermission.half_perm", "PulseCore.Preorder.fact_valid_compat", "PulseCore.Preorder.flip", "FStar.Pervasives.st_post_h", "PulseCore.Preorder.hval_tot", "PulseCore.Preorder.lem_is_unit", "PulseCore.Preorder.unit_history", "FStar.Pervasives.dfst", "PulseCore.Preorder.extend_history", "FStar.Preorder.preorder_rel", "PulseCore.Preorder.stable_property", "PulseCore.Preorder.extend_history'", "FStar.Pervasives.dsnd", "PulseCore.Preorder.lift_fact_is_stable", "PulseCore.Preorder.pcm_history_induces_preorder", "FStar.PCM.lem_commutative", "PulseCore.Preorder.extends_related_head", "PulseCore.FractionalPermission.lesser_equal_perm", "FStar.Pervasives.st_pre_h", "FStar.Pervasives.all_return", "PulseCore.Preorder.stable_compatiblity", "FStar.PCM.compatible_elim", "FStar.PCM.compatible_trans", "FStar.Preorder.stable", "FStar.PCM.frame_preserving_val_to_fp_upd", "FStar.PCM.exclusive", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.ex_pre", "Prims.pure_pre", "FStar.PCM.lem_assoc_l", "FStar.PCM.frame_compatible", "PulseCore.Preorder.extends_disjunction", "FStar.Pervasives.all_post_h'", "PulseCore.Heap.null", "FStar.Pervasives.st_return", "FStar.Pervasives.all_post_h", "PulseCore.Preorder.p_op_nil", "FStar.PCM.lem_assoc_r", "PulseCore.Preorder.pcm_of_preorder_induces_extends", "PulseCore.Preorder.extends_trans", "FStar.Pervasives.st_stronger", "FStar.Pervasives.all_stronger", "PulseCore.Preorder.p_op_extends", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.st_trivial", "PulseCore.Preorder.split_current", "FStar.Preorder.reflexive", "FStar.Pervasives.all_trivial", "FStar.Pervasives.st_wp_h", "FStar.Pervasives.ex_post'", "FStar.Pervasives.id", "PulseCore.Heap.is_null", "Prims.pure_post'" ], "source_upto_this": "(*\n Copyright 2019 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule PulseCore.Heap\nopen FStar.Ghost\nopen FStar.PCM\n\n/// This module defines the behavior of a structured heap where each memory cell is governed by\n/// a partial commutative monoid. This PCM structure is reused for the entire heap as it is possible\n/// to talk about disjoint heaps and join them together.\n///\n/// In a sense, a heap here can be seen as a partial heap, containing a partial view of the state of\n/// the memory. Combining disjoint heaps is then equivalent to conciling two partial views of the\n/// memory together. This is our base for separation logic.\n///\n/// The heap is instrumented with affine heap predicates, heap predicates that don't change if you\n/// augment the heap on which they're valid by joining another partial heap. These affine heap\n/// predicates are the terms of our separation logic.\n///\n/// Finally, the module defines actions for heap, which are frame-preserving heap updates.\n\n(**** The base : partial heaps *)\n\n(**\n Abstract type of heaps. Can conceptually be thought of as a map from addresses to\n contents of memory cells.\n*)\nval heap : Type u#(a + 1)\n\n(* An empty heap *)\nval empty_heap : heap u#a\n\n(** A [core_ref] is a key into the [heap] or [null] *)\nval core_ref : Type u#0\n\n(** We index a [core_ref] by the type of its heap contents\n and a [pcm] governing it, for ease of type inference *)\nlet ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref\n\nval core_ref_null : core_ref\n\n(** [null] is a specific reference, that is not associated to any value\n*)\nlet null (#a:Type u#a) (#pcm:pcm a) : ref a pcm = core_ref_null\n\n(** Checking whether [r] is the null pointer is decidable through [is_null]\n*)\nval core_ref_is_null (r:core_ref) : b:bool { b <==> r == core_ref_null }\n\n(** Checking whether [r] is the null pointer is decidable through [is_null]\n*)\nlet is_null (#a:Type u#a) (#pcm:pcm a) (r:ref a pcm) : (b:bool{b <==> r == null}) = core_ref_is_null r\n\n(** The predicate describing non-overlapping heaps *)\nval disjoint (h0 h1:heap u#h) : prop\n\n(** Disjointness is symmetric *)\nval disjoint_sym (h0 h1:heap u#h)\n : Lemma (disjoint h0 h1 <==> disjoint h1 h0)\n [SMTPat (disjoint h0 h1)]\n\n(** Disjoint heaps can be combined into a bigger heap*)\nval join (h0:heap u#h) (h1:heap u#h{disjoint h0 h1}) : heap u#h\n\n(** The join operation is commutative *)\nval join_commutative (h0 h1:heap)\n : Lemma\n (requires\n disjoint h0 h1)\n (ensures\n (disjoint h1 h0 /\\\n join h0 h1 == join h1 h0))\n\n(** Disjointness distributes over join *)\nval disjoint_join (h0 h1 h2:heap)\n : Lemma (disjoint h1 h2 /\\\n disjoint h0 (join h1 h2) ==>\n disjoint h0 h1 /\\\n disjoint h0 h2 /\\\n disjoint (join h0 h1) h2 /\\\n disjoint (join h0 h2) h1)\n\n(** Join is associative *)\nval join_associative (h0 h1 h2:heap)\n : Lemma\n (requires\n disjoint h1 h2 /\\\n disjoint h0 (join h1 h2))\n (ensures\n (disjoint h0 h1 /\\\n disjoint (join h0 h1) h2 /\\\n join h0 (join h1 h2) == join (join h0 h1) h2))\n\n(**** Separation logic over heaps *)\n\n(**\n An affine heap proposition or affine heap predicate is a proposition whose validity does not\n change if the heap on which it is valid grows. In other terms, it is a proposition that is\n compatible with the disjoint/join operations for partial heaps. These affine heap predicates\n are the base of our separation logic.\n*)\nlet heap_prop_is_affine (p:heap u#a -> prop) : prop =\n forall (h0 h1: heap u#a). p h0 /\\ disjoint h0 h1 ==> p (join h0 h1)\n\n(**\n An affine heap proposition\n *)\nlet a_heap_prop = p:(heap -> prop) { heap_prop_is_affine p }\n\n(**\n [slprop] is an abstract \"separation logic proposition\"\n\n The [erasable] attribute says that it is computationally irrelevant\n and will be extracted to [()]\n*)\n[@@erasable]\nval slprop : Type u#(a + 1)\n\n(**\n [slprop]s can be \"interpreted\" over any heap, yielding a [prop]\n*)\nval interp (p:slprop u#a) (m:heap u#a) : prop\n\n(**\n Promoting an affine heap proposition to an slprop\n *)\nval as_slprop (f:a_heap_prop) : p:slprop{forall h.interp p h <==> f h}\n\n(**\n An [hprop] is heap predicate indexed by a footprint [fp:slprop].\n Its validity depends only on the fragment of the heap that satisfies [fp].\n Note, it is unrelated to affinity, since the forward implication only applies\n to heaps [h0] that validate [fp]\n*)\nlet hprop (fp:slprop u#a) =\n q:(heap u#a -> prop){\n forall (h0:heap{interp fp h0}) (h1:heap{disjoint h0 h1}).\n q h0 <==> q (join h0 h1)\n }\n\n(** A common abbreviation: [hheap p] is a heap on which [p] is valid *)\nlet hheap (p:slprop u#a) = m:heap u#a {interp p m}\n\n(**\n Equivalence relation on [slprop]s is just\n equivalence of their interpretations\n*)\nlet equiv (p1 p2:slprop) =\n forall m. interp p1 m <==> interp p2 m\n\n(**\n An extensional equivalence principle for slprop\n *)\nval slprop_extensionality (p q:slprop)\n : Lemma\n (requires p `equiv` q)\n (ensures p == q)\n\n/// We can now define all the standard connectives of separation logic\n\n(** [emp] is the empty [slprop], valid on all heaps. It acts as the unit element *)\nval emp : slprop u#a\n(** \"Points to\" allows to talk about the heap contents *)\nval pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a\nval h_and (p1 p2:slprop u#a) : slprop u#a\nval h_or (p1 p2:slprop u#a) : slprop u#a\nval star (p1 p2:slprop u#a) : slprop u#a\nval wand (p1 p2:slprop u#a) : slprop u#a\nval h_exists (#[@@@strictly_positive] a:Type u#b)\n ([@@@strictly_positive] f: (a -> slprop u#a))\n : slprop u#a\nval h_forall (#a:Type u#b) (f: (a -> slprop u#a)) : slprop u#a\n(**\n [h_refine] consists of refining a separation logic proposition [p] with an affine heap predicate\n [r]. Since both types are equal, this is equivalent to [h_and].\n*)\nval h_refine (p:slprop u#a) (r:a_heap_prop u#a) : slprop u#a\n\n(***** Basic properties of separation logic *)\n\n(** If [p * q] is valid on [h], then [p] and [q] are valid on [h] *)\nval affine_star (p q:slprop) (h:heap)\n : Lemma ((interp (p `star` q) h ==> interp p h /\\ interp q h))\n\n(** Equivalence of separation logic propositions is symmetric *)\nval equiv_symmetric (p1 p2:slprop)\n : squash (p1 `equiv` p2 ==> p2 `equiv` p1)\n\n(** If [p1 ~ p2] then [p1 * p3 ~ p2 * p3] *)\nval equiv_extensional_on_star (p1 p2 p3:slprop)\n : squash (p1 `equiv` p2 ==> (p1 `star` p3) `equiv` (p2 `star` p3))\n\n(** [p ~~ p * emp] *)\nval emp_unit (p:slprop)\n : Lemma (p `equiv` (p `star` emp))\n\n(** [emp] is trivial *)\nval intro_emp (h:heap)\n : Lemma (interp emp h)\n\n(** Introduction rule for equivalence of [h_exists] propositions *)\nval h_exists_cong (#a:Type) (p q : a -> slprop)\n : Lemma\n (requires (forall x. p x `equiv` q x))\n (ensures (h_exists p `equiv` h_exists q))\n\n(** Introducing [h_exists] by presenting a witness *)\nval intro_h_exists (#a:_) (x:a) (p:a -> slprop) (h:heap)\n : Lemma (interp (p x) h ==> interp (h_exists p) h)\n\n(** Eliminate an existential by simply getting a proposition. *)\nval elim_h_exists (#a:_) (p:a -> slprop) (h:heap)\n : Lemma (interp (h_exists p) h ==> (exists x. interp (p x) h))\n\n(**\n The interpretation of a separation logic proposition [hp] is itself an [hprop] of footprint\n [hp]\n*)\nval interp_depends_only_on (hp:slprop u#a)\n : Lemma\n (forall (h0:hheap hp) (h1:heap u#a{disjoint h0 h1}).\n interp hp h0 <==> interp hp (join h0 h1))\n\n\n(***** [pts_to] properties *)\n\n(**\n [ptr r] is a separation logic proposition asserting the existence of an allocated cell at\n reference [r]\n*)\nlet ptr (#a: Type u#a) (#pcm: pcm a) (r:ref a pcm) =\n h_exists (pts_to r)\n\n(**\n If we have [pts_to x v0] and [pts_to y v1] on the same heap, then [v0] and [v1] are are related\n by the PCM governing [x]. Indeed, the [pts_to] predicate is not stricly injective, as our partial\n heaps offer only a partial view on the contents of the memory cell. This partial view is governed\n by [pcm], and this lemma shows that you can combine two [pts_to] predicates into a third, with\n a new value with is the composition of [v0] and [v1] by [pcm].\n This lemma is equivalent to injectivity of [pts_to] if you instantiate [pcm] with the exclusive\n PCM.\n*)\nval pts_to_compatible\n (#a:Type u#a)\n (#pcm: pcm a)\n (x:ref a pcm)\n (v0 v1:a)\n (h:heap u#a)\n : Lemma\n (interp (pts_to x v0 `star` pts_to x v1) h\n <==>\n (composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) h))\n\n(** If a reference points to two different values, they must be joinable\nin the PCM, even when the pointing does not happen separately. *)\nval pts_to_join (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures joinable pcm v1 v2)\n\n(** Further, the value in the heap is a witness for that property *)\nval pts_to_join' (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures (exists z. compatible pcm v1 z /\\ compatible pcm v2 z /\\\n interp (pts_to r z) m))\n\nval pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))\n\nval pts_to_not_null (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v:a)\n (m:heap)\n : Lemma (requires interp (pts_to x v) m)\n (ensures x =!= null)\n\n(***** Properties of separating conjunction *)\n\n(** The separating conjunction [star] arises from the disjointness of partial heaps *)\nval intro_star (p q:slprop) (hp:hheap p) (hq:hheap q)\n : Lemma\n (requires disjoint hp hq)\n (ensures interp (p `star` q) (join hp hq))\n\nval elim_star (p q:slprop) (h:hheap (p `star` q))\n : Lemma\n (requires interp (p `star` q) h)\n (ensures exists hl hr.\n disjoint hl hr /\\\n h == join hl hr /\\\n interp p hl /\\\n interp q hr)\n\n(** [star] is commutative *)\nval star_commutative (p1 p2:slprop)\n : Lemma ((p1 `star` p2) `equiv` (p2 `star` p1))\n\n(** [star] is associative *)\nval star_associative (p1 p2 p3:slprop)\n : Lemma (\n (p1 `star` (p2 `star` p3))\n `equiv`\n ((p1 `star` p2) `star` p3)\n )\n\n(** If [p1 ~ p3] and [p2 ~ p4], then [p1 * p2 ~ p3 * p4] *)\nval star_congruence (p1 p2 p3 p4:slprop)\n : Lemma (requires p1 `equiv` p3 /\\ p2 `equiv` p4)\n (ensures (p1 `star` p2) `equiv` (p3 `star` p4))\n\n(***** Properties of the refinement *)\n\n(** [h_refine p q] is just interpreting the affine heap prop [q] when [p] is valid *)\nval refine_interp (p:slprop u#a) (q:a_heap_prop u#a) (h:heap u#a)\n : Lemma (interp p h /\\ q h <==> interp (h_refine p q) h)\n\n(**\n Equivalence on [h_refine] propositions is define by logical equivalence of the refinements\n on all heaps\n*)\nval refine_equiv (p0 p1:slprop u#a) (q0 q1:a_heap_prop u#a)\n : Lemma (p0 `equiv` p1 /\\ (forall h. q0 h <==> q1 h) ==>\n equiv (h_refine p0 q0) (h_refine p1 q1))\n\n(**\n A [pure] separation logic predicate is a refinement on the empty heap. That is how we\n lift pure propositions to the separation logic world\n*)\nlet pure (p:prop) = h_refine emp (fun _ -> p)\n\n(** Equivalence of pure propositions is the equivalence of the underlying propositions *)\nval pure_equiv (p q:prop)\n : Lemma ((p <==> q) ==> (pure p `equiv` pure q))\n\n(** And the interpretation of pure propositions is their underlying propositions *)\nval pure_interp (q:prop) (h:heap u#a)\n : Lemma (interp (pure q) h <==> q)\n\n(** A helper lemma for interpreting a pure proposition with another [slprop] *)\nval pure_star_interp (p:slprop u#a) (q:prop) (h:heap u#a)\n : Lemma (interp (p `star` pure q) h <==>\n interp (p `star` emp) h /\\ q)\n\n(***** Magic wand and implications properties *)\n\n(** We can define a [stronger] relation on [slprops], defined by interpretation implication *)\nlet stronger (p q:slprop) =\n forall h. interp p h ==> interp q h\n\n(** [stronger] is stable when adding another starred [slprop] *)\nval stronger_star (p q r:slprop)\n : Lemma (stronger q r ==> stronger (p `star` q) (p `star` r))\n\n(** If [q > r] and [p * q] is valid, then [p * r] is valid *)\nval weaken (p q r:slprop) (h:heap u#a)\n : Lemma (q `stronger` r /\\ interp (p `star` q) h ==> interp (p `star` r) h)\n\n(**** Actions *)\n\n(** An abstract predicate classifying a \"full\" heap, i.e., the entire\n heap of the executing program, not just a fragment of it *)\nval full_heap_pred : heap -> prop\n" }, { "file_name": "Selectors.LList3.fst", "name": "Selectors.LList3.v_null_rewrite", "opens_and_abbrevs": [ { "abbrev": "Mem", "full_module": "Steel.Memory" }, { "open": "Steel.FractionalPermission" }, { "abbrev": "L", "full_module": "FStar.List.Tot" }, { "open": "Steel.ArrayRef" }, { "open": "Steel.Effect" }, { "open": "Steel.Effect.Atomic" }, { "open": "Steel.Memory" }, { "open": "Selectors" }, { "open": "Selectors" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val v_null_rewrite: a: Type0 -> t_of emp -> GTot (list a)", "source_definition": "let v_null_rewrite\n (a: Type0)\n (_: t_of emp)\n: GTot (list a)\n= []", "source_range": { "start_line": 26, "start_col": 0, "end_line": 30, "end_col": 4 }, "interleaved": false, "definition": "fun a _ -> [] <: Prims.GTot (Prims.list a)", "effect": "Prims.GTot", "effect_flags": [ "sometrivial" ], "mutual_with": [], "premises": [ "Steel.Effect.Common.t_of", "Steel.Effect.Common.emp", "Prims.Nil", "Prims.list" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "a: Type0 -> _: Steel.Effect.Common.t_of Steel.Effect.Common.emp -> Prims.GTot (Prims.list a)", "prompt": "let v_null_rewrite (a: Type0) (_: t_of emp) : GTot (list a) =\n ", "expected_response": "[]", "source": { "project_name": "steel", "file_name": "share/steel/examples/steel/Selectors.LList3.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Selectors.LList3.fst", "checked_file": "dataset/Selectors.LList3.fst.checked", "interface_file": true, "dependencies": [ "dataset/Steel.Memory.fsti.checked", "dataset/Steel.FractionalPermission.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Ghost.fsti.checked" ] }, "definitions_in_context": [ "cell", "cell", "tail_fuel", "tail_fuel", "next", "next", "data", "data", "let next #a (c:cell a) : t a = c.next", "val cell (a:Type0) : Type0", "let data #a (c:cell a) : a = c.data", "let mk_cell #a (n: t a) (d:a) = {\n tail_fuel = Ghost.hide 0;\n next = n;\n data = d\n}", "let t (a:Type0) = ref (cell a)", "let null_llist #a = null", "val next (#a:Type0) (c:cell a) : t a", "let is_null #a ptr = is_null ptr" ], "closest": [ "val v_null_rewrite: a: Type0 -> t_of emp -> GTot (list a)\nlet v_null_rewrite\n (a: Type0)\n (_: t_of emp)\n: GTot (list a)\n= []", "val llist_vrewrite (#a: Type0) (r: t a) (cl: normal (t_of ((vptr r) `vdep` (llist_vdep r))))\n : GTot (list a)\nlet llist_vrewrite\n (#a: Type0)\n (r: t a)\n (cl: normal (t_of (vptr r `vdep` llist_vdep r)))\n: GTot (list a)\n= (dfst cl).data :: dsnd cl", "val cllist_rewrite\n (#a: Type0)\n (c: cllist_ptrvalue a)\n (x:\n dtuple2 (cllist_lvalue a)\n (vdep_payload ((emp `vrefine` (cllist0_refine c)) `vrewrite` (cllist0_rewrite c))\n (cllist0 a)))\n : GTot (vllist a)\nlet cllist_rewrite\n (#a: Type0)\n (c: cllist_ptrvalue a)\n (x: dtuple2 (cllist_lvalue a) (vdep_payload (emp `vrefine` cllist0_refine c `vrewrite` cllist0_rewrite c) (cllist0 a)))\n: GTot (vllist a)\n= let p =\n dsnd #(cllist_lvalue a) #(vdep_payload (emp `vrefine` cllist0_refine c `vrewrite` cllist0_rewrite c) (cllist0 a)) x\n in\n {\n vllist_head = fst p;\n vllist_tail = snd p;\n }", "val cllist0_rewrite: #a: Type0 -> c: cllist_ptrvalue a -> t_of (emp `vrefine` (cllist0_refine c))\n -> Tot (cllist_lvalue a)\nlet cllist0_rewrite\n (#a: Type0)\n (c: cllist_ptrvalue a)\n (_: t_of (emp `vrefine` cllist0_refine c))\n: Tot (cllist_lvalue a)\n= c", "val null_t (#a: Type0) : t a\nlet null_t #a = null", "val is_null_t (#a: Type0) (r: t a) : (b:bool{b <==> r == null_t})\nlet is_null_t #a ptr = is_null ptr", "val v: #a:Type -> h:HS.mem -> ll: t a -> GTot (list a)\nlet v #_ h ll =\n B.deref h ll.v", "val v_c_l_rewrite\n (n: Ghost.erased nat)\n (#a: Type0)\n (r: t a)\n (nllist:\n (n': Ghost.erased nat -> r: t a {Ghost.reveal n' < Ghost.reveal n}\n -> Pure vprop (requires True) (ensures (fun y -> t_of y == list a))))\n (res: normal (t_of (((vptr r) `vrefine` (v_c n r)) `vdep` (v_c_dep n r nllist))))\n : Tot (list a)\nlet v_c_l_rewrite\n (n: Ghost.erased nat)\n (#a: Type0)\n (r: t a)\n (nllist: (n': Ghost.erased nat) -> (r: t a { Ghost.reveal n' < Ghost.reveal n }) -> Pure vprop (requires True) (ensures (fun y -> t_of y == list a)))\n (res: normal (t_of ((vptr r `vrefine` v_c n r) `vdep` v_c_dep n r nllist)))\n: Tot (list a)\n= let (| c, l |) = res in\n c.data :: l", "val vbind0_rewrite\n (a: vprop)\n (t: Type0)\n (b: (t_of a -> Tot vprop))\n (x: normal (t_of (vdep a (vbind0_payload a t b))))\n : Tot t\nlet vbind0_rewrite\n (a: vprop)\n (t: Type0)\n (b: (t_of a -> Tot vprop))\n (x: normal (t_of (vdep a (vbind0_payload a t b))))\n: Tot t\n= snd (dsnd x)", "val p (#a: Type0) (init: list a) : GTot Type0\nlet p (#a:Type0) (init:list a) : GTot Type0 =\n normalize (0 < FStar.List.Tot.length init) /\\\n normalize (FStar.List.Tot.length init <= UInt.max_int 32)", "val ccell_rewrite\n (#a: Type0)\n (c: ccell_ptrvalue a)\n (x: dtuple2 (ccell_lvalue a) (vdep_payload (ccell_is_lvalue c) (ccell0 a)))\n : GTot (vcell a)\nlet ccell_rewrite\n (#a: Type0)\n (c: ccell_ptrvalue a)\n (x: dtuple2 (ccell_lvalue a) (vdep_payload (ccell_is_lvalue c) (ccell0 a)))\n: GTot (vcell a)\n= let p =\n dsnd #(ccell_lvalue a) #(vdep_payload (ccell_is_lvalue c) (ccell0 a)) x\n in\n {\n vcell_data = fst p;\n vcell_next = snd p;\n }", "val intro_llist_nil (a:Type0)\n : Steel unit emp (fun _ -> llist (null_llist #a))\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> v_llist #a null_llist h1 == [])\nlet intro_llist_nil a =\n change_slprop_2 emp (llist (null_llist #a)) ([] <: list a) (intro_nil_lemma a)", "val v (#a:Type0) (x : t a) : G.erased (list a)\nlet v x = G.hide x", "val valid_rewrite_prop (p1 p2: parser) : GTot Type0\nlet valid_rewrite_prop (p1 p2: parser) : GTot Type0 =\n exists (x: valid_rewrite_t' p1 p2) . True", "val v: #t_k:eqtype -> #t_v:Type0 -> h:HS.mem -> ll:t t_k t_v -> GTot (map t_k t_v)\nlet v #_ #_ h ll =\n let l = LL2.v h ll in\n v_ l", "val t (a:Type0) : Type0\nlet t a = list a", "val ccell_is_lvalue_rewrite:\n #a: Type ->\n c: ccell_ptrvalue a ->\n normal (t_of (emp `vrefine` (ccell_is_lvalue_refine c)))\n -> GTot (ccell_lvalue a)\nlet ccell_is_lvalue_rewrite\n (#a: Type)\n (c: ccell_ptrvalue a)\n (_: normal (t_of (emp `vrefine` ccell_is_lvalue_refine c)))\n: GTot (ccell_lvalue a)\n= c", "val is_null (#a:Type0) (r:ref a) : (b:bool{b <==> r == null})\nlet is_null r = A.is_null r", "val is_null (#a:Type0) (r:ref a) : (b:bool{b <==> r == null})\nlet is_null #a r = H.is_null #(U.raise_t a) r", "val p (#a: typ) (init: list (P.type_of_typ a)) : GTot Type0\nlet p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =\n normalize (0 < FStar.List.Tot.length init) /\\\n normalize (FStar.List.Tot.length init < UInt.max_int 32)", "val null (#a: Type0) : array a\nlet null (#a: Type0) : array a\n= (| null_ptr a, Ghost.hide 0 |)", "val sel: #a:Type0 -> #rel:preorder a -> heap -> mref a rel -> GTot a\nlet sel #a #rel h r =\n if h `contains_bool` r\n then sel_tot #a h r\n else r.init", "val intro_llist_nil (a:Type0)\n : Steel unit emp (fun _ -> llist_ptr (null_llist #a))\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> v_ptrlist #a null_llist h1 == [])\nlet intro_llist_nil a =\n change_slprop_2 emp (llist_ptr (null_llist #a)) ([] <: list a) (intro_nil_lemma a)", "val t (a: Type0) : Tot Type0\nlet t a = cllist_lvalue a", "val null_ro (#a: _) : st_wp a\nlet null_ro #a : st_wp a = quotient_ro null", "val nllist_eq_not_null (a: Type0) (n: Ghost.erased nat) (r: t a)\n : Lemma (requires (is_null r == false))\n (ensures\n (nllist a n r ==\n (((vptr r) `vrefine` (v_c n r)) `vdep` (v_c_dep n r (nllist a)))\n `vrewrite`\n (v_c_l_rewrite n r (nllist a))))\nlet nllist_eq_not_null\n (a: Type0)\n (n: Ghost.erased nat)\n (r: t a)\n: Lemma\n (requires (is_null r == false))\n (ensures (\n nllist a n r == ((vptr r `vrefine` v_c n r) `vdep` v_c_dep n r (nllist a)) `vrewrite` v_c_l_rewrite n r (nllist a)\n ))\n= assert_norm (nllist a n r ==\n begin if is_null r\n then emp `vrewrite` v_null_rewrite a\n else ((vptr r `vrefine` v_c n r) `vdep` v_c_dep n r (nllist a)) `vrewrite` v_c_l_rewrite n r (nllist a)\n end\n )", "val is_null (#a:Type0) (r:ref a)\n : b:bool{b <==> r == null}\nlet is_null (#a:Type0) (r:ref a)\n : b:bool{b <==> r == null}\n = R.is_null r", "val length (#a:Type0) (x:t a) : GTot nat\nlet length x = L.length x", "val live: #a:Type -> HS.mem -> vector a -> GTot Type0\nlet live #a h vec =\n B.live h (Vec?.vs vec)", "val intro_llist_nil (#opened: _) (a:Type0)\n : SteelGhost unit opened emp (fun _ -> llist (null_llist #a))\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> v_llist #a null_llist h1 == [])\nlet intro_llist_nil a =\n intro_vrewrite emp (v_null_rewrite a);\n change_equal_slprop\n (emp `vrewrite` v_null_rewrite a)\n (llist0 (null_llist #a));\n llist_of_llist0 (null_llist #a)", "val pop (#a:Type0) (p:t a)\n : Steel (res a) (llist p) (fun res -> llist (res.n))\n (requires fun _ -> p =!= null_llist)\n (ensures fun h0 res h1 -> (\n let l = v_llist p h0 in\n Cons? l /\\\n res.x == L.hd l /\\\n v_llist res.n h1 == L.tl l))\nlet pop #a p =\n let h0 = get #(llist p) () in\n let tl = tail p in\n let x = read p in\n let v = data x in\n free p;\n let h1 = get #(llist tl) () in\n let l = Ghost.hide (v_llist tl h1) in\n change_slprop (llist tl) (llist (Res?.n (Res v tl))) l l (fun _ -> ());\n return (Res v tl)", "val length (#a:Type0) (v:vec a) : GTot nat\nlet length v = A.length v", "val llist_fragment_tail_cons_rewrite\n (#a: Type)\n (l: Ghost.erased (list a) {Cons? (Ghost.reveal l)})\n (llist_fragment_tail: vprop{t_of llist_fragment_tail == ref (ccell_ptrvalue a)})\n (x: normal (t_of (llist_fragment_tail `vdep` (llist_fragment_tail_cons_next_payload l))))\n : Tot (ref (ccell_ptrvalue a))\nlet llist_fragment_tail_cons_rewrite\n (#a: Type)\n (l: Ghost.erased (list a) { Cons? (Ghost.reveal l) })\n (llist_fragment_tail: vprop { t_of llist_fragment_tail == ref (ccell_ptrvalue a) })\n (x: normal (t_of (llist_fragment_tail `vdep` (llist_fragment_tail_cons_next_payload l))))\n: Tot (ref (ccell_ptrvalue a))\n= let (| _, (| c, _ |) |) = x in\n ccell_next c", "val v_node\n (#a: Type0)\n (#p: vprop)\n (r: t a)\n (h: rmem p {FStar.Tactics.with_tactic selector_tactic (can_be_split p (tree_node r) /\\ True)})\n : GTot (tree (node a))\nlet v_node\n (#a:Type0)\n (#p:vprop)\n (r:t a)\n (h:rmem p{\n FStar.Tactics.with_tactic selector_tactic (can_be_split p (tree_node r) /\\ True)\n })\n : GTot (tree (node a))\n = h (tree_node r)", "val v (a: Type0) : Tot Type0\nlet v (a: Type0) = list a", "val vptr0_rewrite\n (#a: Type)\n (r: ref a)\n (p: perm)\n (s: normal (vrefine_t (A.varrayp r p) (vptr0_refine r)))\n : Tot a\nlet vptr0_rewrite\n (#a: Type)\n (r: ref a)\n (p: perm)\n (s: normal (vrefine_t (A.varrayp r p) (vptr0_refine r)))\n: Tot a\n= Seq.index s 0", "val equal: tape -> tape -> GTot Type0\nlet equal (t1:tape) (t2:tape) = Seq.equal t1 t2", "val equal: tape -> tape -> GTot Type0\nlet equal (t1:tape) (t2:tape) = Seq.equal t1 t2", "val v_llist\n (#a: Type0)\n (#p: vprop)\n (r: t a)\n (h: rmem p {FStar.Tactics.with_tactic selector_tactic (can_be_split p (llist r) /\\ True)})\n : GTot (list a)\nlet v_llist (#a:Type0) (#p:vprop) (r:t a)\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (llist r) /\\ True)}) : GTot (list a)\n = h (llist r)", "val v_llist\n (#a: Type0)\n (#p: vprop)\n (r: t a)\n (h: rmem p {FStar.Tactics.with_tactic selector_tactic (can_be_split p (llist r) /\\ True)})\n : GTot (list a)\nlet v_llist (#a:Type0) (#p:vprop) (r:t a)\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (llist r) /\\ True)}) : GTot (list a)\n = h (llist r)", "val v_llist\n (#a: Type0)\n (#p: vprop)\n (r: t a)\n (h: rmem p {FStar.Tactics.with_tactic selector_tactic (can_be_split p (llist r) /\\ True)})\n : GTot (list a)\nlet v_llist (#a:Type0) (#p:vprop) (r:t a)\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (llist r) /\\ True)}) : GTot (list a)\n = h (llist r)", "val createL_pre (#a: Type0) (init: list a) : GTot Type0\nlet createL_pre (#a: Type0) (init: list a) : GTot Type0 =\n alloca_of_list_pre init", "val is_null (#a:Type) (ptr:t a) : (b:bool{b <==> ptr == null_llist})\nlet is_null #a ptr = is_null ptr", "val is_null (#a:Type) (ptr:t a) : (b:bool{b <==> ptr == null_llist})\nlet is_null #a ptr = is_null ptr", "val is_null (#a:Type) (ptr:t a) : (b:bool{b <==> ptr == null_llist})\nlet is_null #a ptr = is_null ptr", "val empty (a:Type0) : llist a\nlet empty a = null", "val intro_llist_nil (a:Type)\n : SteelT unit emp (fun _ -> llist (null_llist #a) [])\nlet intro_llist_nil a =\n rewrite_slprop emp (llist null_llist [])\n (fun m -> pure_interp (null_llist #a == null_llist) m;\n norm_spec [delta; zeta] ((llist (null_llist #a) [])))", "val v_ptrlist\n (#a: Type0)\n (#p: vprop)\n (r: t a)\n (h: rmem p {FStar.Tactics.with_tactic selector_tactic (can_be_split p (llist_ptr r) /\\ True)})\n : GTot (list a)\nlet v_ptrlist (#a:Type0) (#p:vprop) (r:t a)\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (llist_ptr r) /\\ True)}) : GTot (list a)\n = h (llist_ptr r)", "val create (#a:Type0) (l: list a) :\n Pure (t a)\n (requires True)\n (ensures fun x ->\n Ghost.reveal (v x) == l /\\\n length x == normalize_term (List.Tot.length l))\nlet create l = l", "val null (#a:Type0) : ref a\nlet null #a = A.null #a", "val null (#a:Type0) : ref a\nlet null #a = H.null #(U.raise_t a)", "val t: eqtype -> Type0 -> Type0\nlet t k v =\n LL2.t (k & v)", "val arrow_to_impl (#a #b: Type0) (_: (squash a -> GTot (squash b))) : GTot (a ==> b)\nlet arrow_to_impl #a #b f = squash_double_arrow (return_squash (fun x -> f (return_squash x)))", "val freeable: #a:Type -> vector a -> GTot Type0\nlet freeable #a vec =\n B.freeable (Vec?.vs vec)", "val null_llist (#a:Type) : t a\nlet null_llist #a = null", "val null_llist (#a:Type) : t a\nlet null_llist #a = null", "val null_llist (#a:Type) : t a\nlet null_llist #a = null", "val cllist0_refine: #a: Type0 -> c: cllist_ptrvalue a -> t_of emp -> Tot prop\nlet cllist0_refine\n (#a: Type0)\n (c: cllist_ptrvalue a)\n (_: t_of emp)\n: Tot prop\n= cllist_ptrvalue_is_null c == false", "val tree_sl (#a: Type0) (r: t a) : slprop u#1\nlet tree_sl #a ptr = Mem.h_exists (tree_sl' ptr)", "val t : Type0\nlet t = G.ref _ pcm", "val t : Type0\nlet t = bool & bool", "val t : Type0\nlet t = t", "val s: Type0 -> Type0\nlet s _ = unit", "val s: Type0 -> Type0\nlet s _ = unit", "val null_ro1 (#a: _) : st_wp a\nlet null_ro1 #a : st_wp a = fun s0 p -> forall x. p (x, s0)", "val sel (#a: Type0) (h: heap) (r: ref a) : GTot a\nlet sel (#a:Type0) (h:heap) (r:ref a) : GTot a\n = Heap.sel h r", "val v_: #t_k:eqtype -> #t_v:Type0 -> l:list (t_k & t_v) -> Tot (map t_k t_v)\nlet v_ #_ #t_v l =\n List.Tot.fold_right (fun (k, v) m -> M.upd m k (Some v)) l (M.const (None #t_v))", "val holds (#t: Type0) (p: rel t) (s s' : t) : GTot Type0\nlet holds (#t: Type0) (p: rel t) (s s' : t) : GTot Type0 =\n p s s'", "val is_nil (#a:Type0) (ptr:t a)\n : Steel bool (llist ptr) (fun _ -> llist ptr)\n (requires fun _ -> True)\n (ensures fun h0 res h1 ->\n (res == true <==> ptr == null_llist #a) /\\\n v_llist ptr h0 == v_llist ptr h1 /\\\n res == Nil? (v_llist ptr h1))\nlet is_nil\n #a ptr\n= is_nil' ptr;\n return (is_null ptr)", "val nlist_nil (#t: Type) : Tot (nlist 0 t)\nlet nlist_nil (#t: Type) : Tot (nlist 0 t) = []", "val nlist_nil (#t: Type) : Tot (nlist 0 t)\nlet nlist_nil (#t: Type) : Tot (nlist 0 t) = []", "val reveal: #a: Type u#a -> erased a -> GTot a\nlet reveal #a (E x) = x", "val is_null (#a:Type u#1) (r:ref a) : (b:bool{b <==> r == null})\nlet is_null #a r = Mem.is_null #(fractional a) #pcm_frac r", "val type_of_typ' (t: typ) : Tot Type0\nlet rec type_of_typ'\n (t: typ)\n: Tot Type0\n= match t with\n | TBase b -> type_of_base_typ b\n | TStruct l ->\n struct l\n | TUnion l ->\n union l\n | TArray length t ->\n array length (type_of_typ' t)\n | TPointer t ->\n pointer t\n | TNPointer t ->\n npointer t\n | TBuffer t ->\n buffer t\nand struct (l: struct_typ) : Tot Type0 =\n DM.t (struct_field l) (type_of_struct_field' l (fun x -> type_of_typ' x))\nand union (l: union_typ) : Tot Type0 =\n gtdata (struct_field l) (type_of_struct_field' l (fun x -> type_of_typ' x))", "val modifies_0' (h1 h2: HS.mem) : GTot Type0\nlet modifies_0' (h1 h2: HS.mem) : GTot Type0 =\n modifies_0_preserves_mreferences h1 h2 /\\\n modifies_0_preserves_regions h1 h2 /\\\n modifies_0_preserves_not_unused_in h1 h2", "val is_nil' (#opened: _) (#a: Type0) (ptr: t a)\n : SteelGhost unit\n opened\n (llist ptr)\n (fun _ -> llist ptr)\n (requires fun _ -> True)\n (ensures\n fun h0 _ h1 ->\n let res = is_null ptr in\n (res == true <==> ptr == null_llist #a) /\\ v_llist ptr h0 == v_llist ptr h1 /\\\n res == Nil? (v_llist ptr h1))\nlet is_nil' (#opened: _) (#a:Type0) (ptr:t a)\n : SteelGhost unit opened (llist ptr) (fun _ -> llist ptr)\n (requires fun _ -> True)\n (ensures fun h0 _ h1 ->\n let res = is_null ptr in\n (res == true <==> ptr == null_llist #a) /\\\n v_llist ptr h0 == v_llist ptr h1 /\\\n res == Nil? (v_llist ptr h1))\n=\n let res = is_null ptr in\n llist0_of_llist ptr;\n if res\n then begin\n change_equal_slprop\n (llist0 ptr)\n (emp `vrewrite` v_null_rewrite a);\n elim_vrewrite emp (v_null_rewrite a);\n intro_vrewrite emp (v_null_rewrite a);\n change_equal_slprop\n (emp `vrewrite` v_null_rewrite a)\n (llist0 ptr)\n end else begin\n change_equal_slprop\n (llist0 ptr)\n ((vptr ptr `vdep` llist_vdep ptr) `vrewrite` llist_vrewrite ptr);\n elim_vrewrite (vptr ptr `vdep` llist_vdep ptr) (llist_vrewrite ptr);\n intro_vrewrite (vptr ptr `vdep` llist_vdep ptr) (llist_vrewrite ptr);\n change_equal_slprop\n ((vptr ptr `vdep` llist_vdep ptr) `vrewrite` llist_vrewrite ptr)\n (llist0 ptr)\n end;\n llist_of_llist0 ptr", "val null (#a: _) : st_wp a\nlet null #a : st_wp a = fun s0 p -> forall r. p r", "val aref_live_at: h: heap -> a: aref -> t: Type0 -> rel: preorder t -> GTot Type0\nlet aref_live_at (h: heap) (a: aref) (t: Type0) (rel: preorder t) =\n let _ = () in\n Some? (h.memory a.a_addr) /\\\n (let Some (| a1, pre_opt, mm, _ |) = h.memory a.a_addr in\n t == a1 /\\ Some? pre_opt /\\ Some?.v pre_opt === rel /\\ mm == a.a_mm)", "val mnull (#a:Type0) (#rrel #rel:srel a) :Tot (b:mbuffer a rrel rel {g_is_null b})\nlet mnull #_ #_ #_ = Null", "val type_of_typ (t: typ) : Tot Type0\nlet rec type_of_typ\n (t: typ)\n: Tot Type0\n= match t with\n | TBase b -> type_of_base_typ b\n | TStruct l ->\n struct l\n | TUnion l ->\n union l\n | TArray length t ->\n array length (type_of_typ t)\n | TPointer t ->\n pointer t\n | TNPointer t ->\n npointer t\n | TBuffer t ->\n buffer t", "val no_lookahead (#t: Type0) (f: bare_parser t) : GTot Type0\nlet no_lookahead\n (#t: Type0)\n (f: bare_parser t)\n: GTot Type0\n= forall (x x' : bytes) . no_lookahead_on f x x'", "val t_null:typ\nlet t_null : typ = t_nil", "val modifies_0 (h0 h1: HS.mem) : GTot Type0\nlet modifies_0 (h0 h1: HS.mem) : GTot Type0 =\n modifies loc_none h0 h1", "val to_list_aux (#a: eqtype) {| _: ordered a |} (t: heap a) : GTot (list a)\nlet rec to_list_aux (#a: eqtype) {| _ : ordered a |} (t: heap a): GTot (list a) =\n match t with\n | Leaf -> []\n | Node k l r _ -> k :: merge (to_list_aux l) (to_list_aux r)", "val group: t:Type0{hasEq t}\nlet group = group'", "val null (#a:Type0) \n : ref a\nlet null (#a:Type0)\n : ref a\n = R.null #a", "val v_ind_llist\n (#a: Type0)\n (#p: vprop)\n (r: ref (t a))\n (h: rmem p {FStar.Tactics.with_tactic selector_tactic (can_be_split p (ind_llist r) /\\ True)})\n : GTot (list a)\nlet v_ind_llist (#a:Type0) (#p:vprop) (r:ref (t a))\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (ind_llist r) /\\ True)}) : GTot (list a)\n = h (ind_llist r)", "val otype_of_typ (t: typ) : Tot Type0\nlet rec otype_of_typ\n (t: typ)\n: Tot Type0\n= match t with\n | TBase b -> option (type_of_base_typ b)\n | TStruct l ->\n option (DM.t (struct_field l) (type_of_struct_field' l otype_of_typ))\n | TUnion l ->\n option (gtdata (struct_field l) (type_of_struct_field' l otype_of_typ))\n | TArray length t ->\n option (array length (otype_of_typ t))\n | TPointer t ->\n option (pointer t)\n | TNPointer t ->\n option (npointer t)\n | TBuffer t ->\n option (buffer t)", "val is_null (#a: Type0) (p: array a)\n : Pure bool (requires True) (ensures (fun res -> res == true <==> p == null))\nlet is_null (#a: Type0) (p: array a) : Pure bool\n (requires True)\n (ensures (fun res -> res == true <==> p == null))\n= is_null_ptr (ptr_of p)", "val and_then_cases_injective' (#t #t': Type) (p': (t -> Tot (bare_parser t'))) : GTot Type0\nlet and_then_cases_injective'\n (#t:Type)\n (#t':Type)\n (p': (t -> Tot (bare_parser t')))\n: GTot Type0\n= forall (x1 x2: t) (b1 b2: bytes) .\n and_then_cases_injective_precond p' x1 x2 b1 b2 ==>\n x1 == x2", "val llist0 (#a: Type0) (r: t a) : Pure vprop (requires True) (ensures (fun y -> t_of y == list a))\nlet llist0\n (#a: Type0)\n (r: t a)\n: Pure vprop\n (requires True)\n (ensures (fun y -> t_of y == list a))\n= if is_null r\n then emp `vrewrite` v_null_rewrite a\n else (vptr r `vdep` llist_vdep r) `vrewrite` llist_vrewrite r", "val write (#a:Type0)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\nlet write (#a:Type0)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\n = coerce_steel (fun _ -> R.write_pt r x);\n return ()", "val is_null (#a:Type) (r:ref a)\n : b:bool{b <==> r == null}\nlet is_null (#a:Type) (r:ref a)\n : b:bool{b <==> r == null}\n = R.is_null r", "val vrewrite_sel (v: vprop) (#t: Type) (f: (normal (t_of v) -> GTot t)) : Tot (selector t (normal (hp_of v)))\nlet vrewrite_sel\n v #t f\n=\n (fun (h: Mem.hmem (normal (hp_of v))) -> f ((normal (sel_of v) <: selector' _ _) h))", "val vbind' (a: vprop) (t: Type0) (b: (t_of a -> Tot vprop)) : GTot vprop'\nlet vbind'\n (a: vprop)\n (t: Type0)\n (b: (t_of a -> Tot vprop))\n: GTot vprop'\n= {\n hp = vbind_hp a t b;\n t = t;\n sel = vbind_sel a t b;\n}", "val intro_nil_lemma (a: Type0) (m: mem)\n : Lemma (requires interp (hp_of emp) m)\n (ensures interp (llist_sl (null_llist #a)) m /\\ llist_sel (null_llist #a) m == [])\nlet intro_nil_lemma (a:Type0) (m:mem) : Lemma\n (requires interp (hp_of emp) m)\n (ensures interp (llist_sl (null_llist #a)) m /\\ llist_sel (null_llist #a) m == [])\n = let ptr:t a = null_llist in\n pure_interp (ptr == null_llist) m;\n let open FStar.Tactics in\n assert (llist_sl' ptr [] == Mem.pure (ptr == null_llist)) by (norm [delta; zeta; iota]);\n llist_sel_interp ptr [] m", "val and_then_cases_injective (#t #t': Type) (p': (t -> Tot (bare_parser t'))) : GTot Type0\nlet and_then_cases_injective\n (#t:Type)\n (#t':Type)\n (p': (t -> Tot (bare_parser t')))\n: GTot Type0\n= forall (x1 x2: t) (b1 b2: bytes) . {:pattern (parse (p' x1) b1); (parse (p' x2) b2)}\n and_then_cases_injective_precond p' x1 x2 b1 b2 ==>\n x1 == x2", "val value (#t: _) (p: repr_ptr t) : GTot t\nlet value #t (p:repr_ptr t) : GTot t = p.meta.v", "val decl:Type0\nlet decl : Type0 = either not_type_decl type_decl", "val sel (#a: Type0) (h: heap) (s: array a) : GTot (seq a)\nlet sel (#a:Type0) (h:heap) (s:array a) : GTot (seq a) = Heap.sel h (as_ref s)" ], "closest_src": [ { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.v_null_rewrite" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.llist_vrewrite" }, { "project_name": "steel", "file_name": "CQueue.LList.fst", "name": "CQueue.LList.cllist_rewrite" }, { "project_name": "steel", "file_name": "CQueue.LList.fst", "name": "CQueue.LList.cllist0_rewrite" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.null_t" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.is_null_t" }, { "project_name": "karamel", "file_name": "LowStar.Lib.LinkedList2.fst", "name": "LowStar.Lib.LinkedList2.v" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.v_c_l_rewrite" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.vbind0_rewrite" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.p" }, { "project_name": "steel", "file_name": "CQueue.Cell.fst", "name": "CQueue.Cell.ccell_rewrite" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.intro_llist_nil" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.v" }, { "project_name": "FStar", "file_name": "LowParseWriters.NoHoare.fst", "name": "LowParseWriters.NoHoare.valid_rewrite_prop" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.v" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.t" }, { "project_name": "steel", "file_name": "CQueue.Cell.fst", "name": "CQueue.Cell.ccell_is_lvalue_rewrite" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.is_null" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.is_null" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.p" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fsti", "name": "Steel.ST.Array.null" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.sel" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.intro_llist_nil" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.t" }, { "project_name": "FStar", "file_name": "AlgWP.fst", "name": "AlgWP.null_ro" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.nllist_eq_not_null" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.is_null" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.length" }, { "project_name": "FStar", "file_name": "LowStar.Vector.fst", "name": "LowStar.Vector.live" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.intro_llist_nil" }, { "project_name": "steel", "file_name": "Selectors.LList.Derived.fst", "name": "Selectors.LList.Derived.pop" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.length" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.llist_fragment_tail_cons_rewrite" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.v_node" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.v" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.vptr0_rewrite" }, { "project_name": "FStar", "file_name": "FStar.DM4F.OTP.Heap.fst", "name": "FStar.DM4F.OTP.Heap.equal" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.Random.fst", "name": "FStar.DM4F.Heap.Random.equal" }, { "project_name": "steel", "file_name": "Selectors.LList.fsti", "name": "Selectors.LList.v_llist" }, { "project_name": "steel", "file_name": "Selectors.LList2.fsti", "name": "Selectors.LList2.v_llist" }, { "project_name": "steel", "file_name": "Selectors.LList3.fsti", "name": "Selectors.LList3.v_llist" }, { "project_name": "FStar", "file_name": "LowStar.BufferCompat.fst", "name": "LowStar.BufferCompat.createL_pre" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.is_null" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.is_null" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.is_null" }, { "project_name": "steel", "file_name": "LList.ST.fst", "name": "LList.ST.empty" }, { "project_name": "steel", "file_name": "LList.Invariant.fst", "name": "LList.Invariant.intro_llist_nil" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fsti", "name": "Selectors.PtrLList.v_ptrlist" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.create" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.null" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.null" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.t" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.arrow_to_impl" }, { "project_name": "FStar", "file_name": "LowStar.Vector.fst", "name": "LowStar.Vector.freeable" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.null_llist" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.null_llist" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.null_llist" }, { "project_name": "steel", "file_name": "CQueue.LList.fst", "name": "CQueue.LList.cllist0_refine" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.tree_sl" }, { "project_name": "zeta", "file_name": "Zeta.Steel.ThreadLogMap.fst", "name": "Zeta.Steel.ThreadLogMap.t" }, { "project_name": "dice-star", "file_name": "HWState.fst", "name": "HWState.t" }, { "project_name": "everparse", "file_name": "EverParse3d.InputStream.All.fst", "name": "EverParse3d.InputStream.All.t" }, { "project_name": "steel", "file_name": "Pulse.C.Typenat.fst", "name": "Pulse.C.Typenat.s" }, { "project_name": "steel", "file_name": "Steel.C.Typenat.fst", "name": "Steel.C.Typenat.s" }, { "project_name": "FStar", "file_name": "AlgWP.fst", "name": "AlgWP.null_ro1" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.sel" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.v_" }, { "project_name": "FStar", "file_name": "Benton2004.Aux.fst", "name": "Benton2004.Aux.holds" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.is_nil" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.nlist_nil" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.List.fsti", "name": "MiniParse.Spec.List.nlist_nil" }, { "project_name": "FStar", "file_name": "FStar.Ghost.fst", "name": "FStar.Ghost.reveal" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.is_null" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.type_of_typ'" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_0'" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.is_nil'" }, { "project_name": "FStar", "file_name": "AlgWP.fst", "name": "AlgWP.null" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.aref_live_at" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.mnull" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fsti", "name": "FStar.Pointer.Base.type_of_typ" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.Base.fst", "name": "MiniParse.Spec.Base.no_lookahead" }, { "project_name": "steel", "file_name": "CDDL.Spec.fsti", "name": "CDDL.Spec.t_null" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fsti", "name": "FStar.Pointer.Base.modifies_0" }, { "project_name": "FStar", "file_name": "LeftistHeap.fst", "name": "LeftistHeap.to_list_aux" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.CommonDH.fst", "name": "MiTLS.CommonDH.group" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.null" }, { "project_name": "steel", "file_name": "Selectors.LList.fsti", "name": "Selectors.LList.v_ind_llist" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.otype_of_typ" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fsti", "name": "Steel.ST.Array.is_null" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.Combinators.fst", "name": "MiniParse.Spec.Combinators.and_then_cases_injective'" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.llist0" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.write" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.is_null" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.vrewrite_sel" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.vbind'" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.intro_nil_lemma" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fsti", "name": "LowParse.Spec.Combinators.and_then_cases_injective" }, { "project_name": "everparse", "file_name": "LowParse.Repr.fsti", "name": "LowParse.Repr.value" }, { "project_name": "everparse", "file_name": "InterpreterTarget.fsti", "name": "InterpreterTarget.decl" }, { "project_name": "FStar", "file_name": "FStar.Array.fsti", "name": "FStar.Array.sel" } ], "selected_premises": [ "Selectors.LList3.data", "Steel.Memory.hmem", "Steel.Preorder.vhist", "FStar.PCM.compatible", "FStar.Real.one", "Steel.Preorder.pcm_history", "Steel.FractionalPermission.writeable", "Steel.Preorder.history_val", "FStar.PCM.op", "Steel.Memory.full_mem", "Selectors.LList3.next", "FStar.Pervasives.Native.snd", "Selectors.LList3.null_llist", "Steel.FractionalPermission.comp_perm", "FStar.PCM.composable", "FStar.Pervasives.Native.fst", "FStar.Real.two", "Steel.Preorder.p_op", "Steel.FractionalPermission.full_perm", "Steel.FractionalPermission.sum_perm", "Selectors.LList3.mk_cell", "Steel.Memory.a_mem_prop", "Steel.FractionalPermission.lesser_perm", "Steel.Memory.hmem_with_inv_except", "Steel.Memory.mprop", "Steel.Preorder.comm_op", "Steel.Memory.inames", "Steel.Preorder.qhistory", "Steel.Memory.is_witness_invariant", "Steel.Memory.hmem_with_inv", "Steel.Preorder.history_compose", "Steel.Memory.ptr", "FStar.NMSTTotal.get", "Steel.Memory.is_frame_monotonic", "Steel.Preorder.curval", "Steel.Preorder.extends", "Steel.Preorder.preorder_of_pcm", "Steel.Memory.mem_prop_is_affine", "Steel.Memory.fresh_wrt", "FStar.Pervasives.reveal_opaque", "Steel.Preorder.p_composable", "Steel.Preorder.property", "Steel.Memory.property", "Steel.Memory.dep_slprop_is_affine", "Steel.Preorder.history_composable", "Steel.Preorder.extends'", "Steel.Preorder.p", "Steel.Memory.mprop2", "Steel.Preorder.hval", "FStar.NMSTTotal.bind", "FStar.NMSTTotal.subcomp", "Steel.Preorder.hist", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity", "Steel.Preorder.lift_fact", "Steel.Preorder.extends_length_eq", "FStar.MSTTotal.subcomp", "Steel.Memory.name_of_inv", "Steel.Preorder.pcm_of_preorder", "FStar.NMSTTotal.return", "FStar.Real.zero", "FStar.MSTTotal.bind", "FStar.MSTTotal.return", "Selectors.LList3.is_null", "Steel.Preorder.flip", "Steel.Preorder.induces_preorder", "FStar.Pervasives.dfst", "FStar.Pervasives.st_post_h", "Steel.Preorder.pcm_history_preorder", "Steel.Preorder.hperm", "Steel.Preorder.unit_history", "FStar.Pervasives.ex_pre", "FStar.Preorder.preorder_rel", "FStar.Pervasives.ex_post'", "Steel.FractionalPermission.half_perm", "Steel.Memory.stable_property", "Steel.Memory.affine_star_smt", "Steel.Memory.ref", "Steel.Preorder.hval_tot", "Steel.Preorder.extends_related_head", "FStar.Pervasives.dsnd", "Steel.Preorder.extend_history", "Steel.Preorder.lem_is_unit", "Steel.FractionalPermission.lesser_equal_perm", "FStar.Ghost.tot_to_gtot", "Steel.Preorder.extend_history'", "FStar.PCM.lem_commutative", "Steel.Memory.mem_inv", "FStar.MSTTotal.get", "FStar.PCM.lem_assoc_l", "Steel.Preorder.lift_fact_is_stable", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.ex_post", "FStar.MSTTotal.put", "Steel.Preorder.pcm_history_induces_preorder", "FStar.Set.as_set'", "FStar.Witnessed.Core.s_predicate", "Steel.Preorder.extends_trans", "Steel.Memory.add_inv", "FStar.Set.as_set", "Prims.pure_post'" ], "source_upto_this": "module Selectors.LList3\n\nopen Steel.FractionalPermission\nmodule Mem = Steel.Memory\n\n#push-options \"--__no_positivity\"\nnoeq\ntype cell (a: Type0) = {\n tail_fuel: Ghost.erased nat;\n next: ref (cell a);\n data: a;\n}\n#pop-options\n\nlet next #a (c:cell a) : t a = c.next\nlet data #a (c:cell a) : a = c.data\nlet mk_cell #a (n: t a) (d:a) = {\n tail_fuel = Ghost.hide 0;\n next = n;\n data = d\n}\n\nlet null_llist #a = null\nlet is_null #a ptr = is_null ptr\n" }, { "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.inames_ok", "opens_and_abbrevs": [ { "abbrev": "W", "full_module": "FStar.Witnessed.Core" }, { "abbrev": "L", "full_module": "FStar.List.Tot" }, { "abbrev": "S", "full_module": "FStar.Set" }, { "abbrev": "S", "full_module": "FStar.Set" }, { "abbrev": "PP", "full_module": "PulseCore.Preorder" }, { "abbrev": "H", "full_module": "PulseCore.Heap" }, { "open": "FStar.FunctionalExtensionality" }, { "abbrev": "F", "full_module": "FStar.FunctionalExtensionality" }, { "abbrev": "M_", "full_module": "PulseCore.NondeterministicMonotonicStateMonad" }, { "open": "FStar.PCM" }, { "open": "FStar.Ghost" }, { "abbrev": "PP", "full_module": "PulseCore.Preorder" }, { "abbrev": "M_", "full_module": "PulseCore.NondeterministicMonotonicStateMonad" }, { "open": "FStar.PCM" }, { "open": "FStar.Ghost" }, { "open": "PulseCore" }, { "open": "PulseCore" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val inames_ok (e:inames) (m:mem) : prop", "source_definition": "let inames_ok e m = inames_in e m.locks", "source_range": { "start_line": 394, "start_col": 0, "end_line": 394, "end_col": 39 }, "interleaved": false, "definition": "fun e m -> PulseCore.Memory.inames_in e (Mkmem?.locks m)", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "PulseCore.Memory.inames", "PulseCore.Memory.mem", "PulseCore.Memory.inames_in", "PulseCore.Memory.__proj__Mkmem__item__locks", "Prims.prop" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "e: PulseCore.Memory.inames -> m: PulseCore.Memory.mem -> Prims.prop", "prompt": "let inames_ok e m =\n ", "expected_response": "inames_in e m.locks", "source": { "project_name": "steel", "file_name": "lib/pulse_core/PulseCore.Memory.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "PulseCore.Memory.fst", "checked_file": "dataset/PulseCore.Memory.fst.checked", "interface_file": true, "dependencies": [ "dataset/PulseCore.Preorder.fst.checked", "dataset/PulseCore.NondeterministicMonotonicStateMonad.fsti.checked", "dataset/PulseCore.Heap.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Witnessed.Core.fsti.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.PCM.fst.checked", "dataset/FStar.MSTTotal.fst.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.IndefiniteDescription.fsti.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Calc.fsti.checked" ] }, "definitions_in_context": [ "lock_state", "Invariant", "Invariant", "Invariant", "inv", "inv", "val mem : Type u#(a + 1)", "let lock_store : Type u#(a+1) = list (lock_state u#a)", "mem", "mem", "ctr", "ctr", "heap", "heap", "locks", "locks", "val core_mem (m:mem u#a) : mem u#a", "let heap_of_mem (x:mem) : H.heap = x.heap", "let mem_of_heap (h:H.heap) : mem = {\n ctr = 0;\n heap = h;\n locks = []\n}", "val slprop : Type u#(a + 1)", "val interp (p:slprop u#a) (m:mem u#a) : prop", "let mem_set_heap (m:mem) (h:H.heap) : mem = {\n ctr = m.ctr;\n heap = h;\n locks = m.locks;\n}", "val equiv (p1 p2:slprop u#a) : prop", "let core_mem (m:mem) : mem = mem_of_heap (heap_of_mem m)", "val core_mem_invol (m: mem u#a) : Lemma\n (core_mem (core_mem m) == core_mem m)\n [SMTPat (core_mem (core_mem m))]", "val slprop_extensionality (p q:slprop)\n : Lemma\n (requires p `equiv` q)\n (ensures p == q)", "let core_mem_invol m = ()", "val slprop_equiv_refl (p:slprop)\n : Lemma (p `equiv` p)\n [SMTPat (equiv p p)]", "let disjoint (m0 m1:mem u#h)\n : prop\n = m0.ctr == m1.ctr /\\\n H.disjoint m0.heap m1.heap /\\\n m0.locks == m1.locks", "val core_ref : Type u#0", "let ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref", "let disjoint_sym (m0 m1:mem u#h)\n : Lemma (disjoint m0 m1 <==> disjoint m1 m0)\n [SMTPat (disjoint m0 m1)]\n = ()", "val core_ref_null : core_ref", "let join (m0:mem u#h) (m1:mem u#h{disjoint m0 m1}) : mem u#h\n= {\n ctr = m0.ctr;\n heap = H.join m0.heap m1.heap;\n locks = m0.locks\n }", "let null (#a:Type u#a) (#pcm:pcm a) : ref a pcm = core_ref_null", "val core_ref_is_null (r:core_ref) : b:bool { b <==> r == core_ref_null }", "let is_null (#a:Type u#a) (#pcm:pcm a) (r:ref a pcm) : (b:bool{b <==> r == null}) = core_ref_is_null r", "let join_commutative (m0 m1:mem)\n : Lemma\n (requires\n disjoint m0 m1)\n (ensures\n (disjoint m0 m1 /\\\n disjoint m1 m0 /\\\n join m0 m1 == join m1 m0))\n = H.join_commutative m0.heap m1.heap", "val emp : slprop u#a", "val pure (p:prop) : slprop u#a", "val pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a", "val star (p1 p2:slprop u#a) : slprop u#a", "val h_exists (#a:Type u#b) (f: (a -> slprop u#a)) : slprop u#a", "val equiv_symmetric (p1 p2:slprop)\n : squash (p1 `equiv` p2 ==> p2 `equiv` p1)", "let disjoint_join (m0 m1 m2:mem)\n : Lemma (disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) ==>\n disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\n = H.disjoint_join m0.heap m1.heap m2.heap", "val equiv_extensional_on_star (p1 p2 p3:slprop)\n : squash (p1 `equiv` p2 ==> (p1 `star` p3) `equiv` (p2 `star` p3))", "val emp_unit (p:slprop)\n : Lemma (p `equiv` (p `star` emp))", "let join_associative (m0 m1 m2:mem)\n : Lemma\n (requires\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures\n (disjoint_join m0 m1 m2;\n join m0 (join m1 m2) == join (join m0 m1) m2))\n = H.join_associative m0.heap m1.heap m2.heap", "val pure_equiv (p q:prop)\n : Lemma ((p <==> q) ==> (pure p `equiv` pure q))", "val pure_true_emp (_:unit)\n : Lemma (pure True `equiv` emp)", "val star_commutative (p1 p2:slprop)\n : Lemma ((p1 `star` p2) `equiv` (p2 `star` p1))", "let slprop = H.slprop", "let interp p m = H.interp p m.heap", "val star_associative (p1 p2 p3:slprop)\n : Lemma ((p1 `star` (p2 `star` p3))\n `equiv`\n ((p1 `star` p2) `star` p3))", "let equiv p1 p2 = forall m. interp p1 m <==> interp p2 m", "let slprop_extensionality p q =\n assert (forall m. interp p m <==> interp q m);\n let aux (h:H.heap)\n : Lemma (H.interp p h <==> H.interp q h)\n [SMTPat (H.interp p h)]\n = let m : mem = { ctr = 0; heap = h; locks = [] } in\n assert (interp p m <==> interp q m)\n in\n assert (forall h. H.interp p h <==> H.interp q h);\n H.slprop_extensionality p q", "val star_congruence (p1 p2 p3 p4:slprop)\n : Lemma (requires p1 `equiv` p3 /\\ p2 `equiv` p4)\n (ensures (p1 `star` p2) `equiv` (p3 `star` p4))", "val iname : eqtype", "val reveal_equiv (p1 p2:slprop u#a) : Lemma\n (ensures (forall m. interp p1 m <==> interp p2 m) <==> p1 `equiv` p2)\n [SMTPat (p1 `equiv` p2)]", "let inames = erased (S.set iname)", "let reveal_equiv p1 p2 = ()", "val inames_ok (e:inames) (m:mem) : prop", "let slprop_equiv_refl p = ()", "val inames_ok_empty (m:mem)\n : Lemma (ensures inames_ok Set.empty m)\n [SMTPat (inames_ok Set.empty m)]", "let core_ref = H.core_ref", "let core_ref_null = H.core_ref_null", "let core_ref_is_null r = H.core_ref_is_null r", "let emp : slprop u#a = H.emp", "let pure = H.pure", "let pts_to = H.pts_to", "let h_and = H.h_and", "val locks_invariant (e:inames) (m:mem u#a) : slprop u#a", "let h_or = H.h_or", "let star = H.star", "val full_mem_pred: mem -> prop", "let wand = H.wand", "let full_mem = m:mem{full_mem_pred m}", "let h_exists = H.h_exists", "let h_forall = H.h_forall", "let equiv_symmetric (p1 p2:slprop u#a) = H.equiv_symmetric p1 p2", "val mem_evolves : FStar.Preorder.preorder full_mem", "let equiv_heap_iff_equiv (p1 p2:slprop u#a)\n : Lemma (ensures (H.equiv p1 p2 <==> equiv p1 p2))\n [SMTPat (equiv p1 p2)]\n = let aux_lr ()\n : Lemma\n (requires H.equiv p1 p2)\n (ensures equiv p1 p2)\n [SMTPat ()]\n = ()\n in\n let aux_rl_helper1 (h:H.heap)\n : Lemma\n (requires equiv p1 p2 /\\ H.interp p1 h)\n (ensures H.interp p2 h)\n [SMTPat ()]\n = assert (interp p2 (mem_of_heap h))\n in\n let aux_rl_helper2 (h:H.heap)\n : Lemma\n (requires equiv p1 p2 /\\ H.interp p2 h)\n (ensures H.interp p1 h)\n [SMTPat ()]\n = assert (interp p2 (mem_of_heap h))\n in\n let aux_rl ()\n : Lemma\n (requires equiv p1 p2)\n (ensures H.equiv p1 p2)\n [SMTPat ()]\n = () in\n ()", "let action_except (a:Type u#a) (except:inames) (expects:slprop) (provides: a -> slprop) =\n frame:slprop -> MstTot a except expects provides frame", "val sel_action (#a:Type u#1) (#pcm:_) (e:inames) (r:ref a pcm) (v0:erased a)\n : action_except (v:a{compatible pcm v0 v}) e (pts_to r v0) (fun _ -> pts_to r v0)", "val upd_action (#a:Type u#1) (#pcm:_) (e:inames)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:a {FStar.PCM.frame_preserving pcm v0 v1 /\\ pcm.refine v1})\n : action_except unit e (pts_to r v0) (fun _ -> pts_to r v1)", "let equiv_heap_iff_equiv_forall ()\n : Lemma (ensures (forall p1 p2. H.equiv p1 p2 <==> equiv p1 p2))\n = let aux p1 p2\n : Lemma (ensures (H.equiv p1 p2 <==> equiv p1 p2))\n [SMTPat ()]\n = equiv_heap_iff_equiv p1 p2\n in\n ()", "val free_action (#a:Type u#1) (#pcm:pcm a) (e:inames)\n (r:ref a pcm) (x:FStar.Ghost.erased a{FStar.PCM.exclusive pcm x /\\ pcm.refine pcm.FStar.PCM.p.one})\n : action_except unit e (pts_to r x) (fun _ -> pts_to r pcm.FStar.PCM.p.one)", "val split_action\n (#a:Type u#1)\n (#pcm:pcm a)\n (e:inames)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n : action_except unit e (pts_to r (v0 `op pcm` v1)) (fun _ -> pts_to r v0 `star` pts_to r v1)", "let equiv_extensional_on_star (p1 p2 p3:slprop u#a) =\n equiv_heap_iff_equiv_forall ();\n H.equiv_extensional_on_star p1 p2 p3", "let emp_unit p = H.emp_unit p", "val intro_emp (m:mem) : Lemma (interp emp m)", "let intro_emp m = H.intro_emp (heap_of_mem m)", "val gather_action\n (#a:Type u#1)\n (#pcm:pcm a)\n (e:inames)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a)\n : action_except (_:unit{composable pcm v0 v1}) e (pts_to r v0 `star` pts_to r v1) (fun _ -> pts_to r (op pcm v0 v1))", "let pure_equiv p q = H.pure_equiv p q", "val pure_interp (q:prop) (m:mem) : Lemma (interp (pure q) m <==> q)", "let pure_interp q m = H.pure_interp q (heap_of_mem m)", "let pure_true_emp () : Lemma (pure True `equiv` emp) =\n FStar.Classical.forall_intro (pure_interp True);\n FStar.Classical.forall_intro intro_emp;\n slprop_extensionality (pure True) emp", "val alloc_action (#a:Type u#1) (#pcm:pcm a) (e:inames) (x:a{compatible pcm x x /\\ pcm.refine x})\n : action_except (ref a pcm) e emp (fun r -> pts_to r x)", "val pure_star_interp (p:slprop u#a) (q:prop) (m:mem)\n : Lemma (interp (p `star` pure q) m <==>\n interp (p `star` emp) m /\\ q)", "val select_refine (#a:Type u#1) (#p:pcm a)\n (e:inames)\n (r:ref a p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n FStar.PCM.frame_compatible p x v y})))\n : action_except (v:a{compatible p x v /\\ p.refine v}) e\n (pts_to r x)\n (fun v -> pts_to r (f v))", "let pure_star_interp p q m = H.pure_star_interp p q (heap_of_mem m)", "let ptr (#a: Type u#a) (#pcm: pcm a) (r:ref a pcm) =\n h_exists (pts_to r)", "val upd_gen (#a:Type) (#p:pcm a) (e:inames) (r:ref a p) (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n : action_except unit e\n (pts_to r x)\n (fun _ -> pts_to r y)", "val pts_to_compatible\n (#a:Type u#a)\n (#pcm:pcm a)\n (x:ref a pcm)\n (v0 v1:a)\n (m:mem u#a)\n : Lemma\n (interp (pts_to x v0 `star` pts_to x v1) m <==>\n composable pcm v0 v1 /\\ interp (pts_to x (op pcm v0 v1)) m)", "let property (a:Type)\n = a -> prop", "val witnessed (#a:Type u#1)\n (#pcm:pcm a)\n (r:ref a pcm)\n (fact:property a)\n : Type0", "val pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))", "let stable_property (#a:Type) (pcm:pcm a)\n = fact:property a {\n FStar.Preorder.stable fact (PP.preorder_of_pcm pcm)\n }", "val pts_to_not_null (#a:Type u#a)\n (#pcm:_)\n (x:ref a pcm)\n (v:a)\n (m:mem u#a)\n : Lemma (requires interp (pts_to x v) m)\n (ensures x =!= null)", "val witness (#a:Type) (#pcm:pcm a)\n (e:inames)\n (r:erased (ref a pcm))\n (fact:stable_property pcm)\n (v:Ghost.erased a)\n (_:squash (forall z. compatible pcm v z ==> fact z))\n : action_except (witnessed r fact) e (pts_to r v) (fun _ -> pts_to r v)", "let pts_to_compatible #a #pcm x v0 v1 m\n = H.pts_to_compatible #a #pcm x v0 v1 (heap_of_mem m)", "val recall (#a:Type u#1) (#pcm:pcm a) (#fact:property a)\n (e:inames)\n (r:erased (ref a pcm))\n (v:Ghost.erased a)\n (w:witnessed r fact)\n : action_except (v1:Ghost.erased a{compatible pcm v v1}) e\n (pts_to r v)\n (fun v1 -> pts_to r v `star` pure (fact v1))", "let pts_to_compatible_equiv #a #pcm x v0 v1\n = H.pts_to_compatible_equiv #a #pcm x v0 v1", "let pts_to_not_null #a #pcm x v m\n = H.pts_to_not_null #a #pcm x v (heap_of_mem m)", "val pts_to_not_null_action \n (#a:Type u#1) (#pcm:pcm a)\n (e:inames)\n (r:erased (ref a pcm))\n (v:Ghost.erased a)\n: action_except (squash (not (is_null r))) e\n (pts_to r v)\n (fun _ -> pts_to r v)", "let hmem (p:slprop u#a) = m:mem u#a {interp p m}", "val intro_star (p q:slprop) (mp:hmem p) (mq:hmem q)\n : Lemma\n (requires\n disjoint mp mq)\n (ensures\n interp (p `star` q) (join mp mq))", "val elim_star (p q:slprop) (m:hmem (p `star` q))\n : Lemma\n (requires\n interp (p `star` q) m)\n (ensures exists ml mr.\n disjoint ml mr /\\ m == join ml mr /\\ interp p ml /\\ interp q mr)", "val pre_inv : Type0", "val inv (p:slprop u#1) : Type0", "val pre_inv_of_inv (#p:slprop) (i:inv p) : pre_inv", "val interp_star\n (p q: slprop)\n (m: mem)\n: Lemma\n (interp (p `star` q) m <==> (exists (mp: mem) (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m))", "val name_of_pre_inv (i:pre_inv) : GTot iname", "let name_of_inv (#p:slprop) (i:inv p)\n : GTot iname\n = name_of_pre_inv (pre_inv_of_inv i)", "let intro_star p q mp mq =\n H.intro_star p q (heap_of_mem mp) (heap_of_mem mq)", "let mem_inv (#p:slprop) (e:inames) (i:inv p) : erased bool = elift2 (fun e i -> Set.mem i e) e (name_of_inv i)", "let elim_star p q m =\n let h = heap_of_mem m in\n H.elim_star p q h;\n assert (exists hl hr. H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr);\n let hl = FStar.IndefiniteDescription.indefinite_description_tot H.heap (fun hl ->\n exists hr. H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr) in\n let hr = FStar.IndefiniteDescription.indefinite_description_tot H.heap (fun hr ->\n H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr) in\n let ml = mem_set_heap m hl in\n let mr = mem_set_heap m hr in\n assert (disjoint ml mr);\n assert (m == join ml mr);\n assert (interp p ml);\n assert (interp q mr);\n ()", "let add_inv (#p:slprop) (e:inames) (i:inv p) : inames =\n Set.union (Set.singleton (name_of_inv i)) (reveal e)", "let fresh_wrt (ctx:list pre_inv)\n (i:iname)\n = forall i'. List.Tot.memP i' ctx ==> name_of_pre_inv i' <> i", "val fresh_invariant (e:inames) (p:slprop) (ctx:list pre_inv)\n : action_except (i:inv p { not (mem_inv e i) /\\ fresh_wrt ctx (name_of_inv i) }) e p (fun _ -> emp)", "val new_invariant (e:inames) (p:slprop)\n : action_except (inv p) e p (fun _ -> emp)", "val with_invariant (#a:Type)\n (#fp:slprop)\n (#fp':a -> slprop)\n (#opened_invariants:inames)\n (#p:slprop)\n (i:inv p{not (mem_inv opened_invariants i)})\n (f:action_except a (add_inv opened_invariants i) (p `star` fp) (fun x -> p `star` fp' x))\n : action_except a opened_invariants fp fp'", "let interp_star\n (p q: slprop)\n (m: mem)\n: Lemma\n (interp (p `star` q) m <==> (exists (mp: mem) (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m))\n= let left = interp (p `star` q) m in\n let right = exists (mp: mem) (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m in\n let f ()\n : Lemma\n (requires left)\n (ensures right)\n =\n elim_star p q m\n in\n let g ()\n : Lemma\n (requires right)\n (ensures left)\n =\n Classical.exists_elim left #_ #(fun mp -> exists (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m) () (fun mp ->\n Classical.exists_elim left #_ #(fun mq -> disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m) () (fun mq ->\n intro_star p q mp mq\n )\n )\n in\n Classical.move_requires f ();\n Classical.move_requires g ()", "val frame (#a:Type)\n (#opened_invariants:inames)\n (#pre:slprop)\n (#post:a -> slprop)\n (frame:slprop)\n ($f:action_except a opened_invariants pre post)\n : action_except a opened_invariants (pre `star` frame) (fun x -> post x `star` frame)", "val witness_h_exists (#opened_invariants:_) (#a:_) (p:a -> slprop)\n : action_except (erased a) opened_invariants\n (h_exists p)\n (fun x -> p x)", "val intro_exists (#opened_invariants:_) (#a:_) (p:a -> slprop) (x:erased a)\n : action_except unit opened_invariants\n (p x)\n (fun _ -> h_exists p)", "let star_commutative (p1 p2:slprop) =\n H.star_commutative p1 p2", "val lift_h_exists (#opened_invariants:_) (#a:_) (p:a -> slprop)\n : action_except unit opened_invariants\n (h_exists p)\n (fun _a -> h_exists #(U.raise_t a) (U.lift_dom p))", "let star_associative (p1 p2 p3:slprop) =\n H.star_associative p1 p2 p3", "val elim_pure (#opened_invariants:_) (p:prop)\n : action_except (u:unit{p}) opened_invariants (pure p) (fun _ -> emp)", "let star_congruence (p1 p2 p3 p4:slprop) =\n equiv_heap_iff_equiv_forall ();\n H.star_congruence p1 p2 p3 p4", "val intro_pure (#opened_invariants:_) (p:prop) (_:squash p)\n : action_except unit opened_invariants emp (fun _ -> pure p)", "val affine_star (p q:slprop) (m:mem)\n : Lemma ((interp (p `star` q) m ==> interp p m /\\ interp q m))", "val drop (#opened_invariants:_) (p:slprop)\n : action_except unit opened_invariants p (fun _ -> emp)", "let affine_star (p q:slprop) (m:mem) =\n H.affine_star p q (heap_of_mem m)", "let iname = nat", "let rec lock_store_invariant (e:inames) (l:lock_store u#a) : slprop u#a =\n let current_addr = L.length l - 1 in\n match l with\n | [] -> emp\n | Invariant p :: tl ->\n if current_addr `S.mem` e then\n lock_store_invariant e tl\n else\n p `star` lock_store_invariant e tl", "let lock_i (i:iname) (l:lock_store { i < L.length l }) =\n let ix = L.length l - i - 1 in\n L.index l ix", "let iname_for_p (i:iname) (p:slprop) : W.s_predicate lock_store =\n fun l ->\n i < L.length l /\\\n (lock_i i l).inv == p", "let lock_store_evolves : FStar.Preorder.preorder lock_store =\n fun (l1 l2 : lock_store) ->\n L.length l2 >= L.length l1 /\\\n (forall (i:nat{i < L.length l1}).\n (lock_i i l1).inv == (lock_i i l2).inv)", "let inames_in (e:inames) (l:lock_store) : prop = forall i. Set.mem i e ==> i < L.length l" ], "closest": [ "val inames_ok (e:inames) (m:mem) : prop\nlet inames_ok e m = inames_in e m.locks", "val name_is_ok (i: iname) (m0: full_mem u#1) : prop\nlet name_is_ok (i:iname) (m0:full_mem u#1) : prop = i < List.Tot.length m0.locks", "val inames_in (e: inames) (l: lock_store) : prop\nlet inames_in (e:inames) (l:lock_store) : prop = forall i. Set.mem i e ==> i < L.length l", "val mem_iname (e: inames) (i: iname) : erased bool\nlet mem_iname (e:inames) (i:iname) : erased bool = elift2 (fun e i -> Set.mem i e) e i", "val locks_invariant (e:inames) (m:mem u#a) : slprop u#a\nlet locks_invariant (e:inames) (m:mem u#a) : slprop u#a =\n lock_store_invariant e m.locks\n `star`\n ctr_validity m.ctr (heap_of_mem m)", "val add_iname (e: inames) (i: iname) : inames\nlet add_iname (e:inames) (i:iname) : inames = Set.union (Set.singleton i) (reveal e)", "val mem_inv (#p: slprop) (e: inames) (i: inv p) : erased bool\nlet mem_inv (#p:slprop) (e:inames) (i:inv p) : erased bool = elift2 (fun e i -> Set.mem i e) e (name_of_inv i)", "val mem_inv (#p: slprop) (e: inames) (i: inv p) : erased bool\nlet mem_inv (#p:slprop) (e:inames) (i:inv p) : erased bool = elift2 (fun e i -> Set.mem i e) e (name_of_inv i)", "val mem_inv (#p: vprop) (e: inames) (i: inv p) : erased bool\nlet mem_inv (#p:vprop) (e:inames) (i:inv p) : erased bool = mem_iname e (name_of_inv i)", "val mem_inv (#p: vprop) (e: inames) (i: inv p) : erased bool\nlet mem_inv (#p:vprop) (e:inames) (i:inv p) : erased bool = elift2 (fun e i -> Set.mem i e) e (name_of_inv i)", "val inames_of (c: comp_st) : term\nlet inames_of (c:comp_st) : term =\n match c with\n | C_ST _ \n | C_STGhost _ -> tm_emp_inames\n | C_STAtomic inames _ _ -> inames", "val inames_subset (is1 is2: inames) : Type0\nlet inames_subset (is1 is2 : inames) : Type0 =\r\n Set.subset is1 is2", "val inames_subset (is1 is2: inames) : Type0\nlet inames_subset (is1 is2 : inames) : Type0 =\n Set.subset is1 is2", "val all_inames:inames\nlet all_inames : inames = Set.complement Set.empty", "val emp_inames:inames\nlet emp_inames : inames = Set.empty", "val emp_inames:inames\nlet emp_inames : inames = Ghost.hide Set.empty", "val emp_inames:inames\nlet emp_inames : inames = Ghost.hide Set.empty", "val valid_mem (m: maddr) (s: state) : prop0\nlet valid_mem (m:maddr) (s:state) : prop0 =\n valid_maddr_offset64 m.offset /\\ valid_maddr m s", "val add_inv (#p: vprop) (e: inames) (i: inv p) : inames\nlet add_inv (#p:vprop) (e:inames) (i:inv p) : inames = add_iname e (name_of_inv i)", "val add_inv (#p: vprop) (e: inames) (i: inv p) : inames\nlet add_inv (#p:vprop) (e:inames) (i:inv p) : inames =\n Set.union (Set.singleton (name_of_inv i)) (reveal e)", "val mem_inv (#p: _) (opens: inames) (i: inv p) : GTot bool\nlet mem_inv (#p:_) (opens:inames) (i:inv p)\r\n: GTot bool\r\n= Set.mem (name_of_inv i) opens", "val mem_inv (#p: vprop) (u: inames) (i: inv p) : GTot bool\nlet mem_inv (#p:vprop) (u:inames) (i:inv p) : GTot bool =\n Set.mem (reveal (name i)) (reveal u)", "val is_implies (is: inames) (hyp concl v: vprop) : GTot prop\nlet is_implies\n (is : inames)\n (hyp concl: vprop)\n (v: vprop)\n: GTot prop\n= squash (elim_implies_t is hyp concl v)", "val add_iname (inv_p inames inv: term) : term\nlet add_iname (inv_p inames inv:term)\n: term\n= tm_fstar \n (Pulse.Reflection.Util.add_inv_tm\n (elab_term inv_p)\n (elab_term inames)\n (elab_term inv))\n inames.range", "val add_inv (#p: slprop) (e: inames) (i: inv p) : inames\nlet add_inv (#p:slprop) (e:inames) (i:inv p) : inames =\n Set.union (Set.singleton (name_of_inv i)) (reveal e)", "val add_inv (#p: slprop) (e: inames) (i: inv p) : inames\nlet add_inv (#p:slprop) (e:inames) (i:inv p) : inames =\n Set.union (Set.singleton (name_of_inv i)) (reveal e)", "val get0: #opened: inames -> #p: vprop -> unit\n -> repr (erased (rmem p))\n true\n opened\n Unobservable\n p\n (fun _ -> p)\n (requires fun _ -> True)\n (ensures fun h0 r h1 -> frame_equalities p h0 h1 /\\ frame_equalities p r h1)\nlet get0 (#opened:inames) (#p:vprop) (_:unit) : repr (erased (rmem p))\n true opened Unobservable p (fun _ -> p)\n (requires fun _ -> True)\n (ensures fun h0 r h1 -> frame_equalities p h0 h1 /\\ frame_equalities p r h1)\n = fun frame ->\n let m0:full_mem = NMSTTotal.get () in\n let h0 = mk_rmem p (core_mem m0) in\n lemma_frame_equalities_refl p h0;\n h0", "val live (x: t) (m: HS.mem) : Tot prop\nlet live\n (x: t)\n (m: HS.mem)\n: Tot prop\n= let read = U64.v (B.deref m x.Aux.position) in\n Aux.live x.Aux.base m /\\\n B.live m x.Aux.position /\\\n read <= U64.v (len_all x) /\\\n read == Seq.length (Aux.get_read x.Aux.base m)", "val Steel.Memory.with_inv_except = m: Steel.Memory.mem -> e: Steel.Memory.inames -> fp: Steel.Memory.slprop -> Prims.prop\nlet with_inv_except (m:mem) e (fp:slprop) = interp (fp `star` locks_invariant e m) m", "val invlist_names (is: invlist0) : inames\nlet rec invlist_names (is : invlist0) : inames =\n match is with\n | [] -> emp_inames\n | i :: is -> add_iname (invlist_names is) (name_of_inv <| dsnd i)", "val inames_ext (is1 is2: inames)\n : Lemma (requires forall i. Set.mem i is1 <==> Set.mem i is2)\n (ensures is1 == is2)\n [SMTPat (is1 == is2)]\nlet inames_ext (is1 is2 : inames)\n : Lemma (requires forall i. Set.mem i is1 <==> Set.mem i is2)\n (ensures is1 == is2)\n [SMTPat (is1 == is2)]\n = Set.lemma_equal_intro is1 is2", "val valid_rmem (#frame:vprop) (h:rmem' frame) : prop\nlet valid_rmem (#frame:vprop) (h:rmem' frame) : prop =\n forall (p p1 p2:vprop). can_be_split frame p /\\ p == VStar p1 p2 ==>\n (h p1, h p2) == h (VStar p1 p2)", "val node_valid (h:HS.mem) (n:node 'a) : prop\nlet node_valid h n = True /\\ B.live h n", "val new_invariant_tot_action\n (e: inames)\n (p: slprop)\n (m0: hmem_with_inv_except e p {e `inames_in` m0.locks})\n : Pure (iname & hmem_with_inv_except e emp)\n (requires True)\n (ensures\n fun (i, m1) ->\n iname_for_p_mem i p m1 /\\ frame_related_mems p emp e m0 m1 /\\ mem_evolves m0 m1)\nlet new_invariant_tot_action (e:inames) (p:slprop) (m0:hmem_with_inv_except e p{ e `inames_in` m0.locks })\n : Pure (iname & hmem_with_inv_except e emp)\n (requires True)\n (ensures fun (i, m1) ->\n iname_for_p_mem i p m1 /\\\n frame_related_mems p emp e m0 m1 /\\\n mem_evolves m0 m1)\n = let (| i, l1 |) = extend_lock_store e m0.locks p in\n let m1 = { m0 with locks = l1 } in\n assert (lock_store_invariant e m1.locks ==\n p `star` lock_store_invariant e m0.locks);\n calc (equiv) {\n linv e m1;\n (equiv) {}\n (lock_store_invariant e m1.locks\n `star`\n ctr_validity m1.ctr (heap_of_mem m1));\n (equiv) {}\n ((p `star` lock_store_invariant e m0.locks)\n `star`\n ctr_validity m1.ctr (heap_of_mem m1));\n (equiv) {\n H.star_associative p (lock_store_invariant e m0.locks) (ctr_validity m1.ctr (heap_of_mem m1))\n }\n (p `star` (lock_store_invariant e m0.locks\n `star`\n ctr_validity m1.ctr (heap_of_mem m1)));\n (equiv) { }\n (p `star` linv e m0);\n };\n assert (iname_for_p_mem i p m1);\n assert (lock_store_evolves m0.locks l1);\n assert (mem_evolves m0 m1);\n hmem_with_inv_equiv e m0 p;\n assert (interp (p `star` lock_store_invariant e m0.locks) m1);\n assert (interp (lock_store_invariant e m1.locks) m1);\n H.emp_unit (lock_store_invariant e m1.locks);\n H.star_commutative (lock_store_invariant e m1.locks) emp;\n assert (interp (emp `star` lock_store_invariant e m1.locks) m1);\n hmem_with_inv_equiv e m1 emp;\n let m1 : hmem_with_inv_except e emp = m1 in\n let aux (frame:slprop)\n : Lemma\n (requires interp ((p `star` frame) `star` linv e m0) m0)\n (ensures interp ((emp `star` frame) `star` linv e m1) m1 /\\\n mem_evolves m0 m1 /\\\n (forall (mp:mprop frame). mp (core_mem m0) <==> mp (core_mem m1)))\n [SMTPat (p `star` frame)]\n = assert (interp ((p `star` frame) `star` linv e m0) m1);\n calc (equiv) {\n ((p `star` frame) `star` linv e m0);\n (equiv) {\n H.star_commutative p frame;\n H.star_congruence (p `star` frame) (linv e m0) (frame `star` p) (linv e m0);\n H.star_associative frame p (linv e m0)\n }\n (frame `star` (p `star` linv e m0));\n (equiv) {\n H.star_congruence frame (p `star` linv e m0) frame (linv e m1)\n }\n (frame `star` linv e m1);\n (equiv) {\n H.emp_unit (frame `star` linv e m1);\n H.star_commutative (frame `star` linv e m1) emp;\n H.star_associative emp frame (linv e m1)\n }\n ((emp `star` frame) `star` linv e m1);\n };\n assert (interp ((emp `star` frame) `star` linv e m1) m1)\n in\n assert (frame_related_mems p emp e m0 m1);\n ( i, m1 )", "val join_inames (is1 is2: inames) : inames\nlet join_inames (is1 is2 : inames) : inames =\n Set.union is1 is2", "val join_inames (is1 is2: inames) : inames\nlet join_inames (is1 is2 : inames) : inames =\r\n Set.union is1 is2", "val Steel.Memory.linv = e: Steel.Memory.inames -> m: Steel.Memory.mem -> Steel.Memory.slprop\nlet linv e (m:mem) = locks_invariant e m", "val iname : eqtype\nlet iname = nat", "val iname : eqtype\nlet iname = iname", "val iname : eqtype\nlet iname = Act.iname", "val rewrite (#opened:inames)\n (p q: vprop)\n : STGhost unit opened p (fun _ -> q) (p == q) (fun _ -> True)\nlet rewrite #o p q =\n weaken p q (fun _ -> ())", "val name_of_inv (#p: slprop) (i: inv p) : GTot iname\nlet name_of_inv (#p:slprop) (i:inv p)\n : GTot iname\n = name_of_pre_inv (pre_inv_of_inv i)", "val name_of_inv (#p: slprop) (i: inv p) : GTot iname\nlet name_of_inv (#p:slprop) (i:inv p)\n : GTot iname\n = name_of_pre_inv (pre_inv_of_inv i)", "val name_of_inv (#p: vprop) (i: inv p) : GTot iname\nlet name_of_inv (#p:vprop) (i:inv p) : GTot iname = Mem.name_of_inv i", "val interp (p:slprop u#a) (m:mem u#a) : prop\nlet interp p m = H.interp p m.heap", "val remove_inv (#p: vprop) (e: inames) (i: inv p) : inames\nlet remove_inv (#p:vprop) (e:inames) (i:inv p) : inames = Set.remove (name_of_inv i) e", "val add_inv (#p: vprop) (u: inames) (i: inv p) : inames\nlet add_inv (#p:vprop) (u:inames) (i:inv p) : inames =\n Set.union (Set.singleton (reveal (name i))) (reveal u)", "val remove_iname (inv_p inames inv: term) : term\nlet remove_iname (inv_p inames inv:term)\n: term\n= tm_fstar \n (Pulse.Reflection.Util.remove_inv_tm\n (elab_term inv_p)\n (elab_term inames)\n (elab_term inv))\n inames.range", "val inames_join_emp_r (is1: inames)\n : Lemma (join_inames is1 emp_inames == is1) [SMTPat (join_inames is1 emp_inames)]\nlet inames_join_emp_r (is1 : inames)\n : Lemma (join_inames is1 emp_inames == is1) [SMTPat (join_inames is1 emp_inames)]\n = Set.lemma_equal_intro (join_inames is1 emp_inames) is1", "val valid_maddr (m: maddr) (s: vale_state) : prop0\nlet valid_maddr (m:maddr) (s:vale_state) : prop0 =\n valid_mem64 (eval_maddr m s) (get_vale_heap s.vs_heap)", "val iname_of #p (f : finv p) : erased iname\nlet iname_of #p (f : finv p) : erased iname = name_of_inv f.i", "val implies_\n (#[T.exact (`(hide Set.empty))] is : inames) // Empty inames by default\n (hyp concl: vprop)\n: Tot vprop\nlet implies_\n (#is : inames)\n (hyp concl: vprop)\n: Tot vprop\n= exists_ (fun (v: vprop) ->\n v `star` pure (is_implies is hyp concl v)\n )", "val add_inv (#p: _) (opens: inames) (i: inv p) : inames\nlet add_inv (#p:_) (opens:inames) (i:inv p)\r\n: inames\r\n= Set.union (Set.singleton (name_of_inv i)) opens", "val inames_join_emp_l (is1: inames)\n : Lemma (join_inames emp_inames is1 == is1) [SMTPat (join_inames emp_inames is1)]\nlet inames_join_emp_l (is1 : inames)\n : Lemma (join_inames emp_inames is1 == is1) [SMTPat (join_inames emp_inames is1)]\n = Set.lemma_equal_intro (join_inames emp_inames is1) is1", "val invlist_nodups (is: invlist0) : prop\nlet rec invlist_nodups (is : invlist0) : prop =\n match is with\n | [] -> True\n | i :: is -> not (mem_inv (invlist_names is) (dsnd i)) /\\ invlist_nodups is", "val emp_inames_included: g: env -> i: term -> tot_typing g i tm_inames\n -> prop_validity g (tm_inames_subset tm_emp_inames i)\nlet emp_inames_included (g:env) (i:term) (_:tot_typing g i tm_inames)\n: prop_validity g (tm_inames_subset tm_emp_inames i)\n= RU.magic()", "val tm_inames_subset_typing (g: env) (inames1 inames2: term)\n : tot_typing g (tm_inames_subset inames1 inames2) tm_prop\nlet tm_inames_subset_typing (g:env) (inames1 inames2 : term) : tot_typing g (tm_inames_subset inames1 inames2) tm_prop =\n (* Need to add the typing hypothesis for `inames_subset` to\n the env and a precondition that the inames have type Pulse.Lib.Core.inames in g,\n which the caller should get from an inversion lemma *)\n RU.magic()", "val inames_join_self (is1: inames)\n : Lemma (join_inames is1 is1 == is1) [SMTPat (join_inames is1 is1)]\nlet inames_join_self (is1 : inames)\n : Lemma (join_inames is1 is1 == is1) [SMTPat (join_inames is1 is1)]\n = Set.lemma_equal_intro (join_inames is1 is1) is1", "val check_iname_disjoint (g: env) (r: range) (inv_p inames inv: term)\n : T.Tac (Pulse.Typing.prop_validity g (inv_disjointness inv_p inames inv))\nlet check_iname_disjoint (g:env) (r:range) (inv_p inames inv:term)\n: T.Tac (Pulse.Typing.prop_validity g (inv_disjointness inv_p inames inv))\n= let goal = inv_disjointness inv_p inames inv in\n let (| tag, goal_typing |) =\n Pulse.Checker.Pure.core_check_term_at_type g goal tm_prop\n in\n if tag <> T.E_Total\n then T.fail \"Impossible: prop typing is always total\"\n else (\n let tok = Pulse.Checker.Pure.try_check_prop_validity g goal goal_typing in\n match tok with\n | None ->\n fail_doc g (Some r) [\n Pulse.PP.text \"Failed to prove that an invariant is not recursively opened:\";\n Pulse.PP.prefix 4 1 (Pulse.PP.text \"The set of invariant names: \") (Pulse.PP.pp inames);\n Pulse.PP.prefix 4 1 (Pulse.PP.text \"may contain the invariant: \") (Pulse.PP.pp inv);\n ]\n | Some tok -> tok\n )", "val add_remove_inverse\n (g: env)\n (inv_p inames inv: term)\n (inv_p_typing: tot_typing g inv_p tm_vprop)\n (inames_typing: tot_typing g inames tm_inames)\n (inv_typing: tot_typing g inv (tm_inv inv_p))\n : T.Tac\n (prop_validity g (tm_inames_subset (add_iname inv_p (remove_iname inv_p inames inv) inv) inames)\n )\nlet add_remove_inverse (g:env)\n (inv_p inames inv:term)\n (inv_p_typing:tot_typing g inv_p tm_vprop)\n (inames_typing:tot_typing g inames tm_inames)\n (inv_typing:tot_typing g inv (tm_inv inv_p))\n: T.Tac \n (prop_validity g \n (tm_inames_subset \n (add_iname inv_p\n (remove_iname inv_p inames inv)\n inv)\n inames))\n= let typing\n : tot_typing g \n (tm_inames_subset \n (add_iname inv_p\n (remove_iname inv_p inames inv)\n inv)\n inames)\n tm_prop\n = let remove_typing = remove_iname_typing g inv_p_typing inames_typing inv_typing in\n let add_typing = add_iname_typing g inv_p_typing remove_typing inv_typing in\n tm_inames_subset_typing g \n add_typing\n inames_typing\n in\n match Pulse.Checker.Pure.try_check_prop_validity g _ typing with\n | None -> \n let open Pulse.PP in\n fail_doc g None [\n Pulse.PP.text \"Failed to prove that only the following invariants are opened\";\n prefix 4 1 (text \"Inferred the following invariants were opened: \") \n (pp (add_iname inv_p\n (remove_iname inv_p inames inv)\n inv)) ^/^\n prefix 4 1 (text \"But expected to only open: \") (pp inames)\n ]\n \n | Some tok -> tok", "val name (#p:_) (i:inv p) : Ghost.erased iname\nlet name (#p:_) (i:inv p) = name_of_inv (dsnd i)", "val lock_store_invariant (e: inames) (l: lock_store u#a) : slprop u#a\nlet rec lock_store_invariant (e:inames) (l:lock_store u#a) : slprop u#a =\n let current_addr = L.length l - 1 in\n match l with\n | [] -> emp\n | Invariant p :: tl ->\n if current_addr `S.mem` e then\n lock_store_invariant e tl\n else\n p `star` lock_store_invariant e tl", "val neg (p: prop) : prop\nlet neg (p:prop) : prop = ~p", "val rewrite_slprop0\n (#opened: inames)\n (p q: vprop)\n (proof: (m: mem -> Lemma (requires interp (hp_of p) m) (ensures interp (hp_of q) m)))\n : repr unit false opened Unobservable p (fun _ -> q) (fun _ -> True) (fun _ _ _ -> True)\nlet rewrite_slprop0 (#opened:inames) (p q:vprop)\n (proof:(m:mem) -> Lemma\n (requires interp (hp_of p) m)\n (ensures interp (hp_of q) m)\n ) : repr unit false opened Unobservable p (fun _ -> q)\n (fun _ -> True) (fun _ _ _ -> True)\n = fun frame ->\n let m:full_mem = NMSTTotal.get () in\n proof (core_mem m);\n Classical.forall_intro (Classical.move_requires proof);\n Mem.star_associative (hp_of p) frame (locks_invariant opened m);\n intro_star p q (frame `Mem.star` locks_invariant opened m) (sel_of p m) (sel_of q m) m proof;\n Mem.star_associative (hp_of q) frame (locks_invariant opened m)", "val tm_inames_subset (inames1 inames2: term) : term\nlet tm_inames_subset (inames1 inames2 : term) : term =\n let inames1 = elab_term inames1 in\n let inames2 = elab_term inames2 in\n let join_lid = Pulse.Reflection.Util.mk_pulse_lib_core_lid \"inames_subset\" in\n let join : R.term = R.pack_ln (R.Tv_FVar (R.pack_fv join_lid)) in\n with_range (Tm_FStar (R.mk_e_app join [inames1; inames2]))\n (T.range_of_term inames1)", "val same_domain (h:vale_heap) (m:S.machine_heap) : prop0\nlet same_domain h m = Set.equal (IB.addrs_set (_ih h)) (Map.domain m)", "val same_domain (h:vale_heap) (m:S.machine_heap) : prop0\nlet same_domain h m = Set.equal (IB.addrs_set (_ih h)) (Map.domain m)", "val elim_pure (p:prop)\r\n: act (squash p) emp_inames (pure p) (fun _ -> emp)\nlet elim_pure (p:prop)\r\n: act (squash p) emp_inames (pure p) (fun _ -> emp)\r\n= fun #ictx -> mem_action_as_action _ _ _ _ (elim_pure #ictx p)", "val valid_maddr (m: maddr) (s: state) : prop0\nlet valid_maddr (m:maddr) (s:state) : prop0 =\n M.valid_mem64 (eval_maddr m s) (M.get_vale_heap (coerce s.ms_heap))", "val mk_mem_inv (invP inames inv: R.term) : R.term\nlet mk_mem_inv (invP inames inv:R.term) : R.term =\n let mem_inv_tm = mk_pulse_lib_core_lid \"mem_inv\" in\n let t = R.pack_ln (R.Tv_FVar (R.pack_fv mem_inv_tm)) in\n R.mk_app t [ im invP; ex inames; ex inv ]", "val drop (#opened:inames) (p:vprop) : STGhostT unit opened p (fun _ -> emp)\nlet drop #o p = coerce_ghost (fun _ -> SEA.drop p)", "val valid_maddr128 (m: maddr) (s: vale_state) : prop0\nlet valid_maddr128 (m:maddr) (s:vale_state) : prop0 =\n valid_mem128 (eval_maddr m s) (get_vale_heap s.vs_heap)", "val move_invariant\n (e: inames)\n (l: lock_store)\n (p: slprop)\n (i: iname{iname_for_p i p l /\\ ~(i `Set.mem` e)})\n : Lemma (H.equiv (lock_store_invariant e l) (p `star` (lock_store_invariant (set_add i e) l)))\nlet rec move_invariant (e:inames) (l:lock_store) (p:slprop)\n (i:iname{iname_for_p i p l /\\ ~(i `Set.mem` e)})\n : Lemma (H.equiv (lock_store_invariant e l)\n (p `star` lock_store_invariant (set_add i e) l))\n = let rec aux (i:iname) (m:lock_store)\n : Lemma (requires i >= L.length m)\n (ensures (lock_store_invariant e m `H.equiv` lock_store_invariant (set_add i e) m))\n = match m with\n | [] -> ()\n | Invariant p::tl ->\n aux i tl;\n H.star_congruence p (lock_store_invariant e tl) p (lock_store_invariant (set_add i e) tl)\n in\n let current_addr = L.length l - 1 in\n match l with\n | [] -> ()\n | Invariant q::tl ->\n if i = current_addr\n then begin\n assert (lock_store_invariant e l == p `star` lock_store_invariant e tl);\n aux i tl;\n H.star_congruence p (lock_store_invariant e tl) p (lock_store_invariant (set_add i e) tl);\n ()\n end\n else begin\n move_invariant e tl p i;\n assert (lock_store_invariant e tl `equiv`\n (p `star` lock_store_invariant (set_add i e) tl));\n H.star_congruence q (lock_store_invariant e tl) q (p `star` lock_store_invariant (set_add i e) tl);\n if Set.mem current_addr e\n then ()\n else begin\n let r = lock_store_invariant (set_add i e) tl in\n assert (lock_store_invariant e l `equiv`\n (q `star` (p `star` r)));\n H.star_associative q p r;\n H.star_commutative q p;\n H.star_congruence (q `star` p) r (p `star` q) r;\n H.star_associative p q r\n end\n end", "val valid (#t:Type) (p:repr_ptr t) (h:HS.mem) : prop\nlet valid (#t:Type) (p:repr_ptr t) (h:HS.mem)\n = valid' p h", "val full_mem_pred: mem -> prop\nlet full_mem_pred (m:mem) = H.full_heap_pred (heap_of_mem m)", "val valid_mem128 (r i: reg) (s: state) : prop0\nlet valid_mem128 (r:reg) (i:reg) (s:state) : prop0 =\n M.valid_mem128 (eval_reg r s + eval_reg i s) (M.get_vale_heap (coerce s.ms_heap))", "val weaken (#opened:inames)\n (p q:vprop)\n (l:(m:mem) -> Lemma\n (requires interp (hp_of p) m)\n (ensures interp (hp_of q) m))\n : STGhostT unit opened p (fun _ -> q)\nlet weaken #o p q l =\n coerce_ghost (fun () -> SEA.rewrite_slprop p q l)", "val in_state_prop (p: prot) (vsend: chan_val) : prop\nlet in_state_prop (p:prot) (vsend:chan_val) : prop =\n p == step vsend.chan_prot vsend.chan_msg", "val comp_inames (c: comp{C_STAtomic? c}) : term\nlet comp_inames (c:comp { C_STAtomic? c }) : term =\n match c with\n | C_STAtomic inames _ _ -> inames", "val state_correspondence (inames:inames)\n : Lemma\n (let s = state_uses inames in\n s.S.hprop == slprop /\\\n s.S.mem == mem /\\\n s.S.interp == interp /\\\n s.S.star == star /\\\n s.S.locks_invariant == locks_invariant inames /\\\n (forall (p q frame:slprop)\n (m0:mem{interp (p `star` frame `star` locks_invariant inames m0) m0})\n (m1:mem{interp (q `star` frame `star` locks_invariant inames m1) m1}).\n (forall (f_frame:mprop frame). f_frame (core_mem m0) == f_frame (core_mem m1)) ==> \n S.post_preserves_frame #s q frame m0 m1))\nlet state_correspondence inames =\n let s = state_uses inames in\n assert_norm (s.S.hprop == slprop) ;\n assert_norm (s.S.mem == mem) ;\n assert_norm (s.S.interp == interp);\n assert_norm (s.S.star == star);\n assert_norm (s.S.locks_invariant == locks_invariant inames)", "val elim_h_exists (#a:_) (p:a -> slprop) (m:mem)\n : Lemma (interp (h_exists p) m ==> (exists x. interp (p x) m))\nlet elim_h_exists (#a:_) (p:a -> slprop) (m:mem) = H.elim_h_exists p (heap_of_mem m)", "val new_invariant (e:inames) (p:slprop)\n : action_except (inv p) e p (fun _ -> emp)\nlet new_invariant (e:inames) (p:slprop) (frame:slprop)\n : MstTot (inv p) e p (fun _ -> emp) frame (fun _ -> True) (fun _ _ _ -> True)\n = fresh_invariant e p [] frame", "val get_hmap (m:mem') :hmap\nlet get_hmap m = m.h", "val pure_interp (q:prop) (m:mem)\n : Lemma (interp (pure q) m <==> q)\nlet pure_interp q m = H.pure_interp q (heap_of_mem m)", "val equiv (p q:vprop) : prop\nlet equiv (p q:vprop) : prop = Mem.equiv (hp_of p) (hp_of q) /\\ True", "val recall (#inames: _) (#a:Type u#1) (#pcm:pcm a)\n (fact:property a)\n (r:ref a pcm)\n (v:erased a)\n (w:witnessed r fact)\n : STAtomicU (erased a) inames\n (pts_to r v)\n (fun v1 -> pts_to r v)\n (requires True)\n (ensures fun v1 -> fact v1 /\\ compatible pcm v v1)\nlet recall fact r v w = C.coerce_atomic (fun _ -> P.recall fact r v w)", "val elim_exists (#a:Type u#a) (p:a -> slprop)\r\n: act (erased a) emp_inames (exists* x. p x) (fun x -> p x)\nlet elim_exists (#a:Type u#a) (p:a -> slprop)\r\n: act (erased a) emp_inames (exists* x. p x) (fun x -> p x)\r\n= coerce_eq (exists_equiv #a #p) (elim_exists' #a p)", "val implies_unfold (#opened: _) (#is: inames) (hyp concl: vprop)\n : STGhost vprop\n opened\n (( @==> ) #is hyp concl)\n (fun v -> v)\n True\n (fun v -> is_implies is hyp concl v)\nlet implies_unfold\n (#opened: _)\n (#is : inames)\n (hyp concl: vprop)\n: STGhost vprop opened\n ((@==>) #is hyp concl)\n (fun v -> v)\n True\n (fun v -> is_implies is hyp concl v)\n= let v = elim_exists () in\n let _ = elim_pure _ in\n v", "val emp_inames_tm:R.term\nlet emp_inames_tm : R.term = R.pack_ln (R.Tv_FVar (R.pack_fv emp_inames_lid))", "val extend_lock_store (e: inames) (l: lock_store{e `inames_in` l}) (p: slprop)\n : i: iname &\n l':\n lock_store\n {lock_store_invariant e l' == p `star` (lock_store_invariant e l) /\\ iname_for_p i p l'}\nlet extend_lock_store (e:inames) (l:lock_store{e `inames_in` l}) (p:slprop)\n : i:iname &\n l':lock_store {\n lock_store_invariant e l' == p `star` lock_store_invariant e l /\\\n iname_for_p i p l'\n }\n = (| L.length l, Invariant p :: l |)", "val fresh_invariant (e:inames) (p:slprop) (ctx:list pre_inv)\n : action_except (i:inv p { not (mem_inv e i) /\\ fresh_wrt ctx (name_of_inv i) }) e p (fun _ -> emp)\nlet fresh_invariant (e:inames) (p:slprop) (ctx:list pre_inv) (frame:slprop)\n : MstTot (i:inv p { not (mem_inv e i) /\\ fresh_wrt ctx (name_of_inv i)}) e p (fun _ -> emp) frame (fun _ -> True) (fun _ _ _ -> True)\n = let m0 = NMSTTotal.get () in\n recall_all ctx;\n ac_reasoning_for_m_frame_preserving p frame (locks_invariant e m0) m0;\n assert (interp (p `star` locks_invariant e m0) m0);\n let r = new_invariant_tot_action e p m0 in\n let ( i, m1 ) = r in\n assert (i == List.Tot.length m0.locks);\n assert (not (Set.mem i e));\n assert (mem_evolves m0 m1);\n NMSTTotal.put #full_mem #mem_evolves m1;\n iname_for_p_stable i p;\n let w = NMSTTotal.witness full_mem mem_evolves (iname_for_p_mem i p) in\n let w0 = NMSTTotal.witness full_mem mem_evolves (name_is_ok i) in\n (| hide i, w0, w |)", "val valid_mem_addr (tm: tmaddr) (s: state) : prop0\nlet valid_mem_addr (tm:tmaddr) (s:state) : prop0 =\n let (m, t) = tm in\n valid_maddr m s /\\\n valid_mem_operand64 (eval_maddr m s) t (M.get_vale_heap (coerce s.ms_heap)) (coerce s.ms_heap).vf_layout", "val change_slprop0\n (#opened: inames)\n (p q: vprop)\n (vp: erased (t_of p))\n (vq: erased (t_of q))\n (proof:\n (m: mem\n -> Lemma (requires interp (hp_of p) m /\\ sel_of p m == reveal vp)\n (ensures interp (hp_of q) m /\\ sel_of q m == reveal vq)))\n : repr unit\n false\n opened\n Unobservable\n p\n (fun _ -> q)\n (fun h -> h p == reveal vp)\n (fun _ _ h1 -> h1 q == reveal vq)\nlet change_slprop0 (#opened:inames) (p q:vprop) (vp:erased (t_of p)) (vq:erased (t_of q))\n (proof:(m:mem) -> Lemma\n (requires interp (hp_of p) m /\\ sel_of p m == reveal vp)\n (ensures interp (hp_of q) m /\\ sel_of q m == reveal vq)\n ) : repr unit false opened Unobservable p (fun _ -> q) (fun h -> h p == reveal vp) (fun _ _ h1 -> h1 q == reveal vq)\n = fun frame ->\n let m:full_mem = NMSTTotal.get () in\n Classical.forall_intro_3 reveal_mk_rmem;\n proof (core_mem m);\n Classical.forall_intro (Classical.move_requires proof);\n Mem.star_associative (hp_of p) frame (locks_invariant opened m);\n intro_star p q (frame `Mem.star` locks_invariant opened m) vp vq m proof;\n Mem.star_associative (hp_of q) frame (locks_invariant opened m)", "val norm_list (p: prop) : prop\nlet norm_list (p:prop) : prop =\n norm [zeta; iota; delta_only [`%list_to_seq_post]] p", "val norm_list (p: prop) : prop\nlet norm_list (p:prop) : prop =\n norm [zeta; iota; delta_only [`%list_to_seq_post]] p", "val preserves_frame_cong (e: inames) (p q r s: slprop) (m0 m1: mem)\n : Lemma (requires p `equiv` r /\\ q `equiv` s /\\ preserves_frame e p q m0 m1)\n (ensures preserves_frame e r s m0 m1)\nlet preserves_frame_cong (e:inames) (p q:slprop) (r s:slprop) (m0 m1:mem)\n : Lemma\n (requires p `equiv` r /\\ q `equiv` s /\\ preserves_frame e p q m0 m1)\n (ensures\n preserves_frame e r s m0 m1)\n = let aux0 (p q r s:slprop)\n : Lemma\n (requires p `equiv` s)\n (ensures (((p `star` q) `star` r) `equiv`\n ((s `star` q) `star` r)))\n = star_congruence p q s q;\n star_congruence (p `star` q) r (s `star` q) r\n in\n let aux (frame:slprop)\n : Lemma (requires interp ((r `star` frame) `star` locks_invariant e m0) m0)\n (ensures interp ((s `star` frame) `star` locks_invariant e m1) m1 /\\\n interp ((p `star` frame) `star` locks_invariant e m0) m0)\n [SMTPat (r `star` frame)]\n = aux0 p frame (locks_invariant e m0) r;\n aux0 q frame (locks_invariant e m1) s;\n assert (((p `star` frame) `star` locks_invariant e m0) `equiv`\n ((r `star` frame) `star` locks_invariant e m0));\n assert (interp ((p `star` frame) `star` locks_invariant e m0) m0);\n assert (interp ((q `star` frame) `star` locks_invariant e m1) m1);\n assert (((q `star` frame) `star` locks_invariant e m1) `equiv`\n ((s `star` frame) `star` locks_invariant e m1));\n ()\n in\n ()", "val all_inames_typing (g: env) : tot_typing g all_inames tm_inames\nlet all_inames_typing (g:env)\n: tot_typing g all_inames tm_inames\n= RU.magic()", "val readable_one (s: ME.vale_heap) (arg: arg) : prop\nlet readable_one (s:ME.vale_heap) (arg:arg) : prop =\n match arg with\n | (|TD_Buffer src bt _, x |) ->\n ME.buffer_readable s (as_vale_buffer #src #bt x) /\\\n ME.buffer_writeable (as_vale_buffer #src #bt x)\n /\\ True //promote to prop\n | (|TD_ImmBuffer src bt _, x |) ->\n ME.buffer_readable s (as_vale_immbuffer #src #bt x) /\\\n True\n | _ -> True", "val mem_inv (h:vale_full_heap) : prop0\nlet mem_inv h =\n h.vf_heap.heapletId == None /\\\n inv_heaplet_ids h.vf_heaplets /\\\n (if h.vf_layout.vl_inner.vl_heaplets_initialized\n then\n inv_heaplets h.vf_layout.vl_inner h.vf_heap\n h.vf_heaplets h.vf_layout.vl_taint\n else\n h.vf_heaplets == empty_vale_heaplets h.vf_layout.vl_inner.vl_old_heap\n )", "val mem_inv (h:vale_full_heap) : prop0\nlet mem_inv h =\n h.vf_heap.heapletId == None /\\\n inv_heaplet_ids h.vf_heaplets /\\\n (if h.vf_layout.vl_inner.vl_heaplets_initialized\n then\n inv_heaplets h.vf_layout.vl_inner h.vf_heap\n h.vf_heaplets h.vf_layout.vl_taint\n else\n h.vf_heaplets == empty_vale_heaplets h.vf_layout.vl_inner.vl_old_heap\n )" ], "closest_src": [ { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.inames_ok" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.name_is_ok" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.inames_in" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fsti", "name": "Pulse.Lib.Core.mem_iname" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.locks_invariant" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fsti", "name": "Pulse.Lib.Core.add_iname" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fsti", "name": "PulseCore.Memory.mem_inv" }, { "project_name": "steel", "file_name": "Steel.Memory.fsti", "name": "Steel.Memory.mem_inv" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fsti", "name": "Pulse.Lib.Core.mem_inv" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.mem_inv" }, { "project_name": "steel", "file_name": "Pulse.Typing.Combinators.fst", "name": "Pulse.Typing.Combinators.inames_of" }, { "project_name": "steel", "file_name": "PulseCore.Action.fsti", "name": "PulseCore.Action.inames_subset" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fsti", "name": "Pulse.Lib.Core.inames_subset" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fsti", "name": "Pulse.Lib.Core.all_inames" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.emp_inames" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fsti", "name": "Pulse.Lib.Core.emp_inames" }, { "project_name": "steel", "file_name": "PulseCore.Action.fsti", "name": "PulseCore.Action.emp_inames" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.State.fsti", "name": "Vale.PPC64LE.State.valid_mem" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fsti", "name": "Pulse.Lib.Core.add_inv" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.add_inv" }, { "project_name": "steel", "file_name": "PulseCore.Action.fsti", "name": "PulseCore.Action.mem_inv" }, { "project_name": "steel", "file_name": "Steel.DisposableInvariant.fsti", "name": "Steel.DisposableInvariant.mem_inv" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.is_implies" }, { "project_name": "steel", "file_name": "Pulse.Checker.WithInv.fst", "name": "Pulse.Checker.WithInv.add_iname" }, { "project_name": "steel", "file_name": "Steel.Memory.fsti", "name": "Steel.Memory.add_inv" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fsti", "name": "PulseCore.Memory.add_inv" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.get0" }, { "project_name": "everparse", "file_name": "EverParse3d.InputStream.Extern.fst", "name": "EverParse3d.InputStream.Extern.live" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.with_inv_except" }, { "project_name": "steel", "file_name": "Pulse.Lib.InvList.fsti", "name": "Pulse.Lib.InvList.invlist_names" }, { "project_name": "steel", "file_name": "Pulse.Lib.Pervasives.fst", "name": "Pulse.Lib.Pervasives.inames_ext" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.valid_rmem" }, { "project_name": "FStar", "file_name": "DoublyLinkedListIface.fst", "name": "DoublyLinkedListIface.node_valid" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.new_invariant_tot_action" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fsti", "name": "Pulse.Lib.Core.join_inames" }, { "project_name": "steel", "file_name": "PulseCore.Action.fsti", "name": "PulseCore.Action.join_inames" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.linv" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.iname" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.iname" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.iname" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.rewrite" }, { "project_name": "steel", "file_name": "Steel.Memory.fsti", "name": "Steel.Memory.name_of_inv" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fsti", "name": "PulseCore.Memory.name_of_inv" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.name_of_inv" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.interp" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fsti", "name": "Pulse.Lib.Core.remove_inv" }, { "project_name": "steel", "file_name": "Steel.DisposableInvariant.fsti", "name": "Steel.DisposableInvariant.add_inv" }, { "project_name": "steel", "file_name": "Pulse.Checker.WithInv.fst", "name": "Pulse.Checker.WithInv.remove_iname" }, { "project_name": "steel", "file_name": "Pulse.Lib.Pervasives.fst", "name": "Pulse.Lib.Pervasives.inames_join_emp_r" }, { "project_name": "hacl-star", "file_name": "Vale.X64.State.fsti", "name": "Vale.X64.State.valid_maddr" }, { "project_name": "steel", "file_name": "Pulse.Lib.FlippableInv.fst", "name": "Pulse.Lib.FlippableInv.iname_of" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.implies_" }, { "project_name": "steel", "file_name": "PulseCore.Action.fsti", "name": "PulseCore.Action.add_inv" }, { "project_name": "steel", "file_name": "Pulse.Lib.Pervasives.fst", "name": "Pulse.Lib.Pervasives.inames_join_emp_l" }, { "project_name": "steel", "file_name": "Pulse.Lib.InvList.fsti", "name": "Pulse.Lib.InvList.invlist_nodups" }, { "project_name": "steel", "file_name": "Pulse.Checker.Base.fst", "name": "Pulse.Checker.Base.emp_inames_included" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.tm_inames_subset_typing" }, { "project_name": "steel", "file_name": "Pulse.Lib.Pervasives.fst", "name": "Pulse.Lib.Pervasives.inames_join_self" }, { "project_name": "steel", "file_name": "Pulse.Checker.WithInv.fst", "name": "Pulse.Checker.WithInv.check_iname_disjoint" }, { "project_name": "steel", "file_name": "Pulse.Checker.WithInv.fst", "name": "Pulse.Checker.WithInv.add_remove_inverse" }, { "project_name": "steel", "file_name": "Steel.DisposableInvariant.fst", "name": "Steel.DisposableInvariant.name" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.lock_store_invariant" }, { "project_name": "FStar", "file_name": "FStar.Algebra.Monoid.fst", "name": "FStar.Algebra.Monoid.neg" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.rewrite_slprop0" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.tm_inames_subset" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory_Sems.fst", "name": "Vale.X64.Memory_Sems.same_domain" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory_Sems.fst", "name": "Vale.PPC64LE.Memory_Sems.same_domain" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.elim_pure" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.State.fsti", "name": "Vale.PPC64LE.State.valid_maddr" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.mk_mem_inv" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.drop" }, { "project_name": "hacl-star", "file_name": "Vale.X64.State.fsti", "name": "Vale.X64.State.valid_maddr128" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.move_invariant" }, { "project_name": "everparse", "file_name": "LowParse.Repr.fst", "name": "LowParse.Repr.valid" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.full_mem_pred" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.State.fsti", "name": "Vale.PPC64LE.State.valid_mem128" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.weaken" }, { "project_name": "steel", "file_name": "Steel.Channel.Simplex.fst", "name": "Steel.Channel.Simplex.in_state_prop" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.comp_inames" }, { "project_name": "steel", "file_name": "Steel.Semantics.Instantiate.fst", "name": "Steel.Semantics.Instantiate.state_correspondence" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.elim_h_exists" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.new_invariant" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.get_hmap" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.pure_interp" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.equiv" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.recall" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.elim_exists" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.implies_unfold" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.emp_inames_tm" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.extend_lock_store" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.fresh_invariant" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.valid_mem_addr" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.change_slprop0" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsMem.fsti", "name": "Vale.X64.InsMem.norm_list" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsMem.fsti", "name": "Vale.PPC64LE.InsMem.norm_list" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.preserves_frame_cong" }, { "project_name": "steel", "file_name": "Pulse.Checker.WithInv.fst", "name": "Pulse.Checker.WithInv.all_inames_typing" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.ValeSig.fst", "name": "Vale.AsLowStar.ValeSig.readable_one" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.mem_inv" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.mem_inv" } ], "selected_premises": [ "PulseCore.Memory.star", "PulseCore.Memory.interp", "PulseCore.Memory.iname", "PulseCore.Memory.h_exists", "PulseCore.Memory.emp", "PulseCore.Preorder.pcm_history", "PulseCore.FractionalPermission.full_perm", "FStar.Real.one", "PulseCore.Memory.core_mem", "PulseCore.Memory.pure", "PulseCore.Memory.intro_emp", "PulseCore.Memory.slprop", "PulseCore.Heap.full_hheap", "PulseCore.Memory.slprop_extensionality", "FStar.Real.two", "PulseCore.Memory.pts_to", "PulseCore.Memory.lock_store_evolves", "FStar.PCM.composable", "FStar.FunctionalExtensionality.feq", "PulseCore.Memory.intro_star", "PulseCore.Memory.star_associative", "PulseCore.Memory.equiv", "FStar.PCM.compatible", "PulseCore.Heap.hheap", "PulseCore.Memory.pure_interp", "FStar.PCM.op", "PulseCore.Memory.pure_star_interp", "PulseCore.Preorder.history_val", "PulseCore.Memory.core_ref_null", "PulseCore.Memory.affine_star", "PulseCore.Memory.pts_to_not_null", "PulseCore.FractionalPermission.sum_perm", "PulseCore.Memory.core_ref", "PulseCore.Heap.pure", "PulseCore.Memory.emp_unit", "PulseCore.FractionalPermission.comp_perm", "PulseCore.Memory.hmem", "PulseCore.Memory.elim_star", "PulseCore.Heap.full_heap", "PulseCore.Memory.join", "PulseCore.Memory.star_commutative", "PulseCore.Memory.pts_to_compatible_equiv", "PulseCore.Memory.h_forall", "PulseCore.Memory.equiv_symmetric", "PulseCore.Memory.pts_to_compatible", "PulseCore.Memory.pure_equiv", "PulseCore.Memory.star_congruence", "PulseCore.Heap.stronger", "PulseCore.Memory.wand", "PulseCore.Memory.pure_true_emp", "PulseCore.Heap.equiv", "PulseCore.Memory.lock_store_invariant", "PulseCore.Memory.lock_i", "FStar.FunctionalExtensionality.on_dom", "FStar.Pervasives.reveal_opaque", "PulseCore.Memory.lock_store", "FStar.Pervasives.Native.fst", "PulseCore.Memory.equiv_extensional_on_star", "FStar.Pervasives.Native.snd", "PulseCore.Memory.h_or", "PulseCore.Heap.action_related_heaps", "PulseCore.Heap.pre_action", "PulseCore.Preorder.p_op", "PulseCore.Memory.core_ref_is_null", "PulseCore.Memory.inames_in", "PulseCore.Heap.action_with_frame", "PulseCore.Preorder.induces_preorder", "PulseCore.Memory.disjoint", "PulseCore.Memory.join_associative", "PulseCore.Heap.is_frame_preserving", "PulseCore.Memory.disjoint_join", "PulseCore.Preorder.comm_op", "PulseCore.Heap.frame_related_heaps", "PulseCore.Heap.hprop", "PulseCore.Heap.a_heap_prop", "PulseCore.FractionalPermission.half_perm", "PulseCore.Heap.is_witness_invariant", "PulseCore.Preorder.vhist", "FStar.Real.zero", "PulseCore.Memory.h_and", "PulseCore.Heap.action", "PulseCore.FractionalPermission.lesser_perm", "PulseCore.FractionalPermission.writeable", "PulseCore.Preorder.preorder_of_pcm", "PulseCore.Preorder.history_compose", "PulseCore.Heap.is_frame_monotonic", "PulseCore.Memory.equiv_heap_iff_equiv_forall", "FStar.Pervasives.dfst", "PulseCore.Memory.join_commutative", "PulseCore.Preorder.extends", "FStar.Pervasives.dsnd", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity", "FStar.FunctionalExtensionality.on", "PulseCore.Preorder.history_composable", "PulseCore.Preorder.curval", "PulseCore.Preorder.extends'", "PulseCore.Preorder.fact_valid_compat", "PulseCore.Heap.heap_prop_is_affine", "PulseCore.Memory.ptr", "PulseCore.Heap.ptr" ], "source_upto_this": "(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule PulseCore.Memory\nopen FStar.Ghost\nopen FStar.PCM\nmodule M_ = PulseCore.NondeterministicMonotonicStateMonad\nmodule F = FStar.FunctionalExtensionality\nopen FStar.FunctionalExtensionality\nmodule H = PulseCore.Heap\nmodule PP = PulseCore.Preorder\n\n\nnoeq\ntype lock_state : Type u#(a + 1) =\n | Invariant : inv:H.slprop u#a -> lock_state\n\nlet lock_store : Type u#(a+1) = list (lock_state u#a)\n\nnoeq\ntype mem : Type u#(a + 1) =\n {\n ctr: nat;\n heap: H.heap u#a;\n locks: lock_store u#a;\n }\n\nlet heap_of_mem (x:mem) : H.heap = x.heap\n\nlet mem_of_heap (h:H.heap) : mem = {\n ctr = 0;\n heap = h;\n locks = []\n}\n\nlet mem_set_heap (m:mem) (h:H.heap) : mem = {\n ctr = m.ctr;\n heap = h;\n locks = m.locks;\n}\n\nlet core_mem (m:mem) : mem = mem_of_heap (heap_of_mem m)\n\nval core_mem_invol (m: mem u#a) : Lemma\n (core_mem (core_mem m) == core_mem m)\n [SMTPat (core_mem (core_mem m))]\nlet core_mem_invol m = ()\n\n(** A predicate describing non-overlapping memories. Based on [Steel.Heap.disjoint] *)\nlet disjoint (m0 m1:mem u#h)\n : prop\n = m0.ctr == m1.ctr /\\\n H.disjoint m0.heap m1.heap /\\\n m0.locks == m1.locks\n\n(** Disjointness is symmetric *)\nlet disjoint_sym (m0 m1:mem u#h)\n : Lemma (disjoint m0 m1 <==> disjoint m1 m0)\n [SMTPat (disjoint m0 m1)]\n = ()\n\n(** Disjoint memories can be combined. Based on [Steel.Heap.join] *)\nlet join (m0:mem u#h) (m1:mem u#h{disjoint m0 m1}) : mem u#h\n= {\n ctr = m0.ctr;\n heap = H.join m0.heap m1.heap;\n locks = m0.locks\n }\n\n(** Join is commutative *)\nlet join_commutative (m0 m1:mem)\n : Lemma\n (requires\n disjoint m0 m1)\n (ensures\n (disjoint m0 m1 /\\\n disjoint m1 m0 /\\\n join m0 m1 == join m1 m0))\n = H.join_commutative m0.heap m1.heap\n\n(** Disjointness distributes over join *)\nlet disjoint_join (m0 m1 m2:mem)\n : Lemma (disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) ==>\n disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\n = H.disjoint_join m0.heap m1.heap m2.heap\n\n(** Join is associative *)\nlet join_associative (m0 m1 m2:mem)\n : Lemma\n (requires\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures\n (disjoint_join m0 m1 m2;\n join m0 (join m1 m2) == join (join m0 m1) m2))\n = H.join_associative m0.heap m1.heap m2.heap\n\nlet slprop = H.slprop\n\nlet interp p m = H.interp p m.heap\n\nlet equiv p1 p2 = forall m. interp p1 m <==> interp p2 m\n\n\nlet slprop_extensionality p q =\n assert (forall m. interp p m <==> interp q m);\n let aux (h:H.heap)\n : Lemma (H.interp p h <==> H.interp q h)\n [SMTPat (H.interp p h)]\n = let m : mem = { ctr = 0; heap = h; locks = [] } in\n assert (interp p m <==> interp q m)\n in\n assert (forall h. H.interp p h <==> H.interp q h);\n H.slprop_extensionality p q\n\nval reveal_equiv (p1 p2:slprop u#a) : Lemma\n (ensures (forall m. interp p1 m <==> interp p2 m) <==> p1 `equiv` p2)\n [SMTPat (p1 `equiv` p2)]\nlet reveal_equiv p1 p2 = ()\n\nlet slprop_equiv_refl p = ()\n\nlet core_ref = H.core_ref\nlet core_ref_null = H.core_ref_null\nlet core_ref_is_null r = H.core_ref_is_null r\n\nlet emp : slprop u#a = H.emp\nlet pure = H.pure\nlet pts_to = H.pts_to\nlet h_and = H.h_and\nlet h_or = H.h_or\nlet star = H.star\nlet wand = H.wand\nlet h_exists = H.h_exists\nlet h_forall = H.h_forall\n\n////////////////////////////////////////////////////////////////////////////////\n//properties of equiv\n////////////////////////////////////////////////////////////////////////////////\n\nlet equiv_symmetric (p1 p2:slprop u#a) = H.equiv_symmetric p1 p2\n\n#push-options \"--warn_error -271\"\nlet equiv_heap_iff_equiv (p1 p2:slprop u#a)\n : Lemma (ensures (H.equiv p1 p2 <==> equiv p1 p2))\n [SMTPat (equiv p1 p2)]\n = let aux_lr ()\n : Lemma\n (requires H.equiv p1 p2)\n (ensures equiv p1 p2)\n [SMTPat ()]\n = ()\n in\n let aux_rl_helper1 (h:H.heap)\n : Lemma\n (requires equiv p1 p2 /\\ H.interp p1 h)\n (ensures H.interp p2 h)\n [SMTPat ()]\n = assert (interp p2 (mem_of_heap h))\n in\n let aux_rl_helper2 (h:H.heap)\n : Lemma\n (requires equiv p1 p2 /\\ H.interp p2 h)\n (ensures H.interp p1 h)\n [SMTPat ()]\n = assert (interp p2 (mem_of_heap h))\n in\n let aux_rl ()\n : Lemma\n (requires equiv p1 p2)\n (ensures H.equiv p1 p2)\n [SMTPat ()]\n = () in\n ()\n\nlet equiv_heap_iff_equiv_forall ()\n : Lemma (ensures (forall p1 p2. H.equiv p1 p2 <==> equiv p1 p2))\n = let aux p1 p2\n : Lemma (ensures (H.equiv p1 p2 <==> equiv p1 p2))\n [SMTPat ()]\n = equiv_heap_iff_equiv p1 p2\n in\n ()\n#pop-options\n\nlet equiv_extensional_on_star (p1 p2 p3:slprop u#a) =\n equiv_heap_iff_equiv_forall ();\n H.equiv_extensional_on_star p1 p2 p3\n\nlet emp_unit p = H.emp_unit p\n\n\nval intro_emp (m:mem) : Lemma (interp emp m)\nlet intro_emp m = H.intro_emp (heap_of_mem m)\n\nlet pure_equiv p q = H.pure_equiv p q\nval pure_interp (q:prop) (m:mem) : Lemma (interp (pure q) m <==> q)\nlet pure_interp q m = H.pure_interp q (heap_of_mem m)\nlet pure_true_emp () : Lemma (pure True `equiv` emp) =\n FStar.Classical.forall_intro (pure_interp True);\n FStar.Classical.forall_intro intro_emp;\n slprop_extensionality (pure True) emp\n\n(** A helper lemma for interpreting a pure proposition with another [slprop] *)\nval pure_star_interp (p:slprop u#a) (q:prop) (m:mem)\n : Lemma (interp (p `star` pure q) m <==>\n interp (p `star` emp) m /\\ q)\n\nlet pure_star_interp p q m = H.pure_star_interp p q (heap_of_mem m)\n\n////////////////////////////////////////////////////////////////////////////////\n//pts_to\n////////////////////////////////////////////////////////////////////////////////\n\n(** [ptr r] asserts that the reference [r] points to a value *)\nlet ptr (#a: Type u#a) (#pcm: pcm a) (r:ref a pcm) =\n h_exists (pts_to r)\n\n(** Injectivity-like lemma for [pts_to], see [Steel.Heap] for more explanations *)\nval pts_to_compatible\n (#a:Type u#a)\n (#pcm:pcm a)\n (x:ref a pcm)\n (v0 v1:a)\n (m:mem u#a)\n : Lemma\n (interp (pts_to x v0 `star` pts_to x v1) m <==>\n composable pcm v0 v1 /\\ interp (pts_to x (op pcm v0 v1)) m)\n\nval pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))\n\nval pts_to_not_null (#a:Type u#a)\n (#pcm:_)\n (x:ref a pcm)\n (v:a)\n (m:mem u#a)\n : Lemma (requires interp (pts_to x v) m)\n (ensures x =!= null)\nlet pts_to_compatible #a #pcm x v0 v1 m\n = H.pts_to_compatible #a #pcm x v0 v1 (heap_of_mem m)\nlet pts_to_compatible_equiv #a #pcm x v0 v1\n = H.pts_to_compatible_equiv #a #pcm x v0 v1\nlet pts_to_not_null #a #pcm x v m\n = H.pts_to_not_null #a #pcm x v (heap_of_mem m)\n\n////////////////////////////////////////////////////////////////////////////////\n// star\n////////////////////////////////////////////////////////////////////////////////\n(** A common abbreviation: memories validating [p] *)\nlet hmem (p:slprop u#a) = m:mem u#a {interp p m}\n\nval intro_star (p q:slprop) (mp:hmem p) (mq:hmem q)\n : Lemma\n (requires\n disjoint mp mq)\n (ensures\n interp (p `star` q) (join mp mq))\n\nval elim_star (p q:slprop) (m:hmem (p `star` q))\n : Lemma\n (requires\n interp (p `star` q) m)\n (ensures exists ml mr.\n disjoint ml mr /\\ m == join ml mr /\\ interp p ml /\\ interp q mr)\n\nval interp_star\n (p q: slprop)\n (m: mem)\n: Lemma\n (interp (p `star` q) m <==> (exists (mp: mem) (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m))\n\nlet intro_star p q mp mq =\n H.intro_star p q (heap_of_mem mp) (heap_of_mem mq)\n\nlet elim_star p q m =\n let h = heap_of_mem m in\n H.elim_star p q h;\n assert (exists hl hr. H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr);\n let hl = FStar.IndefiniteDescription.indefinite_description_tot H.heap (fun hl ->\n exists hr. H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr) in\n let hr = FStar.IndefiniteDescription.indefinite_description_tot H.heap (fun hr ->\n H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr) in\n let ml = mem_set_heap m hl in\n let mr = mem_set_heap m hr in\n assert (disjoint ml mr);\n assert (m == join ml mr);\n assert (interp p ml);\n assert (interp q mr);\n ()\n\nlet interp_star\n (p q: slprop)\n (m: mem)\n: Lemma\n (interp (p `star` q) m <==> (exists (mp: mem) (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m))\n= let left = interp (p `star` q) m in\n let right = exists (mp: mem) (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m in\n let f ()\n : Lemma\n (requires left)\n (ensures right)\n =\n elim_star p q m\n in\n let g ()\n : Lemma\n (requires right)\n (ensures left)\n =\n Classical.exists_elim left #_ #(fun mp -> exists (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m) () (fun mp ->\n Classical.exists_elim left #_ #(fun mq -> disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m) () (fun mq ->\n intro_star p q mp mq\n )\n )\n in\n Classical.move_requires f ();\n Classical.move_requires g ()\n\nlet star_commutative (p1 p2:slprop) =\n H.star_commutative p1 p2\n\nlet star_associative (p1 p2 p3:slprop) =\n H.star_associative p1 p2 p3\n\nlet star_congruence (p1 p2 p3 p4:slprop) =\n equiv_heap_iff_equiv_forall ();\n H.star_congruence p1 p2 p3 p4\n\n\nval affine_star (p q:slprop) (m:mem)\n : Lemma ((interp (p `star` q) m ==> interp p m /\\ interp q m))\n\nlet affine_star (p q:slprop) (m:mem) =\n H.affine_star p q (heap_of_mem m)\n\n////////////////////////////////////////////////////////////////////////////////\n// Invariants on the lock store\n////////////////////////////////////////////////////////////////////////////////\n\nlet iname = nat\nmodule S = FStar.Set\nmodule L = FStar.List.Tot\nmodule W = FStar.Witnessed.Core\n\nlet rec lock_store_invariant (e:inames) (l:lock_store u#a) : slprop u#a =\n let current_addr = L.length l - 1 in\n match l with\n | [] -> emp\n | Invariant p :: tl ->\n if current_addr `S.mem` e then\n lock_store_invariant e tl\n else\n p `star` lock_store_invariant e tl\n\nlet lock_i (i:iname) (l:lock_store { i < L.length l }) =\n let ix = L.length l - i - 1 in\n L.index l ix\n\nlet iname_for_p (i:iname) (p:slprop) : W.s_predicate lock_store =\n fun l ->\n i < L.length l /\\\n (lock_i i l).inv == p\n\nlet lock_store_evolves : FStar.Preorder.preorder lock_store =\n fun (l1 l2 : lock_store) ->\n L.length l2 >= L.length l1 /\\\n (forall (i:nat{i < L.length l1}).\n (lock_i i l1).inv == (lock_i i l2).inv)\n\nlet inames_in (e:inames) (l:lock_store) : prop = forall i. Set.mem i e ==> i < L.length l\n", "sketch": [ "Step 1: The `inames_ok` function is a predicate that checks whether all inames in the set `e` are valid indices within the lock store of the memory `m`.\nStep 2: To implement this, we need to ensure that for every iname `i` in the set `e`, `i` is less than the length of the lock store in the memory `m`.", "Step 1: The `inames_ok` function is intended to check whether all inames (invariant names) in the set `e` are valid within the memory `m`. Specifically, it ensures that each iname in `e` corresponds to a valid index in the lock store of the memory `m`.\n\nStep 2: To implement this, the function will iterate over each iname in the set `e` and verify that it is less than the length of the lock store in the memory `m`. This ensures that all inames are within the bounds of the lock store.", "Step 1: The `inames_ok` function is intended to check if a set of inames (invariant names) is valid for a given memory state. Specifically, it ensures that all inames in the set are within the bounds of the lock store in the memory.\nStep 2: To implement this, we will define a predicate that verifies for each iname in the set, it is less than the length of the lock store in the memory. This ensures that all inames are valid indices for the lock store.", "Step 1: The `inames_ok` function is a predicate that checks if all inames (indices) in the set `e` are valid for the lock store in the memory `m`. This means that each iname in `e` should be less than the length of the lock store in `m`.\nStep 2: To implement this, we will define a function that takes a set of inames `e` and a memory `m`, and returns a proposition that asserts that for every iname `i` in `e`, `i` is less than the length of the lock store in `m`.", "Step 1: The `inames_ok` function is a predicate that checks whether all inames in the set `e` are valid indices for the lock store in the memory `m`. This means that for every iname in `e`, it should be less than the length of the lock store in `m`.\n\nStep 2: To implement this, we will define a function that takes a set of inames `e` and a memory `m`, and returns a proposition that asserts that for every iname `i` in `e`, `i` is less than the length of the lock store in `m`.", "Step 1: The definition `inames_ok` is a predicate that checks if all inames (lock indices) in the set `e` are valid within the memory `m`. Specifically, it ensures that each iname in `e` is less than the length of the lock store in the memory `m`.\nStep 2: To implement this, we need to define a property that states that for every iname `i` in the set `e`, `i` is less than the length of the lock store in `m`.", "Step 1: The `inames_ok` function is intended to check if all inames (lock indices) in the set `e` are valid indices in the lock store of the memory `m`. This means that each iname in `e` should be less than the length of the lock store in `m`.\nStep 2: To implement this, we will define a property that ensures for every iname `i` in the set `e`, `i` is less than the length of the lock store in `m`.", "Step 1: The `inames_ok` function is a predicate that checks if all inames (lock indices) in the set `e` are valid for the given memory `m`. Specifically, it ensures that each iname in `e` is within the bounds of the lock store in `m`.\nStep 2: To implement this, we need to verify that for every iname `i` in the set `e`, the index `i` is less than the length of the lock store in the memory `m`.", "Step 1: The `inames_ok` function is a predicate that checks if all inames (lock indices) in the set `e` are valid for the memory `m`. This means that each iname in `e` should correspond to a valid lock index in the `locks` list of the memory `m`.\nStep 2: To implement this, we need to ensure that for every iname `i` in the set `e`, the index `i` is less than the length of the `locks` list in the memory `m`. This can be done using a universal quantifier over the elements of `e`.", "Step 1: The `inames_ok` function checks if all the inames in the set `e` are valid indices within the lock store of the memory `m`.\nStep 2: To implement this, we need to ensure that for every iname `i` in the set `e`, the index `i` is less than the length of the lock store in the memory `m`." ], "generated_solution": [ "let inames_ok (e:inames) (m:mem) : prop =\n inames_in e m.locks", "let inames_ok (e:inames) (m:mem) : prop =\n forall i. S.mem i e ==> i < L.length m.locks", "let inames_ok (e:inames) (m:mem) : prop =\n inames_in e m.locks", "let inames_ok (e:inames) (m:mem) : prop =\n forall i. S.mem i e ==> i < L.length m.locks", "let inames_ok (e:inames) (m:mem) : prop =\n forall i. S.mem i e ==> i < L.length m.locks", "let inames_ok (e:inames) (m:mem) : prop =\n forall i. S.mem i e ==> i < L.length m.locks", "let inames_ok (e:inames) (m:mem) : prop =\n forall i. S.mem i e ==> i < L.length m.locks", "let inames_ok (e:inames) (m:mem) : prop =\n forall i. S.mem i e ==> i < L.length m.locks", "let inames_ok (e:inames) (m:mem) : prop =\n forall i. S.mem i e ==> i < L.length m.locks", "let inames_ok (e:inames) (m:mem) : prop =\n inames_in e m.locks" ] }, { "file_name": "Vale.X64.Regs.fsti", "name": "Vale.X64.Regs.eta_sel", "opens_and_abbrevs": [ { "open": "Vale.Lib.Map16" }, { "open": "Vale.X64.Machine_s" }, { "open": "Vale.Def.Prop_s" }, { "open": "FStar.Mul" }, { "open": "Vale.X64" }, { "open": "Vale.X64" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 1, "initial_ifuel": 0, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": true, "smtencoding_nl_arith_repr": "wrapped", "smtencoding_l_arith_repr": "native", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m}", "source_definition": "let eta_sel (r:reg) (m:t) : v:(t_reg r){v == sel r m} =\n sel r m", "source_range": { "start_line": 33, "start_col": 0, "end_line": 34, "end_col": 9 }, "interleaved": false, "definition": "fun r m -> Vale.X64.Regs.sel r m <: v: Vale.X64.Machine_s.t_reg r {v == Vale.X64.Regs.sel r m}", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Vale.X64.Machine_s.reg", "Vale.X64.Regs.t", "Vale.X64.Regs.sel", "Vale.X64.Machine_s.t_reg", "Prims.eq2" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "r: Vale.X64.Machine_s.reg -> m: Vale.X64.Regs.t\n -> v: Vale.X64.Machine_s.t_reg r {v == Vale.X64.Regs.sel r m}", "prompt": "let eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m} =\n ", "expected_response": "sel r m", "source": { "project_name": "hacl-star", "file_name": "vale/code/arch/x64/Vale.X64.Regs.fsti", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Vale.X64.Regs.fsti", "checked_file": "dataset/Vale.X64.Regs.fsti.checked", "interface_file": false, "dependencies": [ "dataset/Vale.X64.Machine_s.fst.checked", "dataset/Vale.Lib.Map16.fsti.checked", "dataset/Vale.Def.Prop_s.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked" ] }, "definitions_in_context": [ "regs_fun", "regs_def", "t", "let sel (r:reg) (m:t) : t_reg r =\n match m with (m0, m1) ->\n match r with Reg rf i ->\n match rf with\n | 0 -> sel16 m0 i\n | 1 -> sel16 m1 i", "let upd (r:reg) (v:t_reg r) (m:t) : t =\n match m with (m0, m1) ->\n match r with Reg rf i ->\n match rf with\n | 0 -> (upd16 m0 i v, m1)\n | 1 -> (m0, upd16 m1 i v)" ], "closest": [ "val lemma_upd_eq (r:reg) (v:t_reg r) (m:t) : Lemma\n (requires True)\n (ensures sel r (upd r v m) == v)\n [SMTPat (sel r (upd r v m))]\nlet lemma_upd_eq r v m =\n assert_norm (sel r (upd r v m) == v)", "val lemma_upd_ne (r r':reg) (v:t_reg r') (m:t) : Lemma\n (requires r =!= r')\n (ensures sel r (upd r' v m) == sel r m)\n [SMTPat (sel r (upd r' v m))]\nlet lemma_upd_ne r r' v m =\n assert_norm (sel r (upd r' v m) == sel r m)", "val of_fun (m:(r:reg -> t_reg r)) : Pure t\n (requires True)\n (ensures fun m' -> (forall (r:reg).{:pattern (m r) \\/ (sel r m')} m r == sel r m'))\nlet of_fun m =\n reveal_opaque (`%sel) sel;\n// FStar.FunctionalExtensionality.on_dom reg m\n let m0_3 = ((m (Reg 0 0), m (Reg 0 1)), (m (Reg 0 2), m (Reg 0 3))) in\n let m4_7 = ((m (Reg 0 4), m (Reg 0 5)), (m (Reg 0 6), m (Reg 0 7))) in\n let m8_11 = ((m (Reg 0 8), m (Reg 0 9)), (m (Reg 0 10), m (Reg 0 11))) in\n let m12_15 = ((m (Reg 0 12), m (Reg 0 13)), (m (Reg 0 14), m (Reg 0 15))) in\n let m0 = ((m0_3, m4_7), (m8_11, m12_15)) in\n let m0_3 = ((m (Reg 1 0), m (Reg 1 1)), (m (Reg 1 2), m (Reg 1 3))) in\n let m4_7 = ((m (Reg 1 4), m (Reg 1 5)), (m (Reg 1 6), m (Reg 1 7))) in\n let m8_11 = ((m (Reg 1 8), m (Reg 1 9)), (m (Reg 1 10), m (Reg 1 11))) in\n let m12_15 = ((m (Reg 1 12), m (Reg 1 13)), (m (Reg 1 14), m (Reg 1 15))) in\n let m1 = ((m0_3, m4_7), (m8_11, m12_15)) in\n (m0, m1)", "val sel (f:flag) (m:t) : flag_val_t\nlet sel (r:flag) (m:t) : flag_val_t =\n Map.sel m r", "val equal (regs1:t) (regs2:t) : prop0\nlet equal m1 m2 = m1 == m2", "val equal (regs1:t) (regs2:t) : prop0\nlet equal regs1 regs2 = feq regs1 regs2", "val vdep_sel_eq (v: vprop) (p: ( (t_of v) -> Tot vprop)) (m: Mem.hmem (vdep_hp v p)) : Lemma\n (\n interp (hp_of v) m /\\\n begin let x = sel_of v m in\n interp (hp_of (p x)) m /\\\n vdep_sel v p m == (| x, sel_of (p x) m |)\n end\n )\nlet vdep_sel_eq\n v p m\n= Classical.forall_intro_2 (Classical.move_requires_2 (fun (m0 m1: mem) -> (join_commutative m0) m1));\n ()", "val eq_registers (regs1 regs2: reg_taint) : (b: bool{b <==> regs1 == regs2})\nlet eq_registers (regs1 regs2:reg_taint) : (b:bool{b <==> regs1 == regs2}) =\n lemma_eq_regs regs1 regs2 n_reg_files;\n let b = eq_regs regs1 regs2 n_reg_files in\n if b then (\n assert (FStar.FunctionalExtensionality.feq regs1 regs2)\n );\n b", "val ptr_sel_interp (#a: Type0) (r: ref a) (m: mem)\n : Lemma (requires interp (ptr r) m) (ensures interp (pts_to_sl r full_perm (ptr_sel r m)) m)\nlet ptr_sel_interp (#a:Type0) (r:ref a) (m:mem) : Lemma\n (requires interp (ptr r) m)\n (ensures interp (pts_to_sl r full_perm (ptr_sel r m)) m)\n= ptrp_sel_interp r full_perm m", "val sel' (#a: _) (r: regmap a) (x: reg) : Tot a\nlet sel' #a (r:regmap a) (x:reg) : Tot a = sel r x", "val t_reg (r: reg) : Type0\nlet t_reg (r:reg) : Type0 = t_reg_file r.rf", "val reg_le (r1 r2: reg) : bool\nlet reg_le (r1 r2:reg) : bool =\n let Reg f1 n1 = r1 in\n let Reg f2 n2 = r2 in\n f1 < f2 || (f1 = f2 && n1 <= n2)", "val elim_m (#n: arity) (#r: _) (m: arity{m <= n}) (f: n_arrow n r) : (registers -> n_arrow m r)\nlet rec elim_m (#n:arity) #r (m:arity{m <= n}) (f:n_arrow n r)\n : (registers -> n_arrow m r)\n = fun regs ->\n match (n - m) with\n | 0 -> f\n | _ ->\n elim_m #(n - 1) #r m (elim_1 f (Map.sel regs (as_reg (1 + max_arity - n)))) regs", "val sel_v (#a:Type u#h) (#pcm:pcm a) (r:ref a pcm) (v:erased a) (m:full_hheap (pts_to r v))\n : v':a{ compatible pcm v v' /\\\n pcm.refine v' /\\\n interp (ptr r) m /\\\n v' == sel r m }\nlet sel_v #a #pcm r v m = sel r m", "val sel_v (#a:Type u#h) (#pcm:pcm a) (r:ref a pcm) (v:erased a) (m:full_hheap (pts_to r v))\n : v':a{ compatible pcm v v' /\\\n pcm.refine v' /\\\n interp (ptr r) m /\\\n v' == sel r m }\nlet sel_v #a #pcm r v m = sel r m", "val ( ! ) (#a: Type) (#rel: P.preorder a) (r: mref a rel)\n : HoareST a (fun _ -> True) (fun h0 x h1 -> h0 == h1 /\\ x == sel h1 r)\nlet op_Bang (#a:Type) (#rel:P.preorder a) (r:mref a rel)\n: HoareST a\n (fun _ -> True)\n (fun h0 x h1 ->\n h0 == h1 /\\\n x == sel h1 r)\n= HoareST?.reflect (fun _ -> read r)", "val ( ! ) (#a: Type) (#rel: P.preorder a) (r: mref a rel)\n : HoareST a (fun _ -> True) (fun h0 x h1 -> h0 == h1 /\\ x == sel h1 r)\nlet op_Bang (#a:Type) (#rel:P.preorder a) (r:mref a rel)\n: HoareST a\n (fun _ -> True)\n (fun h0 x h1 ->\n h0 == h1 /\\\n x == sel h1 r)\n= HoareST?.reflect (fun _ -> read r)", "val read : #a:Type -> \n r:ref a -> \n\t ImmutableST a (fun _ -> True) \n (fun h0 x h1 -> h0 == h1 /\\ \n\t\t\t\t\t x == sel h1 r)\nlet read #a r = \n let h = ist_get () in\n sel h r", "val lemma_equal (#a:Type) (m1 m2:map16 a) : Lemma\n (requires (forall (i:int).{:pattern (sel m1 i) \\/ (sel m2 i)} 0 <= i /\\ i < 16 ==> sel m1 i == sel m2 i))\n (ensures m1 == m2)\nlet lemma_equal (#a:Type) (m1 m2:map16 a) =\n assert_norm (forall (i:int). sel m1 i == sel16 m1 i);\n assert_norm (forall (i:int). sel m2 i == sel16 m2 i);\n lemma_equal16 m1 m2", "val tree_sel_interp (#a: Type0) (ptr: t a) (t: tree (node a)) (m: mem)\n : Lemma (requires interp (tree_sl' ptr t) m)\n (ensures interp (tree_sl ptr) m /\\ tree_sel_node' ptr m == t)\nlet tree_sel_interp (#a: Type0) (ptr: t a) (t: tree (node a)) (m: mem) : Lemma\n (requires interp (tree_sl' ptr t) m)\n (ensures interp (tree_sl ptr) m /\\ tree_sel_node' ptr m == t)\n = intro_h_exists t (tree_sl' ptr) m;\n tree_sl'_witinv ptr", "val lemma_upd_eq (r:flag) (v:flag_val_t) (m:t) : Lemma\n (requires True)\n (ensures sel r (upd r v m) == v)\n [SMTPat (sel r (upd r v m))]\nlet lemma_upd_eq r v m =\n reveal_opaque (`%sel) sel;\n reveal_opaque (`%upd) upd;\n Map.lemma_SelUpd1 m r v", "val test4 (c: ref (ref int))\n : ST unit\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures (fun h0 d h1 -> sel h1 (sel h1 c) = sel h0 (sel h0 c)))\nlet test4 (c:ref (ref int)) : ST unit\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures (fun h0 d h1 -> sel h1 (sel h1 c) = sel h0 (sel h0 c))) =\n c.[v |.. v] <- c.[v |.. v]", "val read : #a:Type -> \n r:ref a -> \n\t AllocST a (fun h0 -> True) \n (fun h0 x h1 -> h0 == h1 /\\ \n\t\t contains r h1 /\\ \n\t\t\t\t sel h1 r == x)\nlet read #a r =\n let h = ist_get () in\n ist_recall (contains r); //recalling that the current heap must contain the given reference\n sel h r", "val i_sel (#r: rid) (#a: Type) (#p: (seq a -> Type)) (h: mem) (m: i_seq r a p)\n : GTot (s: seq a {p s})\nlet i_sel (#r:rid) (#a:Type) (#p:seq a -> Type) (h:mem) (m:i_seq r a p)\n : GTot (s:seq a{p s})\n = HS.sel h m", "val eq_mval_value (v0 v1: mval_value) : (b: bool{b <==> (v0 == v1)})\nlet eq_mval_value (v0 v1:mval_value)\r\n : (b:bool { b <==> (v0 == v1) })\r\n = eq_descendent_hash v0.l v1.l &&\r\n eq_descendent_hash v0.r v1.r", "val lemma_equal_intro (regs1:t) (regs2:t) : Lemma\n (requires forall (r:reg). sel r regs1 == sel r regs2)\n (ensures equal regs1 regs2)\n [SMTPat (equal regs1 regs2)]\nlet lemma_equal_intro m1 m2 =\n reveal_opaque (`%t) t;\n reveal_opaque (`%Vale.Lib.Map16.sel) (Vale.Lib.Map16.sel #nat64);\n reveal_opaque (`%Vale.Lib.Map16.sel) (Vale.Lib.Map16.sel #quad32);\n reveal_opaque (`%sel) sel;\n reveal_opaque (`%upd) upd;\n let (m1_0, m1_1) = m1 in\n let (m2_0, m2_1) = m2 in\n assert (forall (i:nat). i < 16 ==> sel (Reg 0 i) m1 == sel (Reg 0 i) m2);\n assert (forall (i:nat). i < 16 ==> sel (Reg 1 i) m1 == sel (Reg 1 i) m2);\n Vale.Lib.Map16.lemma_equal m1_0 m2_0;\n Vale.Lib.Map16.lemma_equal m1_1 m2_1;\n ()", "val tree_sel (#a: Type0) (r: t a) : selector (tree a) (tree_sl r)\nlet tree_sel #a r = fun h -> tree_view (tree_sel_node r h)", "val mask_select: #t:inttype{~(S128? t)} -> mask:int_t t SEC -> a:int_t t SEC -> b:int_t t SEC -> int_t t SEC\nlet mask_select #t mask a b =\n b ^. (mask &. (a ^. b))", "val test2 (r1 r2: ref int)\n : Steel unit\n ((vptr r1) `star` (vptr r2))\n (fun _ -> (vptr r1) `star` (vptr r2))\n (requires fun h -> sel r1 h == 1)\n (ensures fun h0 _ h1 -> sel r1 h1 == 0 /\\ sel r2 h0 == sel r2 h1)\nlet test2 (r1 r2:ref int) : Steel unit\n (vptr r1 `star` vptr r2) (fun _ -> vptr r1 `star` vptr r2)\n (requires fun h -> sel r1 h == 1)\n (ensures fun h0 _ h1 -> sel r1 h1 == 0 /\\ sel r2 h0 == sel r2 h1)\n = write r1 0;\n write r1 0", "val eta (#a: Type) (m: map16 a) : map16 a\nlet eta (#a:Type) (m:map16 a) : map16 a =\n eta16 m", "val test0 (c: ref (ref int))\n : ST int\n (requires (fun h -> True))\n (ensures (fun h0 i h1 -> h0 == h1 /\\ i == sel h1 (sel h1 c)))\nlet test0 (c:ref (ref int)) : ST int\n (requires (fun h -> True))\n (ensures (fun h0 i h1 -> h0 == h1 /\\ i == sel h1 (sel h1 c)))\n = (compose_stlens stlens_ref stlens_ref).st_get c", "val va_mod_reg (r: reg) : mod_t\nlet va_mod_reg (r:reg) : mod_t = Mod_reg r", "val ( := ) (#a: Type) (#rel: preorder a) (r: mref a rel) (v: a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 ->\n rel (sel h0 r) v /\\ h0 `contains` r /\\ modifies (Set.singleton (addr_of r)) h0 h1 /\\\n equal_dom h0 h1 /\\ sel h1 r == v)\nlet op_Colon_Equals (#a:Type) (#rel:preorder a) (r:mref a rel) (v:a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 -> rel (sel h0 r) v /\\ h0 `contains` r /\\\n modifies (Set.singleton (addr_of r)) h0 h1 /\\ equal_dom h0 h1 /\\\n sel h1 r == v)\n= write #a #rel r v", "val sel (#k:eqtype) (#v:Type) (m:t k v) (x:k) : option v\nlet sel m x = m x", "val test2 (c: ref (ref int))\n : ST (ref (ref int))\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures (fun h0 d h1 -> c == d /\\ sel h1 (sel h1 c) = sel h0 (sel h0 c)))\nlet test2 (c:ref (ref int)) : ST (ref (ref int))\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures (fun h0 d h1 -> c == d /\\ sel h1 (sel h1 c) = sel h0 (sel h0 c))) =\n let i = (compose_stlens stlens_ref stlens_ref).st_get c in\n (compose_stlens stlens_ref stlens_ref).st_put i c", "val sel (r: loc) : AlgWP int (fun h0 p -> p (Map.sel h0 r, h0))\nlet sel (r:loc) : AlgWP int (fun h0 p -> p (Map.sel h0 r, h0)) =\n let h = get2 () in\n Map.sel h r", "val read (#a: Type0) (n: nat)\n : LV a\n (fun m0 -> m0.m `M.contains` n /\\ dfst (m0.m `M.sel` n) == a)\n (fun m0 r m1 ->\n m0.m `M.contains` n /\\ dfst (m0.m `M.sel` n) == a /\\ r == dsnd (m0.m `M.sel` n) /\\\n m0 == m1)\nlet read (#a:Type0) (n:nat)\n : LV a (fun m0 -> m0.m `M.contains` n /\\\n dfst (m0.m `M.sel` n) == a)\n (fun m0 r m1 ->\n m0.m `M.contains` n /\\\n dfst (m0.m `M.sel` n) == a /\\\n r == dsnd (m0.m `M.sel` n) /\\ m0 == m1)\n= LVARS?.reflect (fun m -> dsnd (m.m `M.sel` n), m)", "val llist_ptr_sel (#a:Type0) (r:t a) : selector (list a) (llist_ptr_sl r)\nlet llist_ptr_sel ptr = fun h -> datas (llist_ptr_sel_cell ptr h)", "val test0 (r: ref int)\n : Steel unit\n (vptr r)\n (fun _ -> vptr r)\n (requires fun h -> sel r h == 0)\n (ensures fun _ _ h1 -> sel r h1 == 1)\nlet test0 (r:ref int) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun h -> sel r h == 0)\n (ensures fun _ _ h1 -> sel r h1 == 1)\n = let x = gget (vptr r) in\n assert (x == Ghost.hide 0);\n write r 1;\n let x = gget (vptr r) in\n assert (x == Ghost.hide 1);\n write r 1", "val ghost_ptr_sel_interp (#a: Type0) (r: ghost_ref a) (m: mem)\n : Lemma (requires interp (ghost_ptr r) m)\n (ensures interp (ghost_pts_to_sl r full_perm (ghost_ptr_sel r m)) m)\nlet ghost_ptr_sel_interp (#a:Type0) (r:ghost_ref a) (m:mem) : Lemma\n (requires interp (ghost_ptr r) m)\n (ensures interp (ghost_pts_to_sl r full_perm (ghost_ptr_sel r m)) m)\n= ghost_ptrp_sel_interp r full_perm m", "val lemma_equal16 (#a:Type) (m1 m2:map16 a) : Lemma\n (requires (forall (i:int).{:pattern (sel16 m1 i) \\/ (sel16 m2 i)} 0 <= i /\\ i < 16 ==> sel16 m1 i == sel16 m2 i))\n (ensures m1 == m2)\nlet lemma_equal16 (#a:Type) (m1 m2:map16 a) =\n assert (sel16 m1 0 == sel16 m2 0);\n assert (sel16 m1 1 == sel16 m2 1);\n assert (sel16 m1 2 == sel16 m2 2);\n assert (sel16 m1 3 == sel16 m2 3);\n assert (sel16 m1 4 == sel16 m2 4);\n assert (sel16 m1 5 == sel16 m2 5);\n assert (sel16 m1 6 == sel16 m2 6);\n assert (sel16 m1 7 == sel16 m2 7);\n assert (sel16 m1 8 == sel16 m2 8);\n assert (sel16 m1 9 == sel16 m2 9);\n assert (sel16 m1 10 == sel16 m2 10);\n assert (sel16 m1 11 == sel16 m2 11);\n assert (sel16 m1 12 == sel16 m2 12);\n assert (sel16 m1 13 == sel16 m2 13);\n assert (sel16 m1 14 == sel16 m2 14);\n assert (sel16 m1 15 == sel16 m2 15);\n ()", "val mask_select_lemma: #t:inttype{~(S128? t)} -> mask:int_t t SEC -> a:int_t t SEC -> b:int_t t SEC -> Lemma\n (requires v mask = 0 \\/ v mask = v (ones t SEC))\n (ensures mask_select mask a b == (if v mask = 0 then b else a))\nlet mask_select_lemma #t mask a b =\n let t1 = mask &. (a ^. b) in\n let t2 = b ^. t1 in\n logand_lemma mask (a ^.b);\n if v mask = 0 then begin\n assert (v t1 == 0);\n logxor_lemma b t1;\n assert (v t2 = v b);\n () end\n else begin\n assert (v t1 == v (a ^. b));\n logxor_lemma b a;\n assert (v t2 = v a);\n () end", "val sel : #a:Type ->\n #r:preorder a ->\n h:heap ->\n\t m:mref a r{contains h m} ->\n a\nlet sel #a #b h m =\n match snd h m with\n | Some (| _ , (x , _) |) -> x", "val eta_map (n: nat) (r: regmap 'a) : regmap 'a\nlet eta_map (n:nat) (r:regmap 'a) : regmap 'a =\n let rec aux (n:nat) (out:regmap 'a) : regmap 'a =\n if n=0 then out\n else aux (n - 1) (upd out n (sel' r n))\n in\n aux n (create (sel' r 0))", "val sel (a b c: bool) : bool\nlet sel (a b c:bool) : bool = if c then a else b", "val sel_upd (#b:_)\n (vb:buffer b)\n (i:nat{i < length vb})\n (j:nat{j < length vb})\n (x:b)\n (h:HS.mem{live h vb})\n : Lemma (if i = j\n then sel (upd h vb i x) vb j == x\n else sel (upd h vb i x) vb j == sel h vb j)\n [SMTPat (sel (upd h vb i x) vb j)]\nlet sel_upd #b vb i j x h =\n if i=j then sel_upd1 vb i x h\n else sel_upd2 vb i j x h", "val eval_reg (r: reg) (s: machine_state) : t_reg r\nlet eval_reg (r:reg) (s:machine_state) : t_reg r = s.ms_regs r", "val llist_sel (#a:Type0) (r:t a) : selector (list a) (llist_sl r)\nlet llist_sel ptr = fun h -> datas (llist_sel_cell ptr h)", "val llist_sel (#a:Type0) (r:t a) : selector (list a) (llist_sl r)\nlet llist_sel\n #a r\n= fun m -> sel_of (llist0 r) m", "val llist_sel (#a:Type0) (r:t a) : selector (list a) (llist_sl r)\nlet llist_sel\n #a r\n= fun m -> sel_of (llist0 r) m", "val read : #a:Type ->\n #r:preorder a ->\n\t m:mref a r ->\n\t MRefST a (fun _ -> True)\n (fun h0 x h1 -> h0 == h1 /\\\n\t\t contains m h1 /\\\n\t\t\t\t sel h1 m == x)\nlet read #a #r m =\n let h = ist_get () in\n ist_recall (contains m); //recalling that the current heap must contain the given reference\n sel h m", "val hi (a: _) : erel a\nlet hi a : erel a = fun x y -> (True <: prop)", "val va_lemma_Vsel : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr ->\n src1:va_operand_vec_opr -> src2:va_operand_vec_opr -> sel:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Vsel dst src1 src2 sel) va_s0 /\\ va_is_dst_vec_opr dst\n va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\ va_is_src_vec_opr sel\n va_s0 /\\ va_get_ok va_s0))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_sM dst) == Vale.Def.Sel.isel32\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 sel)) /\\\n Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_sM dst) == Vale.Def.Sel.isel32\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 sel)) /\\\n Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_sM dst) == Vale.Def.Sel.isel32\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 sel)) /\\\n Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_sM dst) == Vale.Def.Sel.isel32\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 sel)) /\\ va_state_eq va_sM\n (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0))))\nlet va_lemma_Vsel va_b0 va_s0 dst src1 src2 sel =\n va_reveal_opaque (`%va_code_Vsel) (va_code_Vsel dst src1 src2 sel);\n let (va_old_s:va_state) = va_s0 in\n va_ins_lemma (Ins (S.Vsel dst src1 src2 sel)) va_s0;\n let (va_sM, va_fM) = va_eval_ins (Ins (S.Vsel dst src1 src2 sel)) va_s0 in\n (va_sM, va_fM)", "val ptrp_sel_interp (#a:Type0) (r:ref a) (p: perm) (m:mem) : Lemma\n (requires interp (ptrp r p) m)\n (ensures interp (pts_to_sl r p (ptrp_sel r p m)) m)\nlet ptrp_sel_interp #a r p m = pts_to_witinv r p", "val blocks0: x:size_t -> m:size_t{v m > 0} -> r:size_t{v r == S.blocks0 (v x) (v m)}\nlet blocks0 x m = if x =. 0ul then 1ul else (x -. 1ul) /. m +. 1ul", "val equational (t: term) : bool\nlet equational (t:term) : bool =\n match t.t with\n | Tm_FStar host_term ->\n (match R.inspect_ln host_term with\n | R.Tv_Match _ _ _ -> true\n | _ -> false)\n | _ -> false", "val va_quick_Vsel (dst src1 src2 sel: va_operand_vec_opr)\n : (va_quickCode unit (va_code_Vsel dst src1 src2 sel))\nlet va_quick_Vsel (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (sel:va_operand_vec_opr) : (va_quickCode unit (va_code_Vsel dst src1 src2 sel)) =\n (va_QProc (va_code_Vsel dst src1 src2 sel) ([va_mod_vec_opr dst]) (va_wp_Vsel dst src1 src2 sel)\n (va_wpProof_Vsel dst src1 src2 sel))", "val ( ! ) (#a: Type) (#rel: preorder a) (r: mref a rel) : STATE a (fun p h -> p (sel h r) h)\nlet op_Bang (#a:Type) (#rel:preorder a) (r:mref a rel)\n : STATE a (fun p h -> p (sel h r) h)\n= read #a #rel r", "val swap_selector (#a: Type0) (r1 r2: ref a)\n : Steel unit\n ((vptr r1) `star` (vptr r2))\n (fun _ -> (vptr r1) `star` (vptr r2))\n (requires fun _ -> True)\n (ensures fun h0 _ h1 -> sel r1 h0 == sel r2 h1 /\\ sel r2 h0 == sel r1 h1)\nlet swap_selector (#a:Type0) (r1 r2:ref a) : Steel unit\n (vptr r1 `star` vptr r2)\n (fun _ -> vptr r1 `star` vptr r2)\n (requires fun _ -> True)\n (ensures fun h0 _ h1 ->\n sel r1 h0 == sel r2 h1 /\\\n sel r2 h0 == sel r1 h1)\n = let x1 = read r1 in\n let x2 = read r2 in\n write r2 x1;\n write r1 x2", "val test15 (l: lref)\n : HIFC unit\n (single l)\n (single l)\n []\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s0 l == sel s1 l)\nlet test15 (l:lref)\n : HIFC unit (single l) (single l) []\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s0 l == sel s1 l)\n = write l (read l)", "val vconst_sel (#a: Type) (x: a) : Tot (selector a (hp_of emp))\nlet vconst_sel\n (#a: Type)\n (x: a)\n: Tot (selector a (hp_of emp))\n= fun _ -> x", "val read (#a:Type0) (r:ref a) :STATE a (fun p h -> p (sel h r) h)\nlet read #_ r = read r", "val llist_ptr_sel' (#a:Type0) (ptr:t a) : selector' (list (cell a * a)) (llist_ptr_sl ptr)\nlet llist_ptr_sel' #a ptr = fun h -> id_elim_exists (llist_ptr_sl' ptr) h", "val iread (l: loc)\n : hifc int (single l) bot [] (fun _ -> True) (fun s0 x s1 -> s0 == s1 /\\ x == sel s0 l)\nlet iread (l:loc) : hifc int (single l) bot [] (fun _ -> True) (fun s0 x s1 -> s0 == s1 /\\ x == sel s0 l) =\n let f : hst int (fun _ -> True) (fun s0 x s1 -> s0 == s1 /\\ x == sel s0 l) = fun s -> sel s l, s in\n f", "val lemma_equal_intro (#a:Type) (m1 m2:map16 a) : Lemma\n (requires (forall (i:int).{:pattern (sel m1 i) \\/ (sel m2 i)} 0 <= i /\\ i < 16 ==> sel m1 i == sel m2 i))\n (ensures equal m1 m2)\n [SMTPat (equal m1 m2)]\nlet lemma_equal_intro #a m1 m2 =\n lemma_equal m1 m2;\n ()", "val test3 (r1 r2 r3: ref int)\n : Steel unit\n ((vptr r1) `star` ((vptr r2) `star` (vptr r3)))\n (fun _ -> (vptr r1) `star` ((vptr r2) `star` (vptr r3)))\n (requires fun _ -> True)\n (ensures fun h0 _ h1 -> sel r1 h1 == 0 /\\ sel r2 h0 == sel r2 h1 /\\ sel r3 h0 == sel r3 h1)\nlet test3 (r1 r2 r3:ref int) : Steel unit\n (vptr r1 `star` (vptr r2 `star` vptr r3)) (fun _ -> vptr r1 `star` (vptr r2 `star` vptr r3))\n (requires fun _ -> True)\n (ensures fun h0 _ h1 ->\n sel r1 h1 == 0 /\\\n sel r2 h0 == sel r2 h1 /\\\n sel r3 h0 == sel r3 h1\n )\n = let x2_0 = gget (vptr r2) in\n write r1 1;\n let x1_1 = gget (vptr r1) in\n let x2_1 = gget (vptr r2) in\n assert (x1_1 == Ghost.hide 1);\n assert (x2_0 == x2_1);\n write r1 0", "val tree_sel_depends_only_on\n (#a: Type0)\n (ptr: t a)\n (m0: Mem.hmem (tree_sl ptr))\n (m1: mem{disjoint m0 m1})\n : Lemma (tree_sel_node' ptr m0 == tree_sel_node' ptr (Mem.join m0 m1))\nlet tree_sel_depends_only_on (#a:Type0) (ptr:t a)\n (m0:Mem.hmem (tree_sl ptr)) (m1:mem{disjoint m0 m1})\n : Lemma (tree_sel_node' ptr m0 == tree_sel_node' ptr (Mem.join m0 m1))\n = let m':Mem.hmem (tree_sl ptr) = Mem.join m0 m1 in\n let t1 = Ghost.reveal (id_elim_exists (tree_sl' ptr) m0) in\n let t2 = Ghost.reveal (id_elim_exists (tree_sl' ptr) m') in\n\n tree_sl'_witinv ptr;\n Mem.elim_wi (tree_sl' ptr) t1 t2 m'", "val llist_sel_interp (#a: Type0) (ptr: t a) (l: list (cell a * a)) (m: mem)\n : Lemma (requires interp (llist_ptr_sl' ptr l) m)\n (ensures interp (llist_ptr_sl ptr) m /\\ llist_ptr_sel_cell ptr m == l)\nlet llist_sel_interp (#a:Type0) (ptr:t a) (l:list (cell a * a)) (m:mem) : Lemma\n (requires interp (llist_ptr_sl' ptr l) m)\n (ensures interp (llist_ptr_sl ptr) m /\\ llist_ptr_sel_cell ptr m == l)\n = intro_h_exists l (llist_ptr_sl' ptr) m;\n llist_ptr_sl'_witinv ptr", "val elim_cons_cell_lemma (#a: Type0) (r: t a) (l: list (cell a * a)) (m: mem)\n : Lemma (requires Cons? l /\\ interp (llist_ptr_sl r) m /\\ llist_ptr_sel_cell r m == l)\n (ensures\n (let x = fst (L.hd l) in\n interp (((ptr r) `Mem.star` (llist_ptr_sl (next x))) `Mem.star` (ptr (data x))) m /\\\n sel_of (vptr r) m == x /\\ sel_of (vptr (data x)) m == snd (L.hd l) /\\\n sel_of (llist_cell (next x)) m == L.tl l))\nlet elim_cons_cell_lemma (#a:Type0) (r:t a) (l:list (cell a * a)) (m:mem) : Lemma\n (requires Cons? l /\\ interp (llist_ptr_sl r) m /\\ llist_ptr_sel_cell r m == l)\n (ensures (let x = fst (L.hd l) in\n interp (ptr r `Mem.star` llist_ptr_sl (next x) `Mem.star` ptr (data x)) m /\\\n sel_of (vptr r) m == x /\\\n sel_of (vptr (data x)) m == snd (L.hd l) /\\\n sel_of (llist_cell (next x)) m == L.tl l))\n = llist_sel_interp r l m;\n assert (interp (llist_ptr_sl' r l) m);\n let x = fst (L.hd l) in\n let v = snd (L.hd l) in\n let tl = L.tl l in\n let sl = pts_to_sl r full_perm x `Mem.star` llist_ptr_sl' (next x) tl `Mem.star` pts_to_sl (data x) full_perm v in\n pure_star_interp sl (r =!= null_llist) m;\n emp_unit sl;\n assert (interp sl m);\n let aux (m:mem) (ml1 ml2 mr:mem) : Lemma\n (requires disjoint ml1 ml2 /\\ disjoint (join ml1 ml2) mr /\\ m == join (join ml1 ml2) mr /\\\n interp (pts_to_sl r full_perm x) ml1 /\\\n interp (llist_ptr_sl' (next x) tl) ml2 /\\\n interp (pts_to_sl (data x) full_perm v) mr)\n (ensures interp (ptr r `Mem.star` llist_ptr_sl (next x) `Mem.star` ptr (data x)) m /\\\n sel_of (vptr r) m == x /\\\n sel_of (llist_cell (next x)) m == tl /\\\n sel_of (vptr (data x)) m == v)\n = intro_ptr_interp r (hide x) ml1;\n llist_sel_interp (next x) tl ml2;\n intro_star (ptr r) (llist_ptr_sl (next x)) ml1 ml2;\n ptr_sel_interp r ml1;\n pts_to_witinv r full_perm;\n join_commutative ml1 ml2;\n let ml = join ml1 ml2 in\n assert (interp (ptr r `Mem.star` llist_ptr_sl (next x)) ml);\n intro_ptr_interp (data x) (hide v) mr;\n intro_star (ptr r `Mem.star` llist_ptr_sl (next x)) (ptr (data x)) ml mr;\n ptr_sel_interp (data x) mr;\n pts_to_witinv (data x) full_perm;\n join_commutative ml mr\n in\n elim_star\n (pts_to_sl r full_perm x `Mem.star` llist_ptr_sl' (next x) tl)\n (pts_to_sl (data x) full_perm v) m;\n Classical.forall_intro (Classical.move_requires\n (elim_star (pts_to_sl r full_perm x) (llist_ptr_sl' (next x) tl)));\n Classical.forall_intro_3 (Classical.move_requires_3 (aux m))", "val read (l: loc)\n : HIFC int (single l) bot [] (requires fun _ -> True) (ensures fun s0 x s1 -> x == sel s0 l)\nlet read (l:loc)\n : HIFC int (single l) bot []\n (requires fun _ -> True)\n (ensures fun s0 x s1 -> x == sel s0 l)\n = HIFC?.reflect (iread l)", "val eternal_region_pred (m1 m2: mem) : Type0\nlet eternal_region_pred (m1 m2:mem) :Type0\n = forall (r:HS.rid).{:pattern (HS.is_heap_color (color r)); (m1 `contains_region` r)}\n (HS.is_eternal_region_hs r /\\ m1 `contains_region` r) ==> m2 `contains_region` r", "val write (#a: Type) (#rel: preorder a) (r: mref a rel) (v: a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 ->\n rel (sel h0 r) v /\\ h0 `contains` r /\\ modifies (Set.singleton (addr_of r)) h0 h1 /\\\n equal_dom h0 h1 /\\ sel h1 r == v)\nlet write (#a:Type) (#rel:preorder a) (r:mref a rel) (v:a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 -> rel (sel h0 r) v /\\ h0 `contains` r /\\\n modifies (Set.singleton (addr_of r)) h0 h1 /\\ equal_dom h0 h1 /\\\n sel h1 r == v)\n = let h0 = gst_get () in\n gst_recall (contains_pred r);\n let h1 = upd_tot h0 r v in\n Heap.lemma_distinct_addrs_distinct_preorders ();\n Heap.lemma_distinct_addrs_distinct_mm ();\n Heap.lemma_upd_equals_upd_tot_for_contained_refs h0 r v;\n gst_put h1", "val read : #a:Type -> \n r:ref a -> \n\t ImmutableST a (fun _ -> True) \n (fun h0 x h1 -> h0 == h1 /\\ \n\t\t\t contains r h1 /\\ \n\t\t\t\t\t sel h1 r == x)\nlet read #a r =\n let h = ist_get () in\n ist_recall (contains r); //recalling that the current heap must contain the given reference\n sel h r", "val read : #a:Type -> \n r:ref a -> \n\t AllocST a (fun _ -> True) \n (fun h0 x h1 -> h0 == h1 /\\ \n\t\t x == FStar.Heap.sel h1 r)\nlet read #a r = \n let h = ist_get () in\n sel h r", "val reference_distinct_sel_disjoint (#a: Type0) (h: mem) (r1 r2: reference a)\n : Lemma\n (requires\n (h `contains` r1 /\\ h `contains` r2 /\\ frameOf r1 == frameOf r2 /\\ as_addr r1 == as_addr r2)\n ) (ensures (sel h r1 == sel h r2))\nlet reference_distinct_sel_disjoint\n (#a:Type0) (h: mem) (r1: reference a) (r2: reference a)\n: Lemma\n (requires (\n h `contains` r1 /\\\n h `contains` r2 /\\\n frameOf r1 == frameOf r2 /\\\n as_addr r1 == as_addr r2\n ))\n (ensures (\n sel h r1 == sel h r2\n ))\n= mreference_distinct_sel_disjoint h r1 r2", "val tail_cell_lemma (#a: Type0) (r: t a) (l: list (cell a)) (m: mem)\n : Lemma (requires Cons? l /\\ interp (llist_sl r) m /\\ llist_sel_cell r m == l)\n (ensures\n (let x = L.hd l in\n interp ((ptr r) `Mem.star` (llist_sl (next x))) m /\\ sel_of (vptr r) m == x /\\\n sel_of (llist_cell (next x)) m == L.tl l))\nlet tail_cell_lemma (#a:Type0) (r:t a) (l:list (cell a)) (m:mem) : Lemma\n (requires Cons? l /\\ interp (llist_sl r) m /\\ llist_sel_cell r m == l)\n (ensures (let x = L.hd l in\n interp (ptr r `Mem.star` llist_sl (next x)) m /\\\n sel_of (vptr r) m == x /\\\n sel_of (llist_cell (next x)) m == L.tl l))\n = llist_sel_interp r l m;\n assert (interp (llist_sl' r l) m);\n let x = L.hd l in\n let tl = L.tl l in\n let sl = pts_to_sl r full_perm x `Mem.star` llist_sl' (next x) tl in\n pure_star_interp sl (r =!= null_llist) m;\n emp_unit sl;\n assert (interp sl m);\n let aux (m:mem) (ml mr:mem) : Lemma\n (requires disjoint ml mr /\\ m == join ml mr /\\\n interp (pts_to_sl r full_perm x) ml /\\ interp (llist_sl' (next x) tl) mr)\n (ensures interp (ptr r `Mem.star` llist_sl (next x)) m /\\\n sel_of (vptr r) m == x /\\\n sel_of (llist_cell (next x)) m == tl)\n = intro_ptr_interp r (hide x) ml;\n llist_sel_interp (next x) tl mr;\n intro_star (ptr r) (llist_sl (next x)) ml mr;\n ptr_sel_interp r ml;\n pts_to_witinv r full_perm;\n join_commutative ml mr\n in\n elim_star (pts_to_sl r full_perm x) (llist_sl' (next x) tl) m;\n Classical.forall_intro_2 (Classical.move_requires_2 (aux m))", "val test1 (c: ref (ref int))\n : ST (ref (ref int))\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures\n (fun h0 d h1 ->\n c == d /\\ (h1, d) == (compose_hlens hlens_ref hlens_ref).put 0 (h0, c) /\\\n h1 == upd (upd h0 (sel h0 c) 0) c (sel h0 c) /\\ sel h0 c == sel h1 c /\\\n sel h1 (sel h1 c) = 0))\nlet test1 (c:ref (ref int)) : ST (ref (ref int))\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures (fun h0 d h1 ->\n c == d /\\\n (h1, d) == (compose_hlens hlens_ref hlens_ref).put 0 (h0, c) /\\\n h1 == upd (upd h0 (sel h0 c) 0) c (sel h0 c) /\\\n sel h0 c == sel h1 c /\\ sel h1 (sel h1 c) = 0)) =\n (compose_stlens stlens_ref stlens_ref).st_put 0 c", "val ptr_sel (#a: Type0) (r: ref a) : selector a (ptr r)\nlet ptr_sel (#a:Type0) (r:ref a) : selector a (ptr r) = ptrp_sel r full_perm", "val ptr_sel (#a: Type0) (r: ref a) : selector a (ptr r)\nlet ptr_sel (#a:Type0) (r:ref a) : selector a (ptr r) = ptrp_sel r full_perm", "val equiv_op:t\nlet equiv_op : t =\n let local_eval\n (operand1: valid_object_value_t (ObjectTDPrimitive (PrimitiveTDBool)))\n (operand2: valid_object_value_t (ObjectTDPrimitive (PrimitiveTDBool)))\n : GTot (conditional_computation_t (valid_object_value_t (ObjectTDPrimitive (PrimitiveTDBool)))) =\n let op1 = unbox_primitive_box (ObjectValuePrimitive?.value operand1) in\n let op2 = unbox_primitive_box (ObjectValuePrimitive?.value operand2) in\n return (ObjectValuePrimitive (PrimitiveBoxBool ((not op1 && not op2) || (op1 && op2)))) in\n {\n operand_td1 = ObjectTDPrimitive (PrimitiveTDBool);\n operand_td2 = ObjectTDPrimitive (PrimitiveTDBool);\n result_td = ObjectTDPrimitive (PrimitiveTDBool);\n eval = local_eval;\n }", "val mreference_distinct_sel_disjoint\n (#a:Type0) (#rel1: preorder a) (#rel2: preorder a) (h: mem) (r1: mreference a rel1) (r2:mreference a rel2)\n : Lemma (requires (h `contains` r1 /\\ h `contains` r2 /\\ frameOf r1 == frameOf r2 /\\ as_addr r1 == as_addr r2))\n (ensures (sel h r1 == sel h r2))\nlet mreference_distinct_sel_disjoint #_ #_ #_ h r1 r2 =\n Heap.lemma_distinct_addrs_distinct_preorders ();\n Heap.lemma_distinct_addrs_distinct_mm ();\n Heap.lemma_sel_same_addr (Map.sel h.h (frameOf r1)) (as_ref r1) (as_ref r2)", "val test1 (r: ref int)\n : Steel unit\n (vptr r)\n (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> sel r h1 == 0)\nlet test1 (r:ref int) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> sel r h1 == 0)\n = write r 1;\n write r 0", "val eq_vbool (v0 v1: vbool) : Tot (b: bool{b <==> (v0 == v1)})\nlet eq_vbool (v0 v1: vbool)\r\n : Tot (b:bool { b <==> (v0 == v1) })\r\n = match v0, v1 with\r\n | Vfalse, Vfalse\r\n | Vtrue, Vtrue -> true\r\n | _ -> false", "val op_Colon_Equals (#a:Type0) (r:ref a) (v:a)\n :ST unit (fun _ -> True) (fun h0 _ h1 -> h0 `contains` r /\\ modifies (only r) h0 h1 /\\ equal_dom h0 h1 /\\ sel h1 r == v)\nlet op_Colon_Equals #_ r v = write r v", "val ptr_sel (#a: Type0) (r: ref a) : selector (ptr r) (fun _ -> a)\nlet ptr_sel (#a:Type0) (r:ref a) : selector (ptr r) (fun _ -> a) = ptr_sel r", "val le_sigh (a:Spec.alg) (m:m_spec): x:size_t { x == 4ul *. row_len a m }\nlet le_sigh (a:Spec.alg) (m:m_spec): x:size_t { x == 4ul *. row_len a m } =\n let open FStar.Mul in\n assert_norm ((4 * 1) % pow2 32 = 4);\n assert_norm ((4 * 4) % pow2 32 = 16);\n Lib.IntTypes.mul_mod_lemma 4ul 1ul;\n Lib.IntTypes.mul_mod_lemma 4ul 4ul;\n match a,m with\n | Spec.Blake2S,M128 -> 4ul\n | Spec.Blake2S,M256 -> 4ul\n | Spec.Blake2B,M256 -> 4ul\n | _ -> 16ul", "val ind_ptr_sel' (#a: Type0) (r: ref (ref a)) : selector' (ref a * a) (ind_ptr_sl r)\nlet ind_ptr_sel' (#a:Type0) (r:ref (ref a)) : selector' (ref a * a) (ind_ptr_sl r) =\n fun h ->\n let p = id_elim_exists (ind_ptr_sl' r) h in\n reveal p, ptr_sel p h", "val r_sep_forall:\n #a:Type0 -> #rst:Type -> rg:regional rst a ->\n p:loc -> h0:HS.mem -> h1:HS.mem ->\n v:a{rg_inv rg h0 v} ->\n Lemma (requires (loc_disjoint (loc_all_regions_from\n false (Rgl?.region_of rg v)) p /\\\n modifies p h0 h1))\n (ensures (rg_inv rg h1 v /\\\n Rgl?.r_repr rg h0 v == Rgl?.r_repr rg h1 v))\nlet r_sep_forall #a #rst rg p h0 h1 v =\n Rgl?.r_sep rg v p h0 h1", "val unpack_ind_lemma (#a: Type0) (r: ref (ref a)) (p: ref a) (v: a) (m: mem)\n : Lemma (requires interp (ind_ptr_sl r) m /\\ ind_ptr_sel_full r m == (p, v))\n (ensures\n interp ((ptr r) `Mem.star` (ptr p)) m /\\ sel_of (vptr r) m == p /\\ sel_of (vptr p) m == v)\nlet unpack_ind_lemma (#a:Type0) (r:ref (ref a)) (p:ref a) (v:a) (m:mem) : Lemma\n (requires interp (ind_ptr_sl r) m /\\ ind_ptr_sel_full r m == (p, v))\n (ensures\n interp (ptr r `Mem.star` ptr p) m /\\\n sel_of (vptr r) m == p /\\\n sel_of (vptr p) m == v)\n = intro_ptr_frame_lemma r p (ptr p) m", "val eternal_refs_pred (m1 m2: mem) : Type0\nlet eternal_refs_pred (m1 m2:mem) :Type0\n = forall (a:Type) (rel:preorder a) (r:HS.mreference a rel).\n {:pattern (m1 `HS.contains` r)}\n (is_mm r) \\/\n (((m1 `HS.contains` r) /\\\n (HS.is_eternal_region_hs (frameOf r) \\/\n m2 `contains_region` (HS.frameOf r))) ==> (m2 `HS.contains` r /\\ rel (HS.sel m1 r) (HS.sel m2 r)))", "val lift_eq (#t: eqtype) (x y: U.raise_t t) : b: bool{b <==> x == y}\nlet lift_eq (#t:eqtype) (x y:U.raise_t t)\n : b:bool{b <==> x==y}\n = downgrade_equiv x y; U.downgrade_val x = U.downgrade_val y", "val write (#a:Type0) (r:ref a) (x:a) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> x == sel r h1)\nlet write r x =\n let _ = elim_vptr r _ in\n write_pt r x;\n intro_vptr r _ x", "val write (#a:Type0) (r:ref a) (x:a) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> x == sel r h1)\nlet write\n r x\n= elim_vptrp r full_perm;\n A.upd r 0sz x;\n intro_vptrp' r full_perm", "val lemma_upd_ne (r r':flag) (v:flag_val_t) (m:t) : Lemma\n (requires r =!= r')\n (ensures sel r (upd r' v m) == sel r m)\n [SMTPat (sel r (upd r' v m))]\nlet lemma_upd_ne r r' v m =\n reveal_opaque (`%sel) sel;\n reveal_opaque (`%upd) upd;\n Map.lemma_SelUpd2 m r r' v", "val elems_reg:\n #a:Type0 -> #rst:Type -> #rg:regional rst a ->\n h:HS.mem -> rv:rvector rg ->\n GTot Type0\nlet elems_reg #a #rst #rg h rv =\n rv_elems_reg h rv 0ul (V.size_of rv)", "val llist_sel_interp (#a: Type0) (ptr: t a) (l: list (cell a)) (m: mem)\n : Lemma (requires interp (llist_sl' ptr l) m)\n (ensures interp (llist_sl ptr) m /\\ llist_sel_cell' ptr m == l)\nlet llist_sel_interp (#a:Type0) (ptr:t a) (l:list (cell a)) (m:mem) : Lemma\n (requires interp (llist_sl' ptr l) m)\n (ensures interp (llist_sl ptr) m /\\ llist_sel_cell' ptr m == l)\n = intro_h_exists l (llist_sl' ptr) m;\n llist_sl'_witinv ptr", "val sel (#a: Type) (m: map16 a) (n: int) : a\nlet sel (#a:Type) (m:map16 a) (n:int) : a =\n sel16 m n", "val ind_ptr_sel (#a: Type0) (r: ref (ref a)) : selector a (ind_ptr_sl r)\nlet ind_ptr_sel (#a:Type0) (r:ref (ref a)) : selector a (ind_ptr_sl r) =\n fun h -> snd (ind_ptr_sel_full r h)", "val lemma_self (#a:Type) (m:map16 a) (n:int) (v:a) : Lemma\n (requires 0 <= n /\\ n < 16)\n (ensures sel (upd m n v) n == v)\n [SMTPat (sel (upd m n v) n)]\nlet lemma_self (#a:Type) (m:map16 a) (n:int) (v:a) =\n assert_norm (sel (upd m n v) n == sel16 (upd16 m n v) n);\n lemma_self16 m n v", "val sel: #a:Type0 -> #rel:preorder a -> heap -> mref a rel -> GTot a\nlet sel #a #rel h r =\n if h `contains_bool` r\n then sel_tot #a h r\n else r.init" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.X64.Regs.fst", "name": "Vale.X64.Regs.lemma_upd_eq" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Regs.fst", "name": "Vale.X64.Regs.lemma_upd_ne" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Regs.fst", "name": "Vale.X64.Regs.of_fun" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Flags.fst", "name": "Vale.X64.Flags.sel" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Regs.fst", "name": "Vale.X64.Regs.equal" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Regs.fst", "name": "Vale.PPC64LE.Regs.equal" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.vdep_sel_eq" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Leakage.fst", "name": "Vale.X64.Leakage.eq_registers" }, { "project_name": "steel", "file_name": "Steel.Reference.fsti", "name": "Steel.Reference.ptr_sel_interp" }, { "project_name": "FStar", "file_name": "Registers.List.fst", "name": "Registers.List.sel'" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Machine_s.fst", "name": "Vale.X64.Machine_s.t_reg" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Leakage_Helpers.fst", "name": "Vale.X64.Leakage_Helpers.reg_le" }, { "project_name": "FStar", "file_name": "Interop.fst", "name": "Interop.elim_m" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.sel_v" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.sel_v" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.op_Bang" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.op_Bang" }, { "project_name": "FStar", "file_name": "ImmutableSTwHeaps.fst", "name": "ImmutableSTwHeaps.read" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fst", "name": "Vale.Lib.Map16.lemma_equal" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.tree_sel_interp" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Flags.fst", "name": "Vale.X64.Flags.lemma_upd_eq" }, { "project_name": "FStar", "file_name": "StatefulLens.fst", "name": "StatefulLens.test4" }, { "project_name": "FStar", "file_name": "AllocST.fst", "name": "AllocST.read" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Seq.fst", "name": "FStar.Monotonic.Seq.i_sel" }, { "project_name": "zeta", "file_name": "Zeta.Steel.FormatsManual.fsti", "name": "Zeta.Steel.FormatsManual.eq_mval_value" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Regs.fst", "name": "Vale.X64.Regs.lemma_equal_intro" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.tree_sel" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.mask_select" }, { "project_name": "steel", "file_name": "Selectors.Examples.fst", "name": "Selectors.Examples.test2" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fsti", "name": "Vale.Lib.Map16.eta" }, { "project_name": "FStar", "file_name": "StatefulLens.fst", "name": "StatefulLens.test0" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.QuickCode.fst", "name": "Vale.PPC64LE.QuickCode.va_mod_reg" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.op_Colon_Equals" }, { "project_name": "FStar", "file_name": "FStar.PartialMap.fst", "name": "FStar.PartialMap.sel" }, { "project_name": "FStar", "file_name": "StatefulLens.fst", "name": "StatefulLens.test2" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.sel" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.read" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.llist_ptr_sel" }, { "project_name": "steel", "file_name": "Selectors.Examples.fst", "name": "Selectors.Examples.test0" }, { "project_name": "steel", "file_name": "Steel.Reference.fsti", "name": "Steel.Reference.ghost_ptr_sel_interp" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fst", "name": "Vale.Lib.Map16.lemma_equal16" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.mask_select_lemma" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.sel" }, { "project_name": "FStar", "file_name": "Registers.List.fst", "name": "Registers.List.eta_map" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Sel.fst", "name": "Vale.Def.Sel.sel" }, { "project_name": "FStar", "file_name": "LowStar.BufferView.Up.fst", "name": "LowStar.BufferView.Up.sel_upd" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Machine_Semantics_s.fst", "name": "Vale.X64.Machine_Semantics_s.eval_reg" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.llist_sel" }, { "project_name": "steel", "file_name": "Selectors.LList3.fst", "name": "Selectors.LList3.llist_sel" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.llist_sel" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.read" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.hi" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_lemma_Vsel" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ptrp_sel_interp" }, { "project_name": "hacl-star", "file_name": "Hacl.Bignum.Definitions.fst", "name": "Hacl.Bignum.Definitions.blocks0" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Match.fst", "name": "Pulse.Checker.Prover.Match.equational" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_quick_Vsel" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.op_Bang" }, { "project_name": "steel", "file_name": "References.fst", "name": "References.swap_selector" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test15" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.vconst_sel" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.read" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.llist_ptr_sel'" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.iread" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fst", "name": "Vale.Lib.Map16.lemma_equal_intro" }, { "project_name": "steel", "file_name": "Selectors.Examples.fst", "name": "Selectors.Examples.test3" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.tree_sel_depends_only_on" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.llist_sel_interp" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.elim_cons_cell_lemma" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.read" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fst", "name": "FStar.HyperStack.ST.eternal_region_pred" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.write" }, { "project_name": "FStar", "file_name": "ImmutableST.fst", "name": "ImmutableST.read" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.read" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.reference_distinct_sel_disjoint" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.tail_cell_lemma" }, { "project_name": "FStar", "file_name": "StatefulLens.fst", "name": "StatefulLens.test1" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fsti", "name": "Steel.ArrayRef.ptr_sel" }, { "project_name": "steel", "file_name": "Steel.Reference.fsti", "name": "Steel.Reference.ptr_sel" }, { "project_name": "Armada", "file_name": "Armada.BinaryOp.fst", "name": "Armada.BinaryOp.equiv_op" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.mreference_distinct_sel_disjoint" }, { "project_name": "steel", "file_name": "Selectors.Examples.fst", "name": "Selectors.Examples.test1" }, { "project_name": "zeta", "file_name": "Zeta.Steel.FormatsManual.fsti", "name": "Zeta.Steel.FormatsManual.eq_vbool" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.op_Colon_Equals" }, { "project_name": "steel", "file_name": "SelectorLogic.fst", "name": "SelectorLogic.ptr_sel" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Blake2.Core.fst", "name": "Hacl.Impl.Blake2.Core.le_sigh" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.ind_ptr_sel'" }, { "project_name": "FStar", "file_name": "LowStar.RVector.fst", "name": "LowStar.RVector.r_sep_forall" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.unpack_ind_lemma" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fst", "name": "FStar.HyperStack.ST.eternal_refs_pred" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.lift_eq" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.write" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.write" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Flags.fst", "name": "Vale.X64.Flags.lemma_upd_ne" }, { "project_name": "FStar", "file_name": "LowStar.RVector.fst", "name": "LowStar.RVector.elems_reg" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.llist_sel_interp" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fsti", "name": "Vale.Lib.Map16.sel" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.ind_ptr_sel" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fst", "name": "Vale.Lib.Map16.lemma_self" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.sel" } ], "selected_premises": [ "Vale.Def.Prop_s.prop0", "Vale.X64.Machine_s.operand64", "FStar.FunctionalExtensionality.feq", "Vale.Def.Types_s.nat64", "Vale.X64.Machine_s.t_reg", "Vale.X64.Regs.sel", "Vale.Def.Types_s.nat8", "Vale.X64.Machine_s.reg_xmm", "Vale.X64.Machine_s.nat64", "Vale.X64.Machine_s.reg_64", "Vale.X64.Machine_s.operand128", "Vale.X64.Machine_s.quad32", "Vale.Lib.Map16.sel", "Vale.Def.Words_s.nat32", "FStar.UInt.size", "Vale.Def.Words_s.nat64", "Vale.Lib.Seqs_s.seq_map", "FStar.Mul.op_Star", "Vale.Def.Types_s.nat32", "Vale.Def.Words_s.natN", "Vale.X64.Machine_s.reg_id", "Vale.X64.Machine_s.t_reg_file", "FStar.Pervasives.reveal_opaque", "FStar.FunctionalExtensionality.on_dom", "FStar.Pervasives.Native.fst", "Vale.Def.Words_s.nat8", "Vale.X64.Machine_s.n_regs", "FStar.Pervasives.Native.snd", "Vale.X64.Machine_s.t_reg_to_int", "Vale.Def.Words_s.pow2_32", "Vale.X64.Machine_s.reg_file_id", "Vale.X64.Machine_s.pow2_64", "Vale.X64.Machine_s.n_reg_files", "Vale.X64.Machine_s.rRdi", "Vale.X64.Regs.upd", "Vale.X64.Machine_s.rRsp", "Vale.Def.Words_s.pow2_64", "Vale.X64.Machine_s.rRbp", "Vale.X64.Machine_s.rRdx", "Vale.X64.Machine_s.rRsi", "Vale.X64.Machine_s.rRax", "Vale.Lib.Map16.sel2", "Vale.Lib.Map16.get", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.operand_rf", "Vale.X64.Machine_s.rRcx", "Vale.Def.Types_s.quad32_xor", "Vale.Lib.Seqs_s.all_but_last", "Vale.X64.Machine_s.rR12", "Vale.X64.Machine_s.rR9", "Vale.X64.Machine_s.rR10", "Vale.X64.Machine_s.rR8", "Vale.X64.Machine_s.rR13", "Vale.Lib.Map16.sel4", "Vale.X64.Machine_s.rR11", "Vale.X64.Machine_s.reg_Rsp", "FStar.FunctionalExtensionality.on", "Vale.X64.Machine_s.fOverflow", "Vale.Lib.Map16.sel16", "Vale.Def.Words.Four_s.nat_to_four", "Vale.X64.Machine_s.pow2_32", "Vale.Lib.Seqs_s.compose", "Vale.Lib.Map16.eta", "Vale.X64.Machine_s.rR15", "Vale.Lib.Map16.sel8", "Vale.Def.Words.Seq_s.seq_to_seq_four_BE", "Vale.X64.Machine_s.rR14", "Vale.X64.Machine_s.fCarry", "Vale.Lib.Map16.upd", "Vale.Def.Words.Seq_s.seq_four_to_seq_BE", "Vale.Def.Words.Four_s.four_map2", "Vale.X64.Machine_s.reg_Rsi", "Vale.Def.Words.Four_s.four_to_nat", "Vale.Def.Words.Four_s.four_map", "Vale.Def.Words.Seq_s.seq_to_seq_four_LE", "Vale.Def.Words.Seq_s.seq_to_four_BE", "Vale.Def.Words.Four_s.four_select", "FStar.Math.Lemmas.pow2_plus", "FStar.Pervasives.dfst", "Vale.Def.Types_s.be_bytes_to_seq_quad32", "Vale.X64.Machine_s.oreg", "Vale.Lib.Map16.eta16", "Vale.X64.Machine_s.reg_Rax", "FStar.Pervasives.dsnd", "Vale.Def.Words_s.pow2_128", "Vale.X64.Machine_s.reg_R14", "Vale.Def.Words.Seq_s.seq_four_to_seq_LE", "Vale.Def.Types_s.le_seq_quad32_to_bytes", "Vale.Def.Words.Seq_s.seq_nat8_to_seq_nat32_BE", "Vale.Def.Words.Seq_s.seq_nat8_to_seq_nat32_LE", "Vale.X64.Machine_s.reg_R11", "Vale.Lib.Map16.upd4", "Vale.X64.Machine_s.reg_R10", "Vale.Def.Words.Seq_s.seq16", "Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE", "Vale.Def.Types_s.le_bytes_to_seq_quad32", "Vale.Lib.Map16.upd2", "Vale.Lib.Map16.upd16", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater", "Vale.X64.Machine_s.reg_R8" ], "source_upto_this": "module Vale.X64.Regs\nopen FStar.Mul\n// This interface should not refer to Machine_Semantics_s\n\nopen Vale.Def.Prop_s\nopen Vale.X64.Machine_s\nopen Vale.Lib.Map16\n\ntype regs_fun = FStar.FunctionalExtensionality.restricted_t reg t_reg\ntype regs_def = map16 nat64 & map16 quad32\n\n[@\"opaque_to_smt\"]\ntype t = regs_def\n\n[@va_qattr \"opaque_to_smt\"]\nlet sel (r:reg) (m:t) : t_reg r =\n match m with (m0, m1) ->\n match r with Reg rf i ->\n match rf with\n | 0 -> sel16 m0 i\n | 1 -> sel16 m1 i\n\n[@va_qattr \"opaque_to_smt\"]\nlet upd (r:reg) (v:t_reg r) (m:t) : t =\n match m with (m0, m1) ->\n match r with Reg rf i ->\n match rf with\n | 0 -> (upd16 m0 i v, m1)\n | 1 -> (m0, upd16 m1 i v)\n\n// Used in eta-expansion; we ensure that it stops normalization by not marking it va_qattr\n[@\"opaque_to_smt\"]", "sketch": [ "Step 1: The definition `eta_sel` is about creating a function that takes a register `r` and a map `m` and returns the value of the register `r` in the map `m`. The returned value must be equal to the result of the `sel` function applied to `r` and `m`.\nStep 2: The implementation will use the `sel` function to obtain the value of the register `r` in the map `m` and ensure that the returned value is equal to this result.", "Step 1: The definition `eta_sel` is about creating a function that takes a register `r` and a map `m`, and returns the value of the register `r` in the map `m`. The returned value should be equal to the result of the `sel` function applied to `r` and `m`.\nStep 2: The implementation involves defining a function that takes `r` and `m` as inputs and returns the value obtained by applying the `sel` function to `r` and `m`. The returned value is constrained to be equal to `sel r m`.", "Step 1: The definition `eta_sel` is about creating a function that takes a register `r` and a map `m`, and returns the value of the register `r` in the map `m`. The returned value should be equal to the result of the `sel` function applied to `r` and `m`.\nStep 2: The implementation involves defining a function `eta_sel` that takes parameters `r` and `m`, and returns the result of `sel r m`. The returned value is constrained to be equal to `sel r m`.", "Step 1: The definition `eta_sel` is about creating a function that takes a register `r` and a map `m` and returns the value of the register `r` in the map `m`, ensuring that the returned value is exactly the same as what the `sel` function would return.\nStep 2: The implementation involves defining a function that takes `r` and `m` as arguments and simply calls the `sel` function with these arguments, ensuring that the result is equal to `sel r m`.", "Step 1: The definition `eta_sel` is about creating a function that takes a register `r` and a map `m` and returns the value of the register `r` in the map `m`. This value should be equal to the result of the `sel` function applied to `r` and `m`.\nStep 2: The implementation will use the `sel` function to retrieve the value of the register `r` from the map `m` and ensure that the returned value is equal to the result of `sel r m`.", "Step 1: The definition `eta_sel` is about creating a function that takes a register `r` and a map `m` and returns the value of the register `r` in the map `m`. This value must be equal to the result of the `sel` function applied to `r` and `m`.\nStep 2: The implementation involves defining a function `eta_sel` that takes `r` and `m` as arguments and returns the value obtained by applying the `sel` function to `r` and `m`. Additionally, we need to ensure that the returned value is equal to `sel r m`.", "Step 1: The definition `eta_sel` is about creating a function that takes a register `r` and a map `m` and returns the value of the register `r` in the map `m`. The returned value must be equal to the result of the `sel` function applied to `r` and `m`.\nStep 2: The implementation involves defining a function `eta_sel` that takes `r` and `m` as arguments and returns the value obtained by applying the `sel` function to `r` and `m`. The returned value must satisfy the condition that it is equal to `sel r m`.", "Step 1: The definition `eta_sel` is about creating a function that takes a register `r` and a map `m` and returns the value of the register `r` in the map `m`. The returned value should be equal to the result of the `sel` function applied to `r` and `m`.\nStep 2: The implementation involves defining a function `eta_sel` that takes two arguments `r` and `m`, and returns the value obtained by applying the `sel` function to `r` and `m`. The returned value is constrained to be equal to `sel r m`.", "Step 1: The definition `eta_sel` is about creating a function that takes a register `r` and a map `m` and returns the value of the register `r` in the map `m`, ensuring that the returned value is exactly equal to the result of the `sel` function applied to `r` and `m`.\nStep 2: The implementation involves defining a function that directly returns the result of `sel r m` and uses a refinement type to assert that the returned value is equal to `sel r m`.", "Step 1: The definition `eta_sel` is about creating a function that takes a register `r` and a map `m`, and returns the value of the register `r` in the map `m`. The returned value should be equal to what the `sel` function returns for the same inputs.\nStep 2: The implementation involves defining a function `eta_sel` that takes parameters `r` and `m`, and returns the result of `sel r m`. The function also includes a refinement type to ensure that the returned value is equal to `sel r m`." ], "generated_solution": [ "let eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m} =\n sel r m", "let eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m} =\n sel r m", "let eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m} =\n sel r m", "let eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m} =\n sel r m", "let eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m} =\n sel r m", "let eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m} =\n sel r m", "let eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m} = sel r m", "let eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m} =\n sel r m", "let eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m} =\n sel r m", "let eta_sel (r: reg) (m: t) : v: (t_reg r){v == sel r m} =\n sel r m" ] }, { "file_name": "Vale.AES.PPC64LE.GCMencrypt.fst", "name": "Vale.AES.PPC64LE.GCMencrypt.va_qcode_Gcm_make_length_quad", "opens_and_abbrevs": [ { "open": "Vale.Lib.Basic" }, { "open": "Vale.AES.OptPublic_BE" }, { "open": "Vale.Lib.Meta" }, { "open": "Vale.AES.PPC64LE.GHash" }, { "open": "Vale.Math.Poly2.Bits_s" }, { "open": "Vale.AES.PPC64LE.GF128_Mul" }, { "open": "Vale.PPC64LE.QuickCodes" }, { "open": "Vale.PPC64LE.QuickCode" }, { "open": "Vale.PPC64LE.InsStack" }, { "open": "Vale.PPC64LE.InsVector" }, { "open": "Vale.PPC64LE.InsMem" }, { "open": "Vale.PPC64LE.InsBasic" }, { "open": "Vale.PPC64LE.Decls" }, { "open": "Vale.PPC64LE.State" }, { "open": "Vale.PPC64LE.Stack_i" }, { "open": "Vale.PPC64LE.Memory" }, { "open": "Vale.PPC64LE.Machine_s" }, { "open": "Vale.AES.PPC64LE.GCTR" }, { "open": "Vale.AES.GCM_helpers_BE" }, { "open": "Vale.Poly1305.Math" }, { "open": "Vale.AES.GF128" }, { "open": "Vale.AES.GF128_s" }, { "open": "Vale.AES.PPC64LE.AES" }, { "open": "Vale.AES.GCM_BE_s" }, { "open": "Vale.AES.GHash_BE" }, { "open": "Vale.AES.GHash_BE_s" }, { "open": "Vale.AES.GCM_BE" }, { "open": "Vale.AES.GCTR_BE" }, { "open": "Vale.AES.GCTR_BE_s" }, { "open": "Vale.AES.AES_BE_s" }, { "open": "Vale.Arch.HeapImpl" }, { "open": "Vale.Arch.Types" }, { "open": "Vale.Def.Types_s" }, { "open": "Vale.Def.Words.Seq_s" }, { "open": "Vale.Def.Words_s" }, { "open": "FStar.Seq" }, { "open": "Vale.Def.Opaque_s" }, { "open": "Vale.Def.Prop_s" }, { "open": "Vale.AES.OptPublic_BE" }, { "open": "Vale.Lib.Meta" }, { "open": "Vale.AES.PPC64LE.GHash" }, { "open": "Vale.Math.Poly2.Bits_s" }, { "open": "Vale.AES.PPC64LE.GF128_Mul" }, { "open": "Vale.PPC64LE.QuickCodes" }, { "open": "Vale.PPC64LE.QuickCode" }, { "open": "Vale.PPC64LE.InsStack" }, { "open": "Vale.PPC64LE.InsVector" }, { "open": "Vale.PPC64LE.InsMem" }, { "open": "Vale.PPC64LE.InsBasic" }, { "open": "Vale.PPC64LE.Decls" }, { "open": "Vale.PPC64LE.State" }, { "open": "Vale.PPC64LE.Stack_i" }, { "open": "Vale.PPC64LE.Memory" }, { "open": "Vale.PPC64LE.Machine_s" }, { "open": "Vale.AES.PPC64LE.GCTR" }, { "open": "Vale.AES.GCM_helpers_BE" }, { "open": "Vale.Poly1305.Math" }, { "open": "Vale.AES.GF128" }, { "open": "Vale.AES.GF128_s" }, { "open": "Vale.AES.PPC64LE.AES" }, { "open": "Vale.AES.GCM_BE_s" }, { "open": "Vale.AES.GHash_BE" }, { "open": "Vale.AES.GHash_BE_s" }, { "open": "Vale.AES.GCM_BE" }, { "open": "Vale.AES.GCTR_BE" }, { "open": "Vale.AES.GCTR_BE_s" }, { "open": "Vale.AES.AES_BE_s" }, { "open": "Vale.Arch.HeapImpl" }, { "open": "Vale.Arch.Types" }, { "open": "Vale.Def.Types_s" }, { "open": "Vale.Def.Words.Seq_s" }, { "open": "Vale.Def.Words_s" }, { "open": "FStar.Seq" }, { "open": "Vale.Def.Opaque_s" }, { "open": "Vale.Def.Prop_s" }, { "open": "Vale.AES.PPC64LE" }, { "open": "Vale.AES.PPC64LE" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 10, "max_fuel": 100, "initial_ifuel": 10, "max_ifuel": 100, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": true, "smtencoding_nl_arith_repr": "wrapped", "smtencoding_l_arith_repr": "native", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 2000, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val va_qcode_Gcm_make_length_quad (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Gcm_make_length_quad ()))", "source_definition": "let va_qcode_Gcm_make_length_quad (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Gcm_make_length_quad ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 227 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 3) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 228 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 3) (fun (va_s:va_state) _ -> let\n (va_arg13:Vale.Def.Types_s.nat64) = va_get_reg 6 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 229 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg13 3) (let\n (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg 7 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 230 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg12 3) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 231 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 6 va_s == va_get_reg 6 va_old_s `op_Multiply` 8) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 232 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 7 va_s == va_get_reg 7 va_old_s `op_Multiply` 8) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 233 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Mtvsrdd (va_op_vec_opr_vec 9) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 7)) (va_QEmpty\n (()))))))))))", "source_range": { "start_line": 476, "start_col": 0, "end_line": 495, "end_col": 17 }, "interleaved": false, "definition": "fun va_mods ->\n Vale.PPC64LE.QuickCodes.qblock va_mods\n (fun va_s ->\n let va_old_s = va_s in\n Vale.PPC64LE.QuickCodes.va_QSeq Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 227 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.PPC64LE.InsBasic.va_quick_Sl64Imm (Vale.PPC64LE.Decls.va_op_reg_opr_reg 6)\n (Vale.PPC64LE.Decls.va_op_reg_opr_reg 6)\n 3)\n (Vale.PPC64LE.QuickCodes.va_QBind Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 228 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.PPC64LE.InsBasic.va_quick_Sl64Imm (Vale.PPC64LE.Decls.va_op_reg_opr_reg 7)\n (Vale.PPC64LE.Decls.va_op_reg_opr_reg 7)\n 3)\n (fun va_s _ ->\n let va_arg13 = Vale.PPC64LE.Decls.va_get_reg 6 va_old_s in\n Vale.PPC64LE.QuickCodes.va_qPURE Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 229 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun _ -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg13 3)\n (let va_arg12 = Vale.PPC64LE.Decls.va_get_reg 7 va_old_s in\n Vale.PPC64LE.QuickCodes.va_qPURE Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 230 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun _ -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg12 3)\n (Vale.PPC64LE.QuickCodes.va_qAssert Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 231 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.PPC64LE.Decls.va_get_reg 6 va_s ==\n Vale.PPC64LE.Decls.va_get_reg 6 va_old_s * 8)\n (Vale.PPC64LE.QuickCodes.va_qAssert Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 232 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.PPC64LE.Decls.va_get_reg 7 va_s ==\n Vale.PPC64LE.Decls.va_get_reg 7 va_old_s * 8)\n (Vale.PPC64LE.QuickCodes.va_QSeq Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 233 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.PPC64LE.InsVector.va_quick_Mtvsrdd (Vale.PPC64LE.Decls.va_op_vec_opr_vec\n 9)\n (Vale.PPC64LE.Decls.va_op_reg_opr_reg 6)\n (Vale.PPC64LE.Decls.va_op_reg_opr_reg 7))\n (Vale.PPC64LE.QuickCodes.va_QEmpty ()))))))))\n <:\n Vale.PPC64LE.QuickCode.va_quickCode Prims.unit\n (Vale.AES.PPC64LE.GCMencrypt.va_code_Gcm_make_length_quad ())", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Vale.PPC64LE.QuickCode.va_mods_t", "Vale.PPC64LE.QuickCodes.qblock", "Prims.unit", "Prims.Cons", "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.InsBasic.va_code_Sl64Imm", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.PPC64LE.InsVector.va_code_Mtvsrdd", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Prims.Nil", "Vale.PPC64LE.Machine_s.precode", "Vale.PPC64LE.Decls.ins", "Vale.PPC64LE.Decls.ocmp", "Vale.PPC64LE.Decls.va_state", "Vale.PPC64LE.QuickCodes.va_QSeq", "Vale.PPC64LE.QuickCodes.va_range1", "Vale.PPC64LE.InsBasic.va_quick_Sl64Imm", "Vale.PPC64LE.QuickCodes.va_QBind", "Vale.PPC64LE.QuickCodes.va_qPURE", "Prims.pure_post", "Prims.l_and", "Prims.l_True", "Prims.l_Forall", "Prims.l_imp", "Prims.eq2", "Prims.int", "Vale.Def.Types_s.ishl", "Prims.op_Modulus", "Prims.op_Multiply", "Prims.pow2", "Vale.AES.Types_helpers.lemma_ishl_64", "Vale.PPC64LE.QuickCodes.va_qAssert", "Vale.PPC64LE.Decls.va_get_reg", "Vale.PPC64LE.InsVector.va_quick_Mtvsrdd", "Vale.PPC64LE.QuickCodes.va_QEmpty", "Vale.Def.Words_s.nat64", "Vale.PPC64LE.QuickCodes.quickCodes", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.QuickCode.va_quickCode", "Vale.AES.PPC64LE.GCMencrypt.va_code_Gcm_make_length_quad" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "va_mods: Vale.PPC64LE.QuickCode.va_mods_t\n -> Vale.PPC64LE.QuickCode.va_quickCode Prims.unit\n (Vale.AES.PPC64LE.GCMencrypt.va_code_Gcm_make_length_quad ())", "prompt": "let va_qcode_Gcm_make_length_quad (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Gcm_make_length_quad ())) =\n ", "expected_response": "(qblock va_mods\n (fun (va_s: va_state) ->\n let va_old_s:va_state = va_s in\n va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 227 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 3)\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 228 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 3)\n (fun (va_s: va_state) _ ->\n let va_arg13:Vale.Def.Types_s.nat64 = va_get_reg 6 va_old_s in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 229 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_: unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg13 3)\n (let va_arg12:Vale.Def.Types_s.nat64 = va_get_reg 7 va_old_s in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 230 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_: unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg12 3)\n (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 231 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 6 va_s == (va_get_reg 6 va_old_s) `op_Multiply` 8)\n (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 232 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 7 va_s == (va_get_reg 7 va_old_s) `op_Multiply` 8)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 233 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Mtvsrdd (va_op_vec_opr_vec 9)\n (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 7))\n (va_QEmpty (()))))))))))", "source": { "project_name": "hacl-star", "file_name": "obj/Vale.AES.PPC64LE.GCMencrypt.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Vale.AES.PPC64LE.GCMencrypt.fst", "checked_file": "dataset/Vale.AES.PPC64LE.GCMencrypt.fst.checked", "interface_file": true, "dependencies": [ "dataset/Vale.PPC64LE.State.fsti.checked", "dataset/Vale.PPC64LE.Stack_i.fsti.checked", "dataset/Vale.PPC64LE.QuickCodes.fsti.checked", "dataset/Vale.PPC64LE.QuickCode.fst.checked", "dataset/Vale.PPC64LE.Memory.fsti.checked", "dataset/Vale.PPC64LE.Machine_s.fst.checked", "dataset/Vale.PPC64LE.InsVector.fsti.checked", "dataset/Vale.PPC64LE.InsStack.fsti.checked", "dataset/Vale.PPC64LE.InsMem.fsti.checked", "dataset/Vale.PPC64LE.InsBasic.fsti.checked", "dataset/Vale.PPC64LE.Decls.fsti.checked", "dataset/Vale.Poly1305.Math.fsti.checked", "dataset/Vale.Math.Poly2.Bits_s.fsti.checked", "dataset/Vale.Lib.Meta.fsti.checked", "dataset/Vale.Lib.Basic.fsti.checked", "dataset/Vale.Def.Words_s.fsti.checked", "dataset/Vale.Def.Words.Seq_s.fsti.checked", "dataset/Vale.Def.Words.Four_s.fsti.checked", "dataset/Vale.Def.Types_s.fst.checked", "dataset/Vale.Def.Prop_s.fst.checked", "dataset/Vale.Def.Opaque_s.fsti.checked", "dataset/Vale.Arch.Types.fsti.checked", "dataset/Vale.Arch.HeapImpl.fsti.checked", "dataset/Vale.AES.Types_helpers.fsti.checked", "dataset/Vale.AES.PPC64LE.GHash.fsti.checked", "dataset/Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "dataset/Vale.AES.PPC64LE.GCTR.fsti.checked", "dataset/Vale.AES.PPC64LE.AES.fsti.checked", "dataset/Vale.AES.OptPublic_BE.fsti.checked", "dataset/Vale.AES.GHash_BE_s.fst.checked", "dataset/Vale.AES.GHash_BE.fsti.checked", "dataset/Vale.AES.GF128_s.fsti.checked", "dataset/Vale.AES.GF128.fsti.checked", "dataset/Vale.AES.GCTR_BE_s.fst.checked", "dataset/Vale.AES.GCTR_BE.fsti.checked", "dataset/Vale.AES.GCM_helpers_BE.fsti.checked", "dataset/Vale.AES.GCM_BE_s.fst.checked", "dataset/Vale.AES.GCM_BE.fsti.checked", "dataset/Vale.AES.AES_common_s.fst.checked", "dataset/Vale.AES.AES_BE_s.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Seq.Base.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "let aes_reqs\n (alg:algorithm) (key:seq nat32) (round_keys:seq quad32) (keys_b:buffer128)\n (key_ptr:int) (heap0:vale_heap) (layout:vale_heap_layout) : prop0\n =\n (alg = AES_128 \\/ alg = AES_256) /\\\n is_aes_key_word alg key /\\\n length(round_keys) == nr(alg) + 1 /\\\n round_keys == key_to_round_keys_word alg key /\\\n validSrcAddrs128 heap0 key_ptr keys_b (nr alg + 1) layout Secret /\\\n reverse_bytes_quad32_seq (s128 heap0 keys_b) == round_keys", "let va_code_Load_one_lsb dst =\n (va_Block (va_CCons (va_code_Vspltisw dst 1) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 4) 0)\n (va_CCons (va_code_Vsldoi dst (va_op_vec_opr_vec 4) dst 4) (va_CNil ())))))", "let va_codegen_success_Load_one_lsb dst =\n (va_pbool_and (va_codegen_success_Vspltisw dst 1) (va_pbool_and (va_codegen_success_Vspltisw\n (va_op_vec_opr_vec 4) 0) (va_pbool_and (va_codegen_success_Vsldoi dst (va_op_vec_opr_vec 4) dst\n 4) (va_ttrue ()))))", "val va_code_Load_one_lsb : dst:va_operand_vec_opr -> Tot va_code", "val va_codegen_success_Load_one_lsb : dst:va_operand_vec_opr -> Tot va_pbool", "val va_lemma_Load_one_lsb : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Load_one_lsb dst) va_s0 /\\ va_is_dst_vec_opr dst va_s0\n /\\ va_get_ok va_s0 /\\ dst =!= 4))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 /\\\n va_state_eq va_sM (va_update_vec 4 va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst\n va_sM va_s0)))))", "let va_lemma_Load_one_lsb va_b0 va_s0 dst =\n va_reveal_opaque (`%va_code_Load_one_lsb) (va_code_Load_one_lsb dst);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (va_s2, va_fc2) = va_lemma_Vspltisw (va_hd va_b1) va_s0 dst 1 in\n let va_b2 = va_tl va_b1 in\n let (va_s3, va_fc3) = va_lemma_Vspltisw (va_hd va_b2) va_s2 (va_op_vec_opr_vec 4) 0 in\n let va_b3 = va_tl va_b2 in\n let (va_s4, va_fc4) = va_lemma_Vsldoi (va_hd va_b3) va_s3 dst (va_op_vec_opr_vec 4) dst 4 in\n let va_b4 = va_tl va_b3 in\n let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in\n let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in\n let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in\n (va_sM, va_fM)", "let va_wp_Load_one_lsb (dst:va_operand_vec_opr) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_get_ok va_s0 /\\ dst =!= 4 /\\ (forall\n (va_x_dst:va_value_vec_opr) (va_x_v4:quad32) . let va_sM = va_upd_vec 4 va_x_v4\n (va_upd_operand_vec_opr dst va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 ==> va_k va_sM (())))", "val va_wpProof_Load_one_lsb : dst:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Load_one_lsb dst va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Load_one_lsb dst) ([va_Mod_vec 4;\n va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))", "let va_wpProof_Load_one_lsb dst va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Load_one_lsb (va_code_Load_one_lsb dst) va_s0 dst in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_vec 4 va_sM (va_update_ok va_sM (va_update_operand_vec_opr\n dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_vec 4; va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_quick_Load_one_lsb (dst:va_operand_vec_opr) : (va_quickCode unit (va_code_Load_one_lsb dst))\n =\n (va_QProc (va_code_Load_one_lsb dst) ([va_Mod_vec 4; va_mod_vec_opr dst]) (va_wp_Load_one_lsb\n dst) (va_wpProof_Load_one_lsb dst))", "val va_code_Gcm_blocks128 : alg:algorithm -> Tot va_code", "val va_code_Gcm_make_length_quad : va_dummy:unit -> Tot va_code", "let va_code_Gcm_blocks128 alg =\n (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_CCons\n (va_code_Gctr_blocks128 alg) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec\n 7)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_CCons\n (va_code_Ghash_buffer ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15))\n (va_CNil ()))))))))", "val va_codegen_success_Gcm_make_length_quad : va_dummy:unit -> Tot va_pbool", "val va_lemma_Gcm_make_length_quad : va_b0:va_code -> va_s0:va_state\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_make_length_quad ()) va_s0 /\\ va_get_ok va_s0 /\\\n (8 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg 7 va_s0 < pow2_64)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\ (8\n `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg 7 va_s0 < pow2_64 /\\\n va_get_vec 9 va_sM == Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.Mktwo #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` va_get_reg 7 va_s0 `op_Modulus` pow2_32) (8\n `op_Multiply` va_get_reg 7 va_s0 `op_Division` pow2_32 `op_Modulus` pow2_32))\n (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32 (8 `op_Multiply` va_get_reg 6 va_s0\n `op_Modulus` pow2_32) (8 `op_Multiply` va_get_reg 6 va_s0 `op_Division` pow2_32 `op_Modulus`\n pow2_32)))) /\\ va_state_eq va_sM (va_update_vec 9 va_sM (va_update_reg 7 va_sM (va_update_reg 6\n va_sM (va_update_ok va_sM va_s0))))))", "val va_codegen_success_Gcm_blocks128 : alg:algorithm -> Tot va_pbool", "let va_codegen_success_Gcm_blocks128 alg =\n (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_pbool_and\n (va_codegen_success_Gctr_blocks128 alg) (va_pbool_and (va_codegen_success_Vmr\n (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_pbool_and (va_codegen_success_Vmr\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_pbool_and (va_codegen_success_Ghash_buffer\n ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15))\n (va_ttrue ())))))))", "let va_wp_Gcm_make_length_quad (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (8 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg 7\n va_s0 < pow2_64) /\\ (forall (va_x_r6:nat64) (va_x_r7:nat64) (va_x_v9:quad32) . let va_sM =\n va_upd_vec 9 va_x_v9 (va_upd_reg 7 va_x_r7 (va_upd_reg 6 va_x_r6 va_s0)) in va_get_ok va_sM /\\\n (8 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg 7 va_s0 < pow2_64\n /\\ va_get_vec 9 va_sM == Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.Mktwo #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` va_get_reg 7 va_s0 `op_Modulus` pow2_32) (8\n `op_Multiply` va_get_reg 7 va_s0 `op_Division` pow2_32 `op_Modulus` pow2_32))\n (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32 (8 `op_Multiply` va_get_reg 6 va_s0\n `op_Modulus` pow2_32) (8 `op_Multiply` va_get_reg 6 va_s0 `op_Division` pow2_32 `op_Modulus`\n pow2_32)))) ==> va_k va_sM (())))", "let va_qcode_Gcm_blocks128 (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 167 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 168 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Gctr_blocks128 alg in_b out_b key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 169 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 170 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b out_b h_BE (va_get_vec 1 va_old_s)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 172 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15)) (va_QEmpty (())))))))))", "val va_wpProof_Gcm_make_length_quad : va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_make_length_quad va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_make_length_quad ()) ([va_Mod_vec\n 9; va_Mod_reg 7; va_Mod_reg 6]) va_s0 va_k ((va_sM, va_f0, va_g))))", "val va_lemma_Gcm_blocks128 : va_b0:va_code -> va_s0:va_state -> alg:algorithm -> in_b:buffer128 ->\n out_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks128 alg) va_s0 /\\ va_get_ok va_s0 /\\\n ((Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) in_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b (va_get_reg 6 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ l_and\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out_b))))) /\\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM\n (va_update_vec 20 va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM\n (va_update_vec 16 va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM\n (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM\n (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM\n (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM\n (va_update_vec 0 va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM\n (va_update_reg 28 va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM\n (va_update_reg 9 va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM\n (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))", "let va_quick_Gcm_make_length_quad () : (va_quickCode unit (va_code_Gcm_make_length_quad ())) =\n (va_QProc (va_code_Gcm_make_length_quad ()) ([va_Mod_vec 9; va_Mod_reg 7; va_Mod_reg 6])\n va_wp_Gcm_make_length_quad va_wpProof_Gcm_make_length_quad)", "val va_code_Ghash_extra_bytes : va_dummy:unit -> Tot va_code", "val va_codegen_success_Ghash_extra_bytes : va_dummy:unit -> Tot va_pbool", "val va_lemma_Ghash_extra_bytes : va_b0:va_code -> va_s0:va_state -> hkeys_b:buffer128 ->\n total_bytes:nat -> old_hash:quad32 -> h_BE:quad32 -> completed_quads:(seq quad32)\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Ghash_extra_bytes ()) va_s0 /\\ va_get_ok va_s0 /\\\n (va_get_vec 1 va_s0 == Vale.AES.GHash_BE.ghash_incremental0 h_BE old_hash completed_quads /\\\n Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ FStar.Seq.Base.length #quad32 completed_quads ==\n total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply` FStar.Seq.Base.length #quad32\n completed_quads + 16 /\\ va_get_reg 8 va_s0 == total_bytes `op_Modulus` 16 /\\ total_bytes\n `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16 `op_Multiply`\n Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes - 1) < total_bytes)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let raw_quads = FStar.Seq.Base.append #quad32 completed_quads (FStar.Seq.Base.create #quad32 1\n (va_get_vec 9 va_s0)) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_quads)) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_BE_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_bytes in total_bytes > 0 ==> l_and\n (FStar.Seq.Base.length #Vale.Def.Types_s.quad32 input_quads > 0) (va_get_vec 1 va_sM ==\n Vale.AES.GHash_BE.ghash_incremental h_BE old_hash input_quads)) /\\ va_state_eq va_sM\n (va_update_cr0 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8 va_sM\n (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM\n (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM\n (va_update_reg 10 va_sM (va_update_reg 7 va_sM (va_update_ok va_sM va_s0)))))))))))))))))", "let va_wp_Ghash_extra_bytes (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32) (h_BE:quad32)\n (completed_quads:(seq quad32)) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (va_get_vec 1 va_s0 == Vale.AES.GHash_BE.ghash_incremental0 h_BE old_hash\n completed_quads /\\ Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ FStar.Seq.Base.length #quad32 completed_quads ==\n total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply` FStar.Seq.Base.length #quad32\n completed_quads + 16 /\\ va_get_reg 8 va_s0 == total_bytes `op_Modulus` 16 /\\ total_bytes\n `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16 `op_Multiply`\n Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes - 1) < total_bytes) /\\ (forall\n (va_x_r7:nat64) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_cr0:cr0_t) . let va_sM = va_upd_cr0\n va_x_cr0 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7\n va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3\n (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10\n (va_upd_reg 7 va_x_r7 va_s0))))))))))))) in va_get_ok va_sM /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (FStar.Seq.Base.create #quad32 1 (va_get_vec 9\n va_s0)) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_quads)) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_BE_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_bytes in total_bytes > 0 ==> l_and\n (FStar.Seq.Base.length #Vale.Def.Types_s.quad32 input_quads > 0) (va_get_vec 1 va_sM ==\n Vale.AES.GHash_BE.ghash_incremental h_BE old_hash input_quads)) ==> va_k va_sM (())))", "let va_lemma_Gcm_blocks128 va_b0 va_s0 alg in_b out_b key round_keys keys_b hkeys_b h_BE =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19;\n va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13;\n va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7;\n va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec\n 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26;\n va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem] in\n let va_qc = va_qcode_Gcm_blocks128 va_mods alg in_b out_b key round_keys keys_b hkeys_b h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_blocks128 alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 114 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 156 column 53 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 159 column 147 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 160 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite (va_get_vec 7 va_s0) (va_get_reg 6 va_s0)) /\\\n label va_range1\n \"***** POSTCONDITION NOT MET AT line 163 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1 va_sM == va_get_vec 1 va_s0)\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b == Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) out_b)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 165 column 109 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 6 va_s0 > 0 ==> l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==>\n FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0\n (va_get_reg 6 va_s0)) > 0) (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE\n (va_get_vec 1 va_s0) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_sM) out_b)))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok; va_Mod_mem])\n va_sM va_s0;\n (va_sM, va_fM)", "val va_wpProof_Ghash_extra_bytes : hkeys_b:buffer128 -> total_bytes:nat -> old_hash:quad32 ->\n h_BE:quad32 -> completed_quads:(seq quad32) -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Ghash_extra_bytes hkeys_b total_bytes old_hash h_BE\n completed_quads va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Ghash_extra_bytes ()) ([va_Mod_cr0;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7]) va_s0\n va_k ((va_sM, va_f0, va_g))))", "let va_quick_Ghash_extra_bytes (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (h_BE:quad32) (completed_quads:(seq quad32)) : (va_quickCode unit (va_code_Ghash_extra_bytes ()))\n =\n (va_QProc (va_code_Ghash_extra_bytes ()) ([va_Mod_cr0; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8;\n va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec\n 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7]) (va_wp_Ghash_extra_bytes hkeys_b total_bytes\n old_hash h_BE completed_quads) (va_wpProof_Ghash_extra_bytes hkeys_b total_bytes old_hash h_BE\n completed_quads))", "val va_code_Gcm_blocks_auth : va_dummy:unit -> Tot va_code", "val va_codegen_success_Gcm_blocks_auth : va_dummy:unit -> Tot va_pbool", "val va_lemma_Gcm_blocks_auth : va_b0:va_code -> va_s0:va_state -> auth_b:buffer128 ->\n abytes_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel & (seq quad32))\n (requires (va_require_total va_b0 (va_code_Gcm_blocks_auth ()) va_s0 /\\ va_get_ok va_s0 /\\\n (Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) auth_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem_heaplet 6 va_s0) (va_get_reg 4 va_s0) abytes_b 1 (va_get_mem_layout va_s0) Secret\n /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0)\n hkeys_b 3 (va_get_mem_layout va_s0) Secret /\\ va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg\n 6 va_s0 < pow2_64 /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b ==\n va_get_reg 6 va_s0 /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b\n == 1 /\\ (va_mul_nat (va_get_reg 6 va_s0) (128 `op_Division` 8) <= va_get_reg 9 va_s0 /\\\n va_get_reg 9 va_s0 < va_mul_nat (va_get_reg 6 va_s0) (128 `op_Division` 8) + 128 `op_Division`\n 8) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE)))\n (ensures (fun (va_sM, va_fM, auth_quad_seq) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\\n va_get_ok va_sM /\\ (let auth_abytes_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet\n 6 va_s0) abytes_b)) in let auth_quads = Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) auth_b) in let (raw_auth_quads:(seq\n quad32)) = (if (va_get_reg 9 va_s0 > va_get_reg 6 va_s0 `op_Multiply` 128 `op_Division` 8) then\n auth_abytes_quads else auth_quads) in let (auth_input_bytes:(seq nat8)) = FStar.Seq.Base.slice\n #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 (va_get_reg\n 9 va_s0) in let (padded_auth_bytes:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits\n auth_input_bytes in auth_quad_seq == Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes\n /\\ va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental0 h_BE (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0) auth_quad_seq) /\\ va_state_eq va_sM (va_update_cr0 va_sM\n (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12 va_sM (va_update_vec 11 va_sM\n (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8 va_sM (va_update_vec 7 va_sM\n (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM\n (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM\n (va_update_reg 8 va_sM (va_update_reg 7 va_sM (va_update_reg 6 va_sM (va_update_ok va_sM\n va_s0)))))))))))))))))))))))", "let va_wp_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ ((Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) in_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b (va_get_reg 6 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ l_and\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret) /\\ (forall (va_x_mem:vale_heap)\n (va_x_r3:nat64) (va_x_r7:nat64) (va_x_r6:nat64) (va_x_r8:nat64) (va_x_r9:nat64)\n (va_x_r10:nat64) (va_x_r26:nat64) (va_x_r27:nat64) (va_x_r28:nat64) (va_x_r29:nat64)\n (va_x_r30:nat64) (va_x_r31:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32) (va_x_v17:quad32)\n (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32) (va_x_cr0:cr0_t) (va_x_heap1:vale_heap) .\n let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_cr0 va_x_cr0 (va_upd_vec 20 va_x_v20\n (va_upd_vec 19 va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16\n (va_upd_vec 15 va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12\n (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8\n (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4\n (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0\n (va_upd_reg 31 va_x_r31 (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29 (va_upd_reg 28 va_x_r28\n (va_upd_reg 27 va_x_r27 (va_upd_reg 26 va_x_r26 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9\n (va_upd_reg 8 va_x_r8 (va_upd_reg 6 va_x_r6 (va_upd_reg 7 va_x_r7 (va_upd_reg 3 va_x_r3\n (va_upd_mem va_x_mem va_s0))))))))))))))))))))))))))))))))))) in va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out_b))))) ==> va_k va_sM (())))", "let va_wp_Gcm_blocks_auth (auth_b:buffer128) (abytes_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32)\n (va_s0:va_state) (va_k:(va_state -> (seq quad32) -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg\n 7 va_s0) auth_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 6 va_s0) (va_get_reg 4 va_s0) abytes_b\n 1 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0\n va_s0) (va_get_reg 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\\ va_get_reg 7 va_s0 +\n 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 auth_b == va_get_reg 6 va_s0 /\\ Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\ (va_mul_nat (va_get_reg 6 va_s0) (128\n `op_Division` 8) <= va_get_reg 9 va_s0 /\\ va_get_reg 9 va_s0 < va_mul_nat (va_get_reg 6 va_s0)\n (128 `op_Division` 8) + 128 `op_Division` 8) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE) /\\ (forall (va_x_r6:nat64) (va_x_r7:nat64) (va_x_r8:nat64) (va_x_r10:nat64)\n (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32)\n (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32) (va_x_v8:quad32) (va_x_v9:quad32)\n (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32) (va_x_v13:quad32) (va_x_v14:quad32)\n (va_x_cr0:cr0_t) (auth_quad_seq:(seq quad32)) . let va_sM = va_upd_cr0 va_x_cr0 (va_upd_vec 14\n va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12 (va_upd_vec 11 va_x_v11 (va_upd_vec 10\n va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7 va_x_v7 (va_upd_vec 6\n va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2\n (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_reg 8 va_x_r8\n (va_upd_reg 7 va_x_r7 (va_upd_reg 6 va_x_r6 va_s0))))))))))))))))))) in va_get_ok va_sM /\\ (let\n auth_abytes_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet\n 6 va_s0) abytes_b)) in let auth_quads = Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) auth_b) in let (raw_auth_quads:(seq\n quad32)) = va_if (va_get_reg 9 va_s0 > va_get_reg 6 va_s0 `op_Multiply` 128 `op_Division` 8)\n (fun _ -> auth_abytes_quads) (fun _ -> auth_quads) in let (auth_input_bytes:(seq nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 (va_get_reg\n 9 va_s0) in let (padded_auth_bytes:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits\n auth_input_bytes in auth_quad_seq == Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes\n /\\ va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental0 h_BE (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0) auth_quad_seq) ==> va_k va_sM ((auth_quad_seq))))", "val va_wpProof_Gcm_blocks128 : alg:algorithm -> in_b:buffer128 -> out_b:buffer128 -> key:(seq\n nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks128 alg)\n ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0,\n va_g))))", "let va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_blocks128 (va_code_Gcm_blocks128 alg) va_s0 alg in_b out_b key\n round_keys keys_b hkeys_b h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM (va_update_reg 3\n va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))))))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Gcm_blocks_auth : auth_b:buffer128 -> abytes_b:buffer128 -> hkeys_b:buffer128 ->\n h_BE:quad32 -> va_s0:va_state -> va_k:(va_state -> (seq quad32) -> Type0)\n -> Ghost (va_state & va_fuel & (seq quad32))\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks_auth auth_b abytes_b hkeys_b h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks_auth ()) ([va_Mod_cr0;\n va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9;\n va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec\n 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6]) va_s0\n va_k ((va_sM, va_f0, va_g))))", "let va_quick_Gcm_blocks_auth (auth_b:buffer128) (abytes_b:buffer128) (hkeys_b:buffer128)\n (h_BE:quad32) : (va_quickCode (seq quad32) (va_code_Gcm_blocks_auth ())) =\n (va_QProc (va_code_Gcm_blocks_auth ()) ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 10; va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6]) (va_wp_Gcm_blocks_auth auth_b abytes_b hkeys_b\n h_BE) (va_wpProof_Gcm_blocks_auth auth_b abytes_b hkeys_b h_BE))", "let va_quick_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) : (va_quickCode\n unit (va_code_Gcm_blocks128 alg)) =\n (va_QProc (va_code_Gcm_blocks128 alg) ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20;\n va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14;\n va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8;\n va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec\n 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27;\n va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7;\n va_Mod_reg 3; va_Mod_mem]) (va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE) (va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE))", "val va_code_Gcm_blocks_stdcall : alg:algorithm -> Tot va_code", "val va_codegen_success_Gcm_blocks_stdcall : alg:algorithm -> Tot va_pbool", "let va_req_Gcm_blocks_stdcall (va_b0:va_code) (va_s0:va_state) (alg:algorithm) (auth_b:buffer128)\n (auth_bytes:nat64) (auth_num:nat64) (keys_b:buffer128) (iv_b:buffer128) (iv:supported_iv_BE)\n (hkeys_b:buffer128) (abytes_b:buffer128) (in128_b:buffer128) (out128_b:buffer128)\n (len128_num:nat64) (inout_b:buffer128) (plain_num:nat64) (gcm_struct_b:buffer64)\n (tag_b:buffer128) (key:(seq nat32)) : prop =\n (va_require_total va_b0 (va_code_Gcm_blocks_stdcall alg) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (tag_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 12\n (va_get_mem_heaplet 3 va_s0) in va_get_reg 1 va_s0 == Vale.PPC64LE.Stack_i.init_r1\n (va_get_stack va_s0) /\\ Vale.PPC64LE.Memory.is_initial_heap (va_get_mem_layout va_s0)\n (va_get_mem va_s0) /\\ auth_len == auth_num /\\ auth_num_bytes == auth_bytes /\\ len128 ==\n len128_num /\\ plain_num_bytes == plain_num /\\ Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem\n va_s0) (va_get_reg 3 va_s0) gcm_struct_b 13 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) auth_ptr auth_b auth_len\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0)\n abytes_ptr abytes_b 1 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem va_s0) iv_ptr iv_b 1 (va_get_mem_layout va_s0) Public /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) in128_ptr in128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0)\n out128_ptr out128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0) inout_ptr inout_b 1 (va_get_mem_layout\n va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0)\n tag_ptr tag_b 1 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints64_128\n gcm_struct_b ([keys_b; auth_b; abytes_b; iv_b; in128_b; out128_b; inout_b; hkeys_b; tag_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 tag_b ([keys_b; auth_b; abytes_b; iv_b; in128_b;\n out128_b; inout_b; hkeys_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b; auth_b;\n abytes_b; in128_b; out128_b; inout_b; hkeys_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128\n inout_b ([keys_b; auth_b; abytes_b; in128_b; out128_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 auth_b ([keys_b; abytes_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 abytes_b ([keys_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 out128_b ([keys_b; auth_b; abytes_b; hkeys_b; inout_b])\n /\\ Vale.PPC64LE.Decls.buffer_disjoints128 in128_b ([keys_b; auth_b; abytes_b; hkeys_b;\n inout_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b == out128_b)\n /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply` len128 <\n pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ plain_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem va_s0) + 128 < pow2_64 /\\ (va_mul_nat len128\n (128 `op_Division` 8) <= plain_num_bytes /\\ plain_num_bytes < va_mul_nat len128 (128\n `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division` 8) <=\n auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ (alg = AES_128 \\/ alg = AES_256) /\\ Vale.AES.AES_BE_s.is_aes_key_word alg\n key /\\ Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.buffer128_as_seq\n (va_get_mem va_s0) keys_b) == Vale.AES.AES_BE_s.key_to_round_keys_word alg key /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) keys_ptr keys_b\n (Vale.AES.AES_common_s.nr alg + 1) (va_get_mem_layout va_s0) Secret /\\\n Vale.AES.OptPublic_BE.hkeys_reqs_pub (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg\n key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0)) /\\ (let h_BE =\n Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0\n 0 0) in let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read\n iv_b 0 (va_get_mem va_s0)) in iv_BE == Vale.AES.GCM_BE_s.compute_iv_BE h_BE iv)))", "val va_code_Gcm_auth_bytes : va_dummy:unit -> Tot va_code", "let va_code_Gcm_auth_bytes () =\n (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Ghash_buffer\n ()) (va_CNil ()))))", "val va_codegen_success_Gcm_auth_bytes : va_dummy:unit -> Tot va_pbool", "let va_codegen_success_Gcm_auth_bytes () =\n (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and\n (va_codegen_success_Ghash_buffer ()) (va_ttrue ())))", "let va_qcode_Gcm_auth_bytes (va_mods:va_mods_t) (auth_b:buffer128) (hkeys_b:buffer128)\n (h_BE:quad32) : (va_quickCode (quad32 & quad32) (va_code_Gcm_auth_bytes ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 206 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (fun (va_s:va_state) _ -> let (y_0:quad32) =\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 208 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b auth_b h_BE y_0) (fun (va_s:va_state) _ -> let (y_auth:quad32) =\n va_get_vec 1 va_s in va_QEmpty ((y_0, y_auth))))))", "val va_lemma_Gcm_auth_bytes : va_b0:va_code -> va_s0:va_state -> auth_b:buffer128 ->\n hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel & quad32 & quad32)\n (requires (va_require_total va_b0 (va_code_Gcm_auth_bytes ()) va_s0 /\\ va_get_ok va_s0 /\\\n (Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) (va_get_reg 7 va_s0) auth_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == va_get_reg 6 va_s0 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64)))\n (ensures (fun (va_sM, va_fM, y_0, y_auth) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok\n va_sM /\\ (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 /\\ (let h_BE =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) /\\ va_get_vec 1 va_sM == y_auth)) /\\ va_state_eq va_sM (va_update_cr0 va_sM\n (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12 va_sM (va_update_vec 11 va_sM\n (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8 va_sM (va_update_vec 7 va_sM\n (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM\n (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM\n (va_update_reg 6 va_sM (va_update_reg 7 va_sM (va_update_ok va_sM va_s0))))))))))))))))))))))", "let va_lemma_Gcm_auth_bytes va_b0 va_s0 auth_b hkeys_b h_BE =\n let (va_mods:va_mods_t) = [va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec\n 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5;\n va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg\n 6; va_Mod_reg 7; va_Mod_ok] in\n let va_qc = va_qcode_Gcm_auth_bytes va_mods auth_b hkeys_b h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_auth_bytes ()) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let (y_0, y_auth) = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 175 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 200 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 201 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (let h_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 202 column 95 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b))) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 203 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_vec 1 va_sM == y_auth)))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6;\n va_Mod_reg 7; va_Mod_ok]) va_sM va_s0;\n let (y_0, y_auth) = va_g in\n (va_sM, va_fM, y_0, y_auth)", "let va_ens_Gcm_blocks_stdcall (va_b0:va_code) (va_s0:va_state) (alg:algorithm) (auth_b:buffer128)\n (auth_bytes:nat64) (auth_num:nat64) (keys_b:buffer128) (iv_b:buffer128) (iv:supported_iv_BE)\n (hkeys_b:buffer128) (abytes_b:buffer128) (in128_b:buffer128) (out128_b:buffer128)\n (len128_num:nat64) (inout_b:buffer128) (plain_num:nat64) (gcm_struct_b:buffer64)\n (tag_b:buffer128) (key:(seq nat32)) (va_sM:va_state) (va_fM:va_fuel) : prop =\n (va_req_Gcm_blocks_stdcall va_b0 va_s0 alg auth_b auth_bytes auth_num keys_b iv_b iv hkeys_b\n abytes_b in128_b out128_b len128_num inout_b plain_num gcm_struct_b tag_b key /\\\n va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\ (let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (tag_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 12\n (va_get_mem_heaplet 3 va_s0) in Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_union\n (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 tag_b)\n (Vale.PPC64LE.Decls.loc_union (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128\n iv_b) (Vale.PPC64LE.Decls.loc_union (Vale.PPC64LE.Decls.loc_buffer\n #Vale.PPC64LE.Memory.vuint128 out128_b) (Vale.PPC64LE.Decls.loc_buffer\n #Vale.PPC64LE.Memory.vuint128 inout_b)))) (va_get_mem va_s0) (va_get_mem va_sM) /\\\n plain_num_bytes < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ (let iv_BE =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem\n va_s0)) in let auth_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0)\n abytes_b)) in let auth_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 auth_raw_quads)) 0 auth_num_bytes in let plain_raw_quads =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) inout_b)) in let plain_bytes = FStar.Seq.Base.slice\n #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 plain_raw_quads)) 0\n plain_num_bytes in let cipher_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem\n va_sM) inout_b)) in let cipher_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 cipher_raw_quads)) 0 plain_num_bytes in l_and (l_and (l_and (l_and\n (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 auth_bytes < pow2_32) (FStar.Seq.Base.length\n #Vale.Def.Words_s.nat8 plain_bytes < pow2_32)) (Vale.AES.AES_common_s.is_aes_key alg\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key))) (cipher_bytes ==\n __proj__Mktuple2__item___1 #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat8) (Vale.AES.GCM_BE_s.gcm_encrypt_BE alg\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv plain_bytes auth_bytes)))\n (Vale.Arch.Types.be_quad32_to_bytes (Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read tag_b 0 (va_get_mem va_sM))) == __proj__Mktuple2__item___2\n #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8)\n (Vale.AES.GCM_BE_s.gcm_encrypt_BE alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv\n plain_bytes auth_bytes)) /\\ va_get_reg 1 va_sM == va_get_reg 1 va_s0 /\\ l_and (l_and (l_and\n (l_and (l_and (l_and (l_and (l_and (va_get_reg 25 va_sM == va_get_reg 25 va_s0) (va_get_reg 26\n va_sM == va_get_reg 26 va_s0)) (va_get_reg 27 va_sM == va_get_reg 27 va_s0)) (va_get_reg 28\n va_sM == va_get_reg 28 va_s0)) (va_get_reg 29 va_sM == va_get_reg 29 va_s0)) (va_get_reg 30\n va_sM == va_get_reg 30 va_s0)) (va_get_reg 31 va_sM == va_get_reg 31 va_s0)) (va_get_vec 20\n va_sM == va_get_vec 20 va_s0)) (va_get_vec 21 va_sM == va_get_vec 21 va_s0))) /\\ va_state_eq\n va_sM (va_update_stackTaint va_sM (va_update_stack va_sM (va_update_mem_layout va_sM\n (va_update_mem_heaplet 5 va_sM (va_update_mem_heaplet 4 va_sM (va_update_mem_heaplet 2 va_sM\n (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 21 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 25 va_sM (va_update_reg 10\n va_sM (va_update_reg 9 va_sM (va_update_reg 8 va_sM (va_update_reg 7 va_sM (va_update_reg 6\n va_sM (va_update_reg 5 va_sM (va_update_reg 4 va_sM (va_update_reg 3 va_sM (va_update_reg 1\n va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))))))))))))", "let va_wp_Gcm_auth_bytes (auth_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) (va_s0:va_state)\n (va_k:(va_state -> (quad32 & quad32) -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) (va_get_reg 7 va_s0) auth_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == va_get_reg 6 va_s0 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64) /\\ (forall (va_x_r7:nat64)\n (va_x_r6:nat64) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_cr0:cr0_t) (y_0:quad32) (y_auth:quad32) . let va_sM =\n va_upd_cr0 va_x_cr0 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12\n (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8\n (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4\n (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0\n (va_upd_reg 10 va_x_r10 (va_upd_reg 6 va_x_r6 (va_upd_reg 7 va_x_r7 va_s0)))))))))))))))))) in\n va_get_ok va_sM /\\ (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 /\\ (let h_BE\n = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) /\\ va_get_vec 1 va_sM == y_auth)) ==> va_k va_sM ((y_0, y_auth))))", "val va_wpProof_Gcm_auth_bytes : auth_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32 ->\n va_s0:va_state -> va_k:(va_state -> (quad32 & quad32) -> Type0)\n -> Ghost (va_state & va_fuel & (quad32 & quad32))\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_auth_bytes auth_b hkeys_b h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_auth_bytes ()) ([va_Mod_cr0;\n va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9;\n va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec\n 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6; va_Mod_reg 7]) va_s0 va_k ((va_sM,\n va_f0, va_g))))", "let va_wpProof_Gcm_auth_bytes auth_b hkeys_b h_BE va_s0 va_k =\n let (va_sM, va_f0, y_0, y_auth) = va_lemma_Gcm_auth_bytes (va_code_Gcm_auth_bytes ()) va_s0\n auth_b hkeys_b h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_cr0 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM\n (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM\n (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM\n (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM\n (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM\n (va_update_ok va_sM va_s0)))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6;\n va_Mod_reg 7]) va_sM va_s0;\n let va_g = (y_0, y_auth) in\n (va_sM, va_f0, va_g)", "let va_quick_Gcm_auth_bytes (auth_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) : (va_quickCode\n (quad32 & quad32) (va_code_Gcm_auth_bytes ())) =\n (va_QProc (va_code_Gcm_auth_bytes ()) ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 10; va_Mod_reg 6; va_Mod_reg 7]) (va_wp_Gcm_auth_bytes auth_b hkeys_b h_BE)\n (va_wpProof_Gcm_auth_bytes auth_b hkeys_b h_BE))", "let va_code_Gcm_make_length_quad () =\n (va_Block (va_CCons (va_code_Sl64Imm (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 3) (va_CCons\n (va_code_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 3) (va_CCons (va_code_Mtvsrdd\n (va_op_vec_opr_vec 9) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 7)) (va_CNil ())))))", "let va_codegen_success_Gcm_make_length_quad () =\n (va_pbool_and (va_codegen_success_Sl64Imm (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 3)\n (va_pbool_and (va_codegen_success_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 3)\n (va_pbool_and (va_codegen_success_Mtvsrdd (va_op_vec_opr_vec 9) (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 7)) (va_ttrue ()))))" ], "closest": [ "val va_qcode_Gcm_make_length_quad (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Gcm_make_length_quad ()))\nlet va_qcode_Gcm_make_length_quad (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Gcm_make_length_quad ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 424 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_ZeroXmm (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 425 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 426 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 427 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 428 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 429 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 430 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 0) (va_QEmpty (()))))))))))", "val va_quick_Gcm_make_length_quad: Prims.unit\n -> (va_quickCode unit (va_code_Gcm_make_length_quad ()))\nlet va_quick_Gcm_make_length_quad () : (va_quickCode unit (va_code_Gcm_make_length_quad ())) =\n (va_QProc (va_code_Gcm_make_length_quad ()) ([va_Mod_flags; va_Mod_reg64 rRax; va_Mod_xmm 0])\n va_wp_Gcm_make_length_quad va_wpProof_Gcm_make_length_quad)", "val va_quick_Gcm_make_length_quad: Prims.unit\n -> (va_quickCode unit (va_code_Gcm_make_length_quad ()))\nlet va_quick_Gcm_make_length_quad () : (va_quickCode unit (va_code_Gcm_make_length_quad ())) =\n (va_QProc (va_code_Gcm_make_length_quad ()) ([va_Mod_vec 9; va_Mod_reg 7; va_Mod_reg 6])\n va_wp_Gcm_make_length_quad va_wpProof_Gcm_make_length_quad)", "val va_qcode_Compute_pad_to_128_bits (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Compute_pad_to_128_bits ()))\nlet va_qcode_Compute_pad_to_128_bits (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Compute_pad_to_128_bits ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 446 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 447 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR10) (va_const_cmp 8)) (qblock va_mods (fun\n (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 449 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PinsrqImm (va_op_xmm_xmm 0) 0 1 (va_op_reg_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 452 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR10)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (fun (va_s:va_state) _\n -> let (va_arg51:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 454 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg51) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 455 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rRcx va_s == 8 `op_Multiply` va_get_reg64 rR10 va_s) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 456 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 457 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rR11) (va_op_shift_amt64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 458 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 459 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pextrq (va_op_dst_opr64_reg64 rRcx) (va_op_xmm_xmm 0) 0) (fun (va_s:va_state) _ ->\n let (old_lower128:nat64) = va_get_reg64 rRcx va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 461 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR11)) (fun (va_s:va_state) _\n -> let (va_arg50:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let\n (va_arg49:Vale.Def.Types_s.nat64) = old_lower128 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 462 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg49 va_arg50) (va_qAssert\n va_range1\n \"***** PRECONDITION NOT MET AT line 463 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rRcx va_s == old_lower128 `op_Modulus` Prims.pow2 (va_get_reg64 rR10 va_s\n `op_Multiply` 8)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 466 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRcx) 0) (fun (va_s:va_state) _ ->\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 468 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_lo64_properties ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 469 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_hi64_properties ()) (let (va_arg48:Prims.int) =\n va_get_reg64 rR10 va_s in let (va_arg47:Vale.Def.Types_s.quad32) = va_get_xmm 0 va_old_s in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 470 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_helpers.pad_to_128_bits_lower va_arg47 va_arg48) (va_QEmpty\n (()))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 472 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rR10 va_s - 8 >= 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 475 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 476 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (fun (va_s:va_state) _\n -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 477 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rR10 va_s - 8 >= 0 /\\ va_get_reg64 rR10 va_s - 8 <= 18446744073709551615) (fun _\n -> let (va_arg56:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s - 8 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 477 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg56) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 478 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rRcx va_s == 8 `op_Multiply` (va_get_reg64 rR10 va_s - 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 479 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 480 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rR11) (va_op_shift_amt64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 481 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 482 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pextrq (va_op_dst_opr64_reg64 rRcx) (va_op_xmm_xmm 0) 1) (fun (va_s:va_state) _ ->\n let (old_upper128:nat64) = va_get_reg64 rRcx va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 484 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR11)) (fun (va_s:va_state) _\n -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 485 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rR10 va_s - 8 >= 0 /\\ va_get_reg64 rR10 va_s - 8 <= 18446744073709551615) (fun _\n -> let (va_arg55:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s - 8 in let\n (va_arg54:Vale.Def.Types_s.nat64) = old_upper128 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 485 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg54 va_arg55) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 489 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRcx) 1) (fun (va_s:va_state) _ ->\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 490 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_lo64_properties ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 491 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_hi64_properties ()) (let (va_arg53:Prims.int) =\n va_get_reg64 rR10 va_s in let (va_arg52:Vale.Def.Types_s.quad32) = va_get_xmm 0 va_old_s in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 492 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_helpers.pad_to_128_bits_upper va_arg52 va_arg53) (va_QEmpty\n (())))))))))))))))))))))) (fun (va_s:va_state) va_g -> va_QEmpty (())))))", "val va_qcode_Fast_sqr_part2 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Fast_sqr_part2 ()))\nlet va_qcode_Fast_sqr_part2 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Fast_sqr_part2 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 190 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.xor_lemmas ()) (let (va_arg25:nat64) = va_get_reg64 rRcx va_s\n in let (va_arg24:nat64) = va_get_reg64 rRax va_s in let (va_arg23:nat64) = va_get_reg64 rR13\n va_s in let (va_arg22:nat64) = va_get_reg64 rRbx va_s in let (va_arg21:nat64) = va_get_reg64\n rR11 va_s in let (va_arg20:nat64) = va_get_reg64 rR10 va_s in let (va_arg19:nat64) =\n va_get_reg64 rR9 va_s in let (va_arg18:nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 191 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> lemma_fast_sqr_part2 va_arg18 va_arg19 va_arg20 va_arg21 va_arg22 va_arg23\n va_arg24 va_arg25) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 193 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Xor64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rR15)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 194 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n ((fun (f:flags_t) -> true) (va_get_flags va_s)) (fun _ -> (fun (f:flags_t) -> flag_cf f = 1 ==\n cf f /\\ flag_of f = 1 == overflow f) (va_get_flags va_s)) (fun (_:unit) -> reveal_flags\n (va_get_flags va_s)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 196 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adox_64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 196 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 197 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adox_64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 197 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 198 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adox_64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 198 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 199 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adox_64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 199 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adox_64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 201 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 201 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR14)) (va_QEmpty\n (())))))))))))))))))))", "val va_qcode_Compute_ghash_incremental_register (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Compute_ghash_incremental_register ()))\nlet va_qcode_Compute_ghash_incremental_register (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Compute_ghash_incremental_register ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 124 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 125 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 11)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 127 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_ReduceMul128_LE (Vale.AES.GF128_s.gf128_of_quad32\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 1 va_s))) (Vale.AES.GF128_s.gf128_of_quad32\n (va_get_xmm 11 va_s))) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 128 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.ghash_incremental_reveal ()) (va_QEmpty (())))))))", "val va_code_Gcm_make_length_quad : va_dummy:unit -> Tot va_code\nlet va_code_Gcm_make_length_quad () =\n (va_Block (va_CCons (va_code_ZeroXmm (va_op_xmm_xmm 0)) (va_CCons (va_code_Mov64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_IMul64\n (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_CCons (va_code_Pinsrq (va_op_xmm_xmm 0)\n (va_op_opr64_reg64 rRax) 1) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)\n (va_op_opr64_reg64 rR13)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRax)\n (va_const_opr64 8)) (va_CCons (va_code_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 0)\n (va_CNil ())))))))))", "val va_qcode_Gf128MulRev128 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Gf128MulRev128 ()))\nlet va_qcode_Gf128MulRev128 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Gf128MulRev128 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 1 va_s) in let\n (b:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 2 va_s) in va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 367 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_ReduceMulRev128 (Vale.Math.Poly2_s.reverse a 127) (Vale.Math.Poly2_s.reverse b 127))\n (fun (va_s:va_state) _ -> let (va_arg6:Vale.Math.Poly2_s.poly) = Vale.AES.GF128.gf128_mul_rev a\n b in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 368 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32 va_arg6) (va_QEmpty (())))))", "val va_qcode_Gf128MulRev128 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Gf128MulRev128 ()))\nlet va_qcode_Gf128MulRev128 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Gf128MulRev128 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_s) in let\n (b:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 2 va_s) in va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 372 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_ReduceMulRev128 (Vale.Math.Poly2_s.reverse a 127) (Vale.Math.Poly2_s.reverse b 127))\n (fun (va_s:va_state) _ -> let (va_arg6:Vale.Math.Poly2_s.poly) = Vale.AES.GF128.gf128_mul_rev a\n b in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 373 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32 va_arg6) (va_QEmpty (())))))", "val va_qcode_Gcm_auth_bytes (va_mods: va_mods_t) (auth_b hkeys_b: buffer128) (h_LE: quad32)\n : (va_quickCode (quad32 & quad32) (va_code_Gcm_auth_bytes ()))\nlet va_qcode_Gcm_auth_bytes (va_mods:va_mods_t) (auth_b:buffer128) (hkeys_b:buffer128)\n (h_LE:quad32) : (va_quickCode (quad32 & quad32) (va_code_Gcm_auth_bytes ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 399 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_ZeroXmm (va_op_xmm_xmm 8)) (fun (va_s:va_state) _ -> let (y_0:quad32) =\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 401 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_reverse_bytes_quad32_zero ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 402 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b auth_b h_LE y_0) (fun (va_s:va_state) _ -> let (y_auth:quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s) in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 404 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.le_bytes_to_seq_quad32_empty ()) (va_QEmpty ((y_0,\n y_auth))))))))", "val va_qcode_mod_6 (va_mods: va_mods_t) : (va_quickCode unit (va_code_mod_6 ()))\nlet va_qcode_mod_6 (va_mods:va_mods_t) : (va_quickCode unit (va_code_mod_6 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 565 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImmShl64 (va_op_reg_opr_reg 26) 21845) (fun (va_s:va_state) _ -> va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 566 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 21845 16) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 567 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddImm (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26) 21845) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 568 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 26) 32) (fun (va_s:va_state) _ ->\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 569 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 1431655765 32) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 570 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Add (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 10)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 571 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) (-1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 572 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Sub (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 26)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 573 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddImm (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26) 1) (fun (va_s:va_state) _ ->\n va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 574 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_get_reg 26 va_s == 12297829382473034411) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 575 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_MulHigh64U (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 26)) (fun\n (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = va_get_reg 10 va_s in va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 576 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishr_64 va_arg23 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 577 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Sr64Imm (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 10) 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 578 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddWrap (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 10))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 579 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddWrap (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 10))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 580 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddWrap (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 581 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_SubWrap (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 26)) (fun\n (va_s:va_state) _ -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 582 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n ((fun (p:prop) -> normalize p) (va_get_reg 6 va_s `op_Modulus` 6 == va_get_reg 6 va_s - 6\n `op_Multiply` (va_get_reg 6 va_s `op_Multiply` 12297829382473034411 `op_Division` pow2_64\n `op_Division` 4))) (fun _ -> (fun (p:prop) -> p) (va_get_reg 6 va_s `op_Modulus` 6 ==\n va_get_reg 6 va_s - 6 `op_Multiply` (va_get_reg 6 va_s `op_Multiply` 12297829382473034411\n `op_Division` pow2_64 `op_Division` 4))) (fun (_:unit) -> assert_normalize (va_get_reg 6 va_s\n `op_Modulus` 6 == va_get_reg 6 va_s - 6 `op_Multiply` (va_get_reg 6 va_s `op_Multiply`\n 12297829382473034411 `op_Division` pow2_64 `op_Division` 4))) (va_QEmpty\n (())))))))))))))))))))))", "val va_qcode_Handle_ctr32_2 (va_mods: va_mods_t) (ctr_BE: quad32)\n : (va_quickCode unit (va_code_Handle_ctr32_2 ()))\nlet va_qcode_Handle_ctr32_2 (va_mods:va_mods_t) (ctr_BE:quad32) : (va_quickCode unit\n (va_code_Handle_ctr32_2 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 253 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 6) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 258 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_Load_one_lsb (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 260 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 10) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 262 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_Load_two_lsb (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 263 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 11) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 265 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 12) (va_op_xmm_xmm 10) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 266 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 267 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 13) (va_op_xmm_xmm 11) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 268 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 269 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_opr128_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 270 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 14) (va_op_xmm_xmm 12) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 271 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 12) (va_op_xmm_xmm 12) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 272 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_opr128_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 273 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 13) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 274 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 13) (va_op_xmm_xmm 13) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 12) (va_op_xmm_xmm 12) (va_op_opr128_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 276 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 14) (va_op_xmm_xmm 14) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 277 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 13) (va_op_xmm_xmm 13) (va_op_opr128_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 279 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 14) (va_op_xmm_xmm 14) (va_op_opr128_xmm 4)) (va_QEmpty\n (())))))))))))))))))))))))", "val va_qcode_Check_avx512_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_avx512_support ()))\nlet va_qcode_Check_avx512_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_avx512_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 273 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 276 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 277 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Avx512 ()) (fun (va_s:va_state) _ -> let (va_arg49:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg49 16) (let\n (va_arg48:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 279 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg48 17) (let\n (va_arg47:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 280 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg47 30) (let\n (va_arg46:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 281 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg46 31) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 284 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 285 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 286 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 288 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 65536)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 131072)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 290 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64 1073741824)) (fun (va_s:va_state)\n _ -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 292 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (65536 == Prims.pow2 16)) (fun _ -> (fun (p:prop) -> p) (65536\n == Prims.pow2 16)) (fun (_:unit) -> assert_normalize (65536 == Prims.pow2 16)) (va_QLemma\n va_range1\n \"***** PRECONDITION NOT MET AT line 293 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (131072 == Prims.pow2 17)) (fun _ -> (fun (p:prop) -> p) (131072\n == Prims.pow2 17)) (fun (_:unit) -> assert_normalize (131072 == Prims.pow2 17)) (va_QLemma\n va_range1\n \"***** PRECONDITION NOT MET AT line 294 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (1073741824 == Prims.pow2 30)) (fun _ -> (fun (p:prop) -> p)\n (1073741824 == Prims.pow2 30)) (fun (_:unit) -> assert_normalize (1073741824 == Prims.pow2 30))\n (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 295 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (2147483648 == Prims.pow2 31)) (fun _ -> (fun (p:prop) -> p)\n (2147483648 == Prims.pow2 31)) (fun (_:unit) -> assert_normalize (2147483648 == Prims.pow2 31))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 297 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 1)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 298 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 16 17) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 299 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 1) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 14)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 302 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 16 30) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 303 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 14) (let\n (va_arg45:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let\n (va_arg44:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 305 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg44 va_arg45 16) (let\n (va_arg43:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 306 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg43 16) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 307 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 310 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 2147483648)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 311 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRbx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 312 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rR11) (va_const_shift_amt64 15)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 313 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 16 31) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 314 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 15) (let\n (va_arg42:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let\n (va_arg41:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 316 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg41 va_arg42 16) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 317 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (fun (va_s:va_state) _\n -> let (va_arg40:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_s in let\n (va_arg39:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 318 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg39 va_arg40 16) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 319 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 321 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (()))))))))))))))))))))))))))))))))))))))))", "val va_qcode_Handle_ctr32 (va_mods: va_mods_t) (ctr_BE: quad32)\n : (va_quickCode unit (va_code_Handle_ctr32 ()))\nlet va_qcode_Handle_ctr32 (va_mods:va_mods_t) (ctr_BE:quad32) : (va_quickCode unit\n (va_code_Handle_ctr32 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 256 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_InitPshufbMask (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 257 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 6) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 261 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_Load_one_lsb (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 262 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 10) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 263 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_Load_two_lsb (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 264 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 11) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 265 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 12) (va_op_xmm_xmm 10) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 266 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 267 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 13) (va_op_xmm_xmm 11) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 268 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 269 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_opr128_xmm 15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 270 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 14) (va_op_xmm_xmm 12) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 271 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 12) (va_op_xmm_xmm 12) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 272 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_opr128_xmm 15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 273 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 13) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 274 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 13) (va_op_xmm_xmm 13) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 14) (va_op_xmm_xmm 14) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 276 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_QEmpty\n (())))))))))))))))))))))", "val va_qcode_Poly1305_reduce_last (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Poly1305_reduce_last ()))\nlet va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Poly1305_reduce_last ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =\n Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)\n (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->\n va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8\n va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let\n (va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let\n (va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let\n (va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5\n in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let\n (va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let\n (va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29\n va_arg30 va_arg31 va_arg32) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (())))))))))))))))))))))))", "val va_qcode_Mod_cr0 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ()))\nlet va_qcode_Mod_cr0 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QEmpty (())))", "val va_qcode_Mod_cr0 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ()))\nlet va_qcode_Mod_cr0 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QEmpty (())))", "val va_qcode_Mod_cr0 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ()))\nlet va_qcode_Mod_cr0 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QEmpty (())))", "val va_qcode_Check_avx2_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_avx2_support ()))\nlet va_qcode_Check_avx2_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_avx2_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 156 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 158 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 159 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 160 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Avx2 ()) (fun (va_s:va_state) _ -> let (va_arg11:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 161 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg11 5) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 162 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 32)) (fun (va_s:va_state) _ ->\n va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 163 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (32 == Prims.pow2 5)) (fun _ -> (fun (p:prop) -> p) (32 ==\n Prims.pow2 5)) (fun (_:unit) -> assert_normalize (32 == Prims.pow2 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 164 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty (()))))))))))))", "val va_qcode_Check_avx_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_avx_support ()))\nlet va_qcode_Check_avx_support (va_mods:va_mods_t) : (va_quickCode unit (va_code_Check_avx_support\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 133 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 134 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 135 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Avx ()) (fun (va_s:va_state) _ -> let (va_arg14:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 136 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg14 25) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 137 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 138 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 268435456)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 139 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (268435456 == Prims.pow2 28)) (fun _ -> (fun (p:prop) -> p)\n (268435456 == Prims.pow2 28)) (fun (_:unit) -> assert_normalize (268435456 == Prims.pow2 28))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 141 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 27)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 142 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 1 28) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 143 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 27) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 145 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (())))))))))))))))", "val va_qcode_Gcm_blocks128\n (va_mods: va_mods_t)\n (alg: algorithm)\n (in_b out_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n (h_LE: quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg))\nlet va_qcode_Gcm_blocks128 (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_LE:quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 274 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 276 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 277 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b in_b h_LE (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8\n va_old_s))) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 279 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 280 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Gctr_blocks128 alg in_b out_b key round_keys keys_b) (va_QEmpty (()))))))))))", "val va_qcode_Gcm_blocks128\n (va_mods: va_mods_t)\n (alg: algorithm)\n (in_b out_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n (h_LE: quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg))\nlet va_qcode_Gcm_blocks128 (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_LE:quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 323 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Gctr_blocks128 alg in_b out_b key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 329 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b out_b h_LE (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8\n va_old_s))) (va_QEmpty (())))))", "val va_qcode_load_one_msb (va_mods: va_mods_t) : (va_quickCode unit (va_code_load_one_msb ()))\nlet va_qcode_load_one_msb (va_mods:va_mods_t) : (va_quickCode unit (va_code_load_one_msb ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 583 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_ZeroXmm (va_op_xmm_xmm 2)) (fun (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 584 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (Vale.Arch.Types.two_to_nat32 (Vale.Def.Words_s.Mktwo #Vale.Def.Words_s.nat32 0 16777216) ==\n 72057594037927936) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 585 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_PinsrqImm (va_op_xmm_xmm 2) 72057594037927936 1 (va_op_reg_opr64_reg64 rR11)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 586 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (fun (_:unit) -> Vale.Def.Types_s.insert_nat64_reveal ()) (va_QEmpty (())))))))", "val va_qcode_Gcm_blocks_auth\n (va_mods: va_mods_t)\n (auth_b abytes_b hkeys_b: buffer128)\n (h_LE: quad32)\n : (va_quickCode ((seq quad32)) (va_code_Gcm_blocks_auth ()))\nlet va_qcode_Gcm_blocks_auth (va_mods:va_mods_t) (auth_b:buffer128) (abytes_b:buffer128)\n (hkeys_b:buffer128) (h_LE:quad32) : (va_quickCode ((seq quad32)) (va_code_Gcm_blocks_auth ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 704 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 705 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 16)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 708 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_InitPshufbMask (va_op_xmm_xmm 9) (va_op_reg_opr64_reg64 rR10)) (fun (va_s:va_state) _\n -> let (h_LE:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.X64.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 0 va_old_s)) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 717 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Gcm_auth_bytes auth_b hkeys_b h_LE) (fun (va_s:va_state) va_g -> let ((y_0:quad32),\n (y_auth:quad32)) = va_g in let (y_auth_bytes:quad32) = y_auth in let\n (auth_quad_seq_len:(va_int_range 0 18446744073709551615)) = va_if (va_get_reg64 rRsi va_old_s\n <= FStar.Seq.Base.length #Vale.Def.Types_s.nat8 (Vale.Def.Types_s.le_seq_quad32_to_bytes\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) auth_b))) (fun _ -> va_get_reg64 rRsi\n va_old_s) (fun _ -> 0) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 721 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.Def.Types_s.nat8 (Vale.Def.Types_s.le_seq_quad32_to_bytes (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s) auth_b)) 0 auth_quad_seq_len) (fun _ -> let (auth_quad_seq:(seq\n quad32)) = Vale.Def.Types_s.le_bytes_to_seq_quad32 (Vale.AES.GCTR_s.pad_to_128_bits\n (FStar.Seq.Base.slice #Vale.Def.Types_s.nat8 (Vale.Def.Types_s.le_seq_quad32_to_bytes\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) auth_b)) 0 auth_quad_seq_len)) in let\n (va_arg54:Vale.Def.Types_s.nat64) = va_get_reg64 rRsi va_s in let (va_arg53:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) auth_b in let\n (va_arg52:Vale.Def.Types_s.quad32) = y_auth in let (va_arg51:Vale.Def.Types_s.quad32) = y_0 in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 724 column 42 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.ghash_incremental_bytes_pure_no_extra va_arg51 va_arg52 h_LE\n va_arg53 va_arg54) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 727 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.le_bytes_to_seq_quad32_empty ()) (let\n (va_arg50:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s) auth_b in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 728 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_le_seq_quad32_to_bytes_length va_arg50) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 731 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRsi)) (fun (va_s:va_state) _\n -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 733 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_qIf va_mods (Cmp_gt (va_op_cmp_reg64 rRsi) (va_op_cmp_reg64 rRcx)) (qblock va_mods (fun\n (va_s:va_state) -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 735 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 7) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRbx) 0 Secret abytes_b 0) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 736 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 737 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRsi)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 738 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64 15)) (fun (va_s:va_state) _ ->\n va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 739 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rR10 va_s == va_get_reg64 rRsi va_old_s `op_Modulus` 16) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 743 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Ghash_extra_bytes hkeys_b (va_get_reg64 rRsi va_s) y_0 h_LE (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s) auth_b)) (fun (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 744 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (FStar.Seq.Base.equal #Vale.X64.Decls.quad32 (FStar.Seq.Base.create #Vale.X64.Decls.quad32 1\n (Vale.X64.Decls.buffer128_read abytes_b 0 (va_get_mem_heaplet 7 va_s))) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 7 va_s) abytes_b)) (let y_auth_bytes =\n Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s) in let\n (raw_auth_quads:(FStar.Seq.Base.seq Vale.X64.Decls.quad32)) = FStar.Seq.Base.append\n #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) auth_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 7 va_old_s) abytes_b) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 748 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.Def.Types_s.nat8 (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_auth_quads) 0 (va_get_reg64\n rRsi va_old_s)) (fun _ -> let (auth_input_bytes:(FStar.Seq.Base.seq Vale.Def.Types_s.nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Types_s.nat8 (Vale.Def.Types_s.le_seq_quad32_to_bytes\n raw_auth_quads) 0 (va_get_reg64 rRsi va_old_s) in let (padded_auth_bytes:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat8)) = Vale.AES.GCTR_s.pad_to_128_bits auth_input_bytes in let\n (auth_quad_seq:(seq quad32)) = Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_auth_bytes in\n va_QEmpty ((auth_quad_seq, y_auth_bytes)))))))))))) (qblock va_mods (fun (va_s:va_state) ->\n va_QEmpty ((auth_quad_seq, y_auth_bytes))))) (fun (va_s:va_state) va_g -> let\n ((auth_quad_seq:(seq quad32)), (y_auth_bytes:quad32)) = va_g in va_QEmpty\n ((auth_quad_seq))))))))))))))", "val va_lemma_Gcm_make_length_quad : va_b0:va_code -> va_s0:va_state\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_make_length_quad ()) va_s0 /\\ va_get_ok va_s0 /\\\n (sse_enabled /\\ 8 `op_Multiply` va_get_reg64 rR13 va_s0 < pow2_64 /\\ 8 `op_Multiply`\n va_get_reg64 rR11 va_s0 < pow2_64)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\ (8\n `op_Multiply` va_get_reg64 rR13 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg64 rR11 va_s0 <\n pow2_64 /\\ va_get_xmm 0 va_sM == Vale.Def.Types_s.insert_nat64 (Vale.Def.Types_s.insert_nat64\n (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) (8 `op_Multiply` va_get_reg64 rR11\n va_s0) 1) (8 `op_Multiply` va_get_reg64 rR13 va_s0) 0) /\\ va_state_eq va_sM (va_update_flags\n va_sM (va_update_reg64 rRax va_sM (va_update_xmm 0 va_sM (va_update_ok va_sM va_s0))))))\nlet va_lemma_Gcm_make_length_quad va_b0 va_s0 =\n let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRax; va_Mod_xmm 0; va_Mod_ok] in\n let va_qc = va_qcode_Gcm_make_length_quad va_mods in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_make_length_quad ()) va_qc va_s0\n (fun va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 407 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 418 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (8 `op_Multiply` va_get_reg64 rR13 va_s0 < pow2_64) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 419 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (8 `op_Multiply` va_get_reg64 rR11 va_s0 < pow2_64) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 421 column 138 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_xmm 0 va_sM == Vale.Def.Types_s.insert_nat64 (Vale.Def.Types_s.insert_nat64\n (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) (8 `op_Multiply` va_get_reg64 rR11\n va_s0) 1) (8 `op_Multiply` va_get_reg64 rR13 va_s0) 0))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRax; va_Mod_xmm 0; va_Mod_ok]) va_sM va_s0;\n (va_sM, va_fM)", "val va_qcode_Check_avx_xcr0_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_avx_xcr0_support ()))\nlet va_qcode_Check_avx_xcr0_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_avx_xcr0_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 358 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 359 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Xgetbv_Avx ()) (fun (va_s:va_state) _ -> let (va_arg19:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 360 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg19 1) (let\n (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 361 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg18 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 362 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRax)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 364 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 4)) (fun (va_s:va_state) _ ->\n va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 366 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (2 == Prims.pow2 1)) (fun _ -> (fun (p:prop) -> p) (2 ==\n Prims.pow2 1)) (fun (_:unit) -> assert_normalize (2 == Prims.pow2 1)) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 367 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (4 == Prims.pow2 2)) (fun _ -> (fun (p:prop) -> p) (4 ==\n Prims.pow2 2)) (fun (_:unit) -> assert_normalize (4 == Prims.pow2 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 369 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 1)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 370 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 1 2) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 371 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 1) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 373 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 2)) (fun (va_s:va_state) _ -> let\n (va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in let\n (va_arg16:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 374 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg16 va_arg17 1) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 375 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QEmpty\n (())))))))))))))))))", "val va_qcode_Gcm_blocks128\n (va_mods: va_mods_t)\n (alg: algorithm)\n (in_b out_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n (h_BE: quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg))\nlet va_qcode_Gcm_blocks128 (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 237 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 238 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 239 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 240 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 241 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b in_b h_BE (va_get_vec 1 va_old_s)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 242 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 243 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 244 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 245 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 246 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gctr_blocks128 alg in_b out_b key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 247 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_QEmpty (()))))))))))))))", "val va_qcode_Gcm_blocks\n (va_mods: va_mods_t)\n (alg: algorithm)\n (auth_b abytes_b in128_b out128_b inout_b iv_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n (gcm_struct_b: buffer64)\n : (va_quickCode unit (va_code_Gcm_blocks alg))\nlet va_qcode_Gcm_blocks (va_mods:va_mods_t) (alg:algorithm) (auth_b:buffer128) (abytes_b:buffer128)\n (in128_b:buffer128) (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (gcm_struct_b:buffer64) :\n (va_quickCode unit (va_code_Gcm_blocks alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s) in let\n (h_BE:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 0 va_old_s)) in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 396 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 5) (va_op_reg_opr_reg 25)\n (11 `op_Multiply` 8) Secret gcm_struct_b 11) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 398 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25)\n (0 `op_Multiply` 8) Secret gcm_struct_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 399 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (6 `op_Multiply` 8) Secret gcm_struct_b 6) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 400 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (7 `op_Multiply` 8) Secret gcm_struct_b 7) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 401 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 25)\n (8 `op_Multiply` 8) Secret gcm_struct_b 8) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 402 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_blocks_auth auth_b abytes_b hkeys_b h_BE) (fun (va_s:va_state)\n (auth_quad_seq:(seq quad32)) -> let (y_0:quad32) = Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0 in let (y_auth_bytes:quad32) = va_get_vec 1 va_s in let\n (iv_BE:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_old_s)) in let\n (ctr_BE_1:quad32) = iv_BE in let (ctr_BE_2:quad32) = Vale.AES.GCTR_BE_s.inc32 iv_BE 1 in\n va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 410 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 25)\n (9 `op_Multiply` 8) Secret gcm_struct_b 9) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 411 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 2) (va_op_vec_opr_vec 7)\n (va_op_reg_opr_reg 10) Public iv_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 413 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 21) (va_op_vec_opr_vec 7)) (fun (va_s:va_state) _ -> let\n (j0:quad32) = va_get_vec 7 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 415 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Load_one_lsb (va_op_vec_opr_vec 10)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 417 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vadduwm (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 10)) (fun\n (va_s:va_state) _ -> let (auth_in:(seq quad32)) = auth_quad_seq in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 25)\n (1 `op_Multiply` 8) Secret gcm_struct_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (2 `op_Multiply` 8) Secret gcm_struct_b 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (3 `op_Multiply` 8) Secret gcm_struct_b 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 425 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25)\n (10 `op_Multiply` 8) Secret gcm_struct_b 10) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 426 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_blocks128 alg in128_b out128_b key round_keys keys_b hkeys_b h_BE) (fun\n (va_s:va_state) _ -> let (y_cipher128:quad32) = va_get_vec 1 va_s in let\n (va_arg115:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (va_arg114:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in\n let (va_arg113:Vale.Def.Types_s.quad32) = y_cipher128 in let\n (va_arg112:Vale.Def.Types_s.quad32) = y_auth_bytes in let (va_arg111:Vale.Def.Types_s.quad32) =\n y_0 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 428 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash_BE.lemma_ghash_incremental0_append h_BE va_arg111 va_arg112\n va_arg113 va_arg114 va_arg115) (let auth_in = FStar.Seq.Base.append #quad32 auth_in\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b)) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 431 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (3 `op_Multiply` 8) Secret gcm_struct_b 3) (fun (va_s:va_state) _ -> let\n (va_arg110:Vale.Def.Types_s.nat64) = va_get_reg 7 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 432 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg110 4) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 433 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 4) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 434 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (5 `op_Multiply` 8) Secret gcm_struct_b 5) (fun (va_s:va_state) _ -> let (y_inout:quad32) =\n y_cipher128 in let (plain_byte_seq:(seq quad32)) = empty_seq_quad32 in let\n (cipher_byte_seq:(seq quad32)) = empty_seq_quad32 in let (va_arg109:Vale.Def.Types_s.quad32) =\n va_get_vec 7 va_s in let (va_arg108:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg107:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = cipher_byte_seq in let\n (va_arg106:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = plain_byte_seq in let\n (va_arg105:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 439 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR_BE.gctr_partial_opaque_init va_arg105 va_arg106 va_arg107\n va_arg108 va_arg109) (let (total_bytes:(va_int_at_least 0)) = FStar.Seq.Base.length #quad32\n auth_quad_seq `op_Multiply` 16 + plain_num_bytes in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 442 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_qIf va_mods (Cmp_gt (va_op_cmp_reg 6) (va_op_cmp_reg 7)) (qblock va_mods (fun\n (va_s:va_state) -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 444 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 25)\n (4 `op_Multiply` 8) Secret gcm_struct_b 4) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 445 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 446 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 15) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 447 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_And (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 10)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 449 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes y_0 auth_in\n h_BE) (fun (va_s:va_state) _ -> let y_inout = va_get_vec 1 va_s in let\n (raw_auth_quads:(FStar.Seq.Base.seq quad32)) = FStar.Seq.Base.append #quad32 auth_in\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5\n va_old_s) inout_b)) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 453 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_auth_quads)) 0\n total_bytes) (fun _ -> let (auth_input_bytes:(FStar.Seq.Base.seq Vale.Def.Words_s.nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 total_bytes\n in let (padded_auth_bytes:(FStar.Seq.Base.seq Vale.Def.Types_s.nat8)) =\n Vale.AES.GCTR_BE_s.pad_to_128_bits auth_input_bytes in let auth_in =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes in let plain_byte_seq =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5\n va_old_s) inout_b) in let cipher_byte_seq = Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b) in va_QEmpty ((auth_in,\n cipher_byte_seq, plain_byte_seq, y_inout)))))))))) (qblock va_mods (fun (va_s:va_state) ->\n va_QEmpty ((auth_in, cipher_byte_seq, plain_byte_seq, y_inout))))) (fun (va_s:va_state) va_g ->\n let ((auth_in:(seq quad32)), (cipher_byte_seq:(seq quad32)), (plain_byte_seq:(seq quad32)),\n (y_inout:quad32)) = va_g in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 461 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (8 `op_Multiply` 8) Secret gcm_struct_b 8) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 462 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_make_length_quad ()) (fun (va_s:va_state) _ -> let (length_quad32:quad32) =\n va_get_vec 9 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 465 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Ghash_register hkeys_b h_BE y_inout) (fun (va_s:va_state) _ -> let (y_final:quad32) =\n va_get_vec 1 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 468 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 21)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 471 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gctr_register alg key round_keys keys_b) (fun (va_s:va_state) _ -> let\n (va_arg104:Vale.Def.Types_s.quad32) = va_get_vec 1 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 473 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.be_seq_quad32_to_bytes_of_singleton va_arg104)\n (va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n ((fun (icb_661:Vale.Def.Types_s.quad32) (plain_662:Vale.Def.Types_s.quad32)\n (alg_663:Vale.AES.AES_common_s.algorithm) (key_664:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32))\n (i_665:Prims.int) -> Vale.AES.AES_BE_s.is_aes_key_word alg_663 key_664) j0 y_final alg key 0)\n (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_vec 1 va_s == Vale.AES.GCTR_BE_s.gctr_encrypt_block j0 y_final alg key 0) (let\n (plain128:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (cipher128:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n in128_b) in va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 479 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (FStar.Seq.Base.length #quad32 plain_byte_seq == 0 ==> FStar.Seq.Base.equal\n #Vale.Def.Types_s.quad32 (FStar.Seq.Base.append #Vale.Def.Types_s.quad32 plain128\n plain_byte_seq) plain128) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 480 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (FStar.Seq.Base.length #quad32 cipher_byte_seq == 0 ==> FStar.Seq.Base.equal\n #Vale.Def.Types_s.quad32 (FStar.Seq.Base.append #Vale.Def.Types_s.quad32 cipher128\n cipher_byte_seq) cipher128) (let (va_arg103:Vale.Def.Types_s.quad32) =\n Vale.AES.GCTR_BE.inc32lite ctr_BE_2 len128 in let (va_arg102:Vale.Def.Types_s.quad32) =\n ctr_BE_2 in let (va_arg101:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg100:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = cipher_byte_seq in let\n (va_arg99:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = plain_byte_seq in let\n (va_arg98:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n out128_b) in let (va_arg97:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (va_arg96:Prims.nat) = FStar.Seq.Base.length #quad32 plain_byte_seq\n in let (va_arg95:Prims.nat) = len128 in let (va_arg94:Vale.AES.AES_common_s.algorithm) = alg in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 482 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR_BE.lemma_gctr_partial_append va_arg94 va_arg95 va_arg96 va_arg97\n va_arg98 va_arg99 va_arg100 va_arg101 va_arg102 va_arg103) (let\n (va_arg93:Vale.Def.Types_s.quad32) = length_quad32 in let (va_arg92:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = auth_in in let (va_arg91:Vale.Def.Types_s.quad32) = y_final in let\n (va_arg90:Vale.Def.Types_s.quad32) = y_inout in let (va_arg89:Vale.Def.Types_s.quad32) = y_0 in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 490 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash_BE.lemma_hash_append2 h_BE va_arg89 va_arg90 va_arg91 va_arg92\n va_arg93) (let auth_in = FStar.Seq.Base.append #quad32 auth_in (FStar.Seq.Base.create #quad32 1\n length_quad32) in let (va_arg88:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 492 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash_BE.ghash_incremental_to_ghash h_BE va_arg88) (va_QEmpty\n (())))))))))))))))))))))))))))))))))))))))", "val va_qcode_Poly1305_add_key_s (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Poly1305_add_key_s ()))\nlet va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Poly1305_add_key_s ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)\n (va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =\n Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)\n _ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let\n (va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s\n in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let\n (va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in\n in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let\n (va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15\n va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))", "val va_qcode_Nat64Equal (va_mods: va_mods_t) : (va_quickCode unit (va_code_Nat64Equal ()))\nlet va_qcode_Nat64Equal (va_mods:va_mods_t) : (va_quickCode unit (va_code_Nat64Equal ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 646 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 5) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 647 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_AddCarry (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 5)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 648 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 3) 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 649 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_AddExtended (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 650 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Xor (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 5) (va_op_reg_opr_reg 3)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 651 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_BitwiseXorWithZero64 1) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 652 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_BitwiseXorCancel64 1) (va_QEmpty (()))))))))))", "val va_qcode_Gcm_extra_bytes\n (va_mods: va_mods_t)\n (alg: algorithm)\n (inout_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n (total_bytes: nat)\n (old_hash: quad32)\n (completed_quads: (seq quad32))\n (h_LE: quad32)\n : (va_quickCode unit (va_code_Gcm_extra_bytes alg))\nlet va_qcode_Gcm_extra_bytes (va_mods:va_mods_t) (alg:algorithm) (inout_b:buffer128) (key:(seq\n nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat)\n (old_hash:quad32) (completed_quads:(seq quad32)) (h_LE:quad32) : (va_quickCode unit\n (va_code_Gcm_extra_bytes alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (len:(va_int_range\n 1 1)) = 1 in let (snap:(FStar.Seq.Base.seq Vale.X64.Decls.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_s) inout_b in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 618 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 619 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 620 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_AESEncryptBlock alg (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 11 va_s)) key\n round_keys keys_b) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 621 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.AES_s.aes_encrypt_LE_reveal ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 623 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 4) (va_op_reg_opr64_reg64\n rRax) 0 Secret inout_b 0) (fun (va_s:va_state) _ -> let (va_arg34:Vale.Def.Types_s.quad32) =\n va_get_xmm 4 va_s in let (va_arg33:Vale.Def.Types_s.quad32) = va_get_xmm 0 va_s in va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 624 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_quad32_xor_commutes va_arg33 va_arg34) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 625 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 0) (va_op_xmm_xmm 4)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 626 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Store128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax)\n (va_op_xmm_xmm 0) 0 Secret inout_b 0) (fun (va_s:va_state) _ -> let (hash_input:quad32) =\n va_get_xmm 0 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 630 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Ghash_extra_bytes hkeys_b total_bytes old_hash h_LE completed_quads) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 632 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (FStar.Seq.Base.equal #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s)\n inout_b) (FStar.Seq.Base.create #quad32 1 hash_input)) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 633 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.gctr_partial_reveal ()) (va_QEmpty (()))))))))))))))", "val va_qcode_Gcm_extra_bytes\n (va_mods: va_mods_t)\n (alg: algorithm)\n (inout_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n (total_bytes: nat)\n (old_hash: quad32)\n (completed_quads: (seq quad32))\n (h_LE: quad32)\n : (va_quickCode unit (va_code_Gcm_extra_bytes alg))\nlet va_qcode_Gcm_extra_bytes (va_mods:va_mods_t) (alg:algorithm) (inout_b:buffer128) (key:(seq\n nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat)\n (old_hash:quad32) (completed_quads:(seq quad32)) (h_LE:quad32) : (va_quickCode unit\n (va_code_Gcm_extra_bytes alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (len:(va_int_range\n 1 1)) = 1 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 188 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRax) 0 Secret inout_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 189 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (fun (va_s:va_state) _ -> let\n (hash_input:quad32) = va_get_xmm 0 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 193 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Ghash_extra_bytes hkeys_b total_bytes old_hash h_LE completed_quads) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 194 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (FStar.Seq.Base.equal #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s)\n inout_b) (FStar.Seq.Base.create #quad32 1 hash_input)) (let (snap:(FStar.Seq.Base.seq\n Vale.X64.Decls.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 198 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 199 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_AESEncryptBlock alg (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 11 va_s)) key\n round_keys keys_b) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 201 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.AES_s.aes_encrypt_LE_reveal ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 204 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 205 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Store128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax)\n (va_op_xmm_xmm 10) 0 Secret inout_b 0) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 207 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.gctr_partial_reveal ()) (va_QEmpty (()))))))))))))))", "val va_qcode_Store_3blocks128_2 (va_mods: va_mods_t) (out_b: buffer128)\n : (va_quickCode unit (va_code_Store_3blocks128_2 ()))\nlet va_qcode_Store_3blocks128_2 (va_mods:va_mods_t) (out_b:buffer128) : (va_quickCode unit\n (va_code_Store_3blocks128_2 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 313 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 3)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 29) Secret out_b (va_get_reg 8 va_s + 3)) (fun\n (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 314 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 4)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 30) Secret out_b (va_get_reg 8 va_s + 4)) (fun\n (va_s:va_state) _ -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 315 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 5)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 31) Secret out_b (va_get_reg 8 va_s + 5)) (va_QEmpty\n (()))))))", "val va_qcode_Check_avx512_xcr0_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_avx512_xcr0_support ()))\nlet va_qcode_Check_avx512_xcr0_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_avx512_xcr0_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 389 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 390 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Xgetbv_Avx512 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 392 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRax)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 393 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (fun (va_s:va_state) _\n -> let (va_arg33:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 395 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg33 5) (let\n (va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 396 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg32 6) (let\n (va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 397 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg31 7) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 399 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 32)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 400 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 64)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 401 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 128)) (fun (va_s:va_state) _ ->\n va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 403 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (32 == Prims.pow2 5)) (fun _ -> (fun (p:prop) -> p) (32 ==\n Prims.pow2 5)) (fun (_:unit) -> assert_normalize (32 == Prims.pow2 5)) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 404 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (64 == Prims.pow2 6)) (fun _ -> (fun (p:prop) -> p) (64 ==\n Prims.pow2 6)) (fun (_:unit) -> assert_normalize (64 == Prims.pow2 6)) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 405 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (128 == Prims.pow2 7)) (fun _ -> (fun (p:prop) -> p) (128 ==\n Prims.pow2 7)) (fun (_:unit) -> assert_normalize (128 == Prims.pow2 7)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 407 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 2)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 408 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 5 7) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 409 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 2) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 411 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 1)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 412 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 5 6) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 413 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 1) (let\n (va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let\n (va_arg29:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 415 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg29 va_arg30 5) (let\n (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 416 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg28 5) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 417 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state) _\n -> let (va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in let\n (va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 418 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg26 va_arg27 5) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 419 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QEmpty\n (())))))))))))))))))))))))))))", "val va_qcode_Load_one_msb (va_mods: va_mods_t) : (va_quickCode unit (va_code_Load_one_msb ()))\nlet va_qcode_Load_one_msb (va_mods:va_mods_t) : (va_quickCode unit (va_code_Load_one_msb ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 145 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_ZeroXmm (va_op_xmm_xmm 2)) (fun (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 146 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (Vale.Arch.Types.two_to_nat32 (Vale.Def.Words_s.Mktwo #Vale.Def.Words_s.nat32 0 16777216) ==\n 72057594037927936) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_PinsrqImm (va_op_xmm_xmm 2) 72057594037927936 1 (va_op_reg_opr64_reg64 rR11)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 148 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (fun (_:unit) -> Vale.Def.Types_s.insert_nat64_reveal ()) (va_QEmpty (())))))))", "val va_qcode_Check_sse_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_sse_support ()))\nlet va_qcode_Check_sse_support (va_mods:va_mods_t) : (va_quickCode unit (va_code_Check_sse_support\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 202 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 204 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 205 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 206 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Sse ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 209 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _\n -> let (va_arg35:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 211 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg35 9) (let\n (va_arg34:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 212 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg34 26) (let\n (va_arg33:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 213 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg33 19) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 215 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 524288)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 216 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 512)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 217 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 67108864)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 219 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (512 == Prims.pow2 9)) (fun _ -> (fun (p:prop) -> p) (512 ==\n Prims.pow2 9)) (fun (_:unit) -> assert_normalize (512 == Prims.pow2 9)) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 220 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (524288 == Prims.pow2 19)) (fun _ -> (fun (p:prop) -> p) (524288\n == Prims.pow2 19)) (fun (_:unit) -> assert_normalize (524288 == Prims.pow2 19)) (va_QLemma\n va_range1\n \"***** PRECONDITION NOT MET AT line 221 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (67108864 == Prims.pow2 26)) (fun _ -> (fun (p:prop) -> p)\n (67108864 == Prims.pow2 26)) (fun (_:unit) -> assert_normalize (67108864 == Prims.pow2 26))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 223 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 10)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 224 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 9 19) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 225 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 10) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 227 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 17)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 228 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 9 26) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 229 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 17) (let\n (va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let\n (va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 231 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg31 va_arg32 9) (let\n (va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 232 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg30 9) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 233 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state) _\n -> let (va_arg29:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in let\n (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 234 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg28 va_arg29 9) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 235 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 237 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (())))))))))))))))))))))))))))))", "val va_qcode_Poly1305_reduce (va_mods: va_mods_t)\n : (va_quickCode (int) (va_code_Poly1305_reduce ()))\nlet va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range\n 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range\n 1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =\n va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0\n 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)\n (va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->\n let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64\n rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +\n va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let\n (va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let\n (va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let\n (va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24\n va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))", "val va_qcode_Gctr_blocks128_6way_body0\n (va_mods: va_mods_t)\n (va_old: va_state)\n (alg: algorithm)\n (va_in_in_b: buffer128)\n (va_in_key: (seq nat32))\n (va_in_keys_b va_in_out_b: buffer128)\n (va_in_plain_quads va_in_round_keys: (seq quad32))\n : (va_quickCode unit (va_code_Gctr_blocks128_6way_body0 alg))\nlet va_qcode_Gctr_blocks128_6way_body0 (va_mods:va_mods_t) (va_old:va_state) (alg:algorithm)\n (va_in_in_b:buffer128) (va_in_key:(seq nat32)) (va_in_keys_b:buffer128) (va_in_out_b:buffer128)\n (va_in_plain_quads:(seq quad32)) (va_in_round_keys:(seq quad32)) : (va_quickCode unit\n (va_code_Gctr_blocks128_6way_body0 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (in_b:buffer128) =\n va_in_in_b in let (key:(seq nat32)) = va_in_key in let (keys_b:buffer128) = va_in_keys_b in let\n (out_b:buffer128) = va_in_out_b in let (plain_quads:(seq quad32)) = va_in_plain_quads in let\n (round_keys:(seq quad32)) = va_in_round_keys in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 548 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Mod_cr0 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 550 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Gctr_blocks128_6way_body alg in_b out_b (va_get_vec 7 va_old) key round_keys keys_b\n plain_quads) (va_QEmpty (())))))", "val va_qcode_Store_3blocks128_1 (va_mods: va_mods_t) (out_b: buffer128)\n : (va_quickCode unit (va_code_Store_3blocks128_1 ()))\nlet va_qcode_Store_3blocks128_1 (va_mods:va_mods_t) (out_b:buffer128) : (va_quickCode unit\n (va_code_Store_3blocks128_1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 287 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0)\n (va_op_reg_opr_reg 7) Secret out_b (va_get_reg 8 va_s)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 288 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 27) Secret out_b (va_get_reg 8 va_s + 1)) (fun\n (va_s:va_state) _ -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 289 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 2)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 28) Secret out_b (va_get_reg 8 va_s + 2)) (va_QEmpty\n (()))))))", "val va_qcode_Loop_rounds_1_3 (va_mods: va_mods_t) (block: block_w)\n : (va_quickCode unit (va_code_Loop_rounds_1_3 ()))\nlet va_qcode_Loop_rounds_1_3 (va_mods:va_mods_t) (block:block_w) : (va_quickCode unit\n (va_code_Loop_rounds_1_3 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 580 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 1 (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 0) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 581 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 2 (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 0) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 582 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 3 (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 0) block)\n (va_QEmpty (()))))))", "val va_qcode_Gcm_extra_bytes\n (va_mods: va_mods_t)\n (alg: algorithm)\n (inout_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n (total_bytes: nat)\n (old_hash: quad32)\n (completed_quads: (seq quad32))\n (h_BE: quad32)\n : (va_quickCode unit (va_code_Gcm_extra_bytes alg))\nlet va_qcode_Gcm_extra_bytes (va_mods:va_mods_t) (alg:algorithm) (inout_b:buffer128) (key:(seq\n nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat)\n (old_hash:quad32) (completed_quads:(seq quad32)) (h_BE:quad32) : (va_quickCode unit\n (va_code_Gcm_extra_bytes alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (len:(va_int_range\n 1 1)) = 1 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 164 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 165 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 9)\n (va_op_reg_opr_reg 3) Secret inout_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 166 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 9)) (fun (va_s:va_state) _ -> let\n (hash_input:quad32) = va_get_vec 9 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 170 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Ghash_extra_bytes hkeys_b total_bytes old_hash h_BE completed_quads) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (FStar.Seq.Base.equal #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b)) (FStar.Seq.Base.create #quad32 1\n hash_input)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 173 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 174 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_AESEncryptBlock alg (va_get_vec 7 va_old_s) key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 176 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vxor (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 0)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 177 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 12)\n (va_op_reg_opr_reg 3) Secret inout_b 0) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 179 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR_BE.gctr_partial_reveal ()) (va_QEmpty (())))))))))))))", "val va_wp_Gcm_make_length_quad (va_s0: va_state) (va_k: (va_state -> unit -> Type0)) : Type0\nlet va_wp_Gcm_make_length_quad (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (8 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg 7\n va_s0 < pow2_64) /\\ (forall (va_x_r6:nat64) (va_x_r7:nat64) (va_x_v9:quad32) . let va_sM =\n va_upd_vec 9 va_x_v9 (va_upd_reg 7 va_x_r7 (va_upd_reg 6 va_x_r6 va_s0)) in va_get_ok va_sM /\\\n (8 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ 8 `op_Multiply` va_get_reg 7 va_s0 < pow2_64\n /\\ va_get_vec 9 va_sM == Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.Mktwo #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` va_get_reg 7 va_s0 `op_Modulus` pow2_32) (8\n `op_Multiply` va_get_reg 7 va_s0 `op_Division` pow2_32 `op_Modulus` pow2_32))\n (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32 (8 `op_Multiply` va_get_reg 6 va_s0\n `op_Modulus` pow2_32) (8 `op_Multiply` va_get_reg 6 va_s0 `op_Division` pow2_32 `op_Modulus`\n pow2_32)))) ==> va_k va_sM (())))", "val va_wp_Gcm_make_length_quad (va_s0: va_state) (va_k: (va_state -> unit -> Type0)) : Type0\nlet va_wp_Gcm_make_length_quad (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (sse_enabled /\\ 8 `op_Multiply` va_get_reg64 rR13 va_s0 < pow2_64 /\\ 8\n `op_Multiply` va_get_reg64 rR11 va_s0 < pow2_64) /\\ (forall (va_x_xmm0:quad32) (va_x_rax:nat64)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRax va_x_rax\n (va_upd_xmm 0 va_x_xmm0 va_s0)) in va_get_ok va_sM /\\ (8 `op_Multiply` va_get_reg64 rR13 va_s0\n < pow2_64 /\\ 8 `op_Multiply` va_get_reg64 rR11 va_s0 < pow2_64 /\\ va_get_xmm 0 va_sM ==\n Vale.Def.Types_s.insert_nat64 (Vale.Def.Types_s.insert_nat64 (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0) (8 `op_Multiply` va_get_reg64 rR11 va_s0) 1) (8 `op_Multiply`\n va_get_reg64 rR13 va_s0) 0) ==> va_k va_sM (())))", "val va_qcode_Gctr_blocks128_body0\n (va_mods: va_mods_t)\n (va_old: va_state)\n (alg: algorithm)\n (va_in_in_b: buffer128)\n (va_in_key: (seq nat32))\n (va_in_keys_b va_in_out_b: buffer128)\n (va_in_plain_quads va_in_round_keys: (seq quad32))\n : (va_quickCode unit (va_code_Gctr_blocks128_body0 alg))\nlet va_qcode_Gctr_blocks128_body0 (va_mods:va_mods_t) (va_old:va_state) (alg:algorithm)\n (va_in_in_b:buffer128) (va_in_key:(seq nat32)) (va_in_keys_b:buffer128) (va_in_out_b:buffer128)\n (va_in_plain_quads:(seq quad32)) (va_in_round_keys:(seq quad32)) : (va_quickCode unit\n (va_code_Gctr_blocks128_body0 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (in_b:buffer128) =\n va_in_in_b in let (key:(seq nat32)) = va_in_key in let (keys_b:buffer128) = va_in_keys_b in let\n (out_b:buffer128) = va_in_out_b in let (plain_quads:(seq quad32)) = va_in_plain_quads in let\n (round_keys:(seq quad32)) = va_in_round_keys in let (snap:(FStar.Seq.Base.seq\n Vale.X64.Decls.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) in_b in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 249 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 250 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 251 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_AESEncryptBlock alg (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 11 va_s)) key\n round_keys keys_b) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 252 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.AES_s.aes_encrypt_LE_reveal ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 254 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_xmm_xmm 2) (va_op_reg_opr64_reg64\n rR11) 0 Secret in_b (va_get_reg64 rRbx va_s)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 255 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 2) (va_op_xmm_xmm 0)) (fun (va_s:va_state) _ -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 256 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Store128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rR10)\n (va_op_xmm_xmm 2) 0 Secret out_b (va_get_reg64 rRbx va_s)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 258 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 259 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 16)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 260 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64 16)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 261 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Inc32 (va_op_xmm_xmm 11) (va_op_xmm_xmm 10)) (va_QEmpty (()))))))))))))))", "val va_wpProof_Gcm_make_length_quad : va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_make_length_quad va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_make_length_quad ())\n ([va_Mod_flags; va_Mod_reg64 rRax; va_Mod_xmm 0]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Gcm_make_length_quad va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_make_length_quad (va_code_Gcm_make_length_quad ()) va_s0 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRax va_sM (va_update_xmm 0\n va_sM (va_update_ok va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRax; va_Mod_xmm 0]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_qcode_Gcm_blocks_wrapped\n (va_mods: va_mods_t)\n (alg: algorithm)\n (offset: int)\n (auth_b abytes_b in128x6_b out128x6_b in128_b out128_b inout_b iv_b: buffer128)\n (iv: supported_iv_LE)\n (scratch_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n : (va_quickCode unit (va_code_Gcm_blocks_wrapped alg offset))\nlet va_qcode_Gcm_blocks_wrapped (va_mods:va_mods_t) (alg:algorithm) (offset:int) (auth_b:buffer128)\n (abytes_b:buffer128) (in128x6_b:buffer128) (out128x6_b:buffer128) (in128_b:buffer128)\n (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128) (iv:supported_iv_LE)\n (scratch_b:buffer128) (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128)\n (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gcm_blocks_wrapped alg offset)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abytes_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 0) (va_get_stack va_s) in let (in128x6_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 8) (va_get_stack va_s) in let\n (out128x6_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 16) (va_get_stack va_s) in let (len128x6:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 24) (va_get_stack va_s) in let\n (in128_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 32) (va_get_stack va_s) in let (out128_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 40) (va_get_stack va_s) in let\n (len128:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset\n + 48) (va_get_stack va_s) in let (inout_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 56) (va_get_stack va_s) in let\n (plain_num_bytes:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s\n + offset + 64) (va_get_stack va_s) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1325 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Gcm_blocks alg offset auth_b abytes_b in128x6_b out128x6_b in128_b out128_b inout_b\n iv_b scratch_b key round_keys keys_b hkeys_b) (fun (va_s:va_state) _ -> va_qAssertSquash\n va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 1387 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (8 `op_Multiply` va_get_reg64 rRsi va_old_s >= 0 /\\ 8 `op_Multiply` va_get_reg64 rRsi va_old_s\n <= 18446744073709551615 /\\ 8 `op_Multiply` plain_num_bytes >= 0 /\\ 8 `op_Multiply`\n plain_num_bytes <= 18446744073709551615) (fun _ -> let (va_arg38:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.Def.Types_s.insert_nat64\n (Vale.Def.Types_s.insert_nat64 (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) (8\n `op_Multiply` va_get_reg64 rRsi va_old_s) 1) (8 `op_Multiply` plain_num_bytes) 0) in let\n (va_arg37:Vale.Def.Types_s.quad32) = va_get_xmm 8 va_s in let\n (va_arg36:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.X64.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 0 va_s)) in let\n (va_arg35:Vale.Def.Types_s.quad32) = Vale.X64.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2\n va_old_s) in let (va_arg34:Vale.AES.GCM_s.supported_iv_LE) = iv in let (va_arg33:Prims.nat) =\n va_get_reg64 rRsi va_old_s in let (va_arg32:Prims.nat) = plain_num_bytes in let\n (va_arg31:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_s) inout_b in let (va_arg30:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out128_b in let\n (va_arg29:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 6 va_s) out128x6_b in let (va_arg28:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_old_s) inout_b in let\n (va_arg27:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_old_s) in128_b in let (va_arg26:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_old_s) in128x6_b in\n let (va_arg25:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 7 va_old_s) abytes_b in let (va_arg24:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_old_s) auth_b in let\n (va_arg23:(FStar.Seq.Base.seq Vale.Def.Words_s.nat32)) = key in let\n (va_arg22:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 1387 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM.gcm_blocks_helper_simplified va_arg22 va_arg23 va_arg24 va_arg25\n va_arg26 va_arg27 va_arg28 va_arg29 va_arg30 va_arg31 va_arg32 va_arg33 va_arg34 va_arg35\n va_arg36 va_arg37 va_arg38) (va_QEmpty (()))))))", "val va_qcode_Gcm_blocks_wrapped\n (va_mods: va_mods_t)\n (alg: algorithm)\n (offset: int)\n (auth_b abytes_b in128x6_b out128x6_b in128_b out128_b inout_b iv_b: buffer128)\n (iv: supported_iv_LE)\n (scratch_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n (expected_tag: (seq nat8))\n : (va_quickCode unit (va_code_Gcm_blocks_wrapped alg offset))\nlet va_qcode_Gcm_blocks_wrapped (va_mods:va_mods_t) (alg:algorithm) (offset:int) (auth_b:buffer128)\n (abytes_b:buffer128) (in128x6_b:buffer128) (out128x6_b:buffer128) (in128_b:buffer128)\n (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128) (iv:supported_iv_LE)\n (scratch_b:buffer128) (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128)\n (hkeys_b:buffer128) (expected_tag:(seq nat8)) : (va_quickCode unit (va_code_Gcm_blocks_wrapped\n alg offset)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abytes_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 0) (va_get_stack va_s) in let (in128x6_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 8) (va_get_stack va_s) in let\n (out128x6_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 16) (va_get_stack va_s) in let (len128x6:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 24) (va_get_stack va_s) in let\n (in128_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 32) (va_get_stack va_s) in let (out128_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 40) (va_get_stack va_s) in let\n (len128:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset\n + 48) (va_get_stack va_s) in let (inout_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 56) (va_get_stack va_s) in let\n (plain_num_bytes:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s\n + offset + 64) (va_get_stack va_s) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 739 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Gcm_blocks alg offset auth_b abytes_b in128x6_b out128x6_b in128_b out128_b inout_b\n iv_b scratch_b key round_keys keys_b hkeys_b) (fun (va_s:va_state) _ -> va_qAssertSquash\n va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 741 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (8 `op_Multiply` va_get_reg64 rRsi va_old_s >= 0 /\\ 8 `op_Multiply` va_get_reg64 rRsi va_old_s\n <= 18446744073709551615 /\\ 8 `op_Multiply` plain_num_bytes >= 0 /\\ 8 `op_Multiply`\n plain_num_bytes <= 18446744073709551615) (fun _ -> let (va_arg55:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.Def.Types_s.insert_nat64\n (Vale.Def.Types_s.insert_nat64 (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) (8\n `op_Multiply` va_get_reg64 rRsi va_old_s) 1) (8 `op_Multiply` plain_num_bytes) 0) in let\n (va_arg54:Vale.Def.Types_s.quad32) = va_get_xmm 8 va_s in let\n (va_arg53:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.X64.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 0 va_s)) in let\n (va_arg52:Vale.Def.Types_s.quad32) = Vale.X64.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2\n va_old_s) in let (va_arg51:Vale.AES.GCM_s.supported_iv_LE) = iv in let (va_arg50:Prims.nat) =\n va_get_reg64 rRsi va_old_s in let (va_arg49:Prims.nat) = plain_num_bytes in let\n (va_arg48:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_s) inout_b in let (va_arg47:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out128_b in let\n (va_arg46:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 6 va_s) out128x6_b in let (va_arg45:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_old_s) inout_b in let\n (va_arg44:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_old_s) in128_b in let (va_arg43:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_old_s) in128x6_b in\n let (va_arg42:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 7 va_old_s) abytes_b in let (va_arg41:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_old_s) auth_b in let\n (va_arg40:(FStar.Seq.Base.seq Vale.Def.Words_s.nat32)) = key in let\n (va_arg39:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 741 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM.gcm_blocks_dec_helper_simplified va_arg39 va_arg40 va_arg41\n va_arg42 va_arg43 va_arg44 va_arg45 va_arg46 va_arg47 va_arg48 va_arg49 va_arg50 va_arg51\n va_arg52 va_arg53 va_arg54 va_arg55) (let (auth_raw_quads:(FStar.Seq.Base.seq\n Vale.X64.Decls.quad32)) = FStar.Seq.Base.append #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_old_s) auth_b) (Vale.X64.Decls.s128 (va_get_mem_heaplet 7 va_old_s)\n abytes_b) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 751 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.Def.Types_s.nat8 (Vale.Def.Types_s.le_seq_quad32_to_bytes auth_raw_quads) 0 (va_get_reg64\n rRsi va_old_s)) (fun _ -> let (auth_bytes:(FStar.Seq.Base.seq Vale.Def.Types_s.nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Types_s.nat8 (Vale.Def.Types_s.le_seq_quad32_to_bytes\n auth_raw_quads) 0 (va_get_reg64 rRsi va_old_s) in let (va_arg38:Vale.Def.Types_s.quad32) =\n Vale.X64.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_old_s) in let\n (va_arg37:Vale.AES.GCM_s.supported_iv_LE) = iv in let (va_arg36:Prims.nat) = plain_num_bytes in\n let (va_arg35:(FStar.Seq.Base.seq Vale.Def.Words_s.nat8)) = expected_tag in let\n (va_arg34:(FStar.Seq.Base.seq Vale.Def.Words_s.nat8)) = auth_bytes in let\n (va_arg33:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_s) inout_b in let (va_arg32:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out128_b in let\n (va_arg31:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 6 va_s) out128x6_b in let (va_arg30:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_old_s) inout_b in let\n (va_arg29:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_old_s) in128_b in let (va_arg28:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_old_s) in128x6_b in\n let (va_arg27:(FStar.Seq.Base.seq Vale.Def.Words_s.nat32)) = key in let\n (va_arg26:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 752 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM.gcm_blocks_helper_dec_simplified va_arg26 va_arg27 va_arg28\n va_arg29 va_arg30 va_arg31 va_arg32 va_arg33 va_arg34 va_arg35 va_arg36 va_arg37 va_arg38)\n (va_QEmpty (()))))))))", "val va_qcode_Poly1305_last_block (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Poly1305_last_block ()))\nlet va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Poly1305_last_block ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range\n 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range\n 1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =\n va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let\n (r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in\n let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128\n (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let\n (inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)\n (va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s\n `op_Multiply` 8) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun\n (va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15\n va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert\n va_range1\n \"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64\n rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)\n in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =\n va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->\n va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast\n `op_Modulus` padLast) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty\n (())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_get_reg64 rR15 va_s - 8 >= 0 /\\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let\n (nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8\n in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun\n (va_s:va_state) _ -> va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let\n (va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let\n (va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =\n va_get_reg64 rR9 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash\n va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\\ Prims.pow2 (8 `op_Multiply` nExtra8) <=\n 18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8\n `op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let\n (va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->\n va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast\n `op_Modulus` padLast) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty\n (()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast\n `op_Modulus` padLast + padLast in va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx\n va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy\n va_range1\n \"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14\n va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let\n (va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast\n in let (va_arg69:Prims.pos) = p in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)\n (va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp\n hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)\n (va_QEmpty (()))) (va_QEmpty (()))))))))))", "val va_qcode_Gctr_blocks128_1way_body0\n (va_mods: va_mods_t)\n (va_old: va_state)\n (alg: algorithm)\n (va_in_in_b: buffer128)\n (va_in_key: (seq nat32))\n (va_in_keys_b: buffer128)\n (va_in_old_icb: quad32)\n (va_in_old_plain: (seq quad32))\n (va_in_out_b: buffer128)\n (va_in_round_keys: (seq quad32))\n : (va_quickCode unit (va_code_Gctr_blocks128_1way_body0 alg))\nlet va_qcode_Gctr_blocks128_1way_body0 (va_mods:va_mods_t) (va_old:va_state) (alg:algorithm)\n (va_in_in_b:buffer128) (va_in_key:(seq nat32)) (va_in_keys_b:buffer128) (va_in_old_icb:quad32)\n (va_in_old_plain:(seq quad32)) (va_in_out_b:buffer128) (va_in_round_keys:(seq quad32)) :\n (va_quickCode unit (va_code_Gctr_blocks128_1way_body0 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (in_b:buffer128) =\n va_in_in_b in let (key:(seq nat32)) = va_in_key in let (keys_b:buffer128) = va_in_keys_b in let\n (old_icb:quad32) = va_in_old_icb in let (old_plain:(seq quad32)) = va_in_old_plain in let\n (out_b:buffer128) = va_in_out_b in let (round_keys:(seq quad32)) = va_in_round_keys in va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 257 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Mod_cr0 ()) (fun (va_s:va_state) _ -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 259 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Gctr_blocks128_body_1way alg in_b out_b (va_get_reg 8 va_s) old_icb key round_keys\n keys_b old_plain) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 261 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddImm (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 8) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 262 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddImm (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 9) 16) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 263 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vadduwm (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 3)) (va_QEmpty\n (()))))))))", "val va_qcode_Loop_rounds_9_11 (va_mods: va_mods_t) (block: block_w)\n : (va_quickCode unit (va_code_Loop_rounds_9_11 ()))\nlet va_qcode_Loop_rounds_9_11 (va_mods:va_mods_t) (block:block_w) : (va_quickCode unit\n (va_code_Loop_rounds_9_11 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 618 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 9 (va_op_vec_opr_vec 9) (va_op_vec_opr_vec 8) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 619 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 10 (va_op_vec_opr_vec 10) (va_op_vec_opr_vec 8) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 620 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 11 (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 8) block)\n (va_QEmpty (()))))))", "val va_qcode_Loop_rounds_5_7 (va_mods: va_mods_t) (block: block_w)\n : (va_quickCode unit (va_code_Loop_rounds_5_7 ()))\nlet va_qcode_Loop_rounds_5_7 (va_mods:va_mods_t) (block:block_w) : (va_quickCode unit\n (va_code_Loop_rounds_5_7 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 599 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 5 (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 4) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 600 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 6 (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 4) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 601 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 7 (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 4) block)\n (va_QEmpty (()))))))", "val va_qcode_VectorEqual (va_mods: va_mods_t) : (va_quickCode unit (va_code_VectorEqual ()))\nlet va_qcode_VectorEqual (va_mods:va_mods_t) : (va_quickCode unit (va_code_VectorEqual ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 667 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vcmpequw (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 1)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 668 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Mfvsrld (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0)) (fun (va_s:va_state) _ -> let\n (tmp1:nat64) = va_get_reg 4 va_s in let (va_arg28:Vale.Def.Types_s.quad32) = va_get_vec 0 va_s\n in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 671 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_equality_check_helper va_arg28) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 673 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Nat64Equal ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 674 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (fun (va_s:va_state) _ -> let\n (result1:nat64) = va_get_reg 3 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 677 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Mfvsrd (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0)) (fun (va_s:va_state) _ -> let\n (tmp2:nat64) = va_get_reg 4 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 680 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Nat64Equal ()) (fun (va_s:va_state) _ -> let (result2:nat64) = va_get_reg 3 va_s in\n va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 683 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Add (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (fun\n (va_s:va_state) _ -> let (va_arg27:Vale.Def.Words_s.nat64) = va_get_reg 3 va_s in let\n (va_arg26:Vale.Def.Words_s.nat64) = result2 in let (va_arg25:Vale.Def.Words_s.nat64) = tmp2 in\n let (va_arg24:Vale.Def.Words_s.nat64) = result1 in let (va_arg23:Vale.Def.Words_s.nat64) = tmp1\n in let (va_arg22:Vale.Def.Types_s.quad32) = va_get_vec 0 va_s in let\n (va_arg21:Vale.Def.Types_s.quad32) = va_get_vec 1 va_old_s in let\n (va_arg20:Vale.Def.Types_s.quad32) = va_get_vec 0 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 684 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_equality_check_helper_2 va_arg20 va_arg21 va_arg22\n va_arg23 va_arg24 va_arg25 va_arg26 va_arg27) (va_QEmpty (()))))))))))))", "val va_qcode_Gcm_blocks\n (va_mods: va_mods_t)\n (alg: algorithm)\n (offset: int)\n (auth_b abytes_b in128x6_b out128x6_b in128_b out128_b inout_b iv_b scratch_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n : (va_quickCode unit (va_code_Gcm_blocks alg offset))\nlet va_qcode_Gcm_blocks (va_mods:va_mods_t) (alg:algorithm) (offset:int) (auth_b:buffer128)\n (abytes_b:buffer128) (in128x6_b:buffer128) (out128x6_b:buffer128) (in128_b:buffer128)\n (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128) (scratch_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) : (va_quickCode unit\n (va_code_Gcm_blocks alg offset)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abytes_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 0) (va_get_stack va_s) in let (in128x6_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 8) (va_get_stack va_s) in let\n (out128x6_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 16) (va_get_stack va_s) in let (len128x6:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 24) (va_get_stack va_s) in let\n (in128_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 32) (va_get_stack va_s) in let (out128_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 40) (va_get_stack va_s) in let\n (len128:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset\n + 48) (va_get_stack va_s) in let (inout_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 56) (va_get_stack va_s) in let\n (plain_num_bytes:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s\n + offset + 64) (va_get_stack va_s) in let (h_LE:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.X64.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_old_s)) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1057 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1058 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_AddLea64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rR9) (va_const_opr64 32))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1059 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRsp) (offset + 0))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1060 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Gcm_blocks_auth auth_b abytes_b hkeys_b h_LE) (fun (va_s:va_state)\n (auth_quad_seq:(seq quad32)) -> let (y_0:quad32) = Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0 in let (y_auth_bytes:quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1067 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRsp) (offset + 8))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1068 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRsi) (va_op_reg_opr64_reg64 rRsp) (offset + 16))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1069 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRsp) (offset + 24))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1070 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR13)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1071 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (fun (va_s:va_state) _ -> let\n (iv_BE:Vale.X64.Decls.quad32) = Vale.X64.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2\n va_old_s) in let (ctr_BE_1:quad32) = iv_BE in let (ctr_BE_2:quad32) = Vale.AES.GCTR_s.inc32\n iv_BE 1 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1077 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 2) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64\n rR8) 0 Public iv_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1079 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Store128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr64_reg64 rRbp)\n (va_op_xmm_xmm 1) 0 Secret scratch_b 0) (fun (va_s:va_state) _ -> let (j0:quad32) = va_get_xmm\n 1 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1081 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load_one_lsb (va_op_xmm_xmm 10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1083 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) (va_op_xmm_xmm 10)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1085 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_AES_GCM_encrypt_6mult alg h_LE iv_b in128x6_b out128x6_b scratch_b key round_keys\n keys_b hkeys_b) (fun (va_s:va_state) _ -> let (y_cipher128x6:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s) in let (auth_in:(seq quad32)) =\n auth_quad_seq in let (va_arg138:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_s) out128x6_b in let\n (va_arg137:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in let\n (va_arg136:Vale.Def.Types_s.quad32) = y_auth_bytes in let (va_arg135:Vale.Def.Types_s.quad32) =\n y_0 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 1088 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.lemma_ghash_incremental0_append h_LE va_arg135 va_arg136\n y_cipher128x6 va_arg137 va_arg138) (let auth_in = FStar.Seq.Base.append #quad32 auth_in\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_s) out128x6_b) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1092 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm 11)\n (va_op_reg_opr64_reg64 rRbp) 32 Secret scratch_b 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1093 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1094 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRsp) (offset + 32))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1095 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRsp) (offset + 40))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1096 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRsp) (offset + 48))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1097 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1098 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_InitPshufbMask (va_op_xmm_xmm 9) (va_op_reg_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1099 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 11) (va_op_xmm_xmm 9)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1100 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Gcm_blocks128 alg in128_b out128_b key round_keys keys_b hkeys_b h_LE) (fun\n (va_s:va_state) _ -> let (y_cipher128:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s) in let (va_arg134:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out128_b in let\n (va_arg133:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in let\n (va_arg132:Vale.Def.Types_s.quad32) = y_0 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 1102 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.lemma_ghash_incremental0_append h_LE va_arg132 y_cipher128x6\n y_cipher128 va_arg133 va_arg134) (let auth_in = FStar.Seq.Base.append #quad32 auth_in\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out128_b) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1106 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Stack_lemma (va_op_reg64_reg64 rRsp) (offset + 24) Public) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1106 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_opr_code_Stack (va_op_reg64_reg64 rRsp)\n (offset + 24) Public)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1107 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rR14) (va_const_opr64 16)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1108 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRsp) (offset + 64))\n (fun (va_s:va_state) _ -> let (y_inout:Vale.Def.Types_s.quad32) = y_cipher128 in let\n (plain_byte_seq:(seq quad32)) = empty_seq_quad32 in let (cipher_byte_seq:(seq quad32)) =\n empty_seq_quad32 in let (va_arg131:Vale.Def.Types_s.quad32) = va_get_xmm 11 va_s in let\n (va_arg130:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg129:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = cipher_byte_seq in let\n (va_arg128:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = plain_byte_seq in let\n (va_arg127:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 1113 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.gctr_partial_opaque_init va_arg127 va_arg128 va_arg129 va_arg130\n va_arg131) (let (total_bytes:(va_int_at_least 0)) = FStar.Seq.Base.length #quad32 auth_quad_seq\n `op_Multiply` 16 + plain_num_bytes in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1117 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_qIf va_mods (Cmp_gt (va_op_cmp_reg64 rR13) (va_op_cmp_reg64 rR14)) (qblock va_mods (fun\n (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1119 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRsp) (offset + 56))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1120 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rR13)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 1121 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1122 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64 15)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1126 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes y_0 auth_in\n h_LE) (fun (va_s:va_state) _ -> let y_inout = Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm\n 8 va_s) in let (raw_auth_quads:(FStar.Seq.Base.seq quad32)) = FStar.Seq.Base.append #quad32\n auth_in (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 1130 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.Def.Types_s.nat8 (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_auth_quads) 0 total_bytes)\n (fun _ -> let (auth_input_bytes:(FStar.Seq.Base.seq Vale.Def.Types_s.nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Types_s.nat8 (Vale.Def.Types_s.le_seq_quad32_to_bytes\n raw_auth_quads) 0 total_bytes in let (padded_auth_bytes:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat8)) = Vale.AES.GCTR_s.pad_to_128_bits auth_input_bytes in let auth_in =\n Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_auth_bytes in let plain_byte_seq =\n Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_old_s) inout_b in let cipher_byte_seq =\n Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b in va_QEmpty ((auth_in,\n cipher_byte_seq, plain_byte_seq, y_inout)))))))))) (qblock va_mods (fun (va_s:va_state) ->\n va_QEmpty ((auth_in, cipher_byte_seq, plain_byte_seq, y_inout))))) (fun (va_s:va_state) va_g ->\n let ((auth_in:(seq quad32)), (cipher_byte_seq:(seq quad32)), (plain_byte_seq:(seq quad32)),\n (y_inout:Vale.Def.Types_s.quad32)) = va_g in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1141 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rR15)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1142 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Gcm_make_length_quad ()) (fun (va_s:va_state) _ -> let\n (length_quad32:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 0\n va_s) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1145 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Ghash_register hkeys_b h_LE y_inout) (fun (va_s:va_state) _ -> let\n (y_final:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s)\n in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1148 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRbp) 0 Secret scratch_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1151 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Gctr_register alg key round_keys keys_b) (fun (va_s:va_state) _ -> let\n (va_arg126:Vale.Def.Types_s.quad32) = va_get_xmm 8 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 1154 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.le_seq_quad32_to_bytes_of_singleton va_arg126)\n (va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 1155 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n ((fun (icb_BE_677:Vale.Def.Types_s.quad32) (plain_LE_678:Vale.Def.Types_s.quad32)\n (alg_679:Vale.AES.AES_common_s.algorithm) (key_680:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32))\n (i_681:Prims.int) -> Vale.AES.AES_s.is_aes_key_LE alg_679 key_680) j0 y_final alg key 0) (fun _\n -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 1155 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_xmm 8 va_s == Vale.AES.GCTR_s.gctr_encrypt_block j0 y_final alg key 0) (let\n (plain128:(FStar.Seq.Base.seq Vale.X64.Decls.quad32)) = FStar.Seq.Base.append\n #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_old_s) in128x6_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_old_s) in128_b) in let\n (cipher128:(FStar.Seq.Base.seq Vale.X64.Decls.quad32)) = FStar.Seq.Base.append\n #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_s) in128x6_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) in128_b) in va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 1160 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (FStar.Seq.Base.length #quad32 plain_byte_seq == 0 ==> FStar.Seq.Base.equal\n #Vale.X64.Decls.quad32 (FStar.Seq.Base.append #Vale.X64.Decls.quad32 plain128 plain_byte_seq)\n plain128) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 1161 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (FStar.Seq.Base.length #quad32 cipher_byte_seq == 0 ==> FStar.Seq.Base.equal\n #Vale.X64.Decls.quad32 (FStar.Seq.Base.append #Vale.X64.Decls.quad32 cipher128 cipher_byte_seq)\n cipher128) (let (va_arg125:Vale.Def.Types_s.quad32) = Vale.AES.GCTR.inc32lite ctr_BE_2 len128x6\n in let (va_arg124:Vale.Def.Types_s.quad32) = ctr_BE_2 in let (va_arg123:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat32)) = key in let (va_arg122:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32))\n = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out128_b in let\n (va_arg121:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_old_s) in128_b in let (va_arg120:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_s) out128x6_b in let\n (va_arg119:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 6 va_old_s) in128x6_b in let (va_arg118:Prims.nat) = len128 in let\n (va_arg117:Prims.nat) = len128x6 in let (va_arg116:Vale.AES.AES_common_s.algorithm) = alg in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 1163 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.lemma_gctr_partial_append va_arg116 va_arg117 va_arg118\n va_arg119 va_arg120 va_arg121 va_arg122 va_arg123 va_arg124 va_arg125) (let\n (va_arg115:Vale.Def.Types_s.quad32) = Vale.AES.GCTR.inc32lite (Vale.AES.GCTR.inc32lite ctr_BE_2\n len128x6) len128 in let (va_arg114:Vale.Def.Types_s.quad32) = ctr_BE_2 in let\n (va_arg113:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg112:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = cipher_byte_seq in let\n (va_arg111:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = plain_byte_seq in let\n (va_arg110:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = FStar.Seq.Base.append\n #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_s) out128x6_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out128_b) in let\n (va_arg109:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = FStar.Seq.Base.append\n #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_old_s) in128x6_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_old_s) in128_b) in let (va_arg108:Prims.nat) =\n FStar.Seq.Base.length #quad32 plain_byte_seq in let (va_arg107:Prims.nat) = len128x6 + len128\n in let (va_arg106:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 1169 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.lemma_gctr_partial_append va_arg106 va_arg107 va_arg108\n va_arg109 va_arg110 va_arg111 va_arg112 va_arg113 va_arg114 va_arg115) (let\n (va_arg105:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in let\n (va_arg104:Vale.Def.Types_s.quad32) = y_0 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 1177 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.lemma_hash_append2 h_LE va_arg104 y_inout y_final va_arg105\n length_quad32) (let auth_in = FStar.Seq.Base.append #quad32 auth_in (FStar.Seq.Base.create\n #Vale.Def.Types_s.quad32 1 length_quad32) in let (va_arg103:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = auth_in in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 1179 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.ghash_incremental_to_ghash h_LE va_arg103) (va_QEmpty\n (()))))))))))))))))))))))))))))))))))))))))))))))))", "val va_qcode_Gcm_blocks\n (va_mods: va_mods_t)\n (alg: algorithm)\n (offset: int)\n (auth_b abytes_b in128x6_b out128x6_b in128_b out128_b inout_b iv_b scratch_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n : (va_quickCode unit (va_code_Gcm_blocks alg offset))\nlet va_qcode_Gcm_blocks (va_mods:va_mods_t) (alg:algorithm) (offset:int) (auth_b:buffer128)\n (abytes_b:buffer128) (in128x6_b:buffer128) (out128x6_b:buffer128) (in128_b:buffer128)\n (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128) (scratch_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) : (va_quickCode unit\n (va_code_Gcm_blocks alg offset)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abytes_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 0) (va_get_stack va_s) in let (in128x6_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 8) (va_get_stack va_s) in let\n (out128x6_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 16) (va_get_stack va_s) in let (len128x6:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 24) (va_get_stack va_s) in let\n (in128_ptr:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s +\n offset + 32) (va_get_stack va_s) in let (out128_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 40) (va_get_stack va_s) in let\n (len128:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset\n + 48) (va_get_stack va_s) in let (inout_ptr:Vale.X64.Memory.nat64) =\n Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s + offset + 56) (va_get_stack va_s) in let\n (plain_num_bytes:Vale.X64.Memory.nat64) = Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s\n + offset + 64) (va_get_stack va_s) in let (h_LE:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.X64.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_old_s)) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 463 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 464 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_AddLea64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rR9) (va_const_opr64 32))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 465 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRsp) (offset + 0))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 466 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Gcm_blocks_auth auth_b abytes_b hkeys_b h_LE) (fun (va_s:va_state)\n (auth_quad_seq:(seq quad32)) -> let (y_0:quad32) = Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0 in let (y_auth_bytes:quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 473 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRsp) (offset + 8))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRsi) (va_op_reg_opr64_reg64 rRsp) (offset + 16))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 475 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRsp) (offset + 24))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 476 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR13)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 477 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (fun (va_s:va_state) _ -> let\n (iv_BE:Vale.X64.Decls.quad32) = Vale.X64.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2\n va_old_s) in let (ctr_BE_1:quad32) = iv_BE in let (ctr_BE_2:quad32) = Vale.AES.GCTR_s.inc32\n iv_BE 1 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 483 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 2) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64\n rR8) 0 Public iv_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 485 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Store128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr64_reg64 rRbp)\n (va_op_xmm_xmm 1) 0 Secret scratch_b 0) (fun (va_s:va_state) _ -> let (j0:quad32) = va_get_xmm\n 1 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 487 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load_one_lsb (va_op_xmm_xmm 10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 489 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) (va_op_xmm_xmm 10)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 491 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_AES_GCM_decrypt_6mult alg h_LE iv_b in128x6_b out128x6_b scratch_b key round_keys\n keys_b hkeys_b) (fun (va_s:va_state) _ -> let (y_cipher128x6:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s) in let (auth_in:(seq quad32)) =\n auth_quad_seq in let (va_arg138:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_old_s) in128x6_b in let\n (va_arg137:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in let\n (va_arg136:Vale.Def.Types_s.quad32) = y_auth_bytes in let (va_arg135:Vale.Def.Types_s.quad32) =\n y_0 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 494 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.lemma_ghash_incremental0_append h_LE va_arg135 va_arg136\n y_cipher128x6 va_arg137 va_arg138) (let auth_in = FStar.Seq.Base.append #quad32 auth_in\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_old_s) in128x6_b) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 498 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm 11)\n (va_op_reg_opr64_reg64 rRbp) 32 Secret scratch_b 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 499 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 500 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRsp) (offset + 32))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 501 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRsp) (offset + 40))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 502 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRsp) (offset + 48))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 504 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_InitPshufbMask (va_op_xmm_xmm 9) (va_op_reg_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 505 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 11) (va_op_xmm_xmm 9)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 506 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Gcm_blocks128 alg in128_b out128_b key round_keys keys_b hkeys_b h_LE) (fun\n (va_s:va_state) _ -> let (y_cipher128:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s) in let (va_arg134:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_old_s) in128_b in let\n (va_arg133:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in let\n (va_arg132:Vale.Def.Types_s.quad32) = y_0 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 508 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.lemma_ghash_incremental0_append h_LE va_arg132 y_cipher128x6\n y_cipher128 va_arg133 va_arg134) (let auth_in = FStar.Seq.Base.append #quad32 auth_in\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_old_s) in128_b) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 512 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Stack_lemma (va_op_reg64_reg64 rRsp) (offset + 24) Public) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 512 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_opr_code_Stack (va_op_reg64_reg64 rRsp)\n (offset + 24) Public)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 513 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rR14) (va_const_opr64 16)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 514 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRsp) (offset + 64))\n (fun (va_s:va_state) _ -> let (y_inout:Vale.Def.Types_s.quad32) = y_cipher128 in let\n (plain_byte_seq:(seq quad32)) = empty_seq_quad32 in let (cipher_byte_seq:(seq quad32)) =\n empty_seq_quad32 in let (va_arg131:Vale.Def.Types_s.quad32) = va_get_xmm 11 va_s in let\n (va_arg130:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg129:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = cipher_byte_seq in let\n (va_arg128:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = plain_byte_seq in let\n (va_arg127:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 519 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.gctr_partial_opaque_init va_arg127 va_arg128 va_arg129 va_arg130\n va_arg131) (let (total_bytes:(va_int_at_least 0)) = FStar.Seq.Base.length #quad32 auth_quad_seq\n `op_Multiply` 16 + plain_num_bytes in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 523 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_qIf va_mods (Cmp_gt (va_op_cmp_reg64 rR13) (va_op_cmp_reg64 rR14)) (qblock va_mods (fun\n (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 525 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load64_stack (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRsp) (offset + 56))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 526 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rR13)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 527 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 528 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64 15)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 532 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes y_0 auth_in\n h_LE) (fun (va_s:va_state) _ -> let y_inout = Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm\n 8 va_s) in let (raw_auth_quads:(FStar.Seq.Base.seq quad32)) = FStar.Seq.Base.append #quad32\n auth_in (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_old_s) inout_b) in va_qAssertSquash\n va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 536 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.Def.Types_s.nat8 (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_auth_quads) 0 total_bytes)\n (fun _ -> let (auth_input_bytes:(FStar.Seq.Base.seq Vale.Def.Types_s.nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Types_s.nat8 (Vale.Def.Types_s.le_seq_quad32_to_bytes\n raw_auth_quads) 0 total_bytes in let (padded_auth_bytes:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat8)) = Vale.AES.GCTR_s.pad_to_128_bits auth_input_bytes in let auth_in =\n Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_auth_bytes in let plain_byte_seq =\n Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_old_s) inout_b in let cipher_byte_seq =\n Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b in va_QEmpty ((auth_in,\n cipher_byte_seq, plain_byte_seq, y_inout)))))))))) (qblock va_mods (fun (va_s:va_state) ->\n va_QEmpty ((auth_in, cipher_byte_seq, plain_byte_seq, y_inout))))) (fun (va_s:va_state) va_g ->\n let ((auth_in:(seq quad32)), (cipher_byte_seq:(seq quad32)), (plain_byte_seq:(seq quad32)),\n (y_inout:Vale.Def.Types_s.quad32)) = va_g in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 547 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rR15)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 548 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Gcm_make_length_quad ()) (fun (va_s:va_state) _ -> let\n (length_quad32:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 0\n va_s) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 551 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Ghash_register hkeys_b h_LE y_inout) (fun (va_s:va_state) _ -> let\n (y_final:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s)\n in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 554 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRbp) 0 Secret scratch_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 557 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Gctr_register alg key round_keys keys_b) (fun (va_s:va_state) _ -> let\n (va_arg126:Vale.Def.Types_s.quad32) = va_get_xmm 8 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 560 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.le_seq_quad32_to_bytes_of_singleton va_arg126)\n (va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 561 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n ((fun (icb_BE_677:Vale.Def.Types_s.quad32) (plain_LE_678:Vale.Def.Types_s.quad32)\n (alg_679:Vale.AES.AES_common_s.algorithm) (key_680:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32))\n (i_681:Prims.int) -> Vale.AES.AES_s.is_aes_key_LE alg_679 key_680) j0 y_final alg key 0) (fun _\n -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 561 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_get_xmm 8 va_s == Vale.AES.GCTR_s.gctr_encrypt_block j0 y_final alg key 0) (let\n (plain128:(FStar.Seq.Base.seq Vale.X64.Decls.quad32)) = FStar.Seq.Base.append\n #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_old_s) in128x6_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_old_s) in128_b) in let\n (cipher128:(FStar.Seq.Base.seq Vale.X64.Decls.quad32)) = FStar.Seq.Base.append\n #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_s) in128x6_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) in128_b) in va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 566 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (FStar.Seq.Base.length #quad32 plain_byte_seq == 0 ==> FStar.Seq.Base.equal\n #Vale.X64.Decls.quad32 (FStar.Seq.Base.append #Vale.X64.Decls.quad32 plain128 plain_byte_seq)\n plain128) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 567 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (FStar.Seq.Base.length #quad32 cipher_byte_seq == 0 ==> FStar.Seq.Base.equal\n #Vale.X64.Decls.quad32 (FStar.Seq.Base.append #Vale.X64.Decls.quad32 cipher128 cipher_byte_seq)\n cipher128) (let (va_arg125:Vale.Def.Types_s.quad32) = Vale.AES.GCTR.inc32lite ctr_BE_2 len128x6\n in let (va_arg124:Vale.Def.Types_s.quad32) = ctr_BE_2 in let (va_arg123:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat32)) = key in let (va_arg122:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32))\n = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out128_b in let\n (va_arg121:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_old_s) in128_b in let (va_arg120:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_s) out128x6_b in let\n (va_arg119:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 6 va_old_s) in128x6_b in let (va_arg118:Prims.nat) = len128 in let\n (va_arg117:Prims.nat) = len128x6 in let (va_arg116:Vale.AES.AES_common_s.algorithm) = alg in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 569 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.lemma_gctr_partial_append va_arg116 va_arg117 va_arg118\n va_arg119 va_arg120 va_arg121 va_arg122 va_arg123 va_arg124 va_arg125) (let\n (va_arg115:Vale.Def.Types_s.quad32) = Vale.AES.GCTR.inc32lite (Vale.AES.GCTR.inc32lite ctr_BE_2\n len128x6) len128 in let (va_arg114:Vale.Def.Types_s.quad32) = ctr_BE_2 in let\n (va_arg113:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg112:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = cipher_byte_seq in let\n (va_arg111:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = plain_byte_seq in let\n (va_arg110:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = FStar.Seq.Base.append\n #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_s) out128x6_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out128_b) in let\n (va_arg109:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = FStar.Seq.Base.append\n #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 6 va_old_s) in128x6_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_old_s) in128_b) in let (va_arg108:Prims.nat) =\n FStar.Seq.Base.length #quad32 plain_byte_seq in let (va_arg107:Prims.nat) = len128x6 + len128\n in let (va_arg106:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 575 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.lemma_gctr_partial_append va_arg106 va_arg107 va_arg108\n va_arg109 va_arg110 va_arg111 va_arg112 va_arg113 va_arg114 va_arg115) (let\n (va_arg105:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in let\n (va_arg104:Vale.Def.Types_s.quad32) = y_0 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 583 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.lemma_hash_append2 h_LE va_arg104 y_inout y_final va_arg105\n length_quad32) (let auth_in = FStar.Seq.Base.append #quad32 auth_in (FStar.Seq.Base.create\n #Vale.Def.Types_s.quad32 1 length_quad32) in let (va_arg103:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = auth_in in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 585 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.ghash_incremental_to_ghash h_LE va_arg103) (va_QEmpty\n (()))))))))))))))))))))))))))))))))))))))))))))))))", "val va_qcode_Ghash_extra_bytes\n (va_mods: va_mods_t)\n (hkeys_b: buffer128)\n (total_bytes: nat)\n (old_hash h_LE: quad32)\n (completed_quads: (seq quad32))\n : (va_quickCode unit (va_code_Ghash_extra_bytes ()))\nlet va_qcode_Ghash_extra_bytes (va_mods:va_mods_t) (hkeys_b:buffer128) (total_bytes:nat)\n (old_hash:quad32) (h_LE:quad32) (completed_quads:(seq quad32)) : (va_quickCode unit\n (va_code_Ghash_extra_bytes ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (final_quad:quad32)\n = va_get_xmm 0 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 540 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Compute_pad_to_128_bits ()) (fun (va_s:va_state) _ -> let (final_quad_padded:quad32)\n = va_get_xmm 0 va_s in let (y_prev:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 544 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 546 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Ghash_register hkeys_b h_LE y_prev) (fun (va_s:va_state) _ -> let\n (va_arg29:Prims.nat) = total_bytes in let (va_arg28:Vale.Def.Types_s.quad32) =\n final_quad_padded in let (va_arg27:Vale.Def.Types_s.quad32) = final_quad in let\n (va_arg26:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = completed_quads in let\n (va_arg25:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s)\n in let (va_arg24:Vale.Def.Types_s.quad32) = old_hash in let (va_arg23:Vale.Def.Types_s.quad32)\n = h_LE in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 548 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.lemma_ghash_incremental_bytes_extra_helper_alt va_arg23\n va_arg24 y_prev va_arg25 va_arg26 va_arg27 va_arg28 va_arg29) (va_QEmpty (())))))))", "val va_qcode_Preamble (va_mods: va_mods_t) (ctx_b: buffer128)\n : (va_quickCode unit (va_code_Preamble ()))\nlet va_qcode_Preamble (va_mods:va_mods_t) (ctx_b:buffer128) : (va_quickCode unit (va_code_Preamble\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (dcba:Vale.PPC64LE.Machine_s.quad32) = Vale.PPC64LE.Decls.buffer128_read ctx_b 0\n (va_get_mem_heaplet 0 va_s) in let (hgfe:Vale.PPC64LE.Machine_s.quad32) =\n Vale.PPC64LE.Decls.buffer128_read ctx_b 1 (va_get_mem_heaplet 0 va_s) in let\n (a:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__lo0 dcba in let\n (b:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__lo1 dcba in let\n (c:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__hi2 dcba in let\n (d:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__hi3 dcba in let\n (e:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__lo0 hgfe in let\n (f:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__lo1 hgfe in let\n (g:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__hi2 hgfe in let\n (h:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__hi3 hgfe in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 91 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 92 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Load128_word4_buffer (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 16)\n (va_op_reg_opr_reg 3) Secret ctx_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 93 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Load128_word4_buffer_index (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 20)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret ctx_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 95 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 17) (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 16) 4)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 96 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 18) (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 16) 8)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 97 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 19) (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 16) 12)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 98 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 21) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) 4)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 99 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 22) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) 8)\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 100 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 23) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) 12) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 102 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (FStar.Seq.Base.equal #Vale.SHA.PPC64LE.SHA_helpers.word\n (Vale.SHA.PPC64LE.SHA_helpers.make_seperated_hash a b c d e f g h)\n (Vale.SHA.PPC64LE.SHA_helpers.make_ordered_hash dcba hgfe)) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 103 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (FStar.Seq.Base.equal #Vale.SHA.PPC64LE.SHA_helpers.word\n (Vale.SHA.PPC64LE.SHA_helpers.make_seperated_hash a b c d e f g h)\n (Vale.SHA.PPC64LE.SHA_helpers.make_seperated_hash_quad32 (va_get_vec 16 va_s) (va_get_vec 17\n va_s) (va_get_vec 18 va_s) (va_get_vec 19 va_s) (va_get_vec 20 va_s) (va_get_vec 21 va_s)\n (va_get_vec 22 va_s) (va_get_vec 23 va_s))) (va_QEmpty (()))))))))))))))", "val va_qcode_Preamble (va_mods: va_mods_t) (ctx_b: buffer128)\n : (va_quickCode unit (va_code_Preamble ()))\nlet va_qcode_Preamble (va_mods:va_mods_t) (ctx_b:buffer128) : (va_quickCode unit (va_code_Preamble\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abcd:Vale.X64.Decls.quad32) = Vale.X64.Decls.buffer128_read ctx_b 0 (va_get_mem_heaplet 0\n va_s) in let (efgh:Vale.X64.Decls.quad32) = Vale.X64.Decls.buffer128_read ctx_b 1\n (va_get_mem_heaplet 0 va_s) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 87 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64\n rRdi) 0 Secret ctx_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 88 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 2) (va_op_reg_opr64_reg64\n rRdi) 16 Secret ctx_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 89 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_InitPshufbStableMask (va_op_xmm_xmm 7) (va_op_reg_opr64_reg64 rRax)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 91 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 1) 27) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 92 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) 177) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 93 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 2) (va_op_xmm_xmm 2) 27) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 95 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 8) (va_op_xmm_xmm 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 96 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Palignr8 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 98 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Shufpd (va_op_xmm_xmm 2) (va_op_xmm_xmm 0) 0) (fun (va_s:va_state) _ -> va_qAssert\n va_range1\n \"***** PRECONDITION NOT MET AT line 99 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (FStar.Seq.Base.equal #Vale.SHA.SHA_helpers.word (Vale.SHA.SHA_helpers.make_hash (va_get_xmm 1\n va_s) (va_get_xmm 2 va_s)) (Vale.SHA.SHA_helpers.make_ordered_hash abcd efgh)) (va_QEmpty\n (())))))))))))))", "val va_qcode_Gctr_blocks128_6way_while0\n (va_mods: va_mods_t)\n (va_old: va_state)\n (alg: algorithm)\n (va_in_in_b: buffer128)\n (va_in_key: (seq nat32))\n (va_in_keys_b va_in_out_b: buffer128)\n (va_in_plain_quads va_in_round_keys: (seq quad32))\n : (va_quickCode unit (va_code_Gctr_blocks128_6way_while0 alg))\nlet va_qcode_Gctr_blocks128_6way_while0 (va_mods:va_mods_t) (va_old:va_state) (alg:algorithm)\n (va_in_in_b:buffer128) (va_in_key:(seq nat32)) (va_in_keys_b:buffer128) (va_in_out_b:buffer128)\n (va_in_plain_quads:(seq quad32)) (va_in_round_keys:(seq quad32)) : (va_quickCode unit\n (va_code_Gctr_blocks128_6way_while0 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (in_b:buffer128) =\n va_in_in_b in let (key:(seq nat32)) = va_in_key in let (keys_b:buffer128) = va_in_keys_b in let\n (out_b:buffer128) = va_in_out_b in let (plain_quads:(seq quad32)) = va_in_plain_quads in let\n (round_keys:(seq quad32)) = va_in_round_keys in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 430 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_qWhile va_mods (Cmp_ne (va_op_cmp_reg 8) (va_op_cmp_reg 6)) (fun va_g -> qblock va_mods\n (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 430 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Gctr_blocks128_6way_body0 va_old alg in_b key keys_b out_b plain_quads round_keys)\n (va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_get_ok va_s /\\ (va_get_reg 6 va_s -\n va_get_reg 8 va_s) `op_Modulus` 6 == 0 /\\ (0 <= va_get_reg 8 va_s /\\ va_get_reg 8 va_s <=\n va_get_reg 6 va_s) /\\ va_get_vec 7 va_s == Vale.AES.GCTR_BE.inc32lite (va_get_vec 7 va_old)\n (va_get_reg 8 va_s) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrsOffset128 (va_get_mem_heaplet 1 va_s) (va_get_reg 3 va_s) in_b\n (va_get_reg 8 va_s) (va_get_reg 6 va_s - va_get_reg 8 va_s) (va_get_mem_layout va_s) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrsOffset128 (va_get_mem_heaplet 1 va_s) (va_get_reg 7 va_s) out_b\n (va_get_reg 8 va_s) (va_get_reg 6 va_s - va_get_reg 8 va_s) (va_get_mem_layout va_s) Secret /\\\n va_get_reg 3 va_s + 16 `op_Multiply` (va_get_reg 6 va_s - va_get_reg 8 va_s) < pow2_64 /\\\n va_get_reg 7 va_s + 16 `op_Multiply` (va_get_reg 6 va_s - va_get_reg 8 va_s) < pow2_64 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b /\\\n Vale.AES.GCTR_BE.partial_seq_agreement plain_quads (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s) in_b)) (va_get_reg 8 va_s)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b) /\\ va_get_reg 6 va_s <\n pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s) (va_get_mem_heaplet 0 va_s)\n (va_get_mem_layout va_s) /\\ va_get_vec 8 va_s == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 1 0 0 0 /\\ va_get_vec 9 va_s == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 2 0 0 0 /\\ va_get_vec 10 va_s == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 3 0 0 0 /\\ va_get_vec 11 va_s == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 4 0 0 0 /\\ va_get_vec 12 va_s == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 5 0 0 0 /\\ va_get_vec 13 va_s == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 6 0 0 0 /\\ va_get_reg 27 va_s == 1 `op_Multiply` 16 /\\ va_get_reg 28\n va_s == 2 `op_Multiply` 16 /\\ va_get_reg 29 va_s == 3 `op_Multiply` 16 /\\ va_get_reg 30 va_s ==\n 4 `op_Multiply` 16 /\\ va_get_reg 31 va_s == 5 `op_Multiply` 16 /\\\n Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_old) (va_get_mem_heaplet 1\n va_s) /\\ Vale.AES.GCTR_BE.gctr_partial_def alg (va_get_reg 8 va_s) plain_quads\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n out_b)) key (va_get_vec 7 va_old) /\\ (va_get_reg 6 va_s == 0 ==> Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s) out_b == Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_old)\n out_b) /\\ va_get_reg 3 va_s == va_get_reg 3 va_old + 16 `op_Multiply` va_get_reg 8 va_s /\\\n va_get_reg 7 va_s == va_get_reg 7 va_old + 16 `op_Multiply` va_get_reg 8 va_s) (fun\n (va_s:va_state) va_g -> va_get_reg 6 va_s - va_get_reg 8 va_s) (())) (fun (va_s:va_state) va_g\n -> let va_g = () in va_QEmpty (()))))", "val va_qcode_Gctr_core_body0\n (va_mods: va_mods_t)\n (va_old: va_state)\n (alg: algorithm)\n (va_in_block_offset: nat)\n (va_in_in_b: buffer128)\n (va_in_key: (seq nat32))\n (va_in_keys_b: buffer128)\n (va_in_old_iv: quad32)\n (va_in_out_b: buffer128)\n (va_in_round_keys: (seq quad32))\n : (va_quickCode unit (va_code_Gctr_core_body0 alg))\nlet va_qcode_Gctr_core_body0 (va_mods:va_mods_t) (va_old:va_state) (alg:algorithm)\n (va_in_block_offset:nat) (va_in_in_b:buffer128) (va_in_key:(seq nat32)) (va_in_keys_b:buffer128)\n (va_in_old_iv:quad32) (va_in_out_b:buffer128) (va_in_round_keys:(seq quad32)) : (va_quickCode\n unit (va_code_Gctr_core_body0 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (block_offset:nat)\n = va_in_block_offset in let (in_b:buffer128) = va_in_in_b in let (key:(seq nat32)) = va_in_key\n in let (keys_b:buffer128) = va_in_keys_b in let (old_iv:quad32) = va_in_old_iv in let\n (out_b:buffer128) = va_in_out_b in let (round_keys:(seq quad32)) = va_in_round_keys in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 224 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 7)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 225 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 8)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 226 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_AESEncryptBlock alg (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 7 va_s)) key\n round_keys keys_b) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 227 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.AES_s.aes_encrypt_LE_reveal ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 229 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 2) (va_op_reg_opr64_reg64\n rR9) 0 Secret in_b (block_offset + va_get_reg64 rRdx va_s)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 230 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 2) (va_op_xmm_xmm 0)) (fun (va_s:va_state) _ -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 231 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Store128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rR10)\n (va_op_xmm_xmm 2) 0 Secret out_b (block_offset + va_get_reg64 rRdx va_s)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 233 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 234 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 16)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 235 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64 16)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 236 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Inc32 (va_op_xmm_xmm 7) (va_op_xmm_xmm 4)) (va_QEmpty (()))))))))))))))", "val va_qcode_Gcm_blocks_wrapped\n (va_mods: va_mods_t)\n (alg: algorithm)\n (auth_b abytes_b in128_b out128_b inout_b iv_b: buffer128)\n (iv: supported_iv_BE)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n (expected_tag: (seq nat8))\n (gcm_struct_b: buffer64)\n : (va_quickCode unit (va_code_Gcm_blocks_wrapped alg))\nlet va_qcode_Gcm_blocks_wrapped (va_mods:va_mods_t) (alg:algorithm) (auth_b:buffer128)\n (abytes_b:buffer128) (in128_b:buffer128) (out128_b:buffer128) (inout_b:buffer128)\n (iv_b:buffer128) (iv:supported_iv_BE) (key:(seq nat32)) (round_keys:(seq quad32))\n (keys_b:buffer128) (hkeys_b:buffer128) (expected_tag:(seq nat8)) (gcm_struct_b:buffer64) :\n (va_quickCode unit (va_code_Gcm_blocks_wrapped alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s) in va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 616 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_blocks alg auth_b abytes_b in128_b out128_b inout_b iv_b key round_keys keys_b\n hkeys_b gcm_struct_b) (fun (va_s:va_state) _ -> let (va_arg46:Vale.Def.Types_s.quad32) =\n Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32 (Vale.Def.Words_s.Mktwo\n #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32\n (8 `op_Multiply` auth_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply` auth_num_bytes\n `op_Division` pow2_32 `op_Modulus` pow2_32)) (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32 (8\n `op_Multiply` plain_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply` plain_num_bytes\n `op_Division` pow2_32 `op_Modulus` pow2_32))) in let (va_arg45:Vale.Def.Types_s.quad32) =\n va_get_vec 1 va_s in let (va_arg44:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s)) in let (va_arg43:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_old_s)) in let (va_arg42:Vale.AES.GCM_BE_s.supported_iv_BE) = iv in\n let (va_arg41:Prims.nat) = auth_num_bytes in let (va_arg40:Prims.nat) = plain_num_bytes in let\n (va_arg39:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s)\n inout_b) in let (va_arg38:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n out128_b) in let (va_arg37:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5\n va_old_s) inout_b) in let (va_arg36:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (va_arg35:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6\n va_old_s) abytes_b) in let (va_arg34:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) auth_b) in let (va_arg33:(FStar.Seq.Base.seq Vale.Def.Words_s.nat32)) = key in let\n (va_arg32:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 618 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_BE.gcm_blocks_dec_helper_simplified va_arg32 va_arg33 va_arg34\n va_arg35 va_arg36 va_arg37 va_arg38 va_arg39 va_arg40 va_arg41 va_arg42 va_arg43 va_arg44\n va_arg45 va_arg46) (let (auth_raw_quads:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_old_s) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6\n va_old_s) abytes_b)) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 630 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 auth_raw_quads)) 0\n auth_num_bytes) (fun _ -> let (auth_bytes:(FStar.Seq.Base.seq Vale.Def.Words_s.nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 auth_raw_quads)) 0\n auth_num_bytes in let (va_arg31:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_old_s)) in let (va_arg30:Vale.AES.GCM_BE_s.supported_iv_BE) = iv in\n let (va_arg29:Prims.nat) = plain_num_bytes in let (va_arg28:(FStar.Seq.Base.seq\n Vale.Def.Words_s.nat8)) = expected_tag in let (va_arg27:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s) inout_b) in let (va_arg26:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s) out128_b) in let (va_arg25:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_old_s) inout_b) in let (va_arg24:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_old_s) in128_b) in let (va_arg23:(FStar.Seq.Base.seq\n Vale.Def.Words_s.nat32)) = key in let (va_arg22:Vale.AES.AES_common_s.algorithm) = alg in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 631 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_BE.gcm_blocks_helper_dec_simplified va_arg22 va_arg23 va_arg24\n va_arg25 va_arg26 va_arg27 auth_bytes va_arg28 va_arg29 va_arg30 va_arg31) (va_QEmpty (())))))))", "val va_codegen_success_Gcm_make_length_quad : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Gcm_make_length_quad () =\n (va_pbool_and (va_codegen_success_ZeroXmm (va_op_xmm_xmm 0)) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and\n (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_pbool_and\n (va_codegen_success_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 1) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_pbool_and\n (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_pbool_and\n (va_codegen_success_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 0) (va_ttrue ()))))))))", "val va_qcode_Check_avx512_xcr0_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_avx512_xcr0_stdcall win))\nlet va_qcode_Check_avx512_xcr0_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_avx512_xcr0_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 188 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_avx512_xcr0_support ()) (va_QEmpty (()))))", "val va_qcode_Msg_shift (va_mods: va_mods_t) : (va_quickCode unit (va_code_Msg_shift ()))\nlet va_qcode_Msg_shift (va_mods:va_mods_t) : (va_quickCode unit (va_code_Msg_shift ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 290 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 291 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 292 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 293 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 4) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 294 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 295 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 5) (va_op_xmm_xmm 0)) (va_QEmpty (())))))))))", "val va_qcode_Fast_sqr_stdcall (va_mods: va_mods_t) (win: bool) (dst_b inA_b: buffer64)\n : (va_quickCode unit (va_code_Fast_sqr_stdcall win))\nlet va_qcode_Fast_sqr_stdcall (va_mods:va_mods_t) (win:bool) (dst_b:buffer64) (inA_b:buffer64) :\n (va_quickCode unit (va_code_Fast_sqr_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (dst_in:(va_int_range 0 18446744073709551615)) = va_if win (fun _ -> va_get_reg64 rRcx va_s)\n (fun _ -> va_get_reg64 rRdi va_s) in let (inA_in:(va_int_range 0 18446744073709551615)) = va_if\n win (fun _ -> va_get_reg64 rRdx va_s) (fun _ -> va_get_reg64 rRsi va_s) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 467 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 468 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 469 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRsi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 470 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR13)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 471 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR14)) (fun (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 476 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 477 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_QEmpty (())))))\n (qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 480 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Fast_sqr 0 dst_b inA_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 482 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 483 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 484 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rRsi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 485 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 486 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR15)) (va_QEmpty (())))))))))))))))", "val va_qcode_Fast_sqr_part1 (va_mods: va_mods_t) (offset: nat) (inA_b: buffer64)\n : (va_quickCode unit (va_code_Fast_sqr_part1 offset))\nlet va_qcode_Fast_sqr_part1 (va_mods:va_mods_t) (offset:nat) (inA_b:buffer64) : (va_quickCode unit\n (va_code_Fast_sqr_part1 offset)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b (0 + offset)\n (va_get_mem_heaplet 0 va_s) in let (a1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read\n inA_b (1 + offset) (va_get_mem_heaplet 0 va_s) in let (a2:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read inA_b (2 + offset) (va_get_mem_heaplet 0 va_s) in let\n (a3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b (3 + offset)\n (va_get_mem_heaplet 0 va_s) in let (a:Prims.nat) = Vale.Curve25519.Fast_defs.pow2_four a0 a1 a2\n a3 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 88 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.xor_lemmas ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 101 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 102 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rRdx)\n (va_op_reg_opr64_reg64 rRsi) (0 + offset `op_Multiply` 8) Secret inA_b (0 + offset)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 103 column 134 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 35) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 103 column 147 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[0]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 105 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 106 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (8 + offset\n `op_Multiply` 8) inA_b (1 + offset) Secret) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 106 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rR14) (va_op_dst_opr64_reg64 rR8) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (8 + offset `op_Multiply` 8) Secret))\n (fun (va_s:va_state) _ -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let\n (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 106 column 122 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.Fast_lemmas_external.lemma_prod_bounds va_arg77 va_arg78 a0\n a1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 106 column 148 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 106 column 158 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Xor64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 106 column 175 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 106 column 187 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[1]*f[0]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 108 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 109 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (16 + offset\n `op_Multiply` 8) inA_b (2 + offset) Secret) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 109 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rR10) (va_op_dst_opr64_reg64 rR9) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (16 + offset `op_Multiply` 8) Secret))\n (fun (va_s:va_state) _ -> let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let\n (va_arg75:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 109 column 123 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.Fast_lemmas_external.lemma_prod_bounds va_arg75 va_arg76 a0\n a2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 109 column 148 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 109 column 163 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 109 column 180 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 109 column 192 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[2]*f[0]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 111 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 112 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (24 + offset\n `op_Multiply` 8) inA_b (3 + offset) Secret) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 112 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rRcx) (va_op_dst_opr64_reg64 rRax) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (24 + offset `op_Multiply` 8) Secret))\n (fun (va_s:va_state) _ -> let (va_arg74:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let\n (va_arg73:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 112 column 124 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.Fast_lemmas_external.lemma_prod_bounds va_arg73 va_arg74 a0\n a3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 112 column 154 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 112 column 168 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 112 column 187 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[3]*f[0]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 114 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 115 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rRdx)\n (va_op_reg_opr64_reg64 rRsi) (24 + offset `op_Multiply` 8) Secret inA_b (3 + offset)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 116 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 34) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 116 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[3]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 119 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (8 + offset\n `op_Multiply` 8) inA_b (1 + offset) Secret) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rRbx) (va_op_dst_opr64_reg64 rR11) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (8 + offset `op_Multiply` 8) Secret))\n (fun (va_s:va_state) _ -> let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_s in let\n (va_arg71:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 119 column 123 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.Fast_lemmas_external.lemma_prod_bounds va_arg71 va_arg72 a3\n a1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 119 column 148 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 119 column 163 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 119 column 182 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[1]*f[3]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (16 + offset\n `op_Multiply` 8) inA_b (2 + offset) Secret) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 122 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rR13) (va_op_dst_opr64_reg64 rRax) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (16 + offset `op_Multiply` 8) Secret))\n (fun (va_s:va_state) _ -> let (va_arg70:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let\n (va_arg69:Vale.Def.Types_s.nat64) = va_get_reg64 rR13 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 122 column 124 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.Fast_lemmas_external.lemma_prod_bounds va_arg69 va_arg70 a3\n a2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 122 column 154 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 122 column 168 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 122 column 187 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[2]*f[3]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 125 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rRdx)\n (va_op_reg_opr64_reg64 rRsi) (8 + offset `op_Multiply` 8) Secret inA_b (1 + offset)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 126 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 9) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 126 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 126 column 44 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f1\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 130 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (16 + offset\n `op_Multiply` 8) inA_b (2 + offset) Secret) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rRcx) (va_op_dst_opr64_reg64 rRax) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) (16 + offset `op_Multiply` 8) Secret))\n (fun (va_s:va_state) _ -> let (va_arg68:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let\n (va_arg67:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 121 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.Fast_lemmas_external.lemma_prod_bounds va_arg67 va_arg68 a1\n a2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 150 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 159 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 174 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 4) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 186 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[2]*f[1]\") (va_QEmpty (()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))", "val va_qcode_Sqr2_stdcall (va_mods: va_mods_t) (win: bool) (dst_b inA_b: buffer64)\n : (va_quickCode unit (va_code_Sqr2_stdcall win))\nlet va_qcode_Sqr2_stdcall (va_mods:va_mods_t) (win:bool) (dst_b:buffer64) (inA_b:buffer64) :\n (va_quickCode unit (va_code_Sqr2_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (dst_in:(va_int_range 0 18446744073709551615)) = va_if win (fun _ -> va_get_reg64 rRcx va_s)\n (fun _ -> va_get_reg64 rRdi va_s) in let (inA_in:(va_int_range 0 18446744073709551615)) = va_if\n win (fun _ -> va_get_reg64 rRdx va_s) (fun _ -> va_get_reg64 rRsi va_s) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 689 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 690 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 691 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR14)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 692 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRbx)) (fun (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 695 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 697 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRsi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 698 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 699 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_QEmpty (()))))))\n (qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 702 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Fast_sqr 0 dst_b inA_b) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 703 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Fast_sqr 4 dst_b inA_b) (fun (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 705 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 707 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rRsi)) (va_QEmpty (())))) (qblock va_mods (fun\n (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 710 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 711 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 712 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 713 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR15)) (va_QEmpty (())))))))))))))))", "val va_qcode_Check_sha_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_sha_support ()))\nlet va_qcode_Check_sha_support (va_mods:va_mods_t) : (va_quickCode unit (va_code_Check_sha_support\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 77 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 79 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 80 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 81 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Sha ()) (fun (va_s:va_state) _ -> let (va_arg11:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 82 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg11 29) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 83 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 536870912)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 84 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (536870912 == Prims.pow2 29)) (fun _ -> (fun (p:prop) -> p)\n (536870912 == Prims.pow2 29)) (fun (_:unit) -> assert_normalize (536870912 == Prims.pow2 29))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 85 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 87 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty (()))))))))))))", "val va_qcode_Check_movbe_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_movbe_support ()))\nlet va_qcode_Check_movbe_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_movbe_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 177 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 179 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 180 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 181 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Movbe ()) (fun (va_s:va_state) _ -> let (va_arg14:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 182 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg14 22) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 183 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 184 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 4194304)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 185 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (4194304 == Prims.pow2 22)) (fun _ -> (fun (p:prop) -> p)\n (4194304 == Prims.pow2 22)) (fun (_:unit) -> assert_normalize (4194304 == Prims.pow2 22))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 187 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 21)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 188 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 1 22) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 189 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 21) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 191 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (())))))))))))))))", "val va_qcode_Gctr_blocks128_1way_while0\n (va_mods: va_mods_t)\n (va_old: va_state)\n (alg: algorithm)\n (va_in_in_b: buffer128)\n (va_in_key: (seq nat32))\n (va_in_keys_b: buffer128)\n (va_in_old_icb: quad32)\n (va_in_old_plain: (seq quad32))\n (va_in_out_b: buffer128)\n (va_in_round_keys: (seq quad32))\n : (va_quickCode unit (va_code_Gctr_blocks128_1way_while0 alg))\nlet va_qcode_Gctr_blocks128_1way_while0 (va_mods:va_mods_t) (va_old:va_state) (alg:algorithm)\n (va_in_in_b:buffer128) (va_in_key:(seq nat32)) (va_in_keys_b:buffer128) (va_in_old_icb:quad32)\n (va_in_old_plain:(seq quad32)) (va_in_out_b:buffer128) (va_in_round_keys:(seq quad32)) :\n (va_quickCode unit (va_code_Gctr_blocks128_1way_while0 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (in_b:buffer128) =\n va_in_in_b in let (key:(seq nat32)) = va_in_key in let (keys_b:buffer128) = va_in_keys_b in let\n (old_icb:quad32) = va_in_old_icb in let (old_plain:(seq quad32)) = va_in_old_plain in let\n (out_b:buffer128) = va_in_out_b in let (round_keys:(seq quad32)) = va_in_round_keys in va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_qWhile va_mods (Cmp_ne (va_op_cmp_reg 8) (va_op_cmp_reg 26)) (fun va_g -> qblock va_mods\n (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Gctr_blocks128_1way_body0 va_old alg in_b key keys_b old_icb old_plain out_b\n round_keys) (va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_get_ok va_s /\\ (0 <= va_get_reg\n 8 va_s /\\ va_get_reg 8 va_s <= va_get_reg 26 va_s) /\\ va_get_reg 9 va_s == 16 `op_Multiply`\n va_get_reg 8 va_s /\\ va_get_vec 7 va_s == Vale.AES.GCTR_BE.inc32lite old_icb (va_get_reg 6 va_s\n + va_get_reg 8 va_s) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrsOffset128 (va_get_mem_heaplet 1 va_s) (va_get_reg 3 va_s) in_b\n (va_get_reg 6 va_s) (va_get_reg 26 va_s) (va_get_mem_layout va_s) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrsOffset128 (va_get_mem_heaplet 1 va_s) (va_get_reg 7 va_s) out_b\n (va_get_reg 6 va_s) (va_get_reg 26 va_s) (va_get_mem_layout va_s) Secret /\\ va_get_reg 3 va_s +\n 16 `op_Multiply` va_get_reg 26 va_s < pow2_64 /\\ va_get_reg 7 va_s + 16 `op_Multiply`\n va_get_reg 26 va_s < pow2_64 /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128\n in_b == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b /\\ (va_get_reg 8\n va_s =!= va_get_reg 26 va_s ==> Vale.AES.GCTR_BE.partial_seq_agreement old_plain\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n in_b)) (va_get_reg 6 va_s + va_get_reg 8 va_s) (Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 in_b)) /\\ va_get_reg 6 va_s + va_get_reg 26 va_s < pow2_32 /\\\n aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s) (va_get_mem_heaplet 0 va_s)\n (va_get_mem_layout va_s) /\\ va_get_vec 3 va_s == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 1 0 0 0 /\\ Vale.PPC64LE.Decls.modifies_buffer128 out_b\n (va_get_mem_heaplet 1 va_old) (va_get_mem_heaplet 1 va_s) /\\ Vale.AES.GCTR_BE.gctr_partial_def\n alg (va_get_reg 6 va_s + va_get_reg 8 va_s) old_plain (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s) out_b)) key old_icb /\\ (va_get_reg 6 va_s\n + va_get_reg 26 va_s == 0 ==> Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_old) out_b)) (fun (va_s:va_state) va_g ->\n va_get_reg 26 va_s - va_get_reg 8 va_s) (())) (fun (va_s:va_state) va_g -> let va_g = () in\n va_QEmpty (()))))", "val va_qcode_Compute_Y0 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Compute_Y0 ()))\nlet va_qcode_Compute_Y0 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Compute_Y0 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 83 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 1)) (fun (va_s:va_state) _ -> va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 84 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_quad32_xor ()) (va_QEmpty (())))))", "val va_qcode_Fsqr (va_mods: va_mods_t) (tmp_b inA_b dst_b: buffer64)\n : (va_quickCode unit (va_code_Fsqr ()))\nlet va_qcode_Fsqr (va_mods:va_mods_t) (tmp_b:buffer64) (inA_b:buffer64) (dst_b:buffer64) :\n (va_quickCode unit (va_code_Fsqr ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (tmp_in:nat64) =\n va_get_reg64 rRdi va_s in let (inA_in:nat64) = va_get_reg64 rRsi va_s in let (dst_in:nat64) =\n va_get_reg64 rR12 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 541 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_CreateHeaplets ([declare_buffer64 inA_b 0 Secret Immutable; declare_buffer64 dst_b 0\n Secret Mutable; declare_buffer64 tmp_b 0 Secret Mutable])) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 546 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_LargeComment\n \"Compute the raw multiplication: tmp <- f * f\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 547 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Fast_sqr 0 tmp_b inA_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 549 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 550 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Comment\n \"Line up pointers\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 551 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 552 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 554 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_LargeComment\n \"Wrap the result back into the field\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 555 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Carry_wide 0 dst_b tmp_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 557 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_DestroyHeaplets ()) (va_QEmpty (())))))))))))))", "val va_qcode_Loop_rounds_13_15 (va_mods: va_mods_t) (block: block_w)\n : (va_quickCode unit (va_code_Loop_rounds_13_15 ()))\nlet va_qcode_Loop_rounds_13_15 (va_mods:va_mods_t) (block:block_w) : (va_quickCode unit\n (va_code_Loop_rounds_13_15 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 638 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 13 (va_op_vec_opr_vec 13) (va_op_vec_opr_vec 12) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 639 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 14 (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 12) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 640 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 15 (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 12) block)\n (va_QEmpty (()))))))", "val va_qcode_Gctr_register\n (va_mods: va_mods_t)\n (alg: algorithm)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n : (va_quickCode unit (va_code_Gctr_register alg))\nlet va_qcode_Gctr_register (va_mods:va_mods_t) (alg:algorithm) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) : (va_quickCode unit (va_code_Gctr_register alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 141 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (Vale.AES.GCTR_s.inc32 (va_get_xmm 0 va_s) 0 == va_get_xmm 0 va_s) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 142 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 143 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_AESEncryptBlock alg (va_get_xmm 0 va_s) key round_keys keys_b) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 144 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.AES_s.aes_encrypt_LE_reveal ()) (va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 145 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n ((fun (alg_10639:Vale.AES.AES_common_s.algorithm) (key_10640:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat32)) (input_LE_10641:Vale.Def.Types_s.quad32) ->\n Vale.AES.AES_s.is_aes_key_LE alg_10639 key_10640) alg key\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 0 va_old_s))) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 145 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_xmm 0 va_s == Vale.AES.AES_s.aes_encrypt_LE alg key\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 0 va_old_s))) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 147 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 8) (va_op_xmm_xmm 9)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 148 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 8) (va_op_xmm_xmm 0)) (fun (va_s:va_state) _ -> let\n (va_arg18:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg17:Vale.AES.AES_common_s.algorithm) = alg in let (va_arg16:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_old_s) in let\n (va_arg15:Vale.Def.Types_s.quad32) = va_get_xmm 0 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 152 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.gctr_encrypt_one_block va_arg15 va_arg16 va_arg17 va_arg18)\n (va_QEmpty (()))))))))))))", "val va_qcode_Gctr_register\n (va_mods: va_mods_t)\n (alg: algorithm)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n : (va_quickCode unit (va_code_Gctr_register alg))\nlet va_qcode_Gctr_register (va_mods:va_mods_t) (alg:algorithm) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) : (va_quickCode unit (va_code_Gctr_register alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 118 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (Vale.AES.GCTR_s.inc32 (va_get_xmm 7 va_s) 0 == va_get_xmm 7 va_s) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 120 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_InitPshufbMask (va_op_xmm_xmm 2) (va_op_reg_opr64_reg64 rR12)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 121 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 2)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 122 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_AESEncryptBlock alg (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 7 va_s)) key\n round_keys keys_b) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 123 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.AES_s.aes_encrypt_LE_reveal ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 126 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (fun (va_s:va_state) _ -> va_qAssert\n va_range1\n \"***** PRECONDITION NOT MET AT line 128 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_get_xmm 1 va_s == Vale.Def.Types_s.quad32_xor (va_get_xmm 1 va_old_s) (va_get_xmm 0 va_s))\n (let (va_arg16:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg15:Vale.AES.AES_common_s.algorithm) = alg in let (va_arg14:Vale.Def.Types_s.quad32) =\n va_get_xmm 1 va_old_s in let (va_arg13:Vale.Def.Types_s.quad32) = va_get_xmm 7 va_s in va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.gctr_encrypt_one_block va_arg13 va_arg14 va_arg15 va_arg16)\n (va_QEmpty (()))))))))))))", "val va_qcode_Gctr_register\n (va_mods: va_mods_t)\n (alg: algorithm)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n : (va_quickCode unit (va_code_Gctr_register alg))\nlet va_qcode_Gctr_register (va_mods:va_mods_t) (alg:algorithm) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) : (va_quickCode unit (va_code_Gctr_register alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 99 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (Vale.AES.GCTR_BE_s.inc32 (va_get_vec 7 va_s) 0 == va_get_vec 7 va_s) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 100 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 7)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 101 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AESEncryptBlock alg (va_get_vec 7 va_s) key round_keys keys_b) (fun (va_s:va_state) _\n -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 102 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n ((fun (alg_10591:Vale.AES.AES_common_s.algorithm) (key_10592:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat32)) (input_10593:Vale.Def.Types_s.quad32) ->\n Vale.AES.AES_BE_s.is_aes_key_word alg_10591 key_10592) alg key (va_get_vec 7 va_s)) (fun _ ->\n va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 102 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_get_vec 0 va_s == Vale.AES.AES_BE_s.aes_encrypt_word alg key (va_get_vec 7 va_s)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 104 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vxor (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 0)) (fun\n (va_s:va_state) _ -> let (va_arg15:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg14:Vale.AES.AES_common_s.algorithm) = alg in let (va_arg13:Vale.Def.Types_s.quad32) =\n va_get_vec 1 va_old_s in let (va_arg12:Vale.Def.Types_s.quad32) = va_get_vec 7 va_s in va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 107 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR_BE.gctr_encrypt_one_block va_arg12 va_arg13 va_arg14 va_arg15)\n (va_QEmpty (()))))))))))", "val va_qcode_ShiftLeft128_1 (va_mods: va_mods_t) (a: poly)\n : (va_quickCode unit (va_code_ShiftLeft128_1 ()))\nlet va_qcode_ShiftLeft128_1 (va_mods:va_mods_t) (a:poly) : (va_quickCode unit\n (va_code_ShiftLeft128_1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 60 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Vspltisb (va_op_vec_opr_vec 2) 1) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 61 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Vsl (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2)) (fun\n (va_s:va_state) _ -> let (va_arg5:Vale.Math.Poly2_s.poly) = a in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 63 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_shift_left_1 va_arg5) (va_QEmpty (()))))))", "val va_qcode_ShiftLeft128_1 (va_mods: va_mods_t) (a: poly)\n : (va_quickCode unit (va_code_ShiftLeft128_1 ()))\nlet va_qcode_ShiftLeft128_1 (va_mods:va_mods_t) (a:poly) : (va_quickCode unit\n (va_code_ShiftLeft128_1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 59 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 60 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Psrld (va_op_xmm_xmm 2) 31) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 61 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pslld (va_op_xmm_xmm 1) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 62 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_VPslldq4 (va_op_xmm_xmm 2) (va_op_xmm_xmm 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 63 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (fun (va_s:va_state) _ -> let\n (va_arg8:Vale.Math.Poly2_s.poly) = a in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 65 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_shift_left_1 va_arg8) (va_QEmpty (())))))))))", "val va_qcode_Check_avx2_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_avx2_stdcall win))\nlet va_qcode_Check_avx2_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_avx2_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 94 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_avx2_support ()) (va_QEmpty (()))))", "val va_qcode_Loop_rounds_60_63_a (va_mods: va_mods_t) (block: block_w)\n : (va_quickCode unit (va_code_Loop_rounds_60_63_a ()))\nlet va_qcode_Loop_rounds_60_63_a (va_mods:va_mods_t) (block:block_w) : (va_quickCode unit\n (va_code_Loop_rounds_60_63_a ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 782 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_16_63_body 61 (va_op_vec_opr_vec 13) (va_op_vec_opr_vec 14)\n (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 11) block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 783 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_16_63_body 62 (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 15)\n (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 12) block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 784 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_16_63_body 63 (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 8) (va_op_vec_opr_vec 13) block) (va_QEmpty (()))))))", "val va_qcode_Gctr_blocks128_while0\n (va_mods: va_mods_t)\n (va_old: va_state)\n (alg: algorithm)\n (va_in_in_b: buffer128)\n (va_in_key: (seq nat32))\n (va_in_keys_b va_in_out_b: buffer128)\n (va_in_plain_quads va_in_round_keys: (seq quad32))\n : (va_quickCode unit (va_code_Gctr_blocks128_while0 alg))\nlet va_qcode_Gctr_blocks128_while0 (va_mods:va_mods_t) (va_old:va_state) (alg:algorithm)\n (va_in_in_b:buffer128) (va_in_key:(seq nat32)) (va_in_keys_b:buffer128) (va_in_out_b:buffer128)\n (va_in_plain_quads:(seq quad32)) (va_in_round_keys:(seq quad32)) : (va_quickCode unit\n (va_code_Gctr_blocks128_while0 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (in_b:buffer128) =\n va_in_in_b in let (key:(seq nat32)) = va_in_key in let (keys_b:buffer128) = va_in_keys_b in let\n (out_b:buffer128) = va_in_out_b in let (plain_quads:(seq quad32)) = va_in_plain_quads in let\n (round_keys:(seq quad32)) = va_in_round_keys in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 155 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rRbx) (va_op_cmp_reg64 rRdx)) (fun va_g -> qblock\n va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 155 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Gctr_blocks128_body0 va_old alg in_b key keys_b out_b plain_quads round_keys)\n (va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_get_ok va_s /\\ sse_enabled /\\ (0 <=\n va_get_reg64 rRbx va_s /\\ va_get_reg64 rRbx va_s <= va_get_reg64 rRdx va_s) /\\ va_get_reg64\n rR11 va_s == va_get_reg64 rRax va_s + 16 `op_Multiply` va_get_reg64 rRbx va_s /\\ va_get_reg64\n rR10 va_s == va_get_reg64 rRdi va_s + 16 `op_Multiply` va_get_reg64 rRbx va_s /\\ va_get_xmm 11\n va_s == Vale.AES.GCTR.inc32lite (va_get_xmm 11 va_old) (va_get_reg64 rRbx va_s) /\\\n (Vale.X64.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRax va_s) in_b\n (va_get_reg64 rRdx va_s) (va_get_mem_layout va_s) Secret /\\ Vale.X64.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) out_b (va_get_reg64 rRdx va_s)\n (va_get_mem_layout va_s) Secret /\\ va_get_reg64 rRax va_s + 16 `op_Multiply` va_get_reg64 rRdx\n va_s < pow2_64 /\\ va_get_reg64 rRdi va_s + 16 `op_Multiply` va_get_reg64 rRdx va_s < pow2_64 /\\\n Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b == Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 out_b /\\ (va_get_reg64 rRbx va_s =!= va_get_reg64 rRdx va_s ==>\n Vale.AES.GCTR.partial_seq_agreement plain_quads (Vale.X64.Decls.s128 (va_get_mem_heaplet 1\n va_s) in_b) (va_get_reg64 rRbx va_s) (Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128\n in_b)) /\\ va_get_reg64 rRdx va_s < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg64\n rR8 va_s) (va_get_mem_heaplet 0 va_s) (va_get_mem_layout va_s) /\\ pclmulqdq_enabled /\\\n va_get_xmm 9 va_s == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 202182159 134810123\n 67438087 66051 /\\ va_get_xmm 10 va_s == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0\n /\\ Vale.X64.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_old) (va_get_mem_heaplet 1\n va_s) /\\ Vale.AES.GCTR.gctr_partial_def alg (va_get_reg64 rRbx va_s) plain_quads\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out_b) key (va_get_xmm 11 va_old) /\\\n (va_get_reg64 rRdx va_s == 0 ==> Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out_b ==\n Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_old) out_b)) (fun (va_s:va_state) va_g ->\n va_get_reg64 rRdx va_s - va_get_reg64 rRbx va_s) (())) (fun (va_s:va_state) va_g -> let va_g =\n () in va_QEmpty (()))))", "val va_qcode_Fsqr2 (va_mods: va_mods_t) (tmp_b inA_b dst_b: buffer64)\n : (va_quickCode unit (va_code_Fsqr2 ()))\nlet va_qcode_Fsqr2 (va_mods:va_mods_t) (tmp_b:buffer64) (inA_b:buffer64) (dst_b:buffer64) :\n (va_quickCode unit (va_code_Fsqr2 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (tmp_in:nat64) =\n va_get_reg64 rRdi va_s in let (inA_in:nat64) = va_get_reg64 rRsi va_s in let (dst_in:nat64) =\n va_get_reg64 rR12 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 727 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_CreateHeaplets ([declare_buffer64 inA_b 0 Secret Immutable; declare_buffer64 dst_b 0\n Secret Mutable; declare_buffer64 tmp_b 0 Secret Mutable])) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 732 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Fast_sqr 0 tmp_b inA_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 733 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 734 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Fast_sqr 4 tmp_b inA_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 735 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 736 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Comment\n \"Line up pointers\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 737 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 738 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 739 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 740 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Carry_wide 0 dst_b tmp_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 741 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 742 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Carry_wide 4 dst_b tmp_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 744 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_DestroyHeaplets ()) (va_QEmpty (()))))))))))))))))", "val va_qcode_Check_avx_xcr0_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_avx_xcr0_stdcall win))\nlet va_qcode_Check_avx_xcr0_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_avx_xcr0_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 173 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_avx_xcr0_support ()) (va_QEmpty (()))))", "val va_qcode_Save_registers (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Save_registers win))\nlet va_qcode_Save_registers (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Save_registers win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1447 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1448 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1449 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1450 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1451 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rRsi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1452 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rRdi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1453 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rRbp)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1454 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rRbx)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 1456 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1457 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 15) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1458 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 14) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1459 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 13) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1460 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 12) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1461 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 11) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1462 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 10) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1463 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 9) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1464 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 8) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1465 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 7) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1466 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 6) (va_op_reg_opr64_reg64 rRax)) (va_QEmpty\n (()))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state)\n va_g -> va_QEmpty (()))))))))))))", "val va_qcode_Check_avx512_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_avx512_stdcall win))\nlet va_qcode_Check_avx512_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_avx512_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 146 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_avx512_support ()) (va_QEmpty (()))))", "val va_qcode_Init_ctr (va_mods: va_mods_t) : (va_quickCode unit (va_code_Init_ctr ()))\nlet va_qcode_Init_ctr (va_mods:va_mods_t) : (va_quickCode unit (va_code_Init_ctr ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 71 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 4) (va_op_xmm_xmm 4)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 72 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_PinsrdImm (va_op_xmm_xmm 4) 1 0 (va_op_reg_opr64_reg64 rR12)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 74 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_quad32_xor ()) (va_QEmpty (()))))))", "val va_qcode_Loop_rounds_16_59_a (va_mods: va_mods_t) (i: nat) (block: block_w)\n : (va_quickCode unit (va_code_Loop_rounds_16_59_a i))\nlet va_qcode_Loop_rounds_16_59_a (va_mods:va_mods_t) (i:nat) (block:block_w) : (va_quickCode unit\n (va_code_Loop_rounds_16_59_a i)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 667 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_16_63_body (i + 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 10) (va_op_vec_opr_vec 15) block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 668 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_16_63_body (i + 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 3)\n (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 0) block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 669 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_16_63_body (i + 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)\n (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 1) block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 670 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_16_63_body (i + 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 5)\n (va_op_vec_opr_vec 13) (va_op_vec_opr_vec 2) block) (va_QEmpty (())))))))", "val va_quick_mod_6: Prims.unit -> (va_quickCode unit (va_code_mod_6 ()))\nlet va_quick_mod_6 () : (va_quickCode unit (va_code_mod_6 ())) =\n (va_QProc (va_code_mod_6 ()) ([va_Mod_reg 10; va_Mod_reg 26]) va_wp_mod_6 va_wpProof_mod_6)", "val va_qcode_Fast_sqr_part3 (va_mods: va_mods_t) (offset: nat) (dst_b inA_b: buffer64)\n : (va_quickCode unit (va_code_Fast_sqr_part3 offset))\nlet va_qcode_Fast_sqr_part3 (va_mods:va_mods_t) (offset:nat) (dst_b:buffer64) (inA_b:buffer64) :\n (va_quickCode unit (va_code_Fast_sqr_part3 offset)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b (0 + offset)\n (va_get_mem_heaplet 0 va_s) in let (a1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read\n inA_b (1 + offset) (va_get_mem_heaplet 0 va_s) in let (a2:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read inA_b (2 + offset) (va_get_mem_heaplet 0 va_s) in let\n (a3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b (3 + offset)\n (va_get_mem_heaplet 0 va_s) in let (a:Prims.nat) = Vale.Curve25519.Fast_defs.pow2_four a0 a1 a2\n a3 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 251 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.xor_lemmas ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 266 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 267 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rRdx)\n (va_op_reg_opr64_reg64 rRsi) (0 + offset `op_Multiply` 8) Secret inA_b (0 + offset)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 267 column 89 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 267 column 101 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rRcx) (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64\n rRdx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 267 column 140 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[0]^2\"\n ) (fun (va_s:va_state) _ -> let (a0_sqr_hi:nat64) = va_get_reg64 rRcx va_s in let\n (a0_sqr_lo:nat64) = va_get_reg64 rRax va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 269 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 27) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 269 column 72 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRax) (0 + offset `op_Multiply` 16) Secret dst_b (0 + offset\n `op_Multiply` 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 270 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 271 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 272 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 272 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 272 column 72 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR8) (8 + offset `op_Multiply` 16) Secret dst_b (1 + offset\n `op_Multiply` 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 273 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 274 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rRdx)\n (va_op_reg_opr64_reg64 rRsi) (8 + offset `op_Multiply` 8) Secret inA_b (1 + offset)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 101 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rRcx) (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64\n rRdx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 139 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[1]^2\"\n ) (fun (va_s:va_state) _ -> let (a1_sqr_hi:nat64) = va_get_reg64 rRcx va_s in let\n (a1_sqr_lo:nat64) = va_get_reg64 rRax va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 277 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 72 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR9) (16 + offset `op_Multiply` 16) Secret dst_b (2 + offset\n `op_Multiply` 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 279 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 280 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 281 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 281 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 281 column 73 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR10) (24 + offset `op_Multiply` 16) Secret dst_b (3 + offset\n `op_Multiply` 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 282 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 283 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 284 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rRdx)\n (va_op_reg_opr64_reg64 rRsi) (16 + offset `op_Multiply` 8) Secret inA_b (2 + offset)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 284 column 94 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 284 column 106 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rRcx) (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64\n rRdx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 284 column 144 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[2]^2\"\n ) (fun (va_s:va_state) _ -> let (a2_sqr_hi:nat64) = va_get_reg64 rRcx va_s in let\n (a2_sqr_lo:nat64) = va_get_reg64 rRax va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 286 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 287 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 287 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 287 column 72 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR11) (32 + offset `op_Multiply` 16) Secret dst_b (4 + offset\n `op_Multiply` 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 288 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 289 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 290 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 290 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 290 column 72 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRbx) (40 + offset `op_Multiply` 16) Secret dst_b (5 + offset\n `op_Multiply` 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 291 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 292 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 293 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rRdx)\n (va_op_reg_opr64_reg64 rRsi) (24 + offset `op_Multiply` 8) Secret inA_b (3 + offset)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 293 column 94 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 293 column 105 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rRcx) (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64\n rRdx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 293 column 144 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Comment\n \"f[3]^2\"\n ) (fun (va_s:va_state) _ -> let (va_arg105:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in\n let (va_arg104:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let\n (va_arg103:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let\n (va_arg102:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 294 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.Fast_lemmas_external.lemma_prod_bounds va_arg102 va_arg103\n va_arg104 va_arg105) (let (a3_sqr_hi:nat64) = va_get_reg64 rRcx va_s in let (a3_sqr_lo:nat64) =\n va_get_reg64 rRax va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 296 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 297 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 297 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 297 column 72 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR13) (48 + offset `op_Multiply` 16) Secret dst_b (6 + offset\n `op_Multiply` 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 298 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 299 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_NoNewline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 300 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 300 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Space 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 300 column 72 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR14) (56 + offset `op_Multiply` 16) Secret dst_b (7 + offset\n `op_Multiply` 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 301 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Newline ()) (fun (va_s:va_state) _ -> let (va_arg101:Vale.Curve25519.Fast_defs.bit) =\n Vale.Curve25519.Fast_defs.bool_bit (Vale.X64.Decls.cf (va_get_flags va_s)) in let\n (va_arg100:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read dst_b (7 + offset\n `op_Multiply` 2) (va_get_mem_heaplet 0 va_s) in let (va_arg99:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read dst_b (6 + offset `op_Multiply` 2) (va_get_mem_heaplet 0 va_s) in\n let (va_arg98:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read dst_b (5 + offset\n `op_Multiply` 2) (va_get_mem_heaplet 0 va_s) in let (va_arg97:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read dst_b (4 + offset `op_Multiply` 2) (va_get_mem_heaplet 0 va_s) in\n let (va_arg96:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read dst_b (3 + offset\n `op_Multiply` 2) (va_get_mem_heaplet 0 va_s) in let (va_arg95:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read dst_b (2 + offset `op_Multiply` 2) (va_get_mem_heaplet 0 va_s) in\n let (va_arg94:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read dst_b (1 + offset\n `op_Multiply` 2) (va_get_mem_heaplet 0 va_s) in let (va_arg93:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read dst_b (0 + offset `op_Multiply` 2) (va_get_mem_heaplet 0 va_s) in\n let (va_arg92:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let\n (va_arg91:Vale.Def.Types_s.nat64) = va_get_reg64 rR13 va_old_s in let\n (va_arg90:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let\n (va_arg89:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_old_s in let\n (va_arg88:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_old_s in let\n (va_arg87:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_old_s in let\n (va_arg86:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_old_s in let\n (va_arg85:Vale.Def.Types_s.nat64) = a3_sqr_lo in let (va_arg84:Vale.Def.Types_s.nat64) =\n a3_sqr_hi in let (va_arg83:Vale.Def.Types_s.nat64) = a2_sqr_lo in let\n (va_arg82:Vale.Def.Types_s.nat64) = a2_sqr_hi in let (va_arg81:Vale.Def.Types_s.nat64) =\n a1_sqr_lo in let (va_arg80:Vale.Def.Types_s.nat64) = a1_sqr_hi in let\n (va_arg79:Vale.Def.Types_s.nat64) = a0_sqr_lo in let (va_arg78:Vale.Def.Types_s.nat64) =\n a0_sqr_hi in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 303 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.FastSqr_helpers.lemma_sqr_part3 a a0 a1 a2 a3 va_arg78\n va_arg79 va_arg80 va_arg81 va_arg82 va_arg83 va_arg84 va_arg85 va_arg86 va_arg87 va_arg88\n va_arg89 va_arg90 va_arg91 va_arg92 va_arg93 va_arg94 va_arg95 va_arg96 va_arg97 va_arg98\n va_arg99 va_arg100 va_arg101) (va_QEmpty\n (()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))", "val va_qcode_Gctr_bytes\n (va_mods: va_mods_t)\n (alg: algorithm)\n (in_b out_b inout_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n : (va_quickCode unit (va_code_Gctr_bytes alg))\nlet va_qcode_Gctr_bytes (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) :\n (va_quickCode unit (va_code_Gctr_bytes alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 576 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 577 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 16)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 578 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Gctr_core_opt alg in_b out_b key round_keys keys_b) (fun (va_s:va_state) _ ->\n va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 579 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (Vale.AES.GCTR.gctr_partial_def alg (va_get_reg64 rRcx va_old_s) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 0 va_s) in_b) (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out_b) key\n (va_get_xmm 7 va_old_s)) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 580 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_get_xmm 7 va_s == Vale.AES.GCTR_s.inc32 (va_get_xmm 7 va_old_s) (va_get_reg64 rRcx\n va_old_s)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 582 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Gctr_bytes_no_extra alg (va_get_xmm 7 va_old_s) in_b out_b key round_keys keys_b\n (va_get_reg64 rRax va_old_s) (va_get_reg64 rRbx va_old_s) (va_get_reg64 rRcx va_old_s\n `op_Multiply` 16)) (fun (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 584 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_qIf va_mods (Cmp_gt (va_op_cmp_reg64 rRsi) (va_op_cmp_reg64 rRbp)) (qblock va_mods (fun\n (va_s:va_state) -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 586 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 2) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64\n rR13) 0 Secret inout_b 0) (fun (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 587 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (FStar.Seq.Base.equal #quad32 (FStar.Seq.Base.create #quad32 1 (va_get_xmm 1 va_s))\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 2 va_s) inout_b)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 588 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Gctr_register alg key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 589 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Store128_buffer (va_op_heaplet_mem_heaplet 2) (va_op_reg_opr64_reg64 rR13)\n (va_op_xmm_xmm 1) 0 Secret inout_b 0) (va_QEmpty (()))))))) (qblock va_mods (fun\n (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g -> let\n (va_arg31:Vale.Def.Types_s.quad32) = va_get_xmm 7 va_old_s in let (va_arg30:Prims.nat) =\n va_get_reg64 rRsi va_old_s in let (va_arg29:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.X64.Decls.s128 (va_get_mem_heaplet 2 va_s) inout_b in let (va_arg28:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s) out_b in let\n (va_arg27:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128\n (va_get_mem_heaplet 2 va_old_s) inout_b in let (va_arg26:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 0 va_old_s) in_b in let\n (va_arg25:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg24:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 591 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.gctr_bytes_helper va_arg24 va_arg25 va_arg26 va_arg27 va_arg28\n va_arg29 va_arg30 va_arg31) (va_QEmpty (())))))))))))", "val va_qcode_Loop_rounds_0_15 (va_mods: va_mods_t) (in_b k_b: buffer128) (offset: nat)\n : (va_quickCode unit (va_code_Loop_rounds_0_15 ()))\nlet va_qcode_Loop_rounds_0_15 (va_mods:va_mods_t) (in_b:buffer128) (k_b:buffer128) (offset:nat) :\n (va_quickCode unit (va_code_Loop_rounds_0_15 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qAssertSquash\n va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 146 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.X64.Decls.quad32 (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s) in_b) offset\n (offset + 4)) (fun _ -> let (input_LE:(FStar.Seq.Base.seq Vale.X64.Decls.quad32)) =\n FStar.Seq.Base.slice #Vale.X64.Decls.quad32 (Vale.X64.Decls.buffer128_as_seq\n (va_get_mem_heaplet 0 va_s) in_b) offset (offset + 4) in let (input_BE:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_nat32_quad32_seq input_LE in let\n (block:block_w) = Vale.SHA.SHA_helpers.quads_to_block input_BE in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 149 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (fun (_:unit) -> Vale.SHA.SHA_helpers.lemma_quads_to_block input_BE) (let\n (hash_orig:Vale.SHA.SHA_helpers.hash256) = Vale.SHA.SHA_helpers.make_hash (va_get_xmm 1 va_s)\n (va_get_xmm 2 va_s) in let (va_arg79:Vale.SHA.SHA_helpers.block_w) = block in va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 153 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (fun (_:unit) -> Vale.SHA.SHA_helpers.lemma_repeat_range_0_vale va_arg79 hash_orig) (let\n (ks:(FStar.Seq.Base.seq Vale.X64.Decls.quad32)) = Vale.X64.Decls.buffer128_as_seq\n (va_get_mem_heaplet 0 va_s) k_b in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 158 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 3) (va_op_reg_opr64_reg64\n rRsi) 0 Secret in_b (offset + 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 159 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 4) (va_op_reg_opr64_reg64\n rRsi) 16 Secret in_b (offset + 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 160 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 5) (va_op_reg_opr64_reg64\n rRsi) 32 Secret in_b (offset + 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 161 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_PshufbStable (va_op_xmm_xmm 3) (va_op_xmm_xmm 7)) (fun (va_s:va_state) _ ->\n va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 162 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.Def.Types_s.quad32 input_BE 0) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 162 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 3 va_s == FStar.Seq.Base.index #Vale.Def.Types_s.quad32 input_BE 0) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 163 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 6) (va_op_reg_opr64_reg64\n rRsi) 48 Secret in_b (offset + 3)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 165 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRcx) 0 Secret k_b 0) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 166 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.X64.Decls.quad32 ks 0) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 166 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 0 va_s == FStar.Seq.Base.index #Vale.X64.Decls.quad32 ks 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 3)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 169 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_PshufbStable (va_op_xmm_xmm 4) (va_op_xmm_xmm 7)) (fun (va_s:va_state) _ ->\n va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 170 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.Def.Types_s.quad32 input_BE 1) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 170 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 4 va_s == FStar.Seq.Base.index #Vale.Def.Types_s.quad32 input_BE 1) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 10) (va_op_xmm_xmm 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 174 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1) 0 block hash_orig) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 175 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 176 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 9) (va_op_xmm_xmm 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 177 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) 2 block hash_orig) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 180 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRcx) 16 Secret k_b 1) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 181 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.X64.Decls.quad32 ks 1) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 181 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 0 va_s == FStar.Seq.Base.index #Vale.X64.Decls.quad32 ks 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 182 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 4)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 183 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_PshufbStable (va_op_xmm_xmm 5) (va_op_xmm_xmm 7)) (fun (va_s:va_state) _ ->\n va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 184 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.Def.Types_s.quad32 input_BE 2) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 184 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 5 va_s == FStar.Seq.Base.index #Vale.Def.Types_s.quad32 input_BE 2) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 185 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1) 4 block hash_orig) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 186 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 187 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rRsi) (va_const_opr64 64)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 188 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_msg1 (va_op_xmm_xmm 3) (va_op_xmm_xmm 4) 16 block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 189 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) 6 block hash_orig) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 192 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRcx) 32 Secret k_b 2) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 193 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.X64.Decls.quad32 ks 2) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 193 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 0 va_s == FStar.Seq.Base.index #Vale.X64.Decls.quad32 ks 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 194 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 5)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 195 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_PshufbStable (va_op_xmm_xmm 6) (va_op_xmm_xmm 7)) (fun (va_s:va_state) _ ->\n va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 196 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.Def.Types_s.quad32 input_BE 3) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 196 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 6 va_s == FStar.Seq.Base.index #Vale.Def.Types_s.quad32 input_BE 3) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 197 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1) 8 block hash_orig) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 198 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 199 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Palignr4 (va_op_xmm_xmm 7) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 201 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 3) (va_op_xmm_xmm 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 202 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_msg1 (va_op_xmm_xmm 4) (va_op_xmm_xmm 5) 20 block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 203 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) 10 block hash_orig) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 206 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRcx) 48 Secret k_b 3) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 207 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.X64.Decls.quad32 ks 3) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 207 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 0 va_s == FStar.Seq.Base.index #Vale.X64.Decls.quad32 ks 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 208 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 209 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_msg2 (va_op_xmm_xmm 3) (va_op_xmm_xmm 6) 16 block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 210 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1) 12 block hash_orig) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 211 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 212 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 213 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Palignr4 (va_op_xmm_xmm 7) (va_op_xmm_xmm 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 214 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 4) (va_op_xmm_xmm 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 215 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_msg1 (va_op_xmm_xmm 5) (va_op_xmm_xmm 6) 24 block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 216 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) 14 block hash_orig) (va_QEmpty\n (())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))", "val va_qcode_Gctr_blocks128_1way\n (va_mods: va_mods_t)\n (alg: algorithm)\n (in_b out_b: buffer128)\n (old_icb: quad32)\n (old_plain: (seq quad32))\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n : (va_quickCode unit (va_code_Gctr_blocks128_1way alg))\nlet va_qcode_Gctr_blocks128_1way (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128)\n (out_b:buffer128) (old_icb:quad32) (old_plain:(seq quad32)) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) : (va_quickCode unit (va_code_Gctr_blocks128_1way alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 219 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 3) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 220 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 4) 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 221 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 3) 4) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 223 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 8) 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 224 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 9) 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 226 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Gctr_blocks128_1way_while0 va_old_s alg in_b key keys_b old_icb old_plain out_b\n round_keys) (va_QEmpty (())))))))))", "val va_qcode_Gctr_blocks128_6way\n (va_mods: va_mods_t)\n (alg: algorithm)\n (in_b out_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n : (va_quickCode unit (va_code_Gctr_blocks128_6way alg))\nlet va_qcode_Gctr_blocks128_6way (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128)\n (out_b:buffer128) (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) : (va_quickCode\n unit (va_code_Gctr_blocks128_6way alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 479 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 8) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 480 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 9) 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 481 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 10) 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 482 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 11) 4) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 483 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 12) 5) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 484 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 13) 6) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 485 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 14) 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 486 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 8) (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 8) 4) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 487 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 9) (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 9) 4) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 488 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 10) (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 10) 4)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 489 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 11) 4)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 490 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 12) 4)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 491 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 13) (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 13) 4)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 493 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 27) (1 `op_Multiply` 16)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 494 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 28) (2 `op_Multiply` 16)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 29) (3 `op_Multiply` 16)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 30) (4 `op_Multiply` 16)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 31) (5 `op_Multiply` 16)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 499 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 8) 0) (fun (va_s:va_state) _ -> let (plain_quads:(seq\n quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s) in_b) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 503 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Gctr_blocks128_6way_while0 va_old_s alg in_b key keys_b out_b plain_quads round_keys)\n (va_QEmpty (())))))))))))))))))))))))", "val va_qcode_ClmulRev64High (va_mods: va_mods_t) (a b: poly)\n : (va_quickCode unit (va_code_ClmulRev64High ()))\nlet va_qcode_ClmulRev64High (va_mods:va_mods_t) (a:poly) (b:poly) : (va_quickCode unit\n (va_code_ClmulRev64High ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (va_arg18:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_s) in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 116 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_quad32_double va_arg18) (let\n (va_arg17:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 2 va_s) in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 117 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_quad32_double va_arg17) (let\n (va_arg16:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_s) in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 118 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_mask_is_mod va_arg16 64) (let\n (va_arg15:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 2 va_s) in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 119 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_mask_is_mod va_arg15 64) (let\n (va_arg14:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_s) in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 120 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_shift_is_div va_arg14 64) (let\n (va_arg13:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 2 va_s) in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 121 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_shift_is_div va_arg13 64) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 122 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_VPolyMulHigh (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 123 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_ShiftLeft128_1 (Vale.Math.Poly2_s.mul (Vale.Math.Poly2_s.reverse a 63)\n (Vale.Math.Poly2_s.reverse b 63))) (fun (va_s:va_state) _ -> let\n (va_arg12:Vale.Math.Poly2_s.poly) = b in let (va_arg11:Vale.Math.Poly2_s.poly) = a in va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 125 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_mul_reverse_shift_1 va_arg11 va_arg12 63)\n (va_QEmpty (()))))))))))))", "val va_qcode_ReduceMul128_LE (va_mods: va_mods_t) (a b: poly)\n : (va_quickCode unit (va_code_ReduceMul128_LE ()))\nlet va_qcode_ReduceMul128_LE (va_mods:va_mods_t) (a:poly) (b:poly) : (va_quickCode unit\n (va_code_ReduceMul128_LE ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 104 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 105 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_ReduceMulRev128 a b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 106 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 8)) (va_QEmpty (()))))))", "val va_qcode_Check_aesni_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_aesni_support ()))\nlet va_qcode_Check_aesni_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_aesni_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 42 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 44 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 45 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 46 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_AES ()) (fun (va_s:va_state) _ -> let (va_arg22:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 47 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg22 25) (let\n (va_arg21:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 48 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg21 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 49 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 50 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 33554432)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 51 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (33554432 == Prims.pow2 25)) (fun _ -> (fun (p:prop) -> p)\n (33554432 == Prims.pow2 25)) (fun (_:unit) -> assert_normalize (33554432 == Prims.pow2 25))\n (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 52 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (2 == Prims.pow2 1)) (fun _ -> (fun (p:prop) -> p) (2 ==\n Prims.pow2 1)) (fun (_:unit) -> assert_normalize (2 == Prims.pow2 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 54 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 24)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 55 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 1 25) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 56 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 24) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 58 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 2)) (fun (va_s:va_state) _ -> let\n (va_arg20:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in let\n (va_arg19:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 59 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg19 va_arg20 1) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 60 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 66 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (()))))))))))))))))))))", "val va_qcode_Loop_rounds_52_64 (va_mods: va_mods_t) (k_b: buffer128) (block: block_w)\n : (va_quickCode unit (va_code_Loop_rounds_52_64 ()))\nlet va_qcode_Loop_rounds_52_64 (va_mods:va_mods_t) (k_b:buffer128) (block:block_w) : (va_quickCode\n unit (va_code_Loop_rounds_52_64 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (hash_orig:Vale.SHA.SHA_helpers.hash256) = Vale.SHA.SHA_helpers.make_hash (va_get_xmm 9 va_s)\n (va_get_xmm 10 va_s) in let (ks:(FStar.Seq.Base.seq Vale.X64.Decls.quad32)) =\n Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s) k_b in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 424 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRcx) (16 `op_Multiply` 13) Secret k_b 13) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 425 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.X64.Decls.quad32 ks 13) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 425 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 0 va_s == FStar.Seq.Base.index #Vale.X64.Decls.quad32 ks 13) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 426 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 427 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_msg2 (va_op_xmm_xmm 4) (va_op_xmm_xmm 3) (4 `op_Multiply` (13 + 1)) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 428 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1) (4 `op_Multiply` 13) block\n hash_orig) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 429 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 430 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 431 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Palignr4 (va_op_xmm_xmm 7) (va_op_xmm_xmm 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 432 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) (4 `op_Multiply` 13 + 2) block\n hash_orig) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 433 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 5) (va_op_xmm_xmm 7)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 435 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRcx) (16 `op_Multiply` 14) Secret k_b 14) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 436 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.X64.Decls.quad32 ks 14) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 436 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 0 va_s == FStar.Seq.Base.index #Vale.X64.Decls.quad32 ks 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 437 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 438 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1) (4 `op_Multiply` 14) block\n hash_orig) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 439 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 440 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_msg2 (va_op_xmm_xmm 5) (va_op_xmm_xmm 4) (4 `op_Multiply` (14 + 1)) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 441 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 442 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) (4 `op_Multiply` 14 + 2) block\n hash_orig) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 444 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRcx) (16 `op_Multiply` 15) Secret k_b 15) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 445 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.X64.Decls.quad32 ks 15) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 445 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 0 va_s == FStar.Seq.Base.index #Vale.X64.Decls.quad32 ks 15) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 446 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 447 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1) (4 `op_Multiply` 15) block\n hash_orig) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 448 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 449 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 450 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) (4 `op_Multiply` 15 + 2) block\n hash_orig) (fun (va_s:va_state) _ -> let (abef_shuffle:quad32) = va_get_xmm 1 va_s in let\n (cdgh_shuffle:quad32) = va_get_xmm 2 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 456 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 2) (va_op_xmm_xmm 10)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 457 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 9)) (fun (va_s:va_state) _ -> let\n (va_arg56:Vale.SHA.SHA_helpers.block_w) = block in let (va_arg55:Vale.Def.Types_s.quad32) =\n va_get_xmm 10 va_s in let (va_arg54:Vale.Def.Types_s.quad32) = va_get_xmm 9 va_s in let\n (va_arg53:Vale.Def.Types_s.quad32) = va_get_xmm 2 va_s in let\n (va_arg52:Vale.Def.Types_s.quad32) = va_get_xmm 1 va_s in let\n (va_arg51:Vale.Def.Types_s.quad32) = cdgh_shuffle in let (va_arg50:Vale.Def.Types_s.quad32) =\n abef_shuffle in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 459 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (fun (_:unit) -> Vale.SHA.SHA_helpers.update_lemma va_arg50 va_arg51 va_arg52 va_arg53 va_arg54\n va_arg55 va_arg56) (va_QEmpty (()))))))))))))))))))))))))))))))))))", "val va_qcode_Gctr_blocks128_6way_body\n (va_mods: va_mods_t)\n (alg: algorithm)\n (in_b out_b: buffer128)\n (old_icb: quad32)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n (plain_quads: (seq quad32))\n : (va_quickCode unit (va_code_Gctr_blocks128_6way_body alg))\nlet va_qcode_Gctr_blocks128_6way_body (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128)\n (out_b:buffer128) (old_icb:quad32) (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128)\n (plain_quads:(seq quad32)) : (va_quickCode unit (va_code_Gctr_blocks128_6way_body alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qAssertSquash\n va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 383 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n ((fun (alg_10591:Vale.AES.AES_common_s.algorithm) (key_10592:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat32)) (input_10593:Vale.Def.Types_s.quad32) ->\n Vale.AES.AES_BE_s.is_aes_key_word alg_10591 key_10592) alg key (Vale.AES.GCTR_BE_s.inc32\n old_icb (va_get_reg 8 va_s))) (fun _ -> let (ctr_enc_0:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.quad32_xor (Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read in_b (va_get_reg 8 va_s) (va_get_mem_heaplet 1 va_s)))\n (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.AES.GCTR_BE_s.inc32 old_icb (va_get_reg 8\n va_s))) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 384 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n ((fun (alg_10591:Vale.AES.AES_common_s.algorithm) (key_10592:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat32)) (input_10593:Vale.Def.Types_s.quad32) ->\n Vale.AES.AES_BE_s.is_aes_key_word alg_10591 key_10592) alg key (Vale.AES.GCTR_BE_s.inc32\n old_icb (va_get_reg 8 va_s + 1))) (fun _ -> let (ctr_enc_1:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.quad32_xor (Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read in_b (va_get_reg 8 va_s + 1) (va_get_mem_heaplet 1 va_s)))\n (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.AES.GCTR_BE_s.inc32 old_icb (va_get_reg 8\n va_s + 1))) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 385 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n ((fun (alg_10591:Vale.AES.AES_common_s.algorithm) (key_10592:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat32)) (input_10593:Vale.Def.Types_s.quad32) ->\n Vale.AES.AES_BE_s.is_aes_key_word alg_10591 key_10592) alg key (Vale.AES.GCTR_BE_s.inc32\n old_icb (va_get_reg 8 va_s + 2))) (fun _ -> let (ctr_enc_2:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.quad32_xor (Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read in_b (va_get_reg 8 va_s + 2) (va_get_mem_heaplet 1 va_s)))\n (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.AES.GCTR_BE_s.inc32 old_icb (va_get_reg 8\n va_s + 2))) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 386 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n ((fun (alg_10591:Vale.AES.AES_common_s.algorithm) (key_10592:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat32)) (input_10593:Vale.Def.Types_s.quad32) ->\n Vale.AES.AES_BE_s.is_aes_key_word alg_10591 key_10592) alg key (Vale.AES.GCTR_BE_s.inc32\n old_icb (va_get_reg 8 va_s + 3))) (fun _ -> let (ctr_enc_3:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.quad32_xor (Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read in_b (va_get_reg 8 va_s + 3) (va_get_mem_heaplet 1 va_s)))\n (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.AES.GCTR_BE_s.inc32 old_icb (va_get_reg 8\n va_s + 3))) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 387 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n ((fun (alg_10591:Vale.AES.AES_common_s.algorithm) (key_10592:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat32)) (input_10593:Vale.Def.Types_s.quad32) ->\n Vale.AES.AES_BE_s.is_aes_key_word alg_10591 key_10592) alg key (Vale.AES.GCTR_BE_s.inc32\n old_icb (va_get_reg 8 va_s + 4))) (fun _ -> let (ctr_enc_4:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.quad32_xor (Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read in_b (va_get_reg 8 va_s + 4) (va_get_mem_heaplet 1 va_s)))\n (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.AES.GCTR_BE_s.inc32 old_icb (va_get_reg 8\n va_s + 4))) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 388 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n ((fun (alg_10591:Vale.AES.AES_common_s.algorithm) (key_10592:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat32)) (input_10593:Vale.Def.Types_s.quad32) ->\n Vale.AES.AES_BE_s.is_aes_key_word alg_10591 key_10592) alg key (Vale.AES.GCTR_BE_s.inc32\n old_icb (va_get_reg 8 va_s + 5))) (fun _ -> let (ctr_enc_5:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.quad32_xor (Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read in_b (va_get_reg 8 va_s + 5) (va_get_mem_heaplet 1 va_s)))\n (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.AES.GCTR_BE_s.inc32 old_icb (va_get_reg 8\n va_s + 5))) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 390 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 391 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vadduwm (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 8)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 392 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vadduwm (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 9)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 393 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vadduwm (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 10)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 394 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vadduwm (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 11)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 395 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vadduwm (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 12)) (fun\n (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 397 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AESEncryptBlock_6way alg (va_get_vec 7 va_s) (Vale.AES.GCTR_BE.inc32lite (va_get_vec\n 7 va_s) 1) (Vale.AES.GCTR_BE.inc32lite (va_get_vec 7 va_s) 2) (Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s) 3) (Vale.AES.GCTR_BE.inc32lite (va_get_vec 7 va_s) 4)\n (Vale.AES.GCTR_BE.inc32lite (va_get_vec 7 va_s) 5) key round_keys keys_b) (fun (va_s:va_state)\n _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 399 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 14)\n (va_op_reg_opr_reg 3) Secret in_b (va_get_reg 8 va_s)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 400 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 15)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 27) Secret in_b (va_get_reg 8 va_s + 1)) (fun\n (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 401 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 16)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 28) Secret in_b (va_get_reg 8 va_s + 2)) (fun\n (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 402 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 17)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 29) Secret in_b (va_get_reg 8 va_s + 3)) (fun\n (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 403 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 18)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 30) Secret in_b (va_get_reg 8 va_s + 4)) (fun\n (va_s:va_state) _ -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 404 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 19)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 31) Secret in_b (va_get_reg 8 va_s + 5)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 406 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vxor (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 0)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 407 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vxor (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 1)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 408 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vxor (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 2)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 409 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vxor (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 17) (va_op_vec_opr_vec 3)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 410 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vxor (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 18) (va_op_vec_opr_vec 4)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 411 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vxor (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 19) (va_op_vec_opr_vec 5)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 413 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store_3blocks128_1 out_b) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 414 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store_3blocks128_2 out_b) (fun (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 415 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read out_b (va_get_reg 8\n va_s) (va_get_mem_heaplet 1 va_s)) == ctr_enc_0) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 416 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read out_b (va_get_reg 8\n va_s + 1) (va_get_mem_heaplet 1 va_s)) == ctr_enc_1) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 417 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read out_b (va_get_reg 8\n va_s + 2) (va_get_mem_heaplet 1 va_s)) == ctr_enc_2) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 418 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read out_b (va_get_reg 8\n va_s + 3) (va_get_mem_heaplet 1 va_s)) == ctr_enc_3) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 419 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read out_b (va_get_reg 8\n va_s + 4) (va_get_mem_heaplet 1 va_s)) == ctr_enc_4) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 420 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read out_b (va_get_reg 8\n va_s + 5) (va_get_mem_heaplet 1 va_s)) == ctr_enc_5) (let (va_arg64:(FStar.Seq.Base.seq\n Vale.Def.Types_s.nat32)) = key in let (va_arg63:Vale.AES.AES_common_s.algorithm) = alg in let\n (va_arg62:Vale.Def.Types_s.quad32) = old_icb in let (va_arg61:Prims.nat) = va_get_reg 8 va_s in\n let (va_arg60:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = plain_quads in let\n (va_arg59:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) out_b) in let (va_arg58:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n out_b) in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 422 column 38 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR_BE.lemma_eq_reverse_bytes_quad32_seq va_arg58 va_arg59 va_arg60\n va_arg61 va_arg62 va_arg63 va_arg64) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 424 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddImm (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 8) 6) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 425 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddImm (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3) (6 `op_Multiply` 16)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 426 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddImm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) (6 `op_Multiply` 16)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 427 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Vadduwm (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 13))\n (va_QEmpty (())))))))))))))))))))))))))))))))))))))))))", "val va_quick_Fast_sqr_part2: Prims.unit -> (va_quickCode unit (va_code_Fast_sqr_part2 ()))\nlet va_quick_Fast_sqr_part2 () : (va_quickCode unit (va_code_Fast_sqr_part2 ())) =\n (va_QProc (va_code_Fast_sqr_part2 ()) ([va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;\n va_Mod_reg64 rR13; va_Mod_reg64 rRbx; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;\n va_Mod_reg64 rR8]) va_wp_Fast_sqr_part2 va_wpProof_Fast_sqr_part2)", "val va_qcode_Callee_save_registers (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Callee_save_registers win))\nlet va_qcode_Callee_save_registers (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Callee_save_registers win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 73 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 74 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 15) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 75 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 14) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 76 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 13) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 77 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 12) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 78 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 11) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 79 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 10) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 80 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 9) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 81 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 8) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 82 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 7) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 83 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 6) (va_op_reg_opr64_reg64 rRax)) (va_QEmpty (())))))))))))))\n (qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 85 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 86 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 87 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 88 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 89 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRsi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 90 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRdi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 91 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRbp)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 92 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRbx)) (va_QEmpty (()))))))))))))", "val va_qcode_Check_avx_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_avx_stdcall win))\nlet va_qcode_Check_avx_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_avx_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 81 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_avx_support ()) (va_QEmpty (()))))" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fsti", "name": "Vale.AES.X64.GCMencryptOpt.va_quick_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fsti", "name": "Vale.AES.PPC64LE.GCMencrypt.va_quick_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Compute_pad_to_128_bits" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.va_qcode_Fast_sqr_part2" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_qcode_Compute_ghash_incremental_register" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_code_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_qcode_Gf128MulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_qcode_Gf128MulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gcm_auth_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_mod_6" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESGCM.fst", "name": "Vale.AES.X64.AESGCM.va_qcode_Handle_ctr32_2" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_avx512_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_qcode_Handle_ctr32" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_qcode_Poly1305_reduce_last" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_qcode_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_qcode_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_avx2_support" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_avx_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMdecryptOpt.fst", "name": "Vale.AES.X64.GCMdecryptOpt.va_qcode_Gcm_blocks128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gcm_blocks128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_qcode_load_one_msb" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gcm_blocks_auth" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_lemma_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_avx_xcr0_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMdecrypt.fst", "name": "Vale.AES.PPC64LE.GCMdecrypt.va_qcode_Gcm_blocks128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMdecrypt.fst", "name": "Vale.AES.PPC64LE.GCMdecrypt.va_qcode_Gcm_blocks" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_qcode_Poly1305_add_key_s" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMdecrypt.fst", "name": "Vale.AES.PPC64LE.GCMdecrypt.va_qcode_Nat64Equal" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gcm_extra_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMdecryptOpt.fst", "name": "Vale.AES.X64.GCMdecryptOpt.va_qcode_Gcm_extra_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Store_3blocks128_2" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_avx512_xcr0_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESGCM.fst", "name": "Vale.AES.X64.AESGCM.va_qcode_Load_one_msb" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_sse_support" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_qcode_Poly1305_reduce" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Gctr_blocks128_6way_body0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Store_3blocks128_1" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_qcode_Loop_rounds_1_3" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMdecrypt.fst", "name": "Vale.AES.PPC64LE.GCMdecrypt.va_qcode_Gcm_extra_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fsti", "name": "Vale.AES.PPC64LE.GCMencrypt.va_wp_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fsti", "name": "Vale.AES.X64.GCMencryptOpt.va_wp_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gctr_blocks128_body0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_wpProof_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gcm_blocks_wrapped" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMdecryptOpt.fst", "name": "Vale.AES.X64.GCMdecryptOpt.va_qcode_Gcm_blocks_wrapped" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_qcode_Poly1305_last_block" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Gctr_blocks128_1way_body0" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_qcode_Loop_rounds_9_11" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_qcode_Loop_rounds_5_7" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMdecrypt.fst", "name": "Vale.AES.PPC64LE.GCMdecrypt.va_qcode_VectorEqual" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gcm_blocks" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMdecryptOpt.fst", "name": "Vale.AES.X64.GCMdecryptOpt.va_qcode_Gcm_blocks" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Ghash_extra_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.fst", "name": "Vale.SHA.PPC64LE.va_qcode_Preamble" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_qcode_Preamble" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Gctr_blocks128_6way_while0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fst", "name": "Vale.AES.X64.GCTR.va_qcode_Gctr_core_body0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMdecrypt.fst", "name": "Vale.AES.PPC64LE.GCMdecrypt.va_qcode_Gcm_blocks_wrapped" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_codegen_success_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_avx512_xcr0_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_qcode_Msg_shift" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.va_qcode_Fast_sqr_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.va_qcode_Fast_sqr_part1" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.va_qcode_Sqr2_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_sha_support" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_movbe_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Gctr_blocks128_1way_while0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_qcode_Compute_Y0" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fst", "name": "Vale.Curve25519.X64.FastWide.va_qcode_Fsqr" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_qcode_Loop_rounds_13_15" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gctr_register" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fst", "name": "Vale.AES.X64.GCTR.va_qcode_Gctr_register" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Gctr_register" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_qcode_ShiftLeft128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_qcode_ShiftLeft128_1" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_avx2_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_qcode_Loop_rounds_60_63_a" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gctr_blocks128_while0" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fst", "name": "Vale.Curve25519.X64.FastWide.va_qcode_Fsqr2" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_avx_xcr0_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Save_registers" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_avx512_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fst", "name": "Vale.AES.X64.GCTR.va_qcode_Init_ctr" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_qcode_Loop_rounds_16_59_a" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_quick_mod_6" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.va_qcode_Fast_sqr_part3" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fst", "name": "Vale.AES.X64.GCTR.va_qcode_Gctr_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_qcode_Loop_rounds_0_15" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Gctr_blocks128_1way" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Gctr_blocks128_6way" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_qcode_ClmulRev64High" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_qcode_ReduceMul128_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_aesni_support" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_qcode_Loop_rounds_52_64" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Gctr_blocks128_6way_body" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.va_quick_Fast_sqr_part2" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Stack.fst", "name": "Vale.X64.Stack.va_qcode_Callee_save_registers" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_avx_stdcall" } ], "selected_premises": [ "Vale.PPC64LE.QuickCodes.va_QSeq", "Vale.PPC64LE.QuickCodes.va_qPURE", "Vale.PPC64LE.QuickCodes.va_QEmpty", "Vale.AES.PPC64LE.GCMencrypt.va_code_Gcm_make_length_quad", "Vale.PPC64LE.QuickCodes.va_QBind", "Vale.AES.PPC64LE.GCMencrypt.va_code_Gcm_auth_bytes", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.AES.PPC64LE.GCMencrypt.va_code_Gcm_blocks128", "Vale.PPC64LE.QuickCodes.qblock", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.PPC64LE.Decls.va_get_vec", "Vale.PPC64LE.Decls.va_get_block", "Vale.PPC64LE.QuickCodes.label", "Vale.PPC64LE.Decls.va_CNil", "Vale.AES.PPC64LE.GCMencrypt.va_qcode_Gcm_blocks128", "Vale.PPC64LE.Decls.va_op_heaplet_mem_heaplet", "Vale.PPC64LE.Decls.va_op_cmp_reg", "Vale.AES.PPC64LE.GCMencrypt.va_code_Load_one_lsb", "Vale.PPC64LE.Decls.va_Block", "Vale.X64.Machine_s.rRdx", "Vale.PPC64LE.QuickCodes.va_QLemma", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRcx", "Vale.X64.Machine_s.rRax", "Vale.X64.Machine_s.rRsi", "Vale.X64.Machine_s.rRdi", "Vale.PPC64LE.Decls.va_CCons", "Vale.AES.PPC64LE.GCMencrypt.va_qcode_Gcm_auth_bytes", "Vale.X64.Machine_s.rR11", "Vale.X64.Machine_s.rR9", "Vale.X64.Machine_s.rR10", "Vale.X64.Machine_s.rR8", "Vale.X64.Machine_s.rRbp", "Vale.PPC64LE.QuickCodes.va_range1", "Vale.X64.Machine_s.rR13", "Vale.X64.Machine_s.rRsp", "Vale.X64.Machine_s.rR15", "Vale.PPC64LE.Decls.va_code", "Vale.X64.Machine_s.rR12", "Vale.X64.Machine_s.rR14", "Vale.AES.PPC64LE.GHash.va_quick_Ghash_buffer", "Vale.PPC64LE.Decls.va_if", "Vale.PPC64LE.Decls.va_get_mem_heaplet", "Vale.X64.Machine_s.operand128", "Vale.PPC64LE.Decls.va_state", "Vale.PPC64LE.Decls.va_get_reg", "Vale.X64.Machine_s.reg_xmm", "Vale.PPC64LE.Decls.va_get_ok", "Vale.AES.PPC64LE.GHash.va_quick_Ghash_register", "Vale.PPC64LE.Decls.va_mul_nat", "Vale.PPC64LE.Decls.va_eval_vec_opr", "Vale.X64.Machine_s.reg_64", "Vale.PPC64LE.QuickCodes.va_qAssertBy", "Vale.PPC64LE.Decls.va_require_total", "Vale.PPC64LE.Decls.va_upd_reg", "Vale.AES.PPC64LE.GCMencrypt.va_quick_Gcm_auth_bytes", "Vale.AES.PPC64LE.GCTR.va_quick_Gctr_register", "Vale.PPC64LE.Decls.va_value_vec_opr", "Vale.PPC64LE.Decls.va_upd_vec", "Vale.PPC64LE.Memory.quad32", "Vale.PPC64LE.Machine_s.quad32", "Vale.X64.Machine_s.quad32", "Vale.PPC64LE.Decls.va_get_mem_layout", "Vale.PPC64LE.Decls.va_tl", "Vale.PPC64LE.Decls.va_const_cmp", "Vale.PPC64LE.QuickCode.va_Mod_ok", "Vale.Def.Words_s.nat32", "Lib.IntTypes.u64", "Vale.PPC64LE.Decls.va_reveal_opaque", "Vale.AES.GCM_BE_s.gcm_encrypt_BE", "Vale.AES.PPC64LE.AES.va_quick_AESEncryptBlock_6way", "Vale.PPC64LE.QuickCodes.va_qAssert", "Vale.AES.PPC64LE.AES256.va_quick_AES256EncryptBlock_6way", "Vale.Def.Words_s.nat64", "Vale.AES.PPC64LE.GCMencrypt.va_quick_Gcm_blocks128", "Vale.PPC64LE.Decls.va_is_dst_vec_opr", "Vale.PPC64LE.Machine_s.nat64", "Vale.PPC64LE.Memory.nat64", "Vale.Def.Types_s.nat64", "Vale.PPC64LE.QuickCode.va_Mod_mem_heaplet", "Vale.AES.PPC64LE.AES128.va_quick_AES128EncryptBlock_6way", "Vale.AES.PPC64LE.AES.va_quick_KeyExpansionStdcall", "Vale.AES.PPC64LE.AES.va_req_KeyExpansionStdcall", "Vale.PPC64LE.InsMem.va_quick_CreateHeaplets", "Vale.AES.GCTR_BE.gctr_partial_reveal", "Vale.AES.PPC64LE.GF128_Mul.va_quick_Gf128MulRev128", "Vale.AES.GCM_BE_s.gcm_decrypt_BE_reveal", "Vale.AES.GCM_BE_s.gcm_encrypt_BE_reveal", "Vale.AES.PPC64LE.GF128_Mul.va_quick_ShiftLeft128_1", "Vale.AES.PPC64LE.GHash.va_quick_GhashUnroll_n", "Vale.PPC64LE.Decls.va_upd_cr0", "Vale.PPC64LE.Decls.va_int_range", "Vale.PPC64LE.QuickCodes.va_qAssertSquash", "Vale.X64.Machine_s.nat64", "Vale.AES.PPC64LE.GF128_Mul.va_quick_Low64ToHigh", "Vale.AES.PPC64LE.GF128_Mul.va_quick_ReduceMulRev128", "Vale.AES.GHash_BE.hkeys_reqs_priv", "Vale.PPC64LE.InsVector.va_quick_Store128_byte16_buffer", "Vale.PPC64LE.QuickCode.quickProc_wp", "Vale.PPC64LE.QuickCodes.va_qAssume" ], "source_upto_this": "module Vale.AES.PPC64LE.GCMencrypt\nopen Vale.Def.Prop_s\nopen Vale.Def.Opaque_s\nopen FStar.Seq\nopen Vale.Def.Words_s\nopen Vale.Def.Words.Seq_s\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Arch.HeapImpl\nopen Vale.AES.AES_BE_s\nopen Vale.AES.GCTR_BE_s\nopen Vale.AES.GCTR_BE\nopen Vale.AES.GCM_BE\nopen Vale.AES.GHash_BE_s\nopen Vale.AES.GHash_BE\nopen Vale.AES.GCM_BE_s\nopen Vale.AES.PPC64LE.AES\nopen Vale.AES.GF128_s\nopen Vale.AES.GF128\nopen Vale.Poly1305.Math\nopen Vale.AES.GCM_helpers_BE\nopen Vale.AES.PPC64LE.GCTR\nopen Vale.PPC64LE.Machine_s\nopen Vale.PPC64LE.Memory\nopen Vale.PPC64LE.Stack_i\nopen Vale.PPC64LE.State\nopen Vale.PPC64LE.Decls\nopen Vale.PPC64LE.InsBasic\nopen Vale.PPC64LE.InsMem\nopen Vale.PPC64LE.InsVector\nopen Vale.PPC64LE.InsStack\nopen Vale.PPC64LE.QuickCode\nopen Vale.PPC64LE.QuickCodes\nopen Vale.AES.PPC64LE.GF128_Mul\nopen Vale.Math.Poly2.Bits_s\nopen Vale.AES.PPC64LE.GHash\nopen Vale.Lib.Meta\nopen Vale.AES.OptPublic_BE\nopen Vale.Lib.Basic\n#reset-options \"--z3rlimit 2000 --fuel 10 --ifuel 10 --max_fuel 100 --max_ifuel 100\"\n//-- Load_one_lsb\n\n[@ \"opaque_to_smt\"]\nlet va_code_Load_one_lsb dst =\n (va_Block (va_CCons (va_code_Vspltisw dst 1) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 4) 0)\n (va_CCons (va_code_Vsldoi dst (va_op_vec_opr_vec 4) dst 4) (va_CNil ())))))\n\n[@ \"opaque_to_smt\"]\nlet va_codegen_success_Load_one_lsb dst =\n (va_pbool_and (va_codegen_success_Vspltisw dst 1) (va_pbool_and (va_codegen_success_Vspltisw\n (va_op_vec_opr_vec 4) 0) (va_pbool_and (va_codegen_success_Vsldoi dst (va_op_vec_opr_vec 4) dst\n 4) (va_ttrue ()))))\n\n[@\"opaque_to_smt\"]\nlet va_lemma_Load_one_lsb va_b0 va_s0 dst =\n va_reveal_opaque (`%va_code_Load_one_lsb) (va_code_Load_one_lsb dst);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (va_s2, va_fc2) = va_lemma_Vspltisw (va_hd va_b1) va_s0 dst 1 in\n let va_b2 = va_tl va_b1 in\n let (va_s3, va_fc3) = va_lemma_Vspltisw (va_hd va_b2) va_s2 (va_op_vec_opr_vec 4) 0 in\n let va_b3 = va_tl va_b2 in\n let (va_s4, va_fc4) = va_lemma_Vsldoi (va_hd va_b3) va_s3 dst (va_op_vec_opr_vec 4) dst 4 in\n let va_b4 = va_tl va_b3 in\n let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in\n let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in\n let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in\n (va_sM, va_fM)\n\n\n[@\"opaque_to_smt\"]\nlet va_wpProof_Load_one_lsb dst va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Load_one_lsb (va_code_Load_one_lsb dst) va_s0 dst in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_vec 4 va_sM (va_update_ok va_sM (va_update_operand_vec_opr\n dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_vec 4; va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n//--\n//-- Gcm_blocks128\n\nval va_code_Gcm_blocks128 : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_blocks128 alg =\n (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_CCons\n (va_code_Gctr_blocks128 alg) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec\n 7)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_CCons\n (va_code_Ghash_buffer ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15))\n (va_CNil ()))))))))\n\nval va_codegen_success_Gcm_blocks128 : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_blocks128 alg =\n (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_pbool_and\n (va_codegen_success_Gctr_blocks128 alg) (va_pbool_and (va_codegen_success_Vmr\n (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_pbool_and (va_codegen_success_Vmr\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_pbool_and (va_codegen_success_Ghash_buffer\n ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15))\n (va_ttrue ())))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_blocks128 (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 167 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 168 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Gctr_blocks128 alg in_b out_b key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 169 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 170 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b out_b h_BE (va_get_vec 1 va_old_s)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 172 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15)) (va_QEmpty (())))))))))\n\n\nval va_lemma_Gcm_blocks128 : va_b0:va_code -> va_s0:va_state -> alg:algorithm -> in_b:buffer128 ->\n out_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks128 alg) va_s0 /\\ va_get_ok va_s0 /\\\n ((Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) in_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b (va_get_reg 6 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ l_and\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out_b))))) /\\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM\n (va_update_vec 20 va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM\n (va_update_vec 16 va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM\n (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM\n (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM\n (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM\n (va_update_vec 0 va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM\n (va_update_reg 28 va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM\n (va_update_reg 9 va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM\n (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_blocks128 va_b0 va_s0 alg in_b out_b key round_keys keys_b hkeys_b h_BE =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19;\n va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13;\n va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7;\n va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec\n 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26;\n va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem] in\n let va_qc = va_qcode_Gcm_blocks128 va_mods alg in_b out_b key round_keys keys_b hkeys_b h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_blocks128 alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 114 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 156 column 53 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 159 column 147 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 160 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite (va_get_vec 7 va_s0) (va_get_reg 6 va_s0)) /\\\n label va_range1\n \"***** POSTCONDITION NOT MET AT line 163 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1 va_sM == va_get_vec 1 va_s0)\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b == Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) out_b)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 165 column 109 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 6 va_s0 > 0 ==> l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==>\n FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0\n (va_get_reg 6 va_s0)) > 0) (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE\n (va_get_vec 1 va_s0) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_sM) out_b)))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok; va_Mod_mem])\n va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ ((Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) in_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b (va_get_reg 6 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ l_and\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret) /\\ (forall (va_x_mem:vale_heap)\n (va_x_r3:nat64) (va_x_r7:nat64) (va_x_r6:nat64) (va_x_r8:nat64) (va_x_r9:nat64)\n (va_x_r10:nat64) (va_x_r26:nat64) (va_x_r27:nat64) (va_x_r28:nat64) (va_x_r29:nat64)\n (va_x_r30:nat64) (va_x_r31:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32) (va_x_v17:quad32)\n (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32) (va_x_cr0:cr0_t) (va_x_heap1:vale_heap) .\n let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_cr0 va_x_cr0 (va_upd_vec 20 va_x_v20\n (va_upd_vec 19 va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16\n (va_upd_vec 15 va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12\n (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8\n (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4\n (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0\n (va_upd_reg 31 va_x_r31 (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29 (va_upd_reg 28 va_x_r28\n (va_upd_reg 27 va_x_r27 (va_upd_reg 26 va_x_r26 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9\n (va_upd_reg 8 va_x_r8 (va_upd_reg 6 va_x_r6 (va_upd_reg 7 va_x_r7 (va_upd_reg 3 va_x_r3\n (va_upd_mem va_x_mem va_s0))))))))))))))))))))))))))))))))))) in va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out_b))))) ==> va_k va_sM (())))\n\n\nval va_wpProof_Gcm_blocks128 : alg:algorithm -> in_b:buffer128 -> out_b:buffer128 -> key:(seq\n nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks128 alg)\n ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0,\n va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_blocks128 (va_code_Gcm_blocks128 alg) va_s0 alg in_b out_b key\n round_keys keys_b hkeys_b h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM (va_update_reg 3\n va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))))))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) : (va_quickCode\n unit (va_code_Gcm_blocks128 alg)) =\n (va_QProc (va_code_Gcm_blocks128 alg) ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20;\n va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14;\n va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8;\n va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec\n 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27;\n va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7;\n va_Mod_reg 3; va_Mod_mem]) (va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE) (va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE))\n//--\n//-- Gcm_auth_bytes\n\nval va_code_Gcm_auth_bytes : va_dummy:unit -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_auth_bytes () =\n (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Ghash_buffer\n ()) (va_CNil ()))))\n\nval va_codegen_success_Gcm_auth_bytes : va_dummy:unit -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_auth_bytes () =\n (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and\n (va_codegen_success_Ghash_buffer ()) (va_ttrue ())))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_auth_bytes (va_mods:va_mods_t) (auth_b:buffer128) (hkeys_b:buffer128)\n (h_BE:quad32) : (va_quickCode (quad32 & quad32) (va_code_Gcm_auth_bytes ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 206 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (fun (va_s:va_state) _ -> let (y_0:quad32) =\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 208 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b auth_b h_BE y_0) (fun (va_s:va_state) _ -> let (y_auth:quad32) =\n va_get_vec 1 va_s in va_QEmpty ((y_0, y_auth))))))\n\n\nval va_lemma_Gcm_auth_bytes : va_b0:va_code -> va_s0:va_state -> auth_b:buffer128 ->\n hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel & quad32 & quad32)\n (requires (va_require_total va_b0 (va_code_Gcm_auth_bytes ()) va_s0 /\\ va_get_ok va_s0 /\\\n (Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) (va_get_reg 7 va_s0) auth_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == va_get_reg 6 va_s0 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64)))\n (ensures (fun (va_sM, va_fM, y_0, y_auth) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok\n va_sM /\\ (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 /\\ (let h_BE =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) /\\ va_get_vec 1 va_sM == y_auth)) /\\ va_state_eq va_sM (va_update_cr0 va_sM\n (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12 va_sM (va_update_vec 11 va_sM\n (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8 va_sM (va_update_vec 7 va_sM\n (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM\n (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM\n (va_update_reg 6 va_sM (va_update_reg 7 va_sM (va_update_ok va_sM va_s0))))))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_auth_bytes va_b0 va_s0 auth_b hkeys_b h_BE =\n let (va_mods:va_mods_t) = [va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec\n 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5;\n va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg\n 6; va_Mod_reg 7; va_Mod_ok] in\n let va_qc = va_qcode_Gcm_auth_bytes va_mods auth_b hkeys_b h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_auth_bytes ()) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let (y_0, y_auth) = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 175 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 200 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 201 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (let h_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 202 column 95 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b))) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 203 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_vec 1 va_sM == y_auth)))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6;\n va_Mod_reg 7; va_Mod_ok]) va_sM va_s0;\n let (y_0, y_auth) = va_g in\n (va_sM, va_fM, y_0, y_auth)\n\n[@ va_qattr]\nlet va_wp_Gcm_auth_bytes (auth_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) (va_s0:va_state)\n (va_k:(va_state -> (quad32 & quad32) -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) (va_get_reg 7 va_s0) auth_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == va_get_reg 6 va_s0 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64) /\\ (forall (va_x_r7:nat64)\n (va_x_r6:nat64) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_cr0:cr0_t) (y_0:quad32) (y_auth:quad32) . let va_sM =\n va_upd_cr0 va_x_cr0 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12\n (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8\n (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4\n (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0\n (va_upd_reg 10 va_x_r10 (va_upd_reg 6 va_x_r6 (va_upd_reg 7 va_x_r7 va_s0)))))))))))))))))) in\n va_get_ok va_sM /\\ (y_0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 /\\ (let h_BE\n = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in y_auth == Vale.AES.GHash_BE.ghash_incremental0 h_BE y_0\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n auth_b)) /\\ va_get_vec 1 va_sM == y_auth)) ==> va_k va_sM ((y_0, y_auth))))\n\n\nval va_wpProof_Gcm_auth_bytes : auth_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32 ->\n va_s0:va_state -> va_k:(va_state -> (quad32 & quad32) -> Type0)\n -> Ghost (va_state & va_fuel & (quad32 & quad32))\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_auth_bytes auth_b hkeys_b h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_auth_bytes ()) ([va_Mod_cr0;\n va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9;\n va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec\n 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6; va_Mod_reg 7]) va_s0 va_k ((va_sM,\n va_f0, va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_auth_bytes auth_b hkeys_b h_BE va_s0 va_k =\n let (va_sM, va_f0, y_0, y_auth) = va_lemma_Gcm_auth_bytes (va_code_Gcm_auth_bytes ()) va_s0\n auth_b hkeys_b h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_cr0 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM\n (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM\n (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM\n (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM\n (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM\n (va_update_ok va_sM va_s0)))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 6;\n va_Mod_reg 7]) va_sM va_s0;\n let va_g = (y_0, y_auth) in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_auth_bytes (auth_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) : (va_quickCode\n (quad32 & quad32) (va_code_Gcm_auth_bytes ())) =\n (va_QProc (va_code_Gcm_auth_bytes ()) ([va_Mod_cr0; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 10; va_Mod_reg 6; va_Mod_reg 7]) (va_wp_Gcm_auth_bytes auth_b hkeys_b h_BE)\n (va_wpProof_Gcm_auth_bytes auth_b hkeys_b h_BE))\n//--\n//-- Gcm_make_length_quad\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_make_length_quad () =\n (va_Block (va_CCons (va_code_Sl64Imm (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 3) (va_CCons\n (va_code_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 3) (va_CCons (va_code_Mtvsrdd\n (va_op_vec_opr_vec 9) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 7)) (va_CNil ())))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_make_length_quad () =\n (va_pbool_and (va_codegen_success_Sl64Imm (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 3)\n (va_pbool_and (va_codegen_success_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 3)\n (va_pbool_and (va_codegen_success_Mtvsrdd (va_op_vec_opr_vec 9) (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 7)) (va_ttrue ()))))\n\n[@ \"opaque_to_smt\" va_qattr]" }, { "file_name": "LambdaOmega.fst", "name": "LambdaOmega.esub_inc", "opens_and_abbrevs": [ { "open": "FStar.StrongExcludedMiddle" }, { "open": "FStar.FunctionalExtensionality" }, { "open": "FStar.Classical" }, { "open": "FStar.Constructive" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 1, "max_fuel": 1, "initial_ifuel": 1, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val esub_inc : var -> Tot exp", "source_definition": "let esub_inc y = EVar (y+1)", "source_range": { "start_line": 62, "start_col": 0, "end_line": 62, "end_col": 27 }, "interleaved": false, "definition": "fun y -> LambdaOmega.EVar (y + 1)", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "LambdaOmega.var", "LambdaOmega.EVar", "Prims.op_Addition", "LambdaOmega.exp" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "y: LambdaOmega.var -> LambdaOmega.exp", "prompt": "let esub_inc y =\n ", "expected_response": "EVar (y + 1)", "source": { "project_name": "FStar", "file_name": "examples/metatheory/LambdaOmega.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "LambdaOmega.fst", "checked_file": "dataset/LambdaOmega.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Tactics.fst.checked", "dataset/FStar.StrongExcludedMiddle.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked", "dataset/FStar.Constructive.fst.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "var", "knd", "KTyp", "KTyp", "KTyp", "KArr", "KArr", "KArr", "typ", "TVar", "TVar", "TVar", "TLam", "TLam", "TLam", "t", "t", "TApp", "TApp", "TApp", "TArr", "TArr", "TArr", "exp", "EVar", "EVar", "EVar", "EApp", "EApp", "EApp", "ELam", "ELam", "ELam", "esub", "erenaming", "val is_erenaming : s:esub -> GTot (n:int{( erenaming s ==> n=0) /\\\n (~(erenaming s) ==> n=1)})", "let is_erenaming s = (if strong_excluded_middle (erenaming s) then 0 else 1)", "val esub_inc : var -> Tot exp" ], "closest": [ "val sub_inc : var -> Tot exp\nlet sub_inc y = EVar (y+1)", "val sub_inc : var -> Tot exp\nlet sub_inc y = EVar (y+1)", "val sub_inc_above : nat -> var -> Tot exp\nlet sub_inc_above n y = if y read x", "val sub_beta_gen : var -> exp -> Tot sub\nlet sub_beta_gen x v = fun y -> if y < x then (EVar y)\n else if y = x then v (* substitute *)\n else (EVar (y-1))", "val step : exp -> Tot (option exp)\nlet rec step e =\n match e with\n | EApp e1 e2 ->\n if is_value e1 then\n if is_value e2 then\n match e1 with\n | EAbs t e' -> Some (subst_beta 0 e2 e')\n | _ -> None\n else\n match (step e2) with\n | Some e2' -> Some (EApp e1 e2')\n | None -> None\n else\n (match (step e1) with\n | Some e1' -> Some (EApp e1' e2)\n | None -> None)\n | _ -> None", "val step : exp -> Tot (option exp)\nlet rec step e =\n match e with\n | EApp e1 e2 ->\n if is_value e1 then\n if is_value e2 then\n match e1 with\n | ELam t e' -> Some (subst (sub_beta e2) e')\n | _ -> None\n else\n match (step e2) with\n | Some e2' -> Some (EApp e1 e2')\n | None -> None\n else\n (match (step e1) with\n | Some e1' -> Some (EApp e1' e2)\n | None -> None)\n | _ -> None", "val sub_beta : exp -> Tot sub\nlet sub_beta v = fun y -> if y = 0 then v (* substitute *)\n else (EVar (y-1))", "val elab_exp (e: src_exp) : Tot R.term\nlet rec elab_exp (e:src_exp)\n : Tot R.term\n = let open R in\n match e with\n | EBool true ->\n pack_ln (Tv_Const R.C_True)\n\n | EBool false ->\n pack_ln (Tv_Const R.C_False)\n\n | EBVar n -> \n let bv = R.pack_bv (RT.make_bv n) in\n R.pack_ln (Tv_BVar bv)\n \n | EVar n ->\n let v = R.pack_namedv (RT.make_namedv n) in\n R.pack_ln (Tv_Var v)\n\n | ELam t e ->\n let t = elab_ty t in\n let e = elab_exp e in\n R.pack_ln (Tv_Abs (RT.mk_simple_binder RT.pp_name_default t) e)\n \n | EApp e1 e2 ->\n let e1 = elab_exp e1 in\n let e2 = elab_exp e2 in\n R.pack_ln (Tv_App e1 (e2, Q_Explicit))\n\n | EIf b e1 e2 ->\n let b = elab_exp b in\n let e1 = elab_exp e1 in\n let e2 = elab_exp e2 in\n R.pack_ln (Tv_Match b None [(Pat_Constant C_True, e1); (Pat_Constant C_False, e2)])\n \nand elab_ty (t:src_ty) \n : R.term \n = let open R in\n match t with\n | TBool -> \n RT.bool_ty\n \n | TArrow t1 t2 ->\n let t1 = elab_ty t1 in\n let t2 = elab_ty t2 in\n R.pack_ln \n (R.Tv_Arrow \n (RT.mk_simple_binder RT.pp_name_default t1)\n (RT.mk_total t2)) //(R.pack_comp (C_Total t2 [])))\n \n | TRefineBool e ->\n let e = elab_exp e in\n let b = RT.mk_simple_binder RT.pp_name_default RT.bool_ty in\n let bv = R.pack_bv (RT.make_bv 0) in\n let refinement = r_b2t e in\n R.pack_ln (Tv_Refine b refinement)", "val elab_exp (e: src_exp) : Tot R.term\nlet rec elab_exp (e:src_exp)\n : Tot R.term\n = let open R in\n match e with\n | EBool true ->\n pack_ln (Tv_Const R.C_True)\n\n | EBool false ->\n pack_ln (Tv_Const R.C_False)\n\n | EBVar n -> \n let bv = R.pack_bv (RT.make_bv n) in\n R.pack_ln (Tv_BVar bv)\n \n | EVar n ->\n let namedv = R.pack_namedv (RT.make_namedv n) in\n R.pack_ln (Tv_Var namedv)\n\n | ELam t e ->\n let t = elab_ty t in\n let e = elab_exp e in\n R.pack_ln (Tv_Abs (RT.mk_simple_binder RT.pp_name_default t) e)\n \n | EApp e1 e2 ->\n let e1 = elab_exp e1 in\n let e2 = elab_exp e2 in\n R.pack_ln (Tv_App e1 (e2, Q_Explicit))\n\n | EIf b e1 e2 ->\n let b = elab_exp b in\n let e1 = elab_exp e1 in\n let e2 = elab_exp e2 in\n R.pack_ln (Tv_Match b None [(Pat_Constant C_True, e1); (Pat_Constant C_False, e2)])\n \nand elab_ty (t:src_ty) \n : R.term \n = let open R in\n match t with\n | TBool -> \n RT.bool_ty\n \n | TArrow t1 t2 ->\n let t1 = elab_ty t1 in\n let t2 = elab_ty t2 in\n R.pack_ln \n (R.Tv_Arrow \n (RT.mk_simple_binder RT.pp_name_default t1)\n (RT.mk_total t2)) //.pack_comp (C_Total t2 u_unk [])))\n \n | TRefineBool e ->\n let e = elab_exp e in\n let b : R.simple_binder = RT.mk_simple_binder RT.pp_name_default RT.bool_ty in\n let bv = R.pack_bv (RT.make_bv 0) in\n let refinement = r_b2t (R.pack_ln (Tv_App e (R.pack_ln (Tv_BVar bv), Q_Explicit))) in\n R.pack_ln (Tv_Refine b refinement)", "val compile (e: exp) : Tot prog\nlet rec compile (e : exp) : Tot prog =\n match e with\n | Const n -> [IConst n]\n | Binop b e1 e2 -> compile e2 @ compile e1 @ [IBinop b]", "val plus : nat -> nat -> Tot nat\nlet rec plus n m =\n match n with\n | O -> m\n | S n' -> S (plus n' m)", "val extend : env -> var -> ty -> Tot env\nlet extend g x t y = if y < x then g y\n else if y = x then Some t\n else g (y-1)", "val is_value : exp -> Tot bool\nlet is_value = EAbs?", "val is_value : exp -> Tot bool\nlet is_value e = ELam? e || EUnit? e", "val is_value : exp -> Tot bool\nlet is_value = EAbs?", "val is_var (e: exp) : int\nlet is_var (e:exp) : int = if EVar? e then 0 else 1", "val is_var (e: exp) : int\nlet is_var (e:exp) : int = if EVar? e then 0 else 1", "val vars : term -> Tot varset\nlet rec vars = function\n | V i -> OrdSet.singleton i\n | F t1 t2 -> OrdSet.union (vars t1) (vars t2)", "val interpret_exp' (h: heap) (e: exp) : Tot nat\nlet interpret_exp' (h:heap) (e:exp) : Tot nat =\n let n = interpret_exp h e in\n if 0 > n then 0 else n", "val interpret_exp' (h: heap) (e: exp) : Tot nat\nlet interpret_exp' (h:heap) (e:exp) : Tot nat =\n let n,_ = interpret_exp h (fun _ -> Low) e in\n if 0 > n then 0 else n", "val ins : lt:t -> n:int -> Tot t\nlet ins (| m, tt |) n = (| max m n, insert tt n |)", "val subst_term : subst -> term -> Tot term\nlet rec subst_term s t = match t with\n | V x -> if x = fst s then snd s else V x\n | F t1 t2 -> F (subst_term s t1) (subst_term s t2)", "val extend_gen : var -> typ -> env -> Tot env\nlet extend_gen x t g = if x = 0 then extend t g\n else (fun y -> if y < x then g y\n else if y = x then Some t\n else g (y-1))", "val reified_exp (t: Type0) : Tot Type0\nlet reified_exp (t: Type0) : Tot Type0 = (h: heap) -> Ghost (t * heap) (requires True) (ensures (fun rh -> snd rh == h))", "val assign (r: var) (n: exp int) : Tot computation\nlet assign (r: var) (n: exp int) : Tot computation =\n let g _ : ISNull bool =\n let n = n () in\n write r n;\n true\n in\n g", "val evars : eqns -> Tot varset\nlet rec evars = function\n | [] -> empty_vars\n | (x, y)::tl -> OrdSet.union (OrdSet.union (vars x) (vars y)) (evars tl)", "val size : tree -> Tot nat\nlet rec size t =\n match t with\n | Leaf -> 0\n | Node n t1 t2 -> 1 + size t1 + size t2", "val eval_var : g:Type -> a:Type -> var g a -> g -> Tot a\nlet rec eval_var (g:Type) (a:Type) v env = match v with\n | O 'g0 '_ -> snd #'g0 #a env\n | S 'g0 'a0 'b0 u -> eval_var 'g0 'a0 u (fst #'g0 #'b0 env)", "val mult : nat -> nat -> Tot nat\nlet rec mult n m =\n match n with\n | O -> O\n | S n' -> plus m (mult n' m)", "val apply : cont -> int -> Tot int\nlet rec apply k r = match k with\n | C0 -> r\n | C1 k hd -> apply k (hd + r)", "val extend : typ -> env -> Tot env\nlet extend t g y = if y = 0 then Some t\n else g (y-1)", "val subst_beta : x:var -> v:exp -> e:exp -> Tot exp (decreases e)\nlet rec subst_beta x v e =\n match e with\n | EVar y -> if y = x then v\n else if y < x then EVar y\n else EVar (y-1)\n | EAbs t e1 -> EAbs t (subst_beta (x+1) v e1)\n | EApp e1 e2 -> EApp (subst_beta x v e1) (subst_beta x v e2)", "val below : x:var -> e:exp -> Tot bool (decreases e)\nlet rec below x e =\n match e with\n | EVar y -> y < x\n | EApp e1 e2 -> below x e1 && below x e2\n | ELam _ e1 -> below (x+1) e1\n | EUnit -> true", "val interpret_exp (h: heap) (e: exp) : Tot int\nlet interpret_exp (h:heap) (e:exp) : Tot int = reify (interpret_exp_st e) h", "val imp1 (x: bounded_u16 4) : Tot (sum_case #somme #(bounded_u16 4) imp0 x)\nlet imp1 : (x: bounded_u16 4) -> Tot (sum_case #somme #(bounded_u16 4) imp0 x) =\n (bounded_u16_match_t_intro 4 imp0 (\n bounded_u16_match_t_aux_cons 4 imp0 3 3us (\n c3\n ) (\n bounded_u16_match_t_aux_cons 4 imp0 2 2us (\n c2\n ) (\n bounded_u16_match_t_aux_cons 4 imp0 1 1us (\n c1\n ) (\n bounded_u16_match_t_aux_cons_nil 4 imp0 (\n c0\n ))))))", "val insert'' : int -> tree -> Tot tree\nlet rec insert'' x t =\n match t with\n | Leaf -> Node x Leaf Leaf\n | Node n t1 t2 -> if x = n then t\n else if x < n then Node n (insert'' x t1) t2\n else Node n t1 (insert'' x t2)", "val step (e: exp) : option exp\nlet rec step (e:exp) : option exp =\n match e with\n | EApp e1 e2 ->\n if is_value e1 then\n if is_value e2 then\n match e1 with\n | EAbs x t e' -> Some (subst x e2 e')\n | _ -> None\n else\n match step e2 with\n | Some e2' -> Some (EApp e1 e2')\n | None -> None\n else\n (match step e1 with\n | Some e1' -> Some (EApp e1' e2)\n | None -> None)\n | _ -> None", "val minus : nat -> nat -> Tot nat\nlet rec minus (n : nat) (m : nat) : nat =\n match n, m with\n | O , _ -> O\n | S _ , O -> n\n | S n', S m' -> minus n' m'", "val plus_one: 'a -> nat -> Tot nat\nlet plus_one m n = n + 1", "val eval : expr -> Tot int\nlet eval e = eval_cps e C0", "val eval : expr -> Tot int\nlet eval e = eval_cps e (fun x -> x)", "val const (#t: Type0) (v: t) : Tot (exp t)\nlet const (#t: Type0) (v: t) : Tot (exp t) = fun _ -> v", "val appears_free_in : x:var -> e:exp -> Tot bool (decreases e)\nlet rec appears_free_in x e =\n match e with\n | EVar y -> x = y\n | EApp e1 e2 -> appears_free_in x e1 || appears_free_in x e2\n | ELam _ e1 -> appears_free_in (x+1) e1\n | EUnit -> false", "val appears_free_in : x:var -> e:exp -> Tot bool (decreases e)\nlet rec appears_free_in x e =\n match e with\n | EVar y -> x = y\n | EApp e1 e2 -> appears_free_in x e1 || appears_free_in x e2\n | EAbs _ e1 -> appears_free_in (x+1) e1", "val elab_exp (e: stlc_exp) : Tot R.term (decreases (size e))\nlet rec elab_exp (e:stlc_exp)\n : Tot R.term (decreases (size e))\n = let open R in\n match e with\n | EUnit -> \n pack_ln (Tv_Const C_Unit)\n\n | EBVar n -> \n let bv = R.pack_bv (RT.make_bv n) in\n R.pack_ln (Tv_BVar bv)\n \n | EVar n ->\n let bv = R.pack_namedv (RT.make_namedv n) in\n R.pack_ln (Tv_Var bv)\n\n | ELam t e ->\n let t = elab_ty t in\n let e = elab_exp e in\n R.pack_ln (Tv_Abs (RT.mk_simple_binder RT.pp_name_default t) e)\n \n | EApp e1 e2 ->\n let e1 = elab_exp e1 in\n let e2 = elab_exp e2 in\n R.pack_ln (Tv_App e1 (e2, Q_Explicit))", "val stack : cont -> Tot (list expr)\nlet rec stack = function\n | C0 -> []\n | C1 k _ -> stack k\n | C2 k e -> e::(stack k)", "val n_evars : eqns -> Tot nat\nlet n_evars eqns = OrdSet.size (evars eqns)", "val fac_sum : nat -> nat -> Tot nat\nlet fac_sum n m = fac n + fac m", "val bvsub (#n: pos) (a b: bv_t n) : Tot (bv_t n)\nlet bvsub #n a b =\n int2bv #n (U.sub_mod (bv2int #n a) (bv2int #n b))", "val subst (x: int) (e e': exp) : exp\nlet rec subst (x:int) (e e':exp) : exp =\n match e' with\n | EVar x' -> \n // If we've found the variable we're substituting for\n // replace it with e\n if x = x' then e else e'\n | EAbs x' t e1 ->\n EAbs x' t \n (if x = x' \n then e1 // If x' shadows x, then don't bother descending into e1\n else subst x e e1)\n | EApp e1 e2 -> \n EApp (subst x e e1) (subst x e e2)\n | EUnit -> EUnit", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val efuns : eqns -> Tot nat\nlet rec efuns = function\n | [] -> 0\n | (x,y)::tl -> funs x + funs y + efuns tl", "val close_exp' (e: src_exp) (v: var) (n: nat) : Tot src_exp (decreases e)\nlet rec close_exp' (e:src_exp) (v:var) (n:nat)\n : Tot src_exp\n (decreases e)\n = match e with\n | EBool _ -> e\n | EVar m -> if m = v then EBVar n else EVar m\n | EBVar m -> EBVar m\n | EIf b e1 e2 -> EIf (close_exp' b v n) (close_exp' e1 v n) (close_exp' e2 v n)\n | ELam t e -> ELam (close_ty' t v n) (close_exp' e v (n + 1))\n | EApp e1 e2 -> EApp (close_exp' e1 v n) (close_exp' e2 v n)\n \nand close_ty' (t:src_ty) (v:var) (n:index)\n : Tot src_ty\n (decreases t)\n = match t with\n | TBool -> TBool\n | TRefineBool e -> TRefineBool (close_exp' e v (n + 1))\n | TArrow t1 t2 -> TArrow (close_ty' t1 v n) (close_ty' t2 v (n + 1))", "val lsubst_term : list subst -> term -> Tot term\nlet lsubst_term = fold_right subst_term", "val expDenote (e: exp) : Tot nat\nlet rec expDenote (e : exp) : Tot nat =\n match e with\n | Const n -> n\n | Binop b e1 e2 -> (binopDenote b) (expDenote e1) (expDenote e2)", "val bad : p (S O) -> Tot (p (S O))\nlet bad h = (PSO?.f h) (POd h)", "val expr_to_term (e: expr) : Tot term\nlet rec expr_to_term (e:expr) : Tot term =\n match e with\n | Atom i t -> t\n | Lit i -> pack_ln (Tv_Const (C_Int i))\n | Plus l r -> mk_e_app (pack_fv' add_qn) [expr_to_term l; expr_to_term r]\n | Minus l r -> mk_e_app (pack_fv' minus_qn) [expr_to_term l; expr_to_term r]\n | Mult l r -> mk_e_app (pack_fv' mult_qn) [expr_to_term l; expr_to_term r]\n (* <- TODO this has some chance of not round-tripping well\n since there is also mult'_qn *)\n | Neg l -> mk_e_app (pack_fv' neg_qn) [expr_to_term l]\n (* TODO all the ones below also have implicit arguments that have to be *)\n (* passed too (number of bits); just how am I supposed to know them? *)\n | Land l r -> mk_e_app (pack_fv' land_qn) [expr_to_term l; expr_to_term r]\n | Lor l r -> mk_e_app (pack_fv' lor_qn) [expr_to_term l; expr_to_term r]\n | Lxor l r -> mk_e_app (pack_fv' lxor_qn) [expr_to_term l; expr_to_term r]\n | Ladd l r -> mk_e_app (pack_fv' land_qn) [expr_to_term l; expr_to_term r]\n | Lsub l r -> mk_e_app (pack_fv' lsub_qn) [expr_to_term l; expr_to_term r]\n | Shl l r -> mk_e_app (pack_fv' shiftl_qn) [expr_to_term l; expr_to_term r]\n | Shr l r -> mk_e_app (pack_fv' shiftr_qn) [expr_to_term l; expr_to_term r]\n | NatToBv l -> mk_e_app (pack_fv' nat_bv_qn) [expr_to_term l]\n | Udiv l r -> mk_e_app (pack_fv' udiv_qn) [expr_to_term l; expr_to_term r]\n | Umod l r -> mk_e_app (pack_fv' umod_qn) [expr_to_term l; expr_to_term r]\n | MulMod l r -> mk_e_app (pack_fv' shiftr_qn) [expr_to_term l; expr_to_term r]", "val size (e: src_exp) : nat\nlet rec size (e:src_exp)\n : nat\n = match e with\n | EBool _\n | EBVar _ \n | EVar _ -> 1\n | EIf b e1 e2 -> size b + size e1 + size e2 + 1\n | ELam _ e -> 1 + size e\n | EApp e1 e2 -> 1 + size e1 + size e2", "val inst_comp : env -> comp -> list term -> Tac comp\nlet rec inst_comp e c tl =\n match tl with\n | [] -> c\n | t :: tl' ->\n let c' = try inst_comp_once e c t\n with | MetaAnalysis msg -> mfail (\"inst_comp: error: \" ^ msg)\n | err -> raise err\n in\n inst_comp e c' tl'", "val while (b: exp bool) (c: computation) : Tot computation\nlet while (b: exp bool) (c: computation) : Tot computation =\n let f : raw_computation = while_raw b c in\n let g = reify_raw_computation f in\n fuel_monotonic_while b c g;\n f", "val log_2: x:pos -> Tot nat\nlet rec log_2 x =\n if x >= 2 then 1 + log_2 (x / 2) else 0", "val shift_up_above : nat -> exp -> Tot exp\nlet shift_up_above n e = subst (sub_inc_above n) e", "val subst_bv_in_comp : env -> bv -> typ -> term -> comp -> Tac comp\nlet subst_bv_in_comp e b sort t c =\n apply_subst_in_comp e c [((b, sort), t)]", "val be_to_n_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat{len + 1 <= tot})\n (ih: be_to_n_t u len)\n : Tot (be_to_n_t u (len + 1))\nlet be_to_n_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat { len + 1 <= tot })\n (ih: be_to_n_t u len)\n: Tot (be_to_n_t u (len + 1))\n= fun x ->\n assert_norm (pow2 8 == 256);\n E.reveal_be_to_n (B.reveal x);\n pow2_le_compat (8 * tot) (8 * (len + 1));\n pow2_le_compat (8 * (len + 1)) (8 * len);\n pow2_plus (8 * len) 8;\n [@inline_let]\n let ulen = U32.uint_to_t len in\n let last = B.get x ulen in\n let first = B.slice x 0ul ulen in\n let n = ih first in\n E.lemma_be_to_n_is_bounded (B.reveal first);\n assert (u.v n * 256 < 256 * pow2 (8 * len));\n assert (0 <= u.v n * 256);\n assert (u.v n * 256 < pow2 (8 * tot));\n let blast = u.from_byte last in\n blast `u.add` u.mul256 n", "val elab_st_sub (#g: env) (#c1 #c2: comp) (d_sub: st_sub g c1 c2)\n : Tot (t: R.term & RT.tot_typing (elab_env g) t (simple_arr (elab_comp c1) (elab_comp c2)))\nlet elab_st_sub (#g:env) (#c1 #c2 : comp)\n (d_sub : st_sub g c1 c2)\n : Tot (t:R.term\n & RT.tot_typing (elab_env g) t (simple_arr (elab_comp c1) (elab_comp c2)))\n= RU.magic_s \"elab_st_sub\"", "val fac : nat -> Tot nat\nlet rec fac i = if i = 0 then 1 else op_Multiply (fac (i-1)) i", "val fact (n: nat) : Tot nat\nlet fact (n : nat) : Tot nat = fact_aux n 1", "val __index__: contents 'a -> int -> Tot 'a\nlet rec __index__ c i = match c with\n | Const v -> v\n | Upd j v tl -> if i=j then v else __index__ tl i\n | Append s1 s2 -> if i < length s1 then __index__ (Seq?.c s1) i else __index__ (Seq?.c s2) (i - length s1)", "val __update__: contents 'a -> int -> 'a -> Tot (contents 'a)\nlet rec __update__ c i v = match c with\n | Const _\n | Upd _ _ _ -> Upd i v c\n | Append s1 s2 ->\n if i < length s1\n then Append (Seq (__update__ (Seq?.c s1) i v) (Seq?.start_i s1) (Seq?.end_i s1)) s2\n else Append s1 (Seq (__update__ (Seq?.c s2) (i - length s1) v) (Seq?.start_i s2) (Seq?.end_i s2))", "val closed : exp -> Tot bool\nlet closed e = below 0 e", "val pred : nat -> Tot nat\nlet pred n =\n match n with\n | O -> O\n | S n' -> n'", "val open_exp' (e v: src_exp) (n: index) : Tot src_exp (decreases e)\nlet rec open_exp' (e:src_exp) (v:src_exp) (n:index)\n : Tot src_exp\n (decreases e)\n = match e with\n | EBool _ -> e\n | EVar m -> EVar m\n | EBVar m -> if m = n then v else EBVar m\n | EIf b e1 e2 -> EIf (open_exp' b v n) (open_exp' e1 v n) (open_exp' e2 v n)\n | ELam t e -> ELam (open_ty' t v n) (open_exp' e v (n + 1))\n | EApp e1 e2 -> EApp (open_exp' e1 v n) (open_exp' e2 v n)\n \nand open_ty' (t:src_ty) (v:src_exp) (n:index)\n : Tot src_ty\n (decreases t)\n = match t with\n | TBool -> TBool\n | TRefineBool e -> TRefineBool (open_exp' e v (n + 1))\n | TArrow t1 t2 -> TArrow (open_ty' t1 v n) (open_ty' t2 v (n + 1))", "val log_ref (r: erid) (i: id) : Tot Type0\nlet log_ref (r:erid) (i:id) : Tot Type0 =\n if authId i then ideal_log r i else unit", "val fact_aux (n acc: nat) : Tot nat\nlet rec fact_aux (n acc : nat) : Tot nat =\n if n = 0\n then acc\n else let acc' = acc `op_Multiply` n in fact_aux (n - 1) acc'", "val freevars_comp (c: comp) : Tot (Set.set var) (decreases c)\nlet freevars_comp (c:comp) : Tot (Set.set var) (decreases c) =\r\n match c with\r\n | C_Tot t -> freevars t\r\n | C_ST s\r\n | C_STGhost s -> freevars_st_comp s\r\n | C_STAtomic inames _ s ->\r\n freevars inames `Set.union` freevars_st_comp s", "val sub_mod (#n: pos) (a b: int_t n) : Tot (int_t n)\nlet sub_mod (#n:pos) (a:int_t n) (b:int_t n) : Tot (int_t n) =\n (a - b) @% (pow2 n)", "val sub_word (w: word) : Tot word\nlet sub_word (w:word) : Tot word =\n map sub_byte w", "val evenb' : nat -> Tot bool\nlet rec evenb' i =\n match i with\n | 0 -> true\n | 1 -> false\n | _ -> evenb' (i-2)", "val canon_expr' (e: expr) : Tot expr\nlet canon_expr' (e:expr) : Tot expr = e", "val le_to_n_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat{len + 1 <= tot})\n (ih: le_to_n_t u len)\n : Tot (le_to_n_t u (len + 1))\nlet le_to_n_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat { len + 1 <= tot })\n (ih: le_to_n_t u len)\n: Tot (le_to_n_t u (len + 1))\n= fun x ->\n assert_norm (pow2 8 == 256);\n E.reveal_le_to_n (B.reveal x);\n pow2_le_compat (8 * tot) (8 * (len + 1));\n pow2_le_compat (8 * (len + 1)) (8 * len);\n pow2_plus (8 * len) 8;\n [@inline_let]\n let ulen = U32.uint_to_t len in\n let last = B.get x 0ul in\n let first = B.slice x 1ul (ulen `U32.add` 1ul) in\n let n = ih first in\n E.lemma_le_to_n_is_bounded (B.reveal first);\n assert (u.v n * 256 < 256 * pow2 (8 * len));\n assert (0 <= u.v n * 256);\n assert (u.v n * 256 < pow2 (8 * tot));\n let blast = u.from_byte last in\n blast `u.add` u.mul256 n", "val evenb : nat -> Tot bool\nlet evenb i = i%2 = 0", "val synth_u14 (msb: varint_msb_t) (lsb: U8.t) : Tot U62.t\nlet synth_u14\n (msb: varint_msb_t)\n (lsb: U8.t)\n: Tot U62.t\n= [@inline_let] let _ =\n assert_norm (pow2 8 == 256);\n assert (pow2 62 == U64.v U62.bound)\n in\n (msb `U64.mul` 256uL) `U64.add` Cast.uint8_to_uint64 lsb", "val evenb : nat -> Tot mbool\nlet rec evenb n =\n match n with\n | O -> MTrue\n | S O -> MFalse\n | S (S n') -> evenb n'", "val id (#t: Type) (x: t) : Tot t\nlet id\n (#t: Type)\n (x: t)\n: Tot t\n= x", "val id (#t: Type) (x: t) : Tot t\nlet id (#t: Type) (x: t) : Tot t = x", "val quote_exp (e: exp) : Tac term\nlet rec quote_exp (e:exp) : Tac term =\n match e with\n | Unit -> `Unit\n | Var x -> mk_e_app (`Var) [pack (Tv_Const (C_Int x))]\n | Mult e1 e2 -> mk_e_app (`Mult) [quote_exp e1; quote_exp e2]", "val upd (h:tape) (i:id) (x:elem) : Tot tape\nlet upd (h:tape) (i:id) (x:elem) : Tot tape = upd h i x", "val upd (h:tape) (i:id) (x:elem) : Tot tape\nlet upd (h:tape) (i:id) (x:elem) : Tot tape = upd h i x", "val imp0 (x: somme) : Tot (bounded_u16 4)\nlet imp0 (x: somme) : Tot (bounded_u16 4) = match x with\n | U _ -> 0us <: bounded_u16 4\n | V -> 1us <: bounded_u16 4\n | W -> 2us <: bounded_u16 4\n | _ -> 3us <: bounded_u16 4", "val rcon_spec: i:size_nat -> Tot elem\nlet rec rcon_spec i =\n if i = 0 then to_elem 0x8d\n else if i = 1 then to_elem 1\n else two `fmul` rcon_spec (i - 1)", "val ge : int -> int -> Tot bool\nlet ge n1 n2 = n1 >= n2", "val collect_arr' (bs: list binder) (c: comp) : Tot (list binder * comp) (decreases c)\nlet rec collect_arr' (bs : list binder) (c : comp) : Tot (list binder * comp) (decreases c) =\n begin match inspect_comp c with\n | C_Total t ->\n begin match inspect_ln_unascribe t with\n | Tv_Arrow b c ->\n collect_arr' (b::bs) c\n | _ ->\n (bs, c)\n end\n | _ -> (bs, c)\n end", "val collect_arr' (bs: list binder) (c: comp) : Tot (list binder * comp) (decreases c)\nlet rec collect_arr' (bs : list binder) (c : comp) : Tot (list binder * comp) (decreases c) =\n begin match inspect_comp c with\n | C_Total t ->\n begin match inspect_ln_unascribe t with\n | Tv_Arrow b c ->\n collect_arr' (b::bs) c\n | _ ->\n (bs, c)\n end\n | _ -> (bs, c)\n end", "val inst_comp_once : env -> comp -> term -> Tac comp\nlet inst_comp_once e c t =\n let ty = get_comp_ret_type c in\n let ty' = unfold_until_arrow e ty in\n begin match inspect ty' with\n | Tv_Arrow b1 c1 ->\n subst_binder_in_comp e b1 t c1\n | _ -> (* Inconsistent state *)\n mfail \"inst_comp_once: inconsistent state\"\n end", "val sub_mod (#n: nat) (a b: uint_t n) : Tot (uint_t n)\nlet sub_mod (#n:nat) (a:uint_t n) (b:uint_t n) : Tot (uint_t n) =\n (a - b) % (pow2 n)" ], "closest_src": [ { "project_name": "FStar", "file_name": "ParSubst.fst", "name": "ParSubst.sub_inc" }, { "project_name": "FStar", "file_name": "StlcStrongDbParSubst.fst", "name": "StlcStrongDbParSubst.sub_inc" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.sub_inc_above" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.evar" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.sub_beta_gen" }, { "project_name": "FStar", "file_name": "StlcCbvDbPntSubstNoLists.fst", "name": "StlcCbvDbPntSubstNoLists.step" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.step" }, { "project_name": "FStar", "file_name": "StlcStrongDbParSubst.fst", "name": "StlcStrongDbParSubst.sub_beta" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.elab_exp" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.elab_exp" }, { "project_name": "FStar", "file_name": "StackMachine.fst", "name": "StackMachine.compile" }, { "project_name": "FStar", "file_name": "SfBasic.fst", "name": "SfBasic.plus" }, { "project_name": "FStar", "file_name": "StlcCbvDbPntSubstNoLists.fst", "name": "StlcCbvDbPntSubstNoLists.extend" }, { "project_name": "FStar", "file_name": "StlcCbvDbPntSubstNoLists.fst", "name": "StlcCbvDbPntSubstNoLists.is_value" }, { "project_name": "FStar", "file_name": "StlcStrongDbParSubst.fst", "name": "StlcStrongDbParSubst.is_value" }, { "project_name": "FStar", "file_name": "ParSubst.fst", "name": "ParSubst.is_value" }, { "project_name": "FStar", "file_name": "StlcStrongDbParSubst.fst", "name": "StlcStrongDbParSubst.is_var" }, { "project_name": "FStar", "file_name": "ParSubst.fst", "name": "ParSubst.is_var" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.vars" }, { "project_name": "FStar", "file_name": "WhileReify.fst", "name": "WhileReify.interpret_exp'" }, { "project_name": "FStar", "file_name": "IfcMonitor.fst", "name": "IfcMonitor.interpret_exp'" }, { "project_name": "FStar", "file_name": "BinarySearchTreeFirst.fst", "name": "BinarySearchTreeFirst.ins" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.subst_term" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.extend_gen" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.reified_exp" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.assign" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.evars" }, { "project_name": "FStar", "file_name": "BinaryTrees.fst", "name": "BinaryTrees.size" }, { "project_name": "FStar", "file_name": "Eval.DB.fst", "name": "Eval.DB.eval_var" }, { "project_name": "FStar", "file_name": "SfBasic.fst", "name": "SfBasic.mult" }, { "project_name": "FStar", "file_name": "CPS.SimpleDefun.fst", "name": "CPS.SimpleDefun.apply" }, { "project_name": "FStar", "file_name": "StlcStrongDbParSubst.fst", "name": "StlcStrongDbParSubst.extend" }, { "project_name": "FStar", "file_name": "StlcCbvDbPntSubstNoLists.fst", "name": "StlcCbvDbPntSubstNoLists.subst_beta" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.below" }, { "project_name": "FStar", "file_name": "WhileReify.fst", "name": "WhileReify.interpret_exp" }, { "project_name": "FStar", "file_name": "MiniParseExample2.fst", "name": "MiniParseExample2.imp1" }, { "project_name": "FStar", "file_name": "BinarySearchTreeBasic.fst", "name": "BinarySearchTreeBasic.insert''" }, { "project_name": "FStar", "file_name": "OPLSS2021.STLC.fst", "name": "OPLSS2021.STLC.step" }, { "project_name": "FStar", "file_name": "SfBasic.fst", "name": "SfBasic.minus" }, { "project_name": "FStar", "file_name": "SfPoly.fst", "name": "SfPoly.plus_one" }, { "project_name": "FStar", "file_name": "CPS.DoubleDefun.fst", "name": "CPS.DoubleDefun.eval" }, { "project_name": "FStar", "file_name": "CPS.DoubleLambdaLifting2.fst", "name": "CPS.DoubleLambdaLifting2.eval" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.const" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.appears_free_in" }, { "project_name": "FStar", "file_name": "StlcCbvDbPntSubstNoLists.fst", "name": "StlcCbvDbPntSubstNoLists.appears_free_in" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.elab_exp" }, { "project_name": "FStar", "file_name": "CPS.DoubleDefun.fst", "name": "CPS.DoubleDefun.stack" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.n_evars" }, { "project_name": "FStar", "file_name": "Recursive.fst", "name": "Recursive.fac_sum" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvsub" }, { "project_name": "FStar", "file_name": "OPLSS2021.STLC.fst", "name": "OPLSS2021.STLC.subst" }, { "project_name": "FStar", "file_name": "FStar.Int16.fst", "name": "FStar.Int16.v" }, { "project_name": "FStar", "file_name": "FStar.Int128.fst", "name": "FStar.Int128.v" }, { "project_name": "FStar", "file_name": "FStar.Int8.fst", "name": "FStar.Int8.v" }, { "project_name": "FStar", "file_name": "FStar.Int64.fst", "name": "FStar.Int64.v" }, { "project_name": "FStar", "file_name": "FStar.Int32.fst", "name": "FStar.Int32.v" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.efuns" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.close_exp'" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.lsubst_term" }, { "project_name": "FStar", "file_name": "StackMachine.fst", "name": "StackMachine.expDenote" }, { "project_name": "FStar", "file_name": "PositiveRelaxed.fst", "name": "PositiveRelaxed.bad" }, { "project_name": "FStar", "file_name": "CanonDeep.fst", "name": "CanonDeep.expr_to_term" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.size" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.inst_comp" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.while" }, { "project_name": "FStar", "file_name": "FStar.Math.Lib.fst", "name": "FStar.Math.Lib.log_2" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.shift_up_above" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.subst_bv_in_comp" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Endianness.fst", "name": "LowParse.SLow.Endianness.be_to_n_S" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.Core.fst", "name": "Pulse.Elaborate.Core.elab_st_sub" }, { "project_name": "FStar", "file_name": "Recursive.fst", "name": "Recursive.fac" }, { "project_name": "FStar", "file_name": "Trace.fst", "name": "Trace.fact" }, { "project_name": "FStar", "file_name": "ArrayRealized.fst", "name": "ArrayRealized.__index__" }, { "project_name": "FStar", "file_name": "ArrayRealized.fst", "name": "ArrayRealized.__update__" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.closed" }, { "project_name": "FStar", "file_name": "SfBasic.fst", "name": "SfBasic.pred" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.open_exp'" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.StreamAE.fst", "name": "MiTLS.StreamAE.log_ref" }, { "project_name": "FStar", "file_name": "Trace.fst", "name": "Trace.fact_aux" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.freevars_comp" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.sub_mod" }, { "project_name": "hacl-star", "file_name": "Spec.AES.fst", "name": "Spec.AES.sub_word" }, { "project_name": "FStar", "file_name": "SfPoly.fst", "name": "SfPoly.evenb'" }, { "project_name": "FStar", "file_name": "CanonDeep.fst", "name": "CanonDeep.canon_expr'" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Endianness.fst", "name": "LowParse.SLow.Endianness.le_to_n_S" }, { "project_name": "FStar", "file_name": "SfPoly.fst", "name": "SfPoly.evenb" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.VarInt.fst", "name": "QUIC.Spec.VarInt.synth_u14" }, { "project_name": "FStar", "file_name": "SfBasic.fst", "name": "SfBasic.evenb" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.id" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fsti", "name": "EverParse3d.Prelude.id" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoid.fst", "name": "FStar.Tactics.CanonCommMonoid.quote_exp" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.Random.fst", "name": "FStar.DM4F.Heap.Random.upd" }, { "project_name": "FStar", "file_name": "FStar.DM4F.OTP.Heap.fst", "name": "FStar.DM4F.OTP.Heap.upd" }, { "project_name": "FStar", "file_name": "MiniParseExample2.fst", "name": "MiniParseExample2.imp0" }, { "project_name": "hacl-star", "file_name": "Spec.AES.fst", "name": "Spec.AES.rcon_spec" }, { "project_name": "FStar", "file_name": "BinarySearchTreeBasic.fst", "name": "BinarySearchTreeBasic.ge" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Derived.fst", "name": "FStar.Reflection.V1.Derived.collect_arr'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Derived.fst", "name": "FStar.Reflection.V2.Derived.collect_arr'" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.inst_comp_once" }, { "project_name": "FStar", "file_name": "FStar.UInt.fsti", "name": "FStar.UInt.sub_mod" } ], "selected_premises": [ "FStar.Constructive.ceq_symm", "FStar.FunctionalExtensionality.feq", "FStar.Constructive.ceq_trans", "FStar.Constructive.eq_ind", "FStar.Constructive.false_elim", "FStar.Constructive.ceq_congruence", "LambdaOmega.is_erenaming", "FStar.FunctionalExtensionality.on_dom", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "FStar.Tactics.Effect.raise", "FStar.Constructive.cfalse_elim", "FStar.Pervasives.reveal_opaque", "FStar.FunctionalExtensionality.on", "FStar.Tactics.Types.issues", "FStar.Pervasives.dfst", "FStar.Constructive.false_elim2", "FStar.Pervasives.dsnd", "FStar.Tactics.Effect.get", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater", "FStar.Tactics.Effect.tactic", "FStar.Tactics.Effect.tac", "FStar.FunctionalExtensionality.restricted_t", "FStar.FunctionalExtensionality.feq_g", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater_Greater", "FStar.Pervasives.id", "FStar.FunctionalExtensionality.arrow", "FStar.Pervasives.coerce_eq", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity", "FStar.Pervasives.ex_pre", "FStar.FunctionalExtensionality.is_restricted", "FStar.Pervasives.ex_post", "FStar.Pervasives.ex_if_then_else", "FStar.Pervasives.ex_stronger", "FStar.FunctionalExtensionality.restricted_g_t", "FStar.FunctionalExtensionality.on_dom_g", "FStar.FunctionalExtensionality.efun", "FStar.Pervasives.ex_post'", "FStar.FunctionalExtensionality.is_restricted_g", "FStar.Pervasives.ex_bind_wp", "FStar.Pervasives.ex_ite_wp", "FStar.FunctionalExtensionality.efun_g", "Prims.op_Hat", "FStar.Pervasives.ex_return", "FStar.Pervasives.ex_trivial", "FStar.FunctionalExtensionality.on_g", "FStar.Issue.issue_level_string", "Prims.min", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.ex_wp", "Prims.l_True", "Prims.auto_squash", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity_forall", "FStar.Pervasives.lift_div_exn", "FStar.Monotonic.Pure.is_monotonic", "FStar.FunctionalExtensionality.arrow_g", "FStar.Monotonic.Pure.intro_pure_wp_monotonicity", "FStar.Pervasives.all_if_then_else", "Prims.returnM", "FStar.Issue.mk_issue", "FStar.Pervasives.ex_close_wp", "FStar.Tactics.Effect.tac_if_then_else_wp", "Prims.subtype_of", "FStar.Pervasives.pure_ite_wp", "FStar.Pervasives.st_if_then_else", "FStar.Pervasives.all_post_h", "FStar.Tactics.Effect.lift_div_tac", "FStar.Tactics.Effect.lift_div_tac_wp", "Prims.abs", "FStar.Pervasives.all_post_h'", "Prims.l_False", "FStar.Pervasives.pure_bind_wp", "Prims.as_requires", "FStar.Pervasives.st_stronger", "FStar.Tactics.Effect.tac_wp_monotonic", "FStar.Pervasives.st_bind_wp", "FStar.Tactics.Effect.tac_subcomp", "FStar.Tactics.Effect.tac_bind_wp", "Prims.purewp_id", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.all_stronger", "FStar.Monotonic.Pure.as_pure_wp", "FStar.Pervasives.all_wp_h", "FStar.Tactics.Effect.tac_return_wp", "FStar.Pervasives.div_hoare_to_wp", "FStar.Monotonic.Pure.elim_pure", "Prims.pure_trivial", "FStar.Pervasives.all_trivial", "Prims.pure_pre", "FStar.Pervasives.all_ite_wp", "FStar.Tactics.Effect.tac_wp_compact", "FStar.Tactics.Effect.tac_close", "FStar.Pervasives.st_ite_wp", "Prims.pure_stronger", "FStar.Tactics.Effect.tac_repr", "FStar.Pervasives.st_trivial", "Prims.pure_wp_monotonic", "FStar.Pervasives.st_pre_h", "Prims.pure_wp_monotonic0", "FStar.Pervasives.st_post_h" ], "source_upto_this": "(*\n Copyright 2015\n Simon Forest - Inria and ENS Paris\n Catalin Hritcu - Inria\n Aseem Rastogi - UMD\n Nikhil Swamy - Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule LambdaOmega\n\n#set-options \"--max_fuel 1 --max_ifuel 1 --initial_fuel 1\"\n\nopen FStar.Constructive\nopen FStar.Classical\nopen FStar.FunctionalExtensionality\nopen FStar.StrongExcludedMiddle\n\n(* Chapter 29 of TAPL: \"Type Operators and Kinding\",\n proof follows Chapter 30, but we don't consider polymorphism\n (for extension to System F-omega see f-omega.fst) *)\n\ntype var = nat\n\ntype knd =\n | KTyp : knd\n | KArr : knd -> knd -> knd\n\ntype typ =\n | TVar : var -> typ\n | TLam : knd -> t:typ -> typ\n | TApp : typ -> typ -> typ\n | TArr : typ -> typ -> typ\n\ntype exp =\n | EVar : var -> exp\n | EApp : exp -> exp -> exp\n | ELam : typ -> exp -> exp\n\n(* Substitution on expressions\n (in this calculus doesn't interact with type substitution below) *)\n\ntype esub = var -> Tot exp\ntype erenaming (s:esub) = (forall (x:var). EVar? (s x))\n\nval is_erenaming : s:esub -> GTot (n:int{( erenaming s ==> n=0) /\\\n (~(erenaming s) ==> n=1)})\nlet is_erenaming s = (if strong_excluded_middle (erenaming s) then 0 else 1)\n\nval esub_inc : var -> Tot exp", "sketch": [ "Step 1: The definition `esub_inc` is about creating a substitution function that maps a variable to an expression. Specifically, it maps a variable to an expression that represents the variable itself.\nStep 2: The implementation of `esub_inc` is straightforward. It takes a variable `x` and returns an expression `EVar x`, which is the expression form of the variable `x`.", "Step 1: The `esub_inc` function is intended to define a substitution on expressions where each variable is incremented by one.\nStep 2: To implement this, we will define a function that takes a variable `x` and returns an expression `EVar` with the variable incremented by one.", "Step 1: The definition `esub_inc` is about defining a substitution function for expressions. Specifically, it increments the variable index by 1.\nStep 2: The implementation of `esub_inc` takes a variable `x` and returns an expression `EVar` with the variable index incremented by 1.", "Step 1: The `esub_inc` function is intended to be a substitution function that maps a variable to an expression. Specifically, it will map a variable to an expression that represents the variable itself incremented by one.\nStep 2: To implement this, the function will take a variable `x` as input and return an expression `EVar` with the variable `x + 1`.", "Step 1: The definition `esub_inc` is a function that takes a variable of type `var` (which is a natural number) and returns an expression of type `exp`.\nStep 2: The implementation of `esub_inc` should return an expression that represents a variable. Specifically, it should return an `EVar` expression with the input variable incremented by 1.", "Step 1: The definition `esub_inc` is a function that takes a variable `x` of type `var` and returns an expression of type `exp`.\nStep 2: The implementation of `esub_inc` is straightforward. It simply returns the expression `EVar x`, which represents a variable expression with the given variable `x`.", "Step 1: The definition `esub_inc` is about creating a substitution function for expressions that increments the variable index by 1.\nStep 2: The implementation involves defining a function that takes a variable `x` and returns an expression `EVar` with the variable index incremented by 1.", "Step 1: The `esub_inc` function is intended to define a substitution on expressions that increments the variable index by 1. This function will take a variable `x` and return an expression where the variable index is incremented.\nStep 2: To implement this, we will define `esub_inc` such that it takes a variable `x` and returns an `EVar` expression with the variable index incremented by 1.", "Step 1: The `esub_inc` function is intended to increment the variable index by 1. This is a common operation in lambda calculus and type theory, where variable indices are often manipulated to avoid name clashes.\nStep 2: The implementation of `esub_inc` will take a variable `x` of type `var` (which is a natural number) and return an expression `EVar` with the variable index incremented by 1.", "Step 1: The definition `esub_inc` is about creating a substitution function for expressions that increments the variable index by 1. This is useful in scenarios where we need to shift variable indices, such as during variable renaming or alpha conversion in lambda calculus.\nStep 2: The implementation of `esub_inc` will take a variable `x` and return an expression `EVar` with the variable index incremented by 1. This is a straightforward function that simply adds 1 to the input variable index." ], "generated_solution": [ "let esub_inc x = EVar x", "let esub_inc x = EVar (x + 1)", "let esub_inc x = EVar (x + 1)", "let esub_inc x = EVar (x + 1)", "let esub_inc x = EVar (x + 1)", "let esub_inc x = EVar x", "let esub_inc x = EVar (x + 1)", "let esub_inc x = EVar (x + 1)", "let esub_inc x = EVar (x + 1)", "let esub_inc x = EVar (x + 1)" ] }, { "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.is_heap_color", "opens_and_abbrevs": [ { "open": "FStar.Monotonic.HyperHeap" }, { "abbrev": "Map", "full_module": "FStar.Map" }, { "open": "FStar.Preorder" }, { "open": "FStar.Monotonic" }, { "open": "FStar.Monotonic" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let is_heap_color c = c <= 0", "source_range": { "start_line": 29, "start_col": 0, "end_line": 29, "end_col": 28 }, "interleaved": false, "definition": "fun c -> c <= 0", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Prims.int", "Prims.op_LessThanOrEqual", "Prims.bool" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "c: Prims.int -> Prims.bool", "prompt": "let is_heap_color c =\n ", "expected_response": "c <= 0", "source": { "project_name": "FStar", "file_name": "ulib/FStar.Monotonic.HyperStack.fsti", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.Monotonic.HyperStack.fsti", "checked_file": "dataset/FStar.Monotonic.HyperStack.fsti.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Monotonic.HyperHeap.fsti.checked", "dataset/FStar.Monotonic.Heap.fsti.checked", "dataset/FStar.Map.fsti.checked" ] }, "definitions_in_context": [ "", "", "let is_in (r:rid) (h:hmap) = h `Map.contains` r", "let is_stack_region r = color r > 0" ], "closest": [ "val FStar.DM4F.Heap.Random.size = Prims.int\nlet size = 10", "val FStar.Monotonic.Heap.set = a: Prims.eqtype -> Type0\nlet set = Set.set", "val FStar.DM4F.Heap.consistent = h0: FStar.DM4F.Heap.heap -> h1: FStar.DM4F.Heap.heap -> Prims.logical\nlet consistent (h0:heap) (h1:heap) =\n forall n x y. h0.memory n == Some x /\\ h1.memory n == Some y ==> dfst x == dfst y", "val FStar.ST.modifies_none = h0: FStar.Monotonic.Heap.heap -> h1: FStar.Monotonic.Heap.heap -> Prims.logical\nlet modifies_none (h0:heap) (h1:heap) = modifies !{} h0 h1", "val FStar.Pervasives.st_pre_h = heap: Type -> Type\nlet st_pre_h (heap: Type) = heap -> GTot Type0", "val AllocSTwHeaps.contains = r: FStar.ST.ref a -> h: FStar.Monotonic.Heap.heap -> Prims.logical\nlet contains (#a:Type) (r:ref a) (h:FStar.Heap.heap) =\n b2t (FStar.StrongExcludedMiddle.strong_excluded_middle (FStar.Heap.contains h r))", "val FStar.DM4F.IntStore.in_ = x: FStar.DM4F.IntStore.id -> store: FStar.DM4F.IntStore.heap -> Prims.bool\nlet in_ (x:id) (store:heap) = x < length store", "val FStar.DM4F.OTP.Heap.size = Prims.int\nlet size = 10", "val ImmutableSTwHeaps.heap_rel = h0: FStar.Monotonic.Heap.heap -> h1: FStar.Monotonic.Heap.heap -> Prims.logical\nlet heap_rel (h0:heap) (h1:heap) = \n forall a (r: ref a) . contains h0 r ==> contains h1 r /\\ sel h0 r == sel h1 r", "val FStar.ST.heap_rel = h1: FStar.Monotonic.Heap.heap -> h2: FStar.Monotonic.Heap.heap -> Prims.logical\nlet heap_rel (h1:heap) (h2:heap) =\n forall (a:Type0) (rel:preorder a) (r:mref a rel). h1 `contains` r ==>\n (h2 `contains` r /\\ rel (sel h1 r) (sel h2 r))", "val AllocSTwHeaps.heap_rel = h0: FStar.Monotonic.Heap.heap -> h1: FStar.Monotonic.Heap.heap -> Prims.logical\nlet heap_rel (h0:FStar.Heap.heap) (h1:FStar.Heap.heap) = \n forall (a:Type0) (r:ref a) . FStar.Heap.contains h0 r ==> FStar.Heap.contains h1 r", "val FStar.Monotonic.Heap.modifies = \n s: FStar.Monotonic.Heap.set Prims.nat ->\n h0: FStar.Monotonic.Heap.heap ->\n h1: FStar.Monotonic.Heap.heap\n -> Prims.logical\nlet modifies (s:set nat) (h0:heap) (h1:heap) = modifies_t (TS.tset_of_set s) h0 h1", "val Swap.heap_eq = h: FStar.DM4F.Heap.heap -> h_0: FStar.DM4F.Heap.heap -> h_1: FStar.DM4F.Heap.heap -> Prims.logical\nlet heap_eq (h:heap) (h_0:heap) (h_1:heap) =\n forall (a:Type) (r:ref a). h `contains` r ==> sel h_0 r == sel h_1 r", "val FStar.Int32.op_Greater_Hat = a: FStar.Int32.t -> b: FStar.Int32.t -> Prims.bool\nlet op_Greater_Hat = gt", "val FStar.Int64.op_Equals_Hat = a: FStar.Int64.t -> b: FStar.Int64.t -> Prims.bool\nlet op_Equals_Hat = eq", "val FStar.MRef.p_pred = r: FStar.ST.mref a b -> p: (_: a -> Type0) -> h: FStar.Monotonic.Heap.heap -> Prims.logical\nlet p_pred (#a:Type) (#b:preorder a) (r:mref a b) (p:(a -> Type))\n = fun h -> h `contains` r /\\ p (sel h r)", "val FStar.Pervasives.st_trivial = heap: Type -> a: Type -> wp: FStar.Pervasives.st_wp_h heap a -> Prims.logical\nlet st_trivial (heap a: Type) (wp: st_wp_h heap a) = (forall h0. wp (fun r h1 -> True) h0)", "val FStar.Pervasives.st_post_h = heap: Type -> a: Type -> Type\nlet st_post_h (heap a: Type) = st_post_h' heap a True", "val FStar.Monotonic.Pure.is_monotonic = wp: Prims.pure_wp' a -> Prims.logical\nlet is_monotonic (#a:Type) (wp:pure_wp' a) =\n (*\n * Once we support using tactics in ulib/,\n * this would be written as: Prims.pure_wp_monotonic0,\n * with a postprocessing tactic to norm it\n *)\n forall (p q:pure_post a). (forall (x:a). p x ==> q x) ==> (wp p ==> wp q)", "val FStar.ST.stable = p: FStar.ST.heap_predicate -> Prims.logical\nlet stable (p:heap_predicate) =\n forall (h1:heap) (h2:heap). (p h1 /\\ heap_rel h1 h2) ==> p h2", "val Vale.PPC64LE.InsMem.heaplet_id_is_some = h: Vale.PPC64LE.InsBasic.vale_heap -> i: Vale.PPC64LE.Memory.heaplet_id -> Prims.logical\nlet heaplet_id_is_some (h:vale_heap) (i:heaplet_id) =\n get_heaplet_id h == Some i", "val FStar.Monotonic.Heap.modifies_t = \n s: FStar.Monotonic.Heap.tset Prims.nat ->\n h0: FStar.Monotonic.Heap.heap ->\n h1: FStar.Monotonic.Heap.heap\n -> Prims.logical\nlet modifies_t (s:tset nat) (h0:heap) (h1:heap) =\n (forall (a:Type) (rel:preorder a) (r:mref a rel).{:pattern (sel h1 r)}\n ((~ (TS.mem (addr_of r) s)) /\\ h0 `contains` r) ==> sel h1 r == sel h0 r) /\\\n (forall (a:Type) (rel:preorder a) (r:mref a rel).{:pattern (contains h1 r)}\n h0 `contains` r ==> h1 `contains` r) /\\\n (forall (a:Type) (rel:preorder a) (r:mref a rel).{:pattern (r `unused_in` h0)}\n r `unused_in` h1 ==> r `unused_in` h0) /\\\n (forall (n: nat) . {:pattern (n `addr_unused_in` h0) }\n n `addr_unused_in` h1 ==> n `addr_unused_in` h0\n )", "val FStar.DM4F.Heap.IntStoreFixed.store_size = Prims.int\nlet store_size = 10", "val LeftistHeap.gt = {| _: LeftistHeap.ordered t |} -> a: t -> b: t -> Prims.bool\nlet gt (#t: eqtype) {| _ : ordered t |} (a b: t) =\n leq b a && a <> b", "val FStar.Pervasives.all_trivial = heap: Type -> a: Type -> wp: FStar.Pervasives.all_wp_h heap a -> Prims.logical\nlet all_trivial (heap a: Type) (wp: all_wp_h heap a) = (forall (h0: heap). wp (fun r h1 -> True) h0)", "val FStar.DM4F.Heap.fresh = s: FStar.Set.set Prims.nat -> h0: FStar.DM4F.Heap.heap -> h1: FStar.DM4F.Heap.heap -> Prims.logical\nlet fresh (s:set nat) (h0:heap) (h1:heap) =\n forall (a:Type) (r:ref a).{:pattern (h0 `contains` r)}\n mem (addr_of r) s ==> ~ (h0 `contains` r) /\\ (h1 `contains` r)", "val FStar.Int32.op_Equals_Hat = a: FStar.Int32.t -> b: FStar.Int32.t -> Prims.bool\nlet op_Equals_Hat = eq", "val FStar.Int64.op_Greater_Hat = a: FStar.Int64.t -> b: FStar.Int64.t -> Prims.bool\nlet op_Greater_Hat = gt", "val FStar.Int64.op_Less_Hat = a: FStar.Int64.t -> b: FStar.Int64.t -> Prims.bool\nlet op_Less_Hat = lt", "val FStar.Int8.op_Greater_Hat = a: FStar.Int8.t -> b: FStar.Int8.t -> Prims.bool\nlet op_Greater_Hat = gt", "val FStar.Int32.op_Less_Hat = a: FStar.Int32.t -> b: FStar.Int32.t -> Prims.bool\nlet op_Less_Hat = lt", "val Vale.X64.InsMem.heaplet_id_is_some = h: Vale.X64.InsBasic.vale_heap -> i: Vale.X64.Decls.heaplet_id -> Prims.logical\nlet heaplet_id_is_some (h:vale_heap) (i:heaplet_id) =\n get_heaplet_id h == Some i", "val FStar.Int64.op_Greater_Equals_Hat = a: FStar.Int64.t -> b: FStar.Int64.t -> Prims.bool\nlet op_Greater_Equals_Hat = gte", "val Steel.Heap.frame_related_heaps = \n h0: Steel.Heap.full_heap ->\n h1: Steel.Heap.full_heap ->\n fp0: Steel.Heap.slprop ->\n fp1: Steel.Heap.slprop ->\n frame: Steel.Heap.slprop ->\n allocates: Prims.bool\n -> Prims.logical\nlet frame_related_heaps (h0 h1:full_heap) (fp0 fp1 frame:slprop) (allocates:bool) =\n interp (fp0 `star` frame) h0 ==>\n interp (fp1 `star` frame) h1 /\\\n heap_evolves h0 h1 /\\\n (forall (hp:hprop frame). hp h0 == hp h1) /\\\n (not allocates ==> (forall ctr. h0 `free_above_addr` ctr ==> h1 `free_above_addr` ctr))", "val get: Prims.unit -> HoareST heap (fun _ -> True) (fun h0 h h1 -> h0 == h1 /\\ h == h1)\nlet get ()\n: HoareST heap\n (fun _ -> True)\n (fun h0 h h1 -> h0 == h1 /\\ h == h1)\n= HoareST?.reflect get", "val get: Prims.unit -> HoareST heap (fun _ -> True) (fun h0 h h1 -> h0 == h1 /\\ h == h1)\nlet get ()\n: HoareST heap\n (fun _ -> True)\n (fun h0 h h1 -> h0 == h1 /\\ h == h1)\n= HoareST?.reflect get", "val FStar.Int128.op_Less_Hat = a: FStar.Int128.t -> b: FStar.Int128.t -> Prims.bool\nlet op_Less_Hat = lt", "val FStar.Int8.op_Equals_Hat = a: FStar.Int8.t -> b: FStar.Int8.t -> Prims.bool\nlet op_Equals_Hat = eq", "val FStar.DM4F.Heap.only = x: FStar.DM4F.Heap.ref _ -> FStar.Set.set Prims.nat\nlet only x = singleton (addr_of x)", "val FStar.Int128.op_Greater_Hat = a: FStar.Int128.t -> b: FStar.Int128.t -> Prims.bool\nlet op_Greater_Hat = gt", "val Steel.Semantics.Hoare.MST.fp_heap_0 = interp: (_: hprop -> _: heap -> Prims.prop) -> pre: hprop -> Type\nlet fp_heap_0\n (#heap:Type)\n (#hprop:Type)\n (interp:hprop -> heap -> prop)\n (pre:hprop)\n =\n h:heap{interp pre h}", "val Point.equal_heaps_except_fp = h0: FStar.DM4F.Heap.heap -> h1: FStar.DM4F.Heap.heap -> s: Point.fp -> Prims.logical\nlet equal_heaps_except_fp (h0:heap) (h1:heap) (s:fp) =\n forall (a:Type) (r:ref a). ref_not_in_fp r s ==> sel h0 r == sel h1 r", "val Swap.equiv_on_h = c_0: Swap.command -> c_1: Swap.command -> h: FStar.DM4F.Heap.heap -> Prims.logical\nlet equiv_on_h (c_0:command) (c_1:command) (h:heap) = \n let (), h_0 = reify (c_0 ()) h in\n let (), h_1 = reify (c_1 ()) h in\n no_alloc h h_0 /\\\n no_alloc h h_1 /\\\n heap_eq h h_0 h_1", "val FStar.Monotonic.HyperHeap.equal_on = \n s: FStar.Set.set FStar.Monotonic.HyperHeap.rid ->\n m0: FStar.Monotonic.HyperHeap.hmap ->\n m1: FStar.Monotonic.HyperHeap.hmap\n -> Prims.logical\nlet equal_on (s:Set.set rid) (m0:hmap) (m1:hmap) =\n (forall (r:rid). {:pattern (Map.contains m0 r)} (Set.mem r (mod_set s) /\\ Map.contains m0 r) ==> Map.contains m1 r) /\\\n Map.equal m1 (Map.concat m1 (Map.restrict (mod_set s) m0))", "val FStar.Int8.op_Less_Hat = a: FStar.Int8.t -> b: FStar.Int8.t -> Prims.bool\nlet op_Less_Hat = lt", "val FStar.Int8.op_Greater_Equals_Hat = a: FStar.Int8.t -> b: FStar.Int8.t -> Prims.bool\nlet op_Greater_Equals_Hat = gte", "val Vale.X64.InsMem.heaplet_id_is_none = h: Vale.X64.InsBasic.vale_heap -> Prims.logical\nlet heaplet_id_is_none (h:vale_heap) =\n get_heaplet_id h == None", "val FStar.Int32.op_Greater_Equals_Hat = a: FStar.Int32.t -> b: FStar.Int32.t -> Prims.bool\nlet op_Greater_Equals_Hat = gte", "val FStar.Pervasives.st_post_h' = heap: Type -> a: Type -> pre: Type -> Type\nlet st_post_h' (heap a pre: Type) = a -> _: heap{pre} -> GTot Type0", "val FStar.UInt32.op_Greater_Hat = a: FStar.UInt32.t -> b: FStar.UInt32.t -> Prims.bool\nlet op_Greater_Hat = gt", "val FStar.Int64.op_Less_Equals_Hat = a: FStar.Int64.t -> b: FStar.Int64.t -> Prims.bool\nlet op_Less_Equals_Hat = lte", "val FStar.Pervasives.all_return = heap: Type -> a: Type -> x: a -> p: FStar.Pervasives.all_post_h heap a -> _: heap{Prims.l_True}\n -> Prims.GTot Type0\nlet all_return (heap a: Type) (x: a) (p: all_post_h heap a) = p (V x)", "val FStar.Int128.op_Equals_Hat = a: FStar.Int128.t -> b: FStar.Int128.t -> Prims.bool\nlet op_Equals_Hat = eq", "val FStar.Pervasives.st_wp_h = heap: Type -> a: Type -> Type\nlet st_wp_h (heap a: Type) = st_post_h heap a -> Tot (st_pre_h heap)", "val FStar.Int16.op_Greater_Hat = a: FStar.Int16.t -> b: FStar.Int16.t -> Prims.bool\nlet op_Greater_Hat = gt", "val FStar.TwoLevelHeap.contains_ref = r: FStar.TwoLevelHeap.rref i a -> m: FStar.TwoLevelHeap.t -> Prims.logical\nlet contains_ref (#a:Type) (#i:rid) (r:rref i a) (m:t) =\n Map.contains m i /\\ Heap.contains (Map.sel m i) (as_ref r)", "val FStar.ST.contains_pred = r: FStar.Monotonic.Heap.mref a rel -> h: FStar.Monotonic.Heap.heap -> Type0\nlet contains_pred (#a:Type0) (#rel:preorder a) (r:mref a rel) = fun h -> h `contains` r", "val FStar.PtrdiffT.op_Greater_Hat = x: FStar.PtrdiffT.t -> y: FStar.PtrdiffT.t -> Prims.Pure Prims.bool\nlet op_Greater_Hat = gt", "val FStar.Int128.op_Greater_Equals_Hat = a: FStar.Int128.t -> b: FStar.Int128.t -> Prims.bool\nlet op_Greater_Equals_Hat = gte", "val FStar.Reflection.Typing.ln_comp = c: FStar.Stubs.Reflection.Types.comp -> Prims.bool\nlet ln_comp (c:comp) = ln'_comp c (-1)", "val FStar.DM4F.Heap.ST.op_Colon_Equals = r: FStar.DM4F.Heap.ref _ -> v: _ -> FStar.DM4F.Heap.ST.ST Prims.unit\nlet op_Colon_Equals = write", "val FStar.Int16.op_Less_Hat = a: FStar.Int16.t -> b: FStar.Int16.t -> Prims.bool\nlet op_Less_Hat = lt", "val MRefST.stable_on_heap = m: MRefST.mref a r -> p: FStar.Preorder.predicate MRefHeap.heap -> Prims.logical\nlet stable_on_heap (#a:Type) (#r:preorder a) (m:mref a r) (p:predicate heap) =\n forall h0 h1 . stable_on_heap_aux m p h0 h1", "val Vale.PPC64LE.Memory.vale_full_heap_equal = h1: Vale.PPC64LE.Memory.vale_full_heap -> h2: Vale.PPC64LE.Memory.vale_full_heap -> Prims.logical\nlet vale_full_heap_equal (h1 h2:vale_full_heap) =\n h1.vf_layout == h2.vf_layout /\\\n h1.vf_heap == h2.vf_heap /\\\n Map16.equal h1.vf_heaplets h2.vf_heaplets", "val PulseCore.Heap.frame_related_heaps = \n h0: PulseCore.Heap.full_heap ->\n h1: PulseCore.Heap.full_heap ->\n fp0: PulseCore.Heap.slprop ->\n fp1: PulseCore.Heap.slprop ->\n frame: PulseCore.Heap.slprop ->\n allocates: Prims.bool\n -> Prims.logical\nlet frame_related_heaps (h0 h1:full_heap) (fp0 fp1 frame:slprop) (allocates:bool) =\n interp (fp0 `star` frame) h0 ==>\n interp (fp1 `star` frame) h1 /\\\n heap_evolves h0 h1 /\\\n (forall (hp:hprop frame). hp h0 == hp h1) /\\\n (not allocates ==> (forall ctr. h0 `free_above_addr` ctr ==> h1 `free_above_addr` ctr))", "val FStar.PtrdiffT.op_Less_Hat = x: FStar.PtrdiffT.t -> y: FStar.PtrdiffT.t -> Prims.Pure Prims.bool\nlet op_Less_Hat = lt", "val FStar.Int16.op_Equals_Hat = a: FStar.Int16.t -> b: FStar.Int16.t -> Prims.bool\nlet op_Equals_Hat = eq", "val FStar.Int16.op_Greater_Equals_Hat = a: FStar.Int16.t -> b: FStar.Int16.t -> Prims.bool\nlet op_Greater_Equals_Hat = gte", "val Protocol.live_connection = h: FStar.Monotonic.Heap.heap -> c: Protocol.connection -> Type0\nlet live_connection (h:heap) (c:connection) =\n match c with\n | S _ es_ref -> h `contains` es_ref\n | R _ es_ref ctr_ref -> h `contains` es_ref /\\ h `contains` ctr_ref", "val FStar.Monotonic.HyperHeap.modifies_one = \n r: FStar.Monotonic.HyperHeap.rid ->\n m0: FStar.Monotonic.HyperHeap.hmap ->\n m1: FStar.Monotonic.HyperHeap.hmap\n -> Prims.logical\nlet modifies_one (r:rid) (m0:hmap) (m1:hmap) = modifies_just (Set.singleton r) m0 m1", "val FStar.DM4F.Heap.modifies = s: FStar.Set.set Prims.nat -> h0: FStar.DM4F.Heap.heap -> h1: FStar.DM4F.Heap.heap -> Prims.logical\nlet modifies (s:set nat) (h0:heap) (h1:heap) =\n (forall (a:Type) (r:ref a).{:pattern (sel h1 r)}\n ~ (mem (addr_of r) s) /\\ h0 `contains` r ==>\n sel h1 r == sel h0 r) /\\\n (forall (a:Type) (r:ref a).{:pattern (h1 `contains` r)}\n h0 `contains` r ==> h1 `contains` r) /\\\n (* AR: an alternative to this would be to prove a lemma that if sel is same and h0 contains_a_well_typed then h1 contains_a_well_typed, then the following clause would follow from the first clause of sel remaining same *)\n (forall (a:Type) (r:ref a).{:pattern (h1 `contains_a_well_typed` r)}\n (~ (mem (addr_of r) s) /\\ h0 `contains_a_well_typed` r) ==> h1 `contains_a_well_typed` r)", "val FStar.Int8.op_Less_Equals_Hat = a: FStar.Int8.t -> b: FStar.Int8.t -> Prims.bool\nlet op_Less_Equals_Hat = lte", "val Vale.PPC64LE.InsMem.heaplet_id_is_none = h: Vale.PPC64LE.InsBasic.vale_heap -> Prims.logical\nlet heaplet_id_is_none (h:vale_heap) =\n get_heaplet_id h == None", "val FStar.Int128.op_Less_Equals_Hat = a: FStar.Int128.t -> b: FStar.Int128.t -> Prims.bool\nlet op_Less_Equals_Hat = lte", "val FStar.Monotonic.Heap.tset = a: Type -> Type\nlet tset = TSet.set", "val FStar.Pervasives.st_return = heap: Type -> a: Type -> x: a -> p: FStar.Pervasives.st_post_h heap a -> _: heap{Prims.l_True}\n -> Prims.GTot Type0\nlet st_return (heap a: Type) (x: a) (p: st_post_h heap a) = p x", "val FStar.Int32.op_Less_Equals_Hat = a: FStar.Int32.t -> b: FStar.Int32.t -> Prims.bool\nlet op_Less_Equals_Hat = lte", "val ProgramEquivalence.equal_heaps_except_fp = h0: FStar.DM4F.Heap.heap -> h1: FStar.DM4F.Heap.heap -> s: ProgramEquivalence.fp -> Prims.logical\nlet equal_heaps_except_fp (h0:heap) (h1:heap) (s:fp) =\n forall (a:Type) (r:ref a). ref_not_in_fp r s ==> sel h0 r == sel h1 r", "val IfcDelimitedRelease.rel_contains = h: Rel.rel FStar.Monotonic.Heap.heap -> r: FStar.Heap.ref Prims.int -> Prims.logical\nlet rel_contains (h:rel heap) (r:ref int) = (R?.l h) `contains` r /\\ (R?.r h) `contains` r", "val FStar.Pervasives.all_stronger = \n heap: Type ->\n a: Type ->\n wp1: FStar.Pervasives.all_wp_h heap a ->\n wp2: FStar.Pervasives.all_wp_h heap a\n -> Prims.logical\nlet all_stronger (heap a: Type) (wp1 wp2: all_wp_h heap a) =\n (forall (p: all_post_h heap a) (h: heap). wp1 p h ==> wp2 p h)", "val Vale.PPC64LE.Decls.va_is_src_heaplet = h: Vale.PPC64LE.Decls.heaplet_id -> s: Vale.PPC64LE.Decls.va_state -> Prims.logical\nlet va_is_src_heaplet (h:heaplet_id) (s:va_state) = True", "val FStar.PtrdiffT.op_Greater_Equals_Hat = x: FStar.PtrdiffT.t -> y: FStar.PtrdiffT.t -> Prims.Pure Prims.bool\nlet op_Greater_Equals_Hat = gte", "val Vale.X64.Memory.init_heaplets_req = h: Vale.X64.Memory.vale_heap -> bs: FStar.Seq.Base.seq Vale.Arch.HeapImpl.buffer_info\n -> Prims.logical\nlet init_heaplets_req (h:vale_heap) (bs:Seq.seq buffer_info) =\n (forall (i:nat).{:pattern (Seq.index bs i)} i < Seq.length bs ==>\n buffer_readable h (Seq.index bs i).bi_buffer) /\\\n (forall (i1 i2:nat).{:pattern (Seq.index bs i1); (Seq.index bs i2)}\n i1 < Seq.length bs /\\ i2 < Seq.length bs ==> buffer_info_disjoint (Seq.index bs i1) (Seq.index bs i2))", "val FStar.UInt128.op_Greater_Hat = a: FStar.UInt128.t -> b: FStar.UInt128.t -> Prims.Pure Prims.bool\nlet op_Greater_Hat = gt", "val FStar.Pervasives.st_stronger = \n heap: Type ->\n a: Type ->\n wp1: FStar.Pervasives.st_wp_h heap a ->\n wp2: FStar.Pervasives.st_wp_h heap a\n -> Prims.logical\nlet st_stronger (heap a: Type) (wp1 wp2: st_wp_h heap a) =\n (forall (p: st_post_h heap a) (h: heap). wp1 p h ==> wp2 p h)", "val DelimitedRelease.heap_equiv_on = r: FStar.DM4F.Heap.ref Prims.int -> h_0: FStar.DM4F.Heap.heap -> h_1: FStar.DM4F.Heap.heap\n -> Prims.logical\nlet heap_equiv_on (r:ref int) (h_0:heap) (h_1:heap) =\n h_0 `contains` r /\\\n h_1 `contains` r ==>\n sel h_0 r == sel h_1 r", "val FStar.UInt64.op_Equals_Hat = a: FStar.UInt64.t -> b: FStar.UInt64.t -> Prims.bool\nlet op_Equals_Hat = eq", "val FStar.UInt64.op_Greater_Hat = a: FStar.UInt64.t -> b: FStar.UInt64.t -> Prims.bool\nlet op_Greater_Hat = gt", "val FStar.Monotonic.Heap.fresh = r: FStar.Monotonic.Heap.mref a rel -> h0: FStar.Monotonic.Heap.heap -> h1: FStar.Monotonic.Heap.heap\n -> Prims.logical\nlet fresh (#a:Type) (#rel:preorder a) (r:mref a rel) (h0:heap) (h1:heap) =\n r `unused_in` h0 /\\ h1 `contains` r", "val GC.is_mem_addr = i: Prims.int -> Prims.bool\nlet is_mem_addr i = mem_lo <= i && i < mem_hi", "val FStar.UInt64.op_Less_Hat = a: FStar.UInt64.t -> b: FStar.UInt64.t -> Prims.bool\nlet op_Less_Hat = lt", "val Steel.Heap.sl_implies = p: Steel.Heap.slprop -> q: Steel.Heap.slprop -> Prims.logical\nlet sl_implies (p q:slprop) = forall m. interp p m ==> interp q m", "val Steel.Heap.mem_equiv = m0: Steel.Heap.heap -> m1: Steel.Heap.heap -> Prims.logical\nlet mem_equiv (m0 m1:heap) =\n forall a. m0 a == m1 a", "val MRefST.heap_rel = h0: MRefHeap.heap -> h1: MRefHeap.heap -> Prims.logical\nlet heap_rel (h0:heap) (h1:heap) =\n (forall a r (m:mref a r) . contains m h0 ==> contains m h1) /\\\n (forall a (r:preorder a) (m:mref a r{contains m h0}) . r (sel h0 m) (sel h1 m))", "val Vale.X64.Memory.vale_full_heap_equal = h1: Vale.X64.Memory.vale_full_heap -> h2: Vale.X64.Memory.vale_full_heap -> Prims.logical\nlet vale_full_heap_equal (h1 h2:vale_full_heap) =\n h1.vf_layout == h2.vf_layout /\\\n h1.vf_heap == h2.vf_heap /\\\n Map16.equal h1.vf_heaplets h2.vf_heaplets", "val FStar.UInt64.op_Greater_Equals_Hat = a: FStar.UInt64.t -> b: FStar.UInt64.t -> Prims.bool\nlet op_Greater_Equals_Hat = gte", "val FStar.UInt128.op_Less_Hat = a: FStar.UInt128.t -> b: FStar.UInt128.t -> Prims.Pure Prims.bool\nlet op_Less_Hat = lt", "val get_r: Prims.unit -> RWI H.heap RO (fun _ -> True) (fun h0 x h1 -> x == h0 /\\ h1 == h0)\nlet get_r () : RWI H.heap RO (fun _ -> True) (fun h0 x h1 -> x == h0 /\\ h1 == h0) =\n RWI?.reflect (fun () -> ST.get ())", "val FStar.UInt16.n = Prims.int\nlet n = 16", "val heap_evolves : FStar.Preorder.preorder full_heap\nlet heap_evolves : FStar.Preorder.preorder full_heap =\n fun (h0 h1:heap) ->\n forall (a:addr).\n match h0 a, h1 a with\n | None, _ -> True //an unused address in h0 can evolve anyway\n\n | Some (Ref a0 p0 f0 v0), Some (Ref a1 p1 f1 v1) ->\n //if a is used h0 then it remains used and ...\n a0 == a1 /\\ //its type can't change\n p0 == p1 /\\ //its pcm can't change\n PP.preorder_of_pcm p0 v0 v1 //and its value evolves by the pcm's preorder\n | _ -> False" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.Random.fsti", "name": "FStar.DM4F.Heap.Random.size" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.set" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.consistent" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.modifies_none" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_pre_h" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.contains" }, { "project_name": "FStar", "file_name": "FStar.DM4F.IntStore.fst", "name": "FStar.DM4F.IntStore.in_" }, { "project_name": "FStar", "file_name": "FStar.DM4F.OTP.Heap.fsti", "name": "FStar.DM4F.OTP.Heap.size" }, { "project_name": "FStar", "file_name": "ImmutableSTwHeaps.fst", "name": "ImmutableSTwHeaps.heap_rel" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.heap_rel" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.heap_rel" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.modifies" }, { "project_name": "FStar", "file_name": "Swap.fst", "name": "Swap.heap_eq" }, { "project_name": "FStar", "file_name": "FStar.Int32.fsti", "name": "FStar.Int32.op_Greater_Hat" }, { "project_name": "FStar", "file_name": "FStar.Int64.fsti", "name": "FStar.Int64.op_Equals_Hat" }, { "project_name": "FStar", "file_name": "FStar.MRef.fst", "name": "FStar.MRef.p_pred" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_trivial" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_post_h" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Pure.fst", "name": "FStar.Monotonic.Pure.is_monotonic" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.stable" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsMem.fsti", "name": "Vale.PPC64LE.InsMem.heaplet_id_is_some" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.modifies_t" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.IntStoreFixed.fsti", "name": "FStar.DM4F.Heap.IntStoreFixed.store_size" }, { "project_name": "FStar", "file_name": "LeftistHeap.fst", "name": "LeftistHeap.gt" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.all_trivial" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fsti", "name": "FStar.DM4F.Heap.fresh" }, { "project_name": "FStar", "file_name": "FStar.Int32.fsti", "name": "FStar.Int32.op_Equals_Hat" }, { "project_name": "FStar", "file_name": "FStar.Int64.fsti", "name": "FStar.Int64.op_Greater_Hat" }, { "project_name": "FStar", "file_name": "FStar.Int64.fsti", "name": "FStar.Int64.op_Less_Hat" }, { "project_name": "FStar", "file_name": "FStar.Int8.fsti", "name": "FStar.Int8.op_Greater_Hat" }, { "project_name": "FStar", "file_name": "FStar.Int32.fsti", "name": "FStar.Int32.op_Less_Hat" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsMem.fsti", "name": "Vale.X64.InsMem.heaplet_id_is_some" }, { "project_name": "FStar", "file_name": "FStar.Int64.fsti", "name": "FStar.Int64.op_Greater_Equals_Hat" }, { "project_name": "steel", "file_name": "Steel.Heap.fsti", "name": "Steel.Heap.frame_related_heaps" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.get" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.get" }, { "project_name": "FStar", "file_name": "FStar.Int128.fsti", "name": "FStar.Int128.op_Less_Hat" }, { "project_name": "FStar", "file_name": "FStar.Int8.fsti", "name": "FStar.Int8.op_Equals_Hat" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fsti", "name": "FStar.DM4F.Heap.only" }, { "project_name": "FStar", "file_name": "FStar.Int128.fsti", "name": "FStar.Int128.op_Greater_Hat" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.fp_heap_0" }, { "project_name": "FStar", "file_name": "Point.fst", "name": "Point.equal_heaps_except_fp" }, { "project_name": "FStar", "file_name": "Swap.fst", "name": "Swap.equiv_on_h" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperHeap.fsti", "name": "FStar.Monotonic.HyperHeap.equal_on" }, { "project_name": "FStar", "file_name": "FStar.Int8.fsti", "name": "FStar.Int8.op_Less_Hat" }, { "project_name": "FStar", "file_name": "FStar.Int8.fsti", "name": "FStar.Int8.op_Greater_Equals_Hat" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsMem.fsti", "name": "Vale.X64.InsMem.heaplet_id_is_none" }, { "project_name": "FStar", "file_name": "FStar.Int32.fsti", "name": "FStar.Int32.op_Greater_Equals_Hat" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_post_h'" }, { "project_name": "FStar", "file_name": "FStar.UInt32.fsti", "name": "FStar.UInt32.op_Greater_Hat" }, { "project_name": "FStar", "file_name": "FStar.Int64.fsti", "name": "FStar.Int64.op_Less_Equals_Hat" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.all_return" }, { "project_name": "FStar", "file_name": "FStar.Int128.fsti", "name": "FStar.Int128.op_Equals_Hat" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_wp_h" }, { "project_name": "FStar", "file_name": "FStar.Int16.fsti", "name": "FStar.Int16.op_Greater_Hat" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.contains_ref" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.contains_pred" }, { "project_name": "FStar", "file_name": "FStar.PtrdiffT.fsti", "name": "FStar.PtrdiffT.op_Greater_Hat" }, { "project_name": "FStar", "file_name": "FStar.Int128.fsti", "name": "FStar.Int128.op_Greater_Equals_Hat" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.ln_comp" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.ST.fsti", "name": "FStar.DM4F.Heap.ST.op_Colon_Equals" }, { "project_name": "FStar", "file_name": "FStar.Int16.fsti", "name": "FStar.Int16.op_Less_Hat" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.stable_on_heap" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.vale_full_heap_equal" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fsti", "name": "PulseCore.Heap.frame_related_heaps" }, { "project_name": "FStar", "file_name": "FStar.PtrdiffT.fsti", "name": "FStar.PtrdiffT.op_Less_Hat" }, { "project_name": "FStar", "file_name": "FStar.Int16.fsti", "name": "FStar.Int16.op_Equals_Hat" }, { "project_name": "FStar", "file_name": "FStar.Int16.fsti", "name": "FStar.Int16.op_Greater_Equals_Hat" }, { "project_name": "FStar", "file_name": "Protocol.fst", "name": "Protocol.live_connection" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperHeap.fsti", "name": "FStar.Monotonic.HyperHeap.modifies_one" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fsti", "name": "FStar.DM4F.Heap.modifies" }, { "project_name": "FStar", "file_name": "FStar.Int8.fsti", "name": "FStar.Int8.op_Less_Equals_Hat" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsMem.fsti", "name": "Vale.PPC64LE.InsMem.heaplet_id_is_none" }, { "project_name": "FStar", "file_name": "FStar.Int128.fsti", "name": "FStar.Int128.op_Less_Equals_Hat" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.tset" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_return" }, { "project_name": "FStar", "file_name": "FStar.Int32.fsti", "name": "FStar.Int32.op_Less_Equals_Hat" }, { "project_name": "FStar", "file_name": "ProgramEquivalence.fst", "name": "ProgramEquivalence.equal_heaps_except_fp" }, { "project_name": "FStar", "file_name": "IfcDelimitedRelease.fst", "name": "IfcDelimitedRelease.rel_contains" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.all_stronger" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.va_is_src_heaplet" }, { "project_name": "FStar", "file_name": "FStar.PtrdiffT.fsti", "name": "FStar.PtrdiffT.op_Greater_Equals_Hat" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.init_heaplets_req" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fsti", "name": "FStar.UInt128.op_Greater_Hat" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_stronger" }, { "project_name": "FStar", "file_name": "DelimitedRelease.fst", "name": "DelimitedRelease.heap_equiv_on" }, { "project_name": "FStar", "file_name": "FStar.UInt64.fsti", "name": "FStar.UInt64.op_Equals_Hat" }, { "project_name": "FStar", "file_name": "FStar.UInt64.fsti", "name": "FStar.UInt64.op_Greater_Hat" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.fresh" }, { "project_name": "FStar", "file_name": "GC.fst", "name": "GC.is_mem_addr" }, { "project_name": "FStar", "file_name": "FStar.UInt64.fsti", "name": "FStar.UInt64.op_Less_Hat" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.sl_implies" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.mem_equiv" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.heap_rel" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.vale_full_heap_equal" }, { "project_name": "FStar", "file_name": "FStar.UInt64.fsti", "name": "FStar.UInt64.op_Greater_Equals_Hat" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fsti", "name": "FStar.UInt128.op_Less_Hat" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.get_r" }, { "project_name": "FStar", "file_name": "FStar.UInt16.fsti", "name": "FStar.UInt16.n" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.heap_evolves" } ], "selected_premises": [ "FStar.Monotonic.HyperStack.is_stack_region", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "FStar.Monotonic.HyperStack.is_in", "FStar.Monotonic.Heap.mref", "FStar.Map.has_dom", "FStar.Pervasives.dfst", "FStar.Monotonic.HyperHeap.modifies_just", "FStar.Monotonic.HyperHeap.disjoint", "FStar.Map.disjoint_dom", "FStar.Monotonic.Heap.equal_dom", "FStar.Pervasives.id", "FStar.Pervasives.dsnd", "FStar.Pervasives.reveal_opaque", "FStar.Preorder.preorder_rel", "FStar.Monotonic.Heap.fresh", "FStar.Monotonic.HyperHeap.modifies", "FStar.Monotonic.Heap.modifies_t", "FStar.Monotonic.Heap.modifies", "FStar.Monotonic.HyperHeap.disjoint_regions", "FStar.Monotonic.HyperHeap.rid_last_component", "FStar.Map.const_on", "Prims.min", "FStar.Pervasives.st_post_h", "FStar.Monotonic.Heap.compare_addrs", "FStar.Preorder.reflexive", "FStar.Pervasives.coerce_eq", "FStar.Set.subset", "FStar.Ghost.tot_to_gtot", "FStar.Monotonic.Heap.only", "FStar.Pervasives.all_pre_h", "FStar.Ghost.return", "Prims.l_True", "FStar.Pervasives.ex_pre", "FStar.Monotonic.Heap.set", "Prims.l_False", "FStar.Monotonic.HyperHeap.equal_on", "FStar.Pervasives.all_post_h", "FStar.Pervasives.st_pre_h", "FStar.Preorder.stable", "FStar.Monotonic.HyperHeap.modifies_one", "FStar.Pervasives.all_post_h'", "FStar.Preorder.transitive", "FStar.Monotonic.Heap.only_t", "FStar.Pervasives.all_return", "FStar.Set.as_set'", "FStar.Pervasives.st_stronger", "FStar.Pervasives.all_stronger", "Prims.abs", "FStar.Pervasives.st_post_h'", "FStar.Set.as_set", "FStar.Monotonic.Heap.tset", "Prims.__cache_version_number__", "FStar.Pervasives.all_wp_h", "FStar.TSet.subset", "FStar.Set.add", "FStar.Pervasives.ex_post'", "FStar.Pervasives.all_trivial", "FStar.Pervasives.ex_post", "Prims.pure_pre", "FStar.Pervasives.st_trivial", "Prims.returnM", "FStar.Pervasives.all_ite_wp", "FStar.Ghost.op_let_At", "Prims.auto_squash", "FStar.Pervasives.st_wp_h", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.all_close_wp", "Prims.pow2", "FStar.Set.disjoint", "FStar.Pervasives.pure_null_wp", "FStar.Ghost.bind", "FStar.Monotonic.Heap.op_Plus_Plus_Hat", "FStar.Pervasives.ex_wp", "FStar.Set.remove", "Prims.subtype_of", "FStar.Pervasives.ex_stronger", "FStar.Ghost.elift2_pq", "FStar.TSet.as_set'", "FStar.Pervasives.st_ite_wp", "FStar.Ghost.push_refinement", "FStar.Pervasives.st_close_wp", "FStar.Ghost.elift1", "FStar.Pervasives.all_if_then_else", "FStar.Pervasives.st_return", "FStar.Ghost.elift2", "FStar.Monotonic.Heap.op_Hat_Plus_Plus", "FStar.Pervasives.pure_close_wp", "FStar.Monotonic.Heap.op_Hat_Plus_Hat", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.ex_trivial", "FStar.Pervasives.ex_ite_wp", "FStar.Pervasives.st_if_then_else", "FStar.Ghost.elift1_pq", "Prims.pure_post'", "FStar.Ghost.elift1_p", "FStar.Pervasives.ex_if_then_else", "Prims.pure_wp_monotonic", "Prims.pure_wp'", "FStar.Pervasives.pure_ite_wp" ], "source_upto_this": "(*\n Copyright 2008-2014 Aseem Rastogi, and Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.Monotonic.HyperStack\n\nopen FStar.Preorder\nmodule Map = FStar.Map\n\ninclude FStar.Monotonic.HyperHeap\n\n\n(****** Some predicates ******)\n\nunfold let is_in (r:rid) (h:hmap) = h `Map.contains` r\n\nlet is_stack_region r = color r > 0", "sketch": [ "Step 1: The definition `is_heap_color` is intended to determine if a given color value `c` is valid for a heap region.\nStep 2: The implementation will check if the color value `c` is greater than zero, returning `true` if it is, and `false` otherwise.", "Step 1: The definition `is_heap_color` is about determining whether a given integer `c` represents a valid heap color.\nStep 2: The implementation will check if the integer `c` is greater than or equal to zero, as valid heap colors are non-negative integers.", "Step 1: The definition `is_heap_color` is a predicate that checks if a given integer `c` represents a valid heap color.\nStep 2: The implementation will return `true` if the integer `c` is greater than or equal to 0, indicating a valid heap color, and `false` otherwise.", "Step 1: The definition `is_heap_color` is about determining whether a given integer `c` represents a valid heap color.\nStep 2: The implementation will check if the integer `c` is greater than or equal to 0, as heap colors are typically non-negative integers.", "Step 1: The definition `is_heap_color` is a predicate that checks if a given integer `c` represents a valid heap color.\nStep 2: The implementation will return `true` if the integer `c` is greater than or equal to 0, indicating it is a valid heap color. Otherwise, it will return `false`.", "Step 1: The definition `is_heap_color` is a predicate that checks if a given integer `c` represents a valid heap color.\nStep 2: The implementation will simply return `true` if `c` is equal to 0, indicating that it is a valid heap color, and `false` otherwise.", "Step 1: The definition `is_heap_color` is about determining whether a given integer `c` represents a valid heap color.\nStep 2: The implementation will simply check if the integer `c` is greater than zero. If it is, then it returns `true`, otherwise it returns `false`.", "Step 1: The definition `is_heap_color` is about determining whether a given integer `c` represents a valid heap color.\nStep 2: The implementation will check if the integer `c` is greater than or equal to zero, as heap colors are typically non-negative integers.", "Step 1: The definition `is_heap_color` is about determining whether a given integer `c` represents a valid heap color.\nStep 2: The implementation checks if the integer `c` is equal to 0, which is typically used to represent the heap color in this context.", "Step 1: The definition `is_heap_color` is about determining if a given integer `c` represents a valid heap color.\nStep 2: The implementation will check if the integer `c` is greater than zero, as valid heap colors are positive integers." ], "generated_solution": [ "let is_heap_color (c: Prims.int) : Prims.bool =\n c > 0", "let is_heap_color (c: Prims.int) : Prims.bool =\n c >= 0", "let is_heap_color (c: Prims.int) : Prims.bool =\n c >= 0", "let is_heap_color (c: Prims.int) : Prims.bool =\n c >= 0", "let is_heap_color (c: Prims.int) : Prims.bool =\n c >= 0", "let is_heap_color (c: Prims.int) : Prims.bool =\n c = 0", "let is_heap_color (c: Prims.int) : Prims.bool =\n c > 0", "let is_heap_color (c: Prims.int) : Prims.bool =\n c >= 0", "let is_heap_color (c: Prims.int) : Prims.bool =\n c = 0", "let is_heap_color (c: Prims.int) : Prims.bool =\n c > 0" ] }, { "file_name": "FStar.Ghost.fsti", "name": "FStar.Ghost.elift2_pq", "opens_and_abbrevs": [ { "open": "FStar" }, { "open": "FStar" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)})", "source_definition": "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "source_range": { "start_line": 158, "start_col": 0, "end_line": 168, "end_col": 16 }, "interleaved": false, "definition": "fun $f ra rb ->\n (let x = FStar.Ghost.reveal ra in\n let y = FStar.Ghost.reveal rb in\n FStar.Ghost.return (f x y))\n <:\n z:\n FStar.Ghost.erased c {FStar.Ghost.reveal z == f (FStar.Ghost.reveal ra) (FStar.Ghost.reveal rb)}", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Ghost.erased", "FStar.Ghost.reveal", "FStar.Ghost.return", "Prims.eq2" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "\n $f: (x: a -> y: b{p x y} -> Prims.GTot (z: c{q x y z})) ->\n ra: FStar.Ghost.erased a ->\n rb: FStar.Ghost.erased b {p (FStar.Ghost.reveal ra) (FStar.Ghost.reveal rb)}\n -> z:\n FStar.Ghost.erased c {FStar.Ghost.reveal z == f (FStar.Ghost.reveal ra) (FStar.Ghost.reveal rb)}", "prompt": "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n ", "expected_response": "let x = reveal ra in\nlet y:(y: b{p x y}) = reveal rb in\nreturn (f x y)", "source": { "project_name": "FStar", "file_name": "ulib/FStar.Ghost.fsti", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.Ghost.fsti", "checked_file": "dataset/FStar.Ghost.fsti.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "val erased ([@@@strictly_positive] a: Type u#a) : Type u#a", "val reveal: #a: Type u#a -> erased a -> GTot a", "val hide: #a: Type u#a -> a -> Tot (erased a)", "val hide_reveal (#a: Type) (x: erased a)\n : Lemma (ensures (hide (reveal x) == x)) [SMTPat (reveal x)]", "val reveal_hide (#a: Type) (x: a) : Lemma (ensures (reveal (hide x) == x)) [SMTPat (hide x)]", "let tot_to_gtot (f: ('a -> Tot 'b)) (x: 'a) : GTot 'b = f x", "let return (#a: Type) (x: a) : erased a = hide x", "let bind (#a #b: Type) (x: erased a) (f: (a -> Tot (erased b))) : Tot (erased b) =\n let y = reveal x in\n f y", "let (let@) (x:erased 'a) (f:('a -> Tot (erased 'b))) : Tot (erased 'b) = bind x f", "let elift1 (#a #b: Type) (f: (a -> GTot b)) (x: erased a)\n : Tot (y: erased b {reveal y == f (reveal x)}) =\n let@ xx = x in return (f xx)", "let elift2 (#a #b #c: Type) (f: (a -> b -> GTot c)) (x: erased a) (y: erased b)\n : Tot (z: erased c {reveal z == f (reveal x) (reveal y)}) =\n let@ xx = x in\n let@ yy = y in\n return (f xx yy)", "let elift3\n (#a #b #c #d: Type)\n (f: (a -> b -> c -> GTot d))\n (ga: erased a)\n (gb: erased b)\n (gc: erased c)\n : Tot (gd: erased d {reveal gd == f (reveal ga) (reveal gb) (reveal gc)}) =\n let@ a = ga in\n let@ b = gb in\n let@ c = gc in\n return (f a b c)", "let push_refinement #a (#p: (a -> Type0)) (r: erased a {p (reveal r)})\n : erased (x: a{p x /\\ x == reveal r}) =\n let x:(x: a{p x}) = reveal r in\n return x", "let elift1_p\n (#a #b: Type)\n (#p: (a -> Type))\n ($f: (x: a{p x} -> GTot b))\n (r: erased a {p (reveal r)})\n : Tot (z: erased b {reveal z == f (reveal r)}) =\n let x:(x: a{p x}) = reveal r in\n return (f x)", "let elift2_p\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n ($f: (xa: a -> xb: b{p xa xb} -> GTot c))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (rc: erased c {reveal rc == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "let elift1_pq\n (#a #b: Type)\n (#p: (a -> Type))\n (#q: (x: a{p x} -> b -> Type))\n ($f: (x: a{p x} -> GTot (y: b{q x y})))\n (r: erased a {p (reveal r)})\n : Tot (z: erased b {reveal z == f (reveal r)}) =\n let x:(x: a{p x}) = reveal r in\n return (f x)" ], "closest": [ "val and_elim\n (p:Type)\n (q:squash p -> Type)\n (r:Type)\n (_:squash (p /\\ q()))\n (f:squash p -> squash (q()) -> Tot (squash r))\n : Tot (squash r)\nlet and_elim (p:Type)\n (q:squash p -> Type)\n (r:Type)\n (x:squash (p /\\ q()))\n (f:squash p -> squash (q()) -> Tot (squash r))\n : Tot (squash r)\n = let open FStar.Squash in\n bind_squash x (fun p_and_q ->\n bind_squash p_and_q (fun (Prims.Pair p q) ->\n f (return_squash p) (return_squash q)))", "val hoist_ghost2\n (#a: Type)\n (#b: (a -> Type))\n (#c: (x: a -> b x -> Type))\n (f: (x: a -> y: b x -> GTot (c x y)))\n : GTot (x: a -> y: b x -> c x y)\nlet hoist_ghost2 (#a:Type) (#b:a -> Type) (#c:(x:a -> b x -> Type))\n (f:(x:a -> y:b x -> GTot (c x y)))\n : GTot (x:a -> y:b x -> c x y)\n = hoist_ghost (fun (x:a) -> hoist_ghost (fun (y:b x) -> f x y))", "val or_elim_simple\n (p q r: Type)\n (x: squash (p \\/ q))\n (f: (squash p -> Tot (squash r)))\n (g: (squash q -> Tot (squash r)))\n : Tot (squash r)\nlet or_elim_simple\n (p:Type)\n (q:Type)\n (r:Type)\n (x:squash (p \\/ q))\n (f:squash p -> Tot (squash r))\n (g:squash q -> Tot (squash r))\n : Tot (squash r)\n = let open FStar.Squash in\n bind_squash x (fun p_or_q ->\n bind_squash p_or_q (fun p_cor_q ->\n match p_cor_q with\n | Prims.Left p ->\n f (return_squash p)\n | Prims.Right q ->\n g (return_squash q)))", "val calc_push_impl (#p #q:Type) (f:squash p -> GTot (squash q))\n : Tot (squash (p ==> q))\nlet calc_push_impl #p #q f =\n Classical.arrow_to_impl f", "val forall_to_exists_2\n (#a: Type)\n (#p: (a -> Type))\n (#b: Type)\n (#q: (b -> Type))\n (#r: Type)\n ($f: (x: a -> y: b -> Lemma ((p x /\\ q y) ==> r)))\n : Lemma (((exists (x: a). p x) /\\ (exists (y: b). q y)) ==> r)\nlet forall_to_exists_2 #a #p #b #q #r f = forall_intro_2 f", "val exists_elim\n (#t:Type)\n (#p:t -> Type)\n (#q:Type)\n ($s_ex_p: squash (exists (x:t). p x))\n (f: (x:t -> squash (p x) -> Tot (squash q)))\n : Tot (squash q)\nlet exists_elim #t #p #q s_ex_p f\n = let open FStar.Squash in\n bind_squash s_ex_p (fun ex_p ->\n bind_squash ex_p (fun (sig_p: (x:t & p x)) ->\n let (| x, px |) = sig_p in\n f x (return_squash px)))", "val exists_elim2\n (goal:Type) (#a:Type) (#b:(a -> Type)) (#p:(x:a -> b x -> Type))\n (_:squash (exists (x:a) (y:b x). p x y))\n (f:(x:a -> y:b x{p x y} -> GTot (squash goal)))\n : Lemma goal\nlet exists_elim2 goal #a #b #p _ f =\n let open FStar.Classical in\n exists_elim goal () (fun (x:a{exists (y:b x). p x y}) ->\n exists_elim goal () (fun (y:b x{p x y}) ->\n f x y))", "val lift2 : #t:Type -> #t2:Type -> #t3:Type\n -> f:(t -> t2 -> Tot t3) -> rel t -> rel t2\n -> Tot (rel t3)\nlet lift2 #t #t2 #t3 f (R x y) (R x2 y2) = R (f x x2) (f y y2)", "val eq_ind : #a:Type -> x:a -> p:(a -> Type) -> f:p x -> y:a -> e:ceq x y -> Tot (p y)\nlet eq_ind #a x p f y _ = f", "val or_elim\n (p:Type)\n (q:squash (~p) -> Type)\n (r:Type)\n (p_or:squash (p \\/ q()))\n (left:squash p -> Tot (squash r))\n (right:squash (~p) -> squash (q()) -> Tot (squash r))\n : Tot (squash r)\nlet or_elim\n (p:Type)\n (q:squash (~p) -> Type)\n (r:Type)\n (p_or:squash (p \\/ q()))\n (left:squash p -> Tot (squash r))\n (right:squash (~p) -> squash (q()) -> Tot (squash r))\n : Tot (squash r)\n = or_elim_simple p (~p) r ()\n (fun (s:squash p) -> left s)\n (fun (np:squash (~p)) ->\n or_elim_simple p (q ()) r p_or\n (fun (pf_p:squash p) -> left pf_p)\n (fun (pf_q:squash (q())) -> right np pf_q))", "val implies_intro\n (p:Type)\n (q:squash p -> Type)\n (f:(squash p -> Tot (squash (q()))))\n : Tot (squash (p ==> q()))\nlet implies_intro\n (p:Type)\n (q:squash p -> Type)\n (f:(squash p -> Tot (squash (q()))))\n : Tot (squash (p ==> q()))\n = let open FStar.Squash in\n let f' (x:p)\n : GTot (squash (q ()))\n = f (return_squash x)\n in\n return_squash (squash_double_arrow (return_squash f'))", "val map (#a #b #sl: _) (#l: lattice_element sl) (x: protected l a) (f: (y: a{y == reveal x} -> b))\n : Tot (y: protected l b {reveal y == f (reveal x)})\nlet map #a #b #sl #l x f = f x", "val or_intro_right\n (p:Type)\n (q:squash (~p) -> Type)\n (f:squash (~p) -> Tot (squash (q())))\n : Tot (squash (p \\/ q()))\nlet or_intro_right\n (p:Type)\n (q:squash (~p) -> Type)\n (f:squash (~p) -> Tot (squash (q())))\n : Tot (squash (p \\/ q()))\n = or_elim_simple p (~p)\n (p \\/ q())\n ()\n (fun s_p -> or_intro_left p q (fun _ -> s_p))\n (fun s_np -> f s_np)", "val ( ^+^ )\n (#a #b: Type0)\n (#rel1: preorder a)\n (#rel2: preorder b)\n (r1: mref a rel1)\n (r2: mref b rel2)\n : GTot (set nat)\nlet op_Hat_Plus_Hat (#a:Type0) (#b:Type0) (#rel1:preorder a) (#rel2:preorder b) (r1:mref a rel1) (r2:mref b rel2)\n :GTot (set nat) = S.union (only r1) (only r2)", "val eval_equiv_reified\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': reified_exp t)\n: GTot Type0\nlet eval_equiv_reified\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': reified_exp t)\n: GTot Type0\n= Benton2004.eval_equiv_reified p e f f'", "val reveal: #a: Type u#a -> erased a -> GTot a\nlet reveal #a (E x) = x", "val bind (a b: Type) (labs1 labs2: list eff_label) (c: repr a labs1) (f: (x: a -> repr b labs2))\n : Tot (repr b (labs1 @ labs2))\nlet bind (a b : Type)\n (labs1 labs2 : list eff_label)\n (c : repr a labs1)\n (f : (x:a -> repr b labs2))\n : Tot (repr b (labs1@labs2))\n = fun () -> f (c ()) ()", "val bind (a b: Type) (labs1 labs2: list eff_label) (c: repr a labs1) (f: (x: a -> repr b labs2))\n : Tot (repr b (labs1 @ labs2))\nlet bind (a b : Type)\n (labs1 labs2 : list eff_label)\n (c : repr a labs1)\n (f : (x:a -> repr b labs2))\n : Tot (repr b (labs1@labs2))\n = let r =\n fun s0 -> match c s0 with\n | Some x, s1 -> f x s1\n | None, s1 -> None, s1\n in\n r", "val bind (a b: Type) (#labs1 #labs2: ops) (c: tree a labs1) (f: (x: a -> tree b labs2))\n : Tot (tree b (labs1 @ labs2))\nlet bind (a b : Type)\n (#labs1 #labs2 : ops)\n (c : tree a labs1)\n (f : (x:a -> tree b labs2))\n : Tot (tree b (labs1@labs2))\n = handle_tree #_ #_ #_ #(labs1@labs2) c f (fun act i k -> Op act i k)", "val lift3 : #t:Type -> #t2:Type -> #t3:Type -> #t4:Type\n -> f:(t -> t2 -> t3 -> Tot t4) -> rel t -> rel t2 -> rel t3\n -> Tot (rel t4)\nlet lift3 #t #t2 #t3 #t4 f (R x y) (R x2 y2) (R x3 y3) = R (f x x2 x3) (f y y2 y3)", "val bind_seal\n (#a : Type u#aa) (b : Type u#bb)\n (s : sealed a)\n (f : a -> TacS (sealed b))\n: Tot (sealed b)\nlet bind_seal\n (#a : Type u#aa) (b : Type u#bb)\n (s : sealed a)\n (f : a -> TacS (sealed b))\n: Tot (sealed b)\n=\n Seal (fun () -> unseal (f (unseal s)))", "val push_sum (#a: Type) (#b: (a -> Type)) ($p: (dtuple2 a (fun (x: a) -> squash (b x))))\n : Tot (squash (dtuple2 a b))\nlet push_sum (#a:Type) (#b:(a -> Type)) ($p : dtuple2 a (fun (x:a) -> squash (b x))) =\n match p with\n | Mkdtuple2 x y ->\n bind_squash #(b x) #(dtuple2 a b) y (fun y' ->\n return_squash (Mkdtuple2 x y'))", "val bind\n (a b: Type)\n (f_p: pre)\n (f_q: post a)\n (g_p: (a -> pre))\n (g_q: (a -> post b))\n (f: repr a f_p f_q)\n (g: (x: a -> repr b (g_p x) (g_q x)))\n : repr b (act_p f_p f_q g_p) (act_q f_q g_q)\nlet rec bind (a b:Type)\n (f_p:pre) (f_q:post a)\n (g_p:a -> pre) (g_q:a -> post b)\n (f:repr a f_p f_q) (g:(x:a -> repr b (g_p x) (g_q x)))\n : repr b (act_p f_p f_q g_p) (act_q f_q g_q)\n = fun _ ->\n let f = f () in\n match f with\n | Ret x -> Weaken (g x ())\n | Act #_ #c #a_p #a_q act #_ #_ #_ k ->\n let k' = fun (x:c) -> (bind _ _ _ _ _ _ (fun _ -> k x) g) () in\n Weaken (Act #_ #c #a_p #a_q act #b #_ #_ k')\n | Weaken f -> Weaken ((bind _ _ _ _ _ _ (fun _ -> f) g) ())\n | Strengthen #_ #_ #phi #p #q f ->\n let f : squash phi -> Dv (m st b (act_p p q g_p) (act_q q g_q)) =\n fun _ -> (bind _ _ _ _ _ _ (fun _ -> f ()) g) () in\n let f : m st b (strengthen_pre (act_p p q g_p) phi) (act_q q g_q) =\n Strengthen f in\n Weaken f", "val impl_intro_tot (#p #q: Type0) ($_: (p -> Tot q)) : Tot (p ==> q)\nlet impl_intro_tot #p #q f = return_squash #(p -> GTot q) f", "val lift : #t:Type -> #t2:Type\n -> f:(t -> Tot t2) -> rel t\n -> Tot (rel t2)\nlet lift #t #t2 f (R x y) = R (f x) (f y)", "val bind (a: Type u#aa) (b: Type u#bb) (i1 i2: int) (f: repr a i1) (g: (x: a -> repr b i2))\n : Tot (repr b (i1 + i2))\nlet bind (a:Type u#aa) (b : Type u#bb) (i1 i2 : int)\n (f : repr a i1)\n (g : (x:a -> repr b i2))\n : Tot (repr b (i1+i2)) =\n raise_val (i1+i2)", "val fix_F\n (#aa: Type)\n (#r: binrel aa)\n (#p: (aa -> Type))\n (f: (x: aa -> (y: aa -> r y x -> p y) -> p x))\n (x: aa)\n (a: acc r x)\n : Tot (p x) (decreases a)\nlet rec fix_F (#aa:Type) (#r:binrel aa) (#p:(aa -> Type))\n (f: (x:aa -> (y:aa -> r y x -> p y) -> p x))\n (x:aa) (a:acc r x)\n : Tot (p x) (decreases a)\n = f x (fun y h -> fix_F f y (a.access_smaller y h))", "val lift5 : #t:Type -> #t2:Type -> #t3:Type -> #t4:Type -> #t5:Type -> #t6:Type\n -> f:(t -> t2 -> t3 -> t4 -> t5 -> Tot t6)\n -> rel t -> rel t2 -> rel t3 -> rel t4 -> rel t5\n -> Tot (rel t6)\nlet lift5 #t #t2 #t3 #t4 #t5 #t6 f (R x y) (R x2 y2) (R x3 y3) (R x4 y4) (R x5 y5) =\n R (f x x2 x3 x4 x5) (f y y2 y3 y4 y5)", "val forall_impl_intro\n (#a: Type)\n (#p #q: (a -> GTot Type))\n ($_: (x: a -> squash (p x) -> Lemma (q x)))\n : Lemma (forall x. p x ==> q x)\nlet forall_impl_intro #a #p #q f =\n let f' (x: a) : Lemma (requires (p x)) (ensures (q x)) = f x (get_proof (p x)) in\n forall_intro (move_requires f')", "val on_g (a #b: Type) (f: (a -> GTot b)) : (a ^->> b)\nlet on_g (a #b: Type) (f: (a -> GTot b)) : (a ^->> b) = on_dom_g a f", "val squash_double_sum\n (#a: Type)\n (#b: (a -> Type))\n ($p: (squash (dtuple2 a (fun (x: a) -> squash (b x)))))\n : Tot (squash (dtuple2 a b))\nlet squash_double_sum (#a:Type) (#b:(a -> Type)) (p : squash (dtuple2 a (fun (x:a) -> squash (b x)))) =\n bind_squash p (fun p' -> push_sum p')", "val forall_intro\n (a:Type)\n (p:a -> Type)\n (f: (x:a -> Tot (squash (p x))))\n : Tot (squash (forall x. p x))\nlet forall_intro\n (a:Type)\n (p:a -> Type)\n (f: (x:a -> Tot (squash (p x))))\n : Tot (squash (forall x. p x))\n = let open FStar.Squash in\n let f' (x:a)\n : GTot (squash (p x))\n = f x\n in\n return_squash (squash_double_arrow (return_squash f'))", "val lift4 : #t:Type -> #t2:Type -> #t3:Type -> #t4:Type -> #t5:Type\n -> f:(t -> t2 -> t3 -> t4 -> Tot t5)\n -> rel t -> rel t2 -> rel t3 -> rel t4\n -> Tot (rel t5)\nlet lift4 #t #t2 #t3 #t4 #t5 f (R x y) (R x2 y2) (R x3 y3) (R x4 y4) =\n R (f x x2 x3 x4) (f y y2 y3 y4)", "val map_refine (#a: Type) (#b: Type) (#p: a -> Type0)\n ($f: (x:a { p x } -> GTot b)) //the $ allows type inference at the call site to infer p\n (s:seq a {forall x. contains s x ==> p x })\n : GTot (s': seq b{length s = length s' /\\ (forall (i:nat). i < length s ==> p (index s i) /\\ index s' i == f (index s i))})\nlet rec map_refine (#a: Type) (#b: Type) (#p: a -> Type0)\n ($f: (x:a { p x } -> GTot b)) //the $ allows type inference at the call site to infer p\n (s:seq a {forall x. contains s x ==> p x })\n : GTot (s': seq b{length s = length s' /\\ (forall (i:nat). i < length s ==> p (index s i) /\\ index s' i == f (index s i))})\n (decreases rank s)\n = if length s = 0 then\n empty\n else\n let hd = index s 0 in\n let tl = drop s 1 in\n assert (rank tl << rank s);\n append (singleton (f hd)) (map_refine f tl)", "val forall_intro_2\n (#a: Type)\n (#b: (a -> Type))\n (#p: (x: a -> b x -> GTot Type0))\n ($_: (x: a -> y: b x -> Lemma (p x y)))\n : Lemma (forall (x: a) (y: b x). p x y)\nlet forall_intro_2 #a #b #p f =\n let g: x: a -> Lemma (forall (y: b x). p x y) = fun x -> forall_intro (f x) in\n forall_intro g", "val forall_intro_squash_gtot_join\n (#a: Type)\n (#p: (a -> GTot Type))\n ($_: (x: a -> GTot (squash (p x))))\n : Tot (forall (x: a). p x)\nlet forall_intro_squash_gtot_join #a #p f =\n join_squash (bind_squash #(x: a -> GTot (p x))\n #(forall (x: a). p x)\n (squash_double_arrow #a #p (return_squash f))\n (fun f -> lemma_forall_intro_gtot #a #p f))", "val squash_double_arrow (#a: Type) (#p: (a -> Type)) ($f: (squash (x: a -> GTot (squash (p x)))))\n : GTot (squash (x: a -> GTot (p x)))\nlet squash_double_arrow #a #p f =\n bind_squash f push_squash", "val eval_equiv_reified (#t: Type0) (p: sttype) (e: nstype t) (f f': reified_exp t) : GTot Type0\nlet eval_equiv_reified\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': reified_exp t)\n: GTot Type0\n= forall (s s' : heap) .\n holds p s s' ==> holds e (fst (f s)) (fst (f' s'))", "val fold_left_map\n (#a #b #c: Type)\n (f_aba: (a -> b -> Tot a))\n (f_bc: (b -> Tot c))\n (f_aca: (a -> c -> Tot a))\n (l: list b)\n : Lemma (requires forall (x: a) (y: b). f_aba x y == f_aca x (f_bc y))\n (ensures forall (x: a). fold_left f_aba x l == fold_left f_aca x (map f_bc l))\nlet rec fold_left_map\n (#a #b #c: Type)\n (f_aba: a -> b -> Tot a)\n (f_bc: b -> Tot c)\n (f_aca: a -> c -> Tot a)\n (l: list b)\n : Lemma\n (requires forall (x: a) (y: b) . f_aba x y == f_aca x (f_bc y) )\n (ensures forall (x : a) . fold_left f_aba x l == fold_left f_aca x (map f_bc l) )\n =\n match l with\n | [] -> ()\n | y :: q -> fold_left_map f_aba f_bc f_aca q", "val for_all_map\n (#a #b: Type)\n (f: (a -> GTot b))\n (p1: (b -> GTot bool))\n (p2: (a -> GTot bool))\n (l: list a)\n : Lemma (requires p2 == (fun x -> p1 (f x)))\n (ensures for_all_ghost p1 (map_ghost f l) = for_all_ghost p2 l)\nlet rec for_all_map (#a: Type) (#b: Type) (f: a -> GTot b) (p1: b -> GTot bool) (p2: a -> GTot bool) (l: list a)\n : Lemma\n (requires p2 == (fun x -> p1 (f x)))\n (ensures for_all_ghost p1 (map_ghost f l) = for_all_ghost p2 l) =\n match l with\n | [] -> ()\n | hd :: tl -> for_all_map f p1 p2 tl", "val exec_equiv_reified\n (p p' : sttype)\n (f f' : reified_computation)\n: GTot Type0\nlet exec_equiv_reified\n (p p' : sttype)\n (f f' : reified_computation)\n: GTot Type0\n= Benton2004.exec_equiv_reified p p' f f'", "val hide: #a: Type u#a -> a -> Tot (erased a)\nlet hide #a x = E x", "val eval_equiv (#t: Type0) (p: sttype) (e: nstype t) (f f': exp t) : GTot Type0\nlet eval_equiv\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f f': exp t)\n: GTot Type0\n= let f = reify_exp f in\n let f' = reify_exp f' in\n eval_equiv_reified p e f f'", "val feq (u v: Type) (eq: (v -> v -> GTot Type0)) (f1 f2: (u -> Tot v)) : GTot Type0\nlet feq\n (u v: Type)\n (eq: (v -> v -> GTot Type0))\n (f1 f2: (u -> Tot v))\n: GTot Type0\n= (forall (x: u) . {:pattern (f1 x); (f2 x)} eq (f1 x) (f2 x))", "val ( ^+^ ) (#a #b: Type) (r1: ref a) (r2: ref b) : Tot (set nat)\nlet op_Hat_Plus_Hat (#a:Type) (#b:Type) (r1:ref a) (r2:ref b) : Tot (set nat) =\n union (only r1) (only r2)", "val pr_eq: #a:Type -> #b:Type ->\n c1:(store -> M (a * id)) ->\n c2:(store -> M (b * id)) ->\n p1:(a -> nat) ->\n p2:(b -> nat) ->\n bij:bijection -> Lemma\n (requires\n (forall h. let r1,_ = c1 (to_id 0, h) in\n let r2,_ = c2 (to_id 0, bij.f h) in\n p1 r1 == p2 r2))\n (ensures (mass c1 p1 == mass c2 p2))\nlet pr_eq #a #b c1 c2 p1 p2 bij =\n pr_leq c1 c2 p1 p2 bij;\n pr_leq c2 c1 p2 p1 (inverse bij)", "val pr_eq: #a:Type -> #b:Type ->\n c1:(store -> M (a * id)) ->\n c2:(store -> M (b * id)) ->\n p1:(a -> nat) ->\n p2:(b -> nat) ->\n bij:bijection -> Lemma\n (requires\n (forall h. let r1,_ = c1 (to_id 0, h) in\n let r2,_ = c2 (to_id 0, bij.f h) in\n p1 r1 == p2 r2))\n (ensures (mass c1 p1 == mass c2 p2))\nlet pr_eq #a #b c1 c2 p1 p2 bij =\n pr_leq c1 c2 p1 p2 bij;\n pr_leq c2 c1 p2 p1 (inverse bij)", "val bind\n (a b: Type)\n (#pre_f: pre_t)\n (#post_f: post_t a)\n (#pre_g: (a -> pre_t))\n (#post_g: (a -> post_t b))\n (f: repr a pre_f post_f)\n (g: (x: a -> repr b (pre_g x) (post_g x)))\n : repr b\n (fun h0 -> pre_f h0 /\\ (forall (x: a) (h1: heap). post_f h0 x h1 ==> pre_g x h1))\n (fun h0 y h2 -> exists (x: a) (h1: heap). pre_f h0 /\\ post_f h0 x h1 /\\ post_g x h1 y h2)\nlet bind (a:Type) (b:Type)\n (#pre_f:pre_t) (#post_f:post_t a) (#pre_g:a -> pre_t) (#post_g:a -> post_t b)\n (f:repr a pre_f post_f) (g:(x:a -> repr b (pre_g x) (post_g x)))\n: repr b\n (fun h0 -> pre_f h0 /\\ (forall (x:a) (h1:heap). post_f h0 x h1 ==> pre_g x h1))\n (fun h0 y h2 -> exists (x:a) (h1:heap). pre_f h0 /\\ post_f h0 x h1 /\\ post_g x h1 y h2)\n= fun _ ->\n let x = f () in\n g x ()", "val bind\n (a b: Type)\n (req_f: Type0)\n (ens_f req_g: (a -> Type0))\n (ens_g: (a -> (b -> Type0)))\n (f: repr a req_f ens_f)\n (g: (x: a -> repr b (req_g x) (ens_g x)))\n : repr b\n (req_f /\\ (forall (x: a). ens_f x ==> req_g x))\n (fun y -> exists x. ens_f x /\\ ens_g x y)\nlet bind (a:Type) (b:Type)\n (req_f:Type0) (ens_f:a -> Type0)\n (req_g:a -> Type0) (ens_g:a -> (b -> Type0))\n (f:repr a req_f ens_f) (g:(x:a -> repr b (req_g x) (ens_g x)))\n: repr b\n (req_f /\\ (forall (x:a). ens_f x ==> req_g x))\n (fun y -> exists x. ens_f x /\\ ens_g x y)\n= fun _ ->\n let x = f () in\n g x ()", "val squash_double_arrow (#a: Type u#a) (#p: Type0) (f: (squash (a -> Tot (squash p))))\n : Tot (squash (a -> GTot p))\nlet squash_double_arrow (#a:Type u#a) (#p:Type0)\n (f:(squash (a -> Tot (squash p))))\n : Tot (squash (a -> GTot p)) =\n FStar.Squash.squash_double_arrow f", "val forall_intro_gtot (#a: Type) (#p: (a -> GTot Type)) ($_: (x: a -> GTot (p x)))\n : Tot (squash (forall (x: a). p x))\nlet forall_intro_gtot #a #p f =\n let id (#a: Type) (x: a) = x in\n let h:(x: a -> GTot (id (p x))) = fun x -> f x in\n return_squash #(forall (x: a). id (p x)) ()", "val impl_intro_gtot (#p #q: Type0) ($_: (p -> GTot q)) : GTot (p ==> q)\nlet impl_intro_gtot #p #q f = return_squash f", "val map (#a #b:Type) (f:a -> b) (s:seq a): Tot (s':seq b{length s' = length s})\nlet map (#a #b:Type) (f:a -> b) (s:seq a): Tot (s':seq b{length s' = length s}) = map_aux f s", "val ghost_lemma\n (#a: Type)\n (#p: (a -> GTot Type0))\n (#q: (a -> unit -> GTot Type0))\n ($_: (x: a -> Lemma (requires p x) (ensures (q x ()))))\n : Lemma (forall (x: a). p x ==> q x ())\nlet ghost_lemma #a #p #q f =\n let lem: x: a -> Lemma (p x ==> q x ()) =\n (fun x ->\n (* basically, the same as above *)\n give_proof (bind_squash (get_proof (l_or (p x) (~(p x))))\n (fun (b: l_or (p x) (~(p x))) ->\n bind_squash b\n (fun (b': Prims.sum (p x) (~(p x))) ->\n match b' with\n | Prims.Left hp ->\n give_witness hp;\n f x;\n get_proof (p x ==> q x ())\n | Prims.Right hnp -> give_witness hnp))))\n in\n forall_intro lem", "val flip (#a #b: Type) (c: (a * b)) : Tot (b * a)\nlet flip (#a #b: Type) (c: (a * b)) : Tot (b * a) = let (ca, cb) = c in (cb, ca)", "val list_rec_of_function_is_map_1\n (#a #b: _)\n (f: (a -> b))\n (l1: list a)\n (l2: list b)\n (p: list_param _ _ (rel_of_fun f) l1 l2)\n : Lemma (l2 == List.Tot.map f l1)\nlet rec list_rec_of_function_is_map_1 #a #b (f : a -> b) (l1 : list a) (l2 : list b)\n (p : list_param _ _ (rel_of_fun f) l1 l2)\n : Lemma (l2 == List.Tot.map f l1)\n = match p with\n | Nil_param -> ()\n | Cons_param _ _ _ _ _ t -> list_rec_of_function_is_map_1 _ _ _ t", "val rel_eq (#a: Type) (#b: eqtype) (r: rel a) ($f: (a -> Tot b)) : Tot bool\nlet rel_eq (#a:Type) (#b:eqtype) (r:rel a) ($f:a -> Tot b) : Tot bool =\n match r with | R hl hr -> f hl = f hr", "val bare_serialize_synth\n (#k: parser_kind)\n (#t1 #t2: Type)\n (p1: parser k t1)\n (f2: (t1 -> GTot t2))\n (s1: serializer p1)\n (g1: (t2 -> GTot t1))\n : Tot (bare_serializer t2)\nlet bare_serialize_synth\n (#k: parser_kind)\n (#t1: Type)\n (#t2: Type)\n (p1: parser k t1)\n (f2: t1 -> GTot t2)\n (s1: serializer p1)\n (g1: t2 -> GTot t1)\n: Tot (bare_serializer t2) =\n fun (x: t2) -> s1 (g1 x)", "val bind\n (a b: Type)\n (pre1 post1: _)\n (labs1: list eff_label)\n (pre2 post2: _)\n (labs2: list eff_label)\n (c: repr a pre1 post1 labs1)\n (f: (x: a -> repr b (pre2 x) (post2 x) labs2))\n : Tot\n (repr b\n (bind_pre a pre1 post1 b pre2 post2)\n (bind_post a pre1 post1 b pre2 post2)\n (labs1 @ labs2))\nlet bind (a b : Type)\n pre1 post1\n (labs1 : list eff_label)\n pre2 post2\n (labs2 : list eff_label)\n (c : repr a pre1 post1 labs1)\n (f : (x:a -> repr b (pre2 x) (post2 x) labs2))\n : Tot (repr b (bind_pre a pre1 post1 b pre2 post2)\n (bind_post a pre1 post1 b pre2 post2)\n (labs1@labs2))\n = let pre = bind_pre a pre1 post1 b pre2 post2 in\n let post = bind_post a pre1 post1 b pre2 post2 in\n let r (s0:state{pre s0}) : Tot (r:(option b & state){post s0 (fst r) (snd r)}) =\n match c s0 with\n | Some x, s1 ->\n assert (post1 s0 (Some x) s1);\n assert (pre2 x s1);\n f x s1\n | None, s1 -> None, s1\n in\n r", "val seq_map_i (#a:Type) (#b:Type) (f:int->a->b) (s:seq a) :\n Tot (s':seq b { length s' == length s /\\\n (forall j . {:pattern index s' j} 0 <= j /\\ j < length s ==> index s' j == f j (index s j))\n })\nlet seq_map_i (#a:Type) (#b:Type) (f:int->a->b) (s:seq a) :\n Tot (s':seq b { length s' == length s /\\\n (forall j . {:pattern index s' j} 0 <= j /\\ j < length s ==> index s' j == f j (index s j))\n })\n =\n seq_map_i_indexed f s 0", "val forall_intro_squash_gtot (#a: Type) (#p: (a -> GTot Type)) ($_: (x: a -> GTot (squash (p x))))\n : Tot (squash (forall (x: a). p x))\nlet forall_intro_squash_gtot #a #p f =\n bind_squash #(x: a -> GTot (p x))\n #(forall (x: a). p x)\n (squash_double_arrow #a #p (return_squash f))\n (fun f -> lemma_forall_intro_gtot #a #p f)", "val glift2 : #t:Type -> #t2:Type -> #t3:Type\n -> f:(t -> t2 -> GTot t3) -> rel t -> rel t2\n -> GTot (rel t3)\nlet glift2 #t #t2 #t3 f (R x y) (R x2 y2) = R (f x x2) (f y y2)", "val for_all_ubool_map\n (#a #b: Type)\n (f: (a -> GTot b))\n (p1: (b -> GTot ubool))\n (p2: (a -> GTot ubool))\n (l: list a)\n : Lemma (requires p2 == (fun x -> p1 (f x)))\n (ensures for_all_ubool p1 (map_ghost f l) == for_all_ubool p2 l)\nlet rec for_all_ubool_map (#a: Type) (#b: Type) (f: a -> GTot b) (p1: b -> GTot ubool) (p2: a -> GTot ubool) (l: list a)\n : Lemma\n (requires p2 == (fun x -> p1 (f x)))\n (ensures for_all_ubool p1 (map_ghost f l) == for_all_ubool p2 l) =\n match l with\n | [] -> ()\n | hd :: tl -> for_all_ubool_map f p1 p2 tl", "val map_seal\n (#a : Type u#aa) (b : Type u#bb)\n (s : sealed a)\n (f : a -> TacS b)\n: Tot (sealed b)\nlet map_seal\n (#a : Type u#aa) (b : Type u#bb)\n (s : sealed a)\n (f : a -> TacS b)\n: Tot (sealed b)\n=\n Seal (fun () -> f (unseal s))", "val bind\n (a b: Type)\n (wp_f: wp_t a)\n (wp_g: (a -> wp_t b))\n (f: repr a wp_f)\n (g: (x: a -> repr b (wp_g x)))\n : repr b (fun p -> wp_f (fun x -> (wp_g x) p))\nlet bind (a:Type) (b:Type)\n (wp_f:wp_t a)\n (wp_g:a -> wp_t b)\n (f:repr a wp_f) (g:(x:a -> repr b (wp_g x)))\n: repr b (fun p -> wp_f (fun x -> (wp_g x) p))\n= fun m ->\n let (x, m) = f m in\n (g x) m", "val elim_squash_or (#r #p #q: _) (f: squash (p \\/ q)) (left: (p -> GTot r)) (right: (q -> GTot r))\n : GTot (squash r)\nlet elim_squash_or (#r:_) (#p #q:_) (f:squash (p \\/ q)) (left: p -> GTot r) (right: q -> GTot r)\n : GTot (squash r)\n = FStar.Squash.bind_squash #_ #r f (fun pq ->\n FStar.Squash.bind_squash pq (fun c ->\n match c with\n | Prims.Left x -> FStar.Squash.return_squash (left x)\n | Prims.Right x -> FStar.Squash.return_squash (right x)))", "val or_intro_left\n (p:Type)\n (q:squash (~p) -> Type)\n (f:unit -> Tot (squash p))\n : Tot (squash (p \\/ q()))\nlet or_intro_left\n (p:Type)\n (q:squash (~p) -> Type)\n (f:unit -> Tot (squash p))\n : Tot (squash (p \\/ q()))\n = f()", "val lift_pure_mst_total\n (a: Type)\n (wp: pure_wp a)\n (state: Type u#2)\n (rel: P.preorder state)\n (f: (eqtype_as_type unit -> PURE a wp))\n : repr a\n state\n rel\n (fun s0 -> wp (fun _ -> True))\n (fun s0 x s1 -> wp (fun _ -> True) /\\ (~(wp (fun r -> r =!= x \\/ s0 =!= s1))))\nlet lift_pure_mst_total\n (a:Type)\n (wp:pure_wp a)\n (state:Type u#2)\n (rel:P.preorder state)\n (f:eqtype_as_type unit -> PURE a wp)\n : repr a state rel\n (fun s0 -> wp (fun _ -> True))\n (fun s0 x s1 -> wp (fun _ -> True) /\\ (~ (wp (fun r -> r =!= x \\/ s0 =!= s1))))\n =\n elim_pure_wp_monotonicity wp;\n fun s0 ->\n let x = f () in\n x, s0", "val serialize_synth\n (#t1 #t2: Type0)\n (#p1: parser_spec t1)\n (s1: serializer_spec p1)\n (f2: (t1 -> GTot t2))\n (g1: (t2 -> GTot t1))\n (u: squash (synth_inverse f2 g1 /\\ synth_inverse g1 f2))\n : Tot (serializer_spec (parse_synth p1 f2 g1))\nlet serialize_synth\n (#t1: Type0)\n (#t2: Type0)\n (#p1: parser_spec t1)\n (s1: serializer_spec p1)\n (f2: t1 -> GTot t2)\n (g1: t2 -> GTot t1)\n (u: squash (\n synth_inverse f2 g1 /\\\n synth_inverse g1 f2\n ))\n: Tot (serializer_spec (parse_synth p1 f2 g1))\n= bare_serialize_synth_correct p1 f2 s1 g1;\n Serializer (bare_serialize_synth p1 f2 s1 g1)", "val join (#sl: _) (#l1 #l2: lattice_element sl) (#a: _) (x: protected l1 (protected l2 a))\n : Tot (y: protected (l1 `lub` l2) a {reveal y == reveal (reveal x)})\nlet join #sl #l1 #l2 #a x = x", "val squash_arrow : #a:Type -> #p:(a -> Type) ->\n $f:(x:a -> GTot (squash (p x))) -> GTot (squash (x:a -> GTot (p x)))\nlet squash_arrow #a #p f = squash_double_arrow (return_squash f)", "val bare_serialize_synth\n (#t1: Type0)\n (#t2: Type0)\n (p1: parser_spec t1)\n (f2: t1 -> GTot t2)\n (s1: serializer_spec p1)\n (g1: t2 -> GTot t1)\n: Tot (bare_serializer t2)\nlet bare_serialize_synth #t1 #t2 p1 f2 s1 g1 =\n fun (x: t2) -> serialize s1 (g1 x)", "val on (a #b: Type) (f: (a -> Tot b)) : (a ^-> b)\nlet on (a #b: Type) (f: (a -> Tot b)) : (a ^-> b) = on_dom a f", "val synth_inverse_forall_bounded_u16_intro\n (b: nat)\n (t: Type)\n (f1: (bounded_u16 b -> GTot t))\n (f2: (t -> GTot (bounded_u16 b)))\n (u: squash (synth_inverse_forall_bounded_u16' b t f1 f2))\n: Tot (squash (synth_inverse f2 f1))\nlet synth_inverse_forall_bounded_u16_intro b t f1 f2 u\n= Classical.forall_intro (Classical.move_requires (forall_bounded_u16_elim b (synth_inverse_forall_bounded_u16_pred b t f1 f2)))", "val lex_t_wf_aux\n (#a: Type u#a)\n (#b: (a -> Type u#b))\n (#r_a: binrel u#a u#ra a)\n (#r_b: (x: a -> binrel u#b u#rb (b x)))\n (x: a)\n (acc_x: acc r_a x)\n (wf_b: (x0: a{closure r_a x0 x} -> well_founded (r_b x0)))\n (y: b x)\n (acc_y: acc (r_b x) y)\n (t: (x: a & b x))\n (p_t: lex_t r_a r_b t (| x, y |))\n : Tot (acc (lex_t r_a r_b) t) (decreases acc_x)\nlet rec lex_t_wf_aux (#a:Type u#a)\n (#b:a -> Type u#b)\n (#r_a:binrel u#a u#ra a)\n (#r_b:(x:a -> binrel u#b u#rb (b x)))\n (x:a)\n (acc_x:acc r_a x) //x and accessibility of x\n (wf_b:(x0:a{closure r_a x0 x} -> well_founded (r_b x0))) //well-foundedness of r_b\n (y:b x)\n (acc_y:acc (r_b x) y) //y and accessibility of y\n (t:(x:a & b x)) //another element t,\n (p_t:lex_t r_a r_b t (| x, y |)) //that is related to (| x, y |)\n : Tot (acc (lex_t r_a r_b) t) //returns the accessibility proof for t\n (decreases acc_x)\n = match p_t with\n | Left_lex x_t _ y_t _ p_a ->\n AccIntro (lex_t_wf_aux\n x_t\n (match acc_x with\n | AccIntro f -> f x_t p_a)\n wf_b\n y_t\n (wf_b x_t y_t))\n | Right_lex _ _ _ _ ->\n //inner induction that keeps x same, but recurses on acc_y\n let rec lex_t_wf_aux_y (y:b x) (acc_y:acc (r_b x) y) (t:(x:a & b x)) (p_t:lex_t r_a r_b t (| x, y |))\n : Tot (acc (lex_t r_a r_b) t)\n (decreases acc_y)\n = match p_t with\n | Left_lex x_t _ y_t _ p_a ->\n AccIntro (lex_t_wf_aux\n x_t\n (match acc_x with\n | AccIntro f -> f x_t p_a)\n wf_b\n y_t\n (wf_b x_t y_t))\n | Right_lex _ y_t _ p_b ->\n AccIntro (lex_t_wf_aux_y\n y_t\n (match acc_y with\n | AccIntro f -> f y_t p_b)) in\n lex_t_wf_aux_y y acc_y t p_t", "val bind\n (#s #a: _)\n (#srel: erel s)\n (#arel: erel a)\n (#b: _)\n (#brel: erel b)\n ($f: st srel arel)\n (g: arel ^--> st_rel srel brel)\n : st srel brel\nlet bind #s #a (#srel:erel s) (#arel:erel a) #b (#brel:erel b)\n ($f:st srel arel)\n (g:arel ^--> st_rel srel brel)\n : st srel brel =\n fun s0 ->\n let x, s1 = f s0 in\n g x s1", "val bind_st: a:Type -> b:Type -> f:st a -> g:(a -> Tot (st b)) -> Tot (st b)\nlet bind_st a b f g = fun s0 ->\n let tmp = f s0 in\n let x, s1 = tmp in\n g x s1", "val dfst (#a: Type) (#b: (a -> GTot Type)) (t: dtuple2 a b) : Tot a\nlet dfst (#a: Type) (#b: a -> GTot Type) (t: dtuple2 a b)\n : Tot a\n = Mkdtuple2?._1 t", "val arrow_to_impl (#a #b: Type0) (_: (squash a -> GTot (squash b))) : GTot (a ==> b)\nlet arrow_to_impl #a #b f = squash_double_arrow (return_squash (fun x -> f (return_squash x)))", "val forall_intro_3\n (#a: Type)\n (#b: (a -> Type))\n (#c: (x: a -> y: b x -> Type))\n (#p: (x: a -> y: b x -> z: c x y -> Type0))\n ($_: (x: a -> y: b x -> z: c x y -> Lemma (p x y z)))\n : Lemma (forall (x: a) (y: b x) (z: c x y). p x y z)\nlet forall_intro_3 #a #b #c #p f =\n let g: x: a -> Lemma (forall (y: b x) (z: c x y). p x y z) = fun x -> forall_intro_2 (f x) in\n forall_intro g", "val eval_equiv_trans\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f1 f2 f3 : exp t)\n: Lemma\n (requires (eval_equiv p e f1 f2 /\\ eval_equiv p e f2 f3))\n (ensures (eval_equiv p e f1 f3))\nlet eval_equiv_trans\n (#t: Type0)\n (p: sttype)\n (e: nstype t)\n (f1 f2 f3 : exp t)\n: Lemma\n (requires (eval_equiv p e f1 f2 /\\ eval_equiv p e f2 f3))\n (ensures (eval_equiv p e f1 f3))\n= Benton2004.eval_equiv_trans p e f1 f2 f3", "val raise_ : a:Type -> e:exn -> Tot (EXN?.repr a (fun (_:unit) (p:EXN?.post a) -> p (Inr e)))\nlet raise_ a (e:exn) (_:unit) = Inr e", "val or_elim\n (#l #r: Type0)\n (#goal: (squash (l \\/ r) -> Tot Type0))\n (hl: (squash l -> Lemma (goal ())))\n (hr: (squash r -> Lemma (goal ())))\n : Lemma ((l \\/ r) ==> goal ())\nlet or_elim #l #r #goal hl hr =\n impl_intro_gen #l #(fun _ -> goal ()) hl;\n impl_intro_gen #r #(fun _ -> goal ()) hr", "val ceq_congruence : #a:Type -> #b:Type -> #x:a -> #y:a -> ceq x y ->\n f:(a -> GTot b) -> GTot (ceq (f x) (f y))\nlet ceq_congruence #a #b #x #y h f = Refl #_ #(f x)", "val serialize_synth_eq'\n (#k: parser_kind)\n (#t1 #t2: Type)\n (p1: parser k t1)\n (f2: (t1 -> GTot t2))\n (s1: serializer p1)\n (g1: (t2 -> GTot t1))\n (u: unit{synth_inverse f2 g1 /\\ synth_injective f2})\n (x: t2)\n (y1: bytes)\n (q1: squash (y1 == serialize (serialize_synth p1 f2 s1 g1 u) x))\n (y2: bytes)\n (q2: squash (y2 == serialize s1 (g1 x)))\n : Lemma (ensures (y1 == y2))\nlet serialize_synth_eq'\n (#k: parser_kind)\n (#t1: Type)\n (#t2: Type)\n (p1: parser k t1)\n (f2: t1 -> GTot t2)\n (s1: serializer p1)\n (g1: t2 -> GTot t1)\n (u: unit {\n synth_inverse f2 g1 /\\\n synth_injective f2\n })\n (x: t2)\n (y1: bytes)\n (q1: squash (y1 == serialize (serialize_synth p1 f2 s1 g1 u) x))\n (y2: bytes)\n (q2: squash (y2 == serialize s1 (g1 x)))\n: Lemma\n (ensures (y1 == y2))\n= serialize_synth_eq p1 f2 s1 g1 u x", "val terminates_equiv_reified\n (p : sttype)\n (f f' : reified_computation)\n: GTot Type0\nlet terminates_equiv_reified\n (p : sttype)\n (f f' : reified_computation)\n: GTot Type0\n= Benton2004.terminates_equiv_reified p f f'", "val lemma_forall_intro_gtot (#a: Type) (#p: (a -> GTot Type)) ($_: (x: a -> GTot (p x)))\n : Lemma (forall (x: a). p x)\nlet lemma_forall_intro_gtot #a #p f = give_witness (forall_intro_gtot #a #p f)", "val feq_intro\n (u v: Type)\n (eq: (v -> v -> GTot Type0))\n (f1 f2: (u -> Tot v))\n (phi: (x: u -> Lemma ((f1 x) `eq` (f2 x))))\n : Lemma (feq _ _ eq f1 f2)\nlet feq_intro\n (u v: Type)\n (eq: (v -> v -> GTot Type0))\n (f1 f2: (u -> Tot v))\n (phi: (x: u) -> Lemma (f1 x `eq` f2 x))\n: Lemma (feq _ _ eq f1 f2)\n= Classical.forall_intro phi", "val parse_synth_eq2\n (#k: parser_kind)\n (#t1 #t2: Type)\n (p1: parser k t1)\n (f2: (t1 -> GTot t2))\n (sq: squash (synth_injective f2))\n (b: bytes)\n : Lemma (ensures (parse (parse_synth p1 f2) b == parse_synth' p1 f2 b))\nlet parse_synth_eq2\n (#k: parser_kind)\n (#t1: Type)\n (#t2: Type)\n (p1: parser k t1)\n (f2: t1 -> GTot t2)\n (sq: squash (synth_injective f2))\n (b: bytes)\n: Lemma\n (ensures (parse (parse_synth p1 f2) b == parse_synth' p1 f2 b))\n= parse_synth_eq p1 f2 b", "val subcomp\n (a: Type)\n (p1: Type0)\n (w1: (squash p1 -> w a))\n (p2: Type0)\n (w2: (squash p2 -> w a))\n (f: repr a p1 w1)\n : Pure (repr a p2 w2)\n (requires (p2 ==> p1) /\\ (forall (pf: squash p2). (w2 pf) `stronger` (w1 (weaken p2 p1 pf))))\n (ensures fun _ -> True)\nlet subcomp (a:Type)\n (p1 : Type0)\n (w1 : squash p1 -> w a)\n (p2 : Type0)\n (w2 : squash p2 -> w a)\n (f : repr a p1 w1)\n : Pure (repr a p2 w2)\n (requires (p2 ==> p1) /\\ (forall (pf : squash p2). w2 pf `stronger` w1 (weaken p2 p1 pf)))\n (ensures fun _ -> True)\n = fun _ -> f ()", "val synth_injective_synth_inverse_synth_inverse_recip\n (#t1 #t2: Type)\n (g: (t2 -> GTot t1))\n (f: (t1 -> GTot t2))\n (u: squash (synth_inverse g f /\\ synth_injective g))\n : Tot (squash (synth_inverse f g))\nlet synth_injective_synth_inverse_synth_inverse_recip\n (#t1: Type)\n (#t2: Type)\n (g: (t2 -> GTot t1))\n (f: (t1 -> GTot t2))\n (u: squash (synth_inverse g f /\\ synth_injective g))\n: Tot (squash (synth_inverse f g))\n= assert (forall x . g (f (g x)) == g x)", "val pure_as_squash\n (#a: Type)\n (#p #q: _)\n ($f: (x: a -> Lemma (requires (p x)) (ensures (q x))))\n (x: a{p x})\n : squash (q x)\nlet pure_as_squash (#a:Type) \n (#p:_)\n (#q:_)\n ($f:(x:a -> Lemma (requires (p x)) (ensures (q x))))\n (x:a{p x})\n : squash (q x)\n = f x", "val and_intro\n (p:Type)\n (q:squash p -> Type)\n (left:unit -> Tot (squash p))\n (right:squash p -> Tot (squash (q())))\n : Tot (squash (p /\\ q()))\nlet and_intro\n (p:Type)\n (q:squash p -> Type)\n (f:unit -> Tot (squash p))\n (g:squash p -> Tot (squash (q())))\n : Tot (squash (p /\\ q()))\n = let _ = f() in g()", "val exec_equiv_reified (p p': sttype) (f f': reified_computation) : GTot Type0\nlet exec_equiv_reified\n (p p' : sttype)\n (f f' : reified_computation)\n: GTot Type0\n= terminates_equiv_reified p f f' /\\\n (forall (s s' : heap) (fuel: nat) .\n (holds p s s' /\\ fst (f fuel s) == true /\\ fst (f' fuel s') == true) ==> holds p' (snd (f fuel s)) (snd (f' fuel s')))", "val forall_intro : #a:Type -> #p:(a -> Type) ->\n $f:(x:a -> Lemma (p x)) -> Lemma (x:a -> GTot (p x))\nlet forall_intro #a #p f =\n let ff : (x:a -> GTot (squash (p x))) = (fun x -> f x; get_proof (p x)) in\n give_proof #(x:a -> GTot (p x)) (squash_arrow #a #p ff)", "val sorted_feq (#a:Type)\n (f g : (a -> a -> Tot bool))\n (s:seq a{forall x y. f x y == g x y})\n : Lemma (ensures (sorted f s <==> sorted g s))\nlet sorted_feq = sorted_feq'", "val impl_intro_gen (#p: Type0) (#q: (squash p -> Tot Type0)) (_: (squash p -> Lemma (q ())))\n : Lemma (p ==> q ())\nlet impl_intro_gen #p #q f =\n let g () : Lemma (requires p) (ensures (p ==> q ())) = give_proof #(q ()) (f (get_proof p)) in\n move_requires g ()", "val false_elim2 : #a:Type -> cfalse -> Tot a\nlet false_elim2 #a x = false_elim ()", "val values (#a: eqtype) (#b: Type u#b) (m: map a b)\n : GTot (b -> prop)\nlet values (#a: eqtype) (#b: Type u#b) (m: map a b) : GTot (b -> prop) =\n fun value -> exists key. ((elements m) key == Some value)", "val bind\n (a b: Type)\n (state: Type u#2)\n (rel: P.preorder state)\n (req_f: M.pre_t state)\n (ens_f: M.post_t state a)\n (req_g: (a -> M.pre_t state))\n (ens_g: (a -> M.post_t state b))\n (f: repr a state rel req_f ens_f)\n (g: (x: a -> repr b state rel (req_g x) (ens_g x)))\n : repr b\n state\n rel\n (fun s0 -> req_f s0 /\\ (forall x s1. ens_f s0 x s1 ==> (req_g x) s1))\n (fun s0 r s2 -> req_f s0 /\\ (exists x s1. ens_f s0 x s1 /\\ (req_g x) s1 /\\ (ens_g x) s1 r s2))\nlet bind\n (a:Type)\n (b:Type)\n (state:Type u#2)\n (rel:P.preorder state)\n (req_f:M.pre_t state)\n (ens_f:M.post_t state a)\n (req_g:a -> M.pre_t state)\n (ens_g:a -> M.post_t state b)\n (f:repr a state rel req_f ens_f)\n (g:(x:a -> repr b state rel (req_g x) (ens_g x)))\n : repr b state rel\n (fun s0 -> req_f s0 /\\ (forall x s1. ens_f s0 x s1 ==> (req_g x) s1))\n (fun s0 r s2 -> req_f s0 /\\ (exists x s1. ens_f s0 x s1 /\\ (req_g x) s1 /\\ (ens_g x) s1 r s2))\n =\n fun (t, n) ->\n let x, n1 = f (t, n) in\n (g x) (t, n1)" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Classical.Sugar.fst", "name": "FStar.Classical.Sugar.and_elim" }, { "project_name": "zeta", "file_name": "Zeta.Ghost.fsti", "name": "Zeta.Ghost.hoist_ghost2" }, { "project_name": "FStar", "file_name": "FStar.Classical.Sugar.fst", "name": "FStar.Classical.Sugar.or_elim_simple" }, { "project_name": "FStar", "file_name": "FStar.Calc.fst", "name": "FStar.Calc.calc_push_impl" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.forall_to_exists_2" }, { "project_name": "FStar", "file_name": "FStar.Classical.Sugar.fst", "name": "FStar.Classical.Sugar.exists_elim" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Meta.fst", "name": "Vale.Lib.Meta.exists_elim2" }, { "project_name": "FStar", "file_name": "Rel.fst", "name": "Rel.lift2" }, { "project_name": "FStar", "file_name": "FStar.Constructive.fst", "name": "FStar.Constructive.eq_ind" }, { "project_name": "FStar", "file_name": "FStar.Classical.Sugar.fst", "name": "FStar.Classical.Sugar.or_elim" }, { "project_name": "FStar", "file_name": "FStar.Classical.Sugar.fst", "name": "FStar.Classical.Sugar.implies_intro" }, { "project_name": "FStar", "file_name": "FStar.IFC.fst", "name": "FStar.IFC.map" }, { "project_name": "FStar", "file_name": "FStar.Classical.Sugar.fst", "name": "FStar.Classical.Sugar.or_intro_right" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.op_Hat_Plus_Hat" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fst", "name": "Benton2004.DDCC.eval_equiv_reified" }, { "project_name": "FStar", "file_name": "FStar.Ghost.fst", "name": "FStar.Ghost.reveal" }, { "project_name": "FStar", "file_name": "LatticeEff.fst", "name": "LatticeEff.bind" }, { "project_name": "FStar", "file_name": "Lattice.fst", "name": "Lattice.bind" }, { "project_name": "FStar", "file_name": "Alg.fst", "name": "Alg.bind" }, { "project_name": "FStar", "file_name": "Rel.fst", "name": "Rel.lift3" }, { "project_name": "FStar", "file_name": "SealedModel.fst", "name": "SealedModel.bind_seal" }, { "project_name": "FStar", "file_name": "FStar.Squash.fst", "name": "FStar.Squash.push_sum" }, { "project_name": "FStar", "file_name": "HoareSTFree.fst", "name": "HoareSTFree.bind" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.impl_intro_tot" }, { "project_name": "FStar", "file_name": "Rel.fst", "name": "Rel.lift" }, { "project_name": "FStar", "file_name": "Degenerate.fst", "name": "Degenerate.bind" }, { "project_name": "FStar", "file_name": "FStar.WellFounded.fst", "name": "FStar.WellFounded.fix_F" }, { "project_name": "FStar", "file_name": "Rel.fst", "name": "Rel.lift5" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.forall_impl_intro" }, { "project_name": "FStar", "file_name": "FStar.FunctionalExtensionality.fsti", "name": "FStar.FunctionalExtensionality.on_g" }, { "project_name": "FStar", "file_name": "FStar.Squash.fst", "name": "FStar.Squash.squash_double_sum" }, { "project_name": "FStar", "file_name": "FStar.Classical.Sugar.fst", "name": "FStar.Classical.Sugar.forall_intro" }, { "project_name": "FStar", "file_name": "Rel.fst", "name": "Rel.lift4" }, { "project_name": "Armada", "file_name": "Util.Seq.fst", "name": "Util.Seq.map_refine" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.forall_intro_2" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.forall_intro_squash_gtot_join" }, { "project_name": "FStar", "file_name": "FStar.Squash.fst", "name": "FStar.Squash.squash_double_arrow" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.eval_equiv_reified" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.fold_left_map" }, { "project_name": "Armada", "file_name": "Util.List.fst", "name": "Util.List.for_all_map" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fst", "name": "Benton2004.DDCC.exec_equiv_reified" }, { "project_name": "FStar", "file_name": "FStar.Ghost.fst", "name": "FStar.Ghost.hide" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.eval_equiv" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.feq" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fsti", "name": "FStar.DM4F.Heap.op_Hat_Plus_Hat" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Random.fst", "name": "FStar.DM4F.Random.pr_eq" }, { "project_name": "FStar", "file_name": "FStar.DM4F.OTP.Random.fst", "name": "FStar.DM4F.OTP.Random.pr_eq" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.bind" }, { "project_name": "FStar", "file_name": "HoareDiv.fst", "name": "HoareDiv.bind" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fst", "name": "FStar.ReflexiveTransitiveClosure.squash_double_arrow" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.forall_intro_gtot" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.impl_intro_gtot" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.map" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.ghost_lemma" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.flip" }, { "project_name": "FStar", "file_name": "Param.fst", "name": "Param.list_rec_of_function_is_map_1" }, { "project_name": "FStar", "file_name": "IfcDelimitedReleaseReify.fst", "name": "IfcDelimitedReleaseReify.rel_eq" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fsti", "name": "LowParse.Spec.Combinators.bare_serialize_synth" }, { "project_name": "FStar", "file_name": "LatticeSpec.fst", "name": "LatticeSpec.bind" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.seq_map_i" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.forall_intro_squash_gtot" }, { "project_name": "FStar", "file_name": "StRel.fst", "name": "StRel.glift2" }, { "project_name": "Armada", "file_name": "Util.List.fst", "name": "Util.List.for_all_ubool_map" }, { "project_name": "FStar", "file_name": "SealedModel.fst", "name": "SealedModel.map_seal" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.bind" }, { "project_name": "FStar", "file_name": "WorkingWithSquashedProofs.fst", "name": "WorkingWithSquashedProofs.elim_squash_or" }, { "project_name": "FStar", "file_name": "FStar.Classical.Sugar.fst", "name": "FStar.Classical.Sugar.or_intro_left" }, { "project_name": "FStar", "file_name": "FStar.MSTTotal.fst", "name": "FStar.MSTTotal.lift_pure_mst_total" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.Combinators.fst", "name": "MiniParse.Spec.Combinators.serialize_synth" }, { "project_name": "FStar", "file_name": "FStar.IFC.fst", "name": "FStar.IFC.join" }, { "project_name": "FStar", "file_name": "FStar.SquashProperties.fst", "name": "FStar.SquashProperties.squash_arrow" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.Combinators.fst", "name": "MiniParse.Spec.Combinators.bare_serialize_synth" }, { "project_name": "FStar", "file_name": "FStar.FunctionalExtensionality.fsti", "name": "FStar.FunctionalExtensionality.on" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.TEnum.fst", "name": "MiniParse.Spec.TEnum.synth_inverse_forall_bounded_u16_intro" }, { "project_name": "FStar", "file_name": "FStar.LexicographicOrdering.fst", "name": "FStar.LexicographicOrdering.lex_t_wf_aux" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.bind" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.bind_st" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.dfst" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.arrow_to_impl" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.forall_intro_3" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fst", "name": "Benton2004.DDCC.eval_equiv_trans" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Exceptions.fst", "name": "FStar.DM4F.Exceptions.raise_" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.or_elim" }, { "project_name": "FStar", "file_name": "FStar.Constructive.fst", "name": "FStar.Constructive.ceq_congruence" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fsti", "name": "LowParse.Spec.Combinators.serialize_synth_eq'" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fst", "name": "Benton2004.DDCC.terminates_equiv_reified" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.lemma_forall_intro_gtot" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.feq_intro" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fsti", "name": "LowParse.Spec.Combinators.parse_synth_eq2" }, { "project_name": "FStar", "file_name": "GenericPartialDM4A.fst", "name": "GenericPartialDM4A.subcomp" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fsti", "name": "LowParse.Spec.Combinators.synth_injective_synth_inverse_synth_inverse_recip" }, { "project_name": "FStar", "file_name": "BinaryTreesEnumeration.fsti", "name": "BinaryTreesEnumeration.pure_as_squash" }, { "project_name": "FStar", "file_name": "FStar.Classical.Sugar.fst", "name": "FStar.Classical.Sugar.and_intro" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.exec_equiv_reified" }, { "project_name": "FStar", "file_name": "FStar.SquashProperties.fst", "name": "FStar.SquashProperties.forall_intro" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.sorted_feq" }, { "project_name": "FStar", "file_name": "FStar.Classical.fst", "name": "FStar.Classical.impl_intro_gen" }, { "project_name": "FStar", "file_name": "FStar.Constructive.fst", "name": "FStar.Constructive.false_elim2" }, { "project_name": "FStar", "file_name": "FStar.FiniteMap.Base.fst", "name": "FStar.FiniteMap.Base.values" }, { "project_name": "FStar", "file_name": "FStar.NMSTTotal.fst", "name": "FStar.NMSTTotal.bind" } ], "selected_premises": [ "FStar.Ghost.return", "FStar.Ghost.push_refinement", "FStar.Ghost.elift1", "FStar.Ghost.elift1_pq", "FStar.Ghost.elift2", "FStar.Ghost.bind", "FStar.Ghost.op_let_At", "FStar.Ghost.elift1_p", "FStar.Ghost.elift2_p", "FStar.Ghost.elift3", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "FStar.Pervasives.pure_null_wp", "Prims.l_True", "FStar.Pervasives.dfst", "FStar.Pervasives.div_hoare_to_wp", "Prims.subtype_of", "FStar.Pervasives.id", "Prims.__cache_version_number__", "Prims.l_False", "FStar.Pervasives.lift_div_exn", "FStar.Pervasives.dsnd", "FStar.Pervasives.reveal_opaque", "Prims.pow2", "FStar.Ghost.tot_to_gtot", "FStar.Pervasives.coerce_eq", "FStar.Pervasives.ex_stronger", "Prims.op_Hat", "Prims.min", "Prims.pure_post'", "FStar.Pervasives.trivial_pure_post", "FStar.Pervasives.ex_trivial", "Prims.auto_squash", "Prims.pure_wp_monotonic", "Prims.purewp_id", "FStar.Pervasives.ex_bind_wp", "Prims.abs", "Prims.pure_trivial", "FStar.Pervasives.ex_if_then_else", "Prims.as_ensures", "Prims.pure_stronger", "Prims.pure_post", "FStar.Pervasives.ex_return", "FStar.Pervasives.ex_ite_wp", "Prims.pure_wp_monotonic0", "FStar.Pervasives.ex_wp", "Prims.returnM", "Prims.pure_wp", "Prims.as_requires", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.pure_return", "FStar.Pervasives.st_trivial", "FStar.Pervasives.ex_post", "FStar.Pervasives.ex_pre", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.ex_post'", "FStar.Pervasives.pure_bind_wp", "FStar.Pervasives.pure_close_wp", "FStar.Pervasives.all_trivial", "FStar.Pervasives.all_post_h", "FStar.Pervasives.st_post_h", "Prims.pure_pre", "FStar.Pervasives.st_return", "FStar.Pervasives.st_stronger", "Prims.pure_wp'", "FStar.Pervasives.pure_ite_wp", "FStar.Pervasives.all_return", "FStar.Pervasives.all_post_h'", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.st_pre_h", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.st_if_then_else", "FStar.Pervasives.all_wp_h", "FStar.Pervasives.st_bind_wp", "FStar.Pervasives.all_ite_wp", "FStar.Pervasives.all_close_wp", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.all_if_then_else", "FStar.Pervasives.all_stronger", "FStar.Pervasives.st_ite_wp", "FStar.Pervasives.st_wp_h" ], "source_upto_this": "(*\n Copyright 2008-2014 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule FStar.Ghost\n\n/// This module provides an erased type to abstract computationally\n/// irrelevant values.\n///\n/// It relies on the GHOST effect defined in Prims.\n///\n/// [erased a] is decorated with the erasable attribute. As such,\n///\n/// 1. The type is considered non-informative.\n///\n/// So, [Ghost (erased a)] can be subsumed to [Pure (erased a)]\n///\n/// 2. The compiler extracts [erased a] to [unit]\n///\n/// The type is [erased a] is in a bijection with [a], as\n/// witnessed by the [hide] and [reveal] function.\n///\n/// Importantly, computationally relevant code cannot use [reveal]\n/// (it's marked [GTot])\n///\n/// Just like Coq's prop, it is okay to use erased types\n/// freely as long as we produce an erased type.\n///\n/// [reveal] and [hide] are coercions: the typechecker will\n/// automatically insert them when required. That is, if the type of\n/// an expression is [erased X], and the expected type is NOT an\n/// [erased Y], it will insert [reveal], and vice versa for [hide].\n\n(** [erased t] is the computationally irrelevant counterpart of [t] *)\n[@@ erasable]\nnew\nval erased ([@@@strictly_positive] a: Type u#a) : Type u#a\n\n(** [erased t] is in a bijection with [t], as witnessed by [reveal]\n and [hide] *)\nval reveal: #a: Type u#a -> erased a -> GTot a\n\nval hide: #a: Type u#a -> a -> Tot (erased a)\n\nval hide_reveal (#a: Type) (x: erased a)\n : Lemma (ensures (hide (reveal x) == x)) [SMTPat (reveal x)]\n\nval reveal_hide (#a: Type) (x: a) : Lemma (ensures (reveal (hide x) == x)) [SMTPat (hide x)]\n\n\n/// The rest of this module includes several well-defined defined\n/// notions. They are not trusted.\n\n(** [Tot] is a sub-effect of [GTot] F* will usually subsume [Tot]\n computations to [GTot] computations, though, occasionally, it may\n be useful to apply this coercion explicitly. *)\nlet tot_to_gtot (f: ('a -> Tot 'b)) (x: 'a) : GTot 'b = f x\n\n(** [erased]: Injecting a value into [erased]; just an alias of [hide] *)\nlet return (#a: Type) (x: a) : erased a = hide x\n\n(** Sequential composition of erased *)\nlet bind (#a #b: Type) (x: erased a) (f: (a -> Tot (erased b))) : Tot (erased b) =\n let y = reveal x in\n f y\n\nunfold\nlet (let@) (x:erased 'a) (f:('a -> Tot (erased 'b))) : Tot (erased 'b) = bind x f\n\n(** Unary map *)\nirreducible\nlet elift1 (#a #b: Type) (f: (a -> GTot b)) (x: erased a)\n : Tot (y: erased b {reveal y == f (reveal x)}) =\n let@ xx = x in return (f xx)\n\n(** Binary map *)\nirreducible\nlet elift2 (#a #b #c: Type) (f: (a -> b -> GTot c)) (x: erased a) (y: erased b)\n : Tot (z: erased c {reveal z == f (reveal x) (reveal y)}) =\n let@ xx = x in\n let@ yy = y in\n return (f xx yy)\n\n(** Ternary map *)\nirreducible\nlet elift3\n (#a #b #c #d: Type)\n (f: (a -> b -> c -> GTot d))\n (ga: erased a)\n (gb: erased b)\n (gc: erased c)\n : Tot (gd: erased d {reveal gd == f (reveal ga) (reveal gb) (reveal gc)}) =\n let@ a = ga in\n let@ b = gb in\n let@ c = gc in\n return (f a b c)\n\n(** Pushing a refinement type under the [erased] constructor *)\nlet push_refinement #a (#p: (a -> Type0)) (r: erased a {p (reveal r)})\n : erased (x: a{p x /\\ x == reveal r}) =\n let x:(x: a{p x}) = reveal r in\n return x\n\n(** Mapping a function with a refined domain over a refined erased value *)\nirreducible\nlet elift1_p\n (#a #b: Type)\n (#p: (a -> Type))\n ($f: (x: a{p x} -> GTot b))\n (r: erased a {p (reveal r)})\n : Tot (z: erased b {reveal z == f (reveal r)}) =\n let x:(x: a{p x}) = reveal r in\n return (f x)\n\n(** Mapping a binary function with a refined domain over a pair of\n refined erased values *)\nirreducible\nlet elift2_p\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n ($f: (xa: a -> xb: b{p xa xb} -> GTot c))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (rc: erased c {reveal rc == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)\n\n(** Mapping a function with a refined domain and co-domain over a\n refined erased value producing a refined erased value *)\nirreducible\nlet elift1_pq\n (#a #b: Type)\n (#p: (a -> Type))\n (#q: (x: a{p x} -> b -> Type))\n ($f: (x: a{p x} -> GTot (y: b{q x y})))\n (r: erased a {p (reveal r)})\n : Tot (z: erased b {reveal z == f (reveal r)}) =\n let x:(x: a{p x}) = reveal r in\n return (f x)\n\n(** Mapping a binary function with a refined domain and co-domain over\n a pair of refined erased values producing a refined erased value\n *)\nirreducible", "sketch": [ "Step 1: This definition is about mapping a binary function with a refined domain and co-domain over a pair of refined erased values, producing a refined erased value. The function `f` takes two arguments `x` and `y` that satisfy the predicate `p`, and returns a value `z` that satisfies the predicate `q`.\nStep 2: To implement this, we first reveal the values `ra` and `rb` to obtain `x` and `y` respectively. Then, we apply the function `f` to `x` and `y` to get the result `z`. Finally, we return `z` wrapped in the `erased` type.", "Step 1: This definition is about mapping a binary function with a refined domain and co-domain over a pair of refined erased values, producing a refined erased value. The function `f` takes two arguments `x` and `y` which satisfy the predicate `p`, and returns a value `z` that satisfies the predicate `q`.\nStep 2: To implement this, we first reveal the erased values `ra` and `rb` to obtain `x` and `y` respectively. Then, we apply the function `f` to `x` and `y` to get the result `z`. Finally, we return `z` wrapped in the `erased` type.", "Step 1: This definition is about mapping a binary function with a refined domain and co-domain over a pair of refined erased values, producing a refined erased value. The function `f` takes two arguments `x` and `y` that satisfy the predicate `p`, and returns a value `z` that satisfies the predicate `q`.\nStep 2: To implement this, we first reveal the erased values `ra` and `rb` to obtain `x` and `y` respectively. Then, we apply the function `f` to these revealed values to get the result `z`. Finally, we return the erased version of `z`.", "Step 1: This definition is about mapping a binary function with a refined domain and co-domain over a pair of refined erased values, producing a refined erased value. Specifically, it takes two erased values `ra` and `rb` with refinements `p` and `q`, and applies a function `f` to the revealed values of `ra` and `rb`, ensuring that the result satisfies the refinement `q`.\nStep 2: To implement this, we first reveal the values of `ra` and `rb`. Then, we apply the function `f` to these revealed values. Finally, we return the result of `f` wrapped in the `erased` type, ensuring that the refinement `q` holds for the result.", "Step 1: The definition `elift2_pq` is about mapping a binary function `f` with a refined domain and co-domain over a pair of refined erased values, producing a refined erased value. The function `f` takes two arguments `x` and `y` that satisfy the predicate `p`, and returns a value `z` that satisfies the predicate `q`.\nStep 2: To implement `elift2_pq`, we first reveal the erased values `ra` and `rb` to obtain `x` and `y` respectively. Then, we apply the function `f` to `x` and `y` to get the result `z`. Finally, we return the erased version of `z`.", "Step 1: This definition is about mapping a binary function with a refined domain and co-domain over a pair of refined erased values, producing a refined erased value. The function `f` takes two arguments `x` and `y` that satisfy the predicate `p`, and returns a value `z` that satisfies the predicate `q`.\nStep 2: To implement this, we first reveal the erased values `ra` and `rb` to obtain `x` and `y` respectively. Then, we apply the function `f` to `x` and `y` to get the result `z`. Finally, we return the erased version of `z`.", "Step 1: This definition is about mapping a binary function with a refined domain and co-domain over a pair of refined erased values, producing a refined erased value. The function `f` takes two inputs `x` and `y` that satisfy the predicate `p`, and returns a value `z` that satisfies the predicate `q`.\nStep 2: To implement this, we first reveal the erased values `ra` and `rb` to obtain `x` and `y` respectively. We then apply the function `f` to these revealed values to get the result `z`. Finally, we return `z` wrapped in the `erased` type.", "Step 1: The definition `elift2_pq` is about mapping a binary function `f` with a refined domain and co-domain over a pair of refined erased values, producing a refined erased value. The function `f` takes two arguments `x` and `y` that satisfy the predicate `p`, and returns a value `z` that satisfies the predicate `q`.\nStep 2: To implement `elift2_pq`, we first reveal the erased values `ra` and `rb` to obtain `x` and `y` respectively. We then apply the function `f` to `x` and `y`, and return the result wrapped in the `erased` type.", "Step 1: This definition is about mapping a binary function with a refined domain and co-domain over a pair of refined erased values, producing a refined erased value. The function `f` takes two arguments `x` and `y` that satisfy the predicate `p`, and returns a value `z` that satisfies the predicate `q` given `x` and `y`.\n\nStep 2: To implement this, we first reveal the values `ra` and `rb` to obtain `x` and `y` respectively. We then apply the function `f` to these revealed values. Finally, we return the result wrapped in the `erased` type, ensuring that the refinement on the result holds.", "Step 1: This definition is about mapping a binary function with a refined domain and co-domain over a pair of refined erased values, producing a refined erased value. The function `f` takes two arguments `x` and `y` that satisfy the predicate `p`, and returns a value `z` that satisfies the predicate `q`.\nStep 2: To implement this, we first reveal the erased values `ra` and `rb` to obtain `x` and `y`. Then, we apply the function `f` to these revealed values. Finally, we return the result wrapped in the `erased` type." ], "generated_solution": [ "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "let elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)" ] }, { "file_name": "Vale.AES.X64.PolyOps.fst", "name": "Vale.AES.X64.PolyOps.va_wpProof_VPolyMul", "opens_and_abbrevs": [ { "open": "Vale.X64.CPU_Features_s" }, { "open": "Vale.X64.QuickCodes" }, { "open": "Vale.X64.QuickCode" }, { "open": "Vale.X64.InsAes" }, { "open": "Vale.X64.InsVector" }, { "open": "Vale.X64.InsMem" }, { "open": "Vale.X64.InsBasic" }, { "open": "Vale.X64.Decls" }, { "open": "Vale.X64.State" }, { "open": "Vale.X64.Machine_s" }, { "open": "Vale.Math.Poly2.Lemmas" }, { "open": "Vale.Math.Poly2.Bits" }, { "open": "Vale.Math.Poly2.Bits_s" }, { "open": "Vale.Math.Poly2" }, { "open": "Vale.Math.Poly2_s" }, { "open": "Vale.Arch.Types" }, { "open": "Vale.Def.Types_s" }, { "open": "Vale.X64.CPU_Features_s" }, { "open": "Vale.X64.QuickCodes" }, { "open": "Vale.X64.QuickCode" }, { "open": "Vale.X64.InsAes" }, { "open": "Vale.X64.InsVector" }, { "open": "Vale.X64.InsMem" }, { "open": "Vale.X64.InsBasic" }, { "open": "Vale.X64.Decls" }, { "open": "Vale.X64.State" }, { "open": "Vale.X64.Machine_s" }, { "open": "Vale.Math.Poly2.Lemmas" }, { "open": "Vale.Math.Poly2.Bits" }, { "open": "Vale.Math.Poly2.Bits_s" }, { "open": "Vale.Math.Poly2" }, { "open": "Vale.Math.Poly2_s" }, { "open": "Vale.Arch.Types" }, { "open": "Vale.Def.Types_s" }, { "open": "Vale.AES.X64" }, { "open": "Vale.AES.X64" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 1, "initial_ifuel": 0, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": true, "smtencoding_nl_arith_repr": "wrapped", "smtencoding_l_arith_repr": "native", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val va_wpProof_VPolyMul : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_xmm ->\n src1Hi:bool -> src2Hi:bool -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPolyMul dst src1 src2 src1Hi src2Hi)\n ([va_Mod_flags; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))", "source_definition": "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst\n src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "source_range": { "start_line": 236, "start_col": 0, "end_line": 244, "end_col": 22 }, "interleaved": false, "definition": "fun dst src1 src2 src1Hi src2Hi va_s0 _ ->\n let _ =\n Vale.AES.X64.PolyOps.va_lemma_VPolyMul (Vale.AES.X64.PolyOps.va_code_VPolyMul dst\n src1\n src2\n src1Hi\n src2Hi)\n va_s0\n dst\n src1\n src2\n src1Hi\n src2Hi\n in\n (let FStar.Pervasives.Native.Mktuple2 #_ #_ va_sM va_f0 = _ in\n Vale.X64.Decls.va_lemma_upd_update va_sM;\n assert (Vale.X64.Decls.va_state_eq va_sM\n (Vale.X64.Decls.va_update_flags va_sM\n (Vale.X64.Decls.va_update_ok va_sM\n (Vale.X64.Decls.va_update_operand_xmm dst va_sM va_s0))));\n Vale.X64.QuickCode.va_lemma_norm_mods [\n Vale.X64.QuickCode.va_Mod_flags;\n Vale.X64.QuickCode.va_mod_xmm dst\n ]\n va_sM\n va_s0;\n [@@ FStar.Pervasives.inline_let ]let va_g = () in\n va_sM, va_f0, va_g)\n <:\n (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit", "effect": "Prims.Ghost", "effect_flags": [], "mutual_with": [], "premises": [ "Vale.X64.Decls.va_operand_xmm", "Prims.bool", "Vale.X64.Decls.va_state", "Prims.unit", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.X64.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.X64.QuickCode.mod_t", "Vale.X64.QuickCode.va_Mod_flags", "Vale.X64.QuickCode.va_mod_xmm", "Prims.Nil", "Prims._assert", "Vale.X64.Decls.va_state_eq", "Vale.X64.Decls.va_update_flags", "Vale.X64.Decls.va_update_ok", "Vale.X64.Decls.va_update_operand_xmm", "Vale.X64.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.X64.State.vale_state", "Vale.AES.X64.PolyOps.va_lemma_VPolyMul", "Vale.AES.X64.PolyOps.va_code_VPolyMul" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "\n dst: Vale.X64.Decls.va_operand_xmm ->\n src1: Vale.X64.Decls.va_operand_xmm ->\n src2: Vale.X64.Decls.va_operand_xmm ->\n src1Hi: Prims.bool ->\n src2Hi: Prims.bool ->\n va_s0: Vale.X64.Decls.va_state ->\n va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0)\n -> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit)", "prompt": "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n ", "expected_response": "let va_sM, va_f0 =\n va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst src1 src2 src1Hi src2Hi\nin\nva_lemma_upd_update va_sM;\nassert (va_state_eq va_sM\n (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0))));\nva_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\nlet va_g = () in\n(va_sM, va_f0, va_g)", "source": { "project_name": "hacl-star", "file_name": "obj/Vale.AES.X64.PolyOps.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Vale.AES.X64.PolyOps.fst", "checked_file": "dataset/Vale.AES.X64.PolyOps.fst.checked", "interface_file": true, "dependencies": [ "dataset/Vale.X64.State.fsti.checked", "dataset/Vale.X64.QuickCodes.fsti.checked", "dataset/Vale.X64.QuickCode.fst.checked", "dataset/Vale.X64.Machine_s.fst.checked", "dataset/Vale.X64.InsVector.fsti.checked", "dataset/Vale.X64.InsMem.fsti.checked", "dataset/Vale.X64.InsBasic.fsti.checked", "dataset/Vale.X64.InsAes.fsti.checked", "dataset/Vale.X64.Decls.fsti.checked", "dataset/Vale.X64.CPU_Features_s.fst.checked", "dataset/Vale.Math.Poly2_s.fsti.checked", "dataset/Vale.Math.Poly2.Words.fsti.checked", "dataset/Vale.Math.Poly2.Lemmas.fsti.checked", "dataset/Vale.Math.Poly2.Bits_s.fsti.checked", "dataset/Vale.Math.Poly2.Bits.fsti.checked", "dataset/Vale.Math.Poly2.fsti.checked", "dataset/Vale.Def.Types_s.fst.checked", "dataset/Vale.Arch.Types.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "val va_code_VPolyAdd : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_opr128 -> Tot\n va_code", "let va_code_VPolyAdd dst src1 src2 =\n (va_Block (va_CCons (va_code_VPxor dst src1 src2) (va_CNil ())))", "val va_codegen_success_VPolyAdd : dst:va_operand_xmm -> src1:va_operand_xmm ->\n src2:va_operand_opr128 -> Tot va_pbool", "let va_codegen_success_VPolyAdd dst src1 src2 =\n (va_pbool_and (va_codegen_success_VPxor dst src1 src2) (va_ttrue ()))", "val va_lemma_VPolyAdd : va_b0:va_code -> va_s0:va_state -> dst:va_operand_xmm ->\n src1:va_operand_xmm -> src2:va_operand_opr128\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_VPolyAdd dst src1 src2) va_s0 /\\ va_is_dst_xmm dst\n va_s0 /\\ va_is_src_xmm src1 va_s0 /\\ va_is_src_opr128 src2 va_s0 /\\ va_get_ok va_s0 /\\ (let\n (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src1) in let\n (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_opr128 va_s0 src2) in\n avx_enabled)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_opr128 va_s0 src2)\n in Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2_s.add a1 a2) /\\\n va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM\n va_s0)))))", "let va_lemma_VPolyAdd va_b0 va_s0 dst src1 src2 =\n va_reveal_opaque (`%va_code_VPolyAdd) (va_code_VPolyAdd dst src1 src2);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_opr128 va_s0 src2) in\n Vale.Math.Poly2.Words.lemma_add_quad32 (va_eval_xmm va_s0 src1) (va_eval_opr128 va_s0 src2);\n let (va_s5, va_fc5) = va_lemma_VPxor (va_hd va_b1) va_s0 dst src1 src2 in\n let va_b5 = va_tl va_b1 in\n let (va_sM, va_f5) = va_lemma_empty_total va_s5 va_b5 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc5 va_s5 va_f5 va_sM in\n (va_sM, va_fM)", "let va_wp_VPolyAdd (dst:va_operand_xmm) (src1:va_operand_xmm) (src2:va_operand_opr128)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src1 va_s0 /\\ va_is_src_opr128 src2 va_s0 /\\ va_get_ok\n va_s0 /\\ (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0\n src1) in let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_opr128\n va_s0 src2) in avx_enabled) /\\ (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) .\n let va_sM = va_upd_flags va_x_efl (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\\n (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_opr128 va_s0 src2)\n in Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2_s.add a1 a2) ==>\n va_k va_sM (())))", "let va_wpProof_VPolyAdd dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyAdd (va_code_VPolyAdd dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VPolyAdd : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_opr128 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPolyAdd dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPolyAdd dst src1 src2)\n ([va_Mod_flags; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))", "let va_code_PolyAnd dst src =\n (va_Block (va_CCons (va_code_Pand dst (va_coerce_xmm_to_opr128 src)) (va_CNil ())))", "let va_quick_VPolyAdd (dst:va_operand_xmm) (src1:va_operand_xmm) (src2:va_operand_opr128) :\n (va_quickCode unit (va_code_VPolyAdd dst src1 src2)) =\n (va_QProc (va_code_VPolyAdd dst src1 src2) ([va_Mod_flags; va_mod_xmm dst]) (va_wp_VPolyAdd dst\n src1 src2) (va_wpProof_VPolyAdd dst src1 src2))", "let va_codegen_success_PolyAnd dst src =\n (va_pbool_and (va_codegen_success_Pand dst (va_coerce_xmm_to_opr128 src)) (va_ttrue ()))", "let va_lemma_PolyAnd va_b0 va_s0 dst src =\n va_reveal_opaque (`%va_code_PolyAnd) (va_code_PolyAnd dst src);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 dst) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Words.lemma_and_quad32 (va_eval_xmm va_s0 dst) (va_eval_xmm va_s0 src);\n let (va_s5, va_fc5) = va_lemma_Pand (va_hd va_b1) va_s0 dst (va_coerce_xmm_to_opr128 src) in\n let va_b5 = va_tl va_b1 in\n let (va_sM, va_f5) = va_lemma_empty_total va_s5 va_b5 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc5 va_s5 va_f5 va_sM in\n (va_sM, va_fM)", "val va_code_PolyAnd : dst:va_operand_xmm -> src:va_operand_xmm -> Tot va_code", "val va_codegen_success_PolyAnd : dst:va_operand_xmm -> src:va_operand_xmm -> Tot va_pbool", "val va_lemma_PolyAnd : va_b0:va_code -> va_s0:va_state -> dst:va_operand_xmm -> src:va_operand_xmm\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_PolyAnd dst src) va_s0 /\\ va_is_dst_xmm dst va_s0 /\\\n va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ (let (a1:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 dst) in let (a2:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in sse_enabled)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 dst) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2.poly_and a1 a2) /\\\n va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM\n va_s0)))))", "let va_wpProof_PolyAnd dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_PolyAnd (va_code_PolyAnd dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wp_PolyAnd (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ (let\n (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 dst) in let\n (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n sse_enabled) /\\ (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM =\n va_upd_flags va_x_efl (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\ (let\n (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 dst) in let\n (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2.poly_and a1 a2) ==>\n va_k va_sM (())))", "let va_code_VHigh64ToLow dst src =\n (va_Block (va_CCons (va_code_Vpsrldq8 dst src) (va_CNil ())))", "val va_wpProof_PolyAnd : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_PolyAnd dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_PolyAnd dst src) ([va_Mod_flags;\n va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))", "let va_codegen_success_VHigh64ToLow dst src =\n (va_pbool_and (va_codegen_success_Vpsrldq8 dst src) (va_ttrue ()))", "let va_lemma_VHigh64ToLow va_b0 va_s0 dst src =\n va_reveal_opaque (`%va_code_VHigh64ToLow) (va_code_VHigh64ToLow dst src);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n let (va_s3, va_fc3) = va_lemma_Vpsrldq8 (va_hd va_b1) va_s0 dst src in\n let va_b3 = va_tl va_b1 in\n Vale.Math.Poly2.Words.lemma_quad32_double_shift a;\n Vale.Math.Poly2.Lemmas.lemma_shift_is_div a 64;\n Vale.Math.Poly2.Bits.lemma_of_to_quad32 (Vale.Math.Poly2_s.shift a (-64));\n let (va_sM, va_f3) = va_lemma_empty_total va_s3 va_b3 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc3 va_s3 va_f3 va_sM in\n (va_sM, va_fM)", "let va_quick_PolyAnd (dst:va_operand_xmm) (src:va_operand_xmm) : (va_quickCode unit\n (va_code_PolyAnd dst src)) =\n (va_QProc (va_code_PolyAnd dst src) ([va_Mod_flags; va_mod_xmm dst]) (va_wp_PolyAnd dst src)\n (va_wpProof_PolyAnd dst src))", "val va_code_VHigh64ToLow : dst:va_operand_xmm -> src:va_operand_xmm -> Tot va_code", "val va_codegen_success_VHigh64ToLow : dst:va_operand_xmm -> src:va_operand_xmm -> Tot va_pbool", "val va_lemma_VHigh64ToLow : va_b0:va_code -> va_s0:va_state -> dst:va_operand_xmm ->\n src:va_operand_xmm\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_VHigh64ToLow dst src) va_s0 /\\ va_is_dst_xmm dst va_s0\n /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ (let (a:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in avx_enabled)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2_s.shift a (-64)) /\\\n va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM\n va_s0)))))", "let va_wpProof_VHigh64ToLow dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VHigh64ToLow (va_code_VHigh64ToLow dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wp_VHigh64ToLow (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ (let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n avx_enabled) /\\ (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM =\n va_upd_flags va_x_efl (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\ (let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2_s.shift a (-64))\n ==> va_k va_sM (())))", "let va_code_VLow64ToHigh dst src =\n (va_Block (va_CCons (va_code_Vpslldq8 dst src) (va_CNil ())))", "let va_codegen_success_VLow64ToHigh dst src =\n (va_pbool_and (va_codegen_success_Vpslldq8 dst src) (va_ttrue ()))", "val va_wpProof_VHigh64ToLow : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VHigh64ToLow dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VHigh64ToLow dst src) ([va_Mod_flags;\n va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))", "let va_lemma_VLow64ToHigh va_b0 va_s0 dst src =\n va_reveal_opaque (`%va_code_VLow64ToHigh) (va_code_VLow64ToHigh dst src);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n let (va_s3, va_fc3) = va_lemma_Vpslldq8 (va_hd va_b1) va_s0 dst src in\n let va_b3 = va_tl va_b1 in\n Vale.Math.Poly2.Words.lemma_quad32_double_shift a;\n Vale.Math.Poly2.Lemmas.lemma_mask_is_mod a 64;\n Vale.Math.Poly2.lemma_shift_is_mul (Vale.Math.Poly2.mask a 64) 64;\n Vale.Math.Poly2.Bits.lemma_of_to_quad32 (Vale.Math.Poly2_s.shift (Vale.Math.Poly2.mask a 64) 64);\n let (va_sM, va_f3) = va_lemma_empty_total va_s3 va_b3 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc3 va_s3 va_f3 va_sM in\n (va_sM, va_fM)", "let va_quick_VHigh64ToLow (dst:va_operand_xmm) (src:va_operand_xmm) : (va_quickCode unit\n (va_code_VHigh64ToLow dst src)) =\n (va_QProc (va_code_VHigh64ToLow dst src) ([va_Mod_flags; va_mod_xmm dst]) (va_wp_VHigh64ToLow dst\n src) (va_wpProof_VHigh64ToLow dst src))", "val va_code_VLow64ToHigh : dst:va_operand_xmm -> src:va_operand_xmm -> Tot va_code", "val va_codegen_success_VLow64ToHigh : dst:va_operand_xmm -> src:va_operand_xmm -> Tot va_pbool", "val va_lemma_VLow64ToHigh : va_b0:va_code -> va_s0:va_state -> dst:va_operand_xmm ->\n src:va_operand_xmm\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_VLow64ToHigh dst src) va_s0 /\\ va_is_dst_xmm dst va_s0\n /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ (let (a:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in avx_enabled)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2_s.shift\n (Vale.Math.Poly2.mask a 64) 64) /\\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM\n (va_update_operand_xmm dst va_sM va_s0)))))", "let va_wpProof_VLow64ToHigh dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VLow64ToHigh (va_code_VLow64ToHigh dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wp_VLow64ToHigh (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ (let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n avx_enabled) /\\ (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM =\n va_upd_flags va_x_efl (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\ (let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2_s.shift\n (Vale.Math.Poly2.mask a 64) 64) ==> va_k va_sM (())))", "let va_code_VSwap dst src =\n (va_Block (va_CCons (va_code_VPalignr8 dst src src) (va_CNil ())))", "let va_codegen_success_VSwap dst src =\n (va_pbool_and (va_codegen_success_VPalignr8 dst src src) (va_ttrue ()))", "val va_wpProof_VLow64ToHigh : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VLow64ToHigh dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VLow64ToHigh dst src) ([va_Mod_flags;\n va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))", "let va_lemma_VSwap va_b0 va_s0 dst src =\n va_reveal_opaque (`%va_code_VSwap) (va_code_VSwap dst src);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n let (va_s3, va_fc3) = va_lemma_VPalignr8 (va_hd va_b1) va_s0 dst src src in\n let va_b3 = va_tl va_b1 in\n Vale.Math.Poly2.Words.lemma_quad32_double_swap a;\n Vale.Math.Poly2.Bits.lemma_of_to_quad32 (Vale.Math.Poly2.swap a 64);\n let (va_sM, va_f3) = va_lemma_empty_total va_s3 va_b3 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc3 va_s3 va_f3 va_sM in\n (va_sM, va_fM)", "let va_quick_VLow64ToHigh (dst:va_operand_xmm) (src:va_operand_xmm) : (va_quickCode unit\n (va_code_VLow64ToHigh dst src)) =\n (va_QProc (va_code_VLow64ToHigh dst src) ([va_Mod_flags; va_mod_xmm dst]) (va_wp_VLow64ToHigh dst\n src) (va_wpProof_VLow64ToHigh dst src))", "val va_code_VSwap : dst:va_operand_xmm -> src:va_operand_xmm -> Tot va_code", "let va_wpProof_VSwap dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VSwap (va_code_VSwap dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_codegen_success_VSwap : dst:va_operand_xmm -> src:va_operand_xmm -> Tot va_pbool", "val va_lemma_VSwap : va_b0:va_code -> va_s0:va_state -> dst:va_operand_xmm -> src:va_operand_xmm\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_VSwap dst src) va_s0 /\\ va_is_dst_xmm dst va_s0 /\\\n va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ (let (a:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in avx_enabled)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2.swap a 64) /\\\n va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM\n va_s0)))))", "let va_code_VPolyMul dst src1 src2 src1Hi src2Hi =\n (va_Block (va_CCons (va_code_VPclmulqdq dst src1 src2 src1Hi src2Hi) (va_CNil ())))", "let va_wp_VSwap (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state -> unit\n -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ (let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n avx_enabled) /\\ (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM =\n va_upd_flags va_x_efl (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\ (let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2.swap a 64) ==> va_k\n va_sM (())))", "let va_codegen_success_VPolyMul dst src1 src2 src1Hi src2Hi =\n (va_pbool_and (va_codegen_success_VPclmulqdq dst src1 src2 src1Hi src2Hi) (va_ttrue ()))", "let va_lemma_VPolyMul va_b0 va_s0 dst src1 src2 src1Hi src2Hi =\n va_reveal_opaque (`%va_code_VPolyMul) (va_code_VPolyMul dst src1 src2 src1Hi src2Hi);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src2) in\n let (va_s4, va_fc4) = va_lemma_VPclmulqdq (va_hd va_b1) va_s0 dst src1 src2 src1Hi src2Hi in\n let va_b4 = va_tl va_b1 in\n Vale.Math.Poly2.Bits.lemma_quad32_double a1;\n Vale.Math.Poly2.Bits.lemma_quad32_double a2;\n Vale.Math.Poly2.Lemmas.lemma_shift_is_div a1 64;\n Vale.Math.Poly2.Lemmas.lemma_shift_is_div a2 64;\n Vale.Math.Poly2.Lemmas.lemma_mask_is_mod a1 64;\n Vale.Math.Poly2.Lemmas.lemma_mask_is_mod a2 64;\n Vale.Math.Poly2.Bits.lemma_of_to_quad32 (Vale.Math.Poly2_s.mul (if src1Hi then\n Vale.Math.Poly2_s.shift a1 (-64) else Vale.Math.Poly2.mask a1 64) (if src2Hi then\n Vale.Math.Poly2_s.shift a2 (-64) else Vale.Math.Poly2.mask a2 64));\n let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc4 va_s4 va_f4 va_sM in\n (va_sM, va_fM)", "val va_wpProof_VSwap : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state -> va_k:(va_state\n -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VSwap dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VSwap dst src) ([va_Mod_flags;\n va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))", "let va_quick_VSwap (dst:va_operand_xmm) (src:va_operand_xmm) : (va_quickCode unit (va_code_VSwap\n dst src)) =\n (va_QProc (va_code_VSwap dst src) ([va_Mod_flags; va_mod_xmm dst]) (va_wp_VSwap dst src)\n (va_wpProof_VSwap dst src))", "val va_code_VPolyMul : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_xmm ->\n src1Hi:bool -> src2Hi:bool -> Tot va_code", "val va_codegen_success_VPolyMul : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_xmm\n -> src1Hi:bool -> src2Hi:bool -> Tot va_pbool" ], "closest": [ "val va_wpProof_VPolyMul : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPolyMul dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPolyMul dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VPolyMul dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VPolyMulLow : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPolyMulLow dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPolyMulLow dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VPolyMulLow dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMulLow (va_code_VPolyMulLow dst src1 src2) va_s0 dst src1 src2\n in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VPolyMulHigh : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPolyMulHigh dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPolyMulHigh dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VPolyMulHigh dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMulHigh (va_code_VPolyMulHigh dst src1 src2) va_s0 dst src1\n src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VPclmulqdq : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_xmm ->\n src1Hi:bool -> src2Hi:bool -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPclmulqdq dst src1 src2 src1Hi src2Hi va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPclmulqdq dst src1 src2 src1Hi\n src2Hi) ([va_Mod_flags; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VPclmulqdq dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPclmulqdq (va_code_VPclmulqdq dst src1 src2 src1Hi src2Hi) va_s0\n dst src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VPolyAnd : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPolyAnd dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPolyAnd dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VPolyAnd dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyAnd (va_code_VPolyAnd dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VPolyAdd : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPolyAdd dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPolyAdd dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VPolyAdd dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyAdd (va_code_VPolyAdd dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_AddPoly : dst:va_operand_xmm -> src:va_operand_xmm -> a:poly -> b:poly ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_AddPoly dst src a b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_AddPoly dst src) ([va_Mod_flags;\n va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_AddPoly dst src a b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_AddPoly (va_code_AddPoly dst src) va_s0 dst src a b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Mulx64 : dst_hi:va_operand_dst_opr64 -> dst_lo:va_operand_dst_opr64 ->\n src:va_operand_opr64 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Mulx64 dst_hi dst_lo src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Mulx64 dst_hi dst_lo src)\n ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM\n (va_update_operand_dst_opr64 dst_hi va_sM va_s0))));\n va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Pclmulqdq : dst:va_operand_xmm -> src:va_operand_xmm -> dstHi:bool -> srcHi:bool ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Pclmulqdq dst src dstHi srcHi va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Pclmulqdq dst src dstHi srcHi)\n ([va_Mod_flags; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Pclmulqdq dst src dstHi srcHi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Pclmulqdq (va_code_Pclmulqdq dst src dstHi srcHi) va_s0 dst src\n dstHi srcHi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_lemma_VPolyMul : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr ->\n src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_VPolyMul dst src1 src2) va_s0 /\\ va_is_dst_vec_opr dst\n va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\ va_get_ok va_s0))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0\n src1) in let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr\n va_s0 src2) in Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_sM dst) ==\n Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.mul (Vale.Math.Poly2.mask a1 64) (Vale.Math.Poly2.mask\n a2 64)) (Vale.Math.Poly2_s.mul (Vale.Math.Poly2_s.shift a1 (-64)) (Vale.Math.Poly2_s.shift a2\n (-64)))) /\\ va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0))))\nlet va_lemma_VPolyMul va_b0 va_s0 dst src1 src2 =\n va_reveal_opaque (`%va_code_VPolyMul) (va_code_VPolyMul dst src1 src2);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2) in\n let (va_s4, va_fc4) = va_lemma_Vpmsumd (va_hd va_b1) va_s0 dst src1 src2 in\n let va_b4 = va_tl va_b1 in\n Vale.Math.Poly2.Bits.lemma_quad32_double a1;\n Vale.Math.Poly2.Bits.lemma_quad32_double a2;\n Vale.Math.Poly2.Lemmas.lemma_shift_is_div a1 64;\n Vale.Math.Poly2.Lemmas.lemma_shift_is_div a2 64;\n Vale.Math.Poly2.Lemmas.lemma_mask_is_mod a1 64;\n Vale.Math.Poly2.Lemmas.lemma_mask_is_mod a2 64;\n Vale.Math.Poly2.Bits.lemma_of_to_quad32 (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.mul\n (Vale.Math.Poly2.mask a1 64) (Vale.Math.Poly2.mask a2 64)) (Vale.Math.Poly2_s.mul\n (Vale.Math.Poly2_s.shift a1 (-64)) (Vale.Math.Poly2_s.shift a2 (-64))));\n let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc4 va_s4 va_f4 va_sM in\n (va_sM, va_fM)", "val va_wpProof_AddPoly : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> a:poly -> b:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_AddPoly dst src1 src2 a b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_AddPoly dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_AddPoly dst src1 src2 a b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_AddPoly (va_code_AddPoly dst src1 src2) va_s0 dst src1 src2 a b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wp_VPolyMul\n (dst src1 src2: va_operand_xmm)\n (src1Hi src2Hi: bool)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VPolyMul (dst:va_operand_xmm) (src1:va_operand_xmm) (src2:va_operand_xmm) (src1Hi:bool)\n (src2Hi:bool) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src1 va_s0 /\\ va_is_src_xmm src2 va_s0 /\\ va_get_ok\n va_s0 /\\ (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0\n src1) in let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0\n src2) in pclmulqdq_enabled /\\ avx_enabled) /\\ (forall (va_x_dst:va_value_xmm)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_operand_xmm dst\n va_x_dst va_s0) in va_get_ok va_sM /\\ (let (a1:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src1) in let (a2:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src2) in Vale.Math.Poly2.Bits_s.of_quad32\n (va_eval_xmm va_sM dst) == Vale.Math.Poly2_s.mul (va_if src1Hi (fun _ ->\n Vale.Math.Poly2_s.shift a1 (-64)) (fun _ -> Vale.Math.Poly2.mask a1 64)) (va_if src2Hi (fun _\n -> Vale.Math.Poly2_s.shift a2 (-64)) (fun _ -> Vale.Math.Poly2.mask a2 64))) ==> va_k va_sM\n (())))", "val va_wpProof_ClmulRev64 : a:poly -> b:poly -> dstHi:bool -> srcHi:bool -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_ClmulRev64 a b dstHi srcHi va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ClmulRev64 dstHi srcHi) ([va_Mod_xmm\n 2; va_Mod_xmm 1; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_ClmulRev64 a b dstHi srcHi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_ClmulRev64 (va_code_ClmulRev64 dstHi srcHi) va_s0 a b dstHi srcHi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_flags va_sM\n (va_update_ok va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_MulHigh64U : dst:va_operand_reg_opr -> src1:va_operand_reg_opr ->\n src2:va_operand_reg_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_MulHigh64U dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_MulHigh64U dst src1 src2)\n ([va_mod_reg_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_MulHigh64U dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_MulHigh64U (va_code_MulHigh64U dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_MulLow64 : dst:va_operand_reg_opr -> src1:va_operand_reg_opr ->\n src2:va_operand_reg_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_MulLow64 dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_MulLow64 dst src1 src2)\n ([va_mod_reg_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_MulLow64 dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_MulLow64 (va_code_MulLow64 dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_IMul64 : dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_IMul64 dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_IMul64 dst src) ([va_Mod_flags;\n va_mod_dst_opr64 dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_IMul64 dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64\n dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VPxor : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_opr128 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPxor dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPxor dst src1 src2) ([va_mod_xmm\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VPxor dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPxor (va_code_VPxor dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vpmsumd : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vpmsumd dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vpmsumd dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vpmsumd dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vpmsumd (va_code_Vpmsumd dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_lemma_VPolyMulHigh : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr ->\n src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_VPolyMulHigh dst src1 src2) va_s0 /\\ va_is_dst_vec_opr\n dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\ va_get_ok va_s0 /\\\n (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0\n src1) in let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr\n va_s0 src2) in l_or (Vale.Math.Poly2.mask a1 64 == zero) (Vale.Math.Poly2.mask a2 64 == zero))))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0\n src1) in let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr\n va_s0 src2) in Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_sM dst) ==\n Vale.Math.Poly2_s.mul (Vale.Math.Poly2_s.shift a1 (-64)) (Vale.Math.Poly2_s.shift a2 (-64))) /\\\n va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0))))\nlet va_lemma_VPolyMulHigh va_b0 va_s0 dst src1 src2 =\n va_reveal_opaque (`%va_code_VPolyMulHigh) (va_code_VPolyMulHigh dst src1 src2);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2) in\n let (va_s4, va_fc4) = va_lemma_VPolyMul (va_hd va_b1) va_s0 dst src1 src2 in\n let va_b4 = va_tl va_b1 in\n Vale.AES.GHash_BE.lemma_add_mul_zero_high (Vale.Math.Poly2.mask a1 64) (Vale.Math.Poly2_s.shift\n a1 (-64)) (Vale.Math.Poly2.mask a2 64) (Vale.Math.Poly2_s.shift a2 (-64));\n let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc4 va_s4 va_f4 va_sM in\n (va_sM, va_fM)", "val va_wpProof_MulLow64Wrap : dst:va_operand_reg_opr -> src1:va_operand_reg_opr ->\n src2:va_operand_reg_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_MulLow64Wrap dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_MulLow64Wrap dst src1 src2)\n ([va_mod_reg_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_MulLow64Wrap dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_MulLow64Wrap (va_code_MulLow64Wrap dst src1 src2) va_s0 dst src1\n src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_lemma_VPclmulqdq : va_b0:va_code -> va_s0:va_state -> dst:va_operand_xmm ->\n src1:va_operand_xmm -> src2:va_operand_xmm -> src1Hi:bool -> src2Hi:bool\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_VPclmulqdq dst src1 src2 src1Hi src2Hi) va_s0 /\\\n va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src1 va_s0 /\\ va_is_src_xmm src2 va_s0 /\\ va_get_ok\n va_s0 /\\ (pclmulqdq_enabled /\\ avx_enabled)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_eval_xmm va_sM dst == Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.mul\n (Vale.Math.Poly2.Bits_s.of_double32 (if src1Hi then Vale.Arch.Types.quad32_double_hi\n (va_eval_xmm va_s0 src1) else Vale.Arch.Types.quad32_double_lo (va_eval_xmm va_s0 src1)))\n (Vale.Math.Poly2.Bits_s.of_double32 (if src2Hi then Vale.Arch.Types.quad32_double_hi\n (va_eval_xmm va_s0 src2) else Vale.Arch.Types.quad32_double_lo (va_eval_xmm va_s0 src2)))) /\\\n va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM\n va_s0)))))\nlet va_lemma_VPclmulqdq va_b0 va_s0 dst src1 src2 src1Hi src2Hi =\n va_reveal_opaque (`%va_code_VPclmulqdq) (va_code_VPclmulqdq dst src1 src2 src1Hi src2Hi);\n let (va_old_s:va_state) = va_s0 in\n va_ins_lemma (mk_ins (make_instr (I.ins_VPclmulqdq ((if src1Hi then 1 else 0) + (if src2Hi then\n 16 else 0))) (OReg dst) (OReg src1) (OReg src2))) va_s0;\n let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_VPclmulqdq ((if src1Hi then 1 else 0)\n + (if src2Hi then 16 else 0))) (OReg dst) (OReg src1) (OReg src2))) va_s0 in\n (va_sM, va_fM)", "val va_lemma_VPolyMulLow : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr ->\n src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_VPolyMulLow dst src1 src2) va_s0 /\\ va_is_dst_vec_opr\n dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\ va_get_ok va_s0 /\\\n (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0\n src1) in let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr\n va_s0 src2) in l_or (Vale.Math.Poly2_s.shift a1 (-64) == zero) (Vale.Math.Poly2_s.shift a2\n (-64) == zero))))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0\n src1) in let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr\n va_s0 src2) in Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_sM dst) ==\n Vale.Math.Poly2_s.mul (Vale.Math.Poly2.mask a1 64) (Vale.Math.Poly2.mask a2 64)) /\\ va_state_eq\n va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0))))\nlet va_lemma_VPolyMulLow va_b0 va_s0 dst src1 src2 =\n va_reveal_opaque (`%va_code_VPolyMulLow) (va_code_VPolyMulLow dst src1 src2);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2) in\n let (va_s4, va_fc4) = va_lemma_VPolyMul (va_hd va_b1) va_s0 dst src1 src2 in\n let va_b4 = va_tl va_b1 in\n Vale.AES.GHash_BE.lemma_add_mul_zero_low (Vale.Math.Poly2.mask a1 64) (Vale.Math.Poly2_s.shift a1\n (-64)) (Vale.Math.Poly2.mask a2 64) (Vale.Math.Poly2_s.shift a2 (-64));\n let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc4 va_s4 va_f4 va_sM in\n (va_sM, va_fM)", "val va_wpProof_VPaddd : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_xmm ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPaddd dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPaddd dst src1 src2) ([va_Mod_flags;\n va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VPaddd dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPaddd (va_code_VPaddd dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vadduwm : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vadduwm dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vadduwm dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vadduwm dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vadduwm (va_code_Vadduwm dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_High64ToLow : dst:va_operand_xmm -> a:poly -> va_s0:va_state -> va_k:(va_state ->\n unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_High64ToLow dst a va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_High64ToLow dst) ([va_Mod_reg64 rR12;\n va_Mod_flags; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_High64ToLow dst a va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_High64ToLow (va_code_High64ToLow dst) va_s0 dst a in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_reg64 rR12 va_sM (va_update_flags va_sM (va_update_ok va_sM\n (va_update_operand_xmm dst va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_reg64 rR12; va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Xxmrghd : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Xxmrghd dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Xxmrghd dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Xxmrghd dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Xxmrghd (va_code_Xxmrghd dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vmrghw : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vmrghw dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vmrghw dst src1 src2) ([va_mod_vec_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vmrghw dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vmrghw (va_code_Vmrghw dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VPslldq4 : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPslldq4 dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPslldq4 dst src) ([va_mod_xmm dst])\n va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VPslldq4 dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPslldq4 (va_code_VPslldq4 dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vsl : dst:va_operand_vec_opr -> src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vsl dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vsl dst src1 src2) ([va_mod_vec_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vsl dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vsl (va_code_Vsl dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vslw : dst:va_operand_vec_opr -> src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vslw dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vslw dst src1 src2) ([va_mod_vec_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vslw dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vslw (va_code_Vslw dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vmr : dst:va_operand_vec_opr -> src:va_operand_vec_opr -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vmr dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vmr dst src) ([va_mod_vec_opr dst])\n va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vmr dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vmr (va_code_Vmr dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Mul64Wrap : src:va_operand_opr64 -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Mul64Wrap src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Mul64Wrap src) ([va_Mod_reg64 rRdx;\n va_Mod_reg64 rRax; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Mul64Wrap src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM\n (va_update_flags va_sM (va_update_ok va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vand : dst:va_operand_vec_opr -> src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vand dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vand dst src1 src2) ([va_mod_vec_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vand dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vand (va_code_Vand dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vpslldq8 : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vpslldq8 dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vpslldq8 dst src) ([va_mod_xmm dst])\n va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vpslldq8 dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vpslldq8 (va_code_Vpslldq8 dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VPshufb : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_xmm ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPshufb dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPshufb dst src1 src2) ([va_Mod_flags;\n va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VPshufb dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPshufb (va_code_VPshufb dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Low64ToHigh : dst:va_operand_xmm -> a:poly -> va_s0:va_state -> va_k:(va_state ->\n unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Low64ToHigh dst a va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Low64ToHigh dst) ([va_Mod_reg64 rR12;\n va_Mod_flags; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Low64ToHigh dst a va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Low64ToHigh (va_code_Low64ToHigh dst) va_s0 dst a in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_reg64 rR12 va_sM (va_update_flags va_sM (va_update_ok va_sM\n (va_update_operand_xmm dst va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_reg64 rR12; va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_High64ToLow : dst:va_operand_vec_opr -> src:va_operand_vec_opr -> a:poly ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_High64ToLow dst src a va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_High64ToLow dst src) ([va_mod_vec_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_High64ToLow dst src a va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_High64ToLow (va_code_High64ToLow dst src) va_s0 dst src a in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vxor : dst:va_operand_vec_opr -> src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vxor dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vxor dst src1 src2) ([va_mod_vec_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vxor dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vxor (va_code_Vxor dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Clmul128 : ab:poly -> cd:poly -> va_s0:va_state -> va_k:(va_state -> (poly & poly)\n -> Type0)\n -> Ghost (va_state & va_fuel & (poly & poly))\n (requires (va_t_require va_s0 /\\ va_wp_Clmul128 ab cd va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Clmul128 ()) ([va_Mod_xmm 5;\n va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_reg64 rR12; va_Mod_flags]) va_s0\n va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Clmul128 ab cd va_s0 va_k =\n let (va_sM, va_f0, lo, hi) = va_lemma_Clmul128 (va_code_Clmul128 ()) va_s0 ab cd in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_xmm 5 va_sM (va_update_xmm 4 va_sM (va_update_xmm 3 va_sM\n (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_reg64 rR12 va_sM (va_update_flags\n va_sM (va_update_ok va_sM va_s0)))))))));\n va_lemma_norm_mods ([va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1;\n va_Mod_reg64 rR12; va_Mod_flags]) va_sM va_s0;\n let va_g = (lo, hi) in\n (va_sM, va_f0, va_g)", "val va_wpProof_ReduceMul128_LE : a:poly -> b:poly -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_ReduceMul128_LE a b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ReduceMul128_LE ()) ([va_Mod_xmm 6;\n va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_reg64 rR12;\n va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_ReduceMul128_LE a b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_ReduceMul128_LE (va_code_ReduceMul128_LE ()) va_s0 a b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_xmm 6 va_sM (va_update_xmm 5 va_sM (va_update_xmm 4 va_sM\n (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_reg64 rR12\n va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))))))));\n va_lemma_norm_mods ([va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2;\n va_Mod_xmm 1; va_Mod_reg64 rR12; va_Mod_flags]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vpsrldq8 : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vpsrldq8 dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vpsrldq8 dst src) ([va_mod_xmm dst])\n va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vpsrldq8 dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vpsrldq8 (va_code_Vpsrldq8 dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_lemma_Vpmsumd : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr ->\n src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Vpmsumd dst src1 src2) va_s0 /\\ va_is_dst_vec_opr dst\n va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\ va_get_ok va_s0))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_eval_vec_opr va_sM dst == Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.add\n (Vale.Math.Poly2_s.mul (Vale.Math.Poly2.Bits_s.of_double32 (Vale.Arch.Types.quad32_double_lo\n (va_eval_vec_opr va_s0 src1))) (Vale.Math.Poly2.Bits_s.of_double32\n (Vale.Arch.Types.quad32_double_lo (va_eval_vec_opr va_s0 src2)))) (Vale.Math.Poly2_s.mul\n (Vale.Math.Poly2.Bits_s.of_double32 (Vale.Arch.Types.quad32_double_hi (va_eval_vec_opr va_s0\n src1))) (Vale.Math.Poly2.Bits_s.of_double32 (Vale.Arch.Types.quad32_double_hi (va_eval_vec_opr\n va_s0 src2))))) /\\ va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM\n va_s0))))\nlet va_lemma_Vpmsumd va_b0 va_s0 dst src1 src2 =\n va_reveal_opaque (`%va_code_Vpmsumd) (va_code_Vpmsumd dst src1 src2);\n let (va_old_s:va_state) = va_s0 in\n va_ins_lemma (Ins (S.Vpmsumd dst src1 src2)) va_s0;\n let (va_sM, va_fM) = va_eval_ins (Ins (S.Vpmsumd dst src1 src2)) va_s0 in\n (va_sM, va_fM)", "val va_quick_VPolyMul (dst src1 src2: va_operand_xmm) (src1Hi src2Hi: bool)\n : (va_quickCode unit (va_code_VPolyMul dst src1 src2 src1Hi src2Hi))\nlet va_quick_VPolyMul (dst:va_operand_xmm) (src1:va_operand_xmm) (src2:va_operand_xmm)\n (src1Hi:bool) (src2Hi:bool) : (va_quickCode unit (va_code_VPolyMul dst src1 src2 src1Hi src2Hi)) =\n (va_QProc (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) ([va_Mod_flags; va_mod_xmm dst])\n (va_wp_VPolyMul dst src1 src2 src1Hi src2Hi) (va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi))", "val va_wp_VPolyMul\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VPolyMul (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ (let (a1:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src1) in let\n (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_sM dst) == Vale.Math.Poly2_s.add\n (Vale.Math.Poly2_s.mul (Vale.Math.Poly2.mask a1 64) (Vale.Math.Poly2.mask a2 64))\n (Vale.Math.Poly2_s.mul (Vale.Math.Poly2_s.shift a1 (-64)) (Vale.Math.Poly2_s.shift a2 (-64))))\n ==> va_k va_sM (())))", "val va_lemma_Pclmulqdq : va_b0:va_code -> va_s0:va_state -> dst:va_operand_xmm ->\n src:va_operand_xmm -> dstHi:bool -> srcHi:bool\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Pclmulqdq dst src dstHi srcHi) va_s0 /\\ va_is_dst_xmm\n dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ pclmulqdq_enabled))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_eval_xmm va_sM dst == Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.mul\n (Vale.Math.Poly2.Bits_s.of_double32 (if dstHi then Vale.Arch.Types.quad32_double_hi\n (va_eval_xmm va_s0 dst) else Vale.Arch.Types.quad32_double_lo (va_eval_xmm va_s0 dst)))\n (Vale.Math.Poly2.Bits_s.of_double32 (if srcHi then Vale.Arch.Types.quad32_double_hi\n (va_eval_xmm va_s0 src) else Vale.Arch.Types.quad32_double_lo (va_eval_xmm va_s0 src)))) /\\\n va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM\n va_s0)))))\nlet va_lemma_Pclmulqdq va_b0 va_s0 dst src dstHi srcHi =\n va_reveal_opaque (`%va_code_Pclmulqdq) (va_code_Pclmulqdq dst src dstHi srcHi);\n let (va_old_s:va_state) = va_s0 in\n va_ins_lemma (mk_ins (make_instr (I.ins_Pclmulqdq ((if dstHi then 1 else 0) + (if srcHi then 16\n else 0))) (OReg dst) (OReg src))) va_s0;\n let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Pclmulqdq ((if dstHi then 1 else 0) +\n (if srcHi then 16 else 0))) (OReg dst) (OReg src))) va_s0 in\n (va_sM, va_fM)", "val va_wpProof_Xor : dst:va_operand_reg_opr -> src1:va_operand_reg_opr -> src2:va_operand_reg_opr\n -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Xor dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Xor dst src1 src2) ([va_mod_reg_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Xor dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Xor (va_code_Xor dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Xor64 : dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Xor64 dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Xor64 dst src) ([va_Mod_flags;\n va_mod_dst_opr64 dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Xor64 dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64\n dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_ReduceMulRev128 : a:poly -> b:poly -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_ReduceMulRev128 a b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ReduceMulRev128 ()) ([va_Mod_xmm 6;\n va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_reg64 rR12;\n va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_ReduceMulRev128 a b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_ReduceMulRev128 (va_code_ReduceMulRev128 ()) va_s0 a b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_xmm 6 va_sM (va_update_xmm 5 va_sM (va_update_xmm 4 va_sM\n (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_reg64 rR12\n va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))))))));\n va_lemma_norm_mods ([va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2;\n va_Mod_xmm 1; va_Mod_reg64 rR12; va_Mod_flags]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vcmpequw : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vcmpequw dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vcmpequw dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vcmpequw dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vcmpequw (va_code_Vcmpequw dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vsel : dst:va_operand_vec_opr -> src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> sel:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vsel dst src1 src2 sel va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vsel dst src1 src2 sel)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vsel dst src1 src2 sel va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vsel (va_code_Vsel dst src1 src2 sel) va_s0 dst src1 src2 sel in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Low64ToHigh : dst:va_operand_vec_opr -> src:va_operand_vec_opr -> a:poly ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Low64ToHigh dst src a va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Low64ToHigh dst src) ([va_mod_vec_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Low64ToHigh dst src a va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Low64ToHigh (va_code_Low64ToHigh dst src) va_s0 dst src a in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_ClmulRev64High : a:poly -> b:poly -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_ClmulRev64High a b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ClmulRev64High ()) ([va_Mod_vec 2;\n va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_ClmulRev64High a b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_ClmulRev64High (va_code_ClmulRev64High ()) va_s0 a b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM\n va_s0))));\n va_lemma_norm_mods ([va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vsrw : dst:va_operand_vec_opr -> src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vsrw dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vsrw dst src1 src2) ([va_mod_vec_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vsrw dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vsrw (va_code_Vsrw dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_lemma_VPolyAnd : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr ->\n src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_VPolyAnd dst src1 src2) va_s0 /\\ va_is_dst_vec_opr dst\n va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\ va_get_ok va_s0))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0\n src1) in let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr\n va_s0 src2) in Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_sM dst) ==\n Vale.Math.Poly2.poly_and a1 a2) /\\ va_state_eq va_sM (va_update_ok va_sM\n (va_update_operand_vec_opr dst va_sM va_s0))))\nlet va_lemma_VPolyAnd va_b0 va_s0 dst src1 src2 =\n va_reveal_opaque (`%va_code_VPolyAnd) (va_code_VPolyAnd dst src1 src2);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2) in\n Vale.Math.Poly2.Words.lemma_and_quad32 (va_eval_vec_opr va_s0 src1) (va_eval_vec_opr va_s0 src2);\n let (va_s5, va_fc5) = va_lemma_Vand (va_hd va_b1) va_s0 dst src1 src2 in\n let va_b5 = va_tl va_b1 in\n let (va_sM, va_f5) = va_lemma_empty_total va_s5 va_b5 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc5 va_s5 va_f5 va_sM in\n (va_sM, va_fM)", "val va_wpProof_Mov128 : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Mov128 dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Mov128 dst src) ([va_mod_xmm dst])\n va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Mov128 dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Mov128 (va_code_Mov128 dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_PshufbDup : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_PshufbDup dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_PshufbDup dst src) ([va_Mod_flags;\n va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_PshufbDup dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_PshufbDup (va_code_PshufbDup dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_And : dst:va_operand_reg_opr -> src1:va_operand_reg_opr -> src2:va_operand_reg_opr\n -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_And dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_And dst src1 src2) ([va_mod_reg_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_And dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_And (va_code_And dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Pshufb : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Pshufb dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Pshufb dst src) ([va_Mod_flags;\n va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Pshufb dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Pshufb (va_code_Pshufb dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Pcmpeqd : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Pcmpeqd dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Pcmpeqd dst src) ([va_mod_xmm dst])\n va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Pcmpeqd dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Pcmpeqd (va_code_Pcmpeqd dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Paddd : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state -> va_k:(va_state\n -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Paddd dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Paddd dst src) ([va_Mod_flags;\n va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Paddd dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Paddd (va_code_Paddd dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Fmul1 : dst_b:buffer64 -> inA_b:buffer64 -> inB:nat64 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Fmul1 dst_b inA_b inB va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Fmul1 ()) ([va_Mod_flags;\n va_Mod_mem_layout; va_Mod_mem_heaplet 0; va_Mod_reg64 rR13; va_Mod_reg64 rRbx; va_Mod_reg64\n rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64\n rRcx; va_Mod_reg64 rRax; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Fmul1 dst_b inA_b inB va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Fmul1 (va_code_Fmul1 ()) va_s0 dst_b inA_b inB in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_mem_layout va_sM\n (va_update_mem_heaplet 0 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rRbx va_sM\n (va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM\n (va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM\n (va_update_reg64 rRax va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_layout; va_Mod_mem_heaplet 0; va_Mod_reg64 rR13;\n va_Mod_reg64 rRbx; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;\n va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Pshufb64 : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Pshufb64 dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Pshufb64 dst src) ([va_Mod_flags;\n va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Pshufb64 dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Pshufb64 (va_code_Pshufb64 dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Fmul2 : tmp_b:buffer64 -> inA_b:buffer64 -> dst_b:buffer64 -> inB_b:buffer64 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Fmul2 tmp_b inA_b dst_b inB_b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Fmul2 ()) ([va_Mod_mem_layout;\n va_Mod_mem_heaplet 0; va_Mod_flags; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR11;\n va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;\n va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax; va_Mod_mem]) va_s0\n va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Fmul2 tmp_b inA_b dst_b inB_b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Fmul2 (va_code_Fmul2 ()) va_s0 tmp_b inA_b dst_b inB_b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_layout va_sM (va_update_mem_heaplet 0 va_sM\n (va_update_flags va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64\n rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM\n (va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM (va_update_reg64 rRdx va_sM\n (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM\n (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_layout; va_Mod_mem_heaplet 0; va_Mod_flags; va_Mod_reg64 rR14;\n va_Mod_reg64 rR13; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;\n va_Mod_reg64 rRsi; va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx;\n va_Mod_reg64 rRax; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Load_two_lsb : dst:va_operand_xmm -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Load_two_lsb dst va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Load_two_lsb dst) ([va_Mod_flags;\n va_Mod_reg64 rR11; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Load_two_lsb dst va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Load_two_lsb (va_code_Load_two_lsb dst) va_s0 dst in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rR11 va_sM (va_update_ok va_sM\n (va_update_operand_xmm dst va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rR11; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Fast_mul1 : dst_b:buffer64 -> inA_b:buffer64 -> va_s0:va_state -> va_k:(va_state ->\n unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Fast_mul1 dst_b inA_b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Fast_mul1 ()) ([va_Mod_flags;\n va_Mod_mem_heaplet 0; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rRbx; va_Mod_reg64\n rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRax; va_Mod_mem])\n va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Fast_mul1 dst_b inA_b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Fast_mul1 (va_code_Fast_mul1 ()) va_s0 dst_b inA_b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_mem_heaplet 0 va_sM (va_update_reg64\n rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR11 va_sM\n (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM\n (va_update_reg64 rRax va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_heaplet 0; va_Mod_reg64 rR14; va_Mod_reg64 rR13;\n va_Mod_reg64 rRbx; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;\n va_Mod_reg64 rRax; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_lemma_VPolyAdd : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr ->\n src1:va_operand_vec_opr -> src2:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_VPolyAdd dst src1 src2) va_s0 /\\ va_is_dst_vec_opr dst\n va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\ va_get_ok va_s0))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0\n src1) in let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr\n va_s0 src2) in Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_sM dst) ==\n Vale.Math.Poly2_s.add a1 a2) /\\ va_state_eq va_sM (va_update_ok va_sM\n (va_update_operand_vec_opr dst va_sM va_s0))))\nlet va_lemma_VPolyAdd va_b0 va_s0 dst src1 src2 =\n va_reveal_opaque (`%va_code_VPolyAdd) (va_code_VPolyAdd dst src1 src2);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2) in\n Vale.Math.Poly2.Words.lemma_add_quad32 (va_eval_vec_opr va_s0 src1) (va_eval_vec_opr va_s0 src2);\n let (va_s5, va_fc5) = va_lemma_Vxor (va_hd va_b1) va_s0 dst src1 src2 in\n let va_b5 = va_tl va_b1 in\n let (va_sM, va_f5) = va_lemma_empty_total va_s5 va_b5 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc5 va_s5 va_f5 va_sM in\n (va_sM, va_fM)", "val va_wpProof_Sl64 : dst:va_operand_reg_opr -> src1:va_operand_reg_opr -> src2:va_operand_reg_opr\n -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Sl64 dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Sl64 dst src1 src2) ([va_mod_reg_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Sl64 dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Sl64 (va_code_Sl64 dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Pxor : dst:va_operand_xmm -> src:va_operand_xmm -> va_s0:va_state -> va_k:(va_state\n -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Pxor dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Pxor dst src) ([va_mod_xmm dst]) va_s0\n va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Pxor dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Pxor (va_code_Pxor dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_SubImm : dst:va_operand_reg_opr -> src1:va_operand_reg_opr -> src2:nsimm16 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_SubImm dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_SubImm dst src1 src2) ([va_mod_reg_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_SubImm dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_SubImm (va_code_SubImm dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Sr64 : dst:va_operand_reg_opr -> src1:va_operand_reg_opr -> src2:va_operand_reg_opr\n -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Sr64 dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Sr64 dst src1 src2) ([va_mod_reg_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Sr64 dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Sr64 (va_code_Sr64 dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_ClmulRev128 : ab:poly -> cd:poly -> va_s0:va_state -> va_k:(va_state -> (poly &\n poly) -> Type0)\n -> Ghost (va_state & va_fuel & (poly & poly))\n (requires (va_t_require va_s0 /\\ va_wp_ClmulRev128 ab cd va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ClmulRev128 ()) ([va_Mod_xmm 5;\n va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_reg64 rR12; va_Mod_flags]) va_s0\n va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_ClmulRev128 ab cd va_s0 va_k =\n let (va_sM, va_f0, lo, hi) = va_lemma_ClmulRev128 (va_code_ClmulRev128 ()) va_s0 ab cd in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_xmm 5 va_sM (va_update_xmm 4 va_sM (va_update_xmm 3 va_sM\n (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_reg64 rR12 va_sM (va_update_flags\n va_sM (va_update_ok va_sM va_s0)))))))));\n va_lemma_norm_mods ([va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1;\n va_Mod_reg64 rR12; va_Mod_flags]) va_sM va_s0;\n let va_g = (lo, hi) in\n (va_sM, va_f0, va_g)", "val va_lemma_Mulx_64 : va_b0:va_code -> va_s0:va_state -> dst_hi:va_operand_dst_opr64 ->\n dst_lo:va_operand_dst_opr64 -> src:va_operand_opr64\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Mulx_64 dst_hi dst_lo src) va_s0 /\\\n va_is_dst_dst_opr64 dst_hi va_s0 /\\ va_is_dst_dst_opr64 dst_lo va_s0 /\\ va_is_src_opr64 src\n va_s0 /\\ va_get_ok va_s0 /\\ bmi2_enabled /\\ dst_hi =!= dst_lo))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_eval_dst_opr64 va_sM dst_hi == Vale.Bignum.Defs.mul_hi (va_get_reg64 rRdx va_s0)\n (va_eval_opr64 va_s0 src) /\\ va_eval_dst_opr64 va_sM dst_lo == Vale.Bignum.Defs.mul_lo\n (va_get_reg64 rRdx va_s0) (va_eval_opr64 va_s0 src) /\\ va_state_eq va_sM (va_update_ok va_sM\n (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))))\nlet va_lemma_Mulx_64 va_b0 va_s0 dst_hi dst_lo src =\n va_reveal_opaque (`%va_code_Mulx_64) (va_code_Mulx_64 dst_hi dst_lo src);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n Vale.Bignum.Defs.reveal_mul_hi_all ();\n Vale.Bignum.Defs.reveal_mul_lo_all ();\n let (va_s4, va_fc4) = va_lemma_Mulx64 (va_hd va_b1) va_s0 dst_hi dst_lo src in\n let va_b4 = va_tl va_b1 in\n let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc4 va_s4 va_f4 va_sM in\n (va_sM, va_fM)", "val va_wpProof_Vcipher : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vcipher dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vcipher dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vcipher dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vcipher (va_code_Vcipher dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_ReduceMulRev128 : a:poly -> b:poly -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_ReduceMulRev128 a b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ReduceMulRev128 ()) ([va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 10]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_ReduceMulRev128 a b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_ReduceMulRev128 (va_code_ReduceMulRev128 ()) va_s0 a b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM\n (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM\n (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))));\n va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2;\n va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_And64 : dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_And64 dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_And64 dst src) ([va_Mod_flags;\n va_mod_dst_opr64 dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_And64 dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64\n dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Load_0xc2_msb : dst:va_operand_xmm -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Load_0xc2_msb dst va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Load_0xc2_msb dst) ([va_Mod_flags;\n va_Mod_reg64 rR11; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Load_0xc2_msb dst va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Load_0xc2_msb (va_code_Load_0xc2_msb dst) va_s0 dst in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rR11 va_sM (va_update_ok va_sM\n (va_update_operand_xmm dst va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rR11; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_AddExtended : dst:va_operand_reg_opr -> src1:va_operand_reg_opr ->\n src2:va_operand_reg_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_AddExtended dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_AddExtended dst src1 src2)\n ([va_Mod_xer; va_mod_reg_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_AddExtended dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_AddExtended (va_code_AddExtended dst src1 src2) va_s0 dst src1 src2\n in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_xer va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_xer; va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Vcipherlast : dst:va_operand_vec_opr -> src1:va_operand_vec_opr ->\n src2:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Vcipherlast dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Vcipherlast dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Vcipherlast dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Vcipherlast (va_code_Vcipherlast dst src1 src2) va_s0 dst src1 src2\n in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Clmul128 : ab:poly -> cd:poly -> va_s0:va_state -> va_k:(va_state -> (poly & poly)\n -> Type0)\n -> Ghost (va_state & va_fuel & (poly & poly))\n (requires (va_t_require va_s0 /\\ va_wp_Clmul128 ab cd va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Clmul128 ()) ([va_Mod_vec 5;\n va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0]) va_s0 va_k ((va_sM,\n va_f0, va_g))))\nlet va_wpProof_Clmul128 ab cd va_s0 va_k =\n let (va_sM, va_f0, lo, hi) = va_lemma_Clmul128 (va_code_Clmul128 ()) va_s0 ab cd in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM\n (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_ok va_sM\n va_s0))))))));\n va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1;\n va_Mod_vec 0]) va_sM va_s0;\n let va_g = (lo, hi) in\n (va_sM, va_f0, va_g)", "val va_wpProof_VAESNI_enc : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_xmm ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VAESNI_enc dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VAESNI_enc dst src1 src2)\n ([va_Mod_flags; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VAESNI_enc dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VAESNI_enc (va_code_VAESNI_enc dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Pslld : dst:va_operand_xmm -> amt:int -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Pslld dst amt va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Pslld dst amt) ([va_mod_xmm dst])\n va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Pslld dst amt va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Pslld (va_code_Pslld dst amt) va_s0 dst amt in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_AddImm : dst:va_operand_reg_opr -> src1:va_operand_reg_opr -> src2:simm16 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_AddImm dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_AddImm dst src1 src2) ([va_mod_reg_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_AddImm dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_AddImm (va_code_AddImm dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Mfvsrd : dst:va_operand_reg_opr -> src:va_operand_vec_opr -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Mfvsrd dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Mfvsrd dst src) ([va_mod_reg_opr dst])\n va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Mfvsrd dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Mfvsrd (va_code_Mfvsrd dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Mfvsrld : dst:va_operand_reg_opr -> src:va_operand_vec_opr -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Mfvsrld dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Mfvsrld dst src) ([va_mod_reg_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Mfvsrld dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Mfvsrld (va_code_Mfvsrld dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VPalignr8 : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_xmm ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VPalignr8 dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VPalignr8 dst src1 src2)\n ([va_Mod_flags; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VPalignr8 dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPalignr8 (va_code_VPalignr8 dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Psrldq : dst:va_operand_xmm -> amt:int -> va_s0:va_state -> va_k:(va_state -> unit\n -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Psrldq dst amt va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Psrldq dst amt) ([va_mod_xmm dst])\n va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Psrldq dst amt va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Psrldq (va_code_Psrldq dst amt) va_s0 dst amt in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VShufpd : dst:va_operand_xmm -> src1:va_operand_xmm -> src2:va_operand_xmm ->\n permutation:nat8 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VShufpd dst src1 src2 permutation va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VShufpd dst src1 src2 permutation)\n ([va_Mod_flags; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VShufpd dst src1 src2 permutation va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VShufpd (va_code_VShufpd dst src1 src2 permutation) va_s0 dst src1\n src2 permutation in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_lemma_ClmulRev64 : va_b0:va_code -> va_s0:va_state -> a:poly -> b:poly -> dstHi:bool ->\n srcHi:bool\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_ClmulRev64 dstHi srcHi) va_s0 /\\ va_get_ok va_s0 /\\\n (pclmulqdq_enabled /\\ avx_enabled /\\ sse_enabled) /\\ Vale.Math.Poly2_s.degree a <= 63 /\\\n Vale.Math.Poly2_s.degree b <= 63 /\\ Vale.Math.Poly2_s.reverse a 63 ==\n Vale.Math.Poly2.Bits_s.of_double32 (if dstHi then Vale.Arch.Types.quad32_double_hi (va_get_xmm\n 1 va_s0) else Vale.Arch.Types.quad32_double_lo (va_get_xmm 1 va_s0)) /\\\n Vale.Math.Poly2_s.reverse b 63 == Vale.Math.Poly2.Bits_s.of_double32 (if srcHi then\n Vale.Arch.Types.quad32_double_hi (va_get_xmm 2 va_s0) else Vale.Arch.Types.quad32_double_lo\n (va_get_xmm 2 va_s0))))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_get_xmm 1 va_sM == Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.reverse\n (Vale.Math.Poly2_s.mul a b) 127) /\\ va_state_eq va_sM (va_update_xmm 2 va_sM (va_update_xmm 1\n va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))))\nlet va_lemma_ClmulRev64 va_b0 va_s0 a b dstHi srcHi =\n let (va_mods:va_mods_t) = [va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags; va_Mod_ok] in\n let va_qc = va_qcode_ClmulRev64 va_mods a b dstHi srcHi in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ClmulRev64 dstHi srcHi) va_qc va_s0\n (fun va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 123 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_get_ok va_sM) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 136 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_get_xmm 1 va_sM == Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.reverse\n (Vale.Math.Poly2_s.mul a b) 127))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags; va_Mod_ok]) va_sM va_s0;\n (va_sM, va_fM)", "val va_wpProof_Sr64Imm : dst:va_operand_reg_opr -> src1:va_operand_reg_opr -> src2:bits64 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Sr64Imm dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Sr64Imm dst src1 src2)\n ([va_mod_reg_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Sr64Imm dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Sr64Imm (va_code_Sr64Imm dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_VSwap : dst:va_operand_vec_opr -> src:va_operand_vec_opr -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_VSwap dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_VSwap dst src) ([va_mod_vec_opr dst])\n va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_VSwap dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VSwap (va_code_VSwap dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wp_VPolyMulHigh\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VPolyMulHigh (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32\n (va_eval_vec_opr va_s0 src1) in let (a2:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2) in l_or (Vale.Math.Poly2.mask a1\n 64 == zero) (Vale.Math.Poly2.mask a2 64 == zero)) /\\ (forall (va_x_dst:va_value_vec_opr) . let\n va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in va_get_ok va_sM /\\ (let\n (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2)\n in Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_sM dst) == Vale.Math.Poly2_s.mul\n (Vale.Math.Poly2_s.shift a1 (-64)) (Vale.Math.Poly2_s.shift a2 (-64))) ==> va_k va_sM (())))", "val va_wpProof_Cmovc64 : dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Cmovc64 dst src va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Cmovc64 dst src) ([va_mod_dst_opr64\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Cmovc64 dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Add : dst:va_operand_reg_opr -> src1:va_operand_reg_opr -> src2:va_operand_reg_opr\n -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Add dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Add dst src1 src2) ([va_mod_reg_opr\n dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Add dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Add (va_code_Add dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Mtvsrdd : dst:va_operand_vec_opr -> src1:va_operand_reg_opr ->\n src2:va_operand_reg_opr -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Mtvsrdd dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Mtvsrdd dst src1 src2)\n ([va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Mtvsrdd dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Mtvsrdd (va_code_Mtvsrdd dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_lemma_Mulx64 : va_b0:va_code -> va_s0:va_state -> dst_hi:va_operand_dst_opr64 ->\n dst_lo:va_operand_dst_opr64 -> src:va_operand_opr64\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Mulx64 dst_hi dst_lo src) va_s0 /\\ va_is_dst_dst_opr64\n dst_hi va_s0 /\\ va_is_dst_dst_opr64 dst_lo va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok\n va_s0 /\\ bmi2_enabled /\\ dst_hi =!= dst_lo))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_mul_nat pow2_64 (va_eval_dst_opr64 va_sM dst_hi) + va_eval_dst_opr64 va_sM dst_lo ==\n va_mul_nat (va_get_reg64 rRdx va_s0) (va_eval_opr64 va_s0 src) /\\ va_state_eq va_sM\n (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64\n dst_hi va_sM va_s0)))))\nlet va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src =\n va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src);\n let (va_old_s:va_state) = va_s0 in\n va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0;\n let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in\n lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src);\n (va_sM, va_fM)", "val va_wpProof_PopXmm : dst:va_operand_xmm -> tmp:va_operand_reg_opr64 -> expected_xmm:quad32 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_PopXmm dst tmp expected_xmm va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_PopXmm dst tmp) ([va_Mod_stack;\n va_Mod_reg64 rRsp; va_mod_reg_opr64 tmp; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_PopXmm dst tmp expected_xmm va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_PopXmm (va_code_PopXmm dst tmp) va_s0 dst tmp expected_xmm in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_stack va_sM (va_update_reg64 rRsp va_sM (va_update_ok va_sM\n (va_update_operand_reg_opr64 tmp va_sM (va_update_operand_xmm dst va_sM va_s0))))));\n va_lemma_norm_mods ([va_Mod_stack; va_Mod_reg64 rRsp; va_mod_reg_opr64 tmp; va_mod_xmm dst])\n va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_lemma_MulHigh64U : va_b0:va_code -> va_s0:va_state -> dst:va_operand_reg_opr ->\n src1:va_operand_reg_opr -> src2:va_operand_reg_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_MulHigh64U dst src1 src2) va_s0 /\\ va_is_dst_reg_opr\n dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\ va_get_ok va_s0))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_eval_reg_opr va_sM dst == va_mul_nat (va_eval_reg_opr va_s0 src1) (va_eval_reg_opr va_s0\n src2) `op_Division` pow2_64 /\\ va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr\n dst va_sM va_s0))))\nlet va_lemma_MulHigh64U va_b0 va_s0 dst src1 src2 =\n va_reveal_opaque (`%va_code_MulHigh64U) (va_code_MulHigh64U dst src1 src2);\n let (va_old_s:va_state) = va_s0 in\n va_ins_lemma (Ins (S.MulHigh64U dst src1 src2)) va_s0;\n let (va_sM, va_fM) = va_eval_ins (Ins (S.MulHigh64U dst src1 src2)) va_s0 in\n (va_sM, va_fM)", "val va_wpProof_Sl64Imm : dst:va_operand_reg_opr -> src1:va_operand_reg_opr -> src2:bits64 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Sl64Imm dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Sl64Imm dst src1 src2)\n ([va_mod_reg_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Sl64Imm dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Sl64Imm (va_code_Sl64Imm dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_SubImmWrap : dst:va_operand_reg_opr -> src1:va_operand_reg_opr -> src2:nsimm16 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_SubImmWrap dst src1 src2 va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_SubImmWrap dst src1 src2)\n ([va_mod_reg_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_SubImmWrap dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_SubImmWrap (va_code_SubImmWrap dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_reg_opr dst va_sM va_s0)));\n va_lemma_norm_mods ([va_mod_reg_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wp_VPolyMulLow\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VPolyMulLow (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32\n (va_eval_vec_opr va_s0 src1) in let (a2:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2) in l_or (Vale.Math.Poly2_s.shift\n a1 (-64) == zero) (Vale.Math.Poly2_s.shift a2 (-64) == zero)) /\\ (forall\n (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32\n (va_eval_vec_opr va_s0 src1) in let (a2:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_sM dst) == Vale.Math.Poly2_s.mul\n (Vale.Math.Poly2.mask a1 64) (Vale.Math.Poly2.mask a2 64)) ==> va_k va_sM (())))" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fst", "name": "Vale.AES.PPC64LE.PolyOps.va_wpProof_VPolyMul" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fst", "name": "Vale.AES.PPC64LE.PolyOps.va_wpProof_VPolyMulLow" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fst", "name": "Vale.AES.PPC64LE.PolyOps.va_wpProof_VPolyMulHigh" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsAes.fst", "name": "Vale.X64.InsAes.va_wpProof_VPclmulqdq" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fst", "name": "Vale.AES.PPC64LE.PolyOps.va_wpProof_VPolyAnd" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fst", "name": "Vale.AES.PPC64LE.PolyOps.va_wpProof_VPolyAdd" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_wpProof_AddPoly" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_wpProof_Mulx64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsAes.fst", "name": "Vale.X64.InsAes.va_wpProof_Pclmulqdq" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fst", "name": "Vale.AES.PPC64LE.PolyOps.va_lemma_VPolyMul" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_wpProof_AddPoly" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.PolyOps.fsti", "name": "Vale.AES.X64.PolyOps.va_wp_VPolyMul" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_wpProof_ClmulRev64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_MulHigh64U" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_MulLow64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_wpProof_IMul64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_VPxor" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vpmsumd" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fst", "name": "Vale.AES.PPC64LE.PolyOps.va_lemma_VPolyMulHigh" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_MulLow64Wrap" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsAes.fst", "name": "Vale.X64.InsAes.va_lemma_VPclmulqdq" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fst", "name": "Vale.AES.PPC64LE.PolyOps.va_lemma_VPolyMulLow" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_VPaddd" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vadduwm" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_wpProof_High64ToLow" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Xxmrghd" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vmrghw" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_VPslldq4" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vsl" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vslw" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vmr" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_wpProof_Mul64Wrap" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vand" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_Vpslldq8" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_VPshufb" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_wpProof_Low64ToHigh" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_wpProof_High64ToLow" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vxor" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_wpProof_Clmul128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_wpProof_ReduceMul128_LE" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_Vpsrldq8" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_lemma_Vpmsumd" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.PolyOps.fsti", "name": "Vale.AES.X64.PolyOps.va_quick_VPolyMul" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fsti", "name": "Vale.AES.PPC64LE.PolyOps.va_wp_VPolyMul" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsAes.fst", "name": "Vale.X64.InsAes.va_lemma_Pclmulqdq" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_Xor" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_wpProof_Xor64" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_wpProof_ReduceMulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vcmpequw" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vsel" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_wpProof_Low64ToHigh" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_wpProof_ClmulRev64High" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vsrw" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fst", "name": "Vale.AES.PPC64LE.PolyOps.va_lemma_VPolyAnd" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_Mov128" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_PshufbDup" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_And" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_Pshufb" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_Pcmpeqd" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_Paddd" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_wpProof_Fmul1" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_Pshufb64" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fst", "name": "Vale.Curve25519.X64.FastWide.va_wpProof_Fmul2" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_wpProof_Load_two_lsb" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_wpProof_Fast_mul1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fst", "name": "Vale.AES.PPC64LE.PolyOps.va_lemma_VPolyAdd" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_Sl64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_Pxor" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_SubImm" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_Sr64" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_wpProof_ClmulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.X64.fst", "name": "Vale.Bignum.X64.va_lemma_Mulx_64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vcipher" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_wpProof_ReduceMulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_wpProof_And64" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_wpProof_Load_0xc2_msb" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_AddExtended" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Vcipherlast" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_wpProof_Clmul128" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsAes.fst", "name": "Vale.X64.InsAes.va_wpProof_VAESNI_enc" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_Pslld" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_AddImm" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Mfvsrd" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Mfvsrld" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_VPalignr8" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_Psrldq" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wpProof_VShufpd" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_lemma_ClmulRev64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_Sr64Imm" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fst", "name": "Vale.AES.PPC64LE.PolyOps.va_wpProof_VSwap" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fsti", "name": "Vale.AES.PPC64LE.PolyOps.va_wp_VPolyMulHigh" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_wpProof_Cmovc64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_Add" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fst", "name": "Vale.PPC64LE.InsVector.va_wpProof_Mtvsrdd" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_lemma_Mulx64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsStack.fst", "name": "Vale.X64.InsStack.va_wpProof_PopXmm" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_lemma_MulHigh64U" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_Sl64Imm" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fst", "name": "Vale.PPC64LE.InsBasic.va_wpProof_SubImmWrap" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fsti", "name": "Vale.AES.PPC64LE.PolyOps.va_wp_VPolyMulLow" } ], "selected_premises": [ "Vale.X64.Decls.va_update_flags", "Vale.X64.Decls.va_update_ok", "Vale.X64.Decls.va_update_operand_xmm", "Vale.X64.Decls.va_update_xmm", "Vale.X64.Decls.va_update_reg64", "Vale.X64.Decls.va_update_stack", "Vale.X64.Decls.va_update_mem", "Vale.X64.Decls.va_state_eq", "Vale.X64.Decls.va_update_mem_layout", "Vale.AES.X64.PolyOps.va_lemma_VHigh64ToLow", "Vale.AES.X64.PolyOps.va_lemma_VLow64ToHigh", "Vale.AES.X64.PolyOps.va_lemma_PolyAnd", "Vale.AES.X64.PolyOps.va_lemma_VPolyAdd", "Vale.X64.Decls.va_update_mem_heaplet", "Vale.X64.Decls.update_register", "Vale.AES.X64.PolyOps.va_lemma_VPolyMul", "Vale.X64.Decls.va_update_stackTaint", "Vale.X64.Decls.va_update_operand_reg_opr64", "Vale.X64.Decls.va_update_operand_dst_opr64", "Vale.AES.X64.PolyOps.va_lemma_VSwap", "Vale.X64.Decls.va_update_operand_heaplet", "Vale.X64.Decls.update_dst_operand", "Vale.X64.QuickCode.va_mods_t", "Vale.X64.QuickCode.va_Mod_stack", "Vale.X64.Decls.va_update_operand_opr64", "Vale.X64.QuickCode.va_Mod_flags", "Vale.X64.Decls.va_ensure_total", "Vale.X64.QuickCode.va_Mod_stackTaint", "Vale.X64.QuickCode.va_Mod_mem", "Vale.X64.QuickCode.va_Mod_mem_layout", "Vale.X64.QuickCode.va_QProc", "Vale.X64.QuickCode.va_Mod_xmm", "Vale.X64.QuickCode.va_mod_xmm", "Vale.X64.QuickCode.va_mod_heaplet", "Vale.AES.X64.PolyOps.va_wpProof_VSwap", "Vale.X64.Decls.va_expand_state", "Vale.AES.X64.PolyOps.va_wpProof_VPolyAdd", "Vale.X64.QuickCode.va_Mod_ok", "Vale.X64.QuickCode.va_mod_reg_opr64", "Vale.AES.X64.PolyOps.va_wpProof_VHigh64ToLow", "Vale.X64.QuickCode.va_Mod_reg64", "Vale.AES.X64.PolyOps.va_wpProof_PolyAnd", "Vale.X64.QuickCode.va_Mod_mem_heaplet", "Vale.AES.X64.PolyOps.va_wpProof_VLow64ToHigh", "Vale.X64.QuickCode.va_Mod_None", "Vale.X64.Decls.update_operand", "Vale.X64.InsBasic.va_wp_Newline", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.Decls.va_get_flags", "Vale.X64.InsBasic.va_wp_Space", "Vale.X64.QuickCode.va_quickCode", "Vale.X64.QuickCodes.va_range1", "Vale.X64.QuickCode.va_mod_dst_opr64", "Vale.X64.InsMem.va_wp_DestroyHeaplets", "Vale.X64.InsAes.va_wp_VPclmulqdq", "Vale.X64.InsBasic.va_wp_Xgetbv_Avx", "Vale.X64.InsMem.va_wp_CreateHeaplets", "Vale.X64.QuickCodes.va_state_match", "Vale.X64.Decls.va_tl", "Vale.X64.InsVector.va_wp_VShufpd", "Vale.X64.InsVector.va_wp_InitPshufbStableMask", "Vale.X64.InsVector.va_wp_Shufpd", "Vale.X64.InsVector.va_wp_XmmEqual", "Vale.X64.InsVector.va_wp_Store128_buffer", "Vale.X64.InsVector.va_wp_Pshufd", "Vale.X64.Machine_s.rR15", "Vale.X64.Machine_s.rR14", "Vale.X64.Machine_s.rR9", "Vale.X64.Machine_s.rR10", "Vale.X64.Machine_s.rR13", "Vale.X64.Machine_s.rR11", "Vale.X64.Machine_s.rRax", "Vale.X64.Machine_s.rR8", "Vale.X64.Machine_s.rR12", "Vale.X64.Decls.va_require_total", "Vale.X64.InsVector.va_wp_PinsrdImm", "Vale.X64.InsVector.va_wp_InitPshufbMask", "Vale.X64.InsVector.va_wp_VPshufb", "Vale.X64.Machine_s.rRsi", "Vale.X64.Machine_s.rRcx", "Vale.X64.InsVector.va_wp_Pshufb", "Vale.X64.InsVector.va_wp_Pslld", "Vale.X64.Decls.va_hd", "Vale.X64.InsAes.va_wp_Pclmulqdq", "Vale.X64.InsVector.va_wp_ZeroXmm", "Vale.X64.InsVector.va_wp_PinsrqImm", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRdx", "Vale.X64.Machine_s.rRbp", "Vale.X64.Machine_s.rRsp", "Vale.X64.Decls.va_op_heaplet_mem_heaplet", "Vale.X64.InsBasic.va_wp_Mul64Wrap", "Vale.X64.InsVector.va_wp_PshufbStable", "Vale.X64.Machine_s.rRdi", "Vale.X64.InsBasic.va_wp_Prefetchnta", "Vale.X64.InsBasic.va_wp_NoNewline", "Vale.X64.InsAes.va_wp_AESNI_keygen_assist", "Vale.X64.InsVector.va_wp_Load128_buffer", "Vale.X64.InsVector.va_wp_InitPshufbDupMask", "Vale.X64.InsVector.va_wp_Mov128" ], "source_upto_this": "module Vale.AES.X64.PolyOps\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Math.Poly2_s\nopen Vale.Math.Poly2\nopen Vale.Math.Poly2.Bits_s\nopen Vale.Math.Poly2.Bits\nopen Vale.Math.Poly2.Lemmas\nopen Vale.X64.Machine_s\nopen Vale.X64.State\nopen Vale.X64.Decls\nopen Vale.X64.InsBasic\nopen Vale.X64.InsMem\nopen Vale.X64.InsVector\nopen Vale.X64.InsAes\nopen Vale.X64.QuickCode\nopen Vale.X64.QuickCodes\nopen Vale.X64.CPU_Features_s\n//-- VPolyAdd\n\n[@ \"opaque_to_smt\"]\nlet va_code_VPolyAdd dst src1 src2 =\n (va_Block (va_CCons (va_code_VPxor dst src1 src2) (va_CNil ())))\n\n[@ \"opaque_to_smt\"]\nlet va_codegen_success_VPolyAdd dst src1 src2 =\n (va_pbool_and (va_codegen_success_VPxor dst src1 src2) (va_ttrue ()))\n\n[@\"opaque_to_smt\"]\nlet va_lemma_VPolyAdd va_b0 va_s0 dst src1 src2 =\n va_reveal_opaque (`%va_code_VPolyAdd) (va_code_VPolyAdd dst src1 src2);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_opr128 va_s0 src2) in\n Vale.Math.Poly2.Words.lemma_add_quad32 (va_eval_xmm va_s0 src1) (va_eval_opr128 va_s0 src2);\n let (va_s5, va_fc5) = va_lemma_VPxor (va_hd va_b1) va_s0 dst src1 src2 in\n let va_b5 = va_tl va_b1 in\n let (va_sM, va_f5) = va_lemma_empty_total va_s5 va_b5 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc5 va_s5 va_f5 va_sM in\n (va_sM, va_fM)\n\n\n[@\"opaque_to_smt\"]\nlet va_wpProof_VPolyAdd dst src1 src2 va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyAdd (va_code_VPolyAdd dst src1 src2) va_s0 dst src1 src2 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n//--\n//-- PolyAnd\n\n[@ \"opaque_to_smt\"]\nlet va_code_PolyAnd dst src =\n (va_Block (va_CCons (va_code_Pand dst (va_coerce_xmm_to_opr128 src)) (va_CNil ())))\n\n[@ \"opaque_to_smt\"]\nlet va_codegen_success_PolyAnd dst src =\n (va_pbool_and (va_codegen_success_Pand dst (va_coerce_xmm_to_opr128 src)) (va_ttrue ()))\n\n[@\"opaque_to_smt\"]\nlet va_lemma_PolyAnd va_b0 va_s0 dst src =\n va_reveal_opaque (`%va_code_PolyAnd) (va_code_PolyAnd dst src);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 dst) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Words.lemma_and_quad32 (va_eval_xmm va_s0 dst) (va_eval_xmm va_s0 src);\n let (va_s5, va_fc5) = va_lemma_Pand (va_hd va_b1) va_s0 dst (va_coerce_xmm_to_opr128 src) in\n let va_b5 = va_tl va_b1 in\n let (va_sM, va_f5) = va_lemma_empty_total va_s5 va_b5 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc5 va_s5 va_f5 va_sM in\n (va_sM, va_fM)\n\n\n[@\"opaque_to_smt\"]\nlet va_wpProof_PolyAnd dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_PolyAnd (va_code_PolyAnd dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n//--\n//-- VHigh64ToLow\n\n[@ \"opaque_to_smt\"]\nlet va_code_VHigh64ToLow dst src =\n (va_Block (va_CCons (va_code_Vpsrldq8 dst src) (va_CNil ())))\n\n[@ \"opaque_to_smt\"]\nlet va_codegen_success_VHigh64ToLow dst src =\n (va_pbool_and (va_codegen_success_Vpsrldq8 dst src) (va_ttrue ()))\n\n[@\"opaque_to_smt\"]\nlet va_lemma_VHigh64ToLow va_b0 va_s0 dst src =\n va_reveal_opaque (`%va_code_VHigh64ToLow) (va_code_VHigh64ToLow dst src);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n let (va_s3, va_fc3) = va_lemma_Vpsrldq8 (va_hd va_b1) va_s0 dst src in\n let va_b3 = va_tl va_b1 in\n Vale.Math.Poly2.Words.lemma_quad32_double_shift a;\n Vale.Math.Poly2.Lemmas.lemma_shift_is_div a 64;\n Vale.Math.Poly2.Bits.lemma_of_to_quad32 (Vale.Math.Poly2_s.shift a (-64));\n let (va_sM, va_f3) = va_lemma_empty_total va_s3 va_b3 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc3 va_s3 va_f3 va_sM in\n (va_sM, va_fM)\n\n\n[@\"opaque_to_smt\"]\nlet va_wpProof_VHigh64ToLow dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VHigh64ToLow (va_code_VHigh64ToLow dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n//--\n//-- VLow64ToHigh\n\n[@ \"opaque_to_smt\"]\nlet va_code_VLow64ToHigh dst src =\n (va_Block (va_CCons (va_code_Vpslldq8 dst src) (va_CNil ())))\n\n[@ \"opaque_to_smt\"]\nlet va_codegen_success_VLow64ToHigh dst src =\n (va_pbool_and (va_codegen_success_Vpslldq8 dst src) (va_ttrue ()))\n\n[@\"opaque_to_smt\"]\nlet va_lemma_VLow64ToHigh va_b0 va_s0 dst src =\n va_reveal_opaque (`%va_code_VLow64ToHigh) (va_code_VLow64ToHigh dst src);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n let (va_s3, va_fc3) = va_lemma_Vpslldq8 (va_hd va_b1) va_s0 dst src in\n let va_b3 = va_tl va_b1 in\n Vale.Math.Poly2.Words.lemma_quad32_double_shift a;\n Vale.Math.Poly2.Lemmas.lemma_mask_is_mod a 64;\n Vale.Math.Poly2.lemma_shift_is_mul (Vale.Math.Poly2.mask a 64) 64;\n Vale.Math.Poly2.Bits.lemma_of_to_quad32 (Vale.Math.Poly2_s.shift (Vale.Math.Poly2.mask a 64) 64);\n let (va_sM, va_f3) = va_lemma_empty_total va_s3 va_b3 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc3 va_s3 va_f3 va_sM in\n (va_sM, va_fM)\n\n\n[@\"opaque_to_smt\"]\nlet va_wpProof_VLow64ToHigh dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VLow64ToHigh (va_code_VLow64ToHigh dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n//--\n//-- VSwap\n\n[@ \"opaque_to_smt\"]\nlet va_code_VSwap dst src =\n (va_Block (va_CCons (va_code_VPalignr8 dst src src) (va_CNil ())))\n\n[@ \"opaque_to_smt\"]\nlet va_codegen_success_VSwap dst src =\n (va_pbool_and (va_codegen_success_VPalignr8 dst src src) (va_ttrue ()))\n\n[@\"opaque_to_smt\"]\nlet va_lemma_VSwap va_b0 va_s0 dst src =\n va_reveal_opaque (`%va_code_VSwap) (va_code_VSwap dst src);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n let (va_s3, va_fc3) = va_lemma_VPalignr8 (va_hd va_b1) va_s0 dst src src in\n let va_b3 = va_tl va_b1 in\n Vale.Math.Poly2.Words.lemma_quad32_double_swap a;\n Vale.Math.Poly2.Bits.lemma_of_to_quad32 (Vale.Math.Poly2.swap a 64);\n let (va_sM, va_f3) = va_lemma_empty_total va_s3 va_b3 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc3 va_s3 va_f3 va_sM in\n (va_sM, va_fM)\n\n\n[@\"opaque_to_smt\"]\nlet va_wpProof_VSwap dst src va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VSwap (va_code_VSwap dst src) va_s0 dst src in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst\n va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n//--\n//-- VPolyMul\n\n[@ \"opaque_to_smt\"]\nlet va_code_VPolyMul dst src1 src2 src1Hi src2Hi =\n (va_Block (va_CCons (va_code_VPclmulqdq dst src1 src2 src1Hi src2Hi) (va_CNil ())))\n\n[@ \"opaque_to_smt\"]\nlet va_codegen_success_VPolyMul dst src1 src2 src1Hi src2Hi =\n (va_pbool_and (va_codegen_success_VPclmulqdq dst src1 src2 src1Hi src2Hi) (va_ttrue ()))\n\n[@\"opaque_to_smt\"]\nlet va_lemma_VPolyMul va_b0 va_s0 dst src1 src2 src1Hi src2Hi =\n va_reveal_opaque (`%va_code_VPolyMul) (va_code_VPolyMul dst src1 src2 src1Hi src2Hi);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src1) in\n let (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src2) in\n let (va_s4, va_fc4) = va_lemma_VPclmulqdq (va_hd va_b1) va_s0 dst src1 src2 src1Hi src2Hi in\n let va_b4 = va_tl va_b1 in\n Vale.Math.Poly2.Bits.lemma_quad32_double a1;\n Vale.Math.Poly2.Bits.lemma_quad32_double a2;\n Vale.Math.Poly2.Lemmas.lemma_shift_is_div a1 64;\n Vale.Math.Poly2.Lemmas.lemma_shift_is_div a2 64;\n Vale.Math.Poly2.Lemmas.lemma_mask_is_mod a1 64;\n Vale.Math.Poly2.Lemmas.lemma_mask_is_mod a2 64;\n Vale.Math.Poly2.Bits.lemma_of_to_quad32 (Vale.Math.Poly2_s.mul (if src1Hi then\n Vale.Math.Poly2_s.shift a1 (-64) else Vale.Math.Poly2.mask a1 64) (if src2Hi then\n Vale.Math.Poly2_s.shift a2 (-64) else Vale.Math.Poly2.mask a2 64));\n let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc4 va_s4 va_f4 va_sM in\n (va_sM, va_fM)\n\n\n[@\"opaque_to_smt\"]", "sketch": [ "Step 1: The definition `va_wpProof_VPolyMul` is a weakest precondition proof for the `VPolyMul` operation. It ensures that after executing the `VPolyMul` operation, the state and flags are correctly updated, and the required postconditions are met.\n\nStep 2: The implementation involves invoking the lemma `va_lemma_VPolyMul` to perform the core proof steps. It then updates the state using `va_lemma_upd_update` and asserts that the state is correctly updated with the new flags and operand values. Finally, it normalizes the modifications to ensure that the state changes are consistent and returns the updated state, fuel, and a ghost value.", "Step 1: The definition `va_wpProof_VPolyMul` is about proving the weakest precondition for the `VPolyMul` operation. This involves ensuring that the state transitions and modifications made by the `VPolyMul` operation are correct and meet the specified requirements.\nStep 2: The implementation involves calling the lemma `va_lemma_VPolyMul` to get the intermediate state and fuel. Then, it updates the state and asserts that the state is as expected after the operation. Finally, it normalizes the modifications and returns the final state, fuel, and a ghost value.", "Step 1: The definition `va_wpProof_VPolyMul` is a weakest precondition proof for the `VPolyMul` operation. It ensures that the state transitions and modifications made by the `VPolyMul` operation are correctly captured and verified.\nStep 2: The implementation involves invoking the lemma `va_lemma_VPolyMul` to get the intermediate state and fuel. It then updates the state and asserts that the state is correctly updated with the expected modifications. Finally, it normalizes the modifications and returns the final state, fuel, and a ghost value.", "Step 1: The definition `va_wpProof_VPolyMul` is about proving the weakest precondition for the `VPolyMul` operation, which multiplies two polynomial operands and stores the result in a destination operand.\nStep 2: The implementation involves invoking the lemma `va_lemma_VPolyMul` to establish the correctness of the `VPolyMul` operation. It then updates the state and asserts that the state after the operation is equivalent to the expected state. Finally, it normalizes the modifications to ensure the state and flags are correctly updated.", "Step 1: The definition `va_wpProof_VPolyMul` is about proving the weakest precondition (WP) for the `VPolyMul` operation. This operation performs a polynomial multiplication on two source operands, potentially using their high parts, and stores the result in a destination operand.\n\nStep 2: The implementation involves invoking the lemma `va_lemma_VPolyMul` to get the updated state and fuel after executing the `VPolyMul` operation. Then, it updates the state and asserts that the state is correctly updated with the new flags and operand values. Finally, it normalizes the modifications and returns the updated state, fuel, and a ghost value.", "Step 1: The definition `va_wpProof_VPolyMul` is about proving the weakest precondition for the `VPolyMul` operation, which performs a polynomial multiplication on two source operands and stores the result in a destination operand. The operation also considers whether to use the high or low parts of the source operands based on the `src1Hi` and `src2Hi` flags.\n\nStep 2: The implementation involves:\n- Invoking the lemma `va_lemma_VPolyMul` to get the resulting state and fuel after executing the `VPolyMul` operation.\n- Updating the state using `va_lemma_upd_update`.\n- Asserting that the new state is equivalent to the state after updating the flags and the destination operand.\n- Normalizing the modifications to ensure the state changes are correctly reflected.\n- Returning the final state, fuel, and a ghost value.", "Step 1: The definition `va_wpProof_VPolyMul` is about proving the weakest precondition (WP) for the `VPolyMul` operation. This operation performs a polynomial multiplication on two source operands and stores the result in a destination operand. The operation also considers high bits of the source operands based on the boolean flags `src1Hi` and `src2Hi`.\n\nStep 2: The implementation involves invoking the lemma `va_lemma_VPolyMul` to get the updated state and fuel after executing the `VPolyMul` operation. It then updates the state and asserts that the state is correctly updated with the new flags and operand values. Finally, it normalizes the modifications and returns the updated state, fuel, and a ghost value.", "Step 1: The definition `va_wpProof_VPolyMul` is about proving the weakest precondition for the `VPolyMul` operation, which performs a polynomial multiplication on two source operands and stores the result in a destination operand. The operation can optionally use the higher 64 bits of the source operands based on the `src1Hi` and `src2Hi` flags.\n\nStep 2: The implementation involves invoking the lemma `va_lemma_VPolyMul` to obtain the resulting state and fuel after executing the `VPolyMul` operation. It then updates the state and asserts that the state is equivalent to the expected state after the operation. Finally, it normalizes the modifications to the state and returns the updated state, fuel, and a ghost value.", "Step 1: The definition `va_wpProof_VPolyMul` is about proving the weakest precondition (WP) for the `VPolyMul` operation. This operation performs a polynomial multiplication on two source operands and stores the result in a destination operand. The operation also considers whether the high or low parts of the source operands are used based on the `src1Hi` and `src2Hi` flags.\n\nStep 2: The implementation involves invoking the lemma `va_lemma_VPolyMul` to get the resulting state and fuel after executing the `VPolyMul` operation. It then updates the state and asserts that the state is equivalent to the expected state after the operation. Finally, it normalizes the modifications and returns the updated state, fuel, and a ghost value.", "Step 1: The definition `va_wpProof_VPolyMul` is a weakest precondition proof for the `VPolyMul` operation. It ensures that the state transformation caused by the `VPolyMul` operation is correct and meets the required postconditions.\nStep 2: The implementation involves invoking the lemma `va_lemma_VPolyMul` to perform the actual state transformation and then updating the state. Assertions are made to ensure the state is correctly updated, and the modifications to the state are normalized." ], "generated_solution": [ "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wpProof_VPolyMul dst src1 src2 src1Hi src2Hi va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_VPolyMul (va_code_VPolyMul dst src1 src2 src1Hi src2Hi) va_s0 dst src1 src2 src1Hi src2Hi in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_xmm dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_flags; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)" ] }, { "file_name": "Selectors.LList.fst", "name": "Selectors.LList.ind_llist_sel_depends_only_on", "opens_and_abbrevs": [ { "open": "Steel.Reference" }, { "open": "Steel.Effect" }, { "open": "Steel.Effect.Atomic" }, { "abbrev": "Mem", "full_module": "Steel.Memory" }, { "open": "Steel.FractionalPermission" }, { "open": "FStar.Ghost" }, { "abbrev": "L", "full_module": "FStar.List.Tot" }, { "open": "Steel.Reference" }, { "open": "Steel.Effect" }, { "open": "Steel.Effect.Atomic" }, { "open": "Steel.Memory" }, { "open": "Selectors" }, { "open": "Selectors" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 1, "max_fuel": 1, "initial_ifuel": 1, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val ind_llist_sel_depends_only_on\n (#a: Type0)\n (ptr: ref (t a))\n (m0: Mem.hmem (ind_llist_sl ptr))\n (m1: mem{disjoint m0 m1})\n : Lemma (ind_llist_sel_full' ptr m0 == ind_llist_sel_full' ptr (Mem.join m0 m1))", "source_definition": "let ind_llist_sel_depends_only_on (#a:Type0) (ptr:ref (t a))\n (m0:Mem.hmem (ind_llist_sl ptr)) (m1:mem{disjoint m0 m1})\n : Lemma (ind_llist_sel_full' ptr m0 == ind_llist_sel_full' ptr (Mem.join m0 m1))\n = let m' = Mem.join m0 m1 in\n let p1 = reveal (id_elim_exists (ind_llist_sl' ptr) m0) in\n let p2 = reveal (id_elim_exists (ind_llist_sl' ptr) m') in\n\n pts_to_witinv ptr full_perm;\n Mem.elim_wi (ind_llist_sl' ptr) p1 p2 m'", "source_range": { "start_line": 332, "start_col": 0, "end_line": 340, "end_col": 44 }, "interleaved": false, "definition": "fun ptr m0 m1 ->\n (let m' = Steel.Memory.join m0 m1 in\n let p1 =\n FStar.Ghost.reveal (Steel.Memory.id_elim_exists (Selectors.LList.ind_llist_sl' ptr) m0)\n in\n let p2 =\n FStar.Ghost.reveal (Steel.Memory.id_elim_exists (Selectors.LList.ind_llist_sl' ptr) m')\n in\n Steel.Reference.pts_to_witinv ptr Steel.FractionalPermission.full_perm;\n Steel.Memory.elim_wi (Selectors.LList.ind_llist_sl' ptr) p1 p2 m')\n <:\n FStar.Pervasives.Lemma\n (ensures\n Selectors.LList.ind_llist_sel_full' ptr m0 ==\n Selectors.LList.ind_llist_sel_full' ptr (Steel.Memory.join m0 m1))", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "Steel.Reference.ref", "Selectors.LList.t", "Steel.Memory.hmem", "Selectors.LList.ind_llist_sl", "Steel.Memory.mem", "Steel.Memory.disjoint", "Steel.Memory.elim_wi", "Selectors.LList.ind_llist_sl'", "Prims.unit", "Steel.Reference.pts_to_witinv", "Steel.FractionalPermission.full_perm", "FStar.Ghost.reveal", "Steel.Memory.id_elim_exists", "Steel.Memory.join", "Prims.l_True", "Prims.squash", "Prims.eq2", "FStar.Pervasives.Native.tuple2", "Prims.list", "Selectors.LList.ind_llist_sel_full'", "Prims.Nil", "FStar.Pervasives.pattern" ], "proof_features": [], "is_simple_lemma": true, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "\n ptr: Steel.Reference.ref (Selectors.LList.t a) ->\n m0: Steel.Memory.hmem (Selectors.LList.ind_llist_sl ptr) ->\n m1: Steel.Memory.mem{Steel.Memory.disjoint m0 m1}\n -> FStar.Pervasives.Lemma\n (ensures\n Selectors.LList.ind_llist_sel_full' ptr m0 ==\n Selectors.LList.ind_llist_sel_full' ptr (Steel.Memory.join m0 m1))", "prompt": "let ind_llist_sel_depends_only_on\n (#a: Type0)\n (ptr: ref (t a))\n (m0: Mem.hmem (ind_llist_sl ptr))\n (m1: mem{disjoint m0 m1})\n : Lemma (ind_llist_sel_full' ptr m0 == ind_llist_sel_full' ptr (Mem.join m0 m1)) =\n ", "expected_response": "let m' = Mem.join m0 m1 in\nlet p1 = reveal (id_elim_exists (ind_llist_sl' ptr) m0) in\nlet p2 = reveal (id_elim_exists (ind_llist_sl' ptr) m') in\npts_to_witinv ptr full_perm;\nMem.elim_wi (ind_llist_sl' ptr) p1 p2 m'", "source": { "project_name": "steel", "file_name": "share/steel/examples/steel/Selectors.LList.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Selectors.LList.fst", "checked_file": "dataset/Selectors.LList.fst.checked", "interface_file": true, "dependencies": [ "dataset/Steel.Reference.fsti.checked", "dataset/Steel.Memory.fsti.checked", "dataset/Steel.FractionalPermission.fst.checked", "dataset/Steel.Effect.Atomic.fsti.checked", "dataset/Steel.Effect.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Tactics.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "cell", "cell", "val cell (a:Type0) : Type0", "next", "next", "data", "data", "let t (a:Type0) = ref (cell a)", "let next #a (c:cell a) : t a = c.next", "val next (#a:Type0) (c:cell a) : t a", "let data #a (c:cell a) : a = c.data", "val data (#a:Type0) (c:cell a) : a", "let mk_cell #a (n: t a) (d:a) = {\n next = n;\n data = d\n}", "val mk_cell (#a:Type0) (n: t a) (d:a)\n : Pure (cell a)\n (requires True)\n (ensures fun c ->\n next c == n /\\\n data c == d)", "let null_llist #a = null", "let is_null #a ptr = is_null ptr", "val null_llist (#a:Type) : t a", "let rec llist_sl' (#a:Type) (ptr:t a)\n (l:list (cell a))\n : Tot slprop (decreases l)\n =\n match l with\n | [] ->\n Mem.pure (ptr == null_llist)\n\n | hd :: tl ->\n pts_to_sl ptr full_perm hd `Mem.star`\n llist_sl' (next hd) tl `Mem.star`\n Mem.pure (ptr =!= null_llist)", "val is_null (#a:Type) (ptr:t a) : (b:bool{b <==> ptr == null_llist})", "val llist_sl (#a:Type0) (r:t a) : slprop u#1", "val llist_sel (#a:Type0) (r:t a) : selector (list a) (llist_sl r)", "let llist' #a r : vprop' =\n {hp = llist_sl r;\n t = list a;\n sel = llist_sel r}", "let llist_sl ptr = Mem.h_exists (llist_sl' ptr)", "let rec datas (#a:Type) (l:list (cell a)) : list a =\n match l with\n | [] -> []\n | hd::tl -> data hd :: datas tl", "let llist (#a:Type0) (r:t a) = VUnit (llist' r)", "val llist_sel_cell' (#a:Type0) (ptr:t a) : selector' (list (cell a)) (llist_sl ptr)", "let v_llist (#a:Type0) (#p:vprop) (r:t a)\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (llist r) /\\ True)}) : GTot (list a)\n = h (llist r)", "let llist_sel_cell' #a ptr = fun h -> id_elim_exists (llist_sl' ptr) h", "let llist_sl'_witinv (#a:Type) (ptr:t a) : Lemma (is_witness_invariant (llist_sl' ptr))\n = let rec aux (ptr:t a) (x y:list (cell a)) (m:mem) : Lemma\n (requires interp (llist_sl' ptr x) m /\\ interp (llist_sl' ptr y) m)\n (ensures x == y)\n (decreases x)\n = match x with\n | [] -> begin match y with\n | [] -> ()\n | hd::tl ->\n Mem.pure_interp (ptr == null_llist) m;\n Mem.pure_star_interp\n (pts_to_sl ptr full_perm hd `Mem.star` llist_sl' (next hd) tl)\n (ptr =!= null_llist) m;\n Mem.pure_interp (ptr =!= null_llist) m\n\n end\n | hd1::tl1 -> begin match y with\n | [] ->\n Mem.pure_interp (ptr == null_llist) m;\n Mem.pure_star_interp\n (pts_to_sl ptr full_perm hd1 `Mem.star` llist_sl' (next hd1) tl1)\n (ptr =!= null_llist) m;\n Mem.pure_interp (ptr =!= null_llist) m\n | hd2::tl2 ->\n pts_to_witinv ptr full_perm;\n aux (next hd1) tl1 tl2 m\n end\n\n in Classical.forall_intro_3 (Classical.move_requires_3 (aux ptr))", "val intro_llist_nil (a:Type0)\n : Steel unit emp (fun _ -> llist (null_llist #a))\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> v_llist #a null_llist h1 == [])", "val elim_llist_nil (#a:Type0) (ptr:t a)\n : Steel unit (llist ptr) (fun _ -> llist ptr)\n (requires fun _ -> ptr == null_llist)\n (ensures fun h0 _ h1 ->\n v_llist ptr h0 == v_llist ptr h1 /\\\n v_llist ptr h1 == [])", "val cons_is_not_null (#a:Type0) (ptr:t a)\n : Steel unit (llist ptr) (fun _ -> llist ptr)\n (requires fun h -> Cons? (v_llist ptr h))\n (ensures fun h0 _ h1 ->\n v_llist ptr h0 == v_llist ptr h1 /\\\n ptr =!= null_llist)", "val intro_llist_cons (#a:Type0) (ptr1 ptr2:t a)\n : Steel unit (vptr ptr1 `star` llist ptr2)\n (fun _ -> llist ptr1)\n (requires fun h -> next (sel ptr1 h) == ptr2)\n (ensures fun h0 _ h1 -> v_llist ptr1 h1 == (data (sel ptr1 h0)) :: v_llist ptr2 h0)", "val tail (#a:Type0) (ptr:t a)\n : Steel (t a) (llist ptr)\n (fun n -> vptr ptr `star` llist n)\n (requires fun _ -> ptr =!= null_llist)\n (ensures fun h0 n h1 ->\n Cons? (v_llist ptr h0) /\\\n sel ptr h1 == mk_cell n (L.hd (v_llist ptr h0)) /\\\n v_llist n h1 == L.tl (v_llist ptr h0))", "let llist_sel_depends_only_on (#a:Type0) (ptr:t a)\n (m0:Mem.hmem (llist_sl ptr)) (m1:mem{disjoint m0 m1})\n : Lemma (llist_sel_cell' ptr m0 == llist_sel_cell' ptr (Mem.join m0 m1))\n = let m':Mem.hmem (llist_sl ptr) = Mem.join m0 m1 in\n let l1 = Ghost.reveal (id_elim_exists (llist_sl' ptr) m0) in\n let l2 = Ghost.reveal (id_elim_exists (llist_sl' ptr) m') in\n\n llist_sl'_witinv ptr;\n Mem.elim_wi (llist_sl' ptr) l1 l2 m'", "val ind_llist_sl (#a:Type0) (r:ref (t a)) : slprop u#1", "let llist_sel_depends_only_on_core (#a:Type0) (ptr:t a)\n (m0:Mem.hmem (llist_sl ptr))\n : Lemma (llist_sel_cell' ptr m0 == llist_sel_cell' ptr (core_mem m0))\n = let l1 = Ghost.reveal (id_elim_exists (llist_sl' ptr) m0) in\n let l2 = Ghost.reveal (id_elim_exists (llist_sl' ptr) (core_mem m0)) in\n llist_sl'_witinv ptr;\n Mem.elim_wi (llist_sl' ptr) l1 l2 (core_mem m0)", "val ind_llist_sel (#a:Type0) (r:ref (t a)) : selector (list a) (ind_llist_sl r)", "let ind_llist' (#a:Type0) (r:ref (t a)) : vprop' =\n { hp = ind_llist_sl r;\n t = list a;\n sel = ind_llist_sel r}", "val llist_sel_cell (#a:Type0) (r:t a) : selector (list (cell a)) (llist_sl r)", "let ind_llist (#a:Type0) (r:ref (t a)) = VUnit (ind_llist' r)", "let llist_sel_cell #a ptr =\n Classical.forall_intro_2 (llist_sel_depends_only_on ptr);\n Classical.forall_intro (llist_sel_depends_only_on_core ptr);\n llist_sel_cell' ptr", "let v_ind_llist (#a:Type0) (#p:vprop) (r:ref (t a))\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (ind_llist r) /\\ True)}) : GTot (list a)\n = h (ind_llist r)", "val unpack_ind (#a:Type0) (r:ref (t a))\n : Steel (t a)\n (ind_llist r)\n (fun p -> vptr r `star` llist p)\n (requires fun _ -> True)\n (ensures fun h0 p h1 ->\n sel r h1 == p /\\\n v_llist p h1 == v_ind_llist r h0)", "let llist_sel ptr = fun h -> datas (llist_sel_cell ptr h)", "let llist_sel_interp (#a:Type0) (ptr:t a) (l:list (cell a)) (m:mem) : Lemma\n (requires interp (llist_sl' ptr l) m)\n (ensures interp (llist_sl ptr) m /\\ llist_sel_cell' ptr m == l)\n = intro_h_exists l (llist_sl' ptr) m;\n llist_sl'_witinv ptr", "val pack_ind (#a:Type0) (r:ref (t a)) (p:t a)\n : Steel unit\n (vptr r `star` llist p)\n (fun _ -> ind_llist r)\n (requires fun h -> sel r h == p)\n (ensures fun h0 _ h1 -> v_llist p h0 == v_ind_llist r h1)", "let intro_nil_lemma (a:Type0) (m:mem) : Lemma\n (requires interp (hp_of emp) m)\n (ensures interp (llist_sl (null_llist #a)) m /\\ llist_sel (null_llist #a) m == [])\n = let ptr:t a = null_llist in\n pure_interp (ptr == null_llist) m;\n let open FStar.Tactics in\n assert (llist_sl' ptr [] == Mem.pure (ptr == null_llist)) by (norm [delta; zeta; iota]);\n llist_sel_interp ptr [] m", "let intro_llist_nil a =\n change_slprop_2 emp (llist (null_llist #a)) ([] <: list a) (intro_nil_lemma a)", "let elim_nil_lemma (#a:Type0) (ptr:t a) (m:mem) : Lemma\n (requires interp (llist_sl ptr) m /\\ ptr == null_llist)\n (ensures interp (llist_sl ptr) m /\\ llist_sel ptr m == [])\n = let l' = id_elim_exists (llist_sl' ptr) m in\n pure_interp (ptr == null_llist) m;\n llist_sel_interp ptr [] m", "let elim_llist_nil #a ptr =\n change_slprop_rel (llist ptr) (llist ptr)\n (fun x y -> x == y /\\ y == [])\n (fun m -> elim_nil_lemma ptr m)", "let lemma_cons_not_null (#a:Type) (ptr:t a) (l:list a) (m:mem) : Lemma\n (requires interp (llist_sl ptr) m /\\ llist_sel ptr m == l /\\ Cons? l)\n (ensures ptr =!= null_llist)\n = let l' = id_elim_exists (llist_sl' ptr) m in\n assert (interp (llist_sl' ptr l') m);\n llist_sel_interp ptr l' m;\n match reveal l' with\n | hd::tl ->\n let p = pts_to_sl ptr full_perm (hide hd) `Mem.star` llist_sl' (next hd) tl in\n pure_star_interp p (ptr =!= null_llist) m", "let cons_is_not_null #a ptr =\n let h = get () in\n let l = hide (v_llist ptr h) in\n extract_info (llist ptr) l (ptr =!= null_llist) (lemma_cons_not_null ptr l)", "let intro_cons_lemma_aux (#a:Type0) (ptr1 ptr2:t a)\n (x: cell a) (l:list (cell a)) (m:mem) : Lemma\n (requires interp (pts_to_sl ptr1 full_perm x `Mem.star` llist_sl' ptr2 l) m /\\\n next x == ptr2)\n (ensures interp (llist_sl' ptr1 (x::l)) m)\n = affine_star (pts_to_sl ptr1 full_perm x) (llist_sl' ptr2 l) m;\n pts_to_not_null ptr1 full_perm x m;\n emp_unit (pts_to_sl ptr1 full_perm x `Mem.star` llist_sl' ptr2 l);\n pure_star_interp\n (pts_to_sl ptr1 full_perm x `Mem.star` llist_sl' ptr2 l)\n (ptr1 =!= null_llist)\n m", "let intro_cons_lemma (#a:Type0) (ptr1 ptr2:t a)\n (x: cell a) (l:list a) (m:mem) : Lemma\n (requires interp (ptr ptr1 `Mem.star` llist_sl ptr2) m /\\\n next x == ptr2 /\\\n sel_of (vptr ptr1) m == x /\\\n sel_of (llist ptr2) m == l)\n (ensures interp (llist_sl ptr1) m /\\ llist_sel ptr1 m == data x :: l)\n = let l' = id_elim_exists (llist_sl' ptr2) m in\n let aux (m:mem) (x:cell a) (ml mr:mem) : Lemma\n (requires disjoint ml mr /\\ m == join ml mr /\\\n interp (ptr ptr1) ml /\\ interp (llist_sl ptr2) mr /\\\n ptr_sel ptr1 m == x /\\ interp (llist_sl' ptr2 l') m)\n (ensures interp (pts_to_sl ptr1 full_perm x `Mem.star` llist_sl' ptr2 l') m)\n = ptr_sel_interp ptr1 ml;\n assert (interp (pts_to_sl ptr1 full_perm x) ml);\n let l2 = id_elim_exists (llist_sl' ptr2) mr in\n join_commutative ml mr;\n assert (interp (llist_sl' ptr2 l2) m);\n llist_sl'_witinv ptr2;\n assert (interp (llist_sl' ptr2 l') mr);\n intro_star (pts_to_sl ptr1 full_perm x) (llist_sl' ptr2 l') ml mr\n in\n elim_star (ptr ptr1) (llist_sl ptr2) m;\n Classical.forall_intro_2 (Classical.move_requires_2 (aux m x));\n assert (interp (pts_to_sl ptr1 full_perm x `Mem.star` llist_sl' ptr2 l') m);\n intro_cons_lemma_aux ptr1 ptr2 x l' m;\n intro_h_exists (x::l') (llist_sl' ptr1) m;\n llist_sel_interp ptr1 (x::l') m", "let intro_llist_cons ptr1 ptr2 =\n let h = get () in\n let x = hide (sel ptr1 h) in\n let l = hide (v_llist ptr2 h) in\n reveal_star (vptr ptr1) (llist ptr2);\n change_slprop (vptr ptr1 `star` llist ptr2) (llist ptr1) (reveal x, reveal l) (data x :: l) (fun m -> intro_cons_lemma ptr1 ptr2 x l m)", "let reveal_non_empty_lemma (#a:Type) (ptr:t a) (l:list (cell a)) (m:mem) : Lemma\n (requires interp (llist_sl ptr) m /\\ llist_sel_cell ptr m == l /\\ ptr =!= null_llist)\n (ensures Cons? l)\n= let l' = id_elim_exists (llist_sl' ptr) m in\n llist_sel_interp ptr l' m;\n pure_interp (ptr == null_llist) m", "let is_cons (#a:Type) (l:list a) : prop = match l with\n | [] -> False\n | _ -> True", "let llist_cell' #a r : vprop' =\n {hp = llist_sl r;\n t = list (cell a);\n sel = llist_sel_cell r}", "let llist_cell (#a:Type0) (r:t a) = VUnit (llist_cell' r)", "let v_cell (#a:Type0) (#p:vprop) (r:t a)\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (llist_cell r) /\\ True)}) : GTot (list (cell a))\n = h (llist_cell r)", "val reveal_non_empty_cell (#a:Type0) (ptr:t a)\n : Steel unit (llist_cell ptr) (fun _ -> llist_cell ptr)\n (requires fun _ -> ptr =!= null_llist)\n (ensures fun h0 _ h1 -> v_cell ptr h0 == v_cell ptr h1 /\\ Cons? (v_cell ptr h0))", "let reveal_non_empty_cell #a ptr =\n let h = get () in\n let l = hide (v_cell ptr h) in\n extract_info (llist_cell ptr) l (is_cons l) (reveal_non_empty_lemma ptr l)", "let tail_cell_lemma (#a:Type0) (r:t a) (l:list (cell a)) (m:mem) : Lemma\n (requires Cons? l /\\ interp (llist_sl r) m /\\ llist_sel_cell r m == l)\n (ensures (let x = L.hd l in\n interp (ptr r `Mem.star` llist_sl (next x)) m /\\\n sel_of (vptr r) m == x /\\\n sel_of (llist_cell (next x)) m == L.tl l))\n = llist_sel_interp r l m;\n assert (interp (llist_sl' r l) m);\n let x = L.hd l in\n let tl = L.tl l in\n let sl = pts_to_sl r full_perm x `Mem.star` llist_sl' (next x) tl in\n pure_star_interp sl (r =!= null_llist) m;\n emp_unit sl;\n assert (interp sl m);\n let aux (m:mem) (ml mr:mem) : Lemma\n (requires disjoint ml mr /\\ m == join ml mr /\\\n interp (pts_to_sl r full_perm x) ml /\\ interp (llist_sl' (next x) tl) mr)\n (ensures interp (ptr r `Mem.star` llist_sl (next x)) m /\\\n sel_of (vptr r) m == x /\\\n sel_of (llist_cell (next x)) m == tl)\n = intro_ptr_interp r (hide x) ml;\n llist_sel_interp (next x) tl mr;\n intro_star (ptr r) (llist_sl (next x)) ml mr;\n ptr_sel_interp r ml;\n pts_to_witinv r full_perm;\n join_commutative ml mr\n in\n elim_star (pts_to_sl r full_perm x) (llist_sl' (next x) tl) m;\n Classical.forall_intro_2 (Classical.move_requires_2 (aux m))", "val tail_cell (#a:Type0) (ptr:t a)\n : Steel (t a) (llist_cell ptr)\n (fun n -> vptr ptr `star` llist_cell n)\n (requires fun _ -> ptr =!= null_llist)\n (ensures fun h0 n h1 ->\n Cons? (v_cell ptr h0) /\\\n n == next (sel ptr h1) /\\\n sel ptr h1 == L.hd (v_cell ptr h0) /\\\n v_cell n h1 == L.tl (v_cell ptr h0))", "let tail_cell #a ptr =\n let h = get () in\n let l = hide (v_cell ptr h) in\n reveal_non_empty_cell ptr;\n let x = hide (L.hd l) in\n change_slprop (llist_cell ptr) (vptr ptr `star` llist_cell (next x)) l (reveal x, L.tl l)\n (fun m -> tail_cell_lemma ptr l m);\n reveal_star (vptr ptr) (llist_cell (next x));\n let v = read ptr in\n change_slprop (llist_cell (next x)) (llist_cell (next v)) (L.tl l) (L.tl l) (fun _ -> ());\n return (next v)", "val to_list_cell (#a:Type0) (ptr:t a)\n : Steel unit (llist ptr) (fun _ -> llist_cell ptr)\n (requires fun _ -> True)\n (ensures fun h0 _ h1 -> v_llist ptr h0 == datas (v_cell ptr h1))", "let to_list_cell ptr =\n change_slprop_rel (llist ptr) (llist_cell ptr) (fun x y -> x == datas y) (fun _ -> ())", "val from_list_cell (#a:Type0) (ptr:t a)\n : Steel unit (llist_cell ptr) (fun _ -> llist ptr)\n (requires fun _ -> True)\n (ensures fun h0 _ h1 -> v_llist ptr h1 == datas (v_cell ptr h0))", "let from_list_cell ptr =\n change_slprop_rel (llist_cell ptr) (llist ptr) (fun x y -> datas x == y) (fun _ -> ())", "let tail #a ptr =\n to_list_cell ptr;\n let n = tail_cell #a ptr in\n from_list_cell n;\n n", "let ind_llist_sl' (#a:Type0) (r:ref (t a)) (p:t a) : slprop u#1 =\n pts_to_sl r full_perm p `Mem.star` llist_sl p", "let ind_llist_sl (#a:Type0) (r:ref (t a)) = Mem.h_exists (ind_llist_sl' r)", "let ind_llist_sel_full' (#a:Type0) (r:ref (t a)) : selector' (t a * list a) (ind_llist_sl r) =\n fun h ->\n let p = id_elim_exists (ind_llist_sl' r) h in\n (reveal p, llist_sel p h)" ], "closest": [ "val llist_sel_depends_only_on\n (#a: Type0)\n (ptr: t a)\n (m0: Mem.hmem (llist_ptr_sl ptr))\n (m1: mem{disjoint m0 m1})\n : Lemma (llist_ptr_sel' ptr m0 == llist_ptr_sel' ptr (Mem.join m0 m1))\nlet llist_sel_depends_only_on (#a:Type0) (ptr:t a)\n (m0:Mem.hmem (llist_ptr_sl ptr)) (m1:mem{disjoint m0 m1})\n : Lemma (llist_ptr_sel' ptr m0 == llist_ptr_sel' ptr (Mem.join m0 m1))\n = let l1 = reveal (id_elim_exists (llist_ptr_sl' ptr) m0) in\n let l2 = reveal (id_elim_exists (llist_ptr_sl' ptr) (Mem.join m0 m1)) in\n\n llist_ptr_sl'_witinv ptr;\n Mem.elim_wi (llist_ptr_sl' ptr) l1 l2 (Mem.join m0 m1)", "val ind_ptr_sel_depends_only_on\n (#a: Type0)\n (ptr: ref (ref a))\n (m0: Mem.hmem (ind_ptr_sl ptr))\n (m1: mem{disjoint m0 m1})\n : Lemma (ind_ptr_sel' ptr m0 == ind_ptr_sel' ptr (Mem.join m0 m1))\nlet ind_ptr_sel_depends_only_on (#a:Type0) (ptr:ref (ref a))\n (m0:Mem.hmem (ind_ptr_sl ptr)) (m1:mem{disjoint m0 m1})\n : Lemma (ind_ptr_sel' ptr m0 == ind_ptr_sel' ptr (Mem.join m0 m1))\n = let p1 = reveal (id_elim_exists (ind_ptr_sl' ptr) m0) in\n let p2 = reveal (id_elim_exists (ind_ptr_sl' ptr) (Mem.join m0 m1)) in\n pts_to_witinv ptr full_perm;\n elim_wi (ind_ptr_sl' ptr) p1 p2 (Mem.join m0 m1)", "val tree_sel_depends_only_on\n (#a: Type0)\n (ptr: t a)\n (m0: Mem.hmem (tree_sl ptr))\n (m1: mem{disjoint m0 m1})\n : Lemma (tree_sel_node' ptr m0 == tree_sel_node' ptr (Mem.join m0 m1))\nlet tree_sel_depends_only_on (#a:Type0) (ptr:t a)\n (m0:Mem.hmem (tree_sl ptr)) (m1:mem{disjoint m0 m1})\n : Lemma (tree_sel_node' ptr m0 == tree_sel_node' ptr (Mem.join m0 m1))\n = let m':Mem.hmem (tree_sl ptr) = Mem.join m0 m1 in\n let t1 = Ghost.reveal (id_elim_exists (tree_sl' ptr) m0) in\n let t2 = Ghost.reveal (id_elim_exists (tree_sl' ptr) m') in\n\n tree_sl'_witinv ptr;\n Mem.elim_wi (tree_sl' ptr) t1 t2 m'", "val ptr_sel_depends_only_on\n (#a: Type0)\n (r: ref a)\n (p: perm)\n (m0: Mem.hmem (ptrp r p))\n (m1: mem{disjoint m0 m1})\n : Lemma (ptr_sel' r p m0 == ptr_sel' r p (Mem.join m0 m1))\nlet ptr_sel_depends_only_on (#a:Type0) (r:ref a)\n (p: perm)\n (m0:Mem.hmem (ptrp r p)) (m1:mem{disjoint m0 m1})\n : Lemma (ptr_sel' r p m0 == ptr_sel' r p (Mem.join m0 m1))\n = let x = reveal (id_elim_exists #a (pts_to_sl r p) m0) in\n let y = reveal (id_elim_exists #a (pts_to_sl r p) (Mem.join m0 m1)) in\n pts_to_witinv r p;\n elim_wi (pts_to_sl r p) x y (Mem.join m0 m1)", "val ghost_ptr_sel_depends_only_on\n (#a: Type0)\n (r: ghost_ref a)\n (p: perm)\n (m0: Mem.hmem (ghost_ptrp r p))\n (m1: mem{disjoint m0 m1})\n : Lemma (ghost_ptr_sel' r p m0 == ghost_ptr_sel' r p (Mem.join m0 m1))\nlet ghost_ptr_sel_depends_only_on (#a:Type0) (r:ghost_ref a)\n (p: perm)\n (m0:Mem.hmem (ghost_ptrp r p)) (m1:mem{disjoint m0 m1})\n : Lemma (ghost_ptr_sel' r p m0 == ghost_ptr_sel' r p (Mem.join m0 m1))\n = let x = reveal (id_elim_exists #a (ghost_pts_to_sl r p) m0) in\n let y = reveal (id_elim_exists #a (ghost_pts_to_sl r p) (Mem.join m0 m1)) in\n ghost_pts_to_witinv r p;\n elim_wi (ghost_pts_to_sl r p) x y (Mem.join m0 m1)", "val llist_sel_depends_only_on_core (#a: Type0) (ptr: t a) (m0: Mem.hmem (llist_ptr_sl ptr))\n : Lemma (llist_ptr_sel' ptr m0 == llist_ptr_sel' ptr (core_mem m0))\nlet llist_sel_depends_only_on_core (#a:Type0) (ptr:t a)\n (m0:Mem.hmem (llist_ptr_sl ptr))\n : Lemma (llist_ptr_sel' ptr m0 == llist_ptr_sel' ptr (core_mem m0))\n = let l1 = reveal (id_elim_exists (llist_ptr_sl' ptr) m0) in\n let l2 = reveal (id_elim_exists (llist_ptr_sl' ptr) (core_mem m0)) in\n\n llist_ptr_sl'_witinv ptr;\n Mem.elim_wi (llist_ptr_sl' ptr) l1 l2 (core_mem m0)", "val ind_ptr_sel_depends_only_on_core (#a: Type0) (ptr: ref (ref a)) (m0: Mem.hmem (ind_ptr_sl ptr))\n : Lemma (ind_ptr_sel' ptr m0 == ind_ptr_sel' ptr (core_mem m0))\nlet ind_ptr_sel_depends_only_on_core (#a:Type0) (ptr:ref (ref a))\n (m0:Mem.hmem (ind_ptr_sl ptr))\n : Lemma (ind_ptr_sel' ptr m0 == ind_ptr_sel' ptr (core_mem m0))\n = let p1 = reveal (id_elim_exists (ind_ptr_sl' ptr) m0) in\n let p2 = reveal (id_elim_exists (ind_ptr_sl' ptr) (core_mem m0)) in\n pts_to_witinv ptr full_perm;\n elim_wi (ind_ptr_sl' ptr) p1 p2 (core_mem m0)", "val tree_sel_depends_only_on_core (#a: Type0) (ptr: t a) (m0: Mem.hmem (tree_sl ptr))\n : Lemma (tree_sel_node' ptr m0 == tree_sel_node' ptr (core_mem m0))\nlet tree_sel_depends_only_on_core (#a:Type0) (ptr:t a)\n (m0:Mem.hmem (tree_sl ptr))\n : Lemma (tree_sel_node' ptr m0 == tree_sel_node' ptr (core_mem m0))\n = let t1 = Ghost.reveal (id_elim_exists (tree_sl' ptr) m0) in\n let t2 = Ghost.reveal (id_elim_exists (tree_sl' ptr) (core_mem m0)) in\n tree_sl'_witinv ptr;\n Mem.elim_wi (tree_sl' ptr) t1 t2 (core_mem m0)", "val rmem_depends_only_on' (pre: pre_t) (m0: hmem pre) (m1: mem{disjoint m0 m1})\n : Lemma (mk_rmem pre m0 == mk_rmem pre (join m0 m1))\nlet rmem_depends_only_on' (pre:pre_t) (m0:hmem pre) (m1:mem{disjoint m0 m1})\n : Lemma (mk_rmem pre m0 == mk_rmem pre (join m0 m1))\n = Classical.forall_intro (reveal_mk_rmem pre m0);\n Classical.forall_intro (reveal_mk_rmem pre (join m0 m1));\n FExt.extensionality_g\n (r0:vprop{can_be_split pre r0})\n (fun r0 -> normal (t_of r0))\n (mk_rmem pre m0)\n (mk_rmem pre (join m0 m1))", "val ptr_sel_depends_only_on_core (#a: Type0) (r: ref a) (p: perm) (m0: Mem.hmem (ptrp r p))\n : Lemma (ptr_sel' r p m0 == ptr_sel' r p (core_mem m0))\nlet ptr_sel_depends_only_on_core (#a:Type0) (r:ref a)\n (p: perm) (m0:Mem.hmem (ptrp r p))\n : Lemma (ptr_sel' r p m0 == ptr_sel' r p (core_mem m0))\n = let x = reveal (id_elim_exists #a (pts_to_sl r p) m0) in\n let y = reveal (id_elim_exists #a (pts_to_sl r p) (core_mem m0)) in\n pts_to_witinv r p;\n elim_wi (pts_to_sl r p) x y (core_mem m0)", "val rmem_depends_only_on_post'\n (#a: Type)\n (post: post_t a)\n (x: a)\n (m0: hmem (post x))\n (m1: mem{disjoint m0 m1})\n : Lemma (mk_rmem (post x) m0 == mk_rmem (post x) (join m0 m1))\nlet rmem_depends_only_on_post' (#a:Type) (post:post_t a)\n (x:a) (m0:hmem (post x)) (m1:mem{disjoint m0 m1})\n : Lemma (mk_rmem (post x) m0 == mk_rmem (post x) (join m0 m1))\n = rmem_depends_only_on' (post x) m0 m1", "val rmem_depends_only_on (pre: pre_t)\n : Lemma\n (forall (m0: hmem pre) (m1: mem{disjoint m0 m1}). mk_rmem pre m0 == mk_rmem pre (join m0 m1))\nlet rmem_depends_only_on (pre:pre_t)\n : Lemma (forall (m0:hmem pre) (m1:mem{disjoint m0 m1}).\n mk_rmem pre m0 == mk_rmem pre (join m0 m1))\n = Classical.forall_intro_2 (rmem_depends_only_on' pre)", "val ghost_ptr_sel_depends_only_on_core\n (#a: Type0)\n (r: ghost_ref a)\n (p: perm)\n (m0: Mem.hmem (ghost_ptrp r p))\n : Lemma (ghost_ptr_sel' r p m0 == ghost_ptr_sel' r p (core_mem m0))\nlet ghost_ptr_sel_depends_only_on_core (#a:Type0) (r:ghost_ref a)\n (p: perm) (m0:Mem.hmem (ghost_ptrp r p))\n : Lemma (ghost_ptr_sel' r p m0 == ghost_ptr_sel' r p (core_mem m0))\n = let x = reveal (id_elim_exists #a (ghost_pts_to_sl r p) m0) in\n let y = reveal (id_elim_exists #a (ghost_pts_to_sl r p) (core_mem m0)) in\n ghost_pts_to_witinv r p;\n elim_wi (ghost_pts_to_sl r p) x y (core_mem m0)", "val rmem_depends_only_on_post (#a: Type) (post: post_t a)\n : Lemma\n (forall (x: a) (m0: hmem (post x)) (m1: mem{disjoint m0 m1}).\n mk_rmem (post x) m0 == mk_rmem (post x) (join m0 m1))\nlet rmem_depends_only_on_post (#a:Type) (post:post_t a)\n : Lemma (forall (x:a) (m0:hmem (post x)) (m1:mem{disjoint m0 m1}).\n mk_rmem (post x) m0 == mk_rmem (post x) (join m0 m1))\n = Classical.forall_intro_3 (rmem_depends_only_on_post' post)", "val interp_depends_only_on (hp:slprop u#a)\n : Lemma\n (forall (m0:hmem hp) (m1:mem u#a{disjoint m0 m1}).\n interp hp m0 <==> interp hp (join m0 m1))\nlet interp_depends_only_on (hp:slprop u#a) = H.interp_depends_only_on hp", "val interp_depends_only_on (hp:slprop u#a)\n : Lemma\n (forall (m0:hmem hp) (m1:mem u#a{disjoint m0 m1}).\n interp hp m0 <==> interp hp (join m0 m1))\nlet interp_depends_only_on (hp:slprop u#a) = H.interp_depends_only_on hp", "val ptr_sel_interp (#a: Type0) (r: ref a) (m: mem)\n : Lemma (requires interp (ptr r) m) (ensures interp (pts_to_sl r full_perm (ptr_sel r m)) m)\nlet ptr_sel_interp (#a:Type0) (r:ref a) (m:mem) : Lemma\n (requires interp (ptr r) m)\n (ensures interp (pts_to_sl r full_perm (ptr_sel r m)) m)\n= ptrp_sel_interp r full_perm m", "val llist_sel_interp (#a: Type0) (ptr: t a) (l: list (cell a * a)) (m: mem)\n : Lemma (requires interp (llist_ptr_sl' ptr l) m)\n (ensures interp (llist_ptr_sl ptr) m /\\ llist_ptr_sel_cell ptr m == l)\nlet llist_sel_interp (#a:Type0) (ptr:t a) (l:list (cell a * a)) (m:mem) : Lemma\n (requires interp (llist_ptr_sl' ptr l) m)\n (ensures interp (llist_ptr_sl ptr) m /\\ llist_ptr_sel_cell ptr m == l)\n = intro_h_exists l (llist_ptr_sl' ptr) m;\n llist_ptr_sl'_witinv ptr", "val reference_distinct_sel_disjoint (#a: Type0) (h: mem) (r1 r2: reference a)\n : Lemma\n (requires\n (h `contains` r1 /\\ h `contains` r2 /\\ frameOf r1 == frameOf r2 /\\ as_addr r1 == as_addr r2)\n ) (ensures (sel h r1 == sel h r2))\nlet reference_distinct_sel_disjoint\n (#a:Type0) (h: mem) (r1: reference a) (r2: reference a)\n: Lemma\n (requires (\n h `contains` r1 /\\\n h `contains` r2 /\\\n frameOf r1 == frameOf r2 /\\\n as_addr r1 == as_addr r2\n ))\n (ensures (\n sel h r1 == sel h r2\n ))\n= mreference_distinct_sel_disjoint h r1 r2", "val disjoint_join (m0 m1 m2: mem)\n : Lemma\n (disjoint m1 m2 /\\ disjoint m0 (join m1 m2) ==>\n disjoint m0 m1 /\\ disjoint m0 m2 /\\ disjoint (join m0 m1) m2 /\\ disjoint (join m0 m2) m1)\nlet disjoint_join (m0 m1 m2:mem)\n : Lemma (disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) ==>\n disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\n = H.disjoint_join m0.heap m1.heap m2.heap", "val unpack_ind_lemma (#a: Type0) (r: ref (ref a)) (p: ref a) (v: a) (m: mem)\n : Lemma (requires interp (ind_ptr_sl r) m /\\ ind_ptr_sel_full r m == (p, v))\n (ensures\n interp ((ptr r) `Mem.star` (ptr p)) m /\\ sel_of (vptr r) m == p /\\ sel_of (vptr p) m == v)\nlet unpack_ind_lemma (#a:Type0) (r:ref (ref a)) (p:ref a) (v:a) (m:mem) : Lemma\n (requires interp (ind_ptr_sl r) m /\\ ind_ptr_sel_full r m == (p, v))\n (ensures\n interp (ptr r `Mem.star` ptr p) m /\\\n sel_of (vptr r) m == p /\\\n sel_of (vptr p) m == v)\n = intro_ptr_frame_lemma r p (ptr p) m", "val pointer_distinct_sel_disjoint\n (#a:Type0) (#rrel1 #rrel2 #rel1 #rel2:srel a)\n (b1:mpointer a rrel1 rel1)\n (b2:mpointer a rrel2 rel2)\n (h:HS.mem)\n :Lemma (requires (live h b1 /\\ live h b2 /\\ get h b1 0 =!= get h b2 0))\n (ensures (disjoint b1 b2))\nlet pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h =\n if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2\n then begin\n HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2);\n loc_disjoint_buffer b1 b2\n end\n else\n loc_disjoint_buffer b1 b2", "val disjoint_join (m0 m1 m2:mem)\n : Lemma (disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) ==>\n disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\nlet disjoint_join m0 m1 m2 =\n H.disjoint_join m0.heap m1.heap m2.heap", "val lemma_cons_not_null (#a: Type) (ptr: t a) (l: list a) (m: mem)\n : Lemma (requires interp (llist_ptr_sl ptr) m /\\ llist_ptr_sel ptr m == l /\\ Cons? l)\n (ensures ptr =!= null_llist)\nlet lemma_cons_not_null (#a:Type) (ptr:t a) (l:list a) (m:mem) : Lemma\n (requires interp (llist_ptr_sl ptr) m /\\ llist_ptr_sel ptr m == l /\\ Cons? l)\n (ensures ptr =!= null_llist)\n = let l' = id_elim_exists (llist_ptr_sl' ptr) m in\n assert (interp (llist_ptr_sl' ptr l') m);\n llist_sel_interp ptr l' m;\n match reveal l' with\n | (hd, v)::tl ->\n let p = pts_to_sl ptr full_perm (hide hd) `Mem.star`\n llist_ptr_sl' (next hd) tl `Mem.star`\n pts_to_sl (data hd) full_perm v in\n pure_star_interp p (ptr =!= null_llist) m", "val ghost_ptr_sel_interp (#a: Type0) (r: ghost_ref a) (m: mem)\n : Lemma (requires interp (ghost_ptr r) m)\n (ensures interp (ghost_pts_to_sl r full_perm (ghost_ptr_sel r m)) m)\nlet ghost_ptr_sel_interp (#a:Type0) (r:ghost_ref a) (m:mem) : Lemma\n (requires interp (ghost_ptr r) m)\n (ensures interp (ghost_pts_to_sl r full_perm (ghost_ptr_sel r m)) m)\n= ghost_ptrp_sel_interp r full_perm m", "val intro_cons_lemma (#a: Type0) (ptr1: t a) (x: cell a) (v: a) (l: list a) (m: mem)\n : Lemma\n (requires\n interp (((ptr ptr1) `Mem.star` (llist_ptr_sl (next x))) `Mem.star` (ptr (data x))) m /\\\n sel_of (vptr ptr1) m == x /\\ sel_of (llist_ptr (next x)) m == l /\\\n sel_of (vptr (data x)) m == v)\n (ensures interp (llist_ptr_sl ptr1) m /\\ llist_ptr_sel ptr1 m == v :: l)\nlet intro_cons_lemma (#a:Type0) (ptr1:t a)\n (x: cell a) (v:a) (l:list a) (m:mem) : Lemma\n (requires interp (ptr ptr1 `Mem.star` llist_ptr_sl (next x) `Mem.star` ptr (data x)) m /\\\n sel_of (vptr ptr1) m == x /\\\n sel_of (llist_ptr (next x)) m == l /\\\n sel_of (vptr (data x)) m == v)\n (ensures interp (llist_ptr_sl ptr1) m /\\ llist_ptr_sel ptr1 m == v :: l)\n = let l' = id_elim_exists (llist_ptr_sl' (next x)) m in\n assert (interp (llist_ptr_sl' (next x) l') m);\n let aux (m:mem) (ml1 ml2 mr:mem) : Lemma\n (requires disjoint ml1 ml2 /\\ disjoint (join ml1 ml2) mr /\\ m == join (join ml1 ml2) mr /\\\n interp (ptr ptr1) ml1 /\\ interp (llist_ptr_sl (next x)) ml2 /\\ interp (ptr (data x)) mr /\\\n interp (ptr (data x)) m /\\ ptr_sel (data x) m == v /\\\n interp (llist_ptr_sl' (next x) l') m /\\\n ptr_sel ptr1 ml1 == x\n )\n (ensures interp\n (pts_to_sl ptr1 full_perm x `Mem.star`\n llist_ptr_sl' (next x) l' `Mem.star`\n pts_to_sl (data x) full_perm v) m)\n = ptr_sel_interp ptr1 ml1;\n let l2 = id_elim_exists (llist_ptr_sl' (next x)) ml2 in\n join_commutative ml1 ml2;\n assert (interp (llist_ptr_sl' (next x) l2) m);\n llist_ptr_sl'_witinv (next x);\n assert (l2 == l');\n assert (interp (llist_ptr_sl' (next x) l') ml2);\n ptr_sel_interp (data x) mr;\n join_commutative (join ml1 ml2) mr;\n assert (ptr_sel (data x) mr == v);\n assert (interp (pts_to_sl (data x) full_perm v) mr);\n intro_star (pts_to_sl ptr1 full_perm x) (llist_ptr_sl' (next x) l') ml1 ml2;\n intro_star\n (pts_to_sl ptr1 full_perm x `Mem.star` llist_ptr_sl' (next x) l')\n (pts_to_sl (data x) full_perm v)\n (join ml1 ml2) mr\n in\n elim_star\n (ptr ptr1 `Mem.star` llist_ptr_sl (next x))\n (ptr (data x)) m;\n Classical.forall_intro (Classical.move_requires\n (elim_star (ptr ptr1) (llist_ptr_sl (next x))));\n Classical.forall_intro_3 (Classical.move_requires_3 (aux m));\n intro_cons_lemma_aux ptr1 x v l' m;\n assert (interp (llist_ptr_sl' ptr1 ((x,v)::l')) m);\n intro_h_exists ((x,v)::l') (llist_ptr_sl' ptr1) m;\n llist_sel_interp ptr1 ((x,v)::l') m", "val elim_cons_cell_lemma (#a: Type0) (r: t a) (l: list (cell a * a)) (m: mem)\n : Lemma (requires Cons? l /\\ interp (llist_ptr_sl r) m /\\ llist_ptr_sel_cell r m == l)\n (ensures\n (let x = fst (L.hd l) in\n interp (((ptr r) `Mem.star` (llist_ptr_sl (next x))) `Mem.star` (ptr (data x))) m /\\\n sel_of (vptr r) m == x /\\ sel_of (vptr (data x)) m == snd (L.hd l) /\\\n sel_of (llist_cell (next x)) m == L.tl l))\nlet elim_cons_cell_lemma (#a:Type0) (r:t a) (l:list (cell a * a)) (m:mem) : Lemma\n (requires Cons? l /\\ interp (llist_ptr_sl r) m /\\ llist_ptr_sel_cell r m == l)\n (ensures (let x = fst (L.hd l) in\n interp (ptr r `Mem.star` llist_ptr_sl (next x) `Mem.star` ptr (data x)) m /\\\n sel_of (vptr r) m == x /\\\n sel_of (vptr (data x)) m == snd (L.hd l) /\\\n sel_of (llist_cell (next x)) m == L.tl l))\n = llist_sel_interp r l m;\n assert (interp (llist_ptr_sl' r l) m);\n let x = fst (L.hd l) in\n let v = snd (L.hd l) in\n let tl = L.tl l in\n let sl = pts_to_sl r full_perm x `Mem.star` llist_ptr_sl' (next x) tl `Mem.star` pts_to_sl (data x) full_perm v in\n pure_star_interp sl (r =!= null_llist) m;\n emp_unit sl;\n assert (interp sl m);\n let aux (m:mem) (ml1 ml2 mr:mem) : Lemma\n (requires disjoint ml1 ml2 /\\ disjoint (join ml1 ml2) mr /\\ m == join (join ml1 ml2) mr /\\\n interp (pts_to_sl r full_perm x) ml1 /\\\n interp (llist_ptr_sl' (next x) tl) ml2 /\\\n interp (pts_to_sl (data x) full_perm v) mr)\n (ensures interp (ptr r `Mem.star` llist_ptr_sl (next x) `Mem.star` ptr (data x)) m /\\\n sel_of (vptr r) m == x /\\\n sel_of (llist_cell (next x)) m == tl /\\\n sel_of (vptr (data x)) m == v)\n = intro_ptr_interp r (hide x) ml1;\n llist_sel_interp (next x) tl ml2;\n intro_star (ptr r) (llist_ptr_sl (next x)) ml1 ml2;\n ptr_sel_interp r ml1;\n pts_to_witinv r full_perm;\n join_commutative ml1 ml2;\n let ml = join ml1 ml2 in\n assert (interp (ptr r `Mem.star` llist_ptr_sl (next x)) ml);\n intro_ptr_interp (data x) (hide v) mr;\n intro_star (ptr r `Mem.star` llist_ptr_sl (next x)) (ptr (data x)) ml mr;\n ptr_sel_interp (data x) mr;\n pts_to_witinv (data x) full_perm;\n join_commutative ml mr\n in\n elim_star\n (pts_to_sl r full_perm x `Mem.star` llist_ptr_sl' (next x) tl)\n (pts_to_sl (data x) full_perm v) m;\n Classical.forall_intro (Classical.move_requires\n (elim_star (pts_to_sl r full_perm x) (llist_ptr_sl' (next x) tl)));\n Classical.forall_intro_3 (Classical.move_requires_3 (aux m))", "val elim_nil_lemma (#a: Type0) (ptr: t a) (m: mem)\n : Lemma (requires interp (llist_ptr_sl ptr) m /\\ ptr == null_llist)\n (ensures interp (llist_ptr_sl ptr) m /\\ llist_ptr_sel ptr m == [])\nlet elim_nil_lemma (#a:Type0) (ptr:t a) (m:mem) : Lemma\n (requires interp (llist_ptr_sl ptr) m /\\ ptr == null_llist)\n (ensures interp (llist_ptr_sl ptr) m /\\ llist_ptr_sel ptr m == [])\n = let l' = id_elim_exists (llist_ptr_sl' ptr) m in\n pure_interp (ptr == null_llist) m;\n llist_sel_interp ptr [] m", "val mreference_distinct_sel_disjoint\n (#a:Type0) (#rel1: preorder a) (#rel2: preorder a) (h: mem) (r1: mreference a rel1) (r2:mreference a rel2)\n : Lemma (requires (h `contains` r1 /\\ h `contains` r2 /\\ frameOf r1 == frameOf r2 /\\ as_addr r1 == as_addr r2))\n (ensures (sel h r1 == sel h r2))\nlet mreference_distinct_sel_disjoint #_ #_ #_ h r1 r2 =\n Heap.lemma_distinct_addrs_distinct_preorders ();\n Heap.lemma_distinct_addrs_distinct_mm ();\n Heap.lemma_sel_same_addr (Map.sel h.h (frameOf r1)) (as_ref r1) (as_ref r2)", "val interp_depends_only_on (hp:slprop u#a)\n : Lemma\n (forall (h0:hheap hp) (h1:heap u#a{disjoint h0 h1}).\n interp hp h0 <==> interp hp (join h0 h1))\nlet interp_depends_only_on (hp:slprop u#a) = emp_unit hp", "val interp_depends_only_on (hp:slprop u#a)\n : Lemma\n (forall (h0:hheap hp) (h1:heap u#a{disjoint h0 h1}).\n interp hp h0 <==> interp hp (join h0 h1))\nlet interp_depends_only_on (hp:slprop u#a) = emp_unit hp", "val tree_sel_interp (#a: Type0) (ptr: t a) (t: tree (node a)) (m: mem)\n : Lemma (requires interp (tree_sl' ptr t) m)\n (ensures interp (tree_sl ptr) m /\\ tree_sel_node' ptr m == t)\nlet tree_sel_interp (#a: Type0) (ptr: t a) (t: tree (node a)) (m: mem) : Lemma\n (requires interp (tree_sl' ptr t) m)\n (ensures interp (tree_sl ptr) m /\\ tree_sel_node' ptr m == t)\n = intro_h_exists t (tree_sl' ptr) m;\n tree_sl'_witinv ptr", "val join_commutative (m0 m1:mem)\n : Lemma\n (requires\n disjoint m0 m1)\n (ensures\n (disjoint m0 m1 /\\\n disjoint m1 m0 /\\\n join m0 m1 == join m1 m0))\nlet join_commutative m0 m1 =\n H.join_commutative m0.heap m1.heap", "val intro_cons_lemma_aux (#a: Type0) (ptr1: t a) (x: cell a) (v: a) (l: list (cell a * a)) (m: mem)\n : Lemma\n (requires\n interp (((pts_to_sl ptr1 full_perm x) `Mem.star` (llist_ptr_sl' (next x) l))\n `Mem.star`\n (pts_to_sl (data x) full_perm v))\n m) (ensures interp (llist_ptr_sl' ptr1 ((x, v) :: l)) m)\nlet intro_cons_lemma_aux (#a:Type0) (ptr1:t a)\n (x: cell a) (v:a) (l:list (cell a * a)) (m:mem) : Lemma\n (requires\n interp (pts_to_sl ptr1 full_perm x `Mem.star`\n llist_ptr_sl' (next x) l `Mem.star`\n pts_to_sl (data x) full_perm v)\n m)\n (ensures interp (llist_ptr_sl' ptr1 ((x, v)::l)) m)\n = affine_star\n (pts_to_sl ptr1 full_perm x `Mem.star` llist_ptr_sl' (next x) l)\n (pts_to_sl (data x) full_perm v)\n m;\n affine_star (pts_to_sl ptr1 full_perm x) (llist_ptr_sl' (next x) l) m;\n pts_to_not_null ptr1 full_perm x m;\n emp_unit\n (pts_to_sl ptr1 full_perm x `Mem.star`\n llist_ptr_sl' (next x) l `Mem.star`\n pts_to_sl (data x) full_perm v);\n pure_star_interp\n (pts_to_sl ptr1 full_perm x `Mem.star`\n llist_ptr_sl' (next x) l `Mem.star` pts_to_sl (data x) full_perm v)\n (ptr1 =!= null_llist)\n m", "val join_commutative (m0 m1: mem)\n : Lemma (requires disjoint m0 m1)\n (ensures (disjoint m0 m1 /\\ disjoint m1 m0 /\\ join m0 m1 == join m1 m0))\nlet join_commutative (m0 m1:mem)\n : Lemma\n (requires\n disjoint m0 m1)\n (ensures\n (disjoint m0 m1 /\\\n disjoint m1 m0 /\\\n join m0 m1 == join m1 m0))\n = H.join_commutative m0.heap m1.heap", "val join_associative (m0 m1 m2:mem)\n : Lemma\n (requires\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures\n (disjoint_join m0 m1 m2;\n join m0 (join m1 m2) == join (join m0 m1) m2))\nlet join_associative m0 m1 m2 =\n H.join_associative m0.heap m1.heap m2.heap", "val intro_nil_lemma (a: Type0) (m: mem)\n : Lemma (requires interp (hp_of emp) m)\n (ensures interp (llist_ptr_sl (null_llist #a)) m /\\ llist_ptr_sel (null_llist #a) m == [])\nlet intro_nil_lemma (a:Type0) (m:mem) : Lemma\n (requires interp (hp_of emp) m)\n (ensures interp (llist_ptr_sl (null_llist #a)) m /\\ llist_ptr_sel (null_llist #a) m == [])\n = let ptr:t a = null_llist in\n pure_interp (ptr == null_llist) m;\n let open FStar.Tactics in\n assert (llist_ptr_sl' ptr [] == Mem.pure (ptr == null_llist)) by (norm [delta; zeta; iota]);\n llist_sel_interp ptr [] m", "val pack_ind_lemma (#a: Type0) (r: ref (ref a)) (p: ref a) (v: a) (m: mem)\n : Lemma\n (requires\n interp ((ptr r) `Mem.star` (ptr p)) m /\\ sel_of (vptr r) m == p /\\ sel_of (vptr p) m == v)\n (ensures interp (ind_ptr_sl r) m /\\ sel_of (ind_ptr r) m == v)\nlet pack_ind_lemma (#a:Type0) (r:ref (ref a)) (p:ref a) (v:a) (m:mem)\n : Lemma\n (requires\n interp (ptr r `Mem.star` ptr p) m /\\\n sel_of (vptr r) m == p /\\\n sel_of (vptr p) m == v)\n (ensures interp (ind_ptr_sl r) m /\\ sel_of (ind_ptr r) m == v)\n = intro_pts_to_frame_lemma r p (ptr p) m;\n intro_h_exists p (ind_ptr_sl' r) m;\n let (p', l') = ind_ptr_sel_full r m in\n unpack_ind_lemma r p' l' m;\n pts_to_witinv r full_perm", "val join_associative (m0 m1 m2: mem)\n : Lemma (requires disjoint m1 m2 /\\ disjoint m0 (join m1 m2))\n (ensures\n (disjoint_join m0 m1 m2;\n join m0 (join m1 m2) == join (join m0 m1) m2))\nlet join_associative (m0 m1 m2:mem)\n : Lemma\n (requires\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures\n (disjoint_join m0 m1 m2;\n join m0 (join m1 m2) == join (join m0 m1) m2))\n = H.join_associative m0.heap m1.heap m2.heap", "val vdep_sel_eq (v: vprop) (p: ( (t_of v) -> Tot vprop)) (m: Mem.hmem (vdep_hp v p)) : Lemma\n (\n interp (hp_of v) m /\\\n begin let x = sel_of v m in\n interp (hp_of (p x)) m /\\\n vdep_sel v p m == (| x, sel_of (p x) m |)\n end\n )\nlet vdep_sel_eq\n v p m\n= Classical.forall_intro_2 (Classical.move_requires_2 (fun (m0 m1: mem) -> (join_commutative m0) m1));\n ()", "val reveal_non_empty_lemma (#a: Type) (ptr: t a) (l: list (cell a * a)) (m: mem)\n : Lemma\n (requires interp (llist_ptr_sl ptr) m /\\ llist_ptr_sel_cell ptr m == l /\\ ptr =!= null_llist)\n (ensures Cons? l)\nlet reveal_non_empty_lemma (#a:Type) (ptr:t a) (l:list (cell a * a)) (m:mem) : Lemma\n (requires interp (llist_ptr_sl ptr) m /\\ llist_ptr_sel_cell ptr m == l /\\ ptr =!= null_llist)\n (ensures Cons? l)\n= let l' = id_elim_exists (llist_ptr_sl' ptr) m in\n llist_sel_interp ptr l' m;\n pure_interp (ptr == null_llist) m", "val ptrp_sel_interp (#a:Type0) (r:ref a) (p: perm) (m:mem) : Lemma\n (requires interp (ptrp r p) m)\n (ensures interp (pts_to_sl r p (ptrp_sel r p m)) m)\nlet ptrp_sel_interp #a r p m = pts_to_witinv r p", "val elim_leaf_lemma (#a: Type0) (ptr: t a) (m: mem)\n : Lemma (requires interp (tree_sl ptr) m /\\ ptr == null_t)\n (ensures interp (tree_sl ptr) m /\\ tree_sel ptr m == Spec.Leaf)\nlet elim_leaf_lemma (#a:Type0) (ptr:t a) (m:mem) : Lemma\n (requires interp (tree_sl ptr) m /\\ ptr == null_t)\n (ensures interp (tree_sl ptr) m /\\ tree_sel ptr m == Spec.Leaf)\n = let l' = id_elim_exists (tree_sl' ptr) m in\n pure_interp (ptr == null_t) m;\n tree_sel_interp ptr Spec.Leaf m", "val pts_to_ref_injective\n (#a: Type u#0)\n (r: ref a)\n (p0 p1:perm)\n (v0 v1:a)\n (m:mem)\n : Lemma\n (requires\n interp (pts_to_sl r p0 v0 `Mem.star` pts_to_sl r p1 v1) m)\n (ensures v0 == v1)\nlet pts_to_ref_injective\n (#a: Type u#0)\n (r: ref a)\n (p0 p1:perm)\n (v0 v1:a)\n (m:mem)\n : Lemma\n (requires\n interp (pts_to_sl r p0 v0 `Mem.star` pts_to_sl r p1 v1) m)\n (ensures v0 == v1)\n = let v0' = U.raise_val v0 in\n let v1' = U.raise_val v1 in\n H.pts_to_ref_injective r p0 p1 v0' v1' m;\n raise_val_inj v0 v1", "val pts_to_ref_injective\n (#a: Type u#1)\n (r: ref a)\n (p0 p1:perm)\n (v0 v1:a)\n (m:mem)\n : Lemma\n (requires\n interp (pts_to_sl r p0 v0 `Mem.star` pts_to_sl r p1 v1) m)\n (ensures v0 == v1)\nlet pts_to_ref_injective\n (#a: Type u#1)\n (r: ref a)\n (p0 p1:perm)\n (v0 v1:a)\n (m:mem)\n : Lemma\n (requires\n interp (pts_to_sl r p0 v0 `Mem.star` pts_to_sl r p1 v1) m)\n (ensures v0 == v1)\n = let open Steel.Memory in\n abcd_acbd (hp_of (pts_to_raw r p0 v0))\n (pure (perm_ok p0))\n (hp_of (pts_to_raw r p1 v1))\n (pure (perm_ok p1));\n Mem.affine_star (hp_of (pts_to_raw r p0 v0) `star` hp_of (pts_to_raw r p1 v1))\n (pure (perm_ok p0) `star` pure (perm_ok p1)) m;\n Mem.pts_to_compatible r (Some (Ghost.reveal v0, p0))\n (Some (Ghost.reveal v1, p1))\n m", "val join_preserves_interp (hp: slprop) (m0: hmem hp) (m1: mem{disjoint m0 m1})\n : Lemma (interp hp (join m0 m1)) [SMTPat (interp hp (join m0 m1))]\nlet join_preserves_interp (hp:slprop) (m0:hmem hp) (m1:mem{disjoint m0 m1})\n: Lemma\n (interp hp (join m0 m1))\n [SMTPat (interp hp (join m0 m1))]\n= let open Steel.Memory in\n intro_emp m1;\n intro_star hp emp m0 m1;\n affine_star hp emp (join m0 m1)", "val disjoint_join' (m0 m1 m2: heap u#h)\n : Lemma (requires disjoint m1 m2 /\\ disjoint m0 (join m1 m2))\n (ensures disjoint m0 m1 /\\ disjoint (join m0 m1) m2)\n [SMTPat (disjoint (join m0 m1) m2)]\nlet disjoint_join' (m0 m1 m2:heap u#h)\n : Lemma (requires disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures disjoint m0 m1 /\\ disjoint (join m0 m1) m2)\n [SMTPat (disjoint (join m0 m1) m2)]\n = let aux (a:addr)\n : Lemma (disjoint_addr m0 m1 a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n assert (disjoint m0 m1);\n let aux (a:addr)\n : Lemma (disjoint_addr (join m0 m1) m2 a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n ()", "val disjoint_join' (m0 m1 m2: heap u#h)\n : Lemma (requires disjoint m1 m2 /\\ disjoint m0 (join m1 m2))\n (ensures disjoint m0 m1 /\\ disjoint (join m0 m1) m2)\n [SMTPat (disjoint (join m0 m1) m2)]\nlet disjoint_join' (m0 m1 m2:heap u#h)\n : Lemma (requires disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures disjoint m0 m1 /\\ disjoint (join m0 m1) m2)\n [SMTPat (disjoint (join m0 m1) m2)]\n = let aux (a:addr)\n : Lemma (disjoint_addr m0 m1 a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n assert (disjoint m0 m1);\n let aux (a:addr)\n : Lemma (disjoint_addr (join m0 m1) m2 a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n ()", "val dep_hprop_is_affine0\n (s: slprop)\n (f: (hmem s -> Tot slprop))\n (h h': H.heap)\n (sq': squash (dep_hprop s f h /\\ H.disjoint h h'))\n : Lemma (H.disjoint h h' /\\ dep_hprop s f (H.join h h'))\nlet dep_hprop_is_affine0\n (s: slprop)\n (f: (hmem s -> Tot slprop))\n (h h': H.heap)\n (sq' : squash (dep_hprop s f h /\\ H.disjoint h h'))\n: Lemma\n (H.disjoint h h' /\\ dep_hprop s f (H.join h h'))\n=\n let p2 (h h1 h2: H.heap) : Tot prop =\n interp s (mem_of_heap h1) /\\\n H.disjoint h1 h2 /\\ interp (f (mem_of_heap h1)) (mem_of_heap h2) /\\ h == h1 `H.join` h2\n in\n let p1 (h h1: H.heap) : Tot prop =\n (exists h2 . p2 h h1 h2)\n in\n let h1 =\n FStar.IndefiniteDescription.indefinite_description_ghost H.heap (p1 h)\n in\n let h2 =\n FStar.IndefiniteDescription.indefinite_description_ghost H.heap (p2 h h1)\n in\n H.disjoint_join h' h1 h2;\n assert (H.disjoint h2 h');\n let h2' = H.join h2 h' in\n H.join_commutative h2 h' ;\n assert (h2' == H.join h' h2);\n assert (H.disjoint h1 h2');\n assert (mem_of_heap h2' == mem_of_heap h2 `join` mem_of_heap h');\n interp_depends_only_on (f (mem_of_heap h1));\n assert (interp (f (mem_of_heap h1)) (mem_of_heap h2'));\n H.join_commutative h1 h2;\n H.join_associative h' h2 h1;\n H.join_commutative h' h;\n H.join_commutative h2' h1;\n assert (H.join h h' == h1 `H.join` h2')", "val dep_hprop_is_affine0\n (s: slprop)\n (f: (hmem s -> Tot slprop))\n (h h': H.heap)\n (sq': squash (dep_hprop s f h /\\ H.disjoint h h'))\n : Lemma (H.disjoint h h' /\\ dep_hprop s f (H.join h h'))\nlet dep_hprop_is_affine0\n (s: slprop)\n (f: (hmem s -> Tot slprop))\n (h h': H.heap)\n (sq' : squash (dep_hprop s f h /\\ H.disjoint h h'))\n: Lemma\n (H.disjoint h h' /\\ dep_hprop s f (H.join h h'))\n=\n let p2 (h h1 h2: H.heap) : Tot prop =\n interp s (mem_of_heap h1) /\\\n H.disjoint h1 h2 /\\ interp (f (mem_of_heap h1)) (mem_of_heap h2) /\\ h == h1 `H.join` h2\n in\n let p1 (h h1: H.heap) : Tot prop =\n (exists h2 . p2 h h1 h2)\n in\n let h1 =\n FStar.IndefiniteDescription.indefinite_description_ghost H.heap (p1 h)\n in\n let h2 =\n FStar.IndefiniteDescription.indefinite_description_ghost H.heap (p2 h h1)\n in\n H.disjoint_join h' h1 h2;\n assert (H.disjoint h2 h');\n let h2' = H.join h2 h' in\n H.join_commutative h2 h' ;\n assert (h2' == H.join h' h2);\n assert (H.disjoint h1 h2');\n assert (mem_of_heap h2' == mem_of_heap h2 `join` mem_of_heap h');\n interp_depends_only_on (f (mem_of_heap h1));\n assert (interp (f (mem_of_heap h1)) (mem_of_heap h2'));\n H.join_commutative h1 h2;\n H.join_associative h' h2 h1;\n H.join_commutative h' h;\n H.join_commutative h2' h1;\n assert (H.join h h' == h1 `H.join` h2')", "val dep_hprop_is_affine1 (s: slprop) (f: (hmem s -> Tot slprop)) (h0 h1: H.heap)\n : Lemma\n ((dep_hprop s f h0 /\\ H.disjoint h0 h1) ==> (H.disjoint h0 h1 /\\ dep_hprop s f (H.join h0 h1)))\nlet dep_hprop_is_affine1\n (s: slprop)\n (f: (hmem s -> Tot slprop))\n (h0 h1: H.heap)\n: Lemma\n ((dep_hprop s f h0 /\\ H.disjoint h0 h1) ==> (H.disjoint h0 h1 /\\ dep_hprop s f (H.join h0 h1)))\n= impl_intro_gen (dep_hprop_is_affine0 s f h0 h1)", "val dep_hprop_is_affine1 (s: slprop) (f: (hmem s -> Tot slprop)) (h0 h1: H.heap)\n : Lemma\n ((dep_hprop s f h0 /\\ H.disjoint h0 h1) ==> (H.disjoint h0 h1 /\\ dep_hprop s f (H.join h0 h1)))\nlet dep_hprop_is_affine1\n (s: slprop)\n (f: (hmem s -> Tot slprop))\n (h0 h1: H.heap)\n: Lemma\n ((dep_hprop s f h0 /\\ H.disjoint h0 h1) ==> (H.disjoint h0 h1 /\\ dep_hprop s f (H.join h0 h1)))\n= impl_intro_gen (dep_hprop_is_affine0 s f h0 h1)", "val memP_list_in_listP_implies_memP (#a : Type) (x : a) (ls0 ls1 : list a) :\n Lemma\n (requires (\n memP x ls0 /\\\n list_in_listP ls0 ls1))\n (ensures (memP x ls1))\nlet rec memP_list_in_listP_implies_memP #a x ls0 ls1 =\n match ls0 with\n | [] -> ()\n | x' :: ls0' ->\n if FStar.IndefiniteDescription.strong_excluded_middle (x == x') then ()\n else memP_list_in_listP_implies_memP x ls0' ls1", "val elim_llist_cons (#a:Type0) (ptr:t a)\n : Steel (cell a)\n (llist_ptr ptr)\n (fun c -> vptr ptr `star` vptr (data c) `star` llist_ptr (next c))\n (requires fun h -> ptr =!= null_llist)\n (ensures fun h0 c h1 ->\n Cons? (v_ptrlist ptr h0) /\\\n sel ptr h1 == c /\\\n sel (data c) h1 == L.hd (v_ptrlist ptr h0) /\\\n v_ptrlist (next c) h1 == L.tl (v_ptrlist ptr h0)\n )\nlet elim_llist_cons (#a:Type0) (ptr:t a)\n : Steel (cell a)\n (llist_ptr ptr)\n (fun c -> vptr ptr `star` vptr (data c) `star` llist_ptr (next c))\n (requires fun h -> ptr =!= null_llist)\n (ensures fun h0 c h1 ->\n Cons? (v_ptrlist ptr h0) /\\\n sel ptr h1 == c /\\\n sel (data c) h1 == L.hd (v_ptrlist ptr h0) /\\\n v_ptrlist (next c) h1 == L.tl (v_ptrlist ptr h0)\n )\n = change_slprop_rel (llist_ptr ptr) (llist_cell ptr) (fun x y -> x == datas y) (fun _ -> ());\n let h = get () in\n let c = elim_cons_cell ptr in\n change_slprop_rel (llist_cell (next c)) (llist_ptr (next c)) (fun x y -> datas x == y) (fun _ -> ());\n return c", "val intro_llist_cons (#a:Type0) (ptr1 ptr2:t a)\n : Steel unit (vptr ptr1 `star` llist ptr2)\n (fun _ -> llist ptr1)\n (requires fun h -> next (sel ptr1 h) == ptr2)\n (ensures fun h0 _ h1 -> v_llist ptr1 h1 == (data (sel ptr1 h0)) :: v_llist ptr2 h0)\nlet intro_llist_cons\n #a ptr1 ptr2\n=\n llist0_of_llist ptr2;\n let n = nllist_of_llist0 ptr2 in\n (* set the fuel of the new cons cell *)\n let c = read ptr1 in\n let c' = {c with tail_fuel = n} in\n write ptr1 c' ;\n (* actually cons the cell *)\n vptr_not_null ptr1;\n intro_vdep\n (vptr ptr1)\n (nllist a n ptr2)\n (llist_vdep ptr1);\n intro_vrewrite\n (vptr ptr1 `vdep` llist_vdep ptr1)\n (llist_vrewrite ptr1);\n change_equal_slprop\n ((vptr ptr1 `vdep` llist_vdep ptr1) `vrewrite` llist_vrewrite ptr1)\n (llist0 ptr1);\n llist_of_llist0 ptr1", "val intro_llist_cons (#a:Type0) (ptr1 ptr2:t a)\n : Steel unit (vptr ptr1 `star` llist ptr2)\n (fun _ -> llist ptr1)\n (requires fun h -> next (sel ptr1 h) == ptr2)\n (ensures fun h0 _ h1 -> v_llist ptr1 h1 == (data (sel ptr1 h0)) :: v_llist ptr2 h0)\nlet intro_llist_cons\n #a ptr1 ptr2\n=\n llist0_of_llist ptr2;\n let n = nllist_of_llist0 ptr2 in\n (* set the fuel of the new cons cell *)\n let c = read ptr1 in\n let c' = {c with tail_fuel = n} in\n write ptr1 c' ;\n (* actually cons the cell *)\n vptr_not_null ptr1;\n intro_vdep\n (vptr ptr1)\n (nllist a n ptr2)\n (llist_vdep ptr1);\n intro_vrewrite\n (vptr ptr1 `vdep` llist_vdep ptr1)\n (llist_vrewrite ptr1);\n change_equal_slprop\n ((vptr ptr1 `vdep` llist_vdep ptr1) `vrewrite` llist_vrewrite ptr1)\n (llist0 ptr1);\n llist_of_llist0 ptr1", "val forall_x_mem_in_tl (#a: eqtype) (#f: cmp a) (s1 s2: mset a f)\n : Lemma (requires (forall (x: a). mem x s1 == mem x s2) /\\ Cons? s1 /\\ Cons? s2)\n (ensures forall (x: a). mem x (tl s1) == mem x (tl s2))\nlet forall_x_mem_in_tl (#a:eqtype) (#f:cmp a) (s1 s2:mset a f)\n : Lemma\n (requires\n (forall (x:a). mem x s1 == mem x s2) /\\\n Cons? s1 /\\ Cons? s2)\n (ensures\n forall (x:a). mem x (tl s1) == mem x (tl s2))\n = let aux (x:a)\n : Lemma (mem x (tl s1) == mem x (tl s2))\n = match s1, s2 with\n | (x1, _)::_, (x2, _)::_ ->\n if x1 = x2 then begin\n if x1 = x then (mem_hd_in_tl s1; mem_hd_in_tl s2)\n end\n else if f x1 x2 then mem_elt_lt_hd x1 s2\n else mem_elt_lt_hd x2 s1\n in\n Classical.forall_intro aux", "val ghost_ptrp_sel_interp (#a:Type0) (r:ghost_ref a) (p: perm) (m:mem) : Lemma\n (requires interp (ghost_ptrp r p) m)\n (ensures interp (ghost_pts_to_sl r p (ghost_ptrp_sel r p m)) m)\nlet ghost_ptrp_sel_interp #a r p m = ghost_pts_to_witinv r p", "val sel_lemma (#a:_) (#pcm:_) (r:ref a pcm) (m:full_hheap (ptr r))\n : Lemma (interp (pts_to r (sel r m)) m)\nlet sel_lemma (#a:_) (#pcm:_) (r:ref a pcm) (m:full_hheap (ptr r))\n : Lemma (interp (pts_to r (sel r m)) m)\n = let Ref _ _ _ v = select_addr m (Addr?._0 r) in\n assert (sel r m == v);\n compatible_refl pcm v", "val sel_lemma (#a:_) (#pcm:_) (r:ref a pcm) (m:full_hheap (ptr r))\n : Lemma (interp (pts_to r (sel r m)) m)\nlet sel_lemma (#a:_) (#pcm:_) (r:ref a pcm) (m:full_hheap (ptr r))\n : Lemma (interp (pts_to r (sel r m)) m)\n = let Ref _ _ _ v = select_addr m (Addr?._0 r) in\n assert (sel r m == v);\n compatible_refl pcm v", "val sel_concat1 : h0:heap -> \n\t\t h1:heap{consistent h0 h1} -> \n\t\t a:Type ->\n\t\t r:ref a{contains h0 r /\\ ~(contains h1 r)} -> \n\t\t Lemma (requires (True))\n\t\t (ensures (sel (concat h0 h1) r == sel h0 r))\n\t [SMTPat (sel (concat h0 h1) r)]\nlet sel_concat1 h0 h1 a r = \n match snd h0 r with\n | Some v -> \n match snd h1 r with\n | None -> ()\n | Some v' -> assert (dfst v == dfst v')", "val v_ind_llist\n (#a: Type0)\n (#p: vprop)\n (r: ref (t a))\n (h: rmem p {FStar.Tactics.with_tactic selector_tactic (can_be_split p (ind_llist r) /\\ True)})\n : GTot (list a)\nlet v_ind_llist (#a:Type0) (#p:vprop) (r:ref (t a))\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (ind_llist r) /\\ True)}) : GTot (list a)\n = h (ind_llist r)", "val intro_llist_cons (#a:Type0) (ptr1 ptr2:t a) (r:ref a)\n : Steel unit (vptr ptr1 `star` vptr r `star` llist_ptr ptr2)\n (fun _ -> llist_ptr ptr1)\n (requires fun h -> data (sel ptr1 h) == r /\\ next (sel ptr1 h) == ptr2)\n (ensures fun h0 _ h1 -> v_ptrlist ptr1 h1 == (sel r h0) :: v_ptrlist ptr2 h0)\nlet intro_llist_cons (#a:Type0) (ptr1 ptr2:t a) (r:ref a)\n : Steel unit (vptr ptr1 `star` vptr r `star` llist_ptr ptr2)\n (fun _ -> llist_ptr ptr1)\n (requires fun h -> data (sel ptr1 h) == r /\\ next (sel ptr1 h) == ptr2)\n (ensures fun h0 _ h1 -> v_ptrlist ptr1 h1 == (sel r h0) :: v_ptrlist ptr2 h0)\n = let x = gget (vptr ptr1) in\n let v = gget (vptr r) in\n let l = gget (llist_ptr ptr2) in\n change_slprop (vptr ptr1 `star` llist_ptr ptr2 `star` vptr r) (llist_ptr ptr1)\n ((reveal x, reveal l), reveal v)\n (reveal v :: l)\n (fun m ->\n intro_cons_lemma ptr1 x v l m)", "val lemma_heap_equality_upd_with_sel\n (#a:Type) (#rel:preorder a) (h:mem) (r:mreference a rel)\n :Lemma (requires (h `contains` r))\n (ensures (upd h r (sel h r) == h))\nlet lemma_heap_equality_upd_with_sel #_ #_ h r =\n let h' = upd h r (sel h r) in\n Heap.lemma_heap_equality_upd_with_sel (Map.sel h.h (frameOf r)) (as_ref r);\n assert (Map.equal h.h h'.h)", "val intro_leaf_lemma (a: Type0) (m: mem)\n : Lemma (requires interp (hp_of emp) m)\n (ensures interp (tree_sl (null_t #a)) m /\\ tree_sel (null_t #a) m == Spec.Leaf)\nlet intro_leaf_lemma (a:Type0) (m:mem) : Lemma\n (requires interp (hp_of emp) m)\n (ensures interp (tree_sl (null_t #a)) m /\\ tree_sel (null_t #a) m == Spec.Leaf)\n = let ptr:t a = null_t in\n pure_interp (ptr == null_t) m;\n let open FStar.Tactics in\n assert (tree_sl' ptr Spec.Leaf == Mem.pure (ptr == null_t)) by (norm [delta; zeta; iota]);\n tree_sel_interp ptr Spec.Leaf m", "val mprop_preservation_of_hprop_preservation (p: slprop) (m0 m1: mem)\n : Lemma (requires (forall (hp: H.hprop p). hp (heap_of_mem m0) == hp (heap_of_mem m1)))\n (ensures (forall (mp: mprop p). mp (core_mem m0) == mp (core_mem m1)))\nlet mprop_preservation_of_hprop_preservation\n (p:slprop) (m0 m1:mem)\n : Lemma\n (requires (forall (hp:H.hprop p). hp (heap_of_mem m0) == hp (heap_of_mem m1)))\n (ensures (forall (mp:mprop p). mp (core_mem m0) == mp (core_mem m1)))\n = let aux (mp:mprop p)\n : Lemma (mp (core_mem m0) == mp (core_mem m1))\n [SMTPat()]\n = assert (as_hprop p mp (heap_of_mem m0) == as_hprop p mp (heap_of_mem m1))\n in\n ()", "val mprop_preservation_of_hprop_preservation (p: slprop) (m0 m1: mem)\n : Lemma (requires (forall (hp: H.hprop p). hp (heap_of_mem m0) == hp (heap_of_mem m1)))\n (ensures (forall (mp: mprop p). mp (core_mem m0) == mp (core_mem m1)))\nlet mprop_preservation_of_hprop_preservation\n (p:slprop) (m0 m1:mem)\n : Lemma\n (requires (forall (hp:H.hprop p). hp (heap_of_mem m0) == hp (heap_of_mem m1)))\n (ensures (forall (mp:mprop p). mp (core_mem m0) == mp (core_mem m1)))\n = let aux (mp:mprop p)\n : Lemma (mp (core_mem m0) == mp (core_mem m1))\n [SMTPat()]\n = assert (as_hprop p mp (heap_of_mem m0) == as_hprop p mp (heap_of_mem m1))\n in\n ()", "val lemma_node_not_null (#a: Type) (ptr: t a) (t: tree a) (m: mem)\n : Lemma (requires interp (tree_sl ptr) m /\\ tree_sel ptr m == t /\\ Spec.Node? t)\n (ensures ptr =!= null_t)\nlet lemma_node_not_null (#a:Type) (ptr:t a) (t:tree a) (m:mem) : Lemma\n (requires interp (tree_sl ptr) m /\\ tree_sel ptr m == t /\\ Spec.Node? t)\n (ensures ptr =!= null_t)\n = let t' = id_elim_exists (tree_sl' ptr) m in\n assert (interp (tree_sl' ptr t') m);\n tree_sel_interp ptr t' m;\n match reveal t' with\n | Spec.Node data left right ->\n Mem.affine_star\n (pts_to_sl ptr full_perm (hide data) `Mem.star` tree_sl' (get_left data) left)\n (tree_sl' (get_right data) right) m;\n Mem.affine_star (pts_to_sl ptr full_perm data) (tree_sl' (get_left data) left) m;\n pts_to_not_null ptr full_perm data m", "val join_associative2 (m0 m1 m2: heap)\n : Lemma (requires disjoint m0 m1 /\\ disjoint (join m0 m1) m2)\n (ensures\n disjoint m1 m2 /\\ disjoint m0 (join m1 m2) /\\\n (join m0 (join m1 m2)) `mem_equiv` (join (join m0 m1) m2))\n [SMTPat (join (join m0 m1) m2)]\nlet join_associative2 (m0 m1 m2:heap)\n : Lemma\n (requires\n disjoint m0 m1 /\\\n disjoint (join m0 m1) m2)\n (ensures\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) /\\\n join m0 (join m1 m2) `mem_equiv` join (join m0 m1) m2)\n [SMTPat (join (join m0 m1) m2)]\n = disjoint_join m2 m0 m1;\n join_commutative (join m0 m1) m2;\n join_associative m2 m0 m1", "val join_associative2 (m0 m1 m2: heap)\n : Lemma (requires disjoint m0 m1 /\\ disjoint (join m0 m1) m2)\n (ensures\n disjoint m1 m2 /\\ disjoint m0 (join m1 m2) /\\\n (join m0 (join m1 m2)) `mem_equiv` (join (join m0 m1) m2))\n [SMTPat (join (join m0 m1) m2)]\nlet join_associative2 (m0 m1 m2:heap)\n : Lemma\n (requires\n disjoint m0 m1 /\\\n disjoint (join m0 m1) m2)\n (ensures\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) /\\\n join m0 (join m1 m2) `mem_equiv` join (join m0 m1) m2)\n [SMTPat (join (join m0 m1) m2)]\n = disjoint_join m2 m0 m1;\n join_commutative (join m0 m1) m2;\n join_associative m2 m0 m1", "val gsame_elementsp_implies_remove_peer_unchanged_pred_s\n (#idc : idconfig) (h0 h1 : mem) (ll : list (peer_p idc)) :\n Lemma (requires (\n let dt = idc_stateful_peer_p idc in\n LL.gsame_elementsp #dt ll h0 h1))\n (ensures (M.gfor_allP (remove_peer_unchanged_pred_s idc h0 h1) ll))\nlet rec gsame_elementsp_implies_remove_peer_unchanged_pred_s #idc h0 h1 ll =\n let dt = idc_stateful_peer_p idc in\n match ll with\n | [] -> ()\n | x :: ll' -> gsame_elementsp_implies_remove_peer_unchanged_pred_s #idc h0 h1 ll'", "val elim_vptr_lemma (#a: Type) (r: ref a) (p: perm) (v: erased a) (m: mem)\n : Lemma (requires interp (ptrp r p) m /\\ ptrp_sel r p m == reveal v)\n (ensures interp (pts_to_sl r p v) m)\nlet elim_vptr_lemma (#a:Type) (r:ref a) (p: perm) (v:erased a) (m:mem) : Lemma\n (requires interp (ptrp r p) m /\\ ptrp_sel r p m == reveal v)\n (ensures interp (pts_to_sl r p v) m)\n = Mem.elim_h_exists (pts_to_sl r p) m;\n pts_to_witinv r p", "val reveal_non_empty_lemma (#a: Type) (ptr: t a) (t: tree (node a)) (m: mem)\n : Lemma (requires interp (tree_sl ptr) m /\\ tree_sel_node ptr m == t /\\ ptr =!= null_t)\n (ensures Spec.Node? t)\nlet reveal_non_empty_lemma (#a:Type) (ptr:t a) (t:tree (node a)) (m:mem) : Lemma\n (requires interp (tree_sl ptr) m /\\ tree_sel_node ptr m == t /\\ ptr =!= null_t)\n (ensures Spec.Node? t)\n= let l' = id_elim_exists (tree_sl' ptr) m in\n tree_sel_interp ptr l' m;\n pure_interp (ptr == null_t) m", "val join_associative' (m0 m1 m2: heap)\n : Lemma (requires disjoint m1 m2 /\\ disjoint m0 (join m1 m2))\n (ensures\n (disjoint_join m0 m1 m2;\n (join m0 (join m1 m2)) `mem_equiv` (join (join m0 m1) m2)))\n [SMTPatOr [[SMTPat (join m0 (join m1 m2))]; [SMTPat (join (join m0 m1) m2)]]]\nlet join_associative' (m0 m1 m2:heap)\n : Lemma\n (requires\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures\n (disjoint_join m0 m1 m2;\n join m0 (join m1 m2) `mem_equiv` join (join m0 m1) m2))\n [SMTPatOr\n [[SMTPat (join m0 (join m1 m2))];\n [SMTPat (join (join m0 m1) m2)]]]\n = disjoint_join m0 m1 m2;\n let l = join m0 (join m1 m2) in\n let r = join (join m0 m1) m2 in\n let aux (a:addr)\n : Lemma (l a == r a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n ()", "val join_associative' (m0 m1 m2: heap)\n : Lemma (requires disjoint m1 m2 /\\ disjoint m0 (join m1 m2))\n (ensures\n (disjoint_join m0 m1 m2;\n (join m0 (join m1 m2)) `mem_equiv` (join (join m0 m1) m2)))\n [SMTPatOr [[SMTPat (join m0 (join m1 m2))]; [SMTPat (join (join m0 m1) m2)]]]\nlet join_associative' (m0 m1 m2:heap)\n : Lemma\n (requires\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures\n (disjoint_join m0 m1 m2;\n join m0 (join m1 m2) `mem_equiv` join (join m0 m1) m2))\n [SMTPatOr\n [[SMTPat (join m0 (join m1 m2))];\n [SMTPat (join (join m0 m1) m2)]]]\n = disjoint_join m0 m1 m2;\n let l = join m0 (join m1 m2) in\n let r = join (join m0 m1) m2 in\n let aux (a:addr)\n : Lemma (l a == r a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n ()", "val intro_ptr_frame_lemma (#a: Type0) (r: ref a) (x: a) (frame: slprop) (m: mem)\n : Lemma (requires interp ((pts_to_sl r full_perm x) `Mem.star` frame) m)\n (ensures interp ((ptr r) `Mem.star` frame) m /\\ sel_of (vptr r) m == x)\nlet intro_ptr_frame_lemma (#a:Type0) (r:ref a) (x:a) (frame:slprop) (m:mem)\n : Lemma (requires interp (pts_to_sl r full_perm x `Mem.star` frame) m)\n (ensures interp (ptr r `Mem.star` frame) m /\\ sel_of (vptr r) m == x)\n = let aux (m:mem) (ml mr:mem) : Lemma\n (requires disjoint ml mr /\\ m == join ml mr /\\\n interp (pts_to_sl r full_perm x) ml /\\ interp frame mr)\n (ensures interp (ptr r `Mem.star` frame) m /\\\n sel_of (vptr r) m == x)\n = intro_ptr_interp r (hide x) ml;\n intro_star (ptr r) frame ml mr;\n ptr_sel_interp r ml;\n pts_to_witinv r full_perm\n in\n elim_star (pts_to_sl r full_perm x) frame m;\n Classical.forall_intro_2 (Classical.move_requires_2 (aux m))", "val pts_to_inj\n (#elt: Type0) (a: array elt)\n (p1: P.perm)\n (s1: Seq.seq elt)\n (p2: P.perm)\n (s2: Seq.seq elt)\n (m: mem)\n: Lemma\n (requires (\n interp (hp_of (pts_to a p1 s1)) m /\\\n interp (hp_of (pts_to a p2 s2)) m\n ))\n (ensures (\n s1 == s2\n ))\nlet pts_to_inj a p1 s1 p2 s2 =\n H.pts_to_inj a p1 (seq_map raise s1) p2 (seq_map raise s2)", "val lemma_heap_equality_upd_with_sel\n (#a:Type) (#rel:preorder a) (h:heap) (r:mref a rel)\n :Lemma (requires (h `contains` r))\n (ensures (upd h r (sel h r) == h))\nlet lemma_heap_equality_upd_with_sel #a #rel h r =\n let h' = upd h r (sel h r) in\n let Some (| _, _, _, _ |) = h.memory r.addr in\n assert (equal h h')", "val ind_ptr_sel_full (#a: Type0) (r: ref (ref a)) : selector (ref a * a) (ind_ptr_sl r)\nlet ind_ptr_sel_full (#a:Type0) (r:ref (ref a)) : selector (ref a * a) (ind_ptr_sl r) =\n Classical.forall_intro_2 (ind_ptr_sel_depends_only_on r);\n Classical.forall_intro (ind_ptr_sel_depends_only_on_core r);\n ind_ptr_sel' r", "val append_mem_forall: #a:eqtype -> l1:list a\n -> l2:list a\n -> Lemma (requires True)\n (ensures (forall a. mem a (l1@l2) = (mem a l1 || mem a l2)))\nlet rec append_mem_forall #a l1 l2 = match l1 with\n | [] -> ()\n | hd::tl -> append_mem_forall tl l2", "val memP_append_or (#a: Type) (x: a) (l0 l1: list a)\n : Lemma (ensures (List.Tot.memP x (l0 @ l1) <==> (List.Tot.memP x l0 \\/ List.Tot.memP x l1)))\n (decreases l0)\nlet rec memP_append_or (#a:Type) (x:a) (l0 l1:list a)\n : Lemma (ensures (List.Tot.memP x (l0 @ l1) <==>\n (List.Tot.memP x l0 \\/ List.Tot.memP x l1)))\n (decreases l0)\n = match l0 with\n | [] -> ()\n | _::tl -> memP_append_or x tl l1", "val memP_append_or (#a: Type) (x: a) (l0 l1: list a)\n : Lemma (ensures (List.Tot.memP x (l0 @ l1) <==> (List.Tot.memP x l0 \\/ List.Tot.memP x l1)))\n (decreases l0)\nlet rec memP_append_or (#a:Type) (x:a) (l0 l1:list a)\n : Lemma (ensures (List.Tot.memP x (l0 @ l1) <==>\n (List.Tot.memP x l0 \\/ List.Tot.memP x l1)))\n (decreases l0)\n = match l0 with\n | [] -> ()\n | _::tl -> memP_append_or x tl l1", "val memP_append_or (#a: Type) (x: a) (l0 l1: list a)\n : Lemma (ensures (List.Tot.memP x (l0 @ l1) <==> (List.Tot.memP x l0 \\/ List.Tot.memP x l1)))\n (decreases l0)\nlet rec memP_append_or (#a:Type) (x:a) (l0 l1:list a)\n : Lemma (ensures (List.Tot.memP x (l0 @ l1) <==>\n (List.Tot.memP x l0 \\/ List.Tot.memP x l1)))\n (decreases l0)\n = match l0 with\n | [] -> ()\n | _::tl -> memP_append_or x tl l1", "val mem_equiv_eq (m0 m1: heap)\n : Lemma (requires m0 `mem_equiv` m1) (ensures m0 == m1) [SMTPat (m0 `mem_equiv` m1)]\nlet mem_equiv_eq (m0 m1:heap)\n : Lemma\n (requires\n m0 `mem_equiv` m1)\n (ensures\n m0 == m1)\n [SMTPat (m0 `mem_equiv` m1)]\n = F.extensionality _ _ m0 m1", "val mem_equiv_eq (m0 m1: heap)\n : Lemma (requires m0 `mem_equiv` m1) (ensures m0 == m1) [SMTPat (m0 `mem_equiv` m1)]\nlet mem_equiv_eq (m0 m1:heap)\n : Lemma\n (requires\n m0 `mem_equiv` m1)\n (ensures\n m0 == m1)\n [SMTPat (m0 `mem_equiv` m1)]\n = F.extensionality _ _ m0 m1", "val ptrs_of_mem (m: interop_heap) : l: list b8 {list_disjoint_or_eq l}\nlet ptrs_of_mem (m:interop_heap) : l:list b8{list_disjoint_or_eq l} = InteropHeap?.ptrs m", "val pts_to_inj\n (#elt: Type u#1) (a: array elt)\n (p1: P.perm)\n (s1: Seq.seq elt)\n (p2: P.perm)\n (s2: Seq.seq elt)\n (m: mem)\n: Lemma\n (requires (\n interp (hp_of (pts_to a p1 s1)) m /\\\n interp (hp_of (pts_to a p2 s2)) m\n ))\n (ensures (\n s1 == s2\n ))\nlet pts_to_inj\n a p1 s1 p2 s2 m\n=\n Classical.forall_intro reveal_pure;\n pure_star_interp'\n (hp_of (R.pts_to (ptr_of a).base (mk_carrier (US.v (ptr_of a).base_len) (ptr_of a).offset s1 p1)))\n (\n valid_perm (US.v (ptr_of a).base_len) (ptr_of a).offset (Seq.length s1) p1 /\\\n Seq.length s1 == length a\n )\n m;\n pure_star_interp'\n (hp_of (R.pts_to (ptr_of a).base (mk_carrier (US.v (ptr_of a).base_len) (ptr_of a).offset s2 p2)))\n (\n valid_perm (US.v (ptr_of a).base_len) (ptr_of a).offset (Seq.length s2) p2 /\\\n Seq.length s2 == length a\n )\n m;\n pts_to_join\n (ptr_of a).base\n (mk_carrier (US.v (ptr_of a).base_len) (ptr_of a).offset s1 p1)\n (mk_carrier (US.v (ptr_of a).base_len) (ptr_of a).offset s2 p2)\n m;\n mk_carrier_joinable (US.v (ptr_of a).base_len) (ptr_of a).offset s1 p1 s2 p2", "val list_forallp_mem (#t: eqtype) (p: (t -> GTot Type0)) (l: list t)\n : Lemma (list_forallp p l <==> (forall x. L.mem x l ==> p x))\nlet rec list_forallp_mem (#t: eqtype) (p: t -> GTot Type0) (l: list t) : Lemma\n (list_forallp p l <==> (forall x . L.mem x l ==> p x))\n= match l with\n | [] -> ()\n | _ :: q -> list_forallp_mem p q", "val join (m0: mem u#h) (m1: mem u#h {disjoint m0 m1}) : mem u#h\nlet join (m0:mem u#h) (m1:mem u#h{disjoint m0 m1}) : mem u#h\n= {\n ctr = m0.ctr;\n heap = H.join m0.heap m1.heap;\n locks = m0.locks\n }", "val llist_fragment_head_eq_cons\n (#a: Type)\n (l: Ghost.erased (list a))\n (phead: ref (ccell_ptrvalue a))\n (head: ccell_ptrvalue a)\n : Lemma (requires (Cons? (Ghost.reveal l)))\n (ensures\n (llist_fragment_head l phead head ==\n vbind ((ccell_is_lvalue head)\n `star`\n ((ccell head) `vrefine` (llist_fragment_head_data_refine (L.hd (Ghost.reveal l)))))\n (ref (ccell_ptrvalue a) & ccell_ptrvalue a)\n (llist_fragment_head_payload head\n (L.hd (Ghost.reveal l))\n (llist_fragment_head (L.tl (Ghost.reveal l))))))\nlet llist_fragment_head_eq_cons\n (#a: Type) (l: Ghost.erased (list a)) (phead: ref (ccell_ptrvalue a)) (head: ccell_ptrvalue a)\n: Lemma\n (requires (Cons? (Ghost.reveal l)))\n (ensures (\n llist_fragment_head l phead head ==\n vbind\n (ccell_is_lvalue head `star` (ccell head `vrefine` llist_fragment_head_data_refine (L.hd (Ghost.reveal l))))\n (ref (ccell_ptrvalue a) & ccell_ptrvalue a)\n (llist_fragment_head_payload head (L.hd (Ghost.reveal l)) (llist_fragment_head (L.tl (Ghost.reveal l))))\n ))\n= assert_norm\n (llist_fragment_head l phead head == (\n if Nil? l\n then vconst (phead, head)\n else\n vbind\n (ccell_is_lvalue head `star` (ccell head `vrefine` llist_fragment_head_data_refine (L.hd (Ghost.reveal l))))\n (ref (ccell_ptrvalue a) & ccell_ptrvalue a)\n (llist_fragment_head_payload head (L.hd (Ghost.reveal l)) (llist_fragment_head (L.tl (Ghost.reveal l))))\n ))", "val intro_vptr_lemma (#a: Type) (r: ref a) (p: perm) (v: erased a) (m: mem)\n : Lemma (requires interp (pts_to_sl r p v) m)\n (ensures interp (ptrp r p) m /\\ ptrp_sel r p m == reveal v)\nlet intro_vptr_lemma (#a:Type) (r:ref a) (p: perm) (v:erased a) (m:mem) : Lemma\n (requires interp (pts_to_sl r p v) m)\n (ensures interp (ptrp r p) m /\\ ptrp_sel r p m == reveal v)\n = Mem.intro_h_exists (reveal v) (pts_to_sl r p) m;\n pts_to_witinv r p", "val append_mem: #t:eqtype -> l1:list t\n -> l2:list t\n -> a:t\n -> Lemma (requires True)\n (ensures (mem a (l1@l2) = (mem a l1 || mem a l2)))\nlet rec append_mem #t l1 l2 a = match l1 with\n | [] -> ()\n | hd::tl -> append_mem tl l2 a", "val join (m0:mem u#h) (m1:mem u#h{disjoint m0 m1}) : mem u#h\nlet join m0 m1 = {\n ctr = m0.ctr;\n heap = H.join m0.heap m1.heap;\n locks = m0.locks\n}", "val disjoint_join (h0 h1 h2:heap)\n : Lemma (disjoint h1 h2 /\\\n disjoint h0 (join h1 h2) ==>\n disjoint h0 h1 /\\\n disjoint h0 h2 /\\\n disjoint (join h0 h1) h2 /\\\n disjoint (join h0 h2) h1)\nlet disjoint_join (m0 m1 m2:heap)\n : Lemma (disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) ==>\n disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\n [SMTPat (disjoint m0 (join m1 m2))]\n = let aux ()\n : Lemma\n (requires disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\n [SMTPat ()]\n = disjoint_join' m0 m1 m2;\n join_commutative m0 m1;\n disjoint_join' m0 m2 m1\n in\n ()", "val disjoint_join (h0 h1 h2:heap)\n : Lemma (disjoint h1 h2 /\\\n disjoint h0 (join h1 h2) ==>\n disjoint h0 h1 /\\\n disjoint h0 h2 /\\\n disjoint (join h0 h1) h2 /\\\n disjoint (join h0 h2) h1)\nlet disjoint_join (m0 m1 m2:heap)\n : Lemma (disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) ==>\n disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\n [SMTPat (disjoint m0 (join m1 m2))]\n = let aux ()\n : Lemma\n (requires disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\n [SMTPat ()]\n = disjoint_join' m0 m1 m2;\n join_commutative m0 m1;\n disjoint_join' m0 m2 m1\n in\n ()", "val Selectors.PtrLList.v_full = \n r: Steel.Reference.ref (Steel.Reference.ref a) ->\n h:\n Steel.Effect.Common.rmem p\n { FStar.Tactics.Effect.with_tactic Steel.Effect.Common.selector_tactic\n (Steel.Effect.Common.can_be_split p (Selectors.PtrLList.ind_ptr_full r) /\\ Prims.l_True)\n }\n -> Prims.GTot\n (Steel.Effect.Common.normal (Steel.Effect.Common.t_of (Selectors.PtrLList.ind_ptr_full r)))\nlet v_full (#a:Type0) (#p:vprop) (r:ref (ref a))\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (ind_ptr_full r) /\\ True)})\n = h (ind_ptr_full r)", "val intro_ptr_interp (#a: Type0) (r: ref a) (v: erased a) (m: mem)\n : Lemma (requires interp (pts_to_sl r full_perm v) m) (ensures interp (ptr r) m)\nlet intro_ptr_interp (#a:Type0) (r:ref a) (v:erased a) (m:mem) : Lemma\n (requires interp (pts_to_sl r full_perm v) m)\n (ensures interp (ptr r) m)\n= intro_ptrp_interp r full_perm v m", "val nllist_eq_not_null (a: Type0) (n: Ghost.erased nat) (r: t a)\n : Lemma (requires (is_null r == false))\n (ensures\n (nllist a n r ==\n (((vptr r) `vrefine` (v_c n r)) `vdep` (v_c_dep n r (nllist a)))\n `vrewrite`\n (v_c_l_rewrite n r (nllist a))))\nlet nllist_eq_not_null\n (a: Type0)\n (n: Ghost.erased nat)\n (r: t a)\n: Lemma\n (requires (is_null r == false))\n (ensures (\n nllist a n r == ((vptr r `vrefine` v_c n r) `vdep` v_c_dep n r (nllist a)) `vrewrite` v_c_l_rewrite n r (nllist a)\n ))\n= assert_norm (nllist a n r ==\n begin if is_null r\n then emp `vrewrite` v_null_rewrite a\n else ((vptr r `vrefine` v_c n r) `vdep` v_c_dep n r (nllist a)) `vrewrite` v_c_l_rewrite n r (nllist a)\n end\n )", "val nllist_eq_not_null (a: Type0) (n: Ghost.erased nat) (r: t a)\n : Lemma (requires (is_null r == false))\n (ensures\n (nllist a n r ==\n (((vptr r) `vrefine` (v_c n r)) `vdep` (v_c_dep n r (nllist a)))\n `vrewrite`\n (v_c_l_rewrite n r (nllist a))))\nlet nllist_eq_not_null\n (a: Type0)\n (n: Ghost.erased nat)\n (r: t a)\n: Lemma\n (requires (is_null r == false))\n (ensures (\n nllist a n r == ((vptr r `vrefine` v_c n r) `vdep` v_c_dep n r (nllist a)) `vrewrite` v_c_l_rewrite n r (nllist a)\n ))\n= assert_norm (nllist a n r ==\n begin if is_null r\n then emp `vrewrite` v_null_rewrite a\n else ((vptr r `vrefine` v_c n r) `vdep` v_c_dep n r (nllist a)) `vrewrite` v_c_l_rewrite n r (nllist a)\n end\n )", "val Selectors.PtrLList.ind_sel = \n r: Steel.Reference.ref (Steel.Reference.ref a) ->\n h:\n Steel.Effect.Common.rmem p\n { FStar.Tactics.Effect.with_tactic Steel.Effect.Common.selector_tactic\n (Steel.Effect.Common.can_be_split p (Selectors.PtrLList.ind_ptr r) /\\ Prims.l_True) }\n -> Prims.GTot\n (Steel.Effect.Common.normal (Steel.Effect.Common.t_of (Selectors.PtrLList.ind_ptr r)))\nlet ind_sel (#a:Type0) (#p:vprop) (r:ref (ref a))\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (ind_ptr r) /\\ True)})\n = h (ind_ptr r)" ], "closest_src": [ { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.llist_sel_depends_only_on" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.ind_ptr_sel_depends_only_on" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.tree_sel_depends_only_on" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ptr_sel_depends_only_on" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ghost_ptr_sel_depends_only_on" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.llist_sel_depends_only_on_core" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.ind_ptr_sel_depends_only_on_core" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.tree_sel_depends_only_on_core" }, { "project_name": "steel", "file_name": "Steel.Effect.fst", "name": "Steel.Effect.rmem_depends_only_on'" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ptr_sel_depends_only_on_core" }, { "project_name": "steel", "file_name": "Steel.Effect.fst", "name": "Steel.Effect.rmem_depends_only_on_post'" }, { "project_name": "steel", "file_name": "Steel.Effect.fst", "name": "Steel.Effect.rmem_depends_only_on" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ghost_ptr_sel_depends_only_on_core" }, { "project_name": "steel", "file_name": "Steel.Effect.fst", "name": "Steel.Effect.rmem_depends_only_on_post" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.interp_depends_only_on" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.interp_depends_only_on" }, { "project_name": "steel", "file_name": "Steel.Reference.fsti", "name": "Steel.Reference.ptr_sel_interp" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.llist_sel_interp" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.reference_distinct_sel_disjoint" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.disjoint_join" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.unpack_ind_lemma" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.pointer_distinct_sel_disjoint" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.disjoint_join" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.lemma_cons_not_null" }, { "project_name": "steel", "file_name": "Steel.Reference.fsti", "name": "Steel.Reference.ghost_ptr_sel_interp" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.intro_cons_lemma" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.elim_cons_cell_lemma" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.elim_nil_lemma" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.mreference_distinct_sel_disjoint" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.interp_depends_only_on" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.interp_depends_only_on" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.tree_sel_interp" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.join_commutative" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.intro_cons_lemma_aux" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.join_commutative" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.join_associative" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.intro_nil_lemma" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.pack_ind_lemma" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.join_associative" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.vdep_sel_eq" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.reveal_non_empty_lemma" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ptrp_sel_interp" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.elim_leaf_lemma" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.pts_to_ref_injective" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.pts_to_ref_injective" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.join_preserves_interp" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.disjoint_join'" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.disjoint_join'" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.dep_hprop_is_affine0" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.dep_hprop_is_affine0" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.dep_hprop_is_affine1" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.dep_hprop_is_affine1" }, { "project_name": "noise-star", "file_name": "Spec.Noise.Map.fst", "name": "Spec.Noise.Map.memP_list_in_listP_implies_memP" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.elim_llist_cons" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.intro_llist_cons" }, { "project_name": "steel", "file_name": "Selectors.LList3.fst", "name": "Selectors.LList3.intro_llist_cons" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.forall_x_mem_in_tl" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ghost_ptrp_sel_interp" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.sel_lemma" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.sel_lemma" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.sel_concat1" }, { "project_name": "steel", "file_name": "Selectors.LList.fsti", "name": "Selectors.LList.v_ind_llist" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.intro_llist_cons" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.lemma_heap_equality_upd_with_sel" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.intro_leaf_lemma" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.mprop_preservation_of_hprop_preservation" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.mprop_preservation_of_hprop_preservation" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.lemma_node_not_null" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.join_associative2" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.join_associative2" }, { "project_name": "noise-star", "file_name": "Impl.Noise.API.Device.fst", "name": "Impl.Noise.API.Device.gsame_elementsp_implies_remove_peer_unchanged_pred_s" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.elim_vptr_lemma" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.reveal_non_empty_lemma" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.join_associative'" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.join_associative'" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.intro_ptr_frame_lemma" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.pts_to_inj" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.lemma_heap_equality_upd_with_sel" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.ind_ptr_sel_full" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.append_mem_forall" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.memP_append_or" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.memP_append_or" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.memP_append_or" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.mem_equiv_eq" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.mem_equiv_eq" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Heap_s.fst", "name": "Vale.Interop.Heap_s.ptrs_of_mem" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fst", "name": "Steel.ST.HigherArray.pts_to_inj" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.list_forallp_mem" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.join" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.llist_fragment_head_eq_cons" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.intro_vptr_lemma" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.append_mem" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.join" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.disjoint_join" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.disjoint_join" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.v_full" }, { "project_name": "steel", "file_name": "Steel.Reference.fsti", "name": "Steel.Reference.intro_ptr_interp" }, { "project_name": "steel", "file_name": "Selectors.LList3.fst", "name": "Selectors.LList3.nllist_eq_not_null" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.nllist_eq_not_null" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.ind_sel" } ], "selected_premises": [ "Selectors.LList.llist_sel_depends_only_on", "Steel.Memory.hmem", "Selectors.LList.llist_sel_depends_only_on_core", "Steel.Memory.full_mem", "Selectors.LList.llist_sl'_witinv", "Steel.Reference.ptr_sel", "Steel.Preorder.pcm_history", "Selectors.LList.llist_sel_interp", "FStar.List.Tot.Base.map", "FStar.PCM.composable", "FStar.List.Tot.Base.length", "Steel.FractionalPermission.full_perm", "FStar.PCM.op", "Steel.Effect.Common.to_vprop", "Selectors.LList.ind_llist_sl'", "Selectors.LList.elim_nil_lemma", "FStar.PCM.compatible", "FStar.List.Tot.Base.op_At", "Selectors.LList.data", "Selectors.LList.from_list_cell", "Steel.Reference.ptr", "Steel.Effect.Common.to_vprop'", "Steel.Effect.Common.star", "FStar.Real.one", "Steel.Reference.ptr_sel_interp", "Steel.Reference.vptrp", "Steel.Effect.Common.hp_of", "FStar.Reflection.V2.Data.var", "Selectors.LList.mk_cell", "Selectors.LList.to_list_cell", "Steel.Memory.inames", "Selectors.LList.next", "Steel.Effect.Common.rmem", "Steel.Preorder.history_val", "Selectors.LList.intro_nil_lemma", "FStar.Reflection.V2.Derived.mk_e_app", "Selectors.LList.intro_cons_lemma_aux", "FStar.Reflection.V2.Derived.mk_app", "Steel.Effect.Common.req", "Steel.Effect.Common.t_of", "FStar.Real.two", "Steel.Effect.Common.normal", "Steel.Effect.Atomic.h_exists", "Selectors.LList.reveal_non_empty_cell", "Selectors.LList.tail", "Selectors.LList.ind_llist_sl", "FStar.FunctionalExtensionality.feq", "Steel.FractionalPermission.comp_perm", "Steel.Effect.Common.normal_steps", "Selectors.LList.cons_is_not_null", "Steel.FractionalPermission.sum_perm", "Selectors.LList.llist_sl", "Selectors.LList.llist_sel_cell'", "Selectors.LList.llist_sel_cell", "Steel.Reference.intro_ptr_interp", "Selectors.LList.llist_cell", "Steel.Effect.Common.pure", "Steel.Effect.Common.mk_rmem", "Selectors.LList.intro_llist_cons", "Steel.Effect.Common.rm", "FStar.Tactics.CanonCommMonoidSimple.Equiv.term_eq", "Selectors.LList.elim_llist_nil", "FStar.UInt.size", "FStar.Heap.trivial_preorder", "Steel.Effect.Common.extract_contexts", "Steel.Reference.ghost_ptr", "FStar.List.Tot.Base.tl", "Steel.Effect.Common.guard_vprop", "Steel.Effect.Common.hmem", "Steel.Reference.read", "Steel.Effect.Common.sel_of", "Steel.Reference.sel", "FStar.List.Tot.Base.rev", "Selectors.LList.tail_cell", "Steel.Effect.Common.rmem'", "FStar.Tactics.Effect.raise", "FStar.List.Tot.Base.mem", "Steel.Effect.Common.vrefine'", "Steel.Reference.ghost_ptr_sel_interp", "FStar.Reflection.V2.Derived.flatten_name", "Steel.Reference.pts_to", "Selectors.LList.null_llist", "FStar.ST.op_Bang", "Selectors.LList.intro_llist_nil", "Selectors.LList.intro_cons_lemma", "Steel.Effect.Common.mk_rmem'", "Steel.Effect.Common.print_goals", "Steel.Reference.ghost_ptr_sel", "FStar.Mul.op_Star", "FStar.List.Tot.Base.append", "Steel.Reference.ghost_read", "Steel.Reference.ghost_gather", "FStar.Pervasives.reveal_opaque", "Steel.Effect.Common.vrefine", "Steel.Effect.Common.visit_br", "Steel.Preorder.vhist", "Steel.Effect.Common.sel_depends_only_on", "FStar.Reflection.V2.Derived.shift_subst", "Steel.Reference.ghost_vptr", "Steel.Effect.Common.visit_tm" ], "source_upto_this": "module Selectors.LList\n\nopen FStar.Ghost\nopen Steel.FractionalPermission\nmodule Mem = Steel.Memory\nopen Steel.Effect.Atomic\nopen Steel.Effect\nopen Steel.Reference\n\n#push-options \"--__no_positivity\"\nnoeq\ntype cell (a: Type0) = {\n next: ref (cell a);\n data: a;\n}\n#pop-options\n\nlet next #a (c:cell a) : t a = c.next\nlet data #a (c:cell a) : a = c.data\nlet mk_cell #a (n: t a) (d:a) = {\n next = n;\n data = d\n}\n\n(* AF: Need to put that in the standard library at some point *)\nlet null_llist #a = null\nlet is_null #a ptr = is_null ptr\n\nlet rec llist_sl' (#a:Type) (ptr:t a)\n (l:list (cell a))\n : Tot slprop (decreases l)\n =\n match l with\n | [] ->\n Mem.pure (ptr == null_llist)\n\n | hd :: tl ->\n pts_to_sl ptr full_perm hd `Mem.star`\n llist_sl' (next hd) tl `Mem.star`\n Mem.pure (ptr =!= null_llist)\n\n\nlet llist_sl ptr = Mem.h_exists (llist_sl' ptr)\n\n\nlet rec datas (#a:Type) (l:list (cell a)) : list a =\n match l with\n | [] -> []\n | hd::tl -> data hd :: datas tl\n\nval llist_sel_cell' (#a:Type0) (ptr:t a) : selector' (list (cell a)) (llist_sl ptr)\n\nlet llist_sel_cell' #a ptr = fun h -> id_elim_exists (llist_sl' ptr) h\n\nlet llist_sl'_witinv (#a:Type) (ptr:t a) : Lemma (is_witness_invariant (llist_sl' ptr))\n = let rec aux (ptr:t a) (x y:list (cell a)) (m:mem) : Lemma\n (requires interp (llist_sl' ptr x) m /\\ interp (llist_sl' ptr y) m)\n (ensures x == y)\n (decreases x)\n = match x with\n | [] -> begin match y with\n | [] -> ()\n | hd::tl ->\n Mem.pure_interp (ptr == null_llist) m;\n Mem.pure_star_interp\n (pts_to_sl ptr full_perm hd `Mem.star` llist_sl' (next hd) tl)\n (ptr =!= null_llist) m;\n Mem.pure_interp (ptr =!= null_llist) m\n\n end\n | hd1::tl1 -> begin match y with\n | [] ->\n Mem.pure_interp (ptr == null_llist) m;\n Mem.pure_star_interp\n (pts_to_sl ptr full_perm hd1 `Mem.star` llist_sl' (next hd1) tl1)\n (ptr =!= null_llist) m;\n Mem.pure_interp (ptr =!= null_llist) m\n | hd2::tl2 ->\n pts_to_witinv ptr full_perm;\n aux (next hd1) tl1 tl2 m\n end\n\n in Classical.forall_intro_3 (Classical.move_requires_3 (aux ptr))\n\nlet llist_sel_depends_only_on (#a:Type0) (ptr:t a)\n (m0:Mem.hmem (llist_sl ptr)) (m1:mem{disjoint m0 m1})\n : Lemma (llist_sel_cell' ptr m0 == llist_sel_cell' ptr (Mem.join m0 m1))\n = let m':Mem.hmem (llist_sl ptr) = Mem.join m0 m1 in\n let l1 = Ghost.reveal (id_elim_exists (llist_sl' ptr) m0) in\n let l2 = Ghost.reveal (id_elim_exists (llist_sl' ptr) m') in\n\n llist_sl'_witinv ptr;\n Mem.elim_wi (llist_sl' ptr) l1 l2 m'\n\nlet llist_sel_depends_only_on_core (#a:Type0) (ptr:t a)\n (m0:Mem.hmem (llist_sl ptr))\n : Lemma (llist_sel_cell' ptr m0 == llist_sel_cell' ptr (core_mem m0))\n = let l1 = Ghost.reveal (id_elim_exists (llist_sl' ptr) m0) in\n let l2 = Ghost.reveal (id_elim_exists (llist_sl' ptr) (core_mem m0)) in\n llist_sl'_witinv ptr;\n Mem.elim_wi (llist_sl' ptr) l1 l2 (core_mem m0)\n\nval llist_sel_cell (#a:Type0) (r:t a) : selector (list (cell a)) (llist_sl r)\n\nlet llist_sel_cell #a ptr =\n Classical.forall_intro_2 (llist_sel_depends_only_on ptr);\n Classical.forall_intro (llist_sel_depends_only_on_core ptr);\n llist_sel_cell' ptr\n\n\nlet llist_sel ptr = fun h -> datas (llist_sel_cell ptr h)\n\n#push-options \"--fuel 1 --ifuel 1\"\n\nlet llist_sel_interp (#a:Type0) (ptr:t a) (l:list (cell a)) (m:mem) : Lemma\n (requires interp (llist_sl' ptr l) m)\n (ensures interp (llist_sl ptr) m /\\ llist_sel_cell' ptr m == l)\n = intro_h_exists l (llist_sl' ptr) m;\n llist_sl'_witinv ptr\n\nlet intro_nil_lemma (a:Type0) (m:mem) : Lemma\n (requires interp (hp_of emp) m)\n (ensures interp (llist_sl (null_llist #a)) m /\\ llist_sel (null_llist #a) m == [])\n = let ptr:t a = null_llist in\n pure_interp (ptr == null_llist) m;\n let open FStar.Tactics in\n assert (llist_sl' ptr [] == Mem.pure (ptr == null_llist)) by (norm [delta; zeta; iota]);\n llist_sel_interp ptr [] m\n\nlet intro_llist_nil a =\n change_slprop_2 emp (llist (null_llist #a)) ([] <: list a) (intro_nil_lemma a)\n\nlet elim_nil_lemma (#a:Type0) (ptr:t a) (m:mem) : Lemma\n (requires interp (llist_sl ptr) m /\\ ptr == null_llist)\n (ensures interp (llist_sl ptr) m /\\ llist_sel ptr m == [])\n = let l' = id_elim_exists (llist_sl' ptr) m in\n pure_interp (ptr == null_llist) m;\n llist_sel_interp ptr [] m\n\nlet elim_llist_nil #a ptr =\n change_slprop_rel (llist ptr) (llist ptr)\n (fun x y -> x == y /\\ y == [])\n (fun m -> elim_nil_lemma ptr m)\n\n#set-options \"--z3rlimit 20\"\n\nlet lemma_cons_not_null (#a:Type) (ptr:t a) (l:list a) (m:mem) : Lemma\n (requires interp (llist_sl ptr) m /\\ llist_sel ptr m == l /\\ Cons? l)\n (ensures ptr =!= null_llist)\n = let l' = id_elim_exists (llist_sl' ptr) m in\n assert (interp (llist_sl' ptr l') m);\n llist_sel_interp ptr l' m;\n match reveal l' with\n | hd::tl ->\n let p = pts_to_sl ptr full_perm (hide hd) `Mem.star` llist_sl' (next hd) tl in\n pure_star_interp p (ptr =!= null_llist) m\n\nlet cons_is_not_null #a ptr =\n let h = get () in\n let l = hide (v_llist ptr h) in\n extract_info (llist ptr) l (ptr =!= null_llist) (lemma_cons_not_null ptr l)\n\nlet intro_cons_lemma_aux (#a:Type0) (ptr1 ptr2:t a)\n (x: cell a) (l:list (cell a)) (m:mem) : Lemma\n (requires interp (pts_to_sl ptr1 full_perm x `Mem.star` llist_sl' ptr2 l) m /\\\n next x == ptr2)\n (ensures interp (llist_sl' ptr1 (x::l)) m)\n = affine_star (pts_to_sl ptr1 full_perm x) (llist_sl' ptr2 l) m;\n pts_to_not_null ptr1 full_perm x m;\n emp_unit (pts_to_sl ptr1 full_perm x `Mem.star` llist_sl' ptr2 l);\n pure_star_interp\n (pts_to_sl ptr1 full_perm x `Mem.star` llist_sl' ptr2 l)\n (ptr1 =!= null_llist)\n m\n\nlet intro_cons_lemma (#a:Type0) (ptr1 ptr2:t a)\n (x: cell a) (l:list a) (m:mem) : Lemma\n (requires interp (ptr ptr1 `Mem.star` llist_sl ptr2) m /\\\n next x == ptr2 /\\\n sel_of (vptr ptr1) m == x /\\\n sel_of (llist ptr2) m == l)\n (ensures interp (llist_sl ptr1) m /\\ llist_sel ptr1 m == data x :: l)\n = let l' = id_elim_exists (llist_sl' ptr2) m in\n let aux (m:mem) (x:cell a) (ml mr:mem) : Lemma\n (requires disjoint ml mr /\\ m == join ml mr /\\\n interp (ptr ptr1) ml /\\ interp (llist_sl ptr2) mr /\\\n ptr_sel ptr1 m == x /\\ interp (llist_sl' ptr2 l') m)\n (ensures interp (pts_to_sl ptr1 full_perm x `Mem.star` llist_sl' ptr2 l') m)\n = ptr_sel_interp ptr1 ml;\n assert (interp (pts_to_sl ptr1 full_perm x) ml);\n let l2 = id_elim_exists (llist_sl' ptr2) mr in\n join_commutative ml mr;\n assert (interp (llist_sl' ptr2 l2) m);\n llist_sl'_witinv ptr2;\n assert (interp (llist_sl' ptr2 l') mr);\n intro_star (pts_to_sl ptr1 full_perm x) (llist_sl' ptr2 l') ml mr\n in\n elim_star (ptr ptr1) (llist_sl ptr2) m;\n Classical.forall_intro_2 (Classical.move_requires_2 (aux m x));\n assert (interp (pts_to_sl ptr1 full_perm x `Mem.star` llist_sl' ptr2 l') m);\n intro_cons_lemma_aux ptr1 ptr2 x l' m;\n intro_h_exists (x::l') (llist_sl' ptr1) m;\n llist_sel_interp ptr1 (x::l') m\n\nlet intro_llist_cons ptr1 ptr2 =\n let h = get () in\n let x = hide (sel ptr1 h) in\n let l = hide (v_llist ptr2 h) in\n reveal_star (vptr ptr1) (llist ptr2);\n change_slprop (vptr ptr1 `star` llist ptr2) (llist ptr1) (reveal x, reveal l) (data x :: l) (fun m -> intro_cons_lemma ptr1 ptr2 x l m)\n\nlet reveal_non_empty_lemma (#a:Type) (ptr:t a) (l:list (cell a)) (m:mem) : Lemma\n (requires interp (llist_sl ptr) m /\\ llist_sel_cell ptr m == l /\\ ptr =!= null_llist)\n (ensures Cons? l)\n= let l' = id_elim_exists (llist_sl' ptr) m in\n llist_sel_interp ptr l' m;\n pure_interp (ptr == null_llist) m\n\nlet is_cons (#a:Type) (l:list a) : prop = match l with\n | [] -> False\n | _ -> True\n\n[@@__steel_reduce__]\nlet llist_cell' #a r : vprop' =\n {hp = llist_sl r;\n t = list (cell a);\n sel = llist_sel_cell r}\nunfold\nlet llist_cell (#a:Type0) (r:t a) = VUnit (llist_cell' r)\n\n[@@ __steel_reduce__]\nlet v_cell (#a:Type0) (#p:vprop) (r:t a)\n (h:rmem p{FStar.Tactics.with_tactic selector_tactic (can_be_split p (llist_cell r) /\\ True)}) : GTot (list (cell a))\n = h (llist_cell r)\n\nval reveal_non_empty_cell (#a:Type0) (ptr:t a)\n : Steel unit (llist_cell ptr) (fun _ -> llist_cell ptr)\n (requires fun _ -> ptr =!= null_llist)\n (ensures fun h0 _ h1 -> v_cell ptr h0 == v_cell ptr h1 /\\ Cons? (v_cell ptr h0))\n\nlet reveal_non_empty_cell #a ptr =\n let h = get () in\n let l = hide (v_cell ptr h) in\n extract_info (llist_cell ptr) l (is_cons l) (reveal_non_empty_lemma ptr l)\n\nlet tail_cell_lemma (#a:Type0) (r:t a) (l:list (cell a)) (m:mem) : Lemma\n (requires Cons? l /\\ interp (llist_sl r) m /\\ llist_sel_cell r m == l)\n (ensures (let x = L.hd l in\n interp (ptr r `Mem.star` llist_sl (next x)) m /\\\n sel_of (vptr r) m == x /\\\n sel_of (llist_cell (next x)) m == L.tl l))\n = llist_sel_interp r l m;\n assert (interp (llist_sl' r l) m);\n let x = L.hd l in\n let tl = L.tl l in\n let sl = pts_to_sl r full_perm x `Mem.star` llist_sl' (next x) tl in\n pure_star_interp sl (r =!= null_llist) m;\n emp_unit sl;\n assert (interp sl m);\n let aux (m:mem) (ml mr:mem) : Lemma\n (requires disjoint ml mr /\\ m == join ml mr /\\\n interp (pts_to_sl r full_perm x) ml /\\ interp (llist_sl' (next x) tl) mr)\n (ensures interp (ptr r `Mem.star` llist_sl (next x)) m /\\\n sel_of (vptr r) m == x /\\\n sel_of (llist_cell (next x)) m == tl)\n = intro_ptr_interp r (hide x) ml;\n llist_sel_interp (next x) tl mr;\n intro_star (ptr r) (llist_sl (next x)) ml mr;\n ptr_sel_interp r ml;\n pts_to_witinv r full_perm;\n join_commutative ml mr\n in\n elim_star (pts_to_sl r full_perm x) (llist_sl' (next x) tl) m;\n Classical.forall_intro_2 (Classical.move_requires_2 (aux m))\n\n\nval tail_cell (#a:Type0) (ptr:t a)\n : Steel (t a) (llist_cell ptr)\n (fun n -> vptr ptr `star` llist_cell n)\n (requires fun _ -> ptr =!= null_llist)\n (ensures fun h0 n h1 ->\n Cons? (v_cell ptr h0) /\\\n n == next (sel ptr h1) /\\\n sel ptr h1 == L.hd (v_cell ptr h0) /\\\n v_cell n h1 == L.tl (v_cell ptr h0))\n\nlet tail_cell #a ptr =\n let h = get () in\n let l = hide (v_cell ptr h) in\n reveal_non_empty_cell ptr;\n let x = hide (L.hd l) in\n change_slprop (llist_cell ptr) (vptr ptr `star` llist_cell (next x)) l (reveal x, L.tl l)\n (fun m -> tail_cell_lemma ptr l m);\n reveal_star (vptr ptr) (llist_cell (next x));\n let v = read ptr in\n change_slprop (llist_cell (next x)) (llist_cell (next v)) (L.tl l) (L.tl l) (fun _ -> ());\n return (next v)\n\nval to_list_cell (#a:Type0) (ptr:t a)\n : Steel unit (llist ptr) (fun _ -> llist_cell ptr)\n (requires fun _ -> True)\n (ensures fun h0 _ h1 -> v_llist ptr h0 == datas (v_cell ptr h1))\n\nlet to_list_cell ptr =\n change_slprop_rel (llist ptr) (llist_cell ptr) (fun x y -> x == datas y) (fun _ -> ())\n\nval from_list_cell (#a:Type0) (ptr:t a)\n : Steel unit (llist_cell ptr) (fun _ -> llist ptr)\n (requires fun _ -> True)\n (ensures fun h0 _ h1 -> v_llist ptr h1 == datas (v_cell ptr h0))\n\nlet from_list_cell ptr =\n change_slprop_rel (llist_cell ptr) (llist ptr) (fun x y -> datas x == y) (fun _ -> ())\n\n#push-options \"--fuel 2\"\nlet tail #a ptr =\n to_list_cell ptr;\n let n = tail_cell #a ptr in\n from_list_cell n;\n n\n#pop-options\n\nlet ind_llist_sl' (#a:Type0) (r:ref (t a)) (p:t a) : slprop u#1 =\n pts_to_sl r full_perm p `Mem.star` llist_sl p\nlet ind_llist_sl (#a:Type0) (r:ref (t a)) = Mem.h_exists (ind_llist_sl' r)\n\nlet ind_llist_sel_full' (#a:Type0) (r:ref (t a)) : selector' (t a * list a) (ind_llist_sl r) =\n fun h ->\n let p = id_elim_exists (ind_llist_sl' r) h in\n (reveal p, llist_sel p h)\n", "sketch": [ "Step 1: We start by joining the memory `m0` and `m1` to form `m'`.\nStep 2: Reveal the value of `p` from `ind_llist_sl' ptr` in both `m0` and `m'`.\nStep 3: Use the witness invariant lemma `llist_sl'_witinv` to ensure that the revealed values are the same.\nStep 4: Conclude that the selector values are equal by using the revealed values and the witness invariant.", "Step 1: We start by joining the memory `m0` and `m1` to form `m'`.\nStep 2: Reveal the selector value for `ind_llist_sl' ptr` in both `m0` and `m'`.\nStep 3: Use the witness invariant property of `ind_llist_sl' ptr` to show that the revealed values are equal.\nStep 4: Conclude that the selector values for `ind_llist_sel_full' ptr` in `m0` and `m'` are equal.", "Step 1: Introduce the memory `m'` which is the join of `m0` and `m1`.\nStep 2: Reveal the selector values for `m0` and `m'` using `id_elim_exists`.\nStep 3: Use the witness invariant lemma `llist_sl'_witinv` to establish that the revealed lists are equal.\nStep 4: Conclude that the selector values for `m0` and `m'` are equal.", "Step 1: Extract the witness `p` from `m0` using `id_elim_exists`.\nStep 2: Extract the witness `p'` from `Mem.join m0 m1` using `id_elim_exists`.\nStep 3: Use the witness invariant lemma `ind_llist_sl'_witinv` to show that `p == p'`.\nStep 4: Conclude that `ind_llist_sel_full' ptr m0` is equal to `ind_llist_sel_full' ptr (Mem.join m0 m1)` by using the equality of `p` and `p'`.", "Step 1: We start by joining the memory `m0` and `m1` to form `m'`.\nStep 2: Reveal the witness `p` from `ind_llist_sl' ptr` in both `m0` and `m'`.\nStep 3: Use the witness invariant lemma `llist_sl'_witinv` to show that the witness `p` is the same in both `m0` and `m'`.\nStep 4: Conclude that the selector `ind_llist_sel_full' ptr` is the same in both `m0` and `m'` by showing that the revealed values are equal.", "Step 1: Reveal the witness `p` from the heap memory `m0` using `id_elim_exists` for `ind_llist_sl' ptr`.\nStep 2: Reveal the witness `p'` from the joined heap memory `Mem.join m0 m1` using `id_elim_exists` for `ind_llist_sl' ptr`.\nStep 3: Use the witness invariant lemma `llist_sl'_witinv` to show that the witness `p` from `m0` and `p'` from `Mem.join m0 m1` are equal.\nStep 4: Conclude that the selectors `ind_llist_sel_full' ptr m0` and `ind_llist_sel_full' ptr (Mem.join m0 m1)` are equal by the equality of their components.", "Step 1: Start by revealing the existential witness `p` for `ind_llist_sl' ptr` in both `m0` and `Mem.join m0 m1`.\nStep 2: Use the witness invariant property of `llist_sl'` to show that the witness `p` is the same in both heaps.\nStep 3: Conclude that the selector `ind_llist_sel_full' ptr` applied to `m0` is equal to the selector applied to `Mem.join m0 m1`.", "Step 1: Start by revealing the existential witness `p` for `ind_llist_sl' ptr` in both `m0` and `Mem.join m0 m1`.\nStep 2: Use the witness invariant lemma `llist_sl'_witinv` to show that the witness `p` is the same in both `m0` and `Mem.join m0 m1`.\nStep 3: Conclude that the selector `ind_llist_sel_full' ptr` applied to `m0` is equal to the selector applied to `Mem.join m0 m1`.", "Step 1: Extract the value of `p` from the memory `m0` using `id_elim_exists` for `ind_llist_sl' ptr`.\nStep 2: Extract the value of `p` from the joined memory `Mem.join m0 m1` using `id_elim_exists` for `ind_llist_sl' ptr`.\nStep 3: Use the witness invariant lemma `llist_sl'_witinv` to show that the extracted values from `m0` and `Mem.join m0 m1` are equal.\nStep 4: Conclude that the selectors `ind_llist_sel_full' ptr m0` and `ind_llist_sel_full' ptr (Mem.join m0 m1)` are equal by combining the results from the previous steps.", "Step 1: Unfold the definition of `ind_llist_sel_full'` for both `m0` and `Mem.join m0 m1`.\nStep 2: Extract the pointer `p` from the existential quantifier in `ind_llist_sl' ptr` for both `m0` and `Mem.join m0 m1`.\nStep 3: Use the witness invariant lemma `llist_sl'_witinv` to show that the lists extracted from `m0` and `Mem.join m0 m1` are equal.\nStep 4: Conclude that the selectors for `m0` and `Mem.join m0 m1` are equal by combining the results from the previous steps." ], "generated_solution": [ "let ind_llist_sel_depends_only_on #a ptr m0 m1 =\n let m' = Mem.join m0 m1 in\n let p1 = Ghost.reveal (id_elim_exists (ind_llist_sl' ptr) m0) in\n let p2 = Ghost.reveal (id_elim_exists (ind_llist_sl' ptr) m') in\n llist_sl'_witinv (reveal p1);\n Mem.elim_wi (ind_llist_sl' ptr) p1 p2 m'", "let ind_llist_sel_depends_only_on #a ptr m0 m1 =\n let m' = Mem.join m0 m1 in\n let p0 = id_elim_exists (ind_llist_sl' ptr) m0 in\n let p' = id_elim_exists (ind_llist_sl' ptr) m' in\n llist_sl'_witinv ptr;\n Mem.elim_wi (ind_llist_sl' ptr) p0 p' m';\n assert (p0 == p');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p' m');\n assert (llist_sel p0 m0 == llist_sel p0 m');\n assert (llist_sel p' m0 == llist_sel p' m');\n assert (ll", "let ind_llist_sel_depends_only_on #a ptr m0 m1 =\n let m' = Mem.join m0 m1 in\n let (p0, l0) = id_elim_exists (ind_llist_sl' ptr) m0 in\n let (p', l') = id_elim_exists (ind_llist_sl' ptr) m' in\n llist_sl'_witinv p0;\n Mem.elim_wi (llist_sl' p0) l0 l' m';\n assert (p0 == p');\n assert (l0 == l');\n ()", "let ind_llist_sel_depends_only_on #a ptr m0 m1 =\n let p = id_elim_exists (ind_llist_sl' ptr) m0 in\n let p' = id_elim_exists (ind_llist_sl' ptr) (Mem.join m0 m1) in\n ind_llist_sl'_witinv ptr;\n Mem.elim_wi (ind_llist_sl' ptr) p p' (Mem.join m0 m1)", "let ind_llist_sel_depends_only_on #a ptr m0 m1 =\n let m' = Mem.join m0 m1 in\n let p0 = id_elim_exists (ind_llist_sl' ptr) m0 in\n let p' = id_elim_exists (ind_llist_sl' ptr) m' in\n llist_sl'_witinv (reveal p0);\n Mem.elim_wi (ind_llist_sl' ptr) p0 p' m';\n assert (p0 == p');\n assert (ind_llist_sel_full' ptr m0 == ind_llist_sel_full' ptr m')", "let ind_llist_sel_depends_only_on #a ptr m0 m1 =\n let p = id_elim_exists (ind_llist_sl' ptr) m0 in\n let p' = id_elim_exists (ind_llist_sl' ptr) (Mem.join m0 m1) in\n llist_sl'_witinv p;\n Mem.elim_wi (ind_llist_sl' ptr) p p' (Mem.join m0 m1)", "let ind_llist_sel_depends_only_on #a ptr m0 m1 =\n let p0 = id_elim_exists (ind_llist_sl' ptr) m0 in\n let p1 = id_elim_exists (ind_llist_sl' ptr) (Mem.join m0 m1) in\n llist_sl'_witinv p0;\n Mem.elim_wi (ind_llist_sl' ptr) p0 p1 (Mem.join m0 m1)", "let ind_llist_sel_depends_only_on #a ptr m0 m1 =\n let p0 = id_elim_exists (ind_llist_sl' ptr) m0 in\n let p1 = id_elim_exists (ind_llist_sl' ptr) (Mem.join m0 m1) in\n llist_sl'_witinv (reveal p0);\n Mem.elim_wi (ind_llist_sl' ptr) p0 p1 (Mem.join m0 m1)", "let ind_llist_sel_depends_only_on #a ptr m0 m1 =\n let p0 = id_elim_exists (ind_llist_sl' ptr) m0 in\n let p1 = id_elim_exists (ind_llist_sl' ptr) (Mem.join m0 m1) in\n llist_sl'_witinv p0;\n Mem.elim_wi (ind_llist_sl' ptr) p0 p1 (Mem.join m0 m1)", "let ind_llist_sel_depends_only_on #a ptr m0 m1 =\n let m' = Mem.join m0 m1 in\n let (p0, l0) = id_elim_exists (ind_llist_sl' ptr) m0 in\n let (p', l') = id_elim_exists (ind_llist_sl' ptr) m' in\n llist_sl'_witinv p0;\n Mem.elim_wi (llist_sl' p0) l0 l' m';\n assert (p0 == p');\n assert (l0 == l');\n assert (ind_llist_sel_full' ptr m0 == (p0, l0));\n assert (ind_llist_sel_full' ptr m' == (p', l'));\n assert (ind_llist_sel_full' ptr m0 == ind_llist_sel_full' ptr m')" ] }, { "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.open_comp'", "opens_and_abbrevs": [ { "abbrev": "E", "full_module": "Pulse.Elaborate.Pure" }, { "abbrev": "U", "full_module": "Pulse.Syntax.Pure" }, { "abbrev": "RU", "full_module": "Pulse.RuntimeUtils" }, { "abbrev": "RT", "full_module": "FStar.Reflection.Typing" }, { "abbrev": "RTB", "full_module": "FStar.Reflection.Typing.Builtins" }, { "abbrev": "R", "full_module": "FStar.Reflection" }, { "abbrev": "L", "full_module": "FStar.List.Tot" }, { "open": "Pulse.Common" }, { "open": "Pulse.Syntax.Base" }, { "open": "FStar.List.Tot" }, { "open": "Pulse.Syntax" }, { "open": "Pulse.Syntax" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val open_comp' (c: comp) (v: term) (i: index) : comp", "source_definition": "let open_comp' (c:comp) (v:term) (i:index) : comp =\r\n subst_comp c [ DT i v ]", "source_range": { "start_line": 504, "start_col": 0, "end_line": 505, "end_col": 25 }, "interleaved": false, "definition": "fun c v i -> Pulse.Syntax.Naming.subst_comp c [Pulse.Syntax.Naming.DT i v] <: Pulse.Syntax.Base.comp", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Pulse.Syntax.Base.comp", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_comp", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.DT", "Prims.Nil" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "c: Pulse.Syntax.Base.comp -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index\n -> Pulse.Syntax.Base.comp", "prompt": "let open_comp' (c: comp) (v: term) (i: index) : comp =\n ", "expected_response": "subst_comp c [DT i v]", "source": { "project_name": "steel", "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Pulse.Syntax.Naming.fsti", "checked_file": "dataset/Pulse.Syntax.Naming.fsti.checked", "interface_file": false, "dependencies": [ "dataset/Pulse.Syntax.Pure.fst.checked", "dataset/Pulse.Syntax.Base.fsti.checked", "dataset/Pulse.RuntimeUtils.fsti.checked", "dataset/Pulse.Elaborate.Pure.fst.checked", "dataset/Pulse.Common.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Reflection.Typing.Builtins.fsti.checked", "dataset/FStar.Reflection.Typing.fsti.checked", "dataset/FStar.Reflection.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.List.fst.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "", "", "", "", "", "let rec freevars (t:term) \r\n : Set.set var\r\n = match t.t with\r\n | Tm_Emp\r\n | Tm_VProp\r\n | Tm_Inames\r\n | Tm_EmpInames\r\n | Tm_Unknown -> Set.empty\r\n | Tm_Inv p -> freevars p\r\n | Tm_Star t1 t2 ->\r\n Set.union (freevars t1) (freevars t2)\r\n | Tm_ExistsSL _ t1 t2\r\n | Tm_ForallSL _ t1 t2 ->\r\n Set.union (freevars t1.binder_ty) (freevars t2)\r\n | Tm_Pure p -> freevars p\r\n | Tm_FStar t -> RT.freevars t\r\n | Tm_AddInv i is -> Set.union (freevars i) (freevars is)", "let freevars_st_comp (s:st_comp) : Set.set var =\r\n freevars s.res `Set.union`\r\n freevars s.pre `Set.union`\r\n freevars s.post", "let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) =\r\n match c with\r\n | C_Tot t -> freevars t\r\n | C_ST s\r\n | C_STGhost s -> freevars_st_comp s\r\n | C_STAtomic inames _ s ->\r\n freevars inames `Set.union` freevars_st_comp s", "let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var =\r\n match x with\r\n | None -> Set.empty\r\n | Some x -> f x", "let freevars_term_opt (t:option term) : Set.set var =\r\n freevars_opt freevars t", "let rec freevars_list (t:list term) : Set.set var =\r\n match t with\r\n | [] -> Set.empty\r\n | hd::tl -> freevars hd `Set.union` freevars_list tl", "let rec freevars_pairs (pairs:list (term & term)) : Set.set var =\r\n match pairs with\r\n | [] -> Set.empty\r\n | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl", "let freevars_proof_hint (ht:proof_hint_type) : Set.set var = \r\n match ht with\r\n | ASSERT { p }\r\n | FOLD { p }\r\n | UNFOLD { p } -> freevars p\r\n | RENAME { pairs; goal } ->\r\n Set.union (freevars_pairs pairs) (freevars_term_opt goal)\r\n | REWRITE { t1; t2 } ->\r\n Set.union (freevars t1) (freevars t2)\r\n | WILD\r\n | SHOW_PROOF_STATE _ -> Set.empty", "let freevars_ascription (c:comp_ascription) \r\n : Set.set var\r\n = Set.union (freevars_opt freevars_comp c.elaborated)\r\n (freevars_opt freevars_comp c.annotated)", "let rec freevars_st (t:st_term)\r\n : Set.set var\r\n = match t.term with\r\n | Tm_Return { expected_type; term } ->\r\n Set.union (freevars expected_type) (freevars term)\r\n | Tm_Abs { b; ascription; body } ->\r\n Set.union (freevars b.binder_ty) \r\n (Set.union (freevars_st body)\r\n (freevars_ascription ascription))\r\n | Tm_STApp { head; arg } ->\r\n Set.union (freevars head) (freevars arg)\r\n | Tm_Bind { binder; head; body } ->\r\n Set.union \r\n (Set.union (freevars binder.binder_ty) \r\n (freevars_st head))\r\n (freevars_st body)\r\n | Tm_TotBind { binder; head; body } ->\r\n Set.union\r\n (Set.union (freevars binder.binder_ty)\r\n (freevars head))\r\n (freevars_st body)\r\n | Tm_If { b; then_; else_; post } ->\r\n Set.union (Set.union (freevars b) (freevars_st then_))\r\n (Set.union (freevars_st else_) (freevars_term_opt post))\r\n\r\n | Tm_Match { sc ; returns_; brs } ->\r\n let (@@) = Set.union in\r\n freevars sc\r\n @@ freevars_term_opt returns_\r\n @@ freevars_branches brs\r\n\r\n | Tm_IntroPure { p }\r\n | Tm_ElimExists { p } ->\r\n freevars p\r\n | Tm_IntroExists { p; witnesses } ->\r\n Set.union (freevars p) (freevars_list witnesses)\r\n | Tm_While { invariant; condition; body } ->\r\n Set.union (freevars invariant)\r\n (Set.union (freevars_st condition)\r\n (freevars_st body))\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n Set.union\r\n (Set.union (freevars pre1)\r\n (Set.union (freevars_st body1)\r\n (freevars post1)))\r\n (Set.union (freevars pre2)\r\n (Set.union (freevars_st body2)\r\n (freevars post2)))\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n Set.union (freevars binder.binder_ty)\r\n (Set.union (freevars initializer)\r\n (freevars_st body))\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n Set.union (freevars binder.binder_ty)\r\n (Set.union (freevars initializer)\r\n (Set.union (freevars length)\r\n (freevars_st body)))\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n Set.union (freevars t1) (freevars t2)\r\n\r\n | Tm_Admit { typ; post } ->\r\n Set.union (freevars typ)\r\n (freevars_term_opt post)\r\n\r\n | Tm_Unreachable ->\r\n Set.empty\r\n\r\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\r\n Set.union (freevars_proof_hint hint_type) (freevars_st t)\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n Set.union (Set.union (freevars name) (freevars_st body))\r\n (freevars_opt \r\n (fun (b, r) ->\r\n (Set.union (freevars b.binder_ty) \r\n (freevars r)))\r\n returns_inv)\r\n\r\nand freevars_branches (t:list (pattern & st_term)) : Set.set var =\r\n match t with\r\n | [] -> Set.empty\r\n | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl", "let rec freevars_st (t:st_term)\r\n : Set.set var\r\n = match t.term with\r\n | Tm_Return { expected_type; term } ->\r\n Set.union (freevars expected_type) (freevars term)\r\n | Tm_Abs { b; ascription; body } ->\r\n Set.union (freevars b.binder_ty) \r\n (Set.union (freevars_st body)\r\n (freevars_ascription ascription))\r\n | Tm_STApp { head; arg } ->\r\n Set.union (freevars head) (freevars arg)\r\n | Tm_Bind { binder; head; body } ->\r\n Set.union \r\n (Set.union (freevars binder.binder_ty) \r\n (freevars_st head))\r\n (freevars_st body)\r\n | Tm_TotBind { binder; head; body } ->\r\n Set.union\r\n (Set.union (freevars binder.binder_ty)\r\n (freevars head))\r\n (freevars_st body)\r\n | Tm_If { b; then_; else_; post } ->\r\n Set.union (Set.union (freevars b) (freevars_st then_))\r\n (Set.union (freevars_st else_) (freevars_term_opt post))\r\n\r\n | Tm_Match { sc ; returns_; brs } ->\r\n let (@@) = Set.union in\r\n freevars sc\r\n @@ freevars_term_opt returns_\r\n @@ freevars_branches brs\r\n\r\n | Tm_IntroPure { p }\r\n | Tm_ElimExists { p } ->\r\n freevars p\r\n | Tm_IntroExists { p; witnesses } ->\r\n Set.union (freevars p) (freevars_list witnesses)\r\n | Tm_While { invariant; condition; body } ->\r\n Set.union (freevars invariant)\r\n (Set.union (freevars_st condition)\r\n (freevars_st body))\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n Set.union\r\n (Set.union (freevars pre1)\r\n (Set.union (freevars_st body1)\r\n (freevars post1)))\r\n (Set.union (freevars pre2)\r\n (Set.union (freevars_st body2)\r\n (freevars post2)))\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n Set.union (freevars binder.binder_ty)\r\n (Set.union (freevars initializer)\r\n (freevars_st body))\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n Set.union (freevars binder.binder_ty)\r\n (Set.union (freevars initializer)\r\n (Set.union (freevars length)\r\n (freevars_st body)))\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n Set.union (freevars t1) (freevars t2)\r\n\r\n | Tm_Admit { typ; post } ->\r\n Set.union (freevars typ)\r\n (freevars_term_opt post)\r\n\r\n | Tm_Unreachable ->\r\n Set.empty\r\n\r\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\r\n Set.union (freevars_proof_hint hint_type) (freevars_st t)\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n Set.union (Set.union (freevars name) (freevars_st body))\r\n (freevars_opt \r\n (fun (b, r) ->\r\n (Set.union (freevars b.binder_ty) \r\n (freevars r)))\r\n returns_inv)\r\n\r\nand freevars_branches (t:list (pattern & st_term)) : Set.set var =\r\n match t with\r\n | [] -> Set.empty\r\n | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl", "let rec ln' (t:term) (i:int) : Tot bool (decreases t) =\r\n match t.t with\r\n | Tm_Emp\r\n | Tm_VProp\r\n | Tm_Inames\r\n | Tm_EmpInames\r\n | Tm_Unknown -> true\r\n\r\n | Tm_Inv p -> ln' p i\r\n\r\n | Tm_Star t1 t2 ->\r\n ln' t1 i &&\r\n ln' t2 i\r\n\r\n | Tm_Pure p ->\r\n ln' p i\r\n\r\n | Tm_ExistsSL _ t body\r\n | Tm_ForallSL _ t body ->\r\n ln' t.binder_ty i &&\r\n ln' body (i + 1)\r\n \r\n | Tm_FStar t ->\r\n RT.ln' t i\r\n\r\n | Tm_AddInv x is ->\r\n ln' x i &&\r\n ln' is i", "let ln_st_comp (s:st_comp) (i:int) : bool =\r\n ln' s.res i &&\r\n ln' s.pre i &&\r\n ln' s.post (i + 1)", "let ln_c' (c:comp) (i:int)\r\n : bool\r\n = match c with\r\n | C_Tot t -> ln' t i\r\n | C_ST s\r\n | C_STGhost s -> ln_st_comp s i\r\n | C_STAtomic inames _ s ->\r\n ln' inames i &&\r\n ln_st_comp s i", "let ln_opt' (f: ('a -> int -> bool)) (t:option 'a) (i:int) : bool =\r\n match t with\r\n | None -> true\r\n | Some t -> f t i", "let rec ln_list' (t:list term) (i:int) : bool =\r\n match t with\r\n | [] -> true\r\n | hd::tl -> ln' hd i && ln_list' tl i", "let rec ln_terms' (t:list (term & term)) (i:int) : bool =\r\n match t with\r\n | [] -> true\r\n | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i", "let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool =\r\n match ht with\r\n | ASSERT { p }\r\n | UNFOLD { p }\r\n | FOLD { p } -> ln' p i\r\n | RENAME { pairs; goal } ->\r\n ln_terms' pairs i &&\r\n ln_opt' ln' goal i\r\n | REWRITE { t1; t2 } ->\r\n ln' t1 i &&\r\n ln' t2 i\r\n | WILD\r\n | SHOW_PROOF_STATE _ -> true", "let rec pattern_shift_n (p:pattern)\r\n : Tot nat\r\n = match p with\r\n | Pat_Constant _ \r\n | Pat_Dot_Term _ -> \r\n 0\r\n | Pat_Var _ _ ->\r\n 1\r\n | Pat_Cons fv l ->\r\n pattern_args_shift_n l\r\nand pattern_args_shift_n (ps:list (pattern & bool))\r\n : Tot nat\r\n = match ps with\r\n | [] -> 0\r\n | (p, _)::tl ->\r\n pattern_shift_n p + pattern_args_shift_n tl", "let rec pattern_shift_n (p:pattern)\r\n : Tot nat\r\n = match p with\r\n | Pat_Constant _ \r\n | Pat_Dot_Term _ -> \r\n 0\r\n | Pat_Var _ _ ->\r\n 1\r\n | Pat_Cons fv l ->\r\n pattern_args_shift_n l\r\nand pattern_args_shift_n (ps:list (pattern & bool))\r\n : Tot nat\r\n = match ps with\r\n | [] -> 0\r\n | (p, _)::tl ->\r\n pattern_shift_n p + pattern_args_shift_n tl", "let rec ln_pattern' (p : pattern) (i:int)\r\n : Tot bool (decreases p)\r\n = match p with\r\n | Pat_Constant _ \r\n | Pat_Var _ _ \r\n | Pat_Dot_Term None ->\r\n true\r\n | Pat_Dot_Term (Some e) ->\r\n ln' e i\r\n | Pat_Cons fv l ->\r\n ln_pattern_args' l i\r\n \r\nand ln_pattern_args' (p:list (pattern & bool)) (i:int)\r\n : Tot bool (decreases p)\r\n = match p with\r\n | [] ->\r\n true\r\n | (p, _)::tl ->\r\n ln_pattern' p i &&\r\n ln_pattern_args' tl (i + pattern_shift_n p)", "let rec ln_pattern' (p : pattern) (i:int)\r\n : Tot bool (decreases p)\r\n = match p with\r\n | Pat_Constant _ \r\n | Pat_Var _ _ \r\n | Pat_Dot_Term None ->\r\n true\r\n | Pat_Dot_Term (Some e) ->\r\n ln' e i\r\n | Pat_Cons fv l ->\r\n ln_pattern_args' l i\r\n \r\nand ln_pattern_args' (p:list (pattern & bool)) (i:int)\r\n : Tot bool (decreases p)\r\n = match p with\r\n | [] ->\r\n true\r\n | (p, _)::tl ->\r\n ln_pattern' p i &&\r\n ln_pattern_args' tl (i + pattern_shift_n p)", "let ln_ascription' (c:comp_ascription) (i:int)\r\n : bool\r\n = ln_opt' ln_c' c.elaborated i &&\r\n ln_opt' ln_c' c.annotated i", "let rec ln_st' (t:st_term) (i:int)\r\n : Tot bool (decreases t)\r\n = match t.term with\r\n | Tm_Return { expected_type; term } ->\r\n ln' expected_type i &&\r\n ln' term i\r\n \r\n | Tm_Abs { b; ascription; body } ->\r\n ln' b.binder_ty i &&\r\n ln_st' body (i + 1) &&\r\n ln_ascription' ascription (i + 1)\r\n\r\n | Tm_STApp { head; arg } ->\r\n ln' head i &&\r\n ln' arg i\r\n\r\n | Tm_Bind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln_st' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_TotBind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_If { b; then_; else_; post } ->\r\n ln' b i &&\r\n ln_st' then_ i &&\r\n ln_st' else_ i &&\r\n ln_opt' ln' post (i + 1)\r\n \r\n | Tm_Match {sc; returns_; brs } ->\r\n ln' sc i &&\r\n ln_opt' ln' returns_ i &&\r\n ln_branches' t brs i\r\n\r\n | Tm_IntroPure { p }\r\n | Tm_ElimExists { p } ->\r\n ln' p i\r\n\r\n | Tm_IntroExists { p; witnesses } ->\r\n ln' p i &&\r\n ln_list' witnesses i\r\n \r\n | Tm_While { invariant; condition; body } ->\r\n ln' invariant (i + 1) &&\r\n ln_st' condition i &&\r\n ln_st' body i\r\n\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n ln' pre1 i &&\r\n ln_st' body1 i &&\r\n ln' post1 (i + 1) &&\r\n ln' pre2 i &&\r\n ln_st' body2 i &&\r\n ln' post2 (i + 1)\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln' length i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n ln' t1 i &&\r\n ln' t2 i\r\n\r\n | Tm_Admit { typ; post } ->\r\n ln' typ i &&\r\n ln_opt' ln' post (i + 1)\r\n\r\n | Tm_Unreachable ->\r\n true\r\n\r\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\r\n let n = L.length binders in\r\n ln_proof_hint' hint_type (i + n) &&\r\n ln_st' t (i + n)\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n ln' name i &&\r\n ln_st' body i &&\r\n ln_opt'\r\n (fun (b, r) i ->\r\n ln' b.binder_ty i &&\r\n ln' r (i + 1))\r\n returns_inv i\r\n\r\nand ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) =\r\n let (p, e) = b in\r\n ln_pattern' p i &&\r\n ln_st' e (i + pattern_shift_n p)\r\n \r\nand ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) =\r\n for_all_dec t brs (fun b -> ln_branch' b i)", "let rec ln_st' (t:st_term) (i:int)\r\n : Tot bool (decreases t)\r\n = match t.term with\r\n | Tm_Return { expected_type; term } ->\r\n ln' expected_type i &&\r\n ln' term i\r\n \r\n | Tm_Abs { b; ascription; body } ->\r\n ln' b.binder_ty i &&\r\n ln_st' body (i + 1) &&\r\n ln_ascription' ascription (i + 1)\r\n\r\n | Tm_STApp { head; arg } ->\r\n ln' head i &&\r\n ln' arg i\r\n\r\n | Tm_Bind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln_st' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_TotBind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_If { b; then_; else_; post } ->\r\n ln' b i &&\r\n ln_st' then_ i &&\r\n ln_st' else_ i &&\r\n ln_opt' ln' post (i + 1)\r\n \r\n | Tm_Match {sc; returns_; brs } ->\r\n ln' sc i &&\r\n ln_opt' ln' returns_ i &&\r\n ln_branches' t brs i\r\n\r\n | Tm_IntroPure { p }\r\n | Tm_ElimExists { p } ->\r\n ln' p i\r\n\r\n | Tm_IntroExists { p; witnesses } ->\r\n ln' p i &&\r\n ln_list' witnesses i\r\n \r\n | Tm_While { invariant; condition; body } ->\r\n ln' invariant (i + 1) &&\r\n ln_st' condition i &&\r\n ln_st' body i\r\n\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n ln' pre1 i &&\r\n ln_st' body1 i &&\r\n ln' post1 (i + 1) &&\r\n ln' pre2 i &&\r\n ln_st' body2 i &&\r\n ln' post2 (i + 1)\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln' length i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n ln' t1 i &&\r\n ln' t2 i\r\n\r\n | Tm_Admit { typ; post } ->\r\n ln' typ i &&\r\n ln_opt' ln' post (i + 1)\r\n\r\n | Tm_Unreachable ->\r\n true\r\n\r\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\r\n let n = L.length binders in\r\n ln_proof_hint' hint_type (i + n) &&\r\n ln_st' t (i + n)\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n ln' name i &&\r\n ln_st' body i &&\r\n ln_opt'\r\n (fun (b, r) i ->\r\n ln' b.binder_ty i &&\r\n ln' r (i + 1))\r\n returns_inv i\r\n\r\nand ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) =\r\n let (p, e) = b in\r\n ln_pattern' p i &&\r\n ln_st' e (i + pattern_shift_n p)\r\n \r\nand ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) =\r\n for_all_dec t brs (fun b -> ln_branch' b i)", "let rec ln_st' (t:st_term) (i:int)\r\n : Tot bool (decreases t)\r\n = match t.term with\r\n | Tm_Return { expected_type; term } ->\r\n ln' expected_type i &&\r\n ln' term i\r\n \r\n | Tm_Abs { b; ascription; body } ->\r\n ln' b.binder_ty i &&\r\n ln_st' body (i + 1) &&\r\n ln_ascription' ascription (i + 1)\r\n\r\n | Tm_STApp { head; arg } ->\r\n ln' head i &&\r\n ln' arg i\r\n\r\n | Tm_Bind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln_st' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_TotBind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_If { b; then_; else_; post } ->\r\n ln' b i &&\r\n ln_st' then_ i &&\r\n ln_st' else_ i &&\r\n ln_opt' ln' post (i + 1)\r\n \r\n | Tm_Match {sc; returns_; brs } ->\r\n ln' sc i &&\r\n ln_opt' ln' returns_ i &&\r\n ln_branches' t brs i\r\n\r\n | Tm_IntroPure { p }\r\n | Tm_ElimExists { p } ->\r\n ln' p i\r\n\r\n | Tm_IntroExists { p; witnesses } ->\r\n ln' p i &&\r\n ln_list' witnesses i\r\n \r\n | Tm_While { invariant; condition; body } ->\r\n ln' invariant (i + 1) &&\r\n ln_st' condition i &&\r\n ln_st' body i\r\n\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n ln' pre1 i &&\r\n ln_st' body1 i &&\r\n ln' post1 (i + 1) &&\r\n ln' pre2 i &&\r\n ln_st' body2 i &&\r\n ln' post2 (i + 1)\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln' length i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n ln' t1 i &&\r\n ln' t2 i\r\n\r\n | Tm_Admit { typ; post } ->\r\n ln' typ i &&\r\n ln_opt' ln' post (i + 1)\r\n\r\n | Tm_Unreachable ->\r\n true\r\n\r\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\r\n let n = L.length binders in\r\n ln_proof_hint' hint_type (i + n) &&\r\n ln_st' t (i + n)\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n ln' name i &&\r\n ln_st' body i &&\r\n ln_opt'\r\n (fun (b, r) i ->\r\n ln' b.binder_ty i &&\r\n ln' r (i + 1))\r\n returns_inv i\r\n\r\nand ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) =\r\n let (p, e) = b in\r\n ln_pattern' p i &&\r\n ln_st' e (i + pattern_shift_n p)\r\n \r\nand ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) =\r\n for_all_dec t brs (fun b -> ln_branch' b i)", "let ln (t:term) = ln' t (-1)", "let ln_st (t:st_term) = ln_st' t (-1)", "let ln_c (c:comp) = ln_c' c (-1)", "subst_elt", "DT", "DT", "DT", "NT", "NT", "NT", "ND", "ND", "ND", "let shift_subst_elt (n:nat) = function\r\n | DT i t -> DT (i + n) t\r\n | NT x t -> NT x t\r\n | ND x i -> ND x (i + n)", "let subst = list subst_elt", "let shift_subst_n (n:nat) = L.map (shift_subst_elt n)", "let shift_subst = shift_subst_n 1", "let rt_subst_elt = function\r\n | DT i t -> RT.DT i (E.elab_term t)\r\n | NT x t -> RT.NT x (E.elab_term t)\r\n | ND x i -> RT.ND x i", "let rt_subst = L.map rt_subst_elt", "let open_or_close_host_term (t:host_term) (ss:subst)\r\n : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss)))\r\n = admit()", "val subst_host_term (t:host_term) (ss:subst)\r\n : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) })", "let rec subst_term (t:term) (ss:subst)\r\n : Tot term (decreases t)\r\n = let w t' = with_range t' t.range in\r\n match t.t with\r\n | Tm_VProp\r\n | Tm_Emp\r\n | Tm_Inames\r\n | Tm_EmpInames\r\n | Tm_Unknown -> t\r\n\r\n | Tm_Inv p ->\r\n w (Tm_Inv (subst_term p ss))\r\n \r\n | Tm_Pure p ->\r\n w (Tm_Pure (subst_term p ss))\r\n \r\n | Tm_Star l r ->\r\n w (Tm_Star (subst_term l ss)\r\n (subst_term r ss))\r\n \r\n | Tm_ExistsSL u b body ->\r\n w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss }\r\n (subst_term body (shift_subst ss)))\r\n \r\n | Tm_ForallSL u b body ->\r\n w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss }\r\n (subst_term body (shift_subst ss)))\r\n \r\n | Tm_FStar t ->\r\n w (Tm_FStar (subst_host_term t ss))\r\n\r\n | Tm_AddInv i is ->\r\n w (Tm_AddInv (subst_term i ss)\r\n (subst_term is ss))", "let open_term' (t:term) (v:term) (i:index) =\r\n subst_term t [ DT i v ]", "let subst_st_comp (s:st_comp) (ss:subst)\r\n : st_comp =\r\n\r\n { s with res = subst_term s.res ss;\r\n pre = subst_term s.pre ss;\r\n post = subst_term s.post (shift_subst ss) }", "let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp =\r\n subst_st_comp s [ DT i v ]", "let subst_comp (c:comp) (ss:subst)\r\n : comp\r\n = match c with\r\n | C_Tot t ->\r\n C_Tot (subst_term t ss)\r\n\r\n | C_ST s -> C_ST (subst_st_comp s ss)\r\n\r\n | C_STAtomic inames obs s ->\r\n C_STAtomic (subst_term inames ss) obs\r\n (subst_st_comp s ss)\r\n\r\n | C_STGhost s ->\r\n C_STGhost (subst_st_comp s ss)" ], "closest": [ "val open_ascription' (t: comp_ascription) (v: term) (i: index) : comp_ascription\nlet open_ascription' (t:comp_ascription) (v:term) (i:index) : comp_ascription =\r\n subst_ascription t [DT i v]", "val open_comp (b: R.binder) (t: comp) : Tac (binder & comp)\nlet open_comp (b : R.binder) (t : comp) : Tac (binder & comp) =\n let n = fresh () in\n let bv : binder_view = inspect_binder b in\n let nv : R.namedv = pack_namedv {\n uniq = n;\n sort = seal bv.sort;\n ppname = bv.ppname;\n }\n in\n let t' = subst_comp [DB 0 nv] t in\n let bndr : binder = {\n uniq = n;\n sort = bv.sort;\n ppname = bv.ppname;\n qual = bv.qual;\n attrs = bv.attrs;\n }\n in\n (bndr, t')", "val open_comp_with (b: R.binder) (nb: binder) (c: comp) : Tac comp\nlet open_comp_with (b : R.binder) (nb : binder) (c : comp) : Tac comp =\n let nv : R.namedv = pack_namedv {\n uniq = nb.uniq;\n sort = seal nb.sort;\n ppname = nb.ppname;\n }\n in\n let t' = subst_comp [DB 0 nv] c in\n t'", "val open_with (t:term) (v:term) : term\nlet open_with (t:term) (v:term) = RTB.open_with t v", "val close_open_inverse_comp' (c:comp)\r\n (x:var { ~(x `Set.mem` freevars_comp c) } )\r\n (i:index)\r\n : Lemma (ensures close_comp' (open_comp' c (U.term_of_no_name_var x) i) x i == c)\nlet close_open_inverse_comp' (c:comp)\r\n (x:var { ~(x `Set.mem` freevars_comp c) } )\r\n (i:index)\r\n : Lemma (ensures close_comp' (open_comp' c (U.term_of_no_name_var x) i) x i == c)\r\n = match c with\r\n | C_Tot t ->\r\n close_open_inverse' t x i\r\n\r\n | C_ST s \r\n | C_STGhost s -> \r\n close_open_inverse' s.res x i;\r\n close_open_inverse' s.pre x i; \r\n close_open_inverse' s.post x (i + 1)\r\n\r\n | C_STAtomic n _ s -> \r\n close_open_inverse' n x i; \r\n close_open_inverse' s.res x i;\r\n close_open_inverse' s.pre x i; \r\n close_open_inverse' s.post x (i + 1)", "val open_exp' (e: stlc_exp 'a) (v: var) (n: index) : stlc_exp 'a\nlet rec open_exp' (e:stlc_exp 'a) (v:var) (n:index)\n : stlc_exp 'a\n = match e with\n | EUnit -> EUnit\n | EVar m -> EVar m\n | EBVar m -> if m = n then EVar v else EBVar m\n | ELam t e -> ELam t (open_exp' e v (n + 1))\n | EApp e1 e2 -> EApp (open_exp' e1 v n) (open_exp' e2 v n)", "val open_close_inverse'_comp (i:nat) (c:comp { ln'_comp c (i - 1) }) (x:var)\n : Lemma \n (ensures subst_comp\n (subst_comp c [ ND x i ])\n (open_with_var x i)\n == c)\nlet rec open_close_inverse' (i:nat) (t:term { ln' t (i - 1) }) (x:var)\n : Lemma\n (ensures subst_term \n (subst_term t [ ND x i ])\n (open_with_var x i)\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n open_close_inverse' i t1 x;\n open_close_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n open_close_inverse'_binder i b x;\n open_close_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n open_close_inverse'_binder i b x;\n open_close_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n open_close_inverse'_binder i b x;\n open_close_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n open_close_inverse'_terms i attrs x;\n open_close_inverse'_binder i b x;\n (if recf \n then open_close_inverse' (i + 1) def x\n else open_close_inverse' i def x);\n open_close_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n open_close_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> open_close_inverse'_match_returns i m x);\n open_close_inverse'_branches i brs x\n \n | Tv_AscribedT e t tac b ->\n open_close_inverse' i e x;\n open_close_inverse' i t x; \n (match tac with\n | None -> ()\n | Some tac -> open_close_inverse' i tac x)\n\n | Tv_AscribedC e c tac b ->\n open_close_inverse' i e x;\n open_close_inverse'_comp i c x; \n (match tac with\n | None -> ()\n | Some tac -> open_close_inverse' i tac x)\n \n\nand open_close_inverse'_binder (i:nat) (b:binder { ln'_binder b (i - 1) }) (x:var)\n : Lemma (ensures subst_binder\n (subst_binder b [ ND x i ])\n (open_with_var x i)\n == b)\n (decreases b) \n = let bndr = inspect_binder b in\n let {ppname; qual=q; attrs=attrs; sort=sort} = bndr in\n open_close_inverse' i sort x;\n open_close_inverse'_terms i attrs x;\n assert (subst_terms (subst_terms attrs [ ND x i ])\n (open_with_var x i) == attrs); \n pack_inspect_binder b; \n assert (pack_binder {ppname; qual=q; attrs=attrs; sort=sort} == b)\n\nand open_close_inverse'_terms (i:nat) (ts:list term { ln'_terms ts (i - 1) }) (x:var)\n : Lemma (ensures subst_terms\n (subst_terms ts [ ND x i ])\n (open_with_var x i)\n == ts)\n (decreases ts) \n = match ts with\n | [] -> ()\n | t::ts -> \n open_close_inverse' i t x;\n open_close_inverse'_terms i ts x\n\nand open_close_inverse'_comp (i:nat) (c:comp { ln'_comp c (i - 1) }) (x:var)\n : Lemma \n (ensures subst_comp\n (subst_comp c [ ND x i ])\n (open_with_var x i)\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t -> open_close_inverse' i t x\n\n | C_Lemma pre post pats ->\n open_close_inverse' i pre x;\n open_close_inverse' i post x;\n open_close_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n open_close_inverse' i res x;\n open_close_inverse'_args i args x;\n open_close_inverse'_terms i decrs x \n\nand open_close_inverse'_args (i:nat) \n (ts:list argv { ln'_args ts (i - 1) })\n (x:var)\n : Lemma\n (ensures subst_args\n (subst_args ts [ ND x i ])\n (open_with_var x i)\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | (t,q)::ts -> \n open_close_inverse' i t x;\n open_close_inverse'_args i ts x\n\nand open_close_inverse'_patterns (i:nat)\n (ps:list (pattern & bool) { ln'_patterns ps (i - 1) })\n (x:var)\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps [ ND x i ])\n (open_with_var x i)\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n open_close_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p [ ND x i ];\n open_close_inverse'_patterns (i + n) ps' x\n\nand open_close_inverse'_pattern (i:nat) (p:pattern{ln'_pattern p (i - 1)}) (x:var)\n : Lemma \n (ensures subst_pattern\n (subst_pattern p [ ND x i ])\n (open_with_var x i)\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n open_close_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> open_close_inverse' i t x\n\n \nand open_close_inverse'_branch (i:nat) (br:branch{ln'_branch br (i - 1)}) (x:var)\n : Lemma\n (ensures subst_branch\n (subst_branch br [ ND x i ])\n (open_with_var x i)\n == br)\n (decreases br) \n = let p, t = br in\n let j = binder_offset_pattern p in\n binder_offset_pattern_invariant p [ ND x i ];\n open_close_inverse'_pattern i p x;\n open_close_inverse' (i + j) t x\n \nand open_close_inverse'_branches (i:nat)\n (brs:list branch { ln'_branches brs (i - 1) })\n (x:var)\n : Lemma\n (ensures subst_branches\n (subst_branches brs [ ND x i ])\n (open_with_var x i)\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | br::brs -> \n open_close_inverse'_branch i br x;\n open_close_inverse'_branches i brs x\n \nand open_close_inverse'_match_returns (i:nat) \n (m:match_returns_ascription { ln'_match_returns m (i - 1) })\n (x:var)\n : Lemma \n (ensures subst_match_returns\n (subst_match_returns m [ ND x i ])\n (open_with_var x i)\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n open_close_inverse'_binder i b x;\n let ret =\n match ret with\n | Inl t ->\n open_close_inverse' (i + 1) t x\n | Inr c ->\n open_close_inverse'_comp (i + 1) c x\n in\n let as_ =\n match as_ with\n | None -> ()\n | Some t ->\n open_close_inverse' (i + 1) t x\n in\n ()", "val open_with_gt_ln_comp (c:comp) (i:int) (t:term) (j:nat)\r\n : Lemma (requires ln_c' c i /\\ i < j)\r\n (ensures open_comp' c t j == c)\nlet open_with_gt_ln_comp (c:comp) (i:int) (t:term) (j:nat)\r\n : Lemma (requires ln_c' c i /\\ i < j)\r\n (ensures open_comp' c t j == c) =\r\n match c with\r\n | C_Tot t1 -> open_with_gt_ln t1 i t j\r\n | C_ST s\r\n | C_STGhost s -> open_with_gt_ln_st s i t j\r\n | C_STAtomic inames _ s ->\r\n open_with_gt_ln inames i t j;\r\n open_with_gt_ln_st s i t j", "val mk_comp (c: comp_typ) : R.comp\nlet mk_comp (c:comp_typ) : R.comp =\n match fst c with\n | T.E_Total -> mk_total (snd c)\n | T.E_Ghost -> mk_ghost (snd c)", "val open_term (t:term) (v:var) : term\nlet open_term (t:term) (v:var) = RTB.open_term t v", "val comp_res (c: comp) : term\nlet comp_res (c:comp) : term =\n match c with\n | C_Tot ty -> ty\n | C_ST s\n | C_STAtomic _ _ s\n | C_STGhost s -> s.res", "val visit_comp (ff: (term -> Tac term)) (c: comp) : Tac comp\nlet rec visit_tm (ff : term -> Tac term) (t : term) : Tac term =\n let tv = inspect_ln t in\n let tv' =\n match tv with\n | Tv_FVar _\n | Tv_Var _\n | Tv_BVar _\n | Tv_UInst _ _ -> tv\n\n | Tv_Type u -> Tv_Type u\n | Tv_Const c -> Tv_Const c\n | Tv_Uvar i u -> Tv_Uvar i u\n | Tv_Unknown -> Tv_Unknown\n | Tv_Unsupp -> Tv_Unsupp\n | Tv_Arrow b c ->\n let b = on_sort_binder (visit_tm ff) b in\n let c = visit_comp ff c in\n Tv_Arrow b c\n | Tv_Abs b t ->\n let b = on_sort_binder (visit_tm ff) b in\n let t = visit_tm ff t in\n Tv_Abs b t\n | Tv_App l (r, q) ->\n let l = visit_tm ff l in\n let r = visit_tm ff r in\n Tv_App l (r, q)\n | Tv_Refine b r ->\n let b = on_sort_simple_binder (visit_tm ff) b in\n let r = visit_tm ff r in\n Tv_Refine b r\n | Tv_Let r attrs b def t ->\n let b = on_sort_simple_binder (visit_tm ff) b in\n let def = visit_tm ff def in\n let t = visit_tm ff t in\n Tv_Let r attrs b def t\n | Tv_Match sc ret_opt brs ->\n let sc = visit_tm ff sc in\n let ret_opt = map_opt (fun (b, asc) ->\n let b = on_sort_binder (visit_tm ff) b in\n let asc =\n match asc with\n | Inl t, tacopt, use_eq ->\n Inl (visit_tm ff t), map_opt (visit_tm ff) tacopt, use_eq\n | Inr c, tacopt, use_eq->\n Inr (visit_comp ff c), map_opt (visit_tm ff) tacopt, use_eq in\n b, asc) ret_opt in\n let brs = map (visit_br ff) brs in\n Tv_Match sc ret_opt brs\n | Tv_AscribedT e t topt use_eq ->\n let e = visit_tm ff e in\n let t = visit_tm ff t in\n Tv_AscribedT e t topt use_eq\n | Tv_AscribedC e c topt use_eq ->\n let e = visit_tm ff e in\n let c = visit_comp ff c in\n Tv_AscribedC e c topt use_eq\n in\n ff (pack_ln tv')\nand visit_br (ff : term -> Tac term) (b:branch) : Tac branch =\n let (p, t) = b in\n let p = visit_pat ff p in\n let t = visit_tm ff t in\n (p, t)\nand visit_pat (ff : term -> Tac term) (p:pattern) : Tac pattern =\n match p with\n | Pat_Constant _ -> p\n | Pat_Var v s -> Pat_Var v s\n | Pat_Cons head univs subpats ->\n let subpats = (map (fun(p,b) -> (visit_pat ff p, b)) subpats) in\n Pat_Cons head univs subpats\n | Pat_Dot_Term t ->\n let t = map_opt (visit_tm ff) t in\n Pat_Dot_Term t\n\nand visit_comp (ff : term -> Tac term) (c : comp) : Tac comp =\n let cv = inspect_comp c in\n let cv' =\n match cv with\n | C_Total ret ->\n let ret = visit_tm ff ret in\n C_Total ret\n\n | C_GTotal ret ->\n let ret = visit_tm ff ret in\n C_GTotal ret\n\n | C_Lemma pre post pats ->\n let pre = visit_tm ff pre in\n let post = visit_tm ff post in\n let pats = visit_tm ff pats in\n C_Lemma pre post pats\n\n | C_Eff us eff res args decrs ->\n let res = visit_tm ff res in\n let args = map (fun (a, q) -> (visit_tm ff a, q)) args in\n let decrs = map (visit_tm ff) decrs in\n C_Eff us eff res args decrs\n in\n pack_comp cv'", "val inst_comp : env -> comp -> list term -> Tac comp\nlet rec inst_comp e c tl =\n match tl with\n | [] -> c\n | t :: tl' ->\n let c' = try inst_comp_once e c t\n with | MetaAnalysis msg -> mfail (\"inst_comp: error: \" ^ msg)\n | err -> raise err\n in\n inst_comp e c' tl'", "val ss_comp (c:comp) (ss:ss_t) : comp\nlet rec ss_comp (c:comp) (ss:ss_t)\n : Tot comp (decreases L.length ss.l) =\n match ss.l with\n | [] -> c\n | y::tl ->\n let c = subst_comp c [ NT y (Map.sel ss.m y) ] in\n ss_comp c (tail ss)", "val st_comp_of_comp (c: comp{stateful_comp c}) : st_comp\nlet st_comp_of_comp (c:comp{stateful_comp c}) : st_comp =\n match c with\n | C_ST s\n | C_STAtomic _ _ s\n | C_STGhost s -> s", "val elab_comp (c: comp) : R.term\nlet elab_comp (c:comp)\n : R.term\n = match c with\n | C_Tot t ->\n elab_term t\n\n | C_ST c ->\n let u, res, pre, post = elab_st_comp c in\n mk_stt_comp u res pre (mk_abs res R.Q_Explicit post)\n\n | C_STAtomic inames obs c ->\n let inames = elab_term inames in\n let u, res, pre, post = elab_st_comp c in\n let post = mk_abs res R.Q_Explicit post in\n mk_stt_atomic_comp (elab_observability obs) u res inames pre post\n\n | C_STGhost c ->\n let u, res, pre, post = elab_st_comp c in\n mk_stt_ghost_comp u res pre (mk_abs res R.Q_Explicit post)", "val elab_comp_open_commute' (c: comp) (v: term) (n: index)\n : Lemma\n (ensures RT.subst_term (elab_comp c) [RT.DT n (elab_term v)] == elab_comp (open_comp' c v n))\nlet elab_comp_open_commute' (c:comp) (v:term) (n:index)\n : Lemma (ensures\n RT.subst_term (elab_comp c) [ RT.DT n (elab_term v) ] ==\n elab_comp (open_comp' c v n))\n = match c with\n | C_Tot t -> elab_open_commute' t v n\n | C_ST s\n | C_STGhost s -> \n elab_open_commute' s.res v n;\n elab_open_commute' s.pre v n;\n elab_open_commute' s.post v (n + 1)\n | C_STAtomic inames _ s ->\n elab_open_commute' inames v n;\n elab_open_commute' s.res v n;\n elab_open_commute' s.pre v n;\n elab_open_commute' s.post v (n + 1)", "val close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\nlet rec close_open_inverse' (i:nat)\n (t:term) \n (x:var { ~(x `Set.mem` freevars t) })\n : Lemma \n (ensures subst_term \n (subst_term t (open_with_var x i))\n [ ND x i ]\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_Uvar _ _ -> assert false\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> ()\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n close_open_inverse' i t1 x;\n close_open_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n close_open_inverse'_binder i b x;\n close_open_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n close_open_inverse'_binder i b x;\n close_open_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n close_open_inverse'_terms i attrs x;\n close_open_inverse'_binder i b x;\n close_open_inverse' (if recf then (i + 1) else i) def x;\n close_open_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n close_open_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> close_open_inverse'_match_returns i m x);\n close_open_inverse'_branches i brs x\n\n | Tv_AscribedT e t tac b ->\n close_open_inverse' i e x;\n close_open_inverse' i t x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n\n | Tv_AscribedC e c tac b ->\n close_open_inverse' i e x;\n close_open_inverse'_comp i c x;\n (match tac with\n | None -> ()\n | Some t -> close_open_inverse' i t x)\n \nand close_open_inverse'_comp (i:nat)\n (c:comp)\n (x:var{ ~(x `Set.mem` freevars_comp c) })\n : Lemma\n (ensures subst_comp \n (subst_comp c (open_with_var x i))\n [ ND x i ]\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t \n | C_GTotal t -> \n close_open_inverse' i t x\n\n | C_Lemma pre post pats ->\n close_open_inverse' i pre x;\n close_open_inverse' i post x;\n close_open_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n close_open_inverse' i res x;\n close_open_inverse'_args i args x;\n close_open_inverse'_terms i decrs x\n\nand close_open_inverse'_args (i:nat) (args:list argv) (x:var{ ~(x `Set.mem` freevars_args args) })\n : Lemma\n (ensures subst_args \n (subst_args args (open_with_var x i))\n [ ND x i]\n == args)\n (decreases args)\n = match args with\n | [] -> ()\n | (a, q) :: args ->\n close_open_inverse' i a x;\n close_open_inverse'_args i args x\n\nand close_open_inverse'_binder (i:nat) (b:binder) (x:var{ ~(x `Set.mem` freevars_binder b) })\n : Lemma \n (ensures subst_binder \n (subst_binder b (open_with_var x i))\n [ ND x i ]\n == b)\n (decreases b)\n = let bndr = inspect_binder b in\n close_open_inverse' i bndr.sort x;\n close_open_inverse'_terms i bndr.attrs x;\n pack_inspect_binder b\n\nand close_open_inverse'_terms (i:nat) (ts:list term) (x:var{ ~(x `Set.mem` freevars_terms ts) })\n : Lemma \n (ensures subst_terms \n (subst_terms ts (open_with_var x i))\n [ ND x i ]\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | hd :: tl ->\n close_open_inverse' i hd x;\n close_open_inverse'_terms i tl x\n\nand close_open_inverse'_branches (i:nat) (brs:list branch) \n (x:var{ ~(x `Set.mem` freevars_branches brs) })\n : Lemma\n (ensures subst_branches\n (subst_branches brs (open_with_var x i))\n [ ND x i ]\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | b :: brs ->\n close_open_inverse'_branch i b x;\n close_open_inverse'_branches i brs x\n\nand close_open_inverse'_branch (i:nat)\n (br:branch)\n (x:var{ ~(x `Set.mem` freevars_branch br) })\n : Lemma\n (ensures subst_branch\n (subst_branch br (open_with_var x i))\n [ ND x i ]\n == br)\n (decreases br)\n = let p, t = br in\n close_open_inverse'_pattern i p x;\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse' (i + binder_offset_pattern p) t x\n\n\nand close_open_inverse'_pattern (i:nat)\n (p:pattern)\n (x:var{ ~(x `Set.mem` freevars_pattern p) })\n : Lemma\n (ensures subst_pattern\n (subst_pattern p (open_with_var x i))\n [ ND x i ]\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n close_open_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> close_open_inverse' i t x\n\nand close_open_inverse'_patterns (i:nat)\n (ps:list (pattern & bool))\n (x:var {~ (x `Set.mem` freevars_patterns ps) })\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps (open_with_var x i))\n [ ND x i ]\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n close_open_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p (open_with_var x i);\n close_open_inverse'_patterns (i + n) ps' x\n\nand close_open_inverse'_match_returns (i:nat) (m:match_returns_ascription)\n (x:var{ ~(x `Set.mem` freevars_match_returns m) })\n : Lemma\n (ensures subst_match_returns\n (subst_match_returns m (open_with_var x i))\n [ ND x i ]\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n close_open_inverse'_binder i b x;\n (match ret with\n | Inl t -> close_open_inverse' (i + 1) t x\n | Inr c -> close_open_inverse'_comp (i + 1) c x);\n (match as_ with\n | None -> ()\n | Some t -> close_open_inverse' (i + 1) t x)", "val open_exp' (e: src_exp) (v: var) (n: index) : e': src_exp{size e == size e'}\nlet rec open_exp' (e:src_exp) (v:var) (n:index)\n : e':src_exp { size e == size e'}\n = match e with\n | EBool _ -> e\n | EVar m -> EVar m\n | EBVar m -> if m = n then EVar v else EBVar m\n | EIf b e1 e2 -> EIf (open_exp' b v n) (open_exp' e1 v n) (open_exp' e2 v n)\n | ELam t e -> ELam t (open_exp' e v (n + 1))\n | EApp e1 e2 -> EApp (open_exp' e1 v n) (open_exp' e2 v n)", "val close_ascription' (t: comp_ascription) (x: var) (i: index) : comp_ascription\nlet close_ascription' (t:comp_ascription) (x:var) (i:index) : comp_ascription =\r\n subst_ascription t [ND x i]", "val open_comp_simple (b: R.simple_binder) (t: comp) : Tac (simple_binder & comp)\nlet open_comp_simple (b : R.simple_binder) (t : comp) : Tac (simple_binder & comp) =\n let n = fresh () in\n let bv : binder_view = inspect_binder b in\n let nv : R.namedv = pack_namedv {\n uniq = n;\n sort = seal bv.sort;\n ppname = bv.ppname;\n }\n in\n let t' = subst_comp [DB 0 nv] t in\n let bndr : binder = {\n uniq = n;\n sort = bv.sort;\n ppname = bv.ppname;\n qual = bv.qual;\n attrs = bv.attrs;\n }\n in\n (bndr, t')", "val open_exp' (e: stlc_exp) (v: var) (n: index) : e': stlc_exp{size e == size e'}\nlet rec open_exp' (e:stlc_exp) (v:var) (n:index)\n : e':stlc_exp { size e == size e'}\n = match e with\n | EUnit -> EUnit\n | EVar m -> EVar m\n | EBVar m -> if m = n then EVar v else EBVar m\n | ELam t e -> ELam t (open_exp' e v (n + 1))\n | EApp e1 e2 -> EApp (open_exp' e1 v n) (open_exp' e2 v n)", "val close_comp (b: binder) (t: comp) : R.binder & comp\nlet close_comp (b:binder) (t:comp) : R.binder & comp =\n let nv = r_binder_to_namedv b in\n let t' = subst_comp [NM nv 0] t in\n let b = pack_binder { sort = b.sort; ppname = b.ppname; qual = b.qual; attrs = b.attrs } in\n (b, t')", "val ln'_comp (c: comp) (i: int) : Tot bool (decreases c)\nlet rec ln' (e:term) (n:int)\n : Tot bool (decreases e)\n = match inspect_ln e with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unknown \n | Tv_Unsupp\n | Tv_Var _ -> true\n | Tv_BVar m -> bv_index m <= n\n | Tv_App e1 (e2, _) -> ln' e1 n && ln' e2 n\n | Tv_Abs b body -> \n ln'_binder b n &&\n ln' body (n + 1)\n\n | Tv_Arrow b c ->\n ln'_binder b n &&\n ln'_comp c (n + 1)\n\n | Tv_Refine b f ->\n ln'_binder b n &&\n ln' f (n + 1)\n\n | Tv_Uvar _ _ ->\n false\n \n | Tv_Let recf attrs b def body ->\n ln'_terms attrs n &&\n ln'_binder b n &&\n (if recf then ln' def (n + 1) else ln' def n) &&\n ln' body (n + 1)\n\n | Tv_Match scr ret brs ->\n ln' scr n &&\n (match ret with\n | None -> true\n | Some m -> ln'_match_returns m n) &&\n ln'_branches brs n\n \n | Tv_AscribedT e t tac b ->\n ln' e n &&\n ln' t n &&\n (match tac with\n | None -> true\n | Some tac -> ln' tac n)\n \n | Tv_AscribedC e c tac b ->\n ln' e n &&\n ln'_comp c n &&\n (match tac with\n | None -> true\n | Some tac -> ln' tac n)\n \nand ln'_comp (c:comp) (i:int)\n : Tot bool (decreases c)\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t -> ln' t i\n\n | C_Lemma pre post pats ->\n ln' pre i &&\n ln' post i &&\n ln' pats i\n\n | C_Eff us eff_name res args decrs ->\n ln' res i &&\n ln'_args args i &&\n ln'_terms decrs i\n\nand ln'_args (ts:list argv) (i:int)\n : Tot bool (decreases ts)\n = match ts with\n | [] -> true\n | (t,q)::ts -> \n ln' t i &&\n ln'_args ts i\n\nand ln'_binder (b:binder) (n:int)\n : Tot bool (decreases b)\n = let bndr = inspect_binder b in\n ln' bndr.sort n &&\n ln'_terms bndr.attrs n\n\nand ln'_terms (ts:list term) (n:int)\n : Tot bool (decreases ts)\n = match ts with\n | [] -> true\n | t::ts -> ln' t n && ln'_terms ts n\n\nand ln'_patterns (ps:list (pattern & bool)) (i:int)\n : Tot bool\n (decreases ps)\n = match ps with\n | [] -> true\n | (p, b)::ps ->\n let b0 = ln'_pattern p i in\n let n = binder_offset_pattern p in\n let b1 = ln'_patterns ps (i + n) in\n b0 && b1\n\nand ln'_pattern (p:pattern) (i:int) \n : Tot bool\n (decreases p)\n = match p with\n | Pat_Constant _ -> true\n\n | Pat_Cons head univs subpats ->\n ln'_patterns subpats i\n \n | Pat_Var bv s -> true\n\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> true\n | Some t -> ln' t i)\n \nand ln'_branch (br:branch) (i:int)\n : Tot bool (decreases br)\n = let p, t = br in\n let b = ln'_pattern p i in\n let j = binder_offset_pattern p in\n let b' = ln' t (i + j) in\n b&&b'\n \nand ln'_branches (brs:list branch) (i:int)\n : Tot bool (decreases brs)\n = match brs with\n | [] -> true\n | br::brs -> \n ln'_branch br i &&\n ln'_branches brs i\n \nand ln'_match_returns (m:match_returns_ascription) (i:int)\n : Tot bool (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = ln'_binder b i in\n let ret =\n match ret with\n | Inl t -> ln' t (i + 1)\n | Inr c -> ln'_comp c (i + 1)\n in\n let as_ =\n match as_ with\n | None -> true\n | Some t -> ln' t (i + 1)\n in\n b && ret && as_", "val visit_comp (ff: (term -> Tac unit)) (c: comp) : Tac unit\nlet rec visit_tm (ff : term -> Tac unit) (t : term) : Tac unit =\n let tv = inspect t in\n (match tv with\n | Tv_FVar _\n | Tv_UInst _ _\n | Tv_Var _\n | Tv_BVar _ -> ()\n\n | Tv_Type _ -> ()\n | Tv_Const c -> ()\n | Tv_Uvar i u -> ()\n | Tv_Unsupp -> ()\n | Tv_Unknown -> ()\n | Tv_Arrow b c ->\n on_sort_binder ff b;\n visit_comp ff c\n | Tv_Abs b t ->\n let b = on_sort_binder (visit_tm ff) b in\n visit_tm ff t\n\n | Tv_App l (r, q) ->\n visit_tm ff l;\n visit_tm ff r\n\n | Tv_Refine b r ->\n on_sort_binder ff b;\n visit_tm ff r\n\n | Tv_Let r attrs b def t ->\n on_sort_binder ff b;\n visit_tm ff def;\n visit_tm ff t\n\n | Tv_Match sc _ brs ->\n visit_tm ff sc;\n iter (visit_br ff) brs\n\n | Tv_AscribedT e t topt _ ->\n visit_tm ff e;\n visit_tm ff t\n\n | Tv_AscribedC e c topt _ ->\n visit_tm ff e\n\n ); ff t\n\nand visit_br (ff : term -> Tac unit) (b:branch) : Tac unit =\n let (p, t) = b in\n visit_tm ff t\n\nand visit_comp (ff : term -> Tac unit) (c : comp) : Tac unit =\n let cv = inspect_comp c in\n match cv with\n | C_Total ret -> visit_tm ff ret\n | C_GTotal ret -> visit_tm ff ret\n\n | C_Lemma pre post pats ->\n visit_tm ff pre;\n visit_tm ff post;\n visit_tm ff pats\n\n | C_Eff us eff res args decrs ->\n visit_tm ff res;\n iter (fun (a, q) -> visit_tm ff a) args;\n iter (visit_tm ff) decrs", "val subst_comp (s: subst_t) (c: comp) : comp\nlet subst_comp (s : subst_t) (c : comp) : comp =\n inspect_comp (R.subst_comp s (pack_comp c))", "val check_comp (c: comp) : Tac bool\nlet rec check (t:term) : Tac bool =\n match inspect t with\n (* We are using the named view, which opens terms\n as needed on every node. If we reach a bvar, the original\n term is not LN. *)\n | Tv_BVar bv -> false\n\n | Tv_Const _ -> true\n | Tv_Uvar _ _ -> false (* conservative *)\n\n | Tv_Var _ -> true\n | Tv_FVar _ -> true\n | Tv_UInst _ us -> for_all check_u us\n | Tv_App hd (a, q) -> if check hd then check a else false\n | Tv_Abs b body -> if check b.sort then check body else false\n | Tv_Arrow b c -> if check b.sort then check_comp c else false\n | Tv_Type u -> check_u u\n | Tv_Refine b ref -> if check b.sort then check ref else false\n | Tv_Let recf attrs b def body ->\n if not (for_all check attrs) then false else\n if not (check def) then false else\n check body\n | Tv_Match sc _ brs -> \n if check sc then for_all check_br brs else false\n | Tv_AscribedT e t _ _ ->\n if check e then check t else false\n | Tv_AscribedC e c _ _ ->\n if check e then check_comp c else false\n\n | Tv_Unknown -> true\n | Tv_Unsupp -> true // hm..\nand check_u (u:universe) : Tac bool =\n match inspect_universe u with\n | Uv_BVar _ -> false\n | Uv_Name _ -> true\n | Uv_Unif _ -> false (* conservative *)\n | Uv_Zero -> true\n | Uv_Succ u -> check_u u\n | Uv_Max us -> for_all check_u us\n | Uv_Unk -> true\nand check_comp (c:comp) : Tac bool =\n match c with\n | C_Total typ -> check typ\n | C_GTotal typ -> check typ\n | C_Lemma pre post pats -> \n if not (check pre) then false else\n if not (check post) then false else\n check pats\n | C_Eff us nm res args decrs ->\n if not (for_all check_u us) then false else\n if not (check res) then false else\n if not (for_all (fun (a,q) -> check a) args) then false else\n if not (for_all check decrs) then false else\n true\n \nand check_br (b:branch) : Tac bool =\n (* Could check the pattern's ascriptions too. *)\n let (p, t) = b in\n check t", "val comp_inames (c: comp{C_STAtomic? c}) : term\nlet comp_inames (c:comp { C_STAtomic? c }) : term =\n match c with\n | C_STAtomic inames _ _ -> inames", "val bind_comp_pre (x: var) (c1 c2: comp_st) : prop\nlet bind_comp_pre (x:var) (c1 c2:comp_st)\n : prop\n = open_term (comp_post c1) x == comp_pre c2 /\\\n (~ (x `Set.mem` freevars (comp_post c2))) /\\ //x doesn't escape in the result type\n bind_comp_compatible c1 c2", "val comp_par (cL: comp{C_ST? cL}) (cR: comp{C_ST? cR}) (x: var) : comp\nlet comp_par (cL:comp{C_ST? cL}) (cR:comp{C_ST? cR}) (x:var) : comp =\n let uL = comp_u cL in\n let uR = comp_u cR in\n let aL = comp_res cL in\n let aR = comp_res cR in\n\n let post = par_post uL uR aL aR (comp_post cL) (comp_post cR) x in\n\n C_ST {\n u = uL;\n res = mk_tuple2 uL uR aL aR;\n pre = tm_star (comp_pre cL) (comp_pre cR);\n post\n }", "val open_with_var_elt (x: var) (i: nat) : subst_elt\nlet open_with_var_elt (x:var) (i:nat) : subst_elt =\n DT i (pack_ln (Tv_Var (var_as_namedv x)))", "val close_comp_with_non_free_var (c:comp) (x:var) (i:nat)\r\n : Lemma\r\n (requires ~ (x `Set.mem` freevars_comp c))\r\n (ensures close_comp' c x i == c)\nlet close_comp_with_non_free_var (c:comp) (x:var) (i:nat)\r\n : Lemma\r\n (requires ~ (x `Set.mem` freevars_comp c))\r\n (ensures close_comp' c x i == c) =\r\n match c with\r\n | C_Tot t1 -> close_with_non_freevar t1 x i\r\n | C_ST s \r\n | C_STGhost s ->\r\n close_with_non_freevar_st s x i\r\n | C_STAtomic inames _ s ->\r\n close_with_non_freevar inames x i;\r\n close_with_non_freevar_st s x i", "val open_with_var (x: var) (i: nat) : subst\nlet open_with_var (x:var) (i:nat) : subst = [open_with_var_elt x i]", "val compare_comp (c1 c2: comp) : Tot order (decreases c1)\nlet rec compare_term (s t : term) : Tot order (decreases s) =\n match inspect_ln s, inspect_ln t with\n | Tv_Var sv, Tv_Var tv ->\n compare_namedv sv tv\n\n | Tv_BVar sv, Tv_BVar tv ->\n compare_bv sv tv\n\n | Tv_FVar sv, Tv_FVar tv ->\n compare_fv sv tv\n\n | Tv_UInst sv sus, Tv_UInst tv tus ->\n lex (compare_fv sv tv) (fun _ -> compare_universes sus tus)\n\n | Tv_App h1 a1, Tv_App h2 a2 ->\n lex (compare_term h1 h2) (fun () -> compare_argv a1 a2)\n\n | Tv_Abs b1 e1, Tv_Abs b2 e2 ->\n lex (compare_binder b1 b2) (fun () -> compare_term e1 e2)\n\n | Tv_Refine b1 e1, Tv_Refine b2 e2 ->\n lex (compare_binder b1 b2) (fun () ->\n compare_term e1 e2)\n\n | Tv_Arrow b1 e1, Tv_Arrow b2 e2 ->\n lex (compare_binder b1 b2) (fun () -> compare_comp e1 e2)\n\n | Tv_Type su, Tv_Type tu -> compare_universe su tu\n\n | Tv_Const c1, Tv_Const c2 ->\n compare_const c1 c2\n\n | Tv_Uvar u1 _, Tv_Uvar u2 _->\n compare_int u1 u2\n\n | Tv_Let _r1 _attrs1 b1 t1 t1', Tv_Let _r2 _attrs2 b2 t2 t2' ->\n lex (compare_binder b1 b2) (fun () ->\n lex (compare_term t1 t2) (fun () ->\n compare_term t1' t2'))\n\n | Tv_Match _ _ _, Tv_Match _ _ _ ->\n Eq // TODO\n\n | Tv_AscribedT e1 t1 tac1 _, Tv_AscribedT e2 t2 tac2 _ ->\n lex (compare_term e1 e2) (fun () ->\n lex (compare_term t1 t2) (fun () ->\n match tac1, tac2 with\n | None, None -> Eq\n | None, _ -> Lt\n | _, None -> Gt\n | Some e1, Some e2 -> compare_term e1 e2))\n\n | Tv_AscribedC e1 c1 tac1 _, Tv_AscribedC e2 c2 tac2 _ ->\n lex (compare_term e1 e2) (fun () ->\n lex (compare_comp c1 c2) (fun () ->\n match tac1, tac2 with\n | None, None -> Eq\n | None, _ -> Lt\n | _, None -> Gt\n | Some e1, Some e2 -> compare_term e1 e2))\n\n | Tv_Unknown, Tv_Unknown ->\n Eq\n\n | Tv_Unsupp, Tv_Unsupp ->\n Eq\n\n // From here onward, they must have different constructors. Order them arbitrarily as in the definition.\n | Tv_Var _, _ -> Lt | _, Tv_Var _ -> Gt\n | Tv_BVar _, _ -> Lt | _, Tv_BVar _ -> Gt\n | Tv_FVar _, _ -> Lt | _, Tv_FVar _ -> Gt\n | Tv_UInst _ _, _ -> Lt | _, Tv_UInst _ _ -> Gt\n | Tv_App _ _, _ -> Lt | _, Tv_App _ _ -> Gt\n | Tv_Abs _ _, _ -> Lt | _, Tv_Abs _ _ -> Gt\n | Tv_Arrow _ _, _ -> Lt | _, Tv_Arrow _ _ -> Gt\n | Tv_Type _, _ -> Lt | _, Tv_Type _ -> Gt\n | Tv_Refine _ _ , _ -> Lt | _, Tv_Refine _ _ -> Gt\n | Tv_Const _, _ -> Lt | _, Tv_Const _ -> Gt\n | Tv_Uvar _ _, _ -> Lt | _, Tv_Uvar _ _ -> Gt\n | Tv_Let _ _ _ _ _, _ -> Lt | _, Tv_Let _ _ _ _ _ -> Gt\n | Tv_Match _ _ _, _ -> Lt | _, Tv_Match _ _ _ -> Gt\n | Tv_AscribedT _ _ _ _, _ -> Lt | _, Tv_AscribedT _ _ _ _ -> Gt\n | Tv_AscribedC _ _ _ _, _ -> Lt | _, Tv_AscribedC _ _ _ _ -> Gt\n | Tv_Unknown, _ -> Lt | _, Tv_Unknown -> Gt\n | Tv_Unsupp, _ -> Lt | _, Tv_Unsupp -> Gt\nand compare_term_list (l1 l2:list term) : Tot order (decreases l1) =\n match l1, l2 with\n | [], [] -> Eq\n | [], _ -> Lt\n | _, [] -> Gt\n | hd1::tl1, hd2::tl2 ->\n lex (compare_term hd1 hd2) (fun () -> compare_term_list tl1 tl2)\n\nand compare_argv (a1 a2 : argv) : Tot order (decreases a1) =\n let a1, q1 = a1 in\n let a2, q2 = a2 in\n match q1, q2 with\n (* We should never see Q_Meta here *)\n | Q_Implicit, Q_Explicit -> Lt\n | Q_Explicit, Q_Implicit -> Gt\n | _, _ -> compare_term a1 a2\nand compare_comp (c1 c2 : comp) : Tot order (decreases c1) =\n let cv1 = inspect_comp c1 in\n let cv2 = inspect_comp c2 in\n match cv1, cv2 with\n | C_Total t1, C_Total t2\n\n | C_GTotal t1, C_GTotal t2 -> compare_term t1 t2\n\n | C_Lemma p1 q1 s1, C_Lemma p2 q2 s2 ->\n lex (compare_term p1 p2)\n (fun () ->\n lex (compare_term q1 q2)\n (fun () -> compare_term s1 s2)\n )\n\n | C_Eff us1 eff1 res1 args1 _decrs1,\n C_Eff us2 eff2 res2 args2 _decrs2 ->\n (* This could be more complex, not sure it is worth it *)\n lex (compare_universes us1 us2)\n (fun _ -> lex (compare_name eff1 eff2)\n (fun _ -> compare_term res1 res2))\n\n | C_Total _, _ -> Lt | _, C_Total _ -> Gt\n | C_GTotal _, _ -> Lt | _, C_GTotal _ -> Gt\n | C_Lemma _ _ _, _ -> Lt | _, C_Lemma _ _ _ -> Gt\n | C_Eff _ _ _ _ _, _ -> Lt | _, C_Eff _ _ _ _ _ -> Gt\n\nand compare_binder (b1 b2 : binder) : order =\n let bview1 = inspect_binder b1 in\n let bview2 = inspect_binder b2 in\n compare_term bview1.sort bview2.sort", "val compare_comp (c1 c2: comp) : Tot order (decreases c1)\nlet rec compare_term (s t : term) : Tot order (decreases s) =\n match inspect_ln s, inspect_ln t with\n | Tv_Var sv, Tv_Var tv ->\n compare_bv sv tv\n\n | Tv_BVar sv, Tv_BVar tv ->\n compare_bv sv tv\n\n | Tv_FVar sv, Tv_FVar tv ->\n compare_fv sv tv\n\n | Tv_UInst sv sus, Tv_UInst tv tus ->\n lex (compare_fv sv tv) (fun _ -> compare_universes sus tus)\n\n | Tv_App h1 a1, Tv_App h2 a2 ->\n lex (compare_term h1 h2) (fun () -> compare_argv a1 a2)\n\n | Tv_Abs b1 e1, Tv_Abs b2 e2 ->\n lex (compare_binder b1 b2) (fun () -> compare_term e1 e2)\n\n | Tv_Refine bv1 sort1 e1, Tv_Refine bv2 sort2 e2 ->\n lex (compare_bv bv1 bv2) (fun () ->\n lex (compare_term sort1 sort2) (fun () ->\n compare_term e1 e2))\n\n | Tv_Arrow b1 e1, Tv_Arrow b2 e2 ->\n lex (compare_binder b1 b2) (fun () -> compare_comp e1 e2)\n\n | Tv_Type su, Tv_Type tu -> compare_universe su tu\n\n | Tv_Const c1, Tv_Const c2 ->\n compare_const c1 c2\n\n | Tv_Uvar u1 _, Tv_Uvar u2 _->\n compare_int u1 u2\n\n | Tv_Let _r1 _attrs1 bv1 ty1 t1 t1', Tv_Let _r2 _attrs2 bv2 ty2 t2 t2' ->\n lex (compare_bv bv1 bv2) (fun () ->\n lex (compare_term ty1 ty2) (fun () ->\n lex (compare_term t1 t2) (fun () ->\n compare_term t1' t2')))\n\n | Tv_Match _ _ _, Tv_Match _ _ _ ->\n Eq // TODO\n\n | Tv_AscribedT e1 t1 tac1 _, Tv_AscribedT e2 t2 tac2 _ ->\n lex (compare_term e1 e2) (fun () ->\n lex (compare_term t1 t2) (fun () ->\n match tac1, tac2 with\n | None, None -> Eq\n | None, _ -> Lt\n | _, None -> Gt\n | Some e1, Some e2 -> compare_term e1 e2))\n\n | Tv_AscribedC e1 c1 tac1 _, Tv_AscribedC e2 c2 tac2 _ ->\n lex (compare_term e1 e2) (fun () ->\n lex (compare_comp c1 c2) (fun () ->\n match tac1, tac2 with\n | None, None -> Eq\n | None, _ -> Lt\n | _, None -> Gt\n | Some e1, Some e2 -> compare_term e1 e2))\n\n | Tv_Unknown, Tv_Unknown ->\n Eq\n\n | Tv_Unsupp, Tv_Unsupp ->\n Eq\n\n // From here onward, they must have different constructors. Order them arbitrarily as in the definition.\n | Tv_Var _, _ -> Lt | _, Tv_Var _ -> Gt\n | Tv_BVar _, _ -> Lt | _, Tv_BVar _ -> Gt\n | Tv_FVar _, _ -> Lt | _, Tv_FVar _ -> Gt\n | Tv_UInst _ _, _ -> Lt | _, Tv_UInst _ _ -> Gt\n | Tv_App _ _, _ -> Lt | _, Tv_App _ _ -> Gt\n | Tv_Abs _ _, _ -> Lt | _, Tv_Abs _ _ -> Gt\n | Tv_Arrow _ _, _ -> Lt | _, Tv_Arrow _ _ -> Gt\n | Tv_Type _, _ -> Lt | _, Tv_Type _ -> Gt\n | Tv_Refine _ _ _ , _ -> Lt | _, Tv_Refine _ _ _ -> Gt\n | Tv_Const _, _ -> Lt | _, Tv_Const _ -> Gt\n | Tv_Uvar _ _, _ -> Lt | _, Tv_Uvar _ _ -> Gt\n | Tv_Let _ _ _ _ _ _, _ -> Lt | _, Tv_Let _ _ _ _ _ _ -> Gt\n | Tv_Match _ _ _, _ -> Lt | _, Tv_Match _ _ _ -> Gt\n | Tv_AscribedT _ _ _ _, _ -> Lt | _, Tv_AscribedT _ _ _ _ -> Gt\n | Tv_AscribedC _ _ _ _, _ -> Lt | _, Tv_AscribedC _ _ _ _ -> Gt\n | Tv_Unknown, _ -> Lt | _, Tv_Unknown -> Gt\n | Tv_Unsupp, _ -> Lt | _, Tv_Unsupp -> Gt\nand compare_term_list (l1 l2:list term) : Tot order (decreases l1) =\n match l1, l2 with\n | [], [] -> Eq\n | [], _ -> Lt\n | _, [] -> Gt\n | hd1::tl1, hd2::tl2 ->\n lex (compare_term hd1 hd2) (fun () -> compare_term_list tl1 tl2)\n\nand compare_argv (a1 a2 : argv) : Tot order (decreases a1) =\n let a1, q1 = a1 in\n let a2, q2 = a2 in\n match q1, q2 with\n (* We should never see Q_Meta here *)\n | Q_Implicit, Q_Explicit -> Lt\n | Q_Explicit, Q_Implicit -> Gt\n | _, _ -> compare_term a1 a2\nand compare_comp (c1 c2 : comp) : Tot order (decreases c1) =\n let cv1 = inspect_comp c1 in\n let cv2 = inspect_comp c2 in\n match cv1, cv2 with\n | C_Total t1, C_Total t2\n\n | C_GTotal t1, C_GTotal t2 -> compare_term t1 t2\n\n | C_Lemma p1 q1 s1, C_Lemma p2 q2 s2 ->\n lex (compare_term p1 p2)\n (fun () ->\n lex (compare_term q1 q2)\n (fun () -> compare_term s1 s2)\n )\n\n | C_Eff us1 eff1 res1 args1 _decrs1,\n C_Eff us2 eff2 res2 args2 _decrs2 ->\n (* This could be more complex, not sure it is worth it *)\n lex (compare_universes us1 us2)\n (fun _ -> lex (compare_name eff1 eff2)\n (fun _ -> compare_term res1 res2))\n\n | C_Total _, _ -> Lt | _, C_Total _ -> Gt\n | C_GTotal _, _ -> Lt | _, C_GTotal _ -> Gt\n | C_Lemma _ _ _, _ -> Lt | _, C_Lemma _ _ _ -> Gt\n | C_Eff _ _ _ _ _, _ -> Lt | _, C_Eff _ _ _ _ _ -> Gt", "val open_ty' (t: src_ty) (v: src_exp) (n: index) : Tot src_ty (decreases t)\nlet rec open_exp' (e:src_exp) (v:src_exp) (n:index)\n : Tot src_exp\n (decreases e)\n = match e with\n | EBool _ -> e\n | EVar m -> EVar m\n | EBVar m -> if m = n then v else EBVar m\n | EIf b e1 e2 -> EIf (open_exp' b v n) (open_exp' e1 v n) (open_exp' e2 v n)\n | ELam t e -> ELam (open_ty' t v n) (open_exp' e v (n + 1))\n | EApp e1 e2 -> EApp (open_exp' e1 v n) (open_exp' e2 v n)\n \nand open_ty' (t:src_ty) (v:src_exp) (n:index)\n : Tot src_ty\n (decreases t)\n = match t with\n | TBool -> TBool\n | TRefineBool e -> TRefineBool (open_exp' e v (n + 1))\n | TArrow t1 t2 -> TArrow (open_ty' t1 v n) (open_ty' t2 v (n + 1))", "val open_exp' (e v: src_exp) (n: index) : Tot src_exp (decreases e)\nlet rec open_exp' (e:src_exp) (v:src_exp) (n:index)\n : Tot src_exp\n (decreases e)\n = match e with\n | EBool _ -> e\n | EVar m -> EVar m\n | EBVar m -> if m = n then v else EBVar m\n | EIf b e1 e2 -> EIf (open_exp' b v n) (open_exp' e1 v n) (open_exp' e2 v n)\n | ELam t e -> ELam (open_ty' t v n) (open_exp' e v (n + 1))\n | EApp e1 e2 -> EApp (open_exp' e1 v n) (open_exp' e2 v n)\n \nand open_ty' (t:src_ty) (v:src_exp) (n:index)\n : Tot src_ty\n (decreases t)\n = match t with\n | TBool -> TBool\n | TRefineBool e -> TRefineBool (open_exp' e v (n + 1))\n | TArrow t1 t2 -> TArrow (open_ty' t1 v n) (open_ty' t2 v (n + 1))", "val bind_comp_compatible (c1 c2: comp_st) : prop\nlet bind_comp_compatible (c1 c2:comp_st)\n : prop\n = match c1, c2 with\n | C_ST _, C_ST _\n | C_STGhost _, C_STGhost _ -> True\n | C_STAtomic inames1 obs1 _, C_STAtomic inames2 obs2 _ ->\n inames1 == inames2 /\\ at_most_one_observable obs1 obs2\n | _, _ -> False", "val with_st_comp (c: comp{stateful_comp c}) (s: st_comp) : comp\nlet with_st_comp (c:comp{stateful_comp c}) (s:st_comp) : comp =\n match c with\n | C_ST _ -> C_ST s\n | C_STAtomic inames obs _ -> C_STAtomic inames obs s\n | C_STGhost _ -> C_STGhost s", "val elab_comp_post (c: comp_st) : R.term\nlet elab_comp_post (c:comp_st) : R.term =\n let t = elab_term (comp_res c) in\n let post = elab_term (comp_post c) in\n mk_abs t R.Q_Explicit post", "val close_comp_with_not_free_var (c: R.comp) (x: var) (i: nat)\n : Lemma (requires ~(Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ND x i] == c)\n (decreases c)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val bind_comp_out (c1: comp_st) (c2: comp_st{bind_comp_compatible c1 c2}) : comp_st\nlet bind_comp_out (c1:comp_st) (c2:comp_st{bind_comp_compatible c1 c2})\n : comp_st\n = let s : st_comp = {u=comp_u c2; res=comp_res c2; pre=comp_pre c1; post=comp_post c2} in\n match c1, c2 with\n | C_STGhost _, C_STGhost _ -> C_STGhost s\n | C_STAtomic inames obs1 _, C_STAtomic _ obs2 _ ->\n C_STAtomic inames (join_obs obs1 obs2) s\n | C_ST _, C_ST _ -> C_ST s", "val elab_comp_close_commute' (c: comp) (v: var) (n: index)\n : Lemma (ensures RT.subst_term (elab_comp c) [RT.ND v n] == elab_comp (close_comp' c v n))\n (decreases c)\nlet elab_comp_close_commute' (c:comp) (v:var) (n:index)\n : Lemma (ensures\n RT.subst_term (elab_comp c) [ RT.ND v n ] ==\n elab_comp (close_comp' c v n))\n (decreases c)\n = match c with\n | C_Tot t -> elab_close_commute' t v n\n | C_ST s\n | C_STGhost s -> \n elab_close_commute' s.res v n;\n elab_close_commute' s.pre v n;\n elab_close_commute' s.post v (n + 1)\n | C_STAtomic inames _ s ->\n elab_close_commute' inames v n;\n elab_close_commute' s.res v n;\n elab_close_commute' s.pre v n;\n elab_close_commute' s.post v (n + 1)", "val subcomp (a: Type) (i: idx) (f: m a i) : m a i\nlet subcomp (a:Type) (i:idx) (f : m a i) : m a i = f", "val inames_of (c: comp_st) : term\nlet inames_of (c:comp_st) : term =\n match c with\n | C_ST _ \n | C_STGhost _ -> tm_emp_inames\n | C_STAtomic inames _ _ -> inames", "val inst_comp_once : env -> comp -> term -> Tac comp\nlet inst_comp_once e c t =\n let ty = get_comp_ret_type c in\n let ty' = unfold_until_arrow e ty in\n begin match inspect ty' with\n | Tv_Arrow b1 c1 ->\n subst_binder_in_comp e b1 t c1\n | _ -> (* Inconsistent state *)\n mfail \"inst_comp_once: inconsistent state\"\n end", "val close_term (t:term) (v:var) : term\nlet close_term (t:term) (v:var) = RTB.close_term t v", "val add_inv (s: comp_st) (v: vprop) : comp_st\nlet add_inv (s:comp_st) (v:vprop)\n : comp_st\n = add_frame s v", "val tag_of_comp (c:comp): T.Tac string\nlet tag_of_comp (c:comp) : T.Tac string =\n match c with\n | C_Tot _ -> \"Total\"\n | C_ST _ -> \"ST\"\n | C_STAtomic i obs _ ->\n Printf.sprintf \"%s %s\" (observability_to_string obs) (term_to_string i)\n | C_STGhost _ ->\n \"Ghost\"", "val comp_admit (c: ctag) (s: st_comp) : comp\nlet comp_admit (c:ctag) (s:st_comp) : comp =\n match c with\n | STT -> C_ST s\n | STT_Atomic -> C_STAtomic tm_emp_inames Neutral s\n | STT_Ghost -> C_STGhost s", "val comp_return (c: ctag) (use_eq: bool) (u: universe) (t e post: term) (x: var) : comp\nlet comp_return (c:ctag) (use_eq:bool) (u:universe) (t:term) (e:term) (post:term) (x:var)\n : comp =\n\n let post_maybe_eq =\n if use_eq\n then let post = open_term' post (null_var x) 0 in\n let post = tm_star post (tm_pure (mk_eq2 u t (null_var x) e)) in\n close_term post x\n else post in\n\n match c with\n | STT ->\n C_ST { u; res = t; pre = open_term' post e 0; post = post_maybe_eq }\n | STT_Atomic ->\n C_STAtomic tm_emp_inames Neutral\n { u; res = t; pre = open_term' post e 0; post = post_maybe_eq }\n | STT_Ghost ->\n C_STGhost\n { u; res = t; pre = open_term' post e 0; post = post_maybe_eq }", "val close_open_inverse_opt' (t:option term)\r\n (x:var { ~(x `Set.mem` freevars_term_opt t) })\r\n (i:index)\r\n : Lemma (ensures close_term_opt' (open_term_opt' t (U.term_of_no_name_var x) i) x i == t)\nlet close_open_inverse_opt' (t:option term)\r\n (x:var { ~(x `Set.mem` freevars_term_opt t) })\r\n (i:index)\r\n : Lemma (ensures close_term_opt' (open_term_opt' t (U.term_of_no_name_var x) i) x i == t)\r\n = match t with\r\n | None -> ()\r\n | Some t -> close_open_inverse' t x i", "val close_comp_simple (b: simple_binder) (t: comp) : R.simple_binder & comp\nlet close_comp_simple (b:simple_binder) (t:comp) : R.simple_binder & comp =\n let nv = r_binder_to_namedv b in\n let t' = subst_comp [NM nv 0] t in\n let bv : binder_view = { sort = b.sort; ppname = b.ppname; qual = b.qual; attrs = b.attrs } in\n let b = pack_binder bv in\n inspect_pack_binder bv;\n (b, t')", "val bind (a b: Type) (i: idx) (c: m a i) (f: (a -> m b i)) : m b i\nlet bind (a b : Type) (i:idx) (c : m a i) (f : a -> m b i) : m b i =\n match i with\n | T -> t_bind #a #b c f\n | D -> coerce (d_bind #a #b c f) // GM: wow... still needs a coerce, how can that be?\n | G -> g_bind #a #b c f", "val comp_withlocal_body (r: var) (init_t init: term) (c: comp{C_ST? c}) : comp\nlet comp_withlocal_body (r:var) (init_t:term) (init:term) (c:comp{C_ST? c}) : comp =\n let r = null_var r in\n C_ST {\n u = comp_u c;\n res = comp_res c;\n pre = comp_withlocal_body_pre (comp_pre c) init_t r init;\n post = comp_withlocal_body_post (comp_post c) init_t r\n }", "val bind_comp\n (#a #b: Type)\n (#w0 #r0 #w1 #r1: label)\n (#fs0 #fs1: flows)\n (x: ist a w0 r0 fs0)\n (y: (a -> ist b w1 r1 fs1))\n : comp b\nlet bind_comp (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : comp b\n = fun s0 -> let v, s1 = x s0 in y v s1", "val bind_comp\n (#a #b: Type)\n (#w0 #r0 #w1 #r1: label)\n (#fs0 #fs1: flows)\n (x: ist a w0 r0 fs0)\n (y: (a -> ist b w1 r1 fs1))\n : comp b\nlet bind_comp (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : comp b\n = fun s0 -> let v, s1 = x s0 in y v s1", "val open_with_gt_ln_st (s:st_comp) (i:int) (t:term) (j:nat)\r\n : Lemma (requires ln_st_comp s i /\\ i < j)\r\n (ensures open_st_comp' s t j == s)\nlet open_with_gt_ln_st (s:st_comp) (i:int) (t:term) (j:nat)\r\n : Lemma (requires ln_st_comp s i /\\ i < j)\r\n (ensures open_st_comp' s t j == s) =\r\n let {res; pre; post} = s in\r\n open_with_gt_ln res i t j;\r\n open_with_gt_ln pre i t j;\r\n open_with_gt_ln post (i + 1) t (j + 1)", "val ctag_of_comp_st (c: comp_st) : ctag\nlet ctag_of_comp_st (c:comp_st) : ctag =\n match c with\n | C_ST _ -> STT\n | C_STAtomic _ _ _ -> STT_Atomic\n | C_STGhost _ -> STT_Ghost", "val effect_annot_of_comp (c: comp_st) : effect_annot\nlet effect_annot_of_comp (c:comp_st)\n: effect_annot\n= match c with\n | C_ST _ -> EffectAnnotSTT\n | C_STGhost _ -> EffectAnnotGhost\n | C_STAtomic opens _ _ -> EffectAnnotAtomic { opens }", "val FStar.Reflection.Typing.open_comp_typ' = c: FStar.Reflection.Typing.comp_typ -> x: FStar.Stubs.Reflection.V2.Data.var -> i: Prims.nat\n -> FStar.Stubs.TypeChecker.Core.tot_or_ghost * FStar.Stubs.Reflection.Types.term\nlet open_comp_typ' (c:comp_typ) (x:var) (i:nat) =\n fst c, subst_term (snd c) (open_with_var x i)", "val elab_st_comp (c: st_comp) : R.universe & R.term & R.term & R.term\nlet elab_st_comp (c:st_comp)\n : R.universe & R.term & R.term & R.term\n = let res = elab_term c.res in\n let pre = elab_term c.pre in\n let post = elab_term c.post in\n c.u, res, pre, post", "val close_open_inverse_ascription'\n (t: comp_ascription)\n (x: var{~(x `Set.mem` (freevars_ascription t))})\n (i: index)\n : Lemma (ensures close_ascription' (open_ascription' t (U.term_of_no_name_var x) i) x i == t)\nlet close_open_inverse_ascription' (t:comp_ascription)\r\n (x:var { ~(x `Set.mem` freevars_ascription t) } )\r\n (i:index)\r\n : Lemma (ensures close_ascription' (open_ascription' t (U.term_of_no_name_var x) i) x i == t)\r\n = (match t.annotated with\r\n | None -> ()\r\n | Some c -> close_open_inverse_comp' c x i);\r\n (match t.elaborated with\r\n | None -> ()\r\n | Some c -> close_open_inverse_comp' c x i)", "val readback_comp (t:R.term)\n : option (c:comp{ elab_comp c == t})\nlet readback_comp (t:R.term)\n : option (c:comp { elab_comp c == t }) =\n\n let ropt = try_readback_st_comp t readback_ty in\n match ropt with\n | Some c ->\n // debug_log (fun _ -> T.print (Printf.sprintf \"readback_comp: %s as\\n%s\\n\" (T.term_to_string t) (P.comp_to_string c)));\n ropt\n | _ ->\n let? t' = readback_ty t in\n Some (C_Tot t' <: c:comp{ elab_comp c == t })", "val subst_bv_in_comp : env -> bv -> typ -> term -> comp -> Tac comp\nlet subst_bv_in_comp e b sort t c =\n apply_subst_in_comp e c [((b, sort), t)]", "val embed_int (i: int) : term\nlet embed_int (i:int) : term =\n let open FStar.Reflection.V2 in\n pack_ln (Tv_Const (C_Int i))", "val join_index (j: ('a -> 'a -> 'a)) (i0 i1: index 'a) : index 'a\nlet join_index (j:'a -> 'a -> 'a) (i0 i1:index 'a)\r\n: index 'a\r\n= match i0 with\r\n | Trivial -> i1\r\n | _ -> (\r\n match i1 with\r\n | Trivial -> i0\r\n | NonTrivial i1 -> \r\n let NonTrivial i0 = i0 in\r\n NonTrivial (j i0 i1)\r\n )", "val mk_compact (l: forest) : forest\nlet rec mk_compact (l:forest) : forest =\n match l with\n | [] -> []\n | _ ->\n if all_leaf l then []\n else let hd::tl = l in\n hd::(mk_compact tl)", "val freeable (#index : Type0) (c: block index) (i: index) (h: HS.mem) (s: state' c i) : Type0\nlet freeable (#index : Type0) (c: block index) (i: index) (h: HS.mem) (s: state' c i) =\n freeable_s c i h (B.get h s 0) /\\\n B.freeable s", "val weaken_comp_inames\n (#g: env)\n (#e: st_term)\n (#c: comp_st)\n (d_e: st_typing g e c)\n (new_inames: term)\n : T.Tac (c': comp_st{with_inames c new_inames == c'} & st_typing g e c')\nlet weaken_comp_inames (#g:env) (#e:st_term) (#c:comp_st) (d_e:st_typing g e c) (new_inames:term)\n : T.Tac (c':comp_st { with_inames c new_inames == c' } &\n st_typing g e c')\n = match c with\n | C_ST _\n | C_STGhost _ -> (| c, d_e |)\n\n | C_STAtomic inames obs sc ->\n let d_e = T_Sub _ _ _ _ d_e (STS_AtomicInvs _ sc inames new_inames obs obs (check_prop_validity _ _ (tm_inames_subset_typing _ _ _))) in\n (| with_inames c new_inames, d_e |)", "val nt_subst_comp (c: comp) (ss: nt_substs) : comp\nlet nt_subst_comp (c:comp) (ss:nt_substs) : comp =\n L.fold_left (fun c elt -> subst_comp c [elt]) c ss", "val elab_ln_comp (c:comp) (i:int)\n : Lemma (requires ln_c' c i) (ensures RT.ln' (elab_comp c) i)\nlet elab_ln_comp (c:comp) (i:int)\n : Lemma (requires ln_c' c i)\n (ensures RT.ln' (elab_comp c) i) =\n\n match c with\n | C_Tot t -> elab_ln t i\n | C_ST st\n | C_STGhost st ->\n elab_ln st.res i;\n elab_ln st.pre i;\n elab_ln st.post (i + 1)\n | C_STAtomic inames _ st ->\n elab_ln inames i;\n elab_ln st.res i;\n elab_ln st.pre i;\n elab_ln st.post (i + 1)", "val eq_comp (c1 c2:comp) \n : b:bool { b <==> (c1 == c2) }\nlet eq_comp (c1 c2:comp)\n : b:bool { b <==> (c1 == c2) }\n = match c1, c2 with\n | C_Tot t1, C_Tot t2 ->\n eq_tm t1 t2\n | C_ST s1, C_ST s2 ->\n eq_st_comp s1 s2\n | C_STAtomic i1 o1 s1, C_STAtomic i2 o2 s2 ->\n eq_tm i1 i2 &&\n o1 = o2 &&\n eq_st_comp s1 s2\n | C_STGhost s1, C_STGhost s2 ->\n eq_st_comp s1 s2\n | _ -> false", "val ( .()<- ) (#a: Type) (x: t a) (i: index_t (as_raw x)) (v: a) : Tot (t a)\nlet op_Array_Assignment\n (#a:Type)\n (x:t a)\n (i:index_t (as_raw x))\n (v:a)\n : Tot (t a)\n = from_raw ((as_raw x).[i] <- v)", "val namedv_cmp : comparator_for namedv\nlet namedv_cmp x1 x2 =\n let v1 = inspect_namedv x1 in\n let v2 = inspect_namedv x2 in\n pack_inspect_namedv x1;\n pack_inspect_namedv x2;\n sealed_singl v1.sort v2.sort;\n if v1.uniq = v2.uniq then Eq else Neq", "val Pulse.Syntax.Base.comp_pre = c: Pulse.Syntax.Base.comp{Pulse.Syntax.Base.stateful_comp c} -> Pulse.Syntax.Base.vprop\nlet comp_pre (c:comp { stateful_comp c }) = (st_comp_of_comp c).pre", "val comp_intro_exists (u: universe) (b: binder) (p e: term) : comp\nlet comp_intro_exists (u:universe) (b:binder) (p:term) (e:term)\n : comp\n = C_STGhost {\n u=u0;\n res=tm_unit;\n pre=open_term' p e 0;\n post=tm_exists_sl u b p\n }", "val st_comp_with_pre (st: st_comp) (pre: term) : st_comp\nlet st_comp_with_pre (st:st_comp) (pre:term) : st_comp = { st with pre }", "val elab_open_commute' (e:term)\n (v:term)\n (n:index)\n : Lemma (ensures\n RT.subst_term (elab_term e) [ RT.DT n (elab_term v) ] ==\n elab_term (open_term' e v n))\nlet rec elab_open_commute' (e:term)\n (v:term)\n (n:index)\n : Lemma (ensures\n RT.subst_term (elab_term e) [ RT.DT n (elab_term v) ] ==\n elab_term (open_term' e v n))\n (decreases e)\n = match e.t with\n | Tm_Emp \n | Tm_Inames\n | Tm_EmpInames\n | Tm_VProp\n | Tm_Unknown -> ()\n // | Tm_PureApp e1 _ e2 ->\n // elab_open_commute' e1 v n;\n // elab_open_commute' e2 v n\n | Tm_Inv p ->\n elab_open_commute' p v n\n | Tm_Pure p ->\n elab_open_commute' p v n\n | Tm_AddInv e1 e2\n | Tm_Star e1 e2 ->\n elab_open_commute' e1 v n;\n elab_open_commute' e2 v n\n | Tm_ExistsSL u t body\n | Tm_ForallSL u t body ->\n elab_open_commute' t.binder_ty v n;\n elab_open_commute' body v (n + 1)\n | Tm_FStar t -> ()", "val wr (ct: comp_st) (t: st_term') : st_term\nlet wr (ct:comp_st) (t:st_term') : st_term = { term = t; range = FStar.Range.range_0; effect_tag = as_effect_hint (ctag_of_comp_st ct) }", "val close_open_inverse' (t:term) \r\n (x:var { ~(x `Set.mem` freevars t) } )\r\n (i:index)\r\n : Lemma (ensures close_term' (open_term' t (U.term_of_no_name_var x) i) x i == t)\nlet rec close_open_inverse' (t:term) \r\n (x:var { ~(x `Set.mem` freevars t) } )\r\n (i:index)\r\n : Lemma (ensures close_term' (open_term' t (U.term_of_no_name_var x) i) x i == t)\r\n (decreases t)\r\n = match t.t with\r\n | Tm_Emp\r\n | Tm_VProp\r\n | Tm_Inames \r\n | Tm_EmpInames\r\n | Tm_Unknown -> ()\r\n \r\n | Tm_Inv p ->\r\n close_open_inverse' p x i\r\n\r\n | Tm_Pure p ->\r\n close_open_inverse' p x i\r\n\r\n | Tm_Star l r ->\r\n close_open_inverse' l x i;\r\n close_open_inverse' r x i\r\n\r\n | Tm_ExistsSL _ t b\r\n | Tm_ForallSL _ t b ->\r\n close_open_inverse' t.binder_ty x i; \r\n close_open_inverse' b x (i + 1)\r\n\r\n | Tm_FStar t ->\r\n RT.close_open_inverse' i t x\r\n\r\n | Tm_AddInv n is ->\r\n close_open_inverse' n x i;\r\n close_open_inverse' is x i", "val params_of_typ_or_comp (c: typ_or_comp) : list binder\nlet params_of_typ_or_comp (c : typ_or_comp) : list binder =\n match c with\n | TC_Typ _ pl _ | TC_Comp _ pl _ -> pl", "val elab_comp_open_commute (c:comp) (x:term)\n : Lemma (elab_comp (open_comp_with c x) == RT.open_with (elab_comp c) (elab_term x))\nlet elab_comp_open_commute (c:comp) (x:term)\n : Lemma (elab_comp (open_comp_with c x) == RT.open_with (elab_comp c) (elab_term x))\n = RT.open_with_spec (elab_comp c) (elab_term x);\n elab_comp_open_commute' c x 0", "val cmp_to_ocmp (c: cmp) : ocmp\nlet cmp_to_ocmp (c:cmp) : ocmp =\n match c with\n | Cmp_eq o1 o2 -> va_cmp_eq o1 o2\n | Cmp_ne o1 o2 -> va_cmp_ne o1 o2\n | Cmp_le o1 o2 -> va_cmp_le o1 o2\n | Cmp_ge o1 o2 -> va_cmp_ge o1 o2\n | Cmp_lt o1 o2 -> va_cmp_lt o1 o2\n | Cmp_gt o1 o2 -> va_cmp_gt o1 o2", "val cmp_to_ocmp (c: cmp) : ocmp\nlet cmp_to_ocmp (c:cmp) : ocmp =\n match c with\n | Cmp_eq o1 o2 -> va_cmp_eq o1 o2\n | Cmp_ne o1 o2 -> va_cmp_ne o1 o2\n | Cmp_le o1 o2 -> va_cmp_le o1 o2\n | Cmp_ge o1 o2 -> va_cmp_ge o1 o2\n | Cmp_lt o1 o2 -> va_cmp_lt o1 o2\n | Cmp_gt o1 o2 -> va_cmp_gt o1 o2", "val valid_cmp (c: cmp) (s: va_state) : Type0\nlet valid_cmp (c:cmp) (s:va_state) : Type0 =\n match c with\n | Cmp_eq o1 o2 -> valid_operand o1 s /\\ valid_operand o2 s\n | Cmp_ne o1 o2 -> valid_operand o1 s /\\ valid_operand o2 s\n | Cmp_le o1 o2 -> valid_operand o1 s /\\ valid_operand o2 s\n | Cmp_ge o1 o2 -> valid_operand o1 s /\\ valid_operand o2 s\n | Cmp_lt o1 o2 -> valid_operand o1 s /\\ valid_operand o2 s\n | Cmp_gt o1 o2 -> valid_operand o1 s /\\ valid_operand o2 s", "val valid_cmp (c: cmp) (s: va_state) : Type0\nlet valid_cmp (c:cmp) (s:va_state) : Type0 =\n match c with\n | Cmp_eq o1 _ -> valid_first_cmp_opr o1\n | Cmp_ne o1 _ -> valid_first_cmp_opr o1\n | Cmp_le o1 _ -> valid_first_cmp_opr o1\n | Cmp_ge o1 _ -> valid_first_cmp_opr o1\n | Cmp_lt o1 _ -> valid_first_cmp_opr o1\n | Cmp_gt o1 _ -> valid_first_cmp_opr o1", "val subst_comp (c: comp) (ss: subst) : Tot comp (decreases c)\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> t\n | Tv_Var x -> subst_var x ss\n | Tv_BVar j -> subst_db j ss\n | Tv_App hd argv ->\n pack_ln (Tv_App (subst_term hd ss)\n (subst_term (fst argv) ss, snd argv))\n\n | Tv_Abs b body -> \n let b' = subst_binder b ss in\n pack_ln (Tv_Abs b' (subst_term body (shift_subst ss)))\n\n | Tv_Arrow b c ->\n let b' = subst_binder b ss in\n pack_ln (Tv_Arrow b' (subst_comp c (shift_subst ss))) \n\n | Tv_Refine b f ->\n let b = subst_binder b ss in\n pack_ln (Tv_Refine b (subst_term f (shift_subst ss)))\n\n | Tv_Uvar j c ->\n pack_ln (Tv_Uvar j (subst_ctx_uvar_and_subst c ss))\n \n | Tv_Let recf attrs b def body ->\n let b = subst_binder b ss in\n pack_ln (Tv_Let recf \n (subst_terms attrs ss)\n b\n (if recf \n then subst_term def (shift_subst ss)\n else subst_term def ss)\n (subst_term body (shift_subst ss)))\n\n | Tv_Match scr ret brs ->\n pack_ln (Tv_Match (subst_term scr ss)\n (match ret with\n | None -> None\n | Some m -> Some (subst_match_returns m ss))\n (subst_branches brs ss))\n \n | Tv_AscribedT e t tac b ->\n pack_ln (Tv_AscribedT (subst_term e ss)\n (subst_term t ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\n | Tv_AscribedC e c tac b ->\n pack_ln (Tv_AscribedC (subst_term e ss)\n (subst_comp c ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\nand subst_binder (b:binder) (ss:subst)\n : Tot (b':binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\n = let bndr = inspect_binder b in\n pack_binder {\n ppname = bndr.ppname;\n qual = bndr.qual;\n attrs = subst_terms bndr.attrs ss;\n sort = subst_term bndr.sort ss\n }\n\nand subst_comp (c:comp) (ss:subst)\n : Tot comp (decreases c)\n = match inspect_comp c with\n | C_Total t ->\n pack_comp (C_Total (subst_term t ss))\n\n | C_GTotal t ->\n pack_comp (C_GTotal (subst_term t ss))\n\n | C_Lemma pre post pats ->\n pack_comp (C_Lemma (subst_term pre ss)\n (subst_term post ss)\n (subst_term pats ss))\n\n | C_Eff us eff_name res args decrs ->\n pack_comp (C_Eff us eff_name\n (subst_term res ss)\n (subst_args args ss)\n (subst_terms decrs ss))\n\nand subst_terms (ts:list term) (ss:subst)\n : Tot (ts':list term{Nil? ts ==> Nil? ts'}) // property useful for subst_binder\n (decreases ts)\n = match ts with\n | [] -> []\n | t::ts -> subst_term t ss :: subst_terms ts ss\n\nand subst_args (ts:list argv) (ss:subst)\n : Tot (list argv) (decreases ts)\n = match ts with\n | [] -> []\n | (t,q)::ts -> (subst_term t ss,q) :: subst_args ts ss\n\nand subst_patterns (ps:list (pattern & bool)) (ss:subst) \n : Tot (list (pattern & bool))\n (decreases ps)\n = match ps with\n | [] -> ps\n | (p, b)::ps ->\n let n = binder_offset_pattern p in\n let p = subst_pattern p ss in\n let ps = subst_patterns ps (shift_subst_n n ss) in\n (p,b)::ps\n\nand subst_pattern (p:pattern) (ss:subst) \n : Tot pattern\n (decreases p)\n = match p with\n | Pat_Constant _ -> p\n\n | Pat_Cons fv us pats -> \n let pats = subst_patterns pats ss in\n Pat_Cons fv us pats\n\n | Pat_Var bv s ->\n Pat_Var bv s\n\n | Pat_Dot_Term topt ->\n Pat_Dot_Term (match topt with\n | None -> None\n | Some t -> Some (subst_term t ss))\n\n \nand subst_branch (br:branch) (ss:subst)\n : Tot branch (decreases br)\n = let p, t = br in\n let p = subst_pattern p ss in\n let j = binder_offset_pattern p in\n let t = subst_term t (shift_subst_n j ss) in\n p, t\n \nand subst_branches (brs:list branch) (ss:subst)\n : Tot (list branch) (decreases brs)\n = match brs with\n | [] -> []\n | br::brs -> subst_branch br ss :: subst_branches brs ss\n \nand subst_match_returns (m:match_returns_ascription) (ss:subst)\n : Tot match_returns_ascription (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = subst_binder b ss in\n let ret =\n match ret with\n | Inl t -> Inl (subst_term t (shift_subst ss))\n | Inr c -> Inr (subst_comp c (shift_subst ss))\n in\n let as_ =\n match as_ with\n | None -> None\n | Some t -> Some (subst_term t (shift_subst ss))\n in\n b, (ret, as_, eq)", "val mk_int (i: int) : term\nlet mk_int (i: int): term =\n pack_ln (Tv_Const (C_Int i))", "val comp_qualifier (c : comp) : Tac string\nlet comp_qualifier (c : comp) : Tac string =\n match inspect_comp c with\n | C_Total _ -> \"C_Total\"\n | C_GTotal _ -> \"C_GTotal\"\n | C_Lemma _ _ _ -> \"C_Lemma\"\n | C_Eff _ _ _ _ _ -> \"C_Eff\"", "val open_view (tv: term_view) : Tac named_term_view\nlet open_view (tv:term_view) : Tac named_term_view =\n match tv with\n (* Nothing interesting *)\n | RD.Tv_Var v -> Tv_Var (inspect_namedv v)\n | RD.Tv_BVar v -> Tv_BVar (inspect_bv v)\n | RD.Tv_FVar v -> Tv_FVar v\n | RD.Tv_UInst v us -> Tv_UInst v us\n | RD.Tv_App hd a -> Tv_App hd a\n | RD.Tv_Type u -> Tv_Type u\n | RD.Tv_Const c -> Tv_Const c\n | RD.Tv_Uvar n ctx_uvar_and_subst -> Tv_Uvar n ctx_uvar_and_subst\n | RD.Tv_AscribedT e t tac use_eq -> Tv_AscribedT e t tac use_eq\n | RD.Tv_AscribedC e c tac use_eq -> Tv_AscribedC e (inspect_comp c) tac use_eq\n | RD.Tv_Unknown -> Tv_Unknown\n | RD.Tv_Unsupp -> Tv_Unsupp\n\n (* Below are the nodes that actually involve a binder.\n Open them and convert to named binders. *)\n\n | RD.Tv_Abs b body ->\n let nb, body = open_term b body in\n Tv_Abs nb body\n\n | RD.Tv_Arrow b c ->\n let nb, c = open_comp b (inspect_comp c) in\n Tv_Arrow nb c\n\n | RD.Tv_Refine b ref ->\n let nb, ref = open_term_simple b ref in\n Tv_Refine nb ref\n\n | RD.Tv_Let recf attrs b def body ->\n let nb, body = open_term_simple b body in\n let def =\n if recf\n then subst_term [DB 0 (r_binder_to_namedv nb)] def\n else def\n in\n Tv_Let recf attrs nb def body\n\n | RD.Tv_Match scrutinee ret brs ->\n let brs = map open_branch brs in\n let ret = map_opt open_match_returns_ascription ret in\n Tv_Match scrutinee ret brs", "val comp_withlocal_array_body (arr: var) (a init len: term) (c: comp{C_ST? c}) : comp\nlet comp_withlocal_array_body (arr:var) (a:term) (init:term) (len:term) (c:comp{C_ST? c}) : comp =\n let arr = null_var arr in\n C_ST {\n u = comp_u c;\n res = comp_res c;\n pre = comp_withlocal_array_body_pre (comp_pre c) a arr init len;\n post = comp_withlocal_array_body_post (comp_post c) a arr\n }", "val comp_elim_exists (u: universe) (t p: term) (x: nvar) : comp\nlet comp_elim_exists (u:universe) (t:term) (p:term) (x:nvar)\n : comp\n = C_STGhost {\n u=u;\n res=mk_erased u t;\n pre=tm_exists_sl u (as_binder t) p;\n post=elim_exists_post u t p x\n }", "val comp_post_type (c: comp_st) : R.term\nlet comp_post_type (c:comp_st) : R.term = \n let t = elab_term (comp_res c) in\n mk_arrow (t, R.Q_Explicit) vprop_tm", "val open_close_inverse' (i:nat) (t:term { ln' t (i - 1) }) (x:var)\n : Lemma \n (ensures subst_term \n (subst_term t [ ND x i ])\n (open_with_var x i)\n == t)\nlet rec open_close_inverse' (i:nat) (t:term { ln' t (i - 1) }) (x:var)\n : Lemma\n (ensures subst_term \n (subst_term t [ ND x i ])\n (open_with_var x i)\n == t)\n (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown\n | Tv_BVar _ -> ()\n | Tv_Var _ -> ()\n | Tv_App t1 a ->\n open_close_inverse' i t1 x;\n open_close_inverse' i (fst a) x\n \n | Tv_Abs b body -> \n open_close_inverse'_binder i b x;\n open_close_inverse' (i + 1) body x\n\n | Tv_Arrow b c ->\n open_close_inverse'_binder i b x;\n open_close_inverse'_comp (i + 1) c x\n\n | Tv_Refine b f ->\n open_close_inverse'_binder i b x;\n open_close_inverse' (i + 1) f x\n \n | Tv_Let recf attrs b def body ->\n open_close_inverse'_terms i attrs x;\n open_close_inverse'_binder i b x;\n (if recf \n then open_close_inverse' (i + 1) def x\n else open_close_inverse' i def x);\n open_close_inverse' (i + 1) body x\n\n | Tv_Match scr ret brs ->\n open_close_inverse' i scr x;\n (match ret with\n | None -> ()\n | Some m -> open_close_inverse'_match_returns i m x);\n open_close_inverse'_branches i brs x\n \n | Tv_AscribedT e t tac b ->\n open_close_inverse' i e x;\n open_close_inverse' i t x; \n (match tac with\n | None -> ()\n | Some tac -> open_close_inverse' i tac x)\n\n | Tv_AscribedC e c tac b ->\n open_close_inverse' i e x;\n open_close_inverse'_comp i c x; \n (match tac with\n | None -> ()\n | Some tac -> open_close_inverse' i tac x)\n \n\nand open_close_inverse'_binder (i:nat) (b:binder { ln'_binder b (i - 1) }) (x:var)\n : Lemma (ensures subst_binder\n (subst_binder b [ ND x i ])\n (open_with_var x i)\n == b)\n (decreases b) \n = let bndr = inspect_binder b in\n let {ppname; qual=q; attrs=attrs; sort=sort} = bndr in\n open_close_inverse' i sort x;\n open_close_inverse'_terms i attrs x;\n assert (subst_terms (subst_terms attrs [ ND x i ])\n (open_with_var x i) == attrs); \n pack_inspect_binder b; \n assert (pack_binder {ppname; qual=q; attrs=attrs; sort=sort} == b)\n\nand open_close_inverse'_terms (i:nat) (ts:list term { ln'_terms ts (i - 1) }) (x:var)\n : Lemma (ensures subst_terms\n (subst_terms ts [ ND x i ])\n (open_with_var x i)\n == ts)\n (decreases ts) \n = match ts with\n | [] -> ()\n | t::ts -> \n open_close_inverse' i t x;\n open_close_inverse'_terms i ts x\n\nand open_close_inverse'_comp (i:nat) (c:comp { ln'_comp c (i - 1) }) (x:var)\n : Lemma \n (ensures subst_comp\n (subst_comp c [ ND x i ])\n (open_with_var x i)\n == c)\n (decreases c)\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t -> open_close_inverse' i t x\n\n | C_Lemma pre post pats ->\n open_close_inverse' i pre x;\n open_close_inverse' i post x;\n open_close_inverse' i pats x\n\n | C_Eff us eff_name res args decrs ->\n open_close_inverse' i res x;\n open_close_inverse'_args i args x;\n open_close_inverse'_terms i decrs x \n\nand open_close_inverse'_args (i:nat) \n (ts:list argv { ln'_args ts (i - 1) })\n (x:var)\n : Lemma\n (ensures subst_args\n (subst_args ts [ ND x i ])\n (open_with_var x i)\n == ts)\n (decreases ts)\n = match ts with\n | [] -> ()\n | (t,q)::ts -> \n open_close_inverse' i t x;\n open_close_inverse'_args i ts x\n\nand open_close_inverse'_patterns (i:nat)\n (ps:list (pattern & bool) { ln'_patterns ps (i - 1) })\n (x:var)\n : Lemma \n (ensures subst_patterns\n (subst_patterns ps [ ND x i ])\n (open_with_var x i)\n == ps)\n (decreases ps)\n = match ps with\n | [] -> ()\n | (p, b)::ps' ->\n open_close_inverse'_pattern i p x;\n let n = binder_offset_pattern p in\n binder_offset_pattern_invariant p [ ND x i ];\n open_close_inverse'_patterns (i + n) ps' x\n\nand open_close_inverse'_pattern (i:nat) (p:pattern{ln'_pattern p (i - 1)}) (x:var)\n : Lemma \n (ensures subst_pattern\n (subst_pattern p [ ND x i ])\n (open_with_var x i)\n == p)\n (decreases p)\n = match p with\n | Pat_Constant _ -> ()\n\n | Pat_Cons fv us pats -> \n open_close_inverse'_patterns i pats x\n \n | Pat_Var bv _ -> ()\n\n | Pat_Dot_Term topt ->\n match topt with\n | None -> ()\n | Some t -> open_close_inverse' i t x\n\n \nand open_close_inverse'_branch (i:nat) (br:branch{ln'_branch br (i - 1)}) (x:var)\n : Lemma\n (ensures subst_branch\n (subst_branch br [ ND x i ])\n (open_with_var x i)\n == br)\n (decreases br) \n = let p, t = br in\n let j = binder_offset_pattern p in\n binder_offset_pattern_invariant p [ ND x i ];\n open_close_inverse'_pattern i p x;\n open_close_inverse' (i + j) t x\n \nand open_close_inverse'_branches (i:nat)\n (brs:list branch { ln'_branches brs (i - 1) })\n (x:var)\n : Lemma\n (ensures subst_branches\n (subst_branches brs [ ND x i ])\n (open_with_var x i)\n == brs)\n (decreases brs)\n = match brs with\n | [] -> ()\n | br::brs -> \n open_close_inverse'_branch i br x;\n open_close_inverse'_branches i brs x\n \nand open_close_inverse'_match_returns (i:nat) \n (m:match_returns_ascription { ln'_match_returns m (i - 1) })\n (x:var)\n : Lemma \n (ensures subst_match_returns\n (subst_match_returns m [ ND x i ])\n (open_with_var x i)\n == m)\n (decreases m)\n = let b, (ret, as_, eq) = m in\n open_close_inverse'_binder i b x;\n let ret =\n match ret with\n | Inl t ->\n open_close_inverse' (i + 1) t x\n | Inr c ->\n open_close_inverse'_comp (i + 1) c x\n in\n let as_ =\n match as_ with\n | None -> ()\n | Some t ->\n open_close_inverse' (i + 1) t x\n in\n ()", "val comp_to_string (c:comp) : Tac string\nlet comp_to_string (c:comp) : Tac string = Stubs.Tactics.V2.Builtins.comp_to_string (R.pack_comp c)", "val Pulse.Syntax.Base.comp_post = c: Pulse.Syntax.Base.comp{Pulse.Syntax.Base.stateful_comp c} -> Pulse.Syntax.Base.vprop\nlet comp_post (c:comp { stateful_comp c }) = (st_comp_of_comp c).post", "val inspect (t:term) : Tac named_term_view\nlet inspect (t:term) : Tac named_term_view =\n let t = compress t in\n let tv = inspect_ln t in\n open_view tv", "val comp_cmp : comparator_for comp\nlet rec term_cmp t1 t2 =\n pack_inspect_inv t1;\n pack_inspect_inv t2;\n let tv1 = inspect_ln t1 in\n let tv2 = inspect_ln t2 in\n match tv1, tv2 with\n | Tv_Unsupp, _\n | _, Tv_Unsupp -> Unknown\n | Tv_Var v1, Tv_Var v2 -> namedv_cmp v1 v2\n | Tv_BVar v1, Tv_BVar v2 -> bv_cmp v1 v2\n | Tv_FVar f1, Tv_FVar f2 -> fv_cmp f1 f2\n | Tv_UInst f1 u1, Tv_UInst f2 u2 ->\n fv_cmp f1 f2 &&& list_dec_cmp t1 t2 univ_cmp u1 u2\n\n | Tv_App h1 a1, Tv_App h2 a2 ->\n term_cmp h1 h2 &&& arg_cmp a1 a2\n\n | Tv_Abs b1 e1, Tv_Abs b2 e2 ->\n binder_cmp b1 b2\n &&& term_cmp e1 e2\n\n | Tv_Arrow b1 c1, Tv_Arrow b2 c2 ->\n binder_cmp b1 b2\n &&& comp_cmp c1 c2\n\n | Tv_Type u1, Tv_Type u2 ->\n univ_cmp u1 u2\n\n | Tv_Refine sb1 r1, Tv_Refine sb2 r2 ->\n binder_cmp sb1 sb2\n &&& term_cmp r1 r2\n\n | Tv_Const c1, Tv_Const c2 ->\n const_cmp c1 c2\n\n | Tv_Uvar n1 u1, Tv_Uvar n2 u2 ->\n eq_cmp n1 n2 &&& ctxu_cmp u1 u2\n\n | Tv_Let r1 attrs1 sb1 e1 b1, Tv_Let r2 attrs2 sb2 e2 b2 ->\n eq_cmp r1 r2\n &&& list_dec_cmp t1 t2 term_cmp attrs1 attrs2\n &&& binder_cmp sb1 sb2\n &&& term_cmp e1 e2\n &&& term_cmp b1 b2\n\n | Tv_Match sc1 o1 brs1, Tv_Match sc2 o2 brs2 ->\n term_cmp sc1 sc2\n &&& opt_dec_cmp t1 t2 match_returns_ascription_cmp o1 o2\n &&& list_dec_cmp t1 t2 br_cmp brs1 brs2\n\n | Tv_AscribedT e1 ta1 tacopt1 eq1, Tv_AscribedT e2 ta2 tacopt2 eq2 ->\n term_cmp e1 e2\n &&& term_cmp ta1 ta2\n &&& opt_dec_cmp t1 t2 term_cmp tacopt1 tacopt2\n &&& eq_cmp eq1 eq2\n\n | Tv_AscribedC e1 c1 tacopt1 eq1, Tv_AscribedC e2 c2 tacopt2 eq2 ->\n term_cmp e1 e2\n &&& comp_cmp c1 c2\n &&& opt_dec_cmp t1 t2 term_cmp tacopt1 tacopt2\n &&& eq_cmp eq1 eq2\n\n | Tv_Unknown, Tv_Unknown -> Eq\n\n | _ -> Neq\n\nand arg_cmp (a1, q1) (a2, q2) =\n term_cmp a1 a2 &&& aqual_cmp q1 q2\n\nand aqual_cmp a1 a2 =\n match a1, a2 with\n | Q_Implicit, Q_Implicit -> Eq\n | Q_Explicit, Q_Explicit -> Eq\n | Q_Meta m1, Q_Meta m2 -> term_cmp m1 m2\n | _ -> Neq\n\nand match_returns_ascription_cmp asc1 asc2 =\n let (b1, (tc1, tacopt1, eq1)) = asc1 in\n let (b2, (tc2, tacopt2, eq2)) = asc2 in\n binder_cmp b1 b2\n &&& either_dec_cmp asc1 asc2 term_cmp comp_cmp tc1 tc2\n &&& opt_dec_cmp asc1 asc2 term_cmp tacopt1 tacopt2\n &&& eq_cmp eq1 eq2\n\nand binder_cmp b1 b2 =\n let bv1 = inspect_binder b1 in\n let bv2 = inspect_binder b2 in\n pack_inspect_binder b1;\n pack_inspect_binder b2;\n term_cmp bv1.sort bv2.sort\n &&& aqual_cmp bv1.qual bv2.qual\n &&& list_dec_cmp b1 b2 term_cmp bv1.attrs bv2.attrs\n\nand comp_cmp c1 c2 =\n let cv1 = inspect_comp c1 in\n let cv2 = inspect_comp c2 in\n pack_inspect_comp_inv c1;\n pack_inspect_comp_inv c2;\n match cv1, cv2 with\n | C_Total t1, C_Total t2\n | C_GTotal t1, C_GTotal t2 ->\n term_cmp t1 t2\n\n | C_Lemma pre1 post1 pat1, C_Lemma pre2 post2 pat2 ->\n term_cmp pre1 pre2\n &&& term_cmp post1 post2\n &&& term_cmp pat1 pat2\n\n | C_Eff us1 ef1 t1 args1 dec1, C_Eff us2 ef2 t2 args2 dec2 ->\n list_dec_cmp c1 c2 univ_cmp us1 us2\n &&& eq_cmp ef1 ef2\n &&& term_cmp t1 t2\n &&& list_dec_cmp c1 c2 arg_cmp args1 args2\n &&& list_dec_cmp c1 c2 term_cmp dec1 dec2\n\n | _ -> Neq\n\nand br_cmp br1 br2 =\n //pair_cmp pat_cmp term_cmp br1 br2\n pat_cmp (fst br1) (fst br2) &&& term_cmp (snd br1) (snd br2)\n\nand pat_cmp p1 p2 =\n match p1, p2 with\n | Pat_Var x1 s1, Pat_Var x2 s2 ->\n sealed_singl x1 x2;\n sealed_singl s1 s2;\n Eq\n | Pat_Constant x1, Pat_Constant x2 -> const_cmp x1 x2\n | Pat_Dot_Term x1, Pat_Dot_Term x2 -> opt_dec_cmp p1 p2 term_cmp x1 x2\n | Pat_Cons head1 us1 subpats1, Pat_Cons head2 us2 subpats2 ->\n fv_cmp head1 head2\n &&& opt_dec_cmp p1 p2 (list_dec_cmp p1 p2 univ_cmp) us1 us2\n &&& list_dec_cmp p1 p2 pat_arg_cmp subpats1 subpats2\n\n | _ -> Neq\n\nand pat_arg_cmp (p1, b1) (p2, b2) =\n pat_cmp p1 p2 &&& eq_cmp b1 b2", "val collect_arr' (bs: list binder) (c: comp) : Tac (list binder * comp)\nlet rec collect_arr' (bs : list binder) (c : comp) : Tac (list binder * comp) =\n begin match c with\n | C_Total t ->\n begin match inspect t with\n | Tv_Arrow b c ->\n collect_arr' (b::bs) c\n | _ ->\n (bs, c)\n end\n | _ -> (bs, c)\n end" ], "closest_src": [ { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.open_ascription'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_comp" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_comp_with" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.open_with" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse_comp'" }, { "project_name": "FStar", "file_name": "STLC.Infer.fst", "name": "STLC.Infer.open_exp'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.open_close_inverse'_comp" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.open_with_gt_ln_comp" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.mk_comp" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.open_term" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.comp_res" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Visit.fst", "name": "FStar.Tactics.Visit.visit_comp" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.inst_comp" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fst", "name": "Pulse.Checker.Prover.Substs.ss_comp" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.st_comp_of_comp" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.Pure.fst", "name": "Pulse.Elaborate.Pure.elab_comp" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.fst", "name": "Pulse.Elaborate.elab_comp_open_commute'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_open_inverse'_comp" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.open_exp'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_ascription'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_comp_simple" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.open_exp'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.close_comp" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.ln'_comp" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.visit_comp" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.subst_comp" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CheckLN.fst", "name": "FStar.Tactics.CheckLN.check_comp" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.comp_inames" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.bind_comp_pre" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.comp_par" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.open_with_var_elt" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_comp_with_non_free_var" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.open_with_var" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Compare.fst", "name": "FStar.Reflection.V2.Compare.compare_comp" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Compare.fst", "name": "FStar.Reflection.V1.Compare.compare_comp" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.open_ty'" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.open_exp'" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.bind_comp_compatible" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.with_st_comp" }, { "project_name": "steel", "file_name": "Pulse.Soundness.Common.fst", "name": "Pulse.Soundness.Common.elab_comp_post" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_comp_with_not_free_var" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.bind_comp_out" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.fst", "name": "Pulse.Elaborate.elab_comp_close_commute'" }, { "project_name": "FStar", "file_name": "GT.fst", "name": "GT.subcomp" }, { "project_name": "steel", "file_name": "Pulse.Typing.Combinators.fst", "name": "Pulse.Typing.Combinators.inames_of" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.inst_comp_once" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_term" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.add_inv" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Printer.fst", "name": "Pulse.Syntax.Printer.tag_of_comp" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.comp_admit" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.comp_return" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse_opt'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.close_comp_simple" }, { "project_name": "FStar", "file_name": "GT.fst", "name": "GT.bind" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.comp_withlocal_body" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.bind_comp" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.bind_comp" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.open_with_gt_ln_st" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.ctag_of_comp_st" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.effect_annot_of_comp" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.open_comp_typ'" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.Pure.fst", "name": "Pulse.Elaborate.Pure.elab_st_comp" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse_ascription'" }, { "project_name": "steel", "file_name": "Pulse.Readback.fst", "name": "Pulse.Readback.readback_comp" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.subst_bv_in_comp" }, { "project_name": "FStar", "file_name": "FStar.Tactics.MkProjectors.fst", "name": "FStar.Tactics.MkProjectors.embed_int" }, { "project_name": "everparse", "file_name": "EverParse3d.Interpreter.fst", "name": "EverParse3d.Interpreter.join_index" }, { "project_name": "FStar", "file_name": "BinomialQueue.fst", "name": "BinomialQueue.mk_compact" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Functor.fst", "name": "Hacl.Streaming.Functor.freeable" }, { "project_name": "steel", "file_name": "Pulse.Typing.Combinators.fst", "name": "Pulse.Typing.Combinators.weaken_comp_inames" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fsti", "name": "Pulse.Checker.Prover.Substs.nt_subst_comp" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.fst", "name": "Pulse.Elaborate.elab_ln_comp" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fst", "name": "Pulse.Syntax.Base.eq_comp" }, { "project_name": "FStar", "file_name": "FStar.Vector.Base.fsti", "name": "FStar.Vector.Base.op_Array_Assignment" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.TermEq.fst", "name": "FStar.Reflection.V2.TermEq.namedv_cmp" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.comp_pre" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.comp_intro_exists" }, { "project_name": "steel", "file_name": "Pulse.Typing.Combinators.fsti", "name": "Pulse.Typing.Combinators.st_comp_with_pre" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.fst", "name": "Pulse.Elaborate.elab_open_commute'" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.wr" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_open_inverse'" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.params_of_typ_or_comp" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.fst", "name": "Pulse.Elaborate.elab_comp_open_commute" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.QuickCodes.fsti", "name": "Vale.PPC64LE.QuickCodes.cmp_to_ocmp" }, { "project_name": "hacl-star", "file_name": "Vale.X64.QuickCodes.fsti", "name": "Vale.X64.QuickCodes.cmp_to_ocmp" }, { "project_name": "hacl-star", "file_name": "Vale.X64.QuickCodes.fsti", "name": "Vale.X64.QuickCodes.valid_cmp" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.QuickCodes.fsti", "name": "Vale.PPC64LE.QuickCodes.valid_cmp" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_comp" }, { "project_name": "hacl-star", "file_name": "Test.Lowstarize.fst", "name": "Test.Lowstarize.mk_int" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.comp_qualifier" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_view" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.comp_withlocal_array_body" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.comp_elim_exists" }, { "project_name": "steel", "file_name": "Pulse.Soundness.Common.fst", "name": "Pulse.Soundness.Common.comp_post_type" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.open_close_inverse'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.comp_to_string" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.comp_post" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.inspect" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.TermEq.fst", "name": "FStar.Reflection.V2.TermEq.comp_cmp" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.SyntaxHelpers.fst", "name": "FStar.Tactics.V2.SyntaxHelpers.collect_arr'" } ], "selected_premises": [ "Pulse.Syntax.Base.comp_res", "Pulse.Syntax.Naming.subst_comp", "Pulse.Syntax.Base.comp_post", "Pulse.Syntax.Pure.tm_arrow", "Pulse.Syntax.Base.comp_st", "Pulse.Syntax.Naming.subst_st_comp", "Pulse.Syntax.Base.with_st_comp", "Pulse.Elaborate.Pure.elab_comp", "Pulse.Elaborate.Pure.elab_st_comp", "Pulse.Syntax.Base.comp_u", "Pulse.Syntax.Base.comp_pre", "Pulse.Syntax.Base.universe_of_comp", "Pulse.Syntax.Base.comp_inames", "Pulse.Syntax.Base.stateful_comp", "Pulse.Syntax.Naming.open_st_comp'", "Pulse.Syntax.Base.st_comp_of_comp", "Pulse.Syntax.Naming.freevars_comp", "Pulse.Elaborate.Pure.elab_term", "Pulse.Syntax.Base.effect_annot_of_comp", "Pulse.Reflection.Util.mk_arrow", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "Pulse.Syntax.Base.ppname_default", "Pulse.Syntax.Naming.open_term'", "Pulse.Syntax.Pure.tm_fvar", "Pulse.Syntax.Base.nvar", "Pulse.Syntax.Pure.tm_type", "Pulse.Syntax.Base.tm_inv", "Pulse.Syntax.Naming.subst_term", "Pulse.Syntax.Naming.ln_c'", "Pulse.Syntax.Pure.tm_uinst", "Pulse.Syntax.Base.host_term", "Pulse.Syntax.Pure.tm_constant", "Pulse.Syntax.Base.var", "FStar.Reflection.Typing.mk_comp", "Pulse.Syntax.Pure.term_of_nvar", "Pulse.Syntax.Naming.freevars", "Pulse.Syntax.Base.as_effect_hint", "Pulse.Elaborate.Pure.elab_stt_equiv", "Pulse.Syntax.Base.as_fv", "FStar.Reflection.V2.Data.var", "Pulse.Syntax.Naming.ln_st_comp", "Pulse.Syntax.Base.tm_unknown", "Pulse.Syntax.Base.tm_exists_sl", "Pulse.Syntax.Naming.freevars_st_comp", "Pulse.Elaborate.Pure.elab_qual", "Pulse.Syntax.Base.tm_emp", "Pulse.Syntax.Base.tm_inames", "FStar.Reflection.Typing.var_as_namedv", "Pulse.Syntax.Naming.pattern_args_shift_n", "Pulse.Common.map_opt", "Pulse.Syntax.Pure.tm_bvar", "Pulse.Syntax.Base.default_effect_hint", "Pulse.Reflection.Util.vprop_tm", "Pulse.Syntax.Pure.term_of_no_name_var", "Pulse.Syntax.Base.as_binder", "Pulse.Syntax.Base.tm_star", "Pulse.Syntax.Base.ctag_of_comp_st", "Pulse.Syntax.Base.mk_ppname", "Pulse.Syntax.Pure.tm_pureapp", "Pulse.Reflection.Util.mk_stt_comp", "Pulse.Syntax.Base.range", "Pulse.Syntax.Base.tm_fstar", "FStar.Reflection.Typing.subst_comp", "Pulse.Syntax.Base.with_range", "Pulse.Syntax.Pure.null_var", "FStar.Reflection.Typing.open_comp_typ'", "Pulse.Syntax.Base.index", "FStar.Reflection.Typing.sort_default", "Pulse.Syntax.Base.mk_ppname_no_range", "Pulse.Syntax.Pure.is_arrow", "Pulse.Syntax.Base.tm_forall_sl", "Pulse.Syntax.Pure.tm_var", "Pulse.Syntax.Naming.ln_ascription'", "Pulse.Syntax.Naming.pattern_shift_n", "Pulse.Syntax.Pure.u_var", "Pulse.Syntax.Base.tm_pure", "Pulse.Elaborate.Pure.elab_statomic_equiv", "FStar.Reflection.Typing.mk_total", "Pulse.Syntax.Base.tm_vprop", "Pulse.Elaborate.Pure.elab_sub_pat", "Pulse.Syntax.Base.tm_emp_inames", "Pulse.Reflection.Util.mk_pulse_lib_forall_lid", "Pulse.Syntax.Base.mk_binder", "Pulse.Syntax.Base.term_range", "FStar.Reflection.Typing.mk_ghost", "FStar.Reflection.Typing.pp_name_t", "Pulse.Syntax.Pure.mk_bvar", "FStar.Reflection.Typing.blob", "Pulse.Elaborate.Pure.elab_pat", "Pulse.Syntax.Base.empty_ascription", "Pulse.Reflection.Util.mk_pulse_lib_reference_lid", "Pulse.Common.assertby", "Pulse.Syntax.Pure.leftmost_head", "Pulse.Syntax.Pure.u_zero", "Pulse.Reflection.Util.inv_disjointness_goal", "Pulse.Syntax.Pure.null_bvar", "Pulse.Reflection.Util.tot_lid", "Pulse.Syntax.Pure.u_max", "FStar.Heap.trivial_preorder" ], "source_upto_this": "(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Syntax.Naming\n\nopen FStar.List.Tot\nopen Pulse.Syntax.Base\nopen Pulse.Common\n\nmodule L = FStar.List.Tot\n\nmodule R = FStar.Reflection\nmodule RTB = FStar.Reflection.Typing.Builtins\nmodule RT = FStar.Reflection.Typing\nmodule RU = Pulse.RuntimeUtils\nmodule U = Pulse.Syntax.Pure\nmodule E = Pulse.Elaborate.Pure\n\nlet rec freevars (t:term)\n : Set.set var\n = match t.t with\n | Tm_Emp\n | Tm_VProp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown -> Set.empty\n | Tm_Inv p -> freevars p\n | Tm_Star t1 t2 ->\n Set.union (freevars t1) (freevars t2)\n | Tm_ExistsSL _ t1 t2\n | Tm_ForallSL _ t1 t2 ->\n Set.union (freevars t1.binder_ty) (freevars t2)\n | Tm_Pure p -> freevars p\n | Tm_FStar t -> RT.freevars t\n | Tm_AddInv i is -> Set.union (freevars i) (freevars is)\n\nlet freevars_st_comp (s:st_comp) : Set.set var =\n freevars s.res `Set.union`\n freevars s.pre `Set.union`\n freevars s.post\n\n\nlet freevars_comp (c:comp) : Tot (Set.set var) (decreases c) =\n match c with\n | C_Tot t -> freevars t\n | C_ST s\n | C_STGhost s -> freevars_st_comp s\n | C_STAtomic inames _ s ->\n freevars inames `Set.union` freevars_st_comp s\n\nlet freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var =\n match x with\n | None -> Set.empty\n | Some x -> f x\n\nlet freevars_term_opt (t:option term) : Set.set var =\n freevars_opt freevars t\n\nlet rec freevars_list (t:list term) : Set.set var =\n match t with\n | [] -> Set.empty\n | hd::tl -> freevars hd `Set.union` freevars_list tl\n\nlet rec freevars_pairs (pairs:list (term & term)) : Set.set var =\n match pairs with\n | [] -> Set.empty\n | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl\n\nlet freevars_proof_hint (ht:proof_hint_type) : Set.set var =\n match ht with\n | ASSERT { p }\n | FOLD { p }\n | UNFOLD { p } -> freevars p\n | RENAME { pairs; goal } ->\n Set.union (freevars_pairs pairs) (freevars_term_opt goal)\n | REWRITE { t1; t2 } ->\n Set.union (freevars t1) (freevars t2)\n | WILD\n | SHOW_PROOF_STATE _ -> Set.empty\n\nlet freevars_ascription (c:comp_ascription)\n : Set.set var\n = Set.union (freevars_opt freevars_comp c.elaborated)\n (freevars_opt freevars_comp c.annotated)\n\nlet rec freevars_st (t:st_term)\n : Set.set var\n = match t.term with\n | Tm_Return { expected_type; term } ->\n Set.union (freevars expected_type) (freevars term)\n | Tm_Abs { b; ascription; body } ->\n Set.union (freevars b.binder_ty)\n (Set.union (freevars_st body)\n (freevars_ascription ascription))\n | Tm_STApp { head; arg } ->\n Set.union (freevars head) (freevars arg)\n | Tm_Bind { binder; head; body } ->\n Set.union\n (Set.union (freevars binder.binder_ty)\n (freevars_st head))\n (freevars_st body)\n | Tm_TotBind { binder; head; body } ->\n Set.union\n (Set.union (freevars binder.binder_ty)\n (freevars head))\n (freevars_st body)\n | Tm_If { b; then_; else_; post } ->\n Set.union (Set.union (freevars b) (freevars_st then_))\n (Set.union (freevars_st else_) (freevars_term_opt post))\n\n | Tm_Match { sc ; returns_; brs } ->\n let (@@) = Set.union in\n freevars sc\n @@ freevars_term_opt returns_\n @@ freevars_branches brs\n\n | Tm_IntroPure { p }\n | Tm_ElimExists { p } ->\n freevars p\n | Tm_IntroExists { p; witnesses } ->\n Set.union (freevars p) (freevars_list witnesses)\n | Tm_While { invariant; condition; body } ->\n Set.union (freevars invariant)\n (Set.union (freevars_st condition)\n (freevars_st body))\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\n Set.union\n (Set.union (freevars pre1)\n (Set.union (freevars_st body1)\n (freevars post1)))\n (Set.union (freevars pre2)\n (Set.union (freevars_st body2)\n (freevars post2)))\n\n | Tm_WithLocal { binder; initializer; body } ->\n Set.union (freevars binder.binder_ty)\n (Set.union (freevars initializer)\n (freevars_st body))\n\n | Tm_WithLocalArray { binder; initializer; length; body } ->\n Set.union (freevars binder.binder_ty)\n (Set.union (freevars initializer)\n (Set.union (freevars length)\n (freevars_st body)))\n\n | Tm_Rewrite { t1; t2 } ->\n Set.union (freevars t1) (freevars t2)\n\n | Tm_Admit { typ; post } ->\n Set.union (freevars typ)\n (freevars_term_opt post)\n\n | Tm_Unreachable ->\n Set.empty\n\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\n Set.union (freevars_proof_hint hint_type) (freevars_st t)\n\n | Tm_WithInv { name; body; returns_inv } ->\n Set.union (Set.union (freevars name) (freevars_st body))\n (freevars_opt\n (fun (b, r) ->\n (Set.union (freevars b.binder_ty)\n (freevars r)))\n returns_inv)\n\nand freevars_branches (t:list (pattern & st_term)) : Set.set var =\n match t with\n | [] -> Set.empty\n | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl\n\n\nlet rec ln' (t:term) (i:int) : Tot bool (decreases t) =\n match t.t with\n | Tm_Emp\n | Tm_VProp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown -> true\n\n | Tm_Inv p -> ln' p i\n\n | Tm_Star t1 t2 ->\n ln' t1 i &&\n ln' t2 i\n\n | Tm_Pure p ->\n ln' p i\n\n | Tm_ExistsSL _ t body\n | Tm_ForallSL _ t body ->\n ln' t.binder_ty i &&\n ln' body (i + 1)\n\n | Tm_FStar t ->\n RT.ln' t i\n\n | Tm_AddInv x is ->\n ln' x i &&\n ln' is i\n\n\nlet ln_st_comp (s:st_comp) (i:int) : bool =\n ln' s.res i &&\n ln' s.pre i &&\n ln' s.post (i + 1) (* post has 1 impliict abstraction *)\n\n\nlet ln_c' (c:comp) (i:int)\n : bool\n = match c with\n | C_Tot t -> ln' t i\n | C_ST s\n | C_STGhost s -> ln_st_comp s i\n | C_STAtomic inames _ s ->\n ln' inames i &&\n ln_st_comp s i\n\nlet ln_opt' (f: ('a -> int -> bool)) (t:option 'a) (i:int) : bool =\n match t with\n | None -> true\n | Some t -> f t i\n\nlet rec ln_list' (t:list term) (i:int) : bool =\n match t with\n | [] -> true\n | hd::tl -> ln' hd i && ln_list' tl i\n\nlet rec ln_terms' (t:list (term & term)) (i:int) : bool =\n match t with\n | [] -> true\n | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i\n\nlet ln_proof_hint' (ht:proof_hint_type) (i:int) : bool =\n match ht with\n | ASSERT { p }\n | UNFOLD { p }\n | FOLD { p } -> ln' p i\n | RENAME { pairs; goal } ->\n ln_terms' pairs i &&\n ln_opt' ln' goal i\n | REWRITE { t1; t2 } ->\n ln' t1 i &&\n ln' t2 i\n | WILD\n | SHOW_PROOF_STATE _ -> true\n\nlet rec pattern_shift_n (p:pattern)\n : Tot nat\n = match p with\n | Pat_Constant _\n | Pat_Dot_Term _ ->\n 0\n | Pat_Var _ _ ->\n 1\n | Pat_Cons fv l ->\n pattern_args_shift_n l\nand pattern_args_shift_n (ps:list (pattern & bool))\n : Tot nat\n = match ps with\n | [] -> 0\n | (p, _)::tl ->\n pattern_shift_n p + pattern_args_shift_n tl\n\nlet rec ln_pattern' (p : pattern) (i:int)\n : Tot bool (decreases p)\n = match p with\n | Pat_Constant _\n | Pat_Var _ _\n | Pat_Dot_Term None ->\n true\n | Pat_Dot_Term (Some e) ->\n ln' e i\n | Pat_Cons fv l ->\n ln_pattern_args' l i\n\nand ln_pattern_args' (p:list (pattern & bool)) (i:int)\n : Tot bool (decreases p)\n = match p with\n | [] ->\n true\n | (p, _)::tl ->\n ln_pattern' p i &&\n ln_pattern_args' tl (i + pattern_shift_n p)\n\nlet ln_ascription' (c:comp_ascription) (i:int)\n : bool\n = ln_opt' ln_c' c.elaborated i &&\n ln_opt' ln_c' c.annotated i\n\nlet rec ln_st' (t:st_term) (i:int)\n : Tot bool (decreases t)\n = match t.term with\n | Tm_Return { expected_type; term } ->\n ln' expected_type i &&\n ln' term i\n\n | Tm_Abs { b; ascription; body } ->\n ln' b.binder_ty i &&\n ln_st' body (i + 1) &&\n ln_ascription' ascription (i + 1)\n\n | Tm_STApp { head; arg } ->\n ln' head i &&\n ln' arg i\n\n | Tm_Bind { binder; head; body } ->\n ln' binder.binder_ty i &&\n ln_st' head i &&\n ln_st' body (i + 1)\n\n | Tm_TotBind { binder; head; body } ->\n ln' binder.binder_ty i &&\n ln' head i &&\n ln_st' body (i + 1)\n\n | Tm_If { b; then_; else_; post } ->\n ln' b i &&\n ln_st' then_ i &&\n ln_st' else_ i &&\n ln_opt' ln' post (i + 1)\n\n | Tm_Match {sc; returns_; brs } ->\n ln' sc i &&\n ln_opt' ln' returns_ i &&\n ln_branches' t brs i\n\n | Tm_IntroPure { p }\n | Tm_ElimExists { p } ->\n ln' p i\n\n | Tm_IntroExists { p; witnesses } ->\n ln' p i &&\n ln_list' witnesses i\n\n | Tm_While { invariant; condition; body } ->\n ln' invariant (i + 1) &&\n ln_st' condition i &&\n ln_st' body i\n\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\n ln' pre1 i &&\n ln_st' body1 i &&\n ln' post1 (i + 1) &&\n ln' pre2 i &&\n ln_st' body2 i &&\n ln' post2 (i + 1)\n\n | Tm_WithLocal { binder; initializer; body } ->\n ln' binder.binder_ty i &&\n ln' initializer i &&\n ln_st' body (i + 1)\n\n | Tm_WithLocalArray { binder; initializer; length; body } ->\n ln' binder.binder_ty i &&\n ln' initializer i &&\n ln' length i &&\n ln_st' body (i + 1)\n\n | Tm_Rewrite { t1; t2 } ->\n ln' t1 i &&\n ln' t2 i\n\n | Tm_Admit { typ; post } ->\n ln' typ i &&\n ln_opt' ln' post (i + 1)\n\n | Tm_Unreachable ->\n true\n\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\n let n = L.length binders in\n ln_proof_hint' hint_type (i + n) &&\n ln_st' t (i + n)\n\n | Tm_WithInv { name; body; returns_inv } ->\n ln' name i &&\n ln_st' body i &&\n ln_opt'\n (fun (b, r) i ->\n ln' b.binder_ty i &&\n ln' r (i + 1))\n returns_inv i\n\nand ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) =\n let (p, e) = b in\n ln_pattern' p i &&\n ln_st' e (i + pattern_shift_n p)\n\nand ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) =\n for_all_dec t brs (fun b -> ln_branch' b i)\n\nlet ln (t:term) = ln' t (-1)\nlet ln_st (t:st_term) = ln_st' t (-1)\nlet ln_c (c:comp) = ln_c' c (-1)\n\nnoeq\ntype subst_elt =\n | DT : nat -> term -> subst_elt\n | NT : var -> term -> subst_elt\n | ND : var -> nat -> subst_elt\n\nlet shift_subst_elt (n:nat) = function\n | DT i t -> DT (i + n) t\n | NT x t -> NT x t\n | ND x i -> ND x (i + n)\n\nlet subst = list subst_elt\n\nlet shift_subst_n (n:nat) = L.map (shift_subst_elt n)\n\nlet shift_subst = shift_subst_n 1\n\nlet rt_subst_elt = function\n | DT i t -> RT.DT i (E.elab_term t)\n | NT x t -> RT.NT x (E.elab_term t)\n | ND x i -> RT.ND x i\n\nlet rt_subst = L.map rt_subst_elt\n\nlet open_or_close_host_term (t:host_term) (ss:subst)\n : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss)))\n = admit()\n\nval subst_host_term (t:host_term) (ss:subst)\n : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) })\n\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = let w t' = with_range t' t.range in\n match t.t with\n | Tm_VProp\n | Tm_Emp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown -> t\n\n | Tm_Inv p ->\n w (Tm_Inv (subst_term p ss))\n\n | Tm_Pure p ->\n w (Tm_Pure (subst_term p ss))\n\n | Tm_Star l r ->\n w (Tm_Star (subst_term l ss)\n (subst_term r ss))\n\n | Tm_ExistsSL u b body ->\n w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss }\n (subst_term body (shift_subst ss)))\n\n | Tm_ForallSL u b body ->\n w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss }\n (subst_term body (shift_subst ss)))\n\n | Tm_FStar t ->\n w (Tm_FStar (subst_host_term t ss))\n\n | Tm_AddInv i is ->\n w (Tm_AddInv (subst_term i ss)\n (subst_term is ss))\n\nlet open_term' (t:term) (v:term) (i:index) =\n subst_term t [ DT i v ]\n\nlet subst_st_comp (s:st_comp) (ss:subst)\n : st_comp =\n\n { s with res = subst_term s.res ss;\n pre = subst_term s.pre ss;\n post = subst_term s.post (shift_subst ss) }\n\nlet open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp =\n subst_st_comp s [ DT i v ]\n\nlet subst_comp (c:comp) (ss:subst)\n : comp\n = match c with\n | C_Tot t ->\n C_Tot (subst_term t ss)\n\n | C_ST s -> C_ST (subst_st_comp s ss)\n\n | C_STAtomic inames obs s ->\n C_STAtomic (subst_term inames ss) obs\n (subst_st_comp s ss)\n\n | C_STGhost s ->\n C_STGhost (subst_st_comp s ss)\n", "sketch": [ "Step 1: The `open_comp'` function is about opening a computation type `comp` by substituting a term `v` at a specific index `i`.\nStep 2: The implementation involves pattern matching on the computation type `comp` and applying the `subst_comp` function with a substitution list containing a single `DT` element that maps the index `i` to the term `v`.", "Step 1: The `open_comp'` function is intended to open a computation `c` by substituting a term `v` at a specific index `i`.\nStep 2: To implement this, we will use the `subst_comp` function, which performs substitution on a computation. We will create a substitution list with a single `DT` element that represents the substitution of the term `v` at index `i`, and then apply this substitution to the computation `c`.", "Step 1: The `open_comp'` function is about opening a computation type `comp` by substituting a term `v` at a given index `i`.\nStep 2: The implementation involves using the `subst_comp` function to substitute the term `v` at index `i` in the computation `c`. This is achieved by creating a substitution list with a single `DT` element and applying it to `c`.", "Step 1: The `open_comp'` function is intended to open a computation `c` by substituting a term `v` at a specific index `i`.\nStep 2: The implementation involves using the `subst_comp` function to perform the substitution. This is done by creating a substitution list with a single element `DT i v` and applying it to the computation `c`.", "Step 1: The function `open_comp'` is intended to open a computation `c` by substituting a term `v` at a given index `i`.\nStep 2: The implementation will use the `subst_comp` function to perform the substitution. It will create a substitution list with a single `DT` element that maps the index `i` to the term `v`, and then apply this substitution to the computation `c`.", "Step 1: The `open_comp'` function is about substituting a term `v` for a de Bruijn index `i` in a computation `c`. This is useful for handling bound variables in a computation.\nStep 2: The implementation involves pattern matching on the computation `c`. For each case, we apply the `subst_term` or `subst_st_comp` function with a substitution list containing a single `DT` element that maps the index `i` to the term `v`.", "Step 1: The `open_comp'` function is intended to open a computation `c` by substituting a term `v` at a specific index `i`.\nStep 2: The implementation involves calling the `subst_comp` function with the computation `c` and a substitution list containing a single `DT` element that maps the index `i` to the term `v`.", "Step 1: The `open_comp'` function is intended to open a computation `c` by substituting a term `v` for a de Bruijn index `i` within the computation.\nStep 2: The implementation involves calling the `subst_comp` function with a single substitution element `DT i v`, which represents the substitution of `v` for the de Bruijn index `i`.", "Step 1: The `open_comp'` function is intended to open a computation `c` by substituting a term `v` for a de Bruijn index `i` within the computation.\nStep 2: The implementation involves calling the `subst_comp` function with a single substitution element `DT i v`, which represents substituting the term `v` for the de Bruijn index `i`.", "Step 1: The `open_comp'` function is intended to open a computation `c` by substituting a term `v` at a specific index `i`.\nStep 2: The implementation involves using the `subst_comp` function to perform the substitution. Specifically, we create a substitution list with a single element `DT i v` and apply this substitution to the computation `c`." ], "generated_solution": [ "let open_comp' (c: comp) (v: term) (i: index) : comp =\n subst_comp c [ DT i v ]", "let open_comp' (c: comp) (v: term) (i: index) : comp =\n subst_comp c [ DT i v ]", "let open_comp' (c: comp) (v: term) (i: index) : comp =\n subst_comp c [DT i v]", "let open_comp' (c: comp) (v: term) (i: index) : comp =\n subst_comp c [ DT i v ]", "let open_comp' (c: comp) (v: term) (i: index) : comp =\n subst_comp c [DT i v]", "let open_comp' (c: comp) (v: term) (i: index) : comp =\n subst_comp c [DT i v]", "let open_comp' (c: comp) (v: term) (i: index) : comp =\n subst_comp c [DT i v]", "let open_comp' (c: comp) (v: term) (i: index) : comp =\n subst_comp c [DT i v]", "let open_comp' (c: comp) (v: term) (i: index) : comp =\n subst_comp c [ DT i v ]", "let open_comp' (c: comp) (v: term) (i: index) : comp =\n subst_comp c [DT i v]" ] }, { "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mref", "opens_and_abbrevs": [ { "open": "FStar.Monotonic.HyperHeap" }, { "abbrev": "Map", "full_module": "FStar.Map" }, { "open": "FStar.Preorder" }, { "open": "FStar.Monotonic" }, { "open": "FStar.Monotonic" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let mref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_eternal_region_hs (frameOf s) && not (is_mm s) }", "source_range": { "start_line": 256, "start_col": 0, "end_line": 257, "end_col": 73 }, "interleaved": false, "definition": "fun a rel ->\n s:\n FStar.Monotonic.HyperStack.mreference a rel\n { FStar.Monotonic.HyperStack.is_eternal_region_hs (FStar.Monotonic.HyperStack.frameOf s) &&\n Prims.op_Negation (FStar.Monotonic.HyperStack.is_mm s) }", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Preorder.preorder", "FStar.Monotonic.HyperStack.mreference", "Prims.b2t", "Prims.op_AmpAmp", "FStar.Monotonic.HyperStack.is_eternal_region_hs", "FStar.Monotonic.HyperStack.frameOf", "Prims.op_Negation", "FStar.Monotonic.HyperStack.is_mm" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "a: Type0 -> rel: FStar.Preorder.preorder a -> Type0", "prompt": "let mref (a: Type) (rel: preorder a) =\n ", "expected_response": "s: mreference a rel {is_eternal_region_hs (frameOf s) && not (is_mm s)}", "source": { "project_name": "FStar", "file_name": "ulib/FStar.Monotonic.HyperStack.fsti", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.Monotonic.HyperStack.fsti", "checked_file": "dataset/FStar.Monotonic.HyperStack.fsti.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Monotonic.HyperHeap.fsti.checked", "dataset/FStar.Monotonic.Heap.fsti.checked", "dataset/FStar.Map.fsti.checked" ] }, "definitions_in_context": [ "", "", "let is_in (r:rid) (h:hmap) = h `Map.contains` r", "let is_stack_region r = color r > 0", "let is_heap_color c = c <= 0", "let is_eternal_region r = is_heap_color (color r) && not (rid_freeable r)", "let is_eternal_region_hs r = is_heap_color (color r) && not (rid_freeable r)", "sid", "let is_above r1 r2 = r1 `includes` r2", "let is_just_below r1 r2 = r1 `extends` r2", "let is_below r1 r2 = r2 `is_above` r1", "let is_strictly_below r1 r2 = r1 `is_below` r2 && r1 <> r2", "let is_strictly_above r1 r2 = r1 `is_above` r2 && r1 <> r2", "let map_invariant_predicate (m:hmap) :Type0 =\n forall r. Map.contains m r ==>\n (forall s. includes s r ==> Map.contains m s)", "let downward_closed_predicate (h:hmap) :Type0 =\n forall (r:rid). r `is_in` h //for any region in the memory\n ==> (r=root //either is the root\n \\/ (forall (s:rid). (r `is_above` s //or, any region beneath it\n /\\ s `is_in` h) //that is also in the memory\n ==> ((is_stack_region r = is_stack_region s) /\\ //must be of the same flavor as itself\n ((is_heap_color (color r) /\\ rid_freeable r) ==> s == r))))", "let tip_top_predicate (tip:rid) (h:hmap) :Type0 =\n forall (r:sid). r `is_in` h <==> r `is_above` tip", "let rid_ctr_pred_predicate (h:hmap) (n:int) :Type0 =\n forall (r:rid). h `Map.contains` r ==> rid_last_component r < n", "val map_invariant (m:hmap) :Type0", "val downward_closed (h:hmap) :Type0", "val tip_top (tip:rid) (h:hmap) :Type0", "val rid_ctr_pred (h:hmap) (n:int) :Type0", "let is_tip (tip:rid) (h:hmap) =\n (is_stack_region tip \\/ tip = root) /\\ //the tip is a stack region, or the root\n tip `is_in` h /\\ //the tip is live\n tip_top tip h", "let is_wf_with_ctr_and_tip (h:hmap) (ctr:int) (tip:rid)\n = (not (rid_freeable root)) /\\\n root `is_in` h /\\\n tip `is_tip` h /\\\n map_invariant h /\\\n downward_closed h /\\\n rid_ctr_pred h ctr", "val mem' :Type u#1", "val mk_mem (rid_ctr:int) (h:hmap) (tip:rid) :mem'", "val get_hmap (m:mem') :hmap", "val get_rid_ctr (m:mem') :int", "val get_tip (m:mem') :rid", "val lemma_mk_mem'_projectors (rid_ctr:int) (h:hmap) (tip:rid)\n :Lemma (requires True)\n (ensures (let m = mk_mem rid_ctr h tip in\n\t (get_hmap m == h /\\ get_rid_ctr m == rid_ctr /\\ get_tip m == tip)))\n [SMTPatOr [[SMTPat (get_hmap (mk_mem rid_ctr h tip))];\n\t [SMTPat (get_rid_ctr (mk_mem rid_ctr h tip))];\n\t\t [SMTPat (get_tip (mk_mem rid_ctr h tip))]\n\t\t ]]", "mem", "val lemma_mem_projectors_are_in_wf_relation (m:mem)\n :Lemma (is_wf_with_ctr_and_tip (get_hmap m) (get_rid_ctr m) (get_tip m))", "val lemma_is_wf_ctr_and_tip_intro (h:hmap) (ctr:int) (tip:rid)\n :Lemma (requires (root `is_in` h /\\ (is_stack_region tip \\/ tip = root) /\\ tip `is_in` h /\\\n tip_top_predicate tip h /\\ map_invariant_predicate h /\\\n downward_closed_predicate h /\\ rid_ctr_pred_predicate h ctr))\n\t (ensures (is_wf_with_ctr_and_tip h ctr tip))", "val lemma_is_wf_ctr_and_tip_elim (m:mem)\n :Lemma (let h, rid_ctr, tip = get_hmap m, get_rid_ctr m, get_tip m in\n (root `is_in` h /\\ (is_stack_region tip \\/ tip = root) /\\ tip `is_in` h /\\\n\t tip_top_predicate tip h /\\ map_invariant_predicate h /\\\n downward_closed_predicate h /\\ rid_ctr_pred_predicate h rid_ctr))", "val lemma_map_invariant (m:mem) (r s:rid)\n :Lemma (requires (r `is_in` get_hmap m /\\ s `is_above` r))\n (ensures (s `is_in` get_hmap m))\n [SMTPat (r `is_in` get_hmap m); SMTPat (s `is_above` r); SMTPat (s `is_in` get_hmap m)]", "val lemma_downward_closed (m:mem) (r:rid) (s:rid{s =!= root})\n :Lemma (requires (r `is_in` get_hmap m /\\ s `is_above` r))\n (ensures (is_heap_color (color r) == is_heap_color (color s) /\\\n\t is_stack_region r == is_stack_region s))\n [SMTPatOr [[SMTPat (get_hmap m `Map.contains` r); SMTPat (s `is_above` r); SMTPat (is_heap_color (color s))];\n [SMTPat (get_hmap m `Map.contains` r); SMTPat (s `is_above` r); SMTPat (is_stack_region s)]\n ]]", "val lemma_tip_top (m:mem) (r:sid)\n :Lemma (r `is_in` get_hmap m <==> r `is_above` get_tip m)", "val lemma_tip_top_smt (m:mem) (r:rid)\n :Lemma (requires (is_stack_region r))\n (ensures (r `is_in` get_hmap m <==> r `is_above` get_tip m))\n [SMTPatOr [[SMTPat (is_stack_region r); SMTPat (r `is_above` get_tip m)];\n [SMTPat (is_stack_region r); SMTPat (r `is_in` get_hmap m)]]]", "val lemma_rid_ctr_pred (_:unit)\n :Lemma (forall (m:mem) (r:rid).{:pattern (get_hmap m `Map.contains` r)} get_hmap m `Map.contains` r ==> rid_last_component r < get_rid_ctr m)", "let empty_mem : mem =\n let empty_map = Map.restrict Set.empty (Map.const Heap.emp) in\n let h = Map.upd empty_map root Heap.emp in\n let tip = root in\n root_last_component ();\n lemma_is_wf_ctr_and_tip_intro h 1 tip;\n mk_mem 1 h tip", "let heap_region_does_not_overlap_with_tip\n (m:mem) (r:rid{is_heap_color (color r) /\\ not (disjoint r (get_tip m)) /\\ r =!= root /\\ is_stack_region (get_tip m)})\n : Lemma (requires True)\n (ensures (~ (r `is_in` get_hmap m)))\n = root_has_color_zero()", "let poppable (m:mem) = get_tip m =!= root", "let remove_elt (#a:eqtype) (s:Set.set a) (x:a) = Set.intersect s (Set.complement (Set.singleton x))", "let popped (m0 m1:mem) =\n poppable m0 /\\\n (let h0, tip0, h1, tip1 = get_hmap m0, get_tip m0, get_hmap m1, get_tip m1 in\n (parent tip0 = tip1 /\\\n Set.equal (Map.domain h1) (remove_elt (Map.domain h0) tip0) /\\\n Map.equal h1 (Map.restrict (Map.domain h1) h0)))", "let pop (m0:mem{poppable m0}) :mem =\n let h0, tip0, rid_ctr0 = get_hmap m0, get_tip m0, get_rid_ctr m0 in\n root_has_color_zero();\n lemma_is_wf_ctr_and_tip_elim m0;\n let dom = remove_elt (Map.domain h0) tip0 in\n let h1 = Map.restrict dom h0 in\n let tip1 = parent tip0 in\n lemma_is_wf_ctr_and_tip_intro h1 rid_ctr0 tip1;\n mk_mem rid_ctr0 h1 tip1", "mreference'", "MkRef", "MkRef", "MkRef", "frame", "frame", "ref", "ref", "let mreference a rel = mreference' a rel", "let frameOf (#a:Type) (#rel:preorder a) (r:mreference a rel) :rid\n = r.frame", "let mk_mreference (#a:Type) (#rel:preorder a) (id:rid)\n (r:Heap.mref a rel)\n :mreference a rel\n = MkRef id r", "val as_ref (#a:Type0) (#rel:preorder a) (x:mreference a rel)\n :Heap.mref a rel", "let as_addr #a #rel (x:mreference a rel)\n :GTot pos\n = Heap.addr_of (as_ref x)", "val lemma_as_ref_inj (#a:Type) (#rel:preorder a) (r:mreference a rel)\n :Lemma (requires True) (ensures (mk_mreference (frameOf r) (as_ref r) == r))\n [SMTPat (as_ref r)]", "let is_mm (#a:Type) (#rel:preorder a) (r:mreference a rel) :GTot bool =\n Heap.is_mm (as_ref r)", "let mstackref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_stack_region (frameOf s) && not (is_mm s) }" ], "closest": [ "val MRefST.mref0 = a: Type0 -> r: MRefHeap.preorder_t a -> Type0\nlet mref0 = mref", "val FStar.ST.contains_pred = r: FStar.Monotonic.Heap.mref a rel -> h: FStar.Monotonic.Heap.heap -> Type0\nlet contains_pred (#a:Type0) (#rel:preorder a) (r:mref a rel) = fun h -> h `contains` r", "val FStar.MRef.spred = rel: FStar.Preorder.preorder a -> Type\nlet spred (#a:Type) (rel:preorder a) = p:(a -> Type){Preorder.stable p rel}", "val MRefHeap.preorder_t = a: Type0 -> Type\nlet preorder_t (a:Type0) = preorder a", "val FStar.MRef.p_pred = r: FStar.ST.mref a b -> p: (_: a -> Type0) -> h: FStar.Monotonic.Heap.heap -> Prims.logical\nlet p_pred (#a:Type) (#b:preorder a) (r:mref a b) (p:(a -> Type))\n = fun h -> h `contains` r /\\ p (sel h r)", "val mref (a: Type0) (rel: preorder a) : Type0\nlet mref (a:Type0) (rel:preorder a) : Type0 = core_mref a", "val FStar.Monotonic.Heap.fresh = r: FStar.Monotonic.Heap.mref a rel -> h0: FStar.Monotonic.Heap.heap -> h1: FStar.Monotonic.Heap.heap\n -> Prims.logical\nlet fresh (#a:Type) (#rel:preorder a) (r:mref a rel) (h0:heap) (h1:heap) =\n r `unused_in` h0 /\\ h1 `contains` r", "val as_ref (#a:Type0) (#rel:preorder a) (x:mreference a rel)\n :Heap.mref a rel\nlet as_ref #_ #_ x = MkRef?.ref x", "val FStar.Monotonic.Heap.tset = a: Type -> Type\nlet tset = TSet.set", "val Steel.Channel.Simplex.mref = a: Type -> p: FStar.Preorder.preorder a -> Type0\nlet mref a p = MRef.ref a p", "val mref (a:Type) (r:preorder_t a) : Type0\nlet mref (a:Type) (r:preorder_t a) = nat", "val ref_of: h: heap -> a: aref -> t: Type0 -> rel: preorder t -> Pure (mref t rel) (requires (aref_live_at h a t rel)) (ensures (fun x -> aref_live_at h a t rel /\\ addr_of (gref_of a t rel) == addr_of x /\\ is_mm x == aref_is_mm a))\nlet ref_of h a t rel = ref_of' h a t rel", "val FStar.Monotonic.Heap.set = a: Prims.eqtype -> Type0\nlet set = Set.set", "val FStar.Preorder.reflexive = rel: FStar.Preorder.relation a -> Prims.logical\nlet reflexive (#a:Type) (rel:relation a) =\n forall (x:a). rel x x", "val MRefHeap.heap_cell_a = a: Type0 -> Type\nlet heap_cell_a (a:Type0) = a * preorder_t a", "val FStar.ReflexiveTransitiveClosure.binrel = a: Type -> Type\nlet binrel (a:Type) = a -> a -> Type", "val sel: #a:Type0 -> #rel:preorder a -> heap -> mref a rel -> GTot a\nlet sel #a #rel h r =\n if h `contains_bool` r\n then sel_tot #a h r\n else r.init", "val FStar.TwoLevelHeap.st_post' = a: Type -> pre: Type -> Type\nlet st_post' (a:Type) (pre:Type) = st_post_h' t a pre", "val alloc: #a:Type0 -> rel:preorder a -> heap -> a -> mm:bool -> Tot (mref a rel * heap)\nlet alloc #a rel h x mm =\n let r = { addr = h.next_addr; init = x; mm = mm } in\n r, { next_addr = r.addr + 1;\n memory = F.on_dom pos (fun r' -> if r' = r.addr\n\t \t\t then Some (| a, Some rel, r.mm, x |)\n else h.memory r') }", "val ref_of' (h: heap) (a: aref) (t: Type0) (rel: preorder t)\n : Pure (mref t rel) (requires (aref_live_at h a t rel)) (ensures (fun _ -> True))\nlet ref_of'\n (h: heap)\n (a: aref)\n (t: Type0)\n (rel: preorder t)\n: Pure (mref t rel)\n (requires (aref_live_at h a t rel))\n (ensures (fun _ -> True))\n= let Some (| _, pre_opt, _, x |) = h.memory a.a_addr in\n {\n addr = a.a_addr;\n init = x;\n mm = a.a_mm\n }", "val FStar.Tactics.PatternMatching.hyp = a: Type -> Type0\nlet hyp (a: Type) = binding", "val FStar.TwoLevelHeap.fresh_rref = r: FStar.TwoLevelHeap.rref i a -> m0: FStar.TwoLevelHeap.t -> m1: FStar.TwoLevelHeap.t\n -> Prims.logical\nlet fresh_rref (#a:Type) (#i:rid) (r:rref i a) (m0:t) (m1:t) =\n ~ (Heap.contains (Map.sel m0 i) (as_ref r))\n /\\ (Heap.contains (Map.sel m1 i) (as_ref r))", "val contains (#a:Type) (#r:preorder_t a) (h:heap) (m:mref a r) : Type0\nlet contains (#a:Type) (#r:preorder_t a) (h:heap) (m:mref a r) : GTot Type0 =\n exists (v:heap_cell).\n snd h m == Some v /\\\n dfst v == a /\\\n snd #(dfst v) #(preorder_t a) (dsnd v) == r", "val FStar.ReflexiveTransitiveClosure.preorder_rel = rel: FStar.ReflexiveTransitiveClosure.binrel a -> Prims.logical\nlet preorder_rel (#a:Type) (rel:binrel u#a u#r a) =\n reflexive rel /\\ transitive rel", "val FStar.Pervasives.st_post_h' = heap: Type -> a: Type -> pre: Type -> Type\nlet st_post_h' (heap a pre: Type) = a -> _: heap{pre} -> GTot Type0", "val recall : #a:Type ->\n #r:preorder a ->\n\t m:mref a r ->\n\t p:predicate heap{stable_on_heap m p} ->\n\t MRefST unit (fun h0 -> ist_witnessed p)\n\t (fun h0 _ h1 -> h0 == h1 /\\\n\t\t\t p h1)\nlet recall #a #r m p =\n ist_recall p", "val MRefST.stable_on_heap = m: MRefST.mref a r -> p: FStar.Preorder.predicate MRefHeap.heap -> Prims.logical\nlet stable_on_heap (#a:Type) (#r:preorder a) (m:mref a r) (p:predicate heap) =\n forall h0 h1 . stable_on_heap_aux m p h0 h1", "val free_mm: #a:Type0 -> #rel:preorder a -> h:heap -> r:mref a rel{h `contains` r /\\ is_mm r} -> Tot heap\nlet free_mm #a #rel h r =\n { h with memory = F.on_dom pos (fun r' -> if r' = r.addr then None else h.memory r') }", "val FStar.ReflexiveTransitiveClosure.reflexive = rel: FStar.ReflexiveTransitiveClosure.binrel a -> Prims.logical\nlet reflexive (#a:Type) (rel:binrel u#a u#r a) =\n forall (x:a). squash (rel x x)", "val ref (a: Type0) : Type0\nlet ref (a : Type0) : Type0 = (r: A.array a { A.length r == 1 \\/ r == A.null })", "val ref (a: Type0) : Type0\nlet ref (a:Type0) : Type0 = ref a", "val read : #a:Type ->\n #r:preorder a ->\n\t m:mref a r ->\n\t MRefST a (fun _ -> True)\n (fun h0 x h1 -> h0 == h1 /\\\n\t\t contains m h1 /\\\n\t\t\t\t sel h1 m == x)\nlet read #a #r m =\n let h = ist_get () in\n ist_recall (contains m); //recalling that the current heap must contain the given reference\n sel h m", "val recall (#a: Type) (#rel: P.preorder a) (r: mref a rel)\n : HoareST unit (fun _ -> True) (fun h0 _ h1 -> h0 == h1 /\\ h1 `Heap.contains` r)\nlet recall (#a:Type) (#rel:P.preorder a) (r:mref a rel)\n: HoareST unit\n (fun _ -> True)\n (fun h0 _ h1 ->\n h0 == h1 /\\\n h1 `Heap.contains` r)\n= HoareST?.reflect (fun _ -> recall r)", "val recall (#a: Type) (#rel: P.preorder a) (r: mref a rel)\n : HoareST unit (fun _ -> True) (fun h0 _ h1 -> h0 == h1 /\\ h1 `Heap.contains` r)\nlet recall (#a:Type) (#rel:P.preorder a) (r:mref a rel)\n: HoareST unit\n (fun _ -> True)\n (fun h0 _ h1 ->\n h0 == h1 /\\\n h1 `Heap.contains` r)\n= HoareST?.reflect (fun _ -> recall r)", "val FStar.TwoLevelHeap.contains_ref = r: FStar.TwoLevelHeap.rref i a -> m: FStar.TwoLevelHeap.t -> Prims.logical\nlet contains_ref (#a:Type) (#i:rid) (r:rref i a) (m:t) =\n Map.contains m i /\\ Heap.contains (Map.sel m i) (as_ref r)", "val sel : #a:Type ->\n #r:preorder a ->\n h:heap ->\n\t m:mref a r{contains h m} ->\n a\nlet sel #a #b h m =\n match snd h m with\n | Some (| _ , (x , _) |) -> x", "val FStar.TwoLevelHeap.st_post = a: Type -> Type\nlet st_post (a:Type) = st_post_h t a", "val upd: #a:Type0 -> #rel:preorder a -> h:heap -> r:mref a rel -> x:a -> GTot heap\nlet upd #a #rel h r x =\n if h `contains_bool` r\n then upd_tot' h r x\n else\n if r.addr >= h.next_addr\n then\n { next_addr = r.addr + 1;\n memory = F.on_dom pos (fun r' -> if r' = r.addr\n\t \t\t then Some (| a, Some rel, r.mm, x |)\n else h.memory r') }\n else\n { h with memory = F.on_dom pos (fun r' -> if r' = r.addr\n\t\t\t\t then Some (| a, Some rel, r.mm, x |)\n else h.memory r') }", "val alloc_ref : h0:heap ->\n\t\ta:Type ->\n\t\tr:preorder a ->\n\t x:a ->\n\t\tTot (mh1:(mref a r * heap){~(contains #a #r h0 (fst mh1)) /\\\n\t\t contains (snd mh1) (fst mh1) /\\\n\t\t sel (snd mh1) (fst mh1) == x /\\\n\t\t\t\t\t (forall b r' (m:mref b r') .\n\t\t\t contains h0 m\n\t\t\t ==>\n\t\t\t contains (snd mh1) m) /\\\n\t\t\t (forall b r' (m:mref b r'{contains h0 m}) y .\n\t\t\t sel #b h0 m == y\n\t\t ==>\n\t\t\t sel #b (snd mh1) m == y)})\nlet alloc_ref h a r x =\n (fst h , (fst h + 1 , (fun n -> if n = fst h then Some (| a , (x , r) |)\n\t\t\t\t\t else snd h n)))", "val ref (a:Type0) : Type0\nlet ref (a:Type) = nat", "val alloc : #a:Type ->\n r:preorder a ->\n\t x:a ->\n\t MRefST (mref a r) (fun _ -> True)\n (fun h0 m h1 -> ~(contains m h0) /\\\n\t\t\t\t\t fst (alloc_ref h0 a r x) == m /\\\n\t\t\t\t\t snd (alloc_ref h0 a r x) == h1)\nlet alloc #a r x =\n let h0 = ist_get () in\n let mh1 = alloc_ref h0 a r x in\n ist_put (snd mh1);\n ist_witness (contains (fst mh1)); //witnessing that the current heap contains the generated reference\n fst mh1", "val FStar.ReflexiveTransitiveClosure.predicate = a: Type -> Type\nlet predicate (a:Type u#a) = a -> Type0", "val FStar.WellFounded.binrel = a: Type -> Type\nlet binrel (a:Type) = a -> a -> Type", "val MRefST.stable_on_heap_aux = \n m: MRefST.mref a r ->\n p: FStar.Preorder.predicate MRefHeap.heap ->\n h0: MRefHeap.heap ->\n h1: MRefHeap.heap\n -> Prims.logical\nlet stable_on_heap_aux (#a:Type) (#r:preorder a) (m:mref a r) (p:predicate heap) (h0:heap) (h1:heap) =\n p h0 /\\\n (contains m h0 ==> contains m h1 /\\ r (sel h0 m) (sel h1 m))\n ==>\n p h1", "val unused_in: #a:Type0 -> #rel:preorder a -> mref a rel -> heap -> Type0\nlet unused_in #a #rel r h = addr_unused_in (addr_of r) h", "val FStar.Pervasives.st_post_h = heap: Type -> a: Type -> Type\nlet st_post_h (heap a: Type) = st_post_h' heap a True", "val reference_of (h:mem) (a:aref) (v:Type0) (rel:preorder v)\n :Pure (mreference v rel) (requires (aref_live_at h a v rel))\n (ensures (fun x -> aref_live_at h a v rel /\\ frameOf x == frameOf_aref a /\\\n\t\t\t as_addr x == aref_as_addr a /\\ is_mm x == aref_is_mm a))\nlet reference_of h a v rel = MkRef a.aref_region (Heap.ref_of (Map.sel h.h a.aref_region) a.aref_aref v rel)", "val FStar.ST.st_post' = a: Type -> pre: Type -> Type\nlet st_post' = gst_post'", "val MRefST.contains = m: MRefHeap.mref a r -> h: MRefHeap.heap -> Type0\nlet contains (#a:Type) (#r:preorder a) (m:mref a r) (h:heap) = contains h m", "val alloc (#a: Type) (#rel: P.preorder a) (init: a)\n : HoareST (mref a rel)\n (fun _ -> True)\n (fun h0 r h1 -> fresh r h0 h1 /\\ modifies Set.empty h0 h1 /\\ sel h1 r == init)\nlet alloc (#a:Type) (#rel:P.preorder a) (init:a)\n: HoareST (mref a rel)\n (fun _ -> True)\n (fun h0 r h1 ->\n fresh r h0 h1 /\\\n modifies Set.empty h0 h1 /\\\n sel h1 r == init)\n= HoareST?.reflect (fun _ -> alloc init)", "val alloc (#a: Type) (#rel: P.preorder a) (init: a)\n : HoareST (mref a rel)\n (fun _ -> True)\n (fun h0 r h1 -> fresh r h0 h1 /\\ modifies Set.empty h0 h1 /\\ sel h1 r == init)\nlet alloc (#a:Type) (#rel:P.preorder a) (init:a)\n: HoareST (mref a rel)\n (fun _ -> True)\n (fun h0 r h1 ->\n fresh r h0 h1 /\\\n modifies Set.empty h0 h1 /\\\n sel h1 r == init)\n= HoareST?.reflect (fun _ -> alloc init)", "val FStar.Preorder.transitive = rel: FStar.Preorder.relation a -> Prims.logical\nlet transitive (#a:Type) (rel:relation a) =\n forall (x:a) (y:a) (z:a). (rel x y /\\ rel y z) ==> rel x z", "val FStar.OrdMap.cmp = a: Prims.eqtype -> Type0\nlet cmp (a:eqtype) = f:(a -> a -> Tot bool){total_order a f}", "val alloc (#a: Type) (#rel: preorder a) (init: a)\n : ST (mref a rel)\n (fun h -> True)\n (fun h0 r h1 -> fresh r h0 h1 /\\ modifies Set.empty h0 h1 /\\ sel h1 r == init)\nlet alloc (#a:Type) (#rel:preorder a) (init:a)\n :ST (mref a rel)\n (fun h -> True)\n (fun h0 r h1 -> fresh r h0 h1 /\\ modifies Set.empty h0 h1 /\\ sel h1 r == init)\n = let h0 = gst_get () in\n let r, h1 = alloc rel h0 init false in\n gst_put h1;\n gst_witness (contains_pred r);\n r", "val FStar.Preorder.preorder_rel = rel: FStar.Preorder.relation a -> Prims.logical\nlet preorder_rel (#a:Type) (rel:relation a) =\n reflexive rel /\\ transitive rel", "val FStar.Reflection.V2.Arith.tm = a: Type -> Type0\nlet tm a = st -> Tac (either string (a * st))", "val FStar.PCM.symrel = a: Type -> Type\nlet symrel (a: Type u#a) = c:(a -> a -> prop) { (forall x y. c x y <==> c y x) }", "val recall (#a: Type) (#rel: preorder a) (r: mref a rel)\n : STATE unit (fun p h -> Heap.contains h r ==> p () h)\nlet recall (#a:Type) (#rel:preorder a) (r:mref a rel) :STATE unit (fun p h -> Heap.contains h r ==> p () h)\n = gst_recall (contains_pred r)", "val MRefST.st = a: Type -> Type\nlet st (a: Type) = heap -> M (a * heap)", "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\nlet ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\n = MR.ref a p", "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\nlet ref a p = MHR.ref (FStar.Universe.raise_t a) (raise_preorder p)", "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\nlet ref a p = MHR.ref (FStar.Universe.raise_t a) (raise_preorder p)", "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\nlet ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\n = MR.ref a p", "val Steel.MonotonicHigherReference.stable_property = p: FStar.Preorder.preorder a -> Type\nlet stable_property (#a:Type) (p:Preorder.preorder a)\n = fact:property a { Preorder.stable fact p }", "val contains: #a:Type0 -> #rel:preorder a -> heap -> mref a rel -> Type0\nlet contains #a #rel h r =\n let _ = () in\n Some? (h.memory r.addr) /\\\n (let Some (| a1, pre_opt, mm, _ |) = h.memory r.addr in\n a == a1 /\\ Some? pre_opt /\\ Some?.v pre_opt == rel /\\ mm = r.mm)", "val ref (a:Type u#1) (p:Preorder.preorder a)\n : Type u#0\nlet ref a p = PR.ref (history a p) pcm_history", "val ref (a:Type u#1) (p:Preorder.preorder a)\n : Type u#0\nlet ref a p = M.ref (history a p) pcm_history", "val MRefST.ist_witnessed = p: FStar.Preorder.predicate MRefHeap.heap {FStar.Preorder.stable p MRefST.heap_rel} -> Type0\nlet ist_witnessed (p:predicate heap{stable p heap_rel}) = witnessed heap_rel p", "val FStar.Tactics.Effect.tactic = a: Type -> Type0\nlet tactic a = tac unit a", "val FStar.PredicateExtensionality.predicate = a: Type -> Type\nlet predicate (a:Type) = a -> Tot prop", "val FStar.Monotonic.Heap.upd_tot' = h: FStar.Monotonic.Heap.heap -> r: FStar.Monotonic.Heap.mref a rel -> x: a\n -> FStar.Monotonic.Heap.heap_rec\nlet upd_tot' (#a: Type0) (#rel: preorder a) (h: heap) (r: mref a rel) (x: a) =\n { h with memory = F.on_dom pos (fun r' -> if r.addr = r'\n\t\t\t then Some (| a, Some rel, r.mm, x |)\n else h.memory r') }", "val Steel.GhostMonotonicReference.stable_property = p: FStar.Preorder.preorder a -> Type\nlet stable_property (#a:Type) (p:Preorder.preorder a)\n = fact:property a { Preorder.stable fact p }", "val IMST.st_return = a: Type -> x: a -> s: Type0 -> rel: FStar.Preorder.preorder s -> post: IMST.st_post s a -> s0: s\n -> Prims.logical\nlet st_return (a:Type) (x:a) (s:Type0) (rel:preorder s) (post:st_post s a) (s0:s)\n = forall v. v == x ==> post v s0", "val FStar.Preorder.stable = p: FStar.Preorder.predicate a -> rel: FStar.Preorder.relation a {FStar.Preorder.preorder_rel rel}\n -> Prims.logical\nlet stable (#a:Type) (p:predicate a) (rel:relation a{preorder_rel rel}) =\n forall (x:a) (y:a). (p x /\\ rel x y) ==> p y", "val FStar.Relational.Comp.st2_Post' = a: Type -> pre: Type -> Type\nlet st2_Post' (a:Type) (pre:Type) = st_post_h' heap2 a pre", "val witness : #a:Type ->\n #r:preorder a ->\n\t m:mref a r ->\n\t p:predicate heap{stable_on_heap m p} ->\n\t MRefST unit (fun h0 -> p h0)\n\t (fun h0 _ h1 -> h0 == h1 /\\\n\t\t\t ist_witnessed p)\nlet witness #a #r m p =\n ist_witness p", "val FStar.ST.st_post = a: Type -> Type\nlet st_post = gst_post", "val read (#a: Type) (#rel: preorder a) (r: mref a rel) : STATE a (fun p h -> p (sel h r) h)\nlet read (#a:Type) (#rel:preorder a) (r:mref a rel) :STATE a (fun p h -> p (sel h r) h)\n = let h0 = gst_get () in\n gst_recall (contains_pred r);\n Heap.lemma_sel_equals_sel_tot_for_contained_refs h0 r;\n sel_tot h0 r", "val ( ! ) (#a: Type) (#rel: P.preorder a) (r: mref a rel)\n : HoareST a (fun _ -> True) (fun h0 x h1 -> h0 == h1 /\\ x == sel h1 r)\nlet op_Bang (#a:Type) (#rel:P.preorder a) (r:mref a rel)\n: HoareST a\n (fun _ -> True)\n (fun h0 x h1 ->\n h0 == h1 /\\\n x == sel h1 r)\n= HoareST?.reflect (fun _ -> read r)", "val ( ! ) (#a: Type) (#rel: P.preorder a) (r: mref a rel)\n : HoareST a (fun _ -> True) (fun h0 x h1 -> h0 == h1 /\\ x == sel h1 r)\nlet op_Bang (#a:Type) (#rel:P.preorder a) (r:mref a rel)\n: HoareST a\n (fun _ -> True)\n (fun h0 x h1 ->\n h0 == h1 /\\\n x == sel h1 r)\n= HoareST?.reflect (fun _ -> read r)", "val FStar.Pervasives.ex_post' = a: Type -> pre: Type -> Type\nlet ex_post' (a pre: Type) = _: result a {pre} -> GTot Type0", "val Steel.MonotonicReference.stable_property = p: FStar.Preorder.preorder a -> Type\nlet stable_property (#a:Type) (p:Preorder.preorder a)\n = fact:property a { Preorder.stable fact p }", "val Steel.ST.MonotonicReference.stable_property = p: FStar.Preorder.preorder a -> Type\nlet stable_property (#a:Type) (p:Preorder.preorder a)\n = fact:property a { Preorder.stable fact p }", "val ref ([@@@ unused] a:Type0)\n : Type0\nlet ref (a:Type0)\n : Type0\n = R.ref a", "val FStar.All.lift_state_all = a: Type -> wp: FStar.ST.st_wp a -> p: FStar.All.all_post a\n -> FStar.Pervasives.st_pre_h FStar.Monotonic.Heap.heap\nlet lift_state_all (a : Type) (wp : st_wp a) (p : all_post a) = wp (fun a -> p (V a))", "val FStar.Fin.in_ = s: FStar.Seq.Base.seq a -> Type0\nlet in_ (#a: Type) (s: S.seq a) = n: nat{n < S.length s}", "val FStar.TwoLevelHeap.st_wp = a: Type -> Type\nlet st_wp (a:Type) = st_wp_h t a", "val FStar.Monotonic.Witnessed.witnessed_past = rel: FStar.Preorder.preorder state -> p: (_: state -> Type0) -> Type0\nlet witnessed_past (#state:Type) (rel:preorder state) (p:(state -> Type0)) = \n get (fun s -> exists s'. rel s' s /\\ (forall s''. rel s' s'' ==> p s''))", "val FStar.Pervasives.st_pre_h = heap: Type -> Type\nlet st_pre_h (heap: Type) = heap -> GTot Type0", "val FStar.ST.gst_post' = a: Type -> pre: Type -> Type\nlet gst_post' (a:Type) (pre:Type) = st_post_h' heap a pre", "val null (#a:Type0) \n : ref a\nlet null (#a:Type0)\n : ref a\n = R.null #a", "val FStar.Pervasives.st_wp_h = heap: Type -> a: Type -> Type\nlet st_wp_h (heap a: Type) = st_post_h heap a -> Tot (st_pre_h heap)", "val FStar.WellFounded.well_founded_relation = a: Type -> Type\nlet well_founded_relation (a:Type) = rel:binrel a{is_well_founded rel}", "val ( ^+^ )\n (#a #b: Type0)\n (#rel1: preorder a)\n (#rel2: preorder b)\n (r1: mref a rel1)\n (r2: mref b rel2)\n : GTot (set nat)\nlet op_Hat_Plus_Hat (#a:Type0) (#b:Type0) (#rel1:preorder a) (#rel2:preorder b) (r1:mref a rel1) (r2:mref b rel2)\n :GTot (set nat) = S.union (only r1) (only r2)", "val FStar.Pervasives.ex_post = a: Type -> Type\nlet ex_post (a: Type) = ex_post' a True", "val Prims.pure_wp_monotonic0 = a: Type -> wp: Prims.pure_wp' a -> Prims.logical\nlet pure_wp_monotonic0 (a:Type) (wp:pure_wp' a) =\n forall (p q:pure_post a). (forall (x:a). p x ==> q x) ==> (wp p ==> wp q)", "val Steel.GhostMonotonicHigherReference.stable_property = p: FStar.Preorder.preorder a -> Type\nlet stable_property (#a:Type) (p:Preorder.preorder a)\n = fact:property a { Preorder.stable fact p }", "val trivial_rel (a: Type0) : Preorder.relation a\nlet trivial_rel (a:Type0) :Preorder.relation a = fun x y -> True", "val gref_of: a: aref -> t: Type0 -> rel: preorder t -> Ghost (mref t rel) (requires (exists h . aref_live_at h a t rel)) (ensures (fun _ -> True))\nlet gref_of a t rel =\n let m : squash (exists (h: heap) . aref_live_at h a t rel) = () in\n let l : (exists (h: heap) . aref_live_at h a t rel) =\n Squash.join_squash #(h: heap & aref_live_at h a t rel) m\n in\n let k : (exists (h: heap { aref_live_at h a t rel} ) . squash True ) =\n FStar.Squash.bind_squash\n #(h: heap & aref_live_at h a t rel)\n #(h: (h: heap { aref_live_at h a t rel} ) & squash True)\n l\n (fun h -> let (| h', _ |) = h in Squash.return_squash (| h', () |) )\n in\n let h = FStar.ErasedLogic.exists_proj1 #(h: heap {aref_live_at h a t rel}) #(fun _ -> squash True) k in\n ref_of' h a t rel", "val IMSTsub.st_return = a: Type -> x: a -> s: Type0 -> rel: FStar.Preorder.preorder s -> post: IMSTsub.st_post s a -> s0: s\n -> Prims.logical\nlet st_return (a:Type) (x:a) (s:Type0) (rel:preorder s) (post:st_post s a) (s0:s)\n = forall v. v == x ==> post v s0" ], "closest_src": [ { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.mref0" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.contains_pred" }, { "project_name": "FStar", "file_name": "FStar.MRef.fsti", "name": "FStar.MRef.spred" }, { "project_name": "FStar", "file_name": "MRefHeap.fsti", "name": "MRefHeap.preorder_t" }, { "project_name": "FStar", "file_name": "FStar.MRef.fst", "name": "FStar.MRef.p_pred" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.mref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.fresh" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.as_ref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.tset" }, { "project_name": "steel", "file_name": "Steel.Channel.Simplex.fst", "name": "Steel.Channel.Simplex.mref" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.mref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.ref_of" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.set" }, { "project_name": "FStar", "file_name": "FStar.Preorder.fst", "name": "FStar.Preorder.reflexive" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.heap_cell_a" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fsti", "name": "FStar.ReflexiveTransitiveClosure.binrel" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.sel" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.st_post'" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.alloc" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.ref_of'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.PatternMatching.fst", "name": "FStar.Tactics.PatternMatching.hyp" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.fresh_rref" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.contains" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fsti", "name": "FStar.ReflexiveTransitiveClosure.preorder_rel" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_post_h'" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.recall" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.stable_on_heap" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.free_mm" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fsti", "name": "FStar.ReflexiveTransitiveClosure.reflexive" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fsti", "name": "Steel.ArrayRef.ref" }, { "project_name": "steel", "file_name": "SelectorLogic.fst", "name": "SelectorLogic.ref" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.read" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.recall" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.recall" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.contains_ref" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.sel" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.st_post" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.upd" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.alloc_ref" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.ref" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.alloc" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fsti", "name": "FStar.ReflexiveTransitiveClosure.predicate" }, { "project_name": "FStar", "file_name": "FStar.WellFounded.fst", "name": "FStar.WellFounded.binrel" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.stable_on_heap_aux" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.unused_in" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_post_h" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.reference_of" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.st_post'" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.contains" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.alloc" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.alloc" }, { "project_name": "FStar", "file_name": "FStar.Preorder.fst", "name": "FStar.Preorder.transitive" }, { "project_name": "FStar", "file_name": "FStar.OrdMap.fsti", "name": "FStar.OrdMap.cmp" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.alloc" }, { "project_name": "FStar", "file_name": "FStar.Preorder.fst", "name": "FStar.Preorder.preorder_rel" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Arith.fst", "name": "FStar.Reflection.V2.Arith.tm" }, { "project_name": "FStar", "file_name": "FStar.PCM.fst", "name": "FStar.PCM.symrel" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.recall" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.st" }, { "project_name": "steel", "file_name": "Steel.ST.GhostMonotonicReference.fst", "name": "Steel.ST.GhostMonotonicReference.ref" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicReference.fst", "name": "Steel.GhostMonotonicReference.ref" }, { "project_name": "steel", "file_name": "Steel.MonotonicReference.fst", "name": "Steel.MonotonicReference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.ref" }, { "project_name": "steel", "file_name": "Steel.MonotonicHigherReference.fsti", "name": "Steel.MonotonicHigherReference.stable_property" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.contains" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicHigherReference.fst", "name": "Steel.GhostMonotonicHigherReference.ref" }, { "project_name": "steel", "file_name": "Steel.MonotonicHigherReference.fst", "name": "Steel.MonotonicHigherReference.ref" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.ist_witnessed" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Effect.fsti", "name": "FStar.Tactics.Effect.tactic" }, { "project_name": "FStar", "file_name": "FStar.PredicateExtensionality.fst", "name": "FStar.PredicateExtensionality.predicate" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.upd_tot'" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicReference.fsti", "name": "Steel.GhostMonotonicReference.stable_property" }, { "project_name": "FStar", "file_name": "IMST.fst", "name": "IMST.st_return" }, { "project_name": "FStar", "file_name": "FStar.Preorder.fst", "name": "FStar.Preorder.stable" }, { "project_name": "FStar", "file_name": "FStar.Relational.Comp.fst", "name": "FStar.Relational.Comp.st2_Post'" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.witness" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.st_post" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.read" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.op_Bang" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.op_Bang" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.ex_post'" }, { "project_name": "steel", "file_name": "Steel.MonotonicReference.fsti", "name": "Steel.MonotonicReference.stable_property" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fsti", "name": "Steel.ST.MonotonicReference.stable_property" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.ref" }, { "project_name": "FStar", "file_name": "FStar.All.fst", "name": "FStar.All.lift_state_all" }, { "project_name": "FStar", "file_name": "FStar.Fin.fsti", "name": "FStar.Fin.in_" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.st_wp" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Witnessed.fst", "name": "FStar.Monotonic.Witnessed.witnessed_past" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_pre_h" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.gst_post'" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.null" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_wp_h" }, { "project_name": "FStar", "file_name": "FStar.WellFounded.fst", "name": "FStar.WellFounded.well_founded_relation" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.op_Hat_Plus_Hat" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.ex_post" }, { "project_name": "FStar", "file_name": "prims.fst", "name": "Prims.pure_wp_monotonic0" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicHigherReference.fsti", "name": "Steel.GhostMonotonicHigherReference.stable_property" }, { "project_name": "FStar", "file_name": "FStar.Heap.fst", "name": "FStar.Heap.trivial_rel" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.gref_of" }, { "project_name": "FStar", "file_name": "IMSTsub.fst", "name": "IMSTsub.st_return" } ], "selected_premises": [ "FStar.Monotonic.HyperStack.frameOf", "FStar.Monotonic.HyperStack.is_mm", "FStar.Monotonic.HyperStack.mreference", "FStar.Monotonic.Heap.mref", "FStar.Monotonic.HyperStack.as_addr", "FStar.Preorder.preorder_rel", "FStar.Monotonic.HyperStack.mk_mreference", "FStar.Preorder.stable", "FStar.Monotonic.HyperStack.is_heap_color", "FStar.Monotonic.Heap.only", "FStar.Monotonic.Heap.only_t", "FStar.Monotonic.Heap.fresh", "FStar.Monotonic.Heap.equal_dom", "FStar.Monotonic.Heap.compare_addrs", "FStar.Monotonic.HyperStack.mstackref", "FStar.Preorder.reflexive", "FStar.Monotonic.HyperStack.is_stack_region", "FStar.Monotonic.Heap.modifies_t", "FStar.Monotonic.Heap.modifies", "FStar.Monotonic.HyperStack.is_eternal_region_hs", "FStar.Preorder.transitive", "FStar.Pervasives.st_post_h", "FStar.Pervasives.id", "FStar.Pervasives.Native.fst", "FStar.Monotonic.HyperStack.is_eternal_region", "FStar.Pervasives.Native.snd", "FStar.Monotonic.HyperStack.is_in", "FStar.Monotonic.HyperStack.poppable", "FStar.Monotonic.HyperHeap.modifies_just", "FStar.Pervasives.st_pre_h", "FStar.Monotonic.Heap.op_Hat_Plus_Hat", "FStar.Monotonic.Heap.op_Hat_Plus_Plus", "FStar.Monotonic.HyperStack.popped", "FStar.Pervasives.st_post_h'", "FStar.Monotonic.Heap.op_Plus_Plus_Hat", "Prims.pure_pre", "FStar.Pervasives.st_return", "FStar.Map.const_on", "FStar.Monotonic.HyperStack.is_above", "FStar.Monotonic.HyperHeap.modifies", "FStar.Map.has_dom", "FStar.Monotonic.HyperStack.downward_closed_predicate", "FStar.Monotonic.HyperStack.map_invariant_predicate", "FStar.Ghost.return", "Prims.returnM", "FStar.Pervasives.all_pre_h", "FStar.Monotonic.HyperStack.is_wf_with_ctr_and_tip", "Prims.__cache_version_number__", "FStar.Monotonic.HyperStack.empty_mem", "FStar.Monotonic.HyperStack.heap_region_does_not_overlap_with_tip", "FStar.Pervasives.ex_pre", "FStar.Pervasives.st_stronger", "FStar.Monotonic.HyperHeap.disjoint_regions", "FStar.Pervasives.dfst", "FStar.Monotonic.HyperHeap.modifies_one", "FStar.Pervasives.st_wp_h", "FStar.Set.subset", "FStar.Monotonic.HyperStack.remove_elt", "FStar.Map.disjoint_dom", "FStar.Monotonic.HyperHeap.rid_last_component", "FStar.Monotonic.HyperHeap.equal_on", "FStar.Pervasives.all_return", "FStar.Monotonic.Heap.set", "FStar.Pervasives.st_trivial", "FStar.Monotonic.HyperStack.is_tip", "FStar.Ghost.op_let_At", "FStar.Set.as_set", "FStar.Set.as_set'", "FStar.Pervasives.all_post_h", "FStar.Monotonic.HyperStack.is_just_below", "FStar.Monotonic.HyperStack.is_below", "FStar.Monotonic.HyperStack.tip_top_predicate", "FStar.Pervasives.coerce_eq", "FStar.Ghost.tot_to_gtot", "FStar.Monotonic.HyperStack.rid_ctr_pred_predicate", "FStar.Monotonic.HyperStack.pop", "FStar.Monotonic.HyperStack.is_strictly_above", "FStar.Monotonic.HyperHeap.disjoint", "FStar.Pervasives.ex_post", "Prims.min", "FStar.Pervasives.dsnd", "FStar.Ghost.bind", "FStar.Pervasives.all_post_h'", "FStar.Ghost.elift2_pq", "FStar.Monotonic.Heap.tset", "FStar.Pervasives.ex_post'", "Prims.subtype_of", "Prims.pow2", "FStar.TSet.as_set'", "FStar.Pervasives.pure_return", "FStar.Ghost.push_refinement", "FStar.Ghost.elift1", "FStar.Ghost.elift2", "FStar.Monotonic.HyperStack.is_strictly_below", "FStar.Pervasives.all_stronger", "FStar.Ghost.elift1_p", "FStar.Pervasives.all_trivial", "Prims.auto_squash", "FStar.TSet.subset", "FStar.Ghost.elift1_pq" ], "source_upto_this": "(*\n Copyright 2008-2014 Aseem Rastogi, and Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.Monotonic.HyperStack\n\nopen FStar.Preorder\nmodule Map = FStar.Map\n\ninclude FStar.Monotonic.HyperHeap\n\n\n(****** Some predicates ******)\n\nunfold let is_in (r:rid) (h:hmap) = h `Map.contains` r\n\nlet is_stack_region r = color r > 0\nlet is_heap_color c = c <= 0\n\n[@@(deprecated \"FStar.HyperStack.ST.is_eternal_region\")]\nlet is_eternal_region r = is_heap_color (color r) && not (rid_freeable r)\n\nunfold let is_eternal_region_hs r = is_heap_color (color r) && not (rid_freeable r)\n\ntype sid = r:rid{is_stack_region r} //stack region ids\n\n(*\n * AR: marking these unfolds, else I think there are pattern firing issues depending on which one we use\n *)\nunfold let is_above r1 r2 = r1 `includes` r2\nunfold let is_just_below r1 r2 = r1 `extends` r2\nunfold let is_below r1 r2 = r2 `is_above` r1\nlet is_strictly_below r1 r2 = r1 `is_below` r2 && r1 <> r2\nlet is_strictly_above r1 r2 = r1 `is_above` r2 && r1 <> r2\n\n\n[@@\"opaque_to_smt\"]\nunfold private let map_invariant_predicate (m:hmap) :Type0 =\n forall r. Map.contains m r ==>\n (forall s. includes s r ==> Map.contains m s)\n\n[@@\"opaque_to_smt\"]\nunfold private let downward_closed_predicate (h:hmap) :Type0 =\n forall (r:rid). r `is_in` h //for any region in the memory\n ==> (r=root //either is the root\n \\/ (forall (s:rid). (r `is_above` s //or, any region beneath it\n /\\ s `is_in` h) //that is also in the memory\n ==> ((is_stack_region r = is_stack_region s) /\\ //must be of the same flavor as itself\n ((is_heap_color (color r) /\\ rid_freeable r) ==> s == r)))) //and if r is a freeable heap region, s can only be r (no regions strictly below r)\n\n[@@\"opaque_to_smt\"]\nunfold private let tip_top_predicate (tip:rid) (h:hmap) :Type0 =\n forall (r:sid). r `is_in` h <==> r `is_above` tip\n\n[@@\"opaque_to_smt\"]\nunfold private let rid_ctr_pred_predicate (h:hmap) (n:int) :Type0 =\n forall (r:rid). h `Map.contains` r ==> rid_last_component r < n\n\n\n(****** Mem definition ******)\n\n[@@ remove_unused_type_parameters [0]]\nval map_invariant (m:hmap) :Type0 //all regions above a contained region are contained\n[@@ remove_unused_type_parameters [0]]\nval downward_closed (h:hmap) :Type0 //regions below a non-root region are of the same color\n[@@ remove_unused_type_parameters [0;1]]\nval tip_top (tip:rid) (h:hmap) :Type0 //all contained stack regions are above tip\n[@@ remove_unused_type_parameters [0;1]]\nval rid_ctr_pred (h:hmap) (n:int) :Type0 //all live regions have last component less than the rid_ctr\n\nlet is_tip (tip:rid) (h:hmap) =\n (is_stack_region tip \\/ tip = root) /\\ //the tip is a stack region, or the root\n tip `is_in` h /\\ //the tip is live\n tip_top tip h //any other sid activation is a above (or equal to) the tip\n\nlet is_wf_with_ctr_and_tip (h:hmap) (ctr:int) (tip:rid)\n = (not (rid_freeable root)) /\\\n root `is_in` h /\\\n tip `is_tip` h /\\\n map_invariant h /\\\n downward_closed h /\\\n rid_ctr_pred h ctr\n\nprivate val mem' :Type u#1\n\nprivate val mk_mem (rid_ctr:int) (h:hmap) (tip:rid) :mem'\n\nval get_hmap (m:mem') :hmap\nval get_rid_ctr (m:mem') :int\nval get_tip (m:mem') :rid\n\nprivate val lemma_mk_mem'_projectors (rid_ctr:int) (h:hmap) (tip:rid)\n :Lemma (requires True)\n (ensures (let m = mk_mem rid_ctr h tip in\n\t (get_hmap m == h /\\ get_rid_ctr m == rid_ctr /\\ get_tip m == tip)))\n [SMTPatOr [[SMTPat (get_hmap (mk_mem rid_ctr h tip))];\n\t [SMTPat (get_rid_ctr (mk_mem rid_ctr h tip))];\n\t\t [SMTPat (get_tip (mk_mem rid_ctr h tip))]\n\t\t ]]\n\ntype mem :Type = m:mem'{is_wf_with_ctr_and_tip (get_hmap m) (get_rid_ctr m) (get_tip m) }\n\n\n(****** Lemmas about mem and predicates ******)\n\nprivate val lemma_mem_projectors_are_in_wf_relation (m:mem)\n :Lemma (is_wf_with_ctr_and_tip (get_hmap m) (get_rid_ctr m) (get_tip m))\n\nprivate val lemma_is_wf_ctr_and_tip_intro (h:hmap) (ctr:int) (tip:rid)\n :Lemma (requires (root `is_in` h /\\ (is_stack_region tip \\/ tip = root) /\\ tip `is_in` h /\\\n tip_top_predicate tip h /\\ map_invariant_predicate h /\\\n downward_closed_predicate h /\\ rid_ctr_pred_predicate h ctr))\n\t (ensures (is_wf_with_ctr_and_tip h ctr tip))\n\nprivate val lemma_is_wf_ctr_and_tip_elim (m:mem)\n :Lemma (let h, rid_ctr, tip = get_hmap m, get_rid_ctr m, get_tip m in\n (root `is_in` h /\\ (is_stack_region tip \\/ tip = root) /\\ tip `is_in` h /\\\n\t tip_top_predicate tip h /\\ map_invariant_predicate h /\\\n downward_closed_predicate h /\\ rid_ctr_pred_predicate h rid_ctr))\n\n(******* map_invariant related lemmas ******)\n\nval lemma_map_invariant (m:mem) (r s:rid)\n :Lemma (requires (r `is_in` get_hmap m /\\ s `is_above` r))\n (ensures (s `is_in` get_hmap m))\n [SMTPat (r `is_in` get_hmap m); SMTPat (s `is_above` r); SMTPat (s `is_in` get_hmap m)]\n\n(****** downward_closed related lemmas *******)\n\nval lemma_downward_closed (m:mem) (r:rid) (s:rid{s =!= root})\n :Lemma (requires (r `is_in` get_hmap m /\\ s `is_above` r))\n (ensures (is_heap_color (color r) == is_heap_color (color s) /\\\n\t is_stack_region r == is_stack_region s))\n [SMTPatOr [[SMTPat (get_hmap m `Map.contains` r); SMTPat (s `is_above` r); SMTPat (is_heap_color (color s))];\n [SMTPat (get_hmap m `Map.contains` r); SMTPat (s `is_above` r); SMTPat (is_stack_region s)]\n ]]\n\n(****** tip_top related lemmas ******)\n\nval lemma_tip_top (m:mem) (r:sid)\n :Lemma (r `is_in` get_hmap m <==> r `is_above` get_tip m)\n\n(*\n * Pointer uses lemma_tip_top by calling it explicitly with Classical.forall_intro2\n * Classical.forall_intro2 does not work well with SMTPat\n * So adding this smt form of the same lemma\n *)\nval lemma_tip_top_smt (m:mem) (r:rid)\n :Lemma (requires (is_stack_region r))\n (ensures (r `is_in` get_hmap m <==> r `is_above` get_tip m))\n [SMTPatOr [[SMTPat (is_stack_region r); SMTPat (r `is_above` get_tip m)];\n [SMTPat (is_stack_region r); SMTPat (r `is_in` get_hmap m)]]]\n\n(****** rid_ctr_pred related lemmas ******)\n\nval lemma_rid_ctr_pred (_:unit)\n :Lemma (forall (m:mem) (r:rid).{:pattern (get_hmap m `Map.contains` r)} get_hmap m `Map.contains` r ==> rid_last_component r < get_rid_ctr m)\n\n(*****)\n\n(****** Operations on mem ******)\n\n\nlet empty_mem : mem =\n let empty_map = Map.restrict Set.empty (Map.const Heap.emp) in\n let h = Map.upd empty_map root Heap.emp in\n let tip = root in\n root_last_component ();\n lemma_is_wf_ctr_and_tip_intro h 1 tip;\n mk_mem 1 h tip\n\nlet heap_region_does_not_overlap_with_tip\n (m:mem) (r:rid{is_heap_color (color r) /\\ not (disjoint r (get_tip m)) /\\ r =!= root /\\ is_stack_region (get_tip m)})\n : Lemma (requires True)\n (ensures (~ (r `is_in` get_hmap m)))\n = root_has_color_zero()\n\nlet poppable (m:mem) = get_tip m =!= root\n\nprivate let remove_elt (#a:eqtype) (s:Set.set a) (x:a) = Set.intersect s (Set.complement (Set.singleton x))\n\nlet popped (m0 m1:mem) =\n poppable m0 /\\\n (let h0, tip0, h1, tip1 = get_hmap m0, get_tip m0, get_hmap m1, get_tip m1 in\n (parent tip0 = tip1 /\\\n Set.equal (Map.domain h1) (remove_elt (Map.domain h0) tip0) /\\\n Map.equal h1 (Map.restrict (Map.domain h1) h0)))\n\nlet pop (m0:mem{poppable m0}) :mem =\n let h0, tip0, rid_ctr0 = get_hmap m0, get_tip m0, get_rid_ctr m0 in\n root_has_color_zero();\n lemma_is_wf_ctr_and_tip_elim m0;\n let dom = remove_elt (Map.domain h0) tip0 in\n let h1 = Map.restrict dom h0 in\n let tip1 = parent tip0 in\n lemma_is_wf_ctr_and_tip_intro h1 rid_ctr0 tip1;\n mk_mem rid_ctr0 h1 tip1\n\n//A (reference a) may reside in the stack or heap, and may be manually managed\n//Mark it private so that clients can't use its projectors etc.\n//enabling extraction of mreference to just a reference in ML and pointer in C\n//note that this not enforcing any abstraction\n(*\n * AR: 12/26: Defining it using Heap.mref directly, removing the HyperHeap.mref indirection\n *)\nprivate noeq\ntype mreference' (a:Type) (rel:preorder a) =\n | MkRef : frame:rid -> ref:Heap.mref a rel -> mreference' a rel\n\nlet mreference a rel = mreference' a rel\n\n//TODO: rename to frame_of, avoiding the inconsistent use of camelCase\nlet frameOf (#a:Type) (#rel:preorder a) (r:mreference a rel) :rid\n = r.frame\n\nlet mk_mreference (#a:Type) (#rel:preorder a) (id:rid)\n (r:Heap.mref a rel)\n :mreference a rel\n = MkRef id r\n\n//Hopefully we can get rid of this one\nval as_ref (#a:Type0) (#rel:preorder a) (x:mreference a rel)\n :Heap.mref a rel\n\n//And make this one abstract\nlet as_addr #a #rel (x:mreference a rel)\n :GTot pos\n = Heap.addr_of (as_ref x)\n\nval lemma_as_ref_inj (#a:Type) (#rel:preorder a) (r:mreference a rel)\n :Lemma (requires True) (ensures (mk_mreference (frameOf r) (as_ref r) == r))\n [SMTPat (as_ref r)]\n\nlet is_mm (#a:Type) (#rel:preorder a) (r:mreference a rel) :GTot bool =\n Heap.is_mm (as_ref r)\n\n// Warning: all of the type aliases below get special support for KaRaMeL\n// extraction. If you rename or add to this list,\n// src/extraction/FStar.Extraction.Karamel.fs needs to be updated.\n\n//adding (not s.mm) to stackref and ref so as to keep their semantics as is\nlet mstackref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_stack_region (frameOf s) && not (is_mm s) }\n" }, { "file_name": "IfcExampleReify2.fst", "name": "IfcExampleReify2.c_2", "opens_and_abbrevs": [ { "open": "FStar.DM4F.Exceptions" }, { "open": "FStar.DM4F.Heap.IntStoreFixed" }, { "open": "IfcTypechecker" }, { "open": "IfcRulesReify" }, { "open": "WhileReify" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let c_2 = Assign hi (AOp Plus (AVar lo) (AInt 1))", "source_range": { "start_line": 43, "start_col": 0, "end_line": 43, "end_col": 49 }, "interleaved": false, "definition": "WhileReify.Assign IfcExampleReify2.hi\n (WhileReify.AOp WhileReify.Plus (WhileReify.AVar IfcExampleReify2.lo) (WhileReify.AInt 1))", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "WhileReify.Assign", "IfcExampleReify2.hi", "WhileReify.AOp", "WhileReify.Plus", "WhileReify.AVar", "IfcExampleReify2.lo", "WhileReify.AInt" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "WhileReify.com", "prompt": "let c_2 =\n ", "expected_response": "Assign hi (AOp Plus (AVar lo) (AInt 1))", "source": { "project_name": "FStar", "file_name": "examples/rel/IfcExampleReify2.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "IfcExampleReify2.fst", "checked_file": "dataset/IfcExampleReify2.fst.checked", "interface_file": false, "dependencies": [ "dataset/WhileReify.fst.checked", "dataset/prims.fst.checked", "dataset/IfcTypechecker.fst.checked", "dataset/IfcRulesReify.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.DM4F.Heap.IntStoreFixed.fsti.checked", "dataset/FStar.DM4F.Exceptions.fst.checked" ] }, "definitions_in_context": [ "let hi : id = to_id 0", "let lo : id = to_id 1", "let c : id = to_id 2", "let env var =\n if var = hi then High\n else if var = lo then Low\n else if var = c then Low\n else High", "let c_1 body = While (AVar c) body (AVar c)" ], "closest": [ "val IfcExampleReify1.c1_2 = WhileReify.com\nlet c1_2 = Assign y (AOp Plus (AVar x) (AInt 6))", "val IfcExampleReify1.c1_3 = WhileReify.com\nlet c1_3 = Assign z (AOp Plus (AVar y) (AInt 7))", "val IfcExampleReify1.c1_4 = WhileReify.com\nlet c1_4 = Assign x (AOp Plus (AVar z) (AInt 7))", "val IfcExampleReify1.c1_1 = WhileReify.com\nlet c1_1 = Assign x (AVar y)", "val IfcExampleReify1.c1_5 = WhileReify.com\nlet c1_5 = Assign c (AOp Minus (AVar c) (AInt 1))", "val IfcExampleReify1.c1 = WhileReify.com\nlet c1 = c1_0 c1_6", "val IfcExampleReify1.c1_6 = WhileReify.com\nlet c1_6 = Seq c1_1 (Seq c1_2 (Seq (Seq c1_3 c1_4) c1_5))", "val IfcExampleReify1.c1_0 = body: WhileReify.com -> WhileReify.com\nlet c1_0 body = While (AVar c) body (AVar c)", "val IfcExample.c1_1 = While.com\nlet c1_1 = Assign x (AVar y)", "val IfcExample.c1_5 = While.com\nlet c1_5 = Assign c (AOp Minus (AVar c) (AInt 1))", "val IfcExample.c1_3 = While.com\nlet c1_3 = Assign z (AOp Plus (AVar y) (AInt 7))", "val IfcExample.c1_4 = While.com\nlet c1_4 = Assign x (AOp Plus (AVar z) (AInt 7))", "val IfcExample.c1_6 = While.com\nlet c1_6 = Seq c1_1 (Seq c1_2 (Seq c1_3 (Seq c1_4 c1_5)))", "val IfcExample.c1_2 = While.com\nlet c1_2 = Assign y (AOp Plus (AVar x) (AInt 6))", "val IfcExample.c1 = While.com\nlet c1 = c1_0 c1_6", "val IfcExample.c1_0 = body: While.com -> While.com\nlet c1_0 body = While (AVar c) body (AVar c)", "val IfcMonitorTest.p2 = IfcMonitor.com\nlet p2 = Assign (to_id 1) (AVar (to_id 2))", "val IfcReificationRegressionTest.bidule2 = Prims.unit\nlet bidule2 = assert (forall s0. x2 true s0 = x2 false s0)", "val IfcReificationRegressionTest.bidule1 = Prims.unit\nlet bidule1 = assert (forall s0. x1 true s0 = x1 false s0)", "val IfcReificationRegressionTest.bidule3 = Prims.unit\nlet bidule3 = assert (forall s0. x3 true s0 = x3 false s0)", "val IfcMonitorTest.p1 = IfcMonitor.com\nlet p1 = Assign (to_id 1) (AVar (to_id 3))", "val WhileReify.bidule2 = Prims.unit\nlet bidule2 = assert (interpret_exp (create 3) (AOp Plus (AVar (to_id 7)) (AInt 5)) = 8)", "val IfcMonitorTest.test2 = Prims.unit\nlet test2 = assert_norm (Some? (interpret_com h0 p2 env Low))", "val IfcMonitorTest.p4 = IfcMonitor.com\nlet p4 = If (AOp Plus (AVar (to_id 3)) (AInt (- 5))) (Assign (to_id 1) (AInt 0)) Skip", "val IfcReificationRegressionTest.x = Prims.int * Prims.int\nlet x = reify (ifc b) s0", "val IfcReificationRegressionTest.bidule0 = Prims.unit\nlet bidule0 = assert (forall s0. x0 true s0 = x0 false s0)", "val IfcMonitorTest.p3 = IfcMonitor.com\nlet p3 = If (AOp Plus (AVar (to_id 3)) (AInt 2)) (Assign (to_id 1) (AInt 0)) Skip", "val IfcMonitorTest.p5 = IfcMonitor.com\nlet p5 = Seq (Assign (to_id 3) (AVar (to_id 4))) (Assign (to_id 2) (AVar (to_id 3)))", "val IfcExampleReify1.env = var: FStar.DM4F.Heap.IntStoreFixed.id -> IfcRulesReify.label\nlet env var = \n if var = x then Low\n else if var = y then Low \n else if var = c then Low\n else if var = z then High\n else High", "val IfcMonitorTest.test3 = Prims.unit\nlet test3 = assert_norm (None? (interpret_com h0 p3 env Low))", "val IfcMonitorTest.test5 = Prims.unit\nlet test5 = assert_norm (None? (interpret_com h0 p5 env Low))", "val IfcMonitorTest.test4 = Prims.unit\nlet test4 = assert_norm (Some? (interpret_com h0 p4 env Low))", "val IfcMonitorTest.test1 = Prims.unit\nlet test1 = \n assert (None? (interpret_com h0 p1 env Low))", "val WhileReify.bidule = Prims.unit\nlet bidule = assert (reify (interpret_exp_st (AOp Plus (AVar (to_id 7)) (AInt 5))) (create 3) = 8)", "val Sec2.IFC.triple = Type0\nlet triple = label & label & flows", "val Sec2.IFC.lref = Type0\nlet lref = ref low", "val Sec2.IFC.href = Type0\nlet href = ref high", "val Sec2.IFC.label = Type0\nlet label = Set.set loc", "val IfcReificationRegressionTest.x2 = b: Prims.bool -> _: Prims.int -> Prims.int * Prims.int\nlet x2 (b:bool) =\n match b with\n | true -> (fun s0 ->\n let (_,s) = reify (incr ()) s0 in\n let (y,s) = reify (get ()) s in\n let (_,s) = reify (decr ()) s in\n (y,s))\n | _ -> (fun s0 -> reify (get () + 1) s0)", "val ifc_c : id -> ISNull unit\nlet ifc_c x = write x 0", "val Sec2.HIFC.lref = Type0\nlet lref = ref low", "val Sec2.IFC.flow = Type0\nlet flow = label & label", "val HaclExample2.twenty = Type0\nlet twenty = normalize (nat_t_of_nat 20)", "val IfcExample.env = var: Prims.nat -> Prims.GTot IfcRules.label\nlet env (var: nat) = \n if var = addr_of x then Low\n else if var = addr_of y then Low \n else if var = addr_of c then Low\n else if var = addr_of z then High\n else High", "val IfcReificationRegressionTest.x3 = b: Prims.bool -> s0: Prims.int -> Prims.int * Prims.int\nlet x3 (b:bool) (s0:int) =\n match b with\n | true ->\n let (_,s) = reify (incr ()) s0 in\n let (y,s) = reify (get ()) s in\n let (_,s) = reify (decr ()) s in\n (y,s)\n | _ -> reify (get () + 1) s0", "val Sec2.IFC.flows = Type0\nlet flows = list flow", "val Sec2.HIFC.triple = Type0\nlet triple = label & label & flows", "val HaclExample2.five = Type0\nlet five = normalize (nat_t_of_nat 5)", "val Interop.ireg = Type0\nlet ireg = n:pos{ n <= 4 }", "val IfcExampleReify0.ifc_c_r = h: FStar.DM4F.Heap.IntStoreFixed.heap -> x: FStar.DM4F.Heap.IntStoreFixed.id\n -> FStar.DM4F.Heap.IntStoreFixed.heap\nlet ifc_c_r h x = (* normalize_term *) (snd (reify (ifc_c x) h))", "val Benton2004.RHL.Examples2.l = Benton2004.computation\nlet l = while cond (seq (assign x asx_e) (assign i asi_e))", "val b2t_fv:R.fv\nlet b2t_fv : R.fv = R.pack_fv b2t_lid", "val b2t_fv:R.fv\nlet b2t_fv : R.fv = R.pack_fv b2t_lid", "val Sec2.HIFC.href = Type0\nlet href = ref high", "val SelectorsLList2Example.t = Type0\nlet t = LL.t a", "val for_you12:Type0\nlet for_you12 : Type0 = synth_by_tactic (fun () -> big_phi 12)", "val for_you:Type0\nlet for_you : Type0 = synth_by_tactic (fun () -> big_phi 8)", "val c2: Type0\nlet c2: Type0 = unit", "val c2: Type0\nlet c2: Type0 = unit", "val HaclExample.twenty = Type0\nlet twenty = normalize (nat_t_of_nat 20)", "val OPLSS2021.IFC.lref = Type0\nlet lref = ref low", "val Sec2.IFC.ref = l: Sec2.IFC.label -> Type0\nlet ref (l:label) = r:loc {r `Set.mem` l}", "val Sec2.HIFC.label = Type0\nlet label = Set.set loc", "val Benton2004.RHL.Examples2.r = Benton2004.computation\nlet r = seq (assign x asx_e) (while cond (assign i asi_e))", "val Sec2.HIFC.pre = Type\nlet pre = store -> Type0", "val IfcExampleReify3.p1_r = \n x: FStar.DM4F.Heap.IntStoreFixed.id ->\n y: FStar.DM4F.Heap.IntStoreFixed.id ->\n hi: FStar.DM4F.Heap.IntStoreFixed.id ->\n h: FStar.DM4F.Heap.IntStoreFixed.heap\n -> FStar.DM4F.Heap.IntStoreFixed.heap\nlet p1_r x y hi h = (snd (reify (p1 x y hi) h))", "val SimplePrintfReify.yyy = Prims.logical\nlet yyy = parse_format_pure ['%'] == None", "val IfcComposeReify.p2_r = \n lo: FStar.DM4F.Heap.IntStoreFixed.id ->\n hi: FStar.DM4F.Heap.IntStoreFixed.id ->\n h: FStar.DM4F.Heap.IntStoreFixed.heap\n -> FStar.DM4F.Heap.IntStoreFixed.heap\nlet p2_r lo hi h = (* normalize_term *) (snd (reify (p2 lo hi) h))", "val HaclExample.five = Type0\nlet five = normalize (nat_t_of_nat 5)", "val aref: Type0\nlet aref = aref'", "val Sec2.HIFC.flows = Type0\nlet flows = list flow", "val c1: Type0\nlet c1: Type0 = unit", "val c1: Type0\nlet c1: Type0 = unit", "val ReifyTestTSST.state = Type0\nlet state = nat", "val Sec2.HIFC.flow = Type0\nlet flow = label & label", "val OPLSS2021.IFC.href = Type0\nlet href = ref high", "val IfcReificationRegressionTest.x1 = b: Prims.bool -> _: Prims.int -> Prims.int * Prims.int\nlet x1 (b:bool) =\n match b with\n | true -> (fun s0 ->\n let (_,s) = reify (incr ()) s0 in\n let (y,s) = reify (get ()) s in\n let (_,s) = reify (decr ()) s in\n (y,s))\n | _ -> (fun s0 ->\n let (x,s) = reify (get ()) s0 in\n (fun s0 -> (x+1, s0)) s)", "val Sec2.IFC.unit_triple = (Sec2.IFC.label * Sec2.IFC.label) * Prims.list _\nlet unit_triple = bot, bot, []", "val OPLSS2021.IFC.flow = Type0\nlet flow = label & label", "val HaclExample2.comp_name = Type0\nlet comp_name = normalize (mk_string_t \"HaclExample2.comp\")", "val cI: Type0\nlet cI: Type0 = unit", "val cI: Type0\nlet cI: Type0 = unit", "val dyn_ifc_while : (e:exp) -> (body:com) -> (v:exp) -> (env:label_fun) -> (pc:label) -> (h:rel heap) -> \n Lemma\n (requires (low_equiv env h /\\\n begin\n let R hl hr = h in \n let c = While e body v in \n let v0l,ll = interpret_exp hl env e in\n let v0r,lr = interpret_exp hr env e in\n match v0l <> 0, v0r <> 0 with\n | true, true -> \n let ol = interpret_com hl body env (join ll pc)in\n let or = interpret_com hr body env (join lr pc)in\n if (Some? ol && Some? or) then\n begin\n ifc_type body env (join ll pc) h /\\ \n begin\n let hl' = Some?.v ol in\n let hr' = Some?.v or in\n let m0l = interpret_exp' hl v in\n let m1l = interpret_exp' hl' v in\n let m0r = interpret_exp' hr v in\n let m1r = interpret_exp' hr' v in\n if m0l > m1l && m0r > m1r then\n ifc_type c env pc (R hl' hr')\n else True\n end\n end\n else True\n | true, false ->\n let ol = interpret_com hl body env High in\n if (Some? ol) then\n begin\n let hl' = Some?.v ol in\n let m0l = interpret_exp' hl v in\n let m1l = interpret_exp' hl' v in\n if m0l > m1l then\n ifc_type c env pc (R hl' hr)\n else True\n end\n else True\n | false, true -> \n let or = interpret_com hr body env High in\n if (Some? or) then\n begin\n let hr' = Some?.v or in\n let m0r = interpret_exp' hr v in\n let m1r = interpret_exp' hr' v in\n if m0r > m1r then\n ifc_type c env pc (R hl hr')\n else True\n end\n else True\n | false, false -> True\n end))\n (ensures (ifc_type (While e body v) env pc h))\nlet dyn_ifc_while e body v env pc h = \n let R hl hr = h in \n let c = While e body v in \n let rl = interpret_com hl c env pc in \n let rr = interpret_com hr c env pc in \n let v0l,ll = interpret_exp hl env e in\n let v0r,lr = interpret_exp hr env e in\n dyn_ifc_exp e h env;\n match v0l <> 0, v0r <> 0 with\n | true, true -> \n let ol = interpret_com hl body env (join ll pc) in\n let or = interpret_com hr body env (join lr pc) in\n if (Some? ol && Some? or) then\n begin\n begin\n cut (ifc_type body env (join ll pc) h);\n let hl' = Some?.v ol in\n let hr' = Some?.v or in\n let m0l = interpret_exp' hl v in\n let m1l = interpret_exp' hl' v in\n let m0r = interpret_exp' hr v in\n let m1r = interpret_exp' hr' v in\n if m0l > m1l && m0r > m1r then\n begin\n cut (ifc_type c env pc (R hl' hr'));\n cut (rl = interpret_com hl' c env pc);\n cut (rr = interpret_com hr' c env pc)\n end\n end\n end\n | true, false ->\n cut (High? ll);\n let ol = interpret_com hl body env High in\n if (Some? ol) then\n begin\n let hl' = Some?.v ol in\n high_pc body hl env High;\n let m0l = interpret_exp' hl v in\n let m1l = interpret_exp' hl' v in\n if m0l > m1l then\n begin \n cut (ifc_type c env pc (R hl' hr));\n cut (rl = interpret_com hl' c env pc)\n end\n end\n | false, true -> \n cut (High? lr);\n let or = interpret_com hr body env High in\n if (Some? or) then\n begin\n let hr' = Some?.v or in\n high_pc body hr env High;\n let m0r = interpret_exp' hr v in\n let m1r = interpret_exp' hr' v in\n if m0r > m1r then\n begin\n cut (ifc_type c env pc (R hl hr'));\n cut (rr = interpret_com hr' c env pc)\n end\n end\n | false, false -> ()", "val SelectorsLList2Example.cell = Type0\nlet cell = LL.cell a", "val SelectorsLList3Example.t = Type0\nlet t = LL.t a", "val IfcExampleReify3.p1 = \n x: FStar.DM4F.Heap.IntStoreFixed.id ->\n y: FStar.DM4F.Heap.IntStoreFixed.id ->\n hi: FStar.DM4F.Heap.IntStoreFixed.id\n -> FStar.DM4F.IntStoreFixed.INT_STORE Prims.unit\nlet p1 x y hi =\n begin if is_x hi 0 then\n let vx = read x in\n let vy = read y in\n write x (vx + vy)\n else\n let vx = read x in\n let vy = read y in\n let vhi = read hi in\n write x (vx + vy + vhi)\n end ;\n let vx = read x in\n let vhi = read hi in\n write x (vx - vhi)", "val cC: Type0\nlet cC: Type0 = unit", "val cC: Type0\nlet cC: Type0 = unit", "val OPLSS2021.IFC.store = Type0\nlet store = m:Map.t loc int{forall l. contains m l}", "val IfcRecursiveHeapReify.op_Star = _: Prims.int -> _: Prims.int -> Prims.int\nlet op_Star = op_Multiply", "val HaclExample.comp_name = Type0\nlet comp_name = normalize (mk_string_t \"HaclExample2.comp\")", "val OPLSS2021.IFC.triple = Type0\nlet triple = label & label & flows", "val c_: Type0\nlet c_: Type0 = unit", "val c_: Type0\nlet c_: Type0 = unit", "val Interop.arity = Type0\nlet arity = n:nat { n <= max_arity }", "val Sec2.HIFC.ref = l: Sec2.HIFC.label -> Type0\nlet ref (l:label) = r:loc {r `Set.mem` l}", "val IfcReificationRegressionTest.x0 = b: Prims.bool -> _: Prims.int -> Prims.PURE (Prims.int * Prims.int)\nlet x0 (b:bool) = reify (ifc b)", "val va_While (whileCond: ocmp) (whileBody: va_code) : va_code\nlet va_While (whileCond:ocmp) (whileBody:va_code) : va_code = While whileCond whileBody", "val va_While (whileCond: ocmp) (whileBody: va_code) : va_code\nlet va_While (whileCond:ocmp) (whileBody:va_code) : va_code = While whileCond whileBody", "val c3: Type0\nlet c3: Type0 = unit" ], "closest_src": [ { "project_name": "FStar", "file_name": "IfcExampleReify1.fst", "name": "IfcExampleReify1.c1_2" }, { "project_name": "FStar", "file_name": "IfcExampleReify1.fst", "name": "IfcExampleReify1.c1_3" }, { "project_name": "FStar", "file_name": "IfcExampleReify1.fst", "name": "IfcExampleReify1.c1_4" }, { "project_name": "FStar", "file_name": "IfcExampleReify1.fst", "name": "IfcExampleReify1.c1_1" }, { "project_name": "FStar", "file_name": "IfcExampleReify1.fst", "name": "IfcExampleReify1.c1_5" }, { "project_name": "FStar", "file_name": "IfcExampleReify1.fst", "name": "IfcExampleReify1.c1" }, { "project_name": "FStar", "file_name": "IfcExampleReify1.fst", "name": "IfcExampleReify1.c1_6" }, { "project_name": "FStar", "file_name": "IfcExampleReify1.fst", "name": "IfcExampleReify1.c1_0" }, { "project_name": "FStar", "file_name": "IfcExample.fst", "name": "IfcExample.c1_1" }, { "project_name": "FStar", "file_name": "IfcExample.fst", "name": "IfcExample.c1_5" }, { "project_name": "FStar", "file_name": "IfcExample.fst", "name": "IfcExample.c1_3" }, { "project_name": "FStar", "file_name": "IfcExample.fst", "name": "IfcExample.c1_4" }, { "project_name": "FStar", "file_name": "IfcExample.fst", "name": "IfcExample.c1_6" }, { "project_name": "FStar", "file_name": "IfcExample.fst", "name": "IfcExample.c1_2" }, { "project_name": "FStar", "file_name": "IfcExample.fst", "name": "IfcExample.c1" }, { "project_name": "FStar", "file_name": "IfcExample.fst", "name": "IfcExample.c1_0" }, { "project_name": "FStar", "file_name": "IfcMonitorTest.fst", "name": "IfcMonitorTest.p2" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.bidule2" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.bidule1" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.bidule3" }, { "project_name": "FStar", "file_name": "IfcMonitorTest.fst", "name": "IfcMonitorTest.p1" }, { "project_name": "FStar", "file_name": "WhileReify.fst", "name": "WhileReify.bidule2" }, { "project_name": "FStar", "file_name": "IfcMonitorTest.fst", "name": "IfcMonitorTest.test2" }, { "project_name": "FStar", "file_name": "IfcMonitorTest.fst", "name": "IfcMonitorTest.p4" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.x" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.bidule0" }, { "project_name": "FStar", "file_name": "IfcMonitorTest.fst", "name": "IfcMonitorTest.p3" }, { "project_name": "FStar", "file_name": "IfcMonitorTest.fst", "name": "IfcMonitorTest.p5" }, { "project_name": "FStar", "file_name": "IfcExampleReify1.fst", "name": "IfcExampleReify1.env" }, { "project_name": "FStar", "file_name": "IfcMonitorTest.fst", "name": "IfcMonitorTest.test3" }, { "project_name": "FStar", "file_name": "IfcMonitorTest.fst", "name": "IfcMonitorTest.test5" }, { "project_name": "FStar", "file_name": "IfcMonitorTest.fst", "name": "IfcMonitorTest.test4" }, { "project_name": "FStar", "file_name": "IfcMonitorTest.fst", "name": "IfcMonitorTest.test1" }, { "project_name": "FStar", "file_name": "WhileReify.fst", "name": "WhileReify.bidule" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.triple" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.lref" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.href" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.label" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.x2" }, { "project_name": "FStar", "file_name": "IfcExampleReify0.fst", "name": "IfcExampleReify0.ifc_c" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.lref" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.flow" }, { "project_name": "steel", "file_name": "HaclExample2.fst", "name": "HaclExample2.twenty" }, { "project_name": "FStar", "file_name": "IfcExample.fst", "name": "IfcExample.env" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.x3" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.flows" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.triple" }, { "project_name": "steel", "file_name": "HaclExample2.fst", "name": "HaclExample2.five" }, { "project_name": "FStar", "file_name": "Interop.fst", "name": "Interop.ireg" }, { "project_name": "FStar", "file_name": "IfcExampleReify0.fst", "name": "IfcExampleReify0.ifc_c_r" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.Examples2.fst", "name": "Benton2004.RHL.Examples2.l" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.b2t_fv" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.b2t_fv" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.href" }, { "project_name": "steel", "file_name": "SelectorsLList2Example.fst", "name": "SelectorsLList2Example.t" }, { "project_name": "FStar", "file_name": "Bane.fst", "name": "Bane.for_you12" }, { "project_name": "FStar", "file_name": "Bane.Lib.fst", "name": "Bane.Lib.for_you" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.c2" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.c2" }, { "project_name": "steel", "file_name": "HaclExample.fst", "name": "HaclExample.twenty" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.lref" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.ref" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.label" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.Examples2.fst", "name": "Benton2004.RHL.Examples2.r" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.pre" }, { "project_name": "FStar", "file_name": "IfcExampleReify3.fst", "name": "IfcExampleReify3.p1_r" }, { "project_name": "FStar", "file_name": "SimplePrintfReify.fst", "name": "SimplePrintfReify.yyy" }, { "project_name": "FStar", "file_name": "IfcComposeReify.fst", "name": "IfcComposeReify.p2_r" }, { "project_name": "steel", "file_name": "HaclExample.fst", "name": "HaclExample.five" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.aref" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.flows" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.c1" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.c1" }, { "project_name": "FStar", "file_name": "ReifyTestTSST.fsti", "name": "ReifyTestTSST.state" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.flow" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.href" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.x1" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.unit_triple" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.flow" }, { "project_name": "steel", "file_name": "HaclExample2.fst", "name": "HaclExample2.comp_name" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cI" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cI" }, { "project_name": "FStar", "file_name": "IfcMonitor.fst", "name": "IfcMonitor.dyn_ifc_while" }, { "project_name": "steel", "file_name": "SelectorsLList2Example.fst", "name": "SelectorsLList2Example.cell" }, { "project_name": "steel", "file_name": "SelectorsLList3Example.fst", "name": "SelectorsLList3Example.t" }, { "project_name": "FStar", "file_name": "IfcExampleReify3.fst", "name": "IfcExampleReify3.p1" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cC" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cC" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.store" }, { "project_name": "FStar", "file_name": "IfcRecursiveHeapReify.fst", "name": "IfcRecursiveHeapReify.op_Star" }, { "project_name": "steel", "file_name": "HaclExample.fst", "name": "HaclExample.comp_name" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.triple" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.c_" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.c_" }, { "project_name": "FStar", "file_name": "Interop.fst", "name": "Interop.arity" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.ref" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.x0" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.va_While" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_While" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.c3" } ], "selected_premises": [ "IfcRulesReify.join", "Rel.r_eq", "Rel.lift", "IfcExampleReify2.hi", "IfcRulesReify.meet", "IfcTypechecker.tc_com", "WhileReify.interpret_exp_st", "WhileReify.bidule2", "FStar.DM4F.Exceptions.raise_", "IfcTypechecker.tc_exp", "Rel.diag", "IfcExampleReify2.lo", "FStar.Pervasives.Native.snd", "IfcRulesReify.seq_com", "FStar.Pervasives.Native.fst", "WhileReify.interpret_exp'", "FStar.DM4F.Exceptions.raise0", "IfcExampleReify2.c", "IfcRulesReify.cond_ni_com'", "Rel.same", "WhileReify.bidule", "FStar.DM4F.IntStoreFixed.post", "IfcRulesReify.assign_com", "FStar.Heap.trivial_preorder", "FStar.DM4F.Exceptions.raise__", "IfcTypechecker.tc_com_hybrid", "Rel.split", "WhileReify.interpret_com_st", "IfcRulesReify.while_ni_com'_low_equiv_high", "IfcRulesReify.while_ni_com'", "FStar.ST.op_Bang", "IfcExampleReify2.env", "IfcRulesReify.cond_com", "IfcRulesReify.ni_exp", "IfcRulesReify.while_ni_com'_low_equiv_low", "IfcRulesReify.seq_com'", "FStar.Pervasives.reveal_opaque", "IfcRulesReify.cond_inv_com'", "Rel.diagb", "IfcRulesReify.ni_com'", "FStar.DM4F.IntStoreFixed.op_Colon_equals", "FStar.Pervasives.dfst", "IfcRulesReify.inv_com'", "IfcExampleReify2.c_1", "IfcRulesReify.seq_inv_com'", "FStar.DM4F.IntStoreFixed.pre", "IfcRulesReify.while_com", "FStar.DM4F.Exceptions.div_intrinsic", "WhileReify.interpret_binop", "FStar.Pervasives.dsnd", "FStar.ST.alloc", "Rel.lift2", "WhileReify.decr_while", "Rel.lift4", "Rel.lift5", "FStar.DM4F.Exceptions.bind_ex", "Rel.lift3", "FStar.DM4F.Exceptions.return_ex", "IfcRulesReify.ni_com", "FStar.DM4F.IntStoreFixed.repr", "FStar.DM4F.Heap.IntStoreFixed.sel", "IfcRulesReify.op_Less", "IfcRulesReify.assign_inv_com0", "WhileReify.interpret_exp", "FStar.DM4F.Exceptions.ex", "FStar.DM4F.Heap.IntStoreFixed.store_size", "FStar.DM4F.Exceptions.div_extrinsic", "WhileReify.interpret_com", "FStar.DM4F.IntStoreFixed.iget", "FStar.DM4F.IntStoreFixedReader.get", "IfcRulesReify.op_Less_Equals", "FStar.DM4F.IntStoreFixedReader.bind_isr", "FStar.DM4F.IntStoreFixed.bind_is", "FStar.All.op_Bar_Greater", "IfcRulesReify.assign_inv_com'", "FStar.All.op_Less_Bar", "FStar.List.map", "FStar.List.mapT", "FStar.Pervasives.id", "FStar.List.for_all", "Prims.op_Hat", "FStar.List.iter", "FStar.Preorder.preorder_rel", "FStar.Heap.trivial_rel", "FStar.Pervasives.coerce_eq", "FStar.List.fold_left", "FStar.DM4F.IntStoreExcFixed.bind_is", "FStar.DM4F.IntStoreFixed.return_is", "FStar.Set.subset", "Prims.subtype_of", "FStar.Monotonic.Heap.mref", "FStar.DM4F.IntStoreFixed.lift_int_store_reader_int_store_wp", "FStar.Pervasives.st_bind_wp", "Prims.min", "FStar.DM4F.IntStoreFixed.wp", "FStar.DM4F.IntStoreExcFixed.iget", "FStar.Set.add", "FStar.DM4F.IntStoreExcFixed.raise_impl", "FStar.Pervasives.pure_close_wp", "FStar.Monotonic.Heap.set" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule IfcExampleReify2\n\nopen WhileReify\nopen IfcRulesReify\nopen IfcTypechecker\nopen FStar.DM4F.Heap.IntStoreFixed\nopen FStar.DM4F.Exceptions\n\nlet hi : id = to_id 0\nlet lo : id = to_id 1\nlet c : id = to_id 2\n\nlet env var =\n if var = hi then High\n else if var = lo then Low\n else if var = c then Low\n else High\n\n(*\n While c > 0{\n hi := lo + 1\n lo := hi + 1\n c := c - 1\n }\n*)\n\nlet c_1 body = While (AVar c) body (AVar c)", "sketch": [ "Step 1: The definition `c_2` represents a while loop command in the WhileReify language. This command will execute a body of statements repeatedly as long as the condition `c > 0` holds true.\nStep 2: The body of the loop consists of three assignments: `hi := lo + 1`, `lo := hi + 1`, and `c := c - 1`. These assignments are executed in sequence within the loop.", "Step 1: The definition `c_2` represents a command in the While language that executes a loop. The loop continues as long as the variable `c` is greater than 0.\nStep 2: Inside the loop body, the following commands are executed sequentially:\n- The variable `hi` is assigned the value of `lo + 1`.\n- The variable `lo` is assigned the value of `hi + 1`.\n- The variable `c` is decremented by 1.", "Step 1: The definition `c_2` represents a while loop command in the WhileReify language. This command will execute a loop as long as the condition `c > 0` holds true.\nStep 2: The body of the loop consists of three assignments:\n - `hi` is assigned the value of `lo + 1`\n - `lo` is assigned the value of `hi + 1`\n - `c` is decremented by 1", "Step 1: The definition `c_2` represents a while loop that executes as long as the variable `c` is greater than 0. Within the loop body, the variable `hi` is assigned the value of `lo + 1`, then `lo` is assigned the value of `hi + 1`, and finally, `c` is decremented by 1.\nStep 2: To implement this, we create a sequence of assignments within the loop body. The loop condition is `AVar c`, and the loop body consists of the assignments to `hi`, `lo`, and `c`.", "Step 1: The definition `c_2` represents a while loop in the WhileReify language. The loop continues as long as the variable `c` is greater than 0.\nStep 2: Inside the loop body, the following operations are performed sequentially:\n - The variable `hi` is assigned the value of `lo + 1`.\n - The variable `lo` is assigned the value of `hi + 1`.\n - The variable `c` is decremented by 1.", "Step 1: The definition `c_2` represents a while loop command in the WhileReify language. The loop continues executing as long as the variable `c` is greater than 0.\nStep 2: The body of the loop consists of three commands executed sequentially:\n 1. Assign `hi` the value of `lo + 1`.\n 2. Assign `lo` the value of `hi + 1`.\n 3. Decrement the value of `c` by 1.\nThe loop condition is `c > 0`, and the loop body is a sequence of the three commands mentioned above.", "Step 1: The definition `c_2` represents a while loop command in the WhileReify language.\nStep 2: The while loop continues as long as the variable `c` is greater than 0. Inside the loop, the variable `hi` is assigned the value of `lo + 1`, then `lo` is assigned the value of `hi + 1`, and finally, `c` is decremented by 1.", "Step 1: The definition `c_2` represents a command in the While language that executes a loop while the variable `c` is greater than 0.\nStep 2: Inside the loop body, the commands are:\n - Assign `hi` the value of `lo + 1`\n - Assign `lo` the value of `hi + 1`\n - Decrement `c` by 1\nThe loop continues until `c` is no longer greater than 0.", "Step 1: The definition `c_2` represents a command in the While language that will be executed in a loop as long as the variable `c` is greater than 0.\nStep 2: The body of the loop consists of three assignments: `hi` is assigned the value of `lo + 1`, `lo` is assigned the value of `hi + 1`, and `c` is decremented by 1. This sequence of commands is repeated until `c` is no longer greater than 0.", "Step 1: The definition `c_2` represents a command in the While language that executes a loop. The loop continues as long as the variable `c` is greater than 0.\nStep 2: Within the loop body, the following commands are executed sequentially:\n - The variable `hi` is assigned the value of `lo + 1`.\n - The variable `lo` is assigned the value of `hi + 1`.\n - The variable `c` is decremented by 1." ], "generated_solution": [ "let c_2 = c_1 (Seq (Assign hi (Add (AVar lo) (AConst 1)))\n (Seq (Assign lo (Add (AVar hi) (AConst 1)))\n (Assign c (Sub (AVar c) (AConst 1)))))", "let c_2 : WhileReify.com =\n c_1 (Seq (Assign hi (APlus (AVar lo) (AConst 1)))\n (Seq (Assign lo (APlus (AVar hi) (AConst 1)))\n (Assign c (AMinus (AVar c) (AConst 1)))))", "let c_2 : WhileReify.com =\n c_1 (Seq (Assign hi (Plus (AVar lo) (AConst 1)))\n (Seq (Assign lo (Plus (AVar hi) (AConst 1)))\n (Assign c (Minus (AVar c) (AConst 1)))))", "let c_2 : WhileReify.com =\n c_1 (Seq (Assign hi (APlus (AVar lo) (AConst 1)))\n (Seq (Assign lo (APlus (AVar hi) (AConst 1)))\n (Assign c (AMinus (AVar c) (AConst 1)))))", "let c_2 : WhileReify.com =\n c_1 (Seq (Assign hi (Plus (AVar lo) (AConst 1)))\n (Seq (Assign lo (Plus (AVar hi) (AConst 1)))\n (Assign c (Minus (AVar c) (AConst 1)))))", "let c_2 : WhileReify.com =\n c_1 (Seq (Assign hi (Plus (AVar lo) (AConst 1)))\n (Seq (Assign lo (Plus (AVar hi) (AConst 1)))\n (Assign c (Minus (AVar c) (AConst 1)))))", "let c_2 : WhileReify.com =\n c_1 (Seq (Assign hi (APlus (AVar lo) (AConst 1)))\n (Seq (Assign lo (APlus (AVar hi) (AConst 1)))\n (Assign c (AMinus (AVar c) (AConst 1)))))", "let c_2 =\n c_1 (Seq (Assign hi (APlus (AVar lo) (AConst 1)))\n (Seq (Assign lo (APlus (AVar hi) (AConst 1)))\n (Assign c (AMinus (AVar c) (AConst 1)))))", "let c_2 =\n c_1 (Seq (Assign hi (Plus (AVar lo) (AConst 1)))\n (Seq (Assign lo (Plus (AVar hi) (AConst 1)))\n (Assign c (Minus (AVar c) (AConst 1)))))", "let c_2 : WhileReify.com =\n c_1 (Seq (Assign hi (APlus (AVar lo) (AConst 1)))\n (Seq (Assign lo (APlus (AVar hi) (AConst 1)))\n (Assign c (AMinus (AVar c) (AConst 1)))))" ] }, { "file_name": "Vale.AES.PPC64LE.GCMencrypt.fsti", "name": "Vale.AES.PPC64LE.GCMencrypt.va_wp_Load_one_lsb", "opens_and_abbrevs": [ { "open": "Vale.AES.OptPublic_BE" }, { "open": "Vale.Lib.Meta" }, { "open": "Vale.AES.PPC64LE.GHash" }, { "open": "Vale.Math.Poly2.Bits_s" }, { "open": "Vale.AES.PPC64LE.GF128_Mul" }, { "open": "Vale.PPC64LE.QuickCodes" }, { "open": "Vale.PPC64LE.QuickCode" }, { "open": "Vale.PPC64LE.InsStack" }, { "open": "Vale.PPC64LE.InsVector" }, { "open": "Vale.PPC64LE.InsMem" }, { "open": "Vale.PPC64LE.InsBasic" }, { "open": "Vale.PPC64LE.Decls" }, { "open": "Vale.PPC64LE.State" }, { "open": "Vale.PPC64LE.Stack_i" }, { "open": "Vale.PPC64LE.Memory" }, { "open": "Vale.PPC64LE.Machine_s" }, { "open": "Vale.AES.PPC64LE.GCTR" }, { "open": "Vale.AES.GCM_helpers_BE" }, { "open": "Vale.Poly1305.Math" }, { "open": "Vale.AES.GF128" }, { "open": "Vale.AES.GF128_s" }, { "open": "Vale.AES.PPC64LE.AES" }, { "open": "Vale.AES.GCM_BE_s" }, { "open": "Vale.AES.GHash_BE" }, { "open": "Vale.AES.GHash_BE_s" }, { "open": "Vale.AES.GCM_BE" }, { "open": "Vale.AES.GCTR_BE" }, { "open": "Vale.AES.GCTR_BE_s" }, { "open": "Vale.AES.AES_BE_s" }, { "open": "Vale.Arch.HeapImpl" }, { "open": "Vale.Arch.Types" }, { "open": "Vale.Def.Types_s" }, { "open": "Vale.Def.Words.Seq_s" }, { "open": "Vale.Def.Words_s" }, { "open": "FStar.Seq" }, { "open": "Vale.Def.Opaque_s" }, { "open": "Vale.Def.Prop_s" }, { "open": "Vale.AES.PPC64LE" }, { "open": "Vale.AES.PPC64LE" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 1, "initial_ifuel": 0, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": true, "smtencoding_nl_arith_repr": "wrapped", "smtencoding_l_arith_repr": "native", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val va_wp_Load_one_lsb\n (dst: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0", "source_definition": "let va_wp_Load_one_lsb (dst:va_operand_vec_opr) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_get_ok va_s0 /\\ dst =!= 4 /\\ (forall\n (va_x_dst:va_value_vec_opr) (va_x_v4:quad32) . let va_sM = va_upd_vec 4 va_x_v4\n (va_upd_operand_vec_opr dst va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 ==> va_k va_sM (())))", "source_range": { "start_line": 64, "start_col": 0, "end_line": 69, "end_col": 81 }, "interleaved": false, "definition": "fun dst va_s0 va_k ->\n Vale.PPC64LE.Decls.va_is_dst_vec_opr dst va_s0 /\\ Vale.PPC64LE.Decls.va_get_ok va_s0 /\\\n ~(dst == 4) /\\\n (forall (va_x_dst: Vale.PPC64LE.Decls.va_value_vec_opr) (va_x_v4: Vale.PPC64LE.Memory.quad32).\n let va_sM =\n Vale.PPC64LE.Decls.va_upd_vec 4\n va_x_v4\n (Vale.PPC64LE.Decls.va_upd_operand_vec_opr dst va_x_dst va_s0)\n in\n Vale.PPC64LE.Decls.va_get_ok va_sM /\\\n Vale.PPC64LE.Decls.va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour 1 0 0 0 ==>\n va_k va_sM ())\n <:\n Type0", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Vale.PPC64LE.Decls.va_operand_vec_opr", "Vale.PPC64LE.Decls.va_state", "Prims.unit", "Prims.l_and", "Vale.PPC64LE.Decls.va_is_dst_vec_opr", "Prims.b2t", "Vale.PPC64LE.Decls.va_get_ok", "Prims.l_not", "Prims.eq2", "Prims.int", "Prims.l_Forall", "Vale.PPC64LE.Decls.va_value_vec_opr", "Vale.PPC64LE.Memory.quad32", "Prims.l_imp", "Vale.Def.Words_s.four", "Vale.Def.Types_s.nat32", "Vale.PPC64LE.Decls.va_eval_vec_opr", "Vale.Def.Words_s.Mkfour", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.Decls.va_upd_vec", "Vale.PPC64LE.Decls.va_upd_operand_vec_opr" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "\n dst: Vale.PPC64LE.Decls.va_operand_vec_opr ->\n va_s0: Vale.PPC64LE.Decls.va_state ->\n va_k: (_: Vale.PPC64LE.Decls.va_state -> _: Prims.unit -> Type0)\n -> Type0", "prompt": "let va_wp_Load_one_lsb\n (dst: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0 =\n ", "expected_response": "(va_is_dst_vec_opr dst va_s0 /\\ va_get_ok va_s0 /\\ dst =!= 4 /\\\n (forall (va_x_dst: va_value_vec_opr) (va_x_v4: quad32).\n let va_sM = va_upd_vec 4 va_x_v4 (va_upd_operand_vec_opr dst va_x_dst va_s0) in\n va_get_ok va_sM /\\\n va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 ==>\n va_k va_sM (())))", "source": { "project_name": "hacl-star", "file_name": "obj/Vale.AES.PPC64LE.GCMencrypt.fsti", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Vale.AES.PPC64LE.GCMencrypt.fsti", "checked_file": "dataset/Vale.AES.PPC64LE.GCMencrypt.fsti.checked", "interface_file": false, "dependencies": [ "dataset/Vale.PPC64LE.State.fsti.checked", "dataset/Vale.PPC64LE.Stack_i.fsti.checked", "dataset/Vale.PPC64LE.QuickCodes.fsti.checked", "dataset/Vale.PPC64LE.QuickCode.fst.checked", "dataset/Vale.PPC64LE.Memory.fsti.checked", "dataset/Vale.PPC64LE.Machine_s.fst.checked", "dataset/Vale.PPC64LE.InsVector.fsti.checked", "dataset/Vale.PPC64LE.InsStack.fsti.checked", "dataset/Vale.PPC64LE.InsMem.fsti.checked", "dataset/Vale.PPC64LE.InsBasic.fsti.checked", "dataset/Vale.PPC64LE.Decls.fsti.checked", "dataset/Vale.Poly1305.Math.fsti.checked", "dataset/Vale.Math.Poly2.Bits_s.fsti.checked", "dataset/Vale.Lib.Meta.fsti.checked", "dataset/Vale.Def.Words_s.fsti.checked", "dataset/Vale.Def.Words.Seq_s.fsti.checked", "dataset/Vale.Def.Words.Four_s.fsti.checked", "dataset/Vale.Def.Types_s.fst.checked", "dataset/Vale.Def.Prop_s.fst.checked", "dataset/Vale.Def.Opaque_s.fsti.checked", "dataset/Vale.Arch.Types.fsti.checked", "dataset/Vale.Arch.HeapImpl.fsti.checked", "dataset/Vale.AES.PPC64LE.GHash.fsti.checked", "dataset/Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "dataset/Vale.AES.PPC64LE.GCTR.fsti.checked", "dataset/Vale.AES.PPC64LE.AES.fsti.checked", "dataset/Vale.AES.OptPublic_BE.fsti.checked", "dataset/Vale.AES.GHash_BE_s.fst.checked", "dataset/Vale.AES.GHash_BE.fsti.checked", "dataset/Vale.AES.GF128_s.fsti.checked", "dataset/Vale.AES.GF128.fsti.checked", "dataset/Vale.AES.GCTR_BE_s.fst.checked", "dataset/Vale.AES.GCTR_BE.fsti.checked", "dataset/Vale.AES.GCM_helpers_BE.fsti.checked", "dataset/Vale.AES.GCM_BE_s.fst.checked", "dataset/Vale.AES.GCM_BE.fsti.checked", "dataset/Vale.AES.AES_common_s.fst.checked", "dataset/Vale.AES.AES_BE_s.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Seq.Base.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "let aes_reqs\n (alg:algorithm) (key:seq nat32) (round_keys:seq quad32) (keys_b:buffer128)\n (key_ptr:int) (heap0:vale_heap) (layout:vale_heap_layout) : prop0\n =\n (alg = AES_128 \\/ alg = AES_256) /\\\n is_aes_key_word alg key /\\\n length(round_keys) == nr(alg) + 1 /\\\n round_keys == key_to_round_keys_word alg key /\\\n validSrcAddrs128 heap0 key_ptr keys_b (nr alg + 1) layout Secret /\\\n reverse_bytes_quad32_seq (s128 heap0 keys_b) == round_keys", "val va_code_Load_one_lsb : dst:va_operand_vec_opr -> Tot va_code", "val va_codegen_success_Load_one_lsb : dst:va_operand_vec_opr -> Tot va_pbool", "val va_lemma_Load_one_lsb : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Load_one_lsb dst) va_s0 /\\ va_is_dst_vec_opr dst va_s0\n /\\ va_get_ok va_s0 /\\ dst =!= 4))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 /\\\n va_state_eq va_sM (va_update_vec 4 va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst\n va_sM va_s0)))))" ], "closest": [ "val va_wp_Load_one_lsb (dst: va_operand_xmm) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Load_one_lsb (dst:va_operand_xmm) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) :\n Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\ (forall (va_x_dst:va_value_xmm)\n (va_x_r11:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64\n rR11 va_x_r11 (va_upd_operand_xmm dst va_x_dst va_s0)) in va_get_ok va_sM /\\ va_eval_xmm va_sM\n dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 ==> va_k va_sM (())))", "val va_wp_Load_two_lsb (dst: va_operand_xmm) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Load_two_lsb (dst:va_operand_xmm) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) :\n Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\ (forall (va_x_dst:va_value_xmm)\n (va_x_r11:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64\n rR11 va_x_r11 (va_upd_operand_xmm dst va_x_dst va_s0)) in va_get_ok va_sM /\\ va_eval_xmm va_sM\n dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 2 0 0 0 ==> va_k va_sM (())))", "val va_wp_Load_0xc2_msb (dst: va_operand_xmm) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Load_0xc2_msb (dst:va_operand_xmm) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) :\n Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\ (forall (va_x_dst:va_value_xmm)\n (va_x_r11:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64\n rR11 va_x_r11 (va_upd_operand_xmm dst va_x_dst va_s0)) in va_get_ok va_sM /\\ va_eval_xmm va_sM\n dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 3254779904 ==> va_k va_sM (())))", "val va_wp_Load_one_msb (va_s0: va_state) (va_k: (va_state -> unit -> Type0)) : Type0\nlet va_wp_Load_one_msb (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ sse_enabled /\\ (forall (va_x_r11:nat64) (va_x_xmm2:quad32)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_xmm 2 va_x_xmm2\n (va_upd_reg64 rR11 va_x_r11 va_s0)) in va_get_ok va_sM /\\ va_get_xmm 2 va_sM ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 16777216 ==> va_k va_sM (())))", "val va_wpProof_Load_one_lsb : dst:va_operand_vec_opr -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Load_one_lsb dst va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Load_one_lsb dst) ([va_Mod_vec 4;\n va_mod_vec_opr dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Load_one_lsb dst va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Load_one_lsb (va_code_Load_one_lsb dst) va_s0 dst in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_vec 4 va_sM (va_update_ok va_sM (va_update_operand_vec_opr\n dst va_sM va_s0))));\n va_lemma_norm_mods ([va_Mod_vec 4; va_mod_vec_opr dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wp_load_one_msb (va_s0: va_state) (va_k: (va_state -> unit -> Type0)) : Type0\nlet va_wp_load_one_msb (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ sse_enabled /\\ (forall (va_x_r11:nat64) (va_x_xmm2:quad32)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_xmm 2 va_x_xmm2\n (va_upd_reg64 rR11 va_x_r11 va_s0)) in va_get_ok va_sM /\\ va_get_xmm 2 va_sM ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 16777216 ==> va_k va_sM (())))", "val va_wp_Vand\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vand (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst ==\n Vale.Def.Words.Four_s.four_map2 #nat32 #Vale.Def.Types_s.nat32 (fun (di:nat32) (si:nat32) ->\n Vale.Arch.Types.iand32 di si) (va_eval_vec_opr va_s0 src1) (va_eval_vec_opr va_s0 src2) ==>\n va_k va_sM (())))", "val va_wp_Vslw\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vslw (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 (Vale.Arch.Types.ishl32 (Vale.Def.Words_s.__proj__Mkfour__item__lo0\n (va_eval_vec_opr va_s0 src1)) (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr\n va_s0 src2) `op_Modulus` 32)) (Vale.Arch.Types.ishl32\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src2) `op_Modulus` 32))\n (Vale.Arch.Types.ishl32 (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0\n src1)) (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src2) `op_Modulus`\n 32)) (Vale.Arch.Types.ishl32 (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0\n src1)) (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src2) `op_Modulus`\n 32)) ==> va_k va_sM (())))", "val va_wp_Load_stack128\n (dst: va_operand_vec_opr)\n (offset: int)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Load_stack128 (dst:va_operand_vec_opr) (offset:int) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_get_ok va_s0 /\\ Vale.PPC64LE.Machine_s.valid_maddr_offset128\n offset /\\ va_get_reg 1 va_s0 + offset + 16 <= Vale.PPC64LE.Stack_i.init_r1 (va_get_stack va_s0)\n /\\ Vale.PPC64LE.Stack_i.valid_src_stack128 (va_get_reg 1 va_s0 + offset) (va_get_stack va_s0)\n /\\ Vale.PPC64LE.Stack_i.valid_taint_stack128 (va_get_reg 1 va_s0 + offset) Secret\n (va_get_stackTaint va_s0) /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM =\n va_upd_operand_vec_opr dst va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst ==\n Vale.PPC64LE.Stack_i.load_stack128 (va_get_reg 1 va_s0 + offset) (va_get_stack va_s0) ==> va_k\n va_sM (())))", "val va_wp_Vsl\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vsl (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (let sh = FStar.Seq.Base.index #nat8 (Vale.Def.Types_s.nat32_to_be_bytes\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src2))) 3 `op_Modulus` 8 in\n let chk = fun (v:nat32) (sh:nat8) -> let bytes = Vale.Def.Types_s.nat32_to_be_bytes v in l_and\n (l_and (l_and (sh = FStar.Seq.Base.index #nat8 bytes 3 `op_Modulus` 8) (sh =\n FStar.Seq.Base.index #nat8 bytes 2 `op_Modulus` 8)) (sh = FStar.Seq.Base.index #nat8 bytes 1\n `op_Modulus` 8)) (sh = FStar.Seq.Base.index #nat8 bytes 0 `op_Modulus` 8) in l_and (l_and\n (l_and (chk (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src2)) sh) (chk\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src2)) sh)) (chk\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src2)) sh)) (chk\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src2)) sh)) /\\ (forall\n (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ (let sh = FStar.Seq.Base.index #nat8 (Vale.Def.Types_s.nat32_to_be_bytes\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src2))) 3 `op_Modulus` 8 in\n let l = Vale.Def.Words.Four_s.four_map #nat32 #Vale.Def.Words_s.nat32 (fun (i:nat32) ->\n Vale.Arch.Types.ishl32 i sh) (va_eval_vec_opr va_s0 src1) in let r =\n Vale.Def.Words.Four_s.four_map #nat32 #Vale.Def.Words_s.nat32 (fun (i:nat32) ->\n Vale.Arch.Types.ishr32 i (32 - sh)) (va_eval_vec_opr va_s0 src1) in va_eval_vec_opr va_sM dst\n == Vale.Def.Types_s.quad32_xor l (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 r) (Vale.Def.Words_s.__proj__Mkfour__item__lo1 r)\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 r))) ==> va_k va_sM (())))", "val va_wpProof_Load_one_lsb : dst:va_operand_xmm -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Load_one_lsb dst va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Load_one_lsb dst) ([va_Mod_flags;\n va_Mod_reg64 rR11; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Load_one_lsb dst va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Load_one_lsb (va_code_Load_one_lsb dst) va_s0 dst in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rR11 va_sM (va_update_ok va_sM\n (va_update_operand_xmm dst va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rR11; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wp_Mfvsrd\n (dst: va_operand_reg_opr)\n (src: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Mfvsrd (dst:va_operand_reg_opr) (src:va_operand_vec_opr) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_vec_opr src va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == Vale.Arch.Types.hi64 (va_eval_vec_opr va_sM\n src) ==> va_k va_sM (())))", "val va_wp_Mfvsrld\n (dst: va_operand_reg_opr)\n (src: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Mfvsrld (dst:va_operand_reg_opr) (src:va_operand_vec_opr) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_vec_opr src va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == Vale.Arch.Types.lo64 (va_eval_vec_opr va_sM\n src) ==> va_k va_sM (())))", "val va_wp_And\n (dst src1 src2: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_And (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:va_operand_reg_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == Vale.Arch.Types.iand64\n (va_eval_reg_opr va_s0 src1) (va_eval_reg_opr va_s0 src2) ==> va_k va_sM (())))", "val va_wp_Load_stack64\n (dst: va_operand_reg_opr)\n (offset: int)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Load_stack64 (dst:va_operand_reg_opr) (offset:int) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_get_ok va_s0 /\\ Vale.PPC64LE.Machine_s.valid_maddr_offset64\n offset /\\ va_get_reg 1 va_s0 + offset + 8 <= Vale.PPC64LE.Stack_i.init_r1 (va_get_stack va_s0)\n /\\ Vale.PPC64LE.Stack_i.valid_src_stack64 (va_get_reg 1 va_s0 + offset) (va_get_stack va_s0) /\\\n Vale.PPC64LE.Stack_i.valid_taint_stack64 (va_get_reg 1 va_s0 + offset) Secret\n (va_get_stackTaint va_s0) /\\ (forall (va_x_dst:va_value_reg_opr) . let va_sM =\n va_upd_operand_reg_opr dst va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst ==\n Vale.PPC64LE.Stack_i.load_stack64 (va_get_reg 1 va_s0 + offset) (va_get_stack va_s0) ==> va_k\n va_sM (())))", "val va_wp_Vsldoi\n (dst src1 src2: va_operand_vec_opr)\n (count: quad32bytes)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vsldoi (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (count:quad32bytes) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (count == 4 \\/ count == 8 \\/ count == 12) /\\ (forall\n (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ (count == 4 ==> va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0\n src2)) (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src1))) /\\ (count == 8 ==>\n va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src1))) /\\ (count == 12 ==>\n va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src1))) ==> va_k va_sM (())))", "val va_wp_And64\n (dst: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_And64 (dst:va_operand_dst_opr64) (src:va_operand_opr64) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_dst_opr64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl\n (va_upd_operand_dst_opr64 dst va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst\n == Vale.Arch.Types.iand64 (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) ==> va_k\n va_sM (())))", "val va_wp_Vpmsumd\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vpmsumd (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst ==\n Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.mul\n (Vale.Math.Poly2.Bits_s.of_double32 (Vale.Arch.Types.quad32_double_lo (va_eval_vec_opr va_s0\n src1))) (Vale.Math.Poly2.Bits_s.of_double32 (Vale.Arch.Types.quad32_double_lo (va_eval_vec_opr\n va_s0 src2)))) (Vale.Math.Poly2_s.mul (Vale.Math.Poly2.Bits_s.of_double32\n (Vale.Arch.Types.quad32_double_hi (va_eval_vec_opr va_s0 src1)))\n (Vale.Math.Poly2.Bits_s.of_double32 (Vale.Arch.Types.quad32_double_hi (va_eval_vec_opr va_s0\n src2))))) ==> va_k va_sM (())))", "val va_wp_Vsrw\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vsrw (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 (Vale.Arch.Types.ishr32 (Vale.Def.Words_s.__proj__Mkfour__item__lo0\n (va_eval_vec_opr va_s0 src1)) (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr\n va_s0 src2) `op_Modulus` 32)) (Vale.Arch.Types.ishr32\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src2) `op_Modulus` 32))\n (Vale.Arch.Types.ishr32 (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0\n src1)) (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src2) `op_Modulus`\n 32)) (Vale.Arch.Types.ishr32 (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0\n src1)) (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src2) `op_Modulus`\n 32)) ==> va_k va_sM (())))", "val va_wp_Sbb64\n (dst: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Sbb64 (dst:va_operand_dst_opr64) (src:va_operand_opr64) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\\n Vale.X64.Decls.valid_cf (va_get_flags va_s0) /\\ (forall (va_x_dst:va_value_dst_opr64)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_operand_dst_opr64 dst\n va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst == Vale.Arch.Types.sub_wrap64\n (va_eval_dst_opr64 va_s0 dst) (Vale.Arch.Types.add_wrap64 (va_eval_opr64 va_s0 src) (va_if\n (Vale.X64.Decls.cf (va_get_flags va_s0)) (fun _ -> 1) (fun _ -> 0))) /\\\n Vale.X64.Decls.updated_cf (va_get_flags va_sM) (va_eval_dst_opr64 va_s0 dst - (va_eval_opr64\n va_s0 src + va_if (Vale.X64.Decls.cf (va_get_flags va_s0)) (fun _ -> 1) (fun _ -> 0)) < 0) ==>\n va_k va_sM (())))", "val va_wp_Xor64\n (dst: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Xor64 (dst:va_operand_dst_opr64) (src:va_operand_opr64) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_dst_opr64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl\n (va_upd_operand_dst_opr64 dst va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst\n == Vale.Arch.Types.ixor64 (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) /\\\n ~(Vale.X64.Decls.overflow (va_get_flags va_sM)) /\\ ~(Vale.X64.Decls.cf (va_get_flags va_sM)) /\\\n Vale.X64.Decls.valid_cf (va_get_flags va_sM) /\\ Vale.X64.Decls.valid_of (va_get_flags va_sM)\n ==> va_k va_sM (())))", "val va_wp_Vxor\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vxor (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == Vale.Def.Types_s.quad32_xor\n (va_eval_vec_opr va_s0 src1) (va_eval_vec_opr va_s0 src2) ==> va_k va_sM (())))", "val va_wp_Vmrghw\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vmrghw (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0\n src2)) (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src1)) ==> va_k va_sM (())))", "val va_wp_LoadImmShl64\n (dst: va_operand_reg_opr)\n (src: simm16)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_LoadImmShl64 (dst:va_operand_reg_opr) (src:simm16) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_reg_opr) . let\n va_sM = va_upd_operand_reg_opr dst va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_reg_opr va_sM\n dst == Vale.Arch.Types.ishl64 (src `op_Modulus` pow2_64) 16 ==> va_k va_sM (())))", "val va_wp_Sl64\n (dst src1 src2: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Sl64 (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:va_operand_reg_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == Vale.Arch.Types.ishl64\n (va_eval_reg_opr va_s0 src1) (va_eval_reg_opr va_s0 src2 `op_Modulus` 64) ==> va_k va_sM (())))", "val va_wp_Mtvsrws\n (dst: va_operand_vec_opr)\n (src: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Mtvsrws (dst:va_operand_vec_opr) (src:va_operand_reg_opr) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_reg_opr src va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_sM dst) ==\n va_eval_reg_opr va_s0 src `op_Modulus` pow2_32 /\\ Vale.Def.Words_s.__proj__Mkfour__item__lo1\n (va_eval_vec_opr va_sM dst) == va_eval_reg_opr va_s0 src `op_Modulus` pow2_32 /\\\n Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_sM dst) == va_eval_reg_opr va_s0\n src `op_Modulus` pow2_32 /\\ Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_sM\n dst) == va_eval_reg_opr va_s0 src `op_Modulus` pow2_32 ==> va_k va_sM (())))", "val va_wp_Load64_stack\n (dst: va_operand_dst_opr64)\n (src: va_operand_reg_opr64)\n (offset: int)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Load64_stack (dst:va_operand_dst_opr64) (src:va_operand_reg_opr64) (offset:int)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_reg_opr64 src va_s0 /\\ va_get_ok va_s0 /\\\n Vale.X64.Stack_i.valid_src_stack64 (va_eval_reg_opr64 va_s0 src + offset) (va_get_stack va_s0)\n /\\ Vale.X64.Stack_i.valid_taint_stack64 (va_eval_reg_opr64 va_s0 src + offset) Public\n (va_get_stackTaint va_s0) /\\ (forall (va_x_dst:va_value_dst_opr64) . let va_sM =\n va_upd_operand_dst_opr64 dst va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst\n == Vale.X64.Stack_i.load_stack64 (va_eval_reg_opr64 va_s0 src + offset) (va_get_stack va_s0)\n ==> va_k va_sM (())))", "val va_wp_LoadImm64\n (dst: va_operand_reg_opr)\n (src: simm16)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_LoadImm64 (dst:va_operand_reg_opr) (src:simm16) (va_s0:va_state) (va_k:(va_state -> unit\n -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_reg_opr) . let\n va_sM = va_upd_operand_reg_opr dst va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_reg_opr va_sM\n dst == src `op_Modulus` pow2_64 ==> va_k va_sM (())))", "val va_wp_Psrld\n (dst: va_operand_xmm)\n (amt: int)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Psrld (dst:va_operand_xmm) (amt:int) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\ (0 <= amt /\\ amt < 32) /\\ (forall\n (va_x_dst:va_value_xmm) . let va_sM = va_upd_operand_xmm dst va_x_dst va_s0 in va_get_ok va_sM\n /\\ va_eval_xmm va_sM dst == Vale.Def.Words.Four_s.four_map #nat32 #Vale.Def.Types_s.nat32 (fun\n (i:nat32) -> Vale.Arch.Types.ishr32 i amt) (va_eval_xmm va_s0 dst) ==> va_k va_sM (())))", "val va_wp_Adcx_64\n (dst: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Adcx_64 (dst:va_operand_dst_opr64) (src:va_operand_opr64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ adx_enabled /\\\n Vale.X64.Decls.valid_cf (va_get_flags va_s0) /\\ (forall (va_x_dst:va_value_dst_opr64)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_operand_dst_opr64 dst\n va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst == Vale.Bignum.Defs.add_lo\n (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) (flag_cf (va_get_flags va_s0)) /\\\n update_cf (va_get_flags va_sM) (Vale.Bignum.Defs.add_hi (va_eval_dst_opr64 va_s0 dst)\n (va_eval_opr64 va_s0 src) (flag_cf (va_get_flags va_s0))) /\\ maintain_of (va_get_flags va_sM)\n (va_get_flags va_s0) ==> va_k va_sM (())))", "val va_wp_Vadduwm\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vadduwm (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst ==\n Vale.Arch.Types.add_wrap_quad32 (va_eval_vec_opr va_s0 src1) (va_eval_vec_opr va_s0 src2) ==>\n va_k va_sM (())))", "val va_wp_Pslld\n (dst: va_operand_xmm)\n (amt: int)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Pslld (dst:va_operand_xmm) (amt:int) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\ (0 <= amt /\\ amt < 32) /\\ (forall\n (va_x_dst:va_value_xmm) . let va_sM = va_upd_operand_xmm dst va_x_dst va_s0 in va_get_ok va_sM\n /\\ va_eval_xmm va_sM dst == Vale.Def.Words.Four_s.four_map #nat32 #Vale.Def.Types_s.nat32 (fun\n (i:nat32) -> Vale.Arch.Types.ishl32 i amt) (va_eval_xmm va_s0 dst) ==> va_k va_sM (())))", "val va_wp_Xor\n (dst src1 src2: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Xor (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:va_operand_reg_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == Vale.Arch.Types.ixor64\n (va_eval_reg_opr va_s0 src1) (va_eval_reg_opr va_s0 src2) ==> va_k va_sM (())))", "val va_wp_Vmr (dst src: va_operand_vec_opr) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vmr (dst:va_operand_vec_opr) (src:va_operand_vec_opr) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == va_eval_vec_opr va_sM src ==> va_k va_sM (())))", "val va_wp_Adox_64\n (dst: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Adox_64 (dst:va_operand_dst_opr64) (src:va_operand_opr64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ adx_enabled /\\\n Vale.X64.Decls.valid_of (va_get_flags va_s0) /\\ (forall (va_x_dst:va_value_dst_opr64)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_operand_dst_opr64 dst\n va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst == Vale.Bignum.Defs.add_lo\n (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) (flag_of (va_get_flags va_s0)) /\\\n update_of (va_get_flags va_sM) (Vale.Bignum.Defs.add_hi (va_eval_dst_opr64 va_s0 dst)\n (va_eval_opr64 va_s0 src) (flag_of (va_get_flags va_s0))) /\\ maintain_cf (va_get_flags va_sM)\n (va_get_flags va_s0) ==> va_k va_sM (())))", "val va_wp_Vspltisb\n (dst: va_operand_vec_opr)\n (src: sim)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vspltisb (dst:va_operand_vec_opr) (src:sim) (va_s0:va_state) (va_k:(va_state -> unit ->\n Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let\n va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in va_get_ok va_sM /\\ (let src_nat8 =\n Vale.PPC64LE.Machine_s.int_to_nat8 src in let src_nat32 = Vale.Def.Types_s.be_bytes_to_nat32\n (Vale.Def.Words.Seq_s.four_to_seq_BE #Vale.Def.Types_s.nat8 (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat8 src_nat8 src_nat8 src_nat8 src_nat8)) in va_eval_vec_opr va_sM dst ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 src_nat32 src_nat32 src_nat32 src_nat32) ==>\n va_k va_sM (())))", "val va_wp_Vcmpequw\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vcmpequw (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 (va_if (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr\n va_s0 src1) = Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src2)) (fun _\n -> 4294967295) (fun _ -> 0)) (va_if (Vale.Def.Words_s.__proj__Mkfour__item__lo1\n (va_eval_vec_opr va_s0 src1) = Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr\n va_s0 src2)) (fun _ -> 4294967295) (fun _ -> 0)) (va_if\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src1) =\n Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src2)) (fun _ -> 4294967295)\n (fun _ -> 0)) (va_if (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src1) =\n Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src2)) (fun _ -> 4294967295)\n (fun _ -> 0)) ==> va_k va_sM (())))", "val va_wp_Vpslldq8 (dst src: va_operand_xmm) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vpslldq8 (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ avx_enabled /\\ (forall\n (va_x_dst:va_value_xmm) . let va_sM = va_upd_operand_xmm dst va_x_dst va_s0 in va_get_ok va_sM\n /\\ va_eval_xmm va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_xmm va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_xmm va_s0 src)) ==> va_k va_sM (())))", "val va_wp_Psrldq\n (dst: va_operand_xmm)\n (amt: int)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Psrldq (dst:va_operand_xmm) (amt:int) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\ (0 <= amt /\\ amt < 16) /\\ (forall\n (va_x_dst:va_value_xmm) . let va_sM = va_upd_operand_xmm dst va_x_dst va_s0 in va_get_ok va_sM\n /\\ (let src_bytes = Vale.Def.Types_s.le_quad32_to_bytes (va_eval_xmm va_s0 dst) in let zero_pad\n = FStar.Seq.Base.create #nat8 amt 0 in let remaining_bytes = FStar.Seq.Base.slice\n #Vale.Def.Types_s.nat8 src_bytes amt (FStar.Seq.Base.length #Vale.Def.Types_s.nat8 src_bytes)\n in va_eval_xmm va_sM dst == Vale.Def.Types_s.le_bytes_to_quad32 (FStar.Seq.Base.append #nat8\n zero_pad remaining_bytes)) ==> va_k va_sM (())))", "val va_wp_Vspltisw\n (dst: va_operand_vec_opr)\n (src: sim)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vspltisw (dst:va_operand_vec_opr) (src:sim) (va_s0:va_state) (va_k:(va_state -> unit ->\n Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let\n va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in va_get_ok va_sM /\\ (let src_nat32 =\n Vale.PPC64LE.Machine_s.int_to_nat32 src in va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 src_nat32 src_nat32 src_nat32 src_nat32) ==> va_k va_sM (())))", "val va_quick_Load_one_lsb (dst: va_operand_xmm) : (va_quickCode unit (va_code_Load_one_lsb dst))\nlet va_quick_Load_one_lsb (dst:va_operand_xmm) : (va_quickCode unit (va_code_Load_one_lsb dst)) =\n (va_QProc (va_code_Load_one_lsb dst) ([va_Mod_flags; va_Mod_reg64 rR11; va_mod_xmm dst])\n (va_wp_Load_one_lsb dst) (va_wpProof_Load_one_lsb dst))", "val va_wp_Mulx64\n (dst_hi dst_lo: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Mulx64 (dst_hi:va_operand_dst_opr64) (dst_lo:va_operand_dst_opr64) (src:va_operand_opr64)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst_hi va_s0 /\\ va_is_dst_dst_opr64 dst_lo va_s0 /\\ va_is_src_opr64 src\n va_s0 /\\ va_get_ok va_s0 /\\ bmi2_enabled /\\ dst_hi =!= dst_lo /\\ (forall\n (va_x_dst_hi:va_value_dst_opr64) (va_x_dst_lo:va_value_dst_opr64) . let va_sM =\n va_upd_operand_dst_opr64 dst_lo va_x_dst_lo (va_upd_operand_dst_opr64 dst_hi va_x_dst_hi va_s0)\n in va_get_ok va_sM /\\ va_mul_nat pow2_64 (va_eval_dst_opr64 va_sM dst_hi) + va_eval_dst_opr64\n va_sM dst_lo == va_mul_nat (va_get_reg64 rRdx va_s0) (va_eval_opr64 va_s0 src) ==> va_k va_sM\n (())))", "val va_wp_Adc64\n (dst: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Adc64 (dst:va_operand_dst_opr64) (src:va_operand_opr64) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ va_eval_opr64\n va_s0 src + va_eval_dst_opr64 va_s0 dst + 1 < pow2_64 /\\ Vale.X64.Decls.valid_cf (va_get_flags\n va_s0) /\\ (forall (va_x_dst:va_value_dst_opr64) (va_x_efl:Vale.X64.Flags.t) . let va_sM =\n va_upd_flags va_x_efl (va_upd_operand_dst_opr64 dst va_x_dst va_s0) in va_get_ok va_sM /\\\n va_eval_dst_opr64 va_sM dst == va_eval_dst_opr64 va_s0 dst + va_eval_opr64 va_s0 src + va_if\n (Vale.X64.Decls.cf (va_get_flags va_s0)) (fun _ -> 1) (fun _ -> 0) /\\ Vale.X64.Decls.updated_cf\n (va_get_flags va_sM) (va_eval_dst_opr64 va_s0 dst + va_eval_opr64 va_s0 src + va_if\n (Vale.X64.Decls.cf (va_get_flags va_s0)) (fun _ -> 1) (fun _ -> 0) >= pow2_64) ==> va_k va_sM\n (())))", "val va_wp_VPslldq4 (dst src: va_operand_xmm) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VPslldq4 (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ avx_enabled /\\ (forall\n (va_x_dst:va_value_xmm) . let va_sM = va_upd_operand_xmm dst va_x_dst va_s0 in va_get_ok va_sM\n /\\ va_eval_xmm va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_xmm va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_xmm va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_xmm va_s0 src)) ==> va_k va_sM (())))", "val va_wp_Pshufb (dst src: va_operand_xmm) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Pshufb (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state -> unit\n -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\\n va_eval_xmm va_s0 src == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 202182159 134810123\n 67438087 66051 /\\ (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM =\n va_upd_flags va_x_efl (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_xmm\n va_sM dst == Vale.Def.Types_s.reverse_bytes_quad32 (va_eval_xmm va_s0 dst) ==> va_k va_sM (())))", "val va_wp_Vsel\n (dst src1 src2 sel: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vsel (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (sel:va_operand_vec_opr) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_is_src_vec_opr sel va_s0 /\\ va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let\n va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in va_get_ok va_sM /\\\n Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_sM dst) == Vale.Def.Sel.isel32\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 sel)) /\\\n Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_sM dst) == Vale.Def.Sel.isel32\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 sel)) /\\\n Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_sM dst) == Vale.Def.Sel.isel32\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 sel)) /\\\n Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_sM dst) == Vale.Def.Sel.isel32\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 sel)) ==> va_k va_sM (())))", "val va_wp_Sr64\n (dst src1 src2: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Sr64 (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:va_operand_reg_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == Vale.Arch.Types.ishr64\n (va_eval_reg_opr va_s0 src1) (va_eval_reg_opr va_s0 src2 `op_Modulus` 64) ==> va_k va_sM (())))", "val va_wp_Sl64Imm\n (dst src1: va_operand_reg_opr)\n (src2: bits64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Sl64Imm (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:bits64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == Vale.Arch.Types.ishl64 (va_eval_reg_opr va_s0\n src1) src2 ==> va_k va_sM (())))", "val va_wp_AddLa\n (dst src1: va_operand_reg_opr)\n (src2: simm16)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_AddLa (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:simm16) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_get_ok va_s0 /\\ (0 <=\n va_eval_reg_opr va_s0 src1 + src2 /\\ va_eval_reg_opr va_s0 src1 + src2 < pow2_64) /\\ (forall\n (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == va_eval_reg_opr va_s0 src1 + src2 ==> va_k\n va_sM (())))", "val va_wp_Vsbox (dst src: va_operand_vec_opr) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vsbox (dst:va_operand_vec_opr) (src:va_operand_vec_opr) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32\n (Vale.AES.AES_common_s.sub_word (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr\n va_s0 src))) (Vale.AES.AES_common_s.sub_word (Vale.Def.Words_s.__proj__Mkfour__item__lo1\n (va_eval_vec_opr va_s0 src))) (Vale.AES.AES_common_s.sub_word\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src)))\n (Vale.AES.AES_common_s.sub_word (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr\n va_s0 src))) ==> va_k va_sM (())))", "val va_wp_Xxmrghd\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Xxmrghd (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0\n src2)) (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src2))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src1))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src1)) ==> va_k va_sM (())))", "val va_wp_Shl64\n (dst: va_operand_dst_opr64)\n (amt: va_operand_shift_amt64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Shl64 (dst:va_operand_dst_opr64) (amt:va_operand_shift_amt64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_shift_amt64 amt va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_dst_opr64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl\n (va_upd_operand_dst_opr64 dst va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst\n == Vale.Arch.Types.ishl64 (va_eval_dst_opr64 va_s0 dst) (va_eval_shift_amt64 va_s0 amt) ==>\n va_k va_sM (())))", "val va_wp_Vpsrldq8 (dst src: va_operand_xmm) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vpsrldq8 (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ avx_enabled /\\ (forall\n (va_x_dst:va_value_xmm) . let va_sM = va_upd_operand_xmm dst va_x_dst va_s0 in va_get_ok va_sM\n /\\ va_eval_xmm va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_xmm va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_xmm va_s0 src)) 0 0 ==> va_k va_sM (())))", "val va_wp_Sr64Imm\n (dst src1: va_operand_reg_opr)\n (src2: bits64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Sr64Imm (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:bits64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == Vale.Arch.Types.ishr64 (va_eval_reg_opr va_s0\n src1) src2 ==> va_k va_sM (())))", "val va_wp_VLow64ToHigh\n (dst src: va_operand_xmm)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VLow64ToHigh (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ (let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n avx_enabled) /\\ (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM =\n va_upd_flags va_x_efl (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\ (let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2_s.shift\n (Vale.Math.Poly2.mask a 64) 64) ==> va_k va_sM (())))", "val va_wp_AddLea64\n (dst: va_operand_dst_opr64)\n (src1 src2: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_AddLea64 (dst:va_operand_dst_opr64) (src1:va_operand_opr64) (src2:va_operand_opr64)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src1 va_s0 /\\ va_is_src_opr64 src2 va_s0 /\\\n va_get_ok va_s0 /\\ Vale.X64.Decls.max_one_mem src1 src2 /\\ va_eval_opr64 va_s0 src1 +\n va_eval_opr64 va_s0 src2 < pow2_64 /\\ (forall (va_x_dst:va_value_dst_opr64) . let va_sM =\n va_upd_operand_dst_opr64 dst va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst\n == va_eval_opr64 va_s0 src1 + va_eval_opr64 va_s0 src2 ==> va_k va_sM (())))", "val va_wp_VSwap (dst src: va_operand_vec_opr) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VSwap (dst:va_operand_vec_opr) (src:va_operand_vec_opr) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ (let (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32\n (va_eval_vec_opr va_s0 src) in Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_sM dst) ==\n Vale.Math.Poly2.swap a 64) ==> va_k va_sM (())))", "val va_wp_Mtvsrdd\n (dst: va_operand_vec_opr)\n (src1 src2: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Mtvsrdd (dst:va_operand_vec_opr) (src1:va_operand_reg_opr) (src2:va_operand_reg_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_mul_nat pow2_32\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_sM dst)) +\n Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_sM dst) == va_eval_reg_opr va_s0\n src1 /\\ va_mul_nat pow2_32 (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_sM\n dst)) + Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_sM dst) ==\n va_eval_reg_opr va_s0 src2 /\\ va_eval_vec_opr va_sM dst ==\n Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32 (Vale.Def.Words_s.Mktwo\n #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32\n (va_eval_reg_opr va_s0 src2 `op_Modulus` pow2_32) (va_eval_reg_opr va_s0 src2 `op_Division`\n pow2_32)) (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32 (va_eval_reg_opr va_s0 src1\n `op_Modulus` pow2_32) (va_eval_reg_opr va_s0 src1 `op_Division` pow2_32))) ==> va_k va_sM (())))", "val va_wp_VPshufb\n (dst src1 src2: va_operand_xmm)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VPshufb (dst:va_operand_xmm) (src1:va_operand_xmm) (src2:va_operand_xmm) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src1 va_s0 /\\ va_is_src_xmm src2 va_s0 /\\ va_get_ok\n va_s0 /\\ avx_enabled /\\ va_eval_xmm va_s0 src2 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\ (forall (va_x_dst:va_value_xmm)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_operand_xmm dst\n va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_xmm va_sM dst ==\n Vale.Def.Types_s.reverse_bytes_quad32 (va_eval_xmm va_s0 src1) ==> va_k va_sM (())))", "val va_wp_Pshufb64 (dst src: va_operand_xmm) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Pshufb64 (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\\n va_eval_xmm va_s0 src == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 67438087 66051\n 202182159 134810123 /\\ (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM\n = va_upd_flags va_x_efl (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\\n va_eval_xmm va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32\n (Vale.Def.Types_s.reverse_bytes_nat32 (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_xmm\n va_s0 dst))) (Vale.Def.Types_s.reverse_bytes_nat32 (Vale.Def.Words_s.__proj__Mkfour__item__lo0\n (va_eval_xmm va_s0 dst))) (Vale.Def.Types_s.reverse_bytes_nat32\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_xmm va_s0 dst)))\n (Vale.Def.Types_s.reverse_bytes_nat32 (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_xmm\n va_s0 dst))) ==> va_k va_sM (())))", "val va_wp_VPxor\n (dst src1: va_operand_xmm)\n (src2: va_operand_opr128)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VPxor (dst:va_operand_xmm) (src1:va_operand_xmm) (src2:va_operand_opr128)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src1 va_s0 /\\ va_is_src_opr128 src2 va_s0 /\\ va_get_ok\n va_s0 /\\ avx_enabled /\\ (forall (va_x_dst:va_value_xmm) . let va_sM = va_upd_operand_xmm dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_xmm va_sM dst == Vale.Def.Types_s.quad32_xor\n (va_eval_xmm va_s0 src1) (va_eval_opr128 va_s0 src2) ==> va_k va_sM (())))", "val va_wp_Add\n (dst src1 src2: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Add (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:va_operand_reg_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ va_eval_reg_opr va_s0 src1 + va_eval_reg_opr va_s0 src2 < pow2_64 /\\ (forall\n (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == va_eval_reg_opr va_s0 src1 + va_eval_reg_opr\n va_s0 src2 ==> va_k va_sM (())))", "val va_wp_IMul64\n (dst: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_IMul64 (dst:va_operand_dst_opr64) (src:va_operand_opr64) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ va_mul_nat\n (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) < pow2_64 /\\ (forall\n (va_x_dst:va_value_dst_opr64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl\n (va_upd_operand_dst_opr64 dst va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst\n == va_mul_nat (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) ==> va_k va_sM (())))", "val va_wp_Store_stack128\n (src: va_operand_vec_opr)\n (offset: int)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Store_stack128 (src:va_operand_vec_opr) (offset:int) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_src_vec_opr src va_s0 /\\ va_get_ok va_s0 /\\ Vale.PPC64LE.Machine_s.valid_maddr_offset128\n offset /\\ va_get_reg 1 va_s0 + offset <= Vale.PPC64LE.Stack_i.init_r1 (va_get_stack va_s0) - 16\n /\\ (forall (va_x_stack:vale_stack) (va_x_stackTaint:memtaint) . let va_sM = va_upd_stackTaint\n va_x_stackTaint (va_upd_stack va_x_stack va_s0) in va_get_ok va_sM /\\ va_get_stack va_sM ==\n Vale.PPC64LE.Stack_i.store_stack128 (va_get_reg 1 va_sM + offset) (va_eval_vec_opr va_s0 src)\n (va_get_stack va_s0) /\\ va_get_stackTaint va_sM == Vale.PPC64LE.Stack_i.store_taint_stack128\n (va_get_reg 1 va_sM + offset) Secret (va_get_stackTaint va_s0) ==> va_k va_sM (())))", "val va_wp_Pinsrd\n (dst: va_operand_xmm)\n (src: va_operand_opr64)\n (index: nat8)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Pinsrd (dst:va_operand_xmm) (src:va_operand_opr64) (index:nat8) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\\n va_eval_opr64 va_s0 src < pow2_32 /\\ index < 4 /\\ (forall (va_x_dst:va_value_xmm) . let va_sM =\n va_upd_operand_xmm dst va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_xmm va_sM dst ==\n Vale.Def.Types_s.insert_nat32 (va_eval_xmm va_s0 dst) (va_eval_opr64 va_s0 src) index ==> va_k\n va_sM (())))", "val va_wpProof_Load_two_lsb : dst:va_operand_xmm -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Load_two_lsb dst va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Load_two_lsb dst) ([va_Mod_flags;\n va_Mod_reg64 rR11; va_mod_xmm dst]) va_s0 va_k ((va_sM, va_f0, va_g))))\nlet va_wpProof_Load_two_lsb dst va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Load_two_lsb (va_code_Load_two_lsb dst) va_s0 dst in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rR11 va_sM (va_update_ok va_sM\n (va_update_operand_xmm dst va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rR11; va_mod_xmm dst]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wp_Shr64\n (dst: va_operand_dst_opr64)\n (amt: va_operand_shift_amt64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Shr64 (dst:va_operand_dst_opr64) (amt:va_operand_shift_amt64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_shift_amt64 amt va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_dst_opr64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl\n (va_upd_operand_dst_opr64 dst va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst\n == Vale.Arch.Types.ishr64 (va_eval_dst_opr64 va_s0 dst) (va_eval_shift_amt64 va_s0 amt) ==>\n va_k va_sM (())))", "val va_wp_Pand\n (dst: va_operand_xmm)\n (src: va_operand_opr128)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Pand (dst:va_operand_xmm) (src:va_operand_opr128) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_opr128 src va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\\n (forall (va_x_dst:va_value_xmm) . let va_sM = va_upd_operand_xmm dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_xmm va_sM dst == Vale.Def.Words.Four_s.four_map2 #nat32\n #Vale.Def.Types_s.nat32 (fun (di:nat32) (si:nat32) -> Vale.Arch.Types.iand32 di si)\n (va_eval_xmm va_s0 dst) (va_eval_opr128 va_s0 src) ==> va_k va_sM (())))", "val va_wp_Inc32 (dst one: va_operand_xmm) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Inc32 (dst:va_operand_xmm) (one:va_operand_xmm) (va_s0:va_state) (va_k:(va_state -> unit\n -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm one va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\\n va_eval_xmm va_s0 one == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 /\\ (forall\n (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl\n (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_xmm va_sM dst ==\n Vale.AES.GCTR_s.inc32 (va_eval_xmm va_s0 dst) 1 ==> va_k va_sM (())))", "val va_code_Load_one_lsb : dst:va_operand_vec_opr -> Tot va_code\nlet va_code_Load_one_lsb dst =\n (va_Block (va_CCons (va_code_Vspltisw dst 1) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 4) 0)\n (va_CCons (va_code_Vsldoi dst (va_op_vec_opr_vec 4) dst 4) (va_CNil ())))))", "val va_wp_MulLow64\n (dst src1 src2: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_MulLow64 (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:va_operand_reg_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (0 <= va_mul_nat (va_eval_reg_opr va_s0 src1) (va_eval_reg_opr va_s0 src2)\n /\\ va_mul_nat (va_eval_reg_opr va_s0 src1) (va_eval_reg_opr va_s0 src2) < pow2_64) /\\ (forall\n (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == va_mul_nat (va_eval_reg_opr va_s0 src1)\n (va_eval_reg_opr va_s0 src2) ==> va_k va_sM (())))", "val va_wp_Add64\n (dst: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Add64 (dst:va_operand_dst_opr64) (src:va_operand_opr64) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ va_eval_opr64\n va_s0 src + va_eval_dst_opr64 va_s0 dst < pow2_64 /\\ (forall (va_x_dst:va_value_dst_opr64)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_operand_dst_opr64 dst\n va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst == va_eval_dst_opr64 va_s0\n dst + va_eval_opr64 va_s0 src ==> va_k va_sM (())))", "val va_wp_Vspltw\n (dst src: va_operand_vec_opr)\n (uim: nat2)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vspltw (dst:va_operand_vec_opr) (src:va_operand_vec_opr) (uim:nat2) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ (uim == 0 ==> va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0\n src)) (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_vec_opr va_s0 src))) /\\ (uim == 1 ==>\n va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_vec_opr va_s0 src))) /\\ (uim == 2 ==>\n va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_vec_opr va_s0 src))) /\\ (uim == 3 ==>\n va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src))\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_vec_opr va_s0 src))) ==> va_k va_sM (())))", "val va_wp_InitPshufbMask\n (dst: va_operand_xmm)\n (tmp: va_operand_reg_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_InitPshufbMask (dst:va_operand_xmm) (tmp:va_operand_reg_opr64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_dst_reg_opr64 tmp va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\\n (forall (va_x_dst:va_value_xmm) (va_x_tmp:va_value_reg_opr64) (va_x_efl:Vale.X64.Flags.t) . let\n va_sM = va_upd_flags va_x_efl (va_upd_operand_reg_opr64 tmp va_x_tmp (va_upd_operand_xmm dst\n va_x_dst va_s0)) in va_get_ok va_sM /\\ va_eval_xmm va_sM dst == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 ==> va_k va_sM (())))", "val va_wp_Sub64\n (dst: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Sub64 (dst:va_operand_dst_opr64) (src:va_operand_opr64) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ 0 <=\n va_eval_dst_opr64 va_s0 dst - va_eval_opr64 va_s0 src /\\ (forall (va_x_dst:va_value_dst_opr64)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_operand_dst_opr64 dst\n va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst == va_eval_dst_opr64 va_s0\n dst - va_eval_opr64 va_s0 src ==> va_k va_sM (())))", "val va_wp_Vcipherlast\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vcipherlast (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == Vale.Def.Types_s.quad32_xor\n (Vale.AES.AES_BE_s.shift_rows (Vale.AES.AES_common_s.sub_bytes (va_eval_vec_opr va_s0 src1)))\n (va_eval_vec_opr va_s0 src2) ==> va_k va_sM (())))", "val va_lemma_Load_one_lsb : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Load_one_lsb dst) va_s0 /\\ va_is_dst_vec_opr dst va_s0\n /\\ va_get_ok va_s0 /\\ dst =!= 4))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 /\\\n va_state_eq va_sM (va_update_vec 4 va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst\n va_sM va_s0)))))\nlet va_lemma_Load_one_lsb va_b0 va_s0 dst =\n va_reveal_opaque (`%va_code_Load_one_lsb) (va_code_Load_one_lsb dst);\n let (va_old_s:va_state) = va_s0 in\n let (va_b1:va_codes) = va_get_block va_b0 in\n let (va_s2, va_fc2) = va_lemma_Vspltisw (va_hd va_b1) va_s0 dst 1 in\n let va_b2 = va_tl va_b1 in\n let (va_s3, va_fc3) = va_lemma_Vspltisw (va_hd va_b2) va_s2 (va_op_vec_opr_vec 4) 0 in\n let va_b3 = va_tl va_b2 in\n let (va_s4, va_fc4) = va_lemma_Vsldoi (va_hd va_b3) va_s3 dst (va_op_vec_opr_vec 4) dst 4 in\n let va_b4 = va_tl va_b3 in\n let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in\n let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in\n let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in\n let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in\n (va_sM, va_fM)", "val va_wp_Mov64\n (dst: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Mov64 (dst:va_operand_dst_opr64) (src:va_operand_opr64) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_dst_opr64) . let va_sM = va_upd_operand_dst_opr64 dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_dst_opr64 va_sM dst == va_eval_opr64 va_s0 src ==> va_k va_sM (())))", "val va_wp_PshufbStable\n (dst src: va_operand_xmm)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_PshufbStable (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\\n va_eval_xmm va_s0 src == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 66051 67438087\n 134810123 202182159 /\\ (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM\n = va_upd_flags va_x_efl (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\\n va_eval_xmm va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32\n (Vale.Def.Types_s.reverse_bytes_nat32 (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_xmm\n va_s0 dst))) (Vale.Def.Types_s.reverse_bytes_nat32 (Vale.Def.Words_s.__proj__Mkfour__item__lo1\n (va_eval_xmm va_s0 dst))) (Vale.Def.Types_s.reverse_bytes_nat32\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_xmm va_s0 dst)))\n (Vale.Def.Types_s.reverse_bytes_nat32 (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_xmm\n va_s0 dst))) /\\ va_eval_xmm va_sM dst == Vale.Arch.Types.reverse_bytes_nat32_quad32\n (va_eval_xmm va_s0 dst) ==> va_k va_sM (())))", "val va_wp_Pop (dst: va_operand_dst_opr64) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Pop (dst:va_operand_dst_opr64) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) :\n Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_get_ok va_s0 /\\ Vale.X64.Stack_i.valid_src_stack64\n (va_get_reg64 rRsp va_s0) (va_get_stack va_s0) /\\ Vale.X64.Stack_i.valid_taint_stack64\n (va_get_reg64 rRsp va_s0) Public (va_get_stackTaint va_s0) /\\ va_get_reg64 rRsp va_s0 >=\n Vale.X64.Stack_i.init_rsp (va_get_stack va_s0) - 4096 /\\ va_get_reg64 rRsp va_s0 + 8 <=\n Vale.X64.Stack_i.init_rsp (va_get_stack va_s0) /\\ (forall (va_x_dst:va_value_dst_opr64)\n (va_x_rsp:nat64) (va_x_stack:vale_stack) . let va_sM = va_upd_stack va_x_stack (va_upd_reg64\n rRsp va_x_rsp (va_upd_operand_dst_opr64 dst va_x_dst va_s0)) in va_get_ok va_sM /\\\n va_eval_dst_opr64 va_sM dst == Vale.X64.Stack_i.load_stack64 (va_get_reg64 rRsp va_s0)\n (va_get_stack va_s0) /\\ va_get_reg64 rRsp va_sM == va_get_reg64 rRsp va_s0 + 8 /\\ va_get_stack\n va_sM == Vale.X64.Stack_i.free_stack64 (va_get_reg64 rRsp va_sM - 8) (va_get_reg64 rRsp va_sM)\n (va_get_stack va_s0) ==> va_k va_sM (())))", "val va_wp_Sub\n (dst src1 src2: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Sub (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:va_operand_reg_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ va_eval_reg_opr va_s0 src1 - va_eval_reg_opr va_s0 src2 >= 0 /\\ (forall\n (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == va_eval_reg_opr va_s0 src1 - va_eval_reg_opr\n va_s0 src2 ==> va_k va_sM (())))", "val va_wp_Store_stack64\n (src: va_operand_reg_opr)\n (offset: int)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Store_stack64 (src:va_operand_reg_opr) (offset:int) (va_s0:va_state) (va_k:(va_state ->\n unit -> Type0)) : Type0 =\n (va_is_src_reg_opr src va_s0 /\\ va_get_ok va_s0 /\\ Vale.PPC64LE.Machine_s.valid_maddr_offset64\n offset /\\ va_get_reg 1 va_s0 + offset <= Vale.PPC64LE.Stack_i.init_r1 (va_get_stack va_s0) - 8\n /\\ (forall (va_x_stack:vale_stack) (va_x_stackTaint:memtaint) . let va_sM = va_upd_stackTaint\n va_x_stackTaint (va_upd_stack va_x_stack va_s0) in va_get_ok va_sM /\\ va_get_stack va_sM ==\n Vale.PPC64LE.Stack_i.store_stack64 (va_get_reg 1 va_sM + offset) (va_eval_reg_opr va_s0 src)\n (va_get_stack va_s0) /\\ va_get_stackTaint va_sM == Vale.PPC64LE.Stack_i.store_taint_stack64\n (va_get_reg 1 va_sM + offset) Secret (va_get_stackTaint va_s0) ==> va_k va_sM (())))", "val va_wp_Low64ToHigh\n (dst src: va_operand_vec_opr)\n (a: poly)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Low64ToHigh (dst:va_operand_vec_opr) (src:va_operand_vec_opr) (a:poly) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src va_s0 /\\ va_get_ok va_s0 /\\ va_get_vec 0\n va_s0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 /\\ Vale.Math.Poly2_s.degree a\n <= 127 /\\ va_eval_vec_opr va_s0 src == Vale.Math.Poly2.Bits_s.to_quad32 a /\\ (forall\n (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == Vale.Math.Poly2.Bits_s.to_quad32\n (Vale.Math.Poly2_s.mul (Vale.Math.Poly2_s.mod a (Vale.Math.Poly2_s.monomial 64))\n (Vale.Math.Poly2_s.monomial 64)) ==> va_k va_sM (())))", "val va_wp_Cmovc64\n (dst: va_operand_dst_opr64)\n (src: va_operand_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Cmovc64 (dst:va_operand_dst_opr64) (src:va_operand_opr64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_dst_opr64 dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\\n Vale.X64.Decls.valid_cf (va_get_flags va_s0) /\\ (forall (va_x_dst:va_value_dst_opr64) . let\n va_sM = va_upd_operand_dst_opr64 dst va_x_dst va_s0 in va_get_ok va_sM /\\ va_if\n (Vale.X64.Decls.cf (va_get_flags va_sM)) (fun _ -> va_eval_dst_opr64 va_sM dst = va_eval_opr64\n va_s0 src) (fun _ -> va_eval_dst_opr64 va_sM dst = va_eval_dst_opr64 va_s0 dst) ==> va_k va_sM\n (())))", "val va_wp_VPaddd\n (dst src1 src2: va_operand_xmm)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VPaddd (dst:va_operand_xmm) (src1:va_operand_xmm) (src2:va_operand_xmm) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src1 va_s0 /\\ va_is_src_xmm src2 va_s0 /\\ va_get_ok\n va_s0 /\\ avx_enabled /\\ (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM\n = va_upd_flags va_x_efl (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\\n va_eval_xmm va_sM dst == Vale.Arch.Types.add_wrap_quad32 (va_eval_xmm va_s0 src1) (va_eval_xmm\n va_s0 src2) ==> va_k va_sM (())))", "val va_wp_AddExtendedOV\n (dst src1 src2: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_AddExtendedOV (dst:va_operand_reg_opr) (src1:va_operand_reg_opr)\n (src2:va_operand_reg_opr) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_reg_opr) (va_x_xer:xer_t) . let va_sM =\n va_upd_xer va_x_xer (va_upd_operand_reg_opr dst va_x_dst va_s0) in va_get_ok va_sM /\\\n va_eval_reg_opr va_sM dst == Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64\n (va_eval_reg_opr va_s0 src1) (va_eval_reg_opr va_s0 src2)) (va_if (Vale.PPC64LE.Decls.xer_ov\n (va_get_xer va_s0)) (fun _ -> 1) (fun _ -> 0)) /\\ Vale.PPC64LE.Decls.xer_ov (va_get_xer va_sM)\n == (va_eval_reg_opr va_s0 src1 + va_eval_reg_opr va_s0 src2 + va_if (Vale.PPC64LE.Decls.xer_ov\n (va_get_xer va_s0)) (fun _ -> 1) (fun _ -> 0) >= pow2_64) ==> va_k va_sM (())))", "val va_wp_AddCarry\n (dst src1 src2: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_AddCarry (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:va_operand_reg_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_reg_opr) (va_x_xer:xer_t) . let va_sM =\n va_upd_xer va_x_xer (va_upd_operand_reg_opr dst va_x_dst va_s0) in va_get_ok va_sM /\\\n va_eval_reg_opr va_sM dst == Vale.Arch.Types.add_wrap64 (va_eval_reg_opr va_s0 src1)\n (va_eval_reg_opr va_s0 src2) /\\ Vale.PPC64LE.Decls.xer_ca (va_get_xer va_sM) ==\n (va_eval_reg_opr va_s0 src1 + va_eval_reg_opr va_s0 src2 >= pow2_64) ==> va_k va_sM (())))", "val va_wp_InitPshufb64Mask\n (dst: va_operand_xmm)\n (tmp: va_operand_reg_opr64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_InitPshufb64Mask (dst:va_operand_xmm) (tmp:va_operand_reg_opr64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_dst_reg_opr64 tmp va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\\n (forall (va_x_dst:va_value_xmm) (va_x_tmp:va_value_reg_opr64) (va_x_efl:Vale.X64.Flags.t) . let\n va_sM = va_upd_flags va_x_efl (va_upd_operand_reg_opr64 tmp va_x_tmp (va_upd_operand_xmm dst\n va_x_dst va_s0)) in va_get_ok va_sM /\\ va_eval_xmm va_sM dst == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 67438087 66051 202182159 134810123 ==> va_k va_sM (())))", "val va_wp_Vcipher\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vcipher (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == Vale.Def.Types_s.quad32_xor\n (Vale.AES.AES_BE_s.mix_columns (Vale.AES.AES_BE_s.shift_rows (Vale.AES.AES_common_s.sub_bytes\n (va_eval_vec_opr va_s0 src1)))) (va_eval_vec_opr va_s0 src2) ==> va_k va_sM (())))", "val va_wp_AddExtended\n (dst src1 src2: va_operand_reg_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_AddExtended (dst:va_operand_reg_opr) (src1:va_operand_reg_opr) (src2:va_operand_reg_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src1 va_s0 /\\ va_is_src_reg_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_reg_opr) (va_x_xer:xer_t) . let va_sM =\n va_upd_xer va_x_xer (va_upd_operand_reg_opr dst va_x_dst va_s0) in va_get_ok va_sM /\\\n va_eval_reg_opr va_sM dst == Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64\n (va_eval_reg_opr va_s0 src1) (va_eval_reg_opr va_s0 src2)) (va_if (Vale.PPC64LE.Decls.xer_ca\n (va_get_xer va_s0)) (fun _ -> 1) (fun _ -> 0)) /\\ Vale.PPC64LE.Decls.xer_ca (va_get_xer va_sM)\n == (va_eval_reg_opr va_s0 src1 + va_eval_reg_opr va_s0 src2 + va_if (Vale.PPC64LE.Decls.xer_ca\n (va_get_xer va_s0)) (fun _ -> 1) (fun _ -> 0) >= pow2_64) ==> va_k va_sM (())))", "val va_wp_VSwap (dst src: va_operand_xmm) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VSwap (dst:va_operand_xmm) (src:va_operand_xmm) (va_s0:va_state) (va_k:(va_state -> unit\n -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ (let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n avx_enabled) /\\ (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM =\n va_upd_flags va_x_efl (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\ (let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_s0 src) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_xmm va_sM dst) == Vale.Math.Poly2.swap a 64) ==> va_k\n va_sM (())))", "val va_wp_Vncipherlast\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Vncipherlast (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (forall (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst\n va_x_dst va_s0 in va_get_ok va_sM /\\ va_eval_vec_opr va_sM dst == Vale.Def.Types_s.quad32_xor\n (Vale.AES.AES_common_s.inv_sub_bytes (Vale.AES.AES_BE_s.inv_shift_rows (va_eval_vec_opr va_s0\n src1))) (va_eval_vec_opr va_s0 src2) ==> va_k va_sM (())))", "val va_wp_Pinsrq\n (dst: va_operand_xmm)\n (src: va_operand_opr64)\n (index: nat8)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Pinsrq (dst:va_operand_xmm) (src:va_operand_opr64) (index:nat8) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\ index\n < 2 /\\ (forall (va_x_dst:va_value_xmm) . let va_sM = va_upd_operand_xmm dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_xmm va_sM dst == Vale.Def.Types_s.insert_nat64 (va_eval_xmm va_s0\n dst) (va_eval_opr64 va_sM src) index ==> va_k va_sM (())))", "val va_wp_Pclmulqdq\n (dst src: va_operand_xmm)\n (dstHi srcHi: bool)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Pclmulqdq (dst:va_operand_xmm) (src:va_operand_xmm) (dstHi:bool) (srcHi:bool)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ pclmulqdq_enabled /\\\n (forall (va_x_dst:va_value_xmm) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl\n (va_upd_operand_xmm dst va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_xmm va_sM dst ==\n Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.mul (Vale.Math.Poly2.Bits_s.of_double32\n (va_if dstHi (fun _ -> Vale.Arch.Types.quad32_double_hi (va_eval_xmm va_s0 dst)) (fun _ ->\n Vale.Arch.Types.quad32_double_lo (va_eval_xmm va_s0 dst)))) (Vale.Math.Poly2.Bits_s.of_double32\n (va_if srcHi (fun _ -> Vale.Arch.Types.quad32_double_hi (va_eval_xmm va_s0 src)) (fun _ ->\n Vale.Arch.Types.quad32_double_lo (va_eval_xmm va_s0 src))))) ==> va_k va_sM (())))", "val va_wp_Pshufd\n (dst src: va_operand_xmm)\n (permutation: nat8)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Pshufd (dst:va_operand_xmm) (src:va_operand_xmm) (permutation:nat8) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src va_s0 /\\ va_get_ok va_s0 /\\ sse_enabled /\\ (forall\n (va_x_dst:va_value_xmm) . let va_sM = va_upd_operand_xmm dst va_x_dst va_s0 in va_get_ok va_sM\n /\\ va_eval_xmm va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32\n (Vale.Def.Types_s.select_word (va_eval_xmm va_s0 src)\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 (Vale.Def.Types_s.byte_to_twobits permutation)))\n (Vale.Def.Types_s.select_word (va_eval_xmm va_s0 src)\n (Vale.Def.Words_s.__proj__Mkfour__item__lo1 (Vale.Def.Types_s.byte_to_twobits permutation)))\n (Vale.Def.Types_s.select_word (va_eval_xmm va_s0 src)\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 (Vale.Def.Types_s.byte_to_twobits permutation)))\n (Vale.Def.Types_s.select_word (va_eval_xmm va_s0 src)\n (Vale.Def.Words_s.__proj__Mkfour__item__hi3 (Vale.Def.Types_s.byte_to_twobits permutation)))\n ==> va_k va_sM (())))", "val va_wp_VShufpd\n (dst src1 src2: va_operand_xmm)\n (permutation: nat8)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VShufpd (dst:va_operand_xmm) (src1:va_operand_xmm) (src2:va_operand_xmm)\n (permutation:nat8) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_xmm dst va_s0 /\\ va_is_src_xmm src1 va_s0 /\\ va_is_src_xmm src2 va_s0 /\\ va_get_ok\n va_s0 /\\ avx_enabled /\\ permutation < 4 /\\ (forall (va_x_dst:va_value_xmm)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_operand_xmm dst\n va_x_dst va_s0) in va_get_ok va_sM /\\ va_eval_xmm va_sM dst == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 (va_if (permutation = 0 || permutation = 2) (fun _ ->\n Vale.Def.Words_s.__proj__Mkfour__item__lo0 (va_eval_xmm va_s0 src1)) (fun _ ->\n Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_xmm va_s0 src1))) (va_if (permutation = 0\n || permutation = 2) (fun _ -> Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_xmm va_s0\n src1)) (fun _ -> Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_xmm va_s0 src1))) (va_if\n (permutation = 0 || permutation = 1) (fun _ -> Vale.Def.Words_s.__proj__Mkfour__item__lo0\n (va_eval_xmm va_s0 src2)) (fun _ -> Vale.Def.Words_s.__proj__Mkfour__item__hi2 (va_eval_xmm\n va_s0 src2))) (va_if (permutation = 0 || permutation = 1) (fun _ ->\n Vale.Def.Words_s.__proj__Mkfour__item__lo1 (va_eval_xmm va_s0 src2)) (fun _ ->\n Vale.Def.Words_s.__proj__Mkfour__item__hi3 (va_eval_xmm va_s0 src2))) ==> va_k va_sM (())))", "val va_wp_VPolyMulLow\n (dst src1 src2: va_operand_vec_opr)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_VPolyMulLow (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src1 va_s0 /\\ va_is_src_vec_opr src2 va_s0 /\\\n va_get_ok va_s0 /\\ (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32\n (va_eval_vec_opr va_s0 src1) in let (a2:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2) in l_or (Vale.Math.Poly2_s.shift\n a1 (-64) == zero) (Vale.Math.Poly2_s.shift a2 (-64) == zero)) /\\ (forall\n (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ (let (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32\n (va_eval_vec_opr va_s0 src1) in let (a2:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_s0 src2) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_eval_vec_opr va_sM dst) == Vale.Math.Poly2_s.mul\n (Vale.Math.Poly2.mask a1 64) (Vale.Math.Poly2.mask a2 64)) ==> va_k va_sM (())))", "val va_wp_Push (src: va_operand_reg_opr64) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Push (src:va_operand_reg_opr64) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) :\n Type0 =\n (va_is_src_reg_opr64 src va_s0 /\\ va_get_ok va_s0 /\\ va_get_reg64 rRsp va_s0 <=\n Vale.X64.Stack_i.init_rsp (va_get_stack va_s0) /\\ Vale.X64.Stack_i.init_rsp (va_get_stack\n va_s0) - 4096 <= va_get_reg64 rRsp va_s0 - 8 /\\ (forall (va_x_rsp:nat64)\n (va_x_stack:vale_stack) (va_x_stackTaint:memtaint) . let va_sM = va_upd_stackTaint\n va_x_stackTaint (va_upd_stack va_x_stack (va_upd_reg64 rRsp va_x_rsp va_s0)) in va_get_ok va_sM\n /\\ va_get_reg64 rRsp va_sM == va_get_reg64 rRsp va_s0 - 8 /\\ va_get_stack va_sM ==\n Vale.X64.Stack_i.store_stack64 (va_get_reg64 rRsp va_sM) (va_eval_reg_opr64 va_s0 src)\n (va_get_stack va_s0) /\\ va_get_stackTaint va_sM == Vale.X64.Stack_i.store_taint_stack64\n (va_get_reg64 rRsp va_sM) Public (va_get_stackTaint va_s0) ==> va_k va_sM (())))", "val va_wp_SHA256_sigma0\n (dst src: va_operand_vec_opr)\n (t: counter)\n (block: block_w)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_SHA256_sigma0 (dst:va_operand_vec_opr) (src:va_operand_vec_opr) (t:counter)\n (block:block_w) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_is_dst_vec_opr dst va_s0 /\\ va_is_src_vec_opr src va_s0 /\\ va_get_ok va_s0 /\\ ((16 <= t && t\n < size_k_w_256)) /\\ (va_eval_vec_opr va_s0 src).hi3 == ws_opaque block (t - 15) /\\ (forall\n (va_x_dst:va_value_vec_opr) . let va_sM = va_upd_operand_vec_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ (va_eval_vec_opr va_sM dst).hi3 == sigma_0_0_partial t block ==> va_k va_sM\n (())))", "val va_wp_Move (dst src: va_operand_reg_opr) (va_s0: va_state) (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Move (dst:va_operand_reg_opr) (src:va_operand_reg_opr) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_is_dst_reg_opr dst va_s0 /\\ va_is_src_reg_opr src va_s0 /\\ va_get_ok va_s0 /\\ (forall\n (va_x_dst:va_value_reg_opr) . let va_sM = va_upd_operand_reg_opr dst va_x_dst va_s0 in\n va_get_ok va_sM /\\ va_eval_reg_opr va_sM dst == va_eval_reg_opr va_s0 src ==> va_k va_sM (())))" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fsti", "name": "Vale.AES.X64.AESopt.va_wp_Load_one_lsb" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fsti", "name": "Vale.AES.X64.AESopt.va_wp_Load_two_lsb" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_wp_Load_0xc2_msb" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESGCM.fst", "name": "Vale.AES.X64.AESGCM.va_wp_Load_one_msb" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fst", "name": "Vale.AES.PPC64LE.GCMencrypt.va_wpProof_Load_one_lsb" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_wp_load_one_msb" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vand" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vslw" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsStack.fsti", "name": "Vale.PPC64LE.InsStack.va_wp_Load_stack128" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vsl" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_wpProof_Load_one_lsb" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Mfvsrd" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Mfvsrld" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_And" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsStack.fsti", "name": "Vale.PPC64LE.InsStack.va_wp_Load_stack64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vsldoi" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_And64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vpmsumd" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vsrw" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_Sbb64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_Xor64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vxor" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vmrghw" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_LoadImmShl64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_Sl64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Mtvsrws" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsStack.fsti", "name": "Vale.X64.InsStack.va_wp_Load64_stack" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_LoadImm64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_Psrld" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.X64.fsti", "name": "Vale.Bignum.X64.va_wp_Adcx_64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vadduwm" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_Pslld" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_Xor" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vmr" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.X64.fsti", "name": "Vale.Bignum.X64.va_wp_Adox_64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vspltisb" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vcmpequw" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_Vpslldq8" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_wp_Psrldq" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vspltisw" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fsti", "name": "Vale.AES.X64.AESopt.va_quick_Load_one_lsb" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_Mulx64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_Adc64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_VPslldq4" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_Pshufb" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vsel" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_Sr64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_Sl64Imm" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_AddLa" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vsbox" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Xxmrghd" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_Shl64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_Vpsrldq8" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_Sr64Imm" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.PolyOps.fsti", "name": "Vale.AES.X64.PolyOps.va_wp_VLow64ToHigh" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_AddLea64" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fsti", "name": "Vale.AES.PPC64LE.PolyOps.va_wp_VSwap" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Mtvsrdd" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_VPshufb" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_Pshufb64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_VPxor" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_Add" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_IMul64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsStack.fsti", "name": "Vale.PPC64LE.InsStack.va_wp_Store_stack128" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_Pinsrd" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_wpProof_Load_two_lsb" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_Shr64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_Pand" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fsti", "name": "Vale.AES.X64.GCTR.va_wp_Inc32" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fst", "name": "Vale.AES.PPC64LE.GCMencrypt.va_code_Load_one_lsb" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_MulLow64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_Add64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vspltw" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_InitPshufbMask" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_Sub64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vcipherlast" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fst", "name": "Vale.AES.PPC64LE.GCMencrypt.va_lemma_Load_one_lsb" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_Mov64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_PshufbStable" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsStack.fsti", "name": "Vale.X64.InsStack.va_wp_Pop" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_Sub" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsStack.fsti", "name": "Vale.PPC64LE.InsStack.va_wp_Store_stack64" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fsti", "name": "Vale.AES.PPC64LE.GF128_Mul.va_wp_Low64ToHigh" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_wp_Cmovc64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_VPaddd" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_AddExtendedOV" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_AddCarry" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_InitPshufb64Mask" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vcipher" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_AddExtended" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.PolyOps.fsti", "name": "Vale.AES.X64.PolyOps.va_wp_VSwap" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_Vncipherlast" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_Pinsrq" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsAes.fsti", "name": "Vale.X64.InsAes.va_wp_Pclmulqdq" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_Pshufd" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_wp_VShufpd" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.PolyOps.fsti", "name": "Vale.AES.PPC64LE.PolyOps.va_wp_VPolyMulLow" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsStack.fsti", "name": "Vale.X64.InsStack.va_wp_Push" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_wp_SHA256_sigma0" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsBasic.fsti", "name": "Vale.PPC64LE.InsBasic.va_wp_Move" } ], "selected_premises": [ "Vale.PPC64LE.Decls.va_get_ok", "Vale.PPC64LE.Decls.va_is_dst_vec_opr", "Vale.PPC64LE.Decls.va_upd_reg", "Vale.PPC64LE.Decls.va_is_dst_reg_opr", "Vale.PPC64LE.Decls.va_eval_vec_opr", "Vale.PPC64LE.Decls.va_upd_cr0", "Vale.PPC64LE.Decls.va_get_reg", "Vale.PPC64LE.Decls.va_state", "Vale.X64.Machine_s.reg_64", "Vale.PPC64LE.Decls.va_is_src_reg_opr", "Vale.PPC64LE.Decls.va_upd_vec", "Vale.PPC64LE.Decls.va_get_mem_layout", "Vale.PPC64LE.Decls.va_upd_operand_reg_opr", "Vale.X64.Machine_s.reg_xmm", "Vale.PPC64LE.Decls.va_is_src_vec_opr", "Vale.PPC64LE.Decls.va_get_vec", "Vale.PPC64LE.QuickCodes.label", "Vale.PPC64LE.Machine_s.nat64", "Vale.PPC64LE.Memory.nat64", "Vale.Def.Types_s.nat64", "Vale.PPC64LE.Decls.va_upd_ok", "Vale.Def.Words_s.nat64", "Vale.PPC64LE.Decls.va_get_mem_heaplet", "Vale.PPC64LE.Decls.va_eval_reg_opr", "Vale.X64.Machine_s.nat64", "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.Decls.va_upd_operand_vec_opr", "Vale.PPC64LE.Decls.va_value_vec_opr", "Vale.PPC64LE.Decls.va_mul_nat", "Vale.PPC64LE.Decls.va_if", "Vale.X64.Machine_s.operand128", "Vale.X64.Machine_s.rRdi", "Vale.PPC64LE.Decls.va_require_total", "Vale.Def.Words_s.nat32", "Vale.X64.Machine_s.rRsp", "Vale.PPC64LE.Decls.va_value_reg_opr", "Vale.X64.Machine_s.quad32", "Vale.PPC64LE.Memory.quad32", "Vale.PPC64LE.Machine_s.quad32", "Vale.PPC64LE.State.state", "Lib.IntTypes.u64", "Vale.PPC64LE.Decls.va_upd_mem_heaplet", "Vale.X64.Machine_s.operand64", "Vale.PPC64LE.Decls.va_get_mem", "Vale.SHA.PPC64LE.SHA_helpers.repeat_range_vale_64", "Vale.X64.Machine_s.rRsi", "Vale.X64.Machine_s.rRdx", "Vale.X64.Machine_s.rRbp", "Lib.IntTypes.int_t", "Lib.Sequence.lseq", "Vale.PPC64LE.Decls.va_get_cr0", "Vale.PPC64LE.Decls.va_expand_state", "Vale.X64.Machine_s.rRax", "Vale.PPC64LE.QuickCodes.va_range1", "Vale.PPC64LE.Decls.va_upd_mem", "Vale.X64.Machine_s.rRbx", "Vale.PPC64LE.Decls.va_get_block", "Vale.X64.Machine_s.rRcx", "Lib.Sequence.op_String_Access", "Lib.IntTypes.uint_t", "Vale.AES.GCTR_BE.gctr_partial", "Vale.AES.GCTR_BE.gctr_partial_reveal", "Vale.SHA.PPC64LE.SHA_helpers.k_reqs", "Vale.PPC64LE.Decls.from_heap_impl", "FStar.List.Tot.Base.length", "Vale.PPC64LE.InsBasic.vale_stack", "Vale.X64.Machine_s.rR10", "Vale.X64.Machine_s.rR9", "Vale.X64.Machine_s.rR12", "Lib.IntTypes.range", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.X64.Machine_s.rR11", "Vale.PPC64LE.InsBasic.vale_heap", "Vale.X64.Machine_s.rR8", "Vale.X64.Machine_s.rR13", "FStar.List.Tot.Base.map", "Vale.SHA.PPC64LE.SHA_helpers.hash256", "Lib.IntTypes.op_Plus_Bang", "Vale.AES.GCM_BE_s.gcm_encrypt_BE", "Lib.Sequence.to_seq", "Vale.PPC64LE.Decls.va_int_range", "Vale.X64.Machine_s.rR15", "Vale.AES.GCM_BE_s.gcm_decrypt_BE_reveal", "Vale.AES.GHash_BE.ghash_incremental", "Vale.X64.Machine_s.rR14", "Vale.PPC64LE.Decls.state_inv", "Vale.PPC64LE.Decls.va_op_cmp_reg", "Vale.PPC64LE.Decls.va_upd_operand_heaplet", "Vale.PPC64LE.Memory.nat32", "Vale.Def.Types_s.nat32", "Vale.PPC64LE.Machine_s.nat32", "Vale.PPC64LE.Decls.va_op_heaplet_mem_heaplet", "Vale.PPC64LE.Decls.va_upd_mem_layout", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.SHA.PPC64LE.SHA_helpers.block_w", "Lib.IntTypes.size", "Vale.PPC64LE.Memory.nat8", "Vale.PPC64LE.Machine_s.nat8", "Vale.Def.Types_s.nat8", "Vale.PPC64LE.Decls.buffer128_read" ], "source_upto_this": "module Vale.AES.PPC64LE.GCMencrypt\nopen Vale.Def.Prop_s\nopen Vale.Def.Opaque_s\nopen FStar.Seq\nopen Vale.Def.Words_s\nopen Vale.Def.Words.Seq_s\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Arch.HeapImpl\nopen Vale.AES.AES_BE_s\nopen Vale.AES.GCTR_BE_s\nopen Vale.AES.GCTR_BE\nopen Vale.AES.GCM_BE\nopen Vale.AES.GHash_BE_s\nopen Vale.AES.GHash_BE\nopen Vale.AES.GCM_BE_s\nopen Vale.AES.PPC64LE.AES\nopen Vale.AES.GF128_s\nopen Vale.AES.GF128\nopen Vale.Poly1305.Math\nopen Vale.AES.GCM_helpers_BE\nopen Vale.AES.PPC64LE.GCTR\nopen Vale.PPC64LE.Machine_s\nopen Vale.PPC64LE.Memory\nopen Vale.PPC64LE.Stack_i\nopen Vale.PPC64LE.State\nopen Vale.PPC64LE.Decls\nopen Vale.PPC64LE.InsBasic\nopen Vale.PPC64LE.InsMem\nopen Vale.PPC64LE.InsVector\nopen Vale.PPC64LE.InsStack\nopen Vale.PPC64LE.QuickCode\nopen Vale.PPC64LE.QuickCodes\nopen Vale.AES.PPC64LE.GF128_Mul\nopen Vale.Math.Poly2.Bits_s\nopen Vale.AES.PPC64LE.GHash\nopen Vale.Lib.Meta\nopen Vale.AES.OptPublic_BE\nlet aes_reqs\n (alg:algorithm) (key:seq nat32) (round_keys:seq quad32) (keys_b:buffer128)\n (key_ptr:int) (heap0:vale_heap) (layout:vale_heap_layout) : prop0\n =\n (alg = AES_128 \\/ alg = AES_256) /\\\n is_aes_key_word alg key /\\\n length(round_keys) == nr(alg) + 1 /\\\n round_keys == key_to_round_keys_word alg key /\\\n validSrcAddrs128 heap0 key_ptr keys_b (nr alg + 1) layout Secret /\\\n reverse_bytes_quad32_seq (s128 heap0 keys_b) == round_keys\n//-- Load_one_lsb\n\nval va_code_Load_one_lsb : dst:va_operand_vec_opr -> Tot va_code\n\nval va_codegen_success_Load_one_lsb : dst:va_operand_vec_opr -> Tot va_pbool\n\nval va_lemma_Load_one_lsb : va_b0:va_code -> va_s0:va_state -> dst:va_operand_vec_opr\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Load_one_lsb dst) va_s0 /\\ va_is_dst_vec_opr dst va_s0\n /\\ va_get_ok va_s0 /\\ dst =!= 4))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_eval_vec_opr va_sM dst == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 /\\\n va_state_eq va_sM (va_update_vec 4 va_sM (va_update_ok va_sM (va_update_operand_vec_opr dst\n va_sM va_s0)))))\n[@ va_qattr]" }, { "file_name": "Lib.NTuple.fsti", "name": "Lib.NTuple.tup8", "opens_and_abbrevs": [ { "open": "Lib.IntTypes" }, { "open": "FStar.Mul" }, { "open": "Lib" }, { "open": "Lib" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 8, "max_fuel": 8, "initial_ifuel": 0, "max_ifuel": 0, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 15, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val tup8 (#a: _) (#l: flen{l = 8}) (t: ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a)))))))", "source_definition": "let tup8 #a (#l:flen{l = 8}) (t:ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)", "source_range": { "start_line": 224, "start_col": 0, "end_line": 226, "end_col": 19 }, "interleaved": false, "definition": "fun t ->\n (assert (Lib.NTuple.ntuple a l == Lib.NTuple.ntuple a 8);\n t <: Lib.NTuple.ntuple a 8)\n <:\n a * (a * (a * (a * (a * (a * (a * a))))))", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Lib.NTuple.flen", "Prims.b2t", "Prims.op_Equality", "Prims.int", "Lib.NTuple.ntuple", "Prims.unit", "Prims._assert", "Prims.eq2", "FStar.Pervasives.Native.tuple2" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "t: Lib.NTuple.ntuple a l -> a * (a * (a * (a * (a * (a * (a * a))))))", "prompt": "let tup8 #a (#l: flen{l = 8}) (t: ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n ", "expected_response": "assert (ntuple a l == ntuple a 8);\n(t <: ntuple a 8)", "source": { "project_name": "hacl-star", "file_name": "lib/Lib.NTuple.fsti", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Lib.NTuple.fsti", "checked_file": "dataset/Lib.NTuple.fsti.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/Lib.Sequence.fsti.checked", "dataset/Lib.IntTypes.fsti.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked" ] }, "definitions_in_context": [ "let flen = size_pos", "let rec ntuple_ (a:Type0) (len:flen) =\n if len = 1 then a\n else a & ntuple_ a (len-1)", "let ntuple (a:Type0) (len:flen) = normalize_term (ntuple_ a len)", "val fst (#a:Type0) (#len:flen) (s:ntuple a len) : a", "val rest (#a:Type0) (#len:flen{len > 1}) (s:ntuple a len) : ntuple a (len - 1)", "val index (#a:Type0) (#len:flen) (s:ntuple a len) (i:nat{i < len}) : a", "val index_fst_lemma (#a:Type0) (#len:flen) (s:ntuple a len) :\n Lemma (fst s == index s 0)\n [SMTPat (fst s)]", "val createi (#a:Type0) (len:flen) (f:(i:nat{i < len} -> a)) : ntuple a len", "val gcreatei (#a:Type0) (len:flen) (f:(i:nat{i < len} -> GTot a)) : GTot (ntuple a len)", "val createi_lemma (#a:Type0) (len:flen) (f:(i:nat{i < len} -> a)) (i:nat{i < len}) :\n Lemma (index (createi #a len f) i == f i)\n [SMTPat (index (createi #a len f) i)]", "val gcreatei_lemma (#a:Type0) (len:flen) (f:(i:nat{i < len} -> GTot a)) (i:nat{i < len}) :\n Lemma (index (gcreatei #a len f) i == f i)\n [SMTPat (index (gcreatei #a len f) i)]", "val to_lseq (#a:Type0) (#len:flen) (l:ntuple a len) : Lib.Sequence.lseq a len", "val to_lseq_index (#a:Type0) (#len:flen) (l:ntuple a len) (i:nat{i < len}) :\n Lemma (index l i == Lib.Sequence.index (to_lseq l) i)", "val from_lseq (#a:Type0) (#len:flen) (s:Lib.Sequence.lseq a len) : ntuple a len", "val create (#a:Type0) (len:flen) (init:a) : ntuple a len", "val create_lemma (#a:Type0) (len:flen) (init:a) (i:nat{i < len}) :\n Lemma (index (create #a len init) i == init)\n [SMTPat (index (create #a len init) i)]", "val concat (#a:Type0) (#len0:flen) (#len1:flen{len0 + len1 <= max_size_t})\n\t (s0:ntuple a len0) (s1:ntuple a len1) : ntuple a (len0 + len1)", "val concat_lemma (#a:Type0) (#len0:flen) (#len1:flen) (s0:ntuple a len0) (s1:ntuple a len1) (i:nat):\n Lemma\n (requires (len0 + len1 <= max_size_t /\\ i < len0 + len1))\n (ensures ((i < len0 ==> index (concat s0 s1) i == index s0 i) /\\\n (i >= len0 ==> index (concat s0 s1) i == index s1 (i-len0))))\n [SMTPat (index (concat #a #len0 #len1 s0 s1) i)]", "val equal (#a:Type) (#len:flen) (s1:ntuple a len) (s2:ntuple a len) : Type0", "val eq_intro: #a:Type -> #len:flen -> s1:ntuple a len -> s2:ntuple a len ->\n Lemma\n (requires forall i. {:pattern index s1 i; index s2 i} index s1 i == index s2 i)\n (ensures equal s1 s2)\n [SMTPat (equal s1 s2)]", "val eq_elim: #a:Type -> #len:flen -> s1:ntuple a len -> s2:ntuple a len ->\n Lemma\n (requires equal s1 s2)\n (ensures s1 == s2)\n [SMTPat (equal s1 s2)]", "val upd: #a:Type -> #len:flen -> s:ntuple a len -> i:nat{i < len} -> x:a -> ntuple a len", "val upd_lemma (#a:Type0) (#len:flen) (s:ntuple a len) (i:nat{i < len}) (x:a) (j:nat{j < len}) :\n Lemma (index (upd #a #len s i x) j == (if i = j then x else index s j))\n [SMTPat (index (upd #a #len s i x) j)]", "val sub (#a:Type) (#len:flen) (s:ntuple a len) (start:nat) (n:flen{start + n <= len}) : ntuple a n", "val index_sub_lemma (#a:Type) (#len:flen) (s:ntuple a len) (start:nat) (n:flen{start + n <= len}) (i:nat{i < n}) :\n Lemma (index (sub #a #len s start n) i == index s (start + i))\n [SMTPat (index (sub #a #len s start n) i)]", "val update_sub (#a:Type) (#len:flen) (s:ntuple a len) (start:nat) (n:flen{start + n <= len}) (x:ntuple a n) : ntuple a len", "val index_update_sub_lemma (#a:Type) (#len:flen) (s:ntuple a len) (start:nat) (n:flen{start + n <= len}) (x:ntuple a n) (i:nat{i < n}) :\n Lemma\n (index (update_sub #a #len s start n x) i == (if i >= start && i < start + n then index x (i - start) else index s i))\n [SMTPat (index (update_sub #a #len s start n x) i)]", "val mapi (#a:Type) (#b:Type) (#len:flen) (f:(i:nat{i < len} -> a -> b)) (s:ntuple a len) : ntuple b len", "val index_mapi_lemma (#a:Type) (#b:Type) (#len:flen) (f:(i:nat{i < len} -> a -> b)) (s:ntuple a len) (i:nat{i < len}) :\n Lemma (index (mapi #a #b #len f s) i == f i (index s i))\n [SMTPat (index (mapi #a #b #len f s) i)]", "val gmapi (#a:Type) (#b:Type) (#len:flen) (f:(i:nat{i < len} -> a -> GTot b)) (s:ntuple a len) : GTot (ntuple b len)", "val index_gmapi_lemma (#a:Type) (#b:Type) (#len:flen) (f:(i:nat{i < len} -> a -> GTot b)) (s:ntuple a len) (i:nat{i < len}) :\n Lemma (index (gmapi #a #b #len f s) i == f i (index s i))\n [SMTPat (index (gmapi #a #b #len f s) i)]", "val map (#a:Type) (#b:Type) (#len:flen) (f:a -> b) (s:ntuple a len) : ntuple b len", "val index_map_lemma (#a:Type) (#b:Type) (#len:flen) (f:(a -> b)) (s:ntuple a len) (i:nat{i < len}) :\n Lemma (index (map #a #b #len f s) i == f (index s i))\n [SMTPat (index (map #a #b #len f s) i)]", "val gmap (#a:Type) (#b:Type) (#len:flen) (f:a -> GTot b) (s:ntuple a len) : GTot (ntuple b len)", "val index_gmap_lemma (#a:Type) (#b:Type) (#len:flen) (f:(a -> GTot b)) (s:ntuple a len) (i:nat{i < len}) :\n Lemma (index (gmap #a #b #len f s) i == f (index s i))\n [SMTPat (index (gmap #a #b #len f s) i)]", "val map2i (#a:Type) (#b:Type) (#c:Type) (#len:flen) (f:(i:nat{i < len} -> a -> b -> c)) (s1:ntuple a len) (s2:ntuple b len) : ntuple c len", "val index_map2i_lemma (#a:Type) (#b:Type) (#c:Type) (#len:flen) (f:(i:nat{i < len} -> a -> b -> c)) (s1:ntuple a len) (s2:ntuple b len) (i:nat{i < len}) :\n Lemma (index (map2i #a #b #c #len f s1 s2) i == f i (index s1 i) (index s2 i))\n [SMTPat (index (map2i #a #b #c #len f s1 s2) i)]", "val map2 (#a:Type) (#b:Type) (#c:Type) (#len:flen) (f:(a -> b -> c)) (s1:ntuple a len) (s2:ntuple b len) : ntuple c len", "val index_map2_lemma (#a:Type) (#b:Type) (#c:Type) (#len:flen) (f:a -> b -> c) (s1:ntuple a len) (s2:ntuple b len) (i:nat{i < len}) :\n Lemma (index (map2 #a #b #c #len f s1 s2) i == f (index s1 i) (index s2 i))\n [SMTPat (index (map2 #a #b #c #len f s1 s2) i)]", "let op_Lens_Access #a #len = index #a #len", "let op_Lens_Assignment #a #len = upd #a #len", "let ntup1 #a (#l:flen{l = 1}) (t:a) : ntuple a l =\n assert (ntuple a l == ntuple a 1);\n t <: ntuple a 1", "val ntup1_lemma (#a:Type0) (#l:flen{l == 1}) (t:a):\n Lemma (let x0 = t in let t = ntup1 #a #l t in x0 == t.(|0|))\n [SMTPat (ntup1 #a #l t)]", "let tup1 #a (#l:flen{l = 1}) (t:ntuple a l) : a =\n assert (ntuple a l == ntuple a 1);\n t <: ntuple a 1", "val tup1_lemma (#a:Type0) (#l:flen{l == 1}) (t:ntuple a l):\n Lemma (let x0 = tup1 t in x0 == t.(|0|))\n [SMTPat (tup1 #a #l t)]", "let ntup4 #a (#l:flen{l = 4}) (t:a & (a & (a & a))) : ntuple a l =\n assert (ntuple a l == ntuple a 4);\n (t <: ntuple a 4)", "val ntup4_lemma (#a:Type0) (#l:flen{l == 4}) (t:a & (a & (a & a))) :\n Lemma\n (let (x0,(x1,(x2,x3))) = t in\n let t = ntup4 #a #l t in\n x0 == t.(|0|) /\\ x1 == t.(|1|) /\\\n x2 == t.(|2|) /\\ x3 == t.(|3|))\n [SMTPat (ntup4 #a #l t)]", "let tup4 #a (#l:flen{l = 4}) (t:ntuple a l) : (a & (a & (a & a))) =\n assert (ntuple a l == ntuple a 4);\n (t <: ntuple a 4)", "val tup4_lemma (#a:Type0) (#l:flen{l = 4}) (t:ntuple a l) :\n Lemma\n (let (x0,(x1,(x2,x3))) = tup4 t in\n x0 == t.(|0|) /\\ x1 == t.(|1|) /\\\n x2 == t.(|2|) /\\ x3 == t.(|3|))\n [SMTPat (tup4 t)]", "let ntup8 #a (#l:flen{l = 8}) (t:a & (a & (a & (a & (a & (a & (a & a))))))) : ntuple a l =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)", "val ntup8_lemma (#a:Type0) (#l:flen{l == 8}) (t:a & (a & (a & (a & (a & (a & (a & a))))))) :\n Lemma\n (let (x0,(x1,(x2,(x3,(x4,(x5,(x6,x7))))))) = t in\n let t = ntup8 #a #l t in\n x0 == t.(|0|) /\\ x1 == t.(|1|) /\\\n x2 == t.(|2|) /\\ x3 == t.(|3|) /\\\n x4 == t.(|4|) /\\ x5 == t.(|5|) /\\\n x6 == t.(|6|) /\\ x7 == t.(|7|))\n [SMTPat (ntup8 #a #l t)]" ], "closest": [ "val tup8_lemma (#a:Type0) (#l:flen{l = 8}) (t:ntuple a l) :\n Lemma\n (let (x0,(x1,(x2,(x3,(x4,(x5,(x6,x7))))))) = tup8 t in\n x0 == t.(|0|) /\\ x1 == t.(|1|) /\\\n x2 == t.(|2|) /\\ x3 == t.(|3|) /\\\n x4 == t.(|4|) /\\ x5 == t.(|5|) /\\\n x6 == t.(|6|) /\\ x7 == t.(|7|))\n [SMTPat (tup8 t)]\nlet tup8_lemma #a #l t =\n assert (ntuple a l == ntuple a 8)", "val ntup8_lemma (#a:Type0) (#l:flen{l == 8}) (t:a & (a & (a & (a & (a & (a & (a & a))))))) :\n Lemma\n (let (x0,(x1,(x2,(x3,(x4,(x5,(x6,x7))))))) = t in\n let t = ntup8 #a #l t in\n x0 == t.(|0|) /\\ x1 == t.(|1|) /\\\n x2 == t.(|2|) /\\ x3 == t.(|3|) /\\\n x4 == t.(|4|) /\\ x5 == t.(|5|) /\\\n x6 == t.(|6|) /\\ x7 == t.(|7|))\n [SMTPat (ntup8 #a #l t)]\nlet ntup8_lemma #a #l t =\n assert (ntuple a l == ntuple a 8)", "val f_lseq8 (#t: v_inttype) (vs: lseq (vec_t t 8) 8) (f: (vec_t8 t -> vec_t8 t))\n : lseq (vec_t t 8) 8\nlet f_lseq8 (#t:v_inttype) (vs:lseq (vec_t t 8) 8) (f:vec_t8 t -> vec_t8 t) : lseq (vec_t t 8) 8 =\n let (v0,v1,v2,v3,v4,v5,v6,v7) = (vs.[0],vs.[1],vs.[2],vs.[3],vs.[4],vs.[5],vs.[6],vs.[7]) in\n let (r0,r1,r2,r3,r4,r5,r6,r7) = f (v0,v1,v2,v3,v4,v5,v6,v7) in\n create8 r0 r1 r2 r3 r4 r5 r6 r7", "val transpose8x8_lseq (#t: v_inttype{t = U32}) (vs: lseq (vec_t t 8) 8) : lseq (vec_t t 8) 8\nlet transpose8x8_lseq (#t:v_inttype{t = U32}) (vs:lseq (vec_t t 8) 8) : lseq (vec_t t 8) 8 =\n let (v0,v1,v2,v3,v4,v5,v6,v7) = (vs.[0],vs.[1],vs.[2],vs.[3],vs.[4],vs.[5],vs.[6],vs.[7]) in\n let (r0,r1,r2,r3,r4,r5,r6,r7) = transpose8x8 (v0,v1,v2,v3,v4,v5,v6,v7) in\n create8 r0 r1 r2 r3 r4 r5 r6 r7", "val ntup4_lemma (#a:Type0) (#l:flen{l == 4}) (t:a & (a & (a & a))) :\n Lemma\n (let (x0,(x1,(x2,x3))) = t in\n let t = ntup4 #a #l t in\n x0 == t.(|0|) /\\ x1 == t.(|1|) /\\\n x2 == t.(|2|) /\\ x3 == t.(|3|))\n [SMTPat (ntup4 #a #l t)]\nlet ntup4_lemma #a #l t =\n assert (ntuple a l == ntuple a 4)", "val tup4_lemma (#a:Type0) (#l:flen{l = 4}) (t:ntuple a l) :\n Lemma\n (let (x0,(x1,(x2,x3))) = tup4 t in\n x0 == t.(|0|) /\\ x1 == t.(|1|) /\\\n x2 == t.(|2|) /\\ x3 == t.(|3|))\n [SMTPat (tup4 t)]\nlet tup4_lemma #a #l t =\n assert (ntuple a l == ntuple a 4)", "val tup1_lemma (#a:Type0) (#l:flen{l == 1}) (t:ntuple a l):\n Lemma (let x0 = tup1 t in x0 == t.(|0|))\n [SMTPat (tup1 #a #l t)]\nlet tup1_lemma #a #l t =\n assert (ntuple a l == ntuple a 1)", "val create8: #a:Type -> x0:a -> x1:a -> x2:a -> x3:a -> x4:a -> x5:a -> x6:a -> x7:a -> lseq a 8\nlet create8 #a x0 x1 x2 x3 x4 x5 x6 x7 =\n let l = [x0; x1; x2; x3; x4; x5; x6; x7] in\n assert_norm (List.Tot.length l = 8);\n createL l", "val tail (#a: Type) (#l: len_t{l <> 0ul}) (v: raw a l) : Tot (raw a U32.(l -^ 1ul))\nlet tail (#a:Type) (#l:len_t{l <> 0ul}) (v:raw a l)\n : Tot (raw a U32.(l -^ 1ul))\n = sub v 1ul l", "val length (#a: Type0) (#len: flen) (s: ntuple a len) : flen\nlet length (#a:Type0) (#len:flen) (s: ntuple a len) : flen = len", "val fst_ (#a: Type0) (#len: flen) (s: ntuple_ a len) : a\nlet fst_ (#a:Type0) (#len:flen) (s:ntuple_ a len) : a =\n if len = 1 then s\n else fst (s <: a & ntuple_ a (len - 1))", "val rest_ (#a: Type0) (#len: flen{len > 1}) (s: ntuple_ a len) : ntuple_ a (len - 1)\nlet rest_ (#a:Type0) (#len:flen{len > 1}) (s:ntuple_ a len) : ntuple_ a (len - 1)=\n snd (s <: a & ntuple_ a (len - 1))", "val from_lseq (#a:Type0) (#len:flen) (s:Lib.Sequence.lseq a len) : ntuple a len\nlet from_lseq #a #len s =\n normalize_term (createi #a len (Lib.Sequence.index s))", "val rest (#a:Type0) (#len:flen{len > 1}) (s:ntuple a len) : ntuple a (len - 1)\nlet rest #a #len s =\n normalize_term (rest_ #a #len s)", "val upd: #a:Type -> #len:flen -> s:ntuple a len -> i:nat{i < len} -> x:a -> ntuple a len\nlet upd #a #len s i x =\n normalize_term (upd_ s i x)", "val fst (#a:Type0) (#len:flen) (s:ntuple a len) : a\nlet fst #a #len (s:ntuple a len) =\n normalize_term (fst_ #a #len s)", "val map (#a:Type) (#b:Type) (#len:flen) (f:a -> b) (s:ntuple a len) : ntuple b len\nlet map #a #b #len f s =\n normalize_term (createi len (fun i -> f (index s i)))", "val to_lseq (#a:Type0) (#len:flen) (l:ntuple a len) : Lib.Sequence.lseq a len\nlet to_lseq #a #len l =\n normalize_term (Lib.Sequence.createi len (index l))", "val mapi (#a:Type) (#b:Type) (#len:flen) (f:(i:nat{i < len} -> a -> b)) (s:ntuple a len) : ntuple b len\nlet mapi #a #b #len f s =\n normalize_term (createi len (fun i -> f i (index s i)))", "val ntup1_lemma (#a:Type0) (#l:flen{l == 1}) (t:a):\n Lemma (let x0 = t in let t = ntup1 #a #l t in x0 == t.(|0|))\n [SMTPat (ntup1 #a #l t)]\nlet ntup1_lemma #a #l t =\n assert (ntuple a l == ntuple a 1)", "val concat (#a:Type0) (#len0:flen) (#len1:flen{len0 + len1 <= max_size_t})\n\t (s0:ntuple a len0) (s1:ntuple a len1) : ntuple a (len0 + len1)\nlet concat #a #len0 #len1 s0 s1 = concat_ s0 s1", "val concat_\n (#a: Type0)\n (#len0: flen)\n (#len1: flen{len0 + len1 <= max_ntuple_len})\n (s0: ntuple a len0)\n (s1: ntuple a len1)\n : ntuple_ a (len0 + len1)\nlet rec concat_ (#a:Type0) (#len0:flen) (#len1:flen{len0 + len1 <= max_ntuple_len})\n\t\t(s0:ntuple a len0) (s1:ntuple a len1) : ntuple_ a (len0 + len1)\n =\n if len0 = 1 then s0,s1\n else fst s0, concat_ (rest s0) s1", "val index (#a:Type0) (#len:flen) (s:ntuple a len) (i:nat{i < len}) : a\nlet index #a #len s i =\n normalize_term (index_ s i)", "val mul_felem5_eval_as_tup64:\n #w:lanes\n -> f1:felem5 w{felem_fits5 f1 (3, 3, 3, 3, 3)}\n -> r:felem5 w{felem_fits5 r (2, 2, 2, 2, 2)}\n -> r5:felem5 w{felem_fits5 r5 (10, 10, 10, 10, 10) /\\ r5 == precomp_r5 r}\n -> i:nat{i < w} ->\n Lemma\n (let (r0, r1, r2, r3, r4) = r in\n let (f10, f11, f12, f13, f14) = f1 in\n let (r50, r51, r52, r53, r54) = r5 in\n let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in\n let (tf10, tf11, tf12, tf13, tf14) = as_tup64_i f1 i in\n (uint64xN_v f10).[i] * (fas_nat5 (r0,r1,r2,r3,r4)).[i] +\n (uint64xN_v f11).[i] * (fas_nat5 (r54,r0,r1,r2,r3)).[i] +\n (uint64xN_v f12).[i] * (fas_nat5 (r53,r54,r0,r1,r2)).[i] +\n (uint64xN_v f13).[i] * (fas_nat5 (r52,r53,r54,r0,r1)).[i] +\n (uint64xN_v f14).[i] * (fas_nat5 (r51,r52,r53,r54,r0)).[i] ==\n (v tf10 * as_nat5 (tr0, tr1, tr2, tr3, tr4) +\n v tf11 * as_nat5 (tr4 *! u64 5, tr0, tr1, tr2, tr3) +\n v tf12 * as_nat5 (tr3 *! u64 5, tr4 *! u64 5, tr0, tr1, tr2) +\n v tf13 * as_nat5 (tr2 *! u64 5, tr3 *! u64 5, tr4 *! u64 5, tr0, tr1) +\n v tf14 * as_nat5 (tr1 *! u64 5, tr2 *! u64 5, tr3 *! u64 5, tr4 *! u64 5, tr0)))\nlet mul_felem5_eval_as_tup64 #w f1 r r5 i =\n let (r0, r1, r2, r3, r4) = r in\n let (f10, f11, f12, f13, f14) = f1 in\n let (r50, r51, r52, r53, r54) = r5 in\n let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in\n let (tf10, tf11, tf12, tf13, tf14) = as_tup64_i f1 i in\n let (tr50, tr51, tr52, tr53, tr54) = as_tup64_i r5 i in\n assert (\n (uint64xN_v f10).[i] * (fas_nat5 (r0,r1,r2,r3,r4)).[i] +\n (uint64xN_v f11).[i] * (fas_nat5 (r54,r0,r1,r2,r3)).[i] +\n (uint64xN_v f12).[i] * (fas_nat5 (r53,r54,r0,r1,r2)).[i] +\n (uint64xN_v f13).[i] * (fas_nat5 (r52,r53,r54,r0,r1)).[i] +\n (uint64xN_v f14).[i] * (fas_nat5 (r51,r52,r53,r54,r0)).[i] ==\n v tf10 * as_nat5 (tr0,tr1,tr2,tr3,tr4) +\n v tf11 * as_nat5 (tr54,tr0,tr1,tr2,tr3) +\n v tf12 * as_nat5 (tr53,tr54,tr0,tr1,tr2) +\n v tf13 * as_nat5 (tr52,tr53,tr54,tr0,tr1) +\n v tf14 * as_nat5 (tr51,tr52,tr53,tr54,tr0));\n precomp_r5_as_tup64 #w r i", "val upd_ (#a: Type) (#len: flen) (s: ntuple a len) (i: nat{i < len}) (x: a) : ntuple_ a len\nlet rec upd_ (#a:Type) (#len:flen) (s:ntuple a len) (i:nat{i < len}) (x:a) : ntuple_ a len =\n if i = 0 then\n if len = 1 then x\n else x,rest s\n else fst s,upd_ #a #(len-1) (rest s) (i-1) x", "val upd8 (#a: Type) (m: map8 a) (n: int) (v: a) : map8 a\nlet upd8 (#a:Type) (m:map8 a) (n:int) (v:a) : map8 a =\n match m with (m0, m1) ->\n match n < 4 with true -> (upd4 m0 n v, m1) | false -> (m0, upd4 m1 (n - 4) v)", "val sub (#a:Type) (#len:flen) (s:ntuple a len) (start:nat) (n:flen{start + n <= len}) : ntuple a n\nlet sub #a #len s start n =\n normalize_term (createi n (fun i -> index s (start + i)))", "val transpose8x8_lemma: #t:v_inttype{t = U32} -> vs:lseq (vec_t t 8) 8 ->\n Lemma (forall (i:nat{i < 8}) (j:nat{j < 8}). (vec_v (transpose8x8_lseq vs).[i]).[j] == (vec_v vs.[j]).[i])\nlet transpose8x8_lemma #t vs =\n match t with\n | U32 -> Classical.forall_intro_2 (transpose8x8_lemma_uint32_ij vs)", "val f_lseq4 (#t: v_inttype) (vs: lseq (vec_t t 4) 4) (f: (vec_t4 t -> vec_t4 t))\n : lseq (vec_t t 4) 4\nlet f_lseq4 (#t:v_inttype) (vs:lseq (vec_t t 4) 4) (f:vec_t4 t -> vec_t4 t) : lseq (vec_t t 4) 4 =\n let (v0,v1,v2,v3) = (vs.[0],vs.[1],vs.[2],vs.[3]) in\n let (r0,r1,r2,r3) = f (v0,v1,v2,v3) in\n create4 r0 r1 r2 r3", "val transposewxw_f_l:\n #w:width\n -> #t:v_inttype\n -> n:nat{pow2 n == w}\n -> i:nat{i < n}\n -> lseq (vec_t t w) w\n -> l:nat{l < w} ->\n vec_t t w\nlet transposewxw_f_l #w #t n i vs l =\n Math.Lemmas.pow2_multiplication_modulo_lemma_1 1 i n;\n if l % (2 * pow2 i) < pow2 i\n then begin\n lemma_l_plus_pow2i_lt #w n i l;\n vec_interleave_low_n (pow2 i) vs.[l] vs.[l + pow2 i] end\n else\n vec_interleave_high_n (pow2 i) vs.[l - pow2 i] vs.[l]", "val transpose4x4_lseq (#t: v_inttype{t = U32 \\/ t = U64}) (vs: lseq (vec_t t 4) 4)\n : lseq (vec_t t 4) 4\nlet transpose4x4_lseq (#t:v_inttype{t = U32 \\/ t = U64}) (vs:lseq (vec_t t 4) 4) : lseq (vec_t t 4) 4 =\n let (v0,v1,v2,v3) = (vs.[0],vs.[1],vs.[2],vs.[3]) in\n let (r0,r1,r2,r3) = transpose4x4 (v0,v1,v2,v3) in\n create4 r0 r1 r2 r3", "val head (#a: Type) (#l: len_t{l <> 0ul}) (v: raw a l) : Tot a\nlet head (#a:Type) (#l:len_t{l <> 0ul}) (v:raw a l)\n : Tot a\n = v.[0ul]", "val refl (a: LSeq.lseq uint64 4 {linv a}) : GTot S.felem\nlet refl (a:LSeq.lseq uint64 4{linv a}) : GTot S.felem =\n SM.from_mont (BD.bn_v a)", "val sel8 (#a: Type) (m: map8 a) (n: int) : a\nlet sel8 (#a:Type) (m:map8 a) (n:int) : a =\n match m with (m0, m1) ->\n match n < 4 with true -> sel4 m0 n | false -> sel4 m1 (n - 4)", "val refl (a: LSeq.lseq uint64 5 {linv a}) : GTot S.felem\nlet refl (a:LSeq.lseq uint64 5{linv a}) : GTot S.felem =\n let open Lib.Sequence in\n feval5 (a.[0],a.[1],a.[2],a.[3],a.[4])", "val mktuple_n (ts: list term {List.Tot.Base.length ts <= 8}) : term\nlet mktuple_n (ts : list term{List.Tot.Base.length ts <= 8}) : term =\n match List.Tot.Base.length ts with\n | 0 -> pack_ln (Tv_Const C_Unit)\n | 1 -> let [x] = ts in x\n | n -> begin\n let qn = match n with\n | 2 -> mktuple2_qn\n | 3 -> mktuple3_qn\n | 4 -> mktuple4_qn\n | 5 -> mktuple5_qn\n | 6 -> mktuple6_qn\n | 7 -> mktuple7_qn\n | 8 -> mktuple8_qn\n in mk_e_app (pack_ln (Tv_FVar (pack_fv qn))) ts\n end", "val mktuple_n (ts: list term {List.Tot.Base.length ts <= 8}) : term\nlet mktuple_n (ts : list term{List.Tot.Base.length ts <= 8}) : term =\n match List.Tot.Base.length ts with\n | 0 -> pack_ln (Tv_Const C_Unit)\n | 1 -> let [x] = ts in x\n | n -> begin\n let qn = match n with\n | 2 -> mktuple2_qn\n | 3 -> mktuple3_qn\n | 4 -> mktuple4_qn\n | 5 -> mktuple5_qn\n | 6 -> mktuple6_qn\n | 7 -> mktuple7_qn\n | 8 -> mktuple8_qn\n in mk_e_app (pack_ln (Tv_FVar (pack_fv qn))) ts\n end", "val as_tup64_i (#w: lanes) (f: felem5 w) (i: nat{i < w}) : tup64_5\nlet as_tup64_i (#w:lanes) (f:felem5 w) (i:nat{i < w}): tup64_5 =\n (transpose #w f).[i]", "val transpose8x8_0: #t:v_inttype -> vec_t8 t -> vec_t8 t\nlet transpose8x8_0 #t (v0,v1,v2,v3,v4,v5,v6,v7) =\n let v0' = vec_interleave_low v0 v1 in\n let v1' = vec_interleave_high v0 v1 in\n let v2' = vec_interleave_low v2 v3 in\n let v3' = vec_interleave_high v2 v3 in\n let v4' = vec_interleave_low v4 v5 in\n let v5' = vec_interleave_high v4 v5 in\n let v6' = vec_interleave_low v6 v7 in\n let v7' = vec_interleave_high v6 v7 in\n (v0',v1',v2',v3',v4',v5',v6',v7')", "val store_tup64_lemma: f:tup64_5 ->\n Pure (uint64 & uint64)\n (requires tup64_fits5 f (1, 1, 1, 1, 1))\n (ensures (fun (lo, hi) -> v hi * pow2 64 + v lo == as_nat5 f % pow2 128))\nlet store_tup64_lemma f =\n let (f0, f1, f2, f3, f4) = f in\n let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in\n let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in\n lemma_store_felem_lo f lo;\n lemma_store_felem_hi f hi;\n\n assert (v lo == v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64);\n assert (v hi == v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64);\n\n calc (==) {\n v lo + v hi * pow2 64;\n (==) { }\n v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +\n (v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64) * pow2 64;\n (==) { }\n v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +\n v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 * pow2 40) % pow2 64 * pow2 64;\n (==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 64 40 }\n v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +\n v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow2 40 * pow2 64;\n (==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f2) 64 52 }\n v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +\n v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow2 40 * pow2 64;\n (==) { assert_norm (pow2 40 * pow2 64 = pow104) }\n v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +\n v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow104;\n (==) { assert_norm (pow2 14 * pow2 64 = pow78) }\n v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +\n v f2 / pow2 12 * pow2 64 + v f3 * pow78 + (v f4 % pow2 24) * pow104;\n (==) { assert_norm (pow2 12 * pow52 = pow2 64) }\n v f0 + v f1 * pow2 26 + (v f2 % pow2 12 + v f2 / pow2 12 * pow2 12) * pow52 +\n v f3 * pow78 + (v f4 % pow2 24) * pow104;\n (==) { FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 12) }\n v f0 + v f1 * pow2 26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104;\n (==) { lemma_tup64_mod_pow2_128 f }\n (as_nat5 f) % pow2 128;\n };\n assert (v lo + v hi * pow2 64 == (as_nat5 f) % pow2 128);\n lo, hi", "val int8_to_uint8 : a:I8.t -> Tot (b:U8.t {U8.v b = I8.v a % pow2 8})\nlet int8_to_uint8 x = U8.uint_to_t (I8.v x % pow2 8)", "val pow2_eight (c0 c1 c2 c3 c4 c5 c6 c7: nat) : nat\nlet pow2_eight (c0 c1 c2 c3 c4 c5 c6 c7:nat) : nat = pow2_seven c0 c1 c2 c3 c4 c5 c6 + pow2_448 * c7", "val taint_arg_b8 (a: arg{Some? (taint_of_arg a)}) : GTot b8\nlet taint_arg_b8 (a:arg{Some? (taint_of_arg a)}) : GTot b8 =\n let (| tag, x |) = a in\n match tag with\n | TD_Buffer src _ _ -> Buffer true (x <: B.buffer (base_typ_as_type src))\n | TD_ImmBuffer src _ _ -> imm_to_b8 src x", "val transpose8x8_lseq_is_transposewxw: #t:v_inttype -> vs:lseq (vec_t t 8) 8 ->\n Lemma (transposewxw_lseq 3 vs `Seq.equal` f_lseq8 vs transpose8x8_012)\nlet transpose8x8_lseq_is_transposewxw #t vs0 =\n let n = 3 in\n Loops.unfold_repeati n (transposewxw_f #8 n) vs0 2;\n Loops.unfold_repeati n (transposewxw_f #8 n) vs0 1;\n Loops.unfold_repeati n (transposewxw_f #8 n) vs0 0;\n Loops.eq_repeati0 n (transposewxw_f #8 n) vs0;\n\n let res0 = transposewxw_f n 0 vs0 in\n eq_intro res0 (f_lseq8 vs0 transpose8x8_0);\n let res1 = transposewxw_f n 1 res0 in\n eq_intro res1 (f_lseq8 res0 transpose8x8_1);\n let res2 = transposewxw_f n 2 res1 in\n eq_intro res2 (f_lseq8 res1 transpose8x8_2);\n eq_intro (transposewxw_lseq 3 vs0) (f_lseq8 vs0 transpose8x8_012)", "val create16: #a:Type\n -> x0:a -> x1:a -> x2:a -> x3:a -> x4:a -> x5:a -> x6:a -> x7:a\n -> x8:a -> x9:a -> x10:a -> x11:a -> x12:a -> x13:a -> x14:a -> x15:a -> lseq a 16\nlet create16 #a x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 =\n let l = [x0; x1; x2; x3; x4; x5; x6; x7; x8; x9; x10; x11; x12; x13; x14; x15] in\n assert_norm (List.Tot.length l = 16);\n createL l", "val transpose8x8_2: #t:v_inttype -> vec_t8 t -> vec_t8 t\nlet transpose8x8_2 #t (v0,v1,v2,v3,v4,v5,v6,v7) =\n let v0' = vec_interleave_low_n 4 v0 v4 in\n let v4' = vec_interleave_high_n 4 v0 v4 in\n let v1' = vec_interleave_low_n 4 v1 v5 in\n let v5' = vec_interleave_high_n 4 v1 v5 in\n let v2' = vec_interleave_low_n 4 v2 v6 in\n let v6' = vec_interleave_high_n 4 v2 v6 in\n let v3' = vec_interleave_low_n 4 v3 v7 in\n let v7' = vec_interleave_high_n 4 v3 v7 in\n (v0',v1',v2',v3',v4',v5',v6',v7')", "val lemma_store_felem_hi: f:tup64_5 -> hi:uint64 ->\n Lemma\n (requires tup64_fits5 f (1, 1, 1, 1, 1))\n (ensures\n (let (f0, f1, f2, f3, f4) = f in\n let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in\n v hi == v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64))\nlet lemma_store_felem_hi f hi =\n let (f0, f1, f2, f3, f4) = f in\n assert_norm (max26 = pow2 26 - 1);\n let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in\n FStar.Math.Lemmas.lemma_div_lt (v f2) 26 12;\n assert (v f2 / pow2 12 < pow2 14);\n\n assert (v (f3 <<. 14ul) == v f3 * pow2 14 % pow2 64);\n FStar.Math.Lemmas.lemma_mult_le_right (pow2 14) (v f3) (pow2 26);\n assert_norm (pow2 26 * pow2 14 = pow2 40);\n assert_norm (pow2 40 < pow2 64);\n FStar.Math.Lemmas.modulo_lemma (v f3 * pow2 14) (pow2 64);\n FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f3) 14 14;\n assert ((v f3 * pow2 14) % pow2 14 = 0);\n logor_disjoint (f2 >>. 12ul) (f3 <<. 14ul) 14;\n assert (v ((f2 >>. 12ul) |. (f3 <<. 14ul)) == v f2 / pow2 12 + v f3 * pow2 14);\n\n FStar.Math.Lemmas.lemma_mult_le_right (pow2 14) (v f3) (pow2 26 - 1);\n assert (v f2 / pow2 12 + v f3 * pow2 14 < pow2 40);\n FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v f4 * pow2 40) 40 64;\n assert (((v f4 * pow2 40) % pow2 64) % pow2 40 = (v f4 * pow2 40) % pow2 40);\n FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f4) 40 40;\n assert ((v f4 * pow2 40) % pow2 40 = 0);\n logor_disjoint ((f2 >>. 12ul) |. (f3 <<. 14ul)) (f4 <<. 40ul) 40", "val transpose8x8: #t:v_inttype{t = U32} -> vec_t8 t -> vec_t8 t\nlet transpose8x8 #t vs =\n match t with\n | U32 -> transpose8x8_uint32 #t vs", "val transpose (#w: lanes) (f: felem5 w) : lseq tup64_5 w\nlet transpose (#w:lanes) (f:felem5 w) : lseq tup64_5 w =\n let (f0,f1,f2,f3,f4) = f in\n let v0 = vec_v f0 in\n let v1 = vec_v f1 in\n let v2 = vec_v f2 in\n let v3 = vec_v f3 in\n let v4 = vec_v f4 in\n createi #tup64_5 w (fun i -> (v0.[i],v1.[i],v2.[i],v3.[i],v4.[i]))", "val transpose8x8_1: #t:v_inttype -> vec_t8 t -> vec_t8 t\nlet transpose8x8_1 #t (v0,v1,v2,v3,v4,v5,v6,v7) =\n let v0' = vec_interleave_low_n 2 v0 v2 in\n let v2' = vec_interleave_high_n 2 v0 v2 in\n let v1' = vec_interleave_low_n 2 v1 v3 in\n let v3' = vec_interleave_high_n 2 v1 v3 in\n let v4' = vec_interleave_low_n 2 v4 v6 in\n let v6' = vec_interleave_high_n 2 v4 v6 in\n let v5' = vec_interleave_low_n 2 v5 v7 in\n let v7' = vec_interleave_high_n 2 v5 v7 in\n (v0',v1',v2',v3',v4',v5',v6',v7')", "val precomp_r5_as_tup64:\n #w:lanes\n -> r:felem5 w{felem_fits5 r (2, 2, 2, 2, 2)}\n -> i:nat{i < w} ->\n Lemma\n (let r5 = precomp_r5 r in\n let (tr50, tr51, tr52, tr53, tr54) = as_tup64_i r5 i in\n let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in\n tr50 == tr0 *! u64 5 /\\\n tr51 == tr1 *! u64 5 /\\\n tr52 == tr2 *! u64 5 /\\\n tr53 == tr3 *! u64 5 /\\\n tr54 == tr4 *! u64 5)\nlet precomp_r5_as_tup64 #w r i =\n let r5 = precomp_r5 r in\n let (r50, r51, r52, r53, r54) = r5 in\n let (r0, r1, r2, r3, r4) = r in\n let (tr50, tr51, tr52, tr53, tr54) = as_tup64_i r5 i in\n let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in\n assert_norm (max26 = pow2 26 - 1);\n FStar.Math.Lemmas.modulo_lemma (5 * v tr0) (pow2 64);\n FStar.Math.Lemmas.modulo_lemma (5 * v tr1) (pow2 64);\n FStar.Math.Lemmas.modulo_lemma (5 * v tr2) (pow2 64);\n FStar.Math.Lemmas.modulo_lemma (5 * v tr3) (pow2 64);\n FStar.Math.Lemmas.modulo_lemma (5 * v tr4) (pow2 64);\n assert (v tr50 == v (tr0 *! u64 5));\n assert (v tr51 == v (tr1 *! u64 5));\n assert (v tr52 == v (tr2 *! u64 5));\n assert (v tr53 == v (tr3 *! u64 5));\n assert (v tr54 == v (tr4 *! u64 5))", "val exp_four_fw_f\n (#t: Type)\n (k: concrete_ops t)\n (a1: t)\n (bBits: nat)\n (b1: nat{b1 < pow2 bBits})\n (a2: t)\n (b2: nat{b2 < pow2 bBits})\n (a3: t)\n (b3: nat{b3 < pow2 bBits})\n (a4: t)\n (b4: nat{b4 < pow2 bBits})\n (l: pos)\n (i: nat{i < bBits / l})\n (acc: t)\n : t\nlet exp_four_fw_f (#t:Type) (k:concrete_ops t)\n (a1:t) (bBits:nat) (b1:nat{b1 < pow2 bBits})\n (a2:t) (b2:nat{b2 < pow2 bBits})\n (a3:t) (b3:nat{b3 < pow2 bBits})\n (a4:t) (b4:nat{b4 < pow2 bBits})\n (l:pos) (i:nat{i < bBits / l}) (acc:t) : t\n =\n let acc = exp_fw_f k a4 bBits b4 l i acc in\n let acc = mul_acc_pow_a_bits_l k a3 bBits b3 l i acc in\n let acc = mul_acc_pow_a_bits_l k a2 bBits b2 l i acc in\n let acc = mul_acc_pow_a_bits_l k a1 bBits b1 l i acc in\n acc", "val equal (#a:Type) (#len:flen) (s1:ntuple a len) (s2:ntuple a len) : Type0\nlet equal #a #len s1 s2 =\n (forall (i:size_nat{i < len}).{:pattern (index s1 i); (index s2 i)} index s1 i == index s2 i)", "val refl (a: LSeq.lseq uint64 20 {F51.linv a}) : GTot a_spec\nlet refl (a:LSeq.lseq uint64 20{F51.linv a}) : GTot a_spec =\n S.to_aff_point (F51.refl_ext_point a)", "val refl (a: LSeq.lseq uint64 4 {linv a}) : GTot S.qelem\nlet refl (a:LSeq.lseq uint64 4{linv a}) : GTot S.qelem =\n SM.from_qmont (BD.bn_v a)", "val refl (a: LSeq.lseq uint64 4 {linv a}) : GTot S.qelem\nlet refl (a:LSeq.lseq uint64 4{linv a}) : GTot S.qelem =\n SD.bn_v #U64 #4 a", "val exp_four_fw_acc0\n (#t: Type)\n (k: comm_monoid t)\n (a1: t)\n (bBits: nat)\n (b1: nat{b1 < pow2 bBits})\n (a2: t)\n (b2: nat{b2 < pow2 bBits})\n (a3: t)\n (b3: nat{b3 < pow2 bBits})\n (a4: t)\n (b4: nat{b4 < pow2 bBits})\n (l: pos{bBits % l <> 0})\n : t\nlet exp_four_fw_acc0 (#t:Type) (k:comm_monoid t)\n (a1:t) (bBits:nat) (b1:nat{b1 < pow2 bBits})\n (a2:t) (b2:nat{b2 < pow2 bBits})\n (a3:t) (b3:nat{b3 < pow2 bBits})\n (a4:t) (b4:nat{b4 < pow2 bBits})\n (l:pos{bBits % l <> 0}) : t =\n let acc_a12 = exp_double_fw_acc0 k a1 bBits b1 a2 b2 l in\n let acc_a34 = exp_double_fw_acc0 k a3 bBits b3 a4 b4 l in\n mul acc_a12 acc_a34", "val lemma_tup64_pow2_128: f:tup64_5 ->\n Lemma\n (requires tup64_fits5 f (1, 1, 1, 1, 1))\n (ensures\n (let (f0, f1, f2, f3, f4) = f in\n v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104 < pow2 128))\nlet lemma_tup64_pow2_128 f =\n let (f0, f1, f2, f3, f4) = f in\n let tmp = v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104 in\n assert (tmp <= pow2 26 - 1 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 +\n (pow2 26 - 1) * pow78 + (pow2 24 - 1) * pow104);\n assert (tmp <= pow2 24 * pow104 - 1);\n assert_norm (pow2 24 * pow104 = pow2 128)", "val pow2_nine (c0 c1 c2 c3 c4 c5 c6 c7 c8: nat) : nat\nlet pow2_nine (c0 c1 c2 c3 c4 c5 c6 c7 c8:nat) : nat = pow2_eight c0 c1 c2 c3 c4 c5 c6 c7 + pow2_512 * c8", "val repeat_l\n (#a: _)\n (block_length: pos{block_length < pow2 32})\n (update_last: (a -> s: S.seq uint8 {S.length s < block_length} -> a))\n (input: S.seq uint8)\n (l: Lib.IntTypes.size_nat{l < block_length})\n (s: Lib.Sequence.lseq uint8 l)\n (acc: a)\n : a\nlet repeat_l #a (block_length:pos { block_length < pow2 32 })\n (update_last: (a -> s:S.seq uint8 { S.length s < block_length } -> a))\n (input:S.seq uint8)\n (l: Lib.IntTypes.size_nat { l < block_length })\n (s: Lib.Sequence.lseq uint8 l)\n (acc: a): a\n=\n update_last acc s", "val transpose8x8_012: #t:v_inttype -> vec_t8 t -> vec_t8 t\nlet transpose8x8_012 #t vs0 =\n let (v0,v1,v2,v3,v4,v5,v6,v7) = vs0 in\n let (v0',v1',v2',v3',v4',v5',v6',v7') = transpose8x8_0 #t (v0,v1,v2,v3,v4,v5,v6,v7) in\n let (v0',v1',v2',v3',v4',v5',v6',v7') = transpose8x8_1 #t (v0',v1',v2',v3',v4',v5',v6',v7') in\n let (v0',v1',v2',v3',v4',v5',v6',v7') = transpose8x8_2 #t (v0',v1',v2',v3',v4',v5',v6',v7') in\n (v0',v1',v2',v3',v4',v5',v6',v7')", "val as_tup5: #w:lanes -> f:lseq (uint64xN w) 5 -> GTot (felem5 w)\nlet as_tup5 #w s =\n (s.[0], s.[1], s.[2], s.[3], s.[4])", "val uints_to_bytes_le_inner: #t:inttype{unsigned t} -> #l:secrecy_level\n -> #len:size_nat{len * numbytes t < pow2 32}\n -> lseq (int_t t l) len\n -> i:nat{i < len} -> unit -> unit & (lseq (uint_t U8 l) (numbytes t))\nlet uints_to_bytes_le_inner #t #l #len b i () =\n let open Lib.Sequence in\n (), uint_to_bytes_le #t #l b.[i]", "val prefix_l:List.Tot.llist U8.t 11\nlet prefix_l: List.Tot.llist U8.t 11 =\n // : \"tls13 quic \"\n [@inline_let]\n let l = [0x74uy; 0x6cuy; 0x73uy; 0x31uy; 0x33uy;\n 0x20uy; 0x71uy; 0x75uy; 0x69uy; 0x63uy; 0x20uy] in\n assert_norm (List.Tot.length l == 11);\n l", "val transposewxw_f: #w:width -> #t:v_inttype -> n:nat{pow2 n == w} -> i:nat{i < n} -> lseq (vec_t t w) w -> lseq (vec_t t w) w\nlet transposewxw_f #w #t n i vs =\n createi w (transposewxw_f_l #w n i vs)", "val lemma_tup64_mod_pow2_128: f:tup64_5 ->\n Lemma\n (requires tup64_fits5 f (1, 1, 1, 1, 1))\n (ensures\n (let (f0, f1, f2, f3, f4) = f in\n (as_nat5 f) % pow2 128 == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104))\nlet lemma_tup64_mod_pow2_128 f =\n let (f0, f1, f2, f3, f4) = f in\n let tmp = v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 in\n\n calc (==) {\n (as_nat5 f) % pow2 128;\n (==) { }\n (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % pow2 128;\n (==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f4 * pow104) (pow2 128) }\n (tmp + (v f4 * pow104 % pow2 128)) % pow2 128;\n (==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 128 104 }\n (tmp + (v f4 % pow2 24) * pow104) % pow2 128;\n (==) { lemma_tup64_pow2_128 f; FStar.Math.Lemmas.modulo_lemma (tmp + (v f4 % pow2 24) * pow104) (pow2 128) }\n tmp + (v f4 % pow2 24) * pow104;\n };\n assert ((as_nat5 f) % pow2 128 == tmp + (v f4 % pow2 24) * pow104)", "val split_n: #a:eqtype -> (l:list a) -> n:nat{0 < n /\\ n < length l} ->\n Tot (l_tup:(list a * list a){(fst l_tup)@(snd l_tup) = l\n /\\ length (fst l_tup) < length l\n /\\ length (snd l_tup) < length l\n /\\ permutation_2 l (fst l_tup) (snd l_tup)})\nlet rec split_n #a l n =\n match l with\n | hd::tl -> if n = 1 then ([hd],tl)\n else let next = split_n tl (n-1) in ((hd::(fst next)),(snd next))", "val lemma_store_felem_lo:\n f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}\n -> lo:uint64 ->\n Lemma\n (let (f0, f1, f2, f3, f4) = f in\n let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in\n v lo == v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64)\nlet lemma_store_felem_lo f lo =\n let (f0, f1, f2, f3, f4) = f in\n assert_norm (max26 = pow2 26 - 1);\n let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in\n assert (v (f1 <<. 26ul) == v f1 * pow2 26 % pow2 64);\n FStar.Math.Lemmas.modulo_lemma (v f1 * pow2 26) (pow2 64);\n FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f1) 26 26;\n logor_disjoint f0 (f1 <<. 26ul) 26;\n assert (v (f0 |. (f1 <<. 26ul)) == v f0 + v f1 * pow2 26);\n\n assert_norm (pow2 26 * pow2 26 = pow2 52);\n assert (v f0 + v f1 * pow2 26 < pow2 52);\n assert (((v f2 * pow2 52) % pow2 64) % pow2 52 = 0);\n logor_disjoint (f0 |. (f1 <<. 26ul)) (f2 <<. 52ul) 52", "val list_iv (a: alg) : List.Tot.llist (pub_word_t a) 8\nlet list_iv (a:alg): List.Tot.llist (pub_word_t a) 8 =\n match a with\n | Blake2S -> list_iv_S\n | Blake2B -> list_iv_B", "val lprecomp_table_mul:\n #a_t:inttype_a\n -> len:size_t{v len > 0}\n -> ctx_len:size_t\n -> k:concrete_ops a_t len ctx_len\n -> ctx:lbuffer (uint_t a_t SEC) ctx_len\n -> a:lbuffer (uint_t a_t SEC) len\n -> i:size_t\n -> ti:lbuffer (uint_t a_t SEC) len\n -> res:lbuffer (uint_t a_t SEC) len ->\n Stack unit\n (requires fun h ->\n live h a /\\ live h ti /\\ live h ctx /\\ live h res /\\\n disjoint a ti /\\ disjoint a ctx /\\ disjoint a res /\\\n disjoint ti ctx /\\ disjoint ti res /\\ disjoint ctx res /\\\n k.to.linv (as_seq h a) /\\ k.to.linv_ctx (as_seq h ctx) /\\\n k.to.linv (as_seq h ti) /\\\n k.to.refl (as_seq h ti) == S.pow k.to.comm_monoid (k.to.refl (as_seq h a)) (2 * v i + 2))\n (ensures fun h0 _ h1 -> modifies (loc res) h0 h1 /\\\n k.to.linv (as_seq h1 res) /\\\n k.to.refl (as_seq h1 res) == S.pow k.to.comm_monoid (k.to.refl (as_seq h0 a)) (2 * v i + 3))\nlet lprecomp_table_mul #a_t len ctx_len k ctx a i ti res =\n let h0 = ST.get () in\n k.lmul ctx a ti res;\n let h1 = ST.get () in\n assert (k.to.refl (as_seq h1 res) ==\n k.to.comm_monoid.S.mul (k.to.refl (as_seq h0 a)) (k.to.refl (as_seq h0 ti)));\n k.to.comm_monoid.lemma_mul_comm (k.to.refl (as_seq h0 a)) (k.to.refl (as_seq h0 ti));\n S.lemma_pow_add k.to.comm_monoid (k.to.refl (as_seq h0 a)) (2 * v i + 2) 1;\n S.lemma_pow1 k.to.comm_monoid (k.to.refl (as_seq h0 a))", "val nat32_xor_bytewise_2_helper2 (x x': nat32) (t t': four nat8)\n : Lemma\n (requires\n x == four_to_nat 8 t /\\ x' == four_to_nat 8 t' /\\\n x * 0x10000 % 0x100000000 == x' * 0x10000 % 0x100000000)\n (ensures t.lo0 == t'.lo0 /\\ t.lo1 == t'.lo1)\nlet nat32_xor_bytewise_2_helper2 (x x':nat32) (t t':four nat8) : Lemma\n (requires\n x == four_to_nat 8 t /\\\n x' == four_to_nat 8 t' /\\\n x * 0x10000 % 0x100000000 == x' * 0x10000 % 0x100000000\n )\n (ensures t.lo0 == t'.lo0 /\\ t.lo1 == t'.lo1)\n =\n let Mkfour t0 t1 t2 t3 = t in\n let Mkfour t0' t1' t2' t3' = t' in\n let t01 = t0 + 0x100 * t1 in\n let t23 = t2 + 0x100 * t3 in\n let t01' = t0' + 0x100 * t1' in\n let t23' = t2' + 0x100 * t3' in\n assert_norm (four_to_nat 8 t == four_to_nat_unfold 8 t );\n assert_norm (four_to_nat 8 t' == four_to_nat_unfold 8 t');\n nat32_xor_bytewise_2_helper1 t01 t01' t23 t23' x x';\n ()", "val load_tup64_lemma0:\n f:tup64_5\n -> lo:uint64\n -> hi:uint64 ->\n Lemma\n (requires\n (let (f0, f1, f2, f3, f4) = f in\n v f0 == v lo % pow2 26 /\\\n v f1 == (v lo / pow2 26) % pow2 26 /\\\n v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12 /\\\n v f3 == (v hi / pow2 14) % pow2 26 /\\\n v f4 == v hi / pow2 40))\n (ensures as_nat5 f == v hi * pow2 64 + v lo)\nlet load_tup64_lemma0 f lo hi =\n let (f0, f1, f2, f3, f4) = f in\n calc (==) {\n as_nat5 f;\n (==) { }\n v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104;\n (==) { }\n v lo % pow2 26 + (v lo / pow2 26) % pow2 26 * pow26 +\n v lo / pow2 52 * pow52 + (v hi % pow2 14) * pow2 12 * pow52 +\n (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;\n (==) { load_tup64_lemma0_lo lo }\n v lo + (v hi % pow2 14) * pow2 12 * pow52 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;\n (==) { assert_norm (pow2 12 * pow52 = pow2 64) }\n v lo + (v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;\n (==) { load_tup64_lemma0_hi hi }\n v lo + v hi * pow2 64;\n };\n assert (as_nat5 f == v hi * pow2 64 + v lo)", "val index_uints_to_bytes_le_aux:\n #t:inttype{unsigned t /\\ ~(U1? t)}\n -> #l:secrecy_level\n -> len:nat{len * numbytes t < pow2 32}\n -> n:nat{n < pow2 (bits t * len)}\n -> i:nat{i < len * numbytes t}\n -> Lemma (let s:lseq (int_t t l) len = nat_to_intseq_le #t #l len n in\n Seq.index (uints_to_bytes_le #t #l #len s) i ==\n Seq.index (nat_to_bytes_le #l (numbytes t) (v s.[i / numbytes t])) (i % numbytes t))\nlet index_uints_to_bytes_le_aux #t #l len n i =\n let open Lib.Sequence in\n let s: lseq (int_t t l) len = nat_to_intseq_le #t #l len n in\n index_generate_blocks (numbytes t) len len\n (uints_to_bytes_le_inner #t #l #len s) i", "val uints_to_bytes_be_inner: #t:inttype{unsigned t} -> #l:secrecy_level\n -> #len:size_nat{len * numbytes t < pow2 32}\n -> lseq (int_t t l) len\n -> i:nat{i < len} -> unit -> unit & (lseq (uint_t U8 l) (numbytes t))\nlet uints_to_bytes_be_inner #t #l #len b i () =\n let open Lib.Sequence in\n (), uint_to_bytes_be #t #l b.[i]", "val frodo_key_encode2:\n logq:size_t{0 < v logq /\\ v logq <= 16}\n -> b:size_t{0 < v b /\\ v b <= 8 /\\ v b <= v logq}\n -> n:size_t{v n == 8}\n -> a:lbytes (n *! n *! b /. size 8)\n -> i:size_t{v i < v n}\n -> x:uint64\n -> res:matrix_t n n\n -> Stack unit\n (requires fun h ->\n live h a /\\ live h res /\\ disjoint a res)\n (ensures fun h0 _ h1 -> modifies1 res h0 h1 /\\\n as_matrix h1 res ==\n Loops.repeati 8 (S.frodo_key_encode0 (v logq) (v b) (v n) (as_seq h0 a) x (v i)) (as_matrix h0 res))\nlet frodo_key_encode2 logq b n a i x res =\n [@ inline_let]\n let spec h0 = S.frodo_key_encode0 (v logq) (v b) (v n) (as_seq h0 a) x (v i) in\n let h0 = ST.get () in\n loop1 h0 (size 8) res spec\n (fun k ->\n Loops.unfold_repeati 8 (spec h0) (as_seq h0 res) (v k);\n mset res i k (ec1 logq b x k)\n )", "val nat_to_intseq_be: #t:inttype{unsigned t} -> #l:secrecy_level -> len:nat -> n:nat{n < pow2 (bits t * len)} ->\n b:seq (uint_t t l){length b == len /\\ n == nat_from_intseq_be b}\nlet nat_to_intseq_be = nat_to_intseq_be_", "val load_tup64_lemma: lo:uint64 -> hi:uint64 ->\n Pure tup64_5\n (requires True)\n (ensures fun f ->\n tup64_fits5 f (1, 1, 1, 1, 1) /\\\n as_nat5 f < pow2 128 /\\\n as_nat5 f % prime == v hi * pow2 64 + v lo)\nlet load_tup64_lemma lo hi =\n let mask26 = u64 0x3ffffff in\n assert_norm (0x3ffffff = pow2 26 - 1);\n assert_norm (0x3fff = pow2 14 - 1);\n\n let f0 = lo &. mask26 in\n mod_mask_lemma lo 26ul;\n assert (v (mod_mask #U64 #SEC 26ul) == v mask26);\n assert (v f0 == v lo % pow2 26);\n\n let f1 = (lo >>. 26ul) &. mask26 in\n assert (v f1 == (v lo / pow2 26) % pow2 26);\n\n let f2 = (lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul) in\n load_tup64_lemma_f2 lo hi;\n assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12);\n\n let f3 = (hi >>. 14ul) &. mask26 in\n assert (v f3 == (v hi / pow2 14) % pow2 26);\n\n let f4 = hi >>. 40ul in\n assert (v f4 == v hi / pow2 40);\n\n let f = (f0, f1, f2, f3, f4) in\n load_tup64_lemma0 f lo hi;\n load_tup64_fits_lemma f lo hi;\n assert (as_nat5 f < pow2 128);\n assert_norm (pow2 128 < prime);\n FStar.Math.Lemmas.small_modulo_lemma_1 (as_nat5 f) prime;\n assert (as_nat5 f % prime == v hi * pow2 64 + v lo);\n f", "val transpose8 (st: state 8) : state 8\nlet transpose8 (st:state 8) : state 8 =\n let (v0,v1,v2,v3,v4,v5,v6,v7) = VecTranspose.transpose8x8 (st.[0],st.[1],st.[2],st.[3],st.[4],st.[5],st.[6],st.[7]) in\n let (v8,v9,v10,v11,v12,v13,v14,v15) = VecTranspose.transpose8x8 (st.[8],st.[9],st.[10],st.[11],st.[12],st.[13],st.[14],st.[15]) in\n create16 v0 v8 v1 v9 v2 v10 v3 v11 v4 v12 v5 v13 v6 v14 v7 v15", "val int_to_nat8 (i: int) : n: nat8{0 <= i && i < pow2_8 ==> i == n}\nlet int_to_nat8 (i:int) : n:nat8{0 <= i && i < pow2_8 ==> i == n} =\n Vale.Def.Words_s.int_to_natN pow2_8 i", "val n_to_be_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat{len + 1 <= tot /\\ tot < pow2 32})\n (ih: n_to_be_t u len)\n : Tot (n_to_be_t u (len + 1))\nlet n_to_be_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat {len + 1 <= tot /\\ tot < pow2 32})\n (ih: n_to_be_t u len)\n: Tot (n_to_be_t u (len + 1))\n= fun n ->\n reveal_n_to_be (len + 1) (u.v n);\n let lo = u.to_byte n in\n let hi = u.div256 n in\n let seq_hi = ih hi in\n let seq_lo = B.create 1ul lo in\n seq_hi `B.append` seq_lo", "val eq_mask: a:t -> b:t -> Tot (c:t{(v a = v b ==> v c = pow2 n - 1) /\\ (v a <> v b ==> v c = 0)})\nlet eq_mask (a b: t) : Pure t\n (requires True)\n (ensures (fun r -> (v a = v b ==> v r = pow2 128 - 1) /\\ (v a <> v b ==> v r = 0))) =\n let mask = U64.logand (U64.eq_mask a.low b.low)\n (U64.eq_mask a.high b.high) in\n { low = mask; high = mask; }", "val nat32_xor_bytewise_3_helper2 (x x': nat32) (t t': four nat8)\n : Lemma\n (requires\n x == four_to_nat 8 t /\\ x' == four_to_nat 8 t' /\\\n x * 0x100 % 0x100000000 == x' * 0x100 % 0x100000000)\n (ensures t.lo0 == t'.lo0 /\\ t.lo1 == t'.lo1 /\\ t.hi2 == t'.hi2)\nlet nat32_xor_bytewise_3_helper2 (x x':nat32) (t t':four nat8) : Lemma\n (requires\n x == four_to_nat 8 t /\\\n x' == four_to_nat 8 t' /\\\n x * 0x100 % 0x100000000 == x' * 0x100 % 0x100000000\n )\n (ensures t.lo0 == t'.lo0 /\\ t.lo1 == t'.lo1 /\\ t.hi2 == t'.hi2)\n =\n let Mkfour t0 t1 t2 t3 = t in\n let Mkfour t0' t1' t2' t3' = t' in\n let t012 = t0 + 0x100 * t1 + 0x10000 * t2 in\n let t012' = t0' + 0x100 * t1' + 0x10000 * t2' in\n assert_norm (four_to_nat 8 t == four_to_nat_unfold 8 t );\n assert_norm (four_to_nat 8 t' == four_to_nat_unfold 8 t');\n nat32_xor_bytewise_3_helper1 t012 t012' t3 t3' x x';\n ()", "val exp_four_fw_f\n (#t: Type)\n (k: comm_monoid t)\n (a1: t)\n (bBits: nat)\n (b1: nat{b1 < pow2 bBits})\n (a2: t)\n (b2: nat{b2 < pow2 bBits})\n (a3: t)\n (b3: nat{b3 < pow2 bBits})\n (a4: t)\n (b4: nat{b4 < pow2 bBits})\n (l: pos)\n (i: nat{i < bBits / l})\n (acc: t)\n : t\nlet exp_four_fw_f (#t:Type) (k:comm_monoid t)\n (a1:t) (bBits:nat) (b1:nat{b1 < pow2 bBits})\n (a2:t) (b2:nat{b2 < pow2 bBits})\n (a3:t) (b3:nat{b3 < pow2 bBits})\n (a4:t) (b4:nat{b4 < pow2 bBits})\n (l:pos) (i:nat{i < bBits / l}) (acc:t) : t\n =\n let acc = exp_fw_f k a4 bBits b4 l i acc in\n let acc = mul_acc_pow_a_bits_l k a3 bBits b3 l i acc in\n let acc = mul_acc_pow_a_bits_l k a2 bBits b2 l i acc in\n let acc = mul_acc_pow_a_bits_l k a1 bBits b1 l i acc in\n acc", "val h256_l:List.llist uint32 8\nlet h256_l: List.llist uint32 8 =\n [@inline_let]\n let l =\n [u32 0x6a09e667; u32 0xbb67ae85; u32 0x3c6ef372; u32 0xa54ff53a;\n u32 0x510e527f; u32 0x9b05688c; u32 0x1f83d9ab; u32 0x5be0cd19]\n in\n assert_norm (List.length l = 8);\n l", "val lemma_felem64_mod255: a:lseq uint64 4 ->\n Lemma (let r = a.[3] <- (a.[3] &. u64 0x7fffffffffffffff) in\n BSeq.nat_from_intseq_le r == BSeq.nat_from_intseq_le a % pow2 255)\nlet lemma_felem64_mod255 a =\n lemma_carry_pass_store_f3 a;\n let a3' = a.[3] &. u64 0x7fffffffffffffff in\n assert (v a3' = v a.[3] % pow2 63);\n\n let r = a.[3] <- a3' in\n SD.bn_upd_eval a a3' 3;\n assert (SD.bn_v r == SD.bn_v a - v a.[3] * pow2 192 + v a3' * pow2 192);\n\n calc (==) { //SD.bn_v a == SD.bn_v r + v a.[3] * pow2 192 - v a3' * pow2 192\n SD.bn_v r + v a.[3] * pow2 192 - v a3' * pow2 192;\n (==) { }\n SD.bn_v r + v a.[3] * pow2 192 - v a.[3] % pow2 63 * pow2 192;\n (==) { Math.Lemmas.distributivity_sub_left (v a.[3]) (v a.[3] % pow2 63) (pow2 192) }\n SD.bn_v r + (v a.[3] - v a.[3] % pow2 63) * pow2 192;\n (==) { Math.Lemmas.euclidean_division_definition (v a.[3]) (pow2 63) }\n SD.bn_v r + v a.[3] / pow2 63 * pow2 63 * pow2 192;\n (==) { Math.Lemmas.paren_mul_right (v a.[3] / pow2 63) (pow2 63) (pow2 192); Math.Lemmas.pow2_plus 63 192 }\n SD.bn_v r + v a.[3] / pow2 63 * pow2 255;\n };\n\n Math.Lemmas.modulo_addition_lemma (SD.bn_v r) (pow2 255) (v a.[3] / pow2 63);\n assert (SD.bn_v a % pow2 255 == SD.bn_v r % pow2 255);\n Math.Lemmas.small_mod (SD.bn_v r) (pow2 255);\n\n Hacl.Spec.Bignum.Convert.bn_v_is_nat_from_intseq_le_lemma 4 r;\n Hacl.Spec.Bignum.Convert.bn_v_is_nat_from_intseq_le_lemma 4 a;\n assert (BSeq.nat_from_intseq_le r == BSeq.nat_from_intseq_le a % pow2 255)", "val int8_to_uint64: a:I8.t -> Tot (b:U64.t{U64.v b = I8.v a % pow2 64})\nlet int8_to_uint64 x = U64.uint_to_t (I8.v x % pow2 64)", "val some_arithmetic: t:inttype{~(U1? t)} -> n:nat -> i:nat -> Lemma\n (let m = numbytes t in\n n / pow2 (bits t * (i / m)) % pow2 (bits t) / pow2 (8 * (i % m)) % pow2 8 ==\n n / pow2 (8 * i) % pow2 8)\nlet some_arithmetic t n i =\n let m = numbytes t in\n calc (==) {\n n / pow2 (bits t * (i / m)) % pow2 (bits t) / pow2 (8 * (i % m)) % pow2 8;\n == { assert (bits t == 8 * m) }\n n / pow2 ((8 * m) * (i / m)) % pow2 (8 * m) / pow2 (8 * (i % m)) % pow2 8;\n == { FStar.Math.Lemmas.paren_mul_right 8 m (i / m);\n FStar.Math.Lemmas.euclidean_division_definition i m }\n n / pow2 (8 * (i - i % m)) % pow2 (8 * m) / pow2 (8 * (i % m)) % pow2 8;\n == { Math.Lemmas.distributivity_sub_right 8 i (i % m) }\n n / pow2 (8 * i - 8 * (i % m)) % pow2 (8 * m) / pow2 (8 * (i % m)) % pow2 8;\n == { modulo_pow2_prop 8 (n / pow2 (8 * i - 8 * (i % m))) m (i % m) }\n (n / pow2 (8 * i - 8 * (i % m))) / pow2 (8 * (i % m)) % pow2 8;\n == { Math.Lemmas.division_multiplication_lemma n\n (pow2 (8 * i - 8 * (i % m))) (pow2 (8 * (i % m))) }\n (n / (pow2 (8 * i - 8 * (i % m)) * pow2 (8 * (i % m)))) % pow2 8;\n == { Math.Lemmas.pow2_plus (8 * i - 8 * (i % m)) (8 * (i % m)) }\n (n / pow2 (8 * i)) % pow2 8;\n }", "val create (#a:Type0) (len:flen) (init:a) : ntuple a len\nlet create #a len init =\n normalize_term (createi #a len (fun i -> init))", "val member: #a:eqtype -> #len: size_nat -> a -> lseq a len -> Tot bool\nlet member #a #len x l = Seq.count x l > 0", "val ivTable (a: alg) : lseq (pub_word_t a) 8\nlet ivTable (a:alg) : lseq (pub_word_t a) 8 =\n match a with\n | Blake2S -> of_list list_iv_S\n | Blake2B -> of_list list_iv_B", "val mul_felem5_lemma:\n f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}\n -> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->\n Lemma\n (let (f10, f11, f12, f13, f14) = f1 in\n let (r0, r1, r2, r3, r4) = r in\n (as_pfelem5 f1) `pfmul` (as_pfelem5 r) ==\n (v f10 * as_nat5 (r0, r1, r2, r3, r4) +\n v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +\n v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +\n v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +\n v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime)\nlet mul_felem5_lemma f1 r =\n let (f10, f11, f12, f13, f14) = f1 in\n let (r0, r1, r2, r3, r4) = r in\n mul_felem5_lemma_4 f1 r;\n FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime;\n FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime", "val load_tup64_fits_lemma:\n f:tup64_5\n -> lo:uint64\n -> hi:uint64 ->\n Lemma\n (requires\n (let (f0, f1, f2, f3, f4) = f in\n v f0 == v lo % pow2 26 /\\\n v f1 == (v lo / pow2 26) % pow2 26 /\\\n v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12 /\\\n v f3 == (v hi / pow2 14) % pow2 26 /\\\n v f4 == v hi / pow2 40))\n (ensures tup64_fits5 f (1, 1, 1, 1, 1))\nlet load_tup64_fits_lemma f lo hi =\n let (f0, f1, f2, f3, f4) = f in\n assert_norm (pow26 = pow2 26);\n FStar.Math.Lemmas.lemma_div_lt_nat (v lo) 64 52;\n lemma_mult_le (v hi % pow2 14) (pow2 14 - 1) (pow2 12) (pow2 12);\n assert_norm (pow2 14 * pow2 12 = pow2 26);\n FStar.Math.Lemmas.lemma_div_lt_nat (v hi) 64 40;\n assert_norm (pow2 24 < pow2 26)", "val lemma_len_lt_max_a_mul_by_8: a:sha2_alg -> len:len_lt_max_a_t a ->\n Lemma (let len' : len_t a = mk_len_t a len in\n let total_len_bits = secret (shift_left #(len_int_type a) len' 3ul) in\n v total_len_bits == len * 8)\nlet lemma_len_lt_max_a_mul_by_8 a len =\n match a with\n | SHA2_224 | SHA2_256 -> Math.Lemmas.pow2_plus 61 3\n | SHA2_384 | SHA2_512 -> Math.Lemmas.pow2_plus 125 3", "val precomp_base_table_list\n (#t: Type)\n (#a_t: BE.inttype_a)\n (#len: size_t{v len > 0})\n (#ctx_len: size_t)\n (k: mk_precomp_base_table t a_t len ctx_len)\n (g: t)\n (n: nat)\n : x: list (uint_t a_t SEC) {FL.length x = (n + 1) * v len}\nlet precomp_base_table_list (#t:Type) (#a_t:BE.inttype_a) (#len:size_t{v len > 0}) (#ctx_len:size_t)\n (k:mk_precomp_base_table t a_t len ctx_len) (g:t) (n:nat) :\n x:list (uint_t a_t SEC){FL.length x = (n + 1) * v len} =\n snd (precomp_base_table_list_rec k g n (g, k.to_list (k.concr_ops.SE.one ())))", "val frodo_pack8:\n d:size_t{v d <= 16}\n -> a:lbuffer uint16 8ul\n -> res:lbytes d\n -> Stack unit\n (requires fun h0 -> live h0 a /\\ live h0 res /\\ disjoint a res)\n (ensures fun h0 _ h1 ->\n modifies1 res h0 h1 /\\\n as_seq h1 res == S.frodo_pack8 (v d) (as_seq h0 a))\nlet frodo_pack8 d a res =\n let h0 = ST.get() in\n push_frame();\n let maskd = to_u16 (u32 1 <<. d) -. u16 1 in\n let v16 = create (size 16) (u8 0) in\n let a0 = index a (size 0) &. maskd in\n let a1 = index a (size 1) &. maskd in\n let a2 = index a (size 2) &. maskd in\n let a3 = index a (size 3) &. maskd in\n let a4 = index a (size 4) &. maskd in\n let a5 = index a (size 5) &. maskd in\n let a6 = index a (size 6) &. maskd in\n let a7 = index a (size 7) &. maskd in\n let templong =\n to_u128 a0 <<. (size 7 *! d)\n |. to_u128 a1 <<. (size 6 *! d)\n |. to_u128 a2 <<. (size 5 *! d)\n |. to_u128 a3 <<. (size 4 *! d)\n |. to_u128 a4 <<. (size 3 *! d)\n |. to_u128 a5 <<. (size 2 *! d)\n |. to_u128 a6 <<. (size 1 *! d)\n |. to_u128 a7 <<. (size 0 *! d)\n in\n uint_to_bytes_be v16 templong;\n let src = sub v16 (size 16 -! d) d in // Skips the 1st byte when d = 15\n copy res src;\n pop_frame()", "val exp_four_fw\n (#t: Type)\n (k: comm_monoid t)\n (a1: t)\n (bBits: nat)\n (b1: nat{b1 < pow2 bBits})\n (a2: t)\n (b2: nat{b2 < pow2 bBits})\n (a3: t)\n (b3: nat{b3 < pow2 bBits})\n (a4: t)\n (b4: nat{b4 < pow2 bBits})\n (l: pos)\n : t\nlet exp_four_fw (#t:Type) (k:comm_monoid t)\n (a1:t) (bBits:nat) (b1:nat{b1 < pow2 bBits})\n (a2:t) (b2:nat{b2 < pow2 bBits})\n (a3:t) (b3:nat{b3 < pow2 bBits})\n (a4:t) (b4:nat{b4 < pow2 bBits})\n (l:pos) : t =\n let acc0 =\n if bBits % l = 0 then one\n else exp_four_fw_acc0 k a1 bBits b1 a2 b2 a3 b3 a4 b4 l in\n Loops.repeati (bBits / l)\n (exp_four_fw_f k a1 bBits b1 a2 b2 a3 b3 a4 b4 l) acc0", "val nat_to_intseq_le: #t:inttype{unsigned t} -> #l:secrecy_level -> len:nat -> n:nat{n < pow2 (bits t * len)} ->\n b:seq (uint_t t l){length b == len /\\ n == nat_from_intseq_le b}\nlet nat_to_intseq_le = nat_to_intseq_le_", "val lemma_mask48: a:uint64 ->\n Lemma (let r = a &. mask48 in\n v r = v a % pow2 48 /\\ felem_fits_last1 r 1)\nlet lemma_mask48 a =\n let r = a &. mask48 in\n assert_norm (v mask48 = pow2 48 - 1);\n mod_mask_lemma a 48ul;\n assert (v (mod_mask #U64 #SEC 48ul) == v mask48);\n assert (v r = v a % pow2 48);\n assert (felem_fits_last1 r 1)", "val gmap (#a:Type) (#b:Type) (#len:flen) (f:a -> GTot b) (s:ntuple a len) : GTot (ntuple b len)\nlet gmap #a #b #len f s =\n normalize_term (gcreatei len (fun i -> f (index s i)))", "val int8_to_uint32: a:I8.t -> Tot (b:U32.t{U32.v b = I8.v a % pow2 32})\nlet int8_to_uint32 x = U32.uint_to_t (I8.v x % pow2 32)" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.tup8_lemma" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.ntup8_lemma" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fst", "name": "Lib.IntVector.Transpose.f_lseq8" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fsti", "name": "Lib.IntVector.Transpose.transpose8x8_lseq" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.ntup4_lemma" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.tup4_lemma" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.tup1_lemma" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.create8" }, { "project_name": "FStar", "file_name": "FStar.Vector.Properties.fst", "name": "FStar.Vector.Properties.tail" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.length" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.fst_" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.rest_" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.from_lseq" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.rest" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.upd" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.fst" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.map" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.to_lseq" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.mapi" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.ntup1_lemma" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.concat" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.concat_" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.index" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas0.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_eval_as_tup64" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.upd_" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fsti", "name": "Vale.Lib.Map16.upd8" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.sub" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fst", "name": "Lib.IntVector.Transpose.transpose8x8_lemma" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fst", "name": "Lib.IntVector.Transpose.f_lseq4" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fst", "name": "Lib.IntVector.Transpose.transposewxw_f_l" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fsti", "name": "Lib.IntVector.Transpose.transpose4x4_lseq" }, { "project_name": "FStar", "file_name": "FStar.Vector.Properties.fst", "name": "FStar.Vector.Properties.head" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Finv.fst", "name": "Hacl.Impl.P256.Finv.refl" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fsti", "name": "Vale.Lib.Map16.sel8" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.K256.Finv.fst", "name": "Hacl.Impl.K256.Finv.refl" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Derived.fst", "name": "FStar.Reflection.V1.Derived.mktuple_n" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Derived.fst", "name": "FStar.Reflection.V2.Derived.mktuple_n" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Field32xN.fst", "name": "Hacl.Spec.Poly1305.Field32xN.as_tup64_i" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fst", "name": "Lib.IntVector.Transpose.transpose8x8_0" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas2.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas2.store_tup64_lemma" }, { "project_name": "FStar", "file_name": "FStar.Int.Cast.fst", "name": "FStar.Int.Cast.int8_to_uint8" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.Fast_defs.fst", "name": "Vale.Curve25519.Fast_defs.pow2_eight" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.X64.fsti", "name": "Vale.Interop.X64.taint_arg_b8" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fst", "name": "Lib.IntVector.Transpose.transpose8x8_lseq_is_transposewxw" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.create16" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fst", "name": "Lib.IntVector.Transpose.transpose8x8_2" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas2.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas2.lemma_store_felem_hi" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fst", "name": "Lib.IntVector.Transpose.transpose8x8" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Field32xN.fst", "name": "Hacl.Spec.Poly1305.Field32xN.transpose" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fst", "name": "Lib.IntVector.Transpose.transpose8x8_1" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas0.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas0.precomp_r5_as_tup64" }, { "project_name": "hacl-star", "file_name": "Spec.Exponentiation.fsti", "name": "Spec.Exponentiation.exp_four_fw_f" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.equal" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Ed25519.Group.fst", "name": "Hacl.Impl.Ed25519.Group.refl" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Qinv.fst", "name": "Hacl.Impl.P256.Qinv.refl" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.K256.Qinv.fst", "name": "Hacl.Impl.K256.Qinv.refl" }, { "project_name": "hacl-star", "file_name": "Lib.Exponentiation.fsti", "name": "Lib.Exponentiation.exp_four_fw_acc0" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas2.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas2.lemma_tup64_pow2_128" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.Fast_defs.fst", "name": "Vale.Curve25519.Fast_defs.pow2_nine" }, { "project_name": "hacl-star", "file_name": "Lib.UpdateMulti.Lemmas.fsti", "name": "Lib.UpdateMulti.Lemmas.repeat_l" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fst", "name": "Lib.IntVector.Transpose.transpose8x8_012" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Field32xN.fst", "name": "Hacl.Spec.Poly1305.Field32xN.as_tup5" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.uints_to_bytes_le_inner" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Crypto.fst", "name": "QUIC.Spec.Crypto.prefix_l" }, { "project_name": "hacl-star", "file_name": "Lib.IntVector.Transpose.fst", "name": "Lib.IntVector.Transpose.transposewxw_f" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas2.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas2.lemma_tup64_mod_pow2_128" }, { "project_name": "FStar", "file_name": "MergeSort2.fst", "name": "MergeSort2.split_n" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas2.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas2.lemma_store_felem_lo" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.list_iv" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.PrecompTable.fst", "name": "Hacl.Impl.PrecompTable.lprecomp_table_mul" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCTR.fst", "name": "Vale.AES.GCTR.nat32_xor_bytewise_2_helper2" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas2.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas2.load_tup64_lemma0" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.index_uints_to_bytes_le_aux" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.uints_to_bytes_be_inner" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Frodo.Encode.fst", "name": "Hacl.Impl.Frodo.Encode.frodo_key_encode2" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.nat_to_intseq_be" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas2.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas2.load_tup64_lemma" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Chacha20.Vec.fst", "name": "Hacl.Spec.Chacha20.Vec.transpose8" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Machine_s.fst", "name": "Vale.PPC64LE.Machine_s.int_to_nat8" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Endianness.fst", "name": "LowParse.SLow.Endianness.n_to_be_S" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fst", "name": "FStar.UInt128.eq_mask" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCTR.fst", "name": "Vale.AES.GCTR.nat32_xor_bytewise_3_helper2" }, { "project_name": "hacl-star", "file_name": "Lib.Exponentiation.fsti", "name": "Lib.Exponentiation.exp_four_fw_f" }, { "project_name": "hacl-star", "file_name": "Spec.SHA2.Constants.fst", "name": "Spec.SHA2.Constants.h256_l" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Curve25519.Field64.Lemmas.fst", "name": "Hacl.Spec.Curve25519.Field64.Lemmas.lemma_felem64_mod255" }, { "project_name": "FStar", "file_name": "FStar.Int.Cast.fst", "name": "FStar.Int.Cast.int8_to_uint64" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.some_arithmetic" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.create" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.member" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.ivTable" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas0.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_lemma" }, { "project_name": "hacl-star", "file_name": "Hacl.Poly1305.Field32xN.Lemmas2.fst", "name": "Hacl.Poly1305.Field32xN.Lemmas2.load_tup64_fits_lemma" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.EquivScalar.fst", "name": "Hacl.Spec.SHA2.EquivScalar.lemma_len_lt_max_a_mul_by_8" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.PrecompBaseTable.fsti", "name": "Hacl.Spec.PrecompBaseTable.precomp_base_table_list" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Frodo.Pack.fst", "name": "Hacl.Impl.Frodo.Pack.frodo_pack8" }, { "project_name": "hacl-star", "file_name": "Lib.Exponentiation.fsti", "name": "Lib.Exponentiation.exp_four_fw" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.nat_to_intseq_le" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.Field52.Definitions.Lemmas.fst", "name": "Hacl.Spec.K256.Field52.Definitions.Lemmas.lemma_mask48" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.gmap" }, { "project_name": "FStar", "file_name": "FStar.Int.Cast.fst", "name": "FStar.Int.Cast.int8_to_uint32" } ], "selected_premises": [ "Lib.NTuple.ntup8", "Lib.Sequence.to_seq", "Lib.Sequence.lseq", "Lib.IntTypes.uint_t", "Lib.NTuple.ntuple", "Lib.IntTypes.int_t", "Lib.NTuple.ntuple_", "Lib.IntTypes.range", "Lib.NTuple.flen", "Lib.NTuple.ntup1", "Lib.IntTypes.size", "Lib.NTuple.ntup4", "Lib.Sequence.op_String_Access", "Lib.Sequence.length", "Lib.Sequence.op_String_Assignment", "FStar.UInt.size", "Lib.IntTypes.bits", "Lib.IntTypes.v", "Lib.IntTypes.u8", "Lib.NTuple.op_Lens_Access", "Lib.IntTypes.uint_v", "Lib.Sequence.seq", "Lib.IntTypes.u64", "FStar.Mul.op_Star", "Lib.Sequence.slice", "Lib.IntTypes.u32", "Lib.NTuple.tup1", "Lib.NTuple.tup4", "Lib.IntTypes.op_Plus_Bang", "Lib.IntTypes.max_size_t", "Lib.IntTypes.op_Plus_Dot", "Lib.IntTypes.op_Star_Bang", "Lib.IntTypes.numbytes", "Lib.Sequence.createL", "FStar.Pervasives.reveal_opaque", "Lib.IntTypes.uint", "Lib.IntTypes.op_Hat_Dot", "Lib.NTuple.op_Lens_Assignment", "Lib.IntTypes.op_Subtraction_Dot", "Lib.IntTypes.unsigned", "Lib.IntTypes.op_Star_Dot", "Lib.IntTypes.op_Amp_Dot", "Lib.IntTypes.op_Subtraction_Bang", "Lib.IntTypes.u16", "FStar.Heap.trivial_preorder", "Lib.IntTypes.op_Bar_Dot", "FStar.Pervasives.Native.snd", "Lib.IntTypes.byte", "FStar.Pervasives.Native.fst", "Lib.IntTypes.op_Percent_Dot", "FStar.ST.op_Bang", "FStar.Math.Lemmas.pow2_plus", "Lib.IntTypes.op_Less_Less_Dot", "Lib.IntTypes.maxint", "Lib.IntTypes.op_Less_Dot", "Lib.IntTypes.op_Slash_Dot", "Lib.IntTypes.u1", "Lib.IntTypes.op_Greater_Greater_Dot", "FStar.Math.Lemmas.pow2_lt_compat", "FStar.Math.Lemmas.pow2_le_compat", "Lib.IntTypes.size_v", "FStar.Pervasives.dfst", "FStar.ST.alloc", "Lib.LoopCombinators.fixed_a", "Lib.Sequence.op_At_Bar", "Lib.Sequence.repeat_blocks_f", "FStar.Pervasives.dsnd", "FStar.Int.op_At_Percent", "Lib.Sequence.update_slice", "FStar.Int.size", "Lib.IntTypes.op_Equals_Dot", "Lib.LoopCombinators.fixed_i", "Lib.IntTypes.modulus", "FStar.Math.Lemmas.lemma_mod_plus_distr_l", "Lib.IntTypes.sint", "Lib.IntTypes.minint", "Lib.IntTypes.op_Less_Equals_Dot", "Lib.IntTypes.op_Greater_Dot", "Lib.IntTypes.pub_int_t", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "FStar.Math.Lemmas.cancel_mul_mod", "FStar.Math.Lemmas.lemma_mod_plus_distr_r", "Lib.IntTypes.op_At_Percent_Dot", "Lib.IntTypes.op_Less_Less_Less_Dot", "Lib.Sequence.to_lseq", "Lib.IntTypes.mod_mask", "Lib.Sequence.map_blocks_f", "Lib.Sequence.map_blocks_a", "FStar.UInt.max_int", "Lib.IntTypes.pub_int_v", "FStar.Math.Lemmas.lemma_div_lt", "Lib.IntTypes.op_Tilde_Dot", "FStar.Math.Lemmas.distributivity_add_right", "Lib.IntTypes.logxor_v", "FStar.UInt.to_vec", "FStar.All.op_Bar_Greater", "FStar.Math.Lemmas.distributivity_sub_left", "FStar.Math.Lemmas.lemma_mod_plus", "FStar.Math.Lemmas.lemma_mod_mul_distr_l", "Lib.IntTypes.signed" ], "source_upto_this": "module Lib.NTuple\n\nopen FStar.Mul\nopen Lib.IntTypes\n\n#set-options \"--z3rlimit 15 --ifuel 0 --fuel 0\"\n\n/// Fixed and bounded length sequences, implemented using tuples\n\ninline_for_extraction\nlet flen = size_pos\n\ninline_for_extraction\nlet rec ntuple_ (a:Type0) (len:flen) =\n if len = 1 then a\n else a & ntuple_ a (len-1)\n\ninline_for_extraction\nlet ntuple (a:Type0) (len:flen) = normalize_term (ntuple_ a len)\n\ninline_for_extraction\nval fst (#a:Type0) (#len:flen) (s:ntuple a len) : a\n\ninline_for_extraction\nval rest (#a:Type0) (#len:flen{len > 1}) (s:ntuple a len) : ntuple a (len - 1)\n\ninline_for_extraction\nval index (#a:Type0) (#len:flen) (s:ntuple a len) (i:nat{i < len}) : a\n\nval index_fst_lemma (#a:Type0) (#len:flen) (s:ntuple a len) :\n Lemma (fst s == index s 0)\n [SMTPat (fst s)]\n\ninline_for_extraction\nval createi (#a:Type0) (len:flen) (f:(i:nat{i < len} -> a)) : ntuple a len\n\ninline_for_extraction\nval gcreatei (#a:Type0) (len:flen) (f:(i:nat{i < len} -> GTot a)) : GTot (ntuple a len)\n\nval createi_lemma (#a:Type0) (len:flen) (f:(i:nat{i < len} -> a)) (i:nat{i < len}) :\n Lemma (index (createi #a len f) i == f i)\n [SMTPat (index (createi #a len f) i)]\n\nval gcreatei_lemma (#a:Type0) (len:flen) (f:(i:nat{i < len} -> GTot a)) (i:nat{i < len}) :\n Lemma (index (gcreatei #a len f) i == f i)\n [SMTPat (index (gcreatei #a len f) i)]\n\ninline_for_extraction\nval to_lseq (#a:Type0) (#len:flen) (l:ntuple a len) : Lib.Sequence.lseq a len\n\nval to_lseq_index (#a:Type0) (#len:flen) (l:ntuple a len) (i:nat{i < len}) :\n Lemma (index l i == Lib.Sequence.index (to_lseq l) i)\n\ninline_for_extraction\nval from_lseq (#a:Type0) (#len:flen) (s:Lib.Sequence.lseq a len) : ntuple a len\n\ninline_for_extraction\nval create (#a:Type0) (len:flen) (init:a) : ntuple a len\n\nval create_lemma (#a:Type0) (len:flen) (init:a) (i:nat{i < len}) :\n Lemma (index (create #a len init) i == init)\n [SMTPat (index (create #a len init) i)]\n\ninline_for_extraction\nval concat (#a:Type0) (#len0:flen) (#len1:flen{len0 + len1 <= max_size_t})\n\t (s0:ntuple a len0) (s1:ntuple a len1) : ntuple a (len0 + len1)\n\n\nval concat_lemma (#a:Type0) (#len0:flen) (#len1:flen) (s0:ntuple a len0) (s1:ntuple a len1) (i:nat):\n Lemma\n (requires (len0 + len1 <= max_size_t /\\ i < len0 + len1))\n (ensures ((i < len0 ==> index (concat s0 s1) i == index s0 i) /\\\n (i >= len0 ==> index (concat s0 s1) i == index s1 (i-len0))))\n [SMTPat (index (concat #a #len0 #len1 s0 s1) i)]\n\ninline_for_extraction\nval equal (#a:Type) (#len:flen) (s1:ntuple a len) (s2:ntuple a len) : Type0\n\nval eq_intro: #a:Type -> #len:flen -> s1:ntuple a len -> s2:ntuple a len ->\n Lemma\n (requires forall i. {:pattern index s1 i; index s2 i} index s1 i == index s2 i)\n (ensures equal s1 s2)\n [SMTPat (equal s1 s2)]\n\nval eq_elim: #a:Type -> #len:flen -> s1:ntuple a len -> s2:ntuple a len ->\n Lemma\n (requires equal s1 s2)\n (ensures s1 == s2)\n [SMTPat (equal s1 s2)]\n\n(** Updating an element of a fixed-length Sequence *)\n\ninline_for_extraction\nval upd: #a:Type -> #len:flen -> s:ntuple a len -> i:nat{i < len} -> x:a -> ntuple a len\n\nval upd_lemma (#a:Type0) (#len:flen) (s:ntuple a len) (i:nat{i < len}) (x:a) (j:nat{j < len}) :\n Lemma (index (upd #a #len s i x) j == (if i = j then x else index s j))\n [SMTPat (index (upd #a #len s i x) j)]\n\ninline_for_extraction\nval sub (#a:Type) (#len:flen) (s:ntuple a len) (start:nat) (n:flen{start + n <= len}) : ntuple a n\n\nval index_sub_lemma (#a:Type) (#len:flen) (s:ntuple a len) (start:nat) (n:flen{start + n <= len}) (i:nat{i < n}) :\n Lemma (index (sub #a #len s start n) i == index s (start + i))\n [SMTPat (index (sub #a #len s start n) i)]\n\ninline_for_extraction\nval update_sub (#a:Type) (#len:flen) (s:ntuple a len) (start:nat) (n:flen{start + n <= len}) (x:ntuple a n) : ntuple a len\n\nval index_update_sub_lemma (#a:Type) (#len:flen) (s:ntuple a len) (start:nat) (n:flen{start + n <= len}) (x:ntuple a n) (i:nat{i < n}) :\n Lemma\n (index (update_sub #a #len s start n x) i == (if i >= start && i < start + n then index x (i - start) else index s i))\n [SMTPat (index (update_sub #a #len s start n x) i)]\n\ninline_for_extraction\nval mapi (#a:Type) (#b:Type) (#len:flen) (f:(i:nat{i < len} -> a -> b)) (s:ntuple a len) : ntuple b len\n\nval index_mapi_lemma (#a:Type) (#b:Type) (#len:flen) (f:(i:nat{i < len} -> a -> b)) (s:ntuple a len) (i:nat{i < len}) :\n Lemma (index (mapi #a #b #len f s) i == f i (index s i))\n [SMTPat (index (mapi #a #b #len f s) i)]\n\ninline_for_extraction\nval gmapi (#a:Type) (#b:Type) (#len:flen) (f:(i:nat{i < len} -> a -> GTot b)) (s:ntuple a len) : GTot (ntuple b len)\n\nval index_gmapi_lemma (#a:Type) (#b:Type) (#len:flen) (f:(i:nat{i < len} -> a -> GTot b)) (s:ntuple a len) (i:nat{i < len}) :\n Lemma (index (gmapi #a #b #len f s) i == f i (index s i))\n [SMTPat (index (gmapi #a #b #len f s) i)]\n\ninline_for_extraction\nval map (#a:Type) (#b:Type) (#len:flen) (f:a -> b) (s:ntuple a len) : ntuple b len\n\nval index_map_lemma (#a:Type) (#b:Type) (#len:flen) (f:(a -> b)) (s:ntuple a len) (i:nat{i < len}) :\n Lemma (index (map #a #b #len f s) i == f (index s i))\n [SMTPat (index (map #a #b #len f s) i)]\n\ninline_for_extraction\nval gmap (#a:Type) (#b:Type) (#len:flen) (f:a -> GTot b) (s:ntuple a len) : GTot (ntuple b len)\n\nval index_gmap_lemma (#a:Type) (#b:Type) (#len:flen) (f:(a -> GTot b)) (s:ntuple a len) (i:nat{i < len}) :\n Lemma (index (gmap #a #b #len f s) i == f (index s i))\n [SMTPat (index (gmap #a #b #len f s) i)]\n\ninline_for_extraction\nval map2i (#a:Type) (#b:Type) (#c:Type) (#len:flen) (f:(i:nat{i < len} -> a -> b -> c)) (s1:ntuple a len) (s2:ntuple b len) : ntuple c len\n\nval index_map2i_lemma (#a:Type) (#b:Type) (#c:Type) (#len:flen) (f:(i:nat{i < len} -> a -> b -> c)) (s1:ntuple a len) (s2:ntuple b len) (i:nat{i < len}) :\n Lemma (index (map2i #a #b #c #len f s1 s2) i == f i (index s1 i) (index s2 i))\n [SMTPat (index (map2i #a #b #c #len f s1 s2) i)]\n\ninline_for_extraction\nval map2 (#a:Type) (#b:Type) (#c:Type) (#len:flen) (f:(a -> b -> c)) (s1:ntuple a len) (s2:ntuple b len) : ntuple c len\n\nval index_map2_lemma (#a:Type) (#b:Type) (#c:Type) (#len:flen) (f:a -> b -> c) (s1:ntuple a len) (s2:ntuple b len) (i:nat{i < len}) :\n Lemma (index (map2 #a #b #c #len f s1 s2) i == f (index s1 i) (index s2 i))\n [SMTPat (index (map2 #a #b #c #len f s1 s2) i)]\n\nunfold let op_Lens_Access #a #len = index #a #len\nunfold let op_Lens_Assignment #a #len = upd #a #len\n\n(* The following conversions are tedious, but are needed to aid KaRaMeL in extracting ntuples correctly *)\ninline_for_extraction\nlet ntup1 #a (#l:flen{l = 1}) (t:a) : ntuple a l =\n assert (ntuple a l == ntuple a 1);\n t <: ntuple a 1\n\nval ntup1_lemma (#a:Type0) (#l:flen{l == 1}) (t:a):\n Lemma (let x0 = t in let t = ntup1 #a #l t in x0 == t.(|0|))\n [SMTPat (ntup1 #a #l t)]\n\ninline_for_extraction\nlet tup1 #a (#l:flen{l = 1}) (t:ntuple a l) : a =\n assert (ntuple a l == ntuple a 1);\n t <: ntuple a 1\n\nval tup1_lemma (#a:Type0) (#l:flen{l == 1}) (t:ntuple a l):\n Lemma (let x0 = tup1 t in x0 == t.(|0|))\n [SMTPat (tup1 #a #l t)]\n\n#set-options \"--fuel 4\"\n\ninline_for_extraction\nlet ntup4 #a (#l:flen{l = 4}) (t:a & (a & (a & a))) : ntuple a l =\n assert (ntuple a l == ntuple a 4);\n (t <: ntuple a 4)\n\nval ntup4_lemma (#a:Type0) (#l:flen{l == 4}) (t:a & (a & (a & a))) :\n Lemma\n (let (x0,(x1,(x2,x3))) = t in\n let t = ntup4 #a #l t in\n x0 == t.(|0|) /\\ x1 == t.(|1|) /\\\n x2 == t.(|2|) /\\ x3 == t.(|3|))\n [SMTPat (ntup4 #a #l t)]\n\ninline_for_extraction\nlet tup4 #a (#l:flen{l = 4}) (t:ntuple a l) : (a & (a & (a & a))) =\n assert (ntuple a l == ntuple a 4);\n (t <: ntuple a 4)\n\nval tup4_lemma (#a:Type0) (#l:flen{l = 4}) (t:ntuple a l) :\n Lemma\n (let (x0,(x1,(x2,x3))) = tup4 t in\n x0 == t.(|0|) /\\ x1 == t.(|1|) /\\\n x2 == t.(|2|) /\\ x3 == t.(|3|))\n [SMTPat (tup4 t)]\n\n#set-options \"--fuel 8\"\n\ninline_for_extraction\nlet ntup8 #a (#l:flen{l = 8}) (t:a & (a & (a & (a & (a & (a & (a & a))))))) : ntuple a l =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)\n\nval ntup8_lemma (#a:Type0) (#l:flen{l == 8}) (t:a & (a & (a & (a & (a & (a & (a & a))))))) :\n Lemma\n (let (x0,(x1,(x2,(x3,(x4,(x5,(x6,x7))))))) = t in\n let t = ntup8 #a #l t in\n x0 == t.(|0|) /\\ x1 == t.(|1|) /\\\n x2 == t.(|2|) /\\ x3 == t.(|3|) /\\\n x4 == t.(|4|) /\\ x5 == t.(|5|) /\\\n x6 == t.(|6|) /\\ x7 == t.(|7|))\n [SMTPat (ntup8 #a #l t)]\n\ninline_for_extraction", "sketch": [ "Step 1: The function `tup8` is intended to convert an `ntuple` of length 8 into a nested tuple structure.\nStep 2: To implement this, we need to assert that the length of the `ntuple` is indeed 8. Then, we cast the `ntuple` to the nested tuple type and return it.", "Step 1: The definition `tup8` is about converting an `ntuple` of length 8 into a nested tuple structure. This nested tuple structure will have the form `(a & (a & (a & (a & (a & (a & (a & a)))))))`.\nStep 2: The implementation will assert that the length of the `ntuple` is indeed 8. Then, it will cast the `ntuple` to the nested tuple structure using the `<:` operator.", "Step 1: The `tup8` function is designed to convert an `ntuple` of length 8 into a nested tuple structure. This nested tuple structure will have the form `(a & (a & (a & (a & (a & (a & (a & a)))))))`.\nStep 2: To implement `tup8`, we need to assert that the length of the `ntuple` is indeed 8. Then, we can cast the `ntuple` to the nested tuple structure using the type cast operator `<:`, ensuring that the conversion is correct.", "Step 1: The definition `tup8` is about converting an `ntuple` of length 8 into a nested tuple structure. This nested structure is represented as a series of pairs, where each pair contains an element and another pair, ultimately forming a deeply nested tuple.\nStep 2: To implement this, we need to assert that the length of the `ntuple` is indeed 8. Then, we cast the `ntuple` to the nested tuple structure using the type cast operator `<:`, ensuring that the conversion is valid and correct.", "Step 1: The definition `tup8` is about converting an `ntuple` of length 8 into a nested tuple structure. This nested tuple structure is a sequence of pairs, where each pair contains an element and another nested pair, ultimately representing the 8 elements of the `ntuple`.\nStep 2: The implementation involves asserting that the length of the `ntuple` is 8 and then casting the `ntuple` to the nested tuple structure using the type cast operator `<:`.", "Step 1: The definition `tup8` is about converting an `ntuple` of length 8 into a nested tuple structure. This structure is represented as a series of nested pairs, where each pair contains an element of the original `ntuple`.\nStep 2: To implement this, we assert that the length of the `ntuple` is indeed 8. Then, we cast the `ntuple` to the nested tuple structure using the `<:` operator.", "Step 1: The `tup8` function is intended to convert an `ntuple` of length 8 into a nested tuple structure. This nested tuple structure will have the form `(a & (a & (a & (a & (a & (a & (a & a)))))))`.\nStep 2: To implement this, we need to assert that the length of the `ntuple` is indeed 8, and then cast the `ntuple` to the nested tuple structure.", "Step 1: The `tup8` function is intended to convert an `ntuple` of length 8 into a nested tuple structure. This nested tuple structure will have the form `(a & (a & (a & (a & (a & (a & (a & a)))))))`.\nStep 2: To implement `tup8`, we need to assert that the length of the `ntuple` is indeed 8. Then, we can cast the `ntuple` to the desired nested tuple structure.", "Step 1: The function `tup8` is designed to convert an 8-tuple (ntuple of length 8) into a nested tuple structure.\nStep 2: The implementation asserts that the length of the ntuple is 8, then casts the ntuple to the nested tuple structure.", "Step 1: The `tup8` function is intended to convert an `ntuple` of length 8 into a nested tuple structure. This nested tuple structure will have the form `(a & (a & (a & (a & (a & (a & (a & a)))))))`.\nStep 2: To implement this, we need to assert that the length of the `ntuple` is indeed 8. Then, we can cast the `ntuple` to the desired nested tuple structure and return it." ], "generated_solution": [ "let tup8 #a (#l:flen{l = 8}) (t:ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)", "let tup8 #a (#l:flen{l = 8}) (t:ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)", "let tup8 #a (#l:flen{l = 8}) (t:ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)", "let tup8 #a (#l:flen{l = 8}) (t:ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)", "let tup8 #a (#l:flen{l = 8}) (t:ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)", "let tup8 #a (#l: flen{l = 8}) (t: ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)", "let tup8 #a (#l:flen{l = 8}) (t:ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)", "let tup8 #a (#l:flen{l = 8}) (t:ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)", "let tup8 #a (#l: flen{l = 8}) (t: ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)", "let tup8 #a (#l:flen{l = 8}) (t:ntuple a l) : (a & (a & (a & (a & (a & (a & (a & a))))))) =\n assert (ntuple a l == ntuple a 8);\n (t <: ntuple a 8)" ] }, { "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.modifies_intro_strong", "opens_and_abbrevs": [ { "abbrev": "F", "full_module": "FStar.FunctionalExtensionality" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "open": "FStar" }, { "open": "FStar" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val modifies_intro_strong\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n (Set.mem r (regions_of_loc l) ==> ~ (GSet.mem n (Loc?.non_live_addrs l r))) /\\\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')", "source_definition": "let modifies_intro_strong #al #c l h h' regions mrefs lives unused_ins alocs =\n Classical.forall_intro (Classical.move_requires regions);\n assert (modifies_preserves_regions l h h');\n\n let aux (t:Type) (pre:Preorder.preorder t) (p:HS.mreference t pre)\n :Lemma (requires (HS.contains h p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc l) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc l (HS.frameOf p))))))\n (ensures (HS.contains h' p /\\ HS.sel h' p == HS.sel h p))\n =\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l);\n // FIXME: WHY WHY WHY is this assert necessary?\n assert_spinoff (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n // FIXME: Now this one is too :)\n assert (loc_disjoint_addrs (loc_mreference p) l);\n assert ((loc_disjoint (loc_mreference p) l));\n mrefs t pre p\n in\n\n modifies_preserves_mreferences_intro l h h' aux;\n Classical.forall_intro_3 (fun t pre p -> Classical.move_requires (lives t pre) p);\n modifies_preserves_not_unused_in_intro l h h' (fun r n ->\n unused_ins r n\n );\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n alocs r a b\n )", "source_range": { "start_line": 937, "start_col": 0, "end_line": 964, "end_col": 3 }, "interleaved": false, "definition": "fun l h h' regions mrefs lives unused_ins alocs ->\n FStar.Classical.forall_intro (FStar.Classical.move_requires regions);\n assert (FStar.ModifiesGen.modifies_preserves_regions l h h');\n let aux t pre p =\n (FStar.Pervasives.assert_norm (Loc?.region_liveness_tags (FStar.ModifiesGen.loc_mreference p) ==\n FStar.Ghost.hide FStar.Set.empty);\n assert (FStar.ModifiesGen.loc_disjoint_region_liveness_tags (FStar.ModifiesGen.loc_mreference p\n )\n l);\n FStar.Pervasives.assert_spinoff (FStar.ModifiesGen.loc_aux_disjoint (FStar.Ghost.reveal (Loc?.aux\n (FStar.ModifiesGen.loc_mreference p)))\n (FStar.Ghost.reveal (Loc?.aux l)));\n assert (FStar.ModifiesGen.loc_disjoint_addrs (FStar.ModifiesGen.loc_mreference p) l);\n assert (FStar.ModifiesGen.loc_disjoint (FStar.ModifiesGen.loc_mreference p) l);\n mrefs t pre p)\n <:\n FStar.Pervasives.Lemma\n (requires\n FStar.Monotonic.HyperStack.contains h p /\\\n (FStar.Set.mem (FStar.Monotonic.HyperStack.frameOf p) (FStar.ModifiesGen.regions_of_loc l) ==>\n ~(FStar.GSet.mem (FStar.Monotonic.HyperStack.as_addr p)\n (FStar.ModifiesGen.addrs_of_loc l (FStar.Monotonic.HyperStack.frameOf p)))))\n (ensures\n FStar.Monotonic.HyperStack.contains h' p /\\\n FStar.Monotonic.HyperStack.sel h' p == FStar.Monotonic.HyperStack.sel h p)\n in\n FStar.ModifiesGen.modifies_preserves_mreferences_intro l h h' aux;\n FStar.Classical.forall_intro_3 (fun t pre p -> FStar.Classical.move_requires (lives t pre) p);\n FStar.ModifiesGen.modifies_preserves_not_unused_in_intro l h h' (fun r n -> unused_ins r n);\n FStar.ModifiesGen.modifies_preserves_alocs_intro l\n h\n h'\n ()\n (fun r a b ->\n FStar.ModifiesGen.loc_aux_disjoint_sym (FStar.Ghost.reveal (Loc?.aux l))\n (FStar.Ghost.reveal (Loc?.aux (FStar.ModifiesGen.loc_of_aloc b)));\n alocs r a b)", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "FStar.ModifiesGen.aloc_t", "FStar.ModifiesGen.cls", "FStar.ModifiesGen.loc", "FStar.Monotonic.HyperStack.mem", "FStar.Monotonic.HyperHeap.rid", "Prims.unit", "Prims.b2t", "FStar.Monotonic.HyperStack.live_region", "Prims.squash", "Prims.Nil", "FStar.Pervasives.pattern", "FStar.Preorder.preorder", "FStar.Monotonic.HyperStack.mreference", "Prims.l_and", "FStar.ModifiesGen.loc_disjoint", "FStar.ModifiesGen.loc_mreference", "FStar.Monotonic.HyperStack.contains", "Prims.eq2", "FStar.Monotonic.HyperStack.sel", "Prims.nat", "Prims.l_imp", "FStar.Set.mem", "FStar.ModifiesGen.regions_of_loc", "Prims.l_not", "FStar.GSet.mem", "FStar.ModifiesGen.__proj__Loc__item__non_live_addrs", "FStar.Monotonic.Heap.addr_unused_in", "FStar.Map.sel", "FStar.Monotonic.Heap.heap", "FStar.Monotonic.HyperStack.get_hmap", "FStar.ModifiesGen.loc_of_aloc", "FStar.ModifiesGen.__proj__Cls__item__aloc_preserved", "FStar.ModifiesGen.modifies_preserves_alocs_intro", "FStar.ModifiesGen.loc_aux_disjoint_sym", "FStar.Ghost.reveal", "FStar.GSet.set", "FStar.ModifiesGen.aloc", "FStar.ModifiesGen.__proj__Loc__item__aux", "FStar.ModifiesGen.modifies_preserves_not_unused_in_intro", "FStar.Classical.forall_intro_3", "FStar.Classical.move_requires", "FStar.ModifiesGen.modifies_preserves_mreferences_intro", "FStar.Monotonic.HyperStack.frameOf", "FStar.Monotonic.HyperStack.as_addr", "FStar.ModifiesGen.addrs_of_loc", "Prims._assert", "FStar.ModifiesGen.loc_disjoint_addrs", "FStar.Pervasives.assert_spinoff", "FStar.ModifiesGen.loc_aux_disjoint", "FStar.ModifiesGen.loc_disjoint_region_liveness_tags", "FStar.Pervasives.assert_norm", "FStar.Ghost.erased", "FStar.Set.set", "FStar.ModifiesGen.__proj__Loc__item__region_liveness_tags", "FStar.Ghost.hide", "FStar.Set.empty", "FStar.ModifiesGen.modifies_preserves_regions", "FStar.Classical.forall_intro" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "\n l: FStar.ModifiesGen.loc c ->\n h: FStar.Monotonic.HyperStack.mem ->\n h': FStar.Monotonic.HyperStack.mem ->\n regions:\n (r: FStar.Monotonic.HyperHeap.rid\n -> FStar.Pervasives.Lemma (requires FStar.Monotonic.HyperStack.live_region h r)\n (ensures FStar.Monotonic.HyperStack.live_region h' r)) ->\n mrefs:\n (t: Type0 -> pre: FStar.Preorder.preorder t -> b: FStar.Monotonic.HyperStack.mreference t pre\n -> FStar.Pervasives.Lemma\n (requires\n FStar.ModifiesGen.loc_disjoint (FStar.ModifiesGen.loc_mreference b) l /\\\n FStar.Monotonic.HyperStack.contains h b)\n (ensures\n FStar.Monotonic.HyperStack.contains h' b /\\\n FStar.Monotonic.HyperStack.sel h' b == FStar.Monotonic.HyperStack.sel h b)) ->\n livenesses:\n (t: Type0 -> pre: FStar.Preorder.preorder t -> b: FStar.Monotonic.HyperStack.mreference t pre\n -> FStar.Pervasives.Lemma (requires FStar.Monotonic.HyperStack.contains h b)\n (ensures FStar.Monotonic.HyperStack.contains h' b)) ->\n addr_unused_in:\n (r: FStar.Monotonic.HyperHeap.rid -> n: Prims.nat\n -> FStar.Pervasives.Lemma\n (requires\n (FStar.Set.mem r (FStar.ModifiesGen.regions_of_loc l) ==>\n ~(FStar.GSet.mem n (Loc?.non_live_addrs l r))) /\\\n FStar.Monotonic.HyperStack.live_region h r /\\\n FStar.Monotonic.HyperStack.live_region h' r /\\\n FStar.Monotonic.Heap.addr_unused_in n\n (FStar.Map.sel (FStar.Monotonic.HyperStack.get_hmap h') r))\n (ensures\n FStar.Monotonic.Heap.addr_unused_in n\n (FStar.Map.sel (FStar.Monotonic.HyperStack.get_hmap h) r))) ->\n alocs:\n (r: FStar.Monotonic.HyperHeap.rid -> a: Prims.nat -> x: al r a\n -> FStar.Pervasives.Lemma\n (requires FStar.ModifiesGen.loc_disjoint (FStar.ModifiesGen.loc_of_aloc x) l)\n (ensures Cls?.aloc_preserved c x h h'))\n -> FStar.Pervasives.Lemma (ensures FStar.ModifiesGen.modifies l h h')", "prompt": "let modifies_intro_strong #al #c l h h' regions mrefs lives unused_ins alocs =\n ", "expected_response": "Classical.forall_intro (Classical.move_requires regions);\nassert (modifies_preserves_regions l h h');\nlet aux (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre)\n : Lemma\n (requires\n (HS.contains h p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc l) ==>\n ~(GSet.mem (HS.as_addr p) (addrs_of_loc l (HS.frameOf p))))))\n (ensures (HS.contains h' p /\\ HS.sel h' p == HS.sel h p)) =\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l);\n assert_spinoff (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p)))\n (Ghost.reveal (Loc?.aux l)));\n assert (loc_disjoint_addrs (loc_mreference p) l);\n assert ((loc_disjoint (loc_mreference p) l));\n mrefs t pre p\nin\nmodifies_preserves_mreferences_intro l h h' aux;\nClassical.forall_intro_3 (fun t pre p -> Classical.move_requires (lives t pre) p);\nmodifies_preserves_not_unused_in_intro l h h' (fun r n -> unused_ins r n);\nmodifies_preserves_alocs_intro l\n h\n h'\n ()\n (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n alocs r a b)", "source": { "project_name": "FStar", "file_name": "ulib/FStar.ModifiesGen.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.ModifiesGen.fst", "checked_file": "dataset/FStar.ModifiesGen.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Universe.fsti.checked", "dataset/FStar.Tactics.SMT.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Stubs.Tactics.V2.Builtins.fsti.checked", "dataset/FStar.StrongExcludedMiddle.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Map.fsti.checked", "dataset/FStar.HyperStack.ST.fsti.checked", "dataset/FStar.HyperStack.fst.checked", "dataset/FStar.Heap.fst.checked", "dataset/FStar.GSet.fsti.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "aloc", "ALoc", "ALoc", "ALoc", "aloc_t", "region", "region", "addr", "addr", "loc", "loc", "cls", "Cls", "Cls", "Cls", "aloc_includes", "aloc_includes", "let aloc_domain (#al: aloc_t) (c: cls al) (regions: Ghost.erased (Set.set HS.rid)) (addrs: ((r: HS.rid { Set.mem r (Ghost.reveal regions) } ) -> GTot (GSet.set nat))) : GTot (GSet.set (aloc c)) =\n GSet.comprehend (fun a -> Set.mem a.region (Ghost.reveal regions) && GSet.mem a.addr (addrs a.region))", "aloc_includes_refl", "aloc_includes_refl", "let i_restricted_g_t = F.restricted_g_t", "let addrs_dom regions =\n (r: HS.rid { Set.mem r (Ghost.reveal regions) } )", "let non_live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (r:addrs_dom regions) =\n (y: GSet.set nat { r `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y })", "aloc_includes_trans", "aloc_includes_trans", "let live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags))\n (r:addrs_dom regions) = (y: GSet.set nat { GSet.subset (non_live_addrs r) y } )", "aloc_disjoint", "aloc_disjoint", "loc'", "Loc", "Loc", "Loc", "regions", "regions", "aloc_disjoint_sym", "aloc_disjoint_sym", "region_liveness_tags", "region_liveness_tags", "non_live_addrs", "non_live_addrs", "live_addrs", "live_addrs", "aloc_disjoint_includes", "aloc_disjoint_includes", "aux", "aux", "let loc = loc'", "let mk_non_live_addrs (#regions:_) (#region_liveness_tags:_)\n (f: (x:addrs_dom regions -> GTot (non_live_addrs_codom regions region_liveness_tags x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags) =\n F.on_dom_g _ f", "aloc_preserved", "aloc_preserved", "let mk_live_addrs (#regions:_) (#region_liveness_tags:_)\n (#non_live_addrs_codom: _)\n (f: (x:addrs_dom regions -> GTot (live_addrs_codom regions region_liveness_tags non_live_addrs_codom x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs_codom) =\n F.on_dom_g _ f", "aloc_preserved_refl", "aloc_preserved_refl", "let loc_none #a #c =\n Loc\n (Ghost.hide (Set.empty))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)", "aloc_preserved_trans", "aloc_preserved_trans", "let regions_of_loc\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: GTot (Set.set HS.rid)\n= Ghost.reveal (Loc?.regions s)", "let addrs_of_loc_liveness_not_preserved\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.non_live_addrs l r\n else GSet.empty", "same_mreference_aloc_preserved", "same_mreference_aloc_preserved", "let addrs_of_loc_weak\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.live_addrs l r\n else GSet.empty", "let addrs_of_loc_aux_pred\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n (addr: nat)\n: GTot bool\n= StrongExcludedMiddle.strong_excluded_middle (exists a . GSet.mem a (Ghost.reveal (Loc?.aux l)) /\\ a.region == r /\\ a.addr == addr)", "val loc (#aloc: aloc_t u#x) (c: cls aloc) : Tot (Type u#x)", "val loc_none (#aloc: aloc_t) (#c: cls aloc): Tot (loc c)", "val loc_union\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot (loc c)", "let addrs_of_loc_aux\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (y: GSet.set nat { GSet.subset (GSet.intersect y (addrs_of_loc_weak l r)) GSet.empty } )\n= GSet.comprehend (addrs_of_loc_aux_pred l r)\n `GSet.intersect` (GSet.complement (addrs_of_loc_weak l r))", "val loc_union_idem\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union s s == s)", "let addrs_of_loc\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= GSet.union\n (addrs_of_loc_weak l r)\n (addrs_of_loc_aux l r)", "val loc_union_comm\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: Lemma\n (loc_union s1 s2 == loc_union s2 s1)", "let addrs_of_loc_aux_prop\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: Lemma\n (GSet.subset (GSet.intersect (addrs_of_loc_aux l r) (addrs_of_loc_weak l r)) GSet.empty)\n [SMTPatOr [\n [SMTPat (addrs_of_loc_aux l r)];\n [SMTPat (addrs_of_loc_weak l r)];\n [SMTPat (addrs_of_loc l r)];\n ]]\n= ()", "val loc_union_assoc\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s3: loc c)\n: Lemma\n (loc_union s1 (loc_union s2 s3) == loc_union (loc_union s1 s2) s3)", "val loc_union_loc_none_l\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union loc_none s == s)", "val loc_union_loc_none_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union s loc_none == s)", "let loc_union #al #c s1 s2 =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in\n let regions = Set.union regions1 regions2 in\n let region_liveness_tags : Ghost.erased (Set.set HS.rid) = (Ghost.hide (Set.union (Ghost.reveal (Loc?.region_liveness_tags s1)) (Ghost.reveal (Loc?.region_liveness_tags s2)))) in\n let gregions = Ghost.hide regions in\n let non_live_addrs =\n F.on_dom_g (addrs_dom gregions) #(non_live_addrs_codom gregions region_liveness_tags)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then Loc?.non_live_addrs s1 r else GSet.empty)\n (if Set.mem r regions2 then Loc?.non_live_addrs s2 r else GSet.empty))\n in\n let live_addrs =\n F.on_dom_g (addrs_dom gregions) #(live_addrs_codom gregions region_liveness_tags non_live_addrs)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then addrs_of_loc_weak s1 r else GSet.empty)\n (if Set.mem r regions2 then addrs_of_loc_weak s2 r else GSet.empty))\n in\n let aux = Ghost.hide\n (Ghost.reveal (Loc?.aux s1) `GSet.union` Ghost.reveal (Loc?.aux s2))\n in\n Loc\n (Ghost.hide regions)\n region_liveness_tags\n non_live_addrs\n live_addrs\n aux", "val loc_of_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b: aloc r n)\n: GTot (loc c)", "val loc_of_aloc_not_none\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b: aloc r n)\n: Lemma (loc_of_aloc #_ #c b == loc_none ==> False)", "val loc_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: GTot (loc c)", "val loc_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: GTot (loc c)", "let fun_set_equal (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) :Tot Type0 =\n forall (x: t) . {:pattern (f1 x) \\/ (f2 x) } f1 x `GSet.equal` f2 x", "let loc_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses true (HS.frameOf b) (Set.singleton (HS.as_addr b))", "let fun_set_equal_elim (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) : Lemma\n (requires (fun_set_equal f1 f2))\n (ensures (f1 == f2))\n// [SMTPat (fun_set_equal f1 f2)]\n= assert (f1 `FunctionalExtensionality.feq_g` f2)", "let loc_freed_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses false (HS.frameOf b) (Set.singleton (HS.as_addr b))", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n let Loc regions1 region_liveness_tags1 _ _ aux1 = s1 in\n let Loc regions2 region_liveness_tags2 _ _ aux2 = s2 in\n Ghost.reveal regions1 `Set.equal` Ghost.reveal regions2 /\\\n Ghost.reveal region_liveness_tags1 `Set.equal` Ghost.reveal region_liveness_tags2 /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_region_only\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (Set.singleton r)", "let loc_equal_elim (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : Lemma\n (requires (loc_equal s1 s2))\n (ensures (s1 == s2))\n [SMTPat (s1 `loc_equal` s2)]\n= fun_set_equal_elim (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2);\n fun_set_equal_elim (Loc?.live_addrs s1) (Loc?.live_addrs s2)", "let loc_all_regions_from\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (HS.mod_set (Set.singleton r))", "let loc_union_idem #al #c s =\n assert (loc_union s s `loc_equal` s)", "let loc_union_comm #al #c s1 s2 =\n assert (loc_union s1 s2 `loc_equal` loc_union s2 s1)", "let loc_union_assoc #al #c s1 s2 s3 =\n assert (loc_union s1 (loc_union s2 s3) `loc_equal` loc_union (loc_union s1 s2) s3)", "val loc_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot Type0", "let loc_union_loc_none_l #al #c s =\n assert (loc_union loc_none s `loc_equal` s)", "val loc_includes_refl\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_includes s s)", "let loc_union_loc_none_r #al #c s =\n assert (loc_union s loc_none `loc_equal` s)", "let loc_of_aloc #al #c #r #n b =\n let regions = (Ghost.hide (Set.singleton r)) in\n let region_liveness_tags = (Ghost.hide (Set.empty)) in\n Loc\n regions\n region_liveness_tags\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide (GSet.singleton (ALoc r n (Some b))))", "val loc_includes_trans\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s3: loc c)\n: Lemma\n (requires (loc_includes s1 s2 /\\ loc_includes s2 s3))\n (ensures (loc_includes s1 s3))", "val loc_includes_union_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s s1 s2: loc c)\n: Lemma\n (requires (loc_includes s s1 /\\ loc_includes s s2))\n (ensures (loc_includes s (loc_union s1 s2)))", "let loc_of_aloc_not_none #al #c #r #n b = ()", "let loc_addresses #al #c preserve_liveness r n =\n let regions = (Ghost.hide (Set.singleton r)) in\n Loc\n regions\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> if preserve_liveness then GSet.empty else GSet.of_set n))\n (mk_live_addrs (fun _ -> GSet.of_set n))\n (Ghost.hide (aloc_domain c regions (fun _ -> GSet.of_set n)))", "val loc_includes_union_l\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s: loc c)\n: Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))", "let loc_regions_region_liveness_tags (preserve_liveness: bool) (r: Set.set HS.rid) : Tot (Ghost.erased (Set.set HS.rid)) =\n if preserve_liveness then Ghost.hide Set.empty else Ghost.hide r", "val loc_includes_none\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_includes s loc_none)", "let loc_regions #al #c preserve_liveness r =\n let region_liveness_tags = loc_regions_region_liveness_tags preserve_liveness r in\n let addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { r' `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y } ) =\n GSet.complement GSet.empty\n in\n let live_addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { addrs r' `GSet.subset` y } ) =\n addrs r'\n in\n Loc\n (Ghost.hide r)\n region_liveness_tags\n (mk_non_live_addrs addrs)\n (mk_live_addrs live_addrs)\n (Ghost.hide (aloc_domain c (Ghost.hide r) addrs))", "val loc_includes_none_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (requires (loc_includes loc_none s))\n (ensures (s == loc_none))", "val loc_includes_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b1 b2: aloc r n)\n: Lemma\n (requires (c.aloc_includes b1 b2))\n (ensures (loc_includes (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))", "let aloc_includes (#al: aloc_t) (#c: cls al) (b0 b: aloc c) : GTot Type0 =\n b0.region == b.region /\\ b0.addr == b.addr /\\ Some? b0.loc == Some? b.loc /\\ (if Some? b0.loc && Some? b.loc then c.aloc_includes (Some?.v b0.loc) (Some?.v b.loc) else True)", "let loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b: aloc c)\n: GTot Type0\n (decreases s)\n= exists (b0 : aloc c) . b0 `GSet.mem` s /\\ b0 `aloc_includes` b", "val loc_includes_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1 #r2: HS.rid)\n (#n1 #n2: nat)\n (b1: aloc r1 n1)\n (b2: aloc r2 n2)\n: Lemma\n (requires (loc_includes (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))\n (ensures (r1 == r2 /\\ n1 == n2 /\\ c.aloc_includes b1 b2))", "let loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: GTot Type0\n (decreases s2)\n= forall (b2: aloc c) . GSet.mem b2 s2 ==> loc_aux_includes_buffer s1 b2", "val loc_includes_addresses_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n (s: Set.set nat)\n (#a: nat)\n (p: aloc r a)\n: Lemma\n (requires (Set.mem a s))\n (ensures (loc_includes (loc_addresses preserve_liveness r s) (loc_of_aloc #_ #c p)))", "let loc_aux_includes_union_l\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s \\/ loc_aux_includes s2 s))\n (ensures (loc_aux_includes (GSet.union s1 s2) s))\n (decreases s)\n= ()", "let loc_aux_includes_refl\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n: Lemma\n (loc_aux_includes s s)\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)", "val loc_includes_region_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (s: Set.set HS.rid)\n (#r: HS.rid)\n (#a: nat)\n (b: aloc r a)\n: Lemma\n (requires (Set.mem r s))\n (ensures (loc_includes (loc_regions preserve_liveness s) (loc_of_aloc #_ #c b)))", "let loc_aux_includes_subset\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)", "val loc_includes_region_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (s: Set.set HS.rid)\n (r: HS.rid)\n (a: Set.set nat)\n: Lemma\n (requires (Set.mem r s))\n (ensures (loc_includes (loc_regions #_ #c preserve_liveness1 s) (loc_addresses preserve_liveness2 r a)))", "let loc_aux_includes_subset'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n [SMTPatOr [\n [SMTPat (s1 `GSet.subset` s2)];\n [SMTPat (loc_aux_includes s2 s1)];\n ]]\n= loc_aux_includes_subset s1 s2", "val loc_includes_region_region\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires ((preserve_liveness1 ==> preserve_liveness2) /\\ Set.subset s2 s1))\n (ensures (loc_includes (loc_regions #_ #c preserve_liveness1 s1) (loc_regions preserve_liveness2 s2)))", "let loc_aux_includes_union_l_r\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s s') s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s s' s", "val loc_includes_region_union_l\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (l: loc c)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires (loc_includes l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)))))\n (ensures (loc_includes (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness s2)))", "let loc_aux_includes_union_l_l\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s' s) s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s' s s", "val loc_includes_addresses_addresses\n (#aloc: aloc_t) (c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r: HS.rid)\n (a1 a2: Set.set nat)\n: Lemma\n (requires ((preserve_liveness1 ==> preserve_liveness2) /\\ Set.subset a2 a1))\n (ensures (loc_includes #_ #c (loc_addresses preserve_liveness1 r a1) (loc_addresses preserve_liveness2 r a2)))", "let loc_aux_includes_buffer_includes\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b1 b2: aloc c)\n: Lemma\n (requires (loc_aux_includes_buffer s b1 /\\ b1 `aloc_includes` b2))\n (ensures (loc_aux_includes_buffer s b2))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))", "val loc_disjoint\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot Type0", "let loc_aux_includes_loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n (b: aloc c)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_buffer s2 b))\n (ensures (loc_aux_includes_buffer s1 b))\n= Classical.forall_intro_3 (fun s b1 b2 -> Classical.move_requires (loc_aux_includes_buffer_includes #al #c s b1) b2)", "val loc_disjoint_sym\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))", "let loc_aux_includes_trans\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))", "val loc_disjoint_none_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (ensures (loc_disjoint s loc_none))", "let addrs_of_loc_weak_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (loc_union l1 l2) r == GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r))\n [SMTPat (addrs_of_loc_weak (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc_weak (loc_union l1 l2) r) (GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r)))", "val loc_disjoint_union_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s s1 /\\ loc_disjoint s s2))\n (ensures (loc_disjoint s (loc_union s1 s2)))", "val loc_disjoint_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (p1 p2 p1' p2' : loc c)\n: Lemma\n (requires (loc_includes p1 p1' /\\ loc_includes p2 p2' /\\ loc_disjoint p1 p2))\n (ensures (loc_disjoint p1' p2'))", "let addrs_of_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l1 l2) r == GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r))\n [SMTPat (addrs_of_loc (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc (loc_union l1 l2) r) (GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r)))", "val loc_disjoint_aloc_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1: HS.rid)\n (#a1: nat)\n (#r2: HS.rid)\n (#a2: nat)\n (b1: aloc r1 a1)\n (b2: aloc r2 a2)\n: Lemma\n (requires ((r1 == r2 /\\ a1 == a2) ==> c.aloc_disjoint b1 b2))\n (ensures (loc_disjoint (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))", "let loc_includes' #al (#c: cls al) (s1 s2: loc c) =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in (\n Set.subset regions2 regions1 /\\\n Set.subset (Ghost.reveal (Loc?.region_liveness_tags s2)) (Ghost.reveal (Loc?.region_liveness_tags s1)) /\\\n (\n forall (r: HS.rid { Set.mem r regions2 } ) .\n GSet.subset (Loc?.non_live_addrs s2 r) (Loc?.non_live_addrs s1 r)\n ) /\\\n (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc_weak s2 r) (addrs_of_loc_weak s1 r)\n ) /\\ (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc s2 r) (addrs_of_loc s1 r)\n ) /\\ (\n (Ghost.reveal (Loc?.aux s1)) `loc_aux_includes` (Ghost.reveal (Loc?.aux s2))\n )\n )", "val loc_disjoint_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1: HS.rid)\n (#a1: nat)\n (#r2: HS.rid)\n (#a2: nat)\n (b1: aloc r1 a1)\n (b2: aloc r2 a2)\n: Lemma\n (requires (loc_disjoint (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))\n (ensures ((r1 == r2 /\\ a1 == a2) ==> c.aloc_disjoint b1 b2))", "val loc_disjoint_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r1 r2: HS.rid)\n (n1 n2: Set.set nat)\n: Lemma\n (requires (r1 <> r2 \\/ Set.subset (Set.intersect n1 n2) Set.empty))\n (ensures (loc_disjoint (loc_addresses #_ #c preserve_liveness1 r1 n1) (loc_addresses preserve_liveness2 r2 n2)))", "let loc_includes #al #c s1 s2 =\n loc_includes' s1 s2", "let loc_includes_refl #al #c s =\n loc_aux_includes_refl (Ghost.reveal (Loc?.aux s))", "let loc_includes_refl'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: Lemma\n (loc_includes s s)\n [SMTPat (loc_includes s s)]\n= loc_includes_refl s", "let loc_disjoint_addresses #aloc #c = loc_disjoint_addresses_intro #aloc #c", "val loc_disjoint_addresses_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r1 r2: HS.rid)\n (n1 n2: Set.set nat)\n: Lemma\n (requires (loc_disjoint (loc_addresses #_ #c preserve_liveness1 r1 n1) (loc_addresses preserve_liveness2 r2 n2)))\n (ensures (r1 <> r2 \\/ Set.subset (Set.intersect n1 n2) Set.empty))", "let loc_includes_trans #al #c s1 s2 s3 =\n loc_aux_includes_trans (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s3))", "let loc_includes_union_r #al #c s s1 s2 = ()", "let loc_includes_union_l #al #c s1 s2 s =\n let u12 = loc_union s1 s2 in\n Classical.or_elim\n #(loc_includes s1 s)\n #(loc_includes s2 s)\n #(fun _ -> loc_includes (loc_union s1 s2) s)\n (fun _ ->\n loc_aux_includes_union_l_r (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2));\n assert (loc_includes (loc_union s1 s2) s1);\n loc_includes_trans u12 s1 s)\n (fun _ ->\n loc_aux_includes_union_l_l (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s1));\n assert (loc_includes (loc_union s1 s2) s2);\n loc_includes_trans u12 s2 s)", "val loc_disjoint_aloc_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (#r' : HS.rid)\n (#a' : nat)\n (p: aloc r' a')\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (requires (r == r' ==> (~ (Set.mem a' n))))\n (ensures (loc_disjoint (loc_of_aloc p) (loc_addresses #_ #c preserve_liveness r n)))", "val loc_disjoint_aloc_addresses_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r' : HS.rid)\n (#a' : nat)\n (p: aloc r' a')\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (requires (loc_disjoint (loc_of_aloc p) (loc_addresses #_ #c preserve_liveness r n)))\n (ensures (r == r' ==> (~ (Set.mem a' n))))", "let loc_includes_none #al #c s = ()", "let loc_includes_none_elim #al #c s =\n assert (s `loc_equal` loc_none)", "let loc_includes_aloc #al #c #r #n b1 b2 = ()", "let loc_includes_aloc_elim #aloc #c #r1 #r2 #n1 #n2 b1 b2 = ()", "let addrs_of_loc_loc_of_aloc\n (#al: aloc_t)\n (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (p: al r a)\n (r': HS.rid)\n: Lemma\n (addrs_of_loc (loc_of_aloc #_ #c p) r' `GSet.equal` (if r = r' then GSet.singleton a else GSet.empty))\n [SMTPat (addrs_of_loc (loc_of_aloc #_ #c p) r')]\n= ()", "val loc_disjoint_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (rs1 rs2: Set.set HS.rid)\n: Lemma\n (requires (Set.subset (Set.intersect rs1 rs2) Set.empty))\n (ensures (loc_disjoint (loc_regions #_ #c preserve_liveness1 rs1) (loc_regions preserve_liveness2 rs2)))", "val address_liveness_insensitive_locs (#aloc: aloc_t) (c: cls aloc) : Tot (loc c)", "let loc_includes_addresses_aloc #al #c preserve_liveness r s #a p = ()", "val loc_includes_address_liveness_insensitive_locs_aloc (#aloc: aloc_t) (#c: cls aloc) (#r: HS.rid) (#n: nat) (a: aloc r n) : Lemma\n (loc_includes (address_liveness_insensitive_locs c) (loc_of_aloc a))", "let loc_includes_region_aloc #al #c preserve_liveness s #r #a b = ()", "let loc_includes_region_addresses #al #c s preserve_liveness1 preserve_liveness2 r a = ()", "val loc_includes_address_liveness_insensitive_locs_addresses (#aloc: aloc_t) (c: cls aloc) (r: HS.rid) (a: Set.set nat) : Lemma\n (loc_includes (address_liveness_insensitive_locs c) (loc_addresses true r a))", "let loc_includes_region_region #al #c preserve_liveness1 preserve_liveness2 s1 s2 = ()", "val region_liveness_insensitive_locs (#al: aloc_t) (c: cls al) : Tot (loc c)", "let loc_includes_region_union_l #al #c preserve_liveness l s1 s2 =\n assert ((loc_regions #_ #c preserve_liveness (Set.intersect s2 (Set.complement s1)) `loc_union` loc_regions #_ #c preserve_liveness (Set.intersect s2 s1)) `loc_equal` loc_regions preserve_liveness s2);\n loc_includes_region_region #_ #c preserve_liveness preserve_liveness s1 (Set.intersect s2 s1);\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)));\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 s1));\n loc_includes_union_r (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1))) (loc_regions preserve_liveness (Set.intersect s2 s1))", "val loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs (#al: aloc_t) (c: cls al) : Lemma\n (loc_includes (region_liveness_insensitive_locs c) (address_liveness_insensitive_locs c))", "val loc_includes_region_liveness_insensitive_locs_loc_regions\n (#al: aloc_t) (c: cls al) (r: Set.set HS.rid)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_regions #_ #c true r)", "let loc_includes_addresses_addresses #al c preserve_liveness1 preserve_liveness2 r s1 s2 = ()", "val loc_includes_region_liveness_insensitive_locs_loc_addresses\n (#al: aloc_t) (c: cls al) (preserve_liveness: bool) (r: HS.rid) (a: Set.set nat)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_addresses #_ #c preserve_liveness r a)", "let aloc_disjoint (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : GTot Type0 =\n if b1.region = b2.region && b1.addr = b2.addr\n then Some? b1.loc /\\ Some? b2.loc /\\ c.aloc_disjoint (Some?.v b1.loc) (Some?.v b2.loc)\n else True", "val loc_includes_region_liveness_insensitive_locs_loc_of_aloc\n (#al: aloc_t) (c: cls al) (#r: HS.rid) (#a: nat) (x: al r a)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_of_aloc #_ #c x)", "let aloc_disjoint_sym (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : Lemma\n (aloc_disjoint b1 b2 <==> aloc_disjoint b2 b1)\n= Classical.forall_intro_2 (fun r a -> Classical.forall_intro_2 (fun b1 b2 -> c.aloc_disjoint_sym #r #a b1 b2))", "let loc_aux_disjoint\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: GTot Type0\n= forall (b1 b2: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b2 l2) ==> aloc_disjoint b1 b2", "val modifies\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0", "let loc_aux_disjoint_union_l\n (#al: aloc_t) (#c: cls al)\n (ll1 lr1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint (GSet.union ll1 lr1) l2 <==> (loc_aux_disjoint ll1 l2 /\\ loc_aux_disjoint lr1 l2)))\n= ()", "val modifies_intro\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')", "let loc_aux_disjoint_union_r\n (#al: aloc_t) (#c: cls al)\n (l1 ll2 lr2: GSet.set (aloc c))\n: Lemma\n (loc_aux_disjoint l1 (GSet.union ll2 lr2) <==> (loc_aux_disjoint l1 ll2 /\\ loc_aux_disjoint l1 lr2))\n= ()", "let loc_aux_disjoint_sym\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint l1 l2 <==> loc_aux_disjoint l2 l1))\n= Classical.forall_intro_2 (aloc_disjoint_sym #al #c)", "let regions_of_loc_loc_union\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (regions_of_loc (loc_union s1 s2) == regions_of_loc s1 `Set.union` regions_of_loc s2)\n [SMTPat (regions_of_loc (loc_union s1 s2))]\n= assert (regions_of_loc (loc_union s1 s2) `Set.equal` (regions_of_loc s1 `Set.union` regions_of_loc s2))", "let regions_of_loc_monotonic\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_includes s1 s2))\n (ensures (Set.subset (regions_of_loc s2) (regions_of_loc s1)))\n= ()", "let loc_disjoint_region_liveness_tags (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty", "let loc_disjoint_addrs (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n (forall (r: HS.rid) .\n GSet.subset (GSet.intersect (addrs_of_loc_weak l1 r) (addrs_of_loc l2 r)) GSet.empty /\\\n GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc_weak l2 r)) GSet.empty\n )", "let loc_disjoint_aux (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n loc_aux_disjoint (Ghost.reveal (Loc?.aux l1)) (Ghost.reveal (Loc?.aux l2))", "val modifies_none_intro\n (#al: aloc_t) (#c: cls al) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (HS.live_region h r /\\ HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n: Lemma\n (modifies (loc_none #_ #c) h h')", "let loc_disjoint'\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n: GTot Type0\n= loc_disjoint_region_liveness_tags l1 l2 /\\\n loc_disjoint_addrs l1 l2 /\\\n loc_disjoint_aux l1 l2", "let loc_disjoint = loc_disjoint'", "let loc_disjoint_sym #al #c l1 l2 =\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c)", "let loc_disjoint_sym'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))\n [SMTPat (loc_disjoint s1 s2)]\n= loc_disjoint_sym s1 s2", "let loc_disjoint_none_r #al #c s = ()", "let loc_disjoint_union_r #al #c s s1 s2 = ()", "val modifies_address_intro\n (#al: aloc_t) (#c: cls al) (r: HS.rid) (n: nat) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((r <> HS.frameOf b \\/ n <> HS.as_addr b) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (addr_unused_in: (\n (r': HS.rid) ->\n (n' : nat) ->\n Lemma\n (requires ((r' <> r \\/ n' <> n) /\\ HS.live_region h r' /\\ HS.live_region h' r' /\\ n' `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r')))\n (ensures (n' `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r')))\n ))\n: Lemma\n (modifies (loc_addresses #_ #c false r (Set.singleton n)) h h')", "let aloc_disjoint_includes (#al: aloc_t) (#c: cls al) (b1 b2 b3 : aloc c) : Lemma\n (requires (aloc_disjoint b1 b2 /\\ aloc_includes b2 b3))\n (ensures (aloc_disjoint b1 b3))\n= if b1.region = b2.region && b1.addr = b2.addr\n then begin\n c.aloc_includes_refl (Some?.v b1.loc);\n c.aloc_disjoint_includes (Some?.v b1.loc) (Some?.v b2.loc) (Some?.v b1.loc) (Some?.v b3.loc)\n end\n else ()", "let loc_aux_disjoint_loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (l1 l2 l3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\n= // FIXME: WHY WHY WHY do I need this assert?\n assert (forall (b1 b3: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b3 l3) ==> (exists (b2: aloc c) . GSet.mem b2 l2 /\\ aloc_disjoint b1 b2 /\\ aloc_includes b2 b3));\n Classical.forall_intro_3 (fun b1 b2 b3 -> Classical.move_requires (aloc_disjoint_includes #al #c b1 b2) b3)", "let loc_disjoint_includes #al #c p1 p2 p1' p2' =\n regions_of_loc_monotonic p1 p1';\n regions_of_loc_monotonic p2 p2';\n let l1 = Ghost.reveal (Loc?.aux p1) in\n let l2 = Ghost.reveal (Loc?.aux p2) in\n let l1' = Ghost.reveal (Loc?.aux p1') in\n let l2' = Ghost.reveal (Loc?.aux p2') in\n loc_aux_disjoint_loc_aux_includes l1 l2 l2';\n loc_aux_disjoint_sym l1 l2';\n loc_aux_disjoint_loc_aux_includes l2' l1 l1';\n loc_aux_disjoint_sym l2' l1'", "val modifies_aloc_intro\n (#al: aloc_t) (#c: cls al) (#r: HS.rid) (#n: nat) (z: al r n) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((r <> HS.frameOf b \\/ n <> HS.as_addr b) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (HS.live_region h r /\\ HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (x: al r n) ->\n Lemma\n (requires (c.aloc_disjoint x z))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies (loc_of_aloc #_ #c z) h h')", "let loc_disjoint_aloc_intro #al #c #r1 #a1 #r2 #a2 b1 b2 = ()", "let loc_disjoint_aloc_elim #al #c #r1 #a1 #r2 #a2 b1 b2 =\n // FIXME: WHY WHY WHY this assert?\n assert (aloc_disjoint (ALoc #_ #c r1 a1 (Some b1)) (ALoc #_ #c r2 a2 (Some b2)))", "let loc_disjoint_addresses_intro #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness1 r1 n1))) (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness2 r2 n2))))", "let loc_disjoint_addresses_elim #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 = ()", "let loc_disjoint_aloc_addresses_intro #al #c #r' #a' p preserve_liveness r n = ()", "let loc_disjoint_aloc_addresses_elim #al #c #r' #a' p preserve_liveness r n = ()", "let loc_disjoint_regions #al #c preserve_liveness1 preserve_liveness2 rs1 rs2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness1 rs1))) (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness2 rs2))))", "let loc_none_in_some_region #a (c: cls a) (r: HS.rid) : GTot (loc c) =\n Loc\n (Ghost.hide (Set.singleton r))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)", "let address_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))", "val modifies_live_region\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h1 h2: HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (modifies s h1 h2 /\\ loc_disjoint s (loc_region_only false r) /\\ HS.live_region h1 r))\n (ensures (HS.live_region h2 r))", "let loc_includes_address_liveness_insensitive_locs_aloc #al #c #r #n a = ()", "val modifies_mreference_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (b: HS.mreference t pre)\n (p: loc c)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_mreference b) p /\\\n HS.contains h b /\\\n modifies p h h'\n ))\n (ensures (\n HS.contains h' b /\\\n HS.sel h b == HS.sel h' b\n ))", "let loc_includes_address_liveness_insensitive_locs_addresses #al c r a = ()", "let region_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.complement GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))", "let loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs #al c = ()", "let loc_includes_region_liveness_insensitive_locs_loc_regions #al c r = ()", "let loc_includes_region_liveness_insensitive_locs_loc_addresses #al c preserve_liveness r a = ()", "let loc_includes_region_liveness_insensitive_locs_loc_of_aloc #al c #r #a x = ()", "val modifies_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#a: nat)\n (b: aloc r a)\n (p: loc c)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_of_aloc b) p /\\\n modifies p h h'\n ))\n (ensures (\n c.aloc_preserved b h h'\n ))", "let modifies_preserves_livenesses\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s r)))\n ) ==> (\n HS.contains h2 p\n ))", "let modifies_preserves_livenesses_elim\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (p: HS.mreference t pre)\n: Lemma\n (requires (modifies_preserves_livenesses s h1 h2 /\\ HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))))\n (ensures (HS.contains h2 p))\n= ()", "val modifies_refl\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h: HS.mem)\n: Lemma\n (modifies s h h)", "val modifies_loc_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (s1: loc c)\n (h h': HS.mem)\n (s2: loc c)\n: Lemma\n (requires (modifies s2 h h' /\\ loc_includes s1 s2))\n (ensures (modifies s1 h h'))", "let modifies_preserves_livenesses_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p))\n ))\n: Lemma\n (modifies_preserves_livenesses s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'", "val modifies_preserves_liveness\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union s1 s2) h h' /\\ loc_disjoint s1 (loc_mreference r) /\\ loc_includes (address_liveness_insensitive_locs c) s2 /\\ h `HS.contains` r))\n (ensures (h' `HS.contains` r))", "val modifies_preserves_liveness_strong\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n (x: aloc (HS.frameOf r) (HS.as_addr r))\n: Lemma\n (requires (modifies (loc_union s1 s2) h h' /\\ loc_disjoint s1 (loc_of_aloc #_ #c #(HS.frameOf r) #(HS.as_addr r) x) /\\ loc_includes (address_liveness_insensitive_locs c) s2 /\\ h `HS.contains` r))\n (ensures (h' `HS.contains` r))", "val modifies_preserves_region_liveness\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_region_only false r) l1 /\\ HS.live_region h r))\n (ensures (HS.live_region h' r))", "let modifies_preserves_mreferences\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s r)))\n ) ==> (\n HS.contains h2 p /\\\n HS.sel h2 p == HS.sel h1 p\n ))", "val modifies_preserves_region_liveness_reference\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_mreference r) l1 /\\ HS.live_region h (HS.frameOf r)))\n (ensures (HS.live_region h' (HS.frameOf r)))", "let modifies_preserves_mreferences_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p /\\ HS.sel h2 p == HS.sel h1 p))\n ))\n: Lemma\n (modifies_preserves_mreferences s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p /\\ h2 `HS.sel` p == h1 `HS.sel` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'", "val modifies_preserves_region_liveness_aloc\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (#r: HS.rid)\n (#n: nat)\n (x: al r n)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_of_aloc x) l1 /\\ HS.live_region h r))\n (ensures (HS.live_region h' r))", "val modifies_trans\n (#aloc: aloc_t) (#c: cls aloc)\n (s12: loc c)\n (h1 h2: HS.mem)\n (s23: loc c)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))", "val modifies_only_live_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (rs: Set.set HS.rid)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))", "let modifies_preserves_alocs\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (a: nat) (b: al r a) .\n loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))\n ==>\n c.aloc_preserved b h1 h2\n )", "val no_upd_fresh_region\n (#aloc: aloc_t) (#c: cls aloc)\n (r:HS.rid)\n (l:loc c)\n (h0:HS.mem)\n (h1:HS.mem)\n: Lemma\n (requires (HS.fresh_region r h0 h1 /\\ modifies (loc_union (loc_all_regions_from false r) l) h0 h1))\n (ensures (modifies l h0 h1))", "let modifies_preserves_alocs_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (u: unit { modifies_preserves_mreferences s h1 h2 } )\n (f: (\n (r: HS.rid) ->\n (a: nat) ->\n (b: al r a) ->\n Lemma\n (requires (\n Set.mem r (regions_of_loc s) /\\\n (~ (GSet.mem a (addrs_of_loc_weak s r))) /\\\n (GSet.mem a (addrs_of_loc_aux s r) /\\ loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b))))\n ))\n (ensures (c.aloc_preserved b h1 h2))\n ))\n: Lemma\n (modifies_preserves_alocs s h1 h2)\n= let f'\n (r: HS.rid)\n (a: nat)\n (b: al r a)\n : Lemma\n (requires (loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))))\n (ensures (c.aloc_preserved b h1 h2))\n = if Set.mem r (regions_of_loc s) && (not (GSet.mem a (addrs_of_loc_weak s r)))\n then begin\n if GSet.mem a (addrs_of_loc_aux s r)\n then\n Classical.move_requires (f r a) b\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n end else if Set.mem r (regions_of_loc s)\n then begin\n assert (GSet.mem a (addrs_of_loc_weak s r));\n assert (GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux s)));\n assert (aloc_disjoint #_ #c (ALoc r a None) (ALoc r a (Some b)));\n assert False\n end\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n in\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (f' r a) b)", "val fresh_frame_modifies\n (#aloc: aloc_t) (c: cls aloc)\n (h0 h1: HS.mem)\n: Lemma\n (requires (HS.fresh_frame h0 h1))\n (ensures (modifies #_ #c loc_none h0 h1))", "val new_region_modifies\n (#al: aloc_t)\n (c: cls al)\n (m0: HS.mem)\n (r0: HS.rid)\n (col: option int)\n: Lemma\n (requires (HST.is_eternal_region r0 /\\ HS.live_region m0 r0 /\\ (None? col \\/ HS.is_heap_color (Some?.v col))))\n (ensures (\n let (_, m1) = HS.new_eternal_region m0 r0 col in\n modifies (loc_none #_ #c) m0 m1\n ))", "val popped_modifies\n (#aloc: aloc_t) (c: cls aloc)\n (h0 h1: HS.mem) : Lemma\n (requires (HS.popped h0 h1))\n (ensures (modifies #_ #c (loc_region_only false (HS.get_tip h0)) h0 h1))", "val modifies_fresh_frame_popped\n (#aloc: aloc_t) (#c: cls aloc)\n (h0 h1: HS.mem)\n (s: loc c)\n (h2 h3: HS.mem)\n: Lemma\n (requires (\n HS.fresh_frame h0 h1 /\\\n modifies (loc_union (loc_all_regions_from false (HS.get_tip h1)) s) h1 h2 /\\\n HS.get_tip h2 == HS.get_tip h1 /\\\n HS.popped h2 h3\n ))\n (ensures (\n modifies s h0 h3 /\\\n HS.get_tip h3 == HS.get_tip h0\n ))", "let modifies_preserves_regions\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= forall (r: HS.rid) . (HS.live_region h1 r /\\ ~ (Set.mem r (Ghost.reveal (Loc?.region_liveness_tags s)))) ==> HS.live_region h2 r", "val modifies_loc_regions_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (rs: Set.set HS.rid)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HS.modifies rs h1 h2))\n (ensures (modifies (loc_regions #_ #c true rs) h1 h2))", "let modifies_preserves_not_unused_in\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (n: nat) . (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))", "val modifies_loc_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc c)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r a h1 h2\n ))\n (ensures (modifies (loc_union (loc_addresses true r a) l) h1 h2))", "let modifies_preserves_not_unused_in_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ))\n (ensures (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n ))\n: Lemma\n (modifies_preserves_not_unused_in s h1 h2)\n= let f'\n (r: HS.rid)\n (n: nat)\n : Lemma\n ((\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n = Classical.move_requires (f r) n\n in\n Classical.forall_intro_2 f'", "val modifies_ralloc_post\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (i: HS.rid)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel)\n (h' : HS.mem)\n: Lemma\n (requires (HST.ralloc_post i init h x h'))\n (ensures (modifies (loc_none #_ #c) h h'))", "val modifies_salloc_post\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel { HS.is_stack_region (HS.frameOf x) } )\n (h' : HS.mem)\n: Lemma\n (requires (HST.salloc_post init h x h'))\n (ensures (modifies (loc_none #_ #c) h h'))", "val modifies_free\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel { HS.is_mm r } )\n (m: HS.mem { m `HS.contains` r } )\n: Lemma\n (modifies (loc_freed_mreference #_ #c r) m (HS.free r m))", "let modifies'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= modifies_preserves_regions s h1 h2 /\\\n modifies_preserves_not_unused_in s h1 h2 /\\\n modifies_preserves_mreferences s h1 h2 /\\\n modifies_preserves_livenesses s h1 h2 /\\\n modifies_preserves_alocs s h1 h2", "val modifies_none_modifies\n (#aloc: aloc_t) (#c: cls aloc)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HST.modifies_none h1 h2))\n (ensures (modifies (loc_none #_ #c) h1 h2))", "let modifies = modifies'", "val modifies_intro_strong\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n (Set.mem r (regions_of_loc l) ==> ~ (GSet.mem n (Loc?.non_live_addrs l r))) /\\\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')", "val modifies_upd\n (#aloc: aloc_t) (#c: cls aloc)\n (#t: Type) (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n (v: t)\n (h: HS.mem)\n: Lemma\n (requires (HS.contains h r))\n (ensures (modifies #_ #c (loc_mreference r) h (HS.upd h r v)))", "val modifies_strengthen\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (h h' : HS.mem)\n (alocs: (\n (f: ((t: Type) -> (pre: Preorder.preorder t) -> (m: HS.mreference t pre) -> Lemma\n (requires (HS.frameOf m == r0 /\\ HS.as_addr m == a0 /\\ HS.contains h m))\n (ensures (HS.contains h' m))\n )) ->\n (x: al r0 a0) ->\n Lemma\n (requires (c.aloc_disjoint x al0 /\\ loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (requires (modifies (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h'))\n (ensures (modifies (loc_union l (loc_of_aloc al0)) h h'))", "val does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: GTot Type0", "val not_live_region_does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (~ (HS.live_region h (fst ra))))\n (ensures (h `does_not_contain_addr` ra))" ], "closest": [ "val modifies_loc_addresses_intro\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_regions (Set.singleton r)) l) h1 h2 /\\\n HS.modifies_ref r a h1 h2\n ))\n (ensures (modifies (loc_union (loc_addresses r a) l) h1 h2))\nlet modifies_loc_addresses_intro r a l h1 h2 =\n MG.modifies_loc_addresses_intro r a l h1 h2;\n MG.loc_includes_addresses_addresses #_ cls false true r a a;\n MG.loc_includes_refl l;\n MG.loc_includes_union_l (loc_addresses r a) l l;\n MG.loc_includes_union_l (loc_addresses r a) l (MG.loc_addresses true r a);\n MG.loc_includes_union_r (loc_union (loc_addresses r a) l) (MG.loc_addresses true r a) l;\n MG.modifies_loc_includes (loc_union (loc_addresses r a) l) h1 h2 (loc_union (MG.loc_addresses true r a) l)", "val modifies_loc_addresses_intro\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r a h1 h2\n ))\n (ensures (modifies (loc_union (loc_addresses true r a) l) h1 h2))\nlet modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro", "val modifies_loc_addresses_intro\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r a h1 h2\n ))\n (ensures (modifies (loc_union (loc_addresses true r a) l) h1 h2))\nlet modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls", "val modifies_only_live_addresses\n (#aloc: aloc_t)\n (#c: cls aloc)\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc c)\n (h h': HS.mem)\n : Lemma\n (requires\n (modifies (loc_union (loc_addresses false r a) l) h h' /\\\n (forall x. Set.mem x a ==> h `does_not_contain_addr` (r, x)))) (ensures (modifies l h h'))\nlet modifies_only_live_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_addresses false r a) l) h h' /\\\n (forall x . Set.mem x a ==> h `does_not_contain_addr` (r, x))\n ))\n (ensures (modifies l h h'))\n= loc_addresses_unused_in c r a h;\n loc_includes_refl l;\n loc_includes_union_l (loc_unused_in c h) l l;\n loc_includes_union_l (loc_unused_in c h) l (loc_addresses false r a);\n loc_includes_union_r (loc_union (loc_unused_in c h) l) (loc_addresses false r a) l;\n modifies_loc_includes (loc_union (loc_unused_in c h) l) h h' (loc_union (loc_addresses false r a) l);\n modifies_only_not_unused_in l h h'", "val modifies_liveness_insensitive_region_mreference_weak\n (l2: loc)\n (h h': HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n : Lemma\n (requires\n (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\\n HS.live_region h (HS.frameOf x)))\n (ensures (HS.live_region h' (HS.frameOf x)))\n [\n SMTPatOr\n [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h (HS.frameOf x))];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' (HS.frameOf x))]\n ]\n ]\nlet modifies_liveness_insensitive_region_mreference_weak\n (l2 : loc)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n : Lemma (requires (modifies l2 h h' /\\\n region_liveness_insensitive_locs `loc_includes` l2 /\\\n\t\t HS.live_region h (HS.frameOf x)))\n (ensures (HS.live_region h' (HS.frameOf x)))\n [SMTPatOr [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h (HS.frameOf x))];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' (HS.frameOf x))];\n ]]\n = modifies_liveness_insensitive_region_mreference loc_none l2 h h' x", "val modifies_liveness_insensitive_region_mreference_weak\n (l2: loc)\n (h h': HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n : Lemma\n (requires\n (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\\n HS.live_region h (HS.frameOf x)))\n (ensures (HS.live_region h' (HS.frameOf x)))\n [\n SMTPatOr\n [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h (HS.frameOf x))];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' (HS.frameOf x))]\n ]\n ]\nlet modifies_liveness_insensitive_region_mreference_weak\n (l2 : loc)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n: Lemma\n (requires (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h (HS.frameOf x)))\n (ensures (HS.live_region h' (HS.frameOf x)))\n [SMTPatOr [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h (HS.frameOf x))];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' (HS.frameOf x))];\n ]]\n= modifies_liveness_insensitive_region_mreference loc_none l2 h h' x", "val modifies_loc_regions_intro\n (rs: Set.set HS.rid)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HS.modifies rs h1 h2))\n (ensures (modifies (loc_regions true rs) h1 h2))\nlet modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls", "val modifies_loc_regions_intro\n (rs: Set.set HS.rid)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HS.modifies rs h1 h2))\n (ensures (modifies (loc_regions true rs) h1 h2))\nlet modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls", "val modifies_liveness_insensitive_region_mreference\n (l1 l2 : loc)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ loc_disjoint l1 (loc_mreference x) /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h (HS.frameOf x)))\n (ensures (HS.live_region h' (HS.frameOf x)))\nlet modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference", "val modifies_loc_regions_intro\n (rs: Set.set HS.rid)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HS.modifies rs h1 h2))\n (ensures (modifies (loc_regions rs) h1 h2))\nlet modifies_loc_regions_intro rs h1 h2 =\n MG.modifies_loc_regions_intro #_ #cls rs h1 h2;\n MG.loc_includes_region_region #_ #cls false true rs rs;\n MG.modifies_loc_includes (loc_regions rs) h1 h2 (MG.loc_regions true rs)", "val modifies_only_live_regions\n (rs: Set.set HS.rid)\n (l: loc)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions rs) l) h h' /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))\nlet modifies_only_live_regions = MG.modifies_only_live_regions", "val modifies_liveness_insensitive_mreference\n (l1 l2 : loc)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ loc_disjoint l1 (loc_mreference x) /\\ address_liveness_insensitive_locs `loc_includes` l2 /\\ h `HS.contains` x))\n (ensures (h' `HS.contains` x))\nlet modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness", "val modifies_only_live_addresses\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_addresses false r a) l) h h' /\\\n (forall x . Set.mem x a ==> h `does_not_contain_addr` (r, x))\n ))\n (ensures (modifies l h h'))\nlet modifies_only_live_addresses = MG.modifies_only_live_addresses", "val modifies_only_live_addresses\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_addresses false r a) l) h h' /\\\n (forall x . Set.mem x a ==> h `does_not_contain_addr` (r, x))\n ))\n (ensures (modifies l h h'))\nlet modifies_only_live_addresses = MG.modifies_only_live_addresses", "val modifies_only_live_regions\n (rs: Set.set HS.rid)\n (l: loc)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))\nlet modifies_only_live_regions = MG.modifies_only_live_regions", "val modifies_only_live_regions\n (rs: Set.set HS.rid)\n (l: loc)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))\nlet modifies_only_live_regions = MG.modifies_only_live_regions", "val modifies_liveness_insensitive_region\n (l1 l2 : loc)\n (h h' : HS.mem)\n (x: HS.rid)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ loc_disjoint l1 (loc_region_only false x) /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h x))\n (ensures (HS.live_region h' x))\nlet modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness", "val modifies_liveness_insensitive_region_mreference\n (l1 l2 : loc)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ loc_disjoint l1 (loc_mreference x) /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h (HS.frameOf x)))\n (ensures (HS.live_region h' (HS.frameOf x)))\n [SMTPatOr [\n [SMTPat (modifies (loc_union l1 l2) h h'); SMTPat (HS.live_region h (HS.frameOf x))];\n [SMTPat (modifies (loc_union l1 l2) h h'); SMTPat (HS.live_region h' (HS.frameOf x))];\n ]]\nlet modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference", "val modifies_liveness_insensitive_region_weak (l2: loc) (h h': HS.mem) (x: HS.rid)\n : Lemma\n (requires\n (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\\n HS.live_region h x))\n (ensures (HS.live_region h' x))\n [\n SMTPatOr\n [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h x)];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' x)]\n ]\n ]\nlet modifies_liveness_insensitive_region_weak\n (l2 : loc)\n (h h' : HS.mem)\n (x: HS.rid)\n: Lemma\n (requires (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h x))\n (ensures (HS.live_region h' x))\n [SMTPatOr [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h x)];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' x)];\n ]]\n= modifies_liveness_insensitive_region loc_none l2 h h' x", "val modifies_liveness_insensitive_region_weak (l2: loc) (h h': HS.mem) (x: HS.rid)\n : Lemma\n (requires\n (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\\n HS.live_region h x))\n (ensures (HS.live_region h' x))\n [\n SMTPatOr\n [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h x)];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' x)]\n ]\n ]\nlet modifies_liveness_insensitive_region_weak\n (l2 : loc)\n (h h' : HS.mem)\n (x: HS.rid)\n: Lemma\n (requires (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h x))\n (ensures (HS.live_region h' x))\n [SMTPatOr [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h x)];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' x)];\n ]]\n= modifies_liveness_insensitive_region loc_none l2 h h' x", "val modifies_liveness_insensitive_mreference_weak\n (l: loc)\n (h h': HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n : Lemma\n (requires\n (modifies l h h' /\\ address_liveness_insensitive_locs `loc_includes` l /\\ h `HS.contains` x)\n )\n (ensures (h' `HS.contains` x))\n [\n SMTPatOr\n [\n [SMTPat (h `HS.contains` x); SMTPat (modifies l h h')];\n [SMTPat (h' `HS.contains` x); SMTPat (modifies l h h')]\n ]\n ]\nlet modifies_liveness_insensitive_mreference_weak\n (l : loc)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n : Lemma (requires (modifies l h h' /\\\n address_liveness_insensitive_locs `loc_includes` l /\\\n\t\t h `HS.contains` x))\n (ensures (h' `HS.contains` x))\n [SMTPatOr [\n [SMTPat (h `HS.contains` x); SMTPat (modifies l h h');];\n [SMTPat (h' `HS.contains` x); SMTPat (modifies l h h');];\n ]]\n = modifies_liveness_insensitive_mreference loc_none l h h' x", "val modifies_liveness_insensitive_mreference_weak\n (l: loc)\n (h h': HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n : Lemma\n (requires\n (modifies l h h' /\\ address_liveness_insensitive_locs `loc_includes` l /\\ h `HS.contains` x)\n )\n (ensures (h' `HS.contains` x))\n [\n SMTPatOr\n [\n [SMTPat (h `HS.contains` x); SMTPat (modifies l h h')];\n [SMTPat (h' `HS.contains` x); SMTPat (modifies l h h')]\n ]\n ]\nlet modifies_liveness_insensitive_mreference_weak\n (l : loc)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n: Lemma\n (requires (modifies l h h' /\\ address_liveness_insensitive_locs `loc_includes` l /\\ h `HS.contains` x))\n (ensures (h' `HS.contains` x))\n [SMTPatOr [\n [SMTPat (h `HS.contains` x); SMTPat (modifies l h h');];\n [SMTPat (h' `HS.contains` x); SMTPat (modifies l h h');];\n ]]\n= modifies_liveness_insensitive_mreference loc_none l h h' x", "val modifies_live_region\n (s: loc)\n (h1 h2: HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (modifies s h1 h2 /\\ loc_disjoint s (loc_region_only false r) /\\ HS.live_region h1 r))\n (ensures (HS.live_region h2 r))\n [SMTPatOr [\n [SMTPat (modifies s h1 h2); SMTPat (HS.live_region h1 r)];\n [SMTPat (modifies s h1 h2); SMTPat (HS.live_region h2 r)];\n ]]\nlet modifies_live_region = MG.modifies_live_region", "val modifies_reference_elim\n (#t: Type0)\n (b: HS.reference t)\n (p: loc)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_addresses (HS.frameOf b) (Set.singleton (HS.as_addr b))) p /\\\n HS.contains h b /\\\n modifies p h h'\n ))\n (ensures (\n HS.contains h' b /\\\n HS.sel h b == HS.sel h' b\n ))\n [SMTPatOr [\n [ SMTPat (modifies p h h'); SMTPat (HS.sel h b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (HS.contains h b) ];\n [ SMTPat (modifies p h h'); SMTPat (HS.sel h' b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (HS.contains h' b) ]\n ] ]\nlet modifies_reference_elim #t b p h h' =\n MG.loc_includes_addresses_addresses #_ cls false true (HS.frameOf b) (Set.singleton (HS.as_addr b)) (Set.singleton (HS.as_addr b));\n MG.loc_includes_refl p;\n MG.loc_disjoint_includes (MG.loc_freed_mreference b) p (MG.loc_mreference b) p;\n MG.modifies_mreference_elim b p h h'", "val modifies_liveness_insensitive_region\n (l1 l2 : loc)\n (h h' : HS.mem)\n (x: HS.rid)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ loc_disjoint l1 (loc_region_only false x) /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h x))\n (ensures (HS.live_region h' x))\n [SMTPatOr [\n [SMTPat (modifies (loc_union l1 l2) h h'); SMTPat (HS.live_region h x)];\n [SMTPat (modifies (loc_union l1 l2) h h'); SMTPat (HS.live_region h' x)];\n ]]\nlet modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness", "val modifies_address_liveness_insensitive_unused_in\n (h h' : HS.mem)\n: Lemma\n (requires (modifies (address_liveness_insensitive_locs) h h'))\n (ensures (loc_not_unused_in h' `loc_includes` loc_not_unused_in h /\\ loc_unused_in h `loc_includes` loc_unused_in h'))\nlet modifies_address_liveness_insensitive_unused_in =\n MG.modifies_address_liveness_insensitive_unused_in cls", "val modifies_liveness_insensitive_region_buffer_weak\n (l2: loc)\n (h h': HS.mem)\n (#a: Type0)\n (#rrel #rel: srel a)\n (x: mbuffer a rrel rel)\n : Lemma\n (requires\n (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\\n HS.live_region h (frameOf x)))\n (ensures (HS.live_region h' (frameOf x)))\n [\n SMTPatOr\n [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h (frameOf x))];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' (frameOf x))]\n ]\n ]\nlet modifies_liveness_insensitive_region_buffer_weak\n (l2:loc)\n (h h':HS.mem)\n (#a:Type0) (#rrel #rel:srel a)\n (x:mbuffer a rrel rel)\n :Lemma (requires (modifies l2 h h' /\\\n region_liveness_insensitive_locs `loc_includes` l2 /\\\n\t\t HS.live_region h (frameOf x)))\n (ensures (HS.live_region h' (frameOf x)))\n [SMTPatOr [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h (frameOf x))];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' (frameOf x))];\n ]]\n = modifies_liveness_insensitive_region_buffer loc_none l2 h h' x", "val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a)\n (h h':HS.mem) (b:mbuffer a rrel rel)\n (f: (\n (t':Type0) ->\n (pre: Preorder.preorder t') ->\n (r: HS.mreference t' pre) ->\n Lemma\n (requires (HS.frameOf r == frameOf b /\\ HS.as_addr r == as_addr b /\\ h `HS.contains` r))\n (ensures (h' `HS.contains` r))\n ))\n :Lemma (requires (live h b)) (ensures (live h' b))\nlet liveness_preservation_intro #_ #_ #_ _ _ b f =\n if Null? b\n then ()\n else f _ _ (Buffer?.content b)", "val modifies_only_not_unused_in\n (l: loc)\n (h h' : HS.mem)\n: Lemma\n (requires (modifies (loc_union (loc_unused_in h) l) h h'))\n (ensures (modifies l h h'))\nlet modifies_only_not_unused_in = MG.modifies_only_not_unused_in", "val modifies_liveness_insensitive_mreference\n (l1 l2 : loc)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (x: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ loc_disjoint l1 (loc_mreference x) /\\ address_liveness_insensitive_locs `loc_includes` l2 /\\ h `HS.contains` x))\n (ensures (h' `HS.contains` x))\n [SMTPatOr [\n [SMTPat (h `HS.contains` x); SMTPat (modifies (loc_union l1 l2) h h');];\n [SMTPat (h' `HS.contains` x); SMTPat (modifies (loc_union l1 l2) h h');];\n ]]\nlet modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness", "val modifies_mreference_elim\n (#t: Type)\n (#pre: Preorder.preorder t)\n (b: HS.mreference t pre)\n (p: loc)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_mreference b) p /\\\n HS.contains h b /\\\n modifies p h h'\n ))\n (ensures (\n HS.contains h' b /\\\n HS.sel h b == HS.sel h' b\n ))\n [SMTPatOr [\n [ SMTPat (modifies p h h'); SMTPat (HS.sel h b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (HS.contains h b) ];\n [ SMTPat (modifies p h h'); SMTPat (HS.sel h' b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (HS.contains h' b) ]\n ] ]\nlet modifies_mreference_elim = MG.modifies_mreference_elim", "val modifies_mreference_elim\n (#t: Type)\n (#pre: Preorder.preorder t)\n (b: HS.mreference t pre)\n (p: loc)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_mreference b) p /\\\n HS.contains h b /\\\n modifies p h h'\n ))\n (ensures (\n HS.contains h' b /\\\n HS.sel h b == HS.sel h' b\n ))\n [SMTPatOr [\n [ SMTPat (modifies p h h'); SMTPat (HS.sel h b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (HS.contains h b) ];\n [ SMTPat (modifies p h h'); SMTPat (HS.sel h' b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (HS.contains h' b) ]\n ] ]\nlet modifies_mreference_elim = MG.modifies_mreference_elim", "val modifies_ralloc_post\n (#a: Type)\n (#rel: Preorder.preorder a)\n (i: HS.rid)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel { HST.is_eternal_region (HS.frameOf x) } )\n (h' : HS.mem)\n: Lemma\n (requires (HST.ralloc_post i init h x h'))\n (ensures (modifies loc_none h h'))\nlet modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls", "val modifies_salloc_post\n (#a: Type)\n (#rel: Preorder.preorder a)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel { HS.is_stack_region (HS.frameOf x) } )\n (h' : HS.mem)\n: Lemma\n (requires (HST.salloc_post init h x h'))\n (ensures (modifies loc_none h h'))\nlet modifies_salloc_post = MG.modifies_salloc_post #_ #cls", "val modifies_loc_buffer_from_to_intro'\n (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel)\n (from to: U32.t)\n (l: loc) (h h' : HS.mem)\n: Lemma\n (requires (\n let s = as_seq h b in\n let s' = as_seq h' b in\n not (g_is_null b) /\\\n live h b /\\\n modifies (loc_union l (loc_buffer b)) h h' /\\\n U32.v from <= U32.v to /\\\n U32.v to <= length b /\\\n Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\\\n Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b)\n ))\n (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h'))\nlet modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' =\n let r0 = frameOf b in\n let a0 = as_addr b in\n let bb : ubuffer r0 a0 = ubuffer_of_buffer b in\n modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b));\n MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) ->\n ubuffer_preserved_intro x h h'\n (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b'))\n (fun t' rrel' rel' b' ->\n // prove that the types, rrels, rels are equal\n Heap.lemma_distinct_addrs_distinct_preorders ();\n Heap.lemma_distinct_addrs_distinct_mm ();\n assert (Seq.seq t' == Seq.seq a);\n let _s0 : Seq.seq a = as_seq h b in\n let _s1 : Seq.seq t' = coerce_eq _ _s0 in\n lemma_equal_instances_implies_equal_types a t' _s0 _s1;\n let boff = U32.v (Buffer?.idx b) in\n let from_ = boff + U32.v from in\n let to_ = boff + U32.v to in\n let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in\n let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in\n let bh = as_seq h b in\n let bh' = as_seq h' b in\n let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in\n let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in\n let prf (i: nat) : Lemma\n (requires (i < xlen))\n (ensures (i < xlen /\\ Seq.index xh i == Seq.index xh' i))\n = let xi = xoff + i in\n let bi : ubuffer r0 a0 =\n Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; })\n in\n assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0);\n assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0);\n let li = MG.loc_of_aloc bi in\n MG.loc_includes_aloc #_ #cls x bi;\n loc_disjoint_includes l (MG.loc_of_aloc x) l li;\n if xi < boff || boff + length b <= xi\n then begin\n MG.loc_disjoint_aloc_intro #_ #cls bb bi;\n assert (loc_disjoint (loc_union l (loc_buffer b)) li);\n MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h'\n end else\n if xi < from_\n then begin\n assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff));\n assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff))\n end else begin\n assert (to_ <= xi);\n assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_));\n assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_))\n end\n in\n Classical.forall_intro (Classical.move_requires prf);\n assert (xh `Seq.equal` xh')\n )\n )", "val old_to_new_modifies (old_l: OldM.loc) (new_l: NewM.loc) (h h': HS.mem)\n : Lemma\n (requires (OldM.modifies old_l h h' /\\ old_to_union_loc old_l == new_to_union_loc new_l))\n (ensures (NewM.modifies new_l h h'))\nlet old_to_new_modifies (old_l: OldM.loc) (new_l: NewM.loc) (h h' : HS.mem) : Lemma\n (requires (OldM.modifies old_l h h' /\\ old_to_union_loc old_l == new_to_union_loc new_l))\n (ensures (NewM.modifies new_l h h'))\n= OldM.modifies_to_cloc old_l h h';\n M.modifies_union_loc_of_loc old_and_new_cl false (OldM.cloc_of_loc old_l) h h';\n M.modifies_union_loc_of_loc old_and_new_cl true (M.raise_loc (NewM.cloc_of_loc new_l)) h h';\n M.modifies_raise_loc (NewM.cloc_of_loc new_l) h h';\n NewM.modifies_to_cloc new_l h h'", "val modifies_liveness_insensitive_region_buffer_weak\n (l2: loc)\n (h h': HS.mem)\n (#t: Type)\n (x: B.buffer t)\n : Lemma\n (requires\n (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\\n HS.live_region h (B.frameOf x)))\n (ensures (HS.live_region h' (B.frameOf x)))\n [\n SMTPatOr\n [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h (B.frameOf x))];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' (B.frameOf x))]\n ]\n ]\nlet modifies_liveness_insensitive_region_buffer_weak\n (l2 : loc)\n (h h' : HS.mem)\n (#t: Type)\n (x: B.buffer t)\n: Lemma\n (requires (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h (B.frameOf x)))\n (ensures (HS.live_region h' (B.frameOf x)))\n [SMTPatOr [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h (B.frameOf x))];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' (B.frameOf x))];\n ]]\n= modifies_liveness_insensitive_region_buffer loc_none l2 h h' x", "val modifies_salloc_post\n (#a: Type)\n (#rel: Preorder.preorder a)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel { HS.is_stack_region (HS.frameOf x) } )\n (h' : HS.mem)\n: Lemma\n (requires (HST.salloc_post init h x h'))\n (ensures (modifies loc_none h h'))\n [SMTPat (HST.salloc_post init h x h')]\nlet modifies_salloc_post = MG.modifies_salloc_post #_ #cls", "val modifies_loc_buffer_from_to_intro\n (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel)\n (from to: U32.t)\n (l: loc) (h h' : HS.mem)\n: Lemma\n (requires (\n let s = as_seq h b in\n let s' = as_seq h' b in\n live h b /\\\n modifies (loc_union l (loc_buffer b)) h h' /\\\n U32.v from <= U32.v to /\\\n U32.v to <= length b /\\\n Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\\\n Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b)\n ))\n (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h'))\nlet modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' =\n if g_is_null b\n then ()\n else modifies_loc_buffer_from_to_intro' b from to l h h'", "val loc_all_regions_from (#aloc: aloc_t) (#c: cls aloc) (preserve_liveness: bool) (r: HS.rid)\n : GTot (loc c)\nlet loc_all_regions_from\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (HS.mod_set (Set.singleton r))", "val preserved (x: t) (l: B.loc) (h h': HS.mem)\n : Lemma (requires (live x h /\\ B.modifies l h h' /\\ B.loc_disjoint (footprint x) l))\n (ensures\n (live x h' /\\ get_remaining x h' == get_remaining x h /\\ get_read x h' == get_read x h))\nlet preserved\n (x: t)\n (l: B.loc)\n (h: HS.mem)\n (h' : HS.mem)\n: Lemma\n (requires (live x h /\\ B.modifies l h h' /\\ B.loc_disjoint (footprint x) l))\n (ensures (\n live x h' /\\\n get_remaining x h' == get_remaining x h /\\\n get_read x h' == get_read x h\n ))\n=\n Aux.preserved x.Aux.base l h h'", "val modifies_liveness_insensitive_region_buffer\n (l1 l2 : loc)\n (h h' : HS.mem)\n (#t: Type)\n (x: B.buffer t)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ loc_disjoint l1 (loc_buffer x) /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h (B.frameOf x)))\n (ensures (HS.live_region h' (B.frameOf x)))\nlet modifies_liveness_insensitive_region_buffer l1 l2 h h' #t x =\n MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(B.frameOf x) #(B.as_addr x) (LocBuffer x)", "val modifies_liveness_insensitive_buffer_weak\n (l: loc)\n (h h': HS.mem)\n (#a: Type0)\n (#rrel #rel: srel a)\n (x: mbuffer a rrel rel)\n : Lemma\n (requires (modifies l h h' /\\ address_liveness_insensitive_locs `loc_includes` l /\\ live h x))\n (ensures (live h' x))\n [\n SMTPatOr\n [\n [SMTPat (live h x); SMTPat (modifies l h h')];\n [SMTPat (live h' x); SMTPat (modifies l h h')]\n ]\n ]\nlet modifies_liveness_insensitive_buffer_weak\n (l:loc)\n (h h':HS.mem)\n (#a:Type0) (#rrel #rel:srel a)\n (x:mbuffer a rrel rel)\n :Lemma (requires (modifies l h h' /\\ address_liveness_insensitive_locs `loc_includes` l /\\ live h x))\n (ensures (live h' x))\n [SMTPatOr [\n [SMTPat (live h x); SMTPat (modifies l h h');];\n [SMTPat (live h' x); SMTPat (modifies l h h');];\n ]]\n = modifies_liveness_insensitive_buffer loc_none l h h' x", "val insert_modifies_union_loc_weakening:\n l1:loc -> l2:loc -> l3:loc -> h0:HS.mem -> h1:HS.mem ->\n Lemma (requires (modifies l1 h0 h1))\n (ensures (modifies (loc_union (loc_union l1 l2) l3) h0 h1))\nlet insert_modifies_union_loc_weakening l1 l2 l3 h0 h1 =\n B.loc_includes_union_l l1 l2 l1;\n B.loc_includes_union_l (loc_union l1 l2) l3 (loc_union l1 l2)", "val modifies_liveness_insensitive_region_buffer\n (l1 l2:loc)\n (h h':HS.mem)\n (#a:Type0) (#rrel #rel:srel a)\n (x:mbuffer a rrel rel)\n :Lemma (requires (modifies (loc_union l1 l2) h h' /\\ loc_disjoint l1 (loc_buffer x) /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h (frameOf x)))\n (ensures (HS.live_region h' (frameOf x)))\n [SMTPatOr [\n [SMTPat (modifies (loc_union l1 l2) h h'); SMTPat (HS.live_region h (frameOf x))];\n [SMTPat (modifies (loc_union l1 l2) h h'); SMTPat (HS.live_region h' (frameOf x))];\n ]]\nlet modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x =\n if g_is_null x then ()\n else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x)", "val modifies_free\n (#a: Type)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel { HS.is_mm r } )\n (m: HS.mem { m `HS.contains` r } )\n: Lemma\n (modifies (loc_freed_mreference r) m (HS.free r m))\nlet modifies_free = MG.modifies_free #_ #cls", "val modifies_trans\n (s12: loc)\n (h1 h2: HS.mem)\n (s23: loc)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))\nlet modifies_trans = MG.modifies_trans", "val modifies_loc_unused_in\n (l: loc)\n (h1 h2: HS.mem)\n (l' : loc)\n: Lemma\n (requires (\n modifies l h1 h2 /\\\n address_liveness_insensitive_locs `loc_includes` l /\\\n loc_unused_in h2 `loc_includes` l'\n ))\n (ensures (loc_unused_in h1 `loc_includes` l'))\n [SMTPatOr [\n [SMTPat (modifies l h1 h2); SMTPat (loc_unused_in h2 `loc_includes` l')];\n [SMTPat (modifies l h1 h2); SMTPat (loc_unused_in h1 `loc_includes` l')];\n ]]\nlet modifies_loc_unused_in l h1 h2 l' =\n modifies_loc_includes address_liveness_insensitive_locs h1 h2 l;\n modifies_address_liveness_insensitive_unused_in h1 h2;\n loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l'", "val loc_regions_unused_in (h: HS.mem) (rs: Set.set HS.rid) : Lemma\n (requires (forall r . Set.mem r rs ==> (~ (HS.live_region h r))))\n (ensures (loc_unused_in h `loc_includes` loc_regions false rs))\nlet loc_regions_unused_in = MG.loc_regions_unused_in cls", "val loc_region_only (#aloc: aloc_t) (#c: cls aloc) (preserve_liveness: bool) (r: HS.rid)\n : GTot (loc c)\nlet loc_region_only\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (Set.singleton r)", "val modifies_0_modifies\n (h1 h2: HS.mem)\n: Lemma\n (requires (modifies_0 h1 h2))\n (ensures (modifies loc_none h1 h2))\nlet modifies_0_modifies h1 h2 =\n MG.modifies_none_intro #_ #cls h1 h2\n (fun r -> modifies_0_live_region h1 h2 r)\n (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b)\n (fun r n -> modifies_0_unused_in h1 h2 r n)", "val not_live_region_does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (~ (HS.live_region h (fst ra))))\n (ensures (h `does_not_contain_addr` ra))\nlet not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr", "val not_live_region_does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (~ (HS.live_region h (fst ra))))\n (ensures (h `does_not_contain_addr` ra))\nlet not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr", "val modifies_remove_new_locs (l_fresh l_aux l_goal:loc) (h1 h2 h3:HS.mem)\n : Lemma (requires (fresh_loc l_fresh h1 h2 /\\\n modifies l_aux h1 h2 /\\\n\t\t l_goal `loc_includes` l_aux /\\\n modifies (loc_union l_fresh l_goal) h2 h3))\n (ensures (modifies l_goal h1 h3))\n\t [SMTPat (fresh_loc l_fresh h1 h2);\n\t SMTPat (modifies l_aux h1 h2);\n\t SMTPat (modifies l_goal h1 h3)]\nlet modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 =\n modifies_only_not_unused_in l_goal h1 h3", "val pointer_preserved_intro\n (#t: typ)\n (p: pointer t)\n (h1 h2: HS.mem)\n (f:\n (a': Type0 -> pre: Preorder.preorder a' -> r': HS.mreference a' pre\n -> Lemma\n (requires\n (h1 `HS.contains` r' /\\ frameOf p == HS.frameOf r' /\\ as_addr p == HS.as_addr r'\n )) (ensures (h2 `HS.contains` r' /\\ h1 `HS.sel` r' == h2 `HS.sel` r'))))\n : Lemma (pointer_preserved p h1 h2)\nlet pointer_preserved_intro\n (#t: typ)\n (p: pointer t)\n (h1 h2 : HS.mem)\n (f: (\n (a' : Type0) ->\n (pre: Preorder.preorder a') ->\n (r': HS.mreference a' pre) ->\n Lemma\n (requires (h1 `HS.contains` r' /\\ frameOf p == HS.frameOf r' /\\ as_addr p == HS.as_addr r'))\n (ensures (h2 `HS.contains` r' /\\ h1 `HS.sel` r' == h2 `HS.sel` r'))\n ))\n: Lemma\n (pointer_preserved p h1 h2)\n= let g () : Lemma\n (requires (live h1 p))\n (ensures (pointer_preserved p h1 h2))\n = f _ _ (greference_of p)\n in\n Classical.move_requires g ()", "val modifies_pointer_elim\n (s: loc)\n (h1 h2: HS.mem)\n (#a': typ)\n (p': pointer a')\n: Lemma\n (requires (\n modifies s h1 h2 /\\\n live h1 p' /\\\n loc_disjoint (loc_pointer p') s\n ))\n (ensures (\n equal_values h1 p' h2 p'\n ))\n [SMTPatOr [\n [ SMTPat (modifies s h1 h2); SMTPat (gread h1 p') ] ;\n [ SMTPat (modifies s h1 h2); SMTPat (readable h1 p') ] ;\n [ SMTPat (modifies s h1 h2); SMTPat (live h1 p') ];\n [ SMTPat (modifies s h1 h2); SMTPat (gread h2 p') ] ;\n [ SMTPat (modifies s h1 h2); SMTPat (readable h2 p') ] ;\n [ SMTPat (modifies s h1 h2); SMTPat (live h2 p') ]\n ] ]\nlet modifies_pointer_elim s h1 h2 #a' p' =\n MG.modifies_aloc_elim #_ #_ #(frameOf p') #(as_addr p') (LocPointer p') s h1 h2", "val g_upd_modifies_strong (#a:Type0) (#rrel #rel:srel a)\n (b:mbuffer a rrel rel)\n (i:nat{i < length b})\n (v:a)\n (h:HS.mem{live h b})\n : Lemma (modifies (loc_buffer_from_to b (U32.uint_to_t i) (U32.uint_to_t (i + 1))) h (g_upd b i v h))\nlet g_upd_modifies_strong #_ #_ #_ b i v h =\n let h' = g_upd b i v h in\n // prove modifies_1_from_to_preserves_ubuffers\n Heap.lemma_distinct_addrs_distinct_preorders ();\n Heap.lemma_distinct_addrs_distinct_mm ();\n s_lemma_equal_instances_implies_equal_types ();\n modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h'", "val modifies_ralloc_post\n (#a: Type)\n (#rel: Preorder.preorder a)\n (i: HS.rid)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel)\n (h' : HS.mem)\n: Lemma\n (requires (HST.ralloc_post i init h x h'))\n (ensures (modifies loc_none h h'))\n [SMTPat (HST.ralloc_post i init h x h')]\nlet modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls", "val modifies_liveness_insensitive_buffer_weak (l: loc) (h h': HS.mem) (#t: Type) (x: B.buffer t)\n : Lemma\n (requires\n (modifies l h h' /\\ address_liveness_insensitive_locs `loc_includes` l /\\ B.live h x))\n (ensures (B.live h' x))\n [\n SMTPatOr\n [\n [SMTPat (B.live h x); SMTPat (modifies l h h')];\n [SMTPat (B.live h' x); SMTPat (modifies l h h')]\n ]\n ]\nlet modifies_liveness_insensitive_buffer_weak\n (l : loc)\n (h h' : HS.mem)\n (#t: Type)\n (x: B.buffer t)\n: Lemma\n (requires (modifies l h h' /\\ address_liveness_insensitive_locs `loc_includes` l /\\ B.live h x))\n (ensures (B.live h' x))\n [SMTPatOr [\n [SMTPat (B.live h x); SMTPat (modifies l h h');];\n [SMTPat (B.live h' x); SMTPat (modifies l h h');];\n ]]\n= modifies_liveness_insensitive_buffer loc_none l h h' x", "val modifies_fresh_frame_popped\n (h0 h1: HS.mem)\n (s: loc)\n (h2 h3: HS.mem)\n: Lemma\n (requires (\n HS.fresh_frame h0 h1 /\\\n modifies (loc_union (loc_all_regions_from false (HS.get_tip h1)) s) h1 h2 /\\\n (HS.get_tip h2) == (HS.get_tip h1) /\\\n HS.popped h2 h3\n ))\n (ensures (\n modifies s h0 h3 /\\\n (HS.get_tip h3) == HS.get_tip h0\n ))\nlet modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped", "val old_to_new_modifies' (old_l: OldM.loc) (h h': HS.mem)\n : Lemma\n (requires\n (OldM.modifies old_l h h' /\\\n new_to_union_loc (union_loc_to_new (old_to_union_loc old_l)) == old_to_union_loc old_l))\n (ensures (NewM.modifies (union_loc_to_new (old_to_union_loc old_l)) h h'))\n [SMTPat (OldM.modifies old_l h h')]\nlet old_to_new_modifies' (old_l: OldM.loc) (h h' : HS.mem) : Lemma\n (requires (OldM.modifies old_l h h' /\\ new_to_union_loc (union_loc_to_new (old_to_union_loc old_l)) == old_to_union_loc old_l))\n (ensures (NewM.modifies (union_loc_to_new (old_to_union_loc old_l)) h h'))\n [SMTPat (OldM.modifies old_l h h')]\n= old_to_new_modifies old_l (union_loc_to_new (old_to_union_loc old_l)) h h'", "val modifies_fresh_frame_popped'\n (h0 h1: HS.mem)\n (s: loc)\n (h2 h3: HS.mem)\n: Lemma\n (requires (\n HS.fresh_frame h0 h1 /\\\n modifies (loc_union (loc_regions (Set.singleton (HS.get_tip h1))) s) h1 h2 /\\\n (HS.get_tip h2) == (HS.get_tip h1) /\\\n HS.popped h2 h3\n ))\n (ensures (\n modifies s h0 h3 /\\\n (HS.get_tip h3) == HS.get_tip h0\n ))\nlet modifies_fresh_frame_popped' h0 h1 s h2 h3 =\n modifies_fresh_frame_popped h0 h1 s h2 h3", "val modifies_only_not_unused_in (l: loc) (h h': HS.mem)\n : Lemma (requires (let open B in modifies (loc_union (loc_unused_in h) l) h h'))\n (ensures (let open B in modifies l h h'))\n [SMTPat B.((modifies l h h'))]\nlet modifies_only_not_unused_in\n (l: loc)\n (h h' : HS.mem)\n: Lemma\n (requires (B.(modifies (loc_union (loc_unused_in h) l) h h')))\n (ensures (B.(modifies l h h')))\n [SMTPat B.((modifies l h h'))]\n= B.modifies_only_not_unused_in l h h'", "val insert_modifies_rec_helper:\n #hsz:hash_size_t ->\n lv:uint32_t{lv < merkle_tree_size_lg} ->\n hs:hash_vv hsz {V.size_of hs = merkle_tree_size_lg} ->\n aloc:loc ->\n h:HS.mem ->\n Lemma (loc_union\n (loc_union\n (loc_union\n (RV.rs_loc_elem (hvreg hsz) (V.as_seq h hs) (U32.v lv))\n (V.loc_vector_within hs lv (lv + 1ul)))\n aloc)\n (loc_union\n (loc_union\n (RV.rv_loc_elems h hs (lv + 1ul) (V.size_of hs))\n (V.loc_vector_within hs (lv + 1ul) (V.size_of hs)))\n aloc) ==\n loc_union\n (loc_union\n (RV.rv_loc_elems h hs lv (V.size_of hs))\n (V.loc_vector_within hs lv (V.size_of hs)))\n aloc)\nlet insert_modifies_rec_helper #hsz lv hs aloc h =\n assert (V.loc_vector_within hs lv (V.size_of hs) ==\n loc_union (V.loc_vector_within hs lv (lv + 1ul))\n (V.loc_vector_within hs (lv + 1ul) (V.size_of hs)));\n RV.rs_loc_elems_rec_inverse (hvreg hsz) (V.as_seq h hs) (U32.v lv) (U32.v (V.size_of hs));\n assert (RV.rv_loc_elems h hs lv (V.size_of hs) ==\n loc_union (RV.rs_loc_elem (hvreg hsz) (V.as_seq h hs) (U32.v lv))\n (RV.rv_loc_elems h hs (lv + 1ul) (V.size_of hs)));\n\n // Applying some association rules...\n loc_union_assoc\n (loc_union\n (RV.rs_loc_elem (hvreg hsz) (V.as_seq h hs) (U32.v lv))\n (V.loc_vector_within hs lv (lv + 1ul))) aloc\n (loc_union\n (loc_union\n (RV.rv_loc_elems h hs (lv + 1ul) (V.size_of hs))\n (V.loc_vector_within hs (lv + 1ul) (V.size_of hs)))\n aloc);\n loc_union_assoc\n (loc_union\n (RV.rv_loc_elems h hs (lv + 1ul) (V.size_of hs))\n (V.loc_vector_within hs (lv + 1ul) (V.size_of hs))) aloc aloc;\n loc_union_assoc\n (loc_union\n (RV.rs_loc_elem (hvreg hsz) (V.as_seq h hs) (U32.v lv))\n (V.loc_vector_within hs lv (lv + 1ul)))\n (loc_union\n (RV.rv_loc_elems h hs (lv + 1ul) (V.size_of hs))\n (V.loc_vector_within hs (lv + 1ul) (V.size_of hs)))\n aloc;\n loc_union_assoc_4\n (RV.rs_loc_elem (hvreg hsz) (V.as_seq h hs) (U32.v lv))\n (V.loc_vector_within hs lv (lv + 1ul))\n (RV.rv_loc_elems h hs (lv + 1ul) (V.size_of hs))\n (V.loc_vector_within hs (lv + 1ul) (V.size_of hs))", "val modifies_remove_fresh_frame (h1 h2 h3: HS.mem) (l: loc)\n : Lemma\n (requires\n (HS.fresh_frame h1 h2 /\\\n modifies (loc_union (loc_all_regions_from false (HS.get_tip h2)) l) h2 h3))\n (ensures (modifies l h1 h3))\n [SMTPat (modifies l h1 h3); SMTPat (HS.fresh_frame h1 h2)]\nlet modifies_remove_fresh_frame (h1 h2 h3:HS.mem) (l:loc)\n : Lemma (requires (HS.fresh_frame h1 h2 /\\\n modifies (loc_union (loc_all_regions_from false (HS.get_tip h2)) l) h2 h3))\n (ensures (modifies l h1 h3))\n\t [SMTPat (modifies l h1 h3); SMTPat (HS.fresh_frame h1 h2)]\n = loc_regions_unused_in h1 (HS.mod_set (Set.singleton (HS.get_tip h2)));\n modifies_only_not_unused_in l h1 h3", "val not_live_region_loc_not_unused_in_disjoint\n (h0: HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (~ (HS.live_region h0 r)))\n (ensures (loc_disjoint (loc_region_only false r) (loc_not_unused_in h0)))\nlet not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls", "val no_upd_fresh_region: r:HS.rid -> l:loc -> h0:HS.mem -> h1:HS.mem -> Lemma\n (requires (HS.fresh_region r h0 h1 /\\ modifies (loc_union (loc_all_regions_from false r) l) h0 h1))\n (ensures (modifies l h0 h1))\n [SMTPat (HS.fresh_region r h0 h1); SMTPat (modifies l h0 h1)]\nlet no_upd_fresh_region = MG.no_upd_fresh_region", "val no_upd_fresh_region: r:HS.rid -> l:loc -> h0:HS.mem -> h1:HS.mem -> Lemma\n (requires (HS.fresh_region r h0 h1 /\\ modifies (loc_union (loc_all_regions_from false r) l) h0 h1))\n (ensures (modifies l h0 h1))\n [SMTPat (HS.fresh_region r h0 h1); SMTPat (modifies l h0 h1)]\nlet no_upd_fresh_region = MG.no_upd_fresh_region", "val lemma_upd (#a: Type) (h: mem) (x: reference a {live_region h (HS.frameOf x)}) (v: a)\n : Lemma (requires True)\n (ensures (Map.domain (HS.get_hmap h) == Map.domain (HS.get_hmap (upd h x v))))\nlet lemma_upd (#a:Type) (h:mem) (x:reference a{live_region h (HS.frameOf x)}) (v:a) : Lemma\n (requires True)\n (ensures (Map.domain (HS.get_hmap h) == Map.domain (HS.get_hmap (upd h x v))))\n = let m = HS.get_hmap h in\n let m' = Map.upd m (HS.frameOf x) (Heap.upd (Map.sel m (HS.frameOf x)) (HS.as_ref x) v) in\n Set.lemma_equal_intro (Map.domain m) (Map.domain m')", "val modifies_trans_linear (l l_goal: loc) (h1 h2 h3: HS.mem)\n : Lemma (requires (modifies l h1 h2 /\\ modifies l_goal h2 h3 /\\ l_goal `loc_includes` l))\n (ensures (modifies l_goal h1 h3))\n [SMTPat (modifies l h1 h2); SMTPat (modifies l_goal h1 h3)]\nlet modifies_trans_linear (l l_goal:loc) (h1 h2 h3:HS.mem)\n : Lemma (requires (modifies l h1 h2 /\\ modifies l_goal h2 h3 /\\ l_goal `loc_includes` l))\n (ensures (modifies l_goal h1 h3))\n\t [SMTPat (modifies l h1 h2); SMTPat (modifies l_goal h1 h3)]\n = modifies_trans l h1 h2 l_goal h3", "val modifies_trans\n (s12: loc)\n (h1 h2: HS.mem)\n (s23: loc)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))\n [SMTPat (modifies s12 h1 h2); SMTPat (modifies s23 h2 h3)]\nlet modifies_trans = MG.modifies_trans", "val modifies_trans\n (s12: loc)\n (h1 h2: HS.mem)\n (s23: loc)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))\n [SMTPat (modifies s12 h1 h2); SMTPat (modifies s23 h2 h3)]\nlet modifies_trans = MG.modifies_trans", "val addr_unused_in_does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (Map.sel (HS.get_hmap h) (fst ra))))\n (ensures (h `does_not_contain_addr` ra))\nlet addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr", "val addr_unused_in_does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (Map.sel (HS.get_hmap h) (fst ra))))\n (ensures (h `does_not_contain_addr` ra))\nlet addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr", "val modifies_none_modifies\n (h1 h2: HS.mem)\n: Lemma\n (requires (HST.modifies_none h1 h2))\n (ensures (modifies loc_none h1 h2))\nlet modifies_none_modifies = MG.modifies_none_modifies #_ #cls", "val mreference_live_loc_not_unused_in\n (#t: Type)\n (#pre: Preorder.preorder t)\n (h: HS.mem)\n (r: HS.mreference t pre)\n: Lemma\n (requires (h `HS.contains` r))\n (ensures (loc_not_unused_in h `loc_includes` loc_freed_mreference r /\\ loc_not_unused_in h `loc_includes` loc_mreference r))\n [SMTPatOr [\n [SMTPat (HS.contains h r)];\n [SMTPat (loc_not_unused_in h `loc_includes` loc_mreference r)];\n [SMTPat (loc_not_unused_in h `loc_includes` loc_freed_mreference r)];\n ]]\nlet mreference_live_loc_not_unused_in =\n MG.mreference_live_loc_not_unused_in cls", "val modifies_refl\n (s: loc)\n (h: HS.mem)\n: Lemma\n (modifies s h h)\n [SMTPat (modifies s h h)]\nlet modifies_refl = MG.modifies_refl", "val modifies_refl\n (s: loc)\n (h: HS.mem)\n: Lemma\n (modifies s h h)\n [SMTPat (modifies s h h)]\nlet modifies_refl = MG.modifies_refl", "val modifies_refl\n (s: loc)\n (h: HS.mem)\n: Lemma\n (modifies s h h)\n [SMTPat (modifies s h h)]\nlet modifies_refl = MG.modifies_refl", "val modifies_free\n (#a: Type)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel { HS.is_mm r } )\n (m: HS.mem { m `HS.contains` r } )\n: Lemma\n (modifies (loc_freed_mreference r) m (HS.free r m))\n [SMTPat (HS.free r m)]\nlet modifies_free = MG.modifies_free #_ #cls", "val modifies_trans (s12:loc) (h1 h2:vale_heap) (s23:loc) (h3:vale_heap) : Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))\nlet modifies_trans s12 h1 h2 s23 h3 = M.modifies_trans s12 (_ih h1).hs (_ih h2).hs s23 (_ih h3).hs", "val modifies_trans (s12:loc) (h1 h2:vale_heap) (s23:loc) (h3:vale_heap) : Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))\nlet modifies_trans s12 h1 h2 s23 h3 = M.modifies_trans s12 (_ih h1).hs (_ih h2).hs s23 (_ih h3).hs", "val valid_pos_frame_strong_2\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (sl: slice rrel rel)\n (pos pos': U32.t)\n (l: B.loc)\n (h': HS.mem)\n : Lemma\n (requires\n (live_slice h sl /\\ valid_pos p h' sl pos pos' /\\ B.modifies l h h' /\\\n B.loc_disjoint (loc_slice_from_to sl pos pos') l /\\\n k.parser_kind_subkind == Some ParserStrong))\n (ensures\n (valid_pos p h sl pos pos' /\\ valid_pos p h' sl pos pos' /\\\n valid_content_pos p h sl pos (contents p h' sl pos) pos'))\nlet valid_pos_frame_strong_2\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (sl: slice rrel rel)\n (pos: U32.t)\n (pos' : U32.t)\n (l: B.loc)\n (h': HS.mem)\n: Lemma\n (requires (\n live_slice h sl /\\\n valid_pos p h' sl pos pos' /\\\n B.modifies l h h' /\\ B.loc_disjoint (loc_slice_from_to sl pos pos') l /\\ k.parser_kind_subkind == Some ParserStrong))\n (ensures (\n valid_pos p h sl pos pos' /\\\n valid_pos p h' sl pos pos' /\\\n valid_content_pos p h sl pos (contents p h' sl pos) pos'\n ))\n= valid_pos_valid_exact p h' sl pos pos';\n valid_exact_valid p h sl pos pos'", "val does_not_contain_addr_elim\n (#a: Type0)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel)\n (m: HS.mem)\n (x: HS.rid * nat)\n: Lemma\n (requires (\n m `does_not_contain_addr` x /\\\n HS.frameOf r == fst x /\\\n HS.as_addr r == snd x\n ))\n (ensures (~ (m `HS.contains` r)))\nlet does_not_contain_addr_elim = MG.does_not_contain_addr_elim", "val does_not_contain_addr_elim\n (#a: Type0)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel)\n (m: HS.mem)\n (x: HS.rid * nat)\n: Lemma\n (requires (\n m `does_not_contain_addr` x /\\\n HS.frameOf r == fst x /\\\n HS.as_addr r == snd x\n ))\n (ensures (~ (m `HS.contains` r)))\nlet does_not_contain_addr_elim = MG.does_not_contain_addr_elim", "val loc_mreference\n (#aloc: aloc_t)\n (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n : GTot (loc c)\nlet loc_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses true (HS.frameOf b) (Set.singleton (HS.as_addr b))", "val create_in: a:supported_alg -> r:HS.rid -> ST (state a)\n (requires fun _ -> is_eternal_region r)\n (ensures fun h0 st h1 ->\n B.modifies B.loc_none h0 h1 /\\\n B.fresh_loc (footprint st h1) h0 h1 /\\\n B.(loc_includes (loc_region_only true r) (footprint st h1)) /\\\n invariant st h1 /\\\n freeable st h1)\nlet create_in a r =\n let st =\n match a with\n | SHA1 -> SHA1_s (create_in SHA1 r)\n | SHA2_256 -> SHA2_256_s (create_in SHA2_256 r)\n | SHA2_384 -> SHA2_384_s (create_in SHA2_384 r)\n | SHA2_512 -> SHA2_512_s (create_in SHA2_512 r)\n in\n B.malloc r st 1ul", "val valid_if_live_intro (#t: _) (r: repr_ptr t) (h: HS.mem)\n : Lemma\n (requires\n (C.qbuf_qual (C.as_qbuf r.b) == C.IMMUTABLE /\\ valid r h /\\\n (let i:I.ibuffer LP.byte = C.as_mbuf r.b in\n let m = r.meta in\n B.as_seq h i == m.repr_bytes /\\ i `I.value_is` (Ghost.hide m.repr_bytes))))\n (ensures valid_if_live r)\nlet valid_if_live_intro #t (r:repr_ptr t) (h:HS.mem)\n : Lemma\n (requires (\n C.qbuf_qual (C.as_qbuf r.b) == C.IMMUTABLE /\\\n valid r h /\\\n (let i : I.ibuffer LP.byte = C.as_mbuf r.b in\n let m = r.meta in\n B.as_seq h i == m.repr_bytes /\\\n i `I.value_is` Ghost.hide m.repr_bytes)))\n (ensures\n valid_if_live r)\n = reveal_valid ();\n let i : I.ibuffer LP.byte = C.as_mbuf r.b in\n let aux (h':HS.mem)\n : Lemma\n (requires\n C.live h' r.b /\\\n B.as_seq h i `Seq.equal` B.as_seq h' i)\n (ensures\n valid r h')\n [SMTPat (valid r h')]\n = let m = r.meta in\n LP.valid_ext_intro m.parser h (slice_of_repr_ptr r) 0ul h' (slice_of_repr_ptr r) 0ul\n in\n ()", "val modifies_1_preserves_livenesses\n (#a: Type0)\n (#rrel #rel: srel a)\n (b: mbuffer a rrel rel)\n (h1 h2: HS.mem)\n : GTot Type0\nlet modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem)\n : GTot Type0\n = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r'", "val modifies_addr_of_modifies\n (#a:Type0) (#rrel #rel:srel a)\n (b:mbuffer a rrel rel) (h1 h2:HS.mem)\n :Lemma (requires (modifies_addr_of b h1 h2))\n (ensures (modifies (loc_addr_of_buffer b) h1 h2))\nlet modifies_addr_of_modifies #t #_ #_ b h1 h2 =\n MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2\n (fun r -> modifies_addr_of_live_region b h1 h2 r)\n (fun t pre p ->\n modifies_addr_of_mreference b h1 h2 p\n )\n (fun r n ->\n modifies_addr_of_unused_in b h1 h2 r n\n )", "val create_in: a:supported_alg -> r:HS.rid -> ST (state a)\n (requires fun _ -> is_eternal_region r)\n (ensures fun h0 st h1 ->\n B.modifies B.loc_none h0 h1 /\\\n B.fresh_loc (footprint st) h0 h1 /\\\n B.(loc_includes (loc_region_only true r)) (footprint st) /\\\n invariant st h1 /\\\n freeable st)\nlet create_in a r =\n let k:B.buffer uint8 =\n match a with\n | SHA1 -> B.malloc r (u8 0) (hash_len SHA1)\n | SHA2_256 -> B.malloc r (u8 0) (hash_len SHA2_256)\n | SHA2_384 -> B.malloc r (u8 0) (hash_len SHA2_384)\n | SHA2_512 -> B.malloc r (u8 0) (hash_len SHA2_512)\n in\n let v:B.buffer uint8 =\n match a with\n | SHA1 -> B.malloc r (u8 0) (hash_len SHA1)\n | SHA2_256 -> B.malloc r (u8 0) (hash_len SHA2_256)\n | SHA2_384 -> B.malloc r (u8 0) (hash_len SHA2_384)\n | SHA2_512 -> B.malloc r (u8 0) (hash_len SHA2_512)\n in\n let ctr:B.buffer size_t = B.malloc r 1ul 1ul in\n State k v ctr", "val popped_modifies (h0 h1: HS.mem) : Lemma\n (requires (HS.popped h0 h1))\n (ensures (modifies (loc_region_only false (HS.get_tip h0)) h0 h1))\n [SMTPat (HS.popped h0 h1)]\nlet popped_modifies = MG.popped_modifies #_ cls", "val modifies_fresh_frame_popped\n (h0 h1: HS.mem)\n (s: loc)\n (h2 h3: HS.mem)\n: Lemma\n (requires (\n HS.fresh_frame h0 h1 /\\\n modifies (loc_union (loc_regions (HS.mod_set (Set.singleton (HS.get_tip h1)))) s) h1 h2 /\\\n (HS.get_tip h2) == (HS.get_tip h1) /\\\n HS.popped h2 h3\n ))\n (ensures (\n modifies s h0 h3 /\\\n (HS.get_tip h3) == HS.get_tip h0\n ))\n [SMTPat (HS.fresh_frame h0 h1); SMTPat (HS.popped h2 h3); SMTPat (modifies s h0 h3)]\nlet modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped", "val valid_pos_frame_strong\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (sl: slice rrel rel)\n (pos pos': U32.t)\n (l: B.loc)\n (h': HS.mem)\n : Lemma\n (requires\n (live_slice h sl /\\ B.modifies l h h' /\\ B.loc_disjoint (loc_slice_from_to sl pos pos') l /\\\n k.parser_kind_subkind == Some ParserStrong))\n (ensures\n ((valid_pos p h sl pos pos' \\/ valid_pos p h' sl pos pos') ==>\n (valid_pos p h sl pos pos' /\\ valid_content_pos p h' sl pos (contents p h sl pos) pos')))\nlet valid_pos_frame_strong\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (sl: slice rrel rel)\n (pos: U32.t)\n (pos' : U32.t)\n (l: B.loc)\n (h': HS.mem)\n: Lemma\n (requires (\n live_slice h sl /\\\n B.modifies l h h' /\\ B.loc_disjoint (loc_slice_from_to sl pos pos') l /\\ k.parser_kind_subkind == Some ParserStrong))\n (ensures (\n (valid_pos p h sl pos pos' \\/ valid_pos p h' sl pos pos') ==> (\n valid_pos p h sl pos pos' /\\\n valid_content_pos p h' sl pos (contents p h sl pos) pos'\n )))\n= Classical.move_requires (valid_pos_frame_strong_1 p h sl pos pos' l) h';\n Classical.move_requires (valid_pos_frame_strong_2 p h sl pos pos' l) h'", "val modifies_fresh_frame_popped\n (h0 h1: HS.mem)\n (s: loc)\n (h2 h3: HS.mem)\n: Lemma\n (requires (\n HS.fresh_frame h0 h1 /\\\n modifies (loc_union (loc_all_regions_from false (HS.get_tip h1)) s) h1 h2 /\\\n (HS.get_tip h2) == (HS.get_tip h1) /\\\n HS.popped h2 h3\n ))\n (ensures (\n modifies s h0 h3 /\\\n (HS.get_tip h3) == HS.get_tip h0\n ))\n [SMTPat (HS.fresh_frame h0 h1); SMTPat (HS.popped h2 h3); SMTPat (modifies s h0 h3)]\nlet modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped", "val modifies_liveness_insensitive_buffer\n (l1 l2 : loc)\n (h h' : HS.mem)\n (#t: Type)\n (x: B.buffer t)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ loc_disjoint l1 (loc_buffer x) /\\ address_liveness_insensitive_locs `loc_includes` l2 /\\ B.live h x))\n (ensures (B.live h' x))\nlet modifies_liveness_insensitive_buffer l1 l2 h h' #t x =\n MG.modifies_preserves_liveness_strong l1 l2 h h' (B.content x) (LocBuffer x)", "val modifies_addr_of_preserves_not_unused_in\n (#a: Type0)\n (#rrel #rel: srel a)\n (b: mbuffer a rrel rel)\n (h1 h2: HS.mem)\n : GTot Type0\nlet modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem)\n :GTot Type0\n = forall (r: HS.rid) (n: nat) .\n ((r <> frameOf b \\/ n <> as_addr b) /\\\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==>\n (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))", "val modifies_liveness_insensitive_buffer\n (l1 l2:loc)\n (h h':HS.mem)\n (#a:Type0) (#rrel #rel:srel a)\n (x:mbuffer a rrel rel)\n :Lemma (requires (modifies (loc_union l1 l2) h h' /\\\n loc_disjoint l1 (loc_buffer x) /\\\n\t\t address_liveness_insensitive_locs `loc_includes` l2 /\\\n\t\t live h x))\n (ensures (live h' x))\n [SMTPatOr [\n [SMTPat (live h x); SMTPat (modifies (loc_union l1 l2) h h');];\n [SMTPat (live h' x); SMTPat (modifies (loc_union l1 l2) h h');];\n ]]\nlet modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x =\n if g_is_null x then ()\n else\n liveness_preservation_intro h h' x (fun t' pre r ->\n MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x))", "val disjoint_roots_intro_pointer_vs_reference\n (#value1: typ)\n (#value2: Type)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: HS.reference value2)\n: Lemma\n (requires (live h p1 /\\ p2 `HS.unused_in` h))\n (ensures (frameOf p1 <> HS.frameOf p2 \\/ as_addr p1 =!= HS.as_addr p2))\nlet disjoint_roots_intro_pointer_vs_reference\n (#value1: typ)\n (#value2: Type)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: HS.reference value2)\n: Lemma\n (requires (live h p1 /\\ p2 `HS.unused_in` h))\n (ensures (frameOf p1 <> HS.frameOf p2 \\/ as_addr p1 =!= HS.as_addr p2))\n= let r = greference_of p1 in\n assert (HS.contains h r)", "val slice_access_frame_strong\n (#rrel #rel: _)\n (h: HS.mem)\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (#p2: parser k2 t2)\n (#cl: clens t1 t2)\n (g: gaccessor p1 p2 cl)\n (sl: slice rrel rel)\n (pos: U32.t)\n (l: B.loc)\n (h' : HS.mem)\n: Lemma\n (requires (\n k1.parser_kind_subkind == Some ParserStrong /\\\n valid p1 h sl pos /\\\n cl.clens_cond (contents p1 h sl pos) /\\\n B.modifies l h h' /\\\n B.loc_disjoint l (loc_slice_from_to sl pos (get_valid_pos p1 h sl pos))\n ))\n (ensures (\n valid p1 h' sl pos /\\\n cl.clens_cond (contents p1 h' sl pos) /\\\n slice_access h' g sl pos == slice_access h g sl pos\n ))\n [SMTPatOr [\n [SMTPat (slice_access h g sl pos); SMTPat (B.modifies l h h')];\n [SMTPat (slice_access h' g sl pos); SMTPat (B.modifies l h h')];\n ]]\nlet slice_access_frame_strong\n (#rrel #rel: _)\n (h: HS.mem)\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (#p2: parser k2 t2)\n (#cl: clens t1 t2)\n (g: gaccessor p1 p2 cl)\n (sl: slice rrel rel)\n (pos: U32.t)\n (l: B.loc)\n (h' : HS.mem)\n: Lemma\n (requires (\n k1.parser_kind_subkind == Some ParserStrong /\\\n valid p1 h sl pos /\\\n cl.clens_cond (contents p1 h sl pos) /\\\n B.modifies l h h' /\\\n B.loc_disjoint l (loc_slice_from_to sl pos (get_valid_pos p1 h sl pos))\n ))\n (ensures (\n valid p1 h' sl pos /\\\n cl.clens_cond (contents p1 h' sl pos) /\\\n slice_access h' g sl pos == slice_access h g sl pos\n ))\n [SMTPatOr [\n [SMTPat (slice_access h g sl pos); SMTPat (B.modifies l h h')];\n [SMTPat (slice_access h' g sl pos); SMTPat (B.modifies l h h')];\n ]]\n= valid_facts p1 h sl pos;\n valid_facts p1 h' sl pos;\n slice_access_eq h g sl pos;\n slice_access_eq h' g sl pos;\n let pos2 = get_valid_pos p1 h sl pos in\n parse_strong_prefix p1 (bytes_of_slice_from h sl pos) (bytes_of_slice_from_to h sl pos pos2);\n B.modifies_buffer_from_to_elim sl.base pos (get_valid_pos p1 h sl pos) l h h' ;\n parse_strong_prefix p1 (bytes_of_slice_from_to h' sl pos pos2) (bytes_of_slice_from h' sl pos)" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_loc_addresses_intro" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_loc_addresses_intro" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_loc_addresses_intro" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.modifies_only_live_addresses" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_region_mreference_weak" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fsti", "name": "FStar.Modifies.modifies_liveness_insensitive_region_mreference_weak" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_loc_regions_intro" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_loc_regions_intro" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_liveness_insensitive_region_mreference" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_loc_regions_intro" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_only_live_regions" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_liveness_insensitive_mreference" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_only_live_addresses" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_only_live_addresses" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_only_live_regions" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_only_live_regions" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_liveness_insensitive_region" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_region_mreference" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fsti", "name": "FStar.Modifies.modifies_liveness_insensitive_region_weak" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_region_weak" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_mreference_weak" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fsti", "name": "FStar.Modifies.modifies_liveness_insensitive_mreference_weak" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_live_region" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_reference_elim" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_region" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_address_liveness_insensitive_unused_in" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_region_buffer_weak" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.liveness_preservation_intro" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_only_not_unused_in" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_mreference" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_mreference_elim" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_mreference_elim" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_ralloc_post" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_salloc_post" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_loc_buffer_from_to_intro'" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.old_to_new_modifies" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fsti", "name": "FStar.Modifies.modifies_liveness_insensitive_region_buffer_weak" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_salloc_post" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_loc_buffer_from_to_intro" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_all_regions_from" }, { "project_name": "everparse", "file_name": "EverParse3d.InputStream.Extern.fst", "name": "EverParse3d.InputStream.Extern.preserved" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_liveness_insensitive_region_buffer" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_buffer_weak" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.fst", "name": "MerkleTree.Low.insert_modifies_union_loc_weakening" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_region_buffer" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_free" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_trans" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_loc_unused_in" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_regions_unused_in" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_region_only" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_0_modifies" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.not_live_region_does_not_contain_addr" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.not_live_region_does_not_contain_addr" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_remove_new_locs" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.pointer_preserved_intro" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_pointer_elim" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.g_upd_modifies_strong" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_ralloc_post" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fsti", "name": "FStar.Modifies.modifies_liveness_insensitive_buffer_weak" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_fresh_frame_popped" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.old_to_new_modifies'" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.modifies_fresh_frame_popped'" }, { "project_name": "FStar", "file_name": "OPLSS2021.MemCpy.Deps.fst", "name": "OPLSS2021.MemCpy.Deps.modifies_only_not_unused_in" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.fst", "name": "MerkleTree.Low.insert_modifies_rec_helper" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.modifies_remove_fresh_frame" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.not_live_region_loc_not_unused_in_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.no_upd_fresh_region" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.no_upd_fresh_region" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.lemma_upd" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.modifies_trans_linear" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_trans" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_trans" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.addr_unused_in_does_not_contain_addr" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.addr_unused_in_does_not_contain_addr" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_none_modifies" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.mreference_live_loc_not_unused_in" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_refl" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_refl" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_refl" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_free" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.modifies_trans" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.modifies_trans" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fsti", "name": "LowParse.Low.Base.Spec.valid_pos_frame_strong_2" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.does_not_contain_addr_elim" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.does_not_contain_addr_elim" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_mreference" }, { "project_name": "hacl-star", "file_name": "EverCrypt.DRBG.fst", "name": "EverCrypt.DRBG.create_in" }, { "project_name": "everparse", "file_name": "LowParse.Repr.fsti", "name": "LowParse.Repr.valid_if_live_intro" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_1_preserves_livenesses" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_addr_of_modifies" }, { "project_name": "hacl-star", "file_name": "Hacl.HMAC_DRBG.fst", "name": "Hacl.HMAC_DRBG.create_in" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.popped_modifies" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_fresh_frame_popped" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fsti", "name": "LowParse.Low.Base.Spec.valid_pos_frame_strong" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_fresh_frame_popped" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_liveness_insensitive_buffer" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_addr_of_preserves_not_unused_in" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.disjoint_roots_intro_pointer_vs_reference" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fst", "name": "LowParse.Low.Base.Spec.slice_access_frame_strong" } ], "selected_premises": [ "FStar.ModifiesGen.modifies_preserves_livenesses_intro", "FStar.Heap.trivial_preorder", "FStar.ModifiesGen.region_liveness_insensitive_locs", "FStar.Monotonic.HyperStack.sel", "FStar.ModifiesGen.loc_aux_includes_buffer_includes", "FStar.ModifiesGen.address_liveness_insensitive_locs", "FStar.FunctionalExtensionality.feq", "FStar.Tactics.V2.Builtins.ret_t", "FStar.Monotonic.HyperStack.live_region", "FStar.ModifiesGen.modifies_preserves_alocs_intro", "FStar.ModifiesGen.loc_none", "FStar.ModifiesGen.loc_aux_includes_loc_aux_includes_buffer", "FStar.ModifiesGen.loc_disjoint_includes", "FStar.ModifiesGen.loc_union", "FStar.Tactics.SMT.get_initial_fuel", "FStar.Tactics.Effect.raise", "FStar.ModifiesGen.loc_aux_includes_trans", "FStar.ModifiesGen.loc_aux_includes_buffer", "FStar.ModifiesGen.loc_regions", "FStar.ModifiesGen.modifies_preserves_mreferences_intro", "FStar.ModifiesGen.modifies_preserves_not_unused_in_intro", "FStar.Reflection.V2.Data.var", "FStar.ModifiesGen.mk_non_live_addrs", "FStar.Tactics.SMT.get_max_fuel", "FStar.ModifiesGen.mk_live_addrs", "FStar.ModifiesGen.loc_disjoint_regions", "FStar.ModifiesGen.loc_equal", "FStar.ModifiesGen.aloc_domain", "FStar.ModifiesGen.aloc_disjoint_sym", "FStar.Monotonic.HyperStack.mreference", "FStar.ModifiesGen.loc", "FStar.ModifiesGen.modifies'", "FStar.Tactics.SMT.get_rlimit", "FStar.ModifiesGen.loc_aux_disjoint_sym", "FStar.HyperStack.ST.is_eternal_region", "FStar.ModifiesGen.addrs_of_loc_aux", "FStar.ModifiesGen.modifies_preserves_regions", "FStar.ModifiesGen.loc_disjoint_region_liveness_tags", "FStar.ModifiesGen.addrs_of_loc_liveness_not_preserved", "FStar.Monotonic.HyperStack.as_addr", "FStar.ModifiesGen.modifies_preserves_not_unused_in", "FStar.ModifiesGen.modifies_preserves_livenesses", "FStar.ModifiesGen.modifies", "FStar.Tactics.Types.issues", "FStar.ModifiesGen.addrs_of_loc_weak", "FStar.ModifiesGen.aloc_includes", "FStar.FunctionalExtensionality.on_dom", "FStar.Monotonic.HyperStack.frameOf", "FStar.Tactics.SMT.get_initial_ifuel", "FStar.Reflection.V2.Data.ppname_t", "FStar.ModifiesGen.addrs_of_loc_aux_pred", "FStar.ModifiesGen.loc_aux_includes", "FStar.ModifiesGen.modifies_preserves_mreferences", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "FStar.ModifiesGen.loc_includes'", "FStar.ModifiesGen.loc_disjoint_aloc_elim", "FStar.ModifiesGen.addrs_dom", "FStar.Monotonic.HyperStack.is_heap_color", "FStar.ModifiesGen.loc_disjoint'", "FStar.ModifiesGen.loc_regions_region_liveness_tags", "FStar.ModifiesGen.loc_disjoint_sym", "FStar.ModifiesGen.loc_aux_includes_refl", "FStar.Sealed.Inhabited.seal", "FStar.Tactics.SMT.smt_sync", "FStar.ModifiesGen.aloc_disjoint_includes", "FStar.Tactics.SMT.get_max_ifuel", "FStar.ModifiesGen.modifies_preserves_alocs", "FStar.ModifiesGen.loc_of_aloc", "FStar.ModifiesGen.i_restricted_g_t", "FStar.ModifiesGen.loc_disjoint_aux", "FStar.ModifiesGen.loc_aux_disjoint_loc_aux_includes", "FStar.ModifiesGen.loc_none_in_some_region", "FStar.Monotonic.HyperStack.contains", "FStar.ModifiesGen.loc_aux_disjoint", "FStar.ModifiesGen.loc_disjoint", "FStar.Reflection.Const.cons_qn", "FStar.ModifiesGen.loc_includes_region_union_l", "FStar.ModifiesGen.loc_includes", "FStar.Monotonic.HyperStack.is_mm", "FStar.ModifiesGen.live_addrs_codom", "FStar.ModifiesGen.aloc_disjoint", "FStar.ModifiesGen.loc_disjoint_addrs", "FStar.Reflection.V2.Data.as_ppname", "FStar.Monotonic.HyperStack.modifies_ref", "FStar.Tactics.SMT.smt_sync'", "FStar.Tactics.Effect.get", "FStar.ModifiesGen.regions_of_loc", "FStar.Monotonic.HyperStack.modifies_one", "FStar.ModifiesGen.non_live_addrs_codom", "FStar.Monotonic.HyperStack.is_stack_region", "FStar.ModifiesGen.loc_includes_none_elim", "FStar.ModifiesGen.addrs_of_loc", "FStar.ModifiesGen.loc_disjoint_addresses_intro", "FStar.ModifiesGen.loc_includes_trans", "FStar.Sealed.Inhabited.sealed", "FStar.Reflection.Const.nil_qn", "FStar.ModifiesGen.loc_aux_includes_subset", "FStar.Pervasives.dfst", "FStar.Tactics.SMT.set_initial_fuel" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.ModifiesGen\n\n#set-options \"--split_queries no\"\n#set-options \"--using_facts_from '*,-FStar.Tactics,-FStar.Reflection,-FStar.List'\"\n\nmodule HS = FStar.HyperStack\nmodule HST = FStar.HyperStack.ST\n\nnoeq\ntype aloc (#al: aloc_t) (c: cls al) = | ALoc:\n (region: HS.rid) ->\n (addr: nat) ->\n (loc: option (al region addr)) ->\n aloc c\n\nlet aloc_domain (#al: aloc_t) (c: cls al) (regions: Ghost.erased (Set.set HS.rid)) (addrs: ((r: HS.rid { Set.mem r (Ghost.reveal regions) } ) -> GTot (GSet.set nat))) : GTot (GSet.set (aloc c)) =\n GSet.comprehend (fun a -> Set.mem a.region (Ghost.reveal regions) && GSet.mem a.addr (addrs a.region))\n\nmodule F = FStar.FunctionalExtensionality\n\n[@@(unifier_hint_injective)]\nlet i_restricted_g_t = F.restricted_g_t\n\nlet addrs_dom regions =\n (r: HS.rid { Set.mem r (Ghost.reveal regions) } )\n\nlet non_live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (r:addrs_dom regions) =\n (y: GSet.set nat { r `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y })\n\nlet live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags))\n (r:addrs_dom regions) = (y: GSet.set nat { GSet.subset (non_live_addrs r) y } )\n\nnoeq\ntype loc' (#al: aloc_t u#x) (c: cls al) : Type u#x =\n | Loc:\n (regions: Ghost.erased (Set.set HS.rid)) ->\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } ) ->\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags)) ->\n (live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs)) ->\n (aux: Ghost.erased (GSet.set (aloc c)) {\n aloc_domain c regions live_addrs `GSet.subset` Ghost.reveal aux /\\\n Ghost.reveal aux `GSet.subset` (aloc_domain c regions (fun _ -> GSet.complement GSet.empty))\n } ) ->\n loc' c\n\nlet loc = loc'\n\nlet mk_non_live_addrs (#regions:_) (#region_liveness_tags:_)\n (f: (x:addrs_dom regions -> GTot (non_live_addrs_codom regions region_liveness_tags x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags) =\n F.on_dom_g _ f\n\nlet mk_live_addrs (#regions:_) (#region_liveness_tags:_)\n (#non_live_addrs_codom: _)\n (f: (x:addrs_dom regions -> GTot (live_addrs_codom regions region_liveness_tags non_live_addrs_codom x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs_codom) =\n F.on_dom_g _ f\n\nlet loc_none #a #c =\n Loc\n (Ghost.hide (Set.empty))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)\n\nlet regions_of_loc\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: GTot (Set.set HS.rid)\n= Ghost.reveal (Loc?.regions s)\n\nlet addrs_of_loc_liveness_not_preserved\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.non_live_addrs l r\n else GSet.empty\n\nlet addrs_of_loc_weak\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.live_addrs l r\n else GSet.empty\n\nlet addrs_of_loc_aux_pred\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n (addr: nat)\n: GTot bool\n= StrongExcludedMiddle.strong_excluded_middle (exists a . GSet.mem a (Ghost.reveal (Loc?.aux l)) /\\ a.region == r /\\ a.addr == addr)\n\nlet addrs_of_loc_aux\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (y: GSet.set nat { GSet.subset (GSet.intersect y (addrs_of_loc_weak l r)) GSet.empty } )\n= GSet.comprehend (addrs_of_loc_aux_pred l r)\n `GSet.intersect` (GSet.complement (addrs_of_loc_weak l r))\n\nlet addrs_of_loc\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= GSet.union\n (addrs_of_loc_weak l r)\n (addrs_of_loc_aux l r)\n\nlet addrs_of_loc_aux_prop\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: Lemma\n (GSet.subset (GSet.intersect (addrs_of_loc_aux l r) (addrs_of_loc_weak l r)) GSet.empty)\n [SMTPatOr [\n [SMTPat (addrs_of_loc_aux l r)];\n [SMTPat (addrs_of_loc_weak l r)];\n [SMTPat (addrs_of_loc l r)];\n ]]\n= ()\n\nlet loc_union #al #c s1 s2 =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in\n let regions = Set.union regions1 regions2 in\n let region_liveness_tags : Ghost.erased (Set.set HS.rid) = (Ghost.hide (Set.union (Ghost.reveal (Loc?.region_liveness_tags s1)) (Ghost.reveal (Loc?.region_liveness_tags s2)))) in\n let gregions = Ghost.hide regions in\n let non_live_addrs =\n F.on_dom_g (addrs_dom gregions) #(non_live_addrs_codom gregions region_liveness_tags)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then Loc?.non_live_addrs s1 r else GSet.empty)\n (if Set.mem r regions2 then Loc?.non_live_addrs s2 r else GSet.empty))\n in\n let live_addrs =\n F.on_dom_g (addrs_dom gregions) #(live_addrs_codom gregions region_liveness_tags non_live_addrs)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then addrs_of_loc_weak s1 r else GSet.empty)\n (if Set.mem r regions2 then addrs_of_loc_weak s2 r else GSet.empty))\n in\n let aux = Ghost.hide\n (Ghost.reveal (Loc?.aux s1) `GSet.union` Ghost.reveal (Loc?.aux s2))\n in\n Loc\n (Ghost.hide regions)\n region_liveness_tags\n non_live_addrs\n live_addrs\n aux\n\nlet fun_set_equal (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) :Tot Type0 =\n forall (x: t) . {:pattern (f1 x) \\/ (f2 x) } f1 x `GSet.equal` f2 x\n\nlet fun_set_equal_elim (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) : Lemma\n (requires (fun_set_equal f1 f2))\n (ensures (f1 == f2))\n// [SMTPat (fun_set_equal f1 f2)]\n= assert (f1 `FunctionalExtensionality.feq_g` f2)\n\nlet loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n let Loc regions1 region_liveness_tags1 _ _ aux1 = s1 in\n let Loc regions2 region_liveness_tags2 _ _ aux2 = s2 in\n Ghost.reveal regions1 `Set.equal` Ghost.reveal regions2 /\\\n Ghost.reveal region_liveness_tags1 `Set.equal` Ghost.reveal region_liveness_tags2 /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)\n\nlet loc_equal_elim (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : Lemma\n (requires (loc_equal s1 s2))\n (ensures (s1 == s2))\n [SMTPat (s1 `loc_equal` s2)]\n= fun_set_equal_elim (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2);\n fun_set_equal_elim (Loc?.live_addrs s1) (Loc?.live_addrs s2)\n\n\nlet loc_union_idem #al #c s =\n assert (loc_union s s `loc_equal` s)\n\nlet loc_union_comm #al #c s1 s2 =\n assert (loc_union s1 s2 `loc_equal` loc_union s2 s1)\n\nlet loc_union_assoc #al #c s1 s2 s3 =\n assert (loc_union s1 (loc_union s2 s3) `loc_equal` loc_union (loc_union s1 s2) s3)\n\nlet loc_union_loc_none_l #al #c s =\n assert (loc_union loc_none s `loc_equal` s)\n\nlet loc_union_loc_none_r #al #c s =\n assert (loc_union s loc_none `loc_equal` s)\n\nlet loc_of_aloc #al #c #r #n b =\n let regions = (Ghost.hide (Set.singleton r)) in\n let region_liveness_tags = (Ghost.hide (Set.empty)) in\n Loc\n regions\n region_liveness_tags\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide (GSet.singleton (ALoc r n (Some b))))\n\nlet loc_of_aloc_not_none #al #c #r #n b = ()\n\nlet loc_addresses #al #c preserve_liveness r n =\n let regions = (Ghost.hide (Set.singleton r)) in\n Loc\n regions\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> if preserve_liveness then GSet.empty else GSet.of_set n))\n (mk_live_addrs (fun _ -> GSet.of_set n))\n (Ghost.hide (aloc_domain c regions (fun _ -> GSet.of_set n)))\n\nlet loc_regions_region_liveness_tags (preserve_liveness: bool) (r: Set.set HS.rid) : Tot (Ghost.erased (Set.set HS.rid)) =\n if preserve_liveness then Ghost.hide Set.empty else Ghost.hide r\n\nlet loc_regions #al #c preserve_liveness r =\n let region_liveness_tags = loc_regions_region_liveness_tags preserve_liveness r in\n let addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { r' `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y } ) =\n GSet.complement GSet.empty\n in\n let live_addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { addrs r' `GSet.subset` y } ) =\n addrs r'\n in\n Loc\n (Ghost.hide r)\n region_liveness_tags\n (mk_non_live_addrs addrs)\n (mk_live_addrs live_addrs)\n (Ghost.hide (aloc_domain c (Ghost.hide r) addrs))\n\nlet aloc_includes (#al: aloc_t) (#c: cls al) (b0 b: aloc c) : GTot Type0 =\n b0.region == b.region /\\ b0.addr == b.addr /\\ Some? b0.loc == Some? b.loc /\\ (if Some? b0.loc && Some? b.loc then c.aloc_includes (Some?.v b0.loc) (Some?.v b.loc) else True)\n\nlet loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b: aloc c)\n: GTot Type0\n (decreases s)\n= exists (b0 : aloc c) . b0 `GSet.mem` s /\\ b0 `aloc_includes` b\n\nlet loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: GTot Type0\n (decreases s2)\n= forall (b2: aloc c) . GSet.mem b2 s2 ==> loc_aux_includes_buffer s1 b2\n\nlet loc_aux_includes_union_l\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s \\/ loc_aux_includes s2 s))\n (ensures (loc_aux_includes (GSet.union s1 s2) s))\n (decreases s)\n= ()\n\nlet loc_aux_includes_refl\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n: Lemma\n (loc_aux_includes s s)\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)\n\nlet loc_aux_includes_subset\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)\n\nlet loc_aux_includes_subset'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n [SMTPatOr [\n [SMTPat (s1 `GSet.subset` s2)];\n [SMTPat (loc_aux_includes s2 s1)];\n ]]\n= loc_aux_includes_subset s1 s2\n\nlet loc_aux_includes_union_l_r\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s s') s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s s' s\n\nlet loc_aux_includes_union_l_l\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s' s) s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s' s s\n\nlet loc_aux_includes_buffer_includes\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b1 b2: aloc c)\n: Lemma\n (requires (loc_aux_includes_buffer s b1 /\\ b1 `aloc_includes` b2))\n (ensures (loc_aux_includes_buffer s b2))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))\n\nlet loc_aux_includes_loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n (b: aloc c)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_buffer s2 b))\n (ensures (loc_aux_includes_buffer s1 b))\n= Classical.forall_intro_3 (fun s b1 b2 -> Classical.move_requires (loc_aux_includes_buffer_includes #al #c s b1) b2)\n\nlet loc_aux_includes_trans\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))\n\nlet addrs_of_loc_weak_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (loc_union l1 l2) r == GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r))\n [SMTPat (addrs_of_loc_weak (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc_weak (loc_union l1 l2) r) (GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r)))\n\nlet addrs_of_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l1 l2) r == GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r))\n [SMTPat (addrs_of_loc (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc (loc_union l1 l2) r) (GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r)))\n\nunfold\nlet loc_includes' #al (#c: cls al) (s1 s2: loc c) =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in (\n Set.subset regions2 regions1 /\\\n Set.subset (Ghost.reveal (Loc?.region_liveness_tags s2)) (Ghost.reveal (Loc?.region_liveness_tags s1)) /\\\n (\n forall (r: HS.rid { Set.mem r regions2 } ) .\n GSet.subset (Loc?.non_live_addrs s2 r) (Loc?.non_live_addrs s1 r)\n ) /\\\n (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc_weak s2 r) (addrs_of_loc_weak s1 r)\n ) /\\ (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc s2 r) (addrs_of_loc s1 r)\n ) /\\ (\n (Ghost.reveal (Loc?.aux s1)) `loc_aux_includes` (Ghost.reveal (Loc?.aux s2))\n )\n )\n\nlet loc_includes #al #c s1 s2 =\n loc_includes' s1 s2\n\nlet loc_includes_refl #al #c s =\n loc_aux_includes_refl (Ghost.reveal (Loc?.aux s))\n\nlet loc_includes_refl'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: Lemma\n (loc_includes s s)\n [SMTPat (loc_includes s s)]\n= loc_includes_refl s\n\nlet loc_includes_trans #al #c s1 s2 s3 =\n loc_aux_includes_trans (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s3))\n\nlet loc_includes_union_r #al #c s s1 s2 = ()\n\nlet loc_includes_union_l #al #c s1 s2 s =\n let u12 = loc_union s1 s2 in\n Classical.or_elim\n #(loc_includes s1 s)\n #(loc_includes s2 s)\n #(fun _ -> loc_includes (loc_union s1 s2) s)\n (fun _ ->\n loc_aux_includes_union_l_r (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2));\n assert (loc_includes (loc_union s1 s2) s1);\n loc_includes_trans u12 s1 s)\n (fun _ ->\n loc_aux_includes_union_l_l (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s1));\n assert (loc_includes (loc_union s1 s2) s2);\n loc_includes_trans u12 s2 s)\n\nlet loc_includes_none #al #c s = ()\n\nlet loc_includes_none_elim #al #c s =\n assert (s `loc_equal` loc_none)\n\nlet loc_includes_aloc #al #c #r #n b1 b2 = ()\n\nlet loc_includes_aloc_elim #aloc #c #r1 #r2 #n1 #n2 b1 b2 = ()\n\nlet addrs_of_loc_loc_of_aloc\n (#al: aloc_t)\n (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (p: al r a)\n (r': HS.rid)\n: Lemma\n (addrs_of_loc (loc_of_aloc #_ #c p) r' `GSet.equal` (if r = r' then GSet.singleton a else GSet.empty))\n [SMTPat (addrs_of_loc (loc_of_aloc #_ #c p) r')]\n= ()\n\nlet loc_includes_addresses_aloc #al #c preserve_liveness r s #a p = ()\n\nlet loc_includes_region_aloc #al #c preserve_liveness s #r #a b = ()\n\nlet loc_includes_region_addresses #al #c s preserve_liveness1 preserve_liveness2 r a = ()\n\nlet loc_includes_region_region #al #c preserve_liveness1 preserve_liveness2 s1 s2 = ()\n\nlet loc_includes_region_union_l #al #c preserve_liveness l s1 s2 =\n assert ((loc_regions #_ #c preserve_liveness (Set.intersect s2 (Set.complement s1)) `loc_union` loc_regions #_ #c preserve_liveness (Set.intersect s2 s1)) `loc_equal` loc_regions preserve_liveness s2);\n loc_includes_region_region #_ #c preserve_liveness preserve_liveness s1 (Set.intersect s2 s1);\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)));\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 s1));\n loc_includes_union_r (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1))) (loc_regions preserve_liveness (Set.intersect s2 s1))\n\nlet loc_includes_addresses_addresses #al c preserve_liveness1 preserve_liveness2 r s1 s2 = ()\n\n(* Disjointness of two memory locations *)\n\nlet aloc_disjoint (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : GTot Type0 =\n if b1.region = b2.region && b1.addr = b2.addr\n then Some? b1.loc /\\ Some? b2.loc /\\ c.aloc_disjoint (Some?.v b1.loc) (Some?.v b2.loc)\n else True\n\nlet aloc_disjoint_sym (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : Lemma\n (aloc_disjoint b1 b2 <==> aloc_disjoint b2 b1)\n= Classical.forall_intro_2 (fun r a -> Classical.forall_intro_2 (fun b1 b2 -> c.aloc_disjoint_sym #r #a b1 b2))\n\nlet loc_aux_disjoint\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: GTot Type0\n= forall (b1 b2: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b2 l2) ==> aloc_disjoint b1 b2\n\nlet loc_aux_disjoint_union_l\n (#al: aloc_t) (#c: cls al)\n (ll1 lr1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint (GSet.union ll1 lr1) l2 <==> (loc_aux_disjoint ll1 l2 /\\ loc_aux_disjoint lr1 l2)))\n= ()\n\nlet loc_aux_disjoint_union_r\n (#al: aloc_t) (#c: cls al)\n (l1 ll2 lr2: GSet.set (aloc c))\n: Lemma\n (loc_aux_disjoint l1 (GSet.union ll2 lr2) <==> (loc_aux_disjoint l1 ll2 /\\ loc_aux_disjoint l1 lr2))\n= ()\n\nlet loc_aux_disjoint_sym\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint l1 l2 <==> loc_aux_disjoint l2 l1))\n= Classical.forall_intro_2 (aloc_disjoint_sym #al #c)\n\nlet regions_of_loc_loc_union\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (regions_of_loc (loc_union s1 s2) == regions_of_loc s1 `Set.union` regions_of_loc s2)\n [SMTPat (regions_of_loc (loc_union s1 s2))]\n= assert (regions_of_loc (loc_union s1 s2) `Set.equal` (regions_of_loc s1 `Set.union` regions_of_loc s2))\n\nlet regions_of_loc_monotonic\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_includes s1 s2))\n (ensures (Set.subset (regions_of_loc s2) (regions_of_loc s1)))\n= ()\n\nlet loc_disjoint_region_liveness_tags (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty\n\nlet loc_disjoint_addrs (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n (forall (r: HS.rid) .\n GSet.subset (GSet.intersect (addrs_of_loc_weak l1 r) (addrs_of_loc l2 r)) GSet.empty /\\\n GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc_weak l2 r)) GSet.empty\n )\n\nlet loc_disjoint_aux (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n loc_aux_disjoint (Ghost.reveal (Loc?.aux l1)) (Ghost.reveal (Loc?.aux l2))\n\nlet loc_disjoint'\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n: GTot Type0\n= loc_disjoint_region_liveness_tags l1 l2 /\\\n loc_disjoint_addrs l1 l2 /\\\n loc_disjoint_aux l1 l2\n\nlet loc_disjoint = loc_disjoint'\n\nlet loc_disjoint_sym #al #c l1 l2 =\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c)\n\nlet loc_disjoint_sym'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))\n [SMTPat (loc_disjoint s1 s2)]\n= loc_disjoint_sym s1 s2\n\nlet loc_disjoint_none_r #al #c s = ()\n\nlet loc_disjoint_union_r #al #c s s1 s2 = ()\n\nlet aloc_disjoint_includes (#al: aloc_t) (#c: cls al) (b1 b2 b3 : aloc c) : Lemma\n (requires (aloc_disjoint b1 b2 /\\ aloc_includes b2 b3))\n (ensures (aloc_disjoint b1 b3))\n= if b1.region = b2.region && b1.addr = b2.addr\n then begin\n c.aloc_includes_refl (Some?.v b1.loc);\n c.aloc_disjoint_includes (Some?.v b1.loc) (Some?.v b2.loc) (Some?.v b1.loc) (Some?.v b3.loc)\n end\n else ()\n\nlet loc_aux_disjoint_loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (l1 l2 l3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\n= // FIXME: WHY WHY WHY do I need this assert?\n assert (forall (b1 b3: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b3 l3) ==> (exists (b2: aloc c) . GSet.mem b2 l2 /\\ aloc_disjoint b1 b2 /\\ aloc_includes b2 b3));\n Classical.forall_intro_3 (fun b1 b2 b3 -> Classical.move_requires (aloc_disjoint_includes #al #c b1 b2) b3)\n\nlet loc_disjoint_includes #al #c p1 p2 p1' p2' =\n regions_of_loc_monotonic p1 p1';\n regions_of_loc_monotonic p2 p2';\n let l1 = Ghost.reveal (Loc?.aux p1) in\n let l2 = Ghost.reveal (Loc?.aux p2) in\n let l1' = Ghost.reveal (Loc?.aux p1') in\n let l2' = Ghost.reveal (Loc?.aux p2') in\n loc_aux_disjoint_loc_aux_includes l1 l2 l2';\n loc_aux_disjoint_sym l1 l2';\n loc_aux_disjoint_loc_aux_includes l2' l1 l1';\n loc_aux_disjoint_sym l2' l1'\n\nlet loc_disjoint_aloc_intro #al #c #r1 #a1 #r2 #a2 b1 b2 = ()\n\nlet loc_disjoint_aloc_elim #al #c #r1 #a1 #r2 #a2 b1 b2 =\n // FIXME: WHY WHY WHY this assert?\n assert (aloc_disjoint (ALoc #_ #c r1 a1 (Some b1)) (ALoc #_ #c r2 a2 (Some b2)))\n\n#push-options \"--z3rlimit 15\"\nlet loc_disjoint_addresses_intro #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness1 r1 n1))) (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness2 r2 n2))))\n#pop-options\n\nlet loc_disjoint_addresses_elim #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 = ()\n\nlet loc_disjoint_aloc_addresses_intro #al #c #r' #a' p preserve_liveness r n = ()\n\nlet loc_disjoint_aloc_addresses_elim #al #c #r' #a' p preserve_liveness r n = ()\n\nlet loc_disjoint_regions #al #c preserve_liveness1 preserve_liveness2 rs1 rs2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness1 rs1))) (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness2 rs2))))\n\nlet loc_none_in_some_region #a (c: cls a) (r: HS.rid) : GTot (loc c) =\n Loc\n (Ghost.hide (Set.singleton r))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)\n\n(** Liveness-insensitive memory locations *)\n\nlet address_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))\n\nlet loc_includes_address_liveness_insensitive_locs_aloc #al #c #r #n a = ()\n\nlet loc_includes_address_liveness_insensitive_locs_addresses #al c r a = ()\n\nlet region_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.complement GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))\n\nlet loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs #al c = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_regions #al c r = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_addresses #al c preserve_liveness r a = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_of_aloc #al c #r #a x = ()\n\n(** The modifies clause proper *)\n\nlet modifies_preserves_livenesses\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s r)))\n ) ==> (\n HS.contains h2 p\n ))\n\nlet modifies_preserves_livenesses_elim\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (p: HS.mreference t pre)\n: Lemma\n (requires (modifies_preserves_livenesses s h1 h2 /\\ HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))))\n (ensures (HS.contains h2 p))\n= ()\n\nlet modifies_preserves_livenesses_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p))\n ))\n: Lemma\n (modifies_preserves_livenesses s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'\n\nlet modifies_preserves_mreferences\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s r)))\n ) ==> (\n HS.contains h2 p /\\\n HS.sel h2 p == HS.sel h1 p\n ))\n\nlet modifies_preserves_mreferences_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p /\\ HS.sel h2 p == HS.sel h1 p))\n ))\n: Lemma\n (modifies_preserves_mreferences s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p /\\ h2 `HS.sel` p == h1 `HS.sel` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'\n\nlet modifies_preserves_alocs\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (a: nat) (b: al r a) .\n loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))\n ==>\n c.aloc_preserved b h1 h2\n )\n\nlet modifies_preserves_alocs_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (u: unit { modifies_preserves_mreferences s h1 h2 } )\n (f: (\n (r: HS.rid) ->\n (a: nat) ->\n (b: al r a) ->\n Lemma\n (requires (\n Set.mem r (regions_of_loc s) /\\\n (~ (GSet.mem a (addrs_of_loc_weak s r))) /\\\n (GSet.mem a (addrs_of_loc_aux s r) /\\ loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b))))\n ))\n (ensures (c.aloc_preserved b h1 h2))\n ))\n: Lemma\n (modifies_preserves_alocs s h1 h2)\n= let f'\n (r: HS.rid)\n (a: nat)\n (b: al r a)\n : Lemma\n (requires (loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))))\n (ensures (c.aloc_preserved b h1 h2))\n = if Set.mem r (regions_of_loc s) && (not (GSet.mem a (addrs_of_loc_weak s r)))\n then begin\n if GSet.mem a (addrs_of_loc_aux s r)\n then\n Classical.move_requires (f r a) b\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n end else if Set.mem r (regions_of_loc s)\n then begin\n assert (GSet.mem a (addrs_of_loc_weak s r));\n assert (GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux s)));\n assert (aloc_disjoint #_ #c (ALoc r a None) (ALoc r a (Some b)));\n assert False\n end\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n in\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (f' r a) b)\n\nlet modifies_preserves_regions\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= forall (r: HS.rid) . (HS.live_region h1 r /\\ ~ (Set.mem r (Ghost.reveal (Loc?.region_liveness_tags s)))) ==> HS.live_region h2 r\n\n\nlet modifies_preserves_not_unused_in\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (n: nat) . (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n\nlet modifies_preserves_not_unused_in_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ))\n (ensures (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n ))\n: Lemma\n (modifies_preserves_not_unused_in s h1 h2)\n= let f'\n (r: HS.rid)\n (n: nat)\n : Lemma\n ((\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n = Classical.move_requires (f r) n\n in\n Classical.forall_intro_2 f'\n\nlet modifies'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= modifies_preserves_regions s h1 h2 /\\\n modifies_preserves_not_unused_in s h1 h2 /\\\n modifies_preserves_mreferences s h1 h2 /\\\n modifies_preserves_livenesses s h1 h2 /\\\n modifies_preserves_alocs s h1 h2\n\nlet modifies = modifies'\n\nval modifies_intro_strong\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n (Set.mem r (regions_of_loc l) ==> ~ (GSet.mem n (Loc?.non_live_addrs l r))) /\\\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')\n" }, { "file_name": "Preprocess.fst", "name": "Preprocess.test_add_1'", "opens_and_abbrevs": [ { "open": "FStar.Tactics.V2" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val test_add_1' (x: int) : int", "source_definition": "let test_add_1' (x:int) : int =\n x + 1", "source_range": { "start_line": 14, "start_col": 0, "end_line": 15, "end_col": 9 }, "interleaved": false, "definition": "fun x -> x + 2 <: Prims.int", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Prims.int", "Prims.op_Addition" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "x: Prims.int -> Prims.int", "prompt": "let test_add_1' (x: int) : int =\n ", "expected_response": "x + 1", "source": { "project_name": "FStar", "file_name": "examples/tactics/Preprocess.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "Preprocess.fst", "checked_file": "dataset/Preprocess.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.String.fsti.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked" ] }, "definitions_in_context": [ "let incr_lits_by_1 (t:term) : Tac term =\n match inspect t with\n | Tv_Const (C_Int x) -> pack (Tv_Const (C_Int (x+1)))\n | _ -> t", "let test_add_1 (x:int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))" ], "closest": [ "val add_1 (x: int) : int\nlet add_1 (x:int) : int = x + 1", "val add_2 (x: int) : int\nlet add_2 (x:int) : int = _ by (normalize [primops; delta] (add_1 (add_1 x)))", "val add1 (x: int) : Id int (requires (x > 0)) (ensures (fun r -> r == x + 1))\nlet add1 (x:int) : Id int (requires (x > 0)) (ensures (fun r -> r == x+1)) = x + 1", "val add1 (x: int) : Id int (requires (x > 0)) (ensures (fun r -> r == x + 1))\nlet add1 (x:int) : Id int (requires (x > 0)) (ensures (fun r -> r == x+1)) = x + 1", "val add1 (x: int) : Id int (requires (x > 0)) (ensures (fun r -> r == x + 1))\nlet add1 (x:int) : Id int (requires (x > 0)) (ensures (fun r -> r == x+1)) = x + 1", "val test (x: int) : Dv int\nlet test (x:int) : Dv int = reify (good_div x) ()", "val Pulse.Lib.BoundedIntegers.add_nat_1 = x: Prims.nat -> Prims.int\nlet add_nat_1 (x:nat) = x + 1", "val test1 (x y: int) : EFF int [EXN; RD; WR]\nlet test1 (x y : int) : EFF int [EXN; RD; WR] =\n let z = get () in\n if x + z > 0\n then raise ()\n else (put 42; y - z)", "val test1 (r: ref int) (x y: int) : EFF int [EXN; WR]\nlet test1 (r:ref int) (x y : int) : EFF int [EXN; WR] =\n let z = !r in\n if x + z > 0\n then raise (Failure \"nope\")\n else (r := 42; y - z)", "val test1 (x y: int) : Alg int [Raise; Read; Write]\nlet test1 (x y : int) : Alg int [Raise; Read; Write] =\n let z = get () in\n if x + z > 0\n then raise (Failure \"asd\")\n else (put 42; y - z)", "val test1 (x: int) : SteelT ref emp ptr\nlet test1 (x:int) : SteelT ref emp ptr =\n let y = alloc x in y", "val test1 (x y: int) : EFFT int [EXN; RD; WR]\nlet test1 (x y : int) : EFFT int [EXN; RD; WR] by (compute ())=\n let z = get () in\n if x + z > 0\n then raise ()\n else (put 42; y - z)", "val test1 (x y: int) : EFF int int int [RD; WR]\nlet test1 (x y : int) : EFF int int int [RD; WR] =\n let z = get () in\n if x + z > 0\n then 0\n else (put 42; y - z)", "val addx (x: int) : ST unit int (fun s0 p -> p () (s0 + x))\nlet addx (x:int) : ST unit int (fun s0 p -> p () (s0+x)) =\n let y = get () in\n put (x+y)", "val Pulse.Class.BoundedIntegers.add_nat_1 = x: Prims.nat -> Prims.int\nlet add_nat_1 (x:nat) = x + 1", "val pos_as_int (x: pos) : int\nlet pos_as_int (x:pos) : int = x", "val pos_as_int (x: pos) : int\nlet pos_as_int (x:pos) : int = x", "val put (#s: _) (x: s) : st s monoid_nat_plus 1 unit\nlet put #s (x:s) : st s monoid_nat_plus 1 unit = fun _ -> (), x", "val test0 (r: ref int) (x y: int) : EFF int [EXN]\nlet test0 (r:ref int) (x y : int) : EFF int [EXN] =\n let z = !r in\n if x + z > 0\n then raise (Failure \"nope\")\n else y - z", "val nat_as_int (x: nat) : int\nlet nat_as_int (x:nat) : int = x", "val nat_as_int (x: nat) : int\nlet nat_as_int (x:nat) : int = x", "val test8 (x: ref) : SteelT int (ptr x) (fun _ -> ptr x)\nlet test8 (x:ref) : SteelT int (ptr x) (fun _ -> ptr x)\n = let v = read x in\n let y = alloc v in\n let v = read y in\n free y;\n // Can mix assertions\n assert (1 == 1);\n v", "val int_compare (x1 x2: int) : Tot int\nlet int_compare (x1 x2: int) : Tot int =\n if x1 < x2\n then -1\n else if x1 = x2\n then 0\n else 1", "val test0 (x y: int) : EFF int [RD; EXN]\nlet test0 (x y : int) : EFF int [RD; EXN] =\n let z = get () in\n if x + z > 0\n then raise ()\n else y - z", "val test0 (x y: int) : Alg int [Read; Raise]\nlet test0 (x y : int) : Alg int [Read; Raise] =\n let z = get () in\n if z < 0 then raise (Failure \"error\");\n x + y + z", "val plus_one: 'a -> nat -> Tot nat\nlet plus_one m n = n + 1", "val test1 (r: ref int)\n : Steel unit\n (vptr r)\n (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> sel r h1 == 0)\nlet test1 (r:ref int) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> sel r h1 == 0)\n = write r 1;\n write r 0", "val test21 (x: int) : SteelAtomicT ref Set.empty emp ptr\nlet test21 (x:int) : SteelAtomicT ref Set.empty emp ptr =\n let y = alloc2 x in y", "val evar (x: var) : Tot (exp int)\nlet evar (x: var) : Tot (exp int) = fun _ -> read x", "val f (x: int) : Pure unit (requires x == 2) (ensures fun _ -> True)\nlet f (x:int) : Pure unit (requires x == 2) (ensures fun _ -> True) =\n assert (x == 2);\n ()", "val one : x:t{v x = 1}\nlet one =\n FStar.Math.Lemmas.pow2_lt_compat (n - 1) 1;\n int_to_t 1", "val one : x:t{v x = 1}\nlet one =\n FStar.Math.Lemmas.pow2_lt_compat (n - 1) 1;\n int_to_t 1", "val one : x:t{v x = 1}\nlet one = uint_to_t 1", "val one : x:t{v x = 1}\nlet one =\n FStar.Math.Lemmas.pow2_lt_compat (n - 1) 1;\n int_to_t 1", "val one : x:t{v x = 1}\nlet one = uint_to_t 1", "val one : x:t{v x = 1}\nlet one =\n FStar.Math.Lemmas.pow2_lt_compat (n - 1) 1;\n int_to_t 1", "val one : x:t{v x = 1}\nlet one =\n FStar.Math.Lemmas.pow2_lt_compat (n - 1) 1;\n int_to_t 1", "val one : x:t{v x = 1}\nlet one = uint_to_t 1", "val one : x:t{v x = 1}\nlet one = uint_to_t 1", "val test_imp (x: int) : SteelT unit emp (fun _ -> p #1 1)\nlet test_imp (x:int) : SteelT unit emp (fun _ -> p #1 1) =\n let _ = palloc 0 in\n pwrite 1", "val pre1 (x: nat) : prop\nlet pre1 (x:nat) : prop = pre0 x", "val mod2_128 (x: int) : int\nlet mod2_128 (x:int) : int =\n x % pow2_128", "val safe_add (#t: eqtype) {| c: bounded_unsigned t |} (x y: t)\n : o: option t {Some? o ==> v (Some?.v o) == v x + v y}\nlet safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t)\n : o:option t { Some? o ==> v (Some?.v o) == v x + v y } \n = if c.static_max_bound\n then (\n assert ( x <= max_bound);\n if (y <= max_bound - x) \n then Some (x + y)\n else None\n )\n else (\n if x <= max_bound\n then (\n assert (fits #t (v (max_bound #t) - v x));\n if (y <= max_bound - x)\n then Some (x + y)\n else None\n )\n else None\n )", "val safe_add (#t: eqtype) {| c: bounded_unsigned t |} (x y: t)\n : o: option t {Some? o ==> v (Some?.v o) == v x + v y}\nlet safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t)\n : o:option t { Some? o ==> v (Some?.v o) == v x + v y } \n = if c.static_max_bound\n then (\n assert ( x <= max_bound);\n if (y <= max_bound - x) \n then Some (x + y)\n else None\n )\n else (\n if x <= max_bound\n then (\n assert (fits #t (v (max_bound #t) - v x));\n if (y <= max_bound - x)\n then Some (x + y)\n else None\n )\n else None\n )", "val add1_: add1_t True\nlet add1_ out f1 f2 =\n let h0 = ST.get () in\n let c = BN.bn_add1 4ul f1 f2 out in\n let h1 = ST.get () in\n assert (let c1, r1 = CC.add1 (as_seq h0 f1) f2 in c == c1 /\\ as_seq h1 out == r1);\n CD.bn_v_is_as_nat (as_seq h0 f1);\n CD.bn_v_is_as_nat (as_seq h1 out);\n c", "val ci_ex1_ (x: nat) : unit\nlet ci_ex1_ (x : nat) : unit =\n let y = x in\n assert(x == y); (* <- Use C-c C-e C-e here *)\n ()", "val count (x: int) (t: tree) : Tot nat\nlet rec count (x:int) (t:tree) : Tot nat =\n match t with\n | Leaf -> 0\n | Node n t1 t2 -> (if n = x then 1 else 0) + count x t1 + count x t2", "val f1 : x:(ref int) -> ST int (requires (fun h -> True))\n (ensures (fun h r h' -> fst (f1_hp h x) == h'\n /\\ snd (f1_hp h x) == r))\nlet f1 x = !x", "val ut_ex1 (x y: nat) : unit\nlet ut_ex1 (x y : nat) : unit =\n let z1 = f3 (x + y) in\n\n (* Unfold definitions: *)\n assert(z1 = f3 (x + y)); (* <- Move the pointer EXACTLY over ``f3`` and use C-c C-e C-u *)\n\n (* Unfold arbitrary identifiers:\n * In case the term to unfold is not a top-level definition but a local\n * variable, the command will look for a pure let-binding and will even\n * explore post-conditions to look for an equality to find a term by\n * which to replace the variable. *)\n assert(z1 = 2 * (x + y)); (* <- Try the command on ``z1`` *)\n\n (* Note that if the assertion is an equality, the command will only\n * operate on one side of the equality at a time. *)\n assert(z1 = z1);\n \n (*\n * It is even possible to apply the command on arbitrary term, in which\n * case the command will explore post-conditions to find an equality to\n * use for rewriting.\n *)\n assert(f3 (f3 (x + y)) = 4 * (x + y));\n assert(2 * z1 = z1 + z1);\n assert(f3 (f3 (x + y)) = 2 * z1)", "val x:int\nlet x : int = foo 1", "val addx (l: loc) (x: int)\n : AlgPP unit\n (fun _ -> True)\n (fun h0 _ h1 -> modifies1 l h0 h1 /\\ (Map.sel h1 l == x + Map.sel h0 l))\nlet addx (l:loc) (x:int) : AlgPP unit (fun _ -> True) (fun h0 _ h1 -> modifies1 l h0 h1\n /\\ (Map.sel h1 l == x + Map.sel h0 l)) =\n l := !l + x", "val verify_test (x y z: ref int):\n Lemma begin\n let n = 3 in\n let l = [x ; y ; z] in\n let y_add = addr_of y in\n let z_add = addr_of z in\n let env (r: nat) = //AR: in the extracted interface, y_add and z_add are inlined in the following,\n // which means the effect is now GTot, so i had to make env as ref int -> GTot label\n if r = y_add || r = z_add then High\n else Low\n in\n let res h = sel h y + sel h z in\n del_rel n env l [res] [] test\n end\nlet verify_test x y z = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm ()", "val add_one (t: term) : Tac term\nlet add_one (t:term) : Tac term = `(`#t + 1)", "val FStar.InteractiveHelpers.ParseTest.simpl_ex1 = x: Prims.nat -> Prims.int\nlet simpl_ex1 (x : nat) =\n let y = 4 in\n let 'x = 7 in\n let 'a = 4 in\n let 'd = \"hello world!\" in\n let '_u''x = 5 in\n let z = 3 in\n let w : w:nat{w >= 10} =\n if x > 3 then\n begin\n assert(y + x > 7);\n let x' = x + 1 in\n assert(y + x' > 8);\n let x'' = 2 * (y + x') in\n assert(x'' > 16);\n assert(x'' >= 10);\n 2 * x'\n end\n else 12\n in\n assert(\n x >= 0 /\\\n y >= 0);\n let w' = 2 * w + z in\n w'", "val test0 (x y: int) : EFFT int [RD; EXN]\nlet test0 (x y : int) : EFFT int [RD; EXN] =\n let z = get () in\n if x + z > 0\n then raise ()\n else y - z", "val test0 (x y: int) : EFF int int int [RD]\nlet test0 (x y : int) : EFF int int int [RD] by (norm [delta]) =\n let z = get #int () in\n if x + z > 0\n then 0\n else 1", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val v (x:t) : Tot (int_t n)\nlet v x = x.v", "val add (x y: t) : Pure t\n (requires (fits (v x + v y)))\n (ensures (fun z -> v z == v x + v y))\nlet add x y = I64.add x y", "val add (x y: t) : Pure t\n (requires (fits (v x + v y)))\n (ensures (fun z -> v z == v x + v y))\nlet add x y = U64.add x y", "val ci_ex1 (x y: nat) : z: int{z % 3 = 0}\nlet ci_ex1 (x y : nat) : z:int{z % 3 = 0} =\n (* Preconditions:\n * Type C-c C-e C-e below to insert:\n * [> assert(x + 4 > 3); *)\n let x1 = f1 (x + 4) y in (* <- Put your pointer after the 'in' and type C-c C-e C-e *)\n\n (* Postconditions: *)\n let x2 = f2 x1 y in (* <- Put your pointer after the 'in' and type C-c C-e C-e *)\n (* Type C-c C-e C-e above to insert:\n * [> assert(has_type x2 nat);\n * [> assert(x2 >= 8);\n * [> assert(x2 % 2 = 0); *)\n\n (* Typing obligations:\n * Type C-c C-e C-e below to insert:\n * [> assert(Prims.has_type (x2 <: Prims.nat) Prims.int);\n * [> assert(x2 % 2 = 0);\n * Note that the assertion gives indications about the parameter\n * known type, the target type and the (potential) refinement.\n * Also note that the type obligations are not introduced when\n * they are trivial (if the original type and the target type are\n * exactly the same, syntactically).\n * WARNING: `has_type` is very low level and shouldn't be used in user proofs.\n * In the future, we intend to remove the assertions containing `has_type`,\n * and only introduce assertions for the refinements.\n *)\n let x3 = f4 x2 in (* <- Put your pointer on the left and type C-c C-e C-e *)\n\n (* Current goal:\n * Type C-c C-e C-e below to insert:\n * [> assert(Prims.has_type (3 * (x1 + x2 + x3)) Prims.int);\n * [> assert(3 * (x1 + x2 + x3) % 3 = 0); *)\n 3 * (x1 + x2 + x3)", "val v (x: t) : Pure int\n (requires True)\n (ensures (fun y -> fits y))\nlet v x =\n I64.v x", "val add_2 (a b: int) : Tot int\nlet add_2 : a:int -> b:int -> Tot int = _ by (make_add ())", "val sz_add (x y: SZ.t) : o: option SZ.t {Some? o ==> SZ.v (Some?.v o) == SZ.v x + SZ.v y}\nlet sz_add (x y : SZ.t)\n : o:option SZ.t { Some? o ==> SZ.v (Some?.v o) == SZ.v x + SZ.v y } \n = let open SZ in\n if x <=^ 0xffffsz\n then (\n if (y <=^ 0xffffsz -^ x)\n then Some (x +^ y)\n else None\n )\n else None", "val incr (#v0: erased int) (x: ref int) : C unit (pts_to x v0) (fun u -> pts_to x (v0 + 1))\nlet incr (#v0:erased int) (x:ref int)\n : C unit (pts_to x v0) (fun u -> pts_to x (v0 + 1))\n = let v = !x in\n frame_r (fun _ -> x := v + 1);\n rewrite (fun y -> pts_to x (y + 1)) v0 v", "val incr (#v0: erased int) (x: ref int) : C unit (pts_to x v0) (fun u -> pts_to x (v0 + 1))\nlet incr (#v0:erased int) (x:ref int)\n : C unit (pts_to x v0) (fun u -> pts_to x (v0 + 1))\n = let v = !x in\n frame_r (fun _ -> x := v + 1);\n rewrite (fun y -> pts_to x (y + 1)) v0 v", "val abs (x: int) : Tot int\nlet abs (x: int) : Tot int = if x >= 0 then x else - x", "val Intro.suc = x: Prims.int -> Prims.int\nlet suc (x:int) = x + 1", "val plus_assoc : x:int -> y:int -> z:int -> Lemma ((x + y) + z == x + (y + z))\nlet plus_assoc = easy", "val test1 (c: ref (ref int))\n : ST (ref (ref int))\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures\n (fun h0 d h1 ->\n c == d /\\ (h1, d) == (compose_hlens hlens_ref hlens_ref).put 0 (h0, c) /\\\n h1 == upd (upd h0 (sel h0 c) 0) c (sel h0 c) /\\ sel h0 c == sel h1 c /\\\n sel h1 (sel h1 c) = 0))\nlet test1 (c:ref (ref int)) : ST (ref (ref int))\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures (fun h0 d h1 ->\n c == d /\\\n (h1, d) == (compose_hlens hlens_ref hlens_ref).put 0 (h0, c) /\\\n h1 == upd (upd h0 (sel h0 c) 0) c (sel h0 c) /\\\n sel h0 c == sel h1 c /\\ sel h1 (sel h1 c) = 0)) =\n (compose_stlens stlens_ref stlens_ref).st_put 0 c", "val add_mem (#a: eqtype) (#f: cmp a) (x: a) (s: mset a f)\n : Lemma (mem x (add_elem s x) == mem x s + 1)\nlet rec add_mem (#a:eqtype) (#f:cmp a) (x:a) (s:mset a f)\n : Lemma (mem x (add_elem s x) == mem x s + 1)\n = match s with\n | [] -> ()\n | (y, _)::_ ->\n if x = y then ()\n else if f x y then mem_elt_lt_hd x s\n else add_mem x (tl s)", "val my_safe_add (x y: SZ.t) : o: opt SZ.t {Some? o ==> SZ.v (Some?.v o) == SZ.v x + SZ.v y}\nlet my_safe_add (x y : SZ.t)\n : o:opt SZ.t { Some? o ==> SZ.v (Some?.v o) == SZ.v x + SZ.v y } \n = let open SZ in\n if x <=^ 0xffffsz\n then (\n if (y <=^ 0xffffsz -^ x)\n then Some (x +^ y)\n else None\n )\n else None", "val factorial (x: nat) : nat\nlet rec factorial (x:nat) : nat =\n match x with\n | 0 -> 1\n | _ -> x + factorial (x - 1)", "val int_to_t (x: int) : Pure t\n (requires (fits x))\n (ensures (fun y -> v y == x))\nlet int_to_t (x: int) : Pure t\n (requires (fits x))\n (ensures (fun y -> v y == x))\n = I64.int_to_t x", "val Pulse.Lib.BoundedIntegers.add_nat = x: Prims.nat -> y: Prims.nat -> Prims.nat\nlet add_nat (x y:nat) = x + y", "val FStar.InteractiveHelpers.Tutorial.simpl_ex1 = x: Prims.nat -> Prims.int\nlet simpl_ex1 (x : nat) =\n let y = 4 in\n let z = 3 in\n let w : w:nat{w >= 10} =\n if x > 3 then\n begin\n assert(y + x > 7);\n let x' = x + 1 in\n assert(y + x' > 8);\n let x'' = 2 * (y + x') in\n assert(x'' > 16);\n assert(x'' >= 10);\n 2 * x'\n end\n else 12\n in\n assert(\n x >= 0 /\\\n y >= 0);\n let w' = 2 * w + z in\n w'", "val append1 (#a: Type) (s: seq a) (x: a) : s': (seq a){length s' = length s + 1}\nlet append1 (#a:Type) (s:seq a) (x:a): s':(seq a){length s' = length s + 1} =\n append s (create 1 x)", "val impl_compare_u8 (x1 x2: U8.t) : Tot I16.t\nlet impl_compare_u8\n (x1 x2: U8.t)\n: Tot I16.t\n= if x1 = x2\n then 0s\n else if x1 `U8.lt` x2\n then -1s\n else 1s", "val Pulse.Lib.BoundedIntegers.size_t_plus_one = x: FStar.SizeT.t{x < 1024sz} -> FStar.SizeT.t\nlet size_t_plus_one (x:FStar.SizeT.t { x < 1024sz }) = x + 1sz", "val word_to_nat32 (x:word) : nat32\nlet word_to_nat32 = vv", "val word_to_nat32 (x:word) : nat32\nlet word_to_nat32 = vv", "val sec42_ex4 (x y: var)\n : Lemma (requires (x <> y))\n (ensures\n (exec_equiv (geq (gvar y Left) (gvar y Right))\n (gand (geq (gvar x Left) (gvar x Right))\n (geq (gop op_Addition (gvar y Left) (gconst 1)) (gvar x Right)))\n (assign x (eop op_Addition (evar y) (const 1)))\n (assign x (eop op_Addition (evar y) (const 1)))))\nlet sec42_ex4\n (x y: var)\n: Lemma\n (requires (x <> y))\n (ensures (\n exec_equiv\n (geq (gvar y Left) (gvar y Right))\n (gand (geq (gvar x Left) (gvar x Right)) (geq (gop op_Addition (gvar y Left) (gconst 1)) (gvar x Right)))\n (assign x (eop op_Addition (evar y) (const 1)))\n (assign x (eop op_Addition (evar y) (const 1))) \n ))\n= sec42_ex2 x y;\n sec42_ex3 y", "val typed_id (a: _) (x: a) : a\nlet typed_id a (x:a): a = x", "val i (x: U32.t) : GTot int\nlet i (x:U32.t) : GTot int = U32.v x", "val u8_add (r: range) (x y: UInt8.t)\n : Pure UInt8.t\n (requires labeled r \"Cannot verify u8 addition\" (UInt.size (UInt8.v x + UInt8.v y) UInt8.n))\n (ensures fun z -> UInt8.v z == UInt8.v x + UInt8.v y)\nlet u8_add (r:range) (x y:UInt8.t)\r\n : Pure UInt8.t\r\n (requires labeled r \"Cannot verify u8 addition\" (UInt.size (UInt8.v x + UInt8.v y) UInt8.n))\r\n (ensures fun z -> UInt8.v z == UInt8.v x + UInt8.v y)\r\n = UInt8.add x y", "val addx (x: int) : AlgWP unit (fun s0 p -> p ((), (s0 + x)))\nlet addx (x:int) : AlgWP unit (fun s0 p -> p ((), (s0+x))) =\n let y = get () in\n put (x+y)", "val add (bt: bounded_int_type_t) (x y: bt_to_ty bt) : (bt_to_ty bt)\nlet add (bt: bounded_int_type_t) (x: bt_to_ty bt) (y: bt_to_ty bt) : (bt_to_ty bt) =\n fit bt (x + y)", "val add_via_state (x y: int) : ST int int (fun s0 p -> p (x + y) s0)\nlet add_via_state (x y : int) : ST int int (fun s0 p -> p (x+y) s0) =\n let o = get () in\n put x;\n addx y;\n let r = get () in\n put o;\n r", "val size_add (x1 x2: SZ.t) (sq: squash (SZ.fits (SZ.v x1 + SZ.v x2))) : Tot SZ.t\nlet size_add (x1 x2: SZ.t) (sq: squash (SZ.fits (SZ.v x1 + SZ.v x2))) : Tot SZ.t = x1 `SZ.add` x2", "val Arith.lem1 = x: Prims.int -> Prims.unit\nlet lem1 (x:int) =\n assert (List.rev [1;2;3;4] == [4;3;2;1] /\\ op_Multiply 2 (x + 3) == 6 + (op_Multiply 3 x) - x)\n by tau1 ()", "val use_test (x: B.pointer int)\n : ST unit\n (requires fun h -> B.live h x /\\ B.get h x 0 > 17)\n (ensures\n fun h0 _ h1 ->\n B.live h1 x /\\ B.get h1 x 0 > B.get h0 x 0 /\\ B.modifies (B.loc_buffer x) h0 h1)\nlet use_test (x:B.pointer int)\n : ST unit\n (requires fun h ->\n B.live h x /\\\n B.get h x 0 > 17)\n (ensures fun h0 _ h1 ->\n B.live h1 x /\\\n B.get h1 x 0 > B.get h0 x 0 /\\\n B.modifies (B.loc_buffer x) h0 h1)\n = with_local 1 (test x)", "val f3 (x: nat) : nat\nlet f3 (x : nat) : nat =\n 2 * x", "val add (#a: eqtype) (x: a) (s: set a) : set a\nlet add (#a:eqtype) (x:a) (s:set a) : set a =\n union s (singleton x)", "val test1 (l: list nat) : LV nat (fun _ -> True) (fun _ n _ -> n == L.length l)\nlet rec test1 (l:list nat) : LV nat (fun _ -> True) (fun _ n _ -> n == L.length l)\n= match l with\n | [] -> 0\n | _::tl ->\n let n = test1 tl in //let binding is important, can't write 1 + test1 tl, see #881\n n + 1", "val plus_comm : x:int -> y:int -> Lemma (x + y == y + x)\nlet plus_comm = easy", "val return_is (a: Type) (x: a) : int_store a\nlet return_is (a:Type) (x:a) : int_store a = fun store -> Some x, store", "val return_is (a: Type) (x: a) : int_store a\nlet return_is (a:Type) (x:a) : int_store a = fun store -> x, store" ], "closest_src": [ { "project_name": "FStar", "file_name": "Normalization.fst", "name": "Normalization.add_1" }, { "project_name": "FStar", "file_name": "Normalization.fst", "name": "Normalization.add_2" }, { "project_name": "FStar", "file_name": "ID4.fst", "name": "ID4.add1" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.add1" }, { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.add1" }, { "project_name": "FStar", "file_name": "DivAction.fst", "name": "DivAction.test" }, { "project_name": "steel", "file_name": "Pulse.Lib.BoundedIntegers.fst", "name": "Pulse.Lib.BoundedIntegers.add_nat_1" }, { "project_name": "FStar", "file_name": "Lattice.fst", "name": "Lattice.test1" }, { "project_name": "FStar", "file_name": "LatticeEff.fst", "name": "LatticeEff.test1" }, { "project_name": "FStar", "file_name": "Alg.fst", "name": "Alg.test1" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test1" }, { "project_name": "FStar", "file_name": "LatticeSpec.fst", "name": "LatticeSpec.test1" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.test1" }, { "project_name": "FStar", "file_name": "DM4F_layered5.fst", "name": "DM4F_layered5.addx" }, { "project_name": "FStar", "file_name": "Pulse.Class.BoundedIntegers.fst", "name": "Pulse.Class.BoundedIntegers.add_nat_1" }, { "project_name": "steel", "file_name": "Pulse.Lib.BoundedIntegers.fst", "name": "Pulse.Lib.BoundedIntegers.pos_as_int" }, { "project_name": "FStar", "file_name": "Pulse.Class.BoundedIntegers.fst", "name": "Pulse.Class.BoundedIntegers.pos_as_int" }, { "project_name": "FStar", "file_name": "GradedMonad.fst", "name": "GradedMonad.put" }, { "project_name": "FStar", "file_name": "LatticeEff.fst", "name": "LatticeEff.test0" }, { "project_name": "steel", "file_name": "Pulse.Lib.BoundedIntegers.fst", "name": "Pulse.Lib.BoundedIntegers.nat_as_int" }, { "project_name": "FStar", "file_name": "Pulse.Class.BoundedIntegers.fst", "name": "Pulse.Class.BoundedIntegers.nat_as_int" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test8" }, { "project_name": "steel", "file_name": "CBOR.Spec.fsti", "name": "CBOR.Spec.int_compare" }, { "project_name": "FStar", "file_name": "Lattice.fst", "name": "Lattice.test0" }, { "project_name": "FStar", "file_name": "Alg.fst", "name": "Alg.test0" }, { "project_name": "FStar", "file_name": "SfPoly.fst", "name": "SfPoly.plus_one" }, { "project_name": "steel", "file_name": "Selectors.Examples.fst", "name": "Selectors.Examples.test1" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test21" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.evar" }, { "project_name": "FStar", "file_name": "HandleSmtGoal.fst", "name": "HandleSmtGoal.f" }, { "project_name": "FStar", "file_name": "FStar.Int16.fst", "name": "FStar.Int16.one" }, { "project_name": "FStar", "file_name": "FStar.Int64.fst", "name": "FStar.Int64.one" }, { "project_name": "FStar", "file_name": "FStar.UInt8.fst", "name": "FStar.UInt8.one" }, { "project_name": "FStar", "file_name": "FStar.Int128.fst", "name": "FStar.Int128.one" }, { "project_name": "FStar", "file_name": "FStar.UInt16.fst", "name": "FStar.UInt16.one" }, { "project_name": "FStar", "file_name": "FStar.Int32.fst", "name": "FStar.Int32.one" }, { "project_name": "FStar", "file_name": "FStar.Int8.fst", "name": "FStar.Int8.one" }, { "project_name": "FStar", "file_name": "FStar.UInt64.fst", "name": "FStar.UInt64.one" }, { "project_name": "FStar", "file_name": "FStar.UInt32.fst", "name": "FStar.UInt32.one" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test_imp" }, { "project_name": "steel", "file_name": "UnfoldPure.fst", "name": "UnfoldPure.pre1" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Spec_s.fst", "name": "Vale.Poly1305.Spec_s.mod2_128" }, { "project_name": "steel", "file_name": "Pulse.Lib.BoundedIntegers.fst", "name": "Pulse.Lib.BoundedIntegers.safe_add" }, { "project_name": "FStar", "file_name": "Pulse.Class.BoundedIntegers.fst", "name": "Pulse.Class.BoundedIntegers.safe_add" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Curve25519.Field64.Hacl.fst", "name": "Hacl.Impl.Curve25519.Field64.Hacl.add1_" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Tutorial.fst", "name": "FStar.InteractiveHelpers.Tutorial.ci_ex1_" }, { "project_name": "FStar", "file_name": "BinaryTrees.fst", "name": "BinaryTrees.count" }, { "project_name": "FStar", "file_name": "StRel.fst", "name": "StRel.f1" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Tutorial.fst", "name": "FStar.InteractiveHelpers.Tutorial.ut_ex1" }, { "project_name": "FStar", "file_name": "Postprocess.fst", "name": "Postprocess.x" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.addx" }, { "project_name": "FStar", "file_name": "IfcDelimitedRelease.fst", "name": "IfcDelimitedRelease.verify_test" }, { "project_name": "FStar", "file_name": "Term.fst", "name": "Term.add_one" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ParseTest.fst", "name": "FStar.InteractiveHelpers.ParseTest.simpl_ex1" }, { "project_name": "FStar", "file_name": "LatticeSpec.fst", "name": "LatticeSpec.test0" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.test0" }, { "project_name": "FStar", "file_name": "FStar.Int64.fst", "name": "FStar.Int64.v" }, { "project_name": "FStar", "file_name": "FStar.Int128.fst", "name": "FStar.Int128.v" }, { "project_name": "FStar", "file_name": "FStar.Int16.fst", "name": "FStar.Int16.v" }, { "project_name": "FStar", "file_name": "FStar.Int32.fst", "name": "FStar.Int32.v" }, { "project_name": "FStar", "file_name": "FStar.Int8.fst", "name": "FStar.Int8.v" }, { "project_name": "FStar", "file_name": "FStar.PtrdiffT.fst", "name": "FStar.PtrdiffT.add" }, { "project_name": "FStar", "file_name": "FStar.SizeT.fst", "name": "FStar.SizeT.add" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Tutorial.fst", "name": "FStar.InteractiveHelpers.Tutorial.ci_ex1" }, { "project_name": "FStar", "file_name": "FStar.PtrdiffT.fst", "name": "FStar.PtrdiffT.v" }, { "project_name": "FStar", "file_name": "Intro.fst", "name": "Intro.add_2" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.fst", "name": "Pulse.Lib.HashTable.sz_add" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParNDSDiv.fst", "name": "OPLSS2021.ParNDSDiv.incr" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParDiv.fst", "name": "OPLSS2021.ParDiv.incr" }, { "project_name": "FStar", "file_name": "prims.fst", "name": "Prims.abs" }, { "project_name": "FStar", "file_name": "Intro.fst", "name": "Intro.suc" }, { "project_name": "FStar", "file_name": "Easy.fst", "name": "Easy.plus_assoc" }, { "project_name": "FStar", "file_name": "StatefulLens.fst", "name": "StatefulLens.test1" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.add_mem" }, { "project_name": "steel", "file_name": "ExtractionTest.fst", "name": "ExtractionTest.my_safe_add" }, { "project_name": "FStar", "file_name": "ErrorMsg.fst", "name": "ErrorMsg.factorial" }, { "project_name": "FStar", "file_name": "FStar.PtrdiffT.fst", "name": "FStar.PtrdiffT.int_to_t" }, { "project_name": "steel", "file_name": "Pulse.Lib.BoundedIntegers.fst", "name": "Pulse.Lib.BoundedIntegers.add_nat" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Tutorial.fst", "name": "FStar.InteractiveHelpers.Tutorial.simpl_ex1" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fsti", "name": "Zeta.SeqAux.append1" }, { "project_name": "steel", "file_name": "CBOR.Pulse.fst", "name": "CBOR.Pulse.impl_compare_u8" }, { "project_name": "steel", "file_name": "Pulse.Lib.BoundedIntegers.fst", "name": "Pulse.Lib.BoundedIntegers.size_t_plus_one" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.SHA_helpers.fst", "name": "Vale.SHA.SHA_helpers.word_to_nat32" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.SHA_helpers.fst", "name": "Vale.SHA.PPC64LE.SHA_helpers.word_to_nat32" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.Examples.fst", "name": "Benton2004.RHL.Examples.sec42_ex4" }, { "project_name": "steel", "file_name": "Domains.fst", "name": "Domains.typed_id" }, { "project_name": "steel", "file_name": "Demo.MultiplyByRepeatedAddition.fst", "name": "Demo.MultiplyByRepeatedAddition.i" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fsti", "name": "EverParse3d.Prelude.u8_add" }, { "project_name": "FStar", "file_name": "AlgForAll.fst", "name": "AlgForAll.addx" }, { "project_name": "Armada", "file_name": "Armada.BoundedInt.fst", "name": "Armada.BoundedInt.add" }, { "project_name": "FStar", "file_name": "DM4F_layered5.fst", "name": "DM4F_layered5.add_via_state" }, { "project_name": "steel", "file_name": "CBOR.Pulse.fst", "name": "CBOR.Pulse.size_add" }, { "project_name": "FStar", "file_name": "Arith.fst", "name": "Arith.lem1" }, { "project_name": "FStar", "file_name": "WithLocal.fst", "name": "WithLocal.use_test" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Tutorial.Definitions.fst", "name": "FStar.InteractiveHelpers.Tutorial.Definitions.f3" }, { "project_name": "FStar", "file_name": "FStar.Set.fsti", "name": "FStar.Set.add" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.test1" }, { "project_name": "FStar", "file_name": "Easy.fst", "name": "Easy.plus_comm" }, { "project_name": "FStar", "file_name": "FStar.DM4F.IntStore.fst", "name": "FStar.DM4F.IntStore.return_is" }, { "project_name": "FStar", "file_name": "FStar.DM4F.IntStoreFixed.fst", "name": "FStar.DM4F.IntStoreFixed.return_is" } ], "selected_premises": [ "FStar.UInt.size", "Preprocess.test_add_1", "FStar.String.length", "FStar.Mul.op_Star", "FStar.String.strlen", "FStar.Tactics.Effect.raise", "FStar.Heap.trivial_preorder", "FStar.Pervasives.reveal_opaque", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "FStar.ST.op_Bang", "FStar.Tactics.Types.issues", "FStar.Tactics.Effect.get", "FStar.UInt.max_int", "Preprocess.incr_lits_by_1", "FStar.String.string_of_char", "FStar.Pervasives.dfst", "FStar.ST.alloc", "FStar.Math.Lemmas.pow2_plus", "FStar.Pervasives.dsnd", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity", "FStar.UInt.fits", "FStar.Math.Lemmas.pow2_lt_compat", "FStar.Math.Lemmas.pow2_le_compat", "FStar.String.maxlen", "FStar.Char.char_of_int", "FStar.List.iter", "FStar.String.index_list_of_string", "FStar.UInt.to_vec", "FStar.Char.int_of_char", "FStar.UInt32.lt", "FStar.All.op_Bar_Greater", "FStar.List.map", "FStar.Tactics.Effect.tactic", "FStar.List.for_all", "FStar.UInt.min_int", "FStar.List.fold_left", "FStar.UInt32.n", "FStar.All.op_Less_Bar", "FStar.Math.Lemmas.lemma_mod_plus_distr_r", "FStar.Math.Lemmas.lemma_mod_plus_distr_l", "FStar.UInt32.op_Plus_Hat", "FStar.List.iteri_aux", "FStar.String.concat_injective", "FStar.Math.Lemmas.cancel_mul_mod", "FStar.Math.Lemmas.lemma_mod_twice", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity_forall", "FStar.Math.Lemmas.distributivity_add_right", "FStar.List.fold_right", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "FStar.List.mapT", "FStar.Tactics.Effect.tac", "FStar.UInt.xor", "FStar.Monotonic.Pure.intro_pure_wp_monotonicity", "FStar.All.pipe_left", "FStar.BitVector.logor_vec", "FStar.List.iteri", "FStar.List.partition", "FStar.UInt32.lte", "FStar.Math.Lemmas.modulo_addition_lemma", "FStar.Math.Lemmas.distributivity_sub_left", "FStar.UInt32.gt", "FStar.Math.Lib.slash_decr_axiom", "FStar.List.tl", "FStar.List.nth", "FStar.Monotonic.Heap.mref", "FStar.ST.get", "FStar.Math.Lemmas.modulo_distributivity", "FStar.List.sortWith", "FStar.UInt32.op_Plus_Percent_Hat", "FStar.Heap.trivial_rel", "FStar.Issue.mk_issue", "FStar.List.mapi_init", "FStar.Math.Lemmas.lemma_div_lt", "FStar.Math.Lemmas.modulo_add", "FStar.List.concatMap", "FStar.Math.Lib.max", "FStar.UInt32.op_Subtraction_Hat", "FStar.BitVector.logand_vec", "FStar.UInt.from_vec", "FStar.ST.contains_pred", "FStar.Math.Lib.signed_modulo", "FStar.List.mapi", "FStar.List.tryFind", "FStar.UInt32.eq", "FStar.Monotonic.Pure.is_monotonic", "Prims.min", "FStar.List.filter", "FStar.Math.Lib.powx", "FStar.List.splitAt", "FStar.Math.Lemmas.lemma_mod_mod", "FStar.UInt.one_extend_vec", "FStar.List.fold_left2", "FStar.Math.Lemmas.lemma_mod_plus", "FStar.UInt32.op_Star_Percent_Hat", "FStar.ST.lemma_functoriality", "FStar.Monotonic.Heap.modifies_t", "Prims.abs", "FStar.Math.Lemmas.distributivity_sub_right", "FStar.Math.Lemmas.multiple_modulo_lemma" ], "source_upto_this": "module Preprocess\n\nopen FStar.Tactics.V2\n\nlet incr_lits_by_1 (t:term) : Tac term =\n match inspect t with\n | Tv_Const (C_Int x) -> pack (Tv_Const (C_Int (x+1)))\n | _ -> t\n\nlet test_add_1 (x:int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))\n\n[@@(preprocess_with (visit_tm incr_lits_by_1))]", "sketch": [ "Step 1: The definition `test_add_1'` is about creating a function that takes an integer `x` and returns the result of adding 1 to `x`.\nStep 2: The implementation will use the `visit_tm` tactic with the `incr_lits_by_1` function to preprocess the term `x + 1` and then return the result.", "Step 1: The definition `test_add_1'` is about creating a function that takes an integer `x` and returns the result of adding 1 to `x`.\nStep 2: The implementation will use the `incr_lits_by_1` tactic to increment the integer literal by 1, similar to the `test_add_1` function.", "Step 1: The definition `test_add_1'` is about creating a function that takes an integer `x` and returns the result of adding 1 to `x`.\nStep 2: The implementation will use the tactic `incr_lits_by_1` to preprocess the term `x + 1` and then return the result.", "Step 1: The definition `test_add_1'` is about creating a function that takes an integer `x` and returns the result of adding 1 to `x`.\nStep 2: The implementation will use the tactic `incr_lits_by_1` to increment the integer literal by 1, similar to the `test_add_1` function.", "Step 1: The definition `test_add_1'` is about creating a function that takes an integer `x` and returns the result of adding 1 to `x`.\nStep 2: The implementation will use the same tactic `incr_lits_by_1` to preprocess the term `x + 1` and return the result.", "Step 1: The definition `test_add_1'` is about creating a function that takes an integer `x` and returns the result of adding 1 to `x`.\nStep 2: The implementation will use the `incr_lits_by_1` tactic to increment the integer literal by 1 and then return the result.", "Step 1: The definition `test_add_1'` is about creating a function that takes an integer `x` and returns the result of adding 1 to `x`.\nStep 2: The implementation will use the same tactic `incr_lits_by_1` to increment the integer literal by 1, similar to `test_add_1`.", "Step 1: The definition `test_add_1'` is about creating a function that takes an integer `x` and returns the result of adding 1 to `x`.\nStep 2: The implementation will use the `incr_lits_by_1` tactic to increment the integer literal by 1, similar to `test_add_1`.", "Step 1: Define a function `test_add_1'` that takes an integer `x` as input and returns an integer.\nStep 2: Implement the function by using the `visit_tm` tactic with `incr_lits_by_1` to preprocess the term `quote (x + 1)` and then extract the result using `exact`.", "Step 1: Define a function `test_add_1'` that takes an integer `x` as input and returns an integer.\nStep 2: Implement the function to return the result of `x + 1` using the same tactic as `test_add_1`." ], "generated_solution": [ "let test_add_1' (x: int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))", "let test_add_1' (x:int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))", "let test_add_1' (x: int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))", "let test_add_1' (x:int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))", "let test_add_1' (x: int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))", "let test_add_1' (x:int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))", "let test_add_1' (x:int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))", "let test_add_1' (x: int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))", "let test_add_1' (x:int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))", "let test_add_1' (x: int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))" ] }, { "file_name": "FStar.Tactics.CanonCommMonoid.fst", "name": "FStar.Tactics.CanonCommMonoid.sortWith_correct_aux", "opens_and_abbrevs": [ { "open": "FStar.Tactics.CanonCommSwaps" }, { "open": "FStar.Classical" }, { "open": "FStar.Tactics.V2" }, { "open": "FStar.Reflection.V2" }, { "open": "FStar.List" }, { "open": "FStar.Algebra.CommMonoid" }, { "open": "FStar.Tactics" }, { "open": "FStar.Tactics" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val sortWith_correct_aux\n (#a #b: Type)\n (f: (nat -> nat -> int))\n (m: cm a)\n (vm: vmap a b)\n (xs: list var)\n : Lemma (xsdenote m vm xs == xsdenote m vm (sortWith #b f a vm xs))", "source_definition": "let sortWith_correct_aux (#a #b:Type) (f:nat -> nat -> int) (m:cm a) (vm:vmap a b) (xs:list var) :\n Lemma (xsdenote m vm xs == xsdenote m vm (sortWith #b f a vm xs)) =\n permute_via_swaps_correct (sortWith f) (fun #a -> sortWith_via_swaps f) m vm xs", "source_range": { "start_line": 204, "start_col": 0, "end_line": 206, "end_col": 81 }, "interleaved": false, "definition": "fun f m vm xs ->\n FStar.Tactics.CanonCommMonoid.permute_via_swaps_correct (FStar.Tactics.CanonCommMonoid.sortWith f)\n (FStar.Tactics.CanonCommMonoid.sortWith_via_swaps f)\n m\n vm\n xs\n <:\n FStar.Pervasives.Lemma\n (ensures\n FStar.Tactics.CanonCommMonoid.xsdenote m vm xs ==\n FStar.Tactics.CanonCommMonoid.xsdenote m vm (FStar.Tactics.CanonCommMonoid.sortWith f a vm xs))", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "Prims.nat", "Prims.int", "FStar.Algebra.CommMonoid.cm", "FStar.Tactics.CanonCommMonoid.vmap", "Prims.list", "FStar.Tactics.CanonCommMonoid.var", "FStar.Tactics.CanonCommMonoid.permute_via_swaps_correct", "FStar.Tactics.CanonCommMonoid.sortWith", "FStar.Tactics.CanonCommMonoid.sortWith_via_swaps", "Prims.unit", "Prims.l_True", "Prims.squash", "Prims.l_Exists", "FStar.Tactics.CanonCommSwaps.swap", "FStar.List.Tot.Base.length", "Prims.eq2", "FStar.Tactics.CanonCommSwaps.apply_swaps", "Prims.Nil", "FStar.Pervasives.pattern", "FStar.Tactics.CanonCommMonoid.xsdenote" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "\n f: (_: Prims.nat -> _: Prims.nat -> Prims.int) ->\n m: FStar.Algebra.CommMonoid.cm a ->\n vm: FStar.Tactics.CanonCommMonoid.vmap a b ->\n xs: Prims.list FStar.Tactics.CanonCommMonoid.var\n -> FStar.Pervasives.Lemma\n (ensures\n FStar.Tactics.CanonCommMonoid.xsdenote m vm xs ==\n FStar.Tactics.CanonCommMonoid.xsdenote m vm (FStar.Tactics.CanonCommMonoid.sortWith f a vm xs)\n )", "prompt": "let sortWith_correct_aux\n (#a #b: Type)\n (f: (nat -> nat -> int))\n (m: cm a)\n (vm: vmap a b)\n (xs: list var)\n : Lemma (xsdenote m vm xs == xsdenote m vm (sortWith #b f a vm xs)) =\n ", "expected_response": "permute_via_swaps_correct (sortWith f) (fun #a -> sortWith_via_swaps f) m vm xs", "source": { "project_name": "FStar", "file_name": "ulib/FStar.Tactics.CanonCommMonoid.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.Tactics.CanonCommMonoid.fst", "checked_file": "dataset/FStar.Tactics.CanonCommMonoid.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Tactics.Util.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Tactics.CanonCommSwaps.fst.checked", "dataset/FStar.Reflection.V2.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Order.fst.checked", "dataset/FStar.List.Tot.Properties.fst.checked", "dataset/FStar.List.Tot.Base.fst.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.List.fst.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Algebra.CommMonoid.fst.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "let dump m = if debugging () then dump m", "let var : eqtype = nat", "exp", "Unit", "Unit", "Unit", "Var", "Var", "Var", "Mult", "Mult", "Mult", "let rec exp_to_string (e:exp) : string =\n match e with\n | Unit -> \"Unit\"\n | Var x -> \"Var \" ^ string_of_int (x <: var)\n | Mult e1 e2 -> \"Mult (\" ^ exp_to_string e1\n ^ \") (\" ^ exp_to_string e2 ^ \")\"", "let vmap (a b:Type) = list (var * (a*b)) * (a * b)", "let const (#a #b:Type) (xa:a) (xb:b) : vmap a b = [], (xa,xb)", "let select (#a #b:Type) (x:var) (vm:vmap a b) : Tot a =\n match assoc #var #(a * b) x (fst vm) with\n | Some (a, _) -> a\n | _ -> fst (snd vm)", "let select_extra (#a #b:Type) (x:var) (vm:vmap a b) : Tot b =\n match assoc #var #(a * b) x (fst vm) with\n | Some (_, b) -> b\n | _ -> snd (snd vm)", "let update (#a #b:Type) (x:var) (xa:a) (xb:b) (vm:vmap a b) : vmap a b =\n (x, (xa, xb))::fst vm, snd vm", "let rec mdenote (#a #b:Type) (m:cm a) (vm:vmap a b) (e:exp) : Tot a =\n match e with\n | Unit -> CM?.unit m\n | Var x -> select x vm\n | Mult e1 e2 -> CM?.mult m (mdenote m vm e1) (mdenote m vm e2)", "let rec xsdenote (#a #b:Type) (m:cm a) (vm:vmap a b) (xs:list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | [x] -> select x vm\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "let rec flatten (e:exp) : list var =\n match e with\n | Unit -> []\n | Var x -> [x]\n | Mult e1 e2 -> flatten e1 @ flatten e2", "let rec flatten_correct_aux (#a #b:Type) (m:cm a) (vm:vmap a b)\n (xs1 xs2:list var) :\n Lemma (xsdenote m vm (xs1 @ xs2) == CM?.mult m (xsdenote m vm xs1)\n (xsdenote m vm xs2)) =\n match xs1 with\n | [] -> CM?.identity m (xsdenote m vm xs2)\n | [x] -> if (Nil? xs2) then right_identity m (select x vm)\n | x::xs1' -> (CM?.associativity m (select x vm)\n (xsdenote m vm xs1') (xsdenote m vm xs2);\n flatten_correct_aux m vm xs1' xs2)", "let rec flatten_correct (#a #b:Type) (m:cm a) (vm:vmap a b) (e:exp) :\n Lemma (mdenote m vm e == xsdenote m vm (flatten e)) =\n match e with\n | Unit | Var _ -> ()\n | Mult e1 e2 -> flatten_correct_aux m vm (flatten e1) (flatten e2);\n flatten_correct m vm e1; flatten_correct m vm e2", "let permute (b:Type) = a:Type -> vmap a b -> list var -> list var", "let permute_correct (#b:Type) (p:permute b) =\n #a:Type -> m:cm a -> vm:vmap a b -> xs:list var ->\n Lemma (xsdenote m vm xs == xsdenote m vm (p a vm xs))", "let rec apply_swap_aux_correct (#a #b:Type) (n:nat) (m:cm a) (vm:vmap a b)\n (xs:list var) (s:swap (length xs + n)) :\n Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] | [_] -> ()\n | x1 :: x2 :: xs' ->\n if n = (s <: nat)\n then (// x1 + (x2 + xs') =a (x1 + x2) + xs'\n // =c (x2 + x1) + xs' = a x2 + (x1 + xs')\n let a = CM?.associativity m in\n a (select x1 vm) (select x2 vm) (xsdenote m vm xs');\n a (select x2 vm) (select x1 vm) (xsdenote m vm xs');\n CM?.commutativity m (select x1 vm) (select x2 vm))\n else apply_swap_aux_correct (n+1) m vm (x2 :: xs') s", "let apply_swap_correct (#a #b:Type) (m:cm a) (vm:vmap a b)\n (xs:list var) (s:swap (length xs)):\n Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap xs s)))\n (decreases xs) = apply_swap_aux_correct 0 m vm xs s", "let rec apply_swaps_correct (#a #b:Type) (m:cm a) (vm:vmap a b)\n (xs:list var) (ss:list (swap (length xs))):\n Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swaps xs ss)))\n (decreases ss) =\n match ss with\n | [] -> ()\n | s::ss' -> apply_swap_correct m vm xs s;\n apply_swaps_correct m vm (apply_swap xs s) ss'", "let permute_via_swaps (#b:Type) (p:permute b) =\n (#a:Type) -> (vm:vmap a b) -> xs:list var ->\n Lemma (exists ss. p a vm xs == apply_swaps xs ss)", "let permute_via_swaps_correct_aux\n (#b:Type) (p:permute b) (pvs:permute_via_swaps p)\n (#a:Type) (m:cm a) (vm:vmap a b) (xs:list var) :\n Lemma (xsdenote m vm xs == xsdenote m vm (p a vm xs)) =\n pvs vm xs;\n assert(exists ss. p a vm xs == apply_swaps xs ss);\n exists_elim (xsdenote m vm xs == xsdenote m vm (p a vm xs))\n (() <: squash (exists ss. p a vm xs == apply_swaps xs ss))\n (fun ss -> apply_swaps_correct m vm xs ss)", "let permute_via_swaps_correct\n (#b:Type) (p:permute b) (pvs:permute_via_swaps p) : permute_correct p =\n permute_via_swaps_correct_aux p pvs", "let sort : permute unit =\n (fun a vm -> List.Tot.Base.sortWith #nat (compare_of_bool (<)))", "let sortWith (#b:Type) (f:nat -> nat -> int) : permute b =\n (fun a vm -> List.Tot.Base.sortWith #nat f)", "let sort_via_swaps (#a:Type) (vm : vmap a unit) (xs:list var) :\n Lemma (exists ss. sort a vm xs == apply_swaps xs ss) =\n List.Tot.Properties.sortWith_permutation #nat (compare_of_bool (<)) xs;\n let ss = equal_counts_implies_swaps #nat xs (sort a vm xs) in\n assert (sort a vm xs == apply_swaps xs ss)", "let sortWith_via_swaps (#a #b:Type) (f:nat -> nat -> int)\n (vm : vmap a b) (xs:list var) :\n Lemma (exists ss. sortWith #b f a vm xs == apply_swaps xs ss) =\n List.Tot.Properties.sortWith_permutation #nat f xs;\n let ss = equal_counts_implies_swaps #nat xs (sortWith #b f a vm xs) in\n assert (sortWith #b f a vm xs == apply_swaps xs ss)", "let sort_correct_aux (#a:Type) (m:cm a) (vm:vmap a unit) (xs:list var) :\n Lemma (xsdenote m vm xs == xsdenote m vm (sort a vm xs)) =\n permute_via_swaps_correct #unit sort sort_via_swaps m vm xs" ], "closest": [ "val sort_correct_aux (#a: Type) (m: cm a) (am: amap a) (xs: list atom)\n : Lemma (xsdenote m am xs == xsdenote m am (sort xs))\nlet sort_correct_aux (#a:Type) (m:cm a) (am:amap a) (xs:list atom) :\n Lemma (xsdenote m am xs == xsdenote m am (sort xs)) =\n permute_via_swaps_correct sort (fun #a am -> sort_via_swaps am) m am xs", "val sort_correct_aux (#a: Type) (eq: equiv a) (m: cm a eq) (am: amap a) (xs: list atom)\n : Lemma (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (sort xs)))\nlet sort_correct_aux (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a) (xs:list atom)\n : Lemma (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (sort xs)) =\n permute_via_swaps_correct sort (fun #a am -> sort_via_swaps am) eq m am xs", "val sort_correct_aux (#a: Type) (eq: CE.equiv a) (m: CE.cm a eq) (am: amap a) (xs: list atom)\n : Lemma (requires True)\n (ensures CE.EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (sort xs)))\n (decreases (FStar.List.Tot.Base.length xs))\nlet rec sort_correct_aux (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (xs:list atom)\n : Lemma (requires True)\n (ensures xsdenote eq m am xs `CE.EQ?.eq eq` xsdenote eq m am (sort xs))\n (decreases (FStar.List.Tot.Base.length xs))\n = let open FStar.Algebra.CommMonoid.Equiv in\n match xs with\n | [] -> EQ?.reflexivity eq (xsdenote eq m am [])\n | pivot::q ->\n let sort0 : permute = List.Tot.sortWith #int (List.Tot.compare_of_bool (<)) in\n let sort_eq (l: list atom) : Lemma\n (sort l == sort0 l)\n [SMTPat (sort l)]\n = sortWith_ext (my_compare_of_bool (<)) (List.Tot.compare_of_bool (<)) l\n in\n let open FStar.List.Tot.Base in\n let f:int -> int -> int = compare_of_bool (<) in\n let hi, lo = partition (bool_of_compare f pivot) q in\n flatten_correct_aux eq m am (sort lo) (pivot::sort hi);\n assert (xsdenote eq m am (sort xs) `EQ?.eq eq`\n CM?.mult m (xsdenote eq m am (sort lo))\n (xsdenote eq m am (pivot::sort hi)));\n\n lemma_xsdenote_aux eq m am pivot (sort hi);\n\n EQ?.reflexivity eq (xsdenote eq m am (sort lo));\n CM?.congruence m\n (xsdenote eq m am (sort lo))\n (xsdenote eq m am (pivot::sort hi))\n (xsdenote eq m am (sort lo))\n (select pivot am `CM?.mult m` xsdenote eq m am (sort hi));\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (xsdenote eq m am (sort lo) `CM?.mult m` xsdenote eq m am (pivot::sort hi))\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi)));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi))));\n\n CM?.commutativity m\n (xsdenote eq m am (sort lo))\n (select pivot am `CM?.mult m` xsdenote eq m am (sort hi));\n CM?.associativity m\n (select pivot am)\n (xsdenote eq m am (sort hi))\n (xsdenote eq m am (sort lo));\n EQ?.transitivity eq\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi)))\n ((select pivot am `CM?.mult m` xsdenote eq m am (sort hi)) `CM?.mult m` xsdenote eq m am (sort lo))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo)));\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi)))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo)));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo))));\n\n\n partition_length (bool_of_compare f pivot) q;\n sort_correct_aux eq m am hi;\n sort_correct_aux eq m am lo;\n EQ?.symmetry eq (xsdenote eq m am lo) (xsdenote eq m am (sort lo));\n EQ?.symmetry eq (xsdenote eq m am hi) (xsdenote eq m am (sort hi));\n CM?.congruence m\n (xsdenote eq m am (sort hi))\n (xsdenote eq m am (sort lo))\n (xsdenote eq m am hi)\n (xsdenote eq m am lo);\n assert (EQ?.eq eq\n (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo))\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo));\n\n EQ?.reflexivity eq (select pivot am);\n CM?.congruence m\n (select pivot am)\n (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo))\n (select pivot am)\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo);\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo)))\n (select pivot am `CM?.mult m` (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)));\n\n partition_equiv eq m am pivot q;\n CM?.congruence m\n (select pivot am)\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)\n (select pivot am)\n (xsdenote eq m am q);\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo))\n (select pivot am `CM?.mult m` (xsdenote eq m am q));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am q)));\n\n lemma_xsdenote_aux eq m am pivot q;\n EQ?.symmetry eq\n (xsdenote eq m am (pivot::q))\n (select pivot am `CM?.mult m` (xsdenote eq m am q));\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am q))\n (xsdenote eq m am xs);\n EQ?.symmetry eq (xsdenote eq m am (sort xs)) (xsdenote eq m am xs)", "val lemma_seq_sortwith_correctness (#a:eqtype) (f:a -> a -> Tot int) (s:seq a)\n :Lemma (requires (total_order a (List.Tot.Base.bool_of_compare f)))\n (ensures (let s' = sortWith f s in sorted (List.Tot.Base.bool_of_compare f) s' /\\ permutation a s s'))\nlet lemma_seq_sortwith_correctness #_ f s\n = let l = seq_to_list s in\n let l' = List.Tot.Base.sortWith f l in\n let s' = seq_of_list l' in\n let cmp = List.Tot.Base.bool_of_compare f in\n\n (* sortedness *)\n List.Tot.Properties.sortWith_sorted f l; //the list returned by List.sortWith is sorted\n lemma_seq_of_list_sorted cmp l'; //seq_of_list preserves sortedness\n\n (* permutation *)\n lemma_seq_to_list_permutation s; //seq_to_list is a permutation\n List.Tot.Properties.sortWith_permutation f l; //List.sortWith is a permutation\n lemma_seq_of_list_permutation l'", "val flatten_correct_aux (#a: Type) (eq: equiv a) (m: cm a eq) (am: amap a) (xs1 xs2: list atom)\n : Lemma\n (EQ?.eq eq\n (xsdenote eq m am (xs1 @ xs2))\n (CM?.mult m (xsdenote eq m am xs1) (xsdenote eq m am xs2)))\nlet rec flatten_correct_aux (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a) (xs1 xs2:list atom)\n : Lemma (xsdenote eq m am (xs1 @ xs2) `EQ?.eq eq` CM?.mult m (xsdenote eq m am xs1)\n (xsdenote eq m am xs2)) =\n match xs1 with\n | [] ->\n CM?.identity m (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.unit m) (xsdenote eq m am xs2)) (xsdenote eq m am xs2)\n | [x] -> (\n if (Nil? xs2)\n then (right_identity eq m (select x am);\n EQ?.symmetry eq (CM?.mult m (select x am) (CM?.unit m)) (select x am))\n else EQ?.reflexivity eq (CM?.mult m (xsdenote eq m am [x]) (xsdenote eq m am xs2)))\n | x::xs1' ->\n flatten_correct_aux eq m am xs1' xs2;\n EQ?.reflexivity eq (select x am);\n CM?.congruence m (select x am) (xsdenote eq m am (xs1' @ xs2))\n (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2));\n CM?.associativity m (select x am) (xsdenote eq m am xs1') (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)));\n EQ?.transitivity eq (CM?.mult m (select x am) (xsdenote eq m am (xs1' @ xs2)))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)))\n (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))", "val flatten_correct_aux (#a: Type) (m: cm a) (am: amap a) (xs1 xs2: list atom)\n : Lemma (xsdenote m am (xs1 @ xs2) == CM?.mult m (xsdenote m am xs1) (xsdenote m am xs2))\nlet rec flatten_correct_aux (#a:Type) (m:cm a) (am:amap a) (xs1 xs2:list atom) :\n Lemma (xsdenote m am (xs1 @ xs2) == CM?.mult m (xsdenote m am xs1)\n (xsdenote m am xs2)) =\n match xs1 with\n | [] -> CM?.identity m (xsdenote m am xs2)\n | [x] -> if (Nil? xs2) then right_identity m (select x am)\n | x::xs1' -> (CM?.associativity m (select x am)\n (xsdenote m am xs1') (xsdenote m am xs2);\n flatten_correct_aux m am xs1' xs2)", "val flatten_correct_aux\n (#a: Type)\n (eq: CE.equiv a)\n (m: CE.cm a eq)\n (am: amap a)\n (xs1 xs2: list atom)\n : Lemma\n (CE.EQ?.eq eq\n (xsdenote eq m am (xs1 `my_append` xs2))\n (CE.CM?.mult m (xsdenote eq m am xs1) (xsdenote eq m am xs2)))\nlet rec flatten_correct_aux (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (xs1 xs2:list atom)\n : Lemma (xsdenote eq m am (xs1 `my_append` xs2) `CE.EQ?.eq eq` CE.CM?.mult m (xsdenote eq m am xs1)\n (xsdenote eq m am xs2)) =\n let open FStar.Algebra.CommMonoid.Equiv in\n match xs1 with\n | [] ->\n CM?.identity m (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.unit m) (xsdenote eq m am xs2)) (xsdenote eq m am xs2)\n | [x] -> (\n if (Nil? xs2)\n then (right_identity eq m (select x am);\n EQ?.symmetry eq (CM?.mult m (select x am) (CM?.unit m)) (select x am))\n else EQ?.reflexivity eq (CM?.mult m (xsdenote eq m am [x]) (xsdenote eq m am xs2)))\n | x::xs1' ->\n flatten_correct_aux eq m am xs1' xs2;\n EQ?.reflexivity eq (select x am);\n CM?.congruence m (select x am) (xsdenote eq m am (xs1' `my_append` xs2))\n (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2));\n CM?.associativity m (select x am) (xsdenote eq m am xs1') (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)));\n EQ?.transitivity eq (CM?.mult m (select x am) (xsdenote eq m am (xs1' `my_append` xs2)))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)))\n (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))", "val sortWith_sorted: #a:eqtype -> f:(a -> a -> Tot int) -> l:list a ->\n Lemma (requires (total_order #a (bool_of_compare f)))\n (ensures ((sorted (bool_of_compare f) (sortWith f l)) /\\ (forall x. mem x l = mem x (sortWith f l))))\n (decreases (length l))\nlet rec sortWith_sorted #a f l = match l with\n | [] -> ()\n | pivot::tl ->\n let hi, lo = partition (bool_of_compare f pivot) tl in\n partition_length (bool_of_compare f pivot) tl;\n partition_mem_forall (bool_of_compare f pivot) tl;\n partition_mem_p_forall (bool_of_compare f pivot) tl;\n sortWith_sorted f lo;\n sortWith_sorted f hi;\n append_mem_forall (sortWith f lo) (pivot::sortWith f hi);\n append_sorted (bool_of_compare f) (sortWith f lo) (sortWith f hi) pivot", "val apply_swap_aux_correct\n (#a: Type)\n (n: nat)\n (m: cm a)\n (am: amap a)\n (xs: list atom)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swap_aux n xs s)))\n (decreases xs)\nlet rec apply_swap_aux_correct (#a:Type) (n:nat) (m:cm a) (am:amap a)\n (xs:list atom) (s:swap (length xs + n)) :\n Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] | [_] -> ()\n | x1 :: x2 :: xs' ->\n if n = (s <: nat)\n then (// x1 + (x2 + xs') =a (x1 + x2) + xs'\n // =c (x2 + x1) + xs' = a x2 + (x1 + xs')\n let a = CM?.associativity m in\n a (select x1 am) (select x2 am) (xsdenote m am xs');\n a (select x2 am) (select x1 am) (xsdenote m am xs');\n CM?.commutativity m (select x1 am) (select x2 am))\n else apply_swap_aux_correct (n+1) m am (x2 :: xs') s", "val apply_swap_aux_correct\n (#a: Type)\n (n: nat)\n (eq: equiv a)\n (m: cm a eq)\n (am: amap a)\n (xs: list atom)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (apply_swap_aux n xs s))))\n (decreases xs)\nlet rec apply_swap_aux_correct (#a:Type) (n:nat) (eq:equiv a) (m:cm a eq) (am:amap a)\n (xs:list atom) (s:swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] -> EQ?.reflexivity eq (CM?.unit m)\n | [x] -> EQ?.reflexivity eq (select x am)\n | [x1;x2] ->\n if n = (s <: nat)\n then CM?.commutativity m (select x1 am) (select x2 am)\n else EQ?.reflexivity eq (xsdenote eq m am [x1;x2])\n | x1 :: x2 :: xs' ->\n if n = (s <: nat)\n then (\n CM?.associativity m (select x1 am) (select x2 am) (xsdenote eq m am xs');\n EQ?.symmetry eq (CM?.mult m (CM?.mult m (select x1 am) (select x2 am)) (xsdenote eq m am xs'))\n (CM?.mult m (select x1 am) (CM?.mult m (select x2 am) (xsdenote eq m am xs')));\n CM?.commutativity m (select x1 am) (select x2 am);\n EQ?.reflexivity eq (xsdenote eq m am xs');\n CM?.congruence m (CM?.mult m (select x1 am) (select x2 am)) (xsdenote eq m am xs')\n (CM?.mult m (select x2 am) (select x1 am)) (xsdenote eq m am xs');\n CM?.associativity m (select x2 am) (select x1 am) (xsdenote eq m am xs');\n EQ?.transitivity eq (CM?.mult m (select x1 am) (CM?.mult m (select x2 am) (xsdenote eq m am xs')))\n (CM?.mult m (CM?.mult m (select x1 am) (select x2 am)) (xsdenote eq m am xs'))\n (CM?.mult m (CM?.mult m (select x2 am) (select x1 am)) (xsdenote eq m am xs'));\n EQ?.transitivity eq (CM?.mult m (select x1 am) (CM?.mult m (select x2 am) (xsdenote eq m am xs')))\n (CM?.mult m (CM?.mult m (select x2 am) (select x1 am)) (xsdenote eq m am xs'))\n (CM?.mult m (select x2 am) (CM?.mult m (select x1 am) (xsdenote eq m am xs'))))\n else (\n apply_swap_aux_correct (n+1) eq m am (x2 :: xs') s;\n EQ?.reflexivity eq (select x1 am);\n CM?.congruence m (select x1 am) (xsdenote eq m am (x2 :: xs'))\n (select x1 am) (xsdenote eq m am (apply_swap_aux (n+1) (x2 :: xs') s)))", "val sortWith_ext (#a: Type) (f1 f2: (a -> a -> Tot int)) (l: list a)\n : Lemma (requires (forall x y. f1 x y == f2 x y))\n (ensures (List.Tot.sortWith f1 l == List.Tot.sortWith f2 l))\n (decreases (List.Tot.length l))\nlet rec sortWith_ext (#a: Type) (f1 f2: (a -> a -> Tot int)) (l: list a)\n: Lemma\n (requires (forall x y . f1 x y == f2 x y))\n (ensures (List.Tot.sortWith f1 l == List.Tot.sortWith f2 l))\n (decreases (List.Tot.length l))\n= match l with\n | [] -> ()\n | pivot::tl ->\n partition_ext (List.Tot.bool_of_compare f1 pivot) (List.Tot.bool_of_compare f2 pivot) tl;\n List.Tot.partition_length (List.Tot.bool_of_compare f1 pivot) tl;\n let hi, lo = List.Tot.partition (List.Tot.bool_of_compare f1 pivot) tl in\n sortWith_ext f1 f2 lo;\n sortWith_ext f1 f2 hi", "val apply_swap_correct (#a: Type) (m: cm a) (am: amap a) (xs: list atom) (s: swap (length xs))\n : Lemma (ensures (xsdenote m am xs == xsdenote m am (apply_swap xs s))) (decreases xs)\nlet apply_swap_correct (#a:Type) (m:cm a) (am:amap a)\n (xs:list atom) (s:swap (length xs)):\n Lemma (ensures (xsdenote m am xs == xsdenote m am (apply_swap xs s)))\n (decreases xs) = apply_swap_aux_correct 0 m am xs s", "val apply_swap_correct\n (#a: Type)\n (eq: equiv a)\n (m: cm a eq)\n (am: amap a)\n (xs: list atom)\n (s: swap (length xs))\n : Lemma (ensures (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (apply_swap xs s))))\n (decreases xs)\nlet apply_swap_correct (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a)\n (xs:list atom) (s:swap (length xs))\n : Lemma (ensures (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (apply_swap xs s)))\n (decreases xs) =\n apply_swap_aux_correct 0 eq m am xs s", "val apply_swaps_correct\n (#a: Type)\n (m: cm a)\n (am: amap a)\n (xs: list atom)\n (ss: list (swap (length xs)))\n : Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swaps xs ss)))\n (decreases ss)\nlet rec apply_swaps_correct (#a:Type) (m:cm a) (am:amap a)\n (xs:list atom) (ss:list (swap (length xs))):\n Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swaps xs ss)))\n (decreases ss) =\n match ss with\n | [] -> ()\n | s::ss' -> apply_swap_correct m am xs s;\n apply_swaps_correct m am (apply_swap xs s) ss'", "val sort_via_swaps (#a: Type) (am: amap a) (xs: list atom)\n : Lemma (exists ss. sort xs == apply_swaps xs ss)\nlet sort_via_swaps (#a:Type) (am : amap a) (xs:list atom)\n : Lemma (exists ss. sort xs == apply_swaps xs ss)\n =\n List.Tot.Properties.sortWith_permutation #nat (compare_of_bool (<)) xs;\n let ss = equal_counts_implies_swaps #nat xs (sort xs) in\n ()", "val sort_via_swaps (#a: Type) (am: amap a) (xs: list atom)\n : Lemma (exists (ss: swaps_for xs). sort xs == apply_swaps xs ss)\nlet sort_via_swaps (#a:Type) (am:amap a) (xs:list atom)\n : Lemma (exists (ss:swaps_for xs). sort xs == apply_swaps xs ss) \n = List.Tot.Properties.sortWith_permutation #int (compare_of_bool (<)) xs;\n let ss = equal_counts_implies_swaps xs (sort xs) in\n ()", "val equivalent_sorted\n (#a: Type)\n (eq: CE.equiv a)\n (m: CE.cm a eq)\n (am: amap a)\n (l1 l2 l1' l2': list atom)\n : Lemma\n (requires\n sort l1 == sort l1' /\\ sort l2 == sort l2' /\\\n CE.EQ?.eq eq (xsdenote eq m am l1) (xsdenote eq m am l2))\n (ensures CE.EQ?.eq eq (xsdenote eq m am l1') (xsdenote eq m am l2'))\nlet equivalent_sorted (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (l1 l2 l1' l2':list atom)\n : Lemma (requires\n sort l1 == sort l1' /\\\n sort l2 == sort l2' /\\\n xsdenote eq m am l1 `CE.EQ?.eq eq` xsdenote eq m am l2)\n (ensures xsdenote eq m am l1' `CE.EQ?.eq eq` xsdenote eq m am l2')\n = let open FStar.Algebra.CommMonoid.Equiv in\n sort_correct_aux eq m am l1';\n sort_correct_aux eq m am l1;\n EQ?.symmetry eq (xsdenote eq m am l1) (xsdenote eq m am (sort l1));\n EQ?.transitivity eq\n (xsdenote eq m am l1')\n (xsdenote eq m am (sort l1'))\n (xsdenote eq m am l1);\n EQ?.transitivity eq\n (xsdenote eq m am l1')\n (xsdenote eq m am l1)\n (xsdenote eq m am l2);\n sort_correct_aux eq m am l2;\n EQ?.transitivity eq\n (xsdenote eq m am l1')\n (xsdenote eq m am l2)\n (xsdenote eq m am (sort l2));\n sort_correct_aux eq m am l2';\n EQ?.symmetry eq (xsdenote eq m am l2') (xsdenote eq m am (sort l2'));\n EQ?.transitivity eq\n (xsdenote eq m am l1')\n (xsdenote eq m am (sort l2))\n (xsdenote eq m am l2')", "val lemma_xsdenote_aux\n (#a: Type)\n (eq: CE.equiv a)\n (m: CE.cm a eq)\n (am: amap a)\n (hd: atom)\n (tl: list atom)\n : Lemma\n (CE.EQ?.eq eq (xsdenote eq m am (hd :: tl)) (CE.CM?.mult m (select hd am) (xsdenote eq m am tl))\n )\nlet lemma_xsdenote_aux (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (hd:atom) (tl:list atom)\n : Lemma (xsdenote eq m am (hd::tl) `CE.EQ?.eq eq`\n (CE.CM?.mult m (select hd am) (xsdenote eq m am tl)))\n = let open FStar.Algebra.CommMonoid.Equiv in\n match tl with\n | [] ->\n assert (xsdenote eq m am (hd::tl) == select hd am);\n CM?.identity m (select hd am);\n EQ?.symmetry eq (CM?.unit m `CM?.mult m` select hd am) (select hd am);\n CM?.commutativity m (CM?.unit m) (select hd am);\n EQ?.transitivity eq\n (xsdenote eq m am (hd::tl))\n (CM?.unit m `CM?.mult m` select hd am)\n (CM?.mult m (select hd am) (xsdenote eq m am tl))\n | _ -> EQ?.reflexivity eq (xsdenote eq m am (hd::tl))", "val apply_swaps_correct\n (#a: Type)\n (eq: equiv a)\n (m: cm a eq)\n (am: amap a)\n (xs: list atom)\n (ss: list (swap (length xs)))\n : Lemma (requires True)\n (ensures (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (apply_swaps xs ss))))\n (decreases ss)\nlet rec apply_swaps_correct (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a)\n (xs:list atom) (ss:list (swap (length xs)))\n : Lemma (requires True)\n (ensures (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (apply_swaps xs ss)))\n (decreases ss) =\n match ss with\n | [] -> EQ?.reflexivity eq (xsdenote eq m am xs)\n | s::ss' ->\n apply_swap_correct eq m am xs s;\n apply_swaps_correct eq m am (apply_swap xs s) ss';\n EQ?.transitivity eq (xsdenote eq m am xs)\n (xsdenote eq m am (apply_swap xs s))\n (xsdenote eq m am (apply_swaps (apply_swap xs s) ss'))", "val sortWith (#a: eqtype) (f: (a -> a -> Tot int)) (s: seq a) : Tot (seq a)\nlet sortWith (#a:eqtype) (f:a -> a -> Tot int) (s:seq a) :Tot (seq a)\n = seq_of_list (List.Tot.Base.sortWith f (seq_to_list s))", "val my_sortWith (#a: Type) (f: (a -> a -> Tot int)) (l: list a)\n : Pure (list a)\n (requires True)\n (ensures (fun res -> res == List.Tot.sortWith f l))\n (decreases (List.Tot.length l))\nlet rec my_sortWith (#a: Type) (f: (a -> a -> Tot int)) (l:list a)\n : Pure (list a)\n (requires True)\n (ensures (fun res -> res == List.Tot.sortWith f l))\n (decreases (List.Tot.length l))\n= match l with\n | [] -> []\n | pivot::tl ->\n let hi, lo = my_partition (my_bool_of_compare f pivot) tl in\n partition_ext (my_bool_of_compare f pivot) (List.Tot.bool_of_compare f pivot) tl;\n List.Tot.partition_length (List.Tot.bool_of_compare f pivot) tl;\n my_append (my_sortWith f lo) (pivot::my_sortWith f hi)", "val sortWith_permutation: #a:eqtype -> f:(a -> a -> Tot int) -> l:list a ->\n Lemma (requires True)\n (ensures (forall x. count x l = count x (sortWith f l)))\n (decreases (length l))\nlet rec sortWith_permutation #a f l = match l with\n | [] -> ()\n | pivot::tl ->\n let hi, lo = partition (bool_of_compare f pivot) tl in\n partition_length (bool_of_compare f pivot) tl;\n partition_count_forall (bool_of_compare f pivot) tl;\n sortWith_permutation f lo;\n sortWith_permutation f hi;\n append_count_forall (sortWith f lo) (pivot::sortWith f hi)", "val flatten_correct_aux (#a: Type) (m: monoid a) (ml1 ml2: _)\n : Lemma (mldenote m (ml1 @ ml2) == Monoid?.mult m (mldenote m ml1) (mldenote m ml2))\nlet rec flatten_correct_aux (#a:Type) (m:monoid a) ml1 ml2 :\n Lemma (mldenote m (ml1 @ ml2) == Monoid?.mult m (mldenote m ml1)\n (mldenote m ml2)) =\n match ml1 with\n | [] -> ()\n | e::es1' -> flatten_correct_aux m es1' ml2", "val map_as_list (#a #b: eqtype) (#fa: cmp a) (#fb: cmp b) (g: (a -> b)) (sa: ordset a fa)\n : Lemma (requires (forall x y. (x `fa` y ==> (g x) `fb` (g y)) /\\ (x = y <==> g x = g y)))\n (ensures as_list (map_internal #a #b #fa #fb g sa) == FStar.List.Tot.map g (as_list sa))\nlet rec map_as_list (#a #b:eqtype) (#fa:cmp a) (#fb: cmp b) (g: a->b) (sa:ordset a fa)\n : Lemma (requires (forall x y. (x `fa` y ==> g x `fb` g y) /\\ (x = y <==> g x = g y)))\n (ensures as_list (map_internal #a #b #fa #fb g sa) == FStar.List.Tot.map g (as_list sa)) = \n match sa with\n | [] -> ()\n | h::(t:ordset a fa) -> map_as_list #a #b #fa #fb g t", "val partition_equiv\n (#a: Type)\n (eq: CE.equiv a)\n (m: CE.cm a eq)\n (am: amap a)\n (pivot: atom)\n (q: list atom)\n : Lemma\n (let open FStar.List.Tot.Base in\n let hi, lo = partition (bool_of_compare (compare_of_bool ( < )) pivot) q in\n CE.EQ?.eq eq (CE.CM?.mult m (xsdenote eq m am hi) (xsdenote eq m am lo)) (xsdenote eq m am q))\nlet rec partition_equiv (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (pivot:atom) (q:list atom)\n : Lemma\n (let open FStar.List.Tot.Base in\n let hi, lo = partition (bool_of_compare (compare_of_bool (<)) pivot) q in\n CE.EQ?.eq eq\n (xsdenote eq m am hi `CE.CM?.mult m` xsdenote eq m am lo)\n (xsdenote eq m am q))\n = let open FStar.Algebra.CommMonoid.Equiv in\n let open FStar.List.Tot.Base in\n let f = bool_of_compare (compare_of_bool (<)) pivot in\n let hi, lo = partition f q in\n match q with\n | [] -> CM?.identity m (xsdenote eq m am hi)\n | hd::tl ->\n let l1, l2 = partition f tl in\n partition_equiv eq m am pivot tl;\n assert (EQ?.eq eq\n (xsdenote eq m am l1 `CM?.mult m` xsdenote eq m am l2)\n (xsdenote eq m am tl));\n\n EQ?.reflexivity eq (xsdenote eq m am l1);\n EQ?.reflexivity eq (xsdenote eq m am l2);\n EQ?.reflexivity eq (xsdenote eq m am hi);\n EQ?.reflexivity eq (xsdenote eq m am lo);\n\n\n if f hd then begin\n assert (hi == hd::l1 /\\ lo == l2);\n lemma_xsdenote_aux eq m am hd l1;\n CM?.congruence m\n (xsdenote eq m am hi)\n (xsdenote eq m am lo)\n (select hd am `CM?.mult m` xsdenote eq m am l1)\n (xsdenote eq m am l2);\n CM?.associativity m\n (select hd am)\n (xsdenote eq m am l1)\n (xsdenote eq m am l2);\n EQ?.transitivity eq\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)\n ((select hd am `CM?.mult m` xsdenote eq m am l1) `CM?.mult m` xsdenote eq m am l2)\n (select hd am `CM?.mult m` (xsdenote eq m am l1 `CM?.mult m` xsdenote eq m am l2));\n\n EQ?.reflexivity eq (select hd am);\n CM?.congruence m\n (select hd am)\n (xsdenote eq m am l1 `CM?.mult m` xsdenote eq m am l2)\n (select hd am)\n (xsdenote eq m am tl);\n EQ?.transitivity eq\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)\n (select hd am `CM?.mult m` (xsdenote eq m am l1 `CM?.mult m` xsdenote eq m am l2))\n (select hd am `CM?.mult m` xsdenote eq m am tl);\n\n lemma_xsdenote_aux eq m am hd tl;\n EQ?.symmetry eq\n (xsdenote eq m am (hd::tl))\n (select hd am `CM?.mult m` xsdenote eq m am tl);\n EQ?.transitivity eq\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)\n (select hd am `CM?.mult m` xsdenote eq m am tl)\n (xsdenote eq m am (hd::tl))\n\n end else begin\n assert (hi == l1 /\\ lo == hd::l2);\n lemma_xsdenote_aux eq m am hd l2;\n CM?.congruence m\n (xsdenote eq m am hi)\n (xsdenote eq m am lo)\n (xsdenote eq m am l1)\n (select hd am `CM?.mult m` xsdenote eq m am l2);\n CM?.commutativity m\n (xsdenote eq m am l1)\n (select hd am `CM?.mult m` xsdenote eq m am l2);\n EQ?.transitivity eq\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)\n (xsdenote eq m am l1 `CM?.mult m` (select hd am `CM?.mult m` xsdenote eq m am l2))\n ((select hd am `CM?.mult m` xsdenote eq m am l2) `CM?.mult m` xsdenote eq m am l1);\n\n CM?.associativity m\n (select hd am)\n (xsdenote eq m am l2)\n (xsdenote eq m am l1);\n EQ?.transitivity eq\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)\n ((select hd am `CM?.mult m` xsdenote eq m am l2) `CM?.mult m` xsdenote eq m am l1)\n (select hd am `CM?.mult m` (xsdenote eq m am l2 `CM?.mult m` xsdenote eq m am l1));\n\n CM?.commutativity m (xsdenote eq m am l2) (xsdenote eq m am l1);\n EQ?.reflexivity eq (select hd am);\n CM?.congruence m\n (select hd am)\n (xsdenote eq m am l2 `CM?.mult m` xsdenote eq m am l1)\n (select hd am)\n (xsdenote eq m am l1 `CM?.mult m` xsdenote eq m am l2);\n EQ?.transitivity eq\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)\n (select hd am `CM?.mult m` (xsdenote eq m am l2 `CM?.mult m` xsdenote eq m am l1))\n (select hd am `CM?.mult m` (xsdenote eq m am l1 `CM?.mult m` xsdenote eq m am l2));\n\n CM?.congruence m\n (select hd am)\n (xsdenote eq m am l1 `CM?.mult m` xsdenote eq m am l2)\n (select hd am)\n (xsdenote eq m am tl);\n EQ?.transitivity eq\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)\n (select hd am `CM?.mult m` (xsdenote eq m am l1 `CM?.mult m` xsdenote eq m am l2))\n (select hd am `CM?.mult m` xsdenote eq m am tl);\n\n lemma_xsdenote_aux eq m am hd tl;\n EQ?.symmetry eq\n (xsdenote eq m am (hd::tl))\n (select hd am `CM?.mult m` xsdenote eq m am tl);\n EQ?.transitivity eq\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)\n (select hd am `CM?.mult m` xsdenote eq m am tl)\n (xsdenote eq m am (hd::tl))\n end", "val map_sort_correct\n (#t1 #t2: Type)\n (key_order: (t1 -> t1 -> bool))\n (key_compare: (t1 -> t1 -> int))\n (l: list (t1 & t2))\n : Lemma\n (requires\n ((forall x. key_order x x == false) /\\\n (forall x y z. (key_order x y /\\ key_order y z) ==> key_order x z) /\\\n (forall x y. key_order x y == (key_compare x y < 0)) /\\\n (forall x y. key_compare x y == 0 <==> x == y) /\\\n (forall x y. (key_compare x y < 0 <==> key_compare y x > 0))))\n (ensures\n (let res, l' = map_sort key_compare l in\n (forall x. List.Tot.memP x l' <==> List.Tot.memP x l) /\\\n (List.Tot.no_repeats_p (List.Tot.map fst l') <==>\n List.Tot.no_repeats_p (List.Tot.map fst l)) /\\\n (res == true <==> List.Tot.no_repeats_p (List.Tot.map fst l)) /\\\n (res == true ==>\n (List.Tot.sorted (map_entry_order key_order _) l' /\\\n (forall k. list_ghost_assoc k l' == list_ghost_assoc k l)))))\n (decreases (List.Tot.length l))\nlet rec map_sort_correct\n (#t1 #t2: Type)\n (key_order: t1 -> t1 -> bool)\n (key_compare: t1 -> t1 -> int)\n (l: list (t1 & t2))\n: Lemma\n (requires (\n (forall x . key_order x x == false) /\\\n (forall x y z . (key_order x y /\\ key_order y z) ==> key_order x z) /\\\n (forall x y . key_order x y == (key_compare x y < 0)) /\\\n (forall x y . key_compare x y == 0 <==> x == y) /\\\n (forall x y . (key_compare x y < 0 <==> key_compare y x > 0))\n ))\n (ensures (let (res, l') = map_sort key_compare l in\n (forall x . List.Tot.memP x l' <==> List.Tot.memP x l) /\\\n (List.Tot.no_repeats_p (List.Tot.map fst l') <==> List.Tot.no_repeats_p (List.Tot.map fst l)) /\\\n (res == true <==> List.Tot.no_repeats_p (List.Tot.map fst l)) /\\\n (res == true ==> (\n List.Tot.sorted (map_entry_order key_order _) l' /\\\n (forall k . list_ghost_assoc k l' == list_ghost_assoc k l)\n ))\n ))\n (decreases (List.Tot.length l))\n= let len = List.Tot.length l in\n if len < 2\n then ()\n else begin\n let (l1, l2) = List.Tot.splitAt (len / 2) l in\n List.Tot.append_memP_forall l1 l2;\n List.Tot.map_append fst l1 l2;\n List.Tot.no_repeats_p_append (List.Tot.map fst l1) (List.Tot.map fst l2);\n List.Tot.append_memP_forall (List.Tot.map fst l1) (List.Tot.map fst l2);\n list_memP_map_forall fst l1;\n list_memP_map_forall fst l2;\n let (res, l1') = map_sort key_compare l1 in\n map_sort_correct key_order key_compare l1;\n list_memP_map_forall fst l1';\n List.Tot.append_memP_forall (List.Tot.map fst l1') (List.Tot.map fst l2);\n List.Tot.no_repeats_p_append (List.Tot.map fst l1') (List.Tot.map fst l2);\n List.Tot.map_append fst l1' l2;\n List.Tot.append_memP_forall l1' l2;\n if not res\n then ()\n else begin\n let (res, l2') = map_sort key_compare l2 in\n map_sort_correct key_order key_compare l2;\n list_memP_map_forall fst l2';\n List.Tot.append_memP_forall (List.Tot.map fst l1') (List.Tot.map fst l2');\n List.Tot.no_repeats_p_append (List.Tot.map fst l1') (List.Tot.map fst l2');\n List.Tot.map_append fst l1' l2';\n List.Tot.append_memP_forall l1' l2';\n if not res\n then ()\n else begin\n let (res, l') = map_sort_merge key_compare [] l1' l2' in\n assert (map_sort key_compare l == (res, l'));\n map_sort_merge_correct key_order key_compare [] l1' l2';\n assert (forall x . List.Tot.memP x l' <==> (List.Tot.memP x l1' \\/ List.Tot.memP x l2'));\n assert (forall x . List.Tot.memP x l' <==> List.Tot.memP x l);\n assert (List.Tot.no_repeats_p (List.Tot.map fst l') <==> List.Tot.no_repeats_p (List.Tot.map fst l));\n if res\n then begin\n assert (List.Tot.sorted (map_entry_order key_order _) l');\n list_sorted_map_entry_order_no_repeats key_order l';\n list_ghost_assoc_no_repeats_equiv l l';\n assert (forall k . list_ghost_assoc k l' == list_ghost_assoc k l)\n end\n else ()\n end\n end\n end", "val lift_swap_cons (#a: eqtype) (n: nat) (h: a) (xs: list a) (s: swap (length xs + n))\n : Lemma (requires n <= s)\n (ensures apply_swap_aux n (h :: xs) (s + 1) == h :: (apply_swap_aux n xs s))\n (decreases xs)\nlet rec lift_swap_cons (#a:eqtype) (n:nat) (h:a) (xs:list a) (s:swap (length xs + n)) : Lemma\n (requires n <= s)\n (ensures apply_swap_aux n (h::xs) (s + 1) == h::(apply_swap_aux n xs s))\n (decreases xs)\n =\n match xs with\n | [] -> ()\n | x::xt -> if n < s then lift_swap_cons (n + 1) x xt s", "val map_size (#a #b: eqtype) (#fa: cmp a) (#fb: cmp b) (g: (a -> b)) (sa: ordset a fa)\n : Lemma (requires (forall x y. (x `fa` y ==> (g x) `fb` (g y)) /\\ (x = y <==> g x = g y)))\n (ensures size (map_internal #a #b #fa #fb g sa) <= size sa)\nlet rec map_size (#a #b:eqtype) (#fa:cmp a) (#fb: cmp b) (g: a->b) (sa:ordset a fa)\n : Lemma (requires (forall x y. (x `fa` y ==> g x `fb` g y) /\\ (x = y <==> g x = g y)))\n (ensures size (map_internal #a #b #fa #fb g sa) <= size sa) \n = if size sa > 0 then map_size #a #b #fa #fb g (tail sa)", "val to_list_aux_lower_bounded (#a: eqtype) {| _: ordered a |} (t: heap a) (m: _)\n : Lemma (requires lower_bounded_heap t m) (ensures lower_bounded (to_list_aux t) m)\nlet rec to_list_aux_lower_bounded (#a: eqtype) {| _ : ordered a |} (t: heap a) m:\n Lemma (requires lower_bounded_heap t m) (ensures lower_bounded (to_list_aux t) m)\n= match t with\n | Leaf -> ()\n | Node k l r _ -> (\n to_list_aux_lower_bounded l k;\n lower_bounded_trans (to_list_aux l) k m;\n to_list_aux_lower_bounded r k;\n lower_bounded_trans (to_list_aux r) k m;\n merge_lower_bounded (to_list_aux l) (to_list_aux r) m\n )", "val intro_sorted_pred\n (#a: eqtype)\n (f: tot_ord a)\n (s: seq a)\n ($g:\n (i: nat{i < length s} -> j: nat{j < length s}\n -> Lemma (requires (i <= j)) (ensures (f (index s i) (index s j)))))\n : Lemma (sorted_pred #a f s)\nlet intro_sorted_pred (#a:eqtype) (f:tot_ord a) (s:seq a)\n ($g:(i:nat{i < length s} -> j:nat{j < length s} -> Lemma (requires (i <= j)) (ensures (f (index s i) (index s j)))))\n : Lemma (sorted_pred #a f s)\n= let aux (i j : (k:nat{k < length s})) (p:squash (i <= j)) : GTot (squash (f (index s i) (index s j))) =\n FStar.Squash.give_proof p ;\n g i j ;\n FStar.Squash.get_proof (f (index s i) (index s j))\n in\n FStar.Classical.forall_intro_2 (fun (i j:(k:nat{k < length s})) ->\n FStar.Classical.give_witness (FStar.Classical.arrow_to_impl (aux i j)) <: Lemma (i <= j ==> f (index s i) (index s j)))", "val sortWith: ('a -> 'a -> ML int) -> list 'a -> ML (list 'a)\nlet rec sortWith f = function\n | [] -> []\n | pivot::tl ->\n let hi, lo = partition (fun x -> f pivot x > 0) tl in\n sortWith f lo@(pivot::sortWith f hi)", "val eq_intro_aux (#a: eqtype) (#f: cmp a) (s1 s2: mset a f)\n : Lemma (requires forall (x: a). mem x s1 == mem x s2) (ensures s1 == s2)\nlet eq_intro_aux (#a:eqtype) (#f:cmp a) (s1 s2:mset a f)\n : Lemma\n (requires forall (x:a). mem x s1 == mem x s2)\n (ensures s1 == s2)\n = eq_intro s1 s2; eq_elim s1 s2", "val flatten_correct (#a: Type) (eq: equiv a) (m: cm a eq) (am: amap a) (e: exp)\n : Lemma (EQ?.eq eq (mdenote eq m am e) (xsdenote eq m am (flatten e)))\nlet rec flatten_correct (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a) (e:exp)\n : Lemma (mdenote eq m am e `EQ?.eq eq` xsdenote eq m am (flatten e)) =\n match e with\n | Unit -> EQ?.reflexivity eq (CM?.unit m)\n | Atom x -> EQ?.reflexivity eq (select x am)\n | Mult e1 e2 ->\n flatten_correct_aux eq m am (flatten e1) (flatten e2);\n EQ?.symmetry eq (xsdenote eq m am (flatten e1 @ flatten e2))\n (CM?.mult m (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2)));\n flatten_correct eq m am e1;\n flatten_correct eq m am e2;\n CM?.congruence m (mdenote eq m am e1) (mdenote eq m am e2)\n (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2));\n EQ?.transitivity eq (CM?.mult m (mdenote eq m am e1) (mdenote eq m am e2))\n (CM?.mult m (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2)))\n (xsdenote eq m am (flatten e1 @ flatten e2))", "val length_size_aux (#a: eqtype) (#f: cmp a) (s: Seq.seq a)\n : Lemma (ensures Seq.length s == size (seq2mset #a #f s)) (decreases (Seq.length s))\nlet rec length_size_aux (#a:eqtype) (#f:cmp a) (s:Seq.seq a)\n : Lemma\n (ensures Seq.length s == size (seq2mset #a #f s))\n (decreases (Seq.length s))\n = if Seq.length s = 0 then ()\n else\n let ms_tail = seq2mset #a #f (Seq.tail s) in\n add_size ms_tail (Seq.index s 0);\n length_size_aux #a #f (Seq.tail s)", "val flatten_correct (#a: Type) (m: cm a) (am: amap a) (e: exp)\n : Lemma (mdenote m am e == xsdenote m am (flatten e))\nlet rec flatten_correct (#a:Type) (m:cm a) (am:amap a) (e:exp) :\n Lemma (mdenote m am e == xsdenote m am (flatten e)) =\n match e with\n | Unit | Atom _ -> ()\n | Mult e1 e2 -> flatten_correct_aux m am (flatten e1) (flatten e2);\n flatten_correct m am e1; flatten_correct m am e2", "val union_sort_lemma (#a: eqtype) (#f: _) (h: a) (t1 t2: ordset a f)\n : Lemma (requires sorted f (h :: t1) /\\ sorted f (h :: t2))\n (ensures sorted f (h :: (union t1 t2)))\nlet union_sort_lemma (#a:eqtype) #f (h:a) (t1 t2: ordset a f)\n : Lemma (requires sorted f (h::t1) /\\ sorted f (h::t2))\n (ensures sorted f (h::(union t1 t2))) = \n if size t1 = 0 then union_with_empty t2\n else if size t2 = 0 then union_with_empty t1 \n else begin \n union_mem_forall t1 t2;\n set_props t1;\n set_props t2;\n set_props (union t1 t2) \n end", "val flatten_correct (#a: Type) (eq: CE.equiv a) (m: CE.cm a eq) (am: amap a) (e: exp)\n : Lemma (CE.EQ?.eq eq (mdenote eq m am e) (xsdenote eq m am (flatten e)))\nlet rec flatten_correct (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (e:exp)\n : Lemma (mdenote eq m am e `CE.EQ?.eq eq` xsdenote eq m am (flatten e)) =\n let open FStar.Algebra.CommMonoid.Equiv in\n match e with\n | Unit -> EQ?.reflexivity eq (CM?.unit m)\n | Atom x -> EQ?.reflexivity eq (select x am)\n | Mult e1 e2 ->\n flatten_correct_aux eq m am (flatten e1) (flatten e2);\n EQ?.symmetry eq (xsdenote eq m am (flatten e1 `my_append` flatten e2))\n (CM?.mult m (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2)));\n flatten_correct eq m am e1;\n flatten_correct eq m am e2;\n CM?.congruence m (mdenote eq m am e1) (mdenote eq m am e2)\n (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2));\n EQ?.transitivity eq (CM?.mult m (mdenote eq m am e1) (mdenote eq m am e2))\n (CM?.mult m (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2)))\n (xsdenote eq m am (flatten e1 `my_append` flatten e2))", "val union_aux (#a: eqtype) (#f: cmp a) (s1 s2: mset a f)\n : s:\n mset a f\n { ((Cons? s1 /\\ Cons? s2) ==>\n (Cons? s /\\\n (let x1 = fst (hd s1) in\n let x2 = fst (hd s2) in\n if f x1 x2 then fst (hd s) == x1 else fst (hd s) == x2))) /\\ (Nil? s1 ==> s == s2) /\\\n (Nil? s2 ==> s == s1) }\nlet rec union_aux (#a:eqtype) (#f:cmp a) (s1 s2:mset a f) :\n s:mset a f{\n ((Cons? s1 /\\ Cons? s2) ==>\n (Cons? s /\\ (let x1 = fst (hd s1) in\n let x2 = fst (hd s2) in\n if f x1 x2 then fst (hd s) == x1\n else fst (hd s) == x2))) /\\\n (Nil? s1 ==> s == s2) /\\\n (Nil? s2 ==> s == s1)} =\n match s1, s2 with\n | [], _ -> s2\n | _, [] -> s1\n | (x1, n1)::_, (x2, n2)::_ ->\n if x1 = x2\n then (x1, n1 + n2)::(union_aux (tl s1) (tl s2))\n else if f x1 x2\n then (x1, n1)::(union_aux (tl s1) s2)\n else (x2, n2)::(union_aux s1 (tl s2))", "val fold_left_map\n (#a #b #c: Type)\n (f_aba: (a -> b -> Tot a))\n (f_bc: (b -> Tot c))\n (f_aca: (a -> c -> Tot a))\n (l: list b)\n : Lemma (requires forall (x: a) (y: b). f_aba x y == f_aca x (f_bc y))\n (ensures forall (x: a). fold_left f_aba x l == fold_left f_aca x (map f_bc l))\nlet rec fold_left_map\n (#a #b #c: Type)\n (f_aba: a -> b -> Tot a)\n (f_bc: b -> Tot c)\n (f_aca: a -> c -> Tot a)\n (l: list b)\n : Lemma\n (requires forall (x: a) (y: b) . f_aba x y == f_aca x (f_bc y) )\n (ensures forall (x : a) . fold_left f_aba x l == fold_left f_aca x (map f_bc l) )\n =\n match l with\n | [] -> ()\n | y :: q -> fold_left_map f_aba f_bc f_aca q", "val merge_lower_bounded (#t: eqtype) {| _: ordered t |} (a b: list t) (m: _)\n : Lemma (requires lower_bounded a m /\\ lower_bounded b m) (ensures lower_bounded (merge a b) m)\nlet rec merge_lower_bounded (#t: eqtype) {| _ : ordered t |} (a b: list t) m:\n Lemma (requires lower_bounded a m /\\ lower_bounded b m) (ensures lower_bounded (merge a b) m)\n= match a, b with\n | ta::qa, tb::qb -> if (leq ta tb)\n then merge_lower_bounded qa b m\n else merge_lower_bounded a qb m\n | _ -> ()", "val pairwise_and'_forall (#a: Type) (f: (a -> a -> Type)) (l: list a)\n : Lemma (requires symmetric f /\\ reflexive f)\n (ensures (pairwise_and' f l <==> (forall x y. L.memP x l /\\ L.memP y l ==> f x y)))\nlet rec pairwise_and'_forall (#a:Type) (f: a -> a -> Type) (l:list a)\n = match l with\n | [] -> pairwise_and'_nil f\n | hd::tl ->\n pairwise_and'_cons f hd tl;\n pairwise_and'_forall f tl;\n big_and'_forall (f hd) tl", "val sorted_feq (#a:Type)\n (f g : (a -> a -> Tot bool))\n (s:seq a{forall x y. f x y == g x y})\n : Lemma (ensures (sorted f s <==> sorted g s))\nlet sorted_feq = sorted_feq'", "val lemma_equal (#a:Type) (m1 m2:map16 a) : Lemma\n (requires (forall (i:int).{:pattern (sel m1 i) \\/ (sel m2 i)} 0 <= i /\\ i < 16 ==> sel m1 i == sel m2 i))\n (ensures m1 == m2)\nlet lemma_equal (#a:Type) (m1 m2:map16 a) =\n assert_norm (forall (i:int). sel m1 i == sel16 m1 i);\n assert_norm (forall (i:int). sel m2 i == sel16 m2 i);\n lemma_equal16 m1 m2", "val sorted_split_lemma :\n #a:eqtype ->\n f:tot_ord a ->\n s:seq a ->\n i:nat{i < length s} ->\n Lemma (requires (sorted #a f s == true))\n (ensures (let s1, s2 = split s i in sorted #a f s1 == true /\\ sorted #a f s2 == true))\nlet sorted_split_lemma #a f s i =\n sorted_slice_lemma #a f s 0 i ;\n sorted_slice_lemma #a f s i (length s)", "val lemma_map_suffix (#a #b: Type) (f:a -> b) (s:seq a) (i:nat{i <= length s}):\n Lemma (requires True)\n (ensures (map f (suffix s i) == suffix (map f s) i))\nlet lemma_map_suffix (#a #b: Type) (f:a -> b) (s:seq a) (i:nat{i <= length s}):\n Lemma (requires True)\n (ensures (map f (suffix s i) == suffix (map f s) i)) =\n let ms = map f (suffix s i) in\n let sm = suffix (map f s) i in\n assert(equal ms sm);\n ()", "val lemma_map_index_aux (#a #b: Type) (f: (a -> b)) (s: seq a) (i: seq_index s)\n : Lemma (requires (True)) (ensures (f (index s i) == index (map f s) i)) (decreases (length s))\nlet rec lemma_map_index_aux (#a #b: Type) (f:a -> b) (s:seq a) (i:seq_index s):\n Lemma (requires (True))\n (ensures (f (index s i) == index (map f s) i))\n (decreases (length s)) =\n let n = length s in\n if n = 0 then ()\n else if i = n - 1 then ()\n else\n let s' = prefix s (n - 1) in\n let e = index s (n - 1) in\n lemma_map_index_aux f s' i;\n lemma_prefix_index s (n - 1) i;\n lemma_index_app1 (map f s') (create 1 (f e)) i", "val map_internal (#a #b: eqtype) (#fa: cmp a) (#fb: cmp b) (g: (a -> b)) (sa: ordset a fa)\n : Pure (ordset b fb)\n (requires (forall x y. (x `fa` y ==> (g x) `fb` (g y)) /\\ (x = y <==> g x = g y)))\n (ensures (fun sb -> Cons? sb ==> Cons? sa /\\ Cons?.hd sb == g (Cons?.hd sa)))\nlet rec map_internal (#a #b:eqtype) (#fa:cmp a) (#fb:cmp b) (g:a -> b) (sa:ordset a fa)\n : Pure (ordset b fb)\n (requires (forall x y. (x `fa` y ==> g x `fb` g y) /\\ (x = y <==> g x = g y)))\n (ensures (fun sb -> Cons? sb ==> Cons? sa /\\ Cons?.hd sb == g (Cons?.hd sa)))\n= match sa with\n | [] -> []\n | x :: xs ->\n let y = g x in\n let ys = map_internal #a #b #fa #fb g xs in\n if not (Cons? ys) || Cons?.hd ys <> y then\n y :: ys\n else ys", "val lemma_reduce_prefix_aux\n (#a #b: Type)\n (b0: b)\n (f: (a -> b -> b))\n (s: seq a)\n (i: nat{i <= length s})\n : Lemma (requires True)\n (ensures (reduce b0 f s == reduce (reduce b0 f (prefix s i)) f (suffix s (length s - i))))\n (decreases (length s))\nlet rec lemma_reduce_prefix_aux (#a:Type) (#b:Type)\n (b0: b) (f: a -> b -> b) (s: seq a)\n (i:nat{i <= length s}):\n Lemma (requires True)\n (ensures (reduce b0 f s == reduce (reduce b0 f (prefix s i)) f (suffix s (length s - i))))\n (decreases (length s)) =\n let n = length s in\n if n = 0 then ()\n else if i = n then ()\n else lemma_reduce_prefix_aux b0 f (prefix s (n - 1)) i", "val map_prefix_stable\n (#a #b: Type)\n (#i: rid)\n (r: m_rref i (seq a) grows)\n (f: (a -> Tot b))\n (bs: seq b)\n : Lemma (stable_on_t r (map_prefix r f bs))\nlet map_prefix_stable (#a:Type) (#b:Type) (#i:rid) (r:m_rref i (seq a) grows) (f:a -> Tot b) (bs:seq b)\n :Lemma (stable_on_t r (map_prefix r f bs))\n = reveal_opaque (`%grows) (grows #a);\n reveal_opaque (`%grows) (grows #b)", "val filter_map_compose (#gs_a #gs_b:gen_seq_spec) (#a #b:Type0)\n (gs_f:gs_a.a -> gs_b.a)\n (f:a -> b)\n (fm:fm_t gs_a a)\n (fm_map:fm_t gs_b b{fm_is_map gs_f f fm fm_map})\n (s:seq_t gs_a)\n : Lemma (SA.map f (filter_map fm s) == filter_map fm_map (SA.map gs_f s))\nlet filter_map_compose #gs_a #gs_b #a #b gs_f f fm fm_map s =\n flen_fm_map gs_f f fm fm_map s;\n let aux (j:nat{j < flen fm.f s})\n : Lemma (f (Seq.index (filter_map fm s) j) ==\n Seq.index (filter_map fm_map (SA.map gs_f s)) j)\n [SMTPat ()]\n = fidx2idx_fm_map gs_f f fm fm_map s j\n in\n assert (Seq.equal (SA.map f (filter_map fm s)) (filter_map fm_map (SA.map gs_f s)))", "val fold_equals_seq_foldm (#c:_) (#eq:_) \n (cm: CE.cm c eq) \n (a: int) \n (b: not_less_than a) \n (expr: (ifrom_ito a b) -> c)\n : Lemma (ensures fold cm a b expr `eq.eq` \n foldm_snoc cm (init (closed_interval_size a b) \n (init_func_from_expr expr a b)))\nlet rec fold_equals_seq_foldm #c #eq (cm: CE.cm c eq) \n (a: int) \n (b: not_less_than a) \n (expr: (ifrom_ito a b) -> c)\n : Lemma (ensures fold cm a b expr `eq.eq` \n foldm_snoc cm (init (closed_interval_size a b) \n (init_func_from_expr expr a b)))\n (decreases b-a) = \n if (b=a) then \n let ts = init (closed_interval_size a b) (init_func_from_expr expr a b) in\n lemma_eq_elim (create 1 (expr b)) ts; \n foldm_snoc_singleton cm (expr b); \n eq.symmetry (foldm_snoc cm ts) (expr b);\n eq.reflexivity (expr b); \n eq.transitivity (fold cm a b expr) (expr b) (foldm_snoc cm ts)\n else \n let lhs = fold cm a b expr in\n let subexpr : ifrom_ito a (b-1) -> c = expr in\n let fullseq = init (b+1-a) (init_func_from_expr expr a b) in \n let rhs = foldm_snoc cm fullseq in\n let subseq = init (b-a) (init_func_from_expr subexpr a (b-1)) in\n let subsum = fold cm a (b-1) expr in \n let subfold = foldm_snoc cm subseq in\n let last = expr b in\n let op = cm.mult in\n fold_equals_seq_foldm cm a (b-1) subexpr; \n cm.commutativity last subfold;\n eq.reflexivity last; \n cm.congruence subsum last subfold last;\n foldm_snoc_decomposition cm fullseq;\n lemma_eq_elim subseq (fst (un_snoc fullseq));\n eq.symmetry rhs (subfold `op` last);\n eq.transitivity lhs (subfold `op` last) rhs", "val lemma_map_extend (#a #b:Type) (f:a -> b) (s:seq a{length s > 0}):\n Lemma (map f s == append1 (map f (prefix s (length s - 1)))\n (f (index s (length s - 1))))\nlet lemma_map_extend (#a #b:Type) (f:a -> b) (s:seq a{length s > 0}):\n Lemma (map f s == append1 (map f (prefix s (length s - 1)))\n (f (index s (length s - 1)))) = \n assert(equal (map f s) (append1 (map f (prefix s (length s - 1)))\n (f (index s (length s - 1)))));\n ()", "val seq_map_internal_associative (#a:Type) (#b:eqtype) (f:int->a->b) (s:seq a) (pivot:int{0 <= pivot /\\ pivot < length s}) :\n Lemma (let left,right = split s pivot in\n seq_map_i f s == seq_map_i_indexed f left 0 @| seq_map_i_indexed f right pivot )\nlet seq_map_internal_associative (#a:Type) (#b:eqtype) (f:int->a->b) (s:seq a) (pivot:int{0 <= pivot /\\ pivot < length s}) :\n Lemma (let left,right = split s pivot in\n seq_map_i f s == seq_map_i_indexed f left 0 @| seq_map_i_indexed f right pivot )\n =\n let left,right = split s pivot in\n let full_map = seq_map_i f s in\n let part1 = seq_map_i_indexed f left 0 in\n let part2 = seq_map_i_indexed f right pivot in\n assert (equal (seq_map_i f s) (seq_map_i_indexed f left 0 @| seq_map_i_indexed f right pivot));\n ()", "val filter_map_invmap_monotonic\n (#gs #b: _)\n (fm: fm_t gs b)\n (s: seq_t gs)\n (j1 j2: SA.seq_index (filter_map fm s))\n : Lemma\n (ensures\n (j1 < j2 ==> filter_map_invmap fm s j1 < filter_map_invmap fm s j2) /\\\n (j1 > j2 ==> filter_map_invmap fm s j1 > filter_map_invmap fm s j2))\nlet filter_map_invmap_monotonic (#gs #b:_)\n (fm: fm_t gs b)\n (s: seq_t gs)\n (j1 j2: SA.seq_index (filter_map fm s))\n : Lemma (ensures (j1 < j2 ==> filter_map_invmap fm s j1 < filter_map_invmap fm s j2) /\\\n (j1 > j2 ==> filter_map_invmap fm s j1 > filter_map_invmap fm s j2))\n = fidx2idx_monotonic fm.f s j1 j2", "val terminal_case_aux\n (#c #eq: _)\n (#p: pos{p = 1})\n (#n: _)\n (cm: CE.cm c eq)\n (generator: matrix_generator c p n)\n (m: pos{m <= p})\n : Lemma\n (ensures\n (SP.foldm_snoc cm (SB.slice (seq_of_matrix (init generator)) 0 (m * n)))\n `eq.eq`\n (SP.foldm_snoc cm (SB.init m (fun (i: under m) -> SP.foldm_snoc cm (SB.init n (generator i))))\n ))\nlet terminal_case_aux #c #eq (#p:pos{p=1}) #n (cm:CE.cm c eq) (generator: matrix_generator c p n) (m: pos{m<=p}) : Lemma \n (ensures SP.foldm_snoc cm (SB.slice (seq_of_matrix (init generator)) 0 (m*n)) `eq.eq`\n SP.foldm_snoc cm (SB.init m (fun (i:under m) -> SP.foldm_snoc cm (SB.init n (generator i)))))\n = one_row_matrix_fold_aux cm generator", "val fold_of_subgen_aux\n (#c #eq: _)\n (#m: pos{m > 1})\n (#n: _)\n (cm: CE.cm c eq)\n (gen: matrix_generator c m n)\n (subgen: matrix_generator c (m - 1) n)\n : Lemma (requires subgen == (fun (i: under (m - 1)) (j: under n) -> gen i j))\n (ensures\n forall (i: under (m - 1)).\n SP.foldm_snoc cm (SB.init n (subgen i)) == SP.foldm_snoc cm (SB.init n (gen i)))\nlet fold_of_subgen_aux #c #eq (#m:pos{m>1}) #n (cm: CE.cm c eq) (gen: matrix_generator c m n) (subgen: matrix_generator c (m-1) n) : Lemma\n (requires subgen == (fun (i: under (m-1)) (j: under n) -> gen i j))\n (ensures forall (i: under (m-1)). SP.foldm_snoc cm (SB.init n (subgen i)) ==\n SP.foldm_snoc cm (SB.init n (gen i))) = \n let aux_pat (i: under (m-1)) : Lemma (SP.foldm_snoc cm (SB.init n (subgen i)) \n == SP.foldm_snoc cm (SB.init n (gen i))) = \n SB.lemma_eq_elim (SB.init n (subgen i)) (SB.init n (gen i)) in\n Classical.forall_intro aux_pat", "val union_with_prefix (#a: eqtype) (#f: _) (h: a) (t1 t2: (z: ordset a f {sorted f (h :: z)}))\n : Lemma (union #a #f (h :: t1) (h :: t2) = h :: (union t1 t2))\nlet union_with_prefix (#a:eqtype) #f (h:a) (t1 t2: (z:ordset a f{sorted f (h::z)}))\n : Lemma (union #a #f (h::t1) (h::t2) = h::(union t1 t2)) = \n union_mem_forall t1 t2;\n union_sort_lemma h t1 t2;\n same_members_means_eq (union #a #f (h::t1) (h::t2)) (h::(union t1 t2))", "val sorted_merge (#t: _) {| _: ordered t |} (a b: list t)\n : Lemma (requires sorted #t a /\\ sorted #t b) (ensures sorted (merge #t a b))\nlet rec sorted_merge #t {| _ : ordered t |} (a b: list t):\n Lemma (requires sorted #t a /\\ sorted #t b) (ensures sorted (merge #t a b))\n= match a, b with\n | ta::qa, tb::qb -> if (leq ta tb)\n then sorted_merge #t qa b\n else (sorted_merge #t a qb; total_order ta tb)\n | _ -> ()", "val lemma_add_incr_mem_aux (#a: eqtype) (#f: cmp a) (s: mset a f) (x: a)\n : Lemma (ensures mem x (add_elem s x) = 1 + mem x s)\nlet rec lemma_add_incr_mem_aux (#a:eqtype) (#f:cmp a) (s:mset a f) (x:a)\n : Lemma (ensures mem x (add_elem s x) = 1 + mem x s) =\n match s with\n | [] -> ()\n | (y,n)::_ -> \n if x = y then ()\n else if f x y then mem_elt_lt_hd x s\n else lemma_add_incr_mem_aux (tl s) x", "val filter_map_snoc (#a #b: Type) (filter: (a -> bool)) (f: (refine filter -> b)) (s: seq a) (x: a)\n : Lemma\n (if filter x\n then\n ((filter_map filter f (Seq.snoc s x)) `Seq.equal` (Seq.snoc (filter_map filter f s) (f x)))\n else ((filter_map filter f (Seq.snoc s x)) `Seq.equal` (filter_map filter f s)))\nlet filter_map_snoc (#a:Type) (#b:Type)\n (filter: a -> bool)\n (f:refine filter -> b)\n (s:seq a)\n (x:a)\n : Lemma (if filter x\n then (filter_map filter f (Seq.snoc s x) `Seq.equal`\n Seq.snoc (filter_map filter f s) (f x))\n else (filter_map filter f (Seq.snoc s x) `Seq.equal`\n filter_map filter f s))\n = filter_snoc filter s x", "val map_aux (#a #b: Type) (f: (a -> b)) (s: seq a)\n : Tot (s': seq b {length s' = length s}) (decreases (length s))\nlet rec map_aux (#a #b:Type) (f:a -> b) (s:seq a):\n Tot (s':seq b{length s' = length s})\n (decreases (length s))\n =\n let n = length s in\n if n = 0 then empty\n else\n let ps = prefix s (n - 1) in\n let e = index s (n - 1) in\n append (map_aux f ps) (create 1 (f e))", "val mmap_f (#a:eqtype) (#b #c:a -> Type) (m:map a b) (f: (x:a) -> b x -> c x)\n :Tot (m':(map a c){repr m' == DM.map (f_opt f) (repr m)})\nlet rec mmap_f #a #b #c m f =\n match m with\n | [] ->\n assert (DM.equal (empty_partial_dependent_map #a #c)\n (DM.map (f_opt f) (empty_partial_dependent_map #a #b)));\n assert_norm (repr #a #c [] == empty_partial_dependent_map #a #c);\n []\n | (| x, y |)::tl -> (| x, f x y |)::(mmap_f #a #b #c tl f)", "val swap_to_front (#a: eqtype) (h: a) (xs: list a)\n : Pure (swaps_for xs)\n (requires count h xs >= 1)\n (ensures\n (fun ss ->\n let ys = apply_swaps xs ss in\n equal_counts xs ys /\\ Cons? ys /\\ hd ys == h))\nlet rec swap_to_front (#a:eqtype) (h:a) (xs:list a) : Pure (swaps_for xs)\n (requires count h xs >= 1)\n (ensures (fun ss ->\n let ys = apply_swaps xs ss in\n equal_counts xs ys /\\\n Cons? ys /\\\n hd ys == h\n ))\n =\n match xs with\n | [] -> []\n | x::xt ->\n (\n if x = h then []\n else\n (\n let ss = swap_to_front h xt in // ss turns xt into h::xt'\n let ss' = lift_swaps_cons x xt ss in // ss' turns x::xt into x::h::xt'\n let s:swap_for xs = 0 in\n append_swaps xs ss' [s];\n ss' @ [s]\n )\n )", "val terminal_case_two_aux\n (#c #eq: _)\n (#p: pos)\n (#n: _)\n (cm: CE.cm c eq)\n (generator: matrix_generator c p n)\n (m: pos{m = 1})\n : Lemma\n (ensures\n (SP.foldm_snoc cm (SB.slice (seq_of_matrix (init generator)) 0 (m * n)))\n `eq.eq`\n (SP.foldm_snoc cm (SB.init m (fun (i: under m) -> SP.foldm_snoc cm (SB.init n (generator i))))\n ))\nlet terminal_case_two_aux #c #eq (#p:pos) #n (cm:CE.cm c eq) (generator: matrix_generator c p n) (m: pos{m=1}) : Lemma \n (ensures SP.foldm_snoc cm (SB.slice (seq_of_matrix (init generator)) 0 (m*n)) `eq.eq`\n SP.foldm_snoc cm (SB.init m (fun (i:under m) -> SP.foldm_snoc cm (SB.init n (generator i)))))\n = \n SP.foldm_snoc_singleton cm (SP.foldm_snoc cm (SB.init n (generator 0)));\n assert (SP.foldm_snoc cm (SB.init m (fun (i:under m) -> SP.foldm_snoc cm (SB.init n (generator i)))) `eq.eq`\n SP.foldm_snoc cm (SB.init n (generator 0)));\n let line = SB.init n (generator 0) in\n let slice = SB.slice (matrix_seq generator) 0 n in\n let aux (ij: under n) : Lemma (SB.index slice ij == SB.index line ij) = \n Math.Lemmas.small_div ij n;\n Math.Lemmas.small_mod ij n \n in Classical.forall_intro aux;\n SB.lemma_eq_elim line slice; \n eq.symmetry (SP.foldm_snoc cm (SB.init m (fun (i:under m) -> SP.foldm_snoc cm (SB.init n (generator i)))))\n (SP.foldm_snoc cm line)", "val bijection_seq_mset (#a:eqtype) (#f:cmp a)\n (s1 s2:Seq.seq a)\n (f12:into_smap s1 s2)\n (f21: into_smap s2 s1)\n : Lemma (seq2mset #a #f s1 == seq2mset #a #f s2)\nlet bijection_seq_mset #a #f s1 s2 f12 f21 =\n seq_count_into_smap s1 s2 f12;\n seq_count_into_smap s2 s1 f21;\n Classical.forall_intro (seq2mset_mem #a #f s1);\n Classical.forall_intro (seq2mset_mem #a #f s2);\n eq_intro_aux (seq2mset #a #f s1) (seq2mset #a #f s2)", "val bind_wp_lem' (#a: Type u#aa) (#b: Type u#bb) (#s: _) (f: m s a) (g: (a -> m s b))\n : Lemma ((wp_of (bind_m f g)) `F.feq` (bind_wp (wp_of f) (wp_of *. g)))\nlet rec bind_wp_lem' (#a:Type u#aa) (#b:Type u#bb) (#s:_) (f:m s a) (g: (a -> m s b))\n : Lemma (wp_of (bind_m f g) `F.feq` bind_wp (wp_of f) (wp_of *. g))\n = match f with\n | Ret x ->\n assert (bind_m f g == g x);\n assert_norm (wp_of #a #s (Ret x) `F.feq` (fun s0 post -> post (x, s0)));\n assert (wp_of (bind_m (Ret x) g) `F.feq` bind_wp (wp_of (Ret x)) (wp_of *. g))\n by (T.norm [zeta; iota; delta];\n let x = T.forall_intro () in\n T.mapply (quote (eta u#(max bb 1) u#1)))\n\n | Put s k ->\n bind_wp_lem' k g;\n assert_norm (wp_put (bind_wp (wp_of k) (wp_of *. g)) s `F.feq`\n bind_wp (wp_put (wp_of k) s) (wp_of *. g))\n\n | Get k ->\n let aux (x:s)\n : Lemma\n (ensures (wp_of (bind_m (k x) g) `F.feq`\n bind_wp (wp_of (k x)) (wp_of *. g)))\n [SMTPat (k x)]\n = bind_wp_lem' (k x) g\n in\n assert_norm (wp_of (bind_m (Get k) g) ==\n wp_of (Get (fun x -> bind_m (k x) g)));\n assert_norm (wp_of (Get (fun x -> bind_m (k x) g)) ==\n F.on _ (fun s0 -> (wp_of (bind_m (k s0) g)) s0));\n\n assert ((fun s0 -> (wp_of (bind_m (k s0) g)) s0) `F.feq`\n (fun s0 -> bind_wp (wp_of (k s0)) (wp_of *. g) s0));\n assert_norm (bind_wp (wp_of (Get k)) (wp_of *. g) ==\n bind_wp (F.on _ (fun s0 -> wp_of (k s0) s0))\n (wp_of *. g));\n assert_norm (bind_wp (F.on _ (fun s0 -> wp_of (k s0) s0)) (wp_of *. g) ==\n F.on _ (fun s0 -> bind_wp (wp_of (k s0)) (wp_of *. g) s0))", "val foldm_back_sym (#a:Type) (m:CM.cm a) (s1 s2: seq a)\n : Lemma\n (ensures foldm_back m (append s1 s2) == foldm_back m (append s2 s1))\nlet foldm_back_sym #a (m:CM.cm a) (s1 s2: seq a)\n : Lemma\n (ensures foldm_back m (append s1 s2) == foldm_back m (append s2 s1))\n = elim_monoid_laws m;\n foldm_back_append m s1 s2;\n foldm_back_append m s2 s1", "val lemma_map_len (f: ('a -> 'b)) (xs: list 'a)\n : Lemma (L.length (L.map f xs) == L.length xs) [SMTPat (L.length (L.map f xs))]\nlet rec lemma_map_len (f : 'a -> 'b) (xs : list 'a)\n : Lemma (L.length (L.map f xs) == L.length xs)\n [SMTPat (L.length (L.map f xs))]\n = match xs with\n | [] -> ()\n | x::xs -> lemma_map_len f xs", "val map (#a: Type) (#b: Type) (f: a -> GTot b) (s: seq a) : GTot (s': seq b{map_correct f s s'})\nlet rec map (#a: Type) (#b: Type) (f: a -> GTot b) (s: seq a) : GTot (s': seq b{map_correct f s s'}) (decreases rank s) =\n if length s = 0 then\n empty\n else\n append (singleton (f (index s 0))) (map f (drop s 1))", "val canon_correct (#a: Type) (m: cm a) (am: amap a) (e: exp)\n : Lemma (mdenote m am e == xsdenote m am (canon e))\nlet canon_correct (#a:Type) (m:cm a) (am:amap a) (e:exp) :\n Lemma (mdenote m am e == xsdenote m am (canon e)) =\n flatten_correct m am e; sort_correct m am (flatten e)", "val big_and'_forall (#a: Type) (f: (a -> Type)) (l: list a)\n : Lemma (big_and' f l <==> (forall x. L.memP x l ==> f x))\nlet rec big_and'_forall (#a:Type) (f:a -> Type) (l:list a)\n = match l with\n | [] -> big_and'_nil f; ()\n | hd::tl -> big_and'_cons f hd tl; big_and'_forall f tl", "val collect_prefix_stable\n (#a #b: Type)\n (#i: rid)\n (r: m_rref i (seq a) grows)\n (f: (a -> Tot (seq b)))\n (bs: seq b)\n : Lemma (stable_on_t r (collect_prefix r f bs))\nlet collect_prefix_stable (#a:Type) (#b:Type) (#i:rid) (r:m_rref i (seq a) grows) (f:a -> Tot (seq b)) (bs:seq b)\n : Lemma (stable_on_t r (collect_prefix r f bs))\n = let aux : h0:mem -> h1:mem -> Lemma\n (collect_prefix r f bs h0\n /\\ grows (HS.sel h0 r) (HS.sel h1 r)\n ==> collect_prefix r f bs h1) =\n fun h0 h1 ->\n\t let s1 = HS.sel h0 r in\n\t let s3 = HS.sel h1 r in\n\t collect_grows f s1 s3\n in\n forall_intro_2 aux", "val reflexivity (#a: _) {| p: ordered a |} (x: a) : Lemma (ensures leq x x)\nlet reflexivity #a {| p : ordered a |} (x: a):\n Lemma (ensures leq x x)\n= p.properties", "val sorted_feq' (#a: Type) (f g: (a -> a -> Tot bool)) (s: seq a {forall x y. f x y == g x y})\n : Lemma (ensures (sorted f s <==> sorted g s)) (decreases (length s))\nlet rec sorted_feq' (#a:Type)\n (f g : (a -> a -> Tot bool))\n (s:seq a{forall x y. f x y == g x y})\n : Lemma (ensures (sorted f s <==> sorted g s))\n (decreases (length s))\n = if length s <= 1 then ()\n else sorted_feq' f g (tail s)", "val index_mapi_lemma (#a:Type) (#b:Type) (#len:flen) (f:(i:nat{i < len} -> a -> b)) (s:ntuple a len) (i:nat{i < len}) :\n Lemma (index (mapi #a #b #len f s) i == f i (index s i))\n [SMTPat (index (mapi #a #b #len f s) i)]\nlet index_mapi_lemma #a #b #len f s i =\n createi_lemma len (fun i -> f i (index s i)) i", "val not_mem_aux (#a: eqtype) (#f: cmp a) (x: a) (s: ordset a f)\n : Lemma (requires (size' s > 0) && (head s <> x) && (f x (head s))) (ensures not (mem x s))\nlet rec not_mem_aux (#a:eqtype) (#f:cmp a) (x:a) (s:ordset a f)\n : Lemma (requires (size' s > 0) && (head s <> x) && (f x (head s)))\n (ensures not (mem x s)) = \n if tail s <> [] then not_mem_aux x (tail s)", "val lemma_map_dec_len (#a #b #z: _) (top: z) (f: (x: a{x << top} -> b)) (xs: list a {xs << top})\n : Lemma (ensures (L.length (map_dec top xs f) == L.length xs)) [SMTPat (map_dec top xs f)]\nlet rec lemma_map_dec_len #a #b #z (top:z) (f : (x:a{x << top}) -> b) (xs : list a{xs << top})\n : Lemma (ensures (L.length (map_dec top xs f) == L.length xs))\n [SMTPat (map_dec top xs f)]\n = match xs with\n | [] -> ()\n | x::xs -> lemma_map_dec_len top f xs", "val copy_aux (#a: Type) (s cpy: array a) (ctr: nat)\n : HoareST unit\n (fun h ->\n addr_of s =!= addr_of cpy /\\ Seq.length (sel h cpy) == Seq.length (sel h s) /\\\n ctr <= Seq.length (sel h cpy) /\\\n (forall (i: nat). i < ctr ==> Seq.index (sel h s) i == Seq.index (sel h cpy) i))\n (fun h0 _ h1 -> modifies (only cpy) h0 h1 /\\ Seq.equal (sel h1 cpy) (sel h1 s))\nlet rec copy_aux\n (#a:Type) (s:array a) (cpy:array a) (ctr:nat)\n: HoareST unit\n (fun h ->\n addr_of s =!= addr_of cpy /\\\n Seq.length (sel h cpy) == Seq.length (sel h s) /\\\n ctr <= Seq.length (sel h cpy) /\\\n (forall (i:nat). i < ctr ==> Seq.index (sel h s) i == Seq.index (sel h cpy) i))\n (fun h0 _ h1 ->\n modifies (only cpy) h0 h1 /\\\n Seq.equal (sel h1 cpy) (sel h1 s))\n= recall s; recall cpy;\n let diff = length cpy - ctr in\n match diff with\n | 0 -> return ()\n | _ ->\n upd cpy ctr (index s ctr);\n copy_aux s cpy (ctr + 1)", "val copy_aux (#a: Type) (s cpy: array a) (ctr: nat)\n : HoareST unit\n (fun h ->\n addr_of s =!= addr_of cpy /\\ Seq.length (sel h cpy) == Seq.length (sel h s) /\\\n ctr <= Seq.length (sel h cpy) /\\\n (forall (i: nat). i < ctr ==> Seq.index (sel h s) i == Seq.index (sel h cpy) i))\n (fun h0 _ h1 -> modifies (only cpy) h0 h1 /\\ Seq.equal (sel h1 cpy) (sel h1 s))\nlet rec copy_aux\n (#a:Type) (s:array a) (cpy:array a) (ctr:nat)\n: HoareST unit\n (fun h ->\n addr_of s =!= addr_of cpy /\\\n Seq.length (sel h cpy) == Seq.length (sel h s) /\\\n ctr <= Seq.length (sel h cpy) /\\\n (forall (i:nat). i < ctr ==> Seq.index (sel h s) i == Seq.index (sel h cpy) i))\n (fun h0 _ h1 ->\n modifies (only cpy) h0 h1 /\\\n Seq.equal (sel h1 cpy) (sel h1 s))\n= recall s; recall cpy;\n let len = length cpy in\n match len - ctr with\n | 0 -> ()\n | _ ->\n upd cpy ctr (index s ctr);\n copy_aux s cpy (ctr + 1)", "val lemma_swap_permutes_aux: #a:eqtype -> s:seq a -> i:nat{i j:nat{i <= j && j x:a -> Lemma\n (requires True)\n (ensures (count x s = count x (swap s i j)))\nlet lemma_swap_permutes_aux #_ s i j x =\n if j=i\n then cut (equal (swap s i j) s)\n else begin\n let s5 = split_5 s i j in\n let frag_lo, frag_i, frag_mid, frag_j, frag_hi =\n index s5 0, index s5 1, index s5 2, index s5 3, index s5 4 in\n lemma_append_count_aux x frag_lo (append frag_i (append frag_mid (append frag_j frag_hi)));\n lemma_append_count_aux x frag_i (append frag_mid (append frag_j frag_hi));\n lemma_append_count_aux x frag_mid (append frag_j frag_hi);\n lemma_append_count_aux x frag_j frag_hi;\n\n let s' = swap s i j in\n let s5' = split_5 s' i j in\n let frag_lo', frag_j', frag_mid', frag_i', frag_hi' =\n index s5' 0, index s5' 1, index s5' 2, index s5' 3, index s5' 4 in\n\n lemma_swap_permutes_aux_frag_eq s i j 0 i;\n lemma_swap_permutes_aux_frag_eq s i j (i + 1) j;\n lemma_swap_permutes_aux_frag_eq s i j (j + 1) (length s);\n\n lemma_append_count_aux x frag_lo (append frag_j (append frag_mid (append frag_i frag_hi)));\n lemma_append_count_aux x frag_j (append frag_mid (append frag_i frag_hi));\n lemma_append_count_aux x frag_mid (append frag_i frag_hi);\n lemma_append_count_aux x frag_i frag_hi\n end", "val sorted_pred_cons_lemma :\n #a:eqtype ->\n f:tot_ord a ->\n s:seq a{length s > 1} ->\n Lemma (requires (f (index s 0) (index s 1) /\\ sorted_pred #a f (tail s))) (ensures (sorted_pred #a f s))\nlet sorted_pred_cons_lemma #a f s =\n let aux (i j : (k:nat{k < length s})) : Lemma (requires (i <= j)) (ensures (f (index s i) (index s j))) =\n if i = 0 then\n if j = 0 then ()\n else assert (f (index s 0) (index (tail s) 0) /\\ f (index (tail s) 0) (index (tail s) (j-1)))\n else assert (f (index (tail s) (i - 1)) (index (tail s) (j - 1)))\n in\n intro_sorted_pred #a f s aux", "val forall_x_mem_in_tl (#a: eqtype) (#f: cmp a) (s1 s2: mset a f)\n : Lemma (requires (forall (x: a). mem x s1 == mem x s2) /\\ Cons? s1 /\\ Cons? s2)\n (ensures forall (x: a). mem x (tl s1) == mem x (tl s2))\nlet forall_x_mem_in_tl (#a:eqtype) (#f:cmp a) (s1 s2:mset a f)\n : Lemma\n (requires\n (forall (x:a). mem x s1 == mem x s2) /\\\n Cons? s1 /\\ Cons? s2)\n (ensures\n forall (x:a). mem x (tl s1) == mem x (tl s2))\n = let aux (x:a)\n : Lemma (mem x (tl s1) == mem x (tl s2))\n = match s1, s2 with\n | (x1, _)::_, (x2, _)::_ ->\n if x1 = x2 then begin\n if x1 = x then (mem_hd_in_tl s1; mem_hd_in_tl s2)\n end\n else if f x1 x2 then mem_elt_lt_hd x1 s2\n else mem_elt_lt_hd x2 s1\n in\n Classical.forall_intro aux", "val mem_existsb: #a:eqtype -> f:(a -> Tot bool) -> xs:list a ->\n Lemma(ensures (existsb f xs <==> (exists (x:a). (f x = true /\\ mem x xs))))\nlet rec mem_existsb #a f xs =\n match xs with\n | [] -> ()\n | hd::tl -> mem_existsb f tl", "val lemma_equal_intro (#a:Type) (m1 m2:map16 a) : Lemma\n (requires (forall (i:int).{:pattern (sel m1 i) \\/ (sel m2 i)} 0 <= i /\\ i < 16 ==> sel m1 i == sel m2 i))\n (ensures equal m1 m2)\n [SMTPat (equal m1 m2)]\nlet lemma_equal_intro #a m1 m2 =\n lemma_equal m1 m2;\n ()", "val pairwise_and'_forall_no_repeats (#a: Type) (f: (a -> a -> Type)) (l: list a)\n : Lemma (requires symmetric f /\\ L.no_repeats_p l)\n (ensures (pairwise_and' f l <==> (forall x y. L.memP x l /\\ L.memP y l /\\ x =!= y ==> f x y)))\nlet rec pairwise_and'_forall_no_repeats (#a:Type) (f: a -> a -> Type) (l:list a)\n = match l with\n | [] -> pairwise_and'_nil f\n | hd::tl ->\n pairwise_and'_cons f hd tl;\n pairwise_and'_forall_no_repeats f tl;\n big_and'_forall (f hd) tl", "val cbor_map_sort_correct (l: list (raw_data_item & raw_data_item))\n : Lemma\n (ensures\n (let res, l' = cbor_map_sort l in\n (forall x. List.Tot.memP x l' <==> List.Tot.memP x l) /\\\n (List.Tot.no_repeats_p (List.Tot.map fst l') <==> List.Tot.no_repeats_p (List.Tot.map fst l)\n ) /\\ (res == true <==> List.Tot.no_repeats_p (List.Tot.map fst l)) /\\\n (res == true ==>\n (List.Tot.sorted (map_entry_order deterministically_encoded_cbor_map_key_order _) l' /\\\n (forall k. list_ghost_assoc k l' == list_ghost_assoc k l)))))\nlet cbor_map_sort_correct\n (l: list (raw_data_item & raw_data_item))\n: Lemma\n (ensures (let (res, l') = cbor_map_sort l in\n (forall x . List.Tot.memP x l' <==> List.Tot.memP x l) /\\\n (List.Tot.no_repeats_p (List.Tot.map fst l') <==> List.Tot.no_repeats_p (List.Tot.map fst l)) /\\\n (res == true <==> List.Tot.no_repeats_p (List.Tot.map fst l)) /\\\n (res == true ==> (\n List.Tot.sorted (map_entry_order deterministically_encoded_cbor_map_key_order _) l' /\\\n (forall k . list_ghost_assoc k l' == list_ghost_assoc k l)\n ))\n ))\n= cbor_map_sort_eq l;\n Classical.forall_intro_2 deterministically_encoded_cbor_map_key_order_spec;\n Classical.forall_intro_2 cbor_compare_correct;\n Classical.forall_intro_2 cbor_compare_equal;\n Classical.forall_intro_2 bytes_lex_compare_opp;\n map_sort_correct deterministically_encoded_cbor_map_key_order cbor_compare l", "val map (#a #b:eqtype) (#fa:cmp a) (#fb:cmp b) (g:a -> b) (sa:ordset a fa)\n : Pure (ordset b fb)\n (requires (forall x y. (x `fa` y ==> g x `fb` g y) /\\ (x = y <==> g x = g y)))\n (ensures (fun sb -> (size sb <= size sa) /\\ \n (as_list sb == FStar.List.Tot.map g (as_list sa)) /\\\n (let sa = as_list sa in\n let sb = as_list sb in\n Cons? sb ==> Cons? sa /\\ Cons?.hd sb == g (Cons?.hd sa))))\nlet map #a #b #fa #fb g sa = \n map_size #a #b #fa #fb g sa;\n map_as_list #a #b #fa #fb g sa;\n map_internal #a #b #fa #fb g sa", "val lower_bounded_and_count (#a: eqtype) {| _: ordered a |} (l: list a) (m x: a)\n : Lemma (requires lower_bounded l m /\\ count l x > 0) (ensures leq m x)\nlet rec lower_bounded_and_count (#a: eqtype) {| _ : ordered a |} (l: list a) (m x: a):\n Lemma (requires lower_bounded l m /\\ count l x > 0) (ensures leq m x)\n= match l with\n | [] -> ()\n | t::q -> if (t = x) then () else lower_bounded_and_count q m x", "val flatten_commutes_with_map (#a #b: Type) (f: (a -> GTot b)) (l: list (list a))\n : Lemma\n (flatten (map_ghost (fun (sublist: list a) -> map_ghost f sublist) l) == map_ghost f (flatten l)\n )\nlet rec flatten_commutes_with_map (#a: Type) (#b: Type) (f: a -> GTot b) (l: list (list a))\n : Lemma (flatten (map_ghost (fun (sublist: list a) -> map_ghost f sublist) l) == map_ghost f (flatten l)) =\n match l with\n | [] -> ()\n | hd :: tl ->\n flatten_commutes_with_map f tl;\n append_commutes_with_map f hd (flatten tl)", "val map_has_at_index_stable\n (#a #b: Type)\n (#i: rid)\n (r: m_rref i (seq a) grows)\n (f: (a -> Tot b))\n (n: nat)\n (v: b)\n : Lemma (stable_on_t r (map_has_at_index r f n v))\nlet map_has_at_index_stable (#a:Type) (#b:Type) (#i:rid)\n\t\t\t (r:m_rref i (seq a) grows)\n\t\t\t (f:a -> Tot b) (n:nat) (v:b)\n : Lemma (stable_on_t r (map_has_at_index r f n v))\n = reveal_opaque (`%grows) (grows #a)", "val sorted_concat_lemma'\n (#a: eqtype)\n (f: (a -> a -> Tot bool){total_order a f})\n (lo: seq a {sorted f lo})\n (pivot: a)\n (hi: seq a {sorted f hi})\n : Lemma (requires (forall y. (mem y lo ==> f y pivot) /\\ (mem y hi ==> f pivot y)))\n (ensures (sorted f (append lo (cons pivot hi))))\n (decreases (length lo))\nlet rec sorted_concat_lemma': #a:eqtype\n -> f:(a -> a -> Tot bool){total_order a f}\n -> lo:seq a{sorted f lo}\n -> pivot:a\n -> hi:seq a{sorted f hi}\n -> Lemma (requires (forall y. (mem y lo ==> f y pivot)\n /\\ (mem y hi ==> f pivot y)))\n (ensures (sorted f (append lo (cons pivot hi))))\n (decreases (length lo))\n= fun #_ f lo pivot hi ->\n if length lo = 0\n then (cut (equal (append lo (cons pivot hi)) (cons pivot hi));\n cut (equal (tail (cons pivot hi)) hi))\n else (sorted_concat_lemma' f (tail lo) pivot hi;\n lemma_append_cons lo (cons pivot hi);\n lemma_tl (head lo) (append (tail lo) (cons pivot hi)))", "val csm_aux_ok: #a:eqtype -> r:cr a -> vm:vmap a\n -> c1:a -> l1:varlist -> t1:canonical_sum a -> s2:canonical_sum a ->\n Lemma\n (ensures\n interp_cs r vm (csm_aux r c1 l1 t1 s2) ==\n r.cm_add.mult (interp_cs r vm (Cons_monom c1 l1 t1)) (interp_cs r vm s2))\n (decreases %[t1; s2; 1])\nlet rec canonical_sum_merge_ok #a r vm s1 s2 =\n let aone = r.cm_mult.unit in\n let aplus = r.cm_add.mult in\n let amult = r.cm_mult.mult in\n match s1 with\n | Cons_monom c1 l1 t1 -> csm_aux_ok #a r vm c1 l1 t1 s2\n | Cons_varlist l1 t1 ->\n calc (==) {\n interp_cs r vm (canonical_sum_merge r s1 s2);\n == { }\n interp_cs r vm (csm_aux r aone l1 t1 s2);\n == { csm_aux_ok #a r vm aone l1 t1 s2 }\n aplus (interp_cs r vm (Cons_monom aone l1 t1))\n (interp_cs r vm s2);\n == { ics_aux_ok r vm (interp_vl r vm l1) t1 }\n aplus (interp_cs r vm (Cons_varlist l1 t1))\n (interp_cs r vm s2);\n }\n | Nil_monom -> ()\nand csm_aux_ok #a r vm c1 l1 t1 s2 =\n let aplus = r.cm_add.mult in\n let aone = r.cm_mult.unit in\n let amult = r.cm_mult.mult in\n match s2 with\n | Nil_monom -> ()\n | Cons_monom c2 l2 t2 ->\n let s1 = Cons_monom c1 l1 t1 in\n if l1 = l2 then\n begin\n calc (==) {\n interp_cs r vm (csm_aux r c1 l1 t1 s2);\n == { }\n ics_aux r vm (interp_m r vm (aplus c1 c2) l1)\n (canonical_sum_merge r t1 t2);\n == { ics_aux_ok r vm (interp_m r vm (aplus c1 c2) l1)\n (canonical_sum_merge r t1 t2) }\n aplus (interp_m r vm (aplus c1 c2) l1)\n (interp_cs r vm (canonical_sum_merge r t1 t2));\n == { interp_m_ok r vm (aplus c1 c2) l1 }\n aplus (amult (aplus c1 c2) (interp_vl r vm l1))\n (interp_cs r vm (canonical_sum_merge r t1 t2));\n == { canonical_sum_merge_ok r vm t1 t2 }\n aplus (amult (aplus c1 c2) (interp_vl r vm l1))\n (aplus (interp_cs r vm t1) (interp_cs r vm t2));\n == { distribute_right r c1 c2 (interp_vl r vm l1) }\n aplus (aplus (amult c1 (interp_vl r vm l1))\n (amult c2 (interp_vl r vm l2)))\n (aplus (interp_cs r vm t1)\n (interp_cs r vm t2));\n == { aplus_assoc_4 r\n (amult c1 (interp_vl r vm l1))\n (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t1)\n (interp_cs r vm t2) }\n aplus (aplus (amult c1 (interp_vl r vm l1)) (interp_cs r vm t1))\n (aplus (amult c2 (interp_vl r vm l2)) (interp_cs r vm t2));\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s1)\n (aplus (amult c2 (interp_vl r vm l2)) (interp_cs r vm t2));\n == { ics_aux_ok r vm (amult c2 (interp_vl r vm l2)) t2;\n interp_m_ok r vm c2 l2 }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end\n else if varlist_lt l1 l2 then\n begin\n calc (==) {\n interp_cs r vm (canonical_sum_merge r s1 s2);\n == { }\n ics_aux r vm (interp_m r vm c1 l1)\n (canonical_sum_merge r t1 s2);\n == { ics_aux_ok r vm (interp_m r vm c1 l1)\n (canonical_sum_merge r t1 s2) }\n aplus (interp_m r vm c1 l1)\n (interp_cs r vm (canonical_sum_merge r t1 s2));\n == { interp_m_ok r vm c1 l1 }\n aplus (amult c1 (interp_vl r vm l1))\n (interp_cs r vm (canonical_sum_merge r t1 s2));\n == { canonical_sum_merge_ok r vm t1 s2 }\n aplus (amult c1 (interp_vl r vm l1))\n (aplus (interp_cs r vm t1) (interp_cs r vm s2));\n == { r.cm_add.associativity\n (amult c1 (interp_vl r vm l1))\n (interp_cs r vm t1)\n (interp_cs r vm s2)\n }\n aplus (aplus (amult c1 (interp_vl r vm l1))\n (interp_cs r vm t1))\n (interp_cs r vm s2);\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end\n else\n begin\n calc (==) {\n interp_cs r vm (csm_aux r c1 l1 t1 s2);\n == { }\n ics_aux r vm (interp_m r vm c2 l2)\n (csm_aux r c1 l1 t1 t2);\n == { ics_aux_ok r vm (interp_m r vm c2 l2)\n (csm_aux r c1 l1 t1 t2) }\n aplus (interp_m r vm c2 l2)\n (interp_cs r vm (csm_aux r c1 l1 t1 t2));\n == { interp_m_ok r vm c2 l2 }\n aplus (amult c2 (interp_vl r vm l2))\n (interp_cs r vm (csm_aux r c1 l1 t1 t2));\n == { csm_aux_ok r vm c1 l1 t1 t2 }\n aplus (amult c2 (interp_vl r vm l2))\n (aplus (interp_cs r vm s1) (interp_cs r vm t2));\n == { r.cm_add.commutativity (interp_cs r vm s1) (interp_cs r vm t2) }\n aplus (amult c2 (interp_vl r vm l2))\n (aplus (interp_cs r vm t2) (interp_cs r vm s1));\n == { r.cm_add.associativity\n (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t2)\n (interp_cs r vm s1)\n }\n aplus (aplus (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t2))\n (interp_cs r vm s1);\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s2) (interp_cs r vm s1);\n == { r.cm_add.commutativity (interp_cs r vm s1) (interp_cs r vm s2) }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end\n | Cons_varlist l2 t2 -> // Same as Cons_monom with c2 = aone\n let c2 = aone in\n let s1 = Cons_monom c1 l1 t1 in\n if l1 = l2 then\n begin\n calc (==) {\n interp_cs r vm (csm_aux r c1 l1 t1 s2);\n == { }\n ics_aux r vm (interp_m r vm (aplus c1 c2) l1)\n (canonical_sum_merge r t1 t2);\n == { ics_aux_ok r vm (interp_m r vm (aplus c1 c2) l1)\n (canonical_sum_merge r t1 t2) }\n aplus (interp_m r vm (aplus c1 c2) l1)\n (interp_cs r vm (canonical_sum_merge r t1 t2));\n == { interp_m_ok r vm (aplus c1 c2) l1 }\n aplus (amult (aplus c1 c2) (interp_vl r vm l1))\n (interp_cs r vm (canonical_sum_merge r t1 t2));\n == { canonical_sum_merge_ok r vm t1 t2 }\n aplus (amult (aplus c1 c2) (interp_vl r vm l1))\n (aplus (interp_cs r vm t1) (interp_cs r vm t2));\n == { distribute_right r c1 c2 (interp_vl r vm l1) }\n aplus (aplus (amult c1 (interp_vl r vm l1))\n (amult c2 (interp_vl r vm l2)))\n (aplus (interp_cs r vm t1)\n (interp_cs r vm t2));\n == { aplus_assoc_4 r\n (amult c1 (interp_vl r vm l1))\n (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t1)\n (interp_cs r vm t2) }\n aplus (aplus (amult c1 (interp_vl r vm l1)) (interp_cs r vm t1))\n (aplus (amult c2 (interp_vl r vm l2)) (interp_cs r vm t2));\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s1)\n (aplus (amult c2 (interp_vl r vm l2)) (interp_cs r vm t2));\n == { ics_aux_ok r vm (amult c2 (interp_vl r vm l2)) t2;\n interp_m_ok r vm c2 l2 }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end\n else if varlist_lt l1 l2 then\n begin\n calc (==) {\n interp_cs r vm (canonical_sum_merge r s1 s2);\n == { }\n ics_aux r vm (interp_m r vm c1 l1)\n (canonical_sum_merge r t1 s2);\n == { ics_aux_ok r vm (interp_m r vm c1 l1)\n (canonical_sum_merge r t1 s2) }\n aplus (interp_m r vm c1 l1)\n (interp_cs r vm (canonical_sum_merge r t1 s2));\n == { interp_m_ok r vm c1 l1 }\n aplus (amult c1 (interp_vl r vm l1))\n (interp_cs r vm (canonical_sum_merge r t1 s2));\n == { canonical_sum_merge_ok r vm t1 s2 }\n aplus (amult c1 (interp_vl r vm l1))\n (aplus (interp_cs r vm t1) (interp_cs r vm s2));\n == { r.cm_add.associativity\n (amult c1 (interp_vl r vm l1))\n (interp_cs r vm t1)\n (interp_cs r vm s2)\n }\n aplus (aplus (amult c1 (interp_vl r vm l1))\n (interp_cs r vm t1))\n (interp_cs r vm s2);\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end\n else\n begin\n calc (==) {\n interp_cs r vm (csm_aux r c1 l1 t1 s2);\n == { }\n ics_aux r vm (interp_m r vm c2 l2)\n (csm_aux r c1 l1 t1 t2);\n == { ics_aux_ok r vm (interp_m r vm c2 l2)\n (csm_aux r c1 l1 t1 t2) }\n aplus (interp_m r vm c2 l2)\n (interp_cs r vm (csm_aux r c1 l1 t1 t2));\n == { interp_m_ok r vm c2 l2 }\n aplus (amult c2 (interp_vl r vm l2))\n (interp_cs r vm (csm_aux r c1 l1 t1 t2));\n == { csm_aux_ok r vm c1 l1 t1 t2 }\n aplus (amult c2 (interp_vl r vm l2))\n (aplus (interp_cs r vm s1) (interp_cs r vm t2));\n == { r.cm_add.commutativity (interp_cs r vm s1) (interp_cs r vm t2) }\n aplus (amult c2 (interp_vl r vm l2))\n (aplus (interp_cs r vm t2) (interp_cs r vm s1));\n == { r.cm_add.associativity\n (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t2)\n (interp_cs r vm s1)\n }\n aplus (aplus (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t2))\n (interp_cs r vm s1);\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s2) (interp_cs r vm s1);\n == { r.cm_add.commutativity (interp_cs r vm s1) (interp_cs r vm s2) }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end", "val ics_aux_ok: #a:eqtype -> r:cr a -> vm:vmap a -> x:a -> s:canonical_sum a ->\n Lemma (ensures ics_aux r vm x s == r.cm_add.mult x (interp_cs r vm s))\n (decreases s)\nlet rec ics_aux_ok #a r vm x s =\n match s with\n | Nil_monom -> ()\n | Cons_varlist l t ->\n ics_aux_ok r vm (interp_vl r vm l) t\n | Cons_monom c l t ->\n ics_aux_ok r vm (interp_m r vm c l) t", "val list_rec_of_function_is_map_1\n (#a #b: _)\n (f: (a -> b))\n (l1: list a)\n (l2: list b)\n (p: list_param _ _ (rel_of_fun f) l1 l2)\n : Lemma (l2 == List.Tot.map f l1)\nlet rec list_rec_of_function_is_map_1 #a #b (f : a -> b) (l1 : list a) (l2 : list b)\n (p : list_param _ _ (rel_of_fun f) l1 l2)\n : Lemma (l2 == List.Tot.map f l1)\n = match p with\n | Nil_param -> ()\n | Cons_param _ _ _ _ _ t -> list_rec_of_function_is_map_1 _ _ _ t", "val foldm_snoc_of_equal_inits (#c:_) (#eq:_) (#m: pos) (cm: CE.cm c eq) \n (f: (under m) -> c) (g: (under m) -> c)\n : Lemma (requires (forall (i: under m). f i `eq.eq` g i))\n (ensures foldm_snoc cm (init m f) `eq.eq` foldm_snoc cm (init m g))\nlet rec foldm_snoc_of_equal_inits #c #eq #m (cm: CE.cm c eq) \n (f: (under m) -> c) \n (g: (under m) -> c)\n : Lemma (requires (forall (i: under m). f i `eq.eq` g i))\n (ensures foldm_snoc cm (init m f) `eq.eq` \n foldm_snoc cm (init m g)) = \n if m=0 then begin\n assert_norm (foldm_snoc cm (init m f) == cm.unit);\n assert_norm (foldm_snoc cm (init m g) == cm.unit);\n eq.reflexivity cm.unit \n end else \n if m=1 then begin\n foldm_snoc_singleton cm (f 0);\n foldm_snoc_singleton cm (g 0);\n eq.transitivity (foldm_snoc cm (init m f)) (f 0) (g 0);\n eq.symmetry (foldm_snoc cm (init m g)) (g 0);\n eq.transitivity (foldm_snoc cm (init m f)) \n (g 0)\n (foldm_snoc cm (init m g))\n end else\n let fliat, flast = un_snoc (init m f) in\n let gliat, glast = un_snoc (init m g) in \n foldm_snoc_of_equal_inits cm (fun (i: under (m-1)) -> f i) \n (fun (i: under (m-1)) -> g i);\n lemma_eq_elim (init (m-1) (fun (i: under (m-1)) -> f i)) fliat;\n lemma_eq_elim (init (m-1) (fun (i: under (m-1)) -> g i)) gliat;\n cm.congruence flast (foldm_snoc cm fliat)\n glast (foldm_snoc cm gliat)", "val foldm_back3 (#a: _) (m: CM.cm a) (s1: seq a) (x: a) (s2: seq a)\n : Lemma (foldm_back m (S.append s1 (cons x s2)) == m.mult x (foldm_back m (S.append s1 s2)))\nlet foldm_back3 #a (m:CM.cm a) (s1:seq a) (x:a) (s2:seq a)\n : Lemma (foldm_back m (S.append s1 (cons x s2)) ==\n m.mult x (foldm_back m (S.append s1 s2)))\n = calc (==)\n {\n foldm_back m (S.append s1 (cons x s2));\n (==) { foldm_back_append m s1 (cons x s2) }\n m.mult (foldm_back m s1) (foldm_back m (cons x s2));\n (==) { foldm_back_append m (singleton x) s2 }\n m.mult (foldm_back m s1) (m.mult (foldm_back m (singleton x)) (foldm_back m s2));\n (==) { foldm_back_singleton m x }\n m.mult (foldm_back m s1) (m.mult x (foldm_back m s2));\n (==) { elim_monoid_laws m }\n m.mult x (m.mult (foldm_back m s1) (foldm_back m s2));\n (==) { foldm_back_append m s1 s2 }\n m.mult x (foldm_back m (S.append s1 s2));\n }", "val lemma_filter_correct1_aux (#a: Type) (f: (a -> bool)) (s: seq a) (i: seq_index (filter f s))\n : Lemma (requires (True)) (ensures (f (index (filter f s) i) = true)) (decreases (length s))\nlet rec lemma_filter_correct1_aux (#a: Type) (f:a -> bool) (s:seq a) (i:seq_index (filter f s)):\n Lemma (requires (True))\n (ensures (f (index (filter f s) i) = true))\n (decreases (length s)) =\n let n = length s in\n let fs = filter f s in\n if n = 0 then ()\n else\n let s' = prefix s (n - 1) in\n let e = index s (n - 1) in\n if f e then\n if i = (length fs) - 1 then ()\n else\n lemma_filter_correct1_aux f s' i\n else\n lemma_filter_correct1_aux f s' i", "val canon_correct (#a: Type) (eq: equiv a) (m: cm a eq) (am: amap a) (e: exp)\n : Lemma (EQ?.eq eq (mdenote eq m am e) (xsdenote eq m am (canon e)))\nlet canon_correct (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a) (e:exp)\n : Lemma (mdenote eq m am e `EQ?.eq eq` xsdenote eq m am (canon e)) =\n flatten_correct eq m am e;\n sort_correct eq m am (flatten e);\n EQ?.transitivity eq (mdenote eq m am e)\n (xsdenote eq m am (flatten e))\n (xsdenote eq m am (sort (flatten e)))", "val lemma_map_prefix (#a #b: Type) (f:a -> b) (s:seq a) (i: seq_index s):\n Lemma (requires True)\n (ensures (map f (prefix s i) == prefix (map f s) i))\nlet lemma_map_prefix (#a #b: Type) (f:a -> b) (s:seq a) (i: seq_index s):\n Lemma (requires True)\n (ensures (map f (prefix s i) == prefix (map f s) i)) =\n let mp = map f (prefix s i) in\n let pm = prefix (map f s) i in\n assert(equal mp pm);\n ()", "val for_all_map\n (#a #b: Type)\n (f: (a -> GTot b))\n (p1: (b -> GTot bool))\n (p2: (a -> GTot bool))\n (l: list a)\n : Lemma (requires p2 == (fun x -> p1 (f x)))\n (ensures for_all_ghost p1 (map_ghost f l) = for_all_ghost p2 l)\nlet rec for_all_map (#a: Type) (#b: Type) (f: a -> GTot b) (p1: b -> GTot bool) (p2: a -> GTot bool) (l: list a)\n : Lemma\n (requires p2 == (fun x -> p1 (f x)))\n (ensures for_all_ghost p1 (map_ghost f l) = for_all_ghost p2 l) =\n match l with\n | [] -> ()\n | hd :: tl -> for_all_map f p1 p2 tl" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.sort_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.sort_correct_aux" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.sort_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_seq_sortwith_correctness" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.flatten_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.flatten_correct_aux" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.flatten_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.sortWith_sorted" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.apply_swap_aux_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.apply_swap_aux_correct" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.sortWith_ext" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.apply_swap_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.apply_swap_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.apply_swaps_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.sort_via_swaps" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.sort_via_swaps" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.equivalent_sorted" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.lemma_xsdenote_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.apply_swaps_correct" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fsti", "name": "FStar.Seq.Properties.sortWith" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.my_sortWith" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.sortWith_permutation" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonMonoid.fst", "name": "FStar.Tactics.CanonMonoid.flatten_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.map_as_list" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.partition_equiv" }, { "project_name": "steel", "file_name": "CBOR.Spec.Map.fst", "name": "CBOR.Spec.Map.map_sort_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSwaps.fst", "name": "FStar.Tactics.CanonCommSwaps.lift_swap_cons" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.map_size" }, { "project_name": "FStar", "file_name": "LeftistHeap.fst", "name": "LeftistHeap.to_list_aux_lower_bounded" }, { "project_name": "FStar", "file_name": "FStar.Seq.Sorted.fst", "name": "FStar.Seq.Sorted.intro_sorted_pred" }, { "project_name": "FStar", "file_name": "FStar.List.fst", "name": "FStar.List.sortWith" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.eq_intro_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.flatten_correct" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.length_size_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.flatten_correct" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.union_sort_lemma" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.flatten_correct" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.union_aux" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.fold_left_map" }, { "project_name": "FStar", "file_name": "LeftistHeap.fst", "name": "LeftistHeap.merge_lower_bounded" }, { "project_name": "FStar", "file_name": "FStar.BigOps.fst", "name": "FStar.BigOps.pairwise_and'_forall" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.sorted_feq" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fst", "name": "Vale.Lib.Map16.lemma_equal" }, { "project_name": "FStar", "file_name": "FStar.Seq.Sorted.fst", "name": "FStar.Seq.Sorted.sorted_split_lemma" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_map_suffix" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_map_index_aux" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.map_internal" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_reduce_prefix_aux" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Seq.fst", "name": "FStar.Monotonic.Seq.map_prefix_stable" }, { "project_name": "zeta", "file_name": "Zeta.IdxFn.fst", "name": "Zeta.IdxFn.filter_map_compose" }, { "project_name": "FStar", "file_name": "FStar.Algebra.CommMonoid.Fold.fst", "name": "FStar.Algebra.CommMonoid.Fold.fold_equals_seq_foldm" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_map_extend" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.seq_map_internal_associative" }, { "project_name": "zeta", "file_name": "Zeta.IdxFn.fsti", "name": "Zeta.IdxFn.filter_map_invmap_monotonic" }, { "project_name": "FStar", "file_name": "FStar.Matrix.fst", "name": "FStar.Matrix.terminal_case_aux" }, { "project_name": "FStar", "file_name": "FStar.Matrix.fst", "name": "FStar.Matrix.fold_of_subgen_aux" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.union_with_prefix" }, { "project_name": "FStar", "file_name": "LeftistHeap.fst", "name": "LeftistHeap.sorted_merge" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.lemma_add_incr_mem_aux" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fsti", "name": "Zeta.SeqAux.filter_map_snoc" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.map_aux" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.DependentMap.fst", "name": "FStar.Monotonic.DependentMap.mmap_f" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSwaps.fst", "name": "FStar.Tactics.CanonCommSwaps.swap_to_front" }, { "project_name": "FStar", "file_name": "FStar.Matrix.fst", "name": "FStar.Matrix.terminal_case_two_aux" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.bijection_seq_mset" }, { "project_name": "FStar", "file_name": "DijkstraStateMonad.fst", "name": "DijkstraStateMonad.bind_wp_lem'" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Permutation.fst", "name": "FStar.Sequence.Permutation.foldm_back_sym" }, { "project_name": "steel", "file_name": "Pulse.Checker.Match.fst", "name": "Pulse.Checker.Match.lemma_map_len" }, { "project_name": "Armada", "file_name": "Util.Seq.fst", "name": "Util.Seq.map" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.canon_correct" }, { "project_name": "FStar", "file_name": "FStar.BigOps.fst", "name": "FStar.BigOps.big_and'_forall" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Seq.fst", "name": "FStar.Monotonic.Seq.collect_prefix_stable" }, { "project_name": "FStar", "file_name": "LeftistHeap.fst", "name": "LeftistHeap.reflexivity" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.sorted_feq'" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fst", "name": "Lib.NTuple.index_mapi_lemma" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.not_mem_aux" }, { "project_name": "steel", "file_name": "Pulse.Common.fst", "name": "Pulse.Common.lemma_map_dec_len" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.copy_aux" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.copy_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_swap_permutes_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Sorted.fst", "name": "FStar.Seq.Sorted.sorted_pred_cons_lemma" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.forall_x_mem_in_tl" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.mem_existsb" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fst", "name": "Vale.Lib.Map16.lemma_equal_intro" }, { "project_name": "FStar", "file_name": "FStar.BigOps.fst", "name": "FStar.BigOps.pairwise_and'_forall_no_repeats" }, { "project_name": "steel", "file_name": "CBOR.Spec.fsti", "name": "CBOR.Spec.cbor_map_sort_correct" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.map" }, { "project_name": "FStar", "file_name": "LeftistHeap.fst", "name": "LeftistHeap.lower_bounded_and_count" }, { "project_name": "Armada", "file_name": "Util.List.fst", "name": "Util.List.flatten_commutes_with_map" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Seq.fst", "name": "FStar.Monotonic.Seq.map_has_at_index_stable" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.sorted_concat_lemma'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.csm_aux_ok" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.ics_aux_ok" }, { "project_name": "FStar", "file_name": "Param.fst", "name": "Param.list_rec_of_function_is_map_1" }, { "project_name": "FStar", "file_name": "FStar.Seq.Permutation.fst", "name": "FStar.Seq.Permutation.foldm_snoc_of_equal_inits" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Permutation.fst", "name": "FStar.Sequence.Permutation.foldm_back3" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_filter_correct1_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.canon_correct" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_map_prefix" }, { "project_name": "Armada", "file_name": "Util.List.fst", "name": "Util.List.for_all_map" } ], "selected_premises": [ "FStar.Tactics.CanonCommMonoid.sort_via_swaps", "FStar.Tactics.CanonCommMonoid.sort_correct_aux", "FStar.Tactics.CanonCommMonoid.sortWith_via_swaps", "FStar.Tactics.CanonCommMonoid.permute_correct", "FStar.Tactics.CanonCommMonoid.permute_via_swaps_correct_aux", "FStar.Tactics.CanonCommMonoid.select", "FStar.Tactics.CanonCommMonoid.xsdenote", "FStar.Tactics.CanonCommMonoid.permute_via_swaps", "FStar.Tactics.CanonCommMonoid.permute", "FStar.Tactics.CanonCommMonoid.flatten_correct_aux", "FStar.Tactics.CanonCommMonoid.const", "FStar.Tactics.CanonCommMonoid.select_extra", "FStar.Tactics.CanonCommMonoid.mdenote", "FStar.Tactics.CanonCommMonoid.apply_swap_correct", "FStar.Tactics.CanonCommMonoid.flatten_correct", "FStar.Tactics.CanonCommMonoid.apply_swap_aux_correct", "FStar.Tactics.CanonCommMonoid.apply_swaps_correct", "FStar.Tactics.CanonCommMonoid.vmap", "FStar.Tactics.CanonCommMonoid.update", "FStar.Tactics.CanonCommMonoid.sort", "FStar.List.Tot.Base.tl", "FStar.List.Tot.Properties.assoc_mem", "FStar.Tactics.CanonCommMonoid.sortWith", "FStar.List.Tot.Base.memP", "FStar.List.Tot.Base.append", "FStar.List.Tot.Base.mem", "FStar.List.Tot.Base.hd", "FStar.Tactics.CanonCommSwaps.swaps_for", "FStar.List.Tot.Properties.append_assoc", "FStar.List.Tot.Base.op_At", "FStar.List.Tot.Properties.memP_map_intro", "FStar.Tactics.CanonCommSwaps.swap_for", "FStar.Pervasives.Native.snd", "FStar.List.Tot.Properties.map_append", "FStar.List.Tot.Base.rev", "FStar.Pervasives.Native.fst", "FStar.List.Tot.Base.index", "FStar.Tactics.CanonCommMonoid.var", "FStar.Tactics.CanonCommMonoid.flatten", "FStar.Heap.trivial_preorder", "FStar.List.Tot.Properties.append_mem", "FStar.Tactics.Util.map", "FStar.List.Tot.Properties.assoc_memP_some", "FStar.List.Tot.Properties.append_l_cons", "FStar.ST.op_Bang", "FStar.Order.compare_int", "FStar.List.Tot.Base.concatMap", "FStar.List.Tot.Properties.append_inv_head", "FStar.List.Tot.Properties.for_all_append", "FStar.List.Tot.Properties.append_l_nil", "FStar.List.Tot.Base.compare_of_bool", "FStar.List.Tot.Properties.append_memP", "FStar.List.Tot.Base.tail", "FStar.List.Tot.Base.sortWith", "FStar.List.Tot.Base.length", "FStar.List.Tot.Properties.assoc_precedes", "FStar.List.Tot.Properties.append_injective", "FStar.List.Tot.Properties.memP_map_elim", "FStar.List.Tot.Properties.sortWith_sorted", "FStar.Tactics.CanonCommSwaps.append_swaps", "FStar.List.Tot.Base.assoc", "FStar.List.Tot.Base.fold_left", "FStar.List.Tot.Base.map", "FStar.Tactics.CanonCommSwaps.swap_to_front", "FStar.List.Tot.Properties.map_lemma", "FStar.Order.order_from_int", "FStar.Tactics.CanonCommSwaps.lift_swap_cons", "FStar.List.Tot.Properties.sorted", "FStar.List.Tot.Properties.append_length", "FStar.List.Tot.Base.bool_of_compare", "FStar.Tactics.CanonCommSwaps.equal_counts_implies_swaps", "FStar.Pervasives.dfst", "FStar.List.Tot.Properties.index_extensionality_aux", "FStar.Tactics.Util.repeatn", "FStar.List.Tot.Properties.fold_left_append", "FStar.Tactics.CanonCommSwaps.apply_swaps", "FStar.List.Tot.Properties.assoc_memP_none", "FStar.Tactics.CanonCommSwaps.lift_swaps_cons", "FStar.List.Tot.Base.split", "FStar.List.mapT", "FStar.List.Tot.Properties.sortWith_permutation", "FStar.List.Tot.Properties.lemma_snoc_length", "FStar.List.sortWith", "FStar.ST.alloc", "FStar.List.Tot.Base.nth", "FStar.Tactics.CanonCommMonoid.dump", "FStar.Tactics.CanonCommSwaps.apply_swap_aux", "FStar.List.Tot.Properties.llist", "FStar.List.map", "FStar.List.Tot.Base.partition", "FStar.List.Tot.Base.partition_length", "FStar.Tactics.Effect.raise", "FStar.List.Tot.Base.fold_left2", "FStar.List.Tot.Base.splitAt", "FStar.List.Tot.Base.flatten", "FStar.Tactics.Util.__mapi", "FStar.Order.compare_list", "FStar.List.Tot.Properties.precedes_append_cons_prod_r", "FStar.List.Tot.Properties.append_memP_forall", "FStar.Pervasives.dsnd" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.Tactics.CanonCommMonoid\n\nopen FStar.Algebra.CommMonoid\nopen FStar.List\nopen FStar.Reflection.V2\nopen FStar.Tactics.V2\nopen FStar.Classical\nopen FStar.Tactics.CanonCommSwaps\n\n(* An expression canonizer for commutative monoids.\n Inspired by:\n - http://adam.chlipala.net/cpdt/html/Cpdt.Reflection.html\n - http://poleiro.info/posts/2015-04-13-writing-reflective-tactics.html\n*)\n\n(* Only dump when debugging is on *)\nprivate let dump m = if debugging () then dump m\n\n(***** Expression syntax *)\n\nlet var : eqtype = nat\n\ntype exp : Type =\n | Unit : exp\n | Var : var -> exp\n | Mult : exp -> exp -> exp\n\nlet rec exp_to_string (e:exp) : string =\n match e with\n | Unit -> \"Unit\"\n | Var x -> \"Var \" ^ string_of_int (x <: var)\n | Mult e1 e2 -> \"Mult (\" ^ exp_to_string e1\n ^ \") (\" ^ exp_to_string e2 ^ \")\"\n\n(***** Expression denotation *)\n\n// Use a map that stores for each variable\n// (1) its denotation that should be treated abstractly (type a) and\n// (2) user-specified extra information depending on its term (type b)\n\nlet vmap (a b:Type) = list (var * (a*b)) * (a * b)\nlet const (#a #b:Type) (xa:a) (xb:b) : vmap a b = [], (xa,xb)\nlet select (#a #b:Type) (x:var) (vm:vmap a b) : Tot a =\n match assoc #var #(a * b) x (fst vm) with\n | Some (a, _) -> a\n | _ -> fst (snd vm)\nlet select_extra (#a #b:Type) (x:var) (vm:vmap a b) : Tot b =\n match assoc #var #(a * b) x (fst vm) with\n | Some (_, b) -> b\n | _ -> snd (snd vm)\nlet update (#a #b:Type) (x:var) (xa:a) (xb:b) (vm:vmap a b) : vmap a b =\n (x, (xa, xb))::fst vm, snd vm\n\nlet rec mdenote (#a #b:Type) (m:cm a) (vm:vmap a b) (e:exp) : Tot a =\n match e with\n | Unit -> CM?.unit m\n | Var x -> select x vm\n | Mult e1 e2 -> CM?.mult m (mdenote m vm e1) (mdenote m vm e2)\n\nlet rec xsdenote (#a #b:Type) (m:cm a) (vm:vmap a b) (xs:list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | [x] -> select x vm\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')\n\n(***** Flattening expressions to lists of variables *)\n\nlet rec flatten (e:exp) : list var =\n match e with\n | Unit -> []\n | Var x -> [x]\n | Mult e1 e2 -> flatten e1 @ flatten e2\n\nlet rec flatten_correct_aux (#a #b:Type) (m:cm a) (vm:vmap a b)\n (xs1 xs2:list var) :\n Lemma (xsdenote m vm (xs1 @ xs2) == CM?.mult m (xsdenote m vm xs1)\n (xsdenote m vm xs2)) =\n match xs1 with\n | [] -> CM?.identity m (xsdenote m vm xs2)\n | [x] -> if (Nil? xs2) then right_identity m (select x vm)\n | x::xs1' -> (CM?.associativity m (select x vm)\n (xsdenote m vm xs1') (xsdenote m vm xs2);\n flatten_correct_aux m vm xs1' xs2)\n\nlet rec flatten_correct (#a #b:Type) (m:cm a) (vm:vmap a b) (e:exp) :\n Lemma (mdenote m vm e == xsdenote m vm (flatten e)) =\n match e with\n | Unit | Var _ -> ()\n | Mult e1 e2 -> flatten_correct_aux m vm (flatten e1) (flatten e2);\n flatten_correct m vm e1; flatten_correct m vm e2\n\n(***** Permuting the lists of variables\n by swapping adjacent elements *)\n\n(* The user has control over the permutation. He can store extra\n information in the vmap and use that for choosing the\n permutation. This means that permute has access to the vmap. *)\n\nlet permute (b:Type) = a:Type -> vmap a b -> list var -> list var\n\n// high-level correctness criterion for permutations\nlet permute_correct (#b:Type) (p:permute b) =\n #a:Type -> m:cm a -> vm:vmap a b -> xs:list var ->\n Lemma (xsdenote m vm xs == xsdenote m vm (p a vm xs))\n\n// sufficient condition:\n// permutation has to be expressible as swaps of adjacent list elements\n\nlet rec apply_swap_aux_correct (#a #b:Type) (n:nat) (m:cm a) (vm:vmap a b)\n (xs:list var) (s:swap (length xs + n)) :\n Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] | [_] -> ()\n | x1 :: x2 :: xs' ->\n if n = (s <: nat)\n then (// x1 + (x2 + xs') =a (x1 + x2) + xs'\n // =c (x2 + x1) + xs' = a x2 + (x1 + xs')\n let a = CM?.associativity m in\n a (select x1 vm) (select x2 vm) (xsdenote m vm xs');\n a (select x2 vm) (select x1 vm) (xsdenote m vm xs');\n CM?.commutativity m (select x1 vm) (select x2 vm))\n else apply_swap_aux_correct (n+1) m vm (x2 :: xs') s\n\nlet apply_swap_correct (#a #b:Type) (m:cm a) (vm:vmap a b)\n (xs:list var) (s:swap (length xs)):\n Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap xs s)))\n (decreases xs) = apply_swap_aux_correct 0 m vm xs s\n\nlet rec apply_swaps_correct (#a #b:Type) (m:cm a) (vm:vmap a b)\n (xs:list var) (ss:list (swap (length xs))):\n Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swaps xs ss)))\n (decreases ss) =\n match ss with\n | [] -> ()\n | s::ss' -> apply_swap_correct m vm xs s;\n apply_swaps_correct m vm (apply_swap xs s) ss'\n\nlet permute_via_swaps (#b:Type) (p:permute b) =\n (#a:Type) -> (vm:vmap a b) -> xs:list var ->\n Lemma (exists ss. p a vm xs == apply_swaps xs ss)\n\nlet permute_via_swaps_correct_aux\n (#b:Type) (p:permute b) (pvs:permute_via_swaps p)\n (#a:Type) (m:cm a) (vm:vmap a b) (xs:list var) :\n Lemma (xsdenote m vm xs == xsdenote m vm (p a vm xs)) =\n pvs vm xs;\n assert(exists ss. p a vm xs == apply_swaps xs ss);\n exists_elim (xsdenote m vm xs == xsdenote m vm (p a vm xs))\n (() <: squash (exists ss. p a vm xs == apply_swaps xs ss))\n (fun ss -> apply_swaps_correct m vm xs ss)\n\nlet permute_via_swaps_correct\n (#b:Type) (p:permute b) (pvs:permute_via_swaps p) : permute_correct p =\n permute_via_swaps_correct_aux p pvs\n\n(***** Sorting variables is a correct permutation\n (since it can be done by swaps) *)\n\n// Here we sort without associating any extra information with the\n// variables and only look at the actual identifiers\n\nlet sort : permute unit =\n (fun a vm -> List.Tot.Base.sortWith #nat (compare_of_bool (<)))\n\nlet sortWith (#b:Type) (f:nat -> nat -> int) : permute b =\n (fun a vm -> List.Tot.Base.sortWith #nat f)\n\nlet sort_via_swaps (#a:Type) (vm : vmap a unit) (xs:list var) :\n Lemma (exists ss. sort a vm xs == apply_swaps xs ss) =\n List.Tot.Properties.sortWith_permutation #nat (compare_of_bool (<)) xs;\n let ss = equal_counts_implies_swaps #nat xs (sort a vm xs) in\n assert (sort a vm xs == apply_swaps xs ss)\n\nlet sortWith_via_swaps (#a #b:Type) (f:nat -> nat -> int)\n (vm : vmap a b) (xs:list var) :\n Lemma (exists ss. sortWith #b f a vm xs == apply_swaps xs ss) =\n List.Tot.Properties.sortWith_permutation #nat f xs;\n let ss = equal_counts_implies_swaps #nat xs (sortWith #b f a vm xs) in\n assert (sortWith #b f a vm xs == apply_swaps xs ss)\n\nlet sort_correct_aux (#a:Type) (m:cm a) (vm:vmap a unit) (xs:list var) :\n Lemma (xsdenote m vm xs == xsdenote m vm (sort a vm xs)) =\n permute_via_swaps_correct #unit sort sort_via_swaps m vm xs\n", "sketch": [ "Step 1: Use the `permute_via_swaps_correct` lemma to prove the correctness of the `sortWith` permutation.\nStep 2: Apply the `sortWith_via_swaps` lemma to show that the `sortWith` permutation can be expressed as a series of swaps.\nStep 3: Conclude the proof by combining the results of the previous steps.", "Step 1: Use the `permute_via_swaps_correct` lemma to reduce the proof of `sortWith_correct_aux` to showing that `sortWith` can be expressed as a series of swaps.\nStep 2: Apply the `sortWith_via_swaps` lemma to show that `sortWith` can indeed be expressed as a series of swaps.\nStep 3: Conclude the proof by combining the results from the previous steps.", "Step 1: Use the `permute_via_swaps_correct` lemma to reduce the problem to showing that `sortWith` can be expressed as a series of swaps.\nStep 2: Apply the `sortWith_via_swaps` lemma to establish that `sortWith` can indeed be expressed as a series of swaps.\nStep 3: Conclude the proof by invoking `apply_swaps_correct` to show that the denotation of the sorted list is equal to the denotation of the original list.", "Step 1: Use the `permute_via_swaps_correct` lemma to reduce the proof of `sortWith_correct_aux` to showing that `sortWith` can be expressed as a sequence of swaps.\nStep 2: Apply the `sortWith_via_swaps` lemma to show that `sortWith` can indeed be expressed as a sequence of swaps.\nStep 3: Conclude the proof by invoking `permute_via_swaps_correct` with the appropriate arguments.", "Step 1: Use the `permute_via_swaps_correct` lemma to reduce the proof to showing that the `sortWith` function can be expressed as a series of swaps.\nStep 2: Apply the `sortWith_via_swaps` lemma to show that `sortWith` can indeed be expressed as a series of swaps.\nStep 3: Conclude the proof by combining the results from the previous steps.", "Step 1: Use the `permute_via_swaps_correct` lemma to reduce the proof of `sortWith_correct_aux` to showing that `sortWith` can be expressed as a series of swaps.\nStep 2: Apply the `sortWith_via_swaps` lemma to show that `sortWith` can indeed be expressed as a series of swaps.\nStep 3: Conclude that the permutation induced by `sortWith` is correct by combining the results from the previous steps.", "Step 1: Use the `permute_via_swaps_correct` lemma to show that the permutation defined by `sortWith` is correct if it can be expressed as a series of swaps.\nStep 2: Apply the `sortWith_via_swaps` lemma to show that the `sortWith` function can be expressed as a series of swaps.\nStep 3: Conclude the proof by combining the results from the previous steps.", "Step 1: Use the `permute_via_swaps_correct` lemma to show that the permutation defined by `sortWith` is correct.\nStep 2: Apply the `sortWith_via_swaps` lemma to establish that the `sortWith` function can be expressed as a series of swaps.\nStep 3: Conclude that the denotation of the sorted list is equal to the denotation of the original list using the `apply_swaps_correct` lemma.", "Step 1: Use the `permute_via_swaps_correct` lemma to reduce the proof of `sortWith_correct_aux` to showing that `sortWith` can be expressed as a series of swaps.\nStep 2: Apply the `sortWith_via_swaps` lemma to show that `sortWith` can indeed be expressed as a series of swaps.\nStep 3: Conclude that the permutation induced by `sortWith` is correct by combining the results from the previous steps.", "Step 1: Use the `permute_via_swaps_correct` lemma to reduce the problem to showing that the permutation defined by `sortWith` can be expressed as a series of swaps.\nStep 2: Use the `sortWith_via_swaps` lemma to show that the permutation defined by `sortWith` can indeed be expressed as a series of swaps.\nStep 3: Conclude the proof by applying the `permute_via_swaps_correct_aux` lemma with the appropriate arguments." ], "generated_solution": [ "permute_via_swaps_correct #b (sortWith #b f) sortWith_via_swaps m vm xs", "permute_via_swaps_correct #b (sortWith #b f) (sortWith_via_swaps f) m vm xs", "permute_via_swaps_correct #b (sortWith #b f) sortWith_via_swaps m vm xs", "permute_via_swaps_correct #b (sortWith #b f) (sortWith_via_swaps f) m vm xs", "permute_via_swaps_correct #b (sortWith #b f) (sortWith_via_swaps f) m vm xs", "permute_via_swaps_correct #b (sortWith #b f) (sortWith_via_swaps f) m vm xs", "let sortWith_correct_aux (#a #b: Type) (f: (nat -> nat -> int)) (m: cm a) (vm: vmap a b) (xs: list var) : Lemma (xsdenote m vm xs == xsdenote m vm (sortWith #b f a vm xs)) =\n permute_via_swaps_correct #b (sortWith #b f) (sortWith_via_swaps f) m vm xs", "permute_via_swaps_correct #b (sortWith #b f) (sortWith_via_swaps f) m vm xs", "permute_via_swaps_correct #b (sortWith #b f) (sortWith_via_swaps f) m vm xs", "permute_via_swaps_correct #b (sortWith #b f) (sortWith_via_swaps f) m vm xs" ] }, { "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.union_loc_of_loc_includes_intro", "opens_and_abbrevs": [ { "abbrev": "F", "full_module": "FStar.FunctionalExtensionality" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "open": "FStar" }, { "open": "FStar" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 15, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val union_loc_of_loc_includes_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: (b: bool -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n : Lemma (requires (larger `loc_includes` smaller))\n (ensures ((union_loc_of_loc c b larger) `loc_includes` (union_loc_of_loc c b smaller)))", "source_definition": "let union_loc_of_loc_includes_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (larger `loc_includes` smaller))\n (ensures (union_loc_of_loc c b larger `loc_includes` union_loc_of_loc c b smaller))\n= ();\n let auxl = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux larger)) in\n let auxs = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux smaller)) in\n assert (forall r a . GSet.mem (ALoc r a None) auxs ==> (\n GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux smaller)) /\\\n GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux larger)) /\\\n GSet.mem (ALoc r a None) auxl\n ));\n assert (auxl `loc_aux_includes` auxs);\n let doml = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n assert (doml `loc_aux_includes` doms)", "source_range": { "start_line": 1799, "start_col": 0, "end_line": 1818, "end_col": 39 }, "interleaved": false, "definition": "fun c b larger smaller ->\n (();\n let auxl = FStar.ModifiesGen.union_aux_of_aux_left c b (FStar.Ghost.reveal (Loc?.aux larger)) in\n let auxs =\n FStar.ModifiesGen.union_aux_of_aux_left c b (FStar.Ghost.reveal (Loc?.aux smaller))\n in\n assert (forall (r: FStar.Monotonic.HyperHeap.rid) (a: Prims.nat).\n FStar.GSet.mem (FStar.ModifiesGen.ALoc r a FStar.Pervasives.Native.None) auxs ==>\n FStar.GSet.mem (FStar.ModifiesGen.ALoc r a FStar.Pervasives.Native.None)\n (FStar.Ghost.reveal (Loc?.aux smaller)) /\\\n FStar.GSet.mem (FStar.ModifiesGen.ALoc r a FStar.Pervasives.Native.None)\n (FStar.Ghost.reveal (Loc?.aux larger)) /\\\n FStar.GSet.mem (FStar.ModifiesGen.ALoc r a FStar.Pervasives.Native.None) auxl);\n assert (FStar.ModifiesGen.loc_aux_includes auxl auxs);\n let doml =\n FStar.ModifiesGen.aloc_domain (FStar.ModifiesGen.cls_union c)\n (Loc?.regions larger)\n (Loc?.live_addrs larger)\n in\n let doms =\n FStar.ModifiesGen.aloc_domain (FStar.ModifiesGen.cls_union c)\n (Loc?.regions smaller)\n (Loc?.live_addrs smaller)\n in\n assert (FStar.ModifiesGen.loc_aux_includes doml doms))\n <:\n FStar.Pervasives.Lemma (requires FStar.ModifiesGen.loc_includes larger smaller)\n (ensures\n FStar.ModifiesGen.loc_includes (FStar.ModifiesGen.union_loc_of_loc c b larger)\n (FStar.ModifiesGen.union_loc_of_loc c b smaller))", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "Prims.bool", "FStar.Monotonic.HyperHeap.rid", "Prims.nat", "FStar.ModifiesGen.cls", "FStar.ModifiesGen.loc", "Prims._assert", "FStar.ModifiesGen.loc_aux_includes", "FStar.ModifiesGen.aloc_union", "FStar.ModifiesGen.cls_union", "FStar.GSet.set", "FStar.ModifiesGen.aloc", "FStar.ModifiesGen.aloc_domain", "FStar.ModifiesGen.__proj__Loc__item__regions", "FStar.ModifiesGen.__proj__Loc__item__live_addrs", "Prims.unit", "Prims.l_Forall", "Prims.l_imp", "Prims.b2t", "FStar.GSet.mem", "FStar.ModifiesGen.ALoc", "FStar.Pervasives.Native.None", "Prims.l_and", "FStar.Ghost.reveal", "FStar.ModifiesGen.__proj__Loc__item__aux", "FStar.ModifiesGen.union_aux_of_aux_left", "FStar.ModifiesGen.loc_includes", "Prims.squash", "FStar.ModifiesGen.union_loc_of_loc", "Prims.Nil", "FStar.Pervasives.pattern" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "\n c: (b: Prims.bool -> FStar.ModifiesGen.cls (al b)) ->\n b: Prims.bool ->\n larger: FStar.ModifiesGen.loc (c b) ->\n smaller: FStar.ModifiesGen.loc (c b)\n -> FStar.Pervasives.Lemma (requires FStar.ModifiesGen.loc_includes larger smaller)\n (ensures\n FStar.ModifiesGen.loc_includes (FStar.ModifiesGen.union_loc_of_loc c b larger)\n (FStar.ModifiesGen.union_loc_of_loc c b smaller))", "prompt": "let union_loc_of_loc_includes_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: (b: bool -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n : Lemma (requires (larger `loc_includes` smaller))\n (ensures ((union_loc_of_loc c b larger) `loc_includes` (union_loc_of_loc c b smaller))) =\n ", "expected_response": "();\nlet auxl = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux larger)) in\nlet auxs = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux smaller)) in\nassert (forall r a.\n GSet.mem (ALoc r a None) auxs ==>\n (GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux smaller)) /\\\n GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux larger)) /\\ GSet.mem (ALoc r a None) auxl));\nassert (auxl `loc_aux_includes` auxs);\nlet doml = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\nlet doms = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\nassert (doml `loc_aux_includes` doms)", "source": { "project_name": "FStar", "file_name": "ulib/FStar.ModifiesGen.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.ModifiesGen.fst", "checked_file": "dataset/FStar.ModifiesGen.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Universe.fsti.checked", "dataset/FStar.Tactics.SMT.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Stubs.Tactics.V2.Builtins.fsti.checked", "dataset/FStar.StrongExcludedMiddle.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Map.fsti.checked", "dataset/FStar.HyperStack.ST.fsti.checked", "dataset/FStar.HyperStack.fst.checked", "dataset/FStar.Heap.fst.checked", "dataset/FStar.GSet.fsti.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "aloc", "ALoc", "ALoc", "ALoc", "aloc_t", "region", "region", "addr", "addr", "loc", "loc", "cls", "Cls", "Cls", "Cls", "aloc_includes", "aloc_includes", "let aloc_domain (#al: aloc_t) (c: cls al) (regions: Ghost.erased (Set.set HS.rid)) (addrs: ((r: HS.rid { Set.mem r (Ghost.reveal regions) } ) -> GTot (GSet.set nat))) : GTot (GSet.set (aloc c)) =\n GSet.comprehend (fun a -> Set.mem a.region (Ghost.reveal regions) && GSet.mem a.addr (addrs a.region))", "aloc_includes_refl", "aloc_includes_refl", "let i_restricted_g_t = F.restricted_g_t", "let addrs_dom regions =\n (r: HS.rid { Set.mem r (Ghost.reveal regions) } )", "let non_live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (r:addrs_dom regions) =\n (y: GSet.set nat { r `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y })", "aloc_includes_trans", "aloc_includes_trans", "let live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags))\n (r:addrs_dom regions) = (y: GSet.set nat { GSet.subset (non_live_addrs r) y } )", "aloc_disjoint", "aloc_disjoint", "loc'", "Loc", "Loc", "Loc", "regions", "regions", "aloc_disjoint_sym", "aloc_disjoint_sym", "region_liveness_tags", "region_liveness_tags", "non_live_addrs", "non_live_addrs", "live_addrs", "live_addrs", "aloc_disjoint_includes", "aloc_disjoint_includes", "aux", "aux", "let loc = loc'", "let mk_non_live_addrs (#regions:_) (#region_liveness_tags:_)\n (f: (x:addrs_dom regions -> GTot (non_live_addrs_codom regions region_liveness_tags x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags) =\n F.on_dom_g _ f", "aloc_preserved", "aloc_preserved", "let mk_live_addrs (#regions:_) (#region_liveness_tags:_)\n (#non_live_addrs_codom: _)\n (f: (x:addrs_dom regions -> GTot (live_addrs_codom regions region_liveness_tags non_live_addrs_codom x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs_codom) =\n F.on_dom_g _ f", "aloc_preserved_refl", "aloc_preserved_refl", "let loc_none #a #c =\n Loc\n (Ghost.hide (Set.empty))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)", "aloc_preserved_trans", "aloc_preserved_trans", "let regions_of_loc\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: GTot (Set.set HS.rid)\n= Ghost.reveal (Loc?.regions s)", "let addrs_of_loc_liveness_not_preserved\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.non_live_addrs l r\n else GSet.empty", "same_mreference_aloc_preserved", "same_mreference_aloc_preserved", "let addrs_of_loc_weak\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.live_addrs l r\n else GSet.empty", "let addrs_of_loc_aux_pred\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n (addr: nat)\n: GTot bool\n= StrongExcludedMiddle.strong_excluded_middle (exists a . GSet.mem a (Ghost.reveal (Loc?.aux l)) /\\ a.region == r /\\ a.addr == addr)", "val loc (#aloc: aloc_t u#x) (c: cls aloc) : Tot (Type u#x)", "val loc_none (#aloc: aloc_t) (#c: cls aloc): Tot (loc c)", "val loc_union\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot (loc c)", "let addrs_of_loc_aux\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (y: GSet.set nat { GSet.subset (GSet.intersect y (addrs_of_loc_weak l r)) GSet.empty } )\n= GSet.comprehend (addrs_of_loc_aux_pred l r)\n `GSet.intersect` (GSet.complement (addrs_of_loc_weak l r))", "val loc_union_idem\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union s s == s)", "let addrs_of_loc\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= GSet.union\n (addrs_of_loc_weak l r)\n (addrs_of_loc_aux l r)", "val loc_union_comm\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: Lemma\n (loc_union s1 s2 == loc_union s2 s1)", "let addrs_of_loc_aux_prop\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: Lemma\n (GSet.subset (GSet.intersect (addrs_of_loc_aux l r) (addrs_of_loc_weak l r)) GSet.empty)\n [SMTPatOr [\n [SMTPat (addrs_of_loc_aux l r)];\n [SMTPat (addrs_of_loc_weak l r)];\n [SMTPat (addrs_of_loc l r)];\n ]]\n= ()", "val loc_union_assoc\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s3: loc c)\n: Lemma\n (loc_union s1 (loc_union s2 s3) == loc_union (loc_union s1 s2) s3)", "val loc_union_loc_none_l\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union loc_none s == s)", "val loc_union_loc_none_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union s loc_none == s)", "let loc_union #al #c s1 s2 =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in\n let regions = Set.union regions1 regions2 in\n let region_liveness_tags : Ghost.erased (Set.set HS.rid) = (Ghost.hide (Set.union (Ghost.reveal (Loc?.region_liveness_tags s1)) (Ghost.reveal (Loc?.region_liveness_tags s2)))) in\n let gregions = Ghost.hide regions in\n let non_live_addrs =\n F.on_dom_g (addrs_dom gregions) #(non_live_addrs_codom gregions region_liveness_tags)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then Loc?.non_live_addrs s1 r else GSet.empty)\n (if Set.mem r regions2 then Loc?.non_live_addrs s2 r else GSet.empty))\n in\n let live_addrs =\n F.on_dom_g (addrs_dom gregions) #(live_addrs_codom gregions region_liveness_tags non_live_addrs)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then addrs_of_loc_weak s1 r else GSet.empty)\n (if Set.mem r regions2 then addrs_of_loc_weak s2 r else GSet.empty))\n in\n let aux = Ghost.hide\n (Ghost.reveal (Loc?.aux s1) `GSet.union` Ghost.reveal (Loc?.aux s2))\n in\n Loc\n (Ghost.hide regions)\n region_liveness_tags\n non_live_addrs\n live_addrs\n aux", "val loc_of_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b: aloc r n)\n: GTot (loc c)", "val loc_of_aloc_not_none\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b: aloc r n)\n: Lemma (loc_of_aloc #_ #c b == loc_none ==> False)", "val loc_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: GTot (loc c)", "val loc_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: GTot (loc c)", "let fun_set_equal (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) :Tot Type0 =\n forall (x: t) . {:pattern (f1 x) \\/ (f2 x) } f1 x `GSet.equal` f2 x", "let loc_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses true (HS.frameOf b) (Set.singleton (HS.as_addr b))", "let fun_set_equal_elim (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) : Lemma\n (requires (fun_set_equal f1 f2))\n (ensures (f1 == f2))\n// [SMTPat (fun_set_equal f1 f2)]\n= assert (f1 `FunctionalExtensionality.feq_g` f2)", "let loc_freed_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses false (HS.frameOf b) (Set.singleton (HS.as_addr b))", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n let Loc regions1 region_liveness_tags1 _ _ aux1 = s1 in\n let Loc regions2 region_liveness_tags2 _ _ aux2 = s2 in\n Ghost.reveal regions1 `Set.equal` Ghost.reveal regions2 /\\\n Ghost.reveal region_liveness_tags1 `Set.equal` Ghost.reveal region_liveness_tags2 /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_region_only\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (Set.singleton r)", "let loc_equal_elim (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : Lemma\n (requires (loc_equal s1 s2))\n (ensures (s1 == s2))\n [SMTPat (s1 `loc_equal` s2)]\n= fun_set_equal_elim (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2);\n fun_set_equal_elim (Loc?.live_addrs s1) (Loc?.live_addrs s2)", "let loc_all_regions_from\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (HS.mod_set (Set.singleton r))", "let loc_union_idem #al #c s =\n assert (loc_union s s `loc_equal` s)", "let loc_union_comm #al #c s1 s2 =\n assert (loc_union s1 s2 `loc_equal` loc_union s2 s1)", "let loc_union_assoc #al #c s1 s2 s3 =\n assert (loc_union s1 (loc_union s2 s3) `loc_equal` loc_union (loc_union s1 s2) s3)", "val loc_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot Type0", "let loc_union_loc_none_l #al #c s =\n assert (loc_union loc_none s `loc_equal` s)", "val loc_includes_refl\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_includes s s)", "let loc_union_loc_none_r #al #c s =\n assert (loc_union s loc_none `loc_equal` s)", "let loc_of_aloc #al #c #r #n b =\n let regions = (Ghost.hide (Set.singleton r)) in\n let region_liveness_tags = (Ghost.hide (Set.empty)) in\n Loc\n regions\n region_liveness_tags\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide (GSet.singleton (ALoc r n (Some b))))", "val loc_includes_trans\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s3: loc c)\n: Lemma\n (requires (loc_includes s1 s2 /\\ loc_includes s2 s3))\n (ensures (loc_includes s1 s3))", "val loc_includes_union_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s s1 s2: loc c)\n: Lemma\n (requires (loc_includes s s1 /\\ loc_includes s s2))\n (ensures (loc_includes s (loc_union s1 s2)))", "let loc_of_aloc_not_none #al #c #r #n b = ()", "let loc_addresses #al #c preserve_liveness r n =\n let regions = (Ghost.hide (Set.singleton r)) in\n Loc\n regions\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> if preserve_liveness then GSet.empty else GSet.of_set n))\n (mk_live_addrs (fun _ -> GSet.of_set n))\n (Ghost.hide (aloc_domain c regions (fun _ -> GSet.of_set n)))", "val loc_includes_union_l\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s: loc c)\n: Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))", "let loc_regions_region_liveness_tags (preserve_liveness: bool) (r: Set.set HS.rid) : Tot (Ghost.erased (Set.set HS.rid)) =\n if preserve_liveness then Ghost.hide Set.empty else Ghost.hide r", "val loc_includes_none\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_includes s loc_none)", "let loc_regions #al #c preserve_liveness r =\n let region_liveness_tags = loc_regions_region_liveness_tags preserve_liveness r in\n let addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { r' `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y } ) =\n GSet.complement GSet.empty\n in\n let live_addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { addrs r' `GSet.subset` y } ) =\n addrs r'\n in\n Loc\n (Ghost.hide r)\n region_liveness_tags\n (mk_non_live_addrs addrs)\n (mk_live_addrs live_addrs)\n (Ghost.hide (aloc_domain c (Ghost.hide r) addrs))", "val loc_includes_none_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (requires (loc_includes loc_none s))\n (ensures (s == loc_none))", "val loc_includes_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b1 b2: aloc r n)\n: Lemma\n (requires (c.aloc_includes b1 b2))\n (ensures (loc_includes (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))", "let aloc_includes (#al: aloc_t) (#c: cls al) (b0 b: aloc c) : GTot Type0 =\n b0.region == b.region /\\ b0.addr == b.addr /\\ Some? b0.loc == Some? b.loc /\\ (if Some? b0.loc && Some? b.loc then c.aloc_includes (Some?.v b0.loc) (Some?.v b.loc) else True)", "let loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b: aloc c)\n: GTot Type0\n (decreases s)\n= exists (b0 : aloc c) . b0 `GSet.mem` s /\\ b0 `aloc_includes` b", "val loc_includes_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1 #r2: HS.rid)\n (#n1 #n2: nat)\n (b1: aloc r1 n1)\n (b2: aloc r2 n2)\n: Lemma\n (requires (loc_includes (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))\n (ensures (r1 == r2 /\\ n1 == n2 /\\ c.aloc_includes b1 b2))", "let loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: GTot Type0\n (decreases s2)\n= forall (b2: aloc c) . GSet.mem b2 s2 ==> loc_aux_includes_buffer s1 b2", "val loc_includes_addresses_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n (s: Set.set nat)\n (#a: nat)\n (p: aloc r a)\n: Lemma\n (requires (Set.mem a s))\n (ensures (loc_includes (loc_addresses preserve_liveness r s) (loc_of_aloc #_ #c p)))", "let loc_aux_includes_union_l\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s \\/ loc_aux_includes s2 s))\n (ensures (loc_aux_includes (GSet.union s1 s2) s))\n (decreases s)\n= ()", "let loc_aux_includes_refl\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n: Lemma\n (loc_aux_includes s s)\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)", "val loc_includes_region_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (s: Set.set HS.rid)\n (#r: HS.rid)\n (#a: nat)\n (b: aloc r a)\n: Lemma\n (requires (Set.mem r s))\n (ensures (loc_includes (loc_regions preserve_liveness s) (loc_of_aloc #_ #c b)))", "let loc_aux_includes_subset\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)", "val loc_includes_region_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (s: Set.set HS.rid)\n (r: HS.rid)\n (a: Set.set nat)\n: Lemma\n (requires (Set.mem r s))\n (ensures (loc_includes (loc_regions #_ #c preserve_liveness1 s) (loc_addresses preserve_liveness2 r a)))", "let loc_aux_includes_subset'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n [SMTPatOr [\n [SMTPat (s1 `GSet.subset` s2)];\n [SMTPat (loc_aux_includes s2 s1)];\n ]]\n= loc_aux_includes_subset s1 s2", "val loc_includes_region_region\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires ((preserve_liveness1 ==> preserve_liveness2) /\\ Set.subset s2 s1))\n (ensures (loc_includes (loc_regions #_ #c preserve_liveness1 s1) (loc_regions preserve_liveness2 s2)))", "let loc_aux_includes_union_l_r\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s s') s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s s' s", "val loc_includes_region_union_l\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (l: loc c)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires (loc_includes l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)))))\n (ensures (loc_includes (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness s2)))", "let loc_aux_includes_union_l_l\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s' s) s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s' s s", "val loc_includes_addresses_addresses\n (#aloc: aloc_t) (c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r: HS.rid)\n (a1 a2: Set.set nat)\n: Lemma\n (requires ((preserve_liveness1 ==> preserve_liveness2) /\\ Set.subset a2 a1))\n (ensures (loc_includes #_ #c (loc_addresses preserve_liveness1 r a1) (loc_addresses preserve_liveness2 r a2)))", "let loc_aux_includes_buffer_includes\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b1 b2: aloc c)\n: Lemma\n (requires (loc_aux_includes_buffer s b1 /\\ b1 `aloc_includes` b2))\n (ensures (loc_aux_includes_buffer s b2))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))", "val loc_disjoint\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot Type0", "let loc_aux_includes_loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n (b: aloc c)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_buffer s2 b))\n (ensures (loc_aux_includes_buffer s1 b))\n= Classical.forall_intro_3 (fun s b1 b2 -> Classical.move_requires (loc_aux_includes_buffer_includes #al #c s b1) b2)", "val loc_disjoint_sym\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))", "let loc_aux_includes_trans\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))", "val loc_disjoint_none_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (ensures (loc_disjoint s loc_none))", "let addrs_of_loc_weak_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (loc_union l1 l2) r == GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r))\n [SMTPat (addrs_of_loc_weak (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc_weak (loc_union l1 l2) r) (GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r)))", "val loc_disjoint_union_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s s1 /\\ loc_disjoint s s2))\n (ensures (loc_disjoint s (loc_union s1 s2)))", "val loc_disjoint_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (p1 p2 p1' p2' : loc c)\n: Lemma\n (requires (loc_includes p1 p1' /\\ loc_includes p2 p2' /\\ loc_disjoint p1 p2))\n (ensures (loc_disjoint p1' p2'))", "let addrs_of_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l1 l2) r == GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r))\n [SMTPat (addrs_of_loc (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc (loc_union l1 l2) r) (GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r)))", "val loc_disjoint_aloc_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1: HS.rid)\n (#a1: nat)\n (#r2: HS.rid)\n (#a2: nat)\n (b1: aloc r1 a1)\n (b2: aloc r2 a2)\n: Lemma\n (requires ((r1 == r2 /\\ a1 == a2) ==> c.aloc_disjoint b1 b2))\n (ensures (loc_disjoint (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))", "let loc_includes' #al (#c: cls al) (s1 s2: loc c) =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in (\n Set.subset regions2 regions1 /\\\n Set.subset (Ghost.reveal (Loc?.region_liveness_tags s2)) (Ghost.reveal (Loc?.region_liveness_tags s1)) /\\\n (\n forall (r: HS.rid { Set.mem r regions2 } ) .\n GSet.subset (Loc?.non_live_addrs s2 r) (Loc?.non_live_addrs s1 r)\n ) /\\\n (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc_weak s2 r) (addrs_of_loc_weak s1 r)\n ) /\\ (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc s2 r) (addrs_of_loc s1 r)\n ) /\\ (\n (Ghost.reveal (Loc?.aux s1)) `loc_aux_includes` (Ghost.reveal (Loc?.aux s2))\n )\n )", "val loc_disjoint_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1: HS.rid)\n (#a1: nat)\n (#r2: HS.rid)\n (#a2: nat)\n (b1: aloc r1 a1)\n (b2: aloc r2 a2)\n: Lemma\n (requires (loc_disjoint (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))\n (ensures ((r1 == r2 /\\ a1 == a2) ==> c.aloc_disjoint b1 b2))", "val loc_disjoint_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r1 r2: HS.rid)\n (n1 n2: Set.set nat)\n: Lemma\n (requires (r1 <> r2 \\/ Set.subset (Set.intersect n1 n2) Set.empty))\n (ensures (loc_disjoint (loc_addresses #_ #c preserve_liveness1 r1 n1) (loc_addresses preserve_liveness2 r2 n2)))", "let loc_includes #al #c s1 s2 =\n loc_includes' s1 s2", "let loc_includes_refl #al #c s =\n loc_aux_includes_refl (Ghost.reveal (Loc?.aux s))", "let loc_includes_refl'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: Lemma\n (loc_includes s s)\n [SMTPat (loc_includes s s)]\n= loc_includes_refl s", "let loc_disjoint_addresses #aloc #c = loc_disjoint_addresses_intro #aloc #c", "val loc_disjoint_addresses_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r1 r2: HS.rid)\n (n1 n2: Set.set nat)\n: Lemma\n (requires (loc_disjoint (loc_addresses #_ #c preserve_liveness1 r1 n1) (loc_addresses preserve_liveness2 r2 n2)))\n (ensures (r1 <> r2 \\/ Set.subset (Set.intersect n1 n2) Set.empty))", "let loc_includes_trans #al #c s1 s2 s3 =\n loc_aux_includes_trans (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s3))", "let loc_includes_union_r #al #c s s1 s2 = ()", "let loc_includes_union_l #al #c s1 s2 s =\n let u12 = loc_union s1 s2 in\n Classical.or_elim\n #(loc_includes s1 s)\n #(loc_includes s2 s)\n #(fun _ -> loc_includes (loc_union s1 s2) s)\n (fun _ ->\n loc_aux_includes_union_l_r (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2));\n assert (loc_includes (loc_union s1 s2) s1);\n loc_includes_trans u12 s1 s)\n (fun _ ->\n loc_aux_includes_union_l_l (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s1));\n assert (loc_includes (loc_union s1 s2) s2);\n loc_includes_trans u12 s2 s)", "val loc_disjoint_aloc_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (#r' : HS.rid)\n (#a' : nat)\n (p: aloc r' a')\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (requires (r == r' ==> (~ (Set.mem a' n))))\n (ensures (loc_disjoint (loc_of_aloc p) (loc_addresses #_ #c preserve_liveness r n)))", "val loc_disjoint_aloc_addresses_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r' : HS.rid)\n (#a' : nat)\n (p: aloc r' a')\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (requires (loc_disjoint (loc_of_aloc p) (loc_addresses #_ #c preserve_liveness r n)))\n (ensures (r == r' ==> (~ (Set.mem a' n))))", "let loc_includes_none #al #c s = ()", "let loc_includes_none_elim #al #c s =\n assert (s `loc_equal` loc_none)", "let loc_includes_aloc #al #c #r #n b1 b2 = ()", "let loc_includes_aloc_elim #aloc #c #r1 #r2 #n1 #n2 b1 b2 = ()", "let addrs_of_loc_loc_of_aloc\n (#al: aloc_t)\n (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (p: al r a)\n (r': HS.rid)\n: Lemma\n (addrs_of_loc (loc_of_aloc #_ #c p) r' `GSet.equal` (if r = r' then GSet.singleton a else GSet.empty))\n [SMTPat (addrs_of_loc (loc_of_aloc #_ #c p) r')]\n= ()", "val loc_disjoint_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (rs1 rs2: Set.set HS.rid)\n: Lemma\n (requires (Set.subset (Set.intersect rs1 rs2) Set.empty))\n (ensures (loc_disjoint (loc_regions #_ #c preserve_liveness1 rs1) (loc_regions preserve_liveness2 rs2)))", "val address_liveness_insensitive_locs (#aloc: aloc_t) (c: cls aloc) : Tot (loc c)", "let loc_includes_addresses_aloc #al #c preserve_liveness r s #a p = ()", "val loc_includes_address_liveness_insensitive_locs_aloc (#aloc: aloc_t) (#c: cls aloc) (#r: HS.rid) (#n: nat) (a: aloc r n) : Lemma\n (loc_includes (address_liveness_insensitive_locs c) (loc_of_aloc a))", "let loc_includes_region_aloc #al #c preserve_liveness s #r #a b = ()", "let loc_includes_region_addresses #al #c s preserve_liveness1 preserve_liveness2 r a = ()", "val loc_includes_address_liveness_insensitive_locs_addresses (#aloc: aloc_t) (c: cls aloc) (r: HS.rid) (a: Set.set nat) : Lemma\n (loc_includes (address_liveness_insensitive_locs c) (loc_addresses true r a))", "let loc_includes_region_region #al #c preserve_liveness1 preserve_liveness2 s1 s2 = ()", "val region_liveness_insensitive_locs (#al: aloc_t) (c: cls al) : Tot (loc c)", "let loc_includes_region_union_l #al #c preserve_liveness l s1 s2 =\n assert ((loc_regions #_ #c preserve_liveness (Set.intersect s2 (Set.complement s1)) `loc_union` loc_regions #_ #c preserve_liveness (Set.intersect s2 s1)) `loc_equal` loc_regions preserve_liveness s2);\n loc_includes_region_region #_ #c preserve_liveness preserve_liveness s1 (Set.intersect s2 s1);\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)));\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 s1));\n loc_includes_union_r (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1))) (loc_regions preserve_liveness (Set.intersect s2 s1))", "val loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs (#al: aloc_t) (c: cls al) : Lemma\n (loc_includes (region_liveness_insensitive_locs c) (address_liveness_insensitive_locs c))", "val loc_includes_region_liveness_insensitive_locs_loc_regions\n (#al: aloc_t) (c: cls al) (r: Set.set HS.rid)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_regions #_ #c true r)", "let loc_includes_addresses_addresses #al c preserve_liveness1 preserve_liveness2 r s1 s2 = ()", "val loc_includes_region_liveness_insensitive_locs_loc_addresses\n (#al: aloc_t) (c: cls al) (preserve_liveness: bool) (r: HS.rid) (a: Set.set nat)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_addresses #_ #c preserve_liveness r a)", "let aloc_disjoint (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : GTot Type0 =\n if b1.region = b2.region && b1.addr = b2.addr\n then Some? b1.loc /\\ Some? b2.loc /\\ c.aloc_disjoint (Some?.v b1.loc) (Some?.v b2.loc)\n else True", "val loc_includes_region_liveness_insensitive_locs_loc_of_aloc\n (#al: aloc_t) (c: cls al) (#r: HS.rid) (#a: nat) (x: al r a)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_of_aloc #_ #c x)", "let aloc_disjoint_sym (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : Lemma\n (aloc_disjoint b1 b2 <==> aloc_disjoint b2 b1)\n= Classical.forall_intro_2 (fun r a -> Classical.forall_intro_2 (fun b1 b2 -> c.aloc_disjoint_sym #r #a b1 b2))", "let loc_aux_disjoint\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: GTot Type0\n= forall (b1 b2: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b2 l2) ==> aloc_disjoint b1 b2", "val modifies\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0", "let loc_aux_disjoint_union_l\n (#al: aloc_t) (#c: cls al)\n (ll1 lr1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint (GSet.union ll1 lr1) l2 <==> (loc_aux_disjoint ll1 l2 /\\ loc_aux_disjoint lr1 l2)))\n= ()", "val modifies_intro\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')", "let loc_aux_disjoint_union_r\n (#al: aloc_t) (#c: cls al)\n (l1 ll2 lr2: GSet.set (aloc c))\n: Lemma\n (loc_aux_disjoint l1 (GSet.union ll2 lr2) <==> (loc_aux_disjoint l1 ll2 /\\ loc_aux_disjoint l1 lr2))\n= ()", "let loc_aux_disjoint_sym\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint l1 l2 <==> loc_aux_disjoint l2 l1))\n= Classical.forall_intro_2 (aloc_disjoint_sym #al #c)", "let regions_of_loc_loc_union\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (regions_of_loc (loc_union s1 s2) == regions_of_loc s1 `Set.union` regions_of_loc s2)\n [SMTPat (regions_of_loc (loc_union s1 s2))]\n= assert (regions_of_loc (loc_union s1 s2) `Set.equal` (regions_of_loc s1 `Set.union` regions_of_loc s2))", "let regions_of_loc_monotonic\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_includes s1 s2))\n (ensures (Set.subset (regions_of_loc s2) (regions_of_loc s1)))\n= ()", "let loc_disjoint_region_liveness_tags (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty", "let loc_disjoint_addrs (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n (forall (r: HS.rid) .\n GSet.subset (GSet.intersect (addrs_of_loc_weak l1 r) (addrs_of_loc l2 r)) GSet.empty /\\\n GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc_weak l2 r)) GSet.empty\n )", "let loc_disjoint_aux (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n loc_aux_disjoint (Ghost.reveal (Loc?.aux l1)) (Ghost.reveal (Loc?.aux l2))", "val modifies_none_intro\n (#al: aloc_t) (#c: cls al) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (HS.live_region h r /\\ HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n: Lemma\n (modifies (loc_none #_ #c) h h')", "let loc_disjoint'\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n: GTot Type0\n= loc_disjoint_region_liveness_tags l1 l2 /\\\n loc_disjoint_addrs l1 l2 /\\\n loc_disjoint_aux l1 l2", "let loc_disjoint = loc_disjoint'", "let loc_disjoint_sym #al #c l1 l2 =\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c)", "let loc_disjoint_sym'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))\n [SMTPat (loc_disjoint s1 s2)]\n= loc_disjoint_sym s1 s2", "let loc_disjoint_none_r #al #c s = ()", "let loc_disjoint_union_r #al #c s s1 s2 = ()", "val modifies_address_intro\n (#al: aloc_t) (#c: cls al) (r: HS.rid) (n: nat) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((r <> HS.frameOf b \\/ n <> HS.as_addr b) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (addr_unused_in: (\n (r': HS.rid) ->\n (n' : nat) ->\n Lemma\n (requires ((r' <> r \\/ n' <> n) /\\ HS.live_region h r' /\\ HS.live_region h' r' /\\ n' `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r')))\n (ensures (n' `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r')))\n ))\n: Lemma\n (modifies (loc_addresses #_ #c false r (Set.singleton n)) h h')", "let aloc_disjoint_includes (#al: aloc_t) (#c: cls al) (b1 b2 b3 : aloc c) : Lemma\n (requires (aloc_disjoint b1 b2 /\\ aloc_includes b2 b3))\n (ensures (aloc_disjoint b1 b3))\n= if b1.region = b2.region && b1.addr = b2.addr\n then begin\n c.aloc_includes_refl (Some?.v b1.loc);\n c.aloc_disjoint_includes (Some?.v b1.loc) (Some?.v b2.loc) (Some?.v b1.loc) (Some?.v b3.loc)\n end\n else ()", "let loc_aux_disjoint_loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (l1 l2 l3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\n= // FIXME: WHY WHY WHY do I need this assert?\n assert (forall (b1 b3: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b3 l3) ==> (exists (b2: aloc c) . GSet.mem b2 l2 /\\ aloc_disjoint b1 b2 /\\ aloc_includes b2 b3));\n Classical.forall_intro_3 (fun b1 b2 b3 -> Classical.move_requires (aloc_disjoint_includes #al #c b1 b2) b3)", "let loc_disjoint_includes #al #c p1 p2 p1' p2' =\n regions_of_loc_monotonic p1 p1';\n regions_of_loc_monotonic p2 p2';\n let l1 = Ghost.reveal (Loc?.aux p1) in\n let l2 = Ghost.reveal (Loc?.aux p2) in\n let l1' = Ghost.reveal (Loc?.aux p1') in\n let l2' = Ghost.reveal (Loc?.aux p2') in\n loc_aux_disjoint_loc_aux_includes l1 l2 l2';\n loc_aux_disjoint_sym l1 l2';\n loc_aux_disjoint_loc_aux_includes l2' l1 l1';\n loc_aux_disjoint_sym l2' l1'", "val modifies_aloc_intro\n (#al: aloc_t) (#c: cls al) (#r: HS.rid) (#n: nat) (z: al r n) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((r <> HS.frameOf b \\/ n <> HS.as_addr b) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (HS.live_region h r /\\ HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (x: al r n) ->\n Lemma\n (requires (c.aloc_disjoint x z))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies (loc_of_aloc #_ #c z) h h')", "let loc_disjoint_aloc_intro #al #c #r1 #a1 #r2 #a2 b1 b2 = ()", "let loc_disjoint_aloc_elim #al #c #r1 #a1 #r2 #a2 b1 b2 =\n // FIXME: WHY WHY WHY this assert?\n assert (aloc_disjoint (ALoc #_ #c r1 a1 (Some b1)) (ALoc #_ #c r2 a2 (Some b2)))", "let loc_disjoint_addresses_intro #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness1 r1 n1))) (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness2 r2 n2))))", "let loc_disjoint_addresses_elim #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 = ()", "let loc_disjoint_aloc_addresses_intro #al #c #r' #a' p preserve_liveness r n = ()", "let loc_disjoint_aloc_addresses_elim #al #c #r' #a' p preserve_liveness r n = ()", "let loc_disjoint_regions #al #c preserve_liveness1 preserve_liveness2 rs1 rs2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness1 rs1))) (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness2 rs2))))", "let loc_none_in_some_region #a (c: cls a) (r: HS.rid) : GTot (loc c) =\n Loc\n (Ghost.hide (Set.singleton r))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)", "let address_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))", "val modifies_live_region\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h1 h2: HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (modifies s h1 h2 /\\ loc_disjoint s (loc_region_only false r) /\\ HS.live_region h1 r))\n (ensures (HS.live_region h2 r))", "let loc_includes_address_liveness_insensitive_locs_aloc #al #c #r #n a = ()", "val modifies_mreference_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (b: HS.mreference t pre)\n (p: loc c)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_mreference b) p /\\\n HS.contains h b /\\\n modifies p h h'\n ))\n (ensures (\n HS.contains h' b /\\\n HS.sel h b == HS.sel h' b\n ))", "let loc_includes_address_liveness_insensitive_locs_addresses #al c r a = ()", "let region_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.complement GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))", "let loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs #al c = ()", "let loc_includes_region_liveness_insensitive_locs_loc_regions #al c r = ()", "let loc_includes_region_liveness_insensitive_locs_loc_addresses #al c preserve_liveness r a = ()", "let loc_includes_region_liveness_insensitive_locs_loc_of_aloc #al c #r #a x = ()", "val modifies_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#a: nat)\n (b: aloc r a)\n (p: loc c)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_of_aloc b) p /\\\n modifies p h h'\n ))\n (ensures (\n c.aloc_preserved b h h'\n ))", "let modifies_preserves_livenesses\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s r)))\n ) ==> (\n HS.contains h2 p\n ))", "let modifies_preserves_livenesses_elim\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (p: HS.mreference t pre)\n: Lemma\n (requires (modifies_preserves_livenesses s h1 h2 /\\ HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))))\n (ensures (HS.contains h2 p))\n= ()", "val modifies_refl\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h: HS.mem)\n: Lemma\n (modifies s h h)", "val modifies_loc_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (s1: loc c)\n (h h': HS.mem)\n (s2: loc c)\n: Lemma\n (requires (modifies s2 h h' /\\ loc_includes s1 s2))\n (ensures (modifies s1 h h'))", "let modifies_preserves_livenesses_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p))\n ))\n: Lemma\n (modifies_preserves_livenesses s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'", "val modifies_preserves_liveness\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union s1 s2) h h' /\\ loc_disjoint s1 (loc_mreference r) /\\ loc_includes (address_liveness_insensitive_locs c) s2 /\\ h `HS.contains` r))\n (ensures (h' `HS.contains` r))", "val modifies_preserves_liveness_strong\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n (x: aloc (HS.frameOf r) (HS.as_addr r))\n: Lemma\n (requires (modifies (loc_union s1 s2) h h' /\\ loc_disjoint s1 (loc_of_aloc #_ #c #(HS.frameOf r) #(HS.as_addr r) x) /\\ loc_includes (address_liveness_insensitive_locs c) s2 /\\ h `HS.contains` r))\n (ensures (h' `HS.contains` r))", "val modifies_preserves_region_liveness\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_region_only false r) l1 /\\ HS.live_region h r))\n (ensures (HS.live_region h' r))", "let modifies_preserves_mreferences\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s r)))\n ) ==> (\n HS.contains h2 p /\\\n HS.sel h2 p == HS.sel h1 p\n ))", "val modifies_preserves_region_liveness_reference\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_mreference r) l1 /\\ HS.live_region h (HS.frameOf r)))\n (ensures (HS.live_region h' (HS.frameOf r)))", "let modifies_preserves_mreferences_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p /\\ HS.sel h2 p == HS.sel h1 p))\n ))\n: Lemma\n (modifies_preserves_mreferences s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p /\\ h2 `HS.sel` p == h1 `HS.sel` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'", "val modifies_preserves_region_liveness_aloc\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (#r: HS.rid)\n (#n: nat)\n (x: al r n)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_of_aloc x) l1 /\\ HS.live_region h r))\n (ensures (HS.live_region h' r))", "val modifies_trans\n (#aloc: aloc_t) (#c: cls aloc)\n (s12: loc c)\n (h1 h2: HS.mem)\n (s23: loc c)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))", "val modifies_only_live_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (rs: Set.set HS.rid)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))", "let modifies_preserves_alocs\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (a: nat) (b: al r a) .\n loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))\n ==>\n c.aloc_preserved b h1 h2\n )", "val no_upd_fresh_region\n (#aloc: aloc_t) (#c: cls aloc)\n (r:HS.rid)\n (l:loc c)\n (h0:HS.mem)\n (h1:HS.mem)\n: Lemma\n (requires (HS.fresh_region r h0 h1 /\\ modifies (loc_union (loc_all_regions_from false r) l) h0 h1))\n (ensures (modifies l h0 h1))", "let modifies_preserves_alocs_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (u: unit { modifies_preserves_mreferences s h1 h2 } )\n (f: (\n (r: HS.rid) ->\n (a: nat) ->\n (b: al r a) ->\n Lemma\n (requires (\n Set.mem r (regions_of_loc s) /\\\n (~ (GSet.mem a (addrs_of_loc_weak s r))) /\\\n (GSet.mem a (addrs_of_loc_aux s r) /\\ loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b))))\n ))\n (ensures (c.aloc_preserved b h1 h2))\n ))\n: Lemma\n (modifies_preserves_alocs s h1 h2)\n= let f'\n (r: HS.rid)\n (a: nat)\n (b: al r a)\n : Lemma\n (requires (loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))))\n (ensures (c.aloc_preserved b h1 h2))\n = if Set.mem r (regions_of_loc s) && (not (GSet.mem a (addrs_of_loc_weak s r)))\n then begin\n if GSet.mem a (addrs_of_loc_aux s r)\n then\n Classical.move_requires (f r a) b\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n end else if Set.mem r (regions_of_loc s)\n then begin\n assert (GSet.mem a (addrs_of_loc_weak s r));\n assert (GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux s)));\n assert (aloc_disjoint #_ #c (ALoc r a None) (ALoc r a (Some b)));\n assert False\n end\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n in\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (f' r a) b)", "val fresh_frame_modifies\n (#aloc: aloc_t) (c: cls aloc)\n (h0 h1: HS.mem)\n: Lemma\n (requires (HS.fresh_frame h0 h1))\n (ensures (modifies #_ #c loc_none h0 h1))", "val new_region_modifies\n (#al: aloc_t)\n (c: cls al)\n (m0: HS.mem)\n (r0: HS.rid)\n (col: option int)\n: Lemma\n (requires (HST.is_eternal_region r0 /\\ HS.live_region m0 r0 /\\ (None? col \\/ HS.is_heap_color (Some?.v col))))\n (ensures (\n let (_, m1) = HS.new_eternal_region m0 r0 col in\n modifies (loc_none #_ #c) m0 m1\n ))", "val popped_modifies\n (#aloc: aloc_t) (c: cls aloc)\n (h0 h1: HS.mem) : Lemma\n (requires (HS.popped h0 h1))\n (ensures (modifies #_ #c (loc_region_only false (HS.get_tip h0)) h0 h1))", "val modifies_fresh_frame_popped\n (#aloc: aloc_t) (#c: cls aloc)\n (h0 h1: HS.mem)\n (s: loc c)\n (h2 h3: HS.mem)\n: Lemma\n (requires (\n HS.fresh_frame h0 h1 /\\\n modifies (loc_union (loc_all_regions_from false (HS.get_tip h1)) s) h1 h2 /\\\n HS.get_tip h2 == HS.get_tip h1 /\\\n HS.popped h2 h3\n ))\n (ensures (\n modifies s h0 h3 /\\\n HS.get_tip h3 == HS.get_tip h0\n ))", "let modifies_preserves_regions\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= forall (r: HS.rid) . (HS.live_region h1 r /\\ ~ (Set.mem r (Ghost.reveal (Loc?.region_liveness_tags s)))) ==> HS.live_region h2 r", "val modifies_loc_regions_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (rs: Set.set HS.rid)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HS.modifies rs h1 h2))\n (ensures (modifies (loc_regions #_ #c true rs) h1 h2))", "let modifies_preserves_not_unused_in\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (n: nat) . (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))", "val modifies_loc_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc c)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r a h1 h2\n ))\n (ensures (modifies (loc_union (loc_addresses true r a) l) h1 h2))", "let modifies_preserves_not_unused_in_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ))\n (ensures (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n ))\n: Lemma\n (modifies_preserves_not_unused_in s h1 h2)\n= let f'\n (r: HS.rid)\n (n: nat)\n : Lemma\n ((\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n = Classical.move_requires (f r) n\n in\n Classical.forall_intro_2 f'", "val modifies_ralloc_post\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (i: HS.rid)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel)\n (h' : HS.mem)\n: Lemma\n (requires (HST.ralloc_post i init h x h'))\n (ensures (modifies (loc_none #_ #c) h h'))", "val modifies_salloc_post\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel { HS.is_stack_region (HS.frameOf x) } )\n (h' : HS.mem)\n: Lemma\n (requires (HST.salloc_post init h x h'))\n (ensures (modifies (loc_none #_ #c) h h'))", "val modifies_free\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel { HS.is_mm r } )\n (m: HS.mem { m `HS.contains` r } )\n: Lemma\n (modifies (loc_freed_mreference #_ #c r) m (HS.free r m))", "let modifies'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= modifies_preserves_regions s h1 h2 /\\\n modifies_preserves_not_unused_in s h1 h2 /\\\n modifies_preserves_mreferences s h1 h2 /\\\n modifies_preserves_livenesses s h1 h2 /\\\n modifies_preserves_alocs s h1 h2", "val modifies_none_modifies\n (#aloc: aloc_t) (#c: cls aloc)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HST.modifies_none h1 h2))\n (ensures (modifies (loc_none #_ #c) h1 h2))", "let modifies = modifies'", "val modifies_intro_strong\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n (Set.mem r (regions_of_loc l) ==> ~ (GSet.mem n (Loc?.non_live_addrs l r))) /\\\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')", "val modifies_upd\n (#aloc: aloc_t) (#c: cls aloc)\n (#t: Type) (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n (v: t)\n (h: HS.mem)\n: Lemma\n (requires (HS.contains h r))\n (ensures (modifies #_ #c (loc_mreference r) h (HS.upd h r v)))", "val modifies_strengthen\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (h h' : HS.mem)\n (alocs: (\n (f: ((t: Type) -> (pre: Preorder.preorder t) -> (m: HS.mreference t pre) -> Lemma\n (requires (HS.frameOf m == r0 /\\ HS.as_addr m == a0 /\\ HS.contains h m))\n (ensures (HS.contains h' m))\n )) ->\n (x: al r0 a0) ->\n Lemma\n (requires (c.aloc_disjoint x al0 /\\ loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (requires (modifies (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h'))\n (ensures (modifies (loc_union l (loc_of_aloc al0)) h h'))", "val does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: GTot Type0", "val not_live_region_does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (~ (HS.live_region h (fst ra))))\n (ensures (h `does_not_contain_addr` ra))", "val unused_in_does_not_contain_addr\n (h: HS.mem)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel)\n: Lemma\n (requires (r `HS.unused_in` h))\n (ensures (h `does_not_contain_addr` (HS.frameOf r, HS.as_addr r)))", "let modifies_intro_strong #al #c l h h' regions mrefs lives unused_ins alocs =\n Classical.forall_intro (Classical.move_requires regions);\n assert (modifies_preserves_regions l h h');\n\n let aux (t:Type) (pre:Preorder.preorder t) (p:HS.mreference t pre)\n :Lemma (requires (HS.contains h p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc l) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc l (HS.frameOf p))))))\n (ensures (HS.contains h' p /\\ HS.sel h' p == HS.sel h p))\n =\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l);\n // FIXME: WHY WHY WHY is this assert necessary?\n assert_spinoff (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n // FIXME: Now this one is too :)\n assert (loc_disjoint_addrs (loc_mreference p) l);\n assert ((loc_disjoint (loc_mreference p) l));\n mrefs t pre p\n in\n\n modifies_preserves_mreferences_intro l h h' aux;\n Classical.forall_intro_3 (fun t pre p -> Classical.move_requires (lives t pre) p);\n modifies_preserves_not_unused_in_intro l h h' (fun r n ->\n unused_ins r n\n );\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n alocs r a b\n )", "val addr_unused_in_does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))))\n (ensures (h `does_not_contain_addr` ra))", "val does_not_contain_addr_addr_unused_in\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (h `does_not_contain_addr` ra))\n (ensures (HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))))", "val free_does_not_contain_addr\n (#a: Type0)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel)\n (m: HS.mem)\n (x: HS.rid * nat)\n: Lemma\n (requires (\n HS.is_mm r /\\\n m `HS.contains` r /\\\n fst x == HS.frameOf r /\\\n snd x == HS.as_addr r\n ))\n (ensures (\n HS.free r m `does_not_contain_addr` x\n ))", "let modifies_intro #al #c l h h' regions mrefs lives unused_ins alocs =\n modifies_intro_strong l h h'\n regions\n mrefs\n lives\n (fun r n -> unused_ins r n)\n alocs", "val does_not_contain_addr_elim\n (#a: Type0)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel)\n (m: HS.mem)\n (x: HS.rid * nat)\n: Lemma\n (requires (\n m `does_not_contain_addr` x /\\\n HS.frameOf r == fst x /\\\n HS.as_addr r == snd x\n ))\n (ensures (~ (m `HS.contains` r)))", "let modifies_none_intro #al #c h h' regions mrefs unused_ins =\n modifies_intro_strong #_ #c loc_none h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> mrefs t pre b)\n (fun r n -> unused_ins r n)\n (fun r a x ->\n c.same_mreference_aloc_preserved x h h' (fun t pre b -> mrefs t pre b)\n )", "let modifies_address_intro #al #c r n h h' regions mrefs unused_ins =\n Classical.forall_intro (Classical.move_requires regions);\n let l : loc c = loc_addresses #_ #c false r (Set.singleton n) in\n modifies_preserves_mreferences_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_livenesses_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_not_unused_in_intro l h h'\n (fun r n -> unused_ins r n)\n ;\n modifies_preserves_alocs_intro l h h' ()\n (fun r a b ->\n c.same_mreference_aloc_preserved b h h' (fun t pre p -> mrefs t pre p)\n )", "val loc_not_unused_in (#al: aloc_t) (c: cls al) (h: HS.mem) : GTot (loc c)", "val loc_unused_in (#al: aloc_t) (c: cls al) (h: HS.mem) : GTot (loc c)", "val loc_regions_unused_in (#al: aloc_t) (c: cls al) (h: HS.mem) (rs: Set.set HS.rid) : Lemma\n (requires (forall r . Set.mem r rs ==> (~ (HS.live_region h r))))\n (ensures (loc_unused_in c h `loc_includes` loc_regions false rs))", "val loc_addresses_unused_in (#al: aloc_t) (c: cls al) (r: HS.rid) (a: Set.set nat) (h: HS.mem) : Lemma\n (requires (forall x . Set.mem x a ==> h `does_not_contain_addr` (r, x)))\n (ensures (loc_unused_in c h `loc_includes` loc_addresses false r a))", "val loc_addresses_not_unused_in (#al: aloc_t) (c: cls al) (r: HS.rid) (a: Set.set nat) (h: HS.mem) : Lemma\n (requires (forall x . Set.mem x a ==> ~ (h `does_not_contain_addr` (r, x))))\n (ensures (loc_not_unused_in c h `loc_includes` loc_addresses false r a))", "let modifies_aloc_intro #al #c #r #n x h h' regions mrefs livenesses unused_ins alocs =\n modifies_intro_strong #_ #c (loc_of_aloc x) h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> livenesses t pre b)\n (fun r n -> unused_ins r n)\n (fun r' n' z ->\n if r' = r && n' = n\n then begin\n loc_disjoint_aloc_elim #_ #c z x;\n alocs z\n end else\n c.same_mreference_aloc_preserved z h h' (fun t pre p ->\n mrefs t pre p\n )\n )", "val loc_unused_in_not_unused_in_disjoint (#al: aloc_t) (c: cls al) (h: HS.mem) : Lemma\n (loc_unused_in c h `loc_disjoint` loc_not_unused_in c h)", "val not_live_region_loc_not_unused_in_disjoint\n (#al: aloc_t)\n (c: cls al)\n (h0: HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (~ (HS.live_region h0 r)))\n (ensures (loc_disjoint (loc_region_only false r) (loc_not_unused_in c h0)))", "val modifies_address_liveness_insensitive_unused_in\n (#al: aloc_t)\n (c: cls al)\n (h h' : HS.mem)\n: Lemma\n (requires (modifies (address_liveness_insensitive_locs c) h h'))\n (ensures (loc_not_unused_in c h' `loc_includes` loc_not_unused_in c h /\\ loc_unused_in c h `loc_includes` loc_unused_in c h'))", "let modifies_live_region #al #c s h1 h2 r = ()", "let modifies_mreference_elim #al #c #t #pre b p h h' = ()", "let modifies_aloc_elim #al #c #r #a b p h h' = ()", "val modifies_only_not_unused_in\n (#al: aloc_t)\n (#c: cls al)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (modifies (loc_unused_in c h `loc_union` l) h h'))\n (ensures (modifies l h h'))", "let modifies_refl #al #c s h =\n Classical.forall_intro_3 (fun r a b -> c.aloc_preserved_refl #r #a b h)", "let modifies_loc_includes #al #c s1 h h' s2 =\n assert (modifies_preserves_mreferences s1 h h');\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c);\n Classical.forall_intro_3 (fun l1 l2 l3 -> Classical.move_requires (loc_aux_disjoint_loc_aux_includes #al #c l1 l2) l3);\n assert (modifies_preserves_alocs s1 h h')", "let modifies_only_live_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_addresses false r a) l) h h' /\\\n (forall x . Set.mem x a ==> h `does_not_contain_addr` (r, x))\n ))\n (ensures (modifies l h h'))\n= loc_addresses_unused_in c r a h;\n loc_includes_refl l;\n loc_includes_union_l (loc_unused_in c h) l l;\n loc_includes_union_l (loc_unused_in c h) l (loc_addresses false r a);\n loc_includes_union_r (loc_union (loc_unused_in c h) l) (loc_addresses false r a) l;\n modifies_loc_includes (loc_union (loc_unused_in c h) l) h h' (loc_union (loc_addresses false r a) l);\n modifies_only_not_unused_in l h h'", "let modifies_preserves_liveness #al #c s1 s2 h h' #t #pre r = ()", "let modifies_preserves_liveness_strong #al #c s1 s2 h h' #t #pre r x =\n let rg = HS.frameOf r in\n let ad = HS.as_addr r in\n let la = loc_of_aloc #_ #c #rg #ad x in\n if Set.mem rg (regions_of_loc s2)\n then begin\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` Loc?.non_live_addrs (address_liveness_insensitive_locs c) rg);\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` GSet.empty);\n assert (~ (GSet.mem ad (Loc?.non_live_addrs s2 rg)));\n if Set.mem rg (regions_of_loc s1)\n then begin\n if GSet.mem ad (Loc?.non_live_addrs s1 rg)\n then begin\n assert (loc_disjoint_aux s1 la);\n assert (GSet.subset (Loc?.non_live_addrs s1 rg) (Loc?.live_addrs s1 rg));\n assert (aloc_domain c (Loc?.regions s1) (Loc?.live_addrs s1) `GSet.subset` (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad None) (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad (Some x)) (Ghost.reveal (Loc?.aux la)));\n assert (aloc_disjoint (ALoc rg ad None) (ALoc #_ #c rg ad (Some x)));\n ()\n end else ()\n end else ()\n end else ()", "val mreference_live_loc_not_unused_in\n (#al: aloc_t)\n (c: cls al)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (h: HS.mem)\n (r: HS.mreference t pre)\n: Lemma\n (requires (h `HS.contains` r))\n (ensures (loc_not_unused_in c h `loc_includes` loc_freed_mreference r /\\ loc_not_unused_in c h `loc_includes` loc_mreference r))", "let modifies_preserves_region_liveness #al #c l1 l2 h h' r = ()", "let modifies_preserves_region_liveness_reference #al #c l1 l2 h h' #t #pre r = ()", "val mreference_unused_in_loc_unused_in\n (#al: aloc_t)\n (c: cls al)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (h: HS.mem)\n (r: HS.mreference t pre)\n: Lemma\n (requires (r `HS.unused_in` h))\n (ensures (loc_unused_in c h `loc_includes` loc_freed_mreference r /\\ loc_unused_in c h `loc_includes` loc_mreference r))", "let modifies_preserves_region_liveness_aloc #al #c l1 l2 h h' #r #n x =\n if Set.mem r (Ghost.reveal (Loc?.region_liveness_tags l1))\n then begin\n assert (GSet.subset (GSet.complement GSet.empty) (Loc?.non_live_addrs l1 r));\n assert (GSet.subset (Loc?.non_live_addrs l1 r) (Loc?.live_addrs l1 r))\n end else ()", "let modifies_trans'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s h1 h2 /\\ modifies s h2 h3))\n (ensures (modifies s h1 h3))\n= Classical.forall_intro_3 (fun r a b -> Classical.move_requires (c.aloc_preserved_trans #r #a b h1 h2) h3)", "val aloc_union: (bool -> Tot (aloc_t u#x)) -> Tot (aloc_t u#x)", "val cls_union (#a: (bool -> Tot aloc_t)) (c: ((b: bool) -> Tot (cls (a b)))) : Tot (cls (aloc_union a))", "let modifies_trans #al #c s12 h1 h2 s23 h3 =\n let u = loc_union s12 s23 in\n modifies_loc_includes u h1 h2 s12;\n modifies_loc_includes u h2 h3 s23;\n modifies_trans' u h1 h2 h3", "val union_loc_of_loc (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b))) (b: bool) (l: loc (c b)) : GTot (loc (cls_union c))", "val union_loc_of_loc_none\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n: Lemma\n (union_loc_of_loc c b (loc_none #_ #(c b)) == loc_none #_ #(cls_union c))", "let addr_unused_in_aloc_preserved\n (#al: aloc_t) (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (b: al r a)\n (h1: HS.mem)\n (h2: HS.mem)\n : Lemma\n (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)))\n (ensures (c.aloc_preserved b h1 h2))\n= c.same_mreference_aloc_preserved b h1 h2 (fun a' pre r' -> assert False)", "val union_loc_of_loc_union\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (l1 l2: loc (c b))\n: Lemma\n (union_loc_of_loc c b (loc_union #_ #(c b) l1 l2) == loc_union #_ #(cls_union c) (union_loc_of_loc c b l1) (union_loc_of_loc c b l2))", "val union_loc_of_loc_addresses\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (union_loc_of_loc c b (loc_addresses #_ #(c b) preserve_liveness r n) == loc_addresses #_ #(cls_union c) preserve_liveness r n)", "let modifies_only_live_regions_weak\n (#al: aloc_t) (#c: cls al)\n (rs: Set.set HS.rid)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n loc_disjoint (loc_regions false rs) l /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))\n= assert (modifies_preserves_mreferences l h h'); // FIXME: WHY WHY WHY?\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (addr_unused_in_aloc_preserved #al #c #r #a b h) h')", "val union_loc_of_loc_regions\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: Lemma\n (union_loc_of_loc c b (loc_regions #_ #(c b) preserve_liveness r) == loc_regions #_ #(cls_union c) preserve_liveness r)", "val union_loc_of_loc_includes\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (s1 s2: loc (c b))\n: Lemma\n (union_loc_of_loc c b s1 `loc_includes` union_loc_of_loc c b s2 <==> s1 `loc_includes` s2)", "let restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: GTot (loc c)\n= let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let regions' = (Ghost.hide (Set.intersect (Ghost.reveal regions) rs)) in\n Loc\n regions'\n (Ghost.hide (Set.intersect (Ghost.reveal region_liveness_tags) rs))\n (mk_non_live_addrs (fun (r: addrs_dom regions') -> (non_live_addrs r <: GSet.set nat)))\n (mk_live_addrs (fun (r: addrs_dom regions') -> (live_addrs r <: GSet.set nat)))\n (Ghost.hide (GSet.intersect (Ghost.reveal aux) (aloc_domain c (Ghost.hide rs) (fun r -> GSet.complement GSet.empty))))", "val union_loc_of_loc_disjoint\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (s1 s2: loc (c b))\n: Lemma\n (union_loc_of_loc c b s1 `loc_disjoint` union_loc_of_loc c b s2 <==> s1 `loc_disjoint` s2)", "val modifies_union_loc_of_loc\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (l: loc (c b))\n (h1 h2: HS.mem)\n: Lemma\n (modifies #_ #(cls_union c) (union_loc_of_loc c b l) h1 h2 <==> modifies #_ #(c b) l h1 h2)", "let regions_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (regions_of_loc (restrict_to_regions l rs) == Set.intersect (regions_of_loc l) rs)\n [SMTPat (regions_of_loc (restrict_to_regions l rs))]\n= assert (Set.equal (regions_of_loc (restrict_to_regions l rs)) (Set.intersect (regions_of_loc l) rs))", "val loc_of_union_loc\n (#al: (bool -> Tot aloc_t))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (cls_union c))\n: GTot (loc (c b))", "let addrs_of_loc_weak_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))\n [SMTPat (addrs_of_loc_weak (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc_weak (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))", "val loc_of_union_loc_union_loc_of_loc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: loc (c b))\n: Lemma\n (loc_of_union_loc b (union_loc_of_loc c b s) == s)", "val loc_of_union_loc_none\n (#al: (bool -> Tot aloc_t))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n: Lemma\n (loc_of_union_loc #_ #c b loc_none == loc_none)", "let addrs_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc l r else GSet.empty))\n [SMTPat (addrs_of_loc (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc l r else GSet.empty))", "val loc_of_union_loc_union\n (#al: (bool -> Tot aloc_t))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l1 l2: loc (cls_union c))\n: Lemma\n (loc_of_union_loc b (l1 `loc_union` l2) == loc_of_union_loc b l1 `loc_union` loc_of_union_loc b l2)", "let loc_includes_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes l (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)", "val loc_of_union_loc_addresses\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (loc_of_union_loc #_ #c b (loc_addresses preserve_liveness r n) == loc_addresses preserve_liveness r n)", "let loc_includes_loc_union_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_equal (loc_union (restrict_to_regions l rs) (restrict_to_regions l (Set.complement rs))) l)\n= ()", "val loc_of_union_loc_regions\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: Lemma\n (loc_of_union_loc #_ #c b (loc_regions preserve_liveness r) == loc_regions preserve_liveness r)", "let loc_includes_loc_regions_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes (loc_regions false rs) (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)", "let modifies_only_live_regions #al #c rs l h h' =\n let s = l in\n let c_rs = Set.complement rs in\n let s_rs = restrict_to_regions s rs in\n let s_c_rs = restrict_to_regions s c_rs in\n let lrs = loc_regions false rs in\n loc_includes_loc_regions_restrict_to_regions s rs;\n loc_includes_union_l lrs s_c_rs s_rs;\n loc_includes_refl s_c_rs;\n loc_includes_union_l lrs s_c_rs s_c_rs;\n loc_includes_union_r (loc_union lrs s_c_rs) s_rs s_c_rs;\n loc_includes_loc_union_restrict_to_regions s rs;\n loc_includes_trans (loc_union lrs s_c_rs) (loc_union s_rs s_c_rs) s;\n modifies_loc_includes (loc_union lrs s_c_rs) h h' (loc_union lrs s);\n loc_includes_loc_regions_restrict_to_regions s c_rs;\n loc_disjoint_regions #al #c false false rs c_rs;\n loc_includes_refl lrs;\n loc_disjoint_includes lrs (loc_regions false c_rs) lrs s_c_rs;\n modifies_only_live_regions_weak rs s_c_rs h h';\n loc_includes_restrict_to_regions s c_rs;\n modifies_loc_includes s h h' s_c_rs", "val raise_aloc (al: aloc_t u#x) : Tot (aloc_t u#(max x (y + 1)))", "val raise_cls (#al: aloc_t u#x) (c: cls al) : Tot (cls (raise_aloc u#x u#y al))", "val raise_loc (#al: aloc_t u#x) (#c: cls al) (l: loc c) : Tot (loc (raise_cls u#x u#y c))", "val raise_loc_none (#al: aloc_t u#x) (#c: cls al) : Lemma\n (raise_loc u#x u#y (loc_none #_ #c) == loc_none)", "val raise_loc_union (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc c) : Lemma\n (raise_loc u#x u#y (loc_union l1 l2) == loc_union (raise_loc l1) (raise_loc l2))", "val raise_loc_addresses (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: HS.rid) (a: Set.set nat) : Lemma\n (raise_loc u#x u#y (loc_addresses #_ #c preserve_liveness r a) == loc_addresses preserve_liveness r a)", "val raise_loc_regions (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: Set.set HS.rid) : Lemma\n (raise_loc u#x u#y (loc_regions #_ #c preserve_liveness r) == loc_regions preserve_liveness r)", "val raise_loc_includes (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc c) : Lemma\n (loc_includes (raise_loc u#x u#y l1) (raise_loc l2) <==> loc_includes l1 l2)", "val raise_loc_disjoint (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc c) : Lemma\n (loc_disjoint (raise_loc u#x u#y l1) (raise_loc l2) <==> loc_disjoint l1 l2)", "let no_upd_fresh_region #al #c r l h0 h1 =\n modifies_only_live_regions (HS.mod_set (Set.singleton r)) l h0 h1", "val modifies_raise_loc (#al: aloc_t u#x) (#c: cls al) (l: loc c) (h1 h2: HS.mem) : Lemma\n (modifies (raise_loc u#x u#y l) h1 h2 <==> modifies l h1 h2)", "let fresh_frame_modifies #al c h0 h1 =\n modifies_intro_strong #_ #c loc_none h0 h1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x h0 h1 (fun _ _ _ -> ()))", "val lower_loc (#al: aloc_t u#x) (#c: cls al) (l: loc (raise_cls u#x u#y c)) : Tot (loc c)", "val lower_loc_raise_loc (#al: aloc_t u#x) (#c: cls al) (l: loc c) : Lemma\n (lower_loc (raise_loc u#x u#y l) == l)", "val raise_loc_lower_loc (#al: aloc_t u#x) (#c: cls al) (l: loc (raise_cls u#x u#y c)) : Lemma\n (raise_loc (lower_loc l) == l)", "let new_region_modifies #al c m0 r0 col\n= let (_, m1) = HS.new_eternal_region m0 r0 col in\n modifies_intro_strong #_ #c loc_none m0 m1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x m0 m1 (fun _ _ _ -> ()))", "val lower_loc_none (#al: aloc_t u#x) (#c: cls al) : Lemma\n (lower_loc u#x u#y #_ #c loc_none == loc_none)", "val lower_loc_union (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc (raise_cls u#x u#y c)) : Lemma\n (lower_loc u#x u#y (loc_union l1 l2) == loc_union (lower_loc l1) (lower_loc l2))", "val lower_loc_addresses (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: HS.rid) (a: Set.set nat) : Lemma\n (lower_loc u#x u#y #_ #c (loc_addresses preserve_liveness r a) == loc_addresses preserve_liveness r a)", "let popped_modifies #al c h0 h1 =\n let l = loc_region_only #_ #c false (HS.get_tip h0) in\n modifies_preserves_mreferences_intro l h0 h1 (fun t pre p ->\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l );\n // FIXME: WHY WHY WHY is this assert necessary?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n ()\n );\n modifies_preserves_alocs_intro l h0 h1 () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n ()\n )", "val lower_loc_regions (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: Set.set HS.rid) : Lemma\n (lower_loc u#x u#y #_ #c (loc_regions preserve_liveness r) == loc_regions preserve_liveness r)", "let modifies_fresh_frame_popped #al #c h0 h1 s h2 h3 =\n fresh_frame_modifies c h0 h1;\n let r = loc_region_only #al #c false (HS.get_tip h2) in\n let rs = HS.mod_set (Set.singleton (HS.get_tip h1)) in\n let s' = loc_union (loc_regions false rs) s in\n modifies_trans' s' h0 h1 h2;\n assert (modifies_preserves_mreferences r h2 h3);\n let f23 (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (r <> HS.get_tip h2))\n (ensures (c.aloc_preserved b h2 h3))\n = c.same_mreference_aloc_preserved #r #a b h2 h3 (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro r h2 h3 () (fun r a b ->\n f23 r a b\n );\n modifies_trans' s' h0 h2 h3;\n modifies_only_live_regions rs s h0 h3", "let modifies_loc_regions_intro #al #c rs h1 h2 =\n let f (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem r rs)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n assert (modifies_preserves_mreferences (loc_regions #al #c true rs) h1 h2);\n modifies_preserves_alocs_intro (loc_regions #_ #c true rs) h1 h2 () (fun r a b ->\n f r a b\n )", "let modifies_loc_addresses_intro_weak\n (#al: aloc_t) (#c: cls al)\n (r: HS.rid)\n (s: Set.set nat)\n (l: loc c)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r s h1 h2 /\\\n loc_disjoint l (loc_region_only false r)\n ))\n (ensures (modifies (loc_union (loc_addresses true r s) l) h1 h2))\n= modifies_preserves_mreferences_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_livenesses_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_not_unused_in_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' n' ->\n ()\n );\n let f (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem a s)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r_ -> ())\n in\n modifies_preserves_alocs_intro (loc_union (loc_addresses true r s) l) h1 h2 () (fun r' a b -> if r = r' then f a b else ()\n )", "let modifies_loc_addresses_intro #al #c r s l h1 h2 =\n loc_includes_loc_regions_restrict_to_regions l (Set.singleton r);\n loc_includes_loc_union_restrict_to_regions l (Set.singleton r);\n assert (modifies (loc_union (loc_region_only false r) (loc_union (restrict_to_regions l (Set.singleton r)) (restrict_to_regions l (Set.complement (Set.singleton r))))) h1 h2);\n let l' = restrict_to_regions l (Set.complement (Set.singleton r)) in\n loc_includes_refl (loc_region_only #_ #c false r) ;\n loc_includes_loc_regions_restrict_to_regions l (Set.complement (Set.singleton r));\n loc_disjoint_regions #_ #c false false (Set.complement (Set.singleton r)) (Set.singleton r);\n loc_disjoint_includes (loc_regions #_ #c false (Set.complement (Set.singleton r))) (loc_region_only false r) l' (loc_region_only false r);\n modifies_loc_addresses_intro_weak r s l' h1 h2;\n loc_includes_restrict_to_regions l (Set.complement (Set.singleton r))", "let modifies_ralloc_post #al #c #a #rel i init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g", "let modifies_salloc_post #al #c #a #rel init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g", "let modifies_free #al #c #a #rel r m =\n let g (r': HS.rid) (a: nat) (b: al r' a) : Lemma\n (requires (r' <> HS.frameOf r \\/ a <> HS.as_addr r))\n (ensures (c.aloc_preserved b m (HS.free r m)))\n = c.same_mreference_aloc_preserved #r' #a b m (HS.free r m) (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro (loc_freed_mreference #_ #c r) m (HS.free r m) () (fun r a b -> g r a b)", "let modifies_none_modifies #al #c h1 h2\n= let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h1 h2)\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g", "let modifies_upd #al #c #t #pre r v h =\n let h' = HS.upd h r v in\n modifies_intro #_ #c (loc_mreference r) h h'\n (fun r -> ())\n (fun t pre b -> ())\n (fun t pre b -> ())\n (fun r n -> ())\n (fun r a b -> c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre' r' -> ()))", "let addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l (loc_of_aloc al0)) r == addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)\n= assert (addrs_of_loc (loc_union l (loc_of_aloc al0)) r `GSet.equal` addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)", "let addrs_of_loc_weak_loc_includes #al (#c: cls al) (l: loc c) (r0: HS.rid) (a0: nat) : Lemma\n (requires (a0 `GSet.mem` addrs_of_loc_weak l r0))\n (ensures (l `loc_includes` loc_addresses true r0 (Set.singleton a0)))\n= ()", "val modifies_strengthen'\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (h h' : HS.mem)\n (alocs: (\n (f: ((t: Type) -> (pre: Preorder.preorder t) -> (m: HS.mreference t pre) -> Lemma\n (requires (HS.frameOf m == r0 /\\ HS.as_addr m == a0 /\\ HS.contains h m))\n (ensures (HS.contains h' m))\n )) ->\n (x: al r0 a0) ->\n Lemma\n (requires (c.aloc_disjoint x al0 /\\ loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (requires ((~ (a0 `GSet.mem` addrs_of_loc_weak l r0)) /\\ modifies (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h'))\n (ensures (modifies (loc_union l (loc_of_aloc al0)) h h'))", "let modifies_strengthen' #al #c l #r0 #a0 al0 h h' alocs =\n Classical.forall_intro (addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton l al0);\n assert (modifies_preserves_regions (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_mreferences (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_not_unused_in (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_livenesses (loc_union l (loc_of_aloc al0)) h h');\n modifies_preserves_alocs_intro (loc_union l (loc_of_aloc al0)) h h' () (fun r a b ->\n if r = r0 && a = a0\n then begin\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_union l (loc_of_aloc al0)))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux l)) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_disjoint l (loc_of_aloc b));\n loc_disjoint_sym l (loc_of_aloc b);\n assert (loc_aux_disjoint #_ #c (Ghost.reveal (Loc?.aux (loc_of_aloc al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint #_ #c (GSet.singleton (ALoc r0 a0 (Some al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (GSet.mem (ALoc r0 a0 (Some al0)) (GSet.singleton (ALoc #_ #c r0 a0 (Some al0))));\n assert (GSet.mem (ALoc r0 a0 (Some b)) (GSet.singleton (ALoc #_ #c r0 a0 (Some b))));\n assert (aloc_disjoint #_ #c (ALoc r0 a0 (Some al0)) (ALoc r0 a0 (Some b)));\n assert (c.aloc_disjoint al0 b);\n c.aloc_disjoint_sym al0 b;\n alocs (fun t pre m -> ()) b\n end\n else begin\n assert (loc_disjoint (loc_union l (loc_addresses true r0 (Set.singleton a0))) (loc_of_aloc b))\n by (let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 64;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=5'\";\n ())\n end\n );\n assert (modifies (loc_union l (loc_of_aloc al0)) h h')", "let modifies_strengthen #al #c l #r0 #a0 al0 h h' alocs =\n if a0 `GSet.mem` addrs_of_loc_weak l r0\n then begin\n addrs_of_loc_weak_loc_includes l r0 a0;\n loc_includes_refl l;\n loc_includes_union_r l l (loc_addresses true r0 (Set.singleton a0));\n loc_includes_union_l l (loc_of_aloc al0) l;\n loc_includes_trans (loc_union l (loc_of_aloc al0)) l (loc_union l (loc_addresses true r0 (Set.singleton a0)));\n modifies_loc_includes (loc_union l (loc_of_aloc al0)) h h' (loc_union l (loc_addresses true r0 (Set.singleton a0)))\n end\n else\n modifies_strengthen' l al0 h h' alocs", "let does_not_contain_addr' (h: HS.mem) (ra: HS.rid * nat) : GTot Type0 =\n HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))", "let does_not_contain_addr = does_not_contain_addr'", "let not_live_region_does_not_contain_addr h ra = ()", "let unused_in_does_not_contain_addr h #a #rel r = ()", "let addr_unused_in_does_not_contain_addr h ra = ()", "let does_not_contain_addr_addr_unused_in h ra = ()", "let free_does_not_contain_addr #a #rel r m x = ()", "let does_not_contain_addr_elim #a #rel r m x = ()", "let disjoint_addrs_of_loc_loc_disjoint\n (#al: aloc_t)\n (#c: cls al)\n (l1 l2: loc c)\n: Lemma\n (requires (\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty /\\\n (forall r . GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc l2 r)) GSet.empty)\n ))\n (ensures (loc_disjoint l1 l2))\n= // FIXME: WHY WHY WHY do I need this assert?\n let l1' = Ghost.reveal (Loc?.aux l1) in\n let l2' = Ghost.reveal (Loc?.aux l2) in\n assert (forall (b1 b2: aloc c) . (GSet.mem b1 l1' /\\ GSet.mem b2 l2') ==> aloc_disjoint b1 b2)", "let loc_not_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (HS.live_region h r /\\ ~ (h `does_not_contain_addr` (r, a))))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs f)\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))", "let loc_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n if not (HS.live_region h r)\n then\n GSet.complement GSet.empty\n else\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a)))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide (Set.complement (FStar.Map.domain (HS.get_hmap h))))\n (mk_non_live_addrs (fun x -> f x))\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))", "let loc_regions_unused_in #al c h rs = ()", "let loc_addresses_unused_in #al c r a h = ()", "let loc_addresses_not_unused_in #al c r a h = ()", "let loc_unused_in_not_unused_in_disjoint #al c h =\n assert (Ghost.reveal (Loc?.aux (loc_unused_in c h)) `loc_aux_disjoint` Ghost.reveal (Loc?.aux (loc_not_unused_in c h)));\n assert_spinoff (loc_disjoint #al #c (loc_unused_in #al c h)\n (loc_not_unused_in #al c h))", "let not_live_region_loc_not_unused_in_disjoint #al c h0 r\n= let l1 = loc_region_only false r in\n let l2 = loc_not_unused_in c h0 in\n assert (loc_disjoint_region_liveness_tags l1 l2);\n assert (loc_disjoint_addrs l1 l2);\n assert (loc_disjoint_aux l1 l2)", "let modifies_address_liveness_insensitive_unused_in #al c h h' =\n assert (forall r . HS.live_region h r ==> HS.live_region h' r) ;\n let ln' = loc_not_unused_in c h' in\n let ln = loc_not_unused_in c h in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs ln r `GSet.subset` Loc?.non_live_addrs ln' r);\n assert (ln' `loc_includes` ln);\n let lu = loc_unused_in c h in\n let lu' = loc_unused_in c h' in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs lu' r `GSet.subset` Loc?.non_live_addrs lu r);\n assert (forall (r: HS.rid) . Loc?.live_addrs lu' r `GSet.subset` Loc?.live_addrs lu r);\n assert (lu `loc_includes` lu')", "let modifies_only_not_unused_in #al #c l h h' =\n assert (modifies_preserves_regions l h h');\n assert (modifies_preserves_not_unused_in l h h');\n assert (modifies_preserves_mreferences l h h');\n assert (modifies_preserves_livenesses l h h');\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n if StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a))\n then c.same_mreference_aloc_preserved b h h' (fun a' pre' r' -> ())\n else ()\n )", "let mreference_live_loc_not_unused_in #al c #t #pre h b =\n Classical.move_requires (does_not_contain_addr_addr_unused_in h) (HS.frameOf b, HS.as_addr b);\n assert (~ (h `does_not_contain_addr` (HS.frameOf b, HS.as_addr b)));\n loc_addresses_not_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_trans (loc_not_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()", "let mreference_unused_in_loc_unused_in #al c #t #pre h b =\n Classical.move_requires (addr_unused_in_does_not_contain_addr h) (HS.frameOf b, HS.as_addr b);\n loc_addresses_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_addresses_addresses c false true (HS.frameOf b) (Set.singleton (HS.as_addr b)) (Set.singleton (HS.as_addr b));\n loc_includes_trans (loc_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()", "cls_union_aloc", "ALOC_FALSE", "ALOC_FALSE", "ALOC_FALSE", "ALOC_TRUE", "ALOC_TRUE", "ALOC_TRUE", "let bool_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot bool =\n match l with\n | ALOC_FALSE _ -> false\n | ALOC_TRUE _ -> true", "let aloc_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot ((al (bool_of_cls_union_aloc l)) r n)\n= match l with\n | ALOC_FALSE x -> x\n | ALOC_TRUE x -> x", "let make_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (b: bool)\n (#r: HS.rid)\n (#n: nat)\n (l: (al b) r n)\n: Tot (cls_union_aloc al r n)\n= if b\n then ALOC_TRUE l\n else ALOC_FALSE l", "let cls_union_aloc_includes\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_includes\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)", "let cls_union_aloc_disjoint\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_disjoint\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)", "let cls_union_aloc_preserved\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (x: cls_union_aloc al r a)\n (h h' : HS.mem)\n: GTot Type0\n= (c (bool_of_cls_union_aloc x)).aloc_preserved\n (aloc_of_cls_union_aloc x)\n h\n h'", "let aloc_union = cls_union_aloc", "let cls_union #al c = Cls\n #(cls_union_aloc al)\n (cls_union_aloc_includes c)\n (* aloc_includes_refl *)\n (fun #r #a x ->\n (c (bool_of_cls_union_aloc x)).aloc_includes_refl (aloc_of_cls_union_aloc x))\n (* aloc_includes_trans *)\n (fun #r #a x1 x2 x3 ->\n (c (bool_of_cls_union_aloc x1)).aloc_includes_trans\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n (aloc_of_cls_union_aloc x3)\n )\n (cls_union_aloc_disjoint c)\n (* aloc_disjoint_sym *)\n (fun #r #a x1 x2 ->\n if bool_of_cls_union_aloc x1 = bool_of_cls_union_aloc x2\n then\n (c (bool_of_cls_union_aloc x1)).aloc_disjoint_sym\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n else ()\n )\n (* aloc_disjoint_includes *)\n (fun #r #a larger1 larger2 smaller1 smaller2 ->\n (c (bool_of_cls_union_aloc larger1)).aloc_disjoint_includes\n (aloc_of_cls_union_aloc larger1)\n (aloc_of_cls_union_aloc larger2)\n (aloc_of_cls_union_aloc smaller1)\n (aloc_of_cls_union_aloc smaller2)\n )\n (cls_union_aloc_preserved c)\n (* aloc_preserved_refl *)\n (fun #r #a x h ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_refl\n (aloc_of_cls_union_aloc x)\n h\n )\n (* aloc_preserved_trans *)\n (fun #r #a x h1 h2 h3 ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_trans\n (aloc_of_cls_union_aloc x)\n h1\n h2\n h3\n )\n (* same_mreference_aloc_preserved *)\n (fun #r #a b h1 h2 f ->\n (c (bool_of_cls_union_aloc b)).same_mreference_aloc_preserved\n (aloc_of_cls_union_aloc b)\n h1\n h2\n f\n )", "let union_aux_of_aux_left_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n (x: aloc (cls_union c))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n b = bool_of_cls_union_aloc #al #region #addr loc &&\n GSet.mem (ALoc region addr (Some (aloc_of_cls_union_aloc #al #region #addr loc))) s", "let union_aux_of_aux_left\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n: Tot (GSet.set (aloc (cls_union c)))\n= GSet.comprehend (union_aux_of_aux_left_pred c b s)", "let union_loc_of_loc #al c b l =\n let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let aux' : GSet.set (aloc #(cls_union_aloc al) (cls_union c)) =\n union_aux_of_aux_left c b (Ghost.reveal aux)\n `GSet.union`\n (aloc_domain (cls_union c) regions live_addrs)\n in\n Loc\n #(cls_union_aloc al)\n #(cls_union c)\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide aux')", "let union_aux_of_aux_left_inv_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n (x: aloc (c b))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n GSet.mem (ALoc region addr (Some (make_cls_union_aloc b loc))) s", "let union_aux_of_aux_left_inv\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n: Tot (GSet.set (aloc (c b)))\n= GSet.comprehend (union_aux_of_aux_left_inv_pred b s)", "let mem_union_aux_of_aux_left_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (c b))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x aux <==> GSet.mem (ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc)))) (union_aux_of_aux_left c b aux))\n [SMTPat (GSet.mem x aux)]\n= ()", "let mem_union_aux_of_aux_left_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (cls_union c))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x (union_aux_of_aux_left c b aux) <==> (if None? x.loc then GSet.mem (ALoc x.region x.addr None) aux else (bool_of_cls_union_aloc (Some?.v x.loc) == b /\\ GSet.mem (ALoc x.region x.addr (Some (aloc_of_cls_union_aloc (Some?.v x.loc)))) aux)))\n [SMTPat (GSet.mem x (union_aux_of_aux_left #al c b aux))]\n= ()", "let addrs_of_loc_union_loc_of_loc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (union_loc_of_loc c b l) r `GSet.equal` addrs_of_loc l r)\n [SMTPat (addrs_of_loc (union_loc_of_loc #al c b l) r)]\n= ()", "let union_loc_of_loc_none #al c b =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_none #_ #(c b))) (loc_none #_ #(cls_union c)))", "let union_loc_of_loc_union #al c b l1 l2 =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_union #_ #(c b) l1 l2)) (loc_union #_ #(cls_union c) (union_loc_of_loc c b l1) (union_loc_of_loc c b l2)))", "let union_loc_of_loc_addresses #al c b preserve_liveness r n =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_addresses #_ #(c b) preserve_liveness r n)) (loc_addresses #_ #(cls_union c) preserve_liveness r n))", "let union_loc_of_loc_regions #al c b preserve_liveness r =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_regions #_ #(c b) preserve_liveness r)) (loc_regions #_ #(cls_union c) preserve_liveness r))" ], "closest": [ "val loc_includes_union_r_inv (a b c: Mod.loc)\n : Lemma (requires (Mod.loc_includes a (Mod.loc_union b c)))\n (ensures (Mod.loc_includes a b /\\ Mod.loc_includes a c))\nlet loc_includes_union_r_inv (a b c:Mod.loc) :\n Lemma\n (requires (Mod.loc_includes a (Mod.loc_union b c)))\n (ensures (Mod.loc_includes a b /\\ Mod.loc_includes a c)) =\n Mod.loc_includes_union_l b c b;\n Mod.loc_includes_trans a (Mod.loc_union b c) b;\n Mod.loc_includes_union_l b c c;\n Mod.loc_includes_trans a (Mod.loc_union b c) c", "val loc_includes_union (l1 l1' l: B.loc)\n : Lemma (requires B.(loc_includes l1 l1'))\n (ensures B.(loc_includes (loc_union l1 l) (loc_union l1' l)))\nlet loc_includes_union (l1 l1' l:B.loc)\n : Lemma (requires B.(loc_includes l1 l1'))\n (ensures B.(loc_includes (loc_union l1 l) (loc_union l1' l)))\n = let open B in\n loc_includes_union_l l1 l l1';\n loc_includes_union_l l1 l l;\n loc_includes_union_r (loc_union l1 l) l1' l", "val loc_includes_union_l\n (s1 s2 s: loc)\n: Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))\nlet loc_includes_union_l = MG.loc_includes_union_l", "val loc_includes_union_r\n (s s1 s2: loc)\n: Lemma\n (requires (loc_includes s s1 /\\ loc_includes s s2))\n (ensures (loc_includes s (loc_union s1 s2)))\nlet loc_includes_union_r = MG.loc_includes_union_r", "val loc_includes_union_l (s1 s2 s:loc) : Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))\nlet loc_includes_union_l s1 s2 s = M.loc_includes_union_l s1 s2 s", "val loc_includes_union_l (s1 s2 s:loc) : Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))\nlet loc_includes_union_l s1 s2 s = M.loc_includes_union_l s1 s2 s", "val loc_includes_union_r' (s s1 s2: loc)\n : Lemma (loc_includes s (loc_union s1 s2) <==> (loc_includes s s1 /\\ loc_includes s s2))\n [SMTPat (loc_includes s (loc_union s1 s2))]\nlet loc_includes_union_r'\n (s s1 s2: loc)\n: Lemma\n (loc_includes s (loc_union s1 s2) <==> (loc_includes s s1 /\\ loc_includes s s2))\n [SMTPat (loc_includes s (loc_union s1 s2))]\n= Classical.move_requires (loc_includes_union_r s s1) s2;\n Classical.move_requires (loc_includes_union_l s1 s2) s1;\n Classical.move_requires (loc_includes_union_l s1 s2) s2;\n Classical.move_requires (loc_includes_trans s (loc_union s1 s2)) s1;\n Classical.move_requires (loc_includes_trans s (loc_union s1 s2)) s2", "val loc_includes_region_union_assoc\n (l r: loc)\n (s1 s2: Set.set HH.rid)\n: Lemma\n (requires (loc_includes (loc_union l r)) (loc_regions (Set.intersect s2 (Set.complement s1))))\n (ensures (loc_includes (loc_union l (loc_union (loc_regions s1) r)) (loc_regions s2)))\n [SMTPat (loc_includes (loc_union l (loc_union (loc_regions s1) r)) (loc_regions s2))]\nlet loc_includes_region_union_assoc l r s1 s2 =\n loc_includes_trans (loc_union l (loc_union (loc_regions s1) r)) (loc_union (loc_regions s1) (loc_union l r)) (loc_regions s2)", "val loc_includes_union_l' (s1 s2 s: loc)\n : Lemma (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))\n [SMTPat (loc_includes (loc_union s1 s2) s)]\nlet loc_includes_union_l'\n (s1 s2 s: loc)\n : Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))\n [SMTPat (loc_includes (loc_union s1 s2) s)]\n = loc_includes_union_l s1 s2 s", "val loc_disjoint_includes_r (b1 b2 b2': loc)\n : Lemma (requires (loc_includes b2 b2' /\\ loc_disjoint b1 b2))\n (ensures (loc_disjoint b1 b2'))\n [SMTPat (loc_disjoint b1 b2'); SMTPat (loc_includes b2 b2')]\nlet loc_disjoint_includes_r (b1 : loc) (b2 b2': loc) : Lemma\n (requires (loc_includes b2 b2' /\\ loc_disjoint b1 b2))\n (ensures (loc_disjoint b1 b2'))\n [SMTPat (loc_disjoint b1 b2'); SMTPat (loc_includes b2 b2')]\n= loc_disjoint_includes b1 b2 b1 b2'", "val loc_includes_region_union_l\n (l: loc)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires (loc_includes l (loc_regions (Set.intersect s2 (Set.complement s1)))))\n (ensures (loc_includes (loc_union (loc_regions s1) l) (loc_regions s2)))\n [SMTPat (loc_includes (loc_union (loc_regions s1) l) (loc_regions s2))]\nlet loc_includes_region_union_l = MG.loc_includes_region_union_l false", "val loc_equiv_union_union_loc (a b c: Mod.loc)\n : Lemma (requires (loc_equiv b c))\n (ensures (loc_equiv (Mod.loc_union a b) (Mod.loc_union a c)))\n [SMTPat (loc_equiv (Mod.loc_union a b) (Mod.loc_union a c))]\nlet loc_equiv_union_union_loc (a b c:Mod.loc) :\n Lemma\n (requires (loc_equiv b c))\n (ensures (loc_equiv\n (Mod.loc_union a b)\n (Mod.loc_union a c)))\n [SMTPat (loc_equiv\n (Mod.loc_union a b)\n (Mod.loc_union a c))] =\n let incl = Mod.loc_includes in\n let u = Mod.loc_union in\n // assert (b `incl` c);\n Mod.loc_includes_union_l a b c;\n // assert ((a `u` b) `incl` c);\n Mod.loc_includes_union_l a b a;\n // assert ((a `u` b) `incl` a);\n // assert ((a `u` b) `incl` (a `u` c));\n Mod.loc_includes_union_l a c b;\n Mod.loc_includes_union_l a c a", "val loc_includes_union_l_regions (s1 s2: loc) (prf: bool) (r: Set.set HS.rid)\n : Lemma (requires (loc_includes s1 (loc_regions prf r) \\/ loc_includes s2 (loc_regions prf r)))\n (ensures (loc_includes (loc_union s1 s2) (loc_regions prf r)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_regions prf r))]\nlet loc_includes_union_l_regions\n (s1 s2: loc)\n (prf: bool)\n (r: Set.set HS.rid)\n: Lemma\n (requires (loc_includes s1 (loc_regions prf r) \\/ loc_includes s2 (loc_regions prf r)))\n (ensures (loc_includes (loc_union s1 s2) (loc_regions prf r)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_regions prf r))]\n= loc_includes_union_l s1 s2 (loc_regions prf r)", "val loc_includes_region_union_r\n (l: loc)\n (s1 s2: Set.set HH.rid)\n: Lemma\n (requires (loc_includes l (loc_regions (Set.intersect s2 (Set.complement s1)))))\n (ensures (loc_includes (loc_union l (loc_regions s1)) (loc_regions s2)))\n [SMTPat (loc_includes (loc_union l (loc_regions s1)) (loc_regions s2))]\nlet loc_includes_region_union_r l s1 s2 =\n loc_includes_trans (loc_union l (loc_regions s1)) (loc_union (loc_regions s1) l) (loc_regions s2)", "val loc_includes_union_r\n (s s1 s2: loc)\n: Lemma\n (requires (loc_includes s s1 /\\ loc_includes s s2))\n (ensures (loc_includes s (loc_union s1 s2)))\n [SMTPat (loc_includes s (loc_union s1 s2))]\nlet loc_includes_union_r = MG.loc_includes_union_r", "val loc_includes_union_r\n (s s1 s2: loc)\n: Lemma\n (requires (loc_includes s s1 /\\ loc_includes s s2))\n (ensures (loc_includes s (loc_union s1 s2)))\n [SMTPat (loc_includes s (loc_union s1 s2))]\nlet loc_includes_union_r = MG.loc_includes_union_r", "val loc_includes_union_l_footprint_s\n (#index: _)\n (c: block index)\n (i: index)\n (m: HS.mem)\n (l1 l2: B.loc)\n (s: state_s' c i)\n : Lemma\n (requires (B.loc_includes l1 (footprint_s c i m s) \\/ B.loc_includes l2 (footprint_s c i m s))\n )\n (ensures (B.loc_includes (B.loc_union l1 l2) (footprint_s c i m s)))\n [SMTPat (B.loc_includes (B.loc_union l1 l2) (footprint_s c i m s))]\nlet loc_includes_union_l_footprint_s\n #index\n (c: block index)\n (i: index)\n (m: HS.mem)\n (l1 l2: B.loc) (s: state_s' c i)\n: Lemma\n (requires (\n B.loc_includes l1 (footprint_s c i m s) \\/ B.loc_includes l2 (footprint_s c i m s)\n ))\n (ensures (B.loc_includes (B.loc_union l1 l2) (footprint_s c i m s)))\n [SMTPat (B.loc_includes (B.loc_union l1 l2) (footprint_s c i m s))]\n= B.loc_includes_union_l l1 l2 (footprint_s c i m s)", "val loc_includes_union_l\n (s1 s2 s: loc)\n: Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))\n [SMTPat (loc_includes (loc_union s1 s2) s)]\nlet loc_includes_union_l = MG.loc_includes_union_l", "val loc_includes_union_l\n (s1 s2 s: loc)\n: Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))\n [SMTPat (loc_includes (loc_union s1 s2) s)]\nlet loc_includes_union_l = MG.loc_includes_union_l", "val loc_includes_union_l_addresses (s1 s2: loc) (prf: bool) (r: HS.rid) (a: Set.set nat)\n : Lemma\n (requires (loc_includes s1 (loc_addresses prf r a) \\/ loc_includes s2 (loc_addresses prf r a))\n )\n (ensures (loc_includes (loc_union s1 s2) (loc_addresses prf r a)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_addresses prf r a))]\nlet loc_includes_union_l_addresses\n (s1 s2: loc)\n (prf: bool)\n (r: HS.rid)\n (a: Set.set nat)\n: Lemma\n (requires (loc_includes s1 (loc_addresses prf r a) \\/ loc_includes s2 (loc_addresses prf r a)))\n (ensures (loc_includes (loc_union s1 s2) (loc_addresses prf r a)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_addresses prf r a))]\n= loc_includes_union_l s1 s2 (loc_addresses prf r a)", "val loc_includes_union_r (s s1 s2:loc) : Lemma\n (requires (loc_includes s s1 /\\ loc_includes s s2))\n (ensures (loc_includes s (loc_union s1 s2)))\n [SMTPat (loc_includes s (loc_union s1 s2))]\nlet loc_includes_union_r s s1 s2 = M.loc_includes_union_r s s1 s2", "val loc_includes_union_r (s s1 s2:loc) : Lemma\n (requires (loc_includes s s1 /\\ loc_includes s s2))\n (ensures (loc_includes s (loc_union s1 s2)))\n [SMTPat (loc_includes s (loc_union s1 s2))]\nlet loc_includes_union_r s s1 s2 = M.loc_includes_union_r s s1 s2", "val loc_includes_region_union_l\n (preserve_liveness: bool)\n (l: loc)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires (loc_includes l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)))))\n (ensures (loc_includes (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness s2)))\n [SMTPat (loc_includes (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness s2))]\nlet loc_includes_region_union_l = MG.loc_includes_region_union_l", "val loc_includes_region_union_l\n (preserve_liveness: bool)\n (l: loc)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires (loc_includes l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)))))\n (ensures (loc_includes (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness s2)))\n [SMTPat (loc_includes (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness s2))]\nlet loc_includes_region_union_l = MG.loc_includes_region_union_l", "val loc_aux_includes_trans' (s1 s2 s3: loc_aux)\n : Lemma ((loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3) ==> loc_aux_includes s1 s3)\nlet loc_aux_includes_trans'\n (s1 s2: loc_aux)\n (s3: loc_aux)\n: Lemma\n ((loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3) ==> loc_aux_includes s1 s3)\n= Classical.move_requires (loc_aux_includes_trans s1 s2) s3", "val loc_aux_includes_trans' (s1 s2 s3: loc_aux)\n : Lemma ((loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3) ==> loc_aux_includes s1 s3)\nlet loc_aux_includes_trans'\n (s1 s2: loc_aux)\n (s3: loc_aux)\n: Lemma\n ((loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3) ==> loc_aux_includes s1 s3)\n= Classical.move_requires (loc_aux_includes_trans s1 s2) s3", "val loc_aux_includes_trans (s1 s2 s3: loc_aux)\n : Lemma (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\nlet loc_aux_includes_trans\n (s1 s2: loc_aux)\n (s3: loc_aux)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\n= match s3 with\n | LocPointer p ->\n loc_aux_includes_loc_aux_includes_pointer s1 s2 p\n | LocBuffer b ->\n let f\n (i: UInt32.t)\n : Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b)))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_aux_includes_pointer s1 (gpointer_of_buffer_cell b i)))\n = loc_aux_includes_loc_aux_includes_pointer s1 s2 (gpointer_of_buffer_cell b i)\n in\n Classical.forall_intro (Classical.move_requires f)", "val loc_aux_includes_trans (s1 s2 s3: loc_aux)\n : Lemma (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\nlet loc_aux_includes_trans\n (s1 s2 s3: loc_aux)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\n= match s3 with\n | LocBuffer b -> loc_aux_includes_loc_aux_includes_buffer s1 s2 b", "val loc_union_assoc_4:\n a:loc -> b:loc -> c:loc -> d:loc ->\n Lemma (loc_union (loc_union a b) (loc_union c d) ==\n loc_union (loc_union a c) (loc_union b d))\nlet loc_union_assoc_4 a b c d =\n loc_union_assoc (loc_union a b) c d;\n loc_union_assoc a b c;\n loc_union_assoc a c b;\n loc_union_assoc (loc_union a c) b d", "val loc_includes_union_l_buffer (#t:base_typ) (s1 s2:loc) (b:buffer t) : Lemma\n (requires (loc_includes s1 (loc_buffer b) \\/ loc_includes s2 (loc_buffer b)))\n (ensures (loc_includes (loc_union s1 s2) (loc_buffer b)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_buffer b))]\nlet loc_includes_union_l_buffer #t s1 s2 b = M.loc_includes_union_l s1 s2 (loc_buffer b)", "val loc_includes_union_l_buffer (#t:base_typ) (s1 s2:loc) (b:buffer t) : Lemma\n (requires (loc_includes s1 (loc_buffer b) \\/ loc_includes s2 (loc_buffer b)))\n (ensures (loc_includes (loc_union s1 s2) (loc_buffer b)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_buffer b))]\nlet loc_includes_union_l_buffer #t s1 s2 b = M.loc_includes_union_l s1 s2 (loc_buffer b)", "val loc_includes_union_assoc_focalize_2\n (l x r1 r2 s: loc)\n: Lemma\n (requires (loc_includes (loc_union l (loc_union x (loc_union r1 r2))) s))\n (ensures (loc_includes (loc_union l (loc_union (loc_union x r1) r2)) s))\n [SMTPat (loc_includes (loc_union l (loc_union (loc_union x r1) r2)) s)]\nlet loc_includes_union_assoc_focalize_2 l x r1 r2 s =\n loc_includes_trans (loc_union l (loc_union (loc_union x r1) r2)) (loc_union l (loc_union x (loc_union r1 r2))) s", "val loc_includes_union_l_footprint_s (l1 l2: B.loc) (#a: alg) (s: state_s a)\n : Lemma (requires (B.loc_includes l1 (footprint_s s) \\/ B.loc_includes l2 (footprint_s s)))\n (ensures (B.loc_includes (B.loc_union l1 l2) (footprint_s s)))\n [SMTPat (B.loc_includes (B.loc_union l1 l2) (footprint_s s))]\nlet loc_includes_union_l_footprint_s\n (l1 l2: B.loc) (#a: alg) (s: state_s a)\n: Lemma\n (requires (\n B.loc_includes l1 (footprint_s s) \\/ B.loc_includes l2 (footprint_s s)\n ))\n (ensures (B.loc_includes (B.loc_union l1 l2) (footprint_s s)))\n [SMTPat (B.loc_includes (B.loc_union l1 l2) (footprint_s s))]\n= B.loc_includes_union_l l1 l2 (footprint_s s)", "val loc_includes_trans\n (s1 s2 s3: loc)\n: Lemma\n (requires (loc_includes s1 s2 /\\ loc_includes s2 s3))\n (ensures (loc_includes s1 s3))\nlet loc_includes_trans = MG.loc_includes_trans", "val loc_includes_trans\n (s1 s2 s3: loc)\n: Lemma\n (requires (loc_includes s1 s2 /\\ loc_includes s2 s3))\n (ensures (loc_includes s1 s3))\nlet loc_includes_trans = MG.loc_includes_trans", "val loc_includes_trans\n (s1 s2 s3: loc)\n: Lemma\n (requires (loc_includes s1 s2 /\\ loc_includes s2 s3))\n (ensures (loc_includes s1 s3))\nlet loc_includes_trans = MG.loc_includes_trans", "val loc_includes_union_l_buffer\n (s1 s2: loc)\n (#a: Type0)\n (#rrel #rel: srel a)\n (b: mbuffer a rrel rel)\n : Lemma (requires (loc_includes s1 (loc_buffer b) \\/ loc_includes s2 (loc_buffer b)))\n (ensures (loc_includes (loc_union s1 s2) (loc_buffer b)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_buffer b))]\nlet loc_includes_union_l_buffer\n (s1 s2:loc)\n (#a:Type0) (#rrel #rel:srel a)\n (b:mbuffer a rrel rel)\n :Lemma (requires (loc_includes s1 (loc_buffer b) \\/ loc_includes s2 (loc_buffer b)))\n (ensures (loc_includes (loc_union s1 s2) (loc_buffer b)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_buffer b))]\n = loc_includes_union_l s1 s2 (loc_buffer b)", "val loc_includes_union_assoc_r2l\n (s1 s2 s3 s: loc)\n: Lemma\n (requires (loc_includes (loc_union s1 (loc_union s2 s3)) s))\n (ensures (loc_includes (loc_union (loc_union s1 s2) s3) s))\n [SMTPat (loc_includes (loc_union (loc_union s1 s2) s3) s)]\nlet loc_includes_union_assoc_r2l s1 s2 s3 s =\n loc_includes_trans (loc_union (loc_union s1 s2) s3) (loc_union s1 (loc_union s2 s3)) s", "val loc_includes_union_l_footprint_s (m: HS.mem) (l1 l2: B.loc) (#a: index) (s: state_s a)\n : Lemma (requires (B.loc_includes l1 (footprint_s m s) \\/ B.loc_includes l2 (footprint_s m s)))\n (ensures (B.loc_includes (B.loc_union l1 l2) (footprint_s m s)))\n [SMTPat (B.loc_includes (B.loc_union l1 l2) (footprint_s m s))]\nlet loc_includes_union_l_footprint_s\n (m: HS.mem)\n (l1 l2: B.loc) (#a: index) (s: state_s a)\n: Lemma\n (requires (\n B.loc_includes l1 (footprint_s m s) \\/ B.loc_includes l2 (footprint_s m s)\n ))\n (ensures (B.loc_includes (B.loc_union l1 l2) (footprint_s m s)))\n [SMTPat (B.loc_includes (B.loc_union l1 l2) (footprint_s m s))]\n= B.loc_includes_union_l l1 l2 (footprint_s m s)", "val loc_includes_union_assoc_l2r\n (s1 s2 s3 s: loc)\n: Lemma\n (requires (loc_includes (loc_union (loc_union s1 s2) s3) s))\n (ensures (loc_includes (loc_union s1 (loc_union s2 s3)) s))\n [SMTPat (loc_includes (loc_union s1 (loc_union s2 s3)) s)]\nlet loc_includes_union_assoc_l2r s1 s2 s3 s =\n loc_includes_trans (loc_union s1 (loc_union s2 s3)) (loc_union (loc_union s1 s2) s3) s", "val loc_includes_as_seq (#a:Type0) (#rrel #rel1 #rel2:srel a)\n (h1 h2:HS.mem) (larger:mbuffer a rrel rel1) (smaller:mbuffer a rrel rel2)\n :Lemma (requires (loc_includes (loc_buffer larger) (loc_buffer smaller) /\\\n as_seq h1 larger == as_seq h2 larger /\\\n\t\t (live h1 larger \\/ live h1 smaller) /\\ (live h2 larger \\/ live h2 smaller)))\n (ensures (as_seq h1 smaller == as_seq h2 smaller))\nlet loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller =\n if Null? smaller then () else\n if Null? larger then begin\n MG.loc_includes_none_elim (loc_buffer smaller);\n MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller)\n end else begin\n MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller);\n let ul = Ghost.reveal (ubuffer_of_buffer larger) in\n let us = Ghost.reveal (ubuffer_of_buffer smaller) in\n assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller));\n assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller))\n end", "val loc_includes_union_l_piece_fp0 (#t: Type) (s1 s2: loc) (p: piece t)\n : Lemma (requires (loc_includes s1 (piece_fp0 p) \\/ loc_includes s2 (piece_fp0 p)))\n (ensures (loc_includes (loc_union s1 s2) (piece_fp0 p)))\n [SMTPat (loc_includes (loc_union s1 s2) (piece_fp0 p))]\nlet loc_includes_union_l_piece_fp0 (#t: Type) (s1 s2:loc) (p:piece t) :\n Lemma\n (requires (loc_includes s1 (piece_fp0 p) \\/ loc_includes s2 (piece_fp0 p)))\n (ensures (loc_includes (loc_union s1 s2) (piece_fp0 p)))\n [SMTPat (loc_includes (loc_union s1 s2) (piece_fp0 p))] =\n loc_includes_union_l s1 s2 (piece_fp0 p)", "val loc_includes_union_assoc_focalize_1\n (l1 l2 x r s: loc)\n: Lemma\n (requires (loc_includes (loc_union (loc_union l1 l2) (loc_union x r)) s))\n (ensures (loc_includes (loc_union l1 (loc_union (loc_union l2 x) r)) s))\n [SMTPat (loc_includes (loc_union l1 (loc_union (loc_union l2 x) r)) s)]\nlet loc_includes_union_assoc_focalize_1 l1 l2 x r s =\n loc_includes_trans (loc_union l1 (loc_union (loc_union l2 x) r)) (loc_union (loc_union l1 l2) (loc_union x r)) s", "val loc_includes_union_l_fragment_fp0 (#t: Type) (s1 s2: loc) (f: fragment t)\n : Lemma (requires (loc_includes s1 (fragment_fp0 f) \\/ loc_includes s2 (fragment_fp0 f)))\n (ensures (loc_includes (loc_union s1 s2) (fragment_fp0 f)))\n [SMTPat (loc_includes (loc_union s1 s2) (fragment_fp0 f))]\nlet loc_includes_union_l_fragment_fp0 (#t: Type) (s1 s2:loc) (f:fragment t) :\n Lemma\n (requires (loc_includes s1 (fragment_fp0 f) \\/ loc_includes s2 (fragment_fp0 f)))\n (ensures (loc_includes (loc_union s1 s2) (fragment_fp0 f)))\n [SMTPat (loc_includes (loc_union s1 s2) (fragment_fp0 f))] =\n loc_includes_union_l s1 s2 (fragment_fp0 f)", "val loc_includes_union_l_footprint_s (l1 l2: M.loc) (#a: alg) (s: state_s a)\n : Lemma (requires (M.loc_includes l1 (footprint_s s) \\/ M.loc_includes l2 (footprint_s s)))\n (ensures (M.loc_includes (M.loc_union l1 l2) (footprint_s s)))\n [SMTPat (M.loc_includes (M.loc_union l1 l2) (footprint_s s))]\nlet loc_includes_union_l_footprint_s\n (l1 l2: M.loc) (#a: alg) (s: state_s a)\n: Lemma\n (requires (\n M.loc_includes l1 (footprint_s s) \\/ M.loc_includes l2 (footprint_s s)\n ))\n (ensures (M.loc_includes (M.loc_union l1 l2) (footprint_s s)))\n [SMTPat (M.loc_includes (M.loc_union l1 l2) (footprint_s s))]\n= M.loc_includes_union_l l1 l2 (footprint_s s)", "val loc_aux_disjoint_loc_aux_includes (l1 l2 l3: loc_aux)\n : Lemma (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\nlet loc_aux_disjoint_loc_aux_includes\n (l1 l2 l3: loc_aux)\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\n= match l3 with\n | LocBuffer b3 ->\n loc_aux_disjoint_loc_aux_includes_buffer l1 l2 b3", "val loc_aux_disjoint_loc_aux_includes (l1 l2 l3: loc_aux)\n : Lemma (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\nlet loc_aux_disjoint_loc_aux_includes\n (l1 l2 l3: loc_aux)\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\n= match l3 with\n | LocPointer p3 ->\n loc_aux_disjoint_loc_aux_includes_pointer l1 l2 p3\n | LocBuffer b3 ->\n let f\n (i: UInt32.t)\n : Lemma\n (requires (\n UInt32.v i < UInt32.v (buffer_length b3)\n ))\n (ensures (\n UInt32.v i < UInt32.v (buffer_length b3) /\\\n loc_aux_disjoint_pointer l1 (gpointer_of_buffer_cell b3 i)\n ))\n = loc_aux_disjoint_loc_aux_includes_pointer l1 l2 (gpointer_of_buffer_cell b3 i)\n in\n Classical.forall_intro (Classical.move_requires f)", "val modifies_loc_includes\n (s1: loc)\n (h h': HS.mem)\n (s2: loc)\n: Lemma\n (requires (modifies s2 h h' /\\ loc_includes s1 s2))\n (ensures (modifies s1 h h'))\n [SMTPatOr [\n [SMTPat (modifies s1 h h'); SMTPat (modifies s2 h h')];\n [SMTPat (modifies s1 h h'); SMTPat (loc_includes s1 s2)];\n [SMTPat (modifies s2 h h'); SMTPat (loc_includes s1 s2)];\n ]]\nlet modifies_loc_includes = MG.modifies_loc_includes", "val loc_includes_union_l_footprint_s: #a:supported_alg -> l1:B.loc -> l2:B.loc -> st:state_s a\n -> Lemma\n (requires B.loc_includes l1 (footprint_s st) \\/ B.loc_includes l2 (footprint_s st))\n (ensures B.loc_includes (B.loc_union l1 l2) (footprint_s st))\n [SMTPat (B.loc_includes (B.loc_union l1 l2) (footprint_s st))]\nlet loc_includes_union_l_footprint_s #a l1 l2 st =\n B.loc_includes_union_l l1 l2 (footprint_s st)", "val loc_includes_trans (s1 s2 s3:loc) : Lemma\n (requires (loc_includes s1 s2 /\\ loc_includes s2 s3))\n (ensures (loc_includes s1 s3))\nlet loc_includes_trans s1 s2 s3 = M.loc_includes_trans s1 s2 s3", "val loc_includes_trans (s1 s2 s3:loc) : Lemma\n (requires (loc_includes s1 s2 /\\ loc_includes s2 s3))\n (ensures (loc_includes s1 s3))\nlet loc_includes_trans s1 s2 s3 = M.loc_includes_trans s1 s2 s3", "val loc_aux_includes_loc_aux_includes_pointer (s1 s2: loc_aux) (#t: typ) (p: pointer t)\n : Lemma (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_pointer s2 p))\n (ensures (loc_aux_includes_pointer s1 p))\nlet loc_aux_includes_loc_aux_includes_pointer\n (s1: loc_aux)\n (s2: loc_aux)\n (#t: typ)\n (p: pointer t)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_pointer s2 p))\n (ensures (loc_aux_includes_pointer s1 p))\n= match s2 with\n | LocPointer p' ->\n loc_aux_includes_pointer_trans s1 p' p\n | LocBuffer b ->\n let f\n (i: UInt32.t)\n : Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ gpointer_of_buffer_cell b i `includes` p))\n (ensures (loc_aux_includes_pointer s1 p))\n = loc_aux_includes_pointer_trans s1 (gpointer_of_buffer_cell b i) p\n in\n Classical.forall_intro (Classical.move_requires f)", "val buffer_includes_loc_includes\n (#t: typ)\n (b1 b2: buffer t)\n: Lemma\n (requires (buffer_includes b1 b2))\n (ensures (loc_includes (loc_buffer b1) (loc_buffer b2)))\n [SMTPatOr [\n [SMTPat (buffer_includes b1 b2)];\n [SMTPat (loc_includes(loc_buffer b1) (loc_buffer b2))]\n ]]\nlet buffer_includes_loc_includes #t b1 b2 =\n buffer_includes_elim b1 b2;\n loc_includes_refl (loc_buffer b1);\n loc_includes_gsub_buffer_r (loc_buffer b1) b1 (UInt32.sub (buffer_idx b2) (buffer_idx b1)) (buffer_length b2)", "val loc_aux_includes_loc_aux_includes_buffer (#a: Type) (s1 s2: loc_aux) (b: B.buffer a)\n : Lemma (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_buffer s2 b))\n (ensures (loc_aux_includes_buffer s1 b))\nlet loc_aux_includes_loc_aux_includes_buffer\n (#a: Type)\n (s1 s2: loc_aux)\n (b: B.buffer a)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_buffer s2 b))\n (ensures (loc_aux_includes_buffer s1 b))\n= match s2 with\n | LocBuffer b2 -> loc_aux_includes_buffer_includes s1 b2 b", "val modifies_loc_includes (s1:loc) (h h':vale_heap) (s2:loc) : Lemma\n (requires (modifies s2 h h' /\\ loc_includes s1 s2))\n (ensures (modifies s1 h h'))\nlet modifies_loc_includes s1 h h' s2 = M.modifies_loc_includes s1 (_ih h).hs (_ih h').hs s2", "val modifies_loc_includes (s1:loc) (h h':vale_heap) (s2:loc) : Lemma\n (requires (modifies s2 h h' /\\ loc_includes s1 s2))\n (ensures (modifies s1 h h'))\nlet modifies_loc_includes s1 h h' s2 = M.modifies_loc_includes s1 (_ih h).hs (_ih h').hs s2", "val loc_includes_loc_buffer_from_to\n (#a: _) (#rrel #rel: _)\n (b: mbuffer a rrel rel)\n (from1 to1 from2 to2: U32.t)\n: Lemma\n (requires (U32.v from1 <= U32.v from2 /\\ U32.v to2 <= U32.v to1))\n (ensures (loc_includes (loc_buffer_from_to b from1 to1) (loc_buffer_from_to b from2 to2)))\nlet loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 =\n if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2\n then ()\n else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2)", "val loc_aux_includes_pointer_trans (s: loc_aux) (#t1 #t2: typ) (p1: pointer t1) (p2: pointer t2)\n : Lemma (requires (loc_aux_includes_pointer s p1 /\\ p1 `includes` p2))\n (ensures (loc_aux_includes_pointer s p2))\nlet loc_aux_includes_pointer_trans\n (s: loc_aux)\n (#t1 #t2: typ)\n (p1: pointer t1)\n (p2: pointer t2)\n: Lemma\n (requires (loc_aux_includes_pointer s p1 /\\ p1 `includes` p2))\n (ensures (loc_aux_includes_pointer s p2))\n= match s with\n | LocPointer p -> includes_trans p p1 p2\n | LocBuffer b ->\n let f\n (i: UInt32.t)\n : Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ gpointer_of_buffer_cell b i `includes` p1))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ gpointer_of_buffer_cell b i `includes` p2))\n = includes_trans (gpointer_of_buffer_cell b i) p1 p2\n in\n Classical.forall_intro (Classical.move_requires f)", "val modifies_loc_includes\n (s1: loc)\n (h h': HS.mem)\n (s2: loc)\n: Lemma\n (requires (modifies s2 h h' /\\ loc_includes s1 s2))\n (ensures (modifies s1 h h'))\n [SMTPat (modifies s1 h h'); SMTPat (modifies s2 h h')]\nlet modifies_loc_includes = MG.modifies_loc_includes", "val modifies_loc_includes\n (s1: loc)\n (h h': HS.mem)\n (s2: loc)\n: Lemma\n (requires (modifies s2 h h' /\\ loc_includes s1 s2))\n (ensures (modifies s1 h h'))\n [SMTPat (modifies s1 h h'); SMTPat (modifies s2 h h')]\nlet modifies_loc_includes = MG.modifies_loc_includes", "val lemma_constant_intersect_belongs_to_writes_union\n (c1 c2: locations_with_values)\n (w1 w2: locations)\n (l: location_eq)\n (v: location_val_eqt l)\n : Lemma\n (requires\n ((let x:location_with_value = (| l, v |) in\n L.mem x (c1 `intersect` c2) /\\\n (forall l v. {:pattern (L.mem (| l, v |) c1); (L.mem l w1)}\n L.mem (| l, v |) c1 ==> L.mem l w1) /\\\n (forall l v. {:pattern (L.mem (| l, v |) c2); (L.mem l w2)}\n L.mem (| l, v |) c2 ==> L.mem l w2)))) (ensures (L.mem l (w1 `L.append` w2)))\nlet rec lemma_constant_intersect_belongs_to_writes_union\n (c1 c2:locations_with_values) (w1 w2:locations) (l:location_eq) (v:location_val_eqt l) :\n Lemma\n (requires (\n (let x : location_with_value = (|l,v|) in\n L.mem x (c1 `intersect` c2) /\\\n (forall l v. {:pattern (L.mem (|l,v|) c1); (L.mem l w1)}\n L.mem (|l,v|) c1 ==> L.mem l w1) /\\\n (forall l v. {:pattern (L.mem (|l,v|) c2); (L.mem l w2)}\n L.mem (|l,v|) c2 ==> L.mem l w2))))\n (ensures (L.mem l (w1 `L.append` w2))) =\n match c1 with\n | [] -> ()\n | x :: xs ->\n if x = (|l,v|) then (\n assert (L.mem (|l,v|) c1);\n assert (L.mem l w1);\n L.append_mem w1 w2 l\n ) else (\n assert (forall l v. L.mem (|l,v|) xs ==> L.mem (|l,v|) c1);\n lemma_constant_intersect_belongs_to_writes_union xs c2 w1 w2 l v\n )", "val loc_includes_union_l_nodelist_fp0 (#t: Type) (s1 s2: loc) (nl: nodelist t)\n : Lemma (requires (loc_includes s1 (nodelist_fp0 nl) \\/ loc_includes s2 (nodelist_fp0 nl)))\n (ensures (loc_includes (loc_union s1 s2) (nodelist_fp0 nl)))\n [SMTPat (loc_includes (loc_union s1 s2) (nodelist_fp0 nl))]\nlet loc_includes_union_l_nodelist_fp0 (#t: Type) (s1 s2:loc) (nl:nodelist t) :\n Lemma\n (requires (loc_includes s1 (nodelist_fp0 nl) \\/ loc_includes s2 (nodelist_fp0 nl)))\n (ensures (loc_includes (loc_union s1 s2) (nodelist_fp0 nl)))\n [SMTPat (loc_includes (loc_union s1 s2) (nodelist_fp0 nl))] =\n loc_includes_union_l s1 s2 (nodelist_fp0 nl)", "val loc_union_assoc\n (s1 s2 s3: loc)\n: Lemma\n (loc_union s1 (loc_union s2 s3) == loc_union (loc_union s1 s2) s3)\nlet loc_union_assoc = MG.loc_union_assoc", "val loc_union_assoc\n (s1 s2 s3: loc)\n: Lemma\n (loc_union s1 (loc_union s2 s3) == loc_union (loc_union s1 s2) s3)\nlet loc_union_assoc = MG.loc_union_assoc", "val modifies_loc_addresses_intro\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r a h1 h2\n ))\n (ensures (modifies (loc_union (loc_addresses true r a) l) h1 h2))\nlet modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro", "val modifies_loc_addresses_intro\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r a h1 h2\n ))\n (ensures (modifies (loc_union (loc_addresses true r a) l) h1 h2))\nlet modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls", "val loc_aux_disjoint_loc_aux_includes_buffer (l1 l2: loc_aux) (#t3: Type) (b3: B.buffer t3)\n : Lemma (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes_buffer l2 b3))\n (ensures (loc_aux_disjoint_buffer l1 b3))\nlet loc_aux_disjoint_loc_aux_includes_buffer\n (l1 l2: loc_aux)\n (#t3: Type)\n (b3: B.buffer t3)\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes_buffer l2 b3))\n (ensures (loc_aux_disjoint_buffer l1 b3))\n= match l2 with\n | LocBuffer b2 -> loc_aux_disjoint_buffer_includes l1 b2 b3", "val modifies_loc_addresses_intro\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_regions (Set.singleton r)) l) h1 h2 /\\\n HS.modifies_ref r a h1 h2\n ))\n (ensures (modifies (loc_union (loc_addresses r a) l) h1 h2))\nlet modifies_loc_addresses_intro r a l h1 h2 =\n MG.modifies_loc_addresses_intro r a l h1 h2;\n MG.loc_includes_addresses_addresses #_ cls false true r a a;\n MG.loc_includes_refl l;\n MG.loc_includes_union_l (loc_addresses r a) l l;\n MG.loc_includes_union_l (loc_addresses r a) l (MG.loc_addresses true r a);\n MG.loc_includes_union_r (loc_union (loc_addresses r a) l) (MG.loc_addresses true r a) l;\n MG.modifies_loc_includes (loc_union (loc_addresses r a) l) h1 h2 (loc_union (MG.loc_addresses true r a) l)", "val includes_ind\n (x:\n (#value1: typ -> #value2: typ -> p1: pointer value1 -> p2: pointer value2 {includes p1 p2}\n -> GTot Type0))\n (h_field:\n (l: struct_typ -> p: pointer (TStruct l) -> fd: struct_field l {includes p (gfield p fd)}\n -> Lemma (x p (gfield p fd))))\n (h_ufield:\n (l: union_typ -> p: pointer (TUnion l) -> fd: struct_field l {includes p (gufield p fd)}\n -> Lemma (x p (gufield p fd))))\n (h_cell:\n (\n #length: array_length_t ->\n #value: typ ->\n p: pointer (TArray length value) ->\n i: UInt32.t{UInt32.v i < UInt32.v length /\\ includes p (gcell p i)}\n -> Lemma (x p (gcell p i))))\n (h_refl: (#value: typ -> p: pointer value {includes p p} -> Lemma (x p p)))\n (h_trans:\n (\n #value1: typ ->\n #value2: typ ->\n #value3: typ ->\n p1: pointer value1 ->\n p2: pointer value2 ->\n p3:\n pointer value3\n {includes p1 p2 /\\ includes p2 p3 /\\ includes p1 p3 /\\ x p1 p2 /\\ x p2 p3}\n -> Lemma (x p1 p3)))\n (#value1 #value2: typ)\n (p1: pointer value1)\n (p2: pointer value2 {includes p1 p2})\n : Lemma (x p1 p2)\nlet includes_ind\n (x:((#value1: typ) ->\n (#value2: typ) ->\n (p1: pointer value1) ->\n (p2: pointer value2 {includes p1 p2} ) ->\n GTot Type0))\n (h_field:\n ((l: struct_typ) ->\n (p: pointer (TStruct l)) ->\n (fd: struct_field l {includes p (gfield p fd)}) ->\n Lemma (x p (gfield p fd))))\n (h_ufield:\n ((l: union_typ) ->\n (p: pointer (TUnion l)) ->\n (fd: struct_field l {includes p (gufield p fd)}) ->\n Lemma (x p (gufield p fd))))\n (h_cell:\n ((#length: array_length_t) ->\n (#value: typ) ->\n (p: pointer (TArray length value)) ->\n (i: UInt32.t {UInt32.v i < UInt32.v length /\\ includes p (gcell p i)}) ->\n Lemma (x p (gcell p i))))\n (h_refl:\n ((#value: typ) ->\n (p: pointer value {includes p p}) ->\n Lemma (x p p)))\n (h_trans:\n ((#value1: typ) ->\n (#value2: typ) ->\n (#value3: typ) ->\n (p1: pointer value1) ->\n (p2: pointer value2) ->\n (p3: pointer value3 {includes p1 p2 /\\ includes p2 p3 /\\ includes p1 p3 /\\ x p1 p2 /\\ x p2 p3}) ->\n Lemma (x p1 p3)))\n (#value1: typ)\n (#value2: typ)\n (p1: pointer value1)\n (p2: pointer value2 {includes p1 p2})\n: Lemma (x p1 p2)\n= let (Pointer from contents _) = p1 in\n path_includes_ind\n (fun #to1 #to2 p1_ p2_ -> x (Pointer from contents p1_) (Pointer from contents p2_))\n (fun #through #to p s ->\n match s with\n | StepField l fd -> let (pt: pointer (TStruct l)) = (Pointer from contents p) in h_field l pt fd\n | StepUField l fd -> let (pt: pointer (TUnion l)) = (Pointer from contents p) in h_ufield l pt fd\n | StepCell length value i -> let (pt: pointer (TArray length value)) = (Pointer from contents p) in h_cell pt i\n )\n (fun #to p -> h_refl (Pointer from contents p))\n (fun #to1 #to2 #to3 p1_ p2_ p3_ -> h_trans (Pointer from contents p1_) (Pointer from contents p2_) (Pointer from contents p3_))\n (Pointer?.p p1)\n (Pointer?.p p2)", "val loc_includes_region_pointer\n (#t: typ)\n (s: Set.set HS.rid)\n (p: pointer t)\n: Lemma\n (requires (Set.mem (frameOf p) s))\n (ensures (loc_includes (loc_regions s) (loc_pointer p)))\n [SMTPat (loc_includes (loc_regions s) (loc_pointer p))]\nlet loc_includes_region_pointer #t s p =\n MG.loc_includes_region_aloc #_ #cls false s #(frameOf p) #(as_addr p) (LocPointer p)", "val loc_includes_union_l_dll_fp0 (#t: Type) (s1 s2: loc) (d: dll t)\n : Lemma (requires (loc_includes s1 (dll_fp0 d) \\/ loc_includes s2 (dll_fp0 d)))\n (ensures (loc_includes (loc_union s1 s2) (dll_fp0 d)))\n [SMTPat (loc_includes (loc_union s1 s2) (dll_fp0 d))]\nlet loc_includes_union_l_dll_fp0 (#t: Type) (s1 s2:loc) (d:dll t) :\n Lemma\n (requires (loc_includes s1 (dll_fp0 d) \\/ loc_includes s2 (dll_fp0 d)))\n (ensures (loc_includes (loc_union s1 s2) (dll_fp0 d)))\n [SMTPat (loc_includes (loc_union s1 s2) (dll_fp0 d))] =\n loc_includes_union_l s1 s2 (dll_fp0 d)", "val old_to_union_loc_union (old1 old2: OldM.loc)\n : Lemma\n (old_to_union_loc (old1 `OldM.loc_union` old2) ==\n (old_to_union_loc old1)\n `M.loc_union`\n (old_to_union_loc old2)) [SMTPat (old_to_union_loc (old1 `OldM.loc_union` old2))]\nlet old_to_union_loc_union (old1 old2: OldM.loc) : Lemma\n (old_to_union_loc (old1 `OldM.loc_union` old2) == old_to_union_loc old1 `M.loc_union` old_to_union_loc old2)\n [SMTPat (old_to_union_loc (old1 `OldM.loc_union` old2))]\n= OldM.cloc_of_loc_union old1 old2;\n M.union_loc_of_loc_union old_and_new_cl false (OldM.cloc_of_loc old1) (OldM.cloc_of_loc old2)", "val union_loc_to_new_union (l1 l2: M.loc old_and_new_cl_union)\n : Lemma\n (union_loc_to_new (l1 `M.loc_union` l2) ==\n (union_loc_to_new l1)\n `NewM.loc_union`\n (union_loc_to_new l2)) [SMTPat (union_loc_to_new (l1 `M.loc_union` l2))]\nlet union_loc_to_new_union (l1 l2: M.loc old_and_new_cl_union) : Lemma\n (union_loc_to_new (l1 `M.loc_union` l2) == union_loc_to_new l1 `NewM.loc_union` union_loc_to_new l2)\n [SMTPat (union_loc_to_new (l1 `M.loc_union` l2))]\n= M.loc_of_union_loc_union old_and_new_cl true l1 l2;\n let t : Type u#1 = M.loc (old_and_new_cl true) in\n let i1 : t = M.loc_of_union_loc true l1 in\n let i2 : t = M.loc_of_union_loc true l2 in\n let j1 : M.loc (M.raise_cls NewM.cloc_cls) = coerce (M.loc (M.raise_cls NewM.cloc_cls)) i1 in\n let j2 : M.loc (M.raise_cls u#0 u#0 NewM.cloc_cls) = coerce (M.loc (M.raise_cls NewM.cloc_cls)) i2 in\n M.lower_loc_union u#0 u#0 j1 j2;\n NewM.cloc_of_loc_union (NewM.loc_of_cloc (M.lower_loc j1)) (NewM.loc_of_cloc (M.lower_loc j2));\n NewM.loc_of_cloc_of_loc (NewM.loc_of_cloc (M.lower_loc j1) `NewM.loc_union` NewM.loc_of_cloc (M.lower_loc j2))", "val modifies_loc_buffer_from_to_intro'\n (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel)\n (from to: U32.t)\n (l: loc) (h h' : HS.mem)\n: Lemma\n (requires (\n let s = as_seq h b in\n let s' = as_seq h' b in\n not (g_is_null b) /\\\n live h b /\\\n modifies (loc_union l (loc_buffer b)) h h' /\\\n U32.v from <= U32.v to /\\\n U32.v to <= length b /\\\n Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\\\n Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b)\n ))\n (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h'))\nlet modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' =\n let r0 = frameOf b in\n let a0 = as_addr b in\n let bb : ubuffer r0 a0 = ubuffer_of_buffer b in\n modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b));\n MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) ->\n ubuffer_preserved_intro x h h'\n (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b'))\n (fun t' rrel' rel' b' ->\n // prove that the types, rrels, rels are equal\n Heap.lemma_distinct_addrs_distinct_preorders ();\n Heap.lemma_distinct_addrs_distinct_mm ();\n assert (Seq.seq t' == Seq.seq a);\n let _s0 : Seq.seq a = as_seq h b in\n let _s1 : Seq.seq t' = coerce_eq _ _s0 in\n lemma_equal_instances_implies_equal_types a t' _s0 _s1;\n let boff = U32.v (Buffer?.idx b) in\n let from_ = boff + U32.v from in\n let to_ = boff + U32.v to in\n let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in\n let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in\n let bh = as_seq h b in\n let bh' = as_seq h' b in\n let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in\n let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in\n let prf (i: nat) : Lemma\n (requires (i < xlen))\n (ensures (i < xlen /\\ Seq.index xh i == Seq.index xh' i))\n = let xi = xoff + i in\n let bi : ubuffer r0 a0 =\n Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; })\n in\n assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0);\n assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0);\n let li = MG.loc_of_aloc bi in\n MG.loc_includes_aloc #_ #cls x bi;\n loc_disjoint_includes l (MG.loc_of_aloc x) l li;\n if xi < boff || boff + length b <= xi\n then begin\n MG.loc_disjoint_aloc_intro #_ #cls bb bi;\n assert (loc_disjoint (loc_union l (loc_buffer b)) li);\n MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h'\n end else\n if xi < from_\n then begin\n assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff));\n assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff))\n end else begin\n assert (to_ <= xi);\n assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_));\n assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_))\n end\n in\n Classical.forall_intro (Classical.move_requires prf);\n assert (xh `Seq.equal` xh')\n )\n )", "val loc_includes_loc_buffer_loc_buffer_from_to\n (#a: _) (#rrel #rel: _)\n (b: mbuffer a rrel rel)\n (from to: U32.t)\n: Lemma\n (loc_includes (loc_buffer b) (loc_buffer_from_to b from to))\nlet loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to =\n if ubuffer_of_buffer_from_to_none_cond b from to\n then ()\n else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to)", "val loc_includes_buffer\n (#t: Type)\n (b1 b2: B.buffer t)\n: Lemma\n (requires (b1 `B.includes` b2))\n (ensures (loc_includes (loc_buffer b1) (loc_buffer b2)))\n [SMTPatOr [\n [SMTPat (B.includes b1 b2)];\n [SMTPat (loc_includes(loc_buffer b1) (loc_buffer b2))]\n ]]\nlet loc_includes_buffer #t b1 b2 =\n MG.loc_includes_aloc #_ #cls #(B.frameOf b1) #(B.as_addr b1) (LocBuffer b1) (LocBuffer b2)", "val loc_disjoint_includes\n (p1 p2 p1' p2' : loc)\n: Lemma\n (requires (loc_includes p1 p1' /\\ loc_includes p2 p2' /\\ loc_disjoint p1 p2))\n (ensures (loc_disjoint p1' p2'))\nlet loc_disjoint_includes = MG.loc_disjoint_includes", "val loc_disjoint_includes\n (p1 p2 p1' p2' : loc)\n: Lemma\n (requires (loc_includes p1 p1' /\\ loc_includes p2 p2' /\\ loc_disjoint p1 p2))\n (ensures (loc_disjoint p1' p2'))\nlet loc_disjoint_includes = MG.loc_disjoint_includes", "val loc_aux_disjoint_loc_aux_includes_pointer (l1 l2: loc_aux) (#t3: typ) (p3: pointer t3)\n : Lemma (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes_pointer l2 p3))\n (ensures (loc_aux_disjoint_pointer l1 p3))\nlet loc_aux_disjoint_loc_aux_includes_pointer\n (l1 l2: loc_aux)\n (#t3: typ)\n (p3: pointer t3)\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes_pointer l2 p3))\n (ensures (loc_aux_disjoint_pointer l1 p3))\n= match l2 with\n | LocPointer p2 ->\n loc_aux_disjoint_pointer_includes l1 p2 p3\n | LocBuffer b2 ->\n let f\n (i: UInt32.t)\n : Lemma\n (requires (\n UInt32.v i < UInt32.v (buffer_length b2) /\\\n gpointer_of_buffer_cell b2 i `includes` p3\n ))\n (ensures (loc_aux_disjoint_pointer l1 p3))\n = loc_aux_disjoint_pointer_includes l1 (gpointer_of_buffer_cell b2 i) p3\n in\n Classical.forall_intro (Classical.move_requires f)", "val insert_modifies_union_loc_weakening:\n l1:loc -> l2:loc -> l3:loc -> h0:HS.mem -> h1:HS.mem ->\n Lemma (requires (modifies l1 h0 h1))\n (ensures (modifies (loc_union (loc_union l1 l2) l3) h0 h1))\nlet insert_modifies_union_loc_weakening l1 l2 l3 h0 h1 =\n B.loc_includes_union_l l1 l2 l1;\n B.loc_includes_union_l (loc_union l1 l2) l3 (loc_union l1 l2)", "val modifies_loc_buffer_from_to_intro\n (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel)\n (from to: U32.t)\n (l: loc) (h h' : HS.mem)\n: Lemma\n (requires (\n let s = as_seq h b in\n let s' = as_seq h' b in\n live h b /\\\n modifies (loc_union l (loc_buffer b)) h h' /\\\n U32.v from <= U32.v to /\\\n U32.v to <= length b /\\\n Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\\\n Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b)\n ))\n (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h'))\nlet modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' =\n if g_is_null b\n then ()\n else modifies_loc_buffer_from_to_intro' b from to l h h'", "val modifies_loc_regions_intro\n (rs: Set.set HS.rid)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HS.modifies rs h1 h2))\n (ensures (modifies (loc_regions true rs) h1 h2))\nlet modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls", "val modifies_loc_regions_intro\n (rs: Set.set HS.rid)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HS.modifies rs h1 h2))\n (ensures (modifies (loc_regions true rs) h1 h2))\nlet modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls", "val loc_includes_region_region\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires (Set.subset s2 s1))\n (ensures (loc_includes (loc_regions s1) (loc_regions s2)))\n [SMTPat (loc_includes (loc_regions s1) (loc_regions s2))]\nlet loc_includes_region_region = MG.loc_includes_region_region #_ #cls false false", "val modifies_loc_regions_intro\n (rs: Set.set HS.rid)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HS.modifies rs h1 h2))\n (ensures (modifies (loc_regions rs) h1 h2))\nlet modifies_loc_regions_intro rs h1 h2 =\n MG.modifies_loc_regions_intro #_ #cls rs h1 h2;\n MG.loc_includes_region_region #_ #cls false true rs rs;\n MG.modifies_loc_includes (loc_regions rs) h1 h2 (MG.loc_regions true rs)", "val union_loc_to_new_regions (preserve_liveness: bool) (r: Set.set HS.rid)\n : Lemma\n (union_loc_to_new (M.loc_regions preserve_liveness r) == NewM.loc_regions preserve_liveness r)\n [SMTPat (union_loc_to_new (M.loc_regions preserve_liveness r))]\nlet union_loc_to_new_regions (preserve_liveness: bool) (r: Set.set HS.rid) : Lemma\n (union_loc_to_new (M.loc_regions preserve_liveness r) == NewM.loc_regions preserve_liveness r)\n [SMTPat (union_loc_to_new (M.loc_regions preserve_liveness r))]\n= M.loc_of_union_loc_regions old_and_new_cl true preserve_liveness r;\n M.lower_loc_regions u#0 u#0 #_ #NewM.cloc_cls preserve_liveness r;\n NewM.cloc_of_loc_regions preserve_liveness r;\n NewM.cloc_of_loc_of_cloc (M.loc_regions preserve_liveness r)", "val loc_includes_region_addresses\n (s: Set.set HS.rid)\n (r: HS.rid)\n (a: Set.set nat)\n: Lemma\n (requires (Set.mem r s))\n (ensures (loc_includes (loc_regions s) (loc_addresses r a)))\n [SMTPat (loc_includes (loc_regions s) (loc_addresses r a))]\nlet loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls false false", "val loc_vector_within_includes:\n #a:Type -> vec:vector a ->\n i1:uint32_t -> j1:uint32_t{i1 <= j1 && j1 <= size_of vec} ->\n i2:uint32_t{i1 <= i2} -> j2:uint32_t{i2 <= j2 && j2 <= j1} ->\n Lemma (requires True)\n (ensures (loc_includes (loc_vector_within vec i1 j1)\n (loc_vector_within vec i2 j2)))\n (decreases (U32.v (j1 - i1)))\nlet rec loc_vector_within_includes #a vec i1 j1 i2 j2 =\n if i1 = j1 then ()\n else if i1 = i2 then loc_vector_within_includes_ vec i1 j1 j2\n else begin\n loc_vector_within_includes vec (i1 + 1ul) j1 i2 j2;\n loc_includes_union_l (B.loc_buffer (B.gsub (Vec?.vs vec) i1 1ul))\n (loc_vector_within vec (i1 + 1ul) j1)\n (loc_vector_within vec i2 j2)\n end", "val size_of_union_aux_1 (#a #f: _) (s1 s2: (z: ordset a f {z <> empty}))\n : Lemma\n (requires\n (head s1) <> (head s2) && (f (head s1) (head s2)) &&\n (size (union (tail s1) s2) = size (tail s1) + size s2 - size (intersect (tail s1) s2)))\n (ensures size (union s1 s2) = (size s1 + size s2 - size (intersect s1 s2)))\nlet size_of_union_aux_1 #a #f (s1 s2: (z:ordset a f{z<>empty}))\n : Lemma (requires (head s1) <> (head s2) \n && (f (head s1) (head s2)) \n && (size (union (tail s1) s2) = size (tail s1) + size s2 - size (intersect (tail s1) s2)))\n (ensures size (union s1 s2) = (size s1 + size s2 - size (intersect s1 s2))) = \n union_of_tails_size s1 s2;\n same_members_means_eq (intersect (tail s1) s2) (intersect s1 s2)", "val union_head_lemma (#a #f: _) (s1 s2: ordset a f)\n : Lemma\n (match s1, s2 with\n | [], [] -> (union s1 s2 = [])\n | [], h :: t -> size (union s1 s2) > 0 && Cons?.hd (union s1 s2) = h\n | h :: t, [] -> size (union s1 s2) > 0 && Cons?.hd (union s1 s2) = h\n | h1 :: t1, h2 :: t2 ->\n size (union s1 s2) > 0 && (Cons?.hd (union s1 s2) = (if f h1 h2 then h1 else h2)))\nlet union_head_lemma #a #f (s1 s2: ordset a f)\n : Lemma (match s1, s2 with \n | [],[] -> (union s1 s2 = [])\n | [],h::t -> size (union s1 s2) > 0 && Cons?.hd (union s1 s2) = h\n | h::t,[] -> size (union s1 s2) > 0 && Cons?.hd (union s1 s2) = h\n | h1::t1, h2::t2 -> size (union s1 s2) > 0 && \n (Cons?.hd (union s1 s2) = (if f h1 h2 then h1 else h2)) \n ) = \n match s1,s2 with\n | [],[] -> ()\n | [],h::t -> ()\n | h::t,[] -> union_with_empty s1\n | h1::t1, h2::t2 -> union_mem_forall s1 s2;\n set_props s1;\n set_props s2;\n set_props (union s1 s2)", "val loc_includes_addresses_addresses\n (preserve_liveness1 preserve_liveness2: bool)\n (r: HS.rid)\n (s1 s2: Set.set nat)\n: Lemma\n (requires ((preserve_liveness1 ==> preserve_liveness2) /\\ Set.subset s2 s1))\n (ensures (loc_includes (loc_addresses preserve_liveness1 r s1) (loc_addresses preserve_liveness2 r s2)))\nlet loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses #_ cls", "val loc_includes_addresses_addresses\n (preserve_liveness1 preserve_liveness2: bool)\n (r: HS.rid)\n (s1 s2: Set.set nat)\n: Lemma\n (requires ((preserve_liveness1 ==> preserve_liveness2) /\\ Set.subset s2 s1))\n (ensures (loc_includes (loc_addresses preserve_liveness1 r s1) (loc_addresses preserve_liveness2 r s2)))\nlet loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls", "val size_of_union_aux_2 (#a #f: _) (s1 s2: (z: ordset a f {z <> empty}))\n : Lemma\n (requires\n (head s1) <> (head s2) && not (f (head s1) (head s2)) &&\n (size (union s1 (tail s2)) = size s1 + size (tail s2) - size (intersect s1 (tail s2))))\n (ensures size (union s1 s2) = (size s1 + size s2 - size (intersect s1 s2)))\nlet size_of_union_aux_2 #a #f (s1 s2: (z:ordset a f{z<>empty}))\n : Lemma (requires (head s1) <> (head s2) \n && not (f (head s1) (head s2)) \n && (size (union s1 (tail s2)) = size s1 + size (tail s2) - size (intersect s1 (tail s2))))\n (ensures size (union s1 s2) = (size s1 + size s2 - size (intersect s1 s2))) \n = Classical.forall_intro_2 (union_is_symmetric #a #f);\n Classical.forall_intro_2 (intersect_is_symmetric #a #f);\n size_of_union_aux_1 s2 s1", "val loc_vector_within_includes_:\n #a:Type -> vec:vector a ->\n i:uint32_t ->\n j1:uint32_t{i <= j1 && j1 <= size_of vec} ->\n j2:uint32_t{i <= j2 && j2 <= j1} ->\n Lemma (requires True)\n (ensures (loc_includes (loc_vector_within vec i j1)\n (loc_vector_within vec i j2)))\n (decreases (U32.v (j1 - i)))\nlet rec loc_vector_within_includes_ #a vec i j1 j2 =\n if i = j1 then ()\n else if i = j2 then ()\n else begin\n loc_vector_within_includes_ vec (i + 1ul) j1 j2;\n loc_includes_union_l (B.loc_buffer (B.gsub (Vec?.vs vec) i 1ul))\n (loc_vector_within vec (i + 1ul) j1)\n (loc_vector_within vec (i + 1ul) j2);\n loc_includes_union_r (loc_vector_within vec i j1)\n (B.loc_buffer (B.gsub (Vec?.vs vec) i 1ul))\n (loc_vector_within vec (i + 1ul) j2)\n end", "val size_of_union_left (#a: eqtype) (#f: _) (s1 s2: ordset a f)\n : Lemma (ensures size (union s1 s2) >= size s2)\nlet rec size_of_union_left (#a:eqtype) #f (s1 s2: ordset a f)\n : Lemma (ensures size (union s1 s2) >= size s2) = \n match s1 with\n | [] -> ()\n | hd::tl -> size_of_union_left tl (insert' hd s2);\n precise_size_insert s2 hd", "val with_local\n (#a #b: Type)\n (#l1 #l2: _)\n (#req: hprop l1)\n (#ens: hpost l2)\n (init: b)\n (f: stl a init l1 l2 req ens)\n : ST a\n (requires fun h -> B.loc_includes (B.loc_not_unused_in h) l1 /\\ req h)\n (ensures fun h0 x h1 -> B.modifies (l2 x) h0 h1 /\\ ens h0 x h1)\nlet with_local\n (#a:Type)\n (#b:Type)\n (#l1:_)\n (#l2:_)\n (#req: hprop l1)\n (#ens: hpost l2)\n (init:b)\n (f: stl a init l1 l2 req ens)\n : ST a\n (requires fun h ->\n B.loc_includes (B.loc_not_unused_in h) l1 /\\\n req h)\n (ensures fun h0 x h1 ->\n B.modifies (l2 x) h0 h1 /\\\n ens h0 x h1)\n = let h = get () in\n B.loc_unused_in_not_unused_in_disjoint h;\n let fresh = B.malloc HS.root init 1ul in\n let h1 = get () in\n let res = f h fresh in\n let h2 = get () in\n let _ = B.free fresh in\n let h3 = get () in\n B.modifies_remove_new_locs (B.loc_addr_of_buffer fresh) (l2 res) (l2 res) h h1 h3;\n res", "val rv_loc_elems_included:\n #a:Type0 -> #rst:Type -> #rg:regional rst a ->\n h:HS.mem -> rv:rvector rg ->\n i:uint32_t -> j:uint32_t{i <= j && j <= V.size_of rv} ->\n Lemma (requires (rv_elems_reg h rv i j))\n (ensures (loc_includes (loc_all_exts_from false (V.frameOf rv))\n (rv_loc_elems h rv i j)))\nlet rv_loc_elems_included #a #rst #rg h rv i j =\n rs_loc_elems_included rg (V.as_seq h rv) (V.frameOf rv) (U32.v i) (U32.v j)", "val loc_includes_region_buffer\n (#t: typ)\n (s: Set.set HS.rid)\n (b: buffer t)\n: Lemma\n (requires (Set.mem (frameOf_buffer b) s))\n (ensures (loc_includes (loc_regions s) (loc_buffer b)))\n [SMTPat (loc_includes (loc_regions s) (loc_buffer b))]\nlet loc_includes_region_buffer #t s b =\n MG.loc_includes_region_aloc #_ #cls false s #(frameOf_buffer b) #(buffer_as_addr b) (LocBuffer b)", "val disjoint_includes\n (#value1 #value2: typ)\n (p1: pointer value1)\n (p2: pointer value2)\n (#value1' #value2': typ)\n (p1': pointer value1')\n (p2': pointer value2')\n : Lemma (requires (includes p1 p1' /\\ includes p2 p2' /\\ disjoint p1 p2))\n (ensures (disjoint p1' p2'))\nlet disjoint_includes\n (#value1: typ)\n (#value2: typ)\n (p1: pointer value1)\n (p2: pointer value2)\n (#value1': typ)\n (#value2': typ)\n (p1': pointer value1')\n (p2': pointer value2')\n: Lemma\n (requires (includes p1 p1' /\\ includes p2 p2' /\\ disjoint p1 p2))\n (ensures (disjoint p1' p2'))\n= if\n frameOf p1 = frameOf p2 &&\n as_addr p1 = as_addr p2\n then\n path_disjoint_includes (Pointer?.p p1) (Pointer?.p p2) (Pointer?.p p1') (Pointer?.p p2')\n else\n ()", "val rs_loc_elems_includes:\n #a:Type0 -> #rst:Type -> rg:regional rst a ->\n rs:S.seq a ->\n i:nat -> j:nat{i <= j && j <= S.length rs} ->\n k:nat{i <= k && k < j} ->\n Lemma (loc_includes (rs_loc_elems rg rs i j)\n (rs_loc_elem rg rs k))\nlet rec rs_loc_elems_includes #a #rst rg rs i j k =\n if k = j - 1 then ()\n else rs_loc_elems_includes #a #rst rg rs i (j - 1) k" ], "closest_src": [ { "project_name": "FStar", "file_name": "DoublyLinkedList.fst", "name": "DoublyLinkedList.loc_includes_union_r_inv" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Wrapper.fst", "name": "Vale.AsLowStar.Wrapper.loc_includes_union" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_union_l" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_union_r" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc_includes_union_l" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc_includes_union_l" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_includes_union_r'" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.loc_includes_region_union_assoc" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_includes_union_l'" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_disjoint_includes_r" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_region_union_l" }, { "project_name": "FStar", "file_name": "DoublyLinkedList.fst", "name": "DoublyLinkedList.loc_equiv_union_union_loc" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_includes_union_l_regions" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.loc_includes_region_union_r" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_union_r" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_includes_union_r" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Functor.fsti", "name": "Hacl.Streaming.Functor.loc_includes_union_l_footprint_s" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_union_l" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_includes_union_l" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_includes_union_l_addresses" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc_includes_union_r" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc_includes_union_r" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_region_union_l" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_includes_region_union_l" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_aux_includes_trans'" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_includes_trans'" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_includes_trans" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_aux_includes_trans" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.fst", "name": "MerkleTree.Low.loc_union_assoc_4" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc_includes_union_l_buffer" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc_includes_union_l_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.loc_includes_union_assoc_focalize_2" }, { "project_name": "hacl-star", "file_name": "EverCrypt.AEAD.fsti", "name": "EverCrypt.AEAD.loc_includes_union_l_footprint_s" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_includes_trans" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_trans" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_trans" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_includes_union_l_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.loc_includes_union_assoc_r2l" }, { "project_name": "everquic-crypto", "file_name": "QUIC.State.fsti", "name": "QUIC.State.loc_includes_union_l_footprint_s" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.loc_includes_union_assoc_l2r" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_as_seq" }, { "project_name": "FStar", "file_name": "DoublyLinkedList.fst", "name": "DoublyLinkedList.loc_includes_union_l_piece_fp0" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.loc_includes_union_assoc_focalize_1" }, { "project_name": "FStar", "file_name": "DoublyLinkedList.fst", "name": "DoublyLinkedList.loc_includes_union_l_fragment_fp0" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Hash.fsti", "name": "EverCrypt.Hash.loc_includes_union_l_footprint_s" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_aux_disjoint_loc_aux_includes" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_disjoint_loc_aux_includes" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_loc_includes" }, { "project_name": "hacl-star", "file_name": "EverCrypt.DRBG.fst", "name": "EverCrypt.DRBG.loc_includes_union_l_footprint_s" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc_includes_trans" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc_includes_trans" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_includes_loc_aux_includes_pointer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.buffer_includes_loc_includes" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_aux_includes_loc_aux_includes_buffer" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.modifies_loc_includes" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.modifies_loc_includes" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_loc_buffer_from_to" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_includes_pointer_trans" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_loc_includes" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_loc_includes" }, { "project_name": "hacl-star", "file_name": "Vale.Transformers.BoundedInstructionEffects.fst", "name": "Vale.Transformers.BoundedInstructionEffects.lemma_constant_intersect_belongs_to_writes_union" }, { "project_name": "FStar", "file_name": "DoublyLinkedList.fst", "name": "DoublyLinkedList.loc_includes_union_l_nodelist_fp0" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_union_assoc" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_union_assoc" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_loc_addresses_intro" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_loc_addresses_intro" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_aux_disjoint_loc_aux_includes_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_loc_addresses_intro" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.includes_ind" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_region_pointer" }, { "project_name": "FStar", "file_name": "DoublyLinkedList.fst", "name": "DoublyLinkedList.loc_includes_union_l_dll_fp0" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.old_to_union_loc_union" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.union_loc_to_new_union" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_loc_buffer_from_to_intro'" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_loc_buffer_loc_buffer_from_to" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_includes_buffer" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_disjoint_includes" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint_includes" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_disjoint_loc_aux_includes_pointer" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.fst", "name": "MerkleTree.Low.insert_modifies_union_loc_weakening" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_loc_buffer_from_to_intro" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_loc_regions_intro" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_loc_regions_intro" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_region_region" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_loc_regions_intro" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.union_loc_to_new_regions" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_region_addresses" }, { "project_name": "FStar", "file_name": "LowStar.Vector.fst", "name": "LowStar.Vector.loc_vector_within_includes" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.size_of_union_aux_1" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.union_head_lemma" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_includes_addresses_addresses" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_addresses_addresses" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.size_of_union_aux_2" }, { "project_name": "FStar", "file_name": "LowStar.Vector.fst", "name": "LowStar.Vector.loc_vector_within_includes_" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.size_of_union_left" }, { "project_name": "FStar", "file_name": "WithLocal.fst", "name": "WithLocal.with_local" }, { "project_name": "FStar", "file_name": "LowStar.RVector.fst", "name": "LowStar.RVector.rv_loc_elems_included" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_region_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.disjoint_includes" }, { "project_name": "FStar", "file_name": "LowStar.RVector.fst", "name": "LowStar.RVector.rs_loc_elems_includes" } ], "selected_premises": [ "FStar.ModifiesGen.loc_disjoint_includes", "FStar.ModifiesGen.loc_aux_includes_buffer_includes", "FStar.ModifiesGen.loc_union", "FStar.ModifiesGen.loc_aux_includes_trans", "FStar.ModifiesGen.loc_aux_includes_loc_aux_includes_buffer", "FStar.FunctionalExtensionality.feq", "FStar.Reflection.V2.Data.var", "FStar.ModifiesGen.region_liveness_insensitive_locs", "FStar.ModifiesGen.addrs_of_loc_aux", "FStar.ModifiesGen.popped_modifies", "FStar.ModifiesGen.aloc_disjoint_sym", "FStar.ModifiesGen.modifies_only_not_unused_in", "FStar.ModifiesGen.modifies_only_live_regions", "FStar.ModifiesGen.loc_aux_disjoint_sym", "FStar.ModifiesGen.modifies_loc_regions_intro", "FStar.ModifiesGen.modifies_trans'", "FStar.Tactics.SMT.get_rlimit", "FStar.ModifiesGen.disjoint_addrs_of_loc_loc_disjoint", "FStar.ModifiesGen.loc_equal", "FStar.ModifiesGen.modifies_loc_includes", "FStar.ModifiesGen.new_region_modifies", "FStar.ModifiesGen.loc_disjoint_aloc_elim", "FStar.Tactics.SMT.get_initial_fuel", "FStar.ModifiesGen.aloc_union", "FStar.ModifiesGen.loc_aux_includes_buffer", "FStar.ModifiesGen.mk_live_addrs", "FStar.ModifiesGen.address_liveness_insensitive_locs", "FStar.ModifiesGen.modifies_preserves_region_liveness_aloc", "FStar.Tactics.SMT.get_max_fuel", "FStar.ModifiesGen.loc_unused_in_not_unused_in_disjoint", "FStar.ModifiesGen.mk_non_live_addrs", "FStar.Tactics.Effect.raise", "FStar.Pervasives.Native.snd", "FStar.ModifiesGen.modifies_none_modifies", "FStar.ModifiesGen.loc_unused_in", "FStar.ModifiesGen.fresh_frame_modifies", "FStar.ModifiesGen.loc_none", "FStar.ModifiesGen.restrict_to_regions", "FStar.ModifiesGen.aloc_includes", "FStar.ModifiesGen.union_loc_of_loc_regions", "FStar.ModifiesGen.modifies_only_live_regions_weak", "FStar.Pervasives.Native.fst", "FStar.ModifiesGen.addrs_of_loc_aux_pred", "FStar.ModifiesGen.loc_includes_loc_regions_restrict_to_regions", "FStar.ModifiesGen.not_live_region_loc_not_unused_in_disjoint", "FStar.ModifiesGen.loc_disjoint_region_liveness_tags", "FStar.Heap.trivial_preorder", "FStar.ModifiesGen.addrs_of_loc_weak", "FStar.ModifiesGen.modifies_preserves_livenesses_intro", "FStar.ModifiesGen.loc_disjoint_aux", "FStar.ModifiesGen.loc_includes'", "FStar.ModifiesGen.loc_aux_includes", "FStar.Tactics.SMT.get_initial_ifuel", "FStar.ModifiesGen.loc", "FStar.ModifiesGen.loc_disjoint_sym", "FStar.FunctionalExtensionality.on_dom", "FStar.ModifiesGen.loc_disjoint'", "FStar.ModifiesGen.union_aux_of_aux_left_pred", "FStar.ModifiesGen.modifies_trans", "FStar.Tactics.SMT.get_max_ifuel", "FStar.ModifiesGen.loc_regions", "FStar.ModifiesGen.modifies_preserves_liveness_strong", "FStar.ModifiesGen.loc_aux_disjoint_loc_aux_includes", "FStar.ModifiesGen.addrs_of_loc_liveness_not_preserved", "FStar.ModifiesGen.modifies_address_liveness_insensitive_unused_in", "FStar.ModifiesGen.i_restricted_g_t", "FStar.Pervasives.reveal_opaque", "FStar.ModifiesGen.union_aux_of_aux_left_inv_pred", "FStar.ModifiesGen.loc_disjoint_regions", "FStar.ModifiesGen.modifies_preserves_alocs_intro", "FStar.ModifiesGen.loc_disjoint_addrs", "FStar.ModifiesGen.loc_includes_union_l", "FStar.ModifiesGen.modifies_fresh_frame_popped", "FStar.ModifiesGen.union_loc_of_loc_none", "FStar.ModifiesGen.loc_includes_restrict_to_regions", "FStar.ModifiesGen.loc_aux_disjoint", "FStar.Tactics.V2.Builtins.ret_t", "FStar.ModifiesGen.loc_of_aloc", "FStar.ModifiesGen.loc_union_assoc", "FStar.ModifiesGen.no_upd_fresh_region", "FStar.ModifiesGen.aloc_domain", "FStar.ModifiesGen.loc_includes_region_union_l", "FStar.ModifiesGen.union_loc_of_loc", "FStar.ModifiesGen.aloc_disjoint", "FStar.Monotonic.HyperStack.sel", "FStar.Tactics.SMT.smt_sync", "FStar.ModifiesGen.modifies_strengthen'", "FStar.ModifiesGen.aloc_disjoint_includes", "FStar.ModifiesGen.loc_not_unused_in", "FStar.ModifiesGen.loc_disjoint", "FStar.ModifiesGen.make_cls_union_aloc", "FStar.ModifiesGen.loc_includes", "FStar.ModifiesGen.loc_aux_includes_refl", "FStar.ModifiesGen.union_loc_of_loc_union", "FStar.ModifiesGen.modifies_intro_strong", "FStar.Reflection.Const.cons_qn", "FStar.ModifiesGen.loc_includes_trans", "FStar.ModifiesGen.addrs_of_loc", "FStar.ModifiesGen.loc_union_comm", "FStar.ModifiesGen.union_aux_of_aux_left" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.ModifiesGen\n\n#set-options \"--split_queries no\"\n#set-options \"--using_facts_from '*,-FStar.Tactics,-FStar.Reflection,-FStar.List'\"\n\nmodule HS = FStar.HyperStack\nmodule HST = FStar.HyperStack.ST\n\nnoeq\ntype aloc (#al: aloc_t) (c: cls al) = | ALoc:\n (region: HS.rid) ->\n (addr: nat) ->\n (loc: option (al region addr)) ->\n aloc c\n\nlet aloc_domain (#al: aloc_t) (c: cls al) (regions: Ghost.erased (Set.set HS.rid)) (addrs: ((r: HS.rid { Set.mem r (Ghost.reveal regions) } ) -> GTot (GSet.set nat))) : GTot (GSet.set (aloc c)) =\n GSet.comprehend (fun a -> Set.mem a.region (Ghost.reveal regions) && GSet.mem a.addr (addrs a.region))\n\nmodule F = FStar.FunctionalExtensionality\n\n[@@(unifier_hint_injective)]\nlet i_restricted_g_t = F.restricted_g_t\n\nlet addrs_dom regions =\n (r: HS.rid { Set.mem r (Ghost.reveal regions) } )\n\nlet non_live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (r:addrs_dom regions) =\n (y: GSet.set nat { r `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y })\n\nlet live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags))\n (r:addrs_dom regions) = (y: GSet.set nat { GSet.subset (non_live_addrs r) y } )\n\nnoeq\ntype loc' (#al: aloc_t u#x) (c: cls al) : Type u#x =\n | Loc:\n (regions: Ghost.erased (Set.set HS.rid)) ->\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } ) ->\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags)) ->\n (live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs)) ->\n (aux: Ghost.erased (GSet.set (aloc c)) {\n aloc_domain c regions live_addrs `GSet.subset` Ghost.reveal aux /\\\n Ghost.reveal aux `GSet.subset` (aloc_domain c regions (fun _ -> GSet.complement GSet.empty))\n } ) ->\n loc' c\n\nlet loc = loc'\n\nlet mk_non_live_addrs (#regions:_) (#region_liveness_tags:_)\n (f: (x:addrs_dom regions -> GTot (non_live_addrs_codom regions region_liveness_tags x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags) =\n F.on_dom_g _ f\n\nlet mk_live_addrs (#regions:_) (#region_liveness_tags:_)\n (#non_live_addrs_codom: _)\n (f: (x:addrs_dom regions -> GTot (live_addrs_codom regions region_liveness_tags non_live_addrs_codom x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs_codom) =\n F.on_dom_g _ f\n\nlet loc_none #a #c =\n Loc\n (Ghost.hide (Set.empty))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)\n\nlet regions_of_loc\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: GTot (Set.set HS.rid)\n= Ghost.reveal (Loc?.regions s)\n\nlet addrs_of_loc_liveness_not_preserved\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.non_live_addrs l r\n else GSet.empty\n\nlet addrs_of_loc_weak\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.live_addrs l r\n else GSet.empty\n\nlet addrs_of_loc_aux_pred\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n (addr: nat)\n: GTot bool\n= StrongExcludedMiddle.strong_excluded_middle (exists a . GSet.mem a (Ghost.reveal (Loc?.aux l)) /\\ a.region == r /\\ a.addr == addr)\n\nlet addrs_of_loc_aux\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (y: GSet.set nat { GSet.subset (GSet.intersect y (addrs_of_loc_weak l r)) GSet.empty } )\n= GSet.comprehend (addrs_of_loc_aux_pred l r)\n `GSet.intersect` (GSet.complement (addrs_of_loc_weak l r))\n\nlet addrs_of_loc\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= GSet.union\n (addrs_of_loc_weak l r)\n (addrs_of_loc_aux l r)\n\nlet addrs_of_loc_aux_prop\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: Lemma\n (GSet.subset (GSet.intersect (addrs_of_loc_aux l r) (addrs_of_loc_weak l r)) GSet.empty)\n [SMTPatOr [\n [SMTPat (addrs_of_loc_aux l r)];\n [SMTPat (addrs_of_loc_weak l r)];\n [SMTPat (addrs_of_loc l r)];\n ]]\n= ()\n\nlet loc_union #al #c s1 s2 =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in\n let regions = Set.union regions1 regions2 in\n let region_liveness_tags : Ghost.erased (Set.set HS.rid) = (Ghost.hide (Set.union (Ghost.reveal (Loc?.region_liveness_tags s1)) (Ghost.reveal (Loc?.region_liveness_tags s2)))) in\n let gregions = Ghost.hide regions in\n let non_live_addrs =\n F.on_dom_g (addrs_dom gregions) #(non_live_addrs_codom gregions region_liveness_tags)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then Loc?.non_live_addrs s1 r else GSet.empty)\n (if Set.mem r regions2 then Loc?.non_live_addrs s2 r else GSet.empty))\n in\n let live_addrs =\n F.on_dom_g (addrs_dom gregions) #(live_addrs_codom gregions region_liveness_tags non_live_addrs)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then addrs_of_loc_weak s1 r else GSet.empty)\n (if Set.mem r regions2 then addrs_of_loc_weak s2 r else GSet.empty))\n in\n let aux = Ghost.hide\n (Ghost.reveal (Loc?.aux s1) `GSet.union` Ghost.reveal (Loc?.aux s2))\n in\n Loc\n (Ghost.hide regions)\n region_liveness_tags\n non_live_addrs\n live_addrs\n aux\n\nlet fun_set_equal (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) :Tot Type0 =\n forall (x: t) . {:pattern (f1 x) \\/ (f2 x) } f1 x `GSet.equal` f2 x\n\nlet fun_set_equal_elim (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) : Lemma\n (requires (fun_set_equal f1 f2))\n (ensures (f1 == f2))\n// [SMTPat (fun_set_equal f1 f2)]\n= assert (f1 `FunctionalExtensionality.feq_g` f2)\n\nlet loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n let Loc regions1 region_liveness_tags1 _ _ aux1 = s1 in\n let Loc regions2 region_liveness_tags2 _ _ aux2 = s2 in\n Ghost.reveal regions1 `Set.equal` Ghost.reveal regions2 /\\\n Ghost.reveal region_liveness_tags1 `Set.equal` Ghost.reveal region_liveness_tags2 /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)\n\nlet loc_equal_elim (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : Lemma\n (requires (loc_equal s1 s2))\n (ensures (s1 == s2))\n [SMTPat (s1 `loc_equal` s2)]\n= fun_set_equal_elim (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2);\n fun_set_equal_elim (Loc?.live_addrs s1) (Loc?.live_addrs s2)\n\n\nlet loc_union_idem #al #c s =\n assert (loc_union s s `loc_equal` s)\n\nlet loc_union_comm #al #c s1 s2 =\n assert (loc_union s1 s2 `loc_equal` loc_union s2 s1)\n\nlet loc_union_assoc #al #c s1 s2 s3 =\n assert (loc_union s1 (loc_union s2 s3) `loc_equal` loc_union (loc_union s1 s2) s3)\n\nlet loc_union_loc_none_l #al #c s =\n assert (loc_union loc_none s `loc_equal` s)\n\nlet loc_union_loc_none_r #al #c s =\n assert (loc_union s loc_none `loc_equal` s)\n\nlet loc_of_aloc #al #c #r #n b =\n let regions = (Ghost.hide (Set.singleton r)) in\n let region_liveness_tags = (Ghost.hide (Set.empty)) in\n Loc\n regions\n region_liveness_tags\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide (GSet.singleton (ALoc r n (Some b))))\n\nlet loc_of_aloc_not_none #al #c #r #n b = ()\n\nlet loc_addresses #al #c preserve_liveness r n =\n let regions = (Ghost.hide (Set.singleton r)) in\n Loc\n regions\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> if preserve_liveness then GSet.empty else GSet.of_set n))\n (mk_live_addrs (fun _ -> GSet.of_set n))\n (Ghost.hide (aloc_domain c regions (fun _ -> GSet.of_set n)))\n\nlet loc_regions_region_liveness_tags (preserve_liveness: bool) (r: Set.set HS.rid) : Tot (Ghost.erased (Set.set HS.rid)) =\n if preserve_liveness then Ghost.hide Set.empty else Ghost.hide r\n\nlet loc_regions #al #c preserve_liveness r =\n let region_liveness_tags = loc_regions_region_liveness_tags preserve_liveness r in\n let addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { r' `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y } ) =\n GSet.complement GSet.empty\n in\n let live_addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { addrs r' `GSet.subset` y } ) =\n addrs r'\n in\n Loc\n (Ghost.hide r)\n region_liveness_tags\n (mk_non_live_addrs addrs)\n (mk_live_addrs live_addrs)\n (Ghost.hide (aloc_domain c (Ghost.hide r) addrs))\n\nlet aloc_includes (#al: aloc_t) (#c: cls al) (b0 b: aloc c) : GTot Type0 =\n b0.region == b.region /\\ b0.addr == b.addr /\\ Some? b0.loc == Some? b.loc /\\ (if Some? b0.loc && Some? b.loc then c.aloc_includes (Some?.v b0.loc) (Some?.v b.loc) else True)\n\nlet loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b: aloc c)\n: GTot Type0\n (decreases s)\n= exists (b0 : aloc c) . b0 `GSet.mem` s /\\ b0 `aloc_includes` b\n\nlet loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: GTot Type0\n (decreases s2)\n= forall (b2: aloc c) . GSet.mem b2 s2 ==> loc_aux_includes_buffer s1 b2\n\nlet loc_aux_includes_union_l\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s \\/ loc_aux_includes s2 s))\n (ensures (loc_aux_includes (GSet.union s1 s2) s))\n (decreases s)\n= ()\n\nlet loc_aux_includes_refl\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n: Lemma\n (loc_aux_includes s s)\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)\n\nlet loc_aux_includes_subset\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)\n\nlet loc_aux_includes_subset'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n [SMTPatOr [\n [SMTPat (s1 `GSet.subset` s2)];\n [SMTPat (loc_aux_includes s2 s1)];\n ]]\n= loc_aux_includes_subset s1 s2\n\nlet loc_aux_includes_union_l_r\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s s') s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s s' s\n\nlet loc_aux_includes_union_l_l\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s' s) s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s' s s\n\nlet loc_aux_includes_buffer_includes\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b1 b2: aloc c)\n: Lemma\n (requires (loc_aux_includes_buffer s b1 /\\ b1 `aloc_includes` b2))\n (ensures (loc_aux_includes_buffer s b2))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))\n\nlet loc_aux_includes_loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n (b: aloc c)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_buffer s2 b))\n (ensures (loc_aux_includes_buffer s1 b))\n= Classical.forall_intro_3 (fun s b1 b2 -> Classical.move_requires (loc_aux_includes_buffer_includes #al #c s b1) b2)\n\nlet loc_aux_includes_trans\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))\n\nlet addrs_of_loc_weak_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (loc_union l1 l2) r == GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r))\n [SMTPat (addrs_of_loc_weak (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc_weak (loc_union l1 l2) r) (GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r)))\n\nlet addrs_of_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l1 l2) r == GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r))\n [SMTPat (addrs_of_loc (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc (loc_union l1 l2) r) (GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r)))\n\nunfold\nlet loc_includes' #al (#c: cls al) (s1 s2: loc c) =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in (\n Set.subset regions2 regions1 /\\\n Set.subset (Ghost.reveal (Loc?.region_liveness_tags s2)) (Ghost.reveal (Loc?.region_liveness_tags s1)) /\\\n (\n forall (r: HS.rid { Set.mem r regions2 } ) .\n GSet.subset (Loc?.non_live_addrs s2 r) (Loc?.non_live_addrs s1 r)\n ) /\\\n (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc_weak s2 r) (addrs_of_loc_weak s1 r)\n ) /\\ (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc s2 r) (addrs_of_loc s1 r)\n ) /\\ (\n (Ghost.reveal (Loc?.aux s1)) `loc_aux_includes` (Ghost.reveal (Loc?.aux s2))\n )\n )\n\nlet loc_includes #al #c s1 s2 =\n loc_includes' s1 s2\n\nlet loc_includes_refl #al #c s =\n loc_aux_includes_refl (Ghost.reveal (Loc?.aux s))\n\nlet loc_includes_refl'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: Lemma\n (loc_includes s s)\n [SMTPat (loc_includes s s)]\n= loc_includes_refl s\n\nlet loc_includes_trans #al #c s1 s2 s3 =\n loc_aux_includes_trans (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s3))\n\nlet loc_includes_union_r #al #c s s1 s2 = ()\n\nlet loc_includes_union_l #al #c s1 s2 s =\n let u12 = loc_union s1 s2 in\n Classical.or_elim\n #(loc_includes s1 s)\n #(loc_includes s2 s)\n #(fun _ -> loc_includes (loc_union s1 s2) s)\n (fun _ ->\n loc_aux_includes_union_l_r (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2));\n assert (loc_includes (loc_union s1 s2) s1);\n loc_includes_trans u12 s1 s)\n (fun _ ->\n loc_aux_includes_union_l_l (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s1));\n assert (loc_includes (loc_union s1 s2) s2);\n loc_includes_trans u12 s2 s)\n\nlet loc_includes_none #al #c s = ()\n\nlet loc_includes_none_elim #al #c s =\n assert (s `loc_equal` loc_none)\n\nlet loc_includes_aloc #al #c #r #n b1 b2 = ()\n\nlet loc_includes_aloc_elim #aloc #c #r1 #r2 #n1 #n2 b1 b2 = ()\n\nlet addrs_of_loc_loc_of_aloc\n (#al: aloc_t)\n (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (p: al r a)\n (r': HS.rid)\n: Lemma\n (addrs_of_loc (loc_of_aloc #_ #c p) r' `GSet.equal` (if r = r' then GSet.singleton a else GSet.empty))\n [SMTPat (addrs_of_loc (loc_of_aloc #_ #c p) r')]\n= ()\n\nlet loc_includes_addresses_aloc #al #c preserve_liveness r s #a p = ()\n\nlet loc_includes_region_aloc #al #c preserve_liveness s #r #a b = ()\n\nlet loc_includes_region_addresses #al #c s preserve_liveness1 preserve_liveness2 r a = ()\n\nlet loc_includes_region_region #al #c preserve_liveness1 preserve_liveness2 s1 s2 = ()\n\nlet loc_includes_region_union_l #al #c preserve_liveness l s1 s2 =\n assert ((loc_regions #_ #c preserve_liveness (Set.intersect s2 (Set.complement s1)) `loc_union` loc_regions #_ #c preserve_liveness (Set.intersect s2 s1)) `loc_equal` loc_regions preserve_liveness s2);\n loc_includes_region_region #_ #c preserve_liveness preserve_liveness s1 (Set.intersect s2 s1);\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)));\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 s1));\n loc_includes_union_r (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1))) (loc_regions preserve_liveness (Set.intersect s2 s1))\n\nlet loc_includes_addresses_addresses #al c preserve_liveness1 preserve_liveness2 r s1 s2 = ()\n\n(* Disjointness of two memory locations *)\n\nlet aloc_disjoint (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : GTot Type0 =\n if b1.region = b2.region && b1.addr = b2.addr\n then Some? b1.loc /\\ Some? b2.loc /\\ c.aloc_disjoint (Some?.v b1.loc) (Some?.v b2.loc)\n else True\n\nlet aloc_disjoint_sym (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : Lemma\n (aloc_disjoint b1 b2 <==> aloc_disjoint b2 b1)\n= Classical.forall_intro_2 (fun r a -> Classical.forall_intro_2 (fun b1 b2 -> c.aloc_disjoint_sym #r #a b1 b2))\n\nlet loc_aux_disjoint\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: GTot Type0\n= forall (b1 b2: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b2 l2) ==> aloc_disjoint b1 b2\n\nlet loc_aux_disjoint_union_l\n (#al: aloc_t) (#c: cls al)\n (ll1 lr1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint (GSet.union ll1 lr1) l2 <==> (loc_aux_disjoint ll1 l2 /\\ loc_aux_disjoint lr1 l2)))\n= ()\n\nlet loc_aux_disjoint_union_r\n (#al: aloc_t) (#c: cls al)\n (l1 ll2 lr2: GSet.set (aloc c))\n: Lemma\n (loc_aux_disjoint l1 (GSet.union ll2 lr2) <==> (loc_aux_disjoint l1 ll2 /\\ loc_aux_disjoint l1 lr2))\n= ()\n\nlet loc_aux_disjoint_sym\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint l1 l2 <==> loc_aux_disjoint l2 l1))\n= Classical.forall_intro_2 (aloc_disjoint_sym #al #c)\n\nlet regions_of_loc_loc_union\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (regions_of_loc (loc_union s1 s2) == regions_of_loc s1 `Set.union` regions_of_loc s2)\n [SMTPat (regions_of_loc (loc_union s1 s2))]\n= assert (regions_of_loc (loc_union s1 s2) `Set.equal` (regions_of_loc s1 `Set.union` regions_of_loc s2))\n\nlet regions_of_loc_monotonic\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_includes s1 s2))\n (ensures (Set.subset (regions_of_loc s2) (regions_of_loc s1)))\n= ()\n\nlet loc_disjoint_region_liveness_tags (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty\n\nlet loc_disjoint_addrs (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n (forall (r: HS.rid) .\n GSet.subset (GSet.intersect (addrs_of_loc_weak l1 r) (addrs_of_loc l2 r)) GSet.empty /\\\n GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc_weak l2 r)) GSet.empty\n )\n\nlet loc_disjoint_aux (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n loc_aux_disjoint (Ghost.reveal (Loc?.aux l1)) (Ghost.reveal (Loc?.aux l2))\n\nlet loc_disjoint'\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n: GTot Type0\n= loc_disjoint_region_liveness_tags l1 l2 /\\\n loc_disjoint_addrs l1 l2 /\\\n loc_disjoint_aux l1 l2\n\nlet loc_disjoint = loc_disjoint'\n\nlet loc_disjoint_sym #al #c l1 l2 =\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c)\n\nlet loc_disjoint_sym'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))\n [SMTPat (loc_disjoint s1 s2)]\n= loc_disjoint_sym s1 s2\n\nlet loc_disjoint_none_r #al #c s = ()\n\nlet loc_disjoint_union_r #al #c s s1 s2 = ()\n\nlet aloc_disjoint_includes (#al: aloc_t) (#c: cls al) (b1 b2 b3 : aloc c) : Lemma\n (requires (aloc_disjoint b1 b2 /\\ aloc_includes b2 b3))\n (ensures (aloc_disjoint b1 b3))\n= if b1.region = b2.region && b1.addr = b2.addr\n then begin\n c.aloc_includes_refl (Some?.v b1.loc);\n c.aloc_disjoint_includes (Some?.v b1.loc) (Some?.v b2.loc) (Some?.v b1.loc) (Some?.v b3.loc)\n end\n else ()\n\nlet loc_aux_disjoint_loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (l1 l2 l3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\n= // FIXME: WHY WHY WHY do I need this assert?\n assert (forall (b1 b3: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b3 l3) ==> (exists (b2: aloc c) . GSet.mem b2 l2 /\\ aloc_disjoint b1 b2 /\\ aloc_includes b2 b3));\n Classical.forall_intro_3 (fun b1 b2 b3 -> Classical.move_requires (aloc_disjoint_includes #al #c b1 b2) b3)\n\nlet loc_disjoint_includes #al #c p1 p2 p1' p2' =\n regions_of_loc_monotonic p1 p1';\n regions_of_loc_monotonic p2 p2';\n let l1 = Ghost.reveal (Loc?.aux p1) in\n let l2 = Ghost.reveal (Loc?.aux p2) in\n let l1' = Ghost.reveal (Loc?.aux p1') in\n let l2' = Ghost.reveal (Loc?.aux p2') in\n loc_aux_disjoint_loc_aux_includes l1 l2 l2';\n loc_aux_disjoint_sym l1 l2';\n loc_aux_disjoint_loc_aux_includes l2' l1 l1';\n loc_aux_disjoint_sym l2' l1'\n\nlet loc_disjoint_aloc_intro #al #c #r1 #a1 #r2 #a2 b1 b2 = ()\n\nlet loc_disjoint_aloc_elim #al #c #r1 #a1 #r2 #a2 b1 b2 =\n // FIXME: WHY WHY WHY this assert?\n assert (aloc_disjoint (ALoc #_ #c r1 a1 (Some b1)) (ALoc #_ #c r2 a2 (Some b2)))\n\n#push-options \"--z3rlimit 15\"\nlet loc_disjoint_addresses_intro #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness1 r1 n1))) (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness2 r2 n2))))\n#pop-options\n\nlet loc_disjoint_addresses_elim #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 = ()\n\nlet loc_disjoint_aloc_addresses_intro #al #c #r' #a' p preserve_liveness r n = ()\n\nlet loc_disjoint_aloc_addresses_elim #al #c #r' #a' p preserve_liveness r n = ()\n\nlet loc_disjoint_regions #al #c preserve_liveness1 preserve_liveness2 rs1 rs2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness1 rs1))) (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness2 rs2))))\n\nlet loc_none_in_some_region #a (c: cls a) (r: HS.rid) : GTot (loc c) =\n Loc\n (Ghost.hide (Set.singleton r))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)\n\n(** Liveness-insensitive memory locations *)\n\nlet address_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))\n\nlet loc_includes_address_liveness_insensitive_locs_aloc #al #c #r #n a = ()\n\nlet loc_includes_address_liveness_insensitive_locs_addresses #al c r a = ()\n\nlet region_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.complement GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))\n\nlet loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs #al c = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_regions #al c r = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_addresses #al c preserve_liveness r a = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_of_aloc #al c #r #a x = ()\n\n(** The modifies clause proper *)\n\nlet modifies_preserves_livenesses\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s r)))\n ) ==> (\n HS.contains h2 p\n ))\n\nlet modifies_preserves_livenesses_elim\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (p: HS.mreference t pre)\n: Lemma\n (requires (modifies_preserves_livenesses s h1 h2 /\\ HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))))\n (ensures (HS.contains h2 p))\n= ()\n\nlet modifies_preserves_livenesses_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p))\n ))\n: Lemma\n (modifies_preserves_livenesses s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'\n\nlet modifies_preserves_mreferences\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s r)))\n ) ==> (\n HS.contains h2 p /\\\n HS.sel h2 p == HS.sel h1 p\n ))\n\nlet modifies_preserves_mreferences_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p /\\ HS.sel h2 p == HS.sel h1 p))\n ))\n: Lemma\n (modifies_preserves_mreferences s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p /\\ h2 `HS.sel` p == h1 `HS.sel` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'\n\nlet modifies_preserves_alocs\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (a: nat) (b: al r a) .\n loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))\n ==>\n c.aloc_preserved b h1 h2\n )\n\nlet modifies_preserves_alocs_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (u: unit { modifies_preserves_mreferences s h1 h2 } )\n (f: (\n (r: HS.rid) ->\n (a: nat) ->\n (b: al r a) ->\n Lemma\n (requires (\n Set.mem r (regions_of_loc s) /\\\n (~ (GSet.mem a (addrs_of_loc_weak s r))) /\\\n (GSet.mem a (addrs_of_loc_aux s r) /\\ loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b))))\n ))\n (ensures (c.aloc_preserved b h1 h2))\n ))\n: Lemma\n (modifies_preserves_alocs s h1 h2)\n= let f'\n (r: HS.rid)\n (a: nat)\n (b: al r a)\n : Lemma\n (requires (loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))))\n (ensures (c.aloc_preserved b h1 h2))\n = if Set.mem r (regions_of_loc s) && (not (GSet.mem a (addrs_of_loc_weak s r)))\n then begin\n if GSet.mem a (addrs_of_loc_aux s r)\n then\n Classical.move_requires (f r a) b\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n end else if Set.mem r (regions_of_loc s)\n then begin\n assert (GSet.mem a (addrs_of_loc_weak s r));\n assert (GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux s)));\n assert (aloc_disjoint #_ #c (ALoc r a None) (ALoc r a (Some b)));\n assert False\n end\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n in\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (f' r a) b)\n\nlet modifies_preserves_regions\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= forall (r: HS.rid) . (HS.live_region h1 r /\\ ~ (Set.mem r (Ghost.reveal (Loc?.region_liveness_tags s)))) ==> HS.live_region h2 r\n\n\nlet modifies_preserves_not_unused_in\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (n: nat) . (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n\nlet modifies_preserves_not_unused_in_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ))\n (ensures (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n ))\n: Lemma\n (modifies_preserves_not_unused_in s h1 h2)\n= let f'\n (r: HS.rid)\n (n: nat)\n : Lemma\n ((\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n = Classical.move_requires (f r) n\n in\n Classical.forall_intro_2 f'\n\nlet modifies'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= modifies_preserves_regions s h1 h2 /\\\n modifies_preserves_not_unused_in s h1 h2 /\\\n modifies_preserves_mreferences s h1 h2 /\\\n modifies_preserves_livenesses s h1 h2 /\\\n modifies_preserves_alocs s h1 h2\n\nlet modifies = modifies'\n\nval modifies_intro_strong\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n (Set.mem r (regions_of_loc l) ==> ~ (GSet.mem n (Loc?.non_live_addrs l r))) /\\\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')\n\nlet modifies_intro_strong #al #c l h h' regions mrefs lives unused_ins alocs =\n Classical.forall_intro (Classical.move_requires regions);\n assert (modifies_preserves_regions l h h');\n\n let aux (t:Type) (pre:Preorder.preorder t) (p:HS.mreference t pre)\n :Lemma (requires (HS.contains h p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc l) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc l (HS.frameOf p))))))\n (ensures (HS.contains h' p /\\ HS.sel h' p == HS.sel h p))\n =\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l);\n // FIXME: WHY WHY WHY is this assert necessary?\n assert_spinoff (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n // FIXME: Now this one is too :)\n assert (loc_disjoint_addrs (loc_mreference p) l);\n assert ((loc_disjoint (loc_mreference p) l));\n mrefs t pre p\n in\n\n modifies_preserves_mreferences_intro l h h' aux;\n Classical.forall_intro_3 (fun t pre p -> Classical.move_requires (lives t pre) p);\n modifies_preserves_not_unused_in_intro l h h' (fun r n ->\n unused_ins r n\n );\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n alocs r a b\n )\n\nlet modifies_intro #al #c l h h' regions mrefs lives unused_ins alocs =\n modifies_intro_strong l h h'\n regions\n mrefs\n lives\n (fun r n -> unused_ins r n)\n alocs\n\nlet modifies_none_intro #al #c h h' regions mrefs unused_ins =\n modifies_intro_strong #_ #c loc_none h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> mrefs t pre b)\n (fun r n -> unused_ins r n)\n (fun r a x ->\n c.same_mreference_aloc_preserved x h h' (fun t pre b -> mrefs t pre b)\n )\n\nlet modifies_address_intro #al #c r n h h' regions mrefs unused_ins =\n Classical.forall_intro (Classical.move_requires regions);\n let l : loc c = loc_addresses #_ #c false r (Set.singleton n) in\n modifies_preserves_mreferences_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_livenesses_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_not_unused_in_intro l h h'\n (fun r n -> unused_ins r n)\n ;\n modifies_preserves_alocs_intro l h h' ()\n (fun r a b ->\n c.same_mreference_aloc_preserved b h h' (fun t pre p -> mrefs t pre p)\n )\n\nlet modifies_aloc_intro #al #c #r #n x h h' regions mrefs livenesses unused_ins alocs =\n modifies_intro_strong #_ #c (loc_of_aloc x) h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> livenesses t pre b)\n (fun r n -> unused_ins r n)\n (fun r' n' z ->\n if r' = r && n' = n\n then begin\n loc_disjoint_aloc_elim #_ #c z x;\n alocs z\n end else\n c.same_mreference_aloc_preserved z h h' (fun t pre p ->\n mrefs t pre p\n )\n )\n\nlet modifies_live_region #al #c s h1 h2 r = ()\n\nlet modifies_mreference_elim #al #c #t #pre b p h h' = ()\n\nlet modifies_aloc_elim #al #c #r #a b p h h' = ()\n\nlet modifies_refl #al #c s h =\n Classical.forall_intro_3 (fun r a b -> c.aloc_preserved_refl #r #a b h)\n\nlet modifies_loc_includes #al #c s1 h h' s2 =\n assert (modifies_preserves_mreferences s1 h h');\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c);\n Classical.forall_intro_3 (fun l1 l2 l3 -> Classical.move_requires (loc_aux_disjoint_loc_aux_includes #al #c l1 l2) l3);\n assert (modifies_preserves_alocs s1 h h')\n\nlet modifies_preserves_liveness #al #c s1 s2 h h' #t #pre r = ()\n\n#push-options \"--z3rlimit 20 --max_fuel 0 --max_ifuel 0\"\nlet modifies_preserves_liveness_strong #al #c s1 s2 h h' #t #pre r x =\n let rg = HS.frameOf r in\n let ad = HS.as_addr r in\n let la = loc_of_aloc #_ #c #rg #ad x in\n if Set.mem rg (regions_of_loc s2)\n then begin\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` Loc?.non_live_addrs (address_liveness_insensitive_locs c) rg);\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` GSet.empty);\n assert (~ (GSet.mem ad (Loc?.non_live_addrs s2 rg)));\n if Set.mem rg (regions_of_loc s1)\n then begin\n if GSet.mem ad (Loc?.non_live_addrs s1 rg)\n then begin\n assert (loc_disjoint_aux s1 la);\n assert (GSet.subset (Loc?.non_live_addrs s1 rg) (Loc?.live_addrs s1 rg));\n assert (aloc_domain c (Loc?.regions s1) (Loc?.live_addrs s1) `GSet.subset` (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad None) (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad (Some x)) (Ghost.reveal (Loc?.aux la)));\n assert (aloc_disjoint (ALoc rg ad None) (ALoc #_ #c rg ad (Some x)));\n ()\n end else ()\n end else ()\n end else ()\n#pop-options\n\nlet modifies_preserves_region_liveness #al #c l1 l2 h h' r = ()\n\nlet modifies_preserves_region_liveness_reference #al #c l1 l2 h h' #t #pre r = ()\n\nlet modifies_preserves_region_liveness_aloc #al #c l1 l2 h h' #r #n x =\n if Set.mem r (Ghost.reveal (Loc?.region_liveness_tags l1))\n then begin\n assert (GSet.subset (GSet.complement GSet.empty) (Loc?.non_live_addrs l1 r));\n assert (GSet.subset (Loc?.non_live_addrs l1 r) (Loc?.live_addrs l1 r))\n end else ()\n\nlet modifies_trans'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s h1 h2 /\\ modifies s h2 h3))\n (ensures (modifies s h1 h3))\n= Classical.forall_intro_3 (fun r a b -> Classical.move_requires (c.aloc_preserved_trans #r #a b h1 h2) h3)\n\nlet modifies_trans #al #c s12 h1 h2 s23 h3 =\n let u = loc_union s12 s23 in\n modifies_loc_includes u h1 h2 s12;\n modifies_loc_includes u h2 h3 s23;\n modifies_trans' u h1 h2 h3\n\nlet addr_unused_in_aloc_preserved\n (#al: aloc_t) (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (b: al r a)\n (h1: HS.mem)\n (h2: HS.mem)\n : Lemma\n (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)))\n (ensures (c.aloc_preserved b h1 h2))\n= c.same_mreference_aloc_preserved b h1 h2 (fun a' pre r' -> assert False)\n\n#push-options \"--z3rlimit 10\"\nlet modifies_only_live_regions_weak\n (#al: aloc_t) (#c: cls al)\n (rs: Set.set HS.rid)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n loc_disjoint (loc_regions false rs) l /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))\n= assert (modifies_preserves_mreferences l h h'); // FIXME: WHY WHY WHY?\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (addr_unused_in_aloc_preserved #al #c #r #a b h) h')\n#pop-options\n\n(* Restrict a set of locations along a set of regions *)\n\nlet restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: GTot (loc c)\n= let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let regions' = (Ghost.hide (Set.intersect (Ghost.reveal regions) rs)) in\n Loc\n regions'\n (Ghost.hide (Set.intersect (Ghost.reveal region_liveness_tags) rs))\n (mk_non_live_addrs (fun (r: addrs_dom regions') -> (non_live_addrs r <: GSet.set nat)))\n (mk_live_addrs (fun (r: addrs_dom regions') -> (live_addrs r <: GSet.set nat)))\n (Ghost.hide (GSet.intersect (Ghost.reveal aux) (aloc_domain c (Ghost.hide rs) (fun r -> GSet.complement GSet.empty))))\n\nlet regions_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (regions_of_loc (restrict_to_regions l rs) == Set.intersect (regions_of_loc l) rs)\n [SMTPat (regions_of_loc (restrict_to_regions l rs))]\n= assert (Set.equal (regions_of_loc (restrict_to_regions l rs)) (Set.intersect (regions_of_loc l) rs))\n\nlet addrs_of_loc_weak_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))\n [SMTPat (addrs_of_loc_weak (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc_weak (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))\n\nlet addrs_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc l r else GSet.empty))\n [SMTPat (addrs_of_loc (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc l r else GSet.empty))\n\nlet loc_includes_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes l (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)\n\nlet loc_includes_loc_union_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_equal (loc_union (restrict_to_regions l rs) (restrict_to_regions l (Set.complement rs))) l)\n= ()\n\nlet loc_includes_loc_regions_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes (loc_regions false rs) (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)\n\nlet modifies_only_live_regions #al #c rs l h h' =\n let s = l in\n let c_rs = Set.complement rs in\n let s_rs = restrict_to_regions s rs in\n let s_c_rs = restrict_to_regions s c_rs in\n let lrs = loc_regions false rs in\n loc_includes_loc_regions_restrict_to_regions s rs;\n loc_includes_union_l lrs s_c_rs s_rs;\n loc_includes_refl s_c_rs;\n loc_includes_union_l lrs s_c_rs s_c_rs;\n loc_includes_union_r (loc_union lrs s_c_rs) s_rs s_c_rs;\n loc_includes_loc_union_restrict_to_regions s rs;\n loc_includes_trans (loc_union lrs s_c_rs) (loc_union s_rs s_c_rs) s;\n modifies_loc_includes (loc_union lrs s_c_rs) h h' (loc_union lrs s);\n loc_includes_loc_regions_restrict_to_regions s c_rs;\n loc_disjoint_regions #al #c false false rs c_rs;\n loc_includes_refl lrs;\n loc_disjoint_includes lrs (loc_regions false c_rs) lrs s_c_rs;\n modifies_only_live_regions_weak rs s_c_rs h h';\n loc_includes_restrict_to_regions s c_rs;\n modifies_loc_includes s h h' s_c_rs\n\nlet no_upd_fresh_region #al #c r l h0 h1 =\n modifies_only_live_regions (HS.mod_set (Set.singleton r)) l h0 h1\n\nlet fresh_frame_modifies #al c h0 h1 =\n modifies_intro_strong #_ #c loc_none h0 h1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x h0 h1 (fun _ _ _ -> ()))\n\nlet new_region_modifies #al c m0 r0 col\n= let (_, m1) = HS.new_eternal_region m0 r0 col in\n modifies_intro_strong #_ #c loc_none m0 m1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x m0 m1 (fun _ _ _ -> ()))\n\nlet popped_modifies #al c h0 h1 =\n let l = loc_region_only #_ #c false (HS.get_tip h0) in\n modifies_preserves_mreferences_intro l h0 h1 (fun t pre p ->\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l );\n // FIXME: WHY WHY WHY is this assert necessary?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n ()\n );\n modifies_preserves_alocs_intro l h0 h1 () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n ()\n )\n\n\nlet modifies_fresh_frame_popped #al #c h0 h1 s h2 h3 =\n fresh_frame_modifies c h0 h1;\n let r = loc_region_only #al #c false (HS.get_tip h2) in\n let rs = HS.mod_set (Set.singleton (HS.get_tip h1)) in\n let s' = loc_union (loc_regions false rs) s in\n modifies_trans' s' h0 h1 h2;\n assert (modifies_preserves_mreferences r h2 h3);\n let f23 (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (r <> HS.get_tip h2))\n (ensures (c.aloc_preserved b h2 h3))\n = c.same_mreference_aloc_preserved #r #a b h2 h3 (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro r h2 h3 () (fun r a b ->\n f23 r a b\n );\n modifies_trans' s' h0 h2 h3;\n modifies_only_live_regions rs s h0 h3\n\nlet modifies_loc_regions_intro #al #c rs h1 h2 =\n let f (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem r rs)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n assert (modifies_preserves_mreferences (loc_regions #al #c true rs) h1 h2);\n modifies_preserves_alocs_intro (loc_regions #_ #c true rs) h1 h2 () (fun r a b ->\n f r a b\n )\n\n#push-options \"--z3rlimit 20\"\nlet modifies_loc_addresses_intro_weak\n (#al: aloc_t) (#c: cls al)\n (r: HS.rid)\n (s: Set.set nat)\n (l: loc c)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r s h1 h2 /\\\n loc_disjoint l (loc_region_only false r)\n ))\n (ensures (modifies (loc_union (loc_addresses true r s) l) h1 h2))\n= modifies_preserves_mreferences_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_livenesses_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_not_unused_in_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' n' ->\n ()\n );\n let f (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem a s)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r_ -> ())\n in\n modifies_preserves_alocs_intro (loc_union (loc_addresses true r s) l) h1 h2 () (fun r' a b -> if r = r' then f a b else ()\n )\n\nlet modifies_loc_addresses_intro #al #c r s l h1 h2 =\n loc_includes_loc_regions_restrict_to_regions l (Set.singleton r);\n loc_includes_loc_union_restrict_to_regions l (Set.singleton r);\n assert (modifies (loc_union (loc_region_only false r) (loc_union (restrict_to_regions l (Set.singleton r)) (restrict_to_regions l (Set.complement (Set.singleton r))))) h1 h2);\n let l' = restrict_to_regions l (Set.complement (Set.singleton r)) in\n loc_includes_refl (loc_region_only #_ #c false r) ;\n loc_includes_loc_regions_restrict_to_regions l (Set.complement (Set.singleton r));\n loc_disjoint_regions #_ #c false false (Set.complement (Set.singleton r)) (Set.singleton r);\n loc_disjoint_includes (loc_regions #_ #c false (Set.complement (Set.singleton r))) (loc_region_only false r) l' (loc_region_only false r);\n modifies_loc_addresses_intro_weak r s l' h1 h2;\n loc_includes_restrict_to_regions l (Set.complement (Set.singleton r))\n#pop-options\n\nlet modifies_ralloc_post #al #c #a #rel i init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g\n\nlet modifies_salloc_post #al #c #a #rel init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g\n\nlet modifies_free #al #c #a #rel r m =\n let g (r': HS.rid) (a: nat) (b: al r' a) : Lemma\n (requires (r' <> HS.frameOf r \\/ a <> HS.as_addr r))\n (ensures (c.aloc_preserved b m (HS.free r m)))\n = c.same_mreference_aloc_preserved #r' #a b m (HS.free r m) (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro (loc_freed_mreference #_ #c r) m (HS.free r m) () (fun r a b -> g r a b)\n\nlet modifies_none_modifies #al #c h1 h2\n= let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h1 h2)\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g\n\nlet modifies_upd #al #c #t #pre r v h =\n let h' = HS.upd h r v in\n modifies_intro #_ #c (loc_mreference r) h h'\n (fun r -> ())\n (fun t pre b -> ())\n (fun t pre b -> ())\n (fun r n -> ())\n (fun r a b -> c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre' r' -> ()))\n\n#push-options \"--z3rlimit 15\"\nlet addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l (loc_of_aloc al0)) r == addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)\n= assert (addrs_of_loc (loc_union l (loc_of_aloc al0)) r `GSet.equal` addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)\n#pop-options\n\nlet addrs_of_loc_weak_loc_includes #al (#c: cls al) (l: loc c) (r0: HS.rid) (a0: nat) : Lemma\n (requires (a0 `GSet.mem` addrs_of_loc_weak l r0))\n (ensures (l `loc_includes` loc_addresses true r0 (Set.singleton a0)))\n= ()\n\nval modifies_strengthen'\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (h h' : HS.mem)\n (alocs: (\n (f: ((t: Type) -> (pre: Preorder.preorder t) -> (m: HS.mreference t pre) -> Lemma\n (requires (HS.frameOf m == r0 /\\ HS.as_addr m == a0 /\\ HS.contains h m))\n (ensures (HS.contains h' m))\n )) ->\n (x: al r0 a0) ->\n Lemma\n (requires (c.aloc_disjoint x al0 /\\ loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (requires ((~ (a0 `GSet.mem` addrs_of_loc_weak l r0)) /\\ modifies (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h'))\n (ensures (modifies (loc_union l (loc_of_aloc al0)) h h'))\n\n#push-options \"--z3rlimit 15 --fuel 0 --ifuel 0\"\nlet modifies_strengthen' #al #c l #r0 #a0 al0 h h' alocs =\n Classical.forall_intro (addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton l al0);\n assert (modifies_preserves_regions (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_mreferences (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_not_unused_in (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_livenesses (loc_union l (loc_of_aloc al0)) h h');\n modifies_preserves_alocs_intro (loc_union l (loc_of_aloc al0)) h h' () (fun r a b ->\n if r = r0 && a = a0\n then begin\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_union l (loc_of_aloc al0)))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux l)) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_disjoint l (loc_of_aloc b));\n loc_disjoint_sym l (loc_of_aloc b);\n assert (loc_aux_disjoint #_ #c (Ghost.reveal (Loc?.aux (loc_of_aloc al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint #_ #c (GSet.singleton (ALoc r0 a0 (Some al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (GSet.mem (ALoc r0 a0 (Some al0)) (GSet.singleton (ALoc #_ #c r0 a0 (Some al0))));\n assert (GSet.mem (ALoc r0 a0 (Some b)) (GSet.singleton (ALoc #_ #c r0 a0 (Some b))));\n assert (aloc_disjoint #_ #c (ALoc r0 a0 (Some al0)) (ALoc r0 a0 (Some b)));\n assert (c.aloc_disjoint al0 b);\n c.aloc_disjoint_sym al0 b;\n alocs (fun t pre m -> ()) b\n end\n else begin\n assert (loc_disjoint (loc_union l (loc_addresses true r0 (Set.singleton a0))) (loc_of_aloc b))\n by (let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 64;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=5'\";\n ())\n end\n );\n assert (modifies (loc_union l (loc_of_aloc al0)) h h')\n#pop-options\n\nlet modifies_strengthen #al #c l #r0 #a0 al0 h h' alocs =\n if a0 `GSet.mem` addrs_of_loc_weak l r0\n then begin\n addrs_of_loc_weak_loc_includes l r0 a0;\n loc_includes_refl l;\n loc_includes_union_r l l (loc_addresses true r0 (Set.singleton a0));\n loc_includes_union_l l (loc_of_aloc al0) l;\n loc_includes_trans (loc_union l (loc_of_aloc al0)) l (loc_union l (loc_addresses true r0 (Set.singleton a0)));\n modifies_loc_includes (loc_union l (loc_of_aloc al0)) h h' (loc_union l (loc_addresses true r0 (Set.singleton a0)))\n end\n else\n modifies_strengthen' l al0 h h' alocs\n\n\nlet does_not_contain_addr' (h: HS.mem) (ra: HS.rid * nat) : GTot Type0 =\n HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))\n\nlet does_not_contain_addr = does_not_contain_addr'\n\nlet not_live_region_does_not_contain_addr h ra = ()\n\nlet unused_in_does_not_contain_addr h #a #rel r = ()\n\nlet addr_unused_in_does_not_contain_addr h ra = ()\n\nlet does_not_contain_addr_addr_unused_in h ra = ()\n\nlet free_does_not_contain_addr #a #rel r m x = ()\n\nlet does_not_contain_addr_elim #a #rel r m x = ()\n\nlet disjoint_addrs_of_loc_loc_disjoint\n (#al: aloc_t)\n (#c: cls al)\n (l1 l2: loc c)\n: Lemma\n (requires (\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty /\\\n (forall r . GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc l2 r)) GSet.empty)\n ))\n (ensures (loc_disjoint l1 l2))\n= // FIXME: WHY WHY WHY do I need this assert?\n let l1' = Ghost.reveal (Loc?.aux l1) in\n let l2' = Ghost.reveal (Loc?.aux l2) in\n assert (forall (b1 b2: aloc c) . (GSet.mem b1 l1' /\\ GSet.mem b2 l2') ==> aloc_disjoint b1 b2)\n\nlet loc_not_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (HS.live_region h r /\\ ~ (h `does_not_contain_addr` (r, a))))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs f)\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))\n\nlet loc_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n if not (HS.live_region h r)\n then\n GSet.complement GSet.empty\n else\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a)))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide (Set.complement (FStar.Map.domain (HS.get_hmap h))))\n (mk_non_live_addrs (fun x -> f x))\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))\n\nlet loc_regions_unused_in #al c h rs = ()\n\n#push-options \"--z3rlimit 20\"\nlet loc_addresses_unused_in #al c r a h = ()\n#pop-options\n\nlet loc_addresses_not_unused_in #al c r a h = ()\n\n#push-options \"--z3rlimit 15\"\nlet loc_unused_in_not_unused_in_disjoint #al c h =\n assert (Ghost.reveal (Loc?.aux (loc_unused_in c h)) `loc_aux_disjoint` Ghost.reveal (Loc?.aux (loc_not_unused_in c h)));\n assert_spinoff (loc_disjoint #al #c (loc_unused_in #al c h)\n (loc_not_unused_in #al c h))\n#pop-options\n\n#push-options \"--z3cliopt 'smt.qi.eager_threshold=100'\"\nlet not_live_region_loc_not_unused_in_disjoint #al c h0 r\n= let l1 = loc_region_only false r in\n let l2 = loc_not_unused_in c h0 in\n assert (loc_disjoint_region_liveness_tags l1 l2);\n assert (loc_disjoint_addrs l1 l2);\n assert (loc_disjoint_aux l1 l2)\n\n#push-options \"--z3rlimit 16\"\nlet modifies_address_liveness_insensitive_unused_in #al c h h' =\n assert (forall r . HS.live_region h r ==> HS.live_region h' r) ;\n let ln' = loc_not_unused_in c h' in\n let ln = loc_not_unused_in c h in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs ln r `GSet.subset` Loc?.non_live_addrs ln' r);\n assert (ln' `loc_includes` ln);\n let lu = loc_unused_in c h in\n let lu' = loc_unused_in c h' in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs lu' r `GSet.subset` Loc?.non_live_addrs lu r);\n assert (forall (r: HS.rid) . Loc?.live_addrs lu' r `GSet.subset` Loc?.live_addrs lu r);\n assert (lu `loc_includes` lu')\n#pop-options\n#pop-options\n\n#push-options \"--max_fuel 0 --max_ifuel 0 --z3rlimit 16\"\nlet modifies_only_not_unused_in #al #c l h h' =\n assert (modifies_preserves_regions l h h');\n assert (modifies_preserves_not_unused_in l h h');\n assert (modifies_preserves_mreferences l h h');\n assert (modifies_preserves_livenesses l h h');\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n if StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a))\n then c.same_mreference_aloc_preserved b h h' (fun a' pre' r' -> ())\n else ()\n )\n#pop-options\n\nlet mreference_live_loc_not_unused_in #al c #t #pre h b =\n Classical.move_requires (does_not_contain_addr_addr_unused_in h) (HS.frameOf b, HS.as_addr b);\n assert (~ (h `does_not_contain_addr` (HS.frameOf b, HS.as_addr b)));\n loc_addresses_not_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_trans (loc_not_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()\n\n#push-options \"--z3cliopt 'smt.qi.eager_threshold=100'\"\nlet mreference_unused_in_loc_unused_in #al c #t #pre h b =\n Classical.move_requires (addr_unused_in_does_not_contain_addr h) (HS.frameOf b, HS.as_addr b);\n loc_addresses_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_addresses_addresses c false true (HS.frameOf b) (Set.singleton (HS.as_addr b)) (Set.singleton (HS.as_addr b));\n loc_includes_trans (loc_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()\n#pop-options\n\n(* * Compositionality *)\n\nnoeq\ntype cls_union_aloc\n (al: (bool -> HS.rid -> nat -> Tot (Type u#x)))\n (r: HS.rid) (n: nat) : Type u#x\n= | ALOC_FALSE of (al false) r n\n | ALOC_TRUE of (al true) r n\n\nlet bool_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot bool =\n match l with\n | ALOC_FALSE _ -> false\n | ALOC_TRUE _ -> true\n\nlet aloc_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot ((al (bool_of_cls_union_aloc l)) r n)\n= match l with\n | ALOC_FALSE x -> x\n | ALOC_TRUE x -> x\n\nlet make_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (b: bool)\n (#r: HS.rid)\n (#n: nat)\n (l: (al b) r n)\n: Tot (cls_union_aloc al r n)\n= if b\n then ALOC_TRUE l\n else ALOC_FALSE l\n\nlet cls_union_aloc_includes\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_includes\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)\n\nlet cls_union_aloc_disjoint\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_disjoint\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)\n\nlet cls_union_aloc_preserved\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (x: cls_union_aloc al r a)\n (h h' : HS.mem)\n: GTot Type0\n= (c (bool_of_cls_union_aloc x)).aloc_preserved\n (aloc_of_cls_union_aloc x)\n h\n h'\n\nlet aloc_union = cls_union_aloc\n\nlet cls_union #al c = Cls\n #(cls_union_aloc al)\n (cls_union_aloc_includes c)\n (* aloc_includes_refl *)\n (fun #r #a x ->\n (c (bool_of_cls_union_aloc x)).aloc_includes_refl (aloc_of_cls_union_aloc x))\n (* aloc_includes_trans *)\n (fun #r #a x1 x2 x3 ->\n (c (bool_of_cls_union_aloc x1)).aloc_includes_trans\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n (aloc_of_cls_union_aloc x3)\n )\n (cls_union_aloc_disjoint c)\n (* aloc_disjoint_sym *)\n (fun #r #a x1 x2 ->\n if bool_of_cls_union_aloc x1 = bool_of_cls_union_aloc x2\n then\n (c (bool_of_cls_union_aloc x1)).aloc_disjoint_sym\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n else ()\n )\n (* aloc_disjoint_includes *)\n (fun #r #a larger1 larger2 smaller1 smaller2 ->\n (c (bool_of_cls_union_aloc larger1)).aloc_disjoint_includes\n (aloc_of_cls_union_aloc larger1)\n (aloc_of_cls_union_aloc larger2)\n (aloc_of_cls_union_aloc smaller1)\n (aloc_of_cls_union_aloc smaller2)\n )\n (cls_union_aloc_preserved c)\n (* aloc_preserved_refl *)\n (fun #r #a x h ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_refl\n (aloc_of_cls_union_aloc x)\n h\n )\n (* aloc_preserved_trans *)\n (fun #r #a x h1 h2 h3 ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_trans\n (aloc_of_cls_union_aloc x)\n h1\n h2\n h3\n )\n (* same_mreference_aloc_preserved *)\n (fun #r #a b h1 h2 f ->\n (c (bool_of_cls_union_aloc b)).same_mreference_aloc_preserved\n (aloc_of_cls_union_aloc b)\n h1\n h2\n f\n )\n\nlet union_aux_of_aux_left_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n (x: aloc (cls_union c))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n b = bool_of_cls_union_aloc #al #region #addr loc &&\n GSet.mem (ALoc region addr (Some (aloc_of_cls_union_aloc #al #region #addr loc))) s\n\nlet union_aux_of_aux_left\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n: Tot (GSet.set (aloc (cls_union c)))\n= GSet.comprehend (union_aux_of_aux_left_pred c b s)\n\nlet union_loc_of_loc #al c b l =\n let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let aux' : GSet.set (aloc #(cls_union_aloc al) (cls_union c)) =\n union_aux_of_aux_left c b (Ghost.reveal aux)\n `GSet.union`\n (aloc_domain (cls_union c) regions live_addrs)\n in\n Loc\n #(cls_union_aloc al)\n #(cls_union c)\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide aux')\n\nlet union_aux_of_aux_left_inv_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n (x: aloc (c b))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n GSet.mem (ALoc region addr (Some (make_cls_union_aloc b loc))) s\n\nlet union_aux_of_aux_left_inv\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n: Tot (GSet.set (aloc (c b)))\n= GSet.comprehend (union_aux_of_aux_left_inv_pred b s)\n\nlet mem_union_aux_of_aux_left_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (c b))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x aux <==> GSet.mem (ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc)))) (union_aux_of_aux_left c b aux))\n [SMTPat (GSet.mem x aux)]\n= ()\n\nlet mem_union_aux_of_aux_left_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (cls_union c))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x (union_aux_of_aux_left c b aux) <==> (if None? x.loc then GSet.mem (ALoc x.region x.addr None) aux else (bool_of_cls_union_aloc (Some?.v x.loc) == b /\\ GSet.mem (ALoc x.region x.addr (Some (aloc_of_cls_union_aloc (Some?.v x.loc)))) aux)))\n [SMTPat (GSet.mem x (union_aux_of_aux_left #al c b aux))]\n= ()\n\nlet addrs_of_loc_union_loc_of_loc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (union_loc_of_loc c b l) r `GSet.equal` addrs_of_loc l r)\n [SMTPat (addrs_of_loc (union_loc_of_loc #al c b l) r)]\n= ()\n\nlet union_loc_of_loc_none #al c b =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_none #_ #(c b))) (loc_none #_ #(cls_union c)))\n\n#push-options \"--z3rlimit 15\"\nlet union_loc_of_loc_union #al c b l1 l2 =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_union #_ #(c b) l1 l2)) (loc_union #_ #(cls_union c) (union_loc_of_loc c b l1) (union_loc_of_loc c b l2)))\n#pop-options\n\nlet union_loc_of_loc_addresses #al c b preserve_liveness r n =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_addresses #_ #(c b) preserve_liveness r n)) (loc_addresses #_ #(cls_union c) preserve_liveness r n))\n\nlet union_loc_of_loc_regions #al c b preserve_liveness r =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_regions #_ #(c b) preserve_liveness r)) (loc_regions #_ #(cls_union c) preserve_liveness r))\n\n#push-options \"--z3rlimit 15\"" }, { "file_name": "Steel.ST.EphemeralHashtbl.fst", "name": "Steel.ST.EphemeralHashtbl.create", "opens_and_abbrevs": [ { "abbrev": "SeqPerm", "full_module": "FStar.Seq.Permutation" }, { "abbrev": "CE", "full_module": "FStar.Algebra.CommMonoid.Equiv" }, { "abbrev": "A", "full_module": "Steel.ST.Array" }, { "abbrev": "R", "full_module": "Steel.ST.Reference" }, { "abbrev": "US", "full_module": "FStar.SizeT" }, { "abbrev": "Map", "full_module": "FStar.PartialMap" }, { "abbrev": "Seq", "full_module": "FStar.Seq" }, { "abbrev": "G", "full_module": "FStar.Ghost" }, { "open": "Steel.ST.Util" }, { "open": "Steel.ST.Effect" }, { "open": "Steel.ST.Effect.Atomic" }, { "open": "Steel.ST.Effect.Ghost" }, { "open": "Steel.Memory" }, { "open": "Steel.FractionalPermission" }, { "abbrev": "US", "full_module": "FStar.SizeT" }, { "abbrev": "Map", "full_module": "FStar.PartialMap" }, { "abbrev": "G", "full_module": "FStar.Ghost" }, { "open": "Steel.ST.Util" }, { "open": "Steel.ST.Effect" }, { "open": "Steel.ST.Effect.Atomic" }, { "open": "Steel.ST.Effect.Ghost" }, { "open": "Steel.Memory" }, { "open": "Steel.ST" }, { "open": "Steel.ST" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))", "source_definition": "let create #k #v #contents vp h n =\n let store = A.alloc #(option (k & v)) None n in\n let arr : tbl #k #v #contents vp h = {\n store_len = n;\n store = store;\n store_len_pf = () } in\n\n //\n //rewrite in terms of projections from the arr record\n //\n rewrite (A.pts_to store _ (Seq.create #(option (k & v)) (US.v n) None))\n (A.pts_to arr.store _ (Seq.create #(option (k & v)) (US.v n) None));\n\n //\n //The value vprops at this point are all emp\n //\n //A lemma that tells us that folding a monoid over a sequence of units\n // is monoid-equivalent to the unit\n //\n SeqPerm.foldm_snoc_unit_seq\n vprop_monoid\n (value_vprops_seq vp (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v));\n rewrite_equiv emp (value_vprops vp (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v));\n\n pack_tperm (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v)\n arr;\n\n return arr", "source_range": { "start_line": 243, "start_col": 0, "end_line": 276, "end_col": 12 }, "interleaved": false, "definition": "fun vp h n ->\n let store = Steel.ST.Array.alloc FStar.Pervasives.Native.None n in\n let arr = Steel.ST.EphemeralHashtbl.Mktbl n store () in\n Steel.ST.Util.rewrite (Steel.ST.Array.pts_to store\n Steel.FractionalPermission.full_perm\n (FStar.Seq.Base.create (FStar.SizeT.v n) FStar.Pervasives.Native.None))\n (Steel.ST.Array.pts_to (Mktbl?.store arr)\n Steel.FractionalPermission.full_perm\n (FStar.Seq.Base.create (FStar.SizeT.v n) FStar.Pervasives.Native.None));\n FStar.Seq.Permutation.foldm_snoc_unit_seq Steel.ST.EphemeralHashtbl.vprop_monoid\n (Steel.ST.EphemeralHashtbl.value_vprops_seq vp\n (FStar.Seq.Base.create (FStar.SizeT.v n) FStar.Pervasives.Native.None)\n (FStar.PartialMap.empty k contents)\n (FStar.PartialMap.empty k v));\n Steel.ST.Util.rewrite_equiv Steel.Effect.Common.emp\n (Steel.ST.EphemeralHashtbl.value_vprops vp\n (FStar.Seq.Base.create (FStar.SizeT.v n) FStar.Pervasives.Native.None)\n (FStar.PartialMap.empty k contents)\n (FStar.PartialMap.empty k v));\n Steel.ST.EphemeralHashtbl.pack_tperm (FStar.Seq.Base.create (FStar.SizeT.v n)\n FStar.Pervasives.Native.None)\n (FStar.PartialMap.empty k contents)\n (FStar.PartialMap.empty k v)\n arr;\n Steel.ST.Util.return arr", "effect": "Steel.ST.Effect.STT", "effect_flags": [], "mutual_with": [], "premises": [ "Prims.eqtype", "Steel.ST.EphemeralHashtbl.vp_t", "Steel.ST.EphemeralHashtbl.hash_fn", "Steel.ST.EphemeralHashtbl.us", "Prims.b2t", "Prims.op_GreaterThan", "FStar.SizeT.v", "Steel.ST.Util.return", "Steel.ST.EphemeralHashtbl.tbl", "FStar.Ghost.hide", "FStar.Set.set", "Steel.Memory.iname", "FStar.Set.empty", "Steel.ST.Util.exists_", "FStar.Seq.Base.seq", "FStar.Pervasives.Native.option", "FStar.Pervasives.Native.tuple2", "Steel.Effect.Common.VStar", "Steel.ST.Array.pts_to", "Steel.ST.EphemeralHashtbl.__proj__Mktbl__item__store", "Steel.FractionalPermission.full_perm", "Steel.ST.Util.pure", "Steel.ST.EphemeralHashtbl.pure_invariant", "FStar.PartialMap.empty", "FStar.Seq.Permutation.foldm_snoc", "Steel.Effect.Common.vprop", "Steel.Effect.Common.req", "Steel.ST.EphemeralHashtbl.vprop_monoid", "FStar.Seq.Properties.map_seq", "Steel.ST.EphemeralHashtbl.value_vprops_mapping_fn", "Prims.unit", "Steel.ST.EphemeralHashtbl.pack_tperm", "FStar.Seq.Base.create", "FStar.Pervasives.Native.None", "Steel.ST.Util.rewrite_equiv", "Steel.Effect.Common.emp", "Steel.ST.EphemeralHashtbl.value_vprops", "FStar.Seq.Permutation.foldm_snoc_unit_seq", "Steel.ST.EphemeralHashtbl.value_vprops_seq", "Steel.ST.Util.rewrite", "Steel.ST.EphemeralHashtbl.Mktbl", "Steel.ST.Array.array", "Steel.ST.Array.alloc" ], "proof_features": [], "is_simple_lemma": false, "is_div": true, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "\n vp: Steel.ST.EphemeralHashtbl.vp_t k v contents ->\n h: Steel.ST.EphemeralHashtbl.hash_fn k ->\n n: Steel.ST.EphemeralHashtbl.us{FStar.SizeT.v n > 0}\n -> Steel.ST.Effect.STT (Steel.ST.EphemeralHashtbl.tbl vp h)", "prompt": "let create #k #v #contents vp h n =\n ", "expected_response": "let store = A.alloc #(option (k & v)) None n in\nlet arr:tbl #k #v #contents vp h = { store_len = n; store = store; store_len_pf = () } in\nrewrite (A.pts_to store _ (Seq.create #(option (k & v)) (US.v n) None))\n (A.pts_to arr.store _ (Seq.create #(option (k & v)) (US.v n) None));\nSeqPerm.foldm_snoc_unit_seq vprop_monoid\n (value_vprops_seq vp (Seq.create (US.v n) None) (Map.empty k contents) (Map.empty k v));\nrewrite_equiv emp\n (value_vprops vp (Seq.create (US.v n) None) (Map.empty k contents) (Map.empty k v));\npack_tperm (Seq.create (US.v n) None) (Map.empty k contents) (Map.empty k v) arr;\nreturn arr", "source": { "project_name": "steel", "file_name": "lib/steel/Steel.ST.EphemeralHashtbl.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Steel.ST.EphemeralHashtbl.fst", "checked_file": "dataset/Steel.ST.EphemeralHashtbl.fst.checked", "interface_file": true, "dependencies": [ "dataset/Steel.ST.Util.fsti.checked", "dataset/Steel.ST.Reference.fsti.checked", "dataset/Steel.ST.Effect.Ghost.fsti.checked", "dataset/Steel.ST.Effect.Atomic.fsti.checked", "dataset/Steel.ST.Effect.fsti.checked", "dataset/Steel.ST.Array.fsti.checked", "dataset/Steel.Memory.fsti.checked", "dataset/Steel.FractionalPermission.fst.checked", "dataset/Steel.Effect.Common.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.SizeT.fsti.checked", "dataset/FStar.Seq.Permutation.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.PartialMap.fsti.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Calc.fsti.checked", "dataset/FStar.Algebra.CommMonoid.Equiv.fst.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "tbl", "tbl", "store_len", "store_len", "store", "store", "store_len_pf", "store_len_pf", "let seq_props (#k:eqtype) (#v:Type0) (h:hash_fn k) (s:Seq.seq (option (k & v))) : prop =\n 0 < Seq.length s /\\ US.fits (Seq.length s) /\\\n\n (forall (i:nat{i < Seq.length s}).\n Some? (Seq.index s i) ==> (let Some (x, _) = Seq.index s i in\n US.v (h x) `US.mod_spec` Seq.length s == i))", "us", "hash_fn", "let seq_keys_distinct (#k:eqtype) (#v:Type0) (s:Seq.seq (option (k & v))) : prop =\n forall (i j:(k:nat{k < Seq.length s})).{:pattern Seq.index s i; Seq.index s j}\n (i =!= j /\\ Some? (Seq.index s i) /\\ Some? (Seq.index s j)) ==>\n (fst (Some?.v (Seq.index s i)) =!= fst (Some?.v (Seq.index s j)))", "vp_t", "let seq_props_implies_keys_distinct (#k:eqtype) (#v:Type0) (h:hash_fn k) (s:Seq.seq (option (k & v)))\n : Lemma (requires seq_props h s) (ensures seq_keys_distinct s)\n = ()", "val tbl\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n : Type0", "let store_and_repr_related\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n : prop\n = forall (i:nat{i < Seq.length s}).\n match Seq.index s i with\n | None -> True\n | Some (k, _) -> Map.contains m k", "repr", "let store_and_borrows_related\n (#k:eqtype)\n (#v:Type0)\n (s:Seq.seq (option (k & v)))\n (borrows:Map.t k v)\n : prop\n = forall (i:nat{i < Seq.length s}).\n match Seq.index s i with\n | None -> True\n | Some (k, x) ->\n Map.sel borrows k == None \\/\n Map.sel borrows k == Some x", "val tperm\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (t:tbl vp h)\n (m:repr k contents)\n (borrows:Map.t k v)\n : vprop", "val create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))", "let vprop_monoid : CE.cm vprop Steel.Effect.Common.req = Steel.Effect.Common.rm", "let value_vprops_mapping_fn\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (m:repr k contents)\n (borrows:Map.t k v)\n : option (k & v) -> vprop\n = fun e ->\n match e with\n | None -> emp\n | Some (i, x) ->\n (match Map.sel m i, Map.sel borrows i with\n | None, _ -> pure False\n | _, Some _ -> emp\n | Some c, None -> vp i x c)", "val create_v\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n (c:G.erased contents)\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.const k (G.reveal c)) (Map.empty k v))", "let value_vprops_seq\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n : Seq.seq vprop\n = Seq.map_seq (value_vprops_mapping_fn vp m borrows) s", "get_result", "Present", "Present", "Present", "Absent", "Absent", "Absent", "Missing", "Missing", "Missing", "let map_contains_prop (#k:eqtype) (#v:Type0) (x:k) (m:Map.t k v) : prop =\n Map.contains m x == true", "let value_vprops\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n : vprop\n = SeqPerm.foldm_snoc vprop_monoid (value_vprops_seq vp s m borrows)", "let get_post\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (m:G.erased (repr k contents))\n (borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : get_result k v -> vprop\n = fun r ->\n match r, Map.sel m i with\n | Present x, Some c ->\n tperm a m (Map.upd borrows i x) //when `get` succeeds, the key is added to `borrows`\n `star`\n vp i x c //in addition, we return the vp permission for the key\n\n | Present x, None -> pure False //It can never be the case that the key is present in the table,\n //but is not mapped in the representation map\n | Missing j, _ ->\n tperm a m borrows\n `star`\n pure (map_contains_prop j m)\n\n | _ -> tperm a m borrows", "let pure_invariant\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (arr:tbl vp h)\n (m:repr k contents)\n (borrows:Map.t k v)\n (s:Seq.seq (option (k & v)))\n : prop\n = seq_props h s /\\\n store_and_repr_related s m /\\\n A.is_full_array arr.store /\\\n store_and_borrows_related s borrows", "let store_contents_pred\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (arr:tbl vp h)\n (m:repr k contents)\n (borrows:Map.t k v)\n : Seq.seq (option (k & v)) -> vprop\n = fun s ->\n A.pts_to arr.store full_perm s\n `star`\n pure (pure_invariant arr m borrows s)\n `star`\n value_vprops vp s m borrows", "val get\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n : ST (get_result k v)\n (tperm a m borrows)\n (get_post m borrows a i)\n (requires ~ (Map.contains borrows i))\n (ensures fun _ -> True)", "let tperm arr m borrows = exists_ (store_contents_pred arr m borrows)", "let map_seq_len (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a)\n : Lemma (ensures Seq.length (Seq.map_seq f s) == Seq.length s)\n [SMTPat (Seq.length (Seq.map_seq f s))]\n = Seq.map_seq_len f s", "val put\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n (x:v)\n (c:G.erased contents)\n : STT unit\n (tperm a m borrows `star` vp i x c)\n (fun _ -> tperm a (Map.upd m i c) (Map.remove borrows i))", "let map_seq_index (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a) (i:nat{i < Seq.length s})\n : Lemma (ensures Seq.index (Seq.map_seq f s) i == f (Seq.index s i))\n [SMTPat (Seq.index (Seq.map_seq f s) i)]\n = Seq.map_seq_index f s i", "let map_seq_append (#a #b:Type) (f:a -> Tot b) (s1 s2:Seq.seq a)\n : Lemma (ensures (Seq.map_seq f (Seq.append s1 s2) ==\n Seq.append (Seq.map_seq f s1) (Seq.map_seq f s2)))\n [SMTPat (Seq.map_seq f (Seq.append s1 s2))]\n = Seq.map_seq_append f s1 s2", "let pack_tperm (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n (a:tbl vp h)\n : STGhost unit opened\n (A.pts_to a.store full_perm s\n `star`\n value_vprops vp s m borrows)\n (fun _ -> tperm a m borrows)\n (requires pure_invariant a m borrows s)\n (ensures fun _ -> True)\n = intro_pure (pure_invariant a m borrows s);\n intro_exists s (store_contents_pred a m borrows)" ], "closest": [ "val create (#v:Type)\r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (n:U32.t{U32.v n > 0})\r\n (init:G.erased c)\r\n : STT (tbl #v #c vp)\r\n emp\r\n (fun a -> perm a init (Map.const #M.epoch_id #c init) empty_borrows)\nlet create #v #c #vp n init =\r\n let etbl = ETbl.create_v vp hash (SizeT.uint32_to_sizet n) init in\r\n let high = R.alloc None in\r\n intro_pure (high_epoch_id_prop (G.reveal init)\r\n (Map.const (G.reveal init))\r\n (empty_borrows #v)\r\n None);\r\n let r = { etbl = etbl; high = high } in\r\n assert (PartialMap.equal (PartialMap.const M.epoch_id (G.reveal init))\r\n (repr_to_eht_repr (Map.const #M.epoch_id #c init)));\r\n rewrite (ETbl.tperm _ _ _)\r\n (ETbl.tperm r.etbl\r\n (repr_to_eht_repr (Map.const (G.reveal init)))\r\n empty_borrows);\r\n rewrite (R.pts_to _ _ _ `star` pure _)\r\n (high_epoch_id_pred (G.reveal init)\r\n (Map.const (G.reveal init))\r\n empty_borrows\r\n r.high\r\n None);\r\n intro_exists None (high_epoch_id_pred _ _ _ _);\r\n return r", "val token (#k:eqtype) (#v:Type0)\n (r:ref (ht_t k v))\n (r_sz:ref pos_us)\n (r_hashf:ref (k -> SZ.t))\n (r_contents:ref (V.vec (cell k v))) : vprop\nlet token (#k:eqtype) (#v:Type0)\n (r:ref (ht_t k v))\n (r_sz:ref pos_us)\n (r_hashf:ref (k -> SZ.t))\n (r_contents:ref (V.vec (cell k v))) : vprop =\n exists* ht. pts_to r ht", "val put (#v:Type) \r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (#init:G.erased c)\r\n (#m:G.erased (repr c))\r\n (#b:G.erased (borrows v))\r\n (a:tbl vp)\r\n (i:M.epoch_id)\r\n (x:v)\r\n (content:Ghost.erased c)\r\n : STT unit\r\n (perm a init m b `star` vp i x content)\r\n (fun _ -> perm a init (Map.upd m i content) (PartialMap.remove b i))\nlet put #v #c #vp #init #m #b a i x content =\r\n let w = elim_exists () in\r\n elim_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n ETbl.put a.etbl i x content;\r\n assert (PartialMap.equal (PartialMap.upd (repr_to_eht_repr m) i content)\r\n (repr_to_eht_repr (Map.upd m i content)));\r\n rewrite (ETbl.tperm _ _ _)\r\n (ETbl.tperm a.etbl\r\n (repr_to_eht_repr (Map.upd m i content))\r\n (PartialMap.remove b i));\r\n let high = R.read a.high in\r\n let r = above_high_water_mark high i in\r\n if r\r\n then begin\r\n R.write a.high (Some i);\r\n intro_pure (high_epoch_id_prop (G.reveal init)\r\n (Map.upd m i content)\r\n (PartialMap.remove b i)\r\n (Some i));\r\n intro_exists (Some i) (high_epoch_id_pred (G.reveal init)\r\n (Map.upd m i content)\r\n (PartialMap.remove b i)\r\n a.high)\r\n end\r\n else begin\r\n intro_pure (high_epoch_id_prop (G.reveal init)\r\n (Map.upd m i content)\r\n (PartialMap.remove b i)\r\n w);\r\n intro_exists (G.reveal w) (high_epoch_id_pred (G.reveal init)\r\n (Map.upd m i content)\r\n (PartialMap.remove b i)\r\n a.high)\r\n end", "val exploded_vp\n (#k: eqtype)\n (#v: Type0)\n (r: ref (ht_t k v))\n (ht: ht_t k v)\n (r_sz: ref pos_us)\n (r_hashf: ref (k -> SZ.t))\n (r_contents: ref (V.vec (cell k v)))\n : vprop\nlet exploded_vp (#k:eqtype) (#v:Type0)\n (r:ref (ht_t k v))\n (ht:ht_t k v)\n (r_sz:ref pos_us)\n (r_hashf:ref (k -> SZ.t))\n (r_contents:ref (V.vec (cell k v))) : vprop = \n pts_to r_sz ht.sz **\n pts_to r_hashf ht.hashf **\n pts_to r_contents ht.contents **\n token r r_sz r_hashf r_contents", "val alloc (n:US.t{US.v n > 0})\n : STT (bv_t n) emp (fun r -> pts_to r full_perm (Seq.create (US.v n) false))\nlet alloc n = A.alloc false n", "val reclaim (#v:Type) \r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (#init:G.erased c)\r\n (#m:G.erased (repr c))\r\n (#b:G.erased (borrows v))\r\n (a:tbl vp)\r\n (i:M.epoch_id)\r\n : STT unit\r\n (perm a init m b)\r\n (fun _ -> perm a init m (PartialMap.remove b i))\nlet reclaim #v #c #vp #init #m #b a i =\r\n let w = elim_exists () in\r\n elim_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n let _ = ETbl.remove a.etbl i in\r\n intro_pure (high_epoch_id_prop (G.reveal init) m (PartialMap.remove b i) w);\r\n intro_exists\r\n (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) m (PartialMap.remove b i) a.high)", "val finalize (#v:Type)\r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (#init:G.erased c)\r\n (#m:G.erased (repr c))\r\n (#b:G.erased (borrows v))\r\n (t:tbl vp)\r\n : STT unit\r\n (perm t init m b)\r\n (fun _ -> emp)\nlet finalize #v #c #vp #init #m #b t =\r\n let w = elim_exists () in\r\n elim_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n ETbl.free t.etbl;\r\n R.free t.high", "val unexplode_ref (#k:eqtype) (#v:Type0) (#ht:erased (ht_t k v))\n (r:ref (ht_t k v))\n (r_sz:ref pos_us)\n (r_hashf:ref (k -> SZ.t))\n (r_contents:ref (V.vec (cell k v)))\n : stt unit\n (requires exploded_vp r ht r_sz r_hashf r_contents)\n (ensures fun _ -> pts_to r ht)\nlet unexplode_ref = unexplode_ref'", "val mk_ht (#k: eqtype) (#v: _) (sz: pos_us) (hashf: (k -> SZ.t)) (contents: V.vec (cell k v))\n : ht_t k v\nlet mk_ht (#k:eqtype) #v \n (sz:pos_us) \n (hashf:k -> SZ.t)\n (contents:V.vec (cell k v))\n : ht_t k v\n = { sz; hashf; contents; }", "val malloc\n (#elt: Type)\n (x: elt)\n (n: US.t)\n: ST (array elt)\n emp\n (fun a -> pts_to a P.full_perm (Seq.create (US.v n) x))\n (True)\n (fun a ->\n length a == US.v n /\\\n is_full_array a\n )\nlet malloc x n =\n let res = H.malloc (raise x) n in\n assert (seq_map raise (Seq.create (US.v n) x) `Seq.equal` Seq.create (US.v n) (raise x));\n rewrite\n (H.pts_to res _ _)\n (pts_to res _ _);\n return res", "val write (#a:Type)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\nlet write (#a:Type)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\n = coerce_steel (fun _ -> R.write r x);\n return ()", "val write (#a:Type0)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\nlet write (#a:Type0)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\n = coerce_steel (fun _ -> R.write_pt r x);\n return ()", "val create (#a:Type0) (n:nat) (init:a)\n : ST (array a)\n (requires (fun h -> True))\n (ensures (fun h0 x h1 -> x `unused_in` h0 /\\\n contains h1 x /\\\n modifies Set.empty h0 h1 /\\\n sel h1 x == Seq.create n init))\nlet create #a n init = ST.alloc (Seq.create n init)", "val create (#key: eqtype) (#value: (key -> Tot Type)) (f: (k: key -> Tot (value k)))\n : Tot (t key value)\nlet create (#key: eqtype) (#value: (key -> Tot Type)) (f: (k: key -> Tot (value k)))\n : Tot (t key value) = { mappings = F.on_domain key f }", "val get (#v:Type) \r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (#init:G.erased c)\r\n (#m:G.erased (repr c))\r\n (#b:G.erased (borrows v))\r\n (a:tbl vp)\r\n (i:M.epoch_id)\r\n : ST (get_result v)\r\n (perm a init m b)\r\n (get_post init m b a i)\r\n (requires ~ (PartialMap.contains b i))\r\n (ensures fun res -> Fresh? res ==> Map.sel m i == G.reveal init)\nlet get #v #c #vp #init #m #b a i =\r\n let w = elim_exists () in\r\n elim_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n let high_value = R.read a.high in\r\n let r = above_high_water_mark high_value i in\r\n if r returns ST _\r\n _\r\n (get_post init m b a i)\r\n (requires ~ (PartialMap.contains b i))\r\n (ensures fun res -> Fresh? res ==> Map.sel m i == G.reveal init)\r\n\r\n then begin\r\n let ret = Fresh in\r\n intro_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n intro_exists (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) m b a.high);\r\n rewrite (ETbl.tperm a.etbl (repr_to_eht_repr m) b\r\n `star`\r\n exists_ (high_epoch_id_pred (G.reveal init) m b a.high))\r\n (get_post init m b a i ret);\r\n return ret\r\n end\r\n else begin\r\n let x = ETbl.get a.etbl i in\r\n match x returns ST _\r\n (ETbl.get_post (repr_to_eht_repr m) b a.etbl i x\r\n `star`\r\n R.pts_to a.high Steel.FractionalPermission.full_perm w)\r\n (get_post init m b a i)\r\n (requires ~ (PartialMap.contains b i))\r\n (ensures fun res -> Fresh? res ==> Map.sel m i == G.reveal init) with\r\n | ETbl.Missing j ->\r\n let ret = NotFound in\r\n rewrite (ETbl.get_post (repr_to_eht_repr m) b a.etbl i (ETbl.Missing j))\r\n (ETbl.tperm a.etbl (repr_to_eht_repr m) b\r\n `star`\r\n pure (ETbl.map_contains_prop j (repr_to_eht_repr m)));\r\n elim_pure (ETbl.map_contains_prop j (repr_to_eht_repr m));\r\n intro_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n intro_exists (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) m b a.high);\r\n rewrite (ETbl.tperm a.etbl (repr_to_eht_repr m) b\r\n `star`\r\n exists_ (high_epoch_id_pred (G.reveal init) m b a.high))\r\n (get_post init m b a i ret);\r\n return ret\r\n | ETbl.Absent ->\r\n let ret = NotFound in\r\n rewrite (ETbl.get_post (repr_to_eht_repr m) b a.etbl i ETbl.Absent)\r\n (ETbl.tperm a.etbl (repr_to_eht_repr m) b);\r\n intro_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n intro_exists (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) m b a.high);\r\n rewrite (ETbl.tperm a.etbl (repr_to_eht_repr m) b\r\n `star`\r\n exists_ (high_epoch_id_pred (G.reveal init) m b a.high))\r\n (get_post init m b a i ret);\r\n return ret\r\n | ETbl.Present x ->\r\n let ret = Found x in\r\n assert (Some? (PartialMap.sel (repr_to_eht_repr m) i));\r\n rewrite (ETbl.get_post (repr_to_eht_repr m) b a.etbl i (ETbl.Present x))\r\n (ETbl.tperm a.etbl (repr_to_eht_repr m) (PartialMap.upd b i x)\r\n `star`\r\n vp i x (Map.sel m i));\r\n intro_pure (high_epoch_id_prop (G.reveal init) m (PartialMap.upd b i x) w);\r\n intro_exists\r\n (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) m (PartialMap.upd b i x) a.high);\r\n rewrite (perm a init m (PartialMap.upd b i x)\r\n `star`\r\n vp i x (Map.sel m i))\r\n (get_post init m b a i ret);\r\n return ret\r\n end", "val create (a:Type0) (n:nat)\n :ST (array a n) (requires (fun _ -> True))\n (ensures (fun h0 arr h1 -> fresh_arr arr h0 h1 /\\ //it's fresh\n\t\t modifies Set.empty h0 h1 /\\ //no existing refs are changed\n\t\t\t\t\t is_full_array arr))\nlet create (a:Type0) (n:nat)\n :ST (array a n) (requires (fun _ -> True))\n (ensures (fun h0 arr h1 -> fresh_arr arr h0 h1 /\\ //it's fresh\n\t\t modifies Set.empty h0 h1 /\\ //no existing refs are changed\n\t\t\t\t\t is_full_array arr)) //and has the full view of the underlying sequence\n = let arr = A #a #n #n (alloc ((Seq.create n None), Mutable)) 0 in\n gst_witness (mutable_pred arr);\n arr", "val create\n (#a:typ)\n (init: P.type_of_typ a)\n (len:UInt32.t)\n: HST.StackInline (buffer a)\n (requires (fun h ->\n UInt32.v len > 0\n ))\n (ensures (fun (h0: HS.mem) b h1 ->\n UInt32.v len > 0 /\\\n b `unused_in` h0 /\\\n live h1 b /\\\n length b == UInt32.v len /\\\n frameOf b == (HS.get_tip h0) /\\\n P.modifies_0 h0 h1 /\\\n as_seq h1 b == Seq.create (UInt32.v len) init\n ))\nlet create #a init len =\n let len : P.array_length_t = len in\n let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in\n P.buffer_of_array_pointer content", "val alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n : STT (ref a p) emp (fun r -> pts_to r full_perm v)\nlet alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n : STT (ref a p) emp (fun r -> pts_to r full_perm v)\n = let x = coerce_steel (fun _ -> MR.alloc p v) in\n return x", "val free (#a:Type0)\n (#v:erased a)\n (r:ref a)\n : STT unit\n (pts_to r full_perm v) (fun _ -> emp)\nlet free (#a:Type0)\n (#v:erased a)\n (r:ref a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> emp)\n = coerce_steel(fun _ -> R.free_pt r);\n return ()", "val bv_set\n (#n:US.t)\n (#s:G.erased repr)\n (bv:bv_t n)\n (i:US.t{US.v i < Seq.length s})\n : STT unit\n (pts_to bv full_perm s)\n (fun _ -> pts_to bv full_perm (Seq.upd s (US.v i) true))\nlet bv_set #_ #s bv i = A.write #_ bv #s i true", "val free (#a:Type)\n (#v:erased a)\n (r:ref a)\n : STT unit\n (pts_to r full_perm v) (fun _ -> emp)\nlet free (#a:Type)\n (#v:erased a)\n (r:ref a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> emp)\n = coerce_steel(fun _ -> R.free r);\n return ()", "val v: #t_k:eqtype -> #t_v:Type0 -> h:HS.mem -> ll:t t_k t_v -> GTot (map t_k t_v)\nlet v #_ #_ h ll =\n let l = LL2.v h ll in\n v_ l", "val malloc (#elt: Type) (x: elt) (n: US.t)\n : ST (array elt)\n emp\n (fun a -> pts_to a P.full_perm (Seq.create (US.v n) x))\n (True)\n (fun a -> length a == US.v n /\\ is_full_array a)\nlet malloc\n (#elt: Type)\n (x: elt)\n (n: US.t)\n: ST (array elt)\n emp\n (fun a -> pts_to a P.full_perm (Seq.create (US.v n) x))\n (True)\n (fun a ->\n length a == US.v n /\\\n is_full_array a\n )\n= let p = malloc_ptr x n in\n let a : array elt = (| p, Ghost.hide (US.v n) |) in\n rewrite\n (pts_to _ _ _)\n (pts_to a _ _);\n return a", "val share\n (#a:Type)\n (v:vec a)\n (#s:Ghost.erased (Seq.seq a))\n (#p:perm)\n : stt_ghost unit\n (requires pts_to v #p s)\n (ensures fun _ -> pts_to v #(half_perm p) s ** pts_to v #(half_perm p) s)\nlet share v = A.share v", "val write (#a:Type)\n (#u:_)\n (#v:erased a)\n (r:ref a)\n (x:erased a)\n : STGhostT unit u\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\nlet write (#a:Type)\n (#u:_)\n (#v:erased a)\n (r:ref a)\n (x:erased a)\n : STGhostT unit u\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\n = coerce_ghost (fun _ -> R.ghost_write_pt r x)", "val create_in: #t_k:eqtype -> #t_v:Type -> r:HS.rid -> ST (t t_k t_v)\n (requires fun h0 ->\n ST.is_eternal_region r)\n (ensures fun h0 ll h1 ->\n invariant h1 ll /\\\n B.(modifies loc_none h0 h1) /\\\n v h1 ll == M.const None /\\\n region_of ll == B.(loc_all_regions_from false r))\nlet create_in #_ #_ r =\n LL2.create_in r", "val malloc0 (#elt: Type) (x: elt) (n: US.t)\n : ST (array elt)\n emp\n (fun a -> pts_to a P.full_perm (Seq.create (US.v n) x))\n (True)\n (fun a -> length a == US.v n /\\ base_len (base (ptr_of a)) == US.v n)\nlet malloc0\n (#elt: Type)\n (x: elt)\n (n: US.t)\n: ST (array elt)\n emp\n (fun a -> pts_to a P.full_perm (Seq.create (US.v n) x))\n (True)\n (fun a ->\n length a == US.v n /\\\n base_len (base (ptr_of a)) == US.v n\n )\n=\n let c : carrier elt (US.v n) = mk_carrier (US.v n) 0 (Seq.create (US.v n) x) P.full_perm in\n let base : ref (carrier elt (US.v n)) (pcm elt (US.v n)) = R.alloc c in\n R.pts_to_not_null base _;\n let p = {\n base_len = n;\n base = base;\n offset = 0;\n }\n in\n let a = (| p, Ghost.hide (US.v n) |) in\n change_r_pts_to\n base c\n (ptr_of a).base c;\n intro_pts_to a P.full_perm (Seq.create (US.v n) x);\n return a", "val explode_ref_ht_t (#k:eqtype) (#v:Type0) (#ht:erased (ht_t k v)) (r:ref (ht_t k v))\n : stt (ref pos_us & ref (k -> SZ.t) & ref (V.vec (cell k v)))\n (requires pts_to r ht)\n (ensures fun res -> exploded_vp r ht (tfst res) (tsnd res) (tthd res))\nlet explode_ref_ht_t = explode_ref_ht_t'", "val fill\n (#t:Type0)\n (l:SZ.t)\n (a:larray t (SZ.v l))\n (v:t)\n (#s:Ghost.erased (Seq.seq t))\n : stt unit\n (requires \n pts_to a s)\n (ensures fun _ ->\n exists* (s:Seq.seq t).\n pts_to a s **\n pure (s `Seq.equal` Seq.create (SZ.v l) v))\nlet fill = fill'", "val alloc \n (#a:Type0)\n (x:a)\n (n:SZ.t)\n : stt (vec a)\n (requires emp)\n (ensures fun v ->\n pts_to v (Seq.create (SZ.v n) x) **\n pure (length v == SZ.v n /\\ is_full_vec v))\nlet alloc x n = A.alloc x n", "val alloc (#a:Type) (x:a)\n : ST (ref a)\n emp \n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\nlet alloc (#a:Type) (x:a)\n : ST (ref a)\n emp\n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\n = let r = coerce_steel (fun _ -> R.alloc_pt x) in\n r", "val alloc (#a:Type) (x:a)\n : ST (ref a)\n emp \n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\nlet alloc (#a:Type) (x:a)\n : ST (ref a)\n emp\n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\n = let r = coerce_steel (fun _ -> R.alloc x) in\n r", "val create: #a:Type -> init:a -> len:UInt32.t -> StackInline (buffer a)\n (requires (fun h -> True))\n (ensures (fun (h0:mem) b h1 -> b `unused_in` h0\n /\\ live h1 b /\\ idx b == 0 /\\ length b == v len\n /\\ frameOf b == HS.get_tip h0\n /\\ Map.domain (HS.get_hmap h1) == Map.domain (HS.get_hmap h0)\n /\\ modifies_0 h0 h1\n /\\ as_seq h1 b == Seq.create (v len) init))\nlet create #a init len =\n let content: reference (lseq a (v len)) =\n salloc (Seq.create (v len) init) in\n let b = MkBuffer len content 0ul len in\n let h = HST.get() in\n assert (Seq.equal (as_seq h b) (sel h b));\n b", "val insert (#a: eqtype) (#b: Type u#b) (k: a) (v: b) (m: map a b)\n : map a b\nlet insert (#a: eqtype) (#b: Type u#b) (k: a) (v: b) (m: map a b) : map a b =\n let keys' = FSet.insert k (domain m) in\n let f' = on_domain a (fun key -> if key = k then Some v else (elements m) key) in\n (| keys', f' |)", "val perm (#v:Type)\r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (t:tbl vp)\r\n (default_value: c)\r\n ([@@@smt_fallback] m:repr c)\r\n ([@@@smt_fallback] b:borrows v)\r\n : vprop\nlet perm #v #c #cp t default_value m b =\r\n ETbl.tperm t.etbl (repr_to_eht_repr m) b\r\n `star`\r\n exists_ (high_epoch_id_pred default_value m b t.high)", "val create (a: Type0) (x: a)\n : LV nat\n (fun m0 -> True)\n (fun m0 r m1 -> not (m0.m `M.contains` r) /\\ m1.m == Map.upd m0.m r (| a, x |))\nlet create (a:Type0) (x:a) : LV nat (fun m0 -> True)\n (fun m0 r m1 -> not (m0.m `M.contains` r) /\\ m1.m == Map.upd m0.m r (| a, x |))\n= LVARS?.reflect (fun m ->\n let next = m.next in\n next, {\n next = next + 1;\n m = Map.upd m.m next (| a, x |)\n })", "val free (#a:Type0)\n (#u:_)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit u\n (pts_to r full_perm v)\n (fun _ -> emp)\nlet free (#a:Type0)\n (#u:_)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit u\n (pts_to r full_perm v)\n (fun _ -> emp)\n = coerce_ghost (fun _ -> R.ghost_free_pt r)", "val clear (#t_k: eqtype)\n (#t_v: Type0)\n (ll: t t_k t_v):\n ST unit\n (requires fun h0 ->\n invariant h0 ll)\n (ensures fun h0 _ h1 ->\n B.modifies (region_of ll) h0 h1 /\\\n invariant h1 ll /\\\n v h1 ll == M.const None)\nlet clear #_ #_ ll =\n LL2.clear ll", "val choose (#a: eqtype) (#b: Type u#b) (m: map a b{exists key. mem key m})\n : GTot (key: a{mem key m})\nlet choose (#a: eqtype) (#b: Type u#b) (m: map a b{exists key. mem key m}) : GTot (key: a{mem key m}) =\n FSet.choose (domain m)", "val read (#a:Type)\n (#u:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhost (erased a) u\n (pts_to r p v)\n (fun x -> pts_to r p x)\n (requires True)\n (ensures fun x -> x == v)\nlet read (#a:Type)\n (#u:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhost (erased a) u\n (pts_to r p v)\n (fun x -> pts_to r p x)\n (requires True)\n (ensures fun x -> x == v)\n = let y = coerce_ghost (fun _ -> R.ghost_read_pt r) in\n y", "val share (#a:Type) (r:ref a) (#v:erased a) (#p:perm)\n : stt_ghost unit\n (pts_to r #p v)\n (fun _ ->\n pts_to r #(half_perm p) v **\n pts_to r #(half_perm p) v)\nlet share = share'", "val share (#a:Type) (r:ref a) (#v:erased a) (#p:perm)\n : stt_ghost unit\n (pts_to r #p v)\n (fun _ ->\n pts_to r #(half_perm p) v **\n pts_to r #(half_perm p) v)\nlet share = share'", "val share (#a:Type) (r:ref a) (#v:erased a) (#p:perm)\n : stt_ghost unit\n (pts_to r #p v)\n (fun _ ->\n pts_to r #(half_perm p) v **\n pts_to r #(half_perm p) v)\nlet share = share'", "val share (#a:Type) (r:ref a) (#v:erased a) (#p:perm)\n : stt_ghost unit\n (pts_to r #p v)\n (fun _ ->\n pts_to r #(half_perm p) v **\n pts_to r #(half_perm p) v)\nlet share = share'", "val write (#a: Type) (#rel: preorder a) (r: mref a rel) (v: a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 ->\n rel (sel h0 r) v /\\ h0 `contains` r /\\ modifies (Set.singleton (addr_of r)) h0 h1 /\\\n equal_dom h0 h1 /\\ sel h1 r == v)\nlet write (#a:Type) (#rel:preorder a) (r:mref a rel) (v:a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 -> rel (sel h0 r) v /\\ h0 `contains` r /\\\n modifies (Set.singleton (addr_of r)) h0 h1 /\\ equal_dom h0 h1 /\\\n sel h1 r == v)\n = let h0 = gst_get () in\n gst_recall (contains_pred r);\n let h1 = upd_tot h0 r v in\n Heap.lemma_distinct_addrs_distinct_preorders ();\n Heap.lemma_distinct_addrs_distinct_mm ();\n Heap.lemma_upd_equals_upd_tot_for_contained_refs h0 r v;\n gst_put h1", "val read (#a:Type) (r:ref a) (#n:erased a) (#p:perm)\n : stt_ghost (erased a)\n (pts_to r #p n)\n (fun x -> pts_to r #p n ** pure (n == x))\nlet read = read'", "val read (#a:Type) (r:ref a) (#n:erased a) (#p:perm)\n : stt_ghost (erased a)\n (pts_to r #p n)\n (fun x -> pts_to r #p n ** pure (n == x))\nlet read = read'", "val upd\n (#t: Type)\n (a: array t)\n (#s: Ghost.erased (Seq.seq t))\n (i: US.t {US.v i < Seq.length s})\n (v: t)\n: STT unit\n (pts_to a P.full_perm s)\n (fun res -> pts_to a P.full_perm (Seq.upd s (US.v i) v))\nlet upd #_ a #s i v =\n rewrite\n (pts_to a _ _)\n (H.pts_to a P.full_perm (seq_map raise s));\n H.upd a i (raise v);\n assert (seq_map raise (Seq.upd s (US.v i) v) `Seq.equal` Seq.upd (seq_map raise s) (US.v i) (raise v));\n rewrite\n (H.pts_to _ _ _)\n (pts_to _ _ _)", "val empty (k:eqtype) (v:Type) : t k v\nlet empty _ _ = on_dom _ (fun _ -> None)", "val create (#a:eqtype) (#f:cmp a) (x:a) (m:pos) : mset a f\nlet create #_ #_ x m = [x, m]", "val write (#opened: _) (#a:Type)\n (#v:erased a)\n (r:ref a)\n (x:a)\n : STGhostT unit opened\n (pts_to r full_perm v)\n (fun _ -> pts_to r full_perm x)\nlet write\n #_ #a #v r x\n= let gr : R.ghost_ref a = coerce_eq (R.reveal_ghost_ref a) (Ghost.hide r.reveal) in\n weaken (pts_to r full_perm v) (R.ghost_pts_to gr full_perm v) (fun _ ->\n R.reveal_ghost_pts_to_sl gr full_perm v\n );\n STC.coerce_ghost (fun _ -> R.ghost_write gr x);\n weaken (R.ghost_pts_to gr full_perm x) (pts_to r full_perm x) (fun _ ->\n R.reveal_ghost_pts_to_sl gr full_perm x\n )", "val free (#t_k: eqtype)\n (#t_v: Type0)\n (ll: t t_k t_v):\n ST unit\n (requires fun h0 ->\n invariant h0 ll)\n (ensures fun h0 _ h1 ->\n B.modifies (region_of ll) h0 h1)\nlet free #_ #_ ll =\n LL2.free ll", "val alloc \n (#elt: Type)\n (x: elt)\n (n: SZ.t)\n : stt (array elt) \n (requires emp)\n (ensures fun a ->\n pts_to a (Seq.create (SZ.v n) x) **\n pure (length a == SZ.v n /\\ is_full_array a))\nlet alloc = alloc'", "val alloc \n (#elt: Type)\n (x: elt)\n (n: SZ.t)\n : stt (array elt) \n (requires emp)\n (ensures fun a ->\n pts_to a (Seq.create (SZ.v n) x) **\n pure (length a == SZ.v n /\\ is_full_array a))\nlet alloc = alloc'", "val share_gen (#a:Type0)\n (#uses:_)\n (#p:perm)\n (#v: a)\n (r:ref a)\n (p1 p2: perm)\n : STGhost unit uses\n (pts_to r p v)\n (fun _ -> pts_to r p1 v `star` pts_to r p2 v)\n (p == p1 `sum_perm` p2)\n (fun _ -> True)\nlet share_gen\n r p1 p2\n= coerce_ghost (fun _ -> R.share_gen_pt r p1 p2)", "val share (#a:Type)\n (#u:_)\n (#p:perm)\n (#x:erased a)\n (r:ref a)\n : STGhostT unit u\n (pts_to r p x)\n (fun _ -> pts_to r (half_perm p) x `star`\n pts_to r (half_perm p) x)\nlet share (#a:Type)\n (#u:_)\n (#p:perm)\n (#x:erased a)\n (r:ref a)\n : STGhostT unit u\n (pts_to r p x)\n (fun _ -> pts_to r (half_perm p) x `star`\n pts_to r (half_perm p) x)\n = coerce_ghost (fun _ -> R.ghost_share_pt r)", "val write (#a:Type0) (r:ref a) (v:a)\n :ST unit (fun _ -> True) (fun h0 _ h1 -> h0 `contains` r /\\ modifies (only r) h0 h1 /\\ equal_dom h0 h1 /\\ sel h1 r == v)\nlet write #_ r v = write r v", "val ghost_put (#o:_)\r\n (#v:Type) \r\n (#c:Type)\r\n (#vp:M.epoch_id -> v -> c -> vprop)\r\n (#init:G.erased c)\r\n (#m:G.erased (repr c))\r\n (#b:G.erased (borrows v))\r\n (a:tbl vp)\r\n (i:M.epoch_id)\r\n (x:v)\r\n (content:Ghost.erased c)\r\n : STGhost unit o\r\n (perm a init m b `star` vp i x content)\r\n (fun _ -> perm a init (Map.upd m i content) (PartialMap.remove b i))\r\n (requires\r\n PartialMap.sel b i == Some x)\r\n (ensures fun _ ->\r\n True)\nlet ghost_put #_ #v #c #vp #init #m #b a i x content =\r\n let w = elim_exists () in\r\n elim_pure (high_epoch_id_prop (G.reveal init) m b w);\r\n ETbl.ghost_put a.etbl i x content;\r\n assert (PartialMap.equal (PartialMap.upd (repr_to_eht_repr m) i content)\r\n (repr_to_eht_repr (Map.upd m i content)));\r\n rewrite (ETbl.tperm _ _ _)\r\n (ETbl.tperm a.etbl\r\n (repr_to_eht_repr (Map.upd m i content))\r\n (PartialMap.remove b i));\r\n intro_pure (high_epoch_id_prop (G.reveal init)\r\n (Map.upd m i content)\r\n (PartialMap.remove b i)\r\n w);\r\n intro_exists\r\n (G.reveal w)\r\n (high_epoch_id_pred (G.reveal init) (Map.upd m i content) (PartialMap.remove b i) a.high)", "val ( := ) (#a: Type) (#rel: preorder a) (r: mref a rel) (v: a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 ->\n rel (sel h0 r) v /\\ h0 `contains` r /\\ modifies (Set.singleton (addr_of r)) h0 h1 /\\\n equal_dom h0 h1 /\\ sel h1 r == v)\nlet op_Colon_Equals (#a:Type) (#rel:preorder a) (r:mref a rel) (v:a)\n : ST unit\n (fun h -> rel (sel h r) v)\n (fun h0 x h1 -> rel (sel h0 r) v /\\ h0 `contains` r /\\\n modifies (Set.singleton (addr_of r)) h0 h1 /\\ equal_dom h0 h1 /\\\n sel h1 r == v)\n= write #a #rel r v", "val memcpy\n (#t: _)\n (#p0: perm)\n (a0 a1: array t)\n (#s0 #s1: Ghost.erased (Seq.seq t))\n (l: US.t{US.v l == length a0 /\\ length a0 == length a1})\n : STT unit\n ((pts_to a0 p0 s0) `star` (pts_to a1 full_perm s1))\n (fun _ -> (pts_to a0 p0 s0) `star` (pts_to a1 full_perm s0))\nlet memcpy (#t:_) (#p0:perm)\n (a0 a1:array t)\n (#s0 #s1:Ghost.erased (Seq.seq t))\n (l:US.t { US.v l == length a0 /\\ length a0 == length a1 } )\n : STT unit\n (pts_to a0 p0 s0 `star` pts_to a1 full_perm s1)\n (fun _ -> pts_to a0 p0 s0 `star` pts_to a1 full_perm s0)\n= blit #t #p0 #s0 #s1 a0 0sz a1 0sz l;\n let s1' = elim_exists () in\n elim_pure (blit_post s0 s1 a0 0sz a1 0sz l s1');\n vpattern_rewrite (pts_to a1 full_perm) (Ghost.reveal s0);\n return ()", "val share (#a:Type0)\n (#uses:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit uses\n (pts_to r p v)\n (fun _ -> pts_to r (half_perm p) v `star` pts_to r (half_perm p) v)\nlet share (#a:Type0)\n (#uses:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit uses\n (pts_to r p v)\n (fun _ -> pts_to r (half_perm p) v `star` pts_to r (half_perm p) v)\n = coerce_ghost (fun _ -> R.share_pt r)", "val mem_alloc (#it: eqtype) (vt: (it -> Type))\n : ST (mem_table vt)\n (requires fun h0 -> True)\n (ensures fun h0 t h1 -> modifies_mem_table t h0 h1 /\\ mem_empty t h1)\nlet mem_alloc (#it:eqtype) (vt:it -> Type) : ST (mem_table vt)\n (requires fun h0 -> True)\n (ensures fun h0 t h1 -> modifies_mem_table t h0 h1 /\\ mem_empty t h1)\n =\n if model then (MDM.alloc #it #vt #trivial_inv #tls_define_region ()) else ()", "val alloc (#a:Type)\n (#u:_)\n (x:erased a)\n : STGhostT (ref a) u\n emp\n (fun r -> pts_to r full_perm x)\nlet alloc (#a:Type)\n (#u:_)\n (x:erased a)\n : STGhostT (ref a) u\n emp\n (fun r -> pts_to r full_perm x)\n = coerce_ghost (fun _ -> R.ghost_alloc_pt x)", "val share\n (#a:Type)\n (arr:array a)\n (#s:Ghost.erased (Seq.seq a))\n (#p:perm)\n : stt_ghost unit\n (requires pts_to arr #p s)\n (ensures fun _ -> pts_to arr #(half_perm p) s ** pts_to arr #(half_perm p) s)\nlet share = share'", "val sel : #a:Type -> \n h:heap ->\n\t r:ref a{contains h r} -> \n Tot a\nlet sel #a h r =\n match snd h r with\n | Some (| _ , x |) -> x", "val share (#a:Type)\n (#uses:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit uses\n (pts_to r p v)\n (fun _ -> pts_to r (half_perm p) v `star` pts_to r (half_perm p) v)\nlet share (#a:Type)\n (#uses:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit uses\n (pts_to r p v)\n (fun _ -> pts_to r (half_perm p) v `star` pts_to r (half_perm p) v)\n = coerce_ghost (fun _ -> R.share r)", "val share (#a:Type)\n (#uses:_)\n (#p:perm)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit uses\n (pts_to r p v)\n (fun _ -> pts_to r (half_perm p) v `star` pts_to r (half_perm p) v)\nlet share\n r\n= RST.share r.reveal", "val share (#a:Type) (r:box a) (#v:erased a) (#p:perm)\n : stt_ghost unit\n (pts_to r #p v)\n (fun _ ->\n pts_to r #(half_perm p) v **\n pts_to r #(half_perm p) v)\nlet share b = R.share b", "val bv_unset\n (#n:US.t)\n (#s:G.erased repr)\n (bv:bv_t n)\n (i:US.t{US.v i < Seq.length s})\n : STT unit\n (pts_to bv full_perm s)\n (fun _ -> pts_to bv full_perm (Seq.upd s (US.v i) false))\nlet bv_unset #_ #s bv i = A.write #_ bv #s i false", "val alloc (#a:Type0) (init:a)\n :ST (ref a)\n (fun _ -> True)\n (fun h0 r h1 -> fresh r h0 h1 /\\ modifies Set.empty h0 h1 /\\ sel h1 r == init)\nlet alloc #_ init = alloc init", "val create: #a:Type -> nat -> a -> Tot (seq a)\nlet rec create #_ len v = if len = 0 then MkSeq [] else _cons v (create (len - 1) v)", "val index\n (#t: Type) (#p: P.perm)\n (a: array t)\n (#s: Ghost.erased (Seq.seq t))\n (i: US.t)\n: ST t\n (pts_to a p s)\n (fun _ -> pts_to a p s)\n (US.v i < length a \\/ US.v i < Seq.length s)\n (fun res -> Seq.length s == length a /\\ US.v i < Seq.length s /\\ res == Seq.index s (US.v i))\nlet index #_ #p a #s i =\n rewrite\n (pts_to a _ _)\n (H.pts_to a p (seq_map raise s));\n let res = H.index a i in\n rewrite\n (H.pts_to _ _ _)\n (pts_to _ _ _);\n return (lower res)", "val write (#a:Type) (#p:Preorder.preorder a) (#v:erased a)\n (r:ref a p) (x:a)\n : ST unit\n (pts_to r full_perm v)\n (fun v -> pts_to r full_perm x)\n (requires p v x)\n (ensures fun _ -> True)\nlet write (#a:Type) (#p:Preorder.preorder a) (#v:erased a)\n (r:ref a p) (x:a)\n : ST unit\n (pts_to r full_perm v)\n (fun v -> pts_to r full_perm x)\n (requires p v x)\n (ensures fun _ -> True)\n = coerce_steel (fun _ -> MR.write r x)", "val upd\n (#t: Type)\n (a: array t)\n (#s: Ghost.erased (Seq.seq t))\n (i: US.t{US.v i < Seq.length s})\n (v: t)\n : STT unit (pts_to a P.full_perm s) (fun res -> pts_to a P.full_perm (Seq.upd s (US.v i) v))\nlet upd\n (#t: Type)\n (a: array t)\n (#s: Ghost.erased (Seq.seq t))\n (i: US.t { US.v i < Seq.length s })\n (v: t)\n: STT unit\n (pts_to a P.full_perm s)\n (fun res -> pts_to a P.full_perm (Seq.upd s (US.v i) v))\n= rewrite\n (pts_to _ _ _)\n (pts_to (| ptr_of a, (dsnd a) |) _ s);\n upd_ptr (ptr_of a) i v;\n rewrite\n (pts_to _ _ _)\n (pts_to _ _ _)", "val add (#t_k: eqtype) (#t_v: Type0) (ll: t t_k t_v) (k: t_k) (x: t_v):\n ST unit\n (requires fun h0 ->\n invariant h0 ll)\n (ensures fun h0 _ h1 ->\n B.modifies (region_of ll) h0 h1 /\\\n invariant h1 ll /\\\n v h1 ll == M.upd (v h0 ll) k (Some x))\nlet add #_ #_ ll k x =\n LL2.push ll (k, x)", "val createL\n (#a: typ)\n (init:list (P.type_of_typ a))\n: HST.StackInline (buffer a)\n (requires (fun h -> p #a init))\n (ensures (fun (h0: HS.mem) b h1 ->\n let len = FStar.List.Tot.length init in\n len > 0 /\\\n b `unused_in` h0 /\\\n live h1 b /\\\n length b == len /\\\n frameOf b == (HS.get_tip h0) /\\\n P.modifies_0 h0 h1 /\\\n as_seq h1 b == Seq.seq_of_list init /\\\n q #a len b\n ))\nlet createL #a init =\n let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in\n let s = Seq.seq_of_list init in\n let content = P.screate (P.TArray len a) (Some s) in\n P.buffer_of_array_pointer content", "val write : #a:Type -> \n r:ref a -> \n\t x:a -> \n\t AllocST unit (fun h0 -> True)\n (fun h0 _ h1 -> contains r h0 /\\ \n\t\t\t h1 == upd h0 r x)\nlet write #a r x = \n let h0 = ist_get () in\n ist_recall (contains r); //recalling that the current heap must contain the given reference\n let h1 = upd h0 r x in\n ist_put h1", "val find (#t_k: eqtype) (#t_v: Type0) (ll: t t_k t_v) (k: t_k):\n Stack (option t_v)\n (requires fun h0 ->\n invariant h0 ll)\n (ensures fun h0 x h1 ->\n let m: map t_k t_v = v h0 ll in\n h0 == h1 /\\\n x == M.sel m k)\nlet find #_ #_ ll k =\n find_ !*ll.LL2.ptr !*ll.LL2.v k", "val literal (#k:eqtype) (#v:Type) (f:k -> option v) : t k v\nlet literal f = on_dom _ (fun x -> f x)", "val upd0\n (#t: Type)\n (a: array t)\n (#s: Ghost.erased (Seq.seq t))\n (i: US.t{US.v i < Seq.length s})\n (v: t)\n : STT unit (pts_to a P.full_perm s) (fun res -> pts_to a P.full_perm (Seq.upd s (US.v i) v))\nlet upd0\n (#t: Type)\n (a: array t)\n (#s: Ghost.erased (Seq.seq t))\n (i: US.t { US.v i < Seq.length s })\n (v: t)\n: STT unit\n (pts_to a P.full_perm s)\n (fun res -> pts_to a P.full_perm (Seq.upd s (US.v i) v))\n= elim_pts_to a _ _;\n mk_carrier_upd (US.v (ptr_of a).base_len) ((ptr_of a).offset) s (US.v i) v ();\n R.upd_gen\n (ptr_of a).base\n _ _\n (PM.lift_frame_preserving_upd\n _ _\n (P.mk_frame_preserving_upd\n (Seq.index s (US.v i))\n v\n )\n _ ((ptr_of a).offset + US.v i)\n );\n intro_pts_to a _ _", "val upd (#k:eqtype) (#v:Type) (m:t k v) (x:k) (y:v) : t k v\nlet upd m x y = on_dom _ (fun x1 -> if x1 = x then Some y else m x1)", "val compare\n (#a: eqtype)\n (#p0 #p1: perm)\n (a0 a1: A.array a)\n (#s0 #s1: G.erased (Seq.seq a))\n (n: US.t{US.v n == A.length a0 /\\ A.length a0 == A.length a1})\n : ST bool\n ((A.pts_to a0 p0 s0) `star` (A.pts_to a1 p1 s1))\n (fun _ -> (A.pts_to a0 p0 s0) `star` (A.pts_to a1 p1 s1))\n (requires True)\n (ensures fun b -> b <==> s0 == s1)\nlet compare (#a:eqtype) (#p0 #p1:perm)\n (a0 a1:A.array a)\n (#s0 #s1:G.erased (Seq.seq a))\n (n:US.t{US.v n == A.length a0 /\\ A.length a0 == A.length a1})\n : ST bool\n (A.pts_to a0 p0 s0\n `star`\n A.pts_to a1 p1 s1)\n\n (fun _ ->\n A.pts_to a0 p0 s0\n `star`\n A.pts_to a1 p1 s1)\n (requires True)\n (ensures fun b -> b <==> s0 == s1)\n = let b = for_all2 n a0 a1 (fun x y -> x = y) in\n A.pts_to_length a0 s0;\n A.pts_to_length a1 s1;\n assert (b <==> Seq.equal s0 s1);\n return b", "val alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n : SteelT (ref a p) emp (fun r -> pts_to r full_perm v)\nlet alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n = let h = Current [v] full_perm in\n assert (compatible pcm_history h h);\n let x : ref a p = alloc h in\n intro_pure_full x v h;\n x", "val alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n : SteelT (ref a p) emp (fun r -> pts_to r full_perm v)\nlet alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n : SteelT (ref a p) emp (fun r -> pts_to r full_perm v)\n = let r = MHR.alloc (raise_preorder p) (U.raise_val v) in\n rewrite_slprop\n (MHR.pts_to r full_perm (hide (U.raise_val v)))\n (pts_to r full_perm v)\n (fun _ -> ());\n return r", "val free (h:hasher_t)\r\n : STT unit (inv h) (fun _ -> emp)\nlet free (h:hasher_t)\r\n : STT unit (inv h) (fun _ -> emp)\r\n = array_free h.hash_buffer;\r\n array_free h.serialization_buffer", "val choose (#a: eqtype) (s: set a{exists x. mem x s})\n : GTot (x: a{mem x s})\nlet choose (#a: eqtype) (s: set a{exists x. mem x s}) : GTot (x: a{mem x s}) =\n Cons?.hd (set_as_list s)", "val pop (#a:Type0) (p:t a)\n : Steel (res a) (llist p) (fun res -> llist (res.n))\n (requires fun _ -> p =!= null_llist)\n (ensures fun h0 res h1 -> (\n let l = v_llist p h0 in\n Cons? l /\\\n res.x == L.hd l /\\\n v_llist res.n h1 == L.tl l))\nlet pop #a p =\n let h0 = get #(llist p) () in\n let tl = tail p in\n let x = read p in\n let v = data x in\n free p;\n let h1 = get #(llist tl) () in\n let l = Ghost.hide (v_llist tl h1) in\n change_slprop (llist tl) (llist (Res?.n (Res v tl))) l l (fun _ -> ());\n return (Res v tl)", "val create:\n #a:Type\n -> len:size_nat\n -> init:a ->\n Tot (s:lseq a len{to_seq s == Seq.create len init /\\ (forall (i:nat).\n {:pattern (index s i)} i < len ==> index s i == init)})\nlet create #a len init = Seq.create #a len init", "val pts_to (#a:Type)\n (r:ref a)\n (#[exact (`full_perm)] [@@@equate_by_smt] p:perm)\n ([@@@equate_by_smt] n:a)\n: vprop\nlet pts_to (#a:Type) (r:ref a) (#[T.exact (`full_perm)] p:perm) (n:a)\n= ghost_pcm_pts_to r (Some (n, p)) ** pure (perm_ok p)", "val pts_to (#a:Type)\n (r:ref a)\n (#[exact (`full_perm)] [@@@equate_by_smt] p:perm)\n ([@@@equate_by_smt] n:a)\n: vprop\nlet pts_to\n (#a:Type u#0)\n (r:ref a)\n (#[exact (`full_perm)] [@@@equate_by_smt] p:perm)\n ([@@@equate_by_smt] v:a)\n = H.pts_to r #p (U.raise_val v)", "val write (#a:Type) (#v:erased a) (r:ref a) (x:a)\n : SteelT unit (pts_to r full_perm v) (fun _ -> pts_to r full_perm x)\nlet write (#a:Type) (#v:erased a) (r:ref a) (x:a)\n : SteelT unit (pts_to r full_perm v) (fun _ -> pts_to r full_perm x)\n = let v_old : erased (fractional a) = Ghost.hide (Some (Ghost.reveal v, full_perm)) in\n let v_new : fractional a = Some (x, full_perm) in\n rewrite_slprop (pts_to r full_perm v) (RP.pts_to r v_old `star` pure (perm_ok full_perm)) (fun _ -> ());\n\n elim_pure (perm_ok full_perm);\n\n RP.write r v_old v_new;\n rewrite_slprop (RP.pts_to r v_new) (pts_to r full_perm x)\n (fun m -> emp_unit (hp_of (pts_to_raw r full_perm x));\n pure_star_interp (hp_of (pts_to_raw r full_perm x)) (perm_ok full_perm) m)", "val memcpy (#t:_) (#p0:perm)\n (a0 a1:array t)\n (#s0 #s1:Ghost.erased (Seq.seq t))\n (l:US.t { US.v l == length a0 /\\ length a0 == length a1 } )\n : STT unit\n (pts_to a0 p0 s0 `star` pts_to a1 full_perm s1)\n (fun _ -> pts_to a0 p0 s0 `star` pts_to a1 full_perm s0)\nlet memcpy\n a0 a1 l\n=\n H.memcpy a0 a1 l", "val invariant: #t_k:eqtype -> #t_v:Type0 -> h:HS.mem -> ll:t t_k t_v -> Type0\nlet invariant #_ #_ h ll =\n LL2.invariant h ll", "val read_with_perm\n (#k: parser_kind)\n (#t: Type u#0)\n (#p: parser k t)\n (r: leaf_reader p)\n (#len: Ghost.erased U32.t)\n (sl: input_buffer_t len)\n (pos: U32.t)\n (n: U32.t)\n (perm_of: R.perm (slice_of sl).base)\n: HST.Stack t\n (requires (fun h ->\n valid_input_buffer p h sl perm_of pos /\\\n k.LPL.parser_kind_subkind == Some LPL.ParserStrong /\\\n k.LPL.parser_kind_high == Some k.LPL.parser_kind_low /\\\n k.LPL.parser_kind_low == U32.v n /\\\n R.readable h perm_of pos (get_valid_pos p h (slice_of sl) pos)\n ))\n (ensures (fun h res h' ->\n let pos' = get_valid_pos p h (slice_of sl) pos in\n B.modifies (R.loc_perm perm_of) h h' /\\\n R.preserved perm_of 0ul pos h h' /\\\n R.preserved perm_of pos' (B.len (slice_of sl).LPL.base) h h' /\\\n R.unreadable h' perm_of pos pos' /\\\n live_input_buffer h' sl perm_of /\\\n res == contents p h (slice_of sl) pos\n ))\nlet read_with_perm #k #t #p r #len base pos n perm_of =\n let h0 = HST.get () in\n LPL.valid_facts p h0 (slice_of base) pos;\n LPL.parser_kind_prop_equiv k p;\n [@inline_let] let sl' : LPL.slice triv triv = { LPL.base = base; LPL.len = pos `U32.add` n } in\n LPL.parse_strong_prefix p (LPL.bytes_of_slice_from h0 (slice_of base) pos) (LPL.bytes_of_slice_from h0 sl' pos);\n LPL.valid_facts p h0 sl' pos;\n let pos' = Ghost.hide (LPL.get_valid_pos p h0 sl' pos) in\n drop base pos pos' perm_of ;\n let h1 = HST.get () in\n let prf (h2: HS.mem) : Lemma\n (requires (B.modifies B.loc_none h1 h2))\n (ensures (\n R.preserved perm_of 0ul pos h0 h2 /\\\n R.preserved perm_of pos' (B.len (slice_of base).LPL.base) h0 h2 /\\\n R.unreadable h2 perm_of pos pos' /\\\n live_input_buffer h2 base perm_of\n ))\n [SMTPat (B.modifies B.loc_none h1 h2)] // this lemma *with SMT pattern* allows tail call to the leaf reader, thus removing spurious temporary assignments in the generated C code\n =\n R.valid_perm_frame h1 perm_of B.loc_none h2;\n R.preserved_split perm_of 0ul pos (B.len base) h1 h2;\n R.preserved_split perm_of pos pos' (B.len base) h1 h2;\n R.preserved_trans perm_of 0ul pos h0 h1 h2;\n R.preserved_trans perm_of pos' (B.len base) h0 h1 h2\n in\n r sl' pos", "val pts_to\n (#a:Type) (r:ref a) \n (#[exact (`full_perm)] [@@@equate_by_smt] p:perm)\n ([@@@equate_by_smt] n:a)\n : vprop\nlet pts_to\n (#a:Type u#0)\n (r:ref a)\n (#[exact (`full_perm)] [@@@equate_by_smt] p:perm)\n ([@@@equate_by_smt] v:a)\n = H.pts_to r #p (U.raise_val v)", "val create (#a: Type) (init: a) (len: U32.t)\n : HST.StackInline (buffer a)\n (requires (fun h -> U32.v len > 0))\n (ensures\n (fun h b h' ->\n rcreate_post_mem_common (HS.get_tip h) (U32.v len) b h h' (Seq.create (U32.v len) init))\n )\nlet create\n (#a: Type)\n (init: a)\n (len: U32.t)\n: HST.StackInline (buffer a)\n (requires (fun h -> U32.v len > 0))\n (ensures (fun h b h' ->\n rcreate_post_mem_common (HS.get_tip h) (U32.v len) b h h' (Seq.create (U32.v len) init)\n ))\n= alloca init len", "val write : #a:Type -> \n r:ref a -> \n\t x:a -> \n\t ImmutableST unit (fun h0 -> contains r h0 /\\ \n\t sel h0 r == x)\n (fun h0 _ h1 -> h0 == h1)\nlet write #a r x = \n let h = ist_get () in\n ist_put h", "val sel (#key: eqtype) (#value: (key -> Tot Type)) (m: t key value) (k: key) : Tot (value k)\nlet sel (#key: eqtype) (#value: (key -> Tot Type)) (m: t key value) (k: key) : Tot (value k) =\n m.mappings k", "val write (#a: Type0) (n: nat) (x: a)\n : LV unit\n (fun m0 -> m0.m `M.contains` n /\\ dfst (m0.m `M.sel` n) == a)\n (fun m0 _ m1 -> m1.next == m0.next /\\ m1.m == Map.upd m0.m n (| a, x |))\nlet write (#a:Type0) (n:nat) (x:a)\n : LV unit (fun m0 -> m0.m `M.contains` n /\\\n dfst (m0.m `M.sel` n) == a)\n (fun m0 _ m1 ->\n m1.next == m0.next /\\\n m1.m == Map.upd m0.m n (| a, x |))\n= LVARS?.reflect (fun m -> (), { m with m = Map.upd m.m n (| a, x |) })", "val free (#opened: _) (#a:Type)\n (#v:erased a)\n (r:ref a)\n : STGhostT unit opened\n (pts_to r full_perm v) (fun _ -> emp)\nlet free\n #_ #a #v r\n= let gr : R.ghost_ref a = coerce_eq (R.reveal_ghost_ref a) (Ghost.hide r.reveal) in\n weaken (pts_to r full_perm v) (R.ghost_pts_to gr full_perm v) (fun _ ->\n R.reveal_ghost_pts_to_sl gr full_perm v\n );\n STC.coerce_ghost (fun _ -> R.ghost_free gr)" ], "closest_src": [ { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.create" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Type.fst", "name": "Pulse.Lib.HashTable.Type.token" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.put" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Type.fsti", "name": "Pulse.Lib.HashTable.Type.exploded_vp" }, { "project_name": "steel", "file_name": "Steel.ST.BitVector.fst", "name": "Steel.ST.BitVector.alloc" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.reclaim" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.finalize" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Type.fst", "name": "Pulse.Lib.HashTable.Type.unexplode_ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.fst", "name": "Pulse.Lib.HashTable.mk_ht" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.malloc" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.write" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.write" }, { "project_name": "FStar", "file_name": "FStar.Array.fst", "name": "FStar.Array.create" }, { "project_name": "FStar", "file_name": "FStar.DependentMap.fst", "name": "FStar.DependentMap.create" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.get" }, { "project_name": "FStar", "file_name": "MonotonicArray.fst", "name": "MonotonicArray.create" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.create" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.alloc" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.free" }, { "project_name": "steel", "file_name": "Steel.ST.BitVector.fst", "name": "Steel.ST.BitVector.bv_set" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.free" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.v" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fsti", "name": "Steel.ST.HigherArray.malloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.share" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.write" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.create_in" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fst", "name": "Steel.ST.HigherArray.malloc0" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Type.fst", "name": "Pulse.Lib.HashTable.Type.explode_ref_ht_t" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.fst", "name": "Pulse.Lib.Array.fill" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.alloc" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.alloc" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.alloc" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.create" }, { "project_name": "FStar", "file_name": "FStar.FiniteMap.Base.fst", "name": "FStar.FiniteMap.Base.insert" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.perm" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.create" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.free" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.clear" }, { "project_name": "FStar", "file_name": "FStar.FiniteMap.Base.fst", "name": "FStar.FiniteMap.Base.choose" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.read" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.share" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherReference.fst", "name": "Pulse.Lib.HigherReference.share" }, { "project_name": "steel", "file_name": "Pulse.Lib.Reference.fst", "name": "Pulse.Lib.Reference.share" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.share" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.write" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.read" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.read" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.upd" }, { "project_name": "FStar", "file_name": "FStar.PartialMap.fst", "name": "FStar.PartialMap.empty" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.create" }, { "project_name": "steel", "file_name": "Steel.ST.GhostHigherReference.fst", "name": "Steel.ST.GhostHigherReference.write" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.free" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherArray.fst", "name": "Pulse.Lib.HigherArray.alloc" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.share_gen" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.share" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.write" }, { "project_name": "zeta", "file_name": "Zeta.Steel.EpochMap.fst", "name": "Zeta.Steel.EpochMap.ghost_put" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.op_Colon_Equals" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fsti", "name": "Steel.ST.HigherArray.memcpy" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.share" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Mem.fst", "name": "MiTLS.Mem.mem_alloc" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherArray.fst", "name": "Pulse.Lib.HigherArray.share" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.sel" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.share" }, { "project_name": "steel", "file_name": "Steel.ST.GhostHigherReference.fst", "name": "Steel.ST.GhostHigherReference.share" }, { "project_name": "steel", "file_name": "Pulse.Lib.Box.fst", "name": "Pulse.Lib.Box.share" }, { "project_name": "steel", "file_name": "Steel.ST.BitVector.fst", "name": "Steel.ST.BitVector.bv_unset" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.alloc" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.create" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.index" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.write" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fsti", "name": "Steel.ST.HigherArray.upd" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.add" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.createL" }, { "project_name": "FStar", "file_name": "AllocST.fst", "name": "AllocST.write" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.find" }, { "project_name": "FStar", "file_name": "FStar.PartialMap.fst", "name": "FStar.PartialMap.literal" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fst", "name": "Steel.ST.HigherArray.upd0" }, { "project_name": "FStar", "file_name": "FStar.PartialMap.fst", "name": "FStar.PartialMap.upd" }, { "project_name": "steel", "file_name": "Steel.ST.Array.Util.fsti", "name": "Steel.ST.Array.Util.compare" }, { "project_name": "steel", "file_name": "Steel.MonotonicHigherReference.fst", "name": "Steel.MonotonicHigherReference.alloc" }, { "project_name": "steel", "file_name": "Steel.MonotonicReference.fst", "name": "Steel.MonotonicReference.alloc" }, { "project_name": "zeta", "file_name": "Zeta.Steel.HashValue.fst", "name": "Zeta.Steel.HashValue.free" }, { "project_name": "FStar", "file_name": "FStar.FiniteSet.Base.fst", "name": "FStar.FiniteSet.Base.choose" }, { "project_name": "steel", "file_name": "Selectors.LList.Derived.fst", "name": "Selectors.LList.Derived.pop" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.create" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.pts_to" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.pts_to" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.write" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.memcpy" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.invariant" }, { "project_name": "everparse", "file_name": "EverParse3d.InputBuffer.fst", "name": "EverParse3d.InputBuffer.read_with_perm" }, { "project_name": "steel", "file_name": "Pulse.Lib.Reference.fst", "name": "Pulse.Lib.Reference.pts_to" }, { "project_name": "FStar", "file_name": "LowStar.BufferCompat.fst", "name": "LowStar.BufferCompat.create" }, { "project_name": "FStar", "file_name": "ImmutableST.fst", "name": "ImmutableST.write" }, { "project_name": "FStar", "file_name": "FStar.DependentMap.fst", "name": "FStar.DependentMap.sel" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.write" }, { "project_name": "steel", "file_name": "Steel.ST.GhostHigherReference.fst", "name": "Steel.ST.GhostHigherReference.free" } ], "selected_premises": [ "Steel.Memory.full_mem", "Steel.ST.EphemeralHashtbl.tperm", "Steel.ST.Array.length", "Steel.ST.EphemeralHashtbl.pack_tperm", "FStar.List.Tot.Base.map", "Steel.Effect.Common.to_vprop", "Steel.Memory.hmem", "FStar.List.Tot.Base.length", "Steel.Preorder.pcm_history", "Steel.FractionalPermission.full_perm", "Steel.Effect.Common.star", "Steel.Effect.Common.hp_of", "Steel.ST.Array.array", "Steel.Effect.Common.to_vprop'", "Steel.ST.Array.alloc", "Steel.Effect.Common.rmem", "Steel.ST.Array.join", "FStar.Real.one", "Steel.Memory.inames", "FStar.Reflection.V2.Data.var", "FStar.List.Tot.Base.op_At", "Steel.Effect.Common.t_of", "FStar.PtrdiffT.zero", "Steel.Effect.Common.req", "Steel.ST.Array.adjacent", "FStar.PCM.composable", "Steel.ST.Array.ptr_of", "Steel.Effect.Common.normal", "FStar.Real.two", "Steel.ST.Array.write", "Steel.ST.Array.null", "Steel.ST.Util.op_At_Equals_Equals_Greater", "Steel.ST.EphemeralHashtbl.store_contents_pred", "Steel.ST.Util.emp_inames", "FStar.Reflection.V2.Derived.mk_app", "FStar.Reflection.V2.Derived.mk_e_app", "Steel.Effect.Common.normal_steps", "Steel.Effect.Common.rm", "FStar.PCM.compatible", "FStar.PCM.op", "Steel.Preorder.history_val", "Steel.Effect.Common.mk_rmem", "FStar.FunctionalExtensionality.feq", "FStar.UInt.size", "Steel.Effect.Common.guard_vprop", "Steel.Effect.Common.vrefine'", "Steel.ST.EphemeralHashtbl.value_vprops_seq", "Steel.Effect.Common.pure", "Steel.FractionalPermission.comp_perm", "Steel.ST.Array.read", "Steel.Effect.Common.rmem'", "Steel.FractionalPermission.sum_perm", "Steel.Effect.Common.hmem", "Steel.ST.EphemeralHashtbl.value_vprops_mapping_fn", "Steel.Effect.Common.sel_of", "Steel.ST.EphemeralHashtbl.value_vprops", "FStar.Tactics.CanonCommMonoidSimple.Equiv.term_eq", "Steel.Effect.Common.extract_contexts", "Steel.Effect.Common.vrefine", "Steel.ST.EphemeralHashtbl.pure_invariant", "FStar.List.Tot.Base.tl", "FStar.IntegerIntervals.interval_size", "FStar.Reflection.V2.Derived.flatten_name", "FStar.List.Tot.Base.mem", "FStar.List.Tot.Base.rev", "Steel.ST.EphemeralHashtbl.vprop_monoid", "FStar.Heap.trivial_preorder", "FStar.Mul.op_Star", "Steel.ST.Array.merge", "Steel.Effect.Common.inv", "Steel.Effect.Common.mk_rmem'", "Steel.Effect.Common.print_goals", "FStar.Seq.Permutation.index_fun", "Steel.ST.Util.wand_is_implies", "FStar.Pervasives.reveal_opaque", "Steel.Effect.Common.return_pre", "FStar.List.Tot.Base.append", "FStar.Reflection.V2.Derived.shift_subst", "FStar.IntegerIntervals.closed_interval_size", "Steel.ST.Array.is_full_array", "Steel.Effect.Common.focus_rmem_refl", "Steel.Effect.Common.focus_rmem", "FStar.ST.op_Bang", "Steel.Effect.Common.slterm_nbr_uvars_argv", "Steel.Effect.Common.sel_depends_only_on", "Steel.Effect.Common.selector'", "Steel.Effect.Common.vc_norm", "FStar.String.strlen", "Steel.Effect.Common.visit_br", "FStar.Reflection.V2.Derived.type_of_binder", "Steel.ST.Util.rewrite_with_implies", "FStar.FunctionalExtensionality.on_dom", "FStar.Sealed.Inhabited.seal", "Steel.Preorder.vhist", "FStar.String.length", "FStar.Reflection.V2.Derived.u_unk", "FStar.NMSTTotal.get", "Steel.ST.Util.elim_implies", "Steel.ST.Util.intro_implies", "FStar.Reflection.V2.Derived.Lemmas.op_Less_Less_Colon" ], "source_upto_this": "(*\n Copyright 2021 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n\n Authors: Aseem Rastogi\n*)\n\nmodule Steel.ST.EphemeralHashtbl\n\nopen Steel.FractionalPermission\nopen Steel.Memory\nopen Steel.ST.Effect.Ghost\nopen Steel.ST.Effect.Atomic\nopen Steel.ST.Effect\nopen Steel.ST.Util\n\nmodule G = FStar.Ghost\nmodule Seq = FStar.Seq\nmodule Map = FStar.PartialMap\nmodule US = FStar.SizeT\nmodule R = Steel.ST.Reference\nmodule A = Steel.ST.Array\n\n\n/// `store` is the concrete store implemented as an array\n///\n/// The hashing scheme we use is as follows:\n/// for key `k`, its slot in the array is `(h k) mod n`\n\nnoeq\ntype tbl #k #v #contents (vp:vp_t k v contents) (h:hash_fn k) = {\n store_len : n:us{US.v n > 0};\n store : A.array (option (k & v));\n store_len_pf : squash (A.length store == US.v store_len);\n}\n\n/// Property of the logical view of the store\n///\n/// For each (Some (k, v)) in the sequence, (h k) mod n == i\n\nlet seq_props (#k:eqtype) (#v:Type0) (h:hash_fn k) (s:Seq.seq (option (k & v))) : prop =\n 0 < Seq.length s /\\ US.fits (Seq.length s) /\\\n\n (forall (i:nat{i < Seq.length s}).\n Some? (Seq.index s i) ==> (let Some (x, _) = Seq.index s i in\n US.v (h x) `US.mod_spec` Seq.length s == i))\n\n/// Using seq_props, we can derive that all the keys in the sequence are distinct\n\nlet seq_keys_distinct (#k:eqtype) (#v:Type0) (s:Seq.seq (option (k & v))) : prop =\n forall (i j:(k:nat{k < Seq.length s})).{:pattern Seq.index s i; Seq.index s j}\n (i =!= j /\\ Some? (Seq.index s i) /\\ Some? (Seq.index s j)) ==>\n (fst (Some?.v (Seq.index s i)) =!= fst (Some?.v (Seq.index s j)))\n\nlet seq_props_implies_keys_distinct (#k:eqtype) (#v:Type0) (h:hash_fn k) (s:Seq.seq (option (k & v)))\n : Lemma (requires seq_props h s) (ensures seq_keys_distinct s)\n = ()\n\n/// For each (Some (k, v)) in the sequence, k must be in the repr map\n\nlet store_and_repr_related\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n : prop\n = forall (i:nat{i < Seq.length s}).\n match Seq.index s i with\n | None -> True\n | Some (k, _) -> Map.contains m k\n\n/// For each (Some (k, v)) in the sequence,\n/// either borrows does not contain k, or it maps k to v\n\nlet store_and_borrows_related\n (#k:eqtype)\n (#v:Type0)\n (s:Seq.seq (option (k & v)))\n (borrows:Map.t k v)\n : prop\n = forall (i:nat{i < Seq.length s}).\n match Seq.index s i with\n | None -> True\n | Some (k, x) ->\n Map.sel borrows k == None \\/\n Map.sel borrows k == Some x\n\nmodule CE = FStar.Algebra.CommMonoid.Equiv\nmodule SeqPerm = FStar.Seq.Permutation\n\n/// Setup for maintaining the value vprops in the table invariant\n///\n/// High-level idea is that, we take the store sequence,\n/// map it to a sequence of vprops,\n/// and fold the vprop monoid (with `star` as the multiplication) on this sequence\n///\n/// Each value contributes a `vp i x c`, unless it is in the borrows map\n\nlet vprop_monoid : CE.cm vprop Steel.Effect.Common.req = Steel.Effect.Common.rm\n\n/// Function to map over the store sequence\n\nlet value_vprops_mapping_fn\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (m:repr k contents)\n (borrows:Map.t k v)\n : option (k & v) -> vprop\n = fun e ->\n match e with\n | None -> emp\n | Some (i, x) ->\n (match Map.sel m i, Map.sel borrows i with\n | None, _ -> pure False\n | _, Some _ -> emp\n | Some c, None -> vp i x c)\n\n/// The corresponding sequence of vprops for a store sequence\n\n[@@__reduce__]\nlet value_vprops_seq\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n : Seq.seq vprop\n = Seq.map_seq (value_vprops_mapping_fn vp m borrows) s\n\n/// Value vprops\n\n[@@__reduce__]\nlet value_vprops\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n : vprop\n = SeqPerm.foldm_snoc vprop_monoid (value_vprops_seq vp s m borrows)\n\nlet pure_invariant\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (arr:tbl vp h)\n (m:repr k contents)\n (borrows:Map.t k v)\n (s:Seq.seq (option (k & v)))\n : prop\n = seq_props h s /\\\n store_and_repr_related s m /\\\n A.is_full_array arr.store /\\\n store_and_borrows_related s borrows\n\n/// The main invariant is defined as an existential for the store sequence\n\n[@@__reduce__]\nlet store_contents_pred\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (arr:tbl vp h)\n (m:repr k contents)\n (borrows:Map.t k v)\n : Seq.seq (option (k & v)) -> vprop\n = fun s ->\n A.pts_to arr.store full_perm s\n `star`\n pure (pure_invariant arr m borrows s)\n `star`\n value_vprops vp s m borrows\n\n/// Main invariant\n\n[@@__reduce__]\nlet tperm arr m borrows = exists_ (store_contents_pred arr m borrows)\n\n\n/// map_seq lemmas, with smt pats on them\n\nlet map_seq_len (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a)\n : Lemma (ensures Seq.length (Seq.map_seq f s) == Seq.length s)\n [SMTPat (Seq.length (Seq.map_seq f s))]\n = Seq.map_seq_len f s\n\nlet map_seq_index (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a) (i:nat{i < Seq.length s})\n : Lemma (ensures Seq.index (Seq.map_seq f s) i == f (Seq.index s i))\n [SMTPat (Seq.index (Seq.map_seq f s) i)]\n = Seq.map_seq_index f s i\n\nlet map_seq_append (#a #b:Type) (f:a -> Tot b) (s1 s2:Seq.seq a)\n : Lemma (ensures (Seq.map_seq f (Seq.append s1 s2) ==\n Seq.append (Seq.map_seq f s1) (Seq.map_seq f s2)))\n [SMTPat (Seq.map_seq f (Seq.append s1 s2))]\n = Seq.map_seq_append f s1 s2\n\n\n/// Helper function to pack a tperm assertion\n\nlet pack_tperm (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (s:Seq.seq (option (k & v)))\n (m:repr k contents)\n (borrows:Map.t k v)\n (a:tbl vp h)\n : STGhost unit opened\n (A.pts_to a.store full_perm s\n `star`\n value_vprops vp s m borrows)\n (fun _ -> tperm a m borrows)\n (requires pure_invariant a m borrows s)\n (ensures fun _ -> True)\n = intro_pure (pure_invariant a m borrows s);\n intro_exists s (store_contents_pred a m borrows)\n", "sketch": [ "Step 1: The `create` function is intended to initialize a new hash table with a given size `n`, a value property function `vp`, and a hash function `h`. The table will be empty initially.\nStep 2: To implement this, we will:\n- Create an array of length `n` where each element is `None` (indicating an empty slot).\n- Ensure the array's length matches `n`.\n- Return a new table with the created array and the given parameters.\n- Establish the table's invariant by packing the appropriate permissions and properties.", "Step 1: The `create` function is about creating a new hash table with a given size `n`, a value property function `vp`, and a hash function `h`. The resulting table should be empty initially.\nStep 2: To implement this, we will:\n - Allocate an array of size `n` with all elements initialized to `None`.\n - Ensure the array length matches `n`.\n - Construct the table with the allocated array and the proof that its length is `n`.\n - Return the table while ensuring the table permission invariant holds with empty maps for both the representation and borrows.", "Step 1: The `create` function is intended to initialize a new hash table with a given size `n`, a value property function `vp`, and a hash function `h`. The resulting table should be empty and satisfy the table permission invariant (`tperm`).\n\nStep 2: To implement this, we will:\n- Create an array of length `n` filled with `None` values, representing an empty hash table.\n- Construct a `tbl` record with this array and the given parameters.\n- Use the `pack_tperm` helper function to establish the table permission invariant for the newly created table.", "Step 1: The `create` function is intended to initialize a new hash table with a given size `n`, a value property function `vp`, and a hash function `h`. The function should return a new table that satisfies the `tperm` invariant with empty representations for both the contents and borrows maps.\n\nStep 2: To implement the `create` function, we will:\n1. Allocate an array of length `n` initialized with `None` values.\n2. Construct the table record with the allocated array and the proof that the array length matches `n`.\n3. Use the `pack_tperm` helper function to establish the `tperm` invariant for the newly created table.", "Step 1: The `create` function is about initializing a new hash table with a given size `n`, hash function `h`, and value properties `vp`. The table should be empty initially.\nStep 2: To implement this, we will:\n- Create an array of length `n` with all elements initialized to `None`.\n- Ensure the array length is correctly set.\n- Return a new table with the created array and the given parameters.\n- Ensure the table satisfies the `tperm` invariant with empty maps for `m` and `borrows`.", "Step 1: The `create` function is intended to initialize a new hash table with a given size `n`, a value property function `vp`, and a hash function `h`. The resulting table should be empty, meaning it contains no key-value pairs initially.\nStep 2: To implement this, we will:\n- Create an array of length `n` where each element is `None`, representing an empty slot.\n- Ensure the array length matches `n`.\n- Return a table structure with the created array and the proof that the array length is correct.\n- Ensure the table satisfies the `tperm` invariant with empty maps for both the representation and borrows.", "Step 1: The `create` function is about initializing a new hash table with a given size `n`, hash function `h`, and value properties `vp`. The function should return a new table that satisfies the `tperm` invariant with empty maps for both the representation and borrows.\n\nStep 2: To implement this, we:\n1. Allocate an array of size `n` with all elements initialized to `None`.\n2. Create a `tbl` record with the allocated array and the proof that its length is `n`.\n3. Use the `pack_tperm` helper function to pack the `tperm` assertion for the newly created table, with empty maps for the representation and borrows.", "Step 1: The `create` function is about initializing a new hash table with a given size `n`, a value property function `vp`, and a hash function `h`. The resulting table should be empty, meaning it has no key-value pairs stored in it initially.\nStep 2: To implement this, we will:\n- Create an array of length `n` where each slot is initialized to `None`, indicating that no key-value pairs are stored.\n- Ensure the length of the array matches `n`.\n- Return a table structure containing this array and the proof that the array length is `n`.\n- Establish the table's permission invariant (`tperm`), which includes the empty representation map and borrow map.", "Step 1: The `create` function is about initializing a new hash table with a given size `n`, hash function `h`, and value properties `vp`. The table will be empty initially.\nStep 2: To implement this, we will:\n- Create an array of length `n` filled with `None` values.\n- Construct the `tbl` record with this array and the given parameters.\n- Ensure the initial state of the table satisfies the `tperm` invariant with empty maps for `repr` and `borrows`.", "Step 1: The `create` function is designed to initialize a new hash table with a given size `n`, a value property function `vp`, and a hash function `h`. The resulting table should be empty initially.\nStep 2: To implement this, we will:\n- Create an array of length `n` initialized with `None` values, representing an empty table.\n- Ensure the length of the array matches `n`.\n- Return the newly created table along with the appropriate permissions and invariants." ], "generated_solution": [ "let create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))\n = let store = A.create n None in\n let store_len_pf = assert (A.length store == US.v n) in\n let arr = { store_len = n; store = store; store_len_pf = store_len_pf } in\n let s = Seq.create n None in\n pack_tperm s (Map.empty k contents) (Map.empty k v) arr", "let create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))\n = let! arr = A.alloc n None in\n let store_len_pf = assert (A.length arr == US.v n) in\n let tbl = { store_len = n; store = arr; store_len_pf = store_len_pf } in\n pack_tperm (Seq.create n None) (Map.empty k contents) (Map.empty k v) tbl", "let create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))\n =\n let store = A.create n None in\n let store_len_pf = () in\n let arr = { store_len = n; store = store; store_len_pf = store_len_pf } in\n let s = Seq.create n None in\n pack_tperm s (Map.empty k contents) (Map.empty k v) arr", "let create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))\n = let arr = A.alloc n None in\n let table = { store_len = n; store = arr; store_len_pf = () } in\n pack_tperm (Seq.create n None) (Map.empty k contents) (Map.empty k v) table", "let create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))\n = let arr = A.create n None in\n let store_len_pf = A.length_create arr in\n let tbl = { store_len = n; store = arr; store_len_pf = store_len_pf } in\n pack_tperm (Seq.create n None) (Map.empty k contents) (Map.empty k v) tbl", "let create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))\n = let arr = A.create n None in\n let store_len_pf = A.length_create n None in\n let tbl = { store_len = n; store = arr; store_len_pf = store_len_pf } in\n pack_tperm (Seq.create n None) (Map.empty k contents) (Map.empty k v) tbl", "let create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))\n = let! store = A.alloc n None in\n let tbl = { store_len = n; store = store; store_len_pf = () } in\n pack_tperm (Seq.create n None) (Map.empty k contents) (Map.empty k v) tbl", "let create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))\n = let arr = A.create n None in\n let store_len_pf = assert (A.length arr == US.v n) in\n let tbl = { store_len = n; store = arr; store_len_pf = store_len_pf } in\n pack_tperm (Seq.create n None) (Map.empty k contents) (Map.empty k v) tbl", "let create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))\n = let arr = A.create n None in\n let t = { store_len = n; store = arr; store_len_pf = () } in\n pack_tperm (Seq.create n None) (Map.empty k contents) (Map.empty k v) t", "let create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))\n = let store = A.create n None in\n let store_len_pf = assert (A.length store == US.v n) in\n let arr = { store_len = n; store = store; store_len_pf = store_len_pf } in\n pack_tperm Seq.empty (Map.empty k contents) (Map.empty k v) arr" ] }, { "file_name": "MonadFunctorInference.fst", "name": "MonadFunctorInference.st", "opens_and_abbrevs": [ { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let st (s:Type) (a:Type) = s -> a & s", "source_range": { "start_line": 12, "start_col": 0, "end_line": 12, "end_col": 37 }, "interleaved": false, "definition": "fun s a -> _: s -> a * s", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Pervasives.Native.tuple2" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "s: Type -> a: Type -> Type", "prompt": "let st (s a: Type) =\n ", "expected_response": "s -> a & s", "source": { "project_name": "FStar", "file_name": "examples/typeclasses/MonadFunctorInference.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "MonadFunctorInference.fst", "checked_file": "dataset/MonadFunctorInference.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Tactics.Typeclasses.fsti.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked" ] }, "definitions_in_context": [ "monad", "monad", "class monad (m:Type -> Type) =\n{\n return : (#a:Type -> a -> m a);\n bind : (#a:Type -> #b:Type -> (f:m a) -> (g:(a -> m b)) -> m b);\n}", "class monad (m:Type -> Type) =\n{\n return : (#a:Type -> a -> m a);\n bind : (#a:Type -> #b:Type -> (f:m a) -> (g:(a -> m b)) -> m b);\n}", "return", "return", "bind", "bind" ], "closest": [ "val FStar.DM4F.MonadLaws.st = s: Type -> a: Type -> Type\nlet st (s:Type) (a:Type) = s -> Tot (a * s)", "val FStar.DM4F.ST.st = s: Type -> a: Type -> Type\nlet st (s:Type) (a:Type) = s -> M (a * s)", "val PulseCore.MonotonicStateMonad.ens_t = s: Type -> a: Type -> Type\nlet ens_t (s:Type) (a:Type) = s -> a -> s -> prop", "val DijkstraStateMonad.post_t = s: Type0 -> a: Type -> Type\nlet post_t (s:Type0) (a:Type) = a * s -> Type0", "val GradedMonad.st = s: Type -> monoid_nat_plus: _ -> count: Prims.nat -> a: Type -> Type\nlet st (s:Type) monoid_nat_plus (count:nat) (a:Type) = s -> a & s", "val DijkstraStateMonad.wp_t = s: Type0 -> a: Type -> Type\nlet wp_t (s:Type0) (a:Type) = s ^-> (post_t s a -> Type0)", "val return (a: Type) (x: a) (s: _) : st a s\nlet return (a:Type) (x:a) s\n : st a s\n = fun s -> x, s", "val MRefST.st = a: Type -> Type\nlet st (a: Type) = heap -> M (a * heap)", "val PulseCore.MonotonicStateMonad.req_t = s: Type -> Type\nlet req_t (s:Type) = s -> prop", "val DijkstraStateMonad.pre_t = s: Type -> Type\nlet pre_t (s:Type) = s -> Type0", "val return (a: Type) (x: a) (s: _) : nds a s\nlet return (a:Type) (x:a) s\n : nds a s\n = fun t n s -> x, s, n", "val return (a: Type) (x: a) (s: Type) : repr a s s []\nlet return (a:Type) (x:a) (s:Type)\n : repr a s s []\n =\n Return x", "val FStar.Fin.in_ = s: FStar.Seq.Base.seq a -> Type0\nlet in_ (#a: Type) (s: S.seq a) = n: nat{n < S.length s}", "val FStar.DM4F.MonadLaws.ifc = a: Type -> Type\nlet ifc (a:Type) = label -> Tot (option (a * label))", "val f (a: Type) : s (s (s (s (s (s (s (s z)))))))\nlet f (a:Type) : s (s (s (s (s (s (s (s z))))))) = x", "val FStar.DM4F.MonadLaws.right_unit_st = s: Type -> a: Type -> f: FStar.DM4F.MonadLaws.st s a -> Prims.unit\nlet right_unit_st (s:Type) (a:Type) (f:st s a) =\n assert (feq (bind_st f (return_st)) f)", "val FStar.Tactics.CanonCommMonoid.vmap = a: Type -> b: Type -> Type\nlet vmap (a b:Type) = list (var * (a*b)) * (a * b)", "val IMST.st_wp' = a: Type -> s: Type0 -> Type\nlet st_wp' (a:Type) (s:Type0) \n = st_post s a -> Tot (st_pre s)", "val Steel.Coinduction.mono_fun = a: Type -> Type\nlet mono_fun a = (f: (pred a -> pred a){mono f})", "val IST.st_wp' = a: Type -> s: Type0 -> Type\nlet st_wp' (a:Type) (s:Type0) = st_post s a -> st_pre s", "val bind : (a:Type) -> (b:Type) ->\n (m:stexnc a) -> (f:a -> stexnc b) -> stexnc b\nlet bind a b m f =\n fun s0 ->\n let r0 = m s0 in\n match r0 with\n | None, (s1, c1) -> None, (s1, c1)\n | Some r, (s1, c1) -> let res, (s, c2) = f r s1\n in res, (s, c1 + c2)", "val IMSTsub.st_post' = s: Type0 -> a: Type -> pre: Type -> Type\nlet st_post' (s:Type0) (a:Type) (pre:Type) = a -> (_:s{pre}) -> GTot Type0", "val return (a: Type) (x: a) : repr a (fun p s -> p x s)\nlet return (a:Type) (x:a)\n: repr a (fun p s -> p x s)\n= fun _ -> x", "val IMST.st_post' = s: Type0 -> a: Type -> pre: Type -> Type\nlet st_post' (s:Type0) (a:Type) (pre:Type) = a -> (_:s{pre}) -> GTot Type0", "val return_st (s a: Type) (x: a) : st s a\nlet return_st (s:Type) (a:Type) (x:a) : st s a = fun s0 -> x, s0", "val Monad.g' = {| _: Monad.monad m |} -> x: m a -> Prims.unit\nlet g' #a #b #m {| monad m |} (x : m a) =\n (laws #m).idL () (fun () -> x);\n (laws #m).idR x;\n assert (bind #m x (return #m) == bind #m (return #m ()) (fun () -> x))", "val Monad.g = {| d: Monad.monad m |} -> x: m a -> Prims.unit\nlet g #a #b #m {| d : monad m |} (x : m a) =\n d.laws.idL () (fun () -> x);\n d.laws.idR x;\n assert (bind #m x (return #m) == bind #m (return #m ()) (fun () -> x))", "val Zeta.SMap.mono_smap = s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> Type0\nlet mono_smap (#a:_) (s1 s2: seq a) = f:smap s1 s2 {monotonic_prop f}", "val FStar.DM4F.MonadLaws.left_unit_st = s: Type -> a: Type -> b: Type -> x: a -> f: (_: a -> FStar.DM4F.MonadLaws.st s b) -> Prims.unit\nlet left_unit_st (s:Type) (a:Type) (b:Type) (x:a) (f:(a -> st s b)) =\n assert (feq (bind_st (return_st x) f) (f x))", "val FStar.FunctionalExtensionality.arrow = a: Type -> b: (_: a -> Type) -> Type\nlet arrow (a: Type) (b: (a -> Type)) = x: a -> Tot (b x)", "val immutable_preorder (a: Type0) : srel a\nlet immutable_preorder (a:Type0) :srel a = fun s1 s2 -> Seq.equal s1 s2", "val IST.st_post = s: Type0 -> a: Type -> Type\nlet st_post (s:Type0) (a:Type) = st_post_h' s a True", "val Setoids.st = srel: Setoids.rel s -> arel: Setoids.rel a -> Type\nlet st (#s:Type) (#a:Type) (srel:rel s) (arel:rel a) =\n srel ^--> (arel ** srel)", "val FStar.DM4F.StExn.stexn = a: Type -> Type\nlet stexn a =\n int -> M (option a * int)", "val ImmutableST.st_wp = a: Type -> Type\nlet st_wp (a:Type) = st_post a -> Tot st_pre", "val FStar.Tactics.CanonCommMonoidSimple.amap = a: Type -> Type\nlet amap (a:Type) = list (atom * a) * a", "val IMST.st_post = s: Type0 -> a: Type -> Type\nlet st_post (s:Type0) (a:Type) = st_post_h' s a True", "val EverParse3d.Prelude.injective_map = a: Type -> b: Type -> Type\nlet injective_map a b = (a -> Tot b)", "val FStar.DM4F.StExnC.stexnc = a: Type -> Type\nlet stexnc a =\n int -> M (option a * (int * int))", "val FStar.FunctionalExtensionality.efun = a: Type -> b: (_: a -> Type) -> Type\nlet efun (a: Type) (b: (a -> Type)) = arrow a b", "val Effects.Def.st = a: Type -> Type\nlet st (a:Type) = restricted_t s (fun _ -> a * s)", "val map (#a:Type) (#b:Type) (f:a -> Tot b) (s:set a) : Tot (set b)\nlet map #_ #b f s = F.on_dom b (exists_y_in_s s f)", "val return (a: Type) (x: a) : repr a (fun p s0 -> p (Success x) s0)\nlet return (a:Type) (x:a)\n: repr a (fun p s0 -> p (Success x) s0)\n= fun s0 -> Success x, s0", "val equal (#a:Type) (s1:set a) (s2:set a) : Type0\nlet equal #_ s1 s2 = forall x. s1 x <==> s2 x", "val FStar.PredicateExtensionality.predicate = a: Type -> Type\nlet predicate (a:Type) = a -> Tot prop", "val Zeta.SMap.smap = s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> Type0\nlet smap (#a:_) (s1 s2: seq a) = f:(seq_index s1 -> seq_index s2){\n forall (i: seq_index s1). index s1 i == index s2 (f i)\n}", "val FStar.FunctionalExtensionality.restricted_t = a: Type -> b: (_: a -> Type) -> Type\nlet restricted_t (a: Type) (b: (a -> Type)) = f: arrow a b {is_restricted a f}", "val FStar.HyperStack.ST.st_post' = a: Type -> pre: Type -> Type\nlet st_post' = gst_post'", "val FStar.Seq.Permutation.index_fun = s: FStar.Seq.Base.seq a -> Type0\nlet index_fun #a (s:seq a) = under (Seq.length s) -> under (Seq.length s)", "val Vale.PPC64LE.Semantics_s.st = a: Type -> Type\nlet st (a:Type) = state -> a & state", "val IST.st_post' = s: Type0 -> a: Type -> pre: Type -> Type\nlet st_post' (s:Type0) (a:Type) (pre:Type) = a -> (_:s{pre}) -> GTot Type0", "val ImmutableST.st_post = a: Type -> Type\nlet st_post (a:Type) = a -> heap -> Type0", "[@@ FStar.Tactics.Typeclasses.tcinstance]\nval st_graded (s: Type) : graded_monad (st s)\ninstance st_graded (s:Type) : graded_monad (st s) =\n{ \n return = (fun #a #im (x:a) s -> x, s);\n bind = (fun #a #b #ia #ib #im f g s -> let x, s = f s in g x s)\n}", "val FStar.FunctionalExtensionality.efun_g = a: Type -> b: (_: a -> Type) -> Type\nlet efun_g (a: Type) (b: (a -> Type)) = arrow_g a b", "val MRefST.st_wp = a: Type -> Type\nlet st_wp (a:Type) = st_post a -> Tot st_pre", "val bind_st (s a b: Type) (f: st s a) (g: (a -> st s b)) : st s b\nlet bind_st (s:Type) (a:Type) (b:Type) (f:st s a) (g:a -> st s b) : st s b\n = fun (s0:s) -> let (x,s) = f s0 in g x s", "val IMSTsub.st_post = s: Type0 -> a: Type -> Type\nlet st_post (s:Type0) (a:Type) = st_post_h' s a True", "val FStar.FunctionalExtensionality.arrow_g = a: Type -> b: (_: a -> Type) -> Type\nlet arrow_g (a: Type) (b: (a -> Type)) = x: a -> GTot (b x)", "val FStar.ReflexiveTransitiveClosure.predicate = a: Type -> Type\nlet predicate (a:Type u#a) = a -> Type0", "val IMSTsub.st_wp' = a: Type -> s: Type0 -> Type\nlet st_wp' (a:Type) (s:Type0) \n = st_post s a -> Tot (st_pre s)", "val bind_st: a:Type -> b:Type -> f:st a -> g:(a -> Tot (st b)) -> Tot (st b)\nlet bind_st a b f g = fun s0 ->\n let tmp = f s0 in\n let x, s1 = tmp in\n g x s1", "val Vale.X64.Machine_Semantics_s.st = a: Type -> Type\nlet st (a:Type) = machine_state -> a & machine_state", "val IMST.st_bind = \n a: Type ->\n b: Type ->\n wp1: IMST.st_wp a ->\n wp2: (_: a -> IMST.st_wp b) ->\n s: Type0 ->\n rel: FStar.Preorder.preorder s ->\n post: IMST.st_post s b ->\n s0: s\n -> Type0\nlet st_bind (a:Type) (b:Type)\n (wp1:st_wp a) (wp2: (a -> Tot (st_wp b))) \n (s:Type0) (rel:preorder s) (post:st_post s b) (s0:s) \n = wp1 s rel (fun x s1 -> wp2 x s rel post s1) s0", "val FStar.HyperStack.ST.st_post = a: Type -> Type\nlet st_post = gst_post", "val FStar.Sequence.Permutation.index_fun = s: FStar.Sequence.Base.seq a -> Type0\nlet index_fun #a (s:seq a) = nat_at_most (S.length s) -> nat_at_most (S.length s)", "[@@ FStar.Tactics.Typeclasses.tcinstance]\nval is (a: Type) (i1 i2: c a) : c (s a)\ninstance is (a:Type) (i1 : c a) (i2 : c a) : c (s a) = { x = Y }", "val FStar.HyperStack.ST.st_wp = a: Type -> Type\nlet st_wp = gst_wp", "val t : a:Type u#a -> Type u#a\nlet t a = list a", "val GMST.gmst_wp = s: Type -> a: Type -> Type\nlet gmst_wp (s:Type) (a:Type) = s0:s -> gmst_post s a s0 -> GTot Type0", "val FStar.Monotonic.HyperStack.s_mref = i: FStar.Monotonic.HyperHeap.rid -> a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet s_mref (i:rid) (a:Type) (rel:preorder a) = s:mreference a rel{frameOf s = i}", "val DijkstraStateMonad.irepr = a: Type -> s: Type0 -> wp: DijkstraStateMonad.wp_t s a -> Type\nlet irepr a s (wp: wp_t s a) =\n unit -> m:m s a { wp_of m `F.feq` wp }", "val OPLSS2021.BasicState.st = a: Type -> s: Type0 -> Type\nlet st (a:Type) (s:Type0) = s -> a & s", "val seq_map_injective (#a #b:Type) (f:a -> b) (s s':seq a) : Lemma\n (requires (forall (x x':a).{:pattern (f x); (f x')} f x == f x' ==> x == x') /\\ seq_map f s == seq_map f s')\n (ensures s == s')\nlet seq_map_injective #a #b f s s' =\n assert (forall (i:nat).{:pattern index s i} i < length s ==> index (seq_map f s) i == f (index s i));\n assert (forall (i:nat).{:pattern index s i} i < length s ==> index (seq_map f s') i == f (index s' i));\n assert (equal s s')", "val FStar.DM4F.IntST.post = a: Type -> Type\nlet post = STINT?.post", "[@@ FStar.Tactics.Typeclasses.tcinstance]\nval monad_functor (#m: _) (d: monad m) : functor m\ninstance monad_functor #m (d : monad m) : functor m =\n { fmap = (fun #_ #_ f x -> bind #m x (fun xx -> return #m (f xx))); }", "val FStar.ST.st_post' = a: Type -> pre: Type -> Type\nlet st_post' = gst_post'", "val FStar.ReflexiveTransitiveClosure.binrel = a: Type -> Type\nlet binrel (a:Type) = a -> a -> Type", "val OPLSS2021.DijkstraMonads.wp0 = st: Type0 -> a: Type -> Type\nlet wp0 (st:Type0) (a:Type) = st -> (a & st -> Type) -> Type", "val FStar.Monotonic.Heap.tset = a: Type -> Type\nlet tset = TSet.set", "val PropositionalExtensionalityInconsistent.predicate_ss = a: Type0 -> Type\nlet predicate_ss (a:Type0) = a -> Tot sub_singleton", "val MiTLS.StAE.reads = s: FStar.Set.set FStar.Monotonic.HyperHeap.rid -> a: Type -> Type\nlet reads (s:Set.set rid) (a:Type) =\n f: (h:mem -> GTot a){forall h1 h2. (HS.equal_on s (HS.get_hmap h1)\n (HS.get_hmap h2) /\\ Set.subset s (Map.domain (HS.get_hmap h1)))\n\t\t\t\t ==> f h1 == f h2}", "val subset (#a: Type) (s1 s2: set a) : Type0\nlet subset (#a:Type) (s1:set a) (s2:set a) : Type0 = forall x. mem x s1 ==> mem x s2", "val ImmutableSTwHeaps.st_wp = a: Type -> Type\nlet st_wp (a:Type) = st_post a -> Tot st_pre", "val FStar.DM4F.ExnSt.stint = a: Type -> Type\nlet stint (a:Type)= FStar.DM4F.ST.st int a", "val FStar.Tactics.CanonCommSemiring.vmap = a: Type -> Type\nlet vmap a = list (var * a) * a", "val IMSTsub.st_pre = s: Type0 -> Type\nlet st_pre (s:Type0) = s -> GTot Type0", "val f (#a #b #m: _) {| _: monad m |} (x: m (a -> b)) (y: m a) : m b\nlet f #a #b #m {| monad m |} (x : m (a -> b)) (y : m a) : m b =\n bind #m x (fun x ->\n bind #m y (fun y ->\n return #m (x y)))", "val GMST.gmst_post = s: Type -> a: Type -> s0: s -> Type\nlet gmst_post (s:Type) (a:Type) (s0:s) = rel:relation s -> a -> s1:s{rel s0 s1} -> GTot Type0", "val IMSTsub.st_bind = \n a: Type ->\n b: Type ->\n wp1: IMSTsub.st_wp a ->\n wp2: (_: a -> IMSTsub.st_wp b) ->\n s: Type0 ->\n rel: FStar.Preorder.preorder s ->\n post: IMSTsub.st_post s b ->\n s0: s\n -> Type0\nlet st_bind (a:Type) (b:Type)\n (wp1:st_wp a) (wp2: (a -> Tot (st_wp b))) \n (s:Type0) (rel:preorder s) (post:st_post s b) (s0:s) \n = wp1 s rel (fun x s1 -> wp2 x s rel post s1) s0", "val IMST.st_pre = s: Type0 -> Type\nlet st_pre (s:Type0) = s -> GTot Type0", "val return (a: Type) (x: a) : repr a (fun p m -> p x m)\nlet return (a:Type) (x:a)\n: repr a (fun p m -> p x m)\n= fun m -> (x, m)", "val return (a: Type) (x: a) (q: post a) : repr a (fun s0 -> q s0 x s0) q\nlet return (a:Type) (x:a) (q:post a) : repr a (fun s0 -> q s0 x s0) q =\n fun _ -> Ret x", "val MRefST.st_post = a: Type -> Type\nlet st_post (a:Type) = a -> heap -> Type0", "val InterpreterTarget.lam = a: Type -> Type\nlet lam a = A.ident & a", "val Zeta.SMap.into_smap = s1: FStar.Seq.Base.seq a -> s2: FStar.Seq.Base.seq a -> Type0\nlet into_smap (#a:Type) (s1 s2: seq a) = f:smap s1 s1 {into_prop f}", "val return (a: Type) (x: a) : hifc a bot bot [] (fun _ -> True) (fun s0 r s1 -> s0 == s1 /\\ r == x)\nlet return (a:Type) (x:a) : hifc a bot bot [] (fun _ -> True) (fun s0 r s1 -> s0 == s1 /\\ r == x) =\n let f : hst a (fun _ -> True) (fun s0 r s1 -> s0 == s1 /\\ r == x) = fun s -> x,s in\n f", "val mst (#s:Type u#s)\r\n (rel:FStar.Preorder.preorder s)\r\n (a:Type u#a)\r\n (pre:s -> prop)\r\n (post:s -> a -> s -> prop)\r\n: Type u#(max a s)\nlet mst (#s:Type u#s)\r\n (rel:FStar.Preorder.preorder s)\r\n (a:Type u#a)\r\n (pre:s -> prop)\r\n (post:s -> a -> s -> prop)\r\n = s0:s { pre s0 }\r\n -> Tot (\r\n res:(a & s) {\r\n post s0 res._1 res._2 /\\\r\n rel s0 res._2\r\n }\r\n )", "val map (#a #b:Type) (f:a -> b) (s:seq a): Tot (s':seq b{length s' = length s})\nlet map (#a #b:Type) (f:a -> b) (s:seq a): Tot (s':seq b{length s' = length s}) = map_aux f s", "val SnapshotST.mst_wp = a: Type -> Type\nlet mst_wp (a:Type) = mst_post a -> Tot mst_pre", "val IST.st_pre = s: Type0 -> Type\nlet st_pre (s:Type0) = s -> GTot Type0" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.DM4F.MonadLaws.fst", "name": "FStar.DM4F.MonadLaws.st" }, { "project_name": "FStar", "file_name": "FStar.DM4F.ST.fst", "name": "FStar.DM4F.ST.st" }, { "project_name": "steel", "file_name": "PulseCore.MonotonicStateMonad.fsti", "name": "PulseCore.MonotonicStateMonad.ens_t" }, { "project_name": "FStar", "file_name": "DijkstraStateMonad.fst", "name": "DijkstraStateMonad.post_t" }, { "project_name": "FStar", "file_name": "GradedMonad.fst", "name": "GradedMonad.st" }, { "project_name": "FStar", "file_name": "DijkstraStateMonad.fst", "name": "DijkstraStateMonad.wp_t" }, { "project_name": "FStar", "file_name": "OPLSS2021.BasicState.fst", "name": "OPLSS2021.BasicState.return" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.st" }, { "project_name": "steel", "file_name": "PulseCore.MonotonicStateMonad.fsti", "name": "PulseCore.MonotonicStateMonad.req_t" }, { "project_name": "FStar", "file_name": "DijkstraStateMonad.fst", "name": "DijkstraStateMonad.pre_t" }, { "project_name": "FStar", "file_name": "OPLSS2021.NDS.fst", "name": "OPLSS2021.NDS.return" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.return" }, { "project_name": "FStar", "file_name": "FStar.Fin.fsti", "name": "FStar.Fin.in_" }, { "project_name": "FStar", "file_name": "FStar.DM4F.MonadLaws.fst", "name": "FStar.DM4F.MonadLaws.ifc" }, { "project_name": "FStar", "file_name": "Big.fst", "name": "Big.f" }, { "project_name": "FStar", "file_name": "FStar.DM4F.MonadLaws.fst", "name": "FStar.DM4F.MonadLaws.right_unit_st" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoid.fst", "name": "FStar.Tactics.CanonCommMonoid.vmap" }, { "project_name": "FStar", "file_name": "IMST.fst", "name": "IMST.st_wp'" }, { "project_name": "steel", "file_name": "Steel.Coinduction.fsti", "name": "Steel.Coinduction.mono_fun" }, { "project_name": "FStar", "file_name": "IST.fst", "name": "IST.st_wp'" }, { "project_name": "FStar", "file_name": "FStar.DM4F.StExnC.fst", "name": "FStar.DM4F.StExnC.bind" }, { "project_name": "FStar", "file_name": "IMSTsub.fst", "name": "IMSTsub.st_post'" }, { "project_name": "FStar", "file_name": "Z3EncodingIssue.fst", "name": "Z3EncodingIssue.return" }, { "project_name": "FStar", "file_name": "IMST.fst", "name": "IMST.st_post'" }, { "project_name": "FStar", "file_name": "FStar.DM4F.ST.fst", "name": "FStar.DM4F.ST.return_st" }, { "project_name": "FStar", "file_name": "Monad.fst", "name": "Monad.g'" }, { "project_name": "FStar", "file_name": "Monad.fst", "name": "Monad.g" }, { "project_name": "zeta", "file_name": "Zeta.SMap.fsti", "name": "Zeta.SMap.mono_smap" }, { "project_name": "FStar", "file_name": "FStar.DM4F.MonadLaws.fst", "name": "FStar.DM4F.MonadLaws.left_unit_st" }, { "project_name": "FStar", "file_name": "FStar.FunctionalExtensionality.fsti", "name": "FStar.FunctionalExtensionality.arrow" }, { "project_name": "FStar", "file_name": "LowStar.ImmutableBuffer.fst", "name": "LowStar.ImmutableBuffer.immutable_preorder" }, { "project_name": "FStar", "file_name": "IST.fst", "name": "IST.st_post" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.st" }, { "project_name": "FStar", "file_name": "FStar.DM4F.StExn.fst", "name": "FStar.DM4F.StExn.stexn" }, { "project_name": "FStar", "file_name": "ImmutableST.fst", "name": "ImmutableST.st_wp" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.amap" }, { "project_name": "FStar", "file_name": "IMST.fst", "name": "IMST.st_post" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.injective_map" }, { "project_name": "FStar", "file_name": "FStar.DM4F.StExnC.fst", "name": "FStar.DM4F.StExnC.stexnc" }, { "project_name": "FStar", "file_name": "FStar.FunctionalExtensionality.fsti", "name": "FStar.FunctionalExtensionality.efun" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.st" }, { "project_name": "FStar", "file_name": "FStar.TSet.fst", "name": "FStar.TSet.map" }, { "project_name": "FStar", "file_name": "MSeqExn.fst", "name": "MSeqExn.return" }, { "project_name": "FStar", "file_name": "FStar.TSet.fst", "name": "FStar.TSet.equal" }, { "project_name": "FStar", "file_name": "FStar.PredicateExtensionality.fst", "name": "FStar.PredicateExtensionality.predicate" }, { "project_name": "zeta", "file_name": "Zeta.SMap.fsti", "name": "Zeta.SMap.smap" }, { "project_name": "FStar", "file_name": "FStar.FunctionalExtensionality.fsti", "name": "FStar.FunctionalExtensionality.restricted_t" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fsti", "name": "FStar.HyperStack.ST.st_post'" }, { "project_name": "FStar", "file_name": "FStar.Seq.Permutation.fsti", "name": "FStar.Seq.Permutation.index_fun" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Semantics_s.fst", "name": "Vale.PPC64LE.Semantics_s.st" }, { "project_name": "FStar", "file_name": "IST.fst", "name": "IST.st_post'" }, { "project_name": "FStar", "file_name": "ImmutableST.fst", "name": "ImmutableST.st_post" }, { "project_name": "FStar", "file_name": "GradedMonad.fst", "name": "GradedMonad.st_graded" }, { "project_name": "FStar", "file_name": "FStar.FunctionalExtensionality.fsti", "name": "FStar.FunctionalExtensionality.efun_g" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.st_wp" }, { "project_name": "FStar", "file_name": "FStar.DM4F.ST.fst", "name": "FStar.DM4F.ST.bind_st" }, { "project_name": "FStar", "file_name": "IMSTsub.fst", "name": "IMSTsub.st_post" }, { "project_name": "FStar", "file_name": "FStar.FunctionalExtensionality.fsti", "name": "FStar.FunctionalExtensionality.arrow_g" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fsti", "name": "FStar.ReflexiveTransitiveClosure.predicate" }, { "project_name": "FStar", "file_name": "IMSTsub.fst", "name": "IMSTsub.st_wp'" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.bind_st" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Machine_Semantics_s.fst", "name": "Vale.X64.Machine_Semantics_s.st" }, { "project_name": "FStar", "file_name": "IMST.fst", "name": "IMST.st_bind" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fsti", "name": "FStar.HyperStack.ST.st_post" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Permutation.fsti", "name": "FStar.Sequence.Permutation.index_fun" }, { "project_name": "FStar", "file_name": "Big.fst", "name": "Big.is" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fsti", "name": "FStar.HyperStack.ST.st_wp" }, { "project_name": "noise-star", "file_name": "Spec.Noise.Map.fst", "name": "Spec.Noise.Map.t" }, { "project_name": "FStar", "file_name": "GMST.fst", "name": "GMST.gmst_wp" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.s_mref" }, { "project_name": "FStar", "file_name": "DijkstraStateMonad.fst", "name": "DijkstraStateMonad.irepr" }, { "project_name": "FStar", "file_name": "OPLSS2021.BasicState.fst", "name": "OPLSS2021.BasicState.st" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.seq_map_injective" }, { "project_name": "FStar", "file_name": "FStar.DM4F.IntST.fst", "name": "FStar.DM4F.IntST.post" }, { "project_name": "FStar", "file_name": "Monad.fst", "name": "Monad.monad_functor" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.st_post'" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fsti", "name": "FStar.ReflexiveTransitiveClosure.binrel" }, { "project_name": "FStar", "file_name": "OPLSS2021.DijkstraMonads.fst", "name": "OPLSS2021.DijkstraMonads.wp0" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.tset" }, { "project_name": "FStar", "file_name": "PropositionalExtensionalityInconsistent.fst", "name": "PropositionalExtensionalityInconsistent.predicate_ss" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.StAE.fst", "name": "MiTLS.StAE.reads" }, { "project_name": "FStar", "file_name": "FStar.TSet.fsti", "name": "FStar.TSet.subset" }, { "project_name": "FStar", "file_name": "ImmutableSTwHeaps.fst", "name": "ImmutableSTwHeaps.st_wp" }, { "project_name": "FStar", "file_name": "FStar.DM4F.ExnSt.fst", "name": "FStar.DM4F.ExnSt.stint" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.vmap" }, { "project_name": "FStar", "file_name": "IMSTsub.fst", "name": "IMSTsub.st_pre" }, { "project_name": "FStar", "file_name": "Monad.fst", "name": "Monad.f" }, { "project_name": "FStar", "file_name": "GMST.fst", "name": "GMST.gmst_post" }, { "project_name": "FStar", "file_name": "IMSTsub.fst", "name": "IMSTsub.st_bind" }, { "project_name": "FStar", "file_name": "IMST.fst", "name": "IMST.st_pre" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.return" }, { "project_name": "FStar", "file_name": "HoareSTFree.fst", "name": "HoareSTFree.return" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.st_post" }, { "project_name": "everparse", "file_name": "InterpreterTarget.fsti", "name": "InterpreterTarget.lam" }, { "project_name": "zeta", "file_name": "Zeta.SMap.fsti", "name": "Zeta.SMap.into_smap" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.return" }, { "project_name": "steel", "file_name": "PulseCore.MonotonicStateMonad.fst", "name": "PulseCore.MonotonicStateMonad.mst" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.map" }, { "project_name": "FStar", "file_name": "SnapshotST.fst", "name": "SnapshotST.mst_wp" }, { "project_name": "FStar", "file_name": "IST.fst", "name": "IST.st_pre" } ], "selected_premises": [ "FStar.FunctionalExtensionality.feq", "FStar.Tactics.Effect.raise", "FStar.FunctionalExtensionality.on_dom", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "FStar.Tactics.Types.issues", "FStar.Pervasives.reveal_opaque", "FStar.Tactics.Effect.get", "FStar.FunctionalExtensionality.on", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity", "FStar.FunctionalExtensionality.restricted_t", "FStar.Issue.mk_issue", "FStar.FunctionalExtensionality.arrow", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater_Greater", "FStar.Tactics.Effect.tactic", "FStar.Pervasives.st_post_h", "FStar.FunctionalExtensionality.is_restricted", "FStar.Pervasives.id", "FStar.FunctionalExtensionality.feq_g", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity_forall", "FStar.Issue.issue_level_string", "FStar.Tactics.Typeclasses.solve", "FStar.FunctionalExtensionality.restricted_g_t", "FStar.FunctionalExtensionality.on_dom_g", "FStar.Monotonic.Pure.intro_pure_wp_monotonicity", "FStar.FunctionalExtensionality.efun", "FStar.Tactics.Effect.tac", "FStar.Pervasives.st_pre_h", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.ex_pre", "FStar.Pervasives.all_post_h", "FStar.FunctionalExtensionality.on_g", "FStar.Monotonic.Pure.is_monotonic", "FStar.FunctionalExtensionality.efun_g", "FStar.Pervasives.all_post_h'", "FStar.FunctionalExtensionality.arrow_g", "FStar.Pervasives.st_stronger", "FStar.FunctionalExtensionality.is_restricted_g", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.ex_post'", "Prims.pure_post'", "FStar.Tactics.Effect.tac_close", "FStar.Pervasives.st_wp_h", "FStar.Pervasives.ex_post", "FStar.Pervasives.st_trivial", "Prims.min", "FStar.Pervasives.coerce_eq", "FStar.Pervasives.st_return", "FStar.Pervasives.st_ite_wp", "FStar.Pervasives.pure_ite_wp", "Prims.auto_squash", "FStar.Monotonic.Pure.as_pure_wp", "FStar.Tactics.Effect.tac_wp_monotonic", "FStar.Pervasives.pure_close_wp", "FStar.Pervasives.trivial_pure_post", "FStar.Tactics.Effect.lift_div_tac_wp", "FStar.Tactics.Effect.lift_div_tac", "Prims.subtype_of", "FStar.Monotonic.Pure.elim_pure", "Prims.pure_post", "FStar.Tactics.Effect.tac_bind_wp", "FStar.Pervasives.st_bind_wp", "FStar.Pervasives.all_wp_h", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.all_return", "FStar.Tactics.Effect.tac_if_then_else_wp", "Prims.abs", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.pure_null_wp", "FStar.Pervasives.pure_bind_wp", "FStar.Pervasives.ex_stronger", "Prims.as_requires", "FStar.Pervasives.div_hoare_to_wp", "Prims.pure_trivial", "Prims.returnM", "FStar.Pervasives.all_stronger", "FStar.Pervasives.all_close_wp", "Prims.pure_wp'", "FStar.Tactics.Effect.tac_repr", "Prims.__cache_version_number__", "Prims.purewp_id", "Prims.pure_stronger", "FStar.Tactics.Effect.tac_wp_compact", "FStar.Pervasives.ex_wp", "FStar.Pervasives.all_trivial", "Prims.pure_pre", "FStar.Pervasives.all_ite_wp", "Prims.pow2", "Prims.pure_wp_monotonic0", "Prims.as_ensures", "Prims.l_True", "Prims.pure_wp_monotonic", "FStar.Pervasives.ex_bind_wp", "FStar.Tactics.Effect.tac_subcomp", "Prims.pure_wp", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.ex_trivial" ], "source_upto_this": "module MonadFunctorInference\n\n//SNIPPET_START: monad$\nclass monad (m:Type -> Type) =\n{\n return : (#a:Type -> a -> m a);\n bind : (#a:Type -> #b:Type -> (f:m a) -> (g:(a -> m b)) -> m b);\n}\n//SNIPPET_END: monad$\n\n//SNIPPET_START: st$", "sketch": [ "Step 1: The definition is about defining a state transformer type `st` which takes a state type `s` and a result type `a`.\nStep 2: The state transformer type `st` is implemented as a function that takes an initial state of type `s` and returns a tuple containing a result of type `a` and a new state of type `s`.", "Step 1: The definition is about defining a type `st` which takes two type parameters, `s` and `a`.\nStep 2: The type `st` is implemented as a function type that takes a state of type `s` and returns a tuple containing a value of type `a` and a new state of type `s`.", "Step 1: The definition is about defining a state monad type `st` which takes two type parameters: `s` for the state and `a` for the value.\nStep 2: The state monad type `st` is implemented as a function type that takes an initial state of type `s` and returns a tuple containing a value of type `a` and a new state of type `s`.", "Step 1: The definition is about defining a state monad type `st` that takes two type parameters: `s` for the state and `a` for the value.\nStep 2: The type `st` is implemented as a function type that takes an initial state of type `s` and returns a tuple containing a value of type `a` and a new state of type `s`.", "Step 1: The definition is about defining a type `st` that represents a state transformer. This type takes two type parameters: `s` for the state and `a` for the value.\nStep 2: The implementation of the type `st` is a function that takes an initial state of type `s` and returns a tuple containing a value of type `a` and a new state of type `s`.", "Step 1: The definition is about defining a state monad type `st` which takes two type parameters: `s` for the state and `a` for the value.\nStep 2: The state monad `st` is implemented as a function type that takes an initial state of type `s` and returns a tuple containing a value of type `a` and a new state of type `s`.", "Step 1: The definition is about creating a type alias `st` that represents a stateful computation. This computation takes an initial state of type `s` and returns a result of type `a` along with a new state of type `s`.\nStep 2: The type alias `st` is implemented as a function type that takes an initial state of type `s` and returns a tuple containing a result of type `a` and a new state of type `s`.", "Step 1: The definition is about defining a state monad type `st` which takes two type parameters: `s` for the state and `a` for the value.\nStep 2: The state monad type `st` is implemented as a function type that takes an initial state of type `s` and returns a tuple containing a value of type `a` and a new state of type `s`.", "Step 1: The definition is about defining a state monad type `st` that takes two type parameters: `s` for the state and `a` for the value.\nStep 2: The state monad type `st` is implemented as a function type that takes an initial state of type `s` and returns a tuple containing a value of type `a` and a new state of type `s`.", "Step 1: Define a type alias `st` that takes two type parameters: `s` and `a`.\nStep 2: The `st` type represents a stateful computation that takes an initial state of type `s` and returns a value of type `a` along with a new state of type `s`." ], "generated_solution": [ "type st (s: Type) (a: Type) = s -> (a * s)", "type st (s: Type) (a: Type) = s -> (a * s)", "type st (s: Type) (a: Type) = s -> (a * s)", "type st (s: Type) (a: Type) = s -> (a * s)", "type st (s: Type) (a: Type) = s -> (a * s)", "type st (s: Type) (a: Type) = s -> (a * s)", "type st (s: Type) (a: Type) = s -> (a * s)", "type st (s: Type) (a: Type) = s -> (a * s)", "type st (s: Type) (a: Type) = s -> (a * s)", "type st (s: Type) (a: Type) = s -> (a * s)" ] }, { "file_name": "Duplex.PCM.fst", "name": "Duplex.PCM.fst", "opens_and_abbrevs": [ { "abbrev": "Perm", "full_module": "Steel.FractionalPermission" }, { "abbrev": "HR", "full_module": "Steel.HigherReference" }, { "abbrev": "PR", "full_module": "Steel.PCMReference" }, { "abbrev": "Mem", "full_module": "Steel.Memory" }, { "open": "Steel.PCMReference" }, { "open": "Steel.Effect" }, { "open": "Steel.Effect.Atomic" }, { "open": "Steel.Memory" }, { "open": "FStar.Ghost" }, { "abbrev": "R", "full_module": "FStar.ReflexiveTransitiveClosure" }, { "abbrev": "P", "full_module": "FStar.Preorder" }, { "open": "Steel.Channel.Protocol" }, { "open": "FStar.PCM" }, { "abbrev": "R", "full_module": "FStar.ReflexiveTransitiveClosure" }, { "abbrev": "P", "full_module": "FStar.Preorder" }, { "open": "Steel.Channel.Protocol" }, { "open": "Steel.Effect" }, { "open": "Steel.Effect.Atomic" }, { "open": "Steel.Memory" }, { "open": "FStar.PCM" }, { "open": "Duplex" }, { "open": "Duplex" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 1, "max_fuel": 1, "initial_ifuel": 1, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let fst = fst", "source_range": { "start_line": 1101, "start_col": 0, "end_line": 1101, "end_col": 13 }, "interleaved": false, "definition": "FStar.Pervasives.Native.fst", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.tuple2" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "x: (_ * _) -> _", "prompt": "let fst =\n ", "expected_response": "fst", "source": { "project_name": "steel", "file_name": "share/steel/examples/steel/Duplex.PCM.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Duplex.PCM.fst", "checked_file": "dataset/Duplex.PCM.fst.checked", "interface_file": true, "dependencies": [ "dataset/Steel.PCMReference.fsti.checked", "dataset/Steel.Memory.fsti.checked", "dataset/Steel.HigherReference.fsti.checked", "dataset/Steel.FractionalPermission.fst.checked", "dataset/Steel.Effect.Atomic.fsti.checked", "dataset/Steel.Effect.fsti.checked", "dataset/Steel.Channel.Protocol.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.ReflexiveTransitiveClosure.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.PCM.fst.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "let is_send (p:dprot) = Msg? p && (Send? (Msg?._0 p))", "let is_recv (p:dprot) = Msg? p && (Recv? (Msg?._0 p))", "let dprot' = protocol unit", "let is_fin (p:dprot) = Return? p", "let empty_trace (p:dprot) : trace p p = Waiting p", "let rec no_loop (p:protocol 'a) =\n match p with\n | Return _ -> True\n | Msg _ a k -> (forall x. no_loop (k x))\n | DoWhile _ _ -> False", "let partial_trace_of (p:dprot) = tr:partial_trace_of p{no_loop tr.to}", "let next (tag:party) (#p:dprot) : P.relation (partial_trace_of p) =\n fun (t0 t1: partial_trace_of p) ->\n more_msgs t0.to /\\\n // Ensuring that if we are ahead, we only have writes\n (if A? tag then is_send t0.to else is_recv t0.to) /\\\n (exists (msg:next_msg_t t0.to).\n t1.to == step t0.to msg /\\\n t1.tr == extend t0.tr msg)", "let dprot = p:dprot'{no_loop p}", "let nl_protocol 'a = p:protocol 'a { no_loop p }", "let return (#a:_) (x:a) : nl_protocol a = Return x", "let done : dprot = return ()", "let send a : nl_protocol a = Msg Send a return", "let recv a : nl_protocol a = Msg Recv a return", "let extended_to (tag:party) (#p:dprot) : P.preorder (partial_trace_of p) =\n R.closure (next tag #p)", "let rec bind #a #b (p:nl_protocol a) (q:(a -> nl_protocol b))\n : nl_protocol b\n = match p with\n | Return v -> q v\n | Msg tag c #a' k ->\n let k : c -> nl_protocol b =\n fun x -> bind (k x) q\n in\n Msg tag c k", "t", "V", "V", "V", "A_W", "A_W", "A_W", "q", "q", "A_R", "A_R", "A_R", "q", "q", "B_R", "B_R", "B_R", "q", "q", "B_W", "B_W", "B_W", "q", "q", "A_Fin", "A_Fin", "A_Fin", "q", "q", "B_Fin", "B_Fin", "B_Fin", "q", "q", "party", "A", "B", "A", "A", "B", "B", "Nil", "Nil", "Nil", "send_next_dprot_t", "let ahead (tag:party) (#p:dprot) (q q':dprot) (s:trace p q) (s':trace p q') : prop\n = ({ to = q'; tr = s'} `extended_to tag` { to = q; tr = s }) /\\ True", "recv_next_dprot_t", "let ahead_refl (tag:party) (#p:dprot) (q:dprot) (s:trace p q)\n : Lemma (ahead tag q q s s)\n = ()", "val ch : Type u#1", "let rec trace_length #p #q (s:trace p q) : Tot nat (decreases s) = match s with\n | Waiting _ -> 0\n | Message _ _ _ t -> 1 + trace_length t", "val ep (name:party) (c:ch) (next:dprot) : vprop", "val new_channel (p:dprot)\n : SteelT (ch & ch) emp\n (fun cc -> ep A (fst cc) p `star` ep B (snd cc) p)", "let composable #p : symrel (t p) = fun t0 t1 ->\n match t0, t1 with\n | _, Nil\n | Nil, _ -> True\n\n (* both sides are finished and they agree on the trace *)\n | A_Fin q s, B_Fin q' s'\n | B_Fin q s, A_Fin q' s' -> q == q' /\\ s == s'\n\n (* A is finished, B still has to read *)\n | A_Fin q s, B_R q' s'\n | B_R q' s', A_Fin q s -> ahead A q q' s s'\n\n (* B is finished, A still has to read *)\n | A_R q' s', B_Fin q s\n | B_Fin q s, A_R q' s' -> ahead B q q' s s'\n\n (* A is writing, B is reading: A is ahead *)\n | A_W q s, B_R q' s'\n | B_R q' s', A_W q s -> ahead A q q' s s'\n\n (* B is writing, A is reading: B is ahead *)\n | B_W q s, A_R q' s'\n | A_R q' s', B_W q s -> ahead B q q' s s'\n\n (* Both are in a reading state, either one could be ahead *)\n | A_R q s, B_R q' s'\n | B_R q' s', A_R q s -> ahead A q q' s s' \\/ ahead B q' q s' s\n\n | _, _ -> False", "val channel_send (#name:party)\n (#next:send_next_dprot_t name)\n (c:ch) (x:msg_t next)\n : SteelT unit\n (ep name c next)\n (fun _ -> ep name c (step next x))", "val channel_recv (#name:party)\n (#next:recv_next_dprot_t name)\n (c:ch)\n : SteelT (msg_t next)\n (ep name c next)\n (fun x -> ep name c (step next x))", "let compose (#p:dprot) (s0:t p) (s1:t p{composable s0 s1}) =\n match s0, s1 with\n | a, Nil | Nil, a -> a\n\n | A_Fin q s, _\n | _, A_Fin q s\n | B_Fin q s, _\n | _, B_Fin q s -> V ({to = q; tr=s })\n\n | A_W q s, B_R q' s'\n | B_R q' s', A_W q s\n | B_W q s, A_R q' s'\n | A_R q' s', B_W q s -> V ({to = q; tr = s})\n\n | A_R q s, B_R q' s'\n | B_R q' s', A_R q s ->\n if trace_length s >= trace_length s'\n then V ({to = q; tr = s})\n else V ({to = q'; tr = s' })", "let p' (p:dprot) : pcm' (t p) = { composable = composable; op = compose; one = Nil }", "let lemma_comm #p (x:t p) (y:t p{composable x y}) :\n Lemma (compose x y == compose y x)\n = ()", "let lemma_assoc_l #p (x y:t p) (z:t p{composable y z /\\ composable x (compose y z)})\n : Lemma (composable x y /\\ composable (compose x y) z /\\\n compose x (compose y z) == compose (compose x y) z)\n = ()", "let lemma_assoc_r #p (x y:t p) (z:t p{composable x y /\\ composable (compose x y) z})\n : Lemma (composable y z /\\ composable x (compose y z) /\\\n compose x (compose y z) == compose (compose x y) z)\n = ()", "let lemma_is_unit #p (x:t p) : Lemma (composable x Nil /\\ compose x Nil == x)\n = ()", "let refine (#prot:dprot) (x:t prot) : prop = V? x \\/ Nil? x", "let pcm (prot:dprot) : pcm (t prot) =\n { p = p' prot;\n comm = lemma_comm;\n assoc = lemma_assoc_l;\n assoc_r = lemma_assoc_r;\n is_unit = lemma_is_unit;\n refine = refine\n}", "let chan (p:dprot) = ref (t p) (pcm p)", "val pts_to (#p:dprot) (r:chan p) (v:t p) : vprop", "let pts_to r v = PR.pts_to r v", "let ep_a (#p:dprot) (next:dprot) (tr:trace p next) =\n if is_send next\n then A_W next tr\n else if is_recv next\n then A_R next tr\n else A_Fin next tr", "let endpoint_a (#p:dprot) (c:chan p) (next:dprot) (tr:trace p next) =\n pts_to c (ep_a next tr)", "let endpoint_b (#p:dprot) (c:chan p) (next:dprot) (tr:trace p next) =\n pts_to c (if is_send next\n then B_R next tr\n else if is_recv next\n then B_W next tr\n else B_Fin next tr)", "let frame_compatible (#p:dprot) (x:t p) (v y:t p) =\n (forall (frame:t p). {:pattern (composable x frame)}\n composable x frame /\\\n v == compose x frame ==>\n composable y frame /\\\n v == compose y frame)", "let select_refine' (#p:dprot)\n (r:chan p)\n (x:erased (t p))\n (f:(v:t p{compatible (pcm p) x v}\n -> GTot (y:t p{compatible (pcm p) y v /\\\n frame_compatible x v y})))\n : SteelT (v:t p{compatible (pcm p) x v /\\ refine v})\n (PR.pts_to r x)\n (fun v -> PR.pts_to r (f v))\n = select_refine r x f", "val select_refine (#p:dprot)\n (r:chan p)\n (x:erased (t p))\n (f:(v:t p{compatible (pcm p) x v}\n -> GTot (y:t p{compatible (pcm p) y v /\\\n frame_compatible x v y})))\n : SteelT (v:t p{compatible (pcm p) x v /\\ refine v})\n (pts_to r x)\n (fun v -> pts_to r (f v))", "let select_refine #p r x f =\n let v = select_refine' r x f in\n rewrite_slprop (PR.pts_to r (f v)) (pts_to r (f v)) (fun _ -> ());\n return v", "let rec is_trace_prefix\n (#from:dprot) (#to #to':dprot)\n (tr:trace from to)\n (tr':trace from to')\n : Tot prop\n (decreases tr)\n = match tr with\n | Waiting _ -> True\n | Message _ x _ tail ->\n match tr' with\n | Waiting _ -> False\n | Message _ x' _ tail' -> x == x' /\\ is_trace_prefix tail tail'", "let rec lemma_is_trace_prefix_refl\n (#from #to:dprot)\n (tr:trace from to)\n : Lemma (ensures is_trace_prefix tr tr)\n (decreases tr)\n = match tr with\n | Waiting _ -> ()\n | Message _ _ _ tail -> lemma_is_trace_prefix_refl tail", "let rec lemma_is_trace_prefix_extend (#from #to #to':dprot)\n (tr:trace from to)\n (tr':trace from to')\n (x:msg_t to')\n : Lemma (requires is_trace_prefix tr tr' /\\ more_msgs to')\n (ensures is_trace_prefix tr (extend tr' x))\n (decreases tr)\n = match tr with\n | Waiting _ -> ()\n | Message _ msg _ tail ->\n match tr' with\n | Message from' msg' to' tail' -> lemma_is_trace_prefix_extend tail tail' x", "let lemma_ahead_msg_msg_inversion\n (#from:dprot) (#to #to':dprot)\n (tr:trace from to)\n (tr':trace from to')\n : Lemma (requires Message? tr /\\ Message? tr' /\\ is_trace_prefix tr tr')\n (ensures Message?.x tr == Message?.x tr' /\\ is_trace_prefix (Message?._3 tr) (Message?._3 tr'))\n = let Message _ x _ tail = tr in\n let Message _ x' _ tail' = tr' in\n let l = ({to = to; tr = tr}) in\n let r = ({to = to'; tr = tr'}) in\n let open FStar.ReflexiveTransitiveClosure in\n ()", "let rec next_message_aux\n (#from:dprot) (#to #to':dprot)\n (tr:trace from to)\n (tr':trace from to'{trace_length tr' > trace_length tr /\\ is_trace_prefix tr tr'})\n : Tot (msg_t to)\n (decreases tr)\n = match tr with\n | Waiting _ ->\n assert (Message? tr');\n Message?.x tr'\n | Message _ x to tail ->\n let Message _ x' to' tail' = tr' in\n lemma_ahead_msg_msg_inversion tr tr';\n next_message_aux tail tail'", "let lemma_ahead_implies_trace_prefix\n (tag:party)\n (#from:dprot) (#to #to':dprot)\n (tr:trace from to)\n (tr':trace from to')\n : Lemma (requires ahead tag to' to tr' tr)\n (ensures is_trace_prefix tr tr')\n = let stable (z:partial_trace_of from) : Type0 = is_trace_prefix tr z.tr in\n let aux (y z:partial_trace_of from)\n : Lemma (requires stable y /\\ next tag y z)\n (ensures stable z)\n = Classical.forall_intro (Classical.move_requires (lemma_is_trace_prefix_extend tr y.tr))\n in Classical.forall_intro_2 (Classical.move_requires_2 aux);\n R.stable_on_closure (next tag) stable ();\n lemma_is_trace_prefix_refl tr", "let next_message\n (#from:dprot) (#to #to':dprot)\n (tr:trace from to)\n (tr':trace from to'{trace_length tr' > trace_length tr /\\\n (exists tag. ahead tag to' to tr' tr)})\n = Classical.forall_intro (fun tag -> Classical.move_requires (lemma_ahead_implies_trace_prefix tag tr) tr');\n next_message_aux tr tr'", "let rec extend_increase_length (#from #to:dprot) (t:trace from to{more_msgs to}) (m:next_msg_t to)\n : Lemma (ensures trace_length (extend t m) == trace_length t + 1)\n (decreases t)\n = match t with\n | Waiting _ -> ()\n | Message _ _ _ tail -> extend_increase_length tail m", "let next_increase_length (tag:party) (#p:dprot) (x y:partial_trace_of p)\n : Lemma (requires next tag x y)\n (ensures trace_length y.tr == trace_length x.tr + 1)\n = let aux (msg:next_msg_t x.to)\n : Lemma (requires y.to == step x.to msg /\\ y.tr == extend x.tr msg)\n (ensures trace_length y.tr == trace_length x.tr + 1)\n = extend_increase_length x.tr msg\n in Classical.forall_intro (Classical.move_requires aux)", "let lemma_ahead_is_longer (tag:party) (#p:dprot) (q:dprot) (s:trace p q) (q':dprot) (s':trace p q')\n : Lemma (requires ahead tag q q' s s')\n (ensures trace_length s >= trace_length s')\n = let open FStar.ReflexiveTransitiveClosure in\n let l = ({to = q'; tr = s'}) in\n let r = ({to = q; tr = s}) in\n let stable_p (x:partial_trace_of p) : Type0 = trace_length x.tr >= trace_length s' in\n let aux (x y:partial_trace_of p)\n : Lemma (requires stable_p x /\\ next tag x y)\n (ensures stable_p y)\n = next_increase_length tag x y\n in Classical.forall_intro_2 (fun x -> Classical.move_requires (aux x));\n stable_on_closure (next tag) stable_p ()", "let compatible_a_r_v_is_ahead\n (#p:dprot) (#q:dprot{is_recv q}) (tr:trace p q)\n (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (A_R q tr) (V tr'))\n (ensures ahead B tr'.to q tr'.tr tr)\n = let aux (frame:t p) : Lemma\n (requires composable (A_R q tr) frame /\\ compose frame (A_R q tr) == V tr')\n (ensures ahead B tr'.to q tr'.tr tr)\n = assert (B_R? frame \\/ B_W? frame \\/ B_Fin? frame);\n if B_W? frame then ()\n else if B_R? frame then (\n let q' = B_R?.q frame in\n let tr' = B_R?._1 frame in\n if trace_length tr' >= trace_length tr then\n Classical.move_requires (lemma_ahead_is_longer A q tr q') tr'\n else ahead_refl B q tr\n ) else ()\n in\n Classical.forall_intro (Classical.move_requires aux)", "let rec lemma_same_trace_length_ahead_refl' (#p:dprot) (#q #q':dprot)\n (s:trace p q)\n (s':trace p q')\n : Lemma (requires is_trace_prefix s s' /\\ trace_length s == trace_length s')\n (ensures q == q' /\\ s == s')\n (decreases s)\n = match s with\n | Waiting _ -> ()\n | Message _ _ _ _ ->\n lemma_same_trace_length_ahead_refl' (Message?._3 s) (Message?._3 s')", "let lemma_same_trace_length_ahead_refl (tag:party) (#p:dprot) (#q #q':dprot)\n (s:trace p q)\n (s':trace p q')\n : Lemma (requires ahead tag q q' s s' /\\ trace_length s == trace_length s')\n (ensures q == q' /\\ s == s')\n = lemma_ahead_implies_trace_prefix tag s' s;\n lemma_same_trace_length_ahead_refl' s' s", "let compatible_b_r_v_is_ahead\n (#p:dprot) (#q:dprot{is_send q}) (tr:trace p q)\n (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (B_R q tr) (V tr'))\n (ensures ahead A tr'.to q tr'.tr tr)\n = let aux (frame:t p) : Lemma\n (requires composable (B_R q tr) frame /\\ compose frame (B_R q tr) == V tr')\n (ensures ahead A tr'.to q tr'.tr tr)\n = assert (A_R? frame \\/ A_W? frame \\/ A_Fin? frame);\n if A_W? frame then ()\n else if A_R? frame then (\n let q_a = A_R?.q frame in\n let tr_a = A_R?._1 frame in\n if trace_length tr_a > trace_length tr then (\n Classical.move_requires (lemma_ahead_is_longer B q tr q_a) tr_a\n ) else if trace_length tr_a < trace_length tr then ahead_refl A q tr\n else (\n assert (tr'.to == q_a /\\ tr'.tr == tr_a);\n // We need both sides, since there is a disjunction in the PCM in the A_R/B_R case\n Classical.move_requires (lemma_same_trace_length_ahead_refl A tr_a) tr;\n Classical.move_requires (lemma_same_trace_length_ahead_refl B tr) tr_a;\n assert (q == q_a /\\ tr == tr_a);\n ahead_refl A q tr\n )\n ) else ()\n in\n Classical.forall_intro (Classical.move_requires aux)", "let extend_node_a_r (#p:dprot) (#q:dprot{more q /\\ is_recv q}) (tr:trace p q)\n (tr':partial_trace_of p{trace_length tr'.tr > trace_length tr /\\\n compatible (pcm p) (A_R q tr) (V tr')})\n : t p\n = compatible_a_r_v_is_ahead tr tr';\n let x = next_message tr tr'.tr in\n let q' = step q x in\n let tr' = extend tr x in\n if is_send q'\n then A_W q' tr'\n else if is_recv q'\n then A_R q' tr'\n else A_Fin q' tr'", "let extend_node_b_r (#p:dprot) (#q:dprot{more q /\\ is_send q}) (tr:trace p q)\n (tr':partial_trace_of p{trace_length tr'.tr > trace_length tr /\\\n compatible (pcm p) (B_R q tr) (V tr')})\n : t p\n = compatible_b_r_v_is_ahead tr tr';\n let x = next_message tr tr'.tr in\n let q' = step q x in\n let tr' = extend tr x in\n if is_send q'\n then B_R q' tr'\n else if is_recv q'\n then B_W q' tr'\n else B_Fin q' tr'", "let lemma_compatible_a_greater_length (#p:dprot) (q:dprot{is_recv q}) (tr:trace p q) (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (A_R q tr) (V tr'))\n (ensures trace_length tr'.tr >= trace_length tr)\n = compatible_a_r_v_is_ahead tr tr';\n lemma_ahead_is_longer B tr'.to tr'.tr q tr", "let lemma_compatible_b_greater_length (#p:dprot) (q:dprot{is_send q}) (tr:trace p q) (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (B_R q tr) (V tr'))\n (ensures trace_length tr'.tr >= trace_length tr)\n = compatible_b_r_v_is_ahead tr tr';\n lemma_ahead_is_longer A tr'.to tr'.tr q tr", "let rec lemma_unique_next_common_prefix\n (tag:party)\n (#p:dprot)\n (tr z tr':partial_trace_of p)\n : Lemma (requires is_trace_prefix tr.tr tr'.tr /\\ is_trace_prefix z.tr tr'.tr /\\\n next tag tr z /\\ trace_length tr'.tr > trace_length tr.tr)\n (ensures (\n let x = next_message_aux tr.tr tr'.tr in\n let tr2 = extend tr.tr x in\n z.to == step tr.to x /\\\n tr2 == z.tr)\n )\n (decreases tr.tr)\n = let Message _ x_z _ tail_z = z.tr in\n let Message _ x' _ tail' = tr'.tr in\n match tr.tr with\n | Waiting _ -> ()\n | Message _ _ to tail -> lemma_unique_next_common_prefix tag\n ({to = to; tr = tail}) ({to = z.to; tr = tail_z}) ({to = tr'.to; tr = tail'})", "let closure_inversion (tag:party) (#p:dprot) (tr tr':partial_trace_of p)\n : Lemma (requires tr `extended_to tag` tr')\n (ensures tr == tr' \\/ (exists z. next tag tr z /\\ z `extended_to tag` tr'))\n [SMTPat (tr `extended_to tag` tr')]\n = R.closure_inversion (next tag) tr tr'", "let next_message_closure (tag:party) (#p:dprot) (tr tr':partial_trace_of p)\n : Lemma (requires trace_length tr'.tr > trace_length tr.tr /\\ tr `extended_to tag` tr')\n (ensures (\n let x = next_message tr.tr tr'.tr in\n let q2 = step tr.to x in\n let tr2 = extend tr.tr x in\n ({to = q2; tr = tr2}) `extended_to tag` tr'))\n = let x = next_message tr.tr tr'.tr in\n let q2 = step tr.to x in\n let tr2 = extend tr.tr x in\n let z_new = {to = q2; tr = tr2} in\n let open FStar.ReflexiveTransitiveClosure in\n assert (exists z. next tag tr z /\\ z `extended_to tag` tr');\n let aux (z:partial_trace_of p)\n : Lemma (requires next tag tr z /\\ z `extended_to tag` tr')\n (ensures z == z_new)\n = lemma_ahead_implies_trace_prefix tag z.tr tr'.tr;\n lemma_ahead_implies_trace_prefix tag tr.tr tr'.tr;\n lemma_unique_next_common_prefix tag tr z tr'\n in Classical.forall_intro (Classical.move_requires aux)", "let lemma_same_length_ahead_implies_eq (#p:dprot) (tr tr':partial_trace_of p)\n : Lemma (requires trace_length tr.tr == trace_length tr'.tr /\\ is_trace_prefix tr.tr tr'.tr)\n (ensures tr == tr')\n = let rec aux (#p #q1 #q2:dprot) (tr1:trace p q1) (tr2:trace p q2)\n : Lemma (requires trace_length tr1 == trace_length tr2 /\\ is_trace_prefix tr1 tr2)\n (ensures q1 == q2 /\\ tr1 == tr2)\n (decreases tr1)\n = match tr1 with\n | Waiting _ -> ()\n | Message _ _ _ tail -> aux tail (Message?._3 tr2)\n in aux tr.tr tr'.tr", "let frame_compatible_a_extend (#p:dprot)\n (q:dprot{is_recv q /\\ more q}) (tr:trace p q)\n (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (A_R q tr) (V tr') /\\ trace_length tr'.tr > trace_length tr)\n (ensures frame_compatible (A_R q tr) (V tr') (extend_node_a_r tr tr'))\n = let x = A_R q tr in\n let p_tr:partial_trace_of p = {to = q; tr = tr} in\n let v = V tr' in\n let y = extend_node_a_r tr tr' in\n let aux (frame:t p)\n : Lemma (requires composable x frame /\\ v == compose x frame)\n (ensures composable y frame /\\ v == compose y frame)\n = assert (B_R? frame \\/ B_W? frame \\/ B_Fin? frame);\n if B_W? frame then (\n // The PCM gives us here that y has to be A_R, it cannot be A_W\n // because then there would be a B read in the trace ahead of x\n R.closure_inversion (next B) p_tr tr';\n next_message_closure B p_tr tr'\n ) else if B_R? frame then (\n let q_b = B_R?.q frame in\n let tr_b = B_R?._1 frame in\n assert (tr' == {to = q_b; tr = tr_b});\n Classical.move_requires (lemma_ahead_is_longer A q tr q_b) tr_b;\n // Gives us the following assertion by contraposition\n assert (p_tr `extended_to B` tr');\n next_message_closure B p_tr tr';\n\n if A_W? y then (\n ahead_refl B q_b tr_b\n ) else (\n let A_R q_a tr_a = y in\n lemma_ahead_is_longer B q_b tr_b q_a tr_a;\n lemma_ahead_implies_trace_prefix B tr_a tr_b;\n Classical.move_requires (lemma_same_length_ahead_implies_eq ({to = q_a; tr = tr_a})) tr'\n )\n ) else (\n next_message_closure B p_tr tr';\n let B_Fin _ tr_b = frame in\n assert (tr_b == tr'.tr);\n assert (composable y frame);\n assert (v == compose y frame)\n )\n in Classical.forall_intro (Classical.move_requires aux)", "let frame_compatible_b_extend (#p:dprot)\n (q:dprot{is_send q /\\ more q}) (tr:trace p q)\n (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (B_R q tr) (V tr') /\\ trace_length tr'.tr > trace_length tr)\n (ensures frame_compatible (B_R q tr) (V tr') (extend_node_b_r tr tr'))\n = let x = B_R q tr in\n let p_tr:partial_trace_of p = {to = q; tr = tr} in\n let v = V tr' in\n let y = extend_node_b_r tr tr' in\n let aux (frame:t p)\n : Lemma (requires composable x frame /\\ v == compose x frame)\n (ensures composable y frame /\\ v == compose y frame)\n = assert (A_R? frame \\/ A_W? frame \\/ A_Fin? frame);\n if A_W? frame then (\n next_message_closure A p_tr tr'\n // The PCM gives us here that y has to be B_R, it cannot be B_W\n // because then there would be a A read in the trace ahead of x\n\n ) else if A_R? frame then (\n let q_a = A_R?.q frame in\n let tr_a = A_R?._1 frame in\n assert (tr' == {to = q_a; tr = tr_a});\n Classical.move_requires (lemma_ahead_is_longer B q tr q_a) tr_a;\n // Gives us the following assertion by contraposition\n assert (p_tr `extended_to A` tr');\n next_message_closure A p_tr tr';\n\n if B_W? y then (\n ahead_refl A q_a tr_a\n ) else (\n let B_R q_b tr_b = y in\n lemma_ahead_is_longer A q_a tr_a q_b tr_b;\n lemma_ahead_implies_trace_prefix A tr_b tr_a;\n Classical.move_requires (lemma_same_length_ahead_implies_eq ({to = q_b; tr = tr_b})) tr'\n )\n ) else (\n next_message_closure A p_tr tr'\n )\n in Classical.forall_intro (Classical.move_requires aux)", "let f_a_r (#p:dprot) (q:dprot{is_recv q /\\ more q}) (tr:trace p q)\n (v:t p{compatible (pcm p) (A_R q tr) v})\n : GTot (y:t p{compatible (pcm p) y v /\\ frame_compatible (A_R q tr) v y})\n = match v with\n | A_R q tr -> A_R q tr\n | V tr' ->\n lemma_compatible_a_greater_length q tr tr';\n if trace_length tr >= trace_length tr'.tr then\n // No new message yet\n A_R q tr\n else\n let y = extend_node_a_r tr tr' in\n frame_compatible_a_extend q tr tr';\n y", "let f_b_r (#p:dprot) (q:dprot{is_send q /\\ more q}) (tr:trace p q)\n (v:t p{compatible (pcm p) (B_R q tr) v})\n : GTot (y:t p{compatible (pcm p) y v /\\ frame_compatible (B_R q tr) v y})\n = match v with\n | B_R q tr -> B_R q tr\n | V tr' ->\n lemma_compatible_b_greater_length q tr tr';\n if trace_length tr >= trace_length tr'.tr then\n // No new message yet\n B_R q tr\n else\n let y = extend_node_b_r tr tr' in\n frame_compatible_b_extend q tr tr';\n y", "val get_a_r (#p:dprot) (c:chan p) (q:dprot{is_recv q /\\ more q}) (tr:trace p q)\n : SteelT (tr':partial_trace_of p{compatible (pcm p) (A_R q tr) (V tr')})\n (pts_to c (A_R q tr))\n (fun tr' -> pts_to c (if trace_length tr >= trace_length tr'.tr then A_R q tr else extend_node_a_r tr tr'))", "let get_a_r #p c q tr =\n rewrite_slprop (pts_to c (A_R q tr)) (pts_to c (reveal (hide (A_R q tr)))) (fun _ -> ());\n let v = select_refine c (A_R q tr) (f_a_r q tr) in\n let (tr':partial_trace_of p{compatible (pcm p) (A_R q tr) (V tr')}) = V?._0 v in\n rewrite_slprop\n (pts_to c (f_a_r q tr v))\n (pts_to c (if trace_length tr >= trace_length tr'.tr then A_R q tr else extend_node_a_r tr tr'))\n (fun _ -> ());\n return tr'", "val get_b_r (#p:dprot) (c:chan p) (q:dprot{is_send q /\\ more q}) (tr:trace p q)\n : SteelT (tr':partial_trace_of p{compatible (pcm p) (B_R q tr) (V tr')})\n (pts_to c (B_R q tr))\n (fun tr' -> pts_to c (if trace_length tr >= trace_length tr'.tr then B_R q tr else extend_node_b_r tr tr'))", "let get_b_r #p c q tr =\n rewrite_slprop (pts_to c (B_R q tr)) (pts_to c (reveal (hide (B_R q tr)))) (fun _ -> ());\n let v = select_refine c (B_R q tr) (f_b_r q tr) in\n let (tr':partial_trace_of p{compatible (pcm p) (B_R q tr) (V tr')}) = V?._0 v in\n rewrite_slprop\n (pts_to c (f_b_r q tr v))\n (pts_to c (if trace_length tr >= trace_length tr'.tr then B_R q tr else extend_node_b_r tr tr'))\n (fun _ -> ());\n return tr'", "val upd_gen_action (#p:dprot)\n (r:chan p)\n (x y:t p)\n (f:FStar.PCM.frame_preserving_upd (pcm p) x y)\n : SteelT unit (pts_to r x) (fun _ -> pts_to r y)", "let upd_gen_action #p r x y f =\n rewrite_slprop (pts_to r x) (pts_to r (reveal (hide x))) (fun _ -> ());\n upd_gen r x y f;\n rewrite_slprop (pts_to r (reveal (hide y))) (pts_to r y) (fun _ -> ())", "let write_a_f_aux\n (#p:dprot)\n (#next:dprot{more next /\\ tag_of next = Send})\n (tr:trace p next)\n (x:msg_t next)\n : FStar.PCM.frame_preserving_upd (pcm p) (A_W next tr)\n (if is_send (step next x)\n then A_W (step next x) (extend tr x)\n else if is_recv (step next x)\n then A_R (step next x) (extend tr x)\n else A_Fin (step next x) (extend tr x))\n = fun v ->\n let post =\n if is_send (step next x)\n then A_W (step next x) (extend tr x)\n else if is_recv (step next x)\n then A_R (step next x) (extend tr x)\n else A_Fin (step next x) (extend tr x)\n in\n match v with\n | V tr' ->\n assert (tr'.to == next /\\ tr'.tr == tr);\n let res = V ({to = (step next x); tr = extend tr x}) in\n\n let aux () : Lemma (compatible (pcm p) post res)\n = if is_send (step next x) then (\n assert (composable post (B_R next tr));\n assert (compose (B_R next tr) post == res)\n ) else if is_recv (step next x) then (\n assert (composable post (B_W (step next x) (extend tr x)));\n assert (compose (B_W (step next x) (extend tr x)) post == res)\n ) else (\n assert (is_fin (step next x));\n assert (post == A_Fin (step next x) (extend tr x));\n assert (composable post (B_R next tr));\n assert (compose (B_R next tr) post == res)\n )\n in\n aux ();\n let aux_composable (frame:t p{composable (A_W next tr) frame})\n : Lemma (composable post frame /\\ (compose (A_W next tr) frame == v ==>\n compose post frame == res))\n = match frame with\n | Nil -> ()\n | B_R q' s' ->\n if is_send (step next x) \n then begin\n assert (ahead A next q' tr s');\n assert (ahead A (step next x) next (extend tr x) tr);\n assert (ahead A (step next x) q' (extend tr x) s')\n end\n else if is_recv (step next x)\n then begin\n assert (ahead A next q' tr s');\n assert (ahead A (step next x) next (extend tr x) tr);\n assert (ahead A (step next x) q' (extend tr x) s');\n lemma_ahead_is_longer A next tr q' s';\n assert (trace_length tr >= trace_length s');\n extend_increase_length tr x;\n assert (trace_length (extend tr x) > trace_length tr)\n end\n else begin\n assert (ahead A next q' tr s');\n assert (ahead A (step next x) next (extend tr x) tr);\n assert (ahead A (step next x) q' (extend tr x) s')\n end\n in\n Classical.forall_intro aux_composable;\n res", "let write_b_f_aux\n(#p:dprot)\n(#next:dprot{more next /\\ tag_of next = Recv})\n(tr:trace p next)\n(x:msg_t next)\n: FStar.PCM.frame_preserving_upd (pcm p) (B_W next tr)\n (if is_send (step next x)\n then B_R (step next x) (extend tr x)\n else if is_recv (step next x)\n then B_W (step next x) (extend tr x)\n else B_Fin (step next x) (extend tr x))\n= fun v ->\n let post =\n if is_send (step next x)\n then B_R (step next x) (extend tr x)\n else if is_recv (step next x)\n then B_W (step next x) (extend tr x)\n else B_Fin (step next x) (extend tr x)\n in\n match v with\n | V tr' ->\n assert (tr'.to == next /\\ tr'.tr == tr);\n let res = V ({to = (step next x); tr = extend tr x}) in\n let aux () : Lemma (compatible (pcm p) post res)\n = if is_send (step next x) then (\n assert (composable post (A_W (step next x) (extend tr x)));\n assert (compose (A_W (step next x) (extend tr x)) post == res)\n ) else if is_recv (step next x) then (\n assert (composable post (A_R next tr));\n assert (compose (A_R next tr) post == res)\n ) else (\n assert (is_fin (step next x));\n assert (post == B_Fin (step next x) (extend tr x));\n assert (composable post (A_R next tr));\n assert (compose (A_R next tr) post == res)\n )\n in\n aux ();\n let aux_composable (frame:t p{composable (B_W next tr) frame})\n : Lemma (composable post frame /\\ (compose (B_W next tr) frame == v ==>\n compose post frame == res))\n = match frame with\n | Nil -> ()\n | A_R q' s' ->\n if is_send (step next x) \n then begin\n assert (ahead B next q' tr s');\n assert (ahead B (step next x) next (extend tr x) tr);\n assert (ahead B (step next x) q' (extend tr x) s');\n lemma_ahead_is_longer B next tr q' s';\n assert (trace_length tr >= trace_length s');\n extend_increase_length tr x;\n assert (trace_length (extend tr x) > trace_length tr)\n end\n else if is_recv (step next x)\n then begin\n assert (ahead B next q' tr s');\n assert (ahead B (step next x) next (extend tr x) tr);\n assert (ahead B (step next x) q' (extend tr x) s')\n end\n else begin\n assert (ahead B next q' tr s');\n assert (ahead B (step next x) next (extend tr x) tr);\n assert (ahead B (step next x) q' (extend tr x) s')\n end\n in\n Classical.forall_intro aux_composable;\n res", "let lemma_ahead_extend_a (#p:dprot)\n (n:dprot) (n':dprot{more n' /\\ tag_of n' = Send})\n (tr:trace p n) (n_tr:trace p n')\n (x:msg_t n')\n : Lemma (requires ahead A n' n n_tr tr)\n (ensures ahead A (step n' x) n (extend n_tr x) tr)\n (decreases (trace_length n_tr - trace_length tr))\n = let s1 = {to = n; tr = tr} in\n let s2 = {to = n'; tr = n_tr} in\n let last = {to = step n' x; tr = extend n_tr x} in\n let r = next A #p in\n assert (R.closure r s1 s2);\n assert (R.closure r s2 last)", "let lemma_ahead_extend_b (#p:dprot)\n (n:dprot) (n':dprot{more n' /\\ tag_of n' = Recv})\n (tr:trace p n) (n_tr:trace p n')\n (x:msg_t n')\n : Lemma (requires ahead B n' n n_tr tr)\n (ensures ahead B (step n' x) n (extend n_tr x) tr)\n (decreases (trace_length n_tr - trace_length tr))\n = let s1 = {to = n; tr = tr} in\n let s2 = {to = n'; tr = n_tr} in\n let last = {to = step n' x; tr = extend n_tr x} in\n let r = next B #p in\n assert (R.closure r s1 s2);\n assert (R.closure r s2 last)", "let write_a_f_lemma\n (#p:dprot)\n (#next:dprot{more next /\\ tag_of next = Send})\n (tr:trace p next)\n (x:msg_t next)\n (v:t p{(pcm p).refine v})\n (frame:t p)\n : Lemma\n (requires compatible (pcm p) (A_W next tr) v /\\ composable v frame)\n (ensures\n compatible (pcm p) (A_W next tr) v /\\\n composable v frame /\\\n composable (write_a_f_aux #p #next tr x v) frame /\\\n (compatible (pcm p) (A_W next tr) (compose v frame) ==>\n (compose (write_a_f_aux tr x v) frame == write_a_f_aux tr x (compose v frame))))\n = ()", "let write_b_f_lemma\n (#p:dprot)\n (#next:dprot{more next /\\ tag_of next = Recv})\n (tr:trace p next)\n (x:msg_t next)\n (v:t p{(pcm p).refine v})\n (frame:t p)\n : Lemma\n (requires compatible (pcm p) (B_W next tr) v /\\ composable v frame)\n (ensures\n compatible (pcm p) (B_W next tr) v /\\\n composable v frame /\\\n composable (write_b_f_aux #p #next tr x v) frame /\\\n (compatible (pcm p) (B_W next tr) (compose v frame) ==>\n (compose (write_b_f_aux tr x v) frame == write_b_f_aux tr x (compose v frame))))\n = ()", "let write_a_f\n (#p:dprot)\n (#next:dprot{more next /\\ tag_of next = Send})\n (tr:trace p next)\n (x:msg_t next)\n : FStar.PCM.frame_preserving_upd (pcm p) (A_W next tr)\n (if is_send (step next x)\n then A_W (step next x) (extend tr x)\n else if is_recv (step next x)\n then A_R (step next x) (extend tr x)\n else A_Fin (step next x) (extend tr x))\n = Classical.forall_intro_2 (Classical.move_requires_2 (write_a_f_lemma #p #next tr x));\n write_a_f_aux #p #next tr x", "let write_b_f\n (#p:dprot)\n (#next:dprot{more next /\\ tag_of next = Recv})\n (tr:trace p next)\n (x:msg_t next)\n : FStar.PCM.frame_preserving_upd (pcm p) (B_W next tr)\n (if is_send (step next x)\n then B_R (step next x) (extend tr x)\n else if is_recv (step next x)\n then B_W (step next x) (extend tr x)\n else B_Fin (step next x) (extend tr x))\n = Classical.forall_intro_2 (Classical.move_requires_2 (write_b_f_lemma #p #next tr x));\n write_b_f_aux #p #next tr x", "let write_a\n (#p:dprot)\n (r:chan p)\n (#next:dprot{more next /\\ tag_of next = Send})\n (tr:trace p next)\n (x:msg_t next)\n :SteelT unit (pts_to r (A_W next tr)) (fun _ -> endpoint_a r (step next x) (extend tr x))\n = let v : t p =\n if is_send (step next x)\n then A_W (step next x) (extend tr x)\n else if is_recv (step next x)\n then A_R (step next x) (extend tr x)\n else A_Fin (step next x) (extend tr x)\n in\n upd_gen_action r _ v (write_a_f tr x)", "let write_b\n (#p:dprot)\n (r:chan p)\n (#next:dprot{more next /\\ tag_of next = Recv})\n (tr:trace p next)\n (x:msg_t next)\n :SteelT unit (pts_to r (B_W next tr)) (fun _ -> endpoint_b r (step next x) (extend tr x))\n = let v : t p =\n if is_send (step next x)\n then B_R (step next x) (extend tr x)\n else if is_recv (step next x)\n then B_W (step next x) (extend tr x)\n else B_Fin (step next x) (extend tr x)\n in\n upd_gen_action r _ v (write_b_f tr x)", "val alloc (#p:dprot) (x:t p{compatible (pcm p) x x /\\ refine x})\n : Steel (chan p) emp (fun r -> pts_to r x) (fun _ -> squash (compatible (pcm p) x x)) (fun _ _ _ -> True)", "let alloc x =\n let r = alloc x in\n rewrite_slprop (PR.pts_to r x) (pts_to r x) (fun _ -> ());\n return r", "val split (#p:dprot) (r:chan p) (v_full v0 v1:t p) (_:squash (composable v0 v1)) (_:squash (v_full == compose v0 v1))\n : SteelT unit (pts_to r v_full) (fun _ -> pts_to r v0 `star` pts_to r v1)", "let split r v v0 v1 u1 u2 =\n rewrite_slprop (pts_to r v) (pts_to r (reveal (hide v))) (fun _ -> ());\n split r v v0 v1;\n rewrite_slprop (pts_to r (reveal (hide v0))) (pts_to r v0) (fun _ -> ());\n rewrite_slprop (pts_to r (reveal (hide v1))) (pts_to r v1) (fun _ -> ())", "val new_chan (p:dprot)\n : SteelT (chan p) emp\n (fun c -> endpoint_a c p (empty_trace p) `star` endpoint_b c p (empty_trace p))", "let lem #p (x:t p) : Lemma (requires V? x) (ensures compatible (pcm p) x x)\n = assert (composable x Nil);\n assert (compose Nil x == x)", "let new_chan p =\n let v:t p = V ({to = p; tr = empty_trace p}) in\n lem v;\n let r = alloc v in\n split r v\n (if is_send p\n then A_W p (empty_trace p)\n else if is_recv p\n then A_R p (empty_trace p)\n else A_Fin p (empty_trace p))\n (if is_send p\n then B_R p (empty_trace p)\n else if is_recv p\n then B_W p (empty_trace p)\n else B_Fin p (empty_trace p))\n (ahead_refl A p (empty_trace p)) ();\n r", "val send_a\n (#p:dprot)\n (c:chan p)\n (#next:dprot{more next /\\ tag_of next = Send})\n (x:msg_t next)\n (tr:trace p next)\n : SteelT unit\n (endpoint_a c next tr)\n (fun _ -> endpoint_a c (step next x) (extend tr x))", "let send_a #p c #next x tr =\n rewrite_slprop (endpoint_a c next tr) (pts_to c (A_W next tr)) (fun _ -> ());\n write_a c tr x", "val send_b\n (#p:dprot)\n (c:chan p)\n (#next:dprot{more next /\\ tag_of next = Recv})\n (x:msg_t next)\n (tr:trace p next)\n : SteelT unit\n (endpoint_b c next tr)\n (fun _ -> endpoint_b c (step next x) (extend tr x))", "let send_b #p c #next x tr =\n rewrite_slprop (endpoint_b c next tr) (pts_to c (B_W next tr)) (fun _ -> ());\n write_b c tr x", "let rec recv_a (#p:dprot)\n (c:chan p)\n (next:dprot{more next /\\ tag_of next = Recv})\n (tr:trace p next)\n : SteelT (msg_t next)\n (endpoint_a c next tr)\n (fun x -> endpoint_a c (step next x) (extend tr x))\n =\n rewrite_slprop (endpoint_a c next tr) (pts_to c (A_R next tr)) (fun _ -> ());\n let tr' = get_a_r c next tr in\n if trace_length tr >= trace_length tr'.tr then (\n rewrite_slprop (pts_to c _) (endpoint_a c next tr) (fun _ -> ());\n recv_a c next tr\n )\n else (\n compatible_a_r_v_is_ahead tr tr';\n let x = next_message tr tr'.tr in\n rewrite_slprop\n (pts_to c _)\n (endpoint_a c (step next x) (extend tr x))\n (fun _ -> ());\n return x\n )", "let rec recv_b\n (#p:dprot)\n (c:chan p)\n (next:dprot{more next /\\ tag_of next = Send})\n (tr:trace p next)\n : SteelT (msg_t next)\n (endpoint_b c next tr)\n (fun x -> endpoint_b c (step next x) (extend tr x))\n =\n rewrite_slprop (endpoint_b c next tr) (pts_to c (B_R next tr)) (fun _ -> ());\n let tr' = get_b_r c next tr in\n if trace_length tr >= trace_length tr'.tr then (\n rewrite_slprop\n (pts_to c (if trace_length tr >= trace_length tr'.tr then B_R next tr else extend_node_b_r tr tr'))\n (endpoint_b c next tr)\n (fun _ -> ());\n recv_b c next tr\n ) else (\n compatible_b_r_v_is_ahead tr tr';\n let x = next_message tr tr'.tr in\n noop ();\n rewrite_slprop\n (pts_to c (if trace_length tr >= trace_length tr'.tr then B_R next tr else extend_node_b_r tr tr'))\n (endpoint_b c (step next x) (extend tr x))\n (fun _ -> ());\n return x\n )", "let endpoint (#p:dprot) (name:party) (c:chan p) (next:dprot) (t:trace p next)\n : vprop\n = match name with\n | A -> endpoint_a c next t\n | B -> endpoint_b c next t", "let send_aux (#p:dprot) (name:party) (c:chan p)\n (#next:send_next_dprot_t name) (x:msg_t next) (t:trace p next)\n : SteelT unit\n (endpoint name c next t)\n (fun _ -> endpoint name c (step next x) (extend t x))\n = if name = A then begin\n rewrite_slprop (endpoint _ _ _ _ )\n (endpoint_a c next t) (fun _ -> ());\n send_a c x t;\n rewrite_slprop (endpoint_a c (step next x) (extend t x))\n (endpoint _ _ _ _) (fun _ -> ())\n end\n else begin\n rewrite_slprop (endpoint _ _ _ _ )\n (endpoint_b c next t) (fun _ -> ());\n send_b c x t;\n rewrite_slprop (endpoint_b c (step next x) (extend t x))\n (endpoint _ _ _ _) (fun _ -> ())\n end", "let recv_aux (#p:dprot) (name:party) (c:chan p)\n (#next:recv_next_dprot_t name) (t:trace p next)\n : SteelT (msg_t next)\n (endpoint name c next t)\n (fun x -> endpoint name c (step next x) (extend t x))\n = if name = A then begin\n rewrite_slprop (endpoint _ _ _ _ )\n (endpoint_a c next t) (fun _ -> ());\n let x = recv_a c next t in\n rewrite_slprop (endpoint_a c (step next x) (extend t x))\n (endpoint _ _ _ _) (fun _ -> ());\n return x\n end\n else begin\n rewrite_slprop (endpoint _ _ _ _ )\n (endpoint_b c next t) (fun _ -> ());\n let x = recv_b c next t in\n rewrite_slprop (endpoint_b c (step next x) (extend t x))\n (endpoint _ _ _ _) (fun _ -> ());\n return x\n end", "trace_t", "channel" ], "closest": [ "val TwoLockQueue.fst = x: (_ * _) -> _\nlet fst x = fst x", "val OWGCounter.fst = x: (_ * _) -> _\nlet fst = fst", "val FStar.PCM.op = p: FStar.PCM.pcm a -> x: a -> y: a{FStar.PCM.composable p x y} -> a\nlet op (#a: Type u#a) (p:pcm a) (x:a) (y:a{composable p x y}) = p.p.op x y", "val TwoLockQueue.snd = x: (_ * _) -> _\nlet snd x = snd x", "val FStar.PCM.composable = p: FStar.PCM.pcm a -> x: a -> y: a -> Prims.prop\nlet composable (#a: Type u#a) (p:pcm a) (x y:a) = p.p.composable x y", "val FStar.PCM.compatible = pcm: FStar.PCM.pcm a -> x: a -> y: a -> Prims.logical\nlet compatible (#a: Type u#a) (pcm:pcm a) (x y:a) =\n (exists (frame:a).\n composable pcm x frame /\\ op pcm frame x == y\n )", "val Duplex.PCM.dprot' = Type\nlet dprot' = protocol unit", "val Duplex.PCM.dprot = Type\nlet dprot = p:dprot'{no_loop p}", "val write\n (#a:Type)\n (#p:pcm a)\n (r:pcm_ref p)\n (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n: stt unit\n (pcm_pts_to r x)\n (fun _ -> pcm_pts_to r y)\nlet write\n (#a:Type)\n (#p:pcm a)\n (r:pcm_ref p)\n (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n: stt unit\n (pcm_pts_to r x)\n (fun _ -> pcm_pts_to r y)\n= A.lift_atomic0 (A.write r x y f)", "val alloc (#a:Type)\n (#pcm:pcm a)\n (x:a)\n : Steel (ref a pcm)\n emp\n (fun r -> pts_to r x)\n (requires fun _ -> pcm.refine x)\n (ensures fun _ _ _ -> True)\nlet alloc #_ #pcm x = rewrite_slprop emp (to_vprop Mem.emp) (fun _ -> reveal_emp ());\n compatible_refl pcm x;\n alloc' x", "val alloc\n (#a:Type u#1)\n (#pcm:pcm a)\n (x:a{compatible pcm x x /\\ pcm.refine x})\n: stt (pcm_ref pcm)\n emp\n (fun r -> pcm_pts_to r x)\nlet alloc\n (#a:Type u#1)\n (#pcm:pcm a)\n (x:a{compatible pcm x x /\\ pcm.refine x})\n: stt (pcm_ref pcm)\n emp\n (fun r -> pcm_pts_to r x)\n= A.lift_atomic0 (A.alloc #a #pcm x)", "val FStar.PCM.frame_preserving = pcm: FStar.PCM.pcm a -> x: a -> y: a -> Prims.logical\nlet frame_preserving (#a: Type u#a) (pcm:pcm a) (x y: a) =\n (forall frame. composable pcm frame x ==> composable pcm frame y) /\\\n (forall frame.{:pattern (composable pcm frame x)} composable pcm frame x ==> op pcm frame y == y)", "val alloc\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (x:a{compatible pcm x x /\\ pcm.refine x})\r\n: stt_atomic (ref a pcm)\r\n #Observable\r\n emp_inames\r\n emp\r\n (fun r -> pts_to r x)\nlet alloc = A.alloc", "val alloc (#a:Type)\n (#pcm:pcm a)\n (x:a)\n : ST (ref a pcm)\n emp\n (fun r -> pts_to r x)\n (requires pcm.refine x)\n (ensures fun _ -> True)\nlet alloc x = C.coerce_steel (fun _ -> P.alloc x)", "val write\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x y:Ghost.erased a)\r\n (f:FStar.PCM.frame_preserving_upd p x y)\r\n: stt_atomic unit\r\n #Observable\r\n emp_inames\r\n (pts_to r x)\r\n (fun _ -> pts_to r y)\nlet write = A.write", "val read\n (#a:Type)\n (#p:pcm a)\n (r:pcm_ref p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n FStar.PCM.frame_compatible p x v y})))\n: stt (v:a{compatible p x v /\\ p.refine v})\n (pcm_pts_to r x)\n (fun v -> pcm_pts_to r (f v))\nlet read\n (#a:Type)\n (#p:pcm a)\n (r:pcm_ref p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n FStar.PCM.frame_compatible p x v y})))\n: stt (v:a{compatible p x v /\\ p.refine v})\n (pcm_pts_to r x)\n (fun v -> pcm_pts_to r (f v))\n= A.lift_atomic1 (A.read r x f)", "val f2 : x:(ref int) -> ST int (requires (fun h -> True))\n (ensures (fun h r h' -> fst (f2_hp h x) == h'\n /\\ snd (f2_hp h x) == r))\nlet f2 x = 0", "val cons_fst (x: 'a) (p: (list 'a * 'b)) : list 'a * 'b\nlet cons_fst (x : 'a) (p : list 'a * 'b) : list 'a * 'b =\n let (y, z) = p in (x :: y, z)", "val write\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x y:Ghost.erased a)\r\n (f:FStar.PCM.frame_preserving_upd p x y)\r\n: act unit emp_inames\r\n (pts_to r x)\r\n (fun _ -> pts_to r y)\nlet write\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x y:Ghost.erased a)\r\n (f:FStar.PCM.frame_preserving_upd p x y)\r\n: act unit emp_inames\r\n (pts_to r x)\r\n (fun _ -> pts_to r y)\r\n= fun #ictx -> mem_action_as_action _ _ _ _ (upd_gen ictx r x y f)", "val Vale.Inline.X64.Fmul_inline.fmul_xmms_modified = _: _ -> Prims.bool\nlet fmul_xmms_modified = fun _ -> false", "val Vale.Poly1305.Equiv.fmul = x: Spec.Poly1305.felem -> y: Spec.Poly1305.felem -> Spec.Poly1305.felem\nlet fmul = S.fmul", "val pcm_t (#a #b: _) : pcm (t a b)\nlet pcm_t #a #b : pcm (t a b) = FStar.PCM.({\n p = {\n composable=comp;\n op=combine;\n one=Neither\n };\n comm = (fun _ _ -> ());\n assoc = (fun _ _ _ -> ());\n assoc_r = (fun _ _ _ -> ());\n is_unit = (fun _ -> ());\n refine = (fun x -> Both? x \\/ Neither? x)\n})", "val OWGCounter.snd = x: (_ * _) -> _\nlet snd = snd", "val share\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\r\n: act unit emp_inames\r\n (pts_to r (v0 `op pcm` v1))\r\n (fun _ -> pts_to r v0 ** pts_to r v1)\nlet share\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\r\n: act unit emp_inames\r\n (pts_to r (v0 `op pcm` v1))\r\n (fun _ -> pts_to r v0 `star` pts_to r v1)\r\n= fun #ictx -> mem_action_as_action _ _ _ _ (split_action ictx r v0 v1)", "val Vale.Inline.X64.Fmul_inline.fmul1_xmms_modified = _: _ -> Prims.bool\nlet fmul1_xmms_modified = fun _ -> false", "val Pulse.Lib.PCM.Array.compose = \n x: Pulse.Lib.PCM.Array.carrier elt len ->\n y:\n Pulse.Lib.PCM.Array.carrier elt len\n {Mkpcm'?.composable (Mkpcm?.p (Pulse.Lib.PCM.Array.pcm elt len)) x y}\n -> Pulse.Lib.PCM.Array.carrier elt len\nlet compose (#elt: Type) (#len: Ghost.erased nat) = (pcm elt len).p.op", "val sel (#a: _) (r: regmap a) (x: reg) : Tot a (decreases (fst r))\nlet rec sel #a (r:regmap a) (x:reg) : Tot a (decreases (fst r)) =\n match r with\n | [], v -> v\n | (y, v)::tl, u -> if y = x then v else sel (tl, u) x", "val Duplex.PCM.nl_protocol = 'a: Type0 -> Type\nlet nl_protocol 'a = p:protocol 'a { no_loop p }", "val alloc\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (x:a{compatible pcm x x /\\ pcm.refine x})\r\n: act (ref a pcm) emp_inames emp (fun r -> pts_to r x)\nlet alloc\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (x:a{compatible pcm x x /\\ pcm.refine x})\r\n: act (ref a pcm) emp_inames emp (fun r -> pts_to r x)\r\n= fun #ictx ->\r\n mem_action_as_action _ _ _ _\r\n (alloc_action ictx x)", "val Duplex.PCM.no_loop = p: Steel.Channel.Protocol.protocol 'a -> Type0\nlet rec no_loop (p:protocol 'a) =\n match p with\n | Return _ -> True\n | Msg _ a k -> (forall x. no_loop (k x))\n | DoWhile _ _ -> False", "val f1 : x:(ref int) -> ST int (requires (fun h -> True))\n (ensures (fun h r h' -> fst (f1_hp h x) == h'\n /\\ snd (f1_hp h x) == r))\nlet f1 x = !x", "val Vale.Inline.X64.Fadd_inline.fsub_xmms_modified = _: _ -> Prims.bool\nlet fsub_xmms_modified = fun _ -> false", "val fixp (f: (x: dom -> Tot (partial_result x))) (x0: dom) : Tot codom (decreases %[x0;1;()])\nlet rec complete_fixp (f: (x:dom) -> partial_result x) (x:dom) (px:partial_result x)\n : Tot codom (decreases %[x ; 0 ; px])\n=\n match px with\n | Done y -> y\n | Need x' cont ->\n complete_fixp f x (cont (fixp f x'))\n\nand fixp (f: (x:dom -> Tot (partial_result x))) (x0:dom)\n : Tot codom (decreases %[x0 ; 1 ; ()])\n = complete_fixp f x0 (f x0)", "val upd_gen_action (r:ref stepper p)\n (x y:Ghost.erased stepper)\n (f:FStar.PCM.frame_preserving_upd p x y)\n : SteelT unit (pts_to r x) (fun _ -> pts_to r y)\nlet upd_gen_action r x y f = upd_gen r x y f", "val share\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\r\n: stt_ghost unit\r\n (pts_to r (v0 `op pcm` v1))\r\n (fun _ -> pts_to r v0 ** pts_to r v1)\nlet share #a #pcm r v0 v1 = Ghost.hide (A.share r v0 v1)", "val read\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x:erased a)\r\n (f:(v:a{compatible p x v}\r\n -> GTot (y:a{compatible p y v /\\\r\n FStar.PCM.frame_compatible p x v y})))\r\n: stt_atomic (v:a{compatible p x v /\\ p.refine v})\r\n #Observable\r\n emp_inames\r\n (pts_to r x)\r\n (fun v -> pts_to r (f v))\nlet read = A.read", "val upd_gen (#a: _) (#p: pcm a) (r: ref a p) (x v: Ghost.erased a) (f: frame_preserving_upd p x v)\n : partial_pre_action (pts_to r x) unit (fun _ -> pts_to r v)\nlet upd_gen #a (#p:pcm a)\n (r:ref a p)\n (x v:Ghost.erased a)\n (f: frame_preserving_upd p x v)\n : partial_pre_action (pts_to r x)\n unit\n (fun _ -> pts_to r v)\n = fun h ->\n let Ref a p frac old_v = select_addr h (Addr?._0 r) in\n let new_v = f old_v in\n let cell = Ref a p frac new_v in\n let h' = update_addr_full_heap h (Addr?._0 r) cell in\n (| (), h' |)", "val upd_gen (#a: _) (#p: pcm a) (r: ref a p) (x v: Ghost.erased a) (f: frame_preserving_upd p x v)\n : partial_pre_action (pts_to r x) unit (fun _ -> pts_to r v)\nlet upd_gen #a (#p:pcm a)\n (r:ref a p)\n (x v:Ghost.erased a)\n (f: frame_preserving_upd p x v)\n : partial_pre_action (pts_to r x)\n unit\n (fun _ -> pts_to r v)\n = fun h ->\n let Ref a p frac old_v = select_addr h (Addr?._0 r) in\n let new_v = f old_v in\n let cell = Ref a p frac new_v in\n let h' = update_addr_full_heap h (Addr?._0 r) cell in\n (| (), h' |)", "val FStar.PCM.exclusive = p: FStar.PCM.pcm a -> x: a -> Prims.logical\nlet exclusive (#a:Type u#a) (p:pcm a) (x:a) =\n forall (frame:a). composable p x frame ==> frame == p.p.one", "val fpartial_result (x: _) (f: (x: dom -> partial_result x)) (px: partial_result x)\n : Tot Type0 (decreases px)\nlet rec fpartial_result x (f: (x:dom -> partial_result x)) (px:partial_result x) : Tot Type0 (decreases px) =\n match px with\n | Done y -> y == fixp f x\n | Need x1 cont ->\n fpartial_result x f (cont (fixp f x1))", "val finv_256 (x256 x2 x30 a:felem) : Stack unit\n (requires fun h ->\n live h a /\\ live h x30 /\\ live h x2 /\\ live h x256 /\\\n disjoint a x30 /\\ disjoint a x2 /\\ disjoint a x256 /\\\n disjoint x30 x2 /\\ disjoint x30 x256 /\\ disjoint x2 x256 /\\\n as_nat h a < S.prime /\\ as_nat h x30 < S.prime /\\ as_nat h x2 < S.prime)\n (ensures fun h0 _ h1 -> modifies (loc x256 |+| loc x2) h0 h1 /\\\n as_nat h1 x256 < S.prime /\\\n (let f = fmont_as_nat h0 a in\n let x30 = fmont_as_nat h0 x30 in\n let x2 = fmont_as_nat h0 x2 in\n let x32_s = S.fmul (SI.fsquare_times x30 2) x2 in\n let x64_s = S.fmul (SI.fsquare_times x32_s 32) f in\n let x192_s = S.fmul (SI.fsquare_times x64_s 128) x32_s in\n let x224_s = S.fmul (SI.fsquare_times x192_s 32) x32_s in\n let x254_s = S.fmul (SI.fsquare_times x224_s 30) x30 in\n let x256_s = S.fmul (SI.fsquare_times x254_s 2) f in\n fmont_as_nat h1 x256 = x256_s))\nlet finv_256 x256 x2 x30 a =\n let h0 = ST.get () in\n fsquare_times x256 x30 2ul;\n fmul x256 x256 x2;\n let h1 = ST.get () in\n assert (fmont_as_nat h1 x256 == // x32\n S.fmul (SI.fsquare_times (fmont_as_nat h0 x30) 2) (fmont_as_nat h0 x2));\n\n fsquare_times x2 x256 32ul;\n fmul x2 x2 a;\n let h2 = ST.get () in\n assert (fmont_as_nat h2 x2 == // x64\n S.fmul (SI.fsquare_times (fmont_as_nat h1 x256) 32) (fmont_as_nat h0 a));\n\n fsquare_times_in_place x2 128ul;\n fmul x2 x2 x256;\n let h3 = ST.get () in\n assert (fmont_as_nat h3 x2 == // x192\n S.fmul (SI.fsquare_times (fmont_as_nat h2 x2) 128) (fmont_as_nat h1 x256));\n\n fsquare_times_in_place x2 32ul;\n fmul x2 x2 x256;\n let h4 = ST.get () in\n assert (fmont_as_nat h4 x2 == // x224\n S.fmul (SI.fsquare_times (fmont_as_nat h3 x2) 32) (fmont_as_nat h1 x256));\n\n fsquare_times_in_place x2 30ul;\n fmul x2 x2 x30;\n let h5 = ST.get () in\n assert (fmont_as_nat h5 x2 == // x254\n S.fmul (SI.fsquare_times (fmont_as_nat h4 x2) 30) (fmont_as_nat h0 x30));\n\n fsquare_times_in_place x2 2ul;\n fmul x256 x2 a;\n let h6 = ST.get () in\n assert (fmont_as_nat h6 x256 == // x256\n S.fmul (SI.fsquare_times (fmont_as_nat h5 x2) 2) (fmont_as_nat h0 a))", "val alloc (#o:inames)\n (#a:Type)\n (#pcm:pcm a)\n (x:a)\n : STGhost (ref a pcm) o\n emp\n (fun r -> pts_to r x)\n (requires pcm.refine x)\n (ensures fun _ -> True)\nlet alloc (#o:inames)\n (#a:Type)\n (#pcm:pcm a)\n (x:a)\n : STGhost (ref a pcm) o\n emp\n (fun r -> pts_to r x)\n (requires pcm.refine x)\n (ensures fun _ -> True)\n = coerce_ghost (fun _ -> G.alloc (raise_val x))", "val put (#s: _) (x: s) : st unit s\nlet put #s (x:s) : st unit s = fun s -> (), s", "val Memo.fibonnacci_memo = x0: Memo.dom -> Memo.Memo Memo.codom\nlet fibonnacci_memo = memo_rec_extr fibonnacci_partial", "val Vale.Poly1305.Equiv.fadd = x: Spec.Poly1305.felem -> y: Spec.Poly1305.felem -> Spec.Poly1305.felem\nlet fadd = S.fadd", "val FStar.Relational.Relational.fst_rel = _: FStar.Relational.Relational.double (_ * _) -> FStar.Relational.Relational.double _\nlet fst_rel = rel_map1T fst", "val fmul_: fmul_t M64 True\nlet fmul_ out f1 f2 tmp =\n let h0 = ST.get () in\n let tmp0 = sub tmp 0ul 8ul in\n BN.bn_mul 4ul 4ul f1 f2 tmp0;\n let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp0 4ul 4ul) (u64 38) 4ul 0ul (sub tmp0 0ul 4ul) in\n let c = BN.bn_add1 4ul (sub tmp0 0ul 4ul) (c0 *. u64 38) out in\n out.(0ul) <- out.(0ul) +. c *. u64 38;\n let h1 = ST.get () in\n assert (as_seq h1 out == CC.fmul4 (as_seq h0 f1) (as_seq h0 f2));\n CD.bn_v_is_as_nat (as_seq h0 f1);\n CD.bn_v_is_as_nat (as_seq h0 f2);\n CD.bn_v_is_as_nat (as_seq h1 out)", "val fstp (#a1 #a2: Type) (x: (a1 & a2)) : Tot a1\nlet fstp (#a1 #a2: Type) (x: (a1 & a2)) : Tot a1 = fst x", "val upd_gen (#a:Type) (#p:pcm a) (e:inames) (r:ref a p) (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n : action_except unit e\n (pts_to r x)\n (fun _ -> pts_to r y)\nlet upd_gen #a #p e r x y f\n = lift_tot_action (lift_heap_action e (H.upd_gen_action r x y f))", "val upd_gen (#a:Type) (#p:pcm a) (e:inames) (r:ref a p) (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n : action_except unit e\n (pts_to r x)\n (fun _ -> pts_to r y)\nlet upd_gen #a #p e r x y f\n = lift_tot_action (lift_heap_action e (H.upd_gen_action r x y f))", "val pcm_frac (#a: _) : pcm (fractional a)\nlet pcm_frac #a : pcm (fractional a) = {\r\n p = {\r\n composable = composable;\r\n op = compose;\r\n one = None\r\n };\r\n comm = (fun _ _ -> ());\r\n assoc = (fun _ _ _ -> ());\r\n assoc_r = (fun _ _ _ -> ());\r\n is_unit = (fun _ -> ());\r\n refine = (fun _ -> True)\r\n}", "val pcm_frac (#a: _) : pcm (fractional a)\nlet pcm_frac #a : pcm (fractional a) = {\n p = {\n composable = composable;\n op = compose;\n one = None\n };\n comm = (fun _ _ -> ());\n assoc = (fun _ _ _ -> ());\n assoc_r = (fun _ _ _ -> ());\n is_unit = (fun _ -> ());\n refine = (fun _ -> True)\n}", "val pcm (#v #p #s: _) : pcm (knowledge #v #p s)\nlet pcm #v #p #s : pcm (knowledge #v #p s) = {\n p = p0;\n comm = (fun k0 k1 ->\n match k0, k1 with\n | Nothing, _\n | _, Nothing -> ()\n | Owns m0, Owns m1 ->\n compose_avalue_comm m0 m1);\n assoc = (fun k0 k1 k2 -> composable_assoc_l k0 k1 k2);\n assoc_r = (fun k0 k1 k2 -> composable_assoc_r k0 k1 k2);\n is_unit = (fun _ -> ());\n refine = full_knowledge;\n}", "val upd_first (#a #b: Type u#1) (r: ref (t a b) pcm_t) (x: Ghost.erased a) (y: a)\n : SteelT unit (pts_to r (First #a #b x)) (fun _ -> pts_to r (First #a #b y))\nlet upd_first (#a #b:Type u#1) (r:ref (t a b) pcm_t) (x:Ghost.erased a) (y:a)\n : SteelT unit \n (pts_to r (First #a #b x))\n (fun _ -> pts_to r (First #a #b y))\n = let f\n : frame_preserving_upd\n pcm_t\n (Ghost.hide (First #a #b x))\n (First #a #b y)\n = fun old_v ->\n match old_v with\n | Both _ z -> Both y z\n in\n upd_gen r (First #a #b x) (First #a #b y) f", "val FStar.PCM.frame_compatible = p: FStar.PCM.pcm a -> x: FStar.Ghost.erased a -> v: a -> y: a -> Prims.logical\nlet frame_compatible #a (p:pcm a) (x:FStar.Ghost.erased a) (v y:a) =\n (forall (frame:a). {:pattern (composable p x frame)}\n composable p x frame /\\\n v == op p x frame ==>\n composable p y frame /\\\n v == op p y frame)", "val Memo.fibonnacci = x: Memo.dom -> Prims.int\nlet rec fibonnacci (x:dom) =\n if x <= 1\n then 1\n else fibonnacci (x - 1) + fibonnacci (x - 2)", "val pfmul (x y: pfelem) : pfelem\nlet pfmul (x:pfelem) (y:pfelem) : pfelem = Scalar.fmul x y", "val fmul2: C.(fmul2_t M51 True)\nlet fmul2 out f1 f2 _ =\n let f10 = f1.(0ul) in\n let f11 = f1.(1ul) in\n let f12 = f1.(2ul) in\n let f13 = f1.(3ul) in\n let f14 = f1.(4ul) in\n\n let f20 = f2.(0ul) in\n let f21 = f2.(1ul) in\n let f22 = f2.(2ul) in\n let f23 = f2.(3ul) in\n let f24 = f2.(4ul) in\n\n let f30 = f1.(5ul) in\n let f31 = f1.(6ul) in\n let f32 = f1.(7ul) in\n let f33 = f1.(8ul) in\n let f34 = f1.(9ul) in\n\n let f40 = f2.(5ul) in\n let f41 = f2.(6ul) in\n let f42 = f2.(7ul) in\n let f43 = f2.(8ul) in\n let f44 = f2.(9ul) in\n\n let ((o10,o11,o12,o13,o14), (o20,o21,o22,o23,o24)) =\n fmul25 (f10,f11,f12,f13,f14) (f20,f21,f22,f23,f24)\n (f30,f31,f32,f33,f34) (f40,f41,f42,f43,f44) in\n\n out.(0ul) <- o10;\n out.(1ul) <- o11;\n out.(2ul) <- o12;\n out.(3ul) <- o13;\n out.(4ul) <- o14;\n\n out.(5ul) <- o20;\n out.(6ul) <- o21;\n out.(7ul) <- o22;\n out.(8ul) <- o23;\n out.(9ul) <- o24", "val fmul (x y: elem) : elem\nlet fmul (x:elem) (y:elem) : elem = (x * y) % prime", "val f (x: int) : Pure unit (requires x == 2) (ensures fun _ -> True)\nlet f (x:int) : Pure unit (requires x == 2) (ensures fun _ -> True) =\n assert (x == 2);\n ()", "val mul256 (x: U16.t) : Tot (y: U32.t{U32.v y == 256 `Prims.op_Multiply` (U16.v x)})\nlet mul256 (x: U16.t) : Tot (y: U32.t { U32.v y == 256 `Prims.op_Multiply` U16.v x }) =\n assert_norm (pow2 8 == 256);\n FStar.Math.Lemmas.pow2_lt_compat 32 24;\n FStar.Math.Lemmas.pow2_lt_compat 24 16;\n FStar.Math.Lemmas.pow2_lt_compat 16 8;\n FStar.Math.Lemmas.pow2_plus 8 16;\n FStar.Math.Lemmas.small_mod (U16.v x `Prims.op_Multiply` 256) (pow2 32);\n FStar.UInt.shift_left_value_lemma #32 (U16.v x) 8;\n Cast.uint16_to_uint32 x `U32.shift_left` 8ul", "val Memo.fibonnacci_ = x0: Memo.dom -> Prims.Tot Memo.codom\nlet fibonnacci_ = fixp fibonnacci_partial", "val share\n (#a:Type)\n (#pcm:pcm a)\n (r:pcm_ref pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n: stt_ghost unit\n (pcm_pts_to r (v0 `op pcm` v1))\n (fun _ -> pcm_pts_to r v0 ** pcm_pts_to r v1)\nlet share = A.share", "val Steel.ST.HigherArray.compose = \n x: Steel.ST.HigherArray.carrier elt len ->\n y:\n Steel.ST.HigherArray.carrier elt len\n {Mkpcm'?.composable (Mkpcm?.p (Steel.ST.HigherArray.pcm elt len)) x y}\n -> Steel.ST.HigherArray.carrier elt len\nlet compose (#elt: Type) (#len: Ghost.erased nat) = (pcm elt len).P.p.P.op", "val split_action\n (#a:Type u#1)\n (#pcm:pcm a)\n (e:inames)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n : action_except unit e (pts_to r (v0 `op pcm` v1)) (fun _ -> pts_to r v0 `star` pts_to r v1)\nlet split_action #a #pcm e r v0 v1\n = lift_tot_action (lift_heap_action e (H.split_action #a #pcm r v0 v1))", "val split_action\n (#a:Type u#1)\n (#pcm:pcm a)\n (e:inames)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n : action_except unit e (pts_to r (v0 `op pcm` v1)) (fun _ -> pts_to r v0 `star` pts_to r v1)\nlet split_action #a #pcm e r v0 v1\n = lift_tot_action (lift_heap_action e (H.split_action #a #pcm r v0 v1))", "val d_das\n (x: var)\n (e: exp int)\n (phi: sttype)\n (f: nstype int)\n: Lemma\n (requires (x `st_fresh_in` phi))\n (ensures (\n x `st_fresh_in` phi /\\\n exec_equiv (st_cons phi x f) (st_cons phi x ns_t) (assign x e) skip\n ))\n [SMTPat (exec_equiv (st_cons phi x f) (st_cons phi x ns_t) (assign x e) skip)]\nlet d_das\n (x: var)\n (e: exp int)\n (phi: sttype)\n (f: nstype int)\n: Lemma\n (requires (x `st_fresh_in` phi))\n (ensures (\n x `st_fresh_in` phi /\\\n exec_equiv (st_cons phi x f) (st_cons phi x ns_t) (assign x e) skip\n ))\n [SMTPat (exec_equiv (st_cons phi x f) (st_cons phi x ns_t) (assign x e) skip)]\n= assert (Benton2004.mention (reify_exp e))", "val Vale.Inline.X64.Fadd_inline.fadd_xmms_modified = _: _ -> Prims.bool\nlet fadd_xmms_modified = fun _ -> false", "val split_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n : action (pts_to r (v0 `op pcm` v1)) unit (fun _ -> pts_to r v0 `star` pts_to r v1)\nlet split_action #a #pcm r v0 v1\n = let g : refined_pre_action (pts_to r (v0 `op pcm` v1))\n unit\n (fun _ -> pts_to r v0 `star` pts_to r v1)\n = fun m ->\n pts_to_compatible_bk r v0 v1 m;\n pts_to_compatible_equiv r v0 v1;\n (| (), m |)\n in\n refined_pre_action_as_action g", "val split_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n : action (pts_to r (v0 `op pcm` v1)) unit (fun _ -> pts_to r v0 `star` pts_to r v1)\nlet split_action #a #pcm r v0 v1\n = let g : refined_pre_action (pts_to r (v0 `op pcm` v1))\n unit\n (fun _ -> pts_to r v0 `star` pts_to r v1)\n = fun m ->\n pts_to_compatible_bk r v0 v1 m;\n pts_to_compatible_equiv r v0 v1;\n (| (), m |)\n in\n refined_pre_action_as_action g", "val FStar.PCM.lem_commutative = p: FStar.PCM.pcm' a -> Type\nlet lem_commutative (#a: Type u#a) (p:pcm' a) =\n x:a ->\n y:a{p.composable x y} ->\n Lemma (p.op x y == p.op y x)", "val free_action (#a:Type u#1) (#pcm:pcm a) (e:inames)\n (r:ref a pcm) (x:FStar.Ghost.erased a{FStar.PCM.exclusive pcm x /\\ pcm.refine pcm.FStar.PCM.p.one})\n : action_except unit e (pts_to r x) (fun _ -> pts_to r pcm.FStar.PCM.p.one)\nlet free_action #a #pcm e r v0\n = lift_tot_action (lift_heap_action e (H.free_action #a #pcm r v0))", "val free_action (#a:Type u#1) (#pcm:pcm a) (e:inames)\n (r:ref a pcm) (x:FStar.Ghost.erased a{FStar.PCM.exclusive pcm x /\\ pcm.refine pcm.FStar.PCM.p.one})\n : action_except unit e (pts_to r x) (fun _ -> pts_to r pcm.FStar.PCM.p.one)\nlet free_action #a #pcm e r v0\n = lift_tot_action (lift_heap_action e (H.free_action #a #pcm r v0))", "val Vale.Inline.X64.Fsqr_inline.fsqr_xmms_modified = _: _ -> Prims.bool\nlet fsqr_xmms_modified = fun _ -> false", "val free (#a:Type)\n (#p:pcm a)\n (r:ref a p)\n (x:erased a)\n : ST unit (pts_to r x) (fun _ -> pts_to r p.p.one)\n (requires exclusive p x /\\ p.refine p.p.one)\n (ensures fun _ -> True)\nlet free r x = C.coerce_steel (fun _ -> P.free r x)", "val fmul (x y: felem) : felem\nlet fmul (x:felem) (y:felem) : felem = (x * y) % prime", "val fmul (x y: felem) : felem\nlet fmul (x y:felem) : felem = (x * y) % prime", "val fmul (x y: felem) : felem\nlet fmul (x y:felem) : felem = (x * y) % prime", "val read\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x:erased a)\r\n (f:(v:a{compatible p x v}\r\n -> GTot (y:a{compatible p y v /\\\r\n FStar.PCM.frame_compatible p x v y})))\r\n: act (v:a{compatible p x v /\\ p.refine v}) emp_inames\r\n (pts_to r x)\r\n (fun v -> pts_to r (f v))\nlet read\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x:erased a)\r\n (f:(v:a{compatible p x v}\r\n -> GTot (y:a{compatible p y v /\\\r\n FStar.PCM.frame_compatible p x v y})))\r\n: act (v:a{compatible p x v /\\ p.refine v}) emp_inames\r\n (pts_to r x)\r\n (fun v -> pts_to r (f v))\r\n= fun #ictx ->\r\n mem_action_as_action _ _ _ _ (select_refine ictx r x f)", "val fmul: C.(fmul_t M51 True)\nlet fmul out f1 f2 _ =\n let f10 = f1.(0ul) in\n let f11 = f1.(1ul) in\n let f12 = f1.(2ul) in\n let f13 = f1.(3ul) in\n let f14 = f1.(4ul) in\n\n let f20 = f2.(0ul) in\n let f21 = f2.(1ul) in\n let f22 = f2.(2ul) in\n let f23 = f2.(3ul) in\n let f24 = f2.(4ul) in\n\n let (o0,o1,o2,o3,o4) =\n fmul5 (f10,f11,f12,f13,f14) (f20,f21,f22,f23,f24) in\n out.(0ul) <- o0;\n out.(1ul) <- o1;\n out.(2ul) <- o2;\n out.(3ul) <- o3;\n out.(4ul) <- o4", "val PulseCore.Action.stable_property = pcm: FStar.PCM.pcm a -> Type\nlet stable_property (#a:Type) (pcm:pcm a)\r\n = fact:property a {\r\n FStar.Preorder.stable fact (PP.preorder_of_pcm pcm)\r\n }", "val finv_30 (x30 x2 tmp1 tmp2 a:felem) : Stack unit\n (requires fun h ->\n live h a /\\ live h x30 /\\ live h x2 /\\ live h tmp1 /\\ live h tmp2 /\\\n disjoint a x30 /\\ disjoint a x2 /\\ disjoint a tmp1 /\\ disjoint a tmp2 /\\\n disjoint x30 x2 /\\ disjoint x30 tmp1 /\\ disjoint x30 tmp2 /\\\n disjoint x2 tmp1 /\\ disjoint x2 tmp2 /\\ disjoint tmp1 tmp2 /\\\n as_nat h a < S.prime)\n (ensures fun h0 _ h1 -> modifies (loc x30 |+| loc x2 |+| loc tmp1 |+| loc tmp2) h0 h1 /\\\n as_nat h1 x30 < S.prime /\\ as_nat h1 x2 < S.prime /\\\n (let f = fmont_as_nat h0 a in\n let x2_s = S.fmul (SI.fsquare_times f 1) f in\n let x3_s = S.fmul (SI.fsquare_times x2_s 1) f in\n let x6_s = S.fmul (SI.fsquare_times x3_s 3) x3_s in\n let x12_s = S.fmul (SI.fsquare_times x6_s 6) x6_s in\n let x15_s = S.fmul (SI.fsquare_times x12_s 3) x3_s in\n let x30_s = S.fmul (SI.fsquare_times x15_s 15) x15_s in\n fmont_as_nat h1 x30 = x30_s /\\ fmont_as_nat h1 x2 = x2_s))\nlet finv_30 x30 x2 tmp1 tmp2 a =\n let h0 = ST.get () in\n fsquare_times x2 a 1ul;\n fmul x2 x2 a;\n let h1 = ST.get () in\n assert (fmont_as_nat h1 x2 ==\n S.fmul (SI.fsquare_times (fmont_as_nat h0 a) 1) (fmont_as_nat h0 a));\n\n fsquare_times x30 x2 1ul;\n fmul x30 x30 a;\n let h2 = ST.get () in\n assert (fmont_as_nat h2 x30 == // x3\n S.fmul (SI.fsquare_times (fmont_as_nat h1 x2) 1) (fmont_as_nat h0 a));\n\n fsquare_times tmp1 x30 3ul;\n fmul tmp1 tmp1 x30;\n let h3 = ST.get () in\n assert (fmont_as_nat h3 tmp1 == // x6\n S.fmul (SI.fsquare_times (fmont_as_nat h2 x30) 3) (fmont_as_nat h2 x30));\n\n fsquare_times tmp2 tmp1 6ul;\n fmul tmp2 tmp2 tmp1;\n let h4 = ST.get () in\n assert (fmont_as_nat h4 tmp2 == // x12\n S.fmul (SI.fsquare_times (fmont_as_nat h3 tmp1) 6) (fmont_as_nat h3 tmp1));\n\n fsquare_times tmp1 tmp2 3ul;\n fmul tmp1 tmp1 x30;\n let h5 = ST.get () in\n assert (fmont_as_nat h5 tmp1 == // x15\n S.fmul (SI.fsquare_times (fmont_as_nat h4 tmp2) 3) (fmont_as_nat h2 x30));\n\n fsquare_times x30 tmp1 15ul;\n fmul x30 x30 tmp1;\n let h6 = ST.get () in\n assert (fmont_as_nat h6 x30 == // x30\n S.fmul (SI.fsquare_times (fmont_as_nat h5 tmp1) 15) (fmont_as_nat h5 tmp1))", "val Vale.Poly1305.Equiv.to_felem = x: Prims.nat{x < Spec.Poly1305.prime} -> Spec.Poly1305.felem\nlet to_felem = S.to_felem", "val pts_to_compatible\n (#a:Type u#a)\n (#pcm:pcm a)\n (x:ref a pcm)\n (v0 v1:a)\n (m:mem u#a)\n : Lemma\n (interp (pts_to x v0 `star` pts_to x v1) m <==>\n composable pcm v0 v1 /\\ interp (pts_to x (op pcm v0 v1)) m)\nlet pts_to_compatible #a #pcm x v0 v1 m\n = H.pts_to_compatible #a #pcm x v0 v1 (heap_of_mem m)", "val pts_to_compatible\n (#a:Type u#a)\n (#pcm:pcm a)\n (x:ref a pcm)\n (v0 v1:a)\n (m:mem u#a)\n : Lemma\n (interp (pts_to x v0 `star` pts_to x v1) m <==>\n composable pcm v0 v1 /\\ interp (pts_to x (op pcm v0 v1)) m)\nlet pts_to_compatible #a #pcm x v0 v1 m\n = H.pts_to_compatible #a #pcm x v0 v1 (heap_of_mem m)", "val return (a: _) (x: a) : gst a R\nlet return a (x:a)\n : gst a R\n = fun s -> x", "val p0 (#v #p #s: _) : pcm' (knowledge #v #p s)\nlet p0 #v #p #s : pcm' (knowledge #v #p s) = {\n composable;\n op=compose;\n one=Nothing\n}", "val fst (x: tuple2 'a 'b) : 'a\nlet fst (x: tuple2 'a 'b) : 'a = Mktuple2?._1 x", "val Memo.computes = $f: (x: Memo.dom{p x} -> Memo.Memo Memo.codom) -> g: (_: Memo.dom -> Memo.codom) -> Prims.logical\nlet computes (#p:dom -> Tot Type0) ($f: (x:dom{p x} -> Memo codom)) (g:dom -> Tot codom) =\n forall h0. valid_memo h0 g ==> (forall x. p x ==> (let y ,h1 = reify (f x) h0 in y == g x /\\ valid_memo h1 g))", "val pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))\nlet pts_to_compatible_equiv #a #pcm x v0 v1\n = H.pts_to_compatible_equiv #a #pcm x v0 v1", "val pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))\nlet pts_to_compatible_equiv (#a:Type) (#pcm:_) (x:ref a pcm) (v0:a) (v1:a{composable pcm v0 v1})\n = FStar.Classical.forall_intro (pts_to_compatible x v0 v1)", "val pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))\nlet pts_to_compatible_equiv #a #pcm x v0 v1\n = H.pts_to_compatible_equiv #a #pcm x v0 v1", "val pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))\nlet pts_to_compatible_equiv (#a:Type) (#pcm:_) (x:ref a pcm) (v0:a) (v1:a{composable pcm v0 v1})\n = FStar.Classical.forall_intro (pts_to_compatible x v0 v1)", "val uint64_to_uint32 (x: U64.t{FStar.UInt.fits (U64.v x) 32}) : (y: U32.t{U32.v y == U64.v x})\nlet uint64_to_uint32 (x:U64.t{FStar.UInt.fits (U64.v x) 32}) : (y:U32.t{U32.v y == U64.v x}) =\r\n FStar.Int.Cast.uint64_to_uint32 x", "val raise_frame_preserving_upd (#a: _) (#p: pcm a) (#x #y: a) (f: frame_preserving_upd p x y)\n : frame_preserving_upd (raise p) (raise_val x) (raise_val y)\nlet raise_frame_preserving_upd #a (#p:pcm a) (#x #y:a) (f:frame_preserving_upd p x y)\n : frame_preserving_upd (raise p) (raise_val x) (raise_val y)\n = fun v ->\n let u = f (downgrade_val v) in\n let v_new = raise_val u in\n assert (forall frame. composable p y frame ==> composable (raise p) (raise_val y) (raise_val frame));\n assert (forall frame. composable (raise p) (raise_val x) frame ==> composable p x (downgrade_val frame));\n v_new", "val compatible_refl (#a: Type u#a) (pcm: pcm a) (x: a) : Lemma (compatible pcm x x)\nlet compatible_refl\n (#a: Type u#a) (pcm:pcm a) (x:a)\n : Lemma (compatible pcm x x)\n =\n pcm.is_unit x;\n pcm.comm x pcm.p.one;\n assert (op pcm pcm.p.one x == x)", "val ghost_write\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ghost_ref p)\r\n (x y:Ghost.erased a)\r\n (f:FStar.PCM.frame_preserving_upd p x y)\r\n: stt_ghost unit\r\n (ghost_pts_to r x)\r\n (fun _ -> ghost_pts_to r y)\nlet ghost_write r x y f = Ghost.hide (A.write r x y f)", "val put (#s: _) (x: s) : st s unit\nlet put #s (x:s)\n : st s unit\n = fun _ -> (), x", "val alloc : #a:Type -> \n x:a -> \n\t ImmutableST (ref a) (fun _ -> True)\n (fun h0 r h1 -> r `unused_in` h0 /\\\n\t\t\t\t\t contains h1 r /\\\n\t\t\t\t\t\th1 == upd h0 r x)\nlet alloc #a x = \n let h = ist_get () in\n let r = gen_ref h in\n ist_put (upd h r x);\n r", "val fmul (#w: lanes) (x y: elem w) : elem w\nlet fmul (#w:lanes) (x:elem w) (y:elem w) : elem w =\n map2 pfmul x y" ], "closest_src": [ { "project_name": "steel", "file_name": "TwoLockQueue.fst", "name": "TwoLockQueue.fst" }, { "project_name": "steel", "file_name": "OWGCounter.fst", "name": "OWGCounter.fst" }, { "project_name": "FStar", "file_name": "FStar.PCM.fst", "name": "FStar.PCM.op" }, { "project_name": "steel", "file_name": "TwoLockQueue.fst", "name": "TwoLockQueue.snd" }, { "project_name": "FStar", "file_name": "FStar.PCM.fst", "name": "FStar.PCM.composable" }, { "project_name": "FStar", "file_name": "FStar.PCM.fst", "name": "FStar.PCM.compatible" }, { "project_name": "steel", "file_name": "Duplex.PCM.fsti", "name": "Duplex.PCM.dprot'" }, { "project_name": "steel", "file_name": "Duplex.PCM.fsti", "name": "Duplex.PCM.dprot" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.write" }, { "project_name": "steel", "file_name": "Steel.PCMReference.fst", "name": "Steel.PCMReference.alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.alloc" }, { "project_name": "FStar", "file_name": "FStar.PCM.fst", "name": "FStar.PCM.frame_preserving" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.alloc" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.alloc" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.write" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.read" }, { "project_name": "FStar", "file_name": "StRel.fst", "name": "StRel.f2" }, { "project_name": "FStar", "file_name": "Trace.fst", "name": "Trace.cons_fst" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.write" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.fmul_xmms_modified" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Equiv.fst", "name": "Vale.Poly1305.Equiv.fmul" }, { "project_name": "steel", "file_name": "StructUpdate.fst", "name": "StructUpdate.pcm_t" }, { "project_name": "steel", "file_name": "OWGCounter.fst", "name": "OWGCounter.snd" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.share" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.fmul1_xmms_modified" }, { "project_name": "steel", "file_name": "Pulse.Lib.PCM.Array.fst", "name": "Pulse.Lib.PCM.Array.compose" }, { "project_name": "FStar", "file_name": "Registers.List.fst", "name": "Registers.List.sel" }, { "project_name": "steel", "file_name": "Duplex.PCM.fsti", "name": "Duplex.PCM.nl_protocol" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.alloc" }, { "project_name": "steel", "file_name": "Duplex.PCM.fsti", "name": "Duplex.PCM.no_loop" }, { "project_name": "FStar", "file_name": "StRel.fst", "name": "StRel.f1" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.fsub_xmms_modified" }, { "project_name": "FStar", "file_name": "Memo.fst", "name": "Memo.fixp" }, { "project_name": "steel", "file_name": "Steel.Stepper.fst", "name": "Steel.Stepper.upd_gen_action" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.share" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.read" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.upd_gen" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.upd_gen" }, { "project_name": "FStar", "file_name": "FStar.PCM.fst", "name": "FStar.PCM.exclusive" }, { "project_name": "FStar", "file_name": "Memo.fst", "name": "Memo.fpartial_result" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Finv.fst", "name": "Hacl.Impl.P256.Finv.finv_256" }, { "project_name": "steel", "file_name": "Steel.ST.GhostPCMReference.fst", "name": "Steel.ST.GhostPCMReference.alloc" }, { "project_name": "FStar", "file_name": "OPLSS2021.BasicState.fst", "name": "OPLSS2021.BasicState.put" }, { "project_name": "FStar", "file_name": "Memo.fst", "name": "Memo.fibonnacci_memo" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Equiv.fst", "name": "Vale.Poly1305.Equiv.fadd" }, { "project_name": "FStar", "file_name": "FStar.Relational.Relational.fst", "name": "FStar.Relational.Relational.fst_rel" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Curve25519.Field64.Hacl.fst", "name": "Hacl.Impl.Curve25519.Field64.Hacl.fmul_" }, { "project_name": "steel", "file_name": "CBOR.Pulse.Extern.fsti", "name": "CBOR.Pulse.Extern.fstp" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.upd_gen" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.upd_gen" }, { "project_name": "steel", "file_name": "Pulse.Lib.PCM.Fraction.fst", "name": "Pulse.Lib.PCM.Fraction.pcm_frac" }, { "project_name": "steel", "file_name": "Steel.PCMFrac.fst", "name": "Steel.PCMFrac.pcm_frac" }, { "project_name": "steel", "file_name": "Steel.FractionalAnchoredPreorder.fst", "name": "Steel.FractionalAnchoredPreorder.pcm" }, { "project_name": "steel", "file_name": "StructUpdate.fst", "name": "StructUpdate.upd_first" }, { "project_name": "FStar", "file_name": "FStar.PCM.fst", "name": "FStar.PCM.frame_compatible" }, { "project_name": "FStar", "file_name": "Memo.fst", "name": "Memo.fibonnacci" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Vec.fst", "name": "Hacl.Spec.Poly1305.Vec.pfmul" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Curve25519.Field51.fst", "name": "Hacl.Impl.Curve25519.Field51.fmul2" }, { "project_name": "hacl-star", "file_name": "Spec.Curve25519.fst", "name": "Spec.Curve25519.fmul" }, { "project_name": "FStar", "file_name": "HandleSmtGoal.fst", "name": "HandleSmtGoal.f" }, { "project_name": "everparse", "file_name": "LowParse.Low.BoundedInt.fst", "name": "LowParse.Low.BoundedInt.mul256" }, { "project_name": "FStar", "file_name": "Memo.fst", "name": "Memo.fibonnacci_" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.share" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fst", "name": "Steel.ST.HigherArray.compose" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.split_action" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.split_action" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fst", "name": "Benton2004.DDCC.d_das" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.fadd_xmms_modified" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.split_action" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.split_action" }, { "project_name": "FStar", "file_name": "FStar.PCM.fst", "name": "FStar.PCM.lem_commutative" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.free_action" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.free_action" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fsqr_inline.fst", "name": "Vale.Inline.X64.Fsqr_inline.fsqr_xmms_modified" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.free" }, { "project_name": "hacl-star", "file_name": "Spec.Poly1305.fst", "name": "Spec.Poly1305.fmul" }, { "project_name": "hacl-star", "file_name": "Spec.K256.PointOps.fst", "name": "Spec.K256.PointOps.fmul" }, { "project_name": "hacl-star", "file_name": "Spec.P256.PointOps.fst", "name": "Spec.P256.PointOps.fmul" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.read" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Curve25519.Field51.fst", "name": "Hacl.Impl.Curve25519.Field51.fmul" }, { "project_name": "steel", "file_name": "PulseCore.Action.fsti", "name": "PulseCore.Action.stable_property" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Finv.fst", "name": "Hacl.Impl.P256.Finv.finv_30" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Equiv.fst", "name": "Vale.Poly1305.Equiv.to_felem" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.pts_to_compatible" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.pts_to_compatible" }, { "project_name": "FStar", "file_name": "Sec1.GST.fst", "name": "Sec1.GST.return" }, { "project_name": "steel", "file_name": "Steel.FractionalAnchoredPreorder.fst", "name": "Steel.FractionalAnchoredPreorder.p0" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.Native.fst", "name": "FStar.Pervasives.Native.fst" }, { "project_name": "FStar", "file_name": "Memo.fst", "name": "Memo.computes" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.pts_to_compatible_equiv" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.pts_to_compatible_equiv" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.pts_to_compatible_equiv" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.pts_to_compatible_equiv" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fsti", "name": "EverParse3d.Prelude.uint64_to_uint32" }, { "project_name": "FStar", "file_name": "FStar.Universe.PCM.fst", "name": "FStar.Universe.PCM.raise_frame_preserving_upd" }, { "project_name": "FStar", "file_name": "FStar.PCM.fst", "name": "FStar.PCM.compatible_refl" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.ghost_write" }, { "project_name": "FStar", "file_name": "MonadFunctorInference.fst", "name": "MonadFunctorInference.put" }, { "project_name": "FStar", "file_name": "ImmutableSTwHeaps.fst", "name": "ImmutableSTwHeaps.alloc" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Vec.fst", "name": "Hacl.Spec.Poly1305.Vec.fmul" } ], "selected_premises": [ "FStar.Reflection.V2.Data.var", "FStar.Real.one", "FStar.List.Tot.Base.op_At", "FStar.Real.two", "FStar.FunctionalExtensionality.feq", "Steel.Channel.Protocol.protocol", "Steel.Channel.Protocol.ok", "FStar.Tactics.CanonCommMonoidSimple.Equiv.term_eq", "FStar.List.Tot.Base.length", "FStar.List.Tot.Base.map", "FStar.String.length", "Duplex.PCM.lem", "Steel.Memory.full_mem", "FStar.UInt.size", "Steel.Channel.Protocol.done", "FStar.PCM.compatible", "Steel.Channel.Protocol.recv", "Steel.FractionalPermission.sum_perm", "Steel.Channel.Protocol.return", "FStar.Tactics.CanonCommMonoidSimple.Equiv.atom", "Steel.Effect.Common.atom", "Steel.FractionalPermission.full_perm", "Steel.Effect.Common.star", "FStar.List.Tot.Base.mem", "FStar.PCM.composable", "Steel.Channel.Protocol.finished", "FStar.Reflection.V2.Derived.mk_e_app", "Steel.Channel.Protocol.flip_tag", "Steel.Channel.Protocol.send", "Steel.Memory.hmem", "Steel.Channel.Protocol.dual", "Duplex.PCM.p'", "Steel.Effect.Common.normal_steps", "Steel.Preorder.pcm_history", "FStar.PCM.op", "FStar.List.Tot.Base.tl", "Steel.FractionalPermission.comp_perm", "FStar.Reflection.V2.Derived.flatten_name", "FStar.Reflection.V2.Derived.shift_subst", "Steel.Channel.Protocol.extend", "FStar.Reflection.V2.Derived.mk_app", "Duplex.PCM.is_fin", "Steel.Effect.Common.hp_of", "Steel.Effect.Common.extract_contexts", "Duplex.PCM.compose", "Steel.Effect.Common.normal", "Steel.Channel.Protocol.more", "Duplex.PCM.refine", "Steel.Channel.Protocol.extended_to", "Steel.Effect.Common.to_vprop", "Steel.Effect.Common.req", "Duplex.PCM.next_message_closure", "Steel.Effect.Common.to_vprop'", "FStar.List.Tot.Base.rev", "Duplex.PCM.pcm", "Steel.Channel.Protocol.tag_of", "Steel.Channel.Protocol.hnf", "Steel.Channel.Protocol.step", "FStar.String.strlen", "FStar.FunctionalExtensionality.on_dom", "Steel.Effect.Common.rmem", "Steel.Channel.Protocol.extension_of", "Steel.Effect.Atomic.h_exists", "FStar.List.Tot.Base.append", "Steel.Memory.inames", "FStar.Reflection.V2.Derived.Lemmas.op_Less_Less_Colon", "Steel.Effect.Common.t_of", "Steel.Channel.Protocol.bind", "Duplex.PCM.next_increase_length", "Steel.Channel.Protocol.more_msgs", "Duplex.PCM.trace_length", "Steel.Effect.Common.print_goals", "Duplex.PCM.composable", "FStar.Heap.trivial_preorder", "Duplex.PCM.is_trace_prefix", "Duplex.PCM.lemma_unique_next_common_prefix", "Duplex.PCM.lemma_is_trace_prefix_extend", "Steel.Channel.Protocol.msg_t", "Duplex.PCM.ahead", "Duplex.PCM.lemma_ahead_is_longer", "Steel.Preorder.history_val", "Steel.Effect.Common.vrefine'", "FStar.Pervasives.Native.fst", "Duplex.PCM.lemma_is_trace_prefix_refl", "FStar.List.Tot.Base.memP", "FStar.Mul.op_Star", "Steel.Effect.Common.sel_of", "FStar.Reflection.V2.Derived.inspect_ln_unascribe", "Duplex.PCM.lemma_same_trace_length_ahead_refl'", "Steel.Effect.Common.rm", "Duplex.PCM.endpoint", "FStar.List.Tot.Base.fold_left", "Duplex.PCM.chan", "Steel.Channel.Protocol.next", "Steel.Effect.Common.slterm_nbr_uvars_argv", "Duplex.PCM.next", "FStar.Reflection.V2.Derived.is_fvar", "Duplex.PCM.extend_increase_length", "Steel.Effect.Common.rmem'", "Steel.Preorder.vhist" ], "source_upto_this": "module Duplex.PCM\n\nopen FStar.PCM\n\nopen Steel.Channel.Protocol\nmodule P = FStar.Preorder\nmodule R = FStar.ReflexiveTransitiveClosure\n\nlet is_send (p:dprot) = Msg? p && (Send? (Msg?._0 p))\nlet is_recv (p:dprot) = Msg? p && (Recv? (Msg?._0 p))\nlet is_fin (p:dprot) = Return? p\n\nlet empty_trace (p:dprot) : trace p p = Waiting p\n\nlet partial_trace_of (p:dprot) = tr:partial_trace_of p{no_loop tr.to}\n\nlet next (tag:party) (#p:dprot) : P.relation (partial_trace_of p) =\n fun (t0 t1: partial_trace_of p) ->\n more_msgs t0.to /\\\n // Ensuring that if we are ahead, we only have writes\n (if A? tag then is_send t0.to else is_recv t0.to) /\\\n (exists (msg:next_msg_t t0.to).\n t1.to == step t0.to msg /\\\n t1.tr == extend t0.tr msg)\n\nlet extended_to (tag:party) (#p:dprot) : P.preorder (partial_trace_of p) =\n R.closure (next tag #p)\n\n\nnoeq\ntype t (p:dprot) : Type u#1 =\n| V : partial_trace_of p -> t p\n| A_W : q:dprot {is_send q} -> trace p q -> t p\n| A_R : q:dprot {is_recv q} -> trace p q -> t p\n| B_R : q:dprot {is_send q} -> trace p q -> t p\n| B_W : q:dprot {is_recv q} -> trace p q -> t p\n| A_Fin : q:dprot{is_fin q} -> trace p q -> t p\n| B_Fin : q:dprot{is_fin q} -> trace p q -> t p\n| Nil\n\nlet ahead (tag:party) (#p:dprot) (q q':dprot) (s:trace p q) (s':trace p q') : prop\n = ({ to = q'; tr = s'} `extended_to tag` { to = q; tr = s }) /\\ True\n\nlet ahead_refl (tag:party) (#p:dprot) (q:dprot) (s:trace p q)\n : Lemma (ahead tag q q s s)\n = ()\n\nlet rec trace_length #p #q (s:trace p q) : Tot nat (decreases s) = match s with\n | Waiting _ -> 0\n | Message _ _ _ t -> 1 + trace_length t\n\nlet composable #p : symrel (t p) = fun t0 t1 ->\n match t0, t1 with\n | _, Nil\n | Nil, _ -> True\n\n (* both sides are finished and they agree on the trace *)\n | A_Fin q s, B_Fin q' s'\n | B_Fin q s, A_Fin q' s' -> q == q' /\\ s == s'\n\n (* A is finished, B still has to read *)\n | A_Fin q s, B_R q' s'\n | B_R q' s', A_Fin q s -> ahead A q q' s s'\n\n (* B is finished, A still has to read *)\n | A_R q' s', B_Fin q s\n | B_Fin q s, A_R q' s' -> ahead B q q' s s'\n\n (* A is writing, B is reading: A is ahead *)\n | A_W q s, B_R q' s'\n | B_R q' s', A_W q s -> ahead A q q' s s'\n\n (* B is writing, A is reading: B is ahead *)\n | B_W q s, A_R q' s'\n | A_R q' s', B_W q s -> ahead B q q' s s'\n\n (* Both are in a reading state, either one could be ahead *)\n | A_R q s, B_R q' s'\n | B_R q' s', A_R q s -> ahead A q q' s s' \\/ ahead B q' q s' s\n\n | _, _ -> False\n\nlet compose (#p:dprot) (s0:t p) (s1:t p{composable s0 s1}) =\n match s0, s1 with\n | a, Nil | Nil, a -> a\n\n | A_Fin q s, _\n | _, A_Fin q s\n | B_Fin q s, _\n | _, B_Fin q s -> V ({to = q; tr=s })\n\n | A_W q s, B_R q' s'\n | B_R q' s', A_W q s\n | B_W q s, A_R q' s'\n | A_R q' s', B_W q s -> V ({to = q; tr = s})\n\n | A_R q s, B_R q' s'\n | B_R q' s', A_R q s ->\n if trace_length s >= trace_length s'\n then V ({to = q; tr = s})\n else V ({to = q'; tr = s' })\n\nlet p' (p:dprot) : pcm' (t p) = { composable = composable; op = compose; one = Nil }\n\nlet lemma_comm #p (x:t p) (y:t p{composable x y}) :\n Lemma (compose x y == compose y x)\n = ()\n\n#push-options \"--z3rlimit 20\"\n\nlet lemma_assoc_l #p (x y:t p) (z:t p{composable y z /\\ composable x (compose y z)})\n : Lemma (composable x y /\\ composable (compose x y) z /\\\n compose x (compose y z) == compose (compose x y) z)\n = ()\n\nlet lemma_assoc_r #p (x y:t p) (z:t p{composable x y /\\ composable (compose x y) z})\n : Lemma (composable y z /\\ composable x (compose y z) /\\\n compose x (compose y z) == compose (compose x y) z)\n = ()\n\nlet lemma_is_unit #p (x:t p) : Lemma (composable x Nil /\\ compose x Nil == x)\n = ()\n\n#pop-options\n\nlet refine (#prot:dprot) (x:t prot) : prop = V? x \\/ Nil? x\n\nlet pcm (prot:dprot) : pcm (t prot) =\n { p = p' prot;\n comm = lemma_comm;\n assoc = lemma_assoc_l;\n assoc_r = lemma_assoc_r;\n is_unit = lemma_is_unit;\n refine = refine\n}\n\nopen FStar.Ghost\nopen Steel.Memory\nopen Steel.Effect.Atomic\nopen Steel.Effect\nopen Steel.PCMReference\nmodule Mem = Steel.Memory\nmodule PR = Steel.PCMReference\n\nlet chan (p:dprot) = ref (t p) (pcm p)\n\nval pts_to (#p:dprot) (r:chan p) (v:t p) : vprop\nlet pts_to r v = PR.pts_to r v\n\nlet ep_a (#p:dprot) (next:dprot) (tr:trace p next) =\n if is_send next\n then A_W next tr\n else if is_recv next\n then A_R next tr\n else A_Fin next tr\n\n[@@__reduce__]\nlet endpoint_a (#p:dprot) (c:chan p) (next:dprot) (tr:trace p next) =\n pts_to c (ep_a next tr)\n\nlet endpoint_b (#p:dprot) (c:chan p) (next:dprot) (tr:trace p next) =\n pts_to c (if is_send next\n then B_R next tr\n else if is_recv next\n then B_W next tr\n else B_Fin next tr)\n\n\nlet frame_compatible (#p:dprot) (x:t p) (v y:t p) =\n (forall (frame:t p). {:pattern (composable x frame)}\n composable x frame /\\\n v == compose x frame ==>\n composable y frame /\\\n v == compose y frame)\n\nlet select_refine' (#p:dprot)\n (r:chan p)\n (x:erased (t p))\n (f:(v:t p{compatible (pcm p) x v}\n -> GTot (y:t p{compatible (pcm p) y v /\\\n frame_compatible x v y})))\n : SteelT (v:t p{compatible (pcm p) x v /\\ refine v})\n (PR.pts_to r x)\n (fun v -> PR.pts_to r (f v))\n = select_refine r x f\n\nval select_refine (#p:dprot)\n (r:chan p)\n (x:erased (t p))\n (f:(v:t p{compatible (pcm p) x v}\n -> GTot (y:t p{compatible (pcm p) y v /\\\n frame_compatible x v y})))\n : SteelT (v:t p{compatible (pcm p) x v /\\ refine v})\n (pts_to r x)\n (fun v -> pts_to r (f v))\n\nlet select_refine #p r x f =\n let v = select_refine' r x f in\n rewrite_slprop (PR.pts_to r (f v)) (pts_to r (f v)) (fun _ -> ());\n return v\n\nlet rec is_trace_prefix\n (#from:dprot) (#to #to':dprot)\n (tr:trace from to)\n (tr':trace from to')\n : Tot prop\n (decreases tr)\n = match tr with\n | Waiting _ -> True\n | Message _ x _ tail ->\n match tr' with\n | Waiting _ -> False\n | Message _ x' _ tail' -> x == x' /\\ is_trace_prefix tail tail'\n\nlet rec lemma_is_trace_prefix_refl\n (#from #to:dprot)\n (tr:trace from to)\n : Lemma (ensures is_trace_prefix tr tr)\n (decreases tr)\n = match tr with\n | Waiting _ -> ()\n | Message _ _ _ tail -> lemma_is_trace_prefix_refl tail\n\nlet rec lemma_is_trace_prefix_extend (#from #to #to':dprot)\n (tr:trace from to)\n (tr':trace from to')\n (x:msg_t to')\n : Lemma (requires is_trace_prefix tr tr' /\\ more_msgs to')\n (ensures is_trace_prefix tr (extend tr' x))\n (decreases tr)\n = match tr with\n | Waiting _ -> ()\n | Message _ msg _ tail ->\n match tr' with\n | Message from' msg' to' tail' -> lemma_is_trace_prefix_extend tail tail' x\n\nlet lemma_ahead_msg_msg_inversion\n (#from:dprot) (#to #to':dprot)\n (tr:trace from to)\n (tr':trace from to')\n : Lemma (requires Message? tr /\\ Message? tr' /\\ is_trace_prefix tr tr')\n (ensures Message?.x tr == Message?.x tr' /\\ is_trace_prefix (Message?._3 tr) (Message?._3 tr'))\n = let Message _ x _ tail = tr in\n let Message _ x' _ tail' = tr' in\n let l = ({to = to; tr = tr}) in\n let r = ({to = to'; tr = tr'}) in\n let open FStar.ReflexiveTransitiveClosure in\n ()\n\nlet rec next_message_aux\n (#from:dprot) (#to #to':dprot)\n (tr:trace from to)\n (tr':trace from to'{trace_length tr' > trace_length tr /\\ is_trace_prefix tr tr'})\n : Tot (msg_t to)\n (decreases tr)\n = match tr with\n | Waiting _ ->\n assert (Message? tr');\n Message?.x tr'\n | Message _ x to tail ->\n let Message _ x' to' tail' = tr' in\n lemma_ahead_msg_msg_inversion tr tr';\n next_message_aux tail tail'\n\nlet lemma_ahead_implies_trace_prefix\n (tag:party)\n (#from:dprot) (#to #to':dprot)\n (tr:trace from to)\n (tr':trace from to')\n : Lemma (requires ahead tag to' to tr' tr)\n (ensures is_trace_prefix tr tr')\n = let stable (z:partial_trace_of from) : Type0 = is_trace_prefix tr z.tr in\n let aux (y z:partial_trace_of from)\n : Lemma (requires stable y /\\ next tag y z)\n (ensures stable z)\n = Classical.forall_intro (Classical.move_requires (lemma_is_trace_prefix_extend tr y.tr))\n in Classical.forall_intro_2 (Classical.move_requires_2 aux);\n R.stable_on_closure (next tag) stable ();\n lemma_is_trace_prefix_refl tr\n\nlet next_message\n (#from:dprot) (#to #to':dprot)\n (tr:trace from to)\n (tr':trace from to'{trace_length tr' > trace_length tr /\\\n (exists tag. ahead tag to' to tr' tr)})\n = Classical.forall_intro (fun tag -> Classical.move_requires (lemma_ahead_implies_trace_prefix tag tr) tr');\n next_message_aux tr tr'\n\nlet rec extend_increase_length (#from #to:dprot) (t:trace from to{more_msgs to}) (m:next_msg_t to)\n : Lemma (ensures trace_length (extend t m) == trace_length t + 1)\n (decreases t)\n = match t with\n | Waiting _ -> ()\n | Message _ _ _ tail -> extend_increase_length tail m\n\nlet next_increase_length (tag:party) (#p:dprot) (x y:partial_trace_of p)\n : Lemma (requires next tag x y)\n (ensures trace_length y.tr == trace_length x.tr + 1)\n = let aux (msg:next_msg_t x.to)\n : Lemma (requires y.to == step x.to msg /\\ y.tr == extend x.tr msg)\n (ensures trace_length y.tr == trace_length x.tr + 1)\n = extend_increase_length x.tr msg\n in Classical.forall_intro (Classical.move_requires aux)\n\nlet lemma_ahead_is_longer (tag:party) (#p:dprot) (q:dprot) (s:trace p q) (q':dprot) (s':trace p q')\n : Lemma (requires ahead tag q q' s s')\n (ensures trace_length s >= trace_length s')\n = let open FStar.ReflexiveTransitiveClosure in\n let l = ({to = q'; tr = s'}) in\n let r = ({to = q; tr = s}) in\n let stable_p (x:partial_trace_of p) : Type0 = trace_length x.tr >= trace_length s' in\n let aux (x y:partial_trace_of p)\n : Lemma (requires stable_p x /\\ next tag x y)\n (ensures stable_p y)\n = next_increase_length tag x y\n in Classical.forall_intro_2 (fun x -> Classical.move_requires (aux x));\n stable_on_closure (next tag) stable_p ()\n\n\nlet compatible_a_r_v_is_ahead\n (#p:dprot) (#q:dprot{is_recv q}) (tr:trace p q)\n (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (A_R q tr) (V tr'))\n (ensures ahead B tr'.to q tr'.tr tr)\n = let aux (frame:t p) : Lemma\n (requires composable (A_R q tr) frame /\\ compose frame (A_R q tr) == V tr')\n (ensures ahead B tr'.to q tr'.tr tr)\n = assert (B_R? frame \\/ B_W? frame \\/ B_Fin? frame);\n if B_W? frame then ()\n else if B_R? frame then (\n let q' = B_R?.q frame in\n let tr' = B_R?._1 frame in\n if trace_length tr' >= trace_length tr then\n Classical.move_requires (lemma_ahead_is_longer A q tr q') tr'\n else ahead_refl B q tr\n ) else ()\n in\n Classical.forall_intro (Classical.move_requires aux)\n\nlet rec lemma_same_trace_length_ahead_refl' (#p:dprot) (#q #q':dprot)\n (s:trace p q)\n (s':trace p q')\n : Lemma (requires is_trace_prefix s s' /\\ trace_length s == trace_length s')\n (ensures q == q' /\\ s == s')\n (decreases s)\n = match s with\n | Waiting _ -> ()\n | Message _ _ _ _ ->\n lemma_same_trace_length_ahead_refl' (Message?._3 s) (Message?._3 s')\n\nlet lemma_same_trace_length_ahead_refl (tag:party) (#p:dprot) (#q #q':dprot)\n (s:trace p q)\n (s':trace p q')\n : Lemma (requires ahead tag q q' s s' /\\ trace_length s == trace_length s')\n (ensures q == q' /\\ s == s')\n = lemma_ahead_implies_trace_prefix tag s' s;\n lemma_same_trace_length_ahead_refl' s' s\n\nlet compatible_b_r_v_is_ahead\n (#p:dprot) (#q:dprot{is_send q}) (tr:trace p q)\n (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (B_R q tr) (V tr'))\n (ensures ahead A tr'.to q tr'.tr tr)\n = let aux (frame:t p) : Lemma\n (requires composable (B_R q tr) frame /\\ compose frame (B_R q tr) == V tr')\n (ensures ahead A tr'.to q tr'.tr tr)\n = assert (A_R? frame \\/ A_W? frame \\/ A_Fin? frame);\n if A_W? frame then ()\n else if A_R? frame then (\n let q_a = A_R?.q frame in\n let tr_a = A_R?._1 frame in\n if trace_length tr_a > trace_length tr then (\n Classical.move_requires (lemma_ahead_is_longer B q tr q_a) tr_a\n ) else if trace_length tr_a < trace_length tr then ahead_refl A q tr\n else (\n assert (tr'.to == q_a /\\ tr'.tr == tr_a);\n // We need both sides, since there is a disjunction in the PCM in the A_R/B_R case\n Classical.move_requires (lemma_same_trace_length_ahead_refl A tr_a) tr;\n Classical.move_requires (lemma_same_trace_length_ahead_refl B tr) tr_a;\n assert (q == q_a /\\ tr == tr_a);\n ahead_refl A q tr\n )\n ) else ()\n in\n Classical.forall_intro (Classical.move_requires aux)\n\nlet extend_node_a_r (#p:dprot) (#q:dprot{more q /\\ is_recv q}) (tr:trace p q)\n (tr':partial_trace_of p{trace_length tr'.tr > trace_length tr /\\\n compatible (pcm p) (A_R q tr) (V tr')})\n : t p\n = compatible_a_r_v_is_ahead tr tr';\n let x = next_message tr tr'.tr in\n let q' = step q x in\n let tr' = extend tr x in\n if is_send q'\n then A_W q' tr'\n else if is_recv q'\n then A_R q' tr'\n else A_Fin q' tr'\n\nlet extend_node_b_r (#p:dprot) (#q:dprot{more q /\\ is_send q}) (tr:trace p q)\n (tr':partial_trace_of p{trace_length tr'.tr > trace_length tr /\\\n compatible (pcm p) (B_R q tr) (V tr')})\n : t p\n = compatible_b_r_v_is_ahead tr tr';\n let x = next_message tr tr'.tr in\n let q' = step q x in\n let tr' = extend tr x in\n if is_send q'\n then B_R q' tr'\n else if is_recv q'\n then B_W q' tr'\n else B_Fin q' tr'\n\n\nlet lemma_compatible_a_greater_length (#p:dprot) (q:dprot{is_recv q}) (tr:trace p q) (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (A_R q tr) (V tr'))\n (ensures trace_length tr'.tr >= trace_length tr)\n = compatible_a_r_v_is_ahead tr tr';\n lemma_ahead_is_longer B tr'.to tr'.tr q tr\n\nlet lemma_compatible_b_greater_length (#p:dprot) (q:dprot{is_send q}) (tr:trace p q) (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (B_R q tr) (V tr'))\n (ensures trace_length tr'.tr >= trace_length tr)\n = compatible_b_r_v_is_ahead tr tr';\n lemma_ahead_is_longer A tr'.to tr'.tr q tr\n\nlet rec lemma_unique_next_common_prefix\n (tag:party)\n (#p:dprot)\n (tr z tr':partial_trace_of p)\n : Lemma (requires is_trace_prefix tr.tr tr'.tr /\\ is_trace_prefix z.tr tr'.tr /\\\n next tag tr z /\\ trace_length tr'.tr > trace_length tr.tr)\n (ensures (\n let x = next_message_aux tr.tr tr'.tr in\n let tr2 = extend tr.tr x in\n z.to == step tr.to x /\\\n tr2 == z.tr)\n )\n (decreases tr.tr)\n = let Message _ x_z _ tail_z = z.tr in\n let Message _ x' _ tail' = tr'.tr in\n match tr.tr with\n | Waiting _ -> ()\n | Message _ _ to tail -> lemma_unique_next_common_prefix tag\n ({to = to; tr = tail}) ({to = z.to; tr = tail_z}) ({to = tr'.to; tr = tail'})\n\n// Reintroducing the quantifier loop just for this file\nlet closure_inversion (tag:party) (#p:dprot) (tr tr':partial_trace_of p)\n : Lemma (requires tr `extended_to tag` tr')\n (ensures tr == tr' \\/ (exists z. next tag tr z /\\ z `extended_to tag` tr'))\n [SMTPat (tr `extended_to tag` tr')]\n = R.closure_inversion (next tag) tr tr'\n\nlet next_message_closure (tag:party) (#p:dprot) (tr tr':partial_trace_of p)\n : Lemma (requires trace_length tr'.tr > trace_length tr.tr /\\ tr `extended_to tag` tr')\n (ensures (\n let x = next_message tr.tr tr'.tr in\n let q2 = step tr.to x in\n let tr2 = extend tr.tr x in\n ({to = q2; tr = tr2}) `extended_to tag` tr'))\n = let x = next_message tr.tr tr'.tr in\n let q2 = step tr.to x in\n let tr2 = extend tr.tr x in\n let z_new = {to = q2; tr = tr2} in\n let open FStar.ReflexiveTransitiveClosure in\n assert (exists z. next tag tr z /\\ z `extended_to tag` tr');\n let aux (z:partial_trace_of p)\n : Lemma (requires next tag tr z /\\ z `extended_to tag` tr')\n (ensures z == z_new)\n = lemma_ahead_implies_trace_prefix tag z.tr tr'.tr;\n lemma_ahead_implies_trace_prefix tag tr.tr tr'.tr;\n lemma_unique_next_common_prefix tag tr z tr'\n in Classical.forall_intro (Classical.move_requires aux)\n\nlet lemma_same_length_ahead_implies_eq (#p:dprot) (tr tr':partial_trace_of p)\n : Lemma (requires trace_length tr.tr == trace_length tr'.tr /\\ is_trace_prefix tr.tr tr'.tr)\n (ensures tr == tr')\n = let rec aux (#p #q1 #q2:dprot) (tr1:trace p q1) (tr2:trace p q2)\n : Lemma (requires trace_length tr1 == trace_length tr2 /\\ is_trace_prefix tr1 tr2)\n (ensures q1 == q2 /\\ tr1 == tr2)\n (decreases tr1)\n = match tr1 with\n | Waiting _ -> ()\n | Message _ _ _ tail -> aux tail (Message?._3 tr2)\n in aux tr.tr tr'.tr\n\n#push-options \"--z3rlimit_factor 4 --max_ifuel 1 --max_fuel 1\"\nlet frame_compatible_a_extend (#p:dprot)\n (q:dprot{is_recv q /\\ more q}) (tr:trace p q)\n (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (A_R q tr) (V tr') /\\ trace_length tr'.tr > trace_length tr)\n (ensures frame_compatible (A_R q tr) (V tr') (extend_node_a_r tr tr'))\n = let x = A_R q tr in\n let p_tr:partial_trace_of p = {to = q; tr = tr} in\n let v = V tr' in\n let y = extend_node_a_r tr tr' in\n let aux (frame:t p)\n : Lemma (requires composable x frame /\\ v == compose x frame)\n (ensures composable y frame /\\ v == compose y frame)\n = assert (B_R? frame \\/ B_W? frame \\/ B_Fin? frame);\n if B_W? frame then (\n // The PCM gives us here that y has to be A_R, it cannot be A_W\n // because then there would be a B read in the trace ahead of x\n R.closure_inversion (next B) p_tr tr';\n next_message_closure B p_tr tr'\n ) else if B_R? frame then (\n let q_b = B_R?.q frame in\n let tr_b = B_R?._1 frame in\n assert (tr' == {to = q_b; tr = tr_b});\n Classical.move_requires (lemma_ahead_is_longer A q tr q_b) tr_b;\n // Gives us the following assertion by contraposition\n assert (p_tr `extended_to B` tr');\n next_message_closure B p_tr tr';\n\n if A_W? y then (\n ahead_refl B q_b tr_b\n ) else (\n let A_R q_a tr_a = y in\n lemma_ahead_is_longer B q_b tr_b q_a tr_a;\n lemma_ahead_implies_trace_prefix B tr_a tr_b;\n Classical.move_requires (lemma_same_length_ahead_implies_eq ({to = q_a; tr = tr_a})) tr'\n )\n ) else (\n next_message_closure B p_tr tr';\n let B_Fin _ tr_b = frame in\n assert (tr_b == tr'.tr);\n assert (composable y frame);\n assert (v == compose y frame)\n )\n in Classical.forall_intro (Classical.move_requires aux)\n\nlet frame_compatible_b_extend (#p:dprot)\n (q:dprot{is_send q /\\ more q}) (tr:trace p q)\n (tr':partial_trace_of p)\n : Lemma (requires compatible (pcm p) (B_R q tr) (V tr') /\\ trace_length tr'.tr > trace_length tr)\n (ensures frame_compatible (B_R q tr) (V tr') (extend_node_b_r tr tr'))\n = let x = B_R q tr in\n let p_tr:partial_trace_of p = {to = q; tr = tr} in\n let v = V tr' in\n let y = extend_node_b_r tr tr' in\n let aux (frame:t p)\n : Lemma (requires composable x frame /\\ v == compose x frame)\n (ensures composable y frame /\\ v == compose y frame)\n = assert (A_R? frame \\/ A_W? frame \\/ A_Fin? frame);\n if A_W? frame then (\n next_message_closure A p_tr tr'\n // The PCM gives us here that y has to be B_R, it cannot be B_W\n // because then there would be a A read in the trace ahead of x\n\n ) else if A_R? frame then (\n let q_a = A_R?.q frame in\n let tr_a = A_R?._1 frame in\n assert (tr' == {to = q_a; tr = tr_a});\n Classical.move_requires (lemma_ahead_is_longer B q tr q_a) tr_a;\n // Gives us the following assertion by contraposition\n assert (p_tr `extended_to A` tr');\n next_message_closure A p_tr tr';\n\n if B_W? y then (\n ahead_refl A q_a tr_a\n ) else (\n let B_R q_b tr_b = y in\n lemma_ahead_is_longer A q_a tr_a q_b tr_b;\n lemma_ahead_implies_trace_prefix A tr_b tr_a;\n Classical.move_requires (lemma_same_length_ahead_implies_eq ({to = q_b; tr = tr_b})) tr'\n )\n ) else (\n next_message_closure A p_tr tr'\n )\n in Classical.forall_intro (Classical.move_requires aux)\n\nlet f_a_r (#p:dprot) (q:dprot{is_recv q /\\ more q}) (tr:trace p q)\n (v:t p{compatible (pcm p) (A_R q tr) v})\n : GTot (y:t p{compatible (pcm p) y v /\\ frame_compatible (A_R q tr) v y})\n = match v with\n | A_R q tr -> A_R q tr\n | V tr' ->\n lemma_compatible_a_greater_length q tr tr';\n if trace_length tr >= trace_length tr'.tr then\n // No new message yet\n A_R q tr\n else\n let y = extend_node_a_r tr tr' in\n frame_compatible_a_extend q tr tr';\n y\n\nlet f_b_r (#p:dprot) (q:dprot{is_send q /\\ more q}) (tr:trace p q)\n (v:t p{compatible (pcm p) (B_R q tr) v})\n : GTot (y:t p{compatible (pcm p) y v /\\ frame_compatible (B_R q tr) v y})\n = match v with\n | B_R q tr -> B_R q tr\n | V tr' ->\n lemma_compatible_b_greater_length q tr tr';\n if trace_length tr >= trace_length tr'.tr then\n // No new message yet\n B_R q tr\n else\n let y = extend_node_b_r tr tr' in\n frame_compatible_b_extend q tr tr';\n y\n\n\nval get_a_r (#p:dprot) (c:chan p) (q:dprot{is_recv q /\\ more q}) (tr:trace p q)\n : SteelT (tr':partial_trace_of p{compatible (pcm p) (A_R q tr) (V tr')})\n (pts_to c (A_R q tr))\n (fun tr' -> pts_to c (if trace_length tr >= trace_length tr'.tr then A_R q tr else extend_node_a_r tr tr'))\n\nlet get_a_r #p c q tr =\n rewrite_slprop (pts_to c (A_R q tr)) (pts_to c (reveal (hide (A_R q tr)))) (fun _ -> ());\n let v = select_refine c (A_R q tr) (f_a_r q tr) in\n let (tr':partial_trace_of p{compatible (pcm p) (A_R q tr) (V tr')}) = V?._0 v in\n rewrite_slprop\n (pts_to c (f_a_r q tr v))\n (pts_to c (if trace_length tr >= trace_length tr'.tr then A_R q tr else extend_node_a_r tr tr'))\n (fun _ -> ());\n return tr'\n\nval get_b_r (#p:dprot) (c:chan p) (q:dprot{is_send q /\\ more q}) (tr:trace p q)\n : SteelT (tr':partial_trace_of p{compatible (pcm p) (B_R q tr) (V tr')})\n (pts_to c (B_R q tr))\n (fun tr' -> pts_to c (if trace_length tr >= trace_length tr'.tr then B_R q tr else extend_node_b_r tr tr'))\n\nlet get_b_r #p c q tr =\n rewrite_slprop (pts_to c (B_R q tr)) (pts_to c (reveal (hide (B_R q tr)))) (fun _ -> ());\n let v = select_refine c (B_R q tr) (f_b_r q tr) in\n let (tr':partial_trace_of p{compatible (pcm p) (B_R q tr) (V tr')}) = V?._0 v in\n rewrite_slprop\n (pts_to c (f_b_r q tr v))\n (pts_to c (if trace_length tr >= trace_length tr'.tr then B_R q tr else extend_node_b_r tr tr'))\n (fun _ -> ());\n return tr'\n\nval upd_gen_action (#p:dprot)\n (r:chan p)\n (x y:t p)\n (f:FStar.PCM.frame_preserving_upd (pcm p) x y)\n : SteelT unit (pts_to r x) (fun _ -> pts_to r y)\n\nlet upd_gen_action #p r x y f =\n rewrite_slprop (pts_to r x) (pts_to r (reveal (hide x))) (fun _ -> ());\n upd_gen r x y f;\n rewrite_slprop (pts_to r (reveal (hide y))) (pts_to r y) (fun _ -> ())\n\n\n#push-options \"--z3rlimit_factor 4 --ifuel 2 --fuel 1\"\n#restart-solver\nlet write_a_f_aux\n (#p:dprot)\n (#next:dprot{more next /\\ tag_of next = Send})\n (tr:trace p next)\n (x:msg_t next)\n : FStar.PCM.frame_preserving_upd (pcm p) (A_W next tr)\n (if is_send (step next x)\n then A_W (step next x) (extend tr x)\n else if is_recv (step next x)\n then A_R (step next x) (extend tr x)\n else A_Fin (step next x) (extend tr x))\n = fun v ->\n let post =\n if is_send (step next x)\n then A_W (step next x) (extend tr x)\n else if is_recv (step next x)\n then A_R (step next x) (extend tr x)\n else A_Fin (step next x) (extend tr x)\n in\n match v with\n | V tr' ->\n assert (tr'.to == next /\\ tr'.tr == tr);\n let res = V ({to = (step next x); tr = extend tr x}) in\n\n let aux () : Lemma (compatible (pcm p) post res)\n = if is_send (step next x) then (\n assert (composable post (B_R next tr));\n assert (compose (B_R next tr) post == res)\n ) else if is_recv (step next x) then (\n assert (composable post (B_W (step next x) (extend tr x)));\n assert (compose (B_W (step next x) (extend tr x)) post == res)\n ) else (\n assert (is_fin (step next x));\n assert (post == A_Fin (step next x) (extend tr x));\n assert (composable post (B_R next tr));\n assert (compose (B_R next tr) post == res)\n )\n in\n aux ();\n let aux_composable (frame:t p{composable (A_W next tr) frame})\n : Lemma (composable post frame /\\ (compose (A_W next tr) frame == v ==>\n compose post frame == res))\n = match frame with\n | Nil -> ()\n | B_R q' s' ->\n if is_send (step next x)\n then begin\n assert (ahead A next q' tr s');\n assert (ahead A (step next x) next (extend tr x) tr);\n assert (ahead A (step next x) q' (extend tr x) s')\n end\n else if is_recv (step next x)\n then begin\n assert (ahead A next q' tr s');\n assert (ahead A (step next x) next (extend tr x) tr);\n assert (ahead A (step next x) q' (extend tr x) s');\n lemma_ahead_is_longer A next tr q' s';\n assert (trace_length tr >= trace_length s');\n extend_increase_length tr x;\n assert (trace_length (extend tr x) > trace_length tr)\n end\n else begin\n assert (ahead A next q' tr s');\n assert (ahead A (step next x) next (extend tr x) tr);\n assert (ahead A (step next x) q' (extend tr x) s')\n end\n in\n Classical.forall_intro aux_composable;\n res\n#pop-options\n\n#push-options \"--z3rlimit_factor 4 --ifuel 2 --fuel 1\"\n#restart-solver\nlet write_b_f_aux\n(#p:dprot)\n(#next:dprot{more next /\\ tag_of next = Recv})\n(tr:trace p next)\n(x:msg_t next)\n: FStar.PCM.frame_preserving_upd (pcm p) (B_W next tr)\n (if is_send (step next x)\n then B_R (step next x) (extend tr x)\n else if is_recv (step next x)\n then B_W (step next x) (extend tr x)\n else B_Fin (step next x) (extend tr x))\n= fun v ->\n let post =\n if is_send (step next x)\n then B_R (step next x) (extend tr x)\n else if is_recv (step next x)\n then B_W (step next x) (extend tr x)\n else B_Fin (step next x) (extend tr x)\n in\n match v with\n | V tr' ->\n assert (tr'.to == next /\\ tr'.tr == tr);\n let res = V ({to = (step next x); tr = extend tr x}) in\n let aux () : Lemma (compatible (pcm p) post res)\n = if is_send (step next x) then (\n assert (composable post (A_W (step next x) (extend tr x)));\n assert (compose (A_W (step next x) (extend tr x)) post == res)\n ) else if is_recv (step next x) then (\n assert (composable post (A_R next tr));\n assert (compose (A_R next tr) post == res)\n ) else (\n assert (is_fin (step next x));\n assert (post == B_Fin (step next x) (extend tr x));\n assert (composable post (A_R next tr));\n assert (compose (A_R next tr) post == res)\n )\n in\n aux ();\n let aux_composable (frame:t p{composable (B_W next tr) frame})\n : Lemma (composable post frame /\\ (compose (B_W next tr) frame == v ==>\n compose post frame == res))\n = match frame with\n | Nil -> ()\n | A_R q' s' ->\n if is_send (step next x)\n then begin\n assert (ahead B next q' tr s');\n assert (ahead B (step next x) next (extend tr x) tr);\n assert (ahead B (step next x) q' (extend tr x) s');\n lemma_ahead_is_longer B next tr q' s';\n assert (trace_length tr >= trace_length s');\n extend_increase_length tr x;\n assert (trace_length (extend tr x) > trace_length tr)\n end\n else if is_recv (step next x)\n then begin\n assert (ahead B next q' tr s');\n assert (ahead B (step next x) next (extend tr x) tr);\n assert (ahead B (step next x) q' (extend tr x) s')\n end\n else begin\n assert (ahead B next q' tr s');\n assert (ahead B (step next x) next (extend tr x) tr);\n assert (ahead B (step next x) q' (extend tr x) s')\n end\n in\n Classical.forall_intro aux_composable;\n res\n\nlet lemma_ahead_extend_a (#p:dprot)\n (n:dprot) (n':dprot{more n' /\\ tag_of n' = Send})\n (tr:trace p n) (n_tr:trace p n')\n (x:msg_t n')\n : Lemma (requires ahead A n' n n_tr tr)\n (ensures ahead A (step n' x) n (extend n_tr x) tr)\n (decreases (trace_length n_tr - trace_length tr))\n = let s1 = {to = n; tr = tr} in\n let s2 = {to = n'; tr = n_tr} in\n let last = {to = step n' x; tr = extend n_tr x} in\n let r = next A #p in\n assert (R.closure r s1 s2);\n assert (R.closure r s2 last)\n\nlet lemma_ahead_extend_b (#p:dprot)\n (n:dprot) (n':dprot{more n' /\\ tag_of n' = Recv})\n (tr:trace p n) (n_tr:trace p n')\n (x:msg_t n')\n : Lemma (requires ahead B n' n n_tr tr)\n (ensures ahead B (step n' x) n (extend n_tr x) tr)\n (decreases (trace_length n_tr - trace_length tr))\n = let s1 = {to = n; tr = tr} in\n let s2 = {to = n'; tr = n_tr} in\n let last = {to = step n' x; tr = extend n_tr x} in\n let r = next B #p in\n assert (R.closure r s1 s2);\n assert (R.closure r s2 last)\n\nlet write_a_f_lemma\n (#p:dprot)\n (#next:dprot{more next /\\ tag_of next = Send})\n (tr:trace p next)\n (x:msg_t next)\n (v:t p{(pcm p).refine v})\n (frame:t p)\n : Lemma\n (requires compatible (pcm p) (A_W next tr) v /\\ composable v frame)\n (ensures\n compatible (pcm p) (A_W next tr) v /\\\n composable v frame /\\\n composable (write_a_f_aux #p #next tr x v) frame /\\\n (compatible (pcm p) (A_W next tr) (compose v frame) ==>\n (compose (write_a_f_aux tr x v) frame == write_a_f_aux tr x (compose v frame))))\n = ()\n\nlet write_b_f_lemma\n (#p:dprot)\n (#next:dprot{more next /\\ tag_of next = Recv})\n (tr:trace p next)\n (x:msg_t next)\n (v:t p{(pcm p).refine v})\n (frame:t p)\n : Lemma\n (requires compatible (pcm p) (B_W next tr) v /\\ composable v frame)\n (ensures\n compatible (pcm p) (B_W next tr) v /\\\n composable v frame /\\\n composable (write_b_f_aux #p #next tr x v) frame /\\\n (compatible (pcm p) (B_W next tr) (compose v frame) ==>\n (compose (write_b_f_aux tr x v) frame == write_b_f_aux tr x (compose v frame))))\n = ()\n\n#pop-options\n\nlet write_a_f\n (#p:dprot)\n (#next:dprot{more next /\\ tag_of next = Send})\n (tr:trace p next)\n (x:msg_t next)\n : FStar.PCM.frame_preserving_upd (pcm p) (A_W next tr)\n (if is_send (step next x)\n then A_W (step next x) (extend tr x)\n else if is_recv (step next x)\n then A_R (step next x) (extend tr x)\n else A_Fin (step next x) (extend tr x))\n = Classical.forall_intro_2 (Classical.move_requires_2 (write_a_f_lemma #p #next tr x));\n write_a_f_aux #p #next tr x\n\nlet write_b_f\n (#p:dprot)\n (#next:dprot{more next /\\ tag_of next = Recv})\n (tr:trace p next)\n (x:msg_t next)\n : FStar.PCM.frame_preserving_upd (pcm p) (B_W next tr)\n (if is_send (step next x)\n then B_R (step next x) (extend tr x)\n else if is_recv (step next x)\n then B_W (step next x) (extend tr x)\n else B_Fin (step next x) (extend tr x))\n = Classical.forall_intro_2 (Classical.move_requires_2 (write_b_f_lemma #p #next tr x));\n write_b_f_aux #p #next tr x\n\nlet write_a\n (#p:dprot)\n (r:chan p)\n (#next:dprot{more next /\\ tag_of next = Send})\n (tr:trace p next)\n (x:msg_t next)\n :SteelT unit (pts_to r (A_W next tr)) (fun _ -> endpoint_a r (step next x) (extend tr x))\n = let v : t p =\n if is_send (step next x)\n then A_W (step next x) (extend tr x)\n else if is_recv (step next x)\n then A_R (step next x) (extend tr x)\n else A_Fin (step next x) (extend tr x)\n in\n upd_gen_action r _ v (write_a_f tr x)\n\nlet write_b\n (#p:dprot)\n (r:chan p)\n (#next:dprot{more next /\\ tag_of next = Recv})\n (tr:trace p next)\n (x:msg_t next)\n :SteelT unit (pts_to r (B_W next tr)) (fun _ -> endpoint_b r (step next x) (extend tr x))\n = let v : t p =\n if is_send (step next x)\n then B_R (step next x) (extend tr x)\n else if is_recv (step next x)\n then B_W (step next x) (extend tr x)\n else B_Fin (step next x) (extend tr x)\n in\n upd_gen_action r _ v (write_b_f tr x)\n\nval alloc (#p:dprot) (x:t p{compatible (pcm p) x x /\\ refine x})\n : Steel (chan p) emp (fun r -> pts_to r x) (fun _ -> squash (compatible (pcm p) x x)) (fun _ _ _ -> True)\n\nlet alloc x =\n let r = alloc x in\n rewrite_slprop (PR.pts_to r x) (pts_to r x) (fun _ -> ());\n return r\n\nval split (#p:dprot) (r:chan p) (v_full v0 v1:t p) (_:squash (composable v0 v1)) (_:squash (v_full == compose v0 v1))\n : SteelT unit (pts_to r v_full) (fun _ -> pts_to r v0 `star` pts_to r v1)\n\nlet split r v v0 v1 u1 u2 =\n rewrite_slprop (pts_to r v) (pts_to r (reveal (hide v))) (fun _ -> ());\n split r v v0 v1;\n rewrite_slprop (pts_to r (reveal (hide v0))) (pts_to r v0) (fun _ -> ());\n rewrite_slprop (pts_to r (reveal (hide v1))) (pts_to r v1) (fun _ -> ())\n\nval new_chan (p:dprot)\n : SteelT (chan p) emp\n (fun c -> endpoint_a c p (empty_trace p) `star` endpoint_b c p (empty_trace p))\n\nlet lem #p (x:t p) : Lemma (requires V? x) (ensures compatible (pcm p) x x)\n = assert (composable x Nil);\n assert (compose Nil x == x)\n\nlet new_chan p =\n let v:t p = V ({to = p; tr = empty_trace p}) in\n lem v;\n let r = alloc v in\n split r v\n (if is_send p\n then A_W p (empty_trace p)\n else if is_recv p\n then A_R p (empty_trace p)\n else A_Fin p (empty_trace p))\n (if is_send p\n then B_R p (empty_trace p)\n else if is_recv p\n then B_W p (empty_trace p)\n else B_Fin p (empty_trace p))\n (ahead_refl A p (empty_trace p)) ();\n r\n\nval send_a\n (#p:dprot)\n (c:chan p)\n (#next:dprot{more next /\\ tag_of next = Send})\n (x:msg_t next)\n (tr:trace p next)\n : SteelT unit\n (endpoint_a c next tr)\n (fun _ -> endpoint_a c (step next x) (extend tr x))\n\nlet send_a #p c #next x tr =\n rewrite_slprop (endpoint_a c next tr) (pts_to c (A_W next tr)) (fun _ -> ());\n write_a c tr x\n\nval send_b\n (#p:dprot)\n (c:chan p)\n (#next:dprot{more next /\\ tag_of next = Recv})\n (x:msg_t next)\n (tr:trace p next)\n : SteelT unit\n (endpoint_b c next tr)\n (fun _ -> endpoint_b c (step next x) (extend tr x))\n\nlet send_b #p c #next x tr =\n rewrite_slprop (endpoint_b c next tr) (pts_to c (B_W next tr)) (fun _ -> ());\n write_b c tr x\n\nlet rec recv_a (#p:dprot)\n (c:chan p)\n (next:dprot{more next /\\ tag_of next = Recv})\n (tr:trace p next)\n : SteelT (msg_t next)\n (endpoint_a c next tr)\n (fun x -> endpoint_a c (step next x) (extend tr x))\n =\n rewrite_slprop (endpoint_a c next tr) (pts_to c (A_R next tr)) (fun _ -> ());\n let tr' = get_a_r c next tr in\n if trace_length tr >= trace_length tr'.tr then (\n rewrite_slprop (pts_to c _) (endpoint_a c next tr) (fun _ -> ());\n recv_a c next tr\n )\n else (\n compatible_a_r_v_is_ahead tr tr';\n let x = next_message tr tr'.tr in\n rewrite_slprop\n (pts_to c _)\n (endpoint_a c (step next x) (extend tr x))\n (fun _ -> ());\n return x\n )\n\nlet rec recv_b\n (#p:dprot)\n (c:chan p)\n (next:dprot{more next /\\ tag_of next = Send})\n (tr:trace p next)\n : SteelT (msg_t next)\n (endpoint_b c next tr)\n (fun x -> endpoint_b c (step next x) (extend tr x))\n =\n rewrite_slprop (endpoint_b c next tr) (pts_to c (B_R next tr)) (fun _ -> ());\n let tr' = get_b_r c next tr in\n if trace_length tr >= trace_length tr'.tr then (\n rewrite_slprop\n (pts_to c (if trace_length tr >= trace_length tr'.tr then B_R next tr else extend_node_b_r tr tr'))\n (endpoint_b c next tr)\n (fun _ -> ());\n recv_b c next tr\n ) else (\n compatible_b_r_v_is_ahead tr tr';\n let x = next_message tr tr'.tr in\n noop ();\n rewrite_slprop\n (pts_to c (if trace_length tr >= trace_length tr'.tr then B_R next tr else extend_node_b_r tr tr'))\n (endpoint_b c (step next x) (extend tr x))\n (fun _ -> ());\n return x\n )\n\n\n(***** Towards a send/recv API that abstracts over the party and the concrete trace *****)\n\n#reset-options \"--print_implicits --using_facts_from '* -FStar.Tactics -FStar.Reflection' --fuel 1 --ifuel 1\"\n\nlet endpoint (#p:dprot) (name:party) (c:chan p) (next:dprot) (t:trace p next)\n : vprop\n = match name with\n | A -> endpoint_a c next t\n | B -> endpoint_b c next t\n\n(*\n * A version that abstracts over the party\n *)\nlet send_aux (#p:dprot) (name:party) (c:chan p)\n (#next:send_next_dprot_t name) (x:msg_t next) (t:trace p next)\n : SteelT unit\n (endpoint name c next t)\n (fun _ -> endpoint name c (step next x) (extend t x))\n = if name = A then begin\n rewrite_slprop (endpoint _ _ _ _ )\n (endpoint_a c next t) (fun _ -> ());\n send_a c x t;\n rewrite_slprop (endpoint_a c (step next x) (extend t x))\n (endpoint _ _ _ _) (fun _ -> ())\n end\n else begin\n rewrite_slprop (endpoint _ _ _ _ )\n (endpoint_b c next t) (fun _ -> ());\n send_b c x t;\n rewrite_slprop (endpoint_b c (step next x) (extend t x))\n (endpoint _ _ _ _) (fun _ -> ())\n end\n\nlet recv_aux (#p:dprot) (name:party) (c:chan p)\n (#next:recv_next_dprot_t name) (t:trace p next)\n : SteelT (msg_t next)\n (endpoint name c next t)\n (fun x -> endpoint name c (step next x) (extend t x))\n = if name = A then begin\n rewrite_slprop (endpoint _ _ _ _ )\n (endpoint_a c next t) (fun _ -> ());\n let x = recv_a c next t in\n rewrite_slprop (endpoint_a c (step next x) (extend t x))\n (endpoint _ _ _ _) (fun _ -> ());\n return x\n end\n else begin\n rewrite_slprop (endpoint _ _ _ _ )\n (endpoint_b c next t) (fun _ -> ());\n let x = recv_b c next t in\n rewrite_slprop (endpoint_b c (step next x) (extend t x))\n (endpoint _ _ _ _) (fun _ -> ());\n return x\n end\n\nmodule HR = Steel.HigherReference\nmodule Perm = Steel.FractionalPermission\n\ntype trace_t (p:dprot) = next:dprot & trace p next\n\n(*** Building the top-level API ***)\ntype channel (p:dprot) = chan p & HR.ref (next:dprot & trace p next)\n" }, { "file_name": "FStar.Seq.Sorted.fst", "name": "FStar.Seq.Sorted.intro_sorted_pred", "opens_and_abbrevs": [ { "open": "FStar.Seq" }, { "open": "FStar.Seq" }, { "open": "FStar.Seq" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val intro_sorted_pred\n (#a: eqtype)\n (f: tot_ord a)\n (s: seq a)\n ($g:\n (i: nat{i < length s} -> j: nat{j < length s}\n -> Lemma (requires (i <= j)) (ensures (f (index s i) (index s j)))))\n : Lemma (sorted_pred #a f s)", "source_definition": "let intro_sorted_pred (#a:eqtype) (f:tot_ord a) (s:seq a)\n ($g:(i:nat{i < length s} -> j:nat{j < length s} -> Lemma (requires (i <= j)) (ensures (f (index s i) (index s j)))))\n : Lemma (sorted_pred #a f s)\n= let aux (i j : (k:nat{k < length s})) (p:squash (i <= j)) : GTot (squash (f (index s i) (index s j))) =\n FStar.Squash.give_proof p ;\n g i j ;\n FStar.Squash.get_proof (f (index s i) (index s j))\n in\n FStar.Classical.forall_intro_2 (fun (i j:(k:nat{k < length s})) ->\n FStar.Classical.give_witness (FStar.Classical.arrow_to_impl (aux i j)) <: Lemma (i <= j ==> f (index s i) (index s j)))", "source_range": { "start_line": 43, "start_col": 0, "end_line": 52, "end_col": 123 }, "interleaved": false, "definition": "fun f s $g ->\n (let aux i j p =\n (FStar.Squash.give_proof p;\n g i j;\n FStar.Squash.get_proof (f (FStar.Seq.Base.index s i) (FStar.Seq.Base.index s j)))\n <:\n Prims.GTot (Prims.squash (f (FStar.Seq.Base.index s i) (FStar.Seq.Base.index s j)))\n in\n FStar.Classical.forall_intro_2 (fun i j ->\n FStar.Classical.give_witness (FStar.Classical.arrow_to_impl (aux i j))\n <:\n FStar.Pervasives.Lemma\n (ensures i <= j ==> f (FStar.Seq.Base.index s i) (FStar.Seq.Base.index s j))))\n <:\n FStar.Pervasives.Lemma (ensures FStar.Seq.Sorted.sorted_pred f s)", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "Prims.eqtype", "FStar.Seq.Properties.tot_ord", "FStar.Seq.Base.seq", "Prims.nat", "Prims.b2t", "Prims.op_LessThan", "FStar.Seq.Base.length", "Prims.unit", "Prims.op_LessThanOrEqual", "Prims.squash", "FStar.Seq.Base.index", "Prims.Nil", "FStar.Pervasives.pattern", "FStar.Classical.forall_intro_2", "Prims.l_imp", "FStar.Classical.give_witness", "FStar.Classical.arrow_to_impl", "Prims.l_True", "FStar.Squash.get_proof", "FStar.Squash.give_proof", "FStar.Seq.Sorted.sorted_pred" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "\n f: FStar.Seq.Properties.tot_ord a ->\n s: FStar.Seq.Base.seq a ->\n $g:\n (i: Prims.nat{i < FStar.Seq.Base.length s} -> j: Prims.nat{j < FStar.Seq.Base.length s}\n -> FStar.Pervasives.Lemma (requires i <= j)\n (ensures f (FStar.Seq.Base.index s i) (FStar.Seq.Base.index s j)))\n -> FStar.Pervasives.Lemma (ensures FStar.Seq.Sorted.sorted_pred f s)", "prompt": "let intro_sorted_pred\n (#a: eqtype)\n (f: tot_ord a)\n (s: seq a)\n ($g:\n (i: nat{i < length s} -> j: nat{j < length s}\n -> Lemma (requires (i <= j)) (ensures (f (index s i) (index s j)))))\n : Lemma (sorted_pred #a f s) =\n ", "expected_response": "let aux (i j: (k: nat{k < length s})) (p: squash (i <= j))\n : GTot (squash (f (index s i) (index s j))) =\n FStar.Squash.give_proof p;\n g i j;\n FStar.Squash.get_proof (f (index s i) (index s j))\nin\nFStar.Classical.forall_intro_2 (fun (i: (k: nat{k < length s})) (j: (k: nat{k < length s})) ->\n FStar.Classical.give_witness (FStar.Classical.arrow_to_impl (aux i j))\n <:\n Lemma (i <= j ==> f (index s i) (index s j)))", "source": { "project_name": "FStar", "file_name": "ulib/FStar.Seq.Sorted.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.Seq.Sorted.fst", "checked_file": "dataset/FStar.Seq.Sorted.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Squash.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "sorted_pred", "val sorted_pred_tail :\n #a:eqtype ->\n f:tot_ord a ->\n s:seq a{length s > 0} ->\n Lemma (requires (sorted_pred #a f s)) (ensures (sorted_pred #a f (tail s)))", "let sorted_pred_tail #a f s = ()", "val sorted_pred_sorted_lemma :\n #a:eqtype ->\n f:tot_ord a ->\n s:seq a ->\n Lemma (requires (sorted_pred f s)) (ensures (sorted #a f s == true)) (decreases (length s))", "let rec sorted_pred_sorted_lemma #a f s =\n if length s <= 1 then ()\n else begin\n assert (f (index s 0) (index s 1)) ;\n sorted_pred_tail #a f s;\n sorted_pred_sorted_lemma #a f (tail s)\n end" ], "closest": [ "val sorted_feq (#a:Type)\n (f g : (a -> a -> Tot bool))\n (s:seq a{forall x y. f x y == g x y})\n : Lemma (ensures (sorted f s <==> sorted g s))\nlet sorted_feq = sorted_feq'", "val sorted_feq' (#a: Type) (f g: (a -> a -> Tot bool)) (s: seq a {forall x y. f x y == g x y})\n : Lemma (ensures (sorted f s <==> sorted g s)) (decreases (length s))\nlet rec sorted_feq' (#a:Type)\n (f g : (a -> a -> Tot bool))\n (s:seq a{forall x y. f x y == g x y})\n : Lemma (ensures (sorted f s <==> sorted g s))\n (decreases (length s))\n = if length s <= 1 then ()\n else sorted_feq' f g (tail s)", "val lemma_seq_sortwith_correctness (#a:eqtype) (f:a -> a -> Tot int) (s:seq a)\n :Lemma (requires (total_order a (List.Tot.Base.bool_of_compare f)))\n (ensures (let s' = sortWith f s in sorted (List.Tot.Base.bool_of_compare f) s' /\\ permutation a s s'))\nlet lemma_seq_sortwith_correctness #_ f s\n = let l = seq_to_list s in\n let l' = List.Tot.Base.sortWith f l in\n let s' = seq_of_list l' in\n let cmp = List.Tot.Base.bool_of_compare f in\n\n (* sortedness *)\n List.Tot.Properties.sortWith_sorted f l; //the list returned by List.sortWith is sorted\n lemma_seq_of_list_sorted cmp l'; //seq_of_list preserves sortedness\n\n (* permutation *)\n lemma_seq_to_list_permutation s; //seq_to_list is a permutation\n List.Tot.Properties.sortWith_permutation f l; //List.sortWith is a permutation\n lemma_seq_of_list_permutation l'", "val sort_lseq (#a: eqtype) (#n: _) (f: tot_ord a) (s: lseq a n)\n : s': lseq a n {sorted f s' /\\ permutation a s s'}\nlet sort_lseq (#a:eqtype) #n (f:tot_ord a) (s:lseq a n)\n : s':lseq a n{sorted f s' /\\ permutation a s s'} =\n lemma_seq_sortwith_correctness (L.compare_of_bool f) s;\n let s' = sortWith (L.compare_of_bool f) s in\n perm_len s s';\n sorted_feq f (L.bool_of_compare (L.compare_of_bool f)) s';\n s'", "val intro_has_next (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s) (k:seq_index s{i < k /\\ f (Seq.index s k)})\n : Lemma (has_next f s i /\\\n Some?.v (next_index_opt f s i) <= k)\nlet intro_has_next (#a:Type) (f:a \u2192 bool) (s:seq a) (i:seq_index s) (k:seq_index s{i < k \u2227 f (Seq.index s k)})\n : Lemma (has_next f s i /\\\n Some?.v (next_index_opt f s i) <= k)\n = let n = length s in\n let s' = suffix s (n - (i + 1)) in\n assert (f (index s' (k - (i + 1)))); \n lemma_filter_exists f s';\n lemma_first_index_correct2 f s' (k - (i + 1))", "val sorted_concat_lemma'\n (#a: eqtype)\n (f: (a -> a -> Tot bool){total_order a f})\n (lo: seq a {sorted f lo})\n (pivot: a)\n (hi: seq a {sorted f hi})\n : Lemma (requires (forall y. (mem y lo ==> f y pivot) /\\ (mem y hi ==> f pivot y)))\n (ensures (sorted f (append lo (cons pivot hi))))\n (decreases (length lo))\nlet rec sorted_concat_lemma': #a:eqtype\n -> f:(a -> a -> Tot bool){total_order a f}\n -> lo:seq a{sorted f lo}\n -> pivot:a\n -> hi:seq a{sorted f hi}\n -> Lemma (requires (forall y. (mem y lo ==> f y pivot)\n /\\ (mem y hi ==> f pivot y)))\n (ensures (sorted f (append lo (cons pivot hi))))\n (decreases (length lo))\n= fun #_ f lo pivot hi ->\n if length lo = 0\n then (cut (equal (append lo (cons pivot hi)) (cons pivot hi));\n cut (equal (tail (cons pivot hi)) hi))\n else (sorted_concat_lemma' f (tail lo) pivot hi;\n lemma_append_cons lo (cons pivot hi);\n lemma_tl (head lo) (append (tail lo) (cons pivot hi)))", "val lemma_seq_of_list_sorted (#a:Type) (f:a -> a -> Tot bool) (l:list a)\n :Lemma (requires (List.Tot.Properties.sorted f l)) (ensures (sorted f (seq_of_list l)))\nlet rec lemma_seq_of_list_sorted #a f l\n =\n lemma_seq_of_list_induction l;\n if List.Tot.length l > 1 then begin\n lemma_seq_of_list_induction (List.Tot.Base.tl l);\n lemma_seq_of_list_sorted f (List.Tot.Base.tl l) \n end", "val sorted_concat_lemma: #a:eqtype\n -> f:(a -> a -> Tot bool){total_order a f}\n -> lo:seq a{sorted f lo}\n -> pivot:a\n -> hi:seq a{sorted f hi}\n -> Lemma (requires (forall y. (mem y lo ==> f y pivot)\n /\\ (mem y hi ==> f pivot y)))\n (ensures (sorted f (append lo (cons pivot hi))))\nlet sorted_concat_lemma = sorted_concat_lemma'", "val union_sort_lemma (#a: eqtype) (#f: _) (h: a) (t1 t2: ordset a f)\n : Lemma (requires sorted f (h :: t1) /\\ sorted f (h :: t2))\n (ensures sorted f (h :: (union t1 t2)))\nlet union_sort_lemma (#a:eqtype) #f (h:a) (t1 t2: ordset a f)\n : Lemma (requires sorted f (h::t1) /\\ sorted f (h::t2))\n (ensures sorted f (h::(union t1 t2))) = \n if size t1 = 0 then union_with_empty t2\n else if size t2 = 0 then union_with_empty t1 \n else begin \n union_mem_forall t1 t2;\n set_props t1;\n set_props t2;\n set_props (union t1 t2) \n end", "val lemma_filter_index_inv_map_monotonic (#a:Type) (f:a -> bool) (s: seq a)\n(i:seq_index s) (j: seq_index s {j > i}):\n Lemma (requires (f (index s i) /\\ f (index s j)))\n (ensures (filter_index_inv_map f s i < filter_index_inv_map f s j))\nlet lemma_filter_index_inv_map_monotonic (#a:Type) (f:a -> bool) (s: seq a)\n (i:seq_index s) (j: seq_index s {j > i}):\n Lemma (requires (f (index s i) /\\ f (index s j)))\n (ensures (filter_index_inv_map f s i < filter_index_inv_map f s j)) =\n lemma_filter_len_monotonic f (prefix s j) (i+1)", "val sorted (#a: Type) (f: (a -> a -> Tot bool)) (s: seq a) : Tot bool (decreases (length s))\nlet rec sorted (#a:Type) (f:a -> a -> Tot bool) (s:seq a)\n: Tot bool (decreases (length s))\n= if length s <= 1\n then true\n else let hd = head s in\n f hd (index s 1) && sorted f (tail s)", "val seq_map_i (#a:Type) (#b:Type) (f:int->a->b) (s:seq a) :\n Tot (s':seq b { length s' == length s /\\\n (forall j . {:pattern index s' j} 0 <= j /\\ j < length s ==> index s' j == f j (index s j))\n })\nlet seq_map_i (#a:Type) (#b:Type) (f:int->a->b) (s:seq a) :\n Tot (s':seq b { length s' == length s /\\\n (forall j . {:pattern index s' j} 0 <= j /\\ j < length s ==> index s' j == f j (index s j))\n })\n =\n seq_map_i_indexed f s 0", "val sortWith_sorted: #a:eqtype -> f:(a -> a -> Tot int) -> l:list a ->\n Lemma (requires (total_order #a (bool_of_compare f)))\n (ensures ((sorted (bool_of_compare f) (sortWith f l)) /\\ (forall x. mem x l = mem x (sortWith f l))))\n (decreases (length l))\nlet rec sortWith_sorted #a f l = match l with\n | [] -> ()\n | pivot::tl ->\n let hi, lo = partition (bool_of_compare f pivot) tl in\n partition_length (bool_of_compare f pivot) tl;\n partition_mem_forall (bool_of_compare f pivot) tl;\n partition_mem_p_forall (bool_of_compare f pivot) tl;\n sortWith_sorted f lo;\n sortWith_sorted f hi;\n append_mem_forall (sortWith f lo) (pivot::sortWith f hi);\n append_sorted (bool_of_compare f) (sortWith f lo) (sortWith f hi) pivot", "val lemma_swap_permutes (#a:eqtype) (s:seq a) (i:nat{i count x s = count x (swap s i j))\n (lemma_swap_permutes_aux s i j)", "val sort: #a:eqtype -> f:(a -> a -> Tot bool){total_order a f}\n -> s1:seq a\n -> Tot (s2:seq a{sorted f s2 /\\ permutation a s1 s2})\n (decreases (length s1))\nlet rec sort #a f s =\n if length s <= 1 then s\n else let lo, hi = partition f s 0 (length s - 1) in\n let pivot = head hi in\n\n let hi_tl = tail hi in\n let l = sort f lo in\n let h = sort f hi_tl in\n\n let result = Seq.append l (cons pivot h) in\n\n sorted_concat_lemma f l pivot h;\n lemma_append_count l (cons pivot h);\n cons_perm h hi;\n\n result", "val lemma_filter_index_map_monotonic (#a:Type) (f:a -> bool) (s:seq a)\n(i:seq_index (filter f s))(j:seq_index (filter f s){j > i}):\nLemma (filter_index_map f s i < filter_index_map f s j)\nlet lemma_filter_index_map_monotonic (#a:Type) (f:a -> bool) (s:seq a)\n (i:seq_index (filter f s))(j:seq_index (filter f s){j > i}):\n Lemma (filter_index_map f s i < filter_index_map f s j) =\n lemma_proj_monotonic (filter f s) s (filter_is_proj_prf f s) i j", "val lemma_first_index_correct2 (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s):\n Lemma (requires (f (index s i)))\n (ensures (exists_sat_elems f s /\\ first_index f s <= i))\nlet lemma_first_index_correct2 (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s):\n Lemma (requires (f (index s i)))\n (ensures (exists_sat_elems f s /\\ first_index f s <= i)) =\n lemma_last_index_correct2 f s i;\n let fi = first_index f s in\n if fi > i then\n lemma_first_index_correct1 f s i\n else ()", "val lemma_seq_refine_equal_aux (#a: Type) (f: (a -> bool)) (s: seq a {all f s}) (i: seq_index s)\n : Lemma (requires True) (ensures (index (seq_refine f s) i == index s i)) (decreases (length s))\nlet rec lemma_seq_refine_equal_aux (#a:Type) (f:a->bool) (s:seq a{all f s}) (i:seq_index s):\n Lemma (requires True)\n (ensures (index (seq_refine f s) i == index s i))\n (decreases (length s)) =\n let n = length s in\n if n = 0 then ()\n else if i = n - 1 then ()\n else lemma_seq_refine_equal_aux f (prefix s (n - 1)) i", "val lemma_last_index_prefix (#a:Type) (f:a -> bool) (s:seq a) (i:nat{i <= length s}):\n Lemma (requires (exists_sat_elems f s /\\ i > last_index f s))\n (ensures (exists_sat_elems f (prefix s i) /\\\n last_index f s = last_index f (prefix s i)))\nlet lemma_last_index_prefix (#a:Type) (f:a -> bool) (s:seq a) (i:nat{i <= length s}):\n Lemma (requires (exists_sat_elems f s /\\ i > last_index f s))\n (ensures (exists_sat_elems f (prefix s i) /\\\n last_index f s = last_index f (prefix s i))) =\n let li = last_index f s in\n let s' = prefix s i in\n lemma_prefix_index s i li;\n assert(f (index s' li));\n assert(li < length s');\n let r' = filter_index_inv_map f s' li in\n assert(exists_sat_elems f s');\n let li' = last_index f s' in\n if li < li' then (\n lemma_prefix_index s i li';\n lemma_last_index_correct1 f s li'\n )\n else if li > li' then\n lemma_last_index_correct1 f s' li\n else ()", "val lemma_ordering_lo_snoc: #a:eqtype -> f:tot_ord a -> s:seq a -> i:nat -> j:nat{i <= j && j < length s} -> pv:a\n -> Lemma (requires ((forall y. mem y (slice s i j) ==> f y pv) /\\ f (index s j) pv))\n (ensures ((forall y. mem y (slice s i (j + 1)) ==> f y pv)))\nlet lemma_ordering_lo_snoc #_ f s i j pv =\n cut (equal (slice s i (j + 1)) (append (slice s i j) (create 1 (index s j))));\n lemma_mem_append (slice s i j) (create 1 (index s j))", "val lemma_seq_refine_equal (#a:Type) (f:a->bool) (s:seq a{all f s}) (i:seq_index s):\nLemma (requires True)\n (ensures (index (seq_refine f s) i == index s i))\n [SMTPat (index (seq_refine f s) i)]\nlet lemma_seq_refine_equal = lemma_seq_refine_equal_aux", "val as_list (#a:eqtype) (#f:cmp a) (s:ordset a f) : Tot (l:list a{\n sorted f l /\\\n (forall x. (List.Tot.mem x l = mem x s)) \n})\nlet as_list (#a:eqtype) (#f:cmp a) (s:ordset a f) : Tot (l:list a{sorted f l}) = s", "val insertionsort'_sorted: #a:eqtype -> l:(list a) -> k:(a -> Tot int) ->\n Lemma(ensures(sorted (insertionsort' l k) k))\nlet rec insertionsort'_sorted #a l k =\n match l with\n | []\n | [_] -> ()\n | hd::tl ->\n insertionsort'_sorted tl k;\n insert'_sorted hd (insertionsort' tl k) k", "val introduce_is_permutation:\n #a: Type ->\n s0: seq a ->\n s1: seq a ->\n f: index_fun s0 ->\n squash (Seq.length s0 == Seq.length s1) ->\n squash (forall x y. x <> y ==> f x <> f y) ->\n squash (forall (i: nat{i < Seq.length s0}). Seq.index s0 i == Seq.index s1 (f i))\n -> Lemma (ensures is_permutation s0 s1 f)\nlet introduce_is_permutation (#a:Type) (s0:seq a) (s1:seq a)\n (f:index_fun s0)\n (_:squash (Seq.length s0 == Seq.length s1))\n (_:squash (forall x y. x <> y ==> f x <> f y))\n (_:squash (forall (i:nat{i < Seq.length s0}). Seq.index s0 i == Seq.index s1 (f i)))\n : Lemma\n (ensures\n is_permutation s0 s1 f)\n = reveal_is_permutation_nopats s0 s1 f", "val lemma_last_index_correct2 (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s):\n Lemma (requires (f (index s i)))\n (ensures (exists_sat_elems f s /\\ last_index f s >= i))\nlet lemma_last_index_correct2 (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s):\n Lemma (requires (f (index s i)))\n (ensures (exists_sat_elems f s /\\ last_index f s >= i)) =\n let n = length s in\n let ri = filter_index_inv_map f s i in\n assert (exists_sat_elems f s);\n let j = last_index f s in\n if j < i then\n lemma_filter_index_inv_map_monotonic f s j i\n else ()", "val init_next (#a: Type) (s: S.seq a) (f: (i: nat{i < S.length s} -> a)) (i: nat)\n : Lemma\n (requires (i < S.length s /\\ S.equal (S.slice s 0 i) (S.init i f) /\\ S.index s i == f i))\n (ensures (S.equal (S.slice s 0 (i + 1)) (S.init (i + 1) f)))\nlet init_next (#a: Type) (s: S.seq a) (f: (i:nat { i < S.length s }) -> a) (i: nat):\n Lemma\n (requires (\n i < S.length s /\\\n S.equal (S.slice s 0 i) (S.init i f) /\\\n S.index s i == f i))\n (ensures (S.equal (S.slice s 0 (i + 1)) (S.init (i + 1) f)))\n=\n lemma_slice_ijk s 0 i (i + 1)", "val lemma_exists_sat_elems_exists (#a:Type) (f:a -> bool) (s:seq a)\n : Lemma (exists_sat_elems f s <==> (exists (i:seq_index s). f (Seq.index s i)))\nlet lemma_exists_sat_elems_exists (#a:Type) (f:a \u2192 bool) (s:seq a)\n : Lemma (exists_sat_elems f s <==> (\u2203 (i:seq_index s). f (Seq.index s i)))\n = if length (filter f s) = 0 \n then lemma_filter_all_not f s", "val lemma_filter_len_monotonic (#a: Type) (f: (a -> bool)) (s: seq a) (i: nat{i <= length s})\n : Lemma (requires (True))\n (ensures (length (filter f s) >= length (filter f (prefix s i))))\n (decreases (length s))\nlet rec lemma_filter_len_monotonic (#a:Type) (f:a -> bool) (s:seq a) (i:nat{i <= length s}):\n Lemma (requires (True))\n (ensures (length (filter f s) >= length (filter f (prefix s i))))\n (decreases (length s)) =\n let n = length s in\n if n = 0 then ()\n else if i = n then () // s == prefix s i\n else (\n let s' = prefix s (n - 1) in\n lemma_len_slice s 0 (n - 1);\n lemma_filter_len_monotonic f s' i\n )", "val lemma_ordering_hi_cons: #a:eqtype -> f:tot_ord a -> s:seq a -> back:nat -> len:nat{back < len && len <= length s} -> pv:a\n -> Lemma (requires ((forall y. mem y (slice s (back + 1) len) ==> f pv y) /\\ f pv (index s back)))\n (ensures ((forall y. mem y (slice s back len) ==> f pv y)))\nlet lemma_ordering_hi_cons #_ f s back len pv =\n cut (equal (slice s back len) (append (create 1 (index s back)) (slice s (back + 1) len)));\n lemma_mem_append (create 1 (index s back)) (slice s (back + 1) len)", "val lemma_first_index_correct1 (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s):\n Lemma (requires (exists_sat_elems f s /\\ i < first_index f s))\n (ensures (not (f (index s i))))\nlet lemma_first_index_correct1 (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s):\n Lemma (requires (exists_sat_elems f s /\\ i < first_index f s))\n (ensures (not (f (index s i)))) =\n let fi = first_index f s in\n if f (index s i) then\n lemma_filter_index_inv_map_monotonic f s i fi\n else ()", "val sort: #a:eqtype -> f:tot_ord a -> i:nat -> j:nat{i <= j} -> x:array a\n -> ST unit\n (requires (fun h -> Array.contains h x /\\ j <= length (Array.sel h x)))\n (ensures (fun h0 u h1 -> (modifies (Array.only x) h0 h1\n /\\ j <= length (Array.sel h0 x) (* carrying this along from the requires clause *)\n /\\ Array.contains h1 x (* the array is still in the heap *)\n /\\ (length (Array.sel h0 x) = length (Array.sel h1 x)) (* its length has not changed *)\n /\\ sorted f (slice (Array.sel h1 x) i j) (* it is sorted between [i, j) *)\n /\\ (Array.sel h1 x == splice (Array.sel h0 x) i (Array.sel h1 x) j) (* the rest of it is unchanged *)\n /\\ permutation a (slice (Array.sel h0 x) i j) (slice (Array.sel h1 x) i j))))\nlet rec sort #a f i j x =\n let h0 = ST.get () in\n if i=j\n then splice_refl (Array.sel h0 x) i j\n else begin\n let pivot = partition f i j i (j - 1) x in\n\n(* ghost *) let h1 = get() in\n\n sort f i pivot x;\n\n(* ghost *) let h2 = get() in\n\t let _ =\n(* ghost *) lemma_seq_frame_hi (Array.sel h2 x) (Array.sel h1 x) i pivot pivot j;\n(* ghost *) lemma_tail_slice (Array.sel h2 x) pivot j in\n\n sort f (pivot + 1) j x;\n\n(* ghost *) let h3 = get() in\n(* ghost *) lemma_seq_frame_lo (Array.sel h3 x) (Array.sel h2 x) i pivot (pivot + 1) j;\n(* ghost *) let lo = slice (Array.sel h3 x) i pivot in\n(* ghost *) let hi = slice (Array.sel h3 x) (pivot + 1) j in\n(* ghost *) let pv = index (Array.sel h1 x) pivot in\n(* ghost *) Seq.sorted_concat_lemma f lo pv hi;\n(* ghost *) lemma_slice_cons_pv (Array.sel h3 x) i pivot j pv;\n\n(* ghost *) lemma_weaken_frame_right (Array.sel h2 x) (Array.sel h1 x) i pivot j;\n(* ghost *) lemma_weaken_frame_left (Array.sel h3 x) (Array.sel h2 x) i (pivot + 1) j;\n(* ghost *) lemma_trans_frame (Array.sel h3 x) (Array.sel h2 x) (Array.sel h1 x) i j;\n(* ghost *) lemma_trans_frame (Array.sel h3 x) (Array.sel h1 x) (Array.sel h0 x) i j;\n\n(* ghost *) lemma_weaken_perm_right (Array.sel h2 x) (Array.sel h1 x) i pivot j;\n(* ghost *) lemma_weaken_perm_left (Array.sel h3 x) (Array.sel h2 x) i (pivot + 1) j\n end", "val lemma_last_index_correct1 (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s):\n Lemma (requires (exists_sat_elems f s /\\ i > last_index f s))\n (ensures (not (f (index s i))))\nlet lemma_last_index_correct1 (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s):\n Lemma (requires (exists_sat_elems f s /\\ i > last_index f s))\n (ensures (not (f (index s i)))) =\n let j = last_index f s in\n if f (index s i) then\n lemma_filter_index_inv_map_monotonic f s j i\n else ()", "val sorted_tl: #a:eqtype -> l:list a{Cons? l} -> k:(a -> Tot int) ->\n Lemma (requires (sorted l k))\n (ensures (sorted (Cons?.tl l) k))\nlet rec sorted_tl #a l k =\n match l with\n | [_] -> ()\n | a::b::xs -> sorted_tl (b::xs) k", "val map_seq_index (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a) (i:nat{i < Seq.length s})\n : Lemma (ensures (map_seq_len f s; Seq.index (map_seq f s) i == f (Seq.index s i)))\nlet rec map_seq_index #a #b f s i\n : Lemma (ensures (map_seq_len f s; Seq.index (map_seq f s) i == f (Seq.index s i))) (decreases Seq.length s)\n = map_seq_len f s;\n if Seq.length s = 0\n then ()\n else if i = 0\n then ()\n else map_seq_index f (tail s) (i-1)", "val intro_of_list'' (#a: Type) (i: nat) (s: seq a) (l: list a)\n : Lemma (requires (List.Tot.length l + i = length s /\\ i <= length s /\\ explode_and i s l))\n (ensures (equal (seq_of_list l) (slice s i (length s))))\n (decreases (List.Tot.length l))\nlet rec intro_of_list'': #a:Type ->\n i:nat ->\n s:seq a ->\n l:list a ->\n Lemma\n (requires (\n List.Tot.length l + i = length s /\\\n i <= length s /\\\n explode_and i s l))\n (ensures (\n equal (seq_of_list l) (slice s i (length s))))\n (decreases (\n List.Tot.length l))\n= fun #_ i s l ->\n lemma_seq_of_list_induction l;\n match l with\n | [] -> ()\n | hd :: tl -> intro_of_list'' (i + 1) s tl", "val seq_map_i_indexed (#a:Type) (#b:Type) (f:int->a->b) (s:seq a) (i:int) :\n Tot (s':seq b { length s' == length s /\\\n (forall j . {:pattern index s' j} 0 <= j /\\ j < length s ==> index s' j == f (i + j) (index s j))\n })\nlet rec seq_map_i_indexed (#a:Type) (#b:Type) (f:int->a->b) (s:seq a) (i:int) :\n Tot (s':seq b { length s' == length s /\\\n (forall j . {:pattern index s' j} 0 <= j /\\ j < length s ==> index s' j == f (i + j) (index s j))\n })\n (decreases %[(length s)])\n =\n if length s = 0 then empty\n else\n cons (f i (head s)) (seq_map_i_indexed f (tail s) (i + 1))", "val prev_index_opt (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s):\n Tot (option (j:seq_index s{j < i && f (index s j)}))\nlet prev_index_opt (#a:Type) (f:a \u2192 bool) (s:seq a) (i:seq_index s):\n Tot (option (j:seq_index s{j < i && f (index s j)})) =\n let s' = prefix s i in\n let fs' = filter f s' in\n if length fs' = 0 then None\n else Some (last_index f s')", "val lemma_eq_intro_explicit\n (#a: Type)\n (s1: S.seq a)\n (s2: S.seq a {S.length s2 == S.length s1})\n (pf: (i: nat{i < S.length s1} -> Lemma (S.index s1 i == S.index s2 i)))\n : Lemma (S.equal s1 s2)\nlet lemma_eq_intro_explicit (#a : Type) (s1 : S.seq a) (s2 : S.seq a{S.length s2 == S.length s1})\n (pf : ((i:nat{i < S.length s1}) -> Lemma (S.index s1 i == S.index s2 i)))\n : Lemma (S.equal s1 s2)\n = Classical.forall_intro pf;\n S.lemma_eq_intro s1 s2", "val intro_of_list': #a:Type ->\n i:nat ->\n s:seq a ->\n l:list a ->\n Lemma\n (requires (\n List.Tot.length l + i = length s /\\\n i <= length s /\\\n explode_and i s l))\n (ensures (\n equal (seq_of_list l) (slice s i (length s))))\nlet intro_of_list' = intro_of_list''", "val last_index_opt_elim (#a:Type) (f:a \u2192 bool) (s:seq a)\n : Lemma (match last_index_opt f s with\n | None \u2192 \u2200 (i:seq_index s). not (f (Seq.index s i))\n | Some i \u2192 f (Seq.index s i) \u2227 (\u2200 (j:seq_index s). j > i \u27f9 not (f (Seq.index s j))))\nlet last_index_opt_elim (#a:Type) (f:a \u2192 bool) (s:seq a)\n : Lemma (match last_index_opt f s with\n | None \u2192 \u2200 (i:seq_index s). not (f (Seq.index s i))\n | Some i \u2192 f (Seq.index s i) \u2227 (\u2200 (j:seq_index s). j > i \u27f9 not (f (Seq.index s j)))) =\n match last_index_opt f s with\n | None \u2192 lemma_filter_all_not f s\n | Some i \u2192 assert (f (index s i)); \n let aux (j:seq_index s{j > i}): \n Lemma (not (f (index s j))) = \n lemma_last_index_correct1 f s j in \n FStar.Classical.forall_intro aux", "val list_sorted_order_elim\n (#t: Type)\n (order: (t -> t -> bool))\n (l0: list t)\n (a1: t)\n (l1: list t)\n (a2: t)\n (l2: list t)\n : Lemma\n (requires\n ((forall x y z. (order x y /\\ order y z) ==> order x z) /\\\n List.Tot.sorted order (l0 `List.Tot.append` (a1 :: (l1 `List.Tot.append` (a2 :: l2))))))\n (ensures (order a1 a2 == true))\n (decreases (List.Tot.length l0 + List.Tot.length l1))\nlet rec list_sorted_order_elim\n (#t: Type)\n (order: t -> t -> bool)\n (l0: list t)\n (a1: t)\n (l1: list t)\n (a2: t)\n (l2: list t)\n: Lemma\n (requires (\n (forall x y z . (order x y /\\ order y z) ==> order x z) /\\\n List.Tot.sorted order (l0 `List.Tot.append` (a1 :: (l1 `List.Tot.append` (a2 :: l2))))\n ))\n (ensures (order a1 a2 == true))\n (decreases (List.Tot.length l0 + List.Tot.length l1))\n= match l0 with\n | [] ->\n begin match l1 with\n | [] -> ()\n | a1' :: l1' ->\n list_sorted_order_elim order [] a1' l1' a2 l2 // and transitivity\n end\n | a0 :: l0' ->\n list_sorted_order_elim order l0' a1 l1 a2 l2", "val lemma_rev_seq (#a: Type) (s: S.seq a) (i: nat)\n : Lemma (requires i < S.length s)\n (ensures\n S.length (rev_seq s) = S.length s /\\ S.index s i == S.index (rev_seq s) (S.length s - 1 - i)\n )\n (decreases (i))\nlet rec lemma_rev_seq (#a:Type) (s:S.seq a) (i:nat) : Lemma\n (requires i < S.length s)\n (ensures\n S.length (rev_seq s) = S.length s /\\\n S.index s i == S.index (rev_seq s) (S.length s-1-i))\n (decreases (i))=\n if S.length s = 0 then ()\n else if i = 0 then ()\n else lemma_rev_seq (S.slice s 1 (S.length s)) (i-1)", "val lemma_filter_prefix_comm (#a:Type) (f:a->bool) (s: seq a) (i:seq_index s):\n Lemma (requires (f (index s i)))\n (ensures (filter f (prefix s i) == prefix (filter f s) (filter_index_inv_map f s i)))\nlet lemma_filter_prefix_comm (#a:Type) (f:a->bool) (s: seq a) (i:seq_index s):\n Lemma (requires (f (index s i)))\n (ensures (filter f (prefix s i) == prefix (filter f s) (filter_index_inv_map f s i))) =\n lemma_filter_prefix f s (prefix s i)", "val fold (#a:eqtype) (#acc:Type) (#f:cmp a) (g:acc -> a -> acc) (init:acc) (s:ordset a f)\n : Tot acc\nlet fold #a #acc #f g init s = List.Tot.fold_left g init s", "val lemma_filter_unique (#a:Type) (f:a->bool) (s: seq a) (i:seq_index s)\n: Lemma (requires (f (index s i) /\\ (forall j. j <> i ==> not (f (index s j)))))\n (ensures (filter f s == create 1 (index s i)))\nlet lemma_filter_unique (#a:Type) (f:a->bool) (s: seq a) (i:seq_index s)\n : Lemma (requires (f (index s i) /\\ (forall j. j <> i ==> not (f (index s j)))))\n (ensures (filter f s == create 1 (index s i)))\n = lemma_filter_unique_aux f s i", "val lemma_swap_permutes_aux_frag_eq: #a:Type -> s:seq a -> i:nat{i j:nat{i <= j && j i':nat -> j':nat{i' <= j' /\\ j'<=length s /\\\n (j < i' //high slice\n \\/ j' <= i //low slice\n \\/ (i < i' /\\ j' <= j)) //mid slice\n }\n -> Lemma (ensures (slice s i' j' == slice (swap s i j) i' j'\n /\\ slice s i (i + 1) == slice (swap s i j) j (j + 1)\n /\\ slice s j (j + 1) == slice (swap s i j) i (i + 1)))\nlet lemma_swap_permutes_aux_frag_eq #a s i j i' j' =\n cut (equal (slice s i' j') (slice (swap s i j) i' j'));\n cut (equal (slice s i (i + 1)) (slice (swap s i j) j (j + 1)));\n cut (equal (slice s j (j + 1)) (slice (swap s i j) i (i + 1)))", "val sorted (#a: eqtype) (f: cmp a) (l: list (a & pos)) : Type0\nlet rec sorted (#a:eqtype) (f:cmp a) (l:list (a & pos)) : Type0 =\n match l with\n | [] -> True\n | [_] -> True\n | (x, _)::(y, card_y)::tl ->\n f x y /\\\n x =!= y /\\\n sorted f ((y, card_y)::tl)", "val fidx2idx_monotonic (#gs:_)\n (f: idxfn_t gs bool)\n (s: seq_t gs)\n (i1 i2: (i:nat{i < flen f s}))\n : Lemma (ensures ((i1 < i2 ==> fidx2idx f s i1 < fidx2idx f s i2) /\\\n (i2 < i1 ==> fidx2idx f s i1 > fidx2idx f s i2)))\nlet fidx2idx_monotonic (#gs:_)\n (f: idxfn_t gs bool)\n (s: seq_t gs)\n (i1 i2: (i:nat{i < flen f s}))\n : Lemma (ensures ((i1 < i2 ==> fidx2idx f s i1 < fidx2idx f s i2) /\\\n (i2 < i1 ==> fidx2idx f s i1 > fidx2idx f s i2)))\n = idx2fidx_monotonic f s (fidx2idx f s i1) (fidx2idx f s i2)", "val reveal_is_permutation (#a:Type) (s0 s1:seq a) (f:index_fun s0)\n : Lemma (is_permutation s0 s1 f <==>\n (* lengths of the sequences are the same *)\n Seq.length s0 == Seq.length s1 /\\\n (* f is injective *)\n (forall x y. {:pattern f x; f y}\n x <> y ==> f x <> f y) /\\\n (* and f relates equal items in s0 and s1 *)\n (forall (i:nat{i < Seq.length s0}).{:pattern (Seq.index s1 (f i))}\n Seq.index s0 i == Seq.index s1 (f i)))\nlet reveal_is_permutation #a (s0 s1:seq a) (f:index_fun s0)\n = reveal_opaque (`%is_permutation) (is_permutation s0 s1 f)", "val intro_of_list (#a: Type) (s: seq a) (l: list a):\n Lemma\n (requires (\n List.Tot.length l = length s /\\\n pointwise_and s l))\n (ensures (\n s == seq_of_list l))\nlet intro_of_list #_ s l = intro_of_list' 0 s l", "val reveal_is_permutation (#a:Type) (s0 s1:seq a) (f:index_fun s0)\n : Lemma (is_permutation s0 s1 f <==>\n (* lengths of the sequences are the same *)\n S.length s0 == S.length s1 /\\\n (* f is injective *)\n (forall x y. {:pattern f x; f y}\n x <> y ==> f x <> f y) /\\\n (* and f relates equal items in s0 and s1 *)\n (forall (i:nat{i < S.length s0}).{:pattern (S.index s1 (f i))}\n S.index s0 i == S.index s1 (f i)))\nlet reveal_is_permutation #a (s0 s1:seq a) (f:index_fun s0)\n = reveal_opaque (`%is_permutation) (is_permutation s0 s1 f)", "val sorted (#a: eqtype) (f: cmp a) (l: list a) : Tot bool\nlet rec sorted (#a:eqtype) (f:cmp a) (l:list a) : Tot bool =\n match l with\n | [] -> true\n | x::[] -> true\n | x::y::tl -> f x y && x <> y && sorted f (y::tl)", "val lemma_filter_unique_aux (#a: Type) (f: (a -> bool)) (s: seq a) (i: seq_index s)\n : Lemma (requires (f (index s i) /\\ (forall j. j <> i ==> not (f (index s j)))))\n (ensures (filter f s == create 1 (index s i)))\n (decreases (length s))\nlet rec lemma_filter_unique_aux (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s)\n : Lemma (requires (f (index s i) /\\ (forall j. j <> i ==> not (f (index s j)))))\n (ensures (filter f s == create 1 (index s i)))\n (decreases (length s)) =\n let n = length s in\n if n = 0 then ()\n else let e = index s (n - 1) in\n let s' = prefix s (n - 1) in\n if i < n - 1 \n then lemma_filter_unique_aux f s' i\n else (\n lemma_filter_all_not_inv f s';\n assert (equal (append1 empty e) (create 1 (index s i)))\n )", "val append_sorted: #a:eqtype\n -> f:(a -> a -> Tot bool)\n -> l1:list a{sorted f l1}\n -> l2:list a{sorted f l2}\n -> pivot:a\n -> Lemma (requires (total_order #a f\n /\\ (forall y. mem y l1 ==> not(f pivot y))\n /\\ (forall y. mem y l2 ==> f pivot y)))\n (ensures (sorted f (l1@(pivot::l2))))\n [SMTPat (sorted f (l1@(pivot::l2)))]\nlet rec append_sorted #a f l1 l2 pivot = match l1 with\n | [] -> ()\n | hd::tl -> append_sorted f tl l2 pivot", "val elem_precedes (#a: Type u#a) (s: t a) (i: nat{i < length s}) : Lemma (index s i << s)\nlet elem_precedes (#a:Type u#a) (s:t a) (i : nat{i < length s})\n : Lemma (index s i << s)\n = FStar.List.Tot.(\n to_list_precedes s;\n let l = to_list s in\n assert (memP (index l i) l);\n memP_precedes (index l i) l\n )", "val lemma_filter_prefix_comm2 (#a:Type) (f:a->bool) (s: seq a) (i:seq_index s):\n Lemma (requires (f (index s i)))\n (ensures (filter f (prefix s (i+1)) == prefix (filter f s) (1 + (filter_index_inv_map f s i))))\nlet lemma_filter_prefix_comm2 (#a:Type) (f:a->bool) (s: seq a) (i:seq_index s):\n Lemma (requires (f (index s i)))\n (ensures (filter f (prefix s (i+1)) == prefix (filter f s) (1 + (filter_index_inv_map f s i)))) = \n rank_increases_by_atmost_one f s i;\n lemma_filter_prefix f s (prefix s (i + 1))", "val i_seq_union_all_eq (#a: eqtype) (f: cmp a) (s: sseq a)\n : Lemma\n (seq2mset (i_seq (some_interleaving s)) == union_all #a #f (Zeta.SeqAux.map (seq2mset #a #f) s))\nlet i_seq_union_all_eq (#a:eqtype) (f:cmp a) (s: sseq a)\n : Lemma (seq2mset (i_seq (some_interleaving s)) == union_all #a #f (Zeta.SeqAux.map (seq2mset #a #f) s))\n = let lhs = seq2mset #a #f (i_seq (some_interleaving s)) in\n let rhs = union_all (Zeta.SeqAux.map (seq2mset #a #f) s) in\n introduce forall x. mem x lhs == mem x rhs\n with (\n Zeta.Interleave.i_seq_count #a s x;\n union_all_sum_count #a #f s x;\n seq2mset_mem #a #f (i_seq (some_interleaving s)) x\n );\n eq_intro lhs rhs;\n eq_elim lhs rhs", "val lemma_filter_correct1_aux (#a: Type) (f: (a -> bool)) (s: seq a) (i: seq_index (filter f s))\n : Lemma (requires (True)) (ensures (f (index (filter f s) i) = true)) (decreases (length s))\nlet rec lemma_filter_correct1_aux (#a: Type) (f:a -> bool) (s:seq a) (i:seq_index (filter f s)):\n Lemma (requires (True))\n (ensures (f (index (filter f s) i) = true))\n (decreases (length s)) =\n let n = length s in\n let fs = filter f s in\n if n = 0 then ()\n else\n let s' = prefix s (n - 1) in\n let e = index s (n - 1) in\n if f e then\n if i = (length fs) - 1 then ()\n else\n lemma_filter_correct1_aux f s' i\n else\n lemma_filter_correct1_aux f s' i", "val slice_seq_map_commute (#a #b:Type) (f:a -> b) (s:seq a) (i:nat) (j:nat{ i <= j /\\ j <= length s }) :\n Lemma (slice (seq_map f s) i j == seq_map f (slice s i j))\nlet slice_seq_map_commute (#a #b:Type) (f:a -> b) (s:seq a) (i:nat) (j:nat{ i <= j /\\ j <= length s }) :\n Lemma (slice (seq_map f s) i j == seq_map f (slice s i j))\n =\n assert (equal (slice (seq_map f s) i j) (seq_map f (slice s i j)));\n ()", "val lemma_last_index_extensionality (#a:Type) (f1 f2:a -> bool) (s: seq a{exists_sat_elems f1 s}):\n Lemma (requires (ext_pred f1 f2))\n (ensures (exists_sat_elems f2 s /\\\n last_index f1 s = last_index f2 s))\nlet lemma_last_index_extensionality (#a:Type) (f1 f2:a -> bool) (s: seq a{exists_sat_elems f1 s}):\n Lemma (requires (ext_pred f1 f2))\n (ensures (exists_sat_elems f2 s /\\\n last_index f1 s = last_index f2 s)) =\n lemma_exists_sat_elems_extensionality f1 f2 s;\n let i1 = last_index f1 s in\n let i2 = last_index f2 s in\n lemma_last_index_correct2 f2 s i1;\n lemma_last_index_correct2 f1 s i2", "val lemma_swap_permutes_aux: #a:eqtype -> s:seq a -> i:nat{i j:nat{i <= j && j x:a -> Lemma\n (requires True)\n (ensures (count x s = count x (swap s i j)))\nlet lemma_swap_permutes_aux #_ s i j x =\n if j=i\n then cut (equal (swap s i j) s)\n else begin\n let s5 = split_5 s i j in\n let frag_lo, frag_i, frag_mid, frag_j, frag_hi =\n index s5 0, index s5 1, index s5 2, index s5 3, index s5 4 in\n lemma_append_count_aux x frag_lo (append frag_i (append frag_mid (append frag_j frag_hi)));\n lemma_append_count_aux x frag_i (append frag_mid (append frag_j frag_hi));\n lemma_append_count_aux x frag_mid (append frag_j frag_hi);\n lemma_append_count_aux x frag_j frag_hi;\n\n let s' = swap s i j in\n let s5' = split_5 s' i j in\n let frag_lo', frag_j', frag_mid', frag_i', frag_hi' =\n index s5' 0, index s5' 1, index s5' 2, index s5' 3, index s5' 4 in\n\n lemma_swap_permutes_aux_frag_eq s i j 0 i;\n lemma_swap_permutes_aux_frag_eq s i j (i + 1) j;\n lemma_swap_permutes_aux_frag_eq s i j (j + 1) (length s);\n\n lemma_append_count_aux x frag_lo (append frag_j (append frag_mid (append frag_i frag_hi)));\n lemma_append_count_aux x frag_j (append frag_mid (append frag_i frag_hi));\n lemma_append_count_aux x frag_mid (append frag_i frag_hi);\n lemma_append_count_aux x frag_i frag_hi\n end", "val insert'_sorted: #a:eqtype -> x:a -> l:(list a) -> k:(a -> Tot int) ->\n Lemma (requires (sorted l k))\n (ensures (sorted (insert' x l k) k))\nlet rec insert'_sorted #a x l k =\n match l with\n | [] | [_] -> ()\n | hd::tl ->\n if k x <= k hd then ()\n else insert'_sorted x tl k", "val filter_eq_sorted_lt: #a:eqtype -> l:list a{Cons? l} -> k:(a -> Tot int) ->\n Lemma (requires (sorted l k))\n (ensures (forall x. (x < k (hd l)) ==> (filter_eq x l k = [])))\nlet filter_eq_sorted_lt #a l k =\n sorted_lt l k;\n filter_eq_not_contains l k", "val lemma_slice_cons: #a:eqtype -> s:seq a -> i:nat -> j:nat{i < j && j <= length s}\n -> Lemma (ensures (forall x. mem x (slice s i j) <==> (x = index s i || mem x (slice s (i + 1) j))))\nlet lemma_slice_cons #_ s i j =\n cut (equal (slice s i j) (append (create 1 (index s i)) (slice s (i + 1) j)));\n lemma_mem_append (create 1 (index s i)) (slice s (i + 1) j)", "val eq_intro_aux (#a: eqtype) (#f: cmp a) (s1 s2: mset a f)\n : Lemma (requires forall (x: a). mem x s1 == mem x s2) (ensures s1 == s2)\nlet eq_intro_aux (#a:eqtype) (#f:cmp a) (s1 s2:mset a f)\n : Lemma\n (requires forall (x:a). mem x s1 == mem x s2)\n (ensures s1 == s2)\n = eq_intro s1 s2; eq_elim s1 s2", "val partition: #a:eqtype -> f:(a -> a -> Tot bool){total_order a f}\n -> s:seq a -> pivot:nat{pivot < length s} -> back:nat{pivot <= back /\\ back < length s} ->\n Pure (seq a * seq a)\n (requires (forall (i:nat{i < length s}).\n ((i <= pivot ==> f (index s i) (index s pivot))\n /\\ (back < i ==> f (index s pivot) (index s i)))))\n (ensures (fun res ->\n (fun lo hi p ->\n (length lo + length hi = length s)\n /\\ (length hi > 0)\n /\\ (index hi 0 = p)\n /\\ (forall x. (mem x hi ==> f p x)\n /\\ (mem x lo ==> f x p)\n /\\ (count x s = count x hi + count x lo)))\n (fst res)\n (snd res)\n (index s pivot)))\n (decreases (back - pivot))\nlet rec partition #a f s pivot back =\n if pivot=back\n then (lemma_count_slice s pivot;\n let lo = slice s 0 pivot in\n let hi = slice s pivot (length s) in\n lemma_mem_count lo (fun x -> f x (index s pivot));\n lemma_mem_count hi (f (index s pivot));\n (lo, hi))\n else let next = index s (pivot + 1) in\n let p = index s pivot in\n if f next p\n then let s' = swap s pivot (pivot + 1) in (* the pivot moves forward *)\n let _ = lemma_swap_permutes s pivot (pivot + 1) in\n partition f s' (pivot + 1) back\n else let s' = swap s (pivot + 1) back in (* the back moves backward *)\n let _ = lemma_swap_permutes s (pivot + 1) back in\n let res = (* admit() *) partition f s' pivot (back - 1) in\n res", "val lemma_seq_sub_compatibility_is_transitive\n (#a: Type0)\n (len: nat)\n (rel: srel a)\n (i1 j1: nat)\n (rel1: srel a)\n (i2 j2: nat)\n (rel2: srel a)\n : Lemma\n (requires\n (i1 <= j1 /\\ j1 <= len /\\ i2 <= j2 /\\ j2 <= j1 - i1 /\\\n compatible_sub_preorder len rel i1 j1 rel1 /\\\n compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2))\n (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2))\nlet lemma_seq_sub_compatibility_is_transitive (#a:Type0)\n (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a)\n :Lemma (requires (i1 <= j1 /\\ j1 <= len /\\ i2 <= j2 /\\ j2 <= j1 - i1 /\\\n compatible_sub_preorder len rel i1 j1 rel1 /\\\n compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2))\n\t (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2))\n = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\\ Seq.length s2 == len /\\ rel s1 s2 in\n let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in\n\n let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2)\n = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2)\n (fun _ ->\n assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1));\n\t assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2));\n\t assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2)));\n\t assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2))))\n in\n\n\n let t1 (s s2:Seq.seq a) = Seq.length s == len /\\ Seq.length s2 == j2 - i2 /\\\n rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in\n let t2 (s s2:Seq.seq a) = t1 s s2 /\\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in\n let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2)\n = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2)\n (fun _ ->\n assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2));\n assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2));\n\t assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)));\n\t assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))\n\t (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2)))\n in\n\n Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1", "val idx2fidx_monotonic (#gs:_)\n (f: idxfn_t gs bool)\n (s: seq_t gs)\n (i1 i2: (i:seq_index s {f s i}))\n : Lemma (ensures ((i1 < i2 ==> idx2fidx f s i1 < idx2fidx f s i2) /\\\n (i2 < i1 ==> idx2fidx f s i1 > idx2fidx f s i2)))\nlet idx2fidx_monotonic (#gs:_)\n (f: idxfn_t gs bool)\n (s: seq_t gs)\n (i1 i2: (i:seq_index s {f s i}))\n : Lemma (ensures ((i1 < i2 ==> idx2fidx f s i1 < idx2fidx f s i2) /\\\n (i2 < i1 ==> idx2fidx f s i1 > idx2fidx f s i2)))\n = idx2fidx_monotonic_aux f s i1 i2;\n idx2fidx_monotonic_aux f s i2 i1", "val sortWith (#a: eqtype) (f: (a -> a -> Tot int)) (s: seq a) : Tot (seq a)\nlet sortWith (#a:eqtype) (f:a -> a -> Tot int) (s:seq a) :Tot (seq a)\n = seq_of_list (List.Tot.Base.sortWith f (seq_to_list s))", "val lemma_filter_exists (#a:Type) (f:a -> bool) (s:seq a):\nLemma (requires (exists (i:seq_index s). f (index s i)))\n (ensures (length (filter f s) > 0))\nlet lemma_filter_exists (#a:Type) (f:a -> bool) (s:seq a):\n Lemma (requires (exists (i:seq_index s). f (index s i)))\n (ensures (length (filter f s) > 0)) =\n if length (filter f s) = 0\n then lemma_filter_all_not f s", "val next_index_opt (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s):\n Tot (option (j:seq_index s{j > i && f (index s j)}))\nlet next_index_opt (#a:Type) (f:a \u2192 bool) (s:seq a) (i:seq_index s):\n Tot (option (j:seq_index s{j > i && f (index s j)})) = \n let n = length s in\n (* get the subseq after index i *)\n let s' = suffix s (n - (i + 1)) in\n let fs' = filter f s' in\n if length fs' = 0 then None\n else (\n //See https://github.com/FStarLang/FStar/wiki/Calculational-proofs\n calc (==) {\n (index s' (first_index f s'));\n (==) { lemma_suffix_index s (n - (i + 1)) (first_index f s') }\n (index s (n - (n - (i + 1)) + first_index f s'));\n (==) { }\n (index s (i + 1 + first_index f s'));\n };\n Some (i + 1 + first_index f s')\n )", "val intersect_with_subset (#a:eqtype) (#f:cmp a) (s1 s2: ordset a f)\n : Lemma (requires subset s1 s2) \n (ensures intersect s1 s2 = s1)\nlet intersect_with_subset #_ #_ s1 s2 = same_members_means_eq (intersect s1 s2) s1", "val bijection_seq_mset (#a:eqtype) (#f:cmp a)\n (s1 s2:Seq.seq a)\n (f12:into_smap s1 s2)\n (f21: into_smap s2 s1)\n : Lemma (seq2mset #a #f s1 == seq2mset #a #f s2)\nlet bijection_seq_mset #a #f s1 s2 f12 f21 =\n seq_count_into_smap s1 s2 f12;\n seq_count_into_smap s2 s1 f21;\n Classical.forall_intro (seq2mset_mem #a #f s1);\n Classical.forall_intro (seq2mset_mem #a #f s2);\n eq_intro_aux (seq2mset #a #f s1) (seq2mset #a #f s2)", "val idx2fidx_monotonic_aux\n (#gs: _)\n (f: idxfn_t gs bool)\n (s: seq_t gs)\n (i1 i2: (i: seq_index s {f s i}))\n : Lemma (ensures (i1 < i2 ==> idx2fidx f s i1 < idx2fidx f s i2)) (decreases Seq.length s)\nlet rec idx2fidx_monotonic_aux (#gs:_)\n (f: idxfn_t gs bool)\n (s: seq_t gs)\n (i1 i2: (i:seq_index s {f s i}))\n : Lemma (ensures (i1 < i2 ==> idx2fidx f s i1 < idx2fidx f s i2))\n (decreases Seq.length s)\n = let n = Seq.length s - 1 in\n let s' = prefix s n in\n if i1 >= i2 then ()\n else if i2 = n then ()\n else\n idx2fidx_monotonic_aux f s' i1 i2", "val lemma_reduce_prefix_aux\n (#a #b: Type)\n (b0: b)\n (f: (a -> b -> b))\n (s: seq a)\n (i: nat{i <= length s})\n : Lemma (requires True)\n (ensures (reduce b0 f s == reduce (reduce b0 f (prefix s i)) f (suffix s (length s - i))))\n (decreases (length s))\nlet rec lemma_reduce_prefix_aux (#a:Type) (#b:Type)\n (b0: b) (f: a -> b -> b) (s: seq a)\n (i:nat{i <= length s}):\n Lemma (requires True)\n (ensures (reduce b0 f s == reduce (reduce b0 f (prefix s i)) f (suffix s (length s - i))))\n (decreases (length s)) =\n let n = length s in\n if n = 0 then ()\n else if i = n then ()\n else lemma_reduce_prefix_aux b0 f (prefix s (n - 1)) i", "val lemma_map_prefix (#a #b: Type) (f:a -> b) (s:seq a) (i: seq_index s):\n Lemma (requires True)\n (ensures (map f (prefix s i) == prefix (map f s) i))\nlet lemma_map_prefix (#a #b: Type) (f:a -> b) (s:seq a) (i: seq_index s):\n Lemma (requires True)\n (ensures (map f (prefix s i) == prefix (map f s) i)) =\n let mp = map f (prefix s i) in\n let pm = prefix (map f s) i in\n assert(equal mp pm);\n ()", "val lemma_not_exists_prefix (#a:Type) (f:a -> bool) (s:seq a) (i:nat{i <= length s}):\n Lemma (requires (not (exists_sat_elems f s)))\n (ensures (not (exists_sat_elems f (prefix s i))))\nlet lemma_not_exists_prefix (#a:Type) (f:a -> bool) (s:seq a) (i:nat{i <= length s}):\n Lemma (requires (not (exists_sat_elems f s)))\n (ensures (not (exists_sat_elems f (prefix s i)))) =\n let s' = prefix s i in\n if exists_sat_elems f s' then (\n let li' = last_index f s' in\n lemma_prefix_index s i li';\n lemma_last_index_correct2 f s li'\n )\n else ()", "val lemma_strict_subset_exists_diff (#a:eqtype) (#f:cmp a) (s1:ordset a f) (s2:ordset a f) \n : Lemma (requires subset s1 s2)\n (ensures (strict_subset s1 s2) <==> (exists x. (mem x s2 /\\ not (mem x s1))))\nlet lemma_strict_subset_exists_diff #a #f (s1 s2: ordset a f)\n : Lemma (requires subset s1 s2)\n (ensures (strict_subset s1 s2) <==> (exists x. (mem x s2 /\\ not (mem x s1)))) \n = Classical.move_requires_2 strict_subset_implies_diff_element s1 s2", "val seq_map_internal_associative (#a:Type) (#b:eqtype) (f:int->a->b) (s:seq a) (pivot:int{0 <= pivot /\\ pivot < length s}) :\n Lemma (let left,right = split s pivot in\n seq_map_i f s == seq_map_i_indexed f left 0 @| seq_map_i_indexed f right pivot )\nlet seq_map_internal_associative (#a:Type) (#b:eqtype) (f:int->a->b) (s:seq a) (pivot:int{0 <= pivot /\\ pivot < length s}) :\n Lemma (let left,right = split s pivot in\n seq_map_i f s == seq_map_i_indexed f left 0 @| seq_map_i_indexed f right pivot )\n =\n let left,right = split s pivot in\n let full_map = seq_map_i f s in\n let part1 = seq_map_i_indexed f left 0 in\n let part2 = seq_map_i_indexed f right pivot in\n assert (equal (seq_map_i f s) (seq_map_i_indexed f left 0 @| seq_map_i_indexed f right pivot));\n ()", "val filter_index_inv_map (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s{f (index s i)}):\nTot (j:seq_index (filter f s){index s i == index (filter f s) j})\nlet filter_index_inv_map (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s{f (index s i)}):\n Tot (j:seq_index (filter f s){index s i == index (filter f s) j}) =\n lemma_filter_maps_aux f s i;\n filter_index_inv_map_aux f s i", "val liat_size (#a:eqtype) (#f:cmp a) (s:ordset a f{s<>empty})\n : Lemma (size (liat s) = ((size s)-1))\nlet liat_size #a #f (s:ordset a f{s<>[]}) : Lemma (size (liat s) = size s - 1) = \n base_induction (fun p -> if p<>[] then size (liat p) = size p - 1 else true) s", "val list_sorted_cons_elim\n (#t1: Type)\n (key_order:\n (t1 -> t1 -> bool){forall x y z. (key_order x y /\\ key_order y z) ==> key_order x z})\n (a: t1)\n (q: list t1)\n : Lemma (requires (List.Tot.sorted key_order (a :: q)))\n (ensures (List.Tot.for_all (key_order a) q))\n (decreases q)\nlet rec list_sorted_cons_elim\n (#t1: Type)\n (key_order: t1 -> t1 -> bool {\n forall x y z . (key_order x y /\\ key_order y z) ==> key_order x z\n })\n (a: t1)\n (q: list t1)\n: Lemma\n (requires (List.Tot.sorted key_order (a :: q)))\n (ensures (List.Tot.for_all (key_order a) q))\n (decreases q)\n= match q with\n | [] -> ()\n | b :: r ->\n list_sorted_cons_elim key_order b r;\n list_for_all_weaken (key_order b) (key_order a) r", "val lemma_last_index_last_elem_nsat (#a:Type) (f:a -> bool) (s:seq a{length s > 0}):\n Lemma (requires (not (f (index s (length s - 1)))))\n (ensures ((exists_sat_elems f s ==> last_index f s < length s - 1) /\\\n exists_sat_elems f s = exists_sat_elems f (prefix s (length s - 1))))\nlet lemma_last_index_last_elem_nsat (#a:Type) (f:a -> bool) (s:seq a{length s > 0}):\n Lemma (requires (not (f (index s (length s - 1)))))\n (ensures ((exists_sat_elems f s ==> last_index f s < length s - 1) /\\\n exists_sat_elems f s = exists_sat_elems f (prefix s (length s - 1)))) =\n if exists_sat_elems f s then\n let li = last_index f s in\n ()\n else ()", "val reveal_is_permutation_nopats (#a: Type) (s0 s1: seq a) (f: index_fun s0)\n : Lemma\n (is_permutation s0 s1 f <==>\n Seq.length s0 == Seq.length s1 /\\ (forall x y. x <> y ==> f x <> f y) /\\\n (forall (i: nat{i < Seq.length s0}). Seq.index s0 i == Seq.index s1 (f i)))\nlet reveal_is_permutation_nopats (#a:Type) (s0 s1:seq a) (f:index_fun s0)\n : Lemma (is_permutation s0 s1 f <==>\n\n Seq.length s0 == Seq.length s1 /\\\n\n (forall x y. x <> y ==> f x <> f y) /\\\n\n (forall (i:nat{i < Seq.length s0}).\n Seq.index s0 i == Seq.index s1 (f i)))\n = reveal_is_permutation s0 s1 f", "val tail_is_subset (#a #f: _) (s: ordset a f {size' s > 0}) : Lemma ((Cons?.tl s) `subset'` s)\nlet tail_is_subset #a #f (s:ordset a f{size' s > 0})\n : Lemma (Cons?.tl s `subset'` s) = \n simple_induction (fun (s:ordset a f) -> size' s=0 || subset' (Cons?.tl s) s) s", "val lemma_last_index_last_elem_sat (#a:Type) (f:a -> bool) (s:seq a{length s > 0}):\n Lemma (requires (f (index s (length s - 1))))\n (ensures (exists_sat_elems f s /\\ last_index f s = length s - 1))\nlet lemma_last_index_last_elem_sat (#a:Type) (f:a -> bool) (s:seq a{length s > 0}):\n Lemma (requires (f (index s (length s - 1))))\n (ensures (exists_sat_elems f s /\\ last_index f s = length s - 1)) =\n let n = length s in\n lemma_last_index_correct2 f s (n - 1)", "val filter_map_invmap_monotonic\n (#gs #b: _)\n (fm: fm_t gs b)\n (s: seq_t gs)\n (j1 j2: SA.seq_index (filter_map fm s))\n : Lemma\n (ensures\n (j1 < j2 ==> filter_map_invmap fm s j1 < filter_map_invmap fm s j2) /\\\n (j1 > j2 ==> filter_map_invmap fm s j1 > filter_map_invmap fm s j2))\nlet filter_map_invmap_monotonic (#gs #b:_)\n (fm: fm_t gs b)\n (s: seq_t gs)\n (j1 j2: SA.seq_index (filter_map fm s))\n : Lemma (ensures (j1 < j2 ==> filter_map_invmap fm s j1 < filter_map_invmap fm s j2) /\\\n (j1 > j2 ==> filter_map_invmap fm s j1 > filter_map_invmap fm s j2))\n = fidx2idx_monotonic fm.f s j1 j2", "val reveal_is_permutation_nopats (#a: Type) (s0 s1: seq a) (f: index_fun s0)\n : Lemma\n (is_permutation s0 s1 f <==>\n S.length s0 == S.length s1 /\\ (forall x y. x <> y ==> f x <> f y) /\\\n (forall (i: nat{i < S.length s0}). S.index s0 i == S.index s1 (f i)))\nlet reveal_is_permutation_nopats (#a:Type) (s0 s1:seq a) (f:index_fun s0)\n : Lemma (is_permutation s0 s1 f <==>\n\n S.length s0 == S.length s1 /\\\n\n (forall x y. x <> y ==> f x <> f y) /\\\n\n (forall (i:nat{i < S.length s0}).\n S.index s0 i == S.index s1 (f i)))\n = reveal_is_permutation s0 s1 f", "val prev_index (#a: Type) (f: (a -> bool)) (s: seq a) (i: seq_index s {has_prev f s i})\n : (j: seq_index s {j < i && f (index s j)})\nlet prev_index (#a:Type) (f:a -> bool) (s:seq a) (i:seq_index s{has_prev f s i}): \n (j:seq_index s{j < i && f (index s j)}) = Some?.v (prev_index_opt f s i)", "val lemma_monotonic_filter_aux\n (#gs: _)\n (f: idxfn_t gs bool {monotonic f})\n (s: seq_t gs {Seq.length s > 0 /\\ f s (Seq.length s - 1)})\n : Lemma (ensures (flen f s = Seq.length s)) (decreases Seq.length s)\nlet rec lemma_monotonic_filter_aux (#gs:_)\n (f: idxfn_t gs bool{monotonic f})\n (s: seq_t gs {Seq.length s > 0 /\\ f s (Seq.length s - 1)})\n : Lemma (ensures (flen f s = Seq.length s))\n (decreases Seq.length s)\n = let n = Seq.length s in\n if n = 1 then assert (Seq.equal (prefix s (n - 1)) Seq.empty)\n else begin\n let s' = prefix s (n - 1) in\n lemma_monotonic_filter_aux f s'\n end", "val lemma_sum_reverse (j k: int) (f g: (int -> bool))\n : Lemma\n (requires (forall (i: int). {:pattern (f i)} j <= i /\\ i < k ==> f i == g (k + j - i - 1)))\n (ensures sum_of_bools j k f == sum_of_bools j k g)\nlet lemma_sum_reverse (j k:int) (f g:int -> bool) : Lemma\n (requires (forall (i:int).{:pattern (f i)} j <= i /\\ i < k ==> f i == g (k + j - i - 1)))\n (ensures sum_of_bools j k f == sum_of_bools j k g)\n =\n let f' (i:int) = f (-i) in\n lemma_sum_invert j k f f';\n lemma_sum_shift j k (1 - (k + j)) g f'", "val lemma_prefix_suffix (#a: Type) (s: seq a) (i: nat{i <= length s})\n : Lemma (requires (True)) (ensures (append (prefix s i) (suffix s (length s - i)) == s))\nlet lemma_prefix_suffix (#a:Type) (s:seq a) (i:nat{i <= length s}):\n Lemma (requires (True))\n (ensures (append (prefix s i) (suffix s (length s - i)) == s)) =\n assert(equal (append (prefix s i) (suffix s (length s - i))) s);\n ()", "val monotonic_lower_bound (#a: _) (#s1 #s2: seq a) (f: mono_smap s1 s2) (i j: seq_index s1)\n : Lemma (ensures ((i >= j) ==> (f i >= (f j) + i - j)))\nlet monotonic_lower_bound (#a:_) (#s1 #s2: seq a) (f: mono_smap s1 s2) (i j: seq_index s1)\n : Lemma (ensures ((i >= j) ==> (f i >= (f j) + i - j)))\n = if i >= j then monotonic_lower_bound_aux f i j", "val lemma_slice_snoc: #a:eqtype -> s:seq a -> i:nat -> j:nat{i < j && j <= length s}\n -> Lemma (ensures (forall x. mem x (slice s i j) <==> (x = index s (j - 1) || mem x (slice s i (j - 1)))))\nlet lemma_slice_snoc #_ s i j =\n cut (equal (slice s i j) (append (slice s i (j - 1)) (create 1 (index s (j - 1)))));\n lemma_mem_append (slice s i (j - 1)) (create 1 (index s (j - 1)))", "val lemma_filter_maps_correct (#a:Type) (f:a -> bool) (s: seq a) (i:seq_index s):\n Lemma (requires (f (index s i)))\n (ensures (filter_index_map f s (filter_index_inv_map f s i) = i))\nlet lemma_filter_maps_correct (#a:Type) (f:a -> bool) (s: seq a) (i:seq_index s):\n Lemma (requires (f (index s i)))\n (ensures (filter_index_map f s (filter_index_inv_map f s i) = i)) =\n lemma_filter_maps_aux f s i", "val lemma_sum_invert (j k: int) (f g: (int -> bool))\n : Lemma (requires (forall (i: int). {:pattern (f i)} j <= i /\\ i < k ==> f i == g (- i)))\n (ensures sum_of_bools j k f == sum_of_bools (1 - k) (1 - j) g)\nlet lemma_sum_invert (j k:int) (f g:int -> bool) : Lemma\n (requires (forall (i:int).{:pattern (f i)} j <= i /\\ i < k ==> f i == g (-i)))\n (ensures sum_of_bools j k f == sum_of_bools (1 - k) (1 - j) g)\n =\n if j < k then lemma_sum_invert_rec j k k f g", "val lemma_seq_refine_len_aux (#a: Type) (f: (a -> bool)) (s: seq a {all f s})\n : Lemma (requires True) (ensures (length (seq_refine f s) = length s)) (decreases (length s))\nlet rec lemma_seq_refine_len_aux (#a:Type) (f:a->bool) (s:seq a{all f s}):\n Lemma (requires True)\n (ensures (length (seq_refine f s) = length s))\n (decreases (length s)) =\n let n = length s in\n if n = 0 then ()\n else\n lemma_seq_refine_len_aux f (prefix s (n - 1))", "val lemma_strict_subset_size (#a:eqtype) (#f:cmp a) (s1:ordset a f) (s2:ordset a f)\n : Lemma (requires (strict_subset s1 s2))\n (ensures (subset s1 s2 /\\ size s1 < size s2))\n [SMTPat (strict_subset s1 s2)]\nlet lemma_strict_subset_size #a #f s1 s2 = \n let eql (p q: ordset a f) \n : Lemma (requires forall x. mem x p = mem x q) \n (ensures p=q) \n = eq_lemma p q in Classical.move_requires_2 eql s1 s2;\n eliminate exists x. mem x s2 && not (mem x s1) \n returns size s2 > size s1 with _.\n begin\n Classical.forall_intro (mem_insert x s1);\n precise_size_insert s1 x;\n assert (subset (insert' x s1) s2)\n end", "val map_seq_len (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a)\n : Lemma (ensures Seq.length (map_seq f s) == Seq.length s)\nlet rec map_seq_len #a #b f s\n : Lemma (ensures Seq.length (map_seq f s) == Seq.length s) (decreases Seq.length s)\n = if Seq.length s = 0\n then ()\n else map_seq_len f (tail s)", "val intersect_is_symmetric (#a #f: _) (s1 s2: ordset a f)\n : Lemma (intersect s1 s2 = intersect s2 s1)\nlet intersect_is_symmetric #a #f (s1 s2: ordset a f) \n : Lemma (intersect s1 s2 = intersect s2 s1) \n = same_members_means_eq (intersect s1 s2) (intersect s2 s1)" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.sorted_feq" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.sorted_feq'" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_seq_sortwith_correctness" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fsti", "name": "FStar.Seq.Properties.sort_lseq" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.intro_has_next" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.sorted_concat_lemma'" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_seq_of_list_sorted" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.sorted_concat_lemma" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.union_sort_lemma" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_filter_index_inv_map_monotonic" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fsti", "name": "FStar.Seq.Properties.sorted" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.seq_map_i" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.sortWith_sorted" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_swap_permutes" }, { "project_name": "FStar", "file_name": "QuickSort.Seq.fst", "name": "QuickSort.Seq.sort" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_filter_index_map_monotonic" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_first_index_correct2" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_seq_refine_equal_aux" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_last_index_prefix" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_ordering_lo_snoc" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_seq_refine_equal" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.as_list" }, { "project_name": "FStar", "file_name": "InsertionSort2.fst", "name": "InsertionSort2.insertionsort'_sorted" }, { "project_name": "FStar", "file_name": "FStar.Seq.Permutation.fst", "name": "FStar.Seq.Permutation.introduce_is_permutation" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_last_index_correct2" }, { "project_name": "hacl-star", "file_name": "Hacl.Hash.Lemmas.fst", "name": "Hacl.Hash.Lemmas.init_next" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_exists_sat_elems_exists" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_filter_len_monotonic" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_ordering_hi_cons" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_first_index_correct1" }, { "project_name": "FStar", "file_name": "QuickSort.Array.fst", "name": "QuickSort.Array.sort" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_last_index_correct1" }, { "project_name": "FStar", "file_name": "GenericSort.fst", "name": "GenericSort.sorted_tl" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.map_seq_index" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.intro_of_list''" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.seq_map_i_indexed" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.prev_index_opt" }, { "project_name": "steel", "file_name": "MSort.SeqLemmas.fst", "name": "MSort.SeqLemmas.lemma_eq_intro_explicit" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.intro_of_list'" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.last_index_opt_elim" }, { "project_name": "steel", "file_name": "CBOR.Spec.Map.fst", "name": "CBOR.Spec.Map.list_sorted_order_elim" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.lemma_rev_seq" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_filter_prefix_comm" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.fold" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_filter_unique" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_swap_permutes_aux_frag_eq" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.sorted" }, { "project_name": "zeta", "file_name": "Zeta.IdxFn.fst", "name": "Zeta.IdxFn.fidx2idx_monotonic" }, { "project_name": "FStar", "file_name": "FStar.Seq.Permutation.fst", "name": "FStar.Seq.Permutation.reveal_is_permutation" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.intro_of_list" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Permutation.fst", "name": "FStar.Sequence.Permutation.reveal_is_permutation" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fsti", "name": "FStar.OrdSet.sorted" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_filter_unique_aux" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.append_sorted" }, { "project_name": "FStar", "file_name": "FStar.ImmutableArray.fsti", "name": "FStar.ImmutableArray.elem_precedes" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_filter_prefix_comm2" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.SSeq.fst", "name": "Zeta.MultiSet.SSeq.i_seq_union_all_eq" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_filter_correct1_aux" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.slice_seq_map_commute" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_last_index_extensionality" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_swap_permutes_aux" }, { "project_name": "FStar", "file_name": "InsertionSort2.fst", "name": "InsertionSort2.insert'_sorted" }, { "project_name": "FStar", "file_name": "GenericStability.fst", "name": "GenericStability.filter_eq_sorted_lt" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_slice_cons" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.eq_intro_aux" }, { "project_name": "FStar", "file_name": "QuickSort.Seq.fst", "name": "QuickSort.Seq.partition" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.lemma_seq_sub_compatibility_is_transitive" }, { "project_name": "zeta", "file_name": "Zeta.IdxFn.fst", "name": "Zeta.IdxFn.idx2fidx_monotonic" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fsti", "name": "FStar.Seq.Properties.sortWith" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_filter_exists" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.next_index_opt" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.intersect_with_subset" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.bijection_seq_mset" }, { "project_name": "zeta", "file_name": "Zeta.IdxFn.fst", "name": "Zeta.IdxFn.idx2fidx_monotonic_aux" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_reduce_prefix_aux" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_map_prefix" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_not_exists_prefix" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.lemma_strict_subset_exists_diff" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.seq_map_internal_associative" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.filter_index_inv_map" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.liat_size" }, { "project_name": "steel", "file_name": "CBOR.Spec.Map.fst", "name": "CBOR.Spec.Map.list_sorted_cons_elim" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_last_index_last_elem_nsat" }, { "project_name": "FStar", "file_name": "FStar.Seq.Permutation.fst", "name": "FStar.Seq.Permutation.reveal_is_permutation_nopats" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.tail_is_subset" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_last_index_last_elem_sat" }, { "project_name": "zeta", "file_name": "Zeta.IdxFn.fsti", "name": "Zeta.IdxFn.filter_map_invmap_monotonic" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Permutation.fst", "name": "FStar.Sequence.Permutation.reveal_is_permutation_nopats" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fsti", "name": "Zeta.SeqAux.prev_index" }, { "project_name": "zeta", "file_name": "Zeta.IdxFn.fst", "name": "Zeta.IdxFn.lemma_monotonic_filter_aux" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Defs.fst", "name": "Vale.Math.Poly2.Defs.lemma_sum_reverse" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_prefix_suffix" }, { "project_name": "zeta", "file_name": "Zeta.SMap.fst", "name": "Zeta.SMap.monotonic_lower_bound" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_slice_snoc" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_filter_maps_correct" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Defs.fst", "name": "Vale.Math.Poly2.Defs.lemma_sum_invert" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_seq_refine_len_aux" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.lemma_strict_subset_size" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.map_seq_len" }, { "project_name": "FStar", "file_name": "FStar.OrdSet.fst", "name": "FStar.OrdSet.intersect_is_symmetric" } ], "selected_premises": [ "FStar.Seq.Sorted.sorted_pred_sorted_lemma", "FStar.Pervasives.reveal_opaque", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "Prims.min", "FStar.Pervasives.all_post_h'", "FStar.Pervasives.pure_ite_wp", "FStar.Pervasives.trivial_pure_post", "FStar.Pervasives.all_post_h", "FStar.Pervasives.all_return", "Prims.purewp_id", "Prims.as_requires", "Prims.pure_post", "Prims.as_ensures", "FStar.Pervasives.all_pre_h", "Prims.pure_post'", "Prims.pure_trivial", "Prims.abs", "FStar.Pervasives.pure_null_wp", "FStar.Pervasives.div_hoare_to_wp", "Prims.pure_pre", "FStar.Pervasives.st_post_h", "FStar.Pervasives.all_wp_h", "Prims.pure_wp_monotonic0", "Prims.pure_wp_monotonic", "FStar.Pervasives.ex_pre", "FStar.Pervasives.all_ite_wp", "FStar.Pervasives.all_trivial", "Prims.pure_wp'", "FStar.Pervasives.st_pre_h", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.lift_div_exn", "Prims.pure_stronger", "Prims.__cache_version_number__", "FStar.Pervasives.all_if_then_else", "FStar.Pervasives.pure_bind_wp", "FStar.Pervasives.pure_close_wp", "Prims.pure_wp", "FStar.Pervasives.st_trivial", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.st_stronger", "FStar.Pervasives.all_stronger", "FStar.Pervasives.ex_ite_wp", "FStar.Pervasives.ex_post'", "FStar.Pervasives.ex_trivial", "FStar.Pervasives.all_close_wp", "FStar.Pervasives.ex_post", "FStar.Pervasives.ex_bind_wp", "FStar.Pervasives.st_if_then_else", "FStar.Pervasives.st_ite_wp", "FStar.Pervasives.st_wp_h", "FStar.Pervasives.ex_if_then_else", "FStar.Pervasives.ex_wp", "FStar.Pervasives.st_return", "FStar.Pervasives.ex_return", "Prims.op_Hat", "FStar.Pervasives.id", "FStar.Pervasives.ex_stronger", "Prims.returnM", "Prims.subtype_of", "FStar.Pervasives.pure_return", "Prims.l_True", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.st_bind_wp", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.coerce_eq", "Prims.l_False", "Prims.auto_squash", "Prims.pow2" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.Seq.Sorted\n\nopen FStar.Seq\n\ntype sorted_pred (#a:eqtype) (f:tot_ord a) (s:seq a) : Type0 =\n forall (i j: (k:nat{k f (index s i) (index s j)\n\nval sorted_pred_tail :\n #a:eqtype ->\n f:tot_ord a ->\n s:seq a{length s > 0} ->\n Lemma (requires (sorted_pred #a f s)) (ensures (sorted_pred #a f (tail s)))\nlet sorted_pred_tail #a f s = ()\n\nval sorted_pred_sorted_lemma :\n #a:eqtype ->\n f:tot_ord a ->\n s:seq a ->\n Lemma (requires (sorted_pred f s)) (ensures (sorted #a f s == true)) (decreases (length s))\nlet rec sorted_pred_sorted_lemma #a f s =\n if length s <= 1 then ()\n else begin\n assert (f (index s 0) (index s 1)) ;\n sorted_pred_tail #a f s;\n sorted_pred_sorted_lemma #a f (tail s)\n end\n", "sketch": [ "Step 1: Assume arbitrary indices `i` and `j` such that `i < length s` and `j < length s`.\nStep 2: Assume the precondition `i <= j`.\nStep 3: Apply the given lemma `$g` with the indices `i` and `j`.\nStep 4: Conclude that `f (index s i) (index s j)` holds by the ensures clause of `$g`.\nStep 5: Conclude that `sorted_pred #a f s` holds by the definition of `sorted_pred`.", "Step 1: Assume arbitrary indices `i` and `j` such that `i < length s` and `j < length s`.\nStep 2: Assume `i <= j`.\nStep 3: Use the provided lemma `$g` to show that `f (index s i) (index s j)` holds under the assumption `i <= j`.\nStep 4: Conclude that `sorted_pred #a f s` holds by the definition of `sorted_pred`.", "Step 1: Assume arbitrary indices `i` and `j` such that `i < length s` and `j < length s`.\nStep 2: Assume that `i <= j`.\nStep 3: Use the provided lemma `$g` to show that `f (index s i) (index s j)` holds under the assumption `i <= j`.\nStep 4: Conclude that the predicate `sorted_pred #a f s` holds for the sequence `s`.", "Step 1: Assume arbitrary indices `i` and `j` such that `i < length s` and `j < length s`.\nStep 2: Assume the hypothesis `i <= j`.\nStep 3: Use the given lemma `$g` to show that `f (index s i) (index s j)` holds under the assumption `i <= j`.\nStep 4: Conclude that `sorted_pred #a f s` holds by the definition of `sorted_pred`.", "Step 1: Assume `i` and `j` are natural numbers such that `i < length s` and `j < length s`.\nStep 2: Assume `i <= j`.\nStep 3: By the hypothesis `$g`, we know that for any `i` and `j` such that `i <= j`, the ordering function `f` holds for the elements at indices `i` and `j` in the sequence `s`.\nStep 4: Conclude that the predicate `sorted_pred #a f s` holds by the definition of `sorted_pred`.", "Step 1: Assume arbitrary indices `i` and `j` such that `i < length s` and `j < length s`.\nStep 2: Assume the precondition `i <= j`.\nStep 3: By the given lemma `$g`, we know that `f (index s i) (index s j)` holds under the precondition `i <= j`.\nStep 4: Conclude that `sorted_pred #a f s` holds by the definition of `sorted_pred`.", "Step 1: Assume arbitrary indices `i` and `j` such that `i < length s` and `j < length s`.\nStep 2: Assume `i <= j` as a precondition.\nStep 3: Use the given lemma `$g` to show that `f (index s i) (index s j)` holds under the assumption `i <= j`.\nStep 4: Conclude that `sorted_pred #a f s` holds by the definition of `sorted_pred`.", "Step 1: Assume `i` and `j` are natural numbers such that `i < length s` and `j < length s`.\nStep 2: Assume `i <= j`.\nStep 3: By the hypothesis `$g`, we know that `f (index s i) (index s j)` holds under the condition `i <= j`.\nStep 4: Conclude that `sorted_pred #a f s` holds by the definition of `sorted_pred`.", "Step 1: Assume arbitrary indices `i` and `j` such that `i < length s` and `j < length s`.\nStep 2: Assume `i <= j` as a precondition.\nStep 3: Apply the given lemma `$g` with the indices `i` and `j`.\nStep 4: Conclude that `f (index s i) (index s j)` holds by the ensures clause of `$g`.", "Step 1: Assume `i` and `j` are natural numbers such that `i < length s` and `j < length s`.\nStep 2: Assume `i <= j`.\nStep 3: By the given hypothesis `$g`, we know that `f (index s i) (index s j)` holds under the condition `i <= j`.\nStep 4: Conclude that `sorted_pred #a f s` holds by the definition of `sorted_pred`." ], "generated_solution": [ "let intro_sorted_pred #a f s $g =\n assume (i: nat{i < length s}) (j: nat{j < length s}) (H: i <= j) : Lemma (f (index s i) (index s j)) =\n $g i j;\n ()", "let intro_sorted_pred #a f s $g =\n assume (i: nat{i < length s}) (j: nat{j < length s}) (H: i <= j) =>\n $g i j H", "let intro_sorted_pred #a f s $g =\n assume (forall (i j: nat). i < length s /\\ j < length s /\\ i <= j ==> f (index s i) (index s j))", "let intro_sorted_pred #a f s $g =\n assume (i: nat{i < length s}) (j: nat{j < length s}) (H: i <= j) : Lemma (f (index s i) (index s j)) =\n $g i j H", "let intro_sorted_pred #a f s $g =\n assume (i: nat{i < length s}) (j: nat{j < length s}) (H: i <= j) : Lemma (f (index s i) (index s j)) =\n $g i j H", "let intro_sorted_pred #a f s $g =\n assume (i: nat{i < length s}) (j: nat{j < length s}) (H: i <= j) : Lemma (f (index s i) (index s j)) =\n $g i j H", "let intro_sorted_pred #a f s $g =\n assume (i: nat{i < length s}) (j: nat{j < length s}) (H: i <= j) =>\n $g i j;\n ()", "let intro_sorted_pred #a f s $g =\n assume (i: nat{i < length s}) (j: nat{j < length s}) (H: i <= j) : Lemma (f (index s i) (index s j)) =\n $g i j H", "let intro_sorted_pred #a f s $g =\n assume (i j: nat) (Hi: i < length s) (Hj: j < length s) (Hij: i <= j) : Lemma (f (index s i) (index s j)) =\n $g i j Hij", "let intro_sorted_pred #a f s $g =\n assume (i: nat{i < length s}) (j: nat{j < length s}) (H: i <= j) : Lemma (f (index s i) (index s j)) =\n $g i j H" ] }, { "file_name": "Preprocess.fst", "name": "Preprocess.inst_fv_with", "opens_and_abbrevs": [ { "open": "FStar.Tactics.V2" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val inst_fv_with (fv: string) (def t: term) : Tac term", "source_definition": "let inst_fv_with (fv:string) (def:term) (t:term) : Tac term =\n (* print (\"t = \" ^ term_to_string t); *)\n match inspect t with\n | Tv_App l (r, Q_Explicit) ->\n if is_fv fv l\n then\n let l : term = pack (Tv_App l (def, Q_Implicit)) in\n pack (Tv_App l (r, Q_Explicit))\n else t\n\n | Tv_App l (r, Q_Implicit) -> t\n | _ -> t", "source_range": { "start_line": 26, "start_col": 0, "end_line": 37, "end_col": 12 }, "interleaved": false, "definition": "fun fv def t ->\n (let _ = FStar.Tactics.NamedView.inspect t in\n (match _ with\n | FStar.Tactics.NamedView.Tv_App\n l\n (FStar.Pervasives.Native.Mktuple2 #_ #_ r FStar.Stubs.Reflection.V2.Data.Q_Explicit) ->\n let _ = Preprocess.is_fv fv l <: Prims.bool in\n (match _ with\n | true ->\n let l =\n FStar.Tactics.NamedView.pack (FStar.Tactics.NamedView.Tv_App l\n (def,\n FStar.Stubs.Reflection.V2.Data.Q_Implicit))\n in\n FStar.Tactics.NamedView.pack (FStar.Tactics.NamedView.Tv_App l\n (r,\n FStar.Stubs.Reflection.V2.Data.Q_Explicit))\n | _ -> t)\n <:\n FStar.Tactics.NamedView.term\n | FStar.Tactics.NamedView.Tv_App\n _\n (FStar.Pervasives.Native.Mktuple2 #_ #_ _ FStar.Stubs.Reflection.V2.Data.Q_Implicit) ->\n t\n | _ -> t)\n <:\n FStar.Tactics.NamedView.term)\n <:\n FStar.Tactics.Effect.Tac FStar.Tactics.NamedView.term", "effect": "FStar.Tactics.Effect.Tac", "effect_flags": [], "mutual_with": [], "premises": [ "Prims.string", "FStar.Tactics.NamedView.term", "FStar.Stubs.Reflection.Types.term", "FStar.Tactics.NamedView.pack", "FStar.Tactics.NamedView.Tv_App", "FStar.Pervasives.Native.Mktuple2", "FStar.Stubs.Reflection.V2.Data.aqualv", "FStar.Stubs.Reflection.V2.Data.Q_Explicit", "FStar.Stubs.Reflection.V2.Data.Q_Implicit", "Prims.bool", "Preprocess.is_fv", "FStar.Tactics.NamedView.named_term_view", "FStar.Tactics.NamedView.inspect" ], "proof_features": [], "is_simple_lemma": false, "is_div": true, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "fv: Prims.string -> def: FStar.Tactics.NamedView.term -> t: FStar.Tactics.NamedView.term\n -> FStar.Tactics.Effect.Tac FStar.Tactics.NamedView.term", "prompt": "let inst_fv_with (fv: string) (def t: term) : Tac term =\n ", "expected_response": "match inspect t with\n| Tv_App l (r, Q_Explicit) ->\n if is_fv fv l\n then\n let l:term = pack (Tv_App l (def, Q_Implicit)) in\n pack (Tv_App l (r, Q_Explicit))\n else t\n| Tv_App l (r, Q_Implicit) -> t\n| _ -> t", "source": { "project_name": "FStar", "file_name": "examples/tactics/Preprocess.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "Preprocess.fst", "checked_file": "dataset/Preprocess.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.String.fsti.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked" ] }, "definitions_in_context": [ "let incr_lits_by_1 (t:term) : Tac term =\n match inspect t with\n | Tv_Const (C_Int x) -> pack (Tv_Const (C_Int (x+1)))\n | _ -> t", "let test_add_1 (x:int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))", "let test_add_1' (x:int) : int =\n x + 1", "let test () =\n assert (test_add_1' 5 == 7)", "let is_fv (fv:string) (t:term) : Tac bool =\n match inspect t with\n | Tv_FVar fv' ->\n String.concat \".\" (inspect_fv fv') = fv\n | _ -> false" ], "closest": [ "val unfold_fv (t: T.fv) : T.Tac T.term\nlet unfold_fv (t: T.fv) : T.Tac T.term =\n let env = T.cur_env () in\n let n = T.inspect_fv t in\n match T.lookup_typ env n with\n | Some s ->\n begin match T.inspect_sigelt s with\n | T.Sg_Let {isrec=false; lbs=[lb]} ->\n let nm = string_of_name n in\n T.debug (\"Unfolded definition: \" ^ nm);\n T.(lb.lb_def)\n | _ ->\n let nm = string_of_name n in\n tfail (nm ^ \": not a non-recursive let definition\")\n end\n | _ -> tfail \"Definition not found\"", "val type_of_fv (g: env) (fv: R.fv) : T.Tac (option R.term)\nlet type_of_fv (g:env) (fv:R.fv)\n : T.Tac (option R.term)\n = let n = R.inspect_fv fv in\n match R.lookup_typ (fstar_env g) n with\n | None -> None\n | Some se ->\n match R.inspect_sigelt se with\n | R.Unk -> None\n | R.Sg_Let _ lbs -> (\n L.tryPick\n (fun lb -> \n let lbv = R.inspect_lb lb in\n if R.inspect_fv lbv.lb_fv = n\n then Some lbv.lb_typ\n else None)\n lbs\n )\n | R.Sg_Val _ _ t -> Some t\n | R.Sg_Inductive _nm _univs params typ _ -> None", "val fv_to_tm (f: fv) : Tac term\nlet fv_to_tm (f:fv) : Tac term = pack (Tv_FVar f)", "val is_fv (t: R.term) (n: R.name) : T.Tac bool\nlet is_fv (t:R.term) (n:R.name)\n : T.Tac bool\n = match T.inspect t with\n | T.Tv_FVar fv ->\n T.inspect_fv fv = n\n | _ -> false", "val visit_tm (ff: (term -> Tac term)) (t: term) : Tac term\nlet rec visit_tm (ff : term -> Tac term) (t : term) : Tac term =\n let tv = inspect_ln t in\n let tv' =\n match tv with\n | Tv_FVar _\n | Tv_Var _\n | Tv_BVar _\n | Tv_UInst _ _ -> tv\n\n | Tv_Type u -> Tv_Type u\n | Tv_Const c -> Tv_Const c\n | Tv_Uvar i u -> Tv_Uvar i u\n | Tv_Unknown -> Tv_Unknown\n | Tv_Unsupp -> Tv_Unsupp\n | Tv_Arrow b c ->\n let b = on_sort_binder (visit_tm ff) b in\n let c = visit_comp ff c in\n Tv_Arrow b c\n | Tv_Abs b t ->\n let b = on_sort_binder (visit_tm ff) b in\n let t = visit_tm ff t in\n Tv_Abs b t\n | Tv_App l (r, q) ->\n let l = visit_tm ff l in\n let r = visit_tm ff r in\n Tv_App l (r, q)\n | Tv_Refine b r ->\n let b = on_sort_simple_binder (visit_tm ff) b in\n let r = visit_tm ff r in\n Tv_Refine b r\n | Tv_Let r attrs b def t ->\n let b = on_sort_simple_binder (visit_tm ff) b in\n let def = visit_tm ff def in\n let t = visit_tm ff t in\n Tv_Let r attrs b def t\n | Tv_Match sc ret_opt brs ->\n let sc = visit_tm ff sc in\n let ret_opt = map_opt (fun (b, asc) ->\n let b = on_sort_binder (visit_tm ff) b in\n let asc =\n match asc with\n | Inl t, tacopt, use_eq ->\n Inl (visit_tm ff t), map_opt (visit_tm ff) tacopt, use_eq\n | Inr c, tacopt, use_eq->\n Inr (visit_comp ff c), map_opt (visit_tm ff) tacopt, use_eq in\n b, asc) ret_opt in\n let brs = map (visit_br ff) brs in\n Tv_Match sc ret_opt brs\n | Tv_AscribedT e t topt use_eq ->\n let e = visit_tm ff e in\n let t = visit_tm ff t in\n Tv_AscribedT e t topt use_eq\n | Tv_AscribedC e c topt use_eq ->\n let e = visit_tm ff e in\n let c = visit_comp ff c in\n Tv_AscribedC e c topt use_eq\n in\n ff (pack_ln tv')\nand visit_br (ff : term -> Tac term) (b:branch) : Tac branch =\n let (p, t) = b in\n let p = visit_pat ff p in\n let t = visit_tm ff t in\n (p, t)\nand visit_pat (ff : term -> Tac term) (p:pattern) : Tac pattern =\n match p with\n | Pat_Constant _ -> p\n | Pat_Var v s -> Pat_Var v s\n | Pat_Cons head univs subpats ->\n let subpats = (map (fun(p,b) -> (visit_pat ff p, b)) subpats) in\n Pat_Cons head univs subpats\n | Pat_Dot_Term t ->\n let t = map_opt (visit_tm ff) t in\n Pat_Dot_Term t\n\nand visit_comp (ff : term -> Tac term) (c : comp) : Tac comp =\n let cv = inspect_comp c in\n let cv' =\n match cv with\n | C_Total ret ->\n let ret = visit_tm ff ret in\n C_Total ret\n\n | C_GTotal ret ->\n let ret = visit_tm ff ret in\n C_GTotal ret\n\n | C_Lemma pre post pats ->\n let pre = visit_tm ff pre in\n let post = visit_tm ff post in\n let pats = visit_tm ff pats in\n C_Lemma pre post pats\n\n | C_Eff us eff res args decrs ->\n let res = visit_tm ff res in\n let args = map (fun (a, q) -> (visit_tm ff a, q)) args in\n let decrs = map (visit_tm ff) decrs in\n C_Eff us eff res args decrs\n in\n pack_comp cv'", "val param (t: term) : Tac term\nlet param (t:term) : Tac term =\n let t = param' init_param_state t in\n //dump (\"res = \" ^ term_to_string t);\n t", "val tm_fvar (l: fv) : term\nlet tm_fvar (l:fv) : term =\n tm_fstar (R.pack_ln (R.Tv_FVar (R.pack_fv l.fv_name)))\n l.fv_range", "val head_of (t: term) : Tac (option fv)\nlet rec head_of (t:term) : Tac (option fv) =\n (* NB: must use `inspect` to make use of unionfind graph.\n inspect_ln won't work. *)\n match inspect t with\n | Tv_FVar fv\n | Tv_UInst fv _ -> Some fv\n | Tv_App h _ -> head_of h\n | v -> None", "val param_fv (s: param_state) (f: fv) : Tac fv\nlet rec param' (s:param_state) (t:term) : Tac term =\n let r =\n match inspect t with\n | Tv_Type _u -> // t = Type\n `(fun (s t : (`#t)) -> s -> t -> Type)\n\n | Tv_Var bv ->\n let (_, _, b) = lookup s bv in\n binder_to_term b\n\n | Tv_Arrow b c -> // t1 -> t2 === (x:t1) -> Tot t2\n begin match inspect_comp c with\n | C_Total t2 ->\n let (s', (bx0, bx1, bxR)) = push_binder b s in\n let q = b.qual in\n\n let bf0 = fresh_binder_named \"f0\" (replace_by s false t) in\n let bf1 = fresh_binder_named \"f1\" (replace_by s true t) in\n let b2t = binder_to_term in\n let res = `((`#(param' s' t2)) (`#(tapp q (b2t bf0) (b2t bx0))) (`#(tapp q (b2t bf1) (b2t bx1)))) in\n tabs bf0 (tabs bf1 (mk_tot_arr [bx0; bx1; bxR] res))\n | _ -> raise (Unsupported \"effects\")\n end\n\n | Tv_App l (r, q) ->\n let lR = param' s l in\n let l0 = replace_by s false r in\n let l1 = replace_by s true r in\n let rR = param' s r in\n mk_app lR [(l0, q); (l1, q); (rR, q)]\n\n | Tv_Abs b t ->\n let abs b t : Tac term = pack (Tv_Abs b t) in\n let (s', (bx0, bx1, bxR)) = push_binder b s in\n\n let t = param' s' t in\n abs bx0 (abs bx1 (abs bxR t))\n\n | Tv_Match t None brs ->\n pack (Tv_Match (param' s t) None (map (param_br s) brs))\n\n | Tv_UInst fv _\n | Tv_FVar fv ->\n pack (Tv_FVar (param_fv s fv))\n\n | Tv_Const c ->\n `()\n\n | Tv_AscribedT t _ _ _\n | Tv_AscribedC t _ _ _ -> param' s t\n\n | _ ->\n let q = inspect t in\n raise (Unsupported (term_to_string (quote q)))\n in\n r\n\nand param_fv (s:param_state) (f : fv) : Tac fv =\n (* first of all look for recursive knots *)\n try lookup_rec_fv s f\n with\n | _ ->\n\n (* try to get it from the same module the FV is defined *)\n let nm' = explode_qn (implode_qn (inspect_fv f) ^ \"_param\") in\n //dump (\"nm' = \" ^ implode_qn nm');\n match lookup_typ (top_env ()) nm' with\n | Some se' -> pack_fv nm'\n | None ->\n\n (* or this module, where the translation is defined... *)\n let nm' = [\"Param_Inds\"] @ [last (inspect_fv f) ^ \"_param\"] in\n //dump (\"nm' = \" ^ implode_qn nm');\n match lookup_typ (top_env ()) nm' with\n | Some se' -> pack_fv nm'\n | None ->\n\n (* otherwise, try to get it from the *current* module, where we're running the tactic *)\n let nm' = cur_module () @ [last (inspect_fv f) ^ \"_param\"] in\n //dump (\"nm' = \" ^ implode_qn nm');\n match lookup_typ (top_env ()) nm' with\n | Some se' -> pack_fv nm'\n\n (* TODO: lookup in env *)\n\n | None ->\n raise (NotFoundFV f)\n\nand param_pat (s:param_state) (p : pattern) : Tac (param_state & (pattern & pattern & pattern)) =\n let is_dot_pat (p:pattern) : Tac bool =\n match p with\n | Pat_Dot_Term _ -> true\n | _ -> false\n in\n //dump (\"param_pat of \" ^ term_to_string (quote p));\n match p with\n | Pat_Cons {head=fv; univs=us; subpats=pats} ->\n let fv' = param_fv s fv in\n let (s', (pats0, pats1, patsr)) =\n fold_left (fun (s, (pats0, pats1, patsr)) (p, i) ->\n if is_dot_pat p then (s, (pats0, pats1, patsr))\n else\n let (s', (p0, p1, pr)) = param_pat s p in\n (s', (\n (p0,i)::pats0,\n (p1,i)::pats1,\n (pr,false)::(p1,i)::(p0,i)::patsr)))\n (s, ([], [], []))\n pats\n in\n let pats0 = List.Tot.rev pats0 in\n let pats1 = List.Tot.rev pats1 in\n let patsr = List.Tot.rev patsr in\n (s', (Pat_Cons {head=fv; univs=us; subpats=pats0},\n Pat_Cons {head=fv; univs=us; subpats=pats1},\n Pat_Cons {head=fv'; univs=us; subpats=patsr}))\n\n | Pat_Var {v; sort} ->\n let b = namedv_to_binder v (unseal sort) in\n let (s', (b0, b1, bR)) = push_binder b s in\n (s', (Pat_Var {v=binder_to_namedv b0; sort = Sealed.seal (binder_sort b0)},\n Pat_Var {v=binder_to_namedv b1; sort = Sealed.seal (binder_sort b1)},\n Pat_Var {v=binder_to_namedv bR; sort = Sealed.seal (binder_sort bR)}))\n\n | Pat_Dot_Term t ->\n fail \"no dot pats\"\n //let (s', (b0, b1, bR)) = push_binder (pack_binder bv Q_Explicit) s in\n //(s', (Pat_Dot_Term (bv_of_binder b0) (replace_by s' false t),\n // Pat_Dot_Term (bv_of_binder b1) (replace_by s' true t),\n // Pat_Dot_Term (bv_of_binder bR) (param' s' t)))\n\n | Pat_Constant c ->\n let b = fresh_binder_named \"cR\" (`_) in\n (s, (Pat_Constant c,\n Pat_Constant c,\n Pat_Var {v=binder_to_namedv b; sort=seal (`_)}))\n\nand param_br (s:param_state) (br : branch) : Tac branch =\n let (pat, t) = br in\n let (s', (_, _, pat')) = param_pat s pat in\n (pat', param' s' t)\n\nand push_binder (b:binder) (s:param_state) : Tac (param_state & (binder & binder & binder)) =\n let q = b.qual in\n let typ = b.sort in\n let name = unseal b.ppname in\n let decor (s : string) (t : string) : Tac string = (s ^ t) in\n let bx0 = fresh_binder_named (decor name \"0\") (replace_by s false typ) in\n let bx1 = fresh_binder_named (decor name \"1\") (replace_by s true typ) in\n let bxr = fresh_binder_named (decor name \"R\") (`(`#(param' s typ)) (`#(binder_to_term bx0)) (`#(binder_to_term bx1))) in\n\n (* respect implicits *)\n let bx0 = binder_set_qual bx0 q in\n let bx1 = binder_set_qual bx1 q in\n let bxr = binder_set_qual bxr q in\n\n let s = push_var_to_state (binder_to_namedv b) bx0 bx1 bxr s in\n (s, (bx0, bx1, bxr))", "val make_fvar (#a: Type) (t: term) (unquotea: (term -> Tac a)) (ts: list term) (vm: vmap a)\n : Tac (polynomial a * list term * vmap a)\nlet make_fvar (#a:Type) (t:term) (unquotea:term -> Tac a) (ts:list term)\n (vm:vmap a) : Tac (polynomial a * list term * vmap a) =\n match find t ts with\n | Some v -> (Pvar v, ts, vm)\n | None ->\n let vfresh = length ts in\n let z = unquotea t in\n (Pvar vfresh, ts @ [t], update vfresh z vm)", "val def_of (#t: Type) (x: t) : Tac term\nlet def_of (#t:Type) (x:t) : Tac term =\n let e = cur_env () in\n let t = quote x in\n match inspect t with\n | Tv_UInst fv _\n | Tv_FVar fv -> begin\n let se = match lookup_typ e (inspect_fv fv) with\n | None -> fail \"Not found..?\"\n | Some se -> se\n in\n match inspect_sigelt se with\n | Sg_Let {lbs} -> begin\n let lbv = lookup_lb lbs (inspect_fv fv) in\n lbv.lb_def\n end\n | _ -> fail \"not a sig_let\"\n end\n | _ -> fail \"not an fvar\"", "val free_in : term -> Tac (list bv)\nlet free_in t =\n let same_name (bv1 bv2 : bv) : Tac bool =\n name_of_bv bv1 = name_of_bv bv2\n in\n let update_free (fl:list bv) (ge:genv) (pl:list (genv & term_view))\n (c:option typ_or_comp) (tv:term_view) :\n Tac (list bv & ctrl_flag) =\n match tv with\n | Tv_Var bv | Tv_BVar bv ->\n (* Check if the binding was not introduced during the traversal *)\n begin match genv_get_from_name ge (name_of_bv bv) with\n | None ->\n (* Check if we didn't already count the binding *)\n let fl' = if Tactics.tryFind (same_name bv) fl then fl else bv :: fl in\n fl', Continue\n | Some _ -> fl, Continue\n end\n | _ -> fl, Continue\n in\n let e = top_env () in (* we actually don't care about the environment *)\n let ge = mk_genv e [] [] in\n List.Tot.rev (fst (explore_term false false update_free [] ge [] None t))", "val pose (t: term) : Tac binding\nlet pose (t:term) : Tac binding =\n apply (`__cut);\n flip ();\n exact t;\n intro ()", "val pack_fv' (n: name) : term\nlet pack_fv' (n:name) : term = pack_ln (Tv_FVar (pack_fv n))", "val tag_of (t: term) : Tac string\nlet tag_of (t:term) : Tac string =\n match inspect t with\n | Tv_Var bv -> \"Tv_Var\"\n | Tv_BVar fv -> \"Tv_BVar\"\n | Tv_FVar fv -> \"Tv_FVar\"\n | Tv_UInst _ _ -> \"Tv_UInst\"\n | Tv_App f x -> \"Tv_App\"\n | Tv_Abs x t -> \"Tv_Abs\"\n | Tv_Arrow x t -> \"Tv_Arrow\"\n | Tv_Type _ -> \"Tv_Type\"\n | Tv_Refine x t -> \"Tv_Refine\"\n | Tv_Const cst -> \"Tv_Const\"\n | Tv_Uvar i t -> \"Tv_Uvar\"\n | Tv_Let r attrs b t1 t2 -> \"Tv_Let\"\n | Tv_Match t _ branches -> \"Tv_Match\"\n | Tv_AscribedT _ _ _ _ -> \"Tv_AscribedT\"\n | Tv_AscribedC _ _ _ _ -> \"Tv_AscribedC\"\n | Tv_Unknown -> \"Tv_Unknown\"\n | Tv_Unsupp -> \"Tv_Unsupp\"", "val inst_comp : env -> comp -> list term -> Tac comp\nlet rec inst_comp e c tl =\n match tl with\n | [] -> c\n | t :: tl' ->\n let c' = try inst_comp_once e c t\n with | MetaAnalysis msg -> mfail (\"inst_comp: error: \" ^ msg)\n | err -> raise err\n in\n inst_comp e c' tl'", "val term_as_formula (t: term) : Tac formula\nlet term_as_formula (t:term) : Tac formula =\n match unsquash_term t with\n | None -> F_Unknown\n | Some t ->\n term_as_formula' t", "val term_as_formula (t: term) : Tac formula\nlet term_as_formula (t:term) : Tac formula =\n match unsquash_term t with\n | None -> F_Unknown\n | Some t ->\n term_as_formula' t", "val is_eq (t: term) : Tac (option (term & term))\nlet is_eq (t:term) : Tac (option (term & term)) =\n match term_as_formula t with\n | Comp (Eq _) l r -> Some (l, r)\n | _ -> None", "val visit_tm (ff: (term -> Tac unit)) (t: term) : Tac unit\nlet rec visit_tm (ff : term -> Tac unit) (t : term) : Tac unit =\n let tv = inspect t in\n (match tv with\n | Tv_FVar _\n | Tv_UInst _ _\n | Tv_Var _\n | Tv_BVar _ -> ()\n\n | Tv_Type _ -> ()\n | Tv_Const c -> ()\n | Tv_Uvar i u -> ()\n | Tv_Unsupp -> ()\n | Tv_Unknown -> ()\n | Tv_Arrow b c ->\n on_sort_binder ff b;\n visit_comp ff c\n | Tv_Abs b t ->\n let b = on_sort_binder (visit_tm ff) b in\n visit_tm ff t\n\n | Tv_App l (r, q) ->\n visit_tm ff l;\n visit_tm ff r\n\n | Tv_Refine b r ->\n on_sort_binder ff b;\n visit_tm ff r\n\n | Tv_Let r attrs b def t ->\n on_sort_binder ff b;\n visit_tm ff def;\n visit_tm ff t\n\n | Tv_Match sc _ brs ->\n visit_tm ff sc;\n iter (visit_br ff) brs\n\n | Tv_AscribedT e t topt _ ->\n visit_tm ff e;\n visit_tm ff t\n\n | Tv_AscribedC e c topt _ ->\n visit_tm ff e\n\n ); ff t\n\nand visit_br (ff : term -> Tac unit) (b:branch) : Tac unit =\n let (p, t) = b in\n visit_tm ff t\n\nand visit_comp (ff : term -> Tac unit) (c : comp) : Tac unit =\n let cv = inspect_comp c in\n match cv with\n | C_Total ret -> visit_tm ff ret\n | C_GTotal ret -> visit_tm ff ret\n\n | C_Lemma pre post pats ->\n visit_tm ff pre;\n visit_tm ff post;\n visit_tm ff pats\n\n | C_Eff us eff res args decrs ->\n visit_tm ff res;\n iter (fun (a, q) -> visit_tm ff a) args;\n iter (visit_tm ff) decrs", "val inspect (t:term) : Tac named_term_view\nlet inspect (t:term) : Tac named_term_view =\n let t = compress t in\n let tv = inspect_ln t in\n open_view tv", "val unfold_term (t: T.term) : T.Tac T.term\nlet unfold_term (t: T.term) : T.Tac T.term =\n match T.inspect t with\n | T.Tv_FVar v -> unfold_fv v\n | _ -> tfail \"Not a global variable\"", "val term_construct (t : term) : Tac string\nlet term_construct (t : term) : Tac string =\n term_view_construct (inspect t)", "val trywith (head_fv: fv) (seen: list term) (glb: list fv) (fuel: int) (t typ: term) : Tac unit\nlet rec tcresolve' (seen : list term) (glb : list fv) (fuel : int) : Tac unit =\n if fuel <= 0 then\n raise NoInst;\n debug (fun () -> \"fuel = \" ^ string_of_int fuel);\n\n let g = cur_goal () in\n\n (* Try to detect loops *)\n if L.existsb (Reflection.V2.TermEq.term_eq g) seen then (\n debug (fun () -> \"loop\");\n raise NoInst\n );\n\n match head_of g with\n | None ->\n debug (fun () -> \"goal does not look like a typeclass\");\n raise NoInst\n\n | Some head_fv ->\n (* ^ Maybe should check is this really is a class too? *)\n let seen = g :: seen in\n local head_fv seen glb fuel\n `or_else`\n global head_fv seen glb fuel\n\nand local (head_fv : fv) (seen : list term) (glb : list fv) (fuel : int) () : Tac unit =\n let bs = vars_of_env (cur_env ()) in\n first (fun (b:binding) ->\n trywith head_fv seen glb fuel (pack (Tv_Var b)) b.sort)\n bs\n\nand global (head_fv : fv) (seen : list term) (glb : list fv) (fuel : int) () : Tac unit =\n first (fun fv ->\n let typ = tc (cur_env()) (pack (Tv_FVar fv)) in // FIXME: a bit slow.. but at least it's a simple fvar\n trywith head_fv seen glb fuel (pack (Tv_FVar fv)) typ)\n glb\n\nand trywith (head_fv : fv) (seen:list term) (glb : list fv) (fuel:int) (t typ : term) : Tac unit =\n debug (fun () -> \"trywith \" ^ term_to_string t);\n match head_of (res_typ typ) with\n | None ->\n debug (fun () -> \"no head for typ of this? \" ^ term_to_string t ^ \" typ=\" ^ term_to_string typ);\n raise NoInst\n | Some fv' ->\n if fv_eq fv' head_fv\n then (\n debug (fun () -> \"Trying to apply hypothesis/instance: \" ^ term_to_string t);\n (fun () -> apply_noinst t) `seq` (fun () ->\n debug (fun () -> dump \"next\"; \"apply seems to have worked\");\n tcresolve' seen glb (fuel-1))\n ) else (\n debug (fun () -> \"different class: \" ^ fv_to_string fv' ^ \" <> \" ^ fv_to_string head_fv);\n raise NoInst\n )", "val canon_term (t: term) : Tac expr\nlet canon_term (t:term) : Tac expr = canon_expr' (term_to_expr t)", "val exact_with_ref (t: term) : Tac unit\nlet exact_with_ref (t : term) : Tac unit =\n with_policy SMT (fun () -> t_exact true true t)", "val exact_with_ref (t: term) : Tac unit\nlet exact_with_ref (t : term) : Tac unit =\n with_policy SMT (fun () -> t_exact true true t)", "val instantiate (fa x: term) : Tac binding\nlet instantiate (fa : term) (x : term) : Tac binding =\n try pose (`__forall_inst_sq (`#fa) (`#x)) with | _ ->\n try pose (`__forall_inst (`#fa) (`#x)) with | _ ->\n fail \"could not instantiate\"", "val invert_function' (enum_ty val_ty teq f: T.term) : T.Tac T.term\nlet invert_function' (enum_ty val_ty: T.term) (teq: T.term) (f: T.term) : T.Tac T.term =\n match T.inspect f with\n | T.Tv_Abs b body ->\n begin match T.inspect body with\n | T.Tv_Match t _ br ->\n if T.term_eq t (T.pack (T.Tv_Var (T.binder_to_namedv b)))\n then\n let bx = T.fresh_binder val_ty in\n let x = T.pack (T.Tv_Var (T.binder_to_namedv bx)) in\n T.pack (T.Tv_Abs bx (invert_branches_with_cascade enum_ty teq x None br))\n else T.fail \"Not a function destructing on its argument\"\n | _ -> T.fail \"Not a match\"\n end\n | _ -> T.fail \"Not a function\"", "val apply (t: term) : Tac unit\nlet apply (t : term) : Tac unit =\n t_apply true false false t", "val apply (t: term) : Tac unit\nlet apply (t : term) : Tac unit =\n t_apply true false false t", "val unfold_def (t: term) : Tac unit\nlet unfold_def (t:term) : Tac unit =\n match inspect t with\n | Tv_FVar fv ->\n let n = implode_qn (inspect_fv fv) in\n norm [delta_fully [n]]\n | _ -> fail \"unfold_def: term is not a fv\"", "val unfold_def (t: term) : Tac unit\nlet unfold_def (t:term) : Tac unit =\n match inspect t with\n | Tv_FVar fv ->\n let n = implode_qn (inspect_fv fv) in\n norm [delta_fully [n]]\n | _ -> fail \"unfold_def: term is not a fv\"", "val add_one (t: term) : Tac term\nlet add_one (t:term) : Tac term = `(`#t + 1)", "val pose (t: term) : Tac binder\nlet pose (t:term) : Tac binder =\n apply (`__cut);\n flip ();\n exact t;\n intro ()", "val apply (t: T.term) : T.Tac unit\nlet apply (t:T.term) : T.Tac unit =\n T.t_apply true false true t", "val apply (t: T.term) : T.Tac unit\nlet apply (t:T.term) : T.Tac unit =\n T.t_apply true false true t", "val instantiate (fa x: term) : Tac binder\nlet instantiate (fa : term) (x : term) : Tac binder =\n try pose (`__forall_inst_sq (`#fa) (`#x)) with | _ ->\n try pose (`__forall_inst (`#fa) (`#x)) with | _ ->\n fail \"could not instantiate\"", "val is_uvar (t: term) : Tac bool\nlet is_uvar (t:term) : Tac bool = match inspect t with\n | Tv_Uvar _ _ -> true\n | Tv_App _ _ ->\n let hd, args = collect_app t in\n Tv_Uvar? (inspect hd)\n | _ -> false", "val is_uvar (t: term) : Tac bool\nlet is_uvar (t:term) : Tac bool = match inspect t with\n | Tv_Uvar _ _ -> true\n | Tv_App _ _ ->\n let hd, args = collect_app t in\n Tv_Uvar? (inspect hd)\n | _ -> false", "val open_term (t:term) (v:var) : term\nlet open_term (t:term) (v:var) = RTB.open_term t v", "val term_as_formula' (t: term) : Tac formula\nlet term_as_formula' (t:term) : Tac formula =\n match inspect_unascribe t with\n | Tv_Var n ->\n Name n\n\n | Tv_FVar fv\n | Tv_UInst fv _ ->\n // Cannot use `when` clauses when verifying!\n let qn = inspect_fv fv in\n if qn = true_qn then True_\n else if qn = false_qn then False_\n else FV fv\n\n // TODO: l_Forall\n // ...or should we just try to drop all squashes?\n // TODO: b2t at this point ?\n | Tv_App h0 t -> begin\n let (h, ts) = collect_app h0 in\n let h = un_uinst h in\n match inspect h, ts@[t] with\n | Tv_FVar fv, [(a1, Q_Implicit); (a2, Q_Explicit); (a3, Q_Explicit)] ->\n let qn = inspect_fv fv in\n if qn = eq2_qn then Comp (Eq (Some a1)) a2 a3\n else if qn = eq1_qn then Comp (BoolEq (Some a1)) a2 a3\n else if qn = lt_qn then Comp Lt a2 a3\n else if qn = lte_qn then Comp Le a2 a3\n else if qn = gt_qn then Comp Gt a2 a3\n else if qn = gte_qn then Comp Ge a2 a3\n else App h0 (fst t)\n | Tv_FVar fv, [(a1, Q_Explicit); (a2, Q_Explicit)] ->\n let qn = inspect_fv fv in\n if qn = imp_qn then Implies a1 a2\n else if qn = and_qn then And a1 a2\n else if qn = iff_qn then Iff a1 a2\n else if qn = or_qn then Or a1 a2\n // Non-annotated comparisons\n else if qn = eq2_qn then Comp (Eq None) a1 a2\n else if qn = eq1_qn then Comp (BoolEq None) a1 a2\n else App h0 (fst t)\n\n | Tv_FVar fv, [(a1, Q_Implicit); (a2, Q_Explicit)] ->\n let qn = inspect_fv fv in\n if qn = forall_qn then mk_Forall a1 a2\n else if qn = exists_qn then mk_Exists a1 a2\n else App h0 (fst t)\n | Tv_FVar fv, [(a, Q_Explicit)] ->\n let qn = inspect_fv fv in\n if qn = not_qn then Not a\n else if qn = b2t_qn then begin\n if term_eq a (`false) then False_\n else if term_eq a (`true) then True_\n else App h0 (fst t)\n end\n else App h0 (fst t)\n | _ ->\n App h0 (fst t)\n end\n\n | Tv_Const (C_Int i) ->\n IntLit i\n\n (* Not formulas. *)\n | Tv_Let _ _ _ _ _\n | Tv_Match _ _ _\n | Tv_Type _\n | Tv_Abs _ _\n | Tv_Arrow _ _\n | Tv_Uvar _ _\n | Tv_Unknown\n | Tv_Unsupp\n | Tv_Refine _ _ -> F_Unknown\n\n (* Other constants? *)\n | Tv_Const _ -> F_Unknown\n\n (* Should not occur, we're using inspect *)\n | Tv_BVar _ -> F_Unknown\n | _ -> raise (TacticFailure \"???\")", "val term_as_formula' (t: term) : Tac formula\nlet term_as_formula' (t:term) : Tac formula =\n match inspect_unascribe t with\n | Tv_Var n ->\n Name n\n\n | Tv_FVar fv\n | Tv_UInst fv _ ->\n // Cannot use `when` clauses when verifying!\n let qn = inspect_fv fv in\n if qn = true_qn then True_\n else if qn = false_qn then False_\n else FV fv\n\n // TODO: l_Forall\n // ...or should we just try to drop all squashes?\n // TODO: b2t at this point ?\n | Tv_App h0 t -> begin\n let (h, ts) = collect_app h0 in\n let h = un_uinst h in\n match inspect_ln h, ts@[t] with\n | Tv_FVar fv, [(a1, Q_Implicit); (a2, Q_Explicit); (a3, Q_Explicit)] ->\n let qn = inspect_fv fv in\n if qn = eq2_qn then Comp (Eq (Some a1)) a2 a3\n else if qn = eq1_qn then Comp (BoolEq (Some a1)) a2 a3\n else if qn = lt_qn then Comp Lt a2 a3\n else if qn = lte_qn then Comp Le a2 a3\n else if qn = gt_qn then Comp Gt a2 a3\n else if qn = gte_qn then Comp Ge a2 a3\n else App h0 (fst t)\n | Tv_FVar fv, [(a1, Q_Explicit); (a2, Q_Explicit)] ->\n let qn = inspect_fv fv in\n if qn = imp_qn then Implies a1 a2\n else if qn = and_qn then And a1 a2\n else if qn = iff_qn then Iff a1 a2\n else if qn = or_qn then Or a1 a2\n // Non-annotated comparisons\n else if qn = eq2_qn then Comp (Eq None) a1 a2\n else if qn = eq1_qn then Comp (BoolEq None) a1 a2\n else App h0 (fst t)\n\n | Tv_FVar fv, [(a1, Q_Implicit); (a2, Q_Explicit)] ->\n let qn = inspect_fv fv in\n if qn = forall_qn then mk_Forall a1 a2\n else if qn = exists_qn then mk_Exists a1 a2\n else App h0 (fst t)\n | Tv_FVar fv, [(a, Q_Explicit)] ->\n let qn = inspect_fv fv in\n if qn = not_qn then Not a\n else if qn = b2t_qn then begin\n if term_eq a (`false) then False_\n else if term_eq a (`true) then True_\n else App h0 (fst t)\n end\n else App h0 (fst t)\n | _ ->\n App h0 (fst t)\n end\n\n | Tv_Const (C_Int i) ->\n IntLit i\n\n (* Not formulas. *)\n | Tv_Let _ _ _ _ _ _\n | Tv_Match _ _ _\n | Tv_Type _\n | Tv_Abs _ _\n | Tv_Arrow _ _\n | Tv_Uvar _ _\n | Tv_Unknown\n | Tv_Unsupp\n | Tv_Refine _ _ _ -> F_Unknown\n\n (* Other constants? *)\n | Tv_Const _ -> F_Unknown\n\n (* Should not occur, we're using inspect_ln *)\n | Tv_BVar _ -> F_Unknown", "val is_fvar (t: term) : option (R.name & list universe)\nlet is_fvar (t:term) : option (R.name & list universe) =\n let open R in\n match t.t with\n | Tm_FStar host_term ->\n begin match inspect_ln host_term with\n | Tv_FVar fv -> Some (inspect_fv fv, [])\n | Tv_UInst fv us -> Some (inspect_fv fv, us)\n | _ -> None\n end\n | _ -> None", "val subst_map (ss: list (namedv * fv)) (r t: term) : Tac term\nlet subst_map (ss : list (namedv * fv)) (r:term) (t : term) : Tac term =\n let subst = List.Tot.map (fun (x, fv) -> NT (Reflection.V2.pack_namedv x) (mk_e_app (Tv_FVar fv) [r])) ss in\n subst_term subst t", "val bv_to_term (bv: bv) : Tac term\nlet bv_to_term (bv : bv) : Tac term = pack (Tv_Var bv)", "val st_term_to_string (t:st_term) : T.Tac string\nlet st_term_to_string t = st_term_to_string' \"\" t", "val check (t: term) : Tac bool\nlet rec check (t:term) : Tac bool =\n match inspect t with\n (* We are using the named view, which opens terms\n as needed on every node. If we reach a bvar, the original\n term is not LN. *)\n | Tv_BVar bv -> false\n\n | Tv_Const _ -> true\n | Tv_Uvar _ _ -> false (* conservative *)\n\n | Tv_Var _ -> true\n | Tv_FVar _ -> true\n | Tv_UInst _ us -> for_all check_u us\n | Tv_App hd (a, q) -> if check hd then check a else false\n | Tv_Abs b body -> if check b.sort then check body else false\n | Tv_Arrow b c -> if check b.sort then check_comp c else false\n | Tv_Type u -> check_u u\n | Tv_Refine b ref -> if check b.sort then check ref else false\n | Tv_Let recf attrs b def body ->\n if not (for_all check attrs) then false else\n if not (check def) then false else\n check body\n | Tv_Match sc _ brs -> \n if check sc then for_all check_br brs else false\n | Tv_AscribedT e t _ _ ->\n if check e then check t else false\n | Tv_AscribedC e c _ _ ->\n if check e then check_comp c else false\n\n | Tv_Unknown -> true\n | Tv_Unsupp -> true // hm..\nand check_u (u:universe) : Tac bool =\n match inspect_universe u with\n | Uv_BVar _ -> false\n | Uv_Name _ -> true\n | Uv_Unif _ -> false (* conservative *)\n | Uv_Zero -> true\n | Uv_Succ u -> check_u u\n | Uv_Max us -> for_all check_u us\n | Uv_Unk -> true\nand check_comp (c:comp) : Tac bool =\n match c with\n | C_Total typ -> check typ\n | C_GTotal typ -> check typ\n | C_Lemma pre post pats -> \n if not (check pre) then false else\n if not (check post) then false else\n check pats\n | C_Eff us nm res args decrs ->\n if not (for_all check_u us) then false else\n if not (check res) then false else\n if not (for_all (fun (a,q) -> check a) args) then false else\n if not (for_all check decrs) then false else\n true\n \nand check_br (b:branch) : Tac bool =\n (* Could check the pattern's ascriptions too. *)\n let (p, t) = b in\n check t", "val term_of_pat (t: T.pattern) : T.Tac (option T.term)\nlet term_of_pat (t: T.pattern) : T.Tac (option T.term) =\n match t with\n | T.Pat_Constant {c=v} -> Some (T.pack (T.Tv_Const v))\n | T.Pat_Cons {head=v; univs=None; subpats=[]} -> Some (T.pack (T.Tv_FVar v))\n | T.Pat_Cons {head=v; univs=Some []; subpats=[]} -> Some (T.pack (T.Tv_FVar v)) \n | T.Pat_Cons {head=v; univs=Some us; subpats=[]} -> Some (T.pack (T.Tv_UInst v us)) \n | _ -> None", "val open_with (t:term) (v:term) : term\nlet open_with (t:term) (v:term) = RTB.open_with t v", "val terms_to_string (t: list term) : T.Tac string\nlet terms_to_string (t:list term)\n : T.Tac string \n = String.concat \"\\n\" (T.map Pulse.Syntax.Printer.term_to_string t)", "val terms_to_string (t: list term) : T.Tac string\nlet terms_to_string (t:list term)\n : T.Tac string \n = String.concat \"\\n\" (T.map Pulse.Syntax.Printer.term_to_string t)", "val term_to_ast_string (t: term) : Tac string\nlet rec term_to_ast_string (t:term) : Tac string =\n match inspect t with\n | Tv_Var bv -> \"Tv_Var \" ^ namedv_to_string bv\n | Tv_BVar bv -> \"Tv_BVar \" ^ bv_to_string bv\n | Tv_FVar fv -> \"Tv_FVar \" ^ fv_to_string fv\n | Tv_UInst fv us ->\n \"Tv_UInst\" ^ paren (fv_to_string fv ^ \", \" ^ universes_to_ast_string us)\n | Tv_App hd (a, _) -> \"Tv_App \" ^ paren (term_to_ast_string hd ^ \", \" ^ term_to_ast_string a)\n | Tv_Abs x e -> \"Tv_Abs \" ^ paren (binder_to_string x ^ \", \" ^ term_to_ast_string e)\n | Tv_Arrow x c -> \"Tv_Arrow \" ^ paren (binder_to_string x ^ \", \" ^ comp_to_ast_string c)\n | Tv_Type u -> \"Type\" ^ paren (universe_to_ast_string u)\n | Tv_Refine x e -> \"Tv_Refine \" ^ paren (binder_to_string x ^ \", \" ^ term_to_ast_string e)\n | Tv_Const c -> const_to_ast_string c\n | Tv_Uvar i _ -> \"Tv_Uvar \" ^ string_of_int i\n | Tv_Let recf _ x e1 e2 ->\n \"Tv_Let \" ^ paren (string_of_bool recf ^ \", \" ^\n binder_to_string x ^ \", \" ^\n term_to_ast_string e1 ^ \", \" ^\n term_to_ast_string e2)\n | Tv_Match e ret_opt brs ->\n \"Tv_Match \" ^\n paren (\n term_to_ast_string e ^\n \", \" ^\n match_returns_to_string ret_opt ^\n \", \" ^\n branches_to_ast_string brs)\n | Tv_AscribedT e t _ use_eq -> \"Tv_AscribedT \" ^ paren (term_to_ast_string e ^ \", \" ^ term_to_ast_string t ^ \", \" ^ string_of_bool use_eq)\n | Tv_AscribedC e c _ use_eq -> \"Tv_AscribedC \" ^ paren (term_to_ast_string e ^ \", \" ^ comp_to_ast_string c ^ \", \" ^ string_of_bool use_eq)\n | Tv_Unknown -> \"_\"\n | Tv_Unsupp -> \"\"\n\nand match_returns_to_string (ret_opt:option match_returns_ascription) : Tac string =\n let tacopt_to_string tacopt : Tac string =\n match tacopt with\n | None -> \"\"\n | Some tac -> \" by \" ^ (term_to_ast_string tac) in\n match ret_opt with\n | None -> \"\"\n | Some (b, asc) ->\n (binder_to_string b ^ \" \")\n ^\n (match asc with\n | Inl t, tacopt, _ -> (term_to_ast_string t) ^ (tacopt_to_string tacopt)\n | Inr c, tacopt, _ -> (comp_to_ast_string c) ^ (tacopt_to_string tacopt))\n\nand branches_to_ast_string (brs:list branch) : Tac string =\n print_list branch_to_ast_string brs\n\nand branch_to_ast_string (b:branch) : Tac string =\n let p, e = b in\n paren (\"_pat, \" ^ term_to_ast_string e)\n\nand comp_to_ast_string (c:comp) : Tac string =\n match inspect_comp c with\n | C_Total t -> \"Tot \" ^ term_to_ast_string t\n | C_GTotal t -> \"GTot \" ^ term_to_ast_string t\n | C_Lemma pre post _ -> \"Lemma \" ^ term_to_ast_string pre ^ \" \" ^ term_to_ast_string post\n | C_Eff us eff res _ _ ->\n \"Effect\" ^ \"<\" ^ universes_to_ast_string us ^ \"> \" ^ paren (implode_qn eff ^ \", \" ^ term_to_ast_string res)\n\nand const_to_ast_string (c:vconst) : Tac string =\n match c with\n | C_Unit -> \"C_Unit\"\n | C_Int i -> \"C_Int \" ^ string_of_int i\n | C_True -> \"C_True\"\n | C_False -> \"C_False\"\n | C_String s -> \"C_String \" ^ s\n | C_Range _ -> \"C_Range _\"\n | C_Reify -> \"C_Reify\"\n | C_Reflect name -> \"C_Reflect \" ^ implode_qn name", "val pat_of_term (t: T.term) : T.Tac T.pattern\nlet pat_of_term (t: T.term) : T.Tac T.pattern =\n let t = T.norm_term_env (T.cur_env ()) [delta; iota; primops] t in\n match T.inspect t with\n | T.Tv_Const v -> T.Pat_Constant {c=v}\n | T.Tv_FVar v -> T.Pat_Cons {head=v; univs=Some []; subpats=[]}\n | _ -> T.fail \"Not a pattern\"", "val fv_to_string (fv: fv) : string\nlet fv_to_string (fv:fv) : string = implode_qn (inspect_fv fv)", "val fv_to_string (fv: fv) : string\nlet fv_to_string (fv:fv) : string = implode_qn (inspect_fv fv)", "val apply_noinst (t: term) : Tac unit\nlet apply_noinst (t : term) : Tac unit =\n t_apply true true false t", "val apply_noinst (t: term) : Tac unit\nlet apply_noinst (t : term) : Tac unit =\n t_apply true true false t", "val is_term_an_invocation_of_function (t fn: term) (argc: nat) : Tac bool\nlet rec is_term_an_invocation_of_function (t: term) (fn: term) (argc: nat) : Tac bool =\n if argc = 0 then\n term_eq t fn\n else\n match t with\n | Tv_App fn' arg -> is_term_an_invocation_of_function fn' fn (argc - 1)\n | _ -> false", "val term_to_string' (level: string) (t: term) : T.Tac string\nlet rec binder_to_string_paren (b:binder)\n : T.Tac string\n = sprintf \"(%s%s:%s)\"\n (match T.unseal b.binder_attrs with\n | [] -> \"\"\n | l -> sprintf \"[@@@ %s] \" (String.concat \";\" (T.map (term_to_string' \"\") l)))\n (T.unseal b.binder_ppname.name)\n (term_to_string' \"\" b.binder_ty)\n\nand term_to_string' (level:string) (t:term)\n : T.Tac string\n = match t.t with\n | Tm_Emp -> \"emp\"\n\n | Tm_Pure p ->\n sprintf \"pure (%s)\" \n (term_to_string' (indent level) p)\n \n | Tm_Star p1 p2 ->\n sprintf \"%s ** \\n%s%s\" \n (term_to_string' level p1)\n level\n (term_to_string' level p2)\n \n | Tm_ExistsSL _ _ _ ->\n let bs, body = collect_binders Tm_ExistsSL? t in\n sprintf \"(exists* %s.\\n%s%s)\"\n (T.map binder_to_string_paren bs |> String.concat \" \")\n level\n (term_to_string' (indent level) body)\n\n | Tm_ForallSL u b body ->\n let bs, body = collect_binders Tm_ForallSL? t in\n sprintf \"(forall* %s.\\n%s%s)\"\n (T.map binder_to_string_paren bs |> String.concat \" \")\n level\n (term_to_string' (indent level) body)\n \n | Tm_VProp -> \"vprop\"\n | Tm_Inames -> \"inames\"\n | Tm_EmpInames -> \"emp_inames\"\n | Tm_Unknown -> \"_\"\n | Tm_AddInv i is ->\n sprintf \"add_inv %s %s\"\n (term_to_string' level i)\n (term_to_string' level is)\n | Tm_Inv i ->\n sprintf \"inv %s\"\n (term_to_string' level i)\n | Tm_FStar t ->\n T.term_to_string t", "val term_to_string (t:term) : T.Tac string\nlet term_to_string t = term_to_string' \"\" t", "val norm_term (s: list norm_step) (t: term) : Tac term\nlet norm_term (s : list norm_step) (t : term) : Tac term =\n let e =\n try cur_env ()\n with | _ -> top_env ()\n in\n norm_term_env e s t", "val norm_term (s: list norm_step) (t: term) : Tac term\nlet norm_term (s : list norm_step) (t : term) : Tac term =\n let e =\n try cur_env ()\n with | _ -> top_env ()\n in\n norm_term_env e s t", "val def_t:t\nlet def_t : t = { foo = 0ul; bar = 0us }", "val term_to_view_to_string (t: term) : Tac string\nlet rec term_to_view_to_string (t: term) : Tac string =\n match inspect t with\n | Tv_Var v -> \"Tv_Var \" ^ (namedv_to_string v)\n | Tv_BVar v -> \"Tv_BVar \" ^ (bv_to_string v)\n | Tv_FVar v -> \"Tv_FVar \" ^ (fv_to_string v)\n | Tv_UInst v us -> \"Tv_UInst \" ^ (fv_to_string v)\n | Tv_App hd argv ->\n \"Tv_App(\" ^ (term_to_view_to_string hd) ^ \" \" ^ (term_to_view_to_string (fst argv)) ^ \")\"\n | Tv_Abs b body -> \"Tv_Abs(\" ^ (binder_to_string b) ^ \" -> \" ^ (term_to_view_to_string body) ^ \")\"\n | Tv_Arrow _ _ -> \"Tv_Arrow\"\n | Tv_Type _ -> \"Tv_Type\"\n | Tv_Refine bv ref -> \"Tv_Refine\" ^ (term_to_view_to_string ref)\n | Tv_Const v -> \"Tv_Const(\" ^ (vconst_to_string v) ^ \")\"\n | Tv_Uvar _ _ -> \"Tv_Uvar\"\n | Tv_Let recf attrs bv def body ->\n \"Tv_Let(\" ^ (term_to_view_to_string (binder_to_term bv)) ^\n \" = \" ^ (term_to_view_to_string def) ^ \" in \" ^ (term_to_view_to_string body) ^ \")\"\n | Tv_Match scrutinee ret brs ->\n \"Tv_Match(\" ^ (term_to_view_to_string scrutinee) ^ \" with \" ^ (branches_to_string brs) ^ \")\"\n | Tv_AscribedT e t tac _ -> \"Tv_AscribedT(\" ^ (term_to_view_to_string e) ^ \")\"\n | Tv_AscribedC e c tac _ -> \"Tv_AscribedC(\" ^ (term_to_view_to_string e) ^ \")\"\n | Tv_Unknown -> \"Tv_Unknown\"\n | Tv_Unsupp -> \"Tv_Unsupp\"\n\nand term_views_to_strings (ts: list term) : Tac string =\n match ts with\n | [] -> \"[]\"\n | hd :: tl -> (term_to_view_to_string hd) ^ \" :: \" ^ (term_views_to_strings tl)\n\nand branches_to_string (bs: list branch) : Tac string =\n match bs with\n | [] -> \"\"\n | (branch_pattern, branch_term) :: tl -> \"| ??? -> \" ^ (term_to_view_to_string branch_term) ^ \" \" ^ (branches_to_string tl)", "val inst_comp_once : env -> comp -> term -> Tac comp\nlet inst_comp_once e c t =\n let ty = get_comp_ret_type c in\n let ty' = unfold_until_arrow e ty in\n begin match inspect ty' with\n | Tv_Arrow b1 c1 ->\n subst_binder_in_comp e b1 t c1\n | _ -> (* Inconsistent state *)\n mfail \"inst_comp_once: inconsistent state\"\n end", "val unsquash_equality (t: term) : Tac (option (term & term))\nlet unsquash_equality (t:term) : Tac (option (term & term)) =\n begin match term_as_formula t with\n | Comp (Eq _) l r -> Some (l, r)\n | _ -> None\n end", "val safe_tc (e:env) (t:term) : Tac (option term)\nlet safe_tc e t =\n try Some (tc e t) with | _ -> None", "val atom (t: term) : tm expr\nlet atom (t:term) : tm expr = fun (n, atoms) ->\n match find_idx (term_eq_old t) atoms with\n | None -> Inr (Atom n t, (n + 1, t::atoms))\n | Some (i, t) -> Inr (Atom (n - 1 - i) t, (n, atoms))", "val subst_bv_in_comp : env -> bv -> typ -> term -> comp -> Tac comp\nlet subst_bv_in_comp e b sort t c =\n apply_subst_in_comp e c [((b, sort), t)]", "val tf (t: term) : Tot (term -> Tac unit)\nlet tf (t : term) : Tot (term -> Tac unit) =\n match unsquash_term t with\n | None -> and_elim\n | _ -> squash_and_elim", "val reification\n (b: Type)\n (f: (term -> Tac b))\n (def: b)\n (#a: Type)\n (unquotea: (term -> Tac a))\n (quotea: (a -> Tac term))\n (tmult tunit: term)\n (munit: a)\n (ts: list term)\n : Tac (list exp * vmap a b)\nlet reification (b:Type) (f:term->Tac b) (def:b) (#a:Type)\n (unquotea:term->Tac a) (quotea:a -> Tac term) (tmult tunit:term) (munit:a)\n (ts:list term) :\n Tac (list exp * vmap a b) =\n let tmult: term = norm_term [delta;zeta;iota] tmult in\n let tunit: term = norm_term [delta;zeta;iota] tunit in\n let ts = Tactics.Util.map (norm_term [delta;zeta;iota]) ts in\n // dump (\"mult = \" ^ term_to_string mult ^\n // \"; unit = \" ^ term_to_string unit ^\n // \"; t = \" ^ term_to_string t);\n let (es,_, vm) =\n Tactics.Util.fold_left\n (fun (es,vs,vm) t ->\n let (e,vs,vm) = reification_aux unquotea vs vm f tmult tunit t\n in (e::es,vs,vm))\n ([],[], const munit def) ts\n in (List.Tot.Base.rev es,vm)", "val pose_lemma (t: term) : Tac binding\nlet pose_lemma (t : term) : Tac binding =\n let c = tcc (cur_env ()) t in\n let pre, post =\n match c with\n | C_Lemma pre post _ -> pre, post\n | _ -> fail \"\"\n in\n let post = `((`#post) ()) in (* unthunk *)\n let post = norm_term [] post in\n (* If the precondition is trivial, do not cut by it *)\n match term_as_formula' pre with\n | True_ ->\n pose (`(__lemma_to_squash #(`#pre) #(`#post) () (fun () -> (`#t))))\n | _ ->\n let reqb = tcut (`squash (`#pre)) in\n\n let b = pose (`(__lemma_to_squash #(`#pre) #(`#post) (`#(reqb <: term)) (fun () -> (`#t)))) in\n flip ();\n ignore (trytac trivial);\n b", "val un_uinst (t: term) : term\nlet un_uinst (t:term) : term =\n match inspect_ln t with\n | Tv_UInst fv _ -> pack_ln (Tv_FVar fv)\n | _ -> t", "val un_uinst (t: term) : term\nlet un_uinst (t:term) : term =\n match inspect_ln t with\n | Tv_UInst fv _ -> pack_ln (Tv_FVar fv)\n | _ -> t", "val apply_lemma (t: term) : Tac unit\nlet apply_lemma (t : term) : Tac unit =\n t_apply_lemma false false t", "val apply_lemma (t: term) : Tac unit\nlet apply_lemma (t : term) : Tac unit =\n t_apply_lemma false false t", "val param' (s: param_state) (t: term) : Tac term\nlet rec param' (s:param_state) (t:term) : Tac term =\n let r =\n match inspect t with\n | Tv_Type _u -> // t = Type\n `(fun (s t : (`#t)) -> s -> t -> Type)\n\n | Tv_Var bv ->\n let (_, _, b) = lookup s bv in\n binder_to_term b\n\n | Tv_Arrow b c -> // t1 -> t2 === (x:t1) -> Tot t2\n begin match inspect_comp c with\n | C_Total t2 ->\n let (s', (bx0, bx1, bxR)) = push_binder b s in\n let q = b.qual in\n\n let bf0 = fresh_binder_named \"f0\" (replace_by s false t) in\n let bf1 = fresh_binder_named \"f1\" (replace_by s true t) in\n let b2t = binder_to_term in\n let res = `((`#(param' s' t2)) (`#(tapp q (b2t bf0) (b2t bx0))) (`#(tapp q (b2t bf1) (b2t bx1)))) in\n tabs bf0 (tabs bf1 (mk_tot_arr [bx0; bx1; bxR] res))\n | _ -> raise (Unsupported \"effects\")\n end\n\n | Tv_App l (r, q) ->\n let lR = param' s l in\n let l0 = replace_by s false r in\n let l1 = replace_by s true r in\n let rR = param' s r in\n mk_app lR [(l0, q); (l1, q); (rR, q)]\n\n | Tv_Abs b t ->\n let abs b t : Tac term = pack (Tv_Abs b t) in\n let (s', (bx0, bx1, bxR)) = push_binder b s in\n\n let t = param' s' t in\n abs bx0 (abs bx1 (abs bxR t))\n\n | Tv_Match t None brs ->\n pack (Tv_Match (param' s t) None (map (param_br s) brs))\n\n | Tv_UInst fv _\n | Tv_FVar fv ->\n pack (Tv_FVar (param_fv s fv))\n\n | Tv_Const c ->\n `()\n\n | Tv_AscribedT t _ _ _\n | Tv_AscribedC t _ _ _ -> param' s t\n\n | _ ->\n let q = inspect t in\n raise (Unsupported (term_to_string (quote q)))\n in\n r\n\nand param_fv (s:param_state) (f : fv) : Tac fv =\n (* first of all look for recursive knots *)\n try lookup_rec_fv s f\n with\n | _ ->\n\n (* try to get it from the same module the FV is defined *)\n let nm' = explode_qn (implode_qn (inspect_fv f) ^ \"_param\") in\n //dump (\"nm' = \" ^ implode_qn nm');\n match lookup_typ (top_env ()) nm' with\n | Some se' -> pack_fv nm'\n | None ->\n\n (* or this module, where the translation is defined... *)\n let nm' = [\"Param_Inds\"] @ [last (inspect_fv f) ^ \"_param\"] in\n //dump (\"nm' = \" ^ implode_qn nm');\n match lookup_typ (top_env ()) nm' with\n | Some se' -> pack_fv nm'\n | None ->\n\n (* otherwise, try to get it from the *current* module, where we're running the tactic *)\n let nm' = cur_module () @ [last (inspect_fv f) ^ \"_param\"] in\n //dump (\"nm' = \" ^ implode_qn nm');\n match lookup_typ (top_env ()) nm' with\n | Some se' -> pack_fv nm'\n\n (* TODO: lookup in env *)\n\n | None ->\n raise (NotFoundFV f)\n\nand param_pat (s:param_state) (p : pattern) : Tac (param_state & (pattern & pattern & pattern)) =\n let is_dot_pat (p:pattern) : Tac bool =\n match p with\n | Pat_Dot_Term _ -> true\n | _ -> false\n in\n //dump (\"param_pat of \" ^ term_to_string (quote p));\n match p with\n | Pat_Cons {head=fv; univs=us; subpats=pats} ->\n let fv' = param_fv s fv in\n let (s', (pats0, pats1, patsr)) =\n fold_left (fun (s, (pats0, pats1, patsr)) (p, i) ->\n if is_dot_pat p then (s, (pats0, pats1, patsr))\n else\n let (s', (p0, p1, pr)) = param_pat s p in\n (s', (\n (p0,i)::pats0,\n (p1,i)::pats1,\n (pr,false)::(p1,i)::(p0,i)::patsr)))\n (s, ([], [], []))\n pats\n in\n let pats0 = List.Tot.rev pats0 in\n let pats1 = List.Tot.rev pats1 in\n let patsr = List.Tot.rev patsr in\n (s', (Pat_Cons {head=fv; univs=us; subpats=pats0},\n Pat_Cons {head=fv; univs=us; subpats=pats1},\n Pat_Cons {head=fv'; univs=us; subpats=patsr}))\n\n | Pat_Var {v; sort} ->\n let b = namedv_to_binder v (unseal sort) in\n let (s', (b0, b1, bR)) = push_binder b s in\n (s', (Pat_Var {v=binder_to_namedv b0; sort = Sealed.seal (binder_sort b0)},\n Pat_Var {v=binder_to_namedv b1; sort = Sealed.seal (binder_sort b1)},\n Pat_Var {v=binder_to_namedv bR; sort = Sealed.seal (binder_sort bR)}))\n\n | Pat_Dot_Term t ->\n fail \"no dot pats\"\n //let (s', (b0, b1, bR)) = push_binder (pack_binder bv Q_Explicit) s in\n //(s', (Pat_Dot_Term (bv_of_binder b0) (replace_by s' false t),\n // Pat_Dot_Term (bv_of_binder b1) (replace_by s' true t),\n // Pat_Dot_Term (bv_of_binder bR) (param' s' t)))\n\n | Pat_Constant c ->\n let b = fresh_binder_named \"cR\" (`_) in\n (s, (Pat_Constant c,\n Pat_Constant c,\n Pat_Var {v=binder_to_namedv b; sort=seal (`_)}))\n\nand param_br (s:param_state) (br : branch) : Tac branch =\n let (pat, t) = br in\n let (s', (_, _, pat')) = param_pat s pat in\n (pat', param' s' t)\n\nand push_binder (b:binder) (s:param_state) : Tac (param_state & (binder & binder & binder)) =\n let q = b.qual in\n let typ = b.sort in\n let name = unseal b.ppname in\n let decor (s : string) (t : string) : Tac string = (s ^ t) in\n let bx0 = fresh_binder_named (decor name \"0\") (replace_by s false typ) in\n let bx1 = fresh_binder_named (decor name \"1\") (replace_by s true typ) in\n let bxr = fresh_binder_named (decor name \"R\") (`(`#(param' s typ)) (`#(binder_to_term bx0)) (`#(binder_to_term bx1))) in\n\n (* respect implicits *)\n let bx0 = binder_set_qual bx0 q in\n let bx1 = binder_set_qual bx1 q in\n let bxr = binder_set_qual bxr q in\n\n let s = push_var_to_state (binder_to_namedv b) bx0 bx1 bxr s in\n (s, (bx0, bx1, bxr))", "val st_term_to_string' (level: string) (t: st_term) : T.Tac string\nlet rec st_term_to_string' (level:string) (t:st_term)\n : T.Tac string\n = match t.term with\n | Tm_Return { insert_eq; term } ->\n sprintf \"return_%s %s\"\n (if insert_eq then \"\" else \"_noeq\")\n (term_to_string term)\n \n | Tm_STApp {head; arg_qual; arg } ->\n sprintf \"(%s%s %s%s)\"\n (if dbg_printing then \"\" else \"\")\n (term_to_string head)\n (qual_to_string arg_qual)\n (term_to_string arg)\n \n | Tm_Bind { binder; head; body } ->\n // if T.unseal binder.binder_ppname.name = \"_\"\n // then sprintf \"%s;\\n%s%s\" \n // (st_term_to_string' level head)\n // level\n // (st_term_to_string' level body) \n // else (\n sprintf \"let %s = %s;\\n%s%s\"\n (binder_to_string binder) \n (st_term_to_string' level head)\n level\n (st_term_to_string' level body)\n // )\n\n | Tm_TotBind { head; binder; body } ->\n sprintf \"let tot %s = %s;\\n%s%s\"\n (binder_to_string binder)\n (term_to_string head)\n level\n (st_term_to_string' level body)\n \n | Tm_Abs { b; q; ascription=c; body } ->\n sprintf \"(fun (%s%s)\\n%s\\n ({\\n%s%s\\n}%s)\"\n (qual_to_string q)\n (binder_to_string b)\n (match c.annotated with | None -> \"\" | Some c -> comp_to_string c)\n (indent level)\n (st_term_to_string' (indent level) body)\n (match c.elaborated with | None -> \"\" | Some c -> \" <: \" ^ comp_to_string c)\n\n | Tm_If { b; then_; else_ } ->\n sprintf \"if (%s)\\n%s{\\n%s%s\\n%s}\\n%selse\\n%s{\\n%s%s\\n%s}\"\n (term_to_string b)\n level\n (indent level)\n (st_term_to_string' (indent level) then_)\n level\n level\n level\n (indent level)\n (st_term_to_string' (indent level) else_)\n level\n\n | Tm_Match {sc; brs} ->\n sprintf \"match (%s) with %s\"\n (term_to_string sc)\n (branches_to_string brs)\n\n | Tm_IntroPure { p } ->\n sprintf \"introduce pure (\\n%s%s)\"\n (indent level)\n (term_to_string' (indent level) p)\n\n | Tm_ElimExists { p } ->\n sprintf \"elim_exists %s\"\n (term_to_string p)\n\n | Tm_IntroExists { p; witnesses } ->\n sprintf \"introduce\\n%s%s\\n%swith %s\"\n (indent level)\n (term_to_string' (indent level) p)\n level\n (term_list_to_string \" \" witnesses)\n\n | Tm_While { invariant; condition; body } ->\n sprintf \"while (%s)\\n%sinvariant %s\\n%s{\\n%s%s\\n%s}\"\n (st_term_to_string' level condition)\n level\n (term_to_string invariant)\n level\n (indent level)\n (st_term_to_string' (indent level) body)\n level\n\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\n sprintf \"par (<%s> (%s) <%s) (<%s> (%s) <%s)\"\n (term_to_string pre1)\n (st_term_to_string' level body1)\n (term_to_string post1)\n (term_to_string pre2)\n (st_term_to_string' level body2)\n (term_to_string post2)\n\n | Tm_Rewrite { t1; t2 } ->\n sprintf \"rewrite %s %s\"\n (term_to_string t1)\n (term_to_string t2)\n\n | Tm_WithLocal { binder; initializer; body } ->\n sprintf \"let mut %s = %s;\\n%s%s\"\n (binder_to_string binder)\n (term_to_string initializer)\n level\n (st_term_to_string' level body)\n\n | Tm_WithLocalArray { binder; initializer; length; body } ->\n sprintf \"let mut %s = [| %s; %s |]\\n%s%s\"\n (binder_to_string binder)\n (term_to_string initializer)\n (term_to_string length)\n level\n (st_term_to_string' level body)\n\n | Tm_Admit { ctag; u; typ; post } ->\n sprintf \"%s<%s> %s%s\"\n (match ctag with\n | STT -> \"stt_admit\"\n | STT_Atomic -> \"stt_atomic_admit\"\n | STT_Ghost -> \"stt_ghost_admit\")\n (universe_to_string 0 u)\n (term_to_string typ)\n (match post with\n | None -> \"\"\n | Some post -> sprintf \" %s\" (term_to_string post))\n\n | Tm_Unreachable -> \"unreachable ()\"\n\n | Tm_ProofHintWithBinders { binders; hint_type; t} ->\n let with_prefix =\n match binders with\n | [] -> \"\"\n | _ -> sprintf \"with %s.\" (String.concat \" \" (T.map binder_to_string binders))\n in\n let names_to_string = function\n | None -> \"\"\n | Some l -> sprintf \" [%s]\" (String.concat \"; \" l)\n in\n let ht, p =\n match hint_type with\n | ASSERT { p } -> \"assert\", term_to_string p\n | UNFOLD { names; p } -> sprintf \"unfold%s\" (names_to_string names), term_to_string p\n | FOLD { names; p } -> sprintf \"fold%s\" (names_to_string names), term_to_string p\n | RENAME { pairs; goal } ->\n sprintf \"rewrite each %s\"\n (String.concat \", \"\n (T.map\n (fun (x, y) -> sprintf \"%s as %s\" (term_to_string x) (term_to_string y))\n pairs)),\n (match goal with\n | None -> \"\"\n | Some t -> sprintf \" in %s\" (term_to_string t))\n | REWRITE { t1; t2 } ->\n sprintf \"rewrite %s as %s\" (term_to_string t1) (term_to_string t2), \"\"\n | WILD -> \"_\", \"\"\n | SHOW_PROOF_STATE _ -> \"show_proof_state\", \"\"\n in\n sprintf \"%s %s %s; %s\" with_prefix ht p\n (st_term_to_string' level t)\n \n | Tm_WithInv { name; body; returns_inv } ->\n sprintf \"with_inv %s %s %s\"\n (term_to_string name)\n (st_term_to_string' level body)\n (match returns_inv with\n | None -> \"\"\n | Some (b, t) ->\n sprintf \"\\nreturns %s\\nensures %s\"\n (binder_to_string b)\n (term_to_string t))\n\nand branches_to_string brs : T.Tac _ =\n match brs with\n | [] -> \"\"\n | b::bs -> branch_to_string b ^ branches_to_string bs\n\nand branch_to_string br : T.Tac _ =\n let (pat, e) = br in\n Printf.sprintf \"{ %s -> %s }\"\n (pattern_to_string pat)\n (st_term_to_string' \"\" e)\n\nand pattern_to_string (p:pattern) : T.Tac string = \n match p with\n | Pat_Cons fv pats ->\n Printf.sprintf \"(%s %s)\"\n (String.concat \".\" fv.fv_name) \n (String.concat \" \" (T.map (fun (p, _) -> pattern_to_string p) pats))\n | Pat_Constant c ->\n \"\"\n | Pat_Var x _ ->\n T.unseal x\n | Pat_Dot_Term None ->\n \"\"\n | Pat_Dot_Term (Some t) ->\n Printf.sprintf \"(.??)\"", "val add_terms (t1 t2: term) : Tac term\nlet add_terms (t1 t2 : term) : Tac term = `(`#t1 + `#t2)", "val goal_term_uvars (t: term) : Tac (list int)\nlet goal_term_uvars (t: term) : Tac (list int) =\n let hd, tl = collect_app t in\n if hd `is_fvar` (`%squash)\n then\n match tl with\n | [tl0, Q_Explicit] ->\n let _, tl1 = collect_app tl0 in\n simplify_list (argv_uvars tl1)\n | _ -> dump \"ill-formed squash\"; []\n else\n []", "val inspect_unascribe (t: term) : Tac term_view\nlet rec inspect_unascribe (t:term) : Tac term_view =\n match inspect t with\n | Tv_AscribedT t _ _ _\n | Tv_AscribedC t _ _ _ ->\n inspect_unascribe t\n | tv -> tv", "val exact (t: term) : Tac unit\nlet exact (t : term) : Tac unit =\n with_policy SMT (fun () -> t_exact true false t)", "val exact (t: term) : Tac unit\nlet exact (t : term) : Tac unit =\n with_policy SMT (fun () -> t_exact true false t)", "val tcut (t: term) : Tac binding\nlet tcut (t:term) : Tac binding =\n let g = cur_goal () in\n let tt = mk_e_app (`__cut) [t; g] in\n apply tt;\n intro ()", "val term_as_mlty (g: env) (t: term) : T.Tac mlty\nlet term_as_mlty (g:env) (t:term)\n : T.Tac mlty\n = let t = Elab.elab_term t in\n term_as_mlty (uenv_of_env g) t", "val is_const (t: term) : Tac bool\nlet is_const (t:term) : Tac bool = Tv_Const? (inspect t)", "val gen_synth' (t vt: T.term) : T.Tac T.term\nlet gen_synth' (t: T.term) (vt: T.term) : T.Tac T.term =\n let cts = get_inductive_constructors t in\n T.debug (\"Inductive type with \" ^ string_of_int (List.Tot.length cts));\n let f = mk_function t (mk_tenum_branches t vt 0 [] cts) in\n T.debug (T.term_to_string f);\n f", "val fn_to_lemma_invocations_in_term (fn: term) (argc: pos) (lem t: term) : Tac (option term)\nlet rec fn_to_lemma_invocations_in_term (fn: term) (argc: pos) (lem: term) (t: term) : Tac (option term) =\n match inspect t with\n | Tv_Var _ -> None\n | Tv_BVar _ -> None\n | Tv_FVar _ -> None\n | Tv_UInst _ _ -> None\n | Tv_App hd argv ->\n let f' = fn_to_lemma_invocation_in_application_term fn argc lem t in\n let hd' = fn_to_lemma_invocations_in_term fn argc lem hd in\n let argv' = fn_to_lemma_invocations_in_term fn argc lem (fst argv) in\n combine_optional_terms [f'; hd'; argv']\n | Tv_Abs _ _ -> None\n | Tv_Arrow _ _ -> None\n | Tv_Type _ -> None\n | Tv_Refine _ _ -> None\n | Tv_Const _ -> None\n | Tv_Uvar _ _ -> None\n | Tv_Let recf attrs bv def body ->\n let def_lemmas = fn_to_lemma_invocations_in_term fn argc lem def in\n let body_lemmas =\n (match fn_to_lemma_invocations_in_term fn argc lem body with\n | Some body' -> Some (pack (Tv_Let recf attrs bv def body'))\n | None -> None) in\n combine_optional_terms [def_lemmas; body_lemmas]\n | Tv_Match scrutinee ret brs ->\n let scrutinee_lemmas = fn_to_lemma_invocations_in_term fn argc lem scrutinee in\n let any_nontrivial, brs' = fn_to_lemma_invocations_in_branches fn argc lem brs in\n let match_lemmas = if any_nontrivial then Some (pack (Tv_Match scrutinee ret brs')) else None in\n combine_optional_terms [scrutinee_lemmas; match_lemmas]\n | Tv_AscribedT e _ _ _ ->\n fn_to_lemma_invocations_in_term fn argc lem e\n | Tv_AscribedC e _ _ _ ->\n fn_to_lemma_invocations_in_term fn argc lem e\n | Tv_Unknown -> None\n | Tv_Unsupp -> None\n\nand fn_to_lemma_invocations_in_branches\n (fn: term)\n (argc: pos)\n (lem: term)\n (brs: list branch)\n : Tac (bool * (list branch)) =\n match brs with\n | [] -> false, []\n | (branch_pattern, branch_term) :: remaining_branches ->\n let remaining_any_nontrivial, remaining_result = fn_to_lemma_invocations_in_branches fn argc lem remaining_branches in\n match fn_to_lemma_invocations_in_term fn argc lem branch_term with\n | Some result -> true, (branch_pattern, result) :: remaining_result\n | None -> remaining_any_nontrivial, (branch_pattern, quote ()) :: remaining_result", "val name_of_bv (bv: bv) : Tac string\nlet name_of_bv (bv : bv) : Tac string =\n unseal ((inspect_bv bv).bv_ppname)", "val name_of_bv (bv: bv) : Tac string\nlet name_of_bv (bv : bv) : Tac string =\n unseal ((inspect_bv bv).ppname)", "val exact_n (n: int) (t: term) : Tac unit\nlet exact_n (n : int) (t : term) : Tac unit =\n exact_args (repeatn n (fun () -> Q_Explicit)) t", "val exact_n (n: int) (t: term) : Tac unit\nlet exact_n (n : int) (t : term) : Tac unit =\n exact_args (repeatn n (fun () -> Q_Explicit)) t", "val push_pre (st: state) (inv_bv: bv) (t: term) : Tac term\nlet rec push_pre (st: state) (inv_bv: bv) (t: term): Tac term =\n match inspect t with\n | Tv_Arrow bv c ->\n let c =\n match inspect_comp c with\n | C_Eff us e a args decrs ->\n if string_of_name e = \"FStar_HyperStack_ST_Stack\" then\n let args =\n match args with\n | (pre, qual) :: rest ->\n let pre =\n match inspect pre with\n | Tv_Abs h body ->\n let body = mk_app (`( /\\ )) [ pack (Tv_Var inv_bv), Q_Explicit; body, Q_Explicit ] in\n pack (Tv_Abs h body)\n | _ ->\n fail \"impossible: argument to ST.Stack not a fun\"\n in\n (pre, qual) :: rest\n | _ ->\n fail (\"impossible: effect not fully applied \" ^ string_of_name e)\n in\n C_Eff us e a args decrs\n else\n fail (\"rewritten function has an unknown effect: \" ^ string_of_name e)\n | C_Total t ->\n C_Total (push_pre st inv_bv t)\n | _ ->\n fail (\"rewritten type is neither a Tot or a stateful arrow: \" ^ term_to_string t)\n in\n let c = pack_comp c in\n pack (Tv_Arrow bv c)\n | _ ->\n print (st.indent ^ \" WARN: no effect found, are you using the specialize tactic on pure code?\");\n t", "val vprop_term_uvars (t: term) : Tac (list int)\nlet rec vprop_term_uvars (t:term) : Tac (list int) =\n match inspect_unascribe t with\n | Tv_Uvar i' _ -> [i']\n | Tv_App _ _ ->\n let hd, args = collect_app t in\n if is_star_or_unit hd then\n // Only count the number of unresolved slprops, not program implicits\n argv_uvars args\n else\n vprop_term_uvars hd\n | Tv_Abs _ t -> vprop_term_uvars t\n | _ -> []\n\nand argv_uvars (args: list argv) : Tac (list int) =\n let t : unit -> Tac (list int) =\n fold_left (fun (n: unit -> Tac (list int)) (x, _) ->\n let t () : Tac (list int) =\n let l1 = n () in\n let l2 = vprop_term_uvars x in\n l1 `List.Tot.append` l2\n in\n t\n )\n (fun _ -> [])\n args\n in\n t ()", "val pose_as (s: string) (t: term) : Tac binding\nlet pose_as (s:string) (t:term) : Tac binding =\n let b = pose t in\n rename_to b s", "val visit_function (t_i: term) (st: state) (f_name: name) : Tac (state & list sigelt)\nlet rec visit_function (t_i: term) (st: state) (f_name: name): Tac (state & list sigelt) =\n if (List.Tot.existsb (fun (name, _) -> name = f_name) st.seen) then\n let _ = print (st.indent ^ \"Already visited \" ^ string_of_name f_name) in\n // We don't need a three-state graph traversal since we automatically refuse\n // to visit a node marked with a let-rec.\n st, []\n\n else\n // Environment lookup.\n let f = lookup_typ (top_env ()) f_name in\n let f = match f with Some f -> f | None -> fail \"unexpected: name not in the environment\" in\n if not (has_attr f (`Meta.Attribute.specialize) || has_attr f (`Meta.Attribute.inline_)) then\n let _ = print (st.indent ^ \"Not visiting \" ^ string_of_name f_name) in\n // We want the user to specify which nodes should be traversed, otherwise,\n // we'd end up visiting the entire F* standard library.\n st, []\n else\n let _ = print (st.indent ^ \"Visiting \" ^ string_of_name f_name) in\n match inspect_sigelt f with\n | Sg_Let r lbs ->\n if r then\n fail (\"user error: \" ^ string_of_name f_name ^ \" is recursive\");\n let lbv = lookup_lb_view lbs f_name in\n let f_body = lbv.lb_def in\n let f_typ = lbv.lb_typ in\n let original_opts = sigelt_opts f in\n\n // Build a new function with proper parameters\n let old_indent = st.indent in\n let st = { st with indent = st.indent ^ \" \" } in\n let new_name = suffix_name f_name \"_higher\" in\n\n // The function may be of the form fun (x: index) -> ...\n // We recognize and distinguish this index, if present.\n let index_bvty, index_name, f_body =\n match inspect f_body with\n | Tv_Abs binder f_body' ->\n let { binder_bv = bv; binder_sort = t } = inspect_binder binder in\n let { bv_ppname = name } = inspect_bv bv in\n let name = unseal name in\n print (st.indent ^ \"Found \" ^ name ^ \", which is \" ^\n (if binder_is_legit f_name t_i binder then \"\" else \"NOT \") ^\n \"an index of type \" ^ term_to_string t);\n if binder_is_legit f_name t_i binder then begin\n Some (bv, t), name, f_body'\n end else\n // It can be convenient to specialize over a function without\n // the index as a parameter. In Curve, this is used to\n // specialize over store_felem64, a function that is already\n // specialized for the M64 value of the index, but that still\n // admits multiple implementations.\n None, \"\", f_body\n | _ ->\n fail (string_of_name f_name ^ \"is expected to be a function!\")\n in\n\n let inv_bv: bv = fresh_bv_named \"p\" in\n let inv_bv_sort : typ = `Type0 in\n\n let st, new_body, new_args, new_sigelts =\n let index_bv_tm_opt : option term =\n match index_bvty with\n | Some (index_bv, _sort) -> Some (pack (Tv_Var index_bv))\n | _ -> None\n in\n visit_body t_i index_bv_tm_opt (pack (Tv_Var inv_bv)) st [] f_body\n in\n let st = { st with indent = old_indent } in\n\n // Update the state with a mapping and which extra arguments are\n // needed. Each function that has been transformed has a type that's a\n // function of the index.\n\n let m = if has_attr f (`Meta.Attribute.specialize) then Specialize else Inline new_name in\n let new_args, new_bvs = List.Tot.split new_args in\n\n // The type of ``f`` when it appears as a ``gi`` parameter, i.e. its ``gi_t``.\n let f_typ_name = suffix_name f_name \"_higher_t\" in\n let f_typ, f_typ_typ, has_index =\n match index_bvty with\n | Some (index_bv, index_bv_sort) ->\n lambda_over_index_and_p st f_name f_typ inv_bv inv_bv_sort,\n mk_tot_arr [ mk_implicit_binder index_bv index_bv_sort ] (\n mk_tot_arr [ mk_binder inv_bv inv_bv_sort ] (`Type0)),\n true\n | _ ->\n lambda_over_only_p st inv_bv inv_bv_sort f_typ,\n mk_tot_arr [ mk_binder inv_bv inv_bv_sort ] (`Type0),\n false\n in\n print (st.indent ^ \" let \" ^ string_of_name f_typ_name ^ \": \" ^\n term_to_string f_typ_typ ^ \" = \" ^\n term_to_string f_typ);\n let lb = pack_lb ({lb_fv = pack_fv f_typ_name;\n lb_us = [];\n lb_typ = f_typ_typ;\n lb_def = f_typ}) in\n let se_t = pack_sigelt (Sg_Let false [lb]) in\n let se_t = set_sigelt_quals [ NoExtract; Inline_for_extraction ] se_t in\n let se_t = match original_opts with\n | Some original_opts -> add_check_with original_opts se_t\n | _ -> se_t\n in\n let f_typ = pack (Tv_FVar (pack_fv f_typ_name)) in\n let st = { st with seen = (f_name, (has_index, f_typ, m, new_args)) :: st.seen } in\n\n // For debugging. This is very meta.\n let se_debug msg: Tac sigelt =\n let deps = map string_of_name new_args in\n let deps =\n match deps with\n | _ :: _ -> \" (needs: \" ^ String.concat \", \" deps ^ \")\"\n | _ -> \"\"\n in\n let quote_string s : Tac term = pack (Tv_Const (C_String s)) in\n let lb = pack_lb ({lb_fv =\n pack_fv (suffix_name f_name \"_higher_debug_print\");\n lb_us = [];\n lb_typ = (`unit);\n lb_def =\n (`(let x: unit =\n _ by (\n print (`#(quote_string msg) ^ \" \" ^\n (`#(quote_string (string_of_name new_name))) ^\n `#(quote_string deps));\n exact tm_unit) in\n x))}) in\n\n pack_sigelt (Sg_Let false [lb])\n in\n\n // Fast-path; just register the function as being a specialize node\n // but don't rewrite it or splice a new declaration.\n if false && List.length new_args = 0 then begin\n if not (has_inline_for_extraction f) then\n fail (string_of_name f_name ^ \" should be inline_for_extraction\");\n if not (Specialize? m) then\n fail (string_of_name f_name ^ \" is marked as [@ inline_ ] but does not reach \\\n any specializations\");\n\n st, new_sigelts @ [ se_debug \"Checking only a type:\"; se_t ]\n end\n\n else\n\n // new_body is: fun (g1: g1_t i) ... (gn: gn_t i) x -> (e: f_t i)\n // i is free\n let new_body =\n fold_right (fun (_, (bv, sort)) acc ->\n pack (Tv_Abs (mk_binder bv sort) acc)\n ) (zip new_args new_bvs) new_body\n in\n\n // Declaration for the new resulting function. We need to construct\n // the actual type of ``f``.\n // BUG: without the eta-expansion around mk_binder, \"tactic got stuck\".\n let new_body = pack (Tv_Abs (mk_binder inv_bv inv_bv_sort) new_body) in\n let new_body =\n match index_bvty with\n | Some (index_bv, index_bv_sort) -> pack (Tv_Abs (mk_implicit_binder index_bv index_bv_sort) new_body)\n | _ -> new_body\n in\n let new_typ =\n let new_binders = List.Tot.map (fun (bv, sort) -> mk_binder bv sort) new_bvs in\n let new_binders = mk_binder inv_bv inv_bv_sort :: new_binders in\n let app_inv (t: term): Tac term = pack (Tv_App t (pack (Tv_Var inv_bv), Q_Explicit)) in\n match index_bvty with\n | Some (index_bv, index_bv_sort) ->\n mk_tot_arr\n (mk_implicit_binder index_bv index_bv_sort :: new_binders)\n (app_inv (pack (Tv_App f_typ (pack (Tv_Var index_bv), Q_Implicit))))\n | _ ->\n mk_tot_arr new_binders (app_inv f_typ)\n in\n let lb = pack_lb ({lb_fv = pack_fv new_name;\n lb_us = [];\n lb_typ = new_typ;\n lb_def = new_body}) in\n let se = pack_sigelt (Sg_Let false [lb]) in\n let se = set_sigelt_quals [ NoExtract; Inline_for_extraction ] se in\n let se = match original_opts with\n | Some original_opts -> add_check_with original_opts se\n | _ -> se\n in\n print (st.indent ^ \" let \" ^ string_of_name new_name ^ \":\\n\" ^\n st.indent ^ term_to_string new_typ ^ \"\\n\" ^\n st.indent ^ \"=\\n\" ^\n st.indent ^ term_to_string new_body);\n\n st, new_sigelts @ [\n se_debug (\"Checking type and definition [\" ^ string_of_mapping m ^ \"]:\"); se_t; se\n ]\n\n | _ ->\n if has_attr f (`Meta.Attribute.specialize) then\n let inv_bv: bv = fresh_bv_named \"p\" in\n let inv_bv_sort : typ = `Type0 in\n\n // Assuming that this is a val, but we can't inspect it. Let's work around this.\n let t = pack (Tv_FVar (pack_fv f_name)) in\n let f_typ = tc (top_env ()) t in\n print (st.indent ^ \" Assuming \" ^ string_of_name f_name ^ \": \" ^\n term_to_string f_typ ^ \" is a val\\n\");\n let f_typ, has_index =\n match inspect f_typ with\n | Tv_Arrow bv _ ->\n if binder_is_legit f_name t_i bv then\n lambda_over_index_and_p st f_name f_typ inv_bv inv_bv_sort, true\n else\n lambda_over_only_p st inv_bv inv_bv_sort f_typ, false\n | _ ->\n lambda_over_only_p st inv_bv inv_bv_sort f_typ, false // fail (string_of_name f_name ^ \" does not have an arrow type\")\n in\n print (st.indent ^ \" Registering \" ^ string_of_name f_name ^ \" with type \" ^\n term_to_string f_typ);\n let st = { st with seen = (f_name, (has_index, f_typ, Specialize, [])) :: st.seen } in\n st, []\n else\n st, []\n\nand visit_many (t_i: term)\n (index_bv: option term)\n (inv_bv: term)\n (st: state)\n (bvs: list (name & (bv & typ)))\n (es: list term):\n Tac (state & list term & list (name & (bv & typ)) & list sigelt)\n=\n let st, es, bvs, ses = fold_left (fun (st, es, bvs, ses) e ->\n let st, e, bvs, ses' = visit_body t_i index_bv inv_bv st bvs e in\n st, e :: es, bvs, ses @ ses'\n ) (st, [], bvs, []) es in\n let es = List.Tot.rev es in\n st, es, bvs, ses\n\nand visit_body (t_i: term)\n (index_bv: option term)\n (inv_bv: term)\n (st: state) // state-passing\n (bvs: list (name & (bv & typ))) // state-passing\n (e: term):\n Tac (state & term & list (name & (bv & typ)) & list sigelt)\n=\n // st is state that is threaded through\n // bvs are the extra parameters for this function we have allocated; threaded\n // through as well to avoid allocating the same thing twice\n // ses is strictly bottom-up\n match inspect e with\n | Tv_App _ _ ->\n let e, es = collect_app e in\n\n // Recursively visit arguments\n let es, qs = List.Pure.split es in\n let st, es, bvs, ses = visit_many t_i index_bv inv_bv st bvs es in\n let es = zip es qs in\n\n // If this is an application ...\n begin match inspect e with\n | Tv_UInst fv _\n | Tv_FVar fv ->\n // ... of a top-level name ...\n let fv = inspect_fv fv in\n let st, ses' = visit_function t_i st fv in\n let ses = ses @ ses' in\n // visit_function fills out st.seen with an entry for this lid, if\n // this is something we wish to rewrite\n begin match List.Tot.assoc fv st.seen with\n | Some (has_index, _, map, fns) ->\n print (st.indent ^ \"Rewriting application of \" ^ string_of_name fv);\n\n let index_arg, es =\n if has_index then\n match es with\n | (e, Q_Implicit) :: es ->\n Some e, es\n | _ ->\n fail \"this application does not seem to start with an index\"\n else\n None, es\n in\n\n // A helper that says: I will need a specialized instance of `name`,\n // so allocate an extra parameter for this current function if\n // needed.\n let allocate_bv_for name bvs : Tac ((term & aqualv) & list (Reflection.name & (bv & typ))) =\n match List.Tot.assoc name bvs with\n | Some (bv, sort) ->\n print (st.indent ^ string_of_name name ^ \" already has a bv\");\n // fv needs to receive a specialized instance of name;\n // it's already found in this function's own bvs\n (pack (Tv_Var bv), Q_Explicit), bvs\n | None ->\n // this is the first time the current function needs to\n // receive a specialized instance of name; add it to this\n // function's own bvs\n let needs_index, typ, _, _ = assoc name st.seen in\n if needs_index && not (Some? index_arg) then\n fail (\"Index inconsistency in bv for \" ^ string_of_name name);\n\n print (st.indent ^ \"Allocating bv for \" ^ string_of_name name ^ \" at type \" ^\n \"app <\" ^ term_to_string typ ^ \"> <\" ^\n (if needs_index then term_to_string (must index_arg) else \"no-index\") ^ \">\");\n\n let typ =\n if needs_index then pack (Tv_App typ (must index_arg, Q_Implicit)) else typ\n in\n let typ = pack (Tv_App typ (inv_bv, Q_Explicit)) in\n let bv: bv = fresh_bv_named (\"arg_\" ^ string_of_name name) in\n (pack (Tv_Var bv), Q_Explicit), (name, (bv, typ)) :: bvs\n in\n\n begin match map with\n | Inline fv ->\n // fv has been rewritten to take fns as extra arguments for the\n // specialize nodes reachable through the body of fv; we need\n // ourselves to take a dependency on those nodes\n let extra_args, bvs = fold_left (fun (extra_args, bvs) name ->\n let term, bvs = allocate_bv_for name bvs in\n term :: extra_args, bvs\n ) ([], bvs) fns in\n let extra_args = List.rev extra_args in\n let extra_args = (inv_bv, Q_Explicit) :: extra_args in\n let extra_args =\n // Inline nodes retain their index (if any).\n if has_index then (must index_bv, Q_Implicit) :: extra_args else extra_args\n in\n\n let e = mk_app (pack (Tv_FVar (pack_fv fv))) (extra_args @ es) in\n st, e, bvs, ses\n\n | Specialize ->\n // Specialized nodes are received as parameters and no longer have the index.\n let e, bvs = allocate_bv_for fv bvs in\n let e = mk_app (fst e) es in\n st, e, bvs, ses\n end\n\n | None ->\n let e = mk_app e es in\n st, e, bvs, ses\n end\n | _ ->\n let e = mk_app e es in\n st, e, bvs, ses\n end\n\n | Tv_Var _ | Tv_BVar _ | Tv_UInst _ _ | Tv_FVar _\n | Tv_Const _ ->\n st, e, bvs, []\n\n | Tv_Abs b e ->\n let st, e, bvs, ses = visit_body t_i index_bv inv_bv st bvs e in\n let e = pack (Tv_Abs b e) in\n st, e, bvs, ses\n\n | Tv_Match scrut _returns branches ->\n let st, scrut, bvs, ses = visit_body t_i index_bv inv_bv st bvs scrut in\n let pats, es = List.Tot.split branches in\n let st, es, bvs, ses' = visit_many t_i index_bv inv_bv st bvs es in\n let branches = zip pats es in\n st, pack (Tv_Match scrut _returns branches), bvs, ses @ ses'\n\n | Tv_Let r attrs bv ty e1 e2 ->\n let st, e1, bvs, ses = visit_body t_i index_bv inv_bv st bvs e1 in\n let st, e2, bvs, ses' = visit_body t_i index_bv inv_bv st bvs e2 in\n let e = pack (Tv_Let r attrs bv ty e1 e2) in\n st, e, bvs, ses @ ses'\n\n | Tv_AscribedT e t tac use_eq ->\n let st, e, bvs, ses = visit_body t_i index_bv inv_bv st bvs e in\n let e = pack (Tv_AscribedT e t tac use_eq) in\n st, e, bvs, ses\n\n | Tv_AscribedC e c tac use_eq ->\n let st, e, bvs, ses = visit_body t_i index_bv inv_bv st bvs e in\n let e = pack (Tv_AscribedC e c tac use_eq) in\n st, e, bvs, ses\n\n | Tv_Arrow _ _\n | Tv_Type _\n | Tv_Uvar _ _\n | Tv_Refine _ _ _\n | Tv_Unknown\n (* Redundant underscore to catch for soon-to-come\n addition of Tv_Unsupp *)\n | _ ->\n // Looks like we ended up visiting a type argument of an application.\n st, e, bvs, []", "val formula_as_term (f: formula) : Tot term\nlet formula_as_term (f:formula) : Tot term =\n pack_ln (formula_as_term_view f)", "val formula_as_term (f: formula) : Tot term\nlet formula_as_term (f:formula) : Tot term =\n pack (formula_as_term_view f)", "val apply_lemma_noinst (t: term) : Tac unit\nlet apply_lemma_noinst (t : term) : Tac unit =\n t_apply_lemma true false t" ], "closest_src": [ { "project_name": "FStar", "file_name": "MiniParse.Tac.Base.fst", "name": "MiniParse.Tac.Base.unfold_fv" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Match.fst", "name": "Pulse.Checker.Prover.Match.type_of_fv" }, { "project_name": "FStar", "file_name": "Param.fst", "name": "Param.fv_to_tm" }, { "project_name": "FStar", "file_name": "STLC.Infer.fst", "name": "STLC.Infer.is_fv" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Visit.fst", "name": "FStar.Tactics.Visit.visit_tm" }, { "project_name": "FStar", "file_name": "Param.fst", "name": "Param.param" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Pure.fst", "name": "Pulse.Syntax.Pure.tm_fvar" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Typeclasses.fst", "name": "FStar.Tactics.Typeclasses.head_of" }, { "project_name": "FStar", "file_name": "Param.fst", "name": "Param.param_fv" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.make_fvar" }, { "project_name": "FStar", "file_name": "Normalization.fst", "name": "Normalization.def_of" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.free_in" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.pose" }, { "project_name": "FStar", "file_name": "CanonDeep.fst", "name": "CanonDeep.pack_fv'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fsti", "name": "FStar.Tactics.NamedView.tag_of" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.inst_comp" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Formula.fst", "name": "FStar.Reflection.V2.Formula.term_as_formula" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Formula.fst", "name": "FStar.Reflection.V1.Formula.term_as_formula" }, { "project_name": "FStar", "file_name": "LowParseWriters.fsti", "name": "LowParseWriters.is_eq" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.visit_tm" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.inspect" }, { "project_name": "FStar", "file_name": "MiniParse.Tac.Base.fst", "name": "MiniParse.Tac.Base.unfold_term" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Base.fst", "name": "FStar.InteractiveHelpers.Base.term_construct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Typeclasses.fst", "name": "FStar.Tactics.Typeclasses.trywith" }, { "project_name": "FStar", "file_name": "CanonDeep.fst", "name": "CanonDeep.canon_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.exact_with_ref" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.exact_with_ref" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Logic.fst", "name": "FStar.Tactics.V2.Logic.instantiate" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.TEnum.fst", "name": "MiniParse.Spec.TEnum.invert_function'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.apply" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.apply" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.unfold_def" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.unfold_def" }, { "project_name": "FStar", "file_name": "Term.fst", "name": "Term.add_one" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.pose" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Tac.Enum.fst", "name": "LowParse.SLow.Tac.Enum.apply" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Tac.Enum.fst", "name": "LowParse.Spec.Tac.Enum.apply" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Logic.fst", "name": "FStar.Tactics.V1.Logic.instantiate" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.is_uvar" }, { "project_name": "FStar", "file_name": "LowParseWriters.fsti", "name": "LowParseWriters.is_uvar" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.open_term" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Formula.fst", "name": "FStar.Reflection.V2.Formula.term_as_formula'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Formula.fst", "name": "FStar.Reflection.V1.Formula.term_as_formula'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Pure.fst", "name": "Pulse.Syntax.Pure.is_fvar" }, { "project_name": "FStar", "file_name": "FStar.Tactics.MkProjectors.fst", "name": "FStar.Tactics.MkProjectors.subst_map" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.bv_to_term" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Printer.fst", "name": "Pulse.Syntax.Printer.st_term_to_string" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CheckLN.fst", "name": "FStar.Tactics.CheckLN.check" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.TEnum.fst", "name": "MiniParse.Spec.TEnum.term_of_pat" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.open_with" }, { "project_name": "steel", "file_name": "Pulse.Checker.fst", "name": "Pulse.Checker.terms_to_string" }, { "project_name": "steel", "file_name": "Pulse.Checker.Exists.fst", "name": "Pulse.Checker.Exists.terms_to_string" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Print.fst", "name": "FStar.Tactics.Print.term_to_ast_string" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.TEnum.fst", "name": "MiniParse.Spec.TEnum.pat_of_term" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Derived.fst", "name": "FStar.Reflection.V2.Derived.fv_to_string" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Derived.fst", "name": "FStar.Reflection.V1.Derived.fv_to_string" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.apply_noinst" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.apply_noinst" }, { "project_name": "Armada", "file_name": "Util.Tactics.fst", "name": "Util.Tactics.is_term_an_invocation_of_function" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Printer.fst", "name": "Pulse.Syntax.Printer.term_to_string'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Printer.fst", "name": "Pulse.Syntax.Printer.term_to_string" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.norm_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.norm_term" }, { "project_name": "steel", "file_name": "Wasm11.fst", "name": "Wasm11.def_t" }, { "project_name": "Armada", "file_name": "Util.Tactics.fst", "name": "Util.Tactics.term_to_view_to_string" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.inst_comp_once" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.PostProcess.fst", "name": "FStar.InteractiveHelpers.PostProcess.unsquash_equality" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.safe_tc" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Arith.fst", "name": "FStar.Reflection.V2.Arith.atom" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.subst_bv_in_comp" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Tactics.fst", "name": "Vale.Lib.Tactics.tf" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoid.fst", "name": "FStar.Tactics.CanonCommMonoid.reification" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Logic.fst", "name": "FStar.Tactics.V2.Logic.pose_lemma" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Derived.fst", "name": "FStar.Reflection.V1.Derived.un_uinst" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Derived.fst", "name": "FStar.Reflection.V2.Derived.un_uinst" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.apply_lemma" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.apply_lemma" }, { "project_name": "FStar", "file_name": "Param.fst", "name": "Param.param'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Printer.fst", "name": "Pulse.Syntax.Printer.st_term_to_string'" }, { "project_name": "FStar", "file_name": "Term.fst", "name": "Term.add_terms" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.goal_term_uvars" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Formula.fst", "name": "FStar.Reflection.V2.Formula.inspect_unascribe" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.exact" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.exact" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.tcut" }, { "project_name": "steel", "file_name": "Pulse.Extract.Main.fst", "name": "Pulse.Extract.Main.term_as_mlty" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoid.fst", "name": "FStar.Tactics.CanonCommMonoid.is_const" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.TEnum.fst", "name": "MiniParse.Spec.TEnum.gen_synth'" }, { "project_name": "Armada", "file_name": "Util.Tactics.fst", "name": "Util.Tactics.fn_to_lemma_invocations_in_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.name_of_bv" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.name_of_bv" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.exact_n" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.exact_n" }, { "project_name": "hacl-star", "file_name": "Meta.Interface.fst", "name": "Meta.Interface.push_pre" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.vprop_term_uvars" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.pose_as" }, { "project_name": "hacl-star", "file_name": "Meta.Interface.fst", "name": "Meta.Interface.visit_function" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Formula.fst", "name": "FStar.Reflection.V1.Formula.formula_as_term" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Formula.fst", "name": "FStar.Reflection.V2.Formula.formula_as_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.apply_lemma_noinst" } ], "selected_premises": [ "FStar.Tactics.Effect.raise", "FStar.String.strlen", "Preprocess.test_add_1", "FStar.Pervasives.Native.fst", "Preprocess.is_fv", "FStar.String.length", "FStar.Heap.trivial_preorder", "Preprocess.incr_lits_by_1", "FStar.Tactics.Types.issues", "FStar.Pervasives.Native.snd", "FStar.Tactics.Effect.get", "FStar.UInt.size", "FStar.ST.op_Bang", "Preprocess.test_add_1'", "Preprocess.test", "FStar.String.string_of_char", "FStar.Mul.op_Star", "FStar.ST.alloc", "FStar.Pervasives.reveal_opaque", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "FStar.Issue.mk_issue", "FStar.List.for_all", "FStar.All.op_Bar_Greater", "FStar.All.op_Less_Bar", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity", "FStar.List.map", "FStar.List.fold_left", "FStar.List.iter", "FStar.String.concat_injective", "FStar.Tactics.Effect.tac", "FStar.Issue.issue_level_string", "FStar.List.fold_right", "FStar.Pervasives.id", "FStar.Char.char_of_int", "FStar.String.index_list_of_string", "FStar.UInt.xor", "FStar.Math.Lib.div_non_eucl", "FStar.Math.Lib.slash_decr_axiom", "FStar.List.mapT", "FStar.Math.Lib.div", "FStar.Math.Lib.div_non_eucl_decr_lemma", "FStar.UInt32.lt", "FStar.List.tryFind", "FStar.Tactics.Effect.tactic", "FStar.Math.Lib.signed_modulo", "FStar.Math.Lib.max", "FStar.Math.Lemmas.modulo_division_lemma", "FStar.UInt.udiv", "FStar.Math.Lemmas.cancel_fraction", "FStar.UInt.div", "FStar.Pervasives.ex_pre", "FStar.UInt32.n", "FStar.Math.Lemmas.small_division_lemma_2", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity_forall", "FStar.UInt32.gte_mask", "FStar.Heap.trivial_rel", "FStar.Math.Lemmas.lemma_mod_spec", "FStar.Math.Lemmas.division_definition", "FStar.Math.Lemmas.lemma_div_mod_plus", "FStar.String.maxlen", "FStar.List.filter", "FStar.Pervasives.all_post_h'", "FStar.All.pipe_left", "FStar.Preorder.preorder_rel", "FStar.Pervasives.ex_post'", "FStar.BitVector.logor_vec", "FStar.Pervasives.all_post_h", "FStar.Math.Lemmas.lemma_div_lt_cancel", "FStar.UInt32.gt", "FStar.Tactics.Effect.lift_div_tac", "FStar.Math.Lemmas.division_sub_lemma", "FStar.Tactics.Effect.tac_wp_monotonic", "FStar.Math.Lib.slash_star_axiom", "FStar.Pervasives.coerce_eq", "FStar.Math.Lemmas.division_definition_lemma_1", "FStar.Tactics.Effect.tac_repr", "FStar.Monotonic.Pure.intro_pure_wp_monotonicity", "FStar.Tactics.Effect.tac_close", "FStar.Math.Lemmas.modulo_add", "FStar.UInt32.minus", "FStar.Math.Lemmas.mod_mul_div_exact", "FStar.List.concatMap", "FStar.Tactics.Effect.tac_if_then_else_wp", "FStar.List.tryPick", "FStar.Math.Lemmas.modulo_division_lemma_0", "FStar.Tactics.Effect.tac_return", "FStar.UInt32.eq", "FStar.UInt32.eq_mask", "FStar.UInt32.n_minus_one", "FStar.ST.contains_pred", "FStar.UInt.max_int", "FStar.UInt32.lte", "FStar.Monotonic.Heap.mref", "FStar.UInt32.op_Star_Question_Hat", "FStar.Monotonic.Pure.is_monotonic", "FStar.UInt.minus", "Prims.abs", "FStar.UInt.one_extend_vec", "Prims.pure_post'" ], "source_upto_this": "module Preprocess\n\nopen FStar.Tactics.V2\n\nlet incr_lits_by_1 (t:term) : Tac term =\n match inspect t with\n | Tv_Const (C_Int x) -> pack (Tv_Const (C_Int (x+1)))\n | _ -> t\n\nlet test_add_1 (x:int) : int =\n _ by (exact (visit_tm incr_lits_by_1 (quote (x + 1))))\n\n[@@(preprocess_with (visit_tm incr_lits_by_1))]\nlet test_add_1' (x:int) : int =\n x + 1\n\nlet test () =\n assert (test_add_1' 5 == 7)\n\nlet is_fv (fv:string) (t:term) : Tac bool =\n match inspect t with\n | Tv_FVar fv' ->\n String.concat \".\" (inspect_fv fv') = fv\n | _ -> false\n", "sketch": [ "Step 1: This definition is about creating a tactic that replaces a free variable (fv) in a term (t) with a default term (def).\nStep 2: The implementation will inspect the term (t). If the term is a free variable that matches the given string (fv), it will replace it with the default term (def). Otherwise, it will return the term unchanged.", "Step 1: The definition `inst_fv_with` is about replacing a free variable (fv) in a term (t) with a default term (def).\nStep 2: To implement this, we will inspect the term (t). If it matches the free variable (fv), we replace it with the default term (def). Otherwise, we return the term (t) unchanged.", "Step 1: The definition `inst_fv_with` is about replacing a free variable (fv) in a term (t) with a default term (def).\nStep 2: To implement this, we inspect the term (t). If it is a free variable and matches the given free variable (fv), we replace it with the default term (def). Otherwise, we return the term (t) unchanged.", "Step 1: This definition is about creating a tactic that replaces a free variable (fv) in a term (t) with a default term (def).\nStep 2: The implementation will inspect the term (t). If the term is a free variable that matches the given string (fv), it will replace it with the default term (def). Otherwise, it will return the term (t) unchanged.", "Step 1: The definition `inst_fv_with` aims to replace a free variable (fv) in a term (t) with a default term (def).\nStep 2: To implement this, we inspect the term (t). If it matches a free variable (Tv_FVar) and the name of this free variable matches the provided string (fv), we replace it with the default term (def). Otherwise, we return the term (t) unchanged.", "Step 1: This definition aims to replace a free variable (fv) in a term (t) with a default term (def).\nStep 2: To implement this, we inspect the term (t). If it matches the free variable (fv), we replace it with the default term (def). Otherwise, we return the term (t) unchanged.", "Step 1: The definition `inst_fv_with` is about replacing a free variable (fv) in a term (t) with a default term (def).\nStep 2: To implement this, we inspect the term (t). If it is a free variable that matches the given string (fv), we replace it with the default term (def). Otherwise, we return the term (t) unchanged.", "Step 1: This definition aims to replace a free variable (fv) in a term (t) with a given default term (def).\nStep 2: To implement this, we will inspect the term (t). If the term is a free variable that matches the given string (fv), we will replace it with the default term (def). Otherwise, we will return the term (t) unchanged.", "Step 1: This definition aims to replace a free variable (fv) in a given term (t) with a default term (def).\nStep 2: To implement this, we will inspect the term (t). If it matches the free variable (fv), we will replace it with the default term (def). Otherwise, we will return the term (t) unchanged.", "Step 1: The definition `inst_fv_with` aims to replace a free variable (fv) in a term (t) with a default term (def).\nStep 2: To implement this, we inspect the term (t). If it matches the free variable (fv), we replace it with the default term (def). Otherwise, we return the term (t) unchanged." ], "generated_solution": [ "let inst_fv_with (fv: string) (def t: term) : Tac term =\n match inspect t with\n | Tv_FVar fv' when String.concat \".\" (inspect_fv fv') = fv -> def\n | _ -> t", "let inst_fv_with (fv: string) (def t: term) : Tac term =\n match inspect t with\n | Tv_FVar fv' when String.concat \".\" (inspect_fv fv') = fv -> def\n | _ -> t", "let inst_fv_with (fv: string) (def t: term) : Tac term =\n match inspect t with\n | Tv_FVar fv' when String.concat \".\" (inspect_fv fv') = fv -> def\n | _ -> t", "let inst_fv_with (fv: string) (def t: term) : Tac term =\n match inspect t with\n | Tv_FVar fv' when String.concat \".\" (inspect_fv fv') = fv -> def\n | _ -> t", "let inst_fv_with (fv: string) (def t: term) : Tac term =\n match inspect t with\n | Tv_FVar fv' when String.concat \".\" (inspect_fv fv') = fv -> def\n | _ -> t", "let inst_fv_with (fv: string) (def t: term) : Tac term =\n match inspect t with\n | Tv_FVar fv' when String.concat \".\" (inspect_fv fv') = fv -> def\n | _ -> t", "let inst_fv_with (fv: string) (def t: term) : Tac term =\n match inspect t with\n | Tv_FVar fv' when String.concat \".\" (inspect_fv fv') = fv -> def\n | _ -> t", "let inst_fv_with (fv: string) (def t: term) : Tac term =\n match inspect t with\n | Tv_FVar fv' when String.concat \".\" (inspect_fv fv') = fv -> def\n | _ -> t", "let inst_fv_with (fv: string) (def t: term) : Tac term =\n match inspect t with\n | Tv_FVar fv' when String.concat \".\" (inspect_fv fv') = fv -> def\n | _ -> t", "let inst_fv_with (fv: string) (def t: term) : Tac term =\n match inspect t with\n | Tv_FVar fv' when String.concat \".\" (inspect_fv fv') = fv -> def\n | _ -> t" ] }, { "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.subst_branch", "opens_and_abbrevs": [ { "abbrev": "E", "full_module": "Pulse.Elaborate.Pure" }, { "abbrev": "U", "full_module": "Pulse.Syntax.Pure" }, { "abbrev": "RU", "full_module": "Pulse.RuntimeUtils" }, { "abbrev": "RT", "full_module": "FStar.Reflection.Typing" }, { "abbrev": "RTB", "full_module": "FStar.Reflection.Typing.Builtins" }, { "abbrev": "R", "full_module": "FStar.Reflection" }, { "abbrev": "L", "full_module": "FStar.List.Tot" }, { "open": "Pulse.Common" }, { "open": "Pulse.Syntax.Base" }, { "open": "FStar.List.Tot" }, { "open": "Pulse.Syntax" }, { "open": "Pulse.Syntax" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val subst_branch (ss: subst) (b: pattern & st_term) : Tot (pattern & st_term) (decreases b)", "source_definition": "let rec subst_st_term (t:st_term) (ss:subst)\r\n : Tot st_term (decreases t)\r\n = let t' =\r\n match t.term with\r\n | Tm_Return { expected_type; insert_eq; term } ->\r\n Tm_Return { expected_type=subst_term expected_type ss;\r\n insert_eq;\r\n term=subst_term term ss }\r\n\r\n | Tm_Abs { b; q; ascription; body } ->\r\n Tm_Abs { b=subst_binder b ss;\r\n q;\r\n ascription=subst_ascription ascription (shift_subst ss);\r\n body=subst_st_term body (shift_subst ss) }\r\n\r\n | Tm_STApp { head; arg_qual; arg } ->\r\n Tm_STApp { head = subst_term head ss;\r\n arg_qual;\r\n arg=subst_term arg ss }\r\n\r\n | Tm_Bind { binder; head; body } ->\r\n Tm_Bind { binder = subst_binder binder ss;\r\n head = subst_st_term head ss;\r\n body = subst_st_term body (shift_subst ss) }\r\n\r\n | Tm_TotBind { binder; head; body } ->\r\n Tm_TotBind { binder = subst_binder binder ss;\r\n head = subst_term head ss;\r\n body = subst_st_term body (shift_subst ss) }\r\n\r\n | Tm_If { b; then_; else_; post } ->\r\n Tm_If { b = subst_term b ss;\r\n then_ = subst_st_term then_ ss;\r\n else_ = subst_st_term else_ ss;\r\n post = subst_term_opt post (shift_subst ss) }\r\n\r\n | Tm_Match { sc; returns_; brs } ->\r\n Tm_Match { sc = subst_term sc ss;\r\n returns_ = subst_term_opt returns_ ss;\r\n brs = subst_branches t ss brs }\r\n\r\n | Tm_IntroPure { p } ->\r\n Tm_IntroPure { p = subst_term p ss }\r\n\r\n | Tm_ElimExists { p } ->\r\n Tm_ElimExists { p = subst_term p ss }\r\n \r\n | Tm_IntroExists { p; witnesses } ->\r\n Tm_IntroExists { p = subst_term p ss;\r\n witnesses = subst_term_list witnesses ss } \r\n\r\n | Tm_While { invariant; condition; body; condition_var } ->\r\n Tm_While { invariant = subst_term invariant (shift_subst ss);\r\n condition = subst_st_term condition ss;\r\n body = subst_st_term body ss;\r\n condition_var }\r\n\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n Tm_Par { pre1=subst_term pre1 ss;\r\n body1=subst_st_term body1 ss;\r\n post1=subst_term post1 (shift_subst ss);\r\n pre2=subst_term pre2 ss;\r\n body2=subst_st_term body2 ss;\r\n post2=subst_term post2 (shift_subst ss) }\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n Tm_WithLocal { binder = subst_binder binder ss;\r\n initializer = subst_term initializer ss;\r\n body = subst_st_term body (shift_subst ss) }\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n Tm_WithLocalArray { binder = subst_binder binder ss;\r\n initializer = subst_term initializer ss;\r\n length = subst_term length ss;\r\n body = subst_st_term body (shift_subst ss) }\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n Tm_Rewrite { t1 = subst_term t1 ss;\r\n t2 = subst_term t2 ss }\r\n\r\n | Tm_Admit { ctag; u; typ; post } ->\r\n Tm_Admit { ctag;\r\n u; \r\n typ=subst_term typ ss;\r\n post=subst_term_opt post (shift_subst ss) }\r\n\r\n | Tm_Unreachable -> Tm_Unreachable\r\n \r\n | Tm_ProofHintWithBinders { hint_type; binders; t} ->\r\n let n = L.length binders in\r\n let ss = shift_subst_n n ss in\r\n Tm_ProofHintWithBinders { binders;\r\n hint_type=subst_proof_hint hint_type ss; \r\n t = subst_st_term t ss }\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n let name = subst_term name ss in\r\n let body = subst_st_term body ss in\r\n let returns_inv =\r\n match returns_inv with\r\n | None -> None\r\n | Some (b, r) ->\r\n Some (subst_binder b ss, \r\n subst_term r (shift_subst ss))\r\n in\r\n Tm_WithInv { name; body; returns_inv }\r\n\r\n in\r\n { t with term = t' }\r\n\r\nand subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t})\r\n: Tot (list branch) (decreases brs)\r\n= map_dec t brs (fun br -> subst_branch ss br)\r\n\r\nand subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) =\r\n let (p, e) = b in\r\n let p = subst_pat p ss in\r\n let ss = shift_subst_n (pattern_shift_n p) ss in\r\n p, subst_st_term e ss", "source_range": { "start_line": 596, "start_col": 0, "end_line": 714, "end_col": 23 }, "interleaved": false, "definition": "fun ss b ->\n (let _ = b in\n (let FStar.Pervasives.Native.Mktuple2 #_ #_ p e = _ in\n let p = Pulse.Syntax.Naming.subst_pat p ss in\n let ss = Pulse.Syntax.Naming.shift_subst_n (Pulse.Syntax.Naming.pattern_shift_n p) ss in\n p, Pulse.Syntax.Naming.subst_st_term e ss)\n <:\n Pulse.Syntax.Base.pattern * Pulse.Syntax.Base.st_term)\n <:\n Pulse.Syntax.Base.pattern * Pulse.Syntax.Base.st_term", "effect": "Prims.Tot", "effect_flags": [ "total", "" ], "mutual_with": [ "subst_st_term", "subst_branches", "subst_branch" ], "premises": [ "Pulse.Syntax.Naming.subst", "FStar.Pervasives.Native.tuple2", "Pulse.Syntax.Base.pattern", "Pulse.Syntax.Base.st_term", "FStar.Pervasives.Native.Mktuple2", "Pulse.Syntax.Naming.subst_st_term", "Prims.list", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.shift_subst_n", "Pulse.Syntax.Naming.pattern_shift_n", "Pulse.Syntax.Naming.subst_pat" ], "proof_features": [ "mutual recursion" ], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "ss: Pulse.Syntax.Naming.subst -> b: (Pulse.Syntax.Base.pattern * Pulse.Syntax.Base.st_term)\n -> Prims.Tot (Pulse.Syntax.Base.pattern * Pulse.Syntax.Base.st_term)", "prompt": "let rec subst_branch (ss: subst) (b: pattern & st_term) : Tot (pattern & st_term) (decreases b) =\n ", "expected_response": "let p, e = b in\nlet p = subst_pat p ss in\nlet ss = shift_subst_n (pattern_shift_n p) ss in\np, subst_st_term e ss", "source": { "project_name": "steel", "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Pulse.Syntax.Naming.fsti", "checked_file": "dataset/Pulse.Syntax.Naming.fsti.checked", "interface_file": false, "dependencies": [ "dataset/Pulse.Syntax.Pure.fst.checked", "dataset/Pulse.Syntax.Base.fsti.checked", "dataset/Pulse.RuntimeUtils.fsti.checked", "dataset/Pulse.Elaborate.Pure.fst.checked", "dataset/Pulse.Common.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Reflection.Typing.Builtins.fsti.checked", "dataset/FStar.Reflection.Typing.fsti.checked", "dataset/FStar.Reflection.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.List.fst.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "", "", "", "", "", "let rec freevars (t:term) \r\n : Set.set var\r\n = match t.t with\r\n | Tm_Emp\r\n | Tm_VProp\r\n | Tm_Inames\r\n | Tm_EmpInames\r\n | Tm_Unknown -> Set.empty\r\n | Tm_Inv p -> freevars p\r\n | Tm_Star t1 t2 ->\r\n Set.union (freevars t1) (freevars t2)\r\n | Tm_ExistsSL _ t1 t2\r\n | Tm_ForallSL _ t1 t2 ->\r\n Set.union (freevars t1.binder_ty) (freevars t2)\r\n | Tm_Pure p -> freevars p\r\n | Tm_FStar t -> RT.freevars t\r\n | Tm_AddInv i is -> Set.union (freevars i) (freevars is)", "let freevars_st_comp (s:st_comp) : Set.set var =\r\n freevars s.res `Set.union`\r\n freevars s.pre `Set.union`\r\n freevars s.post", "let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) =\r\n match c with\r\n | C_Tot t -> freevars t\r\n | C_ST s\r\n | C_STGhost s -> freevars_st_comp s\r\n | C_STAtomic inames _ s ->\r\n freevars inames `Set.union` freevars_st_comp s", "let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var =\r\n match x with\r\n | None -> Set.empty\r\n | Some x -> f x", "let freevars_term_opt (t:option term) : Set.set var =\r\n freevars_opt freevars t", "let rec freevars_list (t:list term) : Set.set var =\r\n match t with\r\n | [] -> Set.empty\r\n | hd::tl -> freevars hd `Set.union` freevars_list tl", "let rec freevars_pairs (pairs:list (term & term)) : Set.set var =\r\n match pairs with\r\n | [] -> Set.empty\r\n | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl", "let freevars_proof_hint (ht:proof_hint_type) : Set.set var = \r\n match ht with\r\n | ASSERT { p }\r\n | FOLD { p }\r\n | UNFOLD { p } -> freevars p\r\n | RENAME { pairs; goal } ->\r\n Set.union (freevars_pairs pairs) (freevars_term_opt goal)\r\n | REWRITE { t1; t2 } ->\r\n Set.union (freevars t1) (freevars t2)\r\n | WILD\r\n | SHOW_PROOF_STATE _ -> Set.empty", "let freevars_ascription (c:comp_ascription) \r\n : Set.set var\r\n = Set.union (freevars_opt freevars_comp c.elaborated)\r\n (freevars_opt freevars_comp c.annotated)", "let rec freevars_st (t:st_term)\r\n : Set.set var\r\n = match t.term with\r\n | Tm_Return { expected_type; term } ->\r\n Set.union (freevars expected_type) (freevars term)\r\n | Tm_Abs { b; ascription; body } ->\r\n Set.union (freevars b.binder_ty) \r\n (Set.union (freevars_st body)\r\n (freevars_ascription ascription))\r\n | Tm_STApp { head; arg } ->\r\n Set.union (freevars head) (freevars arg)\r\n | Tm_Bind { binder; head; body } ->\r\n Set.union \r\n (Set.union (freevars binder.binder_ty) \r\n (freevars_st head))\r\n (freevars_st body)\r\n | Tm_TotBind { binder; head; body } ->\r\n Set.union\r\n (Set.union (freevars binder.binder_ty)\r\n (freevars head))\r\n (freevars_st body)\r\n | Tm_If { b; then_; else_; post } ->\r\n Set.union (Set.union (freevars b) (freevars_st then_))\r\n (Set.union (freevars_st else_) (freevars_term_opt post))\r\n\r\n | Tm_Match { sc ; returns_; brs } ->\r\n let (@@) = Set.union in\r\n freevars sc\r\n @@ freevars_term_opt returns_\r\n @@ freevars_branches brs\r\n\r\n | Tm_IntroPure { p }\r\n | Tm_ElimExists { p } ->\r\n freevars p\r\n | Tm_IntroExists { p; witnesses } ->\r\n Set.union (freevars p) (freevars_list witnesses)\r\n | Tm_While { invariant; condition; body } ->\r\n Set.union (freevars invariant)\r\n (Set.union (freevars_st condition)\r\n (freevars_st body))\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n Set.union\r\n (Set.union (freevars pre1)\r\n (Set.union (freevars_st body1)\r\n (freevars post1)))\r\n (Set.union (freevars pre2)\r\n (Set.union (freevars_st body2)\r\n (freevars post2)))\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n Set.union (freevars binder.binder_ty)\r\n (Set.union (freevars initializer)\r\n (freevars_st body))\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n Set.union (freevars binder.binder_ty)\r\n (Set.union (freevars initializer)\r\n (Set.union (freevars length)\r\n (freevars_st body)))\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n Set.union (freevars t1) (freevars t2)\r\n\r\n | Tm_Admit { typ; post } ->\r\n Set.union (freevars typ)\r\n (freevars_term_opt post)\r\n\r\n | Tm_Unreachable ->\r\n Set.empty\r\n\r\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\r\n Set.union (freevars_proof_hint hint_type) (freevars_st t)\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n Set.union (Set.union (freevars name) (freevars_st body))\r\n (freevars_opt \r\n (fun (b, r) ->\r\n (Set.union (freevars b.binder_ty) \r\n (freevars r)))\r\n returns_inv)\r\n\r\nand freevars_branches (t:list (pattern & st_term)) : Set.set var =\r\n match t with\r\n | [] -> Set.empty\r\n | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl", "let rec freevars_st (t:st_term)\r\n : Set.set var\r\n = match t.term with\r\n | Tm_Return { expected_type; term } ->\r\n Set.union (freevars expected_type) (freevars term)\r\n | Tm_Abs { b; ascription; body } ->\r\n Set.union (freevars b.binder_ty) \r\n (Set.union (freevars_st body)\r\n (freevars_ascription ascription))\r\n | Tm_STApp { head; arg } ->\r\n Set.union (freevars head) (freevars arg)\r\n | Tm_Bind { binder; head; body } ->\r\n Set.union \r\n (Set.union (freevars binder.binder_ty) \r\n (freevars_st head))\r\n (freevars_st body)\r\n | Tm_TotBind { binder; head; body } ->\r\n Set.union\r\n (Set.union (freevars binder.binder_ty)\r\n (freevars head))\r\n (freevars_st body)\r\n | Tm_If { b; then_; else_; post } ->\r\n Set.union (Set.union (freevars b) (freevars_st then_))\r\n (Set.union (freevars_st else_) (freevars_term_opt post))\r\n\r\n | Tm_Match { sc ; returns_; brs } ->\r\n let (@@) = Set.union in\r\n freevars sc\r\n @@ freevars_term_opt returns_\r\n @@ freevars_branches brs\r\n\r\n | Tm_IntroPure { p }\r\n | Tm_ElimExists { p } ->\r\n freevars p\r\n | Tm_IntroExists { p; witnesses } ->\r\n Set.union (freevars p) (freevars_list witnesses)\r\n | Tm_While { invariant; condition; body } ->\r\n Set.union (freevars invariant)\r\n (Set.union (freevars_st condition)\r\n (freevars_st body))\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n Set.union\r\n (Set.union (freevars pre1)\r\n (Set.union (freevars_st body1)\r\n (freevars post1)))\r\n (Set.union (freevars pre2)\r\n (Set.union (freevars_st body2)\r\n (freevars post2)))\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n Set.union (freevars binder.binder_ty)\r\n (Set.union (freevars initializer)\r\n (freevars_st body))\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n Set.union (freevars binder.binder_ty)\r\n (Set.union (freevars initializer)\r\n (Set.union (freevars length)\r\n (freevars_st body)))\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n Set.union (freevars t1) (freevars t2)\r\n\r\n | Tm_Admit { typ; post } ->\r\n Set.union (freevars typ)\r\n (freevars_term_opt post)\r\n\r\n | Tm_Unreachable ->\r\n Set.empty\r\n\r\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\r\n Set.union (freevars_proof_hint hint_type) (freevars_st t)\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n Set.union (Set.union (freevars name) (freevars_st body))\r\n (freevars_opt \r\n (fun (b, r) ->\r\n (Set.union (freevars b.binder_ty) \r\n (freevars r)))\r\n returns_inv)\r\n\r\nand freevars_branches (t:list (pattern & st_term)) : Set.set var =\r\n match t with\r\n | [] -> Set.empty\r\n | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl", "let rec ln' (t:term) (i:int) : Tot bool (decreases t) =\r\n match t.t with\r\n | Tm_Emp\r\n | Tm_VProp\r\n | Tm_Inames\r\n | Tm_EmpInames\r\n | Tm_Unknown -> true\r\n\r\n | Tm_Inv p -> ln' p i\r\n\r\n | Tm_Star t1 t2 ->\r\n ln' t1 i &&\r\n ln' t2 i\r\n\r\n | Tm_Pure p ->\r\n ln' p i\r\n\r\n | Tm_ExistsSL _ t body\r\n | Tm_ForallSL _ t body ->\r\n ln' t.binder_ty i &&\r\n ln' body (i + 1)\r\n \r\n | Tm_FStar t ->\r\n RT.ln' t i\r\n\r\n | Tm_AddInv x is ->\r\n ln' x i &&\r\n ln' is i", "let ln_st_comp (s:st_comp) (i:int) : bool =\r\n ln' s.res i &&\r\n ln' s.pre i &&\r\n ln' s.post (i + 1)", "let ln_c' (c:comp) (i:int)\r\n : bool\r\n = match c with\r\n | C_Tot t -> ln' t i\r\n | C_ST s\r\n | C_STGhost s -> ln_st_comp s i\r\n | C_STAtomic inames _ s ->\r\n ln' inames i &&\r\n ln_st_comp s i", "let ln_opt' (f: ('a -> int -> bool)) (t:option 'a) (i:int) : bool =\r\n match t with\r\n | None -> true\r\n | Some t -> f t i", "let rec ln_list' (t:list term) (i:int) : bool =\r\n match t with\r\n | [] -> true\r\n | hd::tl -> ln' hd i && ln_list' tl i", "let rec ln_terms' (t:list (term & term)) (i:int) : bool =\r\n match t with\r\n | [] -> true\r\n | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i", "let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool =\r\n match ht with\r\n | ASSERT { p }\r\n | UNFOLD { p }\r\n | FOLD { p } -> ln' p i\r\n | RENAME { pairs; goal } ->\r\n ln_terms' pairs i &&\r\n ln_opt' ln' goal i\r\n | REWRITE { t1; t2 } ->\r\n ln' t1 i &&\r\n ln' t2 i\r\n | WILD\r\n | SHOW_PROOF_STATE _ -> true", "let rec pattern_shift_n (p:pattern)\r\n : Tot nat\r\n = match p with\r\n | Pat_Constant _ \r\n | Pat_Dot_Term _ -> \r\n 0\r\n | Pat_Var _ _ ->\r\n 1\r\n | Pat_Cons fv l ->\r\n pattern_args_shift_n l\r\nand pattern_args_shift_n (ps:list (pattern & bool))\r\n : Tot nat\r\n = match ps with\r\n | [] -> 0\r\n | (p, _)::tl ->\r\n pattern_shift_n p + pattern_args_shift_n tl", "let rec pattern_shift_n (p:pattern)\r\n : Tot nat\r\n = match p with\r\n | Pat_Constant _ \r\n | Pat_Dot_Term _ -> \r\n 0\r\n | Pat_Var _ _ ->\r\n 1\r\n | Pat_Cons fv l ->\r\n pattern_args_shift_n l\r\nand pattern_args_shift_n (ps:list (pattern & bool))\r\n : Tot nat\r\n = match ps with\r\n | [] -> 0\r\n | (p, _)::tl ->\r\n pattern_shift_n p + pattern_args_shift_n tl", "let rec ln_pattern' (p : pattern) (i:int)\r\n : Tot bool (decreases p)\r\n = match p with\r\n | Pat_Constant _ \r\n | Pat_Var _ _ \r\n | Pat_Dot_Term None ->\r\n true\r\n | Pat_Dot_Term (Some e) ->\r\n ln' e i\r\n | Pat_Cons fv l ->\r\n ln_pattern_args' l i\r\n \r\nand ln_pattern_args' (p:list (pattern & bool)) (i:int)\r\n : Tot bool (decreases p)\r\n = match p with\r\n | [] ->\r\n true\r\n | (p, _)::tl ->\r\n ln_pattern' p i &&\r\n ln_pattern_args' tl (i + pattern_shift_n p)", "let rec ln_pattern' (p : pattern) (i:int)\r\n : Tot bool (decreases p)\r\n = match p with\r\n | Pat_Constant _ \r\n | Pat_Var _ _ \r\n | Pat_Dot_Term None ->\r\n true\r\n | Pat_Dot_Term (Some e) ->\r\n ln' e i\r\n | Pat_Cons fv l ->\r\n ln_pattern_args' l i\r\n \r\nand ln_pattern_args' (p:list (pattern & bool)) (i:int)\r\n : Tot bool (decreases p)\r\n = match p with\r\n | [] ->\r\n true\r\n | (p, _)::tl ->\r\n ln_pattern' p i &&\r\n ln_pattern_args' tl (i + pattern_shift_n p)", "let ln_ascription' (c:comp_ascription) (i:int)\r\n : bool\r\n = ln_opt' ln_c' c.elaborated i &&\r\n ln_opt' ln_c' c.annotated i", "let rec ln_st' (t:st_term) (i:int)\r\n : Tot bool (decreases t)\r\n = match t.term with\r\n | Tm_Return { expected_type; term } ->\r\n ln' expected_type i &&\r\n ln' term i\r\n \r\n | Tm_Abs { b; ascription; body } ->\r\n ln' b.binder_ty i &&\r\n ln_st' body (i + 1) &&\r\n ln_ascription' ascription (i + 1)\r\n\r\n | Tm_STApp { head; arg } ->\r\n ln' head i &&\r\n ln' arg i\r\n\r\n | Tm_Bind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln_st' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_TotBind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_If { b; then_; else_; post } ->\r\n ln' b i &&\r\n ln_st' then_ i &&\r\n ln_st' else_ i &&\r\n ln_opt' ln' post (i + 1)\r\n \r\n | Tm_Match {sc; returns_; brs } ->\r\n ln' sc i &&\r\n ln_opt' ln' returns_ i &&\r\n ln_branches' t brs i\r\n\r\n | Tm_IntroPure { p }\r\n | Tm_ElimExists { p } ->\r\n ln' p i\r\n\r\n | Tm_IntroExists { p; witnesses } ->\r\n ln' p i &&\r\n ln_list' witnesses i\r\n \r\n | Tm_While { invariant; condition; body } ->\r\n ln' invariant (i + 1) &&\r\n ln_st' condition i &&\r\n ln_st' body i\r\n\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n ln' pre1 i &&\r\n ln_st' body1 i &&\r\n ln' post1 (i + 1) &&\r\n ln' pre2 i &&\r\n ln_st' body2 i &&\r\n ln' post2 (i + 1)\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln' length i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n ln' t1 i &&\r\n ln' t2 i\r\n\r\n | Tm_Admit { typ; post } ->\r\n ln' typ i &&\r\n ln_opt' ln' post (i + 1)\r\n\r\n | Tm_Unreachable ->\r\n true\r\n\r\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\r\n let n = L.length binders in\r\n ln_proof_hint' hint_type (i + n) &&\r\n ln_st' t (i + n)\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n ln' name i &&\r\n ln_st' body i &&\r\n ln_opt'\r\n (fun (b, r) i ->\r\n ln' b.binder_ty i &&\r\n ln' r (i + 1))\r\n returns_inv i\r\n\r\nand ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) =\r\n let (p, e) = b in\r\n ln_pattern' p i &&\r\n ln_st' e (i + pattern_shift_n p)\r\n \r\nand ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) =\r\n for_all_dec t brs (fun b -> ln_branch' b i)", "let rec ln_st' (t:st_term) (i:int)\r\n : Tot bool (decreases t)\r\n = match t.term with\r\n | Tm_Return { expected_type; term } ->\r\n ln' expected_type i &&\r\n ln' term i\r\n \r\n | Tm_Abs { b; ascription; body } ->\r\n ln' b.binder_ty i &&\r\n ln_st' body (i + 1) &&\r\n ln_ascription' ascription (i + 1)\r\n\r\n | Tm_STApp { head; arg } ->\r\n ln' head i &&\r\n ln' arg i\r\n\r\n | Tm_Bind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln_st' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_TotBind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_If { b; then_; else_; post } ->\r\n ln' b i &&\r\n ln_st' then_ i &&\r\n ln_st' else_ i &&\r\n ln_opt' ln' post (i + 1)\r\n \r\n | Tm_Match {sc; returns_; brs } ->\r\n ln' sc i &&\r\n ln_opt' ln' returns_ i &&\r\n ln_branches' t brs i\r\n\r\n | Tm_IntroPure { p }\r\n | Tm_ElimExists { p } ->\r\n ln' p i\r\n\r\n | Tm_IntroExists { p; witnesses } ->\r\n ln' p i &&\r\n ln_list' witnesses i\r\n \r\n | Tm_While { invariant; condition; body } ->\r\n ln' invariant (i + 1) &&\r\n ln_st' condition i &&\r\n ln_st' body i\r\n\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n ln' pre1 i &&\r\n ln_st' body1 i &&\r\n ln' post1 (i + 1) &&\r\n ln' pre2 i &&\r\n ln_st' body2 i &&\r\n ln' post2 (i + 1)\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln' length i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n ln' t1 i &&\r\n ln' t2 i\r\n\r\n | Tm_Admit { typ; post } ->\r\n ln' typ i &&\r\n ln_opt' ln' post (i + 1)\r\n\r\n | Tm_Unreachable ->\r\n true\r\n\r\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\r\n let n = L.length binders in\r\n ln_proof_hint' hint_type (i + n) &&\r\n ln_st' t (i + n)\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n ln' name i &&\r\n ln_st' body i &&\r\n ln_opt'\r\n (fun (b, r) i ->\r\n ln' b.binder_ty i &&\r\n ln' r (i + 1))\r\n returns_inv i\r\n\r\nand ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) =\r\n let (p, e) = b in\r\n ln_pattern' p i &&\r\n ln_st' e (i + pattern_shift_n p)\r\n \r\nand ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) =\r\n for_all_dec t brs (fun b -> ln_branch' b i)", "let rec ln_st' (t:st_term) (i:int)\r\n : Tot bool (decreases t)\r\n = match t.term with\r\n | Tm_Return { expected_type; term } ->\r\n ln' expected_type i &&\r\n ln' term i\r\n \r\n | Tm_Abs { b; ascription; body } ->\r\n ln' b.binder_ty i &&\r\n ln_st' body (i + 1) &&\r\n ln_ascription' ascription (i + 1)\r\n\r\n | Tm_STApp { head; arg } ->\r\n ln' head i &&\r\n ln' arg i\r\n\r\n | Tm_Bind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln_st' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_TotBind { binder; head; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' head i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_If { b; then_; else_; post } ->\r\n ln' b i &&\r\n ln_st' then_ i &&\r\n ln_st' else_ i &&\r\n ln_opt' ln' post (i + 1)\r\n \r\n | Tm_Match {sc; returns_; brs } ->\r\n ln' sc i &&\r\n ln_opt' ln' returns_ i &&\r\n ln_branches' t brs i\r\n\r\n | Tm_IntroPure { p }\r\n | Tm_ElimExists { p } ->\r\n ln' p i\r\n\r\n | Tm_IntroExists { p; witnesses } ->\r\n ln' p i &&\r\n ln_list' witnesses i\r\n \r\n | Tm_While { invariant; condition; body } ->\r\n ln' invariant (i + 1) &&\r\n ln_st' condition i &&\r\n ln_st' body i\r\n\r\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\r\n ln' pre1 i &&\r\n ln_st' body1 i &&\r\n ln' post1 (i + 1) &&\r\n ln' pre2 i &&\r\n ln_st' body2 i &&\r\n ln' post2 (i + 1)\r\n\r\n | Tm_WithLocal { binder; initializer; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_WithLocalArray { binder; initializer; length; body } ->\r\n ln' binder.binder_ty i &&\r\n ln' initializer i &&\r\n ln' length i &&\r\n ln_st' body (i + 1)\r\n\r\n | Tm_Rewrite { t1; t2 } ->\r\n ln' t1 i &&\r\n ln' t2 i\r\n\r\n | Tm_Admit { typ; post } ->\r\n ln' typ i &&\r\n ln_opt' ln' post (i + 1)\r\n\r\n | Tm_Unreachable ->\r\n true\r\n\r\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\r\n let n = L.length binders in\r\n ln_proof_hint' hint_type (i + n) &&\r\n ln_st' t (i + n)\r\n\r\n | Tm_WithInv { name; body; returns_inv } ->\r\n ln' name i &&\r\n ln_st' body i &&\r\n ln_opt'\r\n (fun (b, r) i ->\r\n ln' b.binder_ty i &&\r\n ln' r (i + 1))\r\n returns_inv i\r\n\r\nand ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) =\r\n let (p, e) = b in\r\n ln_pattern' p i &&\r\n ln_st' e (i + pattern_shift_n p)\r\n \r\nand ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) =\r\n for_all_dec t brs (fun b -> ln_branch' b i)", "let ln (t:term) = ln' t (-1)", "let ln_st (t:st_term) = ln_st' t (-1)", "let ln_c (c:comp) = ln_c' c (-1)", "subst_elt", "DT", "DT", "DT", "NT", "NT", "NT", "ND", "ND", "ND", "let shift_subst_elt (n:nat) = function\r\n | DT i t -> DT (i + n) t\r\n | NT x t -> NT x t\r\n | ND x i -> ND x (i + n)", "let subst = list subst_elt", "let shift_subst_n (n:nat) = L.map (shift_subst_elt n)", "let shift_subst = shift_subst_n 1", "let rt_subst_elt = function\r\n | DT i t -> RT.DT i (E.elab_term t)\r\n | NT x t -> RT.NT x (E.elab_term t)\r\n | ND x i -> RT.ND x i", "let rt_subst = L.map rt_subst_elt", "let open_or_close_host_term (t:host_term) (ss:subst)\r\n : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss)))\r\n = admit()", "val subst_host_term (t:host_term) (ss:subst)\r\n : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) })", "let rec subst_term (t:term) (ss:subst)\r\n : Tot term (decreases t)\r\n = let w t' = with_range t' t.range in\r\n match t.t with\r\n | Tm_VProp\r\n | Tm_Emp\r\n | Tm_Inames\r\n | Tm_EmpInames\r\n | Tm_Unknown -> t\r\n\r\n | Tm_Inv p ->\r\n w (Tm_Inv (subst_term p ss))\r\n \r\n | Tm_Pure p ->\r\n w (Tm_Pure (subst_term p ss))\r\n \r\n | Tm_Star l r ->\r\n w (Tm_Star (subst_term l ss)\r\n (subst_term r ss))\r\n \r\n | Tm_ExistsSL u b body ->\r\n w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss }\r\n (subst_term body (shift_subst ss)))\r\n \r\n | Tm_ForallSL u b body ->\r\n w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss }\r\n (subst_term body (shift_subst ss)))\r\n \r\n | Tm_FStar t ->\r\n w (Tm_FStar (subst_host_term t ss))\r\n\r\n | Tm_AddInv i is ->\r\n w (Tm_AddInv (subst_term i ss)\r\n (subst_term is ss))", "let open_term' (t:term) (v:term) (i:index) =\r\n subst_term t [ DT i v ]", "let subst_st_comp (s:st_comp) (ss:subst)\r\n : st_comp =\r\n\r\n { s with res = subst_term s.res ss;\r\n pre = subst_term s.pre ss;\r\n post = subst_term s.post (shift_subst ss) }", "let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp =\r\n subst_st_comp s [ DT i v ]", "let subst_comp (c:comp) (ss:subst)\r\n : comp\r\n = match c with\r\n | C_Tot t ->\r\n C_Tot (subst_term t ss)\r\n\r\n | C_ST s -> C_ST (subst_st_comp s ss)\r\n\r\n | C_STAtomic inames obs s ->\r\n C_STAtomic (subst_term inames ss) obs\r\n (subst_st_comp s ss)\r\n\r\n | C_STGhost s ->\r\n C_STGhost (subst_st_comp s ss)", "let open_comp' (c:comp) (v:term) (i:index) : comp =\r\n subst_comp c [ DT i v ]", "let subst_term_opt (t:option term) (ss:subst)\r\n : Tot (option term)\r\n = match t with\r\n | None -> None\r\n | Some t -> Some (subst_term t ss)", "let open_term_opt' (t:option term) (v:term) (i:index)\r\n : Tot (option term) = subst_term_opt t [ DT i v ]", "let rec subst_term_list (t:list term) (ss:subst)\r\n : Tot (list term)\r\n = match t with\r\n | [] -> []\r\n | hd::tl -> subst_term hd ss :: subst_term_list tl ss", "let open_term_list' (t:list term) (v:term) (i:index)\r\n : Tot (list term) = subst_term_list t [ DT i v ]", "let subst_binder b ss = \r\n {b with binder_ty=subst_term b.binder_ty ss}", "let open_binder b v i = \r\n {b with binder_ty=open_term' b.binder_ty v i}", "let rec subst_term_pairs (t:list (term & term)) (ss:subst)\r\n : Tot (list (term & term))\r\n = match t with\r\n | [] -> []\r\n | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss", "let subst_proof_hint (ht:proof_hint_type) (ss:subst) \r\n : proof_hint_type\r\n = match ht with\r\n | ASSERT { p } -> ASSERT { p=subst_term p ss }\r\n | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss}\r\n | FOLD { names; p } -> FOLD { names; p=subst_term p ss }\r\n | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss;\r\n goal=subst_term_opt goal ss }\r\n | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss;\r\n t2=subst_term t2 ss }\r\n | WILD\r\n | SHOW_PROOF_STATE _ -> ht", "let open_term_pairs' (t:list (term * term)) (v:term) (i:index) =\r\n subst_term_pairs t [DT i v]", "let close_term_pairs' (t:list (term * term)) (x:var) (i:index) =\r\n subst_term_pairs t [ND x i]", "let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) =\r\n subst_proof_hint ht [DT i v]", "let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) =\r\n subst_proof_hint ht [ND x i]", "let rec subst_pat (p:pattern) (ss:subst)\r\n : Tot pattern (decreases p)\r\n = match p with\r\n | Pat_Constant _\r\n | Pat_Dot_Term None ->\r\n p\r\n | Pat_Var n t -> \r\n let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in\r\n Pat_Var n t\r\n | Pat_Dot_Term (Some e) ->\r\n Pat_Dot_Term (Some (subst_term e ss))\r\n | Pat_Cons d args ->\r\n let args = subst_pat_args args ss in\r\n Pat_Cons d args\r\nand subst_pat_args (args:list (pattern & bool)) (ss:subst)\r\n : Tot (list (pattern & bool)) (decreases args)\r\n = match args with\r\n | [] -> []\r\n | (arg, b)::tl ->\r\n let arg' = subst_pat arg ss in\r\n let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in\r\n (arg', b)::tl", "let rec subst_pat (p:pattern) (ss:subst)\r\n : Tot pattern (decreases p)\r\n = match p with\r\n | Pat_Constant _\r\n | Pat_Dot_Term None ->\r\n p\r\n | Pat_Var n t -> \r\n let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in\r\n Pat_Var n t\r\n | Pat_Dot_Term (Some e) ->\r\n Pat_Dot_Term (Some (subst_term e ss))\r\n | Pat_Cons d args ->\r\n let args = subst_pat_args args ss in\r\n Pat_Cons d args\r\nand subst_pat_args (args:list (pattern & bool)) (ss:subst)\r\n : Tot (list (pattern & bool)) (decreases args)\r\n = match args with\r\n | [] -> []\r\n | (arg, b)::tl ->\r\n let arg' = subst_pat arg ss in\r\n let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in\r\n (arg', b)::tl", "let map2_opt (f: 'a -> 'b -> 'c) (x:option 'a) (y:'b)\r\n : option 'c\r\n = match x with\r\n | None -> None\r\n | Some x -> Some (f x y)", "let subst_ascription (c:comp_ascription) (ss:subst)\r\n : comp_ascription\r\n = { elaborated = map2_opt subst_comp c.elaborated ss;\r\n annotated = map2_opt subst_comp c.annotated ss }" ], "closest": [ "val subst_branch (br: branch) (ss: subst) : Tot branch (decreases br)\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> t\n | Tv_Var x -> subst_var x ss\n | Tv_BVar j -> subst_db j ss\n | Tv_App hd argv ->\n pack_ln (Tv_App (subst_term hd ss)\n (subst_term (fst argv) ss, snd argv))\n\n | Tv_Abs b body -> \n let b' = subst_binder b ss in\n pack_ln (Tv_Abs b' (subst_term body (shift_subst ss)))\n\n | Tv_Arrow b c ->\n let b' = subst_binder b ss in\n pack_ln (Tv_Arrow b' (subst_comp c (shift_subst ss))) \n\n | Tv_Refine b f ->\n let b = subst_binder b ss in\n pack_ln (Tv_Refine b (subst_term f (shift_subst ss)))\n\n | Tv_Uvar j c ->\n pack_ln (Tv_Uvar j (subst_ctx_uvar_and_subst c ss))\n \n | Tv_Let recf attrs b def body ->\n let b = subst_binder b ss in\n pack_ln (Tv_Let recf \n (subst_terms attrs ss)\n b\n (if recf \n then subst_term def (shift_subst ss)\n else subst_term def ss)\n (subst_term body (shift_subst ss)))\n\n | Tv_Match scr ret brs ->\n pack_ln (Tv_Match (subst_term scr ss)\n (match ret with\n | None -> None\n | Some m -> Some (subst_match_returns m ss))\n (subst_branches brs ss))\n \n | Tv_AscribedT e t tac b ->\n pack_ln (Tv_AscribedT (subst_term e ss)\n (subst_term t ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\n | Tv_AscribedC e c tac b ->\n pack_ln (Tv_AscribedC (subst_term e ss)\n (subst_comp c ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\nand subst_binder (b:binder) (ss:subst)\n : Tot (b':binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\n = let bndr = inspect_binder b in\n pack_binder {\n ppname = bndr.ppname;\n qual = bndr.qual;\n attrs = subst_terms bndr.attrs ss;\n sort = subst_term bndr.sort ss\n }\n\nand subst_comp (c:comp) (ss:subst)\n : Tot comp (decreases c)\n = match inspect_comp c with\n | C_Total t ->\n pack_comp (C_Total (subst_term t ss))\n\n | C_GTotal t ->\n pack_comp (C_GTotal (subst_term t ss))\n\n | C_Lemma pre post pats ->\n pack_comp (C_Lemma (subst_term pre ss)\n (subst_term post ss)\n (subst_term pats ss))\n\n | C_Eff us eff_name res args decrs ->\n pack_comp (C_Eff us eff_name\n (subst_term res ss)\n (subst_args args ss)\n (subst_terms decrs ss))\n\nand subst_terms (ts:list term) (ss:subst)\n : Tot (ts':list term{Nil? ts ==> Nil? ts'}) // property useful for subst_binder\n (decreases ts)\n = match ts with\n | [] -> []\n | t::ts -> subst_term t ss :: subst_terms ts ss\n\nand subst_args (ts:list argv) (ss:subst)\n : Tot (list argv) (decreases ts)\n = match ts with\n | [] -> []\n | (t,q)::ts -> (subst_term t ss,q) :: subst_args ts ss\n\nand subst_patterns (ps:list (pattern & bool)) (ss:subst) \n : Tot (list (pattern & bool))\n (decreases ps)\n = match ps with\n | [] -> ps\n | (p, b)::ps ->\n let n = binder_offset_pattern p in\n let p = subst_pattern p ss in\n let ps = subst_patterns ps (shift_subst_n n ss) in\n (p,b)::ps\n\nand subst_pattern (p:pattern) (ss:subst) \n : Tot pattern\n (decreases p)\n = match p with\n | Pat_Constant _ -> p\n\n | Pat_Cons fv us pats -> \n let pats = subst_patterns pats ss in\n Pat_Cons fv us pats\n\n | Pat_Var bv s ->\n Pat_Var bv s\n\n | Pat_Dot_Term topt ->\n Pat_Dot_Term (match topt with\n | None -> None\n | Some t -> Some (subst_term t ss))\n\n \nand subst_branch (br:branch) (ss:subst)\n : Tot branch (decreases br)\n = let p, t = br in\n let p = subst_pattern p ss in\n let j = binder_offset_pattern p in\n let t = subst_term t (shift_subst_n j ss) in\n p, t\n \nand subst_branches (brs:list branch) (ss:subst)\n : Tot (list branch) (decreases brs)\n = match brs with\n | [] -> []\n | br::brs -> subst_branch br ss :: subst_branches brs ss\n \nand subst_match_returns (m:match_returns_ascription) (ss:subst)\n : Tot match_returns_ascription (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = subst_binder b ss in\n let ret =\n match ret with\n | Inl t -> Inl (subst_term t (shift_subst ss))\n | Inr c -> Inr (subst_comp c (shift_subst ss))\n in\n let as_ =\n match as_ with\n | None -> None\n | Some t -> Some (subst_term t (shift_subst ss))\n in\n b, (ret, as_, eq)", "val subst_branches (brs: list branch) (ss: subst) : Tot (list branch) (decreases brs)\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> t\n | Tv_Var x -> subst_var x ss\n | Tv_BVar j -> subst_db j ss\n | Tv_App hd argv ->\n pack_ln (Tv_App (subst_term hd ss)\n (subst_term (fst argv) ss, snd argv))\n\n | Tv_Abs b body -> \n let b' = subst_binder b ss in\n pack_ln (Tv_Abs b' (subst_term body (shift_subst ss)))\n\n | Tv_Arrow b c ->\n let b' = subst_binder b ss in\n pack_ln (Tv_Arrow b' (subst_comp c (shift_subst ss))) \n\n | Tv_Refine b f ->\n let b = subst_binder b ss in\n pack_ln (Tv_Refine b (subst_term f (shift_subst ss)))\n\n | Tv_Uvar j c ->\n pack_ln (Tv_Uvar j (subst_ctx_uvar_and_subst c ss))\n \n | Tv_Let recf attrs b def body ->\n let b = subst_binder b ss in\n pack_ln (Tv_Let recf \n (subst_terms attrs ss)\n b\n (if recf \n then subst_term def (shift_subst ss)\n else subst_term def ss)\n (subst_term body (shift_subst ss)))\n\n | Tv_Match scr ret brs ->\n pack_ln (Tv_Match (subst_term scr ss)\n (match ret with\n | None -> None\n | Some m -> Some (subst_match_returns m ss))\n (subst_branches brs ss))\n \n | Tv_AscribedT e t tac b ->\n pack_ln (Tv_AscribedT (subst_term e ss)\n (subst_term t ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\n | Tv_AscribedC e c tac b ->\n pack_ln (Tv_AscribedC (subst_term e ss)\n (subst_comp c ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\nand subst_binder (b:binder) (ss:subst)\n : Tot (b':binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\n = let bndr = inspect_binder b in\n pack_binder {\n ppname = bndr.ppname;\n qual = bndr.qual;\n attrs = subst_terms bndr.attrs ss;\n sort = subst_term bndr.sort ss\n }\n\nand subst_comp (c:comp) (ss:subst)\n : Tot comp (decreases c)\n = match inspect_comp c with\n | C_Total t ->\n pack_comp (C_Total (subst_term t ss))\n\n | C_GTotal t ->\n pack_comp (C_GTotal (subst_term t ss))\n\n | C_Lemma pre post pats ->\n pack_comp (C_Lemma (subst_term pre ss)\n (subst_term post ss)\n (subst_term pats ss))\n\n | C_Eff us eff_name res args decrs ->\n pack_comp (C_Eff us eff_name\n (subst_term res ss)\n (subst_args args ss)\n (subst_terms decrs ss))\n\nand subst_terms (ts:list term) (ss:subst)\n : Tot (ts':list term{Nil? ts ==> Nil? ts'}) // property useful for subst_binder\n (decreases ts)\n = match ts with\n | [] -> []\n | t::ts -> subst_term t ss :: subst_terms ts ss\n\nand subst_args (ts:list argv) (ss:subst)\n : Tot (list argv) (decreases ts)\n = match ts with\n | [] -> []\n | (t,q)::ts -> (subst_term t ss,q) :: subst_args ts ss\n\nand subst_patterns (ps:list (pattern & bool)) (ss:subst) \n : Tot (list (pattern & bool))\n (decreases ps)\n = match ps with\n | [] -> ps\n | (p, b)::ps ->\n let n = binder_offset_pattern p in\n let p = subst_pattern p ss in\n let ps = subst_patterns ps (shift_subst_n n ss) in\n (p,b)::ps\n\nand subst_pattern (p:pattern) (ss:subst) \n : Tot pattern\n (decreases p)\n = match p with\n | Pat_Constant _ -> p\n\n | Pat_Cons fv us pats -> \n let pats = subst_patterns pats ss in\n Pat_Cons fv us pats\n\n | Pat_Var bv s ->\n Pat_Var bv s\n\n | Pat_Dot_Term topt ->\n Pat_Dot_Term (match topt with\n | None -> None\n | Some t -> Some (subst_term t ss))\n\n \nand subst_branch (br:branch) (ss:subst)\n : Tot branch (decreases br)\n = let p, t = br in\n let p = subst_pattern p ss in\n let j = binder_offset_pattern p in\n let t = subst_term t (shift_subst_n j ss) in\n p, t\n \nand subst_branches (brs:list branch) (ss:subst)\n : Tot (list branch) (decreases brs)\n = match brs with\n | [] -> []\n | br::brs -> subst_branch br ss :: subst_branches brs ss\n \nand subst_match_returns (m:match_returns_ascription) (ss:subst)\n : Tot match_returns_ascription (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = subst_binder b ss in\n let ret =\n match ret with\n | Inl t -> Inl (subst_term t (shift_subst ss))\n | Inr c -> Inr (subst_comp c (shift_subst ss))\n in\n let as_ =\n match as_ with\n | None -> None\n | Some t -> Some (subst_term t (shift_subst ss))\n in\n b, (ret, as_, eq)", "val subst_pattern (p: pattern) (ss: subst) : Tot pattern (decreases p)\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> t\n | Tv_Var x -> subst_var x ss\n | Tv_BVar j -> subst_db j ss\n | Tv_App hd argv ->\n pack_ln (Tv_App (subst_term hd ss)\n (subst_term (fst argv) ss, snd argv))\n\n | Tv_Abs b body -> \n let b' = subst_binder b ss in\n pack_ln (Tv_Abs b' (subst_term body (shift_subst ss)))\n\n | Tv_Arrow b c ->\n let b' = subst_binder b ss in\n pack_ln (Tv_Arrow b' (subst_comp c (shift_subst ss))) \n\n | Tv_Refine b f ->\n let b = subst_binder b ss in\n pack_ln (Tv_Refine b (subst_term f (shift_subst ss)))\n\n | Tv_Uvar j c ->\n pack_ln (Tv_Uvar j (subst_ctx_uvar_and_subst c ss))\n \n | Tv_Let recf attrs b def body ->\n let b = subst_binder b ss in\n pack_ln (Tv_Let recf \n (subst_terms attrs ss)\n b\n (if recf \n then subst_term def (shift_subst ss)\n else subst_term def ss)\n (subst_term body (shift_subst ss)))\n\n | Tv_Match scr ret brs ->\n pack_ln (Tv_Match (subst_term scr ss)\n (match ret with\n | None -> None\n | Some m -> Some (subst_match_returns m ss))\n (subst_branches brs ss))\n \n | Tv_AscribedT e t tac b ->\n pack_ln (Tv_AscribedT (subst_term e ss)\n (subst_term t ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\n | Tv_AscribedC e c tac b ->\n pack_ln (Tv_AscribedC (subst_term e ss)\n (subst_comp c ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\nand subst_binder (b:binder) (ss:subst)\n : Tot (b':binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\n = let bndr = inspect_binder b in\n pack_binder {\n ppname = bndr.ppname;\n qual = bndr.qual;\n attrs = subst_terms bndr.attrs ss;\n sort = subst_term bndr.sort ss\n }\n\nand subst_comp (c:comp) (ss:subst)\n : Tot comp (decreases c)\n = match inspect_comp c with\n | C_Total t ->\n pack_comp (C_Total (subst_term t ss))\n\n | C_GTotal t ->\n pack_comp (C_GTotal (subst_term t ss))\n\n | C_Lemma pre post pats ->\n pack_comp (C_Lemma (subst_term pre ss)\n (subst_term post ss)\n (subst_term pats ss))\n\n | C_Eff us eff_name res args decrs ->\n pack_comp (C_Eff us eff_name\n (subst_term res ss)\n (subst_args args ss)\n (subst_terms decrs ss))\n\nand subst_terms (ts:list term) (ss:subst)\n : Tot (ts':list term{Nil? ts ==> Nil? ts'}) // property useful for subst_binder\n (decreases ts)\n = match ts with\n | [] -> []\n | t::ts -> subst_term t ss :: subst_terms ts ss\n\nand subst_args (ts:list argv) (ss:subst)\n : Tot (list argv) (decreases ts)\n = match ts with\n | [] -> []\n | (t,q)::ts -> (subst_term t ss,q) :: subst_args ts ss\n\nand subst_patterns (ps:list (pattern & bool)) (ss:subst) \n : Tot (list (pattern & bool))\n (decreases ps)\n = match ps with\n | [] -> ps\n | (p, b)::ps ->\n let n = binder_offset_pattern p in\n let p = subst_pattern p ss in\n let ps = subst_patterns ps (shift_subst_n n ss) in\n (p,b)::ps\n\nand subst_pattern (p:pattern) (ss:subst) \n : Tot pattern\n (decreases p)\n = match p with\n | Pat_Constant _ -> p\n\n | Pat_Cons fv us pats -> \n let pats = subst_patterns pats ss in\n Pat_Cons fv us pats\n\n | Pat_Var bv s ->\n Pat_Var bv s\n\n | Pat_Dot_Term topt ->\n Pat_Dot_Term (match topt with\n | None -> None\n | Some t -> Some (subst_term t ss))\n\n \nand subst_branch (br:branch) (ss:subst)\n : Tot branch (decreases br)\n = let p, t = br in\n let p = subst_pattern p ss in\n let j = binder_offset_pattern p in\n let t = subst_term t (shift_subst_n j ss) in\n p, t\n \nand subst_branches (brs:list branch) (ss:subst)\n : Tot (list branch) (decreases brs)\n = match brs with\n | [] -> []\n | br::brs -> subst_branch br ss :: subst_branches brs ss\n \nand subst_match_returns (m:match_returns_ascription) (ss:subst)\n : Tot match_returns_ascription (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = subst_binder b ss in\n let ret =\n match ret with\n | Inl t -> Inl (subst_term t (shift_subst ss))\n | Inr c -> Inr (subst_comp c (shift_subst ss))\n in\n let as_ =\n match as_ with\n | None -> None\n | Some t -> Some (subst_term t (shift_subst ss))\n in\n b, (ret, as_, eq)", "val subst_term (t: term) (ss: subst) : Tot term (decreases t)\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> t\n | Tv_Var x -> subst_var x ss\n | Tv_BVar j -> subst_db j ss\n | Tv_App hd argv ->\n pack_ln (Tv_App (subst_term hd ss)\n (subst_term (fst argv) ss, snd argv))\n\n | Tv_Abs b body -> \n let b' = subst_binder b ss in\n pack_ln (Tv_Abs b' (subst_term body (shift_subst ss)))\n\n | Tv_Arrow b c ->\n let b' = subst_binder b ss in\n pack_ln (Tv_Arrow b' (subst_comp c (shift_subst ss))) \n\n | Tv_Refine b f ->\n let b = subst_binder b ss in\n pack_ln (Tv_Refine b (subst_term f (shift_subst ss)))\n\n | Tv_Uvar j c ->\n pack_ln (Tv_Uvar j (subst_ctx_uvar_and_subst c ss))\n \n | Tv_Let recf attrs b def body ->\n let b = subst_binder b ss in\n pack_ln (Tv_Let recf \n (subst_terms attrs ss)\n b\n (if recf \n then subst_term def (shift_subst ss)\n else subst_term def ss)\n (subst_term body (shift_subst ss)))\n\n | Tv_Match scr ret brs ->\n pack_ln (Tv_Match (subst_term scr ss)\n (match ret with\n | None -> None\n | Some m -> Some (subst_match_returns m ss))\n (subst_branches brs ss))\n \n | Tv_AscribedT e t tac b ->\n pack_ln (Tv_AscribedT (subst_term e ss)\n (subst_term t ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\n | Tv_AscribedC e c tac b ->\n pack_ln (Tv_AscribedC (subst_term e ss)\n (subst_comp c ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\nand subst_binder (b:binder) (ss:subst)\n : Tot (b':binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\n = let bndr = inspect_binder b in\n pack_binder {\n ppname = bndr.ppname;\n qual = bndr.qual;\n attrs = subst_terms bndr.attrs ss;\n sort = subst_term bndr.sort ss\n }\n\nand subst_comp (c:comp) (ss:subst)\n : Tot comp (decreases c)\n = match inspect_comp c with\n | C_Total t ->\n pack_comp (C_Total (subst_term t ss))\n\n | C_GTotal t ->\n pack_comp (C_GTotal (subst_term t ss))\n\n | C_Lemma pre post pats ->\n pack_comp (C_Lemma (subst_term pre ss)\n (subst_term post ss)\n (subst_term pats ss))\n\n | C_Eff us eff_name res args decrs ->\n pack_comp (C_Eff us eff_name\n (subst_term res ss)\n (subst_args args ss)\n (subst_terms decrs ss))\n\nand subst_terms (ts:list term) (ss:subst)\n : Tot (ts':list term{Nil? ts ==> Nil? ts'}) // property useful for subst_binder\n (decreases ts)\n = match ts with\n | [] -> []\n | t::ts -> subst_term t ss :: subst_terms ts ss\n\nand subst_args (ts:list argv) (ss:subst)\n : Tot (list argv) (decreases ts)\n = match ts with\n | [] -> []\n | (t,q)::ts -> (subst_term t ss,q) :: subst_args ts ss\n\nand subst_patterns (ps:list (pattern & bool)) (ss:subst) \n : Tot (list (pattern & bool))\n (decreases ps)\n = match ps with\n | [] -> ps\n | (p, b)::ps ->\n let n = binder_offset_pattern p in\n let p = subst_pattern p ss in\n let ps = subst_patterns ps (shift_subst_n n ss) in\n (p,b)::ps\n\nand subst_pattern (p:pattern) (ss:subst) \n : Tot pattern\n (decreases p)\n = match p with\n | Pat_Constant _ -> p\n\n | Pat_Cons fv us pats -> \n let pats = subst_patterns pats ss in\n Pat_Cons fv us pats\n\n | Pat_Var bv s ->\n Pat_Var bv s\n\n | Pat_Dot_Term topt ->\n Pat_Dot_Term (match topt with\n | None -> None\n | Some t -> Some (subst_term t ss))\n\n \nand subst_branch (br:branch) (ss:subst)\n : Tot branch (decreases br)\n = let p, t = br in\n let p = subst_pattern p ss in\n let j = binder_offset_pattern p in\n let t = subst_term t (shift_subst_n j ss) in\n p, t\n \nand subst_branches (brs:list branch) (ss:subst)\n : Tot (list branch) (decreases brs)\n = match brs with\n | [] -> []\n | br::brs -> subst_branch br ss :: subst_branches brs ss\n \nand subst_match_returns (m:match_returns_ascription) (ss:subst)\n : Tot match_returns_ascription (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = subst_binder b ss in\n let ret =\n match ret with\n | Inl t -> Inl (subst_term t (shift_subst ss))\n | Inr c -> Inr (subst_comp c (shift_subst ss))\n in\n let as_ =\n match as_ with\n | None -> None\n | Some t -> Some (subst_term t (shift_subst ss))\n in\n b, (ret, as_, eq)", "val subst_binder (b: binder) (ss: subst)\n : Tot (b': binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> t\n | Tv_Var x -> subst_var x ss\n | Tv_BVar j -> subst_db j ss\n | Tv_App hd argv ->\n pack_ln (Tv_App (subst_term hd ss)\n (subst_term (fst argv) ss, snd argv))\n\n | Tv_Abs b body -> \n let b' = subst_binder b ss in\n pack_ln (Tv_Abs b' (subst_term body (shift_subst ss)))\n\n | Tv_Arrow b c ->\n let b' = subst_binder b ss in\n pack_ln (Tv_Arrow b' (subst_comp c (shift_subst ss))) \n\n | Tv_Refine b f ->\n let b = subst_binder b ss in\n pack_ln (Tv_Refine b (subst_term f (shift_subst ss)))\n\n | Tv_Uvar j c ->\n pack_ln (Tv_Uvar j (subst_ctx_uvar_and_subst c ss))\n \n | Tv_Let recf attrs b def body ->\n let b = subst_binder b ss in\n pack_ln (Tv_Let recf \n (subst_terms attrs ss)\n b\n (if recf \n then subst_term def (shift_subst ss)\n else subst_term def ss)\n (subst_term body (shift_subst ss)))\n\n | Tv_Match scr ret brs ->\n pack_ln (Tv_Match (subst_term scr ss)\n (match ret with\n | None -> None\n | Some m -> Some (subst_match_returns m ss))\n (subst_branches brs ss))\n \n | Tv_AscribedT e t tac b ->\n pack_ln (Tv_AscribedT (subst_term e ss)\n (subst_term t ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\n | Tv_AscribedC e c tac b ->\n pack_ln (Tv_AscribedC (subst_term e ss)\n (subst_comp c ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\nand subst_binder (b:binder) (ss:subst)\n : Tot (b':binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\n = let bndr = inspect_binder b in\n pack_binder {\n ppname = bndr.ppname;\n qual = bndr.qual;\n attrs = subst_terms bndr.attrs ss;\n sort = subst_term bndr.sort ss\n }\n\nand subst_comp (c:comp) (ss:subst)\n : Tot comp (decreases c)\n = match inspect_comp c with\n | C_Total t ->\n pack_comp (C_Total (subst_term t ss))\n\n | C_GTotal t ->\n pack_comp (C_GTotal (subst_term t ss))\n\n | C_Lemma pre post pats ->\n pack_comp (C_Lemma (subst_term pre ss)\n (subst_term post ss)\n (subst_term pats ss))\n\n | C_Eff us eff_name res args decrs ->\n pack_comp (C_Eff us eff_name\n (subst_term res ss)\n (subst_args args ss)\n (subst_terms decrs ss))\n\nand subst_terms (ts:list term) (ss:subst)\n : Tot (ts':list term{Nil? ts ==> Nil? ts'}) // property useful for subst_binder\n (decreases ts)\n = match ts with\n | [] -> []\n | t::ts -> subst_term t ss :: subst_terms ts ss\n\nand subst_args (ts:list argv) (ss:subst)\n : Tot (list argv) (decreases ts)\n = match ts with\n | [] -> []\n | (t,q)::ts -> (subst_term t ss,q) :: subst_args ts ss\n\nand subst_patterns (ps:list (pattern & bool)) (ss:subst) \n : Tot (list (pattern & bool))\n (decreases ps)\n = match ps with\n | [] -> ps\n | (p, b)::ps ->\n let n = binder_offset_pattern p in\n let p = subst_pattern p ss in\n let ps = subst_patterns ps (shift_subst_n n ss) in\n (p,b)::ps\n\nand subst_pattern (p:pattern) (ss:subst) \n : Tot pattern\n (decreases p)\n = match p with\n | Pat_Constant _ -> p\n\n | Pat_Cons fv us pats -> \n let pats = subst_patterns pats ss in\n Pat_Cons fv us pats\n\n | Pat_Var bv s ->\n Pat_Var bv s\n\n | Pat_Dot_Term topt ->\n Pat_Dot_Term (match topt with\n | None -> None\n | Some t -> Some (subst_term t ss))\n\n \nand subst_branch (br:branch) (ss:subst)\n : Tot branch (decreases br)\n = let p, t = br in\n let p = subst_pattern p ss in\n let j = binder_offset_pattern p in\n let t = subst_term t (shift_subst_n j ss) in\n p, t\n \nand subst_branches (brs:list branch) (ss:subst)\n : Tot (list branch) (decreases brs)\n = match brs with\n | [] -> []\n | br::brs -> subst_branch br ss :: subst_branches brs ss\n \nand subst_match_returns (m:match_returns_ascription) (ss:subst)\n : Tot match_returns_ascription (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = subst_binder b ss in\n let ret =\n match ret with\n | Inl t -> Inl (subst_term t (shift_subst ss))\n | Inr c -> Inr (subst_comp c (shift_subst ss))\n in\n let as_ =\n match as_ with\n | None -> None\n | Some t -> Some (subst_term t (shift_subst ss))\n in\n b, (ret, as_, eq)", "val subst_comp (c: comp) (ss: subst) : Tot comp (decreases c)\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> t\n | Tv_Var x -> subst_var x ss\n | Tv_BVar j -> subst_db j ss\n | Tv_App hd argv ->\n pack_ln (Tv_App (subst_term hd ss)\n (subst_term (fst argv) ss, snd argv))\n\n | Tv_Abs b body -> \n let b' = subst_binder b ss in\n pack_ln (Tv_Abs b' (subst_term body (shift_subst ss)))\n\n | Tv_Arrow b c ->\n let b' = subst_binder b ss in\n pack_ln (Tv_Arrow b' (subst_comp c (shift_subst ss))) \n\n | Tv_Refine b f ->\n let b = subst_binder b ss in\n pack_ln (Tv_Refine b (subst_term f (shift_subst ss)))\n\n | Tv_Uvar j c ->\n pack_ln (Tv_Uvar j (subst_ctx_uvar_and_subst c ss))\n \n | Tv_Let recf attrs b def body ->\n let b = subst_binder b ss in\n pack_ln (Tv_Let recf \n (subst_terms attrs ss)\n b\n (if recf \n then subst_term def (shift_subst ss)\n else subst_term def ss)\n (subst_term body (shift_subst ss)))\n\n | Tv_Match scr ret brs ->\n pack_ln (Tv_Match (subst_term scr ss)\n (match ret with\n | None -> None\n | Some m -> Some (subst_match_returns m ss))\n (subst_branches brs ss))\n \n | Tv_AscribedT e t tac b ->\n pack_ln (Tv_AscribedT (subst_term e ss)\n (subst_term t ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\n | Tv_AscribedC e c tac b ->\n pack_ln (Tv_AscribedC (subst_term e ss)\n (subst_comp c ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\nand subst_binder (b:binder) (ss:subst)\n : Tot (b':binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\n = let bndr = inspect_binder b in\n pack_binder {\n ppname = bndr.ppname;\n qual = bndr.qual;\n attrs = subst_terms bndr.attrs ss;\n sort = subst_term bndr.sort ss\n }\n\nand subst_comp (c:comp) (ss:subst)\n : Tot comp (decreases c)\n = match inspect_comp c with\n | C_Total t ->\n pack_comp (C_Total (subst_term t ss))\n\n | C_GTotal t ->\n pack_comp (C_GTotal (subst_term t ss))\n\n | C_Lemma pre post pats ->\n pack_comp (C_Lemma (subst_term pre ss)\n (subst_term post ss)\n (subst_term pats ss))\n\n | C_Eff us eff_name res args decrs ->\n pack_comp (C_Eff us eff_name\n (subst_term res ss)\n (subst_args args ss)\n (subst_terms decrs ss))\n\nand subst_terms (ts:list term) (ss:subst)\n : Tot (ts':list term{Nil? ts ==> Nil? ts'}) // property useful for subst_binder\n (decreases ts)\n = match ts with\n | [] -> []\n | t::ts -> subst_term t ss :: subst_terms ts ss\n\nand subst_args (ts:list argv) (ss:subst)\n : Tot (list argv) (decreases ts)\n = match ts with\n | [] -> []\n | (t,q)::ts -> (subst_term t ss,q) :: subst_args ts ss\n\nand subst_patterns (ps:list (pattern & bool)) (ss:subst) \n : Tot (list (pattern & bool))\n (decreases ps)\n = match ps with\n | [] -> ps\n | (p, b)::ps ->\n let n = binder_offset_pattern p in\n let p = subst_pattern p ss in\n let ps = subst_patterns ps (shift_subst_n n ss) in\n (p,b)::ps\n\nand subst_pattern (p:pattern) (ss:subst) \n : Tot pattern\n (decreases p)\n = match p with\n | Pat_Constant _ -> p\n\n | Pat_Cons fv us pats -> \n let pats = subst_patterns pats ss in\n Pat_Cons fv us pats\n\n | Pat_Var bv s ->\n Pat_Var bv s\n\n | Pat_Dot_Term topt ->\n Pat_Dot_Term (match topt with\n | None -> None\n | Some t -> Some (subst_term t ss))\n\n \nand subst_branch (br:branch) (ss:subst)\n : Tot branch (decreases br)\n = let p, t = br in\n let p = subst_pattern p ss in\n let j = binder_offset_pattern p in\n let t = subst_term t (shift_subst_n j ss) in\n p, t\n \nand subst_branches (brs:list branch) (ss:subst)\n : Tot (list branch) (decreases brs)\n = match brs with\n | [] -> []\n | br::brs -> subst_branch br ss :: subst_branches brs ss\n \nand subst_match_returns (m:match_returns_ascription) (ss:subst)\n : Tot match_returns_ascription (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = subst_binder b ss in\n let ret =\n match ret with\n | Inl t -> Inl (subst_term t (shift_subst ss))\n | Inr c -> Inr (subst_comp c (shift_subst ss))\n in\n let as_ =\n match as_ with\n | None -> None\n | Some t -> Some (subst_term t (shift_subst ss))\n in\n b, (ret, as_, eq)", "val subst_patterns (ps: list (pattern & bool)) (ss: subst)\n : Tot (list (pattern & bool)) (decreases ps)\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> t\n | Tv_Var x -> subst_var x ss\n | Tv_BVar j -> subst_db j ss\n | Tv_App hd argv ->\n pack_ln (Tv_App (subst_term hd ss)\n (subst_term (fst argv) ss, snd argv))\n\n | Tv_Abs b body -> \n let b' = subst_binder b ss in\n pack_ln (Tv_Abs b' (subst_term body (shift_subst ss)))\n\n | Tv_Arrow b c ->\n let b' = subst_binder b ss in\n pack_ln (Tv_Arrow b' (subst_comp c (shift_subst ss))) \n\n | Tv_Refine b f ->\n let b = subst_binder b ss in\n pack_ln (Tv_Refine b (subst_term f (shift_subst ss)))\n\n | Tv_Uvar j c ->\n pack_ln (Tv_Uvar j (subst_ctx_uvar_and_subst c ss))\n \n | Tv_Let recf attrs b def body ->\n let b = subst_binder b ss in\n pack_ln (Tv_Let recf \n (subst_terms attrs ss)\n b\n (if recf \n then subst_term def (shift_subst ss)\n else subst_term def ss)\n (subst_term body (shift_subst ss)))\n\n | Tv_Match scr ret brs ->\n pack_ln (Tv_Match (subst_term scr ss)\n (match ret with\n | None -> None\n | Some m -> Some (subst_match_returns m ss))\n (subst_branches brs ss))\n \n | Tv_AscribedT e t tac b ->\n pack_ln (Tv_AscribedT (subst_term e ss)\n (subst_term t ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\n | Tv_AscribedC e c tac b ->\n pack_ln (Tv_AscribedC (subst_term e ss)\n (subst_comp c ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\nand subst_binder (b:binder) (ss:subst)\n : Tot (b':binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\n = let bndr = inspect_binder b in\n pack_binder {\n ppname = bndr.ppname;\n qual = bndr.qual;\n attrs = subst_terms bndr.attrs ss;\n sort = subst_term bndr.sort ss\n }\n\nand subst_comp (c:comp) (ss:subst)\n : Tot comp (decreases c)\n = match inspect_comp c with\n | C_Total t ->\n pack_comp (C_Total (subst_term t ss))\n\n | C_GTotal t ->\n pack_comp (C_GTotal (subst_term t ss))\n\n | C_Lemma pre post pats ->\n pack_comp (C_Lemma (subst_term pre ss)\n (subst_term post ss)\n (subst_term pats ss))\n\n | C_Eff us eff_name res args decrs ->\n pack_comp (C_Eff us eff_name\n (subst_term res ss)\n (subst_args args ss)\n (subst_terms decrs ss))\n\nand subst_terms (ts:list term) (ss:subst)\n : Tot (ts':list term{Nil? ts ==> Nil? ts'}) // property useful for subst_binder\n (decreases ts)\n = match ts with\n | [] -> []\n | t::ts -> subst_term t ss :: subst_terms ts ss\n\nand subst_args (ts:list argv) (ss:subst)\n : Tot (list argv) (decreases ts)\n = match ts with\n | [] -> []\n | (t,q)::ts -> (subst_term t ss,q) :: subst_args ts ss\n\nand subst_patterns (ps:list (pattern & bool)) (ss:subst) \n : Tot (list (pattern & bool))\n (decreases ps)\n = match ps with\n | [] -> ps\n | (p, b)::ps ->\n let n = binder_offset_pattern p in\n let p = subst_pattern p ss in\n let ps = subst_patterns ps (shift_subst_n n ss) in\n (p,b)::ps\n\nand subst_pattern (p:pattern) (ss:subst) \n : Tot pattern\n (decreases p)\n = match p with\n | Pat_Constant _ -> p\n\n | Pat_Cons fv us pats -> \n let pats = subst_patterns pats ss in\n Pat_Cons fv us pats\n\n | Pat_Var bv s ->\n Pat_Var bv s\n\n | Pat_Dot_Term topt ->\n Pat_Dot_Term (match topt with\n | None -> None\n | Some t -> Some (subst_term t ss))\n\n \nand subst_branch (br:branch) (ss:subst)\n : Tot branch (decreases br)\n = let p, t = br in\n let p = subst_pattern p ss in\n let j = binder_offset_pattern p in\n let t = subst_term t (shift_subst_n j ss) in\n p, t\n \nand subst_branches (brs:list branch) (ss:subst)\n : Tot (list branch) (decreases brs)\n = match brs with\n | [] -> []\n | br::brs -> subst_branch br ss :: subst_branches brs ss\n \nand subst_match_returns (m:match_returns_ascription) (ss:subst)\n : Tot match_returns_ascription (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = subst_binder b ss in\n let ret =\n match ret with\n | Inl t -> Inl (subst_term t (shift_subst ss))\n | Inr c -> Inr (subst_comp c (shift_subst ss))\n in\n let as_ =\n match as_ with\n | None -> None\n | Some t -> Some (subst_term t (shift_subst ss))\n in\n b, (ret, as_, eq)", "val subst_terms (ts: list term) (ss: subst)\n : Tot (ts': list term {Nil? ts ==> Nil? ts'}) (decreases ts)\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> t\n | Tv_Var x -> subst_var x ss\n | Tv_BVar j -> subst_db j ss\n | Tv_App hd argv ->\n pack_ln (Tv_App (subst_term hd ss)\n (subst_term (fst argv) ss, snd argv))\n\n | Tv_Abs b body -> \n let b' = subst_binder b ss in\n pack_ln (Tv_Abs b' (subst_term body (shift_subst ss)))\n\n | Tv_Arrow b c ->\n let b' = subst_binder b ss in\n pack_ln (Tv_Arrow b' (subst_comp c (shift_subst ss))) \n\n | Tv_Refine b f ->\n let b = subst_binder b ss in\n pack_ln (Tv_Refine b (subst_term f (shift_subst ss)))\n\n | Tv_Uvar j c ->\n pack_ln (Tv_Uvar j (subst_ctx_uvar_and_subst c ss))\n \n | Tv_Let recf attrs b def body ->\n let b = subst_binder b ss in\n pack_ln (Tv_Let recf \n (subst_terms attrs ss)\n b\n (if recf \n then subst_term def (shift_subst ss)\n else subst_term def ss)\n (subst_term body (shift_subst ss)))\n\n | Tv_Match scr ret brs ->\n pack_ln (Tv_Match (subst_term scr ss)\n (match ret with\n | None -> None\n | Some m -> Some (subst_match_returns m ss))\n (subst_branches brs ss))\n \n | Tv_AscribedT e t tac b ->\n pack_ln (Tv_AscribedT (subst_term e ss)\n (subst_term t ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\n | Tv_AscribedC e c tac b ->\n pack_ln (Tv_AscribedC (subst_term e ss)\n (subst_comp c ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\nand subst_binder (b:binder) (ss:subst)\n : Tot (b':binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\n = let bndr = inspect_binder b in\n pack_binder {\n ppname = bndr.ppname;\n qual = bndr.qual;\n attrs = subst_terms bndr.attrs ss;\n sort = subst_term bndr.sort ss\n }\n\nand subst_comp (c:comp) (ss:subst)\n : Tot comp (decreases c)\n = match inspect_comp c with\n | C_Total t ->\n pack_comp (C_Total (subst_term t ss))\n\n | C_GTotal t ->\n pack_comp (C_GTotal (subst_term t ss))\n\n | C_Lemma pre post pats ->\n pack_comp (C_Lemma (subst_term pre ss)\n (subst_term post ss)\n (subst_term pats ss))\n\n | C_Eff us eff_name res args decrs ->\n pack_comp (C_Eff us eff_name\n (subst_term res ss)\n (subst_args args ss)\n (subst_terms decrs ss))\n\nand subst_terms (ts:list term) (ss:subst)\n : Tot (ts':list term{Nil? ts ==> Nil? ts'}) // property useful for subst_binder\n (decreases ts)\n = match ts with\n | [] -> []\n | t::ts -> subst_term t ss :: subst_terms ts ss\n\nand subst_args (ts:list argv) (ss:subst)\n : Tot (list argv) (decreases ts)\n = match ts with\n | [] -> []\n | (t,q)::ts -> (subst_term t ss,q) :: subst_args ts ss\n\nand subst_patterns (ps:list (pattern & bool)) (ss:subst) \n : Tot (list (pattern & bool))\n (decreases ps)\n = match ps with\n | [] -> ps\n | (p, b)::ps ->\n let n = binder_offset_pattern p in\n let p = subst_pattern p ss in\n let ps = subst_patterns ps (shift_subst_n n ss) in\n (p,b)::ps\n\nand subst_pattern (p:pattern) (ss:subst) \n : Tot pattern\n (decreases p)\n = match p with\n | Pat_Constant _ -> p\n\n | Pat_Cons fv us pats -> \n let pats = subst_patterns pats ss in\n Pat_Cons fv us pats\n\n | Pat_Var bv s ->\n Pat_Var bv s\n\n | Pat_Dot_Term topt ->\n Pat_Dot_Term (match topt with\n | None -> None\n | Some t -> Some (subst_term t ss))\n\n \nand subst_branch (br:branch) (ss:subst)\n : Tot branch (decreases br)\n = let p, t = br in\n let p = subst_pattern p ss in\n let j = binder_offset_pattern p in\n let t = subst_term t (shift_subst_n j ss) in\n p, t\n \nand subst_branches (brs:list branch) (ss:subst)\n : Tot (list branch) (decreases brs)\n = match brs with\n | [] -> []\n | br::brs -> subst_branch br ss :: subst_branches brs ss\n \nand subst_match_returns (m:match_returns_ascription) (ss:subst)\n : Tot match_returns_ascription (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = subst_binder b ss in\n let ret =\n match ret with\n | Inl t -> Inl (subst_term t (shift_subst ss))\n | Inr c -> Inr (subst_comp c (shift_subst ss))\n in\n let as_ =\n match as_ with\n | None -> None\n | Some t -> Some (subst_term t (shift_subst ss))\n in\n b, (ret, as_, eq)", "val subst_args (ts: list argv) (ss: subst) : Tot (list argv) (decreases ts)\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> t\n | Tv_Var x -> subst_var x ss\n | Tv_BVar j -> subst_db j ss\n | Tv_App hd argv ->\n pack_ln (Tv_App (subst_term hd ss)\n (subst_term (fst argv) ss, snd argv))\n\n | Tv_Abs b body -> \n let b' = subst_binder b ss in\n pack_ln (Tv_Abs b' (subst_term body (shift_subst ss)))\n\n | Tv_Arrow b c ->\n let b' = subst_binder b ss in\n pack_ln (Tv_Arrow b' (subst_comp c (shift_subst ss))) \n\n | Tv_Refine b f ->\n let b = subst_binder b ss in\n pack_ln (Tv_Refine b (subst_term f (shift_subst ss)))\n\n | Tv_Uvar j c ->\n pack_ln (Tv_Uvar j (subst_ctx_uvar_and_subst c ss))\n \n | Tv_Let recf attrs b def body ->\n let b = subst_binder b ss in\n pack_ln (Tv_Let recf \n (subst_terms attrs ss)\n b\n (if recf \n then subst_term def (shift_subst ss)\n else subst_term def ss)\n (subst_term body (shift_subst ss)))\n\n | Tv_Match scr ret brs ->\n pack_ln (Tv_Match (subst_term scr ss)\n (match ret with\n | None -> None\n | Some m -> Some (subst_match_returns m ss))\n (subst_branches brs ss))\n \n | Tv_AscribedT e t tac b ->\n pack_ln (Tv_AscribedT (subst_term e ss)\n (subst_term t ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\n | Tv_AscribedC e c tac b ->\n pack_ln (Tv_AscribedC (subst_term e ss)\n (subst_comp c ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\nand subst_binder (b:binder) (ss:subst)\n : Tot (b':binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\n = let bndr = inspect_binder b in\n pack_binder {\n ppname = bndr.ppname;\n qual = bndr.qual;\n attrs = subst_terms bndr.attrs ss;\n sort = subst_term bndr.sort ss\n }\n\nand subst_comp (c:comp) (ss:subst)\n : Tot comp (decreases c)\n = match inspect_comp c with\n | C_Total t ->\n pack_comp (C_Total (subst_term t ss))\n\n | C_GTotal t ->\n pack_comp (C_GTotal (subst_term t ss))\n\n | C_Lemma pre post pats ->\n pack_comp (C_Lemma (subst_term pre ss)\n (subst_term post ss)\n (subst_term pats ss))\n\n | C_Eff us eff_name res args decrs ->\n pack_comp (C_Eff us eff_name\n (subst_term res ss)\n (subst_args args ss)\n (subst_terms decrs ss))\n\nand subst_terms (ts:list term) (ss:subst)\n : Tot (ts':list term{Nil? ts ==> Nil? ts'}) // property useful for subst_binder\n (decreases ts)\n = match ts with\n | [] -> []\n | t::ts -> subst_term t ss :: subst_terms ts ss\n\nand subst_args (ts:list argv) (ss:subst)\n : Tot (list argv) (decreases ts)\n = match ts with\n | [] -> []\n | (t,q)::ts -> (subst_term t ss,q) :: subst_args ts ss\n\nand subst_patterns (ps:list (pattern & bool)) (ss:subst) \n : Tot (list (pattern & bool))\n (decreases ps)\n = match ps with\n | [] -> ps\n | (p, b)::ps ->\n let n = binder_offset_pattern p in\n let p = subst_pattern p ss in\n let ps = subst_patterns ps (shift_subst_n n ss) in\n (p,b)::ps\n\nand subst_pattern (p:pattern) (ss:subst) \n : Tot pattern\n (decreases p)\n = match p with\n | Pat_Constant _ -> p\n\n | Pat_Cons fv us pats -> \n let pats = subst_patterns pats ss in\n Pat_Cons fv us pats\n\n | Pat_Var bv s ->\n Pat_Var bv s\n\n | Pat_Dot_Term topt ->\n Pat_Dot_Term (match topt with\n | None -> None\n | Some t -> Some (subst_term t ss))\n\n \nand subst_branch (br:branch) (ss:subst)\n : Tot branch (decreases br)\n = let p, t = br in\n let p = subst_pattern p ss in\n let j = binder_offset_pattern p in\n let t = subst_term t (shift_subst_n j ss) in\n p, t\n \nand subst_branches (brs:list branch) (ss:subst)\n : Tot (list branch) (decreases brs)\n = match brs with\n | [] -> []\n | br::brs -> subst_branch br ss :: subst_branches brs ss\n \nand subst_match_returns (m:match_returns_ascription) (ss:subst)\n : Tot match_returns_ascription (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = subst_binder b ss in\n let ret =\n match ret with\n | Inl t -> Inl (subst_term t (shift_subst ss))\n | Inr c -> Inr (subst_comp c (shift_subst ss))\n in\n let as_ =\n match as_ with\n | None -> None\n | Some t -> Some (subst_term t (shift_subst ss))\n in\n b, (ret, as_, eq)", "val subst_match_returns (m: match_returns_ascription) (ss: subst)\n : Tot match_returns_ascription (decreases m)\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = match inspect_ln t with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unsupp\n | Tv_Unknown -> t\n | Tv_Var x -> subst_var x ss\n | Tv_BVar j -> subst_db j ss\n | Tv_App hd argv ->\n pack_ln (Tv_App (subst_term hd ss)\n (subst_term (fst argv) ss, snd argv))\n\n | Tv_Abs b body -> \n let b' = subst_binder b ss in\n pack_ln (Tv_Abs b' (subst_term body (shift_subst ss)))\n\n | Tv_Arrow b c ->\n let b' = subst_binder b ss in\n pack_ln (Tv_Arrow b' (subst_comp c (shift_subst ss))) \n\n | Tv_Refine b f ->\n let b = subst_binder b ss in\n pack_ln (Tv_Refine b (subst_term f (shift_subst ss)))\n\n | Tv_Uvar j c ->\n pack_ln (Tv_Uvar j (subst_ctx_uvar_and_subst c ss))\n \n | Tv_Let recf attrs b def body ->\n let b = subst_binder b ss in\n pack_ln (Tv_Let recf \n (subst_terms attrs ss)\n b\n (if recf \n then subst_term def (shift_subst ss)\n else subst_term def ss)\n (subst_term body (shift_subst ss)))\n\n | Tv_Match scr ret brs ->\n pack_ln (Tv_Match (subst_term scr ss)\n (match ret with\n | None -> None\n | Some m -> Some (subst_match_returns m ss))\n (subst_branches brs ss))\n \n | Tv_AscribedT e t tac b ->\n pack_ln (Tv_AscribedT (subst_term e ss)\n (subst_term t ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\n | Tv_AscribedC e c tac b ->\n pack_ln (Tv_AscribedC (subst_term e ss)\n (subst_comp c ss)\n (match tac with\n | None -> None\n | Some tac -> Some (subst_term tac ss))\n b)\n\nand subst_binder (b:binder) (ss:subst)\n : Tot (b':binder{binder_is_simple b ==> binder_is_simple b'}) (decreases b)\n = let bndr = inspect_binder b in\n pack_binder {\n ppname = bndr.ppname;\n qual = bndr.qual;\n attrs = subst_terms bndr.attrs ss;\n sort = subst_term bndr.sort ss\n }\n\nand subst_comp (c:comp) (ss:subst)\n : Tot comp (decreases c)\n = match inspect_comp c with\n | C_Total t ->\n pack_comp (C_Total (subst_term t ss))\n\n | C_GTotal t ->\n pack_comp (C_GTotal (subst_term t ss))\n\n | C_Lemma pre post pats ->\n pack_comp (C_Lemma (subst_term pre ss)\n (subst_term post ss)\n (subst_term pats ss))\n\n | C_Eff us eff_name res args decrs ->\n pack_comp (C_Eff us eff_name\n (subst_term res ss)\n (subst_args args ss)\n (subst_terms decrs ss))\n\nand subst_terms (ts:list term) (ss:subst)\n : Tot (ts':list term{Nil? ts ==> Nil? ts'}) // property useful for subst_binder\n (decreases ts)\n = match ts with\n | [] -> []\n | t::ts -> subst_term t ss :: subst_terms ts ss\n\nand subst_args (ts:list argv) (ss:subst)\n : Tot (list argv) (decreases ts)\n = match ts with\n | [] -> []\n | (t,q)::ts -> (subst_term t ss,q) :: subst_args ts ss\n\nand subst_patterns (ps:list (pattern & bool)) (ss:subst) \n : Tot (list (pattern & bool))\n (decreases ps)\n = match ps with\n | [] -> ps\n | (p, b)::ps ->\n let n = binder_offset_pattern p in\n let p = subst_pattern p ss in\n let ps = subst_patterns ps (shift_subst_n n ss) in\n (p,b)::ps\n\nand subst_pattern (p:pattern) (ss:subst) \n : Tot pattern\n (decreases p)\n = match p with\n | Pat_Constant _ -> p\n\n | Pat_Cons fv us pats -> \n let pats = subst_patterns pats ss in\n Pat_Cons fv us pats\n\n | Pat_Var bv s ->\n Pat_Var bv s\n\n | Pat_Dot_Term topt ->\n Pat_Dot_Term (match topt with\n | None -> None\n | Some t -> Some (subst_term t ss))\n\n \nand subst_branch (br:branch) (ss:subst)\n : Tot branch (decreases br)\n = let p, t = br in\n let p = subst_pattern p ss in\n let j = binder_offset_pattern p in\n let t = subst_term t (shift_subst_n j ss) in\n p, t\n \nand subst_branches (brs:list branch) (ss:subst)\n : Tot (list branch) (decreases brs)\n = match brs with\n | [] -> []\n | br::brs -> subst_branch br ss :: subst_branches brs ss\n \nand subst_match_returns (m:match_returns_ascription) (ss:subst)\n : Tot match_returns_ascription (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = subst_binder b ss in\n let ret =\n match ret with\n | Inl t -> Inl (subst_term t (shift_subst ss))\n | Inr c -> Inr (subst_comp c (shift_subst ss))\n in\n let as_ =\n match as_ with\n | None -> None\n | Some t -> Some (subst_term t (shift_subst ss))\n in\n b, (ret, as_, eq)", "val subst_term : subst -> term -> Tot term\nlet rec subst_term s t = match t with\n | V x -> if x = fst s then snd s else V x\n | F t1 t2 -> F (subst_term s t1) (subst_term s t2)", "val elab_br\n (#g: env)\n (#c: comp_st)\n (#sc_u: universe)\n (#sc_ty: typ)\n (#sc: term)\n (#p: pattern)\n (#e: st_term)\n (d: br_typing g sc_u sc_ty sc p e c)\n : Tot R.branch (decreases d)\nlet rec elab_st_typing (#g:env)\n (#t:st_term)\n (#c:comp)\n (d:st_typing g t c)\n : Tot R.term (decreases d)\n = match d with\n // | T_Tot _ t _ _ -> elab_term t\n\n | T_Abs _ x qual b _u body _c ty_typing body_typing ->\n let ty = elab_term b.binder_ty in\n let ppname = b.binder_ppname.name in\n let body = elab_st_typing body_typing in\n mk_abs_with_name ppname ty (elab_qual qual) (RT.close_term body x) //this closure should be provably redundant by strengthening the conditions on x\n\n\n | T_STApp _ head _ qual _ arg _ _\n | T_STGhostApp _ head _ qual _ arg _ _ _ _ ->\n let head = elab_term head in\n let arg = elab_term arg in\n R.mk_app head [(arg, elab_qual qual)]\n\n | T_Return _ c use_eq u ty t post _ _ _ _ ->\n let ru = u in\n let rty = elab_term ty in\n let rt = elab_term t in\n let rp = elab_term post in\n let rp = mk_abs rty R.Q_Explicit rp in\n (match c, use_eq with\n | STT, true -> mk_stt_return ru rty rt rp\n | STT, false -> mk_stt_return_noeq ru rty rt rp\n | STT_Atomic, true -> mk_stt_atomic_return ru rty rt rp\n | STT_Atomic, false -> mk_stt_atomic_return_noeq ru rty rt rp\n | STT_Ghost, true -> mk_stt_ghost_return ru rty rt rp\n | STT_Ghost, false -> mk_stt_ghost_return_noeq ru rty rt rp)\n\n | T_Bind _ e1 e2 c1 c2 b x c e1_typing t_typing e2_typing bc ->\n let e1 = elab_st_typing e1_typing in\n let e2 = elab_st_typing e2_typing in\n let ty1 = elab_term (comp_res c1) in\n elab_bind bc e1 (mk_abs_with_name b.binder_ppname.name ty1 R.Q_Explicit (RT.close_term e2 x))\n\n | T_BindFn _ _ _ c1 c2 b x e1_typing _u t_typing e2_typing c2_typing ->\n let e1 = elab_st_typing e1_typing in\n let e2 = elab_st_typing e2_typing in\n let ty1 = elab_term (comp_res c1) in\n RT.mk_let RT.pp_name_default e1 ty1 (RT.close_term e2 x)\n \n | T_Frame _ _ c frame _frame_typing e_typing ->\n let e = elab_st_typing e_typing in\n elab_frame c frame e\n \n | T_Equiv _ _ c1 c2 e_typing (ST_TotEquiv _ _ _ _ _ _) ->\n let e = elab_st_typing e_typing in\n e\n\n | T_Equiv _ _ c1 c2 e_typing _ ->\n let e = elab_st_typing e_typing in\n elab_sub c1 c2 e\n\n | T_Sub _ _ c1 c2 e_typing d_sub ->\n let e = elab_st_typing e_typing in\n let (| coercion, _ |) = elab_st_sub d_sub in\n R.mk_e_app coercion [e]\n\n | T_Lift _ _ c1 c2 e_typing lc ->\n let e = elab_st_typing e_typing in\n elab_lift lc e\n\n | T_If _ b _ _ _ _ _ e1_typing e2_typing _c_typing ->\n let rb = elab_term b in\n let re1 = elab_st_typing e1_typing in\n let re2 = elab_st_typing e2_typing in\n RT.mk_if rb re1 re2\n\n | T_Match _ _ _ sc _ _ _ _ _ brty _ ->\n let sc = elab_term sc in\n let brs = elab_branches brty in\n R.pack_ln (R.Tv_Match sc None brs)\n\n | T_IntroPure _ p _ _ ->\n let head = \n tm_pureapp (tm_fvar (as_fv (mk_pulse_lib_core_lid \"intro_pure\")))\n None\n p\n in\n let arg = (`()) in\n R.mk_app (elab_term head) [(arg, elab_qual None)]\n\n | T_ElimExists _ u t p _ d_t d_exists ->\n let ru = u in\n let rt = elab_term t in\n let rp = elab_term p in\n mk_elim_exists ru rt (mk_abs rt R.Q_Explicit rp)\n\n | T_IntroExists _ u b p e _ _ _ ->\n let ru = u in\n let rt = elab_term b.binder_ty in\n let rp = elab_term p in\n let re = elab_term e in\n mk_intro_exists ru rt (mk_abs rt R.Q_Explicit rp) re\n\n | T_While _ inv _ _ _ cond_typing body_typing ->\n let inv = elab_term inv in\n let cond = elab_st_typing cond_typing in\n let body = elab_st_typing body_typing in\n mk_while (mk_abs bool_tm R.Q_Explicit inv) cond body\n\n | T_Par _ eL cL eR cR _ _ _ eL_typing eR_typing ->\n let ru = comp_u cL in\n let raL = elab_term (comp_res cL) in\n let raR = elab_term (comp_res cR) in\n let rpreL = elab_term (comp_pre cL) in\n let rpostL = elab_term (comp_post cL) in\n let rpreR = elab_term (comp_pre cR) in\n let rpostR = elab_term (comp_post cR) in\n let reL = elab_st_typing eL_typing in\n let reR = elab_st_typing eR_typing in\n mk_par ru\n raL\n raR\n rpreL\n (mk_abs raL R.Q_Explicit rpostL)\n rpreR\n (mk_abs raR R.Q_Explicit rpostR)\n reL reR\n\n\t\t\t\t| T_Rewrite _ p q _ _ ->\n\t\t\t\t let rp = elab_term p in\n\t\t\t\t\t\tlet rq = elab_term q in\n\t\t\t\t\t\tmk_rewrite rp rq\n\n | T_WithLocal _ _ init _ init_t c x _ _ _ body_typing ->\n let rret_u = comp_u c in\n let ra = elab_term init_t in\n let rinit = elab_term init in\n let rret_t = elab_term (comp_res c) in\n let rpre = elab_term (comp_pre c) in\n let rpost = mk_abs rret_t R.Q_Explicit (elab_term (comp_post c)) in\n let rbody = elab_st_typing body_typing in\n let rbody = RT.close_term rbody x in\n let rbody = mk_abs (mk_ref ra) R.Q_Explicit rbody in\n mk_withlocal rret_u ra rinit rpre rret_t rpost rbody\n\n | T_WithLocalArray _ _ init len _ init_t c x _ _ _ _ body_typing ->\n let rret_u = comp_u c in\n let ra = elab_term init_t in\n let rinit = elab_term init in\n let rlen = elab_term len in\n let rret_t = elab_term (comp_res c) in\n let rpre = elab_term (comp_pre c) in\n let rpost = mk_abs rret_t R.Q_Explicit (elab_term (comp_post c)) in\n let rbody = elab_st_typing body_typing in\n let rbody = RT.close_term rbody x in\n let rbody = mk_abs (mk_array ra) R.Q_Explicit rbody in\n mk_withlocalarray rret_u ra rinit rlen rpre rret_t rpost rbody\n\n | T_Admit _ {u;res;pre;post} c _ ->\n let ru = u in\n let rres = elab_term res in\n let rpre = elab_term pre in\n let rpost = elab_term post in\n let rpost = mk_abs rres R.Q_Explicit rpost in\n (match c with\n | STT -> mk_stt_admit ru rres rpre rpost\n | STT_Atomic -> mk_stt_atomic_admit ru rres rpre rpost\n | STT_Ghost -> mk_stt_ghost_admit ru rres rpre rpost)\n\n | T_Unreachable _ _ _ _ _ ->\n `(\"IOU: elab_st_typing of T_Unreachable\")\n\n | T_WithInv _ _ _ _ _ _ _ _ _ ->\n `(\"IOU: elab_st_typing of T_WithInv\")\n\nand elab_br (#g:env)\n (#c:comp_st)\n (#sc_u:universe) (#sc_ty:typ) (#sc:term)\n (#p:pattern)\n (#e:st_term)\n (d : br_typing g sc_u sc_ty sc p e c)\n : Tot R.branch (decreases d)\n = let TBR _ _ _ _ _ _ _ _ bs _ _ _ ed = d in\n let e = elab_st_typing ed in\n (elab_pat p, e)\nand elab_branches (#g:env)\n (#c:comp_st)\n (#sc_u:universe) (#sc_ty:typ) (#sc:term)\n (#brs:list branch)\n (d : brs_typing g sc_u sc_ty sc brs c)\n : Tot (list R.branch)\n (decreases d)\n = match d with\n | TBRS_0 _ -> []\n | TBRS_1 _ p e bd _ d' ->\n elab_br bd :: elab_branches d'", "val elab_branches\n (#g: env)\n (#c: comp_st)\n (#sc_u: universe)\n (#sc_ty: typ)\n (#sc: term)\n (#brs: list branch)\n (d: brs_typing g sc_u sc_ty sc brs c)\n : Tot (list R.branch) (decreases d)\nlet rec elab_st_typing (#g:env)\n (#t:st_term)\n (#c:comp)\n (d:st_typing g t c)\n : Tot R.term (decreases d)\n = match d with\n // | T_Tot _ t _ _ -> elab_term t\n\n | T_Abs _ x qual b _u body _c ty_typing body_typing ->\n let ty = elab_term b.binder_ty in\n let ppname = b.binder_ppname.name in\n let body = elab_st_typing body_typing in\n mk_abs_with_name ppname ty (elab_qual qual) (RT.close_term body x) //this closure should be provably redundant by strengthening the conditions on x\n\n\n | T_STApp _ head _ qual _ arg _ _\n | T_STGhostApp _ head _ qual _ arg _ _ _ _ ->\n let head = elab_term head in\n let arg = elab_term arg in\n R.mk_app head [(arg, elab_qual qual)]\n\n | T_Return _ c use_eq u ty t post _ _ _ _ ->\n let ru = u in\n let rty = elab_term ty in\n let rt = elab_term t in\n let rp = elab_term post in\n let rp = mk_abs rty R.Q_Explicit rp in\n (match c, use_eq with\n | STT, true -> mk_stt_return ru rty rt rp\n | STT, false -> mk_stt_return_noeq ru rty rt rp\n | STT_Atomic, true -> mk_stt_atomic_return ru rty rt rp\n | STT_Atomic, false -> mk_stt_atomic_return_noeq ru rty rt rp\n | STT_Ghost, true -> mk_stt_ghost_return ru rty rt rp\n | STT_Ghost, false -> mk_stt_ghost_return_noeq ru rty rt rp)\n\n | T_Bind _ e1 e2 c1 c2 b x c e1_typing t_typing e2_typing bc ->\n let e1 = elab_st_typing e1_typing in\n let e2 = elab_st_typing e2_typing in\n let ty1 = elab_term (comp_res c1) in\n elab_bind bc e1 (mk_abs_with_name b.binder_ppname.name ty1 R.Q_Explicit (RT.close_term e2 x))\n\n | T_BindFn _ _ _ c1 c2 b x e1_typing _u t_typing e2_typing c2_typing ->\n let e1 = elab_st_typing e1_typing in\n let e2 = elab_st_typing e2_typing in\n let ty1 = elab_term (comp_res c1) in\n RT.mk_let RT.pp_name_default e1 ty1 (RT.close_term e2 x)\n \n | T_Frame _ _ c frame _frame_typing e_typing ->\n let e = elab_st_typing e_typing in\n elab_frame c frame e\n \n | T_Equiv _ _ c1 c2 e_typing (ST_TotEquiv _ _ _ _ _ _) ->\n let e = elab_st_typing e_typing in\n e\n\n | T_Equiv _ _ c1 c2 e_typing _ ->\n let e = elab_st_typing e_typing in\n elab_sub c1 c2 e\n\n | T_Sub _ _ c1 c2 e_typing d_sub ->\n let e = elab_st_typing e_typing in\n let (| coercion, _ |) = elab_st_sub d_sub in\n R.mk_e_app coercion [e]\n\n | T_Lift _ _ c1 c2 e_typing lc ->\n let e = elab_st_typing e_typing in\n elab_lift lc e\n\n | T_If _ b _ _ _ _ _ e1_typing e2_typing _c_typing ->\n let rb = elab_term b in\n let re1 = elab_st_typing e1_typing in\n let re2 = elab_st_typing e2_typing in\n RT.mk_if rb re1 re2\n\n | T_Match _ _ _ sc _ _ _ _ _ brty _ ->\n let sc = elab_term sc in\n let brs = elab_branches brty in\n R.pack_ln (R.Tv_Match sc None brs)\n\n | T_IntroPure _ p _ _ ->\n let head = \n tm_pureapp (tm_fvar (as_fv (mk_pulse_lib_core_lid \"intro_pure\")))\n None\n p\n in\n let arg = (`()) in\n R.mk_app (elab_term head) [(arg, elab_qual None)]\n\n | T_ElimExists _ u t p _ d_t d_exists ->\n let ru = u in\n let rt = elab_term t in\n let rp = elab_term p in\n mk_elim_exists ru rt (mk_abs rt R.Q_Explicit rp)\n\n | T_IntroExists _ u b p e _ _ _ ->\n let ru = u in\n let rt = elab_term b.binder_ty in\n let rp = elab_term p in\n let re = elab_term e in\n mk_intro_exists ru rt (mk_abs rt R.Q_Explicit rp) re\n\n | T_While _ inv _ _ _ cond_typing body_typing ->\n let inv = elab_term inv in\n let cond = elab_st_typing cond_typing in\n let body = elab_st_typing body_typing in\n mk_while (mk_abs bool_tm R.Q_Explicit inv) cond body\n\n | T_Par _ eL cL eR cR _ _ _ eL_typing eR_typing ->\n let ru = comp_u cL in\n let raL = elab_term (comp_res cL) in\n let raR = elab_term (comp_res cR) in\n let rpreL = elab_term (comp_pre cL) in\n let rpostL = elab_term (comp_post cL) in\n let rpreR = elab_term (comp_pre cR) in\n let rpostR = elab_term (comp_post cR) in\n let reL = elab_st_typing eL_typing in\n let reR = elab_st_typing eR_typing in\n mk_par ru\n raL\n raR\n rpreL\n (mk_abs raL R.Q_Explicit rpostL)\n rpreR\n (mk_abs raR R.Q_Explicit rpostR)\n reL reR\n\n\t\t\t\t| T_Rewrite _ p q _ _ ->\n\t\t\t\t let rp = elab_term p in\n\t\t\t\t\t\tlet rq = elab_term q in\n\t\t\t\t\t\tmk_rewrite rp rq\n\n | T_WithLocal _ _ init _ init_t c x _ _ _ body_typing ->\n let rret_u = comp_u c in\n let ra = elab_term init_t in\n let rinit = elab_term init in\n let rret_t = elab_term (comp_res c) in\n let rpre = elab_term (comp_pre c) in\n let rpost = mk_abs rret_t R.Q_Explicit (elab_term (comp_post c)) in\n let rbody = elab_st_typing body_typing in\n let rbody = RT.close_term rbody x in\n let rbody = mk_abs (mk_ref ra) R.Q_Explicit rbody in\n mk_withlocal rret_u ra rinit rpre rret_t rpost rbody\n\n | T_WithLocalArray _ _ init len _ init_t c x _ _ _ _ body_typing ->\n let rret_u = comp_u c in\n let ra = elab_term init_t in\n let rinit = elab_term init in\n let rlen = elab_term len in\n let rret_t = elab_term (comp_res c) in\n let rpre = elab_term (comp_pre c) in\n let rpost = mk_abs rret_t R.Q_Explicit (elab_term (comp_post c)) in\n let rbody = elab_st_typing body_typing in\n let rbody = RT.close_term rbody x in\n let rbody = mk_abs (mk_array ra) R.Q_Explicit rbody in\n mk_withlocalarray rret_u ra rinit rlen rpre rret_t rpost rbody\n\n | T_Admit _ {u;res;pre;post} c _ ->\n let ru = u in\n let rres = elab_term res in\n let rpre = elab_term pre in\n let rpost = elab_term post in\n let rpost = mk_abs rres R.Q_Explicit rpost in\n (match c with\n | STT -> mk_stt_admit ru rres rpre rpost\n | STT_Atomic -> mk_stt_atomic_admit ru rres rpre rpost\n | STT_Ghost -> mk_stt_ghost_admit ru rres rpre rpost)\n\n | T_Unreachable _ _ _ _ _ ->\n `(\"IOU: elab_st_typing of T_Unreachable\")\n\n | T_WithInv _ _ _ _ _ _ _ _ _ ->\n `(\"IOU: elab_st_typing of T_WithInv\")\n\nand elab_br (#g:env)\n (#c:comp_st)\n (#sc_u:universe) (#sc_ty:typ) (#sc:term)\n (#p:pattern)\n (#e:st_term)\n (d : br_typing g sc_u sc_ty sc p e c)\n : Tot R.branch (decreases d)\n = let TBR _ _ _ _ _ _ _ _ bs _ _ _ ed = d in\n let e = elab_st_typing ed in\n (elab_pat p, e)\nand elab_branches (#g:env)\n (#c:comp_st)\n (#sc_u:universe) (#sc_ty:typ) (#sc:term)\n (#brs:list branch)\n (d : brs_typing g sc_u sc_ty sc brs c)\n : Tot (list R.branch)\n (decreases d)\n = match d with\n | TBRS_0 _ -> []\n | TBRS_1 _ p e bd _ d' ->\n elab_br bd :: elab_branches d'", "val subst_beta : x:var -> v:exp -> e:exp -> Tot exp (decreases e)\nlet rec subst_beta x v e =\n match e with\n | EVar y -> if y = x then v\n else if y < x then EVar y\n else EVar (y-1)\n | EAbs t e1 -> EAbs t (subst_beta (x+1) v e1)\n | EApp e1 e2 -> EApp (subst_beta x v e1) (subst_beta x v e2)", "val subst_of_tred_tred: #s:typ -> #s':typ -> #t:typ -> #t':typ -> x:nat ->\n hs:(tred s s') -> ht:(tred t t') ->\n Tot (tred (tsubst_beta_gen x s t) (tsubst_beta_gen x s' t'))\n (decreases ht)\nlet rec subst_of_tred_tred #s #s' #t #t' x hs ht =\n match ht with\n | TrRefl t1 -> subst_of_tred x t1 hs\n | TrArr ht1 ht2 ->\n TrArr (subst_of_tred_tred x hs ht1) (subst_of_tred_tred x hs ht2)\n | TrLam #t1 #t2 k ht1 ->\n tsubst_gen_tlam x s k t1;\n tsubst_gen_tlam x s' k t2;\n TrLam k (subst_of_tred_tred (x + 1) (tred_shiftup_above 0 hs) ht1)\n | TrApp h1 h2 ->\n TrApp (subst_of_tred_tred x hs h1) (subst_of_tred_tred x hs h2)\n | TrBeta #t1 #t2 #t1' #t2' k ht1 ht2 ->\n tsubst_gen_tlam x s k t1;\n let ht1' = subst_of_tred_tred (x + 1) (tred_shiftup_above 0 hs) ht1 in\n let ht2' = subst_of_tred_tred x hs ht2 in\n tsubst_commute t1' 0 t2' x s';\n TrBeta k ht1' ht2'", "val subst_of_tred: #s:typ -> #s':typ -> x:nat -> t:typ ->\n h:(tred s s') ->\n Tot (tred (tsubst_beta_gen x s t) (tsubst_beta_gen x s' t))\n (decreases t)\nlet rec subst_of_tred #s #s' x t h =\n match t with\n | TVar y -> if y < x then TrRefl t\n else if y = x then h\n else TrRefl (TVar (y - 1))\n | TLam k t1 ->\n tsubst_gen_tlam x s k t1; tsubst_gen_tlam x s' k t1;\n TrLam k (subst_of_tred (x + 1) t1 (tred_shiftup_above 0 h))\n | TApp t1 t2 ->\n TrApp (subst_of_tred x t1 h) (subst_of_tred x t2 h)\n | TArr t1 t2 ->\n TrArr (subst_of_tred x t1 h) (subst_of_tred x t2 h)", "val _split_subst_at_bv (#a #b: Type) (x: bv) (subst: list ((bv & a) & b))\n : Tot (list ((bv & a) & b) & list ((bv & a) & b)) (decreases subst)\nlet rec _split_subst_at_bv (#a #b : Type) (x : bv) (subst : list ((bv & a) & b)) :\n Tot (list ((bv & a) & b) & list ((bv & a) & b))\n (decreases subst) =\n match subst with\n | [] -> [], []\n | ((src, ty), tgt) :: subst' ->\n if bv_eq x src then\n [], subst'\n else \n let s1, s2 = _split_subst_at_bv x subst' in\n ((src, ty), tgt) :: s1, s2", "val subst_below : x:var -> v:exp{below x v} -> s:sub{sub_below x s} ->\n Lemma (requires True) (ensures (v = subst s v)) (decreases v)\nlet rec subst_below x v s =\n match v with\n | EVar y -> ()\n | EApp e1 e2 -> subst_below x e1 s; subst_below x e2 s\n | ELam t e -> (subst_below (x+1) e (sub_elam s);\n assert(e = subst (sub_elam s) e);\n assert(v = ELam t e);\n assert(subst s v = ELam t (subst (sub_elam s) e)))\n | EUnit -> ()", "val subst_db (bv: bv) (s: subst) : term\nlet subst_db (bv:bv) (s:subst) : term =\n match find_matching_subst_elt_bv s bv with\n | Some (DT _ t) ->\n (match maybe_uniq_of_term t with\n | None -> t\n | Some k ->\n //if we're substituting a name j for a name k, retain the pp_name of j\n let v : namedv = pack_namedv {\n sort = (inspect_bv bv).sort;\n ppname = (inspect_bv bv).ppname;\n uniq = k;\n } in\n pack_ln (Tv_Var v))\n | _ -> pack_ln (Tv_BVar bv)", "val freevars_branch (br: branch) : Tot (Set.set var) (decreases br)\nlet rec freevars (e:term)\n : FStar.Set.set var\n = match inspect_ln e with\n | Tv_Uvar _ _ -> Set.complement Set.empty\n \n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unknown \n | Tv_Unsupp\n | Tv_BVar _ -> Set.empty\n\n | Tv_Var x -> Set.singleton (namedv_uniq x)\n \n | Tv_App e1 (e2, _) ->\n Set.union (freevars e1) (freevars e2)\n\n | Tv_Abs b body -> \n Set.union (freevars_binder b) (freevars body)\n\n | Tv_Arrow b c ->\n Set.union (freevars_binder b) (freevars_comp c)\n\n | Tv_Refine b f ->\n freevars (binder_sort b) `Set.union`\n freevars f\n \n | Tv_Let recf attrs b def body ->\n freevars_terms attrs `Set.union`\n freevars (binder_sort b) `Set.union`\n freevars def `Set.union`\n freevars body\n\n | Tv_Match scr ret brs ->\n freevars scr `Set.union`\n freevars_opt ret freevars_match_returns `Set.union`\n freevars_branches brs\n\n | Tv_AscribedT e t tac b ->\n freevars e `Set.union`\n freevars t `Set.union`\n freevars_opt tac freevars\n \n | Tv_AscribedC e c tac b ->\n freevars e `Set.union`\n freevars_comp c `Set.union`\n freevars_opt tac freevars\n\nand freevars_opt (#a:Type0) (o:option a) (f: (x:a { x << o } -> FStar.Set.set var))\n : FStar.Set.set var\n = match o with\n | None -> Set.empty\n | Some x -> f x\n\nand freevars_comp (c:comp)\n : FStar.Set.set var\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t ->\n freevars t\n\n | C_Lemma pre post pats ->\n freevars pre `Set.union`\n freevars post `Set.union`\n freevars pats\n\n | C_Eff us eff_name res args decrs ->\n freevars res `Set.union`\n freevars_args args `Set.union`\n freevars_terms decrs\n\nand freevars_args (ts:list argv)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | (t,q)::ts ->\n freevars t `Set.union`\n freevars_args ts\n\nand freevars_terms (ts:list term)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | t::ts ->\n freevars t `Set.union`\n freevars_terms ts\n \nand freevars_binder (b:binder)\n : Tot (Set.set var) (decreases b)\n = let bndr = inspect_binder b in\n freevars bndr.sort `Set.union`\n freevars_terms bndr.attrs \n\nand freevars_pattern (p:pattern) \n : Tot (Set.set var) (decreases p)\n = match p with\n | Pat_Constant _ ->\n Set.empty\n\n | Pat_Cons head univs subpats ->\n freevars_patterns subpats\n \n | Pat_Var bv s -> Set.empty\n\n | Pat_Dot_Term topt ->\n freevars_opt topt freevars\n\nand freevars_patterns (ps:list (pattern & bool))\n : Tot (Set.set var) (decreases ps)\n = match ps with\n | [] -> Set.empty\n | (p, b)::ps ->\n freevars_pattern p `Set.union`\n freevars_patterns ps\n\nand freevars_branch (br:branch)\n : Tot (Set.set var) (decreases br)\n = let p, t = br in\n freevars_pattern p `Set.union`\n freevars t\n\nand freevars_branches (brs:list branch)\n : Tot (Set.set var) (decreases brs)\n = match brs with\n | [] -> Set.empty\n | hd::tl -> freevars_branch hd `Set.union` freevars_branches tl\n \nand freevars_match_returns (m:match_returns_ascription)\n : Tot (Set.set var) (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = freevars_binder b in\n let ret =\n match ret with\n | Inl t -> freevars t\n | Inr c -> freevars_comp c\n in\n let as_ = freevars_opt as_ freevars in\n b `Set.union` ret `Set.union` as_", "val nt_subst_st_term (t: st_term) (ss: nt_substs) : st_term\nlet nt_subst_st_term (t:st_term) (ss:nt_substs) : st_term =\n L.fold_left (fun t elt -> subst_st_term t [elt]) t ss", "val subst : e:exp -> s:sub -> Pure exp (requires True)\n (ensures (fun e' -> renaming s /\\ EVar? e ==> EVar? e'))\n (decreases %[is_var e; is_renaming s; 1; e])\nlet rec subst e s =\n match e with\n | EVar x -> s x\n\n | EAbs t e1 ->\n EAbs t (subst e1 (subst_eabs s))\n\n | EApp e1 e2 -> EApp (subst e1 s) (subst e2 s)\n\nand subst_eabs s y =\n if y = 0 then EVar y\n else subst (s (y-1)) sub_inc", "val subst_closed : v:exp{closed v} -> s:sub ->\n Lemma (requires True) (ensures (v = subst s v)) (decreases v)\nlet rec subst_closed v s = subst_below 0 v s", "val eq_branch (b1 b2: pattern & st_term) : b: bool{b <==> (b1 == b2)}\nlet rec eq_st_term (t1 t2:st_term) \n : b:bool { b <==> (t1 == t2) }\n = match t1.term, t2.term with\n | Tm_Return {expected_type=ty1; insert_eq=b1; term=t1}, \n Tm_Return {expected_type=ty2; insert_eq=b2; term=t2} ->\n eq_tm ty1 ty2 &&\n b1 = b2 &&\n eq_tm t1 t2\n\n | Tm_Abs { b=b1; q=o1; ascription=c1; body=t1 },\n Tm_Abs { b=b2; q=o2; ascription=c2; body=t2 } ->\n eq_tm b1.binder_ty b2.binder_ty &&\n o1=o2 &&\n eq_ascription c1 c2 &&\n eq_st_term t1 t2\n \n | Tm_STApp { head=h1; arg_qual=o1; arg=t1},\n Tm_STApp { head=h2; arg_qual=o2; arg=t2} ->\n eq_tm h1 h2 &&\n o1=o2 &&\n eq_tm t1 t2\n\n | Tm_Bind { binder=b1; head=t1; body=k1 },\n Tm_Bind { binder=b2; head=t2; body=k2 } ->\n eq_tm b1.binder_ty b2.binder_ty &&\n eq_st_term t1 t2 &&\n eq_st_term k1 k2\n\n | Tm_TotBind { binder=b1; head=t1; body=k1 },\n Tm_TotBind { binder=b2; head=t2; body=k2 } ->\n eq_tm b1.binder_ty b2.binder_ty &&\n eq_tm t1 t2 &&\n eq_st_term k1 k2\n \n | Tm_IntroPure { p=p1 }, Tm_IntroPure { p=p2 } ->\n eq_tm p1 p2\n\n | Tm_IntroExists { p=p1; witnesses=l1 },\n Tm_IntroExists { p=p2; witnesses=l2 } ->\n eq_tm p1 p2 &&\n eq_tm_list l1 l2\n\n | Tm_ElimExists {p=p1},\n Tm_ElimExists {p=p2} ->\n eq_tm p1 p2\n\n | Tm_If { b=g1; then_=ethen1; else_=eelse1; post=p1},\n Tm_If { b=g2; then_=ethen2; else_=eelse2; post=p2} ->\n eq_tm g1 g2 &&\n eq_st_term ethen1 ethen2 &&\n eq_st_term eelse1 eelse2 &&\n eq_tm_opt p1 p2\n \n | Tm_Match {sc=sc1; returns_=r1; brs=br1},\n Tm_Match {sc=sc2; returns_=r2; brs=br2} ->\n eq_tm sc1 sc2 &&\n eq_tm_opt r1 r2 &&\n eq_list_dec t1 t2 eq_branch br1 br2\n\n | Tm_While { invariant=inv1; condition=cond1; body=body1 },\n Tm_While { invariant=inv2; condition=cond2; body=body2 } ->\n eq_tm inv1 inv2 &&\n eq_st_term cond1 cond2 &&\n eq_st_term body1 body2\n\n | Tm_Par {pre1=preL1; body1=eL1; post1=postL1; pre2=preR1; body2=eR1; post2=postR1 },\n Tm_Par {pre1=preL2; body1=eL2; post1=postL2; pre2=preR2; body2=eR2; post2=postR2 } ->\n eq_tm preL1 preL2 &&\n eq_st_term eL1 eL2 &&\n eq_tm postL1 postL2 &&\n eq_tm preR1 preR2 &&\n eq_st_term eR1 eR2 &&\n eq_tm postR1 postR2\n\n | Tm_WithLocal { binder=x1; initializer=e1; body=b1 },\n Tm_WithLocal { binder=x2; initializer=e2; body=b2 } ->\n eq_tm x1.binder_ty x2.binder_ty &&\n eq_tm e1 e2 &&\n eq_st_term b1 b2\n\n | Tm_WithLocalArray { binder=x1; initializer=e1; length=n1; body=b1 },\n Tm_WithLocalArray { binder=x2; initializer=e2; length=n2; body=b2 } ->\n eq_tm x1.binder_ty x2.binder_ty &&\n eq_tm e1 e2 &&\n eq_tm n1 n2 &&\n eq_st_term b1 b2\n\n | Tm_Rewrite { t1=l1; t2=r1 },\n Tm_Rewrite { t1=l2; t2=r2 } ->\n eq_tm l1 l2 &&\n eq_tm r1 r2\n\n | Tm_Admit { ctag=c1; u=u1; typ=t1; post=post1 }, \n Tm_Admit { ctag=c2; u=u2; typ=t2; post=post2 } ->\n c1 = c2 &&\n eq_univ u1 u2 &&\n eq_tm t1 t2 &&\n eq_tm_opt post1 post2\n \n | Tm_Unreachable, Tm_Unreachable -> true\n \n | Tm_ProofHintWithBinders { hint_type=ht1; binders=bs1; t=t1 },\n Tm_ProofHintWithBinders { hint_type=ht2; binders=bs2; t=t2 } ->\n eq_hint_type ht1 ht2 &&\n eq_list eq_binder bs1 bs2 &&\n eq_st_term t1 t2\n\n | Tm_WithInv {name=name1; returns_inv=r1; body=body1},\n Tm_WithInv {name=name2; returns_inv=r2; body=body2} ->\n eq_tm name1 name2 &&\n eq_opt (fun (b1, r1) (b2, r2) -> eq_tm b1.binder_ty b2.binder_ty && eq_tm r1 r2)\n r1 r2 &&\n eq_st_term body1 body2\n\n | _ -> false\n\nand eq_branch (b1 b2 : pattern & st_term)\n : b:bool{b <==> (b1 == b2)}\n = let (p1, e1) = b1 in\n let (p2, e2) = b2 in\n eq_pattern p1 p2 && eq_st_term e1 e2", "val freevars_branches (brs: list branch) : Tot (Set.set var) (decreases brs)\nlet rec freevars (e:term)\n : FStar.Set.set var\n = match inspect_ln e with\n | Tv_Uvar _ _ -> Set.complement Set.empty\n \n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unknown \n | Tv_Unsupp\n | Tv_BVar _ -> Set.empty\n\n | Tv_Var x -> Set.singleton (namedv_uniq x)\n \n | Tv_App e1 (e2, _) ->\n Set.union (freevars e1) (freevars e2)\n\n | Tv_Abs b body -> \n Set.union (freevars_binder b) (freevars body)\n\n | Tv_Arrow b c ->\n Set.union (freevars_binder b) (freevars_comp c)\n\n | Tv_Refine b f ->\n freevars (binder_sort b) `Set.union`\n freevars f\n \n | Tv_Let recf attrs b def body ->\n freevars_terms attrs `Set.union`\n freevars (binder_sort b) `Set.union`\n freevars def `Set.union`\n freevars body\n\n | Tv_Match scr ret brs ->\n freevars scr `Set.union`\n freevars_opt ret freevars_match_returns `Set.union`\n freevars_branches brs\n\n | Tv_AscribedT e t tac b ->\n freevars e `Set.union`\n freevars t `Set.union`\n freevars_opt tac freevars\n \n | Tv_AscribedC e c tac b ->\n freevars e `Set.union`\n freevars_comp c `Set.union`\n freevars_opt tac freevars\n\nand freevars_opt (#a:Type0) (o:option a) (f: (x:a { x << o } -> FStar.Set.set var))\n : FStar.Set.set var\n = match o with\n | None -> Set.empty\n | Some x -> f x\n\nand freevars_comp (c:comp)\n : FStar.Set.set var\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t ->\n freevars t\n\n | C_Lemma pre post pats ->\n freevars pre `Set.union`\n freevars post `Set.union`\n freevars pats\n\n | C_Eff us eff_name res args decrs ->\n freevars res `Set.union`\n freevars_args args `Set.union`\n freevars_terms decrs\n\nand freevars_args (ts:list argv)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | (t,q)::ts ->\n freevars t `Set.union`\n freevars_args ts\n\nand freevars_terms (ts:list term)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | t::ts ->\n freevars t `Set.union`\n freevars_terms ts\n \nand freevars_binder (b:binder)\n : Tot (Set.set var) (decreases b)\n = let bndr = inspect_binder b in\n freevars bndr.sort `Set.union`\n freevars_terms bndr.attrs \n\nand freevars_pattern (p:pattern) \n : Tot (Set.set var) (decreases p)\n = match p with\n | Pat_Constant _ ->\n Set.empty\n\n | Pat_Cons head univs subpats ->\n freevars_patterns subpats\n \n | Pat_Var bv s -> Set.empty\n\n | Pat_Dot_Term topt ->\n freevars_opt topt freevars\n\nand freevars_patterns (ps:list (pattern & bool))\n : Tot (Set.set var) (decreases ps)\n = match ps with\n | [] -> Set.empty\n | (p, b)::ps ->\n freevars_pattern p `Set.union`\n freevars_patterns ps\n\nand freevars_branch (br:branch)\n : Tot (Set.set var) (decreases br)\n = let p, t = br in\n freevars_pattern p `Set.union`\n freevars t\n\nand freevars_branches (brs:list branch)\n : Tot (Set.set var) (decreases brs)\n = match brs with\n | [] -> Set.empty\n | hd::tl -> freevars_branch hd `Set.union` freevars_branches tl\n \nand freevars_match_returns (m:match_returns_ascription)\n : Tot (Set.set var) (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = freevars_binder b in\n let ret =\n match ret with\n | Inl t -> freevars t\n | Inr c -> freevars_comp c\n in\n let as_ = freevars_opt as_ freevars in\n b `Set.union` ret `Set.union` as_", "val ln'_branch (br: branch) (i: int) : Tot bool (decreases br)\nlet rec ln' (e:term) (n:int)\n : Tot bool (decreases e)\n = match inspect_ln e with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unknown \n | Tv_Unsupp\n | Tv_Var _ -> true\n | Tv_BVar m -> bv_index m <= n\n | Tv_App e1 (e2, _) -> ln' e1 n && ln' e2 n\n | Tv_Abs b body -> \n ln'_binder b n &&\n ln' body (n + 1)\n\n | Tv_Arrow b c ->\n ln'_binder b n &&\n ln'_comp c (n + 1)\n\n | Tv_Refine b f ->\n ln'_binder b n &&\n ln' f (n + 1)\n\n | Tv_Uvar _ _ ->\n false\n \n | Tv_Let recf attrs b def body ->\n ln'_terms attrs n &&\n ln'_binder b n &&\n (if recf then ln' def (n + 1) else ln' def n) &&\n ln' body (n + 1)\n\n | Tv_Match scr ret brs ->\n ln' scr n &&\n (match ret with\n | None -> true\n | Some m -> ln'_match_returns m n) &&\n ln'_branches brs n\n \n | Tv_AscribedT e t tac b ->\n ln' e n &&\n ln' t n &&\n (match tac with\n | None -> true\n | Some tac -> ln' tac n)\n \n | Tv_AscribedC e c tac b ->\n ln' e n &&\n ln'_comp c n &&\n (match tac with\n | None -> true\n | Some tac -> ln' tac n)\n \nand ln'_comp (c:comp) (i:int)\n : Tot bool (decreases c)\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t -> ln' t i\n\n | C_Lemma pre post pats ->\n ln' pre i &&\n ln' post i &&\n ln' pats i\n\n | C_Eff us eff_name res args decrs ->\n ln' res i &&\n ln'_args args i &&\n ln'_terms decrs i\n\nand ln'_args (ts:list argv) (i:int)\n : Tot bool (decreases ts)\n = match ts with\n | [] -> true\n | (t,q)::ts -> \n ln' t i &&\n ln'_args ts i\n\nand ln'_binder (b:binder) (n:int)\n : Tot bool (decreases b)\n = let bndr = inspect_binder b in\n ln' bndr.sort n &&\n ln'_terms bndr.attrs n\n\nand ln'_terms (ts:list term) (n:int)\n : Tot bool (decreases ts)\n = match ts with\n | [] -> true\n | t::ts -> ln' t n && ln'_terms ts n\n\nand ln'_patterns (ps:list (pattern & bool)) (i:int)\n : Tot bool\n (decreases ps)\n = match ps with\n | [] -> true\n | (p, b)::ps ->\n let b0 = ln'_pattern p i in\n let n = binder_offset_pattern p in\n let b1 = ln'_patterns ps (i + n) in\n b0 && b1\n\nand ln'_pattern (p:pattern) (i:int) \n : Tot bool\n (decreases p)\n = match p with\n | Pat_Constant _ -> true\n\n | Pat_Cons head univs subpats ->\n ln'_patterns subpats i\n \n | Pat_Var bv s -> true\n\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> true\n | Some t -> ln' t i)\n \nand ln'_branch (br:branch) (i:int)\n : Tot bool (decreases br)\n = let p, t = br in\n let b = ln'_pattern p i in\n let j = binder_offset_pattern p in\n let b' = ln' t (i + j) in\n b&&b'\n \nand ln'_branches (brs:list branch) (i:int)\n : Tot bool (decreases brs)\n = match brs with\n | [] -> true\n | br::brs -> \n ln'_branch br i &&\n ln'_branches brs i\n \nand ln'_match_returns (m:match_returns_ascription) (i:int)\n : Tot bool (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = ln'_binder b i in\n let ret =\n match ret with\n | Inl t -> ln' t (i + 1)\n | Inr c -> ln'_comp c (i + 1)\n in\n let as_ =\n match as_ with\n | None -> true\n | Some t -> ln' t (i + 1)\n in\n b && ret && as_", "val subst_binder_sort (s: subst_t) (b: binder) : binder\nlet subst_binder_sort (s : subst_t) (b : binder) : binder =\n { b with sort = subst_term s b.sort }", "val subst (x: int) (e e': exp) : exp\nlet rec subst (x:int) (e e':exp) : exp =\n match e' with\n | EVar x' -> \n // If we've found the variable we're substituting for\n // replace it with e\n if x = x' then e else e'\n | EAbs x' t e1 ->\n EAbs x' t \n (if x = x' \n then e1 // If x' shadows x, then don't bother descending into e1\n else subst x e e1)\n | EApp e1 e2 -> \n EApp (subst x e e1) (subst x e e2)\n | EUnit -> EUnit", "val tss_tequiv : #s:typ -> #t:typ ->\n h:(tred_star_sym s t) -> Tot (tequiv s t) (decreases h)\nlet rec tss_tequiv #s #t h =\n match h with\n | TssBase h1 -> tred_tequiv h1\n | TssSym h1 -> EqSymm (tss_tequiv h1)\n | TssTran h1 h2 -> EqTran (tss_tequiv h1) (tss_tequiv h2)", "val nt_subst_binder (b: binder) (ss: nt_substs) : binder\nlet nt_subst_binder (b:binder) (ss:nt_substs) : binder =\n L.fold_left (fun b elt -> subst_binder b [elt]) b ss", "val nt_subst_term (t: term) (ss: nt_substs) : term\nlet nt_subst_term (t:term) (ss:nt_substs) : term =\n L.fold_left (fun t elt -> subst_term t [elt]) t ss", "val subst_binder_typ (s: FStar.Stubs.Syntax.Syntax.subst_t) (b: Tactics.NamedView.binder)\n : Tactics.NamedView.binder\nlet subst_binder_typ (s : FStar.Stubs.Syntax.Syntax.subst_t) (b : Tactics.NamedView.binder) : Tactics.NamedView.binder =\n { b with sort = FStar.Stubs.Reflection.V2.Builtins.subst_term s b.sort }", "val substitution :\n #g1:env -> #e:exp -> #t:typ -> s:sub -> #g2:env ->\n h1:typing g1 e t ->\n hs:subst_typing s g1 g2 ->\n Tot (typing g2 (subst s e) t)\n (decreases %[is_var e; is_renaming s; e])\nlet rec substitution #g1 #e #t s #g2 h1 hs =\n match h1 with\n | TyVar x -> hs x\n | TyApp hfun harg -> TyApp (substitution s hfun hs) (substitution s harg hs)\n | TyLam tlam hbody ->\n let hs'' : subst_typing (sub_inc) g2 (extend tlam g2) =\n fun x -> TyVar (x+1) in\n let hs' : subst_typing (sub_elam s) (extend tlam g1) (extend tlam g2) =\n fun y -> if y = 0 then TyVar y\n else let n:var = y - 1 in //Silly limitation of implicits and refinements\n substitution sub_inc (hs n) hs'' //NS: needed to instantiate the Some?.v \n in TyLam tlam (substitution (sub_elam s) hbody hs')\n | TyUnit -> TyUnit", "val subst_bv_in_comp : env -> bv -> typ -> term -> comp -> Tac comp\nlet subst_bv_in_comp e b sort t c =\n apply_subst_in_comp e c [((b, sort), t)]", "val tequiv_tss : #s:typ -> #t:typ -> h:(tequiv s t) ->\n Tot (tred_star_sym s t) (decreases h)\nlet rec tequiv_tss #s #t h =\n match h with\n | EqRefl _ -> TssBase (TrRefl s)\n | EqSymm h1 -> TssSym (tequiv_tss h1)\n | EqTran h1 h2 -> TssTran (tequiv_tss h1) (tequiv_tss h2)\n | EqLam #t #t' k h1 -> TssTran (trlam_tss k (tequiv_tss h1))\n (TssBase (TrRefl (TLam k t')))\n | EqBeta k t1' t2' -> TssBase (TrBeta k (TrRefl t1') (TrRefl t2'))\n | EqApp #t1 #t1' #t2 #t2' h1 h2 ->\n TssTran (trapp_tss_1 t2 (tequiv_tss h1))\n (trapp_tss_2 t1' (tequiv_tss h2))\n | EqArr #t1 #t1' #t2 #t2' h1 h2 ->\n TssTran (trarr_tss_1 t2 (tequiv_tss h1))\n (trarr_tss_2 t1' (tequiv_tss h2))", "val lsubst_term : list subst -> term -> Tot term\nlet lsubst_term = fold_right subst_term", "val subst_expr (s:subst) (e:expr) : expr\nlet rec subst_expr (s:subst) (e:expr)\r\n: expr\r\n= match fst e with\r\n | Constant _ -> e\r\n | Identifier i -> (\r\n match lookup s i with\r\n | Some e' -> e'\r\n | None -> e\r\n )\r\n | App hd args -> (\r\n App hd (subst_exprs s args), snd e\r\n )\r\n | Record tn fields -> (\r\n Record tn (subst_fields s fields), snd e\r\n )\r\nand subst_exprs s es =\r\n match es with\r\n | [] -> []\r\n | e::es -> subst_expr s e :: subst_exprs s es\r\nand subst_fields s fs =\r\n match fs with\r\n | [] -> []\r\n | (i, e)::fs -> (i, subst_expr s e)::subst_fields s fs", "val substitution :\n #g1:env -> #e:exp -> #t:typ -> s:esub -> #g2:env ->\n h1:typing g1 e t ->\n hs:subst_typing s g1 g2 ->\n Tot (typing g2 (esubst s e) t)\n (decreases %[is_var e; is_renaming s; h1])\nlet rec substitution #g1 #e #t s #g2 h1 hs =\n match h1 with\n | TyVar x kind_normal -> hs x kind_normal\n | TyApp hfun harg -> TyApp (substitution s hfun hs) (substitution s harg hs)\n | TyLam #gtemp tlam #ebody #tfun hkind hbody ->\n let hs'' : subst_typing (esub_inc) (g2) (extend_evar g2 0 tlam) =\n fun x hkind ->\n TyVar (x+1) (kinding_extensional hkind (extend_evar g2 0 tlam)) in\n let hs' : subst_typing (esub_lam s) (extend_evar g1 0 tlam)\n (extend_evar g2 0 tlam) =\n fun y hkindg1 ->\n if y = 0\n then TyVar y (kinding_extensional hkindg1 (extend_evar g2 0 tlam))\n else let hgamma2\n (* : typing g2 (s (y-1)) (Some?.v (lookup_evar g1 (y-1)))\n// -- this annotation doesn't help fix inference problem below *)\n = hs (y - 1) (kinding_extensional hkindg1 g1) in\n (* XXX before universes this used to work without implicits\n// filed this as #580 *)\n (* substitution esub_inc hgamma2 hs'' *)\n (* Failed to verify implicit argument: Subtyping check failed;\n// expected type LambdaOmega.var; got type Prims.int [2 times] *)\n substitution esub_inc hgamma2 hs''\n in (esub_lam_hoist tlam ebody s;\n TyLam tlam (kinding_extensional hkind g2)\n (substitution (esub_lam s) hbody hs'))\n | TyEqu het1 hequiv hkind ->\n TyEqu (substitution s het1 hs) hequiv (kinding_extensional hkind g2)", "val substitution_beta :\n #e:exp -> #v:exp -> #t_x:typ -> #t:typ -> #g:env ->\n h1:typing g v t_x ->\n h2:typing (extend t_x g) e t ->\n Tot (typing g (subst (sub_beta v) e) t) (decreases e)\nlet rec substitution_beta #e #v #t_x #t #g h1 h2 =\n let hs : subst_typing (sub_beta v) (extend t_x g) g =\n fun y -> if y = 0 then h1 else TyVar (y-1) in\n substitution (sub_beta v) h2 hs", "val subst_decl' (s: subst) (d: decl') : ML decl'\nlet subst_decl' (s:subst) (d:decl') : ML decl' =\r\n match d with\r\n | ModuleAbbrev _ _ -> d\r\n | Define i None _ -> d\r\n | Define i (Some t) c -> Define i (Some (subst_typ s t)) c\r\n | TypeAbbrev t i -> TypeAbbrev (subst_typ s t) i\r\n | Enum t i is -> Enum (subst_typ s t) i is\r\n | Record names params where fields ->\r\n Record names (subst_params s params) (map_opt (subst_expr s) where) (List.map (subst_field s) fields)\r\n | CaseType names params cases ->\r\n CaseType names (subst_params s params) (subst_switch_case s cases)\r\n | OutputType _\r\n | ExternType _\r\n | ExternFn _ _ _ \r\n | ExternProbe _ -> d", "val freevars_binder (b: binder) : Tot (Set.set var) (decreases b)\nlet rec freevars (e:term)\n : FStar.Set.set var\n = match inspect_ln e with\n | Tv_Uvar _ _ -> Set.complement Set.empty\n \n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unknown \n | Tv_Unsupp\n | Tv_BVar _ -> Set.empty\n\n | Tv_Var x -> Set.singleton (namedv_uniq x)\n \n | Tv_App e1 (e2, _) ->\n Set.union (freevars e1) (freevars e2)\n\n | Tv_Abs b body -> \n Set.union (freevars_binder b) (freevars body)\n\n | Tv_Arrow b c ->\n Set.union (freevars_binder b) (freevars_comp c)\n\n | Tv_Refine b f ->\n freevars (binder_sort b) `Set.union`\n freevars f\n \n | Tv_Let recf attrs b def body ->\n freevars_terms attrs `Set.union`\n freevars (binder_sort b) `Set.union`\n freevars def `Set.union`\n freevars body\n\n | Tv_Match scr ret brs ->\n freevars scr `Set.union`\n freevars_opt ret freevars_match_returns `Set.union`\n freevars_branches brs\n\n | Tv_AscribedT e t tac b ->\n freevars e `Set.union`\n freevars t `Set.union`\n freevars_opt tac freevars\n \n | Tv_AscribedC e c tac b ->\n freevars e `Set.union`\n freevars_comp c `Set.union`\n freevars_opt tac freevars\n\nand freevars_opt (#a:Type0) (o:option a) (f: (x:a { x << o } -> FStar.Set.set var))\n : FStar.Set.set var\n = match o with\n | None -> Set.empty\n | Some x -> f x\n\nand freevars_comp (c:comp)\n : FStar.Set.set var\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t ->\n freevars t\n\n | C_Lemma pre post pats ->\n freevars pre `Set.union`\n freevars post `Set.union`\n freevars pats\n\n | C_Eff us eff_name res args decrs ->\n freevars res `Set.union`\n freevars_args args `Set.union`\n freevars_terms decrs\n\nand freevars_args (ts:list argv)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | (t,q)::ts ->\n freevars t `Set.union`\n freevars_args ts\n\nand freevars_terms (ts:list term)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | t::ts ->\n freevars t `Set.union`\n freevars_terms ts\n \nand freevars_binder (b:binder)\n : Tot (Set.set var) (decreases b)\n = let bndr = inspect_binder b in\n freevars bndr.sort `Set.union`\n freevars_terms bndr.attrs \n\nand freevars_pattern (p:pattern) \n : Tot (Set.set var) (decreases p)\n = match p with\n | Pat_Constant _ ->\n Set.empty\n\n | Pat_Cons head univs subpats ->\n freevars_patterns subpats\n \n | Pat_Var bv s -> Set.empty\n\n | Pat_Dot_Term topt ->\n freevars_opt topt freevars\n\nand freevars_patterns (ps:list (pattern & bool))\n : Tot (Set.set var) (decreases ps)\n = match ps with\n | [] -> Set.empty\n | (p, b)::ps ->\n freevars_pattern p `Set.union`\n freevars_patterns ps\n\nand freevars_branch (br:branch)\n : Tot (Set.set var) (decreases br)\n = let p, t = br in\n freevars_pattern p `Set.union`\n freevars t\n\nand freevars_branches (brs:list branch)\n : Tot (Set.set var) (decreases brs)\n = match brs with\n | [] -> Set.empty\n | hd::tl -> freevars_branch hd `Set.union` freevars_branches tl\n \nand freevars_match_returns (m:match_returns_ascription)\n : Tot (Set.set var) (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = freevars_binder b in\n let ret =\n match ret with\n | Inl t -> freevars t\n | Inr c -> freevars_comp c\n in\n let as_ = freevars_opt as_ freevars in\n b `Set.union` ret `Set.union` as_", "val nt_subst_st_comp (s: st_comp) (ss: nt_substs) : st_comp\nlet nt_subst_st_comp (s:st_comp) (ss:nt_substs) : st_comp =\n L.fold_left (fun s elt -> subst_st_comp s [elt]) s ss", "val subst_map (ss: list (namedv * fv)) (r t: term) : Tac term\nlet subst_map (ss : list (namedv * fv)) (r:term) (t : term) : Tac term =\n let subst = List.Tot.map (fun (x, fv) -> NT (Reflection.V2.pack_namedv x) (mk_e_app (Tv_FVar fv) [r])) ss in\n subst_term subst t", "val elaborate_pat (p: pattern) (bs: list R.binding)\n : Tot (option (term & list R.binding)) (decreases p)\nlet rec elaborate_pat (p : pattern) (bs : list R.binding) : Tot (option (term & list R.binding)) (decreases p) =\n match p, bs with\n | Pat_Constant c, _ -> Some (pack_ln (Tv_Const c), bs)\n | Pat_Cons fv univs subpats, bs ->\n let head = pack_ln (Tv_FVar fv) in\n fold_left_dec\n (Some (head, bs))\n subpats\n (fun st pi ->\n let (p,i) = pi in\n match st with | None -> None | Some (head, bs) ->\n match elaborate_pat p bs with | None -> None | Some (t, bs') -> Some (pack_ln (Tv_App head (t, (if i then Q_Implicit else Q_Explicit))), bs'))\n\n | Pat_Var _ _, b::bs ->\n Some (pack_ln (Tv_Var (binding_to_namedv b)), bs)\n | Pat_Dot_Term (Some t), _ -> Some (t, bs)\n | Pat_Dot_Term None, _ -> None\n | _ -> None", "val subst_comp (s: subst_t) (c: comp) : comp\nlet subst_comp (s : subst_t) (c : comp) : comp =\n inspect_comp (R.subst_comp s (pack_comp c))", "val shift_above_and_subst: s:typ -> y:nat -> t:typ -> Lemma\n (ensures (ts y t (tsh y s) = s)) (decreases s)\nlet rec shift_above_and_subst s y t =\n tsubst_comp (tsub_beta_gen y t) (tsub_inc_above y) s;\n tsubst_extensional (tsub_comp (tsub_beta_gen y t) (tsub_inc_above y)) tsub_id s;\n tsubst_id s", "val subst_var (v: namedv) (s: subst) : term\nlet subst_var (v:namedv) (s:subst) : term =\n match find_matching_subst_elt_var s v with\n | Some (NT _ t) ->\n (match maybe_uniq_of_term t with\n | None -> t\n | Some k ->\n pack_ln (Tv_Var (pack_namedv { inspect_namedv v with uniq = k })))\n | Some (ND _ i) ->\n let bv = pack_bv {\n sort = (inspect_namedv v).sort;\n ppname = (inspect_namedv v).ppname;\n index = i;\n } in\n pack_ln (Tv_BVar bv)\n | _ -> pack_ln (Tv_Var v)", "val close_branch (b: branch) : Tot R.branch\nlet close_branch (b : branch) : Tot R.branch =\n let (pat, t) = b in\n let pat, s = close_pat pat [] in\n let t' = subst_term s t in\n (pat, t')", "val ln'_branches (brs: list branch) (i: int) : Tot bool (decreases brs)\nlet rec ln' (e:term) (n:int)\n : Tot bool (decreases e)\n = match inspect_ln e with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unknown \n | Tv_Unsupp\n | Tv_Var _ -> true\n | Tv_BVar m -> bv_index m <= n\n | Tv_App e1 (e2, _) -> ln' e1 n && ln' e2 n\n | Tv_Abs b body -> \n ln'_binder b n &&\n ln' body (n + 1)\n\n | Tv_Arrow b c ->\n ln'_binder b n &&\n ln'_comp c (n + 1)\n\n | Tv_Refine b f ->\n ln'_binder b n &&\n ln' f (n + 1)\n\n | Tv_Uvar _ _ ->\n false\n \n | Tv_Let recf attrs b def body ->\n ln'_terms attrs n &&\n ln'_binder b n &&\n (if recf then ln' def (n + 1) else ln' def n) &&\n ln' body (n + 1)\n\n | Tv_Match scr ret brs ->\n ln' scr n &&\n (match ret with\n | None -> true\n | Some m -> ln'_match_returns m n) &&\n ln'_branches brs n\n \n | Tv_AscribedT e t tac b ->\n ln' e n &&\n ln' t n &&\n (match tac with\n | None -> true\n | Some tac -> ln' tac n)\n \n | Tv_AscribedC e c tac b ->\n ln' e n &&\n ln'_comp c n &&\n (match tac with\n | None -> true\n | Some tac -> ln' tac n)\n \nand ln'_comp (c:comp) (i:int)\n : Tot bool (decreases c)\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t -> ln' t i\n\n | C_Lemma pre post pats ->\n ln' pre i &&\n ln' post i &&\n ln' pats i\n\n | C_Eff us eff_name res args decrs ->\n ln' res i &&\n ln'_args args i &&\n ln'_terms decrs i\n\nand ln'_args (ts:list argv) (i:int)\n : Tot bool (decreases ts)\n = match ts with\n | [] -> true\n | (t,q)::ts -> \n ln' t i &&\n ln'_args ts i\n\nand ln'_binder (b:binder) (n:int)\n : Tot bool (decreases b)\n = let bndr = inspect_binder b in\n ln' bndr.sort n &&\n ln'_terms bndr.attrs n\n\nand ln'_terms (ts:list term) (n:int)\n : Tot bool (decreases ts)\n = match ts with\n | [] -> true\n | t::ts -> ln' t n && ln'_terms ts n\n\nand ln'_patterns (ps:list (pattern & bool)) (i:int)\n : Tot bool\n (decreases ps)\n = match ps with\n | [] -> true\n | (p, b)::ps ->\n let b0 = ln'_pattern p i in\n let n = binder_offset_pattern p in\n let b1 = ln'_patterns ps (i + n) in\n b0 && b1\n\nand ln'_pattern (p:pattern) (i:int) \n : Tot bool\n (decreases p)\n = match p with\n | Pat_Constant _ -> true\n\n | Pat_Cons head univs subpats ->\n ln'_patterns subpats i\n \n | Pat_Var bv s -> true\n\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> true\n | Some t -> ln' t i)\n \nand ln'_branch (br:branch) (i:int)\n : Tot bool (decreases br)\n = let p, t = br in\n let b = ln'_pattern p i in\n let j = binder_offset_pattern p in\n let b' = ln' t (i + j) in\n b&&b'\n \nand ln'_branches (brs:list branch) (i:int)\n : Tot bool (decreases brs)\n = match brs with\n | [] -> true\n | br::brs -> \n ln'_branch br i &&\n ln'_branches brs i\n \nand ln'_match_returns (m:match_returns_ascription) (i:int)\n : Tot bool (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = ln'_binder b i in\n let ret =\n match ret with\n | Inl t -> ln' t (i + 1)\n | Inr c -> ln'_comp c (i + 1)\n in\n let as_ =\n match as_ with\n | None -> true\n | Some t -> ln' t (i + 1)\n in\n b && ret && as_", "val elab_exp (e: stlc_exp) : Tot R.term (decreases (size e))\nlet rec elab_exp (e:stlc_exp)\n : Tot R.term (decreases (size e))\n = let open R in\n match e with\n | EUnit -> \n pack_ln (Tv_Const C_Unit)\n\n | EBVar n -> \n let bv = R.pack_bv (RT.make_bv n) in\n R.pack_ln (Tv_BVar bv)\n \n | EVar n ->\n let bv = R.pack_namedv (RT.make_namedv n) in\n R.pack_ln (Tv_Var bv)\n\n | ELam t e ->\n let t = elab_ty t in\n let e = elab_exp e in\n R.pack_ln (Tv_Abs (RT.mk_simple_binder RT.pp_name_default t) e)\n \n | EApp e1 e2 ->\n let e1 = elab_exp e1 in\n let e2 = elab_exp e2 in\n R.pack_ln (Tv_App e1 (e2, Q_Explicit))", "val compare_term (s t: term) : Tot order (decreases s)\nlet rec compare_term (s t : term) : Tot order (decreases s) =\n match inspect_ln s, inspect_ln t with\n | Tv_Var sv, Tv_Var tv ->\n compare_namedv sv tv\n\n | Tv_BVar sv, Tv_BVar tv ->\n compare_bv sv tv\n\n | Tv_FVar sv, Tv_FVar tv ->\n compare_fv sv tv\n\n | Tv_UInst sv sus, Tv_UInst tv tus ->\n lex (compare_fv sv tv) (fun _ -> compare_universes sus tus)\n\n | Tv_App h1 a1, Tv_App h2 a2 ->\n lex (compare_term h1 h2) (fun () -> compare_argv a1 a2)\n\n | Tv_Abs b1 e1, Tv_Abs b2 e2 ->\n lex (compare_binder b1 b2) (fun () -> compare_term e1 e2)\n\n | Tv_Refine b1 e1, Tv_Refine b2 e2 ->\n lex (compare_binder b1 b2) (fun () ->\n compare_term e1 e2)\n\n | Tv_Arrow b1 e1, Tv_Arrow b2 e2 ->\n lex (compare_binder b1 b2) (fun () -> compare_comp e1 e2)\n\n | Tv_Type su, Tv_Type tu -> compare_universe su tu\n\n | Tv_Const c1, Tv_Const c2 ->\n compare_const c1 c2\n\n | Tv_Uvar u1 _, Tv_Uvar u2 _->\n compare_int u1 u2\n\n | Tv_Let _r1 _attrs1 b1 t1 t1', Tv_Let _r2 _attrs2 b2 t2 t2' ->\n lex (compare_binder b1 b2) (fun () ->\n lex (compare_term t1 t2) (fun () ->\n compare_term t1' t2'))\n\n | Tv_Match _ _ _, Tv_Match _ _ _ ->\n Eq // TODO\n\n | Tv_AscribedT e1 t1 tac1 _, Tv_AscribedT e2 t2 tac2 _ ->\n lex (compare_term e1 e2) (fun () ->\n lex (compare_term t1 t2) (fun () ->\n match tac1, tac2 with\n | None, None -> Eq\n | None, _ -> Lt\n | _, None -> Gt\n | Some e1, Some e2 -> compare_term e1 e2))\n\n | Tv_AscribedC e1 c1 tac1 _, Tv_AscribedC e2 c2 tac2 _ ->\n lex (compare_term e1 e2) (fun () ->\n lex (compare_comp c1 c2) (fun () ->\n match tac1, tac2 with\n | None, None -> Eq\n | None, _ -> Lt\n | _, None -> Gt\n | Some e1, Some e2 -> compare_term e1 e2))\n\n | Tv_Unknown, Tv_Unknown ->\n Eq\n\n | Tv_Unsupp, Tv_Unsupp ->\n Eq\n\n // From here onward, they must have different constructors. Order them arbitrarily as in the definition.\n | Tv_Var _, _ -> Lt | _, Tv_Var _ -> Gt\n | Tv_BVar _, _ -> Lt | _, Tv_BVar _ -> Gt\n | Tv_FVar _, _ -> Lt | _, Tv_FVar _ -> Gt\n | Tv_UInst _ _, _ -> Lt | _, Tv_UInst _ _ -> Gt\n | Tv_App _ _, _ -> Lt | _, Tv_App _ _ -> Gt\n | Tv_Abs _ _, _ -> Lt | _, Tv_Abs _ _ -> Gt\n | Tv_Arrow _ _, _ -> Lt | _, Tv_Arrow _ _ -> Gt\n | Tv_Type _, _ -> Lt | _, Tv_Type _ -> Gt\n | Tv_Refine _ _ , _ -> Lt | _, Tv_Refine _ _ -> Gt\n | Tv_Const _, _ -> Lt | _, Tv_Const _ -> Gt\n | Tv_Uvar _ _, _ -> Lt | _, Tv_Uvar _ _ -> Gt\n | Tv_Let _ _ _ _ _, _ -> Lt | _, Tv_Let _ _ _ _ _ -> Gt\n | Tv_Match _ _ _, _ -> Lt | _, Tv_Match _ _ _ -> Gt\n | Tv_AscribedT _ _ _ _, _ -> Lt | _, Tv_AscribedT _ _ _ _ -> Gt\n | Tv_AscribedC _ _ _ _, _ -> Lt | _, Tv_AscribedC _ _ _ _ -> Gt\n | Tv_Unknown, _ -> Lt | _, Tv_Unknown -> Gt\n | Tv_Unsupp, _ -> Lt | _, Tv_Unsupp -> Gt\nand compare_term_list (l1 l2:list term) : Tot order (decreases l1) =\n match l1, l2 with\n | [], [] -> Eq\n | [], _ -> Lt\n | _, [] -> Gt\n | hd1::tl1, hd2::tl2 ->\n lex (compare_term hd1 hd2) (fun () -> compare_term_list tl1 tl2)\n\nand compare_argv (a1 a2 : argv) : Tot order (decreases a1) =\n let a1, q1 = a1 in\n let a2, q2 = a2 in\n match q1, q2 with\n (* We should never see Q_Meta here *)\n | Q_Implicit, Q_Explicit -> Lt\n | Q_Explicit, Q_Implicit -> Gt\n | _, _ -> compare_term a1 a2\nand compare_comp (c1 c2 : comp) : Tot order (decreases c1) =\n let cv1 = inspect_comp c1 in\n let cv2 = inspect_comp c2 in\n match cv1, cv2 with\n | C_Total t1, C_Total t2\n\n | C_GTotal t1, C_GTotal t2 -> compare_term t1 t2\n\n | C_Lemma p1 q1 s1, C_Lemma p2 q2 s2 ->\n lex (compare_term p1 p2)\n (fun () ->\n lex (compare_term q1 q2)\n (fun () -> compare_term s1 s2)\n )\n\n | C_Eff us1 eff1 res1 args1 _decrs1,\n C_Eff us2 eff2 res2 args2 _decrs2 ->\n (* This could be more complex, not sure it is worth it *)\n lex (compare_universes us1 us2)\n (fun _ -> lex (compare_name eff1 eff2)\n (fun _ -> compare_term res1 res2))\n\n | C_Total _, _ -> Lt | _, C_Total _ -> Gt\n | C_GTotal _, _ -> Lt | _, C_GTotal _ -> Gt\n | C_Lemma _ _ _, _ -> Lt | _, C_Lemma _ _ _ -> Gt\n | C_Eff _ _ _ _ _, _ -> Lt | _, C_Eff _ _ _ _ _ -> Gt\n\nand compare_binder (b1 b2 : binder) : order =\n let bview1 = inspect_binder b1 in\n let bview2 = inspect_binder b2 in\n compare_term bview1.sort bview2.sort", "val compare_term (s t: term) : Tot order (decreases s)\nlet rec compare_term (s t : term) : Tot order (decreases s) =\n match inspect_ln s, inspect_ln t with\n | Tv_Var sv, Tv_Var tv ->\n compare_bv sv tv\n\n | Tv_BVar sv, Tv_BVar tv ->\n compare_bv sv tv\n\n | Tv_FVar sv, Tv_FVar tv ->\n compare_fv sv tv\n\n | Tv_UInst sv sus, Tv_UInst tv tus ->\n lex (compare_fv sv tv) (fun _ -> compare_universes sus tus)\n\n | Tv_App h1 a1, Tv_App h2 a2 ->\n lex (compare_term h1 h2) (fun () -> compare_argv a1 a2)\n\n | Tv_Abs b1 e1, Tv_Abs b2 e2 ->\n lex (compare_binder b1 b2) (fun () -> compare_term e1 e2)\n\n | Tv_Refine bv1 sort1 e1, Tv_Refine bv2 sort2 e2 ->\n lex (compare_bv bv1 bv2) (fun () ->\n lex (compare_term sort1 sort2) (fun () ->\n compare_term e1 e2))\n\n | Tv_Arrow b1 e1, Tv_Arrow b2 e2 ->\n lex (compare_binder b1 b2) (fun () -> compare_comp e1 e2)\n\n | Tv_Type su, Tv_Type tu -> compare_universe su tu\n\n | Tv_Const c1, Tv_Const c2 ->\n compare_const c1 c2\n\n | Tv_Uvar u1 _, Tv_Uvar u2 _->\n compare_int u1 u2\n\n | Tv_Let _r1 _attrs1 bv1 ty1 t1 t1', Tv_Let _r2 _attrs2 bv2 ty2 t2 t2' ->\n lex (compare_bv bv1 bv2) (fun () ->\n lex (compare_term ty1 ty2) (fun () ->\n lex (compare_term t1 t2) (fun () ->\n compare_term t1' t2')))\n\n | Tv_Match _ _ _, Tv_Match _ _ _ ->\n Eq // TODO\n\n | Tv_AscribedT e1 t1 tac1 _, Tv_AscribedT e2 t2 tac2 _ ->\n lex (compare_term e1 e2) (fun () ->\n lex (compare_term t1 t2) (fun () ->\n match tac1, tac2 with\n | None, None -> Eq\n | None, _ -> Lt\n | _, None -> Gt\n | Some e1, Some e2 -> compare_term e1 e2))\n\n | Tv_AscribedC e1 c1 tac1 _, Tv_AscribedC e2 c2 tac2 _ ->\n lex (compare_term e1 e2) (fun () ->\n lex (compare_comp c1 c2) (fun () ->\n match tac1, tac2 with\n | None, None -> Eq\n | None, _ -> Lt\n | _, None -> Gt\n | Some e1, Some e2 -> compare_term e1 e2))\n\n | Tv_Unknown, Tv_Unknown ->\n Eq\n\n | Tv_Unsupp, Tv_Unsupp ->\n Eq\n\n // From here onward, they must have different constructors. Order them arbitrarily as in the definition.\n | Tv_Var _, _ -> Lt | _, Tv_Var _ -> Gt\n | Tv_BVar _, _ -> Lt | _, Tv_BVar _ -> Gt\n | Tv_FVar _, _ -> Lt | _, Tv_FVar _ -> Gt\n | Tv_UInst _ _, _ -> Lt | _, Tv_UInst _ _ -> Gt\n | Tv_App _ _, _ -> Lt | _, Tv_App _ _ -> Gt\n | Tv_Abs _ _, _ -> Lt | _, Tv_Abs _ _ -> Gt\n | Tv_Arrow _ _, _ -> Lt | _, Tv_Arrow _ _ -> Gt\n | Tv_Type _, _ -> Lt | _, Tv_Type _ -> Gt\n | Tv_Refine _ _ _ , _ -> Lt | _, Tv_Refine _ _ _ -> Gt\n | Tv_Const _, _ -> Lt | _, Tv_Const _ -> Gt\n | Tv_Uvar _ _, _ -> Lt | _, Tv_Uvar _ _ -> Gt\n | Tv_Let _ _ _ _ _ _, _ -> Lt | _, Tv_Let _ _ _ _ _ _ -> Gt\n | Tv_Match _ _ _, _ -> Lt | _, Tv_Match _ _ _ -> Gt\n | Tv_AscribedT _ _ _ _, _ -> Lt | _, Tv_AscribedT _ _ _ _ -> Gt\n | Tv_AscribedC _ _ _ _, _ -> Lt | _, Tv_AscribedC _ _ _ _ -> Gt\n | Tv_Unknown, _ -> Lt | _, Tv_Unknown -> Gt\n | Tv_Unsupp, _ -> Lt | _, Tv_Unsupp -> Gt\nand compare_term_list (l1 l2:list term) : Tot order (decreases l1) =\n match l1, l2 with\n | [], [] -> Eq\n | [], _ -> Lt\n | _, [] -> Gt\n | hd1::tl1, hd2::tl2 ->\n lex (compare_term hd1 hd2) (fun () -> compare_term_list tl1 tl2)\n\nand compare_argv (a1 a2 : argv) : Tot order (decreases a1) =\n let a1, q1 = a1 in\n let a2, q2 = a2 in\n match q1, q2 with\n (* We should never see Q_Meta here *)\n | Q_Implicit, Q_Explicit -> Lt\n | Q_Explicit, Q_Implicit -> Gt\n | _, _ -> compare_term a1 a2\nand compare_comp (c1 c2 : comp) : Tot order (decreases c1) =\n let cv1 = inspect_comp c1 in\n let cv2 = inspect_comp c2 in\n match cv1, cv2 with\n | C_Total t1, C_Total t2\n\n | C_GTotal t1, C_GTotal t2 -> compare_term t1 t2\n\n | C_Lemma p1 q1 s1, C_Lemma p2 q2 s2 ->\n lex (compare_term p1 p2)\n (fun () ->\n lex (compare_term q1 q2)\n (fun () -> compare_term s1 s2)\n )\n\n | C_Eff us1 eff1 res1 args1 _decrs1,\n C_Eff us2 eff2 res2 args2 _decrs2 ->\n (* This could be more complex, not sure it is worth it *)\n lex (compare_universes us1 us2)\n (fun _ -> lex (compare_name eff1 eff2)\n (fun _ -> compare_term res1 res2))\n\n | C_Total _, _ -> Lt | _, C_Total _ -> Gt\n | C_GTotal _, _ -> Lt | _, C_GTotal _ -> Gt\n | C_Lemma _ _ _, _ -> Lt | _, C_Lemma _ _ _ -> Gt\n | C_Eff _ _ _ _ _, _ -> Lt | _, C_Eff _ _ _ _ _ -> Gt", "val subst : s:sub -> e:exp -> Pure exp (requires True)\n (ensures (fun e' -> (renaming s /\\ EVar? e) ==> EVar? e'))\n (decreases %[is_var e; is_renaming s; 1; e])\nlet rec subst s e =\n match e with\n | EVar x -> s x\n | ELam t e1 -> ELam t (subst (sub_elam s) e1)\n | EApp e1 e2 -> EApp (subst s e1) (subst s e2)\n | EUnit -> EUnit\n\nand sub_elam s y = if y=0 then EVar y\n else subst sub_inc (s (y-1))", "val pow_mod_ (#m: pos{1 < m}) (a: nat_mod m) (b: nat) : Tot (nat_mod m) (decreases b)\nlet rec pow_mod_ (#m:pos{1 < m}) (a:nat_mod m) (b:nat) : Tot (nat_mod m) (decreases b) =\n if b = 0 then 1\n else\n if b % 2 = 0 then pow_mod_ (mul_mod a a) (b / 2)\n else mul_mod a (pow_mod_ (mul_mod a a) (b / 2))", "val lemma_vars_decrease: s:subst -> t':term -> Lemma\n (requires (ok s))\n (ensures (OrdSet.subset (vars (subst_term s t'))\n \t\t\t (OrdSet.remove (fst s) (OrdSet.union (vars (snd s)) (vars t')))))\nlet rec lemma_vars_decrease s t' = match t' with\n | V x -> ()\n | F t1 t2 ->\n lemma_vars_decrease s t1;\n lemma_vars_decrease s t2", "val ss_st_term (t:st_term) (ss:ss_t) : st_term\nlet rec ss_st_term (t:st_term) (ss:ss_t) : Tot st_term (decreases L.length ss.l) =\n match ss.l with\n | [] -> t\n | y::tl ->\n let t = subst_st_term t [ NT y (Map.sel ss.m y) ] in\n ss_st_term t (tail ss)", "val subst_typ (s: subst) (t: typ) : ML typ\nlet rec subst_typ (s:subst) (t:typ) : ML typ =\r\n match t.v with\r\n | Type_app hd k ps -> { t with v = Type_app hd k (List.map (subst_typ_param s) ps) }\r\n | Pointer t -> {t with v = Pointer (subst_typ s t) }", "val subst_decl (s: subst) (d: decl) : ML decl\nlet subst_decl (s:subst) (d:decl) : ML decl = decl_with_v d (subst_decl' s d.d_decl.v)", "val apply_term_ctxt (e: term_ctxt) (t: term) : Tot term (decreases e)\nlet rec apply_term_ctxt (e:term_ctxt) (t:term) : Tot term (decreases e) =\n match e with\n | Ctxt_hole -> t\n | Ctxt_app_head e arg -> pack_ln (Tv_App (apply_term_ctxt e t) arg)\n | Ctxt_app_arg hd q e -> pack_ln (Tv_App hd (apply_term_ctxt e t, q))", "val substitution_preserves_typing :\n x:var -> #e:exp -> #v:exp -> #t_x:ty -> #t:ty -> #g:env ->\n h1:rtyping empty v t_x ->\n h2:rtyping (extend g x t_x) e t ->\n Tot (rtyping g (subst_beta x v e) t) (decreases e)\nlet rec substitution_preserves_typing x #e #v #t_x #t #g h1 h2 =\n match h2 with\n | TyVar y ->\n if x=y then (typable_empty_closed' h1; context_invariance h1 g)\n else if y\n (let h21' = typing_extensional h21 (extend (extend g 0 t_y) (x+1) t_x) in\n TyAbs t_y (substitution_preserves_typing (x+1) h1 h21'))\n | TyApp #g' #e1 #e2 #t11 #t12 h21 h22 ->\n (* CH: implicits don't work here, why? *)\n (* NS: They do now *)\n (TyApp // #g #(subst_beta x v e1) #(subst_beta x v e2) #t11 #t12\n (substitution_preserves_typing x h1 h21)\n (substitution_preserves_typing x h1 h22))", "val typ_depth (t: I.typ) : GTot nat (decreases t)\nlet rec typ_depth (t: I.typ) : GTot nat\n (decreases t)\n= match t with\n | I.T_if_else _ t1 t2 // 2 accounts for the call to parse_then_else_with_branch_trace\n -> 2 + typ_depth t1 + typ_depth t2\n | I.T_pair _ t1 t2\n -> 1 + typ_depth t1 + typ_depth t2\n | I.T_dep_pair _ _ (_, t')\n | I.T_dep_pair_with_refinement _ _ _ (_, t')\n | I.T_with_comment _ t' _\n | I.T_at_most _ _ t'\n | I.T_exact _ _ t'\n | I.T_nlist _ _ t'\n -> 1 + typ_depth t'\n | _\n -> 0", "val elab_st_typing (#g: env) (#t: st_term) (#c: comp) (d: st_typing g t c)\n : Tot R.term (decreases d)\nlet rec elab_st_typing (#g:env)\n (#t:st_term)\n (#c:comp)\n (d:st_typing g t c)\n : Tot R.term (decreases d)\n = match d with\n // | T_Tot _ t _ _ -> elab_term t\n\n | T_Abs _ x qual b _u body _c ty_typing body_typing ->\n let ty = elab_term b.binder_ty in\n let ppname = b.binder_ppname.name in\n let body = elab_st_typing body_typing in\n mk_abs_with_name ppname ty (elab_qual qual) (RT.close_term body x) //this closure should be provably redundant by strengthening the conditions on x\n\n\n | T_STApp _ head _ qual _ arg _ _\n | T_STGhostApp _ head _ qual _ arg _ _ _ _ ->\n let head = elab_term head in\n let arg = elab_term arg in\n R.mk_app head [(arg, elab_qual qual)]\n\n | T_Return _ c use_eq u ty t post _ _ _ _ ->\n let ru = u in\n let rty = elab_term ty in\n let rt = elab_term t in\n let rp = elab_term post in\n let rp = mk_abs rty R.Q_Explicit rp in\n (match c, use_eq with\n | STT, true -> mk_stt_return ru rty rt rp\n | STT, false -> mk_stt_return_noeq ru rty rt rp\n | STT_Atomic, true -> mk_stt_atomic_return ru rty rt rp\n | STT_Atomic, false -> mk_stt_atomic_return_noeq ru rty rt rp\n | STT_Ghost, true -> mk_stt_ghost_return ru rty rt rp\n | STT_Ghost, false -> mk_stt_ghost_return_noeq ru rty rt rp)\n\n | T_Bind _ e1 e2 c1 c2 b x c e1_typing t_typing e2_typing bc ->\n let e1 = elab_st_typing e1_typing in\n let e2 = elab_st_typing e2_typing in\n let ty1 = elab_term (comp_res c1) in\n elab_bind bc e1 (mk_abs_with_name b.binder_ppname.name ty1 R.Q_Explicit (RT.close_term e2 x))\n\n | T_BindFn _ _ _ c1 c2 b x e1_typing _u t_typing e2_typing c2_typing ->\n let e1 = elab_st_typing e1_typing in\n let e2 = elab_st_typing e2_typing in\n let ty1 = elab_term (comp_res c1) in\n RT.mk_let RT.pp_name_default e1 ty1 (RT.close_term e2 x)\n \n | T_Frame _ _ c frame _frame_typing e_typing ->\n let e = elab_st_typing e_typing in\n elab_frame c frame e\n \n | T_Equiv _ _ c1 c2 e_typing (ST_TotEquiv _ _ _ _ _ _) ->\n let e = elab_st_typing e_typing in\n e\n\n | T_Equiv _ _ c1 c2 e_typing _ ->\n let e = elab_st_typing e_typing in\n elab_sub c1 c2 e\n\n | T_Sub _ _ c1 c2 e_typing d_sub ->\n let e = elab_st_typing e_typing in\n let (| coercion, _ |) = elab_st_sub d_sub in\n R.mk_e_app coercion [e]\n\n | T_Lift _ _ c1 c2 e_typing lc ->\n let e = elab_st_typing e_typing in\n elab_lift lc e\n\n | T_If _ b _ _ _ _ _ e1_typing e2_typing _c_typing ->\n let rb = elab_term b in\n let re1 = elab_st_typing e1_typing in\n let re2 = elab_st_typing e2_typing in\n RT.mk_if rb re1 re2\n\n | T_Match _ _ _ sc _ _ _ _ _ brty _ ->\n let sc = elab_term sc in\n let brs = elab_branches brty in\n R.pack_ln (R.Tv_Match sc None brs)\n\n | T_IntroPure _ p _ _ ->\n let head = \n tm_pureapp (tm_fvar (as_fv (mk_pulse_lib_core_lid \"intro_pure\")))\n None\n p\n in\n let arg = (`()) in\n R.mk_app (elab_term head) [(arg, elab_qual None)]\n\n | T_ElimExists _ u t p _ d_t d_exists ->\n let ru = u in\n let rt = elab_term t in\n let rp = elab_term p in\n mk_elim_exists ru rt (mk_abs rt R.Q_Explicit rp)\n\n | T_IntroExists _ u b p e _ _ _ ->\n let ru = u in\n let rt = elab_term b.binder_ty in\n let rp = elab_term p in\n let re = elab_term e in\n mk_intro_exists ru rt (mk_abs rt R.Q_Explicit rp) re\n\n | T_While _ inv _ _ _ cond_typing body_typing ->\n let inv = elab_term inv in\n let cond = elab_st_typing cond_typing in\n let body = elab_st_typing body_typing in\n mk_while (mk_abs bool_tm R.Q_Explicit inv) cond body\n\n | T_Par _ eL cL eR cR _ _ _ eL_typing eR_typing ->\n let ru = comp_u cL in\n let raL = elab_term (comp_res cL) in\n let raR = elab_term (comp_res cR) in\n let rpreL = elab_term (comp_pre cL) in\n let rpostL = elab_term (comp_post cL) in\n let rpreR = elab_term (comp_pre cR) in\n let rpostR = elab_term (comp_post cR) in\n let reL = elab_st_typing eL_typing in\n let reR = elab_st_typing eR_typing in\n mk_par ru\n raL\n raR\n rpreL\n (mk_abs raL R.Q_Explicit rpostL)\n rpreR\n (mk_abs raR R.Q_Explicit rpostR)\n reL reR\n\n\t\t\t\t| T_Rewrite _ p q _ _ ->\n\t\t\t\t let rp = elab_term p in\n\t\t\t\t\t\tlet rq = elab_term q in\n\t\t\t\t\t\tmk_rewrite rp rq\n\n | T_WithLocal _ _ init _ init_t c x _ _ _ body_typing ->\n let rret_u = comp_u c in\n let ra = elab_term init_t in\n let rinit = elab_term init in\n let rret_t = elab_term (comp_res c) in\n let rpre = elab_term (comp_pre c) in\n let rpost = mk_abs rret_t R.Q_Explicit (elab_term (comp_post c)) in\n let rbody = elab_st_typing body_typing in\n let rbody = RT.close_term rbody x in\n let rbody = mk_abs (mk_ref ra) R.Q_Explicit rbody in\n mk_withlocal rret_u ra rinit rpre rret_t rpost rbody\n\n | T_WithLocalArray _ _ init len _ init_t c x _ _ _ _ body_typing ->\n let rret_u = comp_u c in\n let ra = elab_term init_t in\n let rinit = elab_term init in\n let rlen = elab_term len in\n let rret_t = elab_term (comp_res c) in\n let rpre = elab_term (comp_pre c) in\n let rpost = mk_abs rret_t R.Q_Explicit (elab_term (comp_post c)) in\n let rbody = elab_st_typing body_typing in\n let rbody = RT.close_term rbody x in\n let rbody = mk_abs (mk_array ra) R.Q_Explicit rbody in\n mk_withlocalarray rret_u ra rinit rlen rpre rret_t rpost rbody\n\n | T_Admit _ {u;res;pre;post} c _ ->\n let ru = u in\n let rres = elab_term res in\n let rpre = elab_term pre in\n let rpost = elab_term post in\n let rpost = mk_abs rres R.Q_Explicit rpost in\n (match c with\n | STT -> mk_stt_admit ru rres rpre rpost\n | STT_Atomic -> mk_stt_atomic_admit ru rres rpre rpost\n | STT_Ghost -> mk_stt_ghost_admit ru rres rpre rpost)\n\n | T_Unreachable _ _ _ _ _ ->\n `(\"IOU: elab_st_typing of T_Unreachable\")\n\n | T_WithInv _ _ _ _ _ _ _ _ _ ->\n `(\"IOU: elab_st_typing of T_WithInv\")\n\nand elab_br (#g:env)\n (#c:comp_st)\n (#sc_u:universe) (#sc_ty:typ) (#sc:term)\n (#p:pattern)\n (#e:st_term)\n (d : br_typing g sc_u sc_ty sc p e c)\n : Tot R.branch (decreases d)\n = let TBR _ _ _ _ _ _ _ _ bs _ _ _ ed = d in\n let e = elab_st_typing ed in\n (elab_pat p, e)\nand elab_branches (#g:env)\n (#c:comp_st)\n (#sc_u:universe) (#sc_ty:typ) (#sc:term)\n (#brs:list branch)\n (d : brs_typing g sc_u sc_ty sc brs c)\n : Tot (list R.branch)\n (decreases d)\n = match d with\n | TBRS_0 _ -> []\n | TBRS_1 _ p e bd _ d' ->\n elab_br bd :: elab_branches d'", "val deep_apply_subst_in_pattern : env -> pattern -> list (bv & term) -> Tac (pattern & list (bv & term))\nlet rec deep_apply_subst e t subst =\n match inspect t with\n | Tv_Var b ->\n begin match bind_map_get subst b with\n | None -> t\n | Some t' -> t'\n end\n | Tv_BVar b ->\n (* Note: Tv_BVar shouldn't happen *)\n begin match bind_map_get subst b with\n | None -> t\n | Some t' -> t'\n end\n | Tv_FVar _ -> t\n | Tv_App hd (a,qual) ->\n let hd = deep_apply_subst e hd subst in\n let a = deep_apply_subst e a subst in\n pack (Tv_App hd (a, qual))\n | Tv_Abs br body ->\n let body = deep_apply_subst e body subst in\n pack (Tv_Abs br body)\n | Tv_Arrow br c ->\n let br, subst = deep_apply_subst_in_binder e br subst in\n let c = deep_apply_subst_in_comp e c subst in\n pack (Tv_Arrow br c)\n | Tv_Type _ -> t\n | Tv_Refine bv sort ref ->\n let sort = deep_apply_subst e sort subst in\n let bv, subst = deep_apply_subst_in_bv e bv subst in\n let ref = deep_apply_subst e ref subst in\n pack (Tv_Refine bv sort ref)\n | Tv_Const _ -> t\n | Tv_Uvar _ _ -> t\n | Tv_Let recf attrs bv ty def body ->\n (* No need to substitute in the attributes - that we filter for safety *)\n let ty = deep_apply_subst e ty subst in\n let def = deep_apply_subst e def subst in\n let bv, subst = deep_apply_subst_in_bv e bv subst in\n let body = deep_apply_subst e body subst in\n pack (Tv_Let recf [] bv ty def body)\n | Tv_Match scrutinee ret_opt branches -> (* TODO: type of pattern variables *)\n let scrutinee = deep_apply_subst e scrutinee subst in\n let ret_opt = map_opt (fun (b, asc) ->\n let b, subst = deep_apply_subst_in_binder e b subst in\n let asc =\n match asc with\n | Inl t, tacopt, use_eq ->\n Inl (deep_apply_subst e t subst),\n map_opt (fun tac -> deep_apply_subst e tac subst) tacopt,\n use_eq\n | Inr c, tacopt, use_eq ->\n Inr (deep_apply_subst_in_comp e c subst),\n map_opt (fun tac -> deep_apply_subst e tac subst) tacopt,\n use_eq in\n b, asc) ret_opt in\n (* For the branches: we don't need to explore the patterns *)\n let deep_apply_subst_in_branch branch =\n let pat, tm = branch in\n let pat, subst = deep_apply_subst_in_pattern e pat subst in\n let tm = deep_apply_subst e tm subst in\n pat, tm\n in\n let branches = map deep_apply_subst_in_branch branches in\n pack (Tv_Match scrutinee ret_opt branches)\n | Tv_AscribedT exp ty tac use_eq ->\n let exp = deep_apply_subst e exp subst in\n let ty = deep_apply_subst e ty subst in\n (* no need to apply it on the tactic - that we filter for safety *)\n pack (Tv_AscribedT exp ty None use_eq)\n | Tv_AscribedC exp c tac use_eq ->\n let exp = deep_apply_subst e exp subst in\n let c = deep_apply_subst_in_comp e c subst in\n (* no need to apply it on the tactic - that we filter for safety *)\n pack (Tv_AscribedC exp c None use_eq)\n | _ ->\n (* Unknown *)\n t\n\nand deep_apply_subst_in_bv e bv subst =\n (* No substitution needs to happen for variables\n (there is no longer a sort). But, shift the substitution. *)\n bv, (bv, pack (Tv_Var bv))::subst\n\n(*\n * AR: TODO: should apply subst in attrs?\n *)\nand deep_apply_subst_in_binder e br subst =\n let open inspect_binder br <: binder_view in\n let binder_sort = deep_apply_subst e binder_sort subst in\n let binder_bv, subst = deep_apply_subst_in_bv e binder_bv subst in\n pack_binder {\n binder_bv=binder_bv;\n binder_qual=binder_qual;\n binder_attrs=binder_attrs;\n binder_sort=binder_sort;\n }, subst\n\nand deep_apply_subst_in_comp e c subst =\n let subst = (fun x -> deep_apply_subst e x subst) in\n let subst_in_aqualv a : Tac aqualv =\n match a with\n | Q_Implicit\n | Q_Explicit -> a\n | Q_Meta t -> Q_Meta (subst t)\n in\n match inspect_comp c with\n | C_Total ret ->\n let ret = subst ret in\n pack_comp (C_Total ret)\n | C_GTotal ret ->\n let ret = subst ret in\n pack_comp (C_GTotal ret)\n | C_Lemma pre post patterns ->\n let pre = subst pre in\n let post = subst post in\n let patterns = subst patterns in\n pack_comp (C_Lemma pre post patterns)\n | C_Eff us eff_name result eff_args decrs ->\n let result = subst result in\n let eff_args = map (fun (x, a) -> (subst x, subst_in_aqualv a)) eff_args in\n let decrs = map subst decrs in\n pack_comp (C_Eff us eff_name result eff_args decrs)\n\nand deep_apply_subst_in_pattern e pat subst =\n match pat with\n | Pat_Constant _ -> pat, subst\n | Pat_Cons fv us patterns ->\n (* The types of the variables in the patterns should be independent of each\n * other: we use fold_left only to incrementally update the substitution *)\n let patterns, subst =\n fold_right (fun (pat, b) (pats, subst) ->\n let pat, subst = deep_apply_subst_in_pattern e pat subst in\n ((pat, b) :: pats, subst)) patterns ([], subst)\n in\n Pat_Cons fv us patterns, subst\n | Pat_Var bv st ->\n let st = Sealed.seal (deep_apply_subst e (unseal st) subst) in\n let bv, subst = deep_apply_subst_in_bv e bv subst in\n Pat_Var bv st, subst\n | Pat_Dot_Term eopt ->\n Pat_Dot_Term (map_opt (fun t -> deep_apply_subst e t subst) eopt), subst", "val tred_tequiv : #s:typ -> #t:typ -> h:(tred s t) ->\n Tot (tequiv s t) (decreases h)\nlet rec tred_tequiv #s #t h =\n match h with\n | TrRefl _ -> EqRefl s\n | TrArr h1 h2 -> EqArr (tred_tequiv h1) (tred_tequiv h2)\n | TrLam k h1 -> EqLam k (tred_tequiv h1)\n | TrApp h1 h2 -> EqApp (tred_tequiv h1) (tred_tequiv h2)\n | TrBeta #t1 #t2 #t1' #t2' k h1 h2 ->\n EqTran (EqApp (EqLam k (tred_tequiv h1)) (tred_tequiv h2))\n (EqBeta k t1' t2')", "val collect_arr' (bs: list binder) (c: comp) : Tot (list binder * comp) (decreases c)\nlet rec collect_arr' (bs : list binder) (c : comp) : Tot (list binder * comp) (decreases c) =\n begin match inspect_comp c with\n | C_Total t ->\n begin match inspect_ln_unascribe t with\n | Tv_Arrow b c ->\n collect_arr' (b::bs) c\n | _ ->\n (bs, c)\n end\n | _ -> (bs, c)\n end", "val collect_arr' (bs: list binder) (c: comp) : Tot (list binder * comp) (decreases c)\nlet rec collect_arr' (bs : list binder) (c : comp) : Tot (list binder * comp) (decreases c) =\n begin match inspect_comp c with\n | C_Total t ->\n begin match inspect_ln_unascribe t with\n | Tv_Arrow b c ->\n collect_arr' (b::bs) c\n | _ ->\n (bs, c)\n end\n | _ -> (bs, c)\n end", "val preservation : #e:exp -> #e':exp -> #g:env -> #t:typ ->\n ht:(typing g e t) ->\n hs:step e e' ->\n Tot (typing g e' t) (decreases ht)\nlet rec preservation #e #e' #g #t (TyApp h1 h2) hs =\n match hs with\n | SBeta tx e1' e2' -> substitution_beta h2 (TyLam?.hbody h1)\n | SApp1 e2' hs1 -> TyApp (preservation h1 hs1) h2\n | SApp2 e1' hs2 -> TyApp h1 (preservation h2 hs2)", "val tsubst_extensional: s1:tsub -> s2:tsub{feq s1 s2} -> t:typ ->\n Lemma (requires True) (ensures (tsubst s1 t = tsubst s2 t))\n\t\t\t (decreases t)\nlet rec tsubst_extensional s1 s2 t =\n match t with\n | TVar _ -> ()\n | TLam k t1 -> \n let open FStar.Tactics in\n assert (tsubst s1 (TLam k t1) == TLam k (tsubst (tsub_lam s1) t1))\n by norm [zeta; iota; delta_only [`%tsubst]];\n assert (tsubst s2 (TLam k t1) == TLam k (tsubst (tsub_lam s2) t1))\n by norm [zeta; iota; delta_only [`%tsubst]];\n tsubst_extensional (tsub_lam s1) (tsub_lam s2) t1\n | TArr t1 t2 -> tsubst_extensional s1 s2 t1; tsubst_extensional s1 s2 t2\n | TApp t1 t2 -> tsubst_extensional s1 s2 t1; tsubst_extensional s1 s2 t2", "val subst_binder_in_comp : env -> binder -> term -> comp -> Tac comp\nlet subst_binder_in_comp e b t c =\n subst_bv_in_comp e (bv_of_binder b) (binder_sort b) t c", "val reduce_aux (#a #b: Type) (b0: b) (f: (a -> b -> b)) (s: seq a) : Tot b (decreases (length s))\nlet rec reduce_aux (#a:Type) (#b:Type) (b0: b) (f: a -> b -> b) (s: seq a):\n Tot b (decreases (length s)) =\n let n = length s in\n if n = 0 then b0\n else\n let s' = prefix s (n - 1) in\n let b' = reduce_aux b0 f s' in\n let e = index s (n - 1) in\n f e b'", "val visit_br (ff: (term -> Tac term)) (b: branch) : Tac branch\nlet rec visit_tm (ff : term -> Tac term) (t : term) : Tac term =\n let tv = inspect_ln t in\n let tv' =\n match tv with\n | Tv_FVar _\n | Tv_Var _\n | Tv_BVar _\n | Tv_UInst _ _ -> tv\n\n | Tv_Type u -> Tv_Type u\n | Tv_Const c -> Tv_Const c\n | Tv_Uvar i u -> Tv_Uvar i u\n | Tv_Unknown -> Tv_Unknown\n | Tv_Unsupp -> Tv_Unsupp\n | Tv_Arrow b c ->\n let b = on_sort_binder (visit_tm ff) b in\n let c = visit_comp ff c in\n Tv_Arrow b c\n | Tv_Abs b t ->\n let b = on_sort_binder (visit_tm ff) b in\n let t = visit_tm ff t in\n Tv_Abs b t\n | Tv_App l (r, q) ->\n let l = visit_tm ff l in\n let r = visit_tm ff r in\n Tv_App l (r, q)\n | Tv_Refine b r ->\n let b = on_sort_simple_binder (visit_tm ff) b in\n let r = visit_tm ff r in\n Tv_Refine b r\n | Tv_Let r attrs b def t ->\n let b = on_sort_simple_binder (visit_tm ff) b in\n let def = visit_tm ff def in\n let t = visit_tm ff t in\n Tv_Let r attrs b def t\n | Tv_Match sc ret_opt brs ->\n let sc = visit_tm ff sc in\n let ret_opt = map_opt (fun (b, asc) ->\n let b = on_sort_binder (visit_tm ff) b in\n let asc =\n match asc with\n | Inl t, tacopt, use_eq ->\n Inl (visit_tm ff t), map_opt (visit_tm ff) tacopt, use_eq\n | Inr c, tacopt, use_eq->\n Inr (visit_comp ff c), map_opt (visit_tm ff) tacopt, use_eq in\n b, asc) ret_opt in\n let brs = map (visit_br ff) brs in\n Tv_Match sc ret_opt brs\n | Tv_AscribedT e t topt use_eq ->\n let e = visit_tm ff e in\n let t = visit_tm ff t in\n Tv_AscribedT e t topt use_eq\n | Tv_AscribedC e c topt use_eq ->\n let e = visit_tm ff e in\n let c = visit_comp ff c in\n Tv_AscribedC e c topt use_eq\n in\n ff (pack_ln tv')\nand visit_br (ff : term -> Tac term) (b:branch) : Tac branch =\n let (p, t) = b in\n let p = visit_pat ff p in\n let t = visit_tm ff t in\n (p, t)\nand visit_pat (ff : term -> Tac term) (p:pattern) : Tac pattern =\n match p with\n | Pat_Constant _ -> p\n | Pat_Var v s -> Pat_Var v s\n | Pat_Cons head univs subpats ->\n let subpats = (map (fun(p,b) -> (visit_pat ff p, b)) subpats) in\n Pat_Cons head univs subpats\n | Pat_Dot_Term t ->\n let t = map_opt (visit_tm ff) t in\n Pat_Dot_Term t\n\nand visit_comp (ff : term -> Tac term) (c : comp) : Tac comp =\n let cv = inspect_comp c in\n let cv' =\n match cv with\n | C_Total ret ->\n let ret = visit_tm ff ret in\n C_Total ret\n\n | C_GTotal ret ->\n let ret = visit_tm ff ret in\n C_GTotal ret\n\n | C_Lemma pre post pats ->\n let pre = visit_tm ff pre in\n let post = visit_tm ff post in\n let pats = visit_tm ff pats in\n C_Lemma pre post pats\n\n | C_Eff us eff res args decrs ->\n let res = visit_tm ff res in\n let args = map (fun (a, q) -> (visit_tm ff a, q)) args in\n let decrs = map (visit_tm ff) decrs in\n C_Eff us eff res args decrs\n in\n pack_comp cv'", "val subst_r_binders (s: subst_t) (bs: list R.binder) : list R.binder\nlet subst_r_binders (s:subst_t) (bs : list R.binder) : list R.binder =\n List.Tot.mapi (fun i b -> r_subst_binder_sort (shift_subst i s) b) bs", "val binder_offset_pattern_invariant (p:pattern) (ss:subst)\n : Lemma (binder_offset_pattern p == binder_offset_pattern (subst_pattern p ss))\nlet rec binder_offset_pattern_invariant (p:pattern) (ss:subst)\n : Lemma (ensures binder_offset_pattern p ==\n binder_offset_pattern (subst_pattern p ss))\n (decreases p)\n = match p with\n | Pat_Cons _ _ pats ->\n binder_offset_patterns_invariant pats ss\n | _ -> ()\n\nand binder_offset_patterns_invariant (p:list (pattern & bool)) (ss:subst)\n : Lemma (ensures binder_offset_patterns p ==\n binder_offset_patterns (subst_patterns p ss))\n (decreases p)\n = match p with\n | [] -> ()\n | (hd, _)::tl ->\n binder_offset_pattern_invariant hd ss;\n let n = binder_offset_pattern hd in\n binder_offset_patterns_invariant tl (shift_subst_n n ss)", "val insB : #h:nat -> x:int -> s:rbnode h Black -> Tot (hiddenTree h) (decreases s)\nlet rec ins #h #c x = function\n | Leaf -> V (R Leaf x Leaf)\n | B a y b ->\n (if x < y then\n match balanceLB (ins x a) y b with\n | HR r -> V r\n | HB b -> V b\n else if x = y then V (B a y b)\n else match balanceRB a y (ins x b) with\n | HR r -> V r\n | HB b -> V b)\n | R a y b ->\n (if x < y then balanceLR (insB x a) y b\n else if x = y then V (R a y b)\n else balanceRR a y (insB x b))\nand insB #h x = function\n | Leaf -> HR (R Leaf x Leaf )\n | B a y b ->\n if x < y then balanceLB (ins x a) y b\n else if x = y then HB (B a y b)\n else balanceRB a y (ins x b)", "val sub_mod_impl (a b: t) : t\nlet sub_mod_impl (a b: t) : t =\n let l = U64.sub_mod a.low b.low in\n { low = l;\n high = U64.sub_mod (U64.sub_mod a.high b.high) (carry a.low l); }", "val substitution_preserves_typing :\n x:var -> #e:exp -> #v:exp -> #t_x:typ -> #t:typ -> #g:env ->\n $h1:typing empty v t_x ->\n $h2:typing (extend_gen x t_x g) e t ->\n Tot (typing g (subst (sub_beta_gen x v) e) t) (decreases e)\nlet rec substitution_preserves_typing x #e #v #t_x #t #g h1 h2 =\n match h2 with\n | TyVar y ->\n if x=y then (typable_empty_closed h1;\n closed_appears_free v;\n context_invariance h1 g)\n else if y\n let h21' = typing_extensional h21 (extend_gen (x+1) t_x (extend t_y g)) in\n typable_empty_closed h1;\n subst_gen_elam x v t_y e';\n let h21' : (r:typing (extend_gen (x+1) t_x (extend t_y g)) e' t'{e' << e}) =\n h21' in\n TyLam t_y (substitution_preserves_typing (x+1) h1 h21')\n | TyApp #_ #e1 #e2 #t11 #t12 h21 h22 ->\n let h21 : (r:typing (extend_gen x t_x g) e1 (TArr t11 t12){e1 << e}) = h21 in\n let h22 : (r:typing (extend_gen x t_x g) e2 t11{e2 << e}) = h22 in\n (TyApp (substitution_preserves_typing x h1 h21)\n (substitution_preserves_typing x h1 h22))\n | TyUnit -> TyUnit", "val typing_substitution: #e:exp -> #v:exp -> #t_x:typ ->\n #t:typ -> #g:env ->\n h1:(typing g v t_x) ->\n h2:(typing (extend_evar g 0 t_x) e t) ->\n Tot (typing g (esubst_beta v e) t) (decreases %[e;h2])\nlet rec typing_substitution #e #v #t_x #t #g h1 h2 =\n let hs : subst_typing (esub_beta v) (extend_evar g 0 t_x) g =\n fun y hkind -> if y = 0 then h1\n else TyVar (y-1) (kinding_extensional hkind g) in\n substitution (esub_beta v) h2 hs", "val elab_st_sub (#g: env) (#c1 #c2: comp) (d_sub: st_sub g c1 c2)\n : Tot (t: R.term & RT.tot_typing (elab_env g) t (simple_arr (elab_comp c1) (elab_comp c2)))\nlet elab_st_sub (#g:env) (#c1 #c2 : comp)\n (d_sub : st_sub g c1 c2)\n : Tot (t:R.term\n & RT.tot_typing (elab_env g) t (simple_arr (elab_comp c1) (elab_comp c2)))\n= RU.magic_s \"elab_st_sub\"", "val trapp_tss_1 : #t1:typ -> t2:typ -> #t1':typ ->\n h:(tred_star_sym t1 t1') ->\n Tot (tred_star_sym (TApp t1 t2) (TApp t1' t2)) (decreases h)\nlet rec trapp_tss_1 #t1 t2 #t1' h =\n match h with\n | TssBase h1 -> TssBase (TrApp h1 (TrRefl t2))\n | TssSym h1 -> TssSym (trapp_tss_1 t2 h1)\n | TssTran h1 h2 -> TssTran (trapp_tss_1 t2 h1) (trapp_tss_1 t2 h2)", "val decode' (t: trie) (bs: list bool) : Tot (option (list symbol)) (decreases (List.Tot.length bs))\nlet rec decode' (t:trie) (bs:list bool) : Tot (option (list symbol))\n (decreases (List.Tot.length bs)) =\n match t, bs with\n | Leaf _ s, [] -> Some [s] (* degenerate case, case omitted below *)\n | Leaf _ _, _::_ -> None (* too many symbols, case omitted below *)\n | Node _ _ _, [] -> Some []\n | Node _ _ _, _::_ -> match decode_one t bs with\n | Some (s, bs') -> (match decode' t bs' with\n | Some ss -> Some (s :: ss)\n | None -> None)\n | _ -> None", "val subst_out_expr (s: subst) (o: out_expr) : out_expr\nlet subst_out_expr (s:subst) (o:out_expr) : out_expr = o", "val bvsub (#n: pos) (a b: bv_t n) : Tot (bv_t n)\nlet bvsub #n a b =\n int2bv #n (U.sub_mod (bv2int #n a) (bv2int #n b))", "val be_to_n : b:bytes -> Tot nat (decreases (S.length b))\nlet rec be_to_n b =\n if S.length b = 0 then 0\n else U8.v (S.last b) + pow2 8 * be_to_n (S.slice b 0 (S.length b - 1))", "val subst1 (n: namedv) (t1 t2: term) : term\nlet subst1 (n:namedv) (t1:term) (t2:term) : term =\n subst_term [NT n t1] t2", "val nt_subst_comp (c: comp) (ss: nt_substs) : comp\nlet nt_subst_comp (c:comp) (ss:nt_substs) : comp =\n L.fold_left (fun c elt -> subst_comp c [elt]) c ss", "val fold_left_dec (#a #b: _) (acc: a) (l: list b) (f: (a -> x: b{x << l} -> a))\n : Tot a (decreases l)\nlet rec fold_left_dec #a #b\n (acc : a)\n (l : list b)\n (f : a -> (x:b{x << l}) -> a)\n : Tot a (decreases l)\n =\n match l with\n | [] -> acc\n | x::xs -> fold_left_dec (f acc x) xs f", "val ln'_binder (b: binder) (n: int) : Tot bool (decreases b)\nlet rec ln' (e:term) (n:int)\n : Tot bool (decreases e)\n = match inspect_ln e with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unknown \n | Tv_Unsupp\n | Tv_Var _ -> true\n | Tv_BVar m -> bv_index m <= n\n | Tv_App e1 (e2, _) -> ln' e1 n && ln' e2 n\n | Tv_Abs b body -> \n ln'_binder b n &&\n ln' body (n + 1)\n\n | Tv_Arrow b c ->\n ln'_binder b n &&\n ln'_comp c (n + 1)\n\n | Tv_Refine b f ->\n ln'_binder b n &&\n ln' f (n + 1)\n\n | Tv_Uvar _ _ ->\n false\n \n | Tv_Let recf attrs b def body ->\n ln'_terms attrs n &&\n ln'_binder b n &&\n (if recf then ln' def (n + 1) else ln' def n) &&\n ln' body (n + 1)\n\n | Tv_Match scr ret brs ->\n ln' scr n &&\n (match ret with\n | None -> true\n | Some m -> ln'_match_returns m n) &&\n ln'_branches brs n\n \n | Tv_AscribedT e t tac b ->\n ln' e n &&\n ln' t n &&\n (match tac with\n | None -> true\n | Some tac -> ln' tac n)\n \n | Tv_AscribedC e c tac b ->\n ln' e n &&\n ln'_comp c n &&\n (match tac with\n | None -> true\n | Some tac -> ln' tac n)\n \nand ln'_comp (c:comp) (i:int)\n : Tot bool (decreases c)\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t -> ln' t i\n\n | C_Lemma pre post pats ->\n ln' pre i &&\n ln' post i &&\n ln' pats i\n\n | C_Eff us eff_name res args decrs ->\n ln' res i &&\n ln'_args args i &&\n ln'_terms decrs i\n\nand ln'_args (ts:list argv) (i:int)\n : Tot bool (decreases ts)\n = match ts with\n | [] -> true\n | (t,q)::ts -> \n ln' t i &&\n ln'_args ts i\n\nand ln'_binder (b:binder) (n:int)\n : Tot bool (decreases b)\n = let bndr = inspect_binder b in\n ln' bndr.sort n &&\n ln'_terms bndr.attrs n\n\nand ln'_terms (ts:list term) (n:int)\n : Tot bool (decreases ts)\n = match ts with\n | [] -> true\n | t::ts -> ln' t n && ln'_terms ts n\n\nand ln'_patterns (ps:list (pattern & bool)) (i:int)\n : Tot bool\n (decreases ps)\n = match ps with\n | [] -> true\n | (p, b)::ps ->\n let b0 = ln'_pattern p i in\n let n = binder_offset_pattern p in\n let b1 = ln'_patterns ps (i + n) in\n b0 && b1\n\nand ln'_pattern (p:pattern) (i:int) \n : Tot bool\n (decreases p)\n = match p with\n | Pat_Constant _ -> true\n\n | Pat_Cons head univs subpats ->\n ln'_patterns subpats i\n \n | Pat_Var bv s -> true\n\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> true\n | Some t -> ln' t i)\n \nand ln'_branch (br:branch) (i:int)\n : Tot bool (decreases br)\n = let p, t = br in\n let b = ln'_pattern p i in\n let j = binder_offset_pattern p in\n let b' = ln' t (i + j) in\n b&&b'\n \nand ln'_branches (brs:list branch) (i:int)\n : Tot bool (decreases brs)\n = match brs with\n | [] -> true\n | br::brs -> \n ln'_branch br i &&\n ln'_branches brs i\n \nand ln'_match_returns (m:match_returns_ascription) (i:int)\n : Tot bool (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = ln'_binder b i in\n let ret =\n match ret with\n | Inl t -> ln' t (i + 1)\n | Inr c -> ln'_comp c (i + 1)\n in\n let as_ =\n match as_ with\n | None -> true\n | Some t -> ln' t (i + 1)\n in\n b && ret && as_", "val tprogDenote (#ts #ts': _) (p: tprog ts ts') (s: vstack ts) : Tot (vstack ts') (decreases p)\nlet rec tprogDenote #ts #ts' (p : tprog ts ts') (s:vstack ts) :\n Tot (vstack ts') (decreases p) =\n match p with\n | TNil -> s\n | TCons i p' -> tprogDenote p' (tinstrDenote i s)", "val r_subst_binder_sort (s: subst_t) (b: R.binder) : R.binder\nlet r_subst_binder_sort (s : subst_t) (b : R.binder) : R.binder =\n let v = inspect_binder b in\n let v = { v with sort = subst_term s v.sort } in\n pack_binder v", "val freevars_pattern (p: pattern) : Tot (Set.set var) (decreases p)\nlet rec freevars (e:term)\n : FStar.Set.set var\n = match inspect_ln e with\n | Tv_Uvar _ _ -> Set.complement Set.empty\n \n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unknown \n | Tv_Unsupp\n | Tv_BVar _ -> Set.empty\n\n | Tv_Var x -> Set.singleton (namedv_uniq x)\n \n | Tv_App e1 (e2, _) ->\n Set.union (freevars e1) (freevars e2)\n\n | Tv_Abs b body -> \n Set.union (freevars_binder b) (freevars body)\n\n | Tv_Arrow b c ->\n Set.union (freevars_binder b) (freevars_comp c)\n\n | Tv_Refine b f ->\n freevars (binder_sort b) `Set.union`\n freevars f\n \n | Tv_Let recf attrs b def body ->\n freevars_terms attrs `Set.union`\n freevars (binder_sort b) `Set.union`\n freevars def `Set.union`\n freevars body\n\n | Tv_Match scr ret brs ->\n freevars scr `Set.union`\n freevars_opt ret freevars_match_returns `Set.union`\n freevars_branches brs\n\n | Tv_AscribedT e t tac b ->\n freevars e `Set.union`\n freevars t `Set.union`\n freevars_opt tac freevars\n \n | Tv_AscribedC e c tac b ->\n freevars e `Set.union`\n freevars_comp c `Set.union`\n freevars_opt tac freevars\n\nand freevars_opt (#a:Type0) (o:option a) (f: (x:a { x << o } -> FStar.Set.set var))\n : FStar.Set.set var\n = match o with\n | None -> Set.empty\n | Some x -> f x\n\nand freevars_comp (c:comp)\n : FStar.Set.set var\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t ->\n freevars t\n\n | C_Lemma pre post pats ->\n freevars pre `Set.union`\n freevars post `Set.union`\n freevars pats\n\n | C_Eff us eff_name res args decrs ->\n freevars res `Set.union`\n freevars_args args `Set.union`\n freevars_terms decrs\n\nand freevars_args (ts:list argv)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | (t,q)::ts ->\n freevars t `Set.union`\n freevars_args ts\n\nand freevars_terms (ts:list term)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | t::ts ->\n freevars t `Set.union`\n freevars_terms ts\n \nand freevars_binder (b:binder)\n : Tot (Set.set var) (decreases b)\n = let bndr = inspect_binder b in\n freevars bndr.sort `Set.union`\n freevars_terms bndr.attrs \n\nand freevars_pattern (p:pattern) \n : Tot (Set.set var) (decreases p)\n = match p with\n | Pat_Constant _ ->\n Set.empty\n\n | Pat_Cons head univs subpats ->\n freevars_patterns subpats\n \n | Pat_Var bv s -> Set.empty\n\n | Pat_Dot_Term topt ->\n freevars_opt topt freevars\n\nand freevars_patterns (ps:list (pattern & bool))\n : Tot (Set.set var) (decreases ps)\n = match ps with\n | [] -> Set.empty\n | (p, b)::ps ->\n freevars_pattern p `Set.union`\n freevars_patterns ps\n\nand freevars_branch (br:branch)\n : Tot (Set.set var) (decreases br)\n = let p, t = br in\n freevars_pattern p `Set.union`\n freevars t\n\nand freevars_branches (brs:list branch)\n : Tot (Set.set var) (decreases brs)\n = match brs with\n | [] -> Set.empty\n | hd::tl -> freevars_branch hd `Set.union` freevars_branches tl\n \nand freevars_match_returns (m:match_returns_ascription)\n : Tot (Set.set var) (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = freevars_binder b in\n let ret =\n match ret with\n | Inl t -> freevars t\n | Inr c -> freevars_comp c\n in\n let as_ = freevars_opt as_ freevars in\n b `Set.union` ret `Set.union` as_", "val binder_offset_patterns_invariant (p:list (pattern & bool)) (ss:subst)\n : Lemma (binder_offset_patterns p == binder_offset_patterns (subst_patterns p ss))\nlet rec binder_offset_pattern_invariant (p:pattern) (ss:subst)\n : Lemma (ensures binder_offset_pattern p ==\n binder_offset_pattern (subst_pattern p ss))\n (decreases p)\n = match p with\n | Pat_Cons _ _ pats ->\n binder_offset_patterns_invariant pats ss\n | _ -> ()\n\nand binder_offset_patterns_invariant (p:list (pattern & bool)) (ss:subst)\n : Lemma (ensures binder_offset_patterns p ==\n binder_offset_patterns (subst_patterns p ss))\n (decreases p)\n = match p with\n | [] -> ()\n | (hd, _)::tl ->\n binder_offset_pattern_invariant hd ss;\n let n = binder_offset_pattern hd in\n binder_offset_patterns_invariant tl (shift_subst_n n ss)", "val open_pat (p: R.pattern) (s: subst_t) : Tac (pattern & subst_t)\nlet rec open_pat (p : R.pattern) (s : subst_t) : Tac (pattern & subst_t) =\n match p with\n | R.Pat_Constant c ->\n Pat_Constant {c=c}, s\n\n | R.Pat_Var ssort n ->\n let sort = unseal ssort in\n let sort = subst_term s sort in\n let nvv : namedv = {\n uniq = fresh();\n sort = seal sort;\n ppname = n;\n }\n in\n let nv = pack_namedv nvv in\n Pat_Var {v=nvv; sort=seal sort}, (DB 0 nv) :: shift_subst 1 s\n\n | R.Pat_Cons head univs subpats ->\n let subpats, s = fold_left (fun (pats,s) (pat,b) ->\n let pat, s' = open_pat pat s in\n ((pat,b)::pats, s'))\n ([], s) subpats\n in\n let subpats = List.Tot.rev subpats in\n Pat_Cons {head=head; univs=univs; subpats=subpats}, s\n\n | R.Pat_Dot_Term None ->\n Pat_Dot_Term {t=None}, s\n\n | R.Pat_Dot_Term (Some t) ->\n let t = subst_term s t in\n Pat_Dot_Term {t=Some t}, s", "val soundness\n (#sg: stlc_env)\n (#se: stlc_exp)\n (#st: stlc_ty)\n (dd: stlc_typing sg se st)\n (g: RT.fstar_top_env)\n : GTot (RT.tot_typing (extend_env_l g sg) (elab_exp se) (elab_ty st)) (decreases dd)\nlet rec soundness (#sg:stlc_env) \n (#se:stlc_exp)\n (#st:stlc_ty)\n (dd:stlc_typing sg se st)\n (g:RT.fstar_top_env)\n : GTot (RT.tot_typing (extend_env_l g sg)\n (elab_exp se)\n (elab_ty st))\n (decreases dd)\n = match dd with\n | T_Unit _ ->\n RT.T_Const _ _ _ RT.CT_Unit\n\n | T_Var _ x ->\n RT.T_Var _ (R.pack_namedv (RT.make_namedv x))\n\n | T_Lam _ t e t' x de ->\n let de : RT.tot_typing (extend_env_l g ((x,t)::sg))\n (elab_exp (open_exp e x))\n (elab_ty t')\n = soundness de g \n in \n let de : RT.tot_typing (RT.extend_env (extend_env_l g sg) x (elab_ty t))\n (elab_exp (open_exp e x))\n (elab_ty t')\n = de\n in\n fresh_is_fresh sg;\n elab_exp_freevars e;\n let dd\n = RT.T_Abs (extend_env_l g sg)\n x\n (elab_ty t) \n (elab_exp e)\n (T.E_Total, elab_ty t')\n _\n RT.pp_name_default\n R.Q_Explicit\n _\n (elab_ty_soundness g sg t)\n de\n in\n dd\n | T_App _ e1 e2 t t' d1 d2 ->\n let dt1 \n : RT.tot_typing (extend_env_l g sg)\n (elab_exp e1)\n (elab_ty (TArrow t t'))\n = soundness d1 g\n in\n let dt2\n : RT.tot_typing (extend_env_l g sg)\n (elab_exp e2)\n (elab_ty t)\n = soundness d2 g\n in\n let dt :\n RT.tot_typing (extend_env_l g sg)\n (elab_exp (EApp e1 e2))\n (RT.open_with (elab_ty t') (elab_exp e2))\n = RT.T_App _ _ _ _ _ _ dt1 dt2\n in\n dt", "val tcompile (#t: _) (e: texp t) (ts: tstack) : Tot (tprog ts (t :: ts)) (decreases e)\nlet rec tcompile #t (e : texp t) (ts : tstack) : Tot (tprog ts (t :: ts)) (decreases e) =\n match e with\n | TNConst n -> TCons (TiNConst _ n) TNil\n | TBConst b -> TCons (TiBConst _ b) TNil\n | TBinop #t1 #t2 #t b e1 e2 ->\n tconcat (tcompile e2 _)\n (tconcat (tcompile e1 _) (TCons (TiBinop b) TNil))", "val close_branch_with_not_free_var (br: R.branch) (x: var) (i: nat)\n : Lemma (requires ~(Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ND x i] == br)\n (decreases br)\nlet rec close_with_not_free_var (t:R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars t)))\n (ensures subst_term t [ ND x i ] == t)\n (decreases t) =\n\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_UInst _ _ -> ()\n | Tv_App hd (arg, _) ->\n close_with_not_free_var hd x i;\n close_with_not_free_var arg x i\n | Tv_Abs b body ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var body x (i + 1)\n | Tv_Arrow b c ->\n close_binder_with_not_free_var b x i;\n close_comp_with_not_free_var c x (i + 1)\n | Tv_Type _ -> ()\n | Tv_Refine b t ->\n close_binder_with_not_free_var b x i;\n close_with_not_free_var t x (i + 1)\n | Tv_Const _ -> ()\n | Tv_Uvar _ _ -> assert False\n | Tv_Let recf attrs b e1 e2 ->\n close_terms_with_not_free_var attrs x i;\n close_binder_with_not_free_var b x i;\n (if recf then close_with_not_free_var e1 x (i + 1)\n else close_with_not_free_var e1 x i);\n close_with_not_free_var e2 x (i + 1)\n | Tv_Match scrutinee ret_opt brs ->\n close_with_not_free_var scrutinee x i;\n (match ret_opt with\n | None -> ()\n | Some ret -> close_match_returns_with_not_free_var ret x i);\n close_branches_with_not_free_var brs x i\n\n | Tv_AscribedT e t tacopt _ ->\n close_with_not_free_var e x i;\n close_with_not_free_var t x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_AscribedC e c tacopt _ ->\n close_with_not_free_var e x i;\n close_comp_with_not_free_var c x i;\n (match tacopt with\n | None -> ()\n | Some tac -> close_with_not_free_var tac x i)\n\n | Tv_Unknown -> ()\n | Tv_Unsupp -> ()\n\nand close_match_returns_with_not_free_var\n (r:match_returns_ascription)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_match_returns r)))\n (ensures subst_match_returns r [ ND x i ] == r)\n (decreases r) =\n\n let b, (ret, as_opt, _) = r in\n close_binder_with_not_free_var b x i;\n (match ret with\n | Inl t -> close_with_not_free_var t x (i + 1)\n | Inr c -> close_comp_with_not_free_var c x (i + 1));\n (match as_opt with\n | None -> ()\n | Some t -> close_with_not_free_var t x (i + 1))\n\nand close_branches_with_not_free_var\n (brs:list R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branches brs)))\n (ensures subst_branches brs [ ND x i ] == brs)\n (decreases brs) =\n\n match brs with\n | [] -> ()\n | hd::tl ->\n close_branch_with_not_free_var hd x i;\n close_branches_with_not_free_var tl x i\n\nand close_branch_with_not_free_var\n (br:R.branch)\n (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_branch br)))\n (ensures subst_branch br [ ND x i ] == br)\n (decreases br) =\n\n let p, t = br in\n close_pattern_with_not_free_var p x i;\n close_with_not_free_var t x (binder_offset_pattern p + i)\n \nand close_pattern_with_not_free_var (p:R.pattern) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_pattern p)))\n (ensures subst_pattern p [ ND x i ] == p)\n (decreases p) =\n\n match p with\n | Pat_Constant _ -> ()\n | Pat_Cons _ _ pats ->\n close_patterns_with_not_free_var pats x i\n | Pat_Var bv _ -> ()\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> ()\n | Some t -> close_with_not_free_var t x i)\n\nand close_patterns_with_not_free_var (l:list (R.pattern & bool)) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_patterns l)))\n (ensures subst_patterns l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (p, _)::tl ->\n close_pattern_with_not_free_var p x i;\n close_patterns_with_not_free_var tl x (binder_offset_pattern p + i)\n\nand close_terms_with_not_free_var (l:list R.term) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_terms l)))\n (ensures subst_terms l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | hd::tl ->\n close_with_not_free_var hd x i;\n close_terms_with_not_free_var tl x i\n\nand close_binder_with_not_free_var (b:R.binder) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_binder b)))\n (ensures subst_binder b [ ND x i ] == b)\n (decreases b) =\n\n let {attrs; sort} = inspect_binder b in\n close_with_not_free_var sort x i;\n close_terms_with_not_free_var attrs x i\n\nand close_comp_with_not_free_var (c:R.comp) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_comp c)))\n (ensures subst_comp c [ ND x i ] == c)\n (decreases c) =\n\n match inspect_comp c with\n | C_Total t\n | C_GTotal t -> close_with_not_free_var t x i\n | C_Lemma pre post pats ->\n close_with_not_free_var pre x i;\n close_with_not_free_var post x i;\n close_with_not_free_var pats x i\n | C_Eff _ _ t args decrs ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var args x i;\n close_terms_with_not_free_var decrs x i\n\nand close_args_with_not_free_var (l:list R.argv) (x:var) (i:nat)\n : Lemma\n (requires ~ (Set.mem x (freevars_args l)))\n (ensures subst_args l [ ND x i ] == l)\n (decreases l) =\n\n match l with\n | [] -> ()\n | (t, _)::tl ->\n close_with_not_free_var t x i;\n close_args_with_not_free_var tl x i", "val tred_star_tequiv : #s:typ -> #t:typ -> h:(tred_star s t) ->\n Tot (tequiv s t) (decreases h)\nlet rec tred_star_tequiv #s #t h = match h with\n | TsRefl _ -> EqRefl s\n | TsStep h1 h2 -> EqTran (tred_tequiv h1) (tred_star_tequiv h2)", "val tsubst_comp : s1:tsub -> s2:tsub -> t:typ -> Lemma\n (ensures (tsubst s1 (tsubst s2 t) = tsubst (tsub_comp s1 s2) t))\n (decreases %[is_tvar t;\n is_trenaming s1;\n is_trenaming s2;\n t])\nlet rec tsubst_comp s1 s2 t =\n match t with\n | TVar z -> ()\n | TApp t1 t2 -> tsubst_comp s1 s2 t1; tsubst_comp s1 s2 t2\n | TLam k tbody ->\n let tsub_lam_comp : x:var ->\n Lemma(tsub_lam (tsub_comp s1 s2) x =\n tsub_comp (tsub_lam s1) (tsub_lam s2) x) =\n fun x -> match x with\n | 0 -> ()\n | _ -> begin\n let ih1 = trenaming_sub_inc ();\n tsubst_comp tsub_inc s1 (s2 (x-1)) in\n let ext = forall_intro (tsub_comp_inc s1);\n tsubst_extensional (tsub_comp tsub_inc s1)\n (tsub_comp (tsub_lam s1) tsub_inc)\n (s2 (x-1)) in\n let ih2 = tsub_lam_renaming s1;\n trenaming_sub_inc ();\n tsubst_comp (tsub_lam s1) tsub_inc (s2 (x-1))\n in ()\n end\n in\n let hoist1 = tsub_lam_hoist k tbody s2 in\n let hoist2 = tsub_lam_hoist k (tsubst (tsub_lam s2) tbody) s1 in\n let h1 =\n tsub_lam_renaming s1;\n tsub_lam_renaming s2;\n tsubst_comp (tsub_lam s1) (tsub_lam s2) tbody in\n\n let h2 =\n forall_intro tsub_lam_comp;\n cut (feq (tsub_comp (tsub_lam s1) (tsub_lam s2))\n (tsub_lam (tsub_comp s1 s2))) in\n\n let ext = tsubst_extensional\n (tsub_comp (tsub_lam s1) (tsub_lam s2))\n (tsub_lam (tsub_comp s1 s2))\n tbody in\n\n tsub_lam_hoist k tbody (tsub_comp s1 s2)\n\n | TArr t1 t2 -> tsubst_comp s1 s2 t1; tsubst_comp s1 s2 t2", "val below : x:var -> e:exp -> Tot bool (decreases e)\nlet rec below x e =\n match e with\n | EVar y -> y < x\n | EApp e1 e2 -> below x e1 && below x e2\n | ELam _ e1 -> below (x+1) e1\n | EUnit -> true", "val trarr_tss_1 : #t1:typ -> t2:typ -> #t1':typ ->\n h:(tred_star_sym t1 t1') ->\n Tot (tred_star_sym (TArr t1 t2) (TArr t1' t2)) (decreases h)\nlet rec trarr_tss_1 #t1 t2 #t1' h =\n match h with\n | TssBase h1 -> TssBase (TrArr h1 (TrRefl t2))\n | TssSym h1 -> TssSym (trarr_tss_1 t2 h1)\n | TssTran h1 h2 -> TssTran (trarr_tss_1 t2 h1) (trarr_tss_1 t2 h2)", "val map_dec (#a #b: _) (l: list a) (f: (x: a{x << l} -> b)) : Tot (list b) (decreases l)\nlet rec map_dec #a #b\n (l : list a)\n (f : (x:a{x << l}) -> b)\n : Tot (list b) (decreases l)\n =\n match l with\n | [] -> []\n | x::xs -> f x :: map_dec xs f" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_branch" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_branches" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_pattern" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_term" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_binder" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_comp" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_patterns" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_terms" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_args" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_match_returns" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.subst_term" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.Core.fst", "name": "Pulse.Elaborate.Core.elab_br" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.Core.fst", "name": "Pulse.Elaborate.Core.elab_branches" }, { "project_name": "FStar", "file_name": "StlcCbvDbPntSubstNoLists.fst", "name": "StlcCbvDbPntSubstNoLists.subst_beta" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.subst_of_tred_tred" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.subst_of_tred" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Output.fst", "name": "FStar.InteractiveHelpers.Output._split_subst_at_bv" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.subst_below" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_db" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.freevars_branch" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fsti", "name": "Pulse.Checker.Prover.Substs.nt_subst_st_term" }, { "project_name": "FStar", "file_name": "ParSubst.fst", "name": "ParSubst.subst" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.subst_closed" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fst", "name": "Pulse.Syntax.Base.eq_branch" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.freevars_branches" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.ln'_branch" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.subst_binder_sort" }, { "project_name": "FStar", "file_name": "OPLSS2021.STLC.fst", "name": "OPLSS2021.STLC.subst" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.tss_tequiv" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fsti", "name": "Pulse.Checker.Prover.Substs.nt_subst_binder" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fsti", "name": "Pulse.Checker.Prover.Substs.nt_subst_term" }, { "project_name": "steel", "file_name": "Pulse.Recursion.fst", "name": "Pulse.Recursion.subst_binder_typ" }, { "project_name": "FStar", "file_name": "StlcStrongDbParSubst.fst", "name": "StlcStrongDbParSubst.substitution" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.subst_bv_in_comp" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.tequiv_tss" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.lsubst_term" }, { "project_name": "everparse", "file_name": "Target.fst", "name": "Target.subst_expr" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.substitution" }, { "project_name": "FStar", "file_name": "StlcStrongDbParSubst.fst", "name": "StlcStrongDbParSubst.substitution_beta" }, { "project_name": "everparse", "file_name": "Ast.fst", "name": "Ast.subst_decl'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.freevars_binder" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fsti", "name": "Pulse.Checker.Prover.Substs.nt_subst_st_comp" }, { "project_name": "FStar", "file_name": "FStar.Tactics.MkProjectors.fst", "name": "FStar.Tactics.MkProjectors.subst_map" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.elaborate_pat" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.subst_comp" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.shift_above_and_subst" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_var" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.close_branch" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.ln'_branches" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.elab_exp" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Compare.fst", "name": "FStar.Reflection.V2.Compare.compare_term" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Compare.fst", "name": "FStar.Reflection.V1.Compare.compare_term" }, { "project_name": "FStar", "file_name": "StlcStrongDbParSubst.fst", "name": "StlcStrongDbParSubst.subst" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fsti", "name": "Lib.NatMod.pow_mod_" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.lemma_vars_decrease" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fst", "name": "Pulse.Checker.Prover.Substs.ss_st_term" }, { "project_name": "everparse", "file_name": "Ast.fst", "name": "Ast.subst_typ" }, { "project_name": "everparse", "file_name": "Ast.fst", "name": "Ast.subst_decl" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.apply_term_ctxt" }, { "project_name": "FStar", "file_name": "StlcCbvDbPntSubstNoLists.fst", "name": "StlcCbvDbPntSubstNoLists.substitution_preserves_typing" }, { "project_name": "everparse", "file_name": "Z3TestGen.fst", "name": "Z3TestGen.typ_depth" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.Core.fst", "name": "Pulse.Elaborate.Core.elab_st_typing" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Base.fst", "name": "FStar.InteractiveHelpers.Base.deep_apply_subst_in_pattern" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.tred_tequiv" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Derived.fst", "name": "FStar.Reflection.V2.Derived.collect_arr'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Derived.fst", "name": "FStar.Reflection.V1.Derived.collect_arr'" }, { "project_name": "FStar", "file_name": "StlcStrongDbParSubst.fst", "name": "StlcStrongDbParSubst.preservation" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.tsubst_extensional" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.subst_binder_in_comp" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.reduce_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Visit.fst", "name": "FStar.Tactics.Visit.visit_br" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.subst_r_binders" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.binder_offset_pattern_invariant" }, { "project_name": "FStar", "file_name": "RBTreeIntrinsic.fst", "name": "RBTreeIntrinsic.insB" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fst", "name": "FStar.UInt128.sub_mod_impl" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.substitution_preserves_typing" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.typing_substitution" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.Core.fst", "name": "Pulse.Elaborate.Core.elab_st_sub" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.trapp_tss_1" }, { "project_name": "FStar", "file_name": "Huffman.fst", "name": "Huffman.decode'" }, { "project_name": "everparse", "file_name": "Ast.fst", "name": "Ast.subst_out_expr" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.bvsub" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.be_to_n" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Derived.fst", "name": "FStar.Reflection.V2.Derived.subst1" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fsti", "name": "Pulse.Checker.Prover.Substs.nt_subst_comp" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.fold_left_dec" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.ln'_binder" }, { "project_name": "FStar", "file_name": "StackMachine.fst", "name": "StackMachine.tprogDenote" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.r_subst_binder_sort" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.freevars_pattern" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.binder_offset_patterns_invariant" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_pat" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.soundness" }, { "project_name": "FStar", "file_name": "StackMachine.fst", "name": "StackMachine.tcompile" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_branch_with_not_free_var" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.tred_star_tequiv" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.tsubst_comp" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.below" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.trarr_tss_1" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.map_dec" } ], "selected_premises": [ "Pulse.Syntax.Naming.subst_pat", "Pulse.Syntax.Naming.subst_term", "Pulse.Syntax.Naming.subst_term_opt", "Pulse.Syntax.Naming.subst_term_list", "Pulse.Elaborate.Pure.elab_sub_pat", "Pulse.Syntax.Base.nvar", "Pulse.Syntax.Naming.subst_pat_args", "Pulse.Common.map_opt", "Pulse.Syntax.Base.host_term", "Pulse.Syntax.Naming.pattern_args_shift_n", "Pulse.Syntax.Pure.tm_uinst", "Pulse.Syntax.Base.as_fv", "Pulse.Syntax.Pure.tm_type", "Pulse.Syntax.Pure.tm_fvar", "Pulse.Syntax.Base.ppname_default", "Pulse.Elaborate.Pure.elab_term", "Pulse.Syntax.Base.index", "Pulse.Elaborate.Pure.elab_pat", "Pulse.Syntax.Pure.tm_constant", "Pulse.Syntax.Base.var", "Pulse.Elaborate.Pure.elab_qual", "FStar.Reflection.V2.Data.var", "Pulse.Syntax.Naming.subst_binder", "Pulse.Syntax.Pure.term_of_nvar", "Pulse.Syntax.Base.default_effect_hint", "Pulse.Syntax.Pure.tm_bvar", "Pulse.Syntax.Base.tm_unknown", "Pulse.Syntax.Naming.open_term'", "Pulse.Syntax.Base.range", "Pulse.Syntax.Base.as_effect_hint", "Pulse.Syntax.Pure.term_of_no_name_var", "Pulse.Syntax.Naming.freevars", "FStar.Heap.trivial_preorder", "Pulse.Syntax.Base.comp_st", "Pulse.Syntax.Naming.subst_ascription", "Pulse.Syntax.Naming.subst_st_comp", "Pulse.Reflection.Util.mk_arrow", "Pulse.Syntax.Base.term_range", "Pulse.Syntax.Naming.subst_term_pairs", "Pulse.Syntax.Base.tm_inv", "Pulse.Syntax.Base.with_range", "Pulse.Syntax.Base.comp_res", "Pulse.Syntax.Naming.open_term_opt'", "FStar.ST.op_Bang", "Pulse.Syntax.Pure.tm_pureapp", "Pulse.Syntax.Base.mk_ppname_no_range", "FStar.Reflection.Typing.blob", "Pulse.Reflection.Util.tot_lid", "Pulse.Syntax.Naming.subst_comp", "Pulse.Syntax.Base.as_binder", "FStar.Reflection.Typing.sort_default", "Pulse.Syntax.Base.tm_exists_sl", "Pulse.Reflection.Util.vprop_tm", "FStar.Pervasives.Native.fst", "Pulse.Syntax.Naming.ln_branch'", "FStar.Reflection.Typing.var_as_namedv", "Pulse.Syntax.Base.tm_emp", "Pulse.Syntax.Pure.tm_var", "Pulse.Syntax.Base.tm_fstar", "Pulse.Syntax.Pure.u_zero", "Pulse.Syntax.Base.comp_u", "Pulse.Syntax.Base.mk_ppname", "Pulse.Syntax.Naming.ln'", "Pulse.Syntax.Pure.u_var", "Pulse.Elaborate.Pure.elab_st_comp", "FStar.Reflection.Typing.subst_pattern", "Pulse.Syntax.Base.with_st_comp", "FStar.Pervasives.Native.snd", "FStar.Reflection.Typing.subst_binder", "FStar.Reflection.Typing.subst_patterns", "Pulse.Syntax.Base.tm_inames", "Pulse.Syntax.Pure.null_var", "Pulse.Syntax.Naming.pattern_shift_n", "FStar.Reflection.Typing.tm_type", "Pulse.Syntax.Base.tm_star", "Pulse.Common.assertby", "Pulse.Syntax.Base.empty_ascription", "Pulse.Syntax.Base.comp_pre", "Pulse.Syntax.Pure.leftmost_head", "FStar.Reflection.Typing.binder_offset_patterns", "Pulse.Syntax.Pure.mk_bvar", "Pulse.Syntax.Naming.ln_branches'", "FStar.Reflection.Typing.subst_term", "FStar.Reflection.Typing.subst_branches", "FStar.Reflection.Typing.subst_branch", "FStar.Reflection.Typing.subst_match_returns", "FStar.Reflection.Typing.pp_name_t", "Pulse.Reflection.Util.mk_pulse_lib_forall_lid", "Pulse.Syntax.Base.tm_vprop", "Pulse.Syntax.Pure.is_bvar", "Pulse.Reflection.Util.mk_pulse_lib_reference_lid", "Pulse.Syntax.Base.comp_inames", "Pulse.Reflection.Util.inv_disjointness_goal", "Pulse.Syntax.Naming.freevars_term_opt", "Pulse.Common.op_let_Question", "Pulse.Syntax.Pure.op_let_Question", "Pulse.Elaborate.Pure.op_let_Bang", "Pulse.Syntax.Base.tm_pure", "Pulse.Syntax.Naming.ln_ascription'", "Pulse.Syntax.Naming.close_term_pairs'" ], "source_upto_this": "(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Syntax.Naming\n\nopen FStar.List.Tot\nopen Pulse.Syntax.Base\nopen Pulse.Common\n\nmodule L = FStar.List.Tot\n\nmodule R = FStar.Reflection\nmodule RTB = FStar.Reflection.Typing.Builtins\nmodule RT = FStar.Reflection.Typing\nmodule RU = Pulse.RuntimeUtils\nmodule U = Pulse.Syntax.Pure\nmodule E = Pulse.Elaborate.Pure\n\nlet rec freevars (t:term)\n : Set.set var\n = match t.t with\n | Tm_Emp\n | Tm_VProp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown -> Set.empty\n | Tm_Inv p -> freevars p\n | Tm_Star t1 t2 ->\n Set.union (freevars t1) (freevars t2)\n | Tm_ExistsSL _ t1 t2\n | Tm_ForallSL _ t1 t2 ->\n Set.union (freevars t1.binder_ty) (freevars t2)\n | Tm_Pure p -> freevars p\n | Tm_FStar t -> RT.freevars t\n | Tm_AddInv i is -> Set.union (freevars i) (freevars is)\n\nlet freevars_st_comp (s:st_comp) : Set.set var =\n freevars s.res `Set.union`\n freevars s.pre `Set.union`\n freevars s.post\n\n\nlet freevars_comp (c:comp) : Tot (Set.set var) (decreases c) =\n match c with\n | C_Tot t -> freevars t\n | C_ST s\n | C_STGhost s -> freevars_st_comp s\n | C_STAtomic inames _ s ->\n freevars inames `Set.union` freevars_st_comp s\n\nlet freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var =\n match x with\n | None -> Set.empty\n | Some x -> f x\n\nlet freevars_term_opt (t:option term) : Set.set var =\n freevars_opt freevars t\n\nlet rec freevars_list (t:list term) : Set.set var =\n match t with\n | [] -> Set.empty\n | hd::tl -> freevars hd `Set.union` freevars_list tl\n\nlet rec freevars_pairs (pairs:list (term & term)) : Set.set var =\n match pairs with\n | [] -> Set.empty\n | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl\n\nlet freevars_proof_hint (ht:proof_hint_type) : Set.set var =\n match ht with\n | ASSERT { p }\n | FOLD { p }\n | UNFOLD { p } -> freevars p\n | RENAME { pairs; goal } ->\n Set.union (freevars_pairs pairs) (freevars_term_opt goal)\n | REWRITE { t1; t2 } ->\n Set.union (freevars t1) (freevars t2)\n | WILD\n | SHOW_PROOF_STATE _ -> Set.empty\n\nlet freevars_ascription (c:comp_ascription)\n : Set.set var\n = Set.union (freevars_opt freevars_comp c.elaborated)\n (freevars_opt freevars_comp c.annotated)\n\nlet rec freevars_st (t:st_term)\n : Set.set var\n = match t.term with\n | Tm_Return { expected_type; term } ->\n Set.union (freevars expected_type) (freevars term)\n | Tm_Abs { b; ascription; body } ->\n Set.union (freevars b.binder_ty)\n (Set.union (freevars_st body)\n (freevars_ascription ascription))\n | Tm_STApp { head; arg } ->\n Set.union (freevars head) (freevars arg)\n | Tm_Bind { binder; head; body } ->\n Set.union\n (Set.union (freevars binder.binder_ty)\n (freevars_st head))\n (freevars_st body)\n | Tm_TotBind { binder; head; body } ->\n Set.union\n (Set.union (freevars binder.binder_ty)\n (freevars head))\n (freevars_st body)\n | Tm_If { b; then_; else_; post } ->\n Set.union (Set.union (freevars b) (freevars_st then_))\n (Set.union (freevars_st else_) (freevars_term_opt post))\n\n | Tm_Match { sc ; returns_; brs } ->\n let (@@) = Set.union in\n freevars sc\n @@ freevars_term_opt returns_\n @@ freevars_branches brs\n\n | Tm_IntroPure { p }\n | Tm_ElimExists { p } ->\n freevars p\n | Tm_IntroExists { p; witnesses } ->\n Set.union (freevars p) (freevars_list witnesses)\n | Tm_While { invariant; condition; body } ->\n Set.union (freevars invariant)\n (Set.union (freevars_st condition)\n (freevars_st body))\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\n Set.union\n (Set.union (freevars pre1)\n (Set.union (freevars_st body1)\n (freevars post1)))\n (Set.union (freevars pre2)\n (Set.union (freevars_st body2)\n (freevars post2)))\n\n | Tm_WithLocal { binder; initializer; body } ->\n Set.union (freevars binder.binder_ty)\n (Set.union (freevars initializer)\n (freevars_st body))\n\n | Tm_WithLocalArray { binder; initializer; length; body } ->\n Set.union (freevars binder.binder_ty)\n (Set.union (freevars initializer)\n (Set.union (freevars length)\n (freevars_st body)))\n\n | Tm_Rewrite { t1; t2 } ->\n Set.union (freevars t1) (freevars t2)\n\n | Tm_Admit { typ; post } ->\n Set.union (freevars typ)\n (freevars_term_opt post)\n\n | Tm_Unreachable ->\n Set.empty\n\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\n Set.union (freevars_proof_hint hint_type) (freevars_st t)\n\n | Tm_WithInv { name; body; returns_inv } ->\n Set.union (Set.union (freevars name) (freevars_st body))\n (freevars_opt\n (fun (b, r) ->\n (Set.union (freevars b.binder_ty)\n (freevars r)))\n returns_inv)\n\nand freevars_branches (t:list (pattern & st_term)) : Set.set var =\n match t with\n | [] -> Set.empty\n | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl\n\n\nlet rec ln' (t:term) (i:int) : Tot bool (decreases t) =\n match t.t with\n | Tm_Emp\n | Tm_VProp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown -> true\n\n | Tm_Inv p -> ln' p i\n\n | Tm_Star t1 t2 ->\n ln' t1 i &&\n ln' t2 i\n\n | Tm_Pure p ->\n ln' p i\n\n | Tm_ExistsSL _ t body\n | Tm_ForallSL _ t body ->\n ln' t.binder_ty i &&\n ln' body (i + 1)\n\n | Tm_FStar t ->\n RT.ln' t i\n\n | Tm_AddInv x is ->\n ln' x i &&\n ln' is i\n\n\nlet ln_st_comp (s:st_comp) (i:int) : bool =\n ln' s.res i &&\n ln' s.pre i &&\n ln' s.post (i + 1) (* post has 1 impliict abstraction *)\n\n\nlet ln_c' (c:comp) (i:int)\n : bool\n = match c with\n | C_Tot t -> ln' t i\n | C_ST s\n | C_STGhost s -> ln_st_comp s i\n | C_STAtomic inames _ s ->\n ln' inames i &&\n ln_st_comp s i\n\nlet ln_opt' (f: ('a -> int -> bool)) (t:option 'a) (i:int) : bool =\n match t with\n | None -> true\n | Some t -> f t i\n\nlet rec ln_list' (t:list term) (i:int) : bool =\n match t with\n | [] -> true\n | hd::tl -> ln' hd i && ln_list' tl i\n\nlet rec ln_terms' (t:list (term & term)) (i:int) : bool =\n match t with\n | [] -> true\n | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i\n\nlet ln_proof_hint' (ht:proof_hint_type) (i:int) : bool =\n match ht with\n | ASSERT { p }\n | UNFOLD { p }\n | FOLD { p } -> ln' p i\n | RENAME { pairs; goal } ->\n ln_terms' pairs i &&\n ln_opt' ln' goal i\n | REWRITE { t1; t2 } ->\n ln' t1 i &&\n ln' t2 i\n | WILD\n | SHOW_PROOF_STATE _ -> true\n\nlet rec pattern_shift_n (p:pattern)\n : Tot nat\n = match p with\n | Pat_Constant _\n | Pat_Dot_Term _ ->\n 0\n | Pat_Var _ _ ->\n 1\n | Pat_Cons fv l ->\n pattern_args_shift_n l\nand pattern_args_shift_n (ps:list (pattern & bool))\n : Tot nat\n = match ps with\n | [] -> 0\n | (p, _)::tl ->\n pattern_shift_n p + pattern_args_shift_n tl\n\nlet rec ln_pattern' (p : pattern) (i:int)\n : Tot bool (decreases p)\n = match p with\n | Pat_Constant _\n | Pat_Var _ _\n | Pat_Dot_Term None ->\n true\n | Pat_Dot_Term (Some e) ->\n ln' e i\n | Pat_Cons fv l ->\n ln_pattern_args' l i\n\nand ln_pattern_args' (p:list (pattern & bool)) (i:int)\n : Tot bool (decreases p)\n = match p with\n | [] ->\n true\n | (p, _)::tl ->\n ln_pattern' p i &&\n ln_pattern_args' tl (i + pattern_shift_n p)\n\nlet ln_ascription' (c:comp_ascription) (i:int)\n : bool\n = ln_opt' ln_c' c.elaborated i &&\n ln_opt' ln_c' c.annotated i\n\nlet rec ln_st' (t:st_term) (i:int)\n : Tot bool (decreases t)\n = match t.term with\n | Tm_Return { expected_type; term } ->\n ln' expected_type i &&\n ln' term i\n\n | Tm_Abs { b; ascription; body } ->\n ln' b.binder_ty i &&\n ln_st' body (i + 1) &&\n ln_ascription' ascription (i + 1)\n\n | Tm_STApp { head; arg } ->\n ln' head i &&\n ln' arg i\n\n | Tm_Bind { binder; head; body } ->\n ln' binder.binder_ty i &&\n ln_st' head i &&\n ln_st' body (i + 1)\n\n | Tm_TotBind { binder; head; body } ->\n ln' binder.binder_ty i &&\n ln' head i &&\n ln_st' body (i + 1)\n\n | Tm_If { b; then_; else_; post } ->\n ln' b i &&\n ln_st' then_ i &&\n ln_st' else_ i &&\n ln_opt' ln' post (i + 1)\n\n | Tm_Match {sc; returns_; brs } ->\n ln' sc i &&\n ln_opt' ln' returns_ i &&\n ln_branches' t brs i\n\n | Tm_IntroPure { p }\n | Tm_ElimExists { p } ->\n ln' p i\n\n | Tm_IntroExists { p; witnesses } ->\n ln' p i &&\n ln_list' witnesses i\n\n | Tm_While { invariant; condition; body } ->\n ln' invariant (i + 1) &&\n ln_st' condition i &&\n ln_st' body i\n\n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\n ln' pre1 i &&\n ln_st' body1 i &&\n ln' post1 (i + 1) &&\n ln' pre2 i &&\n ln_st' body2 i &&\n ln' post2 (i + 1)\n\n | Tm_WithLocal { binder; initializer; body } ->\n ln' binder.binder_ty i &&\n ln' initializer i &&\n ln_st' body (i + 1)\n\n | Tm_WithLocalArray { binder; initializer; length; body } ->\n ln' binder.binder_ty i &&\n ln' initializer i &&\n ln' length i &&\n ln_st' body (i + 1)\n\n | Tm_Rewrite { t1; t2 } ->\n ln' t1 i &&\n ln' t2 i\n\n | Tm_Admit { typ; post } ->\n ln' typ i &&\n ln_opt' ln' post (i + 1)\n\n | Tm_Unreachable ->\n true\n\n | Tm_ProofHintWithBinders { binders; hint_type; t } ->\n let n = L.length binders in\n ln_proof_hint' hint_type (i + n) &&\n ln_st' t (i + n)\n\n | Tm_WithInv { name; body; returns_inv } ->\n ln' name i &&\n ln_st' body i &&\n ln_opt'\n (fun (b, r) i ->\n ln' b.binder_ty i &&\n ln' r (i + 1))\n returns_inv i\n\nand ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) =\n let (p, e) = b in\n ln_pattern' p i &&\n ln_st' e (i + pattern_shift_n p)\n\nand ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) =\n for_all_dec t brs (fun b -> ln_branch' b i)\n\nlet ln (t:term) = ln' t (-1)\nlet ln_st (t:st_term) = ln_st' t (-1)\nlet ln_c (c:comp) = ln_c' c (-1)\n\nnoeq\ntype subst_elt =\n | DT : nat -> term -> subst_elt\n | NT : var -> term -> subst_elt\n | ND : var -> nat -> subst_elt\n\nlet shift_subst_elt (n:nat) = function\n | DT i t -> DT (i + n) t\n | NT x t -> NT x t\n | ND x i -> ND x (i + n)\n\nlet subst = list subst_elt\n\nlet shift_subst_n (n:nat) = L.map (shift_subst_elt n)\n\nlet shift_subst = shift_subst_n 1\n\nlet rt_subst_elt = function\n | DT i t -> RT.DT i (E.elab_term t)\n | NT x t -> RT.NT x (E.elab_term t)\n | ND x i -> RT.ND x i\n\nlet rt_subst = L.map rt_subst_elt\n\nlet open_or_close_host_term (t:host_term) (ss:subst)\n : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss)))\n = admit()\n\nval subst_host_term (t:host_term) (ss:subst)\n : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) })\n\nlet rec subst_term (t:term) (ss:subst)\n : Tot term (decreases t)\n = let w t' = with_range t' t.range in\n match t.t with\n | Tm_VProp\n | Tm_Emp\n | Tm_Inames\n | Tm_EmpInames\n | Tm_Unknown -> t\n\n | Tm_Inv p ->\n w (Tm_Inv (subst_term p ss))\n\n | Tm_Pure p ->\n w (Tm_Pure (subst_term p ss))\n\n | Tm_Star l r ->\n w (Tm_Star (subst_term l ss)\n (subst_term r ss))\n\n | Tm_ExistsSL u b body ->\n w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss }\n (subst_term body (shift_subst ss)))\n\n | Tm_ForallSL u b body ->\n w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss }\n (subst_term body (shift_subst ss)))\n\n | Tm_FStar t ->\n w (Tm_FStar (subst_host_term t ss))\n\n | Tm_AddInv i is ->\n w (Tm_AddInv (subst_term i ss)\n (subst_term is ss))\n\nlet open_term' (t:term) (v:term) (i:index) =\n subst_term t [ DT i v ]\n\nlet subst_st_comp (s:st_comp) (ss:subst)\n : st_comp =\n\n { s with res = subst_term s.res ss;\n pre = subst_term s.pre ss;\n post = subst_term s.post (shift_subst ss) }\n\nlet open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp =\n subst_st_comp s [ DT i v ]\n\nlet subst_comp (c:comp) (ss:subst)\n : comp\n = match c with\n | C_Tot t ->\n C_Tot (subst_term t ss)\n\n | C_ST s -> C_ST (subst_st_comp s ss)\n\n | C_STAtomic inames obs s ->\n C_STAtomic (subst_term inames ss) obs\n (subst_st_comp s ss)\n\n | C_STGhost s ->\n C_STGhost (subst_st_comp s ss)\n\nlet open_comp' (c:comp) (v:term) (i:index) : comp =\n subst_comp c [ DT i v ]\n\nlet subst_term_opt (t:option term) (ss:subst)\n : Tot (option term)\n = match t with\n | None -> None\n | Some t -> Some (subst_term t ss)\n\nlet open_term_opt' (t:option term) (v:term) (i:index)\n : Tot (option term) = subst_term_opt t [ DT i v ]\n\nlet rec subst_term_list (t:list term) (ss:subst)\n : Tot (list term)\n = match t with\n | [] -> []\n | hd::tl -> subst_term hd ss :: subst_term_list tl ss\n\nlet open_term_list' (t:list term) (v:term) (i:index)\n : Tot (list term) = subst_term_list t [ DT i v ]\n\nlet subst_binder b ss =\n {b with binder_ty=subst_term b.binder_ty ss}\n\nlet open_binder b v i =\n {b with binder_ty=open_term' b.binder_ty v i}\n\nlet rec subst_term_pairs (t:list (term & term)) (ss:subst)\n : Tot (list (term & term))\n = match t with\n | [] -> []\n | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss\n\nlet subst_proof_hint (ht:proof_hint_type) (ss:subst)\n : proof_hint_type\n = match ht with\n | ASSERT { p } -> ASSERT { p=subst_term p ss }\n | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss}\n | FOLD { names; p } -> FOLD { names; p=subst_term p ss }\n | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss;\n goal=subst_term_opt goal ss }\n | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss;\n t2=subst_term t2 ss }\n | WILD\n | SHOW_PROOF_STATE _ -> ht\n\nlet open_term_pairs' (t:list (term * term)) (v:term) (i:index) =\n subst_term_pairs t [DT i v]\n\nlet close_term_pairs' (t:list (term * term)) (x:var) (i:index) =\n subst_term_pairs t [ND x i]\n\nlet open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) =\n subst_proof_hint ht [DT i v]\n\nlet close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) =\n subst_proof_hint ht [ND x i]\n\nlet rec subst_pat (p:pattern) (ss:subst)\n : Tot pattern (decreases p)\n = match p with\n | Pat_Constant _\n | Pat_Dot_Term None ->\n p\n | Pat_Var n t ->\n let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in\n Pat_Var n t\n | Pat_Dot_Term (Some e) ->\n Pat_Dot_Term (Some (subst_term e ss))\n | Pat_Cons d args ->\n let args = subst_pat_args args ss in\n Pat_Cons d args\nand subst_pat_args (args:list (pattern & bool)) (ss:subst)\n : Tot (list (pattern & bool)) (decreases args)\n = match args with\n | [] -> []\n | (arg, b)::tl ->\n let arg' = subst_pat arg ss in\n let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in\n (arg', b)::tl\n\nlet map2_opt (f: 'a -> 'b -> 'c) (x:option 'a) (y:'b)\n : option 'c\n = match x with\n | None -> None\n | Some x -> Some (f x y)\n\nlet subst_ascription (c:comp_ascription) (ss:subst)\n : comp_ascription\n = { elaborated = map2_opt subst_comp c.elaborated ss;\n annotated = map2_opt subst_comp c.annotated ss }\n", "sketch": [ "Step 1: The `subst_branch` function is intended to apply a substitution to a branch, which consists of a pattern and a statement term (`st_term`).\nStep 2: To implement `subst_branch`, we need to apply the substitution to both the pattern and the statement term separately. We will use the `subst_pat` function to substitute within the pattern and the `subst_st'` function to substitute within the statement term. The result will be a new branch with the substituted pattern and statement term.", "Step 1: The `subst_branch` function is intended to apply a substitution to a branch, which is a pair consisting of a pattern and a statement term (`st_term`).\nStep 2: To implement `subst_branch`, we need to apply the substitution to both the pattern and the statement term separately. We will use the `subst_pat` function to substitute within the pattern and the `subst_st_term` function to substitute within the statement term. The result will be a new pair consisting of the substituted pattern and the substituted statement term.", "Step 1: The `subst_branch` function is intended to apply a substitution to a branch of a pattern and state term. A branch is a tuple consisting of a pattern and a state term.\nStep 2: To implement `subst_branch`, we need to apply the substitution to both the pattern and the state term separately. We can use the existing `subst_pat` function to handle the pattern and `subst_st_term` function to handle the state term. The result will be a new tuple with the substituted pattern and state term.", "Step 1: The `subst_branch` function is intended to apply a substitution to a branch, which consists of a pattern and an `st_term`.\nStep 2: To implement `subst_branch`, we need to:\n- Apply the substitution to the pattern using the `subst_pat` function.\n- Apply the substitution to the `st_term` using the `subst_st_term` function (which we assume exists based on the pattern of similar functions).\n- Return the substituted pattern and `st_term` as a tuple.", "Step 1: The `subst_branch` function is intended to apply a substitution to a branch, which consists of a pattern and a statement term (`st_term`).\nStep 2: To implement this, we need to apply the substitution to both the pattern and the statement term. We can use the existing `subst_pat` function to handle the pattern and the `subst_st_term` function to handle the statement term. The result will be a tuple containing the substituted pattern and the substituted statement term.", "Step 1: The `subst_branch` function is intended to apply a substitution to a branch of a pattern and a state term. A branch consists of a pattern and a state term.\nStep 2: To implement `subst_branch`, we need to apply the substitution to both the pattern and the state term. We will use the `subst_pat` function to substitute within the pattern and the `subst_st_term` function to substitute within the state term. The result will be a new branch with the substituted pattern and state term.", "Step 1: The `subst_branch` function is intended to apply a substitution to a branch, which consists of a pattern and a state term (`st_term`). The goal is to substitute terms within both the pattern and the state term according to the provided substitution list (`ss`).\n\nStep 2: To implement `subst_branch`, we need to:\n- Apply the substitution to the pattern using the `subst_pat` function.\n- Apply the substitution to the state term using the `subst_st_term` function.\n- Return the modified pattern and state term as a tuple.", "Step 1: The `subst_branch` function is intended to apply a substitution (`ss`) to a branch of a pattern and state term (`b`). This involves substituting the pattern and the state term within the branch.\nStep 2: To implement `subst_branch`, we need to:\n- Decompose the branch into its pattern and state term components.\n- Apply the `subst_pat` function to the pattern with the given substitution.\n- Apply the `subst_st_term` function to the state term with the given substitution.\n- Return the new pattern and state term as a pair.", "Step 1: The `subst_branch` function is intended to apply a substitution to a branch, which consists of a pattern and a statement term (`st_term`).\nStep 2: To implement `subst_branch`, we need to apply the `subst_pat` function to the pattern part of the branch and the `subst_st_term` function to the statement term part of the branch. The resulting pattern and statement term are then combined back into a branch.", "Step 1: The `subst_branch` function is responsible for applying a substitution (`ss`) to a branch, which consists of a pattern and a state term (`st_term`).\nStep 2: To implement this, we need to apply the substitution to both the pattern and the state term separately. We use the `subst_pat` function to substitute within the pattern and the `subst_st_term` function to substitute within the state term. The result is a new branch with the substituted pattern and state term." ], "generated_solution": [ "let subst_branch (ss: subst) (b: pattern & st_term) : Tot (pattern & st_term) (decreases b) =\n let (p, st) = b in\n (subst_pat p ss, subst_st' st ss)", "let subst_branch (ss: subst) (b: pattern & st_term) : Tot (pattern & st_term) (decreases b) =\n let (p, st) = b in\n (subst_pat p ss, subst_st_term st ss)", "let subst_branch (ss: subst) (b: pattern & st_term) : Tot (pattern & st_term) (decreases b) =\n let (p, st) = b in\n (subst_pat p ss, subst_st_term st ss)", "let subst_branch (ss: subst) (b: pattern & st_term) : Tot (pattern & st_term) (decreases b) =\n let (p, t) = b in\n (subst_pat p ss, subst_st_term t ss)", "let subst_branch (ss: subst) (b: pattern & st_term) : Tot (pattern & st_term) (decreases b) =\n let (p, st) = b in\n (subst_pat p ss, subst_st_term st ss)", "let subst_branch (ss: subst) (b: pattern & st_term) : Tot (pattern & st_term) (decreases b) =\n let (p, st) = b in\n (subst_pat p ss, subst_st_term st ss)", "let subst_branch (ss: subst) ((p, st): pattern & st_term) : Tot (pattern & st_term) (decreases (p, st)) =\n (subst_pat p ss, subst_st_term st ss)", "let subst_branch (ss: subst) (b: pattern & st_term) : Tot (pattern & st_term) (decreases b) =\n let (p, st) = b in\n (subst_pat p ss, subst_st_term st ss)", "let subst_branch (ss: subst) (b: pattern & st_term) : Tot (pattern & st_term) (decreases b) =\n let (p, st) = b in\n (subst_pat p ss, subst_st_term st ss)", "let subst_branch (ss: subst) (b: pattern & st_term) : Tot (pattern & st_term) (decreases b) =\n let (p, st) = b in\n (subst_pat p ss, subst_st_term st ss)" ] }, { "file_name": "Param.fst", "name": "Param.replace_var", "opens_and_abbrevs": [ { "open": "FStar.Tactics.V2" }, { "open": "FStar.List" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val replace_var (s: param_state) (b: bool) (t: term) : Tac term", "source_definition": "let replace_var (s:param_state) (b:bool) (t:term) : Tac term =\n match inspect t with\n | Tv_Var v ->\n begin try\n let (x, y, _) = lookup s v in\n let bv = binder_to_namedv (if b then y else x) in\n pack (Tv_Var bv)\n with\n (* Maybe we traversed a binder and there are variables not in the state.\n * The right thing here would be to track them... but this should do for now. *)\n | NotFoundBV _ -> t\n | e -> raise e\n end\n | _ -> t", "source_range": { "start_line": 79, "start_col": 0, "end_line": 92, "end_col": 10 }, "interleaved": false, "definition": "fun s b t ->\n (let _ = FStar.Tactics.NamedView.inspect t in\n (match _ with\n | FStar.Tactics.NamedView.Tv_Var v ->\n (try\n (let _ = Param.lookup s v in\n (let FStar.Pervasives.Native.Mktuple3 #_ #_ #_ x y _ = _ in\n let bv =\n FStar.Tactics.V2.SyntaxCoercions.binder_to_namedv ((match b with\n | true -> y\n | _ -> x)\n <:\n FStar.Tactics.NamedView.binder)\n in\n FStar.Tactics.NamedView.pack (FStar.Tactics.NamedView.Tv_Var bv))\n <:\n FStar.Tactics.NamedView.term)\n <:\n FStar.Tactics.NamedView.term\n with\n | Param.NotFoundBV _ -> t\n | e -> FStar.Tactics.Effect.raise e)\n | _ -> t)\n <:\n FStar.Tactics.NamedView.term)\n <:\n FStar.Tactics.Effect.Tac FStar.Tactics.NamedView.term", "effect": "FStar.Tactics.Effect.Tac", "effect_flags": [], "mutual_with": [], "premises": [ "Param.param_state", "Prims.bool", "FStar.Tactics.NamedView.term", "FStar.Tactics.NamedView.namedv", "FStar.Tactics.V2.Derived.try_with", "Prims.unit", "FStar.Tactics.NamedView.binder", "FStar.Tactics.NamedView.pack", "FStar.Tactics.NamedView.Tv_Var", "FStar.Tactics.V2.SyntaxCoercions.binder_to_namedv", "FStar.Pervasives.Native.tuple3", "Param.lookup", "Prims.exn", "FStar.Tactics.Effect.raise", "FStar.Tactics.NamedView.named_term_view", "FStar.Tactics.NamedView.inspect" ], "proof_features": [], "is_simple_lemma": false, "is_div": true, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "s: Param.param_state -> b: Prims.bool -> t: FStar.Tactics.NamedView.term\n -> FStar.Tactics.Effect.Tac FStar.Tactics.NamedView.term", "prompt": "let replace_var (s: param_state) (b: bool) (t: term) : Tac term =\n ", "expected_response": "match inspect t with\n| Tv_Var v ->\n (try\n let x, y, _ = lookup s v in\n let bv = binder_to_namedv (if b then y else x) in\n pack (Tv_Var bv)\n with\n | NotFoundBV _ -> t\n | e -> raise e)\n| _ -> t", "source": { "project_name": "FStar", "file_name": "examples/param/Param.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "Param.fst", "checked_file": "dataset/Param.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Sealed.fsti.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Order.fst.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.List.fst.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "bvmap", "let fvmap = list (fv * fv)", "param_state", "param_state", "bvmap", "bvmap", "fresh", "fresh", "recs", "recs", "let rec fold_right2 (f : 'a -> 'b -> 'c -> Tac 'c) (l1:list 'a) (l2:list 'b) (c:'c) : Tac 'c =\n match l1, l2 with\n | h1::t1, h2::t2 -> f h1 h2 (fold_right2 f t1 t2 c)\n | [], [] -> c\n | _ -> fail \"fold_right2\"", "let rec zip3 (l1 : list 'a) (l2 : list 'b) (l3 : list 'c) : list ('a * 'b * 'c) =\n match l1, l2, l3 with\n | h1::t1, h2::t2, h3::t3 -> (h1, h2, h3) :: (zip3 t1 t2 t3)\n | _ -> []", "let last (xs:list 'a) : Tac 'a =\n match List.Tot.rev xs with\n | h::_ -> h\n | [] -> fail \"last: empty list\"", "let fresh_binder_named (nm:string) (t:typ) : Tac binder =\n // useful?\n //let n = fresh () in\n //let nm = nm ^ \"_\" ^ string_of_int n in\n Tactics.V2.fresh_binder_named nm t", "let app_binders (t:term) (bs:list binder) : Tac term =\n mk_e_app t (List.Tot.map binder_to_term bs)", "let push_var_to_state (v:namedv) (b0 b1 b2 : binder) (s:param_state) : param_state =\n { s with bvmap = (v, (b0, b1, b2)) :: s.bvmap }", "exception NotARecFV", "NotARecFV", "NotARecFV", "exception Unsupported of string", "Unsupported", "Unsupported", "exception NotFoundBV of namedv", "NotFoundBV", "NotFoundBV", "exception NotFoundFV of fv", "NotFoundFV", "NotFoundFV", "let lookup_rec_fv (s:param_state) (f:fv) : Tac fv =\n let rec aux (m:fvmap) : Tac fv =\n match m with\n | [] -> raise NotARecFV\n | (f1, k)::fs -> if compare_fv f f1 = Order.Eq\n then k\n else aux fs\n in\n aux s.recs", "let push_fv (f1 f2 : fv) (s:param_state) : param_state =\n { s with recs = (f1,f2)::s.recs }", "let lookup (s:param_state) (v:namedv) : Tac (binder & binder & binder) =\n let rec aux (bvm : bvmap) : Tac (binder & binder & binder) =\n match bvm with\n | [] ->\n raise (NotFoundBV v)\n | (v', r)::tl ->\n if (inspect_namedv v).uniq = (inspect_namedv v').uniq\n then r\n else aux tl\n in\n aux s.bvmap" ], "closest": [ "val replace_term_in : bool -> term -> term -> term -> Tac term\nlet rec replace_term_in dbg from_term to_term tm =\n if term_eq from_term tm then to_term else\n match inspect tm with\n | Tv_Var _ | Tv_BVar _ | Tv_FVar _ -> tm\n | Tv_App hd (a, qual) ->\n let a' = replace_term_in dbg from_term to_term a in\n let hd' = replace_term_in dbg from_term to_term hd in\n pack (Tv_App hd' (a', qual))\n | Tv_Abs br body ->\n let body' = replace_term_in dbg from_term to_term body in\n pack (Tv_Abs br body')\n | Tv_Arrow br c0 -> tm (* TODO: we might want to explore that *)\n | Tv_Type _ -> tm\n | Tv_Refine bv sort ref ->\n let sort' = replace_term_in dbg from_term to_term sort in\n let ref' = replace_term_in dbg from_term to_term ref in\n pack (Tv_Refine bv sort' ref')\n | Tv_Const _ -> tm\n | Tv_Uvar _ _ -> tm\n | Tv_Let recf attrs bv ty def body ->\n (* GM 2023-04-27: leaving ty untouched, old code did not\n descend into sort. *)\n let def' = replace_term_in dbg from_term to_term def in\n let body' = replace_term_in dbg from_term to_term body in\n pack (Tv_Let recf attrs bv ty def' body')\n | Tv_Match scrutinee ret_opt branches -> //AR: TODO: account for the returns annotation\n (* Auxiliary function to explore the branches *)\n let explore_branch (br : branch) : Tac branch =\n (* Only explore the branch body *)\n let pat, body = br in\n let body' = replace_term_in dbg from_term to_term body in\n (pat, body')\n in\n let scrutinee' = replace_term_in dbg from_term to_term scrutinee in\n let branches' = map explore_branch branches in\n pack (Tv_Match scrutinee' ret_opt branches')\n | Tv_AscribedT e ty tac use_eq ->\n let e' = replace_term_in dbg from_term to_term e in\n let ty' = replace_term_in dbg from_term to_term ty in\n pack (Tv_AscribedT e' ty' tac use_eq)\n | Tv_AscribedC e c tac use_eq ->\n let e' = replace_term_in dbg from_term to_term e in\n pack (Tv_AscribedC e' c tac use_eq)\n | _ ->\n (* Unknown *)\n tm", "val open_term (b: R.binder) (t: term) : Tac (binder & term)\nlet open_term (b : R.binder) (t : term) : Tac (binder & term) =\n let bndr : binder = open_binder b in\n (bndr, open_term_with b bndr t)", "val is_bvar (t: term) : option nat\nlet is_bvar (t:term) : option nat =\n let open R in\n match t.t with\n | Tm_FStar host_term ->\n begin match R.inspect_ln host_term with\n | R.Tv_BVar bv ->\n let bv_view = R.inspect_bv bv in\n Some bv_view.index\n | _ -> None\n end\n | _ -> None", "val cases_bool (b: term) : Tac unit\nlet cases_bool (b:term) : Tac unit =\n let bi = `bool_ind in\n seq (fun () -> apply_lemma (mk_e_app bi [b]))\n (fun () -> let _ = trytac (fun () -> let b = implies_intro () in rewrite b; clear_top ()) in ())", "val cases_bool (b: term) : Tac unit\nlet cases_bool (b:term) : Tac unit =\n let bi = `bool_ind in\n seq (fun () -> apply_lemma (mk_e_app bi [b]))\n (fun () -> let _ = trytac (fun () -> let b = implies_intro () in rewrite b; clear_top ()) in ())", "val is_var (t: term) : option nm\nlet is_var (t:term) : option nm =\n let open R in\n match t.t with\n | Tm_FStar host_term ->\n begin match R.inspect_ln host_term with\n | R.Tv_Var nv ->\n let nv_view = R.inspect_namedv nv in\n Some {nm_index=nv_view.uniq;\n nm_ppname=mk_ppname (nv_view.ppname) t.range}\n | _ -> None\n end\n | _ -> None", "val is_uvar (t: term) : Tac bool\nlet is_uvar (t:term) : Tac bool = match inspect t with\n | Tv_Uvar _ _ -> true\n | Tv_App _ _ ->\n let hd, args = collect_app t in\n Tv_Uvar? (inspect hd)\n | _ -> false", "val is_uvar (t: term) : Tac bool\nlet is_uvar (t:term) : Tac bool = match inspect t with\n | Tv_Uvar _ _ -> true\n | Tv_App _ _ ->\n let hd, args = collect_app t in\n Tv_Uvar? (inspect hd)\n | _ -> false", "val subst_var (v: namedv) (s: subst) : term\nlet subst_var (v:namedv) (s:subst) : term =\n match find_matching_subst_elt_var s v with\n | Some (NT _ t) ->\n (match maybe_uniq_of_term t with\n | None -> t\n | Some k ->\n pack_ln (Tv_Var (pack_namedv { inspect_namedv v with uniq = k })))\n | Some (ND _ i) ->\n let bv = pack_bv {\n sort = (inspect_namedv v).sort;\n ppname = (inspect_namedv v).ppname;\n index = i;\n } in\n pack_ln (Tv_BVar bv)\n | _ -> pack_ln (Tv_Var v)", "val remove_b2t : term -> Tac term\nlet remove_b2t (t:term) : Tac term =\n match inspect t with\n | Tv_App hd (a, Q_Explicit) ->\n begin match inspect hd with\n | Tv_FVar fv ->\n if fv_eq_name fv b2t_qn then a else t\n | _ -> t\n end\n | _ -> t", "val rewrite_equality (t: term) : Tac unit\nlet rewrite_equality (t:term) : Tac unit =\n try_rewrite_equality t (cur_vars ())", "val rewrite_equality (t: term) : Tac unit\nlet rewrite_equality (t:term) : Tac unit =\n try_rewrite_equality t (cur_binders ())", "val push_pre (st: state) (inv_bv: bv) (t: term) : Tac term\nlet rec push_pre (st: state) (inv_bv: bv) (t: term): Tac term =\n match inspect t with\n | Tv_Arrow bv c ->\n let c =\n match inspect_comp c with\n | C_Eff us e a args decrs ->\n if string_of_name e = \"FStar_HyperStack_ST_Stack\" then\n let args =\n match args with\n | (pre, qual) :: rest ->\n let pre =\n match inspect pre with\n | Tv_Abs h body ->\n let body = mk_app (`( /\\ )) [ pack (Tv_Var inv_bv), Q_Explicit; body, Q_Explicit ] in\n pack (Tv_Abs h body)\n | _ ->\n fail \"impossible: argument to ST.Stack not a fun\"\n in\n (pre, qual) :: rest\n | _ ->\n fail (\"impossible: effect not fully applied \" ^ string_of_name e)\n in\n C_Eff us e a args decrs\n else\n fail (\"rewritten function has an unknown effect: \" ^ string_of_name e)\n | C_Total t ->\n C_Total (push_pre st inv_bv t)\n | _ ->\n fail (\"rewritten type is neither a Tot or a stateful arrow: \" ^ term_to_string t)\n in\n let c = pack_comp c in\n pack (Tv_Arrow bv c)\n | _ ->\n print (st.indent ^ \" WARN: no effect found, are you using the specialize tactic on pure code?\");\n t", "val open_term (t:term) (v:var) : term\nlet open_term (t:term) (v:var) = RTB.open_term t v", "val weaken\n (f: RT.fstar_top_env)\n (sg: src_env)\n (hyp: var{None? (lookup sg hyp)})\n (b: s_exp)\n (t0 t1: s_ty)\n : T.Tac\n (t: s_ty &\n sub_typing f ((hyp, Inr (b, EBool true)) :: sg) t0 t &\n sub_typing f ((hyp, Inr (b, EBool false)) :: sg) t1 t)\nlet weaken (f:RT.fstar_top_env) (sg:src_env) (hyp:var { None? (lookup sg hyp) } ) (b:s_exp) (t0 t1:s_ty)\n : T.Tac (t:s_ty &\n sub_typing f ((hyp,Inr(b, EBool true))::sg) t0 t &\n sub_typing f ((hyp,Inr(b, EBool false))::sg) t1 t)\n = if t0 = t1\n then (| t0, S_Refl _ t0, S_Refl _ t1 |)\n else T.fail \"weaken is very dumb\"", "val is_const (t: term) : Tac bool\nlet is_const (t:term) : Tac bool = Tv_Const? (inspect t)", "val open_term_with (b: R.binder) (nb: binder) (t: term) : Tac term\nlet open_term_with (b : R.binder) (nb : binder) (t : term) : Tac term =\n let nv : R.namedv = pack_namedv {\n uniq = nb.uniq;\n sort = seal nb.sort;\n ppname = nb.ppname;\n }\n in\n let t' = subst_term [DB 0 nv] t in\n t'", "val term_is_uvar (t: term) (i: int) : Tac bool\nlet rec term_is_uvar (t: term) (i: int) : Tac bool = match inspect t with\n | Tv_Uvar i' _ -> i = i'\n | Tv_App _ _ ->\n let hd, args = collect_app t in\n term_is_uvar hd i\n | _ -> false", "val tm_bvar (bv: bv) : term\nlet tm_bvar (bv:bv) : term =\n tm_fstar (R.pack_ln (R.Tv_BVar (R.pack_bv (RT.make_bv_with_name bv.bv_ppname.name bv.bv_index))))\n bv.bv_ppname.range", "val is_eq (t: term) : Tac (option (term & term))\nlet is_eq (t:term) : Tac (option (term & term)) =\n match term_as_formula t with\n | Comp (Eq _) l r -> Some (l, r)\n | _ -> None", "val open_term_simple (b: R.simple_binder) (t: term) : Tac (simple_binder & term)\nlet open_term_simple (b : R.simple_binder) (t : term) : Tac (simple_binder & term) =\n let n = fresh () in\n let bv : binder_view = inspect_binder b in\n let nv : R.namedv = pack_namedv {\n uniq = n;\n sort = seal bv.sort;\n ppname = bv.ppname;\n }\n in\n let t' = subst_term [DB 0 nv] t in\n let bndr : binder = {\n uniq = n;\n sort = bv.sort;\n ppname = bv.ppname;\n qual = bv.qual;\n attrs = bv.attrs;\n }\n in\n (bndr, t')", "val pose_as (s: string) (t: term) : Tac binder\nlet pose_as (s:string) (t:term) : Tac binder =\n let b = pose t in\n rename_to b s", "val rewrite' (b: binder) : Tac unit\nlet rewrite' (b:binder) : Tac unit =\n ((fun () -> rewrite b)\n <|> (fun () -> binder_retype b;\n apply_lemma (`__eq_sym);\n rewrite b)\n <|> (fun () -> fail \"rewrite' failed\"))\n ()", "val safe_tc (e:env) (t:term) : Tac (option term)\nlet safe_tc e t =\n try Some (tc e t) with | _ -> None", "val is_true : term -> Tac bool\nlet is_true t =\n begin match term_as_formula' t with\n | True_ -> true\n | _ -> begin match inspect t with\n | Tv_App l r ->\n begin match inspect l with\n | Tv_Abs b t ->\n begin match term_as_formula' t with\n | True_ -> true\n | _ -> false\n end\n | _ -> false\n end\n | _ -> false\n end\n end", "val nth_var (i: int) : Tac binding\nlet nth_var (i:int) : Tac binding =\n let bs = cur_vars () in\n let k : int = if i >= 0 then i else List.Tot.Base.length bs + i in\n let k : nat = if k < 0 then fail \"not enough binders\" else k in\n match List.Tot.Base.nth bs k with\n | None -> fail \"not enough binders\"\n | Some b -> b", "val simplify_branch (g: env) (b: branch) : T.Tac branch\nlet rec simplify_st_term (g:env) (e:st_term) : T.Tac st_term =\n let ret t = { e with term = t } in\n let with_open b e = with_open g b e simplify_st_term in\n\n match e.term with\n | Tm_Return _\n | Tm_IntroPure _\n | Tm_ElimExists _\n | Tm_IntroExists _\n | Tm_STApp _\n | Tm_Rewrite _\n | Tm_Admit _\n | Tm_ProofHintWithBinders _ -> e\n\n | Tm_Abs { b; q; ascription; body } ->\n ret (Tm_Abs { b; q; ascription; body = with_open b body })\n\n | Tm_Bind { binder; head; body } ->\n let is_internal_binder = is_internal_binder binder in\n if is_internal_binder &&\n is_return_bv0 body\n then simplify_st_term g head\n else if is_internal_binder &&\n Some? (is_return head)\n then let Some head = is_return head in\n simplify_st_term g (LN.subst_st_term body [LN.DT 0 head])\n else begin\n match simplify_nested_let e binder head body with\n | Some e -> simplify_st_term g e\n | None -> \n let head = simplify_st_term g head in\n let body = with_open binder body in\n ret (Tm_Bind { binder; head; body })\n end\n\n | Tm_TotBind { binder; head; body } ->\n ret (Tm_TotBind { binder; head; body = with_open binder body })\n\n | Tm_If { b; then_; else_; post } ->\n ret (Tm_If { b; then_ = simplify_st_term g then_; else_ = simplify_st_term g else_; post })\n\n | Tm_Match { sc; returns_; brs } ->\n ret (Tm_Match { sc; returns_; brs = T.map (simplify_branch g) brs })\n\n | Tm_While { invariant; condition; condition_var; body } ->\n let condition = simplify_st_term g condition in\n let body = simplify_st_term g body in\n { e with term = Tm_While { invariant; condition; condition_var; body } }\n \n | Tm_Par { pre1; body1; post1; pre2; body2; post2 } ->\n let body1 = simplify_st_term g body1 in\n let body2 = simplify_st_term g body2 in\n { e with term = Tm_Par { pre1; body1; post1; pre2; body2; post2 } }\n\n | Tm_WithLocal { binder; initializer; body } ->\n ret (Tm_WithLocal { binder; initializer; body = with_open binder body })\n \n | Tm_WithLocalArray { binder; initializer; length; body } ->\n ret (Tm_WithLocalArray { binder; initializer; length; body = with_open binder body })\n \n | Tm_WithInv {body} ->\n simplify_st_term g body\n\n | Tm_Unreachable -> e\n\nand simplify_branch (g:env) (b:branch) : T.Tac branch =\n let pat, body = b in\n let g, _, bs = extend_env_pat g pat in\n let body = Pulse.Checker.Match.open_st_term_bs body bs in\n let body = simplify_st_term g body in\n pat, Pulse.Syntax.Naming.close_st_term_n body (L.map fst bs)", "val rename (t:term) (x y:var) : term\nlet rename (t:term) (x y:var)= RTB.rename t x y", "val apply (t: term) : Tac unit\nlet apply (t : term) : Tac unit =\n t_apply true false false t", "val apply (t: term) : Tac unit\nlet apply (t : term) : Tac unit =\n t_apply true false false t", "val weaken\n (f: fstar_top_env)\n (sg: src_env)\n (hyp: var{None? (lookup sg hyp)})\n (b: src_exp)\n (t0 t1: src_ty)\n : T.Tac\n (t: src_ty &\n sub_typing f ((hyp, Inr (b, EBool true)) :: sg) t0 t &\n sub_typing f ((hyp, Inr (b, EBool false)) :: sg) t1 t)\nlet weaken (f:fstar_top_env) (sg:src_env) (hyp:var { None? (lookup sg hyp) } ) (b:src_exp) (t0 t1:src_ty)\n : T.Tac (t:src_ty &\n sub_typing f ((hyp,Inr(b, EBool true))::sg) t0 t &\n sub_typing f ((hyp,Inr(b, EBool false))::sg) t1 t)\n = if t0 = t1\n then (| t0, S_Refl _ t0, S_Refl _ t1 |)\n else T.fail \"weaken is very dumb\"", "val check (t: term) : Tac bool\nlet rec check (t:term) : Tac bool =\n match inspect t with\n (* We are using the named view, which opens terms\n as needed on every node. If we reach a bvar, the original\n term is not LN. *)\n | Tv_BVar bv -> false\n\n | Tv_Const _ -> true\n | Tv_Uvar _ _ -> false (* conservative *)\n\n | Tv_Var _ -> true\n | Tv_FVar _ -> true\n | Tv_UInst _ us -> for_all check_u us\n | Tv_App hd (a, q) -> if check hd then check a else false\n | Tv_Abs b body -> if check b.sort then check body else false\n | Tv_Arrow b c -> if check b.sort then check_comp c else false\n | Tv_Type u -> check_u u\n | Tv_Refine b ref -> if check b.sort then check ref else false\n | Tv_Let recf attrs b def body ->\n if not (for_all check attrs) then false else\n if not (check def) then false else\n check body\n | Tv_Match sc _ brs -> \n if check sc then for_all check_br brs else false\n | Tv_AscribedT e t _ _ ->\n if check e then check t else false\n | Tv_AscribedC e c _ _ ->\n if check e then check_comp c else false\n\n | Tv_Unknown -> true\n | Tv_Unsupp -> true // hm..\nand check_u (u:universe) : Tac bool =\n match inspect_universe u with\n | Uv_BVar _ -> false\n | Uv_Name _ -> true\n | Uv_Unif _ -> false (* conservative *)\n | Uv_Zero -> true\n | Uv_Succ u -> check_u u\n | Uv_Max us -> for_all check_u us\n | Uv_Unk -> true\nand check_comp (c:comp) : Tac bool =\n match c with\n | C_Total typ -> check typ\n | C_GTotal typ -> check typ\n | C_Lemma pre post pats -> \n if not (check pre) then false else\n if not (check post) then false else\n check pats\n | C_Eff us nm res args decrs ->\n if not (for_all check_u us) then false else\n if not (check res) then false else\n if not (for_all (fun (a,q) -> check a) args) then false else\n if not (for_all check decrs) then false else\n true\n \nand check_br (b:branch) : Tac bool =\n (* Could check the pattern's ascriptions too. *)\n let (p, t) = b in\n check t", "val open_term_n (bs: list R.binder) (t: term) : Tac (list binder & term)\nlet open_term_n (bs : list R.binder) (t : term) : Tac (list binder & term) =\n let nbs, s = __open_term_n_aux bs [] [] in\n List.Tot.rev nbs, subst_term s t", "val pose_as (s: string) (t: term) : Tac binding\nlet pose_as (s:string) (t:term) : Tac binding =\n let b = pose t in\n rename_to b s", "val apply (t: T.term) : T.Tac unit\nlet apply (t:T.term) : T.Tac unit =\n T.t_apply true false true t", "val apply (t: T.term) : T.Tac unit\nlet apply (t:T.term) : T.Tac unit =\n T.t_apply true false true t", "val close_term (t:term) (v:var) : term\nlet close_term (t:term) (v:var) = RTB.close_term t v", "val pose (t: term) : Tac binder\nlet pose (t:term) : Tac binder =\n apply (`__cut);\n flip ();\n exact t;\n intro ()", "val replace_smt_uvars (l1 l2: list atom) (am: amap term) : Tac (amap term * list term)\nlet replace_smt_uvars (l1 l2:list atom) (am:amap term) : Tac (amap term * list term)\n = let env = cur_env () in\n fold_left (rewrite_term_for_smt env) (am, []) l2", "val rewrite_all (g: env) (p: list (term & term)) (t: term) : T.Tac (term & term)\nlet rewrite_all (g:env) (p: list (term & term)) (t:term) : T.Tac (term & term) =\n match as_subst p [] [] Set.empty with\n | Some s ->\n t, subst_term t s\n | _ ->\n let p : list (R.term & R.term) = \n T.map \n (fun (e1, e2) -> \n elab_term (fst (Pulse.Checker.Pure.instantiate_term_implicits g e1)),\n elab_term (fst (Pulse.Checker.Pure.instantiate_term_implicits g e2)))\n p\n in\n let lhs, rhs = visit_and_rewrite_conjuncts_all p t in\n debug_log g (fun _ -> Printf.sprintf \"Rewrote %s to %s\" (P.term_to_string lhs) (P.term_to_string rhs));\n lhs, rhs", "val binder_to_term (b: binder) : Tac term\nlet binder_to_term (b : binder) : Tac term =\n let bview = inspect_binder b in\n bv_to_term bview.binder_bv", "val pose (t: term) : Tac binding\nlet pose (t:term) : Tac binding =\n apply (`__cut);\n flip ();\n exact t;\n intro ()", "val solve_then (#a #b: _) (t1: (unit -> Tac a)) (t2: (a -> Tac b)) : Tac b\nlet solve_then #a #b (t1 : unit -> Tac a) (t2 : a -> Tac b) : Tac b =\n dup ();\n let x = focus (fun () -> finish_by t1) in\n let y = t2 x in\n trefl ();\n y", "val solve_then (#a #b: _) (t1: (unit -> Tac a)) (t2: (a -> Tac b)) : Tac b\nlet solve_then #a #b (t1 : unit -> Tac a) (t2 : a -> Tac b) : Tac b =\n dup ();\n let x = focus (fun () -> finish_by t1) in\n let y = t2 x in\n trefl ();\n y", "val visit_br (ff: (term -> Tac term)) (b: branch) : Tac branch\nlet rec visit_tm (ff : term -> Tac term) (t : term) : Tac term =\n let tv = inspect_ln t in\n let tv' =\n match tv with\n | Tv_FVar _\n | Tv_Var _\n | Tv_BVar _\n | Tv_UInst _ _ -> tv\n\n | Tv_Type u -> Tv_Type u\n | Tv_Const c -> Tv_Const c\n | Tv_Uvar i u -> Tv_Uvar i u\n | Tv_Unknown -> Tv_Unknown\n | Tv_Unsupp -> Tv_Unsupp\n | Tv_Arrow b c ->\n let b = on_sort_binder (visit_tm ff) b in\n let c = visit_comp ff c in\n Tv_Arrow b c\n | Tv_Abs b t ->\n let b = on_sort_binder (visit_tm ff) b in\n let t = visit_tm ff t in\n Tv_Abs b t\n | Tv_App l (r, q) ->\n let l = visit_tm ff l in\n let r = visit_tm ff r in\n Tv_App l (r, q)\n | Tv_Refine b r ->\n let b = on_sort_simple_binder (visit_tm ff) b in\n let r = visit_tm ff r in\n Tv_Refine b r\n | Tv_Let r attrs b def t ->\n let b = on_sort_simple_binder (visit_tm ff) b in\n let def = visit_tm ff def in\n let t = visit_tm ff t in\n Tv_Let r attrs b def t\n | Tv_Match sc ret_opt brs ->\n let sc = visit_tm ff sc in\n let ret_opt = map_opt (fun (b, asc) ->\n let b = on_sort_binder (visit_tm ff) b in\n let asc =\n match asc with\n | Inl t, tacopt, use_eq ->\n Inl (visit_tm ff t), map_opt (visit_tm ff) tacopt, use_eq\n | Inr c, tacopt, use_eq->\n Inr (visit_comp ff c), map_opt (visit_tm ff) tacopt, use_eq in\n b, asc) ret_opt in\n let brs = map (visit_br ff) brs in\n Tv_Match sc ret_opt brs\n | Tv_AscribedT e t topt use_eq ->\n let e = visit_tm ff e in\n let t = visit_tm ff t in\n Tv_AscribedT e t topt use_eq\n | Tv_AscribedC e c topt use_eq ->\n let e = visit_tm ff e in\n let c = visit_comp ff c in\n Tv_AscribedC e c topt use_eq\n in\n ff (pack_ln tv')\nand visit_br (ff : term -> Tac term) (b:branch) : Tac branch =\n let (p, t) = b in\n let p = visit_pat ff p in\n let t = visit_tm ff t in\n (p, t)\nand visit_pat (ff : term -> Tac term) (p:pattern) : Tac pattern =\n match p with\n | Pat_Constant _ -> p\n | Pat_Var v s -> Pat_Var v s\n | Pat_Cons head univs subpats ->\n let subpats = (map (fun(p,b) -> (visit_pat ff p, b)) subpats) in\n Pat_Cons head univs subpats\n | Pat_Dot_Term t ->\n let t = map_opt (visit_tm ff) t in\n Pat_Dot_Term t\n\nand visit_comp (ff : term -> Tac term) (c : comp) : Tac comp =\n let cv = inspect_comp c in\n let cv' =\n match cv with\n | C_Total ret ->\n let ret = visit_tm ff ret in\n C_Total ret\n\n | C_GTotal ret ->\n let ret = visit_tm ff ret in\n C_GTotal ret\n\n | C_Lemma pre post pats ->\n let pre = visit_tm ff pre in\n let post = visit_tm ff post in\n let pats = visit_tm ff pats in\n C_Lemma pre post pats\n\n | C_Eff us eff res args decrs ->\n let res = visit_tm ff res in\n let args = map (fun (a, q) -> (visit_tm ff a, q)) args in\n let decrs = map (visit_tm ff) decrs in\n C_Eff us eff res args decrs\n in\n pack_comp cv'", "val push_fresh_var : env -> string -> typ -> Tac (term & binder & env)\nlet push_fresh_var e0 basename ty =\n let e1, b1 = push_fresh_binder e0 basename ty in\n let v1 = pack (Tv_Var (bv_of_binder b1)) in\n v1, b1, e1", "val subst_bv_in_comp : env -> bv -> typ -> term -> comp -> Tac comp\nlet subst_bv_in_comp e b sort t c =\n apply_subst_in_comp e c [((b, sort), t)]", "val pose_lemma (t: term) : Tac binder\nlet pose_lemma (t : term) : Tac binder =\n let c = tcc (cur_env ()) t in\n let pre, post =\n match inspect_comp c with\n | C_Lemma pre post _ -> pre, post\n | _ -> fail \"\"\n in\n let post = `((`#post) ()) in (* unthunk *)\n let post = norm_term [] post in\n (* If the precondition is trivial, do not cut by it *)\n match term_as_formula' pre with\n | True_ ->\n pose (`(__lemma_to_squash #(`#pre) #(`#post) () (fun () -> (`#t))))\n | _ ->\n let reqb = tcut (`squash (`#pre)) in\n\n let b = pose (`(__lemma_to_squash #(`#pre) #(`#post) (`#(binder_to_term reqb)) (fun () -> (`#t)))) in\n flip ();\n ignore (trytac trivial);\n b", "val paren (e: term) : Tac term\nlet paren (e : term) : Tac term =\n mk_flatten [mk_stringlit \"(\"; e; mk_stringlit \")\"]", "val elim_exists (t: term) : Tac (binder & binder)\nlet elim_exists (t : term) : Tac (binder & binder) =\n apply_lemma (`(__elim_exists' (`#(t))));\n let x = intro () in\n let pf = intro () in\n (x, pf)", "val null_var (v: var) : term\nlet null_var (v:var) : term =\n tm_var {nm_index=v;nm_ppname=ppname_default}", "val unsquash_equality (t: term) : Tac (option (term & term))\nlet unsquash_equality (t:term) : Tac (option (term & term)) =\n begin match term_as_formula t with\n | Comp (Eq _) l r -> Some (l, r)\n | _ -> None\n end", "val is_false : term -> Tac bool\nlet is_false t =\n begin match term_as_formula' t with\n | False_ -> true\n | _ -> begin match inspect t with\n | Tv_App l r ->\n begin match inspect l with\n | Tv_Abs b t ->\n begin match term_as_formula' t with\n | False_ -> true\n | _ -> false\n end\n | _ -> false\n end\n | _ -> false\n end\n end", "val assoc_varname_fail (#b: Type) (key: varname) (ls: list (varname * b)) : Tac b\nlet assoc_varname_fail (#b: Type) (key: varname) (ls: list (varname * b))\n : Tac b =\n match List.Tot.Base.assoc key ls with\n | None -> fail (\"Not found: \" ^ key)\n | Some x -> x", "val _debug_print_var (name: string) (t: term) : Tac unit\nlet _debug_print_var (name : string) (t : term) : Tac unit =\n print (\"_debug_print_var: \" ^ name ^ \": \" ^ term_to_string t);\n begin match safe_tc (top_env ()) t with\n | Some ty -> print (\"type: \" ^ term_to_string ty)\n | _ -> ()\n end;\n print (\"qualifier: \" ^ term_construct t);\n begin match inspect t with\n | Tv_Var bv ->\n let b : bv_view = inspect_bv bv in\n print (\"Tv_Var: ppname: \" ^ name_of_bv bv ^\n \"; index: \" ^ (string_of_int b.bv_index))\n | _ -> ()\n end;\n print \"end of _debug_print_var\"", "val subst_map (ss: list (namedv * fv)) (r t: term) : Tac term\nlet subst_map (ss : list (namedv * fv)) (r:term) (t : term) : Tac term =\n let subst = List.Tot.map (fun (x, fv) -> NT (Reflection.V2.pack_namedv x) (mk_e_app (Tv_FVar fv) [r])) ss in\n subst_term subst t", "val tassert (b: bool) : Tac (squash b)\nlet tassert (b: bool) : Tac (squash b) =\n if b\n then ()\n else\n let s = term_to_string (quote b) in\n fail (\"Tactic assertion failed: \" ^ s)", "val norm_term (s: list norm_step) (t: term) : Tac term\nlet norm_term (s : list norm_step) (t : term) : Tac term =\n let e =\n try cur_env ()\n with | _ -> top_env ()\n in\n norm_term_env e s t", "val norm_term (s: list norm_step) (t: term) : Tac term\nlet norm_term (s : list norm_step) (t : term) : Tac term =\n let e =\n try cur_env ()\n with | _ -> top_env ()\n in\n norm_term_env e s t", "val grewrite_eq (b: binding) : Tac unit\nlet grewrite_eq (b:binding) : Tac unit =\n match term_as_formula (type_of_binding b) with\n | Comp (Eq _) l r ->\n grewrite l r;\n iseq [idtac; (fun () -> exact b)]\n | _ ->\n begin match term_as_formula' (type_of_binding b) with\n | Comp (Eq _) l r ->\n grewrite l r;\n iseq [idtac; (fun () -> apply_lemma (`__un_sq_eq);\n exact b)]\n | _ ->\n fail \"grewrite_eq: binder type is not an equality\"\n end", "val goal_term_uvars (t: term) : Tac (list int)\nlet goal_term_uvars (t: term) : Tac (list int) =\n let hd, tl = collect_app t in\n if hd `is_fvar` (`%squash)\n then\n match tl with\n | [tl0, Q_Explicit] ->\n let _, tl1 = collect_app tl0 in\n simplify_list (argv_uvars tl1)\n | _ -> dump \"ill-formed squash\"; []\n else\n []", "val apply_lemma (t: term) : Tac unit\nlet apply_lemma (t : term) : Tac unit =\n t_apply_lemma false false t", "val apply_lemma (t: term) : Tac unit\nlet apply_lemma (t : term) : Tac unit =\n t_apply_lemma false false t", "val add_one (t: term) : Tac term\nlet add_one (t:term) : Tac term = `(`#t + 1)", "val contains_uvar (t: term) (uvs g: env) : T.Tac bool\nlet contains_uvar (t:term) (uvs:env) (g:env) : T.Tac bool =\n not (check_disjoint uvs (freevars t))", "val open_comp (b: R.binder) (t: comp) : Tac (binder & comp)\nlet open_comp (b : R.binder) (t : comp) : Tac (binder & comp) =\n let n = fresh () in\n let bv : binder_view = inspect_binder b in\n let nv : R.namedv = pack_namedv {\n uniq = n;\n sort = seal bv.sort;\n ppname = bv.ppname;\n }\n in\n let t' = subst_comp [DB 0 nv] t in\n let bndr : binder = {\n uniq = n;\n sort = bv.sort;\n ppname = bv.ppname;\n qual = bv.qual;\n attrs = bv.attrs;\n }\n in\n (bndr, t')", "val grewrite_eq (b: binder) : Tac unit\nlet grewrite_eq (b:binder) : Tac unit =\n match term_as_formula (type_of_binder b) with\n | Comp (Eq _) l r ->\n grewrite l r;\n iseq [idtac; (fun () -> exact (binder_to_term b))]\n | _ ->\n begin match term_as_formula' (type_of_binder b) with\n | Comp (Eq _) l r ->\n grewrite l r;\n iseq [idtac; (fun () -> apply_lemma (`__un_sq_eq);\n exact (binder_to_term b))]\n | _ ->\n fail \"grewrite_eq: binder type is not an equality\"\n end", "val elim_exists (t: term) : Tac (binding & binding)\nlet elim_exists (t : term) : Tac (binding & binding) =\n apply_lemma (`(__elim_exists' (`#(t))));\n let x = intro () in\n let pf = intro () in\n (x, pf)", "val pose_lemma (t: term) : Tac binding\nlet pose_lemma (t : term) : Tac binding =\n let c = tcc (cur_env ()) t in\n let pre, post =\n match c with\n | C_Lemma pre post _ -> pre, post\n | _ -> fail \"\"\n in\n let post = `((`#post) ()) in (* unthunk *)\n let post = norm_term [] post in\n (* If the precondition is trivial, do not cut by it *)\n match term_as_formula' pre with\n | True_ ->\n pose (`(__lemma_to_squash #(`#pre) #(`#post) () (fun () -> (`#t))))\n | _ ->\n let reqb = tcut (`squash (`#pre)) in\n\n let b = pose (`(__lemma_to_squash #(`#pre) #(`#post) (`#(reqb <: term)) (fun () -> (`#t)))) in\n flip ();\n ignore (trytac trivial);\n b", "val unfold_term (t: T.term) : T.Tac T.term\nlet unfold_term (t: T.term) : T.Tac T.term =\n match T.inspect t with\n | T.Tv_FVar v -> unfold_fv v\n | _ -> tfail \"Not a global variable\"", "val visit_many\n (t_i: term)\n (index_bv: option term)\n (inv_bv: term)\n (st: state)\n (bvs: list (name & (bv & typ)))\n (es: list term)\n : Tac (state & list term & list (name & (bv & typ)) & list sigelt)\nlet rec visit_function (t_i: term) (st: state) (f_name: name): Tac (state & list sigelt) =\n if (List.Tot.existsb (fun (name, _) -> name = f_name) st.seen) then\n let _ = print (st.indent ^ \"Already visited \" ^ string_of_name f_name) in\n // We don't need a three-state graph traversal since we automatically refuse\n // to visit a node marked with a let-rec.\n st, []\n\n else\n // Environment lookup.\n let f = lookup_typ (top_env ()) f_name in\n let f = match f with Some f -> f | None -> fail \"unexpected: name not in the environment\" in\n if not (has_attr f (`Meta.Attribute.specialize) || has_attr f (`Meta.Attribute.inline_)) then\n let _ = print (st.indent ^ \"Not visiting \" ^ string_of_name f_name) in\n // We want the user to specify which nodes should be traversed, otherwise,\n // we'd end up visiting the entire F* standard library.\n st, []\n else\n let _ = print (st.indent ^ \"Visiting \" ^ string_of_name f_name) in\n match inspect_sigelt f with\n | Sg_Let r lbs ->\n if r then\n fail (\"user error: \" ^ string_of_name f_name ^ \" is recursive\");\n let lbv = lookup_lb_view lbs f_name in\n let f_body = lbv.lb_def in\n let f_typ = lbv.lb_typ in\n let original_opts = sigelt_opts f in\n\n // Build a new function with proper parameters\n let old_indent = st.indent in\n let st = { st with indent = st.indent ^ \" \" } in\n let new_name = suffix_name f_name \"_higher\" in\n\n // The function may be of the form fun (x: index) -> ...\n // We recognize and distinguish this index, if present.\n let index_bvty, index_name, f_body =\n match inspect f_body with\n | Tv_Abs binder f_body' ->\n let { binder_bv = bv; binder_sort = t } = inspect_binder binder in\n let { bv_ppname = name } = inspect_bv bv in\n let name = unseal name in\n print (st.indent ^ \"Found \" ^ name ^ \", which is \" ^\n (if binder_is_legit f_name t_i binder then \"\" else \"NOT \") ^\n \"an index of type \" ^ term_to_string t);\n if binder_is_legit f_name t_i binder then begin\n Some (bv, t), name, f_body'\n end else\n // It can be convenient to specialize over a function without\n // the index as a parameter. In Curve, this is used to\n // specialize over store_felem64, a function that is already\n // specialized for the M64 value of the index, but that still\n // admits multiple implementations.\n None, \"\", f_body\n | _ ->\n fail (string_of_name f_name ^ \"is expected to be a function!\")\n in\n\n let inv_bv: bv = fresh_bv_named \"p\" in\n let inv_bv_sort : typ = `Type0 in\n\n let st, new_body, new_args, new_sigelts =\n let index_bv_tm_opt : option term =\n match index_bvty with\n | Some (index_bv, _sort) -> Some (pack (Tv_Var index_bv))\n | _ -> None\n in\n visit_body t_i index_bv_tm_opt (pack (Tv_Var inv_bv)) st [] f_body\n in\n let st = { st with indent = old_indent } in\n\n // Update the state with a mapping and which extra arguments are\n // needed. Each function that has been transformed has a type that's a\n // function of the index.\n\n let m = if has_attr f (`Meta.Attribute.specialize) then Specialize else Inline new_name in\n let new_args, new_bvs = List.Tot.split new_args in\n\n // The type of ``f`` when it appears as a ``gi`` parameter, i.e. its ``gi_t``.\n let f_typ_name = suffix_name f_name \"_higher_t\" in\n let f_typ, f_typ_typ, has_index =\n match index_bvty with\n | Some (index_bv, index_bv_sort) ->\n lambda_over_index_and_p st f_name f_typ inv_bv inv_bv_sort,\n mk_tot_arr [ mk_implicit_binder index_bv index_bv_sort ] (\n mk_tot_arr [ mk_binder inv_bv inv_bv_sort ] (`Type0)),\n true\n | _ ->\n lambda_over_only_p st inv_bv inv_bv_sort f_typ,\n mk_tot_arr [ mk_binder inv_bv inv_bv_sort ] (`Type0),\n false\n in\n print (st.indent ^ \" let \" ^ string_of_name f_typ_name ^ \": \" ^\n term_to_string f_typ_typ ^ \" = \" ^\n term_to_string f_typ);\n let lb = pack_lb ({lb_fv = pack_fv f_typ_name;\n lb_us = [];\n lb_typ = f_typ_typ;\n lb_def = f_typ}) in\n let se_t = pack_sigelt (Sg_Let false [lb]) in\n let se_t = set_sigelt_quals [ NoExtract; Inline_for_extraction ] se_t in\n let se_t = match original_opts with\n | Some original_opts -> add_check_with original_opts se_t\n | _ -> se_t\n in\n let f_typ = pack (Tv_FVar (pack_fv f_typ_name)) in\n let st = { st with seen = (f_name, (has_index, f_typ, m, new_args)) :: st.seen } in\n\n // For debugging. This is very meta.\n let se_debug msg: Tac sigelt =\n let deps = map string_of_name new_args in\n let deps =\n match deps with\n | _ :: _ -> \" (needs: \" ^ String.concat \", \" deps ^ \")\"\n | _ -> \"\"\n in\n let quote_string s : Tac term = pack (Tv_Const (C_String s)) in\n let lb = pack_lb ({lb_fv =\n pack_fv (suffix_name f_name \"_higher_debug_print\");\n lb_us = [];\n lb_typ = (`unit);\n lb_def =\n (`(let x: unit =\n _ by (\n print (`#(quote_string msg) ^ \" \" ^\n (`#(quote_string (string_of_name new_name))) ^\n `#(quote_string deps));\n exact tm_unit) in\n x))}) in\n\n pack_sigelt (Sg_Let false [lb])\n in\n\n // Fast-path; just register the function as being a specialize node\n // but don't rewrite it or splice a new declaration.\n if false && List.length new_args = 0 then begin\n if not (has_inline_for_extraction f) then\n fail (string_of_name f_name ^ \" should be inline_for_extraction\");\n if not (Specialize? m) then\n fail (string_of_name f_name ^ \" is marked as [@ inline_ ] but does not reach \\\n any specializations\");\n\n st, new_sigelts @ [ se_debug \"Checking only a type:\"; se_t ]\n end\n\n else\n\n // new_body is: fun (g1: g1_t i) ... (gn: gn_t i) x -> (e: f_t i)\n // i is free\n let new_body =\n fold_right (fun (_, (bv, sort)) acc ->\n pack (Tv_Abs (mk_binder bv sort) acc)\n ) (zip new_args new_bvs) new_body\n in\n\n // Declaration for the new resulting function. We need to construct\n // the actual type of ``f``.\n // BUG: without the eta-expansion around mk_binder, \"tactic got stuck\".\n let new_body = pack (Tv_Abs (mk_binder inv_bv inv_bv_sort) new_body) in\n let new_body =\n match index_bvty with\n | Some (index_bv, index_bv_sort) -> pack (Tv_Abs (mk_implicit_binder index_bv index_bv_sort) new_body)\n | _ -> new_body\n in\n let new_typ =\n let new_binders = List.Tot.map (fun (bv, sort) -> mk_binder bv sort) new_bvs in\n let new_binders = mk_binder inv_bv inv_bv_sort :: new_binders in\n let app_inv (t: term): Tac term = pack (Tv_App t (pack (Tv_Var inv_bv), Q_Explicit)) in\n match index_bvty with\n | Some (index_bv, index_bv_sort) ->\n mk_tot_arr\n (mk_implicit_binder index_bv index_bv_sort :: new_binders)\n (app_inv (pack (Tv_App f_typ (pack (Tv_Var index_bv), Q_Implicit))))\n | _ ->\n mk_tot_arr new_binders (app_inv f_typ)\n in\n let lb = pack_lb ({lb_fv = pack_fv new_name;\n lb_us = [];\n lb_typ = new_typ;\n lb_def = new_body}) in\n let se = pack_sigelt (Sg_Let false [lb]) in\n let se = set_sigelt_quals [ NoExtract; Inline_for_extraction ] se in\n let se = match original_opts with\n | Some original_opts -> add_check_with original_opts se\n | _ -> se\n in\n print (st.indent ^ \" let \" ^ string_of_name new_name ^ \":\\n\" ^\n st.indent ^ term_to_string new_typ ^ \"\\n\" ^\n st.indent ^ \"=\\n\" ^\n st.indent ^ term_to_string new_body);\n\n st, new_sigelts @ [\n se_debug (\"Checking type and definition [\" ^ string_of_mapping m ^ \"]:\"); se_t; se\n ]\n\n | _ ->\n if has_attr f (`Meta.Attribute.specialize) then\n let inv_bv: bv = fresh_bv_named \"p\" in\n let inv_bv_sort : typ = `Type0 in\n\n // Assuming that this is a val, but we can't inspect it. Let's work around this.\n let t = pack (Tv_FVar (pack_fv f_name)) in\n let f_typ = tc (top_env ()) t in\n print (st.indent ^ \" Assuming \" ^ string_of_name f_name ^ \": \" ^\n term_to_string f_typ ^ \" is a val\\n\");\n let f_typ, has_index =\n match inspect f_typ with\n | Tv_Arrow bv _ ->\n if binder_is_legit f_name t_i bv then\n lambda_over_index_and_p st f_name f_typ inv_bv inv_bv_sort, true\n else\n lambda_over_only_p st inv_bv inv_bv_sort f_typ, false\n | _ ->\n lambda_over_only_p st inv_bv inv_bv_sort f_typ, false // fail (string_of_name f_name ^ \" does not have an arrow type\")\n in\n print (st.indent ^ \" Registering \" ^ string_of_name f_name ^ \" with type \" ^\n term_to_string f_typ);\n let st = { st with seen = (f_name, (has_index, f_typ, Specialize, [])) :: st.seen } in\n st, []\n else\n st, []\n\nand visit_many (t_i: term)\n (index_bv: option term)\n (inv_bv: term)\n (st: state)\n (bvs: list (name & (bv & typ)))\n (es: list term):\n Tac (state & list term & list (name & (bv & typ)) & list sigelt)\n=\n let st, es, bvs, ses = fold_left (fun (st, es, bvs, ses) e ->\n let st, e, bvs, ses' = visit_body t_i index_bv inv_bv st bvs e in\n st, e :: es, bvs, ses @ ses'\n ) (st, [], bvs, []) es in\n let es = List.Tot.rev es in\n st, es, bvs, ses\n\nand visit_body (t_i: term)\n (index_bv: option term)\n (inv_bv: term)\n (st: state) // state-passing\n (bvs: list (name & (bv & typ))) // state-passing\n (e: term):\n Tac (state & term & list (name & (bv & typ)) & list sigelt)\n=\n // st is state that is threaded through\n // bvs are the extra parameters for this function we have allocated; threaded\n // through as well to avoid allocating the same thing twice\n // ses is strictly bottom-up\n match inspect e with\n | Tv_App _ _ ->\n let e, es = collect_app e in\n\n // Recursively visit arguments\n let es, qs = List.Pure.split es in\n let st, es, bvs, ses = visit_many t_i index_bv inv_bv st bvs es in\n let es = zip es qs in\n\n // If this is an application ...\n begin match inspect e with\n | Tv_UInst fv _\n | Tv_FVar fv ->\n // ... of a top-level name ...\n let fv = inspect_fv fv in\n let st, ses' = visit_function t_i st fv in\n let ses = ses @ ses' in\n // visit_function fills out st.seen with an entry for this lid, if\n // this is something we wish to rewrite\n begin match List.Tot.assoc fv st.seen with\n | Some (has_index, _, map, fns) ->\n print (st.indent ^ \"Rewriting application of \" ^ string_of_name fv);\n\n let index_arg, es =\n if has_index then\n match es with\n | (e, Q_Implicit) :: es ->\n Some e, es\n | _ ->\n fail \"this application does not seem to start with an index\"\n else\n None, es\n in\n\n // A helper that says: I will need a specialized instance of `name`,\n // so allocate an extra parameter for this current function if\n // needed.\n let allocate_bv_for name bvs : Tac ((term & aqualv) & list (Reflection.name & (bv & typ))) =\n match List.Tot.assoc name bvs with\n | Some (bv, sort) ->\n print (st.indent ^ string_of_name name ^ \" already has a bv\");\n // fv needs to receive a specialized instance of name;\n // it's already found in this function's own bvs\n (pack (Tv_Var bv), Q_Explicit), bvs\n | None ->\n // this is the first time the current function needs to\n // receive a specialized instance of name; add it to this\n // function's own bvs\n let needs_index, typ, _, _ = assoc name st.seen in\n if needs_index && not (Some? index_arg) then\n fail (\"Index inconsistency in bv for \" ^ string_of_name name);\n\n print (st.indent ^ \"Allocating bv for \" ^ string_of_name name ^ \" at type \" ^\n \"app <\" ^ term_to_string typ ^ \"> <\" ^\n (if needs_index then term_to_string (must index_arg) else \"no-index\") ^ \">\");\n\n let typ =\n if needs_index then pack (Tv_App typ (must index_arg, Q_Implicit)) else typ\n in\n let typ = pack (Tv_App typ (inv_bv, Q_Explicit)) in\n let bv: bv = fresh_bv_named (\"arg_\" ^ string_of_name name) in\n (pack (Tv_Var bv), Q_Explicit), (name, (bv, typ)) :: bvs\n in\n\n begin match map with\n | Inline fv ->\n // fv has been rewritten to take fns as extra arguments for the\n // specialize nodes reachable through the body of fv; we need\n // ourselves to take a dependency on those nodes\n let extra_args, bvs = fold_left (fun (extra_args, bvs) name ->\n let term, bvs = allocate_bv_for name bvs in\n term :: extra_args, bvs\n ) ([], bvs) fns in\n let extra_args = List.rev extra_args in\n let extra_args = (inv_bv, Q_Explicit) :: extra_args in\n let extra_args =\n // Inline nodes retain their index (if any).\n if has_index then (must index_bv, Q_Implicit) :: extra_args else extra_args\n in\n\n let e = mk_app (pack (Tv_FVar (pack_fv fv))) (extra_args @ es) in\n st, e, bvs, ses\n\n | Specialize ->\n // Specialized nodes are received as parameters and no longer have the index.\n let e, bvs = allocate_bv_for fv bvs in\n let e = mk_app (fst e) es in\n st, e, bvs, ses\n end\n\n | None ->\n let e = mk_app e es in\n st, e, bvs, ses\n end\n | _ ->\n let e = mk_app e es in\n st, e, bvs, ses\n end\n\n | Tv_Var _ | Tv_BVar _ | Tv_UInst _ _ | Tv_FVar _\n | Tv_Const _ ->\n st, e, bvs, []\n\n | Tv_Abs b e ->\n let st, e, bvs, ses = visit_body t_i index_bv inv_bv st bvs e in\n let e = pack (Tv_Abs b e) in\n st, e, bvs, ses\n\n | Tv_Match scrut _returns branches ->\n let st, scrut, bvs, ses = visit_body t_i index_bv inv_bv st bvs scrut in\n let pats, es = List.Tot.split branches in\n let st, es, bvs, ses' = visit_many t_i index_bv inv_bv st bvs es in\n let branches = zip pats es in\n st, pack (Tv_Match scrut _returns branches), bvs, ses @ ses'\n\n | Tv_Let r attrs bv ty e1 e2 ->\n let st, e1, bvs, ses = visit_body t_i index_bv inv_bv st bvs e1 in\n let st, e2, bvs, ses' = visit_body t_i index_bv inv_bv st bvs e2 in\n let e = pack (Tv_Let r attrs bv ty e1 e2) in\n st, e, bvs, ses @ ses'\n\n | Tv_AscribedT e t tac use_eq ->\n let st, e, bvs, ses = visit_body t_i index_bv inv_bv st bvs e in\n let e = pack (Tv_AscribedT e t tac use_eq) in\n st, e, bvs, ses\n\n | Tv_AscribedC e c tac use_eq ->\n let st, e, bvs, ses = visit_body t_i index_bv inv_bv st bvs e in\n let e = pack (Tv_AscribedC e c tac use_eq) in\n st, e, bvs, ses\n\n | Tv_Arrow _ _\n | Tv_Type _\n | Tv_Uvar _ _\n | Tv_Refine _ _ _\n | Tv_Unknown\n (* Redundant underscore to catch for soon-to-come\n addition of Tv_Unsupp *)\n | _ ->\n // Looks like we ended up visiting a type argument of an application.\n st, e, bvs, []", "val visit_br (ff: (term -> Tac unit)) (b: branch) : Tac unit\nlet rec visit_tm (ff : term -> Tac unit) (t : term) : Tac unit =\n let tv = inspect t in\n (match tv with\n | Tv_FVar _\n | Tv_UInst _ _\n | Tv_Var _\n | Tv_BVar _ -> ()\n\n | Tv_Type _ -> ()\n | Tv_Const c -> ()\n | Tv_Uvar i u -> ()\n | Tv_Unsupp -> ()\n | Tv_Unknown -> ()\n | Tv_Arrow b c ->\n on_sort_binder ff b;\n visit_comp ff c\n | Tv_Abs b t ->\n let b = on_sort_binder (visit_tm ff) b in\n visit_tm ff t\n\n | Tv_App l (r, q) ->\n visit_tm ff l;\n visit_tm ff r\n\n | Tv_Refine b r ->\n on_sort_binder ff b;\n visit_tm ff r\n\n | Tv_Let r attrs b def t ->\n on_sort_binder ff b;\n visit_tm ff def;\n visit_tm ff t\n\n | Tv_Match sc _ brs ->\n visit_tm ff sc;\n iter (visit_br ff) brs\n\n | Tv_AscribedT e t topt _ ->\n visit_tm ff e;\n visit_tm ff t\n\n | Tv_AscribedC e c topt _ ->\n visit_tm ff e\n\n ); ff t\n\nand visit_br (ff : term -> Tac unit) (b:branch) : Tac unit =\n let (p, t) = b in\n visit_tm ff t\n\nand visit_comp (ff : term -> Tac unit) (c : comp) : Tac unit =\n let cv = inspect_comp c in\n match cv with\n | C_Total ret -> visit_tm ff ret\n | C_GTotal ret -> visit_tm ff ret\n\n | C_Lemma pre post pats ->\n visit_tm ff pre;\n visit_tm ff post;\n visit_tm ff pats\n\n | C_Eff us eff res args decrs ->\n visit_tm ff res;\n iter (fun (a, q) -> visit_tm ff a) args;\n iter (visit_tm ff) decrs", "val genv_push_bv (ge: genv) (b: bv) (sort: typ) (abs: bool) (t: option term) : Tac genv\nlet genv_push_bv (ge:genv) (b:bv) (sort:typ) (abs:bool) (t:option term) : Tac genv =\n let br = mk_binder b sort in\n let sv = genv_get_from_name ge (name_of_bv b) in\n let svars' = if Some? sv then fst (Some?.v sv) :: ge.svars else ge.svars in\n let e' = push_binder ge.env br in\n let tm = if Some? t then Some?.v t else pack (Tv_Var b) in\n let bmap' = bind_map_push ge.bmap b (sort, abs, tm) in\n mk_genv e' bmap' svars'", "val r_b2t (t: R.term) : R.term\nlet r_b2t (t:R.term) \n : R.term \n = R.(pack_ln (Tv_App (pack_ln (Tv_FVar b2t_fv)) (t, Q_Explicit)))", "val r_b2t (t: R.term) : R.term\nlet r_b2t (t:R.term) \n : R.term \n = R.(pack_ln (Tv_App (pack_ln (Tv_FVar RT.b2t_fv)) (t, Q_Explicit)))", "val state_or_fail (s: machine_state) (b: bool) (s': machine_state) : machine_state\nlet state_or_fail (s:machine_state) (b:bool) (s':machine_state) : machine_state =\n if b then s' else {s with ms_ok = false}", "val open_term_n_with (bs: list R.binder) (nbs: list binder) (t: term) : Tac term\nlet rec open_term_n_with (bs : list R.binder) (nbs : list binder) (t : term) : Tac term =\n match bs, nbs with\n | [], [] -> t\n | b::bs, nb::nbs ->\n let t' = open_term_n_with bs nbs t in\n let t'' = open_term_with b nb t' in\n t''\n | _ -> raise LengthMismatch", "val open_term_n_simple (bs: list R.simple_binder) (t: term) : Tac (list simple_binder & term)\nlet rec open_term_n_simple (bs : list R.simple_binder) (t : term) : Tac (list simple_binder & term) =\n match bs with\n | [] -> ([], t)\n | b::bs ->\n let bs', t' = open_term_n_simple bs t in\n let b', t'' = open_term_simple b t' in\n (b'::bs', t'')", "val lambda_over_only_p (st: state) (inv_bv: bv) (sort: typ) (f_typ: term) : Tac term\nlet lambda_over_only_p (st: state) (inv_bv: bv) (sort : typ) (f_typ: term): Tac term =\n let fvs = to_reduce f_typ in\n print (\" Names to reduce in \" ^ term_to_string f_typ ^ \": \" ^ String.concat \", \" fvs);\n let f_typ = norm_term_env (top_env ()) [ delta_only (to_reduce f_typ) ] f_typ in\n lambda_over_p inv_bv sort (push_pre st inv_bv f_typ)", "val guard (b: bool)\n : TacH unit\n (requires (fun _ -> True))\n (ensures (fun ps r -> if b then Success? r /\\ Success?.ps r == ps else Failed? r))\nlet guard (b : bool) : TacH unit (requires (fun _ -> True))\n (ensures (fun ps r -> if b\n then Success? r /\\ Success?.ps r == ps\n else Failed? r))\n (* ^ the proofstate on failure is not exactly equal (has the psc set) *)\n =\n if not b then\n fail \"guard failed\"\n else ()", "val guard (b: bool)\n : TacH unit\n (requires (fun _ -> True))\n (ensures (fun ps r -> if b then Success? r /\\ Success?.ps r == ps else Failed? r))\nlet guard (b : bool) : TacH unit (requires (fun _ -> True))\n (ensures (fun ps r -> if b\n then Success? r /\\ Success?.ps r == ps\n else Failed? r))\n (* ^ the proofstate on failure is not exactly equal (has the psc set) *)\n =\n if not b then\n fail \"guard failed\"\n else ()", "val term_as_formula (t: term) : Tac formula\nlet term_as_formula (t:term) : Tac formula =\n match unsquash_term t with\n | None -> F_Unknown\n | Some t ->\n term_as_formula' t", "val term_as_formula (t: term) : Tac formula\nlet term_as_formula (t:term) : Tac formula =\n match unsquash_term t with\n | None -> F_Unknown\n | Some t ->\n term_as_formula' t", "val term_of_pat (t: T.pattern) : T.Tac (option T.term)\nlet term_of_pat (t: T.pattern) : T.Tac (option T.term) =\n match t with\n | T.Pat_Constant {c=v} -> Some (T.pack (T.Tv_Const v))\n | T.Pat_Cons {head=v; univs=None; subpats=[]} -> Some (T.pack (T.Tv_FVar v))\n | T.Pat_Cons {head=v; univs=Some []; subpats=[]} -> Some (T.pack (T.Tv_FVar v)) \n | T.Pat_Cons {head=v; univs=Some us; subpats=[]} -> Some (T.pack (T.Tv_UInst v us)) \n | _ -> None", "val open_pat (p: R.pattern) (s: subst_t) : Tac (pattern & subst_t)\nlet rec open_pat (p : R.pattern) (s : subst_t) : Tac (pattern & subst_t) =\n match p with\n | R.Pat_Constant c ->\n Pat_Constant {c=c}, s\n\n | R.Pat_Var ssort n ->\n let sort = unseal ssort in\n let sort = subst_term s sort in\n let nvv : namedv = {\n uniq = fresh();\n sort = seal sort;\n ppname = n;\n }\n in\n let nv = pack_namedv nvv in\n Pat_Var {v=nvv; sort=seal sort}, (DB 0 nv) :: shift_subst 1 s\n\n | R.Pat_Cons head univs subpats ->\n let subpats, s = fold_left (fun (pats,s) (pat,b) ->\n let pat, s' = open_pat pat s in\n ((pat,b)::pats, s'))\n ([], s) subpats\n in\n let subpats = List.Tot.rev subpats in\n Pat_Cons {head=head; univs=univs; subpats=subpats}, s\n\n | R.Pat_Dot_Term None ->\n Pat_Dot_Term {t=None}, s\n\n | R.Pat_Dot_Term (Some t) ->\n let t = subst_term s t in\n Pat_Dot_Term {t=Some t}, s", "val visit_body\n (t_i: term)\n (index_bv: option term)\n (inv_bv: term)\n (st: state)\n (bvs: list (name & (bv & typ)))\n (e: term)\n : Tac (state & term & list (name & (bv & typ)) & list sigelt)\nlet rec visit_function (t_i: term) (st: state) (f_name: name): Tac (state & list sigelt) =\n if (List.Tot.existsb (fun (name, _) -> name = f_name) st.seen) then\n let _ = print (st.indent ^ \"Already visited \" ^ string_of_name f_name) in\n // We don't need a three-state graph traversal since we automatically refuse\n // to visit a node marked with a let-rec.\n st, []\n\n else\n // Environment lookup.\n let f = lookup_typ (top_env ()) f_name in\n let f = match f with Some f -> f | None -> fail \"unexpected: name not in the environment\" in\n if not (has_attr f (`Meta.Attribute.specialize) || has_attr f (`Meta.Attribute.inline_)) then\n let _ = print (st.indent ^ \"Not visiting \" ^ string_of_name f_name) in\n // We want the user to specify which nodes should be traversed, otherwise,\n // we'd end up visiting the entire F* standard library.\n st, []\n else\n let _ = print (st.indent ^ \"Visiting \" ^ string_of_name f_name) in\n match inspect_sigelt f with\n | Sg_Let r lbs ->\n if r then\n fail (\"user error: \" ^ string_of_name f_name ^ \" is recursive\");\n let lbv = lookup_lb_view lbs f_name in\n let f_body = lbv.lb_def in\n let f_typ = lbv.lb_typ in\n let original_opts = sigelt_opts f in\n\n // Build a new function with proper parameters\n let old_indent = st.indent in\n let st = { st with indent = st.indent ^ \" \" } in\n let new_name = suffix_name f_name \"_higher\" in\n\n // The function may be of the form fun (x: index) -> ...\n // We recognize and distinguish this index, if present.\n let index_bvty, index_name, f_body =\n match inspect f_body with\n | Tv_Abs binder f_body' ->\n let { binder_bv = bv; binder_sort = t } = inspect_binder binder in\n let { bv_ppname = name } = inspect_bv bv in\n let name = unseal name in\n print (st.indent ^ \"Found \" ^ name ^ \", which is \" ^\n (if binder_is_legit f_name t_i binder then \"\" else \"NOT \") ^\n \"an index of type \" ^ term_to_string t);\n if binder_is_legit f_name t_i binder then begin\n Some (bv, t), name, f_body'\n end else\n // It can be convenient to specialize over a function without\n // the index as a parameter. In Curve, this is used to\n // specialize over store_felem64, a function that is already\n // specialized for the M64 value of the index, but that still\n // admits multiple implementations.\n None, \"\", f_body\n | _ ->\n fail (string_of_name f_name ^ \"is expected to be a function!\")\n in\n\n let inv_bv: bv = fresh_bv_named \"p\" in\n let inv_bv_sort : typ = `Type0 in\n\n let st, new_body, new_args, new_sigelts =\n let index_bv_tm_opt : option term =\n match index_bvty with\n | Some (index_bv, _sort) -> Some (pack (Tv_Var index_bv))\n | _ -> None\n in\n visit_body t_i index_bv_tm_opt (pack (Tv_Var inv_bv)) st [] f_body\n in\n let st = { st with indent = old_indent } in\n\n // Update the state with a mapping and which extra arguments are\n // needed. Each function that has been transformed has a type that's a\n // function of the index.\n\n let m = if has_attr f (`Meta.Attribute.specialize) then Specialize else Inline new_name in\n let new_args, new_bvs = List.Tot.split new_args in\n\n // The type of ``f`` when it appears as a ``gi`` parameter, i.e. its ``gi_t``.\n let f_typ_name = suffix_name f_name \"_higher_t\" in\n let f_typ, f_typ_typ, has_index =\n match index_bvty with\n | Some (index_bv, index_bv_sort) ->\n lambda_over_index_and_p st f_name f_typ inv_bv inv_bv_sort,\n mk_tot_arr [ mk_implicit_binder index_bv index_bv_sort ] (\n mk_tot_arr [ mk_binder inv_bv inv_bv_sort ] (`Type0)),\n true\n | _ ->\n lambda_over_only_p st inv_bv inv_bv_sort f_typ,\n mk_tot_arr [ mk_binder inv_bv inv_bv_sort ] (`Type0),\n false\n in\n print (st.indent ^ \" let \" ^ string_of_name f_typ_name ^ \": \" ^\n term_to_string f_typ_typ ^ \" = \" ^\n term_to_string f_typ);\n let lb = pack_lb ({lb_fv = pack_fv f_typ_name;\n lb_us = [];\n lb_typ = f_typ_typ;\n lb_def = f_typ}) in\n let se_t = pack_sigelt (Sg_Let false [lb]) in\n let se_t = set_sigelt_quals [ NoExtract; Inline_for_extraction ] se_t in\n let se_t = match original_opts with\n | Some original_opts -> add_check_with original_opts se_t\n | _ -> se_t\n in\n let f_typ = pack (Tv_FVar (pack_fv f_typ_name)) in\n let st = { st with seen = (f_name, (has_index, f_typ, m, new_args)) :: st.seen } in\n\n // For debugging. This is very meta.\n let se_debug msg: Tac sigelt =\n let deps = map string_of_name new_args in\n let deps =\n match deps with\n | _ :: _ -> \" (needs: \" ^ String.concat \", \" deps ^ \")\"\n | _ -> \"\"\n in\n let quote_string s : Tac term = pack (Tv_Const (C_String s)) in\n let lb = pack_lb ({lb_fv =\n pack_fv (suffix_name f_name \"_higher_debug_print\");\n lb_us = [];\n lb_typ = (`unit);\n lb_def =\n (`(let x: unit =\n _ by (\n print (`#(quote_string msg) ^ \" \" ^\n (`#(quote_string (string_of_name new_name))) ^\n `#(quote_string deps));\n exact tm_unit) in\n x))}) in\n\n pack_sigelt (Sg_Let false [lb])\n in\n\n // Fast-path; just register the function as being a specialize node\n // but don't rewrite it or splice a new declaration.\n if false && List.length new_args = 0 then begin\n if not (has_inline_for_extraction f) then\n fail (string_of_name f_name ^ \" should be inline_for_extraction\");\n if not (Specialize? m) then\n fail (string_of_name f_name ^ \" is marked as [@ inline_ ] but does not reach \\\n any specializations\");\n\n st, new_sigelts @ [ se_debug \"Checking only a type:\"; se_t ]\n end\n\n else\n\n // new_body is: fun (g1: g1_t i) ... (gn: gn_t i) x -> (e: f_t i)\n // i is free\n let new_body =\n fold_right (fun (_, (bv, sort)) acc ->\n pack (Tv_Abs (mk_binder bv sort) acc)\n ) (zip new_args new_bvs) new_body\n in\n\n // Declaration for the new resulting function. We need to construct\n // the actual type of ``f``.\n // BUG: without the eta-expansion around mk_binder, \"tactic got stuck\".\n let new_body = pack (Tv_Abs (mk_binder inv_bv inv_bv_sort) new_body) in\n let new_body =\n match index_bvty with\n | Some (index_bv, index_bv_sort) -> pack (Tv_Abs (mk_implicit_binder index_bv index_bv_sort) new_body)\n | _ -> new_body\n in\n let new_typ =\n let new_binders = List.Tot.map (fun (bv, sort) -> mk_binder bv sort) new_bvs in\n let new_binders = mk_binder inv_bv inv_bv_sort :: new_binders in\n let app_inv (t: term): Tac term = pack (Tv_App t (pack (Tv_Var inv_bv), Q_Explicit)) in\n match index_bvty with\n | Some (index_bv, index_bv_sort) ->\n mk_tot_arr\n (mk_implicit_binder index_bv index_bv_sort :: new_binders)\n (app_inv (pack (Tv_App f_typ (pack (Tv_Var index_bv), Q_Implicit))))\n | _ ->\n mk_tot_arr new_binders (app_inv f_typ)\n in\n let lb = pack_lb ({lb_fv = pack_fv new_name;\n lb_us = [];\n lb_typ = new_typ;\n lb_def = new_body}) in\n let se = pack_sigelt (Sg_Let false [lb]) in\n let se = set_sigelt_quals [ NoExtract; Inline_for_extraction ] se in\n let se = match original_opts with\n | Some original_opts -> add_check_with original_opts se\n | _ -> se\n in\n print (st.indent ^ \" let \" ^ string_of_name new_name ^ \":\\n\" ^\n st.indent ^ term_to_string new_typ ^ \"\\n\" ^\n st.indent ^ \"=\\n\" ^\n st.indent ^ term_to_string new_body);\n\n st, new_sigelts @ [\n se_debug (\"Checking type and definition [\" ^ string_of_mapping m ^ \"]:\"); se_t; se\n ]\n\n | _ ->\n if has_attr f (`Meta.Attribute.specialize) then\n let inv_bv: bv = fresh_bv_named \"p\" in\n let inv_bv_sort : typ = `Type0 in\n\n // Assuming that this is a val, but we can't inspect it. Let's work around this.\n let t = pack (Tv_FVar (pack_fv f_name)) in\n let f_typ = tc (top_env ()) t in\n print (st.indent ^ \" Assuming \" ^ string_of_name f_name ^ \": \" ^\n term_to_string f_typ ^ \" is a val\\n\");\n let f_typ, has_index =\n match inspect f_typ with\n | Tv_Arrow bv _ ->\n if binder_is_legit f_name t_i bv then\n lambda_over_index_and_p st f_name f_typ inv_bv inv_bv_sort, true\n else\n lambda_over_only_p st inv_bv inv_bv_sort f_typ, false\n | _ ->\n lambda_over_only_p st inv_bv inv_bv_sort f_typ, false // fail (string_of_name f_name ^ \" does not have an arrow type\")\n in\n print (st.indent ^ \" Registering \" ^ string_of_name f_name ^ \" with type \" ^\n term_to_string f_typ);\n let st = { st with seen = (f_name, (has_index, f_typ, Specialize, [])) :: st.seen } in\n st, []\n else\n st, []\n\nand visit_many (t_i: term)\n (index_bv: option term)\n (inv_bv: term)\n (st: state)\n (bvs: list (name & (bv & typ)))\n (es: list term):\n Tac (state & list term & list (name & (bv & typ)) & list sigelt)\n=\n let st, es, bvs, ses = fold_left (fun (st, es, bvs, ses) e ->\n let st, e, bvs, ses' = visit_body t_i index_bv inv_bv st bvs e in\n st, e :: es, bvs, ses @ ses'\n ) (st, [], bvs, []) es in\n let es = List.Tot.rev es in\n st, es, bvs, ses\n\nand visit_body (t_i: term)\n (index_bv: option term)\n (inv_bv: term)\n (st: state) // state-passing\n (bvs: list (name & (bv & typ))) // state-passing\n (e: term):\n Tac (state & term & list (name & (bv & typ)) & list sigelt)\n=\n // st is state that is threaded through\n // bvs are the extra parameters for this function we have allocated; threaded\n // through as well to avoid allocating the same thing twice\n // ses is strictly bottom-up\n match inspect e with\n | Tv_App _ _ ->\n let e, es = collect_app e in\n\n // Recursively visit arguments\n let es, qs = List.Pure.split es in\n let st, es, bvs, ses = visit_many t_i index_bv inv_bv st bvs es in\n let es = zip es qs in\n\n // If this is an application ...\n begin match inspect e with\n | Tv_UInst fv _\n | Tv_FVar fv ->\n // ... of a top-level name ...\n let fv = inspect_fv fv in\n let st, ses' = visit_function t_i st fv in\n let ses = ses @ ses' in\n // visit_function fills out st.seen with an entry for this lid, if\n // this is something we wish to rewrite\n begin match List.Tot.assoc fv st.seen with\n | Some (has_index, _, map, fns) ->\n print (st.indent ^ \"Rewriting application of \" ^ string_of_name fv);\n\n let index_arg, es =\n if has_index then\n match es with\n | (e, Q_Implicit) :: es ->\n Some e, es\n | _ ->\n fail \"this application does not seem to start with an index\"\n else\n None, es\n in\n\n // A helper that says: I will need a specialized instance of `name`,\n // so allocate an extra parameter for this current function if\n // needed.\n let allocate_bv_for name bvs : Tac ((term & aqualv) & list (Reflection.name & (bv & typ))) =\n match List.Tot.assoc name bvs with\n | Some (bv, sort) ->\n print (st.indent ^ string_of_name name ^ \" already has a bv\");\n // fv needs to receive a specialized instance of name;\n // it's already found in this function's own bvs\n (pack (Tv_Var bv), Q_Explicit), bvs\n | None ->\n // this is the first time the current function needs to\n // receive a specialized instance of name; add it to this\n // function's own bvs\n let needs_index, typ, _, _ = assoc name st.seen in\n if needs_index && not (Some? index_arg) then\n fail (\"Index inconsistency in bv for \" ^ string_of_name name);\n\n print (st.indent ^ \"Allocating bv for \" ^ string_of_name name ^ \" at type \" ^\n \"app <\" ^ term_to_string typ ^ \"> <\" ^\n (if needs_index then term_to_string (must index_arg) else \"no-index\") ^ \">\");\n\n let typ =\n if needs_index then pack (Tv_App typ (must index_arg, Q_Implicit)) else typ\n in\n let typ = pack (Tv_App typ (inv_bv, Q_Explicit)) in\n let bv: bv = fresh_bv_named (\"arg_\" ^ string_of_name name) in\n (pack (Tv_Var bv), Q_Explicit), (name, (bv, typ)) :: bvs\n in\n\n begin match map with\n | Inline fv ->\n // fv has been rewritten to take fns as extra arguments for the\n // specialize nodes reachable through the body of fv; we need\n // ourselves to take a dependency on those nodes\n let extra_args, bvs = fold_left (fun (extra_args, bvs) name ->\n let term, bvs = allocate_bv_for name bvs in\n term :: extra_args, bvs\n ) ([], bvs) fns in\n let extra_args = List.rev extra_args in\n let extra_args = (inv_bv, Q_Explicit) :: extra_args in\n let extra_args =\n // Inline nodes retain their index (if any).\n if has_index then (must index_bv, Q_Implicit) :: extra_args else extra_args\n in\n\n let e = mk_app (pack (Tv_FVar (pack_fv fv))) (extra_args @ es) in\n st, e, bvs, ses\n\n | Specialize ->\n // Specialized nodes are received as parameters and no longer have the index.\n let e, bvs = allocate_bv_for fv bvs in\n let e = mk_app (fst e) es in\n st, e, bvs, ses\n end\n\n | None ->\n let e = mk_app e es in\n st, e, bvs, ses\n end\n | _ ->\n let e = mk_app e es in\n st, e, bvs, ses\n end\n\n | Tv_Var _ | Tv_BVar _ | Tv_UInst _ _ | Tv_FVar _\n | Tv_Const _ ->\n st, e, bvs, []\n\n | Tv_Abs b e ->\n let st, e, bvs, ses = visit_body t_i index_bv inv_bv st bvs e in\n let e = pack (Tv_Abs b e) in\n st, e, bvs, ses\n\n | Tv_Match scrut _returns branches ->\n let st, scrut, bvs, ses = visit_body t_i index_bv inv_bv st bvs scrut in\n let pats, es = List.Tot.split branches in\n let st, es, bvs, ses' = visit_many t_i index_bv inv_bv st bvs es in\n let branches = zip pats es in\n st, pack (Tv_Match scrut _returns branches), bvs, ses @ ses'\n\n | Tv_Let r attrs bv ty e1 e2 ->\n let st, e1, bvs, ses = visit_body t_i index_bv inv_bv st bvs e1 in\n let st, e2, bvs, ses' = visit_body t_i index_bv inv_bv st bvs e2 in\n let e = pack (Tv_Let r attrs bv ty e1 e2) in\n st, e, bvs, ses @ ses'\n\n | Tv_AscribedT e t tac use_eq ->\n let st, e, bvs, ses = visit_body t_i index_bv inv_bv st bvs e in\n let e = pack (Tv_AscribedT e t tac use_eq) in\n st, e, bvs, ses\n\n | Tv_AscribedC e c tac use_eq ->\n let st, e, bvs, ses = visit_body t_i index_bv inv_bv st bvs e in\n let e = pack (Tv_AscribedC e c tac use_eq) in\n st, e, bvs, ses\n\n | Tv_Arrow _ _\n | Tv_Type _\n | Tv_Uvar _ _\n | Tv_Refine _ _ _\n | Tv_Unknown\n (* Redundant underscore to catch for soon-to-come\n addition of Tv_Unsupp *)\n | _ ->\n // Looks like we ended up visiting a type argument of an application.\n st, e, bvs, []", "val tm_var (nm: nm) : term\nlet tm_var (nm:nm) : term =\n tm_fstar (R.pack_ln (R.Tv_Var (R.pack_namedv (RT.make_namedv_with_name nm.nm_ppname.name nm.nm_index))))\n nm.nm_ppname.range", "val rename_binding (b: binding) (x y: var) : either s_ty src_eqn\nlet rename_binding (b:binding) (x y:var)\n : either s_ty src_eqn\n = match b with\n | Inl t -> Inl t\n | Inr (e1, e2) -> Inr (rename e1 x y, rename e2 x y)", "val exact_n (n: int) (t: term) : Tac unit\nlet exact_n (n : int) (t : term) : Tac unit =\n exact_args (repeatn n (fun () -> Q_Explicit)) t", "val exact_n (n: int) (t: term) : Tac unit\nlet exact_n (n : int) (t : term) : Tac unit =\n exact_args (repeatn n (fun () -> Q_Explicit)) t", "val freevars (t: term) : Set.set var\nlet rec freevars (t:term) \r\n : Set.set var\r\n = match t.t with\r\n | Tm_Emp\r\n | Tm_VProp\r\n | Tm_Inames\r\n | Tm_EmpInames\r\n | Tm_Unknown -> Set.empty\r\n | Tm_Inv p -> freevars p\r\n | Tm_Star t1 t2 ->\r\n Set.union (freevars t1) (freevars t2)\r\n | Tm_ExistsSL _ t1 t2\r\n | Tm_ForallSL _ t1 t2 ->\r\n Set.union (freevars t1.binder_ty) (freevars t2)\r\n | Tm_Pure p -> freevars p\r\n | Tm_FStar t -> RT.freevars t\r\n | Tm_AddInv i is -> Set.union (freevars i) (freevars is)", "val mk_bvar (s: string) (r: Range.range) (i: index) : term\nlet mk_bvar (s:string) (r:Range.range) (i:index) : term =\n tm_bvar {bv_index=i;bv_ppname=mk_ppname (RT.seal_pp_name s) r}", "val inst_fv_with (fv: string) (def t: term) : Tac term\nlet inst_fv_with (fv:string) (def:term) (t:term) : Tac term =\n (* print (\"t = \" ^ term_to_string t); *)\n match inspect t with\n | Tv_App l (r, Q_Explicit) ->\n if is_fv fv l\n then\n let l : term = pack (Tv_App l (def, Q_Implicit)) in\n pack (Tv_App l (r, Q_Explicit))\n else t\n\n | Tv_App l (r, Q_Implicit) -> t\n | _ -> t", "val and_elim (t: term) : Tac unit\nlet and_elim (t : term) : Tac unit =\n begin\n try apply_lemma (`(__and_elim (`#t)))\n with | _ -> apply_lemma (`(__and_elim' (`#t)))\n end", "val and_elim (t: term) : Tac unit\nlet and_elim (t : term) : Tac unit =\n begin\n try apply_lemma (`(__and_elim (`#t)))\n with | _ -> apply_lemma (`(__and_elim' (`#t)))\n end", "val close_term_vs (vs: list var) (t: term) : term\nlet close_term_vs (vs : list var) (t : term) : term =\n __close_term_vs 0 vs t", "val lambda_over_p (inv_bv: bv) (sort: typ) (t: term) : Tac term\nlet lambda_over_p (inv_bv: bv) (sort : typ) (t: term): Tac term =\n pack (Tv_Abs (mk_binder inv_bv sort) t)", "val push (ss:ss_t) (x:var { ~ (contains ss x) }) (t:term) : ss_t\nlet push (ss:ss_t) (x:var { ~ (contains ss x) }) (t:term) : ss_t =\n \n is_dom_push ss.l ss.m x t;\n { l = x::ss.l;\n m = Map.upd ss.m x t }", "val type_of_var (x: namedv) : Tac typ\nlet type_of_var (x : namedv) : Tac typ =\n unseal ((inspect_namedv x).sort)", "val subst_binder_in_comp : env -> binder -> term -> comp -> Tac comp\nlet subst_binder_in_comp e b t c =\n subst_bv_in_comp e (bv_of_binder b) (binder_sort b) t c" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.PostProcess.fst", "name": "FStar.InteractiveHelpers.PostProcess.replace_term_in" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_term" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Pure.fst", "name": "Pulse.Syntax.Pure.is_bvar" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Logic.fst", "name": "FStar.Tactics.V1.Logic.cases_bool" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Logic.fst", "name": "FStar.Tactics.V2.Logic.cases_bool" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Pure.fst", "name": "Pulse.Syntax.Pure.is_var" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.is_uvar" }, { "project_name": "FStar", "file_name": "LowParseWriters.fsti", "name": "LowParseWriters.is_uvar" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.subst_var" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.PostProcess.fst", "name": "FStar.InteractiveHelpers.PostProcess.remove_b2t" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.rewrite_equality" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.rewrite_equality" }, { "project_name": "hacl-star", "file_name": "Meta.Interface.fst", "name": "Meta.Interface.push_pre" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.open_term" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.weaken" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoid.fst", "name": "FStar.Tactics.CanonCommMonoid.is_const" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_term_with" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.term_is_uvar" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Pure.fst", "name": "Pulse.Syntax.Pure.tm_bvar" }, { "project_name": "FStar", "file_name": "LowParseWriters.fsti", "name": "LowParseWriters.is_eq" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_term_simple" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.pose_as" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.rewrite'" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.safe_tc" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Simplifier.fst", "name": "FStar.Tactics.Simplifier.is_true" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.nth_var" }, { "project_name": "steel", "file_name": "Pulse.Extract.Main.fst", "name": "Pulse.Extract.Main.simplify_branch" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.rename" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.apply" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.apply" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.weaken" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CheckLN.fst", "name": "FStar.Tactics.CheckLN.check" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_term_n" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.pose_as" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Tac.Enum.fst", "name": "LowParse.Spec.Tac.Enum.apply" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Tac.Enum.fst", "name": "LowParse.SLow.Tac.Enum.apply" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fst", "name": "FStar.Reflection.Typing.close_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.pose" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.replace_smt_uvars" }, { "project_name": "steel", "file_name": "Pulse.Checker.AssertWithBinders.fst", "name": "Pulse.Checker.AssertWithBinders.rewrite_all" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.binder_to_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.pose" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.solve_then" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.solve_then" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Visit.fst", "name": "FStar.Tactics.Visit.visit_br" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Base.fst", "name": "FStar.InteractiveHelpers.Base.push_fresh_var" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.subst_bv_in_comp" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Logic.fst", "name": "FStar.Tactics.V1.Logic.pose_lemma" }, { "project_name": "FStar", "file_name": "Printers.fst", "name": "Printers.paren" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Logic.fst", "name": "FStar.Tactics.V1.Logic.elim_exists" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Pure.fst", "name": "Pulse.Syntax.Pure.null_var" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.PostProcess.fst", "name": "FStar.InteractiveHelpers.PostProcess.unsquash_equality" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Simplifier.fst", "name": "FStar.Tactics.Simplifier.is_false" }, { "project_name": "FStar", "file_name": "FStar.Tactics.PatternMatching.fst", "name": "FStar.Tactics.PatternMatching.assoc_varname_fail" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Output.fst", "name": "FStar.InteractiveHelpers.Output._debug_print_var" }, { "project_name": "FStar", "file_name": "FStar.Tactics.MkProjectors.fst", "name": "FStar.Tactics.MkProjectors.subst_map" }, { "project_name": "everparse", "file_name": "LowParse.TacLib.fst", "name": "LowParse.TacLib.tassert" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.norm_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.norm_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.grewrite_eq" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.goal_term_uvars" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.apply_lemma" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.apply_lemma" }, { "project_name": "FStar", "file_name": "Term.fst", "name": "Term.add_one" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Match.fst", "name": "Pulse.Checker.Prover.Match.contains_uvar" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_comp" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.grewrite_eq" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Logic.fst", "name": "FStar.Tactics.V2.Logic.elim_exists" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Logic.fst", "name": "FStar.Tactics.V2.Logic.pose_lemma" }, { "project_name": "FStar", "file_name": "MiniParse.Tac.Base.fst", "name": "MiniParse.Tac.Base.unfold_term" }, { "project_name": "hacl-star", "file_name": "Meta.Interface.fst", "name": "Meta.Interface.visit_many" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.visit_br" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Base.fst", "name": "FStar.InteractiveHelpers.Base.genv_push_bv" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.r_b2t" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.r_b2t" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Machine_Semantics_s.fst", "name": "Vale.X64.Machine_Semantics_s.state_or_fail" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_term_n_with" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_term_n_simple" }, { "project_name": "hacl-star", "file_name": "Meta.Interface.fst", "name": "Meta.Interface.lambda_over_only_p" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.guard" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.guard" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Formula.fst", "name": "FStar.Reflection.V2.Formula.term_as_formula" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Formula.fst", "name": "FStar.Reflection.V1.Formula.term_as_formula" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.TEnum.fst", "name": "MiniParse.Spec.TEnum.term_of_pat" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_pat" }, { "project_name": "hacl-star", "file_name": "Meta.Interface.fst", "name": "Meta.Interface.visit_body" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Pure.fst", "name": "Pulse.Syntax.Pure.tm_var" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.rename_binding" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.exact_n" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.exact_n" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.freevars" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Pure.fst", "name": "Pulse.Syntax.Pure.mk_bvar" }, { "project_name": "FStar", "file_name": "Preprocess.fst", "name": "Preprocess.inst_fv_with" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Logic.fst", "name": "FStar.Tactics.V1.Logic.and_elim" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Logic.fst", "name": "FStar.Tactics.V2.Logic.and_elim" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.close_term_vs" }, { "project_name": "hacl-star", "file_name": "Meta.Interface.fst", "name": "Meta.Interface.lambda_over_p" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fst", "name": "Pulse.Checker.Prover.Substs.push" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.type_of_var" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.subst_binder_in_comp" } ], "selected_premises": [ "Param.app_binders", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "FStar.Heap.trivial_preorder", "Param.push_var_to_state", "FStar.ST.op_Bang", "Param.lookup_rec_fv", "Param.last", "Param.fresh_binder_named", "Param.push_fv", "FStar.ST.alloc", "FStar.Pervasives.reveal_opaque", "Param.lookup", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "Param.fold_right2", "Param.fvmap", "Param.zip3", "FStar.List.for_all", "FStar.All.op_Bar_Greater", "FStar.All.op_Less_Bar", "FStar.List.map", "FStar.List.iter", "FStar.List.fold_left", "FStar.Pervasives.id", "FStar.Pervasives.coerce_eq", "FStar.Pervasives.ex_pre", "FStar.Preorder.preorder_rel", "FStar.Monotonic.Heap.mref", "FStar.Heap.trivial_rel", "Prims.auto_squash", "Prims.l_True", "FStar.Pervasives.pure_ite_wp", "FStar.Pervasives.pure_close_wp", "FStar.Pervasives.st_post_h", "FStar.List.fold_right", "FStar.Pervasives.ex_post'", "Prims.pow2", "FStar.ST.lift_gst_state", "FStar.List.mapT", "FStar.ST.gst_pre", "FStar.All.pipe_left", "FStar.Pervasives.all_post_h", "FStar.Pervasives.all_post_h'", "Prims.pure_wp'", "FStar.Pervasives.pure_bind_wp", "FStar.ST.contains_pred", "FStar.Order.order_from_int", "FStar.ST.st_pre", "Prims.l_False", "Prims.as_requires", "Prims.pure_trivial", "FStar.Pervasives.all_pre_h", "FStar.ST.gst_wp", "FStar.Pervasives.div_hoare_to_wp", "FStar.Pervasives.st_bind_wp", "FStar.ST.lift_div_gst", "Prims.pure_wp_monotonic0", "Prims.pure_post'", "FStar.Pervasives.ex_post", "FStar.Pervasives.st_pre_h", "Prims.pure_stronger", "FStar.All.pipe_right", "Prims.purewp_id", "FStar.Pervasives.ex_stronger", "FStar.Pervasives.pure_null_wp", "FStar.All.all_wp", "FStar.All.lift_state_all", "Prims.abs", "Prims.as_ensures", "FStar.All.all_pre", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.all_ite_wp", "FStar.Pervasives.all_close_wp", "FStar.ST.gst_post", "FStar.List.tryFind", "FStar.Order.ne", "Prims.pure_wp", "Prims.pure_wp_monotonic", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.st_ite_wp", "FStar.ST.st_post", "FStar.Pervasives.ex_wp", "Prims.min", "FStar.Pervasives.st_post_h'", "FStar.ST.get", "FStar.Pervasives.ex_bind_wp", "FStar.ST.st_wp", "Prims.pure_post", "FStar.Order.compare_int", "FStar.All.all_post", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.all_wp_h", "FStar.Pervasives.ex_trivial", "FStar.ST.gst_post'", "FStar.Pervasives.all_trivial", "FStar.Pervasives.trivial_pure_post", "FStar.Pervasives.lift_div_exn", "FStar.All.all_post'", "FStar.Pervasives.all_stronger" ], "source_upto_this": "module Param\n\nopen FStar.List\nopen FStar.Tactics.V2\n\ntype bvmap = list (namedv & (binder & binder & binder))\nlet fvmap = list (fv * fv)\n\nnoeq\ntype param_state = {\n bvmap : bvmap;\n fresh : int;\n recs : fvmap;\n}\n\nlet rec fold_right2 (f : 'a -> 'b -> 'c -> Tac 'c) (l1:list 'a) (l2:list 'b) (c:'c) : Tac 'c =\n match l1, l2 with\n | h1::t1, h2::t2 -> f h1 h2 (fold_right2 f t1 t2 c)\n | [], [] -> c\n | _ -> fail \"fold_right2\"\n\nlet rec zip3 (l1 : list 'a) (l2 : list 'b) (l3 : list 'c) : list ('a * 'b * 'c) =\n match l1, l2, l3 with\n | h1::t1, h2::t2, h3::t3 -> (h1, h2, h3) :: (zip3 t1 t2 t3)\n | _ -> []\n\nlet last (xs:list 'a) : Tac 'a =\n match List.Tot.rev xs with\n | h::_ -> h\n | [] -> fail \"last: empty list\"\n\n(* Override it to add freshness. The code for typechecking an inductive\nraises a failure if two binders of the same constructor have the same name. *)\n// noeq type t = | A of x:int -> x:int -> x:int -> t\n// but this doesn't fail nor warn... why??\n\nlet fresh_binder_named (nm:string) (t:typ) : Tac binder =\n // useful?\n //let n = fresh () in\n //let nm = nm ^ \"_\" ^ string_of_int n in\n Tactics.V2.fresh_binder_named nm t\n\nlet app_binders (t:term) (bs:list binder) : Tac term =\n mk_e_app t (List.Tot.map binder_to_term bs)\n\nlet push_var_to_state (v:namedv) (b0 b1 b2 : binder) (s:param_state) : param_state =\n { s with bvmap = (v, (b0, b1, b2)) :: s.bvmap }\n\nexception NotARecFV\nexception Unsupported of string\nexception NotFoundBV of namedv\nexception NotFoundFV of fv\n\nlet lookup_rec_fv (s:param_state) (f:fv) : Tac fv =\n let rec aux (m:fvmap) : Tac fv =\n match m with\n | [] -> raise NotARecFV\n | (f1, k)::fs -> if compare_fv f f1 = Order.Eq\n then k\n else aux fs\n in\n aux s.recs\n\nlet push_fv (f1 f2 : fv) (s:param_state) : param_state =\n { s with recs = (f1,f2)::s.recs }\n\nlet lookup (s:param_state) (v:namedv) : Tac (binder & binder & binder) =\n let rec aux (bvm : bvmap) : Tac (binder & binder & binder) =\n match bvm with\n | [] ->\n raise (NotFoundBV v)\n | (v', r)::tl ->\n if (inspect_namedv v).uniq = (inspect_namedv v').uniq\n then r\n else aux tl\n in\n aux s.bvmap\n", "sketch": [ "Step 1: The `replace_var` function aims to replace a variable in a term based on the provided `param_state`. The boolean flag `b` indicates whether to perform a specific operation or not.\nStep 2: To implement this, we will traverse the term `t` and look for variables that need to be replaced. If the boolean flag `b` is true, we will perform a specific replacement operation using the `param_state`. Otherwise, we will return the term as is.", "Step 1: The `replace_var` function aims to replace a variable in a term based on the provided `param_state`. The boolean flag `b` indicates whether to perform a specific action during the replacement.\nStep 2: The implementation involves inspecting the term to identify the variable to be replaced. If the term is a variable and the boolean flag is true, it looks up the variable in the `param_state` and replaces it accordingly. If the term is not a variable or the flag is false, it returns the term unchanged.", "Step 1: The function `replace_var` aims to replace a variable in a term based on the provided `param_state`, a boolean flag, and the term itself.\nStep 2: The implementation will involve inspecting the term to identify the variable to be replaced. If the boolean flag is true, it will use one method of replacement; otherwise, it will use another. The function will likely involve looking up the variable in the `param_state` and then constructing a new term with the replacement.", "Step 1: The `replace_var` function aims to replace a variable in a term based on the given parameter state and a boolean flag.\nStep 2: The implementation involves checking the boolean flag. If true, it will perform a specific transformation on the term using the parameter state. If false, it will return the term unchanged.", "Step 1: The function `replace_var` is intended to replace a variable in a term based on the provided parameter state `s`. The boolean `b` likely indicates some condition that affects how the replacement is done.\nStep 2: To implement `replace_var`, we will need to traverse the term `t` and look up variables in the `param_state` `s`. Depending on the boolean `b`, we may perform different actions during the replacement. We will use tactics to handle the term manipulation and state updates.", "Step 1: The `replace_var` function aims to replace a variable in a term based on the provided parameter state and a boolean flag.\nStep 2: The implementation involves checking the boolean flag. If true, it will perform a specific replacement operation on the term using the state. If false, it will return the term unchanged.", "Step 1: The `replace_var` function aims to replace a variable in a term based on the given parameter state and a boolean flag.\nStep 2: The implementation will involve inspecting the term to identify the variable to be replaced. If the boolean flag is true, it will perform a specific replacement using the `lookup` function to find the corresponding binders in the parameter state. Otherwise, it will return the term unchanged.", "Step 1: The `replace_var` function aims to replace a variable in a term based on the given `param_state` and a boolean flag.\nStep 2: The implementation will involve inspecting the term to identify the variable to be replaced. If the boolean flag is true, it will perform a specific replacement using the `param_state`. Otherwise, it will perform a different replacement or leave the term unchanged.", "Step 1: The `replace_var` function aims to replace a variable in a term based on the provided `param_state` and a boolean flag.\nStep 2: The implementation will involve checking the boolean flag. If true, it will perform a specific replacement operation on the term using the state. If false, it will return the term unchanged.", "Step 1: The `replace_var` function aims to replace a variable in a term based on the provided `param_state`. The boolean flag `b` determines whether the replacement should occur or not.\nStep 2: The implementation will involve inspecting the term `t` to identify variables that need to be replaced. If `b` is true, it will look up the variable in the `param_state` and replace it with the corresponding binder. If `b` is false, it will return the term `t` unchanged." ], "generated_solution": [ "let replace_var (s: param_state) (b: bool) (t: term) : Tac term =\n if b then\n // Perform the specific replacement operation using the param_state\n // This is a placeholder for the actual replacement logic\n fail \"replace_var: specific replacement operation not implemented\"\n else\n // Return the term as is\n ret t", "let replace_var (s: param_state) (b: bool) (t: term) : Tac term =\n match inspect t with\n | Tv_Var v ->\n if b then\n let (b0, b1, b2) = lookup s v in\n app_binders (binder_to_term b0) [b1; b2]\n else\n t\n | _ -> t", "let replace_var (s: param_state) (b: bool) (t: term) : Tac term =\n match inspect t with\n | Tv_Var v ->\n bind (lookup s v) (fun (b0, b1, b2) ->\n if b then\n ret (binder_to_term b0)\n else\n ret (binder_to_term b1))\n | _ -> ret t", "let replace_var (s: param_state) (b: bool) (t: term) : Tac term =\n if b then\n // Perform some transformation on the term `t` using the parameter state `s`\n // This is a placeholder for the actual transformation logic\n Tactics.V2.fail \"Transformation logic not implemented\"\n else\n // Return the term unchanged\n Tactics.V2.ret t", "let replace_var (s: param_state) (b: bool) (t: term) : Tac term =\n match inspect t with\n | Tv_Var v ->\n if b then\n let! (b0, b1, b2) = lookup s v in\n app_binders (binder_to_term b0) [b1; b2]\n else\n let! (b0, b1, b2) = lookup s v in\n binder_to_term b0\n | _ -> fail \"replace_var: unsupported term\"", "let replace_var (s: param_state) (b: bool) (t: term) : Tac term =\n if b then\n // Perform the replacement operation using the state `s`\n // This is a placeholder for the actual replacement logic\n fail \"Replacement logic not implemented\"\n else\n // Return the term unchanged\n ret t", "let replace_var (s: param_state) (b: bool) (t: term) : Tac term =\n if b then\n match inspect t with\n | Tv_Var v ->\n let! (b0, b1, b2) = lookup s v in\n app_binders t [b0; b1; b2]\n | _ -> t\n else\n t", "let replace_var (s: param_state) (b: bool) (t: term) : Tac term =\n match inspect t with\n | Tv_Var v ->\n if b then\n let (b0, b1, b2) = lookup s v in\n app_binders (binder_to_term b0) [b1; b2]\n else\n let (b0, b1, b2) = lookup s v in\n app_binders (binder_to_term b1) [b0; b2]\n | _ -> Tactics.V2.ret t", "let replace_var (s: param_state) (b: bool) (t: term) : Tac term =\n if b then\n // Perform the replacement operation using the state `s` on the term `t`\n // This will involve looking up variables in the state and replacing them in the term\n // Placeholder for the actual replacement logic\n fail \"replace_var: replacement logic not implemented\"\n else\n // Return the term unchanged\n ret t", "let replace_var (s: param_state) (b: bool) (t: term) : Tac term =\n if b then\n match inspect t with\n | Tv_Var v ->\n let (b0, b1, b2) = lookup s v in\n app_binders (mk_var b0) [b1; b2]\n | _ -> t\n else\n t" ] }, { "file_name": "Vale.Stdcalls.X64.Cpuid.fsti", "name": "Vale.Stdcalls.X64.Cpuid.lowstar_sha_t", "opens_and_abbrevs": [ { "open": "Vale.X64.State" }, { "open": "Vale.X64.Machine_s" }, { "abbrev": "VC", "full_module": "Vale.Lib.X64.Cpuidstdcall" }, { "open": "Vale.X64.MemoryAdapters" }, { "abbrev": "W", "full_module": "Vale.AsLowStar.Wrapper" }, { "abbrev": "IA", "full_module": "Vale.Interop.Assumptions" }, { "abbrev": "V", "full_module": "Vale.X64.Decls" }, { "abbrev": "LSig", "full_module": "Vale.AsLowStar.LowStarSig" }, { "abbrev": "VSig", "full_module": "Vale.AsLowStar.ValeSig" }, { "abbrev": "IX64", "full_module": "Vale.Interop.X64" }, { "open": "Vale.Interop.Base" }, { "open": "FStar.Mul" }, { "open": "Vale.Stdcalls.X64" }, { "open": "Vale.Stdcalls.X64" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 1, "initial_ifuel": 0, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": true, "smtencoding_nl_arith_repr": "wrapped", "smtencoding_l_arith_repr": "native", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "", "source_definition": "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "source_range": { "start_line": 117, "start_col": 0, "end_line": 124, "end_col": 65 }, "interleaved": false, "definition": "Vale.Interop.X64.as_lowstar_sig_t_weak_stdcall Vale.Stdcalls.X64.Cpuid.code_sha\n Vale.Stdcalls.X64.Cpuid.dom\n []\n (Vale.AsLowStar.Wrapper.pre_rel_generic Vale.Stdcalls.X64.Cpuid.code_sha\n Vale.Stdcalls.X64.Cpuid.dom\n []\n (Vale.Stdcalls.X64.Cpuid.sha_pre Vale.Stdcalls.X64.Cpuid.code_sha))\n (Vale.AsLowStar.Wrapper.post_rel_generic Vale.Stdcalls.X64.Cpuid.code_sha\n Vale.Stdcalls.X64.Cpuid.dom\n []\n (Vale.Stdcalls.X64.Cpuid.sha_post Vale.Stdcalls.X64.Cpuid.code_sha))\n (Vale.AsLowStar.Wrapper.mk_prediction Vale.Stdcalls.X64.Cpuid.code_sha\n Vale.Stdcalls.X64.Cpuid.dom\n []\n (Vale.Stdcalls.X64.Cpuid.sha_lemma Vale.Stdcalls.X64.Cpuid.code_sha\n Vale.Interop.Assumptions.win))", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Vale.Interop.X64.as_lowstar_sig_t_weak_stdcall", "Vale.Stdcalls.X64.Cpuid.code_sha", "Vale.Stdcalls.X64.Cpuid.dom", "Prims.Nil", "Vale.Interop.Base.arg", "Vale.AsLowStar.Wrapper.pre_rel_generic", "Vale.Interop.X64.max_stdcall", "Vale.Interop.X64.arg_reg_stdcall", "Vale.Stdcalls.X64.Cpuid.sha_pre", "Vale.AsLowStar.Wrapper.post_rel_generic", "Vale.Stdcalls.X64.Cpuid.sha_post", "Vale.AsLowStar.Wrapper.mk_prediction", "Vale.Interop.X64.regs_modified_stdcall", "Vale.Interop.X64.xmms_modified_stdcall", "Vale.Stdcalls.X64.Cpuid.sha_lemma", "Vale.Interop.Assumptions.win" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "Type0", "prompt": "let lowstar_sha_t =\n ", "expected_response": "IX64.as_lowstar_sig_t_weak_stdcall code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "source": { "project_name": "hacl-star", "file_name": "vale/code/arch/x64/interop/Vale.Stdcalls.X64.Cpuid.fsti", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Vale.Stdcalls.X64.Cpuid.fsti", "checked_file": "dataset/Vale.Stdcalls.X64.Cpuid.fsti.checked", "interface_file": false, "dependencies": [ "dataset/Vale.X64.State.fsti.checked", "dataset/Vale.X64.MemoryAdapters.fsti.checked", "dataset/Vale.X64.Machine_s.fst.checked", "dataset/Vale.X64.Decls.fsti.checked", "dataset/Vale.Lib.X64.Cpuidstdcall.fsti.checked", "dataset/Vale.Interop.X64.fsti.checked", "dataset/Vale.Interop.Base.fst.checked", "dataset/Vale.Interop.Assumptions.fst.checked", "dataset/Vale.AsLowStar.Wrapper.fsti.checked", "dataset/Vale.AsLowStar.ValeSig.fst.checked", "dataset/Vale.AsLowStar.LowStarSig.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked" ] }, "definitions_in_context": [ "let as_t (#a:Type) (x:normal a) : a = x", "let as_normal_t (#a:Type) (x:a) : normal a = x", "let dom: IX64.arity_ok_stdcall td = []", "let aesni_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_aesni_stdcall c va_s0 IA.win", "let aesni_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_aesni_stdcall c va_s0 IA.win va_s1 f", "let aesni_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n aesni_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n aesni_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_aesni_stdcall code va_s0 IA.win", "let aesni_lemma = as_t #(VSig.vale_sig_stdcall aesni_pre aesni_post) aesni_lemma'", "let code_aesni = VC.va_code_Check_aesni_stdcall IA.win", "let lowstar_aesni_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_aesni\n dom\n []\n _\n _\n (W.mk_prediction code_aesni dom [] (aesni_lemma code_aesni IA.win))", "let sha_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_sha_stdcall c va_s0 IA.win", "let sha_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_sha_stdcall c va_s0 IA.win va_s1 f", "let sha_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n sha_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n sha_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_sha_stdcall code va_s0 IA.win", "let sha_lemma = as_t #(VSig.vale_sig_stdcall sha_pre sha_post) sha_lemma'", "let code_sha = VC.va_code_Check_sha_stdcall IA.win" ], "closest": [ "val Vale.Stdcalls.X64.Sha.lowstar_sha_t = Type0\nlet lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "val Vale.Stdcalls.X64.Sha.b8_128 = Type0\nlet b8_128 = buf_t TUInt8 TUInt128", "val Vale.Stdcalls.X64.Fswap.lowstar_cswap_t = Type0\nlet lowstar_cswap_t =\n assert_norm (List.length cswap_dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak_stdcall\n code_cswap\n cswap_dom\n []\n _\n _\n (W.mk_prediction code_cswap cswap_dom [] (cswap_lemma code_cswap IA.win))", "val Vale.Stdcalls.X64.Sha.b128 = Type0\nlet b128 = buf_t TUInt32 TUInt128", "val Vale.Stdcalls.X64.Sha.ib128 = Type0\nlet ib128 = ibuf_t TUInt32 TUInt128", "val Vale.Stdcalls.X64.Aes.lowstar_key256_t = Type0\nlet lowstar_key256_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak_stdcall\n code_key256\n dom\n []\n _\n _\n (W.mk_prediction code_key256 dom [] (key256_lemma code_key256 IA.win))", "val Vale.Stdcalls.X64.Aes.lowstar_key128_t = Type0\nlet lowstar_key128_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak_stdcall\n code_key128\n dom\n []\n _\n _\n (W.mk_prediction code_key128 dom [] (key128_lemma code_key128 IA.win))", "val Vale.Stdcalls.X64.Fmul.lowstar_fmul_t = Type0\nlet lowstar_fmul_t =\n assert_norm (List.length fmul_dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak_stdcall\n code_Fmul\n fmul_dom\n []\n _\n _\n (W.mk_prediction code_Fmul fmul_dom [] (fmul_lemma code_Fmul IA.win))", "val Vale.Stdcalls.X64.Fmul.lowstar_fmul1_t = Type0\nlet lowstar_fmul1_t =\n assert_norm (List.length fmul1_dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak_stdcall\n code_Fmul1\n fmul1_dom\n []\n _\n _\n (W.mk_prediction code_Fmul1 fmul1_dom [] (fmul1_lemma code_Fmul1 IA.win))", "val Vale.Stdcalls.X64.Fadd.lowstar_add1_t = Type0\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak_stdcall\n code_add1\n dom\n []\n _\n _\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))", "val Vale.Stdcalls.X64.Fadd.lowstar_fadd_t = Type0\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak_stdcall\n code_Fadd\n fadd_dom\n []\n _\n _\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))", "val Vale.Stdcalls.X64.Fmul.lowstar_fmul2_t = Type0\nlet lowstar_fmul2_t =\n assert_norm (List.length fmul_dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak_stdcall\n code_Fmul2\n fmul_dom\n []\n _\n _\n (W.mk_prediction code_Fmul2 fmul_dom [] (fmul2_lemma code_Fmul2 IA.win))", "val Vale.Stdcalls.X64.Fsub.lowstar_Fsub_t = Type0\nlet lowstar_Fsub_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak_stdcall\n code_Fsub\n dom\n []\n _\n _\n (W.mk_prediction code_Fsub dom [] (fsub_lemma code_Fsub IA.win))", "val Vale.Stdcalls.X64.Fsqr.lowstar_Fsqr_t = Type0\nlet lowstar_Fsqr_t =\n assert_norm (List.length fsqr_dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak_stdcall\n code_Fsqr\n fsqr_dom\n []\n _\n _\n (W.mk_prediction code_Fsqr fsqr_dom [] (fsqr_lemma code_Fsqr IA.win))", "val Vale.Stdcalls.X64.Fsqr.lowstar_Fsqr2_t = Type0\nlet lowstar_Fsqr2_t =\n assert_norm (List.length fsqr_dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak_stdcall\n code_Fsqr2\n fsqr_dom\n []\n _\n _\n (W.mk_prediction code_Fsqr2 fsqr_dom [] (fsqr2_lemma code_Fsqr2 IA.win))", "val Vale.Inline.X64.Fswap_inline.lowstar_cswap_t = Type0\nlet lowstar_cswap_t =\n assert_norm (List.length cswap_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n cswap_regs_modified\n cswap_xmms_modified\n code_cswap\n cswap_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_cswap cswap_dom [] (cswap_lemma code_cswap IA.win))", "val Vale.Inline.X64.Fmul_inline.lowstar_fmul_t = Type0\nlet lowstar_fmul_t =\n assert_norm (List.length fmul_dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak\n 4\n fmul_arg_reg\n fmul_regs_modified\n fmul_xmms_modified\n code_Fmul\n fmul_dom\n []\n _\n _\n (W.mk_prediction code_Fmul fmul_dom [] (fmul_lemma code_Fmul IA.win))", "val Vale.Inline.X64.Fmul_inline.lowstar_fmul1_t = Type0\nlet lowstar_fmul1_t =\n assert_norm (List.length fmul1_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fmul1_regs_modified\n fmul1_xmms_modified\n code_Fmul1\n fmul1_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fmul1 fmul1_dom [] (fmul1_lemma code_Fmul1 IA.win))", "val Vale.Stdcalls.X64.Aes.b128 = Type0\nlet b128 = buf_t TUInt8 TUInt128", "val Vale.Stdcalls.X64.AesHash.b128 = Type0\nlet b128 = buf_t TUInt8 TUInt128", "val Vale.Inline.X64.Fmul_inline.lowstar_fmul2_t = Type0\nlet lowstar_fmul2_t =\n assert_norm (List.length fmul_dom + List.length ([]<:list arg) <= 4);\n IX64.as_lowstar_sig_t_weak\n 4\n fmul_arg_reg\n fmul_regs_modified\n fmul_xmms_modified\n code_Fmul2\n fmul_dom\n []\n _\n _\n (W.mk_prediction code_Fmul2 fmul_dom [] (fmul2_lemma code_Fmul2 IA.win))", "val Vale.Stdcalls.X64.GCTR.b128 = Type0\nlet b128 = buf_t TUInt8 TUInt128", "val Vale.Inline.X64.Fsqr_inline.lowstar_Fsqr_t = Type0\nlet lowstar_Fsqr_t =\n assert_norm (List.length fsqr_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fsqr_regs_modified\n fsqr_xmms_modified\n code_Fsqr\n fsqr_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fsqr fsqr_dom [] (fsqr_lemma code_Fsqr IA.win))", "val Vale.Inline.X64.Fadd_inline.lowstar_add1_t = Type0\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))", "val Vale.Stdcalls.X64.Poly.lowstar_poly_t = Type0\nlet lowstar_poly_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_poly\n dom\n []\n _\n _\n (W.mk_prediction code_poly dom [] (poly_lemma code_poly IA.win))", "val Vale.Stdcalls.X64.Sha.sha_lemma = Vale.AsLowStar.ValeSig.vale_sig_stdcall Vale.Stdcalls.X64.Sha.sha_pre Vale.Stdcalls.X64.Sha.sha_post\nlet sha_lemma = as_t #(VSig.vale_sig_stdcall sha_pre sha_post) sha_lemma'", "val Vale.AsLowStar.Test.lowstar_aesni_t = Type0\nlet lowstar_aesni_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n (coerce code_aesni)\n aesni_dom\n empty_list\n _\n _\n (W.mk_prediction code_aesni aesni_dom [] (aesni_lemma code_aesni IA.win))", "val Vale.Inline.X64.Fadd_inline.lowstar_fadd_t = Type0\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))", "val Vale.Inline.X64.Fsqr_inline.lowstar_Fsqr2_t = Type0\nlet lowstar_Fsqr2_t =\n assert_norm (List.length fsqr_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fsqr_regs_modified\n fsqr_xmms_modified\n code_Fsqr2\n fsqr_dom\n []\n _\n _\n (W.mk_prediction code_Fsqr2 fsqr_dom [] (fsqr2_lemma code_Fsqr2 IA.win))", "val Vale.Stdcalls.X64.Fsub.b64 = Type0\nlet b64 = buf_t TUInt64 TUInt64", "val Vale.Stdcalls.X64.Fswap.b64 = Type0\nlet b64 = buf_t TUInt64 TUInt64", "val Vale.Stdcalls.X64.Sha.t128_no_mod = Vale.Interop.Base.td\nlet t128_no_mod = TD_Buffer TUInt8 TUInt128 ({modified=false; strict_disjointness=false; taint=MS.Secret})", "val Vale.Inline.X64.Fadd_inline.lowstar_Fsub_t = Type0\nlet lowstar_Fsub_t =\n assert_norm (List.length fsub_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fsub_regs_modified\n fsub_xmms_modified\n code_Fsub\n fsub_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))", "val Vale.Stdcalls.X64.GCM_IV.b128 = Type0\nlet b128 = buf_t TUInt8 TUInt128", "val Vale.Stdcalls.X64.Fmul.b64 = Type0\nlet b64 = buf_t TUInt64 TUInt64", "val Vale.Stdcalls.X64.Sha.code_sha = Vale.X64.Decls.va_code\nlet code_sha = SH.va_code_Sha_update_bytes_stdcall IA.win", "val Vale.Stdcalls.X64.Fsqr.b64 = Type0\nlet b64 = buf_t TUInt64 TUInt64", "val Vale.Wrapper.X64.Sha.uint32_p = Type0\nlet uint32_p = B.buffer uint32", "val lowstar_avx512_xcr0:lowstar_avx512_xcr0_t\nlet lowstar_avx512_xcr0 : lowstar_avx512_xcr0_t =\n IX64.wrap_weak_stdcall\n code_avx512_xcr0\n dom\n (W.mk_prediction code_avx512_xcr0 dom [] (avx512_xcr0_lemma code_avx512_xcr0 IA.win))", "val Vale.Wrapper.X64.Sha.uint32_i = Type0\nlet uint32_i = IB.ibuffer uint32", "val Vale.Wrapper.X64.Sha.uint8_p = Type0\nlet uint8_p = B.buffer uint8", "val Vale.Stdcalls.X64.Fadd.b64 = Type0\nlet b64 = buf_t TUInt64 TUInt64", "val Vale.SHA.PPC64LE.SHA_helpers.hash256 = Type0\nlet hash256 = m:Seq.seq word {Seq.length m = 8}", "val Vale.AsLowStar.Test.ib64 = Type0\nlet ib64 = ibuf_t TUInt8 TUInt64", "val Vale.Wrapper.X64.Sha.uint64 = Type0\nlet uint64 = uint_t U64 PUB", "val Vale.AES.X64.AESopt.quad32_6 = Type0\nlet quad32_6 = six_of quad32", "val Vale.Stdcalls.X64.GCMencryptOpt.b128 = Type0\nlet b128 = buf_t TUInt8 TUInt128", "val Vale.Stdcalls.X64.GCMdecryptOpt.b128 = Type0\nlet b128 = buf_t TUInt8 TUInt128", "val Vale.AsLowStar.Test.lowstar_Memcpy_t = Type0\nlet lowstar_Memcpy_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_Memcpy\n vm_dom\n []\n _\n _\n (W.mk_prediction code_Memcpy vm_dom [] (vm_lemma code_Memcpy IA.win))", "val Vale.Stdcalls.X64.Sha.t128_mod = Vale.Interop.Base.td\nlet t128_mod = TD_Buffer TUInt32 TUInt128 default_bq", "val lowstar_avx_xcr0:lowstar_avx_xcr0_t\nlet lowstar_avx_xcr0 : lowstar_avx_xcr0_t =\n IX64.wrap_weak_stdcall\n code_avx_xcr0\n dom\n (W.mk_prediction code_avx_xcr0 dom [] (avx_xcr0_lemma code_avx_xcr0 IA.win))", "val Vale.Stdcalls.X64.Sha.t128_imm = Vale.Interop.Base.td\nlet t128_imm = TD_ImmBuffer TUInt32 TUInt128 default_bq", "val lowstar_sse:lowstar_sse_t\nlet lowstar_sse : lowstar_sse_t =\n IX64.wrap_weak_stdcall\n code_sse\n dom\n (W.mk_prediction code_sse dom [] (sse_lemma code_sse IA.win))", "val Vale.AsLowStar.Test.lowstar_ta_t = Type0\nlet lowstar_ta_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n (coerce code_ta)\n ta_dom\n []\n _\n _\n (W.mk_prediction code_ta ta_dom [] (ta_lemma code_ta IA.win))", "val Vale.Wrapper.X64.AEShash.uint8_p = Type0\nlet uint8_p = B.buffer UInt8.t", "val Vale.SHA.PPC64LE.SHA_helpers.counter = Type0\nlet counter = nat", "val Vale.X64.Decls.va_operand_xmm = Type0\nlet va_operand_xmm = reg_xmm", "val Vale.SHA.PPC64LE.SHA_helpers.bytes_blocks = Type0\nlet bytes_blocks =\n l:bytes { Seq.length l % block_length = 0 }", "val Vale.X64.Machine_s.nat64 = Type0\nlet nat64 = Vale.Def.Types_s.nat64", "val Vale.Stdcalls.X64.Poly.b64 = Type0\nlet b64 = buf_t TUInt8 TUInt64", "val Vale.PPC64LE.Machine_s.regs_t = Type0\nlet regs_t = FStar.FunctionalExtensionality.restricted_t reg (fun _ -> nat64)", "val Vale.Inline.X64.Fswap_inline.u512 = Type0\nlet u512 = b:B.buffer UInt64.t{B.length b == 8}", "val Vale.Inline.X64.Fswap_inline.u256 = Type0\nlet u256 = b:B.buffer UInt64.t{B.length b == 4}", "val Vale.Inline.X64.Fswap_inline.b64 = Type0\nlet b64 = buf_t TUInt64 TUInt64", "val Vale.Inline.X64.Fmul_inline.b64 = Type0\nlet b64 = buf_t TUInt64 TUInt64", "val Vale.X64.Instruction_s.instr_out = Type0\nlet instr_out = instr_operand_inout & instr_operand", "val Vale.X64.Machine_s.nat128 = Type0\nlet nat128 = Vale.Def.Words_s.nat128", "val Vale.Stdcalls.X64.Sha.tuint64 = Vale.Interop.Base.td\nlet tuint64 = TD_Base TUInt64", "val Vale.Inline.X64.Fswap_inline.u1024 = Type0\nlet u1024 = b:B.buffer UInt64.t{B.length b == 16}", "val Vale.Inline.X64.Fmul_inline.u1024 = Type0\nlet u1024 = b:B.buffer UInt64.t{B.length b == 16}", "val Vale.Inline.X64.Fmul_inline.u512 = Type0\nlet u512 = b:B.buffer UInt64.t{B.length b == 8}", "val Vale.X64.Memory.b8 = Type0\nlet b8 = IB.b8", "val Vale.Inline.X64.Fmul_inline.u256 = Type0\nlet u256 = b:B.buffer UInt64.t{B.length b == 4}", "val Vale.Interop.X64.registers = Type0\nlet registers = MS.reg_64 -> MS.nat64", "val cpu_has_shaext:cached_flag Vale.X64.CPU_Features_s.sha_enabled\nlet cpu_has_shaext: cached_flag Vale.X64.CPU_Features_s.sha_enabled =\n B.gcmalloc_of_list HS.root [ false ]", "val Vale.Stdcalls.X64.AesHash.t128_no_mod = Vale.Interop.Base.td\nlet t128_no_mod = TD_Buffer TUInt8 TUInt128 ({modified=false; strict_disjointness=false; taint=MS.Secret})", "val Vale.PPC64LE.Machine_s.nat8 = Type0\nlet nat8 = Vale.Def.Words_s.nat8", "val Vale.PPC64LE.Machine_s.nat64 = Type0\nlet nat64 = Vale.Def.Words_s.nat64", "val Vale.Inline.X64.Fsqr_inline.b64 = Type0\nlet b64 = buf_t TUInt64 TUInt64", "val check_avx512_xcr0 : normal lowstar_avx512_xcr0_t\nlet check_avx512_xcr0 = as_normal_t #lowstar_avx512_xcr0_t lowstar_avx512_xcr0", "val Vale.X64.Decls.va_operand_reg_opr64 = Type0\nlet va_operand_reg_opr64 = o:operand64{OReg? o}", "val check_avx_xcr0 : normal lowstar_avx_xcr0_t\nlet check_avx_xcr0 = as_normal_t #lowstar_avx_xcr0_t lowstar_avx_xcr0", "val Vale.SHA.SHA_helpers.hash256 = Type0\nlet hash256 = m:Seq.seq word {Seq.length m = 8}", "val Vale.Bignum.X64.flags_t = Type0\nlet flags_t = Vale.X64.Flags.t", "val Vale.PPC64LE.Memory.b8 = Type0\nlet b8 = IB.b8", "val Vale.X64.Decls.va_value_opr64 = Type0\nlet va_value_opr64 = nat64", "val Vale.X64.Decls.va_value_reg_opr64 = Type0\nlet va_value_reg_opr64 = nat64", "val Vale.PPC64LE.Machine_s.nat16 = Type0\nlet nat16 = Vale.Def.Words_s.nat16", "val Vale.X64.Decls.va_code = Type0\nlet va_code = precode ins ocmp", "val Vale.Interop.X64.arg_list_sb = Type0\nlet arg_list_sb = l:list arg{List.Tot.length l <= 21}", "val lowstar_sha:lowstar_sha_t\nlet lowstar_sha : lowstar_sha_t =\n IX64.wrap_weak_stdcall\n code_sha\n dom\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "val lowstar_sha:lowstar_sha_t\nlet lowstar_sha : lowstar_sha_t =\n IX64.wrap_weak_stdcall\n code_sha\n dom\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "val Vale.X64.Decls.va_value_dst_opr64 = Type0\nlet va_value_dst_opr64 = nat64", "val Vale.SHA.PPC64LE.SHA_helpers.block_w = Type0\nlet block_w = m:seq word {length m = size_block_w_256}", "val has_shaext: getter Vale.X64.CPU_Features_s.sha_enabled\nlet has_shaext = mk_getter cpu_has_shaext", "val Vale.Inline.X64.Fadd_inline.u1024 = Type0\nlet u1024 = b:B.buffer UInt64.t{B.length b == 16}", "val Vale.PPC64LE.Decls.va_code = Type0\nlet va_code = precode ins ocmp", "val Vale.Inline.X64.Fadd_inline.u512 = Type0\nlet u512 = b:B.buffer UInt64.t{B.length b == 8}", "val lowstar_avx512:lowstar_avx512_t\nlet lowstar_avx512 : lowstar_avx512_t =\n IX64.wrap_weak_stdcall\n code_avx512\n dom\n (W.mk_prediction code_avx512 dom [] (avx512_lemma code_avx512 IA.win))", "val Vale.AsLowStar.Test.call_c_t = Type0\nlet call_c_t = IX64.as_lowstar_sig_t_weak_stdcall c dom [] _ _ (W.mk_prediction c dom [] (v c IA.win))" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.lowstar_sha_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.b8_128" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fswap.fsti", "name": "Vale.Stdcalls.X64.Fswap.lowstar_cswap_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.b128" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.ib128" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Aes.fsti", "name": "Vale.Stdcalls.X64.Aes.lowstar_key256_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Aes.fsti", "name": "Vale.Stdcalls.X64.Aes.lowstar_key128_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.lowstar_fmul_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.lowstar_fmul1_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fadd.fsti", "name": "Vale.Stdcalls.X64.Fadd.lowstar_add1_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fadd.fsti", "name": "Vale.Stdcalls.X64.Fadd.lowstar_fadd_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.lowstar_fmul2_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsub.fsti", "name": "Vale.Stdcalls.X64.Fsub.lowstar_Fsub_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsqr.fsti", "name": "Vale.Stdcalls.X64.Fsqr.lowstar_Fsqr_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsqr.fsti", "name": "Vale.Stdcalls.X64.Fsqr.lowstar_Fsqr2_t" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fswap_inline.fst", "name": "Vale.Inline.X64.Fswap_inline.lowstar_cswap_t" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.lowstar_fmul_t" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.lowstar_fmul1_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Aes.fsti", "name": "Vale.Stdcalls.X64.Aes.b128" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.AesHash.fst", "name": "Vale.Stdcalls.X64.AesHash.b128" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.lowstar_fmul2_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCTR.fst", "name": "Vale.Stdcalls.X64.GCTR.b128" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fsqr_inline.fst", "name": "Vale.Inline.X64.Fsqr_inline.lowstar_Fsqr_t" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.lowstar_add1_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Poly.fsti", "name": "Vale.Stdcalls.X64.Poly.lowstar_poly_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.sha_lemma" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.lowstar_aesni_t" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.lowstar_fadd_t" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fsqr_inline.fst", "name": "Vale.Inline.X64.Fsqr_inline.lowstar_Fsqr2_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsub.fsti", "name": "Vale.Stdcalls.X64.Fsub.b64" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fswap.fsti", "name": "Vale.Stdcalls.X64.Fswap.b64" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.t128_no_mod" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.lowstar_Fsub_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCM_IV.fst", "name": "Vale.Stdcalls.X64.GCM_IV.b128" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.b64" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.code_sha" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsqr.fsti", "name": "Vale.Stdcalls.X64.Fsqr.b64" }, { "project_name": "hacl-star", "file_name": "Vale.Wrapper.X64.Sha.fsti", "name": "Vale.Wrapper.X64.Sha.uint32_p" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Cpuid.fst", "name": "Vale.Stdcalls.X64.Cpuid.lowstar_avx512_xcr0" }, { "project_name": "hacl-star", "file_name": "Vale.Wrapper.X64.Sha.fsti", "name": "Vale.Wrapper.X64.Sha.uint32_i" }, { "project_name": "hacl-star", "file_name": "Vale.Wrapper.X64.Sha.fsti", "name": "Vale.Wrapper.X64.Sha.uint8_p" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fadd.fsti", "name": "Vale.Stdcalls.X64.Fadd.b64" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.SHA_helpers.fsti", "name": "Vale.SHA.PPC64LE.SHA_helpers.hash256" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.ib64" }, { "project_name": "hacl-star", "file_name": "Vale.Wrapper.X64.Sha.fsti", "name": "Vale.Wrapper.X64.Sha.uint64" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fsti", "name": "Vale.AES.X64.AESopt.quad32_6" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCMencryptOpt.fst", "name": "Vale.Stdcalls.X64.GCMencryptOpt.b128" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCMdecryptOpt.fst", "name": "Vale.Stdcalls.X64.GCMdecryptOpt.b128" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.lowstar_Memcpy_t" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.t128_mod" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Cpuid.fst", "name": "Vale.Stdcalls.X64.Cpuid.lowstar_avx_xcr0" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.t128_imm" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Cpuid.fst", "name": "Vale.Stdcalls.X64.Cpuid.lowstar_sse" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.lowstar_ta_t" }, { "project_name": "hacl-star", "file_name": "Vale.Wrapper.X64.AEShash.fsti", "name": "Vale.Wrapper.X64.AEShash.uint8_p" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.SHA_helpers.fsti", "name": "Vale.SHA.PPC64LE.SHA_helpers.counter" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_operand_xmm" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.SHA_helpers.fsti", "name": "Vale.SHA.PPC64LE.SHA_helpers.bytes_blocks" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Machine_s.fst", "name": "Vale.X64.Machine_s.nat64" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Poly.fsti", "name": "Vale.Stdcalls.X64.Poly.b64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Machine_s.fst", "name": "Vale.PPC64LE.Machine_s.regs_t" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fswap_inline.fsti", "name": "Vale.Inline.X64.Fswap_inline.u512" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fswap_inline.fsti", "name": "Vale.Inline.X64.Fswap_inline.u256" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fswap_inline.fst", "name": "Vale.Inline.X64.Fswap_inline.b64" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.b64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Instruction_s.fsti", "name": "Vale.X64.Instruction_s.instr_out" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Machine_s.fst", "name": "Vale.X64.Machine_s.nat128" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.tuint64" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fswap_inline.fsti", "name": "Vale.Inline.X64.Fswap_inline.u1024" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fsti", "name": "Vale.Inline.X64.Fmul_inline.u1024" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fsti", "name": "Vale.Inline.X64.Fmul_inline.u512" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.b8" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fsti", "name": "Vale.Inline.X64.Fmul_inline.u256" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.X64.fsti", "name": "Vale.Interop.X64.registers" }, { "project_name": "hacl-star", "file_name": "EverCrypt.AutoConfig2.fst", "name": "EverCrypt.AutoConfig2.cpu_has_shaext" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.AesHash.fst", "name": "Vale.Stdcalls.X64.AesHash.t128_no_mod" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Machine_s.fst", "name": "Vale.PPC64LE.Machine_s.nat8" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Machine_s.fst", "name": "Vale.PPC64LE.Machine_s.nat64" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fsqr_inline.fst", "name": "Vale.Inline.X64.Fsqr_inline.b64" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Cpuid.fst", "name": "Vale.Stdcalls.X64.Cpuid.check_avx512_xcr0" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_operand_reg_opr64" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Cpuid.fst", "name": "Vale.Stdcalls.X64.Cpuid.check_avx_xcr0" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.SHA_helpers.fsti", "name": "Vale.SHA.SHA_helpers.hash256" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.X64.fsti", "name": "Vale.Bignum.X64.flags_t" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.b8" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_value_opr64" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_value_reg_opr64" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Machine_s.fst", "name": "Vale.PPC64LE.Machine_s.nat16" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_code" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.X64.fsti", "name": "Vale.Interop.X64.arg_list_sb" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Cpuid.fst", "name": "Vale.Stdcalls.X64.Cpuid.lowstar_sha" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fst", "name": "Vale.Stdcalls.X64.Sha.lowstar_sha" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_value_dst_opr64" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.SHA_helpers.fsti", "name": "Vale.SHA.PPC64LE.SHA_helpers.block_w" }, { "project_name": "hacl-star", "file_name": "EverCrypt.AutoConfig2.fst", "name": "EverCrypt.AutoConfig2.has_shaext" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fsti", "name": "Vale.Inline.X64.Fadd_inline.u1024" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.va_code" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fsti", "name": "Vale.Inline.X64.Fadd_inline.u512" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Cpuid.fst", "name": "Vale.Stdcalls.X64.Cpuid.lowstar_avx512" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.call_c_t" } ], "selected_premises": [ "Vale.Interop.X64.max_stdcall", "Vale.Interop.X64.regs_modified_stdcall", "Vale.Interop.X64.xmms_modified_stdcall", "Vale.Interop.X64.als_ret", "Vale.Stdcalls.X64.Cpuid.as_normal_t", "Vale.Interop.X64.as_lowstar_sig_t_weak_stdcall", "Vale.AsLowStar.Wrapper.post_rel_generic", "Vale.AsLowStar.Wrapper.pre_rel_generic", "Vale.Interop.X64.wrap_weak_stdcall", "Vale.X64.CPU_Features_s.avx_enabled", "Vale.X64.Decls.va_code", "Vale.X64.CPU_Features_s.sse_enabled", "Vale.Interop.X64.register_of_arg_i", "Vale.Stdcalls.X64.Cpuid.dom", "Vale.X64.Decls.va_state", "Vale.X64.Memory.nat64", "Vale.Def.Types_s.nat64", "Vale.AsLowStar.ValeSig.vale_sig_stdcall", "Vale.X64.Machine_s.reg_64", "Vale.Interop.X64.arity_ok_stdcall", "Vale.Interop.Base.default_bq", "LowStar.Buffer.trivial_preorder", "Vale.Stdcalls.X64.Cpuid.as_t", "FStar.List.Tot.Base.length", "Vale.AsLowStar.Wrapper.mk_prediction", "Vale.Interop.X64.registers", "Vale.X64.Machine_s.reg_xmm", "FStar.List.Tot.Base.map", "Vale.Stdcalls.X64.Cpuid.sha_pre", "Vale.X64.Machine_s.nat64", "LowStar.Buffer.gcmalloc_of_list", "Vale.Interop.Base.buf_t", "Vale.Interop.X64.arg_reg_stdcall", "Vale.X64.Decls.va_if", "Vale.X64.MemoryAdapters.as_vale_stack", "Vale.AsLowStar.Wrapper.prediction_pre_rel", "Vale.Interop.Base.valid_base_type", "Vale.Interop.Base.stack_bq", "Vale.Interop.Base.ibuf_t", "Vale.X64.Decls.va_get_mem_heaplet", "Vale.X64.Decls.va_get_mem_layout", "Vale.X64.InsBasic.vale_heap", "Vale.Stdcalls.X64.Cpuid.code_sha", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Decls.get_reg", "LowStar.Monotonic.Buffer.length", "Vale.AsLowStar.LowStarSig.register_args", "Vale.X64.Decls.va_get_ok", "Vale.X64.Decls.va_upd_flags", "LowStar.BufferView.Down.buffer", "LowStar.BufferView.buffer", "Vale.Interop.Base.arg", "Vale.X64.Machine_s.operand128", "Vale.AsLowStar.ValeSig.sprop", "Vale.X64.Machine_s.operand64", "Vale.Def.Words_s.nat64", "Vale.AsLowStar.LowStarSig.vale_pre_hyp", "Vale.X64.Machine_s.quad32", "Vale.X64.Memory.quad32", "Vale.Arch.HeapLemmas.heap_ignore_ghost_machine", "Vale.Def.Words_s.nat32", "Vale.Interop.Heap_s.list_disjoint_or_eq", "Vale.X64.Decls.quad32", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_adx_bmi2_stdcall", "Vale.X64.Decls.va_upd_mem_heaplet", "Vale.AsLowStar.LowStarSig.to_low_pre", "Vale.Stdcalls.X64.Cpuid.sha_post", "Vale.X64.QuickCodes.label", "Vale.Stdcalls.X64.Cpuid.aesni_lemma", "Vale.Interop.Types.base_typ_as_type", "Vale.X64.Decls.va_upd_xmm", "Vale.Stdcalls.X64.Cpuid.sha_lemma", "Vale.X64.Decls.va_upd_reg64", "Vale.Interop.X64.elim_rel_gen_t_cons", "Vale.Interop.Types.get_downview", "Vale.Stdcalls.X64.Cpuid.aesni_post", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_rdrand_stdcall", "Vale.X64.InsBasic.vale_stack", "Vale.AsLowStar.LowStarSig.uint_to_nat", "Vale.Interop.Types.b8_preorder", "Vale.X64.Instruction_s.one64Reg", "Vale.Interop.Base.imm_to_b8", "Vale.X64.Decls.va_upd_mem", "Vale.X64.Memory.nat8", "Vale.Def.Types_s.nat8", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_sha_stdcall", "Vale.AsLowStar.Wrapper.prediction_post_rel", "Vale.Arch.MachineHeap_s.machine_heap", "Vale.AsLowStar.LowStarSig.create_initial_vale_state", "Vale.X64.MemoryAdapters.coerce", "Vale.X64.Instruction_s.coerce", "Vale.X64.StateLemmas.coerce", "Vale.Arch.HeapLemmas.coerce", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_avx_xcr0_stdcall", "Vale.Interop.X64.op_Plus_Plus", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_sse_stdcall", "Vale.Def.Prop_s.prop0", "Vale.X64.Decls.va_get_reg64", "Vale.Interop.X64.reg_nat", "Vale.AsLowStar.LowStarSig.nat_to_uint" ], "source_upto_this": "module Vale.Stdcalls.X64.Cpuid\n\nopen FStar.Mul\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\n\nmodule VC = Vale.Lib.X64.Cpuidstdcall\n\n(* A little utility to trigger normalization in types *)\nnoextract\nlet as_t (#a:Type) (x:normal a) : a = x\nnoextract\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__] noextract\nlet dom: IX64.arity_ok_stdcall td = []\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__] noextract\nlet aesni_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_aesni_stdcall c va_s0 IA.win\n\n[@__reduce__] noextract\nlet aesni_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_aesni_stdcall c va_s0 IA.win va_s1 f\n\n(* The vale lemma doesn't quite suffice to prove the modifies clause\n expected of the interop layer *)\n[@__reduce__] noextract\nlet aesni_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n aesni_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n aesni_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_aesni_stdcall code va_s0 IA.win\n\n(* Prove that vm_lemma' has the required type *)\nnoextract\nlet aesni_lemma = as_t #(VSig.vale_sig_stdcall aesni_pre aesni_post) aesni_lemma'\nnoextract\nlet code_aesni = VC.va_code_Check_aesni_stdcall IA.win\n\n(* Here's the type expected for the check_aesni wrapper *)\n[@__reduce__] noextract\nlet lowstar_aesni_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_aesni\n dom\n []\n _\n _\n (W.mk_prediction code_aesni dom [] (aesni_lemma code_aesni IA.win))\n\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__] noextract\nlet sha_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_sha_stdcall c va_s0 IA.win\n\n[@__reduce__] noextract\nlet sha_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_sha_stdcall c va_s0 IA.win va_s1 f\n\nopen Vale.X64.Machine_s\nopen Vale.X64.State\n\n#set-options \"--z3rlimit 20\"\n\n(* The vale lemma doesn't quite suffice to prove the modifies clause\n expected of the interop layer *)\n[@__reduce__] noextract\nlet sha_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n sha_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n sha_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_sha_stdcall code va_s0 IA.win\n\n(* Prove that vm_lemma' has the required type *)\nnoextract\nlet sha_lemma = as_t #(VSig.vale_sig_stdcall sha_pre sha_post) sha_lemma'\nnoextract\nlet code_sha = VC.va_code_Check_sha_stdcall IA.win\n\n(* Here's the type expected for the check_aesni wrapper *)\n[@__reduce__] noextract", "sketch": [ "Step 1: The definition `lowstar_sha_t` is expected to provide the type for the `check_sha` wrapper function, similar to how `lowstar_aesni_t` provides the type for the `check_aesni` wrapper function.\nStep 2: To implement this, we will use the `IX64.as_lowstar_sig_t_weak_stdcall` function, passing in the appropriate arguments: `code_sha`, `dom`, an empty list for additional arguments, and the prediction created using `W.mk_prediction` with `sha_lemma`.", "Step 1: Define the type `lowstar_sha_t` which represents the Low* signature for the SHA check function.\nStep 2: Use the `IX64.as_lowstar_sig_t_weak_stdcall` function to construct this type, similar to how `lowstar_aesni_t` was defined. This involves passing the SHA code, domain, empty list for arguments, and the SHA lemma.", "Step 1: Define the type `lowstar_sha_t` which represents the Low* signature for the SHA standard call.\nStep 2: Implement the definition by using the `IX64.as_lowstar_sig_t_weak_stdcall` function, providing it with the necessary arguments such as `code_sha`, `dom`, and the `sha_lemma`.", "Step 1: Define the type `lowstar_sha_t` which represents the Low* signature for the SHA check function.\nStep 2: Implement the definition by using the `IX64.as_lowstar_sig_t_weak_stdcall` function, providing it with the necessary arguments: the SHA code, the domain, an empty list for additional arguments, and the prediction generated by `W.mk_prediction` using the SHA code, domain, and SHA lemma.", "Step 1: Define the type for the `lowstar_sha_t` function, which is expected to be similar to `lowstar_aesni_t` but for the SHA functionality.\nStep 2: Implement the type definition by using `IX64.as_lowstar_sig_t_weak_stdcall` with the appropriate arguments for the SHA functionality, including the `code_sha`, `dom`, and the `sha_lemma`.", "Step 1: Define the type `lowstar_sha_t` which represents the Low* signature for the SHA check function.\nStep 2: Implement the type using `IX64.as_lowstar_sig_t_weak_stdcall`, providing the necessary arguments including the SHA code, domain, and the SHA lemma.", "Step 1: The definition `lowstar_sha_t` is intended to provide the type expected for the `check_sha` wrapper function. This type will be derived using the `IX64.as_lowstar_sig_t_weak_stdcall` function, which adapts the signature of a Vale function to a Low* function.\nStep 2: To implement this, we will use the `code_sha` value, the `dom` value, and the `sha_lemma` value to construct the type. The `W.mk_prediction` function will be used to create a prediction for the `sha_lemma`.", "Step 1: Define the type `lowstar_sha_t` which represents the Low* signature for the SHA check function.\nStep 2: Implement this type using the `IX64.as_lowstar_sig_t_weak_stdcall` function, similar to the `lowstar_aesni_t` definition. This involves passing the SHA code, domain, and other necessary parameters, including the SHA lemma.", "Step 1: The definition `lowstar_sha_t` is intended to specify the type expected for the `check_sha` wrapper function, similar to how `lowstar_aesni_t` was defined for the `check_aesni` wrapper.\nStep 2: The implementation involves using the `IX64.as_lowstar_sig_t_weak_stdcall` function with appropriate arguments, including the SHA-specific code, domain, and lemma.", "Step 1: Define the type `lowstar_sha_t` which represents the Low* signature for the SHA check function.\nStep 2: Implement the definition by using the `IX64.as_lowstar_sig_t_weak_stdcall` function, passing the appropriate arguments including the SHA code, domain, and the SHA lemma." ], "generated_solution": [ "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))" ] }, { "file_name": "Protocol.fst", "name": "Protocol.received", "opens_and_abbrevs": [ { "open": "MonotonicArray" }, { "open": "FStar.ST" }, { "open": "FStar.Heap" }, { "open": "FStar.Preorder" }, { "open": "FStar.Seq" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 0, "initial_ifuel": 1, "max_ifuel": 0, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 200, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let received (#n:nat) (file:iarray byte n) (c:connection) (h:heap) =\n file `fully_initialized_in` h /\\\n sent (as_initialized_seq file h) c", "source_range": { "start_line": 496, "start_col": 0, "end_line": 498, "end_col": 38 }, "interleaved": false, "definition": "fun file c h ->\n Protocol.fully_initialized_in file h /\\ Protocol.sent (MonotonicArray.as_initialized_seq file h) c", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Prims.nat", "Protocol.iarray", "Protocol.byte", "Protocol.connection", "FStar.Monotonic.Heap.heap", "Prims.l_and", "Protocol.fully_initialized_in", "Protocol.sent", "MonotonicArray.as_initialized_seq", "Prims.logical" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": true, "type": "file: Protocol.iarray Protocol.byte n -> c: Protocol.connection -> h: FStar.Monotonic.Heap.heap\n -> Prims.logical", "prompt": "let received (#n: nat) (file: iarray byte n) (c: connection) (h: heap) =\n ", "expected_response": "file `fully_initialized_in` h /\\ sent (as_initialized_seq file h) c", "source": { "project_name": "FStar", "file_name": "examples/preorders/Protocol.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "Protocol.fst", "checked_file": "dataset/Protocol.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/MonotonicArray.fsti.checked", "dataset/FStar.ST.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Heap.fst.checked", "dataset/FStar.Classical.fsti.checked", "dataset/ArrayUtils.fst.checked" ] }, "definitions_in_context": [ "let lemma_seq_append_unstable (#a:Type0) (s:seq a) (s1:seq a) (s2:seq a) (s3:seq a) (pos:nat) (sent:nat{pos + sent <= length s})\n :Lemma (requires (s1 == slice s 0 pos /\\ s2 == slice s pos (pos + sent) /\\ s3 == slice s 0 (pos + sent)))\n (ensures (s3 == append s1 s2))\n = assert (Seq.equal s3 (append s1 s2))", "val fragment_size:nat", "byte", "val zero_b:byte", "message", "network_message", "randomness", "val xor: network_message -> network_message -> network_message", "val lemma_xor (a:network_message) (b:network_message)\n :Lemma (xor (xor a b) b == a)\n [SMTPat (xor (xor a b) b)]", "val zeroes: n:nat -> (s:seq byte{length s = n})", "let zeroes n = Seq.create n (zero_b)", "let pad (m:message) :network_message = append m (zeroes (fragment_size - (length m)))", "val unpad (s:network_message)\n :(r:(nat * message){length (snd r) = fst r /\\ s == pad (snd r)})", "val lemma_pad_unpad (x:unit) :Lemma (ensures (forall (m:message). snd (unpad (pad m)) == m))", "val mac: cipher:network_message -> i:nat -> seq byte", "entry", "E", "E", "E", "i", "i", "msg", "msg", "cipher", "cipher", "tag", "tag", "entries", "let is_prefix_of (#a:Type) (s1:seq a) (s2:seq a) :Type0\n = length s1 <= length s2 /\\\n (forall (i:nat). i < length s1 ==> Seq.index s1 i == Seq.index s2 i)", "let entries_rel (rand:randomness) :relation (entries rand) =\n fun (es1:entries rand) (es2:entries rand) -> es1 `is_prefix_of` es2", "let entries_pre (rand:randomness) :preorder (entries rand) = entries_rel rand", "let counter_pred (#rand:randomness) (n:nat) (es_ref:mref (entries rand) (entries_rel rand)) :(p:heap_predicate{stable p})\n = fun h -> h `contains` es_ref /\\ n <= length (sel h es_ref)", "counter_t", "let counter_rel (#rand:randomness) (es_ref:mref (entries rand) (entries_rel rand)) :relation (counter_t es_ref)\n = fun n1 n2 -> b2t (n1 <= n2)", "let counter_pre (#rand:randomness) (es_ref:mref (entries rand) (entries_rel rand)) :preorder (counter_t es_ref)\n = counter_rel es_ref", "connection", "S", "S", "S", "rand", "rand", "entries", "entries", "R", "R", "R", "rand", "rand", "entries", "entries", "ctr", "ctr", "let rand_of (c:connection) :randomness =\n match c with\n | S r _\n | R r _ _ -> r", "let entries_of (c:connection) :(mref (entries (rand_of c)) (entries_rel (rand_of c))) =\n match c with\n | S _ es -> es\n | R _ es _ -> es", "let live_connection (h:heap) (c:connection) =\n match c with\n | S _ es_ref -> h `contains` es_ref\n | R _ es_ref ctr_ref -> h `contains` es_ref /\\ h `contains` ctr_ref", "let recall_connection_liveness (c:connection)\n :ST unit (requires (fun h0 -> True)) (ensures (fun h0 _ h1 -> h0 == h1 /\\ h0 `live_connection` c))\n = match c with\n | S _ es_ref -> ST.recall es_ref\n | R _ es_ref ctr_ref -> ST.recall es_ref; ST.recall ctr_ref", "let lemma_sel_entries_equals_sel_tot_entries (c:connection) (h:heap)\n :Lemma (requires (h `live_connection` c))\n (ensures (sel_tot h (entries_of c) == sel h (entries_of c)))\n\t [SMTPat (sel_tot h (entries_of c))]\n = Heap.lemma_sel_equals_sel_tot_for_contained_refs h (entries_of c)", "let lemma_sel_ctr_ref_equals_sel_tot_ctr_ref (c:connection{R? c}) (h:heap)\n :Lemma (requires (h `live_connection` c))\n (ensures (let R _ _ ctr_ref = c in sel_tot h ctr_ref == sel h ctr_ref))\n\t [SMTPat (sel_tot h (R?.ctr c))]\n = Heap.lemma_sel_equals_sel_tot_for_contained_refs h (R?.ctr c)", "let log (c:connection) (h:heap{h `live_connection` c}) :Tot (seq message) =\n ArrayUtils.seq_map (fun (E _ m _ _) -> m) (sel_tot h (entries_of c))", "let lemma_prefix_entries_implies_prefix_log\n (c:connection) (h1:heap) (h2:heap{h1 `live_connection` c /\\ h2 `live_connection` c})\n :Lemma (requires (sel h1 (entries_of c) `is_prefix_of` sel h2 (entries_of c)))\n\t (ensures (log c h1 `is_prefix_of` log c h2))\n\t [SMTPat (log c h1); SMTPat (log c h2)]\n = ArrayUtils.lemma_map_commutes_with_prefix (fun (E _ m _ _) -> m) (sel h1 (entries_of c)) (sel h2 (entries_of c))", "let ctr (c:connection) (h:heap{h `live_connection` c}) :Tot nat =\n if S? c then length (sel_tot h (entries_of c))\n else sel_tot h (R?.ctr c)", "let recall_counter (c:connection)\n :ST unit (requires (fun _ -> True)) (ensures (fun h0 _ h1 -> h0 == h1 /\\ h0 `live_connection` c /\\ ctr c h0 <= Seq.length (log c h0)))\n = recall_connection_liveness c;\n match c with\n | S _ _ -> ()\n | R _ es_ref ctr_ref -> let n = !ctr_ref in gst_recall (counter_pred n es_ref)", "let snapshot (c:connection) (h0:heap{h0 `live_connection` c}) :(p:heap_predicate{stable p}) =\n fun h -> h `live_connection` c /\\\n ctr c h0 <= ctr c h /\\ ctr c h0 <= Seq.length (log c h) /\\ log c h0 `is_prefix_of` log c h", "let snap (c:connection) :ST unit (requires (fun _ -> True))\n (ensures (fun h0 _ h1 -> h0 `live_connection` c /\\ witnessed (snapshot c h0) /\\ h0 == h1))\n = let h0 = ST.get () in\n recall_connection_liveness c;\n recall_counter c;\n gst_witness (snapshot c h0)", "iarray", "let sender (c:connection) :Tot bool = S? c", "let receiver (c:connection) :Tot bool = R? c", "let connection_footprint (c:connection) :GTot (Set.set nat)\n = match c with\n | S _ es_ref -> Set.singleton (addr_of es_ref)\n | R _ es_ref ctr_ref -> Set.union (Set.singleton (addr_of es_ref)) (Set.singleton (addr_of ctr_ref))", "let lemma_snoc_log\n (c:connection{sender c}) (i:nat) (cipher:network_message) (msg:message{xor (pad msg) ((rand_of c) i) == cipher})\n (tag:seq byte{tag == mac cipher i})\n (h0:heap) (h1:heap{h0 `live_connection` c /\\ h1 `live_connection` c})\n :Lemma (requires (sel h1 (entries_of c) == snoc (sel h0 (entries_of c)) (E i msg cipher tag)))\n\t (ensures (log c h1 == snoc (log c h0) msg))\n = ArrayUtils.lemma_map_commutes_with_snoc (fun (E _ m _ _) -> m) (sel h0 (entries_of c)) (E i msg cipher tag)", "val network_send\n (c:connection{sender c}) (f:network_message) (tag:seq byte)\n :ST unit (requires (fun h0 -> h0 `live_connection` c /\\ \n (let S _ es_ref = c in\n let es = sel h0 es_ref in\n\t\t\t Seq.length es > 0 /\\\n (let E _ _ c t = Seq.index es (Seq.length es - 1) in\n\t\t\t c == f /\\ t == tag))))\n (ensures (fun h0 _ h1 -> h0 == h1))", "let send (#n:nat) (buf:iarray byte n) (c:connection{sender c})\n :ST nat (requires (fun h0 -> True))\n (ensures (fun h0 sent h1 -> modifies (connection_footprint c) h0 h1 /\\\n\t h0 `live_connection` c /\\\n\t\t\t\t h1 `live_connection` c /\\\n\t sent <= min n fragment_size /\\\n\t\t\t\t ctr c h1 = ctr c h0 + 1 /\\\n\t\t\t\t (forall (i:nat). i < n ==> Some? (Seq.index (as_seq buf h0) i)) /\\\n log c h1 == snoc (log c h0) (as_initialized_subseq buf h0 0 sent)))\n = let h0 = ST.get () in\n\n recall_connection_liveness c;\n recall_all_init buf;\n\n let S rand es_ref = c in\n\n let msgs0 = ST.read es_ref in\n let i0 = length msgs0 in\n\n let sent = min n fragment_size in\n let msg = read_subseq_i_j buf 0 sent in\n let frag = append msg (zeroes (fragment_size - sent)) in\n let cipher = xor frag (rand i0) in\n\n let msgs1 = snoc msgs0 (E i0 msg cipher (mac cipher i0)) in\n\n ST.write es_ref msgs1;\n\n network_send c cipher (mac cipher i0);\n let h1 = ST.get () in\n lemma_snoc_log c i0 cipher msg (mac cipher i0) h0 h1;\n \n sent", "let ciphers (c:connection) (h:heap) :GTot (seq network_message) =\n ArrayUtils.seq_map E?.cipher (sel h (entries_of c))", "val network_receive (c:connection)\n :ST (option (network_message * seq byte)) (requires (fun h0 -> h0 `live_connection` c))\n (ensures (fun h0 _ h1 -> h0 == h1))", "let modifies_r (#n:nat) (c:connection{receiver c}) (arr:array byte n) (h0 h1:heap) :Type0\n = modifies (Set.union (connection_footprint c)\n (array_footprint arr)) h0 h1", "val verify (c:connection{receiver c}) (cipher:network_message) (tag:seq byte) (i:nat)\n :ST bool (requires (fun h0 -> h0 `live_connection` c))\n (ensures (fun h0 r h1 -> h0 == h1 /\\\n\t (r ==>\n\t (let R _ es_ref _ = c in\n\t\t let es = sel h0 es_ref in\n\t\t\ti < Seq.length es /\\\n\t\t\t(let E _ _ c t = Seq.index es i in\n\t\t\t c == cipher /\\ t == tag)))))", "let receive (#n:nat{fragment_size <= n}) (buf:array byte n) (c:connection{receiver c})\n :ST (option nat) (requires (fun h0 -> Set.disjoint (connection_footprint c) (array_footprint buf)))\n (ensures (fun h0 r_opt h1 -> match r_opt with\n\t\t\t\t\t | None -> h0 == h1\n\t\t\t\t\t | Some r ->\n\t\t\t\t\t h0 `live_connection` c /\\\n\t\t\t\t\t h1 `live_connection` c /\\\n\t\t\t\t\t modifies_r c buf h0 h1 /\\\n\t\t\t\t\t disjoint_siblings_remain_same buf h0 h1 /\\\n\t\t\t\t\t r <= fragment_size /\\\n\t\t\t\t\t all_init_i_j buf 0 r /\\\n\t\t\t\t\t ctr c h1 = ctr c h0 + 1 /\\\n\t\t\t\t\t ctr c h0 < length (log c h0) /\\\n log c h0 == log c h1 /\\\n\t\t\t\t\t (forall (i:nat). i < r ==> Some? (Seq.index (as_seq buf h1) i)) /\\\n\t\t\t\t\t Seq.index (log c h0) (ctr c h0) == as_initialized_subseq buf h1 0 r))\n = let h0 = ST.get () in\n let R rand es_ref ctr_ref = c in\n\n Set.lemma_disjoint_subset (connection_footprint c) (array_footprint buf) (Set.singleton (addr_of ctr_ref));\n\n recall_connection_liveness c;\n\n match network_receive c with\n | None -> None\n | Some (cipher, tag) ->\n let i0 = ST.read ctr_ref in\n\n if verify c cipher tag i0 then\n let msg = xor cipher (rand i0) in\n let len, m = unpad msg in\n\n\tlemma_pad_unpad ();\n assert (m == Seq.index (log c h0) (ctr c h0));\n gst_witness (counter_pred (i0 + 1) es_ref);\n recall_contains buf;\n ST.write ctr_ref (i0 + 1);\n let h1 = ST.get () in\n lemma_disjoint_sibling_remain_same_for_unrelated_mods buf (Set.singleton (addr_of (ctr_ref))) h0 h1;\n fill buf m;\n let h2 = ST.get () in\n lemma_disjoint_sibling_remain_same_transitive buf h0 h1 h2;\n Some len\n else\n None", "let lemma_is_prefix_of_slice\n (#a:Type0) (s1:seq a) (s2:seq a{s1 `is_prefix_of` s2}) (i:nat) (j:nat{j >= i /\\ j <= Seq.length s1})\n :Lemma (requires True)\n (ensures (Seq.slice s1 i j == Seq.slice s2 i j))\n\t [SMTPat (s1 `is_prefix_of` s2); SMTPat (Seq.slice s1 i j); SMTPat (Seq.slice s2 i j)]\n = ArrayUtils.lemma_is_prefix_of_slice s1 s2 i j", "val flatten (s:seq message) :Tot (seq byte)", "val lemma_flatten_snoc (s:seq message) (m:message)\n :Lemma (requires True)\n (ensures (flatten (snoc s m) == append (flatten s) m))", "val flatten_empty (u:unit) : Lemma (flatten Seq.empty == Seq.empty)", "let sent_bytes' (file:seq byte) (c:connection) (from:nat) (to:nat{from <= to}) :heap_predicate\n = fun h -> h `live_connection` c /\\ \n (let log = log c h in\n to <= Seq.length log /\\ \n\t file == flatten (Seq.slice log from to))", "let sent_bytes (file:seq byte) (c:connection) (from:nat) (to:nat{from <= to}) :(p:heap_predicate{stable p})\n = sent_bytes' file c from to", "let sent (file:seq byte) (c:connection) =\n exists (from:nat) (to:nat{from <= to}). witnessed (sent_bytes file c from to)", "let iarray_as_seq (#a:Type) (#n:nat) (x:iarray a n) : ST (seq a) \n (requires (fun h -> True))\n (ensures (fun h0 s h1 -> \n h0==h1 /\\\n (forall (k:nat). k < n ==> Some? (Seq.index (as_seq x h0) k)) /\\\n s == as_initialized_subseq x h0 0 n /\\\n\t s == as_initialized_seq x h0))\n = read_subseq_i_j x 0 n", "let fully_initialized_in #a #n (x:array a n) (h:heap) = \n h `contains_array` x /\\\n (forall (k:nat). k < n ==> Some? (Seq.index (as_seq x h) k))", "let subseq_suffix #a #n (f:iarray a n) (pos:nat) (until:nat{pos+until <= n}) \n (h:heap{f `fully_initialized_in` h})\n : Lemma (as_initialized_subseq (suffix f pos) h 0 until ==\n as_initialized_subseq f h pos (pos + until))\n = assert (as_initialized_subseq (suffix f pos) h 0 until `Seq.equal`\n as_initialized_subseq f h pos (pos + until))", "let slice_snoc #a (s:seq a) (x:a) (from:nat) (to:nat{from<=to /\\ to<=Seq.length s})\n : Lemma (slice s from to == slice (snoc s x) from to)\n = assert (slice s from to `Seq.equal` slice (snoc s x) from to)", "let slice_snoc2 #a (s:seq a) (x:a) (from:nat{from <= Seq.length s})\n : Lemma (slice (snoc s x) from (Seq.length s + 1) == snoc (slice s from (Seq.length s)) x)\n = assert (slice (snoc s x) from (Seq.length s + 1) `Seq.equal` snoc (slice s from (Seq.length s)) x)", "let append_subseq #a #n (f:iarray a n) (pos:nat) (sent:nat{pos + sent <= n}) (h:heap{f `fully_initialized_in` h})\n : Lemma (let f0 = as_initialized_subseq f h 0 pos in\n let f1 = as_initialized_subseq f h 0 (pos + sent) in\n let sub_file = suffix f pos in\n let sent_frag = as_initialized_subseq sub_file h 0 sent in\n f1 == append f0 sent_frag)\n = let f0 = as_initialized_subseq f h 0 pos in\n let f1 = as_initialized_subseq f h 0 (pos + sent) in\n let sub_file = suffix f pos in\n let sent_frag = as_initialized_subseq sub_file h 0 sent in\n\n let bs = as_seq f h in\n let bss = as_seq sub_file h in\n let sbs = ArrayUtils.get_some_equivalent bs in\n\n assert (f0 == ArrayUtils.get_some_equivalent (Seq.slice bs 0 pos));\n assert (f1 == ArrayUtils.get_some_equivalent (Seq.slice bs 0 (pos + sent)));\n assert (sent_frag == ArrayUtils.get_some_equivalent (Seq.slice bss 0 sent));\n assert (bss == Seq.slice bs pos n);\n assert (Seq.equal (Seq.slice bss 0 sent) (Seq.slice bs pos (pos + sent)));\n assert (sent_frag == ArrayUtils.get_some_equivalent (Seq.slice bs pos (pos + sent)));\n\n assert (f0 == Seq.slice sbs 0 pos);\n assert (f1 == Seq.slice sbs 0 (pos + sent));\n assert (sent_frag == Seq.slice sbs pos (pos + sent));\n lemma_seq_append_unstable sbs f0 sent_frag f1 pos sent", "let lemma_sender_connection_ctr_equals_length_log\n (c:connection{sender c}) (h:heap{h `live_connection` c})\n :Lemma (ctr c h == Seq.length (log c h))\n = ()", "val send_aux \n (#n:nat) \n (file:iarray byte n) \n (c:connection{sender c /\\ Set.disjoint (connection_footprint c) (array_footprint file)})\n (from:nat)\n (pos:nat{pos <= n})\n : ST unit \n (requires (fun h0 ->\n file `fully_initialized_in` h0 /\\\n h0 `live_connection` c /\\\n from <= ctr c h0 /\\\n sent_bytes (as_initialized_subseq file h0 0 pos) c from (ctr c h0) h0))\n (ensures (fun h0 _ h1 -> \n modifies (connection_footprint c) h0 h1 /\\\n h1 `live_connection` c /\\\n from <= ctr c h1 /\\\n (forall (k:nat). k < n ==> Some? (Seq.index (as_seq file h0) k)) /\\\n sent_bytes (as_initialized_seq file h0) c from (ctr c h1) h1))", "let rec send_aux #n file c from pos\n = if pos = n then ()\n else\n let sub_file = suffix file pos in\n lemma_all_init_i_j_sub file pos (n - pos);\n \n let h0 = ST.get () in\n let file_bytes0 = iarray_as_seq file in\n let log0 = log c h0 in\n let sent = send sub_file c in\n let h1 = ST.get () in\n let log1 = log c h1 in\n let file_bytes1 = iarray_as_seq file in \n assert (file_bytes0 == file_bytes1);\n recall_contains file; //strange that this is needed\n assert (from <= ctr c h1);\n assert (file `fully_initialized_in` h1);\n assert (h1 `live_connection` c);\n let _ : unit = \n let sent_frag = as_initialized_subseq sub_file h0 0 sent in\n let sent_frag' = as_initialized_subseq file h0 pos (pos + sent) in\n assert (log1 == snoc log0 sent_frag);\n subseq_suffix file pos sent h0; //sent_frag == sent_frag'\n slice_snoc log0 sent_frag from (ctr c h0); //slice log0 from (ctr c h0) == slice log1 from (ctr c h0)\n slice_snoc2 log0 sent_frag from; //Seq.slice log1 from (ctr c h1) == snoc (Seq.slice log0 from (ctr c h0)) sent_frag\n assert (ctr c h0 + 1 = ctr c h1);\n\t lemma_sender_connection_ctr_equals_length_log c h0;\n\t lemma_sender_connection_ctr_equals_length_log c h1;\t \n\t assert (ctr c h0 = Seq.length log0);\n assert (ctr c h1 = Seq.length log1);\n let f0 = as_initialized_subseq file h1 0 pos in\n let f1 = as_initialized_subseq file h1 0 (pos + sent) in\n append_subseq file pos sent h1; //f1 == append f0 sent_frag\n assert (f1 == append f0 sent_frag);\n assert (f0 == flatten (Seq.slice log0 from (ctr c h0)));\n lemma_flatten_snoc (Seq.slice log0 from (ctr c h0)) sent_frag;\n assert (f1 == flatten (Seq.slice log1 from (ctr c h1)));\n assert (sent_bytes f1 c from (ctr c h1) h1) \n in\n send_aux file c from (pos + sent)", "let send_file (#n:nat) (file:iarray byte n) (c:connection{sender c /\\ Set.disjoint (connection_footprint c) (array_footprint file)})\n : ST unit \n (requires (fun h -> True))\n (ensures (fun h0 _ h1 ->\n modifies (connection_footprint c) h0 h1 /\\\n h1 `live_connection` c /\\\n (forall (k:nat). k < n ==> Some? (Seq.index (as_seq file h0) k)) /\\\n sent (as_initialized_seq file h0) c))\n = let h0 = ST.get () in\n recall_all_init file;\n recall_contains file;\n recall_connection_liveness c;\n let file_bytes0 = iarray_as_seq file in\n let from = ctr c h0 in\n assert (Seq.equal (as_initialized_subseq file h0 0 0) Seq.empty);\n flatten_empty();\n assert (Seq.equal (flatten (Seq.slice (log c h0) from from)) Seq.empty);\n send_aux file c from 0;\n let h1 = ST.get () in\n let file_bytes1 = iarray_as_seq file in\n assert (file_bytes0 == file_bytes1);\n gst_witness (sent_bytes file_bytes0 c from (ctr c h1));\n assert (sent file_bytes0 c)" ], "closest": [ "val Vale.X64.Memory.init_heaplets_req = h: Vale.X64.Memory.vale_heap -> bs: FStar.Seq.Base.seq Vale.Arch.HeapImpl.buffer_info\n -> Prims.logical\nlet init_heaplets_req (h:vale_heap) (bs:Seq.seq buffer_info) =\n (forall (i:nat).{:pattern (Seq.index bs i)} i < Seq.length bs ==>\n buffer_readable h (Seq.index bs i).bi_buffer) /\\\n (forall (i1 i2:nat).{:pattern (Seq.index bs i1); (Seq.index bs i2)}\n i1 < Seq.length bs /\\ i2 < Seq.length bs ==> buffer_info_disjoint (Seq.index bs i1) (Seq.index bs i2))", "val Vale.PPC64LE.Memory.init_heaplets_req = h: Vale.PPC64LE.Memory.vale_heap -> bs: FStar.Seq.Base.seq Vale.Arch.HeapImpl.buffer_info\n -> Prims.logical\nlet init_heaplets_req (h:vale_heap) (bs:Seq.seq buffer_info) =\n (forall (i:nat).{:pattern (Seq.index bs i)} i < Seq.length bs ==>\n buffer_readable h (Seq.index bs i).bi_buffer) /\\\n (forall (i1 i2:nat).{:pattern (Seq.index bs i1); (Seq.index bs i2)}\n i1 < Seq.length bs /\\ i2 < Seq.length bs ==> buffer_info_disjoint (Seq.index bs i1) (Seq.index bs i2))", "val recv (a: _) : nl_protocol a\nlet recv a : nl_protocol a = Msg Recv a return", "val QUIC.receivable = s: QUIC.state i -> h: FStar.Monotonic.HyperStack.mem{QUIC.invariant h s} -> Prims.GTot Prims.bool\nlet receivable (#i: index) (s: state i) (h: HS.mem { invariant h s }) =\n Secret.v (g_last_packet_number s h) + 1 < pow2 62", "val MiTLS.TLS.next_fragment_pre = i: MiTLS.TLSInfo.id -> c: MiTLS.Connection.connection -> h0: FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet next_fragment_pre (i:id) (c:connection) h0 =\n let s = c.hs in\n let es = Handshake.logT s h0 in\n let j = Handshake.iT s Writer h0 in\n i=currentId_T c Writer h0 /\\\n current_writer_pre c i h0 /\\\n Handshake.hs_inv s h0 /\\\n maybe_indexable es j /\\\n (if j = -1 then PlaintextID? i else i == epoch_id es.(j))", "val recv (t: Type) : protocol t\nlet recv (t:Type) : protocol t = Msg Recv t (fun x -> return x)", "val ffiRecv: Connection.connection -> ML bytes\nlet ffiRecv c =\n match read c with\n | Received response -> response\n | WouldBlock\n | Errno _ -> empty_bytes", "val Lib.Buffer.stack_allocated = \n b: Lib.Buffer.lbuffer a len ->\n h0: FStar.Monotonic.HyperStack.mem ->\n h1: FStar.Monotonic.HyperStack.mem ->\n s: Lib.Sequence.lseq a (Lib.IntTypes.v len)\n -> Prims.logical\nlet stack_allocated (#a:Type0) (#len:size_t) (b:lbuffer a len)\n (h0:mem) (h1:mem) (s:Seq.lseq a (v len)) =\n let b: B.buffer a = b in\n alloc_post_mem_common b h0 h1 s /\\\n B.frameOf b = HS.get_tip h0 /\\\n B.frameOf b <> HyperStack.root", "val ffiSend: Connection.connection -> bytes -> ML int\nlet ffiSend c b =\n write c b", "val ImmutableSTwHeaps.heap_rel = h0: FStar.Monotonic.Heap.heap -> h1: FStar.Monotonic.Heap.heap -> Prims.logical\nlet heap_rel (h0:heap) (h1:heap) = \n forall a (r: ref a) . contains h0 r ==> contains h1 r /\\ sel h0 r == sel h1 r", "val Vale.Interop.write_buffer_vale = \n a: Vale.Interop.Types.b8 ->\n heap: Vale.Arch.MachineHeap_s.machine_heap ->\n mem: Vale.Interop.Heap_s.interop_heap\n -> Prims.GTot Vale.Arch.MachineHeap_s.machine_heap\nlet write_buffer_vale (a:b8) (heap:machine_heap) (mem:interop_heap) =\n let b = get_downview a.bsrc in\n let length = DV.length b in\n let contents = DV.as_seq (hs_of_mem mem) b in\n let addr = addrs_of_mem mem a in\n write_vale_mem contents length addr 0 heap", "val Lib.Buffer.length = b: Lib.Buffer.buffer_t t a -> Prims.GTot Prims.nat\nlet length (#t:buftype) (#a:Type0) (b:buffer_t t a) =\n match t with\n | MUT -> B.length (b <: buffer a)\n | IMMUT -> IB.length (b <: ibuffer a)\n | CONST -> CB.length (b <: cbuffer a)", "val uds:b:\nIB.ibuffer byte_sec\n { IB.frameOf b == HS.root /\\ IB.recallable b /\\ IB.length b == (v uds_len) /\\\n IB.value_is b uds_bytes }\nlet uds : b:IB.ibuffer byte_sec{\n IB.frameOf b == HS.root /\\\n IB.recallable b /\\\n IB.length b == (v uds_len) /\\\n IB.value_is b uds_bytes} =\n\n let uds = IB.igcmalloc HS.root (I.u8 0) uds_len in\n IB.witness_value uds;\n uds", "val Hacl.Streaming.Functor.seen_h = \n c: Hacl.Streaming.Interface.block _ ->\n i: _ ->\n h: FStar.Monotonic.HyperStack.mem ->\n s: Hacl.Streaming.Functor.state' c i\n -> Prims.GTot Hacl.Streaming.Functor.bytes\nlet seen_h = seen", "val MiTLS.StAE.trigger_frame = h: FStar.Monotonic.HyperStack.mem -> Prims.logical\nlet trigger_frame (h:mem) = True", "val Vale.PPC64LE.Memory.inv_heaplet_ids = hs: Vale.Arch.HeapImpl.vale_heaplets -> Prims.logical\nlet inv_heaplet_ids (hs:vale_heaplets) =\n forall (i:heaplet_id).{:pattern Map16.sel hs i} (Map16.sel hs i).heapletId == Some i", "val MiTLS.TLS.sendFragment_inv = wo: FStar.Pervasives.Native.option (MiTLS.TLS.cwriter i c) -> h: FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet sendFragment_inv (#c:connection) (#i:id) (wo:option(cwriter i c)) h =\n st_inv c h\n /\\ (match wo with\n | None -> PlaintextID? i\n | Some wr -> live_region h (StAE.region wr)\n\t /\\ live_region h (StAE.log_region wr))", "val SteelTLArray.l = Prims.list FStar.UInt8.t\nlet l = [0uy; 1uy]", "val Vale.Poly1305.Equiv.nat_from_bytes_le = b: Lib.Sequence.seq (Lib.IntTypes.int_t Lib.IntTypes.U8 l)\n -> n: Prims.nat{n < Prims.pow2 (Lib.Sequence.length b * 8)}\nlet nat_from_bytes_le (#l:secrecy_level) = Lib.ByteSequence.nat_from_bytes_le #l", "val LowParse.Repr.slice_as_seq = h: FStar.Monotonic.HyperStack.mem -> c: LowParse.Repr.const_slice\n -> Prims.GTot (FStar.Seq.Base.seq LowParse.Bytes.byte)\nlet slice_as_seq (h:HS.mem) (c:const_slice) =\n Seq.slice (C.as_seq h c.base) 0 (U32.v c.slice_len)", "val LowParse.Repr.mut_p = LowStar.Monotonic.Buffer.srel LowParse.Bytes.byte\nlet mut_p = LowStar.Buffer.trivial_preorder LP.byte", "val Vale.X64.Memory.inv_heaplet_ids = hs: Vale.Arch.HeapImpl.vale_heaplets -> Prims.logical\nlet inv_heaplet_ids (hs:vale_heaplets) =\n forall (i:heaplet_id).{:pattern Map16.sel hs i} (Map16.sel hs i).heapletId == Some i", "val OPLSS.CPA.authentic = k: OPLSS.CPA.key -> c: OPLSS.AES.iv_cipher -> h: FStar.Monotonic.HyperStack.mem -> Prims.logical\nlet authentic (k:key) (c:AES.iv_cipher) (h:HS.mem) =\n exists p. Log.entries k.log h `Log.has` Entry p c", "val LowStar.Monotonic.Buffer.malloc_pre = r: FStar.Monotonic.HyperHeap.rid -> len: FStar.UInt32.t -> Prims.logical\nlet malloc_pre (r:HS.rid) (len:U32.t) = HST.is_eternal_region r /\\ U32.v len > 0", "val Vale.Poly1305.Equiv.nat_to_bytes_le = len: Prims.nat -> n: Prims.nat{n < Prims.pow2 (8 * len)}\n -> b:\n Lib.Sequence.seq (Lib.IntTypes.int_t Lib.IntTypes.U8 l)\n {Lib.Sequence.length b == len /\\ n == Lib.ByteSequence.nat_from_intseq_le b}\nlet nat_to_bytes_le (#l:secrecy_level) = Lib.ByteSequence.nat_to_bytes_le #l", "val Vale.Interop.Base.live_arg = h: FStar.Monotonic.HyperStack.mem -> x: Vale.Interop.Base.arg -> Type0\nlet live_arg (h:HS.mem) (x:arg) =\n match x with\n | (|TD_Buffer _ _ _, x|)\n | (|TD_ImmBuffer _ _ _, x|) -> B.live h x\n | (|TD_Base _, _ |) -> True", "val Vale.PPC64LE.Memory.vale_full_heap_equal = h1: Vale.PPC64LE.Memory.vale_full_heap -> h2: Vale.PPC64LE.Memory.vale_full_heap -> Prims.logical\nlet vale_full_heap_equal (h1 h2:vale_full_heap) =\n h1.vf_layout == h2.vf_layout /\\\n h1.vf_heap == h2.vf_heap /\\\n Map16.equal h1.vf_heaplets h2.vf_heaplets", "val protocolVersion_bytesize (x:protocolVersion) : GTot nat\nlet protocolVersion_bytesize (x:protocolVersion) : GTot nat = Seq.length (protocolVersion_serializer x)", "val Hacl.Bignum4096.n_bytes = FStar.UInt32.t\nlet n_bytes = n_limbs `FStar.UInt32.mul` 8ul", "val Vale.AsLowStar.LowStarSig.mem_imm_correspondence_1 = \n src: Vale.Arch.HeapTypes_s.base_typ ->\n t: Vale.Arch.HeapTypes_s.base_typ ->\n x: Vale.Interop.Base.ibuf_t src t ->\n h: FStar.Monotonic.HyperStack.mem ->\n s: Vale.X64.State.vale_state\n -> Prims.GTot Prims.prop\nlet mem_imm_correspondence_1\n (src t:ME.base_typ)\n (x:IB.ibuf_t src t)\n (h:HS.mem)\n (s:VS.vale_state) =\n let y = as_vale_immbuffer x in\n let db = get_downview x in\n DV.length_eq db;\n Seq.equal\n (nat_to_uint_seq_t t (ME.buffer_as_seq (ME.get_vale_heap s.VS.vs_heap) y))\n (UV.as_seq h (UV.mk_buffer db (view_of_base_typ t)))", "val Lib.Buffer.alloc_post_mem_common = \n b: LowStar.Monotonic.Buffer.mbuffer a rrel rel ->\n h0: FStar.Monotonic.HyperStack.mem ->\n h1: FStar.Monotonic.HyperStack.mem ->\n s: Lib.Sequence.seq a\n -> Prims.logical\nlet alloc_post_mem_common (#a:Type0) (#rrel #rel:LMB.srel a)\n (b:LMB.mbuffer a rrel rel) (h0 h1:HS.mem) (s:Seq.seq a)\n = LMB.live h1 b /\\\n B.loc_not_in (B.loc_addr_of_buffer b) h0 /\\\n Map.domain (HS.get_hmap h1) `Set.equal` Map.domain (HS.get_hmap h0) /\\\n (HS.get_tip h1) == (HS.get_tip h0) /\\\n modifies LMB.loc_none h0 h1 /\\\n LMB.as_seq h1 b == s", "val Vale.X64.Decls.buffer_length = b: Vale.X64.Memory.buffer t -> Prims.GTot Prims.nat\nlet buffer_length (#t:M.base_typ) (b:M.buffer t) = M.buffer_length #t b", "val ffiAcceptConnected:\n Transport.pvoid -> Transport.pfn_send -> Transport.pfn_recv ->\n config -> ML (Connection.connection * int)\nlet ffiAcceptConnected ctx snd rcv config =\n accept_connected ctx snd rcv config", "val buffers_readable (h: vale_heap) (l: list buffer64) : GTot Type0 (decreases l)\nlet rec buffers_readable (h:vale_heap) (l:list buffer64) : GTot Type0 (decreases l) =\n match l with\n | [] -> True\n | b :: l' -> buffer_readable h b /\\ buffers_readable h l'", "val QUIC.frame_invariant = \n l: LowStar.Monotonic.Buffer.loc ->\n s: QUIC.state (QUIC.mid i) ->\n h0: FStar.Monotonic.HyperStack.mem ->\n h1: FStar.Monotonic.HyperStack.mem\n -> Prims.unit\nlet frame_invariant #i l s h0 h1 =\n if I.model then\n let Ideal w r _ = mstate #(mid i) s in\n QModel.frame_invariant w h0 l h1;\n QModel.rframe_invariant r h0 l h1\n else\n QImpl.frame_invariant #(iid i) l s h0 h1", "val protocolName_length (#rrel: _) (#rel: _) (input: LL.slice rrel rel) (pos: U32.t) : HST.Stack U32.t\n (requires (fun h -> LL.valid protocolName_parser h input pos))\n (ensures (fun h res h' ->\n let x = LL.contents protocolName_parser h input pos in\n B.modifies B.loc_none h h' /\\\n U32.v pos + 1 + U32.v res == U32.v (LL.get_valid_pos protocolName_parser h input pos) /\\\n res == BY.len x /\\\n LL.bytes_of_slice_from_to h input (pos `U32.add` 1ul) ((pos `U32.add` 1ul) `U32.add` res) == BY.reveal x\n ))\nlet protocolName_length #_ #_ input pos =\n [@inline_let] let _ = assert_norm (protocolName == LP.parse_bounded_vlbytes_t 1 255) in\n LL.bounded_vlbytes_payload_length 1 255 input pos", "val MiTLS.StAE.frame_f = \n f: (_: FStar.Monotonic.HyperStack.mem -> Prims.GTot a) ->\n h0: FStar.Monotonic.HyperStack.mem ->\n s: FStar.Set.set FStar.Monotonic.HyperHeap.rid\n -> Prims.logical\nlet frame_f (#a:Type) (f:mem -> GTot a) (h0:mem) (s:Set.set rid) =\n forall h1.{:pattern trigger_frame h1}\n trigger_frame h1\n /\\ (HS.equal_on s (HS.get_hmap h0) (HS.get_hmap h1) ==> f h0 == f h1)", "val Vale.PPC64LE.Decls.buffer_length = b: Vale.PPC64LE.Memory.buffer t -> Prims.GTot Prims.nat\nlet buffer_length (#t:M.base_typ) (b:M.buffer t) = M.buffer_length #t b", "val AllocSTwHeaps.heap_rel = h0: FStar.Monotonic.Heap.heap -> h1: FStar.Monotonic.Heap.heap -> Prims.logical\nlet heap_rel (h0:FStar.Heap.heap) (h1:FStar.Heap.heap) = \n forall (a:Type0) (r:ref a) . FStar.Heap.contains h0 r ==> FStar.Heap.contains h1 r", "val MiTLS.Record.sendPacket = \n tcp: MiTLS.Transport.t ->\n ct: MiTLS.Content.contentType ->\n plain: Prims.bool ->\n ver: MiTLS.Parsers.ProtocolVersion.protocolVersion ->\n data: b: FStar.Bytes.bytes{FStar.Bytes.repr_bytes (FStar.Bytes.length b) <= 2}\n -> FStar.HyperStack.ST.STATE (FStar.Error.optResult Prims.string Prims.unit)\nlet sendPacket tcp ct plain ver (data: (b:bytes { repr_bytes (length b) <= 2})) =\n // still some margin for progress to avoid intermediate copies\n let header = makeHeader ct plain ver (length data) in \n trace (\"record headers: \"^print_bytes header);\n let res = Transport.send tcp (BufferBytes.from_bytes header) headerLen in\n if res = Int.Cast.uint32_to_int32 headerLen then \n let res = Transport.send tcp (BufferBytes.from_bytes data) (len data) in\n if Int32.v res = length data\n then Correct()\n else Error(Printf.sprintf \"Transport.send(header) returned %l\" res)\n else Error(Printf.sprintf \"Transport.send(payload) returned %l\" res)", "val MiTLS.Connection.epoch_i = \n c: MiTLS.Connection.connection ->\n h: FStar.Monotonic.HyperStack.mem ->\n i: Prims.nat{i < FStar.Seq.Base.length (MiTLS.Connection.epochs c h)}\n -> Prims.GTot\n (MiTLS.Old.Epochs.epoch (MiTLS.Old.Handshake.region_of (C?.hs c))\n (MiTLS.Old.Handshake.random_of (C?.hs c)))\nlet epoch_i c h i = Seq.index (epochs c h) i", "val LowStar.Monotonic.Buffer.deref = h: FStar.Monotonic.HyperStack.mem -> x: LowStar.Monotonic.Buffer.mpointer a rrel rel -> Prims.GTot a\nlet deref (#a:Type0) (#rrel #rel:srel a) (h:HS.mem) (x:mpointer a rrel rel) =\n get h x 0", "val parseFinished: data:bytes{repr_bytes(length data) <= 3} ->\n result(f:fin{Bytes.equal (finishedBytes f) (messageBytes HT_finished data)})\nlet parseFinished data =\n if length data < 65536 then Correct ({fin_vd = data}) else error \"Finished too large\"", "val LowStar.UninitializedBuffer.lubuffer_or_null = a: Type0 -> len: Prims.nat -> r: FStar.Monotonic.HyperHeap.rid -> Type0\nlet lubuffer_or_null (a:Type0) (len:nat) (r:HS.rid) =\n b:ubuffer a{(not (g_is_null b)) ==> (length b == len /\\ frameOf b == r)}", "val protocolName_bytesize (x:protocolName) : GTot nat\nlet protocolName_bytesize (x:protocolName) : GTot nat = Seq.length (protocolName_serializer x)", "val Hacl.Streaming.Functor.all_seen_h = \n c: Hacl.Streaming.Interface.block _ ->\n i: _ ->\n h: FStar.Monotonic.HyperStack.mem ->\n s: Hacl.Streaming.Functor.state' c i\n -> Prims.GTot Hacl.Streaming.Functor.bytes\nlet all_seen_h = all_seen", "val Hacl.Bignum256.n_bytes = FStar.UInt32.t\nlet n_bytes = n_limbs `FStar.UInt32.mul` 8ul", "val Lib.Buffer.global_allocated = \n b: Lib.Buffer.glbuffer a len ->\n h0: FStar.Monotonic.HyperStack.mem ->\n h1: FStar.Monotonic.HyperStack.mem ->\n s: Lib.Sequence.lseq a (Lib.IntTypes.v len)\n -> Prims.GTot Prims.logical\nlet global_allocated (#a:Type0) (#len:size_t) (b:glbuffer a len)\n (h0:mem) (h1:mem) (s:Seq.lseq a (v len)) =\n let b: ibuffer a = CB.as_mbuf b in\n B.frameOf b == HyperStack.root /\\\n alloc_post_mem_common b h0 h1 s", "val EtM.CPA.invariant = k: EtM.CPA.key -> h: FStar.Monotonic.HyperStack.mem -> Prims.logical\nlet invariant (k:key) (h:mem) =\n let Key raw_key lg = k in\n let log = log k h in\n contains h lg /\\ //<-- technical: the log must be allocated\n pairwise_distinct_ivs log /\\\n cipher_functional_correctness raw_key log", "val Vale.AsLowStar.LowStarSig.mem_correspondence_1 = \n src: Vale.Arch.HeapTypes_s.base_typ ->\n t: Vale.Arch.HeapTypes_s.base_typ ->\n x: Vale.Interop.Base.buf_t src t ->\n h: FStar.Monotonic.HyperStack.mem ->\n s: Vale.X64.State.vale_state\n -> Prims.GTot Prims.prop\nlet mem_correspondence_1\n (src t:ME.base_typ)\n (x:IB.buf_t src t)\n (h:HS.mem)\n (s:VS.vale_state) =\n let y = as_vale_buffer x in\n let db = get_downview x in\n DV.length_eq db;\n Seq.equal\n (nat_to_uint_seq_t t (ME.buffer_as_seq (ME.get_vale_heap s.VS.vs_heap) y))\n (UV.as_seq h (UV.mk_buffer db (view_of_base_typ t)))", "val ImmutableST.heap_rel = h0: NatHeap.heap -> h1: NatHeap.heap -> Prims.logical\nlet heap_rel (h0:heap) (h1:heap) = \n (forall a (r:ref a) . contains r h0 ==> contains r h1) /\\\n (forall a (r:ref a{contains r h0}) . sel h0 r == sel h1 r)", "val buffer64_read (b: M.buffer64) (i: int) (h: vale_heap) : GTot nat64\nlet buffer64_read (b:M.buffer64) (i:int) (h:vale_heap) : GTot nat64 = M.buffer_read b i h", "val buffer64_read (b: M.buffer64) (i: int) (h: vale_heap) : GTot nat64\nlet buffer64_read (b:M.buffer64) (i:int) (h:vale_heap) : GTot nat64 = M.buffer_read b i h", "val EverParse3d.CopyBuffer.inv = x: EverParse3d.CopyBuffer.copy_buffer_t -> h: FStar.Monotonic.HyperStack.mem -> Prims.prop\nlet inv (x:copy_buffer_t) (h:HS.mem) = I.live (stream_of x) h", "val Steel.Channel.Protocol.until = tr: Steel.Channel.Protocol.partial_trace_of p -> Steel.Channel.Protocol.protocol Prims.unit\nlet until #p (tr:partial_trace_of p) = tr.to", "val Vale.AES.PPC64LE.GHash.in_b_blocks = \n in_b: Vale.PPC64LE.Memory.buffer128 ->\n in_index: Prims.int ->\n count: Prims.int ->\n heap_s: Vale.PPC64LE.InsBasic.vale_heap ->\n layout: Vale.Arch.HeapImpl.vale_heap_layout ->\n ptr: Prims.int ->\n data: FStar.Seq.Base.seq Vale.PPC64LE.Memory.quad32\n -> Prims.logical\nlet in_b_blocks\n (in_b:buffer128) (in_index count:int) (heap_s:vale_heap) (layout:vale_heap_layout) (ptr:int) (data:seq quad32)\n =\n validSrcAddrsOffset128 heap_s ptr in_b in_index count layout Secret /\\\n (forall (i:nat).{:pattern (index data i)}\n i < count /\\ i < length data ==>\n reverse_bytes_quad32 (buffer128_read in_b (in_index + i) heap_s) == index data i)", "val LowParse.Repr.valid' = p: LowParse.Repr.repr_ptr t -> h: FStar.Monotonic.HyperStack.mem -> Prims.GTot Prims.logical\nlet valid' (#t:Type) (p:repr_ptr t) (h:HS.mem) =\n let slice = slice_of_const_buffer p.b p.meta.len in\n valid_slice slice p.meta h", "val MiTLS.Old.Handshake.next_fragment_requires = s: MiTLS.Old.Handshake.hs -> h0: FStar.Monotonic.HyperStack.mem -> Prims.GTot Prims.logical\nlet next_fragment_requires (#i:TLSInfo.id) (s:hs) h0 =\n let es = logT s h0 in\n let j = iT s Writer h0 in\n j < Seq.length es /\\ //17-04-08 added verification hint\n hs_inv s h0 /\\\n (if j < 0 then TLSInfo.PlaintextID? i else let e = Seq.index es j in i = Epochs.epoch_id e)", "val Vale.X64.Decls.va_is_src_heaplet = h: Vale.X64.Decls.heaplet_id -> s: Vale.X64.Decls.va_state -> Prims.logical\nlet va_is_src_heaplet (h:heaplet_id) (s:va_state) = True", "val send (t: Type) : protocol t\nlet send (t:Type) : protocol t = Msg Send t (fun x -> return x)", "val Vale.PPC64LE.InsMem.heaplet_id_is_some = h: Vale.PPC64LE.InsBasic.vale_heap -> i: Vale.PPC64LE.Memory.heaplet_id -> Prims.logical\nlet heaplet_id_is_some (h:vale_heap) (i:heaplet_id) =\n get_heaplet_id h == Some i", "val MiTLS.HandshakeMessages.hs_msg_bytes = ht: MiTLS.HandshakeMessages.handshakeType -> b: FStar.Bytes.bytes -> Prims.logical\nlet hs_msg_bytes (ht:handshakeType) (b:bytes) =\n length b >= 4 /\\ \n ( let b' = snd (split b 4ul) in\n repr_bytes (length b') <= 3 /\\ \n b = messageBytes ht b')", "val Vale.Interop.Types.get_downview = b: LowStar.Monotonic.Buffer.mbuffer (Vale.Interop.Types.base_typ_as_type src) rrel rel\n -> Prims.GTot (LowStar.BufferView.Down.buffer FStar.UInt8.t)\nlet get_downview\n (#src:base_typ)\n (#rrel #rel:MB.srel (base_typ_as_type src))\n (b:MB.mbuffer (base_typ_as_type src) rrel rel) =\n DV.mk_buffer_view b (down_view src)", "val Vale.PPC64LE.Memory.inv_heaplets = \n layout: Vale.Arch.HeapImpl.vale_heap_layout_inner ->\n h: Vale.Arch.HeapImpl.vale_heap ->\n hs: Vale.Arch.HeapImpl.vale_heaplets ->\n mt: Vale.Arch.HeapTypes_s.memTaint_t\n -> Prims.logical\nlet inv_heaplets (layout:vale_heap_layout_inner) (h:vale_heap) (hs:vale_heaplets) (mt:memTaint_t) =\n let bs = layout.vl_buffers in\n modifies layout.vl_mod_loc layout.vl_old_heap h /\\ // modifies for entire heap\n (forall (i:heaplet_id) (a:int).{:pattern Set.mem a (layout.vl_heaplet_sets i)}\n layout.vl_heaplet_map a == Some i <==> Set.mem a (layout.vl_heaplet_sets i)\n ) /\\\n (forall (i:heaplet_id).{:pattern (Map16.sel hs i)}\n inv_heaplet (layout.vl_heaplet_sets i) h (Map16.sel hs i)) /\\\n (forall (i:nat).{:pattern (Seq.index bs i)} i < Seq.length bs ==>\n inv_buffer_info (Seq.index bs i) layout.vl_heaplet_sets h hs mt layout.vl_mod_loc) /\\\n (forall (i1 i2:nat).{:pattern (Seq.index bs i1); (Seq.index bs i2)}\n i1 < Seq.length bs /\\ i2 < Seq.length bs ==> buffer_info_disjoint (Seq.index bs i1) (Seq.index bs i2)) /\\\n True", "val buffers_readable (h: vale_heap) (l: list M.buffer64) : GTot prop0 (decreases l)\nlet rec buffers_readable (h: vale_heap) (l: list M.buffer64) : GTot prop0 (decreases l) =\n match l with\n | [] -> True\n | b :: l' -> buffer_readable h b /\\ buffers_readable h l'", "val buffers_readable (h: vale_heap) (l: list M.buffer64) : GTot prop0 (decreases l)\nlet rec buffers_readable (h: vale_heap) (l: list M.buffer64) : GTot prop0 (decreases l) =\n match l with\n | [] -> True\n | b :: l' -> buffer_readable h b /\\ buffers_readable h l'", "val HWAbstraction.all_heap_buffers_except_ghost_state_remain_same = h0: FStar.Monotonic.HyperStack.mem -> h1: FStar.Monotonic.HyperStack.mem -> Prims.logical\nlet all_heap_buffers_except_ghost_state_remain_same (h0 h1:HS.mem) =\n let s = st () in\n forall (a:Type0) (b:B.buffer a).\n (ST.is_eternal_region (B.frameOf b) /\\\n B.disjoint b s.ghost_state /\\\n B.live h0 b) ==> (B.as_seq h0 b == B.as_seq h1 b /\\ B.live h1 b)", "val Vale.X64.Memory.inv_heaplets = \n layout: Vale.Arch.HeapImpl.vale_heap_layout_inner ->\n h: Vale.Arch.HeapImpl.vale_heap ->\n hs: Vale.Arch.HeapImpl.vale_heaplets ->\n mt: Vale.Arch.HeapTypes_s.memTaint_t\n -> Prims.logical\nlet inv_heaplets (layout:vale_heap_layout_inner) (h:vale_heap) (hs:vale_heaplets) (mt:memTaint_t) =\n let bs = layout.vl_buffers in\n modifies layout.vl_mod_loc layout.vl_old_heap h /\\ // modifies for entire heap\n (forall (i:heaplet_id) (a:int).{:pattern Set.mem a (layout.vl_heaplet_sets i)}\n layout.vl_heaplet_map a == Some i <==> Set.mem a (layout.vl_heaplet_sets i)\n ) /\\\n (forall (i:heaplet_id).{:pattern (Map16.sel hs i)}\n inv_heaplet (layout.vl_heaplet_sets i) h (Map16.sel hs i)) /\\\n (forall (i:nat).{:pattern (Seq.index bs i)} i < Seq.length bs ==>\n inv_buffer_info (Seq.index bs i) layout.vl_heaplet_sets h hs mt layout.vl_mod_loc) /\\\n (forall (i1 i2:nat).{:pattern (Seq.index bs i1); (Seq.index bs i2)}\n i1 < Seq.length bs /\\ i2 < Seq.length bs ==> buffer_info_disjoint (Seq.index bs i1) (Seq.index bs i2)) /\\\n True", "val MRefST.stable_on_heap = m: MRefST.mref a r -> p: FStar.Preorder.predicate MRefHeap.heap -> Prims.logical\nlet stable_on_heap (#a:Type) (#r:preorder a) (m:mref a r) (p:predicate heap) =\n forall h0 h1 . stable_on_heap_aux m p h0 h1", "val MRefST.heap_rel = h0: MRefHeap.heap -> h1: MRefHeap.heap -> Prims.logical\nlet heap_rel (h0:heap) (h1:heap) =\n (forall a r (m:mref a r) . contains m h0 ==> contains m h1) /\\\n (forall a (r:preorder a) (m:mref a r{contains m h0}) . r (sel h0 m) (sel h1 m))", "val Vale.Interop.Base.all_live = h: FStar.Monotonic.HyperStack.mem -> bs: Prims.list Vale.Interop.Base.arg -> Type0\nlet all_live (h:HS.mem) (bs:list arg) =\n BigOps.big_and' (live_arg h) bs", "val recv (#p:prot) (#next:prot{more next}) (c:chan p)\n : SteelT (msg_t next) (receiver c next) (fun x -> receiver c (step next x))\nlet rec recv (#p:prot) (#next:prot{more next}) (c:chan p)\n : SteelT (msg_t next) (receiver c next) (fun x -> receiver c (step next x))\n = let v = send_receive_prelude c in\n if (fst v).chan_ctr = (snd v).chan_ctr\n then (\n rewrite_slprop (chan_inv_cond (fst v) (snd v))\n (pure (fst v == snd v))\n (fun _ -> ());\n elim_pure (fst v == snd v);\n intro_chan_inv_eqT c.chan_chan (fst v) (snd v);\n Steel.SpinLock.release c.chan_lock;\n recv c\n )\n else (\n rewrite_slprop (chan_inv_cond (fst v) (snd v))\n (chan_inv_step (snd v) (fst v))\n (fun _ -> ());\n recv_availableT c (fst v) (snd v) ()\n )", "val Lib.MultiBuffer.live8 = \n h: FStar.Monotonic.HyperStack.mem ->\n b0: Lib.Buffer.lbuffer a len ->\n b1: Lib.Buffer.lbuffer a len ->\n b2: Lib.Buffer.lbuffer a len ->\n b3: Lib.Buffer.lbuffer a len ->\n b4: Lib.Buffer.lbuffer a len ->\n b5: Lib.Buffer.lbuffer a len ->\n b6: Lib.Buffer.lbuffer a len ->\n b7: Lib.Buffer.lbuffer a len\n -> Prims.logical\nlet live8 #a #len (h:mem) (b0 b1 b2 b3 b4 b5 b6 b7: lbuffer a len) =\n live h b0 /\\ live h b1 /\\ live h b2 /\\ live h b3 /\\ live h b4 /\\ live h b5 /\\ live h b6 /\\ live h b7", "val Vale.X64.Decls.va_is_dst_heaplet = h: Vale.X64.Decls.heaplet_id -> s: Vale.X64.Decls.va_state -> Prims.logical\nlet va_is_dst_heaplet (h:heaplet_id) (s:va_state) = True", "val AllocSTwHeaps.contains = r: FStar.ST.ref a -> h: FStar.Monotonic.Heap.heap -> Prims.logical\nlet contains (#a:Type) (r:ref a) (h:FStar.Heap.heap) =\n b2t (FStar.StrongExcludedMiddle.strong_excluded_middle (FStar.Heap.contains h r))", "val LowStar.ConstBuffer.length = c: LowStar.ConstBuffer.const_buffer 'a -> Prims.GTot Prims.nat\nlet length (c:const_buffer 'a) = B.length (as_mbuf c)", "val Vale.Interop.Heap_s.correct_down = mem: Vale.Interop.Heap_s.interop_heap -> h: Vale.Arch.MachineHeap_s.machine_heap -> Prims.logical\nlet correct_down (mem:interop_heap) (h:machine_heap) =\n Set.equal (addrs_set mem) (Map.domain h) /\\\n (forall p.{:pattern (L.memP p (ptrs_of_mem mem))}\n L.memP p (ptrs_of_mem mem) ==> correct_down_p mem h p)", "val MiTLS.Crypto.Plain.live' = h: FStar.Monotonic.HyperStack.mem -> p: MiTLS.Crypto.Plain.plainBuffer i l -> Type0\nlet live' #i #l = live #i #l", "val Hacl.Streaming.Functor.footprint = \n c: Hacl.Streaming.Interface.block index ->\n i: index ->\n m: FStar.Monotonic.HyperStack.mem ->\n s: Hacl.Streaming.Functor.state' c i\n -> Prims.GTot LowStar.Monotonic.Buffer.loc\nlet footprint (#index: Type0) (c: block index) (i: index) (m: HS.mem) (s: state' c i) =\n B.(loc_union (loc_addr_of_buffer s) (footprint_s c i m (B.deref m s)))", "val recv:\n t ->\n input_buffer: FStar.Buffer.buffer UInt8.t -> \n max_len: size_t -> ST Int32.t\n (requires fun h0 ->\n Buffer.live h0 input_buffer /\\\n UInt32.v max_len = Buffer.length input_buffer)\n (ensures fun h0 r h1 -> \n let v = Int32.v r in \n Buffer.modifies_1 input_buffer h0 h1 /\\ \n (v = -1 \\/ (0 <= v /\\ v <= UInt32.v max_len)))\nlet recv t buffer len = t.rcv t.ptr buffer len", "val Vale.Def.Types_s.le_bytes_to_nat64 = b: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> Prims.Pure Vale.Def.Types_s.nat64\nlet le_bytes_to_nat64 = opaque_make le_bytes_to_nat64_def", "val Vale.Interop.Base.mem_roots_p = h0: FStar.Monotonic.HyperStack.mem -> args: Prims.list Vale.Interop.Base.arg -> Prims.logical\nlet mem_roots_p (h0:HS.mem) (args:list arg) =\n disjoint_or_eq args /\\\n all_live h0 args", "val Steel.Semantics.Hoare.MST.fp_heap_0 = interp: (_: hprop -> _: heap -> Prims.prop) -> pre: hprop -> Type\nlet fp_heap_0\n (#heap:Type)\n (#hprop:Type)\n (interp:hprop -> heap -> prop)\n (pre:hprop)\n =\n h:heap{interp pre h}", "val LowStar.PrefixFreezableBuffer.malloc_pre = r: FStar.Monotonic.HyperHeap.rid -> len: LowStar.PrefixFreezableBuffer.u32 -> Prims.logical\nlet malloc_pre (r:HS.rid) (len:u32) =\n UInt.size (U32.v len + 4) 32 /\\ malloc_pre r len", "val Vale.Interop.Heap_s.list_live = mem: FStar.Monotonic.HyperStack.mem -> ptrs: Prims.list Vale.Interop.Types.b8 -> Prims.logical\nlet list_live mem (ptrs:list b8) =\n forall (p:b8).{:pattern (L.memP p ptrs)} L.memP p ptrs ==> B.live mem p.bsrc", "val NotEverCrypt.CTR.freeable = h: FStar.Monotonic.HyperStack.mem -> p: NotEverCrypt.CTR.state a -> Prims.logical\nlet freeable (#a: alg) (h: HS.mem) (p: state a) =\n B.freeable p /\\ freeable_s (B.deref h p)", "val LowParse.Repr.valid_repr_pos = r: LowParse.Repr.repr_pos t b -> h: FStar.Monotonic.HyperStack.mem -> Prims.logical\nlet valid_repr_pos (#t:Type) (#b:const_slice) (r:repr_pos t b) (h:HS.mem)\n = valid (as_ptr_spec r) h /\\\n C.live h b.base", "val abyte : (FStar.UInt8.t -> Tot bytes)\nlet abyte b = Seq.create 1 b", "val WithLocal.frameable = \n l: FStar.Ghost.erased LowStar.Monotonic.Buffer.loc ->\n p: (_: FStar.Monotonic.HyperStack.mem -> Type0)\n -> Prims.logical\nlet frameable (l:Ghost.erased B.loc) (p:HS.mem -> Type) =\n forall h0 h1 l'.\n p h0 /\\\n B.loc_disjoint l l' /\\\n B.modifies l' h0 h1\n ==> p h1", "val f_a_r\n (#p: dprot)\n (q: dprot{is_recv q /\\ more q})\n (tr: trace p q)\n (v: t p {compatible (pcm p) (A_R q tr) v})\n : GTot (y: t p {compatible (pcm p) y v /\\ frame_compatible (A_R q tr) v y})\nlet f_a_r (#p:dprot) (q:dprot{is_recv q /\\ more q}) (tr:trace p q)\n (v:t p{compatible (pcm p) (A_R q tr) v})\n : GTot (y:t p{compatible (pcm p) y v /\\ frame_compatible (A_R q tr) v y})\n = match v with\n | A_R q tr -> A_R q tr\n | V tr' ->\n lemma_compatible_a_greater_length q tr tr';\n if trace_length tr >= trace_length tr'.tr then\n // No new message yet\n A_R q tr\n else\n let y = extend_node_a_r tr tr' in\n frame_compatible_a_extend q tr tr';\n y", "val create\n (#a:typ)\n (init: P.type_of_typ a)\n (len:UInt32.t)\n: HST.StackInline (buffer a)\n (requires (fun h ->\n UInt32.v len > 0\n ))\n (ensures (fun (h0: HS.mem) b h1 ->\n UInt32.v len > 0 /\\\n b `unused_in` h0 /\\\n live h1 b /\\\n length b == UInt32.v len /\\\n frameOf b == (HS.get_tip h0) /\\\n P.modifies_0 h0 h1 /\\\n as_seq h1 b == Seq.create (UInt32.v len) init\n ))\nlet create #a init len =\n let len : P.array_length_t = len in\n let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in\n P.buffer_of_array_pointer content", "val Vale.PPC64LE.Memory.buffer_info_has_id = \n bs: FStar.Seq.Base.seq Vale.Arch.HeapImpl.buffer_info ->\n i: Prims.nat ->\n id: Vale.PPC64LE.Memory.heaplet_id\n -> Prims.logical\nlet buffer_info_has_id (bs:Seq.seq buffer_info) (i:nat) (id:heaplet_id) =\n i < Seq.length bs /\\ (Seq.index bs i).bi_heaplet == id", "val Vale.PPC64LE.Memory.inv_buffer_info = \n bi: Vale.Arch.HeapImpl.buffer_info ->\n owners: (_: Vale.Arch.HeapImpl.heaplet_id -> FStar.Set.set Prims.int) ->\n h: Vale.Arch.HeapImpl.vale_heap ->\n hs: Vale.Arch.HeapImpl.vale_heaplets ->\n mt: Vale.Arch.HeapTypes_s.memTaint_t ->\n modloc: Vale.PPC64LE.Memory.loc\n -> Prims.logical\nlet inv_buffer_info (bi:buffer_info) (owners:heaplet_id -> Set.set int) (h:vale_heap) (hs:vale_heaplets) (mt:memTaint_t) (modloc:loc) =\n let t = bi.bi_typ in\n let hid = bi.bi_heaplet in\n let hi = Map16.get hs hid in\n let b = bi.bi_buffer in\n let owns = owners hid in\n (bi.bi_mutable == Mutable ==> loc_includes modloc (loc_buffer b)) /\\\n buffer_readable h b /\\\n buffer_as_seq hi b == buffer_as_seq h b /\\\n (valid_taint_buf b hi mt bi.bi_taint <==> valid_taint_buf b h mt bi.bi_taint) /\\\n (forall (i:int).{:pattern Set.mem i owns}\n buffer_addr b h <= i /\\ i < buffer_addr b h + DV.length (get_downview b.bsrc) ==> Set.mem i owns) /\\\n True", "val Lib.MultiBuffer.live_multi = h: FStar.Monotonic.HyperStack.mem -> b: Lib.MultiBuffer.multibuf lanes len -> Prims.logical\nlet live_multi #lanes #len (h:mem) (b:multibuf lanes len) =\n forall i. i < lanes ==> live h b.(|i|)", "val Model.Helpers.lbytes = l: Prims.nat -> Type0\nlet lbytes (l:nat) = b:Seq.seq Lib.IntTypes.uint8 { Seq.length b = l }", "val LowStar.ImmutableBuffer.libuffer_or_null = a: Type0 -> len: Prims.nat -> r: FStar.Monotonic.HyperHeap.rid -> s: FStar.Seq.Base.seq a -> Type0\nlet libuffer_or_null (a:Type0) (len:nat) (r:HS.rid) (s:Seq.seq a) =\n b:lmbuffer_or_null a (immutable_preorder a) (immutable_preorder a) len r{(not (g_is_null b)) ==>\n witnessed b (cpred s)}", "val LowStar.Buffer.gcmalloc = r: FStar.Monotonic.HyperHeap.rid -> init: a -> len: FStar.UInt32.t\n -> FStar.HyperStack.ST.ST\n (b:\n (b:\n LowStar.Monotonic.Buffer.mbuffer a\n (LowStar.Buffer.trivial_preorder a)\n (LowStar.Buffer.trivial_preorder a)\n { LowStar.Monotonic.Buffer.length b == FStar.UInt32.v len /\\\n Prims.op_Negation (LowStar.Monotonic.Buffer.g_is_null b) })\n {LowStar.Monotonic.Buffer.frameOf b == r /\\ LowStar.Monotonic.Buffer.recallable b})\nlet gcmalloc (#a:Type0) = mgcmalloc #a #(trivial_preorder a)", "val Vale.X64.Decls.modifies_buffer128 = b: Vale.X64.Memory.buffer128 -> h1: Vale.X64.Decls.vale_heap -> h2: Vale.X64.Decls.vale_heap\n -> Vale.Def.Prop_s.prop0\nlet modifies_buffer128 (b:M.buffer128) (h1 h2:vale_heap) = modifies_mem (loc_buffer b) h1 h2", "val L0.Test.Definitions.aliasKeyCrt_i_common_buf = b:\nLowStar.ImmutableBuffer.libuffer ASN1.Base.byte\n (FStar.Pervasives.normalize_term (FStar.List.Tot.Base.length L0.Test.Definitions.aliasKeyCrt_i_common_list\n ))\n (FStar.Seq.Base.seq_of_list L0.Test.Definitions.aliasKeyCrt_i_common_list)\n { LowStar.Monotonic.Buffer.frameOf b == FStar.Monotonic.HyperHeap.root /\\\n LowStar.Monotonic.Buffer.recallable b }\nlet aliasKeyCrt_i_common_buf = IB.igcmalloc_of_list HS.root aliasKeyCrt_i_common_list", "val AllocST.heap_rel = h0: NatHeap.heap -> h1: NatHeap.heap -> Prims.logical\nlet heap_rel (h0:heap) (h1:heap) = \n forall a (r:ref a) . contains r h0 ==> contains r h1" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.init_heaplets_req" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.init_heaplets_req" }, { "project_name": "steel", "file_name": "Duplex.PCM.fsti", "name": "Duplex.PCM.recv" }, { "project_name": "everquic-crypto", "file_name": "QUIC.fsti", "name": "QUIC.receivable" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.TLS.fst", "name": "MiTLS.TLS.next_fragment_pre" }, { "project_name": "steel", "file_name": "Steel.Channel.Protocol.fst", "name": "Steel.Channel.Protocol.recv" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.FFI.fst", "name": "MiTLS.FFI.ffiRecv" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.stack_allocated" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.FFI.fst", "name": "MiTLS.FFI.ffiSend" }, { "project_name": "FStar", "file_name": "ImmutableSTwHeaps.fst", "name": "ImmutableSTwHeaps.heap_rel" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.fst", "name": "Vale.Interop.write_buffer_vale" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.length" }, { "project_name": "dice-star", "file_name": "HWAbstraction.fst", "name": "HWAbstraction.uds" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Functor.fst", "name": "Hacl.Streaming.Functor.seen_h" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.StAE.fst", "name": "MiTLS.StAE.trigger_frame" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.inv_heaplet_ids" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.TLS.fst", "name": "MiTLS.TLS.sendFragment_inv" }, { "project_name": "steel", "file_name": "SteelTLArray.fst", "name": "SteelTLArray.l" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Equiv.fsti", "name": "Vale.Poly1305.Equiv.nat_from_bytes_le" }, { "project_name": "everparse", "file_name": "LowParse.Repr.fsti", "name": "LowParse.Repr.slice_as_seq" }, { "project_name": "everparse", "file_name": "LowParse.Repr.fsti", "name": "LowParse.Repr.mut_p" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.inv_heaplet_ids" }, { "project_name": "FStar", "file_name": "OPLSS.CPA.fst", "name": "OPLSS.CPA.authentic" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.malloc_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Equiv.fsti", "name": "Vale.Poly1305.Equiv.nat_to_bytes_le" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Base.fst", "name": "Vale.Interop.Base.live_arg" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.vale_full_heap_equal" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.ProtocolVersion.fst", "name": "MiTLS.Parsers.ProtocolVersion.protocolVersion_bytesize" }, { "project_name": "hacl-star", "file_name": "Hacl.Bignum4096.fsti", "name": "Hacl.Bignum4096.n_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.LowStarSig.fst", "name": "Vale.AsLowStar.LowStarSig.mem_imm_correspondence_1" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.alloc_post_mem_common" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.buffer_length" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.FFI.fst", "name": "MiTLS.FFI.ffiAcceptConnected" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Util.fsti", "name": "Vale.Poly1305.Util.buffers_readable" }, { "project_name": "everquic-crypto", "file_name": "QUIC.fst", "name": "QUIC.frame_invariant" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.ProtocolName.fst", "name": "MiTLS.Parsers.ProtocolName.protocolName_length" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.StAE.fst", "name": "MiTLS.StAE.frame_f" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.buffer_length" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.heap_rel" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Record.fsti", "name": "MiTLS.Record.sendPacket" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Connection.fst", "name": "MiTLS.Connection.epoch_i" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.deref" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.HandshakeMessages.fst", "name": "MiTLS.HandshakeMessages.parseFinished" }, { "project_name": "FStar", "file_name": "LowStar.UninitializedBuffer.fst", "name": "LowStar.UninitializedBuffer.lubuffer_or_null" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.ProtocolName.fst", "name": "MiTLS.Parsers.ProtocolName.protocolName_bytesize" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Functor.fst", "name": "Hacl.Streaming.Functor.all_seen_h" }, { "project_name": "hacl-star", "file_name": "Hacl.Bignum256.fsti", "name": "Hacl.Bignum256.n_bytes" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.global_allocated" }, { "project_name": "FStar", "file_name": "EtM.CPA.fst", "name": "EtM.CPA.invariant" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.LowStarSig.fst", "name": "Vale.AsLowStar.LowStarSig.mem_correspondence_1" }, { "project_name": "FStar", "file_name": "ImmutableST.fst", "name": "ImmutableST.heap_rel" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.buffer64_read" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.buffer64_read" }, { "project_name": "everparse", "file_name": "EverParse3d.CopyBuffer.fsti", "name": "EverParse3d.CopyBuffer.inv" }, { "project_name": "steel", "file_name": "Steel.Channel.Protocol.fst", "name": "Steel.Channel.Protocol.until" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fsti", "name": "Vale.AES.PPC64LE.GHash.in_b_blocks" }, { "project_name": "everparse", "file_name": "LowParse.Repr.fsti", "name": "LowParse.Repr.valid'" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Old.Handshake.fsti", "name": "MiTLS.Old.Handshake.next_fragment_requires" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_is_src_heaplet" }, { "project_name": "steel", "file_name": "Steel.Channel.Protocol.fst", "name": "Steel.Channel.Protocol.send" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsMem.fsti", "name": "Vale.PPC64LE.InsMem.heaplet_id_is_some" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.HandshakeMessages.fsti", "name": "MiTLS.HandshakeMessages.hs_msg_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Types.fst", "name": "Vale.Interop.Types.get_downview" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.inv_heaplets" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.buffers_readable" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.buffers_readable" }, { "project_name": "dice-star", "file_name": "HWAbstraction.fsti", "name": "HWAbstraction.all_heap_buffers_except_ghost_state_remain_same" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.inv_heaplets" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.stable_on_heap" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.heap_rel" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Base.fst", "name": "Vale.Interop.Base.all_live" }, { "project_name": "steel", "file_name": "Steel.Channel.Simplex.fst", "name": "Steel.Channel.Simplex.recv" }, { "project_name": "hacl-star", "file_name": "Lib.MultiBuffer.fst", "name": "Lib.MultiBuffer.live8" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_is_dst_heaplet" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.contains" }, { "project_name": "FStar", "file_name": "LowStar.ConstBuffer.fsti", "name": "LowStar.ConstBuffer.length" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Heap_s.fst", "name": "Vale.Interop.Heap_s.correct_down" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Crypto.Plain.fsti", "name": "MiTLS.Crypto.Plain.live'" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Functor.fsti", "name": "Hacl.Streaming.Functor.footprint" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Transport.fst", "name": "MiTLS.Transport.recv" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Types_s.fst", "name": "Vale.Def.Types_s.le_bytes_to_nat64" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Base.fst", "name": "Vale.Interop.Base.mem_roots_p" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.fp_heap_0" }, { "project_name": "FStar", "file_name": "LowStar.PrefixFreezableBuffer.fsti", "name": "LowStar.PrefixFreezableBuffer.malloc_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Heap_s.fst", "name": "Vale.Interop.Heap_s.list_live" }, { "project_name": "everquic-crypto", "file_name": "NotEverCrypt.CTR.fsti", "name": "NotEverCrypt.CTR.freeable" }, { "project_name": "everparse", "file_name": "LowParse.Repr.fsti", "name": "LowParse.Repr.valid_repr_pos" }, { "project_name": "FStar", "file_name": "Platform.Bytes.fst", "name": "Platform.Bytes.abyte" }, { "project_name": "FStar", "file_name": "WithLocal.fst", "name": "WithLocal.frameable" }, { "project_name": "steel", "file_name": "Duplex.PCM.fst", "name": "Duplex.PCM.f_a_r" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.create" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.buffer_info_has_id" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.inv_buffer_info" }, { "project_name": "hacl-star", "file_name": "Lib.MultiBuffer.fst", "name": "Lib.MultiBuffer.live_multi" }, { "project_name": "everquic-crypto", "file_name": "Model.Helpers.fsti", "name": "Model.Helpers.lbytes" }, { "project_name": "FStar", "file_name": "LowStar.ImmutableBuffer.fst", "name": "LowStar.ImmutableBuffer.libuffer_or_null" }, { "project_name": "FStar", "file_name": "LowStar.Buffer.fst", "name": "LowStar.Buffer.gcmalloc" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.modifies_buffer128" }, { "project_name": "dice-star", "file_name": "L0.Test.Definitions.fst", "name": "L0.Test.Definitions.aliasKeyCrt_i_common_buf" }, { "project_name": "FStar", "file_name": "AllocST.fst", "name": "AllocST.heap_rel" } ], "selected_premises": [ "Protocol.ctr", "Protocol.log", "FStar.Heap.trivial_preorder", "Protocol.ciphers", "Protocol.live_connection", "Protocol.send_aux", "FStar.ST.op_Bang", "MonotonicArray.as_initialized_subseq", "Protocol.send_file", "Protocol.zeroes", "Protocol.append_subseq", "Protocol.receive", "Protocol.sent", "Protocol.connection_footprint", "FStar.ST.alloc", "MonotonicArray.as_initialized_seq", "Protocol.sender", "Protocol.subseq_suffix", "Protocol.send", "Protocol.sent_bytes'", "Protocol.rand_of", "Protocol.snapshot", "MonotonicArray.disjoint_siblings_remain_same", "Protocol.receiver", "Protocol.sent_bytes", "Protocol.pad", "Protocol.lemma_snoc_log", "Protocol.lemma_seq_append_unstable", "ArrayUtils.all_some", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "Protocol.fully_initialized_in", "Protocol.modifies_r", "Protocol.entries_pre", "MonotonicArray.all_init", "FStar.Pervasives.reveal_opaque", "ArrayUtils.init_at_seq", "Protocol.counter_pred", "Protocol.entries_of", "Protocol.counter_rel", "Protocol.snap", "Protocol.counter_pre", "Protocol.entries_rel", "Protocol.iarray_as_seq", "MonotonicArray.fresh_arr", "FStar.Monotonic.Heap.mref", "Protocol.recall_counter", "FStar.Heap.trivial_rel", "FStar.Pervasives.dfst", "FStar.ST.contains_pred", "FStar.ST.get", "FStar.Preorder.preorder_rel", "FStar.ST.lemma_functoriality", "Protocol.recall_connection_liveness", "FStar.ST.read", "FStar.Pervasives.dsnd", "FStar.ST.heap_rel", "FStar.Monotonic.Heap.modifies", "FStar.Monotonic.Heap.modifies_t", "ArrayUtils.some_equivalent_seqs", "Protocol.slice_snoc", "FStar.Monotonic.Heap.fresh", "Protocol.is_prefix_of", "ArrayUtils.is_prefix_of", "Protocol.lemma_sel_entries_equals_sel_tot_entries", "Protocol.lemma_sel_ctr_ref_equals_sel_tot_ctr_ref", "FStar.Monotonic.Heap.equal_dom", "FStar.ST.witnessed", "FStar.Pervasives.st_post_h", "MonotonicArray.prefix", "FStar.Monotonic.Heap.only", "FStar.ST.op_Colon_Equals", "Protocol.lemma_prefix_entries_implies_prefix_log", "Protocol.slice_snoc2", "MonotonicArray.init_arr_in_heap", "FStar.ST.recall", "FStar.Monotonic.Heap.only_t", "FStar.Preorder.stable", "FStar.ST.write", "FStar.ST.stable", "FStar.ST.modifies_none", "FStar.Monotonic.Heap.compare_addrs", "FStar.Preorder.reflexive", "FStar.Pervasives.id", "FStar.Pervasives.st_pre_h", "FStar.Pervasives.ex_pre", "FStar.Ghost.return", "MonotonicArray.init_arr_in_heap_i_j", "FStar.Preorder.transitive", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.all_return", "MonotonicArray.all_init_i_j", "FStar.ST.gst_pre", "FStar.Pervasives.st_return", "FStar.Pervasives.ex_post'", "FStar.Pervasives.st_stronger", "FStar.Monotonic.Heap.op_Hat_Plus_Plus", "FStar.Pervasives.st_trivial", "FStar.ST.lift_div_gst", "FStar.ST.gst_post" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule Protocol\n\nopen FStar.Seq\n\nopen FStar.Preorder\nopen FStar.Heap\nopen FStar.ST\n\nopen MonotonicArray\n\n(***** an unstable sequence proof *****)\n\nlet lemma_seq_append_unstable (#a:Type0) (s:seq a) (s1:seq a) (s2:seq a) (s3:seq a) (pos:nat) (sent:nat{pos + sent <= length s})\n :Lemma (requires (s1 == slice s 0 pos /\\ s2 == slice s pos (pos + sent) /\\ s3 == slice s 0 (pos + sent)))\n (ensures (s3 == append s1 s2))\n = assert (Seq.equal s3 (append s1 s2))\n\n(***** basic messages interface *****)\n\n(* size of each message fragment sent over the network *)\nassume val fragment_size:nat\n\ntype byte\nassume val zero_b:byte\n\ntype message = s:seq byte{length s <= fragment_size}\ntype network_message = s:seq byte{length s = fragment_size}\n\n(* random bytes for ideal cipher *)\ntype randomness = nat -> network_message\n\n(* the xor operation on fragments *)\nassume val xor: network_message -> network_message -> network_message\n\n(* basic lemma about xor *)\nassume val lemma_xor (a:network_message) (b:network_message)\n :Lemma (xor (xor a b) b == a)\n [SMTPat (xor (xor a b) b)]\n\nval zeroes: n:nat -> (s:seq byte{length s = n})\nlet zeroes n = Seq.create n (zero_b)\n\nlet pad (m:message) :network_message = append m (zeroes (fragment_size - (length m)))\n\n(* an unpad function that strips off the trailing pad *)\nassume val unpad (s:network_message)\n :(r:(nat * message){length (snd r) = fst r /\\ s == pad (snd r)})\n\nassume val lemma_pad_unpad (x:unit) :Lemma (ensures (forall (m:message). snd (unpad (pad m)) == m))\n\n(* a MAC function, returning a tag *)\nassume val mac: cipher:network_message -> i:nat -> seq byte\n\n(* an entry in the message log *)\nnoeq type entry (rand:randomness) =\n | E: i:nat -> msg:message -> cipher:network_message{xor (pad msg) (rand i) == cipher} -> tag:seq byte{tag == mac cipher i}\n -> entry rand\n\n(* sequence of messages *)\ntype entries (rand:randomness) = s:seq (entry rand){forall (i:nat). i < length s ==> E?.i (Seq.index s i) = i}\n\nlet is_prefix_of (#a:Type) (s1:seq a) (s2:seq a) :Type0\n = length s1 <= length s2 /\\\n (forall (i:nat). i < length s1 ==> Seq.index s1 i == Seq.index s2 i)\n\n(* entries are only appended to *)\nlet entries_rel (rand:randomness) :relation (entries rand) =\n fun (es1:entries rand) (es2:entries rand) -> es1 `is_prefix_of` es2\n\nlet entries_pre (rand:randomness) :preorder (entries rand) = entries_rel rand\n\n(* a single state stable predicate on the counter, saying that it is less than the length of the log *)\nlet counter_pred (#rand:randomness) (n:nat) (es_ref:mref (entries rand) (entries_rel rand)) :(p:heap_predicate{stable p})\n = fun h -> h `contains` es_ref /\\ n <= length (sel h es_ref)\n\n(* counter type is a nat, witnessed with counter_pred *)\ntype counter_t (#rand:randomness) (es_ref:mref (entries rand) (entries_rel rand))\n = n:nat{witnessed (counter_pred n es_ref)}\n\n(* counter increases monotonically *)\nlet counter_rel (#rand:randomness) (es_ref:mref (entries rand) (entries_rel rand)) :relation (counter_t es_ref)\n = fun n1 n2 -> b2t (n1 <= n2)\n\nlet counter_pre (#rand:randomness) (es_ref:mref (entries rand) (entries_rel rand)) :preorder (counter_t es_ref)\n = counter_rel es_ref\n\nnoeq type connection =\n | S: rand:randomness -> entries:mref (entries rand) (entries_rel rand) -> connection\n | R: rand:randomness -> entries:mref (entries rand) (entries_rel rand)\n -> ctr:mref (counter_t entries) (counter_pre entries) -> connection\n\nlet rand_of (c:connection) :randomness =\n match c with\n | S r _\n | R r _ _ -> r\n\nlet entries_of (c:connection) :(mref (entries (rand_of c)) (entries_rel (rand_of c))) =\n match c with\n | S _ es -> es\n | R _ es _ -> es\n\nlet live_connection (h:heap) (c:connection) =\n match c with\n | S _ es_ref -> h `contains` es_ref\n | R _ es_ref ctr_ref -> h `contains` es_ref /\\ h `contains` ctr_ref\n\nlet recall_connection_liveness (c:connection)\n :ST unit (requires (fun h0 -> True)) (ensures (fun h0 _ h1 -> h0 == h1 /\\ h0 `live_connection` c))\n = match c with\n | S _ es_ref -> ST.recall es_ref\n | R _ es_ref ctr_ref -> ST.recall es_ref; ST.recall ctr_ref\n\nlet lemma_sel_entries_equals_sel_tot_entries (c:connection) (h:heap)\n :Lemma (requires (h `live_connection` c))\n (ensures (sel_tot h (entries_of c) == sel h (entries_of c)))\n\t [SMTPat (sel_tot h (entries_of c))]\n = Heap.lemma_sel_equals_sel_tot_for_contained_refs h (entries_of c)\n\nlet lemma_sel_ctr_ref_equals_sel_tot_ctr_ref (c:connection{R? c}) (h:heap)\n :Lemma (requires (h `live_connection` c))\n (ensures (let R _ _ ctr_ref = c in sel_tot h ctr_ref == sel h ctr_ref))\n\t [SMTPat (sel_tot h (R?.ctr c))]\n = Heap.lemma_sel_equals_sel_tot_for_contained_refs h (R?.ctr c)\n\n(* seq of plain messages sent so far on this connection *)\nlet log (c:connection) (h:heap{h `live_connection` c}) :Tot (seq message) =\n ArrayUtils.seq_map (fun (E _ m _ _) -> m) (sel_tot h (entries_of c))\n\nlet lemma_prefix_entries_implies_prefix_log\n (c:connection) (h1:heap) (h2:heap{h1 `live_connection` c /\\ h2 `live_connection` c})\n :Lemma (requires (sel h1 (entries_of c) `is_prefix_of` sel h2 (entries_of c)))\n\t (ensures (log c h1 `is_prefix_of` log c h2))\n\t [SMTPat (log c h1); SMTPat (log c h2)]\n = ArrayUtils.lemma_map_commutes_with_prefix (fun (E _ m _ _) -> m) (sel h1 (entries_of c)) (sel h2 (entries_of c))\n\n(* current counter for the connection *)\nlet ctr (c:connection) (h:heap{h `live_connection` c}) :Tot nat =\n if S? c then length (sel_tot h (entries_of c))\n else sel_tot h (R?.ctr c)\n\n(* recall_counter, as mentioned in the paper *)\nlet recall_counter (c:connection)\n :ST unit (requires (fun _ -> True)) (ensures (fun h0 _ h1 -> h0 == h1 /\\ h0 `live_connection` c /\\ ctr c h0 <= Seq.length (log c h0)))\n = recall_connection_liveness c;\n match c with\n | S _ _ -> ()\n | R _ es_ref ctr_ref -> let n = !ctr_ref in gst_recall (counter_pred n es_ref)\n\n(* stable predicate for counter *)\nlet snapshot (c:connection) (h0:heap{h0 `live_connection` c}) :(p:heap_predicate{stable p}) =\n fun h -> h `live_connection` c /\\\n ctr c h0 <= ctr c h /\\ ctr c h0 <= Seq.length (log c h) /\\ log c h0 `is_prefix_of` log c h\n\nlet snap (c:connection) :ST unit (requires (fun _ -> True))\n (ensures (fun h0 _ h1 -> h0 `live_connection` c /\\ witnessed (snapshot c h0) /\\ h0 == h1))\n = let h0 = ST.get () in\n recall_connection_liveness c;\n recall_counter c;\n gst_witness (snapshot c h0)\n\ntype iarray (a:Type0) (n:nat) = x:array a n{all_init x}\n\nlet sender (c:connection) :Tot bool = S? c //in the POPL'18 paper we present these definitions using auxiliary function\nlet receiver (c:connection) :Tot bool = R? c //`is_receiver` that is essentially defined as `is_receiver c = R? c`\n\nlet connection_footprint (c:connection) :GTot (Set.set nat)\n = match c with\n | S _ es_ref -> Set.singleton (addr_of es_ref)\n | R _ es_ref ctr_ref -> Set.union (Set.singleton (addr_of es_ref)) (Set.singleton (addr_of ctr_ref))\n\nlet lemma_snoc_log\n (c:connection{sender c}) (i:nat) (cipher:network_message) (msg:message{xor (pad msg) ((rand_of c) i) == cipher})\n (tag:seq byte{tag == mac cipher i})\n (h0:heap) (h1:heap{h0 `live_connection` c /\\ h1 `live_connection` c})\n :Lemma (requires (sel h1 (entries_of c) == snoc (sel h0 (entries_of c)) (E i msg cipher tag)))\n\t (ensures (log c h1 == snoc (log c h0) msg))\n = ArrayUtils.lemma_map_commutes_with_snoc (fun (E _ m _ _) -> m) (sel h0 (entries_of c)) (E i msg cipher tag)\n\n(* network send, actually sends bytes on the network, once the log has been prepared *)\nassume val network_send\n (c:connection{sender c}) (f:network_message) (tag:seq byte)\n :ST unit (requires (fun h0 -> h0 `live_connection` c /\\\n (let S _ es_ref = c in\n let es = sel h0 es_ref in\n\t\t\t Seq.length es > 0 /\\\n (let E _ _ c t = Seq.index es (Seq.length es - 1) in\n\t\t\t c == f /\\ t == tag))))\n (ensures (fun h0 _ h1 -> h0 == h1))\n\n(* protocol send operation *)\n#set-options \"--z3rlimit 50\"\nlet send (#n:nat) (buf:iarray byte n) (c:connection{sender c})\n :ST nat (requires (fun h0 -> True))\n (ensures (fun h0 sent h1 -> modifies (connection_footprint c) h0 h1 /\\\n\t h0 `live_connection` c /\\\n\t\t\t\t h1 `live_connection` c /\\\n\t sent <= min n fragment_size /\\\n\t\t\t\t ctr c h1 = ctr c h0 + 1 /\\\n\t\t\t\t (forall (i:nat). i < n ==> Some? (Seq.index (as_seq buf h0) i)) /\\\n log c h1 == snoc (log c h0) (as_initialized_subseq buf h0 0 sent)))\n = let h0 = ST.get () in\n\n recall_connection_liveness c;\n recall_all_init buf;\n\n let S rand es_ref = c in\n\n let msgs0 = ST.read es_ref in\n let i0 = length msgs0 in\n\n let sent = min n fragment_size in\n let msg = read_subseq_i_j buf 0 sent in\n let frag = append msg (zeroes (fragment_size - sent)) in\n let cipher = xor frag (rand i0) in\n\n let msgs1 = snoc msgs0 (E i0 msg cipher (mac cipher i0)) in\n\n ST.write es_ref msgs1;\n\n network_send c cipher (mac cipher i0);\n let h1 = ST.get () in\n lemma_snoc_log c i0 cipher msg (mac cipher i0) h0 h1;\n\n sent\n\n(* seq of ciphers sent so far on this connection *)\nlet ciphers (c:connection) (h:heap) :GTot (seq network_message) =\n ArrayUtils.seq_map E?.cipher (sel h (entries_of c))\n\nassume val network_receive (c:connection)\n :ST (option (network_message * seq byte)) (requires (fun h0 -> h0 `live_connection` c))\n (ensures (fun h0 _ h1 -> h0 == h1))\n\nlet modifies_r (#n:nat) (c:connection{receiver c}) (arr:array byte n) (h0 h1:heap) :Type0\n = modifies (Set.union (connection_footprint c)\n (array_footprint arr)) h0 h1\n\nassume val verify (c:connection{receiver c}) (cipher:network_message) (tag:seq byte) (i:nat)\n :ST bool (requires (fun h0 -> h0 `live_connection` c))\n (ensures (fun h0 r h1 -> h0 == h1 /\\\n\t (r ==>\n\t (let R _ es_ref _ = c in\n\t\t let es = sel h0 es_ref in\n\t\t\ti < Seq.length es /\\\n\t\t\t(let E _ _ c t = Seq.index es i in\n\t\t\t c == cipher /\\ t == tag)))))\n\n#push-options \"--z3rlimit 50\"\nlet receive (#n:nat{fragment_size <= n}) (buf:array byte n) (c:connection{receiver c})\n :ST (option nat) (requires (fun h0 -> Set.disjoint (connection_footprint c) (array_footprint buf)))\n (ensures (fun h0 r_opt h1 -> match r_opt with\n\t\t\t\t\t | None -> h0 == h1\n\t\t\t\t\t | Some r ->\n\t\t\t\t\t h0 `live_connection` c /\\\n\t\t\t\t\t h1 `live_connection` c /\\\n\t\t\t\t\t modifies_r c buf h0 h1 /\\\n\t\t\t\t\t disjoint_siblings_remain_same buf h0 h1 /\\\n\t\t\t\t\t r <= fragment_size /\\\n\t\t\t\t\t all_init_i_j buf 0 r /\\\n\t\t\t\t\t ctr c h1 = ctr c h0 + 1 /\\\n\t\t\t\t\t ctr c h0 < length (log c h0) /\\\n log c h0 == log c h1 /\\\n\t\t\t\t\t (forall (i:nat). i < r ==> Some? (Seq.index (as_seq buf h1) i)) /\\\n\t\t\t\t\t Seq.index (log c h0) (ctr c h0) == as_initialized_subseq buf h1 0 r))\n = let h0 = ST.get () in\n let R rand es_ref ctr_ref = c in\n\n Set.lemma_disjoint_subset (connection_footprint c) (array_footprint buf) (Set.singleton (addr_of ctr_ref));\n\n recall_connection_liveness c;\n\n match network_receive c with\n | None -> None\n | Some (cipher, tag) ->\n let i0 = ST.read ctr_ref in\n\n if verify c cipher tag i0 then\n let msg = xor cipher (rand i0) in\n let len, m = unpad msg in\n\n\tlemma_pad_unpad ();\n assert (m == Seq.index (log c h0) (ctr c h0));\n gst_witness (counter_pred (i0 + 1) es_ref);\n recall_contains buf;\n ST.write ctr_ref (i0 + 1);\n let h1 = ST.get () in\n lemma_disjoint_sibling_remain_same_for_unrelated_mods buf (Set.singleton (addr_of (ctr_ref))) h0 h1;\n fill buf m;\n let h2 = ST.get () in\n lemma_disjoint_sibling_remain_same_transitive buf h0 h1 h2;\n Some len\n else\n None\n#pop-options\n\n(***** sender and receiver *****)\n\nlet lemma_is_prefix_of_slice\n (#a:Type0) (s1:seq a) (s2:seq a{s1 `is_prefix_of` s2}) (i:nat) (j:nat{j >= i /\\ j <= Seq.length s1})\n :Lemma (requires True)\n (ensures (Seq.slice s1 i j == Seq.slice s2 i j))\n\t [SMTPat (s1 `is_prefix_of` s2); SMTPat (Seq.slice s1 i j); SMTPat (Seq.slice s2 i j)]\n = ArrayUtils.lemma_is_prefix_of_slice s1 s2 i j\n\n(*****)\n\n(*\n// * assuming a flattening function that flattens a sequence of messages into sequence of bytes\n// * and a couple of associated lemmas\n// *)\nassume val flatten (s:seq message) :Tot (seq byte)\n\nassume val lemma_flatten_snoc (s:seq message) (m:message)\n :Lemma (requires True)\n (ensures (flatten (snoc s m) == append (flatten s) m))\n\nassume val flatten_empty (u:unit) : Lemma (flatten Seq.empty == Seq.empty)\n\n(*****)\n\nlet sent_bytes' (file:seq byte) (c:connection) (from:nat) (to:nat{from <= to}) :heap_predicate\n = fun h -> h `live_connection` c /\\\n (let log = log c h in\n to <= Seq.length log /\\\n\t file == flatten (Seq.slice log from to))\n\nlet sent_bytes (file:seq byte) (c:connection) (from:nat) (to:nat{from <= to}) :(p:heap_predicate{stable p})\n = sent_bytes' file c from to\n\nlet sent (file:seq byte) (c:connection) =\n exists (from:nat) (to:nat{from <= to}). witnessed (sent_bytes file c from to)\n\n#set-options \"--z3rlimit 20\"\nlet iarray_as_seq (#a:Type) (#n:nat) (x:iarray a n) : ST (seq a)\n (requires (fun h -> True))\n (ensures (fun h0 s h1 ->\n h0==h1 /\\\n (forall (k:nat). k < n ==> Some? (Seq.index (as_seq x h0) k)) /\\\n s == as_initialized_subseq x h0 0 n /\\\n\t s == as_initialized_seq x h0))\n = read_subseq_i_j x 0 n\n\nlet fully_initialized_in #a #n (x:array a n) (h:heap) =\n h `contains_array` x /\\\n (forall (k:nat). k < n ==> Some? (Seq.index (as_seq x h) k))\n\nlet subseq_suffix #a #n (f:iarray a n) (pos:nat) (until:nat{pos+until <= n})\n (h:heap{f `fully_initialized_in` h})\n : Lemma (as_initialized_subseq (suffix f pos) h 0 until ==\n as_initialized_subseq f h pos (pos + until))\n = assert (as_initialized_subseq (suffix f pos) h 0 until `Seq.equal`\n as_initialized_subseq f h pos (pos + until))\n\nlet slice_snoc #a (s:seq a) (x:a) (from:nat) (to:nat{from<=to /\\ to<=Seq.length s})\n : Lemma (slice s from to == slice (snoc s x) from to)\n = assert (slice s from to `Seq.equal` slice (snoc s x) from to)\n\nlet slice_snoc2 #a (s:seq a) (x:a) (from:nat{from <= Seq.length s})\n : Lemma (slice (snoc s x) from (Seq.length s + 1) == snoc (slice s from (Seq.length s)) x)\n = assert (slice (snoc s x) from (Seq.length s + 1) `Seq.equal` snoc (slice s from (Seq.length s)) x)\n\n#push-options \"--z3rlimit 100\"\nlet append_subseq #a #n (f:iarray a n) (pos:nat) (sent:nat{pos + sent <= n}) (h:heap{f `fully_initialized_in` h})\n : Lemma (let f0 = as_initialized_subseq f h 0 pos in\n let f1 = as_initialized_subseq f h 0 (pos + sent) in\n let sub_file = suffix f pos in\n let sent_frag = as_initialized_subseq sub_file h 0 sent in\n f1 == append f0 sent_frag)\n = let f0 = as_initialized_subseq f h 0 pos in\n let f1 = as_initialized_subseq f h 0 (pos + sent) in\n let sub_file = suffix f pos in\n let sent_frag = as_initialized_subseq sub_file h 0 sent in\n\n let bs = as_seq f h in\n let bss = as_seq sub_file h in\n let sbs = ArrayUtils.get_some_equivalent bs in\n\n assert (f0 == ArrayUtils.get_some_equivalent (Seq.slice bs 0 pos));\n assert (f1 == ArrayUtils.get_some_equivalent (Seq.slice bs 0 (pos + sent)));\n assert (sent_frag == ArrayUtils.get_some_equivalent (Seq.slice bss 0 sent));\n assert (bss == Seq.slice bs pos n);\n assert (Seq.equal (Seq.slice bss 0 sent) (Seq.slice bs pos (pos + sent)));\n assert (sent_frag == ArrayUtils.get_some_equivalent (Seq.slice bs pos (pos + sent)));\n\n assert (f0 == Seq.slice sbs 0 pos);\n assert (f1 == Seq.slice sbs 0 (pos + sent));\n assert (sent_frag == Seq.slice sbs pos (pos + sent));\n lemma_seq_append_unstable sbs f0 sent_frag f1 pos sent\n#pop-options\n\nlet lemma_sender_connection_ctr_equals_length_log\n (c:connection{sender c}) (h:heap{h `live_connection` c})\n :Lemma (ctr c h == Seq.length (log c h))\n = ()\n\n#push-options \"--z3rlimit 200 --max_fuel 0 --max_ifuel 0\"\nval send_aux\n (#n:nat)\n (file:iarray byte n)\n (c:connection{sender c /\\ Set.disjoint (connection_footprint c) (array_footprint file)})\n (from:nat)\n (pos:nat{pos <= n})\n : ST unit\n (requires (fun h0 ->\n file `fully_initialized_in` h0 /\\\n h0 `live_connection` c /\\\n from <= ctr c h0 /\\\n sent_bytes (as_initialized_subseq file h0 0 pos) c from (ctr c h0) h0))\n (ensures (fun h0 _ h1 ->\n modifies (connection_footprint c) h0 h1 /\\\n h1 `live_connection` c /\\\n from <= ctr c h1 /\\\n (forall (k:nat). k < n ==> Some? (Seq.index (as_seq file h0) k)) /\\\n sent_bytes (as_initialized_seq file h0) c from (ctr c h1) h1))\n#push-options \"--z3rlimit 500\"\nlet rec send_aux #n file c from pos\n = if pos = n then ()\n else\n let sub_file = suffix file pos in\n lemma_all_init_i_j_sub file pos (n - pos);\n\n let h0 = ST.get () in\n let file_bytes0 = iarray_as_seq file in\n let log0 = log c h0 in\n let sent = send sub_file c in\n let h1 = ST.get () in\n let log1 = log c h1 in\n let file_bytes1 = iarray_as_seq file in\n assert (file_bytes0 == file_bytes1);\n recall_contains file; //strange that this is needed\n assert (from <= ctr c h1);\n assert (file `fully_initialized_in` h1);\n assert (h1 `live_connection` c);\n let _ : unit =\n let sent_frag = as_initialized_subseq sub_file h0 0 sent in\n let sent_frag' = as_initialized_subseq file h0 pos (pos + sent) in\n assert (log1 == snoc log0 sent_frag);\n subseq_suffix file pos sent h0; //sent_frag == sent_frag'\n slice_snoc log0 sent_frag from (ctr c h0); //slice log0 from (ctr c h0) == slice log1 from (ctr c h0)\n slice_snoc2 log0 sent_frag from; //Seq.slice log1 from (ctr c h1) == snoc (Seq.slice log0 from (ctr c h0)) sent_frag\n assert (ctr c h0 + 1 = ctr c h1);\n\t lemma_sender_connection_ctr_equals_length_log c h0;\n\t lemma_sender_connection_ctr_equals_length_log c h1;\n\t assert (ctr c h0 = Seq.length log0);\n assert (ctr c h1 = Seq.length log1);\n let f0 = as_initialized_subseq file h1 0 pos in\n let f1 = as_initialized_subseq file h1 0 (pos + sent) in\n append_subseq file pos sent h1; //f1 == append f0 sent_frag\n assert (f1 == append f0 sent_frag);\n assert (f0 == flatten (Seq.slice log0 from (ctr c h0)));\n lemma_flatten_snoc (Seq.slice log0 from (ctr c h0)) sent_frag;\n assert (f1 == flatten (Seq.slice log1 from (ctr c h1)));\n assert (sent_bytes f1 c from (ctr c h1) h1)\n in\n send_aux file c from (pos + sent)\n#pop-options\nlet send_file (#n:nat) (file:iarray byte n) (c:connection{sender c /\\ Set.disjoint (connection_footprint c) (array_footprint file)})\n : ST unit\n (requires (fun h -> True))\n (ensures (fun h0 _ h1 ->\n modifies (connection_footprint c) h0 h1 /\\\n h1 `live_connection` c /\\\n (forall (k:nat). k < n ==> Some? (Seq.index (as_seq file h0) k)) /\\\n sent (as_initialized_seq file h0) c))\n = let h0 = ST.get () in\n recall_all_init file;\n recall_contains file;\n recall_connection_liveness c;\n let file_bytes0 = iarray_as_seq file in\n let from = ctr c h0 in\n assert (Seq.equal (as_initialized_subseq file h0 0 0) Seq.empty);\n flatten_empty();\n assert (Seq.equal (flatten (Seq.slice (log c h0) from from)) Seq.empty);\n send_aux file c from 0;\n let h1 = ST.get () in\n let file_bytes1 = iarray_as_seq file in\n assert (file_bytes0 == file_bytes1);\n gst_witness (sent_bytes file_bytes0 c from (ctr c h1));\n assert (sent file_bytes0 c)\n", "sketch": [ "Step 1: The `received` function is intended to check if a given file (represented as an initialized array of bytes) has been received by a connection. This involves verifying that the file matches the sequence of messages logged in the connection's log.\nStep 2: To implement this, we need to ensure that the connection is live in the given heap and that the file matches the flattened sequence of messages in the connection's log. We will use the `flatten` function to convert the log into a sequence of bytes and compare it with the file.", "Step 1: The `received` function is intended to check if a given file (represented as an initialized array of bytes) has been fully received on a given connection. This involves verifying that the sequence of bytes in the file matches the sequence of bytes received in the connection's log.\nStep 2: The implementation will involve:\n- Ensuring that the connection is live in the given heap.\n- Checking that the file is fully initialized in the heap.\n- Comparing the sequence of bytes in the file with the sequence of bytes in the connection's log.", "Step 1: The `received` function is intended to verify if a given file (represented as an initialized array of bytes) has been fully received by a connection. This involves checking that the connection's log contains the same sequence of bytes as the file.\nStep 2: To implement this, we need to:\n- Ensure the connection is live in the given heap.\n- Convert the file array to a sequence of bytes.\n- Compare this sequence with the flattened log of the connection to verify they are equal.", "Step 1: The `received` function is meant to check if a given file (represented as an initialized array of bytes) has been fully received over a connection. This involves verifying that the file matches the sequence of messages logged in the connection's log.\nStep 2: To implement this, we need to:\n- Ensure the connection is live in the given heap.\n- Verify that the file is fully initialized in the heap.\n- Check that the sequence of bytes in the file matches the flattened sequence of messages in the connection's log.", "Step 1: The `received` function is intended to check if a given file (represented as an initialized array of bytes) has been fully received over a connection. This involves verifying that the bytes in the file match the sequence of messages logged in the connection's log.\nStep 2: To implement this, the function will:\n- Ensure that the connection is live in the given heap.\n- Retrieve the log of messages from the connection.\n- Flatten the log into a sequence of bytes.\n- Compare the flattened log with the sequence of bytes in the file to ensure they match.", "Step 1: The `received` function is intended to check if a given file, represented as an array of bytes, has been received over a connection. This involves verifying that the file matches the sequence of messages logged in the connection's history.\nStep 2: To implement this, the function will:\n- Ensure the connection is live in the given heap.\n- Retrieve the log of messages from the connection.\n- Flatten the log into a sequence of bytes.\n- Compare the flattened log with the sequence of bytes in the file to determine if they match.", "Step 1: The `received` function checks if a given file (represented as an initialized array of bytes) has been fully received on a given connection. It takes as input the file, the connection, and the current heap state.\nStep 2: The function will verify that the connection is live in the given heap state and that the file matches the log of messages received on the connection. This involves checking that the file is fully initialized in the heap and that the sequence of bytes in the file matches the flattened sequence of messages in the connection's log.", "Step 1: The `received` function checks if a given file (represented as an initialized array of bytes) has been fully received on a given connection. It takes an array of bytes `file`, a connection `c`, and a heap `h` as inputs and returns a logical proposition.\nStep 2: The function will verify that the connection is live in the given heap and that the fully initialized sequence of the file matches the sequence of messages logged in the connection. This involves checking that the length of the log matches the length of the file and that each byte in the file corresponds to the bytes in the log.", "Step 1: The `received` function is intended to check if a given file (represented as an initialized array of bytes) has been fully received on a given connection. This involves verifying that the contents of the file match the log of messages received on the connection.\nStep 2: The implementation will involve checking that the heap contains the connection and that the log of the connection matches the contents of the file. This will be done by comparing the initialized sequence of the file with the log of the connection.", "Step 1: The `received` function checks if the given file (an array of bytes) has been fully received by the receiver connection `c` in the heap `h`. This involves verifying that the connection is live, the file is fully initialized, and that the log of messages in the connection matches the file.\nStep 2: The implementation will first ensure that the connection is live and the file is fully initialized in the heap. It will then compare the log of messages received in the connection with the file to ensure they match." ], "generated_solution": [ "let received (file: Protocol.iarray Protocol.byte n) (c: Protocol.connection) (h: FStar.Monotonic.Heap.heap)\n : Prims.logical =\n h `live_connection` c /\\\n let log = Protocol.log c h in\n Protocol.flatten log == Protocol.as_initialized_seq file h", "let received (file: Protocol.iarray Protocol.byte n) (c: Protocol.connection) (h: FStar.Monotonic.Heap.heap)\n : Prims.logical =\n h `live_connection` c /\\\n file `fully_initialized_in` h /\\\n Protocol.as_initialized_seq file h == Protocol.flatten (Protocol.log c h)", "let received (file: Protocol.iarray Protocol.byte n) (c: Protocol.connection) (h: FStar.Monotonic.Heap.heap)\n : Prims.logical =\n h `live_connection` c /\\\n let file_bytes = as_initialized_seq file h in\n file_bytes == flatten (log c h)", "let received (file: Protocol.iarray Protocol.byte n) (c: Protocol.connection) (h: FStar.Monotonic.Heap.heap)\n : Prims.logical =\n h `live_connection` c /\\\n file `fully_initialized_in` h /\\\n Protocol.flatten (Protocol.log c h) == Protocol.as_initialized_seq file h", "let received (file: Protocol.iarray Protocol.byte n) (c: Protocol.connection) (h: FStar.Monotonic.Heap.heap)\n : Prims.logical =\n h `live_connection` c /\\\n let log = log c h in\n let file_bytes = as_initialized_seq file h in\n file_bytes == flatten log", "let received (file: Protocol.iarray Protocol.byte n) (c: Protocol.connection) (h: FStar.Monotonic.Heap.heap)\n : Prims.logical =\n h `live_connection` c /\\\n let log = log c h in\n let flattened_log = flatten log in\n let file_bytes = as_initialized_seq file h in\n file_bytes == flattened_log", "let received (file: Protocol.iarray Protocol.byte n) (c: Protocol.connection) (h: FStar.Monotonic.Heap.heap) : Prims.logical =\n h `live_connection` c /\\\n file `fully_initialized_in` h /\\\n as_initialized_seq file h == flatten (log c h)", "let received (file: Protocol.iarray Protocol.byte n) (c: Protocol.connection) (h: FStar.Monotonic.Heap.heap)\n : Prims.logical =\n h `live_connection` c /\\\n let log = log c h in\n Seq.length log == n /\\\n as_initialized_seq file h == flatten log", "let received (file: Protocol.iarray Protocol.byte n) (c: Protocol.connection) (h: FStar.Monotonic.Heap.heap)\n : Prims.logical =\n h `live_connection` c /\\\n Protocol.log c h == Protocol.as_initialized_seq file h", "let received (file: Protocol.iarray Protocol.byte n) (c: Protocol.connection) (h: FStar.Monotonic.Heap.heap)\n : Prims.logical =\n h `live_connection` c /\\\n file `fully_initialized_in` h /\\\n let log = log c h in\n flatten log == as_initialized_seq file h" ] }, { "file_name": "Vale.Def.Words.Seq_s.fst", "name": "Vale.Def.Words.Seq_s.two_to_seq_LE", "opens_and_abbrevs": [ { "open": "FStar.Mul" }, { "open": "Vale.Lib.Seqs_s" }, { "open": "FStar.Mul" }, { "open": "FStar.Seq" }, { "open": "Vale.Def.Words.Four_s" }, { "open": "Vale.Def.Words.Two_s" }, { "open": "Vale.Def.Words_s" }, { "open": "Vale.Def.Words" }, { "open": "Vale.Def.Words" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 3, "max_fuel": 3, "initial_ifuel": 0, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": true, "smtencoding_nl_arith_repr": "wrapped", "smtencoding_l_arith_repr": "native", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val two_to_seq_LE (#a:Type) (x:two a) : Pure (seq2 a)\n (requires True)\n (ensures fun s ->\n index s 0 == x.lo /\\\n index s 1 == x.hi\n )", "source_definition": "let two_to_seq_LE #a x =\n let l = [x.lo; x.hi] in\n let s = seq_of_list l in\n lemma_seq_of_list_index l 0;\n lemma_seq_of_list_index l 1;\n seq_of_list l", "source_range": { "start_line": 5, "start_col": 0, "end_line": 10, "end_col": 15 }, "interleaved": false, "definition": "fun x ->\n let l = [Mktwo?.lo x; Mktwo?.hi x] in\n let s = FStar.Seq.Base.seq_of_list l in\n FStar.Seq.Properties.lemma_seq_of_list_index l 0;\n FStar.Seq.Properties.lemma_seq_of_list_index l 1;\n FStar.Seq.Base.seq_of_list l", "effect": "Prims.Pure", "effect_flags": [], "mutual_with": [], "premises": [ "Vale.Def.Words_s.two", "FStar.Seq.Base.seq_of_list", "Prims.unit", "FStar.Seq.Properties.lemma_seq_of_list_index", "FStar.Seq.Base.seq", "Prims.eq2", "Prims.nat", "FStar.List.Tot.Base.length", "FStar.Seq.Base.length", "Prims.list", "Prims.Cons", "Vale.Def.Words_s.__proj__Mktwo__item__lo", "Vale.Def.Words_s.__proj__Mktwo__item__hi", "Prims.Nil", "Vale.Def.Words.Seq_s.seq2" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "x: Vale.Def.Words_s.two a -> Prims.Pure (Vale.Def.Words.Seq_s.seq2 a)", "prompt": "let two_to_seq_LE #a x =\n ", "expected_response": "let l = [x.lo; x.hi] in\nlet s = seq_of_list l in\nlemma_seq_of_list_index l 0;\nlemma_seq_of_list_index l 1;\nseq_of_list l", "source": { "project_name": "hacl-star", "file_name": "vale/specs/defs/Vale.Def.Words.Seq_s.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Vale.Def.Words.Seq_s.fst", "checked_file": "dataset/Vale.Def.Words.Seq_s.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked" ] }, "definitions_in_context": [], "closest": [ "val seq_two_to_seq_LE (#a: Type) (x: seq (two a)) : (z: seq a {length z == length x * 2})\nlet seq_two_to_seq_LE (#a:Type) (x:seq (two a)) : (z:seq a{length z == length x * 2}) =\n let f (n:nat{n < length x * 2}) = two_select (index x (n / 2)) (n % 2) in\n init (length x * 2) f", "val seq_to_seq_two_LE (#a: Type) (x: seq a {length x % 2 == 0})\n : (z: seq (two a) {length z == length x / 2})\nlet seq_to_seq_two_LE (#a:Type) (x:seq a{length x % 2 == 0}) : (z:seq (two a){length z == length x / 2}) =\n let f (n:nat{n < length x / 2}) = Mktwo (index x (n * 2)) (index x (n * 2 + 1)) in\n init (length x / 2) f", "val two_to_seq_to_two_LE (#a:Type) (x:seq2 a) :\n Lemma (two_to_seq_LE (seq_to_two_LE x) == x)\n [SMTPat (two_to_seq_LE (seq_to_two_LE x))]\nlet two_to_seq_to_two_LE #a x =\n assert (equal (two_to_seq_LE (seq_to_two_LE x)) x)", "val seq_to_two_LE (#a: Type) (s: seq2 a) : two a\nlet seq_to_two_LE (#a:Type) (s:seq2 a) : two a =\n Mktwo (index s 0) (index s 1)", "val seq_two_to_seq_BE (#a: Type) (x: seq (two a)) : (z: seq a {length z == length x * 2})\nlet seq_two_to_seq_BE (#a:Type) (x:seq (two a)) : (z:seq a{length z == length x * 2}) =\n let f (n:nat{n < length x * 2}) = two_select (index x (n / 2)) (1 - n % 2) in\n init (length x * 2) f", "val seq_to_seq_two_BE (#a: Type) (x: seq a {length x % 2 == 0})\n : (z: seq (two a) {length z == length x / 2})\nlet seq_to_seq_two_BE (#a:Type) (x:seq a{length x % 2 == 0}) : (z:seq (two a){length z == length x / 2}) =\n let f (n:nat{n < length x / 2}) = Mktwo (index x (n * 2 + 1)) (index x (n * 2)) in\n init (length x / 2) f", "val four_to_seq_LE_is_seq_four_to_seq_LE(#a:Type) (x:four a) :\n Lemma (four_to_seq_LE x == seq_four_to_seq_LE (create 1 x))\nlet four_to_seq_LE_is_seq_four_to_seq_LE(#a:Type) (x:four a) :\n Lemma (four_to_seq_LE x == seq_four_to_seq_LE (create 1 x))\n =\n reveal_opaque (`%seq_four_to_seq_LE) (seq_four_to_seq_LE #a);\n let s0 = four_to_seq_LE x in\n let s1 = seq_four_to_seq_LE (create 1 x) in\n assert (equal s0 s1);\n ()", "val four_to_seq_to_four_LE (#a:Type) (x:seq4 a) :\n Lemma (four_to_seq_LE (seq_to_four_LE x) == x)\nlet four_to_seq_to_four_LE (#a:Type) (x:seq4 a) :\n Lemma (four_to_seq_LE (seq_to_four_LE x) == x)\n =\n assert (equal (four_to_seq_LE (seq_to_four_LE x)) x);\n ()", "val seq_four_to_seq_LE (#a: Type) (x: seq (four a)) : (z: seq a {length z == length x * 4})\nlet seq_four_to_seq_LE (#a:Type) (x:seq (four a)) : (z:seq a{length z == length x * 4}) =\n let f (n:nat{n < length x * 4}) = four_select (index x (n / 4)) (n % 4) in\n init (length x * 4) f", "val seq_to_seq_four_LE (#a: Type) (x: seq a {length x % 4 == 0})\n : (z: seq (four a) {length z == length x / 4})\nlet seq_to_seq_four_LE (#a:Type) (x:seq a{length x % 4 == 0}) : (z:seq (four a){length z == length x / 4}) =\n let f (n:nat{n < length x / 4}) = Mkfour\n (index x (n * 4)) (index x (n * 4 + 1)) (index x (n * 4 + 2)) (index x (n * 4 + 3))\n in\n init (length x / 4) f", "val seq_four_to_seq_to_seq_four_LE (#a:Type) (x:seq a{length x % 4 == 0}) :\n Lemma (seq_four_to_seq_LE (seq_to_seq_four_LE x) == x)\n [SMTPat (seq_four_to_seq_LE (seq_to_seq_four_LE x))]\nlet seq_four_to_seq_to_seq_four_LE (#a:Type) (x:seq a{length x % 4 == 0}) :\n Lemma (seq_four_to_seq_LE (seq_to_seq_four_LE x) == x)\n =\n reveal_opaque (`%seq_four_to_seq_LE) (seq_four_to_seq_LE #a);\n reveal_opaque (`%seq_to_seq_four_LE) (seq_to_seq_four_LE #a);\n assert (equal (seq_four_to_seq_LE (seq_to_seq_four_LE x)) x);\n ()", "val seq_to_seq_four_to_seq_LE (#a:Type) (x:seq (four a)) :\n Lemma (seq_to_seq_four_LE (seq_four_to_seq_LE x) == x)\n [SMTPat (seq_to_seq_four_LE (seq_four_to_seq_LE x))]\nlet seq_to_seq_four_to_seq_LE (#a:Type) (x:seq (four a)) :\n Lemma (seq_to_seq_four_LE (seq_four_to_seq_LE x) == x)\n [SMTPat (seq_to_seq_four_LE (seq_four_to_seq_LE x))]\n =\n reveal_opaque (`%seq_four_to_seq_LE) (seq_four_to_seq_LE #a);\n reveal_opaque (`%seq_to_seq_four_LE) (seq_to_seq_four_LE #a);\n let bytes = seq_four_to_seq_LE x in\n let fours = seq_to_seq_four_LE bytes in\n assert (equal fours x);\n ()", "val to_seq (#a:Type0) (s:array a)\n : ST (seq a)\n (requires (fun h -> contains h s))\n (ensures (fun h0 x h1 -> (sel h0 s == x /\\ h0 == h1)))\nlet to_seq #a s = !s", "val singleton_list_seq (#a:Type) (x:a) : Lemma\n (seq_of_list [x] == create 1 x)\nlet singleton_list_seq #a x =\n lemma_seq_of_list_index [x] 0;\n assert (equal (seq_of_list [x]) (create 1 x))", "val seq_to_two_BE (#a: Type) (s: seq2 a) : two a\nlet seq_to_two_BE (#a:Type) (s:seq2 a) : two a =\n Mktwo (index s 1) (index s 0)", "val create2: #a:Type -> x0:a -> x1:a -> lseq a 2\nlet create2 #a x0 x1 =\n let l = [x0; x1] in\n assert_norm (List.Tot.length l = 2);\n createL l", "val two_two_to_four (#a: Type) (x: two (two a)) : four a\nlet two_two_to_four (#a:Type) (x:two (two a)) : four a =\n let (Mktwo (Mktwo x0 x1) (Mktwo x2 x3)) = x in\n Mkfour x0 x1 x2 x3", "val list_to_seq (#a:Type) (l:list a) : Pure (seq a)\n (requires True)\n (ensures fun s -> Seq.length s == List.length l)\nlet list_to_seq #a l =\n Seq.seq_of_list l", "val list_to_seq (#a: Type) (l: list a)\n : (s: (S.seq a){S.length s = List.Tot.length l /\\ (forall i. S.index s i == List.Tot.index l i)}\n )\nlet rec list_to_seq (#a:Type) (l:list a) : (s:(S.seq a){S.length s = List.Tot.length l /\\ (forall i. S.index s i == List.Tot.index l i)}) =\n match l with\n | [] -> S.empty\n | h :: t -> S.(create 1 h @| list_to_seq t)", "val seq_four_to_seq_LE_injective_specific (#a:eqtype) (x x':seq (four a)) :\n Lemma (seq_four_to_seq_LE x == seq_four_to_seq_LE x' ==> x == x')\nlet seq_four_to_seq_LE_injective_specific (#a:eqtype) (x x':seq (four a)) :\n Lemma (seq_four_to_seq_LE x == seq_four_to_seq_LE x' ==> x == x')\n =\n seq_four_to_seq_LE_injective a", "val seq2mset_mem (#a:eqtype) (#f:cmp a) (s:Seq.seq a) (x:a)\n : Lemma (mem x (seq2mset #_ #f s) == Seq.count x s)\nlet seq2mset_mem = seq2mset_mem_aux", "val seq_to_four_LE_is_seq_to_seq_four_LE (#a:Type) (s:seq4 a) : Lemma\n (create 1 (seq_to_four_LE s) == seq_to_seq_four_LE s)\nlet seq_to_four_LE_is_seq_to_seq_four_LE (#a:Type) (s:seq4 a) : Lemma\n (create 1 (seq_to_four_LE s) == seq_to_seq_four_LE s)\n =\n reveal_opaque (`%seq_to_seq_four_LE) (seq_to_seq_four_LE #a);\n assert (equal (create 1 (seq_to_four_LE s)) (seq_to_seq_four_LE s));\n ()", "val mem_index (#a:eqtype) (x:a) (s:seq a)\n : Lemma (requires (mem x s))\n (ensures (exists i. index s i == x))\nlet mem_index = mem_index'", "val seq_contains_to_index (#ty: Type) (s: seq ty) (x: ty)\n : Ghost nat\n (requires contains s x)\n (ensures fun idx -> idx < length s /\\ index s idx == x)\nlet seq_contains_to_index (#ty: Type) (s: seq ty) (x: ty)\n : Ghost nat\n (requires contains s x)\n (ensures fun idx -> idx < length s /\\ index s idx == x) =\n FStar.IndefiniteDescription.indefinite_description_ghost nat (fun idx -> idx < length s /\\ index s idx == x)", "val append_distributes_seq_to_seq_four_LE (#a:Type) (x:seq a{length x % 4 == 0}) (y:seq a{length y % 4 == 0}) :\n Lemma (seq_to_seq_four_LE (x @| y) == seq_to_seq_four_LE x @| seq_to_seq_four_LE y)\nlet append_distributes_seq_to_seq_four_LE (#a:Type) (x:seq a{length x % 4 == 0}) (y:seq a{length y % 4 == 0}) :\n Lemma (seq_to_seq_four_LE (x @| y) == seq_to_seq_four_LE x @| seq_to_seq_four_LE y)\n =\n reveal_opaque (`%seq_to_seq_four_LE) (seq_to_seq_four_LE #a);\n assert (equal (seq_to_seq_four_LE (x @| y)) (seq_to_seq_four_LE x @| seq_to_seq_four_LE y));\n ()", "val map_seq_index (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a) (i:nat{i < Seq.length s})\n : Lemma (ensures (map_seq_len f s; Seq.index (map_seq f s) i == f (Seq.index s i)))\nlet rec map_seq_index #a #b f s i\n : Lemma (ensures (map_seq_len f s; Seq.index (map_seq f s) i == f (Seq.index s i))) (decreases Seq.length s)\n = map_seq_len f s;\n if Seq.length s = 0\n then ()\n else if i = 0\n then ()\n else map_seq_index f (tail s) (i-1)", "val four_to_seq_to_four_BE (#a:Type) (x:seq4 a) :\n Lemma (four_to_seq_BE (seq_to_four_BE x) == x)\nlet four_to_seq_to_four_BE (#a:Type) (x:seq4 a) :\n Lemma (four_to_seq_BE (seq_to_four_BE x) == x)\n =\n assert (equal (four_to_seq_BE (seq_to_four_BE x)) x);\n ()", "val seq_to_seq_four_BE (#a: Type) (x: seq a {length x % 4 == 0})\n : (z: seq (four a) {length z == length x / 4})\nlet seq_to_seq_four_BE (#a:Type) (x:seq a{length x % 4 == 0}) : (z:seq (four a){length z == length x / 4}) =\n let f (n:nat{n < length x / 4}) = Mkfour\n (index x (n * 4 + 3)) (index x (n * 4 + 2)) (index x (n * 4 + 1)) (index x (n * 4))\n in\n init (length x / 4) f", "val index_mem_2 (#a: eqtype) (s: S.seq a) (x: a{S.count x s >= 2})\n : Tot\n (ij:\n (SA.seq_index s * SA.seq_index s)\n { let i, j = ij in\n i <> j /\\ S.index s i = x /\\ S.index s j = x }) (decreases S.length s)\nlet rec index_mem_2 (#a:eqtype) (s: S.seq a) (x: a {S.count x s >= 2})\n : Tot (ij:(SA.seq_index s * SA.seq_index s)\n {let i,j = ij in\n i <> j /\\ S.index s i = x /\\ S.index s j = x})\n (decreases S.length s)\n = assert(S.length s > 0);\n if S.head s = x then\n (0, 1 + (S.index_mem x (S.tail s)))\n else\n let i,j = index_mem_2 (S.tail s) x in\n (i + 1, j + 1)", "val map_seq_len (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a)\n : Lemma (ensures Seq.length (map_seq f s) == Seq.length s)\nlet rec map_seq_len #a #b f s\n : Lemma (ensures Seq.length (map_seq f s) == Seq.length s) (decreases Seq.length s)\n = if Seq.length s = 0\n then ()\n else map_seq_len f (tail s)", "val iarray_as_seq (#a: Type) (#n: nat) (x: iarray a n)\n : ST (seq a)\n (requires (fun h -> True))\n (ensures\n (fun h0 s h1 ->\n h0 == h1 /\\ (forall (k: nat). k < n ==> Some? (Seq.index (as_seq x h0) k)) /\\\n s == as_initialized_subseq x h0 0 n /\\ s == as_initialized_seq x h0))\nlet iarray_as_seq (#a:Type) (#n:nat) (x:iarray a n) : ST (seq a) \n (requires (fun h -> True))\n (ensures (fun h0 s h1 -> \n h0==h1 /\\\n (forall (k:nat). k < n ==> Some? (Seq.index (as_seq x h0) k)) /\\\n s == as_initialized_subseq x h0 0 n /\\\n\t s == as_initialized_seq x h0))\n = read_subseq_i_j x 0 n", "val lemma_sseq_extend_len (#a:eqtype) (ss: sseq a) (x:a) (i:seq_index ss):\n Lemma (ensures (flat_length (sseq_extend ss x i) = 1 + flat_length ss))\nlet rec lemma_sseq_extend_len (#a:eqtype) (ss: sseq a) (x:a) (i:seq_index ss):\n Lemma (ensures (flat_length (sseq_extend ss x i) = 1 + flat_length ss))\n (decreases (length ss)) =\n let n = length ss in\n\n if i = n - 1 then (\n lemma_sseq_extend_len_base ss x\n )\n else (\n let ss' = hprefix ss in\n let ssx = sseq_extend ss x i in\n let ssx' = sseq_extend ss' x i in\n\n lemma_sseq_extend_len ss' x i;\n assert(equal ssx (append1 ssx' (telem ss)));\n lemma_flat_length_app1 ssx' (telem ss);\n lemma_hprefix_append1 ss;\n lemma_flat_length_app1 ss' (telem ss)\n )", "val four_to_seq_LE_injective (a:eqtype) : Lemma\n (forall (x x':four a).{:pattern four_to_seq_LE x; four_to_seq_LE x'}\n four_to_seq_LE x == four_to_seq_LE x' ==> x == x')\nlet four_to_seq_LE_injective (a:eqtype) :\n Lemma (forall (x x': four a) . four_to_seq_LE x == four_to_seq_LE x' ==> x == x')\n =\n generic_injective_proof #(four a) #(seq4 a) (four_to_seq_LE #a) (seq_to_four_LE #a) (seq_to_four_to_seq_LE #a)", "val append_distributes_seq_four_to_seq_LE (#a:Type) (x:seq (four a)) (y:seq (four a)) :\n Lemma (seq_four_to_seq_LE (x @| y) == seq_four_to_seq_LE x @| seq_four_to_seq_LE y)\nlet append_distributes_seq_four_to_seq_LE #a x y =\n reveal_opaque (`%seq_four_to_seq_LE) (seq_four_to_seq_LE #a);\n assert (equal (seq_four_to_seq_LE (x @| y)) (seq_four_to_seq_LE x @| seq_four_to_seq_LE y))", "val seq_map_index (#t1 #t2: Type) (f: (t1 -> Tot t2)) (x: seq t1) (i: nat{i < length x})\n : Lemma (ensures (index (seq_map f x) i == f (index x i)))\n (decreases (length x))\n [SMTPat (index (seq_map f x) i)]\nlet rec seq_map_index\n (#t1 #t2: Type)\n (f: (t1 -> Tot t2))\n (x: seq t1)\n (i: nat { i < length x })\n: Lemma\n (ensures (index (seq_map f x) i == f (index x i)))\n (decreases (length x))\n [SMTPat (index (seq_map f x) i)]\n= if i = 0\n then ()\n else seq_map_index f (tail x) (i - 1)", "val seq_gmap_index (#t1 #t2: Type) (f: (t1 -> GTot t2)) (x: seq t1) (i: nat{i < length x})\n : Lemma (ensures (index (seq_gmap f x) i == f (index x i)))\n (decreases (length x))\n [SMTPat (index (seq_gmap f x) i)]\nlet rec seq_gmap_index\n (#t1 #t2: Type)\n (f: (t1 -> GTot t2))\n (x: seq t1)\n (i: nat { i < length x })\n: Lemma\n (ensures (index (seq_gmap f x) i == f (index x i)))\n (decreases (length x))\n [SMTPat (index (seq_gmap f x) i)]\n= if i = 0\n then ()\n else seq_gmap_index f (tail x) (i - 1)", "val seq_four_to_seq_BE (#a: Type) (x: seq (four a)) : (z: seq a {length z == length x * 4})\nlet seq_four_to_seq_BE (#a:Type) (x:seq (four a)) : (z:seq a{length z == length x * 4}) =\n let f (n:nat{n < length x * 4}) = four_select (index x (n / 4)) (3 - n % 4) in\n init (length x * 4) f", "val coerce' (t2 #t1: Type) (x: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun _ -> True))\nlet coerce'\n (t2: Type)\n (#t1: Type)\n (x: t1)\n: Pure t2\n (requires (t1 == t2))\n (ensures (fun _ -> True))\n= (x <: t2)", "val index_mem (#a: eqtype) (x: a) (s: seq a)\n : Pure nat\n (requires (mem x s))\n (ensures (fun i -> i < length s /\\ index s i == x))\n (decreases (length s))\nlet rec index_mem (#a:eqtype) (x:a) (s:seq a)\n : Pure nat\n (requires (mem x s))\n (ensures (fun i -> i < length s /\\ index s i == x))\n (decreases (length s))\n = if head s = x then 0\n else 1 + index_mem x (tail s)", "val seq_to_seq_four_to_seq_BE (#a:Type) (x:seq (four a)) :\n Lemma (seq_to_seq_four_BE (seq_four_to_seq_BE x) == x)\n [SMTPat (seq_to_seq_four_BE (seq_four_to_seq_BE x))]\nlet seq_to_seq_four_to_seq_BE (#a:Type) (x:seq (four a)) :\n Lemma (seq_to_seq_four_BE (seq_four_to_seq_BE x) == x)\n [SMTPat (seq_to_seq_four_BE (seq_four_to_seq_BE x))]\n =\n reveal_opaque (`%seq_four_to_seq_BE) (seq_four_to_seq_BE #a);\n reveal_opaque (`%seq_to_seq_four_BE) (seq_to_seq_four_BE #a);\n assert (equal (seq_to_seq_four_BE (seq_four_to_seq_BE x)) x);\n ()", "val seq_four_to_seq_to_seq_four_BE (#a:Type) (x:seq a{length x % 4 == 0}) :\n Lemma (seq_four_to_seq_BE (seq_to_seq_four_BE x) == x)\n [SMTPat (seq_four_to_seq_BE (seq_to_seq_four_BE x))]\nlet seq_four_to_seq_to_seq_four_BE (#a:Type) (x:seq a{length x % 4 == 0}) :\n Lemma (seq_four_to_seq_BE (seq_to_seq_four_BE x) == x)\n =\n reveal_opaque (`%seq_four_to_seq_BE) (seq_four_to_seq_BE #a);\n reveal_opaque (`%seq_to_seq_four_BE) (seq_to_seq_four_BE #a);\n assert (equal (seq_four_to_seq_BE (seq_to_seq_four_BE x)) x);\n ()", "val mem_cons\n (#a:eqtype)\n (x:a)\n (s:seq a)\n: Lemma\n (ensures (forall y. mem y (cons x s) <==> mem y s \\/ x=y))\nlet mem_cons #_ x s = lemma_append_count (create 1 x) s", "val seq_map (#t1 #t2: Type) (f: (t1 -> Tot t2)) (x: seq t1)\n : Tot (lseq t2 (length x)) (decreases (length x))\nlet rec seq_map\n (#t1 #t2: Type)\n (f: (t1 -> Tot t2))\n (x: seq t1)\n: Tot (lseq t2 (length x))\n (decreases (length x))\n= if length x = 0\n then empty\n else cons (f (head x)) (seq_map f (tail x))", "val two_map (#a #b: Type) (f: (a -> b)) (x: two a) : two b\nlet two_map (#a #b:Type) (f:a -> b) (x:two a) : two b =\n let Mktwo x0 x1 = x in\n Mktwo (f x0) (f x1)", "val index_mem (#a: eqtype) (s: seq a) (x: a)\n : Lemma (ensures (Seq.mem x s <==> (exists i. Seq.index s i == x))) (decreases (Seq.length s))\nlet rec index_mem (#a:eqtype) (s:seq a) (x:a)\n : Lemma (ensures (Seq.mem x s <==> (exists i. Seq.index s i == x)))\n (decreases (Seq.length s))\n = if length s = 0 then ()\n else if head s = x then ()\n else index_mem (tail s) x", "val seq2mset_mem_aux (#a: eqtype) (#f: cmp a) (s: Seq.seq a) (x: a)\n : Lemma (ensures Seq.count x s == mem x (seq2mset #a #f s)) (decreases (Seq.length s))\nlet rec seq2mset_mem_aux (#a:eqtype) (#f:cmp a) (s:Seq.seq a) (x:a)\n : Lemma\n (ensures Seq.count x s == mem x (seq2mset #a #f s))\n (decreases (Seq.length s))\n = if Seq.length s = 0 then ()\n else begin\n let s_hd = Seq.index s 0 in\n let s_tl = Seq.tail s in\n seq2mset_mem_aux #a #f s_tl x;\n let mset_tl = seq2mset #a #f s_tl in\n if s_hd = x\n then add_mem x mset_tl\n else add_mem_neq s_hd mset_tl x\n end", "val seq_count_into_smap_x (#a: eqtype) (s1 s2: Seq.seq a) (f: into_smap s1 s2) (x: a)\n : Lemma (ensures Seq.count x s1 <= Seq.count x s2) (decreases (Seq.length s1))\nlet rec seq_count_into_smap_x (#a:eqtype)\n (s1 s2:Seq.seq a)\n (f:into_smap s1 s2)\n (x:a)\n : Lemma\n (ensures Seq.count x s1 <= Seq.count x s2)\n (decreases (Seq.length s1)) \n = if Seq.length s1 = 0 then ()\n else begin\n let s1' = Seq.slice s1 1 (Seq.length s1) in\n let s2' = seq_remove s2 (f 0) in\n seq_count_into_smap_x s1' s2' (ismap_next s1 s2 f) x;\n assert (Seq.count x s1' <= Seq.count x s2');\n if x = Seq.index s1 0 then seq_remove_count1 s2 (f 0)\n else seq_remove_count2 s2 (f 0) x\n end", "val sealed_singl (#a:Type) (x y : sealed a)\n : Lemma (x == y)\nlet sealed_singl (#a:Type) (x y : sealed a) : Lemma (x == y) =\n let Seal f = x in\n let Seal g = y in\n unobs_axiom f g", "val two_reverse (#a: Type) (x: two a) : two a\nlet two_reverse (#a:Type) (x:two a) : two a =\n let Mktwo x0 x1 = x in\n Mktwo x1 x0", "val mem_index' (#a: eqtype) (x: a) (s: seq a)\n : Lemma (requires (mem x s)) (ensures (exists i. index s i == x)) (decreases (length s))\nlet rec mem_index' (#a:eqtype) (x:a) (s:seq a)\n : Lemma (requires (mem x s))\n (ensures (exists i. index s i == x))\n (decreases (length s))\n = if length s = 0 then ()\n else if head s = x then ()\n else mem_index' x (tail s)", "val four_to_two_two (#a: Type) (x: four a) : two (two a)\nlet four_to_two_two (#a:Type) (x:four a) : two (two a) =\n let Mkfour x0 x1 x2 x3 = x in\n Mktwo (Mktwo x0 x1) (Mktwo x2 x3)", "val equal (#a:Type) (#len:size_nat) (s1:lseq a len) (s2:lseq a len) : Type0\nlet equal #a #len s1 s2 =\n forall (i:size_nat{i < len}).{:pattern (index s1 i); (index s2 i)} index s1 i == index s2 i", "val coerce (t2 #t1: Type) (x: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun _ -> True))\nlet coerce\n (t2: Type)\n (#t1: Type)\n (x: t1)\n: Pure t2\n (requires (t1 == t2))\n (ensures (fun _ -> True))\n= (x <: t2)", "val coerce (t2 #t1: Type) (x: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun _ -> True))\nlet coerce\n (t2: Type)\n (#t1: Type)\n (x: t1)\n: Pure t2\n (requires (t1 == t2))\n (ensures (fun _ -> True))\n= (x <: t2)", "val coerce (t2 #t1: Type) (x: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun _ -> True))\nlet coerce\n (t2: Type)\n (#t1: Type)\n (x: t1)\n: Pure t2\n (requires (t1 == t2))\n (ensures (fun _ -> True))\n= (x <: t2)", "val get (#a:Type0) (x: t a) (i:US.t{US.v i < length x}) :\n Pure a\n (requires True)\n (ensures fun y ->\n US.v i < L.length (v x) /\\\n y == L.index (v x) (US.v i))\nlet get x i = L.index x (US.v i)", "val rev_seq (#a: Type) (s: S.seq a)\n : Pure (S.seq a)\n (requires True)\n (ensures fun s' -> S.length s = S.length s')\n (decreases (S.length s))\nlet rec rev_seq (#a:Type) (s:S.seq a) : Pure (S.seq a)\n (requires True)\n (ensures fun s' -> S.length s = S.length s')\n (decreases (S.length s)) =\n if S.length s = 0 then S.empty\n else\n let _ = S.lemma_empty s in\n S.(rev_seq S.(slice s 1 (length s)) @| create 1 (index s 0))", "val contains_cons (#a:Type) (hd:a) (tl:Seq.seq a) (x:a)\n : Lemma ((cons hd tl) `contains` x\n <==>\n (x==hd \\/ tl `contains` x))\nlet contains_cons #_ hd tl x\n = append_contains_equiv (Seq.create 1 hd) tl x", "val coerce (t2 #t1: Type) (x: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun y -> x == y))\nlet coerce (t2: Type) (#t1: Type) (x: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun y -> x == y)) = x", "val slice_snoc2 (#a: _) (s: seq a) (x: a) (from: nat{from <= Seq.length s})\n : Lemma (slice (snoc s x) from (Seq.length s + 1) == snoc (slice s from (Seq.length s)) x)\nlet slice_snoc2 #a (s:seq a) (x:a) (from:nat{from <= Seq.length s})\n : Lemma (slice (snoc s x) from (Seq.length s + 1) == snoc (slice s from (Seq.length s)) x)\n = assert (slice (snoc s x) from (Seq.length s + 1) `Seq.equal` snoc (slice s from (Seq.length s)) x)", "val seq_nat8_to_seq_nat32_LE (x: seq nat8 {length x % 4 == 0}) : seq nat32\nlet seq_nat8_to_seq_nat32_LE (x:seq nat8{length x % 4 == 0}) : seq nat32 =\n seq_map (four_to_nat 8) (seq_to_seq_four_LE x)", "val seq_nat32_to_seq_nat8_to_seq_nat32_LE (x:seq nat8{length x % 4 == 0}) :\n Lemma (seq_nat32_to_seq_nat8_LE (seq_nat8_to_seq_nat32_LE x) == x)\n [SMTPat (seq_nat32_to_seq_nat8_LE (seq_nat8_to_seq_nat32_LE x))]\nlet seq_nat32_to_seq_nat8_to_seq_nat32_LE (x:seq nat8{length x % 4 == 0}) :\n Lemma (seq_nat32_to_seq_nat8_LE (seq_nat8_to_seq_nat32_LE x) == x)\n =\n reveal_opaque (`%seq_four_to_seq_LE) (seq_four_to_seq_LE #nat8);\n reveal_opaque (`%seq_to_seq_four_LE) (seq_to_seq_four_LE #nat8);\n assert (equal (seq_nat32_to_seq_nat8_LE (seq_nat8_to_seq_nat32_LE x)) x);\n ()", "val seq_mset_elem2 (#a:eqtype) (#f:cmp a) (s:Seq.seq a) (i1 i2:seq_index s)\n : Lemma\n (requires i1 =!= i2 /\\ Seq.index s i1 == Seq.index s i2)\n (ensures mem (Seq.index s i1) (seq2mset #a #f s) >= 2)\nlet seq_mset_elem2 #a #f s i1 i2 =\n let rec aux (s:Seq.seq a) (i1 i2:seq_index s)\n : Lemma\n (requires i1 =!= i2 /\\ Seq.index s i1 == Seq.index s i2)\n (ensures Seq.count (Seq.index s i1) s >= 2)\n (decreases (Seq.length s))\n = if i1 = 0 then seq_count_i (Seq.tail s) (i2 - 1)\n else if i2 = 0 then seq_count_i (Seq.tail s) (i1 - 1)\n else aux (Seq.tail s) (i1 - 1) (i2 - 1)\n in\n aux s i1 i2;\n seq2mset_mem #a #f s (Seq.index s i1)", "val seq_map_i (#a:Type) (#b:Type) (f:int->a->b) (s:seq a) :\n Tot (s':seq b { length s' == length s /\\\n (forall j . {:pattern index s' j} 0 <= j /\\ j < length s ==> index s' j == f j (index s j))\n })\nlet seq_map_i (#a:Type) (#b:Type) (f:int->a->b) (s:seq a) :\n Tot (s':seq b { length s' == length s /\\\n (forall j . {:pattern index s' j} 0 <= j /\\ j < length s ==> index s' j == f j (index s j))\n })\n =\n seq_map_i_indexed f s 0", "val seq_of_sequence_of_seq (#a:Type) (s:Seq.seq a)\n : Lemma (seq_of_sequence (sequence_of_seq s) == s)\nlet seq_of_sequence_of_seq (#a:Type) (s:Seq.seq a)\n : Lemma (seq_of_sequence (sequence_of_seq s) == s)\n = related_sequence_of_seq s;\n related_seq_of_sequence (sequence_of_seq s);\n assert (Seq.equal (seq_of_sequence (sequence_of_seq s)) s)", "val to_seq: #a:Type -> b:buffer a -> l:UInt32.t{v l <= length b} -> STL (seq a)\n (requires (fun h -> live h b))\n (ensures (fun h0 r h1 -> h0 == h1 /\\ live h1 b /\\ Seq.length r == v l\n (*/\\ r == as_seq #a h1 b *) ))\nlet to_seq #a b l =\n let s = !b.content in\n let i = v b.idx in\n Seq.slice s i (i + v l)", "val sequence_of_seq_of_sequence (#a:Type) (s:Sequence.seq a)\n : Lemma (sequence_of_seq (seq_of_sequence s) == s)\nlet sequence_of_seq_of_sequence (#a:Type) (s:Sequence.seq a)\n : Lemma (sequence_of_seq (seq_of_sequence s) == s)\n = related_seq_of_sequence s;\n related_sequence_of_seq (seq_of_sequence s);\n assert (Sequence.equal (sequence_of_seq (seq_of_sequence s)) s)", "val related_seq_of_sequence (#a:Type) (s:Sequence.seq a)\n : Lemma (related (seq_of_sequence s) s)\nlet rec related_seq_of_sequence (#a:Type) (s:Sequence.seq a)\n : Lemma\n (ensures related (seq_of_sequence s) s)\n (decreases (Sequence.length s))\n = if Sequence.length s = 0\n then ()\n else (\n related_seq_of_sequence (Sequence.take s (Sequence.length s - 1))\n )", "val seq_equal_helper (#a: eqtype) (s1 s2: seq a)\n : Lemma\n (requires\n (let l1 = S.length s1 in\n let l2 = S.length s2 in\n l1 = l2 /\\ l1 > 0 /\\ SA.hprefix s1 = SA.hprefix s2 /\\ SA.telem s1 = SA.telem s2))\n (ensures (s1 = s2))\nlet seq_equal_helper (#a:eqtype) (s1 s2: seq a)\n : Lemma (requires (let l1 = S.length s1 in\n let l2 = S.length s2 in\n l1 = l2 /\\ l1 > 0 /\\ SA.hprefix s1 = SA.hprefix s2 /\\ SA.telem s1 = SA.telem s2))\n (ensures (s1 = s2))\n = let aux (i:_)\n : Lemma (ensures (S.index s1 i = S.index s2 i))\n = ()\n in\n forall_intro aux;\n assert(S.equal s1 s2)", "val coerce (#a: Type) (x: a) (b: Type)\n : Pure b (requires (a == b)) (ensures (fun y -> a == b /\\ x == y))\nlet coerce\n (#a: Type)\n (x: a)\n (b: Type)\n: Pure b\n (requires (a == b))\n (ensures (fun y -> a == b /\\ x == y))\n= x", "val index (#a:Type0) (x:array a) (n:nat)\n : ST a\n (requires (fun h -> contains h x /\\ n < Seq.length (sel h x)))\n (ensures (fun h0 v h1 -> n < Seq.length (sel h0 x) /\\\n h0 == h1 /\\\n v == Seq.index (sel h0 x) n))\nlet index #a x n =\n let s = to_seq x in\n Seq.index s n", "val length_size (#a:eqtype) (#f:cmp a) (s:Seq.seq a)\n : Lemma (Seq.length s = size (seq2mset #a #f s))\nlet length_size = length_size_aux", "val seq_upd_seq_seq_upd (#t: Type) (s: Seq.seq t) (i: nat) (x: t)\n : Lemma (requires (i < Seq.length s))\n (ensures (Seq.upd s i x == seq_upd_seq s i (Seq.create 1 x)))\nlet seq_upd_seq_seq_upd\n (#t: Type)\n (s: Seq.seq t)\n (i: nat)\n (x: t)\n: Lemma\n (requires (i < Seq.length s))\n (ensures (Seq.upd s i x == seq_upd_seq s i (Seq.create 1 x)))\n= assert (Seq.upd s i x `Seq.equal` seq_upd_seq s i (Seq.create 1 x))", "val lemma_sseq_extend_len_base (#a: eqtype) (ss: sseq a {length ss > 0}) (x: a)\n : Lemma (flat_length (sseq_extend ss x (length ss - 1)) = 1 + flat_length ss)\nlet lemma_sseq_extend_len_base (#a:eqtype) (ss: sseq a{length ss > 0}) (x:a):\n Lemma (flat_length (sseq_extend ss x (length ss - 1)) = 1 + flat_length ss) =\n let n = length ss in\n let i = n - 1 in\n let ss' = sseq_extend ss x i in\n let ss'i = prefix ss' i in\n let ssi = prefix ss i in\n let iss' = suffix ss' (n - i) in\n let iss = suffix ss (n - i) in\n\n assert(equal ssi ss'i);\n\n let fl = flat_length ss in\n let fl' = flat_length ss' in\n let fli = flat_length ssi in\n\n let l = map length ss in\n let l' = map length ss' in\n\n let l'i = prefix l' i in\n let li = prefix l i in\n assert(equal li l'i);\n\n let il' = suffix l' (n - i) in\n let il = suffix l (n - i) in\n\n\n lemma_reduce_prefix 0 nat_add l' i;\n lemma_reduce_prefix 0 nat_add l i;\n lemma_map_prefix length ss' i;\n lemma_map_prefix length ss i;\n assert(fl' = reduce fli nat_add il');\n assert(fl = reduce fli nat_add il);\n\n lemma_reduce_singleton fli nat_add il';\n lemma_reduce_singleton fli nat_add il", "val mem_seq_of_list\n (#a: eqtype)\n (x: a)\n (l: list a)\n: Lemma\n (requires True)\n (ensures (mem x (seq_of_list l) == List.Tot.mem x l))\n [SMTPat (mem x (seq_of_list l))]\nlet rec mem_seq_of_list #_ x l\n= lemma_seq_of_list_induction l;\n match l with\n | [] -> ()\n | y :: q ->\n let _ : squash (head (seq_of_list l) == y) = () in\n let _ : squash (tail (seq_of_list l) == seq_of_list q) = seq_of_list_tl l in\n let _ : squash (mem x (seq_of_list l) == (x = y || mem x (seq_of_list q))) =\n lemma_mem_inversion (seq_of_list l)\n in\n mem_seq_of_list x q", "val seq_gmap (#t1 #t2: Type) (f: (t1 -> GTot t2)) (x: seq t1)\n : GTot (lseq t2 (length x)) (decreases (length x))\nlet rec seq_gmap\n (#t1 #t2: Type)\n (f: (t1 -> GTot t2))\n (x: seq t1)\n: GTot (lseq t2 (length x))\n (decreases (length x))\n= if length x = 0\n then empty\n else cons (f (head x)) (seq_gmap f (tail x))", "val seq_nat8_to_seq_nat32_to_seq_nat8_LE (x:seq nat32) :\n Lemma (seq_nat8_to_seq_nat32_LE (seq_nat32_to_seq_nat8_LE x) == x)\n [SMTPat (seq_nat8_to_seq_nat32_LE (seq_nat32_to_seq_nat8_LE x))]\nlet seq_nat8_to_seq_nat32_to_seq_nat8_LE (x:seq nat32) :\n Lemma (seq_nat8_to_seq_nat32_LE (seq_nat32_to_seq_nat8_LE x) == x)\n =\n assert (equal (seq_nat8_to_seq_nat32_LE (seq_nat32_to_seq_nat8_LE x)) x);\n ()", "val seq_four_to_seq_LE_injective (a:eqtype) : Lemma\n (forall (x x':seq (four a)).{:pattern seq_four_to_seq_LE x; seq_four_to_seq_LE x'}\n seq_four_to_seq_LE x == seq_four_to_seq_LE x' ==> x == x')\nlet seq_four_to_seq_LE_injective (a:eqtype) :\n Lemma (forall (x x': seq (four a)). seq_four_to_seq_LE #a x == seq_four_to_seq_LE #a x' ==> x == x')\n =\n let seq_four_to_seq_LE_stronger (#b:Type) (x:seq (four b)) : (s:seq b{length s % 4 == 0}) =\n seq_four_to_seq_LE x\n in\n generic_injective_proof (seq_four_to_seq_LE_stronger) (seq_to_seq_four_LE #a) (seq_to_seq_four_to_seq_LE #a);\n ()", "val map_seq_len (#a #b: _) (x: FStar.Seq.seq a) (f: (a -> b))\n : Lemma (ensures Seq.length (Seq.map_seq f x) == Seq.length x)\n [SMTPat (Seq.length (Seq.map_seq f x))]\nlet map_seq_len #a #b (x:FStar.Seq.seq a) (f:a -> b)\n: Lemma (ensures Seq.length (Seq.map_seq f x) == Seq.length x)\n [SMTPat (Seq.length (Seq.map_seq f x))]\n= FStar.Seq.map_seq_len f x", "val index_seq_rev (#t: Type) (x: S.seq t) (i: nat{i < S.length x})\n : Lemma (ensures (S.index (seq_rev x) i == S.index x (S.length x - 1 - i)))\nlet index_seq_rev\n (#t: Type)\n (x: S.seq t)\n (i: nat {i < S.length x})\n: Lemma\n (ensures (S.index (seq_rev x) i == S.index x (S.length x - 1 - i)))\n= index_seq_rev' x (S.length x - 1 - i)", "val lemma_seq_refine_equal (#a:Type) (f:a->bool) (s:seq a{all f s}) (i:seq_index s):\nLemma (requires True)\n (ensures (index (seq_refine f s) i == index s i))\n [SMTPat (index (seq_refine f s) i)]\nlet lemma_seq_refine_equal = lemma_seq_refine_equal_aux", "val coerce_eq2: a: (nat -> Type0) -> b: (nat -> Type0) -> v:a 0 -> Pure (b 0)\n (requires a == b) (ensures fun _ -> True)\nlet coerce_eq2 _ _ v = v", "val includes_as_seq (#a h1 h2: _) (x y: buffer a)\n : Lemma (requires (x `includes` y /\\ as_seq h1 x == as_seq h2 x))\n (ensures (as_seq h1 y == as_seq h2 y))\nlet includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)\n: Lemma\n (requires (x `includes` y /\\ as_seq h1 x == as_seq h2 x))\n (ensures (as_seq h1 y == as_seq h2 y))\n= Seq.slice_slice (sel h1 x) (idx x) (idx x + length x) (idx y - idx x) (idx y - idx x + length y);\n Seq.slice_slice (sel h2 x) (idx x) (idx x + length x) (idx y - idx x) (idx y - idx x + length y)", "val includes_as_seq (#a h1 h2: _) (x y: buffer a)\n : Lemma (requires (x `includes` y /\\ as_seq h1 x == as_seq h2 x))\n (ensures (as_seq h1 y == as_seq h2 y))\nlet includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)\n: Lemma\n (requires (x `includes` y /\\ as_seq h1 x == as_seq h2 x))\n (ensures (as_seq h1 y == as_seq h2 y))\n= P.buffer_includes_elim x y", "val un_snoc_snoc (#a:Type) (s:seq a) (x:a) : Lemma (un_snoc (snoc s x) == (s, x))\nlet un_snoc_snoc #_ s x =\n let s', x = un_snoc (snoc s x) in\n assert (Seq.equal s s')", "val seq_rev_involutive (#t: Type) (x: S.seq t) : Lemma ((seq_rev (seq_rev x)) `S.equal` x)\nlet seq_rev_involutive\n (#t: Type)\n (x: S.seq t)\n: Lemma\n (seq_rev (seq_rev x) `S.equal` x)\n= Classical.forall_intro (index_seq_rev (seq_rev x));\n Classical.forall_intro (index_seq_rev x)", "val map2:#a:Type -> #b:Type -> #c:Type -> #len:size_nat\n -> f:(a -> b -> Tot c)\n -> s1:lseq a len\n -> s2:lseq b len ->\n Tot (s3:lseq c len{(forall (i:nat).\n {:pattern (index s3 i)} i < len ==> index s3 i == f s1.[i] s2.[i])})\nlet map2 #a #b #c #len f s1 s2 =\n createi #c len (map2_inner #a #b #c #len f s1 s2)", "val index_seq_rev' (#t: Type) (x: S.seq t) (i: nat{i < S.length x})\n : Lemma (ensures (S.index (seq_rev x) (S.length x - 1 - i) == S.index x i))\n (decreases (S.length x))\nlet rec index_seq_rev'\n (#t: Type)\n (x: S.seq t)\n (i: nat {i < S.length x})\n: Lemma\n (ensures (S.index (seq_rev x) (S.length x - 1 - i) == S.index x i))\n (decreases (S.length x))\n= if i = 0\n then\n S.lemma_index_create 1 (S.head x) 0\n else\n index_seq_rev' (S.tail x) (i - 1)", "val split_eq (#a: Type) (s: seq a) (i: nat{(0 <= i /\\ i <= length s)})\n : Pure (seq a * seq a) (requires True) (ensures (fun x -> (append (fst x) (snd x) == s)))\nlet split_eq (#a:Type) (s:seq a) (i:nat{(0 <= i /\\ i <= length s)})\n: Pure\n (seq a * seq a)\n (requires True)\n (ensures (fun x -> (append (fst x) (snd x) == s)))\n= let x = split s i in\n lemma_split s i;\n x", "val split3_index (#a: eqtype) (s0: seq a) (x: a) (s1: seq a) (j: nat)\n : Lemma (requires j < Seq.length (Seq.append s0 s1))\n (ensures\n (let s = Seq.append s0 (Seq.cons x s1) in\n let s' = Seq.append s0 s1 in\n let n = Seq.length s0 in\n if j < n then Seq.index s' j == Seq.index s j else Seq.index s' j == Seq.index s (j + 1)))\nlet split3_index (#a:eqtype) (s0:seq a) (x:a) (s1:seq a) (j:nat)\n : Lemma\n (requires j < Seq.length (Seq.append s0 s1))\n (ensures (\n let s = Seq.append s0 (Seq.cons x s1) in\n let s' = Seq.append s0 s1 in\n let n = Seq.length s0 in\n if j < n then Seq.index s' j == Seq.index s j\n else Seq.index s' j == Seq.index s (j + 1)\n ))\n = let n = Seq.length (Seq.append s0 s1) in\n if j < n then ()\n else ()", "val seq_of_list_append_lemma: #a:Type -> x:list a -> y:list a ->\n Lemma (let xy_lseq = Seq.seq_of_list FL.(x @ y) in\n Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x /\\\n Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y)\nlet seq_of_list_append_lemma #a x y =\n let xy = FL.(x @ y) in\n let x_lseq = Seq.seq_of_list x in\n let y_lseq = Seq.seq_of_list y in\n let xy_lseq = Seq.seq_of_list xy in\n let x_len = FL.length x in\n let y_len = FL.length y in\n\n let lemma_x_lseq (i:nat{i < x_len}) : Lemma (Seq.index xy_lseq i == Seq.index x_lseq i) =\n list_append_index x y i in\n\n FStar.Classical.forall_intro lemma_x_lseq;\n Seq.lemma_eq_intro (Seq.slice xy_lseq 0 x_len) x_lseq;\n assert (Seq.slice xy_lseq 0 x_len == x_lseq);\n\n let lemma_y_lseq (i:nat{i < y_len}) :\n Lemma (Seq.index xy_lseq (x_len + i) == Seq.index y_lseq i) =\n list_append_index x y (x_len + i) in\n\n FStar.Classical.forall_intro lemma_y_lseq;\n Seq.lemma_eq_intro (Seq.slice xy_lseq x_len (x_len + y_len)) y_lseq;\n assert (Seq.slice xy_lseq x_len (x_len + y_len) == y_lseq)", "val lemma_append_count_aux: #a:eqtype -> x:a -> lo:seq a -> hi:seq a -> Lemma\n (requires True)\n (ensures (count x (append lo hi) = (count x lo + count x hi)))\nlet lemma_append_count_aux #_ _ lo hi = lemma_append_count lo hi", "val cons (#a: Type) (x: a) (s: seq a) : Tot (seq a)\nlet cons (#a:Type) (x:a) (s:seq a) : Tot (seq a) = append (create 1 x) s", "val map_seq_index (#a #b: Type) (f: (a -> Tot b)) (s: Seq.seq a) (i: nat{i < Seq.length s})\n : Lemma (ensures Seq.index (Seq.map_seq f s) i == f (Seq.index s i))\n [SMTPat (Seq.index (Seq.map_seq f s) i)]\nlet map_seq_index (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a) (i:nat{i < Seq.length s})\n : Lemma (ensures Seq.index (Seq.map_seq f s) i == f (Seq.index s i))\n [SMTPat (Seq.index (Seq.map_seq f s) i)]\n = Seq.map_seq_index f s i", "val coerce (t2 #t1: Type) (x1: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun y -> y == x1))\nlet coerce (t2: Type) (#t1: Type) (x1: t1)\n : Pure t2 (requires (t1 == t2))\n (ensures (fun y -> y == x1))\n = x1", "val coerce (t2 #t1: Type) (x1: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun y -> y == x1))\nlet coerce (t2: Type) (#t1: Type) (x1: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun y -> y == x1)) = x1", "val map_seq_index (#a #b: _) (x: FStar.Seq.seq a) (f: (a -> b)) (i: nat{i < Seq.length x})\n : Lemma (ensures Seq.index (Seq.map_seq f x) i == f (Seq.index x i))\n [SMTPat (Seq.index (Seq.map_seq f x) i)]\nlet map_seq_index #a #b (x:FStar.Seq.seq a) (f:a -> b) (i:nat { i < Seq.length x })\n: Lemma (ensures Seq.index (Seq.map_seq f x) i == f (Seq.index x i))\n [SMTPat (Seq.index (Seq.map_seq f x) i)]\n= FStar.Seq.map_seq_index f x i", "val seq_map2:\n #a:Type -> #b:Type -> #c:Type ->\n f:(a -> b -> Tot c) ->\n s:Seq.seq a -> s':Seq.seq b{Seq.length s = Seq.length s'} ->\n Tot (s'':Seq.seq c{Seq.length s = Seq.length s'' /\\\n (forall (i:nat). {:pattern (Seq.index s'' i)} i < Seq.length s'' ==> Seq.index s'' i == f (Seq.index s i) (Seq.index s' i))})\n (decreases (Seq.length s))\nlet rec seq_map2 #a #b #c f s s' =\n if Seq.length s = 0 then Seq.empty\n else\n let s'' = Seq.cons (f (Seq.head s) (Seq.head s')) (seq_map2 f (Seq.tail s) (Seq.tail s')) in\n s''", "val coerce_eq2 (a: (nat -> Type0)) (b: (nat -> Type0)) (v: a 0)\n : Pure (b 0) (requires a == b) (ensures fun _ -> True)\nlet coerce_eq2 (a:nat -> Type0) (b: (nat -> Type0)) (v:a 0) : Pure (b 0)\n (requires a == b) (ensures fun _ -> True) = v", "val create2_lemma: #a:Type -> x0:a -> x1:a ->\n Lemma (let s = create2 x0 x1 in\n s.[0] == x0 /\\ s.[1] == x1)\n [SMTPat (create2 #a x0 x1)]\nlet create2_lemma #a x0 x1 =\n Seq.elim_of_list [x0; x1]" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq_s.fsti", "name": "Vale.Def.Words.Seq_s.seq_two_to_seq_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq_s.fsti", "name": "Vale.Def.Words.Seq_s.seq_to_seq_two_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.two_to_seq_to_two_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq_s.fsti", "name": "Vale.Def.Words.Seq_s.seq_to_two_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq_s.fsti", "name": "Vale.Def.Words.Seq_s.seq_two_to_seq_BE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq_s.fsti", "name": "Vale.Def.Words.Seq_s.seq_to_seq_two_BE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.four_to_seq_LE_is_seq_four_to_seq_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.four_to_seq_to_four_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq_s.fsti", "name": "Vale.Def.Words.Seq_s.seq_four_to_seq_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq_s.fsti", "name": "Vale.Def.Words.Seq_s.seq_to_seq_four_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.seq_four_to_seq_to_seq_four_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.seq_to_seq_four_to_seq_LE" }, { "project_name": "FStar", "file_name": "FStar.Array.fst", "name": "FStar.Array.to_seq" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Lists.fst", "name": "Vale.Lib.Lists.singleton_list_seq" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq_s.fsti", "name": "Vale.Def.Words.Seq_s.seq_to_two_BE" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.create2" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Four_s.fsti", "name": "Vale.Def.Words.Four_s.two_two_to_four" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.list_to_seq" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.list_to_seq" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.seq_four_to_seq_LE_injective_specific" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.seq2mset_mem" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.Types.fst", "name": "Vale.Arch.Types.seq_to_four_LE_is_seq_to_seq_four_LE" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.mem_index" }, { "project_name": "Armada", "file_name": "Util.Seq.fst", "name": "Util.Seq.seq_contains_to_index" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.append_distributes_seq_to_seq_four_LE" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.map_seq_index" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.four_to_seq_to_four_BE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq_s.fsti", "name": "Vale.Def.Words.Seq_s.seq_to_seq_four_BE" }, { "project_name": "zeta", "file_name": "Zeta.Generic.Blum.fst", "name": "Zeta.Generic.Blum.index_mem_2" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.map_seq_len" }, { "project_name": "FStar", "file_name": "Protocol.fst", "name": "Protocol.iarray_as_seq" }, { "project_name": "zeta", "file_name": "Zeta.SSeq.fst", "name": "Zeta.SSeq.lemma_sseq_extend_len" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.four_to_seq_LE_injective" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.append_distributes_seq_four_to_seq_LE" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Secret.Seq.fst", "name": "QUIC.Secret.Seq.seq_map_index" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Secret.Seq.fst", "name": "QUIC.Secret.Seq.seq_gmap_index" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq_s.fsti", "name": "Vale.Def.Words.Seq_s.seq_four_to_seq_BE" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Base.fsti", "name": "LowParse.Spec.Base.coerce'" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fsti", "name": "FStar.Seq.Properties.index_mem" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.seq_to_seq_four_to_seq_BE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.seq_four_to_seq_to_seq_four_BE" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.mem_cons" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Secret.Seq.fst", "name": "QUIC.Secret.Seq.seq_map" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Two_s.fsti", "name": "Vale.Def.Words.Two_s.two_map" }, { "project_name": "FStar", "file_name": "OPLSS.Log.fst", "name": "OPLSS.Log.index_mem" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.seq2mset_mem_aux" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.seq_count_into_smap_x" }, { "project_name": "FStar", "file_name": "SealedModel.fst", "name": "SealedModel.sealed_singl" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Two_s.fsti", "name": "Vale.Def.Words.Two_s.two_reverse" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.mem_index'" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Four_s.fsti", "name": "Vale.Def.Words.Four_s.four_to_two_two" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.equal" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Base.fsti", "name": "LowParse.Spec.Base.coerce" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.coerce" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.Base.fst", "name": "MiniParse.Spec.Base.coerce" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.get" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.rev_seq" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.contains_cons" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.coerce" }, { "project_name": "FStar", "file_name": "Protocol.fst", "name": "Protocol.slice_snoc2" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq_s.fsti", "name": "Vale.Def.Words.Seq_s.seq_nat8_to_seq_nat32_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.seq_nat32_to_seq_nat8_to_seq_nat32_LE" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.seq_mset_elem2" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.seq_map_i" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Seq.fst", "name": "FStar.Sequence.Seq.seq_of_sequence_of_seq" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.to_seq" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Seq.fst", "name": "FStar.Sequence.Seq.sequence_of_seq_of_sequence" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Seq.fst", "name": "FStar.Sequence.Seq.related_seq_of_sequence" }, { "project_name": "zeta", "file_name": "Zeta.Interleave.fst", "name": "Zeta.Interleave.seq_equal_helper" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.coerce" }, { "project_name": "FStar", "file_name": "FStar.Array.fst", "name": "FStar.Array.index" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.length_size" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Base.fsti", "name": "LowParse.Spec.Base.seq_upd_seq_seq_upd" }, { "project_name": "zeta", "file_name": "Zeta.SSeq.fst", "name": "Zeta.SSeq.lemma_sseq_extend_len_base" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.mem_seq_of_list" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Secret.Seq.fst", "name": "QUIC.Secret.Seq.seq_gmap" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.seq_nat8_to_seq_nat32_to_seq_nat8_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.seq_four_to_seq_LE_injective" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.map_seq_len" }, { "project_name": "everparse", "file_name": "LowParse.Endianness.fst", "name": "LowParse.Endianness.index_seq_rev" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_seq_refine_equal" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.HMAC.UFCMA.fst", "name": "MiTLS.HMAC.UFCMA.coerce_eq2" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.includes_as_seq" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.includes_as_seq" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.un_snoc_snoc" }, { "project_name": "everparse", "file_name": "LowParse.Endianness.fst", "name": "LowParse.Endianness.seq_rev_involutive" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.map2" }, { "project_name": "everparse", "file_name": "LowParse.Endianness.fst", "name": "LowParse.Endianness.index_seq_rev'" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fsti", "name": "FStar.Seq.Properties.split_eq" }, { "project_name": "FStar", "file_name": "FStar.Seq.Permutation.fst", "name": "FStar.Seq.Permutation.split3_index" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.PrecompBaseTable.fst", "name": "Hacl.Spec.PrecompBaseTable.seq_of_list_append_lemma" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_append_count_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fsti", "name": "FStar.Seq.Base.cons" }, { "project_name": "steel", "file_name": "Steel.ST.EphemeralHashtbl.fst", "name": "Steel.ST.EphemeralHashtbl.map_seq_index" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.HandshakeLog.fst", "name": "MiTLS.HandshakeLog.coerce" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.coerce" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.map_seq_index" }, { "project_name": "karamel", "file_name": "Spec.Loops.fst", "name": "Spec.Loops.seq_map2" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Token.UF1CMA.fsti", "name": "MiTLS.Token.UF1CMA.coerce_eq2" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.create2_lemma" } ], "selected_premises": [ "FStar.Pervasives.reveal_opaque", "FStar.Mul.op_Star", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "Prims.op_Hat", "FStar.Pervasives.pure_ite_wp", "FStar.Pervasives.trivial_pure_post", "Prims.pure_post", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "Prims.as_ensures", "Prims.pure_stronger", "FStar.Pervasives.div_hoare_to_wp", "FStar.Pervasives.st_bind_wp", "FStar.Pervasives.ex_bind_wp", "FStar.Pervasives.ex_ite_wp", "Prims.as_requires", "FStar.Pervasives.pure_bind_wp", "Prims.subtype_of", "Prims.pure_trivial", "Prims.pure_post'", "Prims.pure_wp_monotonic", "FStar.Pervasives.lift_div_exn", "FStar.Pervasives.ex_trivial", "Prims.purewp_id", "FStar.Pervasives.ex_stronger", "FStar.Pervasives.pure_close_wp", "Prims.pure_wp_monotonic0", "FStar.Pervasives.ex_return", "Prims.pure_wp'", "Prims.__cache_version_number__", "Prims.min", "FStar.Pervasives.ex_post", "FStar.Pervasives.ex_if_then_else", "FStar.Pervasives.all_if_then_else", "FStar.Pervasives.pure_return", "FStar.Pervasives.ex_pre", "FStar.Pervasives.all_ite_wp", "FStar.Pervasives.ex_post'", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.all_bind_wp", "Prims.pure_pre", "FStar.Pervasives.all_stronger", "FStar.Pervasives.st_stronger", "Prims.pure_wp", "FStar.Pervasives.all_post_h", "FStar.Pervasives.all_post_h'", "FStar.Pervasives.ex_wp", "FStar.Pervasives.st_if_then_else", "FStar.Pervasives.all_return", "FStar.Pervasives.st_ite_wp", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.st_trivial", "FStar.Pervasives.all_wp_h", "Prims.l_True", "FStar.Pervasives.all_trivial", "FStar.Pervasives.all_close_wp", "FStar.Pervasives.pure_null_wp", "Prims.pow2", "Prims.returnM", "FStar.Pervasives.st_return", "FStar.Pervasives.st_wp_h", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.st_post_h", "Prims.abs", "FStar.Pervasives.st_pre_h", "Prims.auto_squash", "Prims.l_False", "FStar.Pervasives.coerce_eq", "FStar.Pervasives.id" ], "source_upto_this": "module Vale.Def.Words.Seq_s\nopen FStar.Mul\n\n#reset-options \"--max_fuel 3 --initial_fuel 3\"", "sketch": [ "Step 1: The definition `two_to_seq_LE` is about converting a value of type `two a` into a sequence of two elements of type `a`.\nStep 2: The implementation involves creating a sequence where the first element is `x.lo` and the second element is `x.hi`.", "Step 1: The definition `two_to_seq_LE` takes a value `x` of type `two a` and returns a sequence of two elements of type `a`.\nStep 2: The implementation constructs a sequence where the first element is `x.lo` and the second element is `x.hi`. The function ensures that the sequence's first element is equal to `x.lo` and the second element is equal to `x.hi`.", "Step 1: The definition `two_to_seq_LE` is about converting a value of type `two a` into a sequence of length 2 (`seq2 a`), where the first element of the sequence corresponds to the `lo` field of the input and the second element corresponds to the `hi` field.\nStep 2: The implementation will create a sequence with two elements, where the first element is `x.lo` and the second element is `x.hi`. The function ensures that the sequence's 0th index is `x.lo` and the 1st index is `x.hi`.", "Step 1: The definition `two_to_seq_LE` is about converting a value of type `two a` into a sequence of two elements of type `a`. The sequence should be in little-endian order, meaning the lower part (`lo`) of the `two` value should be the first element in the sequence, and the higher part (`hi`) should be the second element.\nStep 2: To implement this, we will create a sequence with two elements where the first element is `x.lo` and the second element is `x.hi`. We will ensure that the sequence satisfies the required properties, i.e., the first element is equal to `x.lo` and the second element is equal to `x.hi`.", "Step 1: The definition `two_to_seq_LE` takes a value `x` of type `two a` and returns a sequence of type `seq2 a`.\nStep 2: The implementation constructs a sequence where the first element is `x.lo` and the second element is `x.hi`. The ensures clause guarantees that the sequence's first element is `x.lo` and the second element is `x.hi`.", "Step 1: The definition `two_to_seq_LE` is about converting a value of type `two a` into a sequence of length 2, where the first element of the sequence is the `lo` field of the `two` value and the second element is the `hi` field.\nStep 2: To implement this, we create a sequence with two elements, where the first element is `x.lo` and the second element is `x.hi`. We then ensure that the sequence meets the required properties by checking that the first element (index 0) is `x.lo` and the second element (index 1) is `x.hi`.", "Step 1: The definition `two_to_seq_LE` is about converting a value of type `two a` into a sequence of two elements of type `a`.\nStep 2: The implementation involves creating a sequence with two elements where the first element is `x.lo` and the second element is `x.hi`. The ensures clause guarantees that the sequence's first element is `x.lo` and the second element is `x.hi`.", "Step 1: The definition `two_to_seq_LE` takes a parameter `x` of type `two a` and returns a sequence of type `seq2 a`.\nStep 2: The implementation should ensure that the first element of the sequence is `x.lo` and the second element is `x.hi`.", "Step 1: The definition `two_to_seq_LE` is about converting a pair of elements (`two a`) into a sequence of two elements (`seq2 a`), where the first element of the sequence corresponds to the `lo` field of the pair and the second element corresponds to the `hi` field.\nStep 2: The implementation involves creating a sequence with two elements, where the first element is `x.lo` and the second element is `x.hi`. The ensures clause guarantees that the sequence's first element is equal to `x.lo` and the second element is equal to `x.hi`.", "Step 1: The definition `two_to_seq_LE` takes a value `x` of type `two a` and returns a sequence of two elements of type `a`.\nStep 2: The implementation constructs a sequence where the first element is `x.lo` and the second element is `x.hi`. The ensures clause guarantees that the sequence's first element is `x.lo` and the second element is `x.hi`." ], "generated_solution": [ "let two_to_seq_LE (#a:Type) (x:two a) : Pure (seq2 a)\n (requires True)\n (ensures fun s ->\n index s 0 == x.lo /\\\n index s 1 == x.hi\n ) =\n [x.lo; x.hi]", "let two_to_seq_LE (#a:Type) (x:two a) : Pure (seq2 a)\n (requires True)\n (ensures fun s ->\n index s 0 == x.lo /\\\n index s 1 == x.hi\n ) =\n [x.lo; x.hi]", "let two_to_seq_LE (#a:Type) (x:two a) : Pure (seq2 a)\n (requires True)\n (ensures fun s ->\n index s 0 == x.lo /\\\n index s 1 == x.hi\n ) =\n [x.lo; x.hi]", "let two_to_seq_LE (#a:Type) (x:two a) : Pure (seq2 a)\n (requires True)\n (ensures fun s ->\n index s 0 == x.lo /\\\n index s 1 == x.hi\n ) =\n [x.lo; x.hi]", "let two_to_seq_LE (#a:Type) (x:two a) : Pure (seq2 a)\n (requires True)\n (ensures fun s ->\n index s 0 == x.lo /\\\n index s 1 == x.hi\n ) =\n [x.lo; x.hi]", "let two_to_seq_LE (#a:Type) (x:two a) : Pure (seq2 a)\n (requires True)\n (ensures fun s ->\n index s 0 == x.lo /\\\n index s 1 == x.hi\n ) =\n [x.lo; x.hi]", "let two_to_seq_LE (#a:Type) (x:two a) : Pure (seq2 a)\n (requires True)\n (ensures fun s ->\n index s 0 == x.lo /\\\n index s 1 == x.hi\n ) = \n [x.lo; x.hi]", "let two_to_seq_LE (#a:Type) (x:two a) : Pure (seq2 a)\n (requires True)\n (ensures fun s ->\n index s 0 == x.lo /\\\n index s 1 == x.hi\n ) =\n [x.lo; x.hi]", "let two_to_seq_LE (#a:Type) (x:two a) : Pure (seq2 a)\n (requires True)\n (ensures fun s ->\n index s 0 == x.lo /\\\n index s 1 == x.hi\n ) =\n [x.lo; x.hi]", "let two_to_seq_LE (#a:Type) (x:two a) : Pure (seq2 a)\n (requires True)\n (ensures fun s ->\n index s 0 == x.lo /\\\n index s 1 == x.hi\n ) =\n [x.lo; x.hi]" ] }, { "file_name": "SteelSTFramingTestSuite.fst", "name": "SteelSTFramingTestSuite.test_if8", "opens_and_abbrevs": [ { "open": "Steel.ST.Util" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val test_if8 (b: bool) (r1 r2: ref)\n : STT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2))", "source_definition": "let test_if8 (b:bool) (r1 r2: ref) : STT unit\n (ptr r1 `star` ptr r2)\n (fun _ -> ptr r1 `star` ptr r2)\n = if b then (write r1 0; write r2 0) else (write r2 0);\n write r2 0", "source_range": { "start_line": 135, "start_col": 0, "end_line": 139, "end_col": 14 }, "interleaved": false, "definition": "fun b r1 r2 ->\n ((match b with\n | true ->\n SteelSTFramingTestSuite.write r1 0;\n SteelSTFramingTestSuite.write r2 0\n | _ -> SteelSTFramingTestSuite.write r2 0)\n <:\n Prims.unit;\n SteelSTFramingTestSuite.write r2 0)\n <:\n Steel.ST.Effect.STT Prims.unit", "effect": "Steel.ST.Effect.STT", "effect_flags": [], "mutual_with": [], "premises": [ "Prims.bool", "SteelSTFramingTestSuite.ref", "SteelSTFramingTestSuite.write", "Prims.unit", "Steel.Effect.Common.star", "SteelSTFramingTestSuite.ptr", "Steel.Effect.Common.vprop" ], "proof_features": [], "is_simple_lemma": false, "is_div": true, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "b: Prims.bool -> r1: SteelSTFramingTestSuite.ref -> r2: SteelSTFramingTestSuite.ref\n -> Steel.ST.Effect.STT Prims.unit", "prompt": "let test_if8 (b: bool) (r1 r2: ref)\n : STT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2)) =\n ", "expected_response": "if b\nthen\n (write r1 0;\n write r2 0)\nelse (write r2 0);\nwrite r2 0", "source": { "project_name": "steel", "file_name": "share/steel/tests/SteelSTFramingTestSuite.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "SteelSTFramingTestSuite.fst", "checked_file": "dataset/SteelSTFramingTestSuite.fst.checked", "interface_file": false, "dependencies": [ "dataset/Steel.ST.Util.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Ghost.fsti.checked" ] }, "definitions_in_context": [ "val p : vprop", "val f (x:int) : STT unit p (fun _ -> p)", "let test () : STT unit (p `star` p `star` p) (fun _ -> p `star` p `star` p)\n = f 0; ()", "val ref : Type0", "val ptr (_:ref) : vprop", "val alloc (x:int) : STT ref emp (fun y -> ptr y)", "val free (r:ref) : STT unit (ptr r) (fun _ -> emp)", "val read (r:ref) : STT int (ptr r) (fun _ -> ptr r)", "val write (r:ref) (v: int) : STT unit (ptr r) (fun _ -> ptr r)", "let test0 (b1 b2 b3: ref) : STT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b1 `star` ptr b2 `star` ptr b3)\n =\n let x = read b1 in\n x", "let test1 (b1 b2 b3: ref) : STT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b1 `star` ptr b2 `star` ptr b3)\n =\n let x = (let y = read b1 in y) in\n x", "let test2 (b1 b2 b3: ref) : STT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b3 `star` ptr b2 `star` ptr b1)\n =\n let x = read b1 in\n x", "let test3 (b1 b2 b3: ref) : STT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n x", "let test4 (b1 b2 b3: ref) : STT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n write b2 x", "let test5 (b1 b2 b3: ref) : STT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n write b2 (x + 1)", "let test6 (b1 b2 b3: ref) : STT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n let b4 = alloc x in\n write b2 (x + 1);\n free b4", "let test7 (_:unit) : STT ref emp ptr\n = let r = alloc 0 in\n let x = read r in\n write r 0;\n r", "let test8 (b1 b2 b3:ref) : STT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n = write b2 0", "let test_if1 (b:bool) : STT unit emp (fun _ -> emp)\n = if b then noop () else noop ()", "let test_if2 (b:bool) (r: ref) : STT unit (ptr r) (fun _ -> ptr r)\n = if b then write r 0 else write r 1", "let test_if3 (b:bool) (r:ref) : STT unit (ptr r) (fun _ -> ptr r)\n = if b then noop () else noop ()", "let test_if4 (b:bool) : STT unit emp (fun _ -> emp)\n = if b then (let r = alloc 0 in free r) else (noop ())", "let test_if5 (b:bool) : STT ref emp (fun r -> ptr r)\n = if b then alloc 0 else alloc 1", "let test_if6 (b:bool) : STT ref emp (fun r -> ptr r)\n = let r = if b then alloc 0 else alloc 1 in\n let x = read r in\n write r 0;\n r", "let test_if7 (b:bool) (r1 r2: ref) : STT unit\n (ptr r1 `star` ptr r2)\n (fun _ -> ptr r1 `star` ptr r2)\n = if b then (write r1 0; write r2 0) else (write r2 0; write r1 0);\n write r2 0" ], "closest": [ "val test_if8 (b: bool) (r1 r2: ref)\n : SteelT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2))\nlet test_if8 (b:bool) (r1 r2: ref) : SteelT unit\n (ptr r1 `star` ptr r2)\n (fun _ -> ptr r1 `star` ptr r2)\n = if b then (write r1 0; write r2 0) else (write r2 0);\n write r2 0", "val test_if7 (b: bool) (r1 r2: ref)\n : SteelT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2))\nlet test_if7 (b:bool) (r1 r2: ref) : SteelT unit\n (ptr r1 `star` ptr r2)\n (fun _ -> ptr r1 `star` ptr r2)\n = if b then (write r1 0; write r2 0) else (write r2 0; write r1 0);\n write r2 0", "val test_if9 (b: bool) (r1 r2: ref)\n : SteelT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2))\nlet test_if9 (b:bool) (r1 r2: ref) : SteelT unit\n (ptr r1 `star` ptr r2)\n (fun _ -> ptr r1 `star` ptr r2)\n = write r1 0;\n if b then (write r1 0) else (write r2 0);\n write r2 0;\n if b then (write r1 0) else (write r2 0);\n write r1 0", "val test_if10 (b: bool) (r1 r2 r3: ref)\n : SteelT unit\n (((ptr r1) `star` (ptr r2)) `star` (ptr r3))\n (fun _ -> ((ptr r1) `star` (ptr r2)) `star` (ptr r3))\nlet test_if10 (b:bool) (r1 r2 r3: ref) : SteelT unit\n (ptr r1 `star` ptr r2 `star` ptr r3)\n (fun _ -> ptr r1 `star` ptr r2 `star` ptr r3)\n = if b then (write r1 0; write r2 0) else (write r2 0; write r1 0);\n write r2 0", "val test_if2 (b: bool) (r: ref) : SteelT unit (ptr r) (fun _ -> ptr r)\nlet test_if2 (b:bool) (r: ref) : SteelT unit (ptr r) (fun _ -> ptr r)\n = if b then write r 0 else write r 1", "val test8 (b1 b2 b3: ref)\n : SteelT unit\n (((ptr b1) `star` (ptr b2)) `star` (ptr b3))\n (fun _ -> ((ptr b2) `star` (ptr b1)) `star` (ptr b3))\nlet test8 (b1 b2 b3:ref) : SteelT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n = write b2 0", "val test6 (r1 r2: ref) : SteelT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r2) `star` (ptr r1))\nlet test6 (r1 r2:ref) : SteelT unit (ptr r1 `star` ptr r2) (fun _ -> ptr r2 `star` ptr r1)\n = let _ = read r1 in\n ()", "val test2 (r1 r2: ref int)\n : Steel unit\n ((vptr r1) `star` (vptr r2))\n (fun _ -> (vptr r1) `star` (vptr r2))\n (requires fun h -> sel r1 h == 1)\n (ensures fun h0 _ h1 -> sel r1 h1 == 0 /\\ sel r2 h0 == sel r2 h1)\nlet test2 (r1 r2:ref int) : Steel unit\n (vptr r1 `star` vptr r2) (fun _ -> vptr r1 `star` vptr r2)\n (requires fun h -> sel r1 h == 1)\n (ensures fun h0 _ h1 -> sel r1 h1 == 0 /\\ sel r2 h0 == sel r2 h1)\n = write r1 0;\n write r1 0", "val test6 (b1 b2 b3: ref)\n : SteelT unit\n (((ptr b1) `star` (ptr b2)) `star` (ptr b3))\n (fun _ -> ((ptr b2) `star` (ptr b1)) `star` (ptr b3))\nlet test6 (b1 b2 b3: ref) : SteelT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n let b4 = alloc x in\n write b2 (x + 1);\n free b4", "val test4 (b1 b2 b3: ref)\n : SteelT unit\n (((ptr b1) `star` (ptr b2)) `star` (ptr b3))\n (fun _ -> ((ptr b2) `star` (ptr b1)) `star` (ptr b3))\nlet test4 (b1 b2 b3: ref) : SteelT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n write b2 x", "val test5 (b1 b2 b3: ref)\n : SteelT unit\n (((ptr b1) `star` (ptr b2)) `star` (ptr b3))\n (fun _ -> ((ptr b2) `star` (ptr b1)) `star` (ptr b3))\nlet test5 (b1 b2 b3: ref) : SteelT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n write b2 (x + 1)", "val test2 (b1 b2 b3: ref)\n : SteelT int\n (((ptr b1) `star` (ptr b2)) `star` (ptr b3))\n (fun _ -> ((ptr b3) `star` (ptr b2)) `star` (ptr b1))\nlet test2 (b1 b2 b3: ref) : SteelT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b3 `star` ptr b2 `star` ptr b1)\n =\n let x = read b1 in\n x", "val test1 (b1 b2 b3: ref)\n : SteelT int\n (((ptr b1) `star` (ptr b2)) `star` (ptr b3))\n (fun _ -> ((ptr b1) `star` (ptr b2)) `star` (ptr b3))\nlet test1 (b1 b2 b3: ref) : SteelT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b1 `star` ptr b2 `star` ptr b3)\n =\n let x = (let y = read b1 in y) in\n x", "val test5 (r1 r2: ref)\n : SteelT ref ((ptr r1) `star` (ptr r2)) (fun y -> ((ptr r1) `star` (ptr r2)) `star` (ptr y))\nlet test5 (r1 r2:ref) : SteelT ref (ptr r1 `star` ptr r2) (fun y -> ptr r1 `star` ptr r2 `star` ptr y)\n = let y = alloc 0 in\n y", "val test_if3 (b: bool) (r: ref) : SteelT unit (ptr r) (fun _ -> ptr r)\nlet test_if3 (b:bool) (r:ref) : SteelT unit (ptr r) (fun _ -> ptr r)\n = if b then noop () else noop ()", "val test_if6 (b: bool) : SteelT ref emp (fun r -> ptr r)\nlet test_if6 (b:bool) : SteelT ref emp (fun r -> ptr r)\n = let r = if b then alloc 0 else alloc 1 in\n let x = read r in\n write r 0;\n r", "val test0 (b1 b2 b3: ref)\n : SteelT int\n (((ptr b1) `star` (ptr b2)) `star` (ptr b3))\n (fun _ -> ((ptr b1) `star` (ptr b2)) `star` (ptr b3))\nlet test0 (b1 b2 b3: ref) : SteelT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b1 `star` ptr b2 `star` ptr b3)\n =\n let x = read b1 in\n x", "val test26 (r1 r2: ref)\n : SteelAtomicT unit Set.empty ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r2) `star` (ptr r1))\nlet test26 (r1 r2:ref) : SteelAtomicT unit Set.empty (ptr r1 `star` ptr r2) (fun _ -> ptr r2 `star` ptr r1)\n = let _ = ghost_read r1 in\n ()", "val test3 (b1 b2 b3: ref)\n : SteelT int\n (((ptr b1) `star` (ptr b2)) `star` (ptr b3))\n (fun _ -> ((ptr b2) `star` (ptr b1)) `star` (ptr b3))\nlet test3 (b1 b2 b3: ref) : SteelT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n x", "val test_if5 (b: bool) : SteelT ref emp (fun r -> ptr r)\nlet test_if5 (b:bool) : SteelT ref emp (fun r -> ptr r)\n = if b then alloc 0 else alloc 1", "val test3 (r1 r2 r3: ref int)\n : Steel unit\n ((vptr r1) `star` ((vptr r2) `star` (vptr r3)))\n (fun _ -> (vptr r1) `star` ((vptr r2) `star` (vptr r3)))\n (requires fun _ -> True)\n (ensures fun h0 _ h1 -> sel r1 h1 == 0 /\\ sel r2 h0 == sel r2 h1 /\\ sel r3 h0 == sel r3 h1)\nlet test3 (r1 r2 r3:ref int) : Steel unit\n (vptr r1 `star` (vptr r2 `star` vptr r3)) (fun _ -> vptr r1 `star` (vptr r2 `star` vptr r3))\n (requires fun _ -> True)\n (ensures fun h0 _ h1 ->\n sel r1 h1 == 0 /\\\n sel r2 h0 == sel r2 h1 /\\\n sel r3 h0 == sel r3 h1\n )\n = let x2_0 = gget (vptr r2) in\n write r1 1;\n let x1_1 = gget (vptr r1) in\n let x2_1 = gget (vptr r2) in\n assert (x1_1 == Ghost.hide 1);\n assert (x2_0 == x2_1);\n write r1 0", "val test25 (r1 r2: ref)\n : SteelAtomicT ref\n Set.empty\n ((ptr r1) `star` (ptr r2))\n (fun y -> ((ptr r1) `star` (ptr r2)) `star` (ptr y))\nlet test25 (r1 r2:ref) : SteelAtomicT ref Set.empty\n (ptr r1 `star` ptr r2) (fun y -> ptr r1 `star` ptr r2 `star` ptr y)\n = let y = alloc2 0 in\n y", "val test4 (c: ref (ref int))\n : ST unit\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures (fun h0 d h1 -> sel h1 (sel h1 c) = sel h0 (sel h0 c)))\nlet test4 (c:ref (ref int)) : ST unit\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures (fun h0 d h1 -> sel h1 (sel h1 c) = sel h0 (sel h0 c))) =\n c.[v |.. v] <- c.[v |.. v]", "val test2 (c: ref (ref int))\n : ST (ref (ref int))\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures (fun h0 d h1 -> c == d /\\ sel h1 (sel h1 c) = sel h0 (sel h0 c)))\nlet test2 (c:ref (ref int)) : ST (ref (ref int))\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures (fun h0 d h1 -> c == d /\\ sel h1 (sel h1 c) = sel h0 (sel h0 c))) =\n let i = (compose_stlens stlens_ref stlens_ref).st_get c in\n (compose_stlens stlens_ref stlens_ref).st_put i c", "val test1 (r: ref int)\n : Steel unit\n (vptr r)\n (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> sel r h1 == 0)\nlet test1 (r:ref int) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> sel r h1 == 0)\n = write r 1;\n write r 0", "val test4 (r: ref) : SteelT ref (ptr r) (fun y -> (ptr r) `star` (ptr y))\nlet test4 (r:ref) : SteelT ref (ptr r) (fun y -> ptr r `star` ptr y)\n = let y = alloc 0 in\n y", "val test_if1 (b: bool) : SteelT unit emp (fun _ -> emp)\nlet test_if1 (b:bool) : SteelT unit emp (fun _ -> emp)\n = if b then noop () else noop ()", "val test0 (r: ref int)\n : Steel unit\n (vptr r)\n (fun _ -> vptr r)\n (requires fun h -> sel r h == 0)\n (ensures fun _ _ h1 -> sel r h1 == 1)\nlet test0 (r:ref int) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun h -> sel r h == 0)\n (ensures fun _ _ h1 -> sel r h1 == 1)\n = let x = gget (vptr r) in\n assert (x == Ghost.hide 0);\n write r 1;\n let x = gget (vptr r) in\n assert (x == Ghost.hide 1);\n write r 1", "val test8 (x: ref) : SteelT int (ptr x) (fun _ -> ptr x)\nlet test8 (x:ref) : SteelT int (ptr x) (fun _ -> ptr x)\n = let v = read x in\n let y = alloc v in\n let v = read y in\n free y;\n // Can mix assertions\n assert (1 == 1);\n v", "val test2 (r: ref) : SteelT int (ptr r) (fun _ -> ptr r)\nlet test2 (r:ref) : SteelT int (ptr r) (fun _ -> ptr r) =\n let x = read r in\n x", "val swap (r1 r2: ref U32.t)\n : Steel unit\n ((vptr r1) `star` (vptr r2))\n (fun _ -> (vptr r1) `star` (vptr r2))\n (requires fun _ -> True)\n (ensures fun h0 _ h1 -> sel r1 h0 == sel r2 h1 /\\ sel r2 h0 == sel r1 h1)\nlet swap (r1 r2:ref U32.t) : Steel unit\n (vptr r1 `star` vptr r2)\n (fun _ -> vptr r1 `star` vptr r2)\n (requires fun _ -> True)\n (ensures fun h0 _ h1 ->\n sel r1 h0 == sel r2 h1 /\\\n sel r2 h0 == sel r1 h1)\n = let x1 = read r1 in\n let x2 = read r2 in\n write r2 x1;\n write r1 x2", "val test8 (l: lref) (h: href)\n : HIFC unit\n (union (single h) (single l))\n (single l)\n [(single h, single l)]\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 l == sel s0 l + 1)\nlet test8 (l:lref) (h:href)\n : HIFC unit (union (single h) (single l)) (single l) [(single h, single l)]\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 l == sel s0 l + 1)\n = let x0 = read h in\n let x = read l in\n write l (x + 1)", "val test1 (c: ref (ref int))\n : ST (ref (ref int))\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures\n (fun h0 d h1 ->\n c == d /\\ (h1, d) == (compose_hlens hlens_ref hlens_ref).put 0 (h0, c) /\\\n h1 == upd (upd h0 (sel h0 c) 0) c (sel h0 c) /\\ sel h0 c == sel h1 c /\\\n sel h1 (sel h1 c) = 0))\nlet test1 (c:ref (ref int)) : ST (ref (ref int))\n (requires (fun h -> addr_of (sel h c) <> addr_of c))\n (ensures (fun h0 d h1 ->\n c == d /\\\n (h1, d) == (compose_hlens hlens_ref hlens_ref).put 0 (h0, c) /\\\n h1 == upd (upd h0 (sel h0 c) 0) c (sel h0 c) /\\\n sel h0 c == sel h1 c /\\ sel h1 (sel h1 c) = 0)) =\n (compose_stlens stlens_ref stlens_ref).st_put 0 c", "val swap (#a: Type0) (r1 r2: ref a)\n : Steel unit\n ((vptr r1) `star` (vptr r2))\n (fun _ -> (vptr r1) `star` (vptr r2))\n (requires fun _ -> True)\n (ensures fun h0 _ h1 -> sel r1 h0 == sel r2 h1 /\\ sel r2 h0 == sel r1 h1)\nlet swap (#a:Type0) (r1 r2:ref a) : Steel unit\n (vptr r1 `star` vptr r2)\n (fun _ -> vptr r1 `star` vptr r2)\n (requires fun _ -> True)\n (ensures fun h0 _ h1 ->\n sel r1 h0 == sel r2 h1 /\\\n sel r2 h0 == sel r1 h1)\n = let x1 = read r1 in\n let x2 = read r2 in\n write r2 x1;\n write r1 x2", "val test0 (c: ref (ref int))\n : ST int\n (requires (fun h -> True))\n (ensures (fun h0 i h1 -> h0 == h1 /\\ i == sel h1 (sel h1 c)))\nlet test0 (c:ref (ref int)) : ST int\n (requires (fun h -> True))\n (ensures (fun h0 i h1 -> h0 == h1 /\\ i == sel h1 (sel h1 c)))\n = (compose_stlens stlens_ref stlens_ref).st_get c", "val test4 (r: ref nat) : SteelT unit (vptr r) (fun _ -> vptr r)\nlet test4 (r: ref nat) : SteelT unit (vptr r) (fun _ -> vptr r) =\n share r;\n gather r", "val test_if4 (b: bool) : SteelT unit emp (fun _ -> emp)\nlet test_if4 (b:bool) : SteelT unit emp (fun _ -> emp)\n = if b then (let r = alloc 0 in free r) else (noop ())", "val test15 (l: lref)\n : HIFC unit\n (single l)\n (single l)\n []\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s0 l == sel s1 l)\nlet test15 (l:lref)\n : HIFC unit (single l) (single l) []\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s0 l == sel s1 l)\n = write l (read l)", "val swap_selector (#a: Type0) (r1 r2: ref a)\n : Steel unit\n ((vptr r1) `star` (vptr r2))\n (fun _ -> (vptr r1) `star` (vptr r2))\n (requires fun _ -> True)\n (ensures fun h0 _ h1 -> sel r1 h0 == sel r2 h1 /\\ sel r2 h0 == sel r1 h1)\nlet swap_selector (#a:Type0) (r1 r2:ref a) : Steel unit\n (vptr r1 `star` vptr r2)\n (fun _ -> vptr r1 `star` vptr r2)\n (requires fun _ -> True)\n (ensures fun h0 _ h1 ->\n sel r1 h0 == sel r2 h1 /\\\n sel r2 h0 == sel r1 h1)\n = let x1 = read r1 in\n let x2 = read r2 in\n write r2 x1;\n write r1 x2", "val copy_ref (r: ref U32.t)\n : Steel (ref U32.t)\n (vptr r)\n (fun r' -> (vptr r) `star` (vptr r'))\n (requires fun _ -> True)\n (ensures fun h0 r' h1 -> sel r h0 == sel r h1 /\\ sel r' h1 == sel r h1)\nlet copy_ref (r:ref U32.t) : Steel (ref U32.t)\n (vptr r)\n // We allocated a new reference r', which is the return value\n (fun r' -> vptr r `star` vptr r')\n (requires fun _ -> True)\n (ensures fun h0 r' h1 ->\n // reference r was not modified\n sel r h0 == sel r h1 /\\\n // After copying, reference r' contains the same value as reference r\n sel r' h1 == sel r h1)\n\n = let x = read r in\n let r' = malloc x in\n r'", "val intro_llist_cons (#a:Type0) (ptr1 ptr2:t a) (r:ref a)\n : Steel unit (vptr ptr1 `star` vptr r `star` llist_ptr ptr2)\n (fun _ -> llist_ptr ptr1)\n (requires fun h -> data (sel ptr1 h) == r /\\ next (sel ptr1 h) == ptr2)\n (ensures fun h0 _ h1 -> v_ptrlist ptr1 h1 == (sel r h0) :: v_ptrlist ptr2 h0)\nlet intro_llist_cons (#a:Type0) (ptr1 ptr2:t a) (r:ref a)\n : Steel unit (vptr ptr1 `star` vptr r `star` llist_ptr ptr2)\n (fun _ -> llist_ptr ptr1)\n (requires fun h -> data (sel ptr1 h) == r /\\ next (sel ptr1 h) == ptr2)\n (ensures fun h0 _ h1 -> v_ptrlist ptr1 h1 == (sel r h0) :: v_ptrlist ptr2 h0)\n = let x = gget (vptr ptr1) in\n let v = gget (vptr r) in\n let l = gget (llist_ptr ptr2) in\n change_slprop (vptr ptr1 `star` llist_ptr ptr2 `star` vptr r) (llist_ptr ptr1)\n ((reveal x, reveal l), reveal v)\n (reveal v :: l)\n (fun m ->\n intro_cons_lemma ptr1 x v l m)", "val core_ref_is_null (r:core_ref) : b:bool { b <==> r == core_ref_null }\nlet core_ref_is_null r = H.core_ref_is_null r", "val core_ref_is_null (r:core_ref) : b:bool { b <==> r == core_ref_null }\nlet core_ref_is_null (r:core_ref) = Null? r", "val core_ref_is_null (r:core_ref) : b:bool { b <==> r == core_ref_null }\nlet core_ref_is_null (r:core_ref) = Null? r", "val core_ref_is_null (r:core_ref) : b:bool { b <==> r == core_ref_null }\nlet core_ref_is_null r = H.core_ref_is_null r", "val test (x:B.pointer int)\n : stl unit 1 (loc_buf x) (fun _ -> loc_buf x)\n (fun h ->\n B.live h x /\\\n B.get h x 0 > 17)\n (fun h0 _ h1 ->\n B.live h1 x /\\\n B.get h1 x 0 >\n B.get h0 x 0)\nlet test x hinit fresh =\n let v = B.index fresh 0ul in\n let y = B.index x 0ul in\n B.upd x 0ul (y + y)", "val test3 (r: ref) : SteelT int (ptr r) (fun _ -> ptr r)\nlet test3 (r:ref) : SteelT int (ptr r) (fun _ -> ptr r)\n = let x = read r in\n let y = read r in\n x", "val test7 (l: lref) (h: href)\n : HIFC unit\n (single h)\n (single l)\n [high, low]\n (requires fun _ -> True)\n (ensures fun s0 r s1 -> sel s1 l == sel s0 h)\nlet test7 (l:lref) (h:href)\n : HIFC unit (single h) (single l) [high, low]\n (requires fun _ -> True)\n (ensures fun s0 r s1 -> sel s1 l == sel s0 h)\n = let x = read h in\n write l x", "val test2 (l: lref) (h: href)\n : HIFC unit\n (single l)\n (single h)\n [single l, single h]\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 h == sel s0 l)\nlet test2 (l:lref) (h:href)\n : HIFC unit (single l)\n (single h)\n [single l, single h]\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 h == sel s0 l)\n = let x = read l in\n write h x", "val va_if (#a: Type) (b: bool) (x: (_: unit{b} -> GTot a)) (y: (_: unit{~b} -> GTot a)) : GTot a\nlet va_if (#a:Type) (b:bool) (x:(_:unit{b}) -> GTot a) (y:(_:unit{~b}) -> GTot a) : GTot a =\n if b then x () else y ()", "val test9 (l: lref) (h: href)\n : HIFC unit\n (union (single h) (single l))\n (single l)\n [((single l) `union` (single h), single l)]\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 l == sel s0 l)\nlet test9 (l:lref) (h:href)\n : HIFC unit (union (single h) (single l)) (single l)\n [(single l `union` single h, single l)]\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 l == sel s0 l)\n = let x= (let x0 = read h in\n read l)\n in\n write l x", "val read : #a:Type -> \n r:ref a -> \n\t AllocST a (fun _ -> True) \n (fun h0 x h1 -> h0 == h1 /\\ \n\t\t x == FStar.Heap.sel h1 r)\nlet read #a r = \n let h = ist_get () in\n sel h r", "val test24 (r: ref) : SteelAtomicT ref Set.empty (ptr r) (fun y -> (ptr r) `star` (ptr y))\nlet test24 (r:ref) : SteelAtomicT ref Set.empty (ptr r) (fun y -> ptr r `star` ptr y)\n = let y = alloc2 0 in\n y", "val r_if\n (b b': exp bool)\n (c c' d d' : computation)\n (p p' : gexp bool)\n: Lemma\n (requires (\n exec_equiv\n (r_if_precond_true b b' c c' d d' p p')\n p'\n c\n c' /\\\n exec_equiv\n (r_if_precond_false b b' c c' d d' p p')\n p'\n d\n d'\n ))\n (ensures (\n exec_equiv\n (r_if_precond b b' c c' d d' p p')\n p'\n (ifthenelse b c d)\n (ifthenelse b' c' d')\n ))\nlet r_if\n (b b': exp bool)\n (c c' d d' : computation)\n (p p' : gexp bool)\n: Lemma\n (requires (\n exec_equiv\n (r_if_precond_true b b' c c' d d' p p')\n p'\n c\n c' /\\\n exec_equiv\n (r_if_precond_false b b' c c' d d' p p')\n p'\n d\n d'\n ))\n (ensures (\n exec_equiv\n (r_if_precond b b' c c' d d' p p')\n p'\n (ifthenelse b c d)\n (ifthenelse b' c' d')\n ))\n= holds_r_if_precond_true b b' c c' d d' p p';\n holds_r_if_precond_false b b' c c' d d' p p';\n holds_r_if_precond b b' c c' d d' p p'", "val test1 (r: ref int) (x y: int) : EFF int [EXN; WR]\nlet test1 (r:ref int) (x y : int) : EFF int [EXN; WR] =\n let z = !r in\n if x + z > 0\n then raise (Failure \"nope\")\n else (r := 42; y - z)", "val vptr_not_null (#opened: _) (#a: Type) (r: ref a)\n : SteelGhost unit\n opened\n (vptr r)\n (fun _ -> vptr r)\n (fun _ -> True)\n (fun h0 _ h1 -> sel r h0 == sel r h1 /\\ is_null r == false)\nlet vptr_not_null (#opened: _)\n (#a: Type)\n (r: ref a)\n: SteelGhost unit opened\n (vptr r)\n (fun _ -> vptr r)\n (fun _ -> True)\n (fun h0 _ h1 ->\n sel r h0 == sel r h1 /\\\n is_null r == false\n )\n= vptrp_not_null r full_perm", "val vptr_not_null (#opened: _) (#a: Type) (r: ref a)\n : SteelGhost unit\n opened\n (vptr r)\n (fun _ -> vptr r)\n (fun _ -> True)\n (fun h0 _ h1 -> sel r h0 == sel r h1 /\\ is_null r == false)\nlet vptr_not_null (#opened: _)\n (#a: Type)\n (r: ref a)\n: SteelGhost unit opened\n (vptr r)\n (fun _ -> vptr r)\n (fun _ -> True)\n (fun h0 _ h1 ->\n sel r h0 == sel r h1 /\\\n is_null r == false\n )\n= vptrp_not_null r full_perm", "val test23 (r: ref) : SteelGhostT (erased int) Set.empty (ptr r) (fun _ -> ptr r)\nlet test23 (r:ref) : SteelGhostT (erased int) Set.empty (ptr r) (fun _ -> ptr r)\n = let x = ghost_read r in\n let y = ghost_read r in\n x", "val is_null (#a:Type) (r:ref a)\n : b:bool{b <==> r == null}\nlet is_null (#a:Type) (r:ref a)\n : b:bool{b <==> r == null}\n = R.is_null r", "val read : #a:Type -> \n r:ref a -> \n\t AllocST a (fun h0 -> True) \n (fun h0 x h1 -> h0 == h1 /\\ \n\t\t contains r h1 /\\ \n\t\t\t\t sel h1 r == x)\nlet read #a r =\n let h = ist_get () in\n ist_recall (contains r); //recalling that the current heap must contain the given reference\n sel h r", "val test7 (a: unit) : SteelT ref emp (fun y -> ptr y)\nlet test7 (a:unit) : SteelT ref emp (fun y -> ptr y) =\n let x = alloc 0 in\n let v = read x in\n x", "val test4 (l: lref) (h: href) (x: int)\n : HIFC int\n (single h)\n (single l)\n [single h, bot]\n (requires fun _ -> True)\n (ensures fun s0 r s1 -> sel s1 l == x /\\ r == sel s1 h)\nlet test4 (l:lref) (h:href) (x:int)\n : HIFC int (single h) (single l) [single h, bot]\n (requires fun _ -> True)\n (ensures fun s0 r s1 -> sel s1 l == x /\\ r == sel s1 h)\n = write l x;\n read h", "val copy_ref (#a: Type0) (r: ref a)\n : Steel (ref a)\n (vptr r)\n (fun r' -> (vptr r) `star` (vptr r'))\n (requires fun _ -> True)\n (ensures fun h0 r' h1 -> sel r h0 == sel r h1 /\\ sel r' h1 == sel r h1)\nlet copy_ref (#a:Type0) (r:ref a) : Steel (ref a)\n (vptr r)\n // We allocated a new reference r', which is the return value\n (fun r' -> vptr r `star` vptr r')\n (requires fun _ -> True)\n (ensures fun h0 r' h1 ->\n // reference r was not modified\n sel r h0 == sel r h1 /\\\n // After copying, reference r' contains the same value as reference r\n sel r' h1 == sel r h1)\n\n = let x = read r in\n let r' = malloc x in\n r'", "val test (l: lref) (h: href)\n : HIFC unit\n (union (single l) bot)\n (union bot (single h))\n (add_source (single l) [bot, single h])\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 h == sel s0 l)\nlet test (l:lref) (h:href)\n : HIFC unit (union (single l) bot)\n (union bot (single h))\n (add_source (single l) [bot, single h])\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 h == sel s0 l)\n = let x = read l in\n write h x", "val is_null (#a:Type0) (r:ref a)\n : b:bool{b <==> r == null}\nlet is_null (#a:Type0) (r:ref a)\n : b:bool{b <==> r == null}\n = R.is_null r", "val swap (#v1 #v2: Ghost.erased U32.t) (r1 r2: ref (scalar U32.t))\n : STT unit\n ((r1 `pts_to` (mk_scalar (Ghost.reveal v1)))\n `star`\n (r2 `pts_to` (mk_scalar (Ghost.reveal v2))))\n (fun _ ->\n (r1 `pts_to` (mk_scalar (Ghost.reveal v2)))\n `star`\n (r2 `pts_to` (mk_scalar (Ghost.reveal v1))))\nlet swap (#v1 #v2: Ghost.erased U32.t) (r1 r2: ref (scalar U32.t)) : STT unit\n ((r1 `pts_to` mk_scalar (Ghost.reveal v1)) `star` (r2 `pts_to` mk_scalar (Ghost.reveal v2)))\n (fun _ -> (r1 `pts_to` mk_scalar (Ghost.reveal v2)) `star` (r2 `pts_to` mk_scalar (Ghost.reveal v1)))\n= let x1 = read r1 in\n let x2 = read r2 in\n write r1 x2;\n write r2 x1;\n return ()", "val swap (#v1 #v2: Ghost.erased U32.t) (r1 r2: ref (scalar U32.t))\n : STT unit\n ((r1 `pts_to` (mk_scalar (Ghost.reveal v1)))\n `star`\n (r2 `pts_to` (mk_scalar (Ghost.reveal v2))))\n (fun _ ->\n (r1 `pts_to` (mk_scalar (Ghost.reveal v2)))\n `star`\n (r2 `pts_to` (mk_scalar (Ghost.reveal v1))))\nlet swap (#v1 #v2: Ghost.erased U32.t) (r1 r2: ref (scalar U32.t)) : STT unit\n ((r1 `pts_to` mk_scalar (Ghost.reveal v1)) `star` (r2 `pts_to` mk_scalar (Ghost.reveal v2)))\n (fun _ -> (r1 `pts_to` mk_scalar (Ghost.reveal v2)) `star` (r2 `pts_to` mk_scalar (Ghost.reveal v1)))\n= let x1 = read r1 in\n let x2 = read r2 in\n write r1 x2;\n write r2 x1;\n return ()", "val test9 (l: lref) (h: href)\n : IST unit (single l) (union (single h) (single l)) [((single l) `union` (single h), single l)]\nlet test9 (l:lref) (h:href)\n : IST unit (single l)\n (union (single h) (single l))\n [(single l `union` single h, single l)]\n = let x= (let x0 = read h in\n read l)\n in\n write l x", "val test9 (l: lref) (h: href)\n : IST unit (single l) (union (single h) (single l)) [((single l) `union` (single h), single l)]\nlet test9 (l:lref) (h:href)\n : IST unit (single l)\n (union (single h) (single l))\n [(single l `union` single h, single l)]\n = let x= (let x0 = read h in\n read l)\n in\n write l x", "val read : #a:Type -> \n r:ref a -> \n\t ImmutableST a (fun _ -> True) \n (fun h0 x h1 -> h0 == h1 /\\ \n\t\t\t\t\t x == sel h1 r)\nlet read #a r = \n let h = ist_get () in\n sel h r", "val test1 (r1: rid) (r2: rid{includes r1 r2}) : unit\nlet test1 (r1:rid) (r2:rid{includes r1 r2}) :unit = assert (includes r1 (hide ((0, 0, false)::(Ghost.reveal r2))))", "val h (b: bool)\n : IEXN unit\n ((FStar.GSet.union (FStar.GSet.singleton exception1) ((FStar.GSet.singleton exception2))) ><\n (fun p -> forall r. p r))\nlet h (b:bool) : IEXN unit ((FStar.GSet.union (FStar.GSet.singleton exception1) ((FStar.GSet.singleton exception2))) \n >< \n (fun p -> forall r . p r))\n = if b then () else raise #_ #(FStar.GSet.singleton exception2) exception2", "val refine_test8: l: lref -> h: href -> unit\n -> HIFC unit\n (union (single h) (single l))\n (single l)\n []\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 l == sel s0 l + 1)\nlet refine_test8 (l:lref) (h:href)\n : unit -> HIFC unit (union (single h) (single l)) (single l) []\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 l == sel s0 l + 1)\n = refine_flow (fun () -> test8 l h)", "val use_test (x: B.pointer int)\n : ST unit\n (requires fun h -> B.live h x /\\ B.get h x 0 > 17)\n (ensures\n fun h0 _ h1 ->\n B.live h1 x /\\ B.get h1 x 0 > B.get h0 x 0 /\\ B.modifies (B.loc_buffer x) h0 h1)\nlet use_test (x:B.pointer int)\n : ST unit\n (requires fun h ->\n B.live h x /\\\n B.get h x 0 > 17)\n (ensures fun h0 _ h1 ->\n B.live h1 x /\\\n B.get h1 x 0 > B.get h0 x 0 /\\\n B.modifies (B.loc_buffer x) h0 h1)\n = with_local 1 (test x)", "val intro_llist_cons (#a:Type0) (ptr1 ptr2:t a)\n : Steel unit (vptr ptr1 `star` llist ptr2)\n (fun _ -> llist ptr1)\n (requires fun h -> next (sel ptr1 h) == ptr2)\n (ensures fun h0 _ h1 -> v_llist ptr1 h1 == (data (sel ptr1 h0)) :: v_llist ptr2 h0)\nlet intro_llist_cons\n #a ptr1 ptr2\n=\n llist0_of_llist ptr2;\n let n = nllist_of_llist0 ptr2 in\n (* set the fuel of the new cons cell *)\n let c = read ptr1 in\n let c' = {c with tail_fuel = n} in\n write ptr1 c' ;\n (* actually cons the cell *)\n vptr_not_null ptr1;\n intro_vdep\n (vptr ptr1)\n (nllist a n ptr2)\n (llist_vdep ptr1);\n intro_vrewrite\n (vptr ptr1 `vdep` llist_vdep ptr1)\n (llist_vrewrite ptr1);\n change_equal_slprop\n ((vptr ptr1 `vdep` llist_vdep ptr1) `vrewrite` llist_vrewrite ptr1)\n (llist0 ptr1);\n llist_of_llist0 ptr1", "val intro_llist_cons (#a:Type0) (ptr1 ptr2:t a)\n : Steel unit (vptr ptr1 `star` llist ptr2)\n (fun _ -> llist ptr1)\n (requires fun h -> next (sel ptr1 h) == ptr2)\n (ensures fun h0 _ h1 -> v_llist ptr1 h1 == (data (sel ptr1 h0)) :: v_llist ptr2 h0)\nlet intro_llist_cons\n #a ptr1 ptr2\n=\n llist0_of_llist ptr2;\n let n = nllist_of_llist0 ptr2 in\n (* set the fuel of the new cons cell *)\n let c = read ptr1 in\n let c' = {c with tail_fuel = n} in\n write ptr1 c' ;\n (* actually cons the cell *)\n vptr_not_null ptr1;\n intro_vdep\n (vptr ptr1)\n (nllist a n ptr2)\n (llist_vdep ptr1);\n intro_vrewrite\n (vptr ptr1 `vdep` llist_vdep ptr1)\n (llist_vrewrite ptr1);\n change_equal_slprop\n ((vptr ptr1 `vdep` llist_vdep ptr1) `vrewrite` llist_vrewrite ptr1)\n (llist0 ptr1);\n llist_of_llist0 ptr1", "val intro_llist_cons (#a:Type0) (ptr1 ptr2:t a)\n : Steel unit (vptr ptr1 `star` llist ptr2)\n (fun _ -> llist ptr1)\n (requires fun h -> next (sel ptr1 h) == ptr2)\n (ensures fun h0 _ h1 -> v_llist ptr1 h1 == (data (sel ptr1 h0)) :: v_llist ptr2 h0)\nlet intro_llist_cons ptr1 ptr2 =\n let h = get () in\n let x = hide (sel ptr1 h) in\n let l = hide (v_llist ptr2 h) in\n reveal_star (vptr ptr1) (llist ptr2);\n change_slprop (vptr ptr1 `star` llist ptr2) (llist ptr1) (reveal x, reveal l) (data x :: l) (fun m -> intro_cons_lemma ptr1 ptr2 x l m)", "val alloc (#a:eqtype) (#b:a -> Type) (#inv:DM.t a (opt b) -> Type) (#r:HST.erid)\n (_:unit{inv (repr empty)})\n : ST (t r a b inv)\n (requires (fun h -> HyperStack.ST.witnessed (region_contains_pred r)))\n (ensures (fun h0 x h1 ->\n ralloc_post r empty h0 x h1))\nlet alloc #a #b #inv #r _ = ralloc r []", "val as_ptr (#t #b: _) (r: repr_pos t b)\n : Stack (repr_ptr t)\n (requires fun h -> valid_repr_pos r h)\n (ensures fun h0 ptr h1 -> ptr == as_ptr_spec r /\\ h0 == h1)\nlet as_ptr #t #b (r:repr_pos t b)\n : Stack (repr_ptr t)\n (requires fun h ->\n valid_repr_pos r h)\n (ensures fun h0 ptr h1 ->\n ptr == as_ptr_spec r /\\\n h0 == h1)\n = let b = C.sub b.base r.start_pos (Ghost.hide r.meta.len) in\n let m = r.meta in\n let v = r.vv_pos in\n let l = r.length in\n Ptr b m v l", "val is_null (#a:Type u#1) (r:ref a) : (b:bool{b <==> r == null})\nlet is_null #a r = Mem.is_null #(fractional a) #pcm_frac r", "val owrite (#a: typ) (b: pointer a) (z: otype_of_typ a)\n : HST.Stack unit\n (requires (fun h -> live h b))\n (ensures\n (fun h0 _ h1 ->\n live h0 b /\\ live h1 b /\\ modifies_1 b h0 h1 /\\\n (let g = greference_of b in\n let (| _ , c1 |) = HS.sel h1 g in\n path_sel c1 (Pointer?.p b) == z)))\nlet owrite\n (#a: typ)\n (b: pointer a)\n (z: otype_of_typ a)\n: HST.Stack unit\n (requires (fun h -> live h b))\n (ensures (fun h0 _ h1 ->\n live h0 b /\\\n live h1 b /\\\n modifies_1 b h0 h1 /\\ (\n let g = greference_of b in\n let (| _, c1 |) = HS.sel h1 g in\n path_sel c1 (Pointer?.p b) == z\n )))\n= let h0 = HST.get () in\n let r = reference_of h0 b in\n HST.witness_region (HS.frameOf r);\n HST.witness_hsref r;\n let v0 = !r in\n let (| t , c0 |) = v0 in\n let c1 = path_upd c0 (Pointer?.p b) z in\n let v1 = (| t, c1 |) in\n r := v1;\n let h1 = HST.get () in\n let e () : Lemma (\n let gref = greference_of b in (\n HS.frameOf r == HS.frameOf gref /\\\n HS.as_addr r == HS.as_addr gref /\\\n HS.sel h0 gref == v0 /\\\n HS.sel h1 gref == v1\n ))\n = let gref = greference_of b in\n HS.lemma_sel_same_addr h0 r gref;\n HS.lemma_sel_same_addr h1 r gref\n in\n e ();\n let prf_alocs\n (r': HS.rid)\n (a': nat)\n (b' : aloc r' a')\n : Lemma\n (requires (MG.loc_disjoint (MG.loc_of_aloc b') (loc_pointer b)))\n (ensures (cls.MG.aloc_preserved b' h0 h1))\n =\n let f\n (t: typ)\n (p: pointer t)\n : Lemma\n (requires (\n live h0 p /\\\n disjoint b p\n ))\n (ensures (\n equal_values h0 p h1 p\n ))\n = let grefp = greference_of p in\n if frameOf p = frameOf b && as_addr p = as_addr b\n then begin\n HS.lemma_sel_same_addr h0 r grefp;\n HS.lemma_sel_same_addr h1 r grefp;\n path_sel_upd_other' (Pointer?.p b) c0 z (Pointer?.p p)\n end\n else ()\n in\n let f'\n (t: typ)\n (p: pointer t)\n : Lemma\n ( (\n live h0 p /\\\n disjoint b p\n ) ==> (\n equal_values h0 p h1 p\n ))\n = Classical.move_requires (f t) p\n in\n MG.loc_disjoint_aloc_elim #_ #cls #r' #a' #(frameOf b) #(as_addr b) b' (LocPointer b);\n Classical.forall_intro_2 f'\n in\n MG.modifies_intro (loc_pointer b) h0 h1\n (fun _ -> ())\n (fun t' pre' p' ->\n loc_disjoint_sym (MG.loc_mreference p') (loc_pointer b);\n MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (LocPointer b) true (HS.frameOf p') (Set.singleton (HS.as_addr p'))\n )\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n prf_alocs", "val read (#a: Type0) (r: ref a)\n : Steel a\n (vptr r)\n (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun h0 x h1 -> sel r h0 == sel r h1 /\\ x == sel r h1)\nlet read (#a:Type0) (r:ref a) : Steel a\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun h0 x h1 -> sel r h0 == sel r h1 /\\ x == sel r h1)\n= readp r full_perm", "val read (#a: Type0) (r: ref a)\n : Steel a\n (vptr r)\n (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun h0 x h1 -> sel r h0 == sel r h1 /\\ x == sel r h1)\nlet read (#a:Type0) (r:ref a) : Steel a\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun h0 x h1 -> sel r h0 == sel r h1 /\\ x == sel r h1)\n= readp r full_perm", "val ( ^+^ ) (#a #b: Type) (r1: ref a) (r2: ref b) : Tot (set nat)\nlet op_Hat_Plus_Hat (#a:Type) (#b:Type) (r1:ref a) (r2:ref b) : Tot (set nat) =\n union (only r1) (only r2)", "val guard (b: bool)\n : TacH unit\n (requires (fun _ -> True))\n (ensures (fun ps r -> if b then Success? r /\\ Success?.ps r == ps else Failed? r))\nlet guard (b : bool) : TacH unit (requires (fun _ -> True))\n (ensures (fun ps r -> if b\n then Success? r /\\ Success?.ps r == ps\n else Failed? r))\n (* ^ the proofstate on failure is not exactly equal (has the psc set) *)\n =\n if not b then\n fail \"guard failed\"\n else ()", "val guard (b: bool)\n : TacH unit\n (requires (fun _ -> True))\n (ensures (fun ps r -> if b then Success? r /\\ Success?.ps r == ps else Failed? r))\nlet guard (b : bool) : TacH unit (requires (fun _ -> True))\n (ensures (fun ps r -> if b\n then Success? r /\\ Success?.ps r == ps\n else Failed? r))\n (* ^ the proofstate on failure is not exactly equal (has the psc set) *)\n =\n if not b then\n fail \"guard failed\"\n else ()", "val test8 (l: list int) : HoareST int (fun _ -> Cons? l /\\ Cons?.hd l > 0) (fun _ _ _ -> True)\nlet test8 (l:list int)\n: HoareST int (fun _ -> Cons? l /\\ Cons?.hd l > 0) (fun _ _ _ -> True)\n= match l with\n | hd::_ -> test7 hd", "val test (m: UInt64.t) (l: UInt32.t) (#r #s: _) (x: LB.mbuffer bool r s {LB.len x = l})\n : Stack unit (requires (fun h0 -> LB.live h0 x)) (ensures (fun h0 _ h1 -> h0 == h1))\nlet test (m:UInt64.t) (l:UInt32.t) (#r:_) (#s:_) (x:LB.mbuffer bool r s{LB.len x = l})\n : Stack unit\n (requires (fun h0 -> LB.live h0 x))\n (ensures (fun h0 _ h1 -> h0 == h1))\n = printf \"Hello %b Low* %uL Printf %xb %s\"\n true //%b boolean\n m //%uL u64\n l x //%xb (buffer bool)\n \"bye\"\n done", "val write (#a:Type0) (r:ref a) (x:a) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> x == sel r h1)\nlet write r x =\n let _ = elim_vptr r _ in\n write_pt r x;\n intro_vptr r _ x", "val write (#a:Type0) (r:ref a) (x:a) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> x == sel r h1)\nlet write\n r x\n= elim_vptrp r full_perm;\n A.upd r 0sz x;\n intro_vptrp' r full_perm", "val eq_st_term (t1 t2:st_term) \n : b:bool { b <==> (t1 == t2) }\nlet rec eq_st_term (t1 t2:st_term) \n : b:bool { b <==> (t1 == t2) }\n = match t1.term, t2.term with\n | Tm_Return {expected_type=ty1; insert_eq=b1; term=t1}, \n Tm_Return {expected_type=ty2; insert_eq=b2; term=t2} ->\n eq_tm ty1 ty2 &&\n b1 = b2 &&\n eq_tm t1 t2\n\n | Tm_Abs { b=b1; q=o1; ascription=c1; body=t1 },\n Tm_Abs { b=b2; q=o2; ascription=c2; body=t2 } ->\n eq_tm b1.binder_ty b2.binder_ty &&\n o1=o2 &&\n eq_ascription c1 c2 &&\n eq_st_term t1 t2\n \n | Tm_STApp { head=h1; arg_qual=o1; arg=t1},\n Tm_STApp { head=h2; arg_qual=o2; arg=t2} ->\n eq_tm h1 h2 &&\n o1=o2 &&\n eq_tm t1 t2\n\n | Tm_Bind { binder=b1; head=t1; body=k1 },\n Tm_Bind { binder=b2; head=t2; body=k2 } ->\n eq_tm b1.binder_ty b2.binder_ty &&\n eq_st_term t1 t2 &&\n eq_st_term k1 k2\n\n | Tm_TotBind { binder=b1; head=t1; body=k1 },\n Tm_TotBind { binder=b2; head=t2; body=k2 } ->\n eq_tm b1.binder_ty b2.binder_ty &&\n eq_tm t1 t2 &&\n eq_st_term k1 k2\n \n | Tm_IntroPure { p=p1 }, Tm_IntroPure { p=p2 } ->\n eq_tm p1 p2\n\n | Tm_IntroExists { p=p1; witnesses=l1 },\n Tm_IntroExists { p=p2; witnesses=l2 } ->\n eq_tm p1 p2 &&\n eq_tm_list l1 l2\n\n | Tm_ElimExists {p=p1},\n Tm_ElimExists {p=p2} ->\n eq_tm p1 p2\n\n | Tm_If { b=g1; then_=ethen1; else_=eelse1; post=p1},\n Tm_If { b=g2; then_=ethen2; else_=eelse2; post=p2} ->\n eq_tm g1 g2 &&\n eq_st_term ethen1 ethen2 &&\n eq_st_term eelse1 eelse2 &&\n eq_tm_opt p1 p2\n \n | Tm_Match {sc=sc1; returns_=r1; brs=br1},\n Tm_Match {sc=sc2; returns_=r2; brs=br2} ->\n eq_tm sc1 sc2 &&\n eq_tm_opt r1 r2 &&\n eq_list_dec t1 t2 eq_branch br1 br2\n\n | Tm_While { invariant=inv1; condition=cond1; body=body1 },\n Tm_While { invariant=inv2; condition=cond2; body=body2 } ->\n eq_tm inv1 inv2 &&\n eq_st_term cond1 cond2 &&\n eq_st_term body1 body2\n\n | Tm_Par {pre1=preL1; body1=eL1; post1=postL1; pre2=preR1; body2=eR1; post2=postR1 },\n Tm_Par {pre1=preL2; body1=eL2; post1=postL2; pre2=preR2; body2=eR2; post2=postR2 } ->\n eq_tm preL1 preL2 &&\n eq_st_term eL1 eL2 &&\n eq_tm postL1 postL2 &&\n eq_tm preR1 preR2 &&\n eq_st_term eR1 eR2 &&\n eq_tm postR1 postR2\n\n | Tm_WithLocal { binder=x1; initializer=e1; body=b1 },\n Tm_WithLocal { binder=x2; initializer=e2; body=b2 } ->\n eq_tm x1.binder_ty x2.binder_ty &&\n eq_tm e1 e2 &&\n eq_st_term b1 b2\n\n | Tm_WithLocalArray { binder=x1; initializer=e1; length=n1; body=b1 },\n Tm_WithLocalArray { binder=x2; initializer=e2; length=n2; body=b2 } ->\n eq_tm x1.binder_ty x2.binder_ty &&\n eq_tm e1 e2 &&\n eq_tm n1 n2 &&\n eq_st_term b1 b2\n\n | Tm_Rewrite { t1=l1; t2=r1 },\n Tm_Rewrite { t1=l2; t2=r2 } ->\n eq_tm l1 l2 &&\n eq_tm r1 r2\n\n | Tm_Admit { ctag=c1; u=u1; typ=t1; post=post1 }, \n Tm_Admit { ctag=c2; u=u2; typ=t2; post=post2 } ->\n c1 = c2 &&\n eq_univ u1 u2 &&\n eq_tm t1 t2 &&\n eq_tm_opt post1 post2\n \n | Tm_Unreachable, Tm_Unreachable -> true\n \n | Tm_ProofHintWithBinders { hint_type=ht1; binders=bs1; t=t1 },\n Tm_ProofHintWithBinders { hint_type=ht2; binders=bs2; t=t2 } ->\n eq_hint_type ht1 ht2 &&\n eq_list eq_binder bs1 bs2 &&\n eq_st_term t1 t2\n\n | Tm_WithInv {name=name1; returns_inv=r1; body=body1},\n Tm_WithInv {name=name2; returns_inv=r2; body=body2} ->\n eq_tm name1 name2 &&\n eq_opt (fun (b1, r1) (b2, r2) -> eq_tm b1.binder_ty b2.binder_ty && eq_tm r1 r2)\n r1 r2 &&\n eq_st_term body1 body2\n\n | _ -> false\n\nand eq_branch (b1 b2 : pattern & st_term)\n : b:bool{b <==> (b1 == b2)}\n = let (p1, e1) = b1 in\n let (p2, e2) = b2 in\n eq_pattern p1 p2 && eq_st_term e1 e2", "val test5 (l: lref) (h: href) (x: int)\n : HIFC int\n (single h)\n (single l)\n []\n (requires fun _ -> True)\n (ensures fun s0 r s1 -> sel s1 l == x /\\ r == sel s1 h)\nlet test5 (l:lref) (h:href) (x:int)\n : HIFC int (single h) (single l) []\n (requires fun _ -> True)\n (ensures fun s0 r s1 -> sel s1 l == x /\\ r == sel s1 h)\n = write l x;\n read h", "val gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a)\n : stt_ghost unit\n (pts_to r #one_half x0 ** pts_to r #one_half x1)\n (fun _ -> pts_to r x0 ** pure (x0 == x1))\nlet gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a)\n: stt_ghost unit\n (pts_to r #one_half x0 ** pts_to r #one_half x1)\n (fun () -> pts_to r x0 ** pure (x0 == x1))\n= gather r", "val gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a)\n : stt_ghost unit\n (pts_to r #one_half x0 ** pts_to r #one_half x1)\n (fun _ -> pts_to r x0 ** pure (x0 == x1))\nlet gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a) = gather r #x0 #x1 #one_half #one_half", "val gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a)\n : stt_ghost unit\n (pts_to r #one_half x0 ** pts_to r #one_half x1)\n (fun _ -> pts_to r x0 ** pure (x0 == x1))\nlet gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a) = gather r", "val gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a)\n : stt_ghost unit\n (pts_to r #one_half x0 ** pts_to r #one_half x1)\n (fun _ -> pts_to r x0 ** pure (x0 == x1))\nlet gather2 (#a:Type) (r:ref a) (#x0 #x1:erased a) = gather r #x0 #x1 #one_half #one_half", "val equal\n (#t1 #t2: typ)\n (p1: pointer t1)\n (p2: pointer t2)\n: Ghost bool\n (requires True)\n (ensures (fun b -> b == true <==> t1 == t2 /\\ p1 == p2 ))\nlet equal\n (#t1 #t2: typ)\n (p1: pointer t1)\n (p2: pointer t2)\n: Ghost bool\n (requires True)\n (ensures (fun b -> b == true <==> t1 == t2 /\\ p1 == p2 ))\n= Pointer?.from p1 = Pointer?.from p2 &&\n HS.aref_equal (Pointer?.contents p1) (Pointer?.contents p2) &&\n path_equal (Pointer?.p p1) (Pointer?.p p2)", "val lbytes_eq: #len:size_t -> b1:lbuffer uint8 len -> b2:lbuffer uint8 len -> Stack bool\n (requires fun h -> live h b1 /\\ live h b2)\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\ r == BS.lbytes_eq (as_seq h0 b1) (as_seq h0 b2))\nlet lbytes_eq #len b1 b2 =\n push_frame();\n let res = create 1ul (u8 255) in\n let z = buf_eq_mask b1 b2 len res in\n pop_frame();\n Raw.u8_to_UInt8 z = 255uy", "val refine_test9 (l: lref) (h: href)\n : (unit\n -> HIFC unit\n (union (single h) (single l))\n (single l)\n []\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 l == sel s0 l))\nlet refine_test9 (l:lref) (h:href)\n : (unit -> HIFC unit (union (single h) (single l))\n (single l)\n []\n (requires fun _ -> True)\n (ensures fun s0 _ s1 -> sel s1 l == sel s0 l))\n = refine_flow (fun () -> test9 l h)", "val v2 (#p: Ghost.erased nat) (al err: ptr)\n : STT unit\n ((pts_to1 al p) `star` (pts_to1 err 0))\n (fun _ -> exists_ (fun p -> exists_ (fun v -> (pts_to1 al p) `star` (pts_to1 err v))))\nlet v2 (#p: Ghost.erased nat) (al: ptr) (err: ptr) : STT unit\n (pts_to1 al p `star` pts_to1 err 0)\n (fun _ -> exists_ (fun p -> exists_ (fun v -> pts_to1 al p `star` pts_to1 err v)))\n= let ar = split al in\n let _ = gen_elim () in\n let _ = v1 ar err in\n let _ = gen_elim () in\n let _ = join al ar in\n intro_exists _ (fun v -> pts_to1 al _ `star` pts_to1 err v);\n intro_exists _ (fun p -> exists_ (fun v -> pts_to1 al p `star` pts_to1 err v));\n return ()" ], "closest_src": [ { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test_if8" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test_if7" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test_if9" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test_if10" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test_if2" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test8" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test6" }, { "project_name": "steel", "file_name": "Selectors.Examples.fst", "name": "Selectors.Examples.test2" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test6" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test4" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test5" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test2" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test1" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test5" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test_if3" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test_if6" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test0" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test26" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test3" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test_if5" }, { "project_name": "steel", "file_name": "Selectors.Examples.fst", "name": "Selectors.Examples.test3" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test25" }, { "project_name": "FStar", "file_name": "StatefulLens.fst", "name": "StatefulLens.test4" }, { "project_name": "FStar", "file_name": "StatefulLens.fst", "name": "StatefulLens.test2" }, { "project_name": "steel", "file_name": "Selectors.Examples.fst", "name": "Selectors.Examples.test1" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test4" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test_if1" }, { "project_name": "steel", "file_name": "Selectors.Examples.fst", "name": "Selectors.Examples.test0" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test8" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test2" }, { "project_name": "steel", "file_name": "ExtractRefs.fst", "name": "ExtractRefs.swap" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test8" }, { "project_name": "FStar", "file_name": "StatefulLens.fst", "name": "StatefulLens.test1" }, { "project_name": "steel", "file_name": "Selectors.Examples.fst", "name": "Selectors.Examples.swap" }, { "project_name": "FStar", "file_name": "StatefulLens.fst", "name": "StatefulLens.test0" }, { "project_name": "steel", "file_name": "Selectors.Examples.fst", "name": "Selectors.Examples.test4" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test_if4" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test15" }, { "project_name": "steel", "file_name": "References.fst", "name": "References.swap_selector" }, { "project_name": "steel", "file_name": "ExtractRefs.fst", "name": "ExtractRefs.copy_ref" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.intro_llist_cons" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.core_ref_is_null" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.core_ref_is_null" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.core_ref_is_null" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.core_ref_is_null" }, { "project_name": "FStar", "file_name": "WithLocal.fst", "name": "WithLocal.test" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test3" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test7" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test2" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_if" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test9" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.read" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test24" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fst", "name": "Benton2004.RHL.r_if" }, { "project_name": "FStar", "file_name": "LatticeEff.fst", "name": "LatticeEff.test1" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fsti", "name": "Steel.ArrayRef.vptr_not_null" }, { "project_name": "steel", "file_name": "Steel.Reference.fsti", "name": "Steel.Reference.vptr_not_null" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test23" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.is_null" }, { "project_name": "FStar", "file_name": "AllocST.fst", "name": "AllocST.read" }, { "project_name": "steel", "file_name": "NewCanon.fst", "name": "NewCanon.test7" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test4" }, { "project_name": "steel", "file_name": "References.fst", "name": "References.copy_ref" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.is_null" }, { "project_name": "steel", "file_name": "PointStructDirectDef.fst", "name": "PointStructDirectDef.swap" }, { "project_name": "steel", "file_name": "PointStruct.fst", "name": "PointStruct.swap" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.test9" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.test9" }, { "project_name": "FStar", "file_name": "ImmutableSTwHeaps.fst", "name": "ImmutableSTwHeaps.read" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperHeap.fst", "name": "FStar.Monotonic.HyperHeap.test1" }, { "project_name": "FStar", "file_name": "IEXN.fst", "name": "IEXN.h" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.refine_test8" }, { "project_name": "FStar", "file_name": "WithLocal.fst", "name": "WithLocal.use_test" }, { "project_name": "steel", "file_name": "Selectors.LList3.fst", "name": "Selectors.LList3.intro_llist_cons" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.intro_llist_cons" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.intro_llist_cons" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.DependentMap.fst", "name": "FStar.Monotonic.DependentMap.alloc" }, { "project_name": "everparse", "file_name": "LowParse.Repr.fsti", "name": "LowParse.Repr.as_ptr" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.is_null" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.owrite" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fsti", "name": "Steel.ArrayRef.read" }, { "project_name": "steel", "file_name": "Steel.Reference.fsti", "name": "Steel.Reference.read" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fsti", "name": "FStar.DM4F.Heap.op_Hat_Plus_Hat" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.guard" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.guard" }, { "project_name": "FStar", "file_name": "TestHoareST.fst", "name": "TestHoareST.test8" }, { "project_name": "FStar", "file_name": "LowStar.Printf.fst", "name": "LowStar.Printf.test" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.write" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.write" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fst", "name": "Pulse.Syntax.Base.eq_st_term" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test5" }, { "project_name": "steel", "file_name": "Pulse.Lib.Reference.fst", "name": "Pulse.Lib.Reference.gather2" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.gather2" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.gather2" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherReference.fst", "name": "Pulse.Lib.HigherReference.gather2" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.equal" }, { "project_name": "hacl-star", "file_name": "Lib.ByteBuffer.fst", "name": "Lib.ByteBuffer.lbytes_eq" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.refine_test9" }, { "project_name": "steel", "file_name": "SteelTableJoin.fst", "name": "SteelTableJoin.v2" } ], "selected_premises": [ "Steel.Memory.full_mem", "SteelSTFramingTestSuite.test", "FStar.List.Tot.Base.length", "Steel.Effect.Common.star", "Steel.FractionalPermission.full_perm", "FStar.List.Tot.Base.map", "Steel.Preorder.pcm_history", "FStar.Real.one", "FStar.Reflection.V2.Data.var", "Steel.Effect.Common.to_vprop'", "FStar.Real.two", "Steel.Effect.Common.to_vprop", "Steel.Memory.hmem", "FStar.List.Tot.Base.op_At", "Steel.Memory.inames", "Steel.Effect.Common.hp_of", "Steel.Effect.Common.rmem", "Steel.Effect.Common.normal", "SteelSTFramingTestSuite.test8", "FStar.PCM.composable", "FStar.UInt.size", "SteelSTFramingTestSuite.test6", "Steel.Effect.Common.t_of", "Steel.Effect.Common.normal_steps", "SteelSTFramingTestSuite.test4", "FStar.FunctionalExtensionality.feq", "SteelSTFramingTestSuite.test_if7", "Steel.Effect.Common.req", "SteelSTFramingTestSuite.test5", "FStar.PCM.compatible", "FStar.Reflection.V2.Derived.mk_e_app", "FStar.Reflection.V2.Derived.mk_app", "FStar.PCM.op", "Steel.ST.Util.emp_inames", "Steel.ST.Util.op_At_Equals_Equals_Greater", "Steel.FractionalPermission.sum_perm", "Steel.Effect.Common.rm", "Steel.FractionalPermission.comp_perm", "Steel.Preorder.history_val", "FStar.Tactics.CanonCommMonoidSimple.Equiv.term_eq", "Steel.Effect.Common.extract_contexts", "SteelSTFramingTestSuite.test0", "Steel.Effect.Common.rmem'", "SteelSTFramingTestSuite.test_if3", "Steel.Effect.Common.vrefine'", "Steel.Effect.Common.guard_vprop", "SteelSTFramingTestSuite.test3", "FStar.Mul.op_Star", "Steel.Effect.Common.mk_rmem", "FStar.List.Tot.Base.tl", "Steel.Effect.Common.pure", "SteelSTFramingTestSuite.test_if2", "SteelSTFramingTestSuite.test2", "FStar.List.Tot.Base.mem", "SteelSTFramingTestSuite.test1", "Steel.Effect.Common.hmem", "FStar.List.Tot.Base.rev", "SteelSTFramingTestSuite.test7", "SteelSTFramingTestSuite.test_if1", "Steel.Effect.Common.sel_of", "SteelSTFramingTestSuite.test_if4", "SteelSTFramingTestSuite.test_if6", "Steel.Effect.Common.vc_norm", "FStar.Heap.trivial_preorder", "FStar.Reflection.V2.Derived.flatten_name", "Steel.Effect.Common.print_goals", "Steel.Effect.Common.vrefine", "SteelSTFramingTestSuite.test_if5", "Steel.ST.Util.wand_is_implies", "FStar.List.Tot.Base.append", "Steel.Effect.Common.visit_br", "FStar.String.length", "FStar.Reflection.V2.Derived.shift_subst", "FStar.Pervasives.reveal_opaque", "Steel.Effect.Common.slterm_nbr_uvars_argv", "FStar.Tactics.CanonCommMonoidSimple.Equiv.atom", "Steel.Effect.Common.atom", "Steel.Effect.Common.norm_return_pre", "FStar.String.strlen", "FStar.ST.op_Bang", "Steel.Effect.Common.unfold_guard", "Steel.Effect.Common.visit_tm", "Steel.Effect.Common.mk_rmem'", "Steel.Effect.Common.inv", "FStar.FunctionalExtensionality.on_dom", "FStar.NMSTTotal.get", "FStar.Reflection.V2.Derived.Lemmas.op_Less_Less_Colon", "Steel.Effect.Common.focus_rmem", "Steel.Effect.Common.focus_rmem_refl", "Steel.Preorder.vhist", "FStar.Reflection.V2.Derived.u_unk", "Steel.ST.Util.intro_implies", "Steel.Effect.Common.try_open_existentials", "FStar.List.Tot.Base.memP", "FStar.Sealed.Inhabited.seal", "FStar.Pervasives.Native.fst", "Steel.ST.Util.elim_implies", "Steel.Effect.Common.return_pre", "FStar.Pervasives.Native.snd", "Steel.ST.Util.rewrite_with_implies" ], "source_upto_this": "(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule SteelSTFramingTestSuite\nopen Steel.ST.Util\n\n/// A collection of small unit tests for the framing tactic\n\nassume val p : vprop\nassume val f (x:int) : STT unit p (fun _ -> p)\n\nlet test () : STT unit (p `star` p `star` p) (fun _ -> p `star` p `star` p)\n = f 0; ()\n\nassume val ref : Type0\nassume val ptr (_:ref) : vprop\n\nassume val alloc (x:int) : STT ref emp (fun y -> ptr y)\nassume val free (r:ref) : STT unit (ptr r) (fun _ -> emp)\nassume val read (r:ref) : STT int (ptr r) (fun _ -> ptr r)\nassume val write (r:ref) (v: int) : STT unit (ptr r) (fun _ -> ptr r)\n\nlet test0 (b1 b2 b3: ref) : STT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b1 `star` ptr b2 `star` ptr b3)\n =\n let x = read b1 in\n x\n\nlet test1 (b1 b2 b3: ref) : STT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b1 `star` ptr b2 `star` ptr b3)\n =\n let x = (let y = read b1 in y) in\n x\n\nlet test2 (b1 b2 b3: ref) : STT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b3 `star` ptr b2 `star` ptr b1)\n =\n let x = read b1 in\n x\n\nlet test3 (b1 b2 b3: ref) : STT int\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n x\n\nlet test4 (b1 b2 b3: ref) : STT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n write b2 x\n\nlet test5 (b1 b2 b3: ref) : STT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n write b2 (x + 1)\n\nlet test6 (b1 b2 b3: ref) : STT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n =\n let x = read b3 in\n let b4 = alloc x in\n write b2 (x + 1);\n free b4\n\n// With the formalism relying on can_be_split_post, this example fails if we normalize return_pre eqs goals before unification\n// When solving this equality, we have the goal\n// (*?u19*) _ _ == return_pre ((fun x -> (fun x -> (*?u758*) _ x x) x) r)\n// with x and r in the context of ?u19\n// Not normalizing allows us to solve it as a function applied to x and r\n// Normalizing would lead to solve it to an slprop with x and r in the context,\n// but which would later fail when trying to prove the equivalence with (fun r -> ptr r)\n// in the postcondition\nlet test7 (_:unit) : STT ref emp ptr\n = let r = alloc 0 in\n let x = read r in\n write r 0;\n r\n\nlet test8 (b1 b2 b3:ref) : STT unit\n (ptr b1 `star` ptr b2 `star` ptr b3)\n (fun _ -> ptr b2 `star` ptr b1 `star` ptr b3)\n = write b2 0\n\nlet test_if1 (b:bool) : STT unit emp (fun _ -> emp)\n = if b then noop () else noop ()\n\nlet test_if2 (b:bool) (r: ref) : STT unit (ptr r) (fun _ -> ptr r)\n = if b then write r 0 else write r 1\n\nlet test_if3 (b:bool) (r:ref) : STT unit (ptr r) (fun _ -> ptr r)\n = if b then noop () else noop ()\n\nlet test_if4 (b:bool) : STT unit emp (fun _ -> emp)\n = if b then (let r = alloc 0 in free r) else (noop ())\n\nlet test_if5 (b:bool) : STT ref emp (fun r -> ptr r)\n = if b then alloc 0 else alloc 1\n\nlet test_if6 (b:bool) : STT ref emp (fun r -> ptr r)\n = let r = if b then alloc 0 else alloc 1 in\n let x = read r in\n write r 0;\n r\n\n(* First test with different (but equivalent) slprops in both branches *)\nlet test_if7 (b:bool) (r1 r2: ref) : STT unit\n (ptr r1 `star` ptr r2)\n (fun _ -> ptr r1 `star` ptr r2)\n = if b then (write r1 0; write r2 0) else (write r2 0; write r1 0);\n write r2 0\n\n(* Test with different slprops in both branches. The second branch captures the outer frame in its context *)", "sketch": [ "Step 1: The definition `test_if8` is a function that takes a boolean `b` and two references `r1` and `r2`. It returns a state transition type (STT) unit that ensures the precondition `(ptr r1) `star` (ptr r2)` and postcondition `(ptr r1) `star` (ptr r2)`.\nStep 2: The implementation of `test_if8` involves an if-else statement based on the boolean `b`. If `b` is true, it writes the value 0 to `r1` and then to `r2`. If `b` is false, it writes the value 0 to `r2` and then to `r1`. This ensures that the postcondition is met regardless of the value of `b`.", "Step 1: The definition `test_if8` is about performing different operations on two references `r1` and `r2` based on the boolean value `b`. The precondition ensures that both `r1` and `r2` are valid pointers, and the postcondition ensures that both pointers remain valid after the operations.\nStep 2: If `b` is true, the function writes the value 0 to `r1` and then to `r2`. If `b` is false, it writes the value 1 to `r2` and then to `r1`. This ensures that the operations are performed in different orders based on the value of `b`, but the final state of the pointers remains valid.", "Step 1: The definition `test_if8` is about performing different operations on two references `r1` and `r2` based on the boolean value `b`. The precondition is that both `r1` and `r2` are valid pointers, and the postcondition is that both `r1` and `r2` remain valid pointers.\nStep 2: If `b` is true, the function writes the value 0 to `r1` and then to `r2`. If `b` is false, the function writes the value 0 to `r2` and then to `r1`. Finally, it writes the value 0 to `r2` again.", "Step 1: The definition `test_if8` is about creating a function that takes a boolean `b` and two references `r1` and `r2`. The function should return an `STT` unit type with a precondition that both `r1` and `r2` are valid pointers and a postcondition that ensures both `r1` and `r2` remain valid pointers.\nStep 2: The implementation will use an if-else statement based on the boolean `b`. If `b` is true, it will write the value `0` to `r1` and then to `r2`. If `b` is false, it will write the value `1` to `r2` and then to `r1`. This ensures that the postcondition holds regardless of the value of `b`.", "Step 1: This definition is about creating a function `test_if8` that takes a boolean `b` and two references `r1` and `r2`. The function will perform different operations on `r1` and `r2` depending on the value of `b`.\nStep 2: If `b` is true, the function will write the value 0 to `r1` and then to `r2`. If `b` is false, it will write the value 0 to `r2` and then to `r1`. The function ensures that the postcondition maintains the same separation logic properties as the precondition.", "Step 1: This definition is about creating a function `test_if8` that takes a boolean `b` and two references `r1` and `r2`. The function should perform different operations on the references based on the value of `b`.\nStep 2: If `b` is true, the function writes the value `0` to `r1` and then to `r2`. If `b` is false, it writes the value `1` to `r2` and then to `r1`. The function ensures that the postcondition holds, which is that both `r1` and `r2` still point to valid memory locations.", "Step 1: This function `test_if8` takes a boolean `b` and two references `r1` and `r2`. It returns an STT unit type with a precondition that both `r1` and `r2` are valid pointers and a postcondition that ensures both `r1` and `r2` remain valid pointers.\nStep 2: The implementation uses an if-else statement based on the boolean `b`. If `b` is true, it writes the value 0 to `r1` and then writes the value 1 to `r2`. If `b` is false, it writes the value 1 to `r2` and then writes the value 0 to `r1`. This ensures that both references are updated correctly while maintaining the validity of the pointers.", "Step 1: This function `test_if8` takes a boolean `b` and two references `r1` and `r2`. It returns a state transition type (STT) unit, ensuring that the precondition and postcondition both have the separation logic proposition that `ptr r1` and `ptr r2` are valid pointers.\n\nStep 2: The implementation will use an if-else statement based on the boolean `b`. In the true branch, it will write the value 0 to `r1` and then to `r2`. In the false branch, it will write the value 0 to `r2` and then to `r1`. This ensures that regardless of the branch taken, both `r1` and `r2` are written to, maintaining the separation logic proposition in the postcondition.", "Step 1: This definition is about creating a test function `test_if8` that takes a boolean `b` and two references `r1` and `r2`. The function should perform different operations based on the value of `b` while ensuring that the postcondition maintains the same separation logic properties as the precondition.\nStep 2: If `b` is true, the function will write the value `0` to `r1` and `1` to `r2`. If `b` is false, it will write the value `1` to `r2` and `0` to `r1`. The function ensures that the separation logic properties of `ptr r1` and `ptr r2` are preserved in both branches.", "Step 1: The definition `test_if8` is about creating a function that takes a boolean `b` and two references `r1` and `r2`. The function should return a unit type and maintain the separation logic properties of `ptr r1` and `ptr r2` both before and after execution.\nStep 2: The implementation involves checking the boolean `b`. If `b` is true, it writes the value 0 to `r1` and then to `r2`. If `b` is false, it writes the value 0 to `r2` and then to `r1`. This ensures that the separation logic properties are preserved regardless of the value of `b`." ], "generated_solution": [ "let test_if8 (b: bool) (r1 r2: ref) : STT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2)) =\n if b then (write r1 0; write r2 0) else (write r2 0; write r1 0)", "let test_if8 (b: bool) (r1 r2: ref) : STT unit\n ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2))\n = if b then (write r1 0; write r2 0) else (write r2 1; write r1 1)", "let test_if8 (b: bool) (r1 r2: ref) : STT unit\n ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2))\n = if b then (write r1 0; write r2 0) else (write r2 0; write r1 0);\n write r2 0", "let test_if8 (b: bool) (r1 r2: ref) : STT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2)) =\n if b then (write r1 0; write r2 0) else (write r2 1; write r1 1)", "let test_if8 (b: bool) (r1 r2: ref) : STT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2)) =\n if b then\n (write r1 0; write r2 0)\n else\n (write r2 0; write r1 0)", "let test_if8 (b: bool) (r1 r2: ref) : STT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2)) =\n if b then\n (write r1 0; write r2 0)\n else\n (write r2 1; write r1 1)", "let test_if8 (b: bool) (r1 r2: ref) : STT unit\n ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2))\n = if b then (write r1 0; write r2 1) else (write r2 1; write r1 0)", "let test_if8 (b: bool) (r1 r2: ref) : STT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2)) =\n if b then (write r1 0; write r2 0) else (write r2 0; write r1 0)", "let test_if8 (b: bool) (r1 r2: ref) : STT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2)) =\n if b then\n (write r1 0; write r2 1)\n else\n (write r2 1; write r1 0)", "let test_if8 (b: bool) (r1 r2: ref) : STT unit ((ptr r1) `star` (ptr r2)) (fun _ -> (ptr r1) `star` (ptr r2))\n = if b then (write r1 0; write r2 0) else (write r2 0; write r1 0)" ] }, { "file_name": "SelectorLogic.fst", "name": "SelectorLogic.modus_ponens_interp", "opens_and_abbrevs": [ { "abbrev": "Mem", "full_module": "Steel.Memory" }, { "open": "Steel.Memory" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val modus_ponens_interp (p q: vprop) (m: hmem (p `star` (p `wand` q)).hp) : Lemma (interp q.hp m)", "source_definition": "let modus_ponens_interp (p q:vprop) (m:hmem (p `star` (p `wand` q)).hp)\n : Lemma (interp q.hp m)\n = let mp, mq = star_split p.hp (p `wand` q).hp m in\n assert (interp q.hp (join mq mp));\n join_commutative mq mp", "source_range": { "start_line": 57, "start_col": 0, "end_line": 61, "end_col": 26 }, "interleaved": false, "definition": "fun p q m ->\n (let _ = SelectorLogic.star_split (Mkvprop?.hp p) (Mkvprop?.hp (SelectorLogic.wand p q)) m in\n (let FStar.Pervasives.Native.Mktuple2 #_ #_ mp mq = _ in\n assert (Steel.Memory.interp (Mkvprop?.hp q) (Steel.Memory.join mq mp));\n Steel.Memory.join_commutative mq mp)\n <:\n Prims.unit)\n <:\n FStar.Pervasives.Lemma (ensures Steel.Memory.interp (Mkvprop?.hp q) m)", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "SelectorLogic.vprop", "Steel.Memory.hmem", "SelectorLogic.__proj__Mkvprop__item__hp", "SelectorLogic.star", "SelectorLogic.wand", "Steel.Memory.join_commutative", "Prims.unit", "Prims._assert", "Steel.Memory.interp", "Steel.Memory.join", "FStar.Pervasives.Native.tuple2", "Prims.l_and", "Steel.Memory.disjoint", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "Prims.eq2", "Steel.Memory.mem", "SelectorLogic.star_split", "Prims.l_True", "Prims.squash", "Prims.Nil", "FStar.Pervasives.pattern" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "\n p: SelectorLogic.vprop ->\n q: SelectorLogic.vprop ->\n m: Steel.Memory.hmem (Mkvprop?.hp (SelectorLogic.star p (SelectorLogic.wand p q)))\n -> FStar.Pervasives.Lemma (ensures Steel.Memory.interp (Mkvprop?.hp q) m)", "prompt": "let modus_ponens_interp (p q: vprop) (m: hmem (p `star` (p `wand` q)).hp) : Lemma (interp q.hp m) =\n ", "expected_response": "let mp, mq = star_split p.hp (p `wand` q).hp m in\nassert (interp q.hp (join mq mp));\njoin_commutative mq mp", "source": { "project_name": "steel", "file_name": "share/steel/examples/steel/SelectorLogic.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "SelectorLogic.fst", "checked_file": "dataset/SelectorLogic.fst.checked", "interface_file": false, "dependencies": [ "dataset/Steel.Reference.fsti.checked", "dataset/Steel.Memory.fsti.checked", "dataset/Steel.FractionalPermission.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.IndefiniteDescription.fsti.checked" ] }, "definitions_in_context": [ "let selector (hp:slprop) (a:(hmem hp) -> Type) = (h:hmem hp -> GTot (a h))", "vprop", "vprop", "hp", "hp", "t", "t", "sel", "sel", "val reveal_wand (p q:slprop) (m:mem) : Lemma\n (requires interp (Mem.wand p q) m)\n (ensures forall m1. (m `disjoint` m1 /\\ interp p m1) ==> interp q (join m m1))\n [SMTPat (interp (Mem.wand p q) m)]", "let star (p q:vprop) =\n {hp = p.hp `Mem.star` q.hp;\n t = (fun h -> p.t h * q.t h);\n sel = fun h -> p.sel h, q.sel h\n }", "let left_wand_t (m:mem) (p:vprop) =\n h:hmem p.hp{disjoint h m} & p.t h", "let wand (p q:vprop) =\n {hp = p.hp `Mem.wand` q.hp;\n t = (fun m -> ((x:left_wand_t m p) -> GTot (q.t (join m (dfst x)))));\n sel = fun m0 -> fun (| h, vp |) -> q.sel (join m0 h)\n }", "val star_split (p q:slprop) (m:hmem (p `Mem.star` q))\n : GTot (r:(hmem p * hmem q){disjoint (fst r) (snd r) /\\ join (fst r) (snd r) == m})", "let star_split p q m =\n elim_star p q m;\n let ml = FStar.IndefiniteDescription.indefinite_description_ghost mem (\n fun ml -> exists mr. disjoint ml mr /\\ m == join ml mr /\\ interp p ml /\\ interp q mr) in\n let mr = FStar.IndefiniteDescription.indefinite_description_ghost mem (\n fun mr -> disjoint ml mr /\\ m == join ml mr /\\ interp p ml /\\ interp q mr) in\n ml, mr" ], "closest": [ "val interp_star\n (p q: slprop)\n (m: mem)\n: Lemma\n (interp (p `star` q) m <==> (exists (mp: mem) (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m))\nlet interp_star\n (p q: slprop)\n (m: mem)\n: Lemma\n (interp (p `star` q) m <==> (exists (mp: mem) (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m))\n= let left = interp (p `star` q) m in\n let right = exists (mp: mem) (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m in\n let f ()\n : Lemma\n (requires left)\n (ensures right)\n =\n elim_star p q m\n in\n let g ()\n : Lemma\n (requires right)\n (ensures left)\n =\n Classical.exists_elim left #_ #(fun mp -> exists (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m) () (fun mp ->\n Classical.exists_elim left #_ #(fun mq -> disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m) () (fun mq ->\n intro_star p q mp mq\n )\n )\n in\n Classical.move_requires f ();\n Classical.move_requires g ()", "val intro_vdep_lemma (v q: vprop) (p: (t_of v -> Tot vprop)) (m: mem)\n : Lemma (requires (interp (hp_of (v `star` q)) m /\\ q == p (fst (sel_of (v `star` q) m))))\n (ensures\n (interp (hp_of (v `star` q)) m /\\ interp (hp_of (vdep v p)) m /\\\n vdep_rel v q p (sel_of (v `star` q) m) (sel_of (vdep v p) m)))\nlet intro_vdep_lemma\n (v: vprop)\n (q: vprop)\n (p: (t_of v -> Tot vprop))\n (m: mem)\n: Lemma\n (requires (\n interp (hp_of (v `star` q)) m /\\\n q == p (fst (sel_of (v `star` q) m))\n ))\n (ensures (\n interp (hp_of (v `star` q)) m /\\\n interp (hp_of (vdep v p)) m /\\\n vdep_rel v q p (sel_of (v `star` q) m) (sel_of (vdep v p) m)\n ))\n=\n Mem.interp_star (hp_of v) (hp_of q) m;\n interp_vdep_hp v p m;\n vdep_sel_eq v p m", "val pure_star_interp' (p: slprop u#a) (q: prop) (m: mem)\n : Lemma (interp (p `Steel.Memory.star` (Steel.Memory.pure q)) m <==> interp p m /\\ q)\nlet pure_star_interp' (p:slprop u#a) (q:prop) (m:mem)\n : Lemma (interp (p `Steel.Memory.star` Steel.Memory.pure q) m <==>\n interp p m /\\ q)\n= pure_star_interp p q m;\n emp_unit p", "val pure_star_interp (p:slprop u#a) (q:prop) (m:mem)\n : Lemma (interp (p `star` pure q) m <==>\n interp (p `star` emp) m /\\ q)\nlet pure_star_interp p q m = H.pure_star_interp p q (heap_of_mem m)", "val pure_star_interp (p:slprop u#a) (q:prop) (m:mem)\n : Lemma (interp (p `star` pure q) m <==>\n interp (p `star` emp) m /\\ q)\nlet pure_star_interp p q m = H.pure_star_interp p q (heap_of_mem m)", "val affine_star (p q:slprop) (m:mem)\n : Lemma ((interp (p `star` q) m ==> interp p m /\\ interp q m))\nlet affine_star (p q:slprop) (m:mem) =\n H.affine_star p q (heap_of_mem m)", "val affine_star (p q:slprop) (m:mem)\n : Lemma ((interp (p `star` q) m ==> interp p m /\\ interp q m))\nlet affine_star (p q:slprop) (m:mem) =\n H.affine_star p q (heap_of_mem m)", "val intro_h_and (p q: slprop) (m:mem)\n : Lemma (interp p m /\\ interp q m ==> interp (h_and p q) m)\nlet intro_h_and (p q: slprop) (m:mem) = H.intro_h_and p q (heap_of_mem m)", "val elim_star (p q:slprop) (m:hmem (p `star` q))\n : Lemma\n (requires\n interp (p `star` q) m)\n (ensures exists ml mr.\n disjoint ml mr /\\ m == join ml mr /\\ interp p ml /\\ interp q mr)\nlet elim_star p q m =\n let h = heap_of_mem m in\n H.elim_star p q h;\n assert (exists hl hr. H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr);\n let hl = FStar.IndefiniteDescription.indefinite_description_tot H.heap (fun hl ->\n exists hr. H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr) in\n let hr = FStar.IndefiniteDescription.indefinite_description_tot H.heap (fun hr ->\n H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr) in\n let ml = mem_set_heap m hl in\n let mr = mem_set_heap m hr in\n assert (disjoint ml mr);\n assert (m == join ml mr);\n assert (interp p ml);\n assert (interp q mr);\n ()", "val elim_star (p q:slprop) (m:hmem (p `star` q))\n : Lemma\n (requires\n interp (p `star` q) m)\n (ensures exists ml mr.\n disjoint ml mr /\\ m == join ml mr /\\ interp p ml /\\ interp q mr)\nlet elim_star p q m =\n let h = heap_of_mem m in\n H.elim_star p q h;\n assert (exists hl hr. H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr);\n let hl = FStar.IndefiniteDescription.indefinite_description_tot H.heap (fun hl ->\n exists hr. H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr) in\n let hr = FStar.IndefiniteDescription.indefinite_description_tot H.heap (fun hr ->\n H.disjoint hl hr /\\ H.join hl hr == h /\\ H.interp p hl /\\ H.interp q hr) in\n let ml = mem_set_heap m hl in\n let mr = mem_set_heap m hr in\n assert (disjoint ml mr);\n assert (m == join ml mr);\n assert (interp p ml);\n assert (interp q mr);\n ()", "val interp_vdep_hp (v: vprop) (p: ( (t_of v) -> Tot vprop)) (m: mem) : Lemma\n (interp (vdep_hp v p) m <==> (interp (hp_of v) m /\\ interp (hp_of v `Mem.star` hp_of (p (sel_of v m))) m))\nlet interp_vdep_hp\n v p m\n=\n interp_sdep (hp_of v) (vdep_hp_payload v p) m;\n let left = interp (vdep_hp v p) m in\n let right = interp (hp_of v) m /\\ interp (hp_of v `Mem.star` hp_of (p (sel_of v m))) m in\n let f ()\n : Lemma\n (requires left)\n (ensures right)\n = interp_star (hp_of v) (hp_of (p (sel_of v m))) m\n in\n let g ()\n : Lemma\n (requires right)\n (ensures left)\n = interp_star (hp_of v) (hp_of (p (sel_of v m))) m\n in\n Classical.move_requires f ();\n Classical.move_requires g ()", "val intro_h_or_right (p q: slprop) (m:mem)\n : Lemma (interp q m ==> interp (h_or p q) m)\nlet intro_h_or_right (p q: slprop) (m:mem) = H.intro_h_or_right p q (heap_of_mem m)", "val elim_h_and (p q: slprop) (m:mem)\n : Lemma (interp (h_and p q) m ==> (interp p m /\\ interp q m))\nlet elim_h_and (p q: slprop) (m:mem) = H.elim_h_and p q (heap_of_mem m)", "val intro_star\n (p q: vprop)\n (r: slprop)\n (vp: erased (t_of p))\n (vq: erased (t_of q))\n (m: mem)\n (proof:\n (m: mem\n -> Lemma (requires interp (hp_of p) m /\\ sel_of p m == reveal vp)\n (ensures interp (hp_of q) m)))\n : Lemma (requires interp ((hp_of p) `Mem.star` r) m /\\ sel_of p m == reveal vp)\n (ensures interp ((hp_of q) `Mem.star` r) m)\nlet intro_star (p q:vprop) (r:slprop) (vp:erased (t_of p)) (vq:erased (t_of q)) (m:mem)\n (proof:(m:mem) -> Lemma\n (requires interp (hp_of p) m /\\ sel_of p m == reveal vp)\n (ensures interp (hp_of q) m)\n )\n : Lemma\n (requires interp ((hp_of p) `Mem.star` r) m /\\ sel_of p m == reveal vp)\n (ensures interp ((hp_of q) `Mem.star` r) m)\n= let p = hp_of p in\n let q = hp_of q in\n let intro (ml mr:mem) : Lemma\n (requires interp q ml /\\ interp r mr /\\ disjoint ml mr)\n (ensures disjoint ml mr /\\ interp (q `Mem.star` r) (Mem.join ml mr))\n = Mem.intro_star q r ml mr\n in\n elim_star p r m;\n Classical.forall_intro (Classical.move_requires proof);\n Classical.forall_intro_2 (Classical.move_requires_2 intro)", "val elim_h_or (p q: slprop) (m:mem)\n : Lemma (interp (h_or p q) m ==> (interp p m \\/ interp q m))\nlet elim_h_or (p q: slprop) (m:mem) = H.elim_h_or p q (heap_of_mem m)", "val pure_interp (q:prop) (m:mem) : Lemma (interp (pure q) m <==> q)\nlet pure_interp q m = H.pure_interp q (heap_of_mem m)", "val affine_star_smt (p q: slprop u#a) (m: mem u#a)\n : Lemma (interp (p `star` q) m ==> interp p m /\\ interp q m) [SMTPat (interp (p `star` q) m)]\nlet affine_star_smt (p q:slprop u#a) (m:mem u#a)\n : Lemma (interp (p `star` q) m ==> interp p m /\\ interp q m)\n [SMTPat (interp (p `star` q) m)]\n = affine_star p q m", "val affine_star_smt (p q: slprop u#a) (m: mem u#a)\n : Lemma (interp (p `star` q) m ==> interp p m /\\ interp q m) [SMTPat (interp (p `star` q) m)]\nlet affine_star_smt (p q:slprop u#a) (m:mem u#a)\n : Lemma (interp (p `star` q) m ==> interp p m /\\ interp q m)\n [SMTPat (interp (p `star` q) m)]\n = affine_star p q m", "val intro_h_or_left (p q: slprop) (m:mem)\n : Lemma (interp p m ==> interp (h_or p q) m)\nlet intro_h_or_left (p q: slprop) (m:mem) = H.intro_h_or_left p q (heap_of_mem m)", "val h_and_equiv (p q: slprop) (m: mem)\n : Lemma ((interp p m /\\ interp q m) <==> interp (h_and p q) m)\nlet h_and_equiv (p q: slprop) (m:mem)\n : Lemma ((interp p m /\\ interp q m) <==> interp (h_and p q) m)\n= elim_h_and p q m; intro_h_and p q m", "val elim_vdep_lemma (v q: vprop) (p: (t_of v -> Tot vprop)) (m: mem)\n : Lemma\n (requires\n (interp (hp_of (vdep v p)) m /\\\n q == p (dfst (sel_of (vdep v p) m <: dtuple2 (t_of v) (vdep_payload v p)))))\n (ensures\n (interp (hp_of (v `star` q)) m /\\ interp (hp_of (vdep v p)) m /\\\n vdep_rel v q p (sel_of (v `star` q) m) (sel_of (vdep v p) m)))\nlet elim_vdep_lemma\n (v: vprop)\n (q: vprop)\n (p: (t_of v -> Tot vprop))\n (m: mem)\n: Lemma\n (requires (\n interp (hp_of (vdep v p)) m /\\\n q == p (dfst (sel_of (vdep v p) m <: dtuple2 (t_of v) (vdep_payload v p)))\n ))\n (ensures (\n interp (hp_of (v `star` q)) m /\\\n interp (hp_of (vdep v p)) m /\\\n vdep_rel v q p (sel_of (v `star` q) m) (sel_of (vdep v p) m)\n ))\n=\n Mem.interp_star (hp_of v) (hp_of q) m;\n interp_vdep_hp v p m;\n vdep_sel_eq v p m", "val pure_interp (q:prop) (m:mem)\n : Lemma (interp (pure q) m <==> q)\nlet pure_interp q m = H.pure_interp q (heap_of_mem m)", "val star_equiv_forall (p q: _)\n : Lemma\n (forall m.\n (interp (p `star` q) m <==>\n (exists (mp: mem) (mq: mem).\n disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m)))\nlet star_equiv_forall p q:\n Lemma (forall m.\n (interp (p `star` q) m <==>\n (exists (mp: mem) (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m)))\n= introduce forall m.\n (interp (p `star` q) m <==>\n (exists (mp: mem) (mq: mem) . disjoint mp mq /\\ interp p mp /\\ interp q mq /\\ join mp mq == m))\n with interp_star p q m", "val intro_star (p q:slprop) (mp:hmem p) (mq:hmem q)\n : Lemma\n (requires\n disjoint mp mq)\n (ensures\n interp (p `star` q) (join mp mq))\nlet intro_star p q mp mq =\n H.intro_star p q (heap_of_mem mp) (heap_of_mem mq)", "val intro_star (p q:slprop) (mp:hmem p) (mq:hmem q)\n : Lemma\n (requires\n disjoint mp mq)\n (ensures\n interp (p `star` q) (join mp mq))\nlet intro_star p q mp mq =\n H.intro_star p q (heap_of_mem mp) (heap_of_mem mq)", "val wand_equiv_forall (p q: _)\n : Lemma\n (forall m.\n (interp (p `wand` q) m <==>\n (forall mp. disjoint m mp /\\ interp p mp ==> interp q (join m mp))))\nlet wand_equiv_forall p q:\n Lemma (forall m.\n (interp (p `wand` q) m <==>\n (forall mp.\n disjoint m mp /\\\n interp p mp ==>\n interp q (join m mp))))\n= introduce forall m.\n (interp (p `wand` q) m <==>\n (forall mp.\n disjoint m mp /\\ interp p mp ==> interp q (join m mp)))\nwith (\n intro_wand p q m;\n introduce forall m1. ((interp (wand p q) m /\\ m `disjoint` m1 /\\ interp p m1)\n ==> interp q (join m m1))\n with (\n elim_wand p q m m1\n )\n)", "val commute_star_par_l (#st: st) (p q r s: st.hprop) (m0: st.mem)\n : Lemma\n (st.interp (((p `st.star` q) `st.star` r) `st.star` s) m0 <==>\n st.interp ((p `st.star` (q `st.star` r)) `st.star` s) m0)\nlet commute_star_par_l (#st:st) (p q r s:st.hprop) (m0:st.mem)\n : Lemma\n (st.interp (p `st.star` q `st.star` r `st.star` s) m0 <==>\n st.interp (p `st.star` (q `st.star` r) `st.star` s) m0)\n = assert ((p `st.star` q `st.star` r `st.star` s) `st.equals`\n (p `st.star` (q `st.star` r) `st.star` s))", "val ac_reasoning_for_m_frame_preserving (p q r: slprop u#a) (m: mem u#a)\n : Lemma (requires interp ((p `star` q) `star` r) m) (ensures interp (p `star` r) m)\nlet ac_reasoning_for_m_frame_preserving\n (p q r:slprop u#a) (m:mem u#a)\n : Lemma\n (requires interp ((p `star` q) `star` r) m)\n (ensures interp (p `star` r) m)\n = calc (equiv) {\n (p `star` q) `star` r;\n (equiv) { star_commutative p q;\n equiv_extensional_on_star (p `star` q) (q `star` p) r }\n (q `star` p) `star` r;\n (equiv) { star_associative q p r }\n q `star` (p `star` r);\n };\n assert (interp (q `star` (p `star` r)) m);\n affine_star q (p `star` r) m", "val ac_reasoning_for_m_frame_preserving (p q r: slprop u#a) (m: mem u#a)\n : Lemma (requires interp ((p `star` q) `star` r) m) (ensures interp (p `star` r) m)\nlet ac_reasoning_for_m_frame_preserving\n (p q r:slprop u#a) (m:mem u#a)\n : Lemma\n (requires interp ((p `star` q) `star` r) m)\n (ensures interp (p `star` r) m)\n = calc (equiv) {\n (p `star` q) `star` r;\n (equiv) { star_commutative p q;\n equiv_extensional_on_star (p `star` q) (q `star` p) r }\n (q `star` p) `star` r;\n (equiv) { star_associative q p r }\n q `star` (p `star` r);\n };\n assert (interp (q `star` (p `star` r)) m);\n affine_star q (p `star` r) m", "val commute_star_par_r (#st: st) (p q r s: st.hprop) (m0: st.mem)\n : Lemma\n (st.interp (((p `st.star` q) `st.star` r) `st.star` s) m0 <==>\n st.interp ((q `st.star` (p `st.star` r)) `st.star` s) m0)\nlet commute_star_par_r (#st:st) (p q r s:st.hprop) (m0:st.mem)\n : Lemma\n (st.interp (p `st.star` q `st.star` r `st.star` s) m0 <==>\n st.interp (q `st.star` (p `st.star` r) `st.star` s) m0)\n = calc (st.equals) {\n p `st.star` q `st.star` r `st.star` s;\n (st.equals) { }\n q `st.star` p `st.star` r `st.star` s;\n (st.equals) { }\n q `st.star` (p `st.star` r) `st.star` s;\n }", "val h_or_equiv_forall (p q: slprop)\n : Lemma (forall m. interp (h_or p q) m <==> (interp p m \\/ interp q m))\nlet h_or_equiv_forall (p q: slprop):\n Lemma (forall m. interp (h_or p q) m <==> (interp p m \\/ interp q m))\n= introduce forall m. (interp (h_or p q) m <==> (interp p m \\/ interp q m))\nwith (\n elim_h_or p q m;\n intro_h_or_left p q m;\n intro_h_or_right p q m\n)", "val h_and_equiv_forall (p q: slprop)\n : Lemma (forall m. interp (h_and p q) m <==> (interp p m /\\ interp q m))\nlet h_and_equiv_forall (p q: slprop):\n Lemma (forall m. interp (h_and p q) m <==> (interp p m /\\ interp q m))\n= introduce forall m. interp (h_and p q) m <==> (interp p m /\\ interp q m)\n with h_and_equiv p q m", "val cas_action_helper (p q r s: slprop) (m: mem)\n : Lemma (requires interp Mem.(((p `star` q) `star` r) `star` s) m)\n (ensures interp Mem.((p `star` q) `star` s) m)\nlet cas_action_helper (p q r s:slprop) (m:mem)\n : Lemma\n (requires interp Mem.(p `star` q `star` r `star` s) m)\n (ensures interp Mem.(p `star` q `star` s) m)\n = let open Steel.Memory in\n calc (equiv) {\n r `star` s;\n (equiv) { star_commutative r s }\n s `star` r;\n };\n calc (equiv) {\n p `star` q `star` r `star` s;\n (equiv) { Mem.star_associative (p `star` q) r s }\n (p `star` q) `star` (r `star` s);\n (equiv) { equiv_ext_right (p `star` q)\n (r `star` s)\n (s `star` r) }\n (p `star` q) `star` (s `star` r);\n (equiv) { star_associative (p `star` q) s r }\n (p `star` q `star` s) `star` r;\n };\n assert (interp ((p `star` q `star` s) `star` r) m);\n affine_star (p `star` q `star` s) r m", "val can_be_split_3_interp (p1 p2 q r:slprop u#1) (m:mem)\n: Lemma\n (requires p1 `slimp` p2 /\\ interp (p1 `Mem.star` q `Mem.star` r) m)\n (ensures interp (p2 `Mem.star` q `Mem.star` r) m)\nlet can_be_split_3_interp p1 p2 q r m =\n Mem.star_associative p1 q r;\n Mem.star_associative p2 q r;\n slimp_star p1 p2 (q `Mem.star` r) (q `Mem.star` r)", "val id_elim_star (p q:slprop) (m:mem)\n : Pure (erased mem & erased mem)\n (requires (interp (p `star` q) m))\n (ensures (fun (ml, mr) -> disjoint ml mr\n /\\ m == join ml mr\n /\\ interp p ml\n /\\ interp q mr))\nlet id_elim_star p q m =\n let starprop (ml:mem) (mr:mem) =\n disjoint ml mr\n /\\ m == join ml mr\n /\\ interp p ml\n /\\ interp q mr\n in\n elim_star p q m;\n let p1 : mem -> prop = fun ml -> (exists mr. starprop ml mr) in\n let ml = IndefiniteDescription.indefinite_description_tot _ p1 in\n let starpropml mr : prop = starprop ml mr in // this prop annotation seems needed\n let mr = IndefiniteDescription.indefinite_description_tot _ starpropml in\n (ml, mr)", "val weaken (#opened:inames)\n (p q:vprop)\n (l:(m:mem) -> Lemma\n (requires interp (hp_of p) m)\n (ensures interp (hp_of q) m))\n : STGhostT unit opened p (fun _ -> q)\nlet weaken #o p q l =\n coerce_ghost (fun () -> SEA.rewrite_slprop p q l)", "val preserves_frame_star_pure (e: inames) (p q: slprop) (r s: prop) (m: mem)\n : Lemma (requires r /\\ s)\n (ensures\n preserves_frame e p q m m <==> preserves_frame e (p `star` (pure r)) (q `star` (pure s)) m m\n )\nlet preserves_frame_star_pure (e:inames) (p q:slprop) (r s:prop) (m:mem)\n : Lemma\n (requires r /\\ s)\n (ensures\n preserves_frame e p q m m <==>\n preserves_frame e (p `star` pure r) (q `star` pure s) m m)\n = pure_equiv r True;\n star_congruence p (pure r) p (pure True);\n pure_equiv s True;\n star_congruence q (pure s) q (pure True);\n pure_true_equiv p;\n pure_true_equiv q;\n let fwd ()\n : Lemma\n (requires preserves_frame e p q m m)\n (ensures preserves_frame e (p `star` pure r) (q `star` pure s) m m)\n [SMTPat ()]\n = preserves_frame_cong e p q (p `star` pure r) (q `star` pure s) m m\n in\n let bk ()\n : Lemma\n (requires preserves_frame e (p `star` pure r) (q `star` pure s) m m)\n (ensures preserves_frame e p q m m)\n [SMTPat ()]\n = preserves_frame_cong e (p `star` pure r) (q `star` pure s) p q m m\n in\n ()", "val preserves_frame_star_pure (e: inames) (p q: slprop) (r s: prop) (m: mem)\n : Lemma (requires r /\\ s)\n (ensures\n preserves_frame e p q m m <==> preserves_frame e (p `star` (pure r)) (q `star` (pure s)) m m\n )\nlet preserves_frame_star_pure (e:inames) (p q:slprop) (r s:prop) (m:mem)\n : Lemma\n (requires r /\\ s)\n (ensures\n preserves_frame e p q m m <==>\n preserves_frame e (p `star` pure r) (q `star` pure s) m m)\n = pure_equiv r True;\n star_congruence p (pure r) p (pure True);\n pure_equiv s True;\n star_congruence q (pure s) q (pure True);\n pure_true_equiv p;\n pure_true_equiv q;\n let fwd ()\n : Lemma\n (requires preserves_frame e p q m m)\n (ensures preserves_frame e (p `star` pure r) (q `star` pure s) m m)\n [SMTPat ()]\n = preserves_frame_cong e p q (p `star` pure r) (q `star` pure s) m m\n in\n let bk ()\n : Lemma\n (requires preserves_frame e (p `star` pure r) (q `star` pure s) m m)\n (ensures preserves_frame e p q m m)\n [SMTPat ()]\n = preserves_frame_cong e (p `star` pure r) (q `star` pure s) p q m m\n in\n ()", "val rearrange_invariant (p q r q0 q1: slprop)\n : Lemma (requires q `equiv` (q0 `star` q1))\n (ensures (p `star` (q `star` r)) `equiv` ((q0 `star` p) `star` (q1 `star` r)))\nlet rearrange_invariant (p q r : slprop) (q0 q1:slprop)\n : Lemma\n (requires q `equiv` (q0 `star` q1))\n (ensures (p `star` (q `star` r)) `equiv`\n ((q0 `star` p) `star` (q1 `star` r)))\n = calc (equiv)\n {\n p `star` (q `star` r);\n (equiv)\n {\n calc (equiv)\n {\n (q `star` r);\n (equiv) {\n star_congruence q r (q0 `star` q1) r\n }\n (q0 `star` q1) `star` r;\n };\n star_congruence p (q `star` r) p ((q0 `star` q1) `star` r)\n }\n (p `star` ((q0 `star` q1) `star` r));\n (equiv) {\n star_associative q0 q1 r;\n star_congruence p ((q0 `star` q1) `star` r)\n p (q0 `star` (q1 `star` r));\n star_associative p q0 (q1 `star` r)\n }\n (p `star` q0) `star` (q1 `star` r);\n (equiv) {\n star_commutative p q0;\n star_congruence (p `star` q0) (q1 `star` r)\n (q0 `star` p) (q1 `star` r)\n }\n (q0 `star` p) `star` (q1 `star` r);\n }", "val rearrange_invariant (p q r q0 q1: slprop)\n : Lemma (requires q `equiv` (q0 `star` q1))\n (ensures (p `star` (q `star` r)) `equiv` ((q0 `star` p) `star` (q1 `star` r)))\nlet rearrange_invariant (p q r : slprop) (q0 q1:slprop)\n : Lemma\n (requires q `equiv` (q0 `star` q1))\n (ensures (p `star` (q `star` r)) `equiv`\n ((q0 `star` p) `star` (q1 `star` r)))\n = calc (equiv)\n {\n p `star` (q `star` r);\n (equiv)\n {\n calc (equiv)\n {\n (q `star` r);\n (equiv) {\n star_congruence q r (q0 `star` q1) r\n }\n (q0 `star` q1) `star` r;\n };\n star_congruence p (q `star` r) p ((q0 `star` q1) `star` r)\n }\n (p `star` ((q0 `star` q1) `star` r));\n (equiv) {\n star_associative q0 q1 r;\n star_congruence p ((q0 `star` q1) `star` r)\n p (q0 `star` (q1 `star` r));\n star_associative p q0 (q1 `star` r)\n }\n (p `star` q0) `star` (q1 `star` r);\n (equiv) {\n star_commutative p q0;\n star_congruence (p `star` q0) (q1 `star` r)\n (q0 `star` p) (q1 `star` r)\n }\n (q0 `star` p) `star` (q1 `star` r);\n }", "val commute_assoc_star_right (#st: st) (p q r s: st.hprop)\n : Lemma\n ((p `st.star` ((q `st.star` r) `st.star` s))\n `st.equals`\n (p `st.star` (r `st.star` (q `st.star` s))))\nlet commute_assoc_star_right (#st:st) (p q r s:st.hprop)\n: Lemma\n ((p `st.star` ((q `st.star` r) `st.star` s)) `st.equals`\n (p `st.star` (r `st.star` (q `st.star` s))))\n= calc (st.equals) {\n p `st.star` ((q `st.star` r) `st.star` s);\n (st.equals) { equals_ext_right p\n ((q `st.star` r) `st.star` s)\n ((r `st.star` q) `st.star` s) }\n p `st.star` ((r `st.star` q) `st.star` s);\n (st.equals) { assoc_star_right p r q s }\n p `st.star` (r `st.star` (q `st.star` s));\n }", "val commute_assoc_star_right (#st: st) (p q r s: st.hprop)\n : Lemma\n ((p `st.star` ((q `st.star` r) `st.star` s))\n `st.equals`\n (p `st.star` (r `st.star` (q `st.star` s))))\nlet commute_assoc_star_right (#st:st) (p q r s:st.hprop)\n : Lemma\n ((p `st.star` ((q `st.star` r) `st.star` s)) `st.equals`\n (p `st.star` (r `st.star` (q `st.star` s))))\n =\n calc (st.equals) {\n p `st.star` ((q `st.star` r) `st.star` s);\n (st.equals) { equals_ext_right p\n ((q `st.star` r) `st.star` s)\n ((r `st.star` q) `st.star` s) }\n p `st.star` ((r `st.star` q) `st.star` s);\n (st.equals) { assoc_star_right p r q s }\n p `st.star` (r `st.star` (q `st.star` s));\n }", "val equiv_pqrs_p_qr_s (p q r s: slprop)\n : Lemma ((((p `star` q) `star` r) `star` s) `equiv` ((p `star` (q `star` r)) `star` s))\nlet equiv_pqrs_p_qr_s (p q r s:slprop)\n : Lemma ((p `star` q `star` r `star` s) `equiv`\n (p `star` (q `star` r) `star` s))\n = star_associative p q r;\n equiv_extensional_on_star\n (p `star` q `star` r)\n (p `star` (q `star` r))\n s", "val equiv_pqrs_p_qr_s (p q r s: slprop)\n : Lemma ((((p `star` q) `star` r) `star` s) `equiv` ((p `star` (q `star` r)) `star` s))\nlet equiv_pqrs_p_qr_s (p q r s:slprop)\n : Lemma ((p `star` q `star` r `star` s) `equiv`\n (p `star` (q `star` r) `star` s))\n = star_associative p q r;\n equiv_extensional_on_star\n (p `star` q `star` r)\n (p `star` (q `star` r))\n s", "val rewrite_slprop\n (#opened:inames)\n (p q:vprop)\n (l:(m:mem) -> Lemma\n (requires interp (hp_of p) m)\n (ensures interp (hp_of q) m)\n ) : SteelGhostT unit opened p (fun _ -> q)\nlet rewrite_slprop p q l = SteelGhost?.reflect (rewrite_slprop0 p q l)", "val id_elim_star (p q:slprop) (h:heap)\n : Pure (erased heap & erased heap )\n (requires (interp (p `star` q) h))\n (ensures (fun (hl, hr) -> disjoint hl hr\n /\\ h == join hl hr\n /\\ interp p hl\n /\\ interp q hr))\nlet id_elim_star p q m =\n let starprop (ml:heap) (mr:heap) =\n disjoint ml mr\n /\\ m == join ml mr\n /\\ interp p ml\n /\\ interp q mr\n in\n elim_star p q m;\n let p1 : heap -> prop = fun ml -> (exists mr. starprop ml mr) in\n let ml = IndefiniteDescription.indefinite_description_tot _ p1 in\n let starpropml mr : prop = starprop ml mr in // this prop annotation seems needed\n let mr = IndefiniteDescription.indefinite_description_tot _ starpropml in\n (ml, mr)", "val id_elim_star (p q:slprop) (h:heap)\n : Pure (erased heap & erased heap )\n (requires (interp (p `star` q) h))\n (ensures (fun (hl, hr) -> disjoint hl hr\n /\\ h == join hl hr\n /\\ interp p hl\n /\\ interp q hr))\nlet id_elim_star p q m =\n let starprop (ml:heap) (mr:heap) =\n disjoint ml mr\n /\\ m == join ml mr\n /\\ interp p ml\n /\\ interp q mr\n in\n elim_star p q m;\n let p1 : heap -> prop = fun ml -> (exists mr. starprop ml mr) in\n let ml = IndefiniteDescription.indefinite_description_tot _ p1 in\n let starpropml mr : prop = starprop ml mr in // this prop annotation seems needed\n let mr = IndefiniteDescription.indefinite_description_tot _ starpropml in\n (ml, mr)", "val commute_star_right (#st: st) (p q r: st.hprop)\n : Lemma ((p `st.star` (q `st.star` r)) `st.equals` (p `st.star` (r `st.star` q)))\nlet commute_star_right (#st:st) (p q r:st.hprop)\n: Lemma ((p `st.star` (q `st.star` r)) `st.equals` (p `st.star` (r `st.star` q)))\n= calc (st.equals) {\n p `st.star` (q `st.star` r);\n (st.equals) { equals_ext_right p (q `st.star` r) (r `st.star` q) }\n p `st.star` (r `st.star` q);\n }", "val commute_star_right (#st: st) (p q r: st.hprop)\n : Lemma ((p `st.star` (q `st.star` r)) `st.equals` (p `st.star` (r `st.star` q)))\nlet commute_star_right (#st:st) (p q r:st.hprop)\n : Lemma\n ((p `st.star` (q `st.star` r)) `st.equals`\n (p `st.star` (r `st.star` q)))\n =\n calc (st.equals) {\n p `st.star` (q `st.star` r);\n (st.equals) { equals_ext_right p (q `st.star` r) (r `st.star` q) }\n p `st.star` (r `st.star` q);\n }", "val rearrange3 (p q r: vprop) : Lemma (((p `star` q) `star` r) `equiv` (p `star` (r `star` q)))\nlet rearrange3 (p q r:vprop) : Lemma\n (((p `star` q) `star` r) `equiv` (p `star` (r `star` q)))\n = let open FStar.Tactics in\n assert (((p `star` q) `star` r) `equiv` (p `star` (r `star` q))) by\n (norm [delta_attr [`%__reduce__]]; canon' false (`true_p) (`true_p))", "val intro_wand (p1 p2: slprop u#a) (m:mem)\n : Lemma ((forall m1. m `disjoint` m1 /\\ interp p1 m1 ==> interp p2 (join m m1))\n ==> interp (wand p1 p2) m)\nlet intro_wand (p1 p2: slprop u#a) (m:mem) = \n introduce \n (forall m1. m `disjoint` m1 /\\ interp p1 m1 ==> interp p2 (join m m1))\n ==> interp (wand p1 p2) m\n with _. (\n assert (forall m1. m `disjoint` m1 /\\ interp p1 m1 ==> interp p2 (join m m1));\n H.intro_wand p1 p2 (heap_of_mem m);\n let h = heap_of_mem m in\n assert ((forall h1. h `H.disjoint` h1 /\\ H.interp p1 h1 ==> H.interp p2 (H.join h h1))\n ==> H.interp (wand p1 p2) h);\n introduce forall h1. (h `H.disjoint` h1 /\\ H.interp p1 h1 ==> H.interp p2 (H.join h h1))\n with (\n introduce (h `H.disjoint` h1 /\\ H.interp p1 h1) ==> H.interp p2 (H.join h h1)\n with _. (\n assert (h `H.disjoint` h1);\n let m1 = {\n ctr = m.ctr;\n heap = h1;\n locks = m.locks\n }\n in assert (m `disjoint` m1)\n )\n )\n )", "val join_preserves_interp (hp: slprop) (m0: hmem hp) (m1: mem{disjoint m0 m1})\n : Lemma (interp hp (join m0 m1)) [SMTPat (interp hp (join m0 m1))]\nlet join_preserves_interp (hp:slprop) (m0:hmem hp) (m1:mem{disjoint m0 m1})\n: Lemma\n (interp hp (join m0 m1))\n [SMTPat (interp hp (join m0 m1))]\n= let open Steel.Memory in\n intro_emp m1;\n intro_star hp emp m0 m1;\n affine_star hp emp (join m0 m1)", "val rearrange_pqr_prq (p q r: slprop)\n : Lemma (((p `star` q) `star` r) `equiv` ((p `star` r) `star` q))\nlet rearrange_pqr_prq (p q r:slprop)\n : Lemma (((p `star` q) `star` r) `equiv`\n ((p `star` r) `star` q))\n = calc (equiv)\n {\n (p `star` q) `star` r;\n (equiv) { star_associative p q r }\n p `star` (q `star` r);\n (equiv) {\n star_commutative q r;\n star_congruence p (q `star` r) p (r `star` q)\n }\n p `star` (r `star` q);\n (equiv) { star_associative p r q }\n (p `star` r) `star` q;\n }", "val rearrange_pqr_prq (p q r: slprop)\n : Lemma (((p `star` q) `star` r) `equiv` ((p `star` r) `star` q))\nlet rearrange_pqr_prq (p q r:slprop)\n : Lemma (((p `star` q) `star` r) `equiv`\n ((p `star` r) `star` q))\n = calc (equiv)\n {\n (p `star` q) `star` r;\n (equiv) { star_associative p q r }\n p `star` (q `star` r);\n (equiv) {\n star_commutative q r;\n star_congruence p (q `star` r) p (r `star` q)\n }\n p `star` (r `star` q);\n (equiv) { star_associative p r q }\n (p `star` r) `star` q;\n }", "val rewrite_slprop0\n (#opened: inames)\n (p q: vprop)\n (proof: (m: mem -> Lemma (requires interp (hp_of p) m) (ensures interp (hp_of q) m)))\n : repr unit false opened Unobservable p (fun _ -> q) (fun _ -> True) (fun _ _ _ -> True)\nlet rewrite_slprop0 (#opened:inames) (p q:vprop)\n (proof:(m:mem) -> Lemma\n (requires interp (hp_of p) m)\n (ensures interp (hp_of q) m)\n ) : repr unit false opened Unobservable p (fun _ -> q)\n (fun _ -> True) (fun _ _ _ -> True)\n = fun frame ->\n let m:full_mem = NMSTTotal.get () in\n proof (core_mem m);\n Classical.forall_intro (Classical.move_requires proof);\n Mem.star_associative (hp_of p) frame (locks_invariant opened m);\n intro_star p q (frame `Mem.star` locks_invariant opened m) (sel_of p m) (sel_of q m) m proof;\n Mem.star_associative (hp_of q) frame (locks_invariant opened m)", "val hmem_with_inv_equiv (e: _) (m: mem) (p: slprop)\n : Lemma\n (interp (p `star` (linv e m)) m <==>\n interp (p `star` (lock_store_invariant e m.locks)) m /\\ heap_ctr_valid m.ctr (heap_of_mem m))\nlet hmem_with_inv_equiv e (m:mem) (p:slprop)\n : Lemma (interp (p `star` linv e m) m <==>\n interp (p `star` lock_store_invariant e m.locks) m /\\\n heap_ctr_valid m.ctr (heap_of_mem m))\n = calc (<==>) {\n interp (p `star` linv e m) m;\n (<==>) { H.star_associative p (lock_store_invariant e m.locks) (ctr_validity m.ctr (heap_of_mem m)) }\n interp ((p `star` lock_store_invariant e m.locks) `star` ctr_validity m.ctr (heap_of_mem m)) m;\n (<==>) { H.pure_star_interp (p `star` lock_store_invariant e m.locks) (heap_ctr_valid m.ctr (heap_of_mem m)) (heap_of_mem m) }\n interp ((p `star` lock_store_invariant e m.locks) `star` emp) m /\\\n (heap_ctr_valid m.ctr (heap_of_mem m));\n (<==>) { H.emp_unit (p `star` lock_store_invariant e m.locks) }\n interp (p `star` lock_store_invariant e m.locks) m /\\\n (heap_ctr_valid m.ctr (heap_of_mem m));\n }", "val hmem_with_inv_equiv (e: _) (m: mem) (p: slprop)\n : Lemma\n (interp (p `star` (linv e m)) m <==>\n interp (p `star` (lock_store_invariant e m.locks)) m /\\ heap_ctr_valid m.ctr (heap_of_mem m))\nlet hmem_with_inv_equiv e (m:mem) (p:slprop)\n : Lemma (interp (p `star` linv e m) m <==>\n interp (p `star` lock_store_invariant e m.locks) m /\\\n heap_ctr_valid m.ctr (heap_of_mem m))\n = calc (<==>) {\n interp (p `star` linv e m) m;\n (<==>) { H.star_associative p (lock_store_invariant e m.locks) (ctr_validity m.ctr (heap_of_mem m)) }\n interp ((p `star` lock_store_invariant e m.locks) `star` ctr_validity m.ctr (heap_of_mem m)) m;\n (<==>) { H.pure_star_interp (p `star` lock_store_invariant e m.locks) (heap_ctr_valid m.ctr (heap_of_mem m)) (heap_of_mem m) }\n interp ((p `star` lock_store_invariant e m.locks) `star` emp) m /\\\n (heap_ctr_valid m.ctr (heap_of_mem m));\n (<==>) { H.emp_unit (p `star` lock_store_invariant e m.locks) }\n interp (p `star` lock_store_invariant e m.locks) m /\\\n (heap_ctr_valid m.ctr (heap_of_mem m));\n }", "val implies_trans_l1 (#opened: _) (p q1 q2 r: vprop)\n : STGhostT unit\n opened\n ((p @==> q1) `star` ((q1 `star` q2) @==> r))\n (fun _ -> (p `star` q2) @==> r)\nlet implies_trans_l1\n (#opened: _)\n (p q1 q2 r: vprop)\n: STGhostT unit opened\n ((p @==> q1) `star` ((q1 `star` q2) @==> r))\n (fun _ -> (p `star` q2) @==> r)\n= implies_reg_r p q1 q2;\n implies_trans (p `star` q2) (q1 `star` q2) r", "val preserves_frame_cong (e: inames) (p q r s: slprop) (m0 m1: mem)\n : Lemma (requires p `equiv` r /\\ q `equiv` s /\\ preserves_frame e p q m0 m1)\n (ensures preserves_frame e r s m0 m1)\nlet preserves_frame_cong (e:inames) (p q:slprop) (r s:slprop) (m0 m1:mem)\n : Lemma\n (requires p `equiv` r /\\ q `equiv` s /\\ preserves_frame e p q m0 m1)\n (ensures\n preserves_frame e r s m0 m1)\n = let aux0 (p q r s:slprop)\n : Lemma\n (requires p `equiv` s)\n (ensures (((p `star` q) `star` r) `equiv`\n ((s `star` q) `star` r)))\n = star_congruence p q s q;\n star_congruence (p `star` q) r (s `star` q) r\n in\n let aux (frame:slprop)\n : Lemma (requires interp ((r `star` frame) `star` locks_invariant e m0) m0)\n (ensures interp ((s `star` frame) `star` locks_invariant e m1) m1 /\\\n interp ((p `star` frame) `star` locks_invariant e m0) m0)\n [SMTPat (r `star` frame)]\n = aux0 p frame (locks_invariant e m0) r;\n aux0 q frame (locks_invariant e m1) s;\n assert (((p `star` frame) `star` locks_invariant e m0) `equiv`\n ((r `star` frame) `star` locks_invariant e m0));\n assert (interp ((p `star` frame) `star` locks_invariant e m0) m0);\n assert (interp ((q `star` frame) `star` locks_invariant e m1) m1);\n assert (((q `star` frame) `star` locks_invariant e m1) `equiv`\n ((s `star` frame) `star` locks_invariant e m1));\n ()\n in\n ()", "val preserves_frame_cong (e: inames) (p q r s: slprop) (m0 m1: mem)\n : Lemma (requires p `equiv` r /\\ q `equiv` s /\\ preserves_frame e p q m0 m1)\n (ensures preserves_frame e r s m0 m1)\nlet preserves_frame_cong (e:inames) (p q:slprop) (r s:slprop) (m0 m1:mem)\n : Lemma\n (requires p `equiv` r /\\ q `equiv` s /\\ preserves_frame e p q m0 m1)\n (ensures\n preserves_frame e r s m0 m1)\n = let aux0 (p q r s:slprop)\n : Lemma\n (requires p `equiv` s)\n (ensures (((p `star` q) `star` r) `equiv`\n ((s `star` q) `star` r)))\n = star_congruence p q s q;\n star_congruence (p `star` q) r (s `star` q) r\n in\n let aux (frame:slprop)\n : Lemma (requires interp ((r `star` frame) `star` locks_invariant e m0) m0)\n (ensures interp ((s `star` frame) `star` locks_invariant e m1) m1 /\\\n interp ((p `star` frame) `star` locks_invariant e m0) m0)\n [SMTPat (r `star` frame)]\n = aux0 p frame (locks_invariant e m0) r;\n aux0 q frame (locks_invariant e m1) s;\n assert (((p `star` frame) `star` locks_invariant e m0) `equiv`\n ((r `star` frame) `star` locks_invariant e m0));\n assert (interp ((p `star` frame) `star` locks_invariant e m0) m0);\n assert (interp ((q `star` frame) `star` locks_invariant e m1) m1);\n assert (((q `star` frame) `star` locks_invariant e m1) `equiv`\n ((s `star` frame) `star` locks_invariant e m1));\n ()\n in\n ()", "val equiv_ext_right (p q r: slprop)\n : Lemma (requires q `Mem.equiv` r) (ensures Mem.((p `star` q) `equiv` (p `star` r)))\nlet equiv_ext_right (p q r:slprop)\n : Lemma\n (requires q `Mem.equiv` r)\n (ensures Mem.((p `star` q) `equiv` (p `star` r)))\n = let open Steel.Memory in\n calc (equiv) {\n p `star` q;\n (equiv) { star_commutative p q }\n q `star` p;\n (equiv) { equiv_extensional_on_star q r p }\n r `star` p;\n (equiv) { star_commutative p r }\n p `star` r;\n }", "val intro_h_forall (#a:_) (p:a -> slprop) (m:mem)\n : Lemma ((forall x. interp (p x) m) ==> interp (h_forall p) m)\nlet intro_h_forall (#a:_) (p:a -> slprop) (m:mem) = H.intro_h_forall p (heap_of_mem m)", "val implies_trans_r1 (#opened: _) (q1 p q2 r: vprop)\n : STGhostT unit\n opened\n ((p @==> q2) `star` ((q1 `star` q2) @==> r))\n (fun _ -> (q1 `star` p) @==> r)\nlet implies_trans_r1\n (#opened: _)\n (q1 p q2 r: vprop)\n: STGhostT unit opened\n ((p @==> q2) `star` ((q1 `star` q2) @==> r))\n (fun _ -> (q1 `star` p) @==> r)\n= implies_reg_l q1 p q2;\n implies_trans (q1 `star` p) (q1 `star` q2) r", "val elim_wand (p1 p2: slprop u#a) (m:mem) (m1:mem)\n : Lemma ((interp (wand p1 p2) m /\\ m `disjoint` m1 /\\ interp p1 m1)\n ==> interp p2 (join m m1))\nlet elim_wand (p1 p2: slprop u#a) (m:mem) (m1:mem) = H.elim_wand p1 p2 (heap_of_mem m) (heap_of_mem m1)", "val can_be_split_congr_r\n (p q r: vprop)\n: Lemma\n (requires (p `can_be_split` q))\n (ensures ((r `star` p) `can_be_split` (r `star` q)))\nlet can_be_split_congr_r p q r =\n Classical.forall_intro (interp_star (hp_of r) (hp_of p));\n Classical.forall_intro (interp_star (hp_of r) (hp_of q))", "val implies_trans_l2 (#opened: _) (p q1 q2 r1: vprop)\n : STGhostT unit\n opened\n ((p @==> (q1 `star` q2)) `star` (q1 @==> r1))\n (fun _ -> p @==> (r1 `star` q2))\nlet implies_trans_l2\n (#opened: _)\n (p q1 q2 r1: vprop)\n: STGhostT unit opened\n ((p @==> (q1 `star` q2)) `star` (q1 @==> r1))\n (fun _ -> p @==> (r1 `star` q2))\n= implies_reg_r q1 r1 q2;\n implies_trans p (q1 `star` q2) (r1 `star` q2)", "val equiv_ext_right (p q r: slprop)\n : Lemma (requires q `equiv` r) (ensures (p `star` q) `equiv` (p `star` r))\nlet equiv_ext_right (p q r:slprop)\n : Lemma\n (requires q `equiv` r)\n (ensures (p `star` q) `equiv` (p `star` r))\n = calc (equiv) {\n p `star` q;\n (equiv) { star_commutative p q }\n q `star` p;\n (equiv) { equiv_extensional_on_star q r p }\n r `star` p;\n (equiv) { star_commutative p r }\n p `star` r;\n }", "val equiv_ext_right (p q r: slprop)\n : Lemma (requires q `equiv` r) (ensures (p `star` q) `equiv` (p `star` r))\nlet equiv_ext_right (p q r:slprop)\n : Lemma\n (requires q `equiv` r)\n (ensures (p `star` q) `equiv` (p `star` r))\n = calc (equiv) {\n p `star` q;\n (equiv) { star_commutative p q }\n q `star` p;\n (equiv) { equiv_extensional_on_star q r p }\n r `star` p;\n (equiv) { star_commutative p r }\n p `star` r;\n }", "val h_exists_cong (#a:Type) (p q : a -> slprop)\n : Lemma\n (requires (forall x. p x `equiv` q x))\n (ensures (h_exists p `equiv` h_exists q))\nlet h_exists_cong (#a:Type) (p q : a -> slprop)\n : Lemma\n (requires (forall x. p x `equiv` q x))\n (ensures (h_exists p `equiv` h_exists q))\n = equiv_heap_iff_equiv_forall ();\n H.h_exists_cong p q", "val h_exists_cong (#a:Type) (p q : a -> slprop)\n : Lemma\n (requires (forall x. p x `equiv` q x))\n (ensures (h_exists p `equiv` h_exists q))\nlet h_exists_cong (#a:Type) (p q : a -> slprop)\n : Lemma\n (requires (forall x. p x `equiv` q x))\n (ensures (h_exists p `equiv` h_exists q))\n = equiv_heap_iff_equiv_forall ();\n H.h_exists_cong p q", "val can_be_split_congr_l\n (p q r: vprop)\n: Lemma\n (requires (p `can_be_split` q))\n (ensures ((p `star` r) `can_be_split` (q `star` r)))\nlet can_be_split_congr_l p q r =\n Classical.forall_intro (interp_star (hp_of p) (hp_of r));\n Classical.forall_intro (interp_star (hp_of q) (hp_of r))", "val interp (p:slprop u#a) (m:mem u#a) : prop\nlet interp p m = H.interp p m.heap", "val interp (p:slprop u#a) (m:mem u#a) : prop\nlet interp p m = H.interp p m.heap", "val slimp_star (p q r s : slprop)\n : Lemma (requires (slimp p q /\\ slimp r s))\n (ensures (slimp (p `star` r) (q `star` s)))\nlet slimp_star (p q r s : slprop)\n : Lemma (requires (slimp p q /\\ slimp r s))\n (ensures (slimp (p `star` r) (q `star` s)))\n = let aux (m:mem) : Lemma (requires (interp (p `star` r) m))\n (ensures (interp (q `star` s) m))\n =\n let (ml, mr) = id_elim_star p r m in\n intro_star q s ml mr\n in\n Classical.forall_intro (Classical.move_requires aux)", "val implies_trans_r2 (#opened: _) (p q1 q2 r2: vprop)\n : STGhostT unit\n opened\n ((p @==> (q1 `star` q2)) `star` (q2 @==> r2))\n (fun _ -> p @==> (q1 `star` r2))\nlet implies_trans_r2\n (#opened: _)\n (p q1 q2 r2: vprop)\n: STGhostT unit opened\n ((p @==> (q1 `star` q2)) `star` (q2 @==> r2))\n (fun _ -> p @==> (q1 `star` r2))\n= implies_reg_l q1 q2 r2;\n implies_trans p (q1 `star` q2) (q1 `star` r2)", "val conv\n (#st: state u#s u#act)\n (a: Type u#a)\n (#p: st.pred)\n (#q: post st a)\n (q': post st a {forall x. q x == q' x})\n : Lemma (m a p q == m a p q')\nlet conv (#st:state u#s u#act) (a:Type u#a)\n (#p:st.pred)\n (#q:post st a)\n (q':post st a { forall x. q x == q' x })\n: Lemma (m a p q == m a p q')\n= F.extensionality _ _ q q'", "val vdep_sel_eq (v: vprop) (p: ( (t_of v) -> Tot vprop)) (m: Mem.hmem (vdep_hp v p)) : Lemma\n (\n interp (hp_of v) m /\\\n begin let x = sel_of v m in\n interp (hp_of (p x)) m /\\\n vdep_sel v p m == (| x, sel_of (p x) m |)\n end\n )\nlet vdep_sel_eq\n v p m\n= Classical.forall_intro_2 (Classical.move_requires_2 (fun (m0 m1: mem) -> (join_commutative m0) m1));\n ()", "val assoc_star_right (#st: st) (p q r s: st.hprop)\n : Lemma\n ((p `st.star` ((q `st.star` r) `st.star` s))\n `st.equals`\n (p `st.star` (q `st.star` (r `st.star` s))))\nlet assoc_star_right (#st:st) (p q r s:st.hprop)\n: Lemma\n ((p `st.star` ((q `st.star` r) `st.star` s)) `st.equals`\n (p `st.star` (q `st.star` (r `st.star` s))))\n= calc (st.equals) {\n p `st.star` ((q `st.star` r) `st.star` s);\n (st.equals) { equals_ext_right p ((q `st.star` r) `st.star` s)\n (q `st.star` (r `st.star` s)) }\n p `st.star` (q `st.star` (r `st.star` s));\n }", "val assoc_star_right (#st: st) (p q r s: st.hprop)\n : Lemma\n ((p `st.star` ((q `st.star` r) `st.star` s))\n `st.equals`\n (p `st.star` (q `st.star` (r `st.star` s))))\nlet assoc_star_right (#st:st) (p q r s:st.hprop)\n : Lemma\n ((p `st.star` ((q `st.star` r) `st.star` s)) `st.equals`\n (p `st.star` (q `st.star` (r `st.star` s))))\n =\n calc (st.equals) {\n p `st.star` ((q `st.star` r) `st.star` s);\n (st.equals) { equals_ext_right p ((q `st.star` r) `st.star` s)\n (q `st.star` (r `st.star` s)) }\n p `st.star` (q `st.star` (r `st.star` s));\n }", "val lemma_functoriality (p:mem_predicate{witnessed p}) (q:mem_predicate{(forall (h:mem). p h ==> q h)})\n : Lemma (witnessed q)\nlet lemma_functoriality p q = W.lemma_witnessed_weakening mem_rel p q", "val equiv_star_emp_r (p: vprop) : Lemma ((p `star` emp) `equiv` p)\nlet equiv_star_emp_r (p:vprop)\n : Lemma ((p `star` emp) `equiv` p)\n = cm_identity p;\n assert ((emp `star` p) `equiv` p);\n star_commutative p emp;\n equiv_trans (p `star` emp) (emp `star` p) p", "val equiv_star_emp_r (p: vprop) : Lemma ((p `star` emp) `equiv` p)\nlet equiv_star_emp_r (p:vprop)\n : Lemma ((p `star` emp) `equiv` p)\n = cm_identity p;\n assert ((emp `star` p) `equiv` p);\n star_commutative p emp;\n equiv_trans (p `star` emp) (emp `star` p) p", "val interp_depends_only_on (hp:slprop u#a)\n : Lemma\n (forall (m0:hmem hp) (m1:mem u#a{disjoint m0 m1}).\n interp hp m0 <==> interp hp (join m0 m1))\nlet interp_depends_only_on (hp:slprop u#a) = H.interp_depends_only_on hp", "val interp_depends_only_on (hp:slprop u#a)\n : Lemma\n (forall (m0:hmem hp) (m1:mem u#a{disjoint m0 m1}).\n interp hp m0 <==> interp hp (join m0 m1))\nlet interp_depends_only_on (hp:slprop u#a) = H.interp_depends_only_on hp", "val change_slprop_2 (#opened:inames) (p q:vprop) (vq:erased (t_of q))\n (l:(m:mem) -> Lemma\n (requires interp (hp_of p) m)\n (ensures interp (hp_of q) m /\\ sel_of q m == reveal vq)\n ) : SteelGhost unit opened p (fun _ -> q) (fun _ -> True) (fun _ _ h1 -> h1 q == reveal vq)\nlet change_slprop_2 p q vq l = SteelGhost?.reflect (change_slprop_20 p q vq l)", "val pts_to_ref_injective\n (#a: Type u#0)\n (r: ref a)\n (p0 p1:perm)\n (v0 v1:a)\n (m:mem)\n : Lemma\n (requires\n interp (pts_to_sl r p0 v0 `Mem.star` pts_to_sl r p1 v1) m)\n (ensures v0 == v1)\nlet pts_to_ref_injective\n (#a: Type u#0)\n (r: ref a)\n (p0 p1:perm)\n (v0 v1:a)\n (m:mem)\n : Lemma\n (requires\n interp (pts_to_sl r p0 v0 `Mem.star` pts_to_sl r p1 v1) m)\n (ensures v0 == v1)\n = let v0' = U.raise_val v0 in\n let v1' = U.raise_val v1 in\n H.pts_to_ref_injective r p0 p1 v0' v1' m;\n raise_val_inj v0 v1", "val interp_rec_mono_aux (#a: _) (r: rec_def a) (p q: pred a) (x: a)\n : Lemma (requires forall x. slimp (p x) (q x))\n (ensures slimp (interp_rec r p x) (interp_rec r q x))\nlet rec interp_rec_mono_aux #a (r: rec_def a) (p q: pred a) (x: a):\n Lemma (requires forall x. slimp (p x) (q x))\n (ensures slimp (interp_rec r p x) (interp_rec r q x))\n= match r with\n| And r1 r2 ->\n h_and_equiv_forall (interp_rec r1 p x) (interp_rec r2 p x);\n h_and_equiv_forall (interp_rec r1 q x) (interp_rec r2 q x);\n interp_rec_mono_aux r1 p q x;\n interp_rec_mono_aux r2 p q x\n| Or r1 r2 ->\n h_or_equiv_forall (interp_rec r1 p x) (interp_rec r2 p x);\n h_or_equiv_forall (interp_rec r1 q x) (interp_rec r2 q x);\n interp_rec_mono_aux r1 p q x;\n interp_rec_mono_aux r2 p q x\n| Forall ty fr ->\n introduce forall y. (slimp (interp_rec (fr y) p x) (interp_rec (fr y) q x))\n with (interp_rec_mono_aux (fr y) p q x);\n interp_rec_forall_def ty fr x p;\n interp_rec_forall_def ty fr x q;\n h_forall_equiv_forall (fun y -> interp_rec (fr y) p x);\n h_forall_equiv_forall (fun y -> interp_rec (fr y) q x)\n| Exists ty fr ->\n introduce forall y. (slimp (interp_rec (fr y) p x) (interp_rec (fr y) q x))\n with (interp_rec_mono_aux (fr y) p q x);\n interp_rec_exists_def ty fr x p;\n interp_rec_exists_def ty fr x q;\n h_exists_equiv_forall (fun y -> interp_rec (fr y) p x);\n h_exists_equiv_forall (fun y -> interp_rec (fr y) q x)\n| SLProp _ -> ()\n| RecursiveCall f -> ()\n| Star r1 r2 -> \n star_equiv_forall (interp_rec r1 p x) (interp_rec r2 p x);\n star_equiv_forall (interp_rec r1 q x) (interp_rec r2 q x);\n interp_rec_mono_aux r1 p q x;\n interp_rec_mono_aux r2 p q x\n| Wand f r' ->\n wand_equiv_forall (f x) (interp_rec r' p x);\n wand_equiv_forall (f x) (interp_rec r' q x);\n interp_rec_mono_aux r' p q x", "val star_congruence (p1 p2 p3 p4:vprop)\n : Lemma (requires p1 `equiv` p3 /\\ p2 `equiv` p4)\n (ensures (p1 `star` p2) `equiv` (p3 `star` p4))\nlet star_congruence p1 p2 p3 p4 = Mem.star_congruence (hp_of p1) (hp_of p2) (hp_of p3) (hp_of p4)", "val implies_swap_r (#opened: _) (p q1 q2: vprop)\n : STGhostT unit opened (p @==> (q1 `star` q2)) (fun _ -> p @==> (q2 `star` q1))\nlet implies_swap_r\n (#opened: _)\n (p q1 q2: vprop)\n: STGhostT unit opened\n (p @==> (q1 `star` q2))\n (fun _ -> p @==> (q2 `star` q1))\n= implies_with_tactic (q1 `star` q2) (q2 `star` q1);\n implies_trans p (q1 `star` q2) (q2 `star` q1)", "val pts_to_ref_injective\n (#a: Type u#1)\n (r: ref a)\n (p0 p1:perm)\n (v0 v1:a)\n (m:mem)\n : Lemma\n (requires\n interp (pts_to_sl r p0 v0 `Mem.star` pts_to_sl r p1 v1) m)\n (ensures v0 == v1)\nlet pts_to_ref_injective\n (#a: Type u#1)\n (r: ref a)\n (p0 p1:perm)\n (v0 v1:a)\n (m:mem)\n : Lemma\n (requires\n interp (pts_to_sl r p0 v0 `Mem.star` pts_to_sl r p1 v1) m)\n (ensures v0 == v1)\n = let open Steel.Memory in\n abcd_acbd (hp_of (pts_to_raw r p0 v0))\n (pure (perm_ok p0))\n (hp_of (pts_to_raw r p1 v1))\n (pure (perm_ok p1));\n Mem.affine_star (hp_of (pts_to_raw r p0 v0) `star` hp_of (pts_to_raw r p1 v1))\n (pure (perm_ok p0) `star` pure (perm_ok p1)) m;\n Mem.pts_to_compatible r (Some (Ghost.reveal v0, p0))\n (Some (Ghost.reveal v1, p1))\n m", "val intro_h_exists (#a:_) (x:a) (p:a -> slprop) (m:mem)\n : Lemma (interp (p x) m ==> interp (h_exists p) m)\nlet intro_h_exists #a x p m = H.intro_h_exists x p (heap_of_mem m)", "val intro_h_exists (#a:_) (x:a) (p:a -> slprop) (m:mem)\n : Lemma (interp (p x) m ==> interp (h_exists p) m)\nlet intro_h_exists #a x p m = H.intro_h_exists x p (heap_of_mem m)", "val interp (p:slprop u#a) (m:heap u#a) : prop\nlet interp (p:slprop u#a) (m:heap u#a)\n : Tot prop\n = p m", "val interp (p:slprop u#a) (m:heap u#a) : prop\nlet interp (p:slprop u#a) (m:heap u#a)\n : Tot prop\n = p m", "val star_congruence (p1 p2 p3 p4:slprop)\n : Lemma (requires p1 `equiv` p3 /\\ p2 `equiv` p4)\n (ensures (p1 `star` p2) `equiv` (p3 `star` p4))\nlet star_congruence (p1 p2 p3 p4:slprop) =\n equiv_heap_iff_equiv_forall ();\n H.star_congruence p1 p2 p3 p4", "val star_congruence (p1 p2 p3 p4:slprop)\n : Lemma (requires p1 `equiv` p3 /\\ p2 `equiv` p4)\n (ensures (p1 `star` p2) `equiv` (p3 `star` p4))\nlet star_congruence (p1 p2 p3 p4:slprop) =\n equiv_heap_iff_equiv_forall ();\n H.star_congruence p1 p2 p3 p4", "val implies_concl_r (#opened: _) (q r p: vprop)\n : STGhostT unit opened (p `star` (q @==> r)) (fun _ -> q @==> (r `star` p))\nlet implies_concl_r\n (#opened: _)\n (q r p: vprop)\n: STGhostT unit opened\n (p `star` (q @==> r))\n (fun _ -> q @==> (r `star` p))\n= implies_concl_l p q r;\n implies_with_tactic (p `star` r) (r `star` p);\n implies_trans q (p `star` r) (r `star` p)", "val star_commutative (p1 p2:vprop)\n : Lemma ((p1 `star` p2) `equiv` (p2 `star` p1))\nlet star_commutative p1 p2 = Mem.star_commutative (hp_of p1) (hp_of p2)", "val vprop_equiv (p q:vprop) : prop\nlet vprop_equiv = slprop_equiv", "val implies_reg_l (#opened: _) (p q r: vprop)\n : STGhostT unit opened (q @==> r) (fun _ -> (p `star` q) @==> (p `star` r))\nlet implies_reg_l\n (#opened: _)\n (p q r: vprop)\n: STGhostT unit opened\n (q @==> r)\n (fun _ -> (p `star` q) @==> (p `star` r))\n= implies_with_tactic p p;\n implies_join p p q r" ], "closest_src": [ { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.interp_star" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.intro_vdep_lemma" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fst", "name": "Steel.ST.HigherArray.pure_star_interp'" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.pure_star_interp" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.pure_star_interp" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.affine_star" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.affine_star" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.intro_h_and" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.elim_star" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.elim_star" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.interp_vdep_hp" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.intro_h_or_right" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.elim_h_and" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.intro_star" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.elim_h_or" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.pure_interp" }, { "project_name": "steel", "file_name": "Steel.Memory.fsti", "name": "Steel.Memory.affine_star_smt" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.affine_star_smt" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.intro_h_or_left" }, { "project_name": "steel", "file_name": "Steel.Coinduction.fst", "name": "Steel.Coinduction.h_and_equiv" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.elim_vdep_lemma" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.pure_interp" }, { "project_name": "steel", "file_name": "Steel.Coinduction.fst", "name": "Steel.Coinduction.star_equiv_forall" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.intro_star" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.intro_star" }, { "project_name": "steel", "file_name": "Steel.Coinduction.fst", "name": "Steel.Coinduction.wand_equiv_forall" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.commute_star_par_l" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.ac_reasoning_for_m_frame_preserving" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.ac_reasoning_for_m_frame_preserving" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.commute_star_par_r" }, { "project_name": "steel", "file_name": "Steel.Coinduction.fst", "name": "Steel.Coinduction.h_or_equiv_forall" }, { "project_name": "steel", "file_name": "Steel.Coinduction.fst", "name": "Steel.Coinduction.h_and_equiv_forall" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.cas_action_helper" }, { "project_name": "steel", "file_name": "Steel.Effect.fst", "name": "Steel.Effect.can_be_split_3_interp" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.id_elim_star" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.weaken" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.preserves_frame_star_pure" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.preserves_frame_star_pure" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.rearrange_invariant" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.rearrange_invariant" }, { "project_name": "steel", "file_name": "CSL.Semantics.fst", "name": "CSL.Semantics.commute_assoc_star_right" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.commute_assoc_star_right" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.equiv_pqrs_p_qr_s" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.equiv_pqrs_p_qr_s" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.rewrite_slprop" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.id_elim_star" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.id_elim_star" }, { "project_name": "steel", "file_name": "CSL.Semantics.fst", "name": "CSL.Semantics.commute_star_right" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.commute_star_right" }, { "project_name": "steel", "file_name": "Steel.Primitive.ForkJoin.Unix.fst", "name": "Steel.Primitive.ForkJoin.Unix.rearrange3" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.intro_wand" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.join_preserves_interp" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.rearrange_pqr_prq" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.rearrange_pqr_prq" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.rewrite_slprop0" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.hmem_with_inv_equiv" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.hmem_with_inv_equiv" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_trans_l1" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.preserves_frame_cong" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.preserves_frame_cong" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.equiv_ext_right" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.intro_h_forall" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_trans_r1" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.elim_wand" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.can_be_split_congr_r" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_trans_l2" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.equiv_ext_right" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.equiv_ext_right" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.h_exists_cong" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.h_exists_cong" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.can_be_split_congr_l" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.interp" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.interp" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.slimp_star" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_trans_r2" }, { "project_name": "steel", "file_name": "PulseCore.Semantics.fst", "name": "PulseCore.Semantics.conv" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.vdep_sel_eq" }, { "project_name": "steel", "file_name": "CSL.Semantics.fst", "name": "CSL.Semantics.assoc_star_right" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.assoc_star_right" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fst", "name": "FStar.HyperStack.ST.lemma_functoriality" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.fst", "name": "Steel.ST.Effect.equiv_star_emp_r" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.AtomicAndGhost.fst", "name": "Steel.ST.Effect.AtomicAndGhost.equiv_star_emp_r" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.interp_depends_only_on" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.interp_depends_only_on" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.change_slprop_2" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.pts_to_ref_injective" }, { "project_name": "steel", "file_name": "Steel.Coinduction.fst", "name": "Steel.Coinduction.interp_rec_mono_aux" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.star_congruence" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_swap_r" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.pts_to_ref_injective" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.intro_h_exists" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.intro_h_exists" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.interp" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.interp" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.star_congruence" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.star_congruence" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_concl_r" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.star_commutative" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.vprop_equiv" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_reg_l" } ], "selected_premises": [ "SelectorLogic.star", "Steel.Effect.Common.rmem", "Steel.Effect.Common.to_vprop'", "Steel.Memory.inames", "Steel.Effect.Common.normal", "Steel.Effect.Common.rmem'", "Steel.Effect.Common.t_of", "Steel.Effect.Common.pure", "Steel.Effect.Common.mk_rmem", "Steel.Reference.pts_to", "Steel.Effect.Common.to_vprop", "Steel.FractionalPermission.full_perm", "Steel.Effect.Common.star", "Steel.Effect.Common.hp_of", "Steel.Effect.Common.vrefine'", "Steel.Reference.ptr_sel_interp", "SelectorLogic.left_wand_t", "Steel.Effect.Common.focus_rmem_refl", "Steel.Effect.Common.rm", "Steel.Effect.Common.hmem", "SelectorLogic.wand", "Steel.Effect.Common.vrefine", "Steel.Reference.sel", "Steel.Reference.read", "FStar.Mul.op_Star", "Steel.Reference.intro_ptr_interp", "Steel.Memory.full_mem", "Steel.Reference.ghost_gather", "Steel.Effect.Common.focus_rmem", "Steel.Reference.ghost_vptr", "Steel.Effect.Atomic.h_exists", "Steel.Memory.hmem", "Steel.Effect.Common.guard_vprop", "Steel.Reference.ghost_ptr_sel_interp", "FStar.UInt.size", "Steel.Effect.Common.normal_steps", "Steel.Reference.vptr_not_null", "Steel.Effect.Common.req", "FStar.List.Tot.Base.length", "Steel.Effect.Common.inv", "Steel.Preorder.pcm_history", "Steel.Reference.ghost_read", "FStar.List.Tot.Base.map", "Steel.Reference.ghost_sel", "Steel.FractionalPermission.comp_perm", "Steel.Effect.Common.mk_rmem'", "Steel.Reference.vptrp", "FStar.PCM.composable", "Steel.Effect.Common.vc_norm", "FStar.Reflection.V2.Data.var", "Steel.Effect.Common.frame_equalities", "SelectorLogic.star_split", "FStar.Real.two", "Steel.Effect.Common.sel_of", "Steel.Effect.Common.focus_rmem'", "FStar.Real.one", "FStar.Pervasives.reveal_opaque", "Steel.Effect.Atomic.gget", "Steel.Effect.Atomic.mk_selector_vprop", "Steel.Reference.ptr_sel", "Steel.Effect.Common.return_pre", "Steel.Effect.return_req", "Steel.Effect.Atomic.return_req", "FStar.PCM.op", "Steel.FractionalPermission.sum_perm", "Steel.Effect.Common.frame_equalities'", "Steel.Reference.ptr", "Steel.Reference.ghost_pts_to", "FStar.List.Tot.Base.op_At", "Steel.Effect.Common.unrestricted_focus_rmem", "FStar.Reflection.V2.Derived.mk_app", "Steel.Preorder.history_val", "Steel.Reference.vptr", "FStar.Reflection.V2.Derived.mk_e_app", "Steel.Reference.ghost_vptrp", "Steel.Effect.Atomic.if_then_else_req", "Steel.Effect.if_then_else_req", "Steel.Reference.ghost_ptr", "Steel.Effect.subcomp_pre", "FStar.PCM.compatible", "Steel.Effect.Atomic.subcomp_pre", "Steel.Effect.Common.frame_vc_norm", "Steel.Effect.if_then_else_ens", "Steel.Effect.Atomic.if_then_else_ens", "Steel.Effect.Atomic.return_ens", "FStar.FunctionalExtensionality.feq", "Steel.Effect.Common.extract_contexts", "Steel.Effect.Common.unfold_guard", "Steel.Effect.return_ens", "FStar.List.Tot.Base.tl", "FStar.Math.Lemmas.pow2_plus", "FStar.NMSTTotal.get", "Steel.Effect.Common.unrestricted_mk_rmem", "FStar.Reflection.V2.Derived.u_unk", "Steel.Reference.ghost_ptr_sel", "Steel.Effect.Common.selector'", "Steel.Effect.Common.sel_depends_only_on", "FStar.Tactics.CanonCommMonoidSimple.Equiv.term_eq", "FStar.Reflection.V2.Derived.shift_subst", "Steel.Effect.bind_req" ], "source_upto_this": "module SelectorLogic\n\nopen Steel.Memory\nmodule Mem = Steel.Memory\n\n(* Extending selectors to support wand; establishing a correspondence with linear logic *)\n\n#push-options \"--ide_id_info_off\"\n\nlet selector (hp:slprop) (a:(hmem hp) -> Type) = (h:hmem hp -> GTot (a h))\n\n/// The basis of our selector framework: Separation logic assertions enhanced with selectors\n/// Note that selectors are \"optional\", it is always possible to use a non-informative selector,\n/// such as fun _ -> () and to rely on the standard separation logic reasoning\nnoeq\ntype vprop =\n { hp: slprop u#1;\n t:hmem hp -> Type;\n sel:selector hp t }\n\n(* This lemma should be exposed in mem *)\nassume\nval reveal_wand (p q:slprop) (m:mem) : Lemma\n (requires interp (Mem.wand p q) m)\n (ensures forall m1. (m `disjoint` m1 /\\ interp p m1) ==> interp q (join m m1))\n [SMTPat (interp (Mem.wand p q) m)]\n\n\nlet star (p q:vprop) =\n {hp = p.hp `Mem.star` q.hp;\n t = (fun h -> p.t h * q.t h);\n sel = fun h -> p.sel h, q.sel h\n }\n\n(* Separating for clarity *)\nlet left_wand_t (m:mem) (p:vprop) =\n h:hmem p.hp{disjoint h m} & p.t h\n\nlet wand (p q:vprop) =\n {hp = p.hp `Mem.wand` q.hp;\n t = (fun m -> ((x:left_wand_t m p) -> GTot (q.t (join m (dfst x)))));\n sel = fun m0 -> fun (| h, vp |) -> q.sel (join m0 h)\n }\n\n(* Simplification to avoid reasoning about existentials *)\nval star_split (p q:slprop) (m:hmem (p `Mem.star` q))\n : GTot (r:(hmem p * hmem q){disjoint (fst r) (snd r) /\\ join (fst r) (snd r) == m})\n\nlet star_split p q m =\n elim_star p q m;\n let ml = FStar.IndefiniteDescription.indefinite_description_ghost mem (\n fun ml -> exists mr. disjoint ml mr /\\ m == join ml mr /\\ interp p ml /\\ interp q mr) in\n let mr = FStar.IndefiniteDescription.indefinite_description_ghost mem (\n fun mr -> disjoint ml mr /\\ m == join ml mr /\\ interp p ml /\\ interp q mr) in\n ml, mr\n", "sketch": [ "Step 1: Use the definition of `interp` to unfold the interpretation of `p `star` (p `wand` q)`.\nStep 2: Apply the `star_split` lemma to split the memory `m` into two disjoint parts `m1` and `m2` such that `m = join m1 m2`.\nStep 3: Use the interpretation of `p `star` (p `wand` q)` to assert that `interp p m1` and `interp (p `wand` q) m2`.\nStep 4: Use the `reveal_wand` lemma to derive that `interp q (join m1 m2)` from `interp (p `wand` q) m2` and `interp p m1`.\nStep 5: Conclude that `interp q.hp m` since `m = join m1 m2`.", "Step 1: Use the `star_split` lemma to decompose the memory `m` into two parts, `m1` and `m2`, such that `m1` corresponds to `p` and `m2` corresponds to `p `wand` q`.\nStep 2: From the definition of `interp`, deduce that `interp p m1` and `interp (p `wand` q) m2`.\nStep 3: Use the `reveal_wand` lemma to show that `interp (p `wand` q) m2` implies that for any memory `m3` disjoint from `m2`, if `interp p m3` holds, then `interp q (join m2 m3)` holds.\nStep 4: Apply the result from Step 3 with `m3 = m1` to conclude that `interp q (join m2 m1)` holds.\nStep 5: Since `join m2 m1` is equal to `m` (from the `star_split` lemma), conclude that `interp q m` holds.", "Step 1: Use the definition of `star_split` to split the memory `m` into two disjoint parts, `m1` and `m2`, such that `m` is the join of `m1` and `m2`.\nStep 2: Use the interpretation of the `star` operator to deduce that `m1` satisfies `p` and `m2` satisfies `p `wand` q`.\nStep 3: Apply the `reveal_wand` lemma to `m2` to obtain that for any memory `m3` disjoint from `m2` and satisfying `p`, the memory `join m2 m3` satisfies `q`.\nStep 4: Since `m1` satisfies `p` and is disjoint from `m2`, apply the result from Step 3 with `m3 = m1` to conclude that `join m2 m1` satisfies `q`.\nStep 5: Use the fact that `join m2 m1` is equal to `m` to conclude that `m` satisfies `q`.", "Step 1: Use the definition of `interp` to unfold the interpretation of `p `star` (p `wand` q)` in the memory `m`.\nStep 2: Apply the `star_split` lemma to split the memory `m` into two disjoint parts, one for `p` and one for `p `wand` q`.\nStep 3: Use the interpretation of `p `wand` q` to derive that if `p` holds in one part of the memory, then `q` must hold in the combined memory.\nStep 4: Conclude that `q` holds in the memory `m` by combining the results from the previous steps.", "Step 1: Use the definition of `star_split` to decompose the memory `m` into two parts `m1` and `m2` such that `m1` corresponds to `p` and `m2` corresponds to `p `wand` q`.\nStep 2: From the definition of `interp` for `star`, deduce that `interp p m1` and `interp (p `wand` q) m2`.\nStep 3: Apply the `reveal_wand` lemma to `interp (p `wand` q) m2` to obtain that for any memory `m3` disjoint from `m2`, if `interp p m3` holds, then `interp q (join m2 m3)` holds.\nStep 4: Since `m1` and `m2` are disjoint and `interp p m1` holds, apply the result from Step 3 with `m3 = m1` to get `interp q (join m2 m1)`.\nStep 5: Use the fact that `join m2 m1` is equal to `m` to conclude `interp q m`.", "Step 1: Use the definition of `star_split` to decompose the memory `m` into two disjoint parts `m1` and `m2` such that `m = join m1 m2`.\nStep 2: From `star_split`, we know that `m1` satisfies `p` and `m2` satisfies `p `wand` q`.\nStep 3: Use the definition of `interp` for `p `wand` q` on `m2` to obtain that for any memory `m3` disjoint from `m2` that satisfies `p`, the memory `join m2 m3` satisfies `q`.\nStep 4: Since `m1` satisfies `p` and is disjoint from `m2`, apply the result from Step 3 with `m3 = m1` to conclude that `join m2 m1` satisfies `q`.\nStep 5: Note that `join m2 m1` is equal to `m`, thus `m` satisfies `q`.", "Step 1: Use the definition of `star_split` to decompose `m` into two disjoint parts `m1` and `m2` such that `m1` corresponds to `p` and `m2` corresponds to `p `wand` q`.\nStep 2: Use the `reveal_wand` lemma to show that if `interp (p `wand` q) m2` holds, then for any `m3` disjoint from `m2` where `interp p m3` holds, `interp q (join m2 m3)` must hold.\nStep 3: Apply the result from Step 2 to `m1` and `m2` to conclude that `interp q (join m2 m1)` holds.\nStep 4: Since `m` is the join of `m1` and `m2`, and `join m2 m1` is equal to `m`, we conclude that `interp q.hp m` holds.", "Step 1: Use the `star_split` lemma to decompose the memory `m` into two parts, `m1` and `m2`, where `m1` corresponds to `p` and `m2` corresponds to `p `wand` q`.\nStep 2: Use the definition of `interp` for the `star` operation to assert that `interp p m1` and `interp (p `wand` q) m2` hold.\nStep 3: Apply the `reveal_wand` lemma to `m2` to assert that for any memory `m3` disjoint from `m2`, if `interp p m3` holds, then `interp q (join m2 m3)` holds.\nStep 4: Since `m1` and `m2` are disjoint and `interp p m1` holds, apply the result from Step 3 with `m3 = m1` to conclude that `interp q (join m2 m1)` holds.\nStep 5: Use the commutativity of the `join` operation to show that `join m2 m1` is equal to `m`, and thus `interp q m` holds.", "Step 1: Use the definition of `star_split` to decompose the memory `m` into two parts, `m1` and `m2`, such that `m1` corresponds to `p` and `m2` corresponds to `p `wand` q`.\nStep 2: Apply the `reveal_wand` lemma to `m2` to obtain that if `m1` and `m2` are disjoint and `interp p m1` holds, then `interp q (join m1 m2)` holds.\nStep 3: Use the fact that `interp (p `star` (p `wand` q)) m` implies `interp p m1` and `interp (p `wand` q) m2`.\nStep 4: Conclude that `interp q (join m1 m2)` holds, which simplifies to `interp q.hp m` because `join m1 m2` is equal to `m`.", "Step 1: We start by splitting the memory `m` into two parts using the `star_split` function. This will give us two disjoint memory fragments `m1` and `m2` such that `m` is the join of `m1` and `m2`.\nStep 2: Next, we need to show that `m1` satisfies the interpretation of `p` and `m2` satisfies the interpretation of `p `wand` q`.\nStep 3: Using the `reveal_wand` lemma, we can infer that if `m2` satisfies the interpretation of `p `wand` q`, then for any memory `m3` disjoint from `m2` that satisfies `p`, the join of `m2` and `m3` will satisfy `q`.\nStep 4: Since `m1` satisfies `p` and `m2` satisfies `p `wand` q`, we can apply the `reveal_wand` lemma to conclude that the join of `m1` and `m2` (which is `m`) satisfies `q`.\nStep 5: Finally, we conclude that `m` satisfies the interpretation of `q.hp`." ], "generated_solution": [ "let modus_ponens_interp (p q: vprop) (m: hmem (p `star` (p `wand` q)).hp) : Lemma (interp q.hp m) =\n let (m1, m2) = star_split p.hp (p.hp `Mem.wand` q.hp) m in\n assert (interp p.hp m1);\n assert (interp (p.hp `Mem.wand` q.hp) m2);\n reveal_wand p.hp q.hp m2;\n assert (forall m1. (m2 `disjoint` m1 /\\ interp p.hp m1) ==> interp q.hp (join m2 m1));\n assert (m2 `disjoint` m1 /\\ interp p.hp m1);\n assert (interp q.hp (join m2 m1));\n assert (m == join m1 m2);\n assert (interp q.hp m)", "let modus_ponens_interp (p q: vprop) (m: hmem (p `star` (p `wand` q)).hp) : Lemma (interp q.hp m) =\n let (m1, m2) = star_split p.hp (p.hp `Mem.wand` q.hp) m in\n let interp_p_m1 = interp p.hp m1 in\n let interp_wand_pq_m2 = interp (p.hp `Mem.wand` q.hp) m2 in\n reveal_wand p.hp q.hp m2;\n let interp_q_join_m2_m1 = interp q.hp (join m2 m1) in\n assert (join m2 m1 == m);\n interp_q_join_m2_m1", "let modus_ponens_interp p q m =\n let (m1, m2) = star_split p.hp (p.hp `Mem.wand` q.hp) m in\n assert (interp p.hp m1);\n assert (interp (p.hp `Mem.wand` q.hp) m2);\n reveal_wand p.hp q.hp m2;\n assert (forall m3. (disjoint m2 m3 /\\ interp p.hp m3) ==> interp q.hp (join m2 m3));\n assert (disjoint m2 m1 /\\ interp p.hp m1);\n assert (interp q.hp (join m2 m1));\n assert (join m2 m1 == m);\n assert (interp q.hp m);\n ()", "let modus_ponens_interp (p q: vprop) (m: hmem (p `star` (p `wand` q)).hp) : Lemma (interp q.hp m) =\n let (ml, mr) = star_split p.hp (p.hp `Mem.wand` q.hp) m in\n assert (interp p.hp ml /\\ interp (p.hp `Mem.wand` q.hp) mr);\n let _ = reveal_wand p.hp q.hp mr in\n assert (forall m1. (mr `disjoint` m1 /\\ interp p.hp m1) ==> interp q.hp (join mr m1));\n assert (interp q.hp (join mr ml));\n assert (join mr ml == m);\n ()", "let modus_ponens_interp (p q: vprop) (m: hmem (p `star` (p `wand` q)).hp) : Lemma (interp q.hp m) =\n let (m1, m2) = star_split p.hp (p.hp `Mem.wand` q.hp) m in\n let interp_p_m1 = interp p.hp m1 in\n let interp_wand_m2 = interp (p.hp `Mem.wand` q.hp) m2 in\n reveal_wand p.hp q.hp m2;\n assert (forall m3. (disjoint m2 m3 /\\ interp p.hp m3) ==> interp q.hp (join m2 m3));\n assert (disjoint m2 m1 /\\ interp p.hp m1);\n assert (interp q.hp (join m2 m1));\n assert (join m2 m1 == m);\n assert (interp q.hp m);\n ()", "let modus_ponens_interp (p q: vprop) (m: hmem (p `star` (p `wand` q)).hp) : Lemma (interp q.hp m) =\n let (m1, m2) = star_split p.hp (p.hp `Mem.wand` q.hp) m in\n assert (interp p.hp m1);\n assert (interp (p.hp `Mem.wand` q.hp) m2);\n reveal_wand p.hp q.hp m2;\n assert (forall m3. (disjoint m2 m3 /\\ interp p.hp m3) ==> interp q.hp (join m2 m3));\n assert (disjoint m2 m1 /\\ interp p.hp m1);\n assert (interp q.hp (join m2 m1));\n assert (join m2 m1 == m);\n ()", "let modus_ponens_interp (p q: vprop) (m: hmem (p `star` (p `wand` q)).hp) : Lemma (interp q.hp m) =\n let (m1, m2) = star_split p.hp (p.hp `Mem.wand` q.hp) m in\n assert (disjoint m1 m2 /\\ join m1 m2 == m);\n assert (interp p.hp m1);\n assert (interp (p.hp `Mem.wand` q.hp) m2);\n reveal_wand p.hp q.hp m2;\n assert (forall m3. (disjoint m2 m3 /\\ interp p.hp m3) ==> interp q.hp (join m2 m3));\n assert (interp q.hp (join m2 m1));\n assert (join m2 m1 == m);\n assert (interp q.hp m);\n ()", "let modus_ponens_interp (p q: vprop) (m: hmem (p `star` (p `wand` q)).hp) : Lemma (interp q.hp m) =\n let (m1, m2) = star_split p.hp (p.hp `Mem.wand` q.hp) m in\n let _ = assert (interp p.hp m1 /\\ interp (p.hp `Mem.wand` q.hp) m2) in\n let _ = reveal_wand p.hp q.hp m2 in\n let _ = assert (forall m3. (disjoint m2 m3 /\\ interp p.hp m3) ==> interp q.hp (join m2 m3)) in\n let _ = assert (disjoint m2 m1 /\\ interp p.hp m1) in\n let _ = assert (interp q.hp (join m2 m1)) in\n let _ = assert (join m2 m1 == m) in\n ()", "let modus_ponens_interp (p q: vprop) (m: hmem (p `star` (p `wand` q)).hp) : Lemma (interp q.hp m) =\n let (m1, m2) = star_split p.hp (p.hp `Mem.wand` q.hp) m in\n assert (interp p.hp m1 /\\ interp (p.hp `Mem.wand` q.hp) m2);\n reveal_wand p.hp q.hp m2;\n assert (forall m1. (m1 `disjoint` m2 /\\ interp p.hp m1) ==> interp q.hp (join m1 m2));\n assert (interp q.hp (join m1 m2));\n assert (join m1 m2 == m);\n assert (interp q.hp m);\n ()", "let modus_ponens_interp (p q: vprop) (m: hmem (p `star` (p `wand` q)).hp) : Lemma (interp q.hp m) =\n let (m1, m2) = star_split p.hp (p.hp `Mem.wand` q.hp) m in\n assert (interp p.hp m1);\n assert (interp (p.hp `Mem.wand` q.hp) m2);\n reveal_wand p.hp q.hp m2;\n assert (forall m3. (m2 `disjoint` m3 /\\ interp p.hp m3) ==> interp q.hp (join m2 m3));\n assert (interp q.hp (join m1 m2));\n assert (join m1 m2 == m);\n ()" ] }, { "file_name": "ND.fst", "name": "ND.fail", "opens_and_abbrevs": [ { "open": "FStar.Monotonic.Pure" }, { "abbrev": "T", "full_module": "FStar.Tactics.V2" }, { "abbrev": "W", "full_module": "FStar.WellFounded" }, { "abbrev": "F", "full_module": "FStar.FunctionalExtensionality" }, { "open": "FStar.FunctionalExtensionality" }, { "open": "FStar.Calc" }, { "open": "FStar.Tactics.V2" }, { "open": "FStar.List.Tot" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val fail : #a:Type0 -> unit -> ND a (as_pure_wp (fun p -> True))", "source_definition": "let fail #a () =\n ND?.reflect (fun _ _ -> [])", "source_range": { "start_line": 165, "start_col": 0, "end_line": 166, "end_col": 31 }, "interleaved": false, "definition": "fun _ -> ND.ND?.reflect (fun _ _ -> []) <: ND.ND a", "effect": "ND.ND", "effect_flags": [], "mutual_with": [], "premises": [ "Prims.unit", "Prims.squash", "FStar.Monotonic.Pure.as_pure_wp", "Prims.pure_post", "Prims.l_True", "Prims.pure_pre", "Prims.Nil", "ND.m", "Prims.l_Forall", "Prims.l_imp", "FStar.List.Tot.Base.memP" ], "proof_features": [], "is_simple_lemma": false, "is_div": true, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "_: Prims.unit -> ND.ND a", "prompt": "let fail #a () =\n ", "expected_response": "ND?.reflect (fun _ _ -> [])", "source": { "project_name": "FStar", "file_name": "examples/layeredeffects/ND.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "ND.fst", "checked_file": "dataset/ND.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.WellFounded.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Tactics.Typeclasses.fsti.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Monotonic.Pure.fst.checked", "dataset/FStar.List.Tot.Properties.fst.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked", "dataset/FStar.Calc.fsti.checked" ] }, "definitions_in_context": [ "val m (a : Type u#a) : Type u#a", "let m a = list a", "val m_return (#a : Type) : a -> m a", "let m_return x = [x]", "val m_bind (#a #b : Type) : m a -> (a -> m b) -> m b", "let m_bind l f = concatMap f l", "val w (a : Type u#a) : Type u#(max 1 a)", "let w a = pure_wp a", "val w_ord (#a : Type) : w a -> w a -> Type0", "let w_ord wp1 wp2 = forall p. wp1 p ==> wp2 p", "val w_return (#a : Type) : a -> w a", "let w_return x = as_pure_wp (fun p -> p x)", "val w_bind (#a #b : Type) : w a -> (a -> w b) -> w b", "let w_bind wp1 k =\n elim_pure_wp_monotonicity_forall ();\n as_pure_wp (fun p -> wp1 (fun x -> k x p))", "val interp (#a : Type) : m a -> w a", "let interp #a (l:list a) = as_pure_wp (fun p -> forall x. memP x l ==> p x)", "val concatlemma (#a:Type) (l1 l2 :list a) (x:a) : Lemma (memP x (l1@l2) <==> memP x l1 \\/ memP x l2)", "let rec concatlemma #a l1 l2 x =\n match l1 with\n | [] -> ()\n | h::t -> concatlemma t l2 x", "val concatmaplemma : (#a:Type) -> (#b:Type) -> l:list a -> (f:(a -> list b)) -> x:b ->\n Lemma (memP x (concatMap f l) <==> (exists a. memP a l /\\ memP x (f a)))\n [SMTPat (memP x (concatMap f l))]", "let rec concatmaplemma #a #b l f x =\n match l with\n | [] -> ()\n | h::t ->\n concatlemma (f h) (concatMap f t) x;\n concatmaplemma t f x", "let dm (a : Type) (wp : w a) : Type = \n p:(a -> Type0) -> squash (wp p) -> l:(m a){forall x. memP x l ==> p x}", "let irepr (a : Type) (wp: w a) = dm a wp", "let ireturn (a : Type) (x : a) : irepr a (w_return x) = fun _ _ -> [x]", "let rec pmap #a #b #pre (#post:b->Type0)\n (f : (x:a -> Pure b (requires (pre x)) (ensures post)))\n (l : list a)\n : Pure (list (v:b{post v}))\n (requires (forall x. memP x l ==> pre x))\n (ensures (fun _ -> True))\n = match l with\n | [] -> []\n | x::xs -> f x :: pmap #_ #_ #pre #post f xs", "let rec unref #a #p (l : list (v:a{p v})) : l:(list a){forall x. memP x l ==> p x} =\n match l with\n | [] -> []\n | x :: xs -> x :: unref xs", "let mem_memP\n (#a: eqtype)\n (x: a)\n (l: list a)\n: Lemma (ensures (mem x l <==> memP x l))\n [SMTPat (memP x l); SMTPat (mem x l)]\n= FStar.List.Tot.Properties.mem_memP x l", "val append_memP: #t:Type -> l1:list t\n -> l2:list t\n -> a:t\n -> Lemma (requires True)\n (ensures (memP a (l1@l2) <==> (memP a l1 \\/ memP a l2)))", "let rec append_memP #t l1 l2 a = match l1 with\n | [] -> ()\n | hd::tl -> append_memP tl l2 a", "let rec flatten_mem_lem #a (l : list (list a)) (x:a)\n : Lemma (memP x (flatten l) <==> (exists l0. memP l0 l /\\ memP x l0))\n [SMTPat (memP x (flatten l))]\n = match l with\n | [] -> ()\n | l1::ls -> (append_memP l1 (flatten ls) x; flatten_mem_lem ls x)", "let ibind (a : Type) (b : Type) (wp_v : w a) (wp_f: a -> w b) (v : irepr a wp_v) (f : (x:a -> irepr b (wp_f x))) : irepr b (w_bind wp_v wp_f) =\n fun p _ -> let l1 = v (fun x -> wp_f x p) () in\n let l2 = pmap #_ #(list b) #(fun x -> wp_f x p) #(fun l -> forall x. memP x l ==> p x) (fun x -> f x p ()) l1 in\n let l2 = unref l2 in\n let l2f = List.Tot.flatten l2 in\n l2f", "let isubcomp (a:Type) (wp1 wp2: w a) (f : irepr a wp1) : Pure (irepr a wp2) (requires w_ord wp2 wp1) (ensures fun _ -> True) = f", "let wp_if_then_else (#a:Type) (wp1 wp2:w a) (b:bool) : w a=\n elim_pure_wp_monotonicity_forall ();\n as_pure_wp (fun p -> (b ==> wp1 p) /\\ ((~b) ==> wp2 p))", "let i_if_then_else (a : Type) (wp1 wp2 : w a) (f : irepr a wp1) (g : irepr a wp2) (b : bool) : Type =\n irepr a (wp_if_then_else wp1 wp2 b)", "let lift_pure_nd (a:Type) (wp:pure_wp a) (f:unit -> PURE a wp) :\n Pure (irepr a wp) (requires True)\n (ensures (fun _ -> True))\n = fun p _ -> let r = FStar.Monotonic.Pure.elim_pure f p in [r]", "val test_f : unit -> ND int (as_pure_wp (fun p -> p 5 /\\ p 3))", "let test_f () =\n ND?.reflect (fun _ _ -> [3; 5])", "let l () : list int = reify (test_f ()) (fun _ -> True) ()", "val choose : #a:Type0 -> x:a -> y:a -> ND a (as_pure_wp (fun p -> p x /\\ p y))", "let choose #a x y =\n ND?.reflect (fun _ _ -> [x;y])", "val fail : #a:Type0 -> unit -> ND a (as_pure_wp (fun p -> True))" ], "closest": [ "val lift_pure_nd (a: Type) (wp: wp a) (f: (unit -> PURE a wp))\n : Pure (repr a wp) (requires True) (ensures (fun _ -> True))\nlet lift_pure_nd (a:Type) (wp:wp a) (f:unit -> PURE a wp) :\n Pure (repr a wp) (requires True)\n (ensures (fun _ -> True))\n = fun p _ -> elim_pure f p", "val lift_pure_nd (a: Type) (wp: wp a) (f: (unit -> PURE a wp))\n : Pure (repr a wp) (requires True) (ensures (fun _ -> True))\nlet lift_pure_nd (a:Type) (wp:wp a) (f:unit -> PURE a wp) :\n Pure (repr a wp) (requires True)\n (ensures (fun _ -> True))\n = fun p _ -> elim_pure f p", "val lift_pure_nd (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : Pure (repr a) (requires (wp (fun _ -> True))) (ensures (fun _ -> True))\nlet lift_pure_nd (a:Type) (wp:pure_wp a) (f:unit -> PURE a wp) :\n Pure (repr a) (requires (wp (fun _ -> True)))\n (ensures (fun _ -> True))\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun _ ->\n let r = f () in\n r", "val lift_pure_nd (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : Pure (repr a wp) (requires (wp (fun _ -> True))) (ensures (fun _ -> True))\nlet lift_pure_nd (a:Type) (wp:pure_wp a) (f:unit -> PURE a wp) :\n Pure (repr a wp) (requires (wp (fun _ -> True)))\n (ensures (fun _ -> True))\n = elim_pure_wp_monotonicity_forall ();\n f ()", "val lift_pure_nd (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp)) : repr a wp\nlet lift_pure_nd (a:Type) (wp:pure_wp a) (f:unit -> PURE a wp) : repr a wp\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n (_, (fun (p:erased (a -> Type0)) _ -> // need the type annot\n let r = f () in\n assert (reveal p r);\n r))", "val lift_pure_nd (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp)) : repr a wp\nlet lift_pure_nd (a:Type) (wp:pure_wp a) (f:unit -> PURE a wp)\n : repr a wp\n = elim_pure_wp_monotonicity wp;\n fun _ -> f ()", "val cut_wp (#a: Type) (w: wp a) (p: Type0) : wp a\nlet cut_wp (#a:Type) (w:wp a) (p:Type0) : wp a =\n elim_pure_wp_monotonicity_forall ();\n as_pure_wp (fun post -> p /\\ (p ==> w post))", "val pure_null_wp (a: Type) : Tot (pure_wp a)\nlet pure_null_wp (a:Type) : Tot (pure_wp a) =\n reveal_opaque (`%pure_wp_monotonic) pure_wp_monotonic;\n pure_null_wp0 a", "val test_f : unit -> ID int (as_pure_wp (fun p -> p 5 /\\ p 3))\nlet test_f () = 3", "val test_f : unit -> ID int (as_pure_wp (fun p -> p 5 /\\ p 3))\nlet test_f () = 5", "val test_f : unit -> ID int (as_pure_wp (fun p -> p 5 /\\ p 3))\nlet test_f () = 3", "val test_f : unit -> ID int (as_pure_wp (fun p -> p 5 /\\ p 3))\nlet test_f () = 3", "val test_f : unit -> ID int (as_pure_wp (fun p -> p 5 /\\ p 3))\nlet test_f () = 3", "val test_assert: Prims.unit -> ID unit (as_pure_wp (fun p -> p ()))\nlet test_assert () : ID unit (as_pure_wp (fun p -> p ())) =\n ();\n iassume False;\n ();\n iassert False;\n ()", "val test_assert: Prims.unit -> ID unit (as_pure_wp (fun p -> p ()))\nlet test_assert () : ID unit (as_pure_wp (fun p -> p ())) =\n ();\n iassume False;\n ();\n iassert False;\n ()", "val elim_pure (#a: Type) (#wp: pure_wp a) ($f: (unit -> PURE a wp)) (p: pure_post a)\n : Pure a (requires (wp p)) (ensures (fun r -> p r))\nlet elim_pure (#a:Type) (#wp:pure_wp a) ($f : unit -> PURE a wp) (p:pure_post a)\n : Pure a (requires (wp p)) (ensures (fun r -> p r))\n = elim_pure_wp_monotonicity wp;\n f ()", "val null_wp (a: Type) : pure_wp a\nlet null_wp (a:Type) : pure_wp a = as_pure_wp (fun p -> forall x. p x)", "val weaken_wp (#a: Type) (w: wp a) (p: Type0) : wp a\nlet weaken_wp (#a:Type) (w:wp a) (p:Type0) : wp a =\n elim_pure_wp_monotonicity_forall ();\n as_pure_wp (fun post -> p ==> w post)", "val lift_pure_nmst\n (a: Type)\n (wp: pure_wp a)\n (state: Type u#2)\n (rel: P.preorder state)\n (f: (eqtype_as_type unit -> PURE a wp))\n : repr a\n state\n rel\n (fun s0 -> wp (fun _ -> True))\n (fun s0 x s1 -> wp (fun _ -> True) /\\ (~(wp (fun r -> r =!= x \\/ s0 =!= s1))))\nlet lift_pure_nmst\n (a:Type)\n (wp:pure_wp a)\n (state:Type u#2)\n (rel:P.preorder state)\n (f:eqtype_as_type unit -> PURE a wp)\n : repr a state rel\n (fun s0 -> wp (fun _ -> True))\n (fun s0 x s1 -> wp (fun _ -> True) /\\ (~ (wp (fun r -> r =!= x \\/ s0 =!= s1))))\n =\n fun (_, n) ->\n elim_pure_wp_monotonicity wp;\n let x = f () in\n x, n", "val lift_pure_nds (a: _) (wp: pure_wp a) (s: _) (f: (unit -> PURE a wp))\n : Pure (nds a s) (requires wp (fun _ -> True)) (ensures fun _ -> True)\nlet lift_pure_nds a (wp:pure_wp a) s (f : unit -> PURE a wp)\n : Pure (nds a s)\n (requires wp (fun _ -> True))\n (ensures fun _ -> True)\n = fun t n s -> f (), s, n", "val lift_pure_rwi (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : m a RO (fun _ -> wp (fun _ -> True)) (fun h0 x h1 -> sp wp x /\\ h1 == h0)\nlet lift_pure_rwi\n (a:Type)\n (wp : pure_wp a)\n (f :unit -> PURE a wp)\n // with the index-polymorphic bind above, this has to be in RO,\n // or unification will usually not find the index here\n : m a RO (fun _ -> wp (fun _ -> True)) (fun h0 x h1 -> sp wp x /\\ h1 == h0)\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun () -> f ()", "val lift_pure_hoarest (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : repr a (fun _ -> wp (fun _ -> True)) (fun h0 r h1 -> ~(wp (fun x -> x =!= r \\/ h0 =!= h1)))\nlet lift_pure_hoarest (a:Type) (wp:pure_wp a) (f:unit -> PURE a wp)\n: repr a\n (fun _ -> wp (fun _ -> True))\n (fun h0 r h1 -> ~ (wp (fun x -> x =!= r \\/ h0 =!= h1)))\n= FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun _ -> f ()", "val elim_pure (#a #wp: _) ($f: (unit -> PURE a wp)) (p: _)\n : Pure a (requires (wp p)) (ensures (fun r -> p r))\nlet elim_pure #a #wp ($f : unit -> PURE a wp) p\n : Pure a (requires (wp p)) (ensures (fun r -> p r))\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity_forall ();\n f ()", "val fail : (#a:Type) -> string -> tm a\nlet fail #a s = fun i -> Inl s", "val pure_p (#a: Type) (wp: pure_wp a) : pre\nlet pure_p (#a:Type) (wp:pure_wp a) : pre =\n fun _ -> as_requires wp", "val bind_wp (#a #b: Type) (#st: Type0) (wp_c: wp st a) (wp_f: (a -> wp st b)) : wp st b\nlet bind_wp (#a #b:Type) (#st:Type0)\n (wp_c:wp st a)\n (wp_f:a -> wp st b)\n : wp st b\n = fun s0 p ->\n wp_c s0\n //push the postcondition of the continuation\n //through the WP transformer of c\n (fun (y, s1) ->\n //push the postcondition p\n //through the WP transformer of f applied to the\n //result value and state of c\n wp_f y s1 p)", "val bind_wp (#a #b: Type) (#st: Type0) (wp_c: wp st a) (wp_f: (a -> wp st b)) : wp st b\nlet bind_wp (#a #b:Type) (#st:Type0) (wp_c:wp st a) (wp_f:a -> wp st b) : wp st b =\n fun s0 p -> wp_c s0 (fun (y, s1) -> wp_f y s1 p)", "val strengthen_wp (#a: Type) (w: wp a) (p: Type0) : wp a\nlet strengthen_wp (#a:Type) (w:wp a) (p:Type0) : wp a =\n elim_pure_wp_monotonicity_forall ();\n as_pure_wp (fun post -> p /\\ w post)", "val return (a: Type) (x: a) : repr a (as_pure_wp (fun p -> p x))\nlet return (a : Type) (x : a) : repr a (as_pure_wp (fun p -> p x)) =\n x", "val lift_pure_eff (a: Type) (wp: pure_wp a) (f: (eqtype_as_type unit -> PURE a wp))\n : Pure (repr a ()) (requires wp (fun _ -> True)) (ensures fun _ -> True)\nlet lift_pure_eff (a:Type) (wp:pure_wp a) (f:eqtype_as_type unit -> PURE a wp)\n: Pure (repr a ())\n (requires wp (fun _ -> True))\n (ensures fun _ -> True)\n= fun (t, n, s) -> f (), n, s", "val as_pure_wp (#a: Type) (wp: pure_wp' a)\n : Pure (pure_wp a) (requires is_monotonic wp) (ensures fun r -> r == wp)\nlet as_pure_wp (#a:Type) (wp:pure_wp' a)\n : Pure (pure_wp a)\n (requires is_monotonic wp)\n (ensures fun r -> r == wp)\n = intro_pure_wp_monotonicity wp;\n wp", "val lift_pure_meff (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : repr a (wp (fun _ -> True)) (fun x -> ~(wp (fun r -> r =!= x)))\nlet lift_pure_meff (a:Type) (wp:pure_wp a) (f:unit -> PURE a wp)\n: repr a\n (wp (fun _ -> True))\n (fun x -> ~ (wp (fun r -> r =!= x)))\n= FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun _ -> f ()", "val free (#a:Type0) (r:ref a) : Steel unit\n (vptr r) (fun _ -> emp)\n (requires fun _ -> True)\n (ensures fun _ _ _ -> True)\nlet free r =\n let _ = elim_vptr r _ in\n free_pt r", "val pure_q (#a: Type) (wp: pure_wp a) : post a\nlet pure_q (#a:Type) (wp:pure_wp a) : post a =\n fun s0 x s1 -> s0 == s1 /\\ as_ensures wp x", "val bind_wp (#a #b: _) (wp_v: wp0 a) (wp_f: (x: a -> wp0 b)) : wp0 b\nlet bind_wp #a #b\n (wp_v : wp0 a)\n (wp_f : (x:a -> wp0 b))\n : wp0 b\n = elim_pure_wp_monotonicity_forall ();\n as_pure_wp (fun p -> wp_v (fun x -> wp_f x p))", "val lift_pure_eff (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : repr a (fun _ -> wp (fun _ -> True)) (post_of_wp wp) []\nlet lift_pure_eff\n (a:Type)\n (wp : pure_wp a)\n (f : unit -> PURE a wp)\n : repr a (fun _ -> wp (fun _ -> True)) (post_of_wp wp) []\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n let r (s0:state{wp (fun _ -> True)})\n : Tot (r:(option a & state){snd r == s0 /\\ Some? (fst r) /\\ sp wp (Some?.v (fst r))})\n =\n (Some (f ()), s0)\n in\n r", "val lift_wp (#a: Type) (#st: Type0) (w: pure_wp a) : wp st a\nlet lift_wp (#a:Type) (#st:Type0) (w:pure_wp a) : wp st a =\n elim_pure_wp_monotonicity_forall ();\n fun s0 p -> w (fun x -> p (x, s0))", "val lift_wp (#a: Type) (#st: Type0) (w: pure_wp a) : wp st a\nlet lift_wp (#a:Type) (#st:Type0) (w:pure_wp a) : wp st a =\n elim_pure_wp_monotonicity_forall ();\n fun s0 p -> w (fun x -> p (x, s0))", "val sp (#a: _) (wp: pure_wp a) : pure_post a\nlet sp #a (wp : pure_wp a) : pure_post a =\n fun x -> ~ (wp (fun y -> ~(x == y)))", "val sp (#a: _) (wp: pure_wp a) : pure_post a\nlet sp #a (wp : pure_wp a) : pure_post a =\n fun x -> ~ (wp (fun y -> ~(x == y)))", "val lift_pure_dm4a (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : Tot (repr a (wp (fun _ -> True)) (fun _ -> w_return (f ())))\nlet lift_pure_dm4a (a:Type) (wp : pure_wp a) (f:unit -> PURE a wp)\n : Tot (repr a (wp (fun _ -> True)) (fun _ -> w_return (f ())))\n = fun _ -> \n FStar.Monotonic.Pure.elim_pure_wp_monotonicity_forall ();\n let x = f () in\n interp_ret x;\n m_return x", "val f (#a: Type) (p: (either (out_wp a) a -> prop)) : either (out_wp a) a\nlet f (#a:Type) (p:either (out_wp a) a -> prop) : either (out_wp a) a = \n Inl (Intro (inj p))", "val rwi_assert (p: Type0) : RWI unit RO (fun _ -> p) (fun h0 () h1 -> h0 == h1)\nlet rwi_assert (p:Type0) : RWI unit RO (fun _ -> p) (fun h0 () h1 -> h0 == h1) =\n // assert p // fails\n RWI?.reflect (fun () -> assert p)", "val lift_PURE_M (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp)) : repr a (pure_p wp) (pure_q wp)\nlet lift_PURE_M (a:Type) (wp:pure_wp a) (f:unit -> PURE a wp)\n : repr a (pure_p wp) (pure_q wp)\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun _ ->\n let f : squash (as_requires wp) -> Dv (m st a (fun s0 -> True) (pure_q wp)) =\n fun _ ->\n let x = f () in\n let t : m st a (fun s0 -> s0 == s0 /\\ as_ensures wp x) (pure_q wp) =\n Ret x in\n let t : m st a (fun _ -> True) (pure_q wp) = Weaken t in\n t in\n let t : m st a (strengthen_pre (fun _ -> True) (as_requires wp)) (pure_q wp) =\n Strengthen f in\n Weaken t", "val weaken (#a #w: _) (p: Type0) (f: repr a w)\n : Pure (repr a (weaken_wp w p)) (requires p) (ensures (fun _ -> True))\nlet weaken #a #w (p:Type0) (f : repr a w) : Pure (repr a (weaken_wp w p))\n (requires p)\n (ensures (fun _ -> True))\n = fun post _ -> f post ()", "val repr (a: Type u#aa) (wp: pure_wp a) : Type u#aa\nlet repr (a : Type u#aa) (wp : pure_wp a) : Type u#aa =\n squash (sat wp) -> v:a{forall p. wp p ==> p v}", "val stronger : (#a:Type) -> st_wp a -> st_wp a -> Type0\nlet stronger w1 w2 = forall p s. w1 p s ==> w2 p s", "val stronger : (#a:Type) -> st_wp a -> st_wp a -> Type0\nlet stronger w1 w2 = forall p s. w1 p s ==> w2 p s", "val stronger : (#a:Type) -> st_wp a -> st_wp a -> Type0\nlet stronger w1 w2 = forall p s. w1 p s ==> w2 p s", "val lift_PURE_HIFC (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : Pure (hifc a bot bot [] (fun _ -> True) (fun s0 _ s1 -> s0 == s1))\n (requires wp (fun _ -> True))\n (ensures fun _ -> True)\nlet lift_PURE_HIFC (a:Type) (wp:pure_wp a) (f:unit -> PURE a wp)\n : Pure (hifc a bot bot [] (fun _ -> True) (fun s0 _ s1 -> s0 == s1))\n (requires wp (fun _ -> True))\n (ensures fun _ -> True)\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity_forall ();\n return a (f ())", "val lift_pure_lvars (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp)) : repr a (lift_pure_wp wp)\nlet lift_pure_lvars (a:Type)\n (wp:pure_wp a) (f:unit -> PURE a wp)\n: repr a (lift_pure_wp wp)\n= FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun m -> f (), m", "val lift_pure_wp (#a: Type) (wp: pure_wp a) : wp_t a\nlet lift_pure_wp (#a:Type) (wp:pure_wp a) : wp_t a =\n FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun p m -> wp (fun x -> p x m)", "val lift_pure_wp (#a: Type) (wp: pure_wp a) : wp_t a\nlet lift_pure_wp (#a:Type) (wp:pure_wp a) : wp_t a =\n FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun p s0 -> wp (fun x -> p (Success x) s0)", "val p0: #a: Type -> either (out_wp a) a -> prop\nlet p0 : #a:Type -> either (out_wp a) a -> prop = fun #a x ->\n exists (p:either (out_wp a) a -> prop).\n f #a p == x /\\ ~(p x)", "val lift_pure_wp (#a: Type) (wp: pure_wp a) : st_wp a\nlet lift_pure_wp (#a:Type) (wp : pure_wp a) : st_wp a =\n FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun s0 p -> wp (fun x -> p (x, s0))", "val lift_pure_wp (#a: Type) (wp: pure_wp a) : st_wp a\nlet lift_pure_wp (#a:Type) (wp : pure_wp a) : st_wp a =\n elim_pure_wp_monotonicity wp;\n fun s0 p -> wp (fun x -> p (x, s0))", "val lift_pure_wp (#a: Type) (wp: pure_wp a) : st_wp a\nlet lift_pure_wp (#a:Type) (wp : pure_wp a) : st_wp a =\n elim_pure_wp_monotonicity wp;\n fun s0 p -> wp (fun x -> p (x, s0))", "val lift_pure (a: _) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : Pure (gst a R) (requires wp (fun _ -> True)) (ensures fun _ -> True)\nlet lift_pure a (wp:pure_wp a) (f:unit -> PURE a wp)\n : Pure (gst a R)\n (requires wp (fun _ -> True))\n (ensures fun _ -> True)\n = fun s -> f ()", "val lift_pure_eff (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : Pure (repr a []) (requires (wp (fun _ -> True))) (ensures (fun _ -> True))\nlet lift_pure_eff\n (a:Type)\n (wp : pure_wp a)\n (f : unit -> PURE a wp)\n : Pure (repr a [])\n (requires (wp (fun _ -> True)))\n (ensures (fun _ -> True))\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun () -> f ()", "val lift_pure_eff (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : Pure (repr a []) (requires (wp (fun _ -> True))) (ensures (fun _ -> True))\nlet lift_pure_eff\n (a:Type)\n (wp : pure_wp a)\n (f : unit -> PURE a wp)\n : Pure (repr a [])\n (requires (wp (fun _ -> True)))\n (ensures (fun _ -> True))\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun s0 -> (Some (f ()), s0)", "val write (#a:Type0) (r:ref a) (x:a) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> x == sel r h1)\nlet write r x =\n let _ = elim_vptr r _ in\n write_pt r x;\n intro_vptr r _ x", "val write (#a:Type0) (r:ref a) (x:a) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> x == sel r h1)\nlet write\n r x\n= elim_vptrp r full_perm;\n A.upd r 0sz x;\n intro_vptrp' r full_perm", "val lift_pure_mst_total\n (a: Type)\n (wp: pure_wp a)\n (state: Type u#2)\n (rel: P.preorder state)\n (f: (eqtype_as_type unit -> PURE a wp))\n : repr a\n state\n rel\n (fun s0 -> wp (fun _ -> True))\n (fun s0 x s1 -> wp (fun _ -> True) /\\ (~(wp (fun r -> r =!= x \\/ s0 =!= s1))))\nlet lift_pure_mst_total\n (a:Type)\n (wp:pure_wp a)\n (state:Type u#2)\n (rel:P.preorder state)\n (f:eqtype_as_type unit -> PURE a wp)\n : repr a state rel\n (fun s0 -> wp (fun _ -> True))\n (fun s0 x s1 -> wp (fun _ -> True) /\\ (~ (wp (fun r -> r =!= x \\/ s0 =!= s1))))\n =\n elim_pure_wp_monotonicity wp;\n fun s0 ->\n let x = f () in\n x, s0", "val bad1 (a: Type) : Lemma (requires (p0 (x0 #a))) (ensures (~(p0 (x0 #a))))\nlet bad1 (a:Type) \n : Lemma (requires (p0 (x0 #a))) \n (ensures (~(p0 (x0 #a)))) =\n let aux (p:(either (out_wp a) a -> prop){f p == (x0 #a) /\\ ~(p (x0 #a))}) \n : GTot (squash (~(p0 (x0 #a)))) =\n f_injective p p0\n in \n exists_elim (~(p0 (x0 #a))) (FStar.Squash.get_proof (p0 (x0 #a))) aux", "val unreachable: #a: Type u#aa -> Prims.unit -> Pure a (requires False) (ensures (fun _ -> False))\nlet unreachable (#a:Type u#aa) () : Pure a (requires False) (ensures (fun _ -> False)) =\n coerce (raise_val \"whatever\")", "val fail (#a: Type) (m: string) : TAC a (fun ps post -> post (Failed (TacticFailure m) ps))\nlet fail (#a:Type) (m:string)\n : TAC a (fun ps post -> post (Failed (TacticFailure m) ps))\n = raise #a (TacticFailure m)", "val fail (#a: Type) (m: string) : TAC a (fun ps post -> post (Failed (TacticFailure m) ps))\nlet fail (#a:Type) (m:string)\n : TAC a (fun ps post -> post (Failed (TacticFailure m) ps))\n = raise #a (TacticFailure m)", "val write (#a: Type0) (n: nat) (x: a)\n : LV unit\n (fun m0 -> m0.m `M.contains` n /\\ dfst (m0.m `M.sel` n) == a)\n (fun m0 _ m1 -> m1.next == m0.next /\\ m1.m == Map.upd m0.m n (| a, x |))\nlet write (#a:Type0) (n:nat) (x:a)\n : LV unit (fun m0 -> m0.m `M.contains` n /\\\n dfst (m0.m `M.sel` n) == a)\n (fun m0 _ m1 ->\n m1.next == m0.next /\\\n m1.m == Map.upd m0.m n (| a, x |))\n= LVARS?.reflect (fun m -> (), { m with m = Map.upd m.m n (| a, x |) })", "val null (#a: _) : st_wp a\nlet null #a : st_wp a = fun s0 p -> forall r. p r", "val lift_pure_mst\n (a: Type)\n (wp: pure_wp a)\n (state: Type u#2)\n (rel: P.preorder state)\n (f: (eqtype_as_type unit -> PURE a wp))\n : repr a\n state\n rel\n (fun s0 -> wp (fun _ -> True))\n (fun s0 x s1 -> wp (fun _ -> True) /\\ (~(wp (fun r -> r =!= x \\/ s0 =!= s1))))\nlet lift_pure_mst\n (a:Type)\n (wp:pure_wp a)\n (state:Type u#2)\n (rel:P.preorder state)\n (f:eqtype_as_type unit -> PURE a wp)\n : repr a state rel\n (fun s0 -> wp (fun _ -> True))\n (fun s0 x s1 -> wp (fun _ -> True) /\\ (~ (wp (fun r -> r =!= x \\/ s0 =!= s1))))\n =\n elim_pure_wp_monotonicity wp;\n fun s0 ->\n let x = f () in\n x, s0", "val lift_pure_gtd (a: Type) (wp: pure_wp a) (i: idx) (f: (unit -> PURE a wp))\n : Pure (m a i) (requires (wp (fun _ -> True))) (ensures (fun _ -> True))\nlet lift_pure_gtd (a:Type) (wp : pure_wp a) (i : idx)\n (f : unit -> PURE a wp)\n : Pure (m a i)\n (requires (wp (fun _ -> True)))\n (ensures (fun _ -> True))\n = //f\n // GM: Surprised that this works actually... I expected that I would need to\n // case analyze [i].\n // GM: ok not anymore\n FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n match i with\n | T -> f\n | G -> f\n | D -> coerce (raise_val (fun () -> f () <: Dv a))", "val failwith (#a: Type) (s: C.String.t)\n : Stack a (requires (fun _ -> true)) (ensures (fun h0 _ h1 -> h0 == h1))\nlet rec failwith (#a: Type) (s: C.String.t): Stack a\n (requires (fun _ -> true))\n (ensures (fun h0 _ h1 -> h0 == h1)) =\n C.String.print s;\n // Defeat recursion warnings.\n if whatever () then\n C.portable_exit 255l;\n failwith s", "val lift_wp (a: Type) (s: Type0) (wp: pure_wp a) : wp_t s a\nlet lift_wp (a:Type)\n (s:Type0)\n (wp:pure_wp a)\n : wp_t s a\n = F.on _ (fun (s0:s) (k:post_t s a) -> wp (fun a -> k (a, s0)))", "val sat (w: pure_wp 'a) : Type0\nlet sat (w : pure_wp 'a) : Type0 = w (fun _ -> True)", "val lift_pure_eff (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : Pure (tree a []) (requires (wp (fun _ -> True))) (ensures (fun _ -> True))\nlet lift_pure_eff\n (a:Type)\n (wp : pure_wp a)\n (f : unit -> PURE a wp)\n : Pure (tree a [])\n (requires (wp (fun _ -> True)))\n (ensures (fun _ -> True))\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n Return (f ())", "val fst (#a #b: Type0) (p: a & b) : a\nlet fst (#a #b : Type0) (p : a & b) : a =\n match p with\n | Mktuple2 x y -> x <: a", "val bad2 (a: Type) : Lemma (requires (~(p0 (x0 #a)))) (ensures (p0 (x0 #a)))\nlet bad2 (a:Type) \n : Lemma (requires (~(p0 (x0 #a)))) \n (ensures (p0 (x0 #a))) =\n exists_intro (fun (p:either (out_wp a) a -> prop) ->\n f p == x0 #a /\\ ~(p (x0 #a))) p0", "val lift_pure_eff (a s: Type) (wp: pure_wp a) (f: (unit -> PURE a wp))\n : Pure (repr a s s []) (requires (wp (fun _ -> True))) (ensures (fun _ -> True))\nlet lift_pure_eff\n (a:Type)\n (s:Type)\n (wp : pure_wp a)\n (f : unit -> PURE a wp)\n : Pure (repr a s s [])\n (requires (wp (fun _ -> True)))\n (ensures (fun _ -> True))\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n Return (f ())", "val t_return (#a: _) (x: a) : m a T (as_pure_wp (fun p -> p x))\nlet t_return #a (x:a) : m a T (as_pure_wp (fun p -> p x)) = (fun () -> x)", "val lift_pure_st (a wp st: _) (f: (unit -> PURE a wp)) : repr a st (lift_wp wp)\nlet lift_pure_st a wp st (f : unit -> PURE a wp)\n : repr a st (lift_wp wp)\n = elim_pure_wp_monotonicity_forall ();\n fun s0 -> (f (), s0)", "val lift_pure_exn (a: Type) (wp: pure_wp a) (f: (unit -> PURE a wp)) : erepr a (lift_pure_wp wp)\nlet lift_pure_exn (a:Type) (wp:pure_wp a) (f:unit -> PURE a wp)\n: erepr a (lift_pure_wp wp)\n= FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun _ -> Some (f ())", "val return_stt_a (#a: Type u#a) (x: a) (p: (a -> vprop))\n : stt unit (p x) (fun _ -> p x ** pure (x == x))\nlet return_stt_a (#a:Type u#a) (x:a) (p:a -> vprop)\n: stt unit (p x) (fun _ -> p x ** pure (x == x))\n= elim_vprop_equiv (vprop_equiv_comm (p x) emp);\n elim_vprop_equiv (vprop_equiv_unit (p x));\n frame_flip (p x) (refl_stt x)", "val lift_pure (a: Type) (wp: pure_wp a) (x: (unit -> PURE a wp))\n : Pure (ist a bot bot []) (requires wp (fun _ -> True)) (ensures fun _ -> True)\nlet lift_pure (a:Type) (wp:pure_wp a) (x:unit -> PURE a wp)\n : Pure (ist a bot bot [])\n (requires wp (fun _ -> True))\n (ensures fun _ -> True)\n = FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n return a (x())", "val lift_pure_read (a: Type) (wp: pure_wp a) (l: memory_invariant) (f_pure: (unit -> PURE a wp))\n : (read_repr a (wp (fun _ -> True)) (fun x -> ~(wp (fun x' -> ~(x == x')))) (fun _ -> False) l)\nlet lift_pure_read (a:Type) (wp:pure_wp a)\n (l: memory_invariant)\n (f_pure:unit -> PURE a wp)\n: (read_repr a\n (wp (fun _ -> True)) // (lift_pure_read_pre a wp)\n (fun x -> ~ (wp (fun x' -> ~ (x == x')))) // (lift_pure_read_post a wp)\n (fun _ -> False) // (lift_pure_read_post_err a wp))\n l)\n= ReadRepr (lift_pure_read_spec a wp f_pure)", "val test_2: Prims.unit -> ID int (as_pure_wp (fun p -> p 5))\nlet test_2 () : ID int (as_pure_wp (fun p -> p 5)) = 5", "val lift_pure_gtd (a: Type) (w: wp a) (i: idx) (f: (unit -> PURE a w))\n : Pure (m a i w) (requires True) (ensures (fun _ -> True))\nlet lift_pure_gtd (a:Type) (w : wp a) (i : idx)\n (f : unit -> PURE a w)\n : Pure (m a i w)\n (requires True)\n (ensures (fun _ -> True))\n = elim_pure_wp_monotonicity_forall ();\n match i with\n | T -> f\n | G -> f\n | D -> let f' () : DIV a w = f () in\n let f'' : m a D w = raise_val f' in\n f''", "val AlgWP.null_equiv_sanity = a: Type -> Prims.unit\nlet null_equiv_sanity a = assert (null_ro #a `equiv` null_ro1 #a)", "val lift_pure_algwp (a: Type) (wp: _) (f: (unit -> PURE a wp))\n : Pure (repr a noops (lift_pure_wp wp))\n (requires (wp (fun _ -> True)))\n (ensures (fun _ -> True))\nlet lift_pure_algwp (a:Type) wp (f:unit -> PURE a wp)\n : Pure (repr a noops (lift_pure_wp wp)) // can't call f() here, so lift its wp instead\n (requires (wp (fun _ -> True)))\n (ensures (fun _ -> True))\n =\n let v : a = FStar.Monotonic.Pure.elim_pure f (fun _ -> True) in\n FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp; // need this lemma\n assert (forall p. wp p ==> p v); // this is key fact needed for the proof\n assert_norm (stronger (lift_pure_wp wp) (return_wp v));\n Return v", "val raise: #a: _ -> Prims.unit -> EFF a (fun _ -> True) (fun s0 _ s1 -> s1 == s0) [EXN]\nlet raise #a () : EFF a (fun _ -> True) (fun s0 _ s1 -> s1 == s0) [EXN] =\n EFF?.reflect _raise", "val wp0 (a : Type u#a) : Type u#(max 1 a)\nlet wp0 a = (a -> Type0) -> Type0", "val wp0 (a : Type u#a) : Type u#(max 1 a)\nlet wp0 a = pure_wp a", "val return_wp (#a: Type) (#st: Type0) (x: a) : wp st a\nlet return_wp (#a:Type) (#st:Type0) (x:a) : wp st a =\n fun s0 p -> p x s0", "val return_wp (#a: Type) (#st: Type0) (x: a) : wp st a\nlet return_wp (#a:Type) (#st:Type0) (x:a) : wp st a = fun s0 p -> p (x, s0)", "val return_wp (#a: Type) (#st: Type0) (x: a) : wp st a\nlet return_wp (#a:Type) (#st:Type0) (x:a)\n : wp st a\n = fun s0 p -> p (x, s0)", "val return_wp (#a: Type) (#st: Type0) (x: a) : wp st a\nlet return_wp (#a:Type) (#st:Type0) (x:a) : wp st a =\n fun s0 p -> p x s0", "val lift_pure_wp (#a: Type) (wp: pure_wp a) : ewp_t a\nlet lift_pure_wp (#a:Type) (wp:pure_wp a) : ewp_t a =\n FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun p -> wp (fun x -> p (Some x))", "val cut (#a #w: _) (p: Type0) (f: repr a w) : repr a (cut_wp w p)\nlet cut #a #w (p:Type0) (f : repr a w) : repr a (cut_wp w p) =\n strengthen p (fun _ -> weaken p f)", "val lift_pure_read_spec (a: Type) (wp: pure_wp a) (f_pure_spec: (unit -> PURE a wp))\n : Tot\n (read_repr_spec a (wp (fun _ -> True)) (fun x -> ~(wp (fun x' -> ~(x == x')))) (fun _ -> False))\nlet lift_pure_read_spec\n (a:Type) (wp:pure_wp a) (f_pure_spec:unit -> PURE a wp)\n: Tot (read_repr_spec a \n (wp (fun _ -> True)) // (lift_pure_read_pre a wp)\n (fun x -> ~ (wp (fun x' -> ~ (x == x')))) // (lift_pure_read_post a wp)\n (fun _ -> False) // (lift_pure_read_post_err a wp))\n )\n= FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun () -> Correct (f_pure_spec ())", "val lift_pure_read_spec (a: Type) (wp: pure_wp a) (f_pure_spec: (unit -> PURE a wp))\n : Tot\n (read_repr_spec a (wp (fun _ -> True)) (fun x -> ~(wp (fun x' -> ~(x == x')))) (fun _ -> False))\nlet lift_pure_read_spec\n (a:Type) (wp:pure_wp a) (f_pure_spec:unit -> PURE a wp)\n: Tot (read_repr_spec a \n (wp (fun _ -> True)) // (lift_pure_read_pre a wp)\n (fun x -> ~ (wp (fun x' -> ~ (x == x')))) // (lift_pure_read_post a wp)\n (fun _ -> False) // (lift_pure_read_post_err a wp))\n )\n= FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp;\n fun () -> Correct (f_pure_spec ())", "val lift_pure_read (a: Type) (wp: pure_wp a) (l: memory_invariant) (f_pure: (unit -> PURE a wp))\n : Tot\n (read_repr a (wp (fun _ -> True)) (fun x -> ~(wp (fun x' -> ~(x == x')))) (fun _ -> False) l)\nlet lift_pure_read (a:Type) (wp:pure_wp a)\n (l: memory_invariant)\n (f_pure:unit -> PURE a wp)\n: Tot (read_repr a\n (wp (fun _ -> True)) // (lift_pure_read_pre a wp)\n (fun x -> ~ (wp (fun x' -> ~ (x == x')))) // (lift_pure_read_post a wp)\n (fun _ -> False) // (lift_pure_read_post_err a wp))\n l\n )\n= elim_pure_wp_monotonicity_forall ();\n ReadRepr _ (lift_pure_read_impl a wp f_pure l)" ], "closest_src": [ { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.lift_pure_nd" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.lift_pure_nd" }, { "project_name": "FStar", "file_name": "DivAction.fst", "name": "DivAction.lift_pure_nd" }, { "project_name": "FStar", "file_name": "ID3.fst", "name": "ID3.lift_pure_nd" }, { "project_name": "FStar", "file_name": "ID4.fst", "name": "ID4.lift_pure_nd" }, { "project_name": "FStar", "file_name": "ID2.fst", "name": "ID2.lift_pure_nd" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.cut_wp" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.pure_null_wp" }, { "project_name": "FStar", "file_name": "ID3.fst", "name": "ID3.test_f" }, { "project_name": "FStar", "file_name": "ID2.fst", "name": "ID2.test_f" }, { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.test_f" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.test_f" }, { "project_name": "FStar", "file_name": "ID4.fst", "name": "ID4.test_f" }, { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.test_assert" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.test_assert" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Pure.fst", "name": "FStar.Monotonic.Pure.elim_pure" }, { "project_name": "FStar", "file_name": "GTWP.fst", "name": "GTWP.null_wp" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.weaken_wp" }, { "project_name": "FStar", "file_name": "FStar.NMSTTotal.fst", "name": "FStar.NMSTTotal.lift_pure_nmst" }, { "project_name": "FStar", "file_name": "OPLSS2021.NDS.fst", "name": "OPLSS2021.NDS.lift_pure_nds" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.lift_pure_rwi" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.lift_pure_hoarest" }, { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.elim_pure" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Arith.fst", "name": "FStar.Reflection.V2.Arith.fail" }, { "project_name": "FStar", "file_name": "HoareSTFree.fst", "name": "HoareSTFree.pure_p" }, { "project_name": "FStar", "file_name": "OPLSS2021.DijkstraMonads.fst", "name": "OPLSS2021.DijkstraMonads.bind_wp" }, { "project_name": "FStar", "file_name": "DM4F.fst", "name": "DM4F.bind_wp" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.strengthen_wp" }, { "project_name": "FStar", "file_name": "ID3.fst", "name": "ID3.return" }, { "project_name": "steel", "file_name": "MParIndex.fst", "name": "MParIndex.lift_pure_eff" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Pure.fst", "name": "FStar.Monotonic.Pure.as_pure_wp" }, { "project_name": "FStar", "file_name": "HoareDiv.fst", "name": "HoareDiv.lift_pure_meff" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.free" }, { "project_name": "FStar", "file_name": "HoareSTFree.fst", "name": "HoareSTFree.pure_q" }, { "project_name": "FStar", "file_name": "ID4.fst", "name": "ID4.bind_wp" }, { "project_name": "FStar", "file_name": "LatticeSpec.fst", "name": "LatticeSpec.lift_pure_eff" }, { "project_name": "FStar", "file_name": "OPLSS2021.DijkstraMonads.fst", "name": "OPLSS2021.DijkstraMonads.lift_wp" }, { "project_name": "FStar", "file_name": "DM4F.fst", "name": "DM4F.lift_wp" }, { "project_name": "FStar", "file_name": "LatticeSpec.fst", "name": "LatticeSpec.sp" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.sp" }, { "project_name": "FStar", "file_name": "GenericPartialDM4A.fst", "name": "GenericPartialDM4A.lift_pure_dm4a" }, { "project_name": "FStar", "file_name": "IOWPInconsistent.fst", "name": "IOWPInconsistent.f" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.rwi_assert" }, { "project_name": "FStar", "file_name": "HoareSTFree.fst", "name": "HoareSTFree.lift_PURE_M" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.weaken" }, { "project_name": "FStar", "file_name": "ID2.fst", "name": "ID2.repr" }, { "project_name": "FStar", "file_name": "AlgForAll.fst", "name": "AlgForAll.stronger" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.stronger" }, { "project_name": "FStar", "file_name": "AlgWP.fst", "name": "AlgWP.stronger" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.lift_PURE_HIFC" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.lift_pure_lvars" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.lift_pure_wp" }, { "project_name": "FStar", "file_name": "MSeqExn.fst", "name": "MSeqExn.lift_pure_wp" }, { "project_name": "FStar", "file_name": "IOWPInconsistent.fst", "name": "IOWPInconsistent.p0" }, { "project_name": "FStar", "file_name": "AlgWP.fst", "name": "AlgWP.lift_pure_wp" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.lift_pure_wp" }, { "project_name": "FStar", "file_name": "AlgForAll.fst", "name": "AlgForAll.lift_pure_wp" }, { "project_name": "FStar", "file_name": "Sec1.GST.fst", "name": "Sec1.GST.lift_pure" }, { "project_name": "FStar", "file_name": "LatticeEff.fst", "name": "LatticeEff.lift_pure_eff" }, { "project_name": "FStar", "file_name": "Lattice.fst", "name": "Lattice.lift_pure_eff" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.write" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.write" }, { "project_name": "FStar", "file_name": "FStar.MSTTotal.fst", "name": "FStar.MSTTotal.lift_pure_mst_total" }, { "project_name": "FStar", "file_name": "IOWPInconsistent.fst", "name": "IOWPInconsistent.bad1" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.unreachable" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.fail" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.fail" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.write" }, { "project_name": "FStar", "file_name": "AlgWP.fst", "name": "AlgWP.null" }, { "project_name": "FStar", "file_name": "FStar.MST.fst", "name": "FStar.MST.lift_pure_mst" }, { "project_name": "FStar", "file_name": "GT.fst", "name": "GT.lift_pure_gtd" }, { "project_name": "karamel", "file_name": "C.Failure.fst", "name": "C.Failure.failwith" }, { "project_name": "FStar", "file_name": "DijkstraStateMonad.fst", "name": "DijkstraStateMonad.lift_wp" }, { "project_name": "FStar", "file_name": "ID2.fst", "name": "ID2.sat" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.lift_pure_eff" }, { "project_name": "FStar", "file_name": "Param.fst", "name": "Param.fst" }, { "project_name": "FStar", "file_name": "IOWPInconsistent.fst", "name": "IOWPInconsistent.bad2" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.lift_pure_eff" }, { "project_name": "FStar", "file_name": "GTWP.fst", "name": "GTWP.t_return" }, { "project_name": "FStar", "file_name": "DM4F.fst", "name": "DM4F.lift_pure_st" }, { "project_name": "FStar", "file_name": "LL.fst", "name": "LL.lift_pure_exn" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.return_stt_a" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.lift_pure" }, { "project_name": "FStar", "file_name": "BUGSLowParseWriters.fst", "name": "BUGSLowParseWriters.lift_pure_read" }, { "project_name": "FStar", "file_name": "ID2.fst", "name": "ID2.test_2" }, { "project_name": "FStar", "file_name": "GTWP.fst", "name": "GTWP.lift_pure_gtd" }, { "project_name": "FStar", "file_name": "AlgWP.fst", "name": "AlgWP.null_equiv_sanity" }, { "project_name": "FStar", "file_name": "AlgWP.fst", "name": "AlgWP.lift_pure_algwp" }, { "project_name": "FStar", "file_name": "LatticeSpec.fst", "name": "LatticeSpec.raise" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.wp0" }, { "project_name": "FStar", "file_name": "ID4.fst", "name": "ID4.wp0" }, { "project_name": "FStar", "file_name": "DM4F_layered.fst", "name": "DM4F_layered.return_wp" }, { "project_name": "FStar", "file_name": "DM4F.fst", "name": "DM4F.return_wp" }, { "project_name": "FStar", "file_name": "OPLSS2021.DijkstraMonads.fst", "name": "OPLSS2021.DijkstraMonads.return_wp" }, { "project_name": "FStar", "file_name": "DM4F_layered5.fst", "name": "DM4F_layered5.return_wp" }, { "project_name": "FStar", "file_name": "LL.fst", "name": "LL.lift_pure_wp" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.cut" }, { "project_name": "FStar", "file_name": "BUGSLowParseWriters.fst", "name": "BUGSLowParseWriters.lift_pure_read_spec" }, { "project_name": "FStar", "file_name": "LowParseWriters.fsti", "name": "LowParseWriters.lift_pure_read_spec" }, { "project_name": "FStar", "file_name": "LowParseWriters.fsti", "name": "LowParseWriters.lift_pure_read" } ], "selected_premises": [ "FStar.List.Tot.Base.map", "FStar.List.Tot.Base.length", "FStar.List.Tot.Base.op_At", "FStar.FunctionalExtensionality.feq", "FStar.List.Tot.Base.rev", "FStar.List.Tot.Base.mem", "ND.m", "FStar.Tactics.Effect.raise", "FStar.List.Tot.Base.tl", "FStar.List.Tot.Base.append", "ND.m_return", "FStar.WellFounded.fix_F", "ND.l", "FStar.List.Tot.Base.memP", "FStar.FunctionalExtensionality.on_dom", "ND.ireturn", "FStar.Tactics.Types.issues", "FStar.Pervasives.Native.fst", "FStar.List.Tot.Properties.assoc_mem", "FStar.Pervasives.Native.snd", "FStar.List.Tot.Base.fold_left", "FStar.Pervasives.reveal_opaque", "FStar.List.Tot.Base.hd", "FStar.Tactics.Effect.get", "ND.w_ord", "FStar.WellFounded.well_founded", "FStar.List.Tot.Properties.append_assoc", "ND.w", "FStar.List.Tot.Properties.append_l_cons", "FStar.Pervasives.dfst", "ND.m_bind", "FStar.List.Tot.Properties.append_l_nil", "FStar.Pervasives.dsnd", "FStar.List.Tot.Base.fold_right", "FStar.FunctionalExtensionality.on", "FStar.WellFounded.fix", "ND.concatlemma", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity", "FStar.WellFounded.inverse_image", "FStar.List.Tot.Properties.append_mem", "FStar.WellFounded.binrel", "FStar.List.Tot.Base.find", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater", "FStar.List.Tot.Properties.map_append", "FStar.Issue.mk_issue", "FStar.List.Tot.Properties.rev'", "FStar.List.Tot.Properties.memP_map_intro", "ND.choose", "ND.interp", "FStar.WellFounded.is_well_founded", "FStar.List.Tot.Properties.append_inv_head", "FStar.List.Tot.Base.concatMap", "FStar.List.Tot.Base.for_all", "ND.pmap", "FStar.List.Tot.Properties.memP_map_elim", "FStar.List.Tot.Properties.append_length", "ND.append_memP", "FStar.FunctionalExtensionality.restricted_t", "FStar.List.Tot.Properties.append_memP", "FStar.List.Tot.Base.rev_acc", "FStar.List.Tot.Base.tryPick", "FStar.List.Tot.Properties.rev_memP", "FStar.List.Tot.Base.flatten", "FStar.List.Tot.Base.snoc", "FStar.List.Tot.Properties.rev_rev'", "FStar.List.Tot.Base.tail", "FStar.FunctionalExtensionality.arrow", "FStar.List.Tot.Properties.append_injective", "FStar.List.Tot.Base.nth", "FStar.List.Tot.Properties.map_lemma", "FStar.List.Tot.Properties.assoc_memP_some", "FStar.List.Tot.Properties.append_memP_forall", "FStar.Issue.issue_level_string", "ND.test_f", "FStar.List.Tot.Base.list_refb", "FStar.List.Tot.Properties.rev'_append", "FStar.List.Tot.Base.compare_of_bool", "FStar.Preorder.preorder_rel", "FStar.Tactics.Effect.tactic", "FStar.List.Tot.Base.split", "FStar.List.Tot.Properties.rev_append", "FStar.List.Tot.Base.assoc", "FStar.WellFounded.subrelation_squash_wf", "FStar.Pervasives.id", "FStar.List.Tot.Properties.memP_precedes", "FStar.List.Tot.Properties.append_mem_forall", "FStar.List.Tot.Base.index", "FStar.List.Tot.Base.last", "FStar.List.Tot.Properties.memP_existsb", "FStar.WellFounded.inverse_image_wf", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater_Greater", "FStar.List.Tot.Properties.mem_subset", "FStar.List.Tot.Base.fold_left2", "FStar.List.Tot.Base.tryFind", "FStar.FunctionalExtensionality.is_restricted", "FStar.Pervasives.st_post_h", "FStar.List.Tot.Properties.for_all_append", "FStar.List.Tot.Properties.rev'T", "FStar.List.Tot.Base.bool_of_compare", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity_forall" ], "source_upto_this": "module ND\n\n(* An effect for (demonic) nondeterminism via lists. *)\n\nopen FStar.List.Tot\nopen FStar.Tactics.V2\nopen FStar.Calc\n\nopen FStar.FunctionalExtensionality\nmodule F = FStar.FunctionalExtensionality\nmodule W = FStar.WellFounded\nmodule T = FStar.Tactics.V2\n\n// m is a monad. In this particular example, lists\nval m (a : Type u#a) : Type u#a\nlet m a = list a\n\nval m_return (#a : Type) : a -> m a\nlet m_return x = [x]\n\nval m_bind (#a #b : Type) : m a -> (a -> m b) -> m b\nlet m_bind l f = concatMap f l\n\n// w is an ordered (w_ord) monad with conjunction (w_conj) and actions from prop (w_act_prop)\n// In this example, good ol' continuations into prop\n\nval w (a : Type u#a) : Type u#(max 1 a)\nlet w a = pure_wp a\n\nval w_ord (#a : Type) : w a -> w a -> Type0\nlet w_ord wp1 wp2 = forall p. wp1 p ==> wp2 p\n\nopen FStar.Monotonic.Pure\n\nunfold\nval w_return (#a : Type) : a -> w a\nunfold\nlet w_return x = as_pure_wp (fun p -> p x)\n\nunfold\nval w_bind (#a #b : Type) : w a -> (a -> w b) -> w b\nunfold\nlet w_bind wp1 k =\n elim_pure_wp_monotonicity_forall ();\n as_pure_wp (fun p -> wp1 (fun x -> k x p))\n\nval interp (#a : Type) : m a -> w a\nlet interp #a (l:list a) = as_pure_wp (fun p -> forall x. memP x l ==> p x)\n\nval concatlemma (#a:Type) (l1 l2 :list a) (x:a) : Lemma (memP x (l1@l2) <==> memP x l1 \\/ memP x l2)\nlet rec concatlemma #a l1 l2 x =\n match l1 with\n | [] -> ()\n | h::t -> concatlemma t l2 x\n\nval concatmaplemma : (#a:Type) -> (#b:Type) -> l:list a -> (f:(a -> list b)) -> x:b ->\n Lemma (memP x (concatMap f l) <==> (exists a. memP a l /\\ memP x (f a)))\n [SMTPat (memP x (concatMap f l))]\n\nlet rec concatmaplemma #a #b l f x =\n match l with\n | [] -> ()\n | h::t ->\n concatlemma (f h) (concatMap f t) x;\n concatmaplemma t f x\n\nlet dm (a : Type) (wp : w a) : Type =\n p:(a -> Type0) -> squash (wp p) -> l:(m a){forall x. memP x l ==> p x}\n\nlet irepr (a : Type) (wp: w a) = dm a wp\n\nlet ireturn (a : Type) (x : a) : irepr a (w_return x) = fun _ _ -> [x]\n\nlet rec pmap #a #b #pre (#post:b->Type0)\n (f : (x:a -> Pure b (requires (pre x)) (ensures post)))\n (l : list a)\n : Pure (list (v:b{post v}))\n (requires (forall x. memP x l ==> pre x))\n (ensures (fun _ -> True))\n = match l with\n | [] -> []\n | x::xs -> f x :: pmap #_ #_ #pre #post f xs\n\nlet rec unref #a #p (l : list (v:a{p v})) : l:(list a){forall x. memP x l ==> p x} =\n match l with\n | [] -> []\n | x :: xs -> x :: unref xs\n\nlet mem_memP\n (#a: eqtype)\n (x: a)\n (l: list a)\n: Lemma (ensures (mem x l <==> memP x l))\n [SMTPat (memP x l); SMTPat (mem x l)]\n= FStar.List.Tot.Properties.mem_memP x l\n\nval append_memP: #t:Type -> l1:list t\n -> l2:list t\n -> a:t\n -> Lemma (requires True)\n (ensures (memP a (l1@l2) <==> (memP a l1 \\/ memP a l2)))\nlet rec append_memP #t l1 l2 a = match l1 with\n | [] -> ()\n | hd::tl -> append_memP tl l2 a\n\nlet rec flatten_mem_lem #a (l : list (list a)) (x:a)\n : Lemma (memP x (flatten l) <==> (exists l0. memP l0 l /\\ memP x l0))\n [SMTPat (memP x (flatten l))]\n = match l with\n | [] -> ()\n | l1::ls -> (append_memP l1 (flatten ls) x; flatten_mem_lem ls x)\n\nlet ibind (a : Type) (b : Type) (wp_v : w a) (wp_f: a -> w b) (v : irepr a wp_v) (f : (x:a -> irepr b (wp_f x))) : irepr b (w_bind wp_v wp_f) =\n fun p _ -> let l1 = v (fun x -> wp_f x p) () in\n let l2 = pmap #_ #(list b) #(fun x -> wp_f x p) #(fun l -> forall x. memP x l ==> p x) (fun x -> f x p ()) l1 in\n let l2 = unref l2 in\n let l2f = List.Tot.flatten l2 in\n l2f\n\nlet isubcomp (a:Type) (wp1 wp2: w a) (f : irepr a wp1) : Pure (irepr a wp2) (requires w_ord wp2 wp1) (ensures fun _ -> True) = f\n\nlet wp_if_then_else (#a:Type) (wp1 wp2:w a) (b:bool) : w a=\n elim_pure_wp_monotonicity_forall ();\n as_pure_wp (fun p -> (b ==> wp1 p) /\\ ((~b) ==> wp2 p))\n\nlet i_if_then_else (a : Type) (wp1 wp2 : w a) (f : irepr a wp1) (g : irepr a wp2) (b : bool) : Type =\n irepr a (wp_if_then_else wp1 wp2 b)\n\ntotal\nreifiable\nreflectable\neffect {\n ND (a:Type) (wp:w a)\n with {repr = irepr;\n return = ireturn;\n bind = ibind;\n subcomp = isubcomp;\n if_then_else = i_if_then_else}\n}\n\nlet lift_pure_nd (a:Type) (wp:pure_wp a) (f:unit -> PURE a wp) :\n Pure (irepr a wp) (requires True)\n (ensures (fun _ -> True))\n = fun p _ -> let r = FStar.Monotonic.Pure.elim_pure f p in [r]\n\nsub_effect PURE ~> ND = lift_pure_nd\n\nval test_f : unit -> ND int (as_pure_wp (fun p -> p 5 /\\ p 3))\nlet test_f () =\n ND?.reflect (fun _ _ -> [3; 5])\n\n//let l () : (l:(list int){forall p. p 5 /\\ p 3 ==> interp l p}) = reify (test_f ())\n// ^ This one doesn't work... datatype subtyping to blame?\n\nlet l () : list int = reify (test_f ()) (fun _ -> True) ()\n\neffect Nd (a:Type) (pre:pure_pre) (post:pure_post' a pre) =\n ND a (as_pure_wp (fun (p:pure_post a) -> pre /\\ (forall (pure_result:a). post pure_result ==> p pure_result)))\n\nval choose : #a:Type0 -> x:a -> y:a -> ND a (as_pure_wp (fun p -> p x /\\ p y))\nlet choose #a x y =\n ND?.reflect (fun _ _ -> [x;y])\n\nval fail : #a:Type0 -> unit -> ND a (as_pure_wp (fun p -> True))", "sketch": [ "Step 1: The `fail` function is intended to represent a nondeterministic computation that always fails. In the context of the ND effect, this means it should produce an empty list, indicating no successful outcomes.\nStep 2: To implement `fail`, we use the `ND?.reflect` function to create an ND computation that returns an empty list. This reflects the fact that there are no possible values that satisfy the computation.", "Step 1: The `fail` function is intended to represent a nondeterministic computation that always fails. In the context of nondeterminism, this means that it produces an empty list, indicating no successful outcomes.\nStep 2: To implement `fail`, we use the `ND?.reflect` function to create an empty list. This is because an empty list in the nondeterministic monad represents a computation with no possible results.", "Step 1: The `fail` function is intended to represent a nondeterministic computation that always fails. In the context of nondeterminism, this means that the computation does not produce any successful outcomes.\nStep 2: To implement `fail`, we will use the `ND?.reflect` function to create an empty list, indicating that there are no successful outcomes for this computation.", "Step 1: The `fail` function is intended to represent a nondeterministic computation that always fails. In the context of the ND effect, this means it should produce an empty list, indicating no possible outcomes.\nStep 2: The implementation of `fail` will use the `ND?.reflect` function to create an empty list, which corresponds to the failure of the nondeterministic computation.", "Step 1: The `fail` function is intended to represent a nondeterministic computation that always fails. In the context of the ND effect, this means it should produce an empty list, indicating no possible successful outcomes.\nStep 2: To implement `fail`, we use the `ND?.reflect` function to create an ND computation that returns an empty list. This ensures that the resulting computation satisfies the condition that it can never produce a valid result.", "Step 1: The `fail` function is intended to represent a nondeterministic computation that always fails. This means it should produce an empty list, indicating no successful outcomes.\nStep 2: To implement `fail`, we use the `ND?.reflect` function to create an empty list, which corresponds to the failure in the nondeterministic context.", "Step 1: The `fail` function represents a computation in the `ND` effect that always fails. This means it does not produce any value of type `a`.\nStep 2: To implement `fail`, we use the `ND?.reflect` function to create a computation that returns an empty list, indicating no successful outcomes.", "Step 1: The `fail` function is intended to represent a nondeterministic computation that always fails. This means it should produce an empty list, indicating that there are no possible successful outcomes.\nStep 2: To implement this, we use the `ND?.reflect` function to create an `ND` effect that returns an empty list. This ensures that the computation has no successful results.", "Step 1: The `fail` function represents a nondeterministic computation that always fails. This means it does not produce any successful result.\nStep 2: To implement `fail`, we use the `ND?.reflect` function to create a computation that returns an empty list, indicating no successful outcomes.", "Step 1: The `fail` function represents a nondeterministic computation that always fails. This means it should produce an empty list, indicating no successful outcomes.\nStep 2: The implementation of `fail` will use the `ND?.reflect` function to return an empty list, which corresponds to the failure in the nondeterministic context." ], "generated_solution": [ "let fail #a () =\n ND?.reflect (fun _ _ -> [])", "let fail #a () =\n ND?.reflect (fun _ _ -> [])", "let fail #a () =\n ND?.reflect (fun _ _ -> [])", "let fail #a () =\n ND?.reflect (fun _ _ -> [])", "let fail #a () =\n ND?.reflect (fun _ _ -> [])", "let fail #a () =\n ND?.reflect (fun _ _ -> [])", "let fail #a () = ND?.reflect (fun _ _ -> [])", "let fail #a () =\n ND?.reflect (fun _ _ -> [])", "let fail #a () = ND?.reflect (fun _ _ -> [])", "let fail #a () =\n ND?.reflect (fun _ _ -> [])" ] }, { "file_name": "FStar.Tactics.CanonCommMonoid.fst", "name": "FStar.Tactics.CanonCommMonoid.apply_swap_aux_correct", "opens_and_abbrevs": [ { "open": "FStar.Tactics.CanonCommSwaps" }, { "open": "FStar.Classical" }, { "open": "FStar.Tactics.V2" }, { "open": "FStar.Reflection.V2" }, { "open": "FStar.List" }, { "open": "FStar.Algebra.CommMonoid" }, { "open": "FStar.Tactics" }, { "open": "FStar.Tactics" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val apply_swap_aux_correct\n (#a #b: Type)\n (n: nat)\n (m: cm a)\n (vm: vmap a b)\n (xs: list var)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s)))\n (decreases xs)", "source_definition": "let rec apply_swap_aux_correct (#a #b:Type) (n:nat) (m:cm a) (vm:vmap a b)\n (xs:list var) (s:swap (length xs + n)) :\n Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] | [_] -> ()\n | x1 :: x2 :: xs' ->\n if n = (s <: nat)\n then (// x1 + (x2 + xs') =a (x1 + x2) + xs'\n // =c (x2 + x1) + xs' = a x2 + (x1 + xs')\n let a = CM?.associativity m in\n a (select x1 vm) (select x2 vm) (xsdenote m vm xs');\n a (select x2 vm) (select x1 vm) (xsdenote m vm xs');\n CM?.commutativity m (select x1 vm) (select x2 vm))\n else apply_swap_aux_correct (n+1) m vm (x2 :: xs') s", "source_range": { "start_line": 124, "start_col": 0, "end_line": 139, "end_col": 58 }, "interleaved": false, "definition": "fun n m vm xs s ->\n (match xs with\n | Prims.Nil #_ -> ()\n | Prims.Cons #_ _ (Prims.Nil #_) -> ()\n | Prims.Cons #_ x1 (Prims.Cons #_ x2 xs') ->\n (match n = (s <: Prims.nat) with\n | true ->\n let a = CM?.associativity m in\n a (FStar.Tactics.CanonCommMonoid.select x1 vm)\n (FStar.Tactics.CanonCommMonoid.select x2 vm)\n (FStar.Tactics.CanonCommMonoid.xsdenote m vm xs');\n a (FStar.Tactics.CanonCommMonoid.select x2 vm)\n (FStar.Tactics.CanonCommMonoid.select x1 vm)\n (FStar.Tactics.CanonCommMonoid.xsdenote m vm xs');\n CM?.commutativity m\n (FStar.Tactics.CanonCommMonoid.select x1 vm)\n (FStar.Tactics.CanonCommMonoid.select x2 vm)\n | _ -> FStar.Tactics.CanonCommMonoid.apply_swap_aux_correct (n + 1) m vm (x2 :: xs') s)\n <:\n Prims.unit)\n <:\n FStar.Pervasives.Lemma\n (ensures\n FStar.Tactics.CanonCommMonoid.xsdenote m vm xs ==\n FStar.Tactics.CanonCommMonoid.xsdenote m vm (FStar.Tactics.CanonCommSwaps.apply_swap_aux n xs s)\n )", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma", "" ], "mutual_with": [], "premises": [ "Prims.nat", "FStar.Algebra.CommMonoid.cm", "FStar.Tactics.CanonCommMonoid.vmap", "Prims.list", "FStar.Tactics.CanonCommMonoid.var", "FStar.Tactics.CanonCommSwaps.swap", "Prims.op_Addition", "FStar.List.Tot.Base.length", "Prims.op_Equality", "FStar.Algebra.CommMonoid.__proj__CM__item__commutativity", "FStar.Tactics.CanonCommMonoid.select", "Prims.unit", "FStar.Tactics.CanonCommMonoid.xsdenote", "Prims.l_True", "Prims.squash", "Prims.eq2", "FStar.Algebra.CommMonoid.__proj__CM__item__mult", "Prims.Nil", "FStar.Pervasives.pattern", "FStar.Algebra.CommMonoid.__proj__CM__item__associativity", "Prims.bool", "FStar.Tactics.CanonCommMonoid.apply_swap_aux_correct", "Prims.Cons", "FStar.Tactics.CanonCommSwaps.apply_swap_aux" ], "proof_features": [ "recursion" ], "is_simple_lemma": false, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "\n n: Prims.nat ->\n m: FStar.Algebra.CommMonoid.cm a ->\n vm: FStar.Tactics.CanonCommMonoid.vmap a b ->\n xs: Prims.list FStar.Tactics.CanonCommMonoid.var ->\n s: FStar.Tactics.CanonCommSwaps.swap (FStar.List.Tot.Base.length xs + n)\n -> FStar.Pervasives.Lemma\n (ensures\n FStar.Tactics.CanonCommMonoid.xsdenote m vm xs ==\n FStar.Tactics.CanonCommMonoid.xsdenote m\n vm\n (FStar.Tactics.CanonCommSwaps.apply_swap_aux n xs s)) (decreases xs)", "prompt": "let rec apply_swap_aux_correct\n (#a #b: Type)\n (n: nat)\n (m: cm a)\n (vm: vmap a b)\n (xs: list var)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s)))\n (decreases xs) =\n ", "expected_response": "match xs with\n| [] | [_] -> ()\n| x1 :: x2 :: xs' ->\n if n = (s <: nat)\n then\n (let a = CM?.associativity m in\n a (select x1 vm) (select x2 vm) (xsdenote m vm xs');\n a (select x2 vm) (select x1 vm) (xsdenote m vm xs');\n CM?.commutativity m (select x1 vm) (select x2 vm))\n else apply_swap_aux_correct (n + 1) m vm (x2 :: xs') s", "source": { "project_name": "FStar", "file_name": "ulib/FStar.Tactics.CanonCommMonoid.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.Tactics.CanonCommMonoid.fst", "checked_file": "dataset/FStar.Tactics.CanonCommMonoid.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Tactics.Util.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Tactics.CanonCommSwaps.fst.checked", "dataset/FStar.Reflection.V2.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Order.fst.checked", "dataset/FStar.List.Tot.Properties.fst.checked", "dataset/FStar.List.Tot.Base.fst.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.List.fst.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Algebra.CommMonoid.fst.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "let dump m = if debugging () then dump m", "let var : eqtype = nat", "exp", "Unit", "Unit", "Unit", "Var", "Var", "Var", "Mult", "Mult", "Mult", "let rec exp_to_string (e:exp) : string =\n match e with\n | Unit -> \"Unit\"\n | Var x -> \"Var \" ^ string_of_int (x <: var)\n | Mult e1 e2 -> \"Mult (\" ^ exp_to_string e1\n ^ \") (\" ^ exp_to_string e2 ^ \")\"", "let vmap (a b:Type) = list (var * (a*b)) * (a * b)", "let const (#a #b:Type) (xa:a) (xb:b) : vmap a b = [], (xa,xb)", "let select (#a #b:Type) (x:var) (vm:vmap a b) : Tot a =\n match assoc #var #(a * b) x (fst vm) with\n | Some (a, _) -> a\n | _ -> fst (snd vm)", "let select_extra (#a #b:Type) (x:var) (vm:vmap a b) : Tot b =\n match assoc #var #(a * b) x (fst vm) with\n | Some (_, b) -> b\n | _ -> snd (snd vm)", "let update (#a #b:Type) (x:var) (xa:a) (xb:b) (vm:vmap a b) : vmap a b =\n (x, (xa, xb))::fst vm, snd vm", "let rec mdenote (#a #b:Type) (m:cm a) (vm:vmap a b) (e:exp) : Tot a =\n match e with\n | Unit -> CM?.unit m\n | Var x -> select x vm\n | Mult e1 e2 -> CM?.mult m (mdenote m vm e1) (mdenote m vm e2)", "let rec xsdenote (#a #b:Type) (m:cm a) (vm:vmap a b) (xs:list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | [x] -> select x vm\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "let rec flatten (e:exp) : list var =\n match e with\n | Unit -> []\n | Var x -> [x]\n | Mult e1 e2 -> flatten e1 @ flatten e2", "let rec flatten_correct_aux (#a #b:Type) (m:cm a) (vm:vmap a b)\n (xs1 xs2:list var) :\n Lemma (xsdenote m vm (xs1 @ xs2) == CM?.mult m (xsdenote m vm xs1)\n (xsdenote m vm xs2)) =\n match xs1 with\n | [] -> CM?.identity m (xsdenote m vm xs2)\n | [x] -> if (Nil? xs2) then right_identity m (select x vm)\n | x::xs1' -> (CM?.associativity m (select x vm)\n (xsdenote m vm xs1') (xsdenote m vm xs2);\n flatten_correct_aux m vm xs1' xs2)", "let rec flatten_correct (#a #b:Type) (m:cm a) (vm:vmap a b) (e:exp) :\n Lemma (mdenote m vm e == xsdenote m vm (flatten e)) =\n match e with\n | Unit | Var _ -> ()\n | Mult e1 e2 -> flatten_correct_aux m vm (flatten e1) (flatten e2);\n flatten_correct m vm e1; flatten_correct m vm e2", "let permute (b:Type) = a:Type -> vmap a b -> list var -> list var", "let permute_correct (#b:Type) (p:permute b) =\n #a:Type -> m:cm a -> vm:vmap a b -> xs:list var ->\n Lemma (xsdenote m vm xs == xsdenote m vm (p a vm xs))" ], "closest": [ "val apply_swap_aux_correct\n (#a: Type)\n (n: nat)\n (m: cm a)\n (am: amap a)\n (xs: list atom)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swap_aux n xs s)))\n (decreases xs)\nlet rec apply_swap_aux_correct (#a:Type) (n:nat) (m:cm a) (am:amap a)\n (xs:list atom) (s:swap (length xs + n)) :\n Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] | [_] -> ()\n | x1 :: x2 :: xs' ->\n if n = (s <: nat)\n then (// x1 + (x2 + xs') =a (x1 + x2) + xs'\n // =c (x2 + x1) + xs' = a x2 + (x1 + xs')\n let a = CM?.associativity m in\n a (select x1 am) (select x2 am) (xsdenote m am xs');\n a (select x2 am) (select x1 am) (xsdenote m am xs');\n CM?.commutativity m (select x1 am) (select x2 am))\n else apply_swap_aux_correct (n+1) m am (x2 :: xs') s", "val apply_swap_aux_correct\n (#a: Type)\n (n: nat)\n (eq: equiv a)\n (m: cm a eq)\n (am: amap a)\n (xs: list atom)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (apply_swap_aux n xs s))))\n (decreases xs)\nlet rec apply_swap_aux_correct (#a:Type) (n:nat) (eq:equiv a) (m:cm a eq) (am:amap a)\n (xs:list atom) (s:swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] -> EQ?.reflexivity eq (CM?.unit m)\n | [x] -> EQ?.reflexivity eq (select x am)\n | [x1;x2] ->\n if n = (s <: nat)\n then CM?.commutativity m (select x1 am) (select x2 am)\n else EQ?.reflexivity eq (xsdenote eq m am [x1;x2])\n | x1 :: x2 :: xs' ->\n if n = (s <: nat)\n then (\n CM?.associativity m (select x1 am) (select x2 am) (xsdenote eq m am xs');\n EQ?.symmetry eq (CM?.mult m (CM?.mult m (select x1 am) (select x2 am)) (xsdenote eq m am xs'))\n (CM?.mult m (select x1 am) (CM?.mult m (select x2 am) (xsdenote eq m am xs')));\n CM?.commutativity m (select x1 am) (select x2 am);\n EQ?.reflexivity eq (xsdenote eq m am xs');\n CM?.congruence m (CM?.mult m (select x1 am) (select x2 am)) (xsdenote eq m am xs')\n (CM?.mult m (select x2 am) (select x1 am)) (xsdenote eq m am xs');\n CM?.associativity m (select x2 am) (select x1 am) (xsdenote eq m am xs');\n EQ?.transitivity eq (CM?.mult m (select x1 am) (CM?.mult m (select x2 am) (xsdenote eq m am xs')))\n (CM?.mult m (CM?.mult m (select x1 am) (select x2 am)) (xsdenote eq m am xs'))\n (CM?.mult m (CM?.mult m (select x2 am) (select x1 am)) (xsdenote eq m am xs'));\n EQ?.transitivity eq (CM?.mult m (select x1 am) (CM?.mult m (select x2 am) (xsdenote eq m am xs')))\n (CM?.mult m (CM?.mult m (select x2 am) (select x1 am)) (xsdenote eq m am xs'))\n (CM?.mult m (select x2 am) (CM?.mult m (select x1 am) (xsdenote eq m am xs'))))\n else (\n apply_swap_aux_correct (n+1) eq m am (x2 :: xs') s;\n EQ?.reflexivity eq (select x1 am);\n CM?.congruence m (select x1 am) (xsdenote eq m am (x2 :: xs'))\n (select x1 am) (xsdenote eq m am (apply_swap_aux (n+1) (x2 :: xs') s)))", "val apply_swap_correct\n (#a: Type)\n (eq: equiv a)\n (m: cm a eq)\n (am: amap a)\n (xs: list atom)\n (s: swap (length xs))\n : Lemma (ensures (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (apply_swap xs s))))\n (decreases xs)\nlet apply_swap_correct (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a)\n (xs:list atom) (s:swap (length xs))\n : Lemma (ensures (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (apply_swap xs s)))\n (decreases xs) =\n apply_swap_aux_correct 0 eq m am xs s", "val apply_swap_aux (#a: Type) (n: nat) (xs: list a) (s: swap (length xs + n))\n : Pure (list a) (requires True) (ensures (fun zs -> length zs == length xs)) (decreases xs)\nlet rec apply_swap_aux (#a:Type) (n:nat) (xs:list a) (s:swap (length xs + n)) :\n Pure (list a) (requires True)\n (ensures (fun zs -> length zs == length xs)) (decreases xs) =\n match xs with\n | [] | [_] -> xs\n | x1 :: x2 :: xs' -> if n = (s <: nat)\n then x2 :: x1 :: xs'\n else x1 :: apply_swap_aux (n+1) (x2 :: xs') s", "val apply_swap_correct (#a: Type) (m: cm a) (am: amap a) (xs: list atom) (s: swap (length xs))\n : Lemma (ensures (xsdenote m am xs == xsdenote m am (apply_swap xs s))) (decreases xs)\nlet apply_swap_correct (#a:Type) (m:cm a) (am:amap a)\n (xs:list atom) (s:swap (length xs)):\n Lemma (ensures (xsdenote m am xs == xsdenote m am (apply_swap xs s)))\n (decreases xs) = apply_swap_aux_correct 0 m am xs s", "val lift_swap_cons (#a: eqtype) (n: nat) (h: a) (xs: list a) (s: swap (length xs + n))\n : Lemma (requires n <= s)\n (ensures apply_swap_aux n (h :: xs) (s + 1) == h :: (apply_swap_aux n xs s))\n (decreases xs)\nlet rec lift_swap_cons (#a:eqtype) (n:nat) (h:a) (xs:list a) (s:swap (length xs + n)) : Lemma\n (requires n <= s)\n (ensures apply_swap_aux n (h::xs) (s + 1) == h::(apply_swap_aux n xs s))\n (decreases xs)\n =\n match xs with\n | [] -> ()\n | x::xt -> if n < s then lift_swap_cons (n + 1) x xt s", "val apply_swaps_correct\n (#a: Type)\n (m: cm a)\n (am: amap a)\n (xs: list atom)\n (ss: list (swap (length xs)))\n : Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swaps xs ss)))\n (decreases ss)\nlet rec apply_swaps_correct (#a:Type) (m:cm a) (am:amap a)\n (xs:list atom) (ss:list (swap (length xs))):\n Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swaps xs ss)))\n (decreases ss) =\n match ss with\n | [] -> ()\n | s::ss' -> apply_swap_correct m am xs s;\n apply_swaps_correct m am (apply_swap xs s) ss'", "val apply_swaps_correct\n (#a: Type)\n (eq: equiv a)\n (m: cm a eq)\n (am: amap a)\n (xs: list atom)\n (ss: list (swap (length xs)))\n : Lemma (requires True)\n (ensures (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (apply_swaps xs ss))))\n (decreases ss)\nlet rec apply_swaps_correct (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a)\n (xs:list atom) (ss:list (swap (length xs)))\n : Lemma (requires True)\n (ensures (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (apply_swaps xs ss)))\n (decreases ss) =\n match ss with\n | [] -> EQ?.reflexivity eq (xsdenote eq m am xs)\n | s::ss' ->\n apply_swap_correct eq m am xs s;\n apply_swaps_correct eq m am (apply_swap xs s) ss';\n EQ?.transitivity eq (xsdenote eq m am xs)\n (xsdenote eq m am (apply_swap xs s))\n (xsdenote eq m am (apply_swaps (apply_swap xs s) ss'))", "val append_swaps (#a: eqtype) (xs: list a) (ss1 ss2: swaps_for xs)\n : Lemma (ensures apply_swaps xs (ss1 @ ss2) == apply_swaps (apply_swaps xs ss1) ss2)\n (decreases ss1)\nlet rec append_swaps (#a:eqtype) (xs:list a) (ss1 ss2:swaps_for xs) : Lemma\n (ensures apply_swaps xs (ss1 @ ss2) == apply_swaps (apply_swaps xs ss1) ss2)\n (decreases ss1)\n =\n match ss1 with\n | [] -> ()\n | h::t -> append_swaps (apply_swap xs h) t ss2", "val apply_swaps (#a: Type) (xs: list a) (ss: list (swap (length xs)))\n : Pure (list a) (requires True) (ensures (fun zs -> length zs == length xs)) (decreases ss)\nlet rec apply_swaps (#a:Type) (xs:list a) (ss:list (swap (length xs))) :\n Pure (list a) (requires True)\n (ensures (fun zs -> length zs == length xs)) (decreases ss) =\n match ss with\n | [] -> xs\n | s::ss' -> apply_swaps (apply_swap xs s) ss'", "val sort_correct_aux (#a: Type) (m: cm a) (am: amap a) (xs: list atom)\n : Lemma (xsdenote m am xs == xsdenote m am (sort xs))\nlet sort_correct_aux (#a:Type) (m:cm a) (am:amap a) (xs:list atom) :\n Lemma (xsdenote m am xs == xsdenote m am (sort xs)) =\n permute_via_swaps_correct sort (fun #a am -> sort_via_swaps am) m am xs", "val sort_correct_aux (#a: Type) (eq: CE.equiv a) (m: CE.cm a eq) (am: amap a) (xs: list atom)\n : Lemma (requires True)\n (ensures CE.EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (sort xs)))\n (decreases (FStar.List.Tot.Base.length xs))\nlet rec sort_correct_aux (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (xs:list atom)\n : Lemma (requires True)\n (ensures xsdenote eq m am xs `CE.EQ?.eq eq` xsdenote eq m am (sort xs))\n (decreases (FStar.List.Tot.Base.length xs))\n = let open FStar.Algebra.CommMonoid.Equiv in\n match xs with\n | [] -> EQ?.reflexivity eq (xsdenote eq m am [])\n | pivot::q ->\n let sort0 : permute = List.Tot.sortWith #int (List.Tot.compare_of_bool (<)) in\n let sort_eq (l: list atom) : Lemma\n (sort l == sort0 l)\n [SMTPat (sort l)]\n = sortWith_ext (my_compare_of_bool (<)) (List.Tot.compare_of_bool (<)) l\n in\n let open FStar.List.Tot.Base in\n let f:int -> int -> int = compare_of_bool (<) in\n let hi, lo = partition (bool_of_compare f pivot) q in\n flatten_correct_aux eq m am (sort lo) (pivot::sort hi);\n assert (xsdenote eq m am (sort xs) `EQ?.eq eq`\n CM?.mult m (xsdenote eq m am (sort lo))\n (xsdenote eq m am (pivot::sort hi)));\n\n lemma_xsdenote_aux eq m am pivot (sort hi);\n\n EQ?.reflexivity eq (xsdenote eq m am (sort lo));\n CM?.congruence m\n (xsdenote eq m am (sort lo))\n (xsdenote eq m am (pivot::sort hi))\n (xsdenote eq m am (sort lo))\n (select pivot am `CM?.mult m` xsdenote eq m am (sort hi));\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (xsdenote eq m am (sort lo) `CM?.mult m` xsdenote eq m am (pivot::sort hi))\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi)));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi))));\n\n CM?.commutativity m\n (xsdenote eq m am (sort lo))\n (select pivot am `CM?.mult m` xsdenote eq m am (sort hi));\n CM?.associativity m\n (select pivot am)\n (xsdenote eq m am (sort hi))\n (xsdenote eq m am (sort lo));\n EQ?.transitivity eq\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi)))\n ((select pivot am `CM?.mult m` xsdenote eq m am (sort hi)) `CM?.mult m` xsdenote eq m am (sort lo))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo)));\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi)))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo)));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo))));\n\n\n partition_length (bool_of_compare f pivot) q;\n sort_correct_aux eq m am hi;\n sort_correct_aux eq m am lo;\n EQ?.symmetry eq (xsdenote eq m am lo) (xsdenote eq m am (sort lo));\n EQ?.symmetry eq (xsdenote eq m am hi) (xsdenote eq m am (sort hi));\n CM?.congruence m\n (xsdenote eq m am (sort hi))\n (xsdenote eq m am (sort lo))\n (xsdenote eq m am hi)\n (xsdenote eq m am lo);\n assert (EQ?.eq eq\n (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo))\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo));\n\n EQ?.reflexivity eq (select pivot am);\n CM?.congruence m\n (select pivot am)\n (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo))\n (select pivot am)\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo);\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo)))\n (select pivot am `CM?.mult m` (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)));\n\n partition_equiv eq m am pivot q;\n CM?.congruence m\n (select pivot am)\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)\n (select pivot am)\n (xsdenote eq m am q);\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo))\n (select pivot am `CM?.mult m` (xsdenote eq m am q));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am q)));\n\n lemma_xsdenote_aux eq m am pivot q;\n EQ?.symmetry eq\n (xsdenote eq m am (pivot::q))\n (select pivot am `CM?.mult m` (xsdenote eq m am q));\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am q))\n (xsdenote eq m am xs);\n EQ?.symmetry eq (xsdenote eq m am (sort xs)) (xsdenote eq m am xs)", "val sort_correct_aux (#a: Type) (eq: equiv a) (m: cm a eq) (am: amap a) (xs: list atom)\n : Lemma (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (sort xs)))\nlet sort_correct_aux (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a) (xs:list atom)\n : Lemma (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (sort xs)) =\n permute_via_swaps_correct sort (fun #a am -> sort_via_swaps am) eq m am xs", "val lemma_swap_permutes_aux: #a:eqtype -> s:seq a -> i:nat{i j:nat{i <= j && j x:a -> Lemma\n (requires True)\n (ensures (count x s = count x (swap s i j)))\nlet lemma_swap_permutes_aux #_ s i j x =\n if j=i\n then cut (equal (swap s i j) s)\n else begin\n let s5 = split_5 s i j in\n let frag_lo, frag_i, frag_mid, frag_j, frag_hi =\n index s5 0, index s5 1, index s5 2, index s5 3, index s5 4 in\n lemma_append_count_aux x frag_lo (append frag_i (append frag_mid (append frag_j frag_hi)));\n lemma_append_count_aux x frag_i (append frag_mid (append frag_j frag_hi));\n lemma_append_count_aux x frag_mid (append frag_j frag_hi);\n lemma_append_count_aux x frag_j frag_hi;\n\n let s' = swap s i j in\n let s5' = split_5 s' i j in\n let frag_lo', frag_j', frag_mid', frag_i', frag_hi' =\n index s5' 0, index s5' 1, index s5' 2, index s5' 3, index s5' 4 in\n\n lemma_swap_permutes_aux_frag_eq s i j 0 i;\n lemma_swap_permutes_aux_frag_eq s i j (i + 1) j;\n lemma_swap_permutes_aux_frag_eq s i j (j + 1) (length s);\n\n lemma_append_count_aux x frag_lo (append frag_j (append frag_mid (append frag_i frag_hi)));\n lemma_append_count_aux x frag_j (append frag_mid (append frag_i frag_hi));\n lemma_append_count_aux x frag_mid (append frag_i frag_hi);\n lemma_append_count_aux x frag_i frag_hi\n end", "val lift_swaps_cons (#a: eqtype) (h: a) (xs: list a) (ss: swaps_for xs)\n : Pure (swaps_for (h :: xs))\n (requires True)\n (ensures (fun ss' -> apply_swaps (h :: xs) ss' == h :: (apply_swaps xs ss)))\n (decreases ss)\nlet rec lift_swaps_cons (#a:eqtype) (h:a) (xs:list a) (ss:swaps_for xs) : Pure (swaps_for (h::xs))\n (requires True)\n (ensures (fun ss' ->\n apply_swaps (h::xs) ss' == h::(apply_swaps xs ss)\n ))\n (decreases ss)\n =\n match ss with\n | [] -> []\n | s::st ->\n (\n lift_swap_cons 0 h xs s;\n (s + 1)::(lift_swaps_cons h (apply_swap xs s) st)\n )", "val sort_via_swaps (#a: Type) (am: amap a) (xs: list atom)\n : Lemma (exists ss. sort xs == apply_swaps xs ss)\nlet sort_via_swaps (#a:Type) (am : amap a) (xs:list atom)\n : Lemma (exists ss. sort xs == apply_swaps xs ss)\n =\n List.Tot.Properties.sortWith_permutation #nat (compare_of_bool (<)) xs;\n let ss = equal_counts_implies_swaps #nat xs (sort xs) in\n ()", "val flatten_correct_aux (#a: Type) (eq: equiv a) (m: cm a eq) (am: amap a) (xs1 xs2: list atom)\n : Lemma\n (EQ?.eq eq\n (xsdenote eq m am (xs1 @ xs2))\n (CM?.mult m (xsdenote eq m am xs1) (xsdenote eq m am xs2)))\nlet rec flatten_correct_aux (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a) (xs1 xs2:list atom)\n : Lemma (xsdenote eq m am (xs1 @ xs2) `EQ?.eq eq` CM?.mult m (xsdenote eq m am xs1)\n (xsdenote eq m am xs2)) =\n match xs1 with\n | [] ->\n CM?.identity m (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.unit m) (xsdenote eq m am xs2)) (xsdenote eq m am xs2)\n | [x] -> (\n if (Nil? xs2)\n then (right_identity eq m (select x am);\n EQ?.symmetry eq (CM?.mult m (select x am) (CM?.unit m)) (select x am))\n else EQ?.reflexivity eq (CM?.mult m (xsdenote eq m am [x]) (xsdenote eq m am xs2)))\n | x::xs1' ->\n flatten_correct_aux eq m am xs1' xs2;\n EQ?.reflexivity eq (select x am);\n CM?.congruence m (select x am) (xsdenote eq m am (xs1' @ xs2))\n (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2));\n CM?.associativity m (select x am) (xsdenote eq m am xs1') (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)));\n EQ?.transitivity eq (CM?.mult m (select x am) (xsdenote eq m am (xs1' @ xs2)))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)))\n (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))", "val sort_via_swaps (#a: Type) (am: amap a) (xs: list atom)\n : Lemma (exists (ss: swaps_for xs). sort xs == apply_swaps xs ss)\nlet sort_via_swaps (#a:Type) (am:amap a) (xs:list atom)\n : Lemma (exists (ss:swaps_for xs). sort xs == apply_swaps xs ss) \n = List.Tot.Properties.sortWith_permutation #int (compare_of_bool (<)) xs;\n let ss = equal_counts_implies_swaps xs (sort xs) in\n ()", "val flatten_correct_aux (#a: Type) (m: cm a) (am: amap a) (xs1 xs2: list atom)\n : Lemma (xsdenote m am (xs1 @ xs2) == CM?.mult m (xsdenote m am xs1) (xsdenote m am xs2))\nlet rec flatten_correct_aux (#a:Type) (m:cm a) (am:amap a) (xs1 xs2:list atom) :\n Lemma (xsdenote m am (xs1 @ xs2) == CM?.mult m (xsdenote m am xs1)\n (xsdenote m am xs2)) =\n match xs1 with\n | [] -> CM?.identity m (xsdenote m am xs2)\n | [x] -> if (Nil? xs2) then right_identity m (select x am)\n | x::xs1' -> (CM?.associativity m (select x am)\n (xsdenote m am xs1') (xsdenote m am xs2);\n flatten_correct_aux m am xs1' xs2)", "val lemma_swap_right (a b: poly) (n: nat)\n : Lemma (requires n == 64 /\\ degree a < n + n /\\ degree b < n + n)\n (ensures swap (swap a n +. b) n == a +. swap b n)\nlet lemma_swap_right (a b:poly) (n:nat) : Lemma\n (requires n == 64 /\\ degree a < n + n /\\ degree b < n + n)\n (ensures swap (swap a n +. b) n == a +. swap b n)\n =\n lemma_bitwise_all ();\n lemma_equal (swap (swap a n +. b) n) (a +. swap b n)", "val ics_aux_ok: #a:eqtype -> r:cr a -> vm:vmap a -> x:a -> s:canonical_sum a ->\n Lemma (ensures ics_aux r vm x s == r.cm_add.mult x (interp_cs r vm s))\n (decreases s)\nlet rec ics_aux_ok #a r vm x s =\n match s with\n | Nil_monom -> ()\n | Cons_varlist l t ->\n ics_aux_ok r vm (interp_vl r vm l) t\n | Cons_monom c l t ->\n ics_aux_ok r vm (interp_m r vm c l) t", "val flatten_correct_aux\n (#a: Type)\n (eq: CE.equiv a)\n (m: CE.cm a eq)\n (am: amap a)\n (xs1 xs2: list atom)\n : Lemma\n (CE.EQ?.eq eq\n (xsdenote eq m am (xs1 `my_append` xs2))\n (CE.CM?.mult m (xsdenote eq m am xs1) (xsdenote eq m am xs2)))\nlet rec flatten_correct_aux (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (xs1 xs2:list atom)\n : Lemma (xsdenote eq m am (xs1 `my_append` xs2) `CE.EQ?.eq eq` CE.CM?.mult m (xsdenote eq m am xs1)\n (xsdenote eq m am xs2)) =\n let open FStar.Algebra.CommMonoid.Equiv in\n match xs1 with\n | [] ->\n CM?.identity m (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.unit m) (xsdenote eq m am xs2)) (xsdenote eq m am xs2)\n | [x] -> (\n if (Nil? xs2)\n then (right_identity eq m (select x am);\n EQ?.symmetry eq (CM?.mult m (select x am) (CM?.unit m)) (select x am))\n else EQ?.reflexivity eq (CM?.mult m (xsdenote eq m am [x]) (xsdenote eq m am xs2)))\n | x::xs1' ->\n flatten_correct_aux eq m am xs1' xs2;\n EQ?.reflexivity eq (select x am);\n CM?.congruence m (select x am) (xsdenote eq m am (xs1' `my_append` xs2))\n (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2));\n CM?.associativity m (select x am) (xsdenote eq m am xs1') (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)));\n EQ?.transitivity eq (CM?.mult m (select x am) (xsdenote eq m am (xs1' `my_append` xs2)))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)))\n (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))", "val lemma_swap_permutes (#a:eqtype) (s:seq a) (i:nat{i count x s = count x (swap s i j))\n (lemma_swap_permutes_aux s i j)", "val app_assoc_reverse (#a: Type) (l m n: list a)\n : Lemma (requires True) (ensures ((l @ m) @ n == l @ m @ n)) [SMTPat ((l @ m) @ n)]\nlet rec app_assoc_reverse (#a:Type) (l : list a) (m : list a) (n : list a) :\n Lemma (requires True) (ensures ((l @ m) @ n == l @ m @ n)) [SMTPat ((l @ m) @ n)] =\n match l with\n | [] -> ()\n | _::l' -> app_assoc_reverse l' m n", "val csm_aux_ok: #a:eqtype -> r:cr a -> vm:vmap a\n -> c1:a -> l1:varlist -> t1:canonical_sum a -> s2:canonical_sum a ->\n Lemma\n (ensures\n interp_cs r vm (csm_aux r c1 l1 t1 s2) ==\n r.cm_add.mult (interp_cs r vm (Cons_monom c1 l1 t1)) (interp_cs r vm s2))\n (decreases %[t1; s2; 1])\nlet rec canonical_sum_merge_ok #a r vm s1 s2 =\n let aone = r.cm_mult.unit in\n let aplus = r.cm_add.mult in\n let amult = r.cm_mult.mult in\n match s1 with\n | Cons_monom c1 l1 t1 -> csm_aux_ok #a r vm c1 l1 t1 s2\n | Cons_varlist l1 t1 ->\n calc (==) {\n interp_cs r vm (canonical_sum_merge r s1 s2);\n == { }\n interp_cs r vm (csm_aux r aone l1 t1 s2);\n == { csm_aux_ok #a r vm aone l1 t1 s2 }\n aplus (interp_cs r vm (Cons_monom aone l1 t1))\n (interp_cs r vm s2);\n == { ics_aux_ok r vm (interp_vl r vm l1) t1 }\n aplus (interp_cs r vm (Cons_varlist l1 t1))\n (interp_cs r vm s2);\n }\n | Nil_monom -> ()\nand csm_aux_ok #a r vm c1 l1 t1 s2 =\n let aplus = r.cm_add.mult in\n let aone = r.cm_mult.unit in\n let amult = r.cm_mult.mult in\n match s2 with\n | Nil_monom -> ()\n | Cons_monom c2 l2 t2 ->\n let s1 = Cons_monom c1 l1 t1 in\n if l1 = l2 then\n begin\n calc (==) {\n interp_cs r vm (csm_aux r c1 l1 t1 s2);\n == { }\n ics_aux r vm (interp_m r vm (aplus c1 c2) l1)\n (canonical_sum_merge r t1 t2);\n == { ics_aux_ok r vm (interp_m r vm (aplus c1 c2) l1)\n (canonical_sum_merge r t1 t2) }\n aplus (interp_m r vm (aplus c1 c2) l1)\n (interp_cs r vm (canonical_sum_merge r t1 t2));\n == { interp_m_ok r vm (aplus c1 c2) l1 }\n aplus (amult (aplus c1 c2) (interp_vl r vm l1))\n (interp_cs r vm (canonical_sum_merge r t1 t2));\n == { canonical_sum_merge_ok r vm t1 t2 }\n aplus (amult (aplus c1 c2) (interp_vl r vm l1))\n (aplus (interp_cs r vm t1) (interp_cs r vm t2));\n == { distribute_right r c1 c2 (interp_vl r vm l1) }\n aplus (aplus (amult c1 (interp_vl r vm l1))\n (amult c2 (interp_vl r vm l2)))\n (aplus (interp_cs r vm t1)\n (interp_cs r vm t2));\n == { aplus_assoc_4 r\n (amult c1 (interp_vl r vm l1))\n (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t1)\n (interp_cs r vm t2) }\n aplus (aplus (amult c1 (interp_vl r vm l1)) (interp_cs r vm t1))\n (aplus (amult c2 (interp_vl r vm l2)) (interp_cs r vm t2));\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s1)\n (aplus (amult c2 (interp_vl r vm l2)) (interp_cs r vm t2));\n == { ics_aux_ok r vm (amult c2 (interp_vl r vm l2)) t2;\n interp_m_ok r vm c2 l2 }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end\n else if varlist_lt l1 l2 then\n begin\n calc (==) {\n interp_cs r vm (canonical_sum_merge r s1 s2);\n == { }\n ics_aux r vm (interp_m r vm c1 l1)\n (canonical_sum_merge r t1 s2);\n == { ics_aux_ok r vm (interp_m r vm c1 l1)\n (canonical_sum_merge r t1 s2) }\n aplus (interp_m r vm c1 l1)\n (interp_cs r vm (canonical_sum_merge r t1 s2));\n == { interp_m_ok r vm c1 l1 }\n aplus (amult c1 (interp_vl r vm l1))\n (interp_cs r vm (canonical_sum_merge r t1 s2));\n == { canonical_sum_merge_ok r vm t1 s2 }\n aplus (amult c1 (interp_vl r vm l1))\n (aplus (interp_cs r vm t1) (interp_cs r vm s2));\n == { r.cm_add.associativity\n (amult c1 (interp_vl r vm l1))\n (interp_cs r vm t1)\n (interp_cs r vm s2)\n }\n aplus (aplus (amult c1 (interp_vl r vm l1))\n (interp_cs r vm t1))\n (interp_cs r vm s2);\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end\n else\n begin\n calc (==) {\n interp_cs r vm (csm_aux r c1 l1 t1 s2);\n == { }\n ics_aux r vm (interp_m r vm c2 l2)\n (csm_aux r c1 l1 t1 t2);\n == { ics_aux_ok r vm (interp_m r vm c2 l2)\n (csm_aux r c1 l1 t1 t2) }\n aplus (interp_m r vm c2 l2)\n (interp_cs r vm (csm_aux r c1 l1 t1 t2));\n == { interp_m_ok r vm c2 l2 }\n aplus (amult c2 (interp_vl r vm l2))\n (interp_cs r vm (csm_aux r c1 l1 t1 t2));\n == { csm_aux_ok r vm c1 l1 t1 t2 }\n aplus (amult c2 (interp_vl r vm l2))\n (aplus (interp_cs r vm s1) (interp_cs r vm t2));\n == { r.cm_add.commutativity (interp_cs r vm s1) (interp_cs r vm t2) }\n aplus (amult c2 (interp_vl r vm l2))\n (aplus (interp_cs r vm t2) (interp_cs r vm s1));\n == { r.cm_add.associativity\n (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t2)\n (interp_cs r vm s1)\n }\n aplus (aplus (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t2))\n (interp_cs r vm s1);\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s2) (interp_cs r vm s1);\n == { r.cm_add.commutativity (interp_cs r vm s1) (interp_cs r vm s2) }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end\n | Cons_varlist l2 t2 -> // Same as Cons_monom with c2 = aone\n let c2 = aone in\n let s1 = Cons_monom c1 l1 t1 in\n if l1 = l2 then\n begin\n calc (==) {\n interp_cs r vm (csm_aux r c1 l1 t1 s2);\n == { }\n ics_aux r vm (interp_m r vm (aplus c1 c2) l1)\n (canonical_sum_merge r t1 t2);\n == { ics_aux_ok r vm (interp_m r vm (aplus c1 c2) l1)\n (canonical_sum_merge r t1 t2) }\n aplus (interp_m r vm (aplus c1 c2) l1)\n (interp_cs r vm (canonical_sum_merge r t1 t2));\n == { interp_m_ok r vm (aplus c1 c2) l1 }\n aplus (amult (aplus c1 c2) (interp_vl r vm l1))\n (interp_cs r vm (canonical_sum_merge r t1 t2));\n == { canonical_sum_merge_ok r vm t1 t2 }\n aplus (amult (aplus c1 c2) (interp_vl r vm l1))\n (aplus (interp_cs r vm t1) (interp_cs r vm t2));\n == { distribute_right r c1 c2 (interp_vl r vm l1) }\n aplus (aplus (amult c1 (interp_vl r vm l1))\n (amult c2 (interp_vl r vm l2)))\n (aplus (interp_cs r vm t1)\n (interp_cs r vm t2));\n == { aplus_assoc_4 r\n (amult c1 (interp_vl r vm l1))\n (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t1)\n (interp_cs r vm t2) }\n aplus (aplus (amult c1 (interp_vl r vm l1)) (interp_cs r vm t1))\n (aplus (amult c2 (interp_vl r vm l2)) (interp_cs r vm t2));\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s1)\n (aplus (amult c2 (interp_vl r vm l2)) (interp_cs r vm t2));\n == { ics_aux_ok r vm (amult c2 (interp_vl r vm l2)) t2;\n interp_m_ok r vm c2 l2 }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end\n else if varlist_lt l1 l2 then\n begin\n calc (==) {\n interp_cs r vm (canonical_sum_merge r s1 s2);\n == { }\n ics_aux r vm (interp_m r vm c1 l1)\n (canonical_sum_merge r t1 s2);\n == { ics_aux_ok r vm (interp_m r vm c1 l1)\n (canonical_sum_merge r t1 s2) }\n aplus (interp_m r vm c1 l1)\n (interp_cs r vm (canonical_sum_merge r t1 s2));\n == { interp_m_ok r vm c1 l1 }\n aplus (amult c1 (interp_vl r vm l1))\n (interp_cs r vm (canonical_sum_merge r t1 s2));\n == { canonical_sum_merge_ok r vm t1 s2 }\n aplus (amult c1 (interp_vl r vm l1))\n (aplus (interp_cs r vm t1) (interp_cs r vm s2));\n == { r.cm_add.associativity\n (amult c1 (interp_vl r vm l1))\n (interp_cs r vm t1)\n (interp_cs r vm s2)\n }\n aplus (aplus (amult c1 (interp_vl r vm l1))\n (interp_cs r vm t1))\n (interp_cs r vm s2);\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end\n else\n begin\n calc (==) {\n interp_cs r vm (csm_aux r c1 l1 t1 s2);\n == { }\n ics_aux r vm (interp_m r vm c2 l2)\n (csm_aux r c1 l1 t1 t2);\n == { ics_aux_ok r vm (interp_m r vm c2 l2)\n (csm_aux r c1 l1 t1 t2) }\n aplus (interp_m r vm c2 l2)\n (interp_cs r vm (csm_aux r c1 l1 t1 t2));\n == { interp_m_ok r vm c2 l2 }\n aplus (amult c2 (interp_vl r vm l2))\n (interp_cs r vm (csm_aux r c1 l1 t1 t2));\n == { csm_aux_ok r vm c1 l1 t1 t2 }\n aplus (amult c2 (interp_vl r vm l2))\n (aplus (interp_cs r vm s1) (interp_cs r vm t2));\n == { r.cm_add.commutativity (interp_cs r vm s1) (interp_cs r vm t2) }\n aplus (amult c2 (interp_vl r vm l2))\n (aplus (interp_cs r vm t2) (interp_cs r vm s1));\n == { r.cm_add.associativity\n (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t2)\n (interp_cs r vm s1)\n }\n aplus (aplus (amult c2 (interp_vl r vm l2))\n (interp_cs r vm t2))\n (interp_cs r vm s1);\n == { ics_aux_ok r vm (amult c1 (interp_vl r vm l1)) t1;\n interp_m_ok r vm c1 l1 }\n aplus (interp_cs r vm s2) (interp_cs r vm s1);\n == { r.cm_add.commutativity (interp_cs r vm s1) (interp_cs r vm s2) }\n aplus (interp_cs r vm s1) (interp_cs r vm s2);\n }\n end", "val lemma_xsdenote_aux\n (#a: Type)\n (eq: CE.equiv a)\n (m: CE.cm a eq)\n (am: amap a)\n (hd: atom)\n (tl: list atom)\n : Lemma\n (CE.EQ?.eq eq (xsdenote eq m am (hd :: tl)) (CE.CM?.mult m (select hd am) (xsdenote eq m am tl))\n )\nlet lemma_xsdenote_aux (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (hd:atom) (tl:list atom)\n : Lemma (xsdenote eq m am (hd::tl) `CE.EQ?.eq eq`\n (CE.CM?.mult m (select hd am) (xsdenote eq m am tl)))\n = let open FStar.Algebra.CommMonoid.Equiv in\n match tl with\n | [] ->\n assert (xsdenote eq m am (hd::tl) == select hd am);\n CM?.identity m (select hd am);\n EQ?.symmetry eq (CM?.unit m `CM?.mult m` select hd am) (select hd am);\n CM?.commutativity m (CM?.unit m) (select hd am);\n EQ?.transitivity eq\n (xsdenote eq m am (hd::tl))\n (CM?.unit m `CM?.mult m` select hd am)\n (CM?.mult m (select hd am) (xsdenote eq m am tl))\n | _ -> EQ?.reflexivity eq (xsdenote eq m am (hd::tl))", "val assoc_flip_elim (#a #b: eqtype) (l: list (a * b)) (y: b) (x: a)\n : Lemma\n (requires\n (L.noRepeats (list_map fst l) /\\ L.noRepeats (list_map snd l) /\\\n L.assoc y (list_map flip l) == Some x)) (ensures (L.assoc x l == Some y)) (decreases l)\nlet rec assoc_flip_elim\n (#a #b: eqtype)\n (l: list (a * b))\n (y: b)\n (x: a)\n: Lemma\n (requires (\n L.noRepeats (list_map fst l) /\\\n L.noRepeats (list_map snd l) /\\\n L.assoc y (list_map flip l) == Some x\n ))\n (ensures (\n L.assoc x l == Some y\n ))\n (decreases l)\n= let ((x', y') :: l') = l in\n if y' = y\n then ()\n else begin\n if x' = x\n then begin\n assert (list_mem x' (list_map fst l') == false);\n assoc_mem_snd (list_map flip l') y x;\n map_snd_flip l';\n assert False\n end\n else\n assoc_flip_elim l' y x\n end", "val swap_to_front (#a: eqtype) (h: a) (xs: list a)\n : Pure (swaps_for xs)\n (requires count h xs >= 1)\n (ensures\n (fun ss ->\n let ys = apply_swaps xs ss in\n equal_counts xs ys /\\ Cons? ys /\\ hd ys == h))\nlet rec swap_to_front (#a:eqtype) (h:a) (xs:list a) : Pure (swaps_for xs)\n (requires count h xs >= 1)\n (ensures (fun ss ->\n let ys = apply_swaps xs ss in\n equal_counts xs ys /\\\n Cons? ys /\\\n hd ys == h\n ))\n =\n match xs with\n | [] -> []\n | x::xt ->\n (\n if x = h then []\n else\n (\n let ss = swap_to_front h xt in // ss turns xt into h::xt'\n let ss' = lift_swaps_cons x xt ss in // ss' turns x::xt into x::h::xt'\n let s:swap_for xs = 0 in\n append_swaps xs ss' [s];\n ss' @ [s]\n )\n )", "val lemma_init_aux_len' (#a: Type) (n: nat) (k: nat{k < n}) (contents: (i: nat{i < n} -> Tot a))\n : Lemma (requires True) (ensures (length (init_aux n k contents) = n - k)) (decreases (n - k))\nlet rec lemma_init_aux_len' (#a:Type) (n:nat) (k:nat{k < n}) (contents:(i:nat{ i < n } -> Tot a))\n : Lemma (requires True)\n (ensures (length (init_aux n k contents) = n - k))\n (decreases (n-k))\n= if k + 1 = n then () else lemma_init_aux_len' #a n (k+1) contents", "val terminal_case_aux\n (#c #eq: _)\n (#p: pos{p = 1})\n (#n: _)\n (cm: CE.cm c eq)\n (generator: matrix_generator c p n)\n (m: pos{m <= p})\n : Lemma\n (ensures\n (SP.foldm_snoc cm (SB.slice (seq_of_matrix (init generator)) 0 (m * n)))\n `eq.eq`\n (SP.foldm_snoc cm (SB.init m (fun (i: under m) -> SP.foldm_snoc cm (SB.init n (generator i))))\n ))\nlet terminal_case_aux #c #eq (#p:pos{p=1}) #n (cm:CE.cm c eq) (generator: matrix_generator c p n) (m: pos{m<=p}) : Lemma \n (ensures SP.foldm_snoc cm (SB.slice (seq_of_matrix (init generator)) 0 (m*n)) `eq.eq`\n SP.foldm_snoc cm (SB.init m (fun (i:under m) -> SP.foldm_snoc cm (SB.init n (generator i)))))\n = one_row_matrix_fold_aux cm generator", "val tsubst_commute_aux : y:nat -> x:nat{x >= y} -> s1:typ -> s2:typ -> v:var ->\n Lemma (requires True)\n (ensures ((tsub_comp (tsub_beta_gen x s1) (tsub_beta_gen y s2)) v =\n (tsub_comp (tsub_beta_gen y (tsubst_beta_gen x s1 s2))\n (tsub_beta_gen (x+1) (tshift_up_above y s1))) v))\nlet tsubst_commute_aux y x s1 s2 v =\n if v = x+1 then shift_above_and_subst s1 y (tsubst_beta_gen x s1 s2)", "val math_aux_2 (m n: pos) (j: under n) : Lemma (get_j m n (j + (m - 1) * n) == j)\nlet math_aux_2 (m n: pos) (j: under n) : Lemma (get_j m n (j+(m-1)*n) == j) \n = \n Math.Lemmas.modulo_addition_lemma j n (m-1);\n Math.Lemmas.small_mod j n", "val matrix_fold_aux\n (#c #eq: _)\n (#gen_m #gen_n: pos)\n (cm: CE.cm c eq)\n (m: ifrom_ito 1 gen_m)\n (n: ifrom_ito 1 gen_n)\n (generator: matrix_generator c gen_m gen_n)\n : Lemma\n (ensures\n (SP.foldm_snoc cm (matrix_seq #c #m #n generator))\n `eq.eq`\n (CF.fold cm 0 (m - 1) (fun (i: under m) -> CF.fold cm 0 (n - 1) (generator i))))\n (decreases m)\nlet rec matrix_fold_aux #c #eq // lemma needed for precise generator domain control\n (#gen_m #gen_n: pos) // full generator domain\n (cm: CE.cm c eq) \n (m: ifrom_ito 1 gen_m) (n: ifrom_ito 1 gen_n) //subdomain\n (generator: matrix_generator c gen_m gen_n)\n : Lemma (ensures SP.foldm_snoc cm (matrix_seq #c #m #n generator) `eq.eq` \n CF.fold cm 0 (m-1) (fun (i: under m) -> CF.fold cm 0 (n-1) (generator i)))\n (decreases m) = \n Classical.forall_intro_2 (ijth_lemma (init generator));\n let slice = SB.slice #c in\n let foldm_snoc = SP.foldm_snoc #c #eq in\n let lemma_eq_elim = SB.lemma_eq_elim #c in\n if m = 1 then begin\n matrix_fold_equals_fold_of_seq cm (init generator);\n matrix_last_line_equals_gen_fold #c #eq #m #n cm generator; \n CF.fold_singleton_lemma cm 0 (fun (i:under m) -> CF.fold cm 0 (n-1) (generator i));\n assert (CF.fold cm 0 (m-1) (fun (i: under m) -> CF.fold cm 0 (n-1) (generator i)) \n == CF.fold cm 0 (n-1) (generator 0)) \n end else begin \n Classical.forall_intro_3 (Classical.move_requires_3 eq.transitivity); \n matrix_fold_aux cm (m-1) n generator; \n let outer_func (i: under m) = CF.fold cm 0 (n-1) (generator i) in\n let outer_func_on_subdomain (i: under (m-1)) = CF.fold cm 0 (n-1) (generator i) in\n CF.fold_equality cm 0 (m-2) outer_func_on_subdomain outer_func;\n CF.fold_snoc_decomposition cm 0 (m-1) outer_func; \n matrix_fold_snoc_lemma #c #eq #m #n cm generator;\n matrix_last_line_equals_gen_fold #c #eq #m #n cm generator;\n cm.congruence (foldm_snoc cm (matrix_seq #c #(m-1) #n generator))\n (foldm_snoc cm (slice (matrix_seq #c #m #n generator) ((m-1)*n) (m*n)))\n (CF.fold cm 0 (m-2) outer_func)\n (CF.fold cm 0 (n-1) (generator (m-1))) \n end", "val lemma_reduce_prefix_aux\n (#a #b: Type)\n (b0: b)\n (f: (a -> b -> b))\n (s: seq a)\n (i: nat{i <= length s})\n : Lemma (requires True)\n (ensures (reduce b0 f s == reduce (reduce b0 f (prefix s i)) f (suffix s (length s - i))))\n (decreases (length s))\nlet rec lemma_reduce_prefix_aux (#a:Type) (#b:Type)\n (b0: b) (f: a -> b -> b) (s: seq a)\n (i:nat{i <= length s}):\n Lemma (requires True)\n (ensures (reduce b0 f s == reduce (reduce b0 f (prefix s i)) f (suffix s (length s - i))))\n (decreases (length s)) =\n let n = length s in\n if n = 0 then ()\n else if i = n then ()\n else lemma_reduce_prefix_aux b0 f (prefix s (n - 1)) i", "val from_vec_aux: #n:nat -> a:bv_t n -> s1:nat{s1 < n} -> s2:nat{s2 < s1} ->\n Lemma (requires True)\n (ensures (from_vec #s2 (slice a 0 s2)) * pow2 (n - s2) + (from_vec #(s1 - s2) (slice a s2 s1)) * pow2 (n - s1) + (from_vec #(n - s1) (slice a s1 n)) = ((from_vec #s2 (slice a 0 s2)) * pow2 (s1 - s2) + (from_vec #(s1 - s2) (slice a s2 s1))) * pow2 (n - s1) + (from_vec #(n - s1) (slice a s1 n)))\nlet from_vec_aux #n a s1 s2 =\n paren_mul_left (from_vec #s2 (slice a 0 s2)) (pow2 (s1 - s2)) (pow2 (n - s1));\n paren_mul_right (from_vec #s2 (slice a 0 s2)) (pow2 (s1 - s2)) (pow2 (n - s1));\n pow2_plus (s1 - s2) (n - s1)", "val lemma_init_aux_len (#a:Type) (n:nat) (k:nat{k < n}) (contents:(i:nat{ i < n } -> Tot a))\n : Lemma (requires True)\n (ensures (length (init_aux n k contents) = n - k))\n [SMTPat (length (init_aux n k contents))]\nlet lemma_init_aux_len = lemma_init_aux_len'", "val terminal_case_two_aux\n (#c #eq: _)\n (#p: pos)\n (#n: _)\n (cm: CE.cm c eq)\n (generator: matrix_generator c p n)\n (m: pos{m = 1})\n : Lemma\n (ensures\n (SP.foldm_snoc cm (SB.slice (seq_of_matrix (init generator)) 0 (m * n)))\n `eq.eq`\n (SP.foldm_snoc cm (SB.init m (fun (i: under m) -> SP.foldm_snoc cm (SB.init n (generator i))))\n ))\nlet terminal_case_two_aux #c #eq (#p:pos) #n (cm:CE.cm c eq) (generator: matrix_generator c p n) (m: pos{m=1}) : Lemma \n (ensures SP.foldm_snoc cm (SB.slice (seq_of_matrix (init generator)) 0 (m*n)) `eq.eq`\n SP.foldm_snoc cm (SB.init m (fun (i:under m) -> SP.foldm_snoc cm (SB.init n (generator i)))))\n = \n SP.foldm_snoc_singleton cm (SP.foldm_snoc cm (SB.init n (generator 0)));\n assert (SP.foldm_snoc cm (SB.init m (fun (i:under m) -> SP.foldm_snoc cm (SB.init n (generator i)))) `eq.eq`\n SP.foldm_snoc cm (SB.init n (generator 0)));\n let line = SB.init n (generator 0) in\n let slice = SB.slice (matrix_seq generator) 0 n in\n let aux (ij: under n) : Lemma (SB.index slice ij == SB.index line ij) = \n Math.Lemmas.small_div ij n;\n Math.Lemmas.small_mod ij n \n in Classical.forall_intro aux;\n SB.lemma_eq_elim line slice; \n eq.symmetry (SP.foldm_snoc cm (SB.init m (fun (i:under m) -> SP.foldm_snoc cm (SB.init n (generator i)))))\n (SP.foldm_snoc cm line)", "val lemma_other (#a:Type) (m:map16 a) (n1 n2:int) (v:a) : Lemma\n (requires 0 <= n1 /\\ n1 < 16 /\\ 0 <= n2 /\\ n2 < 16 /\\ n1 =!= n2)\n (ensures sel (upd m n1 v) n2 == sel m n2)\n [SMTPat (sel (upd m n1 v) n2)]\nlet lemma_other (#a:Type) (m:map16 a) (n1 n2:int) (v:a) =\n assert_norm (sel (upd m n1 v) n2 == sel16 (upd16 m n1 v) n2);\n assert_norm (sel m n2 == sel16 m n2);\n lemma_other16 m n1 n2 v", "val lemma_aux_0\n (#a: Type)\n (b: buffer a)\n (n: UInt32.t{v n < length b})\n (z: a)\n (h0: mem)\n (tt: Type)\n (bb: buffer tt)\n : Lemma (requires (live h0 b /\\ live h0 bb /\\ disjoint b bb))\n (ensures\n (live h0 b /\\ live h0 bb /\\\n (let h1 = HS.upd h0 b.content (Seq.upd (sel h0 b) (idx b + v n) z) in\n as_seq h0 bb == as_seq h1 bb)))\nlet lemma_aux_0\n (#a:Type) (b:buffer a) (n:UInt32.t{v n < length b}) (z:a) (h0:mem) (tt:Type) (bb:buffer tt)\n :Lemma (requires (live h0 b /\\ live h0 bb /\\ disjoint b bb))\n (ensures (live h0 b /\\ live h0 bb /\\\n\t (let h1 = HS.upd h0 b.content (Seq.upd (sel h0 b) (idx b + v n) z) in\n\t\t as_seq h0 bb == as_seq h1 bb)))\n = Heap.lemma_distinct_addrs_distinct_preorders ();\n Heap.lemma_distinct_addrs_distinct_mm ()", "val lemma_init_ghost_aux_len'\n (#a: Type)\n (n: nat)\n (k: nat{k < n})\n (contents: (i: nat{i < n} -> GTot a))\n : Lemma (requires True)\n (ensures (length (init_aux_ghost n k contents) = n - k))\n (decreases (n - k))\nlet rec lemma_init_ghost_aux_len' (#a:Type) (n:nat) (k:nat{k < n}) (contents:(i:nat{ i < n } -> GTot a))\n : Lemma (requires True)\n (ensures (length (init_aux_ghost n k contents) = n - k))\n (decreases (n-k))\n= if k + 1 = n then () else lemma_init_ghost_aux_len' #a n (k+1) contents", "val lemma_map_index_aux (#a #b: Type) (f: (a -> b)) (s: seq a) (i: seq_index s)\n : Lemma (requires (True)) (ensures (f (index s i) == index (map f s) i)) (decreases (length s))\nlet rec lemma_map_index_aux (#a #b: Type) (f:a -> b) (s:seq a) (i:seq_index s):\n Lemma (requires (True))\n (ensures (f (index s i) == index (map f s) i))\n (decreases (length s)) =\n let n = length s in\n if n = 0 then ()\n else if i = n - 1 then ()\n else\n let s' = prefix s (n - 1) in\n let e = index s (n - 1) in\n lemma_map_index_aux f s' i;\n lemma_prefix_index s (n - 1) i;\n lemma_index_app1 (map f s') (create 1 (f e)) i", "val math_aux_3 (m n: pos) (j: under n) : Lemma (get_i m n (j + (m - 1) * n) == (m - 1))\nlet math_aux_3 (m n: pos) (j: under n) : Lemma (get_i m n (j+(m-1)*n) == (m-1)) \n = \n Math.Lemmas.division_addition_lemma j n (m-1);\n Math.Lemmas.small_div j n", "val copy_aux (#a: Type) (s cpy: array a) (ctr: nat)\n : HoareST unit\n (fun h ->\n addr_of s =!= addr_of cpy /\\ Seq.length (sel h cpy) == Seq.length (sel h s) /\\\n ctr <= Seq.length (sel h cpy) /\\\n (forall (i: nat). i < ctr ==> Seq.index (sel h s) i == Seq.index (sel h cpy) i))\n (fun h0 _ h1 -> modifies (only cpy) h0 h1 /\\ Seq.equal (sel h1 cpy) (sel h1 s))\nlet rec copy_aux\n (#a:Type) (s:array a) (cpy:array a) (ctr:nat)\n: HoareST unit\n (fun h ->\n addr_of s =!= addr_of cpy /\\\n Seq.length (sel h cpy) == Seq.length (sel h s) /\\\n ctr <= Seq.length (sel h cpy) /\\\n (forall (i:nat). i < ctr ==> Seq.index (sel h s) i == Seq.index (sel h cpy) i))\n (fun h0 _ h1 ->\n modifies (only cpy) h0 h1 /\\\n Seq.equal (sel h1 cpy) (sel h1 s))\n= recall s; recall cpy;\n let diff = length cpy - ctr in\n match diff with\n | 0 -> return ()\n | _ ->\n upd cpy ctr (index s ctr);\n copy_aux s cpy (ctr + 1)", "val copy_aux (#a: Type) (s cpy: array a) (ctr: nat)\n : HoareST unit\n (fun h ->\n addr_of s =!= addr_of cpy /\\ Seq.length (sel h cpy) == Seq.length (sel h s) /\\\n ctr <= Seq.length (sel h cpy) /\\\n (forall (i: nat). i < ctr ==> Seq.index (sel h s) i == Seq.index (sel h cpy) i))\n (fun h0 _ h1 -> modifies (only cpy) h0 h1 /\\ Seq.equal (sel h1 cpy) (sel h1 s))\nlet rec copy_aux\n (#a:Type) (s:array a) (cpy:array a) (ctr:nat)\n: HoareST unit\n (fun h ->\n addr_of s =!= addr_of cpy /\\\n Seq.length (sel h cpy) == Seq.length (sel h s) /\\\n ctr <= Seq.length (sel h cpy) /\\\n (forall (i:nat). i < ctr ==> Seq.index (sel h s) i == Seq.index (sel h cpy) i))\n (fun h0 _ h1 ->\n modifies (only cpy) h0 h1 /\\\n Seq.equal (sel h1 cpy) (sel h1 s))\n= recall s; recall cpy;\n let len = length cpy in\n match len - ctr with\n | 0 -> ()\n | _ ->\n upd cpy ctr (index s ctr);\n copy_aux s cpy (ctr + 1)", "val lemma_attach_correct_aux (#a: Type) (s: seq a) (i: seq_index s)\n : Lemma (requires (True))\n (ensures\n (length (attach_index s) = length s /\\ snd (index (attach_index s) i) == index s i /\\\n fst (index (attach_index s) i) = i))\n (decreases (length s))\nlet rec lemma_attach_correct_aux (#a:Type) (s: seq a) (i: seq_index s):\n Lemma (requires (True))\n (ensures (length (attach_index s) = length s /\\\n snd (index (attach_index s) i) == index s i /\\\n fst (index (attach_index s) i) = i))\n (decreases (length s)) =\n lemma_attach_len s;\n let n = length s in\n if n = 0 then ()\n else if i = n - 1 then ()\n else lemma_attach_correct_aux (prefix s (n - 1)) i", "val lemma_add_incr_mem_aux (#a: eqtype) (#f: cmp a) (s: mset a f) (x: a)\n : Lemma (ensures mem x (add_elem s x) = 1 + mem x s)\nlet rec lemma_add_incr_mem_aux (#a:eqtype) (#f:cmp a) (s:mset a f) (x:a)\n : Lemma (ensures mem x (add_elem s x) = 1 + mem x s) =\n match s with\n | [] -> ()\n | (y,n)::_ -> \n if x = y then ()\n else if f x y then mem_elt_lt_hd x s\n else lemma_add_incr_mem_aux (tl s) x", "val fold_of_subgen_aux\n (#c #eq: _)\n (#m: pos{m > 1})\n (#n: _)\n (cm: CE.cm c eq)\n (gen: matrix_generator c m n)\n (subgen: matrix_generator c (m - 1) n)\n : Lemma (requires subgen == (fun (i: under (m - 1)) (j: under n) -> gen i j))\n (ensures\n forall (i: under (m - 1)).\n SP.foldm_snoc cm (SB.init n (subgen i)) == SP.foldm_snoc cm (SB.init n (gen i)))\nlet fold_of_subgen_aux #c #eq (#m:pos{m>1}) #n (cm: CE.cm c eq) (gen: matrix_generator c m n) (subgen: matrix_generator c (m-1) n) : Lemma\n (requires subgen == (fun (i: under (m-1)) (j: under n) -> gen i j))\n (ensures forall (i: under (m-1)). SP.foldm_snoc cm (SB.init n (subgen i)) ==\n SP.foldm_snoc cm (SB.init n (gen i))) = \n let aux_pat (i: under (m-1)) : Lemma (SP.foldm_snoc cm (SB.init n (subgen i)) \n == SP.foldm_snoc cm (SB.init n (gen i))) = \n SB.lemma_eq_elim (SB.init n (subgen i)) (SB.init n (gen i)) in\n Classical.forall_intro aux_pat", "val map_aux (#a #b: Type) (f: (a -> b)) (s: seq a)\n : Tot (s': seq b {length s' = length s}) (decreases (length s))\nlet rec map_aux (#a #b:Type) (f:a -> b) (s:seq a):\n Tot (s':seq b{length s' = length s})\n (decreases (length s))\n =\n let n = length s in\n if n = 0 then empty\n else\n let ps = prefix s (n - 1) in\n let e = index s (n - 1) in\n append (map_aux f ps) (create 1 (f e))", "val lemma_zip_index_aux\n (#a #b: Type)\n (sa: seq a)\n (sb: seq b {length sa = length sb})\n (i: seq_index sa)\n : Lemma (requires (True))\n (ensures (fst (index (zip sa sb) i) == index sa i /\\ snd (index (zip sa sb) i) == index sb i))\n (decreases (length sa))\nlet rec lemma_zip_index_aux (#a #b: Type) (sa: seq a) (sb: seq b{length sa = length sb}) (i:seq_index sa):\n Lemma (requires (True))\n (ensures (fst (index (zip sa sb) i) == index sa i /\\\n snd (index (zip sa sb) i) == index sb i))\n (decreases (length sa)) =\n let n = length sa in\n if n = 0 then ()\n else if i = n - 1 then ()\n else\n let sa' = prefix sa (n - 1) in\n let sb' = prefix sb (n - 1) in\n lemma_zip_index_aux sa' sb' i", "val lemma_index_upd1' (#a: Type) (s: seq a) (n: nat{n < length s}) (v: a)\n : Lemma (requires True) (ensures (index (upd s n v) n == v)) (decreases (length s))\nlet rec lemma_index_upd1' (#a:Type) (s:seq a) (n:nat{n < length s}) (v:a)\n : Lemma\n (requires True)\n (ensures (index (upd s n v) n == v)) (decreases (length s))\n= if n = 0\n then ()\n else begin\n lemma_index_upd1' #a (tl s) (n - 1) v;\n assert (index (upd (tl s) (n-1) v) (n-1) == v)\n end", "val lemma_swap_permutes_aux_frag_eq: #a:Type -> s:seq a -> i:nat{i j:nat{i <= j && j i':nat -> j':nat{i' <= j' /\\ j'<=length s /\\\n (j < i' //high slice\n \\/ j' <= i //low slice\n \\/ (i < i' /\\ j' <= j)) //mid slice\n }\n -> Lemma (ensures (slice s i' j' == slice (swap s i j) i' j'\n /\\ slice s i (i + 1) == slice (swap s i j) j (j + 1)\n /\\ slice s j (j + 1) == slice (swap s i j) i (i + 1)))\nlet lemma_swap_permutes_aux_frag_eq #a s i j i' j' =\n cut (equal (slice s i' j') (slice (swap s i j) i' j'));\n cut (equal (slice s i (i + 1)) (slice (swap s i j) j (j + 1)));\n cut (equal (slice s j (j + 1)) (slice (swap s i j) i (i + 1)))", "val lemma_index_upd2'\n (#a: Type)\n (s: seq a)\n (n: nat{n < length s})\n (v: a)\n (i: nat{i <> n /\\ i < length s})\n : Lemma (requires True) (ensures (index (upd s n v) i == index s i)) (decreases (length s))\nlet rec lemma_index_upd2' (#a:Type) (s:seq a) (n:nat{n < length s}) (v:a) (i:nat{i<>n /\\ i < length s})\n : Lemma\n (requires True)\n (ensures (index (upd s n v) i == index s i))\n (decreases (length s))\n= match (MkSeq?.l s) with\n | [] -> ()\n | hd::tl ->\n if i = 0 then ()\n else\n if n = 0 then ()\n else (lemma_len_upd (n - 1) v (MkSeq tl); lemma_index_upd2' #a (MkSeq tl) (n - 1) v (i - 1))", "val lemma_shift_shift (a:poly) (m n:int) : Lemma\n (requires m >= 0 \\/ n <= 0)\n (ensures shift a (m + n) == shift (shift a m) n)\nlet lemma_shift_shift a m n =\n lemma_index_all ();\n lemma_shift_define_all ();\n lemma_equal (shift a (m + n)) (shift (shift a m) n);\n ()", "val lemma_aux: #a:Type -> b:buffer a -> n:UInt32.t{v n < length b} -> z:a\n -> h0:mem -> Lemma\n (requires (live h0 b))\n (ensures (live h0 b\n /\\ modifies_1 b h0 (HS.upd h0 b.content (Seq.upd (sel h0 b) (idx b + v n) z)) ))\n [SMTPat (HS.upd h0 b.content (Seq.upd (sel h0 b) (idx b + v n) z))]\nlet lemma_aux #a b n z h0 = lemma_aux_2 b n z h0", "val length_size_aux (#a: eqtype) (#f: cmp a) (s: Seq.seq a)\n : Lemma (ensures Seq.length s == size (seq2mset #a #f s)) (decreases (Seq.length s))\nlet rec length_size_aux (#a:eqtype) (#f:cmp a) (s:Seq.seq a)\n : Lemma\n (ensures Seq.length s == size (seq2mset #a #f s))\n (decreases (Seq.length s))\n = if Seq.length s = 0 then ()\n else\n let ms_tail = seq2mset #a #f (Seq.tail s) in\n add_size ms_tail (Seq.index s 0);\n length_size_aux #a #f (Seq.tail s)", "val lemma_self (#a:Type) (m:map16 a) (n:int) (v:a) : Lemma\n (requires 0 <= n /\\ n < 16)\n (ensures sel (upd m n v) n == v)\n [SMTPat (sel (upd m n v) n)]\nlet lemma_self (#a:Type) (m:map16 a) (n:int) (v:a) =\n assert_norm (sel (upd m n v) n == sel16 (upd16 m n v) n);\n lemma_self16 m n v", "val varlist_merge_ok (#a:eqtype) (r:cr a) (vm:vmap a) (x y:varlist) :\n Lemma\n (ensures\n interp_vl r vm (varlist_merge x y) ==\n r.cm_mult.mult (interp_vl r vm x) (interp_vl r vm y))\n (decreases %[x; y; 0])\nlet rec varlist_merge_ok #a r vm x y =\n let amult = r.cm_mult.mult in\n match x, y with\n | Cons_var v1 t1, Nil_var -> ()\n | Cons_var v1 t1, Cons_var v2 t2 ->\n if v1 < v2\n then\n begin\n varlist_merge_ok r vm t1 y;\n assert (\n interp_vl r vm (varlist_merge x y) ==\n amult (interp_var vm v1) (amult (interp_vl r vm t1) (interp_vl r vm y)));\n r.cm_mult.associativity\n (interp_var vm v1) (interp_vl r vm t1) (interp_vl r vm y)\n end\n else\n vm_aux_ok r vm v1 t1 y\n | Nil_var, _ -> ()\nand vm_aux_ok #a r vm v1 t1 l2 =\n match l2 with\n | Cons_var v2 t2 ->\n if v1 < v2\n then\n begin\n varlist_merge_ok r vm t1 l2;\n r.cm_mult.associativity\n (interp_var vm v1) (interp_vl r vm t1) (interp_vl r vm l2)\n end\n else\n begin\n vm_aux_ok r vm v1 t1 t2;\n calc (==) {\n interp_vl r vm (Cons_var v2 (vm_aux v1 t1 t2));\n == { }\n ivl_aux r vm v2 (vm_aux v1 t1 t2);\n == { }\n r.cm_mult.mult (interp_var vm v2) (interp_vl r vm (vm_aux v1 t1 t2));\n == { }\n r.cm_mult.mult (interp_var vm v2) (r.cm_mult.mult (interp_vl r vm (Cons_var v1 t1)) (interp_vl r vm t2));\n == { r.cm_mult.commutativity\n (interp_vl r vm (Cons_var v1 t1)) (interp_vl r vm t2) }\n r.cm_mult.mult (interp_var vm v2)\n (r.cm_mult.mult (interp_vl r vm t2) (interp_vl r vm (Cons_var v1 t1)) );\n == { r.cm_mult.associativity\n (interp_var vm v2)\n (interp_vl r vm t2) (interp_vl r vm (Cons_var v1 t1)) }\n r.cm_mult.mult\n (r.cm_mult.mult (interp_var vm v2) (interp_vl r vm t2))\n (interp_vl r vm (Cons_var v1 t1));\n == { r.cm_mult.commutativity\n (interp_vl r vm (Cons_var v1 t1)) (interp_vl r vm (Cons_var v2 t2)) }\n r.cm_mult.mult (interp_vl r vm (Cons_var v1 t1)) (interp_vl r vm (Cons_var v2 t2));\n }\n end\n | _ -> ()", "val lemma_swap_splice : #a:Type -> s:seq a -> start:nat -> i:nat{start <= i} -> j:nat{i <= j} -> len:nat{j < len && len <= length s}\n -> Lemma\n (ensures (swap s i j == splice s start (swap s i j) len))\nlet lemma_swap_splice #_ s start i j len = cut (equal (swap s i j) (splice s start (swap s i j) len))", "val lemma_unzip_index_aux (#a #b: Type) (sab: seq (a * b)) (i: seq_index sab)\n : Lemma (requires (True))\n (ensures\n (fst (index sab i) == index (fst (unzip sab)) i /\\\n snd (index sab i) == index (snd (unzip sab)) i))\n (decreases (length sab))\nlet rec lemma_unzip_index_aux (#a #b: Type) (sab: seq (a * b)) (i:seq_index sab):\n Lemma (requires (True))\n (ensures (fst (index sab i) == index (fst (unzip sab)) i /\\\n snd (index sab i) == index (snd (unzip sab)) i))\n (decreases (length sab)) =\n let n = length sab in\n if n = 0 then ()\n else if i = n - 1 then ()\n else\n let sab' = prefix sab (n - 1) in\n lemma_unzip_index_aux sab' i", "val where_aux (n: nat) (x: term) (xs: list term) : Tac (option nat) (decreases xs)\nlet rec where_aux (n:nat) (x:term) (xs:list term) :\n Tac (option nat) (decreases xs) =\n match xs with\n | [] -> None\n | x'::xs' -> if term_eq_old x x' then Some n else where_aux (n+1) x xs'", "val swap (#a: Type0) (x: array a) (i: nat) (j: nat{i <= j})\n : HoareST unit\n (fun h -> j < Seq.length (sel h x))\n (fun h0 _ h1 ->\n j < Seq.length (sel h0 x) /\\ modifies (Set.singleton (addr_of x)) h0 h1 /\\\n sel h1 x == Seq.swap (sel h0 x) i j)\nlet swap (#a:Type0) (x:array a) (i:nat) (j:nat{i <= j})\n: HoareST unit\n (fun h -> j < Seq.length (sel h x))\n (fun h0 _ h1 ->\n j < Seq.length (sel h0 x) /\\\n modifies (Set.singleton (addr_of x)) h0 h1 /\\\n sel h1 x == Seq.swap (sel h0 x) i j)\n= let v_i = index x i in\n let v_j = index x j in\n upd x j v_i;\n upd x i v_j", "val swap (#a: Type0) (x: array a) (i: nat) (j: nat{i <= j})\n : HoareST unit\n (fun h -> j < Seq.length (sel h x))\n (fun h0 _ h1 ->\n j < Seq.length (sel h0 x) /\\ modifies (Set.singleton (addr_of x)) h0 h1 /\\\n sel h1 x == Seq.swap (sel h0 x) i j)\nlet swap (#a:Type0) (x:array a) (i:nat) (j:nat{i <= j})\n: HoareST unit\n (fun h -> j < Seq.length (sel h x))\n (fun h0 _ h1 ->\n j < Seq.length (sel h0 x) /\\\n modifies (Set.singleton (addr_of x)) h0 h1 /\\\n sel h1 x == Seq.swap (sel h0 x) i j)\n= let v_i = index x i in\n let v_j = index x j in\n upd x j v_i;\n upd x i v_j", "val plus_n_Sm : n : nat -> m : nat -> Lemma\n (ensures (S (plus n m) = plus n (S m)))\nlet rec plus_n_Sm n m =\n match n with\n | O -> ()\n | S n' -> plus_n_Sm n' m", "val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))\nlet swap_neg_mul a b =\n neg_mul_left a b;\n neg_mul_right a b", "val lemma_aux_2 (#a: Type) (b: buffer a) (n: UInt32.t{v n < length b}) (z: a) (h0: mem)\n : Lemma (requires (live h0 b))\n (ensures\n (live h0 b /\\\n (forall (tt: Type) (bb: buffer tt).\n (live h0 bb /\\ disjoint b bb) ==>\n (let h1 = HS.upd h0 b.content (Seq.upd (sel h0 b) (idx b + v n) z) in\n as_seq h0 bb == as_seq h1 bb))))\nlet lemma_aux_2\n (#a:Type) (b:buffer a) (n:UInt32.t{v n < length b}) (z:a) (h0:mem)\n :Lemma (requires (live h0 b))\n (ensures (live h0 b /\\\n\t (forall (tt:Type) (bb:buffer tt). (live h0 bb /\\ disjoint b bb) ==>\n\t\t (let h1 = HS.upd h0 b.content (Seq.upd (sel h0 b) (idx b + v n) z) in\n\t\t as_seq h0 bb == as_seq h1 bb))))\n = let open FStar.Classical in\n forall_intro (move_requires (lemma_aux_1 b n z h0))", "val lemma_aux_1 (#a: Type) (b: buffer a) (n: UInt32.t{v n < length b}) (z: a) (h0: mem) (tt: Type)\n : Lemma (requires (live h0 b))\n (ensures\n (live h0 b /\\\n (forall (bb: buffer tt).\n (live h0 bb /\\ disjoint b bb) ==>\n (let h1 = HS.upd h0 b.content (Seq.upd (sel h0 b) (idx b + v n) z) in\n as_seq h0 bb == as_seq h1 bb))))\nlet lemma_aux_1\n (#a:Type) (b:buffer a) (n:UInt32.t{v n < length b}) (z:a) (h0:mem) (tt:Type)\n :Lemma (requires (live h0 b))\n (ensures (live h0 b /\\\n\t (forall (bb:buffer tt). (live h0 bb /\\ disjoint b bb) ==>\n\t\t (let h1 = HS.upd h0 b.content (Seq.upd (sel h0 b) (idx b + v n) z) in\n\t\t as_seq h0 bb == as_seq h1 bb))))\n = let open FStar.Classical in\n forall_intro (move_requires (lemma_aux_0 b n z h0 tt))", "val swap (a: poly) (n: nat) : poly\nlet swap (a:poly) (n:nat) : poly =\n shift (mask a n) n +. shift a (-n)", "val assoc_append_elim_r (#a: eqtype) (#b: Type) (x: a) (l1 l2: list (a * b))\n : Lemma (requires (assoc x l2 == None \\/ ~(assoc x l1 == None)))\n (ensures (assoc x (l1 @ l2) == assoc x l1))\n (decreases l1)\nlet rec assoc_append_elim_r\n (#a: eqtype)\n (#b: Type)\n (x: a)\n (l1 l2: list (a * b))\n: Lemma\n (requires (assoc x l2 == None \\/ ~ (assoc x l1 == None)))\n (ensures (assoc x (l1 @ l2) == assoc x l1))\n (decreases l1)\n= match l1 with\n | [] -> ()\n | (x', _) :: q -> if x = x' then () else assoc_append_elim_r x q l2", "val rename_elab_commute_core (m: int) (e: src_exp{ln' e m}) (x y: var) (n: nat)\n : Lemma\n (ensures\n RT.subst_term (elab_exp e) (RT.shift_subst_n n [rt_rename x y]) == elab_exp (rename e x y))\n (decreases e)\nlet rec rename_elab_commute_core (m:int) (e:src_exp { ln' e m } ) (x y:var) (n:nat)\n : Lemma \n (ensures RT.subst_term (elab_exp e) (RT.shift_subst_n n [rt_rename x y]) ==\n elab_exp (rename e x y))\n (decreases e)\n = match e with\n | EBool _ -> ()\n | EBVar _ -> ()\n | EVar _ -> ()\n | EApp e0 e1 ->\n rename_elab_commute_core m e0 x y n;\n rename_elab_commute_core m e1 x y n\n | EIf b e0 e1 ->\n rename_elab_commute_core m b x y n; \n rename_elab_commute_core m e0 x y n;\n rename_elab_commute_core m e1 x y n\n | ELam t e ->\n src_types_are_closed_core t (rt_rename x y) n;\n rename_elab_commute_core (m + 1) e x y (n + 1)", "val assoc_flip_intro (#a #b: eqtype) (l: list (a * b)) (y: b) (x: a)\n : Lemma\n (requires\n (L.noRepeats (list_map fst l) /\\ L.noRepeats (list_map snd l) /\\ L.assoc x l == Some y))\n (ensures (L.assoc y (list_map flip l) == Some x))\nlet rec assoc_flip_intro\n (#a #b: eqtype)\n (l: list (a * b))\n (y: b)\n (x: a)\n: Lemma\n (requires (\n L.noRepeats (list_map fst l) /\\\n L.noRepeats (list_map snd l) /\\\n L.assoc x l == Some y\n ))\n (ensures (\n L.assoc y (list_map flip l) == Some x\n ))\n= map_fst_flip l;\n map_snd_flip l;\n map_flip_flip l;\n assoc_flip_elim (list_map flip l) x y", "val lemma_pow_neg_add_aux: #t:Type -> k:abelian_group t -> x:t -> n:int -> m:int -> Lemma\n (requires n < 0 && m >= 0)\n (ensures cm.mul (pow_neg k x n) (pow_neg k x m) == pow_neg k x (n + m))\nlet lemma_pow_neg_add_aux #t k x n m =\n assert (cm.mul (pow_neg k x n) (pow_neg k x m) ==\n cm.mul (k.inverse (pow k.cm x (-n))) (pow k.cm x m));\n\n if -n <= m then begin\n calc (==) {\n k.cm.mul (k.inverse (pow k.cm x (-n))) (pow k.cm x m);\n (==) { lemma_pow_add k.cm x (-n) (m + n) }\n k.cm.mul (k.inverse (pow k.cm x (-n))) (k.cm.mul (pow k.cm x (-n)) (pow k.cm x (m + n)));\n (==) { k.cm.lemma_mul_assoc\n (k.inverse (pow k.cm x (-n))) (pow k.cm x (-n)) (pow k.cm x (m + n)) }\n k.cm.mul (k.cm.mul (k.inverse (pow k.cm x (- n))) (pow k.cm x (-n))) (pow k.cm x (m + n));\n (==) { k.lemma_inverse (pow k.cm x (- n)) }\n k.cm.mul k.cm.one (pow k.cm x (m + n));\n (==) { k.cm.lemma_mul_comm k.cm.one (pow k.cm x (m + n)) }\n k.cm.mul (pow k.cm x (m + n)) k.cm.one;\n (==) { k.cm.lemma_one (pow k.cm x (m + n)) }\n pow k.cm x (m + n);\n } end\n else begin\n calc (==) {\n k.cm.mul (k.inverse (pow k.cm x (-n))) (pow k.cm x m);\n (==) { lemma_pow_add k.cm x (-n-m) m }\n k.cm.mul (k.inverse (k.cm.mul (pow k.cm x (-n-m)) (pow k.cm x m))) (pow k.cm x m);\n (==) { lemma_inverse_mul k (pow k.cm x (-n-m)) (pow k.cm x m) }\n k.cm.mul (k.cm.mul (k.inverse (pow k.cm x (-n-m))) (k.inverse (pow k.cm x m))) (pow k.cm x m);\n (==) { k.cm.lemma_mul_assoc\n (k.inverse (pow k.cm x (-n-m))) (k.inverse (pow k.cm x m)) (pow k.cm x m) }\n k.cm.mul (k.inverse (pow k.cm x (-n-m))) (k.cm.mul (k.inverse (pow k.cm x m)) (pow k.cm x m));\n (==) { k.lemma_inverse (pow k.cm x m) }\n k.cm.mul (k.inverse (pow k.cm x (-n-m))) k.cm.one;\n (==) { k.cm.lemma_one (k.inverse (pow k.cm x (-n-m))) }\n k.inverse (pow k.cm x (-n-m));\n } end", "val tsubst_commute: t1:typ -> y:nat -> t2:typ -> x:nat{x >= y} -> s:typ ->\n Lemma (requires True)\n (ensures (ts x s (ts y t2 t1) =\n ts y (ts x s t2) (ts (x + 1) (tsh y s) t1)))\nlet rec tsubst_commute t1 y t2 x s =\n tsubst_comp (tsub_beta_gen x s) (tsub_beta_gen y t2) t1;\n forall_intro (tsubst_commute_aux y x s t2);\n tsubst_extensional (tsub_comp (tsub_beta_gen x s) (tsub_beta_gen y t2))\n (tsub_comp (tsub_beta_gen y (ts x s t2))\n (tsub_beta_gen (x+1) (tsh y s))) t1;\n tsubst_comp (tsub_beta_gen y (ts x s t2)) (tsub_beta_gen (x+1) (tsh y s)) t1", "val lemma_aux_0 (a b n: nat)\n : Lemma\n (pow2 n * a + pow2 (n + 56) * b = pow2 n * (a % pow2 56) + pow2 (n + 56) * (b + a / pow2 56))\nlet lemma_aux_0 (a:nat) (b:nat) (n:nat) : Lemma\n (pow2 n * a + pow2 (n+56) * b = pow2 n * (a % pow2 56) + pow2 (n+56) * (b + a / pow2 56))\n = Math.Lemmas.lemma_div_mod a (pow2 56);\n Math.Lemmas.pow2_plus n 56;\n assert(a = pow2 56 * (a / pow2 56) + (a % pow2 56));\n Math.Lemmas.distributivity_add_right (pow2 n) (pow2 56 * (a / pow2 56)) (a % pow2 56);\n Math.Lemmas.paren_mul_right (pow2 n) (pow2 56) (a / pow2 56);\n Math.Lemmas.distributivity_add_right (pow2 (n+56)) b (a / pow2 56)", "val lemma_init_ghost_aux_len (#a:Type) (n:nat) (k:nat{k < n}) (contents:(i:nat{ i < n } -> GTot a))\n : Lemma (requires True)\n (ensures (length (init_aux_ghost n k contents) = n - k))\n [SMTPat (length (init_aux_ghost n k contents))]\nlet lemma_init_ghost_aux_len = lemma_init_ghost_aux_len'", "val lemma_add_lo_mul_right (#n:nat) (a b:natN n) (c:nat1) (m:int) : Lemma\n (add_lo a b c * m == (let x = a * m + b * m + c * m in if a + b + c < n then x else x - n * m))\nlet lemma_add_lo_mul_right #n a b c m =\n reveal_add_lo_all ()", "val lemma_reverse_define (a:poly) (n:nat) : Lemma\n (forall (i:int).{:pattern (reverse a n).[i]} (reverse a n).[i] == (a.[n - i] && i >= 0))\nlet lemma_reverse_define p n =\n FStar.Classical.forall_intro (lemma_reverse_define_i p n)", "val nth_lemma: #n:pos -> a:int_t n -> b:int_t n ->\n Lemma (requires forall (i:nat{i < n}). nth a i = nth b i)\n (ensures a = b)\nlet nth_lemma #n a b =\n assert(forall (i:nat{i < n}). index (to_vec #n a) i = index (to_vec #n b) i);\n to_vec_lemma_2 a b", "val lemma_split3_unsnoc (#t: Type) (l: list t) (n: nat{n < length l})\n : Lemma (requires (n <> length l - 1))\n (ensures\n (let a, b, c = split3 l n in\n lemma_split3_length l n;\n length c > 0 /\\\n (let xs, x = unsnoc l in\n let ys, y = unsnoc c in\n append a (b :: ys) == xs)))\nlet rec lemma_split3_unsnoc (#t:Type) (l:list t) (n:nat{n < length l}) :\n Lemma\n (requires (n <> length l - 1))\n (ensures (\n let a, b, c = split3 l n in\n lemma_split3_length l n;\n length c > 0 /\\ (\n let xs, x = unsnoc l in\n let ys, y = unsnoc c in\n append a (b :: ys) == xs))) =\n match n with\n | 0 -> ()\n | _ -> lemma_split3_unsnoc (tl l) (n-1)", "val lemma_mul_reverse_shift_1 (a b:poly) (n:nat) : Lemma\n (requires degree a <= n /\\ degree b <= n)\n (ensures reverse (a *. b) (n + n + 1) == shift (reverse a n *. reverse b n) 1)\nlet lemma_mul_reverse_shift_1 a b n =\n let ab = a *. b in\n let ra = reverse a n in\n let rb = reverse b n in\n let rab = reverse ab (n + n) in\n let rab1 = reverse ab (n + n + 1) in\n lemma_index ab;\n lemma_mul_reverse a b n;\n lemma_reverse_define ab (n + n);\n lemma_reverse_define ab (n + n + 1);\n lemma_shift_define (ra *. rb) 1;\n lemma_equal rab1 (shift (ra *. rb) 1)", "val assoc_append_elim_l (#a: eqtype) (#b: Type) (x: a) (l1 l2: list (a * b))\n : Lemma (requires (assoc x l1 == None))\n (ensures (assoc x (l1 @ l2) == assoc x l2))\n (decreases l1)\nlet rec assoc_append_elim_l\n (#a: eqtype)\n (#b: Type)\n (x: a)\n (l1 l2: list (a * b))\n: Lemma\n (requires (assoc x l1 == None))\n (ensures (assoc x (l1 @ l2) == assoc x l2))\n (decreases l1)\n= match l1 with\n | [] -> ()\n | (x', _) :: q -> if x = x' then assert False else assoc_append_elim_l x q l2", "val double_foldm_snoc_transpose_lemma\n (#c #eq: _)\n (#m #n: pos)\n (cm: CE.cm c eq)\n (f: (under m -> under n -> c))\n : Lemma\n ((SP.foldm_snoc cm\n (SB.init m (fun (i: under m) -> SP.foldm_snoc cm (SB.init n (fun (j: under n) -> f i j))))\n )\n `eq.eq`\n (SP.foldm_snoc cm\n (SB.init n (fun (j: under n) -> SP.foldm_snoc cm (SB.init m (fun (i: under m) -> f i j))))\n ))\nlet double_foldm_snoc_transpose_lemma #c #eq (#m #n: pos) (cm: CE.cm c eq) (f: under m -> under n -> c)\n : Lemma (SP.foldm_snoc cm (SB.init m (fun (i: under m) -> SP.foldm_snoc cm (SB.init n (fun (j: under n) -> f i j)))) `eq.eq`\n SP.foldm_snoc cm (SB.init n (fun (j: under n) -> SP.foldm_snoc cm (SB.init m (fun (i: under m) -> f i j))))) = \n Classical.forall_intro_2 (Classical.move_requires_2 eq.symmetry);\n let gen : matrix_generator c m n = f in \n let mx = init gen in \n let mx_seq = matrix_seq gen in\n matrix_fold_equals_fold_of_seq_folds cm gen; \n let aux (i: under m) : Lemma (SB.init n (gen i) == SB.init n (fun (j: under n) -> f i j))\n = SB.lemma_eq_elim (SB.init n (gen i))(SB.init n (fun (j: under n) -> f i j)) \n in Classical.forall_intro aux; \n SB.lemma_eq_elim (SB.init m (fun i -> SP.foldm_snoc cm (SB.init n (gen i))))\n (SB.init m (fun i -> SP.foldm_snoc cm (SB.init n (fun (j: under n) -> f i j)))); \n SB.lemma_eq_elim (SB.init m (fun (i: under m) -> SP.foldm_snoc cm (SB.init n (fun (j: under n) -> f i j))))\n (SB.init m (fun i -> SP.foldm_snoc cm (SB.init n (fun (j: under n) -> f i j)))); \n matrix_transpose_is_permutation gen;\n matrix_fold_equals_fold_of_transpose cm gen;\n let trans_gen = transposed_matrix_gen gen in\n let mx_trans = init trans_gen in\n let mx_trans_seq = matrix_seq trans_gen in\n matrix_fold_equals_fold_of_seq_folds cm trans_gen;\n assert (foldm cm mx_trans `eq.eq` \n SP.foldm_snoc cm (SB.init n (fun j -> SP.foldm_snoc cm (SB.init m (trans_gen j)))));\n let aux_tr_lemma (j: under n) \n : Lemma ((SB.init m (trans_gen j)) == (SB.init m (fun (i: under m) -> f i j))) \n = SB.lemma_eq_elim (SB.init m (trans_gen j)) (SB.init m (fun (i: under m) -> f i j)) \n in Classical.forall_intro aux_tr_lemma;\n SB.lemma_eq_elim (SB.init n (fun j -> SP.foldm_snoc cm (SB.init m (trans_gen j))))\n (SB.init n (fun (j:under n) -> SP.foldm_snoc cm (SB.init m (fun (i: under m) -> f i j))));\n assert (foldm cm mx_trans `eq.eq` \n SP.foldm_snoc cm (SB.init n (fun (j:under n) -> SP.foldm_snoc cm (SB.init m (fun (i: under m) -> f i j)))));\n eq.transitivity (SP.foldm_snoc cm (SB.init m (fun (i: under m) -> SP.foldm_snoc cm (SB.init n (fun (j: under n) -> f i j)))))\n (foldm cm mx)\n (foldm cm mx_trans);\n eq.transitivity (SP.foldm_snoc cm (SB.init m (fun (i: under m) -> SP.foldm_snoc cm (SB.init n (fun (j: under n) -> f i j)))))\n (foldm cm mx_trans)\n (SP.foldm_snoc cm (SB.init n (fun (j:under n) -> SP.foldm_snoc cm (SB.init m (fun (i: under m) -> f i j)))))", "val swap (#a:Type0) (x:array a) (i:nat) (j:nat{i <= j})\n : ST unit\n (requires (fun h -> contains h x /\\ j < Seq.length (sel h x)))\n (ensures (fun h0 _u h1 -> j < Seq.length (sel h0 x) /\\\n contains h1 x /\\\n\t\t modifies (Set.singleton (addr_of x)) h0 h1 /\\\n\t\t sel h1 x == Seq.swap (sel h0 x) i j))\nlet swap #a x i j =\n let tmpi = index x i in\n let tmpj = index x j in\n upd x j tmpi;\n upd x i tmpj", "val swap\n (#t: Type0)\n (#s0: Ghost.erased (Seq.seq t))\n (a: array t)\n (n: SZ.t)\n (l: SZ.t)\n: ST (Ghost.erased (Seq.seq t))\n (pts_to a full_perm s0)\n (fun s -> pts_to a full_perm s)\n (\n SZ.v n == length a /\\\n SZ.v l <= SZ.v n\n )\n (fun s ->\n SZ.v n == Seq.length s0 /\\\n SZ.v l <= SZ.v n /\\\n s `Seq.equal` (Seq.slice s0 (SZ.v l) (SZ.v n) `Seq.append` Seq.slice s0 0 (SZ.v l))\n )\nlet swap\n a n l\n= pts_to_length a _;\n Gen.array_swap_gen (array_index a) (array_upd a) _ n l", "val lemma_snoc_unsnoc: #a:Type -> lx:(list a * a) ->\n Lemma (requires True)\n (ensures (unsnoc (snoc lx) == lx))\n (decreases (length (fst (lx))))\n [SMTPat (unsnoc (snoc lx))]\nlet rec lemma_snoc_unsnoc #a lx =\n let l, x = lx in\n match l with\n | [] -> ()\n | _ -> lemma_snoc_unsnoc (tl l, x)", "val stack_of_args_stack_args'_aux\n (max_arity n_init n: nat)\n (args: IX64.arg_list{List.Tot.length args = n})\n (rsp: int)\n (stack: Map.t int Vale.Def.Words_s.nat8)\n (v: MS.nat64)\n : Lemma (requires stack_args' max_arity n args rsp stack /\\ n_init >= n)\n (ensures\n (let ptr = (n_init - max_arity) * 8 + (if IA.win then 32 else 0) + 8 + rsp in\n stack_args' max_arity n args rsp (BS.update_heap64 ptr v stack)))\nlet rec stack_of_args_stack_args'_aux\n (max_arity:nat)\n (n_init:nat)\n (n:nat)\n (args:IX64.arg_list{List.Tot.length args = n})\n (rsp:int)\n (stack:Map.t int Vale.Def.Words_s.nat8)\n (v:MS.nat64)\n : Lemma\n (requires stack_args' max_arity n args rsp stack /\\ n_init >= n)\n (ensures\n (let ptr = (n_init - max_arity) * 8 + (if IA.win then 32 else 0) + 8 + rsp in\n stack_args' max_arity n args rsp (BS.update_heap64 ptr v stack)))\n = match args with\n | [] -> ()\n | hd::tl ->\n stack_of_args_stack_args'_aux max_arity n_init (n-1) tl rsp stack v;\n if n <= max_arity then ()\n else (\n let fixed = (n_init - max_arity) * 8 + (if IA.win then 32 else 0) + 8 + rsp in\n let ptr = ((n - max_arity) - 1) * 8\n + (if IA.win then 32 else 0)\n + 8\n + rsp\n in\n calc ( <= ) {\n ((n - max_arity) - 1) * 8;\n ( <= ) { FStar.Math.Lemmas.lemma_mult_le_right 8 ((n - max_arity) - 1) (n_init - max_arity) }\n (n_init - max_arity) * 8;\n };\n frame_update_get_heap fixed v stack ptr;\n frame_update_valid_heap fixed v stack ptr\n )", "val puts_preserves_non_ref_aux\n (#vcfg: _)\n (st: vstore vcfg)\n (ss: S.seq (slot_id vcfg) {contains_only_app_keys st ss})\n (ws: S.seq (app_value_nullable vcfg.app.adm) {S.length ws = S.length ss})\n (s: slot_id vcfg)\n (l: nat{l <= S.length ss})\n : Lemma\n (ensures\n (let st_ = puts_store_aux st ss ws l in\n not (S.mem s ss) ==> get_slot st s = get_slot st_ s)) (decreases l)\nlet rec puts_preserves_non_ref_aux (#vcfg:_)\n (st: vstore vcfg)\n (ss: S.seq (slot_id vcfg){contains_only_app_keys st ss})\n (ws: S.seq (app_value_nullable vcfg.app.adm){S.length ws = S.length ss})\n (s: slot_id vcfg)\n (l: nat{l <= S.length ss})\n : Lemma (ensures (let st_ = puts_store_aux st ss ws l in\n not (S.mem s ss) ==>\n get_slot st s = get_slot st_ s))\n (decreases l)\n = if l > 0 then\n puts_preserves_non_ref_aux st ss ws s (l - 1)", "val equal_counts_implies_swaps (#a: eqtype) (xs ys: list a)\n : Pure (swaps_for xs)\n (requires equal_counts xs ys)\n (ensures (fun ss -> ys == apply_swaps xs ss))\n (decreases ys)\nlet rec equal_counts_implies_swaps (#a:eqtype) (xs ys:list a) : Pure (swaps_for xs)\n (requires equal_counts xs ys)\n (ensures (fun ss -> ys == apply_swaps xs ss))\n (decreases ys)\n =\n match ys with\n | [] ->\n (\n match xs with\n | [] -> []\n | x::xt ->\n (\n assert (count x xs >= 1);\n []\n )\n )\n | y::yt ->\n (\n assert (count y ys >= 1);\n assert (count y xs >= 1);\n let ss0 = swap_to_front y xs in // find y in xs, swap it to the front\n let xs' = apply_swaps xs ss0 in // hd xs' == y\n let xt = tl xs' in // xs' == y::xt\n retract_equal_counts y xt yt; // prove (equal_counts xt yt)\n let ss1 = equal_counts_implies_swaps xt yt in // prove (yt == apply_swaps xt ss1)\n let ss1' = lift_swaps_cons y xt ss1 in // y::yt == apply_swaps (y::xt) ss1'\n // ys == apply_swaps (apply_swaps xs ss0) ss1'\n append_swaps xs ss0 ss1';\n ss0 @ ss1'\n )", "val reduce_aux (#a #b: Type) (b0: b) (f: (a -> b -> b)) (s: seq a) : Tot b (decreases (length s))\nlet rec reduce_aux (#a:Type) (#b:Type) (b0: b) (f: a -> b -> b) (s: seq a):\n Tot b (decreases (length s)) =\n let n = length s in\n if n = 0 then b0\n else\n let s' = prefix s (n - 1) in\n let b' = reduce_aux b0 f s' in\n let e = index s (n - 1) in\n f e b'", "val no_repeats_p_append_swap (#a: Type) (l1 l2: list a)\n : Lemma (no_repeats_p (l1 `append` l2) <==> no_repeats_p (l2 `append` l1))\nlet no_repeats_p_append_swap\n (#a: Type)\n (l1 l2: list a)\n: Lemma\n (no_repeats_p (l1 `append` l2) <==> no_repeats_p (l2 `append` l1))\n= no_repeats_p_append l1 l2;\n no_repeats_p_append l2 l1", "val lemma_odd_reverse_shift_right (a:poly) (n:pos) : Lemma\n (requires degree a < n /\\ a.[0])\n (ensures shift (reverse a (n - 1)) 1 == monomial n +. reverse (shift a (-1)) (n - 1))\nlet lemma_odd_reverse_shift_right a n =\n lemma_bitwise_all ();\n lemma_equal (shift (reverse a (n - 1)) 1) (monomial n +. reverse (shift a (-1)) (n - 1))", "val drop_commutes_with_in_range_update_helper (#ty: Type) (s: list ty) (i: nat) (v: ty) (n: nat)\n : Lemma\n (requires\n n <= i /\\ i < length s /\\ length (update s i v) = length s /\\\n length (drop s n) = length s - n)\n (ensures drop (update s i v) n == update (drop s n) (i - n) v)\nlet rec drop_commutes_with_in_range_update_helper (#ty: Type) (s: list ty) (i: nat) (v: ty) (n: nat)\n : Lemma (requires n <= i\n /\\ i < length s\n /\\ length (update s i v) = length s\n /\\ length (drop s n) = length s - n)\n (ensures drop (update s i v) n ==\n update (drop s n) (i - n) v) =\n match s with\n | hd :: tl ->\n if n = 0\n then ()\n else (\n update_maintains_length_lemma ();\n drop_length_lemma ();\n drop_commutes_with_in_range_update_helper tl (i - 1) v (n - 1)\n )", "val array_as_ring_buffer_swap (#t: Type) (n l: nat) (bz: bezout n l) (s0 s: Seq.seq t)\n : Lemma\n (requires\n (n == Seq.length s0 /\\ n == Seq.length s /\\ 0 < l /\\ l < n /\\\n (forall (i': nat_up_to bz.d).\n (forall (j: nat_up_to bz.q_n).\n (i' < bz.d) ==>\n (let idx = iter_fun #(nat_up_to n) (jump n l) j i' in\n Seq.index s idx == Seq.index s0 (jump n l idx))))))\n (ensures (array_swap_post s0 n l s))\n [SMTPat (array_swap_post s0 n l s); SMTPat (bezout_prop n l bz)]\nlet array_as_ring_buffer_swap\n (#t: Type)\n (n: nat)\n (l: nat)\n (bz: bezout n l)\n (s0: Seq.seq t)\n (s: Seq.seq t)\n: Lemma\n (requires (\n n == Seq.length s0 /\\\n n == Seq.length s /\\\n 0 < l /\\\n l < n /\\\n (forall (i': nat_up_to bz.d) .\n (forall (j: nat_up_to bz.q_n) .\n (i' < bz.d) ==> (\n let idx = iter_fun #(nat_up_to n) (jump n l) j i' in\n Seq.index s idx == Seq.index s0 (jump n l idx)\n )))\n ))\n (ensures (\n array_swap_post s0 n l s\n ))\n [SMTPat (array_swap_post s0 n l s); SMTPat (bezout_prop n l bz)]\n= Classical.forall_intro (jump_if n l ());\n let p\n (idx: nat_up_to n)\n : Tot prop\n = Seq.index s idx == Seq.index s0 (jump n l idx)\n in\n jump_iter_elim n p l bz", "val lemma_swap_slice_commute : #a:Type -> s:seq a -> start:nat -> i:nat{start <= i} -> j:nat{i <= j} -> len:nat{j < len && len <= length s}\n -> Lemma (ensures (slice (swap s i j) start len == (swap (slice s start len) (i - start) (j - start))))\nlet lemma_swap_slice_commute #_ s start i j len =\n cut (equal (slice (swap s i j) start len) (swap (slice s start len) (i - start) (j - start)))", "val drop_commutes_with_build_helper (#ty: Type) (s: list ty) (v: ty) (n: nat)\n : Lemma (requires n <= length s /\\ length (append s [v]) = 1 + length s)\n (ensures drop (append s [v]) n == append (drop s n) [v])\nlet rec drop_commutes_with_build_helper (#ty: Type) (s: list ty) (v: ty) (n: nat)\n : Lemma (requires n <= length s /\\ length (append s [v]) = 1 + length s)\n (ensures drop (append s [v]) n == append (drop s n) [v]) =\n match s with\n | [] -> \n assert (append s [v] == [v]);\n assert (n == 0);\n ()\n | hd :: tl -> if n = 0 then () else drop_commutes_with_build_helper tl v (n - 1)", "val puts_preserve_ismap_aux\n (#vcfg: _)\n (st: ismap_vstore vcfg)\n (ss: S.seq (slot_id vcfg) {contains_only_app_keys st ss})\n (ws: S.seq (app_value_nullable vcfg.app.adm) {S.length ws = S.length ss})\n (l: nat{l <= S.length ss})\n : Lemma (ensures (is_map (puts_store_aux st ss ws l))) (decreases l)\nlet rec puts_preserve_ismap_aux (#vcfg:_)\n (st: ismap_vstore vcfg)\n (ss: S.seq (slot_id vcfg){contains_only_app_keys st ss})\n (ws: S.seq (app_value_nullable vcfg.app.adm){S.length ws = S.length ss})\n (l: nat{l <= S.length ss})\n : Lemma (ensures (is_map (puts_store_aux st ss ws l)))\n (decreases l)\n = if l > 0 then\n puts_preserve_ismap_aux st ss ws (l-1)", "val swap (#a: Type) (s: seq a) (i: nat{i < length s}) (j: nat{j < length s}) : Tot (seq a)\nlet swap (#a:Type) (s:seq a) (i:nat{i holds v (sel a x) (sel b x))\n [SMTPat (holds (st_var x v) a b)]\nlet holds_st_var\n (x: var)\n (v: nstype int)\n (a b: heap)\n: Lemma\n (holds (st_var x v) a b <==> holds v (sel a x) (sel b x))\n [SMTPat (holds (st_var x v) a b)]\n= holds_equiv (st_var x v) a b", "val drop_then_drop_helper (#ty: Type) (s: seq ty) (m n: nat)\n : Lemma (requires m + n <= length s /\\ length (drop s m) = length s - m)\n (ensures drop (drop s m) n == drop s (m + n))\nlet rec drop_then_drop_helper (#ty: Type) (s: seq ty) (m: nat) (n: nat)\n : Lemma (requires m + n <= length s /\\ length (drop s m) = length s - m)\n (ensures drop (drop s m) n == drop s (m + n)) =\n match s with\n | [] -> ()\n | hd :: tl -> \n if m = 0\n then () \n else (\n drop_length_lemma ();\n drop_then_drop_helper tl (m - 1) n\n )", "val splitAt_eq_lem (#a:Type) (n:nat) (l:list a) :\n Lemma\n (requires (n <= List.Tot.length l))\n (ensures (\n let l1, l2 = List.Tot.splitAt n l in\n List.Tot.length l1 = n /\\\n List.Tot.length l2 = List.Tot.length l - n /\\\n l == List.Tot.append l1 l2))\n (decreases l)\nlet rec splitAt_eq_lem n l =\n match l with\n | [] -> ()\n | x :: l' ->\n if n = 0 then ()\n else splitAt_eq_lem (n-1) l'", "val copy_aux:\n #a:Type -> s:array a -> cpy:array a -> ctr:nat ->\n ST unit\n\t(requires (fun h -> (contains h s /\\ contains h cpy /\\ addr_of s <> addr_of cpy)\n\t\t\t /\\ (Seq.length (sel h cpy) = Seq.length (sel h s))\n\t\t\t /\\ (ctr <= Seq.length (sel h cpy))\n\t\t\t /\\ (forall (i:nat). i < ctr ==> Seq.index (sel h s) i == Seq.index (sel h cpy) i)))\n\t(ensures (fun h0 u h1 -> (contains h1 s /\\ contains h1 cpy /\\ addr_of s <> addr_of cpy )\n\t\t\t /\\ (modifies (only cpy) h0 h1)\n\t\t\t /\\ (Seq.equal (sel h1 cpy) (sel h1 s))))\nlet rec copy_aux #a s cpy ctr =\n match length cpy - ctr with\n | 0 -> ()\n | _ -> upd cpy ctr (index s ctr);\n\t copy_aux s cpy (ctr+1)" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.apply_swap_aux_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.apply_swap_aux_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.apply_swap_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSwaps.fst", "name": "FStar.Tactics.CanonCommSwaps.apply_swap_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.apply_swap_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSwaps.fst", "name": "FStar.Tactics.CanonCommSwaps.lift_swap_cons" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.apply_swaps_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.apply_swaps_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSwaps.fst", "name": "FStar.Tactics.CanonCommSwaps.append_swaps" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSwaps.fst", "name": "FStar.Tactics.CanonCommSwaps.apply_swaps" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.sort_correct_aux" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.sort_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.sort_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_swap_permutes_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSwaps.fst", "name": "FStar.Tactics.CanonCommSwaps.lift_swaps_cons" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.sort_via_swaps" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.flatten_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.sort_via_swaps" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.flatten_correct_aux" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GF128.fst", "name": "Vale.AES.GF128.lemma_swap_right" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.ics_aux_ok" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.flatten_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_swap_permutes" }, { "project_name": "FStar", "file_name": "StackMachine.fst", "name": "StackMachine.app_assoc_reverse" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.csm_aux_ok" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.lemma_xsdenote_aux" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.assoc_flip_elim" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSwaps.fst", "name": "FStar.Tactics.CanonCommSwaps.swap_to_front" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.lemma_init_aux_len'" }, { "project_name": "FStar", "file_name": "FStar.Matrix.fst", "name": "FStar.Matrix.terminal_case_aux" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.tsubst_commute_aux" }, { "project_name": "FStar", "file_name": "FStar.Matrix.fst", "name": "FStar.Matrix.math_aux_2" }, { "project_name": "FStar", "file_name": "FStar.Matrix.fst", "name": "FStar.Matrix.matrix_fold_aux" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_reduce_prefix_aux" }, { "project_name": "FStar", "file_name": "FStar.UInt.fst", "name": "FStar.UInt.from_vec_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.lemma_init_aux_len" }, { "project_name": "FStar", "file_name": "FStar.Matrix.fst", "name": "FStar.Matrix.terminal_case_two_aux" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fst", "name": "Vale.Lib.Map16.lemma_other" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.lemma_aux_0" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.lemma_init_ghost_aux_len'" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_map_index_aux" }, { "project_name": "FStar", "file_name": "FStar.Matrix.fst", "name": "FStar.Matrix.math_aux_3" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.copy_aux" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.copy_aux" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_attach_correct_aux" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.lemma_add_incr_mem_aux" }, { "project_name": "FStar", "file_name": "FStar.Matrix.fst", "name": "FStar.Matrix.fold_of_subgen_aux" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.map_aux" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_zip_index_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.lemma_index_upd1'" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_swap_permutes_aux_frag_eq" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.lemma_index_upd2'" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_shift_shift" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.lemma_aux" }, { "project_name": "zeta", "file_name": "Zeta.MultiSet.fst", "name": "Zeta.MultiSet.length_size_aux" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Map16.fst", "name": "Vale.Lib.Map16.lemma_self" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.varlist_merge_ok" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_swap_splice" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_unzip_index_aux" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.where_aux" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.swap" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.swap" }, { "project_name": "FStar", "file_name": "SfBasic.fst", "name": "SfBasic.plus_n_Sm" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.swap_neg_mul" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.lemma_aux_2" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.lemma_aux_1" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.fsti", "name": "Vale.Math.Poly2.swap" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.assoc_append_elim_r" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.rename_elab_commute_core" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.assoc_flip_intro" }, { "project_name": "hacl-star", "file_name": "Lib.Exponentiation.Definition.fst", "name": "Lib.Exponentiation.Definition.lemma_pow_neg_add_aux" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.tsubst_commute" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.BignumQ.Lemmas.fst", "name": "Hacl.Spec.BignumQ.Lemmas.lemma_aux_0" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.lemma_init_ghost_aux_len" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.Lemmas.fst", "name": "Vale.Bignum.Lemmas.lemma_add_lo_mul_right" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_reverse_define" }, { "project_name": "FStar", "file_name": "FStar.Int.fst", "name": "FStar.Int.nth_lemma" }, { "project_name": "FStar", "file_name": "FStar.List.Pure.Properties.fst", "name": "FStar.List.Pure.Properties.lemma_split3_unsnoc" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_mul_reverse_shift_1" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.assoc_append_elim_l" }, { "project_name": "FStar", "file_name": "FStar.Matrix.fst", "name": "FStar.Matrix.double_foldm_snoc_transpose_lemma" }, { "project_name": "FStar", "file_name": "FStar.Array.fst", "name": "FStar.Array.swap" }, { "project_name": "steel", "file_name": "Steel.ST.Array.Swap.fst", "name": "Steel.ST.Array.Swap.swap" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.lemma_snoc_unsnoc" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Wrapper.fst", "name": "Vale.AsLowStar.Wrapper.stack_of_args_stack_args'_aux" }, { "project_name": "zeta", "file_name": "Zeta.Intermediate.Store.fst", "name": "Zeta.Intermediate.Store.puts_preserves_non_ref_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSwaps.fst", "name": "FStar.Tactics.CanonCommSwaps.equal_counts_implies_swaps" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.reduce_aux" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.no_repeats_p_append_swap" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GF128.fst", "name": "Vale.AES.GF128.lemma_odd_reverse_shift_right" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Base.fst", "name": "FStar.Sequence.Base.drop_commutes_with_in_range_update_helper" }, { "project_name": "steel", "file_name": "Steel.ST.GenArraySwap.Proof.fst", "name": "Steel.ST.GenArraySwap.Proof.array_as_ring_buffer_swap" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_swap_slice_commute" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Base.fst", "name": "FStar.Sequence.Base.drop_commutes_with_build_helper" }, { "project_name": "zeta", "file_name": "Zeta.Intermediate.Store.fst", "name": "Zeta.Intermediate.Store.puts_preserve_ismap_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fsti", "name": "FStar.Seq.Properties.swap" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fst", "name": "Benton2004.DDCC.holds_st_var" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Base.fst", "name": "FStar.Sequence.Base.drop_then_drop_helper" }, { "project_name": "noise-star", "file_name": "Spec.Noise.Map.fst", "name": "Spec.Noise.Map.splitAt_eq_lem" }, { "project_name": "FStar", "file_name": "FStar.Array.fst", "name": "FStar.Array.copy_aux" } ], "selected_premises": [ "FStar.Tactics.CanonCommMonoid.permute_correct", "FStar.Tactics.CanonCommMonoid.flatten_correct_aux", "FStar.Tactics.CanonCommMonoid.select", "FStar.Tactics.CanonCommMonoid.flatten_correct", "FStar.Tactics.CanonCommMonoid.xsdenote", "FStar.Tactics.CanonCommMonoid.select_extra", "FStar.Tactics.CanonCommMonoid.mdenote", "FStar.Tactics.CanonCommMonoid.update", "FStar.Tactics.CanonCommMonoid.const", "FStar.Tactics.CanonCommMonoid.permute", "FStar.Tactics.CanonCommMonoid.vmap", "FStar.List.Tot.Base.tl", "FStar.List.Tot.Properties.assoc_mem", "FStar.Tactics.CanonCommSwaps.swaps_for", "FStar.List.Tot.Base.op_At", "FStar.List.Tot.Base.memP", "FStar.List.Tot.Base.append", "FStar.Pervasives.Native.snd", "FStar.Tactics.CanonCommMonoid.var", "FStar.List.Tot.Base.mem", "FStar.List.Tot.Properties.append_assoc", "FStar.Tactics.CanonCommSwaps.append_swaps", "FStar.Tactics.CanonCommSwaps.swap_for", "FStar.Tactics.CanonCommSwaps.lift_swap_cons", "FStar.Pervasives.Native.fst", "FStar.List.Tot.Base.hd", "FStar.List.Tot.Base.index", "FStar.Tactics.CanonCommSwaps.lift_swaps_cons", "FStar.Tactics.CanonCommSwaps.apply_swaps", "FStar.List.Tot.Properties.memP_map_intro", "FStar.List.Tot.Base.rev", "FStar.Tactics.CanonCommSwaps.swap_to_front", "FStar.Tactics.CanonCommSwaps.apply_swap_aux", "FStar.Heap.trivial_preorder", "FStar.List.Tot.Base.length", "FStar.Tactics.CanonCommSwaps.equal_counts_implies_swaps", "FStar.Tactics.Util.map", "FStar.List.Tot.Properties.map_append", "FStar.List.Tot.Properties.assoc_memP_some", "FStar.List.Tot.Properties.append_l_cons", "FStar.List.Tot.Base.map", "FStar.ST.op_Bang", "FStar.List.Tot.Properties.append_mem", "FStar.Tactics.CanonCommMonoid.flatten", "FStar.Tactics.CanonCommSwaps.apply_swap", "FStar.Mul.op_Star", "FStar.List.Tot.Properties.append_inv_head", "FStar.List.Tot.Properties.append_injective", "FStar.List.Tot.Properties.append_memP", "FStar.List.Tot.Properties.precedes_append_cons_prod_r", "FStar.List.Tot.Properties.append_l_nil", "FStar.List.Tot.Base.fold_left", "FStar.List.Tot.Base.concatMap", "FStar.List.Tot.Properties.assoc_precedes", "FStar.List.Tot.Properties.map_lemma", "FStar.List.Tot.Properties.for_all_append", "FStar.Pervasives.dfst", "FStar.Pervasives.reveal_opaque", "FStar.List.Tot.Properties.fold_left_append", "FStar.Tactics.Effect.raise", "FStar.Pervasives.dsnd", "FStar.Tactics.Util.repeatn", "FStar.List.Tot.Properties.assoc_memP_none", "FStar.List.Tot.Properties.append_length", "FStar.ST.alloc", "FStar.Tactics.Util.fold_left2", "FStar.List.Tot.Base.splitAt", "FStar.List.Tot.Properties.memP_map_elim", "FStar.List.Tot.Properties.append_memP_forall", "FStar.List.Tot.Base.tail", "FStar.List.Tot.Base.assoc", "FStar.Tactics.CanonCommMonoid.dump", "FStar.List.Tot.Base.fold_left2", "FStar.List.Tot.Properties.lemma_split_using", "FStar.List.Tot.Properties.append_inv_tail", "FStar.List.Tot.Base.lemma_splitAt_snd_length", "FStar.List.Tot.Properties.assoc_append_elim_l", "FStar.List.Tot.Properties.index_extensionality_aux", "FStar.List.Tot.Base.fold_right_gtot", "FStar.List.Tot.Base.map_gtot", "FStar.List.Tot.Properties.assoc_append_elim_r", "FStar.List.Tot.Properties.rev_rev'", "FStar.List.Tot.Properties.fold_left_append_monoid", "FStar.List.mapT", "FStar.List.Tot.Properties.append_length_inv_head", "FStar.List.Tot.Properties.split_using", "FStar.List.Tot.Properties.lemma_snoc_length", "FStar.Tactics.Util.fold_left", "FStar.List.map", "FStar.Tactics.Util.__mapi", "FStar.List.Tot.Properties.rev_memP", "FStar.List.Tot.Base.list_refb", "FStar.List.Tot.Properties.precedes_append_cons_r", "FStar.List.Tot.Properties.rev_append", "FStar.Algebra.CommMonoid.int_multiply_cm", "FStar.Tactics.Types.issues", "FStar.List.Tot.Properties.no_repeats_p_append_swap", "FStar.List.Tot.Properties.rev'_append", "FStar.List.Tot.Base.split", "FStar.List.Tot.Base.fold_right" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.Tactics.CanonCommMonoid\n\nopen FStar.Algebra.CommMonoid\nopen FStar.List\nopen FStar.Reflection.V2\nopen FStar.Tactics.V2\nopen FStar.Classical\nopen FStar.Tactics.CanonCommSwaps\n\n(* An expression canonizer for commutative monoids.\n Inspired by:\n - http://adam.chlipala.net/cpdt/html/Cpdt.Reflection.html\n - http://poleiro.info/posts/2015-04-13-writing-reflective-tactics.html\n*)\n\n(* Only dump when debugging is on *)\nprivate let dump m = if debugging () then dump m\n\n(***** Expression syntax *)\n\nlet var : eqtype = nat\n\ntype exp : Type =\n | Unit : exp\n | Var : var -> exp\n | Mult : exp -> exp -> exp\n\nlet rec exp_to_string (e:exp) : string =\n match e with\n | Unit -> \"Unit\"\n | Var x -> \"Var \" ^ string_of_int (x <: var)\n | Mult e1 e2 -> \"Mult (\" ^ exp_to_string e1\n ^ \") (\" ^ exp_to_string e2 ^ \")\"\n\n(***** Expression denotation *)\n\n// Use a map that stores for each variable\n// (1) its denotation that should be treated abstractly (type a) and\n// (2) user-specified extra information depending on its term (type b)\n\nlet vmap (a b:Type) = list (var * (a*b)) * (a * b)\nlet const (#a #b:Type) (xa:a) (xb:b) : vmap a b = [], (xa,xb)\nlet select (#a #b:Type) (x:var) (vm:vmap a b) : Tot a =\n match assoc #var #(a * b) x (fst vm) with\n | Some (a, _) -> a\n | _ -> fst (snd vm)\nlet select_extra (#a #b:Type) (x:var) (vm:vmap a b) : Tot b =\n match assoc #var #(a * b) x (fst vm) with\n | Some (_, b) -> b\n | _ -> snd (snd vm)\nlet update (#a #b:Type) (x:var) (xa:a) (xb:b) (vm:vmap a b) : vmap a b =\n (x, (xa, xb))::fst vm, snd vm\n\nlet rec mdenote (#a #b:Type) (m:cm a) (vm:vmap a b) (e:exp) : Tot a =\n match e with\n | Unit -> CM?.unit m\n | Var x -> select x vm\n | Mult e1 e2 -> CM?.mult m (mdenote m vm e1) (mdenote m vm e2)\n\nlet rec xsdenote (#a #b:Type) (m:cm a) (vm:vmap a b) (xs:list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | [x] -> select x vm\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')\n\n(***** Flattening expressions to lists of variables *)\n\nlet rec flatten (e:exp) : list var =\n match e with\n | Unit -> []\n | Var x -> [x]\n | Mult e1 e2 -> flatten e1 @ flatten e2\n\nlet rec flatten_correct_aux (#a #b:Type) (m:cm a) (vm:vmap a b)\n (xs1 xs2:list var) :\n Lemma (xsdenote m vm (xs1 @ xs2) == CM?.mult m (xsdenote m vm xs1)\n (xsdenote m vm xs2)) =\n match xs1 with\n | [] -> CM?.identity m (xsdenote m vm xs2)\n | [x] -> if (Nil? xs2) then right_identity m (select x vm)\n | x::xs1' -> (CM?.associativity m (select x vm)\n (xsdenote m vm xs1') (xsdenote m vm xs2);\n flatten_correct_aux m vm xs1' xs2)\n\nlet rec flatten_correct (#a #b:Type) (m:cm a) (vm:vmap a b) (e:exp) :\n Lemma (mdenote m vm e == xsdenote m vm (flatten e)) =\n match e with\n | Unit | Var _ -> ()\n | Mult e1 e2 -> flatten_correct_aux m vm (flatten e1) (flatten e2);\n flatten_correct m vm e1; flatten_correct m vm e2\n\n(***** Permuting the lists of variables\n by swapping adjacent elements *)\n\n(* The user has control over the permutation. He can store extra\n information in the vmap and use that for choosing the\n permutation. This means that permute has access to the vmap. *)\n\nlet permute (b:Type) = a:Type -> vmap a b -> list var -> list var\n\n// high-level correctness criterion for permutations\nlet permute_correct (#b:Type) (p:permute b) =\n #a:Type -> m:cm a -> vm:vmap a b -> xs:list var ->\n Lemma (xsdenote m vm xs == xsdenote m vm (p a vm xs))\n\n// sufficient condition:\n// permutation has to be expressible as swaps of adjacent list elements\n", "sketch": [ "Step 1: Perform case analysis on the swap `s`. The swap can either be `SwapNil` or `SwapCons`.\nStep 2: If `s` is `SwapNil`, then the swap does nothing, and the lemma holds trivially.\nStep 3: If `s` is `SwapCons`, then we need to show that swapping two adjacent elements in the list `xs` preserves the denotation.\nStep 4: Use the associativity and commutativity properties of the commutative monoid to show that swapping two adjacent elements does not change the denotation.\nStep 5: Recursively apply the lemma to the rest of the swaps in `s`.", "Step 1: Perform induction on the natural number `n`.\nStep 2: In the base case where `n` is 0, show that applying the swap does not change the list.\nStep 3: In the inductive step, assume the lemma holds for `n` and prove it for `n + 1`.\nStep 4: Use the properties of `swap` and `apply_swap_aux` to show that the denotation remains the same after applying the swap.\nStep 5: Conclude the proof by combining the induction hypothesis and the properties of the commutative monoid.", "Step 1: Perform induction on the list `xs`.\nStep 2: For the base case, when `xs` is an empty list, show that both sides of the equality reduce to the unit element of the commutative monoid.\nStep 3: For the inductive case, assume the lemma holds for a list `xs'` and show it holds for `x::xs'`.\nStep 4: Use the properties of the commutative monoid (associativity, identity) to manipulate the expressions and show the equality holds.", "Step 1: Perform induction on the list `xs`. The base case is when `xs` is an empty list.\nStep 2: For the base case, show that `xsdenote m vm []` is equal to `xsdenote m vm (apply_swap_aux n [] s)`.\nStep 3: For the inductive case, assume the lemma holds for a list `xs'` and prove it for `x::xs'`.\nStep 4: Use the properties of `xsdenote` and `apply_swap_aux` to show that the equality holds after applying the swap.", "Step 1: Perform induction on the natural number `n`.\nStep 2: In the base case where `n` is 0, show that `apply_swap_aux 0 xs s` is equivalent to `xs`.\nStep 3: In the inductive case, assume the lemma holds for `n` and prove it for `n + 1`.\nStep 4: Use the properties of the commutative monoid and the definition of `apply_swap_aux` to show that swapping elements preserves the denotation.", "Step 1: Perform induction on the list `xs`.\nStep 2: For the base case where `xs` is empty, show that both sides of the equality reduce to the unit element of the commutative monoid.\nStep 3: For the inductive case where `xs` is non-empty, consider the head `x` and the tail `xs'` of the list `xs`.\nStep 4: Apply the induction hypothesis to the tail `xs'`.\nStep 5: Use the properties of the commutative monoid (associativity, identity) to show that the equality holds after applying the swap.", "Step 1: Perform induction on the list `xs`.\nStep 2: For the base case where `xs` is empty, show that both sides of the equality are equal to the unit element of the commutative monoid.\nStep 3: For the inductive case where `xs` is non-empty, decompose `xs` into its head and tail.\nStep 4: Apply the induction hypothesis to the tail of the list.\nStep 5: Use the properties of the commutative monoid (associativity, identity) to show that the equality holds after applying the swap.", "Step 1: Perform induction on the natural number `n`.\nStep 2: In the base case where `n` is 0, the swap is applied directly to the list `xs`.\nStep 3: Prove that applying the swap directly to `xs` preserves the denotation.\nStep 4: In the inductive case, assume the lemma holds for `n` and prove it for `n + 1`.\nStep 5: Show that applying the swap to the list `xs` with `n + 1` elements preserves the denotation by leveraging the inductive hypothesis.", "Step 1: We perform induction on the list `xs`. The base case is when `xs` is empty.\nStep 2: For the base case, `xs` is `[]`. We need to show that `xsdenote m vm [] == xsdenote m vm (apply_swap_aux n [] s)`. Since both sides denote the unit element of the monoid, this holds trivially.\nStep 3: For the inductive case, assume the lemma holds for a list `xs`. We need to show it holds for `x::xs`.\nStep 4: We consider the structure of the swap `s`. If `s` is a swap that does not affect the first element, we can apply the induction hypothesis directly.\nStep 5: If `s` is a swap that affects the first element, we need to show that swapping the first element with the next one and then applying the induction hypothesis still preserves the denotation.", "Step 1: Perform case analysis on the swap `s`. The swap can either be `Swap i j` or `Id`.\nStep 2: If `s` is `Id`, then the list remains unchanged, and the lemma holds trivially.\nStep 3: If `s` is `Swap i j`, then we need to show that swapping elements at positions `i` and `j` in the list does not change the denotation.\nStep 4: Use the properties of the commutative monoid to show that the order of multiplication does not affect the result.\nStep 5: Conclude the proof by combining the results of the case analysis." ], "generated_solution": [ "match s with\n| SwapNil -> ()\n| SwapCons i j s' ->\n let xs' = swap i j xs in\n let H = flatten_correct_aux m vm (take i xs) (drop (i + 2) xs) in\n let H' = flatten_correct_aux m vm (take i xs') (drop (i + 2) xs') in\n assert (xsdenote m vm xs == xsdenote m vm xs');\n apply_swap_aux_correct n m vm xs' s'", "let rec apply_swap_aux_correct (#a #b: Type) (n: nat) (m: cm a) (vm: vmap a b) (xs: list var) (s: swap (length xs + n)) : Lemma (requires True) (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s))) (decreases xs) =\n match n with\n | 0 -> \n // Base case: when n is 0, applying the swap does not change the list\n ()\n | n' -> \n // Inductive step: assume the lemma holds for n', prove it for n' + 1\n let _ = apply_swap_aux_correct n' m vm xs s in\n // Use properties of swap and apply_swap_aux to show denotation remains the same\n ()", "let rec apply_swap_aux_correct (#a #b: Type) (n: nat) (m: cm a) (vm: vmap a b) (xs: list var) (s: swap (length xs + n)) : Lemma (requires True) (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s))) (decreases xs) =\n match xs with\n | [] -> CM?.identity m (xsdenote m vm [])\n | x::xs' ->\n let IH = apply_swap_aux_correct n m vm xs' s in\n CM?.associativity m (select x vm) (xsdenote m vm xs') (xsdenote m vm (apply_swap_aux n xs' s));\n IH", "let rec apply_swap_aux_correct\n (#a #b: Type)\n (n: nat)\n (m: cm a)\n (vm: vmap a b)\n (xs: list var)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] -> ()\n | x::xs' ->\n let IH = apply_swap_aux_correct n m vm xs' s in\n // Use the properties of xsdenote and apply_swap_aux\n // to show that the equality holds after applying the swap\n ()", "let rec apply_swap_aux_correct (#a #b: Type) (n: nat) (m: cm a) (vm: vmap a b) (xs: list var) (s: swap (length xs + n)) : Lemma (requires True) (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s))) (decreases xs) =\n match n with\n | 0 -> \n // Base case: n = 0\n // apply_swap_aux 0 xs s should be equivalent to xs\n ()\n | _ -> \n // Inductive case: assume the lemma holds for n, prove for n + 1\n let n' = n - 1 in\n apply_swap_aux_correct n' m vm xs s;\n // Use properties of the commutative monoid and apply_swap_aux definition\n // to show that swapping elements preserves the denotation\n ()", "let rec apply_swap_aux_correct\n (#a #b: Type)\n (n: nat)\n (m: cm a)\n (vm: vmap a b)\n (xs: list var)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] -> ()\n | x::xs' ->\n let _ = apply_swap_aux_correct n m vm xs' s in\n // Use properties of the commutative monoid to show the equality\n ()", "let rec apply_swap_aux_correct\n (#a #b: Type)\n (n: nat)\n (m: cm a)\n (vm: vmap a b)\n (xs: list var)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] -> ()\n | x::xs' ->\n let IH = apply_swap_aux_correct n m vm xs' s in\n // Use the induction hypothesis and properties of the commutative monoid\n ()", "let rec apply_swap_aux_correct\n (#a #b: Type)\n (n: nat)\n (m: cm a)\n (vm: vmap a b)\n (xs: list var)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s)))\n (decreases xs) =\n match n with\n | 0 ->\n // Base case: n = 0\n // Applying the swap directly to xs\n ()\n | n' ->\n // Inductive case: assume the lemma holds for n', prove for n' + 1\n // Apply the inductive hypothesis\n apply_swap_aux_correct n' m vm xs s", "let rec apply_swap_aux_correct\n (#a #b: Type)\n (n: nat)\n (m: cm a)\n (vm: vmap a b)\n (xs: list var)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] -> ()\n | x::xs' ->\n match s with\n | Swap i j when i == 0 && j == 1 ->\n let swapped_xs = swap_adjacent xs in\n CM?.commutativity m (select x vm) (xsdenote m vm xs');\n apply_swap_aux_correct n m vm xs' (shift_swap 1 s)\n | _ ->\n apply_swap_aux_correct n m vm xs' (shift_swap 1 s)", "let rec apply_swap_aux_correct (#a #b: Type) (n: nat) (m: cm a) (vm: vmap a b) (xs: list var) (s: swap (length xs + n)) : Lemma (requires True) (ensures (xsdenote m vm xs == xsdenote m vm (apply_swap_aux n xs s))) (decreases xs) =\n match s with\n | Id -> ()\n | Swap i j ->\n let xi = nth xs i in\n let xj = nth xs j in\n let xs' = update_nth i xj (update_nth j xi xs) in\n assert (xsdenote m vm xs == xsdenote m vm xs');\n xsdenote_comm m vm xs i j;\n apply_swap_aux_correct n m vm xs' Id" ] }, { "file_name": "Hacl.K256.ECDSA.fst", "name": "Hacl.K256.ECDSA.secp256k1_ecdsa_sign_hashed_msg", "opens_and_abbrevs": [ { "open": "Hacl.K256.Scalar" }, { "open": "Hacl.K256.Field" }, { "abbrev": "VK", "full_module": "Hacl.Impl.K256.Verify" }, { "abbrev": "SK", "full_module": "Hacl.Impl.K256.Sign" }, { "abbrev": "P", "full_module": "Hacl.Impl.K256.Point" }, { "abbrev": "BDL", "full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas" }, { "abbrev": "S", "full_module": "Spec.K256" }, { "abbrev": "BSeq", "full_module": "Lib.ByteSequence" }, { "abbrev": "LSeq", "full_module": "Lib.Sequence" }, { "abbrev": "ST", "full_module": "FStar.HyperStack.ST" }, { "open": "Lib.Buffer" }, { "open": "Lib.IntTypes" }, { "open": "FStar.Mul" }, { "open": "FStar.HyperStack.ST" }, { "open": "FStar.HyperStack" }, { "abbrev": "BSeq", "full_module": "Lib.ByteSequence" }, { "abbrev": "S", "full_module": "Spec.K256" }, { "open": "Lib.Buffer" }, { "open": "Lib.IntTypes" }, { "open": "FStar.Mul" }, { "open": "FStar.HyperStack.ST" }, { "open": "FStar.HyperStack" }, { "open": "Hacl.K256" }, { "open": "Hacl.K256" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 0, "max_fuel": 0, "initial_ifuel": 0, "max_ifuel": 0, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val secp256k1_ecdsa_sign_hashed_msg (signature:lbytes 64ul)\n (msgHash private_key nonce:lbytes 32ul) : Stack bool\n (requires fun h ->\n live h msgHash /\\ live h private_key /\\ live h nonce /\\ live h signature /\\\n disjoint signature msgHash /\\ disjoint signature private_key /\\ disjoint signature nonce)\n (ensures fun h0 b h1 -> modifies (loc signature) h0 h1 /\\\n (let sgnt = S.secp256k1_ecdsa_sign_hashed_msg (as_seq h0 msgHash) (as_seq h0 private_key) (as_seq h0 nonce) in\n (b <==> Some? sgnt) /\\ (b ==> (as_seq h1 signature == Some?.v sgnt))))", "source_definition": "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n let b = ecdsa_sign_hashed_msg signature msgHash private_key nonce in\n if b then secp256k1_ecdsa_signature_normalize signature else false", "source_range": { "start_line": 83, "start_col": 0, "end_line": 85, "end_col": 68 }, "interleaved": false, "definition": "fun signature msgHash private_key nonce ->\n let b = Hacl.K256.ECDSA.ecdsa_sign_hashed_msg signature msgHash private_key nonce in\n (match b with\n | true -> Hacl.K256.ECDSA.secp256k1_ecdsa_signature_normalize signature\n | _ -> false)\n <:\n Prims.bool", "effect": "FStar.HyperStack.ST.Stack", "effect_flags": [], "mutual_with": [], "premises": [ "Hacl.K256.ECDSA.lbytes", "FStar.UInt32.__uint_to_t", "Hacl.K256.ECDSA.secp256k1_ecdsa_signature_normalize", "Prims.bool", "Hacl.K256.ECDSA.ecdsa_sign_hashed_msg" ], "proof_features": [], "is_simple_lemma": false, "is_div": true, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "\n signature: Hacl.K256.ECDSA.lbytes 64ul ->\n msgHash: Hacl.K256.ECDSA.lbytes 32ul ->\n private_key: Hacl.K256.ECDSA.lbytes 32ul ->\n nonce: Hacl.K256.ECDSA.lbytes 32ul\n -> FStar.HyperStack.ST.Stack Prims.bool", "prompt": "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n ", "expected_response": "let b = ecdsa_sign_hashed_msg signature msgHash private_key nonce in\nif b then secp256k1_ecdsa_signature_normalize signature else false", "source": { "project_name": "hacl-star", "file_name": "code/k256/Hacl.K256.ECDSA.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Hacl.K256.ECDSA.fst", "checked_file": "dataset/Hacl.K256.ECDSA.fst.checked", "interface_file": true, "dependencies": [ "dataset/Spec.K256.fst.checked", "dataset/prims.fst.checked", "dataset/Lib.Sequence.fsti.checked", "dataset/Lib.RawIntTypes.fsti.checked", "dataset/Lib.IntTypes.fsti.checked", "dataset/Lib.ByteSequence.fsti.checked", "dataset/Lib.Buffer.fsti.checked", "dataset/Hacl.Streaming.SHA2.fst.checked", "dataset/Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked", "dataset/Hacl.K256.Scalar.fsti.checked", "dataset/Hacl.K256.Field.fsti.checked", "dataset/Hacl.Impl.K256.Verify.fst.checked", "dataset/Hacl.Impl.K256.Sign.fst.checked", "dataset/Hacl.Impl.K256.PointMul.fsti.checked", "dataset/Hacl.Impl.K256.Point.fsti.checked", "dataset/Hacl.Bignum.Base.fst.checked", "dataset/FStar.UInt8.fsti.checked", "dataset/FStar.UInt32.fsti.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked", "dataset/FStar.HyperStack.ST.fsti.checked", "dataset/FStar.HyperStack.fst.checked" ] }, "definitions_in_context": [ "let lbytes len = lbuffer uint8 len", "let ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n SK.ecdsa_sign_hashed_msg signature msgHash private_key nonce", "let ecdsa_sign_sha256 signature msg_len msg private_key nonce =\n push_frame ();\n let msgHash = create 32ul (u8 0) in\n Hacl.Streaming.SHA2.hash_256 msgHash msg msg_len;\n let b = ecdsa_sign_hashed_msg signature msgHash private_key nonce in\n pop_frame ();\n b", "let ecdsa_verify_hashed_msg m public_key signature =\n VK.ecdsa_verify_hashed_msg m public_key signature", "let ecdsa_verify_sha256 msg_len msg public_key signature =\n push_frame ();\n let mHash = create 32ul (u8 0) in\n Hacl.Streaming.SHA2.hash_256 mHash msg msg_len;\n let b = ecdsa_verify_hashed_msg mHash public_key signature in\n pop_frame ();\n b", "val ecdsa_sign_hashed_msg (signature:lbytes 64ul)\n (msgHash private_key nonce:lbytes 32ul) : Stack bool\n (requires fun h ->\n live h msgHash /\\ live h private_key /\\ live h nonce /\\ live h signature /\\\n disjoint signature msgHash /\\ disjoint signature private_key /\\ disjoint signature nonce)\n (ensures fun h0 b h1 -> modifies (loc signature) h0 h1 /\\\n (let sgnt = S.ecdsa_sign_hashed_msg (as_seq h0 msgHash) (as_seq h0 private_key) (as_seq h0 nonce) in\n (b <==> Some? sgnt) /\\ (b ==> (as_seq h1 signature == Some?.v sgnt))))", "let secp256k1_ecdsa_signature_normalize signature =\n push_frame ();\n let s_q = create_qelem () in\n let s = sub signature 32ul 32ul in\n let is_sk_valid = load_qelem_vartime s_q s in\n let b =\n if not is_sk_valid then false\n else begin\n let is_sk_lt_q_halved = is_qelem_le_q_halved_vartime s_q in\n qnegate_conditional_vartime s_q (not is_sk_lt_q_halved);\n\n let h1 = ST.get () in\n update_sub_f h1 signature 32ul 32ul\n (fun h -> BSeq.nat_to_bytes_be 32 (qas_nat h1 s_q))\n (fun _ -> store_qelem (sub signature 32ul 32ul) s_q);\n true end in\n pop_frame ();\n b", "val ecdsa_sign_sha256 (signature:lbytes 64ul)\n (msg_len:size_t) (msg:lbytes msg_len) (private_key nonce:lbytes 32ul) : Stack bool\n (requires fun h ->\n live h msg /\\ live h private_key /\\ live h nonce /\\ live h signature /\\\n disjoint signature msg /\\ disjoint signature private_key /\\ disjoint signature nonce)\n (ensures fun h0 b h1 -> modifies (loc signature) h0 h1 /\\\n (let sgnt = S.ecdsa_sign_sha256 (v msg_len) (as_seq h0 msg) (as_seq h0 private_key) (as_seq h0 nonce) in\n (b <==> Some? sgnt) /\\ (b ==> (as_seq h1 signature == Some?.v sgnt))))", "let secp256k1_ecdsa_is_signature_normalized signature =\n push_frame ();\n let s_q = create_qelem () in\n let s = sub signature 32ul 32ul in\n let is_s_valid = load_qelem_vartime s_q s in\n let is_s_lt_q_halved = is_qelem_le_q_halved_vartime s_q in\n pop_frame ();\n is_s_valid && is_s_lt_q_halved" ], "closest": [ "val ecdsa_sign_hashed_msg (signature:lbytes 64ul) (msgHash private_key nonce:lbytes 32ul) : Stack bool\n (requires fun h ->\n live h msgHash /\\ live h private_key /\\ live h nonce /\\ live h signature /\\\n disjoint signature msgHash /\\ disjoint signature private_key /\\ disjoint signature nonce)\n (ensures fun h0 b h1 -> modifies (loc signature) h0 h1 /\\\n (let sgnt = S.ecdsa_sign_hashed_msg (as_seq h0 msgHash) (as_seq h0 private_key) (as_seq h0 nonce) in\n (b <==> Some? sgnt) /\\ (b ==> (as_seq h1 signature == Some?.v sgnt))))\nlet ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n push_frame ();\n let oneq = create_one () in\n let rsdk_q = create 16ul (u64 0) in\n let r_q = sub rsdk_q 0ul 4ul in\n let s_q = sub rsdk_q 4ul 4ul in\n let d_a = sub rsdk_q 8ul 4ul in\n let k_q = sub rsdk_q 12ul 4ul in\n\n let are_sk_nonce_valid = ecdsa_sign_load d_a k_q private_key nonce in\n ecdsa_sign_r r_q k_q;\n ecdsa_sign_s s_q k_q r_q d_a msgHash;\n ecdsa_sign_store signature r_q s_q;\n let res = check_signature are_sk_nonce_valid r_q s_q in\n pop_frame ();\n res", "val ecdsa_verify_hashed_msg (msgHash:lbytes 32ul)\n (public_key signature:lbytes 64ul) : Stack bool\n (requires fun h ->\n live h msgHash /\\ live h public_key /\\ live h signature)\n (ensures fun h0 b h1 -> modifies0 h0 h1 /\\\n b == S.ecdsa_verify_hashed_msg (as_seq h0 msgHash) (as_seq h0 public_key) (as_seq h0 signature))\nlet ecdsa_verify_hashed_msg msgHash public_key signature =\n push_frame ();\n let tmp = create 35ul (u64 0) in\n let pk = sub tmp 0ul 15ul in\n let r_q = sub tmp 15ul 4ul in\n let s_q = sub tmp 19ul 4ul in\n let u1 = sub tmp 23ul 4ul in\n let u2 = sub tmp 27ul 4ul in\n let m_q = sub tmp 31ul 4ul in\n\n let is_pk_valid = load_point_vartime pk public_key in\n let is_rs_valid = load_signature r_q s_q signature in\n QA.load_qelem_modq m_q msgHash;\n\n let res =\n if not (is_pk_valid && is_rs_valid) then false\n else begin\n ecdsa_verify_get_u12 u1 u2 r_q s_q m_q;\n ecdsa_verify_cmpr r_q pk u1 u2 end in\n pop_frame ();\n res", "val test_sign_hashed:\n msgHash:lbuffer uint8 32ul\n -> sk:lbuffer uint8 32ul\n -> nonce:lbuffer uint8 32ul\n -> expected_sgnt:lbuffer uint8 64ul\n -> Stack unit\n (requires fun h ->\n live h msgHash /\\ live h sk /\\ live h nonce /\\ live h expected_sgnt)\n (ensures fun h0 r h1 -> modifies0 h0 h1)\nlet test_sign_hashed msgHash sk nonce expected_sgnt =\n push_frame ();\n let sgnt = create 64ul (u8 0) in\n let _ = K256.ecdsa_sign_hashed_msg sgnt msgHash sk nonce in\n\n C.String.print (C.String.of_literal \"\\n Test K256 ecdsa signing:\\n\");\n if not (result_compare_display 64ul (to_const sgnt) (to_const expected_sgnt)) then C.exit 255l;\n pop_frame ()", "val secp256k1_ecdsa_sign_hashed_msg (msgHash private_key nonce: lbytes 32) : option (lbytes 64)\nlet secp256k1_ecdsa_sign_hashed_msg (msgHash private_key nonce:lbytes 32) : option (lbytes 64) =\n let signature = ecdsa_sign_hashed_msg msgHash private_key nonce in\n match signature with\n | Some x -> secp256k1_ecdsa_signature_normalize x\n | None -> None", "val sign:\n signature:lbuffer uint8 64ul\n -> private_key:lbuffer uint8 32ul\n -> msg_len:size_t\n -> msg:lbuffer uint8 msg_len ->\n Stack unit\n (requires fun h ->\n live h signature /\\ live h msg /\\ live h private_key /\\\n disjoint signature msg /\\ disjoint signature private_key)\n (ensures fun h0 _ h1 -> modifies (loc signature) h0 h1 /\\\n as_seq h1 signature == Spec.Ed25519.sign (as_seq h0 private_key) (as_seq h0 msg))\nlet sign signature private_key msg_len msg =\n Hacl.Ed25519.sign signature private_key msg_len msg", "val sign:\n signature:lbuffer uint8 64ul\n -> private_key:lbuffer uint8 32ul\n -> msg_len:size_t\n -> msg:lbuffer uint8 msg_len ->\n Stack unit\n (requires fun h ->\n live h signature /\\ live h msg /\\ live h private_key /\\\n disjoint signature msg /\\ disjoint signature private_key)\n (ensures fun h0 _ h1 -> modifies (loc signature) h0 h1 /\\\n as_seq h1 signature == Spec.Ed25519.sign (as_seq h0 private_key) (as_seq h0 msg))\nlet sign signature private_key msg_len msg =\n push_frame ();\n let expanded_keys = create 96ul (u8 0) in\n expand_keys expanded_keys private_key;\n sign_expanded signature expanded_keys msg_len msg;\n pop_frame ()", "val ecdsa_sign_msg_as_qelem:\n signature:lbuffer uint8 64ul\n -> m_q:felem\n -> private_key:lbuffer uint8 32ul\n -> nonce:lbuffer uint8 32ul ->\n Stack bool\n (requires fun h ->\n live h signature /\\ live h m_q /\\ live h private_key /\\ live h nonce /\\\n disjoint signature m_q /\\ disjoint signature private_key /\\ disjoint signature nonce /\\\n disjoint m_q private_key /\\ disjoint m_q nonce /\\\n as_nat h m_q < S.order)\n (ensures fun h0 flag h1 -> modifies (loc signature |+| loc m_q) h0 h1 /\\\n (let sgnt = S.ecdsa_sign_msg_as_qelem\n (as_nat h0 m_q) (as_seq h0 private_key) (as_seq h0 nonce) in\n (flag <==> Some? sgnt) /\\ (flag ==> (as_seq h1 signature == Some?.v sgnt))))\nlet ecdsa_sign_msg_as_qelem signature m_q private_key nonce =\n push_frame ();\n let rsdk_q = create 16ul (u64 0) in\n let r_q = sub rsdk_q 0ul 4ul in\n let s_q = sub rsdk_q 4ul 4ul in\n let d_a = sub rsdk_q 8ul 4ul in\n let k_q = sub rsdk_q 12ul 4ul in\n let are_sk_nonce_valid = ecdsa_sign_load d_a k_q private_key nonce in\n ecdsa_sign_r r_q k_q;\n ecdsa_sign_s s_q k_q r_q d_a m_q;\n bn2_to_bytes_be4 signature r_q s_q;\n let res = check_signature are_sk_nonce_valid r_q s_q in\n pop_frame ();\n res", "val test_sign_and_verify_hashed:\n msgHash:lbuffer uint8 32ul\n -> sk:lbuffer uint8 32ul\n -> nonce:lbuffer uint8 32ul\n -> pk:lbuffer uint8 64ul\n -> expected_sgnt:lbuffer uint8 64ul\n -> Stack unit\n (requires fun h ->\n live h msgHash /\\ live h sk /\\ live h nonce /\\\n live h pk /\\ live h expected_sgnt)\n (ensures fun h0 r h1 -> modifies0 h0 h1)\nlet test_sign_and_verify_hashed msgHash sk nonce pk expected_sgnt =\n test_verify_hashed msgHash pk expected_sgnt;\n test_sign_hashed msgHash sk nonce expected_sgnt", "val ecdsa_sign_hashed_msg (msgHash private_key nonce: lbytes 32) : option (lbytes 64)\nlet ecdsa_sign_hashed_msg (msgHash private_key nonce:lbytes 32) : option (lbytes 64) =\n let k_q = nat_from_bytes_be nonce in\n let d_a = nat_from_bytes_be private_key in\n let z = nat_from_bytes_be msgHash % q in\n\n let is_privkey_valid = 0 < d_a && d_a < q in\n let is_nonce_valid = 0 < k_q && k_q < q in\n\n if not (is_privkey_valid && is_nonce_valid) then None\n else begin\n let _X, _Y, _Z = point_mul_g k_q in\n let x = _X /% _Z in\n let r = x % q in\n\n let kinv = qinv k_q in\n let s = kinv *^ (z +^ r *^ d_a) in\n\n let rb = nat_to_bytes_be 32 r in\n let sb = nat_to_bytes_be 32 s in\n\n if r = 0 || s = 0 then None else Some (concat #_ #32 #32 rb sb) end", "val secp256k1_ecdsa_sign_sha256\n (msg_len: size_nat)\n (msg: lbytes msg_len)\n (private_key nonce: lbytes 32)\n : option (lbytes 64)\nlet secp256k1_ecdsa_sign_sha256 (msg_len:size_nat) (msg:lbytes msg_len) (private_key nonce:lbytes 32) : option (lbytes 64) =\n let msgHash = Spec.Agile.Hash.hash Spec.Hash.Definitions.SHA2_256 msg in\n secp256k1_ecdsa_sign_hashed_msg msgHash private_key nonce", "val test_verify_hashed:\n msgHash:lbuffer uint8 32ul\n -> pk:lbuffer uint8 64ul\n -> sgnt:lbuffer uint8 64ul\n -> Stack unit\n (requires fun h -> live h msgHash /\\ live h pk /\\ live h sgnt)\n (ensures fun h0 r h1 -> modifies0 h0 h1)\nlet test_verify_hashed msgHash pk sgnt =\n let b = K256.ecdsa_verify_hashed_msg msgHash pk sgnt in\n\n C.String.print (C.String.of_literal \"\\n Test K256 ecdsa verification: \");\n if b then C.String.print (C.String.of_literal \"Success!\\n\")\n else (C.String.print (C.String.of_literal \"Failure :(\\n\"); C.exit 255l)", "val secp256k1_ecdsa_verify_hashed_msg (msgHash: lbytes 32) (public_key signature: lbytes 64) : bool\nlet secp256k1_ecdsa_verify_hashed_msg (msgHash:lbytes 32) (public_key signature:lbytes 64) : bool =\n if not (secp256k1_ecdsa_is_signature_normalized signature) then false\n else ecdsa_verify_hashed_msg msgHash public_key signature", "val verify:\n public_key:lbuffer uint8 32ul\n -> msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> signature:lbuffer uint8 64ul ->\n Stack bool\n (requires fun h -> live h public_key /\\ live h msg /\\ live h signature)\n (ensures fun h0 b h1 -> modifies0 h0 h1 /\\\n b == Spec.Ed25519.verify (as_seq h0 public_key) (as_seq h0 msg) (as_seq h0 signature))\nlet verify public_key msg_len msg signature =\n Hacl.Ed25519.verify public_key msg_len msg signature", "val verify:\n public_key:lbuffer uint8 32ul\n -> msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> signature:lbuffer uint8 64ul ->\n Stack bool\n (requires fun h -> live h public_key /\\ live h msg /\\ live h signature)\n (ensures fun h0 b h1 -> modifies0 h0 h1 /\\\n b == Spec.Ed25519.verify (as_seq h0 public_key) (as_seq h0 msg) (as_seq h0 signature))\nlet verify public_key msg_len msg signature =\n Hacl.Impl.Ed25519.Verify.verify public_key msg_len msg signature", "val ecdsa_verify_hashed_msg (msgHash: lbytes 32) (public_key signature: lbytes 64) : bool\nlet ecdsa_verify_hashed_msg (msgHash:lbytes 32) (public_key signature:lbytes 64) : bool =\n let pk = load_point public_key in\n let r = nat_from_bytes_be (sub signature 0 32) in\n let s = nat_from_bytes_be (sub signature 32 32) in\n let z = nat_from_bytes_be msgHash % q in\n\n let is_r_valid = 0 < r && r < q in\n let is_s_valid = 0 < s && s < q in\n\n if not (Some? pk && is_r_valid && is_s_valid) then false\n else begin\n assert_norm (q < pow2 256);\n let sinv = qinv s in\n let u1 = z *^ sinv in\n let u2 = r *^ sinv in\n let _X, _Y, _Z = point_mul_double_g u1 u2 (Some?.v pk) in\n\n if is_proj_point_at_inf (_X, _Y, _Z) then false\n else begin\n let x = _X /% _Z in\n x % q = r end\n end", "val ecdsa_sign_sha256 (msg_len: size_nat) (msg: lbytes msg_len) (private_key nonce: lbytes 32)\n : option (lbytes 64)\nlet ecdsa_sign_sha256 (msg_len:size_nat) (msg:lbytes msg_len) (private_key nonce:lbytes 32) : option (lbytes 64) =\n let msgHash = Spec.Agile.Hash.hash Spec.Hash.Definitions.SHA2_256 msg in\n ecdsa_sign_hashed_msg msgHash private_key nonce", "val verify:\n public_key:lbuffer uint8 32ul\n -> msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> signature:lbuffer uint8 64ul ->\n Stack bool\n (requires fun h ->\n live h public_key /\\ live h msg /\\ live h signature)\n (ensures fun h0 z h1 -> modifies0 h0 h1 /\\\n z == Spec.Ed25519.verify (as_seq h0 public_key) (as_seq h0 msg) (as_seq h0 signature))\nlet verify public_key msg_len msg signature =\n push_frame ();\n let a' = create 20ul (u64 0) in\n let h0 = ST.get () in\n Spec.Ed25519.Lemmas.point_decompress_lemma (as_seq h0 public_key);\n let b = Hacl.Impl.Ed25519.PointDecompress.point_decompress a' public_key in\n let res = if b then verify_valid_pk public_key msg_len msg signature a' else false in\n pop_frame ();\n res", "val test_verify_sha256:\n msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> pk:lbuffer uint8 64ul\n -> sgnt:lbuffer uint8 64ul\n -> Stack unit\n (requires fun h -> live h msg /\\ live h pk /\\ live h sgnt)\n (ensures fun h0 r h1 -> modifies0 h0 h1)\nlet test_verify_sha256 msg_len msg pk sgnt =\n let b = K256.ecdsa_verify_sha256 msg_len msg pk sgnt in\n\n C.String.print (C.String.of_literal \"\\n Test K256 ecdsa verification: \");\n if b then C.String.print (C.String.of_literal \"Success!\\n\")\n else (C.String.print (C.String.of_literal \"Failure :(\\n\"); C.exit 255l)", "val sign_expanded:\n signature:lbuffer uint8 64ul\n -> expanded_keys:lbuffer uint8 96ul\n -> msg_len:size_t\n -> msg:lbuffer uint8 msg_len ->\n Stack unit\n (requires fun h ->\n live h signature /\\ live h msg /\\ live h expanded_keys /\\\n disjoint signature msg /\\ disjoint signature expanded_keys)\n (ensures fun h0 _ h1 -> modifies (loc signature) h0 h1 /\\\n as_seq h1 signature == Spec.Ed25519.sign_expanded\n (as_seq h0 (gsub expanded_keys 0ul 32ul))\n (as_seq h0 (gsub expanded_keys 32ul 32ul))\n (as_seq h0 (gsub expanded_keys 64ul 32ul))\n (as_seq h0 msg))\nlet sign_expanded signature expanded_keys msg_len msg =\n Hacl.Ed25519.sign_expanded signature expanded_keys msg_len msg", "val sign_expanded:\n signature:lbuffer uint8 64ul\n -> expanded_keys:lbuffer uint8 96ul\n -> msg_len:size_t\n -> msg:lbuffer uint8 msg_len ->\n Stack unit\n (requires fun h ->\n live h signature /\\ live h msg /\\ live h expanded_keys /\\\n disjoint signature msg /\\ disjoint signature expanded_keys)\n (ensures fun h0 _ h1 -> modifies (loc signature) h0 h1 /\\\n as_seq h1 signature == Spec.Ed25519.sign_expanded\n (as_seq h0 (gsub expanded_keys 0ul 32ul))\n (as_seq h0 (gsub expanded_keys 32ul 32ul))\n (as_seq h0 (gsub expanded_keys 64ul 32ul))\n (as_seq h0 msg))\nlet sign_expanded signature expanded_keys msg_len msg =\n Hacl.Impl.Ed25519.Sign.sign_expanded signature expanded_keys msg_len msg", "val sign_expanded:\n signature:lbuffer uint8 64ul\n -> expanded_keys:lbuffer uint8 96ul\n -> msg_len:size_t\n -> msg:lbuffer uint8 msg_len ->\n Stack unit\n (requires fun h ->\n live h signature /\\ live h msg /\\ live h expanded_keys /\\\n disjoint signature msg /\\ disjoint signature expanded_keys)\n (ensures fun h0 _ h1 -> modifies (loc signature) h0 h1 /\\\n as_seq h1 signature == Spec.Ed25519.sign_expanded\n (as_seq h0 (gsub expanded_keys 0ul 32ul))\n (as_seq h0 (gsub expanded_keys 32ul 32ul))\n (as_seq h0 (gsub expanded_keys 64ul 32ul))\n (as_seq h0 msg))\nlet sign_expanded signature expanded_keys msg_len msg =\n push_frame ();\n let rs = sub signature 0ul 32ul in\n let ss = sub signature 32ul 32ul in\n\n let rq = create 5ul (u64 0) in\n let hq = create 5ul (u64 0) in\n let rb = create 32ul (u8 0) in\n\n // expanded_keys = [ public_key; s; prefix ]\n let public_key = sub expanded_keys 0ul 32ul in\n let s = sub expanded_keys 32ul 32ul in\n let prefix = sub expanded_keys 64ul 32ul in\n\n Hacl.Impl.SHA512.ModQ.store_sha512_modq_pre rb rq prefix msg_len msg;\n point_mul_g_compress rs rb;\n Hacl.Impl.SHA512.ModQ.sha512_modq_pre_pre2 hq rs public_key msg_len msg;\n sign_compute_s rq hq s ss;\n let h1 = ST.get () in\n LSeq.eq_intro (as_seq h1 signature)\n (Spec.Ed25519.sign_expanded (as_seq h1 public_key) (as_seq h1 s) (as_seq h1 prefix) (as_seq h1 msg));\n pop_frame ()", "val ecdsa_sign_load (d_a k_q:qelem) (private_key nonce:lbytes 32ul) : Stack uint64\n (requires fun h ->\n live h private_key /\\ live h nonce /\\ live h d_a /\\ live h k_q /\\\n disjoint d_a k_q /\\ disjoint d_a private_key /\\ disjoint d_a nonce /\\\n disjoint k_q private_key /\\ disjoint k_q nonce)\n (ensures fun h0 m h1 -> modifies (loc d_a |+| loc k_q) h0 h1 /\\\n (let d_a_nat = BSeq.nat_from_bytes_be (as_seq h0 private_key) in\n let k_nat = BSeq.nat_from_bytes_be (as_seq h0 nonce) in\n let is_sk_valid = 0 < d_a_nat && d_a_nat < S.q in\n let is_nonce_valid = 0 < k_nat && k_nat < S.q in\n (v m = ones_v U64 \\/ v m = 0) /\\\n (v m = ones_v U64) = (is_sk_valid && is_nonce_valid) /\\\n qas_nat h1 d_a == (if is_sk_valid then d_a_nat else 1) /\\\n qas_nat h1 k_q == (if is_nonce_valid then k_nat else 1)))\nlet ecdsa_sign_load d_a k_q private_key nonce =\n let is_sk_valid = load_qelem_conditional d_a private_key in\n let is_nonce_valid = load_qelem_conditional k_q nonce in\n let m = is_sk_valid &. is_nonce_valid in\n logand_lemma is_sk_valid is_nonce_valid;\n m", "val test_sign:\n msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> sk:lbuffer uint8 32ul\n -> expected_sig:lbuffer uint8 64ul\n -> Stack unit\n (requires fun h ->\n live h msg /\\ live h sk /\\ live h expected_sig)\n (ensures fun h0 r h1 -> modifies0 h0 h1)\nlet test_sign msg_len msg sk expected_sig =\n push_frame ();\n let test_sig = create 64ul (u8 0) in\n Ed25519.sign test_sig sk msg_len msg;\n\n C.String.print (C.String.of_literal \"\\nTest Ed25519 Sign:\\n\");\n if not (result_compare_display 64ul (to_const test_sig) (to_const expected_sig)) then C.exit 255l;\n pop_frame ()", "val ecdsa_verify_msg_as_qelem:\n m_q:felem\n -> public_key:lbuffer uint8 64ul\n -> signature_r:lbuffer uint8 32ul\n -> signature_s:lbuffer uint8 32ul ->\n Stack bool\n (requires fun h ->\n live h public_key /\\ live h signature_r /\\ live h signature_s /\\ live h m_q /\\\n as_nat h m_q < S.order)\n (ensures fun h0 result h1 -> modifies0 h0 h1 /\\\n result == S.ecdsa_verify_msg_as_qelem (as_nat h0 m_q)\n (as_seq h0 public_key) (as_seq h0 signature_r) (as_seq h0 signature_s))\nlet ecdsa_verify_msg_as_qelem m_q public_key signature_r signature_s =\n push_frame ();\n let tmp = create 28ul (u64 0) in\n let pk = sub tmp 0ul 12ul in\n let r_q = sub tmp 12ul 4ul in\n let s_q = sub tmp 16ul 4ul in\n let u1 = sub tmp 20ul 4ul in\n let u2 = sub tmp 24ul 4ul in\n\n let is_pk_valid = load_point_vartime pk public_key in\n let is_rs_valid = load_signature r_q s_q signature_r signature_s in\n\n let res =\n if not (is_pk_valid && is_rs_valid) then false\n else begin\n ecdsa_verification_get_u12 u1 u2 r_q s_q m_q;\n ecdsa_verification_cmpr r_q pk u1 u2 end in\n pop_frame ();\n res", "val ecdsa_sign_load (d_a k_q:felem) (private_key nonce:lbytes 32ul) : Stack uint64\n (requires fun h ->\n live h private_key /\\ live h nonce /\\ live h d_a /\\ live h k_q /\\\n disjoint d_a k_q /\\ disjoint d_a private_key /\\ disjoint d_a nonce /\\\n disjoint k_q private_key /\\ disjoint k_q nonce)\n (ensures fun h0 m h1 -> modifies (loc d_a |+| loc k_q) h0 h1 /\\\n (let d_a_nat = BSeq.nat_from_bytes_be (as_seq h0 private_key) in\n let k_nat = BSeq.nat_from_bytes_be (as_seq h0 nonce) in\n let is_sk_valid = 0 < d_a_nat && d_a_nat < S.order in\n let is_nonce_valid = 0 < k_nat && k_nat < S.order in\n (v m = ones_v U64 \\/ v m = 0) /\\\n (v m = ones_v U64) = (is_sk_valid && is_nonce_valid) /\\\n as_nat h1 d_a == (if is_sk_valid then d_a_nat else 1) /\\\n as_nat h1 k_q == (if is_nonce_valid then k_nat else 1)))\nlet ecdsa_sign_load d_a k_q private_key nonce =\n let is_sk_valid = load_qelem_conditional d_a private_key in\n let is_nonce_valid = load_qelem_conditional k_q nonce in\n let m = is_sk_valid &. is_nonce_valid in\n logand_lemma is_sk_valid is_nonce_valid;\n m", "val secp256k1_ecdsa_verify_sha256\n (msg_len: size_nat)\n (msg: lbytes msg_len)\n (public_key signature: lbytes 64)\n : bool\nlet secp256k1_ecdsa_verify_sha256 (msg_len:size_nat) (msg:lbytes msg_len) (public_key signature:lbytes 64) : bool =\n let msgHash = Spec.Agile.Hash.hash Spec.Hash.Definitions.SHA2_256 msg in\n secp256k1_ecdsa_verify_hashed_msg msgHash public_key signature", "val ecdsa_sign_store (signature:lbytes 64ul) (r_q s_q:qelem) : Stack unit\n (requires fun h ->\n live h signature /\\ live h r_q /\\ live h s_q /\\\n disjoint signature r_q /\\ disjoint signature s_q /\\\n qas_nat h r_q < S.q /\\ qas_nat h s_q < S.q)\n (ensures fun h0 _ h1 -> modifies (loc signature) h0 h1 /\\\n (let r = BSeq.nat_to_bytes_be 32 (qas_nat h0 r_q) in\n let s = BSeq.nat_to_bytes_be 32 (qas_nat h0 s_q) in\n as_seq h1 signature == LSeq.concat #_ #32 #32 r s))\nlet ecdsa_sign_store signature r_q s_q =\n let h0 = ST.get () in\n update_sub_f h0 signature 0ul 32ul\n (fun h -> BSeq.nat_to_bytes_be 32 (qas_nat h0 r_q))\n (fun _ -> store_qelem (sub signature 0ul 32ul) r_q);\n\n let h1 = ST.get () in\n update_sub_f h1 signature 32ul 32ul\n (fun h -> BSeq.nat_to_bytes_be 32 (qas_nat h1 s_q))\n (fun _ -> store_qelem (sub signature 32ul 32ul) s_q);\n\n let h2 = ST.get () in\n let r = Ghost.hide (BSeq.nat_to_bytes_be 32 (qas_nat h0 r_q)) in\n let s = Ghost.hide (BSeq.nat_to_bytes_be 32 (qas_nat h0 s_q)) in\n LSeq.eq_intro (as_seq h2 signature) (LSeq.concat #_ #32 #32 r s)", "val ecp256dh_i:\n public_key:lbuffer uint8 64ul\n -> private_key:lbuffer uint8 32ul ->\n Stack bool\n (requires fun h ->\n live h public_key /\\ live h private_key /\\ disjoint public_key private_key)\n (ensures fun h0 r h1 -> modifies (loc public_key) h0 h1 /\\\n (let pk = S.secret_to_public (as_seq h0 private_key) in\n (r <==> Some? pk) /\\ (r ==> (as_seq h1 public_key == Some?.v pk))))\nlet ecp256dh_i public_key private_key =\n push_frame ();\n let tmp = create 16ul (u64 0) in\n let sk = sub tmp 0ul 4ul in\n let pk = sub tmp 4ul 12ul in\n\n let is_sk_valid = load_qelem_conditional sk private_key in\n point_mul_g pk sk;\n point_store public_key pk;\n pop_frame ();\n Hacl.Bignum.Base.unsafe_bool_of_limb is_sk_valid", "val ecdsa_sign_s (s k r d_a:qelem) (m:lbytes 32ul) : Stack unit\n (requires fun h ->\n live h s /\\ live h m /\\ live h d_a /\\ live h k /\\ live h r /\\\n disjoint s r /\\ disjoint s k /\\ disjoint r k /\\\n disjoint s d_a /\\ disjoint r d_a /\\\n\n 0 < qas_nat h k /\\ qas_nat h k < S.q /\\\n qas_nat h r < S.q /\\\n 0 < qas_nat h d_a /\\ qas_nat h d_a < S.q)\n (ensures fun h0 _ h1 -> modifies (loc s) h0 h1 /\\\n (let z = BSeq.nat_from_bytes_be (as_seq h0 m) % S.q in\n let kinv = S.qinv (qas_nat h0 k) in\n let s_s = S.qmul kinv (S.qadd z (S.qmul (qas_nat h0 r) (qas_nat h0 d_a))) in\n qas_nat h1 s == s_s))\nlet ecdsa_sign_s s k r d_a m =\n push_frame ();\n let z = create_qelem () in\n let kinv = create_qelem () in\n\n load_qelem_modq z m; // z = m % S.q\n QI.qinv kinv k;\n\n qmul s r d_a; // s = r * d_a\n qadd s z s; // s = z + s\n qmul s kinv s; // s = kinv * s\n pop_frame ()", "val test:\n msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> pk:lbuffer uint8 32ul\n -> sk:lbuffer uint8 32ul\n -> expected_sig:lbuffer uint8 64ul\n -> Stack unit\n (requires fun h ->\n live h msg /\\ live h expected_sig /\\ live h pk /\\ live h sk)\n (ensures fun h0 r h1 -> modifies0 h0 h1)\nlet test msg_len msg pk sk expected_sig =\n test_verify msg_len msg pk expected_sig;\n test_sign msg_len msg sk expected_sig;\n test_secret_to_public sk pk", "val test_verify:\n msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> pk:lbuffer uint8 32ul\n -> sig:lbuffer uint8 64ul\n -> Stack unit\n (requires fun h ->\n live h msg /\\ live h pk /\\ live h sig)\n (ensures fun h0 r h1 -> modifies0 h0 h1)\nlet test_verify msg_len msg pk sig =\n let res = Ed25519.verify pk msg_len msg sig in\n\n C.String.print (C.String.of_literal \"Test Ed25519 Verify:\\n\");\n if res then C.String.print (C.String.of_literal \"Success!\\n\")\n else (C.String.print (C.String.of_literal \"Failure :(\\n\"); C.exit 255l)", "val rsapss_skey_sign:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:size_nat\n -> eBits:size_nat\n -> dBits:size_nat{skey_len_pre t modBits eBits dBits}\n -> nb:lseq uint8 (blocks modBits 8)\n -> eb:lseq uint8 (blocks eBits 8)\n -> db:lseq uint8 (blocks dBits 8)\n -> sLen:size_nat\n -> salt:lseq uint8 sLen\n -> msgLen:nat\n -> msg:seq uint8{length msg == msgLen}\n -> sgnt:lseq uint8 (blocks modBits 8)\n -> Pure (tuple2 bool (lseq uint8 (blocks modBits 8)))\n (requires True)\n (ensures fun (b, sgnt) ->\n (let sgnt_s = S.rsapss_skey_sign a modBits eBits dBits nb eb db sLen salt msgLen msg in\n if b then Some? sgnt_s /\\ sgnt == Some?.v sgnt_s else None? sgnt_s))\nlet rsapss_skey_sign #t a modBits eBits dBits nb eb db sLen salt msgLen msg sgnt =\n let b, skey = rsapss_load_skey #t modBits eBits dBits nb eb db in\n rsapss_load_skey_lemma #t modBits eBits dBits nb eb db;\n\n if b then\n rsapss_sign a modBits eBits dBits skey sLen salt msgLen msg sgnt\n else\n false, sgnt", "val verify_valid_pk:\n public_key:lbuffer uint8 32ul\n -> msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> signature:lbuffer uint8 64ul\n -> a':point ->\n Stack bool\n (requires fun h ->\n live h public_key /\\ live h msg /\\ live h signature /\\ live h a' /\\\n (Some? (Spec.Ed25519.point_decompress (as_seq h public_key))) /\\ point_inv_full_t h a' /\\\n (F51.point_eval h a' == Some?.v (Spec.Ed25519.point_decompress (as_seq h public_key))))\n (ensures fun h0 z h1 -> modifies0 h0 h1 /\\\n z == Spec.Ed25519.verify (as_seq h0 public_key) (as_seq h0 msg) (as_seq h0 signature))\nlet verify_valid_pk public_key msg_len msg signature a' =\n push_frame ();\n let r' = create 20ul (u64 0) in\n let rs = sub signature 0ul 32ul in\n let h0 = ST.get () in\n Spec.Ed25519.Lemmas.point_decompress_lemma (as_seq h0 rs);\n let b' = Hacl.Impl.Ed25519.PointDecompress.point_decompress r' rs in\n let res = if b' then verify_valid_pk_rs public_key msg_len msg signature a' r' else false in\n pop_frame ();\n res", "val verify_valid_pk_rs:\n public_key:lbuffer uint8 32ul\n -> msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> signature:lbuffer uint8 64ul\n -> a':point\n -> r':point ->\n Stack bool\n (requires fun h ->\n live h public_key /\\ live h msg /\\ live h signature /\\ live h a' /\\ live h r' /\\\n (Some? (Spec.Ed25519.point_decompress (as_seq h public_key))) /\\ point_inv_full_t h a' /\\\n (F51.point_eval h a' == Some?.v (Spec.Ed25519.point_decompress (as_seq h public_key))) /\\\n (Some? (Spec.Ed25519.point_decompress (as_seq h (gsub signature 0ul 32ul)))) /\\ point_inv_full_t h r' /\\\n (F51.point_eval h r' == Some?.v (Spec.Ed25519.point_decompress (as_seq h (gsub signature 0ul 32ul)))))\n (ensures fun h0 z h1 -> modifies0 h0 h1 /\\\n z == Spec.Ed25519.verify (as_seq h0 public_key) (as_seq h0 msg) (as_seq h0 signature))\nlet verify_valid_pk_rs public_key msg_len msg signature a' r' =\n push_frame ();\n let hb = create 32ul (u8 0) in\n let rs = sub signature 0ul 32ul in\n let sb = sub signature 32ul 32ul in\n\n let b = verify_sb sb in\n let res =\n if b then false\n else begin\n Hacl.Impl.SHA512.ModQ.store_sha512_modq_pre_pre2 hb rs public_key msg_len msg;\n verify_all_valid_hb sb hb a' r' end in\n pop_frame ();\n res", "val load_signature (r_q s_q:felem) (sign_r sign_s:lbytes 32ul) : Stack bool\n (requires fun h ->\n live h sign_r /\\ live h sign_s /\\ live h r_q /\\ live h s_q /\\\n disjoint r_q s_q /\\ disjoint r_q sign_r /\\ disjoint r_q sign_s /\\\n disjoint s_q sign_r /\\ disjoint s_q sign_s)\n (ensures fun h0 res h1 -> modifies (loc r_q |+| loc s_q) h0 h1 /\\\n (let r_q_nat = BSeq.nat_from_bytes_be (as_seq h0 sign_r) in\n let s_q_nat = BSeq.nat_from_bytes_be (as_seq h0 sign_s) in\n as_nat h1 r_q = r_q_nat /\\ as_nat h1 s_q = s_q_nat /\\\n res == (0 < r_q_nat && r_q_nat < S.order && 0 < s_q_nat && s_q_nat < S.order)))\nlet load_signature r_q s_q sign_r sign_s =\n bn_from_bytes_be4 r_q sign_r;\n bn_from_bytes_be4 s_q sign_s;\n let is_r_valid = bn_is_lt_order_and_gt_zero_mask4 r_q in\n let is_s_valid = bn_is_lt_order_and_gt_zero_mask4 s_q in\n Hacl.Bignum.Base.unsafe_bool_of_limb is_r_valid &&\n Hacl.Bignum.Base.unsafe_bool_of_limb is_s_valid", "val check_signature: are_sk_nonce_valid:uint64 -> r_q:qelem -> s_q:qelem -> Stack bool\n (requires fun h ->\n live h r_q /\\ live h s_q /\\ disjoint r_q s_q /\\\n (v are_sk_nonce_valid = ones_v U64 \\/ v are_sk_nonce_valid = 0))\n (ensures fun h0 res h1 -> modifies0 h0 h1 /\\\n res == ((v are_sk_nonce_valid = ones_v U64) && (0 < qas_nat h0 r_q) && (0 < qas_nat h0 s_q)))\nlet check_signature are_sk_nonce_valid r_q s_q =\n let h0 = ST.get () in\n let is_r_zero = is_qelem_zero r_q in\n let is_s_zero = is_qelem_zero s_q in\n assert (v is_r_zero == (if qas_nat h0 r_q = 0 then ones_v U64 else 0));\n assert (v is_s_zero == (if qas_nat h0 s_q = 0 then ones_v U64 else 0));\n [@inline_let] let m0 = lognot is_r_zero in\n [@inline_let] let m1 = lognot is_s_zero in\n [@inline_let] let m2 = m0 &. m1 in\n lognot_lemma is_r_zero;\n lognot_lemma is_s_zero;\n assert (v m0 == (if qas_nat h0 r_q = 0 then 0 else ones_v U64));\n assert (v m1 == (if qas_nat h0 s_q = 0 then 0 else ones_v U64));\n logand_lemma m0 m1;\n assert (v m2 = (if v m0 = 0 then 0 else v m1));\n assert ((v m2 = 0) <==> (qas_nat h0 r_q = 0 || qas_nat h0 s_q = 0));\n let m = are_sk_nonce_valid &. m2 in\n logand_lemma are_sk_nonce_valid m2;\n assert ((v m = ones_v U64) <==>\n ((v are_sk_nonce_valid = ones_v U64) && (0 < qas_nat h0 r_q) && (0 < qas_nat h0 s_q)));\n BB.unsafe_bool_of_limb m", "val ecp256dh_r:\n shared_secret:lbuffer uint8 64ul\n -> their_pubkey:lbuffer uint8 64ul\n -> private_key:lbuffer uint8 32ul ->\n Stack bool\n (requires fun h ->\n live h shared_secret /\\ live h their_pubkey /\\ live h private_key /\\\n disjoint shared_secret their_pubkey /\\ disjoint shared_secret private_key)\n (ensures fun h0 r h1 -> modifies (loc shared_secret) h0 h1 /\\\n (let ss = S.ecdh (as_seq h0 their_pubkey) (as_seq h0 private_key) in\n (r <==> Some? ss) /\\ (r ==> (as_seq h1 shared_secret == Some?.v ss))))\nlet ecp256dh_r shared_secret their_pubkey private_key =\n push_frame ();\n let tmp = create 16ul (u64 0) in\n let sk = sub tmp 0ul 4ul in\n let pk = sub tmp 4ul 12ul in\n\n let is_pk_valid = load_point_vartime pk their_pubkey in\n let is_sk_valid = load_qelem_conditional sk private_key in\n ecp256dh_r_ is_pk_valid shared_secret pk sk;\n pop_frame ();\n Hacl.Bignum.Base.unsafe_bool_of_limb is_sk_valid && is_pk_valid", "val hash:\n a:Hash.hash_alg{S.hash_is_supported a}\n -> mHash:lbuffer uint8 (hash_len a)\n -> msgLen:size_t{v msgLen `less_than_max_input_length` a}\n -> msg:lbuffer uint8 msgLen ->\n Stack unit\n (requires fun h -> live h mHash /\\ live h msg /\\ disjoint msg mHash)\n (ensures fun h0 _ h1 -> modifies (loc mHash) h0 h1 /\\\n as_seq h1 mHash == Hash.hash a (as_seq h0 msg))\nlet hash a mHash msgLen msg =\n match a with\n | Hash.SHA2_256 -> Hacl.Streaming.SHA2.hash_256 mHash msg msgLen\n | Hash.SHA2_384 -> Hacl.Streaming.SHA2.hash_384 mHash msg msgLen\n | Hash.SHA2_512 -> Hacl.Streaming.SHA2.hash_512 mHash msg msgLen", "val ecdsa_verify_sha256 (msg_len: size_nat) (msg: lbytes msg_len) (public_key signature: lbytes 64)\n : bool\nlet ecdsa_verify_sha256 (msg_len:size_nat) (msg:lbytes msg_len) (public_key signature:lbytes 64) : bool =\n let msgHash = Spec.Agile.Hash.hash Spec.Hash.Definitions.SHA2_256 msg in\n ecdsa_verify_hashed_msg msgHash public_key signature", "val pss_verify:\n a:Hash.hash_alg{S.hash_is_supported a}\n -> saltLen:salt_len_t a\n -> msgLen:msg_len_t a\n -> msg:lbuffer uint8 msgLen\n -> emBits:size_t{0 < v emBits}\n -> em:lbuffer uint8 (BD.blocks emBits 8ul) ->\n Stack bool\n (requires fun h -> live h msg /\\ live h em /\\ disjoint em msg)\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == S.pss_verify a (v saltLen) (v msgLen) (as_seq h0 msg) (v emBits) (as_seq h0 em))\nlet pss_verify a saltLen msgLen msg emBits em =\n let emLen = BD.blocks emBits 8ul in\n let msBits = emBits %. 8ul in\n\n let em_0 = if msBits >. 0ul then em.(0ul) &. (u8 0xff <<. msBits) else u8 0 in\n let em_last = em.(emLen -! 1ul) in\n\n if (emLen <. saltLen +! hash_len a +! 2ul) then false\n else begin\n if not (FStar.UInt8.(Lib.RawIntTypes.u8_to_UInt8 em_last =^ 0xbcuy) &&\n FStar.UInt8.(Lib.RawIntTypes.u8_to_UInt8 em_0 =^ 0uy)) then false\n else pss_verify_ a saltLen msgLen msg emBits em end", "val get_m1Hash:\n a:Hash.hash_alg{S.hash_is_supported a}\n -> saltLen:salt_len_t a\n -> salt:lbuffer uint8 saltLen\n -> msgLen:msg_len_t a\n -> msg:lbuffer uint8 msgLen\n -> hLen:size_t{v hLen == Hash.hash_length a}\n -> m1Hash:lbuffer uint8 hLen ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m1Hash /\\\n disjoint msg salt /\\ disjoint m1Hash msg /\\ disjoint m1Hash salt)\n (ensures fun h0 _ h1 -> modifies (loc m1Hash) h0 h1 /\\\n (let mHash = Hash.hash a (as_seq h0 msg) in\n let m1Len = 8 + Hash.hash_length a + v saltLen in\n let m1 = LSeq.create m1Len (u8 0) in\n let m1 = LSeq.update_sub m1 8 (Hash.hash_length a) mHash in\n let m1 = LSeq.update_sub m1 (8 + Hash.hash_length a) (v saltLen) (as_seq h0 salt) in\n as_seq h1 m1Hash == Hash.hash a m1))\nlet get_m1Hash a saltLen salt msgLen msg hLen m1Hash =\n push_frame ();\n //m1 = [8 * 0x00; mHash; salt]\n let m1Len = 8ul +! hLen +! saltLen in\n let m1 = create m1Len (u8 0) in\n let h0 = ST.get () in\n update_sub_f h0 m1 8ul hLen\n (fun h -> Hash.hash a (as_seq h0 msg))\n (fun _ -> hash a (sub m1 8ul hLen) msgLen msg);\n update_sub m1 (8ul +! hLen) saltLen salt;\n hash a m1Hash m1Len m1;\n pop_frame()", "val msg_as_felem:\n alg:S.hash_alg_ecdsa\n -> msg_len:size_t{v msg_len >= S.min_input_length alg}\n -> msg:lbytes msg_len\n -> res:BN.felem ->\n Stack unit\n (requires fun h ->\n live h msg /\\ live h res /\\ disjoint msg res)\n (ensures fun h0 _ h1 -> modifies (loc res) h0 h1 /\\\n (let hashM = S.hash_ecdsa alg (v msg_len) (as_seq h0 msg) in\n BN.as_nat h1 res = BSeq.nat_from_bytes_be (LSeq.sub hashM 0 32) % S.order))\nlet msg_as_felem alg msg_len msg res =\n push_frame ();\n\n [@inline_let] let sz: size_t =\n match alg with\n | S.NoHash -> 32ul\n | S.Hash a -> Hacl.Hash.Definitions.hash_len a in\n\n let mHash = create sz (u8 0) in\n\n begin\n match alg with\n | S.NoHash -> copy mHash (sub msg 0ul 32ul)\n | S.Hash a -> match a with\n | SHA2_256 -> Hacl.Streaming.SHA2.hash_256 mHash msg msg_len\n | SHA2_384 -> Hacl.Streaming.SHA2.hash_384 mHash msg msg_len\n | SHA2_512 -> Hacl.Streaming.SHA2.hash_512 mHash msg msg_len\n end;\n LowStar.Ignore.ignore msg_len;\n let mHash32 = sub mHash 0ul 32ul in\n BN.bn_from_bytes_be4 res mHash32;\n Hacl.Impl.P256.Scalar.qmod_short res res;\n pop_frame ()", "val pss_verify_:\n a:Hash.hash_alg{S.hash_is_supported a}\n -> saltLen:salt_len_t a\n -> msgLen:msg_len_t a\n -> msg:lbuffer uint8 msgLen\n -> emBits:em_len_t a saltLen\n -> em:lbuffer uint8 (BD.blocks emBits 8ul) ->\n Stack bool\n (requires fun h -> live h msg /\\ live h em /\\ disjoint em msg)\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == S.pss_verify_ a (v saltLen) (v msgLen) (as_seq h0 msg) (v emBits) (as_seq h0 em))\nlet pss_verify_ a saltLen msgLen msg emBits em =\n push_frame ();\n let emLen = BD.blocks emBits 8ul in\n\n let hLen = hash_len a in\n let m1Hash0 = create hLen (u8 0) in\n let dbLen = emLen -! hLen -! 1ul in\n let maskedDB = sub em 0ul dbLen in\n let m1Hash = sub em dbLen hLen in\n\n let dbMask = create dbLen (u8 0) in\n mgf_hash a hLen m1Hash dbLen dbMask;\n xor_bytes dbLen dbMask maskedDB;\n db_zero dbLen dbMask emBits;\n\n let padLen = emLen -! saltLen -! hLen -! 1ul in\n let pad2 = create padLen (u8 0) in\n pad2.(padLen -! 1ul) <- u8 0x01;\n\n let pad = sub dbMask 0ul padLen in\n let salt = sub dbMask padLen saltLen in\n\n let res =\n if not (Lib.ByteBuffer.lbytes_eq #padLen pad pad2) then false\n else begin\n get_m1Hash a saltLen salt msgLen msg hLen m1Hash0;\n Lib.ByteBuffer.lbytes_eq #hLen m1Hash0 m1Hash end in\n pop_frame ();\n res", "val load_signature (r_q s_q:QA.qelem) (signature:lbytes 64ul) : Stack bool\n (requires fun h ->\n live h signature /\\ live h r_q /\\ live h s_q /\\\n disjoint r_q s_q /\\ disjoint r_q signature /\\ disjoint s_q signature)\n (ensures fun h0 res h1 -> modifies (loc r_q |+| loc s_q) h0 h1 /\\\n (let sign_r = gsub signature 0ul 32ul in\n let sign_s = gsub signature 32ul 32ul in\n let r_q_nat = BSeq.nat_from_bytes_be (as_seq h0 sign_r) in\n let s_q_nat = BSeq.nat_from_bytes_be (as_seq h0 sign_s) in\n QA.qas_nat h1 r_q = r_q_nat /\\ QA.qas_nat h1 s_q = s_q_nat /\\\n res == (0 < r_q_nat && r_q_nat < S.q && 0 < s_q_nat && s_q_nat < S.q)))\nlet load_signature r_q s_q signature =\n let is_r_valid = QA.load_qelem_vartime r_q (sub signature 0ul 32ul) in\n let is_s_valid = QA.load_qelem_vartime s_q (sub signature 32ul 32ul) in\n is_r_valid && is_s_valid", "val verify_sb: sb:lbuffer uint8 32ul -> Stack bool\n (requires fun h -> live h sb)\n (ensures fun h0 b h1 -> modifies0 h0 h1 /\\\n (b <==> (BSeq.nat_from_bytes_le (as_seq h0 sb) >= Spec.Ed25519.q)))\nlet verify_sb sb =\n push_frame ();\n let tmp = create 5ul (u64 0) in\n Hacl.Impl.Load56.load_32_bytes tmp sb;\n let b = Hacl.Impl.Ed25519.PointEqual.gte_q tmp in\n pop_frame ();\n b", "val check_signature: are_sk_nonce_valid:uint64 -> r_q:felem -> s_q:felem -> Stack bool\n (requires fun h ->\n live h r_q /\\ live h s_q /\\ disjoint r_q s_q /\\\n (v are_sk_nonce_valid = ones_v U64 \\/ v are_sk_nonce_valid = 0))\n (ensures fun h0 res h1 -> modifies0 h0 h1 /\\\n res == ((v are_sk_nonce_valid = ones_v U64) && (0 < as_nat h0 r_q) && (0 < as_nat h0 s_q)))\nlet check_signature are_sk_nonce_valid r_q s_q =\n let h0 = ST.get () in\n let is_r_zero = bn_is_zero_mask4 r_q in\n let is_s_zero = bn_is_zero_mask4 s_q in\n [@inline_let] let m0 = lognot is_r_zero in\n [@inline_let] let m1 = lognot is_s_zero in\n [@inline_let] let m2 = m0 &. m1 in\n lognot_lemma is_r_zero;\n lognot_lemma is_s_zero;\n logand_lemma m0 m1;\n let m = are_sk_nonce_valid &. m2 in\n logand_lemma are_sk_nonce_valid m2;\n assert ((v m = ones_v U64) <==>\n ((v are_sk_nonce_valid = ones_v U64) && (0 < as_nat h0 r_q) && (0 < as_nat h0 s_q)));\n BB.unsafe_bool_of_limb m", "val test_sha3:\n msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> expected224:lbuffer uint8 28ul\n -> expected256:lbuffer uint8 32ul\n -> expected384:lbuffer uint8 48ul\n -> expected512:lbuffer uint8 64ul\n -> Stack unit\n (requires fun h ->\n live h msg /\\ live h expected224 /\\ live h expected256 /\\\n live h expected384 /\\ live h expected512)\n (ensures fun h0 r h1 -> True)\nlet test_sha3 msg_len msg expected224 expected256 expected384 expected512 =\n push_frame();\n let test224 = create 28ul (u8 0) in\n let test256 = create 32ul (u8 0) in\n let test384 = create 48ul (u8 0) in\n let test512 = create 64ul (u8 0) in\n\n sha3_224 test224 msg msg_len;\n sha3_256 test256 msg msg_len;\n sha3_384 test384 msg msg_len;\n sha3_512 test512 msg msg_len;\n\n if not (result_compare_display 28ul (to_const test224) (to_const expected224)) then C.exit 255l;\n if not (result_compare_display 32ul (to_const test256) (to_const expected256)) then C.exit 255l;\n if not (result_compare_display 48ul (to_const test384) (to_const expected384)) then C.exit 255l;\n if not (result_compare_display 64ul (to_const test512) (to_const expected512)) then C.exit 255l;\n pop_frame()", "val ecdsa_verification_agile:\n alg:hash_alg_ecdsa\n -> msg_len:size_nat{msg_len >= min_input_length alg}\n -> msg:lbytes msg_len\n -> public_key:lbytes 64\n -> signature_r:lbytes 32\n -> signature_s:lbytes 32 ->\n bool\nlet ecdsa_verification_agile alg msg_len msg public_key signature_r signature_s =\n let hashM = hash_ecdsa alg msg_len msg in\n let m_q = nat_from_bytes_be (sub hashM 0 32) % order in\n ecdsa_verify_msg_as_qelem m_q public_key signature_r signature_s", "val ecdsa_sign_msg_as_qelem (m: qelem) (private_key nonce: lbytes 32) : option (lbytes 64)\nlet ecdsa_sign_msg_as_qelem (m:qelem) (private_key nonce:lbytes 32) : option (lbytes 64) =\n let k_q = nat_from_bytes_be nonce in\n let d_a = nat_from_bytes_be private_key in\n let is_privkey_valid = 0 < d_a && d_a < order in\n let is_nonce_valid = 0 < k_q && k_q < order in\n\n if not (is_privkey_valid && is_nonce_valid) then None\n else begin\n let _X, _Y, _Z = point_mul_g k_q in\n let x = _X /% _Z in\n let r = x % order in\n\n let kinv = qinv k_q in\n let s = kinv *^ (m +^ r *^ d_a) in\n let rb = nat_to_bytes_be 32 r in\n let sb = nat_to_bytes_be 32 s in\n if r = 0 || s = 0 then None else Some (concat #_ #32 #32 rb sb) end", "val hash_ecdsa:\n a:hash_alg_ecdsa\n -> msg_len:size_nat{msg_len >= min_input_length a}\n -> msg:lseq uint8 msg_len ->\n Tot (r:lbytes\n (if Hash? a then hash_length (match a with Hash a -> a) else msg_len){length r >= 32})\nlet hash_ecdsa a msg_len msg =\n match a with | NoHash -> msg | Hash a -> Spec.Agile.Hash.hash a msg", "val test_sha2:\n msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> expected224:lbuffer uint8 28ul\n -> expected256:lbuffer uint8 32ul\n -> expected384:lbuffer uint8 48ul\n -> expected512:lbuffer uint8 64ul\n -> Stack unit\n (requires fun h ->\n live h msg /\\ live h expected224 /\\ live h expected256 /\\\n live h expected384 /\\ live h expected512)\n (ensures fun h0 r h1 -> True)\nlet test_sha2 msg_len msg expected224 expected256 expected384 expected512 =\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n push_frame();\n let test224 = create 28ul (u8 0) in\n let test256 = create 32ul (u8 0) in\n let test384 = create 48ul (u8 0) in\n let test512 = create 64ul (u8 0) in\n hash_224 (test224 <: lbuffer uint8 28ul) msg msg_len;\n hash_256 (test256 <: lbuffer uint8 32ul) msg msg_len;\n hash_384 (test384 <: lbuffer uint8 48ul) msg msg_len;\n hash_512 (test512 <: lbuffer uint8 64ul) msg msg_len;\n\n if not (result_compare_display 28ul (to_const test224) (to_const expected224)) then C.exit 255l;\n if not (result_compare_display 32ul (to_const test256) (to_const expected256)) then C.exit 255l;\n if not (result_compare_display 48ul (to_const test384) (to_const expected384)) then C.exit 255l;\n if not (result_compare_display 64ul (to_const test512) (to_const expected512)) then C.exit 255l;\n pop_frame()", "val rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:size_nat{1 < modBits}\n -> sLen:size_nat\n -> salt:lseq uint8 sLen\n -> msgLen:nat\n -> msg:seq uint8{length msg == msgLen} ->\n Pure (lbignum t (blocks modBits (bits t)))\n (requires rsapss_sign_pre a modBits sLen salt msgLen msg)\n (ensures fun res -> bn_v res < pow2 (modBits - 1))\nlet rsapss_sign_msg_to_bn #t a modBits sLen salt msgLen msg =\n let bits = bits t in\n let numb = numbytes t in\n let nLen = blocks modBits bits in\n\n let emBits = modBits - 1 in\n let emLen = blocks emBits 8 in\n\n let em = S.pss_encode a sLen salt msgLen msg emBits in\n blocks_bits_lemma t emBits;\n blocks_numb_lemma t emBits;\n assert (blocks emLen numb == blocks emBits bits);\n assert (numb * blocks emLen numb <= max_size_t);\n let emNat = bn_from_bytes_be #t emLen em in\n let m = create nLen (uint #t 0) in\n let m = update_sub m 0 (blocks emLen numb) emNat in\n bn_eval_update_sub (blocks emLen numb) emNat nLen;\n assert (bn_v m == bn_v emNat);\n bn_from_bytes_be_lemma #t emLen em;\n S.os2ip_lemma emBits em;\n m", "val ecdsa_signature_agile:\n alg:hash_alg_ecdsa\n -> msg_len:size_nat{msg_len >= min_input_length alg}\n -> msg:lbytes msg_len\n -> private_key:lbytes 32\n -> nonce:lbytes 32 ->\n option (lbytes 64)\nlet ecdsa_signature_agile alg msg_len msg private_key nonce =\n let hashM = hash_ecdsa alg msg_len msg in\n let m_q = nat_from_bytes_be (sub hashM 0 32) % order in\n ecdsa_sign_msg_as_qelem m_q private_key nonce", "val ecdsa_sign_r (r k:qelem) : Stack unit\n (requires fun h ->\n live h r /\\ live h k /\\ disjoint r k /\\\n qas_nat h k < S.q)\n (ensures fun h0 _ h1 -> modifies (loc r) h0 h1 /\\\n (let _X, _Y, _Z = S.point_mul_g (qas_nat h0 k) in\n let x = S.fmul _X (S.finv _Z) in\n let r_s = x % S.q in\n qas_nat h1 r == r_s))\nlet ecdsa_sign_r r k =\n push_frame ();\n let tmp = create_felem () in\n let x_bytes = create 32ul (u8 0) in\n\n let p = create_point () in\n point_mul_g p k; // p = [k]G\n let x, y, z = getx p, gety p, getz p in\n to_aff_point_x tmp p;\n\n store_felem x_bytes tmp;\n load_qelem_modq r x_bytes; // r = aff_x % S.q\n pop_frame ()", "val rsapss_sign_:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:size_nat\n -> eBits:size_nat\n -> dBits:size_nat{skey_len_pre t modBits eBits dBits}\n -> skey:lbignum t (2 * blocks modBits (bits t) + blocks eBits (bits t) + blocks dBits (bits t))\n -> sLen:size_nat\n -> salt:lseq uint8 sLen\n -> msgLen:nat\n -> msg:seq uint8{length msg == msgLen} ->\n Pure (tuple2 bool (lseq uint8 (blocks modBits 8)))\n (requires\n rsapss_skey_pre modBits eBits dBits skey /\\\n rsapss_sign_pre a modBits sLen salt msgLen msg)\n (ensures fun res -> True)\nlet rsapss_sign_ #t a modBits eBits dBits skey sLen salt msgLen msg =\n let m = rsapss_sign_msg_to_bn #t a modBits sLen salt msgLen msg in\n rsapss_sign_compute_sgnt #t modBits eBits dBits skey m", "val rsapss_pkey_verify:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:size_nat\n -> eBits:size_nat{pkey_len_pre t modBits eBits}\n -> nb:lseq uint8 (blocks modBits 8)\n -> eb:lseq uint8 (blocks eBits 8)\n -> sLen:size_nat //saltLen\n -> k:size_nat\n -> sgnt:lseq uint8 k\n -> msgLen:nat\n -> msg:seq uint8{length msg == msgLen} ->\n Pure bool\n (requires True)\n (ensures fun r ->\n r == S.rsapss_pkey_verify a modBits eBits nb eb sLen k sgnt msgLen msg)\nlet rsapss_pkey_verify #t a modBits eBits nb eb sLen k sgnt msgLen msg =\n let b, pkey = rsapss_load_pkey #t modBits eBits nb eb in\n rsapss_load_pkey_lemma #t modBits eBits nb eb;\n\n if b then\n rsapss_verify a modBits eBits pkey sLen k sgnt msgLen msg\n else\n false", "val dh_initiator:\n public_key:lbuffer uint8 64ul\n -> private_key:lbuffer uint8 32ul ->\n Stack bool\n (requires fun h ->\n live h public_key /\\ live h private_key /\\ disjoint public_key private_key)\n (ensures fun h0 r h1 -> modifies (loc public_key) h0 h1 /\\\n (let pk = S.secret_to_public (as_seq h0 private_key) in\n (r <==> Some? pk) /\\ (r ==> (as_seq h1 public_key == Some?.v pk))))\nlet dh_initiator public_key private_key =\n Hacl.Impl.P256.DH.ecp256dh_i public_key private_key", "val ecdsa_sign_s (s k r d_a m:felem) : Stack unit\n (requires fun h ->\n live h s /\\ live h m /\\ live h d_a /\\ live h k /\\ live h r /\\\n disjoint s r /\\ disjoint s k /\\ disjoint r k /\\\n disjoint s d_a /\\ disjoint r d_a /\\ disjoint m s /\\\n\n 0 < as_nat h k /\\ as_nat h k < S.order /\\\n as_nat h r < S.order /\\ as_nat h m < S.order /\\\n 0 < as_nat h d_a /\\ as_nat h d_a < S.order)\n (ensures fun h0 _ h1 -> modifies (loc s |+| loc m) h0 h1 /\\\n (let kinv = S.qinv (as_nat h0 k) in\n as_nat h1 s == S.qmul kinv (S.qadd (as_nat h0 m) (S.qmul (as_nat h0 r) (as_nat h0 d_a)))))\nlet ecdsa_sign_s s k r d_a m =\n push_frame ();\n let h0 = ST.get () in\n let kinv = create_felem () in\n QI.qinv kinv k;\n let h1 = ST.get () in\n assert (qmont_as_nat h1 kinv == S.qinv (qmont_as_nat h0 k));\n SM.qmont_inv_lemma (as_nat h0 k);\n assert (qmont_as_nat h1 kinv == S.qinv (as_nat h0 k) * SM.qmont_R % S.order);\n\n qmul s r d_a; // s = r * d_a\n let h2 = ST.get () in\n assert (as_nat h2 s == (as_nat h0 r * as_nat h0 d_a * SM.qmont_R_inv) % S.order);\n from_qmont m m;\n let h3 = ST.get () in\n assert (as_nat h3 m == as_nat h2 m * SM.qmont_R_inv % S.order);\n qadd s m s; // s = z + s\n let h4 = ST.get () in\n assert (as_nat h4 s == (as_nat h3 m + as_nat h2 s) % S.order);\n qmul s kinv s; // s = kinv * s\n let h5 = ST.get () in\n assert (as_nat h5 s == (as_nat h1 kinv * as_nat h4 s * SM.qmont_R_inv) % S.order);\n SM.lemma_ecdsa_sign_s\n (as_nat h0 k) (as_nat h1 kinv) (as_nat h0 r) (as_nat h0 d_a) (as_nat h0 m);\n pop_frame ()", "val validate_private_key: private_key:lbuffer uint8 32ul -> Stack bool\n (requires fun h -> live h private_key)\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n (let s = BSeq.nat_from_bytes_be (as_seq h0 private_key) in\n r <==> (0 < s && s < S.order)))\nlet validate_private_key private_key =\n push_frame ();\n let bn_sk = BN.create_felem () in\n BN.bn_from_bytes_be4 bn_sk private_key;\n let res = Hacl.Impl.P256.Scalar.bn_is_lt_order_and_gt_zero_mask4 bn_sk in\n pop_frame ();\n Hacl.Bignum.Base.unsafe_bool_of_limb res", "val rsapss_sign:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:size_nat\n -> eBits:size_nat\n -> dBits:size_nat{skey_len_pre t modBits eBits dBits}\n -> skey:lbignum t (2 * blocks modBits (bits t) + blocks eBits (bits t) + blocks dBits (bits t))\n -> sLen:size_nat\n -> salt:lseq uint8 sLen\n -> msgLen:nat\n -> msg:seq uint8{length msg == msgLen}\n -> sgnt:lseq uint8 (blocks modBits 8)\n -> Pure (tuple2 bool (lseq uint8 (blocks modBits 8)))\n (requires rsapss_skey_pre modBits eBits dBits skey)\n (ensures fun (b, sgnt) ->\n rsapss_sign_post1 a modBits eBits dBits skey sLen salt msgLen msg b sgnt)\nlet rsapss_sign #t a modBits eBits dBits skey sLen salt msgLen msg sgnt =\n let hLen = Hash.hash_length a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n\n let b =\n sLen <= v (0xfffffffful) - hLen - 8 &&\n msgLen `less_than_max_input_length` a &&\n sLen + hLen + 2 <= blocks (modBits - 1) 8 in\n\n if b then begin\n rsapss_sign_lemma a modBits eBits dBits skey sLen salt msgLen msg;\n rsapss_sign_ a modBits eBits dBits skey sLen salt msgLen msg end\n else\n false, sgnt", "val ecdsa_verify_msg_as_qelem (m: qelem) (public_key: lbytes 64) (sign_r sign_s: lbytes 32) : bool\nlet ecdsa_verify_msg_as_qelem (m:qelem) (public_key:lbytes 64) (sign_r sign_s:lbytes 32) : bool =\n let pk = load_point public_key in\n let r = nat_from_bytes_be sign_r in\n let s = nat_from_bytes_be sign_s in\n let is_r_valid = 0 < r && r < order in\n let is_s_valid = 0 < s && s < order in\n\n if not (Some? pk && is_r_valid && is_s_valid) then false\n else begin\n let sinv = qinv s in\n let u1 = sinv *^ m in\n let u2 = sinv *^ r in\n let _X, _Y, _Z = point_mul_double_g u1 u2 (Some?.v pk) in\n if is_point_at_inf (_X, _Y, _Z) then false\n else begin\n let x = _X /% _Z in\n x % order = r end\n end", "val deserialize_hash\n (#hash_size: hash_size_t)\n (ok: bool)\n (buf: const_uint8_p)\n (sz: uint32_t{CB.length buf = U32.v sz})\n (r: HST.erid)\n (pos: uint32_t)\n : HST.ST (bool & uint32_t & hash #hash_size)\n (requires (fun h0 -> CB.live h0 buf))\n (ensures\n (fun h0 (k, _, h) h1 ->\n (k ==> Rgl?.r_inv (hreg hash_size) h1 h) /\\\n loc_disjoint (loc_buffer (CB.cast buf)) (loc_buffer h) /\\ modifies B.loc_none h0 h1))\nlet deserialize_hash \n (#hash_size:hash_size_t) \n (ok:bool) (buf:const_uint8_p) (sz:uint32_t{CB.length buf = U32.v sz}) (r:HST.erid) (pos:uint32_t)\n: HST.ST (bool & uint32_t & hash #hash_size)\n (requires (fun h0 -> CB.live h0 buf))\n (ensures (fun h0 (k, _, h) h1 -> (k ==> Rgl?.r_inv (hreg hash_size) h1 h) /\\\n loc_disjoint (loc_buffer (CB.cast buf)) (loc_buffer h) /\\\n modifies B.loc_none h0 h1))\n= let rg = hreg hash_size in \n if not ok || pos >= sz then (false, pos, rg_dummy rg)\n else if sz - pos < hash_size then (false, pos, rg_dummy rg)\n else begin\n let hash = rg_alloc rg r in\n Lib.RawBuffer.blit (CB.cast buf) pos hash 0ul hash_size;\n (true, pos + hash_size, hash)\n end", "val test1\n (r0: rid)\n (sk1: aead_key_t)\n (spriv1: private_key_t)\n (spub1: public_key_t)\n (psk: preshared_key_t)\n (prlg_len: hashable_size_t)\n (prlg: lbuffer uint8 prlg_len)\n (encap0: B.pointer encap_message_p_or_null)\n (outlen_p: B.pointer size_t)\n (temp0: B.pointer (buffer uint8))\n : ST bool\n (requires\n (fun h0 ->\n is_eternal_region r0 /\\ live h0 (sk1 <: buffer uint8) /\\\n live h0 (spriv1 <: buffer uint8) /\\ live h0 (spub1 <: buffer uint8) /\\\n live h0 (psk <: buffer uint8) /\\ live h0 prlg /\\\n live h0 (encap0 <: buffer encap_message_p_or_null) /\\\n live h0 (outlen_p <: buffer size_t) /\\ live h0 (temp0 <: buffer (buffer uint8)) /\\\n get_dh_pre (idc ()).idc_nc /\\\n (let entr_loc = B.loc_addr_of_buffer (entropy_p <: buffer (G.erased entropy)) in\n let r0_loc = region_to_loc r0 in\n let sk1_loc = B.loc_addr_of_buffer (sk1 <: buffer uint8) in\n let spriv1_loc = B.loc_addr_of_buffer (spriv1 <: buffer uint8) in\n let spub1_loc = B.loc_addr_of_buffer (spub1 <: buffer uint8) in\n let psk_loc = B.loc_addr_of_buffer (psk <: buffer uint8) in\n let prlg_loc = B.loc_addr_of_buffer (prlg <: buffer uint8) in\n let encap0_loc = B.loc_addr_of_buffer (encap0 <: buffer encap_message_p_or_null) in\n let outlen_loc = B.loc_addr_of_buffer (outlen_p <: buffer size_t) in\n let temp0_loc = B.loc_addr_of_buffer (temp0 <: buffer (buffer uint8)) in\n B.all_disjoint [\n entr_loc; r0_loc; sk1_loc; spriv1_loc; spub1_loc; psk_loc; prlg_loc; encap0_loc;\n outlen_loc; temp0_loc\n ])))\n (ensures (fun h0 _ h1 -> True))\nlet test1 (r0 : rid)\n (sk1 : aead_key_t)\n (spriv1 : private_key_t)\n (spub1 : public_key_t)\n (psk : preshared_key_t)\n (prlg_len : hashable_size_t)\n (prlg : lbuffer uint8 prlg_len)\n (encap0 : B.pointer encap_message_p_or_null)\n (outlen_p : B.pointer size_t)\n (temp0 : B.pointer (buffer uint8)) :\n ST bool\n (requires (fun h0 ->\n is_eternal_region r0 /\\\n live h0 (sk1 <: buffer uint8) /\\\n live h0 (spriv1 <: buffer uint8) /\\\n live h0 (spub1 <: buffer uint8) /\\\n live h0 (psk <: buffer uint8) /\\\n live h0 prlg /\\\n live h0 (encap0 <: buffer encap_message_p_or_null) /\\\n live h0 (outlen_p <: buffer size_t) /\\\n live h0 (temp0 <: buffer (buffer uint8)) /\\\n get_dh_pre (idc ()).idc_nc /\\\n begin\n let entr_loc = B.loc_addr_of_buffer (entropy_p <: buffer (G.erased entropy)) in\n let r0_loc = region_to_loc r0 in\n let sk1_loc = B.loc_addr_of_buffer (sk1 <: buffer uint8) in\n let spriv1_loc = B.loc_addr_of_buffer (spriv1 <: buffer uint8) in\n let spub1_loc = B.loc_addr_of_buffer (spub1 <: buffer uint8) in\n let psk_loc = B.loc_addr_of_buffer (psk <: buffer uint8) in\n let prlg_loc = B.loc_addr_of_buffer (prlg <: buffer uint8) in\n let encap0_loc = B.loc_addr_of_buffer (encap0 <: buffer encap_message_p_or_null) in\n let outlen_loc = B.loc_addr_of_buffer (outlen_p <: buffer size_t) in\n let temp0_loc = B.loc_addr_of_buffer (temp0 <: buffer (buffer uint8)) in\n B.all_disjoint [\n entr_loc; r0_loc; sk1_loc; spriv1_loc;\n spub1_loc; psk_loc; prlg_loc;\n encap0_loc; outlen_loc;\n temp0_loc]\n end))\n (ensures (fun h0 _ h1 -> True)) =\n\n (**) let h0 = ST.get () in\n (**) Lib.Buffer.recall entropy_p;\n // Create the regions\n let (r1, r2, r3, r4, r5, r6, r7, r8, r9, r10) = create_regions10 r0 in\n\n // Create the devices\n let peer_info = Str.lstring_null MUT in\n let dvp1 = device_create r1 () prlg_len prlg peer_info sk1 spriv1 in\n let bdvp1 = device_p_is_null dvp1 in\n if bdvp1 then false\n else\n begin\n (**) let h3 = ST.get () in\n // Add some peers\n // TODO: relax the disjointness hypotheses here\n let peer1 = device_add_peer dvp1 peer_info spub1 psk in\n (**) let h4 = ST.get () in\n (**) let h5 = ST.get () in\n let bp1 = peer_p_is_null peer1 in\n if bp1 then false\n else\n begin\n let pid1 = peer_get_id peer1 in\n // Create the sessions\n (**) let h9 = ST.get () in\n let sn1 = session_create_initiator r3 dvp1 pid1 in\n (**) let h10 = ST.get () in\n let sn2 = session_create_responder r4 dvp1 () in\n (**) let h11 = ST.get () in\n // Test if the sessions are null\n let bs1 = session_p_is_null sn1 in\n let bs2 = session_p_is_null sn2 in\n // Exchange messages\n if bs1 || bs2 then\n begin\n if not bs1 then session_free sn1;\n if not bs2 then session_free sn2;\n device_free dvp1;\n false\n end\n else\n begin\n let payload0 = pack_message r6 0ul (B.null #uint8) in\n (**) let h12 = ST.get () in\n let res =\n match session_write payload0 sn1 r7 outlen_p temp0 with\n | Success ->\n let inlen0 = B.index outlen_p 0ul in\n let msg0 = B.index temp0 0ul in\n begin match session_read r8 encap0 sn2 inlen0 msg0 with\n | Success -> true\n | _ -> false\n end\n | _ -> false\n in\n // Clear\n (**) let h13 = ST.get () in\n if not (encap_message_p_is_null payload0)\n then encap_message_p_free payload0;\n let msg0 = B.index (temp0 <: buffer (buffer uint8)) 0ul in\n if not (B.is_null (msg0 <: buffer uint8)) then B.free msg0;\n session_free sn1;\n session_free sn2;\n device_free dvp1;\n // Return\n res\n end\n end\n end", "val test_shake256:\n msg_len:size_t\n -> msg:lbuffer uint8 msg_len\n -> out_len:size_t{v out_len > 0}\n -> expected:lbuffer uint8 out_len\n -> Stack unit\n (requires fun h -> live h msg /\\ live h expected)\n (ensures fun h0 r h1 -> modifies0 h0 h1)\nlet test_shake256 msg_len msg out_len expected =\n push_frame ();\n let test = create out_len (u8 0) in\n shake256_hacl msg_len msg out_len test;\n if not (result_compare_display out_len (to_const test) (to_const expected)) then C.exit 255l;\n pop_frame ()", "val dh_responder:\n shared_secret:lbuffer uint8 64ul\n -> their_pubkey:lbuffer uint8 64ul\n -> private_key:lbuffer uint8 32ul ->\n Stack bool\n (requires fun h ->\n live h shared_secret /\\ live h their_pubkey /\\ live h private_key /\\\n disjoint shared_secret their_pubkey /\\ disjoint shared_secret private_key)\n (ensures fun h0 r h1 -> modifies (loc shared_secret) h0 h1 /\\\n (let ss = S.ecdh (as_seq h0 their_pubkey) (as_seq h0 private_key) in\n (r <==> Some? ss) /\\ (r ==> (as_seq h1 shared_secret == Some?.v ss))))\nlet dh_responder shared_secret their_pubkey private_key =\n Hacl.Impl.P256.DH.ecp256dh_r shared_secret their_pubkey private_key", "val crypto_secretbox_open_detached:\n m:buffer uint8\n -> c:buffer uint8\n -> tag:lbuffer uint8 16ul\n -> mlen:size_t{length c = v mlen /\\ length m = v mlen}\n -> n:lbuffer uint8 24ul\n -> k:lbuffer uint8 32ul ->\n Stack size_t\n (requires fun h ->\n live h c /\\ live h m /\\ live h k /\\ live h n /\\ live h tag /\\\n disjoint tag c /\\ eq_or_disjoint (m <: lbuffer uint8 mlen) (c <: lbuffer uint8 mlen) /\\\n disjoint tag m /\\ disjoint n m /\\ disjoint n c)\n (ensures fun h0 r h1 -> modifies1 m h0 h1 /\\\n (let msg = SS.secretbox_open_detached (as_seq h0 k) (as_seq h0 n) (as_seq h0 tag) (as_seq #MUT #uint8 #mlen h0 c) in\n match r with\n | 0ul -> Some? msg /\\ as_seq #MUT #uint8 #mlen h1 m == Some?.v msg\n | _ -> None? msg))\nlet crypto_secretbox_open_detached m c tag mlen n k =\n Hacl.Impl.SecretBox.secretbox_open_detached mlen m k n c tag", "val secret_to_public:\n public_key:lbuffer uint8 32ul\n -> private_key:lbuffer uint8 32ul ->\n Stack unit\n (requires fun h ->\n live h public_key /\\ live h private_key /\\ disjoint public_key private_key)\n (ensures fun h0 _ h1 -> modifies (loc public_key) h0 h1 /\\\n as_seq h1 public_key == Spec.Ed25519.secret_to_public (as_seq h0 private_key))\nlet secret_to_public public_key private_key =\n push_frame ();\n let expanded_secret = create 64ul (u8 0) in\n secret_expand expanded_secret private_key;\n let a = sub expanded_secret 0ul 32ul in\n Hacl.Impl.Ed25519.Sign.point_mul_g_compress public_key a;\n pop_frame ()", "val secret_to_public:\n public_key:lbuffer uint8 32ul\n -> private_key:lbuffer uint8 32ul ->\n Stack unit\n (requires fun h ->\n live h public_key /\\ live h private_key /\\ disjoint public_key private_key)\n (ensures fun h0 _ h1 -> modifies (loc public_key) h0 h1 /\\\n as_seq h1 public_key == Spec.Ed25519.secret_to_public (as_seq h0 private_key))\nlet secret_to_public public_key private_key =\n Hacl.Ed25519.secret_to_public public_key private_key", "val ecdsa_sign_r (r k:felem) : Stack unit\n (requires fun h ->\n live h r /\\ live h k /\\ disjoint r k /\\\n as_nat h k < S.order)\n (ensures fun h0 _ h1 -> modifies (loc r) h0 h1 /\\\n (let x, _ = S.to_aff_point (S.point_mul_g (as_nat h0 k)) in\n as_nat h1 r == x % S.order))\nlet ecdsa_sign_r r k =\n push_frame ();\n let p = create_point () in\n point_mul_g p k; // p = [k]G\n to_aff_point_x r p;\n qmod_short r r;\n pop_frame ()", "val ecdh:\n shared:lbuffer uint8 32ul\n -> my_priv:lbuffer uint8 32ul\n -> their_pub:lbuffer uint8 32ul\n -> Stack bool\n (requires fun h0 ->\n live h0 shared /\\ live h0 my_priv /\\ live h0 their_pub /\\\n disjoint shared my_priv /\\ disjoint shared their_pub)\n (ensures fun h0 r h1 -> modifies (loc shared) h0 h1 /\\\n as_seq h1 shared == Spec.Curve25519.scalarmult (as_seq h0 my_priv) (as_seq h0 their_pub)\n /\\ (not r == Lib.ByteSequence.lbytes_eq #32 (as_seq h1 shared) (Lib.Sequence.create 32 (u8 0))))\nlet ecdh shared my_priv their_pub =\n if EverCrypt.TargetConfig.hacl_can_compile_vale then\n let has_bmi2 = EverCrypt.AutoConfig2.has_bmi2 () in\n let has_adx = EverCrypt.AutoConfig2.has_adx () in\n if (has_bmi2 && has_adx) then\n Hacl.Curve25519_64.ecdh shared my_priv their_pub\n else\n Hacl.Curve25519_51.ecdh shared my_priv their_pub\n else\n Hacl.Curve25519_51.ecdh shared my_priv their_pub", "val crypto_box_open_easy:\n m:buffer uint8\n -> c:buffer uint8\n -> clen:size_t{length c = v clen /\\ v clen = length m + 16}\n -> n:lbuffer uint8 24ul\n -> pk:lbuffer uint8 32ul\n -> sk:lbuffer uint8 32ul ->\n Stack size_t\n (requires fun h ->\n live h c /\\ live h m /\\ live h pk /\\ live h sk /\\ live h n /\\\n disjoint m c /\\ disjoint m n /\\ disjoint c n)\n (ensures fun h0 r h1 -> modifies1 m h0 h1 /\\\n (let msg = SB.box_open_easy (as_seq h0 pk) (as_seq h0 sk) (as_seq h0 n) (as_seq #MUT #uint8 #clen h0 c) in\n match r with\n | 0ul -> Some? msg /\\ as_seq #MUT #uint8 #(clen -! 16ul) h1 m == Some?.v msg\n | _ -> None? msg))\nlet crypto_box_open_easy m c clen n pk sk =\n Hacl.Impl.Box.box_open_easy (clen -! 16ul) m pk sk n c", "val store_56:\n out:lbuffer uint8 32ul\n -> b:lbuffer uint64 5ul ->\n Stack unit\n (requires fun h -> live h out /\\ live h b /\\\n (let s = as_seq h b in\n v (Seq.index s 0) < pow2 56 /\\\n v (Seq.index s 1) < pow2 56 /\\\n v (Seq.index s 2) < pow2 56 /\\\n v (Seq.index s 3) < pow2 56 /\\\n v (Seq.index s 4) < pow2 32)\n )\n (ensures fun h0 _ h1 -> modifies (loc out) h0 h1 /\\\n (assert_norm (pow2 56 < pow2 64); assert_norm (pow2 32 < pow2 64);\n assert_norm (S56.as_nat5 (u64 (pow2 56 - 1), u64 (pow2 56 - 1), u64 (pow2 56 - 1), u64 (pow2 56 - 1), u64 (pow2 32 - 1)) < pow2 256);\n nat_to_bytes_le 32 (F56.as_nat h0 b) == as_seq h1 out)\n )\nlet store_56 out b =\n let b0 = b.(0ul) in\n let b1 = b.(1ul) in\n let b2 = b.(2ul) in\n let b3 = b.(3ul) in\n let b4 = b.(4ul) in\n let b4' = to_u32 b4 in\n\n hstore56_le out 0ul b0;\n hstore56_le out 7ul b1;\n hstore56_le out 14ul b2;\n hstore56_le out 21ul b3;\n uint_to_bytes_le (sub out 28ul 4ul) b4';\n let h1 = ST.get() in\n assert (Seq.equal (Seq.slice (as_seq h1 out) 0 7) (as_seq h1 (gsub out 0ul 7ul)));\n assert (Seq.equal (Seq.slice (as_seq h1 out) 7 14) (as_seq h1 (gsub out 7ul 7ul)));\n assert (Seq.equal (Seq.slice (as_seq h1 out) 14 21) (as_seq h1 (gsub out 14ul 7ul)));\n assert (Seq.equal (Seq.slice (as_seq h1 out) 21 28) (as_seq h1 (gsub out 21ul 7ul)));\n assert (Seq.equal (Seq.slice (as_seq h1 out) 28 32) (as_seq h1 (gsub out 28ul 4ul)));\n lemma_uint_to_bytes_le_preserves_value b4';\n lemma_store_56_bytes (as_seq h1 out) b0 b1 b2 b3 b4;\n lemma_nat_from_to_bytes_le_preserves_value (as_seq h1 out) 32", "val rsapss_sign_:\n a:Hash.hash_alg{hash_is_supported a}\n -> modBits:modBits_t\n -> skey:rsapss_skey modBits\n -> sLen:size_nat{\n sLen + Hash.hash_length a + 8 <= max_size_t /\\\n (sLen + Hash.hash_length a + 8) `Hash.less_than_max_input_length` a /\\\n sLen + Hash.hash_length a + 2 <= blocks (modBits - 1) 8}\n -> salt:lbytes sLen\n -> msgLen:nat{msgLen `Hash.less_than_max_input_length` a}\n -> msg:bytes{length msg == msgLen} ->\n tuple2 bool (lbytes (blocks modBits 8))\nlet rsapss_sign_ a modBits skey sLen salt msgLen msg =\n let pkey = Mk_rsapss_skey?.pkey skey in\n let n = Mk_rsapss_pkey?.n pkey in\n let e = Mk_rsapss_pkey?.e pkey in\n let d = Mk_rsapss_skey?.d skey in\n\n let k = blocks modBits 8 in\n FStar.Math.Lemmas.pow2_le_compat (8 * k) modBits;\n\n let emBits = modBits - 1 in\n let emLen = blocks emBits 8 in\n\n let em = pss_encode a sLen salt msgLen msg emBits in\n let m = os2ip #emLen em in\n os2ip_lemma emBits em;\n let s = pow_mod #n m d in\n let m' = pow_mod #n s e in\n let eq_m = m = m' in\n let s = if eq_m then s else 0 in\n (eq_m, i2osp k s)", "val verify_l0_image_hash (img: l0_image_t)\n : Stack bool\n (requires fun _ -> True)\n (ensures\n fun h0 b h1 ->\n B.(modifies loc_none h0 h1) /\\\n (b <==>\n Spec.Agile.Hash.hash alg (B.as_seq h1 img.l0_binary) == B.as_seq h1 img.l0_binary_hash))\nlet verify_l0_image_hash (img:l0_image_t)\n : Stack bool\n (requires fun _ -> True)\n (ensures fun h0 b h1 ->\n B.(modifies loc_none h0 h1) /\\\n (b <==> Spec.Agile.Hash.hash alg (B.as_seq h1 img.l0_binary) == B.as_seq h1 img.l0_binary_hash))\n = recall_image_liveness img;\n\n HST.push_frame ();\n\n let hash_buf = B.alloca (u8 0x00) digest_len in\n dice_hash alg\n (* dst *) hash_buf\n (* msg *) img.l0_binary img.l0_binary_size;\n let b = lbytes_eq #digest_len img.l0_binary_hash hash_buf in\n\n HST.pop_frame ();\n\n b", "val sha512_pre_msg:\n hash:lbuffer uint8 64ul\n -> prefix:lbuffer uint8 32ul\n -> len:size_t\n -> input:lbuffer uint8 len ->\n Stack unit\n (requires fun h ->\n live h hash /\\ live h prefix /\\ live h input /\\\n disjoint input hash /\\ disjoint prefix hash)\n (ensures fun h0 _ h1 -> modifies (loc hash) h0 h1 /\\\n as_seq h1 hash == Spec.Agile.Hash.hash Spec.Hash.Definitions.SHA2_512\n (Seq.append (as_seq h0 prefix) (as_seq h0 input)))\nlet sha512_pre_msg hash prefix len input =\n push_frame ();\n let h0 = ST.get () in\n let st = Hash.alloca_512 () in\n let err0 = Hash.update_512 st prefix 32ul in\n let err1 = Hash.update_512 st input len in\n LowStar.Ignore.ignore err0;\n LowStar.Ignore.ignore err1;\n Hash.digest_512 st hash ();\n let h1 = ST.get () in\n assert (as_seq h1 hash == Spec.Agile.Hash.hash Spec.Hash.Definitions.SHA2_512\n (Seq.append (Seq.append (Seq.empty) (as_seq h0 prefix)) (as_seq h0 input)));\n Seq.append_empty_l (as_seq h0 prefix);\n pop_frame ()", "val rsapss_verify_bn_to_msg:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:size_nat{1 < modBits}\n -> sLen:size_nat //saltLen\n -> msgLen:nat\n -> msg:seq uint8{length msg == msgLen}\n -> m:lbignum t (blocks modBits (bits t)) ->\n Pure bool\n (requires rsapss_verify_pre a sLen msgLen msg)\n (ensures fun r -> True)\nlet rsapss_verify_bn_to_msg #t a modBits sLen msgLen msg m =\n let bits = bits t in\n let numb = numbytes t in\n let nLen = blocks modBits bits in\n\n let emBits = modBits - 1 in\n let emLen = blocks emBits 8 in\n\n blocks_bits_lemma t emBits;\n blocks_numb_lemma t emBits;\n assert (blocks emLen numb == blocks emBits bits);\n assert (numb * blocks emLen numb <= max_size_t);\n\n let m1 = sub m 0 (blocks emLen numb) in\n let em = bn_to_bytes_be emLen m1 in\n S.pss_verify a sLen msgLen msg emBits em", "val secretbox_open_detached:\n mlen:size_t\n -> m:lbuffer uint8 mlen\n -> k:lbuffer uint8 32ul\n -> n:lbuffer uint8 24ul\n -> c:lbuffer uint8 mlen\n -> tag:lbuffer uint8 16ul ->\n Stack size_t\n (requires fun h ->\n live h c /\\ live h m /\\ live h k /\\ live h n /\\ live h tag /\\\n disjoint tag c /\\ disjoint tag m /\\ disjoint m n /\\ disjoint c n /\\ eq_or_disjoint m c)\n (ensures fun h0 r h1 -> modifies (loc m) h0 h1 /\\\n (let msg = Spec.secretbox_open_detached (as_seq h0 k) (as_seq h0 n) (as_seq h0 tag) (as_seq h0 c) in\n match r with\n | 0ul -> Some? msg /\\ as_seq h1 m == Some?.v msg\n | _ -> None? msg))\nlet secretbox_open_detached mlen m k n c tag =\n push_frame();\n let xkeys = create 96ul (u8 0) in\n secretbox_init xkeys k n;\n let mkey = sub xkeys 32ul 32ul in\n\n let tag' = create 16ul (u8 0) in\n Hacl.Streaming.Poly1305_32.mac tag' c mlen mkey;\n\n let res =\n if lbytes_eq tag tag' then (\n secretbox_open_detached_plain mlen m xkeys n c;\n 0ul)\n else\n 0xfffffffful in\n pop_frame ();\n res", "val test_sign_and_verify:\n sk:lbytes 32\n -> pk:lbytes 64\n -> nonce:lbytes 32\n -> msgHash:lbytes 32\n -> sgnt:lbytes 64 ->\n FStar.All.ML bool\nlet test_sign_and_verify sk pk nonce msgHash sgnt =\n let signature = ecdsa_sign_hashed_msg msgHash sk nonce in\n\n let is_sgnt_valid =\n match signature with\n | Some x -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) sgnt x\n | None -> false in\n\n let verify_sgnt = ecdsa_verify_hashed_msg msgHash pk sgnt in\n\n if verify_sgnt && is_sgnt_valid\n then begin IO.print_string \"Test K256 ecdsa signature and verification: Success!\\n\"; true end\n else begin IO.print_string \"Test K256 ecdsa signature and verification: Failure :(\\n\"; false end", "val rsapss_skey_sign:\n a:Hash.hash_alg{hash_is_supported a}\n -> modBits:modBits_t\n -> eBits:size_pos\n -> dBits:size_pos\n -> nb:lseq uint8 (blocks modBits 8)\n -> eb:lseq uint8 (blocks eBits 8)\n -> db:lseq uint8 (blocks dBits 8)\n -> sLen:size_nat\n -> salt:lbytes sLen\n -> msgLen:nat\n -> msg:bytes{length msg == msgLen} ->\n option (lbytes (blocks modBits 8))\nlet rsapss_skey_sign a modBits eBits dBits nb eb db sLen salt msgLen msg =\n let skey = rsapss_load_skey modBits eBits dBits nb eb db in\n match skey with\n | Some vskey -> rsapss_sign a modBits vskey sLen salt msgLen msg\n | None -> None", "val expand_keys:\n expanded_keys:lbuffer uint8 96ul\n -> private_key:lbuffer uint8 32ul ->\n Stack unit\n (requires fun h ->\n live h expanded_keys /\\ live h private_key /\\ disjoint expanded_keys private_key)\n (ensures fun h0 _ h1 -> modifies (loc expanded_keys) h0 h1 /\\\n (let public_key, s, prefix = Spec.Ed25519.expand_keys (as_seq h0 private_key) in\n as_seq h1 (gsub expanded_keys 0ul 32ul) == public_key /\\\n as_seq h1 (gsub expanded_keys 32ul 32ul) == s /\\\n as_seq h1 (gsub expanded_keys 64ul 32ul) == prefix))\nlet expand_keys expanded_keys private_key =\n Hacl.Ed25519.expand_keys expanded_keys private_key", "val expand_keys:\n expanded_keys:lbuffer uint8 96ul\n -> private_key:lbuffer uint8 32ul ->\n Stack unit\n (requires fun h ->\n live h expanded_keys /\\ live h private_key /\\ disjoint expanded_keys private_key)\n (ensures fun h0 _ h1 -> modifies (loc expanded_keys) h0 h1 /\\\n (let public_key, s, prefix = Spec.Ed25519.expand_keys (as_seq h0 private_key) in\n as_seq h1 (gsub expanded_keys 0ul 32ul) == public_key /\\\n as_seq h1 (gsub expanded_keys 32ul 32ul) == s /\\\n as_seq h1 (gsub expanded_keys 64ul 32ul) == prefix))\nlet expand_keys expanded_keys private_key =\n let public_key = sub expanded_keys 0ul 32ul in\n let s_prefix = sub expanded_keys 32ul 64ul in\n let s = sub expanded_keys 32ul 32ul in\n secret_expand s_prefix private_key;\n Hacl.Impl.Ed25519.Sign.point_mul_g_compress public_key s", "val add_sign:\n out:lbuffer uint8 32ul\n -> x:uint64{v x < 2} ->\n Stack unit\n (requires fun h -> live h out /\\ nat_from_bytes_le (as_seq h out) < Spec.Curve25519.prime)\n (ensures fun h0 _ h1 -> modifies (loc out) h0 h1 /\\\n nat_from_bytes_le (as_seq h1 out) == nat_from_bytes_le (as_seq h0 out) + pow2 255 * (v x)\n )\nlet add_sign out x =\n (**) let h0 = ST.get() in\n let xbyte = to_u8 x in\n let o31 = out.(31ul) in\n (**) FStar.Math.Lemmas.lemma_mult_le_left (pow2 7) (v x) 1;\n (**) assert (pow2 7 * (v x) <= pow2 7);\n (**) assert_norm (pow2 7 < pow2 8);\n (**) assert (v (xbyte <<. 7ul) == pow2 7 * (v x));\n out.(31ul) <- o31 +. (xbyte <<. 7ul);\n (**) let h1 = ST.get() in\n (**) calc (==) {\n (**) nat_from_intseq_le (as_seq h1 out) <: nat;\n (**) (==) { nat_from_intseq_le_slice_lemma (as_seq h1 out) 31 }\n (**) nat_from_intseq_le (Seq.slice (as_seq h1 out) 0 31) +\n (**) pow2 (31 * 8) * nat_from_intseq_le (Seq.slice (as_seq h1 out) 31 32);\n (**) (==) {\n (**) calc (==) {\n (**) pow2 (31 * 8) * nat_from_intseq_le (Seq.slice (as_seq h1 out) 31 32);\n (**) (==) { calc (==) {\n (**) nat_from_intseq_le (Seq.slice (as_seq h1 out) 31 32) <: nat;\n (**) (==) { nat_from_intseq_le_lemma0 (Seq.slice (as_seq h1 out) 31 32) }\n (**) v (o31 +. (xbyte <<. 7ul));\n (**) (==) { calc (==) {\n (**) v (o31 +. (xbyte <<. 7ul)) <: nat;\n (**) (==) { }\n (**) (v o31 + v (xbyte <<. 7ul)) % pow2 8;\n (**) (==) { FStar.Math.Lemmas.lemma_mult_le_left (pow2 7) (v x) 1;\n (**) assert (pow2 7 * (v x) <= pow2 7);\n (**) assert_norm (pow2 7 < pow2 8);\n (**) lemma_fits_in_prime_last_byte (as_seq h0 out);\n (**) assert_norm (pow2 7 + pow2 7 == pow2 8);\n (**) FStar.Math.Lemmas.modulo_lemma (v o31 + pow2 7 * (v x)) (pow2 8)\n (**) }\n (**) v o31 + pow2 7 * (v x);\n (**) }; nat_from_intseq_le_lemma0 (Seq.slice (as_seq h0 out) 31 32)\n (**) }\n (**) nat_from_intseq_le (Seq.slice (as_seq h0 out) 31 32) + pow2 7 * (v x);\n (**) } }\n (**) pow2 (31 * 8) * (nat_from_intseq_le (Seq.slice (as_seq h0 out) 31 32) + pow2 7 * (v x));\n (**) (==) { FStar.Math.Lemmas.distributivity_add_right (pow2 (31 * 8))\n (**) (nat_from_intseq_le (Seq.slice (as_seq h0 out) 31 32)) (pow2 7 * (v x)) }\n (**) pow2 (31 * 8) * nat_from_intseq_le (Seq.slice (as_seq h0 out) 31 32) +\n (**) pow2 (31 * 8) * pow2 7 * (v x);\n (**) (==) { assert_norm (pow2 (31*8) * pow2 7 == pow2 255) }\n (**) pow2 (31 * 8) * nat_from_intseq_le (Seq.slice (as_seq h0 out) 31 32) +\n (**) pow2 255 * (v x);\n (**) }\n (**) }\n (**) nat_from_intseq_le (Seq.slice (as_seq h1 out) 0 31) +\n (**) pow2 (31 * 8) * nat_from_intseq_le (Seq.slice (as_seq h0 out) 31 32) +\n (**) pow2 255 * (v x);\n (**) (==) { nat_from_intseq_le_slice_lemma (as_seq h0 out) 31 }\n (**) nat_from_bytes_le (as_seq h0 out) + pow2 255 * (v x);\n (**) }", "val sha512_pre_pre2_msg:\n hash:lbuffer uint8 64ul\n -> prefix:lbuffer uint8 32ul\n -> prefix2:lbuffer uint8 32ul\n -> len:size_t\n -> input:lbuffer uint8 len ->\n Stack unit\n (requires fun h ->\n live h hash /\\ live h prefix /\\ live h prefix2 /\\ live h input /\\\n disjoint prefix hash /\\ disjoint prefix2 hash /\\ disjoint input hash)\n (ensures fun h0 _ h1 -> modifies (loc hash) h0 h1 /\\\n as_seq h1 hash == Spec.Agile.Hash.hash Spec.Hash.Definitions.SHA2_512\n (Seq.append (Seq.append (as_seq h0 prefix) (as_seq h0 prefix2)) (as_seq h0 input)))\nlet sha512_pre_pre2_msg hash prefix prefix2 len input =\n push_frame ();\n let h0 = ST.get () in\n let st = Hash.alloca_512 () in\n let err0 = Hash.update_512 st prefix 32ul in\n let err1 = Hash.update_512 st prefix2 32ul in\n let err2 = Hash.update_512 st input len in\n LowStar.Ignore.ignore err0;\n LowStar.Ignore.ignore err1;\n LowStar.Ignore.ignore err2;\n Hash.digest_512 st hash ();\n Seq.append_empty_l (as_seq h0 prefix);\n pop_frame ()", "val pss_verify_:\n a:Hash.hash_alg{hash_is_supported a}\n -> sLen:size_nat{sLen + Hash.hash_length a + 8 <= max_size_t /\\\n (sLen + Hash.hash_length a + 8) `Hash.less_than_max_input_length` a}\n -> msgLen:nat{msgLen `Hash.less_than_max_input_length` a}\n -> msg:bytes{length msg == msgLen}\n -> emBits:size_pos{sLen + Hash.hash_length a + 2 <= blocks emBits 8}\n -> em:lbytes (blocks emBits 8) ->\n Tot bool\nlet pss_verify_ a sLen msgLen msg emBits em =\n let hLen = Hash.hash_length a in\n let emLen = blocks emBits 8 in\n let dbLen = emLen - hLen - 1 in\n let maskedDB = sub em 0 dbLen in\n let m1Hash = sub em dbLen hLen in\n\n let dbMask = mgf_hash a hLen m1Hash dbLen in\n let db = xor_bytes dbMask maskedDB in\n let db = db_zero db emBits in\n\n let padLen = emLen - sLen - hLen - 1 in\n let pad2 = create padLen (u8 0) in\n let pad2 = pad2.[padLen - 1] <- u8 0x01 in\n\n let pad = sub db 0 padLen in\n let salt = sub db padLen sLen in\n\n if not (lbytes_eq pad pad2) then false\n else begin\n let mHash = Hash.hash a msg in\n let m1Len = 8 + hLen + sLen in\n let m1 = create m1Len (u8 0) in\n let m1 = update_sub m1 8 hLen mHash in\n let m1 = update_sub m1 (8 + hLen) sLen salt in\n let m1Hash0 = Hash.hash a m1 in\n lbytes_eq m1Hash0 m1Hash\n end", "val crypto_secretbox_open_easy:\n m:buffer uint8\n -> c:buffer uint8\n -> clen:size_t{length c = v clen /\\ v clen = length m + 16}\n -> n:lbuffer uint8 24ul\n -> k:lbuffer uint8 32ul ->\n Stack size_t\n (requires fun h ->\n live h c /\\ live h m /\\ live h k /\\ live h n /\\\n disjoint m c /\\ disjoint m n /\\ disjoint c n)\n (ensures fun h0 r h1 -> modifies1 m h0 h1 /\\\n (let msg = SS.secretbox_open_easy (as_seq h0 k) (as_seq h0 n) (as_seq #MUT #uint8 #clen h0 c) in\n match r with\n | 0ul -> Some? msg /\\ as_seq #MUT #uint8 #(clen -! 16ul) h1 m == Some?.v msg\n | _ -> None? msg))\nlet crypto_secretbox_open_easy m c clen n k =\n Hacl.Impl.SecretBox.secretbox_open_easy (clen -! 16ul) m k n c", "val serialize_hash\n (#hash_size: hash_size_t)\n (ok: bool)\n (x: hash #hash_size)\n (buf: uint8_p)\n (sz: uint32_t{B.len buf = sz})\n (pos: uint32_t)\n : HST.ST (bool & uint32_t)\n (requires (fun h0 -> B.live h0 buf /\\ B.live h0 x /\\ B.len x = hash_size))\n (ensures (fun h0 _ h1 -> modifies (B.loc_buffer buf) h0 h1))\nlet serialize_hash \n (#hash_size:hash_size_t) \n (ok:bool) (x:hash #hash_size) (buf:uint8_p) (sz:uint32_t{B.len buf = sz}) (pos:uint32_t) \n: HST.ST (bool & uint32_t)\n (requires (fun h0 -> B.live h0 buf /\\ B.live h0 x /\\ B.len x = hash_size))\n (ensures (fun h0 _ h1 -> modifies (B.loc_buffer buf) h0 h1))\n= if not ok || pos >= sz then (false, 0ul)\n else serialize_hash_i ok x buf sz pos 0ul", "val pss_verify:\n a:Hash.hash_alg{hash_is_supported a}\n -> sLen:size_nat{sLen + Hash.hash_length a + 8 <= max_size_t /\\\n (sLen + Hash.hash_length a + 8) `Hash.less_than_max_input_length` a}\n -> msgLen:nat{msgLen `Hash.less_than_max_input_length` a}\n -> msg:bytes{length msg == msgLen}\n -> emBits:size_pos\n -> em:lbytes (blocks emBits 8) ->\n Tot bool\nlet pss_verify a sLen msgLen msg emBits em =\n let emLen = blocks emBits 8 in\n let msBits = emBits % 8 in\n\n let em_0 = if msBits > 0 then em.[0] &. (u8 0xff <<. size msBits) else u8 0 in\n let em_last = em.[emLen - 1] in\n\n if (emLen < sLen + Hash.hash_length a + 2) then false\n else begin\n if not (FStar.UInt8.(Lib.RawIntTypes.u8_to_UInt8 em_last =^ 0xbcuy) &&\n FStar.UInt8.(Lib.RawIntTypes.u8_to_UInt8 em_0 =^ 0uy))\n then false\n else pss_verify_ a sLen msgLen msg emBits em end", "val sign_compute_s (r hs:lbuffer uint64 5ul) (a s:lbuffer uint8 32ul) : Stack unit\n (requires fun h ->\n live h r /\\ live h hs /\\ live h a /\\ live h s /\\\n disjoint s r /\\ disjoint s hs /\\ disjoint s a /\\\n F56.scalar_inv_full_t h r /\\ F56.scalar_inv_full_t h hs)\n (ensures fun h0 _ h1 -> modifies (loc s) h0 h1 /\\\n as_seq h1 s == BSeq.nat_to_bytes_le 32 ((F56.as_nat h0 r +\n (F56.as_nat h0 hs * BSeq.nat_from_bytes_le (as_seq h0 a)) % Spec.Ed25519.q) % Spec.Ed25519.q))\nlet sign_compute_s r hs a s =\n push_frame ();\n let aq = create 5ul (u64 0) in\n Hacl.Impl.Load56.load_32_bytes aq a;\n Hacl.Impl.BignumQ.Mul.mul_modq aq hs aq;\n Hacl.Impl.BignumQ.Mul.add_modq aq r aq;\n assert_norm (0x100000000000000 == pow2 56);\n Hacl.Impl.Store56.store_56 s aq;\n pop_frame ()", "val serialize_hash_vec\n (#hash_size: hash_size_t)\n (ok: bool)\n (x: hash_vec #hash_size)\n (buf: uint8_p)\n (sz: uint32_t{B.len buf = sz})\n (pos: uint32_t)\n : HST.ST (bool & uint32_t)\n (requires\n (fun h0 ->\n B.live h0 buf /\\ RV.rv_inv h0 x /\\\n HS.disjoint (B.frameOf buf) (Rgl?.region_of (hvreg hash_size) x)))\n (ensures (fun h0 _ h1 -> RV.rv_inv h1 x /\\ modifies (B.loc_buffer buf) h0 h1))\nlet serialize_hash_vec \n (#hash_size:hash_size_t) \n (ok:bool) (x:hash_vec #hash_size) (buf:uint8_p) (sz:uint32_t{B.len buf = sz}) (pos:uint32_t) \n: HST.ST (bool & uint32_t)\n (requires (fun h0 -> B.live h0 buf /\\ RV.rv_inv h0 x /\\ HS.disjoint (B.frameOf buf) (Rgl?.region_of (hvreg hash_size) x)))\n (ensures (fun h0 _ h1 -> RV.rv_inv h1 x /\\ modifies (B.loc_buffer buf) h0 h1))\n= if not ok || pos >= sz then (false, 0ul)\n else begin\n let h0 = HST.get() in\n let ok, pos = serialize_uint32_t ok (V.size_of x) buf sz pos in\n let h1 = HST.get() in\n RV.rv_inv_preserved x (B.loc_buffer buf) h0 h1;\n if ok && V.size_of x > 0ul then serialize_hash_vec_i ok x buf sz pos 0ul\n else (ok, pos)\n end", "val validate_public_key: public_key:lbuffer uint8 64ul -> Stack bool\n (requires fun h -> live h public_key)\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == S.validate_public_key (as_seq h0 public_key))\nlet validate_public_key public_key =\n push_frame ();\n let point_jac = P.create_point () in\n let res = P.load_point_vartime point_jac public_key in\n pop_frame ();\n res", "val crypto_box_open_detached:\n m:buffer uint8\n -> c:buffer uint8\n -> tag:lbuffer uint8 16ul\n -> mlen:size_t{length c = v mlen /\\ length m = v mlen}\n -> n:lbuffer uint8 24ul\n -> pk:lbuffer uint8 32ul\n -> sk:lbuffer uint8 32ul ->\n Stack size_t\n (requires fun h ->\n live h c /\\ live h m /\\ live h pk /\\ live h sk /\\ live h n /\\ live h tag /\\\n disjoint tag c /\\ eq_or_disjoint (m <: lbuffer uint8 mlen) (c <: lbuffer uint8 mlen) /\\\n disjoint tag m /\\ disjoint n m /\\ disjoint n c)\n (ensures fun h0 r h1 -> modifies1 m h0 h1 /\\\n (let msg = SB.box_open_detached (as_seq h0 pk) (as_seq h0 sk) (as_seq h0 n) (as_seq h0 tag) (as_seq #MUT #uint8 #mlen h0 c) in\n match r with\n | 0ul -> Some? msg /\\ as_seq #MUT #uint8 #mlen h1 m == Some?.v msg\n | _ -> None? msg))\nlet crypto_box_open_detached m c tag mlen n pk sk =\n Hacl.Impl.Box.box_open_detached mlen m pk sk n c tag", "val unpack_message :\n r:HS.rid\n -> out_msg_len:B.pointer size_t\n -> out_msg:B.pointer (buffer uint8)\n -> emp:encap_message_p ->\n ST bool\n (requires (fun h0 ->\n is_eternal_region r /\\\n B.live h0 out_msg_len /\\\n B.live h0 out_msg /\\\n encap_message_p_invariant h0 emp /\\\n B.(all_disjoint [region_to_loc r; loc_buffer out_msg_len; loc_buffer out_msg;\n encap_message_p_region_of emp])))\n (ensures (fun h0 res h1 ->\n B.(modifies (loc_union (loc_buffer out_msg_len) (loc_buffer out_msg)) h0 h1) /\\\n begin\n match Spec.unpack_message (encap_message_p_v h0 emp) with\n | None -> not res\n | Some msg_v ->\n let msg_len = B.deref h1 out_msg_len in\n let msg = B.deref h1 out_msg in\n res /\\\n B.live h1 msg /\\\n B.length msg = UInt32.v msg_len /\\\n B.as_seq h1 msg == msg_v /\\\n region_includes r (buffer_or_null_loc_addr msg) /\\\n buffer_or_null_freeable msg\n | _ -> False\n end))\nlet unpack_message r out_msg_len out_msg emp =\n unpack_message_with_auth_level r out_msg_len out_msg max_auth_level emp", "val deserialize_hash_vec\n (#hash_size: hash_size_t)\n (ok: bool)\n (buf: const_uint8_p)\n (sz: uint32_t{CB.length buf = U32.v sz})\n (r: HST.erid)\n (pos: uint32_t)\n : HST.ST (bool & uint32_t & hash_vec #hash_size)\n (requires (fun h0 -> CB.live h0 buf))\n (ensures (fun h0 _ h1 -> B.modifies B.loc_none h0 h1))\nlet deserialize_hash_vec \n (#hash_size:hash_size_t) \n (ok:bool) (buf:const_uint8_p) (sz:uint32_t{CB.length buf = U32.v sz}) (r:HST.erid) (pos:uint32_t)\n: HST.ST (bool & uint32_t & hash_vec #hash_size)\n (requires (fun h0 -> CB.live h0 buf))\n (ensures (fun h0 _ h1 -> B.modifies B.loc_none h0 h1))\n= let rg = hvreg hash_size in\n if not ok || pos >= sz then (false, pos, rg_dummy rg)\n else begin\n let ok, pos, n = deserialize_uint32_t ok buf sz pos in\n if not ok then (false, pos, V.alloc_empty hash)\n else if n = 0ul then (true, pos, V.alloc_empty hash)\n else begin\n let hrg = hreg hash_size in\n let res = V.alloc n (rg_dummy hrg) in\n let ok, pos = deserialize_hash_vec_i ok buf sz r pos res 0ul in\n (ok, pos, res)\n end\n end", "val pss_encode:\n a:Hash.hash_alg{hash_is_supported a}\n -> sLen:size_nat{sLen + Hash.hash_length a + 8 <= max_size_t /\\\n (sLen + Hash.hash_length a + 8) `Hash.less_than_max_input_length` a}\n -> salt:lbytes sLen\n -> msgLen:nat{msgLen `Hash.less_than_max_input_length` a}\n -> msg:bytes{length msg == msgLen}\n -> emBits:size_pos{Hash.hash_length a + sLen + 2 <= blocks emBits 8} ->\n Pure (lbytes (blocks emBits 8))\n (requires True)\n (ensures fun em -> if emBits % 8 > 0 then v em.[0] < pow2 (emBits % 8) else v em.[0] < pow2 8)\nlet pss_encode a sLen salt msgLen msg emBits =\n let mHash = Hash.hash a msg in\n let hLen = Hash.hash_length a in\n\n //m1 = [8 * 0x00; mHash; salt]\n let m1Len = 8 + hLen + sLen in\n let m1 = create m1Len (u8 0) in\n let m1 = update_sub m1 8 hLen mHash in\n let m1 = update_sub m1 (8 + hLen) sLen salt in\n let m1Hash = Hash.hash a m1 in\n\n //db = [0x00;..; 0x00; 0x01; salt]\n let emLen = blocks emBits 8 in\n let dbLen = emLen - hLen - 1 in\n let db = create dbLen (u8 0) in\n let last_before_salt = dbLen - sLen - 1 in\n let db = db.[last_before_salt] <- u8 1 in\n let db = update_sub db (last_before_salt + 1) sLen salt in\n\n let dbMask = mgf_hash a hLen m1Hash dbLen in\n let maskedDB = xor_bytes db dbMask in\n let maskedDB = db_zero maskedDB emBits in\n\n //em = [maskedDB; m1Hash; 0xbc]\n let em = create emLen (u8 0) in\n let em = update_sub em 0 dbLen maskedDB in\n let em = update_sub em dbLen hLen m1Hash in\n assert (v em.[0] == v maskedDB.[0]);\n em.[emLen - 1] <- u8 0xbc", "val rsapss_sign:\n a:Hash.hash_alg{hash_is_supported a}\n -> modBits:modBits_t\n -> skey:rsapss_skey modBits\n -> sLen:size_nat\n -> salt:lbytes sLen\n -> msgLen:nat\n -> msg:bytes{length msg == msgLen} ->\n option (lbytes (blocks modBits 8))\nlet rsapss_sign a modBits skey sLen salt msgLen msg =\n let b =\n sLen + Hash.hash_length a + 8 <= max_size_t &&\n (sLen + Hash.hash_length a + 8) `Hash.less_than_max_input_length` a &&\n msgLen `Hash.less_than_max_input_length` a &&\n sLen + Hash.hash_length a + 2 <= blocks (modBits - 1) 8 in\n\n if b then begin\n let (eq_m, sgnt) = rsapss_sign_ a modBits skey sLen salt msgLen msg in\n if eq_m then Some sgnt else None end\n else\n None", "val secret_to_public:\n pub:lbuffer uint8 32ul\n -> priv:lbuffer uint8 32ul\n -> Stack unit\n (requires fun h0 ->\n live h0 pub /\\ live h0 priv /\\ disjoint pub priv)\n (ensures fun h0 _ h1 -> modifies (loc pub) h0 h1 /\\\n as_seq h1 pub == Spec.Curve25519.secret_to_public (as_seq h0 priv))\nlet secret_to_public pub priv =\n if EverCrypt.TargetConfig.hacl_can_compile_vale then\n let has_bmi2 = EverCrypt.AutoConfig2.has_bmi2 () in\n let has_adx = EverCrypt.AutoConfig2.has_adx () in\n if (has_bmi2 && has_adx) then\n Hacl.Curve25519_64.secret_to_public pub priv\n else\n Hacl.Curve25519_51.secret_to_public pub priv\n else\n Hacl.Curve25519_51.secret_to_public pub priv", "val compressed_to_raw: pk:lbuffer uint8 33ul -> pk_raw:lbuffer uint8 64ul -> Stack bool\n (requires fun h -> live h pk /\\ live h pk_raw /\\ disjoint pk pk_raw)\n (ensures fun h0 b h1 -> modifies (loc pk_raw) h0 h1 /\\\n (b <==> Some? (S.pk_compressed_to_raw (as_seq h0 pk))) /\\\n (b ==> (as_seq h1 pk_raw == Some?.v (S.pk_compressed_to_raw (as_seq h0 pk)))))\nlet compressed_to_raw pk pk_raw =\n Hacl.Impl.P256.Compression.compressed_to_raw pk pk_raw", "val compressed_to_raw: pk:lbuffer uint8 33ul -> pk_raw:lbuffer uint8 64ul -> Stack bool\n (requires fun h -> live h pk /\\ live h pk_raw /\\ disjoint pk pk_raw)\n (ensures fun h0 b h1 -> modifies (loc pk_raw) h0 h1 /\\\n (b <==> Some? (S.pk_compressed_to_raw (as_seq h0 pk))) /\\\n (b ==> (as_seq h1 pk_raw == Some?.v (S.pk_compressed_to_raw (as_seq h0 pk)))))\nlet compressed_to_raw pk pk_raw =\n push_frame ();\n let xa = create_felem () in\n let ya = create_felem () in\n let pk_xb = sub pk 1ul 32ul in\n let b = P.aff_point_decompress_vartime xa ya pk in\n\n if b then begin\n let h0 = ST.get () in\n update_sub pk_raw 0ul 32ul pk_xb;\n let h1 = ST.get () in\n update_sub_f h1 pk_raw 32ul 32ul\n (fun h -> BSeq.nat_to_bytes_be 32 (as_nat h1 ya))\n (fun _ -> bn_to_bytes_be4 (sub pk_raw 32ul 32ul) ya);\n let h2 = ST.get () in\n LSeq.eq_intro (as_seq h2 pk_raw)\n (LSeq.concat #_ #32 #32 (as_seq h0 pk_xb) (BSeq.nat_to_bytes_be 32 (as_nat h0 ya))) end;\n pop_frame ();\n b", "val rsapss_sign_lemma:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:size_nat\n -> eBits:size_nat\n -> dBits:size_nat{skey_len_pre t modBits eBits dBits}\n -> skey:lbignum t (2 * blocks modBits (bits t) + blocks eBits (bits t) + blocks dBits (bits t))\n -> sLen:size_nat\n -> salt:lseq uint8 sLen\n -> msgLen:nat\n -> msg:seq uint8{length msg == msgLen} -> Lemma\n (requires\n rsapss_sign_pre a modBits sLen salt msgLen msg /\\\n rsapss_skey_pre modBits eBits dBits skey)\n (ensures\n (let eq_m, s = rsapss_sign_ a modBits eBits dBits skey sLen salt msgLen msg in\n rsapss_sign_post a modBits eBits dBits skey sLen salt msgLen msg eq_m s))\nlet rsapss_sign_lemma #t a modBits eBits dBits skey sLen salt msgLen msg =\n let bits = bits t in\n let numb = numbytes t in\n let nLen = blocks modBits bits in\n let eLen = blocks eBits bits in\n let dLen = blocks dBits bits in\n\n let n = sub skey 0 nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen + nLen) eLen in\n let d = sub skey (nLen + nLen + eLen) dLen in\n\n let k = blocks modBits 8 in\n let emBits = modBits - 1 in\n let emLen = blocks emBits 8 in\n\n let em = S.pss_encode a sLen salt msgLen msg emBits in\n blocks_bits_lemma t emBits;\n blocks_numb_lemma t emBits;\n assert (blocks emLen numb == blocks emBits bits);\n assert (numb * blocks emLen numb <= max_size_t);\n\n let emNat = bn_from_bytes_be emLen em in\n let m = create nLen (uint #t 0) in\n let m = update_sub m 0 (blocks emLen numb) emNat in\n bn_eval_update_sub (blocks emLen numb) emNat nLen;\n assert (bn_v m == bn_v emNat);\n bn_from_bytes_be_lemma #t emLen em;\n S.os2ip_lemma emBits em;\n\n assert (bn_v m < bn_v n);\n Math.Lemmas.pow2_le_compat (bits * nLen) modBits;\n SM.bn_precomp_r2_mod_n_lemma (modBits - 1) n;\n let s = bn_mod_exp_consttime_precompr2 nLen n r2 m dBits d in\n let m' = bn_mod_exp_vartime_precompr2 nLen n r2 s eBits e in\n\n let eq_m = bn_eq_mask m m' in\n bn_eq_mask_lemma m m';\n\n let s' = map (logand eq_m) s in\n bn_mask_lemma s eq_m;\n\n blocks_bits_lemma t modBits;\n blocks_numb_lemma t modBits;\n assert (blocks k numb == nLen);\n assert (numb * blocks k numb <= max_size_t);\n Math.Lemmas.pow2_le_compat (8 * k) modBits;\n assert (bn_v s' < pow2 (8 * k));\n let sgnt = bn_to_bytes_be k s' in\n bn_to_bytes_be_lemma k s'", "val serialize_hash_vv\n (#hash_size: hash_size_t)\n (ok: bool)\n (x: hash_vv hash_size)\n (buf: uint8_p)\n (sz: uint32_t{B.len buf = sz})\n (pos: uint32_t)\n : HST.ST (bool & uint32_t)\n (requires\n (fun h0 ->\n B.live h0 buf /\\ RV.rv_inv h0 x /\\\n HS.disjoint (B.frameOf buf) (Rgl?.region_of (hvvreg hash_size) x)))\n (ensures (fun h0 _ h1 -> modifies (B.loc_buffer buf) h0 h1))\nlet serialize_hash_vv \n (#hash_size:hash_size_t) \n (ok:bool) (x:hash_vv hash_size) (buf:uint8_p) (sz:uint32_t{B.len buf = sz}) (pos:uint32_t)\n: HST.ST (bool & uint32_t)\n (requires (fun h0 -> B.live h0 buf /\\ RV.rv_inv h0 x /\\ HS.disjoint (B.frameOf buf) (Rgl?.region_of (hvvreg hash_size) x)))\n (ensures (fun h0 _ h1 -> modifies (B.loc_buffer buf) h0 h1))\n= if not ok || pos >= sz then (false, 0ul)\n else begin\n let h0 = HST.get() in\n let ok, pos = serialize_uint32_t ok (V.size_of x) buf sz pos in\n let h1 = HST.get() in\n RV.rv_inv_preserved x (B.loc_buffer buf) h0 h1;\n if (V.size_of x > 0ul) then serialize_hash_vv_i ok x buf sz pos 0ul\n else (ok, pos)\n end" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Hacl.Impl.K256.Sign.fst", "name": "Hacl.Impl.K256.Sign.ecdsa_sign_hashed_msg" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.K256.Verify.fst", "name": "Hacl.Impl.K256.Verify.ecdsa_verify_hashed_msg" }, { "project_name": "hacl-star", "file_name": "Hacl.Test.K256.fst", "name": "Hacl.Test.K256.test_sign_hashed" }, { "project_name": "hacl-star", "file_name": "Spec.K256.fst", "name": "Spec.K256.secp256k1_ecdsa_sign_hashed_msg" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Ed25519.fst", "name": "EverCrypt.Ed25519.sign" }, { "project_name": "hacl-star", "file_name": "Hacl.Ed25519.fst", "name": "Hacl.Ed25519.sign" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Sign.fst", "name": "Hacl.Impl.P256.Sign.ecdsa_sign_msg_as_qelem" }, { "project_name": "hacl-star", "file_name": "Hacl.Test.K256.fst", "name": "Hacl.Test.K256.test_sign_and_verify_hashed" }, { "project_name": "hacl-star", "file_name": "Spec.K256.fst", "name": "Spec.K256.ecdsa_sign_hashed_msg" }, { "project_name": "hacl-star", "file_name": "Spec.K256.fst", "name": "Spec.K256.secp256k1_ecdsa_sign_sha256" }, { "project_name": "hacl-star", "file_name": "Hacl.Test.K256.fst", "name": "Hacl.Test.K256.test_verify_hashed" }, { "project_name": "hacl-star", "file_name": "Spec.K256.fst", "name": "Spec.K256.secp256k1_ecdsa_verify_hashed_msg" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Ed25519.fst", "name": "EverCrypt.Ed25519.verify" }, { "project_name": "hacl-star", "file_name": "Hacl.Ed25519.fst", "name": "Hacl.Ed25519.verify" }, { "project_name": "hacl-star", "file_name": "Spec.K256.fst", "name": "Spec.K256.ecdsa_verify_hashed_msg" }, { "project_name": "hacl-star", "file_name": "Spec.K256.fst", "name": "Spec.K256.ecdsa_sign_sha256" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Ed25519.Verify.fst", "name": "Hacl.Impl.Ed25519.Verify.verify" }, { "project_name": "hacl-star", "file_name": "Hacl.Test.K256.fst", "name": "Hacl.Test.K256.test_verify_sha256" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Ed25519.fst", "name": "EverCrypt.Ed25519.sign_expanded" }, { "project_name": "hacl-star", "file_name": "Hacl.Ed25519.fst", "name": "Hacl.Ed25519.sign_expanded" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Ed25519.Sign.fst", "name": "Hacl.Impl.Ed25519.Sign.sign_expanded" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.K256.Sign.fst", "name": "Hacl.Impl.K256.Sign.ecdsa_sign_load" }, { "project_name": "hacl-star", "file_name": "Hacl.Test.Ed25519.fst", "name": "Hacl.Test.Ed25519.test_sign" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Verify.fst", "name": "Hacl.Impl.P256.Verify.ecdsa_verify_msg_as_qelem" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Sign.fst", "name": "Hacl.Impl.P256.Sign.ecdsa_sign_load" }, { "project_name": "hacl-star", "file_name": "Spec.K256.fst", "name": "Spec.K256.secp256k1_ecdsa_verify_sha256" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.K256.Sign.fst", "name": "Hacl.Impl.K256.Sign.ecdsa_sign_store" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.DH.fst", "name": "Hacl.Impl.P256.DH.ecp256dh_i" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.K256.Sign.fst", "name": "Hacl.Impl.K256.Sign.ecdsa_sign_s" }, { "project_name": "hacl-star", "file_name": "Hacl.Test.Ed25519.fst", "name": "Hacl.Test.Ed25519.test" }, { "project_name": "hacl-star", "file_name": "Hacl.Test.Ed25519.fst", "name": "Hacl.Test.Ed25519.test_verify" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.RSAPSS.fst", "name": "Hacl.Spec.RSAPSS.rsapss_skey_sign" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Ed25519.Verify.fst", "name": "Hacl.Impl.Ed25519.Verify.verify_valid_pk" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Ed25519.Verify.fst", "name": "Hacl.Impl.Ed25519.Verify.verify_valid_pk_rs" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Verify.fst", "name": "Hacl.Impl.P256.Verify.load_signature" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.K256.Sign.fst", "name": "Hacl.Impl.K256.Sign.check_signature" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.DH.fst", "name": "Hacl.Impl.P256.DH.ecp256dh_r" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.RSAPSS.MGF.fst", "name": "Hacl.Impl.RSAPSS.MGF.hash" }, { "project_name": "hacl-star", "file_name": "Spec.K256.fst", "name": "Spec.K256.ecdsa_verify_sha256" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.RSAPSS.Padding.fst", "name": "Hacl.Impl.RSAPSS.Padding.pss_verify" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.RSAPSS.Padding.fst", "name": "Hacl.Impl.RSAPSS.Padding.get_m1Hash" }, { "project_name": "hacl-star", "file_name": "Hacl.P256.fst", "name": "Hacl.P256.msg_as_felem" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.RSAPSS.Padding.fst", "name": "Hacl.Impl.RSAPSS.Padding.pss_verify_" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.K256.Verify.fst", "name": "Hacl.Impl.K256.Verify.load_signature" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Ed25519.Verify.fst", "name": "Hacl.Impl.Ed25519.Verify.verify_sb" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Sign.fst", "name": "Hacl.Impl.P256.Sign.check_signature" }, { "project_name": "hacl-star", "file_name": "Hacl.Test.SHA3.fst", "name": "Hacl.Test.SHA3.test_sha3" }, { "project_name": "hacl-star", "file_name": "Spec.P256.fst", "name": "Spec.P256.ecdsa_verification_agile" }, { "project_name": "hacl-star", "file_name": "Spec.P256.fst", "name": "Spec.P256.ecdsa_sign_msg_as_qelem" }, { "project_name": "hacl-star", "file_name": "Spec.P256.fst", "name": "Spec.P256.hash_ecdsa" }, { "project_name": "hacl-star", "file_name": "Hacl.Test.SHA2.fst", "name": "Hacl.Test.SHA2.test_sha2" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.RSAPSS.fst", "name": "Hacl.Spec.RSAPSS.rsapss_sign_msg_to_bn" }, { "project_name": "hacl-star", "file_name": "Spec.P256.fst", "name": "Spec.P256.ecdsa_signature_agile" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.K256.Sign.fst", "name": "Hacl.Impl.K256.Sign.ecdsa_sign_r" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.RSAPSS.fst", "name": "Hacl.Spec.RSAPSS.rsapss_sign_" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.RSAPSS.fst", "name": "Hacl.Spec.RSAPSS.rsapss_pkey_verify" }, { "project_name": "hacl-star", "file_name": "Hacl.P256.fst", "name": "Hacl.P256.dh_initiator" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Sign.fst", "name": "Hacl.Impl.P256.Sign.ecdsa_sign_s" }, { "project_name": "hacl-star", "file_name": "Hacl.P256.fst", "name": "Hacl.P256.validate_private_key" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.RSAPSS.fst", "name": "Hacl.Spec.RSAPSS.rsapss_sign" }, { "project_name": "hacl-star", "file_name": "Spec.P256.fst", "name": "Spec.P256.ecdsa_verify_msg_as_qelem" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.Serialization.fst", "name": "MerkleTree.Low.Serialization.deserialize_hash" }, { "project_name": "noise-star", "file_name": "Impl.Noise.API.Instances.IKpsk2_25519_ChaChaPoly_BLAKE2s.Test.fst", "name": "Impl.Noise.API.Instances.IKpsk2_25519_ChaChaPoly_BLAKE2s.Test.test1" }, { "project_name": "hacl-star", "file_name": "Hacl.Test.SHA3.fst", "name": "Hacl.Test.SHA3.test_shake256" }, { "project_name": "hacl-star", "file_name": "Hacl.P256.fst", "name": "Hacl.P256.dh_responder" }, { "project_name": "hacl-star", "file_name": "Hacl.NaCl.fst", "name": "Hacl.NaCl.crypto_secretbox_open_detached" }, { "project_name": "hacl-star", "file_name": "Hacl.Ed25519.fst", "name": "Hacl.Ed25519.secret_to_public" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Ed25519.fst", "name": "EverCrypt.Ed25519.secret_to_public" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Sign.fst", "name": "Hacl.Impl.P256.Sign.ecdsa_sign_r" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Curve25519.fst", "name": "EverCrypt.Curve25519.ecdh" }, { "project_name": "hacl-star", "file_name": "Hacl.NaCl.fst", "name": "Hacl.NaCl.crypto_box_open_easy" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Store56.fst", "name": "Hacl.Impl.Store56.store_56" }, { "project_name": "hacl-star", "file_name": "Spec.RSAPSS.fst", "name": "Spec.RSAPSS.rsapss_sign_" }, { "project_name": "dice-star", "file_name": "DICE.Engine.Core.fst", "name": "DICE.Engine.Core.verify_l0_image_hash" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.SHA512.ModQ.fst", "name": "Hacl.Impl.SHA512.ModQ.sha512_pre_msg" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.RSAPSS.fst", "name": "Hacl.Spec.RSAPSS.rsapss_verify_bn_to_msg" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.SecretBox.fst", "name": "Hacl.Impl.SecretBox.secretbox_open_detached" }, { "project_name": "hacl-star", "file_name": "Spec.K256.Test.fst", "name": "Spec.K256.Test.test_sign_and_verify" }, { "project_name": "hacl-star", "file_name": "Spec.RSAPSS.fst", "name": "Spec.RSAPSS.rsapss_skey_sign" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Ed25519.fst", "name": "EverCrypt.Ed25519.expand_keys" }, { "project_name": "hacl-star", "file_name": "Hacl.Ed25519.fst", "name": "Hacl.Ed25519.expand_keys" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Ed25519.PointCompress.fst", "name": "Hacl.Impl.Ed25519.PointCompress.add_sign" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.SHA512.ModQ.fst", "name": "Hacl.Impl.SHA512.ModQ.sha512_pre_pre2_msg" }, { "project_name": "hacl-star", "file_name": "Spec.RSAPSS.fst", "name": "Spec.RSAPSS.pss_verify_" }, { "project_name": "hacl-star", "file_name": "Hacl.NaCl.fst", "name": "Hacl.NaCl.crypto_secretbox_open_easy" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.Serialization.fst", "name": "MerkleTree.Low.Serialization.serialize_hash" }, { "project_name": "hacl-star", "file_name": "Spec.RSAPSS.fst", "name": "Spec.RSAPSS.pss_verify" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Ed25519.Sign.fst", "name": "Hacl.Impl.Ed25519.Sign.sign_compute_s" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.Serialization.fst", "name": "MerkleTree.Low.Serialization.serialize_hash_vec" }, { "project_name": "hacl-star", "file_name": "Hacl.P256.fst", "name": "Hacl.P256.validate_public_key" }, { "project_name": "hacl-star", "file_name": "Hacl.NaCl.fst", "name": "Hacl.NaCl.crypto_box_open_detached" }, { "project_name": "noise-star", "file_name": "Impl.Noise.API.Session.fst", "name": "Impl.Noise.API.Session.unpack_message" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.Serialization.fst", "name": "MerkleTree.Low.Serialization.deserialize_hash_vec" }, { "project_name": "hacl-star", "file_name": "Spec.RSAPSS.fst", "name": "Spec.RSAPSS.pss_encode" }, { "project_name": "hacl-star", "file_name": "Spec.RSAPSS.fst", "name": "Spec.RSAPSS.rsapss_sign" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Curve25519.fst", "name": "EverCrypt.Curve25519.secret_to_public" }, { "project_name": "hacl-star", "file_name": "Hacl.P256.fst", "name": "Hacl.P256.compressed_to_raw" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Compression.fst", "name": "Hacl.Impl.P256.Compression.compressed_to_raw" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.RSAPSS.fst", "name": "Hacl.Spec.RSAPSS.rsapss_sign_lemma" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.Serialization.fst", "name": "MerkleTree.Low.Serialization.serialize_hash_vv" } ], "selected_premises": [ "Lib.Buffer.lbuffer", "Lib.Buffer.lbuffer_t", "Hacl.Impl.K256.Qinv.mk_to_k256_scalar_comm_monoid", "Lib.MultiBuffer.as_seq_multi", "Hacl.Spec.Bignum.Definitions.blocks", "Hacl.Spec.Bignum.Definitions.blocks0", "Hacl.Impl.K256.Point.getx", "Lib.NTuple.ntuple", "Hacl.K256.Scalar.qas_nat", "Hacl.K256.ECDSA.secp256k1_ecdsa_is_signature_normalized", "Hacl.Impl.K256.Sign.ecdsa_sign_store", "Hacl.Impl.K256.Finv.mk_to_k256_prime_comm_monoid", "Hacl.Bignum.Definitions.blocks0", "Lib.Buffer.as_seq", "Hacl.Bignum.Definitions.lbignum", "Hacl.Impl.K256.Verify.load_signature", "Hacl.Impl.K256.Qinv.mul_mod", "Lib.NTuple.flen", "Lib.Sequence.lseq", "Hacl.Impl.K256.Qinv.linv", "Hacl.K256.Scalar.qeval", "Hacl.K256.Field.nlimb", "Hacl.K256.Scalar.qnlimb", "Hacl.Bignum.Definitions.blocks", "Hacl.K256.Field.felem", "Hacl.Hash.Definitions.m_spec", "Spec.K256.PointOps.felem", "Lib.IntTypes.uint_t", "Hacl.K256.ECDSA.secp256k1_ecdsa_signature_normalize", "Hacl.Spec.Bignum.Definitions.lbignum", "Hacl.Impl.K256.Point.gety", "LowStar.Buffer.trivial_preorder", "Spec.K256.PointOps.q", "Lib.IntTypes.int_t", "Hacl.Impl.K256.Qinv.qsquare_times_in_place", "Spec.K256.PointOps.g", "Hacl.Impl.K256.Qinv.linv_ctx", "Hacl.Impl.K256.Finv.linv_ctx", "Lib.Buffer.gsub", "Hacl.K256.Field.as_felem4", "Hacl.Impl.K256.Qinv.mk_k256_scalar_concrete_ops", "Hacl.Impl.K256.Qinv.refl", "Hacl.Impl.K256.Point.as_felem5_lseq", "FStar.List.Tot.Base.length", "Hacl.Impl.K256.Sign.lbytes", "Hacl.Impl.K256.Verify.lbytes", "Spec.SHA2.Constants.k384_512", "Hacl.Impl.K256.Finv.fsquare_times_in_place", "Hacl.Impl.K256.Verify.ecdsa_verify_avoid_finv", "Hacl.Impl.K256.Finv.mul_mod", "Hacl.Spec.K256.GLV.g2", "Hacl.Impl.K256.Qinv.qsquare_times", "FStar.Seq.Properties.seq_of_list", "Hacl.Impl.K256.Point.getz", "Hacl.Impl.K256.Finv.fsquare_times", "Hacl.Impl.K256.Qinv.qinv", "Hacl.Impl.K256.Qinv.sqr_mod", "Hacl.K256.Field.as_felem5", "Hacl.Spec.K256.GLV.b2", "Lib.Sequence.to_seq", "FStar.Integers.op_Greater_Equals", "Hacl.Impl.K256.Qinv.one_mod", "Hacl.Bignum.Definitions.bn_v", "Hacl.Impl.K256.Finv.refl", "Hacl.K256.Scalar.qelem", "FStar.List.Tot.Base.map", "Lib.IntTypes.size", "Spec.K256.PointOps.proj_point", "Hacl.Impl.Exponentiation.table_inv_precomp", "Hacl.Spec.K256.Qinv.nat_mod_comm_monoid", "Hacl.Spec.K256.Finv.nat_mod_comm_monoid", "Lib.IntTypes.range", "FStar.Integers.op_Less_Equals", "Hacl.Spec.K256.GLV.g1", "FStar.Integers.op_Greater", "Hacl.Impl.K256.Finv.mk_k256_prime_concrete_ops", "Hacl.Streaming.MD.hacl_md", "FStar.Integers.op_Less", "Hacl.Bignum.Definitions.limb", "LowStar.Monotonic.Buffer.length", "Spec.SHA2.Constants.k224_256", "Hacl.Impl.K256.Finv.sqr_mod", "Hacl.Streaming.SHA2.hacl_sha2_224", "Hacl.Spec.K256.Qinv.one_mod", "Hacl.Impl.K256.Finv.fsqrt", "Hacl.Impl.K256.Finv.finv", "LowStar.Buffer.gcmalloc_of_list", "Hacl.Impl.K256.Point.point_inv_lseq", "Spec.K256.PointOps.prime", "Hacl.Spec.K256.GLV.negate_point_and_scalar_cond", "Hacl.Streaming.SHA2.hacl_sha2_256", "Hacl.Streaming.MD.hacl_sha2_256", "Lib.MultiBuffer.multibuf", "Hacl.Hash.Definitions.mk_impl", "Hacl.Spec.K256.GLV.a2", "Hacl.Spec.K256.Finv.one_mod", "Hacl.Spec.K256.GLV.aff_negate_point_and_scalar_cond", "Hacl.Streaming.SHA2.state_512", "Hacl.Spec.K256.Qinv.qinv", "Hacl.Spec.K256.Field52.Definitions.max52" ], "source_upto_this": "module Hacl.K256.ECDSA\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nmodule ST = FStar.HyperStack.ST\nmodule LSeq = Lib.Sequence\nmodule BSeq = Lib.ByteSequence\n\nmodule S = Spec.K256\nmodule BDL = Hacl.Spec.K256.Field52.Definitions.Lemmas\n\nmodule P = Hacl.Impl.K256.Point\nmodule SK = Hacl.Impl.K256.Sign\nmodule VK = Hacl.Impl.K256.Verify\n\nopen Hacl.K256.Field\nopen Hacl.K256.Scalar\n\n#set-options \"--z3rlimit 50 --fuel 0 --ifuel 0\"\n\nlet ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n SK.ecdsa_sign_hashed_msg signature msgHash private_key nonce\n\n\nlet ecdsa_sign_sha256 signature msg_len msg private_key nonce =\n push_frame ();\n let msgHash = create 32ul (u8 0) in\n Hacl.Streaming.SHA2.hash_256 msgHash msg msg_len;\n let b = ecdsa_sign_hashed_msg signature msgHash private_key nonce in\n pop_frame ();\n b\n\n\nlet ecdsa_verify_hashed_msg m public_key signature =\n VK.ecdsa_verify_hashed_msg m public_key signature\n\n\nlet ecdsa_verify_sha256 msg_len msg public_key signature =\n push_frame ();\n let mHash = create 32ul (u8 0) in\n Hacl.Streaming.SHA2.hash_256 mHash msg msg_len;\n let b = ecdsa_verify_hashed_msg mHash public_key signature in\n pop_frame ();\n b\n\n/// Low-S normalization\n\nlet secp256k1_ecdsa_signature_normalize signature =\n push_frame ();\n let s_q = create_qelem () in\n let s = sub signature 32ul 32ul in\n let is_sk_valid = load_qelem_vartime s_q s in\n let b =\n if not is_sk_valid then false\n else begin\n let is_sk_lt_q_halved = is_qelem_le_q_halved_vartime s_q in\n qnegate_conditional_vartime s_q (not is_sk_lt_q_halved);\n\n let h1 = ST.get () in\n update_sub_f h1 signature 32ul 32ul\n (fun h -> BSeq.nat_to_bytes_be 32 (qas_nat h1 s_q))\n (fun _ -> store_qelem (sub signature 32ul 32ul) s_q);\n true end in\n pop_frame ();\n b\n\n\nlet secp256k1_ecdsa_is_signature_normalized signature =\n push_frame ();\n let s_q = create_qelem () in\n let s = sub signature 32ul 32ul in\n let is_s_valid = load_qelem_vartime s_q s in\n let is_s_lt_q_halved = is_qelem_le_q_halved_vartime s_q in\n pop_frame ();\n is_s_valid && is_s_lt_q_halved\n\n", "sketch": [ "Step 1: The definition is about signing a hashed message using the secp256k1 ECDSA algorithm. It takes a signature buffer, a hashed message, a private key, and a nonce as inputs, and returns a boolean indicating success or failure.\nStep 2: The implementation involves calling the underlying signing function from the Spec.K256 module, checking if the signing was successful, and updating the signature buffer accordingly.", "Step 1: The definition is about signing a hashed message using the secp256k1 ECDSA algorithm. It takes a signature buffer, a hashed message, a private key, and a nonce, and returns a boolean indicating success.\nStep 2: The implementation involves calling the underlying signing function from the Spec.K256 module, ensuring the signature buffer is updated correctly, and verifying the result.", "Step 1: The definition is about signing a hashed message using the secp256k1 ECDSA algorithm. It takes a signature buffer, a hashed message, a private key, and a nonce, and returns a boolean indicating success.\nStep 2: The implementation will call the underlying signing function from the Spec.K256 module, check if the signing was successful, and if so, store the resulting signature in the provided buffer.", "Step 1: This definition is about signing a hashed message using the secp256k1 ECDSA algorithm. It takes a signature buffer, a hashed message, a private key, and a nonce as inputs and returns a boolean indicating success or failure.\nStep 2: The implementation involves calling the underlying signing function from the Spec.K256 module, checking if the signing was successful, and updating the signature buffer accordingly.", "Step 1: The definition is about signing a hashed message using the secp256k1 ECDSA algorithm. It takes a signature buffer, a hashed message, a private key, and a nonce as inputs.\nStep 2: The implementation involves calling the underlying signing function from the Spec.K256 module, checking if the signing operation was successful, and updating the signature buffer accordingly.", "Step 1: The definition is about signing a hashed message using the secp256k1 ECDSA algorithm. It takes a signature buffer, a hashed message, a private key, and a nonce as inputs, and returns a boolean indicating success or failure.\nStep 2: The implementation involves calling the underlying signing function from the Spec.K256 module, updating the signature buffer if the signing is successful, and ensuring the appropriate preconditions and postconditions are met.", "Step 1: The definition is about signing a hashed message using the secp256k1 ECDSA algorithm. It takes a signature buffer, a hashed message, a private key, and a nonce as inputs, and returns a boolean indicating success or failure.\nStep 2: The implementation involves calling the signing function from the SK module, ensuring the signature buffer is updated correctly, and verifying the conditions specified in the ensures clause.", "Step 1: The definition is about signing a hashed message using the secp256k1 ECDSA algorithm. It takes a signature buffer, a hashed message, a private key, and a nonce, and returns a boolean indicating success.\nStep 2: The implementation involves calling the underlying signing function from the Spec.K256 module, checking if the signing was successful, and updating the signature buffer accordingly.", "Step 1: This definition is about signing a hashed message using the secp256k1 ECDSA algorithm. It takes a signature buffer, a hashed message, a private key, and a nonce as inputs and returns a boolean indicating success or failure.\nStep 2: The implementation involves calling the underlying signing function from the Spec.K256 module. It ensures that the signature buffer is updated correctly if the signing is successful and verifies the preconditions and postconditions related to memory safety and disjointness of buffers.", "Step 1: The definition is about signing a hashed message using the secp256k1 ECDSA algorithm. It takes a signature buffer, a hashed message, a private key, and a nonce as inputs, and returns a boolean indicating success or failure.\nStep 2: The implementation involves calling the underlying signing function from the Spec module, checking if the signing was successful, and updating the signature buffer accordingly." ], "generated_solution": [ "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n let sgnt = S.secp256k1_ecdsa_sign_hashed_msg (as_seq msgHash) (as_seq private_key) (as_seq nonce) in\n match sgnt with\n | None -> false\n | Some sgnt_val ->\n update_sub (as_seq signature) 0ul sgnt_val;\n true", "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n let sgnt = S.secp256k1_ecdsa_sign_hashed_msg (as_seq #_ msgHash) (as_seq #_ private_key) (as_seq #_ nonce) in\n match sgnt with\n | None -> false\n | Some s ->\n update_sub_f (ST.get ()) signature 0ul 64ul\n (fun h -> BSeq.nat_to_bytes_be 64 (qas_nat h s))\n (fun _ -> store_qelem signature s);\n true", "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n let sgnt = S.secp256k1_ecdsa_sign_hashed_msg (as_seq h msgHash) (as_seq h private_key) (as_seq h nonce) in\n match sgnt with\n | None -> false\n | Some sgnt_val ->\n store (sub signature 0ul 64ul) sgnt_val;\n true", "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n let sgnt = S.secp256k1_ecdsa_sign_hashed_msg (as_seq h msgHash) (as_seq h private_key) (as_seq h nonce) in\n match sgnt with\n | None -> false\n | Some sgnt_val ->\n update_sub (loc signature) 0ul 64ul (fun _ -> sgnt_val);\n true", "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n let sgnt = S.secp256k1_ecdsa_sign_hashed_msg (as_seq msgHash) (as_seq private_key) (as_seq nonce) in\n match sgnt with\n | None -> false\n | Some sgnt_val ->\n let _ = BSeq.blit (S.seq_to_bytes sgnt_val) 0ul signature 0ul 64ul in\n true", "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n let sgnt = S.secp256k1_ecdsa_sign_hashed_msg (as_seq (ST.get ()) msgHash) (as_seq (ST.get ()) private_key) (as_seq (ST.get ()) nonce) in\n match sgnt with\n | None -> false\n | Some sgnt_val ->\n let h = ST.get () in\n update_sub_f h signature 0ul 64ul\n (fun _ -> sgnt_val)\n (fun _ -> ());\n true", "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n push_frame ();\n let sgnt = S.secp256k1_ecdsa_sign_hashed_msg (as_seq msgHash) (as_seq private_key) (as_seq nonce) in\n let b = match sgnt with\n | Some s -> update_sub signature 0ul 64ul (fun _ -> s); true\n | None -> false\n in\n pop_frame ();\n b", "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n let sgnt = S.secp256k1_ecdsa_sign_hashed_msg (as_seq msgHash) (as_seq private_key) (as_seq nonce) in\n match sgnt with\n | None -> false\n | Some sgnt_val ->\n update_sub signature 0ul 64ul (fun _ -> sgnt_val);\n true", "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n let sgnt = S.secp256k1_ecdsa_sign_hashed_msg (as_seq h msgHash) (as_seq h private_key) (as_seq h nonce) in\n match sgnt with\n | None -> false\n | Some sgnt_val ->\n update_sub_f h signature 0ul 64ul\n (fun h -> BSeq.nat_to_bytes_be 64 sgnt_val)\n (fun _ -> ());\n true", "let secp256k1_ecdsa_sign_hashed_msg signature msgHash private_key nonce =\n let sgnt = S.secp256k1_ecdsa_sign_hashed_msg (as_seq h0 msgHash) (as_seq h0 private_key) (as_seq h0 nonce) in\n match sgnt with\n | None -> false\n | Some sgnt_val ->\n update_sub_f h0 signature 0ul 64ul (fun _ -> sgnt_val);\n true" ] }, { "file_name": "Vale.AES.PPC64LE.GCMdecrypt.fst", "name": "Vale.AES.PPC64LE.GCMdecrypt.va_qcode_VectorEqual", "opens_and_abbrevs": [ { "open": "Vale.Lib.Basic" }, { "open": "Vale.AES.PPC64LE.GCMencrypt" }, { "open": "Vale.Lib.Meta" }, { "open": "Vale.Math.Poly2.Bits_s" }, { "open": "Vale.AES.PPC64LE.GF128_Mul" }, { "open": "Vale.PPC64LE.QuickCodes" }, { "open": "Vale.PPC64LE.QuickCode" }, { "open": "Vale.PPC64LE.InsStack" }, { "open": "Vale.PPC64LE.InsVector" }, { "open": "Vale.PPC64LE.InsMem" }, { "open": "Vale.PPC64LE.InsBasic" }, { "open": "Vale.PPC64LE.Decls" }, { "open": "Vale.PPC64LE.State" }, { "open": "Vale.PPC64LE.Stack_i" }, { "open": "Vale.PPC64LE.Memory" }, { "open": "Vale.PPC64LE.Machine_s" }, { "open": "Vale.AES.PPC64LE.GCTR" }, { "open": "Vale.AES.PPC64LE.GHash" }, { "open": "Vale.AES.GCM_helpers_BE" }, { "open": "Vale.Poly1305.Math" }, { "open": "Vale.AES.GF128" }, { "open": "Vale.AES.GF128_s" }, { "open": "Vale.AES.PPC64LE.AES" }, { "open": "Vale.AES.GCM_BE_s" }, { "open": "Vale.AES.GHash_BE" }, { "open": "Vale.AES.GHash_BE_s" }, { "open": "Vale.AES.GCM_BE" }, { "open": "Vale.AES.GCTR_BE" }, { "open": "Vale.AES.GCTR_BE_s" }, { "open": "Vale.AES.AES_BE_s" }, { "open": "Vale.Arch.HeapImpl" }, { "open": "Vale.Arch.Types" }, { "open": "Vale.Def.Types_s" }, { "open": "Vale.Def.Words.Seq_s" }, { "open": "Vale.Def.Words_s" }, { "open": "FStar.Seq" }, { "open": "Vale.Def.Opaque_s" }, { "open": "Vale.Def.Prop_s" }, { "open": "Vale.AES.PPC64LE.GCMencrypt" }, { "open": "Vale.Lib.Meta" }, { "open": "Vale.Math.Poly2.Bits_s" }, { "open": "Vale.AES.PPC64LE.GF128_Mul" }, { "open": "Vale.PPC64LE.QuickCodes" }, { "open": "Vale.PPC64LE.QuickCode" }, { "open": "Vale.PPC64LE.InsStack" }, { "open": "Vale.PPC64LE.InsVector" }, { "open": "Vale.PPC64LE.InsMem" }, { "open": "Vale.PPC64LE.InsBasic" }, { "open": "Vale.PPC64LE.Decls" }, { "open": "Vale.PPC64LE.State" }, { "open": "Vale.PPC64LE.Stack_i" }, { "open": "Vale.PPC64LE.Memory" }, { "open": "Vale.PPC64LE.Machine_s" }, { "open": "Vale.AES.PPC64LE.GCTR" }, { "open": "Vale.AES.PPC64LE.GHash" }, { "open": "Vale.AES.GCM_helpers_BE" }, { "open": "Vale.Poly1305.Math" }, { "open": "Vale.AES.GF128" }, { "open": "Vale.AES.GF128_s" }, { "open": "Vale.AES.PPC64LE.AES" }, { "open": "Vale.AES.GCM_BE_s" }, { "open": "Vale.AES.GHash_BE" }, { "open": "Vale.AES.GHash_BE_s" }, { "open": "Vale.AES.GCM_BE" }, { "open": "Vale.AES.GCTR_BE" }, { "open": "Vale.AES.GCTR_BE_s" }, { "open": "Vale.AES.AES_BE_s" }, { "open": "Vale.Arch.HeapImpl" }, { "open": "Vale.Arch.Types" }, { "open": "Vale.Def.Types_s" }, { "open": "Vale.Def.Words.Seq_s" }, { "open": "Vale.Def.Words_s" }, { "open": "FStar.Seq" }, { "open": "Vale.Def.Opaque_s" }, { "open": "Vale.Def.Prop_s" }, { "open": "Vale.AES.PPC64LE" }, { "open": "Vale.AES.PPC64LE" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 1, "initial_ifuel": 0, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": true, "smtencoding_nl_arith_repr": "wrapped", "smtencoding_l_arith_repr": "native", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val va_qcode_VectorEqual (va_mods: va_mods_t) : (va_quickCode unit (va_code_VectorEqual ()))", "source_definition": "let va_qcode_VectorEqual (va_mods:va_mods_t) : (va_quickCode unit (va_code_VectorEqual ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 667 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vcmpequw (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 1)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 668 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Mfvsrld (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0)) (fun (va_s:va_state) _ -> let\n (tmp1:nat64) = va_get_reg 4 va_s in let (va_arg28:Vale.Def.Types_s.quad32) = va_get_vec 0 va_s\n in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 671 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_equality_check_helper va_arg28) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 673 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Nat64Equal ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 674 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (fun (va_s:va_state) _ -> let\n (result1:nat64) = va_get_reg 3 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 677 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Mfvsrd (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0)) (fun (va_s:va_state) _ -> let\n (tmp2:nat64) = va_get_reg 4 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 680 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Nat64Equal ()) (fun (va_s:va_state) _ -> let (result2:nat64) = va_get_reg 3 va_s in\n va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 683 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Add (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (fun\n (va_s:va_state) _ -> let (va_arg27:Vale.Def.Words_s.nat64) = va_get_reg 3 va_s in let\n (va_arg26:Vale.Def.Words_s.nat64) = result2 in let (va_arg25:Vale.Def.Words_s.nat64) = tmp2 in\n let (va_arg24:Vale.Def.Words_s.nat64) = result1 in let (va_arg23:Vale.Def.Words_s.nat64) = tmp1\n in let (va_arg22:Vale.Def.Types_s.quad32) = va_get_vec 0 va_s in let\n (va_arg21:Vale.Def.Types_s.quad32) = va_get_vec 1 va_old_s in let\n (va_arg20:Vale.Def.Types_s.quad32) = va_get_vec 0 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 684 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_equality_check_helper_2 va_arg20 va_arg21 va_arg22\n va_arg23 va_arg24 va_arg25 va_arg26 va_arg27) (va_QEmpty (()))))))))))))", "source_range": { "start_line": 1971, "start_col": 0, "end_line": 2003, "end_col": 76 }, "interleaved": false, "definition": "fun va_mods ->\n Vale.PPC64LE.QuickCodes.qblock va_mods\n (fun va_s ->\n let va_old_s = va_s in\n Vale.PPC64LE.QuickCodes.va_QSeq Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 667 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.InsVector.va_quick_Vcmpequw (Vale.PPC64LE.Decls.va_op_vec_opr_vec 0)\n (Vale.PPC64LE.Decls.va_op_vec_opr_vec 0)\n (Vale.PPC64LE.Decls.va_op_vec_opr_vec 1))\n (Vale.PPC64LE.QuickCodes.va_QBind Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 668 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.InsVector.va_quick_Mfvsrld (Vale.PPC64LE.Decls.va_op_reg_opr_reg 4)\n (Vale.PPC64LE.Decls.va_op_vec_opr_vec 0))\n (fun va_s _ ->\n let tmp1 = Vale.PPC64LE.Decls.va_get_reg 4 va_s in\n let va_arg28 = Vale.PPC64LE.Decls.va_get_vec 0 va_s in\n Vale.PPC64LE.QuickCodes.va_qPURE Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 671 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun _ -> Vale.Arch.Types.lemma_equality_check_helper va_arg28)\n (Vale.PPC64LE.QuickCodes.va_QSeq Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 673 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.AES.PPC64LE.GCMdecrypt.va_quick_Nat64Equal ())\n (Vale.PPC64LE.QuickCodes.va_QBind Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 674 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.InsBasic.va_quick_Move (Vale.PPC64LE.Decls.va_op_reg_opr_reg\n 6)\n (Vale.PPC64LE.Decls.va_op_reg_opr_reg 3))\n (fun va_s _ ->\n let result1 = Vale.PPC64LE.Decls.va_get_reg 3 va_s in\n Vale.PPC64LE.QuickCodes.va_QBind Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 677 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.InsVector.va_quick_Mfvsrd (Vale.PPC64LE.Decls.va_op_reg_opr_reg\n 4)\n (Vale.PPC64LE.Decls.va_op_vec_opr_vec 0))\n (fun va_s _ ->\n let tmp2 = Vale.PPC64LE.Decls.va_get_reg 4 va_s in\n Vale.PPC64LE.QuickCodes.va_QBind Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 680 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.AES.PPC64LE.GCMdecrypt.va_quick_Nat64Equal ())\n (fun va_s _ ->\n let result2 = Vale.PPC64LE.Decls.va_get_reg 3 va_s in\n Vale.PPC64LE.QuickCodes.va_QBind Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 683 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.InsBasic.va_quick_Add (Vale.PPC64LE.Decls.va_op_reg_opr_reg\n 3)\n (Vale.PPC64LE.Decls.va_op_reg_opr_reg 6)\n (Vale.PPC64LE.Decls.va_op_reg_opr_reg 3))\n (fun va_s _ ->\n let va_arg27 =\n Vale.PPC64LE.Decls.va_get_reg 3 va_s\n in\n let va_arg26 = result2 in\n let va_arg25 = tmp2 in\n let va_arg24 = result1 in\n let va_arg23 = tmp1 in\n let va_arg22 =\n Vale.PPC64LE.Decls.va_get_vec 0 va_s\n in\n let va_arg21 =\n Vale.PPC64LE.Decls.va_get_vec 1 va_old_s\n in\n let va_arg20 =\n Vale.PPC64LE.Decls.va_get_vec 0 va_old_s\n in\n Vale.PPC64LE.QuickCodes.va_qPURE Vale.PPC64LE.QuickCodes.va_range1\n \"***** PRECONDITION NOT MET AT line 684 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun _ ->\n Vale.Arch.Types.lemma_equality_check_helper_2\n va_arg20\n va_arg21\n va_arg22\n va_arg23\n va_arg24\n va_arg25\n va_arg26\n va_arg27)\n (Vale.PPC64LE.QuickCodes.va_QEmpty ()))))))))))\n <:\n Vale.PPC64LE.QuickCode.va_quickCode Prims.unit\n (Vale.AES.PPC64LE.GCMdecrypt.va_code_VectorEqual ())", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Vale.PPC64LE.QuickCode.va_mods_t", "Vale.PPC64LE.QuickCodes.qblock", "Prims.unit", "Prims.Cons", "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.InsVector.va_code_Vcmpequw", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.PPC64LE.InsVector.va_code_Mfvsrld", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.AES.PPC64LE.GCMdecrypt.va_code_Nat64Equal", "Vale.PPC64LE.InsBasic.va_code_Move", "Vale.PPC64LE.InsVector.va_code_Mfvsrd", "Vale.PPC64LE.InsBasic.va_code_Add", "Prims.Nil", "Vale.PPC64LE.Machine_s.precode", "Vale.PPC64LE.Decls.ins", "Vale.PPC64LE.Decls.ocmp", "Vale.PPC64LE.Decls.va_state", "Vale.PPC64LE.QuickCodes.va_QSeq", "Vale.PPC64LE.QuickCodes.va_range1", "Vale.PPC64LE.InsVector.va_quick_Vcmpequw", "Vale.PPC64LE.QuickCodes.va_QBind", "Vale.PPC64LE.InsVector.va_quick_Mfvsrld", "Vale.PPC64LE.QuickCodes.va_qPURE", "Prims.pure_post", "Prims.l_and", "Prims.l_True", "Prims.l_Forall", "Prims.l_imp", "Prims.eq2", "Prims.int", "Vale.Def.Words_s.__proj__Mkfour__item__lo0", "Vale.Def.Words_s.nat32", "Vale.Def.Words_s.__proj__Mkfour__item__lo1", "Vale.Arch.Types.lo64", "Prims.l_or", "Prims.b2t", "Prims.op_Negation", "Prims.op_Equality", "Vale.Def.Words_s.__proj__Mkfour__item__hi2", "Vale.Def.Words_s.__proj__Mkfour__item__hi3", "Vale.Arch.Types.hi64", "Prims.l_not", "Prims.l_iff", "Vale.Arch.Types.lemma_equality_check_helper", "Vale.AES.PPC64LE.GCMdecrypt.va_quick_Nat64Equal", "Vale.PPC64LE.InsBasic.va_quick_Move", "Vale.PPC64LE.InsVector.va_quick_Mfvsrd", "Vale.PPC64LE.InsBasic.va_quick_Add", "Vale.Def.Words_s.four", "Vale.Def.Words_s.Mkfour", "Prims.bool", "Vale.Def.Words_s.nat64", "Prims.op_Addition", "Vale.Def.Types_s.quad32", "Prims.op_GreaterThan", "Prims.logical", "Vale.Arch.Types.lemma_equality_check_helper_2", "Vale.PPC64LE.QuickCodes.va_QEmpty", "Vale.PPC64LE.Decls.va_get_vec", "Vale.PPC64LE.Decls.va_get_reg", "Vale.PPC64LE.QuickCodes.quickCodes", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.QuickCode.va_quickCode", "Vale.AES.PPC64LE.GCMdecrypt.va_code_VectorEqual" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "va_mods: Vale.PPC64LE.QuickCode.va_mods_t\n -> Vale.PPC64LE.QuickCode.va_quickCode Prims.unit\n (Vale.AES.PPC64LE.GCMdecrypt.va_code_VectorEqual ())", "prompt": "let va_qcode_VectorEqual (va_mods: va_mods_t) : (va_quickCode unit (va_code_VectorEqual ())) =\n ", "expected_response": "(qblock va_mods\n (fun (va_s: va_state) ->\n let va_old_s:va_state = va_s in\n va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 667 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vcmpequw (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 1))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 668 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Mfvsrld (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0))\n (fun (va_s: va_state) _ ->\n let tmp1:nat64 = va_get_reg 4 va_s in\n let va_arg28:Vale.Def.Types_s.quad32 = va_get_vec 0 va_s in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 671 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_: unit) -> Vale.Arch.Types.lemma_equality_check_helper va_arg28)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 673 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Nat64Equal ())\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 674 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3))\n (fun (va_s: va_state) _ ->\n let result1:nat64 = va_get_reg 3 va_s in\n va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 677 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Mfvsrd (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0))\n (fun (va_s: va_state) _ ->\n let tmp2:nat64 = va_get_reg 4 va_s in\n va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 680 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Nat64Equal ())\n (fun (va_s: va_state) _ ->\n let result2:nat64 = va_get_reg 3 va_s in\n va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 683 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Add (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 3))\n (fun (va_s: va_state) _ ->\n let va_arg27:Vale.Def.Words_s.nat64 =\n va_get_reg 3 va_s\n in\n let va_arg26:Vale.Def.Words_s.nat64 = result2 in\n let va_arg25:Vale.Def.Words_s.nat64 = tmp2 in\n let va_arg24:Vale.Def.Words_s.nat64 = result1 in\n let va_arg23:Vale.Def.Words_s.nat64 = tmp1 in\n let va_arg22:Vale.Def.Types_s.quad32 =\n va_get_vec 0 va_s\n in\n let va_arg21:Vale.Def.Types_s.quad32 =\n va_get_vec 1 va_old_s\n in\n let va_arg20:Vale.Def.Types_s.quad32 =\n va_get_vec 0 va_old_s\n in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 684 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_: unit) ->\n Vale.Arch.Types.lemma_equality_check_helper_2\n va_arg20\n va_arg21\n va_arg22\n va_arg23\n va_arg24\n va_arg25\n va_arg26\n va_arg27)\n (va_QEmpty (()))))))))))))", "source": { "project_name": "hacl-star", "file_name": "obj/Vale.AES.PPC64LE.GCMdecrypt.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Vale.AES.PPC64LE.GCMdecrypt.fst", "checked_file": "dataset/Vale.AES.PPC64LE.GCMdecrypt.fst.checked", "interface_file": true, "dependencies": [ "dataset/Vale.PPC64LE.State.fsti.checked", "dataset/Vale.PPC64LE.Stack_i.fsti.checked", "dataset/Vale.PPC64LE.QuickCodes.fsti.checked", "dataset/Vale.PPC64LE.QuickCode.fst.checked", "dataset/Vale.PPC64LE.Memory.fsti.checked", "dataset/Vale.PPC64LE.Machine_s.fst.checked", "dataset/Vale.PPC64LE.InsVector.fsti.checked", "dataset/Vale.PPC64LE.InsStack.fsti.checked", "dataset/Vale.PPC64LE.InsMem.fsti.checked", "dataset/Vale.PPC64LE.InsBasic.fsti.checked", "dataset/Vale.PPC64LE.Decls.fsti.checked", "dataset/Vale.Poly1305.Math.fsti.checked", "dataset/Vale.Math.Poly2.Bits_s.fsti.checked", "dataset/Vale.Lib.Meta.fsti.checked", "dataset/Vale.Lib.Basic.fsti.checked", "dataset/Vale.Def.Words_s.fsti.checked", "dataset/Vale.Def.Words.Seq_s.fsti.checked", "dataset/Vale.Def.Words.Four_s.fsti.checked", "dataset/Vale.Def.Types_s.fst.checked", "dataset/Vale.Def.Prop_s.fst.checked", "dataset/Vale.Def.Opaque_s.fsti.checked", "dataset/Vale.Arch.Types.fsti.checked", "dataset/Vale.Arch.HeapImpl.fsti.checked", "dataset/Vale.AES.Types_helpers.fsti.checked", "dataset/Vale.AES.PPC64LE.GHash.fsti.checked", "dataset/Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "dataset/Vale.AES.PPC64LE.GCTR.fsti.checked", "dataset/Vale.AES.PPC64LE.GCMencrypt.fsti.checked", "dataset/Vale.AES.PPC64LE.AES.fsti.checked", "dataset/Vale.AES.GHash_BE_s.fst.checked", "dataset/Vale.AES.GHash_BE.fsti.checked", "dataset/Vale.AES.GF128_s.fsti.checked", "dataset/Vale.AES.GF128.fsti.checked", "dataset/Vale.AES.GCTR_BE_s.fst.checked", "dataset/Vale.AES.GCTR_BE.fsti.checked", "dataset/Vale.AES.GCM_helpers_BE.fsti.checked", "dataset/Vale.AES.GCM_BE_s.fst.checked", "dataset/Vale.AES.GCM_BE.fsti.checked", "dataset/Vale.AES.AES_common_s.fst.checked", "dataset/Vale.AES.AES_BE_s.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Seq.Base.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "let aes_reqs\n (alg:algorithm) (key:seq nat32) (round_keys:seq quad32) (keys_b:buffer128)\n (key_ptr:int) (heap0:vale_heap) (layout:vale_heap_layout) : prop0\n =\n (alg = AES_128 \\/ alg = AES_256) /\\\n is_aes_key_word alg key /\\\n length(round_keys) == nr(alg) + 1 /\\\n round_keys == key_to_round_keys_word alg key /\\\n validSrcAddrs128 heap0 key_ptr keys_b (nr alg + 1) layout Secret /\\\n reverse_bytes_quad32_seq (s128 heap0 keys_b) == round_keys", "val va_code_Gcm_extra_bytes : alg:algorithm -> Tot va_code", "let va_code_Gcm_extra_bytes alg =\n (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 7)) (va_CCons\n (va_code_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 9)\n (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 12) (va_op_vec_opr_vec\n 9)) (va_CCons (va_code_Ghash_extra_bytes ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 11)) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_Vxor\n (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 0)) (va_CCons\n (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 12)\n (va_op_reg_opr_reg 3) Secret) (va_CNil ()))))))))))", "val va_code_Gcm_blocks_decrypt_stdcall : alg:algorithm -> Tot va_code", "val va_codegen_success_Gcm_blocks_decrypt_stdcall : alg:algorithm -> Tot va_pbool", "val va_codegen_success_Gcm_extra_bytes : alg:algorithm -> Tot va_pbool", "let va_req_Gcm_blocks_decrypt_stdcall (va_b0:va_code) (va_s0:va_state) (alg:algorithm)\n (auth_b:buffer128) (auth_bytes:nat64) (auth_num:nat64) (keys_b:buffer128) (iv_b:buffer128)\n (iv:supported_iv_BE) (hkeys_b:buffer128) (abytes_b:buffer128) (in128_b:buffer128)\n (out128_b:buffer128) (len128_num:nat64) (inout_b:buffer128) (cipher_num:nat64)\n (gcm_struct_b:buffer64) (tag_b:buffer128) (key:(seq nat32)) : prop =\n (va_require_total va_b0 (va_code_Gcm_blocks_decrypt_stdcall alg) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (cipher_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (tag_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 12\n (va_get_mem_heaplet 3 va_s0) in va_get_reg 1 va_s0 == Vale.PPC64LE.Stack_i.init_r1\n (va_get_stack va_s0) /\\ Vale.PPC64LE.Memory.is_initial_heap (va_get_mem_layout va_s0)\n (va_get_mem va_s0) /\\ auth_len == auth_num /\\ auth_num_bytes == auth_bytes /\\ len128 ==\n len128_num /\\ cipher_num_bytes == cipher_num /\\ Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem\n va_s0) (va_get_reg 3 va_s0) gcm_struct_b 13 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) auth_ptr auth_b auth_len\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0)\n abytes_ptr abytes_b 1 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem va_s0) iv_ptr iv_b 1 (va_get_mem_layout va_s0) Public /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) in128_ptr in128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0)\n out128_ptr out128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0) inout_ptr inout_b 1 (va_get_mem_layout\n va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0)\n tag_ptr tag_b 1 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints64_128\n gcm_struct_b ([keys_b; auth_b; abytes_b; iv_b; in128_b; out128_b; inout_b; hkeys_b; tag_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 tag_b ([keys_b; auth_b; abytes_b; iv_b; in128_b;\n out128_b; inout_b; hkeys_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b; auth_b;\n abytes_b; in128_b; out128_b; inout_b; hkeys_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128\n inout_b ([keys_b; auth_b; abytes_b; in128_b; out128_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 auth_b ([keys_b; abytes_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 abytes_b ([keys_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 out128_b ([keys_b; auth_b; abytes_b; hkeys_b; inout_b])\n /\\ Vale.PPC64LE.Decls.buffer_disjoints128 in128_b ([keys_b; auth_b; abytes_b; hkeys_b;\n inout_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b == out128_b)\n /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply` len128 <\n pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ cipher_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem va_s0) + 128 < pow2_64 /\\ (va_mul_nat len128\n (128 `op_Division` 8) <= cipher_num_bytes /\\ cipher_num_bytes < va_mul_nat len128 (128\n `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division` 8) <=\n auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ aes_reqs alg key (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem va_s0) keys_b)) keys_b keys_ptr (va_get_mem\n va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.OptPublic_BE.hkeys_reqs_pub\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) hkeys_b))\n (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0\n 0 0 0)) /\\ (let h_BE = Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0) in let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem va_s0)) in iv_BE ==\n Vale.AES.GCM_BE_s.compute_iv_BE h_BE iv)))", "let va_codegen_success_Gcm_extra_bytes alg =\n (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 7)) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 9)\n (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 12)\n (va_op_vec_opr_vec 9)) (va_pbool_and (va_codegen_success_Ghash_extra_bytes ()) (va_pbool_and\n (va_codegen_success_Vmr (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 11)) (va_pbool_and\n (va_codegen_success_AESEncryptBlock alg) (va_pbool_and (va_codegen_success_Vxor\n (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 0)) (va_pbool_and\n (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 12)\n (va_op_reg_opr_reg 3) Secret) (va_ttrue ())))))))))", "let va_qcode_Gcm_extra_bytes (va_mods:va_mods_t) (alg:algorithm) (inout_b:buffer128) (key:(seq\n nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat)\n (old_hash:quad32) (completed_quads:(seq quad32)) (h_BE:quad32) : (va_quickCode unit\n (va_code_Gcm_extra_bytes alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (len:(va_int_range\n 1 1)) = 1 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 164 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 165 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 9)\n (va_op_reg_opr_reg 3) Secret inout_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 166 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 9)) (fun (va_s:va_state) _ -> let\n (hash_input:quad32) = va_get_vec 9 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 170 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Ghash_extra_bytes hkeys_b total_bytes old_hash h_BE completed_quads) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (FStar.Seq.Base.equal #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b)) (FStar.Seq.Base.create #quad32 1\n hash_input)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 173 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 174 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_AESEncryptBlock alg (va_get_vec 7 va_old_s) key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 176 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vxor (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 0)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 177 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 12)\n (va_op_reg_opr_reg 3) Secret inout_b 0) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 179 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR_BE.gctr_partial_reveal ()) (va_QEmpty (())))))))))))))", "val va_lemma_Gcm_extra_bytes : va_b0:va_code -> va_s0:va_state -> alg:algorithm ->\n inout_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> total_bytes:nat -> old_hash:quad32 -> completed_quads:(seq quad32) ->\n h_BE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_extra_bytes alg) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (len:(va_int_range 1 1)) = 1 in Vale.PPC64LE.Decls.buffers_disjoint128 keys_b inout_b /\\\n Vale.PPC64LE.Decls.buffers_disjoint128 hkeys_b inout_b /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 5 va_s0) (va_get_reg 3 va_s0) inout_b len (va_get_mem_layout va_s0) Secret\n /\\ len == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b /\\ aes_reqs\n alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout\n va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ va_get_vec 1 va_s0 == Vale.AES.GHash_BE.ghash_incremental0\n h_BE old_hash completed_quads /\\ FStar.Seq.Base.length #quad32 completed_quads == total_bytes\n `op_Division` 16 /\\ total_bytes < 16 `op_Multiply` FStar.Seq.Base.length #quad32\n completed_quads + 16 /\\ va_get_reg 8 va_s0 == total_bytes `op_Modulus` 16 /\\ total_bytes\n `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16 `op_Multiply`\n Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes - 1) < total_bytes)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (len:(va_int_range 1 1)) = 1 in Vale.PPC64LE.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg\n len (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5\n va_s0) inout_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) key (va_get_vec 7 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b)) in let input_bytes =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_quads)) 0 total_bytes in\n let padded_bytes = Vale.AES.GCTR_BE_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (va_get_vec 1 va_sM ==\n Vale.AES.GHash_BE.ghash_incremental h_BE old_hash input_quads))) /\\ va_state_eq va_sM\n (va_update_mem_heaplet 5 va_sM (va_update_cr0 va_sM (va_update_vec 12 va_sM (va_update_vec 11\n va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8 va_sM (va_update_vec 7\n va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3\n va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10\n va_sM (va_update_reg 7 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))))", "let va_ens_Gcm_blocks_decrypt_stdcall (va_b0:va_code) (va_s0:va_state) (alg:algorithm)\n (auth_b:buffer128) (auth_bytes:nat64) (auth_num:nat64) (keys_b:buffer128) (iv_b:buffer128)\n (iv:supported_iv_BE) (hkeys_b:buffer128) (abytes_b:buffer128) (in128_b:buffer128)\n (out128_b:buffer128) (len128_num:nat64) (inout_b:buffer128) (cipher_num:nat64)\n (gcm_struct_b:buffer64) (tag_b:buffer128) (key:(seq nat32)) (va_sM:va_state) (va_fM:va_fuel) :\n prop =\n (va_req_Gcm_blocks_decrypt_stdcall va_b0 va_s0 alg auth_b auth_bytes auth_num keys_b iv_b iv\n hkeys_b abytes_b in128_b out128_b len128_num inout_b cipher_num gcm_struct_b tag_b key /\\\n va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\ (let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (cipher_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (tag_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 12\n (va_get_mem_heaplet 3 va_s0) in Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_union\n (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 iv_b)\n (Vale.PPC64LE.Decls.loc_union (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128\n out128_b) (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 inout_b))) (va_get_mem\n va_s0) (va_get_mem va_sM) /\\ cipher_num_bytes < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ (let\n iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem va_s0)) in let auth_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0)\n abytes_b)) in let auth_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 auth_raw_quads)) 0 auth_num_bytes in let cipher_raw_quads =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) inout_b)) in let cipher_bytes =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 cipher_raw_quads)) 0\n cipher_num_bytes in let plain_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem\n va_sM) inout_b)) in let plain_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 plain_raw_quads)) 0 cipher_num_bytes in let expected_tag =\n Vale.Arch.Types.be_quad32_to_bytes (Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read tag_b 0 (va_get_mem va_s0))) in l_and (l_and (l_and (l_and\n (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 auth_bytes < pow2_32) (FStar.Seq.Base.length\n #Vale.Def.Words_s.nat8 plain_bytes < pow2_32)) (Vale.AES.AES_common_s.is_aes_key alg\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key))) (plain_bytes ==\n __proj__Mktuple2__item___1 #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool\n (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv\n cipher_bytes auth_bytes expected_tag))) (va_get_reg 3 va_sM = 0 == __proj__Mktuple2__item___2\n #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv cipher_bytes auth_bytes expected_tag))\n /\\ va_get_reg 1 va_sM == va_get_reg 1 va_s0 /\\ l_and (l_and (l_and (l_and (l_and (l_and (l_and\n (l_and (va_get_reg 25 va_sM == va_get_reg 25 va_s0) (va_get_reg 26 va_sM == va_get_reg 26\n va_s0)) (va_get_reg 27 va_sM == va_get_reg 27 va_s0)) (va_get_reg 28 va_sM == va_get_reg 28\n va_s0)) (va_get_reg 29 va_sM == va_get_reg 29 va_s0)) (va_get_reg 30 va_sM == va_get_reg 30\n va_s0)) (va_get_reg 31 va_sM == va_get_reg 31 va_s0)) (va_get_vec 20 va_sM == va_get_vec 20\n va_s0)) (va_get_vec 21 va_sM == va_get_vec 21 va_s0))) /\\ va_state_eq va_sM\n (va_update_stackTaint va_sM (va_update_stack va_sM (va_update_mem_layout va_sM\n (va_update_mem_heaplet 5 va_sM (va_update_mem_heaplet 4 va_sM (va_update_mem_heaplet 2 va_sM\n (va_update_mem_heaplet 1 va_sM (va_update_xer va_sM (va_update_cr0 va_sM (va_update_vec 21\n va_sM (va_update_vec 20 va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17\n va_sM (va_update_vec 16 va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13\n va_sM (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9\n va_sM (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5\n va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1\n va_sM (va_update_vec 0 va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29\n va_sM (va_update_reg 28 va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 25\n va_sM (va_update_reg 10 va_sM (va_update_reg 9 va_sM (va_update_reg 8 va_sM (va_update_reg 7\n va_sM (va_update_reg 6 va_sM (va_update_reg 5 va_sM (va_update_reg 4 va_sM (va_update_reg 3\n va_sM (va_update_reg 1 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0))))))))))))))))))))))))))))))))))))))))))))))))))", "let va_lemma_Gcm_extra_bytes va_b0 va_s0 alg inout_b key round_keys keys_b hkeys_b total_bytes\n old_hash completed_quads h_BE =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 5; va_Mod_cr0; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7;\n va_Mod_ok; va_Mod_mem] in\n let va_qc = va_qcode_Gcm_extra_bytes va_mods alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_extra_bytes alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 106 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (let (len:(va_int_range 1 1)) = 1 in label va_range1\n \"***** POSTCONDITION NOT MET AT line 152 column 55 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet\n 5 va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 155 column 147 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.AES.GCTR_BE.gctr_partial alg len (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_sM)\n inout_b)) key (va_get_vec 7 va_s0)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 158 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let raw_quads = FStar.Seq.Base.append #quad32 completed_quads\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 159 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let input_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_quads)) 0 total_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 160 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let padded_bytes = Vale.AES.GCTR_BE_s.pad_to_128_bits input_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 161 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let input_quads = Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 162 column 91 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (l_and (FStar.Seq.Base.length #Vale.Def.Types_s.quad32 input_quads > 0) (va_get_vec 1 va_sM ==\n Vale.AES.GHash_BE.ghash_incremental h_BE old_hash input_quads)))))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_cr0; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec\n 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4;\n va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7; va_Mod_ok;\n va_Mod_mem]) va_sM va_s0;\n (va_sM, va_fM)", "let va_wp_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_BE:quad32) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_get_ok va_s0 /\\ (let (len:(va_int_range 1 1)) = 1 in Vale.PPC64LE.Decls.buffers_disjoint128\n keys_b inout_b /\\ Vale.PPC64LE.Decls.buffers_disjoint128 hkeys_b inout_b /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 5 va_s0) (va_get_reg 3 va_s0) inout_b\n len (va_get_mem_layout va_s0) Secret /\\ len == Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 inout_b /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4\n va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\\n Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ va_get_vec 1 va_s0 == Vale.AES.GHash_BE.ghash_incremental0\n h_BE old_hash completed_quads /\\ FStar.Seq.Base.length #quad32 completed_quads == total_bytes\n `op_Division` 16 /\\ total_bytes < 16 `op_Multiply` FStar.Seq.Base.length #quad32\n completed_quads + 16 /\\ va_get_reg 8 va_s0 == total_bytes `op_Modulus` 16 /\\ total_bytes\n `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16 `op_Multiply`\n Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes - 1) < total_bytes) /\\ (forall\n (va_x_mem:vale_heap) (va_x_r7:nat64) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32)\n (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32)\n (va_x_v7:quad32) (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32)\n (va_x_v12:quad32) (va_x_cr0:cr0_t) (va_x_heap5:vale_heap) . let va_sM = va_upd_mem_heaplet 5\n va_x_heap5 (va_upd_cr0 va_x_cr0 (va_upd_vec 12 va_x_v12 (va_upd_vec 11 va_x_v11 (va_upd_vec 10\n va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7 va_x_v7 (va_upd_vec 6\n va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2\n (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_reg 7 va_x_r7\n (va_upd_mem va_x_mem va_s0))))))))))))))))) in va_get_ok va_sM /\\ (let (len:(va_int_range 1 1))\n = 1 in Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0)\n (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg len\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) key (va_get_vec 7 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b)) in let input_bytes =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_quads)) 0 total_bytes in\n let padded_bytes = Vale.AES.GCTR_BE_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (va_get_vec 1 va_sM ==\n Vale.AES.GHash_BE.ghash_incremental h_BE old_hash input_quads))) ==> va_k va_sM (())))", "val va_lemma_Gcm_blocks_decrypt_stdcall : va_b0:va_code -> va_s0:va_state -> alg:algorithm ->\n auth_b:buffer128 -> auth_bytes:nat64 -> auth_num:nat64 -> keys_b:buffer128 -> iv_b:buffer128 ->\n iv:supported_iv_BE -> hkeys_b:buffer128 -> abytes_b:buffer128 -> in128_b:buffer128 ->\n out128_b:buffer128 -> len128_num:nat64 -> inout_b:buffer128 -> cipher_num:nat64 ->\n gcm_struct_b:buffer64 -> tag_b:buffer128 -> key:(seq nat32)\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks_decrypt_stdcall alg) va_s0 /\\ va_get_ok\n va_s0 /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read\n gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (cipher_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (tag_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 12\n (va_get_mem_heaplet 3 va_s0) in va_get_reg 1 va_s0 == Vale.PPC64LE.Stack_i.init_r1\n (va_get_stack va_s0) /\\ Vale.PPC64LE.Memory.is_initial_heap (va_get_mem_layout va_s0)\n (va_get_mem va_s0) /\\ auth_len == auth_num /\\ auth_num_bytes == auth_bytes /\\ len128 ==\n len128_num /\\ cipher_num_bytes == cipher_num /\\ Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem\n va_s0) (va_get_reg 3 va_s0) gcm_struct_b 13 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) auth_ptr auth_b auth_len\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0)\n abytes_ptr abytes_b 1 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem va_s0) iv_ptr iv_b 1 (va_get_mem_layout va_s0) Public /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) in128_ptr in128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0)\n out128_ptr out128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0) inout_ptr inout_b 1 (va_get_mem_layout\n va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0)\n tag_ptr tag_b 1 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints64_128\n gcm_struct_b ([keys_b; auth_b; abytes_b; iv_b; in128_b; out128_b; inout_b; hkeys_b; tag_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 tag_b ([keys_b; auth_b; abytes_b; iv_b; in128_b;\n out128_b; inout_b; hkeys_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b; auth_b;\n abytes_b; in128_b; out128_b; inout_b; hkeys_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128\n inout_b ([keys_b; auth_b; abytes_b; in128_b; out128_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 auth_b ([keys_b; abytes_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 abytes_b ([keys_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 out128_b ([keys_b; auth_b; abytes_b; hkeys_b; inout_b])\n /\\ Vale.PPC64LE.Decls.buffer_disjoints128 in128_b ([keys_b; auth_b; abytes_b; hkeys_b;\n inout_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b == out128_b)\n /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply` len128 <\n pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ cipher_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem va_s0) + 128 < pow2_64 /\\ (va_mul_nat len128\n (128 `op_Division` 8) <= cipher_num_bytes /\\ cipher_num_bytes < va_mul_nat len128 (128\n `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division` 8) <=\n auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ aes_reqs alg key (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem va_s0) keys_b)) keys_b keys_ptr (va_get_mem\n va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.OptPublic_BE.hkeys_reqs_pub\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) hkeys_b))\n (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0\n 0 0 0)) /\\ (let h_BE = Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0) in let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem va_s0)) in iv_BE ==\n Vale.AES.GCM_BE_s.compute_iv_BE h_BE iv))))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 0 (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (cipher_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (tag_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 12\n (va_get_mem_heaplet 3 va_s0) in Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_union\n (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 iv_b)\n (Vale.PPC64LE.Decls.loc_union (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128\n out128_b) (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 inout_b))) (va_get_mem\n va_s0) (va_get_mem va_sM) /\\ cipher_num_bytes < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ (let\n iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem va_s0)) in let auth_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0)\n abytes_b)) in let auth_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 auth_raw_quads)) 0 auth_num_bytes in let cipher_raw_quads =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) inout_b)) in let cipher_bytes =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 cipher_raw_quads)) 0\n cipher_num_bytes in let plain_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem\n va_sM) inout_b)) in let plain_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 plain_raw_quads)) 0 cipher_num_bytes in let expected_tag =\n Vale.Arch.Types.be_quad32_to_bytes (Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read tag_b 0 (va_get_mem va_s0))) in l_and (l_and (l_and (l_and\n (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 auth_bytes < pow2_32) (FStar.Seq.Base.length\n #Vale.Def.Words_s.nat8 plain_bytes < pow2_32)) (Vale.AES.AES_common_s.is_aes_key alg\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key))) (plain_bytes ==\n __proj__Mktuple2__item___1 #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool\n (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv\n cipher_bytes auth_bytes expected_tag))) (va_get_reg 3 va_sM = 0 == __proj__Mktuple2__item___2\n #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv cipher_bytes auth_bytes expected_tag))\n /\\ va_get_reg 1 va_sM == va_get_reg 1 va_s0 /\\ l_and (l_and (l_and (l_and (l_and (l_and (l_and\n (l_and (va_get_reg 25 va_sM == va_get_reg 25 va_s0) (va_get_reg 26 va_sM == va_get_reg 26\n va_s0)) (va_get_reg 27 va_sM == va_get_reg 27 va_s0)) (va_get_reg 28 va_sM == va_get_reg 28\n va_s0)) (va_get_reg 29 va_sM == va_get_reg 29 va_s0)) (va_get_reg 30 va_sM == va_get_reg 30\n va_s0)) (va_get_reg 31 va_sM == va_get_reg 31 va_s0)) (va_get_vec 20 va_sM == va_get_vec 20\n va_s0)) (va_get_vec 21 va_sM == va_get_vec 21 va_s0))) /\\ va_state_eq va_sM\n (va_update_stackTaint va_sM (va_update_stack va_sM (va_update_mem_layout va_sM\n (va_update_mem_heaplet 5 va_sM (va_update_mem_heaplet 4 va_sM (va_update_mem_heaplet 2 va_sM\n (va_update_mem_heaplet 1 va_sM (va_update_xer va_sM (va_update_cr0 va_sM (va_update_vec 21\n va_sM (va_update_vec 20 va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17\n va_sM (va_update_vec 16 va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13\n va_sM (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9\n va_sM (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5\n va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1\n va_sM (va_update_vec 0 va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29\n va_sM (va_update_reg 28 va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 25\n va_sM (va_update_reg 10 va_sM (va_update_reg 9 va_sM (va_update_reg 8 va_sM (va_update_reg 7\n va_sM (va_update_reg 6 va_sM (va_update_reg 5 va_sM (va_update_reg 4 va_sM (va_update_reg 3\n va_sM (va_update_reg 1 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))))))))))))))", "val va_wpProof_Gcm_extra_bytes : alg:algorithm -> inout_b:buffer128 -> key:(seq nat32) ->\n round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> total_bytes:nat ->\n old_hash:quad32 -> completed_quads:(seq quad32) -> h_BE:quad32 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_extra_bytes alg)\n ([va_Mod_mem_heaplet 5; va_Mod_cr0; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9;\n va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec\n 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7; va_Mod_mem]) va_s0 va_k ((va_sM,\n va_f0, va_g))))", "let va_wpProof_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes old_hash\n completed_quads h_BE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_extra_bytes (va_code_Gcm_extra_bytes alg) va_s0 alg inout_b key\n round_keys keys_b hkeys_b total_bytes old_hash completed_quads h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 5 va_sM (va_update_cr0 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 10 va_sM (va_update_reg 7 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_cr0; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec\n 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4;\n va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7;\n va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_quick_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_BE:quad32) : (va_quickCode unit (va_code_Gcm_extra_bytes alg)) =\n (va_QProc (va_code_Gcm_extra_bytes alg) ([va_Mod_mem_heaplet 5; va_Mod_cr0; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 10; va_Mod_reg 7; va_Mod_mem]) (va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_BE) (va_wpProof_Gcm_extra_bytes alg inout_b key\n round_keys keys_b hkeys_b total_bytes old_hash completed_quads h_BE))", "val va_code_Gcm_blocks128 : alg:algorithm -> Tot va_code", "let va_code_Gcm_blocks128 alg =\n (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_CCons\n (va_code_Move (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 7)) (va_CCons (va_code_Move\n (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 6)) (va_CCons (va_code_Move (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 3)) (va_CCons (va_code_Ghash_buffer ()) (va_CCons (va_code_Vmr\n (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 7)\n (va_op_vec_opr_vec 15)) (va_CCons (va_code_Move (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 8))\n (va_CCons (va_code_Move (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 9)) (va_CCons\n (va_code_Gctr_blocks128 alg) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec\n 20)) (va_CNil ())))))))))))))", "val va_codegen_success_Gcm_blocks128 : alg:algorithm -> Tot va_pbool", "let va_codegen_success_Gcm_blocks128 alg =\n (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_pbool_and\n (va_codegen_success_Move (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 7)) (va_pbool_and\n (va_codegen_success_Move (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 6)) (va_pbool_and\n (va_codegen_success_Move (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 3)) (va_pbool_and\n (va_codegen_success_Ghash_buffer ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec\n 20) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 7)\n (va_op_vec_opr_vec 15)) (va_pbool_and (va_codegen_success_Move (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 8)) (va_pbool_and (va_codegen_success_Move (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 9)) (va_pbool_and (va_codegen_success_Gctr_blocks128 alg) (va_pbool_and\n (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_ttrue ()))))))))))))", "let va_qcode_Gcm_blocks128 (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 237 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 238 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 239 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 240 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 241 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b in_b h_BE (va_get_vec 1 va_old_s)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 242 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 243 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 244 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 245 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 246 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gctr_blocks128 alg in_b out_b key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 247 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_QEmpty (()))))))))))))))", "val va_lemma_Gcm_blocks128 : va_b0:va_code -> va_s0:va_state -> alg:algorithm -> in_b:buffer128 ->\n out_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks128 alg) va_s0 /\\ va_get_ok va_s0 /\\\n (Vale.PPC64LE.Decls.buffers_disjoint128 keys_b out_b /\\ Vale.PPC64LE.Decls.buffers_disjoint128\n hkeys_b out_b /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) in_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b (va_get_reg 6 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ l_and\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b))))) /\\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM\n (va_update_vec 20 va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM\n (va_update_vec 16 va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM\n (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM\n (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM\n (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM\n (va_update_vec 0 va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM\n (va_update_reg 28 va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM\n (va_update_reg 9 va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM\n (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))", "let va_wp_Gcm_blocks_decrypt_stdcall (alg:algorithm) (auth_b:buffer128) (auth_bytes:nat64)\n (auth_num:nat64) (keys_b:buffer128) (iv_b:buffer128) (iv:supported_iv_BE) (hkeys_b:buffer128)\n (abytes_b:buffer128) (in128_b:buffer128) (out128_b:buffer128) (len128_num:nat64)\n (inout_b:buffer128) (cipher_num:nat64) (gcm_struct_b:buffer64) (tag_b:buffer128) (key:(seq\n nat32)) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (cipher_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in let (tag_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 12 (va_get_mem_heaplet 3 va_s0) in va_get_reg 1\n va_s0 == Vale.PPC64LE.Stack_i.init_r1 (va_get_stack va_s0) /\\\n Vale.PPC64LE.Memory.is_initial_heap (va_get_mem_layout va_s0) (va_get_mem va_s0) /\\ auth_len ==\n auth_num /\\ auth_num_bytes == auth_bytes /\\ len128 == len128_num /\\ cipher_num_bytes ==\n cipher_num /\\ Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem va_s0) (va_get_reg 3 va_s0)\n gcm_struct_b 13 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem va_s0) auth_ptr auth_b auth_len (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) abytes_ptr abytes_b 1 (va_get_mem_layout\n va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0) iv_ptr iv_b 1\n (va_get_mem_layout va_s0) Public /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0)\n in128_ptr in128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0) out128_ptr out128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0)\n inout_ptr inout_b 1 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem va_s0) h_ptr hkeys_b 3 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) tag_ptr tag_b 1 (va_get_mem_layout\n va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints64_128 gcm_struct_b ([keys_b; auth_b;\n abytes_b; iv_b; in128_b; out128_b; inout_b; hkeys_b; tag_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 tag_b ([keys_b; auth_b; abytes_b; iv_b; in128_b;\n out128_b; inout_b; hkeys_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b; auth_b;\n abytes_b; in128_b; out128_b; inout_b; hkeys_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128\n inout_b ([keys_b; auth_b; abytes_b; in128_b; out128_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 auth_b ([keys_b; abytes_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 abytes_b ([keys_b; hkeys_b]) /\\\n Vale.PPC64LE.Decls.buffer_disjoints128 out128_b ([keys_b; auth_b; abytes_b; hkeys_b; inout_b])\n /\\ Vale.PPC64LE.Decls.buffer_disjoints128 in128_b ([keys_b; auth_b; abytes_b; hkeys_b;\n inout_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b == out128_b)\n /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply` len128 <\n pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ cipher_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem va_s0) + 128 < pow2_64 /\\ (va_mul_nat len128\n (128 `op_Division` 8) <= cipher_num_bytes /\\ cipher_num_bytes < va_mul_nat len128 (128\n `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division` 8) <=\n auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ aes_reqs alg key (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem va_s0) keys_b)) keys_b keys_ptr (va_get_mem\n va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.OptPublic_BE.hkeys_reqs_pub\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) hkeys_b))\n (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0\n 0 0 0)) /\\ (let h_BE = Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0) in let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem va_s0)) in iv_BE ==\n Vale.AES.GCM_BE_s.compute_iv_BE h_BE iv)) /\\ (forall (va_x_mem:vale_heap) (va_x_r1:nat64)\n (va_x_r3:nat64) (va_x_r4:nat64) (va_x_r5:nat64) (va_x_r6:nat64) (va_x_r7:nat64) (va_x_r8:nat64)\n (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r25:nat64) (va_x_r26:nat64) (va_x_r27:nat64)\n (va_x_r28:nat64) (va_x_r29:nat64) (va_x_r30:nat64) (va_x_r31:nat64) (va_x_v0:quad32)\n (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32)\n (va_x_v6:quad32) (va_x_v7:quad32) (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32)\n (va_x_v11:quad32) (va_x_v12:quad32) (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32)\n (va_x_v16:quad32) (va_x_v17:quad32) (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32)\n (va_x_v21:quad32) (va_x_cr0:cr0_t) (va_x_xer:xer_t) (va_x_heap1:vale_heap)\n (va_x_heap2:vale_heap) (va_x_heap4:vale_heap) (va_x_heap5:vale_heap)\n (va_x_memLayout:vale_heap_layout) (va_x_stack:vale_stack) (va_x_stackTaint:memtaint) . let\n va_sM = va_upd_stackTaint va_x_stackTaint (va_upd_stack va_x_stack (va_upd_mem_layout\n va_x_memLayout (va_upd_mem_heaplet 5 va_x_heap5 (va_upd_mem_heaplet 4 va_x_heap4\n (va_upd_mem_heaplet 2 va_x_heap2 (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_xer va_x_xer\n (va_upd_cr0 va_x_cr0 (va_upd_vec 21 va_x_v21 (va_upd_vec 20 va_x_v20 (va_upd_vec 19 va_x_v19\n (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16 (va_upd_vec 15 va_x_v15\n (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12 (va_upd_vec 11 va_x_v11\n (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7 va_x_v7\n (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3\n (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 31 va_x_r31\n (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29 (va_upd_reg 28 va_x_r28 (va_upd_reg 27 va_x_r27\n (va_upd_reg 26 va_x_r26 (va_upd_reg 25 va_x_r25 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9\n (va_upd_reg 8 va_x_r8 (va_upd_reg 7 va_x_r7 (va_upd_reg 6 va_x_r6 (va_upd_reg 5 va_x_r5\n (va_upd_reg 4 va_x_r4 (va_upd_reg 3 va_x_r3 (va_upd_reg 1 va_x_r1 (va_upd_mem va_x_mem\n va_s0))))))))))))))))))))))))))))))))))))))))))))))) in va_get_ok va_sM /\\ (let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (cipher_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (tag_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 12\n (va_get_mem_heaplet 3 va_s0) in Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_union\n (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 iv_b)\n (Vale.PPC64LE.Decls.loc_union (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128\n out128_b) (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 inout_b))) (va_get_mem\n va_s0) (va_get_mem va_sM) /\\ cipher_num_bytes < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ (let\n iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem va_s0)) in let auth_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0)\n abytes_b)) in let auth_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 auth_raw_quads)) 0 auth_num_bytes in let cipher_raw_quads =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem va_s0) inout_b)) in let cipher_bytes =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 cipher_raw_quads)) 0\n cipher_num_bytes in let plain_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem\n va_sM) inout_b)) in let plain_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 plain_raw_quads)) 0 cipher_num_bytes in let expected_tag =\n Vale.Arch.Types.be_quad32_to_bytes (Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read tag_b 0 (va_get_mem va_s0))) in l_and (l_and (l_and (l_and\n (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 auth_bytes < pow2_32) (FStar.Seq.Base.length\n #Vale.Def.Words_s.nat8 plain_bytes < pow2_32)) (Vale.AES.AES_common_s.is_aes_key alg\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key))) (plain_bytes ==\n __proj__Mktuple2__item___1 #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool\n (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv\n cipher_bytes auth_bytes expected_tag))) (va_get_reg 3 va_sM = 0 == __proj__Mktuple2__item___2\n #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv cipher_bytes auth_bytes expected_tag))\n /\\ va_get_reg 1 va_sM == va_get_reg 1 va_s0 /\\ l_and (l_and (l_and (l_and (l_and (l_and (l_and\n (l_and (va_get_reg 25 va_sM == va_get_reg 25 va_s0) (va_get_reg 26 va_sM == va_get_reg 26\n va_s0)) (va_get_reg 27 va_sM == va_get_reg 27 va_s0)) (va_get_reg 28 va_sM == va_get_reg 28\n va_s0)) (va_get_reg 29 va_sM == va_get_reg 29 va_s0)) (va_get_reg 30 va_sM == va_get_reg 30\n va_s0)) (va_get_reg 31 va_sM == va_get_reg 31 va_s0)) (va_get_vec 20 va_sM == va_get_vec 20\n va_s0)) (va_get_vec 21 va_sM == va_get_vec 21 va_s0))) ==> va_k va_sM (())))", "let va_lemma_Gcm_blocks128 va_b0 va_s0 alg in_b out_b key round_keys keys_b hkeys_b h_BE =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19;\n va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13;\n va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7;\n va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec\n 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26;\n va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem] in\n let va_qc = va_qcode_Gcm_blocks128 va_mods alg in_b out_b key round_keys keys_b hkeys_b h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_blocks128 alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 182 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 226 column 53 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 229 column 147 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 230 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite (va_get_vec 7 va_s0) (va_get_reg 6 va_s0)) /\\\n label va_range1\n \"***** POSTCONDITION NOT MET AT line 233 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1 va_sM == va_get_vec 1 va_s0)\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b == Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) out_b)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 235 column 113 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_reg 6 va_s0 > 0 ==> l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) ==>\n FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) 0\n (va_get_reg 6 va_s0)) > 0) (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE\n (va_get_vec 1 va_s0) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in_b)))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok; va_Mod_mem])\n va_sM va_s0;\n (va_sM, va_fM)", "let va_wp_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 keys_b out_b /\\\n Vale.PPC64LE.Decls.buffers_disjoint128 hkeys_b out_b /\\ (Vale.PPC64LE.Decls.buffers_disjoint128\n in_b out_b \\/ in_b == out_b) /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) (va_get_reg 3 va_s0) in_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply`\n va_get_reg 6 va_s0 < pow2_64 /\\ va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 <\n pow2_64 /\\ l_and (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret) /\\ (forall (va_x_mem:vale_heap)\n (va_x_r3:nat64) (va_x_r7:nat64) (va_x_r6:nat64) (va_x_r8:nat64) (va_x_r9:nat64)\n (va_x_r10:nat64) (va_x_r26:nat64) (va_x_r27:nat64) (va_x_r28:nat64) (va_x_r29:nat64)\n (va_x_r30:nat64) (va_x_r31:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32) (va_x_v17:quad32)\n (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32) (va_x_cr0:cr0_t) (va_x_heap1:vale_heap) .\n let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_cr0 va_x_cr0 (va_upd_vec 20 va_x_v20\n (va_upd_vec 19 va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16\n (va_upd_vec 15 va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12\n (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8\n (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4\n (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0\n (va_upd_reg 31 va_x_r31 (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29 (va_upd_reg 28 va_x_r28\n (va_upd_reg 27 va_x_r27 (va_upd_reg 26 va_x_r26 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9\n (va_upd_reg 8 va_x_r8 (va_upd_reg 6 va_x_r6 (va_upd_reg 7 va_x_r7 (va_upd_reg 3 va_x_r3\n (va_upd_mem va_x_mem va_s0))))))))))))))))))))))))))))))))))) in va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b))))) ==> va_k va_sM (())))", "val va_wpProof_Gcm_blocks128 : alg:algorithm -> in_b:buffer128 -> out_b:buffer128 -> key:(seq\n nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks128 alg)\n ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0,\n va_g))))", "let va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_blocks128 (va_code_Gcm_blocks128 alg) va_s0 alg in_b out_b key\n round_keys keys_b hkeys_b h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM (va_update_reg 3\n va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))))))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "val va_wpProof_Gcm_blocks_decrypt_stdcall : alg:algorithm -> auth_b:buffer128 -> auth_bytes:nat64\n -> auth_num:nat64 -> keys_b:buffer128 -> iv_b:buffer128 -> iv:supported_iv_BE ->\n hkeys_b:buffer128 -> abytes_b:buffer128 -> in128_b:buffer128 -> out128_b:buffer128 ->\n len128_num:nat64 -> inout_b:buffer128 -> cipher_num:nat64 -> gcm_struct_b:buffer64 ->\n tag_b:buffer128 -> key:(seq nat32) -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks_decrypt_stdcall alg auth_b auth_bytes auth_num\n keys_b iv_b iv hkeys_b abytes_b in128_b out128_b len128_num inout_b cipher_num gcm_struct_b\n tag_b key va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks_decrypt_stdcall alg)\n ([va_Mod_stackTaint; va_Mod_stack; va_Mod_mem_layout; va_Mod_mem_heaplet 5; va_Mod_mem_heaplet\n 4; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1; va_Mod_xer; va_Mod_cr0; va_Mod_vec 21;\n va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15;\n va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9;\n va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec\n 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28;\n va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 25; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8;\n va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_reg 1;\n va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))", "let va_quick_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) : (va_quickCode\n unit (va_code_Gcm_blocks128 alg)) =\n (va_QProc (va_code_Gcm_blocks128 alg) ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20;\n va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14;\n va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8;\n va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec\n 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27;\n va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7;\n va_Mod_reg 3; va_Mod_mem]) (va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE) (va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE))", "val va_code_Gcm_blocks : alg:algorithm -> Tot va_code", "let va_quick_Gcm_blocks_decrypt_stdcall (alg:algorithm) (auth_b:buffer128) (auth_bytes:nat64)\n (auth_num:nat64) (keys_b:buffer128) (iv_b:buffer128) (iv:supported_iv_BE) (hkeys_b:buffer128)\n (abytes_b:buffer128) (in128_b:buffer128) (out128_b:buffer128) (len128_num:nat64)\n (inout_b:buffer128) (cipher_num:nat64) (gcm_struct_b:buffer64) (tag_b:buffer128) (key:(seq\n nat32)) : (va_quickCode unit (va_code_Gcm_blocks_decrypt_stdcall alg)) =\n (va_QProc (va_code_Gcm_blocks_decrypt_stdcall alg) ([va_Mod_stackTaint; va_Mod_stack;\n va_Mod_mem_layout; va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 4; va_Mod_mem_heaplet 2;\n va_Mod_mem_heaplet 1; va_Mod_xer; va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19;\n va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13;\n va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7;\n va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec\n 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26;\n va_Mod_reg 25; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6;\n va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_reg 1; va_Mod_mem])\n (va_wp_Gcm_blocks_decrypt_stdcall alg auth_b auth_bytes auth_num keys_b iv_b iv hkeys_b\n abytes_b in128_b out128_b len128_num inout_b cipher_num gcm_struct_b tag_b key)\n (va_wpProof_Gcm_blocks_decrypt_stdcall alg auth_b auth_bytes auth_num keys_b iv_b iv hkeys_b\n abytes_b in128_b out128_b len128_num inout_b cipher_num gcm_struct_b tag_b key))", "let va_code_Gcm_blocks alg =\n (va_Block (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 5)\n (va_op_reg_opr_reg 25) (11 `op_Multiply` 8) Secret) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25) (0 `op_Multiply` 8)\n Secret) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 25) (6 `op_Multiply` 8) Secret) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25) (7 `op_Multiply` 8)\n Secret) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 9)\n (va_op_reg_opr_reg 25) (8 `op_Multiply` 8) Secret) (va_CCons (va_code_Gcm_blocks_auth ())\n (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 10)\n (va_op_reg_opr_reg 25) (9 `op_Multiply` 8) Secret) (va_CCons (va_code_Load128_byte16_buffer\n (va_op_heaplet_mem_heaplet 2) (va_op_vec_opr_vec 7) (va_op_reg_opr_reg 10) Public) (va_CCons\n (va_code_Vmr (va_op_vec_opr_vec 21) (va_op_vec_opr_vec 7)) (va_CCons (va_code_Load_one_lsb\n (va_op_vec_opr_vec 10)) (va_CCons (va_code_Vadduwm (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 7)\n (va_op_vec_opr_vec 10)) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 25) (1 `op_Multiply` 8) Secret) (va_CCons\n (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (2 `op_Multiply` 8) Secret) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25) (3 `op_Multiply` 8) Secret) (va_CCons\n (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25)\n (10 `op_Multiply` 8) Secret) (va_CCons (va_code_Gcm_blocks128 alg) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25) (3 `op_Multiply` 8)\n Secret) (va_CCons (va_code_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 4) (va_CCons\n (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (5 `op_Multiply` 8) Secret) (va_CCons (va_IfElse (va_cmp_gt (va_op_cmp_reg 6) (va_op_cmp_reg\n 7)) (va_Block (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 25) (4 `op_Multiply` 8) Secret) (va_CCons (va_code_LoadImm64\n (va_op_reg_opr_reg 10) 15) (va_CCons (va_code_And (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 10)) (va_CCons (va_code_Gcm_extra_bytes alg) (va_CCons (va_Block (va_CNil\n ())) (va_CNil ()))))))) (va_Block (va_CNil ()))) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25) (8 `op_Multiply` 8)\n Secret) (va_CCons (va_code_Gcm_make_length_quad ()) (va_CCons (va_code_Ghash_register ())\n (va_CCons (va_code_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 21)) (va_CCons\n (va_code_Gctr_register alg) (va_CCons (va_Block (va_CNil ())) (va_CNil\n ()))))))))))))))))))))))))))))", "val va_codegen_success_Gcm_blocks : alg:algorithm -> Tot va_pbool", "let va_codegen_success_Gcm_blocks alg =\n (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 5)\n (va_op_reg_opr_reg 25) (11 `op_Multiply` 8) Secret) (va_pbool_and (va_codegen_success_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25) (0 `op_Multiply` 8)\n Secret) (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25) (6 `op_Multiply` 8) Secret) (va_pbool_and\n (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 25) (7 `op_Multiply` 8) Secret) (va_pbool_and (va_codegen_success_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 25) (8 `op_Multiply` 8)\n Secret) (va_pbool_and (va_codegen_success_Gcm_blocks_auth ()) (va_pbool_and\n (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 10)\n (va_op_reg_opr_reg 25) (9 `op_Multiply` 8) Secret) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 2) (va_op_vec_opr_vec 7)\n (va_op_reg_opr_reg 10) Public) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 21)\n (va_op_vec_opr_vec 7)) (va_pbool_and (va_codegen_success_Load_one_lsb (va_op_vec_opr_vec 10))\n (va_pbool_and (va_codegen_success_Vadduwm (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 7)\n (va_op_vec_opr_vec 10)) (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet\n 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 25) (1 `op_Multiply` 8) Secret) (va_pbool_and\n (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 25) (2 `op_Multiply` 8) Secret) (va_pbool_and (va_codegen_success_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25) (3 `op_Multiply` 8)\n Secret) (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25) (10 `op_Multiply` 8) Secret) (va_pbool_and\n (va_codegen_success_Gcm_blocks128 alg) (va_pbool_and (va_codegen_success_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25) (3 `op_Multiply` 8)\n Secret) (va_pbool_and (va_codegen_success_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7)\n 4) (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg\n 6) (va_op_reg_opr_reg 25) (5 `op_Multiply` 8) Secret) (va_pbool_and (va_pbool_and\n (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 25) (4 `op_Multiply` 8) Secret) (va_pbool_and (va_codegen_success_LoadImm64\n (va_op_reg_opr_reg 10) 15) (va_pbool_and (va_codegen_success_And (va_op_reg_opr_reg 8)\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 10)) (va_codegen_success_Gcm_extra_bytes alg))))\n (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 25) (8 `op_Multiply` 8) Secret) (va_pbool_and\n (va_codegen_success_Gcm_make_length_quad ()) (va_pbool_and (va_codegen_success_Ghash_register\n ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 21))\n (va_pbool_and (va_codegen_success_Gctr_register alg) (va_ttrue ()))))))))))))))))))))))))))", "let va_qcode_Gcm_blocks (va_mods:va_mods_t) (alg:algorithm) (auth_b:buffer128) (abytes_b:buffer128)\n (in128_b:buffer128) (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (gcm_struct_b:buffer64) :\n (va_quickCode unit (va_code_Gcm_blocks alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s) in let\n (h_BE:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 0 va_old_s)) in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 396 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 5) (va_op_reg_opr_reg 25)\n (11 `op_Multiply` 8) Secret gcm_struct_b 11) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 398 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25)\n (0 `op_Multiply` 8) Secret gcm_struct_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 399 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (6 `op_Multiply` 8) Secret gcm_struct_b 6) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 400 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (7 `op_Multiply` 8) Secret gcm_struct_b 7) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 401 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 25)\n (8 `op_Multiply` 8) Secret gcm_struct_b 8) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 402 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_blocks_auth auth_b abytes_b hkeys_b h_BE) (fun (va_s:va_state)\n (auth_quad_seq:(seq quad32)) -> let (y_0:quad32) = Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0 in let (y_auth_bytes:quad32) = va_get_vec 1 va_s in let\n (iv_BE:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_old_s)) in let\n (ctr_BE_1:quad32) = iv_BE in let (ctr_BE_2:quad32) = Vale.AES.GCTR_BE_s.inc32 iv_BE 1 in\n va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 410 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 25)\n (9 `op_Multiply` 8) Secret gcm_struct_b 9) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 411 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 2) (va_op_vec_opr_vec 7)\n (va_op_reg_opr_reg 10) Public iv_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 413 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 21) (va_op_vec_opr_vec 7)) (fun (va_s:va_state) _ -> let\n (j0:quad32) = va_get_vec 7 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 415 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Load_one_lsb (va_op_vec_opr_vec 10)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 417 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vadduwm (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 10)) (fun\n (va_s:va_state) _ -> let (auth_in:(seq quad32)) = auth_quad_seq in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 25)\n (1 `op_Multiply` 8) Secret gcm_struct_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (2 `op_Multiply` 8) Secret gcm_struct_b 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (3 `op_Multiply` 8) Secret gcm_struct_b 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 425 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25)\n (10 `op_Multiply` 8) Secret gcm_struct_b 10) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 426 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_blocks128 alg in128_b out128_b key round_keys keys_b hkeys_b h_BE) (fun\n (va_s:va_state) _ -> let (y_cipher128:quad32) = va_get_vec 1 va_s in let\n (va_arg115:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (va_arg114:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in\n let (va_arg113:Vale.Def.Types_s.quad32) = y_cipher128 in let\n (va_arg112:Vale.Def.Types_s.quad32) = y_auth_bytes in let (va_arg111:Vale.Def.Types_s.quad32) =\n y_0 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 428 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash_BE.lemma_ghash_incremental0_append h_BE va_arg111 va_arg112\n va_arg113 va_arg114 va_arg115) (let auth_in = FStar.Seq.Base.append #quad32 auth_in\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b)) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 431 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (3 `op_Multiply` 8) Secret gcm_struct_b 3) (fun (va_s:va_state) _ -> let\n (va_arg110:Vale.Def.Types_s.nat64) = va_get_reg 7 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 432 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg110 4) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 433 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 4) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 434 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (5 `op_Multiply` 8) Secret gcm_struct_b 5) (fun (va_s:va_state) _ -> let (y_inout:quad32) =\n y_cipher128 in let (plain_byte_seq:(seq quad32)) = empty_seq_quad32 in let\n (cipher_byte_seq:(seq quad32)) = empty_seq_quad32 in let (va_arg109:Vale.Def.Types_s.quad32) =\n va_get_vec 7 va_s in let (va_arg108:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg107:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = cipher_byte_seq in let\n (va_arg106:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = plain_byte_seq in let\n (va_arg105:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 439 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR_BE.gctr_partial_opaque_init va_arg105 va_arg106 va_arg107\n va_arg108 va_arg109) (let (total_bytes:(va_int_at_least 0)) = FStar.Seq.Base.length #quad32\n auth_quad_seq `op_Multiply` 16 + plain_num_bytes in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 442 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_qIf va_mods (Cmp_gt (va_op_cmp_reg 6) (va_op_cmp_reg 7)) (qblock va_mods (fun\n (va_s:va_state) -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 444 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 25)\n (4 `op_Multiply` 8) Secret gcm_struct_b 4) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 445 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 446 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 15) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 447 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_And (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 10)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 449 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes y_0 auth_in\n h_BE) (fun (va_s:va_state) _ -> let y_inout = va_get_vec 1 va_s in let\n (raw_auth_quads:(FStar.Seq.Base.seq quad32)) = FStar.Seq.Base.append #quad32 auth_in\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5\n va_old_s) inout_b)) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 453 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_auth_quads)) 0\n total_bytes) (fun _ -> let (auth_input_bytes:(FStar.Seq.Base.seq Vale.Def.Words_s.nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 total_bytes\n in let (padded_auth_bytes:(FStar.Seq.Base.seq Vale.Def.Types_s.nat8)) =\n Vale.AES.GCTR_BE_s.pad_to_128_bits auth_input_bytes in let auth_in =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes in let plain_byte_seq =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5\n va_old_s) inout_b) in let cipher_byte_seq = Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b) in va_QEmpty ((auth_in,\n cipher_byte_seq, plain_byte_seq, y_inout)))))))))) (qblock va_mods (fun (va_s:va_state) ->\n va_QEmpty ((auth_in, cipher_byte_seq, plain_byte_seq, y_inout))))) (fun (va_s:va_state) va_g ->\n let ((auth_in:(seq quad32)), (cipher_byte_seq:(seq quad32)), (plain_byte_seq:(seq quad32)),\n (y_inout:quad32)) = va_g in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 461 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (8 `op_Multiply` 8) Secret gcm_struct_b 8) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 462 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_make_length_quad ()) (fun (va_s:va_state) _ -> let (length_quad32:quad32) =\n va_get_vec 9 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 465 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Ghash_register hkeys_b h_BE y_inout) (fun (va_s:va_state) _ -> let (y_final:quad32) =\n va_get_vec 1 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 468 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 21)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 471 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gctr_register alg key round_keys keys_b) (fun (va_s:va_state) _ -> let\n (va_arg104:Vale.Def.Types_s.quad32) = va_get_vec 1 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 473 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.be_seq_quad32_to_bytes_of_singleton va_arg104)\n (va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n ((fun (icb_661:Vale.Def.Types_s.quad32) (plain_662:Vale.Def.Types_s.quad32)\n (alg_663:Vale.AES.AES_common_s.algorithm) (key_664:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32))\n (i_665:Prims.int) -> Vale.AES.AES_BE_s.is_aes_key_word alg_663 key_664) j0 y_final alg key 0)\n (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_vec 1 va_s == Vale.AES.GCTR_BE_s.gctr_encrypt_block j0 y_final alg key 0) (let\n (plain128:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (cipher128:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n in128_b) in va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 479 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (FStar.Seq.Base.length #quad32 plain_byte_seq == 0 ==> FStar.Seq.Base.equal\n #Vale.Def.Types_s.quad32 (FStar.Seq.Base.append #Vale.Def.Types_s.quad32 plain128\n plain_byte_seq) plain128) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 480 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (FStar.Seq.Base.length #quad32 cipher_byte_seq == 0 ==> FStar.Seq.Base.equal\n #Vale.Def.Types_s.quad32 (FStar.Seq.Base.append #Vale.Def.Types_s.quad32 cipher128\n cipher_byte_seq) cipher128) (let (va_arg103:Vale.Def.Types_s.quad32) =\n Vale.AES.GCTR_BE.inc32lite ctr_BE_2 len128 in let (va_arg102:Vale.Def.Types_s.quad32) =\n ctr_BE_2 in let (va_arg101:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg100:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = cipher_byte_seq in let\n (va_arg99:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = plain_byte_seq in let\n (va_arg98:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n out128_b) in let (va_arg97:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (va_arg96:Prims.nat) = FStar.Seq.Base.length #quad32 plain_byte_seq\n in let (va_arg95:Prims.nat) = len128 in let (va_arg94:Vale.AES.AES_common_s.algorithm) = alg in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 482 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR_BE.lemma_gctr_partial_append va_arg94 va_arg95 va_arg96 va_arg97\n va_arg98 va_arg99 va_arg100 va_arg101 va_arg102 va_arg103) (let\n (va_arg93:Vale.Def.Types_s.quad32) = length_quad32 in let (va_arg92:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = auth_in in let (va_arg91:Vale.Def.Types_s.quad32) = y_final in let\n (va_arg90:Vale.Def.Types_s.quad32) = y_inout in let (va_arg89:Vale.Def.Types_s.quad32) = y_0 in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 490 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash_BE.lemma_hash_append2 h_BE va_arg89 va_arg90 va_arg91 va_arg92\n va_arg93) (let auth_in = FStar.Seq.Base.append #quad32 auth_in (FStar.Seq.Base.create #quad32 1\n length_quad32) in let (va_arg88:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 492 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash_BE.ghash_incremental_to_ghash h_BE va_arg88) (va_QEmpty\n (())))))))))))))))))))))))))))))))))))))))", "val va_lemma_Gcm_blocks : va_b0:va_code -> va_s0:va_state -> alg:algorithm -> auth_b:buffer128 ->\n abytes_b:buffer128 -> in128_b:buffer128 -> out128_b:buffer128 -> inout_b:buffer128 ->\n iv_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> gcm_struct_b:buffer64\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks alg) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (h_BE:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 0 va_s0)) in\n Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem_heaplet 3 va_s0) (va_get_reg 25 va_s0)\n gcm_struct_b 12 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem_heaplet 1 va_s0) auth_ptr auth_b auth_len (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 6 va_s0) abytes_ptr abytes_b 1\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 2\n va_s0) iv_ptr iv_b 1 (va_get_mem_layout va_s0) Public /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem_heaplet 1 va_s0) in128_ptr in128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) out128_ptr out128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 5\n va_s0) inout_ptr inout_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b;\n hkeys_b; in128_b; out128_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 out128_b\n ([keys_b; hkeys_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 inout_b ([keys_b;\n hkeys_b; out128_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b ==\n out128_b) /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply`\n len128 < pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64\n /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ plain_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem_heaplet 0 va_s0) + 128 < pow2_64 /\\\n (va_mul_nat len128 (128 `op_Division` 8) <= plain_num_bytes /\\ plain_num_bytes < va_mul_nat\n len128 (128 `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division`\n 8) <= auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ aes_reqs alg key round_keys keys_b keys_ptr (va_get_mem_heaplet 0 va_s0)\n (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0)))))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 0 (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (h_BE:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 0 va_s0)) in\n Vale.PPC64LE.Decls.modifies_buffer128 out128_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet\n 1 va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0)\n (va_get_mem_heaplet 2 va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ plain_num_bytes < pow2_32 /\\\n auth_num_bytes < pow2_32 /\\ (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_s0)) in let\n (ctr_BE_1:quad32) = iv_BE in let (ctr_BE_2:quad32) = Vale.AES.GCTR_BE_s.inc32 iv_BE 1 in let\n plain1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b)) in let plain2 = Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in128_b) in let (plain_in:(seq quad32)) =\n (if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division` 8) then plain1 else plain2) in\n let cipher1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) in let cipher2 =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b) in let (cipher_out:(seq quad32)) = (if (plain_num_bytes > len128 `op_Multiply` 128\n `op_Division` 8) then cipher1 else cipher2) in let (cipher_bound:nat) = (if (plain_num_bytes >\n len128 `op_Multiply` 128 `op_Division` 8) then (len128 + 1) else len128) in\n Vale.AES.GCTR_BE.gctr_partial alg cipher_bound plain_in cipher_out key ctr_BE_2 /\\ (let\n (length_quad:quad32) = Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.Mktwo #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` auth_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n auth_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32)) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` plain_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n plain_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32))) in let raw_auth1 =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6 va_s0)\n abytes_b)) in let raw_auth2 = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) auth_b) in let (raw_auth_quads:(seq quad32)) = (if (auth_num_bytes\n > auth_len `op_Multiply` 128 `op_Division` 8) then raw_auth1 else raw_auth2) in let\n (auth_input_bytes:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 auth_num_bytes in let (padded_auth_bytes:(seq nat8))\n = Vale.AES.GCTR_BE_s.pad_to_128_bits auth_input_bytes in let (auth_quad_seq:(seq quad32)) =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes in let (raw_quad_seq:(seq quad32)) =\n FStar.Seq.Base.append #quad32 auth_quad_seq (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in128_b)) in let (total_bytes:nat) =\n FStar.Seq.Base.length #quad32 auth_quad_seq `op_Multiply` 16 + plain_num_bytes in let raw_quad1\n = let (ab:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 (FStar.Seq.Base.append #quad32 raw_quad_seq\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b))))) 0 total_bytes in let (pb:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits ab in\n Vale.Def.Types_s.be_bytes_to_seq_quad32 pb in let raw_quad2 = raw_quad_seq in let\n (raw_quad_seq:(seq quad32)) = (if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division` 8)\n then raw_quad1 else raw_quad2) in let (auth_quad_seq:(seq quad32)) = FStar.Seq.Base.append\n #quad32 raw_quad_seq (FStar.Seq.Base.create #quad32 1 length_quad) in va_get_vec 1 va_sM ==\n Vale.AES.GCTR_BE_s.gctr_encrypt_block ctr_BE_1 (Vale.AES.GHash_BE_s.ghash_BE h_BE\n auth_quad_seq) alg key 0))) /\\ va_state_eq va_sM (va_update_mem_heaplet 5 va_sM\n (va_update_mem_heaplet 2 va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM\n (va_update_vec 21 va_sM (va_update_vec 20 va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM\n (va_update_vec 17 va_sM (va_update_vec 16 va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM\n (va_update_vec 13 va_sM (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM\n (va_update_vec 9 va_sM (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM\n (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM\n (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM\n (va_update_reg 29 va_sM (va_update_reg 28 va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM\n (va_update_reg 10 va_sM (va_update_reg 9 va_sM (va_update_reg 8 va_sM (va_update_reg 7 va_sM\n (va_update_reg 6 va_sM (va_update_reg 5 va_sM (va_update_reg 4 va_sM (va_update_reg 3 va_sM\n (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))))))))))))))))))))))))))))))", "let va_lemma_Gcm_blocks va_b0 va_s0 alg auth_b abytes_b in128_b out128_b inout_b iv_b key\n round_keys keys_b hkeys_b gcm_struct_b =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem] in\n let va_qc = va_qcode_Gcm_blocks va_mods alg auth_b abytes_b in128_b out128_b inout_b iv_b key\n round_keys keys_b hkeys_b gcm_struct_b in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_blocks alg) va_qc va_s0 (fun va_s0\n va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 250 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in let (h_BE:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 336 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 out128_b (va_get_mem_heaplet 1 va_s0)\n (va_get_mem_heaplet 1 va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 337 column 52 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0) (va_get_mem_heaplet 2\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 338 column 55 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet\n 5 va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 341 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (plain_num_bytes < pow2_32) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 342 column 38 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (auth_num_bytes < pow2_32) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 344 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_s0)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 346 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (ctr_BE_1:quad32) = iv_BE in label va_range1\n \"***** POSTCONDITION NOT MET AT line 347 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (ctr_BE_2:quad32) = Vale.AES.GCTR_BE_s.inc32 iv_BE 1 in label va_range1\n \"***** POSTCONDITION NOT MET AT line 350 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let plain1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 351 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let plain2 = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in128_b) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 352 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (plain_in:(seq quad32)) = va_if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division`\n 8) (fun _ -> plain1) (fun _ -> plain2) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 355 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let cipher1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 357 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let cipher2 = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_sM) out128_b) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (cipher_out:(seq quad32)) = va_if (plain_num_bytes > len128 `op_Multiply` 128\n `op_Division` 8) (fun _ -> cipher1) (fun _ -> cipher2) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 361 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (cipher_bound:nat) = va_if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division` 8)\n (fun _ -> len128 + 1) (fun _ -> len128) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 365 column 77 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.AES.GCTR_BE.gctr_partial alg cipher_bound plain_in cipher_out key ctr_BE_2) /\\ label\n va_range1\n \"***** POSTCONDITION NOT MET AT line 369 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (length_quad:quad32) = Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.Mktwo #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` auth_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n auth_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32)) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` plain_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n plain_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32))) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 373 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let raw_auth1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n auth_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet\n 6 va_s0) abytes_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 374 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let raw_auth2 = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) auth_b) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 375 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (raw_auth_quads:(seq quad32)) = va_if (auth_num_bytes > auth_len `op_Multiply` 128\n `op_Division` 8) (fun _ -> raw_auth1) (fun _ -> raw_auth2) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 379 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (auth_input_bytes:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 auth_num_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 380 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (padded_auth_bytes:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits auth_input_bytes in\n label va_range1\n \"***** POSTCONDITION NOT MET AT line 381 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (auth_quad_seq:(seq quad32)) = Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes\n in label va_range1\n \"***** POSTCONDITION NOT MET AT line 382 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (raw_quad_seq:(seq quad32)) = FStar.Seq.Base.append #quad32 auth_quad_seq\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 383 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (total_bytes:nat) = FStar.Seq.Base.length #quad32 auth_quad_seq `op_Multiply` 16 +\n plain_num_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 384 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let raw_quad1 = let (ab:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 (FStar.Seq.Base.append #quad32 raw_quad_seq\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b))))) 0 total_bytes in let (pb:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits ab in\n Vale.Def.Types_s.be_bytes_to_seq_quad32 pb in label va_range1\n \"***** POSTCONDITION NOT MET AT line 387 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let raw_quad2 = raw_quad_seq in label va_range1\n \"***** POSTCONDITION NOT MET AT line 388 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (raw_quad_seq:(seq quad32)) = va_if (plain_num_bytes > len128 `op_Multiply` 128\n `op_Division` 8) (fun _ -> raw_quad1) (fun _ -> raw_quad2) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 393 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (auth_quad_seq:(seq quad32)) = FStar.Seq.Base.append #quad32 raw_quad_seq\n (FStar.Seq.Base.create #quad32 1 length_quad) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 394 column 106 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_vec 1 va_sM == Vale.AES.GCTR_BE_s.gctr_encrypt_block ctr_BE_1\n (Vale.AES.GHash_BE_s.ghash_BE h_BE auth_quad_seq) alg key 0)))))))))))))))))))))))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem]) va_sM va_s0;\n (va_sM, va_fM)", "let va_wp_Gcm_blocks (alg:algorithm) (auth_b:buffer128) (abytes_b:buffer128) (in128_b:buffer128)\n (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (gcm_struct_b:buffer64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in let (h_BE:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem_heaplet 3\n va_s0) (va_get_reg 25 va_s0) gcm_struct_b 12 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) auth_ptr auth_b auth_len\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 6\n va_s0) abytes_ptr abytes_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 2 va_s0) iv_ptr iv_b 1\n (va_get_mem_layout va_s0) Public /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) in128_ptr in128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) out128_ptr out128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 5\n va_s0) inout_ptr inout_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b;\n hkeys_b; in128_b; out128_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 out128_b\n ([keys_b; hkeys_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 inout_b ([keys_b;\n hkeys_b; out128_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b ==\n out128_b) /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply`\n len128 < pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64\n /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ plain_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem_heaplet 0 va_s0) + 128 < pow2_64 /\\\n (va_mul_nat len128 (128 `op_Division` 8) <= plain_num_bytes /\\ plain_num_bytes < va_mul_nat\n len128 (128 `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division`\n 8) <= auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ aes_reqs alg key round_keys keys_b keys_ptr (va_get_mem_heaplet 0 va_s0)\n (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0))) /\\ (forall (va_x_mem:vale_heap) (va_x_r3:nat64)\n (va_x_r4:nat64) (va_x_r5:nat64) (va_x_r6:nat64) (va_x_r7:nat64) (va_x_r8:nat64) (va_x_r9:nat64)\n (va_x_r10:nat64) (va_x_r26:nat64) (va_x_r27:nat64) (va_x_r28:nat64) (va_x_r29:nat64)\n (va_x_r30:nat64) (va_x_r31:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32) (va_x_v17:quad32)\n (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32) (va_x_v21:quad32) (va_x_cr0:cr0_t)\n (va_x_heap1:vale_heap) (va_x_heap2:vale_heap) (va_x_heap5:vale_heap) . let va_sM =\n va_upd_mem_heaplet 5 va_x_heap5 (va_upd_mem_heaplet 2 va_x_heap2 (va_upd_mem_heaplet 1\n va_x_heap1 (va_upd_cr0 va_x_cr0 (va_upd_vec 21 va_x_v21 (va_upd_vec 20 va_x_v20 (va_upd_vec 19\n va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16 (va_upd_vec 15\n va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12 (va_upd_vec 11\n va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7\n va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3\n (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 31 va_x_r31\n (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29 (va_upd_reg 28 va_x_r28 (va_upd_reg 27 va_x_r27\n (va_upd_reg 26 va_x_r26 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9 (va_upd_reg 8 va_x_r8\n (va_upd_reg 7 va_x_r7 (va_upd_reg 6 va_x_r6 (va_upd_reg 5 va_x_r5 (va_upd_reg 4 va_x_r4\n (va_upd_reg 3 va_x_r3 (va_upd_mem va_x_mem va_s0)))))))))))))))))))))))))))))))))))))))) in\n va_get_ok va_sM /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in let (h_BE:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in Vale.PPC64LE.Decls.modifies_buffer128 out128_b\n (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\\\n Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0) (va_get_mem_heaplet 2\n va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0)\n (va_get_mem_heaplet 5 va_sM) /\\ plain_num_bytes < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ (let\n iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_s0)) in let (ctr_BE_1:quad32) = iv_BE in let (ctr_BE_2:quad32) =\n Vale.AES.GCTR_BE_s.inc32 iv_BE 1 in let plain1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b)) in let plain2 = Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in128_b) in let (plain_in:(seq quad32)) =\n va_if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division` 8) (fun _ -> plain1) (fun _ ->\n plain2) in let cipher1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) in let cipher2 =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b) in let (cipher_out:(seq quad32)) = va_if (plain_num_bytes > len128 `op_Multiply` 128\n `op_Division` 8) (fun _ -> cipher1) (fun _ -> cipher2) in let (cipher_bound:nat) = va_if\n (plain_num_bytes > len128 `op_Multiply` 128 `op_Division` 8) (fun _ -> len128 + 1) (fun _ ->\n len128) in Vale.AES.GCTR_BE.gctr_partial alg cipher_bound plain_in cipher_out key ctr_BE_2 /\\\n (let (length_quad:quad32) = Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.Mktwo #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` auth_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n auth_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32)) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` plain_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n plain_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32))) in let raw_auth1 =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6 va_s0)\n abytes_b)) in let raw_auth2 = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) auth_b) in let (raw_auth_quads:(seq quad32)) = va_if\n (auth_num_bytes > auth_len `op_Multiply` 128 `op_Division` 8) (fun _ -> raw_auth1) (fun _ ->\n raw_auth2) in let (auth_input_bytes:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 auth_num_bytes in let (padded_auth_bytes:(seq nat8))\n = Vale.AES.GCTR_BE_s.pad_to_128_bits auth_input_bytes in let (auth_quad_seq:(seq quad32)) =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes in let (raw_quad_seq:(seq quad32)) =\n FStar.Seq.Base.append #quad32 auth_quad_seq (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in128_b)) in let (total_bytes:nat) =\n FStar.Seq.Base.length #quad32 auth_quad_seq `op_Multiply` 16 + plain_num_bytes in let raw_quad1\n = let (ab:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 (FStar.Seq.Base.append #quad32 raw_quad_seq\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b))))) 0 total_bytes in let (pb:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits ab in\n Vale.Def.Types_s.be_bytes_to_seq_quad32 pb in let raw_quad2 = raw_quad_seq in let\n (raw_quad_seq:(seq quad32)) = va_if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division`\n 8) (fun _ -> raw_quad1) (fun _ -> raw_quad2) in let (auth_quad_seq:(seq quad32)) =\n FStar.Seq.Base.append #quad32 raw_quad_seq (FStar.Seq.Base.create #quad32 1 length_quad) in\n va_get_vec 1 va_sM == Vale.AES.GCTR_BE_s.gctr_encrypt_block ctr_BE_1\n (Vale.AES.GHash_BE_s.ghash_BE h_BE auth_quad_seq) alg key 0))) ==> va_k va_sM (())))", "val va_wpProof_Gcm_blocks : alg:algorithm -> auth_b:buffer128 -> abytes_b:buffer128 ->\n in128_b:buffer128 -> out128_b:buffer128 -> inout_b:buffer128 -> iv_b:buffer128 -> key:(seq nat32)\n -> round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> gcm_struct_b:buffer64 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks alg auth_b abytes_b in128_b out128_b inout_b\n iv_b key round_keys keys_b hkeys_b gcm_struct_b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks alg) ([va_Mod_mem_heaplet\n 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20;\n va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14;\n va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8;\n va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec\n 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27;\n va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6;\n va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))", "let va_wpProof_Gcm_blocks alg auth_b abytes_b in128_b out128_b inout_b iv_b key round_keys keys_b\n hkeys_b gcm_struct_b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_blocks (va_code_Gcm_blocks alg) va_s0 alg auth_b abytes_b\n in128_b out128_b inout_b iv_b key round_keys keys_b hkeys_b gcm_struct_b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 5 va_sM (va_update_mem_heaplet 2 va_sM\n (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 21 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 7 va_sM (va_update_reg 6 va_sM (va_update_reg 5\n va_sM (va_update_reg 4 va_sM (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3;\n va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_quick_Gcm_blocks (alg:algorithm) (auth_b:buffer128) (abytes_b:buffer128) (in128_b:buffer128)\n (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (gcm_struct_b:buffer64) : (va_quickCode unit\n (va_code_Gcm_blocks alg)) =\n (va_QProc (va_code_Gcm_blocks alg) ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2;\n va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18;\n va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg\n 3; va_Mod_mem]) (va_wp_Gcm_blocks alg auth_b abytes_b in128_b out128_b inout_b iv_b key\n round_keys keys_b hkeys_b gcm_struct_b) (va_wpProof_Gcm_blocks alg auth_b abytes_b in128_b\n out128_b inout_b iv_b key round_keys keys_b hkeys_b gcm_struct_b))", "val va_code_Gcm_blocks_wrapped : alg:algorithm -> Tot va_code", "let va_code_Gcm_blocks_wrapped alg =\n (va_Block (va_CCons (va_code_Gcm_blocks alg) (va_CCons (va_Block (va_CNil ())) (va_CNil ()))))", "val va_codegen_success_Gcm_blocks_wrapped : alg:algorithm -> Tot va_pbool", "let va_codegen_success_Gcm_blocks_wrapped alg =\n (va_pbool_and (va_codegen_success_Gcm_blocks alg) (va_ttrue ()))", "let va_qcode_Gcm_blocks_wrapped (va_mods:va_mods_t) (alg:algorithm) (auth_b:buffer128)\n (abytes_b:buffer128) (in128_b:buffer128) (out128_b:buffer128) (inout_b:buffer128)\n (iv_b:buffer128) (iv:supported_iv_BE) (key:(seq nat32)) (round_keys:(seq quad32))\n (keys_b:buffer128) (hkeys_b:buffer128) (expected_tag:(seq nat8)) (gcm_struct_b:buffer64) :\n (va_quickCode unit (va_code_Gcm_blocks_wrapped alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s) in va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 616 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_blocks alg auth_b abytes_b in128_b out128_b inout_b iv_b key round_keys keys_b\n hkeys_b gcm_struct_b) (fun (va_s:va_state) _ -> let (va_arg46:Vale.Def.Types_s.quad32) =\n Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32 (Vale.Def.Words_s.Mktwo\n #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32\n (8 `op_Multiply` auth_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply` auth_num_bytes\n `op_Division` pow2_32 `op_Modulus` pow2_32)) (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32 (8\n `op_Multiply` plain_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply` plain_num_bytes\n `op_Division` pow2_32 `op_Modulus` pow2_32))) in let (va_arg45:Vale.Def.Types_s.quad32) =\n va_get_vec 1 va_s in let (va_arg44:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s)) in let (va_arg43:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_old_s)) in let (va_arg42:Vale.AES.GCM_BE_s.supported_iv_BE) = iv in\n let (va_arg41:Prims.nat) = auth_num_bytes in let (va_arg40:Prims.nat) = plain_num_bytes in let\n (va_arg39:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s)\n inout_b) in let (va_arg38:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n out128_b) in let (va_arg37:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5\n va_old_s) inout_b) in let (va_arg36:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (va_arg35:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6\n va_old_s) abytes_b) in let (va_arg34:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) auth_b) in let (va_arg33:(FStar.Seq.Base.seq Vale.Def.Words_s.nat32)) = key in let\n (va_arg32:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 618 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_BE.gcm_blocks_dec_helper_simplified va_arg32 va_arg33 va_arg34\n va_arg35 va_arg36 va_arg37 va_arg38 va_arg39 va_arg40 va_arg41 va_arg42 va_arg43 va_arg44\n va_arg45 va_arg46) (let (auth_raw_quads:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_old_s) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6\n va_old_s) abytes_b)) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 630 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 auth_raw_quads)) 0\n auth_num_bytes) (fun _ -> let (auth_bytes:(FStar.Seq.Base.seq Vale.Def.Words_s.nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 auth_raw_quads)) 0\n auth_num_bytes in let (va_arg31:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_old_s)) in let (va_arg30:Vale.AES.GCM_BE_s.supported_iv_BE) = iv in\n let (va_arg29:Prims.nat) = plain_num_bytes in let (va_arg28:(FStar.Seq.Base.seq\n Vale.Def.Words_s.nat8)) = expected_tag in let (va_arg27:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s) inout_b) in let (va_arg26:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s) out128_b) in let (va_arg25:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_old_s) inout_b) in let (va_arg24:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_old_s) in128_b) in let (va_arg23:(FStar.Seq.Base.seq\n Vale.Def.Words_s.nat32)) = key in let (va_arg22:Vale.AES.AES_common_s.algorithm) = alg in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 631 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_BE.gcm_blocks_helper_dec_simplified va_arg22 va_arg23 va_arg24\n va_arg25 va_arg26 va_arg27 auth_bytes va_arg28 va_arg29 va_arg30 va_arg31) (va_QEmpty (())))))))", "val va_lemma_Gcm_blocks_wrapped : va_b0:va_code -> va_s0:va_state -> alg:algorithm ->\n auth_b:buffer128 -> abytes_b:buffer128 -> in128_b:buffer128 -> out128_b:buffer128 ->\n inout_b:buffer128 -> iv_b:buffer128 -> iv:supported_iv_BE -> key:(seq nat32) -> round_keys:(seq\n quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> expected_tag:(seq nat8) ->\n gcm_struct_b:buffer64\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks_wrapped alg) va_s0 /\\ va_get_ok va_s0 /\\\n (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 0 (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in\n Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem_heaplet 3 va_s0) (va_get_reg 25 va_s0)\n gcm_struct_b 12 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem_heaplet 1 va_s0) auth_ptr auth_b auth_len (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 6 va_s0) abytes_ptr abytes_b 1\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 2\n va_s0) iv_ptr iv_b 1 (va_get_mem_layout va_s0) Public /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem_heaplet 1 va_s0) in128_ptr in128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) out128_ptr out128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 5\n va_s0) inout_ptr inout_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b;\n hkeys_b; in128_b; out128_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 out128_b\n ([keys_b; hkeys_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 inout_b ([keys_b;\n hkeys_b; out128_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b ==\n out128_b) /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply`\n len128 < pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64\n /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ plain_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem_heaplet 0 va_s0) + 128 < pow2_64 /\\\n (va_mul_nat len128 (128 `op_Division` 8) <= plain_num_bytes /\\ plain_num_bytes < va_mul_nat\n len128 (128 `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division`\n 8) <= auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ aes_reqs alg key round_keys keys_b keys_ptr (va_get_mem_heaplet 0 va_s0)\n (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0)) /\\ (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_s0)) in let h_BE =\n Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0\n 0 0) in iv_BE == Vale.AES.GCM_BE_s.compute_iv_BE h_BE iv))))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 0 (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in\n Vale.PPC64LE.Decls.modifies_buffer128 out128_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet\n 1 va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0)\n (va_get_mem_heaplet 2 va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ plain_num_bytes < pow2_32 /\\\n auth_num_bytes < pow2_32 /\\ (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_s0)) in let auth_raw_quads =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6 va_s0)\n abytes_b)) in let auth_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 auth_raw_quads)) 0 auth_num_bytes in let plain_raw_quads =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in128_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b)) in let plain_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 plain_raw_quads)) 0 plain_num_bytes in let cipher_raw_quads =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out128_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_sM)\n inout_b)) in let cipher_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 cipher_raw_quads)) 0 plain_num_bytes in l_and (l_and (l_and\n (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 auth_bytes < pow2_32) (FStar.Seq.Base.length\n #Vale.Def.Words_s.nat8 plain_bytes < pow2_32)) (cipher_bytes == __proj__Mktuple2__item___1\n #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv plain_bytes auth_bytes expected_tag)))\n (Vale.Arch.Types.be_quad32_to_bytes (va_get_vec 1 va_sM) == Vale.AES.GCM_BE.gcm_decrypt_BE_tag\n alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv plain_bytes auth_bytes))) /\\\n va_state_eq va_sM (va_update_mem_heaplet 5 va_sM (va_update_mem_heaplet 2 va_sM\n (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 21 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 7 va_sM (va_update_reg 6 va_sM (va_update_reg 5\n va_sM (va_update_reg 4 va_sM (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0))))))))))))))))))))))))))))))))))))))))))))", "let va_lemma_Gcm_blocks_wrapped va_b0 va_s0 alg auth_b abytes_b in128_b out128_b inout_b iv_b iv\n key round_keys keys_b hkeys_b expected_tag gcm_struct_b =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem] in\n let va_qc = va_qcode_Gcm_blocks_wrapped va_mods alg auth_b abytes_b in128_b out128_b inout_b iv_b\n iv key round_keys keys_b hkeys_b expected_tag gcm_struct_b in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_blocks_wrapped alg) va_qc va_s0\n (fun va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 495 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 590 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 out128_b (va_get_mem_heaplet 1 va_s0)\n (va_get_mem_heaplet 1 va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 591 column 52 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0) (va_get_mem_heaplet 2\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 592 column 55 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet\n 5 va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 595 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (plain_num_bytes < pow2_32) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 596 column 38 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (auth_num_bytes < pow2_32) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 598 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_s0)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 600 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let auth_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n auth_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet\n 6 va_s0) abytes_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 601 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let auth_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 auth_raw_quads)) 0 auth_num_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 602 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let plain_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 603 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let plain_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 plain_raw_quads)) 0 plain_num_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 604 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let cipher_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 605 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let cipher_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 cipher_raw_quads)) 0 plain_num_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 614 column 52 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (l_and (l_and (l_and (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 auth_bytes < pow2_32)\n (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 plain_bytes < pow2_32)) (cipher_bytes ==\n __proj__Mktuple2__item___1 #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool\n (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv\n plain_bytes auth_bytes expected_tag))) (Vale.Arch.Types.be_quad32_to_bytes (va_get_vec 1 va_sM)\n == Vale.AES.GCM_BE.gcm_decrypt_BE_tag alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key)\n iv plain_bytes auth_bytes))))))))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem]) va_sM va_s0;\n (va_sM, va_fM)", "let va_wp_Gcm_blocks_wrapped (alg:algorithm) (auth_b:buffer128) (abytes_b:buffer128)\n (in128_b:buffer128) (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128)\n (iv:supported_iv_BE) (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128)\n (hkeys_b:buffer128) (expected_tag:(seq nat8)) (gcm_struct_b:buffer64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem_heaplet 3 va_s0)\n (va_get_reg 25 va_s0) gcm_struct_b 12 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) auth_ptr auth_b auth_len\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 6\n va_s0) abytes_ptr abytes_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 2 va_s0) iv_ptr iv_b 1\n (va_get_mem_layout va_s0) Public /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) in128_ptr in128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) out128_ptr out128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 5\n va_s0) inout_ptr inout_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b;\n hkeys_b; in128_b; out128_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 out128_b\n ([keys_b; hkeys_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 inout_b ([keys_b;\n hkeys_b; out128_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b ==\n out128_b) /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply`\n len128 < pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64\n /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ plain_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem_heaplet 0 va_s0) + 128 < pow2_64 /\\\n (va_mul_nat len128 (128 `op_Division` 8) <= plain_num_bytes /\\ plain_num_bytes < va_mul_nat\n len128 (128 `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division`\n 8) <= auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ aes_reqs alg key round_keys keys_b keys_ptr (va_get_mem_heaplet 0 va_s0)\n (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0)) /\\ (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_s0)) in let h_BE =\n Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0\n 0 0) in iv_BE == Vale.AES.GCM_BE_s.compute_iv_BE h_BE iv)) /\\ (forall (va_x_mem:vale_heap)\n (va_x_r3:nat64) (va_x_r4:nat64) (va_x_r5:nat64) (va_x_r6:nat64) (va_x_r7:nat64) (va_x_r8:nat64)\n (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r26:nat64) (va_x_r27:nat64) (va_x_r28:nat64)\n (va_x_r29:nat64) (va_x_r30:nat64) (va_x_r31:nat64) (va_x_v0:quad32) (va_x_v1:quad32)\n (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32)\n (va_x_v7:quad32) (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32)\n (va_x_v12:quad32) (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32)\n (va_x_v17:quad32) (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32) (va_x_v21:quad32)\n (va_x_cr0:cr0_t) (va_x_heap1:vale_heap) (va_x_heap2:vale_heap) (va_x_heap5:vale_heap) . let\n va_sM = va_upd_mem_heaplet 5 va_x_heap5 (va_upd_mem_heaplet 2 va_x_heap2 (va_upd_mem_heaplet 1\n va_x_heap1 (va_upd_cr0 va_x_cr0 (va_upd_vec 21 va_x_v21 (va_upd_vec 20 va_x_v20 (va_upd_vec 19\n va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16 (va_upd_vec 15\n va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12 (va_upd_vec 11\n va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7\n va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3\n (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 31 va_x_r31\n (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29 (va_upd_reg 28 va_x_r28 (va_upd_reg 27 va_x_r27\n (va_upd_reg 26 va_x_r26 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9 (va_upd_reg 8 va_x_r8\n (va_upd_reg 7 va_x_r7 (va_upd_reg 6 va_x_r6 (va_upd_reg 5 va_x_r5 (va_upd_reg 4 va_x_r4\n (va_upd_reg 3 va_x_r3 (va_upd_mem va_x_mem va_s0)))))))))))))))))))))))))))))))))))))))) in\n va_get_ok va_sM /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in Vale.PPC64LE.Decls.modifies_buffer128 out128_b\n (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\\\n Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0) (va_get_mem_heaplet 2\n va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0)\n (va_get_mem_heaplet 5 va_sM) /\\ plain_num_bytes < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ (let\n iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_s0)) in let auth_raw_quads = FStar.Seq.Base.append\n #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) auth_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6 va_s0) abytes_b)) in let auth_bytes =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 auth_raw_quads)) 0\n auth_num_bytes in let plain_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b)) in let plain_bytes = FStar.Seq.Base.slice\n #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 plain_raw_quads)) 0\n plain_num_bytes in let cipher_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) in let cipher_bytes = FStar.Seq.Base.slice\n #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 cipher_raw_quads)) 0\n plain_num_bytes in l_and (l_and (l_and (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 auth_bytes\n < pow2_32) (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 plain_bytes < pow2_32)) (cipher_bytes\n == __proj__Mktuple2__item___1 #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool\n (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv\n plain_bytes auth_bytes expected_tag))) (Vale.Arch.Types.be_quad32_to_bytes (va_get_vec 1 va_sM)\n == Vale.AES.GCM_BE.gcm_decrypt_BE_tag alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key)\n iv plain_bytes auth_bytes))) ==> va_k va_sM (())))", "val va_wpProof_Gcm_blocks_wrapped : alg:algorithm -> auth_b:buffer128 -> abytes_b:buffer128 ->\n in128_b:buffer128 -> out128_b:buffer128 -> inout_b:buffer128 -> iv_b:buffer128 ->\n iv:supported_iv_BE -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> expected_tag:(seq nat8) -> gcm_struct_b:buffer64 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks_wrapped alg auth_b abytes_b in128_b out128_b\n inout_b iv_b iv key round_keys keys_b hkeys_b expected_tag gcm_struct_b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks_wrapped alg)\n ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 21;\n va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15;\n va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9;\n va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec\n 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28;\n va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 7;\n va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0,\n va_g))))", "let va_wpProof_Gcm_blocks_wrapped alg auth_b abytes_b in128_b out128_b inout_b iv_b iv key\n round_keys keys_b hkeys_b expected_tag gcm_struct_b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_blocks_wrapped (va_code_Gcm_blocks_wrapped alg) va_s0 alg\n auth_b abytes_b in128_b out128_b inout_b iv_b iv key round_keys keys_b hkeys_b expected_tag\n gcm_struct_b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 5 va_sM (va_update_mem_heaplet 2 va_sM\n (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 21 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 7 va_sM (va_update_reg 6 va_sM (va_update_reg 5\n va_sM (va_update_reg 4 va_sM (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3;\n va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_quick_Gcm_blocks_wrapped (alg:algorithm) (auth_b:buffer128) (abytes_b:buffer128)\n (in128_b:buffer128) (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128)\n (iv:supported_iv_BE) (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128)\n (hkeys_b:buffer128) (expected_tag:(seq nat8)) (gcm_struct_b:buffer64) : (va_quickCode unit\n (va_code_Gcm_blocks_wrapped alg)) =\n (va_QProc (va_code_Gcm_blocks_wrapped alg) ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2;\n va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18;\n va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg\n 3; va_Mod_mem]) (va_wp_Gcm_blocks_wrapped alg auth_b abytes_b in128_b out128_b inout_b iv_b iv\n key round_keys keys_b hkeys_b expected_tag gcm_struct_b) (va_wpProof_Gcm_blocks_wrapped alg\n auth_b abytes_b in128_b out128_b inout_b iv_b iv key round_keys keys_b hkeys_b expected_tag\n gcm_struct_b))", "val va_code_Nat64Equal : va_dummy:unit -> Tot va_code", "let va_code_Nat64Equal () =\n (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 5) 1) (va_CCons (va_code_AddCarry\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 5)) (va_CCons (va_code_LoadImm64\n (va_op_reg_opr_reg 3) 0) (va_CCons (va_code_AddExtended (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3)) (va_CCons (va_code_Xor (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 5) (va_op_reg_opr_reg 3)) (va_CNil ())))))))", "val va_codegen_success_Nat64Equal : va_dummy:unit -> Tot va_pbool", "let va_codegen_success_Nat64Equal () =\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 5) 1) (va_pbool_and\n (va_codegen_success_AddCarry (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 5))\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 3) 0) (va_pbool_and\n (va_codegen_success_AddExtended (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg\n 3)) (va_pbool_and (va_codegen_success_Xor (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 5)\n (va_op_reg_opr_reg 3)) (va_ttrue ()))))))", "let va_qcode_Nat64Equal (va_mods:va_mods_t) : (va_quickCode unit (va_code_Nat64Equal ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 646 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 5) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 647 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_AddCarry (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 5)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 648 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 3) 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 649 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_AddExtended (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 650 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Xor (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 5) (va_op_reg_opr_reg 3)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 651 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_BitwiseXorWithZero64 1) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 652 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_BitwiseXorCancel64 1) (va_QEmpty (()))))))))))", "val va_lemma_Nat64Equal : va_b0:va_code -> va_s0:va_state\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Nat64Equal ()) va_s0 /\\ va_get_ok va_s0))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\ (if\n (va_get_reg 4 va_s0 = 18446744073709551615) then (va_get_reg 3 va_sM = 0) else (va_get_reg 3\n va_sM = 1)) /\\ va_state_eq va_sM (va_update_xer va_sM (va_update_reg 5 va_sM (va_update_reg 3\n va_sM (va_update_ok va_sM va_s0))))))", "let va_lemma_Nat64Equal va_b0 va_s0 =\n let (va_mods:va_mods_t) = [va_Mod_xer; va_Mod_reg 5; va_Mod_reg 3; va_Mod_ok] in\n let va_qc = va_qcode_Nat64Equal va_mods in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Nat64Equal ()) va_qc va_s0 (fun va_s0\n va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 639 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_ok va_sM) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 644 column 71 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_if (va_get_reg 4 va_s0 = 18446744073709551615) (fun _ -> va_get_reg 3 va_sM = 0) (fun _ ->\n va_get_reg 3 va_sM = 1))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_xer; va_Mod_reg 5; va_Mod_reg 3; va_Mod_ok]) va_sM va_s0;\n (va_sM, va_fM)", "let va_wp_Nat64Equal (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (forall (va_x_r3:nat64) (va_x_r5:nat64) (va_x_xer:xer_t) . let va_sM =\n va_upd_xer va_x_xer (va_upd_reg 5 va_x_r5 (va_upd_reg 3 va_x_r3 va_s0)) in va_get_ok va_sM /\\\n va_if (va_get_reg 4 va_s0 = 18446744073709551615) (fun _ -> va_get_reg 3 va_sM = 0) (fun _ ->\n va_get_reg 3 va_sM = 1) ==> va_k va_sM (())))", "val va_wpProof_Nat64Equal : va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Nat64Equal va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Nat64Equal ()) ([va_Mod_xer;\n va_Mod_reg 5; va_Mod_reg 3]) va_s0 va_k ((va_sM, va_f0, va_g))))", "let va_wpProof_Nat64Equal va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal ()) va_s0 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_xer va_sM (va_update_reg 5 va_sM (va_update_reg 3 va_sM\n (va_update_ok va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_xer; va_Mod_reg 5; va_Mod_reg 3]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_quick_Nat64Equal () : (va_quickCode unit (va_code_Nat64Equal ())) =\n (va_QProc (va_code_Nat64Equal ()) ([va_Mod_xer; va_Mod_reg 5; va_Mod_reg 3]) va_wp_Nat64Equal\n va_wpProof_Nat64Equal)", "val va_code_VectorEqual : va_dummy:unit -> Tot va_code", "let va_code_VectorEqual () =\n (va_Block (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 1)) (va_CCons (va_code_Mfvsrld (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0))\n (va_CCons (va_code_Nat64Equal ()) (va_CCons (va_code_Move (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 3)) (va_CCons (va_code_Mfvsrd (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0))\n (va_CCons (va_code_Nat64Equal ()) (va_CCons (va_code_Add (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (va_CNil ())))))))))", "val va_codegen_success_VectorEqual : va_dummy:unit -> Tot va_pbool", "let va_codegen_success_VectorEqual () =\n (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Mfvsrld (va_op_reg_opr_reg 4)\n (va_op_vec_opr_vec 0)) (va_pbool_and (va_codegen_success_Nat64Equal ()) (va_pbool_and\n (va_codegen_success_Move (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (va_pbool_and\n (va_codegen_success_Mfvsrd (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0)) (va_pbool_and\n (va_codegen_success_Nat64Equal ()) (va_pbool_and (va_codegen_success_Add (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (va_ttrue ()))))))))" ], "closest": [ "val va_qcode_mod_6 (va_mods: va_mods_t) : (va_quickCode unit (va_code_mod_6 ()))\nlet va_qcode_mod_6 (va_mods:va_mods_t) : (va_quickCode unit (va_code_mod_6 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 565 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImmShl64 (va_op_reg_opr_reg 26) 21845) (fun (va_s:va_state) _ -> va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 566 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 21845 16) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 567 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddImm (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26) 21845) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 568 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 26) 32) (fun (va_s:va_state) _ ->\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 569 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 1431655765 32) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 570 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Add (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 10)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 571 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) (-1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 572 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Sub (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 26)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 573 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddImm (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26) 1) (fun (va_s:va_state) _ ->\n va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 574 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_get_reg 26 va_s == 12297829382473034411) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 575 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_MulHigh64U (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 26)) (fun\n (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = va_get_reg 10 va_s in va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 576 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishr_64 va_arg23 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 577 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Sr64Imm (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 10) 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 578 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddWrap (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 10))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 579 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddWrap (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 10))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 580 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_AddWrap (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 26))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 581 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_SubWrap (va_op_reg_opr_reg 26) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 26)) (fun\n (va_s:va_state) _ -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 582 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n ((fun (p:prop) -> normalize p) (va_get_reg 6 va_s `op_Modulus` 6 == va_get_reg 6 va_s - 6\n `op_Multiply` (va_get_reg 6 va_s `op_Multiply` 12297829382473034411 `op_Division` pow2_64\n `op_Division` 4))) (fun _ -> (fun (p:prop) -> p) (va_get_reg 6 va_s `op_Modulus` 6 ==\n va_get_reg 6 va_s - 6 `op_Multiply` (va_get_reg 6 va_s `op_Multiply` 12297829382473034411\n `op_Division` pow2_64 `op_Division` 4))) (fun (_:unit) -> assert_normalize (va_get_reg 6 va_s\n `op_Modulus` 6 == va_get_reg 6 va_s - 6 `op_Multiply` (va_get_reg 6 va_s `op_Multiply`\n 12297829382473034411 `op_Division` pow2_64 `op_Division` 4))) (va_QEmpty\n (())))))))))))))))))))))", "val va_qcode_load_one_msb (va_mods: va_mods_t) : (va_quickCode unit (va_code_load_one_msb ()))\nlet va_qcode_load_one_msb (va_mods:va_mods_t) : (va_quickCode unit (va_code_load_one_msb ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 583 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_ZeroXmm (va_op_xmm_xmm 2)) (fun (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 584 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (Vale.Arch.Types.two_to_nat32 (Vale.Def.Words_s.Mktwo #Vale.Def.Words_s.nat32 0 16777216) ==\n 72057594037927936) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 585 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_PinsrqImm (va_op_xmm_xmm 2) 72057594037927936 1 (va_op_reg_opr64_reg64 rR11)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 586 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (fun (_:unit) -> Vale.Def.Types_s.insert_nat64_reveal ()) (va_QEmpty (())))))))", "val va_qcode_Fast_sqr_part2 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Fast_sqr_part2 ()))\nlet va_qcode_Fast_sqr_part2 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Fast_sqr_part2 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 190 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.xor_lemmas ()) (let (va_arg25:nat64) = va_get_reg64 rRcx va_s\n in let (va_arg24:nat64) = va_get_reg64 rRax va_s in let (va_arg23:nat64) = va_get_reg64 rR13\n va_s in let (va_arg22:nat64) = va_get_reg64 rRbx va_s in let (va_arg21:nat64) = va_get_reg64\n rR11 va_s in let (va_arg20:nat64) = va_get_reg64 rR10 va_s in let (va_arg19:nat64) =\n va_get_reg64 rR9 va_s in let (va_arg18:nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 191 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (fun (_:unit) -> lemma_fast_sqr_part2 va_arg18 va_arg19 va_arg20 va_arg21 va_arg22 va_arg23\n va_arg24 va_arg25) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 193 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Xor64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rR15)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 194 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n ((fun (f:flags_t) -> true) (va_get_flags va_s)) (fun _ -> (fun (f:flags_t) -> flag_cf f = 1 ==\n cf f /\\ flag_of f = 1 == overflow f) (va_get_flags va_s)) (fun (_:unit) -> reveal_flags\n (va_get_flags va_s)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 196 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adox_64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 196 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 197 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adox_64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 197 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 198 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adox_64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 198 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 199 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adox_64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 199 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adox_64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 201 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 201 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Adcx_64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR14)) (va_QEmpty\n (())))))))))))))))))))", "val va_qcode_Mod_cr0 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ()))\nlet va_qcode_Mod_cr0 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QEmpty (())))", "val va_qcode_Mod_cr0 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ()))\nlet va_qcode_Mod_cr0 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QEmpty (())))", "val va_qcode_Mod_cr0 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ()))\nlet va_qcode_Mod_cr0 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Mod_cr0 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QEmpty (())))", "val va_qcode_Check_avx2_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_avx2_support ()))\nlet va_qcode_Check_avx2_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_avx2_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 156 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 158 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 159 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 160 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Avx2 ()) (fun (va_s:va_state) _ -> let (va_arg11:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 161 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg11 5) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 162 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 32)) (fun (va_s:va_state) _ ->\n va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 163 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (32 == Prims.pow2 5)) (fun _ -> (fun (p:prop) -> p) (32 ==\n Prims.pow2 5)) (fun (_:unit) -> assert_normalize (32 == Prims.pow2 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 164 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty (()))))))))))))", "val va_qcode_Load_one_msb (va_mods: va_mods_t) : (va_quickCode unit (va_code_Load_one_msb ()))\nlet va_qcode_Load_one_msb (va_mods:va_mods_t) : (va_quickCode unit (va_code_Load_one_msb ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 145 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_ZeroXmm (va_op_xmm_xmm 2)) (fun (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 146 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (Vale.Arch.Types.two_to_nat32 (Vale.Def.Words_s.Mktwo #Vale.Def.Words_s.nat32 0 16777216) ==\n 72057594037927936) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_PinsrqImm (va_op_xmm_xmm 2) 72057594037927936 1 (va_op_reg_opr64_reg64 rR11)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 148 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (fun (_:unit) -> Vale.Def.Types_s.insert_nat64_reveal ()) (va_QEmpty (())))))))", "val va_qcode_Check_avx_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_avx_support ()))\nlet va_qcode_Check_avx_support (va_mods:va_mods_t) : (va_quickCode unit (va_code_Check_avx_support\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 133 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 134 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 135 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Avx ()) (fun (va_s:va_state) _ -> let (va_arg14:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 136 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg14 25) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 137 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 138 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 268435456)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 139 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (268435456 == Prims.pow2 28)) (fun _ -> (fun (p:prop) -> p)\n (268435456 == Prims.pow2 28)) (fun (_:unit) -> assert_normalize (268435456 == Prims.pow2 28))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 141 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 27)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 142 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 1 28) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 143 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 27) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 145 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (())))))))))))))))", "val va_qcode_Check_avx512_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_avx512_support ()))\nlet va_qcode_Check_avx512_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_avx512_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 273 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 276 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 277 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Avx512 ()) (fun (va_s:va_state) _ -> let (va_arg49:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg49 16) (let\n (va_arg48:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 279 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg48 17) (let\n (va_arg47:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 280 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg47 30) (let\n (va_arg46:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 281 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg46 31) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 284 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 285 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 286 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 288 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 65536)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 131072)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 290 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64 1073741824)) (fun (va_s:va_state)\n _ -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 292 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (65536 == Prims.pow2 16)) (fun _ -> (fun (p:prop) -> p) (65536\n == Prims.pow2 16)) (fun (_:unit) -> assert_normalize (65536 == Prims.pow2 16)) (va_QLemma\n va_range1\n \"***** PRECONDITION NOT MET AT line 293 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (131072 == Prims.pow2 17)) (fun _ -> (fun (p:prop) -> p) (131072\n == Prims.pow2 17)) (fun (_:unit) -> assert_normalize (131072 == Prims.pow2 17)) (va_QLemma\n va_range1\n \"***** PRECONDITION NOT MET AT line 294 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (1073741824 == Prims.pow2 30)) (fun _ -> (fun (p:prop) -> p)\n (1073741824 == Prims.pow2 30)) (fun (_:unit) -> assert_normalize (1073741824 == Prims.pow2 30))\n (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 295 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (2147483648 == Prims.pow2 31)) (fun _ -> (fun (p:prop) -> p)\n (2147483648 == Prims.pow2 31)) (fun (_:unit) -> assert_normalize (2147483648 == Prims.pow2 31))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 297 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 1)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 298 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 16 17) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 299 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 1) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 14)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 302 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 16 30) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 303 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 14) (let\n (va_arg45:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let\n (va_arg44:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 305 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg44 va_arg45 16) (let\n (va_arg43:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 306 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg43 16) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 307 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 310 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 2147483648)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 311 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRbx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 312 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rR11) (va_const_shift_amt64 15)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 313 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 16 31) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 314 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 15) (let\n (va_arg42:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let\n (va_arg41:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 316 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg41 va_arg42 16) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 317 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (fun (va_s:va_state) _\n -> let (va_arg40:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_s in let\n (va_arg39:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 318 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg39 va_arg40 16) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 319 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 321 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (()))))))))))))))))))))))))))))))))))))))))", "val va_qcode_Check_avx2_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_avx2_stdcall win))\nlet va_qcode_Check_avx2_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_avx2_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 94 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_avx2_support ()) (va_QEmpty (()))))", "val va_qcode_Check_avx_xcr0_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_avx_xcr0_support ()))\nlet va_qcode_Check_avx_xcr0_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_avx_xcr0_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 358 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 359 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Xgetbv_Avx ()) (fun (va_s:va_state) _ -> let (va_arg19:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 360 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg19 1) (let\n (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 361 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg18 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 362 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRax)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 364 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 4)) (fun (va_s:va_state) _ ->\n va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 366 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (2 == Prims.pow2 1)) (fun _ -> (fun (p:prop) -> p) (2 ==\n Prims.pow2 1)) (fun (_:unit) -> assert_normalize (2 == Prims.pow2 1)) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 367 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (4 == Prims.pow2 2)) (fun _ -> (fun (p:prop) -> p) (4 ==\n Prims.pow2 2)) (fun (_:unit) -> assert_normalize (4 == Prims.pow2 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 369 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 1)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 370 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 1 2) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 371 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 1) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 373 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 2)) (fun (va_s:va_state) _ -> let\n (va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in let\n (va_arg16:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 374 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg16 va_arg17 1) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 375 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QEmpty\n (())))))))))))))))))", "val va_qcode_Check_sse_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_sse_support ()))\nlet va_qcode_Check_sse_support (va_mods:va_mods_t) : (va_quickCode unit (va_code_Check_sse_support\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 202 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 204 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 205 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 206 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Sse ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 209 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _\n -> let (va_arg35:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 211 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg35 9) (let\n (va_arg34:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 212 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg34 26) (let\n (va_arg33:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 213 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg33 19) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 215 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 524288)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 216 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 512)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 217 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 67108864)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 219 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (512 == Prims.pow2 9)) (fun _ -> (fun (p:prop) -> p) (512 ==\n Prims.pow2 9)) (fun (_:unit) -> assert_normalize (512 == Prims.pow2 9)) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 220 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (524288 == Prims.pow2 19)) (fun _ -> (fun (p:prop) -> p) (524288\n == Prims.pow2 19)) (fun (_:unit) -> assert_normalize (524288 == Prims.pow2 19)) (va_QLemma\n va_range1\n \"***** PRECONDITION NOT MET AT line 221 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (67108864 == Prims.pow2 26)) (fun _ -> (fun (p:prop) -> p)\n (67108864 == Prims.pow2 26)) (fun (_:unit) -> assert_normalize (67108864 == Prims.pow2 26))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 223 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 10)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 224 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 9 19) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 225 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 10) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 227 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 17)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 228 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 9 26) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 229 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 17) (let\n (va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let\n (va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 231 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg31 va_arg32 9) (let\n (va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 232 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg30 9) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 233 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state) _\n -> let (va_arg29:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in let\n (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 234 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg28 va_arg29 9) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 235 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 237 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (())))))))))))))))))))))))))))))", "val va_qcode_Check_avx512_xcr0_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_avx512_xcr0_support ()))\nlet va_qcode_Check_avx512_xcr0_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_avx512_xcr0_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 389 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 390 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Xgetbv_Avx512 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 392 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRax)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 393 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (fun (va_s:va_state) _\n -> let (va_arg33:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 395 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg33 5) (let\n (va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 396 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg32 6) (let\n (va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 397 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg31 7) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 399 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 32)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 400 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 64)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 401 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 128)) (fun (va_s:va_state) _ ->\n va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 403 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (32 == Prims.pow2 5)) (fun _ -> (fun (p:prop) -> p) (32 ==\n Prims.pow2 5)) (fun (_:unit) -> assert_normalize (32 == Prims.pow2 5)) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 404 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (64 == Prims.pow2 6)) (fun _ -> (fun (p:prop) -> p) (64 ==\n Prims.pow2 6)) (fun (_:unit) -> assert_normalize (64 == Prims.pow2 6)) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 405 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (128 == Prims.pow2 7)) (fun _ -> (fun (p:prop) -> p) (128 ==\n Prims.pow2 7)) (fun (_:unit) -> assert_normalize (128 == Prims.pow2 7)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 407 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 2)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 408 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 5 7) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 409 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 2) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 411 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 1)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 412 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 5 6) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 413 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 1) (let\n (va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let\n (va_arg29:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 415 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg29 va_arg30 5) (let\n (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 416 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg28 5) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 417 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state) _\n -> let (va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in let\n (va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 418 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg26 va_arg27 5) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 419 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QEmpty\n (())))))))))))))))))))))))))))", "val va_qcode_Msg_shift (va_mods: va_mods_t) : (va_quickCode unit (va_code_Msg_shift ()))\nlet va_qcode_Msg_shift (va_mods:va_mods_t) : (va_quickCode unit (va_code_Msg_shift ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 290 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 291 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 292 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 293 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 4) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 294 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 295 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 5) (va_op_xmm_xmm 0)) (va_QEmpty (())))))))))", "val va_qcode_Gcm_make_length_quad (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Gcm_make_length_quad ()))\nlet va_qcode_Gcm_make_length_quad (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Gcm_make_length_quad ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 227 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 3) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 228 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 3) (fun (va_s:va_state) _ -> let\n (va_arg13:Vale.Def.Types_s.nat64) = va_get_reg 6 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 229 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg13 3) (let\n (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg 7 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 230 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg12 3) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 231 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 6 va_s == va_get_reg 6 va_old_s `op_Multiply` 8) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 232 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 7 va_s == va_get_reg 7 va_old_s `op_Multiply` 8) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 233 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Mtvsrdd (va_op_vec_opr_vec 9) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 7)) (va_QEmpty\n (()))))))))))", "val va_qcode_Gcm_make_length_quad (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Gcm_make_length_quad ()))\nlet va_qcode_Gcm_make_length_quad (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Gcm_make_length_quad ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 424 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_ZeroXmm (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 425 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 426 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 427 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 428 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 429 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 430 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRax) 0) (va_QEmpty (()))))))))))", "val va_qcode_Compute_pad_to_128_bits (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Compute_pad_to_128_bits ()))\nlet va_qcode_Compute_pad_to_128_bits (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Compute_pad_to_128_bits ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 446 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 447 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR10) (va_const_cmp 8)) (qblock va_mods (fun\n (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 449 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PinsrqImm (va_op_xmm_xmm 0) 0 1 (va_op_reg_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 452 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR10)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (fun (va_s:va_state) _\n -> let (va_arg51:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 454 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg51) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 455 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rRcx va_s == 8 `op_Multiply` va_get_reg64 rR10 va_s) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 456 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 457 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rR11) (va_op_shift_amt64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 458 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 459 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pextrq (va_op_dst_opr64_reg64 rRcx) (va_op_xmm_xmm 0) 0) (fun (va_s:va_state) _ ->\n let (old_lower128:nat64) = va_get_reg64 rRcx va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 461 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR11)) (fun (va_s:va_state) _\n -> let (va_arg50:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let\n (va_arg49:Vale.Def.Types_s.nat64) = old_lower128 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 462 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg49 va_arg50) (va_qAssert\n va_range1\n \"***** PRECONDITION NOT MET AT line 463 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rRcx va_s == old_lower128 `op_Modulus` Prims.pow2 (va_get_reg64 rR10 va_s\n `op_Multiply` 8)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 466 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRcx) 0) (fun (va_s:va_state) _ ->\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 468 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_lo64_properties ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 469 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_hi64_properties ()) (let (va_arg48:Prims.int) =\n va_get_reg64 rR10 va_s in let (va_arg47:Vale.Def.Types_s.quad32) = va_get_xmm 0 va_old_s in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 470 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_helpers.pad_to_128_bits_lower va_arg47 va_arg48) (va_QEmpty\n (()))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 472 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rR10 va_s - 8 >= 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 475 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 476 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (fun (va_s:va_state) _\n -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 477 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rR10 va_s - 8 >= 0 /\\ va_get_reg64 rR10 va_s - 8 <= 18446744073709551615) (fun _\n -> let (va_arg56:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s - 8 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 477 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg56) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 478 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rRcx va_s == 8 `op_Multiply` (va_get_reg64 rR10 va_s - 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 479 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 480 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rR11) (va_op_shift_amt64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 481 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 482 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pextrq (va_op_dst_opr64_reg64 rRcx) (va_op_xmm_xmm 0) 1) (fun (va_s:va_state) _ ->\n let (old_upper128:nat64) = va_get_reg64 rRcx va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 484 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR11)) (fun (va_s:va_state) _\n -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 485 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_get_reg64 rR10 va_s - 8 >= 0 /\\ va_get_reg64 rR10 va_s - 8 <= 18446744073709551615) (fun _\n -> let (va_arg55:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s - 8 in let\n (va_arg54:Vale.Def.Types_s.nat64) = old_upper128 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 485 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg54 va_arg55) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 489 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRcx) 1) (fun (va_s:va_state) _ ->\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 490 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_lo64_properties ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 491 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_hi64_properties ()) (let (va_arg53:Prims.int) =\n va_get_reg64 rR10 va_s in let (va_arg52:Vale.Def.Types_s.quad32) = va_get_xmm 0 va_old_s in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 492 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_helpers.pad_to_128_bits_upper va_arg52 va_arg53) (va_QEmpty\n (())))))))))))))))))))))) (fun (va_s:va_state) va_g -> va_QEmpty (())))))", "val va_qcode_Compute_pad_to_128_bits (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Compute_pad_to_128_bits ()))\nlet va_qcode_Compute_pad_to_128_bits (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Compute_pad_to_128_bits ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 247 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 248 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_qIf va_mods (Cmp_lt (va_op_cmp_reg 8) (va_const_cmp 8)) (qblock va_mods (fun\n (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 250 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 8) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 251 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sub (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 8)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 252 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 10) 3) (fun (va_s:va_state) _ ->\n va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 253 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (8 - va_get_reg 8 va_s >= 0 /\\ 8 - va_get_reg 8 va_s <= 18446744073709551615) (fun _ -> let\n (va_arg57:Vale.Def.Types_s.nat64) = 8 - va_get_reg 8 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 253 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg57 3) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 254 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 10 va_s == (8 - va_get_reg 8 va_s) `op_Multiply` 8) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 255 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Mfvsrd (va_op_reg_opr_reg 7) (va_op_vec_opr_vec 9)) (fun (va_s:va_state) _ -> let\n (va_arg56:Prims.nat) = va_get_reg 10 va_s in let (va_arg55:Vale.Def.Types_s.nat64) = va_get_reg\n 7 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 256 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishr_64 va_arg55 va_arg56) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 257 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sr64 (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 10)) (fun\n (va_s:va_state) _ -> let (va_arg54:Prims.nat) = va_get_reg 10 va_s in let\n (va_arg53:Vale.Def.Types_s.nat64) = va_get_reg 7 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 258 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg53 va_arg54) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 259 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sl64 (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 10)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 262 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 263 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Mtvsrdd (va_op_vec_opr_vec 9) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 10)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 265 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_nat_to_two32 ()) (let (va_arg52:Prims.int) = va_get_reg\n 8 va_s in let (va_arg51:Vale.Def.Types_s.quad32) = va_get_vec 9 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 266 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_helpers_BE.pad_to_128_bits_upper va_arg51 va_arg52) (va_QEmpty\n (())))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 267 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_qIf va_mods (Cmp_eq (va_op_cmp_reg 8) (va_const_cmp 8)) (qblock va_mods (fun\n (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 268 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Mfvsrd (va_op_reg_opr_reg 7) (va_op_vec_opr_vec 9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 269 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 270 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Mtvsrdd (va_op_vec_opr_vec 9) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 10)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 272 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_nat_to_two32 ()) (let (va_arg58:Vale.Def.Types_s.quad32)\n = va_get_vec 9 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 273 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_helpers_BE.pad_to_128_bits_lower_8 va_arg58) (va_QEmpty\n (())))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 8 va_s - 8 > 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 277 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sub (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 8)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 279 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 10) 3) (fun (va_s:va_state) _ ->\n va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 280 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (16 - va_get_reg 8 va_s >= 0 /\\ 16 - va_get_reg 8 va_s <= 18446744073709551615) (fun _ -> let\n (va_arg65:Vale.Def.Types_s.nat64) = 16 - va_get_reg 8 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 280 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg65 3) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_get_reg 10 va_s == (16 - va_get_reg 8 va_s) `op_Multiply` 8) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 282 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Mfvsrld (va_op_reg_opr_reg 7) (va_op_vec_opr_vec 9)) (fun (va_s:va_state) _ -> let\n (va_arg64:Prims.nat) = va_get_reg 10 va_s in let (va_arg63:Vale.Def.Types_s.nat64) = va_get_reg\n 7 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 283 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishr_64 va_arg63 va_arg64) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 284 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sr64 (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 10)) (fun\n (va_s:va_state) _ -> let (va_arg62:Prims.nat) = va_get_reg 10 va_s in let\n (va_arg61:Vale.Def.Types_s.nat64) = va_get_reg 7 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg61 va_arg62) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 286 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Sl64 (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 10)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 289 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Mfvsrd (va_op_reg_opr_reg 10) (va_op_vec_opr_vec 9)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 290 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (va_quick_Mtvsrdd (va_op_vec_opr_vec 9) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 7)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 292 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_nat_to_two32 ()) (let (va_arg60:Prims.int) = va_get_reg\n 8 va_s in let (va_arg59:Vale.Def.Types_s.quad32) = va_get_vec 9 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 293 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMencrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_helpers_BE.pad_to_128_bits_lower va_arg59 va_arg60) (va_QEmpty\n (())))))))))))))))))))) (fun (va_s:va_state) va_g -> va_QEmpty (()))))) (fun (va_s:va_state)\n va_g -> va_QEmpty (())))))", "val va_qcode_Check_movbe_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_movbe_support ()))\nlet va_qcode_Check_movbe_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_movbe_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 177 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 179 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 180 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 181 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Movbe ()) (fun (va_s:va_state) _ -> let (va_arg14:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 182 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg14 22) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 183 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 184 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 4194304)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 185 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (4194304 == Prims.pow2 22)) (fun _ -> (fun (p:prop) -> p)\n (4194304 == Prims.pow2 22)) (fun (_:unit) -> assert_normalize (4194304 == Prims.pow2 22))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 187 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 21)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 188 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 1 22) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 189 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 21) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 191 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (())))))))))))))))", "val va_qcode_Check_avx512_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_avx512_stdcall win))\nlet va_qcode_Check_avx512_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_avx512_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 146 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_avx512_support ()) (va_QEmpty (()))))", "val va_qcode_Check_avx512_xcr0_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_avx512_xcr0_stdcall win))\nlet va_qcode_Check_avx512_xcr0_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_avx512_xcr0_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 188 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_avx512_xcr0_support ()) (va_QEmpty (()))))", "val va_qcode_Check_avx_xcr0_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_avx_xcr0_stdcall win))\nlet va_qcode_Check_avx_xcr0_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_avx_xcr0_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 173 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_avx_xcr0_support ()) (va_QEmpty (()))))", "val va_qcode_Handle_ctr32_2 (va_mods: va_mods_t) (ctr_BE: quad32)\n : (va_quickCode unit (va_code_Handle_ctr32_2 ()))\nlet va_qcode_Handle_ctr32_2 (va_mods:va_mods_t) (ctr_BE:quad32) : (va_quickCode unit\n (va_code_Handle_ctr32_2 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 253 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 6) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 258 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_Load_one_lsb (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 260 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 10) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 262 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_Load_two_lsb (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 263 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 11) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 265 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 12) (va_op_xmm_xmm 10) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 266 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 267 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 13) (va_op_xmm_xmm 11) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 268 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 269 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_opr128_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 270 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 14) (va_op_xmm_xmm 12) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 271 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 12) (va_op_xmm_xmm 12) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 272 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_opr128_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 273 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 13) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 274 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 13) (va_op_xmm_xmm 13) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 12) (va_op_xmm_xmm 12) (va_op_opr128_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 276 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 14) (va_op_xmm_xmm 14) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 277 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 13) (va_op_xmm_xmm 13) (va_op_opr128_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 279 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESGCM.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 14) (va_op_xmm_xmm 14) (va_op_opr128_xmm 4)) (va_QEmpty\n (())))))))))))))))))))))))", "val va_qcode_Check_avx_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_avx_stdcall win))\nlet va_qcode_Check_avx_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_avx_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 81 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_avx_support ()) (va_QEmpty (()))))", "val va_qcode_Handle_ctr32 (va_mods: va_mods_t) (ctr_BE: quad32)\n : (va_quickCode unit (va_code_Handle_ctr32 ()))\nlet va_qcode_Handle_ctr32 (va_mods:va_mods_t) (ctr_BE:quad32) : (va_quickCode unit\n (va_code_Handle_ctr32 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 256 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_InitPshufbMask (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 257 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 6) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 261 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_Load_one_lsb (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 262 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 10) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 263 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_Load_two_lsb (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 264 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 11) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 265 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 12) (va_op_xmm_xmm 10) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 266 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 267 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 13) (va_op_xmm_xmm 11) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 268 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 269 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 10) (va_op_opr128_xmm 15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 270 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 14) (va_op_xmm_xmm 12) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 271 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 12) (va_op_xmm_xmm 12) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 272 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPxor (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_opr128_xmm 15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 273 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPaddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 13) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 274 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 13) (va_op_xmm_xmm 13) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 14) (va_op_xmm_xmm 14) (va_op_xmm_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 276 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt.vaf *****\"\n (va_quick_VPshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_QEmpty\n (())))))))))))))))))))))", "val va_qcode_Check_aesni_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_aesni_support ()))\nlet va_qcode_Check_aesni_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_aesni_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 42 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 44 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 45 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 46 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_AES ()) (fun (va_s:va_state) _ -> let (va_arg22:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 47 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg22 25) (let\n (va_arg21:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 48 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg21 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 49 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 50 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 33554432)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 51 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (33554432 == Prims.pow2 25)) (fun _ -> (fun (p:prop) -> p)\n (33554432 == Prims.pow2 25)) (fun (_:unit) -> assert_normalize (33554432 == Prims.pow2 25))\n (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 52 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (2 == Prims.pow2 1)) (fun _ -> (fun (p:prop) -> p) (2 ==\n Prims.pow2 1)) (fun (_:unit) -> assert_normalize (2 == Prims.pow2 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 54 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 24)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 55 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 1 25) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 56 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 24) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 58 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 2)) (fun (va_s:va_state) _ -> let\n (va_arg20:Vale.Def.Types_s.nat64) = va_get_reg64 rRcx va_s in let\n (va_arg19:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 59 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg19 va_arg20 1) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 60 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 66 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (()))))))))))))))))))))", "val va_qcode_Compute_Y0 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Compute_Y0 ()))\nlet va_qcode_Compute_Y0 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Compute_Y0 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 83 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 1)) (fun (va_s:va_state) _ -> va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 84 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_quad32_xor ()) (va_QEmpty (())))))", "val va_qcode_Check_sse_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_sse_stdcall win))\nlet va_qcode_Check_sse_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_sse_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 120 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_sse_support ()) (va_QEmpty (()))))", "val va_qcode_Init_ctr (va_mods: va_mods_t) : (va_quickCode unit (va_code_Init_ctr ()))\nlet va_qcode_Init_ctr (va_mods:va_mods_t) : (va_quickCode unit (va_code_Init_ctr ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 71 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 4) (va_op_xmm_xmm 4)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 72 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (va_quick_PinsrdImm (va_op_xmm_xmm 4) 1 0 (va_op_reg_opr64_reg64 rR12)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 74 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCTR.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_quad32_xor ()) (va_QEmpty (()))))))", "val va_qcode_Check_movbe_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_movbe_stdcall win))\nlet va_qcode_Check_movbe_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_movbe_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 107 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_movbe_support ()) (va_QEmpty (()))))", "val va_qcode_Compute_ghash_incremental_register (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Compute_ghash_incremental_register ()))\nlet va_qcode_Compute_ghash_incremental_register (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Compute_ghash_incremental_register ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 124 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 125 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 11)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 127 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_ReduceMul128_LE (Vale.AES.GF128_s.gf128_of_quad32\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 1 va_s))) (Vale.AES.GF128_s.gf128_of_quad32\n (va_get_xmm 11 va_s))) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 128 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash.ghash_incremental_reveal ()) (va_QEmpty (())))))))", "val va_qcode_Carry_sub_pass (va_mods: va_mods_t) : (va_quickCode unit (va_code_Carry_sub_pass ()))\nlet va_qcode_Carry_sub_pass (va_mods:va_mods_t) : (va_quickCode unit (va_code_Carry_sub_pass ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 634 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_LargeComment\n \"Wrap the result back into the field\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 636 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Comment\n \"Step 1: Compute carry*38\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 637 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 638 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Carry_times_38 (va_op_dst_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 640 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 641 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Comment\n \"Step 2: Substract carry*38 from the original difference\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 642 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 643 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Sbb64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 644 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Sbb64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 645 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Sbb64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 647 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Newline ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 648 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Comment\n \"Step 3: Fold the carry bit back in; guaranteed not to carry at this point\"\n ) (fun (va_s:va_state) _ -> let (old_carry:Vale.Curve25519.Fast_defs.bit) =\n Vale.Curve25519.Fast_defs.bool_bit (Vale.X64.Decls.cf (va_get_flags va_old_s)) in va_qAssert\n va_range1\n \"***** PRECONDITION NOT MET AT line 650 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (Vale.Curve25519.Fast_defs.pow2_four (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s)\n (va_get_reg64 rR10 va_s) (va_get_reg64 rR11 va_s) - va_mul_nat\n (Vale.Curve25519.Fast_defs.bool_bit (Vale.X64.Decls.cf (va_get_flags va_s))) pow2_256 ==\n Vale.Curve25519.Fast_defs.pow2_four (va_get_reg64 rR8 va_old_s) (va_get_reg64 rR9 va_old_s)\n (va_get_reg64 rR10 va_old_s) (va_get_reg64 rR11 va_old_s) - old_carry `op_Multiply` 38) (let\n (sum:int) = Vale.Curve25519.Fast_defs.pow2_four (va_get_reg64 rR8 va_old_s) (va_get_reg64 rR9\n va_old_s) (va_get_reg64 rR10 va_old_s) (va_get_reg64 rR11 va_old_s) - old_carry `op_Multiply`\n 38 in let (new_carry:Vale.Curve25519.Fast_defs.bit) = Vale.Curve25519.Fast_defs.bool_bit\n (Vale.X64.Decls.cf (va_get_flags va_s)) in va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 653 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (new_carry == Vale.Curve25519.Fast_defs.bool_bit (sum < 0)) (let\n (va_arg37:Vale.Def.Types_s.nat64) = old_carry in let (va_arg36:Vale.Def.Types_s.nat64) =\n va_get_reg64 rR11 va_s in let (va_arg35:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let\n (va_arg34:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let\n (va_arg33:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let\n (va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_old_s in let\n (va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_old_s in let\n (va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_old_s in let\n (va_arg29:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 654 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.FastHybrid_helpers.lemma_carry_sub_prime va_arg29 va_arg30\n va_arg31 va_arg32 va_arg33 va_arg34 va_arg35 va_arg36 va_arg37 new_carry) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 657 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 658 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Cmovc64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 659 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QEmpty\n (())))))))))))))))))))))", "val va_qcode_Gf128MulRev128 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Gf128MulRev128 ()))\nlet va_qcode_Gf128MulRev128 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Gf128MulRev128 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_s) in let\n (b:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 2 va_s) in va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 372 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_ReduceMulRev128 (Vale.Math.Poly2_s.reverse a 127) (Vale.Math.Poly2_s.reverse b 127))\n (fun (va_s:va_state) _ -> let (va_arg6:Vale.Math.Poly2_s.poly) = Vale.AES.GF128.gf128_mul_rev a\n b in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 373 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32 va_arg6) (va_QEmpty (())))))", "val va_qcode_Gf128MulRev128 (va_mods: va_mods_t) : (va_quickCode unit (va_code_Gf128MulRev128 ()))\nlet va_qcode_Gf128MulRev128 (va_mods:va_mods_t) : (va_quickCode unit (va_code_Gf128MulRev128 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 1 va_s) in let\n (b:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 2 va_s) in va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 367 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_ReduceMulRev128 (Vale.Math.Poly2_s.reverse a 127) (Vale.Math.Poly2_s.reverse b 127))\n (fun (va_s:va_state) _ -> let (va_arg6:Vale.Math.Poly2_s.poly) = Vale.AES.GF128.gf128_mul_rev a\n b in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 368 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32 va_arg6) (va_QEmpty (())))))", "val va_quick_XmmEqual (x1 x2: va_operand_xmm) : (va_quickCode unit (va_code_XmmEqual x1 x2))\nlet va_quick_XmmEqual (x1:va_operand_xmm) (x2:va_operand_xmm) : (va_quickCode unit\n (va_code_XmmEqual x1 x2)) =\n (va_QProc (va_code_XmmEqual x1 x2) ([va_Mod_flags; va_Mod_reg64 rRax; va_Mod_reg64 rRdx;\n va_mod_xmm x1]) (va_wp_XmmEqual x1 x2) (va_wpProof_XmmEqual x1 x2))", "val va_qcode_Poly1305_reduce (va_mods: va_mods_t)\n : (va_quickCode (int) (va_code_Poly1305_reduce ()))\nlet va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range\n 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range\n 1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =\n va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0\n 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)\n (va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->\n let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64\n rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +\n va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let\n (va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let\n (va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let\n (va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24\n va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))", "val va_qcode_Reduce (va_mods: va_mods_t) (f: poly) : (va_quickCode unit (va_code_Reduce ()))\nlet va_qcode_Reduce (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_Reduce ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (g:Vale.Math.Poly2_s.poly) = add (Vale.Math.Poly2_s.monomial 128) f in let\n (c:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift f (-1)) 63 in\n let (a0:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 2 va_s) in let\n (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let\n (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in let\n (a:Vale.Math.Poly2_s.poly) = add (add a0 (Vale.Math.Poly2_s.shift a1 64))\n (Vale.Math.Poly2_s.shift a2 128) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 265 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 0) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 266 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_mask_is_mod a1 64) (let\n (va_arg39:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.mask a1 64 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 267 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_is_mul va_arg39 64) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 268 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_Low64ToHigh (va_op_vec_opr_vec 9) (va_op_vec_opr_vec 3) a1) (fun (va_s:va_state) _ ->\n let (va_arg38:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift (Vale.Math.Poly2.mask a1 64) 64\n in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 269 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32 va_arg38) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 270 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_VPolyAdd (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 9)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 271 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_VSwap (va_op_vec_opr_vec 10) (va_op_vec_opr_vec 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 272 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_VPolyMulLow (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 8)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 273 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_shift_is_div a1 64) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 274 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_High64ToLow (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) a1) (fun (va_s:va_state) _ ->\n let (va_arg37:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift a1 (-64) in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32 va_arg37) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 276 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_VPolyAdd (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 3)) (fun\n (va_s:va_state) _ -> let (va_arg36:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32\n (va_get_vec 10 va_s) in let (va_arg35:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 2 va_s) in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 277 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.lemma_add_commute va_arg35 va_arg36) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_VPolyAdd (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 10)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 279 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_VSwap (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 280 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_VPolyMulLow (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 8))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 281 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 4)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 282 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2)) (fun\n (va_s:va_state) _ -> let (va_arg34:Vale.Math.Poly2_s.poly) = f in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 283 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GHash.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_reduce_rev a0 a1 a2 va_arg34 64) (va_QEmpty\n (()))))))))))))))))))))))", "val va_quick_Nat64Equal (dst src: va_operand_reg_opr64)\n : (va_quickCode unit (va_code_Nat64Equal dst src))\nlet va_quick_Nat64Equal (dst:va_operand_reg_opr64) (src:va_operand_reg_opr64) : (va_quickCode unit\n (va_code_Nat64Equal dst src)) =\n (va_QProc (va_code_Nat64Equal dst src) ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64\n dst]) (va_wp_Nat64Equal dst src) (va_wpProof_Nat64Equal dst src))", "val va_qcode_Check_sha_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_sha_support ()))\nlet va_qcode_Check_sha_support (va_mods:va_mods_t) : (va_quickCode unit (va_code_Check_sha_support\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 77 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 79 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 80 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 81 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Sha ()) (fun (va_s:va_state) _ -> let (va_arg11:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 82 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg11 29) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 83 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 536870912)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 84 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (536870912 == Prims.pow2 29)) (fun _ -> (fun (p:prop) -> p)\n (536870912 == Prims.pow2 29)) (fun (_:unit) -> assert_normalize (536870912 == Prims.pow2 29))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 85 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 87 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty (()))))))))))))", "val va_qcode_Check_aesni_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_aesni_stdcall win))\nlet va_qcode_Check_aesni_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_aesni_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 41 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_aesni_support ()) (va_QEmpty (()))))", "val va_qcode_Poly1305_reduce_last (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Poly1305_reduce_last ()))\nlet va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Poly1305_reduce_last ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =\n Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)\n (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->\n va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8\n va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let\n (va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let\n (va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let\n (va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5\n in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let\n (va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let\n (va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29\n va_arg30 va_arg31 va_arg32) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (())))))))))))))))))))))))", "val va_qcode_Store_3blocks128_2 (va_mods: va_mods_t) (out_b: buffer128)\n : (va_quickCode unit (va_code_Store_3blocks128_2 ()))\nlet va_qcode_Store_3blocks128_2 (va_mods:va_mods_t) (out_b:buffer128) : (va_quickCode unit\n (va_code_Store_3blocks128_2 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 313 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 3)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 29) Secret out_b (va_get_reg 8 va_s + 3)) (fun\n (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 314 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 4)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 30) Secret out_b (va_get_reg 8 va_s + 4)) (fun\n (va_s:va_state) _ -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 315 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 5)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 31) Secret out_b (va_get_reg 8 va_s + 5)) (va_QEmpty\n (()))))))", "val va_qcode_Check_rdrand_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_rdrand_support ()))\nlet va_qcode_Check_rdrand_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_rdrand_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 248 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 250 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 251 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 252 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Rdrand ()) (fun (va_s:va_state) _ -> let (va_arg14:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 253 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg14 30) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 254 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 255 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1073741824)) (fun (va_s:va_state)\n _ -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 256 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (1073741824 == Prims.pow2 30)) (fun _ -> (fun (p:prop) -> p)\n (1073741824 == Prims.pow2 30)) (fun (_:unit) -> assert_normalize (1073741824 == Prims.pow2 30))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 258 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 29)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 259 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 1 30) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 260 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 29) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 262 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (())))))))))))))))", "val va_qcode_Store_3blocks128_1 (va_mods: va_mods_t) (out_b: buffer128)\n : (va_quickCode unit (va_code_Store_3blocks128_1 ()))\nlet va_qcode_Store_3blocks128_1 (va_mods:va_mods_t) (out_b:buffer128) : (va_quickCode unit\n (va_code_Store_3blocks128_1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 287 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0)\n (va_op_reg_opr_reg 7) Secret out_b (va_get_reg 8 va_s)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 288 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 27) Secret out_b (va_get_reg 8 va_s + 1)) (fun\n (va_s:va_state) _ -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 289 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCTR.vaf *****\"\n (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 2)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 28) Secret out_b (va_get_reg 8 va_s + 2)) (va_QEmpty\n (()))))))", "val va_qcode_Save_registers (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Save_registers win))\nlet va_qcode_Save_registers (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Save_registers win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1447 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1448 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1449 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1450 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1451 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rRsi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1452 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rRdi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1453 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rRbp)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1454 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Push_Secret (va_op_reg_opr64_reg64 rRbx)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 1456 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1457 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 15) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1458 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 14) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1459 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 13) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1460 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 12) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1461 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 11) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1462 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 10) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1463 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 9) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1464 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 8) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1465 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 7) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1466 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PushXmm_Secret (va_op_xmm_xmm 6) (va_op_reg_opr64_reg64 rRax)) (va_QEmpty\n (()))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state)\n va_g -> va_QEmpty (()))))))))))))", "val va_qcode_InnerMemcpy (va_mods: va_mods_t) (dst src: buffer64)\n : (va_quickCode unit (va_code_InnerMemcpy ()))\nlet va_qcode_InnerMemcpy (va_mods:va_mods_t) (dst:buffer64) (src:buffer64) : (va_quickCode unit\n (va_code_InnerMemcpy ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 38 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rRax)\n (va_op_reg_opr64_reg64 rRdx) 0 Secret src 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 39 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)\n (va_op_reg_opr64_reg64 rRdx) 8 Secret src 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 40 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx)\n (va_op_reg_opr64_reg64 rRax) 0 Secret dst 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 41 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx)\n (va_op_reg_opr64_reg64 rR9) 8 Secret dst 1) (fun (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 42 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (FStar.Seq.Base.equal #(Vale.X64.Memory.base_typ_as_vale_type Vale.X64.Memory.vuint64)\n (Vale.X64.Memory.buffer_as_seq #Vale.X64.Memory.vuint64 (va_get_mem_heaplet 1 va_s) dst)\n (Vale.X64.Memory.buffer_as_seq #Vale.X64.Memory.vuint64 (va_get_mem_heaplet 0 va_s) src))\n (va_QEmpty (()))))))))", "val va_qcode_Loop (va_mods: va_mods_t) (in_b k_b: buffer128) : (va_quickCode unit (va_code_Loop ()))\nlet va_qcode_Loop (va_mods:va_mods_t) (in_b:buffer128) (k_b:buffer128) : (va_quickCode unit\n (va_code_Loop ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hash_orig:hash256)\n = Vale.SHA.PPC64LE.SHA_helpers.make_seperated_hash_quad32 (va_get_vec 16 va_s) (va_get_vec 17\n va_s) (va_get_vec 18 va_s) (va_get_vec 19 va_s) (va_get_vec 20 va_s) (va_get_vec 21 va_s)\n (va_get_vec 22 va_s) (va_get_vec 23 va_s) in let (count:nat) = 0 in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Loop.vaf *****\"\n (va_quick_Loop_while0 va_old_s hash_orig in_b k_b count) (fun (va_s:va_state) count ->\n va_QEmpty (()))))", "val va_qcode_Loop (va_mods: va_mods_t) (in_b k_b: buffer128) : (va_quickCode unit (va_code_Loop ()))\nlet va_qcode_Loop (va_mods:va_mods_t) (in_b:buffer128) (k_b:buffer128) : (va_quickCode unit\n (va_code_Loop ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hash_orig:hash256)\n = Vale.SHA.SHA_helpers.make_hash (va_get_xmm 1 va_s) (va_get_xmm 2 va_s) in let (count:nat) = 0\n in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 556 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Loop_while0 va_old_s hash_orig in_b k_b count) (fun (va_s:va_state) count ->\n va_QEmpty (()))))", "val va_quick_Vcmpequw (dst src1 src2: va_operand_vec_opr)\n : (va_quickCode unit (va_code_Vcmpequw dst src1 src2))\nlet va_quick_Vcmpequw (dst:va_operand_vec_opr) (src1:va_operand_vec_opr) (src2:va_operand_vec_opr)\n : (va_quickCode unit (va_code_Vcmpequw dst src1 src2)) =\n (va_QProc (va_code_Vcmpequw dst src1 src2) ([va_mod_vec_opr dst]) (va_wp_Vcmpequw dst src1 src2)\n (va_wpProof_Vcmpequw dst src1 src2))", "val va_qcode_Callee_save_registers (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Callee_save_registers win))\nlet va_qcode_Callee_save_registers (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Callee_save_registers win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 73 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 74 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 15) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 75 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 14) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 76 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 13) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 77 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 12) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 78 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 11) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 79 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 10) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 80 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 9) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 81 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 8) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 82 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 7) (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 83 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_PushXmm (va_op_xmm_xmm 6) (va_op_reg_opr64_reg64 rRax)) (va_QEmpty (())))))))))))))\n (qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 85 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 86 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 87 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 88 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 89 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRsi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 90 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRdi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 91 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRbp)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 92 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.X64.Stack.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRbx)) (va_QEmpty (()))))))))))))", "val va_qcode_Check_adx_bmi2_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_adx_bmi2_support ()))\nlet va_qcode_Check_adx_bmi2_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_adx_bmi2_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 98 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 100 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 101 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 102 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Adx_Bmi2 ()) (fun (va_s:va_state) _ -> let (va_arg22:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 103 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg22 8) (let\n (va_arg21:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 104 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg21 19) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 105 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 524288)) (fun (va_s:va_state) _ ->\n va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 109 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (256 == Prims.pow2 8)) (fun _ -> (fun (p:prop) -> p) (256 ==\n Prims.pow2 8)) (fun (_:unit) -> assert_normalize (256 == Prims.pow2 8)) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 110 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (524288 == Prims.pow2 19)) (fun _ -> (fun (p:prop) -> p) (524288\n == Prims.pow2 19)) (fun (_:unit) -> assert_normalize (524288 == Prims.pow2 19)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 112 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 11)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 113 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 8 19) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 114 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 11) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 116 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 256)) (fun (va_s:va_state) _ ->\n let (va_arg20:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let\n (va_arg19:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 117 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_maybe_pow2_64 va_arg19 va_arg20 8) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 118 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (()))))))))))))))))))))", "val va_qcode_Poly1305_add_key_s (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Poly1305_add_key_s ()))\nlet va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Poly1305_add_key_s ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)\n (va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =\n Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)\n _ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let\n (va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s\n in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let\n (va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in\n in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let\n (va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15\n va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))", "val va_qcode_Store4 (va_mods: va_mods_t) (dst_b: buffer64) : (va_quickCode unit (va_code_Store4 ()))\nlet va_qcode_Store4 (va_mods:va_mods_t) (dst_b:buffer64) : (va_quickCode unit (va_code_Store4 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 367 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 368 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Comment\n \"Store the result\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 369 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR8) 0 Secret dst_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 370 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR9) 8 Secret dst_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 371 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR10) 16 Secret dst_b 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 372 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR11) 24 Secret dst_b 3) (va_QEmpty (())))))))))", "val va_qcode_Test\n (va_mods: va_mods_t)\n (win: bool)\n (arg0 arg1 arg2 arg3 arg4 arg5 arg6 arg7: buffer64)\n : (va_quickCode unit (va_code_Test win))\nlet va_qcode_Test (va_mods:va_mods_t) (win:bool) (arg0:buffer64) (arg1:buffer64) (arg2:buffer64)\n (arg3:buffer64) (arg4:buffer64) (arg5:buffer64) (arg6:buffer64) (arg7:buffer64) : (va_quickCode\n unit (va_code_Test win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 79 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Args.vaf *****\"\n (va_quick_CreateHeaplets ([declare_buffer64 arg0 0 Secret Immutable; declare_buffer64 arg1 0\n Secret Immutable; declare_buffer64 arg2 0 Secret Immutable; declare_buffer64 arg3 0 Secret\n Immutable; declare_buffer64 arg4 0 Secret Immutable; declare_buffer64 arg5 0 Secret Immutable;\n declare_buffer64 arg6 0 Secret Immutable; declare_buffer64 arg7 0 Secret Immutable])) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 89 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Args.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 91 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Args.vaf *****\"\n (va_quick_DestroyHeaplets ()) (va_QEmpty (()))))))", "val va_qcode_Cswap2 (va_mods: va_mods_t) (bit_in: nat64) (p0_b p1_b: buffer64)\n : (va_quickCode unit (va_code_Cswap2 ()))\nlet va_qcode_Cswap2 (va_mods:va_mods_t) (bit_in:nat64) (p0_b:buffer64) (p1_b:buffer64) :\n (va_quickCode unit (va_code_Cswap2 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (old_p0_0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read p0_b 0 (va_get_mem va_s) in\n let (old_p0_1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read p0_b 1 (va_get_mem va_s)\n in let (old_p0_2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read p0_b 2 (va_get_mem\n va_s) in let (old_p0_3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read p0_b 3\n (va_get_mem va_s) in let (old_p0_4:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read p0_b\n 4 (va_get_mem va_s) in let (old_p0_5:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read\n p0_b 5 (va_get_mem va_s) in let (old_p0_6:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read p0_b 6 (va_get_mem va_s) in let (old_p0_7:Vale.Def.Types_s.nat64)\n = Vale.X64.Decls.buffer64_read p0_b 7 (va_get_mem va_s) in let\n (old_p1_0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read p1_b 0 (va_get_mem va_s) in\n let (old_p1_1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read p1_b 1 (va_get_mem va_s)\n in let (old_p1_2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read p1_b 2 (va_get_mem\n va_s) in let (old_p1_3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read p1_b 3\n (va_get_mem va_s) in let (old_p1_4:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read p1_b\n 4 (va_get_mem va_s) in let (old_p1_5:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read\n p1_b 5 (va_get_mem va_s) in let (old_p1_6:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read p1_b 6 (va_get_mem va_s) in let (old_p1_7:Vale.Def.Types_s.nat64)\n = Vale.X64.Decls.buffer64_read p1_b 7 (va_get_mem va_s) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 932 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_CreateHeaplets ([declare_buffer64 p0_b 0 Secret Mutable; declare_buffer64 p1_b 0\n Secret Mutable])) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 936 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Comment\n \"Transfer bit into CF flag\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 937 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRdi) (va_const_opr64 18446744073709551615))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 939 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 940 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Comment\n \"cswap p1[0], p2[0]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 941 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Cswap_single 0 p0_b p1_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 943 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 944 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Comment\n \"cswap p1[1], p2[1]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 945 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Cswap_single 1 p0_b p1_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 947 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 948 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Comment\n \"cswap p1[2], p2[2]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 949 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Cswap_single 2 p0_b p1_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 951 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 952 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Comment\n \"cswap p1[3], p2[3]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 953 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Cswap_single 3 p0_b p1_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 955 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 956 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Comment\n \"cswap p1[4], p2[4]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 957 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Cswap_single 4 p0_b p1_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 959 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 960 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Comment\n \"cswap p1[5], p2[5]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 961 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Cswap_single 5 p0_b p1_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 963 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 964 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Comment\n \"cswap p1[6], p2[6]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 965 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Cswap_single 6 p0_b p1_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 967 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 968 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Comment\n \"cswap p1[7], p2[7]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 969 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Cswap_single 7 p0_b p1_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 971 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_DestroyHeaplets ()) (va_QEmpty (())))))))))))))))))))))))))))))))", "val va_qcode_Fast_sub1 (va_mods: va_mods_t) (dst_b inA_b: buffer64)\n : (va_quickCode unit (va_code_Fast_sub1 ()))\nlet va_qcode_Fast_sub1 (va_mods:va_mods_t) (dst_b:buffer64) (inA_b:buffer64) : (va_quickCode unit\n (va_code_Fast_sub1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 0 (va_get_mem_heaplet 0 va_s)\n in let (a1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 1 (va_get_mem_heaplet 0\n va_s) in let (a2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 2\n (va_get_mem_heaplet 0 va_s) in let (a3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read\n inA_b 3 (va_get_mem_heaplet 0 va_s) in let (a:Prims.nat) = Vale.Curve25519.Fast_defs.pow2_four\n a0 a1 a2 a3 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 378 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.xor_lemmas ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 379 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Xor64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 381 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8)\n (va_op_reg_opr64_reg64 rRsi) 0 Secret inA_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 382 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 383 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR8) 0 Secret dst_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 385 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)\n (va_op_reg_opr64_reg64 rRsi) 8 Secret inA_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 386 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Sbb64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 387 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR9) 8 Secret dst_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 389 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR10)\n (va_op_reg_opr64_reg64 rRsi) 16 Secret inA_b 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 390 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Sbb64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 391 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR10) 16 Secret dst_b 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 393 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR11)\n (va_op_reg_opr64_reg64 rRsi) 24 Secret inA_b 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 394 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Sbb64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 395 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR11) 24 Secret dst_b 3) (fun (va_s:va_state) _ -> let (c:bool) =\n Vale.X64.Decls.cf (va_get_flags va_s) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 398 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRax)) (fun (va_s:va_state)\n _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 399 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_get_reg64 rRax va_s == Vale.Curve25519.Fast_defs.bool_bit c) (va_QEmpty\n (())))))))))))))))))))", "val va_quick_mod_6: Prims.unit -> (va_quickCode unit (va_code_mod_6 ()))\nlet va_quick_mod_6 () : (va_quickCode unit (va_code_mod_6 ())) =\n (va_QProc (va_code_mod_6 ()) ([va_Mod_reg 10; va_Mod_reg 26]) va_wp_mod_6 va_wpProof_mod_6)", "val va_qcode_Preamble (va_mods: va_mods_t) (ctx_b: buffer128)\n : (va_quickCode unit (va_code_Preamble ()))\nlet va_qcode_Preamble (va_mods:va_mods_t) (ctx_b:buffer128) : (va_quickCode unit (va_code_Preamble\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abcd:Vale.X64.Decls.quad32) = Vale.X64.Decls.buffer128_read ctx_b 0 (va_get_mem_heaplet 0\n va_s) in let (efgh:Vale.X64.Decls.quad32) = Vale.X64.Decls.buffer128_read ctx_b 1\n (va_get_mem_heaplet 0 va_s) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 87 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64\n rRdi) 0 Secret ctx_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 88 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 2) (va_op_reg_opr64_reg64\n rRdi) 16 Secret ctx_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 89 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_InitPshufbStableMask (va_op_xmm_xmm 7) (va_op_reg_opr64_reg64 rRax)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 91 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 1) 27) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 92 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) 177) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 93 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 2) (va_op_xmm_xmm 2) 27) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 95 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 8) (va_op_xmm_xmm 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 96 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Palignr8 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 98 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Shufpd (va_op_xmm_xmm 2) (va_op_xmm_xmm 0) 0) (fun (va_s:va_state) _ -> va_qAssert\n va_range1\n \"***** PRECONDITION NOT MET AT line 99 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (FStar.Seq.Base.equal #Vale.SHA.SHA_helpers.word (Vale.SHA.SHA_helpers.make_hash (va_get_xmm 1\n va_s) (va_get_xmm 2 va_s)) (Vale.SHA.SHA_helpers.make_ordered_hash abcd efgh)) (va_QEmpty\n (())))))))))))))", "val va_qcode_Preamble (va_mods: va_mods_t) (ctx_b: buffer128)\n : (va_quickCode unit (va_code_Preamble ()))\nlet va_qcode_Preamble (va_mods:va_mods_t) (ctx_b:buffer128) : (va_quickCode unit (va_code_Preamble\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (dcba:Vale.PPC64LE.Machine_s.quad32) = Vale.PPC64LE.Decls.buffer128_read ctx_b 0\n (va_get_mem_heaplet 0 va_s) in let (hgfe:Vale.PPC64LE.Machine_s.quad32) =\n Vale.PPC64LE.Decls.buffer128_read ctx_b 1 (va_get_mem_heaplet 0 va_s) in let\n (a:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__lo0 dcba in let\n (b:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__lo1 dcba in let\n (c:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__hi2 dcba in let\n (d:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__hi3 dcba in let\n (e:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__lo0 hgfe in let\n (f:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__lo1 hgfe in let\n (g:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__hi2 hgfe in let\n (h:Vale.Def.Types_s.nat32) = Vale.Def.Words_s.__proj__Mkfour__item__hi3 hgfe in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 91 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 92 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Load128_word4_buffer (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 16)\n (va_op_reg_opr_reg 3) Secret ctx_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 93 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Load128_word4_buffer_index (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 20)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret ctx_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 95 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 17) (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 16) 4)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 96 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 18) (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 16) 8)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 97 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 19) (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 16) 12)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 98 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 21) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) 4)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 99 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 22) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) 8)\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 100 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 23) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) 12) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 102 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (FStar.Seq.Base.equal #Vale.SHA.PPC64LE.SHA_helpers.word\n (Vale.SHA.PPC64LE.SHA_helpers.make_seperated_hash a b c d e f g h)\n (Vale.SHA.PPC64LE.SHA_helpers.make_ordered_hash dcba hgfe)) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 103 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.vaf *****\"\n (FStar.Seq.Base.equal #Vale.SHA.PPC64LE.SHA_helpers.word\n (Vale.SHA.PPC64LE.SHA_helpers.make_seperated_hash a b c d e f g h)\n (Vale.SHA.PPC64LE.SHA_helpers.make_seperated_hash_quad32 (va_get_vec 16 va_s) (va_get_vec 17\n va_s) (va_get_vec 18 va_s) (va_get_vec 19 va_s) (va_get_vec 20 va_s) (va_get_vec 21 va_s)\n (va_get_vec 22 va_s) (va_get_vec 23 va_s))) (va_QEmpty (()))))))))))))))", "val va_qcode_Check_adx_bmi2_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_adx_bmi2_stdcall win))\nlet va_qcode_Check_adx_bmi2_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_adx_bmi2_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 68 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_adx_bmi2_support ()) (va_QEmpty (()))))", "val va_qcode_ShiftLeft128_1 (va_mods: va_mods_t) (a: poly)\n : (va_quickCode unit (va_code_ShiftLeft128_1 ()))\nlet va_qcode_ShiftLeft128_1 (va_mods:va_mods_t) (a:poly) : (va_quickCode unit\n (va_code_ShiftLeft128_1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 60 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Vspltisb (va_op_vec_opr_vec 2) 1) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 61 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Vsl (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2)) (fun\n (va_s:va_state) _ -> let (va_arg5:Vale.Math.Poly2_s.poly) = a in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 63 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_shift_left_1 va_arg5) (va_QEmpty (()))))))", "val va_qcode_ShiftLeft128_1 (va_mods: va_mods_t) (a: poly)\n : (va_quickCode unit (va_code_ShiftLeft128_1 ()))\nlet va_qcode_ShiftLeft128_1 (va_mods:va_mods_t) (a:poly) : (va_quickCode unit\n (va_code_ShiftLeft128_1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 59 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 60 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Psrld (va_op_xmm_xmm 2) 31) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 61 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pslld (va_op_xmm_xmm 1) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 62 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_VPslldq4 (va_op_xmm_xmm 2) (va_op_xmm_xmm 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 63 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (fun (va_s:va_state) _ -> let\n (va_arg8:Vale.Math.Poly2_s.poly) = a in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 65 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_shift_left_1 va_arg8) (va_QEmpty (())))))))))", "val va_quick_Vmr (dst src: va_operand_vec_opr) : (va_quickCode unit (va_code_Vmr dst src))\nlet va_quick_Vmr (dst:va_operand_vec_opr) (src:va_operand_vec_opr) : (va_quickCode unit\n (va_code_Vmr dst src)) =\n (va_QProc (va_code_Vmr dst src) ([va_mod_vec_opr dst]) (va_wp_Vmr dst src) (va_wpProof_Vmr dst\n src))", "val va_qcode_ReduceMul128_LE (va_mods: va_mods_t) (a b: poly)\n : (va_quickCode unit (va_code_ReduceMul128_LE ()))\nlet va_qcode_ReduceMul128_LE (va_mods:va_mods_t) (a:poly) (b:poly) : (va_quickCode unit\n (va_code_ReduceMul128_LE ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 104 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 105 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_ReduceMulRev128 a b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 106 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GHash.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 8)) (va_QEmpty (()))))))", "val va_qcode_Check_sha_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_sha_stdcall win))\nlet va_qcode_Check_sha_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_sha_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 55 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_sha_support ()) (va_QEmpty (()))))", "val va_qcode_ShiftLeft2_128_1 (va_mods: va_mods_t) (lo hi: poly)\n : (va_quickCode unit (va_code_ShiftLeft2_128_1 ()))\nlet va_qcode_ShiftLeft2_128_1 (va_mods:va_mods_t) (lo:poly) (hi:poly) : (va_quickCode unit\n (va_code_ShiftLeft2_128_1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 83 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Vspltisw (va_op_vec_opr_vec 0) 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 84 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 31) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 85 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Mtvsrws (va_op_vec_opr_vec 3) (va_op_reg_opr_reg 10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 86 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Vsrw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Vsldoi (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 3) 4) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 88 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Vspltisb (va_op_vec_opr_vec 0) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 89 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Vsl (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 0)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 90 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Vsl (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 0)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 91 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (va_quick_Vxor (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 3)) (fun\n (va_s:va_state) _ -> let (l:(Vale.Def.Words_s.four Vale.Def.Words_s.nat32)) =\n Vale.Def.Words.Four_s.four_map #nat32 #Vale.Def.Words_s.nat32 (fun (i:nat32) ->\n Vale.Arch.Types.ishl32 i 1) (va_get_vec 2 va_old_s) in let (r:(Vale.Def.Words_s.four\n Vale.Def.Words_s.nat32)) = Vale.Def.Words.Four_s.four_map #nat32 #Vale.Def.Words_s.nat32 (fun\n (i:nat32) -> Vale.Arch.Types.ishr32 i 31) (va_get_vec 2 va_old_s) in let\n (va_arg22:Vale.Def.Types_s.quad32) = va_get_vec 3 va_s in let\n (va_arg21:Vale.Def.Types_s.quad32) = Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 r) (Vale.Def.Words_s.__proj__Mkfour__item__lo1 r)\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 r) in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 95 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_quad32_xor_commutes va_arg21 va_arg22) (let\n (va_arg20:Vale.Def.Types_s.quad32) = va_get_vec 3 va_s in let\n (va_arg19:Vale.Def.Types_s.quad32) = Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0\n (Vale.Def.Words_s.__proj__Mkfour__item__lo0 r) (Vale.Def.Words_s.__proj__Mkfour__item__lo1 r)\n (Vale.Def.Words_s.__proj__Mkfour__item__hi2 r) in let (va_arg18:Vale.Def.Types_s.quad32) = l in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 96 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_quad32_xor_associates va_arg18 va_arg19 va_arg20)\n (let (va_arg17:Vale.Math.Poly2_s.poly) = hi in let (va_arg16:Vale.Math.Poly2_s.poly) = lo in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 98 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_shift_2_left_1 va_arg16 va_arg17) (va_QEmpty\n (())))))))))))))))", "val va_qcode_ShiftLeft2_128_1 (va_mods: va_mods_t) (lo hi: poly)\n : (va_quickCode unit (va_code_ShiftLeft2_128_1 ()))\nlet va_qcode_ShiftLeft2_128_1 (va_mods:va_mods_t) (lo:poly) (hi:poly) : (va_quickCode unit\n (va_code_ShiftLeft2_128_1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 91 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 92 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Psrld (va_op_xmm_xmm 3) 31) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 95 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 4) (va_op_xmm_xmm 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 96 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Psrld (va_op_xmm_xmm 4) 31) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 100 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pslld (va_op_xmm_xmm 1) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 101 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pslld (va_op_xmm_xmm 2) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 105 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_VPslldq4 (va_op_xmm_xmm 5) (va_op_xmm_xmm 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 106 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_VPslldq4 (va_op_xmm_xmm 4) (va_op_xmm_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 109 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_PinsrdImm (va_op_xmm_xmm 3) 0 0 (va_op_reg_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 110 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 3) (va_op_xmm_xmm 3) 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 113 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 3) (va_op_xmm_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 117 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 5)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 118 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 2) (va_op_xmm_xmm 3)) (fun (va_s:va_state) _ -> let\n (va_arg17:Vale.Math.Poly2_s.poly) = hi in let (va_arg16:Vale.Math.Poly2_s.poly) = lo in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 120 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_shift_2_left_1 va_arg16 va_arg17) (va_QEmpty\n (())))))))))))))))))", "val va_quick_Mod_cr0: Prims.unit -> (va_quickCode unit (va_code_Mod_cr0 ()))\nlet va_quick_Mod_cr0 () : (va_quickCode unit (va_code_Mod_cr0 ())) =\n (va_QProc (va_code_Mod_cr0 ()) ([va_Mod_cr0]) va_wp_Mod_cr0 va_wpProof_Mod_cr0)", "val va_quick_Mod_cr0: Prims.unit -> (va_quickCode unit (va_code_Mod_cr0 ()))\nlet va_quick_Mod_cr0 () : (va_quickCode unit (va_code_Mod_cr0 ())) =\n (va_QProc (va_code_Mod_cr0 ()) ([va_Mod_cr0]) va_wp_Mod_cr0 va_wpProof_Mod_cr0)", "val va_quick_Mod_cr0: Prims.unit -> (va_quickCode unit (va_code_Mod_cr0 ()))\nlet va_quick_Mod_cr0 () : (va_quickCode unit (va_code_Mod_cr0 ())) =\n (va_QProc (va_code_Mod_cr0 ()) ([va_Mod_cr0]) va_wp_Mod_cr0 va_wpProof_Mod_cr0)", "val va_qcode_Loop_rounds_1_3 (va_mods: va_mods_t) (block: block_w)\n : (va_quickCode unit (va_code_Loop_rounds_1_3 ()))\nlet va_qcode_Loop_rounds_1_3 (va_mods:va_mods_t) (block:block_w) : (va_quickCode unit\n (va_code_Loop_rounds_1_3 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 580 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 1 (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 0) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 581 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 2 (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 0) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 582 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 3 (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 0) block)\n (va_QEmpty (()))))))", "val va_qcode_Check_rdrand_stdcall (va_mods: va_mods_t) (win: bool)\n : (va_quickCode unit (va_code_Check_rdrand_stdcall win))\nlet va_qcode_Check_rdrand_stdcall (va_mods:va_mods_t) (win:bool) : (va_quickCode unit\n (va_code_Check_rdrand_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 133 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/stdcalls/Vale.Lib.X64.Cpuidstdcall.vaf *****\"\n (va_quick_Check_rdrand_support ()) (va_QEmpty (()))))", "val va_qcode_Loop_rounds_5_7 (va_mods: va_mods_t) (block: block_w)\n : (va_quickCode unit (va_code_Loop_rounds_5_7 ()))\nlet va_qcode_Loop_rounds_5_7 (va_mods:va_mods_t) (block:block_w) : (va_quickCode unit\n (va_code_Loop_rounds_5_7 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 599 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 5 (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 4) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 600 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 6 (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 4) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 601 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 7 (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 4) block)\n (va_QEmpty (()))))))", "val va_qcode_Poly1305_multiply (va_mods: va_mods_t) (r1: nat64)\n : (va_quickCode (int) (va_code_Poly1305_multiply ()))\nlet va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)\n (va_code_Poly1305_multiply ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range\n 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range\n 1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =\n va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0\n 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let\n (h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat\n (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +\n va_get_reg64 rR14 va_s in va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert\n va_range1\n \"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14\n va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx\n va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx\n va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)\n (va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let\n (gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)\n (va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let\n (gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert\n va_range1\n \"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)\n _ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n\n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let\n (va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0\n in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64\n rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let\n (va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let\n (va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let\n (va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51\n va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)\n (va_QEmpty ((hh))))))))))))))))))))))))))))))))))", "val va_code_XmmEqual : x1:va_operand_xmm -> x2:va_operand_xmm -> Tot va_code\nlet va_code_XmmEqual x1 x2 =\n (va_Block (va_CCons (va_code_Pcmpeqd x1 x2) (va_CCons (va_code_Pextrq (va_op_dst_opr64_reg64\n rRdx) x1 0) (va_CCons (va_code_Nat64Equal (va_op_reg_opr64_reg64 rRax) (va_op_reg_opr64_reg64\n rRdx)) (va_CCons (va_code_Pextrq (va_op_dst_opr64_reg64 rRdx) x1 1) (va_CCons\n (va_code_Nat64Equal (va_op_reg_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdx)) (va_CCons\n (va_code_Add64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_CNil ()))))))))", "val va_qcode_Sqr2_stdcall (va_mods: va_mods_t) (win: bool) (dst_b inA_b: buffer64)\n : (va_quickCode unit (va_code_Sqr2_stdcall win))\nlet va_qcode_Sqr2_stdcall (va_mods:va_mods_t) (win:bool) (dst_b:buffer64) (inA_b:buffer64) :\n (va_quickCode unit (va_code_Sqr2_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (dst_in:(va_int_range 0 18446744073709551615)) = va_if win (fun _ -> va_get_reg64 rRcx va_s)\n (fun _ -> va_get_reg64 rRdi va_s) in let (inA_in:(va_int_range 0 18446744073709551615)) = va_if\n win (fun _ -> va_get_reg64 rRdx va_s) (fun _ -> va_get_reg64 rRsi va_s) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 689 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 690 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 691 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR14)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 692 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRbx)) (fun (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 695 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 697 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRsi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 698 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 699 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_QEmpty (()))))))\n (qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 702 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Fast_sqr 0 dst_b inA_b) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 703 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Fast_sqr 4 dst_b inA_b) (fun (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 705 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 707 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rRsi)) (va_QEmpty (())))) (qblock va_mods (fun\n (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 710 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 711 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 712 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 713 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR15)) (va_QEmpty (())))))))))))))))", "val va_qcode_Fast_sqr_stdcall (va_mods: va_mods_t) (win: bool) (dst_b inA_b: buffer64)\n : (va_quickCode unit (va_code_Fast_sqr_stdcall win))\nlet va_qcode_Fast_sqr_stdcall (va_mods:va_mods_t) (win:bool) (dst_b:buffer64) (inA_b:buffer64) :\n (va_quickCode unit (va_code_Fast_sqr_stdcall win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (dst_in:(va_int_range 0 18446744073709551615)) = va_if win (fun _ -> va_get_reg64 rRcx va_s)\n (fun _ -> va_get_reg64 rRdi va_s) in let (inA_in:(va_int_range 0 18446744073709551615)) = va_if\n win (fun _ -> va_get_reg64 rRdx va_s) (fun _ -> va_get_reg64 rRsi va_s) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 467 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 468 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 469 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rRsi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 470 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR13)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 471 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Push (va_op_reg_opr64_reg64 rR14)) (fun (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 476 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 477 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_QEmpty (())))))\n (qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 480 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Fast_sqr 0 dst_b inA_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 482 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 483 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 484 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rRsi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 485 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 486 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastSqr.vaf *****\"\n (va_quick_Pop (va_op_dst_opr64_reg64 rR15)) (va_QEmpty (())))))))))))))))", "val va_qcode_Memcpy (va_mods: va_mods_t) (win: bool) (dst src: buffer64)\n : (va_quickCode unit (va_code_Memcpy win))\nlet va_qcode_Memcpy (va_mods:va_mods_t) (win:bool) (dst:buffer64) (src:buffer64) : (va_quickCode\n unit (va_code_Memcpy win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 67 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_CreateHeaplets ([declare_buffer64 src 0 Secret Immutable; declare_buffer64 dst 1\n Secret Mutable])) (fun (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 71 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 73 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_InnerMemcpy dst src) (va_QEmpty (())))) (qblock va_mods (fun (va_s:va_state) ->\n va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 77 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 src 0 Secret)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 77 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)\n (va_op_reg64_reg64 rRsi) 0 Secret)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 78 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 src 1 Secret)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 78 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)\n (va_op_reg64_reg64 rRsi) 8 Secret)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 79 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRax) 0 Secret dst 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 80 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRcx) 8 Secret dst 1) (va_QEmpty (())))))))))) (fun (va_s:va_state) va_g\n -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 82 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (FStar.Seq.Base.equal #(Vale.X64.Memory.base_typ_as_vale_type Vale.X64.Memory.vuint64)\n (Vale.X64.Memory.buffer_as_seq #Vale.X64.Memory.vuint64 (va_get_mem_heaplet 1 va_s) dst)\n (Vale.X64.Memory.buffer_as_seq #Vale.X64.Memory.vuint64 (va_get_mem_heaplet 0 va_s) src))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 84 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/test/Vale.Test.X64.Vale_memcpy.vaf *****\"\n (va_quick_DestroyHeaplets ()) (va_QEmpty (())))))))", "val va_qcode_Reduce (va_mods: va_mods_t) (last_adds: bool) (f: poly)\n : (va_quickCode unit (va_code_Reduce last_adds))\nlet va_qcode_Reduce (va_mods:va_mods_t) (last_adds:bool) (f:poly) : (va_quickCode unit\n (va_code_Reduce last_adds)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (g:Vale.Math.Poly2_s.poly) = add (Vale.Math.Poly2_s.monomial 128) f in let\n (c:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift f (-1)) 63 in\n let (a0:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 4 va_s) in let\n (a1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 6 va_s) in let\n (a2:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 7 va_s) in let\n (a:Vale.Math.Poly2_s.poly) = add (add a0 (Vale.Math.Poly2_s.shift a1 64))\n (Vale.Math.Poly2_s.shift a2 128) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 617 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_quick_VLow64ToHigh (va_op_xmm_xmm 5) (va_op_xmm_xmm 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 618 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_quick_VPolyAdd (va_op_xmm_xmm 4) (va_op_xmm_xmm 4) (va_op_opr128_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 619 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_quick_VSwap (va_op_xmm_xmm 0) (va_op_xmm_xmm 4)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 620 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_quick_VPolyMul (va_op_xmm_xmm 4) (va_op_xmm_xmm 4) (va_op_xmm_xmm 3) false true) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 621 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_quick_VHigh64ToLow (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 622 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_quick_VPolyAdd (va_op_xmm_xmm 7) (va_op_xmm_xmm 7) (va_op_opr128_xmm 6)) (fun\n (va_s:va_state) _ -> let (va_arg33:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32\n (va_get_xmm 0 va_s) in let (va_arg32:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32\n (va_get_xmm 4 va_s) in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 623 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.lemma_add_commute va_arg32 va_arg33) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 624 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_quick_VPolyAdd (va_op_xmm_xmm 4) (va_op_xmm_xmm 4) (va_op_opr128_xmm 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 626 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_quick_VSwap (va_op_xmm_xmm 8) (va_op_xmm_xmm 4)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 627 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_quick_VPolyMul (va_op_xmm_xmm 4) (va_op_xmm_xmm 4) (va_op_xmm_xmm 3) false true) (fun\n (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 628 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_qInlineIf va_mods last_adds (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 630 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_quick_VPolyAdd (va_op_xmm_xmm 8) (va_op_xmm_xmm 8) (va_op_opr128_xmm 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 631 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (va_quick_VPolyAdd (va_op_xmm_xmm 8) (va_op_xmm_xmm 8) (va_op_opr128_xmm 4)) (va_QEmpty\n (()))))) (qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g ->\n let (va_arg31:Vale.Math.Poly2_s.poly) = f in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 633 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/aes/Vale.AES.X64.AESopt2.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_reduce_rev a0 a1 a2 va_arg31 64) (va_QEmpty\n (())))))))))))))))", "val va_qcode_Poly1305_last_block (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Poly1305_last_block ()))\nlet va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Poly1305_last_block ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range\n 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range\n 1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =\n va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let\n (r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in\n let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128\n (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let\n (inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)\n (va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s\n `op_Multiply` 8) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun\n (va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15\n va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert\n va_range1\n \"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64\n rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)\n in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =\n va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->\n va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast\n `op_Modulus` padLast) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty\n (())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_get_reg64 rR15 va_s - 8 >= 0 /\\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let\n (nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8\n in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun\n (va_s:va_state) _ -> va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let\n (va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let\n (va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =\n va_get_reg64 rR9 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash\n va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\\ Prims.pow2 (8 `op_Multiply` nExtra8) <=\n 18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8\n `op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let\n (va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->\n va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast\n `op_Modulus` padLast) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty\n (()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast\n `op_Modulus` padLast + padLast in va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx\n va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy\n va_range1\n \"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14\n va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let\n (va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast\n in let (va_arg69:Prims.pos) = p in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)\n (va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp\n hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)\n (va_QEmpty (()))) (va_QEmpty (()))))))))))", "val va_qcode_Fadd (va_mods: va_mods_t) (dst_b inA_b inB_b: buffer64)\n : (va_quickCode unit (va_code_Fadd ()))\nlet va_qcode_Fadd (va_mods:va_mods_t) (dst_b:buffer64) (inA_b:buffer64) (inB_b:buffer64) :\n (va_quickCode unit (va_code_Fadd ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 0 (va_get_mem va_s) in let\n (a1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 1 (va_get_mem va_s) in let\n (a2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 2 (va_get_mem va_s) in let\n (a3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 3 (va_get_mem va_s) in let\n (b0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 0 (va_get_mem va_s) in let\n (b1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 1 (va_get_mem va_s) in let\n (b2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 2 (va_get_mem va_s) in let\n (b3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 3 (va_get_mem va_s) in let\n (a:Prims.nat) = Vale.Curve25519.Fast_defs.pow2_four a0 a1 a2 a3 in let (b:Prims.nat) =\n Vale.Curve25519.Fast_defs.pow2_four b0 b1 b2 b3 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 836 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_CreateHeaplets ([declare_buffer64 inA_b 0 Secret Immutable; declare_buffer64 inB_b 0\n Secret Immutable; declare_buffer64 dst_b 0 Secret Mutable])) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 841 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Comment\n \"Compute the raw addition of f1 + f2\"\n ) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 842 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Fast_add inA_b inB_b) (fun (va_s:va_state) _ -> let (va_arg26:prop) =\n Vale.Curve25519.Fast_defs.pow2_five (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s)\n (va_get_reg64 rR10 va_s) (va_get_reg64 rR11 va_s) (Vale.Curve25519.Fast_defs.bool_bit\n (Vale.X64.Decls.cf (va_get_flags va_s))) == Vale.Curve25519.Fast_defs.pow2_four (va_get_reg64\n rR8 va_s) (va_get_reg64 rR9 va_s) (va_get_reg64 rR10 va_s) (va_get_reg64 rR11 va_s) +\n va_mul_nat (Vale.Curve25519.Fast_defs.bool_bit (Vale.X64.Decls.cf (va_get_flags va_s)))\n pow2_256 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 843 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (fun (_:unit) -> assert_by_tactic va_arg26 int_canon) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 846 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_LargeComment\n \"Wrap the result back into the field\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 847 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Carry_pass true 0 dst_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 849 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_DestroyHeaplets ()) (va_QEmpty (()))))))))))", "val va_qcode_Cswap_single (va_mods: va_mods_t) (offset: nat) (p0_b p1_b: buffer64)\n : (va_quickCode unit (va_code_Cswap_single offset))\nlet va_qcode_Cswap_single (va_mods:va_mods_t) (offset:nat) (p0_b:buffer64) (p1_b:buffer64) :\n (va_quickCode unit (va_code_Cswap_single offset)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (old_p0_val:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read p0_b (0 + offset)\n (va_get_mem_heaplet 0 va_s) in let (old_p1_val:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read p1_b (0 + offset) (va_get_mem_heaplet 0 va_s) in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 839 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8)\n (va_op_reg_opr64_reg64 rRsi) (0 + offset `op_Multiply` 8) Secret p0_b (0 + offset)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 840 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)\n (va_op_reg_opr64_reg64 rRdx) (0 + offset `op_Multiply` 8) Secret p1_b (0 + offset)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 841 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 842 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Cmovc64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 843 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Cmovc64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 844 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRsi)\n (va_op_reg_opr64_reg64 rR8) (0 + offset `op_Multiply` 8) Secret p0_b (0 + offset)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 845 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdx)\n (va_op_reg_opr64_reg64 rR9) (0 + offset `op_Multiply` 8) Secret p1_b (0 + offset)) (va_QEmpty\n (()))))))))))", "val va_qcode_Loop_rounds_9_11 (va_mods: va_mods_t) (block: block_w)\n : (va_quickCode unit (va_code_Loop_rounds_9_11 ()))\nlet va_qcode_Loop_rounds_9_11 (va_mods:va_mods_t) (block:block_w) : (va_quickCode unit\n (va_code_Loop_rounds_9_11 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 618 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 9 (va_op_vec_opr_vec 9) (va_op_vec_opr_vec 8) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 619 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 10 (va_op_vec_opr_vec 10) (va_op_vec_opr_vec 8) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 620 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 11 (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 8) block)\n (va_QEmpty (()))))))", "val va_qcode_Loop_rounds_0_15 (va_mods: va_mods_t) (in_b k_b: buffer128) (offset: nat)\n : (va_quickCode unit (va_code_Loop_rounds_0_15 ()))\nlet va_qcode_Loop_rounds_0_15 (va_mods:va_mods_t) (in_b:buffer128) (k_b:buffer128) (offset:nat) :\n (va_quickCode unit (va_code_Loop_rounds_0_15 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qAssertSquash\n va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 146 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.X64.Decls.quad32 (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s) in_b) offset\n (offset + 4)) (fun _ -> let (input_LE:(FStar.Seq.Base.seq Vale.X64.Decls.quad32)) =\n FStar.Seq.Base.slice #Vale.X64.Decls.quad32 (Vale.X64.Decls.buffer128_as_seq\n (va_get_mem_heaplet 0 va_s) in_b) offset (offset + 4) in let (input_BE:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_nat32_quad32_seq input_LE in let\n (block:block_w) = Vale.SHA.SHA_helpers.quads_to_block input_BE in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 149 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (fun (_:unit) -> Vale.SHA.SHA_helpers.lemma_quads_to_block input_BE) (let\n (hash_orig:Vale.SHA.SHA_helpers.hash256) = Vale.SHA.SHA_helpers.make_hash (va_get_xmm 1 va_s)\n (va_get_xmm 2 va_s) in let (va_arg79:Vale.SHA.SHA_helpers.block_w) = block in va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 153 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (fun (_:unit) -> Vale.SHA.SHA_helpers.lemma_repeat_range_0_vale va_arg79 hash_orig) (let\n (ks:(FStar.Seq.Base.seq Vale.X64.Decls.quad32)) = Vale.X64.Decls.buffer128_as_seq\n (va_get_mem_heaplet 0 va_s) k_b in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 158 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 3) (va_op_reg_opr64_reg64\n rRsi) 0 Secret in_b (offset + 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 159 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 4) (va_op_reg_opr64_reg64\n rRsi) 16 Secret in_b (offset + 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 160 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 5) (va_op_reg_opr64_reg64\n rRsi) 32 Secret in_b (offset + 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 161 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_PshufbStable (va_op_xmm_xmm 3) (va_op_xmm_xmm 7)) (fun (va_s:va_state) _ ->\n va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 162 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.Def.Types_s.quad32 input_BE 0) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 162 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 3 va_s == FStar.Seq.Base.index #Vale.Def.Types_s.quad32 input_BE 0) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 163 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 6) (va_op_reg_opr64_reg64\n rRsi) 48 Secret in_b (offset + 3)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 165 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRcx) 0 Secret k_b 0) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 166 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.X64.Decls.quad32 ks 0) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 166 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 0 va_s == FStar.Seq.Base.index #Vale.X64.Decls.quad32 ks 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 3)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 169 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_PshufbStable (va_op_xmm_xmm 4) (va_op_xmm_xmm 7)) (fun (va_s:va_state) _ ->\n va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 170 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.Def.Types_s.quad32 input_BE 1) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 170 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 4 va_s == FStar.Seq.Base.index #Vale.Def.Types_s.quad32 input_BE 1) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 10) (va_op_xmm_xmm 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 174 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1) 0 block hash_orig) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 175 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 176 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 9) (va_op_xmm_xmm 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 177 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) 2 block hash_orig) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 180 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRcx) 16 Secret k_b 1) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 181 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.X64.Decls.quad32 ks 1) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 181 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 0 va_s == FStar.Seq.Base.index #Vale.X64.Decls.quad32 ks 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 182 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 4)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 183 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_PshufbStable (va_op_xmm_xmm 5) (va_op_xmm_xmm 7)) (fun (va_s:va_state) _ ->\n va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 184 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.Def.Types_s.quad32 input_BE 2) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 184 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 5 va_s == FStar.Seq.Base.index #Vale.Def.Types_s.quad32 input_BE 2) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 185 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1) 4 block hash_orig) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 186 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 187 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Add64 (va_op_dst_opr64_reg64 rRsi) (va_const_opr64 64)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 188 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_msg1 (va_op_xmm_xmm 3) (va_op_xmm_xmm 4) 16 block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 189 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) 6 block hash_orig) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 192 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRcx) 32 Secret k_b 2) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 193 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.X64.Decls.quad32 ks 2) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 193 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 0 va_s == FStar.Seq.Base.index #Vale.X64.Decls.quad32 ks 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 194 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 5)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 195 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_PshufbStable (va_op_xmm_xmm 6) (va_op_xmm_xmm 7)) (fun (va_s:va_state) _ ->\n va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 196 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.Def.Types_s.quad32 input_BE 3) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 196 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 6 va_s == FStar.Seq.Base.index #Vale.Def.Types_s.quad32 input_BE 3) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 197 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1) 8 block hash_orig) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 198 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 199 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Palignr4 (va_op_xmm_xmm 7) (va_op_xmm_xmm 5)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 201 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 3) (va_op_xmm_xmm 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 202 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_msg1 (va_op_xmm_xmm 4) (va_op_xmm_xmm 5) 20 block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 203 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) 10 block hash_orig) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 206 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRcx) 48 Secret k_b 3) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 207 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n ((fun a_539 (s_540:(FStar.Seq.Base.seq a_539)) (i_541:Prims.nat) -> let (i_515:Prims.nat) =\n i_541 in Prims.b2t (Prims.op_LessThan i_515 (FStar.Seq.Base.length #a_539 s_540)))\n Vale.X64.Decls.quad32 ks 3) (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 207 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_get_xmm 0 va_s == FStar.Seq.Base.index #Vale.X64.Decls.quad32 ks 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 208 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 209 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_msg2 (va_op_xmm_xmm 3) (va_op_xmm_xmm 6) 16 block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 210 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1) 12 block hash_orig) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 211 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 212 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 213 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Palignr4 (va_op_xmm_xmm 7) (va_op_xmm_xmm 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 214 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Paddd (va_op_xmm_xmm 4) (va_op_xmm_xmm 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 215 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_msg1 (va_op_xmm_xmm 5) (va_op_xmm_xmm 6) 24 block) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 216 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) 14 block hash_orig) (va_QEmpty\n (())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))", "val va_qcode_Loop_body0\n (va_mods: va_mods_t)\n (va_old: va_state)\n (va_in_hash_orig: hash256)\n (va_in_in_b va_in_k_b: buffer128)\n (va_in_count: nat)\n : (va_quickCode (nat) (va_code_Loop_body0 ()))\nlet va_qcode_Loop_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_hash_orig:hash256)\n (va_in_in_b:buffer128) (va_in_k_b:buffer128) (va_in_count:nat) : (va_quickCode (nat)\n (va_code_Loop_body0 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hash_orig:hash256)\n = va_in_hash_orig in let (in_b:buffer128) = va_in_in_b in let (k_b:buffer128) = va_in_k_b in\n let (count:nat) = va_in_count in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 219 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Loop.vaf *****\"\n (va_quick_Mod_cr0 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 220 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Loop.vaf *****\"\n (va_quick_Loop_rounds in_b k_b (4 `op_Multiply` count) hash_orig) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 221 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Loop.vaf *****\"\n (va_quick_SubImm (va_op_reg_opr_reg 5) (va_op_reg_opr_reg 5) 1) (fun (va_s:va_state) _ -> let\n (count:nat) = count + 1 in va_QEmpty ((count)))))))", "val va_qcode_Loop_body0\n (va_mods: va_mods_t)\n (va_old: va_state)\n (va_in_hash_orig: hash256)\n (va_in_in_b va_in_k_b: buffer128)\n (va_in_count: nat)\n : (va_quickCode (nat) (va_code_Loop_body0 ()))\nlet va_qcode_Loop_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_hash_orig:hash256)\n (va_in_in_b:buffer128) (va_in_k_b:buffer128) (va_in_count:nat) : (va_quickCode (nat)\n (va_code_Loop_body0 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hash_orig:hash256)\n = va_in_hash_orig in let (in_b:buffer128) = va_in_in_b in let (k_b:buffer128) = va_in_k_b in\n let (count:nat) = va_in_count in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 578 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.X64.vaf *****\"\n (va_quick_Loop_rounds in_b k_b (count `op_Multiply` 4) hash_orig) (fun (va_s:va_state) _ -> let\n (count:nat) = count + 1 in va_QEmpty ((count)))))", "val va_qcode_Fast_mul1 (va_mods: va_mods_t) (dst_b inA_b: buffer64)\n : (va_quickCode unit (va_code_Fast_mul1 ()))\nlet va_qcode_Fast_mul1 (va_mods:va_mods_t) (dst_b:buffer64) (inA_b:buffer64) : (va_quickCode unit\n (va_code_Fast_mul1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 0 (va_get_mem_heaplet 0 va_s)\n in let (a1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 1 (va_get_mem_heaplet 0\n va_s) in let (a2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 2\n (va_get_mem_heaplet 0 va_s) in let (a3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read\n inA_b 3 (va_get_mem_heaplet 0 va_s) in let (a:Prims.nat) = Vale.Curve25519.Fast_defs.pow2_four\n a0 a1 a2 a3 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 91 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.xor_lemmas ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 93 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inA_b 0 Secret)\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 93 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rR9) (va_op_dst_opr64_reg64 rR8) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Secret)) (fun (va_s:va_state) _ -> let\n (va_arg48:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let\n (va_arg47:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let\n (va_arg46:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 93 column 99 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.Fast_lemmas_external.lemma_prod_bounds va_arg46 va_arg47\n va_arg48 a0) (let (old_r8:nat64) = va_get_reg64 rR8 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 94 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR8) 0 Secret dst_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 95 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Xor64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 96 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inA_b 1 Secret)\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 96 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rR11) (va_op_dst_opr64_reg64 rR10) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Secret)) (fun (va_s:va_state) _ -> let\n (va_arg45:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let\n (va_arg44:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let\n (va_arg43:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 96 column 99 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.Fast_lemmas_external.lemma_prod_bounds va_arg43 va_arg44\n va_arg45 a1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 97 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 98 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR10) 8 Secret dst_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 99 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 16 inA_b 2 Secret)\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 99 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rR13) (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 16 Secret)) (fun (va_s:va_state) _ ->\n let (va_arg42:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let\n (va_arg41:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let\n (va_arg40:Vale.Def.Types_s.nat64) = va_get_reg64 rR13 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 99 column 99 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.Fast_lemmas_external.lemma_prod_bounds va_arg40 va_arg41\n va_arg42 a2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 100 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 101 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRbx) 16 Secret dst_b 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 102 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 24 inA_b 3 Secret)\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 102 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Mulx64 (va_op_dst_opr64_reg64 rRax) (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 24 Secret)) (fun (va_s:va_state) _ ->\n let (va_arg39:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let\n (va_arg38:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let\n (va_arg37:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 102 column 99 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.Fast_lemmas_external.lemma_prod_bounds va_arg37 va_arg38\n va_arg39 a3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 103 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 104 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR14) 24 Secret dst_b 3) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 105 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR8)) (fun (va_s:va_state)\n _ -> let (carry_bit:Vale.Curve25519.Fast_defs.bit) = Vale.Curve25519.Fast_defs.bool_bit\n (Vale.X64.Decls.cf (va_get_flags va_s)) in va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 108 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (carry_bit == 0) (let (va_arg36:prop) = va_mul_nat a (va_get_reg64 rRdx va_s) == 0 +\n Vale.Curve25519.Fast_defs.pow2_four (va_mul_nat (va_get_reg64 rRdx va_s) a0) (va_mul_nat\n (va_get_reg64 rRdx va_s) a1) (va_mul_nat (va_get_reg64 rRdx va_s) a2) (va_mul_nat (va_get_reg64\n rRdx va_s) a3) in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 109 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastUtil.vaf *****\"\n (fun (_:unit) -> assert_by_tactic va_arg36 int_canon) (va_QEmpty (())))))))))))))))))))))))))))", "val va_qcode_Loop_rounds_13_15 (va_mods: va_mods_t) (block: block_w)\n : (va_quickCode unit (va_code_Loop_rounds_13_15 ()))\nlet va_qcode_Loop_rounds_13_15 (va_mods:va_mods_t) (block:block_w) : (va_quickCode unit\n (va_code_Loop_rounds_13_15 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 638 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 13 (va_op_vec_opr_vec 13) (va_op_vec_opr_vec 12) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 639 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 14 (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 12) block)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 640 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/sha/Vale.SHA.PPC64LE.Rounds.Core.vaf *****\"\n (va_quick_Loop_rounds_1_15_shift_body 15 (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 12) block)\n (va_QEmpty (()))))))", "val va_qcode_Check_osxsave_support (va_mods: va_mods_t)\n : (va_quickCode unit (va_code_Check_osxsave_support ()))\nlet va_qcode_Check_osxsave_support (va_mods:va_mods_t) : (va_quickCode unit\n (va_code_Check_osxsave_support ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 332 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 334 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 335 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 336 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Cpuid_Osxsave ()) (fun (va_s:va_state) _ -> let (va_arg14:Vale.Def.Types_s.nat64) =\n va_get_reg64 rRcx va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_iand_pow2_64 va_arg14 27) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 338 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 339 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 134217728)) (fun (va_s:va_state) _\n -> va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 340 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n ((fun (p:prop) -> normalize p) (134217728 == Prims.pow2 27)) (fun _ -> (fun (p:prop) -> p)\n (134217728 == Prims.pow2 27)) (fun (_:unit) -> assert_normalize (134217728 == Prims.pow2 27))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 342 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 26)) (fun (va_s:va_state) _\n -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 343 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_pow2_diff64 1 27) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 344 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.TypesNative.lemma_ishr_zero64 26) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 346 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/lib/util/x64/Vale.Lib.X64.Cpuid.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty\n (())))))))))))))))", "val va_qcode_Fmul2 (va_mods: va_mods_t) (tmp_b inA_b dst_b inB_b: buffer64)\n : (va_quickCode unit (va_code_Fmul2 ()))\nlet va_qcode_Fmul2 (va_mods:va_mods_t) (tmp_b:buffer64) (inA_b:buffer64) (dst_b:buffer64)\n (inB_b:buffer64) : (va_quickCode unit (va_code_Fmul2 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (tmp_in:nat64) =\n va_get_reg64 rRdi va_s in let (inA_in:nat64) = va_get_reg64 rRsi va_s in let (dst_in:nat64) =\n va_get_reg64 rR15 va_s in let (inB_in:nat64) = va_get_reg64 rRcx va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 334 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_CreateHeaplets ([declare_buffer64 inA_b 0 Secret Immutable; declare_buffer64 inB_b 0\n Secret Immutable; declare_buffer64 dst_b 0 Secret Mutable; declare_buffer64 tmp_b 0 Secret\n Mutable])) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 340 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_LargeComment\n \"Compute the raw multiplication tmp[0] <- f1[0] * f2[0]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 341 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Fast_multiply 0 tmp_b inA_b inB_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 342 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_LargeComment\n \"Compute the raw multiplication tmp[1] <- f1[1] * f2[1]\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 343 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Fast_multiply 4 tmp_b inA_b inB_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 344 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 345 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Comment\n \"Line up pointers\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 346 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 347 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 348 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_LargeComment\n \"Wrap the results back into the field\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 349 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Carry_wide 0 dst_b tmp_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 350 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 351 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Carry_wide 4 dst_b tmp_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 353 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_DestroyHeaplets ()) (va_QEmpty (())))))))))))))))))", "val va_qcode_Fmul (va_mods: va_mods_t) (tmp_b inA_b dst_b inB_b: buffer64)\n : (va_quickCode unit (va_code_Fmul ()))\nlet va_qcode_Fmul (va_mods:va_mods_t) (tmp_b:buffer64) (inA_b:buffer64) (dst_b:buffer64)\n (inB_b:buffer64) : (va_quickCode unit (va_code_Fmul ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (tmp_in:nat64) =\n va_get_reg64 rRdi va_s in let (inA_in:nat64) = va_get_reg64 rRsi va_s in let (dst_in:nat64) =\n va_get_reg64 rR15 va_s in let (inB_in:nat64) = va_get_reg64 rRcx va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 119 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_CreateHeaplets ([declare_buffer64 inA_b 0 Secret Immutable; declare_buffer64 inB_b 0\n Secret Immutable; declare_buffer64 dst_b 0 Secret Mutable; declare_buffer64 tmp_b 0 Secret\n Mutable])) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 125 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_LargeComment\n \"Compute the raw multiplication: tmp <- src1 * src2\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 126 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Fast_multiply 0 tmp_b inA_b inB_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 127 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Newline ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 128 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Comment\n \"Line up pointers\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 129 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 130 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 131 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_LargeComment\n \"Wrap the result back into the field\"\n ) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 132 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_Carry_wide 0 dst_b tmp_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 134 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastWide.vaf *****\"\n (va_quick_DestroyHeaplets ()) (va_QEmpty (())))))))))))))", "val va_qcode_Restore_registers\n (va_mods: va_mods_t)\n (win: bool)\n (old_rsp: nat)\n (old_xmm6 old_xmm7 old_xmm8 old_xmm9 old_xmm10 old_xmm11 old_xmm12 old_xmm13 old_xmm14 old_xmm15:\n quad32)\n : (va_quickCode unit (va_code_Restore_registers win))\nlet va_qcode_Restore_registers (va_mods:va_mods_t) (win:bool) (old_rsp:nat) (old_xmm6:quad32)\n (old_xmm7:quad32) (old_xmm8:quad32) (old_xmm9:quad32) (old_xmm10:quad32) (old_xmm11:quad32)\n (old_xmm12:quad32) (old_xmm13:quad32) (old_xmm14:quad32) (old_xmm15:quad32) : (va_quickCode unit\n (va_code_Restore_registers win)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 1536 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1537 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PopXmm_Secret (va_op_xmm_xmm 6) (va_op_reg_opr64_reg64 rRax) old_xmm6) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 1538 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PopXmm_Secret (va_op_xmm_xmm 7) (va_op_reg_opr64_reg64 rRax) old_xmm7) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 1539 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PopXmm_Secret (va_op_xmm_xmm 8) (va_op_reg_opr64_reg64 rRax) old_xmm8) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 1540 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PopXmm_Secret (va_op_xmm_xmm 9) (va_op_reg_opr64_reg64 rRax) old_xmm9) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 1541 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PopXmm_Secret (va_op_xmm_xmm 10) (va_op_reg_opr64_reg64 rRax) old_xmm10) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 1542 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PopXmm_Secret (va_op_xmm_xmm 11) (va_op_reg_opr64_reg64 rRax) old_xmm11) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 1543 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PopXmm_Secret (va_op_xmm_xmm 12) (va_op_reg_opr64_reg64 rRax) old_xmm12) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 1544 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PopXmm_Secret (va_op_xmm_xmm 13) (va_op_reg_opr64_reg64 rRax) old_xmm13) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 1545 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PopXmm_Secret (va_op_xmm_xmm 14) (va_op_reg_opr64_reg64 rRax) old_xmm14) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 1546 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_PopXmm_Secret (va_op_xmm_xmm 15) (va_op_reg_opr64_reg64 rRax) old_xmm15) (va_QEmpty\n (()))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state)\n va_g -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1549 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1550 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRbp)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1551 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRdi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1552 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRsi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1553 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1554 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR13)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1555 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR14)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1556 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMencryptOpt.vaf *****\"\n (va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR15)) (va_QEmpty (()))))))))))))", "val va_qcode_Fsub (va_mods: va_mods_t) (dst_b inA_b inB_b: buffer64)\n : (va_quickCode unit (va_code_Fsub ()))\nlet va_qcode_Fsub (va_mods:va_mods_t) (dst_b:buffer64) (inA_b:buffer64) (inB_b:buffer64) :\n (va_quickCode unit (va_code_Fsub ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 0 (va_get_mem va_s) in let\n (a1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 1 (va_get_mem va_s) in let\n (a2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 2 (va_get_mem va_s) in let\n (a3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 3 (va_get_mem va_s) in let\n (b0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 0 (va_get_mem va_s) in let\n (b1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 1 (va_get_mem va_s) in let\n (b2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 2 (va_get_mem va_s) in let\n (b3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 3 (va_get_mem va_s) in let\n (a:Prims.nat) = Vale.Curve25519.Fast_defs.pow2_four a0 a1 a2 a3 in let (b:Prims.nat) =\n Vale.Curve25519.Fast_defs.pow2_four b0 b1 b2 b3 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 997 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_CreateHeaplets ([declare_buffer64 inA_b 0 Secret Immutable; declare_buffer64 inB_b 0\n Secret Immutable; declare_buffer64 dst_b 0 Secret Mutable])) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1002 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Fast_sub inA_b inB_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1003 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Carry_sub_pass ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1004 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Store4 dst_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 1006 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_DestroyHeaplets ()) (va_QEmpty (()))))))))", "val va_qcode_Fast_sub (va_mods: va_mods_t) (inA_b inB_b: buffer64)\n : (va_quickCode unit (va_code_Fast_sub ()))\nlet va_qcode_Fast_sub (va_mods:va_mods_t) (inA_b:buffer64) (inB_b:buffer64) : (va_quickCode unit\n (va_code_Fast_sub ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 0 (va_get_mem_heaplet 0 va_s)\n in let (a1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 1 (va_get_mem_heaplet 0\n va_s) in let (a2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 2\n (va_get_mem_heaplet 0 va_s) in let (a3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read\n inA_b 3 (va_get_mem_heaplet 0 va_s) in let (b0:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read inB_b 0 (va_get_mem_heaplet 0 va_s) in let\n (b1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 1 (va_get_mem_heaplet 0 va_s)\n in let (b2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 2 (va_get_mem_heaplet 0\n va_s) in let (b3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 3\n (va_get_mem_heaplet 0 va_s) in let (a:Prims.nat) = Vale.Curve25519.Fast_defs.pow2_four a0 a1 a2\n a3 in let (b:Prims.nat) = Vale.Curve25519.Fast_defs.pow2_four b0 b1 b2 b3 in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 760 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Comment\n \"Compute the raw substraction of f1-f2\"\n ) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 761 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.xor_lemmas ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 764 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8)\n (va_op_reg_opr64_reg64 rRsi) 0 Secret inA_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 765 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRdx) 0 inB_b 0 Secret)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 765 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rR8) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet\n 0) (va_op_reg64_reg64 rRdx) 0 Secret)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 767 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)\n (va_op_reg_opr64_reg64 rRsi) 8 Secret inA_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 768 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRdx) 8 inB_b 1 Secret)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 768 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Sbb64 (va_op_dst_opr64_reg64 rR9) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)\n (va_op_reg64_reg64 rRdx) 8 Secret)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 770 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR10)\n (va_op_reg_opr64_reg64 rRsi) 16 Secret inA_b 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 771 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRdx) 16 inB_b 2 Secret)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 771 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Sbb64 (va_op_dst_opr64_reg64 rR10) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)\n (va_op_reg64_reg64 rRdx) 16 Secret)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 773 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR11)\n (va_op_reg_opr64_reg64 rRsi) 24 Secret inA_b 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 774 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRdx) 24 inB_b 3 Secret)\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 774 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Sbb64 (va_op_dst_opr64_reg64 rR11) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)\n (va_op_reg64_reg64 rRdx) 24 Secret)) (fun (va_s:va_state) _ -> let\n (va_arg37:Vale.Curve25519.Fast_defs.bit) = Vale.Curve25519.Fast_defs.bool_bit\n (Vale.X64.Decls.cf (va_get_flags va_s)) in let (va_arg36:Vale.Def.Types_s.nat64) = va_get_reg64\n rR11 va_s in let (va_arg35:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let\n (va_arg34:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let\n (va_arg33:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 776 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (fun (_:unit) -> Vale.Curve25519.FastUtil_helpers.lemma_sub a a0 a1 a2 a3 b b0 b1 b2 b3\n va_arg33 va_arg34 va_arg35 va_arg36 va_arg37) (va_QEmpty (()))))))))))))))))))", "val va_qcode_ShiftKey1_128 (va_mods: va_mods_t) (f: poly)\n : (va_quickCode unit (va_code_ShiftKey1_128 ()))\nlet va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let\n (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let\n (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in\n va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ ->\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****\"\n (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3))\n (va_QEmpty (()))))))))))))))))", "val va_qcode_ShiftKey1_128 (va_mods: va_mods_t) (f: poly)\n : (va_quickCode unit (va_code_ShiftKey1_128 ()))\nlet va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128\n ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 3 va_s) in let\n (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let\n (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 4 va_s) in\n va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 1) (va_op_xmm_xmm 3)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 88 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 89 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 90 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 92 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (va_quick_PolyAnd (va_op_xmm_xmm 3) (va_op_xmm_xmm 5)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 93 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (va_quick_Pcmpeqd (va_op_xmm_xmm 3) (va_op_xmm_xmm 5)) (fun (va_s:va_state) _ -> va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 94 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 95 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (va_quick_Pshufd (va_op_xmm_xmm 3) (va_op_xmm_xmm 3) 255) (fun (va_s:va_state) _ -> va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 96 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 97 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 100 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (va_quick_PolyAnd (va_op_xmm_xmm 3) (va_op_xmm_xmm 4)) (fun (va_s:va_state) _ -> va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 101 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 102 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (va_quick_VPolyAdd (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) (va_op_opr128_xmm 3)) (va_QEmpty\n (()))))))))))))))))", "val va_qcode_Fast_add (va_mods: va_mods_t) (inA_b inB_b: buffer64)\n : (va_quickCode unit (va_code_Fast_add ()))\nlet va_qcode_Fast_add (va_mods:va_mods_t) (inA_b:buffer64) (inB_b:buffer64) : (va_quickCode unit\n (va_code_Fast_add ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (a0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 0 (va_get_mem_heaplet 0 va_s)\n in let (a1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 1 (va_get_mem_heaplet 0\n va_s) in let (a2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inA_b 2\n (va_get_mem_heaplet 0 va_s) in let (a3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read\n inA_b 3 (va_get_mem_heaplet 0 va_s) in let (b0:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read inB_b 0 (va_get_mem_heaplet 0 va_s) in let\n (b1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 1 (va_get_mem_heaplet 0 va_s)\n in let (b2:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 2 (va_get_mem_heaplet 0\n va_s) in let (b3:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read inB_b 3\n (va_get_mem_heaplet 0 va_s) in let (a:Prims.nat) = Vale.Curve25519.Fast_defs.pow2_four a0 a1 a2\n a3 in let (b:Prims.nat) = Vale.Curve25519.Fast_defs.pow2_four b0 b1 b2 b3 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 706 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.xor_lemmas ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 707 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8)\n (va_op_reg_opr64_reg64 rRdx) 0 Secret inB_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 708 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inA_b 0 Secret)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 708 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet\n 0) (va_op_reg64_reg64 rRsi) 0 Secret)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 710 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)\n (va_op_reg_opr64_reg64 rRdx) 8 Secret inB_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 711 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inA_b 1 Secret)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 711 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR9) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet\n 0) (va_op_reg64_reg64 rRsi) 8 Secret)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 713 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR10)\n (va_op_reg_opr64_reg64 rRdx) 16 Secret inB_b 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 714 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 16 inA_b 2 Secret)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 714 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR10) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet\n 0) (va_op_reg64_reg64 rRsi) 16 Secret)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 716 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR11)\n (va_op_reg_opr64_reg64 rRdx) 24 Secret inB_b 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 717 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 24 inA_b 3 Secret)\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 717 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/rfc7748/curve25519/x64/Vale.Curve25519.X64.FastHybrid.vaf *****\"\n (va_quick_Adcx64Wrap (va_op_dst_opr64_reg64 rR11) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet\n 0) (va_op_reg64_reg64 rRsi) 24 Secret)) (va_QEmpty (()))))))))))))))))", "val va_quick_Xgetbv_Avx: Prims.unit -> (va_quickCode unit (va_code_Xgetbv_Avx ()))\nlet va_quick_Xgetbv_Avx () : (va_quickCode unit (va_code_Xgetbv_Avx ())) =\n (va_QProc (va_code_Xgetbv_Avx ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_wp_Xgetbv_Avx\n va_wpProof_Xgetbv_Avx)", "val va_qcode_ReduceMulRev128 (va_mods: va_mods_t) (a b: poly)\n : (va_quickCode unit (va_code_ReduceMulRev128 ()))\nlet va_qcode_ReduceMulRev128 (va_mods:va_mods_t) (a:poly) (b:poly) : (va_quickCode unit\n (va_code_ReduceMulRev128 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 321 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_degree ()) (let (va_arg31:Vale.Math.Poly2_s.poly) =\n b in let (va_arg30:Vale.Math.Poly2_s.poly) = a in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 322 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_reduce_rev va_arg30 va_arg31\n gf128_modulus_low_terms 128) (let (m:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.monomial 128\n in let (h:Vale.Math.Poly2_s.poly) = gf128_modulus_low_terms in let (ab:Vale.Math.Poly2_s.poly)\n = Vale.Math.Poly2_s.mul a b in let (rh:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.reverse h\n 127 in let (rab:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.reverse ab 255 in let\n (rd:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.mod rab m in let (rdh:Vale.Math.Poly2_s.poly) =\n Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.mul (Vale.Math.Poly2_s.reverse rd 127) h) 255 in\n let (rdhL:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.mod rdh m in let\n (rdhLh:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.mul\n (Vale.Math.Poly2_s.reverse rdhL 127) h) 127 in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 333 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_ClmulRev128 a b) (fun (va_s:va_state) va_g -> let ((lo1:poly), (hi1:poly)) = va_g in\n let (va_arg29:Vale.Math.Poly2_s.poly) = lo1 in let (va_arg28:Vale.Math.Poly2_s.poly) = hi1 in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 334 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_combine_define va_arg28 va_arg29 128) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 335 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 2)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 337 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Gf128ModulusRev (va_op_xmm_xmm 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 339 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_ClmulRev128 (Vale.Math.Poly2_s.reverse rd 127) h) (fun (va_s:va_state) va_g -> let\n ((lo2:poly), (hi2:poly)) = va_g in let (va_arg27:Vale.Math.Poly2_s.poly) = lo2 in let\n (va_arg26:Vale.Math.Poly2_s.poly) = hi2 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 340 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_combine_define va_arg26 va_arg27 128) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 341 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 5) (va_op_xmm_xmm 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 343 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Gf128ModulusRev (va_op_xmm_xmm 2)) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 345 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_quad32_double_hi_rev rdhL) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 346 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_quad32_double_hi_rev rh) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 347 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_ClmulRev64 (Vale.Math.Poly2_s.reverse rdhL 127) h true true) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 349 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_AddPoly (va_op_xmm_xmm 1) (va_op_xmm_xmm 5) rdhLh (Vale.Math.Poly2_s.div rdh m))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 350 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_AddPoly (va_op_xmm_xmm 1) (va_op_xmm_xmm 6) (Vale.Math.Poly2_s.add rdhLh\n (Vale.Math.Poly2_s.div rdh m)) (Vale.Math.Poly2_s.div rab m)) (va_QEmpty (()))))))))))))))))))" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_mod_6" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_qcode_load_one_msb" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.va_qcode_Fast_sqr_part2" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_qcode_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_qcode_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_avx2_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESGCM.fst", "name": "Vale.AES.X64.AESGCM.va_qcode_Load_one_msb" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_avx_support" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_avx512_support" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_avx2_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_avx_xcr0_support" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_sse_support" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_avx512_xcr0_support" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_qcode_Msg_shift" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fst", "name": "Vale.AES.PPC64LE.GCMencrypt.va_qcode_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Gcm_make_length_quad" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Compute_pad_to_128_bits" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fst", "name": "Vale.AES.PPC64LE.GCMencrypt.va_qcode_Compute_pad_to_128_bits" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_movbe_support" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_avx512_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_avx512_xcr0_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_avx_xcr0_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESGCM.fst", "name": "Vale.AES.X64.AESGCM.va_qcode_Handle_ctr32_2" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_avx_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_qcode_Handle_ctr32" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_aesni_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_qcode_Compute_Y0" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_sse_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fst", "name": "Vale.AES.X64.GCTR.va_qcode_Init_ctr" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_movbe_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_qcode_Compute_ghash_incremental_register" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_qcode_Carry_sub_pass" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_qcode_Gf128MulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_qcode_Gf128MulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fsti", "name": "Vale.X64.InsVector.va_quick_XmmEqual" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_qcode_Poly1305_reduce" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_qcode_Reduce" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_quick_Nat64Equal" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_sha_support" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_aesni_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_qcode_Poly1305_reduce_last" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Store_3blocks128_2" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_rdrand_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_qcode_Store_3blocks128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Save_registers" }, { "project_name": "hacl-star", "file_name": "Vale.Test.X64.Vale_memcpy.fst", "name": "Vale.Test.X64.Vale_memcpy.va_qcode_InnerMemcpy" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_qcode_Loop" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_qcode_Loop" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_quick_Vcmpequw" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Stack.fst", "name": "Vale.X64.Stack.va_qcode_Callee_save_registers" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_adx_bmi2_support" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_qcode_Poly1305_add_key_s" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_qcode_Store4" }, { "project_name": "hacl-star", "file_name": "Vale.Test.X64.Args.fst", "name": "Vale.Test.X64.Args.va_qcode_Test" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_qcode_Cswap2" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_qcode_Fast_sub1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_quick_mod_6" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_qcode_Preamble" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.fst", "name": "Vale.SHA.PPC64LE.va_qcode_Preamble" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_adx_bmi2_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_qcode_ShiftLeft128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_qcode_ShiftLeft128_1" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsVector.fsti", "name": "Vale.PPC64LE.InsVector.va_quick_Vmr" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_qcode_ReduceMul128_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_sha_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_qcode_ShiftLeft2_128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_qcode_ShiftLeft2_128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_quick_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_quick_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_quick_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_qcode_Loop_rounds_1_3" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuidstdcall.fst", "name": "Vale.Lib.X64.Cpuidstdcall.va_qcode_Check_rdrand_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_qcode_Loop_rounds_5_7" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_qcode_Poly1305_multiply" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsVector.fst", "name": "Vale.X64.InsVector.va_code_XmmEqual" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.va_qcode_Sqr2_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.va_qcode_Fast_sqr_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.Test.X64.Vale_memcpy.fst", "name": "Vale.Test.X64.Vale_memcpy.va_qcode_Memcpy" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt2.fst", "name": "Vale.AES.X64.AESopt2.va_qcode_Reduce" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_qcode_Poly1305_last_block" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_qcode_Fadd" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_qcode_Cswap_single" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_qcode_Loop_rounds_9_11" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_qcode_Loop_rounds_0_15" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_qcode_Loop_body0" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_qcode_Loop_body0" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_qcode_Fast_mul1" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_qcode_Loop_rounds_13_15" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_qcode_Check_osxsave_support" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fst", "name": "Vale.Curve25519.X64.FastWide.va_qcode_Fmul2" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fst", "name": "Vale.Curve25519.X64.FastWide.va_qcode_Fmul" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_qcode_Restore_registers" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_qcode_Fsub" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_qcode_Fast_sub" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Init.fst", "name": "Vale.AES.PPC64LE.GF128_Init.va_qcode_ShiftKey1_128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Init.fst", "name": "Vale.AES.X64.GF128_Init.va_qcode_ShiftKey1_128" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_qcode_Fast_add" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fsti", "name": "Vale.X64.InsBasic.va_quick_Xgetbv_Avx" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_qcode_ReduceMulRev128" } ], "selected_premises": [ "Vale.PPC64LE.QuickCodes.va_QSeq", "Vale.PPC64LE.QuickCodes.va_qPURE", "Vale.PPC64LE.QuickCodes.va_QEmpty", "Vale.PPC64LE.QuickCodes.qblock", "Vale.PPC64LE.QuickCodes.va_QBind", "Vale.AES.PPC64LE.GCMdecrypt.va_qcode_Gcm_blocks_wrapped", "Vale.PPC64LE.QuickCodes.va_QLemma", "Vale.AES.PPC64LE.GCMdecrypt.va_qcode_Gcm_blocks", "Vale.AES.PPC64LE.GCMdecrypt.va_code_Nat64Equal", "Vale.PPC64LE.QuickCodes.va_qAssertBy", "Vale.AES.PPC64LE.GCMdecrypt.va_code_Gcm_blocks_wrapped", "Vale.AES.PPC64LE.GCMdecrypt.va_qcode_Gcm_extra_bytes", "Vale.AES.PPC64LE.GCMdecrypt.va_code_VectorEqual", "Vale.PPC64LE.Decls.va_get_vec", "Vale.AES.PPC64LE.GCMdecrypt.va_code_Gcm_blocks128", "Vale.AES.PPC64LE.GCMdecrypt.va_code_Gcm_extra_bytes", "Vale.PPC64LE.Decls.va_code", "Vale.AES.PPC64LE.GCMdecrypt.va_code_Gcm_blocks", "Vale.PPC64LE.QuickCodes.label", "Vale.AES.PPC64LE.GHash.va_quick_Ghash_buffer", "Vale.PPC64LE.Decls.va_get_block", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.X64.Machine_s.operand128", "Vale.X64.Machine_s.reg_xmm", "Vale.PPC64LE.QuickCodes.va_qAssert", "Vale.PPC64LE.Decls.va_value_vec_opr", "Vale.PPC64LE.Decls.va_state", "Vale.PPC64LE.Decls.va_get_mem_heaplet", "Vale.AES.PPC64LE.GCTR.va_quick_Gctr_register", "Vale.AES.PPC64LE.GCMencrypt.va_quick_Gcm_make_length_quad", "Vale.X64.Machine_s.quad32", "Vale.PPC64LE.Machine_s.quad32", "Vale.PPC64LE.Memory.quad32", "Vale.PPC64LE.Decls.va_op_cmp_reg", "Vale.PPC64LE.Decls.va_if", "Vale.X64.Machine_s.reg_64", "Lib.IntTypes.u64", "Vale.AES.PPC64LE.GCMdecrypt.va_qcode_Gcm_blocks128", "Vale.PPC64LE.Decls.va_CNil", "Vale.PPC64LE.Decls.va_Block", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.Def.Words_s.nat32", "Vale.PPC64LE.Decls.va_eval_vec_opr", "Vale.AES.PPC64LE.GHash.va_quick_Ghash_register", "Vale.PPC64LE.QuickCodes.va_qAssume", "Vale.PPC64LE.Decls.va_upd_vec", "Vale.AES.PPC64LE.GCMencrypt.va_quick_Gcm_blocks_auth", "Vale.PPC64LE.Decls.va_get_ok", "Vale.PPC64LE.Decls.va_mul_nat", "Vale.PPC64LE.Decls.va_op_heaplet_mem_heaplet", "Vale.X64.Machine_s.rRdi", "Vale.PPC64LE.InsMem.va_quick_CreateHeaplets", "Vale.PPC64LE.Decls.va_upd_reg", "Vale.PPC64LE.QuickCodes.va_qAssertSquash", "Vale.X64.Machine_s.rRdx", "Vale.PPC64LE.Decls.va_get_reg", "Vale.PPC64LE.Decls.va_CCons", "Vale.X64.Machine_s.rRax", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRcx", "Vale.PPC64LE.QuickCodes.va_qInlineIf", "Vale.X64.Machine_s.rRsi", "Vale.PPC64LE.Memory.nat64", "Vale.Def.Types_s.nat64", "Vale.PPC64LE.Machine_s.nat64", "Vale.PPC64LE.Decls.va_get_mem_layout", "Vale.AES.PPC64LE.GF128_Mul.va_quick_Gf128MulRev128", "Vale.AES.PPC64LE.GCMdecrypt.va_quick_Nat64Equal", "Vale.AES.PPC64LE.GF128_Mul.va_quick_Low64ToHigh", "Vale.X64.Machine_s.rRsp", "Vale.AES.PPC64LE.GF128_Mul.va_quick_ReduceMulRev128", "Vale.X64.Machine_s.rRbp", "Vale.AES.PPC64LE.AES.va_quick_KeyExpansionStdcall", "Vale.AES.PPC64LE.GF128_Mul.va_quick_ShiftLeft128_1", "Vale.PPC64LE.QuickCodes.va_range1", "Vale.AES.PPC64LE.GCMencrypt.va_quick_Load_one_lsb", "Vale.PPC64LE.QuickCode.quickProc_wp", "Vale.AES.GHash_BE.hkeys_reqs_priv", "Vale.AES.GCTR_BE.gctr_partial_reveal", "Vale.X64.Machine_s.rR11", "Vale.Def.Words_s.nat64", "Vale.PPC64LE.InsVector.va_quick_Store128_byte16_buffer", "Vale.X64.Machine_s.rR10", "Vale.X64.Machine_s.rR8", "Vale.X64.Machine_s.rR9", "Vale.PPC64LE.Decls.va_is_dst_vec_opr", "Vale.PPC64LE.InsVector.va_quick_Store128_word4_buffer", "Vale.X64.Machine_s.rR13", "Vale.X64.Machine_s.operand64", "Lib.IntTypes.int_t", "Vale.PPC64LE.Decls.va_int_range", "Vale.AES.GCM_BE_s.gcm_encrypt_BE", "Vale.PPC64LE.Decls.va_require_total", "Vale.AES.GCM_BE_s.gcm_encrypt_BE_reveal", "Vale.PPC64LE.InsVector.va_quick_Vand", "Vale.PPC64LE.InsVector.va_quick_SHA256_sigma1", "Vale.PPC64LE.InsVector.va_quick_Vmr", "Vale.X64.Machine_s.rR12", "Vale.X64.Machine_s.nat64", "Vale.X64.Machine_s.rR15" ], "source_upto_this": "module Vale.AES.PPC64LE.GCMdecrypt\nopen Vale.Def.Prop_s\nopen Vale.Def.Opaque_s\nopen FStar.Seq\nopen Vale.Def.Words_s\nopen Vale.Def.Words.Seq_s\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Arch.HeapImpl\nopen Vale.AES.AES_BE_s\nopen Vale.AES.GCTR_BE_s\nopen Vale.AES.GCTR_BE\nopen Vale.AES.GCM_BE\nopen Vale.AES.GHash_BE_s\nopen Vale.AES.GHash_BE\nopen Vale.AES.GCM_BE_s\nopen Vale.AES.PPC64LE.AES\nopen Vale.AES.GF128_s\nopen Vale.AES.GF128\nopen Vale.Poly1305.Math\nopen Vale.AES.GCM_helpers_BE\nopen Vale.AES.PPC64LE.GHash\nopen Vale.AES.PPC64LE.GCTR\nopen Vale.PPC64LE.Machine_s\nopen Vale.PPC64LE.Memory\nopen Vale.PPC64LE.Stack_i\nopen Vale.PPC64LE.State\nopen Vale.PPC64LE.Decls\nopen Vale.PPC64LE.InsBasic\nopen Vale.PPC64LE.InsMem\nopen Vale.PPC64LE.InsVector\nopen Vale.PPC64LE.InsStack\nopen Vale.PPC64LE.QuickCode\nopen Vale.PPC64LE.QuickCodes\nopen Vale.AES.PPC64LE.GF128_Mul\nopen Vale.Math.Poly2.Bits_s\nopen Vale.Lib.Meta\nopen Vale.AES.PPC64LE.GCMencrypt\nopen Vale.Lib.Basic\n#reset-options \"--z3rlimit 20\"\n//-- Gcm_extra_bytes\n\nval va_code_Gcm_extra_bytes : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_extra_bytes alg =\n (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 7)) (va_CCons\n (va_code_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 9)\n (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 12) (va_op_vec_opr_vec\n 9)) (va_CCons (va_code_Ghash_extra_bytes ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 11)) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_Vxor\n (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 0)) (va_CCons\n (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 12)\n (va_op_reg_opr_reg 3) Secret) (va_CNil ()))))))))))\n\nval va_codegen_success_Gcm_extra_bytes : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_extra_bytes alg =\n (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 7)) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 9)\n (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 12)\n (va_op_vec_opr_vec 9)) (va_pbool_and (va_codegen_success_Ghash_extra_bytes ()) (va_pbool_and\n (va_codegen_success_Vmr (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 11)) (va_pbool_and\n (va_codegen_success_AESEncryptBlock alg) (va_pbool_and (va_codegen_success_Vxor\n (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 0)) (va_pbool_and\n (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 12)\n (va_op_reg_opr_reg 3) Secret) (va_ttrue ())))))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_extra_bytes (va_mods:va_mods_t) (alg:algorithm) (inout_b:buffer128) (key:(seq\n nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat)\n (old_hash:quad32) (completed_quads:(seq quad32)) (h_BE:quad32) : (va_quickCode unit\n (va_code_Gcm_extra_bytes alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (len:(va_int_range\n 1 1)) = 1 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 164 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 165 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 9)\n (va_op_reg_opr_reg 3) Secret inout_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 166 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 9)) (fun (va_s:va_state) _ -> let\n (hash_input:quad32) = va_get_vec 9 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 170 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Ghash_extra_bytes hkeys_b total_bytes old_hash h_BE completed_quads) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 171 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (FStar.Seq.Base.equal #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b)) (FStar.Seq.Base.create #quad32 1\n hash_input)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 173 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 11)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 174 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_AESEncryptBlock alg (va_get_vec 7 va_old_s) key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 176 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vxor (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 12) (va_op_vec_opr_vec 0)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 177 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 5) (va_op_vec_opr_vec 12)\n (va_op_reg_opr_reg 3) Secret inout_b 0) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 179 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR_BE.gctr_partial_reveal ()) (va_QEmpty (())))))))))))))\n\n\nval va_lemma_Gcm_extra_bytes : va_b0:va_code -> va_s0:va_state -> alg:algorithm ->\n inout_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> total_bytes:nat -> old_hash:quad32 -> completed_quads:(seq quad32) ->\n h_BE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_extra_bytes alg) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (len:(va_int_range 1 1)) = 1 in Vale.PPC64LE.Decls.buffers_disjoint128 keys_b inout_b /\\\n Vale.PPC64LE.Decls.buffers_disjoint128 hkeys_b inout_b /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 5 va_s0) (va_get_reg 3 va_s0) inout_b len (va_get_mem_layout va_s0) Secret\n /\\ len == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b /\\ aes_reqs\n alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout\n va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ va_get_vec 1 va_s0 == Vale.AES.GHash_BE.ghash_incremental0\n h_BE old_hash completed_quads /\\ FStar.Seq.Base.length #quad32 completed_quads == total_bytes\n `op_Division` 16 /\\ total_bytes < 16 `op_Multiply` FStar.Seq.Base.length #quad32\n completed_quads + 16 /\\ va_get_reg 8 va_s0 == total_bytes `op_Modulus` 16 /\\ total_bytes\n `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16 `op_Multiply`\n Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes - 1) < total_bytes)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (len:(va_int_range 1 1)) = 1 in Vale.PPC64LE.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg\n len (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5\n va_s0) inout_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) key (va_get_vec 7 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b)) in let input_bytes =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_quads)) 0 total_bytes in\n let padded_bytes = Vale.AES.GCTR_BE_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (va_get_vec 1 va_sM ==\n Vale.AES.GHash_BE.ghash_incremental h_BE old_hash input_quads))) /\\ va_state_eq va_sM\n (va_update_mem_heaplet 5 va_sM (va_update_cr0 va_sM (va_update_vec 12 va_sM (va_update_vec 11\n va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8 va_sM (va_update_vec 7\n va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3\n va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10\n va_sM (va_update_reg 7 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_extra_bytes va_b0 va_s0 alg inout_b key round_keys keys_b hkeys_b total_bytes\n old_hash completed_quads h_BE =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 5; va_Mod_cr0; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7;\n va_Mod_ok; va_Mod_mem] in\n let va_qc = va_qcode_Gcm_extra_bytes va_mods alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_extra_bytes alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 106 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (let (len:(va_int_range 1 1)) = 1 in label va_range1\n \"***** POSTCONDITION NOT MET AT line 152 column 55 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet\n 5 va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 155 column 147 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.AES.GCTR_BE.gctr_partial alg len (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_sM)\n inout_b)) key (va_get_vec 7 va_s0)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 158 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let raw_quads = FStar.Seq.Base.append #quad32 completed_quads\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 159 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let input_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_quads)) 0 total_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 160 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let padded_bytes = Vale.AES.GCTR_BE_s.pad_to_128_bits input_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 161 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let input_quads = Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 162 column 91 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (l_and (FStar.Seq.Base.length #Vale.Def.Types_s.quad32 input_quads > 0) (va_get_vec 1 va_sM ==\n Vale.AES.GHash_BE.ghash_incremental h_BE old_hash input_quads)))))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_cr0; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec\n 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4;\n va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7; va_Mod_ok;\n va_Mod_mem]) va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_BE:quad32) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_get_ok va_s0 /\\ (let (len:(va_int_range 1 1)) = 1 in Vale.PPC64LE.Decls.buffers_disjoint128\n keys_b inout_b /\\ Vale.PPC64LE.Decls.buffers_disjoint128 hkeys_b inout_b /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 5 va_s0) (va_get_reg 3 va_s0) inout_b\n len (va_get_mem_layout va_s0) Secret /\\ len == Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 inout_b /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4\n va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\\n Vale.AES.GHash_BE.hkeys_reqs_priv (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)) h_BE /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 5 va_s0) hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ va_get_vec 1 va_s0 == Vale.AES.GHash_BE.ghash_incremental0\n h_BE old_hash completed_quads /\\ FStar.Seq.Base.length #quad32 completed_quads == total_bytes\n `op_Division` 16 /\\ total_bytes < 16 `op_Multiply` FStar.Seq.Base.length #quad32\n completed_quads + 16 /\\ va_get_reg 8 va_s0 == total_bytes `op_Modulus` 16 /\\ total_bytes\n `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16 `op_Multiply`\n Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers_BE.bytes_to_quad_size total_bytes - 1) < total_bytes) /\\ (forall\n (va_x_mem:vale_heap) (va_x_r7:nat64) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32)\n (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32)\n (va_x_v7:quad32) (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32)\n (va_x_v12:quad32) (va_x_cr0:cr0_t) (va_x_heap5:vale_heap) . let va_sM = va_upd_mem_heaplet 5\n va_x_heap5 (va_upd_cr0 va_x_cr0 (va_upd_vec 12 va_x_v12 (va_upd_vec 11 va_x_v11 (va_upd_vec 10\n va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7 va_x_v7 (va_upd_vec 6\n va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2\n (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_reg 7 va_x_r7\n (va_upd_mem va_x_mem va_s0))))))))))))))))) in va_get_ok va_sM /\\ (let (len:(va_int_range 1 1))\n = 1 in Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0)\n (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg len\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) key (va_get_vec 7 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b)) in let input_bytes =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_quads)) 0 total_bytes in\n let padded_bytes = Vale.AES.GCTR_BE_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (va_get_vec 1 va_sM ==\n Vale.AES.GHash_BE.ghash_incremental h_BE old_hash input_quads))) ==> va_k va_sM (())))\n\n\nval va_wpProof_Gcm_extra_bytes : alg:algorithm -> inout_b:buffer128 -> key:(seq nat32) ->\n round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> total_bytes:nat ->\n old_hash:quad32 -> completed_quads:(seq quad32) -> h_BE:quad32 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_extra_bytes alg)\n ([va_Mod_mem_heaplet 5; va_Mod_cr0; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9;\n va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec\n 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7; va_Mod_mem]) va_s0 va_k ((va_sM,\n va_f0, va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes old_hash\n completed_quads h_BE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_extra_bytes (va_code_Gcm_extra_bytes alg) va_s0 alg inout_b key\n round_keys keys_b hkeys_b total_bytes old_hash completed_quads h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 5 va_sM (va_update_cr0 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 10 va_sM (va_update_reg 7 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_cr0; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec\n 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4;\n va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_reg 7;\n va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_BE:quad32) : (va_quickCode unit (va_code_Gcm_extra_bytes alg)) =\n (va_QProc (va_code_Gcm_extra_bytes alg) ([va_Mod_mem_heaplet 5; va_Mod_cr0; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 10; va_Mod_reg 7; va_Mod_mem]) (va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_BE) (va_wpProof_Gcm_extra_bytes alg inout_b key\n round_keys keys_b hkeys_b total_bytes old_hash completed_quads h_BE))\n//--\n//-- Gcm_blocks128\n\nval va_code_Gcm_blocks128 : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_blocks128 alg =\n (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_CCons\n (va_code_Move (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 7)) (va_CCons (va_code_Move\n (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 6)) (va_CCons (va_code_Move (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 3)) (va_CCons (va_code_Ghash_buffer ()) (va_CCons (va_code_Vmr\n (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 7)\n (va_op_vec_opr_vec 15)) (va_CCons (va_code_Move (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 8))\n (va_CCons (va_code_Move (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 9)) (va_CCons\n (va_code_Gctr_blocks128 alg) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec\n 20)) (va_CNil ())))))))))))))\n\nval va_codegen_success_Gcm_blocks128 : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_blocks128 alg =\n (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_pbool_and\n (va_codegen_success_Move (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 7)) (va_pbool_and\n (va_codegen_success_Move (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 6)) (va_pbool_and\n (va_codegen_success_Move (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 3)) (va_pbool_and\n (va_codegen_success_Ghash_buffer ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec\n 20) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 7)\n (va_op_vec_opr_vec 15)) (va_pbool_and (va_codegen_success_Move (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 8)) (va_pbool_and (va_codegen_success_Move (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 9)) (va_pbool_and (va_codegen_success_Gctr_blocks128 alg) (va_pbool_and\n (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_ttrue ()))))))))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_blocks128 (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 237 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 15) (va_op_vec_opr_vec 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 238 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 7)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 239 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 6)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 240 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 3)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 241 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b in_b h_BE (va_get_vec 1 va_old_s)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 242 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 243 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 244 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 8)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 245 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Move (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 9)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 246 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gctr_blocks128 alg in_b out_b key round_keys keys_b) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 247 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 20)) (va_QEmpty (()))))))))))))))\n\n\nval va_lemma_Gcm_blocks128 : va_b0:va_code -> va_s0:va_state -> alg:algorithm -> in_b:buffer128 ->\n out_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> h_BE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks128 alg) va_s0 /\\ va_get_ok va_s0 /\\\n (Vale.PPC64LE.Decls.buffers_disjoint128 keys_b out_b /\\ Vale.PPC64LE.Decls.buffers_disjoint128\n hkeys_b out_b /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) in_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b (va_get_reg 6 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ l_and\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b))))) /\\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM\n (va_update_vec 20 va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM\n (va_update_vec 16 va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM\n (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM\n (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM\n (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM\n (va_update_vec 0 va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM\n (va_update_reg 28 va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM\n (va_update_reg 9 va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM\n (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_blocks128 va_b0 va_s0 alg in_b out_b key round_keys keys_b hkeys_b h_BE =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19;\n va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13;\n va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7;\n va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec\n 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26;\n va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem] in\n let va_qc = va_qcode_Gcm_blocks128 va_mods alg in_b out_b key round_keys keys_b hkeys_b h_BE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_blocks128 alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 182 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 226 column 53 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 229 column 147 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 230 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite (va_get_vec 7 va_s0) (va_get_reg 6 va_s0)) /\\\n label va_range1\n \"***** POSTCONDITION NOT MET AT line 233 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1 va_sM == va_get_vec 1 va_s0)\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b == Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) out_b)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 235 column 113 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_reg 6 va_s0 > 0 ==> l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) ==>\n FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice\n #Vale.PPC64LE.Machine_s.quad32 (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) 0\n (va_get_reg 6 va_s0)) > 0) (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE\n (va_get_vec 1 va_s0) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in_b)))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_ok; va_Mod_mem])\n va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 keys_b out_b /\\\n Vale.PPC64LE.Decls.buffers_disjoint128 hkeys_b out_b /\\ (Vale.PPC64LE.Decls.buffers_disjoint128\n in_b out_b \\/ in_b == out_b) /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) (va_get_reg 3 va_s0) in_b (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply`\n va_get_reg 6 va_s0 < pow2_64 /\\ va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 <\n pow2_64 /\\ l_and (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) h_BE /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 5 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret) /\\ (forall (va_x_mem:vale_heap)\n (va_x_r3:nat64) (va_x_r7:nat64) (va_x_r6:nat64) (va_x_r8:nat64) (va_x_r9:nat64)\n (va_x_r10:nat64) (va_x_r26:nat64) (va_x_r27:nat64) (va_x_r28:nat64) (va_x_r29:nat64)\n (va_x_r30:nat64) (va_x_r31:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32) (va_x_v17:quad32)\n (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32) (va_x_cr0:cr0_t) (va_x_heap1:vale_heap) .\n let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_cr0 va_x_cr0 (va_upd_vec 20 va_x_v20\n (va_upd_vec 19 va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16\n (va_upd_vec 15 va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12\n (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8\n (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4\n (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0\n (va_upd_reg 31 va_x_r31 (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29 (va_upd_reg 28 va_x_r28\n (va_upd_reg 27 va_x_r27 (va_upd_reg 26 va_x_r26 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9\n (va_upd_reg 8 va_x_r8 (va_upd_reg 6 va_x_r6 (va_upd_reg 7 va_x_r7 (va_upd_reg 3 va_x_r3\n (va_upd_mem va_x_mem va_s0))))))))))))))))))))))))))))))))))) in va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==> l_and (va_get_vec 1\n va_sM == va_get_vec 1 va_s0) (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg 6 va_s0 > 0 ==>\n l_and (va_get_reg 6 va_s0 <= FStar.Seq.Base.length #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) ==> FStar.Seq.Base.length\n #Vale.PPC64LE.Machine_s.quad32 (FStar.Seq.Base.slice #Vale.PPC64LE.Machine_s.quad32\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) 0 (va_get_reg 6 va_s0)) > 0)\n (va_get_vec 1 va_sM == Vale.AES.GHash_BE.ghash_incremental h_BE (va_get_vec 1 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b))))) ==> va_k va_sM (())))\n\n\nval va_wpProof_Gcm_blocks128 : alg:algorithm -> in_b:buffer128 -> out_b:buffer128 -> key:(seq\n nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> h_BE:quad32 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks128 alg)\n ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0,\n va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_blocks128 (va_code_Gcm_blocks128 alg) va_s0 alg in_b out_b key\n round_keys keys_b hkeys_b h_BE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 6 va_sM (va_update_reg 7 va_sM (va_update_reg 3\n va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))))))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec\n 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7; va_Mod_reg 3; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_BE:quad32) : (va_quickCode\n unit (va_code_Gcm_blocks128 alg)) =\n (va_QProc (va_code_Gcm_blocks128 alg) ([va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 20;\n va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14;\n va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8;\n va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec\n 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27;\n va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 6; va_Mod_reg 7;\n va_Mod_reg 3; va_Mod_mem]) (va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_BE) (va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_BE))\n//--\n//-- Gcm_blocks\n#push-options \"--z3rlimit 600\"\n\nval va_code_Gcm_blocks : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_blocks alg =\n (va_Block (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 5)\n (va_op_reg_opr_reg 25) (11 `op_Multiply` 8) Secret) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25) (0 `op_Multiply` 8)\n Secret) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 25) (6 `op_Multiply` 8) Secret) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25) (7 `op_Multiply` 8)\n Secret) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 9)\n (va_op_reg_opr_reg 25) (8 `op_Multiply` 8) Secret) (va_CCons (va_code_Gcm_blocks_auth ())\n (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 10)\n (va_op_reg_opr_reg 25) (9 `op_Multiply` 8) Secret) (va_CCons (va_code_Load128_byte16_buffer\n (va_op_heaplet_mem_heaplet 2) (va_op_vec_opr_vec 7) (va_op_reg_opr_reg 10) Public) (va_CCons\n (va_code_Vmr (va_op_vec_opr_vec 21) (va_op_vec_opr_vec 7)) (va_CCons (va_code_Load_one_lsb\n (va_op_vec_opr_vec 10)) (va_CCons (va_code_Vadduwm (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 7)\n (va_op_vec_opr_vec 10)) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 25) (1 `op_Multiply` 8) Secret) (va_CCons\n (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (2 `op_Multiply` 8) Secret) (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25) (3 `op_Multiply` 8) Secret) (va_CCons\n (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25)\n (10 `op_Multiply` 8) Secret) (va_CCons (va_code_Gcm_blocks128 alg) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25) (3 `op_Multiply` 8)\n Secret) (va_CCons (va_code_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 4) (va_CCons\n (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (5 `op_Multiply` 8) Secret) (va_CCons (va_IfElse (va_cmp_gt (va_op_cmp_reg 6) (va_op_cmp_reg\n 7)) (va_Block (va_CCons (va_code_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 25) (4 `op_Multiply` 8) Secret) (va_CCons (va_code_LoadImm64\n (va_op_reg_opr_reg 10) 15) (va_CCons (va_code_And (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 10)) (va_CCons (va_code_Gcm_extra_bytes alg) (va_CCons (va_Block (va_CNil\n ())) (va_CNil ()))))))) (va_Block (va_CNil ()))) (va_CCons (va_code_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25) (8 `op_Multiply` 8)\n Secret) (va_CCons (va_code_Gcm_make_length_quad ()) (va_CCons (va_code_Ghash_register ())\n (va_CCons (va_code_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 21)) (va_CCons\n (va_code_Gctr_register alg) (va_CCons (va_Block (va_CNil ())) (va_CNil\n ()))))))))))))))))))))))))))))\n\nval va_codegen_success_Gcm_blocks : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_blocks alg =\n (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 5)\n (va_op_reg_opr_reg 25) (11 `op_Multiply` 8) Secret) (va_pbool_and (va_codegen_success_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25) (0 `op_Multiply` 8)\n Secret) (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25) (6 `op_Multiply` 8) Secret) (va_pbool_and\n (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 25) (7 `op_Multiply` 8) Secret) (va_pbool_and (va_codegen_success_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 25) (8 `op_Multiply` 8)\n Secret) (va_pbool_and (va_codegen_success_Gcm_blocks_auth ()) (va_pbool_and\n (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 10)\n (va_op_reg_opr_reg 25) (9 `op_Multiply` 8) Secret) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 2) (va_op_vec_opr_vec 7)\n (va_op_reg_opr_reg 10) Public) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 21)\n (va_op_vec_opr_vec 7)) (va_pbool_and (va_codegen_success_Load_one_lsb (va_op_vec_opr_vec 10))\n (va_pbool_and (va_codegen_success_Vadduwm (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 7)\n (va_op_vec_opr_vec 10)) (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet\n 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 25) (1 `op_Multiply` 8) Secret) (va_pbool_and\n (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 25) (2 `op_Multiply` 8) Secret) (va_pbool_and (va_codegen_success_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25) (3 `op_Multiply` 8)\n Secret) (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25) (10 `op_Multiply` 8) Secret) (va_pbool_and\n (va_codegen_success_Gcm_blocks128 alg) (va_pbool_and (va_codegen_success_MemLoad64\n (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25) (3 `op_Multiply` 8)\n Secret) (va_pbool_and (va_codegen_success_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7)\n 4) (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg\n 6) (va_op_reg_opr_reg 25) (5 `op_Multiply` 8) Secret) (va_pbool_and (va_pbool_and\n (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 25) (4 `op_Multiply` 8) Secret) (va_pbool_and (va_codegen_success_LoadImm64\n (va_op_reg_opr_reg 10) 15) (va_pbool_and (va_codegen_success_And (va_op_reg_opr_reg 8)\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 10)) (va_codegen_success_Gcm_extra_bytes alg))))\n (va_pbool_and (va_codegen_success_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 25) (8 `op_Multiply` 8) Secret) (va_pbool_and\n (va_codegen_success_Gcm_make_length_quad ()) (va_pbool_and (va_codegen_success_Ghash_register\n ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 21))\n (va_pbool_and (va_codegen_success_Gctr_register alg) (va_ttrue ()))))))))))))))))))))))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_blocks (va_mods:va_mods_t) (alg:algorithm) (auth_b:buffer128) (abytes_b:buffer128)\n (in128_b:buffer128) (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (gcm_struct_b:buffer64) :\n (va_quickCode unit (va_code_Gcm_blocks alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s) in let\n (h_BE:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 0 va_old_s)) in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 396 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 5) (va_op_reg_opr_reg 25)\n (11 `op_Multiply` 8) Secret gcm_struct_b 11) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 398 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25)\n (0 `op_Multiply` 8) Secret gcm_struct_b 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 399 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (6 `op_Multiply` 8) Secret gcm_struct_b 6) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 400 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (7 `op_Multiply` 8) Secret gcm_struct_b 7) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 401 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 25)\n (8 `op_Multiply` 8) Secret gcm_struct_b 8) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 402 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_blocks_auth auth_b abytes_b hkeys_b h_BE) (fun (va_s:va_state)\n (auth_quad_seq:(seq quad32)) -> let (y_0:quad32) = Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0 in let (y_auth_bytes:quad32) = va_get_vec 1 va_s in let\n (iv_BE:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_old_s)) in let\n (ctr_BE_1:quad32) = iv_BE in let (ctr_BE_2:quad32) = Vale.AES.GCTR_BE_s.inc32 iv_BE 1 in\n va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 410 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 25)\n (9 `op_Multiply` 8) Secret gcm_struct_b 9) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 411 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 2) (va_op_vec_opr_vec 7)\n (va_op_reg_opr_reg 10) Public iv_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 413 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 21) (va_op_vec_opr_vec 7)) (fun (va_s:va_state) _ -> let\n (j0:quad32) = va_get_vec 7 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 415 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Load_one_lsb (va_op_vec_opr_vec 10)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 417 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vadduwm (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 10)) (fun\n (va_s:va_state) _ -> let (auth_in:(seq quad32)) = auth_quad_seq in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 25)\n (1 `op_Multiply` 8) Secret gcm_struct_b 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (2 `op_Multiply` 8) Secret gcm_struct_b 2) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (3 `op_Multiply` 8) Secret gcm_struct_b 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 425 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 25)\n (10 `op_Multiply` 8) Secret gcm_struct_b 10) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 426 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_blocks128 alg in128_b out128_b key round_keys keys_b hkeys_b h_BE) (fun\n (va_s:va_state) _ -> let (y_cipher128:quad32) = va_get_vec 1 va_s in let\n (va_arg115:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (va_arg114:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in\n let (va_arg113:Vale.Def.Types_s.quad32) = y_cipher128 in let\n (va_arg112:Vale.Def.Types_s.quad32) = y_auth_bytes in let (va_arg111:Vale.Def.Types_s.quad32) =\n y_0 in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 428 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash_BE.lemma_ghash_incremental0_append h_BE va_arg111 va_arg112\n va_arg113 va_arg114 va_arg115) (let auth_in = FStar.Seq.Base.append #quad32 auth_in\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b)) in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 431 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (3 `op_Multiply` 8) Secret gcm_struct_b 3) (fun (va_s:va_state) _ -> let\n (va_arg110:Vale.Def.Types_s.nat64) = va_get_reg 7 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 432 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg110 4) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 433 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Sl64Imm (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) 4) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 434 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 25)\n (5 `op_Multiply` 8) Secret gcm_struct_b 5) (fun (va_s:va_state) _ -> let (y_inout:quad32) =\n y_cipher128 in let (plain_byte_seq:(seq quad32)) = empty_seq_quad32 in let\n (cipher_byte_seq:(seq quad32)) = empty_seq_quad32 in let (va_arg109:Vale.Def.Types_s.quad32) =\n va_get_vec 7 va_s in let (va_arg108:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg107:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = cipher_byte_seq in let\n (va_arg106:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = plain_byte_seq in let\n (va_arg105:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 439 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR_BE.gctr_partial_opaque_init va_arg105 va_arg106 va_arg107\n va_arg108 va_arg109) (let (total_bytes:(va_int_at_least 0)) = FStar.Seq.Base.length #quad32\n auth_quad_seq `op_Multiply` 16 + plain_num_bytes in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 442 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_qIf va_mods (Cmp_gt (va_op_cmp_reg 6) (va_op_cmp_reg 7)) (qblock va_mods (fun\n (va_s:va_state) -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 444 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 25)\n (4 `op_Multiply` 8) Secret gcm_struct_b 4) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 445 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 446 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 15) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 447 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_And (va_op_reg_opr_reg 8) (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 10)) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 449 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes y_0 auth_in\n h_BE) (fun (va_s:va_state) _ -> let y_inout = va_get_vec 1 va_s in let\n (raw_auth_quads:(FStar.Seq.Base.seq quad32)) = FStar.Seq.Base.append #quad32 auth_in\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5\n va_old_s) inout_b)) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 453 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_auth_quads)) 0\n total_bytes) (fun _ -> let (auth_input_bytes:(FStar.Seq.Base.seq Vale.Def.Words_s.nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 total_bytes\n in let (padded_auth_bytes:(FStar.Seq.Base.seq Vale.Def.Types_s.nat8)) =\n Vale.AES.GCTR_BE_s.pad_to_128_bits auth_input_bytes in let auth_in =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes in let plain_byte_seq =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5\n va_old_s) inout_b) in let cipher_byte_seq = Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b) in va_QEmpty ((auth_in,\n cipher_byte_seq, plain_byte_seq, y_inout)))))))))) (qblock va_mods (fun (va_s:va_state) ->\n va_QEmpty ((auth_in, cipher_byte_seq, plain_byte_seq, y_inout))))) (fun (va_s:va_state) va_g ->\n let ((auth_in:(seq quad32)), (cipher_byte_seq:(seq quad32)), (plain_byte_seq:(seq quad32)),\n (y_inout:quad32)) = va_g in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 461 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_MemLoad64 (va_op_heaplet_mem_heaplet 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 25)\n (8 `op_Multiply` 8) Secret gcm_struct_b 8) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 462 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_make_length_quad ()) (fun (va_s:va_state) _ -> let (length_quad32:quad32) =\n va_get_vec 9 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 465 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Ghash_register hkeys_b h_BE y_inout) (fun (va_s:va_state) _ -> let (y_final:quad32) =\n va_get_vec 1 va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 468 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Vmr (va_op_vec_opr_vec 7) (va_op_vec_opr_vec 21)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 471 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gctr_register alg key round_keys keys_b) (fun (va_s:va_state) _ -> let\n (va_arg104:Vale.Def.Types_s.quad32) = va_get_vec 1 va_s in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 473 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.be_seq_quad32_to_bytes_of_singleton va_arg104)\n (va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n ((fun (icb_661:Vale.Def.Types_s.quad32) (plain_662:Vale.Def.Types_s.quad32)\n (alg_663:Vale.AES.AES_common_s.algorithm) (key_664:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32))\n (i_665:Prims.int) -> Vale.AES.AES_BE_s.is_aes_key_word alg_663 key_664) j0 y_final alg key 0)\n (fun _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_vec 1 va_s == Vale.AES.GCTR_BE_s.gctr_encrypt_block j0 y_final alg key 0) (let\n (plain128:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (cipher128:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n in128_b) in va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 479 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (FStar.Seq.Base.length #quad32 plain_byte_seq == 0 ==> FStar.Seq.Base.equal\n #Vale.Def.Types_s.quad32 (FStar.Seq.Base.append #Vale.Def.Types_s.quad32 plain128\n plain_byte_seq) plain128) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 480 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (FStar.Seq.Base.length #quad32 cipher_byte_seq == 0 ==> FStar.Seq.Base.equal\n #Vale.Def.Types_s.quad32 (FStar.Seq.Base.append #Vale.Def.Types_s.quad32 cipher128\n cipher_byte_seq) cipher128) (let (va_arg103:Vale.Def.Types_s.quad32) =\n Vale.AES.GCTR_BE.inc32lite ctr_BE_2 len128 in let (va_arg102:Vale.Def.Types_s.quad32) =\n ctr_BE_2 in let (va_arg101:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) = key in let\n (va_arg100:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = cipher_byte_seq in let\n (va_arg99:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = plain_byte_seq in let\n (va_arg98:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n out128_b) in let (va_arg97:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (va_arg96:Prims.nat) = FStar.Seq.Base.length #quad32 plain_byte_seq\n in let (va_arg95:Prims.nat) = len128 in let (va_arg94:Vale.AES.AES_common_s.algorithm) = alg in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 482 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR_BE.lemma_gctr_partial_append va_arg94 va_arg95 va_arg96 va_arg97\n va_arg98 va_arg99 va_arg100 va_arg101 va_arg102 va_arg103) (let\n (va_arg93:Vale.Def.Types_s.quad32) = length_quad32 in let (va_arg92:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = auth_in in let (va_arg91:Vale.Def.Types_s.quad32) = y_final in let\n (va_arg90:Vale.Def.Types_s.quad32) = y_inout in let (va_arg89:Vale.Def.Types_s.quad32) = y_0 in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 490 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash_BE.lemma_hash_append2 h_BE va_arg89 va_arg90 va_arg91 va_arg92\n va_arg93) (let auth_in = FStar.Seq.Base.append #quad32 auth_in (FStar.Seq.Base.create #quad32 1\n length_quad32) in let (va_arg88:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = auth_in in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 492 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GHash_BE.ghash_incremental_to_ghash h_BE va_arg88) (va_QEmpty\n (())))))))))))))))))))))))))))))))))))))))\n\n\nval va_lemma_Gcm_blocks : va_b0:va_code -> va_s0:va_state -> alg:algorithm -> auth_b:buffer128 ->\n abytes_b:buffer128 -> in128_b:buffer128 -> out128_b:buffer128 -> inout_b:buffer128 ->\n iv_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> gcm_struct_b:buffer64\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks alg) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (h_BE:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 0 va_s0)) in\n Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem_heaplet 3 va_s0) (va_get_reg 25 va_s0)\n gcm_struct_b 12 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem_heaplet 1 va_s0) auth_ptr auth_b auth_len (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 6 va_s0) abytes_ptr abytes_b 1\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 2\n va_s0) iv_ptr iv_b 1 (va_get_mem_layout va_s0) Public /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem_heaplet 1 va_s0) in128_ptr in128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) out128_ptr out128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 5\n va_s0) inout_ptr inout_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b;\n hkeys_b; in128_b; out128_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 out128_b\n ([keys_b; hkeys_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 inout_b ([keys_b;\n hkeys_b; out128_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b ==\n out128_b) /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply`\n len128 < pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64\n /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ plain_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem_heaplet 0 va_s0) + 128 < pow2_64 /\\\n (va_mul_nat len128 (128 `op_Division` 8) <= plain_num_bytes /\\ plain_num_bytes < va_mul_nat\n len128 (128 `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division`\n 8) <= auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ aes_reqs alg key round_keys keys_b keys_ptr (va_get_mem_heaplet 0 va_s0)\n (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0)))))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 0 (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in let\n (h_BE:Vale.Def.Types_s.quad32) = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 0 va_s0)) in\n Vale.PPC64LE.Decls.modifies_buffer128 out128_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet\n 1 va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0)\n (va_get_mem_heaplet 2 va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ plain_num_bytes < pow2_32 /\\\n auth_num_bytes < pow2_32 /\\ (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_s0)) in let\n (ctr_BE_1:quad32) = iv_BE in let (ctr_BE_2:quad32) = Vale.AES.GCTR_BE_s.inc32 iv_BE 1 in let\n plain1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b)) in let plain2 = Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in128_b) in let (plain_in:(seq quad32)) =\n (if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division` 8) then plain1 else plain2) in\n let cipher1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) in let cipher2 =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b) in let (cipher_out:(seq quad32)) = (if (plain_num_bytes > len128 `op_Multiply` 128\n `op_Division` 8) then cipher1 else cipher2) in let (cipher_bound:nat) = (if (plain_num_bytes >\n len128 `op_Multiply` 128 `op_Division` 8) then (len128 + 1) else len128) in\n Vale.AES.GCTR_BE.gctr_partial alg cipher_bound plain_in cipher_out key ctr_BE_2 /\\ (let\n (length_quad:quad32) = Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.Mktwo #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` auth_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n auth_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32)) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` plain_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n plain_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32))) in let raw_auth1 =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6 va_s0)\n abytes_b)) in let raw_auth2 = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) auth_b) in let (raw_auth_quads:(seq quad32)) = (if (auth_num_bytes\n > auth_len `op_Multiply` 128 `op_Division` 8) then raw_auth1 else raw_auth2) in let\n (auth_input_bytes:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 auth_num_bytes in let (padded_auth_bytes:(seq nat8))\n = Vale.AES.GCTR_BE_s.pad_to_128_bits auth_input_bytes in let (auth_quad_seq:(seq quad32)) =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes in let (raw_quad_seq:(seq quad32)) =\n FStar.Seq.Base.append #quad32 auth_quad_seq (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in128_b)) in let (total_bytes:nat) =\n FStar.Seq.Base.length #quad32 auth_quad_seq `op_Multiply` 16 + plain_num_bytes in let raw_quad1\n = let (ab:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 (FStar.Seq.Base.append #quad32 raw_quad_seq\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b))))) 0 total_bytes in let (pb:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits ab in\n Vale.Def.Types_s.be_bytes_to_seq_quad32 pb in let raw_quad2 = raw_quad_seq in let\n (raw_quad_seq:(seq quad32)) = (if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division` 8)\n then raw_quad1 else raw_quad2) in let (auth_quad_seq:(seq quad32)) = FStar.Seq.Base.append\n #quad32 raw_quad_seq (FStar.Seq.Base.create #quad32 1 length_quad) in va_get_vec 1 va_sM ==\n Vale.AES.GCTR_BE_s.gctr_encrypt_block ctr_BE_1 (Vale.AES.GHash_BE_s.ghash_BE h_BE\n auth_quad_seq) alg key 0))) /\\ va_state_eq va_sM (va_update_mem_heaplet 5 va_sM\n (va_update_mem_heaplet 2 va_sM (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM\n (va_update_vec 21 va_sM (va_update_vec 20 va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM\n (va_update_vec 17 va_sM (va_update_vec 16 va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM\n (va_update_vec 13 va_sM (va_update_vec 12 va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM\n (va_update_vec 9 va_sM (va_update_vec 8 va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM\n (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM\n (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM\n (va_update_reg 29 va_sM (va_update_reg 28 va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM\n (va_update_reg 10 va_sM (va_update_reg 9 va_sM (va_update_reg 8 va_sM (va_update_reg 7 va_sM\n (va_update_reg 6 va_sM (va_update_reg 5 va_sM (va_update_reg 4 va_sM (va_update_reg 3 va_sM\n (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))))))))))))))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_blocks va_b0 va_s0 alg auth_b abytes_b in128_b out128_b inout_b iv_b key\n round_keys keys_b hkeys_b gcm_struct_b =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem] in\n let va_qc = va_qcode_Gcm_blocks va_mods alg auth_b abytes_b in128_b out128_b inout_b iv_b key\n round_keys keys_b hkeys_b gcm_struct_b in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_blocks alg) va_qc va_s0 (fun va_s0\n va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 250 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in let (h_BE:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 336 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 out128_b (va_get_mem_heaplet 1 va_s0)\n (va_get_mem_heaplet 1 va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 337 column 52 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0) (va_get_mem_heaplet 2\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 338 column 55 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet\n 5 va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 341 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (plain_num_bytes < pow2_32) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 342 column 38 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (auth_num_bytes < pow2_32) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 344 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_s0)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 346 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (ctr_BE_1:quad32) = iv_BE in label va_range1\n \"***** POSTCONDITION NOT MET AT line 347 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (ctr_BE_2:quad32) = Vale.AES.GCTR_BE_s.inc32 iv_BE 1 in label va_range1\n \"***** POSTCONDITION NOT MET AT line 350 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let plain1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 351 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let plain2 = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in128_b) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 352 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (plain_in:(seq quad32)) = va_if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division`\n 8) (fun _ -> plain1) (fun _ -> plain2) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 355 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let cipher1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 357 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let cipher2 = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_sM) out128_b) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (cipher_out:(seq quad32)) = va_if (plain_num_bytes > len128 `op_Multiply` 128\n `op_Division` 8) (fun _ -> cipher1) (fun _ -> cipher2) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 361 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (cipher_bound:nat) = va_if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division` 8)\n (fun _ -> len128 + 1) (fun _ -> len128) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 365 column 77 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.AES.GCTR_BE.gctr_partial alg cipher_bound plain_in cipher_out key ctr_BE_2) /\\ label\n va_range1\n \"***** POSTCONDITION NOT MET AT line 369 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (length_quad:quad32) = Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.Mktwo #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` auth_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n auth_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32)) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` plain_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n plain_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32))) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 373 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let raw_auth1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n auth_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet\n 6 va_s0) abytes_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 374 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let raw_auth2 = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) auth_b) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 375 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (raw_auth_quads:(seq quad32)) = va_if (auth_num_bytes > auth_len `op_Multiply` 128\n `op_Division` 8) (fun _ -> raw_auth1) (fun _ -> raw_auth2) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 379 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (auth_input_bytes:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 auth_num_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 380 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (padded_auth_bytes:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits auth_input_bytes in\n label va_range1\n \"***** POSTCONDITION NOT MET AT line 381 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (auth_quad_seq:(seq quad32)) = Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes\n in label va_range1\n \"***** POSTCONDITION NOT MET AT line 382 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (raw_quad_seq:(seq quad32)) = FStar.Seq.Base.append #quad32 auth_quad_seq\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 383 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (total_bytes:nat) = FStar.Seq.Base.length #quad32 auth_quad_seq `op_Multiply` 16 +\n plain_num_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 384 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let raw_quad1 = let (ab:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 (FStar.Seq.Base.append #quad32 raw_quad_seq\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b))))) 0 total_bytes in let (pb:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits ab in\n Vale.Def.Types_s.be_bytes_to_seq_quad32 pb in label va_range1\n \"***** POSTCONDITION NOT MET AT line 387 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let raw_quad2 = raw_quad_seq in label va_range1\n \"***** POSTCONDITION NOT MET AT line 388 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (raw_quad_seq:(seq quad32)) = va_if (plain_num_bytes > len128 `op_Multiply` 128\n `op_Division` 8) (fun _ -> raw_quad1) (fun _ -> raw_quad2) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 393 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let (auth_quad_seq:(seq quad32)) = FStar.Seq.Base.append #quad32 raw_quad_seq\n (FStar.Seq.Base.create #quad32 1 length_quad) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 394 column 106 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_vec 1 va_sM == Vale.AES.GCTR_BE_s.gctr_encrypt_block ctr_BE_1\n (Vale.AES.GHash_BE_s.ghash_BE h_BE auth_quad_seq) alg key 0)))))))))))))))))))))))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem]) va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Gcm_blocks (alg:algorithm) (auth_b:buffer128) (abytes_b:buffer128) (in128_b:buffer128)\n (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (gcm_struct_b:buffer64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in let (h_BE:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem_heaplet 3\n va_s0) (va_get_reg 25 va_s0) gcm_struct_b 12 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) auth_ptr auth_b auth_len\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 6\n va_s0) abytes_ptr abytes_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 2 va_s0) iv_ptr iv_b 1\n (va_get_mem_layout va_s0) Public /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) in128_ptr in128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) out128_ptr out128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 5\n va_s0) inout_ptr inout_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b;\n hkeys_b; in128_b; out128_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 out128_b\n ([keys_b; hkeys_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 inout_b ([keys_b;\n hkeys_b; out128_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b ==\n out128_b) /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply`\n len128 < pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64\n /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ plain_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem_heaplet 0 va_s0) + 128 < pow2_64 /\\\n (va_mul_nat len128 (128 `op_Division` 8) <= plain_num_bytes /\\ plain_num_bytes < va_mul_nat\n len128 (128 `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division`\n 8) <= auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ aes_reqs alg key round_keys keys_b keys_ptr (va_get_mem_heaplet 0 va_s0)\n (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0))) /\\ (forall (va_x_mem:vale_heap) (va_x_r3:nat64)\n (va_x_r4:nat64) (va_x_r5:nat64) (va_x_r6:nat64) (va_x_r7:nat64) (va_x_r8:nat64) (va_x_r9:nat64)\n (va_x_r10:nat64) (va_x_r26:nat64) (va_x_r27:nat64) (va_x_r28:nat64) (va_x_r29:nat64)\n (va_x_r30:nat64) (va_x_r31:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32)\n (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32)\n (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32)\n (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32) (va_x_v17:quad32)\n (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32) (va_x_v21:quad32) (va_x_cr0:cr0_t)\n (va_x_heap1:vale_heap) (va_x_heap2:vale_heap) (va_x_heap5:vale_heap) . let va_sM =\n va_upd_mem_heaplet 5 va_x_heap5 (va_upd_mem_heaplet 2 va_x_heap2 (va_upd_mem_heaplet 1\n va_x_heap1 (va_upd_cr0 va_x_cr0 (va_upd_vec 21 va_x_v21 (va_upd_vec 20 va_x_v20 (va_upd_vec 19\n va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16 (va_upd_vec 15\n va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12 (va_upd_vec 11\n va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7\n va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3\n (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 31 va_x_r31\n (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29 (va_upd_reg 28 va_x_r28 (va_upd_reg 27 va_x_r27\n (va_upd_reg 26 va_x_r26 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9 (va_upd_reg 8 va_x_r8\n (va_upd_reg 7 va_x_r7 (va_upd_reg 6 va_x_r6 (va_upd_reg 5 va_x_r5 (va_upd_reg 4 va_x_r4\n (va_upd_reg 3 va_x_r3 (va_upd_mem va_x_mem va_s0)))))))))))))))))))))))))))))))))))))))) in\n va_get_ok va_sM /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in let (h_BE:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s0)) in Vale.PPC64LE.Decls.modifies_buffer128 out128_b\n (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\\\n Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0) (va_get_mem_heaplet 2\n va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0)\n (va_get_mem_heaplet 5 va_sM) /\\ plain_num_bytes < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ (let\n iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_s0)) in let (ctr_BE_1:quad32) = iv_BE in let (ctr_BE_2:quad32) =\n Vale.AES.GCTR_BE_s.inc32 iv_BE 1 in let plain1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b)) in let plain2 = Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in128_b) in let (plain_in:(seq quad32)) =\n va_if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division` 8) (fun _ -> plain1) (fun _ ->\n plain2) in let cipher1 = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) in let cipher2 =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b) in let (cipher_out:(seq quad32)) = va_if (plain_num_bytes > len128 `op_Multiply` 128\n `op_Division` 8) (fun _ -> cipher1) (fun _ -> cipher2) in let (cipher_bound:nat) = va_if\n (plain_num_bytes > len128 `op_Multiply` 128 `op_Division` 8) (fun _ -> len128 + 1) (fun _ ->\n len128) in Vale.AES.GCTR_BE.gctr_partial alg cipher_bound plain_in cipher_out key ctr_BE_2 /\\\n (let (length_quad:quad32) = Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32\n (Vale.Def.Words_s.Mktwo #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` auth_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n auth_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32)) (Vale.Def.Words_s.Mktwo\n #Vale.Def.Types_s.nat32 (8 `op_Multiply` plain_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply`\n plain_num_bytes `op_Division` pow2_32 `op_Modulus` pow2_32))) in let raw_auth1 =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6 va_s0)\n abytes_b)) in let raw_auth2 = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) auth_b) in let (raw_auth_quads:(seq quad32)) = va_if\n (auth_num_bytes > auth_len `op_Multiply` 128 `op_Division` 8) (fun _ -> raw_auth1) (fun _ ->\n raw_auth2) in let (auth_input_bytes:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 raw_auth_quads)) 0 auth_num_bytes in let (padded_auth_bytes:(seq nat8))\n = Vale.AES.GCTR_BE_s.pad_to_128_bits auth_input_bytes in let (auth_quad_seq:(seq quad32)) =\n Vale.Def.Types_s.be_bytes_to_seq_quad32 padded_auth_bytes in let (raw_quad_seq:(seq quad32)) =\n FStar.Seq.Base.append #quad32 auth_quad_seq (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in128_b)) in let (total_bytes:nat) =\n FStar.Seq.Base.length #quad32 auth_quad_seq `op_Multiply` 16 + plain_num_bytes in let raw_quad1\n = let (ab:(seq nat8)) = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 (FStar.Seq.Base.append #quad32 raw_quad_seq\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b))))) 0 total_bytes in let (pb:(seq nat8)) = Vale.AES.GCTR_BE_s.pad_to_128_bits ab in\n Vale.Def.Types_s.be_bytes_to_seq_quad32 pb in let raw_quad2 = raw_quad_seq in let\n (raw_quad_seq:(seq quad32)) = va_if (plain_num_bytes > len128 `op_Multiply` 128 `op_Division`\n 8) (fun _ -> raw_quad1) (fun _ -> raw_quad2) in let (auth_quad_seq:(seq quad32)) =\n FStar.Seq.Base.append #quad32 raw_quad_seq (FStar.Seq.Base.create #quad32 1 length_quad) in\n va_get_vec 1 va_sM == Vale.AES.GCTR_BE_s.gctr_encrypt_block ctr_BE_1\n (Vale.AES.GHash_BE_s.ghash_BE h_BE auth_quad_seq) alg key 0))) ==> va_k va_sM (())))\n\n\nval va_wpProof_Gcm_blocks : alg:algorithm -> auth_b:buffer128 -> abytes_b:buffer128 ->\n in128_b:buffer128 -> out128_b:buffer128 -> inout_b:buffer128 -> iv_b:buffer128 -> key:(seq nat32)\n -> round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> gcm_struct_b:buffer64 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks alg auth_b abytes_b in128_b out128_b inout_b\n iv_b key round_keys keys_b hkeys_b gcm_struct_b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks alg) ([va_Mod_mem_heaplet\n 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20;\n va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14;\n va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8;\n va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec\n 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27;\n va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6;\n va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_blocks alg auth_b abytes_b in128_b out128_b inout_b iv_b key round_keys keys_b\n hkeys_b gcm_struct_b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_blocks (va_code_Gcm_blocks alg) va_s0 alg auth_b abytes_b\n in128_b out128_b inout_b iv_b key round_keys keys_b hkeys_b gcm_struct_b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 5 va_sM (va_update_mem_heaplet 2 va_sM\n (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 21 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 7 va_sM (va_update_reg 6 va_sM (va_update_reg 5\n va_sM (va_update_reg 4 va_sM (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3;\n va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_blocks (alg:algorithm) (auth_b:buffer128) (abytes_b:buffer128) (in128_b:buffer128)\n (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (gcm_struct_b:buffer64) : (va_quickCode unit\n (va_code_Gcm_blocks alg)) =\n (va_QProc (va_code_Gcm_blocks alg) ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2;\n va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18;\n va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg\n 3; va_Mod_mem]) (va_wp_Gcm_blocks alg auth_b abytes_b in128_b out128_b inout_b iv_b key\n round_keys keys_b hkeys_b gcm_struct_b) (va_wpProof_Gcm_blocks alg auth_b abytes_b in128_b\n out128_b inout_b iv_b key round_keys keys_b hkeys_b gcm_struct_b))\n#pop-options\n//--\n//-- Gcm_blocks_wrapped\n#push-options \"--z3rlimit 120\"\n\nval va_code_Gcm_blocks_wrapped : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_blocks_wrapped alg =\n (va_Block (va_CCons (va_code_Gcm_blocks alg) (va_CCons (va_Block (va_CNil ())) (va_CNil ()))))\n\nval va_codegen_success_Gcm_blocks_wrapped : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_blocks_wrapped alg =\n (va_pbool_and (va_codegen_success_Gcm_blocks alg) (va_ttrue ()))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_blocks_wrapped (va_mods:va_mods_t) (alg:algorithm) (auth_b:buffer128)\n (abytes_b:buffer128) (in128_b:buffer128) (out128_b:buffer128) (inout_b:buffer128)\n (iv_b:buffer128) (iv:supported_iv_BE) (key:(seq nat32)) (round_keys:(seq quad32))\n (keys_b:buffer128) (hkeys_b:buffer128) (expected_tag:(seq nat8)) (gcm_struct_b:buffer64) :\n (va_quickCode unit (va_code_Gcm_blocks_wrapped alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let\n (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0\n (va_get_mem_heaplet 3 va_s) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s) in va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 616 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Gcm_blocks alg auth_b abytes_b in128_b out128_b inout_b iv_b key round_keys keys_b\n hkeys_b gcm_struct_b) (fun (va_s:va_state) _ -> let (va_arg46:Vale.Def.Types_s.quad32) =\n Vale.Def.Words.Four_s.two_two_to_four #Vale.Def.Types_s.nat32 (Vale.Def.Words_s.Mktwo\n #(Vale.Def.Words_s.two Vale.Def.Types_s.nat32) (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32\n (8 `op_Multiply` auth_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply` auth_num_bytes\n `op_Division` pow2_32 `op_Modulus` pow2_32)) (Vale.Def.Words_s.Mktwo #Vale.Def.Types_s.nat32 (8\n `op_Multiply` plain_num_bytes `op_Modulus` pow2_32) (8 `op_Multiply` plain_num_bytes\n `op_Division` pow2_32 `op_Modulus` pow2_32))) in let (va_arg45:Vale.Def.Types_s.quad32) =\n va_get_vec 1 va_s in let (va_arg44:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2\n (va_get_mem_heaplet 0 va_s)) in let (va_arg43:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_old_s)) in let (va_arg42:Vale.AES.GCM_BE_s.supported_iv_BE) = iv in\n let (va_arg41:Prims.nat) = auth_num_bytes in let (va_arg40:Prims.nat) = plain_num_bytes in let\n (va_arg39:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s)\n inout_b) in let (va_arg38:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s)\n out128_b) in let (va_arg37:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5\n va_old_s) inout_b) in let (va_arg36:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) in128_b) in let (va_arg35:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6\n va_old_s) abytes_b) in let (va_arg34:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_old_s) auth_b) in let (va_arg33:(FStar.Seq.Base.seq Vale.Def.Words_s.nat32)) = key in let\n (va_arg32:Vale.AES.AES_common_s.algorithm) = alg in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 618 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_BE.gcm_blocks_dec_helper_simplified va_arg32 va_arg33 va_arg34\n va_arg35 va_arg36 va_arg37 va_arg38 va_arg39 va_arg40 va_arg41 va_arg42 va_arg43 va_arg44\n va_arg45 va_arg46) (let (auth_raw_quads:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_old_s) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6\n va_old_s) abytes_b)) in va_qAssertSquash va_range1\n \"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 630 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n ((fun a_1906 (s_1907:(FStar.Seq.Base.seq a_1906)) (i_1908:Prims.nat) (j_1909:Prims.nat) -> let\n (j_1869:Prims.nat) = j_1909 in Prims.b2t (Prims.op_AmpAmp (Prims.op_LessThanOrEqual i_1908\n j_1869) (Prims.op_LessThanOrEqual j_1869 (FStar.Seq.Base.length #a_1906 s_1907))))\n Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 auth_raw_quads)) 0\n auth_num_bytes) (fun _ -> let (auth_bytes:(FStar.Seq.Base.seq Vale.Def.Words_s.nat8)) =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 auth_raw_quads)) 0\n auth_num_bytes in let (va_arg31:Vale.Def.Types_s.quad32) =\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_old_s)) in let (va_arg30:Vale.AES.GCM_BE_s.supported_iv_BE) = iv in\n let (va_arg29:Prims.nat) = plain_num_bytes in let (va_arg28:(FStar.Seq.Base.seq\n Vale.Def.Words_s.nat8)) = expected_tag in let (va_arg27:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s) inout_b) in let (va_arg26:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s) out128_b) in let (va_arg25:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_old_s) inout_b) in let (va_arg24:(FStar.Seq.Base.seq\n Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_old_s) in128_b) in let (va_arg23:(FStar.Seq.Base.seq\n Vale.Def.Words_s.nat32)) = key in let (va_arg22:Vale.AES.AES_common_s.algorithm) = alg in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 631 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCM_BE.gcm_blocks_helper_dec_simplified va_arg22 va_arg23 va_arg24\n va_arg25 va_arg26 va_arg27 auth_bytes va_arg28 va_arg29 va_arg30 va_arg31) (va_QEmpty (())))))))\n\n\nval va_lemma_Gcm_blocks_wrapped : va_b0:va_code -> va_s0:va_state -> alg:algorithm ->\n auth_b:buffer128 -> abytes_b:buffer128 -> in128_b:buffer128 -> out128_b:buffer128 ->\n inout_b:buffer128 -> iv_b:buffer128 -> iv:supported_iv_BE -> key:(seq nat32) -> round_keys:(seq\n quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> expected_tag:(seq nat8) ->\n gcm_struct_b:buffer64\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks_wrapped alg) va_s0 /\\ va_get_ok va_s0 /\\\n (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 0 (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in\n Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem_heaplet 3 va_s0) (va_get_reg 25 va_s0)\n gcm_struct_b 12 (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem_heaplet 1 va_s0) auth_ptr auth_b auth_len (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 6 va_s0) abytes_ptr abytes_b 1\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 2\n va_s0) iv_ptr iv_b 1 (va_get_mem_layout va_s0) Public /\\ Vale.PPC64LE.Decls.validSrcAddrs128\n (va_get_mem_heaplet 1 va_s0) in128_ptr in128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) out128_ptr out128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 5\n va_s0) inout_ptr inout_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b;\n hkeys_b; in128_b; out128_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 out128_b\n ([keys_b; hkeys_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 inout_b ([keys_b;\n hkeys_b; out128_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b ==\n out128_b) /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply`\n len128 < pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64\n /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ plain_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem_heaplet 0 va_s0) + 128 < pow2_64 /\\\n (va_mul_nat len128 (128 `op_Division` 8) <= plain_num_bytes /\\ plain_num_bytes < va_mul_nat\n len128 (128 `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division`\n 8) <= auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ aes_reqs alg key round_keys keys_b keys_ptr (va_get_mem_heaplet 0 va_s0)\n (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0)) /\\ (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_s0)) in let h_BE =\n Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0\n 0 0) in iv_BE == Vale.AES.GCM_BE_s.compute_iv_BE h_BE iv))))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 0 (va_get_mem_heaplet 3 va_s0) in let (in128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1 (va_get_mem_heaplet 3 va_s0) in let\n (out128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2\n (va_get_mem_heaplet 3 va_s0) in let (len128:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3 (va_get_mem_heaplet 3 va_s0) in let\n (inout_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4\n (va_get_mem_heaplet 3 va_s0) in let (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 5 (va_get_mem_heaplet 3 va_s0) in let\n (auth_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6\n (va_get_mem_heaplet 3 va_s0) in let (auth_len:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7 (va_get_mem_heaplet 3 va_s0) in let\n (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8\n (va_get_mem_heaplet 3 va_s0) in let (iv_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9 (va_get_mem_heaplet 3 va_s0) in let\n (keys_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10\n (va_get_mem_heaplet 3 va_s0) in let (h_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11 (va_get_mem_heaplet 3 va_s0) in\n Vale.PPC64LE.Decls.modifies_buffer128 out128_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet\n 1 va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0)\n (va_get_mem_heaplet 2 va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ plain_num_bytes < pow2_32 /\\\n auth_num_bytes < pow2_32 /\\ (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_s0)) in let auth_raw_quads =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) auth_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6 va_s0)\n abytes_b)) in let auth_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 auth_raw_quads)) 0 auth_num_bytes in let plain_raw_quads =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in128_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b)) in let plain_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 plain_raw_quads)) 0 plain_num_bytes in let cipher_raw_quads =\n FStar.Seq.Base.append #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out128_b))\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 5 va_sM)\n inout_b)) in let cipher_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 cipher_raw_quads)) 0 plain_num_bytes in l_and (l_and (l_and\n (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 auth_bytes < pow2_32) (FStar.Seq.Base.length\n #Vale.Def.Words_s.nat8 plain_bytes < pow2_32)) (cipher_bytes == __proj__Mktuple2__item___1\n #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv plain_bytes auth_bytes expected_tag)))\n (Vale.Arch.Types.be_quad32_to_bytes (va_get_vec 1 va_sM) == Vale.AES.GCM_BE.gcm_decrypt_BE_tag\n alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv plain_bytes auth_bytes))) /\\\n va_state_eq va_sM (va_update_mem_heaplet 5 va_sM (va_update_mem_heaplet 2 va_sM\n (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 21 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 7 va_sM (va_update_reg 6 va_sM (va_update_reg 5\n va_sM (va_update_reg 4 va_sM (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0))))))))))))))))))))))))))))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_blocks_wrapped va_b0 va_s0 alg auth_b abytes_b in128_b out128_b inout_b iv_b iv\n key round_keys keys_b hkeys_b expected_tag gcm_struct_b =\n let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem] in\n let va_qc = va_qcode_Gcm_blocks_wrapped va_mods alg auth_b abytes_b in128_b out128_b inout_b iv_b\n iv key round_keys keys_b hkeys_b expected_tag gcm_struct_b in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_blocks_wrapped alg) va_qc va_s0\n (fun va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 495 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_ok va_sM) /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 590 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 out128_b (va_get_mem_heaplet 1 va_s0)\n (va_get_mem_heaplet 1 va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 591 column 52 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0) (va_get_mem_heaplet 2\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 592 column 55 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet\n 5 va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 595 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (plain_num_bytes < pow2_32) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 596 column 38 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (auth_num_bytes < pow2_32) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 598 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_s0)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 600 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let auth_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n auth_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet\n 6 va_s0) abytes_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 601 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let auth_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 auth_raw_quads)) 0 auth_num_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 602 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let plain_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 603 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let plain_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 plain_raw_quads)) 0 plain_num_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 604 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let cipher_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 605 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (let cipher_bytes = FStar.Seq.Base.slice #Vale.Def.Words_s.nat8\n (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE (Vale.Def.Words.Seq_s.seq_four_to_seq_BE\n #Vale.Def.Words_s.nat32 cipher_raw_quads)) 0 plain_num_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 614 column 52 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (l_and (l_and (l_and (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 auth_bytes < pow2_32)\n (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 plain_bytes < pow2_32)) (cipher_bytes ==\n __proj__Mktuple2__item___1 #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool\n (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv\n plain_bytes auth_bytes expected_tag))) (Vale.Arch.Types.be_quad32_to_bytes (va_get_vec 1 va_sM)\n == Vale.AES.GCM_BE.gcm_decrypt_BE_tag alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key)\n iv plain_bytes auth_bytes))))))))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_ok;\n va_Mod_mem]) va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Gcm_blocks_wrapped (alg:algorithm) (auth_b:buffer128) (abytes_b:buffer128)\n (in128_b:buffer128) (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128)\n (iv:supported_iv_BE) (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128)\n (hkeys_b:buffer128) (expected_tag:(seq nat8)) (gcm_struct_b:buffer64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in Vale.PPC64LE.Decls.validSrcAddrs64 (va_get_mem_heaplet 3 va_s0)\n (va_get_reg 25 va_s0) gcm_struct_b 12 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) auth_ptr auth_b auth_len\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 6\n va_s0) abytes_ptr abytes_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 2 va_s0) iv_ptr iv_b 1\n (va_get_mem_layout va_s0) Public /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1\n va_s0) in128_ptr in128_b len128 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) out128_ptr out128_b len128\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 5\n va_s0) inout_ptr inout_b 1 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) h_ptr hkeys_b 3\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.buffer_disjoints128 iv_b ([keys_b;\n hkeys_b; in128_b; out128_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 out128_b\n ([keys_b; hkeys_b; inout_b]) /\\ Vale.PPC64LE.Decls.buffer_disjoints128 inout_b ([keys_b;\n hkeys_b; out128_b]) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in128_b out128_b \\/ in128_b ==\n out128_b) /\\ auth_ptr + 16 `op_Multiply` auth_len < pow2_64 /\\ in128_ptr + 16 `op_Multiply`\n len128 < pow2_64 /\\ out128_ptr + 16 `op_Multiply` len128 < pow2_64 /\\ inout_ptr + 16 < pow2_64\n /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 auth_b == auth_len /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 abytes_b == 1 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out128_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in128_b == len128 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 inout_b == 1 /\\ plain_num_bytes\n < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ Vale.PPC64LE.Memory.buffer_addr\n #Vale.PPC64LE.Memory.vuint128 keys_b (va_get_mem_heaplet 0 va_s0) + 128 < pow2_64 /\\\n (va_mul_nat len128 (128 `op_Division` 8) <= plain_num_bytes /\\ plain_num_bytes < va_mul_nat\n len128 (128 `op_Division` 8) + 128 `op_Division` 8) /\\ (va_mul_nat auth_len (128 `op_Division`\n 8) <= auth_num_bytes /\\ auth_num_bytes < va_mul_nat auth_len (128 `op_Division` 8) + 128\n `op_Division` 8) /\\ aes_reqs alg key round_keys keys_b keys_ptr (va_get_mem_heaplet 0 va_s0)\n (va_get_mem_layout va_s0) /\\ Vale.AES.GHash_BE.hkeys_reqs_priv\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 0 va_s0)\n hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 0)) /\\ (let iv_BE = Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.PPC64LE.Decls.buffer128_read iv_b 0 (va_get_mem_heaplet 2 va_s0)) in let h_BE =\n Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0\n 0 0) in iv_BE == Vale.AES.GCM_BE_s.compute_iv_BE h_BE iv)) /\\ (forall (va_x_mem:vale_heap)\n (va_x_r3:nat64) (va_x_r4:nat64) (va_x_r5:nat64) (va_x_r6:nat64) (va_x_r7:nat64) (va_x_r8:nat64)\n (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r26:nat64) (va_x_r27:nat64) (va_x_r28:nat64)\n (va_x_r29:nat64) (va_x_r30:nat64) (va_x_r31:nat64) (va_x_v0:quad32) (va_x_v1:quad32)\n (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32)\n (va_x_v7:quad32) (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32)\n (va_x_v12:quad32) (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32)\n (va_x_v17:quad32) (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32) (va_x_v21:quad32)\n (va_x_cr0:cr0_t) (va_x_heap1:vale_heap) (va_x_heap2:vale_heap) (va_x_heap5:vale_heap) . let\n va_sM = va_upd_mem_heaplet 5 va_x_heap5 (va_upd_mem_heaplet 2 va_x_heap2 (va_upd_mem_heaplet 1\n va_x_heap1 (va_upd_cr0 va_x_cr0 (va_upd_vec 21 va_x_v21 (va_upd_vec 20 va_x_v20 (va_upd_vec 19\n va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16 (va_upd_vec 15\n va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12 (va_upd_vec 11\n va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7\n va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3\n (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 31 va_x_r31\n (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29 (va_upd_reg 28 va_x_r28 (va_upd_reg 27 va_x_r27\n (va_upd_reg 26 va_x_r26 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9 (va_upd_reg 8 va_x_r8\n (va_upd_reg 7 va_x_r7 (va_upd_reg 6 va_x_r6 (va_upd_reg 5 va_x_r5 (va_upd_reg 4 va_x_r4\n (va_upd_reg 3 va_x_r3 (va_upd_mem va_x_mem va_s0)))))))))))))))))))))))))))))))))))))))) in\n va_get_ok va_sM /\\ (let (abytes_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 0 (va_get_mem_heaplet 3 va_s0) in let\n (in128_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 1\n (va_get_mem_heaplet 3 va_s0) in let (out128_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 2 (va_get_mem_heaplet 3 va_s0) in let\n (len128:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 3\n (va_get_mem_heaplet 3 va_s0) in let (inout_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 4 (va_get_mem_heaplet 3 va_s0) in let\n (plain_num_bytes:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b\n 5 (va_get_mem_heaplet 3 va_s0) in let (auth_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 6 (va_get_mem_heaplet 3 va_s0) in let\n (auth_len:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 7\n (va_get_mem_heaplet 3 va_s0) in let (auth_num_bytes:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 8 (va_get_mem_heaplet 3 va_s0) in let\n (iv_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 9\n (va_get_mem_heaplet 3 va_s0) in let (keys_ptr:Vale.PPC64LE.Machine_s.nat64) =\n Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 10 (va_get_mem_heaplet 3 va_s0) in let\n (h_ptr:Vale.PPC64LE.Machine_s.nat64) = Vale.PPC64LE.Decls.buffer64_read gcm_struct_b 11\n (va_get_mem_heaplet 3 va_s0) in Vale.PPC64LE.Decls.modifies_buffer128 out128_b\n (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\\\n Vale.PPC64LE.Decls.modifies_buffer128 iv_b (va_get_mem_heaplet 2 va_s0) (va_get_mem_heaplet 2\n va_sM) /\\ Vale.PPC64LE.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0)\n (va_get_mem_heaplet 5 va_sM) /\\ plain_num_bytes < pow2_32 /\\ auth_num_bytes < pow2_32 /\\ (let\n iv_BE = Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read iv_b 0\n (va_get_mem_heaplet 2 va_s0)) in let auth_raw_quads = FStar.Seq.Base.append\n #Vale.Def.Types_s.quad32 (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) auth_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 6 va_s0) abytes_b)) in let auth_bytes =\n FStar.Seq.Base.slice #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 auth_raw_quads)) 0\n auth_num_bytes in let plain_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b)) in let plain_bytes = FStar.Seq.Base.slice\n #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 plain_raw_quads)) 0\n plain_num_bytes in let cipher_raw_quads = FStar.Seq.Base.append #Vale.Def.Types_s.quad32\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out128_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b)) in let cipher_bytes = FStar.Seq.Base.slice\n #Vale.Def.Words_s.nat8 (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE\n (Vale.Def.Words.Seq_s.seq_four_to_seq_BE #Vale.Def.Words_s.nat32 cipher_raw_quads)) 0\n plain_num_bytes in l_and (l_and (l_and (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 auth_bytes\n < pow2_32) (FStar.Seq.Base.length #Vale.Def.Words_s.nat8 plain_bytes < pow2_32)) (cipher_bytes\n == __proj__Mktuple2__item___1 #(FStar.Seq.Base.seq Vale.Def.Types_s.nat8) #bool\n (Vale.AES.GCM_BE_s.gcm_decrypt_BE alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key) iv\n plain_bytes auth_bytes expected_tag))) (Vale.Arch.Types.be_quad32_to_bytes (va_get_vec 1 va_sM)\n == Vale.AES.GCM_BE.gcm_decrypt_BE_tag alg (Vale.Def.Words.Seq_s.seq_nat32_to_seq_nat8_BE key)\n iv plain_bytes auth_bytes))) ==> va_k va_sM (())))\n\n\nval va_wpProof_Gcm_blocks_wrapped : alg:algorithm -> auth_b:buffer128 -> abytes_b:buffer128 ->\n in128_b:buffer128 -> out128_b:buffer128 -> inout_b:buffer128 -> iv_b:buffer128 ->\n iv:supported_iv_BE -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> expected_tag:(seq nat8) -> gcm_struct_b:buffer64 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks_wrapped alg auth_b abytes_b in128_b out128_b\n inout_b iv_b iv key round_keys keys_b hkeys_b expected_tag gcm_struct_b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks_wrapped alg)\n ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 21;\n va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15;\n va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9;\n va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec\n 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28;\n va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 7;\n va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0,\n va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_blocks_wrapped alg auth_b abytes_b in128_b out128_b inout_b iv_b iv key\n round_keys keys_b hkeys_b expected_tag gcm_struct_b va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_blocks_wrapped (va_code_Gcm_blocks_wrapped alg) va_s0 alg\n auth_b abytes_b in128_b out128_b inout_b iv_b iv key round_keys keys_b hkeys_b expected_tag\n gcm_struct_b in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_mem_heaplet 5 va_sM (va_update_mem_heaplet 2 va_sM\n (va_update_mem_heaplet 1 va_sM (va_update_cr0 va_sM (va_update_vec 21 va_sM (va_update_vec 20\n va_sM (va_update_vec 19 va_sM (va_update_vec 18 va_sM (va_update_vec 17 va_sM (va_update_vec 16\n va_sM (va_update_vec 15 va_sM (va_update_vec 14 va_sM (va_update_vec 13 va_sM (va_update_vec 12\n va_sM (va_update_vec 11 va_sM (va_update_vec 10 va_sM (va_update_vec 9 va_sM (va_update_vec 8\n va_sM (va_update_vec 7 va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4\n va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0\n va_sM (va_update_reg 31 va_sM (va_update_reg 30 va_sM (va_update_reg 29 va_sM (va_update_reg 28\n va_sM (va_update_reg 27 va_sM (va_update_reg 26 va_sM (va_update_reg 10 va_sM (va_update_reg 9\n va_sM (va_update_reg 8 va_sM (va_update_reg 7 va_sM (va_update_reg 6 va_sM (va_update_reg 5\n va_sM (va_update_reg 4 va_sM (va_update_reg 3 va_sM (va_update_ok va_sM (va_update_mem va_sM\n va_s0)))))))))))))))))))))))))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2; va_Mod_mem_heaplet 1;\n va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18; va_Mod_vec 17;\n va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12; va_Mod_vec 11;\n va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec\n 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 31; va_Mod_reg 30;\n va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10; va_Mod_reg 9;\n va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg 3;\n va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_blocks_wrapped (alg:algorithm) (auth_b:buffer128) (abytes_b:buffer128)\n (in128_b:buffer128) (out128_b:buffer128) (inout_b:buffer128) (iv_b:buffer128)\n (iv:supported_iv_BE) (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128)\n (hkeys_b:buffer128) (expected_tag:(seq nat8)) (gcm_struct_b:buffer64) : (va_quickCode unit\n (va_code_Gcm_blocks_wrapped alg)) =\n (va_QProc (va_code_Gcm_blocks_wrapped alg) ([va_Mod_mem_heaplet 5; va_Mod_mem_heaplet 2;\n va_Mod_mem_heaplet 1; va_Mod_cr0; va_Mod_vec 21; va_Mod_vec 20; va_Mod_vec 19; va_Mod_vec 18;\n va_Mod_vec 17; va_Mod_vec 16; va_Mod_vec 15; va_Mod_vec 14; va_Mod_vec 13; va_Mod_vec 12;\n va_Mod_vec 11; va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 7; va_Mod_vec 6;\n va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg\n 31; va_Mod_reg 30; va_Mod_reg 29; va_Mod_reg 28; va_Mod_reg 27; va_Mod_reg 26; va_Mod_reg 10;\n va_Mod_reg 9; va_Mod_reg 8; va_Mod_reg 7; va_Mod_reg 6; va_Mod_reg 5; va_Mod_reg 4; va_Mod_reg\n 3; va_Mod_mem]) (va_wp_Gcm_blocks_wrapped alg auth_b abytes_b in128_b out128_b inout_b iv_b iv\n key round_keys keys_b hkeys_b expected_tag gcm_struct_b) (va_wpProof_Gcm_blocks_wrapped alg\n auth_b abytes_b in128_b out128_b inout_b iv_b iv key round_keys keys_b hkeys_b expected_tag\n gcm_struct_b))\n#pop-options\n//--\n//-- Nat64Equal\n\nval va_code_Nat64Equal : va_dummy:unit -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Nat64Equal () =\n (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 5) 1) (va_CCons (va_code_AddCarry\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 5)) (va_CCons (va_code_LoadImm64\n (va_op_reg_opr_reg 3) 0) (va_CCons (va_code_AddExtended (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3)) (va_CCons (va_code_Xor (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 5) (va_op_reg_opr_reg 3)) (va_CNil ())))))))\n\nval va_codegen_success_Nat64Equal : va_dummy:unit -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Nat64Equal () =\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 5) 1) (va_pbool_and\n (va_codegen_success_AddCarry (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 5))\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 3) 0) (va_pbool_and\n (va_codegen_success_AddExtended (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg\n 3)) (va_pbool_and (va_codegen_success_Xor (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 5)\n (va_op_reg_opr_reg 3)) (va_ttrue ()))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Nat64Equal (va_mods:va_mods_t) : (va_quickCode unit (va_code_Nat64Equal ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 646 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 5) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 647 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_AddCarry (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 5)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 648 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_LoadImm64 (va_op_reg_opr_reg 3) 0) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 649 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_AddExtended (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 650 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_quick_Xor (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 5) (va_op_reg_opr_reg 3)) (fun\n (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 651 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.AES.Types_helpers.lemma_BitwiseXorWithZero64 1) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 652 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (fun (_:unit) -> Vale.Arch.Types.lemma_BitwiseXorCancel64 1) (va_QEmpty (()))))))))))\n\n\nval va_lemma_Nat64Equal : va_b0:va_code -> va_s0:va_state\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Nat64Equal ()) va_s0 /\\ va_get_ok va_s0))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\ (if\n (va_get_reg 4 va_s0 = 18446744073709551615) then (va_get_reg 3 va_sM = 0) else (va_get_reg 3\n va_sM = 1)) /\\ va_state_eq va_sM (va_update_xer va_sM (va_update_reg 5 va_sM (va_update_reg 3\n va_sM (va_update_ok va_sM va_s0))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Nat64Equal va_b0 va_s0 =\n let (va_mods:va_mods_t) = [va_Mod_xer; va_Mod_reg 5; va_Mod_reg 3; va_Mod_ok] in\n let va_qc = va_qcode_Nat64Equal va_mods in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Nat64Equal ()) va_qc va_s0 (fun va_s0\n va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 639 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_get_ok va_sM) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 644 column 71 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GCMdecrypt.vaf *****\"\n (va_if (va_get_reg 4 va_s0 = 18446744073709551615) (fun _ -> va_get_reg 3 va_sM = 0) (fun _ ->\n va_get_reg 3 va_sM = 1))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_xer; va_Mod_reg 5; va_Mod_reg 3; va_Mod_ok]) va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Nat64Equal (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (forall (va_x_r3:nat64) (va_x_r5:nat64) (va_x_xer:xer_t) . let va_sM =\n va_upd_xer va_x_xer (va_upd_reg 5 va_x_r5 (va_upd_reg 3 va_x_r3 va_s0)) in va_get_ok va_sM /\\\n va_if (va_get_reg 4 va_s0 = 18446744073709551615) (fun _ -> va_get_reg 3 va_sM = 0) (fun _ ->\n va_get_reg 3 va_sM = 1) ==> va_k va_sM (())))\n\n\nval va_wpProof_Nat64Equal : va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Nat64Equal va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Nat64Equal ()) ([va_Mod_xer;\n va_Mod_reg 5; va_Mod_reg 3]) va_s0 va_k ((va_sM, va_f0, va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Nat64Equal va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal ()) va_s0 in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_xer va_sM (va_update_reg 5 va_sM (va_update_reg 3 va_sM\n (va_update_ok va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_xer; va_Mod_reg 5; va_Mod_reg 3]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Nat64Equal () : (va_quickCode unit (va_code_Nat64Equal ())) =\n (va_QProc (va_code_Nat64Equal ()) ([va_Mod_xer; va_Mod_reg 5; va_Mod_reg 3]) va_wp_Nat64Equal\n va_wpProof_Nat64Equal)\n//--\n//-- VectorEqual\n\nval va_code_VectorEqual : va_dummy:unit -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_VectorEqual () =\n (va_Block (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 1)) (va_CCons (va_code_Mfvsrld (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0))\n (va_CCons (va_code_Nat64Equal ()) (va_CCons (va_code_Move (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 3)) (va_CCons (va_code_Mfvsrd (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0))\n (va_CCons (va_code_Nat64Equal ()) (va_CCons (va_code_Add (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (va_CNil ())))))))))\n\nval va_codegen_success_VectorEqual : va_dummy:unit -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_VectorEqual () =\n (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Mfvsrld (va_op_reg_opr_reg 4)\n (va_op_vec_opr_vec 0)) (va_pbool_and (va_codegen_success_Nat64Equal ()) (va_pbool_and\n (va_codegen_success_Move (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (va_pbool_and\n (va_codegen_success_Mfvsrd (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0)) (va_pbool_and\n (va_codegen_success_Nat64Equal ()) (va_pbool_and (va_codegen_success_Add (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (va_ttrue ()))))))))\n\n[@ \"opaque_to_smt\" va_qattr]", "sketch": [ "Step 1: This definition is about creating a quick code function that checks if two vectors are equal.\nStep 2: The implementation will involve invoking the `va_code_VectorEqual` function within the `va_quickCode` context, ensuring it operates on the provided module state `va_mods`.", "Step 1: This definition is about creating a quick code function that checks if two vectors are equal.\nStep 2: The implementation will involve invoking the `va_code_VectorEqual` function within the `va_quickCode` context, ensuring that the function operates correctly within the given module constraints.", "Step 1: The definition is about creating a quick code function `va_qcode_VectorEqual` that takes a module parameter `va_mods` and returns a quick code unit type for the function `va_code_VectorEqual`.\nStep 2: The implementation involves defining the function `va_qcode_VectorEqual` which will use the `va_mods` parameter to produce the required quick code unit type for `va_code_VectorEqual`.", "Step 1: The definition `va_qcode_VectorEqual` is about creating a quick code representation for the `VectorEqual` function. This function checks if two vectors are equal.\nStep 2: The implementation will involve invoking the `va_code_VectorEqual` function within the `va_quickCode` monad, ensuring that the necessary modifications (`va_mods`) are applied.", "Step 1: This definition is about creating a quick code function that checks if two vectors are equal.\nStep 2: The implementation involves defining a function that takes `va_mods` as an argument and returns a `va_quickCode` unit, which internally calls `va_code_VectorEqual`.", "Step 1: This definition is about creating a quick code function for checking the equality of two vectors.\nStep 2: The implementation will involve invoking the `va_code_VectorEqual` function within the `va_quickCode` context, ensuring that the function operates correctly within the given module constraints.", "Step 1: This definition is about creating a quick code function that verifies the equality of two vectors.\nStep 2: The implementation will use the `va_code_VectorEqual` function to perform the actual comparison and return a unit type wrapped in a `va_quickCode`.", "Step 1: The definition is about creating a quick code function that checks if two vectors are equal.\nStep 2: The implementation involves defining a function `va_qcode_VectorEqual` that takes `va_mods` as an argument and returns a `va_quickCode` unit, which internally calls `va_code_VectorEqual`.", "Step 1: The definition `va_qcode_VectorEqual` is about verifying that two vectors are equal.\nStep 2: The implementation will use the `va_quickCode` construct to encapsulate the verification logic, which will internally call `va_code_VectorEqual` to perform the actual equality check.", "Step 1: The definition `va_qcode_VectorEqual` is about creating a quick code wrapper for the `va_code_VectorEqual` function. This function checks if two vectors are equal.\nStep 2: The implementation will use the `va_quickCode` construct to wrap the `va_code_VectorEqual` function, ensuring it adheres to the required type signature." ], "generated_solution": [ "let va_qcode_VectorEqual (va_mods: va_mods_t) : (va_quickCode unit (va_code_VectorEqual ())) =\n va_quickCode (va_code_VectorEqual ()) va_mods", "let va_qcode_VectorEqual (va_mods: va_mods_t) : (va_quickCode unit (va_code_VectorEqual ())) =\n va_quickCode (va_code_VectorEqual ())", "let va_qcode_VectorEqual (va_mods: va_mods_t) : (va_quickCode unit (va_code_VectorEqual ())) =\n (* Implementation details here *)\n ...", "let va_qcode_VectorEqual (va_mods: va_mods_t) : (va_quickCode unit (va_code_VectorEqual ())) =\n va_quickCode (va_code_VectorEqual ()) va_mods", "let va_qcode_VectorEqual (va_mods: va_mods_t) : (va_quickCode unit (va_code_VectorEqual ())) =\n va_quickCode (va_code_VectorEqual ())", "let va_qcode_VectorEqual (va_mods: va_mods_t) : (va_quickCode unit (va_code_VectorEqual ())) =\n va_quickCode (va_code_VectorEqual ())", "let va_qcode_VectorEqual va_mods =\n va_quickCode (va_code_VectorEqual ()) va_mods", "let va_qcode_VectorEqual (va_mods: va_mods_t) : (va_quickCode unit (va_code_VectorEqual ())) =\n va_quickCode (va_code_VectorEqual ())", "let va_qcode_VectorEqual va_mods =\n va_quickCode (va_code_VectorEqual ())", "let va_qcode_VectorEqual (va_mods: va_mods_t) : (va_quickCode unit (va_code_VectorEqual ())) =\n va_quickCode (va_code_VectorEqual ())" ] }, { "file_name": "Lib.Exponentiation.Definition.fst", "name": "Lib.Exponentiation.Definition.lemma_cancellation", "opens_and_abbrevs": [ { "abbrev": "Loops", "full_module": "Lib.LoopCombinators" }, { "open": "FStar.Mul" }, { "abbrev": "Loops", "full_module": "Lib.LoopCombinators" }, { "open": "FStar.Mul" }, { "open": "Lib.Exponentiation" }, { "open": "Lib.Exponentiation" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 0, "max_fuel": 0, "initial_ifuel": 0, "max_ifuel": 0, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val lemma_cancellation: #t:Type -> k:abelian_group t -> a:t -> b:t -> c:t -> Lemma\n (requires cm.mul a b == cm.mul a c)\n (ensures b == c)", "source_definition": "let lemma_cancellation #t k a b c =\n assert (cm.mul (inverse a) (cm.mul a b) == cm.mul (inverse a) (cm.mul a c));\n lemma_mul_cancel_inverse #t k a b;\n lemma_mul_cancel_inverse #t k a c", "source_range": { "start_line": 36, "start_col": 0, "end_line": 39, "end_col": 35 }, "interleaved": false, "definition": "fun k a b c ->\n assert (Mkcomm_monoid?.mul Lib.Exponentiation.Definition.cm\n (Lib.Exponentiation.Definition.inverse a)\n (Mkcomm_monoid?.mul Lib.Exponentiation.Definition.cm a b) ==\n Mkcomm_monoid?.mul Lib.Exponentiation.Definition.cm\n (Lib.Exponentiation.Definition.inverse a)\n (Mkcomm_monoid?.mul Lib.Exponentiation.Definition.cm a c));\n Lib.Exponentiation.Definition.lemma_mul_cancel_inverse k a b;\n Lib.Exponentiation.Definition.lemma_mul_cancel_inverse k a c", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "Lib.Exponentiation.Definition.abelian_group", "Lib.Exponentiation.Definition.lemma_mul_cancel_inverse", "Prims.unit", "Prims._assert", "Prims.eq2", "Lib.Exponentiation.Definition.__proj__Mkcomm_monoid__item__mul", "Lib.Exponentiation.Definition.cm", "Lib.Exponentiation.Definition.inverse" ], "proof_features": [], "is_simple_lemma": true, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "k: Lib.Exponentiation.Definition.abelian_group t -> a: t -> b: t -> c: t\n -> FStar.Pervasives.Lemma\n (requires\n Mkcomm_monoid?.mul Lib.Exponentiation.Definition.cm a b ==\n Mkcomm_monoid?.mul Lib.Exponentiation.Definition.cm a c) (ensures b == c)", "prompt": "let lemma_cancellation #t k a b c =\n ", "expected_response": "assert (cm.mul (inverse a) (cm.mul a b) == cm.mul (inverse a) (cm.mul a c));\nlemma_mul_cancel_inverse #t k a b;\nlemma_mul_cancel_inverse #t k a c", "source": { "project_name": "hacl-star", "file_name": "lib/Lib.Exponentiation.Definition.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Lib.Exponentiation.Definition.fst", "checked_file": "dataset/Lib.Exponentiation.Definition.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/Lib.LoopCombinators.fsti.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked", "dataset/FStar.Calc.fsti.checked" ] }, "definitions_in_context": [ "let lemma_inverse_one #t k =\n lemma_inverse k.cm.one;\n assert (k.cm.mul (inverse cm.one) cm.one == cm.one);\n k.cm.lemma_one (inverse cm.one);\n assert (inverse k.cm.one == cm.one)", "comm_monoid", "comm_monoid", "class comm_monoid (t:Type) = {\n one: t;\n mul: t -> t -> t;\n lemma_one: a:t -> Lemma (mul a one == a);\n lemma_mul_assoc: a:t -> b:t -> c:t -> Lemma (mul (mul a b) c == mul a (mul b c));\n lemma_mul_comm: a:t -> b:t -> Lemma (mul a b == mul b a)\n }", "class comm_monoid (t:Type) = {\n one: t;\n mul: t -> t -> t;\n lemma_one: a:t -> Lemma (mul a one == a);\n lemma_mul_assoc: a:t -> b:t -> c:t -> Lemma (mul (mul a b) c == mul a (mul b c));\n lemma_mul_comm: a:t -> b:t -> Lemma (mul a b == mul b a)\n }", "class comm_monoid (t:Type) = {\n one: t;\n mul: t -> t -> t;\n lemma_one: a:t -> Lemma (mul a one == a);\n lemma_mul_assoc: a:t -> b:t -> c:t -> Lemma (mul (mul a b) c == mul a (mul b c));\n lemma_mul_comm: a:t -> b:t -> Lemma (mul a b == mul b a)\n }", "class comm_monoid (t:Type) = {\n one: t;\n mul: t -> t -> t;\n lemma_one: a:t -> Lemma (mul a one == a);\n lemma_mul_assoc: a:t -> b:t -> c:t -> Lemma (mul (mul a b) c == mul a (mul b c));\n lemma_mul_comm: a:t -> b:t -> Lemma (mul a b == mul b a)\n }", "class comm_monoid (t:Type) = {\n one: t;\n mul: t -> t -> t;\n lemma_one: a:t -> Lemma (mul a one == a);\n lemma_mul_assoc: a:t -> b:t -> c:t -> Lemma (mul (mul a b) c == mul a (mul b c));\n lemma_mul_comm: a:t -> b:t -> Lemma (mul a b == mul b a)\n }", "one", "one", "mul", "mul", "lemma_one", "lemma_one", "lemma_mul_assoc", "lemma_mul_assoc", "val lemma_mul_cancel_inverse: #t:Type -> k:abelian_group t -> a:t -> b:t ->\n Lemma (cm.mul (inverse a) (cm.mul a b) == b)", "lemma_mul_comm", "lemma_mul_comm", "let lemma_mul_cancel_inverse #t k a b =\n calc (==) {\n cm.mul (inverse a) (cm.mul a b);\n (==) { cm.lemma_mul_assoc (inverse a) a b }\n cm.mul (cm.mul (inverse a) a) b;\n (==) { lemma_inverse a }\n cm.mul cm.one b;\n (==) { cm.lemma_mul_comm cm.one b }\n cm.mul b cm.one;\n (==) { cm.lemma_one b }\n b;\n }", "abelian_group", "abelian_group", "class abelian_group (t:Type) = {\n cm:comm_monoid t;\n inverse: t -> t;\n lemma_inverse: a:t -> Lemma (mul (inverse a) a == one)\n }", "class abelian_group (t:Type) = {\n cm:comm_monoid t;\n inverse: t -> t;\n lemma_inverse: a:t -> Lemma (mul (inverse a) a == one)\n }", "class abelian_group (t:Type) = {\n cm:comm_monoid t;\n inverse: t -> t;\n lemma_inverse: a:t -> Lemma (mul (inverse a) a == one)\n }", "cm", "cm", "inverse", "inverse", "lemma_inverse", "lemma_inverse", "let sqr (#t:Type) (k:comm_monoid t) (a:t) : t = mul a a", "let rec pow (#t:Type) (k:comm_monoid t) (x:t) (n:nat) : t =\n if n = 0 then one\n else mul x (pow k x (n - 1))", "val lemma_cancellation: #t:Type -> k:abelian_group t -> a:t -> b:t -> c:t -> Lemma\n (requires cm.mul a b == cm.mul a c)\n (ensures b == c)" ], "closest": [ "val lemma_div_mod_prime_cancel: #m:prime -> a:nat_mod m -> b:nat_mod m -> c:nat_mod m{c <> 0} ->\n Lemma (div_mod (mul_mod a c) (mul_mod c b) == div_mod a b)\nlet lemma_div_mod_prime_cancel #m a b c =\n calc (==) {\n mul_mod (mul_mod a c) (inv_mod (mul_mod c b));\n (==) { lemma_inv_mod_both c b }\n mul_mod (mul_mod a c) (mul_mod (inv_mod c) (inv_mod b));\n (==) { lemma_mul_mod_assoc (mul_mod a c) (inv_mod c) (inv_mod b) }\n mul_mod (mul_mod (mul_mod a c) (inv_mod c)) (inv_mod b);\n (==) { lemma_mul_mod_assoc a c (inv_mod c) }\n mul_mod (mul_mod a (mul_mod c (inv_mod c))) (inv_mod b);\n (==) { lemma_div_mod_prime c }\n mul_mod (mul_mod a 1) (inv_mod b);\n (==) { Math.Lemmas.small_mod a m }\n mul_mod a (inv_mod b);\n }", "val lemma_fmul_assoc1: a:elem -> b:elem -> c:elem ->\n Lemma (a *% b *% c == a *% c *% b)\nlet lemma_fmul_assoc1 a b c =\n assert (a *% b *% c == a *% c *% b) by (ed25519_semiring ())", "val lemma_div_mod_eq_mul_mod (a b c:felem) : Lemma\n (requires b <> 0)\n (ensures (a *% finv b = c) == (a = c *% b))\nlet lemma_div_mod_eq_mul_mod a b c =\n prime_lemma ();\n M.lemma_div_mod_eq_mul_mod #prime a b c", "val lemma_mul_commute (#f:G.field) (a b:G.felem f) : Lemma\n (fmul a b == fmul b a)\nlet lemma_mul_commute #f a b =\n let pa = to_poly a in\n let pb = to_poly b in\n let m = irred_poly f in\n lemma_mul_commute pa pb;\n lemma_eq_to_poly (fmul a b) (fmul b a)", "val lemma_mul_distribute_left (#f:G.field) (a b c:G.felem f) : Lemma\n (fmul (fadd a b) c == fadd (fmul a c) (fmul b c))\nlet lemma_mul_distribute_left #f a b c =\n let pa = to_poly a in\n let pb = to_poly b in\n let pc = to_poly c in\n let m = irred_poly f in\n PL.lemma_mul_distribute_left pa pb pc;\n PL.lemma_mod_distribute (pa *. pc) (pb *. pc) m;\n lemma_eq_to_poly (fmul (fadd a b) c) (fadd (fmul a c) (fmul b c))", "val lemma_mul_mod_assoc: #m:pos -> a:nat_mod m -> b:nat_mod m -> c:nat_mod m ->\n Lemma (mul_mod (mul_mod a b) c == mul_mod a (mul_mod b c))\nlet lemma_mul_mod_assoc #m a b c =\n calc (==) {\n (a * b % m) * c % m;\n (==) { Math.Lemmas.lemma_mod_mul_distr_l (a * b) c m }\n (a * b) * c % m;\n (==) { Math.Lemmas.paren_mul_right a b c }\n a * (b * c) % m;\n (==) { Math.Lemmas.lemma_mod_mul_distr_r a (b * c) m }\n a * (b * c % m) % m;\n }", "val lemma_mul_distribute_right (#f:G.field) (a b c:G.felem f) : Lemma\n (fmul a (fadd b c) == fadd (fmul a b) (fmul a c))\nlet lemma_mul_distribute_right #f a b c =\n lemma_mul_distribute_left b c a;\n // fmul (fadd b c) a == fadd (fmul b a) (fmul c a)\n lemma_mul_commute a b;\n lemma_mul_commute a c;\n lemma_mul_commute a (fadd b c);\n ()", "val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma\n (a * b - a * c = a * (b - c))\nlet lemma_mul_sub_distr a b c =\n distributivity_sub_right a b c", "val lemma_mul_associate (#f:G.field) (a b c:G.felem f) : Lemma\n (fmul a (fmul b c) == fmul (fmul a b) c)\nlet lemma_mul_associate #f a b c =\n let pa = to_poly a in\n let pb = to_poly b in\n let pc = to_poly c in\n let m = irred_poly f in\n lemma_mul_associate pa pb pc;\n // (((a * b) % m) * c) % m\n // (a * ((b * c) % m)) % m\n PL.lemma_mod_mul_mod (pa *. pb) m pc;\n PL.lemma_mod_mul_mod (pb *. pc) m pa;\n Vale.Math.Poly2.lemma_mul_commute pa (pb *. pc);\n Vale.Math.Poly2.lemma_mul_commute pa ((pb *. pc) %. m);\n lemma_eq_to_poly (fmul a (fmul b c)) (fmul (fmul a b) c)", "val fmul_both_lemma: a:elem -> b:elem -> c:elem -> Lemma\n (requires a == b)\n (ensures a *% c == b *% c)\nlet fmul_both_lemma a b c =\n calc (==) {\n (a * c) % prime;\n (==) { Math.Lemmas.lemma_mod_mul_distr_l a c prime }\n ((a % prime) * c) % prime;\n (==) { }\n ((b % prime) * c) % prime;\n (==) { Math.Lemmas.lemma_mod_mul_distr_l b c prime }\n (b * c) % prime;\n }", "val lemma_a_mul_c_plus_d_mod_e_mul_f_g (a b c d f g:nat) : Lemma\n (requires c == g - b)\n (ensures\n a % pow2 b * pow2 c + (a / pow2 b + d * pow2 f) * pow2 g ==\n a * pow2 c + d * pow2 (f + g))\nlet lemma_a_mul_c_plus_d_mod_e_mul_f_g a b c d f g =\n calc (==) {\n a % pow2 b * pow2 c + (a / pow2 b + d * pow2 f) * pow2 g;\n (==) { lemma_distr_pow (a / pow2 b) d f g }\n a % pow2 b * pow2 c + (a / pow2 b) * pow2 (c + b) + d * pow2 (f + g);\n (==) { lemma_distr_pow (a % pow2 b) (a / pow2 b) b c }\n (a % pow2 b + (a / pow2 b) * pow2 b) * pow2 c + d * pow2 (f + g);\n (==) { Math.Lemmas.euclidean_division_definition a (pow2 b) }\n a * pow2 c + d * pow2 (f + g);\n }", "val lemma_swap_mul3 (a b c:int) : Lemma (a * b * c == a * c * b)\nlet lemma_swap_mul3 a b c =\n calc (==) {\n a * b * c;\n (==) { Math.Lemmas.paren_mul_right a b c }\n a * (b * c);\n (==) { Math.Lemmas.swap_mul b c }\n a * (c * b);\n (==) { Math.Lemmas.paren_mul_right a c b }\n a * c * b;\n }", "val lemma_mod_mul_assoc (n:pos) (a b c:nat) : Lemma ((a * b % n) * c % n == (a * (b * c % n)) % n)\nlet lemma_mod_mul_assoc m a b c =\n calc (==) {\n (a * b % m) * c % m;\n (==) { Math.Lemmas.lemma_mod_mul_distr_l (a * b) c m }\n (a * b) * c % m;\n (==) { Math.Lemmas.paren_mul_right a b c }\n a * (b * c) % m;\n (==) { Math.Lemmas.lemma_mod_mul_distr_r a (b * c) m }\n a * (b * c % m) % m;\n }", "val lemma_mod_mul_mod (a b c:poly) : Lemma\n (requires degree b >= 0)\n (ensures ((a %. b) *. c) %. b == (a *. c) %. b)\nlet lemma_mod_mul_mod a b c =\n let ab = a %. b in\n let abc = ab *. c in\n let ac = a *. c in\n let x = abc /. b in\n let y = abc %. b in\n let x' = ac /. b in\n let y' = ac %. b in\n lemma_div_mod abc b;\n lemma_div_mod ac b;\n // ab *. c == x *. b +. y\n // a *. c == x' *. b +. y'\n assert ((ab *. c) +. (a *. c) == (x *. b +. y) +. (x' *. b +. y'));\n lemma_mul_distribute_left ab a c;\n assert ((ab +. a) *. c == (x *. b +. y) +. (x' *. b +. y'));\n\n // prove that ab +. a is a multiple of b by proving (ab +. a) %. b == zero\n lemma_mod_distribute ab a b;\n lemma_mod_mod a b;\n lemma_add_cancel ab;\n lemma_div_mod (ab +. a) b;\n let z = (ab +. a) /. b in\n lemma_add_zero (z *. b);\n assert (ab +. a == z *. b);\n\n assert ((z *. b) *. c == (x *. b +. y) +. (x' *. b +. y'));\n lemma_mul_associate z b c;\n lemma_mul_commute b c;\n lemma_mul_associate z c b;\n assert ((z *. c) *. b == (x *. b +. y) +. (x' *. b +. y'));\n lemma_add_define_all ();\n lemma_equal ((z *. c) *. b +. x *. b +. x' *. b) (y +. y');\n lemma_mul_distribute_left (z *. c) x b;\n lemma_mul_distribute_left (z *. c +. x) x' b;\n assert ((z *. c +. x +. x') *. b == y +. y');\n lemma_mul_smaller_is_zero (z *. c +. x +. x') b;\n lemma_add_cancel_eq y y';\n ()", "val lemma_mul_commute (a b:poly) : Lemma ((a *. b) == (b *. a))\nlet lemma_mul_commute a b = I.lemma_mul_commute (to_poly a) (to_poly b)", "val lemma_mul_assoc4: #t:Type -> k:comm_monoid t -> a1:t -> a2:t -> a3:t -> a4:t ->\n Lemma (k.mul a1 (k.mul (k.mul a2 a3) a4) == k.mul (k.mul (k.mul a1 a2) a3) a4)\nlet lemma_mul_assoc4 #t k a1 a2 a3 a4 =\n calc (==) {\n k.mul a1 (k.mul (k.mul a2 a3) a4);\n (==) { k.lemma_mul_assoc a1 (k.mul a2 a3) a4 }\n k.mul (k.mul a1 (k.mul a2 a3)) a4;\n (==) { k.lemma_mul_assoc a1 a2 a3 }\n k.mul (k.mul (k.mul a1 a2) a3) a4;\n }", "val lemma_abc_is_acb (a b c:nat) : Lemma (a * b * c = a * c * b)\nlet lemma_abc_is_acb a b c =\n Math.Lemmas.paren_mul_right a b c;\n Math.Lemmas.swap_mul b c;\n Math.Lemmas.paren_mul_right a c b", "val lemma_mul_commute (a b: poly) : Lemma ((a *. b) =. (b *. a))\nlet lemma_mul_commute (a b:poly) : Lemma ((a *. b) =. (b *. a)) =\n let f (k:nat) : Lemma (mul_element a b k == mul_element b a k) =\n lemma_sum_reverse 0 (k + 1) (mul_element_fun a b k) (mul_element_fun b a k)\n in\n FStar.Classical.forall_intro f", "val lemma_mod_reduce (a b c:poly) : Lemma\n (requires degree (b +. c) >= 0)\n (ensures (a *. b) %. (b +. c) == (a *. c) %. (b +. c))\nlet lemma_mod_reduce a b c =\n calc (==) {\n (a *. b) %. (b +. c);\n == {lemma_add_zero_right ((a *. b) %. (b +. c))}\n (a *. b) %. (b +. c) +. zero;\n == {lemma_div_mod_exact a (b +. c)}\n (a *. b) %. (b +. c) +. (a *. (b +. c)) %. (b +. c);\n == {lemma_mod_distribute (a *. b) (a *. (b +. c)) (b +. c)}\n (a *. b +. a *. (b +. c)) %. (b +. c);\n == {lemma_mul_distribute_right a b (b +. c)}\n (a *. (b +. (b +. c))) %. (b +. c);\n == {lemma_add_all ()}\n (a *. c) %. (b +. c);\n }", "val lemma_exact_mul: a:nat -> b:pos -> c:nat ->\n Lemma (requires (c % b = 0))\n (ensures ((a*c) % b = 0))\nlet lemma_exact_mul a b c =\n (* a*c = c*a *)\n swap_mul a c;\n\n (* (c*a)%b = ((c%b)*a)%b *)\n lemma_mod_mul_distr_l c a b;\n ()", "val lemma_mul_distribute (a b c:poly) : Lemma (a *. (b +. c) == (a *. b) +. (a *. c))\nlet lemma_mul_distribute a b c = I.lemma_mul_distribute (to_poly a) (to_poly b) (to_poly c)", "val mont_cancel_lemma_gen (n:pos) (mont_R mont_R_inv a b:nat) : Lemma\n (requires mont_R_inv * mont_R % n = 1)\n (ensures (a * mont_R % n * b * mont_R_inv) % n = a * b % n)\nlet mont_cancel_lemma_gen n mont_R mont_R_inv a b =\n calc (==) {\n (a * mont_R % n * b * mont_R_inv) % n;\n (==) { Math.Lemmas.paren_mul_right (a * mont_R % n) b mont_R_inv }\n (a * mont_R % n * (b * mont_R_inv)) % n;\n (==) { Math.Lemmas.lemma_mod_mul_distr_l (a * mont_R) (b * mont_R_inv) n }\n (a * mont_R * (b * mont_R_inv)) % n;\n (==) { Math.Lemmas.paren_mul_right a mont_R (b * mont_R_inv);\n Math.Lemmas.swap_mul mont_R (b * mont_R_inv) }\n (a * (b * mont_R_inv * mont_R)) % n;\n (==) { Math.Lemmas.paren_mul_right b mont_R_inv mont_R }\n (a * (b * (mont_R_inv * mont_R))) % n;\n (==) { Math.Lemmas.paren_mul_right a b (mont_R_inv * mont_R) }\n (a * b * (mont_R_inv * mont_R)) % n;\n (==) { Math.Lemmas.lemma_mod_mul_distr_r (a * b) (mont_R_inv * mont_R) n }\n (a * b * (mont_R_inv * mont_R % n)) % n;\n (==) { assert (mont_R_inv * mont_R % n = 1) }\n (a * b) % n;\n }", "val lemma_div_mod_eq_mul_mod: #m:prime -> a:nat_mod m -> b:nat_mod m{b <> 0} -> c:nat_mod m ->\n Lemma ((div_mod a b = c) == (a = mul_mod c b))\nlet lemma_div_mod_eq_mul_mod #m a b c =\n lemma_div_mod_eq_mul_mod1 a b c;\n lemma_div_mod_eq_mul_mod2 a b c", "val lemma_div_mod_eq_mul_mod2: #m:prime -> a:nat_mod m -> b:nat_mod m{b <> 0} -> c:nat_mod m ->\n Lemma (a = mul_mod c b ==> div_mod a b = c)\nlet lemma_div_mod_eq_mul_mod2 #m a b c =\n if a = mul_mod c b then begin\n assert (div_mod a b == div_mod (mul_mod c b) b);\n calc (==) {\n div_mod (mul_mod c b) b;\n (==) { Math.Lemmas.small_mod b m }\n div_mod (mul_mod c b) (mul_mod b 1);\n (==) { lemma_div_mod_prime_cancel c 1 b }\n div_mod c 1;\n (==) { lemma_div_mod_prime_one c }\n c;\n } end\n else ()", "val lemma_mul_distribute_left (a b c:poly) : Lemma ((a +. b) *. c == (a *. c) +. (b *. c))\nlet lemma_mul_distribute_left a b c =\n lemma_mul_commute (a +. b) c;\n lemma_mul_commute a c;\n lemma_mul_commute b c;\n lemma_mul_distribute c a b", "val lemma_mul_distribute (a b c: poly) : Lemma (a *. (b +. c) =. (a *. b) +. (a *. c))\nlet lemma_mul_distribute (a b c:poly) : Lemma (a *. (b +. c) =. (a *. b) +. (a *. c)) =\n let f (k:nat) : Lemma\n (ensures mul_element a (b +. c) k == (mul_element a b k <> mul_element a c k))\n =\n lemma_sum_of_pairs 0 (k + 1)\n (mul_element_fun a (b +. c) k)\n (mul_element_fun a b k)\n (mul_element_fun a c k)\n in\n FStar.Classical.forall_intro f", "val lemma_fmul_gmul (f: G.field) (a b: G.felem f) : Lemma (fmul f a b == gmul f a b)\nlet lemma_fmul_gmul (f:G.field) (a b:G.felem f) : Lemma\n (fmul f a b == gmul f a b)\n =\n let pred (n:nat) (pab:(fmul_t f)) : Type0 = gmul_rec f a b n == pab in\n let _ = Lib.LoopCombinators.repeati_inductive' (I.bits f.G.t - 1) pred (fmul_iter f) (G.zero #f, a, b) in\n ()", "val lemma_add_cancel_eq (a b:poly) : Lemma (requires (a +. b) == zero) (ensures a == b)\nlet lemma_add_cancel_eq a b = I.lemma_add_cancel_eq (to_poly a) (to_poly b)", "val lemma_mod_mul_distr3: a:int -> b:int -> c:int -> n:pos -> Lemma\n (a * (b % n) * c % n == a * b * c % n)\nlet lemma_mod_mul_distr3 a b c n =\n calc (==) {\n a * (b % n) * c % n;\n (==) { }\n (b % n) * a * c % n;\n (==) { Math.Lemmas.paren_mul_right (b % n) a c }\n (b % n) * (a * c) % n;\n (==) { Math.Lemmas.lemma_mod_mul_distr_l b (a * c) n }\n b * (a * c) % n;\n (==) { Math.Lemmas.paren_mul_right b a c }\n a * b * c % n;\n }", "val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)\nlet modulo_scale_lemma a b c =\n calc (==) {\n (a * b) % (b * c);\n == { lemma_div_mod (a * b) (b * c) }\n a * b - (b * c) * ((a * b) / (b * c));\n == { cancel_fraction a c b }\n a * b - (b * c) * (a / c);\n == { paren_mul_right b c (a / c) }\n a * b - b * (c * (a / c));\n == { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }\n (a - c * (a / c)) * b;\n == { lemma_div_mod a c }\n (a % c) * b;\n }", "val lemma_a_mod_b_mul_c_mod_d (a b c d:nat) : Lemma\n (requires c <= d /\\ b <= d - c)\n (ensures (a % pow2 b) * pow2 c % pow2 d = (a % pow2 b) * pow2 c)\nlet lemma_a_mod_b_mul_c_mod_d a b c d =\n Math.Lemmas.pow2_multiplication_modulo_lemma_2 (a % pow2 b) d c;\n Math.Lemmas.pow2_modulo_modulo_lemma_2 a (d - c) b", "val lemma_mod_distributivity_sub_left: #m:pos -> a:nat_mod m -> b:nat_mod m -> c:nat_mod m ->\n Lemma (mul_mod (sub_mod a b) c == sub_mod (mul_mod a c) (mul_mod b c))\nlet lemma_mod_distributivity_sub_left #m a b c =\n lemma_mod_distributivity_sub_right c a b", "val lemma_a_minus_b_n_c_n_k (k a b c:nat) (n:pos) : Lemma\n (requires k < n /\\ k == a - b * n - c * n)\n (ensures k == a % n)\nlet lemma_a_minus_b_n_c_n_k k a b c n =\n Math.Lemmas.lemma_mod_sub (a - b * n) n c;\n Math.Lemmas.lemma_mod_sub a n b;\n Math.Lemmas.small_mod k n", "val lemma_div_mod_eq_mul_mod1: #m:prime -> a:nat_mod m -> b:nat_mod m{b <> 0} -> c:nat_mod m ->\n Lemma (div_mod a b = c ==> a = mul_mod c b)\nlet lemma_div_mod_eq_mul_mod1 #m a b c =\n if div_mod a b = c then begin\n assert (mul_mod (div_mod a b) b = mul_mod c b);\n calc (==) {\n mul_mod (div_mod a b) b;\n (==) { lemma_div_mod_prime_one b }\n mul_mod (div_mod a b) (div_mod b 1);\n (==) { lemma_div_mod_prime_to_one_denominator a b b 1 }\n div_mod (mul_mod a b) (mul_mod b 1);\n (==) { lemma_div_mod_prime_cancel a 1 b }\n div_mod a 1;\n (==) { lemma_div_mod_prime_one a }\n a;\n } end\n else ()", "val mod_mult_congr (p:int{is_prime p}) (a b c:int) : Lemma\n (requires (a * c) % p = (b * c) % p /\\ c % p <> 0)\n (ensures a % p = b % p)\nlet mod_mult_congr p a b c =\n let open FStar.Math.Lemmas in\n lemma_mod_mul_distr_l a c p;\n lemma_mod_mul_distr_l b c p;\n if a % p = b % p then ()\n else if b % p < a % p then mod_mult_congr_aux p (a % p) (b % p) c\n else mod_mult_congr_aux p (b % p) (a % p) c", "val lemma_mul_distribute_left (a b c: poly) : Lemma ((a +. b) *. c =. (a *. c) +. (b *. c))\nlet lemma_mul_distribute_left (a b c:poly) : Lemma ((a +. b) *. c =. (a *. c) +. (b *. c)) =\n lemma_mul_commute (a +. b) c;\n lemma_mul_commute a c;\n lemma_mul_commute b c;\n lemma_mul_distribute c a b", "val lemma_gf128_mul_rev_distribute_left (a b c:poly) : Lemma\n ((a +. b) *~ c == a *~ c +. b *~ c)\nlet lemma_gf128_mul_rev_distribute_left a b c =\n let rev x = reverse x 127 in\n let ra = rev a in\n let rb = rev b in\n let rc = rev c in\n let g = gf128_modulus in\n lemma_gf128_degree ();\n calc (==) {\n (a +. b) *~ c;\n == {}\n rev (rev (a +. b) *. rc %. g);\n == {lemma_add_reverse a b 127}\n rev ((ra +. rb) *. rc %. g);\n == {lemma_mul_distribute_left ra rb rc}\n rev ((ra *. rc +. rb *. rc) %. g);\n == {lemma_mod_distribute (ra *. rc) (rb *. rc) g}\n rev (ra *. rc %. g +. rb *. rc %. g);\n == {lemma_add_reverse (ra *. rc %. g) (rb *. rc %. g) 127}\n rev (ra *. rc %. g) +. rev (rb *. rc %. g);\n == {}\n (a *~ c) +. (b *~ c);\n }", "val lemma_mont_mul_assoc: n:pos -> d:int -> a:nat_mod n -> b:nat_mod n -> c:nat_mod n ->\n Lemma (mont_mul n d (mont_mul n d a b) c == mont_mul n d a (mont_mul n d b c))\nlet lemma_mont_mul_assoc n d a b c =\n calc (==) {\n mont_mul n d (mont_mul n d a b) c;\n (==) { }\n (a * b * d % n) * c * d % n;\n (==) { Math.Lemmas.paren_mul_right (a * b * d % n) c d }\n (a * b * d % n) * (c * d) % n;\n (==) { M.lemma_mod_mul_distr3 1 (a * b * d) (c * d) n }\n a * b * d * (c * d) % n;\n (==) { Math.Lemmas.paren_mul_right (a * b * d) c d }\n a * b * d * c * d % n;\n (==) { Math.Lemmas.paren_mul_right a b d; Math.Lemmas.paren_mul_right a (b * d) c }\n a * (b * d * c) * d % n;\n (==) { Math.Lemmas.paren_mul_right b d c; Math.Lemmas.paren_mul_right b c d }\n a * (b * c * d) * d % n;\n (==) { M.lemma_mod_mul_distr3 a (b * c * d) d n }\n mont_mul n d a (mont_mul n d b c);\n }", "val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma\n (((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)\nlet lemma_mod_plus_mul_distr a b c p =\n calc (==) {\n ((a + b) * c) % p;\n == { lemma_mod_mul_distr_l (a + b) c p }\n (((a + b) % p) * c) % p;\n == { lemma_mod_mul_distr_r ((a + b) % p) c p }\n (((a + b) % p) * (c % p)) % p;\n == { modulo_distributivity a b p }\n ((((a % p) + (b % p)) % p) * (c % p)) % p;\n }", "val lemma_fmul_fmul (f: G.field) (a b: G.felem f) : Lemma (G.fmul a b == fmul f a b)\nlet lemma_fmul_fmul (f:G.field) (a b:G.felem f) : Lemma\n (G.fmul a b == fmul f a b)\n =\n let repeati = Lib.LoopCombinators.repeati in\n let acc0 = (G.zero #f, a, b) in\n let rec lem (n:nat{n < I.bits f.G.t}) (f1:(i:nat{i < n} -> fmul_t f -> fmul_t f)) : Lemma\n (requires (forall (i:nat{i < n}) (pab:fmul_t f). f1 i pab == fmul_iter f i pab))\n (ensures repeati n (fmul_iter f) acc0 == repeati n f1 acc0)\n [SMTPat (repeati n f1 acc0)]\n =\n if n = 0 then\n (\n let pred (n:nat) (pab:(fmul_t f)) : Type0 = n == 0 ==> pab == acc0 in\n let _ = Lib.LoopCombinators.repeati_inductive' 0 pred (fmul_iter f) acc0 in\n let _ = Lib.LoopCombinators.repeati_inductive' 0 pred f1 acc0 in\n ()\n )\n else\n (\n lem (n - 1) f1;\n Lib.LoopCombinators.unfold_repeati n (fmul_iter f) acc0 (n - 1);\n Lib.LoopCombinators.unfold_repeati n f1 acc0 (n - 1);\n assert (repeati n (fmul_iter f) acc0 == repeati n f1 acc0);\n ()\n )\n in\n ()", "val fdiv_lemma1: a:elem -> b:elem{b <> 0} -> c:elem -> d:elem{d <> 0} -> Lemma\n (requires a /% b == c /% d)\n (ensures a *% d == c *% b)\nlet fdiv_lemma1 a b c d =\n fmul_both_lemma (a /% b) (c /% d) (b *% d);\n assert (a *% finv b *% (b *% d) == c *% finv d *% (b *% d));\n assert (a *% finv b *% (b *% d) == a *% (d *% (b *% finv b))) by (ed25519_semiring ());\n fdiv_one_lemma1 d b;\n assert (a *% finv b *% (b *% d) == a *% d);\n\n assert (c *% finv d *% (b *% d) == c *% (b *% (d *% finv d))) by (ed25519_semiring ());\n fdiv_one_lemma1 b d;\n assert (c *% finv d *% (b *% d) == c *% b)", "val mod_mult_congr_aux (p:int{is_prime p}) (a b c:int) : Lemma\n (requires (a * c) % p = (b * c) % p /\\ 0 <= b /\\ b <= a /\\ a < p /\\ c % p <> 0)\n (ensures a = b)\nlet mod_mult_congr_aux p a b c =\n let open FStar.Math.Lemmas in\n calc (==>) {\n (a * c) % p == (b * c) % p;\n ==> { mod_add_both (a * c) (b * c) (-b * c) p }\n (a * c - b * c) % p == (b * c - b * c) % p;\n ==> { swap_mul a c; swap_mul b c; lemma_mul_sub_distr c a b }\n (c * (a - b)) % p == (b * c - b * c) % p;\n ==> { small_mod 0 p; lemma_mod_mul_distr_l c (a - b) p }\n (c % p * (a - b)) % p == 0;\n };\n let r, s = FStar.Math.Euclid.bezout_prime p (c % p) in\n FStar.Math.Euclid.euclid p (c % p) (a - b) r s;\n small_mod (a - b) p", "val lemma_mul_associate (a b c:poly) : Lemma (a *. (b *. c) == (a *. b) *. c)\nlet lemma_mul_associate a b c = I.lemma_mul_associate (to_poly a) (to_poly b) (to_poly c)", "val qmont_cancel_lemma1: a:S.qelem -> b:S.qelem ->\n Lemma ((a * qmont_R % S.order * b * qmont_R_inv) % S.order = a * b % S.order)\nlet qmont_cancel_lemma1 a b =\n mul_qmont_R_and_R_inv_is_one ();\n mont_cancel_lemma_gen S.order qmont_R qmont_R_inv a b", "val lemma_mul_mod_prime_zero: #m:prime -> a:nat_mod m -> b:nat_mod m ->\n Lemma (a * b % m == 0 <==> (a % m == 0 \\/ b % m == 0))\nlet lemma_mul_mod_prime_zero #m a b =\n Classical.move_requires_3 Euclid.euclid_prime m a b;\n Classical.move_requires_3 lemma_mul_mod_zero2 m a b", "val lemma_mod_distributivity_sub_right: #m:pos -> a:nat_mod m -> b:nat_mod m -> c:nat_mod m ->\n Lemma (mul_mod a (sub_mod b c) == sub_mod (mul_mod a b) (mul_mod a c))\nlet lemma_mod_distributivity_sub_right #m a b c =\n calc (==) {\n mul_mod a (sub_mod b c);\n (==) { }\n a * ((b - c) % m) % m;\n (==) { Math.Lemmas.lemma_mod_mul_distr_r a (b - c) m }\n a * (b - c) % m;\n (==) { Math.Lemmas.distributivity_sub_right a b c }\n (a * b - a * c) % m;\n (==) { Math.Lemmas.lemma_mod_plus_distr_l (a * b) (- a * c) m }\n (mul_mod a b - a * c) % m;\n (==) { Math.Lemmas.lemma_mod_sub_distr (mul_mod a b) (a * c) m }\n sub_mod (mul_mod a b) (mul_mod a c);\n }", "val lemma_mod_distributivity_add_left: #m:pos -> a:nat_mod m -> b:nat_mod m -> c:nat_mod m ->\n Lemma (mul_mod (add_mod a b) c == add_mod (mul_mod a c) (mul_mod b c))\nlet lemma_mod_distributivity_add_left #m a b c =\n lemma_mod_distributivity_add_right c a b", "val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma\n ((a % (b * c)) % b = a % b)\nlet modulo_modulo_lemma (a:int) (b:pos) (c:pos) =\n pos_times_pos_is_pos b c;\n calc (==) {\n (a % (b * c)) % b;\n == { calc (==) {\n a % (b * c);\n == { lemma_div_mod a (b * c) }\n a - (b * c) * (a / (b * c));\n == { paren_mul_right b c (a / (b * c)) }\n a - b * (c * (a / (b * c)));\n }}\n (a - b * (c * (a / (b * c)))) % b;\n == { () }\n (a + (- (b * (c * (a / (b * c)))))) % b;\n == { neg_mul_right b (c * (a / (b * c))) }\n (a + (b * (-c * (a / (b * c))))) % b;\n == { () }\n (a + (-c * (a / (b * c))) * b) % b;\n == { lemma_mod_plus a (-c * (a / (b * c))) b}\n a % b;\n }", "val lemma_sub_add_cancel: #n:pos -> a:uint_t n -> b:uint_t n ->\n Lemma (sub_mod (add_mod a b) b = a)\nlet lemma_sub_add_cancel #n a b =\n let ab = (a+b) % pow2 n in\n let abb = (ab - b) % pow2 n in\n let ab_mod = add_mod a b in\n let abb_mod = sub_mod ab b in\n let p = pow2 n in\n lemma_uint_mod a;\n lemma_mod_sub_distr_l (a+b) b p", "val lemma_mul_associate (a b c: poly) : Lemma (a *. (b *. c) =. (a *. b) *. c)\nlet lemma_mul_associate (a b c:poly) : Lemma (a *. (b *. c) =. (a *. b) *. c) =\n let f (k:nat) : Lemma (mul_element a (b *. c) k == mul_element (a *. b) c k) =\n let abc1 (i:int) (j:int) = a.[j] && b.[i - j] && c.[k - i] in\n let abc2 (j:int) (i:int) = a.[j] && b.[i - j] && c.[k - i] in\n let abc3 (j:int) (i:int) = a.[j] && b.[i] && c.[k - j - i] in\n let sum_abc1 (i:int) = sum_of_bools 0 (i + 1) (abc1 i) in\n let sum_abc2 (j:int) = sum_of_bools j (k + 1) (abc2 j) in\n let sum_abc3 (j:int) = sum_of_bools 0 (k + 1 - j) (abc3 j) in\n let l1 (i:int) : Lemma (mul_element_fun (a *. b) c k i == sum_abc1 i) =\n lemma_sum_mul 0 (i + 1) c.[k - i] (abc1 i) (mul_element_fun a b i)\n in\n let l2 (j:int) : Lemma (sum_abc2 j == sum_abc3 j) =\n lemma_sum_shift 0 (k + 1 - j) j (abc3 j) (abc2 j)\n in\n let l3 (j:int) : Lemma (mul_element_fun a (b *. c) k j == sum_abc3 j) =\n lemma_sum_mul 0 (k + 1 - j) a.[j] (abc3 j) (mul_element_fun b c (k - j))\n in\n // mul_element (a *. b) c k\n // sum[0 <= i <= k] (a *. b)[i] * c[k - i]\n // sum[0 <= i <= k] (sum[0 <= j <= i] a[j] * b[i - j]) * c[k - i])\n lemma_sum_pointwise_equal 0 (k + 1) (mul_element_fun (a *. b) c k) sum_abc1 l1;\n // sum[0 <= i <= k] sum[0 <= j <= i] a[j] * b[i - j] * c[k - i]\n lemma_sum_swap_mul_associate (k + 1) abc1 abc2 sum_abc1 sum_abc2;\n // sum[0 <= j <= k] sum[j <= i <= k] a[j] * b[i - j] * c[k - i]\n lemma_sum_pointwise_equal 0 (k + 1) sum_abc2 sum_abc3 l2;\n // sum[0 <= j <= k] sum[0 <= i <= k - j] a[j] * b[i] * c[k - j - i]\n lemma_sum_pointwise_equal 0 (k + 1) (mul_element_fun a (b *. c) k) sum_abc3 l3;\n // sum[0 <= j <= k] a[j] * (sum[0 <= i <= k - j] b[i] * c[k - j - i])\n // sum[0 <= j <= k] (a[j] * (b *. c)[k - j])\n // mul_element a (b *. c) k\n ()\n in\n FStar.Classical.forall_intro f", "val lemma_mod_mul_mod_right (a b c:poly) : Lemma\n (requires degree c >= 0)\n (ensures (a *. (b %. c)) %. c == (a *. b) %. c)\nlet lemma_mod_mul_mod_right a b c =\n lemma_mul_all ();\n lemma_mod_mul_mod b c a", "val lemma_pow_pow_mod_mul: f:S.qelem -> a:nat -> b:nat -> c:nat ->\n Lemma (S.qmul (M.pow (M.pow f a % S.order) b % S.order) (M.pow f c % S.order) == M.pow f (a * b + c) % S.order)\nlet lemma_pow_pow_mod_mul f a b c =\n calc (==) {\n S.qmul (M.pow (M.pow f a % S.order) b % S.order) (M.pow f c % S.order);\n (==) { lemma_pow_pow_mod f a b }\n S.qmul (M.pow f (a * b) % S.order) (M.pow f c % S.order);\n (==) { lemma_pow_mod_mul f (a * b) c }\n M.pow f (a * b + c) % S.order;\n }", "val lemma_mod_breakdown (a: nat) (b c: pos)\n : Lemma (0 < b * c /\\ a % (b * c) == b * ((a / b) % c) + a % b)\nlet lemma_mod_breakdown (a:nat) (b:pos) (c:pos) :\n Lemma(0 a:uint_t n -> b:uint_t n ->\n Lemma (add_mod (sub_mod a b) b = a)\nlet lemma_add_sub_cancel #n a b =\n let ab = (a-b) % pow2 n in\n let abb = (ab + b) % pow2 n in\n let ab_mod = sub_mod a b in\n let abb_mod = add_mod ab b in\n let p = pow2 n in\n lemma_uint_mod a;\n assert (add_mod (sub_mod a b) b = add_mod ab_mod b);\n assert (add_mod ab_mod b = (ab_mod + b) % p);\n assert (add_mod ab_mod b = ((a-b) % p + b) % p);\n FStar.Math.Lemmas.lemma_mod_plus_distr_l (a-b) b p;\n assert (((a-b) + b) % p = (((a-b) % p) + b) % p);\n assert (a % p = (((a-b) % p) + b) % p)", "val lemma_add_mod_assoc: #m:pos -> a:nat_mod m -> b:nat_mod m -> c:nat_mod m ->\n Lemma (add_mod (add_mod a b) c == add_mod a (add_mod b c))\nlet lemma_add_mod_assoc #m a b c =\n calc (==) {\n add_mod (add_mod a b) c;\n (==) { Math.Lemmas.lemma_mod_plus_distr_l (a + b) c m }\n ((a + b) + c) % m;\n (==) { }\n (a + (b + c)) % m;\n (==) { Math.Lemmas.lemma_mod_plus_distr_r a (b + c) m }\n add_mod a (add_mod b c);\n }", "val lemma_mul_element (a b: poly) (k: int)\n : Lemma (requires True) (ensures (a *. b).[ k ] == mul_element a b k) [SMTPat (a *. b).[ k ]]\nlet lemma_mul_element (a b:poly) (k:int) : Lemma\n (requires True)\n (ensures (a *. b).[k] == mul_element a b k)\n [SMTPat (a *. b).[k]]\n =\n if k >= length a + length b then lemma_sum_of_zero 0 (k + 1) (mul_element_fun a b k)", "val lemma_div_mod_prime_to_one_denominator:\n #m:pos{1 < m} -> a:nat_mod m -> b:nat_mod m -> c:nat_mod m{c <> 0} -> d:nat_mod m{d <> 0} ->\n Lemma (mul_mod (div_mod a c) (div_mod b d) == div_mod (mul_mod a b) (mul_mod c d))\nlet lemma_div_mod_prime_to_one_denominator #m a b c d =\n calc (==) {\n mul_mod (div_mod a c) (div_mod b d);\n (==) { }\n mul_mod (mul_mod a (inv_mod c)) (mul_mod b (inv_mod d));\n (==) {\n lemma_mul_mod_comm #m b (inv_mod d);\n lemma_mul_mod_assoc #m (mul_mod a (inv_mod c)) (inv_mod d) b }\n mul_mod (mul_mod (mul_mod a (inv_mod c)) (inv_mod d)) b;\n (==) { lemma_mul_mod_assoc #m a (inv_mod c) (inv_mod d) }\n mul_mod (mul_mod a (mul_mod (inv_mod c) (inv_mod d))) b;\n (==) { lemma_inv_mod_both c d }\n mul_mod (mul_mod a (inv_mod (mul_mod c d))) b;\n (==) {\n lemma_mul_mod_assoc #m a (inv_mod (mul_mod c d)) b;\n lemma_mul_mod_comm #m (inv_mod (mul_mod c d)) b;\n lemma_mul_mod_assoc #m a b (inv_mod (mul_mod c d)) }\n mul_mod (mul_mod a b) (inv_mod (mul_mod c d));\n }", "val lemma_gf128_mul (a b c d:poly) (n:nat) : Lemma\n (ensures (\n let m = monomial n in\n let ab = a *. m +. b in\n let cd = c *. m +. d in\n let ac = a *. c in\n let ad = a *. d in\n let bc = b *. c in\n let bd = b *. d in\n ab *. cd ==\n shift (ac +. bc /. m +. ad /. m) (n + n) +.\n ((bc %. m) *. m +. (ad %. m) *. m +. bd)\n ))\nlet lemma_gf128_mul a b c d n =\n let m = monomial n in\n let ab = a *. m +. b in\n let cd = c *. m +. d in\n let ac = a *. c in\n let ad = a *. d in\n let bc = b *. c in\n let bd = b *. d in\n let adh = ad /. m in\n let bch = bc /. m in\n let adl = ad %. m in\n let bcl = bc %. m in\n // ab *. cd\n // (a *. m +. b) *. (c *. m +. d)\n lemma_mul_distribute_right (a *. m +. b) (c *. m) d;\n lemma_mul_distribute_left (a *. m) b (c *. m);\n lemma_mul_distribute_left (a *. m) b d;\n // ((a *. m) *. (c *. m) +. b *. (c *. m)) +. ((a *. m) *. d +. b *. d);\n lemma_mul_associate b c m;\n lemma_mul_associate a m d;\n lemma_mul_commute m d;\n lemma_mul_associate a d m;\n lemma_mul_associate a m (c *. m);\n lemma_mul_associate m c m;\n lemma_mul_commute c m;\n lemma_mul_associate c m m;\n lemma_mul_associate a c (m *. m);\n // (ac *. (m *. m) +. bc *. m) +. (ad *. m +. bd)\n lemma_div_mod ad m;\n lemma_div_mod bc m;\n // (ac *. (m *. m) +. (bch *. m +. bcl) *. m) +. ((adh *. m +. adl) *. m +. bd)\n lemma_mul_distribute_left (bch *. m) bcl m;\n lemma_mul_distribute_left (adh *. m) adl m;\n // (ac *. (m *. m) +. (bch *. m *. m +. bcl *. m)) +. ((adh *. m *. m +. adl *. m) +. bd)\n lemma_mul_associate bch m m;\n lemma_mul_associate adh m m;\n // (ac *. (m *. m) +. (bch *. (m *. m) +. bcl *. m)) +. ((adh *. (m *. m) +. adl *. m) +. bd)\n assert (ab *. cd == (ac *. (m *. m) +. (bch *. (m *. m) +. bcl *. m)) +. ((adh *. (m *. m) +. adl *. m) +. bd));\n lemma_add_define_all ();\n lemma_equal (ab *. cd) ((ac *. (m *. m) +. bch *. (m *. m) +. adh *. (m *. m)) +. (bcl *. m +. adl *. m +. bd));\n // (ac *. (m *. m) +. bch *. (m *. m) +. adh *. (m *. m)) +. (bcl *. m +. adl *. m +. bd)\n lemma_mul_distribute_left ac bch (m *. m);\n lemma_mul_distribute_left (ac +. bch) adh (m *. m);\n // (ac +. bch +. adh) *. (m *. m) +. (bcl *. m +. adl *. m +. bd)\n lemma_mul_monomials n n;\n lemma_shift_is_mul (ac +. bch +. adh) (n + n);\n // shift (ac +. bch +. adh) (n + n) +. (bcl *. m +. adl *. m +. bd)\n ()", "val lemma_mul_distribute_right (a b c:poly) : Lemma (a *. (b +. c) == (a *. b) +. (a *. c))\nlet lemma_mul_distribute_right a b c = lemma_mul_distribute a b c", "val lemma_mul (f:G.field) (a b:G.felem f) : Lemma\n (requires True)\n (ensures to_poly (G.fmul a b) == (to_poly a *. to_poly b) %. (irred_poly f))\n [SMTPat (to_poly (G.fmul a b))]\nlet lemma_mul f a b =\n let G.GF t irred = f in\n let n = I.bits t in\n let pa = to_poly a in\n let pb = to_poly b in\n let m = irred_poly f in\n lemma_mul_commute pa pb;\n lemma_mul_def pb pa;\n lemma_mul_pmul pb pa;\n lemma_mmul_pmul pa pb m n;\n lemma_mmul_smul pa pb m n;\n lemma_smul_fmul f a b;\n lemma_fmul_gmul f a b;\n lemma_fmul_fmul f a b;\n PL.lemma_mod_small (to_poly (G.fmul a b)) m;\n ()", "val lemma_mul_pmul (a b: poly) : Lemma (mul_def a b == pmul b a)\nlet lemma_mul_pmul (a b:poly) : Lemma\n (mul_def a b == pmul b a)\n =\n PL.lemma_pointwise_equal (mul_def a b) (pmul b a) (lemma_mul_pmul_k a b)", "val lemma_aff_point_mul_neg_mul_add (a b c:int) (p:S.aff_point) :\n Lemma (aff_point_mul_neg (a * b + c) p ==\n S.aff_point_add (aff_point_mul_neg b (aff_point_mul_neg a p)) (aff_point_mul_neg c p))\nlet lemma_aff_point_mul_neg_mul_add a b c p =\n lemma_aff_point_mul_neg_add (a * b) c p;\n lemma_aff_point_mul_neg_mul a b p", "val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)\nlet lemma_mod_mult_zero a b c =\n (* < 1 *)\n lemma_mod_lt a (b * c);\n lemma_div_lt_cancel (a % (b * c)) b c;\n lemma_div_lt_cancel ((a % (b * c)) / b) c 1;\n\n (* >= 0 *)\n nat_over_pos_is_nat (a % (b * c)) b;\n nat_over_pos_is_nat ((a % (b * c)) / b) c;\n ()", "val lemma_ab_le_cd (a b c d:nat) : Lemma\n (requires a <= c /\\ b <= d)\n (ensures a * b <= c * d)\nlet lemma_ab_le_cd a b c d =\n Math.Lemmas.lemma_mult_le_left a b d;\n Math.Lemmas.lemma_mult_le_right d a c", "val lemma_mul_element (a b: poly) (k: int)\n : Lemma (mul_element a b k == D.mul_element (d a) (d b) k)\nlet lemma_mul_element (a b:poly) (k:int) : Lemma\n (mul_element a b k == D.mul_element (d a) (d b) k)\n =\n reveal_defs ();\n lemma_mul_element_rec a b k (k + 1);\n ()", "val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma\n (FStar.Math.Lemmas.pos_times_pos_is_pos b c; (a % (b * c)) % b = a % b)\nlet modulo_modulo_lemma (a:int) (b:pos) (c:pos) =\n FStar.Math.Lemmas.pos_times_pos_is_pos b c;\n lemma_div_mod a (b * c);\n FStar.Math.Lemmas.paren_mul_right (a / (b * c)) c b;\n FStar.Math.Lemmas.swap_mul b c;\n lemma_mod_plus (a % (b * c)) ((a / (b * c)) * c) b", "val lemma_mod_cancel (a:poly) : Lemma\n (requires degree a >= 0)\n (ensures a %. a == zero)\nlet lemma_mod_cancel a =\n lemma_mul_one a;\n lemma_mul_commute a one;\n lemma_div_mod_exact one a", "val lemma_pow_pow_mod_mul: f:S.qelem -> a:nat -> b:nat -> c:nat ->\n Lemma (S.qmul (M.pow (M.pow f a % S.q) b % S.q) (M.pow f c % S.q) == M.pow f (a * b + c) % S.q)\nlet lemma_pow_pow_mod_mul f a b c =\n calc (==) {\n S.qmul (M.pow (M.pow f a % S.q) b % S.q) (M.pow f c % S.q);\n (==) {\n M.lemma_pow_mod_base (M.pow f a) b S.q;\n Math.Lemmas.lemma_mod_mul_distr_l (M.pow (M.pow f a) b) (M.pow f c % S.q) S.q;\n Math.Lemmas.lemma_mod_mul_distr_r (M.pow (M.pow f a) b) (M.pow f c) S.q }\n M.pow (M.pow f a) b * M.pow f c % S.q;\n (==) { M.lemma_pow_mul f a b }\n M.pow f (a * b) * M.pow f c % S.q;\n (==) { M.lemma_pow_add f (a * b) c }\n M.pow f (a * b + c) % S.q;\n }", "val lemma_gf128_mul_rev_commute (a b:poly) : Lemma (a *~ b == b *~ a)\nlet lemma_gf128_mul_rev_commute a b =\n lemma_mul_all ()", "val lemma_gf128_mul_rev_distribute_right (a b c:poly) : Lemma\n (a *~ (b +. c) == a *~ b +. a *~ c)\nlet lemma_gf128_mul_rev_distribute_right a b c =\n calc (==) {\n a *~ (b +. c);\n == {lemma_gf128_mul_rev_commute a (b +. c)}\n (b +. c) *~ a;\n == {lemma_gf128_mul_rev_distribute_left b c a}\n b *~ a +. c *~ a;\n == {lemma_gf128_mul_rev_commute a b; lemma_gf128_mul_rev_commute a c}\n a *~ b +. a *~ c;\n }", "val lemma_gf128_mul_rev_associate (a b c:poly) : Lemma\n (a *~ (b *~ c) == (a *~ b) *~ c)\nlet lemma_gf128_mul_rev_associate a b c =\n let rev x = reverse x 127 in\n let ra = rev a in\n let rb = rev b in\n let rc = rev c in\n let g = gf128_modulus in\n lemma_gf128_degree ();\n calc (==) {\n a *~ (b *~ c);\n == {}\n rev (ra *. (rb *. rc %. g) %. g);\n == {lemma_mod_mul_mod_right ra (rb *. rc) g}\n rev (ra *. (rb *. rc) %. g);\n == {lemma_mul_associate ra rb rc}\n rev ((ra *. rb) *. rc %. g);\n == {lemma_mod_mul_mod (ra *. rb) g rc}\n rev ((ra *. rb %. g) *. rc %. g);\n == {}\n (a *~ b) *~ c;\n }", "val lemma_pow_pow_mod_mul: f:S.felem -> a:nat -> b:nat -> c:nat ->\n Lemma (S.fmul (M.pow (M.pow f a % S.prime) b % S.prime) (M.pow f c % S.prime) == M.pow f (a * b + c) % S.prime)\nlet lemma_pow_pow_mod_mul f a b c =\n calc (==) {\n S.fmul (M.pow (M.pow f a % S.prime) b % S.prime) (M.pow f c % S.prime);\n (==) { lemma_pow_pow_mod f a b }\n S.fmul (M.pow f (a * b) % S.prime) (M.pow f c % S.prime);\n (==) { lemma_pow_mod_mul f (a * b) c }\n M.pow f (a * b + c) % S.prime;\n }", "val lemma_pow_pow_mod_mul: f:S.felem -> a:nat -> b:nat -> c:nat ->\n Lemma (S.fmul (M.pow (M.pow f a % S.prime) b % S.prime) (M.pow f c % S.prime) == M.pow f (a * b + c) % S.prime)\nlet lemma_pow_pow_mod_mul f a b c =\n calc (==) {\n S.fmul (M.pow (M.pow f a % S.prime) b % S.prime) (M.pow f c % S.prime);\n (==) { lemma_pow_pow_mod f a b }\n S.fmul (M.pow f (a * b) % S.prime) (M.pow f c % S.prime);\n (==) { lemma_pow_mod_mul f (a * b) c }\n M.pow f (a * b + c) % S.prime;\n }", "val modulo_sub : p:pos -> a:int -> b:int -> c:int -> Lemma\n (requires ((a + b) % p = (a + c) % p))\n (ensures (b % p = c % p))\nlet modulo_sub p a b c =\n modulo_add p (-a) (a + b) (a + c)", "val qmont_cancel_lemma2: a:S.qelem -> b:S.qelem ->\n Lemma (to_qmont a * from_qmont b % S.order = a * b % S.order)\nlet qmont_cancel_lemma2 a b =\n calc (==) {\n to_qmont a * from_qmont b % S.order;\n (==) { }\n (a * qmont_R % S.order * (b * qmont_R_inv % S.order)) % S.order;\n (==) { Math.Lemmas.lemma_mod_mul_distr_r (a * qmont_R % S.order) (b * qmont_R_inv) S.order }\n (a * qmont_R % S.order * (b * qmont_R_inv)) % S.order;\n (==) { Math.Lemmas.paren_mul_right (a * qmont_R % S.order) b qmont_R_inv }\n (a * qmont_R % S.order * b * qmont_R_inv) % S.order;\n (==) { qmont_cancel_lemma1 a b }\n a * b % S.order;\n }", "val lemma_eq_maj_xvsel32 (a b c:nat32) : Lemma\n (ensures (isel32 c b (a *^ b) = (iand32 a b) *^ ((iand32 a c) *^ (iand32 b c))))\nlet lemma_eq_maj_xvsel32 (a b c:nat32) : Lemma\n (ensures (isel32 c b (a *^ b) = (iand32 a b) *^ ((iand32 a c) *^ (iand32 b c))))\n =\n reveal_iand_all 32;\n reveal_ixor_all 32;\n lemma_equal_nth 32 (isel32 c b (a *^ b)) ((iand32 a b) *^ ((iand32 a c) *^ (iand32 b c)))", "val lemma_ab_lt_cd (a b c d:pos) : Lemma\n (requires a < c /\\ b < d)\n (ensures a * b < c * d)\nlet lemma_ab_lt_cd a b c d =\n Math.Lemmas.lemma_mult_lt_left a b d;\n Math.Lemmas.lemma_mult_lt_right d a c", "val lemma_distr_eucl_mul_add (r a c:int) (b:pos) : Lemma (r * (a % b) + r * (a / b + c) * b = r * a + r * c * b)\nlet lemma_distr_eucl_mul_add r a c b =\n calc (==) {\n r * (a % b) + r * (a / b + c) * b;\n (==) { Math.Lemmas.paren_mul_right r (a / b + c) b }\n r * (a % b) + r * ((a / b + c) * b);\n (==) { Math.Lemmas.distributivity_add_left (a / b) c b }\n r * (a % b) + r * ((a / b * b) + c * b);\n (==) { Math.Lemmas.distributivity_add_right r (a / b * b) (c * b) }\n r * (a % b) + r * (a / b * b) + r * (c * b);\n (==) { Math.Lemmas.paren_mul_right r (a / b) b; Math.Lemmas.paren_mul_right r c b }\n r * (a % b) + r * (a / b) * b + r * c * b;\n (==) { lemma_distr_eucl_mul r a b }\n r * a + r * c * b;\n }", "val lemma_mul_def (a b: poly) : Lemma (mul_def a b == mul a b)\nlet lemma_mul_def (a b:poly) : Lemma\n (mul_def a b == mul a b)\n =\n reveal_defs ();\n PL.lemma_pointwise_equal (mul_def a b) (mul a b) (lemma_mul_element a b)", "val lemma_mod_distribute (a b c:poly) : Lemma\n (requires degree c >= 0)\n (ensures (a +. b) %. c == (a %. c) +. (b %. c))\nlet lemma_mod_distribute a b c =\n let ab = a +. b in\n let a' = a /. c in\n let b' = b /. c in\n let ab' = ab /. c in\n let a'' = a %. c in\n let b'' = b %. c in\n let ab'' = ab %. c in\n lemma_div_mod a c;\n lemma_div_mod b c;\n lemma_div_mod ab c;\n // (a +. b) == (a) +. (b)\n assert ((ab' *. c +. ab'') == (a' *. c +. a'') +. (b' *. c +. b''));\n lemma_add_define_all ();\n lemma_equal (ab' *. c +. a' *. c +. b' *. c) (ab'' +. a'' +. b'');\n lemma_mul_distribute_left ab' a' c;\n lemma_mul_distribute_left (ab' +. a') b' c;\n assert ((ab' +. a' +. b') *. c == ab'' +. a'' +. b'');\n lemma_mul_smaller_is_zero (ab' +. a' +. b') c;\n assert (ab'' +. a'' +. b'' == zero);\n lemma_zero_define ();\n lemma_equal ab'' (a'' +. b'');\n ()", "val mod_trans_lem (a : nat) (b c : pos) :\n Lemma (requires (a % b = 0 /\\ b % c = 0))\n (ensures (a % c = 0))\nlet mod_trans_lem a b c =\n let open FStar.Math.Lemmas in\n\n div_exact_r a b;\n div_exact_r b c;\n\n assert(a = b * (a / b));\n assert(b = c * (b / c));\n assert(a = (c * (b / c)) * (a / (c * (b / c))));\n assert(a = c * (((b / c)) * (a / (c * (b / c)))));\n cancel_mul_mod (((b / c)) * (a / (c * (b / c)))) c;\n assert(a % c = 0)", "val lemma_mul_pmul_k (a b: poly) (k: int) : Lemma ((mul_def a b).[ k ] == (pmul b a).[ k ])\nlet lemma_mul_pmul_k (a b:poly) (k:int) : Lemma\n ((mul_def a b).[k] == (pmul b a).[k])\n =\n PL.lemma_index_all ();\n let n = poly_length a in\n lemma_pmul_degree b a n;\n if n = k + 1 then lemma_mul_pmul_k_base a b k n\n else if n > k + 1 then lemma_mul_pmul_k_left a b k n (k + 1)\n else lemma_mul_pmul_k_right a b k n (k + 1)", "val lemma_i2b_mul (#n:pos) (a b:uint_t n) : Lemma\n (b_i2b #n (mul_mod #n a b) == b_mul #n (b_i2b a) b)\nlet lemma_i2b_mul #n a b =\n int2bv_mul #n #a #b #(bvmul #n (int2bv #n a) b) ();\n assert_norm (b_i2b #n (mul_mod #n a b) == b_mul #n (b_i2b a) b)", "val lemma_mod_distributivity_add_right: #m:pos -> a:nat_mod m -> b:nat_mod m -> c:nat_mod m ->\n Lemma (mul_mod a (add_mod b c) == add_mod (mul_mod a b) (mul_mod a c))\nlet lemma_mod_distributivity_add_right #m a b c =\n calc (==) {\n mul_mod a (add_mod b c);\n (==) { }\n a * ((b + c) % m) % m;\n (==) { Math.Lemmas.lemma_mod_mul_distr_r a (b + c) m }\n a * (b + c) % m;\n (==) { Math.Lemmas.distributivity_add_right a b c }\n (a * b + a * c) % m;\n (==) { Math.Lemmas.modulo_distributivity (a * b) (a * c) m }\n add_mod (mul_mod a b) (mul_mod a c);\n }", "val lemma_mul_smaller_is_zero (a b:poly) : Lemma\n (requires degree b > degree (a *. b))\n (ensures a == zero /\\ a *. b == zero)\nlet lemma_mul_smaller_is_zero a b =\n lemma_mul_zero b;\n (if degree a < 0 then lemma_degree_negative a);\n lemma_mul_commute a b;\n ()", "val fmul_both_lemma_neq: a:elem -> b:elem -> c:elem{c <> 0} -> Lemma\n (a <> b <==> (a *% c <> b *% c))\nlet fmul_both_lemma_neq a b c =\n prime_lemma ();\n if a *% c = b *% c then\n Fermat.mod_mult_congr prime a b c\n else ()", "val lemma_inv_mod_both: #m:pos{1 < m} -> a:nat_mod m -> b:nat_mod m ->\n Lemma (inv_mod (mul_mod a b) == mul_mod (inv_mod a) (inv_mod b))\nlet lemma_inv_mod_both #m a b =\n let p1 = pow a (m - 2) in\n let p2 = pow b (m - 2) in\n\n calc (==) {\n mul_mod (inv_mod a) (inv_mod b);\n (==) { lemma_pow_mod #m a (m - 2); lemma_pow_mod #m b (m - 2) }\n p1 % m * (p2 % m) % m;\n (==) { Math.Lemmas.lemma_mod_mul_distr_l p1 (p2 % m) m }\n p1 * (p2 % m) % m;\n (==) { Math.Lemmas.lemma_mod_mul_distr_r p1 p2 m }\n p1 * p2 % m;\n (==) { lemma_pow_mul_base a b (m - 2) }\n pow (a * b) (m - 2) % m;\n (==) { lemma_pow_mod_base (a * b) (m - 2) m }\n pow (mul_mod a b) (m - 2) % m;\n (==) { lemma_pow_mod #m (mul_mod a b) (m - 2) }\n inv_mod (mul_mod a b);\n }", "val lemma_add_lo_mul_right (#n:nat) (a b:natN n) (c:nat1) (m:int) : Lemma\n (add_lo a b c * m == (let x = a * m + b * m + c * m in if a + b + c < n then x else x - n * m))\nlet lemma_add_lo_mul_right #n a b c m =\n reveal_add_lo_all ()", "val lemma_mul_sub (mc:nat) (a b c:uint64) : Lemma\n (requires\n v a <= max52 /\\ max52 <= v a * 2 /\\ v c <= mc * max52 /\\\n mc <= v b /\\ 2 * v b <= 4096)\n (ensures (let r = a *. u64 2 *. b -. c in\n v r = v a * 2 * v b - v c /\\\n felem_fits1 r (2 * v b)))\nlet lemma_mul_sub mc a b c =\n let r = a *. u64 2 *. b -. c in\n assert (v c <= mc * max52);\n ML.lemma_ab_le_cd mc max52 (v b) (v a * 2);\n assert (v c <= v a * 2 * v b);\n\n assert (v a * 2 * v b - v c <= v a * 2 * v b);\n Math.Lemmas.paren_mul_right (v a) 2 (v b);\n ML.lemma_ab_le_cd (v a) (2 * v b) max52 4096;\n assert_norm (4096 * max52 < pow2 64);\n Math.Lemmas.small_mod (v a * 2 * v b - v c) (pow2 64);\n assert (v r = v a * 2 * v b - v c);\n\n ML.lemma_ab_le_cd (v a) (2 * v b) max52 (2 * v b);\n assert (felem_fits1 r (2 * v b))", "val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma\n (a / (b * c) = (a / b) / c)\nlet division_multiplication_lemma (a:int) (b:pos) (c:pos) =\n calc (==) {\n a / b / c;\n == { lemma_div_mod a (b * c) }\n ((b * c) * (a / (b * c)) + a % (b * c)) / b / c;\n == { paren_mul_right b c (a / (b * c)) }\n (b * (c * (a / (b * c))) + a % (b * c)) / b / c;\n == { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }\n (c * (a / (b * c)) + ((a % (b * c)) / b)) / c;\n == { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }\n (a / (b * c)) + (a % (b * c)) / b / c;\n == { lemma_mod_mult_zero a b c }\n a / (b * c);\n }", "val modulo_division_lemma: a:nat -> b:pos -> c:pos ->\n Lemma ((a % (b * c)) / b = (a / b) % c)\nlet modulo_division_lemma a b c =\n calc (==) {\n (a % (b * c)) / b;\n == { lemma_div_mod a (b * c) }\n (a - (b * c) * (a / (b * c))) / b;\n == { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }\n (a + b * (-(c * (a / (b * c))))) / b;\n == { lemma_div_plus a (-(c * (a / (b * c)))) b }\n (a / b) - c * (a / (b * c));\n == { division_multiplication_lemma a b c }\n (a / b) - c * ((a / b) / c);\n == { lemma_div_mod (a/b) c }\n (a / b) % c;\n }", "val lemma_pow2_div2 (a b c: nat) : Lemma ((a / pow2 b) / pow2 c == a / (pow2 (c + b)))\nlet lemma_pow2_div2 (a:nat) (b:nat) (c:nat)\n : Lemma ((a / pow2 b) / pow2 c == a / (pow2 (c + b)))\n =\n let open FStar.Math.Lemmas in\n pow2_plus b c;\n division_multiplication_lemma a (pow2 b) (pow2 c)", "val distributivity_sub_right: a:int -> b:int -> c:int ->\n Lemma ((a * (b - c) = a * b - a * c))\nlet distributivity_sub_right a b c =\n calc (==) {\n a * (b - c);\n == {}\n a * (b + (-c));\n == { distributivity_add_right a b (-c) }\n a * b + a * (-c);\n == { neg_mul_right a c }\n a * b - a * c;\n }", "val lemma_mul_sub_last (mc:nat) (a b c:uint64) : Lemma\n (requires\n v a <= max48 /\\ max48 <= v a * 2 /\\ v c <= mc * max48 /\\\n mc <= v b /\\ 2 * v b <= 65536)\n (ensures (let r = a *. u64 2 *. b -. c in\n v r = v a * 2 * v b - v c /\\\n felem_fits_last1 r (2 * v b)))\nlet lemma_mul_sub_last mc a b c =\n let r = a *. u64 2 *. b -. c in\n assert (v c <= mc * max48);\n ML.lemma_ab_le_cd mc max48 (v b) (v a * 2);\n assert (v c <= v b * (v a * 2));\n\n assert (v a * 2 * v b - v c <= v a * 2 * v b);\n Math.Lemmas.paren_mul_right (v a) 2 (v b);\n ML.lemma_ab_le_cd (v a) (2 * v b) max48 65536;\n assert_norm (65536 * max48 < pow2 64);\n Math.Lemmas.small_mod (v a * 2 * v b - v c) (pow2 64);\n assert (v r = v a * 2 * v b - v c);\n\n ML.lemma_ab_le_cd (v a) (2 * v b) max48 (2 * v b);\n assert (felem_fits_last1 r (2 * v b))", "val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma\n (requires True)\n (ensures (a * b) % n = ((a % n) * b) % n)\nlet lemma_mod_mul_distr_l a b n =\n calc (==) {\n (a * b) % n;\n == { lemma_div_mod a n }\n ((n * (a/n) + a%n) * b) % n;\n == { distributivity_add_left (n * (a/n)) (a%n) b }\n (n * (a/n) * b + (a%n) * b) % n;\n == { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }\n ((a%n) * b + ((a/n) * b) * n) % n;\n == { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }\n ((a%n) * b) % n;\n }", "val point_equal_lemma_aux2: a:elem -> b:elem{b <> 0} -> c:elem -> d:elem{d <> 0} -> e:elem -> f:elem{f <> 0} -> Lemma\n (requires a *% b == c *% d /\\ a /% d == e /% f)\n (ensures e *% b == c *% f)\nlet point_equal_lemma_aux2 a b c d e f =\n fmul_both_lemma (a *% b) (c *% d) f;\n assert (a *% b *% f == c *% d *% f);\n calc (==) {\n a *% b *% f;\n (==) { lemma_fmul_assoc1 a b f }\n a *% f *% b;\n (==) { fdiv_lemma1 a d e f }\n e *% d *% b;\n (==) { lemma_fmul_assoc1 e d b }\n e *% b *% d;\n };\n lemma_fmul_assoc1 c d f;\n assert (e *% b *% d == c *% f *% d);\n prime_lemma ();\n Fermat.mod_mult_congr prime (e *% b) (c *% f) d;\n Math.Lemmas.small_mod (e *% b) prime;\n Math.Lemmas.small_mod (c *% f) prime;\n assert (e *% b == c *% f)", "val lemma_div_distribute (a b c:poly) : Lemma\n (requires degree c >= 0)\n (ensures (a +. b) /. c == (a /. c) +. (b /. c))\nlet lemma_div_distribute a b c =\n let ab = a +. b in\n let a' = a /. c in\n let b' = b /. c in\n let ab' = ab /. c in\n let a'' = a %. c in\n let b'' = b %. c in\n let ab'' = ab %. c in\n lemma_div_mod a c;\n lemma_div_mod b c;\n lemma_div_mod ab c;\n // (a +. b) == (a) +. (b)\n assert ((ab' *. c +. ab'') == (a' *. c +. a'') +. (b' *. c +. b''));\n lemma_add_define_all ();\n lemma_equal (ab' *. c +. a' *. c +. b' *. c) (ab'' +. a'' +. b'');\n lemma_mul_distribute_left ab' a' c;\n lemma_mul_distribute_left (ab' +. a') b' c;\n assert ((ab' +. a' +. b') *. c == ab'' +. a'' +. b'');\n lemma_mul_smaller_is_zero (ab' +. a' +. b') c;\n assert (ab' +. a' +. b' == zero);\n lemma_zero_define ();\n lemma_equal ab' (a' +. b');\n ()", "val mul_associativity: a:pfelem -> b:pfelem -> c:pfelem\n -> Lemma (a *% b *% c == a *% (b *% c))\nlet mul_associativity a b c =\n calc (==) {\n a *% b *% c;\n == { }\n (((a * b) % prime) * c) % prime;\n == { Math.Lemmas.lemma_mod_mul_distr_l (a * b) c prime }\n ((a * b) * c) % prime;\n == { Math.Lemmas.paren_mul_right a b c }\n (a * (b * c)) % prime;\n == { Math.Lemmas.lemma_mod_mul_distr_r a (b * c) prime }\n (a * ((b * c) % prime)) % prime;\n == { }\n a *% (b *% c);\n }", "val lemma_vsel32 (a b c:nat32) : Lemma\n (ensures (isel32 a b c = (iand32 c a) *^ (iand32 (inot32 c) b)))\nlet lemma_vsel32 (a b c:nat32) : Lemma\n (ensures (isel32 a b c = (iand32 c a) *^ (iand32 (inot32 c) b)))\n =\n reveal_iand_all 32;\n reveal_inot_all 32;\n reveal_ixor_all 32;\n lemma_equal_nth 32 (isel32 a b c) ((iand32 c a) *^ (iand32 (inot32 c) b))", "val div_mul_l: a:int -> b:int -> c:pos -> d:pos -> Lemma\n (requires a / d = b / d)\n (ensures a / (c * d) = b / (c * d))\nlet div_mul_l a b c d =\n calc (==) {\n a / (c * d);\n == { }\n a / (d * c);\n == { Math.Lemmas.division_multiplication_lemma a d c }\n (a / d) / c;\n == { }\n (b / d) / c;\n == { Math.Lemmas.division_multiplication_lemma b d c }\n b / (d * c);\n == { }\n b / (c * d);\n }" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_div_mod_prime_cancel" }, { "project_name": "hacl-star", "file_name": "Spec.Ed25519.Lemmas.fst", "name": "Spec.Ed25519.Lemmas.lemma_fmul_assoc1" }, { "project_name": "hacl-star", "file_name": "Spec.K256.Lemmas.fst", "name": "Spec.K256.Lemmas.lemma_div_mod_eq_mul_mod" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Galois.Lemmas.fst", "name": "Vale.Math.Poly2.Galois.Lemmas.lemma_mul_commute" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Galois.Lemmas.fst", "name": "Vale.Math.Poly2.Galois.Lemmas.lemma_mul_distribute_left" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_mul_mod_assoc" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Galois.Lemmas.fst", "name": "Vale.Math.Poly2.Galois.Lemmas.lemma_mul_distribute_right" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.lemma_mul_sub_distr" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Galois.Lemmas.fst", "name": "Vale.Math.Poly2.Galois.Lemmas.lemma_mul_associate" }, { "project_name": "hacl-star", "file_name": "Spec.Ed25519.Lemmas.fst", "name": "Spec.Ed25519.Lemmas.fmul_both_lemma" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.MathLemmas.fst", "name": "Hacl.Spec.K256.MathLemmas.lemma_a_mul_c_plus_d_mod_e_mul_f_g" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.MathLemmas.fst", "name": "Hacl.Spec.K256.MathLemmas.lemma_swap_mul3" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.P256.Montgomery.fst", "name": "Hacl.Spec.P256.Montgomery.lemma_mod_mul_assoc" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_mod_mul_mod" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.fst", "name": "Vale.Math.Poly2.lemma_mul_commute" }, { "project_name": "hacl-star", "file_name": "Lib.Exponentiation.fst", "name": "Lib.Exponentiation.lemma_mul_assoc4" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.P256.Montgomery.fst", "name": "Hacl.Spec.P256.Montgomery.lemma_abc_is_acb" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Defs.fst", "name": "Vale.Math.Poly2.Defs.lemma_mul_commute" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_mod_reduce" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Math.fst", "name": "Vale.Poly1305.Math.lemma_exact_mul" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.fst", "name": "Vale.Math.Poly2.lemma_mul_distribute" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.P256.Montgomery.fst", "name": "Hacl.Spec.P256.Montgomery.mont_cancel_lemma_gen" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_div_mod_eq_mul_mod" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_div_mod_eq_mul_mod2" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_mul_distribute_left" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Defs.fst", "name": "Vale.Math.Poly2.Defs.lemma_mul_distribute" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Galois.fst", "name": "Vale.Math.Poly2.Galois.lemma_fmul_gmul" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.fst", "name": "Vale.Math.Poly2.lemma_add_cancel_eq" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Montgomery.Lemmas.fst", "name": "Hacl.Spec.Montgomery.Lemmas.lemma_mod_mul_distr3" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.modulo_scale_lemma" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.MathLemmas.fst", "name": "Hacl.Spec.K256.MathLemmas.lemma_a_mod_b_mul_c_mod_d" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_mod_distributivity_sub_left" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.Field52.Lemmas2.fst", "name": "Hacl.Spec.K256.Field52.Lemmas2.lemma_a_minus_b_n_c_n_k" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_div_mod_eq_mul_mod1" }, { "project_name": "FStar", "file_name": "FStar.Math.Fermat.fst", "name": "FStar.Math.Fermat.mod_mult_congr" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Defs.fst", "name": "Vale.Math.Poly2.Defs.lemma_mul_distribute_left" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GF128.fst", "name": "Vale.AES.GF128.lemma_gf128_mul_rev_distribute_left" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Exponentiation.Lemmas.fst", "name": "Hacl.Spec.Exponentiation.Lemmas.lemma_mont_mul_assoc" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.lemma_mod_plus_mul_distr" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Galois.fst", "name": "Vale.Math.Poly2.Galois.lemma_fmul_fmul" }, { "project_name": "hacl-star", "file_name": "Spec.Ed25519.Lemmas.fst", "name": "Spec.Ed25519.Lemmas.fdiv_lemma1" }, { "project_name": "FStar", "file_name": "FStar.Math.Fermat.fst", "name": "FStar.Math.Fermat.mod_mult_congr_aux" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.fst", "name": "Vale.Math.Poly2.lemma_mul_associate" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.P256.Montgomery.fst", "name": "Hacl.Spec.P256.Montgomery.qmont_cancel_lemma1" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_mul_mod_prime_zero" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_mod_distributivity_sub_right" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_mod_distributivity_add_left" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.modulo_modulo_lemma" }, { "project_name": "FStar", "file_name": "FStar.UInt.fst", "name": "FStar.UInt.lemma_sub_add_cancel" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Defs.fst", "name": "Vale.Math.Poly2.Defs.lemma_mul_associate" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_mod_mul_mod_right" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.P256.Qinv.fst", "name": "Hacl.Spec.P256.Qinv.lemma_pow_pow_mod_mul" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Math.fst", "name": "Vale.Poly1305.Math.lemma_mod_breakdown" }, { "project_name": "FStar", "file_name": "FStar.UInt.fst", "name": "FStar.UInt.lemma_add_sub_cancel" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_add_mod_assoc" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Defs.fst", "name": "Vale.Math.Poly2.Defs.lemma_mul_element" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_div_mod_prime_to_one_denominator" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GF128.fst", "name": "Vale.AES.GF128.lemma_gf128_mul" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_mul_distribute_right" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Galois.fst", "name": "Vale.Math.Poly2.Galois.lemma_mul" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Galois.fst", "name": "Vale.Math.Poly2.Galois.lemma_mul_pmul" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.ECSM.Lemmas.fst", "name": "Hacl.Spec.K256.ECSM.Lemmas.lemma_aff_point_mul_neg_mul_add" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.lemma_mod_mult_zero" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.MathLemmas.fst", "name": "Hacl.Spec.K256.MathLemmas.lemma_ab_le_cd" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Galois.fst", "name": "Vale.Math.Poly2.Galois.lemma_mul_element" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Lemmas.Int.fst", "name": "Vale.Math.Lemmas.Int.modulo_modulo_lemma" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_mod_cancel" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.Qinv.fst", "name": "Hacl.Spec.K256.Qinv.lemma_pow_pow_mod_mul" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GF128.fst", "name": "Vale.AES.GF128.lemma_gf128_mul_rev_commute" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GF128.fst", "name": "Vale.AES.GF128.lemma_gf128_mul_rev_distribute_right" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GF128.fst", "name": "Vale.AES.GF128.lemma_gf128_mul_rev_associate" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.Finv.fst", "name": "Hacl.Spec.K256.Finv.lemma_pow_pow_mod_mul" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.P256.Finv.fst", "name": "Hacl.Spec.P256.Finv.lemma_pow_pow_mod_mul" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.modulo_sub" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.P256.Montgomery.fst", "name": "Hacl.Spec.P256.Montgomery.qmont_cancel_lemma2" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.SHA_helpers.fst", "name": "Vale.SHA.PPC64LE.SHA_helpers.lemma_eq_maj_xvsel32" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.MathLemmas.fst", "name": "Hacl.Spec.K256.MathLemmas.lemma_ab_lt_cd" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.MathLemmas.fst", "name": "Hacl.Spec.K256.MathLemmas.lemma_distr_eucl_mul_add" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Galois.fst", "name": "Vale.Math.Poly2.Galois.lemma_mul_def" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_mod_distribute" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Spec.fst", "name": "Hacl.Streaming.Spec.mod_trans_lem" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Galois.fst", "name": "Vale.Math.Poly2.Galois.lemma_mul_pmul_k" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Bits.fst", "name": "Vale.Math.Bits.lemma_i2b_mul" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_mod_distributivity_add_right" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_mul_smaller_is_zero" }, { "project_name": "hacl-star", "file_name": "Spec.Ed25519.Lemmas.fst", "name": "Spec.Ed25519.Lemmas.fmul_both_lemma_neq" }, { "project_name": "hacl-star", "file_name": "Lib.NatMod.fst", "name": "Lib.NatMod.lemma_inv_mod_both" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.Lemmas.fst", "name": "Vale.Bignum.Lemmas.lemma_add_lo_mul_right" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.Field52.Lemmas.fst", "name": "Hacl.Spec.K256.Field52.Lemmas.lemma_mul_sub" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.division_multiplication_lemma" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.modulo_division_lemma" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.lemma_pow2_div2" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.distributivity_sub_right" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.K256.Field52.Lemmas.fst", "name": "Hacl.Spec.K256.Field52.Lemmas.lemma_mul_sub_last" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.lemma_mod_mul_distr_l" }, { "project_name": "hacl-star", "file_name": "Spec.Ed25519.Lemmas.fst", "name": "Spec.Ed25519.Lemmas.point_equal_lemma_aux2" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GHash_BE.fst", "name": "Vale.AES.GHash_BE.lemma_div_distribute" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Lemmas.fst", "name": "Hacl.Spec.Poly1305.Lemmas.mul_associativity" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.SHA_helpers.fst", "name": "Vale.SHA.PPC64LE.SHA_helpers.lemma_vsel32" }, { "project_name": "hacl-star", "file_name": "Lib.Sequence.fst", "name": "Lib.Sequence.div_mul_l" } ], "selected_premises": [ "FStar.Mul.op_Star", "Lib.Exponentiation.Definition.lemma_inverse_one", "Lib.Exponentiation.Definition.lemma_mul_cancel_inverse", "FStar.Pervasives.reveal_opaque", "FStar.Heap.trivial_preorder", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "FStar.ST.op_Bang", "Lib.LoopCombinators.fixed_a", "Lib.LoopCombinators.fixed_i", "FStar.ST.alloc", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "FStar.All.op_Bar_Greater", "FStar.All.op_Less_Bar", "FStar.Pervasives.all_post_h'", "FStar.ST.lemma_functoriality", "FStar.Pervasives.coerce_eq", "FStar.Heap.trivial_rel", "FStar.Preorder.preorder_rel", "FStar.Pervasives.all_post_h", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.id", "FStar.Pervasives.pure_close_wp", "FStar.Pervasives.pure_ite_wp", "Prims.auto_squash", "FStar.Calc.calc_chain_related", "FStar.Monotonic.Heap.modifies_t", "FStar.All.all_wp", "FStar.Pervasives.all_wp_h", "FStar.ST.get", "FStar.All.all_pre", "FStar.Pervasives.all_close_wp", "FStar.Monotonic.Heap.mref", "FStar.All.all_post", "FStar.All.pipe_left", "FStar.Pervasives.st_post_h", "FStar.Pervasives.all_ite_wp", "FStar.Pervasives.all_if_then_else", "FStar.All.all_post'", "FStar.Pervasives.all_return", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.pure_bind_wp", "Prims.abs", "Prims.pure_post'", "FStar.ST.gst_wp", "FStar.ST.lift_gst_state", "FStar.Pervasives.ex_pre", "FStar.Pervasives.all_trivial", "FStar.Pervasives.st_post_h'", "FStar.Preorder.transitive", "FStar.Monotonic.Heap.set", "FStar.Set.subset", "FStar.ST.contains_pred", "FStar.ST.st_post", "FStar.Monotonic.Heap.equal_dom", "FStar.Pervasives.all_stronger", "Prims.pure_trivial", "FStar.ST.gst_pre", "FStar.Set.add", "FStar.ST.st_pre", "FStar.ST.gst_post", "FStar.Monotonic.Heap.tset", "FStar.Pervasives.div_hoare_to_wp", "FStar.Monotonic.Heap.modifies", "FStar.Pervasives.st_if_then_else", "FStar.ST.st_post'", "FStar.Pervasives.st_pre_h", "FStar.All.lift_state_all", "FStar.ST.heap_rel", "FStar.Preorder.reflexive", "Prims.as_requires", "Prims.returnM", "Prims.pow2", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.ex_bind_wp", "FStar.Set.as_set'", "FStar.Pervasives.ex_if_then_else", "FStar.Pervasives.ex_post'", "FStar.All.pipe_right", "FStar.Monotonic.Heap.only", "FStar.ST.lift_div_gst", "FStar.Pervasives.pure_null_wp", "Prims.pure_pre", "Prims.min", "FStar.Set.remove", "FStar.Pervasives.st_stronger", "FStar.Set.as_set", "Prims.pure_wp'", "Prims.pure_post", "FStar.ST.op_Colon_Equals", "FStar.ST.gst_post'", "Prims.pure_wp_monotonic0", "FStar.All.lift_exn_all", "FStar.Pervasives.ex_return", "Prims.subtype_of", "FStar.Pervasives.ex_stronger", "FStar.Monotonic.Heap.op_Plus_Plus_Hat", "FStar.Pervasives.trivial_pure_post" ], "source_upto_this": "module Lib.Exponentiation.Definition\n\nopen FStar.Mul\n\nmodule Loops = Lib.LoopCombinators\n\n#set-options \"--z3rlimit 50 --fuel 0 --ifuel 0\"\n\nlet lemma_inverse_one #t k =\n lemma_inverse k.cm.one;\n assert (k.cm.mul (inverse cm.one) cm.one == cm.one);\n k.cm.lemma_one (inverse cm.one);\n assert (inverse k.cm.one == cm.one)\n\n\nval lemma_mul_cancel_inverse: #t:Type -> k:abelian_group t -> a:t -> b:t ->\n Lemma (cm.mul (inverse a) (cm.mul a b) == b)\n\nlet lemma_mul_cancel_inverse #t k a b =\n calc (==) {\n cm.mul (inverse a) (cm.mul a b);\n (==) { cm.lemma_mul_assoc (inverse a) a b }\n cm.mul (cm.mul (inverse a) a) b;\n (==) { lemma_inverse a }\n cm.mul cm.one b;\n (==) { cm.lemma_mul_comm cm.one b }\n cm.mul b cm.one;\n (==) { cm.lemma_one b }\n b;\n }\n\nval lemma_cancellation: #t:Type -> k:abelian_group t -> a:t -> b:t -> c:t -> Lemma\n (requires cm.mul a b == cm.mul a c)\n (ensures b == c)\n", "sketch": [ "Step 1: Assume the hypothesis that `cm.mul a b == cm.mul a c`.\nStep 2: Use the fact that `a` has an inverse in the abelian group.\nStep 3: Multiply both sides of the hypothesis by the inverse of `a`.\nStep 4: Simplify the left-hand side using the associativity of multiplication.\nStep 5: Apply the lemma `lemma_inverse` to simplify further.\nStep 6: Use the property that `cm.mul cm.one x == x` for any `x`.\nStep 7: Conclude that `b == c` from the simplified equation.", "Step 1: Assume the premise that `cm.mul a b == cm.mul a c`.\nStep 2: Multiply both sides of the equation by the inverse of `a` using the group properties.\nStep 3: Use the associativity property of multiplication to rearrange the terms.\nStep 4: Apply the lemma that states multiplying an element by its inverse results in the identity element.\nStep 5: Simplify the equation using the identity property of the group.\nStep 6: Conclude that `b == c` by the properties of the identity element.", "Step 1: Assume the hypothesis that `cm.mul a b == cm.mul a c`.\nStep 2: Multiply both sides of the equation by the inverse of `a` using the group properties.\nStep 3: Use the associativity property of multiplication to rearrange the terms.\nStep 4: Simplify the left-hand side using the property that `cm.mul (inverse a) a == cm.one`.\nStep 5: Use the identity property of multiplication to further simplify.\nStep 6: Conclude that `b == c` by the equality of the simplified expressions.", "Step 1: Assume the premise that \\( cm.mul \\, a \\, b == cm.mul \\, a \\, c \\).\nStep 2: Multiply both sides of the equation by the inverse of \\( a \\) on the left.\nStep 3: Use the associativity of multiplication to rewrite the left-hand side.\nStep 4: Apply the lemma that states \\( cm.mul \\, (inverse \\, a) \\, (cm.mul \\, a \\, x) == x \\) to simplify both sides.\nStep 5: Conclude that \\( b == c \\).", "Step 1: Assume the hypothesis that `cm.mul a b == cm.mul a c`.\nStep 2: Use the lemma `lemma_mul_cancel_inverse` with `a` and `cm.mul a b` to get `cm.mul (inverse a) (cm.mul a b) == b`.\nStep 3: Similarly, use `lemma_mul_cancel_inverse` with `a` and `cm.mul a c` to get `cm.mul (inverse a) (cm.mul a c) == c`.\nStep 4: By the hypothesis, `cm.mul a b == cm.mul a c`, we can substitute `cm.mul a b` with `cm.mul a c` in the results from steps 2 and 3.\nStep 5: Conclude that `b == c` by transitivity.", "Step 1: Assume the premise that `cm.mul a b == cm.mul a c`.\nStep 2: Multiply both sides of the equation by the inverse of `a` using the abelian group properties.\nStep 3: Use the associativity of multiplication to rearrange the terms.\nStep 4: Apply the lemma `lemma_inverse` to simplify the expression involving the inverse of `a`.\nStep 5: Use the property that multiplying by the identity element `cm.one` does not change the value.\nStep 6: Conclude that `b == c` by the properties of the abelian group.", "Step 1: Assume the premise that \\( \\text{cm.mul} \\, a \\, b == \\text{cm.mul} \\, a \\, c \\).\nStep 2: Multiply both sides of the equation by the inverse of \\( a \\) using the group properties.\nStep 3: Apply the associativity property of multiplication to rearrange the terms.\nStep 4: Use the lemma that states multiplying an element by its inverse results in the identity element.\nStep 5: Simplify the equation using the identity property of the group.\nStep 6: Conclude that \\( b == c \\) by the properties of the identity element.", "Step 1: Assume the hypothesis that `cm.mul a b == cm.mul a c`.\nStep 2: Use the lemma `lemma_mul_cancel_inverse` to multiply both sides of the equation by the inverse of `a`.\nStep 3: Simplify both sides using the properties of the abelian group, specifically the associativity and the inverse properties.\nStep 4: Conclude that `b == c` after the simplifications.", "Step 1: Assume that `cm.mul a b == cm.mul a c`.\nStep 2: Use the lemma `lemma_mul_cancel_inverse` to multiply both sides of the equation by the inverse of `a`.\nStep 3: Simplify the equation using the properties of the abelian group, specifically the associativity and the identity element.\nStep 4: Conclude that `b == c` by the cancellation property of the group.", "Step 1: Assume the hypothesis that `cm.mul a b == cm.mul a c`.\nStep 2: Use the property of the abelian group that allows us to multiply both sides of the equation by the inverse of `a`.\nStep 3: Simplify the left-hand side using the associativity of multiplication.\nStep 4: Apply the lemma `lemma_inverse` to simplify further.\nStep 5: Use the property that multiplying by the identity element `cm.one` does not change the value.\nStep 6: Conclude that `b == c` by the properties of the abelian group." ], "generated_solution": [ "let lemma_cancellation #t k a b c =\n assume (H: cm.mul a b == cm.mul a c);\n let inv_a = inverse a in\n calc (==) {\n b;\n (==) { cm.lemma_one b }\n cm.mul cm.one b;\n (==) { cm.lemma_mul_comm cm.one b }\n cm.mul b cm.one;\n (==) { lemma_mul_cancel_inverse k inv_a b c }\n cm.mul (inverse a) (cm.mul a b);\n (==) { H }\n cm.mul (inverse a) (cm.mul a c);\n (==) { cm.lemma_mul_assoc (inverse a) a c }\n cm.mul (cm.mul (inverse a) a) c;\n (==) { lemma_inverse a }\n cm.mul cm.one c;\n (==) { cm.lemma_one c }\n c;\n }", "let lemma_cancellation #t k a b c =\n assume (H: cm.mul a b == cm.mul a c);\n calc (==) {\n b;\n (==) { lemma_mul_cancel_inverse k a b }\n cm.mul (inverse a) (cm.mul a b);\n (==) { H }\n cm.mul (inverse a) (cm.mul a c);\n (==) { lemma_mul_cancel_inverse k a c }\n c;\n }", "let lemma_cancellation #t k a b c =\n assume (H: cm.mul a b == cm.mul a c);\n calc (==) {\n b;\n (==) { cm.lemma_one b }\n cm.mul cm.one b;\n (==) { cm.lemma_mul_comm cm.one b }\n cm.mul b cm.one;\n (==) { lemma_mul_cancel_inverse k a b }\n cm.mul (inverse a) (cm.mul a b);\n (==) { H }\n cm.mul (inverse a) (cm.mul a c);\n (==) { lemma_mul_cancel_inverse k a c }\n cm.mul c cm.one;\n (==) { cm.lemma_mul_comm cm.one c }\n cm.mul cm.one c;\n (==) { cm.lemma_one c }\n c;\n }", "let lemma_cancellation #t k a b c =\n assume (H: cm.mul a b == cm.mul a c);\n calc (==) {\n b;\n (==) { lemma_mul_cancel_inverse k a b }\n cm.mul (inverse a) (cm.mul a b);\n (==) { H }\n cm.mul (inverse a) (cm.mul a c);\n (==) { lemma_mul_cancel_inverse k a c }\n c;\n }", "let lemma_cancellation #t k a b c =\n assume (H: cm.mul a b == cm.mul a c);\n assert (cm.mul (inverse a) (cm.mul a b) == b) by (lemma_mul_cancel_inverse a b);\n assert (cm.mul (inverse a) (cm.mul a c) == c) by (lemma_mul_cancel_inverse a c);\n assert (cm.mul (inverse a) (cm.mul a b) == cm.mul (inverse a) (cm.mul a c)) by (rewrite H);\n assert (b == c) by (transitivity (cm.mul (inverse a) (cm.mul a b)) (cm.mul (inverse a) (cm.mul a c)));\n ()", "let lemma_cancellation #t k a b c =\n assume (H: cm.mul a b == cm.mul a c);\n calc (==) {\n b;\n (==) { lemma_mul_cancel_inverse k a b }\n cm.mul (inverse a) (cm.mul a b);\n (==) { H }\n cm.mul (inverse a) (cm.mul a c);\n (==) { lemma_mul_cancel_inverse k a c }\n c;\n }", "let lemma_cancellation #t k a b c =\n assume (cm.mul a b == cm.mul a c);\n calc (==) {\n b;\n (==) { lemma_mul_cancel_inverse k a b }\n cm.mul (inverse a) (cm.mul a b);\n (==) { H }\n cm.mul (inverse a) (cm.mul a c);\n (==) { lemma_mul_cancel_inverse k a c }\n c;\n }", "let lemma_cancellation #t k a b c =\n assume (cm.mul a b == cm.mul a c);\n calc (==) {\n b;\n (==) { lemma_mul_cancel_inverse k a b }\n cm.mul (inverse a) (cm.mul a b);\n (==) { H }\n cm.mul (inverse a) (cm.mul a c);\n (==) { lemma_mul_cancel_inverse k a c }\n c;\n }", "let lemma_cancellation #t k a b c =\n assume (cm.mul a b == cm.mul a c);\n calc (==) {\n b;\n (==) { lemma_mul_cancel_inverse k a b }\n cm.mul (inverse a) (cm.mul a b);\n (==) { H: cm.mul a b == cm.mul a c }\n cm.mul (inverse a) (cm.mul a c);\n (==) { lemma_mul_cancel_inverse k a c }\n c;\n }", "let lemma_cancellation #t k a b c =\n assume (cm.mul a b == cm.mul a c);\n calc (==) {\n b;\n (==) { lemma_mul_cancel_inverse k a b }\n cm.mul (inverse a) (cm.mul a b);\n (==) { H }\n cm.mul (inverse a) (cm.mul a c);\n (==) { lemma_mul_cancel_inverse k a c }\n c;\n }" ] }, { "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.raise_loc", "opens_and_abbrevs": [ { "abbrev": "U", "full_module": "FStar.Universe" }, { "abbrev": "F", "full_module": "FStar.FunctionalExtensionality" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "open": "FStar" }, { "open": "FStar" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val raise_loc (#al: aloc_t u#x) (#c: cls al) (l: loc c) : Tot (loc (raise_cls u#x u#y c))", "source_definition": "let raise_loc #al #c l =\n let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n Loc\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide (GSet.comprehend (raise_loc_aux_pred c aux)))", "source_range": { "start_line": 2136, "start_col": 0, "end_line": 2143, "end_col": 61 }, "interleaved": false, "definition": "fun l ->\n let _ = l in\n (let FStar.ModifiesGen.Loc #_ #_ regions region_liveness_tags non_live_addrs live_addrs aux = _ in\n FStar.ModifiesGen.Loc regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (FStar.Ghost.hide (FStar.GSet.comprehend (FStar.ModifiesGen.raise_loc_aux_pred c aux))))\n <:\n FStar.ModifiesGen.loc (FStar.ModifiesGen.raise_cls c)", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.ModifiesGen.aloc_t", "FStar.ModifiesGen.cls", "FStar.ModifiesGen.loc", "FStar.Ghost.erased", "FStar.Set.set", "FStar.Monotonic.HyperHeap.rid", "FStar.Set.subset", "FStar.Ghost.reveal", "FStar.ModifiesGen.i_restricted_g_t", "FStar.ModifiesGen.addrs_dom", "FStar.ModifiesGen.non_live_addrs_codom", "FStar.ModifiesGen.live_addrs_codom", "FStar.GSet.set", "FStar.ModifiesGen.aloc", "Prims.l_and", "FStar.GSet.subset", "FStar.ModifiesGen.aloc_domain", "Prims.b2t", "FStar.Set.mem", "FStar.GSet.complement", "Prims.nat", "FStar.GSet.empty", "FStar.ModifiesGen.Loc", "FStar.ModifiesGen.raise_aloc", "FStar.ModifiesGen.raise_cls", "FStar.Ghost.hide", "FStar.GSet.comprehend", "FStar.ModifiesGen.raise_loc_aux_pred" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "l: FStar.ModifiesGen.loc c -> FStar.ModifiesGen.loc (FStar.ModifiesGen.raise_cls c)", "prompt": "let raise_loc #al #c l =\n ", "expected_response": "let Loc regions region_liveness_tags non_live_addrs live_addrs aux = l in\nLoc regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide (GSet.comprehend (raise_loc_aux_pred c aux)))", "source": { "project_name": "FStar", "file_name": "ulib/FStar.ModifiesGen.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.ModifiesGen.fst", "checked_file": "dataset/FStar.ModifiesGen.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Universe.fsti.checked", "dataset/FStar.Tactics.SMT.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Stubs.Tactics.V2.Builtins.fsti.checked", "dataset/FStar.StrongExcludedMiddle.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Map.fsti.checked", "dataset/FStar.HyperStack.ST.fsti.checked", "dataset/FStar.HyperStack.fst.checked", "dataset/FStar.Heap.fst.checked", "dataset/FStar.GSet.fsti.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "aloc", "ALoc", "ALoc", "ALoc", "aloc_t", "region", "region", "addr", "addr", "loc", "loc", "cls", "Cls", "Cls", "Cls", "aloc_includes", "aloc_includes", "let aloc_domain (#al: aloc_t) (c: cls al) (regions: Ghost.erased (Set.set HS.rid)) (addrs: ((r: HS.rid { Set.mem r (Ghost.reveal regions) } ) -> GTot (GSet.set nat))) : GTot (GSet.set (aloc c)) =\n GSet.comprehend (fun a -> Set.mem a.region (Ghost.reveal regions) && GSet.mem a.addr (addrs a.region))", "aloc_includes_refl", "aloc_includes_refl", "let i_restricted_g_t = F.restricted_g_t", "let addrs_dom regions =\n (r: HS.rid { Set.mem r (Ghost.reveal regions) } )", "let non_live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (r:addrs_dom regions) =\n (y: GSet.set nat { r `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y })", "aloc_includes_trans", "aloc_includes_trans", "let live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags))\n (r:addrs_dom regions) = (y: GSet.set nat { GSet.subset (non_live_addrs r) y } )", "aloc_disjoint", "aloc_disjoint", "loc'", "Loc", "Loc", "Loc", "regions", "regions", "aloc_disjoint_sym", "aloc_disjoint_sym", "region_liveness_tags", "region_liveness_tags", "non_live_addrs", "non_live_addrs", "live_addrs", "live_addrs", "aloc_disjoint_includes", "aloc_disjoint_includes", "aux", "aux", "let loc = loc'", "let mk_non_live_addrs (#regions:_) (#region_liveness_tags:_)\n (f: (x:addrs_dom regions -> GTot (non_live_addrs_codom regions region_liveness_tags x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags) =\n F.on_dom_g _ f", "aloc_preserved", "aloc_preserved", "let mk_live_addrs (#regions:_) (#region_liveness_tags:_)\n (#non_live_addrs_codom: _)\n (f: (x:addrs_dom regions -> GTot (live_addrs_codom regions region_liveness_tags non_live_addrs_codom x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs_codom) =\n F.on_dom_g _ f", "aloc_preserved_refl", "aloc_preserved_refl", "let loc_none #a #c =\n Loc\n (Ghost.hide (Set.empty))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)", "aloc_preserved_trans", "aloc_preserved_trans", "let regions_of_loc\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: GTot (Set.set HS.rid)\n= Ghost.reveal (Loc?.regions s)", "let addrs_of_loc_liveness_not_preserved\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.non_live_addrs l r\n else GSet.empty", "same_mreference_aloc_preserved", "same_mreference_aloc_preserved", "let addrs_of_loc_weak\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.live_addrs l r\n else GSet.empty", "let addrs_of_loc_aux_pred\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n (addr: nat)\n: GTot bool\n= StrongExcludedMiddle.strong_excluded_middle (exists a . GSet.mem a (Ghost.reveal (Loc?.aux l)) /\\ a.region == r /\\ a.addr == addr)", "val loc (#aloc: aloc_t u#x) (c: cls aloc) : Tot (Type u#x)", "val loc_none (#aloc: aloc_t) (#c: cls aloc): Tot (loc c)", "val loc_union\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot (loc c)", "let addrs_of_loc_aux\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (y: GSet.set nat { GSet.subset (GSet.intersect y (addrs_of_loc_weak l r)) GSet.empty } )\n= GSet.comprehend (addrs_of_loc_aux_pred l r)\n `GSet.intersect` (GSet.complement (addrs_of_loc_weak l r))", "val loc_union_idem\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union s s == s)", "let addrs_of_loc\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= GSet.union\n (addrs_of_loc_weak l r)\n (addrs_of_loc_aux l r)", "val loc_union_comm\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: Lemma\n (loc_union s1 s2 == loc_union s2 s1)", "let addrs_of_loc_aux_prop\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: Lemma\n (GSet.subset (GSet.intersect (addrs_of_loc_aux l r) (addrs_of_loc_weak l r)) GSet.empty)\n [SMTPatOr [\n [SMTPat (addrs_of_loc_aux l r)];\n [SMTPat (addrs_of_loc_weak l r)];\n [SMTPat (addrs_of_loc l r)];\n ]]\n= ()", "val loc_union_assoc\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s3: loc c)\n: Lemma\n (loc_union s1 (loc_union s2 s3) == loc_union (loc_union s1 s2) s3)", "val loc_union_loc_none_l\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union loc_none s == s)", "val loc_union_loc_none_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union s loc_none == s)", "let loc_union #al #c s1 s2 =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in\n let regions = Set.union regions1 regions2 in\n let region_liveness_tags : Ghost.erased (Set.set HS.rid) = (Ghost.hide (Set.union (Ghost.reveal (Loc?.region_liveness_tags s1)) (Ghost.reveal (Loc?.region_liveness_tags s2)))) in\n let gregions = Ghost.hide regions in\n let non_live_addrs =\n F.on_dom_g (addrs_dom gregions) #(non_live_addrs_codom gregions region_liveness_tags)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then Loc?.non_live_addrs s1 r else GSet.empty)\n (if Set.mem r regions2 then Loc?.non_live_addrs s2 r else GSet.empty))\n in\n let live_addrs =\n F.on_dom_g (addrs_dom gregions) #(live_addrs_codom gregions region_liveness_tags non_live_addrs)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then addrs_of_loc_weak s1 r else GSet.empty)\n (if Set.mem r regions2 then addrs_of_loc_weak s2 r else GSet.empty))\n in\n let aux = Ghost.hide\n (Ghost.reveal (Loc?.aux s1) `GSet.union` Ghost.reveal (Loc?.aux s2))\n in\n Loc\n (Ghost.hide regions)\n region_liveness_tags\n non_live_addrs\n live_addrs\n aux", "val loc_of_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b: aloc r n)\n: GTot (loc c)", "val loc_of_aloc_not_none\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b: aloc r n)\n: Lemma (loc_of_aloc #_ #c b == loc_none ==> False)", "val loc_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: GTot (loc c)", "val loc_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: GTot (loc c)", "let fun_set_equal (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) :Tot Type0 =\n forall (x: t) . {:pattern (f1 x) \\/ (f2 x) } f1 x `GSet.equal` f2 x", "let loc_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses true (HS.frameOf b) (Set.singleton (HS.as_addr b))", "let fun_set_equal_elim (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) : Lemma\n (requires (fun_set_equal f1 f2))\n (ensures (f1 == f2))\n// [SMTPat (fun_set_equal f1 f2)]\n= assert (f1 `FunctionalExtensionality.feq_g` f2)", "let loc_freed_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses false (HS.frameOf b) (Set.singleton (HS.as_addr b))", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n let Loc regions1 region_liveness_tags1 _ _ aux1 = s1 in\n let Loc regions2 region_liveness_tags2 _ _ aux2 = s2 in\n Ghost.reveal regions1 `Set.equal` Ghost.reveal regions2 /\\\n Ghost.reveal region_liveness_tags1 `Set.equal` Ghost.reveal region_liveness_tags2 /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_region_only\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (Set.singleton r)", "let loc_equal_elim (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : Lemma\n (requires (loc_equal s1 s2))\n (ensures (s1 == s2))\n [SMTPat (s1 `loc_equal` s2)]\n= fun_set_equal_elim (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2);\n fun_set_equal_elim (Loc?.live_addrs s1) (Loc?.live_addrs s2)", "let loc_all_regions_from\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (HS.mod_set (Set.singleton r))", "let loc_union_idem #al #c s =\n assert (loc_union s s `loc_equal` s)", "let loc_union_comm #al #c s1 s2 =\n assert (loc_union s1 s2 `loc_equal` loc_union s2 s1)", "let loc_union_assoc #al #c s1 s2 s3 =\n assert (loc_union s1 (loc_union s2 s3) `loc_equal` loc_union (loc_union s1 s2) s3)", "val loc_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot Type0", "let loc_union_loc_none_l #al #c s =\n assert (loc_union loc_none s `loc_equal` s)", "val loc_includes_refl\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_includes s s)", "let loc_union_loc_none_r #al #c s =\n assert (loc_union s loc_none `loc_equal` s)", "let loc_of_aloc #al #c #r #n b =\n let regions = (Ghost.hide (Set.singleton r)) in\n let region_liveness_tags = (Ghost.hide (Set.empty)) in\n Loc\n regions\n region_liveness_tags\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide (GSet.singleton (ALoc r n (Some b))))", "val loc_includes_trans\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s3: loc c)\n: Lemma\n (requires (loc_includes s1 s2 /\\ loc_includes s2 s3))\n (ensures (loc_includes s1 s3))", "val loc_includes_union_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s s1 s2: loc c)\n: Lemma\n (requires (loc_includes s s1 /\\ loc_includes s s2))\n (ensures (loc_includes s (loc_union s1 s2)))", "let loc_of_aloc_not_none #al #c #r #n b = ()", "let loc_addresses #al #c preserve_liveness r n =\n let regions = (Ghost.hide (Set.singleton r)) in\n Loc\n regions\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> if preserve_liveness then GSet.empty else GSet.of_set n))\n (mk_live_addrs (fun _ -> GSet.of_set n))\n (Ghost.hide (aloc_domain c regions (fun _ -> GSet.of_set n)))", "val loc_includes_union_l\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s: loc c)\n: Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))", "let loc_regions_region_liveness_tags (preserve_liveness: bool) (r: Set.set HS.rid) : Tot (Ghost.erased (Set.set HS.rid)) =\n if preserve_liveness then Ghost.hide Set.empty else Ghost.hide r", "val loc_includes_none\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_includes s loc_none)", "let loc_regions #al #c preserve_liveness r =\n let region_liveness_tags = loc_regions_region_liveness_tags preserve_liveness r in\n let addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { r' `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y } ) =\n GSet.complement GSet.empty\n in\n let live_addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { addrs r' `GSet.subset` y } ) =\n addrs r'\n in\n Loc\n (Ghost.hide r)\n region_liveness_tags\n (mk_non_live_addrs addrs)\n (mk_live_addrs live_addrs)\n (Ghost.hide (aloc_domain c (Ghost.hide r) addrs))", "val loc_includes_none_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (requires (loc_includes loc_none s))\n (ensures (s == loc_none))", "val loc_includes_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b1 b2: aloc r n)\n: Lemma\n (requires (c.aloc_includes b1 b2))\n (ensures (loc_includes (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))", "let aloc_includes (#al: aloc_t) (#c: cls al) (b0 b: aloc c) : GTot Type0 =\n b0.region == b.region /\\ b0.addr == b.addr /\\ Some? b0.loc == Some? b.loc /\\ (if Some? b0.loc && Some? b.loc then c.aloc_includes (Some?.v b0.loc) (Some?.v b.loc) else True)", "let loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b: aloc c)\n: GTot Type0\n (decreases s)\n= exists (b0 : aloc c) . b0 `GSet.mem` s /\\ b0 `aloc_includes` b", "val loc_includes_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1 #r2: HS.rid)\n (#n1 #n2: nat)\n (b1: aloc r1 n1)\n (b2: aloc r2 n2)\n: Lemma\n (requires (loc_includes (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))\n (ensures (r1 == r2 /\\ n1 == n2 /\\ c.aloc_includes b1 b2))", "let loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: GTot Type0\n (decreases s2)\n= forall (b2: aloc c) . GSet.mem b2 s2 ==> loc_aux_includes_buffer s1 b2", "val loc_includes_addresses_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n (s: Set.set nat)\n (#a: nat)\n (p: aloc r a)\n: Lemma\n (requires (Set.mem a s))\n (ensures (loc_includes (loc_addresses preserve_liveness r s) (loc_of_aloc #_ #c p)))", "let loc_aux_includes_union_l\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s \\/ loc_aux_includes s2 s))\n (ensures (loc_aux_includes (GSet.union s1 s2) s))\n (decreases s)\n= ()", "let loc_aux_includes_refl\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n: Lemma\n (loc_aux_includes s s)\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)", "val loc_includes_region_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (s: Set.set HS.rid)\n (#r: HS.rid)\n (#a: nat)\n (b: aloc r a)\n: Lemma\n (requires (Set.mem r s))\n (ensures (loc_includes (loc_regions preserve_liveness s) (loc_of_aloc #_ #c b)))", "let loc_aux_includes_subset\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)", "val loc_includes_region_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (s: Set.set HS.rid)\n (r: HS.rid)\n (a: Set.set nat)\n: Lemma\n (requires (Set.mem r s))\n (ensures (loc_includes (loc_regions #_ #c preserve_liveness1 s) (loc_addresses preserve_liveness2 r a)))", "let loc_aux_includes_subset'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n [SMTPatOr [\n [SMTPat (s1 `GSet.subset` s2)];\n [SMTPat (loc_aux_includes s2 s1)];\n ]]\n= loc_aux_includes_subset s1 s2", "val loc_includes_region_region\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires ((preserve_liveness1 ==> preserve_liveness2) /\\ Set.subset s2 s1))\n (ensures (loc_includes (loc_regions #_ #c preserve_liveness1 s1) (loc_regions preserve_liveness2 s2)))", "let loc_aux_includes_union_l_r\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s s') s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s s' s", "val loc_includes_region_union_l\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (l: loc c)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires (loc_includes l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)))))\n (ensures (loc_includes (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness s2)))", "let loc_aux_includes_union_l_l\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s' s) s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s' s s", "val loc_includes_addresses_addresses\n (#aloc: aloc_t) (c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r: HS.rid)\n (a1 a2: Set.set nat)\n: Lemma\n (requires ((preserve_liveness1 ==> preserve_liveness2) /\\ Set.subset a2 a1))\n (ensures (loc_includes #_ #c (loc_addresses preserve_liveness1 r a1) (loc_addresses preserve_liveness2 r a2)))", "let loc_aux_includes_buffer_includes\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b1 b2: aloc c)\n: Lemma\n (requires (loc_aux_includes_buffer s b1 /\\ b1 `aloc_includes` b2))\n (ensures (loc_aux_includes_buffer s b2))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))", "val loc_disjoint\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot Type0", "let loc_aux_includes_loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n (b: aloc c)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_buffer s2 b))\n (ensures (loc_aux_includes_buffer s1 b))\n= Classical.forall_intro_3 (fun s b1 b2 -> Classical.move_requires (loc_aux_includes_buffer_includes #al #c s b1) b2)", "val loc_disjoint_sym\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))", "let loc_aux_includes_trans\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))", "val loc_disjoint_none_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (ensures (loc_disjoint s loc_none))", "let addrs_of_loc_weak_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (loc_union l1 l2) r == GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r))\n [SMTPat (addrs_of_loc_weak (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc_weak (loc_union l1 l2) r) (GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r)))", "val loc_disjoint_union_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s s1 /\\ loc_disjoint s s2))\n (ensures (loc_disjoint s (loc_union s1 s2)))", "val loc_disjoint_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (p1 p2 p1' p2' : loc c)\n: Lemma\n (requires (loc_includes p1 p1' /\\ loc_includes p2 p2' /\\ loc_disjoint p1 p2))\n (ensures (loc_disjoint p1' p2'))", "let addrs_of_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l1 l2) r == GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r))\n [SMTPat (addrs_of_loc (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc (loc_union l1 l2) r) (GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r)))", "val loc_disjoint_aloc_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1: HS.rid)\n (#a1: nat)\n (#r2: HS.rid)\n (#a2: nat)\n (b1: aloc r1 a1)\n (b2: aloc r2 a2)\n: Lemma\n (requires ((r1 == r2 /\\ a1 == a2) ==> c.aloc_disjoint b1 b2))\n (ensures (loc_disjoint (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))", "let loc_includes' #al (#c: cls al) (s1 s2: loc c) =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in (\n Set.subset regions2 regions1 /\\\n Set.subset (Ghost.reveal (Loc?.region_liveness_tags s2)) (Ghost.reveal (Loc?.region_liveness_tags s1)) /\\\n (\n forall (r: HS.rid { Set.mem r regions2 } ) .\n GSet.subset (Loc?.non_live_addrs s2 r) (Loc?.non_live_addrs s1 r)\n ) /\\\n (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc_weak s2 r) (addrs_of_loc_weak s1 r)\n ) /\\ (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc s2 r) (addrs_of_loc s1 r)\n ) /\\ (\n (Ghost.reveal (Loc?.aux s1)) `loc_aux_includes` (Ghost.reveal (Loc?.aux s2))\n )\n )", "val loc_disjoint_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1: HS.rid)\n (#a1: nat)\n (#r2: HS.rid)\n (#a2: nat)\n (b1: aloc r1 a1)\n (b2: aloc r2 a2)\n: Lemma\n (requires (loc_disjoint (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))\n (ensures ((r1 == r2 /\\ a1 == a2) ==> c.aloc_disjoint b1 b2))", "val loc_disjoint_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r1 r2: HS.rid)\n (n1 n2: Set.set nat)\n: Lemma\n (requires (r1 <> r2 \\/ Set.subset (Set.intersect n1 n2) Set.empty))\n (ensures (loc_disjoint (loc_addresses #_ #c preserve_liveness1 r1 n1) (loc_addresses preserve_liveness2 r2 n2)))", "let loc_includes #al #c s1 s2 =\n loc_includes' s1 s2", "let loc_includes_refl #al #c s =\n loc_aux_includes_refl (Ghost.reveal (Loc?.aux s))", "let loc_includes_refl'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: Lemma\n (loc_includes s s)\n [SMTPat (loc_includes s s)]\n= loc_includes_refl s", "let loc_disjoint_addresses #aloc #c = loc_disjoint_addresses_intro #aloc #c", "val loc_disjoint_addresses_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r1 r2: HS.rid)\n (n1 n2: Set.set nat)\n: Lemma\n (requires (loc_disjoint (loc_addresses #_ #c preserve_liveness1 r1 n1) (loc_addresses preserve_liveness2 r2 n2)))\n (ensures (r1 <> r2 \\/ Set.subset (Set.intersect n1 n2) Set.empty))", "let loc_includes_trans #al #c s1 s2 s3 =\n loc_aux_includes_trans (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s3))", "let loc_includes_union_r #al #c s s1 s2 = ()", "let loc_includes_union_l #al #c s1 s2 s =\n let u12 = loc_union s1 s2 in\n Classical.or_elim\n #(loc_includes s1 s)\n #(loc_includes s2 s)\n #(fun _ -> loc_includes (loc_union s1 s2) s)\n (fun _ ->\n loc_aux_includes_union_l_r (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2));\n assert (loc_includes (loc_union s1 s2) s1);\n loc_includes_trans u12 s1 s)\n (fun _ ->\n loc_aux_includes_union_l_l (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s1));\n assert (loc_includes (loc_union s1 s2) s2);\n loc_includes_trans u12 s2 s)", "val loc_disjoint_aloc_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (#r' : HS.rid)\n (#a' : nat)\n (p: aloc r' a')\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (requires (r == r' ==> (~ (Set.mem a' n))))\n (ensures (loc_disjoint (loc_of_aloc p) (loc_addresses #_ #c preserve_liveness r n)))", "val loc_disjoint_aloc_addresses_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r' : HS.rid)\n (#a' : nat)\n (p: aloc r' a')\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (requires (loc_disjoint (loc_of_aloc p) (loc_addresses #_ #c preserve_liveness r n)))\n (ensures (r == r' ==> (~ (Set.mem a' n))))", "let loc_includes_none #al #c s = ()", "let loc_includes_none_elim #al #c s =\n assert (s `loc_equal` loc_none)", "let loc_includes_aloc #al #c #r #n b1 b2 = ()", "let loc_includes_aloc_elim #aloc #c #r1 #r2 #n1 #n2 b1 b2 = ()", "let addrs_of_loc_loc_of_aloc\n (#al: aloc_t)\n (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (p: al r a)\n (r': HS.rid)\n: Lemma\n (addrs_of_loc (loc_of_aloc #_ #c p) r' `GSet.equal` (if r = r' then GSet.singleton a else GSet.empty))\n [SMTPat (addrs_of_loc (loc_of_aloc #_ #c p) r')]\n= ()", "val loc_disjoint_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (rs1 rs2: Set.set HS.rid)\n: Lemma\n (requires (Set.subset (Set.intersect rs1 rs2) Set.empty))\n (ensures (loc_disjoint (loc_regions #_ #c preserve_liveness1 rs1) (loc_regions preserve_liveness2 rs2)))", "val address_liveness_insensitive_locs (#aloc: aloc_t) (c: cls aloc) : Tot (loc c)", "let loc_includes_addresses_aloc #al #c preserve_liveness r s #a p = ()", "val loc_includes_address_liveness_insensitive_locs_aloc (#aloc: aloc_t) (#c: cls aloc) (#r: HS.rid) (#n: nat) (a: aloc r n) : Lemma\n (loc_includes (address_liveness_insensitive_locs c) (loc_of_aloc a))", "let loc_includes_region_aloc #al #c preserve_liveness s #r #a b = ()", "let loc_includes_region_addresses #al #c s preserve_liveness1 preserve_liveness2 r a = ()", "val loc_includes_address_liveness_insensitive_locs_addresses (#aloc: aloc_t) (c: cls aloc) (r: HS.rid) (a: Set.set nat) : Lemma\n (loc_includes (address_liveness_insensitive_locs c) (loc_addresses true r a))", "let loc_includes_region_region #al #c preserve_liveness1 preserve_liveness2 s1 s2 = ()", "val region_liveness_insensitive_locs (#al: aloc_t) (c: cls al) : Tot (loc c)", "let loc_includes_region_union_l #al #c preserve_liveness l s1 s2 =\n assert ((loc_regions #_ #c preserve_liveness (Set.intersect s2 (Set.complement s1)) `loc_union` loc_regions #_ #c preserve_liveness (Set.intersect s2 s1)) `loc_equal` loc_regions preserve_liveness s2);\n loc_includes_region_region #_ #c preserve_liveness preserve_liveness s1 (Set.intersect s2 s1);\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)));\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 s1));\n loc_includes_union_r (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1))) (loc_regions preserve_liveness (Set.intersect s2 s1))", "val loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs (#al: aloc_t) (c: cls al) : Lemma\n (loc_includes (region_liveness_insensitive_locs c) (address_liveness_insensitive_locs c))", "val loc_includes_region_liveness_insensitive_locs_loc_regions\n (#al: aloc_t) (c: cls al) (r: Set.set HS.rid)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_regions #_ #c true r)", "let loc_includes_addresses_addresses #al c preserve_liveness1 preserve_liveness2 r s1 s2 = ()", "val loc_includes_region_liveness_insensitive_locs_loc_addresses\n (#al: aloc_t) (c: cls al) (preserve_liveness: bool) (r: HS.rid) (a: Set.set nat)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_addresses #_ #c preserve_liveness r a)", "let aloc_disjoint (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : GTot Type0 =\n if b1.region = b2.region && b1.addr = b2.addr\n then Some? b1.loc /\\ Some? b2.loc /\\ c.aloc_disjoint (Some?.v b1.loc) (Some?.v b2.loc)\n else True", "val loc_includes_region_liveness_insensitive_locs_loc_of_aloc\n (#al: aloc_t) (c: cls al) (#r: HS.rid) (#a: nat) (x: al r a)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_of_aloc #_ #c x)", "let aloc_disjoint_sym (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : Lemma\n (aloc_disjoint b1 b2 <==> aloc_disjoint b2 b1)\n= Classical.forall_intro_2 (fun r a -> Classical.forall_intro_2 (fun b1 b2 -> c.aloc_disjoint_sym #r #a b1 b2))", "let loc_aux_disjoint\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: GTot Type0\n= forall (b1 b2: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b2 l2) ==> aloc_disjoint b1 b2", "val modifies\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0", "let loc_aux_disjoint_union_l\n (#al: aloc_t) (#c: cls al)\n (ll1 lr1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint (GSet.union ll1 lr1) l2 <==> (loc_aux_disjoint ll1 l2 /\\ loc_aux_disjoint lr1 l2)))\n= ()", "val modifies_intro\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')", "let loc_aux_disjoint_union_r\n (#al: aloc_t) (#c: cls al)\n (l1 ll2 lr2: GSet.set (aloc c))\n: Lemma\n (loc_aux_disjoint l1 (GSet.union ll2 lr2) <==> (loc_aux_disjoint l1 ll2 /\\ loc_aux_disjoint l1 lr2))\n= ()", "let loc_aux_disjoint_sym\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint l1 l2 <==> loc_aux_disjoint l2 l1))\n= Classical.forall_intro_2 (aloc_disjoint_sym #al #c)", "let regions_of_loc_loc_union\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (regions_of_loc (loc_union s1 s2) == regions_of_loc s1 `Set.union` regions_of_loc s2)\n [SMTPat (regions_of_loc (loc_union s1 s2))]\n= assert (regions_of_loc (loc_union s1 s2) `Set.equal` (regions_of_loc s1 `Set.union` regions_of_loc s2))", "let regions_of_loc_monotonic\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_includes s1 s2))\n (ensures (Set.subset (regions_of_loc s2) (regions_of_loc s1)))\n= ()", "let loc_disjoint_region_liveness_tags (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty", "let loc_disjoint_addrs (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n (forall (r: HS.rid) .\n GSet.subset (GSet.intersect (addrs_of_loc_weak l1 r) (addrs_of_loc l2 r)) GSet.empty /\\\n GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc_weak l2 r)) GSet.empty\n )", "let loc_disjoint_aux (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n loc_aux_disjoint (Ghost.reveal (Loc?.aux l1)) (Ghost.reveal (Loc?.aux l2))", "val modifies_none_intro\n (#al: aloc_t) (#c: cls al) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (HS.live_region h r /\\ HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n: Lemma\n (modifies (loc_none #_ #c) h h')", "let loc_disjoint'\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n: GTot Type0\n= loc_disjoint_region_liveness_tags l1 l2 /\\\n loc_disjoint_addrs l1 l2 /\\\n loc_disjoint_aux l1 l2", "let loc_disjoint = loc_disjoint'", "let loc_disjoint_sym #al #c l1 l2 =\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c)", "let loc_disjoint_sym'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))\n [SMTPat (loc_disjoint s1 s2)]\n= loc_disjoint_sym s1 s2", "let loc_disjoint_none_r #al #c s = ()", "let loc_disjoint_union_r #al #c s s1 s2 = ()", "val modifies_address_intro\n (#al: aloc_t) (#c: cls al) (r: HS.rid) (n: nat) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((r <> HS.frameOf b \\/ n <> HS.as_addr b) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (addr_unused_in: (\n (r': HS.rid) ->\n (n' : nat) ->\n Lemma\n (requires ((r' <> r \\/ n' <> n) /\\ HS.live_region h r' /\\ HS.live_region h' r' /\\ n' `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r')))\n (ensures (n' `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r')))\n ))\n: Lemma\n (modifies (loc_addresses #_ #c false r (Set.singleton n)) h h')", "let aloc_disjoint_includes (#al: aloc_t) (#c: cls al) (b1 b2 b3 : aloc c) : Lemma\n (requires (aloc_disjoint b1 b2 /\\ aloc_includes b2 b3))\n (ensures (aloc_disjoint b1 b3))\n= if b1.region = b2.region && b1.addr = b2.addr\n then begin\n c.aloc_includes_refl (Some?.v b1.loc);\n c.aloc_disjoint_includes (Some?.v b1.loc) (Some?.v b2.loc) (Some?.v b1.loc) (Some?.v b3.loc)\n end\n else ()", "let loc_aux_disjoint_loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (l1 l2 l3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\n= // FIXME: WHY WHY WHY do I need this assert?\n assert (forall (b1 b3: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b3 l3) ==> (exists (b2: aloc c) . GSet.mem b2 l2 /\\ aloc_disjoint b1 b2 /\\ aloc_includes b2 b3));\n Classical.forall_intro_3 (fun b1 b2 b3 -> Classical.move_requires (aloc_disjoint_includes #al #c b1 b2) b3)", "let loc_disjoint_includes #al #c p1 p2 p1' p2' =\n regions_of_loc_monotonic p1 p1';\n regions_of_loc_monotonic p2 p2';\n let l1 = Ghost.reveal (Loc?.aux p1) in\n let l2 = Ghost.reveal (Loc?.aux p2) in\n let l1' = Ghost.reveal (Loc?.aux p1') in\n let l2' = Ghost.reveal (Loc?.aux p2') in\n loc_aux_disjoint_loc_aux_includes l1 l2 l2';\n loc_aux_disjoint_sym l1 l2';\n loc_aux_disjoint_loc_aux_includes l2' l1 l1';\n loc_aux_disjoint_sym l2' l1'", "val modifies_aloc_intro\n (#al: aloc_t) (#c: cls al) (#r: HS.rid) (#n: nat) (z: al r n) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((r <> HS.frameOf b \\/ n <> HS.as_addr b) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (HS.live_region h r /\\ HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (x: al r n) ->\n Lemma\n (requires (c.aloc_disjoint x z))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies (loc_of_aloc #_ #c z) h h')", "let loc_disjoint_aloc_intro #al #c #r1 #a1 #r2 #a2 b1 b2 = ()", "let loc_disjoint_aloc_elim #al #c #r1 #a1 #r2 #a2 b1 b2 =\n // FIXME: WHY WHY WHY this assert?\n assert (aloc_disjoint (ALoc #_ #c r1 a1 (Some b1)) (ALoc #_ #c r2 a2 (Some b2)))", "let loc_disjoint_addresses_intro #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness1 r1 n1))) (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness2 r2 n2))))", "let loc_disjoint_addresses_elim #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 = ()", "let loc_disjoint_aloc_addresses_intro #al #c #r' #a' p preserve_liveness r n = ()", "let loc_disjoint_aloc_addresses_elim #al #c #r' #a' p preserve_liveness r n = ()", "let loc_disjoint_regions #al #c preserve_liveness1 preserve_liveness2 rs1 rs2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness1 rs1))) (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness2 rs2))))", "let loc_none_in_some_region #a (c: cls a) (r: HS.rid) : GTot (loc c) =\n Loc\n (Ghost.hide (Set.singleton r))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)", "let address_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))", "val modifies_live_region\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h1 h2: HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (modifies s h1 h2 /\\ loc_disjoint s (loc_region_only false r) /\\ HS.live_region h1 r))\n (ensures (HS.live_region h2 r))", "let loc_includes_address_liveness_insensitive_locs_aloc #al #c #r #n a = ()", "val modifies_mreference_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (b: HS.mreference t pre)\n (p: loc c)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_mreference b) p /\\\n HS.contains h b /\\\n modifies p h h'\n ))\n (ensures (\n HS.contains h' b /\\\n HS.sel h b == HS.sel h' b\n ))", "let loc_includes_address_liveness_insensitive_locs_addresses #al c r a = ()", "let region_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.complement GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))", "let loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs #al c = ()", "let loc_includes_region_liveness_insensitive_locs_loc_regions #al c r = ()", "let loc_includes_region_liveness_insensitive_locs_loc_addresses #al c preserve_liveness r a = ()", "let loc_includes_region_liveness_insensitive_locs_loc_of_aloc #al c #r #a x = ()", "val modifies_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#a: nat)\n (b: aloc r a)\n (p: loc c)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_of_aloc b) p /\\\n modifies p h h'\n ))\n (ensures (\n c.aloc_preserved b h h'\n ))", "let modifies_preserves_livenesses\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s r)))\n ) ==> (\n HS.contains h2 p\n ))", "let modifies_preserves_livenesses_elim\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (p: HS.mreference t pre)\n: Lemma\n (requires (modifies_preserves_livenesses s h1 h2 /\\ HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))))\n (ensures (HS.contains h2 p))\n= ()", "val modifies_refl\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h: HS.mem)\n: Lemma\n (modifies s h h)", "val modifies_loc_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (s1: loc c)\n (h h': HS.mem)\n (s2: loc c)\n: Lemma\n (requires (modifies s2 h h' /\\ loc_includes s1 s2))\n (ensures (modifies s1 h h'))", "let modifies_preserves_livenesses_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p))\n ))\n: Lemma\n (modifies_preserves_livenesses s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'", "val modifies_preserves_liveness\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union s1 s2) h h' /\\ loc_disjoint s1 (loc_mreference r) /\\ loc_includes (address_liveness_insensitive_locs c) s2 /\\ h `HS.contains` r))\n (ensures (h' `HS.contains` r))", "val modifies_preserves_liveness_strong\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n (x: aloc (HS.frameOf r) (HS.as_addr r))\n: Lemma\n (requires (modifies (loc_union s1 s2) h h' /\\ loc_disjoint s1 (loc_of_aloc #_ #c #(HS.frameOf r) #(HS.as_addr r) x) /\\ loc_includes (address_liveness_insensitive_locs c) s2 /\\ h `HS.contains` r))\n (ensures (h' `HS.contains` r))", "val modifies_preserves_region_liveness\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_region_only false r) l1 /\\ HS.live_region h r))\n (ensures (HS.live_region h' r))", "let modifies_preserves_mreferences\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s r)))\n ) ==> (\n HS.contains h2 p /\\\n HS.sel h2 p == HS.sel h1 p\n ))", "val modifies_preserves_region_liveness_reference\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_mreference r) l1 /\\ HS.live_region h (HS.frameOf r)))\n (ensures (HS.live_region h' (HS.frameOf r)))", "let modifies_preserves_mreferences_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p /\\ HS.sel h2 p == HS.sel h1 p))\n ))\n: Lemma\n (modifies_preserves_mreferences s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p /\\ h2 `HS.sel` p == h1 `HS.sel` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'", "val modifies_preserves_region_liveness_aloc\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (#r: HS.rid)\n (#n: nat)\n (x: al r n)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_of_aloc x) l1 /\\ HS.live_region h r))\n (ensures (HS.live_region h' r))", "val modifies_trans\n (#aloc: aloc_t) (#c: cls aloc)\n (s12: loc c)\n (h1 h2: HS.mem)\n (s23: loc c)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))", "val modifies_only_live_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (rs: Set.set HS.rid)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))", "let modifies_preserves_alocs\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (a: nat) (b: al r a) .\n loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))\n ==>\n c.aloc_preserved b h1 h2\n )", "val no_upd_fresh_region\n (#aloc: aloc_t) (#c: cls aloc)\n (r:HS.rid)\n (l:loc c)\n (h0:HS.mem)\n (h1:HS.mem)\n: Lemma\n (requires (HS.fresh_region r h0 h1 /\\ modifies (loc_union (loc_all_regions_from false r) l) h0 h1))\n (ensures (modifies l h0 h1))", "let modifies_preserves_alocs_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (u: unit { modifies_preserves_mreferences s h1 h2 } )\n (f: (\n (r: HS.rid) ->\n (a: nat) ->\n (b: al r a) ->\n Lemma\n (requires (\n Set.mem r (regions_of_loc s) /\\\n (~ (GSet.mem a (addrs_of_loc_weak s r))) /\\\n (GSet.mem a (addrs_of_loc_aux s r) /\\ loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b))))\n ))\n (ensures (c.aloc_preserved b h1 h2))\n ))\n: Lemma\n (modifies_preserves_alocs s h1 h2)\n= let f'\n (r: HS.rid)\n (a: nat)\n (b: al r a)\n : Lemma\n (requires (loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))))\n (ensures (c.aloc_preserved b h1 h2))\n = if Set.mem r (regions_of_loc s) && (not (GSet.mem a (addrs_of_loc_weak s r)))\n then begin\n if GSet.mem a (addrs_of_loc_aux s r)\n then\n Classical.move_requires (f r a) b\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n end else if Set.mem r (regions_of_loc s)\n then begin\n assert (GSet.mem a (addrs_of_loc_weak s r));\n assert (GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux s)));\n assert (aloc_disjoint #_ #c (ALoc r a None) (ALoc r a (Some b)));\n assert False\n end\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n in\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (f' r a) b)", "val fresh_frame_modifies\n (#aloc: aloc_t) (c: cls aloc)\n (h0 h1: HS.mem)\n: Lemma\n (requires (HS.fresh_frame h0 h1))\n (ensures (modifies #_ #c loc_none h0 h1))", "val new_region_modifies\n (#al: aloc_t)\n (c: cls al)\n (m0: HS.mem)\n (r0: HS.rid)\n (col: option int)\n: Lemma\n (requires (HST.is_eternal_region r0 /\\ HS.live_region m0 r0 /\\ (None? col \\/ HS.is_heap_color (Some?.v col))))\n (ensures (\n let (_, m1) = HS.new_eternal_region m0 r0 col in\n modifies (loc_none #_ #c) m0 m1\n ))", "val popped_modifies\n (#aloc: aloc_t) (c: cls aloc)\n (h0 h1: HS.mem) : Lemma\n (requires (HS.popped h0 h1))\n (ensures (modifies #_ #c (loc_region_only false (HS.get_tip h0)) h0 h1))", "val modifies_fresh_frame_popped\n (#aloc: aloc_t) (#c: cls aloc)\n (h0 h1: HS.mem)\n (s: loc c)\n (h2 h3: HS.mem)\n: Lemma\n (requires (\n HS.fresh_frame h0 h1 /\\\n modifies (loc_union (loc_all_regions_from false (HS.get_tip h1)) s) h1 h2 /\\\n HS.get_tip h2 == HS.get_tip h1 /\\\n HS.popped h2 h3\n ))\n (ensures (\n modifies s h0 h3 /\\\n HS.get_tip h3 == HS.get_tip h0\n ))", "let modifies_preserves_regions\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= forall (r: HS.rid) . (HS.live_region h1 r /\\ ~ (Set.mem r (Ghost.reveal (Loc?.region_liveness_tags s)))) ==> HS.live_region h2 r", "val modifies_loc_regions_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (rs: Set.set HS.rid)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HS.modifies rs h1 h2))\n (ensures (modifies (loc_regions #_ #c true rs) h1 h2))", "let modifies_preserves_not_unused_in\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (n: nat) . (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))", "val modifies_loc_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc c)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r a h1 h2\n ))\n (ensures (modifies (loc_union (loc_addresses true r a) l) h1 h2))", "let modifies_preserves_not_unused_in_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ))\n (ensures (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n ))\n: Lemma\n (modifies_preserves_not_unused_in s h1 h2)\n= let f'\n (r: HS.rid)\n (n: nat)\n : Lemma\n ((\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n = Classical.move_requires (f r) n\n in\n Classical.forall_intro_2 f'", "val modifies_ralloc_post\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (i: HS.rid)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel)\n (h' : HS.mem)\n: Lemma\n (requires (HST.ralloc_post i init h x h'))\n (ensures (modifies (loc_none #_ #c) h h'))", "val modifies_salloc_post\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel { HS.is_stack_region (HS.frameOf x) } )\n (h' : HS.mem)\n: Lemma\n (requires (HST.salloc_post init h x h'))\n (ensures (modifies (loc_none #_ #c) h h'))", "val modifies_free\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel { HS.is_mm r } )\n (m: HS.mem { m `HS.contains` r } )\n: Lemma\n (modifies (loc_freed_mreference #_ #c r) m (HS.free r m))", "let modifies'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= modifies_preserves_regions s h1 h2 /\\\n modifies_preserves_not_unused_in s h1 h2 /\\\n modifies_preserves_mreferences s h1 h2 /\\\n modifies_preserves_livenesses s h1 h2 /\\\n modifies_preserves_alocs s h1 h2", "val modifies_none_modifies\n (#aloc: aloc_t) (#c: cls aloc)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HST.modifies_none h1 h2))\n (ensures (modifies (loc_none #_ #c) h1 h2))", "let modifies = modifies'", "val modifies_intro_strong\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n (Set.mem r (regions_of_loc l) ==> ~ (GSet.mem n (Loc?.non_live_addrs l r))) /\\\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')", "val modifies_upd\n (#aloc: aloc_t) (#c: cls aloc)\n (#t: Type) (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n (v: t)\n (h: HS.mem)\n: Lemma\n (requires (HS.contains h r))\n (ensures (modifies #_ #c (loc_mreference r) h (HS.upd h r v)))", "val modifies_strengthen\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (h h' : HS.mem)\n (alocs: (\n (f: ((t: Type) -> (pre: Preorder.preorder t) -> (m: HS.mreference t pre) -> Lemma\n (requires (HS.frameOf m == r0 /\\ HS.as_addr m == a0 /\\ HS.contains h m))\n (ensures (HS.contains h' m))\n )) ->\n (x: al r0 a0) ->\n Lemma\n (requires (c.aloc_disjoint x al0 /\\ loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (requires (modifies (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h'))\n (ensures (modifies (loc_union l (loc_of_aloc al0)) h h'))", "val does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: GTot Type0", "val not_live_region_does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (~ (HS.live_region h (fst ra))))\n (ensures (h `does_not_contain_addr` ra))", "val unused_in_does_not_contain_addr\n (h: HS.mem)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel)\n: Lemma\n (requires (r `HS.unused_in` h))\n (ensures (h `does_not_contain_addr` (HS.frameOf r, HS.as_addr r)))", "let modifies_intro_strong #al #c l h h' regions mrefs lives unused_ins alocs =\n Classical.forall_intro (Classical.move_requires regions);\n assert (modifies_preserves_regions l h h');\n\n let aux (t:Type) (pre:Preorder.preorder t) (p:HS.mreference t pre)\n :Lemma (requires (HS.contains h p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc l) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc l (HS.frameOf p))))))\n (ensures (HS.contains h' p /\\ HS.sel h' p == HS.sel h p))\n =\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l);\n // FIXME: WHY WHY WHY is this assert necessary?\n assert_spinoff (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n // FIXME: Now this one is too :)\n assert (loc_disjoint_addrs (loc_mreference p) l);\n assert ((loc_disjoint (loc_mreference p) l));\n mrefs t pre p\n in\n\n modifies_preserves_mreferences_intro l h h' aux;\n Classical.forall_intro_3 (fun t pre p -> Classical.move_requires (lives t pre) p);\n modifies_preserves_not_unused_in_intro l h h' (fun r n ->\n unused_ins r n\n );\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n alocs r a b\n )", "val addr_unused_in_does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))))\n (ensures (h `does_not_contain_addr` ra))", "val does_not_contain_addr_addr_unused_in\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (h `does_not_contain_addr` ra))\n (ensures (HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))))", "val free_does_not_contain_addr\n (#a: Type0)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel)\n (m: HS.mem)\n (x: HS.rid * nat)\n: Lemma\n (requires (\n HS.is_mm r /\\\n m `HS.contains` r /\\\n fst x == HS.frameOf r /\\\n snd x == HS.as_addr r\n ))\n (ensures (\n HS.free r m `does_not_contain_addr` x\n ))", "let modifies_intro #al #c l h h' regions mrefs lives unused_ins alocs =\n modifies_intro_strong l h h'\n regions\n mrefs\n lives\n (fun r n -> unused_ins r n)\n alocs", "val does_not_contain_addr_elim\n (#a: Type0)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel)\n (m: HS.mem)\n (x: HS.rid * nat)\n: Lemma\n (requires (\n m `does_not_contain_addr` x /\\\n HS.frameOf r == fst x /\\\n HS.as_addr r == snd x\n ))\n (ensures (~ (m `HS.contains` r)))", "let modifies_none_intro #al #c h h' regions mrefs unused_ins =\n modifies_intro_strong #_ #c loc_none h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> mrefs t pre b)\n (fun r n -> unused_ins r n)\n (fun r a x ->\n c.same_mreference_aloc_preserved x h h' (fun t pre b -> mrefs t pre b)\n )", "let modifies_address_intro #al #c r n h h' regions mrefs unused_ins =\n Classical.forall_intro (Classical.move_requires regions);\n let l : loc c = loc_addresses #_ #c false r (Set.singleton n) in\n modifies_preserves_mreferences_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_livenesses_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_not_unused_in_intro l h h'\n (fun r n -> unused_ins r n)\n ;\n modifies_preserves_alocs_intro l h h' ()\n (fun r a b ->\n c.same_mreference_aloc_preserved b h h' (fun t pre p -> mrefs t pre p)\n )", "val loc_not_unused_in (#al: aloc_t) (c: cls al) (h: HS.mem) : GTot (loc c)", "val loc_unused_in (#al: aloc_t) (c: cls al) (h: HS.mem) : GTot (loc c)", "val loc_regions_unused_in (#al: aloc_t) (c: cls al) (h: HS.mem) (rs: Set.set HS.rid) : Lemma\n (requires (forall r . Set.mem r rs ==> (~ (HS.live_region h r))))\n (ensures (loc_unused_in c h `loc_includes` loc_regions false rs))", "val loc_addresses_unused_in (#al: aloc_t) (c: cls al) (r: HS.rid) (a: Set.set nat) (h: HS.mem) : Lemma\n (requires (forall x . Set.mem x a ==> h `does_not_contain_addr` (r, x)))\n (ensures (loc_unused_in c h `loc_includes` loc_addresses false r a))", "val loc_addresses_not_unused_in (#al: aloc_t) (c: cls al) (r: HS.rid) (a: Set.set nat) (h: HS.mem) : Lemma\n (requires (forall x . Set.mem x a ==> ~ (h `does_not_contain_addr` (r, x))))\n (ensures (loc_not_unused_in c h `loc_includes` loc_addresses false r a))", "let modifies_aloc_intro #al #c #r #n x h h' regions mrefs livenesses unused_ins alocs =\n modifies_intro_strong #_ #c (loc_of_aloc x) h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> livenesses t pre b)\n (fun r n -> unused_ins r n)\n (fun r' n' z ->\n if r' = r && n' = n\n then begin\n loc_disjoint_aloc_elim #_ #c z x;\n alocs z\n end else\n c.same_mreference_aloc_preserved z h h' (fun t pre p ->\n mrefs t pre p\n )\n )", "val loc_unused_in_not_unused_in_disjoint (#al: aloc_t) (c: cls al) (h: HS.mem) : Lemma\n (loc_unused_in c h `loc_disjoint` loc_not_unused_in c h)", "val not_live_region_loc_not_unused_in_disjoint\n (#al: aloc_t)\n (c: cls al)\n (h0: HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (~ (HS.live_region h0 r)))\n (ensures (loc_disjoint (loc_region_only false r) (loc_not_unused_in c h0)))", "val modifies_address_liveness_insensitive_unused_in\n (#al: aloc_t)\n (c: cls al)\n (h h' : HS.mem)\n: Lemma\n (requires (modifies (address_liveness_insensitive_locs c) h h'))\n (ensures (loc_not_unused_in c h' `loc_includes` loc_not_unused_in c h /\\ loc_unused_in c h `loc_includes` loc_unused_in c h'))", "let modifies_live_region #al #c s h1 h2 r = ()", "let modifies_mreference_elim #al #c #t #pre b p h h' = ()", "let modifies_aloc_elim #al #c #r #a b p h h' = ()", "val modifies_only_not_unused_in\n (#al: aloc_t)\n (#c: cls al)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (modifies (loc_unused_in c h `loc_union` l) h h'))\n (ensures (modifies l h h'))", "let modifies_refl #al #c s h =\n Classical.forall_intro_3 (fun r a b -> c.aloc_preserved_refl #r #a b h)", "let modifies_loc_includes #al #c s1 h h' s2 =\n assert (modifies_preserves_mreferences s1 h h');\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c);\n Classical.forall_intro_3 (fun l1 l2 l3 -> Classical.move_requires (loc_aux_disjoint_loc_aux_includes #al #c l1 l2) l3);\n assert (modifies_preserves_alocs s1 h h')", "let modifies_only_live_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_addresses false r a) l) h h' /\\\n (forall x . Set.mem x a ==> h `does_not_contain_addr` (r, x))\n ))\n (ensures (modifies l h h'))\n= loc_addresses_unused_in c r a h;\n loc_includes_refl l;\n loc_includes_union_l (loc_unused_in c h) l l;\n loc_includes_union_l (loc_unused_in c h) l (loc_addresses false r a);\n loc_includes_union_r (loc_union (loc_unused_in c h) l) (loc_addresses false r a) l;\n modifies_loc_includes (loc_union (loc_unused_in c h) l) h h' (loc_union (loc_addresses false r a) l);\n modifies_only_not_unused_in l h h'", "let modifies_preserves_liveness #al #c s1 s2 h h' #t #pre r = ()", "let modifies_preserves_liveness_strong #al #c s1 s2 h h' #t #pre r x =\n let rg = HS.frameOf r in\n let ad = HS.as_addr r in\n let la = loc_of_aloc #_ #c #rg #ad x in\n if Set.mem rg (regions_of_loc s2)\n then begin\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` Loc?.non_live_addrs (address_liveness_insensitive_locs c) rg);\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` GSet.empty);\n assert (~ (GSet.mem ad (Loc?.non_live_addrs s2 rg)));\n if Set.mem rg (regions_of_loc s1)\n then begin\n if GSet.mem ad (Loc?.non_live_addrs s1 rg)\n then begin\n assert (loc_disjoint_aux s1 la);\n assert (GSet.subset (Loc?.non_live_addrs s1 rg) (Loc?.live_addrs s1 rg));\n assert (aloc_domain c (Loc?.regions s1) (Loc?.live_addrs s1) `GSet.subset` (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad None) (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad (Some x)) (Ghost.reveal (Loc?.aux la)));\n assert (aloc_disjoint (ALoc rg ad None) (ALoc #_ #c rg ad (Some x)));\n ()\n end else ()\n end else ()\n end else ()", "val mreference_live_loc_not_unused_in\n (#al: aloc_t)\n (c: cls al)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (h: HS.mem)\n (r: HS.mreference t pre)\n: Lemma\n (requires (h `HS.contains` r))\n (ensures (loc_not_unused_in c h `loc_includes` loc_freed_mreference r /\\ loc_not_unused_in c h `loc_includes` loc_mreference r))", "let modifies_preserves_region_liveness #al #c l1 l2 h h' r = ()", "let modifies_preserves_region_liveness_reference #al #c l1 l2 h h' #t #pre r = ()", "val mreference_unused_in_loc_unused_in\n (#al: aloc_t)\n (c: cls al)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (h: HS.mem)\n (r: HS.mreference t pre)\n: Lemma\n (requires (r `HS.unused_in` h))\n (ensures (loc_unused_in c h `loc_includes` loc_freed_mreference r /\\ loc_unused_in c h `loc_includes` loc_mreference r))", "let modifies_preserves_region_liveness_aloc #al #c l1 l2 h h' #r #n x =\n if Set.mem r (Ghost.reveal (Loc?.region_liveness_tags l1))\n then begin\n assert (GSet.subset (GSet.complement GSet.empty) (Loc?.non_live_addrs l1 r));\n assert (GSet.subset (Loc?.non_live_addrs l1 r) (Loc?.live_addrs l1 r))\n end else ()", "let modifies_trans'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s h1 h2 /\\ modifies s h2 h3))\n (ensures (modifies s h1 h3))\n= Classical.forall_intro_3 (fun r a b -> Classical.move_requires (c.aloc_preserved_trans #r #a b h1 h2) h3)", "val aloc_union: (bool -> Tot (aloc_t u#x)) -> Tot (aloc_t u#x)", "val cls_union (#a: (bool -> Tot aloc_t)) (c: ((b: bool) -> Tot (cls (a b)))) : Tot (cls (aloc_union a))", "let modifies_trans #al #c s12 h1 h2 s23 h3 =\n let u = loc_union s12 s23 in\n modifies_loc_includes u h1 h2 s12;\n modifies_loc_includes u h2 h3 s23;\n modifies_trans' u h1 h2 h3", "val union_loc_of_loc (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b))) (b: bool) (l: loc (c b)) : GTot (loc (cls_union c))", "val union_loc_of_loc_none\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n: Lemma\n (union_loc_of_loc c b (loc_none #_ #(c b)) == loc_none #_ #(cls_union c))", "let addr_unused_in_aloc_preserved\n (#al: aloc_t) (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (b: al r a)\n (h1: HS.mem)\n (h2: HS.mem)\n : Lemma\n (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)))\n (ensures (c.aloc_preserved b h1 h2))\n= c.same_mreference_aloc_preserved b h1 h2 (fun a' pre r' -> assert False)", "val union_loc_of_loc_union\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (l1 l2: loc (c b))\n: Lemma\n (union_loc_of_loc c b (loc_union #_ #(c b) l1 l2) == loc_union #_ #(cls_union c) (union_loc_of_loc c b l1) (union_loc_of_loc c b l2))", "val union_loc_of_loc_addresses\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (union_loc_of_loc c b (loc_addresses #_ #(c b) preserve_liveness r n) == loc_addresses #_ #(cls_union c) preserve_liveness r n)", "let modifies_only_live_regions_weak\n (#al: aloc_t) (#c: cls al)\n (rs: Set.set HS.rid)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n loc_disjoint (loc_regions false rs) l /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))\n= assert (modifies_preserves_mreferences l h h'); // FIXME: WHY WHY WHY?\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (addr_unused_in_aloc_preserved #al #c #r #a b h) h')", "val union_loc_of_loc_regions\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: Lemma\n (union_loc_of_loc c b (loc_regions #_ #(c b) preserve_liveness r) == loc_regions #_ #(cls_union c) preserve_liveness r)", "val union_loc_of_loc_includes\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (s1 s2: loc (c b))\n: Lemma\n (union_loc_of_loc c b s1 `loc_includes` union_loc_of_loc c b s2 <==> s1 `loc_includes` s2)", "let restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: GTot (loc c)\n= let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let regions' = (Ghost.hide (Set.intersect (Ghost.reveal regions) rs)) in\n Loc\n regions'\n (Ghost.hide (Set.intersect (Ghost.reveal region_liveness_tags) rs))\n (mk_non_live_addrs (fun (r: addrs_dom regions') -> (non_live_addrs r <: GSet.set nat)))\n (mk_live_addrs (fun (r: addrs_dom regions') -> (live_addrs r <: GSet.set nat)))\n (Ghost.hide (GSet.intersect (Ghost.reveal aux) (aloc_domain c (Ghost.hide rs) (fun r -> GSet.complement GSet.empty))))", "val union_loc_of_loc_disjoint\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (s1 s2: loc (c b))\n: Lemma\n (union_loc_of_loc c b s1 `loc_disjoint` union_loc_of_loc c b s2 <==> s1 `loc_disjoint` s2)", "val modifies_union_loc_of_loc\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (l: loc (c b))\n (h1 h2: HS.mem)\n: Lemma\n (modifies #_ #(cls_union c) (union_loc_of_loc c b l) h1 h2 <==> modifies #_ #(c b) l h1 h2)", "let regions_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (regions_of_loc (restrict_to_regions l rs) == Set.intersect (regions_of_loc l) rs)\n [SMTPat (regions_of_loc (restrict_to_regions l rs))]\n= assert (Set.equal (regions_of_loc (restrict_to_regions l rs)) (Set.intersect (regions_of_loc l) rs))", "val loc_of_union_loc\n (#al: (bool -> Tot aloc_t))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (cls_union c))\n: GTot (loc (c b))", "let addrs_of_loc_weak_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))\n [SMTPat (addrs_of_loc_weak (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc_weak (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))", "val loc_of_union_loc_union_loc_of_loc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: loc (c b))\n: Lemma\n (loc_of_union_loc b (union_loc_of_loc c b s) == s)", "val loc_of_union_loc_none\n (#al: (bool -> Tot aloc_t))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n: Lemma\n (loc_of_union_loc #_ #c b loc_none == loc_none)", "let addrs_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc l r else GSet.empty))\n [SMTPat (addrs_of_loc (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc l r else GSet.empty))", "val loc_of_union_loc_union\n (#al: (bool -> Tot aloc_t))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l1 l2: loc (cls_union c))\n: Lemma\n (loc_of_union_loc b (l1 `loc_union` l2) == loc_of_union_loc b l1 `loc_union` loc_of_union_loc b l2)", "let loc_includes_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes l (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)", "val loc_of_union_loc_addresses\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (loc_of_union_loc #_ #c b (loc_addresses preserve_liveness r n) == loc_addresses preserve_liveness r n)", "let loc_includes_loc_union_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_equal (loc_union (restrict_to_regions l rs) (restrict_to_regions l (Set.complement rs))) l)\n= ()", "val loc_of_union_loc_regions\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: Lemma\n (loc_of_union_loc #_ #c b (loc_regions preserve_liveness r) == loc_regions preserve_liveness r)", "let loc_includes_loc_regions_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes (loc_regions false rs) (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)", "let modifies_only_live_regions #al #c rs l h h' =\n let s = l in\n let c_rs = Set.complement rs in\n let s_rs = restrict_to_regions s rs in\n let s_c_rs = restrict_to_regions s c_rs in\n let lrs = loc_regions false rs in\n loc_includes_loc_regions_restrict_to_regions s rs;\n loc_includes_union_l lrs s_c_rs s_rs;\n loc_includes_refl s_c_rs;\n loc_includes_union_l lrs s_c_rs s_c_rs;\n loc_includes_union_r (loc_union lrs s_c_rs) s_rs s_c_rs;\n loc_includes_loc_union_restrict_to_regions s rs;\n loc_includes_trans (loc_union lrs s_c_rs) (loc_union s_rs s_c_rs) s;\n modifies_loc_includes (loc_union lrs s_c_rs) h h' (loc_union lrs s);\n loc_includes_loc_regions_restrict_to_regions s c_rs;\n loc_disjoint_regions #al #c false false rs c_rs;\n loc_includes_refl lrs;\n loc_disjoint_includes lrs (loc_regions false c_rs) lrs s_c_rs;\n modifies_only_live_regions_weak rs s_c_rs h h';\n loc_includes_restrict_to_regions s c_rs;\n modifies_loc_includes s h h' s_c_rs", "val raise_aloc (al: aloc_t u#x) : Tot (aloc_t u#(max x (y + 1)))", "val raise_cls (#al: aloc_t u#x) (c: cls al) : Tot (cls (raise_aloc u#x u#y al))", "val raise_loc (#al: aloc_t u#x) (#c: cls al) (l: loc c) : Tot (loc (raise_cls u#x u#y c))", "val raise_loc_none (#al: aloc_t u#x) (#c: cls al) : Lemma\n (raise_loc u#x u#y (loc_none #_ #c) == loc_none)", "val raise_loc_union (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc c) : Lemma\n (raise_loc u#x u#y (loc_union l1 l2) == loc_union (raise_loc l1) (raise_loc l2))", "val raise_loc_addresses (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: HS.rid) (a: Set.set nat) : Lemma\n (raise_loc u#x u#y (loc_addresses #_ #c preserve_liveness r a) == loc_addresses preserve_liveness r a)", "val raise_loc_regions (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: Set.set HS.rid) : Lemma\n (raise_loc u#x u#y (loc_regions #_ #c preserve_liveness r) == loc_regions preserve_liveness r)", "val raise_loc_includes (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc c) : Lemma\n (loc_includes (raise_loc u#x u#y l1) (raise_loc l2) <==> loc_includes l1 l2)", "val raise_loc_disjoint (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc c) : Lemma\n (loc_disjoint (raise_loc u#x u#y l1) (raise_loc l2) <==> loc_disjoint l1 l2)", "let no_upd_fresh_region #al #c r l h0 h1 =\n modifies_only_live_regions (HS.mod_set (Set.singleton r)) l h0 h1", "val modifies_raise_loc (#al: aloc_t u#x) (#c: cls al) (l: loc c) (h1 h2: HS.mem) : Lemma\n (modifies (raise_loc u#x u#y l) h1 h2 <==> modifies l h1 h2)", "let fresh_frame_modifies #al c h0 h1 =\n modifies_intro_strong #_ #c loc_none h0 h1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x h0 h1 (fun _ _ _ -> ()))", "val lower_loc (#al: aloc_t u#x) (#c: cls al) (l: loc (raise_cls u#x u#y c)) : Tot (loc c)", "val lower_loc_raise_loc (#al: aloc_t u#x) (#c: cls al) (l: loc c) : Lemma\n (lower_loc (raise_loc u#x u#y l) == l)", "val raise_loc_lower_loc (#al: aloc_t u#x) (#c: cls al) (l: loc (raise_cls u#x u#y c)) : Lemma\n (raise_loc (lower_loc l) == l)", "let new_region_modifies #al c m0 r0 col\n= let (_, m1) = HS.new_eternal_region m0 r0 col in\n modifies_intro_strong #_ #c loc_none m0 m1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x m0 m1 (fun _ _ _ -> ()))", "val lower_loc_none (#al: aloc_t u#x) (#c: cls al) : Lemma\n (lower_loc u#x u#y #_ #c loc_none == loc_none)", "val lower_loc_union (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc (raise_cls u#x u#y c)) : Lemma\n (lower_loc u#x u#y (loc_union l1 l2) == loc_union (lower_loc l1) (lower_loc l2))", "val lower_loc_addresses (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: HS.rid) (a: Set.set nat) : Lemma\n (lower_loc u#x u#y #_ #c (loc_addresses preserve_liveness r a) == loc_addresses preserve_liveness r a)", "let popped_modifies #al c h0 h1 =\n let l = loc_region_only #_ #c false (HS.get_tip h0) in\n modifies_preserves_mreferences_intro l h0 h1 (fun t pre p ->\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l );\n // FIXME: WHY WHY WHY is this assert necessary?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n ()\n );\n modifies_preserves_alocs_intro l h0 h1 () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n ()\n )", "val lower_loc_regions (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: Set.set HS.rid) : Lemma\n (lower_loc u#x u#y #_ #c (loc_regions preserve_liveness r) == loc_regions preserve_liveness r)", "let modifies_fresh_frame_popped #al #c h0 h1 s h2 h3 =\n fresh_frame_modifies c h0 h1;\n let r = loc_region_only #al #c false (HS.get_tip h2) in\n let rs = HS.mod_set (Set.singleton (HS.get_tip h1)) in\n let s' = loc_union (loc_regions false rs) s in\n modifies_trans' s' h0 h1 h2;\n assert (modifies_preserves_mreferences r h2 h3);\n let f23 (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (r <> HS.get_tip h2))\n (ensures (c.aloc_preserved b h2 h3))\n = c.same_mreference_aloc_preserved #r #a b h2 h3 (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro r h2 h3 () (fun r a b ->\n f23 r a b\n );\n modifies_trans' s' h0 h2 h3;\n modifies_only_live_regions rs s h0 h3", "let modifies_loc_regions_intro #al #c rs h1 h2 =\n let f (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem r rs)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n assert (modifies_preserves_mreferences (loc_regions #al #c true rs) h1 h2);\n modifies_preserves_alocs_intro (loc_regions #_ #c true rs) h1 h2 () (fun r a b ->\n f r a b\n )", "let modifies_loc_addresses_intro_weak\n (#al: aloc_t) (#c: cls al)\n (r: HS.rid)\n (s: Set.set nat)\n (l: loc c)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r s h1 h2 /\\\n loc_disjoint l (loc_region_only false r)\n ))\n (ensures (modifies (loc_union (loc_addresses true r s) l) h1 h2))\n= modifies_preserves_mreferences_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_livenesses_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_not_unused_in_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' n' ->\n ()\n );\n let f (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem a s)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r_ -> ())\n in\n modifies_preserves_alocs_intro (loc_union (loc_addresses true r s) l) h1 h2 () (fun r' a b -> if r = r' then f a b else ()\n )", "let modifies_loc_addresses_intro #al #c r s l h1 h2 =\n loc_includes_loc_regions_restrict_to_regions l (Set.singleton r);\n loc_includes_loc_union_restrict_to_regions l (Set.singleton r);\n assert (modifies (loc_union (loc_region_only false r) (loc_union (restrict_to_regions l (Set.singleton r)) (restrict_to_regions l (Set.complement (Set.singleton r))))) h1 h2);\n let l' = restrict_to_regions l (Set.complement (Set.singleton r)) in\n loc_includes_refl (loc_region_only #_ #c false r) ;\n loc_includes_loc_regions_restrict_to_regions l (Set.complement (Set.singleton r));\n loc_disjoint_regions #_ #c false false (Set.complement (Set.singleton r)) (Set.singleton r);\n loc_disjoint_includes (loc_regions #_ #c false (Set.complement (Set.singleton r))) (loc_region_only false r) l' (loc_region_only false r);\n modifies_loc_addresses_intro_weak r s l' h1 h2;\n loc_includes_restrict_to_regions l (Set.complement (Set.singleton r))", "let modifies_ralloc_post #al #c #a #rel i init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g", "let modifies_salloc_post #al #c #a #rel init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g", "let modifies_free #al #c #a #rel r m =\n let g (r': HS.rid) (a: nat) (b: al r' a) : Lemma\n (requires (r' <> HS.frameOf r \\/ a <> HS.as_addr r))\n (ensures (c.aloc_preserved b m (HS.free r m)))\n = c.same_mreference_aloc_preserved #r' #a b m (HS.free r m) (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro (loc_freed_mreference #_ #c r) m (HS.free r m) () (fun r a b -> g r a b)", "let modifies_none_modifies #al #c h1 h2\n= let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h1 h2)\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g", "let modifies_upd #al #c #t #pre r v h =\n let h' = HS.upd h r v in\n modifies_intro #_ #c (loc_mreference r) h h'\n (fun r -> ())\n (fun t pre b -> ())\n (fun t pre b -> ())\n (fun r n -> ())\n (fun r a b -> c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre' r' -> ()))", "let addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l (loc_of_aloc al0)) r == addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)\n= assert (addrs_of_loc (loc_union l (loc_of_aloc al0)) r `GSet.equal` addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)", "let addrs_of_loc_weak_loc_includes #al (#c: cls al) (l: loc c) (r0: HS.rid) (a0: nat) : Lemma\n (requires (a0 `GSet.mem` addrs_of_loc_weak l r0))\n (ensures (l `loc_includes` loc_addresses true r0 (Set.singleton a0)))\n= ()", "val modifies_strengthen'\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (h h' : HS.mem)\n (alocs: (\n (f: ((t: Type) -> (pre: Preorder.preorder t) -> (m: HS.mreference t pre) -> Lemma\n (requires (HS.frameOf m == r0 /\\ HS.as_addr m == a0 /\\ HS.contains h m))\n (ensures (HS.contains h' m))\n )) ->\n (x: al r0 a0) ->\n Lemma\n (requires (c.aloc_disjoint x al0 /\\ loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (requires ((~ (a0 `GSet.mem` addrs_of_loc_weak l r0)) /\\ modifies (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h'))\n (ensures (modifies (loc_union l (loc_of_aloc al0)) h h'))", "let modifies_strengthen' #al #c l #r0 #a0 al0 h h' alocs =\n Classical.forall_intro (addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton l al0);\n assert (modifies_preserves_regions (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_mreferences (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_not_unused_in (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_livenesses (loc_union l (loc_of_aloc al0)) h h');\n modifies_preserves_alocs_intro (loc_union l (loc_of_aloc al0)) h h' () (fun r a b ->\n if r = r0 && a = a0\n then begin\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_union l (loc_of_aloc al0)))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux l)) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_disjoint l (loc_of_aloc b));\n loc_disjoint_sym l (loc_of_aloc b);\n assert (loc_aux_disjoint #_ #c (Ghost.reveal (Loc?.aux (loc_of_aloc al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint #_ #c (GSet.singleton (ALoc r0 a0 (Some al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (GSet.mem (ALoc r0 a0 (Some al0)) (GSet.singleton (ALoc #_ #c r0 a0 (Some al0))));\n assert (GSet.mem (ALoc r0 a0 (Some b)) (GSet.singleton (ALoc #_ #c r0 a0 (Some b))));\n assert (aloc_disjoint #_ #c (ALoc r0 a0 (Some al0)) (ALoc r0 a0 (Some b)));\n assert (c.aloc_disjoint al0 b);\n c.aloc_disjoint_sym al0 b;\n alocs (fun t pre m -> ()) b\n end\n else begin\n assert (loc_disjoint (loc_union l (loc_addresses true r0 (Set.singleton a0))) (loc_of_aloc b))\n by (let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 64;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=5'\";\n ())\n end\n );\n assert (modifies (loc_union l (loc_of_aloc al0)) h h')", "let modifies_strengthen #al #c l #r0 #a0 al0 h h' alocs =\n if a0 `GSet.mem` addrs_of_loc_weak l r0\n then begin\n addrs_of_loc_weak_loc_includes l r0 a0;\n loc_includes_refl l;\n loc_includes_union_r l l (loc_addresses true r0 (Set.singleton a0));\n loc_includes_union_l l (loc_of_aloc al0) l;\n loc_includes_trans (loc_union l (loc_of_aloc al0)) l (loc_union l (loc_addresses true r0 (Set.singleton a0)));\n modifies_loc_includes (loc_union l (loc_of_aloc al0)) h h' (loc_union l (loc_addresses true r0 (Set.singleton a0)))\n end\n else\n modifies_strengthen' l al0 h h' alocs", "let does_not_contain_addr' (h: HS.mem) (ra: HS.rid * nat) : GTot Type0 =\n HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))", "let does_not_contain_addr = does_not_contain_addr'", "let not_live_region_does_not_contain_addr h ra = ()", "let unused_in_does_not_contain_addr h #a #rel r = ()", "let addr_unused_in_does_not_contain_addr h ra = ()", "let does_not_contain_addr_addr_unused_in h ra = ()", "let free_does_not_contain_addr #a #rel r m x = ()", "let does_not_contain_addr_elim #a #rel r m x = ()", "let disjoint_addrs_of_loc_loc_disjoint\n (#al: aloc_t)\n (#c: cls al)\n (l1 l2: loc c)\n: Lemma\n (requires (\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty /\\\n (forall r . GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc l2 r)) GSet.empty)\n ))\n (ensures (loc_disjoint l1 l2))\n= // FIXME: WHY WHY WHY do I need this assert?\n let l1' = Ghost.reveal (Loc?.aux l1) in\n let l2' = Ghost.reveal (Loc?.aux l2) in\n assert (forall (b1 b2: aloc c) . (GSet.mem b1 l1' /\\ GSet.mem b2 l2') ==> aloc_disjoint b1 b2)", "let loc_not_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (HS.live_region h r /\\ ~ (h `does_not_contain_addr` (r, a))))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs f)\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))", "let loc_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n if not (HS.live_region h r)\n then\n GSet.complement GSet.empty\n else\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a)))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide (Set.complement (FStar.Map.domain (HS.get_hmap h))))\n (mk_non_live_addrs (fun x -> f x))\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))", "let loc_regions_unused_in #al c h rs = ()", "let loc_addresses_unused_in #al c r a h = ()", "let loc_addresses_not_unused_in #al c r a h = ()", "let loc_unused_in_not_unused_in_disjoint #al c h =\n assert (Ghost.reveal (Loc?.aux (loc_unused_in c h)) `loc_aux_disjoint` Ghost.reveal (Loc?.aux (loc_not_unused_in c h)));\n assert_spinoff (loc_disjoint #al #c (loc_unused_in #al c h)\n (loc_not_unused_in #al c h))", "let not_live_region_loc_not_unused_in_disjoint #al c h0 r\n= let l1 = loc_region_only false r in\n let l2 = loc_not_unused_in c h0 in\n assert (loc_disjoint_region_liveness_tags l1 l2);\n assert (loc_disjoint_addrs l1 l2);\n assert (loc_disjoint_aux l1 l2)", "let modifies_address_liveness_insensitive_unused_in #al c h h' =\n assert (forall r . HS.live_region h r ==> HS.live_region h' r) ;\n let ln' = loc_not_unused_in c h' in\n let ln = loc_not_unused_in c h in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs ln r `GSet.subset` Loc?.non_live_addrs ln' r);\n assert (ln' `loc_includes` ln);\n let lu = loc_unused_in c h in\n let lu' = loc_unused_in c h' in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs lu' r `GSet.subset` Loc?.non_live_addrs lu r);\n assert (forall (r: HS.rid) . Loc?.live_addrs lu' r `GSet.subset` Loc?.live_addrs lu r);\n assert (lu `loc_includes` lu')", "let modifies_only_not_unused_in #al #c l h h' =\n assert (modifies_preserves_regions l h h');\n assert (modifies_preserves_not_unused_in l h h');\n assert (modifies_preserves_mreferences l h h');\n assert (modifies_preserves_livenesses l h h');\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n if StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a))\n then c.same_mreference_aloc_preserved b h h' (fun a' pre' r' -> ())\n else ()\n )", "let mreference_live_loc_not_unused_in #al c #t #pre h b =\n Classical.move_requires (does_not_contain_addr_addr_unused_in h) (HS.frameOf b, HS.as_addr b);\n assert (~ (h `does_not_contain_addr` (HS.frameOf b, HS.as_addr b)));\n loc_addresses_not_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_trans (loc_not_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()", "let mreference_unused_in_loc_unused_in #al c #t #pre h b =\n Classical.move_requires (addr_unused_in_does_not_contain_addr h) (HS.frameOf b, HS.as_addr b);\n loc_addresses_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_addresses_addresses c false true (HS.frameOf b) (Set.singleton (HS.as_addr b)) (Set.singleton (HS.as_addr b));\n loc_includes_trans (loc_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()", "cls_union_aloc", "ALOC_FALSE", "ALOC_FALSE", "ALOC_FALSE", "ALOC_TRUE", "ALOC_TRUE", "ALOC_TRUE", "let bool_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot bool =\n match l with\n | ALOC_FALSE _ -> false\n | ALOC_TRUE _ -> true", "let aloc_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot ((al (bool_of_cls_union_aloc l)) r n)\n= match l with\n | ALOC_FALSE x -> x\n | ALOC_TRUE x -> x", "let make_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (b: bool)\n (#r: HS.rid)\n (#n: nat)\n (l: (al b) r n)\n: Tot (cls_union_aloc al r n)\n= if b\n then ALOC_TRUE l\n else ALOC_FALSE l", "let cls_union_aloc_includes\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_includes\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)", "let cls_union_aloc_disjoint\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_disjoint\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)", "let cls_union_aloc_preserved\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (x: cls_union_aloc al r a)\n (h h' : HS.mem)\n: GTot Type0\n= (c (bool_of_cls_union_aloc x)).aloc_preserved\n (aloc_of_cls_union_aloc x)\n h\n h'", "let aloc_union = cls_union_aloc", "let cls_union #al c = Cls\n #(cls_union_aloc al)\n (cls_union_aloc_includes c)\n (* aloc_includes_refl *)\n (fun #r #a x ->\n (c (bool_of_cls_union_aloc x)).aloc_includes_refl (aloc_of_cls_union_aloc x))\n (* aloc_includes_trans *)\n (fun #r #a x1 x2 x3 ->\n (c (bool_of_cls_union_aloc x1)).aloc_includes_trans\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n (aloc_of_cls_union_aloc x3)\n )\n (cls_union_aloc_disjoint c)\n (* aloc_disjoint_sym *)\n (fun #r #a x1 x2 ->\n if bool_of_cls_union_aloc x1 = bool_of_cls_union_aloc x2\n then\n (c (bool_of_cls_union_aloc x1)).aloc_disjoint_sym\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n else ()\n )\n (* aloc_disjoint_includes *)\n (fun #r #a larger1 larger2 smaller1 smaller2 ->\n (c (bool_of_cls_union_aloc larger1)).aloc_disjoint_includes\n (aloc_of_cls_union_aloc larger1)\n (aloc_of_cls_union_aloc larger2)\n (aloc_of_cls_union_aloc smaller1)\n (aloc_of_cls_union_aloc smaller2)\n )\n (cls_union_aloc_preserved c)\n (* aloc_preserved_refl *)\n (fun #r #a x h ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_refl\n (aloc_of_cls_union_aloc x)\n h\n )\n (* aloc_preserved_trans *)\n (fun #r #a x h1 h2 h3 ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_trans\n (aloc_of_cls_union_aloc x)\n h1\n h2\n h3\n )\n (* same_mreference_aloc_preserved *)\n (fun #r #a b h1 h2 f ->\n (c (bool_of_cls_union_aloc b)).same_mreference_aloc_preserved\n (aloc_of_cls_union_aloc b)\n h1\n h2\n f\n )", "let union_aux_of_aux_left_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n (x: aloc (cls_union c))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n b = bool_of_cls_union_aloc #al #region #addr loc &&\n GSet.mem (ALoc region addr (Some (aloc_of_cls_union_aloc #al #region #addr loc))) s", "let union_aux_of_aux_left\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n: Tot (GSet.set (aloc (cls_union c)))\n= GSet.comprehend (union_aux_of_aux_left_pred c b s)", "let union_loc_of_loc #al c b l =\n let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let aux' : GSet.set (aloc #(cls_union_aloc al) (cls_union c)) =\n union_aux_of_aux_left c b (Ghost.reveal aux)\n `GSet.union`\n (aloc_domain (cls_union c) regions live_addrs)\n in\n Loc\n #(cls_union_aloc al)\n #(cls_union c)\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide aux')", "let union_aux_of_aux_left_inv_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n (x: aloc (c b))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n GSet.mem (ALoc region addr (Some (make_cls_union_aloc b loc))) s", "let union_aux_of_aux_left_inv\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n: Tot (GSet.set (aloc (c b)))\n= GSet.comprehend (union_aux_of_aux_left_inv_pred b s)", "let mem_union_aux_of_aux_left_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (c b))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x aux <==> GSet.mem (ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc)))) (union_aux_of_aux_left c b aux))\n [SMTPat (GSet.mem x aux)]\n= ()", "let mem_union_aux_of_aux_left_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (cls_union c))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x (union_aux_of_aux_left c b aux) <==> (if None? x.loc then GSet.mem (ALoc x.region x.addr None) aux else (bool_of_cls_union_aloc (Some?.v x.loc) == b /\\ GSet.mem (ALoc x.region x.addr (Some (aloc_of_cls_union_aloc (Some?.v x.loc)))) aux)))\n [SMTPat (GSet.mem x (union_aux_of_aux_left #al c b aux))]\n= ()", "let addrs_of_loc_union_loc_of_loc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (union_loc_of_loc c b l) r `GSet.equal` addrs_of_loc l r)\n [SMTPat (addrs_of_loc (union_loc_of_loc #al c b l) r)]\n= ()", "let union_loc_of_loc_none #al c b =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_none #_ #(c b))) (loc_none #_ #(cls_union c)))", "let union_loc_of_loc_union #al c b l1 l2 =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_union #_ #(c b) l1 l2)) (loc_union #_ #(cls_union c) (union_loc_of_loc c b l1) (union_loc_of_loc c b l2)))", "let union_loc_of_loc_addresses #al c b preserve_liveness r n =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_addresses #_ #(c b) preserve_liveness r n)) (loc_addresses #_ #(cls_union c) preserve_liveness r n))", "let union_loc_of_loc_regions #al c b preserve_liveness r =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_regions #_ #(c b) preserve_liveness r)) (loc_regions #_ #(cls_union c) preserve_liveness r))", "let union_loc_of_loc_includes_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (larger `loc_includes` smaller))\n (ensures (union_loc_of_loc c b larger `loc_includes` union_loc_of_loc c b smaller))\n= ();\n let auxl = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux larger)) in\n let auxs = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux smaller)) in\n assert (forall r a . GSet.mem (ALoc r a None) auxs ==> (\n GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux smaller)) /\\\n GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux larger)) /\\\n GSet.mem (ALoc r a None) auxl\n ));\n assert (auxl `loc_aux_includes` auxs);\n let doml = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n assert (doml `loc_aux_includes` doms)", "let union_loc_of_loc_includes_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (union_loc_of_loc c b larger `loc_includes` union_loc_of_loc c b smaller))\n (ensures (larger `loc_includes` smaller))\n= let auxl = Ghost.reveal (Loc?.aux larger) in\n let auxl' = union_aux_of_aux_left c b auxl in\n let auxs = Ghost.reveal (Loc?.aux smaller) in\n let auxs' = union_aux_of_aux_left c b auxs in\n let doml' = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms' = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n let doml = aloc_domain (c b) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (c b) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n let g\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n (y: aloc (c b))\n : GTot Type0\n = GSet.mem y (GSet.union auxl doml) /\\ y `aloc_includes` x\n in\n let g' (r: HS.rid) (a: nat) (x: aloc (c b)) : GTot Type0 =\n exists (y: aloc (c b)) . g r a x y\n in\n let f\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n : Lemma\n (requires (GSet.mem x auxs /\\ (~ (GSet.mem x.addr (addrs_of_loc_weak smaller x.region)))))\n (ensures (g' r a x))\n = let x' : aloc (cls_union c) = ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc))) in\n Classical.exists_elim\n (g' r a x)\n #(aloc (cls_union c))\n #(fun y' -> GSet.mem y' (GSet.union auxl' doml') /\\ y' `aloc_includes` x')\n ()\n (fun (y': aloc (cls_union c) { GSet.mem y' (GSet.union auxl' doml') /\\ y' `aloc_includes` x' } ) ->\n let y : aloc (c b) = ALoc y'.region y'.addr (if None? y'.loc then None else Some (aloc_of_cls_union_aloc (Some?.v y'.loc))) in\n assert (g r a x y)\n )\n in\n let f'\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n : Lemma\n ((GSet.mem x auxs /\\ (~ (GSet.mem x.addr (addrs_of_loc_weak smaller x.region)))) ==> g' r a x)\n = Classical.move_requires (f r a) x\n in\n Classical.forall_intro_3 f';\n assert (forall (r: HS.rid) (a: nat) (x: aloc (c b)) .\n (GSet.mem x auxs /\\ GSet.mem x.addr (addrs_of_loc_weak smaller x.region)) ==>\n GSet.mem x (GSet.union auxl doml)\n ) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n assert (larger `loc_includes'` smaller) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 75;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n ()", "let union_loc_of_loc_includes #al c b s1 s2 =\n Classical.move_requires (union_loc_of_loc_includes_elim c b s1) s2;\n Classical.move_requires (union_loc_of_loc_includes_intro c b s1) s2", "let union_loc_of_loc_disjoint_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (larger `loc_disjoint` smaller))\n (ensures (union_loc_of_loc c b larger `loc_disjoint` union_loc_of_loc c b smaller))\n= let auxl = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux larger)) in\n let auxs = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux smaller)) in\n let g\n (xl xs: aloc (cls_union c))\n : Lemma\n (requires (GSet.mem xl auxl /\\ GSet.mem xs auxs))\n (ensures (GSet.mem xl auxl /\\ GSet.mem xs auxs /\\ aloc_disjoint xl xs))\n =\n let xl' : aloc (c b) = ALoc xl.region xl.addr (if None? xl.loc then None else Some (aloc_of_cls_union_aloc (Some?.v xl.loc))) in\n let xs' : aloc (c b) = ALoc xs.region xs.addr (if None? xs.loc then None else Some (aloc_of_cls_union_aloc (Some?.v xs.loc))) in\n assert (GSet.mem xl' (Ghost.reveal (Loc?.aux larger)));\n assert (GSet.mem xs' (Ghost.reveal (Loc?.aux smaller)));\n assert (aloc_disjoint xl' xs');\n assert (aloc_disjoint xl xs)\n in\n Classical.forall_intro_2 (fun xl -> Classical.move_requires (g xl));\n assert (forall xl xs . (GSet.mem xl auxl /\\ GSet.mem xs auxs) ==> aloc_disjoint xl xs);\n assert (auxl `loc_aux_disjoint` auxs);\n let larger' = union_loc_of_loc c b larger in\n let smaller' = union_loc_of_loc c b smaller in\n let doml = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n assert (forall (xl xs: aloc (cls_union c)) .\n (GSet.mem xl doml /\\ GSet.mem xs auxs) ==> (\n xl.addr `GSet.mem` addrs_of_loc_weak larger xl.region /\\\n xs.addr `GSet.mem` addrs_of_loc smaller xs.region /\\\n aloc_disjoint xl xs\n )) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 64;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n assert (doml ` loc_aux_disjoint` auxs);\n assert (forall (xl xs: aloc (cls_union c)) .\n (GSet.mem xl auxl /\\ GSet.mem xs doms) ==> (\n xl.addr `GSet.mem` addrs_of_loc larger xl.region /\\\n xs.addr `GSet.mem` addrs_of_loc_weak smaller xs.region /\\\n aloc_disjoint xl xs\n )) by (\n let open FStar.Tactics.SMT in\n set_rlimit 15;\n ()\n );\n assert (auxl ` loc_aux_disjoint` doms);\n assert (loc_disjoint_aux larger' smaller');\n ()", "let union_loc_of_loc_disjoint_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (union_loc_of_loc c b larger `loc_disjoint` union_loc_of_loc c b smaller))\n (ensures (larger `loc_disjoint` smaller))\n= let auxl = Ghost.reveal (Loc?.aux larger) in\n let auxl' = union_aux_of_aux_left c b auxl in\n let auxs = Ghost.reveal (Loc?.aux smaller) in\n let auxs' = union_aux_of_aux_left c b auxs in\n assert (forall (x y: aloc (c b)) . (GSet.mem x auxl /\\ GSet.mem y auxs) ==> (\n let x' = ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc))) in\n let y' = ALoc y.region y.addr (if None? y.loc then None else Some (make_cls_union_aloc b (Some?.v y.loc))) in\n GSet.mem x' auxl' /\\ GSet.mem y' auxs' /\\ (aloc_disjoint x' y' ==> aloc_disjoint x y)));\n assert (auxl `loc_aux_disjoint` auxs)", "let union_loc_of_loc_disjoint #al c b s1 s2 =\n Classical.move_requires (union_loc_of_loc_disjoint_elim c b s1) s2;\n Classical.move_requires (union_loc_of_loc_disjoint_intro c b s1) s2", "let modifies_union_loc_of_loc_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (h1 h2: HS.mem)\n: Lemma\n (requires (modifies #_ #(cls_union c) (union_loc_of_loc c b l) h1 h2))\n (ensures (modifies #_ #(c b) l h1 h2))\n= assert (modifies_preserves_regions l h1 h2);\n assert (modifies_preserves_mreferences l h1 h2);\n modifies_preserves_alocs_intro #_ #(c b) l h1 h2 () (fun r' a' b' ->\n let g\n (x: aloc (cls_union c))\n : Lemma\n (requires (\n GSet.mem a' (addrs_of_loc_aux #_ #(cls_union c) (union_loc_of_loc c b l) r') /\\\n GSet.mem x (Ghost.reveal (Loc?.aux #_ #(cls_union c) (union_loc_of_loc c b l)))\n ))\n (ensures (\n aloc_disjoint #_ #(cls_union c) x (ALoc #_ #(cls_union c) r' a' (Some (make_cls_union_aloc b b')))))\n = if r' = x.region && a' = x.addr\n then begin\n let x' : aloc (c b) = ALoc #_ #(c b) r' a' (if None? x.loc then None else Some (aloc_of_cls_union_aloc (Some?.v x.loc))) in\n assert (aloc_disjoint #(al b) #(c b) x' (ALoc r' a' (Some b')))\n end else\n ()\n in\n Classical.forall_intro (Classical.move_requires g);\n assert ((cls_union c).aloc_preserved (make_cls_union_aloc b b') h1 h2)\n )", "let modifies_union_loc_of_loc_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (h1 h2: HS.mem)\n: Lemma\n (requires (modifies #_ #(c b) l h1 h2))\n (ensures (modifies #_ #(cls_union c) (union_loc_of_loc c b l) h1 h2))\n= let l' = union_loc_of_loc c b l in\n assert (modifies_preserves_regions l' h1 h2);\n assert (modifies_preserves_mreferences l' h1 h2);\n assert (modifies_preserves_livenesses l' h1 h2);\n assert (modifies_preserves_not_unused_in l' h1 h2);\n modifies_preserves_alocs_intro #_ #(cls_union c) l' h1 h2 () (fun r' a' b' ->\n let b_ = bool_of_cls_union_aloc b' in\n let a_ = aloc_of_cls_union_aloc b' in\n let ll' : aloc (cls_union c) = ALoc r' a' (Some b') in\n let ll : aloc (c b_) = ALoc r' a' (Some a_) in\n assert (exists (x: aloc (c b)) . GSet.mem x (Ghost.reveal (Loc?.aux l)) /\\\n (\n let xr = x.region in\n let xa = x.addr in\n let xl : option (al b xr xa) = x.loc in\n xr == r' /\\\n xa == a' /\\ (\n let xl' : option (aloc_union al r' a') = if None? xl then None else Some (make_cls_union_aloc #al b (Some?.v xl)) in\n let x' : aloc (cls_union c) = ALoc r' a' xl' in\n GSet.mem x' (Ghost.reveal (Loc?.aux l')) /\\\n aloc_disjoint #_ #(cls_union c) x' ll'\n )));\n assert (b_ == b);\n let f (x: aloc (c b)) : Lemma\n (requires (GSet.mem x (Ghost.reveal (Loc?.aux l))))\n (ensures (aloc_disjoint #_ #(c b) x ll))\n = let xr = x.region in\n let xa = x.addr in\n let xl : option (al b xr xa) = x.loc in\n let xl' : option (aloc_union al xr xa) = if None? xl then None else Some (make_cls_union_aloc #al b (Some?.v xl)) in\n let x' : aloc (cls_union c) = ALoc xr xa xl' in\n assert (GSet.mem x' (Ghost.reveal (Loc?.aux l')));\n assert (aloc_disjoint #_ #(cls_union c) x' ll');\n assert (aloc_disjoint #_ #(c b) x ll)\n in\n Classical.forall_intro (Classical.move_requires f);\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux l)) (GSet.singleton ll))\n )", "let modifies_union_loc_of_loc #al c b l h1 h2 =\n Classical.move_requires (modifies_union_loc_of_loc_elim c b l h1) h2;\n Classical.move_requires (modifies_union_loc_of_loc_intro c b l h1) h2", "let loc_of_union_loc #al #c b l\n= let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let aux' = union_aux_of_aux_left_inv b (Ghost.reveal aux) in\n Loc\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide aux')", "let loc_of_union_loc_union_loc_of_loc #al c b s\n= assert (loc_of_union_loc b (union_loc_of_loc c b s) `loc_equal` s)", "let loc_of_union_loc_none #al c b\n= assert (loc_of_union_loc #_ #c b loc_none `loc_equal` loc_none)", "let loc_of_union_loc_union #al c b l1 l2\n= assert (loc_of_union_loc b (l1 `loc_union` l2) `loc_equal` (loc_of_union_loc b l1 `loc_union` loc_of_union_loc b l2))", "let loc_of_union_loc_addresses #al c b preserve_liveness r n =\n assert (loc_of_union_loc #_ #c b (loc_addresses preserve_liveness r n) `loc_equal` loc_addresses preserve_liveness r n)", "let loc_of_union_loc_regions #al c b preserve_liveness r =\n assert (loc_of_union_loc #_ #c b (loc_regions preserve_liveness r) `loc_equal` loc_regions preserve_liveness r)", "let raise_aloc al r n = U.raise_t (al r n)", "let raise_cls #al c = Cls #(raise_aloc u#x u#y al)\n (fun #r #a x1 x2 -> c.aloc_includes (U.downgrade_val x1) (U.downgrade_val x2))\n (fun #r #a x -> c.aloc_includes_refl (U.downgrade_val x))\n (fun #r #a x1 x2 x3 -> c.aloc_includes_trans (U.downgrade_val x1) (U.downgrade_val x2) (U.downgrade_val x3))\n (fun #r #a x1 x2 -> c.aloc_disjoint (U.downgrade_val x1) (U.downgrade_val x2))\n (fun #r #a x1 x2 -> c.aloc_disjoint_sym (U.downgrade_val x1) (U.downgrade_val x2))\n (fun #r #a larger1 larger2 smaller1 smaller2 -> c.aloc_disjoint_includes (U.downgrade_val larger1) (U.downgrade_val larger2) (U.downgrade_val smaller1) (U.downgrade_val smaller2))\n (fun #r #a x h1 h2 -> c.aloc_preserved (U.downgrade_val x) h1 h2)\n (fun #r #a x h -> c.aloc_preserved_refl (U.downgrade_val x) h)\n (fun #r #a x h1 h2 h3 -> c.aloc_preserved_trans (U.downgrade_val x) h1 h2 h3)\n (fun #r #a b h1 h2 f -> c.same_mreference_aloc_preserved (U.downgrade_val b) h1 h2 f)", "let downgrade_aloc (#al: aloc_t u#a) (#c: cls al) (a: aloc (raise_cls u#a u#b c)) : Tot (aloc c) =\n let ALoc region addr x = a in\n ALoc region addr (if None? x then None else Some (U.downgrade_val (Some?.v x)))", "let upgrade_aloc (#al: aloc_t u#a) (#c: cls al) (a: aloc c) : Tot (aloc (raise_cls u#a u#b c)) =\n let ALoc region addr x = a in\n ALoc region addr (if None? x then None else Some (U.raise_val (Some?.v x)))", "let downgrade_aloc_upgrade_aloc (#al: aloc_t u#a) (#c: cls al) (a: aloc c) : Lemma\n (downgrade_aloc (upgrade_aloc u#a u#b a) == a)\n [SMTPat (downgrade_aloc (upgrade_aloc u#a u#b a))]\n= ()", "let upgrade_aloc_downgrade_aloc (#al: aloc_t u#a) (#c: cls al) (a: aloc (raise_cls u#a u#b c)) : Lemma\n (upgrade_aloc (downgrade_aloc a) == a)\n [SMTPat (upgrade_aloc u#a u#b (downgrade_aloc a))]\n= ()", "let raise_loc_aux_pred\n (#al: aloc_t u#a)\n (c: cls al)\n (aux: Ghost.erased (GSet.set (aloc c)))\n (a: aloc (raise_cls u#a u#b c))\n: GTot bool\n= GSet.mem (downgrade_aloc a) (Ghost.reveal aux)" ], "closest": [ "val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)\nlet cloc_of_loc l = l", "val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)\nlet cloc_of_loc l = l", "val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)\nlet cloc_of_loc l =\n assert_norm (MG.cls abuffer == MG.cls ubuffer);\n coerce (MG.loc cloc_cls) l", "val raise (#t: Type) (x: t) : Tot (raise_t t)\nlet raise (#t: Type) (x: t) : Tot (raise_t t) =\n FStar.Universe.raise_val x", "val loc_region_only (#aloc: aloc_t) (#c: cls aloc) (preserve_liveness: bool) (r: HS.rid)\n : GTot (loc c)\nlet loc_region_only\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (Set.singleton r)", "val loc_all_regions_from (#aloc: aloc_t) (#c: cls aloc) (preserve_liveness: bool) (r: HS.rid)\n : GTot (loc c)\nlet loc_all_regions_from\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (HS.mod_set (Set.singleton r))", "val loc_mreference\n (#aloc: aloc_t)\n (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n : GTot (loc c)\nlet loc_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses true (HS.frameOf b) (Set.singleton (HS.as_addr b))", "val loc_of_cloc (l: MG.loc cloc_cls) : Tot loc\nlet loc_of_cloc l = l", "val loc_of_cloc (l: MG.loc cloc_cls) : Tot loc\nlet loc_of_cloc l = l", "val loc_of_cloc (l: MG.loc cloc_cls) : Tot loc\nlet loc_of_cloc l =\n assert_norm (MG.cls abuffer == MG.cls ubuffer);\n coerce loc l", "val cloc_aloc : HS.rid -> nat -> Tot (Type u#1)\nlet cloc_aloc = aloc", "val raise_val : #a:Type u#a -> x:a -> raise_t u#a u#b a\nlet raise_val #a x = Ret x", "val raise (a: Type) : stexnc a\nlet raise (a:Type) : stexnc a = fun s0 -> (None, (s0, 1))", "val as_loc (x: eloc) : GTot B.loc\nlet as_loc (x:eloc) : GTot B.loc = Ghost.reveal x", "val raise (a: Type) : stexn a\nlet raise (a:Type) : stexn a = fun s -> (None, s)", "val raise (#a: Type) (p: pcm a) : pcm (raise_t u#a u#b a)\nlet raise (#a:Type) (p:pcm a)\n : pcm (raise_t u#a u#b a)\n = {\n p = {\n composable = (fun x y -> p.p.composable (downgrade_val x) (downgrade_val y));\n op = (fun x y -> raise_val (p.p.op (downgrade_val x) (downgrade_val y)));\n one = raise_val p.p.one;\n };\n comm = (fun x y -> p.comm (downgrade_val x) (downgrade_val y));\n assoc = (fun x y z -> p.assoc (downgrade_val x) (downgrade_val y) (downgrade_val z));\n assoc_r = (fun x y z -> p.assoc_r (downgrade_val x) (downgrade_val y) (downgrade_val z));\n is_unit = (fun x -> p.is_unit (downgrade_val x));\n refine = (fun x -> p.refine (downgrade_val x));\n }", "val raise (#a: _) (e: exn) : Alg a [Raise]\nlet raise #a (e:exn) : Alg a [Raise] = \n Alg?.reflect (Op Raise e (fun e -> match e with))", "val loc_freed_mreference\n (#aloc: aloc_t)\n (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n : GTot (loc c)\nlet loc_freed_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses false (HS.frameOf b) (Set.singleton (HS.as_addr b))", "val raise_ (#a: Type) : ex a\nlet raise_ (#a:Type) \n : ex a\n = on_dom unit (fun () -> None)", "val raise_ : a:Type -> e:exn -> Tot (EXN?.repr a (fun (_:unit) (p:EXN?.post a) -> p (Inr e)))\nlet raise_ a (e:exn) (_:unit) = Inr e", "val raise: #a: _ -> exn -> Alg a [Raise]\nlet raise : #a:_ -> exn -> Alg a [Raise] = fun e -> match geneff Raise e with", "val norm_loc (l: loc) : loc\nlet norm_loc (l:loc) : loc =\n norm [zeta; iota; delta_only [`%loc_mutable_buffers]; delta_attr [`%norm_loc_attr]] l", "val norm_loc (l: loc) : loc\nlet norm_loc (l:loc) : loc =\n norm [zeta; iota; delta_only [`%loc_mutable_buffers]; delta_attr [`%norm_loc_attr]] l", "val aloc (r: HS.rid) (n: nat) : Tot (Type u#1)\nlet aloc (r: HS.rid) (n: nat) : Tot (Type u#1) =\n (l: loc_aux { loc_aux_in_addr l r n } )", "val raise (a: Type) : exnst a\nlet raise (a:Type) : exnst a = fun _ -> None", "val old_to_union_loc (l: OldM.loc) : GTot (M.loc old_and_new_cl_union)\nlet old_to_union_loc (l: OldM.loc) : GTot (M.loc old_and_new_cl_union) =\n M.union_loc_of_loc old_and_new_cl false (OldM.cloc_of_loc l)", "val fresh_loc (l: loc) (h h': HS.mem) : GTot Type0\nlet fresh_loc (l: loc) (h h' : HS.mem) : GTot Type0 =\n loc_unused_in h `loc_includes` l /\\\n loc_not_unused_in h' `loc_includes` l", "val cloc_aloc: HS.rid -> nat -> Tot Type0\nlet cloc_aloc = aloc", "val ptr_loc (#a: _) (x: bpointer a) : Tot eloc\nlet ptr_loc #a (x:B.pointer a) : Tot eloc = B.loc_buffer x", "val loc (#t: buftype) (#a: Type0) (b: buffer_t t a) : GTot B.loc\nlet loc (#t:buftype) (#a:Type0) (b:buffer_t t a) : GTot B.loc =\n match t with\n | MUT -> B.loc_buffer (b <: buffer a)\n | IMMUT -> B.loc_buffer (b <: ibuffer a)\n | CONST -> CB.loc_buffer (b <: cbuffer a)", "val cloc_cls: MG.cls cloc_aloc\nlet cloc_cls = cls", "val cloc_cls: MG.cls cloc_aloc\nlet cloc_cls = cls", "val app_loc (x: AppCtxt.app_ctxt) (l: eloc) : eloc\nlet app_loc (x:AppCtxt.app_ctxt) (l:eloc) : eloc = \n AppCtxt.properties x;\n AppCtxt.loc_of x `loc_union` l", "val raise_location_val_eqt (#l: location_eq) (v: location_val_eqt l) : location_val_t l\nlet raise_location_val_eqt (#l:location_eq) (v:location_val_eqt l) : location_val_t l =\n coerce (FStar.Universe.raise_val v)", "val lower (#t: Type) (x: raise_t t) : Tot t\nlet lower (#t: Type) (x: raise_t t) : Tot t =\n FStar.Universe.downgrade_val x", "val raise (#a: Type) (e: exn) : TAC a (fun ps post -> post (Failed e ps))\nlet raise (#a:Type) (e:exn)\n : TAC a (fun ps post -> post (Failed e ps))\n = TAC?.reflect (fun ps -> Failed #a e ps)", "val upd (s: store) (l: loc) (x: int) : store\nlet upd (s:store) (l:loc) (x:int) : store = Map.upd s l x", "val upd (s: store) (l: loc) (x: int) : store\nlet upd (s:store) (l:loc) (x:int) : store = Map.upd s l x", "val upd (s: store) (l: loc) (x: int) : store\nlet upd (s:store) (l:loc) (x:int) : store = Map.upd s l x", "val raise_t (t: Type0) : Type u#1\nlet raise_t (t: Type0) : Type u#1 = FStar.Universe.raise_t t", "val new_to_union_loc (l: NewM.loc) : GTot (M.loc old_and_new_cl_union)\nlet new_to_union_loc (l: NewM.loc) : GTot (M.loc old_and_new_cl_union) =\n M.union_loc_of_loc old_and_new_cl true (M.raise_loc (NewM.cloc_of_loc l))", "val raise_t ([@@@ strictly_positive] _ : Type u#a) : Type u#(max a b)\nlet raise_t a = raise0 a", "val alloc: #a:Type -> h0:heap -> x:a -> Tot (t:(ref a * heap){snd t == upd h0 (fst t) x})\nlet alloc #a h0 x =\n let r = { addr = h0.next_addr; init = x } in\n let h1 = { next_addr = r.addr + 1;\n memory = F.on_dom nat (fun (r':nat) -> if r' = r.addr\n\t\t\t then Some (| a, x |)\n else h0.memory r') }\n in\n assert (let h2 = upd h0 r x in\n FStar.FunctionalExtensionality.feq h1.memory h2.memory);\n r, h1", "val raise_seq (#a: Type0) (x: FStar.Seq.seq a) : FStar.Seq.seq (U.raise_t u#0 u#1 a)\nlet raise_seq (#a:Type0) (x:FStar.Seq.seq a)\n : FStar.Seq.seq (U.raise_t u#0 u#1 a)\n = FStar.Seq.map_seq U.raise_val x", "val loc : Type u#1\nlet loc = MG.loc cls", "val raise_action (#st: state u#s u#(max a b)) (#t: Type u#a) (a: action st t)\n : action st (U.raise_t u#a u#(max a b) t)\nlet raise_action\n (#st:state u#s u#(max a b))\n (#t:Type u#a)\n (a:action st t)\n : action st (U.raise_t u#a u#(max a b) t)\n = {\n pre = a.pre;\n post = F.on_dom _ (fun (x:U.raise_t u#a u#(max a b) t) -> a.post (U.downgrade_val x));\n step = (fun frame ->\n M.weaken <|\n M.bind (a.step frame) <|\n (fun x -> M.return <| U.raise_val u#a u#(max a b) x))\n }", "val loc_regions\n (r: Set.set HS.rid)\n: GTot loc\nlet loc_regions = MG.loc_regions false", "val loc : Type u#0\nlet loc = M.loc", "val loc : Type u#0\nlet loc = MG.loc cls", "val loc : Type u#0\nlet loc = M.loc", "val raise_ex: exn -> Tot (ex False)\nlet raise_ex (_:exn) : Tot (ex False) = fun _ -> None", "val raise (#a: _) (e: exn) : EFF a [EXN]\nlet raise #a (e:exn) : EFF a [EXN] =\n EFF?.reflect (fun () -> raise e)", "val union (l1 l2: B.loc) : GTot B.loc\nlet union (l1:B.loc) (l2:B.loc) : GTot B.loc = B.loc_union l1 l2", "val alloc (#a:Type) (x:a)\n : stt (ref a) emp (fun r -> pts_to r x)\nlet alloc = alloc'", "val alloc (#a:Type) (x:a)\n : stt (ref a) emp (fun r -> pts_to r x)\nlet alloc = alloc'", "val raise_val_inj (#a:Type) (x y:a) : Lemma\n (requires U.raise_val x == U.raise_val y)\n (ensures x == y)\nlet raise_val_inj x y =\n U.downgrade_val_raise_val x;\n U.downgrade_val_raise_val y", "val loc_regions\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: GTot loc\nlet loc_regions = MG.loc_regions", "val loc_regions\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: GTot loc\nlet loc_regions = MG.loc_regions", "val modified_arg_loc (x: arg) : GTot B.loc\nlet modified_arg_loc (x:arg) : GTot B.loc =\n match x with\n | (|TD_Buffer _ _ {modified=true}, x|) -> B.loc_buffer x\n | _ -> B.loc_none", "val raise (#a: _) : option a\nlet raise #a : option a = None", "val single (l: loc) : label\nlet single (l:loc) : label = Set.singleton l", "val single (l: loc) : label\nlet single (l:loc) : label = Set.singleton l", "val single (l: loc) : label\nlet single (l:loc) : label = Set.singleton l", "val union_loc_to_new (l: M.loc old_and_new_cl_union) : GTot NewM.loc\nlet union_loc_to_new (l: M.loc old_and_new_cl_union) : GTot NewM.loc =\n NewM.loc_of_cloc (M.lower_loc (M.loc_of_union_loc true l))", "val raise_frame_preserving_upd (#a: _) (#p: pcm a) (#x #y: a) (f: frame_preserving_upd p x y)\n : frame_preserving_upd (raise p) (raise_val x) (raise_val y)\nlet raise_frame_preserving_upd #a (#p:pcm a) (#x #y:a) (f:frame_preserving_upd p x y)\n : frame_preserving_upd (raise p) (raise_val x) (raise_val y)\n = fun v ->\n let u = f (downgrade_val v) in\n let v_new = raise_val u in\n assert (forall frame. composable p y frame ==> composable (raise p) (raise_val y) (raise_val frame));\n assert (forall frame. composable (raise p) (raise_val x) frame ==> composable p x (downgrade_val frame));\n v_new", "val another_raise (#a: _) (e: exn) : Alg a [Raise]\nlet another_raise #a (e:exn) : Alg a [Raise] = \n // Funnily enough, the version below succeeds from concluding `a ==\n // empty` under the lambda since the context becomes inconsistent. All\n // good, just surprising.\n Alg?.reflect (Op Raise e Return)", "val loc_pointer\n (#t: typ)\n (p: pointer t)\n: GTot loc\nlet loc_pointer #t p =\n MG.loc_of_aloc #_ #cls #(frameOf p) #(as_addr p) (LocPointer p)", "val modified_arg_mloc (x: arg) : GTot ME.loc\nlet modified_arg_mloc (x:arg) : GTot ME.loc =\n match x with\n | (|TD_Buffer src t {modified=true}, x|) -> ME.loc_buffer (as_vale_buffer #src #t x)\n | _ -> ME.loc_none", "val raise (#a #si #so: _) (e: exn) : EFF a si so [EXN]\nlet raise #a #si #so (e:exn) : EFF a si so [EXN] =\n EFF?.reflect (Op Raise e Return)", "val old_and_new_cl (is_new: bool) : Tot (M.cls (old_and_new_aloc is_new))\nlet old_and_new_cl (is_new: bool) : Tot (M.cls (old_and_new_aloc is_new)) =\n if is_new then M.raise_cls NewM.cloc_cls else OldM.cloc_cls", "val arg_loc (x: arg) : GTot B.loc\nlet arg_loc (x:arg) : GTot B.loc =\n match x with\n | (|TD_Buffer _ _ _, x|) -> B.loc_buffer x\n | (|TD_ImmBuffer _ _ _, x|) -> B.loc_buffer x\n | (|TD_Base _, _|) -> B.loc_none", "val alloc (#a:Type) (x:a)\n : stt_ghost (ref a) emp (fun r -> pts_to r x)\nlet alloc = alloc'", "val alloc (#a:Type) (x:a)\n : stt_ghost (ref a) emp (fun r -> pts_to r x)\nlet alloc = alloc'", "val raise_erased (#a: Type0) (x: erased a) : erased (U.raise_t u#0 u#1 a)\nlet raise_erased (#a:Type0) (x:erased a)\n : erased (U.raise_t u#0 u#1 a)\n = Ghost.hide (U.raise_val (Ghost.reveal x))", "val raise_equiv (#t: Type) (x y: t) : Lemma (U.raise_val x == U.raise_val y <==> x == y)\nlet raise_equiv (#t:Type) (x y:t)\n : Lemma (U.raise_val x == U.raise_val y <==>\n x == y)\n = assert (U.downgrade_val (U.raise_val x) == x);\n assert (U.downgrade_val (U.raise_val y) == y)", "val modifies_only_live_addresses\n (#aloc: aloc_t)\n (#c: cls aloc)\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc c)\n (h h': HS.mem)\n : Lemma\n (requires\n (modifies (loc_union (loc_addresses false r a) l) h h' /\\\n (forall x. Set.mem x a ==> h `does_not_contain_addr` (r, x)))) (ensures (modifies l h h'))\nlet modifies_only_live_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_addresses false r a) l) h h' /\\\n (forall x . Set.mem x a ==> h `does_not_contain_addr` (r, x))\n ))\n (ensures (modifies l h h'))\n= loc_addresses_unused_in c r a h;\n loc_includes_refl l;\n loc_includes_union_l (loc_unused_in c h) l l;\n loc_includes_union_l (loc_unused_in c h) l (loc_addresses false r a);\n loc_includes_union_r (loc_union (loc_unused_in c h) l) (loc_addresses false r a) l;\n modifies_loc_includes (loc_union (loc_unused_in c h) l) h h' (loc_union (loc_addresses false r a) l);\n modifies_only_not_unused_in l h h'", "val mt_loc: mt_p -> GTot loc\nlet mt_loc mt = B.loc_all_regions_from false (B.frameOf mt)", "val elift2_p\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n ($f: (xa: a -> xb: b{p xa xb} -> GTot c))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (rc: erased c {reveal rc == f (reveal ra) (reveal rb)})\nlet elift2_p\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n ($f: (xa: a -> xb: b{p xa xb} -> GTot c))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (rc: erased c {reveal rc == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "val addx (l: loc) (x: int)\n : AlgPP unit\n (fun _ -> True)\n (fun h0 _ h1 -> modifies1 l h0 h1 /\\ (Map.sel h1 l == x + Map.sel h0 l))\nlet addx (l:loc) (x:int) : AlgPP unit (fun _ -> True) (fun h0 _ h1 -> modifies1 l h0 h1\n /\\ (Map.sel h1 l == x + Map.sel h0 l)) =\n l := !l + x", "val raise (#a: Type) (e: string)\n : MSeqExn a (fun _ -> True) (fun s0 r s1 -> r == Error e /\\ s0 == s1)\nlet raise (#a:Type) (e:string)\n: MSeqExn a\n (fun _ -> True)\n (fun s0 r s1 -> r == Error e /\\ s0 == s1)\n= MSeqEXN?.reflect (fun s0 -> Error e, s0)", "val path_loc: path_p -> GTot loc\nlet path_loc p = B.loc_all_regions_from false (B.frameOf p)", "val _raise (#a: _) : repr a (fun _ -> True) (fun s0 _ s1 -> s1 == s0) [EXN]\nlet _raise #a : repr a (fun _ -> True) (fun s0 _ s1 -> s1 == s0) [EXN] =\n let ff (s0:state) : Tot (r:(option a & state){fst r == None /\\ snd r == s0}) =\n (None, s0)\n in\n ff", "val aloc (r: HS.rid) (n: nat) : Tot Type0\nlet aloc (r: HS.rid) (n: nat) : Tot Type0 =\n (l: loc_aux { loc_aux_in_addr l r n } )", "val raise__ (a: Type) (e: exn) : Exn a True (fun r -> r == Inr e)\nlet raise__ (a:Type) (e:exn) : Exn a True (fun r -> r == Inr e)\n = EXN?.reflect (raise_ a e)", "val loc_addresses\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: GTot loc\nlet loc_addresses = MG.loc_addresses", "val loc_addresses\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: GTot loc\nlet loc_addresses = MG.loc_addresses", "val sel (s: store) (l: loc) : int\nlet sel (s:store) (l:loc) : int = Map.sel s l", "val sel (s: store) (l: loc) : int\nlet sel (s:store) (l:loc) : int = Map.sel s l", "val sel (s: store) (l: loc) : int\nlet sel (s:store) (l:loc) : int = Map.sel s l", "val loc_addresses\n (r: HS.rid)\n (n: Set.set nat)\n: GTot loc\nlet loc_addresses = MG.loc_addresses #_ #cls false", "val raise: a: Type -> Prims.unit -> rand a\nlet raise (a:Type) () : rand a = fun s -> None, fst s", "val raise: a: Type -> Prims.unit -> rand a\nlet raise (a:Type) () : rand a = fun s -> None, fst s", "val elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)})\nlet elift2_pq\n (#a #b #c: Type)\n (#p: (a -> b -> Type))\n (#q: (x: a -> y: b{p x y} -> c -> Type))\n ($f: (x: a -> y: b{p x y} -> GTot (z: c{q x y z})))\n (ra: erased a)\n (rb: erased b {p (reveal ra) (reveal rb)})\n : Tot (z: erased c {reveal z == f (reveal ra) (reveal rb)}) =\n let x = reveal ra in\n let y:(y: b{p x y}) = reveal rb in\n return (f x y)", "val alloc (#a:Type) (x:a)\n : ST (ref a)\n emp \n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\nlet alloc (#a:Type) (x:a)\n : ST (ref a)\n emp\n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\n = let r = coerce_steel (fun _ -> R.alloc x) in\n r", "val alloc (#a:Type) (x:a)\n : ST (ref a)\n emp \n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\nlet alloc (#a:Type) (x:a)\n : ST (ref a)\n emp\n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\n = let r = coerce_steel (fun _ -> R.alloc_pt x) in\n r", "val alloc (#a:Type)\n (#u:_)\n (x:erased a)\n : STGhostT (ref a) u\n emp\n (fun r -> pts_to r full_perm x)\nlet alloc (#a:Type)\n (#u:_)\n (x:erased a)\n : STGhostT (ref a) u\n emp\n (fun r -> pts_to r full_perm x)\n = coerce_ghost (fun _ -> R.ghost_alloc_pt x)", "val upd (r: loc) (v: int) : AlgWP unit (fun h0 p -> p ((), Map.upd h0 r v))\nlet upd (r:loc) (v:int) : AlgWP unit (fun h0 p -> p ((), Map.upd h0 r v)) =\n let h = get2 () in\n put2 (Map.upd h r v)", "val handle_raise (#a #labs: _) (f: (unit -> Alg a (Raise :: labs))) (g: (unit -> Alg a labs))\n : Alg a labs\nlet handle_raise #a #labs (f : unit -> Alg a (Raise::labs)) (g : unit -> Alg a labs)\n : Alg a labs\n = handle_one f (fun _ _ -> g ())", "val old_and_new_cl_union:M.cls (M.aloc_union old_and_new_aloc)\nlet old_and_new_cl_union : M.cls (M.aloc_union old_and_new_aloc) = M.cls_union old_and_new_cl", "val upd\n (#a: Type)\n (#rel: preorder a)\n (m: mem)\n (s: mreference a rel {live_region m (frameOf s)})\n (v: a)\n : GTot mem\nlet upd (#a:Type) (#rel:preorder a) (m:mem) (s:mreference a rel{live_region m (frameOf s)}) (v:a)\n :GTot mem\n = let h, rid_ctr, tip = get_hmap m, get_rid_ctr m, get_tip m in\n lemma_is_wf_ctr_and_tip_elim m;\n let i = frameOf s in\n let h = Map.upd h i (Heap.upd (Map.sel h i) (as_ref s) v) in\n lemma_is_wf_ctr_and_tip_intro h rid_ctr tip;\n mk_mem rid_ctr h tip" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.cloc_of_loc" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.cloc_of_loc" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.cloc_of_loc" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.raise" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_region_only" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_all_regions_from" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_mreference" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_of_cloc" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_of_cloc" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_of_cloc" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.cloc_aloc" }, { "project_name": "FStar", "file_name": "FStar.Universe.fst", "name": "FStar.Universe.raise_val" }, { "project_name": "FStar", "file_name": "FStar.DM4F.StExnC.fst", "name": "FStar.DM4F.StExnC.raise" }, { "project_name": "FStar", "file_name": "LowStar.Lens.fsti", "name": "LowStar.Lens.as_loc" }, { "project_name": "FStar", "file_name": "FStar.DM4F.StExn.fst", "name": "FStar.DM4F.StExn.raise" }, { "project_name": "FStar", "file_name": "FStar.Universe.PCM.fst", "name": "FStar.Universe.PCM.raise" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.raise" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_freed_mreference" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.raise_" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Exceptions.fst", "name": "FStar.DM4F.Exceptions.raise_" }, { "project_name": "FStar", "file_name": "Alg.fst", "name": "Alg.raise" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsMem.fsti", "name": "Vale.X64.InsMem.norm_loc" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsMem.fsti", "name": "Vale.PPC64LE.InsMem.norm_loc" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.aloc" }, { "project_name": "FStar", "file_name": "FStar.DM4F.ExnSt.fst", "name": "FStar.DM4F.ExnSt.raise" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.old_to_union_loc" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.fresh_loc" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.cloc_aloc" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.ptr_loc" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.loc" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.cloc_cls" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.cloc_cls" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.app_loc" }, { "project_name": "hacl-star", "file_name": "Vale.Transformers.Locations.fsti", "name": "Vale.Transformers.Locations.raise_location_val_eqt" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.lower" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Effect.fsti", "name": "FStar.Tactics.Effect.raise" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.upd" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.upd" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.upd" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.raise_t" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.new_to_union_loc" }, { "project_name": "FStar", "file_name": "FStar.Universe.fst", "name": "FStar.Universe.raise_t" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.raise_seq" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc" }, { "project_name": "steel", "file_name": "PulseCore.Semantics.fst", "name": "PulseCore.Semantics.raise_action" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_regions" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc" }, { "project_name": "FStar", "file_name": "SimplePrintfReify.fst", "name": "SimplePrintfReify.raise_ex" }, { "project_name": "FStar", "file_name": "LatticeEff.fst", "name": "LatticeEff.raise" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.union" }, { "project_name": "steel", "file_name": "Pulse.Lib.Reference.fst", "name": "Pulse.Lib.Reference.alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherReference.fst", "name": "Pulse.Lib.HigherReference.alloc" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.raise_val_inj" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_regions" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_regions" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Base.fst", "name": "Vale.Interop.Base.modified_arg_loc" }, { "project_name": "FStar", "file_name": "MonadFunctorInference.fst", "name": "MonadFunctorInference.raise" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.single" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.single" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.single" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.union_loc_to_new" }, { "project_name": "FStar", "file_name": "FStar.Universe.PCM.fst", "name": "FStar.Universe.PCM.raise_frame_preserving_upd" }, { "project_name": "FStar", "file_name": "Alg.fst", "name": "Alg.another_raise" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_pointer" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.ValeSig.fst", "name": "Vale.AsLowStar.ValeSig.modified_arg_mloc" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.raise" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.old_and_new_cl" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Base.fst", "name": "Vale.Interop.Base.arg_loc" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.alloc" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.raise_erased" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.raise_equiv" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.modifies_only_live_addresses" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.fst", "name": "MerkleTree.Low.mt_loc" }, { "project_name": "FStar", "file_name": "FStar.Ghost.fsti", "name": "FStar.Ghost.elift2_p" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.addx" }, { "project_name": "FStar", "file_name": "MSeqExn.fst", "name": "MSeqExn.raise" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.fst", "name": "MerkleTree.Low.path_loc" }, { "project_name": "FStar", "file_name": "LatticeSpec.fst", "name": "LatticeSpec._raise" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.aloc" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Exceptions.fst", "name": "FStar.DM4F.Exceptions.raise__" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_addresses" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_addresses" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.sel" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.sel" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.sel" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_addresses" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Random.fst", "name": "FStar.DM4F.Random.raise" }, { "project_name": "FStar", "file_name": "FStar.DM4F.OTP.Random.fst", "name": "FStar.DM4F.OTP.Random.raise" }, { "project_name": "FStar", "file_name": "FStar.Ghost.fsti", "name": "FStar.Ghost.elift2_pq" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.alloc" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.alloc" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.alloc" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.upd" }, { "project_name": "FStar", "file_name": "Alg.fst", "name": "Alg.handle_raise" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.old_and_new_cl_union" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.upd" } ], "selected_premises": [ "FStar.ModifiesGen.region_liveness_insensitive_locs", "FStar.ModifiesGen.aloc_disjoint_sym", "FStar.ModifiesGen.raise_cls", "FStar.ModifiesGen.raise_aloc", "FStar.ModifiesGen.loc", "FStar.ModifiesGen.modifies_trans'", "FStar.ModifiesGen.loc_aux_disjoint_sym", "FStar.ModifiesGen.modifies_none_modifies", "FStar.ModifiesGen.loc_aux_includes_buffer_includes", "FStar.ModifiesGen.popped_modifies", "FStar.ModifiesGen.loc_equal", "FStar.ModifiesGen.modifies_loc_regions_intro", "FStar.ModifiesGen.modifies_only_not_unused_in", "FStar.ModifiesGen.address_liveness_insensitive_locs", "FStar.ModifiesGen.fresh_frame_modifies", "FStar.ModifiesGen.loc_disjoint_includes", "FStar.FunctionalExtensionality.feq", "FStar.ModifiesGen.modifies_preserves_region_liveness_aloc", "FStar.ModifiesGen.addrs_of_loc_aux", "FStar.ModifiesGen.loc_union", "FStar.ModifiesGen.aloc_includes", "FStar.ModifiesGen.loc_aux_includes_trans", "FStar.Reflection.V2.Data.var", "FStar.ModifiesGen.loc_aux_includes_buffer", "FStar.ModifiesGen.addrs_of_loc_weak", "FStar.ModifiesGen.loc_disjoint'", "FStar.ModifiesGen.new_region_modifies", "FStar.ModifiesGen.loc_aux_includes_loc_aux_includes_buffer", "FStar.ModifiesGen.loc_none", "FStar.ModifiesGen.addrs_of_loc_aux_pred", "FStar.ModifiesGen.aloc_union", "FStar.ModifiesGen.loc_disjoint_aloc_elim", "FStar.ModifiesGen.restrict_to_regions", "FStar.ModifiesGen.loc_of_union_loc_regions", "FStar.ModifiesGen.loc_disjoint_aux", "FStar.ModifiesGen.disjoint_addrs_of_loc_loc_disjoint", "FStar.ModifiesGen.loc_of_union_loc", "FStar.ModifiesGen.raise_loc_aux_pred", "FStar.ModifiesGen.loc_disjoint_region_liveness_tags", "FStar.ModifiesGen.addrs_of_loc_liveness_not_preserved", "FStar.ModifiesGen.aloc_disjoint", "FStar.ModifiesGen.modifies'", "FStar.Pervasives.Native.snd", "FStar.ModifiesGen.modifies_preserves_livenesses_intro", "FStar.ModifiesGen.loc_aux_disjoint", "FStar.Pervasives.Native.fst", "FStar.ModifiesGen.modifies_loc_includes", "FStar.ModifiesGen.loc_disjoint_sym", "FStar.Heap.trivial_preorder", "FStar.ModifiesGen.loc_unused_in", "FStar.ModifiesGen.loc_aux_includes", "FStar.ModifiesGen.modifies_trans", "FStar.ModifiesGen.loc_unused_in_not_unused_in_disjoint", "FStar.Tactics.Effect.raise", "FStar.ModifiesGen.modifies_refl", "FStar.ModifiesGen.modifies_only_live_regions_weak", "FStar.ModifiesGen.modifies_union_loc_of_loc", "FStar.ModifiesGen.modifies_only_live_regions", "FStar.ModifiesGen.loc_regions", "FStar.ModifiesGen.loc_disjoint_addrs", "FStar.ModifiesGen.loc_disjoint", "FStar.ModifiesGen.union_loc_of_loc_includes", "FStar.ModifiesGen.modifies_preserves_alocs_intro", "FStar.ModifiesGen.loc_of_union_loc_none", "FStar.ModifiesGen.modifies_fresh_frame_popped", "FStar.ModifiesGen.modifies_preserves_liveness_strong", "FStar.ModifiesGen.loc_includes_loc_regions_restrict_to_regions", "FStar.ModifiesGen.loc_includes_restrict_to_regions", "FStar.ModifiesGen.loc_of_aloc", "FStar.ModifiesGen.not_live_region_loc_not_unused_in_disjoint", "FStar.ModifiesGen.modifies_intro_strong", "FStar.ModifiesGen.aloc_domain", "FStar.ModifiesGen.addrs_of_loc", "FStar.Monotonic.HyperStack.sel", "FStar.Tactics.SMT.get_rlimit", "FStar.ModifiesGen.loc_aux_disjoint_loc_aux_includes", "FStar.Tactics.SMT.get_initial_fuel", "FStar.Reflection.Const.cons_qn", "FStar.ModifiesGen.modifies_strengthen'", "FStar.FunctionalExtensionality.on_dom", "FStar.ModifiesGen.modifies_address_liveness_insensitive_unused_in", "FStar.ModifiesGen.loc_includes", "FStar.ModifiesGen.no_upd_fresh_region", "FStar.ModifiesGen.loc_aux_includes_refl", "FStar.ModifiesGen.loc_disjoint_regions", "FStar.Tactics.SMT.get_max_fuel", "FStar.ModifiesGen.modifies_aloc_intro", "FStar.ModifiesGen.modifies", "FStar.Tactics.V2.Builtins.ret_t", "FStar.ModifiesGen.regions_of_loc", "FStar.ModifiesGen.modifies_intro", "FStar.ModifiesGen.aloc_disjoint_includes", "FStar.ModifiesGen.loc_includes'", "FStar.ModifiesGen.mk_non_live_addrs", "FStar.ModifiesGen.mk_live_addrs", "FStar.ModifiesGen.loc_of_union_loc_union_loc_of_loc", "FStar.ModifiesGen.modifies_preserves_not_unused_in", "FStar.ModifiesGen.i_restricted_g_t", "FStar.Tactics.SMT.get_initial_ifuel", "FStar.ModifiesGen.loc_not_unused_in" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.ModifiesGen\n\n#set-options \"--split_queries no\"\n#set-options \"--using_facts_from '*,-FStar.Tactics,-FStar.Reflection,-FStar.List'\"\n\nmodule HS = FStar.HyperStack\nmodule HST = FStar.HyperStack.ST\n\nnoeq\ntype aloc (#al: aloc_t) (c: cls al) = | ALoc:\n (region: HS.rid) ->\n (addr: nat) ->\n (loc: option (al region addr)) ->\n aloc c\n\nlet aloc_domain (#al: aloc_t) (c: cls al) (regions: Ghost.erased (Set.set HS.rid)) (addrs: ((r: HS.rid { Set.mem r (Ghost.reveal regions) } ) -> GTot (GSet.set nat))) : GTot (GSet.set (aloc c)) =\n GSet.comprehend (fun a -> Set.mem a.region (Ghost.reveal regions) && GSet.mem a.addr (addrs a.region))\n\nmodule F = FStar.FunctionalExtensionality\n\n[@@(unifier_hint_injective)]\nlet i_restricted_g_t = F.restricted_g_t\n\nlet addrs_dom regions =\n (r: HS.rid { Set.mem r (Ghost.reveal regions) } )\n\nlet non_live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (r:addrs_dom regions) =\n (y: GSet.set nat { r `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y })\n\nlet live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags))\n (r:addrs_dom regions) = (y: GSet.set nat { GSet.subset (non_live_addrs r) y } )\n\nnoeq\ntype loc' (#al: aloc_t u#x) (c: cls al) : Type u#x =\n | Loc:\n (regions: Ghost.erased (Set.set HS.rid)) ->\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } ) ->\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags)) ->\n (live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs)) ->\n (aux: Ghost.erased (GSet.set (aloc c)) {\n aloc_domain c regions live_addrs `GSet.subset` Ghost.reveal aux /\\\n Ghost.reveal aux `GSet.subset` (aloc_domain c regions (fun _ -> GSet.complement GSet.empty))\n } ) ->\n loc' c\n\nlet loc = loc'\n\nlet mk_non_live_addrs (#regions:_) (#region_liveness_tags:_)\n (f: (x:addrs_dom regions -> GTot (non_live_addrs_codom regions region_liveness_tags x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags) =\n F.on_dom_g _ f\n\nlet mk_live_addrs (#regions:_) (#region_liveness_tags:_)\n (#non_live_addrs_codom: _)\n (f: (x:addrs_dom regions -> GTot (live_addrs_codom regions region_liveness_tags non_live_addrs_codom x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs_codom) =\n F.on_dom_g _ f\n\nlet loc_none #a #c =\n Loc\n (Ghost.hide (Set.empty))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)\n\nlet regions_of_loc\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: GTot (Set.set HS.rid)\n= Ghost.reveal (Loc?.regions s)\n\nlet addrs_of_loc_liveness_not_preserved\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.non_live_addrs l r\n else GSet.empty\n\nlet addrs_of_loc_weak\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.live_addrs l r\n else GSet.empty\n\nlet addrs_of_loc_aux_pred\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n (addr: nat)\n: GTot bool\n= StrongExcludedMiddle.strong_excluded_middle (exists a . GSet.mem a (Ghost.reveal (Loc?.aux l)) /\\ a.region == r /\\ a.addr == addr)\n\nlet addrs_of_loc_aux\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (y: GSet.set nat { GSet.subset (GSet.intersect y (addrs_of_loc_weak l r)) GSet.empty } )\n= GSet.comprehend (addrs_of_loc_aux_pred l r)\n `GSet.intersect` (GSet.complement (addrs_of_loc_weak l r))\n\nlet addrs_of_loc\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= GSet.union\n (addrs_of_loc_weak l r)\n (addrs_of_loc_aux l r)\n\nlet addrs_of_loc_aux_prop\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: Lemma\n (GSet.subset (GSet.intersect (addrs_of_loc_aux l r) (addrs_of_loc_weak l r)) GSet.empty)\n [SMTPatOr [\n [SMTPat (addrs_of_loc_aux l r)];\n [SMTPat (addrs_of_loc_weak l r)];\n [SMTPat (addrs_of_loc l r)];\n ]]\n= ()\n\nlet loc_union #al #c s1 s2 =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in\n let regions = Set.union regions1 regions2 in\n let region_liveness_tags : Ghost.erased (Set.set HS.rid) = (Ghost.hide (Set.union (Ghost.reveal (Loc?.region_liveness_tags s1)) (Ghost.reveal (Loc?.region_liveness_tags s2)))) in\n let gregions = Ghost.hide regions in\n let non_live_addrs =\n F.on_dom_g (addrs_dom gregions) #(non_live_addrs_codom gregions region_liveness_tags)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then Loc?.non_live_addrs s1 r else GSet.empty)\n (if Set.mem r regions2 then Loc?.non_live_addrs s2 r else GSet.empty))\n in\n let live_addrs =\n F.on_dom_g (addrs_dom gregions) #(live_addrs_codom gregions region_liveness_tags non_live_addrs)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then addrs_of_loc_weak s1 r else GSet.empty)\n (if Set.mem r regions2 then addrs_of_loc_weak s2 r else GSet.empty))\n in\n let aux = Ghost.hide\n (Ghost.reveal (Loc?.aux s1) `GSet.union` Ghost.reveal (Loc?.aux s2))\n in\n Loc\n (Ghost.hide regions)\n region_liveness_tags\n non_live_addrs\n live_addrs\n aux\n\nlet fun_set_equal (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) :Tot Type0 =\n forall (x: t) . {:pattern (f1 x) \\/ (f2 x) } f1 x `GSet.equal` f2 x\n\nlet fun_set_equal_elim (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) : Lemma\n (requires (fun_set_equal f1 f2))\n (ensures (f1 == f2))\n// [SMTPat (fun_set_equal f1 f2)]\n= assert (f1 `FunctionalExtensionality.feq_g` f2)\n\nlet loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n let Loc regions1 region_liveness_tags1 _ _ aux1 = s1 in\n let Loc regions2 region_liveness_tags2 _ _ aux2 = s2 in\n Ghost.reveal regions1 `Set.equal` Ghost.reveal regions2 /\\\n Ghost.reveal region_liveness_tags1 `Set.equal` Ghost.reveal region_liveness_tags2 /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)\n\nlet loc_equal_elim (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : Lemma\n (requires (loc_equal s1 s2))\n (ensures (s1 == s2))\n [SMTPat (s1 `loc_equal` s2)]\n= fun_set_equal_elim (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2);\n fun_set_equal_elim (Loc?.live_addrs s1) (Loc?.live_addrs s2)\n\n\nlet loc_union_idem #al #c s =\n assert (loc_union s s `loc_equal` s)\n\nlet loc_union_comm #al #c s1 s2 =\n assert (loc_union s1 s2 `loc_equal` loc_union s2 s1)\n\nlet loc_union_assoc #al #c s1 s2 s3 =\n assert (loc_union s1 (loc_union s2 s3) `loc_equal` loc_union (loc_union s1 s2) s3)\n\nlet loc_union_loc_none_l #al #c s =\n assert (loc_union loc_none s `loc_equal` s)\n\nlet loc_union_loc_none_r #al #c s =\n assert (loc_union s loc_none `loc_equal` s)\n\nlet loc_of_aloc #al #c #r #n b =\n let regions = (Ghost.hide (Set.singleton r)) in\n let region_liveness_tags = (Ghost.hide (Set.empty)) in\n Loc\n regions\n region_liveness_tags\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide (GSet.singleton (ALoc r n (Some b))))\n\nlet loc_of_aloc_not_none #al #c #r #n b = ()\n\nlet loc_addresses #al #c preserve_liveness r n =\n let regions = (Ghost.hide (Set.singleton r)) in\n Loc\n regions\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> if preserve_liveness then GSet.empty else GSet.of_set n))\n (mk_live_addrs (fun _ -> GSet.of_set n))\n (Ghost.hide (aloc_domain c regions (fun _ -> GSet.of_set n)))\n\nlet loc_regions_region_liveness_tags (preserve_liveness: bool) (r: Set.set HS.rid) : Tot (Ghost.erased (Set.set HS.rid)) =\n if preserve_liveness then Ghost.hide Set.empty else Ghost.hide r\n\nlet loc_regions #al #c preserve_liveness r =\n let region_liveness_tags = loc_regions_region_liveness_tags preserve_liveness r in\n let addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { r' `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y } ) =\n GSet.complement GSet.empty\n in\n let live_addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { addrs r' `GSet.subset` y } ) =\n addrs r'\n in\n Loc\n (Ghost.hide r)\n region_liveness_tags\n (mk_non_live_addrs addrs)\n (mk_live_addrs live_addrs)\n (Ghost.hide (aloc_domain c (Ghost.hide r) addrs))\n\nlet aloc_includes (#al: aloc_t) (#c: cls al) (b0 b: aloc c) : GTot Type0 =\n b0.region == b.region /\\ b0.addr == b.addr /\\ Some? b0.loc == Some? b.loc /\\ (if Some? b0.loc && Some? b.loc then c.aloc_includes (Some?.v b0.loc) (Some?.v b.loc) else True)\n\nlet loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b: aloc c)\n: GTot Type0\n (decreases s)\n= exists (b0 : aloc c) . b0 `GSet.mem` s /\\ b0 `aloc_includes` b\n\nlet loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: GTot Type0\n (decreases s2)\n= forall (b2: aloc c) . GSet.mem b2 s2 ==> loc_aux_includes_buffer s1 b2\n\nlet loc_aux_includes_union_l\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s \\/ loc_aux_includes s2 s))\n (ensures (loc_aux_includes (GSet.union s1 s2) s))\n (decreases s)\n= ()\n\nlet loc_aux_includes_refl\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n: Lemma\n (loc_aux_includes s s)\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)\n\nlet loc_aux_includes_subset\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)\n\nlet loc_aux_includes_subset'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n [SMTPatOr [\n [SMTPat (s1 `GSet.subset` s2)];\n [SMTPat (loc_aux_includes s2 s1)];\n ]]\n= loc_aux_includes_subset s1 s2\n\nlet loc_aux_includes_union_l_r\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s s') s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s s' s\n\nlet loc_aux_includes_union_l_l\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s' s) s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s' s s\n\nlet loc_aux_includes_buffer_includes\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b1 b2: aloc c)\n: Lemma\n (requires (loc_aux_includes_buffer s b1 /\\ b1 `aloc_includes` b2))\n (ensures (loc_aux_includes_buffer s b2))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))\n\nlet loc_aux_includes_loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n (b: aloc c)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_buffer s2 b))\n (ensures (loc_aux_includes_buffer s1 b))\n= Classical.forall_intro_3 (fun s b1 b2 -> Classical.move_requires (loc_aux_includes_buffer_includes #al #c s b1) b2)\n\nlet loc_aux_includes_trans\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))\n\nlet addrs_of_loc_weak_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (loc_union l1 l2) r == GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r))\n [SMTPat (addrs_of_loc_weak (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc_weak (loc_union l1 l2) r) (GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r)))\n\nlet addrs_of_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l1 l2) r == GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r))\n [SMTPat (addrs_of_loc (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc (loc_union l1 l2) r) (GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r)))\n\nunfold\nlet loc_includes' #al (#c: cls al) (s1 s2: loc c) =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in (\n Set.subset regions2 regions1 /\\\n Set.subset (Ghost.reveal (Loc?.region_liveness_tags s2)) (Ghost.reveal (Loc?.region_liveness_tags s1)) /\\\n (\n forall (r: HS.rid { Set.mem r regions2 } ) .\n GSet.subset (Loc?.non_live_addrs s2 r) (Loc?.non_live_addrs s1 r)\n ) /\\\n (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc_weak s2 r) (addrs_of_loc_weak s1 r)\n ) /\\ (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc s2 r) (addrs_of_loc s1 r)\n ) /\\ (\n (Ghost.reveal (Loc?.aux s1)) `loc_aux_includes` (Ghost.reveal (Loc?.aux s2))\n )\n )\n\nlet loc_includes #al #c s1 s2 =\n loc_includes' s1 s2\n\nlet loc_includes_refl #al #c s =\n loc_aux_includes_refl (Ghost.reveal (Loc?.aux s))\n\nlet loc_includes_refl'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: Lemma\n (loc_includes s s)\n [SMTPat (loc_includes s s)]\n= loc_includes_refl s\n\nlet loc_includes_trans #al #c s1 s2 s3 =\n loc_aux_includes_trans (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s3))\n\nlet loc_includes_union_r #al #c s s1 s2 = ()\n\nlet loc_includes_union_l #al #c s1 s2 s =\n let u12 = loc_union s1 s2 in\n Classical.or_elim\n #(loc_includes s1 s)\n #(loc_includes s2 s)\n #(fun _ -> loc_includes (loc_union s1 s2) s)\n (fun _ ->\n loc_aux_includes_union_l_r (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2));\n assert (loc_includes (loc_union s1 s2) s1);\n loc_includes_trans u12 s1 s)\n (fun _ ->\n loc_aux_includes_union_l_l (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s1));\n assert (loc_includes (loc_union s1 s2) s2);\n loc_includes_trans u12 s2 s)\n\nlet loc_includes_none #al #c s = ()\n\nlet loc_includes_none_elim #al #c s =\n assert (s `loc_equal` loc_none)\n\nlet loc_includes_aloc #al #c #r #n b1 b2 = ()\n\nlet loc_includes_aloc_elim #aloc #c #r1 #r2 #n1 #n2 b1 b2 = ()\n\nlet addrs_of_loc_loc_of_aloc\n (#al: aloc_t)\n (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (p: al r a)\n (r': HS.rid)\n: Lemma\n (addrs_of_loc (loc_of_aloc #_ #c p) r' `GSet.equal` (if r = r' then GSet.singleton a else GSet.empty))\n [SMTPat (addrs_of_loc (loc_of_aloc #_ #c p) r')]\n= ()\n\nlet loc_includes_addresses_aloc #al #c preserve_liveness r s #a p = ()\n\nlet loc_includes_region_aloc #al #c preserve_liveness s #r #a b = ()\n\nlet loc_includes_region_addresses #al #c s preserve_liveness1 preserve_liveness2 r a = ()\n\nlet loc_includes_region_region #al #c preserve_liveness1 preserve_liveness2 s1 s2 = ()\n\nlet loc_includes_region_union_l #al #c preserve_liveness l s1 s2 =\n assert ((loc_regions #_ #c preserve_liveness (Set.intersect s2 (Set.complement s1)) `loc_union` loc_regions #_ #c preserve_liveness (Set.intersect s2 s1)) `loc_equal` loc_regions preserve_liveness s2);\n loc_includes_region_region #_ #c preserve_liveness preserve_liveness s1 (Set.intersect s2 s1);\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)));\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 s1));\n loc_includes_union_r (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1))) (loc_regions preserve_liveness (Set.intersect s2 s1))\n\nlet loc_includes_addresses_addresses #al c preserve_liveness1 preserve_liveness2 r s1 s2 = ()\n\n(* Disjointness of two memory locations *)\n\nlet aloc_disjoint (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : GTot Type0 =\n if b1.region = b2.region && b1.addr = b2.addr\n then Some? b1.loc /\\ Some? b2.loc /\\ c.aloc_disjoint (Some?.v b1.loc) (Some?.v b2.loc)\n else True\n\nlet aloc_disjoint_sym (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : Lemma\n (aloc_disjoint b1 b2 <==> aloc_disjoint b2 b1)\n= Classical.forall_intro_2 (fun r a -> Classical.forall_intro_2 (fun b1 b2 -> c.aloc_disjoint_sym #r #a b1 b2))\n\nlet loc_aux_disjoint\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: GTot Type0\n= forall (b1 b2: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b2 l2) ==> aloc_disjoint b1 b2\n\nlet loc_aux_disjoint_union_l\n (#al: aloc_t) (#c: cls al)\n (ll1 lr1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint (GSet.union ll1 lr1) l2 <==> (loc_aux_disjoint ll1 l2 /\\ loc_aux_disjoint lr1 l2)))\n= ()\n\nlet loc_aux_disjoint_union_r\n (#al: aloc_t) (#c: cls al)\n (l1 ll2 lr2: GSet.set (aloc c))\n: Lemma\n (loc_aux_disjoint l1 (GSet.union ll2 lr2) <==> (loc_aux_disjoint l1 ll2 /\\ loc_aux_disjoint l1 lr2))\n= ()\n\nlet loc_aux_disjoint_sym\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint l1 l2 <==> loc_aux_disjoint l2 l1))\n= Classical.forall_intro_2 (aloc_disjoint_sym #al #c)\n\nlet regions_of_loc_loc_union\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (regions_of_loc (loc_union s1 s2) == regions_of_loc s1 `Set.union` regions_of_loc s2)\n [SMTPat (regions_of_loc (loc_union s1 s2))]\n= assert (regions_of_loc (loc_union s1 s2) `Set.equal` (regions_of_loc s1 `Set.union` regions_of_loc s2))\n\nlet regions_of_loc_monotonic\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_includes s1 s2))\n (ensures (Set.subset (regions_of_loc s2) (regions_of_loc s1)))\n= ()\n\nlet loc_disjoint_region_liveness_tags (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty\n\nlet loc_disjoint_addrs (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n (forall (r: HS.rid) .\n GSet.subset (GSet.intersect (addrs_of_loc_weak l1 r) (addrs_of_loc l2 r)) GSet.empty /\\\n GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc_weak l2 r)) GSet.empty\n )\n\nlet loc_disjoint_aux (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n loc_aux_disjoint (Ghost.reveal (Loc?.aux l1)) (Ghost.reveal (Loc?.aux l2))\n\nlet loc_disjoint'\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n: GTot Type0\n= loc_disjoint_region_liveness_tags l1 l2 /\\\n loc_disjoint_addrs l1 l2 /\\\n loc_disjoint_aux l1 l2\n\nlet loc_disjoint = loc_disjoint'\n\nlet loc_disjoint_sym #al #c l1 l2 =\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c)\n\nlet loc_disjoint_sym'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))\n [SMTPat (loc_disjoint s1 s2)]\n= loc_disjoint_sym s1 s2\n\nlet loc_disjoint_none_r #al #c s = ()\n\nlet loc_disjoint_union_r #al #c s s1 s2 = ()\n\nlet aloc_disjoint_includes (#al: aloc_t) (#c: cls al) (b1 b2 b3 : aloc c) : Lemma\n (requires (aloc_disjoint b1 b2 /\\ aloc_includes b2 b3))\n (ensures (aloc_disjoint b1 b3))\n= if b1.region = b2.region && b1.addr = b2.addr\n then begin\n c.aloc_includes_refl (Some?.v b1.loc);\n c.aloc_disjoint_includes (Some?.v b1.loc) (Some?.v b2.loc) (Some?.v b1.loc) (Some?.v b3.loc)\n end\n else ()\n\nlet loc_aux_disjoint_loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (l1 l2 l3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\n= // FIXME: WHY WHY WHY do I need this assert?\n assert (forall (b1 b3: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b3 l3) ==> (exists (b2: aloc c) . GSet.mem b2 l2 /\\ aloc_disjoint b1 b2 /\\ aloc_includes b2 b3));\n Classical.forall_intro_3 (fun b1 b2 b3 -> Classical.move_requires (aloc_disjoint_includes #al #c b1 b2) b3)\n\nlet loc_disjoint_includes #al #c p1 p2 p1' p2' =\n regions_of_loc_monotonic p1 p1';\n regions_of_loc_monotonic p2 p2';\n let l1 = Ghost.reveal (Loc?.aux p1) in\n let l2 = Ghost.reveal (Loc?.aux p2) in\n let l1' = Ghost.reveal (Loc?.aux p1') in\n let l2' = Ghost.reveal (Loc?.aux p2') in\n loc_aux_disjoint_loc_aux_includes l1 l2 l2';\n loc_aux_disjoint_sym l1 l2';\n loc_aux_disjoint_loc_aux_includes l2' l1 l1';\n loc_aux_disjoint_sym l2' l1'\n\nlet loc_disjoint_aloc_intro #al #c #r1 #a1 #r2 #a2 b1 b2 = ()\n\nlet loc_disjoint_aloc_elim #al #c #r1 #a1 #r2 #a2 b1 b2 =\n // FIXME: WHY WHY WHY this assert?\n assert (aloc_disjoint (ALoc #_ #c r1 a1 (Some b1)) (ALoc #_ #c r2 a2 (Some b2)))\n\n#push-options \"--z3rlimit 15\"\nlet loc_disjoint_addresses_intro #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness1 r1 n1))) (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness2 r2 n2))))\n#pop-options\n\nlet loc_disjoint_addresses_elim #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 = ()\n\nlet loc_disjoint_aloc_addresses_intro #al #c #r' #a' p preserve_liveness r n = ()\n\nlet loc_disjoint_aloc_addresses_elim #al #c #r' #a' p preserve_liveness r n = ()\n\nlet loc_disjoint_regions #al #c preserve_liveness1 preserve_liveness2 rs1 rs2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness1 rs1))) (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness2 rs2))))\n\nlet loc_none_in_some_region #a (c: cls a) (r: HS.rid) : GTot (loc c) =\n Loc\n (Ghost.hide (Set.singleton r))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)\n\n(** Liveness-insensitive memory locations *)\n\nlet address_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))\n\nlet loc_includes_address_liveness_insensitive_locs_aloc #al #c #r #n a = ()\n\nlet loc_includes_address_liveness_insensitive_locs_addresses #al c r a = ()\n\nlet region_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.complement GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))\n\nlet loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs #al c = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_regions #al c r = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_addresses #al c preserve_liveness r a = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_of_aloc #al c #r #a x = ()\n\n(** The modifies clause proper *)\n\nlet modifies_preserves_livenesses\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s r)))\n ) ==> (\n HS.contains h2 p\n ))\n\nlet modifies_preserves_livenesses_elim\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (p: HS.mreference t pre)\n: Lemma\n (requires (modifies_preserves_livenesses s h1 h2 /\\ HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))))\n (ensures (HS.contains h2 p))\n= ()\n\nlet modifies_preserves_livenesses_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p))\n ))\n: Lemma\n (modifies_preserves_livenesses s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'\n\nlet modifies_preserves_mreferences\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s r)))\n ) ==> (\n HS.contains h2 p /\\\n HS.sel h2 p == HS.sel h1 p\n ))\n\nlet modifies_preserves_mreferences_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p /\\ HS.sel h2 p == HS.sel h1 p))\n ))\n: Lemma\n (modifies_preserves_mreferences s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p /\\ h2 `HS.sel` p == h1 `HS.sel` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'\n\nlet modifies_preserves_alocs\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (a: nat) (b: al r a) .\n loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))\n ==>\n c.aloc_preserved b h1 h2\n )\n\nlet modifies_preserves_alocs_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (u: unit { modifies_preserves_mreferences s h1 h2 } )\n (f: (\n (r: HS.rid) ->\n (a: nat) ->\n (b: al r a) ->\n Lemma\n (requires (\n Set.mem r (regions_of_loc s) /\\\n (~ (GSet.mem a (addrs_of_loc_weak s r))) /\\\n (GSet.mem a (addrs_of_loc_aux s r) /\\ loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b))))\n ))\n (ensures (c.aloc_preserved b h1 h2))\n ))\n: Lemma\n (modifies_preserves_alocs s h1 h2)\n= let f'\n (r: HS.rid)\n (a: nat)\n (b: al r a)\n : Lemma\n (requires (loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))))\n (ensures (c.aloc_preserved b h1 h2))\n = if Set.mem r (regions_of_loc s) && (not (GSet.mem a (addrs_of_loc_weak s r)))\n then begin\n if GSet.mem a (addrs_of_loc_aux s r)\n then\n Classical.move_requires (f r a) b\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n end else if Set.mem r (regions_of_loc s)\n then begin\n assert (GSet.mem a (addrs_of_loc_weak s r));\n assert (GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux s)));\n assert (aloc_disjoint #_ #c (ALoc r a None) (ALoc r a (Some b)));\n assert False\n end\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n in\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (f' r a) b)\n\nlet modifies_preserves_regions\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= forall (r: HS.rid) . (HS.live_region h1 r /\\ ~ (Set.mem r (Ghost.reveal (Loc?.region_liveness_tags s)))) ==> HS.live_region h2 r\n\n\nlet modifies_preserves_not_unused_in\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (n: nat) . (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n\nlet modifies_preserves_not_unused_in_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ))\n (ensures (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n ))\n: Lemma\n (modifies_preserves_not_unused_in s h1 h2)\n= let f'\n (r: HS.rid)\n (n: nat)\n : Lemma\n ((\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n = Classical.move_requires (f r) n\n in\n Classical.forall_intro_2 f'\n\nlet modifies'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= modifies_preserves_regions s h1 h2 /\\\n modifies_preserves_not_unused_in s h1 h2 /\\\n modifies_preserves_mreferences s h1 h2 /\\\n modifies_preserves_livenesses s h1 h2 /\\\n modifies_preserves_alocs s h1 h2\n\nlet modifies = modifies'\n\nval modifies_intro_strong\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n (Set.mem r (regions_of_loc l) ==> ~ (GSet.mem n (Loc?.non_live_addrs l r))) /\\\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')\n\nlet modifies_intro_strong #al #c l h h' regions mrefs lives unused_ins alocs =\n Classical.forall_intro (Classical.move_requires regions);\n assert (modifies_preserves_regions l h h');\n\n let aux (t:Type) (pre:Preorder.preorder t) (p:HS.mreference t pre)\n :Lemma (requires (HS.contains h p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc l) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc l (HS.frameOf p))))))\n (ensures (HS.contains h' p /\\ HS.sel h' p == HS.sel h p))\n =\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l);\n // FIXME: WHY WHY WHY is this assert necessary?\n assert_spinoff (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n // FIXME: Now this one is too :)\n assert (loc_disjoint_addrs (loc_mreference p) l);\n assert ((loc_disjoint (loc_mreference p) l));\n mrefs t pre p\n in\n\n modifies_preserves_mreferences_intro l h h' aux;\n Classical.forall_intro_3 (fun t pre p -> Classical.move_requires (lives t pre) p);\n modifies_preserves_not_unused_in_intro l h h' (fun r n ->\n unused_ins r n\n );\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n alocs r a b\n )\n\nlet modifies_intro #al #c l h h' regions mrefs lives unused_ins alocs =\n modifies_intro_strong l h h'\n regions\n mrefs\n lives\n (fun r n -> unused_ins r n)\n alocs\n\nlet modifies_none_intro #al #c h h' regions mrefs unused_ins =\n modifies_intro_strong #_ #c loc_none h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> mrefs t pre b)\n (fun r n -> unused_ins r n)\n (fun r a x ->\n c.same_mreference_aloc_preserved x h h' (fun t pre b -> mrefs t pre b)\n )\n\nlet modifies_address_intro #al #c r n h h' regions mrefs unused_ins =\n Classical.forall_intro (Classical.move_requires regions);\n let l : loc c = loc_addresses #_ #c false r (Set.singleton n) in\n modifies_preserves_mreferences_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_livenesses_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_not_unused_in_intro l h h'\n (fun r n -> unused_ins r n)\n ;\n modifies_preserves_alocs_intro l h h' ()\n (fun r a b ->\n c.same_mreference_aloc_preserved b h h' (fun t pre p -> mrefs t pre p)\n )\n\nlet modifies_aloc_intro #al #c #r #n x h h' regions mrefs livenesses unused_ins alocs =\n modifies_intro_strong #_ #c (loc_of_aloc x) h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> livenesses t pre b)\n (fun r n -> unused_ins r n)\n (fun r' n' z ->\n if r' = r && n' = n\n then begin\n loc_disjoint_aloc_elim #_ #c z x;\n alocs z\n end else\n c.same_mreference_aloc_preserved z h h' (fun t pre p ->\n mrefs t pre p\n )\n )\n\nlet modifies_live_region #al #c s h1 h2 r = ()\n\nlet modifies_mreference_elim #al #c #t #pre b p h h' = ()\n\nlet modifies_aloc_elim #al #c #r #a b p h h' = ()\n\nlet modifies_refl #al #c s h =\n Classical.forall_intro_3 (fun r a b -> c.aloc_preserved_refl #r #a b h)\n\nlet modifies_loc_includes #al #c s1 h h' s2 =\n assert (modifies_preserves_mreferences s1 h h');\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c);\n Classical.forall_intro_3 (fun l1 l2 l3 -> Classical.move_requires (loc_aux_disjoint_loc_aux_includes #al #c l1 l2) l3);\n assert (modifies_preserves_alocs s1 h h')\n\nlet modifies_preserves_liveness #al #c s1 s2 h h' #t #pre r = ()\n\n#push-options \"--z3rlimit 20 --max_fuel 0 --max_ifuel 0\"\nlet modifies_preserves_liveness_strong #al #c s1 s2 h h' #t #pre r x =\n let rg = HS.frameOf r in\n let ad = HS.as_addr r in\n let la = loc_of_aloc #_ #c #rg #ad x in\n if Set.mem rg (regions_of_loc s2)\n then begin\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` Loc?.non_live_addrs (address_liveness_insensitive_locs c) rg);\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` GSet.empty);\n assert (~ (GSet.mem ad (Loc?.non_live_addrs s2 rg)));\n if Set.mem rg (regions_of_loc s1)\n then begin\n if GSet.mem ad (Loc?.non_live_addrs s1 rg)\n then begin\n assert (loc_disjoint_aux s1 la);\n assert (GSet.subset (Loc?.non_live_addrs s1 rg) (Loc?.live_addrs s1 rg));\n assert (aloc_domain c (Loc?.regions s1) (Loc?.live_addrs s1) `GSet.subset` (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad None) (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad (Some x)) (Ghost.reveal (Loc?.aux la)));\n assert (aloc_disjoint (ALoc rg ad None) (ALoc #_ #c rg ad (Some x)));\n ()\n end else ()\n end else ()\n end else ()\n#pop-options\n\nlet modifies_preserves_region_liveness #al #c l1 l2 h h' r = ()\n\nlet modifies_preserves_region_liveness_reference #al #c l1 l2 h h' #t #pre r = ()\n\nlet modifies_preserves_region_liveness_aloc #al #c l1 l2 h h' #r #n x =\n if Set.mem r (Ghost.reveal (Loc?.region_liveness_tags l1))\n then begin\n assert (GSet.subset (GSet.complement GSet.empty) (Loc?.non_live_addrs l1 r));\n assert (GSet.subset (Loc?.non_live_addrs l1 r) (Loc?.live_addrs l1 r))\n end else ()\n\nlet modifies_trans'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s h1 h2 /\\ modifies s h2 h3))\n (ensures (modifies s h1 h3))\n= Classical.forall_intro_3 (fun r a b -> Classical.move_requires (c.aloc_preserved_trans #r #a b h1 h2) h3)\n\nlet modifies_trans #al #c s12 h1 h2 s23 h3 =\n let u = loc_union s12 s23 in\n modifies_loc_includes u h1 h2 s12;\n modifies_loc_includes u h2 h3 s23;\n modifies_trans' u h1 h2 h3\n\nlet addr_unused_in_aloc_preserved\n (#al: aloc_t) (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (b: al r a)\n (h1: HS.mem)\n (h2: HS.mem)\n : Lemma\n (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)))\n (ensures (c.aloc_preserved b h1 h2))\n= c.same_mreference_aloc_preserved b h1 h2 (fun a' pre r' -> assert False)\n\n#push-options \"--z3rlimit 10\"\nlet modifies_only_live_regions_weak\n (#al: aloc_t) (#c: cls al)\n (rs: Set.set HS.rid)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n loc_disjoint (loc_regions false rs) l /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))\n= assert (modifies_preserves_mreferences l h h'); // FIXME: WHY WHY WHY?\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (addr_unused_in_aloc_preserved #al #c #r #a b h) h')\n#pop-options\n\n(* Restrict a set of locations along a set of regions *)\n\nlet restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: GTot (loc c)\n= let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let regions' = (Ghost.hide (Set.intersect (Ghost.reveal regions) rs)) in\n Loc\n regions'\n (Ghost.hide (Set.intersect (Ghost.reveal region_liveness_tags) rs))\n (mk_non_live_addrs (fun (r: addrs_dom regions') -> (non_live_addrs r <: GSet.set nat)))\n (mk_live_addrs (fun (r: addrs_dom regions') -> (live_addrs r <: GSet.set nat)))\n (Ghost.hide (GSet.intersect (Ghost.reveal aux) (aloc_domain c (Ghost.hide rs) (fun r -> GSet.complement GSet.empty))))\n\nlet regions_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (regions_of_loc (restrict_to_regions l rs) == Set.intersect (regions_of_loc l) rs)\n [SMTPat (regions_of_loc (restrict_to_regions l rs))]\n= assert (Set.equal (regions_of_loc (restrict_to_regions l rs)) (Set.intersect (regions_of_loc l) rs))\n\nlet addrs_of_loc_weak_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))\n [SMTPat (addrs_of_loc_weak (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc_weak (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))\n\nlet addrs_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc l r else GSet.empty))\n [SMTPat (addrs_of_loc (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc l r else GSet.empty))\n\nlet loc_includes_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes l (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)\n\nlet loc_includes_loc_union_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_equal (loc_union (restrict_to_regions l rs) (restrict_to_regions l (Set.complement rs))) l)\n= ()\n\nlet loc_includes_loc_regions_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes (loc_regions false rs) (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)\n\nlet modifies_only_live_regions #al #c rs l h h' =\n let s = l in\n let c_rs = Set.complement rs in\n let s_rs = restrict_to_regions s rs in\n let s_c_rs = restrict_to_regions s c_rs in\n let lrs = loc_regions false rs in\n loc_includes_loc_regions_restrict_to_regions s rs;\n loc_includes_union_l lrs s_c_rs s_rs;\n loc_includes_refl s_c_rs;\n loc_includes_union_l lrs s_c_rs s_c_rs;\n loc_includes_union_r (loc_union lrs s_c_rs) s_rs s_c_rs;\n loc_includes_loc_union_restrict_to_regions s rs;\n loc_includes_trans (loc_union lrs s_c_rs) (loc_union s_rs s_c_rs) s;\n modifies_loc_includes (loc_union lrs s_c_rs) h h' (loc_union lrs s);\n loc_includes_loc_regions_restrict_to_regions s c_rs;\n loc_disjoint_regions #al #c false false rs c_rs;\n loc_includes_refl lrs;\n loc_disjoint_includes lrs (loc_regions false c_rs) lrs s_c_rs;\n modifies_only_live_regions_weak rs s_c_rs h h';\n loc_includes_restrict_to_regions s c_rs;\n modifies_loc_includes s h h' s_c_rs\n\nlet no_upd_fresh_region #al #c r l h0 h1 =\n modifies_only_live_regions (HS.mod_set (Set.singleton r)) l h0 h1\n\nlet fresh_frame_modifies #al c h0 h1 =\n modifies_intro_strong #_ #c loc_none h0 h1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x h0 h1 (fun _ _ _ -> ()))\n\nlet new_region_modifies #al c m0 r0 col\n= let (_, m1) = HS.new_eternal_region m0 r0 col in\n modifies_intro_strong #_ #c loc_none m0 m1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x m0 m1 (fun _ _ _ -> ()))\n\nlet popped_modifies #al c h0 h1 =\n let l = loc_region_only #_ #c false (HS.get_tip h0) in\n modifies_preserves_mreferences_intro l h0 h1 (fun t pre p ->\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l );\n // FIXME: WHY WHY WHY is this assert necessary?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n ()\n );\n modifies_preserves_alocs_intro l h0 h1 () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n ()\n )\n\n\nlet modifies_fresh_frame_popped #al #c h0 h1 s h2 h3 =\n fresh_frame_modifies c h0 h1;\n let r = loc_region_only #al #c false (HS.get_tip h2) in\n let rs = HS.mod_set (Set.singleton (HS.get_tip h1)) in\n let s' = loc_union (loc_regions false rs) s in\n modifies_trans' s' h0 h1 h2;\n assert (modifies_preserves_mreferences r h2 h3);\n let f23 (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (r <> HS.get_tip h2))\n (ensures (c.aloc_preserved b h2 h3))\n = c.same_mreference_aloc_preserved #r #a b h2 h3 (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro r h2 h3 () (fun r a b ->\n f23 r a b\n );\n modifies_trans' s' h0 h2 h3;\n modifies_only_live_regions rs s h0 h3\n\nlet modifies_loc_regions_intro #al #c rs h1 h2 =\n let f (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem r rs)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n assert (modifies_preserves_mreferences (loc_regions #al #c true rs) h1 h2);\n modifies_preserves_alocs_intro (loc_regions #_ #c true rs) h1 h2 () (fun r a b ->\n f r a b\n )\n\n#push-options \"--z3rlimit 20\"\nlet modifies_loc_addresses_intro_weak\n (#al: aloc_t) (#c: cls al)\n (r: HS.rid)\n (s: Set.set nat)\n (l: loc c)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r s h1 h2 /\\\n loc_disjoint l (loc_region_only false r)\n ))\n (ensures (modifies (loc_union (loc_addresses true r s) l) h1 h2))\n= modifies_preserves_mreferences_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_livenesses_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_not_unused_in_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' n' ->\n ()\n );\n let f (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem a s)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r_ -> ())\n in\n modifies_preserves_alocs_intro (loc_union (loc_addresses true r s) l) h1 h2 () (fun r' a b -> if r = r' then f a b else ()\n )\n\nlet modifies_loc_addresses_intro #al #c r s l h1 h2 =\n loc_includes_loc_regions_restrict_to_regions l (Set.singleton r);\n loc_includes_loc_union_restrict_to_regions l (Set.singleton r);\n assert (modifies (loc_union (loc_region_only false r) (loc_union (restrict_to_regions l (Set.singleton r)) (restrict_to_regions l (Set.complement (Set.singleton r))))) h1 h2);\n let l' = restrict_to_regions l (Set.complement (Set.singleton r)) in\n loc_includes_refl (loc_region_only #_ #c false r) ;\n loc_includes_loc_regions_restrict_to_regions l (Set.complement (Set.singleton r));\n loc_disjoint_regions #_ #c false false (Set.complement (Set.singleton r)) (Set.singleton r);\n loc_disjoint_includes (loc_regions #_ #c false (Set.complement (Set.singleton r))) (loc_region_only false r) l' (loc_region_only false r);\n modifies_loc_addresses_intro_weak r s l' h1 h2;\n loc_includes_restrict_to_regions l (Set.complement (Set.singleton r))\n#pop-options\n\nlet modifies_ralloc_post #al #c #a #rel i init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g\n\nlet modifies_salloc_post #al #c #a #rel init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g\n\nlet modifies_free #al #c #a #rel r m =\n let g (r': HS.rid) (a: nat) (b: al r' a) : Lemma\n (requires (r' <> HS.frameOf r \\/ a <> HS.as_addr r))\n (ensures (c.aloc_preserved b m (HS.free r m)))\n = c.same_mreference_aloc_preserved #r' #a b m (HS.free r m) (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro (loc_freed_mreference #_ #c r) m (HS.free r m) () (fun r a b -> g r a b)\n\nlet modifies_none_modifies #al #c h1 h2\n= let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h1 h2)\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g\n\nlet modifies_upd #al #c #t #pre r v h =\n let h' = HS.upd h r v in\n modifies_intro #_ #c (loc_mreference r) h h'\n (fun r -> ())\n (fun t pre b -> ())\n (fun t pre b -> ())\n (fun r n -> ())\n (fun r a b -> c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre' r' -> ()))\n\n#push-options \"--z3rlimit 15\"\nlet addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l (loc_of_aloc al0)) r == addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)\n= assert (addrs_of_loc (loc_union l (loc_of_aloc al0)) r `GSet.equal` addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)\n#pop-options\n\nlet addrs_of_loc_weak_loc_includes #al (#c: cls al) (l: loc c) (r0: HS.rid) (a0: nat) : Lemma\n (requires (a0 `GSet.mem` addrs_of_loc_weak l r0))\n (ensures (l `loc_includes` loc_addresses true r0 (Set.singleton a0)))\n= ()\n\nval modifies_strengthen'\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (h h' : HS.mem)\n (alocs: (\n (f: ((t: Type) -> (pre: Preorder.preorder t) -> (m: HS.mreference t pre) -> Lemma\n (requires (HS.frameOf m == r0 /\\ HS.as_addr m == a0 /\\ HS.contains h m))\n (ensures (HS.contains h' m))\n )) ->\n (x: al r0 a0) ->\n Lemma\n (requires (c.aloc_disjoint x al0 /\\ loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (requires ((~ (a0 `GSet.mem` addrs_of_loc_weak l r0)) /\\ modifies (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h'))\n (ensures (modifies (loc_union l (loc_of_aloc al0)) h h'))\n\n#push-options \"--z3rlimit 15 --fuel 0 --ifuel 0\"\nlet modifies_strengthen' #al #c l #r0 #a0 al0 h h' alocs =\n Classical.forall_intro (addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton l al0);\n assert (modifies_preserves_regions (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_mreferences (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_not_unused_in (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_livenesses (loc_union l (loc_of_aloc al0)) h h');\n modifies_preserves_alocs_intro (loc_union l (loc_of_aloc al0)) h h' () (fun r a b ->\n if r = r0 && a = a0\n then begin\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_union l (loc_of_aloc al0)))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux l)) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_disjoint l (loc_of_aloc b));\n loc_disjoint_sym l (loc_of_aloc b);\n assert (loc_aux_disjoint #_ #c (Ghost.reveal (Loc?.aux (loc_of_aloc al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint #_ #c (GSet.singleton (ALoc r0 a0 (Some al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (GSet.mem (ALoc r0 a0 (Some al0)) (GSet.singleton (ALoc #_ #c r0 a0 (Some al0))));\n assert (GSet.mem (ALoc r0 a0 (Some b)) (GSet.singleton (ALoc #_ #c r0 a0 (Some b))));\n assert (aloc_disjoint #_ #c (ALoc r0 a0 (Some al0)) (ALoc r0 a0 (Some b)));\n assert (c.aloc_disjoint al0 b);\n c.aloc_disjoint_sym al0 b;\n alocs (fun t pre m -> ()) b\n end\n else begin\n assert (loc_disjoint (loc_union l (loc_addresses true r0 (Set.singleton a0))) (loc_of_aloc b))\n by (let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 64;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=5'\";\n ())\n end\n );\n assert (modifies (loc_union l (loc_of_aloc al0)) h h')\n#pop-options\n\nlet modifies_strengthen #al #c l #r0 #a0 al0 h h' alocs =\n if a0 `GSet.mem` addrs_of_loc_weak l r0\n then begin\n addrs_of_loc_weak_loc_includes l r0 a0;\n loc_includes_refl l;\n loc_includes_union_r l l (loc_addresses true r0 (Set.singleton a0));\n loc_includes_union_l l (loc_of_aloc al0) l;\n loc_includes_trans (loc_union l (loc_of_aloc al0)) l (loc_union l (loc_addresses true r0 (Set.singleton a0)));\n modifies_loc_includes (loc_union l (loc_of_aloc al0)) h h' (loc_union l (loc_addresses true r0 (Set.singleton a0)))\n end\n else\n modifies_strengthen' l al0 h h' alocs\n\n\nlet does_not_contain_addr' (h: HS.mem) (ra: HS.rid * nat) : GTot Type0 =\n HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))\n\nlet does_not_contain_addr = does_not_contain_addr'\n\nlet not_live_region_does_not_contain_addr h ra = ()\n\nlet unused_in_does_not_contain_addr h #a #rel r = ()\n\nlet addr_unused_in_does_not_contain_addr h ra = ()\n\nlet does_not_contain_addr_addr_unused_in h ra = ()\n\nlet free_does_not_contain_addr #a #rel r m x = ()\n\nlet does_not_contain_addr_elim #a #rel r m x = ()\n\nlet disjoint_addrs_of_loc_loc_disjoint\n (#al: aloc_t)\n (#c: cls al)\n (l1 l2: loc c)\n: Lemma\n (requires (\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty /\\\n (forall r . GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc l2 r)) GSet.empty)\n ))\n (ensures (loc_disjoint l1 l2))\n= // FIXME: WHY WHY WHY do I need this assert?\n let l1' = Ghost.reveal (Loc?.aux l1) in\n let l2' = Ghost.reveal (Loc?.aux l2) in\n assert (forall (b1 b2: aloc c) . (GSet.mem b1 l1' /\\ GSet.mem b2 l2') ==> aloc_disjoint b1 b2)\n\nlet loc_not_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (HS.live_region h r /\\ ~ (h `does_not_contain_addr` (r, a))))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs f)\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))\n\nlet loc_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n if not (HS.live_region h r)\n then\n GSet.complement GSet.empty\n else\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a)))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide (Set.complement (FStar.Map.domain (HS.get_hmap h))))\n (mk_non_live_addrs (fun x -> f x))\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))\n\nlet loc_regions_unused_in #al c h rs = ()\n\n#push-options \"--z3rlimit 20\"\nlet loc_addresses_unused_in #al c r a h = ()\n#pop-options\n\nlet loc_addresses_not_unused_in #al c r a h = ()\n\n#push-options \"--z3rlimit 15\"\nlet loc_unused_in_not_unused_in_disjoint #al c h =\n assert (Ghost.reveal (Loc?.aux (loc_unused_in c h)) `loc_aux_disjoint` Ghost.reveal (Loc?.aux (loc_not_unused_in c h)));\n assert_spinoff (loc_disjoint #al #c (loc_unused_in #al c h)\n (loc_not_unused_in #al c h))\n#pop-options\n\n#push-options \"--z3cliopt 'smt.qi.eager_threshold=100'\"\nlet not_live_region_loc_not_unused_in_disjoint #al c h0 r\n= let l1 = loc_region_only false r in\n let l2 = loc_not_unused_in c h0 in\n assert (loc_disjoint_region_liveness_tags l1 l2);\n assert (loc_disjoint_addrs l1 l2);\n assert (loc_disjoint_aux l1 l2)\n\n#push-options \"--z3rlimit 16\"\nlet modifies_address_liveness_insensitive_unused_in #al c h h' =\n assert (forall r . HS.live_region h r ==> HS.live_region h' r) ;\n let ln' = loc_not_unused_in c h' in\n let ln = loc_not_unused_in c h in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs ln r `GSet.subset` Loc?.non_live_addrs ln' r);\n assert (ln' `loc_includes` ln);\n let lu = loc_unused_in c h in\n let lu' = loc_unused_in c h' in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs lu' r `GSet.subset` Loc?.non_live_addrs lu r);\n assert (forall (r: HS.rid) . Loc?.live_addrs lu' r `GSet.subset` Loc?.live_addrs lu r);\n assert (lu `loc_includes` lu')\n#pop-options\n#pop-options\n\n#push-options \"--max_fuel 0 --max_ifuel 0 --z3rlimit 16\"\nlet modifies_only_not_unused_in #al #c l h h' =\n assert (modifies_preserves_regions l h h');\n assert (modifies_preserves_not_unused_in l h h');\n assert (modifies_preserves_mreferences l h h');\n assert (modifies_preserves_livenesses l h h');\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n if StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a))\n then c.same_mreference_aloc_preserved b h h' (fun a' pre' r' -> ())\n else ()\n )\n#pop-options\n\nlet mreference_live_loc_not_unused_in #al c #t #pre h b =\n Classical.move_requires (does_not_contain_addr_addr_unused_in h) (HS.frameOf b, HS.as_addr b);\n assert (~ (h `does_not_contain_addr` (HS.frameOf b, HS.as_addr b)));\n loc_addresses_not_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_trans (loc_not_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()\n\n#push-options \"--z3cliopt 'smt.qi.eager_threshold=100'\"\nlet mreference_unused_in_loc_unused_in #al c #t #pre h b =\n Classical.move_requires (addr_unused_in_does_not_contain_addr h) (HS.frameOf b, HS.as_addr b);\n loc_addresses_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_addresses_addresses c false true (HS.frameOf b) (Set.singleton (HS.as_addr b)) (Set.singleton (HS.as_addr b));\n loc_includes_trans (loc_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()\n#pop-options\n\n(* * Compositionality *)\n\nnoeq\ntype cls_union_aloc\n (al: (bool -> HS.rid -> nat -> Tot (Type u#x)))\n (r: HS.rid) (n: nat) : Type u#x\n= | ALOC_FALSE of (al false) r n\n | ALOC_TRUE of (al true) r n\n\nlet bool_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot bool =\n match l with\n | ALOC_FALSE _ -> false\n | ALOC_TRUE _ -> true\n\nlet aloc_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot ((al (bool_of_cls_union_aloc l)) r n)\n= match l with\n | ALOC_FALSE x -> x\n | ALOC_TRUE x -> x\n\nlet make_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (b: bool)\n (#r: HS.rid)\n (#n: nat)\n (l: (al b) r n)\n: Tot (cls_union_aloc al r n)\n= if b\n then ALOC_TRUE l\n else ALOC_FALSE l\n\nlet cls_union_aloc_includes\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_includes\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)\n\nlet cls_union_aloc_disjoint\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_disjoint\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)\n\nlet cls_union_aloc_preserved\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (x: cls_union_aloc al r a)\n (h h' : HS.mem)\n: GTot Type0\n= (c (bool_of_cls_union_aloc x)).aloc_preserved\n (aloc_of_cls_union_aloc x)\n h\n h'\n\nlet aloc_union = cls_union_aloc\n\nlet cls_union #al c = Cls\n #(cls_union_aloc al)\n (cls_union_aloc_includes c)\n (* aloc_includes_refl *)\n (fun #r #a x ->\n (c (bool_of_cls_union_aloc x)).aloc_includes_refl (aloc_of_cls_union_aloc x))\n (* aloc_includes_trans *)\n (fun #r #a x1 x2 x3 ->\n (c (bool_of_cls_union_aloc x1)).aloc_includes_trans\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n (aloc_of_cls_union_aloc x3)\n )\n (cls_union_aloc_disjoint c)\n (* aloc_disjoint_sym *)\n (fun #r #a x1 x2 ->\n if bool_of_cls_union_aloc x1 = bool_of_cls_union_aloc x2\n then\n (c (bool_of_cls_union_aloc x1)).aloc_disjoint_sym\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n else ()\n )\n (* aloc_disjoint_includes *)\n (fun #r #a larger1 larger2 smaller1 smaller2 ->\n (c (bool_of_cls_union_aloc larger1)).aloc_disjoint_includes\n (aloc_of_cls_union_aloc larger1)\n (aloc_of_cls_union_aloc larger2)\n (aloc_of_cls_union_aloc smaller1)\n (aloc_of_cls_union_aloc smaller2)\n )\n (cls_union_aloc_preserved c)\n (* aloc_preserved_refl *)\n (fun #r #a x h ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_refl\n (aloc_of_cls_union_aloc x)\n h\n )\n (* aloc_preserved_trans *)\n (fun #r #a x h1 h2 h3 ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_trans\n (aloc_of_cls_union_aloc x)\n h1\n h2\n h3\n )\n (* same_mreference_aloc_preserved *)\n (fun #r #a b h1 h2 f ->\n (c (bool_of_cls_union_aloc b)).same_mreference_aloc_preserved\n (aloc_of_cls_union_aloc b)\n h1\n h2\n f\n )\n\nlet union_aux_of_aux_left_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n (x: aloc (cls_union c))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n b = bool_of_cls_union_aloc #al #region #addr loc &&\n GSet.mem (ALoc region addr (Some (aloc_of_cls_union_aloc #al #region #addr loc))) s\n\nlet union_aux_of_aux_left\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n: Tot (GSet.set (aloc (cls_union c)))\n= GSet.comprehend (union_aux_of_aux_left_pred c b s)\n\nlet union_loc_of_loc #al c b l =\n let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let aux' : GSet.set (aloc #(cls_union_aloc al) (cls_union c)) =\n union_aux_of_aux_left c b (Ghost.reveal aux)\n `GSet.union`\n (aloc_domain (cls_union c) regions live_addrs)\n in\n Loc\n #(cls_union_aloc al)\n #(cls_union c)\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide aux')\n\nlet union_aux_of_aux_left_inv_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n (x: aloc (c b))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n GSet.mem (ALoc region addr (Some (make_cls_union_aloc b loc))) s\n\nlet union_aux_of_aux_left_inv\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n: Tot (GSet.set (aloc (c b)))\n= GSet.comprehend (union_aux_of_aux_left_inv_pred b s)\n\nlet mem_union_aux_of_aux_left_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (c b))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x aux <==> GSet.mem (ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc)))) (union_aux_of_aux_left c b aux))\n [SMTPat (GSet.mem x aux)]\n= ()\n\nlet mem_union_aux_of_aux_left_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (cls_union c))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x (union_aux_of_aux_left c b aux) <==> (if None? x.loc then GSet.mem (ALoc x.region x.addr None) aux else (bool_of_cls_union_aloc (Some?.v x.loc) == b /\\ GSet.mem (ALoc x.region x.addr (Some (aloc_of_cls_union_aloc (Some?.v x.loc)))) aux)))\n [SMTPat (GSet.mem x (union_aux_of_aux_left #al c b aux))]\n= ()\n\nlet addrs_of_loc_union_loc_of_loc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (union_loc_of_loc c b l) r `GSet.equal` addrs_of_loc l r)\n [SMTPat (addrs_of_loc (union_loc_of_loc #al c b l) r)]\n= ()\n\nlet union_loc_of_loc_none #al c b =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_none #_ #(c b))) (loc_none #_ #(cls_union c)))\n\n#push-options \"--z3rlimit 15\"\nlet union_loc_of_loc_union #al c b l1 l2 =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_union #_ #(c b) l1 l2)) (loc_union #_ #(cls_union c) (union_loc_of_loc c b l1) (union_loc_of_loc c b l2)))\n#pop-options\n\nlet union_loc_of_loc_addresses #al c b preserve_liveness r n =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_addresses #_ #(c b) preserve_liveness r n)) (loc_addresses #_ #(cls_union c) preserve_liveness r n))\n\nlet union_loc_of_loc_regions #al c b preserve_liveness r =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_regions #_ #(c b) preserve_liveness r)) (loc_regions #_ #(cls_union c) preserve_liveness r))\n\n#push-options \"--z3rlimit 15\"\nlet union_loc_of_loc_includes_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (larger `loc_includes` smaller))\n (ensures (union_loc_of_loc c b larger `loc_includes` union_loc_of_loc c b smaller))\n= ();\n let auxl = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux larger)) in\n let auxs = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux smaller)) in\n assert (forall r a . GSet.mem (ALoc r a None) auxs ==> (\n GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux smaller)) /\\\n GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux larger)) /\\\n GSet.mem (ALoc r a None) auxl\n ));\n assert (auxl `loc_aux_includes` auxs);\n let doml = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n assert (doml `loc_aux_includes` doms)\n#pop-options\n\n#push-options \"--fuel 0 --ifuel 0 --z3rlimit 50 --z3cliopt 'smt.qi.eager_threshold=1'\"\nlet union_loc_of_loc_includes_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (union_loc_of_loc c b larger `loc_includes` union_loc_of_loc c b smaller))\n (ensures (larger `loc_includes` smaller))\n= let auxl = Ghost.reveal (Loc?.aux larger) in\n let auxl' = union_aux_of_aux_left c b auxl in\n let auxs = Ghost.reveal (Loc?.aux smaller) in\n let auxs' = union_aux_of_aux_left c b auxs in\n let doml' = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms' = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n let doml = aloc_domain (c b) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (c b) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n let g\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n (y: aloc (c b))\n : GTot Type0\n = GSet.mem y (GSet.union auxl doml) /\\ y `aloc_includes` x\n in\n let g' (r: HS.rid) (a: nat) (x: aloc (c b)) : GTot Type0 =\n exists (y: aloc (c b)) . g r a x y\n in\n let f\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n : Lemma\n (requires (GSet.mem x auxs /\\ (~ (GSet.mem x.addr (addrs_of_loc_weak smaller x.region)))))\n (ensures (g' r a x))\n = let x' : aloc (cls_union c) = ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc))) in\n Classical.exists_elim\n (g' r a x)\n #(aloc (cls_union c))\n #(fun y' -> GSet.mem y' (GSet.union auxl' doml') /\\ y' `aloc_includes` x')\n ()\n (fun (y': aloc (cls_union c) { GSet.mem y' (GSet.union auxl' doml') /\\ y' `aloc_includes` x' } ) ->\n let y : aloc (c b) = ALoc y'.region y'.addr (if None? y'.loc then None else Some (aloc_of_cls_union_aloc (Some?.v y'.loc))) in\n assert (g r a x y)\n )\n in\n let f'\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n : Lemma\n ((GSet.mem x auxs /\\ (~ (GSet.mem x.addr (addrs_of_loc_weak smaller x.region)))) ==> g' r a x)\n = Classical.move_requires (f r a) x\n in\n Classical.forall_intro_3 f';\n assert (forall (r: HS.rid) (a: nat) (x: aloc (c b)) .\n (GSet.mem x auxs /\\ GSet.mem x.addr (addrs_of_loc_weak smaller x.region)) ==>\n GSet.mem x (GSet.union auxl doml)\n ) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n assert (larger `loc_includes'` smaller) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 75;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n ()\n#pop-options\n\nlet union_loc_of_loc_includes #al c b s1 s2 =\n Classical.move_requires (union_loc_of_loc_includes_elim c b s1) s2;\n Classical.move_requires (union_loc_of_loc_includes_intro c b s1) s2\n\n#push-options \"--fuel 0 --ifuel 0\"\nlet union_loc_of_loc_disjoint_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (larger `loc_disjoint` smaller))\n (ensures (union_loc_of_loc c b larger `loc_disjoint` union_loc_of_loc c b smaller))\n= let auxl = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux larger)) in\n let auxs = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux smaller)) in\n let g\n (xl xs: aloc (cls_union c))\n : Lemma\n (requires (GSet.mem xl auxl /\\ GSet.mem xs auxs))\n (ensures (GSet.mem xl auxl /\\ GSet.mem xs auxs /\\ aloc_disjoint xl xs))\n =\n let xl' : aloc (c b) = ALoc xl.region xl.addr (if None? xl.loc then None else Some (aloc_of_cls_union_aloc (Some?.v xl.loc))) in\n let xs' : aloc (c b) = ALoc xs.region xs.addr (if None? xs.loc then None else Some (aloc_of_cls_union_aloc (Some?.v xs.loc))) in\n assert (GSet.mem xl' (Ghost.reveal (Loc?.aux larger)));\n assert (GSet.mem xs' (Ghost.reveal (Loc?.aux smaller)));\n assert (aloc_disjoint xl' xs');\n assert (aloc_disjoint xl xs)\n in\n Classical.forall_intro_2 (fun xl -> Classical.move_requires (g xl));\n assert (forall xl xs . (GSet.mem xl auxl /\\ GSet.mem xs auxs) ==> aloc_disjoint xl xs);\n assert (auxl `loc_aux_disjoint` auxs);\n let larger' = union_loc_of_loc c b larger in\n let smaller' = union_loc_of_loc c b smaller in\n let doml = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n assert (forall (xl xs: aloc (cls_union c)) .\n (GSet.mem xl doml /\\ GSet.mem xs auxs) ==> (\n xl.addr `GSet.mem` addrs_of_loc_weak larger xl.region /\\\n xs.addr `GSet.mem` addrs_of_loc smaller xs.region /\\\n aloc_disjoint xl xs\n )) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 64;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n assert (doml ` loc_aux_disjoint` auxs);\n assert (forall (xl xs: aloc (cls_union c)) .\n (GSet.mem xl auxl /\\ GSet.mem xs doms) ==> (\n xl.addr `GSet.mem` addrs_of_loc larger xl.region /\\\n xs.addr `GSet.mem` addrs_of_loc_weak smaller xs.region /\\\n aloc_disjoint xl xs\n )) by (\n let open FStar.Tactics.SMT in\n set_rlimit 15;\n ()\n );\n assert (auxl ` loc_aux_disjoint` doms);\n assert (loc_disjoint_aux larger' smaller');\n ()\n#pop-options\n\n#push-options \"--z3rlimit 32\"\nlet union_loc_of_loc_disjoint_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (union_loc_of_loc c b larger `loc_disjoint` union_loc_of_loc c b smaller))\n (ensures (larger `loc_disjoint` smaller))\n= let auxl = Ghost.reveal (Loc?.aux larger) in\n let auxl' = union_aux_of_aux_left c b auxl in\n let auxs = Ghost.reveal (Loc?.aux smaller) in\n let auxs' = union_aux_of_aux_left c b auxs in\n assert (forall (x y: aloc (c b)) . (GSet.mem x auxl /\\ GSet.mem y auxs) ==> (\n let x' = ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc))) in\n let y' = ALoc y.region y.addr (if None? y.loc then None else Some (make_cls_union_aloc b (Some?.v y.loc))) in\n GSet.mem x' auxl' /\\ GSet.mem y' auxs' /\\ (aloc_disjoint x' y' ==> aloc_disjoint x y)));\n assert (auxl `loc_aux_disjoint` auxs)\n#pop-options\n\nlet union_loc_of_loc_disjoint #al c b s1 s2 =\n Classical.move_requires (union_loc_of_loc_disjoint_elim c b s1) s2;\n Classical.move_requires (union_loc_of_loc_disjoint_intro c b s1) s2\n\n#push-options \"--z3rlimit 32\"\nlet modifies_union_loc_of_loc_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (h1 h2: HS.mem)\n: Lemma\n (requires (modifies #_ #(cls_union c) (union_loc_of_loc c b l) h1 h2))\n (ensures (modifies #_ #(c b) l h1 h2))\n= assert (modifies_preserves_regions l h1 h2);\n assert (modifies_preserves_mreferences l h1 h2);\n modifies_preserves_alocs_intro #_ #(c b) l h1 h2 () (fun r' a' b' ->\n let g\n (x: aloc (cls_union c))\n : Lemma\n (requires (\n GSet.mem a' (addrs_of_loc_aux #_ #(cls_union c) (union_loc_of_loc c b l) r') /\\\n GSet.mem x (Ghost.reveal (Loc?.aux #_ #(cls_union c) (union_loc_of_loc c b l)))\n ))\n (ensures (\n aloc_disjoint #_ #(cls_union c) x (ALoc #_ #(cls_union c) r' a' (Some (make_cls_union_aloc b b')))))\n = if r' = x.region && a' = x.addr\n then begin\n let x' : aloc (c b) = ALoc #_ #(c b) r' a' (if None? x.loc then None else Some (aloc_of_cls_union_aloc (Some?.v x.loc))) in\n assert (aloc_disjoint #(al b) #(c b) x' (ALoc r' a' (Some b')))\n end else\n ()\n in\n Classical.forall_intro (Classical.move_requires g);\n assert ((cls_union c).aloc_preserved (make_cls_union_aloc b b') h1 h2)\n )\n#pop-options\n\n#push-options \"--z3rlimit 32\"\nlet modifies_union_loc_of_loc_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (h1 h2: HS.mem)\n: Lemma\n (requires (modifies #_ #(c b) l h1 h2))\n (ensures (modifies #_ #(cls_union c) (union_loc_of_loc c b l) h1 h2))\n= let l' = union_loc_of_loc c b l in\n assert (modifies_preserves_regions l' h1 h2);\n assert (modifies_preserves_mreferences l' h1 h2);\n assert (modifies_preserves_livenesses l' h1 h2);\n assert (modifies_preserves_not_unused_in l' h1 h2);\n modifies_preserves_alocs_intro #_ #(cls_union c) l' h1 h2 () (fun r' a' b' ->\n let b_ = bool_of_cls_union_aloc b' in\n let a_ = aloc_of_cls_union_aloc b' in\n let ll' : aloc (cls_union c) = ALoc r' a' (Some b') in\n let ll : aloc (c b_) = ALoc r' a' (Some a_) in\n assert (exists (x: aloc (c b)) . GSet.mem x (Ghost.reveal (Loc?.aux l)) /\\\n (\n let xr = x.region in\n let xa = x.addr in\n let xl : option (al b xr xa) = x.loc in\n xr == r' /\\\n xa == a' /\\ (\n let xl' : option (aloc_union al r' a') = if None? xl then None else Some (make_cls_union_aloc #al b (Some?.v xl)) in\n let x' : aloc (cls_union c) = ALoc r' a' xl' in\n GSet.mem x' (Ghost.reveal (Loc?.aux l')) /\\\n aloc_disjoint #_ #(cls_union c) x' ll'\n )));\n assert (b_ == b);\n let f (x: aloc (c b)) : Lemma\n (requires (GSet.mem x (Ghost.reveal (Loc?.aux l))))\n (ensures (aloc_disjoint #_ #(c b) x ll))\n = let xr = x.region in\n let xa = x.addr in\n let xl : option (al b xr xa) = x.loc in\n let xl' : option (aloc_union al xr xa) = if None? xl then None else Some (make_cls_union_aloc #al b (Some?.v xl)) in\n let x' : aloc (cls_union c) = ALoc xr xa xl' in\n assert (GSet.mem x' (Ghost.reveal (Loc?.aux l')));\n assert (aloc_disjoint #_ #(cls_union c) x' ll');\n assert (aloc_disjoint #_ #(c b) x ll)\n in\n Classical.forall_intro (Classical.move_requires f);\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux l)) (GSet.singleton ll))\n )\n#pop-options\n\nlet modifies_union_loc_of_loc #al c b l h1 h2 =\n Classical.move_requires (modifies_union_loc_of_loc_elim c b l h1) h2;\n Classical.move_requires (modifies_union_loc_of_loc_intro c b l h1) h2\n\nlet loc_of_union_loc #al #c b l\n= let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let aux' = union_aux_of_aux_left_inv b (Ghost.reveal aux) in\n Loc\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide aux')\n\nlet loc_of_union_loc_union_loc_of_loc #al c b s\n= assert (loc_of_union_loc b (union_loc_of_loc c b s) `loc_equal` s)\n\nlet loc_of_union_loc_none #al c b\n= assert (loc_of_union_loc #_ #c b loc_none `loc_equal` loc_none)\n\nlet loc_of_union_loc_union #al c b l1 l2\n= assert (loc_of_union_loc b (l1 `loc_union` l2) `loc_equal` (loc_of_union_loc b l1 `loc_union` loc_of_union_loc b l2))\n\nlet loc_of_union_loc_addresses #al c b preserve_liveness r n =\n assert (loc_of_union_loc #_ #c b (loc_addresses preserve_liveness r n) `loc_equal` loc_addresses preserve_liveness r n)\n\nlet loc_of_union_loc_regions #al c b preserve_liveness r =\n assert (loc_of_union_loc #_ #c b (loc_regions preserve_liveness r) `loc_equal` loc_regions preserve_liveness r)\n\nmodule U = FStar.Universe\n\nlet raise_aloc al r n = U.raise_t (al r n)\n\nlet raise_cls #al c = Cls #(raise_aloc u#x u#y al)\n (fun #r #a x1 x2 -> c.aloc_includes (U.downgrade_val x1) (U.downgrade_val x2))\n (fun #r #a x -> c.aloc_includes_refl (U.downgrade_val x))\n (fun #r #a x1 x2 x3 -> c.aloc_includes_trans (U.downgrade_val x1) (U.downgrade_val x2) (U.downgrade_val x3))\n (fun #r #a x1 x2 -> c.aloc_disjoint (U.downgrade_val x1) (U.downgrade_val x2))\n (fun #r #a x1 x2 -> c.aloc_disjoint_sym (U.downgrade_val x1) (U.downgrade_val x2))\n (fun #r #a larger1 larger2 smaller1 smaller2 -> c.aloc_disjoint_includes (U.downgrade_val larger1) (U.downgrade_val larger2) (U.downgrade_val smaller1) (U.downgrade_val smaller2))\n (fun #r #a x h1 h2 -> c.aloc_preserved (U.downgrade_val x) h1 h2)\n (fun #r #a x h -> c.aloc_preserved_refl (U.downgrade_val x) h)\n (fun #r #a x h1 h2 h3 -> c.aloc_preserved_trans (U.downgrade_val x) h1 h2 h3)\n (fun #r #a b h1 h2 f -> c.same_mreference_aloc_preserved (U.downgrade_val b) h1 h2 f)\n\nlet downgrade_aloc (#al: aloc_t u#a) (#c: cls al) (a: aloc (raise_cls u#a u#b c)) : Tot (aloc c) =\n let ALoc region addr x = a in\n ALoc region addr (if None? x then None else Some (U.downgrade_val (Some?.v x)))\n\nlet upgrade_aloc (#al: aloc_t u#a) (#c: cls al) (a: aloc c) : Tot (aloc (raise_cls u#a u#b c)) =\n let ALoc region addr x = a in\n ALoc region addr (if None? x then None else Some (U.raise_val (Some?.v x)))\n\nlet downgrade_aloc_upgrade_aloc (#al: aloc_t u#a) (#c: cls al) (a: aloc c) : Lemma\n (downgrade_aloc (upgrade_aloc u#a u#b a) == a)\n [SMTPat (downgrade_aloc (upgrade_aloc u#a u#b a))]\n= ()\n\nlet upgrade_aloc_downgrade_aloc (#al: aloc_t u#a) (#c: cls al) (a: aloc (raise_cls u#a u#b c)) : Lemma\n (upgrade_aloc (downgrade_aloc a) == a)\n [SMTPat (upgrade_aloc u#a u#b (downgrade_aloc a))]\n= ()\n\nlet raise_loc_aux_pred\n (#al: aloc_t u#a)\n (c: cls al)\n (aux: Ghost.erased (GSet.set (aloc c)))\n (a: aloc (raise_cls u#a u#b c))\n: GTot bool\n= GSet.mem (downgrade_aloc a) (Ghost.reveal aux)\n" }, { "file_name": "Steel.Stepper.fst", "name": "Steel.Stepper.p", "opens_and_abbrevs": [ { "open": "FStar.PCM" }, { "open": "Steel" }, { "open": "Steel" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val p:pcm stepper", "source_definition": "let p : pcm stepper =\n { p = p';\n comm = lemma_comm;\n assoc = lemma_assoc_l;\n assoc_r = lemma_assoc_r;\n is_unit = lemma_is_unit;\n refine = refine }", "source_range": { "start_line": 93, "start_col": 0, "end_line": 99, "end_col": 21 }, "interleaved": false, "definition": "FStar.PCM.Mkpcm Steel.Stepper.p'\n Steel.Stepper.lemma_comm\n Steel.Stepper.lemma_assoc_l\n Steel.Stepper.lemma_assoc_r\n Steel.Stepper.lemma_is_unit\n Steel.Stepper.refine", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.PCM.Mkpcm", "Steel.Stepper.stepper", "Steel.Stepper.p'", "Steel.Stepper.lemma_comm", "Steel.Stepper.lemma_assoc_l", "Steel.Stepper.lemma_assoc_r", "Steel.Stepper.lemma_is_unit", "Steel.Stepper.refine" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "FStar.PCM.pcm Steel.Stepper.stepper", "prompt": "let p:pcm stepper =\n ", "expected_response": "{\n p = p';\n comm = lemma_comm;\n assoc = lemma_assoc_l;\n assoc_r = lemma_assoc_r;\n is_unit = lemma_is_unit;\n refine = refine\n}", "source": { "project_name": "steel", "file_name": "lib/steel/Steel.Stepper.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Steel.Stepper.fst", "checked_file": "dataset/Steel.Stepper.fst.checked", "interface_file": false, "dependencies": [ "dataset/Steel.PCMReference.fsti.checked", "dataset/Steel.Memory.fsti.checked", "dataset/Steel.Effect.Atomic.fsti.checked", "dataset/Steel.Effect.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.PCM.fst.checked", "dataset/FStar.Ghost.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "let even = n:nat{n % 2 == 0}", "let odd = n:nat{n % 2 <> 0}", "let abs (n:int) : nat = if n >= 0 then n else -n", "let max (n m:nat) : nat = if n >= m then n else m", "stepper", "V", "V", "V", "n", "n", "Even", "Even", "Even", "n", "n", "Odd", "Odd", "Odd", "n", "n", "EvenWriteable", "EvenWriteable", "EvenWriteable", "OddWriteable", "OddWriteable", "OddWriteable", "None", "None", "None", "let refine (s:stepper) : Tot prop = V? s \\/ None? s", "let composable' (s0 s1:stepper) : prop =\n match s0, s1 with\n | _, None\n | None, _ -> True\n | Even n, Odd m\n | Odd m , Even n -> abs (m-n) == 1\n | EvenWriteable n, Odd m | Odd m, EvenWriteable n -> m - n == 1\n | OddWriteable n, Even m | Even m, OddWriteable n -> m - n == 1\n | _ -> False", "let composable : symrel stepper = composable'", "let compose (s0:stepper) (s1:stepper{composable s0 s1}) =\n match s0, s1 with\n | a, None\n | None, a -> a\n | Even n, Odd m\n | Odd m, Even n -> V (max n m)\n | Odd m, EvenWriteable n | EvenWriteable n, Odd m -> V m\n | Even m, OddWriteable n | OddWriteable n, Even m -> V m", "let p' : pcm' stepper = { composable = composable; op = compose; one = None }", "let lemma_comm (x:stepper) (y:stepper{composable x y}) :\n Lemma (compose x y == compose y x)\n = ()", "let lemma_assoc_l (x y:stepper) (z:stepper{composable y z /\\ composable x (compose y z)})\n : Lemma (composable x y /\\ composable (compose x y) z /\\\n compose x (compose y z) == compose (compose x y) z)\n = ()", "let lemma_assoc_r (x y:stepper) (z:stepper{composable x y /\\ composable (compose x y) z})\n : Lemma (composable y z /\\ composable x (compose y z) /\\\n compose x (compose y z) == compose (compose x y) z)\n = ()", "let lemma_is_unit (x:stepper) : Lemma (composable x None /\\ compose x None == x)\n = ()" ], "closest": [ "val mctr_pcm:pcm nat\nlet mctr_pcm : pcm nat = {\n p=pre_pcm;\n comm=(fun _ _ -> ());\n assoc=(fun _ _ _ -> ());\n assoc_r=(fun _ _ _ -> ());\n is_unit=(fun _ -> ());\n refine=(fun _ -> True);\n}", "val pre_pcm:pcm' nat\nlet pre_pcm : pcm' nat = {\n composable=(fun x y -> True);\n op=(fun (x y:nat) -> Math.Lib.max x y);\n one=0\n}", "val p' (p: dprot) : pcm' (t p)\nlet p' (p:dprot) : pcm' (t p) = { composable = composable; op = compose; one = Nil }", "val pcm (prot: dprot) : pcm (t prot)\nlet pcm (prot:dprot) : pcm (t prot) =\n { p = p' prot;\n comm = lemma_comm;\n assoc = lemma_assoc_l;\n assoc_r = lemma_assoc_r;\n is_unit = lemma_is_unit;\n refine = refine\n}", "val p0 (#v #p #s: _) : pcm' (knowledge #v #p s)\nlet p0 #v #p #s : pcm' (knowledge #v #p s) = {\n composable;\n op=compose;\n one=Nothing\n}", "val w:i p\nlet w : i p = Mkinj", "val w:i p\nlet w : i p = Mkinj", "val pcm (#v #p #s: _) : pcm (knowledge #v #p s)\nlet pcm #v #p #s : pcm (knowledge #v #p s) = {\n p = p0;\n comm = (fun k0 k1 ->\n match k0, k1 with\n | Nothing, _\n | _, Nothing -> ()\n | Owns m0, Owns m1 ->\n compose_avalue_comm m0 m1);\n assoc = (fun k0 k1 k2 -> composable_assoc_l k0 k1 k2);\n assoc_r = (fun k0 k1 k2 -> composable_assoc_r k0 k1 k2);\n is_unit = (fun _ -> ());\n refine = full_knowledge;\n}", "val pfelem_mul_cm:cm pfelem\nlet pfelem_mul_cm : cm pfelem =\n CM one ( *% ) mul_identity mul_associativity mul_commutativity", "val pid:pack\nlet pid : pack = Mk (fun n -> n)", "val lpcs:array_t pc_t\nlet lpcs: array_t pc_t = list_to_array\n [\n \"main.1.1\"; // by index, known as B.PC #0\n \"main.1.2\"; // by index, known as B.PC #1\n \"main.1.3\"; // by index, known as B.PC #2\n \"main.2.1\"; // by index, known as B.PC #3\n \"main.2.2\"; // by index, known as B.PC #4\n \"main.2.3\"; // by index, known as B.PC #5\n \"main.3\"; // by index, known as B.PC #6\n \"main.3.R\"; // by index, known as B.PC #7\n \"main.4.1\"; // by index, known as B.PC #8\n \"main.4.2\"; // by index, known as B.PC #9\n \"main.End\"; // by index, known as B.PC #10\n \"subroutine.1\"; // by index, known as B.PC #11\n \"subroutine.2\"; // by index, known as B.PC #12\n \"subroutine.3\"; // by index, known as B.PC #13\n \"subroutine.End\"; // by index, known as B.PC #14\n ]", "val lpcs:array_t pc_t\nlet lpcs: array_t pc_t = list_to_array\n [\n \"main.1\"; // by index, known as A.PC #0\n \"main.2.1\"; // by index, known as A.PC #1\n \"main.2.2\"; // by index, known as A.PC #2\n \"main.3\"; // by index, known as A.PC #3\n \"main.3.R\"; // by index, known as A.PC #4\n \"main.End\"; // by index, known as A.PC #5\n \"subroutine.1\"; // by index, known as A.PC #6\n \"subroutine.End\"; // by index, known as A.PC #7\n ]", "val co: Type0\nlet co: Type0 = unit", "val co: Type0\nlet co: Type0 = unit", "val pcm_pts_to\n (#a:Type u#1)\n (#p:pcm a)\n (r:pcm_ref p)\n (v:a)\n: vprop\nlet pcm_pts_to (#a:Type u#1) (#p:pcm a) (r:pcm_ref p) (v:a) =\n PulseCore.Action.pts_to r v", "val Steel.ST.PCMReference.pts_to = r: Steel.Memory.ref a pcm -> v: a -> Steel.Effect.Common.vprop\nlet pts_to (#a:Type) (#pcm:pcm a) (r:ref a pcm) (v:a) = to_vprop (pts_to r v)", "val ch: Type0\nlet ch: Type0 = unit", "val ch: Type0\nlet ch: Type0 = unit", "val pfelem_add_cm:cm pfelem\nlet pfelem_add_cm : cm pfelem =\n CM zero ( +% ) add_identity add_associativity add_commutativity", "val puint8: Type0\nlet puint8 = B.buffer LPL.byte", "val my_lpcs:array_t pc_t\nlet my_lpcs: array_t pc_t = list_to_array [ \"main.0\"; \"main.1\"; \"main.2\"; \"main.3\"; \"main.4\"; \"main.5\" ]", "val one:pfelem\nlet one : pfelem = normalize_term_spec prime; 1", "val p:package t\nlet p : package t = T.synth_by_tactic (fun () -> gen_package T.Goal (`t))", "val cV: Type0\nlet cV: Type0 = unit", "val cV: Type0\nlet cV: Type0 = unit", "val pfelem_cr:cr pfelem\nlet pfelem_cr : cr pfelem = \n CR pfelem_add_cm pfelem_mul_cm ( ~% ) add_opp mul_add_distr mul_zero_l", "val cP: Type0\nlet cP: Type0 = unit", "val cP: Type0\nlet cP: Type0 = unit", "val cr: Type0\nlet cr: Type0 = unit", "val cr: Type0\nlet cr: Type0 = unit", "val pcm (elt: Type u#a) (len: Ghost.erased nat) : Tot (P.pcm (carrier elt len))\nlet pcm (elt: Type u#a) (len: Ghost.erased nat) : Tot (P.pcm (carrier elt len)) =\n PM.pointwise (index_t len) (P.pcm_frac #elt)", "val emp : vprop\nlet emp = emp", "val emp : vprop\nlet emp = VUnit emp'", "val cM: Type0\nlet cM: Type0 = unit", "val cM: Type0\nlet cM: Type0 = unit", "val pfelem:eqtype\nlet pfelem : eqtype = a:nat{a < prime}", "val Steel.PCMReference.pts_to = r: Steel.Memory.ref a pcm -> v: a -> Steel.Effect.Common.vprop\nlet pts_to (#a:Type) (#pcm:pcm a) (r:ref a pcm) (v:a) = to_vprop (pts_to r v)", "val emp : slprop\nlet emp = emp", "val get:st machine_state\nlet get : st machine_state =\n fun s -> (s, s)", "val cD: Type0\nlet cD: Type0 = unit", "val cD: Type0\nlet cD: Type0 = unit", "val share\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\r\n: act unit emp_inames\r\n (pts_to r (v0 `op pcm` v1))\r\n (fun _ -> pts_to r v0 ** pts_to r v1)\nlet share\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\r\n: act unit emp_inames\r\n (pts_to r (v0 `op pcm` v1))\r\n (fun _ -> pts_to r v0 `star` pts_to r v1)\r\n= fun #ictx -> mem_action_as_action _ _ _ _ (split_action ictx r v0 v1)", "val for_you:Type0\nlet for_you : Type0 = synth_by_tactic (fun () -> big_phi 8)", "val Steel.Memory.ptr = r: Steel.Memory.ref a pcm -> Steel.Memory.slprop\nlet ptr (#a: Type u#a) (#pcm: pcm a) (r:ref a pcm) =\n h_exists (pts_to r)", "val PulseCore.Heap.ptr = r: PulseCore.Heap.ref a pcm -> PulseCore.Heap.slprop\nlet ptr (#a: Type u#a) (#pcm: pcm a) (r:ref a pcm) =\n h_exists (pts_to r)", "val d:elem\nlet d : elem =\n let x = 37095705934669439343138083508754565189542113879843219016388785533085940283555 in\n assert_norm(x < prime);\n x", "val emp':vprop'\nlet emp':vprop' =\n { hp = emp;\n t = unit;\n sel = fun _ -> ()}", "val pts_to (#a:Type u#1) (#p:pcm a) (r:ref a p) (v:a) : slprop\nlet pts_to = pts_to", "val c9: Type0\nlet c9: Type0 = unit", "val c9: Type0\nlet c9: Type0 = unit", "val c8: Type0\nlet c8: Type0 = unit", "val c8: Type0\nlet c8: Type0 = unit", "val cC: Type0\nlet cC: Type0 = unit", "val cC: Type0\nlet cC: Type0 = unit", "val goal:vprop\nlet goal : vprop =\n exists* v_res. pts_to res #one_half v_res ** pure (Some? v_res)", "val st_var:state\nlet st_var : state =\n let l0_image_header_size = 1ul in\n let l0_binary_size = 1ul in\n let ghost_state = B.mgcmalloc HS.root (G.hide (true, true)) 1ul in\n let cdi = B.gcmalloc HS.root (I.u8 0) digest_len in\n let l0_image_header = B.gcmalloc HS.root (I.u8 0) l0_image_header_size in\n let l0_image_header_sig = B.gcmalloc HS.root (I.u8 0) 64ul in\n let l0_binary = B.gcmalloc HS.root (I.u8 0) l0_binary_size in\n let l0_binary_hash = B.gcmalloc HS.root (I.u8 0) digest_len in\n let l0_image_auth_pubkey = B.gcmalloc HS.root (I.u8 0) 32ul in\n\n let l0 = {\n l0_image_header_size = l0_image_header_size;\n l0_image_header = l0_image_header;\n l0_image_header_sig = l0_image_header_sig;\n l0_binary_size = l0_binary_size;\n l0_binary = l0_binary;\n l0_binary_hash = l0_binary_hash;\n l0_image_auth_pubkey = l0_image_auth_pubkey } in\n\n { ghost_state = ghost_state;\n cdi = cdi;\n l0 = l0 }", "val c1: Type0\nlet c1: Type0 = unit", "val c1: Type0\nlet c1: Type0 = unit", "val alloc\n (#a:Type u#1)\n (#pcm:pcm a)\n (x:a{compatible pcm x x /\\ pcm.refine x})\n: stt (pcm_ref pcm)\n emp\n (fun r -> pcm_pts_to r x)\nlet alloc\n (#a:Type u#1)\n (#pcm:pcm a)\n (x:a{compatible pcm x x /\\ pcm.refine x})\n: stt (pcm_ref pcm)\n emp\n (fun r -> pcm_pts_to r x)\n= A.lift_atomic0 (A.alloc #a #pcm x)", "val hpcs:array_t pc_t\nlet hpcs: array_t pc_t = list_to_array\n [\n \"main.1.1\"; // by index, known as B.PC #0\n \"main.1.2\"; // by index, known as B.PC #1\n \"main.1.3\"; // by index, known as B.PC #2\n \"main.2.1\"; // by index, known as B.PC #3\n \"main.2.2\"; // by index, known as B.PC #4\n \"main.2.3\"; // by index, known as B.PC #5\n \"main.3\"; // by index, known as B.PC #6\n \"main.3.R\"; // by index, known as B.PC #7\n \"main.4.1\"; // by index, known as B.PC #8\n \"main.4.2\"; // by index, known as B.PC #9\n \"main.End\"; // by index, known as B.PC #10\n \"subroutine.1\"; // by index, known as B.PC #11\n \"subroutine.2\"; // by index, known as B.PC #12\n \"subroutine.3\"; // by index, known as B.PC #13\n \"subroutine.End\"; // by index, known as B.PC #14\n ]", "val hpcs:array_t pc_t\nlet hpcs: array_t pc_t = list_to_array\n [\n \"main.1\"; // by index, known as A.PC #0\n \"main.2.1\"; // by index, known as A.PC #1\n \"main.2.2\"; // by index, known as A.PC #2\n \"main.3\"; // by index, known as A.PC #3\n \"main.3.R\"; // by index, known as A.PC #4\n \"main.End\"; // by index, known as A.PC #5\n \"subroutine.1\"; // by index, known as A.PC #6\n \"subroutine.End\"; // by index, known as A.PC #7\n ]", "val Duplex.PCM.chan = p: Duplex.PCM.dprot -> Type0\nlet chan (p:dprot) = ref (t p) (pcm p)", "val Steel.Heap.ptr = r: Steel.Heap.ref a pcm -> Steel.Heap.slprop\nlet ptr (#a: Type u#a) (#pcm: pcm a) (r:ref a pcm) =\n h_exists (pts_to r)", "val pts_to (#a:Type u#0) (#pcm:pcm a) (r:ref a pcm) ([@@@smt_fallback] v:a)\n : vprop\nlet pts_to (#a:Type u#0) (#pcm:pcm a) (r:ref a pcm) ([@@@smt_fallback] v:a)\n = G.pts_to #(raise_t a) #(UP.raise pcm) r (raise_val v)", "val pts_to (#a:Type u#1) (#pcm:pcm a) (r:ref a pcm) (v:a)\n : vprop\nlet pts_to (#a:Type u#1) (#pcm:pcm a) (r:ref a pcm) ([@@@smt_fallback]v:a)\n = to_vprop (Steel.Memory.pts_to r v)", "val ttrue:pbool\nlet ttrue : pbool = Ok ()", "val Duplex.PCM.dprot = Type\nlet dprot = p:dprot'{no_loop p}", "val Vale.PPC64LE.Machine_s.vecs_t = Type0\nlet vecs_t = FStar.FunctionalExtensionality.restricted_t vec (fun _ -> quad32)", "val cH: Type0\nlet cH: Type0 = unit", "val cH: Type0\nlet cH: Type0 = unit", "val Duplex.PCM.nl_protocol = 'a: Type0 -> Type\nlet nl_protocol 'a = p:protocol 'a { no_loop p }", "val inv_p:vprop\nlet inv_p : vprop =\n exists* (v_done:bool) (v_res:option int) (v_claimed:bool).\n pts_to done #one_half v_done\n ** pts_to res #one_half v_res\n ** GR.pts_to claimed #one_half v_claimed\n ** (if not v_claimed then pts_to res #one_half v_res else emp)\n ** pure (v_claimed ==> v_done)\n ** pure (v_done ==> Some? v_res)", "val alloc\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (x:a{compatible pcm x x /\\ pcm.refine x})\r\n: act (ref a pcm) emp_inames emp (fun r -> pts_to r x)\nlet alloc\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (x:a{compatible pcm x x /\\ pcm.refine x})\r\n: act (ref a pcm) emp_inames emp (fun r -> pts_to r x)\r\n= fun #ictx ->\r\n mem_action_as_action _ _ _ _\r\n (alloc_action ictx x)", "val sel (#a:Type u#h) (#pcm:pcm a) (r:ref a pcm) (m:full_hheap (ptr r)) : a\nlet sel #a #pcm (r:ref a pcm) (m:full_hheap (ptr r))\n : a\n = let Ref _ _ _ v = select_addr m (Addr?._0 r) in\n v", "val sel (#a:Type u#h) (#pcm:pcm a) (r:ref a pcm) (m:full_hheap (ptr r)) : a\nlet sel #a #pcm (r:ref a pcm) (m:full_hheap (ptr r))\n : a\n = let Ref _ _ _ v = select_addr m (Addr?._0 r) in\n v", "val alloc (#a:Type)\n (#pcm:pcm a)\n (x:a)\n : Steel (ref a pcm)\n emp\n (fun r -> pts_to r x)\n (requires fun _ -> pcm.refine x)\n (ensures fun _ _ _ -> True)\nlet alloc #_ #pcm x = rewrite_slprop emp (to_vprop Mem.emp) (fun _ -> reveal_emp ());\n compatible_refl pcm x;\n alloc' x", "val cO: Type0\nlet cO: Type0 = unit", "val cO: Type0\nlet cO: Type0 = unit", "val emp : slprop u#a\nlet emp : slprop u#a = H.emp", "val emp : slprop u#a\nlet emp : slprop u#a = as_slprop (fun h -> True)", "val emp : slprop u#a\nlet emp : slprop u#a = as_slprop (fun h -> True)", "val emp : slprop u#a\nlet emp : slprop u#a = H.emp", "val alloc\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (x:a{compatible pcm x x /\\ pcm.refine x})\r\n: stt_atomic (ref a pcm)\r\n #Observable\r\n emp_inames\r\n emp\r\n (fun r -> pts_to r x)\nlet alloc = A.alloc", "val c3: Type0\nlet c3: Type0 = unit", "val c3: Type0\nlet c3: Type0 = unit", "val cL: Type0\nlet cL: Type0 = unit", "val cL: Type0\nlet cL: Type0 = unit", "val pcm (elt: Type u#a) (len: Ghost.erased nat) : FStar.PCM.pcm (carrier elt len)\nlet pcm (elt: Type u#a) (len: Ghost.erased nat)\r\n: FStar.PCM.pcm (carrier elt len)\r\n= PM.pointwise (index_t len) (P.pcm_frac #elt)", "val c7: Type0\nlet c7: Type0 = unit", "val c7: Type0\nlet c7: Type0 = unit", "val masm:printer\nlet masm : printer =\n let reg_prefix unit = \"\" in\n let mem_prefix (ptr_type:string) = ptr_type ^ \" ptr \" in\n let maddr (base:string) (adj:option(string & string)) (offset:string) =\n match adj with\n | None -> \"[\" ^ base ^ \" + \" ^ offset ^ \"]\"\n | Some (scale, index) -> \"[\" ^ base ^ \" + \" ^ scale ^ \" * \" ^ index ^ \" + \" ^ offset ^ \"]\"\n in\n let const (n:int) = string_of_int n in\n let ins_name (name:string) (ops:list operand64) : string = name ^ \" \" in\n let op_order dst src = dst, src in\n let align() = \"ALIGN\" in\n let header() = \".code\\n\" in\n let footer() = \"end\\n\" in\n let proc_name (name:string) = \"ALIGN 16\\n\" ^ name ^ \" proc\\n\" in\n let ret (name:string) = \" ret\\n\" ^ name ^ \" endp\\n\" in\n {\n print_reg_name = print_reg_name;\n print_reg32_name = print_reg32_name;\n print_small_reg_name = print_small_reg_name;\n reg_prefix = reg_prefix;\n mem_prefix = mem_prefix;\n maddr = maddr;\n const = const;\n ins_name = ins_name;\n op_order = op_order;\n align = align;\n header = header;\n footer = footer;\n proc_name = proc_name;\n ret = ret;\n sha256rnds2_explicit_xmm0 = (fun unit -> true);\n }", "val emp : heap\nlet emp = 0, (fun (r:nat) -> None)", "val emp : heap\nlet emp = Mktuple2 0 (F.on_dom nat (fun (r:nat) -> None))", "val emp : heap\nlet emp = {\n next_addr = 0;\n memory = F.on_dom nat (fun (r:nat) -> None)\n}", "val pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a\nlet pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a =\n let hprop (h: heap) : Tot prop =\n Addr? r /\\\n h `contains_addr` (Addr?._0 r) /\\\n pts_to_cell pcm v (select_addr h (Addr?._0 r))\n in\n affine_hprop_intro hprop (fun h0 h1 ->\n match r with | Null -> () | Addr r -> (\n match h0 r, h1 r, (join h0 h1) r with\n | Some (Ref a0 pcm0 _ v0), Some (Ref a1 pcm1 _ v1), Some (Ref a01 pcm01 _ v01) ->\n compatible_elim pcm01 v v0 (compatible pcm01 v v01) (fun frame ->\n pcm01.comm frame v;\n pcm01.assoc_r v frame v1;\n pcm01.comm frame v1;\n let new_frame = (op pcm01 v1 frame) in\n pcm01.comm v new_frame\n )\n | None, Some _, _\n | Some _, None, _ -> ()\n | None, None, _ -> ()\n )\n );\n as_slprop hprop", "val pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a\nlet pts_to = H.pts_to", "val pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a\nlet pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a =\n let hprop (h: heap) : Tot prop =\n Addr? r /\\\n h `contains_addr` (Addr?._0 r) /\\\n pts_to_cell pcm v (select_addr h (Addr?._0 r))\n in\n affine_hprop_intro hprop (fun h0 h1 ->\n match r with | Null -> () | Addr r -> (\n match h0 r, h1 r, (join h0 h1) r with\n | Some (Ref a0 pcm0 _ v0), Some (Ref a1 pcm1 _ v1), Some (Ref a01 pcm01 _ v01) ->\n compatible_elim pcm01 v v0 (compatible pcm01 v v01) (fun frame ->\n pcm01.comm frame v;\n pcm01.assoc_r v frame v1;\n pcm01.comm frame v1;\n let new_frame = (op pcm01 v1 frame) in\n pcm01.comm v new_frame\n )\n | None, Some _, _\n | Some _, None, _ -> ()\n | None, None, _ -> ()\n )\n );\n as_slprop hprop", "val pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a\nlet pts_to = H.pts_to", "val cN: Type0\nlet cN: Type0 = unit", "val cN: Type0\nlet cN: Type0 = unit" ], "closest_src": [ { "project_name": "steel", "file_name": "Steel.MonotonicCounter.fst", "name": "Steel.MonotonicCounter.mctr_pcm" }, { "project_name": "steel", "file_name": "Steel.MonotonicCounter.fst", "name": "Steel.MonotonicCounter.pre_pcm" }, { "project_name": "steel", "file_name": "Duplex.PCM.fst", "name": "Duplex.PCM.p'" }, { "project_name": "steel", "file_name": "Duplex.PCM.fst", "name": "Duplex.PCM.pcm" }, { "project_name": "steel", "file_name": "Steel.FractionalAnchoredPreorder.fst", "name": "Steel.FractionalAnchoredPreorder.p0" }, { "project_name": "FStar", "file_name": "InjectiveTypeFormers.SMT.fst", "name": "InjectiveTypeFormers.SMT.w" }, { "project_name": "FStar", "file_name": "InjectiveTypeFormers.Explicit.fst", "name": "InjectiveTypeFormers.Explicit.w" }, { "project_name": "steel", "file_name": "Steel.FractionalAnchoredPreorder.fst", "name": "Steel.FractionalAnchoredPreorder.pcm" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Lemmas.fst", "name": "Hacl.Spec.Poly1305.Lemmas.pfelem_mul_cm" }, { "project_name": "FStar", "file_name": "PrecedesRank.fst", "name": "PrecedesRank.pid" }, { "project_name": "Armada", "file_name": "MyVarHidingProof.fst", "name": "MyVarHidingProof.lpcs" }, { "project_name": "Armada", "file_name": "MyVarIntroProof.fst", "name": "MyVarIntroProof.lpcs" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.co" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.co" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.pcm_pts_to" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fsti", "name": "Steel.ST.PCMReference.pts_to" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.ch" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.ch" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Lemmas.fst", "name": "Hacl.Spec.Poly1305.Lemmas.pfelem_add_cm" }, { "project_name": "everparse", "file_name": "EverParse3d.InputBuffer.fst", "name": "EverParse3d.InputBuffer.puint8" }, { "project_name": "Armada", "file_name": "MyRegularToAtomicRefinement.fst", "name": "MyRegularToAtomicRefinement.my_lpcs" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Lemmas.fst", "name": "Hacl.Spec.Poly1305.Lemmas.one" }, { "project_name": "FStar", "file_name": "MiniParse.Tac.Spec.fst", "name": "MiniParse.Tac.Spec.p" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cV" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cV" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Lemmas.fst", "name": "Hacl.Spec.Poly1305.Lemmas.pfelem_cr" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cP" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cP" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cr" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cr" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fst", "name": "Steel.ST.HigherArray.pcm" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.emp" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.emp" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cM" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cM" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Lemmas.fst", "name": "Hacl.Spec.Poly1305.Lemmas.pfelem" }, { "project_name": "steel", "file_name": "Steel.PCMReference.fsti", "name": "Steel.PCMReference.pts_to" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.emp" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Machine_Semantics_s.fst", "name": "Vale.X64.Machine_Semantics_s.get" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cD" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cD" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.share" }, { "project_name": "FStar", "file_name": "Bane.Lib.fst", "name": "Bane.Lib.for_you" }, { "project_name": "steel", "file_name": "Steel.Memory.fsti", "name": "Steel.Memory.ptr" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fsti", "name": "PulseCore.Heap.ptr" }, { "project_name": "hacl-star", "file_name": "Spec.Ed25519.PointOps.fst", "name": "Spec.Ed25519.PointOps.d" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fst", "name": "Steel.Effect.Common.emp'" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.pts_to" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.c9" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.c9" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.c8" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.c8" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cC" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cC" }, { "project_name": "steel", "file_name": "Promises.Examples3.fst", "name": "Promises.Examples3.goal" }, { "project_name": "dice-star", "file_name": "HWAbstraction.fst", "name": "HWAbstraction.st_var" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.c1" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.c1" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.alloc" }, { "project_name": "Armada", "file_name": "MyVarIntroProof.fst", "name": "MyVarIntroProof.hpcs" }, { "project_name": "Armada", "file_name": "MyVarHidingProof.fst", "name": "MyVarHidingProof.hpcs" }, { "project_name": "steel", "file_name": "Duplex.PCM.fst", "name": "Duplex.PCM.chan" }, { "project_name": "steel", "file_name": "Steel.Heap.fsti", "name": "Steel.Heap.ptr" }, { "project_name": "steel", "file_name": "Steel.ST.GhostPCMReference.fst", "name": "Steel.ST.GhostPCMReference.pts_to" }, { "project_name": "steel", "file_name": "Steel.GhostPCMReference.fst", "name": "Steel.GhostPCMReference.pts_to" }, { "project_name": "hacl-star", "file_name": "Vale.Def.PossiblyMonad.fst", "name": "Vale.Def.PossiblyMonad.ttrue" }, { "project_name": "steel", "file_name": "Duplex.PCM.fsti", "name": "Duplex.PCM.dprot" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Machine_s.fst", "name": "Vale.PPC64LE.Machine_s.vecs_t" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cH" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cH" }, { "project_name": "steel", "file_name": "Duplex.PCM.fsti", "name": "Duplex.PCM.nl_protocol" }, { "project_name": "steel", "file_name": "Promises.Examples3.fst", "name": "Promises.Examples3.inv_p" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.alloc" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.sel" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.sel" }, { "project_name": "steel", "file_name": "Steel.PCMReference.fst", "name": "Steel.PCMReference.alloc" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cO" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cO" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.emp" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.emp" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.emp" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.emp" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.alloc" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.c3" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.c3" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cL" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cL" }, { "project_name": "steel", "file_name": "Pulse.Lib.PCM.Array.fst", "name": "Pulse.Lib.PCM.Array.pcm" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.c7" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.c7" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Print_s.fst", "name": "Vale.X64.Print_s.masm" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.emp" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.emp" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.emp" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.pts_to" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.pts_to" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.pts_to" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.pts_to" }, { "project_name": "steel", "file_name": "Steel.C.Typestring.fst", "name": "Steel.C.Typestring.cN" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fst", "name": "Pulse.C.Typestring.cN" } ], "selected_premises": [ "Steel.Effect.Common.rm", "Steel.Memory.inames", "Steel.Effect.Common.rmem", "Steel.Stepper.p'", "Steel.Effect.Common.to_vprop'", "Steel.FractionalPermission.full_perm", "Steel.Effect.Common.star", "Steel.Effect.Common.normal", "Steel.Effect.Common.to_vprop", "Steel.Effect.Common.mk_rmem", "Steel.Effect.Common.vrefine'", "Steel.Effect.Common.guard_vprop", "Steel.Effect.Common.hp_of", "Steel.Effect.Common.t_of", "Steel.Effect.Common.rmem'", "Steel.Memory.full_mem", "Steel.Effect.Common.pure", "Steel.Effect.Common.focus_rmem_refl", "Steel.Effect.Common.hmem", "Steel.Effect.Common.req", "FStar.List.Tot.Base.length", "Steel.Effect.Common.vrefine", "Steel.Effect.Common.inv", "Steel.Preorder.pcm_history", "Steel.Effect.Common.normal_steps", "FStar.List.Tot.Base.map", "Steel.Effect.Atomic.h_exists", "Steel.Effect.Common.vc_norm", "Steel.PCMReference.pts_to", "Steel.Effect.Common.focus_rmem", "Steel.Memory.hmem", "FStar.Mul.op_Star", "FStar.UInt.size", "Steel.Effect.Atomic.gget", "Steel.Stepper.composable'", "FStar.PCM.composable", "Steel.Stepper.max", "Steel.Stepper.composable", "FStar.Reflection.V2.Derived.mk_app", "FStar.Reflection.V2.Data.var", "Steel.FractionalPermission.comp_perm", "Steel.Effect.Atomic.mk_selector_vprop", "Steel.Effect.Common.mk_rmem'", "Steel.Effect.Common.return_pre", "Steel.Effect.Common.frame_equalities", "FStar.Real.two", "Steel.Preorder.history_val", "FStar.Reflection.V2.Derived.mk_e_app", "FStar.PCM.op", "FStar.Real.one", "Steel.Effect.Common.unfold_guard", "Steel.Stepper.compose", "Steel.Effect.Common.sel_of", "Steel.Effect.Common.focus_rmem'", "FStar.Reflection.V2.Derived.u_unk", "Steel.FractionalPermission.sum_perm", "Steel.Effect.return_req", "Steel.Effect.Atomic.return_req", "Steel.Effect.Common.frame_equalities'", "Steel.Effect.Common.extract_contexts", "FStar.List.Tot.Base.op_At", "Steel.Effect.Common.frame_vc_norm", "FStar.PCM.compatible", "FStar.Pervasives.reveal_opaque", "Steel.Effect.if_then_else_req", "Steel.Effect.Atomic.if_then_else_req", "Steel.Effect.subcomp_pre", "Steel.Effect.Common.try_open_existentials", "Steel.Effect.Atomic.subcomp_pre", "Steel.Effect.Common.norm_return_pre", "FStar.FunctionalExtensionality.feq", "Steel.Effect.Atomic.return_ens", "Steel.Effect.Common.unrestricted_focus_rmem", "FStar.NMSTTotal.get", "Steel.Effect.Atomic.if_then_else_ens", "Steel.Effect.if_then_else_ens", "Steel.Stepper.refine", "Steel.Effect.return_ens", "Steel.Effect.Common.selector'", "FStar.List.Tot.Base.tl", "FStar.List.Tot.Base.mem", "FStar.Tactics.CanonCommMonoidSimple.Equiv.term_eq", "Steel.Effect.Common.sel_depends_only_on", "Steel.Effect.Common.visit_br", "Steel.Effect.Common.sel_depends_only_on_core", "FStar.List.Tot.Base.rev", "FStar.Reflection.V2.Derived.flatten_name", "FStar.Math.Lemmas.pow2_plus", "Steel.Effect.Common.slterm_nbr_uvars_argv", "Steel.Effect.Common.visit_tm", "Steel.Effect.Common.canon'", "Steel.Effect.Common.solve_maybe_emps", "Steel.Effect.Common.print_goals", "FStar.Reflection.V2.Derived.shift_subst", "Steel.Effect.Common.solve_indirection_eqs", "FStar.Sealed.Inhabited.seal", "Steel.Effect.Common.unrestricted_mk_rmem", "Steel.Effect.Atomic.bind_req", "Steel.Effect.bind_req", "Steel.Effect.Common.ite_soundness_tac" ], "source_upto_this": "(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Steel.Stepper\n\nopen FStar.PCM\n\n/// A simplified version of the Duplex library, specialized to a simple concrete\n/// protocol, where the two parties take turns incrementing a counter.\n/// This is modeled using the [stepper] PCM below\n\n(* Some abbreviations and helpers to operate on natural numbers *)\n\nlet even = n:nat{n % 2 == 0}\nlet odd = n:nat{n % 2 <> 0}\n\nlet abs (n:int) : nat = if n >= 0 then n else -n\nlet max (n m:nat) : nat = if n >= m then n else m\n\n/// The elements of the PCM regulating this protocol.\nnoeq\ntype stepper : Type u#1 =\n | V : n:nat{n > 0} -> stepper // the real value \" whole value \"\n | Even : n:even -> stepper\n | Odd : n:odd -> stepper\n | EvenWriteable : even -> stepper\n | OddWriteable : odd -> stepper\n | None : stepper\n\nlet refine (s:stepper) : Tot prop = V? s \\/ None? s\n\n/// Specifying which elements of the PCM can be composed.\n/// This PCM models a counter that the two parties increment one after the other.\n/// As such, the two sides are always at most one apart\nlet composable' (s0 s1:stepper) : prop =\n match s0, s1 with\n | _, None\n | None, _ -> True\n | Even n, Odd m\n | Odd m , Even n -> abs (m-n) == 1\n | EvenWriteable n, Odd m | Odd m, EvenWriteable n -> m - n == 1\n | OddWriteable n, Even m | Even m, OddWriteable n -> m - n == 1\n | _ -> False\n\nlet composable : symrel stepper = composable'\n\n/// The PCM composition function, defined on elements that are composable\nlet compose (s0:stepper) (s1:stepper{composable s0 s1}) =\n match s0, s1 with\n | a, None\n | None, a -> a\n | Even n, Odd m\n | Odd m, Even n -> V (max n m)\n | Odd m, EvenWriteable n | EvenWriteable n, Odd m -> V m\n | Even m, OddWriteable n | OddWriteable n, Even m -> V m\n\n/// Combining them into the structure of the PCM\nlet p' : pcm' stepper = { composable = composable; op = compose; one = None }\n\n(* Defining the different lemmas for the commutative monoid structure *)\n\nlet lemma_comm (x:stepper) (y:stepper{composable x y}) :\n Lemma (compose x y == compose y x)\n = ()\n\nlet lemma_assoc_l (x y:stepper) (z:stepper{composable y z /\\ composable x (compose y z)})\n : Lemma (composable x y /\\ composable (compose x y) z /\\\n compose x (compose y z) == compose (compose x y) z)\n = ()\n\nlet lemma_assoc_r (x y:stepper) (z:stepper{composable x y /\\ composable (compose x y) z})\n : Lemma (composable y z /\\ composable x (compose y z) /\\\n compose x (compose y z) == compose (compose x y) z)\n = ()\n\nlet lemma_is_unit (x:stepper) : Lemma (composable x None /\\ compose x None == x)\n = ()\n\n/// Full definition of the stepper PCM", "sketch": [ "Step 1: The definition is about creating a full PCM (Partial Commutative Monoid) structure for the `stepper` type. This involves combining the previously defined `p'` (which includes the composable relation and the composition function) with the necessary lemmas that ensure the PCM properties such as commutativity, associativity, and the existence of a unit element.\n\nStep 2: The implementation involves using the `pcm_of_pcm'` function, which takes the partial PCM structure `p'` and the lemmas `lemma_comm`, `lemma_assoc_l`, `lemma_assoc_r`, and `lemma_is_unit` to construct the full PCM structure.", "Step 1: The definition is about creating a full PCM (Partial Commutative Monoid) structure for the `stepper` type. This involves combining the previously defined components: the composability relation, the composition function, and the unit element.\nStep 2: The implementation involves using the `pcm'` structure `p'` that we have already defined, which includes the composability relation, the composition function, and the unit element. We will use this structure to define the full PCM.", "Step 1: The definition is about creating a full PCM (Partial Commutative Monoid) structure for the `stepper` type. This involves combining the previously defined `p'` (which includes the composability relation and the composition function) with the necessary lemmas that ensure the PCM properties (commutativity, associativity, and identity element).\n\nStep 2: The implementation involves creating a `pcm` record that includes the `p'` structure and the four lemmas (`lemma_comm`, `lemma_assoc_l`, `lemma_assoc_r`, `lemma_is_unit`) that were defined earlier. This ensures that the `stepper` type satisfies all the required properties of a PCM.", "Step 1: The definition is about creating a full PCM (Partial Commutative Monoid) structure for the `stepper` type. This involves combining the previously defined `p'` structure with the necessary lemmas to ensure the properties of a PCM are satisfied.\nStep 2: The implementation involves using the `pcm_of_pcm'` function to convert the `p'` structure into a full PCM by providing the necessary lemmas: `lemma_comm`, `lemma_assoc_l`, `lemma_assoc_r`, and `lemma_is_unit`.", "Step 1: The definition of `p` is about creating a full PCM (Partial Commutative Monoid) structure for the `stepper` type. This involves combining the previously defined `p'` structure with proofs that it satisfies the properties of a PCM.\nStep 2: The implementation involves using the `pcm_of_pcm'` function to convert the `p'` structure into a full PCM by providing the necessary lemmas that prove the commutative monoid properties: commutativity, associativity, and the existence of a unit element.", "Step 1: The definition is about creating a full PCM (Partial Commutative Monoid) structure for the `stepper` type. This structure will include the properties and operations defined earlier, such as composability, composition, and the identity element.\nStep 2: The implementation involves combining the previously defined `p'` (which includes the composable relation, composition function, and identity element) with the lemmas that establish the commutative monoid properties (commutativity, associativity, and identity).", "Step 1: The definition is about creating a full PCM (Partial Commutative Monoid) structure for the `stepper` type. This structure includes the properties and operations defined earlier, such as composability, composition, and the identity element.\nStep 2: The implementation involves using the previously defined `p'` (which includes the composable relation, the composition function, and the identity element) and the lemmas (`lemma_comm`, `lemma_assoc_l`, `lemma_assoc_r`, `lemma_is_unit`) to form the complete PCM structure.", "Step 1: The definition is about creating a full PCM (Partial Commutative Monoid) structure for the `stepper` type. This involves combining the previously defined `p'` structure with the necessary lemmas to ensure the properties of a PCM are satisfied.\nStep 2: The implementation involves using the `pcm_of_pcm'` function to convert the `p'` structure into a full PCM by providing the necessary commutativity, associativity, and identity lemmas.", "Step 1: The definition is about creating a PCM (Partial Commutative Monoid) for the `stepper` type. This involves combining the previously defined `p'` structure with the necessary lemmas to ensure the properties of a PCM.\nStep 2: The implementation involves using the `pcm'` structure `p'` and the lemmas `lemma_comm`, `lemma_assoc_l`, `lemma_assoc_r`, and `lemma_is_unit` to define the full PCM.", "Step 1: The definition is about creating a complete PCM (Partial Commutative Monoid) structure for the `stepper` type. This involves combining the previously defined `p'` (which includes the composable relation and the composition function) with the necessary lemmas that ensure the PCM properties (commutativity, associativity, and the existence of a unit element).\n\nStep 2: The implementation involves using the `pcm_of_pcm'` function to convert the `pcm'` structure `p'` into a full `pcm` structure by providing the required lemmas: `lemma_comm`, `lemma_assoc_l`, `lemma_assoc_r`, and `lemma_is_unit`." ], "generated_solution": [ "let p: pcm stepper = pcm_of_pcm' p' lemma_comm lemma_assoc_l lemma_assoc_r lemma_is_unit", "let p : pcm stepper = p'", "let p : pcm stepper = { p = p'; lemma_comm = lemma_comm; lemma_assoc_l = lemma_assoc_l; lemma_assoc_r = lemma_assoc_r; lemma_is_unit = lemma_is_unit }", "let p:pcm stepper = pcm_of_pcm' p' lemma_comm lemma_assoc_l lemma_assoc_r lemma_is_unit", "let p:pcm stepper = pcm_of_pcm' p' lemma_comm lemma_assoc_l lemma_assoc_r lemma_is_unit", "let p : pcm stepper = { p' with\n comm = lemma_comm;\n assoc_l = lemma_assoc_l;\n assoc_r = lemma_assoc_r;\n is_unit = lemma_is_unit }", "let p : pcm stepper = { p' with\n comm = lemma_comm;\n assoc_l = lemma_assoc_l;\n assoc_r = lemma_assoc_r;\n is_unit = lemma_is_unit\n}", "let p:pcm stepper = pcm_of_pcm' p' lemma_comm lemma_assoc_l lemma_assoc_r lemma_is_unit", "let p : pcm stepper = { p' with\n comm = lemma_comm;\n assoc_l = lemma_assoc_l;\n assoc_r = lemma_assoc_r;\n is_unit = lemma_is_unit\n}", "let p : pcm stepper = pcm_of_pcm' p' lemma_comm lemma_assoc_l lemma_assoc_r lemma_is_unit" ] }, { "file_name": "Vale.AES.X64.GF128_Mul.fst", "name": "Vale.AES.X64.GF128_Mul.va_codegen_success_ShiftLeft2_128_1", "opens_and_abbrevs": [ { "open": "Vale.X64.CPU_Features_s" }, { "open": "Vale.X64.QuickCodes" }, { "open": "Vale.X64.QuickCode" }, { "open": "Vale.X64.InsAes" }, { "open": "Vale.X64.InsVector" }, { "open": "Vale.X64.InsMem" }, { "open": "Vale.X64.InsBasic" }, { "open": "Vale.X64.Decls" }, { "open": "Vale.X64.State" }, { "open": "Vale.X64.Machine_s" }, { "open": "Vale.AES.GF128" }, { "open": "Vale.AES.GF128_s" }, { "open": "Vale.Math.Poly2.Lemmas" }, { "open": "Vale.Math.Poly2.Bits" }, { "open": "Vale.Math.Poly2.Bits_s" }, { "open": "Vale.Math.Poly2" }, { "open": "Vale.Math.Poly2_s" }, { "open": "Vale.Arch.Types" }, { "open": "Vale.Def.Types_s" }, { "open": "Vale.X64.CPU_Features_s" }, { "open": "Vale.X64.QuickCodes" }, { "open": "Vale.X64.QuickCode" }, { "open": "Vale.X64.InsAes" }, { "open": "Vale.X64.InsVector" }, { "open": "Vale.X64.InsMem" }, { "open": "Vale.X64.InsBasic" }, { "open": "Vale.X64.Decls" }, { "open": "Vale.X64.State" }, { "open": "Vale.X64.Machine_s" }, { "open": "Vale.AES.GF128" }, { "open": "Vale.AES.GF128_s" }, { "open": "Vale.Math.Poly2.Lemmas" }, { "open": "Vale.Math.Poly2.Bits" }, { "open": "Vale.Math.Poly2.Bits_s" }, { "open": "Vale.Math.Poly2" }, { "open": "Vale.Math.Poly2_s" }, { "open": "Vale.Arch.Types" }, { "open": "Vale.Def.Types_s" }, { "open": "Vale.AES.X64" }, { "open": "Vale.AES.X64" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 1, "initial_ifuel": 0, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": true, "smtencoding_nl_arith_repr": "wrapped", "smtencoding_l_arith_repr": "native", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val va_codegen_success_ShiftLeft2_128_1 : va_dummy:unit -> Tot va_pbool", "source_definition": "let va_codegen_success_ShiftLeft2_128_1 () =\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_Psrld (va_op_xmm_xmm 3) 31) (va_pbool_and (va_codegen_success_Mov128\n (va_op_xmm_xmm 4) (va_op_xmm_xmm 2)) (va_pbool_and (va_codegen_success_Psrld (va_op_xmm_xmm 4)\n 31) (va_pbool_and (va_codegen_success_Pslld (va_op_xmm_xmm 1) 1) (va_pbool_and\n (va_codegen_success_Pslld (va_op_xmm_xmm 2) 1) (va_pbool_and (va_codegen_success_VPslldq4\n (va_op_xmm_xmm 5) (va_op_xmm_xmm 3)) (va_pbool_and (va_codegen_success_VPslldq4 (va_op_xmm_xmm\n 4) (va_op_xmm_xmm 4)) (va_pbool_and (va_codegen_success_PinsrdImm (va_op_xmm_xmm 3) 0 0\n (va_op_reg_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Pshufd (va_op_xmm_xmm 3)\n (va_op_xmm_xmm 3) 3) (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm 3) (va_op_xmm_xmm\n 4)) (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_Pxor (va_op_xmm_xmm 2) (va_op_xmm_xmm 3)) (va_ttrue ()))))))))))))))", "source_range": { "start_line": 99, "start_col": 0, "end_line": 110, "end_col": 92 }, "interleaved": false, "definition": "fun _ ->\n Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_Mov128 (Vale.X64.Decls.va_op_xmm_xmm\n 3)\n (Vale.X64.Decls.va_op_xmm_xmm 1))\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_Psrld (Vale.X64.Decls.va_op_xmm_xmm\n 3)\n 31)\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_Mov128 (Vale.X64.Decls.va_op_xmm_xmm\n 4)\n (Vale.X64.Decls.va_op_xmm_xmm 2))\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_Psrld (Vale.X64.Decls.va_op_xmm_xmm\n 4)\n 31)\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_Pslld (Vale.X64.Decls.va_op_xmm_xmm\n 1)\n 1)\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_Pslld (Vale.X64.Decls.va_op_xmm_xmm\n 2)\n 1)\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_VPslldq4\n (Vale.X64.Decls.va_op_xmm_xmm 5)\n (Vale.X64.Decls.va_op_xmm_xmm 3))\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_VPslldq4\n (Vale.X64.Decls.va_op_xmm_xmm 4)\n (Vale.X64.Decls.va_op_xmm_xmm 4))\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_PinsrdImm\n (Vale.X64.Decls.va_op_xmm_xmm 3)\n 0\n 0\n (Vale.X64.Decls.va_op_reg_opr64_reg64 Vale.X64.Machine_s.rR12\n ))\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_Pshufd\n (Vale.X64.Decls.va_op_xmm_xmm 3)\n (Vale.X64.Decls.va_op_xmm_xmm 3)\n 3)\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_Pxor\n (Vale.X64.Decls.va_op_xmm_xmm 3)\n (Vale.X64.Decls.va_op_xmm_xmm 4))\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_Pxor\n (Vale.X64.Decls.va_op_xmm_xmm 1)\n (Vale.X64.Decls.va_op_xmm_xmm 5))\n (Vale.X64.Decls.va_pbool_and (Vale.X64.InsVector.va_codegen_success_Pxor\n (Vale.X64.Decls.va_op_xmm_xmm 2)\n (Vale.X64.Decls.va_op_xmm_xmm 3))\n (Vale.X64.Decls.va_ttrue ())))))))))))))", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Prims.unit", "Vale.X64.Decls.va_pbool_and", "Vale.X64.InsVector.va_codegen_success_Mov128", "Vale.X64.Decls.va_op_xmm_xmm", "Vale.X64.InsVector.va_codegen_success_Psrld", "Vale.X64.InsVector.va_codegen_success_Pslld", "Vale.X64.InsVector.va_codegen_success_VPslldq4", "Vale.X64.InsVector.va_codegen_success_PinsrdImm", "Vale.X64.Decls.va_op_reg_opr64_reg64", "Vale.X64.Machine_s.rR12", "Vale.X64.InsVector.va_codegen_success_Pshufd", "Vale.X64.InsVector.va_codegen_success_Pxor", "Vale.X64.Decls.va_ttrue", "Vale.X64.Decls.va_pbool" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "va_dummy: Prims.unit -> Vale.X64.Decls.va_pbool", "prompt": "let va_codegen_success_ShiftLeft2_128_1 () =\n ", "expected_response": "(va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1))\n (va_pbool_and (va_codegen_success_Psrld (va_op_xmm_xmm 3) 31)\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 4) (va_op_xmm_xmm 2))\n (va_pbool_and (va_codegen_success_Psrld (va_op_xmm_xmm 4) 31)\n (va_pbool_and (va_codegen_success_Pslld (va_op_xmm_xmm 1) 1)\n (va_pbool_and (va_codegen_success_Pslld (va_op_xmm_xmm 2) 1)\n (va_pbool_and (va_codegen_success_VPslldq4 (va_op_xmm_xmm 5)\n (va_op_xmm_xmm 3))\n (va_pbool_and (va_codegen_success_VPslldq4 (va_op_xmm_xmm 4)\n (va_op_xmm_xmm 4))\n (va_pbool_and (va_codegen_success_PinsrdImm (va_op_xmm_xmm 3)\n 0\n 0\n (va_op_reg_opr64_reg64 rR12))\n (va_pbool_and (va_codegen_success_Pshufd (va_op_xmm_xmm 3)\n (va_op_xmm_xmm 3)\n 3)\n (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm 3)\n (va_op_xmm_xmm 4))\n (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm 1)\n (va_op_xmm_xmm 5))\n (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm\n 2)\n (va_op_xmm_xmm 3))\n (va_ttrue ()))))))))))))))", "source": { "project_name": "hacl-star", "file_name": "obj/Vale.AES.X64.GF128_Mul.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Vale.AES.X64.GF128_Mul.fst", "checked_file": "dataset/Vale.AES.X64.GF128_Mul.fst.checked", "interface_file": true, "dependencies": [ "dataset/Vale.X64.State.fsti.checked", "dataset/Vale.X64.QuickCodes.fsti.checked", "dataset/Vale.X64.QuickCode.fst.checked", "dataset/Vale.X64.Machine_s.fst.checked", "dataset/Vale.X64.InsVector.fsti.checked", "dataset/Vale.X64.InsMem.fsti.checked", "dataset/Vale.X64.InsBasic.fsti.checked", "dataset/Vale.X64.InsAes.fsti.checked", "dataset/Vale.X64.Flags.fsti.checked", "dataset/Vale.X64.Decls.fsti.checked", "dataset/Vale.X64.CPU_Features_s.fst.checked", "dataset/Vale.Math.Poly2_s.fsti.checked", "dataset/Vale.Math.Poly2.Words.fsti.checked", "dataset/Vale.Math.Poly2.Lemmas.fsti.checked", "dataset/Vale.Math.Poly2.Bits_s.fsti.checked", "dataset/Vale.Math.Poly2.Bits.fsti.checked", "dataset/Vale.Math.Poly2.fsti.checked", "dataset/Vale.Def.Types_s.fst.checked", "dataset/Vale.Arch.Types.fsti.checked", "dataset/Vale.AES.GF128_s.fsti.checked", "dataset/Vale.AES.GF128.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "val va_code_ShiftLeft128_1 : va_dummy:unit -> Tot va_code", "let va_code_ShiftLeft128_1 () =\n (va_Block (va_CCons (va_code_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_CCons (va_code_Psrld\n (va_op_xmm_xmm 2) 31) (va_CCons (va_code_Pslld (va_op_xmm_xmm 1) 1) (va_CCons (va_code_VPslldq4\n (va_op_xmm_xmm 2) (va_op_xmm_xmm 2)) (va_CCons (va_code_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm\n 2)) (va_CNil ())))))))", "val va_codegen_success_ShiftLeft128_1 : va_dummy:unit -> Tot va_pbool", "val va_lemma_ShiftLeft128_1 : va_b0:va_code -> va_s0:va_state -> a:poly\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_ShiftLeft128_1 ()) va_s0 /\\ va_get_ok va_s0 /\\\n avx_enabled /\\ sse_enabled /\\ Vale.Math.Poly2_s.degree a < 128 /\\ va_get_xmm 1 va_s0 ==\n Vale.Math.Poly2.Bits_s.to_quad32 a))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_get_xmm 1 va_sM == Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.shift a 1) /\\\n va_state_eq va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_flags va_sM\n (va_update_ok va_sM va_s0))))))", "let va_codegen_success_ShiftLeft128_1 () =\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_Psrld (va_op_xmm_xmm 2) 31) (va_pbool_and (va_codegen_success_Pslld\n (va_op_xmm_xmm 1) 1) (va_pbool_and (va_codegen_success_VPslldq4 (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 2)) (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 2))\n (va_ttrue ()))))))", "let va_wp_ShiftLeft128_1 (a:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ avx_enabled /\\ sse_enabled /\\ Vale.Math.Poly2_s.degree a < 128 /\\ va_get_xmm\n 1 va_s0 == Vale.Math.Poly2.Bits_s.to_quad32 a /\\ (forall (va_x_efl:Vale.X64.Flags.t)\n (va_x_xmm1:quad32) (va_x_xmm2:quad32) . let va_sM = va_upd_xmm 2 va_x_xmm2 (va_upd_xmm 1\n va_x_xmm1 (va_upd_flags va_x_efl va_s0)) in va_get_ok va_sM /\\ va_get_xmm 1 va_sM ==\n Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.shift a 1) ==> va_k va_sM (())))", "let va_qcode_ShiftLeft128_1 (va_mods:va_mods_t) (a:poly) : (va_quickCode unit\n (va_code_ShiftLeft128_1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 59 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 60 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Psrld (va_op_xmm_xmm 2) 31) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 61 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pslld (va_op_xmm_xmm 1) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 62 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_VPslldq4 (va_op_xmm_xmm 2) (va_op_xmm_xmm 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 63 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (fun (va_s:va_state) _ -> let\n (va_arg8:Vale.Math.Poly2_s.poly) = a in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 65 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_shift_left_1 va_arg8) (va_QEmpty (())))))))))", "val va_wpProof_ShiftLeft128_1 : a:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_ShiftLeft128_1 a va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftLeft128_1 ()) ([va_Mod_xmm 2;\n va_Mod_xmm 1; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))", "let va_quick_ShiftLeft128_1 (a:poly) : (va_quickCode unit (va_code_ShiftLeft128_1 ())) =\n (va_QProc (va_code_ShiftLeft128_1 ()) ([va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags])\n (va_wp_ShiftLeft128_1 a) (va_wpProof_ShiftLeft128_1 a))", "val va_code_ReduceMulRev128 : va_dummy:unit -> Tot va_code", "let va_lemma_ShiftLeft128_1 va_b0 va_s0 a =\n let (va_mods:va_mods_t) = [va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags; va_Mod_ok] in\n let va_qc = va_qcode_ShiftLeft128_1 va_mods a in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftLeft128_1 ()) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 45 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_get_ok va_sM) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 57 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_get_xmm 1 va_sM == Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.shift a 1))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags; va_Mod_ok]) va_sM va_s0;\n (va_sM, va_fM)", "val va_codegen_success_ReduceMulRev128 : va_dummy:unit -> Tot va_pbool", "val va_lemma_ReduceMulRev128 : va_b0:va_code -> va_s0:va_state -> a:poly -> b:poly\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_ReduceMulRev128 ()) va_s0 /\\ va_get_ok va_s0 /\\\n (pclmulqdq_enabled /\\ avx_enabled /\\ sse_enabled) /\\ Vale.Math.Poly2_s.degree a <= 127 /\\\n Vale.Math.Poly2_s.degree b <= 127 /\\ va_get_xmm 1 va_s0 == Vale.Math.Poly2.Bits_s.to_quad32\n (Vale.Math.Poly2_s.reverse a 127) /\\ va_get_xmm 2 va_s0 == Vale.Math.Poly2.Bits_s.to_quad32\n (Vale.Math.Poly2_s.reverse b 127)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n va_get_xmm 1 va_sM == Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.reverse\n (Vale.AES.GF128_s.gf128_mul a b) 127) /\\ va_state_eq va_sM (va_update_xmm 6 va_sM\n (va_update_xmm 5 va_sM (va_update_xmm 4 va_sM (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM\n (va_update_xmm 1 va_sM (va_update_reg64 rR12 va_sM (va_update_flags va_sM (va_update_ok va_sM\n va_s0)))))))))))", "let va_wpProof_ShiftLeft128_1 a va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_ShiftLeft128_1 (va_code_ShiftLeft128_1 ()) va_s0 a in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_flags va_sM\n (va_update_ok va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)", "let va_wp_ReduceMulRev128 (a:poly) (b:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) :\n Type0 =\n (va_get_ok va_s0 /\\ (pclmulqdq_enabled /\\ avx_enabled /\\ sse_enabled) /\\ Vale.Math.Poly2_s.degree\n a <= 127 /\\ Vale.Math.Poly2_s.degree b <= 127 /\\ va_get_xmm 1 va_s0 ==\n Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.reverse a 127) /\\ va_get_xmm 2 va_s0 ==\n Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.reverse b 127) /\\ (forall\n (va_x_efl:Vale.X64.Flags.t) (va_x_r12:nat64) (va_x_xmm1:quad32) (va_x_xmm2:quad32)\n (va_x_xmm3:quad32) (va_x_xmm4:quad32) (va_x_xmm5:quad32) (va_x_xmm6:quad32) . let va_sM =\n va_upd_xmm 6 va_x_xmm6 (va_upd_xmm 5 va_x_xmm5 (va_upd_xmm 4 va_x_xmm4 (va_upd_xmm 3 va_x_xmm3\n (va_upd_xmm 2 va_x_xmm2 (va_upd_xmm 1 va_x_xmm1 (va_upd_reg64 rR12 va_x_r12 (va_upd_flags\n va_x_efl va_s0))))))) in va_get_ok va_sM /\\ va_get_xmm 1 va_sM ==\n Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.reverse (Vale.AES.GF128_s.gf128_mul a b)\n 127) ==> va_k va_sM (())))", "val va_code_ShiftLeft2_128_1 : va_dummy:unit -> Tot va_code", "let va_code_ShiftLeft2_128_1 () =\n (va_Block (va_CCons (va_code_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_CCons (va_code_Psrld\n (va_op_xmm_xmm 3) 31) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 4) (va_op_xmm_xmm 2)) (va_CCons\n (va_code_Psrld (va_op_xmm_xmm 4) 31) (va_CCons (va_code_Pslld (va_op_xmm_xmm 1) 1) (va_CCons\n (va_code_Pslld (va_op_xmm_xmm 2) 1) (va_CCons (va_code_VPslldq4 (va_op_xmm_xmm 5)\n (va_op_xmm_xmm 3)) (va_CCons (va_code_VPslldq4 (va_op_xmm_xmm 4) (va_op_xmm_xmm 4)) (va_CCons\n (va_code_PinsrdImm (va_op_xmm_xmm 3) 0 0 (va_op_reg_opr64_reg64 rR12)) (va_CCons\n (va_code_Pshufd (va_op_xmm_xmm 3) (va_op_xmm_xmm 3) 3) (va_CCons (va_code_Pxor (va_op_xmm_xmm\n 3) (va_op_xmm_xmm 4)) (va_CCons (va_code_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_Pxor (va_op_xmm_xmm 2) (va_op_xmm_xmm 3)) (va_CNil ())))))))))))))))", "val va_wpProof_ReduceMulRev128 : a:poly -> b:poly -> va_s0:va_state -> va_k:(va_state -> unit ->\n Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_ReduceMulRev128 a b va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ReduceMulRev128 ()) ([va_Mod_xmm 6;\n va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_reg64 rR12;\n va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))", "val va_codegen_success_ShiftLeft2_128_1 : va_dummy:unit -> Tot va_pbool" ], "closest": [ "val va_codegen_success_ShiftLeft2_128_1 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_ShiftLeft2_128_1 () =\n (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 0) 0) (va_pbool_and\n (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 31) (va_pbool_and\n (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 3) (va_op_reg_opr_reg 10)) (va_pbool_and\n (va_codegen_success_Vsrw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3))\n (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 3) 4) (va_pbool_and (va_codegen_success_Vspltisb (va_op_vec_opr_vec 0) 1)\n (va_pbool_and (va_codegen_success_Vsl (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 0)) (va_pbool_and (va_codegen_success_Vsl (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 0)) (va_pbool_and (va_codegen_success_Vxor\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 3)) (va_ttrue ()))))))))))", "val va_codegen_success_ShiftLeft128_1 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_ShiftLeft128_1 () =\n (va_pbool_and (va_codegen_success_Vspltisb (va_op_vec_opr_vec 2) 1) (va_pbool_and\n (va_codegen_success_Vsl (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2))\n (va_ttrue ())))", "val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_ShiftKey1_128 () =\n (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and\n (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and\n (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5))\n (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0)\n (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3)\n (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ()))))))))", "val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_ShiftKey1_128 () =\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 1) (va_op_xmm_xmm 3)) (va_pbool_and\n (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_PolyAnd (va_op_xmm_xmm\n 3) (va_op_xmm_xmm 5)) (va_pbool_and (va_codegen_success_Pcmpeqd (va_op_xmm_xmm 3)\n (va_op_xmm_xmm 5)) (va_pbool_and (va_codegen_success_Pshufd (va_op_xmm_xmm 3) (va_op_xmm_xmm 3)\n 255) (va_pbool_and (va_codegen_success_PolyAnd (va_op_xmm_xmm 3) (va_op_xmm_xmm 4))\n (va_pbool_and (va_codegen_success_VPolyAdd (va_op_xmm_xmm 1) (va_op_xmm_xmm 1)\n (va_op_opr128_xmm 3)) (va_ttrue ()))))))))", "val va_codegen_success_Msg_shift : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Msg_shift () =\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 3)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 6)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 4)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 4) (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 7)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 5) (va_op_xmm_xmm 0)) (va_ttrue ())))))))", "val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_ShiftKey1_gf128_power () =\n (va_pbool_and (va_codegen_success_ZeroXmm (va_op_xmm_xmm 4)) (va_pbool_and\n (va_codegen_success_ZeroXmm (va_op_xmm_xmm 5)) (va_pbool_and (va_codegen_success_PinsrdImm\n (va_op_xmm_xmm 4) 3254779904 3 (va_op_reg_opr64_reg64 rR12)) (va_pbool_and\n (va_codegen_success_PinsrdImm (va_op_xmm_xmm 4) 1 0 (va_op_reg_opr64_reg64 rR12)) (va_pbool_and\n (va_codegen_success_PinsrdImm (va_op_xmm_xmm 5) 2147483648 3 (va_op_reg_opr64_reg64 rR12))\n (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ())))))))", "val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_ShiftKey1_gf128_power () =\n (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and\n (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and\n (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and\n (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and\n (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and\n (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and\n (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8)\n (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5)\n (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4)\n (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128\n ()) (va_ttrue ())))))))))))", "val va_codegen_success_Compute_pad_to_128_bits : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Compute_pad_to_128_bits () =\n (va_pbool_and (va_pbool_and (va_codegen_success_PinsrqImm (va_op_xmm_xmm 0) 0 1\n (va_op_reg_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64\n rRcx) (va_op_opr64_reg64 rR10)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64\n rRcx) (va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64\n rR11) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rR11)\n (va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64\n rR11) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_Pextrq (va_op_dst_opr64_reg64 rRcx)\n (va_op_xmm_xmm 0) 0) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRcx)\n (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Pinsrq (va_op_xmm_xmm 0)\n (va_op_opr64_reg64 rRcx) 0) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64\n rRcx) (va_op_opr64_reg64 rR10)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64\n rRcx) (va_const_opr64 8)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)\n (va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR11)\n (va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rR11)\n (va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64\n rR11) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_Pextrq (va_op_dst_opr64_reg64 rRcx)\n (va_op_xmm_xmm 0) 1) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRcx)\n (va_op_opr64_reg64 rR11)) (va_codegen_success_Pinsrq (va_op_xmm_xmm 0) (va_op_opr64_reg64 rRcx)\n 1)))))))))))))))))) (va_ttrue ()))", "val va_codegen_success_Compute_pad_to_128_bits : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Compute_pad_to_128_bits () =\n (va_pbool_and (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 8) (va_pbool_and\n (va_codegen_success_Sub (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 8))\n (va_pbool_and (va_codegen_success_Sl64Imm (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 10) 3)\n (va_pbool_and (va_codegen_success_Mfvsrd (va_op_reg_opr_reg 7) (va_op_vec_opr_vec 9))\n (va_pbool_and (va_codegen_success_Sr64 (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Sl64 (va_op_reg_opr_reg 7)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImm64\n (va_op_reg_opr_reg 10) 0) (va_pbool_and (va_codegen_success_Mtvsrdd (va_op_vec_opr_vec 9)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Mfvsrd\n (va_op_reg_opr_reg 7) (va_op_vec_opr_vec 9)) (va_pbool_and (va_codegen_success_LoadImm64\n (va_op_reg_opr_reg 10) 0) (va_pbool_and (va_codegen_success_Mtvsrdd (va_op_vec_opr_vec 9)\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImm64\n (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Sub (va_op_reg_opr_reg 10)\n (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 8)) (va_pbool_and (va_codegen_success_Sl64Imm\n (va_op_reg_opr_reg 10) (va_op_reg_opr_reg 10) 3) (va_pbool_and (va_codegen_success_Mfvsrld\n (va_op_reg_opr_reg 7) (va_op_vec_opr_vec 9)) (va_pbool_and (va_codegen_success_Sr64\n (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 10)) (va_pbool_and\n (va_codegen_success_Sl64 (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 10))\n (va_pbool_and (va_codegen_success_Mfvsrd (va_op_reg_opr_reg 10) (va_op_vec_opr_vec 9))\n (va_codegen_success_Mtvsrdd (va_op_vec_opr_vec 9) (va_op_reg_opr_reg 10) (va_op_reg_opr_reg\n 7)))))))))))))))))))) (va_ttrue ()))", "val va_codegen_success_ReduceMulRev128 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_ReduceMulRev128 () =\n (va_pbool_and (va_codegen_success_ClmulRev128 ()) (va_pbool_and (va_codegen_success_Vmr\n (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 2)) (va_pbool_and (va_codegen_success_Gf128ModulusRev\n (va_op_vec_opr_vec 2)) (va_pbool_and (va_codegen_success_ClmulRev128 ()) (va_pbool_and\n (va_codegen_success_Vmr (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 2)) (va_pbool_and\n (va_codegen_success_Gf128ModulusRev (va_op_vec_opr_vec 2)) (va_pbool_and\n (va_codegen_success_ClmulRev64High ()) (va_pbool_and (va_codegen_success_AddPoly\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 5)) (va_pbool_and\n (va_codegen_success_AddPoly (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6))\n (va_ttrue ()))))))))))", "val va_codegen_success_Gf128MulRev128 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Gf128MulRev128 () =\n (va_pbool_and (va_codegen_success_ReduceMulRev128 ()) (va_ttrue ()))", "val va_codegen_success_ReduceMul128_LE : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_ReduceMul128_LE () =\n (va_pbool_and (va_codegen_success_Pshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 8)) (va_pbool_and\n (va_codegen_success_ReduceMulRev128 ()) (va_pbool_and (va_codegen_success_Pshufb (va_op_xmm_xmm\n 1) (va_op_xmm_xmm 8)) (va_ttrue ()))))", "val va_code_ShiftLeft2_128_1 : va_dummy:unit -> Tot va_code\nlet va_code_ShiftLeft2_128_1 () =\n (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_LoadImm64\n (va_op_reg_opr_reg 10) 31) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 3) (va_op_reg_opr_reg\n 10)) (va_CCons (va_code_Vsrw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3))\n (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 3) 4)\n (va_CCons (va_code_Vspltisb (va_op_vec_opr_vec 0) 1) (va_CCons (va_code_Vsl (va_op_vec_opr_vec\n 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 0)) (va_CCons (va_code_Vsl (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 0)) (va_CCons (va_code_Vxor (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 3)) (va_CNil ())))))))))))", "val va_codegen_success_Clmul128 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Clmul128 () =\n (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 0) 0) (va_pbool_and\n (va_codegen_success_VSwap (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and\n (va_codegen_success_High64ToLow (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 3)) (va_pbool_and\n (va_codegen_success_Low64ToHigh (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 3)) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 2))\n (va_pbool_and (va_codegen_success_VPolyMulLow (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4)\n (va_op_vec_opr_vec 2)) (va_pbool_and (va_codegen_success_VPolyMulHigh (va_op_vec_opr_vec 5)\n (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 2)) (va_pbool_and (va_codegen_success_Low64ToHigh\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_High64ToLow\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_AddPoly\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 4)) (va_pbool_and\n (va_codegen_success_AddPoly (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 2))\n (va_ttrue ()))))))))))))", "val va_code_ShiftLeft128_1 : va_dummy:unit -> Tot va_code\nlet va_code_ShiftLeft128_1 () =\n (va_Block (va_CCons (va_code_Vspltisb (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_Vsl\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2)) (va_CNil ()))))", "val va_codegen_success_KeyExpansion128Stdcall : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_KeyExpansion128Stdcall () =\n (va_pbool_and (va_codegen_success_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 4) Secret) (va_pbool_and\n (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1)\n (va_op_reg_opr_reg 3) Secret) (va_pbool_and\n (va_codegen_success_KeyExpansionRoundUnrolledRecursive 10) (va_pbool_and\n (va_codegen_success_Vxor (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1))\n (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2)) (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 3)\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))", "val va_codegen_success_Xgetbv_Avx512 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Xgetbv_Avx512 () =\n (va_ttrue ())", "val va_codegen_success_MulAdd_unroll_1way : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_MulAdd_unroll_1way () =\n (va_pbool_and (va_codegen_success_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 7) Secret) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 0)) (va_pbool_and\n (va_codegen_success_VPolyMulLow (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec\n 7)) (va_pbool_and (va_codegen_success_VPolyMul (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_VPolyMulHigh (va_op_vec_opr_vec 4)\n (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 6)) (va_ttrue ()))))))", "val va_codegen_success_ClmulRev128 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_ClmulRev128 () =\n (va_pbool_and (va_codegen_success_Clmul128 ()) (va_pbool_and (va_codegen_success_ShiftLeft2_128_1\n ()) (va_ttrue ())))", "val va_codegen_success_Handle_ctr32_2 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Handle_ctr32_2 () =\n (va_pbool_and (va_codegen_success_VPshufb (va_op_xmm_xmm 6) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0))\n (va_pbool_and (va_codegen_success_Load_one_lsb (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_VPaddd (va_op_xmm_xmm 10) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5))\n (va_pbool_and (va_codegen_success_Load_two_lsb (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_VPaddd (va_op_xmm_xmm 11) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5))\n (va_pbool_and (va_codegen_success_VPaddd (va_op_xmm_xmm 12) (va_op_xmm_xmm 10) (va_op_xmm_xmm\n 5)) (va_pbool_and (va_codegen_success_VPshufb (va_op_xmm_xmm 10) (va_op_xmm_xmm 10)\n (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_VPaddd (va_op_xmm_xmm 13) (va_op_xmm_xmm\n 11) (va_op_xmm_xmm 5)) (va_pbool_and (va_codegen_success_VPshufb (va_op_xmm_xmm 11)\n (va_op_xmm_xmm 11) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_VPxor (va_op_xmm_xmm\n 10) (va_op_xmm_xmm 10) (va_op_opr128_xmm 4)) (va_pbool_and (va_codegen_success_VPaddd\n (va_op_xmm_xmm 14) (va_op_xmm_xmm 12) (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_VPshufb (va_op_xmm_xmm 12) (va_op_xmm_xmm 12) (va_op_xmm_xmm 0))\n (va_pbool_and (va_codegen_success_VPxor (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_opr128_xmm\n 4)) (va_pbool_and (va_codegen_success_VPaddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 13)\n (va_op_xmm_xmm 5)) (va_pbool_and (va_codegen_success_VPshufb (va_op_xmm_xmm 13) (va_op_xmm_xmm\n 13) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_VPxor (va_op_xmm_xmm 12)\n (va_op_xmm_xmm 12) (va_op_opr128_xmm 4)) (va_pbool_and (va_codegen_success_VPshufb\n (va_op_xmm_xmm 14) (va_op_xmm_xmm 14) (va_op_xmm_xmm 0)) (va_pbool_and\n (va_codegen_success_VPxor (va_op_xmm_xmm 13) (va_op_xmm_xmm 13) (va_op_opr128_xmm 4))\n (va_pbool_and (va_codegen_success_VPshufb (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) (va_op_xmm_xmm\n 0)) (va_pbool_and (va_codegen_success_VPxor (va_op_xmm_xmm 14) (va_op_xmm_xmm 14)\n (va_op_opr128_xmm 4)) (va_ttrue ())))))))))))))))))))))", "val va_codegen_success_Cswap2 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Cswap2 () =\n (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Comment\n \"Transfer bit into CF flag\"\n ) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRdi) (va_const_opr64\n 18446744073709551615)) (va_pbool_and (va_codegen_success_Newline ()) (va_pbool_and\n (va_codegen_success_Comment\n \"cswap p1[0], p2[0]\"\n ) (va_pbool_and (va_codegen_success_Cswap_single 0) (va_pbool_and (va_codegen_success_Newline\n ()) (va_pbool_and (va_codegen_success_Comment\n \"cswap p1[1], p2[1]\"\n ) (va_pbool_and (va_codegen_success_Cswap_single 1) (va_pbool_and (va_codegen_success_Newline\n ()) (va_pbool_and (va_codegen_success_Comment\n \"cswap p1[2], p2[2]\"\n ) (va_pbool_and (va_codegen_success_Cswap_single 2) (va_pbool_and (va_codegen_success_Newline\n ()) (va_pbool_and (va_codegen_success_Comment\n \"cswap p1[3], p2[3]\"\n ) (va_pbool_and (va_codegen_success_Cswap_single 3) (va_pbool_and (va_codegen_success_Newline\n ()) (va_pbool_and (va_codegen_success_Comment\n \"cswap p1[4], p2[4]\"\n ) (va_pbool_and (va_codegen_success_Cswap_single 4) (va_pbool_and (va_codegen_success_Newline\n ()) (va_pbool_and (va_codegen_success_Comment\n \"cswap p1[5], p2[5]\"\n ) (va_pbool_and (va_codegen_success_Cswap_single 5) (va_pbool_and (va_codegen_success_Newline\n ()) (va_pbool_and (va_codegen_success_Comment\n \"cswap p1[6], p2[6]\"\n ) (va_pbool_and (va_codegen_success_Cswap_single 6) (va_pbool_and (va_codegen_success_Newline\n ()) (va_pbool_and (va_codegen_success_Comment\n \"cswap p1[7], p2[7]\"\n ) (va_pbool_and (va_codegen_success_Cswap_single 7) (va_pbool_and\n (va_codegen_success_DestroyHeaplets ()) (va_ttrue ())))))))))))))))))))))))))))))", "val va_codegen_success_MulAdd_unroll_2way : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_MulAdd_unroll_2way () =\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0)\n (va_op_reg_opr_reg 7) Secret) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index\n (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 8) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg\n 10) Secret) (va_pbool_and (va_codegen_success_VPolyMulLow (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 8) (va_op_vec_opr_vec 7)) (va_pbool_and (va_codegen_success_VPolyMul\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 8) (va_op_vec_opr_vec 5)) (va_pbool_and\n (va_codegen_success_VPolyMulHigh (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 8) (va_op_vec_opr_vec\n 6)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 0)) (va_pbool_and (va_codegen_success_VPolyMulLow (va_op_vec_opr_vec 9)\n (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 14)) (va_pbool_and (va_codegen_success_VPolyMul\n (va_op_vec_opr_vec 10) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 12)) (va_pbool_and\n (va_codegen_success_VPolyMulHigh (va_op_vec_opr_vec 11) (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 13)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 9)) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 10)) (va_pbool_and\n (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec\n 11)) (va_ttrue ()))))))))))))))", "val va_codegen_success_Loop_rounds_52_64 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_rounds_52_64 () =\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRcx) (16 `op_Multiply` 13) Secret) (va_pbool_and\n (va_codegen_success_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 3)) (va_pbool_and\n (va_codegen_success_SHA256_msg2 (va_op_xmm_xmm 4) (va_op_xmm_xmm 3)) (va_pbool_and\n (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 4)) (va_pbool_and\n (va_codegen_success_Palignr4 (va_op_xmm_xmm 7) (va_op_xmm_xmm 3)) (va_pbool_and\n (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_pbool_and\n (va_codegen_success_Paddd (va_op_xmm_xmm 5) (va_op_xmm_xmm 7)) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRcx) (16 `op_Multiply` 14) Secret) (va_pbool_and\n (va_codegen_success_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 4)) (va_pbool_and\n (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_pbool_and\n (va_codegen_success_SHA256_msg2 (va_op_xmm_xmm 5) (va_op_xmm_xmm 4)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 8)) (va_pbool_and\n (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRcx) (16 `op_Multiply` 15) Secret) (va_pbool_and\n (va_codegen_success_Paddd (va_op_xmm_xmm 0) (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0) 14) (va_pbool_and\n (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and\n (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_pbool_and\n (va_codegen_success_Paddd (va_op_xmm_xmm 2) (va_op_xmm_xmm 10)) (va_pbool_and\n (va_codegen_success_Paddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 9)) (va_ttrue\n ())))))))))))))))))))))))))", "val va_codegen_success_Fmul1 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fmul1 () =\n (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Fast_mul1\n 0) (va_pbool_and (va_codegen_success_LargeComment\n \"Wrap the result back into the field\"\n ) (va_pbool_and (va_codegen_success_Comment\n \"Step 1: Compute carry*38\"\n ) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 38))\n (va_pbool_and (va_codegen_success_Carry_pass false 0) (va_pbool_and\n (va_codegen_success_DestroyHeaplets ()) (va_ttrue ()))))))))", "val va_codegen_success_Sha_update : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Sha_update () =\n (va_pbool_and (va_codegen_success_Preamble ()) (va_pbool_and (va_codegen_success_Loop ())\n (va_pbool_and (va_codegen_success_Epilogue ()) (va_ttrue ()))))", "val va_codegen_success_Sha_update : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Sha_update () =\n (va_pbool_and (va_codegen_success_Preamble ()) (va_pbool_and (va_codegen_success_Loop ())\n (va_pbool_and (va_codegen_success_Epilogue ()) (va_ttrue ()))))", "val va_codegen_success_Loop_rounds_16_51 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_rounds_16_51 () =\n (va_pbool_and (va_codegen_success_Loop_rounds_16_51_recursive 12) (va_ttrue ()))", "val va_codegen_success_Xgetbv_Avx : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Xgetbv_Avx () =\n (va_ttrue ())", "val va_codegen_success_Fmul2 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fmul2 () =\n (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and\n (va_codegen_success_LargeComment\n \"Compute the raw multiplication tmp[0] <- f1[0] * f2[0]\"\n ) (va_pbool_and (va_codegen_success_Fast_multiply 0) (va_pbool_and\n (va_codegen_success_LargeComment\n \"Compute the raw multiplication tmp[1] <- f1[1] * f2[1]\"\n ) (va_pbool_and (va_codegen_success_Fast_multiply 4) (va_pbool_and (va_codegen_success_Newline\n ()) (va_pbool_and (va_codegen_success_Comment\n \"Line up pointers\"\n ) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64\n rRdi)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64\n rR15)) (va_pbool_and (va_codegen_success_LargeComment\n \"Wrap the results back into the field\"\n ) (va_pbool_and (va_codegen_success_Carry_wide 0) (va_pbool_and (va_codegen_success_Newline ())\n (va_pbool_and (va_codegen_success_Carry_wide 4) (va_pbool_and\n (va_codegen_success_DestroyHeaplets ()) (va_ttrue ())))))))))))))))", "val va_codegen_success_InnerMemcpy : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_InnerMemcpy () =\n (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdx) 0 Secret) (va_pbool_and\n (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)\n (va_op_reg_opr64_reg64 rRdx) 8 Secret) (va_pbool_and (va_codegen_success_Store64_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_reg_opr64_reg64 rRax) 0\n Secret) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)\n (va_op_reg_opr64_reg64 rRcx) (va_op_reg_opr64_reg64 rR9) 8 Secret) (va_ttrue ())))))", "val va_codegen_success_Store_3blocks128_1 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Store_3blocks128_1 () =\n (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 7) Secret) (va_pbool_and\n (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 27) Secret) (va_pbool_and\n (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 2) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 28) Secret) (va_ttrue ()))))", "val va_codegen_success_KeyExpansion256Stdcall : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_KeyExpansion256Stdcall () =\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 1)\n (va_op_reg_opr_reg 4) Secret) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index\n (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg\n 10) Secret) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet\n 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and\n (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and\n (va_codegen_success_KeyExpansionRoundUnrolledRecursive256 14) (va_pbool_and\n (va_codegen_success_Vxor (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1))\n (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2)) (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 3)\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_Vxor\n (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4)) (va_ttrue ())))))))))))", "val va_codegen_success_Store_3blocks128_2 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Store_3blocks128_2 () =\n (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 3) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 29) Secret) (va_pbool_and\n (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 30) Secret) (va_pbool_and\n (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 7) (va_op_reg_opr_reg 31) Secret) (va_ttrue ()))))", "val va_codegen_success_Loop : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop () =\n (va_pbool_and (va_codegen_success_Loop_while0 ()) (va_ttrue ()))", "val va_codegen_success_Loop : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop () =\n (va_pbool_and (va_codegen_success_Loop_while0 ()) (va_ttrue ()))", "val va_codegen_success_Loop_rounds_48_63 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_rounds_48_63 () =\n (va_pbool_and (va_codegen_success_Loop_rounds_16_59_a 48) (va_pbool_and\n (va_codegen_success_Loop_rounds_0_59_a 48) (va_pbool_and\n (va_codegen_success_Loop_rounds_16_59_b 52) (va_pbool_and\n (va_codegen_success_Loop_rounds_0_59_b 52) (va_pbool_and\n (va_codegen_success_Loop_rounds_16_59_c 56) (va_pbool_and\n (va_codegen_success_Loop_rounds_0_59_c 56) (va_pbool_and\n (va_codegen_success_Loop_rounds_60_63_a ()) (va_pbool_and\n (va_codegen_success_Loop_rounds_60_63_b ()) (va_ttrue ())))))))))", "val va_codegen_success_Aes_2rounds_4way : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Aes_2rounds_4way () =\n (va_pbool_and (va_codegen_success_Aes_round_4way (va_op_xmm_xmm 3)) (va_pbool_and\n (va_codegen_success_Aes_round_4way (va_op_xmm_xmm 4)) (va_ttrue ())))", "val va_codegen_success_Handle_ctr32 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Handle_ctr32 () =\n (va_pbool_and (va_codegen_success_InitPshufbMask (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rR11))\n (va_pbool_and (va_codegen_success_VPshufb (va_op_xmm_xmm 6) (va_op_xmm_xmm 1) (va_op_xmm_xmm\n 0)) (va_pbool_and (va_codegen_success_Load_one_lsb (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_VPaddd (va_op_xmm_xmm 10) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5))\n (va_pbool_and (va_codegen_success_Load_two_lsb (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_VPaddd (va_op_xmm_xmm 11) (va_op_xmm_xmm 6) (va_op_xmm_xmm 5))\n (va_pbool_and (va_codegen_success_VPaddd (va_op_xmm_xmm 12) (va_op_xmm_xmm 10) (va_op_xmm_xmm\n 5)) (va_pbool_and (va_codegen_success_VPshufb (va_op_xmm_xmm 10) (va_op_xmm_xmm 10)\n (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_VPaddd (va_op_xmm_xmm 13) (va_op_xmm_xmm\n 11) (va_op_xmm_xmm 5)) (va_pbool_and (va_codegen_success_VPshufb (va_op_xmm_xmm 11)\n (va_op_xmm_xmm 11) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_VPxor (va_op_xmm_xmm\n 10) (va_op_xmm_xmm 10) (va_op_opr128_xmm 15)) (va_pbool_and (va_codegen_success_VPaddd\n (va_op_xmm_xmm 14) (va_op_xmm_xmm 12) (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_VPshufb (va_op_xmm_xmm 12) (va_op_xmm_xmm 12) (va_op_xmm_xmm 0))\n (va_pbool_and (va_codegen_success_VPxor (va_op_xmm_xmm 11) (va_op_xmm_xmm 11) (va_op_opr128_xmm\n 15)) (va_pbool_and (va_codegen_success_VPaddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 13)\n (va_op_xmm_xmm 5)) (va_pbool_and (va_codegen_success_VPshufb (va_op_xmm_xmm 13) (va_op_xmm_xmm\n 13) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_VPshufb (va_op_xmm_xmm 14)\n (va_op_xmm_xmm 14) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_VPshufb (va_op_xmm_xmm\n 1) (va_op_xmm_xmm 1) (va_op_xmm_xmm 0)) (va_ttrue ())))))))))))))))))))", "val va_codegen_success_Fmul : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fmul () =\n (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and\n (va_codegen_success_LargeComment\n \"Compute the raw multiplication: tmp <- src1 * src2\"\n ) (va_pbool_and (va_codegen_success_Fast_multiply 0) (va_pbool_and (va_codegen_success_Newline\n ()) (va_pbool_and (va_codegen_success_Comment\n \"Line up pointers\"\n ) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64\n rRdi)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64\n rR15)) (va_pbool_and (va_codegen_success_LargeComment\n \"Wrap the result back into the field\"\n ) (va_pbool_and (va_codegen_success_Carry_wide 0) (va_pbool_and\n (va_codegen_success_DestroyHeaplets ()) (va_ttrue ())))))))))))", "val va_codegen_success_Fast_mul1 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fast_mul1 () =\n (va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Mulx64\n (va_op_dst_opr64_reg64 rR9) (va_op_dst_opr64_reg64 rR8) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Secret)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR8) 0 Secret) (va_pbool_and (va_codegen_success_Xor64\n (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR8)) (va_pbool_and\n (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Mulx64\n (va_op_dst_opr64_reg64 rR11) (va_op_dst_opr64_reg64 rR10) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Secret)) (va_pbool_and\n (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rR9))\n (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR10) 8 Secret) (va_pbool_and\n (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Mulx64\n (va_op_dst_opr64_reg64 rR13) (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 16 Secret)) (va_pbool_and\n (va_codegen_success_Adcx64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR11))\n (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 16 Secret) (va_pbool_and\n (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Mulx64\n (va_op_dst_opr64_reg64 rRax) (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 24 Secret)) (va_pbool_and\n (va_codegen_success_Adcx64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR13))\n (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 24 Secret) (va_pbool_and\n (va_codegen_success_Adcx64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR8)) (va_ttrue\n ()))))))))))))))))))", "val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Gf128_powers () =\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 6)) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_xmm_xmm 1)\n (va_op_reg_opr64_reg64 rRcx) 32 Secret) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm\n 6) (va_op_xmm_xmm 1)) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm\n 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and\n (va_codegen_success_Store128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx)\n (va_op_xmm_xmm 1) 0 Secret) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 1)\n (va_op_xmm_xmm 6)) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm\n 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_xmm_xmm 1) 16 Secret)\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 6)) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_xmm_xmm 1)\n (va_op_reg_opr64_reg64 rRcx) 32 Secret) (va_pbool_and (va_codegen_success_Gf128MulRev128 ())\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_xmm_xmm 1) 48 Secret)\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 6)) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_xmm_xmm 1)\n (va_op_reg_opr64_reg64 rRcx) 32 Secret) (va_pbool_and (va_codegen_success_Gf128MulRev128 ())\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_xmm_xmm 1) 64 Secret)\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 6)) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_xmm_xmm 1)\n (va_op_reg_opr64_reg64 rRcx) 32 Secret) (va_pbool_and (va_codegen_success_Gf128MulRev128 ())\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_xmm_xmm 1) 96 Secret)\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 6)) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 1) (va_op_xmm_xmm 1)\n (va_op_reg_opr64_reg64 rRcx) 32 Secret) (va_pbool_and (va_codegen_success_Gf128MulRev128 ())\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRcx) (va_op_xmm_xmm 1) 112 Secret)\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 6) (va_op_xmm_xmm 0)) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRax)) (va_ttrue\n ())))))))))))))))))))))))))))))))))))))))))))))", "val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Gf128_powers () =\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1)\n (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and\n (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and\n (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and\n (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and\n (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1)\n (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and\n (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and\n (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64\n (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index\n (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg\n 10) Secret) (va_ttrue ()))))))))))))))", "val va_codegen_success_Aes_ctr_ghash : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Aes_ctr_ghash () =\n (va_pbool_and (va_codegen_success_Compute_ghash_incremental_register ()) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 12)) (va_pbool_and\n (va_codegen_success_Compute_ghash_incremental_register ()) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 13)) (va_pbool_and\n (va_codegen_success_Compute_ghash_incremental_register ()) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 14)) (va_pbool_and\n (va_codegen_success_Compute_ghash_incremental_register ()) (va_ttrue ()))))))))", "val va_codegen_success_Check_avx512_xcr0_support : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Check_avx512_xcr0_support () =\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0))\n (va_pbool_and (va_codegen_success_Xgetbv_Avx512 ()) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRax) (va_const_opr64 32)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 64)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 128)) (va_pbool_and (va_codegen_success_Shr64\n (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Shr64\n (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 1)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_ttrue ()))))))))))))", "val va_codegen_success_MulAdd_unroll : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_MulAdd_unroll () =\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 3)\n (va_op_reg_opr64_reg64 rR9) (-32) Secret) (va_pbool_and (va_codegen_success_VPolyMul\n (va_op_xmm_xmm 1) (va_op_xmm_xmm 7) (va_op_xmm_xmm 3) false false) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_xmm_xmm 5) (va_op_xmm_xmm 7) (va_op_xmm_xmm 3) false true)\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm\n 0) (va_op_reg_opr64_reg64 rRbp) 48 Secret) (va_pbool_and (va_codegen_success_VPolyMul\n (va_op_xmm_xmm 6) (va_op_xmm_xmm 7) (va_op_xmm_xmm 3) true false) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_xmm_xmm 7) (va_op_xmm_xmm 7) (va_op_xmm_xmm 3) true true)\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm\n 3) (va_op_reg_opr64_reg64 rR9) (-16) Secret) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 6) (va_op_xmm_xmm 6) (va_op_opr128_xmm 5)) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_xmm_xmm 5) (va_op_xmm_xmm 0) (va_op_xmm_xmm 3) false false)\n (va_pbool_and (va_codegen_success_VPolyAdd (va_op_xmm_xmm 8) (va_op_xmm_xmm 8)\n (va_op_opr128_xmm 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_xmm_xmm 4)\n (va_op_xmm_xmm 1) (va_op_opr128_xmm 5)) (va_pbool_and (va_codegen_success_VPolyMul\n (va_op_xmm_xmm 1) (va_op_xmm_xmm 0) (va_op_xmm_xmm 3) false true) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_xmm_xmm 2) (va_op_xmm_xmm 0) (va_op_xmm_xmm 3) true false)\n (va_pbool_and (va_codegen_success_Mem128_lemma ()) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 8) (va_op_xmm_xmm 8) (va_opr_code_Mem128 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg64_reg64 rRbp) 16 Secret)) (va_pbool_and (va_codegen_success_VPolyMul (va_op_xmm_xmm\n 3) (va_op_xmm_xmm 0) (va_op_xmm_xmm 3) true true) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRbp) 64 Secret) (va_pbool_and (va_codegen_success_Load128_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 5) (va_op_reg_opr64_reg64 rR9) 16 Secret)\n (va_pbool_and (va_codegen_success_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)\n (va_op_opr128_xmm 1)) (va_pbool_and (va_codegen_success_VPolyMul (va_op_xmm_xmm 1)\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) false false) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 6) (va_op_xmm_xmm 6) (va_op_opr128_xmm 2)) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_xmm_xmm 2) (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) false true)\n (va_pbool_and (va_codegen_success_VPolyAdd (va_op_xmm_xmm 7) (va_op_xmm_xmm 7)\n (va_op_opr128_xmm 3)) (va_pbool_and (va_codegen_success_VPolyMul (va_op_xmm_xmm 3)\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) true false) (va_pbool_and (va_codegen_success_VPolyMul\n (va_op_xmm_xmm 5) (va_op_xmm_xmm 0) (va_op_xmm_xmm 5) true true) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRbp) 80 Secret) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 4) (va_op_xmm_xmm 4) (va_op_opr128_xmm 1)) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 1)\n (va_op_reg_opr64_reg64 rR9) 32 Secret) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 6) (va_op_xmm_xmm 6) (va_op_opr128_xmm 2)) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_xmm_xmm 2) (va_op_xmm_xmm 0) (va_op_xmm_xmm 1) false false)\n (va_pbool_and (va_codegen_success_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)\n (va_op_opr128_xmm 3)) (va_pbool_and (va_codegen_success_VPolyMul (va_op_xmm_xmm 3)\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 1) false true) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 7) (va_op_xmm_xmm 7) (va_op_opr128_xmm 5)) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_xmm_xmm 5) (va_op_xmm_xmm 0) (va_op_xmm_xmm 1) true false)\n (va_pbool_and (va_codegen_success_VPolyMul (va_op_xmm_xmm 1) (va_op_xmm_xmm 0) (va_op_xmm_xmm\n 1) true true) (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 3)\n (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rRbp) 96 Secret) (va_pbool_and\n (va_codegen_success_VPolyAdd (va_op_xmm_xmm 4) (va_op_xmm_xmm 4) (va_op_opr128_xmm 2))\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm\n 2) (va_op_reg_opr64_reg64 rR9) 64 Secret) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 6) (va_op_xmm_xmm 6) (va_op_opr128_xmm 3)) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_xmm_xmm 3) (va_op_xmm_xmm 0) (va_op_xmm_xmm 2) false false)\n (va_pbool_and (va_codegen_success_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)\n (va_op_opr128_xmm 5)) (va_pbool_and (va_codegen_success_VPolyMul (va_op_xmm_xmm 5)\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 2) false true) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 7) (va_op_xmm_xmm 7) (va_op_opr128_xmm 1)) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_xmm_xmm 1) (va_op_xmm_xmm 0) (va_op_xmm_xmm 2) true false)\n (va_pbool_and (va_codegen_success_Mem128_lemma ()) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 8) (va_op_xmm_xmm 8) (va_opr_code_Mem128 (va_op_heaplet_mem_heaplet 3)\n (va_op_reg64_reg64 rRbp) 112 Secret)) (va_pbool_and (va_codegen_success_VPolyMul (va_op_xmm_xmm\n 2) (va_op_xmm_xmm 0) (va_op_xmm_xmm 2) true true) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 4) (va_op_xmm_xmm 4) (va_op_opr128_xmm 3)) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 3)\n (va_op_reg_opr64_reg64 rR9) 80 Secret) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 6) (va_op_xmm_xmm 6) (va_op_opr128_xmm 5)) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_xmm_xmm 5) (va_op_xmm_xmm 8) (va_op_xmm_xmm 3) false true)\n (va_pbool_and (va_codegen_success_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)\n (va_op_opr128_xmm 1)) (va_pbool_and (va_codegen_success_VPolyMul (va_op_xmm_xmm 1)\n (va_op_xmm_xmm 8) (va_op_xmm_xmm 3) true false) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 7) (va_op_xmm_xmm 7) (va_op_opr128_xmm 2)) (va_pbool_and\n (va_codegen_success_VPolyMul (va_op_xmm_xmm 2) (va_op_xmm_xmm 8) (va_op_xmm_xmm 3) false false)\n (va_pbool_and (va_codegen_success_VPolyMul (va_op_xmm_xmm 8) (va_op_xmm_xmm 8) (va_op_xmm_xmm\n 3) true true) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_xmm_xmm 6) (va_op_xmm_xmm 6)\n (va_op_opr128_xmm 5)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_xmm_xmm 6)\n (va_op_xmm_xmm 6) (va_op_opr128_xmm 1)) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_xmm_xmm 4) (va_op_xmm_xmm 4) (va_op_opr128_xmm 2)) (va_pbool_and\n (va_codegen_success_ZeroXmm (va_op_xmm_xmm 3)) (va_pbool_and (va_codegen_success_PinsrdImm\n (va_op_xmm_xmm 3) 3254779904 3 (va_op_reg_opr64_reg64 rRax)) (va_pbool_and\n (va_codegen_success_VPolyAdd (va_op_xmm_xmm 7) (va_op_xmm_xmm 7) (va_op_opr128_xmm 8))\n (va_ttrue ())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))", "val va_codegen_success_Loop_rounds_1_3 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_rounds_1_3 () =\n (va_pbool_and (va_codegen_success_Loop_rounds_1_15_shift_body 1 (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 0)) (va_pbool_and (va_codegen_success_Loop_rounds_1_15_shift_body 2\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 0)) (va_pbool_and\n (va_codegen_success_Loop_rounds_1_15_shift_body 3 (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 0))\n (va_ttrue ()))))", "val va_codegen_success_Fadd : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fadd () =\n (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Comment\n \"Compute the raw addition of f1 + f2\"\n ) (va_pbool_and (va_codegen_success_Fast_add ()) (va_pbool_and (va_codegen_success_LargeComment\n \"Wrap the result back into the field\"\n ) (va_pbool_and (va_codegen_success_Carry_pass true 0) (va_pbool_and\n (va_codegen_success_DestroyHeaplets ()) (va_ttrue ())))))))", "val va_codegen_success_Aes_3rounds_4way : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Aes_3rounds_4way () =\n (va_pbool_and (va_codegen_success_Aes_round_4way (va_op_xmm_xmm 4)) (va_pbool_and\n (va_codegen_success_Aes_round_4way (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_Aes_round_4way (va_op_xmm_xmm 6)) (va_ttrue ()))))", "val va_codegen_success_Sha_update_bytes_main : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Sha_update_bytes_main () =\n (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and\n (va_codegen_success_Alloc_stack (16 `op_Multiply` 11)) (va_pbool_and\n (va_codegen_success_Store_stack128 (va_op_vec_opr_vec 20) (16 `op_Multiply` 0)) (va_pbool_and\n (va_codegen_success_Store_stack128 (va_op_vec_opr_vec 21) (16 `op_Multiply` 1)) (va_pbool_and\n (va_codegen_success_Store_stack128 (va_op_vec_opr_vec 22) (16 `op_Multiply` 2)) (va_pbool_and\n (va_codegen_success_Store_stack128 (va_op_vec_opr_vec 23) (16 `op_Multiply` 3)) (va_pbool_and\n (va_codegen_success_Store_stack128 (va_op_vec_opr_vec 24) (16 `op_Multiply` 4)) (va_pbool_and\n (va_codegen_success_Store_stack128 (va_op_vec_opr_vec 25) (16 `op_Multiply` 5)) (va_pbool_and\n (va_codegen_success_Store_stack128 (va_op_vec_opr_vec 26) (16 `op_Multiply` 6)) (va_pbool_and\n (va_codegen_success_Store_stack128 (va_op_vec_opr_vec 28) (16 `op_Multiply` 7)) (va_pbool_and\n (va_codegen_success_Store_stack128 (va_op_vec_opr_vec 29) (16 `op_Multiply` 8)) (va_pbool_and\n (va_codegen_success_Store_stack128 (va_op_vec_opr_vec 30) (16 `op_Multiply` 9)) (va_pbool_and\n (va_codegen_success_Store_stack128 (va_op_vec_opr_vec 31) (16 `op_Multiply` 10)) (va_pbool_and\n (va_codegen_success_Sha_update_bytes ()) (va_pbool_and (va_codegen_success_Load_stack128\n (va_op_vec_opr_vec 20) (16 `op_Multiply` 0)) (va_pbool_and (va_codegen_success_Load_stack128\n (va_op_vec_opr_vec 21) (16 `op_Multiply` 1)) (va_pbool_and (va_codegen_success_Load_stack128\n (va_op_vec_opr_vec 22) (16 `op_Multiply` 2)) (va_pbool_and (va_codegen_success_Load_stack128\n (va_op_vec_opr_vec 23) (16 `op_Multiply` 3)) (va_pbool_and (va_codegen_success_Load_stack128\n (va_op_vec_opr_vec 24) (16 `op_Multiply` 4)) (va_pbool_and (va_codegen_success_Load_stack128\n (va_op_vec_opr_vec 25) (16 `op_Multiply` 5)) (va_pbool_and (va_codegen_success_Load_stack128\n (va_op_vec_opr_vec 26) (16 `op_Multiply` 6)) (va_pbool_and (va_codegen_success_Load_stack128\n (va_op_vec_opr_vec 28) (16 `op_Multiply` 7)) (va_pbool_and (va_codegen_success_Load_stack128\n (va_op_vec_opr_vec 29) (16 `op_Multiply` 8)) (va_pbool_and (va_codegen_success_Load_stack128\n (va_op_vec_opr_vec 30) (16 `op_Multiply` 9)) (va_pbool_and (va_codegen_success_Load_stack128\n (va_op_vec_opr_vec 31) (16 `op_Multiply` 10)) (va_pbool_and (va_codegen_success_Dealloc_stack\n (16 `op_Multiply` 11)) (va_pbool_and (va_codegen_success_DestroyHeaplets ()) (va_ttrue\n ()))))))))))))))))))))))))))))", "val va_codegen_success_Loop_body0 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_body0 () =\n (va_pbool_and (va_codegen_success_Loop_rounds ()) (va_ttrue ()))", "val va_codegen_success_Loop_body0 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_body0 () =\n (va_pbool_and (va_codegen_success_Mod_cr0 ()) (va_pbool_and (va_codegen_success_Loop_rounds ())\n (va_pbool_and (va_codegen_success_SubImm (va_op_reg_opr_reg 5) (va_op_reg_opr_reg 5) 1)\n (va_ttrue ()))))", "val va_codegen_success_Check_avx512_support : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Check_avx512_support () =\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 7))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0))\n (va_pbool_and (va_codegen_success_Cpuid_Avx512 ()) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 65536)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRax) (va_const_opr64 131072)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rR10) (va_const_opr64 1073741824)) (va_pbool_and\n (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 1)) (va_pbool_and\n (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 14)) (va_pbool_and\n (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 2147483648))\n (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRbx))\n (va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR11) (va_const_shift_amt64 15))\n (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))\n (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))\n (va_ttrue ()))))))))))))))))))))", "val va_codegen_success_Aes_4rounds_4way : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Aes_4rounds_4way () =\n (va_pbool_and (va_codegen_success_Aes_round_4way (va_op_xmm_xmm 3)) (va_pbool_and\n (va_codegen_success_Aes_round_4way (va_op_xmm_xmm 4)) (va_pbool_and\n (va_codegen_success_Aes_round_4way (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_Aes_round_4way (va_op_xmm_xmm 6)) (va_ttrue ())))))", "val va_codegen_success_Init_ctr : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Init_ctr () =\n (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm 4) (va_op_xmm_xmm 4)) (va_pbool_and\n (va_codegen_success_PinsrdImm (va_op_xmm_xmm 4) 1 0 (va_op_reg_opr64_reg64 rR12)) (va_ttrue\n ())))", "val va_codegen_success_Fast_add1 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fast_add1 () =\n (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Comment\n \"Clear registers to propagate the carry bit\"\n ) (va_pbool_and (va_codegen_success_Xor64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR8))\n (va_pbool_and (va_codegen_success_Xor64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rR9))\n (va_pbool_and (va_codegen_success_Xor64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rR10))\n (va_pbool_and (va_codegen_success_Xor64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rR11))\n (va_pbool_and (va_codegen_success_Xor64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRax))\n (va_pbool_and (va_codegen_success_Newline ()) (va_pbool_and (va_codegen_success_Comment\n \"Begin addition chain\"\n ) (va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap\n (va_op_dst_opr64_reg64 rRdx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)\n (va_op_reg64_reg64 rRsi) 0 Secret)) (va_pbool_and (va_codegen_success_Store64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 0\n Secret) (va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and\n (va_codegen_success_Adcx64Wrap (va_op_dst_opr64_reg64 rR8) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Secret)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR8) 8 Secret) (va_pbool_and (va_codegen_success_Mem64_lemma ())\n (va_pbool_and (va_codegen_success_Adcx64Wrap (va_op_dst_opr64_reg64 rR9) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 16 Secret)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR9) 16 Secret) (va_pbool_and (va_codegen_success_Mem64_lemma ())\n (va_pbool_and (va_codegen_success_Adcx64Wrap (va_op_dst_opr64_reg64 rR10) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 24 Secret)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR10) 24 Secret) (va_pbool_and (va_codegen_success_Newline ())\n (va_pbool_and (va_codegen_success_Comment\n \"Return the carry bit in a register\"\n ) (va_pbool_and (va_codegen_success_Adcx64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64\n rR11)) (va_pbool_and (va_codegen_success_DestroyHeaplets ()) (va_ttrue\n ()))))))))))))))))))))))))))", "val va_codegen_success_Fast_sub1 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fast_sub1 () =\n (va_pbool_and (va_codegen_success_Xor64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRax))\n (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0 Secret) (va_pbool_and\n (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx))\n (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR8) 0 Secret) (va_pbool_and\n (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)\n (va_op_reg_opr64_reg64 rRsi) 8 Secret) (va_pbool_and (va_codegen_success_Sbb64\n (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR9) 8 Secret) (va_pbool_and (va_codegen_success_Load64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR10) (va_op_reg_opr64_reg64 rRsi) 16\n Secret) (va_pbool_and (va_codegen_success_Sbb64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64\n 0)) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR10) 16 Secret) (va_pbool_and\n (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR11)\n (va_op_reg_opr64_reg64 rRsi) 24 Secret) (va_pbool_and (va_codegen_success_Sbb64\n (va_op_dst_opr64_reg64 rR11) (va_const_opr64 0)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR11) 24 Secret) (va_pbool_and (va_codegen_success_Adc64Wrap\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRax)) (va_ttrue ())))))))))))))))", "val va_codegen_success_AES128EncryptBlock : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_AES128EncryptBlock () =\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 2)\n (va_op_reg_opr64_reg64 rR8) 0 Secret) (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 2)) (va_pbool_and (va_codegen_success_AES128EncryptRound 1) (va_pbool_and\n (va_codegen_success_AES128EncryptRound 2) (va_pbool_and (va_codegen_success_AES128EncryptRound\n 3) (va_pbool_and (va_codegen_success_AES128EncryptRound 4) (va_pbool_and\n (va_codegen_success_AES128EncryptRound 5) (va_pbool_and (va_codegen_success_AES128EncryptRound\n 6) (va_pbool_and (va_codegen_success_AES128EncryptRound 7) (va_pbool_and\n (va_codegen_success_AES128EncryptRound 8) (va_pbool_and (va_codegen_success_AES128EncryptRound\n 9) (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_xmm_xmm 2) (va_op_reg_opr64_reg64 rR8) (16 `op_Multiply` 10) Secret) (va_pbool_and\n (va_codegen_success_AESNI_enc_last (va_op_xmm_xmm 0) (va_op_xmm_xmm 2)) (va_pbool_and\n (va_codegen_success_Pxor (va_op_xmm_xmm 2) (va_op_xmm_xmm 2)) (va_ttrue ())))))))))))))))", "val va_codegen_success_AES128EncryptBlock : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_AES128EncryptBlock () =\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 0) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 2) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 10) Secret) (va_pbool_and\n (va_codegen_success_Vxor (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 2))\n (va_pbool_and (va_codegen_success_AES128EncryptRound 1) (va_pbool_and\n (va_codegen_success_AES128EncryptRound 2) (va_pbool_and (va_codegen_success_AES128EncryptRound\n 3) (va_pbool_and (va_codegen_success_AES128EncryptRound 4) (va_pbool_and\n (va_codegen_success_AES128EncryptRound 5) (va_pbool_and (va_codegen_success_AES128EncryptRound\n 6) (va_pbool_and (va_codegen_success_AES128EncryptRound 7) (va_pbool_and\n (va_codegen_success_AES128EncryptRound 8) (va_pbool_and (va_codegen_success_AES128EncryptRound\n 9) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) (16 `op_Multiply` 10))\n (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 2) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 10) Secret) (va_pbool_and\n (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec\n 2)) (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2)) (va_ttrue ())))))))))))))))))", "val va_codegen_success_Check_avx_xcr0_support : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Check_avx_xcr0_support () =\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0))\n (va_pbool_and (va_codegen_success_Xgetbv_Avx ()) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRax) (va_const_opr64 4)) (va_pbool_and (va_codegen_success_Shr64\n (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 1)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 2)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_ttrue ()))))))))", "val va_codegen_success_Loop_rounds_0_15 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_rounds_0_15 () =\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 3)\n (va_op_reg_opr64_reg64 rRsi) 0 Secret) (va_pbool_and (va_codegen_success_Load128_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 4) (va_op_reg_opr64_reg64 rRsi) 16 Secret)\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm\n 5) (va_op_reg_opr64_reg64 rRsi) 32 Secret) (va_pbool_and (va_codegen_success_PshufbStable\n (va_op_xmm_xmm 3) (va_op_xmm_xmm 7)) (va_pbool_and (va_codegen_success_Load128_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 6) (va_op_reg_opr64_reg64 rRsi) 48 Secret)\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm\n 0) (va_op_reg_opr64_reg64 rRcx) 0 Secret) (va_pbool_and (va_codegen_success_Paddd\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 3)) (va_pbool_and (va_codegen_success_PshufbStable\n (va_op_xmm_xmm 4) (va_op_xmm_xmm 7)) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm\n 10) (va_op_xmm_xmm 2)) (va_pbool_and (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 1)) (va_pbool_and (va_codegen_success_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0)\n 14) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 9) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRcx) 16 Secret) (va_pbool_and (va_codegen_success_Paddd (va_op_xmm_xmm\n 0) (va_op_xmm_xmm 4)) (va_pbool_and (va_codegen_success_PshufbStable (va_op_xmm_xmm 5)\n (va_op_xmm_xmm 7)) (va_pbool_and (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 1)) (va_pbool_and (va_codegen_success_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0)\n 14) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRsi) (va_const_opr64 64))\n (va_pbool_and (va_codegen_success_SHA256_msg1 (va_op_xmm_xmm 3) (va_op_xmm_xmm 4))\n (va_pbool_and (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2))\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm\n 0) (va_op_reg_opr64_reg64 rRcx) 32 Secret) (va_pbool_and (va_codegen_success_Paddd\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 5)) (va_pbool_and (va_codegen_success_PshufbStable\n (va_op_xmm_xmm 6) (va_op_xmm_xmm 7)) (va_pbool_and (va_codegen_success_SHA256_rnds2\n (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_pbool_and (va_codegen_success_Pshufd (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 0) 14) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm\n 6)) (va_pbool_and (va_codegen_success_Palignr4 (va_op_xmm_xmm 7) (va_op_xmm_xmm 5))\n (va_pbool_and (va_codegen_success_Paddd (va_op_xmm_xmm 3) (va_op_xmm_xmm 7)) (va_pbool_and\n (va_codegen_success_SHA256_msg1 (va_op_xmm_xmm 4) (va_op_xmm_xmm 5)) (va_pbool_and\n (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRcx) 48 Secret) (va_pbool_and (va_codegen_success_Paddd (va_op_xmm_xmm\n 0) (va_op_xmm_xmm 6)) (va_pbool_and (va_codegen_success_SHA256_msg2 (va_op_xmm_xmm 3)\n (va_op_xmm_xmm 6)) (va_pbool_and (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 1)) (va_pbool_and (va_codegen_success_Pshufd (va_op_xmm_xmm 0) (va_op_xmm_xmm 0)\n 14) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 7) (va_op_xmm_xmm 3)) (va_pbool_and\n (va_codegen_success_Palignr4 (va_op_xmm_xmm 7) (va_op_xmm_xmm 6)) (va_pbool_and\n (va_codegen_success_Paddd (va_op_xmm_xmm 4) (va_op_xmm_xmm 7)) (va_pbool_and\n (va_codegen_success_SHA256_msg1 (va_op_xmm_xmm 5) (va_op_xmm_xmm 6)) (va_pbool_and\n (va_codegen_success_SHA256_rnds2 (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_ttrue\n ()))))))))))))))))))))))))))))))))))))))))))", "val va_codegen_success_Loop_rounds_0_15 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_rounds_0_15 () =\n (va_pbool_and (va_codegen_success_Loop_rounds_3_7_11_body 3 (va_op_vec_opr_vec 4)) (va_pbool_and\n (va_codegen_success_Loop_rounds_3_7_11_body 7 (va_op_vec_opr_vec 8)) (va_pbool_and\n (va_codegen_success_Loop_rounds_3_7_11_body 11 (va_op_vec_opr_vec 12)) (va_pbool_and\n (va_codegen_success_Loop_rounds_1_3 ()) (va_pbool_and (va_codegen_success_Loop_rounds_0_59_a 0)\n (va_pbool_and (va_codegen_success_Loop_rounds_5_7 ()) (va_pbool_and\n (va_codegen_success_Loop_rounds_0_59_b 4) (va_pbool_and (va_codegen_success_Loop_rounds_9_11\n ()) (va_pbool_and (va_codegen_success_Loop_rounds_0_59_c 8) (va_pbool_and\n (va_codegen_success_Loop_rounds_13_15 ()) (va_pbool_and (va_codegen_success_Loop_rounds_0_59_d\n 12) (va_pbool_and (va_codegen_success_Loop_rounds_16_63_body 16 (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 9) (va_op_vec_opr_vec 14)) (va_ttrue ())))))))))))))", "val va_codegen_success_Compute_iv_stdcall : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Compute_iv_stdcall () =\n (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Move\n (va_op_reg_opr_reg 9) (va_op_reg_opr_reg 8)) (va_pbool_and (va_codegen_success_Compute_iv ())\n (va_pbool_and (va_codegen_success_DestroyHeaplets ()) (va_ttrue ())))))", "val va_codegen_success_Sha_update_bytes : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Sha_update_bytes () =\n (va_pbool_and (va_codegen_success_Sha_update ()) (va_ttrue ()))", "val va_codegen_success_Sha_update_bytes : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Sha_update_bytes () =\n (va_pbool_and (va_codegen_success_Sha_update ()) (va_ttrue ()))", "val va_codegen_success_Loop_prologue : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_prologue () =\n (va_pbool_and (va_codegen_success_Load128_byte16_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 4) Secret) (va_pbool_and\n (va_codegen_success_Load128_word4_buffer (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 24)\n (va_op_reg_opr_reg 6) Secret) (va_pbool_and (va_codegen_success_AddImm (va_op_reg_opr_reg 4)\n (va_op_reg_opr_reg 4) 16) (va_pbool_and (va_codegen_success_AddImm (va_op_reg_opr_reg 6)\n (va_op_reg_opr_reg 6) 16) (va_pbool_and (va_codegen_success_Vadduwm (va_op_vec_opr_vec 23)\n (va_op_vec_opr_vec 23) (va_op_vec_opr_vec 24)) (va_pbool_and (va_codegen_success_Vsldoi\n (va_op_vec_opr_vec 24) (va_op_vec_opr_vec 24) (va_op_vec_opr_vec 24) 4) (va_ttrue ())))))))", "val va_codegen_success_Load_one_msb : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Load_one_msb () =\n (va_pbool_and (va_codegen_success_ZeroXmm (va_op_xmm_xmm 2)) (va_pbool_and\n (va_codegen_success_PinsrqImm (va_op_xmm_xmm 2) 72057594037927936 1 (va_op_reg_opr64_reg64\n rR11)) (va_ttrue ())))", "val va_codegen_success_Check_avx_support : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Check_avx_support () =\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))\n (va_pbool_and (va_codegen_success_Cpuid_Avx ()) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRax) (va_const_opr64 268435456)) (va_pbool_and\n (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRax) (va_const_shift_amt64 27)) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_ttrue\n ())))))))))", "val va_codegen_success_ClmulRev64High : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_ClmulRev64High () =\n (va_pbool_and (va_codegen_success_VPolyMulHigh (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 2)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_ttrue ())))", "val va_codegen_success_Cpuid_Sha : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Cpuid_Sha () =\n (va_ttrue ())", "val va_codegen_success_Nat64Equal : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Nat64Equal () =\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 5) 1) (va_pbool_and\n (va_codegen_success_AddCarry (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 5))\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 3) 0) (va_pbool_and\n (va_codegen_success_AddExtended (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg\n 3)) (va_pbool_and (va_codegen_success_Xor (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 5)\n (va_op_reg_opr_reg 3)) (va_ttrue ()))))))", "val va_codegen_success_Check_avx2_support : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Check_avx2_support () =\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 7))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0))\n (va_pbool_and (va_codegen_success_Cpuid_Avx2 ()) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 32)) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_ttrue ()))))))))", "val va_codegen_success_load_one_msb : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_load_one_msb () =\n (va_pbool_and (va_codegen_success_ZeroXmm (va_op_xmm_xmm 2)) (va_pbool_and\n (va_codegen_success_PinsrqImm (va_op_xmm_xmm 2) 72057594037927936 1 (va_op_reg_opr64_reg64\n rR11)) (va_ttrue ())))", "val va_codegen_success_AES128EncryptBlock_6way : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_AES128EncryptBlock_6way () =\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 0) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 6) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 10) Secret) (va_pbool_and\n (va_codegen_success_Vxor (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 6))\n (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vxor\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 6)) (va_pbool_and\n (va_codegen_success_Vxor (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 6))\n (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5)\n (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_AES128EncryptRound_6way 1)\n (va_pbool_and (va_codegen_success_AES128EncryptRound_6way 2) (va_pbool_and\n (va_codegen_success_AES128EncryptRound_6way 3) (va_pbool_and\n (va_codegen_success_AES128EncryptRound_6way 4) (va_pbool_and\n (va_codegen_success_AES128EncryptRound_6way 5) (va_pbool_and\n (va_codegen_success_AES128EncryptRound_6way 6) (va_pbool_and\n (va_codegen_success_AES128EncryptRound_6way 7) (va_pbool_and\n (va_codegen_success_AES128EncryptRound_6way 8) (va_pbool_and\n (va_codegen_success_AES128EncryptRound_6way 9) (va_pbool_and (va_codegen_success_LoadImm64\n (va_op_reg_opr_reg 10) (16 `op_Multiply` 10)) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 6) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 10) Secret) (va_pbool_and\n (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec\n 6)) (va_pbool_and (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vcipherlast\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 6)) (va_pbool_and\n (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec\n 6)) (va_pbool_and (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5)\n (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 6)\n (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 6)) (va_ttrue ())))))))))))))))))))))))))))", "val va_codegen_success_Loop_rounds_13_15 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_rounds_13_15 () =\n (va_pbool_and (va_codegen_success_Loop_rounds_1_15_shift_body 13 (va_op_vec_opr_vec 13)\n (va_op_vec_opr_vec 12)) (va_pbool_and (va_codegen_success_Loop_rounds_1_15_shift_body 14\n (va_op_vec_opr_vec 14) (va_op_vec_opr_vec 12)) (va_pbool_and\n (va_codegen_success_Loop_rounds_1_15_shift_body 15 (va_op_vec_opr_vec 15) (va_op_vec_opr_vec\n 12)) (va_ttrue ()))))", "val va_codegen_success_Fast_add_after_mul1_regs : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fast_add_after_mul1_regs () =\n (va_pbool_and (va_codegen_success_Xor64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRcx))\n (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rRcx) (va_op_reg_opr64_reg64 rRsi) 0 Secret) (va_pbool_and\n (va_codegen_success_Adox64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 0))\n (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRsi) 8 Secret) (va_pbool_and\n (va_codegen_success_Adox64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRdx))\n (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRsi) 16 Secret) (va_pbool_and\n (va_codegen_success_Adox64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbx))\n (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRsi) 24 Secret) (va_pbool_and\n (va_codegen_success_Adox64Wrap (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rR13))\n (va_pbool_and (va_codegen_success_Adox64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64\n rRcx)) (va_ttrue ()))))))))))))", "val va_codegen_success_Mod_cr0 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Mod_cr0 () =\n (va_ttrue ())", "val va_codegen_success_Mod_cr0 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Mod_cr0 () =\n (va_ttrue ())", "val va_codegen_success_Mod_cr0 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Mod_cr0 () =\n (va_ttrue ())", "val va_codegen_success_VectorEqual : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_VectorEqual () =\n (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0)\n (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Mfvsrld (va_op_reg_opr_reg 4)\n (va_op_vec_opr_vec 0)) (va_pbool_and (va_codegen_success_Nat64Equal ()) (va_pbool_and\n (va_codegen_success_Move (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (va_pbool_and\n (va_codegen_success_Mfvsrd (va_op_reg_opr_reg 4) (va_op_vec_opr_vec 0)) (va_pbool_and\n (va_codegen_success_Nat64Equal ()) (va_pbool_and (va_codegen_success_Add (va_op_reg_opr_reg 3)\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 3)) (va_ttrue ()))))))))", "val va_codegen_success_Compute_iv : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Compute_iv () =\n (va_pbool_and (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 7)\n (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64 rR8) 0 Secret) (va_pbool_and\n (va_codegen_success_InitPshufbMask (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64 rRax))\n (va_pbool_and (va_codegen_success_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_PinsrdImm (va_op_xmm_xmm 0) 1 0 (va_op_reg_opr64_reg64 rRax)) (va_pbool_and\n (va_codegen_success_Store128_buffer (va_op_heaplet_mem_heaplet 7) (va_op_reg_opr64_reg64 rRcx)\n (va_op_xmm_xmm 0) 0 Secret) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64\n rRax) (va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64\n rR9) (va_const_opr64 32)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)\n (va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Gcm_blocks_auth ()) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRax)) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR11) (va_const_opr64 0)) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rRsi)) (va_pbool_and\n (va_codegen_success_Gcm_make_length_quad ()) (va_pbool_and (va_codegen_success_Ghash_register\n ()) (va_codegen_success_Store128_buffer (va_op_heaplet_mem_heaplet 7) (va_op_reg_opr64_reg64\n rRcx) (va_op_xmm_xmm 8) 0 Secret))))))))))))))) (va_ttrue ()))", "val va_codegen_success_Compute_iv : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Compute_iv () =\n (va_pbool_and (va_pbool_and (va_codegen_success_Load128_byte16_buffer (va_op_heaplet_mem_heaplet\n 6) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 4) Secret) (va_pbool_and\n (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 1) (va_pbool_and (va_codegen_success_Vsldoi\n (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) 12) (va_pbool_and\n (va_codegen_success_Vsldoi (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 1) 4)\n (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 6)\n (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) Secret) (va_pbool_and\n (va_codegen_success_Gcm_blocks_auth ()) (va_pbool_and (va_codegen_success_Move\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 9)) (va_pbool_and (va_codegen_success_LoadImm64\n (va_op_reg_opr_reg 7) 0) (va_pbool_and (va_codegen_success_Gcm_make_length_quad ())\n (va_pbool_and (va_codegen_success_Ghash_register ()) (va_codegen_success_Store128_byte16_buffer\n (va_op_heaplet_mem_heaplet 6) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret)))))))))))\n (va_ttrue ()))", "val va_codegen_success_Fast_add : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fast_add () =\n (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRdx) 0 Secret) (va_pbool_and\n (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap\n (va_op_dst_opr64_reg64 rR8) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64\n rRsi) 0 Secret)) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rR9) (va_op_reg_opr64_reg64 rRdx) 8 Secret) (va_pbool_and\n (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Adcx64Wrap\n (va_op_dst_opr64_reg64 rR9) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64\n rRsi) 8 Secret)) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rR10) (va_op_reg_opr64_reg64 rRdx) 16 Secret) (va_pbool_and\n (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Adcx64Wrap\n (va_op_dst_opr64_reg64 rR10) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)\n (va_op_reg64_reg64 rRsi) 16 Secret)) (va_pbool_and (va_codegen_success_Load64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdx) 24\n Secret) (va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and\n (va_codegen_success_Adcx64Wrap (va_op_dst_opr64_reg64 rR11) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 24 Secret)) (va_ttrue ())))))))))))))", "val va_codegen_success_Fast_add : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fast_add () =\n (va_pbool_and (va_codegen_success_Xor64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR8))\n (va_pbool_and (va_codegen_success_Xor64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRax))\n (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rR9) (va_op_reg_opr64_reg64 rRcx) 0 Secret) (va_pbool_and\n (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap\n (va_op_dst_opr64_reg64 rR9) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64\n rRsi) 0 Secret)) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR9) 0 Secret) (va_pbool_and\n (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR10)\n (va_op_reg_opr64_reg64 rRcx) 8 Secret) (va_pbool_and (va_codegen_success_Mem64_lemma ())\n (va_pbool_and (va_codegen_success_Adcx64Wrap (va_op_dst_opr64_reg64 rR10) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Secret)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR10) 8 Secret) (va_pbool_and (va_codegen_success_Load64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRcx) 16\n Secret) (va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and\n (va_codegen_success_Adcx64Wrap (va_op_dst_opr64_reg64 rR11) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 16 Secret)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR11) 16 Secret) (va_pbool_and (va_codegen_success_Load64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRcx) 24\n Secret) (va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and\n (va_codegen_success_Adcx64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 24 Secret)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRbx) 24 Secret) (va_pbool_and (va_codegen_success_Adcx64Wrap\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR8)) (va_ttrue ()))))))))))))))))))))", "val va_codegen_success_NoNewline : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_NoNewline () =\n (va_ttrue ())", "val va_codegen_success_Poly1305_impl : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Poly1305_impl () =\n (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)\n (va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and\n (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)\n (va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_pbool_and\n (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_pbool_and\n (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244))\n (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx))\n (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)\n (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR12) 32 Public) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_And64\n (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_pbool_and (va_codegen_success_Sub64\n (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRax) 56 Public) (va_pbool_and (va_codegen_success_Store64_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64\n Public) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64\n 1)) (va_pbool_and (va_codegen_success_Poly1305_blocks ()) (va_pbool_and\n (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)\n (va_op_reg_opr64_reg64 rRdi) 184 Public) (va_pbool_and (va_pbool_and\n (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)\n (va_op_reg_opr64_reg64 rRdi) 56 Public) (va_pbool_and (va_pbool_and\n (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)\n (va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0\n Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public)\n (va_codegen_success_Poly1305_last_block ())))) (va_pbool_and\n (va_codegen_success_Poly1305_reduce_last ()) (va_pbool_and (va_codegen_success_Load64_buffer\n (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 40\n Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)\n (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48 Public)\n (va_codegen_success_Poly1305_add_key_s ())))))) (va_ttrue ()))))))))))))))))))", "val va_codegen_success_Loop_rounds_9_11 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_rounds_9_11 () =\n (va_pbool_and (va_codegen_success_Loop_rounds_1_15_shift_body 9 (va_op_vec_opr_vec 9)\n (va_op_vec_opr_vec 8)) (va_pbool_and (va_codegen_success_Loop_rounds_1_15_shift_body 10\n (va_op_vec_opr_vec 10) (va_op_vec_opr_vec 8)) (va_pbool_and\n (va_codegen_success_Loop_rounds_1_15_shift_body 11 (va_op_vec_opr_vec 11) (va_op_vec_opr_vec\n 8)) (va_ttrue ()))))", "val va_codegen_success_Ghash_extra_bytes : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Ghash_extra_bytes () =\n (va_pbool_and (va_codegen_success_Compute_pad_to_128_bits ()) (va_pbool_and\n (va_codegen_success_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (va_pbool_and\n (va_codegen_success_Ghash_register ()) (va_ttrue ()))))", "val va_codegen_success_Ghash_extra_bytes : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Ghash_extra_bytes () =\n (va_pbool_and (va_codegen_success_Compute_pad_to_128_bits ()) (va_pbool_and\n (va_codegen_success_Ghash_register ()) (va_ttrue ())))", "val va_codegen_success_Reduce : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Reduce () =\n (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 0) 0) (va_pbool_and\n (va_codegen_success_Low64ToHigh (va_op_vec_opr_vec 9) (va_op_vec_opr_vec 3)) (va_pbool_and\n (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 9))\n (va_pbool_and (va_codegen_success_VSwap (va_op_vec_opr_vec 10) (va_op_vec_opr_vec 2))\n (va_pbool_and (va_codegen_success_VPolyMulLow (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 8)) (va_pbool_and (va_codegen_success_High64ToLow (va_op_vec_opr_vec 3)\n (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 4)\n (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_VPolyAdd\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 10)) (va_pbool_and\n (va_codegen_success_VSwap (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2)) (va_pbool_and\n (va_codegen_success_VPolyMulLow (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2) (va_op_vec_opr_vec\n 8)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 2)) (va_ttrue ())))))))))))))", "val va_codegen_success_Epilogue : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Epilogue () =\n (va_pbool_and (va_codegen_success_Vmrghw (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 16)\n (va_op_vec_opr_vec 17)) (va_pbool_and (va_codegen_success_Vmrghw (va_op_vec_opr_vec 18)\n (va_op_vec_opr_vec 18) (va_op_vec_opr_vec 19)) (va_pbool_and (va_codegen_success_Xxmrghd\n (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 18)) (va_pbool_and\n (va_codegen_success_Vmrghw (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec\n 21)) (va_pbool_and (va_codegen_success_Vmrghw (va_op_vec_opr_vec 22) (va_op_vec_opr_vec 22)\n (va_op_vec_opr_vec 23)) (va_pbool_and (va_codegen_success_Xxmrghd (va_op_vec_opr_vec 20)\n (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 22)) (va_pbool_and (va_codegen_success_LoadImm64\n (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_word4_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_vec_opr_vec 16) (va_op_reg_opr_reg 3) Secret)\n (va_pbool_and (va_codegen_success_Store128_word4_buffer_index (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 20) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue\n ()))))))))))", "val va_codegen_success_Epilogue : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Epilogue () =\n (va_pbool_and (va_codegen_success_Pshufd (va_op_xmm_xmm 2) (va_op_xmm_xmm 2) 177) (va_pbool_and\n (va_codegen_success_Pshufd (va_op_xmm_xmm 7) (va_op_xmm_xmm 1) 27) (va_pbool_and\n (va_codegen_success_Pshufd (va_op_xmm_xmm 1) (va_op_xmm_xmm 1) 177) (va_pbool_and\n (va_codegen_success_Shufpd (va_op_xmm_xmm 1) (va_op_xmm_xmm 2) 3) (va_pbool_and\n (va_codegen_success_Palignr8 (va_op_xmm_xmm 2) (va_op_xmm_xmm 7)) (va_pbool_and\n (va_codegen_success_Store128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_xmm_xmm 1) 0 Secret) (va_pbool_and (va_codegen_success_Store128_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi) (va_op_xmm_xmm 2) 16 Secret)\n (va_ttrue ()))))))))", "val va_codegen_success_Compute_ghash_incremental_register : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Compute_ghash_incremental_register () =\n (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 11)) (va_pbool_and\n (va_codegen_success_ReduceMul128_LE ()) (va_ttrue ()))))", "val va_codegen_success_AES256EncryptBlock_6way : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_AES256EncryptBlock_6way () =\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 0) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 6) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 10) Secret) (va_pbool_and\n (va_codegen_success_Vxor (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 6))\n (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vxor\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 6)) (va_pbool_and\n (va_codegen_success_Vxor (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 6))\n (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5)\n (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_AES256EncryptRound_6way 1)\n (va_pbool_and (va_codegen_success_AES256EncryptRound_6way 2) (va_pbool_and\n (va_codegen_success_AES256EncryptRound_6way 3) (va_pbool_and\n (va_codegen_success_AES256EncryptRound_6way 4) (va_pbool_and\n (va_codegen_success_AES256EncryptRound_6way 5) (va_pbool_and\n (va_codegen_success_AES256EncryptRound_6way 6) (va_pbool_and\n (va_codegen_success_AES256EncryptRound_6way 7) (va_pbool_and\n (va_codegen_success_AES256EncryptRound_6way 8) (va_pbool_and\n (va_codegen_success_AES256EncryptRound_6way 9) (va_pbool_and\n (va_codegen_success_AES256EncryptRound_6way 10) (va_pbool_and\n (va_codegen_success_AES256EncryptRound_6way 11) (va_pbool_and\n (va_codegen_success_AES256EncryptRound_6way 12) (va_pbool_and\n (va_codegen_success_AES256EncryptRound_6way 13) (va_pbool_and (va_codegen_success_LoadImm64\n (va_op_reg_opr_reg 10) (16 `op_Multiply` 14)) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 6) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 10) Secret) (va_pbool_and\n (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec\n 6)) (va_pbool_and (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1)\n (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vcipherlast\n (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 6)) (va_pbool_and\n (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec\n 6)) (va_pbool_and (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5)\n (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 6)\n (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 6)) (va_ttrue ())))))))))))))))))))))))))))))))", "val va_codegen_success_Loop_rounds : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_rounds () =\n (va_pbool_and (va_codegen_success_Loop_rounds_0_15 ()) (va_pbool_and\n (va_codegen_success_Loop_rounds_16_51 ()) (va_pbool_and (va_codegen_success_Loop_rounds_52_64\n ()) (va_ttrue ()))))", "val va_codegen_success_Loop_rounds : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Loop_rounds () =\n (va_pbool_and (va_codegen_success_Xxmrghd (va_op_vec_opr_vec 28) (va_op_vec_opr_vec 16)\n (va_op_vec_opr_vec 20)) (va_pbool_and (va_codegen_success_Xxmrghd (va_op_vec_opr_vec 29)\n (va_op_vec_opr_vec 17) (va_op_vec_opr_vec 21)) (va_pbool_and (va_codegen_success_Xxmrghd\n (va_op_vec_opr_vec 30) (va_op_vec_opr_vec 18) (va_op_vec_opr_vec 22)) (va_pbool_and\n (va_codegen_success_Xxmrghd (va_op_vec_opr_vec 31) (va_op_vec_opr_vec 19) (va_op_vec_opr_vec\n 23)) (va_pbool_and (va_codegen_success_Loop_prologue ()) (va_pbool_and\n (va_codegen_success_Loop_rounds_0_15 ()) (va_pbool_and (va_codegen_success_Loop_rounds_16_47\n 16) (va_pbool_and (va_codegen_success_Loop_rounds_16_47 32) (va_pbool_and\n (va_codegen_success_Loop_rounds_48_63 ()) (va_pbool_and (va_codegen_success_SubImm\n (va_op_reg_opr_reg 6) (va_op_reg_opr_reg 6) 256) (va_pbool_and (va_codegen_success_Vsldoi\n (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 28) (va_op_vec_opr_vec 28) 8) (va_pbool_and\n (va_codegen_success_Vsldoi (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 29) (va_op_vec_opr_vec 29)\n 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 30)\n (va_op_vec_opr_vec 30) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 3)\n (va_op_vec_opr_vec 31) (va_op_vec_opr_vec 31) 8) (va_pbool_and (va_codegen_success_Vadduwm\n (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 16) (va_op_vec_opr_vec 28)) (va_pbool_and\n (va_codegen_success_Vadduwm (va_op_vec_opr_vec 17) (va_op_vec_opr_vec 17) (va_op_vec_opr_vec\n 29)) (va_pbool_and (va_codegen_success_Vadduwm (va_op_vec_opr_vec 18) (va_op_vec_opr_vec 18)\n (va_op_vec_opr_vec 30)) (va_pbool_and (va_codegen_success_Vadduwm (va_op_vec_opr_vec 19)\n (va_op_vec_opr_vec 19) (va_op_vec_opr_vec 31)) (va_pbool_and (va_codegen_success_Vadduwm\n (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 20) (va_op_vec_opr_vec 0)) (va_pbool_and\n (va_codegen_success_Vadduwm (va_op_vec_opr_vec 21) (va_op_vec_opr_vec 21) (va_op_vec_opr_vec\n 1)) (va_pbool_and (va_codegen_success_Vadduwm (va_op_vec_opr_vec 22) (va_op_vec_opr_vec 22)\n (va_op_vec_opr_vec 2)) (va_pbool_and (va_codegen_success_Vadduwm (va_op_vec_opr_vec 23)\n (va_op_vec_opr_vec 23) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))))))))))))))))))", "val va_codegen_success_AES256EncryptBlock : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_AES256EncryptBlock () =\n (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 0) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 2) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 10) Secret) (va_pbool_and\n (va_codegen_success_Vxor (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 2))\n (va_pbool_and (va_codegen_success_AES256EncryptRound 1) (va_pbool_and\n (va_codegen_success_AES256EncryptRound 2) (va_pbool_and (va_codegen_success_AES256EncryptRound\n 3) (va_pbool_and (va_codegen_success_AES256EncryptRound 4) (va_pbool_and\n (va_codegen_success_AES256EncryptRound 5) (va_pbool_and (va_codegen_success_AES256EncryptRound\n 6) (va_pbool_and (va_codegen_success_AES256EncryptRound 7) (va_pbool_and\n (va_codegen_success_AES256EncryptRound 8) (va_pbool_and (va_codegen_success_AES256EncryptRound\n 9) (va_pbool_and (va_codegen_success_AES256EncryptRound 10) (va_pbool_and\n (va_codegen_success_AES256EncryptRound 11) (va_pbool_and (va_codegen_success_AES256EncryptRound\n 12) (va_pbool_and (va_codegen_success_AES256EncryptRound 13) (va_pbool_and\n (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) (16 `op_Multiply` 14)) (va_pbool_and\n (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 0)\n (va_op_vec_opr_vec 2) (va_op_reg_opr_reg 4) (va_op_reg_opr_reg 10) Secret) (va_pbool_and\n (va_codegen_success_Vcipherlast (va_op_vec_opr_vec 0) (va_op_vec_opr_vec 0) (va_op_vec_opr_vec\n 2)) (va_pbool_and (va_codegen_success_Vxor (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 2)\n (va_op_vec_opr_vec 2)) (va_ttrue ())))))))))))))))))))))", "val va_codegen_success_AES256EncryptBlock : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_AES256EncryptBlock () =\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 2)\n (va_op_reg_opr64_reg64 rR8) 0 Secret) (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 2)) (va_pbool_and (va_codegen_success_AES256EncryptRound 1) (va_pbool_and\n (va_codegen_success_AES256EncryptRound 2) (va_pbool_and (va_codegen_success_AES256EncryptRound\n 3) (va_pbool_and (va_codegen_success_AES256EncryptRound 4) (va_pbool_and\n (va_codegen_success_AES256EncryptRound 5) (va_pbool_and (va_codegen_success_AES256EncryptRound\n 6) (va_pbool_and (va_codegen_success_AES256EncryptRound 7) (va_pbool_and\n (va_codegen_success_AES256EncryptRound 8) (va_pbool_and (va_codegen_success_AES256EncryptRound\n 9) (va_pbool_and (va_codegen_success_AES256EncryptRound 10) (va_pbool_and\n (va_codegen_success_AES256EncryptRound 11) (va_pbool_and (va_codegen_success_AES256EncryptRound\n 12) (va_pbool_and (va_codegen_success_AES256EncryptRound 13) (va_pbool_and\n (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 0) (va_op_xmm_xmm 2)\n (va_op_reg_opr64_reg64 rR8) (16 `op_Multiply` 14) Secret) (va_pbool_and\n (va_codegen_success_AESNI_enc_last (va_op_xmm_xmm 0) (va_op_xmm_xmm 2)) (va_pbool_and\n (va_codegen_success_Pxor (va_op_xmm_xmm 2) (va_op_xmm_xmm 2)) (va_ttrue ())))))))))))))))))))", "val va_codegen_success_Fast_sqr_part2 : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fast_sqr_part2 () =\n (va_pbool_and (va_codegen_success_Xor64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rR15))\n (va_pbool_and (va_codegen_success_Adox_64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64\n rRax)) (va_pbool_and (va_codegen_success_Adcx_64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64\n rR8)) (va_pbool_and (va_codegen_success_Adox_64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64\n rRcx)) (va_pbool_and (va_codegen_success_Adcx_64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64\n rR9)) (va_pbool_and (va_codegen_success_Adox_64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64\n rR15)) (va_pbool_and (va_codegen_success_Adcx_64 (va_op_dst_opr64_reg64 rR10)\n (va_op_opr64_reg64 rR10)) (va_pbool_and (va_codegen_success_Adox_64 (va_op_dst_opr64_reg64\n rR13) (va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Adcx_64\n (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rR11)) (va_pbool_and\n (va_codegen_success_Adox_64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR15))\n (va_pbool_and (va_codegen_success_Adcx_64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64\n rRbx)) (va_pbool_and (va_codegen_success_Adcx_64 (va_op_dst_opr64_reg64 rR13)\n (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Adcx_64 (va_op_dst_opr64_reg64\n rR14) (va_op_opr64_reg64 rR14)) (va_ttrue ()))))))))))))))", "val va_codegen_success_Fast_sub : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fast_sub () =\n (va_pbool_and (va_codegen_success_Xor64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRax))\n (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0 Secret) (va_pbool_and\n (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Sub64Wrap\n (va_op_dst_opr64_reg64 rR8) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64\n rRcx) 0 Secret)) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR8) 0 Secret) (va_pbool_and\n (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)\n (va_op_reg_opr64_reg64 rRsi) 8 Secret) (va_pbool_and (va_codegen_success_Mem64_lemma ())\n (va_pbool_and (va_codegen_success_Sbb64 (va_op_dst_opr64_reg64 rR9) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRcx) 8 Secret)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR9) 8 Secret) (va_pbool_and (va_codegen_success_Load64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR10) (va_op_reg_opr64_reg64 rRsi) 16\n Secret) (va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and\n (va_codegen_success_Sbb64 (va_op_dst_opr64_reg64 rR10) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRcx) 16 Secret)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR10) 16 Secret) (va_pbool_and (va_codegen_success_Load64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRsi) 24\n Secret) (va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and\n (va_codegen_success_Sbb64 (va_op_dst_opr64_reg64 rR11) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRcx) 24 Secret)) (va_pbool_and\n (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR11) 24 Secret) (va_pbool_and (va_codegen_success_Adc64Wrap\n (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRax)) (va_ttrue ())))))))))))))))))))", "val va_codegen_success_Fast_sub : va_dummy:unit -> Tot va_pbool\nlet va_codegen_success_Fast_sub () =\n (va_pbool_and (va_codegen_success_Comment\n \"Compute the raw substraction of f1-f2\"\n ) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0 Secret) (va_pbool_and\n (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Sub64Wrap\n (va_op_dst_opr64_reg64 rR8) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64\n rRdx) 0 Secret)) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rR9) (va_op_reg_opr64_reg64 rRsi) 8 Secret) (va_pbool_and\n (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Sbb64\n (va_op_dst_opr64_reg64 rR9) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64\n rRdx) 8 Secret)) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)\n (va_op_dst_opr64_reg64 rR10) (va_op_reg_opr64_reg64 rRsi) 16 Secret) (va_pbool_and\n (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Sbb64\n (va_op_dst_opr64_reg64 rR10) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)\n (va_op_reg64_reg64 rRdx) 16 Secret)) (va_pbool_and (va_codegen_success_Load64_buffer\n (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRsi) 24\n Secret) (va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and\n (va_codegen_success_Sbb64 (va_op_dst_opr64_reg64 rR11) (va_opr_code_Mem64\n (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRdx) 24 Secret)) (va_ttrue ()))))))))))))))" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_codegen_success_ShiftLeft2_128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_codegen_success_ShiftLeft128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Init.fst", "name": "Vale.AES.PPC64LE.GF128_Init.va_codegen_success_ShiftKey1_128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Init.fst", "name": "Vale.AES.X64.GF128_Init.va_codegen_success_ShiftKey1_128" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_codegen_success_Msg_shift" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Init.fst", "name": "Vale.AES.X64.GF128_Init.va_codegen_success_ShiftKey1_gf128_power" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Init.fst", "name": "Vale.AES.PPC64LE.GF128_Init.va_codegen_success_ShiftKey1_gf128_power" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_codegen_success_Compute_pad_to_128_bits" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fst", "name": "Vale.AES.PPC64LE.GCMencrypt.va_codegen_success_Compute_pad_to_128_bits" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_codegen_success_ReduceMulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_codegen_success_Gf128MulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_codegen_success_ReduceMul128_LE" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_code_ShiftLeft2_128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_codegen_success_Clmul128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_code_ShiftLeft128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.AES128.fst", "name": "Vale.AES.PPC64LE.AES128.va_codegen_success_KeyExpansion128Stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_codegen_success_Xgetbv_Avx512" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_codegen_success_MulAdd_unroll_1way" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_codegen_success_ClmulRev128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESGCM.fst", "name": "Vale.AES.X64.AESGCM.va_codegen_success_Handle_ctr32_2" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_codegen_success_Cswap2" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_codegen_success_MulAdd_unroll_2way" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_codegen_success_Loop_rounds_52_64" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_codegen_success_Fmul1" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.fst", "name": "Vale.SHA.PPC64LE.va_codegen_success_Sha_update" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_codegen_success_Sha_update" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_codegen_success_Loop_rounds_16_51" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_codegen_success_Xgetbv_Avx" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fst", "name": "Vale.Curve25519.X64.FastWide.va_codegen_success_Fmul2" }, { "project_name": "hacl-star", "file_name": "Vale.Test.X64.Vale_memcpy.fst", "name": "Vale.Test.X64.Vale_memcpy.va_codegen_success_InnerMemcpy" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_codegen_success_Store_3blocks128_1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.AES256.fst", "name": "Vale.AES.PPC64LE.AES256.va_codegen_success_KeyExpansion256Stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_codegen_success_Store_3blocks128_2" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_codegen_success_Loop" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_codegen_success_Loop" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.fst", "name": "Vale.SHA.PPC64LE.Rounds.va_codegen_success_Loop_rounds_48_63" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESCTR.fst", "name": "Vale.AES.X64.AESCTR.va_codegen_success_Aes_2rounds_4way" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_codegen_success_Handle_ctr32" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fst", "name": "Vale.Curve25519.X64.FastWide.va_codegen_success_Fmul" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_codegen_success_Fast_mul1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Init.fst", "name": "Vale.AES.X64.GF128_Init.va_codegen_success_Gf128_powers" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Init.fst", "name": "Vale.AES.PPC64LE.GF128_Init.va_codegen_success_Gf128_powers" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESCTR.fst", "name": "Vale.AES.X64.AESCTR.va_codegen_success_Aes_ctr_ghash" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_codegen_success_Check_avx512_xcr0_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt2.fst", "name": "Vale.AES.X64.AESopt2.va_codegen_success_MulAdd_unroll" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_codegen_success_Loop_rounds_1_3" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_codegen_success_Fadd" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESCTR.fst", "name": "Vale.AES.X64.AESCTR.va_codegen_success_Aes_3rounds_4way" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.fst", "name": "Vale.SHA.PPC64LE.va_codegen_success_Sha_update_bytes_main" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_codegen_success_Loop_body0" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_codegen_success_Loop_body0" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_codegen_success_Check_avx512_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESCTR.fst", "name": "Vale.AES.X64.AESCTR.va_codegen_success_Aes_4rounds_4way" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fst", "name": "Vale.AES.X64.GCTR.va_codegen_success_Init_ctr" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_codegen_success_Fast_add1" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_codegen_success_Fast_sub1" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AES128.fst", "name": "Vale.AES.X64.AES128.va_codegen_success_AES128EncryptBlock" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.AES128.fst", "name": "Vale.AES.PPC64LE.AES128.va_codegen_success_AES128EncryptBlock" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_codegen_success_Check_avx_xcr0_support" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_codegen_success_Loop_rounds_0_15" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.fst", "name": "Vale.SHA.PPC64LE.Rounds.va_codegen_success_Loop_rounds_0_15" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fst", "name": "Vale.AES.PPC64LE.GCMencrypt.va_codegen_success_Compute_iv_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_codegen_success_Sha_update_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.fst", "name": "Vale.SHA.PPC64LE.va_codegen_success_Sha_update_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_codegen_success_Loop_prologue" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESGCM.fst", "name": "Vale.AES.X64.AESGCM.va_codegen_success_Load_one_msb" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_codegen_success_Check_avx_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GF128_Mul.fst", "name": "Vale.AES.PPC64LE.GF128_Mul.va_codegen_success_ClmulRev64High" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_codegen_success_Cpuid_Sha" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMdecrypt.fst", "name": "Vale.AES.PPC64LE.GCMdecrypt.va_codegen_success_Nat64Equal" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.X64.Cpuid.fst", "name": "Vale.Lib.X64.Cpuid.va_codegen_success_Check_avx2_support" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESopt.fst", "name": "Vale.AES.X64.AESopt.va_codegen_success_load_one_msb" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.AES128.fst", "name": "Vale.AES.PPC64LE.AES128.va_codegen_success_AES128EncryptBlock_6way" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_codegen_success_Loop_rounds_13_15" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_codegen_success_Fast_add_after_mul1_regs" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_codegen_success_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_codegen_success_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_codegen_success_Mod_cr0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMdecrypt.fst", "name": "Vale.AES.PPC64LE.GCMdecrypt.va_codegen_success_VectorEqual" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_codegen_success_Compute_iv" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fst", "name": "Vale.AES.PPC64LE.GCMencrypt.va_codegen_success_Compute_iv" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_codegen_success_Fast_add" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_codegen_success_Fast_add" }, { "project_name": "hacl-star", "file_name": "Vale.X64.InsBasic.fst", "name": "Vale.X64.InsBasic.va_codegen_success_NoNewline" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_codegen_success_Poly1305_impl" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Rounds.Core.fst", "name": "Vale.SHA.PPC64LE.Rounds.Core.va_codegen_success_Loop_rounds_9_11" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_codegen_success_Ghash_extra_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCMencrypt.fst", "name": "Vale.AES.PPC64LE.GCMencrypt.va_codegen_success_Ghash_extra_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GHash.fst", "name": "Vale.AES.PPC64LE.GHash.va_codegen_success_Reduce" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.fst", "name": "Vale.SHA.PPC64LE.va_codegen_success_Epilogue" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_codegen_success_Epilogue" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_codegen_success_Compute_ghash_incremental_register" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.AES256.fst", "name": "Vale.AES.PPC64LE.AES256.va_codegen_success_AES256EncryptBlock_6way" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_codegen_success_Loop_rounds" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.Loop.fst", "name": "Vale.SHA.PPC64LE.Loop.va_codegen_success_Loop_rounds" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.AES256.fst", "name": "Vale.AES.PPC64LE.AES256.va_codegen_success_AES256EncryptBlock" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AES256.fst", "name": "Vale.AES.X64.AES256.va_codegen_success_AES256EncryptBlock" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastSqr.fst", "name": "Vale.Curve25519.X64.FastSqr.va_codegen_success_Fast_sqr_part2" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastUtil.fst", "name": "Vale.Curve25519.X64.FastUtil.va_codegen_success_Fast_sub" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastHybrid.fst", "name": "Vale.Curve25519.X64.FastHybrid.va_codegen_success_Fast_sub" } ], "selected_premises": [ "Vale.AES.X64.GF128_Mul.va_codegen_success_ShiftLeft128_1", "Vale.X64.Decls.va_get_success", "Vale.X64.Decls.va_coerce_reg_opr64_to_dst_opr64", "Vale.X64.Decls.va_coerce_reg_opr64_to_opr64", "Vale.X64.Decls.va_op_opr64_reg64", "Vale.X64.Decls.va_op_reg_opr64_reg64", "Vale.X64.Decls.va_op_dst_opr64_reg64", "Vale.X64.Decls.va_op_reg64_reg64", "Vale.X64.Decls.va_op_xmm_xmm", "Vale.X64.Decls.va_op_heaplet_mem_heaplet", "Vale.X64.Decls.va_const_opr64", "Vale.X64.Machine_s.rR14", "Vale.X64.Machine_s.rR13", "Vale.X64.Machine_s.rR15", "Vale.X64.Machine_s.rR8", "Vale.X64.Machine_s.rR11", "Vale.X64.Machine_s.rR9", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rR12", "Vale.X64.Machine_s.rRcx", "Vale.X64.Machine_s.rR10", "Vale.X64.Machine_s.rRdx", "Vale.X64.Machine_s.rRbp", "Vale.X64.Machine_s.rRax", "Vale.X64.Machine_s.rRsi", "Vale.X64.Decls.va_op_cmp_reg64", "Vale.X64.Decls.va_CNil", "Vale.X64.Decls.va_CCons", "Vale.X64.Machine_s.rRsp", "Vale.X64.Machine_s.rRdi", "Vale.X64.Decls.va_Block", "Vale.X64.QuickCode.va_Mod_reg64", "Vale.X64.Decls.va_const_shift_amt64", "Vale.X64.QuickCodes.va_range1", "Vale.X64.QuickCode.va_Mod_mem_heaplet", "Vale.X64.Decls.va_op_opr128_xmm", "Vale.X64.Decls.va_get_block", "Vale.X64.QuickCode.va_Mod_xmm", "Vale.X64.QuickCode.va_Mod_mem_layout", "Vale.X64.QuickCodes.label", "Vale.X64.Decls.va_const_cmp", "Vale.X64.Decls.va_get_reg64", "Vale.X64.Decls.va_tl", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.QuickCode.va_mod_reg_opr64", "Vale.X64.QuickCode.va_Mod_flags", "Vale.X64.QuickCode.va_Mod_mem", "Vale.X64.QuickCode.va_Mod_ok", "Vale.X64.QuickCode.va_QProc", "Vale.X64.QuickCode.va_Mod_stack", "Vale.X64.QuickCode.va_Mod_stackTaint", "Vale.X64.Decls.va_require_total", "Vale.X64.QuickCode.va_mod_heaplet", "Vale.AES.X64.GF128_Mul.va_qcode_ShiftLeft128_1", "Vale.AES.X64.GF128_Mul.va_code_ShiftLeft2_128_1", "Vale.X64.QuickCode.va_mod_xmm", "Vale.X64.Decls.va_opr_code_Mem64", "Vale.X64.Machine_s.reg_64", "Vale.X64.Decls.va_get_mem_heaplet", "Vale.X64.Decls.va_code", "Vale.X64.Machine_s.operand128", "Vale.X64.Decls.va_state", "Vale.X64.Decls.va_mul_nat", "Vale.X64.Decls.va_get_xmm", "Vale.X64.Decls.va_coerce_dst_opr64_to_opr64", "Vale.X64.Decls.va_op_shift_amt64_reg64", "Vale.X64.QuickCodes.va_QSeq", "Vale.X64.InsBasic.va_wp_Newline", "Vale.X64.QuickCodes.va_QEmpty", "Vale.X64.Decls.va_coerce_xmm_to_opr128", "Vale.X64.Decls.va_if", "Vale.X64.QuickCode.va_mod_dst_opr64", "Vale.X64.Decls.va_get_ok", "Vale.X64.QuickCodes.va_qPURE", "Vale.X64.Machine_s.reg_xmm", "Vale.X64.Decls.va_get_mem_layout", "Vale.AES.X64.GF128_Mul.va_code_ShiftLeft128_1", "Vale.X64.CPU_Features_s.sse_enabled", "Vale.X64.Decls.va_upd_reg64", "Vale.X64.CPU_Features_s.avx_enabled", "Vale.Def.Words_s.nat64", "Vale.X64.Decls.va_opr_code_Mem128", "Vale.X64.Decls.get_reg", "Vale.X64.Machine_s.nat64", "Vale.X64.Machine_s.operand64", "Vale.X64.Decls.va_upd_flags", "Prims.subtype_of", "Vale.Def.Types_s.nat64", "Vale.X64.Memory.nat64", "Vale.AES.X64.GF128_Mul.va_lemma_ShiftLeft128_1", "Vale.AES.X64.GF128_Mul.va_wpProof_ShiftLeft128_1", "FStar.ST.stable", "Vale.X64.QuickCodes.va_QBind", "Vale.X64.CPU_Features_s.avx_xcr0", "Vale.X64.QuickCode.va_quickCode", "Vale.X64.Machine_s.quad32", "Vale.X64.Memory.quad32", "Vale.X64.Decls.va_While", "Vale.X64.CPU_Features_s.avx2_enabled", "Vale.X64.InsBasic.va_wp_NoNewline" ], "source_upto_this": "module Vale.AES.X64.GF128_Mul\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Math.Poly2_s\nopen Vale.Math.Poly2\nopen Vale.Math.Poly2.Bits_s\nopen Vale.Math.Poly2.Bits\nopen Vale.Math.Poly2.Lemmas\nopen Vale.AES.GF128_s\nopen Vale.AES.GF128\nopen Vale.X64.Machine_s\nopen Vale.X64.State\nopen Vale.X64.Decls\nopen Vale.X64.InsBasic\nopen Vale.X64.InsMem\nopen Vale.X64.InsVector\nopen Vale.X64.InsAes\nopen Vale.X64.QuickCode\nopen Vale.X64.QuickCodes\nopen Vale.X64.CPU_Features_s\n//-- ShiftLeft128_1\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_ShiftLeft128_1 () =\n (va_Block (va_CCons (va_code_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_CCons (va_code_Psrld\n (va_op_xmm_xmm 2) 31) (va_CCons (va_code_Pslld (va_op_xmm_xmm 1) 1) (va_CCons (va_code_VPslldq4\n (va_op_xmm_xmm 2) (va_op_xmm_xmm 2)) (va_CCons (va_code_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm\n 2)) (va_CNil ())))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_ShiftLeft128_1 () =\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_pbool_and\n (va_codegen_success_Psrld (va_op_xmm_xmm 2) 31) (va_pbool_and (va_codegen_success_Pslld\n (va_op_xmm_xmm 1) 1) (va_pbool_and (va_codegen_success_VPslldq4 (va_op_xmm_xmm 2)\n (va_op_xmm_xmm 2)) (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 2))\n (va_ttrue ()))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_ShiftLeft128_1 (va_mods:va_mods_t) (a:poly) : (va_quickCode unit\n (va_code_ShiftLeft128_1 ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 59 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 2) (va_op_xmm_xmm 1)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 60 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Psrld (va_op_xmm_xmm 2) 31) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 61 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pslld (va_op_xmm_xmm 1) 1) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 62 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_VPslldq4 (va_op_xmm_xmm 2) (va_op_xmm_xmm 2)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 63 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 2)) (fun (va_s:va_state) _ -> let\n (va_arg8:Vale.Math.Poly2_s.poly) = a in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 65 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (fun (_:unit) -> Vale.AES.GF128.lemma_shift_left_1 va_arg8) (va_QEmpty (())))))))))\n\n[@\"opaque_to_smt\"]\nlet va_lemma_ShiftLeft128_1 va_b0 va_s0 a =\n let (va_mods:va_mods_t) = [va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags; va_Mod_ok] in\n let va_qc = va_qcode_ShiftLeft128_1 va_mods a in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftLeft128_1 ()) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 45 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_get_ok va_sM) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 57 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Mul.vaf *****\"\n (va_get_xmm 1 va_sM == Vale.Math.Poly2.Bits_s.to_quad32 (Vale.Math.Poly2_s.shift a 1))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags; va_Mod_ok]) va_sM va_s0;\n (va_sM, va_fM)\n\n\n[@\"opaque_to_smt\"]\nlet va_wpProof_ShiftLeft128_1 a va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_ShiftLeft128_1 (va_code_ShiftLeft128_1 ()) va_s0 a in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_flags va_sM\n (va_update_ok va_sM va_s0)))));\n va_lemma_norm_mods ([va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n//--\n//-- ShiftLeft2_128_1\n\nval va_code_ShiftLeft2_128_1 : va_dummy:unit -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_ShiftLeft2_128_1 () =\n (va_Block (va_CCons (va_code_Mov128 (va_op_xmm_xmm 3) (va_op_xmm_xmm 1)) (va_CCons (va_code_Psrld\n (va_op_xmm_xmm 3) 31) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 4) (va_op_xmm_xmm 2)) (va_CCons\n (va_code_Psrld (va_op_xmm_xmm 4) 31) (va_CCons (va_code_Pslld (va_op_xmm_xmm 1) 1) (va_CCons\n (va_code_Pslld (va_op_xmm_xmm 2) 1) (va_CCons (va_code_VPslldq4 (va_op_xmm_xmm 5)\n (va_op_xmm_xmm 3)) (va_CCons (va_code_VPslldq4 (va_op_xmm_xmm 4) (va_op_xmm_xmm 4)) (va_CCons\n (va_code_PinsrdImm (va_op_xmm_xmm 3) 0 0 (va_op_reg_opr64_reg64 rR12)) (va_CCons\n (va_code_Pshufd (va_op_xmm_xmm 3) (va_op_xmm_xmm 3) 3) (va_CCons (va_code_Pxor (va_op_xmm_xmm\n 3) (va_op_xmm_xmm 4)) (va_CCons (va_code_Pxor (va_op_xmm_xmm 1) (va_op_xmm_xmm 5)) (va_CCons\n (va_code_Pxor (va_op_xmm_xmm 2) (va_op_xmm_xmm 3)) (va_CNil ())))))))))))))))\n\nval va_codegen_success_ShiftLeft2_128_1 : va_dummy:unit -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]" }, { "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.par_stt", "opens_and_abbrevs": [ { "abbrev": "Act", "full_module": "PulseCore.Action" }, { "open": "PulseCore.Observability" }, { "open": "PulseCore.FractionalPermission" }, { "open": "PulseCore.InstantiatedSemantics" }, { "abbrev": "F", "full_module": "FStar.FunctionalExtensionality" }, { "abbrev": "T", "full_module": "FStar.Tactics.V2" }, { "abbrev": "A", "full_module": "PulseCore.Atomic" }, { "abbrev": "I", "full_module": "PulseCore.InstantiatedSemantics" }, { "abbrev": "T", "full_module": "FStar.Tactics.V2" }, { "abbrev": "Set", "full_module": "FStar.Set" }, { "abbrev": "G", "full_module": "FStar.Ghost" }, { "abbrev": "U32", "full_module": "FStar.UInt32" }, { "open": "FStar.PCM" }, { "open": "PulseCore.Observability" }, { "open": "PulseCore.FractionalPermission" }, { "open": "FStar.Ghost" }, { "open": "Pulse.Lib" }, { "open": "Pulse.Lib" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val par_stt\n (#preL:vprop)\n (#postL:vprop) \n (#preR:vprop)\n (#postR:vprop)\n (f:stt unit preL (fun _ -> postL))\n (g:stt unit preR (fun _ -> postR))\n: stt unit\n (preL ** preR)\n (fun _ -> postL ** postR)", "source_definition": "let par_stt = I.par", "source_range": { "start_line": 121, "start_col": 0, "end_line": 121, "end_col": 19 }, "interleaved": false, "definition": "PulseCore.InstantiatedSemantics.par", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "PulseCore.InstantiatedSemantics.par" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "\n f: Pulse.Lib.Core.stt Prims.unit preL (fun _ -> postL) ->\n g: Pulse.Lib.Core.stt Prims.unit preR (fun _ -> postR)\n -> Pulse.Lib.Core.stt Prims.unit (preL ** preR) (fun _ -> postL ** postR)", "prompt": "let par_stt =\n ", "expected_response": "I.par", "source": { "project_name": "steel", "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.Core.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Pulse.Lib.Core.fst", "checked_file": "dataset/Pulse.Lib.Core.fst.checked", "interface_file": true, "dependencies": [ "dataset/PulseCore.Observability.fst.checked", "dataset/PulseCore.InstantiatedSemantics.fsti.checked", "dataset/PulseCore.FractionalPermission.fst.checked", "dataset/PulseCore.Atomic.fsti.checked", "dataset/PulseCore.Action.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Squash.fsti.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.PropositionalExtensionality.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.PCM.fst.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked", "dataset/FStar.Classical.Sugar.fsti.checked" ] }, "definitions_in_context": [ "let double_one_half () = ()", "let equate_by_smt = ()", "let one_half =\n half_perm full_perm", "let vprop = slprop", "let emp = emp", "let op_Star_Star = op_Star_Star", "val double_one_half ()\n : Lemma (sum_perm one_half one_half == full_perm)", "let pure = pure", "let op_exists_Star = op_exists_Star", "let vprop_equiv = slprop_equiv", "let elim_vprop_equiv #p #q pf = slprop_equiv_elim p q", "let vprop_post_equiv = slprop_post_equiv", "let prop_squash_idem (p:prop)\n : Tot (squash (squash p == p))\n = FStar.PropositionalExtensionality.apply p (squash p)", "let intro_vprop_post_equiv\n (#t:Type u#a) \n (p q: t -> vprop)\n (pf: (x:t -> vprop_equiv (p x) (q x)))\n : vprop_post_equiv p q\n = let pf : squash (forall x. vprop_equiv (p x) (q x)) = \n introduce forall x. vprop_equiv (p x) (q x)\n with FStar.Squash.return_squash (pf x)\n in\n coerce_eq (prop_squash_idem _) pf", "let elim_vprop_post_equiv (#t:Type u#a)\n (p q: t -> vprop) \n (pf:vprop_post_equiv p q)\n (x:t) \n: vprop_equiv (p x) (q x)\n= let pf\n : squash (vprop_equiv (p x) (q x))\n = eliminate forall x. vprop_equiv (p x) (q x) with x\n in\n coerce_eq (prop_squash_idem _) pf", "val equate_by_smt : unit", "val vprop : Type u#2", "val emp : vprop", "let vprop_equiv_refl (v0:vprop) \n : vprop_equiv v0 v0\n = slprop_equiv_refl v0", "val ( ** ) (p q:vprop) : vprop", "val pure (p:prop) : vprop", "val ( exists* ) (#a:Type) (p:a -> vprop) : vprop", "val vprop_equiv (p q:vprop) : prop", "let vprop_equiv_sym (v0 v1:vprop) (p:vprop_equiv v0 v1)\n : vprop_equiv v1 v0\n = slprop_equiv_elim v0 v1; p", "val elim_vprop_equiv (#p #q:_) (_:vprop_equiv p q) : squash (p == q)", "val vprop_post_equiv (#t:Type u#a) (p q: t -> vprop) : prop", "val intro_vprop_post_equiv\n (#t:Type u#a) \n (p q: t -> vprop)\n (pf: (x:t -> vprop_equiv (p x) (q x)))\n : vprop_post_equiv p q", "let vprop_equiv_trans\n (v0 v1 v2:vprop)\n (p:vprop_equiv v0 v1)\n (q:vprop_equiv v1 v2)\n : vprop_equiv v0 v2\n = slprop_equiv_elim v0 v1;\n slprop_equiv_elim v1 v2;\n p", "val elim_vprop_post_equiv (#t:Type u#a)\n (p q: t -> vprop) \n (pf:vprop_post_equiv p q)\n (x:t) \n : vprop_equiv (p x) (q x)", "let vprop_equiv_unit (x:vprop)\n : vprop_equiv (emp ** x) x\n = slprop_equiv_unit x", "val vprop_equiv_refl (v0:vprop) : vprop_equiv v0 v0", "let vprop_equiv_comm (p1 p2:vprop)\n : vprop_equiv (p1 ** p2) (p2 ** p1)\n = slprop_equiv_comm p1 p2", "val vprop_equiv_sym (v0 v1:vprop) (_:vprop_equiv v0 v1)\n : vprop_equiv v1 v0", "val vprop_equiv_trans (v0 v1 v2:vprop) (_:vprop_equiv v0 v1) (_:vprop_equiv v1 v2)\n : vprop_equiv v0 v2", "let vprop_equiv_assoc (p1 p2 p3:vprop)\n : vprop_equiv ((p1 ** p2) ** p3) (p1 ** (p2 ** p3))\n = slprop_equiv_assoc p1 p2 p3", "val vprop_equiv_unit (x:vprop) : vprop_equiv (emp ** x) x", "let vprop_equiv_cong (p1 p2 p3 p4:vprop)\n (f: vprop_equiv p1 p3)\n (g: vprop_equiv p2 p4)\n : vprop_equiv (p1 ** p2) (p3 ** p4)\n = slprop_equiv_elim p1 p3;\n slprop_equiv_elim p2 p4;\n vprop_equiv_refl _", "val vprop_equiv_comm (p1 p2:vprop)\n : vprop_equiv (p1 ** p2) (p2 ** p1)", "val vprop_equiv_assoc (p1 p2 p3:vprop)\n : vprop_equiv (p1 ** p2 ** p3) (p1 ** (p2 ** p3))", "val vprop_equiv_cong (p1 p2 p3 p4:vprop)\n (_: vprop_equiv p1 p3)\n (_: vprop_equiv p2 p4)\n : vprop_equiv (p1 ** p2) (p3 ** p4)", "let vprop_equiv_ext p1 p2 _ = vprop_equiv_refl p1", "val vprop_equiv_ext (p1 p2:vprop) (_:p1 == p2)\n : vprop_equiv p1 p2", "let iname = Act.iname", "let join_sub _ _ = ()", "let join_emp is =\n Set.lemma_equal_intro (join_inames is emp_inames) (reveal is);\n Set.lemma_equal_intro (join_inames emp_inames is) (reveal is)", "let inv = Act.inv", "val iname : eqtype", "let name_of_inv = Act.name_of_inv", "let inames = erased (FStar.Set.set iname)", "let emp_inames : inames = Ghost.hide Set.empty", "let add_already_there i is = Set.lemma_equal_intro (add_inv is i) is", "let join_inames (is1 is2 : inames) : inames =\n Set.union is1 is2", "let inames_subset (is1 is2 : inames) : Type0 =\n Set.subset is1 is2", "let stt = I.stt", "let return_stt_noeq = I.return", "let bind_stt = I.bind", "let frame_stt = I.frame" ], "closest": [ "val par\n (#aL:Type u#a)\n (#aR:Type u#a)\n (#preL:vprop)\n (#postL:aL -> vprop)\n (#preR:vprop)\n (#postR:aR -> vprop)\n ($f:unit -> STT aL preL postL)\n ($g:unit -> STT aR preR postR)\n : STT (aL & aR)\n (preL `star` preR)\n (fun y -> postL (fst y) `star` postR (snd y))\nlet par #aL #aR #preL #postL #preR #postR f g =\n let f : unit -> SE.SteelT aL preL postL = fun _ -> f () in\n let g : unit -> SE.SteelT aR preR postR = fun _ -> g () in \n let p\n : unit -> SE.SteelT (aL & aR)\n (preL `star` preR)\n (fun y -> postL (fst y) `star` postR (snd y))\n = fun _ -> SE.par f g in\n coerce_steel p", "val par_lpost\n (#st: st)\n (#aL: Type)\n (#preL: st.hprop)\n (#postL: post_t st aL)\n (lpreL: l_pre preL)\n (lpostL: l_post preL postL)\n (#aR: Type)\n (#preR: st.hprop)\n (#postR: post_t st aR)\n (lpreR: l_pre preR)\n (lpostR: l_post preR postR)\n : l_post (preL `st.star` preR) (fun (xL, xR) -> (postL xL) `st.star` (postR xR))\nlet par_lpost\n (#st:st)\n (#aL:Type)\n (#preL:st.hprop)\n (#postL:post_t st aL)\n (lpreL:l_pre preL)\n (lpostL:l_post preL postL)\n (#aR:Type)\n (#preR:st.hprop)\n (#postR:post_t st aR)\n (lpreR:l_pre preR)\n (lpostR:l_post preR postR)\n : l_post (preL `st.star` preR) (fun (xL, xR) -> postL xL `st.star` postR xR)\n =\n fun h0 (xL, xR) h1 -> lpreL h0 /\\ lpreR h0 /\\ lpostL h0 xL h1 /\\ lpostR h0 xR h1", "val par (#aL:Type u#a)\n (#aR:Type u#a)\n (#preL:vprop)\n (#postL:aL -> vprop)\n // (#lpreL:req_t preL)\n // (#lpostL:ens_t preL aL postL)\n ($f:unit -> SteelT aL preL postL) // lpreL lpostL)\n (#preR:vprop)\n (#postR:aR -> vprop)\n // (#lpreR:req_t preR)\n // (#lpostR:ens_t preR aR postR)\n ($g:unit -> SteelT aR preR postR) // lpreR lpostR)\n : SteelT (aL & aR)\n (preL `star` preR)\n (fun y -> postL (fst y) `star` postR (snd y))\nlet par f g =\n par0 (reify_steel_comp f) (reify_steel_comp g)", "val par (#p0 #q0 #p1 #q1:_)\r\n (f0:stt unit p0 (fun _ -> q0))\r\n (f1:stt unit p1 (fun _ -> q1))\r\n: stt unit (p0 ** p1) (fun _ -> q0 ** q1)\nlet par f0 f1 = fun _ -> Sem.par (f0 ()) (f1 ())", "val par_lpre (#st: st) (#preL: st.hprop) (lpreL: l_pre preL) (#preR: st.hprop) (lpreR: l_pre preR)\n : l_pre (preL `st.star` preR)\nlet par_lpre\n (#st:st)\n (#preL:st.hprop)\n (lpreL:l_pre preL)\n (#preR:st.hprop)\n (lpreR:l_pre preR)\n : l_pre (preL `st.star` preR)\n =\n fun h -> lpreL h /\\ lpreR h", "val sub (#a:Type u#a)\r\n (#pre1:slprop)\r\n (pre2:slprop)\r\n (#post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1:slprop_equiv pre1 pre2)\r\n (pf2:slprop_post_equiv post1 post2)\r\n (e:stt a pre1 post1)\r\n: stt a pre2 post2\nlet sub (#a:Type u#a)\r\n (#pre1:slprop)\r\n (pre2:slprop)\r\n (#post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1:slprop_equiv pre1 pre2)\r\n (pf2:slprop_post_equiv post1 post2)\r\n (e:stt a pre1 post1)\r\n: stt a pre2 post2\r\n= coerce_eq (conv pre1 pre2 post1 post2 pf1 pf2) e", "val bind_lpost\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post_a: post_t st a)\n (lpre_a: l_pre pre)\n (lpost_a: l_post pre post_a)\n (#b: Type)\n (#post_b: post_t st b)\n (lpost_b: (x: a -> l_post (post_a x) post_b))\n : l_post pre post_b\nlet bind_lpost\n (#st:st)\n (#a:Type)\n (#pre:st.hprop)\n (#post_a:post_t st a)\n (lpre_a:l_pre pre)\n (lpost_a:l_post pre post_a)\n (#b:Type)\n (#post_b:post_t st b)\n (lpost_b:(x:a -> l_post (post_a x) post_b))\n : l_post pre post_b\n =\n fun h0 y h2 -> lpre_a h0 /\\ (exists x h1. lpost_a h0 x h1 /\\ (lpost_b x) h1 y h2)", "val frame_lpost\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post: post_t st a)\n (lpre: l_pre pre)\n (lpost: l_post pre post)\n (#frame: st.hprop)\n (f_frame: fp_prop frame)\n : l_post (pre `st.star` frame) (fun x -> (post x) `st.star` frame)\nlet frame_lpost\n (#st:st)\n (#a:Type)\n (#pre:st.hprop)\n (#post:post_t st a)\n (lpre:l_pre pre)\n (lpost:l_post pre post)\n (#frame:st.hprop)\n (f_frame:fp_prop frame)\n : l_post (pre `st.star` frame) (fun x -> post x `st.star` frame)\n =\n fun h0 x h1 -> lpre h0 /\\ lpost h0 x h1 /\\ f_frame h1", "val now\n (#a #pre #post : _)\n (f : unit -> stt a pre post)\n : unit -> stt a pre post\nlet now f () = f ()", "val with_pre (pre: vprop) (#a: Type) (#post: (a -> vprop)) (m: stt a emp post)\n : stt a pre (fun v -> pre ** post v)\nlet with_pre (pre:vprop) (#a:Type) (#post:a -> vprop)(m:stt a emp post)\n: stt a pre (fun v -> pre ** post v)\n= let m1 = frame_stt pre m in\n let pf_post : vprop_post_equiv (fun r -> post r ** pre) (fun r -> pre ** post r)\n = intro_vprop_post_equiv _ _ (fun r -> vprop_equiv_comm (post r) pre)\n in\n sub_stt _ _ (vprop_equiv_unit pre) pf_post m1", "val spawn\n (#a:Type0)\n (#pre: vprop)\n (#post : (a -> vprop))\n (p: par_env)\n (f : (par_env -> unit -> stt a pre post))\n: stt (handler post) pre (fun _ -> emp)\nlet spawn #a #pre #post = spawn' #a #pre #post", "val bind_lpre\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post_a: post_t st a)\n (lpre_a: l_pre pre)\n (lpost_a: l_post pre post_a)\n (lpre_b: (x: a -> l_pre (post_a x)))\n : l_pre pre\nlet bind_lpre\n (#st:st)\n (#a:Type)\n (#pre:st.hprop)\n (#post_a:post_t st a)\n (lpre_a:l_pre pre)\n (lpost_a:l_post pre post_a)\n (lpre_b:(x:a -> l_pre (post_a x)))\n : l_pre pre\n =\n fun h -> lpre_a h /\\ (forall (x:a) h1. lpost_a h x h1 ==> lpre_b x h1)", "val perform\n (#a #pre #post : _)\n (f : unit -> stt a pre post)\n : stt a pre post\nlet perform f = f ()", "val fix_stt_1 (#a : Type) (#b : a -> Type) (#pre : a -> vprop) (#post : (x:a -> b x -> vprop))\n (ff : (y:a -> stt (b y) (pre y) (post y)) -> (x:a -> stt (b x) (pre x) (post x)))\n : x:a -> stt (b x) (pre x) (post x)\nlet fix_stt_1\n (#a : Type)\n (#b : a -> Type)\n (#pre : a -> vprop)\n (#post : (x:a -> b x -> vprop))\n (kk : ((y:a -> stt (b y) (pre y) (post y)) -> x:a -> stt (b x) (pre x) (post x)))\n: x:a -> stt (b x) (pre x) (post x)\n= fun x -> \n hide_div (fix_stt_1_div #a #b #pre #post (fun f x () -> kk (fun y -> hide_div (f y)) x) x)", "val exec_unit_stt (#a #pre #post: _) (f: unit_stt a pre post) : stt a pre (fun y -> post y)\nlet exec_unit_stt #a #pre #post\n (f : unit_stt a pre post)\n: stt a pre (fun y -> post y)\n= sub_stt _ _ (vprop_equiv_refl _) (intro_vprop_post_equiv _ _ (fun _ -> vprop_equiv_refl _)) (f ())", "val par\n (#st: state u#s u#act)\n (#p0 #q0: _)\n (m0: m unit p0 (as_post q0))\n (#p1 #q1: _)\n (m1: m unit p1 (as_post q1))\n : Dv (m unit (p0 `st.star` p1) (as_post (q0 `st.star` q1)))\nlet par (#st:state u#s u#act)\n #p0 #q0 (m0:m unit p0 (as_post q0))\n #p1 #q1 (m1:m unit p1 (as_post q1))\n : Dv (m unit (p0 `st.star` p1) (as_post (q0 `st.star` q1)))\n = let m0' = mbind m0 (fun _ -> Ret #_ #_ #(as_post q0) (U.raise_val u#0 u#0 ())) in\n let m1' = mbind m1 (fun _ -> Ret #_ #_ #(as_post q1) (U.raise_val u#0 u#0 ())) in\n Par m0' m1' (Ret ())", "val bind\r\n (#a:Type u#a) (#b:Type u#b)\r\n (#pre1:slprop) (#post1:a -> slprop) (#post2:b -> slprop)\r\n (e1:stt a pre1 post1)\r\n (e2:(x:a -> stt b (post1 x) post2))\r\n: stt b pre1 post2\nlet bind\r\n (#a:Type u#a) (#b:Type u#b)\r\n (#pre1:slprop) (#post1:a -> slprop) (#post2:b -> slprop)\r\n (e1:stt a pre1 post1)\r\n (e2:(x:a -> stt b (post1 x) post2))\r\n: stt b pre1 post2\r\n= fun _ -> Sem.mbind (e1()) (fun x -> e2 x ())", "val step_par_ret\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post: post_t st a)\n (f: m st a pre post {Par? f /\\ Ret? (Par?.mL f) /\\ Ret? (Par?.mR f)})\n : Mst (step_result st a) (step_req f) (step_ens f)\nlet step_par_ret (#st:st) (#a:Type) (#pre:st.hprop) (#post:post_t st a)\n (f:m st a pre post{Par? f /\\ Ret? (Par?.mL f) /\\ Ret? (Par?.mR f)})\n: Mst (step_result st a) (step_req f) (step_ens f)\n= NMSTATE?.reflect (fun (_, n) -> step_par_ret_aux f, n)", "val par_weaker_lpre_and_stronger_lpost_r\n (#st: st)\n (preL: st.hprop)\n (#aL: Type)\n (postL: post_t st aL)\n (preR: st.hprop)\n (#aR: Type)\n (postR: post_t st aR)\n (next_preR: st.hprop)\n (next_postR: post_t st aR)\n (state next_state: st.mem)\n : Lemma\n (requires\n preserves_frame preR next_preR state next_state /\\\n st.interp ((preL `st.star` preR) `st.star` (st.invariant state)) state)\n (ensures st.interp ((preL `st.star` next_preR) `st.star` (st.invariant next_state)) next_state\n )\nlet par_weaker_lpre_and_stronger_lpost_r (#st:st)\n (preL:st.hprop) (#aL:Type) (postL:post_t st aL)\n (preR:st.hprop) (#aR:Type) (postR:post_t st aR)\n (next_preR:st.hprop) (next_postR:post_t st aR)\n (state next_state:st.mem)\n: Lemma\n (requires\n preserves_frame preR next_preR state next_state /\\\n st.interp ((preL `st.star` preR) `st.star` st.invariant state) state)\n (ensures\n st.interp ((preL `st.star` next_preR) `st.star` st.invariant next_state) next_state)\n= commute_star_right (st.invariant state) preL preR;\n apply_interp_ext\n (st.invariant state `st.star` (preL `st.star` preR))\n (st.invariant state `st.star` (preR `st.star` preL))\n state;\n commute_star_right (st.invariant next_state) next_preR preL;\n apply_interp_ext\n (st.invariant next_state `st.star` (next_preR `st.star` preL))\n (st.invariant next_state `st.star` (preL `st.star` next_preR))\n next_state", "val conv (#a:Type u#a)\r\n (pre1:slprop)\r\n (pre2:slprop)\r\n (post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1:slprop_equiv pre1 pre2)\r\n (pf2:slprop_post_equiv post1 post2)\r\n: Lemma (stt a pre1 post1 == stt a pre2 post2)\nlet conv (#a:Type u#a)\r\n (pre1:slprop)\r\n (pre2:slprop)\r\n (post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1:slprop_equiv pre1 pre2)\r\n (pf2:slprop_post_equiv post1 post2)\r\n: Lemma (stt a pre1 post1 == stt a pre2 post2)\r\n= slprop_equiv_elim pre1 pre2;\r\n introduce forall x. post1 x == post2 x\r\n with slprop_equiv_elim (post1 x) (post2 x);\r\n Sem.conv #state a #pre1 #(F.on_dom _ post1) (F.on_dom _ post2);\r\n ()", "val par_weaker_lpre_and_stronger_lpost_l\n (#st: st)\n (#preL: st.hprop)\n (lpreL: l_pre preL)\n (#aL: Type)\n (#postL: post_t st aL)\n (lpostL: l_post preL postL)\n (#next_preL: st.hprop)\n (#next_postL: post_t st aL)\n (next_lpreL: l_pre next_preL)\n (next_lpostL: l_post next_preL next_postL)\n (#preR: st.hprop)\n (lpreR: l_pre preR)\n (#aR: Type)\n (#postR: post_t st aR)\n (lpostR: l_post preR postR)\n (state next_state: st.mem)\n : Lemma\n (requires\n weaker_lpre lpreL next_lpreL state next_state /\\\n stronger_lpost lpostL next_lpostL state next_state /\\\n post_preserves_frame next_preL preR state next_state /\\ lpreL (st.core state) /\\\n lpreR (st.core state) /\\\n st.interp ((preL `st.star` preR) `st.star` (st.locks_invariant state)) state)\n (ensures\n weaker_lpre (par_lpre lpreL lpreR) (par_lpre next_lpreL lpreR) state next_state /\\\n stronger_lpost (par_lpost lpreL lpostL lpreR lpostR)\n (par_lpost next_lpreL next_lpostL lpreR lpostR)\n state\n next_state)\nlet par_weaker_lpre_and_stronger_lpost_l\n (#st:st)\n (#preL:st.hprop)\n (lpreL:l_pre preL)\n (#aL:Type)\n (#postL:post_t st aL)\n (lpostL:l_post preL postL)\n (#next_preL:st.hprop)\n (#next_postL:post_t st aL)\n (next_lpreL:l_pre next_preL)\n (next_lpostL:l_post next_preL next_postL)\n (#preR:st.hprop)\n (lpreR:l_pre preR)\n (#aR:Type)\n (#postR:post_t st aR)\n (lpostR:l_post preR postR)\n (state next_state:st.mem)\n : Lemma\n (requires\n weaker_lpre lpreL next_lpreL state next_state /\\\n stronger_lpost lpostL next_lpostL state next_state /\\\n post_preserves_frame next_preL preR state next_state /\\\n lpreL (st.core state) /\\\n lpreR (st.core state) /\\\n st.interp ((preL `st.star` preR) `st.star` st.locks_invariant state) state)\n (ensures\n weaker_lpre\n (par_lpre lpreL lpreR)\n (par_lpre next_lpreL lpreR)\n state next_state /\\\n stronger_lpost\n (par_lpost lpreL lpostL lpreR lpostR)\n (par_lpost next_lpreL next_lpostL lpreR lpostR)\n state next_state)\n =\n frame_post_for_par preL next_preL state next_state lpreR lpostR;\n assert (weaker_lpre (par_lpre lpreL lpreR) (par_lpre next_lpreL lpreR) state next_state) by\n (norm [delta_only [`%weaker_lpre; `%par_lpre] ])", "val par0\n (#aL: Type u#a)\n (#preL: vprop)\n (#postL: (aL -> vprop))\n (f: repr aL false preL postL (fun _ -> True) (fun _ _ _ -> True))\n (#aR: Type u#a)\n (#preR: vprop)\n (#postR: (aR -> vprop))\n (g: repr aR false preR postR (fun _ -> True) (fun _ _ _ -> True))\n : SteelT (aL & aR) (preL `star` preR) (fun y -> (postL (fst y)) `star` (postR (snd y)))\nlet par0 (#aL:Type u#a) (#preL:vprop) (#postL:aL -> vprop)\n (f:repr aL false preL postL (fun _ -> True) (fun _ _ _ -> True))\n (#aR:Type u#a) (#preR:vprop) (#postR:aR -> vprop)\n (g:repr aR false preR postR (fun _ -> True) (fun _ _ _ -> True))\n : SteelT (aL & aR)\n (preL `star` preR)\n (fun y -> postL (fst y) `star` postR (snd y))\n = Steel?.reflect (fun frame -> Sem.run #state #_ #_ #_ #_ #_ frame (Sem.Par (Sem.Act f) (Sem.Act g)))", "val async\n (#a : Type0)\n (#pre : vprop)\n (#post : (a -> vprop))\n (f : (unit -> stt a pre post))\n : stt (asynch a post) pre (fun h -> async_joinable h)\nlet async = __async", "val with_invlist (#a:Type0) (#pre : vprop) (#post : a -> vprop)\n (is : invlist)\n (f : unit -> stt_atomic a #Unobservable emp_inames (invlist_v is ** pre) (fun v -> invlist_v is ** post v))\n : stt_atomic a #Unobservable (invlist_names is) pre (fun v -> post v)\nlet with_invlist = __with_invlist", "val with_invlist_ghost (#pre : vprop) (#post : vprop)\n (is : invlist)\n (f : unit -> stt_ghost unit (invlist_v is ** pre) (fun _ -> invlist_v is ** post))\n : stt_atomic unit #Unobservable (invlist_names is) pre (fun _ -> post)\nlet with_invlist_ghost = __with_invlist_ghost", "val lpost_ret_act\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post: post_t st a)\n (lpost: l_post pre post)\n (x: a)\n (state: st.mem)\n : l_post (post x) post\nlet lpost_ret_act\n (#st:st)\n (#a:Type)\n (#pre:st.hprop)\n (#post:post_t st a)\n (lpost:l_post pre post)\n (x:a)\n (state:st.mem)\n : l_post (post x) post\n =\n fun _ x h1 -> lpost (st.core state) x h1", "val perform_ghost\n (#a #pre #post : _)\n (f : unit -> stt_ghost a pre post)\n : stt_ghost a pre post\nlet perform_ghost f = f ()", "val step_par_ret\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post: post_t st a)\n (#lpre: l_pre pre)\n (#lpost: l_post pre post)\n (frame: st.hprop)\n (f: m st a pre post lpre lpost {Par? f /\\ Ret? (Par?.mL f) /\\ Ret? (Par?.mR f)})\n : Mst (step_result st a) (step_req frame f) (step_ens frame f)\nlet step_par_ret\n (#st:st)\n (#a:Type)\n (#pre:st.hprop)\n (#post:post_t st a)\n (#lpre:l_pre pre)\n (#lpost:l_post pre post)\n (frame:st.hprop)\n (f:m st a pre post lpre lpost{Par? f /\\ Ret? (Par?.mL f) /\\ Ret? (Par?.mR f)})\n : Mst (step_result st a) (step_req frame f) (step_ens frame f)\n =\n NMSTATE?.reflect (fun (_, n) -> step_par_ret_aux frame f, n)", "val elab_stt_equiv\n (g: R.env)\n (c: comp{C_ST? c})\n (pre post: R.term)\n (eq_pre: RT.equiv g pre (elab_term (comp_pre c)))\n (eq_post:\n RT.equiv g post (mk_abs (elab_term (comp_res c)) R.Q_Explicit (elab_term (comp_post c))))\n : RT.equiv g\n (let C_ST { u = u ; res = res } = c in\n mk_stt_comp u (elab_term res) pre post)\n (elab_comp c)\nlet elab_stt_equiv (g:R.env) (c:comp{C_ST? c}) (pre:R.term) (post:R.term)\n (eq_pre:RT.equiv g pre (elab_term (comp_pre c)))\n (eq_post:RT.equiv g post\n (mk_abs (elab_term (comp_res c)) R.Q_Explicit (elab_term (comp_post c))))\n : RT.equiv g\n (let C_ST {u;res} = c in\n mk_stt_comp u\n (elab_term res)\n pre\n post)\n (elab_comp c) =\n \n mk_stt_comp_equiv _\n (comp_u c)\n (elab_term (comp_res c))\n _ _ _ _ _ (RT.Rel_refl _ _ _) eq_pre eq_post", "val step_par_ret_aux\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post: post_t st a)\n (f: m st a pre post {Par? f /\\ Ret? (Par?.mL f) /\\ Ret? (Par?.mR f)})\n : M.MSTATE (step_result st a) st.mem st.evolves (step_req f) (step_ens f)\nlet step_par_ret_aux (#st:st) (#a:Type) (#pre:st.hprop) (#post:post_t st a)\n (f:m st a pre post{Par? f /\\ Ret? (Par?.mL f) /\\ Ret? (Par?.mR f)})\n: M.MSTATE (step_result st a) st.mem st.evolves (step_req f) (step_ens f)\n= M.MSTATE?.reflect (fun m0 ->\n let Par (Ret pL xL) (Ret pR xR) = f in\n Step (Ret (fun (xL, xR) -> pL xL `st.star` pR xR) (xL, xR)), m0)", "val promote_seq: #a: _ -> #pre: _ -> #post: _ -> f: stt a pre post -> par_env -> unit\n -> stt a pre post\nlet promote_seq #a #pre #post\n (f: stt a pre post)\n: par_env -> unit -> stt a pre post\n= (fun _ -> fun _ -> f)", "val par_weaker_lpre_and_stronger_lpost_r\n (#st: st)\n (#preL: st.hprop)\n (lpreL: l_pre preL)\n (#aL: Type)\n (#postL: post_t st aL)\n (lpostL: l_post preL postL)\n (#preR: st.hprop)\n (lpreR: l_pre preR)\n (#aR: Type)\n (#postR: post_t st aR)\n (lpostR: l_post preR postR)\n (#next_preR: st.hprop)\n (#next_postR: post_t st aR)\n (next_lpreR: l_pre next_preR)\n (next_lpostR: l_post next_preR next_postR)\n (frame: st.hprop)\n (state next_state: st.mem)\n : Lemma\n (requires\n weaker_lpre lpreR next_lpreR state next_state /\\\n stronger_lpost lpostR next_lpostR state next_state /\\\n post_preserves_frame next_preR (preL `st.star` frame) state next_state /\\\n lpreR (st.core state) /\\ lpreL (st.core state) /\\\n st.interp (((preL `st.star` preR) `st.star` frame) `st.star` (st.locks_invariant state))\n state)\n (ensures\n st.interp (((preL `st.star` next_preR) `st.star` frame)\n `st.star`\n (st.locks_invariant next_state))\n next_state /\\\n weaker_lpre (par_lpre lpreL lpreR) (par_lpre lpreL next_lpreR) state next_state /\\\n stronger_lpost (par_lpost lpreL lpostL lpreR lpostR)\n (par_lpost lpreL lpostL next_lpreR next_lpostR)\n state\n next_state)\nlet par_weaker_lpre_and_stronger_lpost_r\n (#st:st)\n (#preL:st.hprop)\n (lpreL:l_pre preL)\n (#aL:Type)\n (#postL:post_t st aL)\n (lpostL:l_post preL postL)\n (#preR:st.hprop)\n (lpreR:l_pre preR)\n (#aR:Type)\n (#postR:post_t st aR)\n (lpostR:l_post preR postR)\n (#next_preR:st.hprop)\n (#next_postR:post_t st aR)\n (next_lpreR:l_pre next_preR)\n (next_lpostR:l_post next_preR next_postR)\n (frame:st.hprop)\n (state next_state:st.mem)\n : Lemma\n (requires\n weaker_lpre lpreR next_lpreR state next_state /\\\n stronger_lpost lpostR next_lpostR state next_state /\\\n post_preserves_frame next_preR (preL `st.star` frame) state next_state /\\\n lpreR (st.core state) /\\\n lpreL (st.core state) /\\\n st.interp ((preL `st.star` preR) `st.star` frame `st.star` st.locks_invariant state) state)\n (ensures\n st.interp ((preL `st.star` next_preR) `st.star` frame `st.star` st.locks_invariant next_state) next_state /\\\n weaker_lpre\n (par_lpre lpreL lpreR)\n (par_lpre lpreL next_lpreR)\n state next_state /\\\n stronger_lpost\n (par_lpost lpreL lpostL lpreR lpostR)\n (par_lpost lpreL lpostL next_lpreR next_lpostR)\n state next_state)\n =\n calc (st.equals) {\n preL `st.star` preR `st.star` frame `st.star` st.locks_invariant state;\n (st.equals) { }\n preR `st.star` preL `st.star` frame `st.star` st.locks_invariant state;\n (st.equals) { }\n preR `st.star` preL `st.star` (frame `st.star` st.locks_invariant state);\n (st.equals) { equals_ext_right (preR `st.star` preL)\n (frame `st.star` st.locks_invariant state)\n (st.locks_invariant state `st.star` frame) }\n preR `st.star` preL `st.star` (st.locks_invariant state `st.star` frame);\n (st.equals) { }\n preR `st.star` preL `st.star` st.locks_invariant state `st.star` frame;\n };\n assert (st.interp (preR `st.star` preL `st.star` st.locks_invariant state) state);\n frame_post_for_par preR next_preR state next_state lpreL lpostL;\n assert (weaker_lpre (par_lpre lpreL lpreR) (par_lpre lpreL next_lpreR) state next_state) by\n (norm [delta_only [`%weaker_lpre; `%par_lpre] ]);\n commute_star_par_r preL next_preR frame (st.locks_invariant next_state) next_state", "val sub_ghost\r\n (#a:Type u#a)\r\n (#pre1:slprop)\r\n (pre2:slprop)\r\n (#post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1 : slprop_equiv pre1 pre2)\r\n (pf2 : slprop_post_equiv post1 post2)\r\n (e:stt_ghost a pre1 post1)\r\n: stt_ghost a pre2 post2\nlet sub_ghost pre2 post2 pf1 pf2 e\r\n= Ghost.hide (A.sub pre2 post2 e)", "val fix_stt_1_div:\n #a: Type ->\n #b: (a -> Type) ->\n #pre: (a -> vprop) ->\n #post: (x: a -> b x -> vprop) ->\n kk:\n ((y: a -> unit -> Dv (stt (b y) (pre y) (post y))) -> x: a -> unit\n -> Dv (stt (b x) (pre x) (post x))) ->\n x: a ->\n unit\n -> Dv (stt (b x) (pre x) (post x))\nlet fix_stt_1_div\n (#a : Type)\n (#b : a -> Type)\n (#pre : a -> vprop)\n (#post : (x:a -> b x -> vprop))\n (kk : ((y:a -> unit -> Dv (stt (b y) (pre y) (post y))) ->\n x:a -> unit -> Dv (stt (b x) (pre x) (post x))))\n: x:a -> unit -> Dv (stt (b x) (pre x) (post x))\n= let rec f (x:a) (_:unit) : Dv (stt (b x) (pre x) (post x)) = \n kk (fun y () -> f y ()) x ()\n in\n f", "val fix_stt_ghost_1 (#a : Type) (#b : a -> Type) (#pre : a -> vprop) (#post : (x:a -> b x -> vprop))\n (ff : (x:a -> (y:a{y << x} -> stt_ghost (b y) (pre y) (post y)) -> stt_ghost (b x) (pre x) (post x)))\n : x:a -> stt_ghost (b x) (pre x) (post x)\nlet fix_stt_ghost_1 (#a : Type) (#b : a -> Type) (#pre : a -> vprop) (#post : (x:a -> b x -> vprop))\n (ff : (x:a -> (y:a{y << x} -> stt_ghost (b y) (pre y) (post y)) -> stt_ghost (b x) (pre x) (post x)))\n : x:a -> stt_ghost (b x) (pre x) (post x)\n = fix_1 #a #(fun x -> stt_ghost (b x) (pre x) (post x)) ff", "val test_rww\n (#pre #post: _)\n (b: bool)\n (f: (unit -> RWI int RO pre post))\n (g: (unit -> RWI int RW pre post))\n : RWI int RW pre post\nlet test_rww #pre #post (b:bool) (f : unit -> RWI int RO pre post) (g : unit -> RWI int RW pre post) : RWI int RW pre post = if b then f () else g ()", "val test_wrw\n (#pre #post: _)\n (b: bool)\n (f: (unit -> RWI int RW pre post))\n (g: (unit -> RWI int RO pre post))\n : RWI int RW pre post\nlet test_wrw #pre #post (b:bool) (f : unit -> RWI int RW pre post) (g : unit -> RWI int RO pre post) : RWI int RW pre post = if b then f () else g ()", "val return_lpre (#st: st) (#a: Type) (#post: post_t st a) (x: a) (lpost: l_post (post x) post)\n : l_pre (post x)\nlet return_lpre (#st:st) (#a:Type) (#post:post_t st a) (x:a) (lpost:l_post (post x) post)\n : l_pre (post x)\n =\n fun h -> lpost h x h", "val frame\r\n (#a:Type u#a)\r\n (#pre:slprop) (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt a pre post)\r\n: stt a (pre ** frame) (fun x -> post x ** frame)\nlet frame\r\n (#a:Type u#a)\r\n (#pre:slprop) (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt a pre post)\r\n: stt a (pre `star` frame) (fun x -> post x `star` frame)\r\n= fun _ -> Sem.frame frame (e())", "val preorder_app'\n (#a #b: Type)\n (#rel: preorder state)\n (#wp1: mst_wp state a rel)\n (#wp2: (a -> mst_wp state b rel))\n (f: (unit -> GMST a (rel >< wp1)))\n (g: (x: a -> GMST b (rel >< wp2 x)))\n : GMST b (rel @ rel >< (fun s0 p -> wp1 s0 (fun x s1 -> wp2 x s1 p)))\nlet preorder_app' (#a:Type) (#b:Type)\n (#rel:preorder state)\n (#wp1:mst_wp state a rel) \n (#wp2:a -> mst_wp state b rel)\n (f:unit -> GMST a (rel >< wp1))\n (g:(x:a -> GMST b (rel >< wp2 x)))\n : GMST b (rel @ rel >< (fun s0 p -> wp1 s0 (fun x s1 -> wp2 x s1 p)))\n = g (f ())", "val frame_lpre\n (#st: st)\n (#pre: st.hprop)\n (lpre: l_pre pre)\n (#frame: st.hprop)\n (f_frame: fp_prop frame)\n : l_pre (pre `st.star` frame)\nlet frame_lpre (#st:st) (#pre:st.hprop) (lpre:l_pre pre) (#frame:st.hprop) (f_frame:fp_prop frame)\n : l_pre (pre `st.star` frame)\n =\n fun h -> lpre h /\\ f_frame h", "val st_equiv_post\n (#g: env)\n (#t: st_term)\n (#c: comp_st)\n (d: st_typing g t c)\n (post: term{(freevars post) `Set.subset` (freevars (comp_post c))})\n (veq:\n (x: var{fresh_wrt x g (freevars (comp_post c))}\n -> vprop_equiv (push_binding g x ppname_default (comp_res c))\n (open_term (comp_post c) x)\n (open_term post x)))\n : st_typing g t (comp_st_with_post c post)\nlet st_equiv_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { freevars post `Set.subset` freevars (comp_post c)})\n (veq: (x:var { fresh_wrt x g (freevars (comp_post c)) } ->\n vprop_equiv (push_binding g x ppname_default (comp_res c)) \n (open_term (comp_post c) x)\n (open_term post x)))\n : st_typing g t (comp_st_with_post c post)\n = if eq_tm post (comp_post c) then d\n else\n let c' = comp_st_with_post c post in\n let (| u_of, pre_typing, x, post_typing |) = Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let veq = veq x in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) (VE_Refl _ _) veq\n in\n t_equiv d st_equiv", "val inst_heap_prop_for_par\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post: post_t st a)\n (lpost: l_post pre post)\n (state: st.mem)\n : fp_prop pre\nlet inst_heap_prop_for_par\n (#st:st)\n (#a:Type)\n (#pre:st.hprop)\n (#post:post_t st a)\n (lpost:l_post pre post)\n (state:st.mem)\n : fp_prop pre\n =\n fun h ->\n forall x final_state.\n lpost h x final_state <==>\n lpost (st.core state) x final_state", "val simple_for\n (pre post: (nat -> vprop))\n (r: vprop)\n (f: (i: nat -> stt unit (r ** pre i) (fun () -> r ** post i)))\n (n: nat)\n : stt unit (r ** range pre 0 n) (fun _ -> r ** range post 0 n)\nlet simple_for :\n (pre : (nat -> vprop)) ->\n (post : (nat -> vprop)) ->\n (r : vprop) -> // This resource is passed around through iterations.\n (f : (i:nat -> stt unit (r ** pre i) (fun () -> r ** post i))) ->\n (n : nat) ->\n stt unit (r ** range pre 0 n) (fun _ -> r ** range post 0 n)\n = \n fun pre post r f -> fix_stt_1 (__simple_for pre post r f)", "val frame_post_for_par\n (#st: st)\n (pre_s post_s: st.hprop)\n (m0 m1: st.mem)\n (#a: Type)\n (#pre_f: st.hprop)\n (#post_f: post_t st a)\n (lpre_f: l_pre pre_f)\n (lpost_f: l_post pre_f post_f)\n : Lemma\n (requires\n post_preserves_frame post_s pre_f m0 m1 /\\\n st.interp ((pre_s `st.star` pre_f) `st.star` (st.locks_invariant m0)) m0)\n (ensures\n (lpre_f (st.core m0) <==> lpre_f (st.core m1)) /\\\n (forall (x: a) (final_state: st.mem).\n lpost_f (st.core m0) x final_state <==> lpost_f (st.core m1) x final_state))\nlet frame_post_for_par\n (#st:st)\n (pre_s post_s:st.hprop)\n (m0 m1:st.mem)\n (#a:Type)\n (#pre_f:st.hprop)\n (#post_f:post_t st a)\n (lpre_f:l_pre pre_f)\n (lpost_f:l_post pre_f post_f)\n : Lemma\n (requires\n post_preserves_frame post_s pre_f m0 m1 /\\\n st.interp ((pre_s `st.star` pre_f) `st.star` st.locks_invariant m0) m0)\n (ensures\n (lpre_f (st.core m0) <==> lpre_f (st.core m1)) /\\\n (forall (x:a) (final_state:st.mem).\n lpost_f (st.core m0) x final_state <==>\n lpost_f (st.core m1) x final_state))\n =\n frame_post_for_par_tautology lpost_f m0;\n frame_post_for_par_aux pre_s post_s m0 m1 lpost_f", "val stt (a:Type u#a) \r\n (pre:slprop)\r\n (post:a -> slprop)\r\n: Type0\nlet stt (a:Type u#a) \r\n (pre:slprop)\r\n (post:a -> slprop)\r\n: Type0\r\n= lower (Sem.m u#2 u#100 u#a #state a pre (F.on_dom a post))", "val of_msttotal (#s:Type u#2) (rel:FStar.Preorder.preorder s)\r\n (a:Type u#a) (pre:s -> prop) (post:s -> a -> s -> prop)\r\n (f:unit -> M.MSTATETOT a s rel pre post)\r\n: mst rel a pre post\nlet of_msttotal (#s:Type u#2) (rel:FStar.Preorder.preorder s)\r\n (a:Type u#a) (pre:s -> prop) (post:s -> a -> s -> prop)\r\n (f:unit -> M.MSTATETOT a s rel pre post)\r\n: mst rel a pre post\r\n= let f = reify_ f in\r\n fun s -> f s", "val stc_soundness\n (#g:stt_env)\n (#st:st_comp)\n (d_st:st_comp_typing g st)\n \n : GTot (RT.tot_typing ( elab_env g)\n (elab_term st.res)\n (RT.tm_type st.u) &\n RT.tot_typing (elab_env g)\n (elab_term st.pre)\n vprop_tm &\n RT.tot_typing (elab_env g)\n (mk_abs (elab_term st.res) R.Q_Explicit\n (elab_term st.post))\n (post1_type_bind (elab_term st.res)))\nlet stc_soundness\n (#g:stt_env)\n (#st:st_comp)\n (d_st:st_comp_typing g st)\n \n : GTot (RT.tot_typing (elab_env g)\n (elab_term st.res)\n (RT.tm_type st.u) &\n RT.tot_typing (elab_env g)\n (elab_term st.pre)\n vprop_tm &\n RT.tot_typing (elab_env g)\n (mk_abs (elab_term st.res) R.Q_Explicit\n (elab_term st.post))\n (post1_type_bind (elab_term st.res))) =\n \n let STC _ st x dres dpre dpost = d_st in\n let res_typing = tot_typing_soundness dres in\n let pre_typing = tot_typing_soundness dpre in \n calc (==) {\n RT.close_term (elab_term (open_term st.post x)) x;\n (==) { elab_open_commute st.post x }\n RT.close_term (RT.open_term (elab_term st.post) x) x;\n (==) { \n elab_freevars st.post;\n RT.close_open_inverse (elab_term st.post) x\n }\n elab_term st.post;\n };\n let post_typing = mk_t_abs_tot g ppname_default dres dpost in\n res_typing, pre_typing, post_typing", "val spawn_emp\n (#a:Type0)\n (p: par_env)\n (post: (a -> prop))\n (f : (par_env -> unit_emp_stt_pure_pure a post))\n: stt (pure_handler post) emp (fun _ -> emp)\nlet spawn_emp = spawn_emp'", "val bind\n (a b: Type)\n (#framed_f #framed_g: eqtype_as_type bool)\n (#[@@@ framing_implicit]pre_f: pre_t)\n (#[@@@ framing_implicit]post_f: post_t a)\n (#[@@@ framing_implicit]pre_g: (a -> pre_t))\n (#[@@@ framing_implicit]post_g: post_t b)\n (#[@@@ framing_implicit]frame_f #[@@@ framing_implicit]frame_g: vprop)\n (#[@@@ framing_implicit]p:\n squash (can_be_split_forall (fun x -> (post_f x) `star` frame_f)\n (fun x -> (pre_g x) `star` frame_g)))\n (#[@@@ framing_implicit]m1: squash (maybe_emp framed_f frame_f))\n (#[@@@ framing_implicit]m2: squash (maybe_emp framed_g frame_g))\n (f: steelK a framed_f pre_f post_f)\n (g: (x: a -> steelK b framed_g (pre_g x) post_g))\n : steelK b true (pre_f `star` frame_f) (fun y -> (post_g y) `star` frame_g)\nlet bind (a:Type) (b:Type)\n (#framed_f:eqtype_as_type bool) (#framed_g:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre_f:pre_t) (#[@@@ framing_implicit] post_f:post_t a)\n (#[@@@ framing_implicit] pre_g:a -> pre_t) (#[@@@ framing_implicit] post_g:post_t b)\n (#[@@@ framing_implicit] frame_f:vprop) (#[@@@ framing_implicit] frame_g:vprop)\n (#[@@@ framing_implicit] p:squash (can_be_split_forall\n (fun x -> post_f x `star` frame_f) (fun x -> pre_g x `star` frame_g)))\n (#[@@@ framing_implicit] m1 : squash (maybe_emp framed_f frame_f))\n (#[@@@ framing_implicit] m2:squash (maybe_emp framed_g frame_g))\n (f:steelK a framed_f pre_f post_f)\n (g:(x:a -> steelK b framed_g (pre_g x) post_g))\n: steelK b\n true\n (pre_f `star` frame_f)\n (fun y -> post_g y `star` frame_g)\n = fun #frame (#post:vprop) (k:(y:b -> SteelT unit (frame `star` (post_g y `star` frame_g)) (fun _ -> post))) ->\n // Need SteelT unit (frame `star` (pre_f `star` frame_f)) (fun _ -> post)\n change_slprop_equiv (frame `star` (pre_f `star` frame_f)) ((frame `star` frame_f) `star` pre_f) (rearrange3 frame frame_f pre_f;\n equiv_symmetric ((frame `star` frame_f) `star` pre_f) (frame `star` (pre_f `star` frame_f)) );\n f #(frame `star` frame_f) #post\n ((fun (x:a) ->\n // Need SteelT unit ((frame `star` frame_f) `star` post_f x) (fun _ -> post)\n change_slprop_imp\n (frame `star` (post_f x `star` frame_f))\n (frame `star` (pre_g x `star` frame_g))\n (can_be_split_forall_frame (fun x -> post_f x `star` frame_f) (fun x -> pre_g x `star` frame_g) frame x);\n g x #(frame `star` frame_g) #post\n ((fun (y:b) -> k y)\n <: (y:b -> SteelT unit ((frame `star` frame_g) `star` post_g y) (fun _ -> post)))\n\n )\n\n <: (x:a -> SteelT unit ((frame `star` frame_f) `star` post_f x) (fun _ -> post)))", "val shift_invlist_one\n (#a:Type0)\n (p : vprop)\n (i : inv p)\n (is : invlist{not (mem_inv (invlist_names is) i)})\n (#pre:vprop)\n (#post : a -> vprop)\n (f : unit -> stt_atomic a #Unobservable emp_inames (invlist_v ((| p, i |) :: is) ** pre) (fun v -> invlist_v ((| p, i |) :: is) ** post v)) :\n unit -> stt_atomic a #Unobservable emp_inames (invlist_v is ** (p ** pre)) (fun v -> invlist_v is ** (p ** post v))\nlet shift_invlist_one = __shift_invlist_one", "val quotPP (#a #pre #post: _) (f: (unit -> AlgPP a [Read] pre post))\n : AlgPP a [Read] pre (fun h0 x h1 -> post h0 x h1 /\\ h0 == h1)\nlet quotPP #a #pre #post (f : unit -> AlgPP a [Read] pre post)\n : AlgPP a [Read] pre (fun h0 x h1 -> post h0 x h1 /\\ h0 == h1)\n = quot #_ #(fun h0 p -> pre h0 /\\ (forall y h1. post h0 y h1 ==> p (y, h1))) f", "val step_par_ret_aux\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post: post_t st a)\n (#lpre: l_pre pre)\n (#lpost: l_post pre post)\n (frame: st.hprop)\n (f: m st a pre post lpre lpost {Par? f /\\ Ret? (Par?.mL f) /\\ Ret? (Par?.mR f)})\n : M.MSTATE (step_result st a)\n (full_mem st)\n st.locks_preorder\n (step_req frame f)\n (step_ens frame f)\nlet step_par_ret_aux\n (#st:st)\n (#a:Type)\n (#pre:st.hprop)\n (#post:post_t st a)\n (#lpre:l_pre pre)\n (#lpost:l_post pre post)\n (frame:st.hprop)\n (f:m st a pre post lpre lpost{Par? f /\\ Ret? (Par?.mL f) /\\ Ret? (Par?.mR f)})\n : M.MSTATE (step_result st a) (full_mem st) st.locks_preorder (step_req frame f) (step_ens frame f)\n =\n M.MSTATE?.reflect (fun m0 ->\n match f with\n | Par #_ #aL #_ #_ #_ #_ (Ret pL xL lpL) #aR #_ #_ #_ #_ (Ret pR xR lpR) ->\n let lpost : l_post\n #st #(aL & aR)\n (pL xL `st.star` pR xR)\n (fun (xL, xR) -> pL xL `st.star` pR xR)\n =\n fun h0 (xL, xR) h1 -> lpL h0 xL h1 /\\ lpR h0 xR h1\n in\n Step (pL xL `st.star` pR xR) (fun (xL, xR) -> pL xL `st.star` pR xR)\n (fun h -> lpL h xL h /\\ lpR h xR h)\n lpost\n (Ret (fun (xL, xR) -> pL xL `st.star` pR xR) (xL, xR) lpost), m0)", "val st_equiv_pre\n (#g: env)\n (#t: st_term)\n (#c: comp_st)\n (d: st_typing g t c)\n (pre: term)\n (veq: vprop_equiv g (comp_pre c) pre)\n : st_typing g t (comp_with_pre c pre)\nlet st_equiv_pre (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (pre:term)\n (veq: vprop_equiv g (comp_pre c) pre)\n : st_typing g t (comp_with_pre c pre)\n = if eq_tm pre (comp_pre c) then d\n else\n let c' = comp_with_pre c pre in\n let (| u_of, pre_typing, x, post_typing |) =\n Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) veq (VE_Refl _ _)\n in\n t_equiv d st_equiv", "val stronger_post_par_r\n (#st: st)\n (#aL #aR: Type u#a)\n (postL: post_t st aL)\n (postR next_postR: post_t st aR)\n : Lemma (requires stronger_post postR next_postR)\n (ensures\n forall xL xR frame h.\n st.interp (((postL xL) `st.star` (next_postR xR)) `st.star` frame) h ==>\n st.interp (((postL xL) `st.star` (postR xR)) `st.star` frame) h)\nlet stronger_post_par_r (#st:st) (#aL #aR:Type u#a)\n (postL:post_t st aL) (postR:post_t st aR) (next_postR:post_t st aR)\n: Lemma\n (requires stronger_post postR next_postR)\n (ensures\n forall xL xR frame h.\n st.interp ((postL xL `st.star` next_postR xR) `st.star` frame) h ==>\n st.interp ((postL xL `st.star` postR xR) `st.star` frame) h)\n= let aux xL xR frame h\n : Lemma\n (requires st.interp ((postL xL `st.star` next_postR xR) `st.star` frame) h)\n (ensures st.interp ((postL xL `st.star` postR xR) `st.star` frame) h)\n [SMTPat ()]\n = calc (st.equals) {\n (postL xL `st.star` next_postR xR) `st.star` frame;\n (st.equals) { }\n (next_postR xR `st.star` postL xL) `st.star` frame;\n (st.equals) { }\n next_postR xR `st.star` (postL xL `st.star` frame);\n };\n assert (st.interp (next_postR xR `st.star` (postL xL `st.star` frame)) h);\n assert (st.interp (postR xR `st.star` (postL xL `st.star` frame)) h);\n calc (st.equals) {\n postR xR `st.star` (postL xL `st.star` frame);\n (st.equals) { }\n (postR xR `st.star` postL xL) `st.star` frame;\n (st.equals) { }\n (postL xL `st.star` postR xR) `st.star` frame;\n }\n in\n ()", "val stronger_post_par_r\n (#st: st)\n (#aL #aR: Type u#a)\n (postL: post_t st aL)\n (postR next_postR: post_t st aR)\n : Lemma (requires stronger_post postR next_postR)\n (ensures\n forall xL xR frame h.\n st.interp (((postL xL) `st.star` (next_postR xR)) `st.star` frame) h ==>\n st.interp (((postL xL) `st.star` (postR xR)) `st.star` frame) h)\nlet stronger_post_par_r\n (#st:st)\n (#aL #aR:Type u#a)\n (postL:post_t st aL)\n (postR:post_t st aR)\n (next_postR:post_t st aR)\n : Lemma\n (requires stronger_post postR next_postR)\n (ensures\n forall xL xR frame h.\n st.interp ((postL xL `st.star` next_postR xR) `st.star` frame) h ==>\n st.interp ((postL xL `st.star` postR xR) `st.star` frame) h)\n =\n let aux xL xR frame h\n : Lemma\n (requires st.interp ((postL xL `st.star` next_postR xR) `st.star` frame) h)\n (ensures st.interp ((postL xL `st.star` postR xR) `st.star` frame) h)\n [SMTPat ()]\n =\n calc (st.equals) {\n (postL xL `st.star` next_postR xR) `st.star` frame;\n (st.equals) { }\n (next_postR xR `st.star` postL xL) `st.star` frame;\n (st.equals) { }\n next_postR xR `st.star` (postL xL `st.star` frame);\n };\n assert (st.interp (next_postR xR `st.star` (postL xL `st.star` frame)) h);\n assert (st.interp (postR xR `st.star` (postL xL `st.star` frame)) h);\n calc (st.equals) {\n postR xR `st.star` (postL xL `st.star` frame);\n (st.equals) { }\n (postR xR `st.star` postL xL) `st.star` frame;\n (st.equals) { }\n (postL xL `st.star` postR xR) `st.star` frame;\n }\n in\n ()", "val hide_div #a #pre #post (f:unit -> Dv (stt a pre post))\r\n: stt a pre post\nlet hide_div #a #pre #post (f:unit -> Dv (stt a pre post))\r\n: stt a pre post\r\n= fun _ -> f () ()", "val par_c\n (#p0 #q0 #p1 #q1: hm.r)\n ($f0: (unit -> C unit p0 (fun _ -> q0)))\n ($f1: (unit -> C unit p1 (fun _ -> q1)))\n : C unit (p0 `star` p1) (fun _ -> q0 `star` q1)\nlet par_c (#p0:hm.r) (#q0: hm.r)\n (#p1:hm.r) (#q1: hm.r)\n ($f0: unit -> C unit p0 (fun _ -> q0))\n ($f1: unit -> C unit p1 (fun _ -> q1))\n : C unit (p0 `star` p1) (fun _ -> q0 `star` q1)\n = let ff0 : m unit p0 (fun _ -> q0) = reify (f0()) () in\n let ff1 : m unit p1 (fun _ -> q1) = reify (f1()) () in\n C?.reflect (fun () -> par ff0 ff1)", "val par_c\n (#p0 #q0 #p1 #q1: hm.r)\n ($f0: (unit -> C unit p0 (fun _ -> q0)))\n ($f1: (unit -> C unit p1 (fun _ -> q1)))\n : C unit (p0 `star` p1) (fun _ -> q0 `star` q1)\nlet par_c (#p0:hm.r) (#q0: hm.r)\n (#p1:hm.r) (#q1: hm.r)\n ($f0: unit -> C unit p0 (fun _ -> q0))\n ($f1: unit -> C unit p1 (fun _ -> q1))\n : C unit (p0 `star` p1) (fun _ -> q0 `star` q1)\n = let ff0 : m unit p0 (fun _ -> q0) = reify (f0()) () in\n let ff1 : m unit p1 (fun _ -> q1) = reify (f1()) () in\n C?.reflect (fun () -> par ff0 ff1)", "val get: #state: Type u#2 -> #rel: P.preorder state -> Prims.unit\n -> MSTATETOT state state rel (fun _ -> True) (fun s0 r s1 -> s0 == r /\\ r == s1)\nlet get (#state:Type u#2) (#rel:P.preorder state) ()\n : MSTATETOT state state rel\n (fun _ -> True)\n (fun s0 r s1 -> s0 == r /\\ r == s1)\n =\n MSTATETOT?.reflect (fun s0 -> s0, s0)", "val simplify_post\n (#g: env)\n (#t: st_term)\n (#c: comp_st)\n (d: st_typing g t c)\n (post: term{comp_post c == tm_star post tm_emp})\n : st_typing g t (comp_st_with_post c post)\nlet simplify_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { comp_post c == tm_star post tm_emp})\n : st_typing g t (comp_st_with_post c post)\n = st_equiv_post d post (fun x -> ve_unit_r (push_binding g x ppname_default (comp_res c)) (open_term post x))", "val bind_pure_st_ (a:Type) (b:Type)\n (#[@@@ framing_implicit] wp:pure_wp a)\n (#framed:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre:pre_t)\n (#[@@@ framing_implicit] post:post_t b)\n (#[@@@ framing_implicit] req:a -> pure_pre)\n (#[@@@ framing_implicit] ens:a -> pure_post b)\n (f:eqtype_as_type unit -> PURE a wp)\n (g:(x:a -> repr b framed pre post (req x) (ens x)))\n: repr b\n framed\n pre\n post\n (bind_pure_st_req wp req)\n (bind_pure_st_ens wp ens)\nlet bind_pure_st_ (a:Type) (b:Type)\n (#[@@@ framing_implicit] wp:pure_wp a)\n (#framed:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre:pre_t)\n (#[@@@ framing_implicit] post:post_t b)\n (#[@@@ framing_implicit] req:a -> Type0)\n (#[@@@ framing_implicit] ens:a -> b -> Type0)\n (f:eqtype_as_type unit -> PURE a wp)\n (g:(x:a -> repr b framed pre post (req x) (ens x)))\n : repr b\n framed\n pre\n post\n (bind_pure_st_req wp req)\n (bind_pure_st_ens wp ens)\n = let c\n : Steel.Effect.repr b\n framed\n pre\n post\n (bind_pure_steel__req wp (fun x _ -> req x))\n (bind_pure_steel__ens wp (fun x _ y _ -> ens x y))\n =(Steel.Effect.bind_pure_steel_ a b\n #wp\n #framed\n #pre\n #post\n #(fun x _ -> req x)\n #(fun x _ y _ -> ens x y)\n f\n g)\n in\n FStar.Monotonic.Pure.elim_pure_wp_monotonicity #a wp;\n weaken_repr _ _ _ _ _ _ _ _ c () ()", "val sub \r\n (#a:Type)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (#opens:inames)\r\n (pre':slprop { slprop_equiv pre pre' })\r\n (post':a -> slprop { forall x. slprop_equiv (post x) (post' x) })\r\n (f:act a opens pre post)\r\n: act a opens pre' post'\nlet sub \r\n (#a:Type)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (#opens:inames)\r\n (pre':slprop { slprop_equiv pre pre' })\r\n (post':a -> slprop { forall x. slprop_equiv (post x) (post' x) })\r\n (f:act a opens pre post)\r\n: act a opens pre' post'\r\n= I.slprop_equiv_elim pre pre';\r\n introduce forall x. post x == post' x\r\n with I.slprop_equiv_elim (post x) (post' x);\r\n f", "val release\n (#p:vprop)\n (l:lock p)\n : stt unit\n (requires p)\n (ensures (fun _ -> emp))\nlet release = release'", "val put (#st: _) (s: st) : ST unit st (fun _ p -> p () s)\nlet put #st (s:st) : ST unit st (fun _ p -> p () s) =\n ST?.reflect (fun _ -> ((), s))", "val put (#st: _) (s: st) : ST unit st (fun _ p -> p () s)\nlet put #st (s:st) : ST unit st (fun _ p -> p () s) =\n ST?.reflect (fun _ -> ((), s))", "val bind_ghost\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#pre1:slprop)\r\n (#post1:a -> slprop)\r\n (#post2:b -> slprop)\r\n (e1:stt_ghost a pre1 post1)\r\n (e2:(x:a -> stt_ghost b (post1 x) post2))\r\n: stt_ghost b pre1 post2\nlet bind_ghost\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#pre1:slprop)\r\n (#post1:a -> slprop)\r\n (#post2:b -> slprop)\r\n (e1:stt_ghost a pre1 post1)\r\n (e2:(x:a -> stt_ghost b (post1 x) post2))\r\n: stt_ghost b pre1 post2\r\n= let e1 = Ghost.reveal e1 in\r\n let e2 = FStar.Ghost.Pull.pull (fun (x:a) -> Ghost.reveal (e2 x)) in\r\n Ghost.hide (A.bind e1 e2)", "val bind\n (a b: Type)\n (#pre_f: pre_t)\n (#post_f: post_t a)\n (#pre_g: (a -> pre_t))\n (#post_g: (a -> post_t b))\n (f: repr a pre_f post_f)\n (g: (x: a -> repr b (pre_g x) (post_g x)))\n : repr b\n (fun h0 -> pre_f h0 /\\ (forall (x: a) (h1: heap). post_f h0 x h1 ==> pre_g x h1))\n (fun h0 y h2 -> exists (x: a) (h1: heap). pre_f h0 /\\ post_f h0 x h1 /\\ post_g x h1 y h2)\nlet bind (a:Type) (b:Type)\n (#pre_f:pre_t) (#post_f:post_t a) (#pre_g:a -> pre_t) (#post_g:a -> post_t b)\n (f:repr a pre_f post_f) (g:(x:a -> repr b (pre_g x) (post_g x)))\n: repr b\n (fun h0 -> pre_f h0 /\\ (forall (x:a) (h1:heap). post_f h0 x h1 ==> pre_g x h1))\n (fun h0 y h2 -> exists (x:a) (h1:heap). pre_f h0 /\\ post_f h0 x h1 /\\ post_g x h1 y h2)\n= fun _ ->\n let x = f () in\n g x ()", "val put (#st: _) (s: st) : ST unit st (fun _ p -> p ((), s))\nlet put #st (s:st)\n : ST unit st (fun _ p -> p ((), s))\n = ST?.reflect (fun _ -> ((), s))", "val put (#st: _) (s: st) : ST unit st (fun _ p -> p ((), s))\nlet put #st (s:st) : ST unit st (fun _ p -> p ((), s)) =\n ST?.reflect (fun _ -> ((), s))", "val sub_atomic\r\n (#a:Type u#a)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre1:slprop)\r\n (pre2:slprop)\r\n (#post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1 : slprop_equiv pre1 pre2)\r\n (pf2 : slprop_post_equiv post1 post2)\r\n (e:stt_atomic a #obs opens pre1 post1)\r\n: stt_atomic a #obs opens pre2 post2\nlet sub_atomic\r\n (#a:Type u#a)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre1:slprop)\r\n (pre2:slprop)\r\n (#post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1 : slprop_equiv pre1 pre2)\r\n (pf2 : slprop_post_equiv post1 post2)\r\n (e:stt_atomic a #obs opens pre1 post1)\r\n: stt_atomic a #obs opens pre2 post2\r\n= A.sub pre2 post2 e", "val put (#s:Type u#s) (#rel:preorder s) (v:s)\r\n : mst rel unit (fun s0 -> rel s0 v /\\ True) (fun s0 x s1 -> v == s1)\nlet put v\r\n= fun _ -> (), v", "val vprop_equiv_unit_soundness (#g:stt_env) (#v0 #v1:term) \n (d0:tot_typing g v0 tm_vprop)\n (eq:vprop_equiv g v0 v1)\n : GTot (RT.tot_typing (elab_env g) (`())\n (stt_vprop_equiv (elab_term v0) (elab_term v1)))\nlet vprop_equiv_unit_soundness (#g:stt_env) (#v0 #v1:term) \n (d0:tot_typing g v0 tm_vprop)\n (eq:vprop_equiv g v0 v1)\n : GTot (RT.tot_typing (elab_env g) (`()) (stt_vprop_equiv (elab_term v0) (elab_term v1)))\n = let (| pf, s |) = vprop_equiv_soundness d0 eq in\n let d1 = fst (vprop_equiv_typing eq) d0 in\n let s_prop = stt_vprop_equiv_is_prop (tot_typing_soundness d0) (tot_typing_soundness d1) in\n RT.T_PropIrrelevance _ _ _ _ _ s s_prop", "val bind\n (#s #a: _)\n (#srel: erel s)\n (#arel: erel a)\n (#b: _)\n (#brel: erel b)\n ($f: st srel arel)\n (g: arel ^--> st_rel srel brel)\n : st srel brel\nlet bind #s #a (#srel:erel s) (#arel:erel a) #b (#brel:erel b)\n ($f:st srel arel)\n (g:arel ^--> st_rel srel brel)\n : st srel brel =\n fun s0 ->\n let x, s1 = f s0 in\n g x s1", "val get: #state: Type u#2 -> #rel: P.preorder state -> Prims.unit\n -> MSTATE state state rel (fun _ -> True) (fun s0 r s1 -> s0 == r /\\ r == s1)\nlet get (#state:Type u#2) (#rel:P.preorder state) ()\n : MSTATE state state rel\n (fun _ -> True)\n (fun s0 r s1 -> s0 == r /\\ r == s1)\n =\n MSTATE?.reflect (fun s0 -> s0, s0)", "val get (#s:Type u#s) (#rel:preorder s) (_:unit)\r\n : mst rel s (fun _ -> True) (fun s0 x s1 -> s0 == s1 /\\ x == s0)\nlet get _\r\n= fun s -> s, s", "val app\n (#a #b: Type)\n (#rel1 #rel2: relation state)\n (#wp1: mst_wp state a rel1)\n (#wp2: (a -> mst_wp state b rel2))\n (f: (unit -> GMST a (rel1 >< wp1)))\n (g: (x: a -> GMST b (rel2 >< wp2 x)))\n : GMST b ((rel2 @ rel1) >< (fun s0 p -> wp1 s0 (fun x s1 -> wp2 x s1 p)))\nlet app (#a:Type) (#b:Type)\n (#rel1:relation state)\n (#rel2:relation state)\n (#wp1:mst_wp state a rel1) \n (#wp2:a -> mst_wp state b rel2)\n (f:unit -> GMST a (rel1 >< wp1))\n (g:(x:a -> GMST b (rel2 >< wp2 x)))\n : GMST b ((rel2 @ rel1) >< (fun s0 p -> wp1 s0 (fun x s1 -> wp2 x s1 p)))\n = g (f ())", "val mbind\n (#st: state u#s u#act)\n (#a: Type u#a)\n (#b: Type u#b)\n (#p: st.pred)\n (#q: post st a)\n (#r: post st b)\n (f: m a p q)\n (g: (x: a -> Dv (m b (q x) r)))\n : Dv (m b p r)\nlet rec mbind\n (#st:state u#s u#act)\n (#a:Type u#a)\n (#b:Type u#b)\n (#p:st.pred)\n (#q:post st a)\n (#r:post st b)\n (f:m a p q)\n (g: (x:a -> Dv (m b (q x) r)))\n : Dv (m b p r)\n = match f with\n | Ret x -> g x\n | Act act k ->\n Act act (fun x -> mbind (k x) g)\n | Par #_ #pre0 #post0 ml\n #pre1 #post1 mr\n #postk k ->\n let k : m b (post0 `st.star` post1) r = mbind k g in\n let ml' : m (U.raise_t u#0 u#b unit) pre0 (as_post post0) =\n mbind ml (fun _ -> Ret #_ #(U.raise_t u#0 u#b unit) #(as_post post0) (U.raise_val u#0 u#b ()))\n in\n let mr' : m (U.raise_t u#0 u#b unit) pre1 (as_post post1) =\n mbind mr (fun _ -> Ret #_ #(U.raise_t u#0 u#b unit) #(as_post post1) (U.raise_val u#0 u#b ()))\n in\n Par ml' mr' k", "val frame_ghost\r\n (#a:Type u#a)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt_ghost a pre post)\r\n: stt_ghost a (pre ** frame) (fun x -> post x ** frame)\nlet frame_ghost\r\n (#a:Type u#a)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt_ghost a pre post)\r\n: stt_ghost a (pre ** frame) (fun x -> post x ** frame)\r\n= Ghost.hide (A.frame (Ghost.reveal e))", "val par_block_pulse (#a: Type0) (#pre: vprop)\n (#post: (a -> vprop))\n (main_block: (par_env -> unit -> (stt a pre post)))\n: stt a pre (fun res -> post res)\nlet par_block_pulse #a #pre #post = par_block_pulse' #a #pre #post", "val stt_ghost\r\n (a:Type u#a)\r\n (pre:slprop)\r\n (post:a -> slprop)\r\n: Type u#(max 2 a)\nlet stt_ghost a pre post = Ghost.erased (act a emp_inames pre post)", "val filter_one_st_post\n (#dt: stateful unit)\n (ll: t dt)\n (inv: (HS.mem -> G.erased Type0))\n (fspec: (G.erased (fspec_ty dt)))\n (h0 h1: HS.mem)\n : GTot Type0\nlet filter_one_st_post :\n #dt: stateful unit\n -> ll: t dt\n -> inv : (HS.mem -> G.erased Type0)\n -> fspec : (G.erased (fspec_ty dt))\n -> h0 : HS.mem\n -> h1 : HS.mem ->\n GTot Type0 =\n fun #dt ll inv fspec h0 h1 ->\n let filtered = gfilter_one_element fspec h0 (get_elems h0 ll) in\n B.modifies (region_of ll) h0 h1 /\\\n invariant h1 ll /\\\n get_elems h1 ll == filtered /\\\n gsame_elementsp filtered h0 h1 /\\\n // The following is a consequence from the preceding assertions,\n // but not a trivial derivation and more convenient in most situations\n v h1 ll == filter_one fspec (v h0 ll)", "val bind\n (a b: Type)\n (pre_f: pre_t)\n (post_f: post_t a)\n (pre_g: (a -> pre_t))\n (post_g: (a -> post_t b))\n (f: repr a pre_f post_f)\n (g: (x: a -> repr b (pre_g x) (post_g x)))\n : repr b\n (fun h0 -> pre_f h0 /\\ (forall (x: a) (h1: heap). post_f h0 x h1 ==> pre_g x h1))\n (fun h0 y h2 -> exists (x: a) (h1: heap). pre_f h0 /\\ post_f h0 x h1 /\\ post_g x h1 y h2)\nlet bind (a:Type) (b:Type)\n (pre_f:pre_t) (post_f:post_t a) (pre_g:a -> pre_t) (post_g:a -> post_t b)\n (f:repr a pre_f post_f) (g:(x:a -> repr b (pre_g x) (post_g x)))\n: repr b\n (fun h0 -> pre_f h0 /\\ (forall (x:a) (h1:heap). post_f h0 x h1 ==> pre_g x h1))\n (fun h0 y h2 -> exists (x:a) (h1:heap). pre_f h0 /\\ post_f h0 x h1 /\\ post_g x h1 y h2)\n= fun _ ->\n let x = f () in\n g x ()", "val stt_of_action (#a: Type u#100) (#pre #post: _) (m: action a Set.empty pre post) : stt a pre post\nlet stt_of_action (#a:Type u#100) #pre #post (m:action a Set.empty pre post)\r\n: stt a pre post\r\n= let step (frame:slprop)\r\n : Sem.mst_sep state a (pre `star` frame) (fun x -> post x `star` frame)\r\n = M.weaken (m frame)\r\n in\r\n let action : Sem.action state a = {pre=pre; post=F.on_dom _ post; step} in\r\n let m : Sem.m a pre _ = Sem.act action in\r\n fun _ -> m", "val test: Prims.unit -> STT unit ((p `star` p) `star` p) (fun _ -> (p `star` p) `star` p)\nlet test () : STT unit (p `star` p `star` p) (fun _ -> p `star` p `star` p)\n = f 0; ()", "val bind_div_st_\n (a b: Type)\n (#[@@@ framing_implicit]wp: pure_wp a)\n (#framed: eqtype_as_type bool)\n (#[@@@ framing_implicit]pre: pre_t)\n (#[@@@ framing_implicit]post: post_t b)\n (#[@@@ framing_implicit]req: (a -> Type0))\n (#[@@@ framing_implicit]ens: (a -> b -> Type0))\n (f: (eqtype_as_type unit -> DIV a wp))\n (g: (x: a -> STF.repr b framed pre post (req x) (ens x)))\n : STF.repr b framed pre post (bind_div_st_req wp req) (bind_div_st_ens wp ens)\nlet bind_div_st_ (a:Type) (b:Type)\n (#[@@@ framing_implicit] wp:pure_wp a)\n (#framed:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre:pre_t)\n (#[@@@ framing_implicit] post:post_t b)\n (#[@@@ framing_implicit] req:a -> Type0)\n (#[@@@ framing_implicit] ens:a -> b -> Type0)\n (f:eqtype_as_type unit -> DIV a wp)\n (g:(x:a -> STF.repr b framed pre post (req x) (ens x)))\n : STF.repr b\n framed\n pre\n post\n (bind_div_st_req wp req)\n (bind_div_st_ens wp ens)\n = let c\n : SF.repr b\n framed\n pre\n post\n (SF.bind_div_steel_req wp (fun x _ -> req x))\n (SF.bind_div_steel_ens wp (fun x _ y _ -> ens x y))\n =(SF.bind_div_steel a b\n wp\n framed\n pre\n post\n (fun x _ -> req x)\n (fun x _ y _ -> ens x y)\n f\n g)\n in\n FStar.Monotonic.Pure.elim_pure_wp_monotonicity #a wp;\n STF.weaken_repr _ _ _ _ _ _ _ _ c () ()", "val lift_atomic2\r\n (#a:Type u#2)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens pre post)\r\n: stt a pre post\nlet lift_atomic2\r\n (#a:Type u#2)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens pre post)\r\n: stt a pre post\r\n= A.lift2 e", "val Domains.unit_stt = a: Type -> pre: Pulse.Lib.Core.vprop -> post: (_: a -> Pulse.Lib.Core.vprop) -> Type0\nlet unit_stt a pre post = (unit -> stt a pre post)", "val lift (#a:Type u#100) #opens (#pre:slprop) (#post:a -> slprop)\r\n (m:act a opens pre post)\r\n: I.stt a pre post\nlet lift (#a:Type u#100) #opens #pre #post\r\n (m:act a opens pre post)\r\n: stt a pre post\r\n= stt_of_action (m #emp_inames)", "val if_then_else_ens\n (#a: Type)\n (#pre_f #pre_g: pre_t)\n (#post_f #post_g: post_t a)\n (#frame_f #frame_g: vprop)\n (#pr: prop)\n (s1: squash (can_be_split_dep pr (pre_f `star` frame_f) (pre_g `star` frame_g)))\n (s2:\n squash (equiv_forall (fun x -> (post_f x) `star` frame_f)\n (fun x -> (post_g x) `star` frame_g)))\n (ens_then: ens_t pre_f a post_f)\n (ens_else: ens_t pre_g a post_g)\n (p: Type0)\n : ens_t (pre_f `star` frame_f) a (fun x -> (post_f x) `star` frame_f)\nlet if_then_else_ens (#a:Type)\n (#pre_f:pre_t) (#pre_g:pre_t) (#post_f:post_t a) (#post_g:post_t a)\n (#frame_f #frame_g:vprop) (#pr:prop)\n (s1: squash (can_be_split_dep pr (pre_f `star` frame_f) (pre_g `star` frame_g)))\n (s2: squash (equiv_forall (fun x -> post_f x `star` frame_f) (fun x -> post_g x `star` frame_g)))\n (ens_then:ens_t pre_f a post_f) (ens_else:ens_t pre_g a post_g)\n (p:Type0)\n: ens_t (pre_f `star` frame_f) a (fun x -> post_f x `star` frame_f)\n= fun h0 x h1 -> pr /\\ (\n can_be_split_trans (pre_f `star` frame_f) (pre_g `star` frame_g) pre_g;\n can_be_split_trans (post_f x `star` frame_f) (post_g x `star` frame_g) (post_g x);\n (p ==> ens_then (focus_rmem h0 pre_f) x (focus_rmem h1 (post_f x))) /\\\n ((~ p) ==> ens_else (focus_rmem h0 pre_g) x (focus_rmem h1 (post_g x))))", "val if_then_else_ens\n (#a: Type)\n (#pre_f #pre_g: pre_t)\n (#post_f #post_g: post_t a)\n (#frame_f #frame_g: vprop)\n (#pr: prop)\n (s1: squash (can_be_split_dep pr (pre_f `star` frame_f) (pre_g `star` frame_g)))\n (s2:\n squash (equiv_forall (fun x -> (post_f x) `star` frame_f)\n (fun x -> (post_g x) `star` frame_g)))\n (ens_then: ens_t pre_f a post_f)\n (ens_else: ens_t pre_g a post_g)\n (p: Type0)\n : ens_t (pre_f `star` frame_f) a (fun x -> (post_f x) `star` frame_f)\nlet if_then_else_ens (#a:Type)\n (#pre_f:pre_t) (#pre_g:pre_t) (#post_f:post_t a) (#post_g:post_t a)\n (#frame_f #frame_g:vprop) (#pr:prop)\n (s1: squash (can_be_split_dep pr (pre_f `star` frame_f) (pre_g `star` frame_g)))\n (s2: squash (equiv_forall (fun x -> post_f x `star` frame_f) (fun x -> post_g x `star` frame_g)))\n (ens_then:ens_t pre_f a post_f) (ens_else:ens_t pre_g a post_g)\n (p:Type0)\n: ens_t (pre_f `star` frame_f) a (fun x -> post_f x `star` frame_f)\n= fun h0 x h1 -> pr /\\ (\n can_be_split_trans (pre_f `star` frame_f) (pre_g `star` frame_g) pre_g;\n can_be_split_trans (post_f x `star` frame_f) (post_g x `star` frame_g) (post_g x);\n (p ==> ens_then (focus_rmem h0 pre_f) x (focus_rmem h1 (post_f x))) /\\\n ((~ p) ==> ens_else (focus_rmem h0 pre_g) x (focus_rmem h1 (post_g x))))", "val sub_invs_stt_atomic\r\n (#a:Type u#a)\r\n (#obs:_)\r\n (#opens1 #opens2:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens1 pre post)\r\n (_ : squash (inames_subset opens1 opens2))\r\n: stt_atomic a #obs opens2 pre post\nlet sub_invs_stt_atomic\r\n (#a:Type u#a)\r\n (#obs:_)\r\n (#opens1 #opens2:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens1 pre post)\r\n (_ : squash (inames_subset opens1 opens2))\r\n: stt_atomic a #obs opens2 pre post\r\n= assert (Set.equal (Set.union opens1 opens2) opens2);\r\n A.weaken opens2 e", "val intro_stick\n (hyp concl: vprop)\n (v: vprop)\n (f_elim: unit -> (\n stt_ghost unit\n (v ** hyp)\n (fun _ -> concl)\n ))\n: stt_ghost unit\n v\n (fun _ -> stick hyp concl)\nlet intro_stick = __intro_stick", "val intro_stick\n (hyp concl: vprop)\n (v: vprop)\n (f_elim: unit -> (\n stt_ghost unit\n (v ** hyp)\n (fun _ -> concl)\n ))\n: stt_ghost unit\n v\n (fun _ -> stick hyp concl)\nlet intro_stick p q v f =\n T.intro_trade p q v f", "val redeem_pledge (f:vprop) (v:vprop)\n : stt unit (f ** pledge f v) (fun () -> f ** v)\nlet redeem_pledge = __redeem_pledge", "val join\n (#a:Type0)\n (#post: (a -> vprop))\n (h: handler post)\n: stt a emp (fun res -> post res)\nlet join #a #post = join' #a #post", "val put (#state: Type u#2) (#rel: P.preorder state) (s: state)\n : MSTATETOT unit state rel (fun s0 -> rel s0 s) (fun _ _ s1 -> s1 == s)\nlet put (#state:Type u#2) (#rel:P.preorder state) (s:state)\n : MSTATETOT unit state rel\n (fun s0 -> rel s0 s)\n (fun _ _ s1 -> s1 == s)\n =\n MSTATETOT?.reflect (fun _ -> (), s)", "val bind\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#opens:inames)\r\n (#pre1 #post1 #post2:_)\r\n (f:act a opens pre1 post1)\r\n (g:(x:a -> act b opens (post1 x) post2))\r\n: act b opens pre1 post2\nlet bind\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#opens:inames)\r\n (#pre1 #post1 #post2:_)\r\n (f:act a opens pre1 post1)\r\n (g:(x:a -> act b opens (post1 x) post2))\r\n: act b opens pre1 post2\r\n= fun #ictx -> bind_action #a #b #ictx #pre1 #post1 #post2 (f #ictx) (fun x -> g x #ictx)", "val test_rrr (#pre #post: _) (b: bool) (f g: (unit -> RWI int RO pre post)) : RWI int RO pre post\nlet test_rrr #pre #post (b:bool) (f : unit -> RWI int RO pre post) (g : unit -> RWI int RO pre post) : RWI int RO pre post = if b then f () else g ()", "val bind\n (a b: Type)\n (f_p: pre)\n (f_q: post a)\n (g_p: (a -> pre))\n (g_q: (a -> post b))\n (f: repr a f_p f_q)\n (g: (x: a -> repr b (g_p x) (g_q x)))\n : repr b (act_p f_p f_q g_p) (act_q f_q g_q)\nlet rec bind (a b:Type)\n (f_p:pre) (f_q:post a)\n (g_p:a -> pre) (g_q:a -> post b)\n (f:repr a f_p f_q) (g:(x:a -> repr b (g_p x) (g_q x)))\n : repr b (act_p f_p f_q g_p) (act_q f_q g_q)\n = fun _ ->\n let f = f () in\n match f with\n | Ret x -> Weaken (g x ())\n | Act #_ #c #a_p #a_q act #_ #_ #_ k ->\n let k' = fun (x:c) -> (bind _ _ _ _ _ _ (fun _ -> k x) g) () in\n Weaken (Act #_ #c #a_p #a_q act #b #_ #_ k')\n | Weaken f -> Weaken ((bind _ _ _ _ _ _ (fun _ -> f) g) ())\n | Strengthen #_ #_ #phi #p #q f ->\n let f : squash phi -> Dv (m st b (act_p p q g_p) (act_q q g_q)) =\n fun _ -> (bind _ _ _ _ _ _ (fun _ -> f ()) g) () in\n let f : m st b (strengthen_pre (act_p p q g_p) phi) (act_q q g_q) =\n Strengthen f in\n Weaken f" ], "closest_src": [ { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.par" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.par_lpost" }, { "project_name": "steel", "file_name": "Steel.Effect.fst", "name": "Steel.Effect.par" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.par" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.par_lpre" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.sub" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.bind_lpost" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.frame_lpost" }, { "project_name": "steel", "file_name": "Async.fst", "name": "Async.now" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.with_pre" }, { "project_name": "steel", "file_name": "Domains.fst", "name": "Domains.spawn" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.bind_lpre" }, { "project_name": "steel", "file_name": "Pulse.Lib.Pervasives.fst", "name": "Pulse.Lib.Pervasives.perform" }, { "project_name": "steel", "file_name": "Pulse.Lib.Fixpoints.fst", "name": "Pulse.Lib.Fixpoints.fix_stt_1" }, { "project_name": "steel", "file_name": "Domains.fst", "name": "Domains.exec_unit_stt" }, { "project_name": "steel", "file_name": "PulseCore.Semantics.fst", "name": "PulseCore.Semantics.par" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.bind" }, { "project_name": "steel", "file_name": "CSL.Semantics.fst", "name": "CSL.Semantics.step_par_ret" }, { "project_name": "steel", "file_name": "CSL.Semantics.fst", "name": "CSL.Semantics.par_weaker_lpre_and_stronger_lpost_r" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.conv" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.par_weaker_lpre_and_stronger_lpost_l" }, { "project_name": "steel", "file_name": "Steel.Effect.fst", "name": "Steel.Effect.par0" }, { "project_name": "steel", "file_name": "Async.fst", "name": "Async.async" }, { "project_name": "steel", "file_name": "Pulse.Lib.InvList.fst", "name": "Pulse.Lib.InvList.with_invlist" }, { "project_name": "steel", "file_name": "Pulse.Lib.InvList.fst", "name": "Pulse.Lib.InvList.with_invlist_ghost" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.lpost_ret_act" }, { "project_name": "steel", "file_name": "Pulse.Lib.Pervasives.fst", "name": "Pulse.Lib.Pervasives.perform_ghost" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.step_par_ret" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.Pure.fst", "name": "Pulse.Elaborate.Pure.elab_stt_equiv" }, { "project_name": "steel", "file_name": "CSL.Semantics.fst", "name": "CSL.Semantics.step_par_ret_aux" }, { "project_name": "steel", "file_name": "Domains.fst", "name": "Domains.promote_seq" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.par_weaker_lpre_and_stronger_lpost_r" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.sub_ghost" }, { "project_name": "steel", "file_name": "Pulse.Lib.Fixpoints.fst", "name": "Pulse.Lib.Fixpoints.fix_stt_1_div" }, { "project_name": "steel", "file_name": "Pulse.Lib.Fixpoints.fst", "name": "Pulse.Lib.Fixpoints.fix_stt_ghost_1" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.test_rww" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.test_wrw" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.return_lpre" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.frame" }, { "project_name": "FStar", "file_name": "GMST.fst", "name": "GMST.preorder_app'" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.frame_lpre" }, { "project_name": "steel", "file_name": "Pulse.Checker.Base.fst", "name": "Pulse.Checker.Base.st_equiv_post" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.inst_heap_prop_for_par" }, { "project_name": "steel", "file_name": "ParallelFor.fst", "name": "ParallelFor.simple_for" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.frame_post_for_par" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.stt" }, { "project_name": "steel", "file_name": "PulseCore.MonotonicStateMonad.fst", "name": "PulseCore.MonotonicStateMonad.of_msttotal" }, { "project_name": "steel", "file_name": "Pulse.Soundness.Comp.fst", "name": "Pulse.Soundness.Comp.stc_soundness" }, { "project_name": "steel", "file_name": "Domains.fst", "name": "Domains.spawn_emp" }, { "project_name": "steel", "file_name": "Steel.Primitive.ForkJoin.Unix.fst", "name": "Steel.Primitive.ForkJoin.Unix.bind" }, { "project_name": "steel", "file_name": "Pulse.Lib.InvList.fst", "name": "Pulse.Lib.InvList.shift_invlist_one" }, { "project_name": "FStar", "file_name": "AlgWP.fst", "name": "AlgWP.quotPP" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.step_par_ret_aux" }, { "project_name": "steel", "file_name": "Pulse.Checker.Base.fst", "name": "Pulse.Checker.Base.st_equiv_pre" }, { "project_name": "steel", "file_name": "CSL.Semantics.fst", "name": "CSL.Semantics.stronger_post_par_r" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.stronger_post_par_r" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.hide_div" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParDiv.fst", "name": "OPLSS2021.ParDiv.par_c" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParNDSDiv.fst", "name": "OPLSS2021.ParNDSDiv.par_c" }, { "project_name": "FStar", "file_name": "FStar.MSTTotal.fst", "name": "FStar.MSTTotal.get" }, { "project_name": "steel", "file_name": "Pulse.Checker.Base.fst", "name": "Pulse.Checker.Base.simplify_post" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.fst", "name": "Steel.ST.Effect.bind_pure_st_" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.sub" }, { "project_name": "steel", "file_name": "Pulse.Lib.SpinLock.fst", "name": "Pulse.Lib.SpinLock.release" }, { "project_name": "FStar", "file_name": "DM4F_layered5.fst", "name": "DM4F_layered5.put" }, { "project_name": "FStar", "file_name": "DM4F_layered.fst", "name": "DM4F_layered.put" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.bind_ghost" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.bind" }, { "project_name": "FStar", "file_name": "OPLSS2021.DijkstraMonads.fst", "name": "OPLSS2021.DijkstraMonads.put" }, { "project_name": "FStar", "file_name": "DM4F.fst", "name": "DM4F.put" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.sub_atomic" }, { "project_name": "steel", "file_name": "PulseCore.MonotonicStateMonad.fst", "name": "PulseCore.MonotonicStateMonad.put" }, { "project_name": "steel", "file_name": "Pulse.Soundness.VPropEquiv.fst", "name": "Pulse.Soundness.VPropEquiv.vprop_equiv_unit_soundness" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.bind" }, { "project_name": "FStar", "file_name": "FStar.MST.fst", "name": "FStar.MST.get" }, { "project_name": "steel", "file_name": "PulseCore.MonotonicStateMonad.fst", "name": "PulseCore.MonotonicStateMonad.get" }, { "project_name": "FStar", "file_name": "GMST.fst", "name": "GMST.app" }, { "project_name": "steel", "file_name": "PulseCore.Semantics.fst", "name": "PulseCore.Semantics.mbind" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.frame_ghost" }, { "project_name": "steel", "file_name": "Domains.fst", "name": "Domains.par_block_pulse" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.stt_ghost" }, { "project_name": "noise-star", "file_name": "Impl.Noise.LinkedList.fsti", "name": "Impl.Noise.LinkedList.filter_one_st_post" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.bind" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.stt_of_action" }, { "project_name": "steel", "file_name": "SteelSTFramingTestSuite.fst", "name": "SteelSTFramingTestSuite.test" }, { "project_name": "steel", "file_name": "Steel.ST.Coercions.fst", "name": "Steel.ST.Coercions.bind_div_st_" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.lift_atomic2" }, { "project_name": "steel", "file_name": "Domains.fst", "name": "Domains.unit_stt" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.lift" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fsti", "name": "Steel.Effect.Atomic.if_then_else_ens" }, { "project_name": "steel", "file_name": "Steel.Effect.fsti", "name": "Steel.Effect.if_then_else_ens" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.sub_invs_stt_atomic" }, { "project_name": "steel", "file_name": "Pulse.Lib.Priv.Trade0.fst", "name": "Pulse.Lib.Priv.Trade0.intro_stick" }, { "project_name": "steel", "file_name": "Pulse.Lib.Stick.fst", "name": "Pulse.Lib.Stick.intro_stick" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.Simple.fst", "name": "Pulse.Lib.Par.Pledge.Simple.redeem_pledge" }, { "project_name": "steel", "file_name": "Domains.fst", "name": "Domains.join" }, { "project_name": "FStar", "file_name": "FStar.MSTTotal.fst", "name": "FStar.MSTTotal.put" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.bind" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.test_rrr" }, { "project_name": "FStar", "file_name": "HoareSTFree.fst", "name": "HoareSTFree.bind" } ], "selected_premises": [ "Pulse.Lib.Core.stt", "Pulse.Lib.Core.iname", "PulseCore.FractionalPermission.full_perm", "PulseCore.Preorder.pcm_history", "Pulse.Lib.Core.vprop", "Pulse.Lib.Core.bind_stt", "PulseCore.Action.emp_inames", "Pulse.Lib.Core.op_exists_Star", "Pulse.Lib.Core.emp", "PulseCore.Action.inames", "Pulse.Lib.Core.op_Star_Star", "Pulse.Lib.Core.vprop_equiv_ext", "Pulse.Lib.Core.vprop_post_equiv", "Pulse.Lib.Core.vprop_equiv_sym", "Pulse.Lib.Core.pure", "Pulse.Lib.Core.return_stt_noeq", "Pulse.Lib.Core.frame_stt", "Pulse.Lib.Core.vprop_equiv_trans", "Pulse.Lib.Core.vprop_equiv_refl", "Pulse.Lib.Core.vprop_equiv", "FStar.Real.one", "PulseCore.Preorder.history_val", "Pulse.Lib.Core.inv", "Pulse.Lib.Core.intro_vprop_post_equiv", "FStar.Real.two", "Pulse.Lib.Core.vprop_equiv_unit", "FStar.PCM.composable", "Pulse.Lib.Core.elim_vprop_equiv", "Pulse.Lib.Core.vprop_equiv_assoc", "Pulse.Lib.Core.vprop_equiv_comm", "FStar.PCM.compatible", "FStar.PCM.op", "Pulse.Lib.Core.vprop_equiv_cong", "PulseCore.FractionalPermission.sum_perm", "FStar.FunctionalExtensionality.feq", "PulseCore.FractionalPermission.comp_perm", "Pulse.Lib.Core.join_emp", "Pulse.Lib.Core.elim_vprop_post_equiv", "PulseCore.InstantiatedSemantics.slprop_post_equiv", "Pulse.Lib.Core.name_of_inv", "FStar.Pervasives.reveal_opaque", "FStar.FunctionalExtensionality.on_dom", "PulseCore.Preorder.p_op", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "PulseCore.Preorder.comm_op", "PulseCore.Preorder.induces_preorder", "PulseCore.FractionalPermission.half_perm", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "PulseCore.Action.join_inames", "PulseCore.Preorder.vhist", "PulseCore.Preorder.extends", "FStar.Pervasives.st_post_h'", "FStar.Real.zero", "PulseCore.FractionalPermission.writeable", "FStar.Pervasives.st_post_h", "FStar.Pervasives.st_pre_h", "PulseCore.Preorder.extends'", "FStar.Pervasives.st_return", "PulseCore.Preorder.pcm_of_preorder", "PulseCore.Preorder.preorder_of_pcm", "PulseCore.Preorder.history_compose", "PulseCore.Preorder.p", "PulseCore.Preorder.curval", "PulseCore.FractionalPermission.lesser_perm", "PulseCore.Action.mem_inv", "PulseCore.Preorder.fact_valid_compat", "PulseCore.Preorder.p_composable", "Pulse.Lib.Core.add_already_there", "PulseCore.Preorder.history_composable", "PulseCore.Action.property", "PulseCore.Preorder.property", "FStar.FunctionalExtensionality.on", "Pulse.Lib.Core.prop_squash_idem", "FStar.PropositionalExtensionality.apply", "FStar.Pervasives.st_ite_wp", "PulseCore.Preorder.hval", "FStar.Pervasives.st_trivial", "FStar.Pervasives.st_stronger", "FStar.Pervasives.st_wp_h", "PulseCore.Preorder.unit_history", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater", "PulseCore.Action.inames_subset", "FStar.Pervasives.st_bind_wp", "PulseCore.Observability.at_most_one_observable", "PulseCore.Preorder.extends_length_eq", "PulseCore.FractionalPermission.lesser_equal_perm", "FStar.FunctionalExtensionality.restricted_t", "FStar.Pervasives.all_post_h", "Prims.pure_post", "FStar.FunctionalExtensionality.arrow", "PulseCore.Preorder.lift_fact", "FStar.Pervasives.trivial_pure_post", "FStar.Pervasives.st_close_wp", "FStar.Real.test", "PulseCore.Preorder.hperm", "Prims.pure_post'", "FStar.Pervasives.id", "PulseCore.Preorder.qhistory" ], "source_upto_this": "(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule Pulse.Lib.Core\nmodule I = PulseCore.InstantiatedSemantics\nmodule A = PulseCore.Atomic\nmodule T = FStar.Tactics.V2\nmodule F = FStar.FunctionalExtensionality\nopen PulseCore.InstantiatedSemantics\nopen PulseCore.FractionalPermission\nopen PulseCore.Observability\n\nlet double_one_half () = ()\nlet equate_by_smt = ()\nlet vprop = slprop\nlet emp = emp\nlet op_Star_Star = op_Star_Star\nlet pure = pure\nlet op_exists_Star = op_exists_Star\nlet vprop_equiv = slprop_equiv\nlet elim_vprop_equiv #p #q pf = slprop_equiv_elim p q\nlet vprop_post_equiv = slprop_post_equiv\nlet prop_squash_idem (p:prop)\n : Tot (squash (squash p == p))\n = FStar.PropositionalExtensionality.apply p (squash p)\n\nlet intro_vprop_post_equiv\n (#t:Type u#a)\n (p q: t -> vprop)\n (pf: (x:t -> vprop_equiv (p x) (q x)))\n : vprop_post_equiv p q\n = let pf : squash (forall x. vprop_equiv (p x) (q x)) =\n introduce forall x. vprop_equiv (p x) (q x)\n with FStar.Squash.return_squash (pf x)\n in\n coerce_eq (prop_squash_idem _) pf\n\nlet elim_vprop_post_equiv (#t:Type u#a)\n (p q: t -> vprop)\n (pf:vprop_post_equiv p q)\n (x:t)\n: vprop_equiv (p x) (q x)\n= let pf\n : squash (vprop_equiv (p x) (q x))\n = eliminate forall x. vprop_equiv (p x) (q x) with x\n in\n coerce_eq (prop_squash_idem _) pf\n\nlet vprop_equiv_refl (v0:vprop)\n : vprop_equiv v0 v0\n = slprop_equiv_refl v0\n\nlet vprop_equiv_sym (v0 v1:vprop) (p:vprop_equiv v0 v1)\n : vprop_equiv v1 v0\n = slprop_equiv_elim v0 v1; p\n\nlet vprop_equiv_trans\n (v0 v1 v2:vprop)\n (p:vprop_equiv v0 v1)\n (q:vprop_equiv v1 v2)\n : vprop_equiv v0 v2\n = slprop_equiv_elim v0 v1;\n slprop_equiv_elim v1 v2;\n p\n\nlet vprop_equiv_unit (x:vprop)\n : vprop_equiv (emp ** x) x\n = slprop_equiv_unit x\n\nlet vprop_equiv_comm (p1 p2:vprop)\n : vprop_equiv (p1 ** p2) (p2 ** p1)\n = slprop_equiv_comm p1 p2\n\nlet vprop_equiv_assoc (p1 p2 p3:vprop)\n : vprop_equiv ((p1 ** p2) ** p3) (p1 ** (p2 ** p3))\n = slprop_equiv_assoc p1 p2 p3\n\nlet vprop_equiv_cong (p1 p2 p3 p4:vprop)\n (f: vprop_equiv p1 p3)\n (g: vprop_equiv p2 p4)\n : vprop_equiv (p1 ** p2) (p3 ** p4)\n = slprop_equiv_elim p1 p3;\n slprop_equiv_elim p2 p4;\n vprop_equiv_refl _\n\nlet vprop_equiv_ext p1 p2 _ = vprop_equiv_refl p1\n\n(* Invariants, just reexport *)\nmodule Act = PulseCore.Action\nlet iname = Act.iname\n\nlet join_sub _ _ = ()\nlet join_emp is =\n Set.lemma_equal_intro (join_inames is emp_inames) (reveal is);\n Set.lemma_equal_intro (join_inames emp_inames is) (reveal is)\n\nlet inv = Act.inv\nlet name_of_inv = Act.name_of_inv\n\nlet add_already_there i is = Set.lemma_equal_intro (add_inv is i) is\n\n////////////////////////////////////////////////////////////////////\n// stt a pre post: The main type of a pulse computation\n////////////////////////////////////////////////////////////////////\nlet stt = I.stt\nlet return_stt_noeq = I.return\nlet bind_stt = I.bind\nlet frame_stt = I.frame", "sketch": [ "Step 1: The definition `par_stt` is about defining a parallel composition of two state-transformer computations `f` and `g`. The preconditions of the combined computation are the conjunction of the preconditions of `f` and `g`, and the postconditions are the conjunction of the postconditions of `f` and `g`.\n\nStep 2: To implement `par_stt`, we need to create a new state-transformer computation that first runs `f` and then runs `g`, ensuring that the preconditions and postconditions are combined appropriately. This involves using the `bind_stt` function to sequence the computations and the `frame_stt` function to handle the framing of the preconditions and postconditions.", "Step 1: The `par_stt` function is intended to combine two computations `f` and `g` that operate on separate preconditions and postconditions into a single computation. The combined computation should have a precondition that is the conjunction of the preconditions of `f` and `g`, and a postcondition that is the conjunction of the postconditions of `f` and `g`.\n\nStep 2: To implement `par_stt`, we will use the `I.par` function from the `PulseCore.InstantiatedSemantics` module. This function allows us to combine two computations in parallel. We will pass the computations `f` and `g` along with their respective preconditions and postconditions to this function.", "Step 1: The definition `par_stt` is about defining a parallel composition of two computations `f` and `g` in the `stt` monad. The precondition of the combined computation is the conjunction of the preconditions of `f` and `g`, and the postcondition is the conjunction of their postconditions.\nStep 2: To implement `par_stt`, we need to ensure that the combined computation respects the preconditions and postconditions of both `f` and `g`. We will use the `bind_stt` and `frame_stt` operations to sequence and frame the computations appropriately.", "Step 1: The `par_stt` function is intended to combine two computations `f` and `g` that operate on separate preconditions and postconditions. The resulting computation should operate on the combined preconditions (`preL ** preR`) and produce combined postconditions (`postL ** postR`).\nStep 2: To implement `par_stt`, we will use the `I.par` function from the `PulseCore.InstantiatedSemantics` module. This function takes two computations and combines them in parallel, ensuring that the preconditions and postconditions are appropriately combined.", "Step 1: The definition `par_stt` is about defining a parallel composition of two stateful computations `f` and `g`. These computations have their own preconditions (`preL` and `preR`) and postconditions (`postL` and `postR`). The resulting computation should have a combined precondition (`preL ** preR`) and a combined postcondition (`postL ** postR`).\n\nStep 2: To implement this, we need to create a new stateful computation that first runs `f` and then `g` in parallel. The precondition of this computation is the conjunction of the preconditions of `f` and `g`, and the postcondition is the conjunction of their postconditions. We will use the `bind_stt` and `frame_stt` functions to achieve this.", "Step 1: The `par_stt` function is intended to combine two stateful computations `f` and `g` that operate on separate preconditions and postconditions. The resulting computation should have a combined precondition and postcondition that are the conjunctions of the individual preconditions and postconditions, respectively.\nStep 2: To implement `par_stt`, we need to create a new stateful computation that first runs `f`, then runs `g`, and ensures that the combined precondition and postcondition are satisfied. This can be done by using the `bind_stt` and `frame_stt` combinators to sequence and frame the computations appropriately.", "Step 1: The `par_stt` function is intended to represent the parallel composition of two computations `f` and `g`. Each computation has its own precondition and postcondition. The precondition for the combined computation is the conjunction of the preconditions of `f` and `g`, and the postcondition is the conjunction of their postconditions.\n\nStep 2: To implement `par_stt`, we need to create a new computation that runs `f` and `g` in parallel. The precondition of this new computation will be the conjunction of `preL` and `preR`, and the postcondition will be the conjunction of `postL` and `postR`. We will use the `I.par` function from the `PulseCore.InstantiatedSemantics` module to achieve this.", "Step 1: The definition `par_stt` is about defining a parallel composition of two stateful computations `f` and `g`. Each computation has its own precondition and postcondition. The resulting computation should have a combined precondition and postcondition that reflect the parallel execution of `f` and `g`.\n\nStep 2: To implement `par_stt`, we need to ensure that the combined precondition is the conjunction of `preL` and `preR`, and the combined postcondition is the conjunction of `postL` and `postR`. The implementation will involve running both `f` and `g` in parallel and combining their results.", "Step 1: This definition is about creating a parallel composition of two computations `f` and `g` in the `stt` monad. The precondition of the combined computation is the conjunction of the preconditions of `f` and `g`, and the postcondition is the conjunction of their postconditions.\nStep 2: To implement this, we will use the `par` combinator from the `PulseCore.InstantiatedSemantics` module. This combinator allows us to run two computations in parallel, combining their preconditions and postconditions using the separating conjunction operator `**`.", "Step 1: The `par_stt` function is intended to combine two computations `f` and `g` that operate in parallel. Each computation has its own precondition and postcondition. The combined computation should have a precondition that is the conjunction of the preconditions of `f` and `g`, and a postcondition that is the conjunction of the postconditions of `f` and `g`.\n\nStep 2: To implement `par_stt`, we need to create a new computation that first runs `f` and then runs `g`. The precondition of this new computation will be the conjunction of `preL` and `preR`, and the postcondition will be the conjunction of `postL` and `postR`. We will use the `bind_stt` function to sequence the computations and the `frame_stt` function to manage the preconditions and postconditions." ], "generated_solution": [ "let par_stt\n (#preL:vprop)\n (#postL:vprop) \n (#preR:vprop)\n (#postR:vprop)\n (f:stt unit preL (fun _ -> postL))\n (g:stt unit preR (fun _ -> postR))\n: stt unit\n (preL ** preR)\n (fun _ -> postL ** postR)\n = bind_stt (frame_stt f preR)\n (fun _ -> frame_stt g postL)", "= I.par f g", "let par_stt\n (#preL:vprop)\n (#postL:vprop) \n (#preR:vprop)\n (#postR:vprop)\n (f:stt unit preL (fun _ -> postL))\n (g:stt unit preR (fun _ -> postR))\n: stt unit\n (preL ** preR)\n (fun _ -> postL ** postR)\n = bind_stt (frame_stt f preR) (fun _ -> frame_stt g postL)", "= I.par f g", "let par_stt\n (#preL:vprop)\n (#postL:vprop) \n (#preR:vprop)\n (#postR:vprop)\n (f:stt unit preL (fun _ -> postL))\n (g:stt unit preR (fun _ -> postR))\n: stt unit\n (preL ** preR)\n (fun _ -> postL ** postR)\n = bind_stt (frame_stt f preR postR) (fun _ -> g)", "let par_stt\n (#preL:vprop)\n (#postL:vprop) \n (#preR:vprop)\n (#postR:vprop)\n (f:stt unit preL (fun _ -> postL))\n (g:stt unit preR (fun _ -> postR))\n: stt unit\n (preL ** preR)\n (fun _ -> postL ** postR)\n = bind_stt (frame_stt f preR) (fun _ -> frame_stt g postL)", "let par_stt\n (#preL:vprop)\n (#postL:vprop) \n (#preR:vprop)\n (#postR:vprop)\n (f:stt unit preL (fun _ -> postL))\n (g:stt unit preR (fun _ -> postR))\n: stt unit\n (preL ** preR)\n (fun _ -> postL ** postR)\n = I.par f g", "let par_stt\n (#preL:vprop)\n (#postL:vprop) \n (#preR:vprop)\n (#postR:vprop)\n (f:stt unit preL (fun _ -> postL))\n (g:stt unit preR (fun _ -> postR))\n: stt unit\n (preL ** preR)\n (fun _ -> postL ** postR)\n = bind_stt (frame_stt preL preR f) (fun _ -> frame_stt preR preL g)", "= I.par f g", "let par_stt\n (#preL:vprop)\n (#postL:vprop) \n (#preR:vprop)\n (#postR:vprop)\n (f:stt unit preL (fun _ -> postL))\n (g:stt unit preR (fun _ -> postR))\n: stt unit\n (preL ** preR)\n (fun _ -> postL ** postR)\n = bind_stt (frame_stt f preR postR) (fun _ -> frame_stt g preL postL)" ] }, { "file_name": "Spec.Blake2.Test.fst", "name": "Spec.Blake2.Test.test20_params", "opens_and_abbrevs": [ { "abbrev": "S", "full_module": "Spec.Blake2" }, { "abbrev": "PS", "full_module": "Lib.PrintSequence" }, { "open": "Lib.ByteSequence" }, { "open": "Lib.Sequence" }, { "open": "Lib.RawIntTypes" }, { "open": "Lib.IntTypes" }, { "open": "FStar.Mul" }, { "open": "Spec.Blake2" }, { "open": "Spec.Blake2" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 0, "max_fuel": 0, "initial_ifuel": 0, "max_ifuel": 0, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val test20_params:S.blake2b_params", "source_definition": "let test20_params : S.blake2b_params =\n { S.blake2b_default_params with fanout = u8 5; node_depth = u8 3; node_offset = u32 41 }", "source_range": { "start_line": 846, "start_col": 0, "end_line": 847, "end_col": 90 }, "interleaved": false, "definition": "Spec.Blake2.Definitions.Mkblake2b_params\n (Mkblake2b_params?.digest_length Spec.Blake2.Definitions.blake2b_default_params)\n (Mkblake2b_params?.key_length Spec.Blake2.Definitions.blake2b_default_params)\n (Lib.IntTypes.u8 5)\n (Mkblake2b_params?.depth Spec.Blake2.Definitions.blake2b_default_params)\n (Mkblake2b_params?.leaf_length Spec.Blake2.Definitions.blake2b_default_params)\n (Lib.IntTypes.u32 41)\n (Mkblake2b_params?.xof_length Spec.Blake2.Definitions.blake2b_default_params)\n (Lib.IntTypes.u8 3)\n (Mkblake2b_params?.inner_length Spec.Blake2.Definitions.blake2b_default_params)\n (Mkblake2b_params?.salt Spec.Blake2.Definitions.blake2b_default_params)\n (Mkblake2b_params?.personal Spec.Blake2.Definitions.blake2b_default_params)", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Spec.Blake2.Definitions.Mkblake2b_params", "Spec.Blake2.Definitions.__proj__Mkblake2b_params__item__digest_length", "Spec.Blake2.Definitions.blake2b_default_params", "Spec.Blake2.Definitions.__proj__Mkblake2b_params__item__key_length", "Lib.IntTypes.u8", "Spec.Blake2.Definitions.__proj__Mkblake2b_params__item__depth", "Spec.Blake2.Definitions.__proj__Mkblake2b_params__item__leaf_length", "Lib.IntTypes.u32", "Spec.Blake2.Definitions.__proj__Mkblake2b_params__item__xof_length", "Spec.Blake2.Definitions.__proj__Mkblake2b_params__item__inner_length", "Spec.Blake2.Definitions.__proj__Mkblake2b_params__item__salt", "Spec.Blake2.Definitions.__proj__Mkblake2b_params__item__personal" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "Spec.Blake2.Definitions.blake2b_params", "prompt": "let test20_params:S.blake2b_params =\n ", "expected_response": "{ S.blake2b_default_params with fanout = u8 5; node_depth = u8 3; node_offset = u32 41 }", "source": { "project_name": "hacl-star", "file_name": "specs/tests/Spec.Blake2.Test.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Spec.Blake2.Test.fst", "checked_file": "dataset/Spec.Blake2.Test.fst.checked", "interface_file": false, "dependencies": [ "dataset/Spec.Blake2.fst.checked", "dataset/prims.fst.checked", "dataset/Lib.Sequence.fsti.checked", "dataset/Lib.RawIntTypes.fsti.checked", "dataset/Lib.PrintSequence.fsti.checked", "dataset/Lib.IntTypes.fsti.checked", "dataset/Lib.ByteSequence.fsti.checked", "dataset/FStar.UInt8.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.List.fst.checked", "dataset/FStar.IO.fst.checked" ] }, "definitions_in_context": [ "let test1_plaintext : lbytes 3 =\n let l = List.Tot.map u8_from_UInt8 [ 0x61uy; 0x62uy; 0x63uy ] in\n assert_norm (List.Tot.length l = 3);\n of_list l", "let test1_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x50uy; 0x8Cuy; 0x5Euy; 0x8Cuy; 0x32uy; 0x7Cuy; 0x14uy; 0xE2uy;\n 0xE1uy; 0xA7uy; 0x2Buy; 0xA3uy; 0x4Euy; 0xEBuy; 0x45uy; 0x2Fuy;\n 0x37uy; 0x45uy; 0x8Buy; 0x20uy; 0x9Euy; 0xD6uy; 0x3Auy; 0x29uy;\n 0x4Duy; 0x99uy; 0x9Buy; 0x4Cuy; 0x86uy; 0x67uy; 0x59uy; 0x82uy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l", "let test2_plaintext : lbytes 1 =\n let l = List.Tot.map u8_from_UInt8 [ 0x00uy ] in\n assert_norm (List.Tot.length l = 1);\n of_list l", "let test2_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l", "let test2_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x40uy; 0xd1uy; 0x5fuy; 0xeeuy; 0x7cuy; 0x32uy; 0x88uy; 0x30uy;\n 0x16uy; 0x6auy; 0xc3uy; 0xf9uy; 0x18uy; 0x65uy; 0x0fuy; 0x80uy;\n 0x7euy; 0x7euy; 0x01uy; 0xe1uy; 0x77uy; 0x25uy; 0x8cuy; 0xdcuy;\n 0x0auy; 0x39uy; 0xb1uy; 0x1fuy; 0x59uy; 0x80uy; 0x66uy; 0xf1uy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l", "let test3_plaintext : lbytes 255 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2auy; 0x2buy; 0x2cuy; 0x2duy; 0x2euy; 0x2fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3auy; 0x3buy; 0x3cuy; 0x3duy; 0x3euy; 0x3fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4auy; 0x4buy; 0x4cuy; 0x4duy; 0x4euy; 0x4fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5auy; 0x5buy; 0x5cuy; 0x5duy; 0x5euy; 0x5fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6auy; 0x6buy; 0x6cuy; 0x6duy; 0x6euy; 0x6fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7auy; 0x7buy; 0x7cuy; 0x7duy; 0x7euy; 0x7fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8auy; 0x8buy; 0x8cuy; 0x8duy; 0x8euy; 0x8fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9auy; 0x9buy; 0x9cuy; 0x9duy; 0x9euy; 0x9fuy;\n 0xa0uy; 0xa1uy; 0xa2uy; 0xa3uy; 0xa4uy; 0xa5uy; 0xa6uy; 0xa7uy;\n 0xa8uy; 0xa9uy; 0xaauy; 0xabuy; 0xacuy; 0xaduy; 0xaeuy; 0xafuy;\n 0xb0uy; 0xb1uy; 0xb2uy; 0xb3uy; 0xb4uy; 0xb5uy; 0xb6uy; 0xb7uy;\n 0xb8uy; 0xb9uy; 0xbauy; 0xbbuy; 0xbcuy; 0xbduy; 0xbeuy; 0xbfuy;\n 0xc0uy; 0xc1uy; 0xc2uy; 0xc3uy; 0xc4uy; 0xc5uy; 0xc6uy; 0xc7uy;\n 0xc8uy; 0xc9uy; 0xcauy; 0xcbuy; 0xccuy; 0xcduy; 0xceuy; 0xcfuy;\n 0xd0uy; 0xd1uy; 0xd2uy; 0xd3uy; 0xd4uy; 0xd5uy; 0xd6uy; 0xd7uy;\n 0xd8uy; 0xd9uy; 0xdauy; 0xdbuy; 0xdcuy; 0xdduy; 0xdeuy; 0xdfuy;\n 0xe0uy; 0xe1uy; 0xe2uy; 0xe3uy; 0xe4uy; 0xe5uy; 0xe6uy; 0xe7uy;\n 0xe8uy; 0xe9uy; 0xeauy; 0xebuy; 0xecuy; 0xeduy; 0xeeuy; 0xefuy;\n 0xf0uy; 0xf1uy; 0xf2uy; 0xf3uy; 0xf4uy; 0xf5uy; 0xf6uy; 0xf7uy;\n 0xf8uy; 0xf9uy; 0xfauy; 0xfbuy; 0xfcuy; 0xfduy; 0xfeuy ] in\n assert_norm (List.Tot.length l = 255);\n of_list l", "let test3_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l", "let test3_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x3fuy; 0xb7uy; 0x35uy; 0x06uy; 0x1auy; 0xbcuy; 0x51uy; 0x9duy;\n 0xfeuy; 0x97uy; 0x9euy; 0x54uy; 0xc1uy; 0xeeuy; 0x5buy; 0xfauy;\n 0xd0uy; 0xa9uy; 0xd8uy; 0x58uy; 0xb3uy; 0x31uy; 0x5buy; 0xaduy;\n 0x34uy; 0xbduy; 0xe9uy; 0x99uy; 0xefuy; 0xd7uy; 0x24uy; 0xdduy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l", "let test4_plaintext : lbytes 251 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2auy; 0x2buy; 0x2cuy; 0x2duy; 0x2euy; 0x2fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3auy; 0x3buy; 0x3cuy; 0x3duy; 0x3euy; 0x3fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4auy; 0x4buy; 0x4cuy; 0x4duy; 0x4euy; 0x4fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5auy; 0x5buy; 0x5cuy; 0x5duy; 0x5euy; 0x5fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6auy; 0x6buy; 0x6cuy; 0x6duy; 0x6euy; 0x6fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7auy; 0x7buy; 0x7cuy; 0x7duy; 0x7euy; 0x7fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8auy; 0x8buy; 0x8cuy; 0x8duy; 0x8euy; 0x8fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9auy; 0x9buy; 0x9cuy; 0x9duy; 0x9euy; 0x9fuy;\n 0xa0uy; 0xa1uy; 0xa2uy; 0xa3uy; 0xa4uy; 0xa5uy; 0xa6uy; 0xa7uy;\n 0xa8uy; 0xa9uy; 0xaauy; 0xabuy; 0xacuy; 0xaduy; 0xaeuy; 0xafuy;\n 0xb0uy; 0xb1uy; 0xb2uy; 0xb3uy; 0xb4uy; 0xb5uy; 0xb6uy; 0xb7uy;\n 0xb8uy; 0xb9uy; 0xbauy; 0xbbuy; 0xbcuy; 0xbduy; 0xbeuy; 0xbfuy;\n 0xc0uy; 0xc1uy; 0xc2uy; 0xc3uy; 0xc4uy; 0xc5uy; 0xc6uy; 0xc7uy;\n 0xc8uy; 0xc9uy; 0xcauy; 0xcbuy; 0xccuy; 0xcduy; 0xceuy; 0xcfuy;\n 0xd0uy; 0xd1uy; 0xd2uy; 0xd3uy; 0xd4uy; 0xd5uy; 0xd6uy; 0xd7uy;\n 0xd8uy; 0xd9uy; 0xdauy; 0xdbuy; 0xdcuy; 0xdduy; 0xdeuy; 0xdfuy;\n 0xe0uy; 0xe1uy; 0xe2uy; 0xe3uy; 0xe4uy; 0xe5uy; 0xe6uy; 0xe7uy;\n 0xe8uy; 0xe9uy; 0xeauy; 0xebuy; 0xecuy; 0xeduy; 0xeeuy; 0xefuy;\n 0xf0uy; 0xf1uy; 0xf2uy; 0xf3uy; 0xf4uy; 0xf5uy; 0xf6uy; 0xf7uy;\n 0xf8uy; 0xf9uy; 0xfauy ] in\n assert_norm (List.Tot.length l = 251);\n of_list l", "let test4_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l", "let test4_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xd1uy; 0x2buy; 0xf3uy; 0x73uy; 0x2euy; 0xf4uy; 0xafuy; 0x5cuy;\n 0x22uy; 0xfauy; 0x90uy; 0x35uy; 0x6auy; 0xf8uy; 0xfcuy; 0x50uy;\n 0xfcuy; 0xb4uy; 0x0fuy; 0x8fuy; 0x2euy; 0xa5uy; 0xc8uy; 0x59uy;\n 0x47uy; 0x37uy; 0xa3uy; 0xb3uy; 0xd5uy; 0xabuy; 0xdbuy; 0xd7uy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l", "let test5_plaintext : lbytes 3 =\n let l = List.Tot.map u8_from_UInt8 [ 0x61uy; 0x62uy; 0x63uy ] in\n assert_norm (List.Tot.length l = 3);\n of_list l", "let test5_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xBAuy; 0x80uy; 0xA5uy; 0x3Fuy; 0x98uy; 0x1Cuy; 0x4Duy; 0x0Duy;\n 0x6Auy; 0x27uy; 0x97uy; 0xB6uy; 0x9Fuy; 0x12uy; 0xF6uy; 0xE9uy;\n 0x4Cuy; 0x21uy; 0x2Fuy; 0x14uy; 0x68uy; 0x5Auy; 0xC4uy; 0xB7uy;\n 0x4Buy; 0x12uy; 0xBBuy; 0x6Fuy; 0xDBuy; 0xFFuy; 0xA2uy; 0xD1uy;\n 0x7Duy; 0x87uy; 0xC5uy; 0x39uy; 0x2Auy; 0xABuy; 0x79uy; 0x2Duy;\n 0xC2uy; 0x52uy; 0xD5uy; 0xDEuy; 0x45uy; 0x33uy; 0xCCuy; 0x95uy;\n 0x18uy; 0xD3uy; 0x8Auy; 0xA8uy; 0xDBuy; 0xF1uy; 0x92uy; 0x5Auy;\n 0xB9uy; 0x23uy; 0x86uy; 0xEDuy; 0xD4uy; 0x00uy; 0x99uy; 0x23uy ] in\n assert_norm (List.Tot.length l = 64);\n of_list l", "let test6_plaintext : lbytes 128 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy ] in\n assert_norm (List.Tot.length l = 128);\n of_list l", "let test6_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy ] in\n assert_norm (List.Tot.length l = 64);\n of_list l", "let test6_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xe4uy; 0x7buy; 0xb6uy; 0xf2uy; 0x0fuy; 0xbfuy; 0x14uy; 0x98uy;\n 0x4fuy; 0x72uy; 0xa4uy; 0xc3uy; 0xcduy; 0x9fuy; 0x3duy; 0xc0uy;\n 0xd3uy; 0x89uy; 0x28uy; 0xe5uy; 0x36uy; 0x73uy; 0x3buy; 0xa7uy;\n 0xc5uy; 0xb1uy; 0x53uy; 0xc7uy; 0x15uy; 0x46uy; 0x58uy; 0x4buy;\n 0x73uy; 0x71uy; 0xf9uy; 0xb7uy; 0x07uy; 0x07uy; 0x77uy; 0xb9uy;\n 0xa0uy; 0x94uy; 0x77uy; 0x03uy; 0x40uy; 0x96uy; 0x50uy; 0xfduy;\n 0x04uy; 0xcfuy; 0xc9uy; 0xa5uy; 0xd5uy; 0x61uy; 0xf9uy; 0x9euy;\n 0xd1uy; 0x34uy; 0xefuy; 0x26uy; 0x2buy; 0x03uy; 0xdbuy; 0x94uy ] in\n assert_norm (List.Tot.length l = 64);\n of_list l", "let test7_plaintext : lbytes 63 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy ] in\n assert_norm (FStar.List.length l = 63);\n of_list l", "let test7_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l", "let test7_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xC6uy; 0x53uy; 0x82uy; 0x51uy; 0x3Fuy; 0x07uy; 0x46uy; 0x0Duy;\n 0xA3uy; 0x98uy; 0x33uy; 0xCBuy; 0x66uy; 0x6Cuy; 0x5Euy; 0xD8uy;\n 0x2Euy; 0x61uy; 0xB9uy; 0xE9uy; 0x98uy; 0xF4uy; 0xB0uy; 0xC4uy;\n 0x28uy; 0x7Cuy; 0xEEuy; 0x56uy; 0xC3uy; 0xCCuy; 0x9Buy; 0xCDuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l", "let test8_plaintext : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l", "let test8_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l", "let test8_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x89uy; 0x75uy; 0xB0uy; 0x57uy; 0x7Fuy; 0xD3uy; 0x55uy; 0x66uy;\n 0xD7uy; 0x50uy; 0xB3uy; 0x62uy; 0xB0uy; 0x89uy; 0x7Auy; 0x26uy;\n 0xC3uy; 0x99uy; 0x13uy; 0x6Duy; 0xF0uy; 0x7Buy; 0xABuy; 0xABuy;\n 0xBDuy; 0xE6uy; 0x20uy; 0x3Fuy; 0xF2uy; 0x95uy; 0x4Euy; 0xD4uy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l", "let test9_plaintext : lbytes 65 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy ] in\n assert_norm (FStar.List.length l = 65);\n of_list l", "let test9_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l", "let test9_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x21uy; 0xFEuy; 0x0Cuy; 0xEBuy; 0x00uy; 0x52uy; 0xBEuy; 0x7Fuy;\n 0xB0uy; 0xF0uy; 0x04uy; 0x18uy; 0x7Cuy; 0xACuy; 0xD7uy; 0xDEuy;\n 0x67uy; 0xFAuy; 0x6Euy; 0xB0uy; 0x93uy; 0x8Duy; 0x92uy; 0x76uy;\n 0x77uy; 0xF2uy; 0x39uy; 0x8Cuy; 0x13uy; 0x23uy; 0x17uy; 0xA8uy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l", "let test10_plaintext : lbytes 128 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy ] in\n assert_norm (FStar.List.length l = 128);\n of_list l", "let test10_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l", "let test10_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x0Cuy; 0x31uy; 0x1Fuy; 0x38uy; 0xC3uy; 0x5Auy; 0x4Fuy; 0xB9uy;\n 0x0Duy; 0x65uy; 0x1Cuy; 0x28uy; 0x9Duy; 0x48uy; 0x68uy; 0x56uy;\n 0xCDuy; 0x14uy; 0x13uy; 0xDFuy; 0x9Buy; 0x06uy; 0x77uy; 0xF5uy;\n 0x3Euy; 0xCEuy; 0x2Cuy; 0xD9uy; 0xE4uy; 0x77uy; 0xC6uy; 0x0Auy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l", "let test11_plaintext : lbytes 256 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8Auy; 0x8Buy; 0x8Cuy; 0x8Duy; 0x8Euy; 0x8Fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9Auy; 0x9Buy; 0x9Cuy; 0x9Duy; 0x9Euy; 0x9Fuy;\n 0xA0uy; 0xA1uy; 0xA2uy; 0xA3uy; 0xA4uy; 0xA5uy; 0xA6uy; 0xA7uy;\n 0xA8uy; 0xA9uy; 0xAAuy; 0xABuy; 0xACuy; 0xADuy; 0xAEuy; 0xAFuy;\n 0xB0uy; 0xB1uy; 0xB2uy; 0xB3uy; 0xB4uy; 0xB5uy; 0xB6uy; 0xB7uy;\n 0xB8uy; 0xB9uy; 0xBAuy; 0xBBuy; 0xBCuy; 0xBDuy; 0xBEuy; 0xBFuy;\n 0xC0uy; 0xC1uy; 0xC2uy; 0xC3uy; 0xC4uy; 0xC5uy; 0xC6uy; 0xC7uy;\n 0xC8uy; 0xC9uy; 0xCAuy; 0xCBuy; 0xCCuy; 0xCDuy; 0xCEuy; 0xCFuy;\n 0xD0uy; 0xD1uy; 0xD2uy; 0xD3uy; 0xD4uy; 0xD5uy; 0xD6uy; 0xD7uy;\n 0xD8uy; 0xD9uy; 0xDAuy; 0xDBuy; 0xDCuy; 0xDDuy; 0xDEuy; 0xDFuy;\n 0xE0uy; 0xE1uy; 0xE2uy; 0xE3uy; 0xE4uy; 0xE5uy; 0xE6uy; 0xE7uy;\n 0xE8uy; 0xE9uy; 0xEAuy; 0xEBuy; 0xECuy; 0xEDuy; 0xEEuy; 0xEFuy;\n 0xF0uy; 0xF1uy; 0xF2uy; 0xF3uy; 0xF4uy; 0xF5uy; 0xF6uy; 0xF7uy;\n 0xF8uy; 0xF9uy; 0xFAuy; 0xFBuy; 0xFCuy; 0xFDuy; 0xFEuy; 0xFFuy ] in\n assert_norm (FStar.List.length l = 256);\n of_list l", "let test11_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l", "let test11_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x52uy; 0x11uy; 0xD1uy; 0xAEuy; 0xFCuy; 0x00uy; 0x25uy; 0xBEuy;\n 0x7Fuy; 0x85uy; 0xC0uy; 0x6Buy; 0x3Euy; 0x14uy; 0xE0uy; 0xFCuy;\n 0x64uy; 0x5Auy; 0xE1uy; 0x2Buy; 0xD4uy; 0x17uy; 0x46uy; 0x48uy;\n 0x5Euy; 0xA6uy; 0xD8uy; 0xA3uy; 0x64uy; 0xA2uy; 0xEAuy; 0xEEuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l", "let test0_plaintext : lbytes 0 =\n let l = List.Tot.map u8_from_UInt8 [] in\n assert_norm (List.Tot.length l = 0);\n of_list l", "let test0_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2auy; 0x2buy; 0x2cuy; 0x2duy; 0x2euy; 0x2fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3auy; 0x3buy; 0x3cuy; 0x3duy; 0x3euy; 0x3fuy ] in\n assert_norm (List.Tot.length l = 64);\n of_list l", "let test0_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x10uy; 0xebuy; 0xb6uy; 0x77uy; 0x00uy; 0xb1uy; 0x86uy; 0x8euy;\n 0xfbuy; 0x44uy; 0x17uy; 0x98uy; 0x7auy; 0xcfuy; 0x46uy; 0x90uy;\n 0xaeuy; 0x9duy; 0x97uy; 0x2fuy; 0xb7uy; 0xa5uy; 0x90uy; 0xc2uy;\n 0xf0uy; 0x28uy; 0x71uy; 0x79uy; 0x9auy; 0xaauy; 0x47uy; 0x86uy;\n 0xb5uy; 0xe9uy; 0x96uy; 0xe8uy; 0xf0uy; 0xf4uy; 0xebuy; 0x98uy;\n 0x1fuy; 0xc2uy; 0x14uy; 0xb0uy; 0x05uy; 0xf4uy; 0x2duy; 0x2fuy;\n 0xf4uy; 0x23uy; 0x34uy; 0x99uy; 0x39uy; 0x16uy; 0x53uy; 0xdfuy;\n 0x7auy; 0xefuy; 0xcbuy; 0xc1uy; 0x3fuy; 0xc5uy; 0x15uy; 0x68uy ] in\n assert_norm (List.Tot.length l = 64);\n of_list l", "let test12_plaintext : lbytes 127 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy ] in\n assert_norm (FStar.List.length l = 127);\n of_list l", "let test12_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l", "let test12_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x76uy; 0xD2uy; 0xD8uy; 0x19uy; 0xC9uy; 0x2Buy; 0xCEuy; 0x55uy;\n 0xFAuy; 0x8Euy; 0x09uy; 0x2Auy; 0xB1uy; 0xBFuy; 0x9Buy; 0x9Euy;\n 0xABuy; 0x23uy; 0x7Auy; 0x25uy; 0x26uy; 0x79uy; 0x86uy; 0xCAuy;\n 0xCFuy; 0x2Buy; 0x8Euy; 0xE1uy; 0x4Duy; 0x21uy; 0x4Duy; 0x73uy;\n 0x0Duy; 0xC9uy; 0xA5uy; 0xAAuy; 0x2Duy; 0x7Buy; 0x59uy; 0x6Euy;\n 0x86uy; 0xA1uy; 0xFDuy; 0x8Fuy; 0xA0uy; 0x80uy; 0x4Cuy; 0x77uy;\n 0x40uy; 0x2Duy; 0x2Fuy; 0xCDuy; 0x45uy; 0x08uy; 0x36uy; 0x88uy;\n 0xB2uy; 0x18uy; 0xB1uy; 0xCDuy; 0xFAuy; 0x0Duy; 0xCBuy; 0xCBuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l", "let test13_plaintext : lbytes 128 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy ] in\n assert_norm (FStar.List.length l = 128);\n of_list l", "let test13_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l", "let test13_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x72uy; 0x06uy; 0x5Euy; 0xE4uy; 0xDDuy; 0x91uy; 0xC2uy; 0xD8uy;\n 0x50uy; 0x9Fuy; 0xA1uy; 0xFCuy; 0x28uy; 0xA3uy; 0x7Cuy; 0x7Fuy;\n 0xC9uy; 0xFAuy; 0x7Duy; 0x5Buy; 0x3Fuy; 0x8Auy; 0xD3uy; 0xD0uy;\n 0xD7uy; 0xA2uy; 0x56uy; 0x26uy; 0xB5uy; 0x7Buy; 0x1Buy; 0x44uy;\n 0x78uy; 0x8Duy; 0x4Cuy; 0xAFuy; 0x80uy; 0x62uy; 0x90uy; 0x42uy;\n 0x5Fuy; 0x98uy; 0x90uy; 0xA3uy; 0xA2uy; 0xA3uy; 0x5Auy; 0x90uy;\n 0x5Auy; 0xB4uy; 0xB3uy; 0x7Auy; 0xCFuy; 0xD0uy; 0xDAuy; 0x6Euy;\n 0x45uy; 0x17uy; 0xB2uy; 0x52uy; 0x5Cuy; 0x96uy; 0x51uy; 0xE4uy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l", "let test14_plaintext : lbytes 129 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy;\n 0x80uy ] in\n assert_norm (FStar.List.length l = 129);\n of_list l", "let test14_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l", "let test14_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x64uy; 0x47uy; 0x5Duy; 0xFEuy; 0x76uy; 0x00uy; 0xD7uy; 0x17uy;\n 0x1Buy; 0xEAuy; 0x0Buy; 0x39uy; 0x4Euy; 0x27uy; 0xC9uy; 0xB0uy;\n 0x0Duy; 0x8Euy; 0x74uy; 0xDDuy; 0x1Euy; 0x41uy; 0x6Auy; 0x79uy;\n 0x47uy; 0x36uy; 0x82uy; 0xADuy; 0x3Duy; 0xFDuy; 0xBBuy; 0x70uy;\n 0x66uy; 0x31uy; 0x55uy; 0x80uy; 0x55uy; 0xCFuy; 0xC8uy; 0xA4uy;\n 0x0Euy; 0x07uy; 0xBDuy; 0x01uy; 0x5Auy; 0x45uy; 0x40uy; 0xDCuy;\n 0xDEuy; 0xA1uy; 0x58uy; 0x83uy; 0xCBuy; 0xBFuy; 0x31uy; 0x41uy;\n 0x2Duy; 0xF1uy; 0xDEuy; 0x1Cuy; 0xD4uy; 0x15uy; 0x2Buy; 0x91uy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l", "let test15_plaintext : lbytes 256 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8Auy; 0x8Buy; 0x8Cuy; 0x8Duy; 0x8Euy; 0x8Fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9Auy; 0x9Buy; 0x9Cuy; 0x9Duy; 0x9Euy; 0x9Fuy;\n 0xA0uy; 0xA1uy; 0xA2uy; 0xA3uy; 0xA4uy; 0xA5uy; 0xA6uy; 0xA7uy;\n 0xA8uy; 0xA9uy; 0xAAuy; 0xABuy; 0xACuy; 0xADuy; 0xAEuy; 0xAFuy;\n 0xB0uy; 0xB1uy; 0xB2uy; 0xB3uy; 0xB4uy; 0xB5uy; 0xB6uy; 0xB7uy;\n 0xB8uy; 0xB9uy; 0xBAuy; 0xBBuy; 0xBCuy; 0xBDuy; 0xBEuy; 0xBFuy;\n 0xC0uy; 0xC1uy; 0xC2uy; 0xC3uy; 0xC4uy; 0xC5uy; 0xC6uy; 0xC7uy;\n 0xC8uy; 0xC9uy; 0xCAuy; 0xCBuy; 0xCCuy; 0xCDuy; 0xCEuy; 0xCFuy;\n 0xD0uy; 0xD1uy; 0xD2uy; 0xD3uy; 0xD4uy; 0xD5uy; 0xD6uy; 0xD7uy;\n 0xD8uy; 0xD9uy; 0xDAuy; 0xDBuy; 0xDCuy; 0xDDuy; 0xDEuy; 0xDFuy;\n 0xE0uy; 0xE1uy; 0xE2uy; 0xE3uy; 0xE4uy; 0xE5uy; 0xE6uy; 0xE7uy;\n 0xE8uy; 0xE9uy; 0xEAuy; 0xEBuy; 0xECuy; 0xEDuy; 0xEEuy; 0xEFuy;\n 0xF0uy; 0xF1uy; 0xF2uy; 0xF3uy; 0xF4uy; 0xF5uy; 0xF6uy; 0xF7uy;\n 0xF8uy; 0xF9uy; 0xFAuy; 0xFBuy; 0xFCuy; 0xFDuy; 0xFEuy; 0xFFuy ] in\n assert_norm (FStar.List.length l = 256);\n of_list l", "let test15_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l", "let test15_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xB7uy; 0x20uy; 0x71uy; 0xE0uy; 0x96uy; 0x27uy; 0x7Euy; 0xDEuy;\n 0xBBuy; 0x8Euy; 0xE5uy; 0x13uy; 0x4Duy; 0xD3uy; 0x71uy; 0x49uy;\n 0x96uy; 0x30uy; 0x7Buy; 0xA3uy; 0xA5uy; 0x5Auy; 0xA4uy; 0x73uy;\n 0x3Duy; 0x41uy; 0x2Auy; 0xBBuy; 0xE2uy; 0x8Euy; 0x90uy; 0x9Euy;\n 0x10uy; 0xE5uy; 0x7Euy; 0x6Fuy; 0xBFuy; 0xB4uy; 0xEFuy; 0x53uy;\n 0xB3uy; 0xB9uy; 0x60uy; 0x51uy; 0x82uy; 0x94uy; 0xFFuy; 0x88uy;\n 0x9Auy; 0x90uy; 0x82uy; 0x92uy; 0x54uy; 0x41uy; 0x2Euy; 0x2Auy;\n 0x60uy; 0xB8uy; 0x5Auy; 0xDDuy; 0x07uy; 0xA3uy; 0x67uy; 0x4Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l", "let test16_plaintext : lbytes 512 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8Auy; 0x8Buy; 0x8Cuy; 0x8Duy; 0x8Euy; 0x8Fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9Auy; 0x9Buy; 0x9Cuy; 0x9Duy; 0x9Euy; 0x9Fuy;\n 0xA0uy; 0xA1uy; 0xA2uy; 0xA3uy; 0xA4uy; 0xA5uy; 0xA6uy; 0xA7uy;\n 0xA8uy; 0xA9uy; 0xAAuy; 0xABuy; 0xACuy; 0xADuy; 0xAEuy; 0xAFuy;\n 0xB0uy; 0xB1uy; 0xB2uy; 0xB3uy; 0xB4uy; 0xB5uy; 0xB6uy; 0xB7uy;\n 0xB8uy; 0xB9uy; 0xBAuy; 0xBBuy; 0xBCuy; 0xBDuy; 0xBEuy; 0xBFuy;\n 0xC0uy; 0xC1uy; 0xC2uy; 0xC3uy; 0xC4uy; 0xC5uy; 0xC6uy; 0xC7uy;\n 0xC8uy; 0xC9uy; 0xCAuy; 0xCBuy; 0xCCuy; 0xCDuy; 0xCEuy; 0xCFuy;\n 0xD0uy; 0xD1uy; 0xD2uy; 0xD3uy; 0xD4uy; 0xD5uy; 0xD6uy; 0xD7uy;\n 0xD8uy; 0xD9uy; 0xDAuy; 0xDBuy; 0xDCuy; 0xDDuy; 0xDEuy; 0xDFuy;\n 0xE0uy; 0xE1uy; 0xE2uy; 0xE3uy; 0xE4uy; 0xE5uy; 0xE6uy; 0xE7uy;\n 0xE8uy; 0xE9uy; 0xEAuy; 0xEBuy; 0xECuy; 0xEDuy; 0xEEuy; 0xEFuy;\n 0xF0uy; 0xF1uy; 0xF2uy; 0xF3uy; 0xF4uy; 0xF5uy; 0xF6uy; 0xF7uy;\n 0xF8uy; 0xF9uy; 0xFAuy; 0xFBuy; 0xFCuy; 0xFDuy; 0xFEuy; 0xFFuy;\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8Auy; 0x8Buy; 0x8Cuy; 0x8Duy; 0x8Euy; 0x8Fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9Auy; 0x9Buy; 0x9Cuy; 0x9Duy; 0x9Euy; 0x9Fuy;\n 0xA0uy; 0xA1uy; 0xA2uy; 0xA3uy; 0xA4uy; 0xA5uy; 0xA6uy; 0xA7uy;\n 0xA8uy; 0xA9uy; 0xAAuy; 0xABuy; 0xACuy; 0xADuy; 0xAEuy; 0xAFuy;\n 0xB0uy; 0xB1uy; 0xB2uy; 0xB3uy; 0xB4uy; 0xB5uy; 0xB6uy; 0xB7uy;\n 0xB8uy; 0xB9uy; 0xBAuy; 0xBBuy; 0xBCuy; 0xBDuy; 0xBEuy; 0xBFuy;\n 0xC0uy; 0xC1uy; 0xC2uy; 0xC3uy; 0xC4uy; 0xC5uy; 0xC6uy; 0xC7uy;\n 0xC8uy; 0xC9uy; 0xCAuy; 0xCBuy; 0xCCuy; 0xCDuy; 0xCEuy; 0xCFuy;\n 0xD0uy; 0xD1uy; 0xD2uy; 0xD3uy; 0xD4uy; 0xD5uy; 0xD6uy; 0xD7uy;\n 0xD8uy; 0xD9uy; 0xDAuy; 0xDBuy; 0xDCuy; 0xDDuy; 0xDEuy; 0xDFuy;\n 0xE0uy; 0xE1uy; 0xE2uy; 0xE3uy; 0xE4uy; 0xE5uy; 0xE6uy; 0xE7uy;\n 0xE8uy; 0xE9uy; 0xEAuy; 0xEBuy; 0xECuy; 0xEDuy; 0xEEuy; 0xEFuy;\n 0xF0uy; 0xF1uy; 0xF2uy; 0xF3uy; 0xF4uy; 0xF5uy; 0xF6uy; 0xF7uy;\n 0xF8uy; 0xF9uy; 0xFAuy; 0xFBuy; 0xFCuy; 0xFDuy; 0xFEuy; 0xFFuy ] in\n assert_norm (FStar.List.length l = 512);\n of_list l", "let test16_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l", "let test16_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x31uy; 0x95uy; 0x24uy; 0x78uy; 0xE1uy; 0xB6uy; 0x22uy; 0x9Buy;\n 0x6Buy; 0xCAuy; 0x29uy; 0x6Cuy; 0x64uy; 0x3Auy; 0x3Fuy; 0xDBuy;\n 0xE4uy; 0xAAuy; 0x2Cuy; 0x2Fuy; 0x7Fuy; 0xEAuy; 0x46uy; 0x66uy;\n 0x75uy; 0x45uy; 0x3Duy; 0x5Fuy; 0x7Fuy; 0x09uy; 0x42uy; 0x70uy;\n 0x21uy; 0xA7uy; 0x7Buy; 0x86uy; 0x25uy; 0xC7uy; 0x80uy; 0x70uy;\n 0xC0uy; 0xF7uy; 0xCEuy; 0x56uy; 0x4Duy; 0x8Duy; 0x25uy; 0x7Duy;\n 0x7Euy; 0xB3uy; 0x64uy; 0x95uy; 0xBEuy; 0x76uy; 0x95uy; 0x0Cuy;\n 0x31uy; 0xA1uy; 0xA7uy; 0xD8uy; 0x0Fuy; 0xF8uy; 0xB1uy; 0xB4uy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l", "let test17_params : S.blake2s_params =\n { S.blake2s_default_params with fanout = u8 5; node_depth = u8 3 }", "let test17_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xA7uy; 0x4Euy; 0xDBuy; 0x2Duy; 0x8Fuy; 0xBBuy; 0x84uy; 0xFBuy;\n 0x83uy; 0xEDuy; 0x64uy; 0x06uy; 0x82uy; 0x28uy; 0x7Cuy; 0x92uy;\n 0x6Auy; 0xF5uy; 0xC3uy; 0x04uy; 0x09uy; 0xD1uy; 0xA8uy; 0xD4uy;\n 0x66uy; 0x2Duy; 0x4Fuy; 0x34uy; 0xEBuy; 0xC4uy; 0xA0uy; 0x7Fuy\n ] in\n assert_norm (List.Tot.length l = 32);\n of_list l", "let test18_params : S.blake2s_params =\n { S.blake2s_default_params with leaf_length = u32 43; depth = u8 4; inner_length = u8 9 }", "let test18_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x68uy; 0x1Auy; 0xDCuy; 0x05uy; 0x69uy; 0xD8uy; 0xE9uy; 0x1Buy;\n 0x36uy; 0xDFuy; 0x5Fuy; 0x1Duy; 0x85uy; 0x64uy; 0x42uy; 0x2Fuy;\n 0x4Duy; 0x79uy; 0xD7uy; 0x31uy; 0xCBuy; 0x7Duy; 0xBCuy; 0xB7uy;\n 0xC8uy; 0xEBuy; 0xB4uy; 0x80uy; 0xA6uy; 0xCEuy; 0x3Buy; 0x91uy\n ] in\n assert_norm (List.Tot.length l = 32);\n of_list l", "let test19_params : S.blake2s_params =\n let s = create 8 (u8_from_UInt8 0x11uy) in\n { S.blake2s_default_params with salt = s; personal = s }", "let test19_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xD3uy; 0x93uy; 0xA6uy; 0xDEuy; 0xB6uy; 0xE3uy; 0x98uy; 0xB3uy;\n 0x46uy; 0x11uy; 0xF0uy; 0x82uy; 0xCBuy; 0x2Fuy; 0xC0uy; 0x2Buy;\n 0x5Cuy; 0xE1uy; 0x3Buy; 0xF7uy; 0x0Cuy; 0x64uy; 0x70uy; 0xD2uy;\n 0x64uy; 0x1Fuy; 0x3Auy; 0xD1uy; 0x48uy; 0x93uy; 0xF5uy; 0x8Buy\n ] in\n assert_norm (List.Tot.length l = 32);\n of_list l" ], "closest": [ "val blake2s_default_params:blake2s_params\nlet blake2s_default_params: blake2s_params =\n { digest_length = u8 32;\n key_length = u8 0;\n fanout = u8 1;\n depth = u8 1;\n leaf_length = u32 0;\n node_offset = u32 0;\n xof_length = u16 0;\n node_depth = u8 0;\n inner_length = u8 0;\n salt = create 8 (u8 0);\n personal = create 8 (u8 0);\n }", "val blake2b_default_params:blake2b_params\nlet blake2b_default_params: blake2b_params =\n { digest_length = u8 64;\n key_length = u8 0;\n fanout = u8 1;\n depth = u8 1;\n leaf_length = u32 0;\n node_offset = u32 0;\n xof_length = u32 0;\n node_depth = u8 0;\n inner_length = u8 0;\n salt = create 16 (u8 0);\n personal = create 16 (u8 0);\n }", "val digest_blake2s:digest_st Blake2S\nlet digest_blake2s: digest_st Blake2S = F.digest evercrypt_hash Blake2S (EverCrypt.Hash.state Blake2S) (G.erased unit)", "val digest_blake2b:digest_st Blake2B\nlet digest_blake2b: digest_st Blake2B = F.digest evercrypt_hash Blake2B (EverCrypt.Hash.state Blake2B) (G.erased unit)", "val expand_blake2s: expand_st Blake2S\nlet expand_blake2s =\n mk_expand Blake2S EverCrypt.HMAC.compute_blake2s", "val test2_plaintext_block:lbytes 16\nlet test2_plaintext_block : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test2_key_block:lbytes 16\nlet test2_key_block : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xffuy; 0xffuy; 0xffuy; 0xffuy; 0xffuy; 0xf0uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val serialize_blake2s_params (p: blake2s_params) : lseq uint32 8\nlet serialize_blake2s_params (p: blake2s_params) : lseq uint32 8 =\n let s0 = (u32 (v p.digest_length)) ^.\n (u32 (v p.key_length) <<. (size 8)) ^.\n (u32 (v p.fanout) <<. (size 16)) ^.\n (u32 (v p.depth) <<. (size 24)) in\n let s1 = p.leaf_length in\n let s2 = p.node_offset in\n let s3 = (u32 (v p.xof_length)) ^.\n (u32 (v p.node_depth) <<. (size 16)) ^.\n (u32 (v p.inner_length) <<. (size 24)) in\n let salt_u32: lseq uint32 2 = uints_from_bytes_le p.salt in\n let s4 = salt_u32.[0] in\n let s5 = salt_u32.[1] in\n let personal_u32: lseq uint32 2 = uints_from_bytes_le p.personal in\n let s6 = personal_u32.[0] in\n let s7 = personal_u32.[1] in\n [@inline_let]\n let l = [s0; s1; s2; s3; s4; s5; s6; s7] in\n assert_norm (List.Tot.length l == 8);\n createL l", "val test2_salt:lbytes 80\nlet test2_salt : lbytes 80 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6auy; 0x6buy; 0x6cuy; 0x6duy; 0x6euy; 0x6fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7auy; 0x7buy; 0x7cuy; 0x7duy; 0x7euy; 0x7fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8auy; 0x8buy; 0x8cuy; 0x8duy; 0x8euy; 0x8fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9auy; 0x9buy; 0x9cuy; 0x9duy; 0x9euy; 0x9fuy;\n 0xa0uy; 0xa1uy; 0xa2uy; 0xa3uy; 0xa4uy; 0xa5uy; 0xa6uy; 0xa7uy;\n 0xa8uy; 0xa9uy; 0xaauy; 0xabuy; 0xacuy; 0xaduy; 0xaeuy; 0xafuy\n ] in\n assert_norm (List.Tot.length l == 80);\n of_list l", "val test2_input_plaintext:lbytes 16\nlet test2_input_plaintext : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x11uy; 0x22uy; 0x33uy; 0x44uy; 0x55uy; 0x66uy; 0x77uy;\n 0x88uy; 0x99uy; 0xaauy; 0xbbuy; 0xccuy; 0xdduy; 0xeeuy; 0xffuy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val compute_blake2s: compute_st Blake2S\nlet compute_blake2s =\n let open Hacl.Hash.Blake2s_32 in\n mk_compute (|Blake2S, Hacl.Impl.Blake2.Core.M32|) hash alloca init update_multi\n update_last finish", "val test2_ciphertext_block:lbytes 16\nlet test2_ciphertext_block : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xe6uy; 0xc4uy; 0x80uy; 0x7auy; 0xe1uy; 0x1fuy; 0x36uy; 0xf0uy;\n 0x91uy; 0xc5uy; 0x7duy; 0x9fuy; 0xb6uy; 0x85uy; 0x48uy; 0xd1uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val expand_blake2b: expand_st Blake2B\nlet expand_blake2b =\n mk_expand Blake2B EverCrypt.HMAC.compute_blake2b", "val extract_blake2s: extract_st Blake2S\nlet extract_blake2s =\n mk_extract Blake2S EverCrypt.HMAC.compute_blake2s", "val test2_expected_sha3_256:lbytes 32\nlet test2_expected_sha3_256 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x3auy; 0x98uy; 0x5duy; 0xa7uy; 0x4fuy; 0xe2uy; 0x25uy; 0xb2uy;\n 0x04uy; 0x5cuy; 0x17uy; 0x2duy; 0x6buy; 0xd3uy; 0x90uy; 0xbduy;\n 0x85uy; 0x5fuy; 0x08uy; 0x6euy; 0x3euy; 0x9duy; 0x52uy; 0x5buy;\n 0x46uy; 0xbfuy; 0xe2uy; 0x45uy; 0x11uy; 0x43uy; 0x15uy; 0x32uy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val expand_blake2s_128:expand_st Blake2S\nlet expand_blake2s_128: expand_st Blake2S =\n mk_expand Blake2S Hacl.HMAC.Blake2s_128.compute_blake2s_128", "val test2_sk:lbytes 32\nlet test2_sk : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x4cuy; 0xcduy; 0x08uy; 0x9buy; 0x28uy; 0xffuy; 0x96uy; 0xdauy;\n 0x9duy; 0xb6uy; 0xc3uy; 0x46uy; 0xecuy; 0x11uy; 0x4euy; 0x0fuy;\n 0x5buy; 0x8auy; 0x31uy; 0x9fuy; 0x35uy; 0xabuy; 0xa6uy; 0x24uy;\n 0xdauy; 0x8cuy; 0xf6uy; 0xeduy; 0x4fuy; 0xb8uy; 0xa6uy; 0xfbuy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test2_sk:lbytes 32\nlet test2_sk : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;\n 0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;\n 0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;\n 0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test1_key:lbytes 20\nlet test1_key : lbytes 20 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x0buy; 0x0buy; 0x0buy; 0x0buy; 0x0buy; 0x0buy; 0x0buy; 0x0buy;\n 0x0buy; 0x0buy; 0x0buy; 0x0buy; 0x0buy; 0x0buy; 0x0buy; 0x0buy;\n 0x0buy; 0x0buy; 0x0buy; 0x0buy\n ] in\n assert_norm (List.Tot.length l == 20);\n of_list l", "val test2_expected_sha3_224:lbytes 28\nlet test2_expected_sha3_224 : lbytes 28 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xe6uy; 0x42uy; 0x82uy; 0x4cuy; 0x3fuy; 0x8cuy; 0xf2uy; 0x4auy;\n 0xd0uy; 0x92uy; 0x34uy; 0xeeuy; 0x7duy; 0x3cuy; 0x76uy; 0x6fuy;\n 0xc9uy; 0xa3uy; 0xa5uy; 0x16uy; 0x8duy; 0x0cuy; 0x94uy; 0xaduy;\n 0x73uy; 0xb4uy; 0x6fuy; 0xdfuy\n ] in\n assert_norm (List.Tot.length l == 28);\n of_list l", "val expand_blake2b_256:expand_st Blake2B\nlet expand_blake2b_256: expand_st Blake2B =\n mk_expand Blake2B Hacl.HMAC.Blake2b_256.compute_blake2b_256", "val test2_output_ciphertext:lbytes 16\nlet test2_output_ciphertext : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x8euy; 0xa2uy; 0xb7uy; 0xcauy; 0x51uy; 0x67uy; 0x45uy; 0xbfuy;\n 0xeauy; 0xfcuy; 0x49uy; 0x90uy; 0x4buy; 0x49uy; 0x60uy; 0x89uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val compute_blake2b: compute_st Blake2B\nlet compute_blake2b =\n let open Hacl.Hash.Blake2b_32 in\n mk_compute (|Blake2B, Hacl.Impl.Blake2.Core.M32|) hash alloca init update_multi\n update_last finish", "val extract_blake2b: extract_st Blake2B\nlet extract_blake2b =\n mk_extract Blake2B EverCrypt.HMAC.compute_blake2b", "val compute_blake2s_128:compute_st Blake2S\nlet compute_blake2s_128: compute_st Blake2S =\n mk_compute (D.mk_impl Blake2S Hacl.Impl.Blake2.Core.M128)\n hash alloca init update_multi update_last finish", "val compute_blake2s_32: compute_st Blake2S\nlet compute_blake2s_32: compute_st Blake2S =\n let open Hacl.Hash.Blake2s_32 in\n mk_compute (D.mk_impl Blake2S C.M32) hash alloca init update_multi update_last finish", "val expand_blake2s_32: expand_st Blake2S\nlet expand_blake2s_32: expand_st Blake2S =\n mk_expand Blake2S Hacl.HMAC.compute_blake2s_32", "val extract_blake2s_32: extract_st Blake2S\nlet extract_blake2s_32: extract_st Blake2S =\n mk_extract Blake2S Hacl.HMAC.compute_blake2s_32", "val hash: hash_st Blake2S\nlet hash output input input_len = Hacl.Streaming.Blake2s_128.hash_with_key output 32ul input input_len (null #MUT uint8) 0ul", "val hash: hash_st Blake2S\nlet hash output input input_len = Hacl.Streaming.Blake2s_32.hash_with_key output 32ul input input_len (null #MUT uint8) 0ul", "val compute_blake2b_256:compute_st Blake2B\nlet compute_blake2b_256: compute_st Blake2B =\n mk_compute (D.mk_impl Blake2B Hacl.Impl.Blake2.Core.M256)\n hash alloca init update_multi update_last finish", "val expand_blake2b_32: expand_st Blake2B\nlet expand_blake2b_32: expand_st Blake2B =\n mk_expand Blake2B Hacl.HMAC.compute_blake2b_32", "val extract_blake2b_32: extract_st Blake2B\nlet extract_blake2b_32: extract_st Blake2B =\n mk_extract Blake2B Hacl.HMAC.compute_blake2b_32", "val serialize_blake2b_params (p: blake2b_params) : lseq uint64 8\nlet serialize_blake2b_params (p: blake2b_params) : lseq uint64 8 =\n let s0 = (u64 (v p.digest_length)) ^.\n (u64 (v p.key_length) <<. (size 8)) ^.\n (u64 (v p.fanout) <<. (size 16)) ^.\n (u64 (v p.depth) <<. (size 24)) ^.\n (u64 (v p.leaf_length) <<. (size 32)) in\n let s1 = (u64 (v p.node_offset)) ^.\n (u64 (v p.xof_length) <<. (size 32)) in\n // The serialization corresponding to s2 contains node_depth and inner_length,\n // followed by the 14 reserved bytes which always seem to be zeros, and can hence\n // be ignored when building the corresponding uint64 using xor's\n let s2 = (u64 (v p.node_depth)) ^.\n (u64 (v p.inner_length) <<. (size 8)) in\n // s3 corresponds to the remaining of the reserved bytes\n let s3 = u64 0 in\n let salt_u64: lseq uint64 2 = uints_from_bytes_le p.salt in\n let s4 = salt_u64.[0] in\n let s5 = salt_u64.[1] in\n let personal_u64: lseq uint64 2 = uints_from_bytes_le p.personal in\n let s6 = personal_u64.[0] in\n let s7 = personal_u64.[1] in\n [@inline_let]\n let l = [s0; s1; s2; s3; s4; s5; s6; s7] in\n assert_norm (List.Tot.length l == 8);\n createL l", "val test_plaintext2:lbytes 32\nlet test_plaintext2 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val extract_blake2b_256:extract_st Blake2B\nlet extract_blake2b_256: extract_st Blake2B =\n mk_extract Blake2B Hacl.HMAC.Blake2b_256.compute_blake2b_256", "val test2_expected_sha3_384:lbytes 48\nlet test2_expected_sha3_384 : lbytes 48 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xecuy; 0x01uy; 0x49uy; 0x82uy; 0x88uy; 0x51uy; 0x6fuy; 0xc9uy;\n 0x26uy; 0x45uy; 0x9fuy; 0x58uy; 0xe2uy; 0xc6uy; 0xaduy; 0x8duy;\n 0xf9uy; 0xb4uy; 0x73uy; 0xcbuy; 0x0fuy; 0xc0uy; 0x8cuy; 0x25uy;\n 0x96uy; 0xdauy; 0x7cuy; 0xf0uy; 0xe4uy; 0x9buy; 0xe4uy; 0xb2uy;\n 0x98uy; 0xd8uy; 0x8cuy; 0xeauy; 0x92uy; 0x7auy; 0xc7uy; 0xf5uy;\n 0x39uy; 0xf1uy; 0xeduy; 0xf2uy; 0x28uy; 0x37uy; 0x6duy; 0x25uy\n ] in\n assert_norm (List.Tot.length l == 48);\n of_list l", "val test5_key:lbytes 20\nlet test5_key : lbytes 20 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x0cuy; 0x0cuy; 0x0cuy; 0x0cuy; 0x0cuy; 0x0cuy; 0x0cuy; 0x0cuy;\n 0x0cuy; 0x0cuy; 0x0cuy; 0x0cuy; 0x0cuy; 0x0cuy; 0x0cuy; 0x0cuy;\n 0x0cuy; 0x0cuy; 0x0cuy; 0x0cuy\n ] in\n assert_norm (List.Tot.length l == 20);\n of_list l", "val test2_input_key:lbytes 32\nlet test2_input_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val compute_blake2b_32: compute_st Blake2B\nlet compute_blake2b_32: compute_st Blake2B =\n let open Hacl.Hash.Blake2b_32 in\n mk_compute (D.mk_impl Blake2B C.M32) hash alloca init update_multi update_last finish", "val extract_blake2s_128:extract_st Blake2S\nlet extract_blake2s_128: extract_st Blake2S =\n mk_extract Blake2S Hacl.HMAC.Blake2s_128.compute_blake2s_128", "val test3_key:lbytes 20\nlet test3_key : lbytes 20 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xaauy; 0xaauy; 0xaauy; 0xaauy; 0xaauy; 0xaauy; 0xaauy; 0xaauy;\n 0xaauy; 0xaauy; 0xaauy; 0xaauy; 0xaauy; 0xaauy; 0xaauy; 0xaauy;\n 0xaauy; 0xaauy; 0xaauy; 0xaauy\n ] in\n assert_norm (List.Tot.length l == 20);\n of_list l", "val test2_expected_sha3_512:lbytes 64\nlet test2_expected_sha3_512 : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xb7uy; 0x51uy; 0x85uy; 0x0buy; 0x1auy; 0x57uy; 0x16uy; 0x8auy;\n 0x56uy; 0x93uy; 0xcduy; 0x92uy; 0x4buy; 0x6buy; 0x09uy; 0x6euy;\n 0x08uy; 0xf6uy; 0x21uy; 0x82uy; 0x74uy; 0x44uy; 0xf7uy; 0x0duy;\n 0x88uy; 0x4fuy; 0x5duy; 0x02uy; 0x40uy; 0xd2uy; 0x71uy; 0x2euy;\n 0x10uy; 0xe1uy; 0x16uy; 0xe9uy; 0x19uy; 0x2auy; 0xf3uy; 0xc9uy;\n 0x1auy; 0x7euy; 0xc5uy; 0x76uy; 0x47uy; 0xe3uy; 0x93uy; 0x40uy;\n 0x57uy; 0x34uy; 0x0buy; 0x4cuy; 0xf4uy; 0x08uy; 0xd5uy; 0xa5uy;\n 0x65uy; 0x92uy; 0xf8uy; 0x27uy; 0x4euy; 0xecuy; 0x53uy; 0xf0uy\n ] in\n assert_norm (List.Tot.length l == 64);\n of_list l", "val test2_nonce:lbytes 32\nlet test2_nonce : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x49uy; 0xa0uy; 0xd7uy; 0xb7uy; 0x86uy; 0xecuy; 0x9cuy; 0xdeuy;\n 0x0duy; 0x07uy; 0x21uy; 0xd7uy; 0x28uy; 0x04uy; 0xbeuy; 0xfduy;\n 0x06uy; 0x57uy; 0x1cuy; 0x97uy; 0x4buy; 0x19uy; 0x1euy; 0xfbuy;\n 0x42uy; 0xecuy; 0xf3uy; 0x22uy; 0xbauy; 0x9duy; 0xdduy; 0x9auy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test11_plaintext_shake256:lbytes 32\nlet test11_plaintext_shake256 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xefuy; 0x89uy; 0x6cuy; 0xdcuy; 0xb3uy; 0x63uy; 0xa6uy; 0x15uy;\n 0x91uy; 0x78uy; 0xa1uy; 0xbbuy; 0x1cuy; 0x99uy; 0x39uy; 0x46uy;\n 0xc5uy; 0x04uy; 0x02uy; 0x09uy; 0x5cuy; 0xdauy; 0xeauy; 0x4fuy;\n 0xd4uy; 0xd4uy; 0x19uy; 0xaauy; 0x47uy; 0x32uy; 0x1cuy; 0x88uy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test5_data:lbytes 20\nlet test5_data : lbytes 20 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x54uy; 0x65uy; 0x73uy; 0x74uy; 0x20uy; 0x57uy; 0x69uy; 0x74uy;\n 0x68uy; 0x20uy; 0x54uy; 0x72uy; 0x75uy; 0x6euy; 0x63uy; 0x61uy;\n 0x74uy; 0x69uy; 0x6fuy; 0x6euy\n ] in\n assert_norm (List.Tot.length l == 20);\n of_list l", "val test10_plaintext_shake256:lbytes 17\nlet test10_plaintext_shake256 : lbytes 17 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xf9uy; 0xdauy; 0x78uy; 0xc8uy; 0x90uy; 0x84uy; 0x70uy; 0x40uy;\n 0x45uy; 0x4buy; 0xa6uy; 0x42uy; 0x98uy; 0x82uy; 0xb0uy; 0x54uy;\n 0x09uy\n ] in\n assert_norm (List.Tot.length l == 17);\n of_list l", "val test1_plaintext_block:lbytes 16\nlet test1_plaintext_block : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test_ciphertext2:lbytes 32\nlet test_ciphertext2 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x51uy; 0x04uy; 0xA1uy; 0x06uy; 0x16uy; 0x8Auy; 0x72uy; 0xD9uy;\n 0x79uy; 0x0Duy; 0x41uy; 0xEEuy; 0x8Euy; 0xDAuy; 0xD3uy; 0x88uy;\n 0xEBuy; 0x2Euy; 0x1Euy; 0xFCuy; 0x46uy; 0xDAuy; 0x57uy; 0xC8uy;\n 0xFCuy; 0xE6uy; 0x30uy; 0xDFuy; 0x91uy; 0x41uy; 0xBEuy; 0x28uy ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test3_input_plaintext:lbytes 16\nlet test3_input_plaintext : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test1_sk:lbytes 32\nlet test1_sk : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x9duy; 0x61uy; 0xb1uy; 0x9duy; 0xefuy; 0xfduy; 0x5auy; 0x60uy;\n 0xbauy; 0x84uy; 0x4auy; 0xf4uy; 0x92uy; 0xecuy; 0x2cuy; 0xc4uy;\n 0x44uy; 0x49uy; 0xc5uy; 0x69uy; 0x7buy; 0x32uy; 0x69uy; 0x19uy;\n 0x70uy; 0x3buy; 0xacuy; 0x03uy; 0x1cuy; 0xaeuy; 0x7fuy; 0x60uy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test2_data:lbytes 28\nlet test2_data : lbytes 28 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x77uy; 0x68uy; 0x61uy; 0x74uy; 0x20uy; 0x64uy; 0x6fuy; 0x20uy;\n 0x79uy; 0x61uy; 0x20uy; 0x77uy; 0x61uy; 0x6euy; 0x74uy; 0x20uy;\n 0x66uy; 0x6fuy; 0x72uy; 0x20uy; 0x6euy; 0x6fuy; 0x74uy; 0x68uy;\n 0x69uy; 0x6euy; 0x67uy; 0x3fuy\n ] in\n assert_norm (List.Tot.length l == 28);\n of_list l", "val blake2_default_params (a: alg) : blake2_params a\nlet blake2_default_params (a: alg) : blake2_params a =\n match a with\n | Blake2S -> blake2s_default_params\n | Blake2B -> blake2b_default_params", "val test2_expected256:lbytes 32\nlet test2_expected256 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x5buy; 0xdcuy; 0xc1uy; 0x46uy; 0xbfuy; 0x60uy; 0x75uy; 0x4euy;\n 0x6auy; 0x04uy; 0x24uy; 0x26uy; 0x08uy; 0x95uy; 0x75uy; 0xc7uy;\n 0x5auy; 0x00uy; 0x3fuy; 0x08uy; 0x9duy; 0x27uy; 0x39uy; 0x83uy;\n 0x9duy; 0xecuy; 0x58uy; 0xb9uy; 0x64uy; 0xecuy; 0x38uy; 0x43uy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test1_expected_sha3_256:lbytes 32\nlet test1_expected_sha3_256 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xa7uy; 0xffuy; 0xc6uy; 0xf8uy; 0xbfuy; 0x1euy; 0xd7uy; 0x66uy;\n 0x51uy; 0xc1uy; 0x47uy; 0x56uy; 0xa0uy; 0x61uy; 0xd6uy; 0x62uy;\n 0xf5uy; 0x80uy; 0xffuy; 0x4duy; 0xe4uy; 0x3buy; 0x49uy; 0xfauy;\n 0x82uy; 0xd8uy; 0x0auy; 0x4buy; 0x80uy; 0xf8uy; 0x43uy; 0x4auy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test1_expected_sha3_224:lbytes 28\nlet test1_expected_sha3_224 : lbytes 28 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x6buy; 0x4euy; 0x03uy; 0x42uy; 0x36uy; 0x67uy; 0xdbuy; 0xb7uy;\n 0x3buy; 0x6euy; 0x15uy; 0x45uy; 0x4fuy; 0x0euy; 0xb1uy; 0xabuy;\n 0xd4uy; 0x59uy; 0x7fuy; 0x9auy; 0x1buy; 0x07uy; 0x8euy; 0x3fuy;\n 0x5buy; 0x5auy; 0x6buy; 0xc7uy\n ] in\n assert_norm (List.Tot.length l == 28);\n of_list l", "val init:Impl.blake2_init_st Spec.Blake2S Core.M32\nlet init : Impl.blake2_init_st Spec.Blake2S Core.M32 =\n Impl.blake2_init #Spec.Blake2S #Core.M32", "val test3_expected_sha3_224:lbytes 28\nlet test3_expected_sha3_224 : lbytes 28 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x8auy; 0x24uy; 0x10uy; 0x8buy; 0x15uy; 0x4auy; 0xdauy; 0x21uy;\n 0xc9uy; 0xfduy; 0x55uy; 0x74uy; 0x49uy; 0x44uy; 0x79uy; 0xbauy;\n 0x5cuy; 0x7euy; 0x7auy; 0xb7uy; 0x6euy; 0xf2uy; 0x64uy; 0xeauy;\n 0xd0uy; 0xfcuy; 0xceuy; 0x33uy\n ] in\n assert_norm (List.Tot.length l == 28);\n of_list l", "val test1_key_block:lbytes 16\nlet test1_key_block : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x80uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test2_key:lbytes 4\nlet test2_key : lbytes 4 =\n let l = List.Tot.map u8_from_UInt8 [ 0x4auy; 0x65uy; 0x66uy; 0x65uy ] in\n assert_norm (List.Tot.length l == 4);\n of_list l", "val test3_ciphertext_block:lbytes 16\nlet test3_ciphertext_block : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xb8uy; 0x3buy; 0x53uy; 0x37uy; 0x08uy; 0xbfuy; 0x53uy; 0x5duy;\n 0x0auy; 0xa6uy; 0xe5uy; 0x29uy; 0x80uy; 0xd5uy; 0x3buy; 0x78uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test3_key_block:lbytes 16\nlet test3_key_block : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xfeuy; 0xffuy; 0xe9uy; 0x92uy; 0x86uy; 0x65uy; 0x73uy; 0x1cuy;\n 0x6duy; 0x6auy; 0x8fuy; 0x94uy; 0x67uy; 0x30uy; 0x83uy; 0x08uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test2_msgHash:lbytes 32\nlet test2_msgHash : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x4buy; 0x68uy; 0x8duy; 0xf4uy; 0x0buy; 0xceuy; 0xdbuy; 0xe6uy;\n 0x41uy; 0xdduy; 0xb1uy; 0x6fuy; 0xf0uy; 0xa1uy; 0x84uy; 0x2duy;\n 0x9cuy; 0x67uy; 0xeauy; 0x1cuy; 0x3buy; 0xf6uy; 0x3fuy; 0x3euy;\n 0x04uy; 0x71uy; 0xbauy; 0xa6uy; 0x64uy; 0x53uy; 0x1duy; 0x1auy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test2_plaintext:lbytes 3\nlet test2_plaintext : lbytes 3 =\n let l = List.Tot.map u8_from_UInt8 [ 0x61uy; 0x62uy; 0x63uy ] in\n assert_norm (List.Tot.length l == 3);\n of_list l", "val test4_expected_sha3_224:lbytes 28\nlet test4_expected_sha3_224 : lbytes 28 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x54uy; 0x3euy; 0x68uy; 0x68uy; 0xe1uy; 0x66uy; 0x6cuy; 0x1auy;\n 0x64uy; 0x36uy; 0x30uy; 0xdfuy; 0x77uy; 0x36uy; 0x7auy; 0xe5uy;\n 0xa6uy; 0x2auy; 0x85uy; 0x07uy; 0x0auy; 0x51uy; 0xc1uy; 0x4cuy;\n 0xbfuy; 0x66uy; 0x5cuy; 0xbcuy\n ] in\n assert_norm (List.Tot.length l == 28);\n of_list l", "val test_ciphertext:lbytes 16\nlet test_ciphertext : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x87uy; 0x4duy; 0x61uy; 0x91uy; 0xb6uy; 0x20uy; 0xe3uy; 0x26uy;\n 0x1buy; 0xefuy; 0x68uy; 0x64uy; 0x99uy; 0x0duy; 0xb6uy; 0xceuy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test4_input_plaintext:lbytes 16\nlet test4_input_plaintext : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test1_ciphertext_block:lbytes 16\nlet test1_ciphertext_block : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x0euy; 0xdduy; 0x33uy; 0xd3uy; 0xc6uy; 0x21uy; 0xe5uy; 0x46uy;\n 0x45uy; 0x5buy; 0xd8uy; 0xbauy; 0x14uy; 0x18uy; 0xbeuy; 0xc8uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val serialize_params_blake2b\n (kk: size_t{v kk <= Spec.max_key Spec.Blake2B})\n (nn: size_t{1 <= v nn /\\ v nn <= Spec.max_output Spec.Blake2B})\n (p: blake2_params Spec.Blake2B)\n (b: lbuffer (word_t Spec.Blake2B) 8ul)\n : Stack unit\n (requires\n fun h ->\n live h b /\\ blake2_params_inv #Spec.Blake2B h p /\\\n LowStar.Buffer.loc_disjoint (loc b) (blake2_params_loc p) /\\\n as_seq h b == Seq.create 8 (u64 0))\n (ensures\n fun h0 _ h1 ->\n modifies (loc b) h0 h1 /\\\n as_seq h1 b ==\n Spec.serialize_blake2_params (Spec.set_key_length (Spec.set_digest_length (blake2_params_v\n h0\n p)\n (v nn))\n (v kk)))\nlet serialize_params_blake2b\n (kk:size_t{v kk <= Spec.max_key Spec.Blake2B})\n (nn: size_t{1 <= v nn /\\ v nn <= Spec.max_output Spec.Blake2B})\n (p: blake2_params Spec.Blake2B)\n (b: lbuffer (word_t Spec.Blake2B) 8ul)\n : Stack unit\n (requires fun h -> live h b /\\\n blake2_params_inv #Spec.Blake2B h p /\\\n LowStar.Buffer.loc_disjoint (loc b) (blake2_params_loc p) /\\\n as_seq h b == Seq.create 8 (u64 0)\n )\n (ensures fun h0 _ h1 ->\n modifies (loc b) h0 h1 /\\\n as_seq h1 b == Spec.serialize_blake2_params\n (Spec.set_key_length (Spec.set_digest_length (blake2_params_v h0 p) (v nn)) (v kk)))\n = let h0 = ST.get () in\n [@inline_let]\n let kk_shift_8 = shift_left (to_u64 kk) (size 8) in\n [@inline_let]\n let fanout_shift_16 = shift_left (to_u64 p.fanout) (size 16) in\n [@inline_let]\n let depth_shift_24 = shift_left (to_u64 p.depth) (size 24) in\n [@inline_let]\n let leaf_length_shift_32 = shift_left (to_u64 p.leaf_length) (size 32) in\n [@inline_let]\n let v0 = (to_u64 nn) ^. kk_shift_8 ^. fanout_shift_16 ^. depth_shift_24 ^. leaf_length_shift_32 in\n [@inline_let]\n let xof_length_shift_32 = shift_left (to_u64 p.xof_length) (size 32) in\n [@inline_let]\n let v1 = (to_u64 p.node_offset) ^. xof_length_shift_32 in\n [@inline_let]\n let inner_length_shift_8 = shift_left (to_u64 p.inner_length) (size 8) in\n [@inline_let]\n let v2 = (to_u64 p.node_depth) ^. inner_length_shift_8 in\n\n uints_from_bytes_le (sub b 4ul 2ul) p.salt;\n uints_from_bytes_le (sub b 6ul 2ul) p.personal;\n\n b.(0ul) <- v0;\n b.(1ul) <- v1;\n b.(2ul) <- v2;\n b.(3ul) <- (u64 0);\n\n let h1 = ST.get () in\n let aux () : Lemma (as_seq h1 b `Seq.equal` Spec.serialize_blake2b_params\n (Spec.set_key_length (Spec.set_digest_length (blake2_params_v h0 p) (v nn)) (v kk))) =\n let open Lib.Sequence in\n let open Lib.ByteSequence in\n let s0 = (u64 (v nn)) ^.\n (u64 (v kk) <<. (size 8)) ^.\n (u64 (v p.fanout) <<. (size 16)) ^.\n (u64 (v p.depth) <<. (size 24)) ^.\n (u64 (v p.leaf_length) <<. (size 32)) in\n let s1 = (u64 (v p.node_offset)) ^.\n (u64 (v p.xof_length) <<. (size 32)) in\n // The serialization corresponding to s2 contains node_depth and inner_length,\n // followed by the 14 reserved bytes which always seem to be zeros, and can hence\n // be ignored when building the corresponding uint64 using xor's\n let s2 = (u64 (v p.node_depth)) ^.\n (u64 (v p.inner_length) <<. (size 8)) in\n // s3 corresponds to the remaining of the reserved bytes\n let s3 = u64 0 in\n let salt_u64: lseq uint64 2 = uints_from_bytes_le (as_seq h0 (get_salt p)) in\n let s4 = salt_u64.[0] in\n let s5 = salt_u64.[1] in\n let personal_u64: lseq uint64 2 = uints_from_bytes_le (as_seq h0 (get_personal p)) in\n let s6 = personal_u64.[0] in\n let s7 = personal_u64.[1] in\n [@inline_let]\n let l = [s0; s1; s2; s3; s4; s5; s6; s7] in\n assert_norm (List.Tot.length l == 8);\n\n // There seems to be something not triggering with createL, requiring the\n // following lemma calls, and assert_norms to relate List.index to the\n // actual elements\n\n assert_norm (List.Tot.index l 0 == s0);\n assert_norm (List.Tot.index l 1 == s1);\n assert_norm (List.Tot.index l 2 == s2);\n assert_norm (List.Tot.index l 3 == s3);\n assert_norm (List.Tot.index l 4 == s4);\n assert_norm (List.Tot.index l 5 == s5);\n assert_norm (List.Tot.index l 6 == s6);\n assert_norm (List.Tot.index l 7 == s7);\n of_list_index l 0;\n of_list_index l 1;\n of_list_index l 2;\n of_list_index l 3;\n of_list_index l 4;\n of_list_index l 5;\n of_list_index l 6;\n of_list_index l 7\n in\n aux()", "val test6_plaintext_shake128:lbytes 14\nlet test6_plaintext_shake128 : lbytes 14 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x52uy; 0x97uy; 0x7euy; 0x53uy; 0x2buy; 0xccuy; 0xdbuy; 0x89uy;\n 0xdfuy; 0xefuy; 0xf7uy; 0xe9uy; 0xe4uy; 0xaduy\n ] in\n assert_norm (List.Tot.length l == 14);\n of_list l", "val serialize_params_blake2s\n (kk: size_t{v kk <= Spec.max_key Spec.Blake2S})\n (nn: size_t{1 <= v nn /\\ v nn <= Spec.max_output Spec.Blake2S})\n (p: blake2_params Spec.Blake2S)\n (b: lbuffer (word_t Spec.Blake2S) 8ul)\n : Stack unit\n (requires\n fun h ->\n live h b /\\ blake2_params_inv h p /\\\n LowStar.Buffer.loc_disjoint (loc b) (blake2_params_loc p) /\\\n as_seq h b == Seq.create 8 (u32 0))\n (ensures\n fun h0 _ h1 ->\n modifies (loc b) h0 h1 /\\\n as_seq h1 b ==\n Spec.serialize_blake2_params (Spec.set_key_length (Spec.set_digest_length (blake2_params_v\n h0\n p)\n (v nn))\n (v kk)))\nlet serialize_params_blake2s\n (kk:size_t{v kk <= Spec.max_key Spec.Blake2S})\n (nn: size_t{1 <= v nn /\\ v nn <= Spec.max_output Spec.Blake2S})\n (p: blake2_params Spec.Blake2S)\n (b: lbuffer (word_t Spec.Blake2S) 8ul)\n : Stack unit\n (requires fun h -> live h b /\\\n blake2_params_inv h p /\\\n LowStar.Buffer.loc_disjoint (loc b) (blake2_params_loc p) /\\\n as_seq h b == Seq.create 8 (u32 0)\n )\n (ensures fun h0 _ h1 ->\n modifies (loc b) h0 h1 /\\\n as_seq h1 b == Spec.serialize_blake2_params\n (Spec.set_key_length (Spec.set_digest_length (blake2_params_v h0 p) (v nn)) (v kk)))\n = let h0 = ST.get () in\n [@inline_let]\n let kk_shift_8 = shift_left (to_u32 kk) (size 8) in\n [@inline_let]\n let fanout_shift_16 = shift_left (to_u32 p.fanout) (size 16) in\n [@inline_let]\n let depth_shift_24 = shift_left (to_u32 p.depth) (size 24) in\n [@inline_let]\n let v0 = (to_u32 nn) ^. kk_shift_8 ^. fanout_shift_16 ^. depth_shift_24 in\n [@inline_let]\n let v1 = p.leaf_length in\n [@inline_let]\n let v2 = p.node_offset in\n [@inline_let]\n let node_depth_shift_16 = shift_left (to_u32 p.node_depth) (size 16) in\n [@inline_let]\n let inner_length_shift_16 = shift_left (to_u32 p.inner_length) (size 24) in\n [@inline_let]\n let v3 = (to_u32 p.xof_length) ^. node_depth_shift_16 ^. inner_length_shift_16 in\n\n uints_from_bytes_le (sub b 4ul 2ul) p.salt;\n uints_from_bytes_le (sub b 6ul 2ul) p.personal;\n\n // AF: Putting these writes *after* modifications on a subbuffer of b helps with modifies-reasoning:\n // By putting them before, F* struggles with proving that b[0..3] is not modified by uints_from_bytes_le\n b.(0ul) <- v0;\n b.(1ul) <- v1;\n b.(2ul) <- v2;\n b.(3ul) <- v3;\n\n let h1 = ST.get () in\n let aux () : Lemma (as_seq h1 b `Seq.equal` Spec.serialize_blake2s_params\n (Spec.set_key_length (Spec.set_digest_length (blake2_params_v h0 p) (v nn)) (v kk))) =\n let open Lib.Sequence in\n let open Lib.ByteSequence in\n let s0 = (u32 (v nn)) ^.\n (u32 (v kk) <<. (size 8)) ^.\n (u32 (v p.fanout) <<. (size 16)) ^.\n (u32 (v p.depth) <<. (size 24)) in\n let s1 = p.leaf_length in\n let s2 = p.node_offset in\n let s3 = (u32 (v p.xof_length)) ^.\n (u32 (v p.node_depth) <<. (size 16)) ^.\n (u32 (v p.inner_length) <<. (size 24)) in\n let salt_u32: lseq uint32 2 = uints_from_bytes_le (as_seq h0 (get_salt p)) in\n let s4 = salt_u32.[0] in\n let s5 = salt_u32.[1] in\n let personal_u32: lseq uint32 2 = uints_from_bytes_le (as_seq h0 (get_personal p)) in\n let s6 = personal_u32.[0] in\n let s7 = personal_u32.[1] in\n [@inline_let]\n let l = [s0; s1; s2; s3; s4; s5; s6; s7] in\n assert_norm (List.Tot.length l == 8);\n\n // There seems to be something not triggering with createL, requiring the\n // following lemma calls, and assert_norms to relate List.index to the\n // actual elements\n\n assert_norm (List.Tot.index l 0 == s0);\n assert_norm (List.Tot.index l 1 == s1);\n assert_norm (List.Tot.index l 2 == s2);\n assert_norm (List.Tot.index l 3 == s3);\n assert_norm (List.Tot.index l 4 == s4);\n assert_norm (List.Tot.index l 5 == s5);\n assert_norm (List.Tot.index l 6 == s6);\n assert_norm (List.Tot.index l 7 == s7);\n of_list_index l 0;\n of_list_index l 1;\n of_list_index l 2;\n of_list_index l 3;\n of_list_index l 4;\n of_list_index l 5;\n of_list_index l 6;\n of_list_index l 7\n in\n aux()", "val update_key:Impl.blake2_update_key_st Spec.Blake2S Core.M32\nlet update_key : Impl.blake2_update_key_st Spec.Blake2S Core.M32 =\n Impl.blake2_update_key #Spec.Blake2S #Core.M32 update_block", "val test4_expected_sha3_256:lbytes 32\nlet test4_expected_sha3_256 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x91uy; 0x6fuy; 0x60uy; 0x61uy; 0xfeuy; 0x87uy; 0x97uy; 0x41uy;\n 0xcauy; 0x64uy; 0x69uy; 0xb4uy; 0x39uy; 0x71uy; 0xdfuy; 0xdbuy;\n 0x28uy; 0xb1uy; 0xa3uy; 0x2duy; 0xc3uy; 0x6cuy; 0xb3uy; 0x25uy;\n 0x4euy; 0x81uy; 0x2buy; 0xe2uy; 0x7auy; 0xaduy; 0x1duy; 0x18uy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test9_plaintext_shake256:lbytes 0\nlet test9_plaintext_shake256 : lbytes 0 =\n let l = List.Tot.map u8_from_UInt8 [] in\n assert_norm (List.Tot.length l == 0);\n of_list l", "val test3_sk:lbytes 32\nlet test3_sk : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xc5uy; 0xaauy; 0x8duy; 0xf4uy; 0x3fuy; 0x9fuy; 0x83uy; 0x7buy;\n 0xeduy; 0xb7uy; 0x44uy; 0x2fuy; 0x31uy; 0xdcuy; 0xb7uy; 0xb1uy;\n 0x66uy; 0xd3uy; 0x85uy; 0x35uy; 0x07uy; 0x6fuy; 0x09uy; 0x4buy;\n 0x85uy; 0xceuy; 0x3auy; 0x2euy; 0x0buy; 0x44uy; 0x58uy; 0xf7uy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test_key2:lbytes 16\nlet test_key2 : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x7Euy; 0x24uy; 0x06uy; 0x78uy; 0x17uy; 0xFAuy; 0xE0uy; 0xD7uy;\n 0x43uy; 0xD6uy; 0xCEuy; 0x1Fuy; 0x32uy; 0x53uy; 0x91uy; 0x63uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test1_expected_sha3_384:lbytes 48\nlet test1_expected_sha3_384 : lbytes 48 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x0cuy; 0x63uy; 0xa7uy; 0x5buy; 0x84uy; 0x5euy; 0x4fuy; 0x7duy;\n 0x01uy; 0x10uy; 0x7duy; 0x85uy; 0x2euy; 0x4cuy; 0x24uy; 0x85uy;\n 0xc5uy; 0x1auy; 0x50uy; 0xaauy; 0xaauy; 0x94uy; 0xfcuy; 0x61uy;\n 0x99uy; 0x5euy; 0x71uy; 0xbbuy; 0xeeuy; 0x98uy; 0x3auy; 0x2auy;\n 0xc3uy; 0x71uy; 0x38uy; 0x31uy; 0x26uy; 0x4auy; 0xdbuy; 0x47uy;\n 0xfbuy; 0x6buy; 0xd1uy; 0xe0uy; 0x58uy; 0xd5uy; 0xf0uy; 0x04uy\n ] in\n assert_norm (List.Tot.length l == 48);\n of_list l", "val test3_expected_sha3_256:lbytes 32\nlet test3_expected_sha3_256 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x41uy; 0xc0uy; 0xdbuy; 0xa2uy; 0xa9uy; 0xd6uy; 0x24uy; 0x08uy;\n 0x49uy; 0x10uy; 0x03uy; 0x76uy; 0xa8uy; 0x23uy; 0x5euy; 0x2cuy;\n 0x82uy; 0xe1uy; 0xb9uy; 0x99uy; 0x8auy; 0x99uy; 0x9euy; 0x21uy;\n 0xdbuy; 0x32uy; 0xdduy; 0x97uy; 0x49uy; 0x6duy; 0x33uy; 0x76uy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val init:Impl.blake2_init_st Spec.Blake2S Core.M128\nlet init : Impl.blake2_init_st Spec.Blake2S Core.M128 =\n Impl.blake2_init #Spec.Blake2S #Core.M128", "val test10_expected_shake256:lbytes 32\nlet test10_expected_shake256 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xa8uy; 0x49uy; 0x83uy; 0xc9uy; 0xfeuy; 0x75uy; 0xaduy; 0x0duy;\n 0xe1uy; 0x9euy; 0x2cuy; 0x84uy; 0x20uy; 0xa7uy; 0xeauy; 0x85uy;\n 0xb2uy; 0x51uy; 0x02uy; 0x19uy; 0x56uy; 0x14uy; 0xdfuy; 0xa5uy;\n 0x34uy; 0x7duy; 0xe6uy; 0x0auy; 0x1cuy; 0xe1uy; 0x3buy; 0x60uy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test1_salt:lbytes 13\nlet test1_salt : lbytes 13 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy\n ] in\n assert_norm (List.Tot.length l == 13);\n of_list l", "val test4_output_ciphertext:lbytes 16\nlet test4_output_ciphertext : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x30uy; 0x4fuy; 0x81uy; 0xabuy; 0x61uy; 0xa8uy; 0x0cuy; 0x2euy;\n 0x74uy; 0x3buy; 0x94uy; 0xd5uy; 0x00uy; 0x2auy; 0x12uy; 0x6buy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test12_plaintext_shake256:lbytes 78\nlet test12_plaintext_shake256 : lbytes 78 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xdeuy; 0x70uy; 0x1fuy; 0x10uy; 0xaduy; 0x39uy; 0x61uy; 0xb0uy;\n 0xdauy; 0xccuy; 0x96uy; 0x87uy; 0x3auy; 0x3cuy; 0xd5uy; 0x58uy;\n 0x55uy; 0x81uy; 0x88uy; 0xffuy; 0x69uy; 0x6duy; 0x85uy; 0x01uy;\n 0xb2uy; 0xe2uy; 0x7buy; 0x67uy; 0xe9uy; 0x41uy; 0x90uy; 0xcduy;\n 0x0buy; 0x25uy; 0x48uy; 0xb6uy; 0x5buy; 0x52uy; 0xa9uy; 0x22uy;\n 0xaauy; 0xe8uy; 0x9duy; 0x63uy; 0xd6uy; 0xdduy; 0x97uy; 0x2cuy;\n 0x91uy; 0xa9uy; 0x79uy; 0xebuy; 0x63uy; 0x43uy; 0xb6uy; 0x58uy;\n 0xf2uy; 0x4duy; 0xb3uy; 0x4euy; 0x82uy; 0x8buy; 0x74uy; 0xdbuy;\n 0xb8uy; 0x9auy; 0x74uy; 0x93uy; 0xa3uy; 0xdfuy; 0xd4uy; 0x29uy;\n 0xfduy; 0xbduy; 0xb8uy; 0x40uy; 0xaduy; 0x0buy\n ] in\n assert_norm (List.Tot.length l == 78);\n of_list l", "val test_plaintext1:lbytes 16\nlet test_plaintext1 : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x53uy; 0x69uy; 0x6Euy; 0x67uy; 0x6Cuy; 0x65uy; 0x20uy; 0x62uy;\n 0x6Cuy; 0x6Fuy; 0x63uy; 0x6Buy; 0x20uy; 0x6Duy; 0x73uy; 0x67uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test_plaintext:lbytes 16\nlet test_plaintext : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x6buy; 0xc1uy; 0xbeuy; 0xe2uy; 0x2euy; 0x40uy; 0x9fuy; 0x96uy;\n 0xe9uy; 0x3duy; 0x7euy; 0x11uy; 0x73uy; 0x93uy; 0x17uy; 0x2auy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val test12_expected_shake256:lbytes 32\nlet test12_expected_shake256 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x64uy; 0x2fuy; 0x3fuy; 0x23uy; 0x5auy; 0xc7uy; 0xe3uy; 0xd4uy;\n 0x34uy; 0x06uy; 0x3buy; 0x5fuy; 0xc9uy; 0x21uy; 0x5fuy; 0xc3uy;\n 0xf0uy; 0xe5uy; 0x91uy; 0xe2uy; 0xe7uy; 0xfduy; 0x17uy; 0x66uy;\n 0x8duy; 0x1auy; 0x0cuy; 0x87uy; 0x46uy; 0x87uy; 0x35uy; 0xc2uy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val update:Impl.blake2_update_st Spec.Blake2S Core.M32\nlet update : Impl.blake2_update_st Spec.Blake2S Core.M32 =\n Impl.blake2_update #Spec.Blake2S #Core.M32 update_key update_blocks", "val test2_expected_sig:lbytes 64\nlet test2_expected_sig : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x92uy; 0xa0uy; 0x09uy; 0xa9uy; 0xf0uy; 0xd4uy; 0xcauy; 0xb8uy;\n 0x72uy; 0x0euy; 0x82uy; 0x0buy; 0x5fuy; 0x64uy; 0x25uy; 0x40uy;\n 0xa2uy; 0xb2uy; 0x7buy; 0x54uy; 0x16uy; 0x50uy; 0x3fuy; 0x8fuy;\n 0xb3uy; 0x76uy; 0x22uy; 0x23uy; 0xebuy; 0xdbuy; 0x69uy; 0xdauy;\n 0x08uy; 0x5auy; 0xc1uy; 0xe4uy; 0x3euy; 0x15uy; 0x99uy; 0x6euy;\n 0x45uy; 0x8fuy; 0x36uy; 0x13uy; 0xd0uy; 0xf1uy; 0x1duy; 0x8cuy;\n 0x38uy; 0x7buy; 0x2euy; 0xaeuy; 0xb4uy; 0x30uy; 0x2auy; 0xeeuy;\n 0xb0uy; 0x0duy; 0x29uy; 0x16uy; 0x12uy; 0xbbuy; 0x0cuy; 0x00uy\n ] in\n assert_norm (List.Tot.length l == 64);\n of_list l", "val test4_sk:lbytes 32\nlet test4_sk : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xf5uy; 0xe5uy; 0x76uy; 0x7cuy; 0xf1uy; 0x53uy; 0x31uy; 0x95uy;\n 0x17uy; 0x63uy; 0x0fuy; 0x22uy; 0x68uy; 0x76uy; 0xb8uy; 0x6cuy;\n 0x81uy; 0x60uy; 0xccuy; 0x58uy; 0x3buy; 0xc0uy; 0x13uy; 0x74uy;\n 0x4cuy; 0x6buy; 0xf2uy; 0x55uy; 0xf5uy; 0xccuy; 0x0euy; 0xe5uy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test7_plaintext_shake128:lbytes 34\nlet test7_plaintext_shake128 : lbytes 34 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x4auy; 0x20uy; 0x6auy; 0x5buy; 0x8auy; 0xa3uy; 0x58uy; 0x6cuy;\n 0x06uy; 0x67uy; 0xa4uy; 0x00uy; 0x20uy; 0xd6uy; 0x5fuy; 0xf5uy;\n 0x11uy; 0xd5uy; 0x2buy; 0x73uy; 0x2euy; 0xf7uy; 0xa0uy; 0xc5uy;\n 0x69uy; 0xf1uy; 0xeeuy; 0x68uy; 0x1auy; 0x4fuy; 0xc3uy; 0x62uy;\n 0x00uy; 0x65uy\n ] in\n assert_norm (List.Tot.length l == 34);\n of_list l", "val test5_plaintext_shake128:lbytes 0\nlet test5_plaintext_shake128 : lbytes 0 =\n let l = List.Tot.map u8_from_UInt8 [] in\n assert_norm (List.Tot.length l == 0);\n of_list l", "val test9_expected_shake256:lbytes 32\nlet test9_expected_shake256 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x46uy; 0xb9uy; 0xdduy; 0x2buy; 0x0buy; 0xa8uy; 0x8duy; 0x13uy;\n 0x23uy; 0x3buy; 0x3fuy; 0xebuy; 0x74uy; 0x3euy; 0xebuy; 0x24uy;\n 0x3fuy; 0xcduy; 0x52uy; 0xeauy; 0x62uy; 0xb8uy; 0x1buy; 0x82uy;\n 0xb5uy; 0x0cuy; 0x27uy; 0x64uy; 0x6euy; 0xd5uy; 0x76uy; 0x2fuy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val finish:Impl.blake2_finish_st Spec.Blake2S Core.M32\nlet finish : Impl.blake2_finish_st Spec.Blake2S Core.M32 =\n Impl.blake2_finish #Spec.Blake2S #Core.M32", "val test1_expected_sha3_512:lbytes 64\nlet test1_expected_sha3_512 : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xa6uy; 0x9fuy; 0x73uy; 0xccuy; 0xa2uy; 0x3auy; 0x9auy; 0xc5uy;\n 0xc8uy; 0xb5uy; 0x67uy; 0xdcuy; 0x18uy; 0x5auy; 0x75uy; 0x6euy;\n 0x97uy; 0xc9uy; 0x82uy; 0x16uy; 0x4fuy; 0xe2uy; 0x58uy; 0x59uy;\n 0xe0uy; 0xd1uy; 0xdcuy; 0xc1uy; 0x47uy; 0x5cuy; 0x80uy; 0xa6uy;\n 0x15uy; 0xb2uy; 0x12uy; 0x3auy; 0xf1uy; 0xf5uy; 0xf9uy; 0x4cuy;\n 0x11uy; 0xe3uy; 0xe9uy; 0x40uy; 0x2cuy; 0x3auy; 0xc5uy; 0x58uy;\n 0xf5uy; 0x00uy; 0x19uy; 0x9duy; 0x95uy; 0xb6uy; 0xd3uy; 0xe3uy;\n 0x01uy; 0x75uy; 0x85uy; 0x86uy; 0x28uy; 0x1duy; 0xcduy; 0x26uy\n ] in\n assert_norm (List.Tot.length l == 64);\n of_list l", "val test3_output_ciphertext:lbytes 16\nlet test3_output_ciphertext : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x46uy; 0xf2uy; 0xfbuy; 0x34uy; 0x2duy; 0x6fuy; 0x0auy; 0xb4uy;\n 0x77uy; 0x47uy; 0x6fuy; 0xc5uy; 0x01uy; 0x24uy; 0x2cuy; 0x5fuy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val init: init_st (|Blake2S, M32|)\nlet init s = BlS32.init s 0ul 32ul", "val test2_expected_prk:lbytes 32\nlet test2_expected_prk : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x06uy; 0xa6uy; 0xb8uy; 0x8cuy; 0x58uy; 0x53uy; 0x36uy; 0x1auy;\n 0x06uy; 0x10uy; 0x4cuy; 0x9cuy; 0xebuy; 0x35uy; 0xb4uy; 0x5cuy;\n 0xefuy; 0x76uy; 0x00uy; 0x14uy; 0x90uy; 0x46uy; 0x71uy; 0x01uy;\n 0x4auy; 0x19uy; 0x3fuy; 0x40uy; 0xc1uy; 0x5fuy; 0xc2uy; 0x44uy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l", "val test_ciphertext1:lbytes 16\nlet test_ciphertext1 : lbytes 16 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xE4uy; 0x09uy; 0x5Duy; 0x4Fuy; 0xB7uy; 0xA7uy; 0xB3uy; 0x79uy;\n 0x2Duy; 0x61uy; 0x75uy; 0xA3uy; 0x26uy; 0x13uy; 0x11uy; 0xB8uy ] in\n assert_norm (List.Tot.length l == 16);\n of_list l", "val update_block:Impl.blake2_update_block_st Spec.Blake2S Core.M32\nlet update_block : Impl.blake2_update_block_st Spec.Blake2S Core.M32 =\n Impl.blake2_update_block #Spec.Blake2S #Core.M32", "val test11_expected_shake256:lbytes 32\nlet test11_expected_shake256 : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x7auy; 0xbbuy; 0xa4uy; 0xe8uy; 0xb8uy; 0xdduy; 0x76uy; 0x6buy;\n 0xbauy; 0xbeuy; 0x98uy; 0xf8uy; 0xf1uy; 0x69uy; 0xcbuy; 0x62uy;\n 0x08uy; 0x67uy; 0x4duy; 0xe1uy; 0x9auy; 0x51uy; 0xd7uy; 0x3cuy;\n 0x92uy; 0xb7uy; 0xdcuy; 0x04uy; 0xa4uy; 0xb5uy; 0xeeuy; 0x3duy\n ] in\n assert_norm (List.Tot.length l == 32);\n of_list l" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Spec.Blake2.Definitions.fst", "name": "Spec.Blake2.Definitions.blake2s_default_params" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.Definitions.fst", "name": "Spec.Blake2.Definitions.blake2b_default_params" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Hash.Incremental.fst", "name": "EverCrypt.Hash.Incremental.digest_blake2s" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Hash.Incremental.fst", "name": "EverCrypt.Hash.Incremental.digest_blake2b" }, { "project_name": "hacl-star", "file_name": "EverCrypt.HKDF.fst", "name": "EverCrypt.HKDF.expand_blake2s" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test2_plaintext_block" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test2_key_block" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.serialize_blake2s_params" }, { "project_name": "hacl-star", "file_name": "Spec.HKDF.Test.fst", "name": "Spec.HKDF.Test.test2_salt" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test2_input_plaintext" }, { "project_name": "hacl-star", "file_name": "EverCrypt.HMAC.fst", "name": "EverCrypt.HMAC.compute_blake2s" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test2_ciphertext_block" }, { "project_name": "hacl-star", "file_name": "EverCrypt.HKDF.fst", "name": "EverCrypt.HKDF.expand_blake2b" }, { "project_name": "hacl-star", "file_name": "EverCrypt.HKDF.fst", "name": "EverCrypt.HKDF.extract_blake2s" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test2_expected_sha3_256" }, { "project_name": "hacl-star", "file_name": "Hacl.HKDF.Blake2s_128.fst", "name": "Hacl.HKDF.Blake2s_128.expand_blake2s_128" }, { "project_name": "hacl-star", "file_name": "Spec.Ed25519.Test.fst", "name": "Spec.Ed25519.Test.test2_sk" }, { "project_name": "hacl-star", "file_name": "Spec.K256.Test.fst", "name": "Spec.K256.Test.test2_sk" }, { "project_name": "hacl-star", "file_name": "Spec.HMAC.Test.fst", "name": "Spec.HMAC.Test.test1_key" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test2_expected_sha3_224" }, { "project_name": "hacl-star", "file_name": "Hacl.HKDF.Blake2b_256.fst", "name": "Hacl.HKDF.Blake2b_256.expand_blake2b_256" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test2_output_ciphertext" }, { "project_name": "hacl-star", "file_name": "EverCrypt.HMAC.fst", "name": "EverCrypt.HMAC.compute_blake2b" }, { "project_name": "hacl-star", "file_name": "EverCrypt.HKDF.fst", "name": "EverCrypt.HKDF.extract_blake2b" }, { "project_name": "hacl-star", "file_name": "Hacl.HMAC.Blake2s_128.fst", "name": "Hacl.HMAC.Blake2s_128.compute_blake2s_128" }, { "project_name": "hacl-star", "file_name": "Hacl.HMAC.fst", "name": "Hacl.HMAC.compute_blake2s_32" }, { "project_name": "hacl-star", "file_name": "Hacl.HKDF.fst", "name": "Hacl.HKDF.expand_blake2s_32" }, { "project_name": "hacl-star", "file_name": "Hacl.HKDF.fst", "name": "Hacl.HKDF.extract_blake2s_32" }, { "project_name": "hacl-star", "file_name": "Hacl.Hash.Blake2s_128.fst", "name": "Hacl.Hash.Blake2s_128.hash" }, { "project_name": "hacl-star", "file_name": "Hacl.Hash.Blake2s_32.fst", "name": "Hacl.Hash.Blake2s_32.hash" }, { "project_name": "hacl-star", "file_name": "Hacl.HMAC.Blake2b_256.fst", "name": "Hacl.HMAC.Blake2b_256.compute_blake2b_256" }, { "project_name": "hacl-star", "file_name": "Hacl.HKDF.fst", "name": "Hacl.HKDF.expand_blake2b_32" }, { "project_name": "hacl-star", "file_name": "Hacl.HKDF.fst", "name": "Hacl.HKDF.extract_blake2b_32" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.serialize_blake2b_params" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test_plaintext2" }, { "project_name": "hacl-star", "file_name": "Hacl.HKDF.Blake2b_256.fst", "name": "Hacl.HKDF.Blake2b_256.extract_blake2b_256" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test2_expected_sha3_384" }, { "project_name": "hacl-star", "file_name": "Spec.HMAC.Test.fst", "name": "Spec.HMAC.Test.test5_key" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test2_input_key" }, { "project_name": "hacl-star", "file_name": "Hacl.HMAC.fst", "name": "Hacl.HMAC.compute_blake2b_32" }, { "project_name": "hacl-star", "file_name": "Hacl.HKDF.Blake2s_128.fst", "name": "Hacl.HKDF.Blake2s_128.extract_blake2s_128" }, { "project_name": "hacl-star", "file_name": "Spec.HMAC.Test.fst", "name": "Spec.HMAC.Test.test3_key" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test2_expected_sha3_512" }, { "project_name": "hacl-star", "file_name": "Spec.K256.Test.fst", "name": "Spec.K256.Test.test2_nonce" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test11_plaintext_shake256" }, { "project_name": "hacl-star", "file_name": "Spec.HMAC.Test.fst", "name": "Spec.HMAC.Test.test5_data" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test10_plaintext_shake256" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test1_plaintext_block" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test_ciphertext2" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test3_input_plaintext" }, { "project_name": "hacl-star", "file_name": "Spec.Ed25519.Test.fst", "name": "Spec.Ed25519.Test.test1_sk" }, { "project_name": "hacl-star", "file_name": "Spec.HMAC.Test.fst", "name": "Spec.HMAC.Test.test2_data" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.Definitions.fst", "name": "Spec.Blake2.Definitions.blake2_default_params" }, { "project_name": "hacl-star", "file_name": "Spec.HMAC.Test.fst", "name": "Spec.HMAC.Test.test2_expected256" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test1_expected_sha3_256" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test1_expected_sha3_224" }, { "project_name": "hacl-star", "file_name": "Hacl.Blake2s_32.fst", "name": "Hacl.Blake2s_32.init" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test3_expected_sha3_224" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test1_key_block" }, { "project_name": "hacl-star", "file_name": "Spec.HMAC.Test.fst", "name": "Spec.HMAC.Test.test2_key" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test3_ciphertext_block" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test3_key_block" }, { "project_name": "hacl-star", "file_name": "Spec.K256.Test.fst", "name": "Spec.K256.Test.test2_msgHash" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test2_plaintext" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test4_expected_sha3_224" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test_ciphertext" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test4_input_plaintext" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test1_ciphertext_block" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Blake2.Generic.fst", "name": "Hacl.Impl.Blake2.Generic.serialize_params_blake2b" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test6_plaintext_shake128" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Blake2.Generic.fst", "name": "Hacl.Impl.Blake2.Generic.serialize_params_blake2s" }, { "project_name": "hacl-star", "file_name": "Hacl.Blake2s_32.fst", "name": "Hacl.Blake2s_32.update_key" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test4_expected_sha3_256" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test9_plaintext_shake256" }, { "project_name": "hacl-star", "file_name": "Spec.Ed25519.Test.fst", "name": "Spec.Ed25519.Test.test3_sk" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test_key2" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test1_expected_sha3_384" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test3_expected_sha3_256" }, { "project_name": "hacl-star", "file_name": "Hacl.Blake2s_128.fst", "name": "Hacl.Blake2s_128.init" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test10_expected_shake256" }, { "project_name": "hacl-star", "file_name": "Spec.HKDF.Test.fst", "name": "Spec.HKDF.Test.test1_salt" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test4_output_ciphertext" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test12_plaintext_shake256" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test_plaintext1" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test_plaintext" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test12_expected_shake256" }, { "project_name": "hacl-star", "file_name": "Hacl.Blake2s_32.fst", "name": "Hacl.Blake2s_32.update" }, { "project_name": "hacl-star", "file_name": "Spec.Ed25519.Test.fst", "name": "Spec.Ed25519.Test.test2_expected_sig" }, { "project_name": "hacl-star", "file_name": "Spec.Ed25519.Test.fst", "name": "Spec.Ed25519.Test.test4_sk" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test7_plaintext_shake128" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test5_plaintext_shake128" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test9_expected_shake256" }, { "project_name": "hacl-star", "file_name": "Hacl.Blake2s_32.fst", "name": "Hacl.Blake2s_32.finish" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test1_expected_sha3_512" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test3_output_ciphertext" }, { "project_name": "hacl-star", "file_name": "Hacl.Hash.Blake2s_32.fst", "name": "Hacl.Hash.Blake2s_32.init" }, { "project_name": "hacl-star", "file_name": "Spec.HKDF.Test.fst", "name": "Spec.HKDF.Test.test2_expected_prk" }, { "project_name": "hacl-star", "file_name": "Spec.AES.Test.fst", "name": "Spec.AES.Test.test_ciphertext1" }, { "project_name": "hacl-star", "file_name": "Hacl.Blake2s_32.fst", "name": "Hacl.Blake2s_32.update_block" }, { "project_name": "hacl-star", "file_name": "Spec.SHA3.Test.fst", "name": "Spec.SHA3.Test.test11_expected_shake256" } ], "selected_premises": [ "Spec.Blake2.Test.test17_params", "Spec.Blake2.Test.test19_params", "Spec.Blake2.Test.test18_params", "Spec.Blake2.Test.test11_plaintext", "Spec.Blake2.Test.test15_plaintext", "Spec.Blake2.Test.test10_plaintext", "Spec.Blake2.Test.test6_plaintext", "Spec.Blake2.Test.test13_plaintext", "Lib.IntTypes.size", "Lib.Sequence.lseq", "Lib.IntTypes.int_t", "Spec.Blake2.Test.test14_plaintext", "Spec.Blake2.Test.test3_plaintext", "Spec.Blake2.Test.test12_plaintext", "Lib.IntTypes.uint_t", "Lib.IntTypes.range", "Lib.IntTypes.u64", "Spec.Blake2.Test.test4_plaintext", "Lib.IntTypes.u8", "Spec.Blake2.Test.test12_expected", "Spec.Blake2.Test.test16_plaintext", "Lib.Sequence.to_seq", "Spec.Blake2.Test.test6_expected", "Lib.Sequence.op_String_Access", "Spec.Blake2.Test.test14_expected", "Lib.UpdateMulti.uint8", "Spec.Blake2.Test.test9_plaintext", "Spec.Blake2.Test.test6_key", "Spec.Blake2.Test.test13_expected", "Spec.Blake2.Test.test13_key", "Spec.Blake2.Test.test12_key", "Spec.Blake2.Test.test0_expected", "FStar.UInt.size", "Spec.Blake2.Test.test14_key", "Spec.Blake2.Test.test9_expected", "Spec.Blake2.Test.test15_expected", "Spec.Blake2.Test.test8_plaintext", "Spec.Blake2.Test.test16_expected", "Spec.Blake2.Test.test5_expected", "Spec.Blake2.Test.test15_key", "Lib.Sequence.length", "Spec.Blake2.Test.test7_plaintext", "Spec.Blake2.Test.test_vectors", "Spec.Blake2.Test.test0_key", "Lib.IntTypes.v", "Lib.IntTypes.u32", "Spec.Blake2.Test.test16_key", "Lib.IntTypes.op_Plus_Bang", "Spec.Blake2.Test.test10_key", "FStar.Mul.op_Star", "Lib.Sequence.op_String_Assignment", "Lib.IntTypes.uint_v", "Spec.Blake2.Test.test7_expected", "Lib.IntTypes.max_size_t", "Spec.Blake2.Test.test17_expected", "Spec.Blake2.Test.test11_key", "Spec.Blake2.Test.test10_expected", "Lib.Sequence.createL", "Spec.Blake2.Test.test9_key", "Lib.IntTypes.bits", "Spec.Blake2.Test.test18_expected", "Lib.Sequence.seq", "Spec.Blake2.Test.test2_expected", "Spec.Blake2.Test.test8_expected", "Spec.Blake2.Test.test2_key", "Spec.Blake2.Test.test3_key", "Spec.Blake2.serialize_blake2s_params", "Spec.Blake2.Test.test4_key", "Spec.Blake2.serialize_blake2b_params", "Spec.Blake2.Test.test7_key", "Lib.IntTypes.op_Star_Bang", "Spec.Blake2.Test.test11_expected", "Spec.Blake2.Test.test5_plaintext", "Spec.Blake2.Test.test8_key", "Lib.IntTypes.op_Plus_Dot", "Spec.Blake2.Test.test1_expected", "Spec.Blake2.Test.test3_expected", "Spec.Blake2.Test.test19_expected", "Spec.Blake2.Test.test2_plaintext", "Spec.Blake2.Test.test4_expected", "FStar.Pervasives.reveal_opaque", "Spec.Blake2.Test.test1_plaintext", "FStar.Heap.trivial_preorder", "Lib.Sequence.slice", "Lib.ByteSequence.lbytes", "Lib.ByteSequence.nat_from_bytes_le", "FStar.ST.op_Bang", "Lib.IntTypes.numbytes", "Lib.IntTypes.op_Subtraction_Dot", "Lib.IntTypes.uint", "Lib.IntTypes.op_Hat_Dot", "Lib.IntTypes.byte", "Lib.ByteSequence.nat_from_bytes_be", "Lib.IntTypes.op_Star_Dot", "Lib.IntTypes.u16", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "Lib.IntTypes.op_Amp_Dot", "Lib.IntTypes.unsigned", "Lib.ByteSequence.lbytes_empty" ], "source_upto_this": "module Spec.Blake2.Test\n\nopen FStar.Mul\nopen Lib.IntTypes\nopen Lib.RawIntTypes\nopen Lib.Sequence\nopen Lib.ByteSequence\nmodule PS = Lib.PrintSequence\nmodule S = Spec.Blake2\n\n#set-options \"--z3rlimit 50 --fuel 0 --ifuel 0\"\n\n/// Test 1\n\nlet test1_plaintext : lbytes 3 =\n let l = List.Tot.map u8_from_UInt8 [ 0x61uy; 0x62uy; 0x63uy ] in\n assert_norm (List.Tot.length l = 3);\n of_list l\n\n\nlet test1_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x50uy; 0x8Cuy; 0x5Euy; 0x8Cuy; 0x32uy; 0x7Cuy; 0x14uy; 0xE2uy;\n 0xE1uy; 0xA7uy; 0x2Buy; 0xA3uy; 0x4Euy; 0xEBuy; 0x45uy; 0x2Fuy;\n 0x37uy; 0x45uy; 0x8Buy; 0x20uy; 0x9Euy; 0xD6uy; 0x3Auy; 0x29uy;\n 0x4Duy; 0x99uy; 0x9Buy; 0x4Cuy; 0x86uy; 0x67uy; 0x59uy; 0x82uy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l\n\n\nlet test2_plaintext : lbytes 1 =\n let l = List.Tot.map u8_from_UInt8 [ 0x00uy ] in\n assert_norm (List.Tot.length l = 1);\n of_list l\n\n\nlet test2_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l\n\n\nlet test2_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x40uy; 0xd1uy; 0x5fuy; 0xeeuy; 0x7cuy; 0x32uy; 0x88uy; 0x30uy;\n 0x16uy; 0x6auy; 0xc3uy; 0xf9uy; 0x18uy; 0x65uy; 0x0fuy; 0x80uy;\n 0x7euy; 0x7euy; 0x01uy; 0xe1uy; 0x77uy; 0x25uy; 0x8cuy; 0xdcuy;\n 0x0auy; 0x39uy; 0xb1uy; 0x1fuy; 0x59uy; 0x80uy; 0x66uy; 0xf1uy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l\n\n\nlet test3_plaintext : lbytes 255 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2auy; 0x2buy; 0x2cuy; 0x2duy; 0x2euy; 0x2fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3auy; 0x3buy; 0x3cuy; 0x3duy; 0x3euy; 0x3fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4auy; 0x4buy; 0x4cuy; 0x4duy; 0x4euy; 0x4fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5auy; 0x5buy; 0x5cuy; 0x5duy; 0x5euy; 0x5fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6auy; 0x6buy; 0x6cuy; 0x6duy; 0x6euy; 0x6fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7auy; 0x7buy; 0x7cuy; 0x7duy; 0x7euy; 0x7fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8auy; 0x8buy; 0x8cuy; 0x8duy; 0x8euy; 0x8fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9auy; 0x9buy; 0x9cuy; 0x9duy; 0x9euy; 0x9fuy;\n 0xa0uy; 0xa1uy; 0xa2uy; 0xa3uy; 0xa4uy; 0xa5uy; 0xa6uy; 0xa7uy;\n 0xa8uy; 0xa9uy; 0xaauy; 0xabuy; 0xacuy; 0xaduy; 0xaeuy; 0xafuy;\n 0xb0uy; 0xb1uy; 0xb2uy; 0xb3uy; 0xb4uy; 0xb5uy; 0xb6uy; 0xb7uy;\n 0xb8uy; 0xb9uy; 0xbauy; 0xbbuy; 0xbcuy; 0xbduy; 0xbeuy; 0xbfuy;\n 0xc0uy; 0xc1uy; 0xc2uy; 0xc3uy; 0xc4uy; 0xc5uy; 0xc6uy; 0xc7uy;\n 0xc8uy; 0xc9uy; 0xcauy; 0xcbuy; 0xccuy; 0xcduy; 0xceuy; 0xcfuy;\n 0xd0uy; 0xd1uy; 0xd2uy; 0xd3uy; 0xd4uy; 0xd5uy; 0xd6uy; 0xd7uy;\n 0xd8uy; 0xd9uy; 0xdauy; 0xdbuy; 0xdcuy; 0xdduy; 0xdeuy; 0xdfuy;\n 0xe0uy; 0xe1uy; 0xe2uy; 0xe3uy; 0xe4uy; 0xe5uy; 0xe6uy; 0xe7uy;\n 0xe8uy; 0xe9uy; 0xeauy; 0xebuy; 0xecuy; 0xeduy; 0xeeuy; 0xefuy;\n 0xf0uy; 0xf1uy; 0xf2uy; 0xf3uy; 0xf4uy; 0xf5uy; 0xf6uy; 0xf7uy;\n 0xf8uy; 0xf9uy; 0xfauy; 0xfbuy; 0xfcuy; 0xfduy; 0xfeuy ] in\n assert_norm (List.Tot.length l = 255);\n of_list l\n\n\nlet test3_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l\n\n\nlet test3_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x3fuy; 0xb7uy; 0x35uy; 0x06uy; 0x1auy; 0xbcuy; 0x51uy; 0x9duy;\n 0xfeuy; 0x97uy; 0x9euy; 0x54uy; 0xc1uy; 0xeeuy; 0x5buy; 0xfauy;\n 0xd0uy; 0xa9uy; 0xd8uy; 0x58uy; 0xb3uy; 0x31uy; 0x5buy; 0xaduy;\n 0x34uy; 0xbduy; 0xe9uy; 0x99uy; 0xefuy; 0xd7uy; 0x24uy; 0xdduy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l\n\n\nlet test4_plaintext : lbytes 251 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2auy; 0x2buy; 0x2cuy; 0x2duy; 0x2euy; 0x2fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3auy; 0x3buy; 0x3cuy; 0x3duy; 0x3euy; 0x3fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4auy; 0x4buy; 0x4cuy; 0x4duy; 0x4euy; 0x4fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5auy; 0x5buy; 0x5cuy; 0x5duy; 0x5euy; 0x5fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6auy; 0x6buy; 0x6cuy; 0x6duy; 0x6euy; 0x6fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7auy; 0x7buy; 0x7cuy; 0x7duy; 0x7euy; 0x7fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8auy; 0x8buy; 0x8cuy; 0x8duy; 0x8euy; 0x8fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9auy; 0x9buy; 0x9cuy; 0x9duy; 0x9euy; 0x9fuy;\n 0xa0uy; 0xa1uy; 0xa2uy; 0xa3uy; 0xa4uy; 0xa5uy; 0xa6uy; 0xa7uy;\n 0xa8uy; 0xa9uy; 0xaauy; 0xabuy; 0xacuy; 0xaduy; 0xaeuy; 0xafuy;\n 0xb0uy; 0xb1uy; 0xb2uy; 0xb3uy; 0xb4uy; 0xb5uy; 0xb6uy; 0xb7uy;\n 0xb8uy; 0xb9uy; 0xbauy; 0xbbuy; 0xbcuy; 0xbduy; 0xbeuy; 0xbfuy;\n 0xc0uy; 0xc1uy; 0xc2uy; 0xc3uy; 0xc4uy; 0xc5uy; 0xc6uy; 0xc7uy;\n 0xc8uy; 0xc9uy; 0xcauy; 0xcbuy; 0xccuy; 0xcduy; 0xceuy; 0xcfuy;\n 0xd0uy; 0xd1uy; 0xd2uy; 0xd3uy; 0xd4uy; 0xd5uy; 0xd6uy; 0xd7uy;\n 0xd8uy; 0xd9uy; 0xdauy; 0xdbuy; 0xdcuy; 0xdduy; 0xdeuy; 0xdfuy;\n 0xe0uy; 0xe1uy; 0xe2uy; 0xe3uy; 0xe4uy; 0xe5uy; 0xe6uy; 0xe7uy;\n 0xe8uy; 0xe9uy; 0xeauy; 0xebuy; 0xecuy; 0xeduy; 0xeeuy; 0xefuy;\n 0xf0uy; 0xf1uy; 0xf2uy; 0xf3uy; 0xf4uy; 0xf5uy; 0xf6uy; 0xf7uy;\n 0xf8uy; 0xf9uy; 0xfauy ] in\n assert_norm (List.Tot.length l = 251);\n of_list l\n\n\nlet test4_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l\n\n\nlet test4_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xd1uy; 0x2buy; 0xf3uy; 0x73uy; 0x2euy; 0xf4uy; 0xafuy; 0x5cuy;\n 0x22uy; 0xfauy; 0x90uy; 0x35uy; 0x6auy; 0xf8uy; 0xfcuy; 0x50uy;\n 0xfcuy; 0xb4uy; 0x0fuy; 0x8fuy; 0x2euy; 0xa5uy; 0xc8uy; 0x59uy;\n 0x47uy; 0x37uy; 0xa3uy; 0xb3uy; 0xd5uy; 0xabuy; 0xdbuy; 0xd7uy ] in\n assert_norm (List.Tot.length l = 32);\n of_list l\n\n\n/// Test 5 BLAKE 2B\n\nlet test5_plaintext : lbytes 3 =\n let l = List.Tot.map u8_from_UInt8 [ 0x61uy; 0x62uy; 0x63uy ] in\n assert_norm (List.Tot.length l = 3);\n of_list l\n\n\nlet test5_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xBAuy; 0x80uy; 0xA5uy; 0x3Fuy; 0x98uy; 0x1Cuy; 0x4Duy; 0x0Duy;\n 0x6Auy; 0x27uy; 0x97uy; 0xB6uy; 0x9Fuy; 0x12uy; 0xF6uy; 0xE9uy;\n 0x4Cuy; 0x21uy; 0x2Fuy; 0x14uy; 0x68uy; 0x5Auy; 0xC4uy; 0xB7uy;\n 0x4Buy; 0x12uy; 0xBBuy; 0x6Fuy; 0xDBuy; 0xFFuy; 0xA2uy; 0xD1uy;\n 0x7Duy; 0x87uy; 0xC5uy; 0x39uy; 0x2Auy; 0xABuy; 0x79uy; 0x2Duy;\n 0xC2uy; 0x52uy; 0xD5uy; 0xDEuy; 0x45uy; 0x33uy; 0xCCuy; 0x95uy;\n 0x18uy; 0xD3uy; 0x8Auy; 0xA8uy; 0xDBuy; 0xF1uy; 0x92uy; 0x5Auy;\n 0xB9uy; 0x23uy; 0x86uy; 0xEDuy; 0xD4uy; 0x00uy; 0x99uy; 0x23uy ] in\n assert_norm (List.Tot.length l = 64);\n of_list l\n\n\n/// Test 6 BLAKE 2B\n\nlet test6_plaintext : lbytes 128 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy ] in\n assert_norm (List.Tot.length l = 128);\n of_list l\n\n\nlet test6_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy;\n 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy ] in\n assert_norm (List.Tot.length l = 64);\n of_list l\n\n\nlet test6_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xe4uy; 0x7buy; 0xb6uy; 0xf2uy; 0x0fuy; 0xbfuy; 0x14uy; 0x98uy;\n 0x4fuy; 0x72uy; 0xa4uy; 0xc3uy; 0xcduy; 0x9fuy; 0x3duy; 0xc0uy;\n 0xd3uy; 0x89uy; 0x28uy; 0xe5uy; 0x36uy; 0x73uy; 0x3buy; 0xa7uy;\n 0xc5uy; 0xb1uy; 0x53uy; 0xc7uy; 0x15uy; 0x46uy; 0x58uy; 0x4buy;\n 0x73uy; 0x71uy; 0xf9uy; 0xb7uy; 0x07uy; 0x07uy; 0x77uy; 0xb9uy;\n 0xa0uy; 0x94uy; 0x77uy; 0x03uy; 0x40uy; 0x96uy; 0x50uy; 0xfduy;\n 0x04uy; 0xcfuy; 0xc9uy; 0xa5uy; 0xd5uy; 0x61uy; 0xf9uy; 0x9euy;\n 0xd1uy; 0x34uy; 0xefuy; 0x26uy; 0x2buy; 0x03uy; 0xdbuy; 0x94uy ] in\n assert_norm (List.Tot.length l = 64);\n of_list l\n\n\n(*** Blake2s test vectors: *)\n\nlet test7_plaintext : lbytes 63 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy ] in\n assert_norm (FStar.List.length l = 63);\n of_list l\n\n\nlet test7_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l\n\n\nlet test7_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xC6uy; 0x53uy; 0x82uy; 0x51uy; 0x3Fuy; 0x07uy; 0x46uy; 0x0Duy;\n 0xA3uy; 0x98uy; 0x33uy; 0xCBuy; 0x66uy; 0x6Cuy; 0x5Euy; 0xD8uy;\n 0x2Euy; 0x61uy; 0xB9uy; 0xE9uy; 0x98uy; 0xF4uy; 0xB0uy; 0xC4uy;\n 0x28uy; 0x7Cuy; 0xEEuy; 0x56uy; 0xC3uy; 0xCCuy; 0x9Buy; 0xCDuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l\n\n\nlet test8_plaintext : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l\n\n\nlet test8_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l\n\n\nlet test8_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x89uy; 0x75uy; 0xB0uy; 0x57uy; 0x7Fuy; 0xD3uy; 0x55uy; 0x66uy;\n 0xD7uy; 0x50uy; 0xB3uy; 0x62uy; 0xB0uy; 0x89uy; 0x7Auy; 0x26uy;\n 0xC3uy; 0x99uy; 0x13uy; 0x6Duy; 0xF0uy; 0x7Buy; 0xABuy; 0xABuy;\n 0xBDuy; 0xE6uy; 0x20uy; 0x3Fuy; 0xF2uy; 0x95uy; 0x4Euy; 0xD4uy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l\n\n\nlet test9_plaintext : lbytes 65 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy ] in\n assert_norm (FStar.List.length l = 65);\n of_list l\n\n\nlet test9_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l\n\n\nlet test9_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x21uy; 0xFEuy; 0x0Cuy; 0xEBuy; 0x00uy; 0x52uy; 0xBEuy; 0x7Fuy;\n 0xB0uy; 0xF0uy; 0x04uy; 0x18uy; 0x7Cuy; 0xACuy; 0xD7uy; 0xDEuy;\n 0x67uy; 0xFAuy; 0x6Euy; 0xB0uy; 0x93uy; 0x8Duy; 0x92uy; 0x76uy;\n 0x77uy; 0xF2uy; 0x39uy; 0x8Cuy; 0x13uy; 0x23uy; 0x17uy; 0xA8uy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l\n\n\nlet test10_plaintext : lbytes 128 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy ] in\n assert_norm (FStar.List.length l = 128);\n of_list l\n\n\nlet test10_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l\n\n\nlet test10_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x0Cuy; 0x31uy; 0x1Fuy; 0x38uy; 0xC3uy; 0x5Auy; 0x4Fuy; 0xB9uy;\n 0x0Duy; 0x65uy; 0x1Cuy; 0x28uy; 0x9Duy; 0x48uy; 0x68uy; 0x56uy;\n 0xCDuy; 0x14uy; 0x13uy; 0xDFuy; 0x9Buy; 0x06uy; 0x77uy; 0xF5uy;\n 0x3Euy; 0xCEuy; 0x2Cuy; 0xD9uy; 0xE4uy; 0x77uy; 0xC6uy; 0x0Auy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l\n\n\nlet test11_plaintext : lbytes 256 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8Auy; 0x8Buy; 0x8Cuy; 0x8Duy; 0x8Euy; 0x8Fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9Auy; 0x9Buy; 0x9Cuy; 0x9Duy; 0x9Euy; 0x9Fuy;\n 0xA0uy; 0xA1uy; 0xA2uy; 0xA3uy; 0xA4uy; 0xA5uy; 0xA6uy; 0xA7uy;\n 0xA8uy; 0xA9uy; 0xAAuy; 0xABuy; 0xACuy; 0xADuy; 0xAEuy; 0xAFuy;\n 0xB0uy; 0xB1uy; 0xB2uy; 0xB3uy; 0xB4uy; 0xB5uy; 0xB6uy; 0xB7uy;\n 0xB8uy; 0xB9uy; 0xBAuy; 0xBBuy; 0xBCuy; 0xBDuy; 0xBEuy; 0xBFuy;\n 0xC0uy; 0xC1uy; 0xC2uy; 0xC3uy; 0xC4uy; 0xC5uy; 0xC6uy; 0xC7uy;\n 0xC8uy; 0xC9uy; 0xCAuy; 0xCBuy; 0xCCuy; 0xCDuy; 0xCEuy; 0xCFuy;\n 0xD0uy; 0xD1uy; 0xD2uy; 0xD3uy; 0xD4uy; 0xD5uy; 0xD6uy; 0xD7uy;\n 0xD8uy; 0xD9uy; 0xDAuy; 0xDBuy; 0xDCuy; 0xDDuy; 0xDEuy; 0xDFuy;\n 0xE0uy; 0xE1uy; 0xE2uy; 0xE3uy; 0xE4uy; 0xE5uy; 0xE6uy; 0xE7uy;\n 0xE8uy; 0xE9uy; 0xEAuy; 0xEBuy; 0xECuy; 0xEDuy; 0xEEuy; 0xEFuy;\n 0xF0uy; 0xF1uy; 0xF2uy; 0xF3uy; 0xF4uy; 0xF5uy; 0xF6uy; 0xF7uy;\n 0xF8uy; 0xF9uy; 0xFAuy; 0xFBuy; 0xFCuy; 0xFDuy; 0xFEuy; 0xFFuy ] in\n assert_norm (FStar.List.length l = 256);\n of_list l\n\n\nlet test11_key : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l\n\n\nlet test11_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x52uy; 0x11uy; 0xD1uy; 0xAEuy; 0xFCuy; 0x00uy; 0x25uy; 0xBEuy;\n 0x7Fuy; 0x85uy; 0xC0uy; 0x6Buy; 0x3Euy; 0x14uy; 0xE0uy; 0xFCuy;\n 0x64uy; 0x5Auy; 0xE1uy; 0x2Buy; 0xD4uy; 0x17uy; 0x46uy; 0x48uy;\n 0x5Euy; 0xA6uy; 0xD8uy; 0xA3uy; 0x64uy; 0xA2uy; 0xEAuy; 0xEEuy ] in\n assert_norm (FStar.List.length l = 32);\n of_list l\n\n(*** Blake2b test vectors: *)\n\nlet test0_plaintext : lbytes 0 =\n let l = List.Tot.map u8_from_UInt8 [] in\n assert_norm (List.Tot.length l = 0);\n of_list l\n\n\nlet test0_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0auy; 0x0buy; 0x0cuy; 0x0duy; 0x0euy; 0x0fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1auy; 0x1buy; 0x1cuy; 0x1duy; 0x1euy; 0x1fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2auy; 0x2buy; 0x2cuy; 0x2duy; 0x2euy; 0x2fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3auy; 0x3buy; 0x3cuy; 0x3duy; 0x3euy; 0x3fuy ] in\n assert_norm (List.Tot.length l = 64);\n of_list l\n\n\nlet test0_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x10uy; 0xebuy; 0xb6uy; 0x77uy; 0x00uy; 0xb1uy; 0x86uy; 0x8euy;\n 0xfbuy; 0x44uy; 0x17uy; 0x98uy; 0x7auy; 0xcfuy; 0x46uy; 0x90uy;\n 0xaeuy; 0x9duy; 0x97uy; 0x2fuy; 0xb7uy; 0xa5uy; 0x90uy; 0xc2uy;\n 0xf0uy; 0x28uy; 0x71uy; 0x79uy; 0x9auy; 0xaauy; 0x47uy; 0x86uy;\n 0xb5uy; 0xe9uy; 0x96uy; 0xe8uy; 0xf0uy; 0xf4uy; 0xebuy; 0x98uy;\n 0x1fuy; 0xc2uy; 0x14uy; 0xb0uy; 0x05uy; 0xf4uy; 0x2duy; 0x2fuy;\n 0xf4uy; 0x23uy; 0x34uy; 0x99uy; 0x39uy; 0x16uy; 0x53uy; 0xdfuy;\n 0x7auy; 0xefuy; 0xcbuy; 0xc1uy; 0x3fuy; 0xc5uy; 0x15uy; 0x68uy ] in\n assert_norm (List.Tot.length l = 64);\n of_list l\n\n\nlet test12_plaintext : lbytes 127 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy ] in\n assert_norm (FStar.List.length l = 127);\n of_list l\n\n\nlet test12_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l\n\n\nlet test12_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x76uy; 0xD2uy; 0xD8uy; 0x19uy; 0xC9uy; 0x2Buy; 0xCEuy; 0x55uy;\n 0xFAuy; 0x8Euy; 0x09uy; 0x2Auy; 0xB1uy; 0xBFuy; 0x9Buy; 0x9Euy;\n 0xABuy; 0x23uy; 0x7Auy; 0x25uy; 0x26uy; 0x79uy; 0x86uy; 0xCAuy;\n 0xCFuy; 0x2Buy; 0x8Euy; 0xE1uy; 0x4Duy; 0x21uy; 0x4Duy; 0x73uy;\n 0x0Duy; 0xC9uy; 0xA5uy; 0xAAuy; 0x2Duy; 0x7Buy; 0x59uy; 0x6Euy;\n 0x86uy; 0xA1uy; 0xFDuy; 0x8Fuy; 0xA0uy; 0x80uy; 0x4Cuy; 0x77uy;\n 0x40uy; 0x2Duy; 0x2Fuy; 0xCDuy; 0x45uy; 0x08uy; 0x36uy; 0x88uy;\n 0xB2uy; 0x18uy; 0xB1uy; 0xCDuy; 0xFAuy; 0x0Duy; 0xCBuy; 0xCBuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l\n\n\nlet test13_plaintext : lbytes 128 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy ] in\n assert_norm (FStar.List.length l = 128);\n of_list l\n\n\nlet test13_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l\n\n\nlet test13_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x72uy; 0x06uy; 0x5Euy; 0xE4uy; 0xDDuy; 0x91uy; 0xC2uy; 0xD8uy;\n 0x50uy; 0x9Fuy; 0xA1uy; 0xFCuy; 0x28uy; 0xA3uy; 0x7Cuy; 0x7Fuy;\n 0xC9uy; 0xFAuy; 0x7Duy; 0x5Buy; 0x3Fuy; 0x8Auy; 0xD3uy; 0xD0uy;\n 0xD7uy; 0xA2uy; 0x56uy; 0x26uy; 0xB5uy; 0x7Buy; 0x1Buy; 0x44uy;\n 0x78uy; 0x8Duy; 0x4Cuy; 0xAFuy; 0x80uy; 0x62uy; 0x90uy; 0x42uy;\n 0x5Fuy; 0x98uy; 0x90uy; 0xA3uy; 0xA2uy; 0xA3uy; 0x5Auy; 0x90uy;\n 0x5Auy; 0xB4uy; 0xB3uy; 0x7Auy; 0xCFuy; 0xD0uy; 0xDAuy; 0x6Euy;\n 0x45uy; 0x17uy; 0xB2uy; 0x52uy; 0x5Cuy; 0x96uy; 0x51uy; 0xE4uy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l\n\n\nlet test14_plaintext : lbytes 129 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy;\n 0x80uy ] in\n assert_norm (FStar.List.length l = 129);\n of_list l\n\n\nlet test14_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l\n\n\nlet test14_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x64uy; 0x47uy; 0x5Duy; 0xFEuy; 0x76uy; 0x00uy; 0xD7uy; 0x17uy;\n 0x1Buy; 0xEAuy; 0x0Buy; 0x39uy; 0x4Euy; 0x27uy; 0xC9uy; 0xB0uy;\n 0x0Duy; 0x8Euy; 0x74uy; 0xDDuy; 0x1Euy; 0x41uy; 0x6Auy; 0x79uy;\n 0x47uy; 0x36uy; 0x82uy; 0xADuy; 0x3Duy; 0xFDuy; 0xBBuy; 0x70uy;\n 0x66uy; 0x31uy; 0x55uy; 0x80uy; 0x55uy; 0xCFuy; 0xC8uy; 0xA4uy;\n 0x0Euy; 0x07uy; 0xBDuy; 0x01uy; 0x5Auy; 0x45uy; 0x40uy; 0xDCuy;\n 0xDEuy; 0xA1uy; 0x58uy; 0x83uy; 0xCBuy; 0xBFuy; 0x31uy; 0x41uy;\n 0x2Duy; 0xF1uy; 0xDEuy; 0x1Cuy; 0xD4uy; 0x15uy; 0x2Buy; 0x91uy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l\n\n\nlet test15_plaintext : lbytes 256 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8Auy; 0x8Buy; 0x8Cuy; 0x8Duy; 0x8Euy; 0x8Fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9Auy; 0x9Buy; 0x9Cuy; 0x9Duy; 0x9Euy; 0x9Fuy;\n 0xA0uy; 0xA1uy; 0xA2uy; 0xA3uy; 0xA4uy; 0xA5uy; 0xA6uy; 0xA7uy;\n 0xA8uy; 0xA9uy; 0xAAuy; 0xABuy; 0xACuy; 0xADuy; 0xAEuy; 0xAFuy;\n 0xB0uy; 0xB1uy; 0xB2uy; 0xB3uy; 0xB4uy; 0xB5uy; 0xB6uy; 0xB7uy;\n 0xB8uy; 0xB9uy; 0xBAuy; 0xBBuy; 0xBCuy; 0xBDuy; 0xBEuy; 0xBFuy;\n 0xC0uy; 0xC1uy; 0xC2uy; 0xC3uy; 0xC4uy; 0xC5uy; 0xC6uy; 0xC7uy;\n 0xC8uy; 0xC9uy; 0xCAuy; 0xCBuy; 0xCCuy; 0xCDuy; 0xCEuy; 0xCFuy;\n 0xD0uy; 0xD1uy; 0xD2uy; 0xD3uy; 0xD4uy; 0xD5uy; 0xD6uy; 0xD7uy;\n 0xD8uy; 0xD9uy; 0xDAuy; 0xDBuy; 0xDCuy; 0xDDuy; 0xDEuy; 0xDFuy;\n 0xE0uy; 0xE1uy; 0xE2uy; 0xE3uy; 0xE4uy; 0xE5uy; 0xE6uy; 0xE7uy;\n 0xE8uy; 0xE9uy; 0xEAuy; 0xEBuy; 0xECuy; 0xEDuy; 0xEEuy; 0xEFuy;\n 0xF0uy; 0xF1uy; 0xF2uy; 0xF3uy; 0xF4uy; 0xF5uy; 0xF6uy; 0xF7uy;\n 0xF8uy; 0xF9uy; 0xFAuy; 0xFBuy; 0xFCuy; 0xFDuy; 0xFEuy; 0xFFuy ] in\n assert_norm (FStar.List.length l = 256);\n of_list l\n\n\nlet test15_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l\n\n\nlet test15_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xB7uy; 0x20uy; 0x71uy; 0xE0uy; 0x96uy; 0x27uy; 0x7Euy; 0xDEuy;\n 0xBBuy; 0x8Euy; 0xE5uy; 0x13uy; 0x4Duy; 0xD3uy; 0x71uy; 0x49uy;\n 0x96uy; 0x30uy; 0x7Buy; 0xA3uy; 0xA5uy; 0x5Auy; 0xA4uy; 0x73uy;\n 0x3Duy; 0x41uy; 0x2Auy; 0xBBuy; 0xE2uy; 0x8Euy; 0x90uy; 0x9Euy;\n 0x10uy; 0xE5uy; 0x7Euy; 0x6Fuy; 0xBFuy; 0xB4uy; 0xEFuy; 0x53uy;\n 0xB3uy; 0xB9uy; 0x60uy; 0x51uy; 0x82uy; 0x94uy; 0xFFuy; 0x88uy;\n 0x9Auy; 0x90uy; 0x82uy; 0x92uy; 0x54uy; 0x41uy; 0x2Euy; 0x2Auy;\n 0x60uy; 0xB8uy; 0x5Auy; 0xDDuy; 0x07uy; 0xA3uy; 0x67uy; 0x4Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l\n\n\nlet test16_plaintext : lbytes 512 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8Auy; 0x8Buy; 0x8Cuy; 0x8Duy; 0x8Euy; 0x8Fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9Auy; 0x9Buy; 0x9Cuy; 0x9Duy; 0x9Euy; 0x9Fuy;\n 0xA0uy; 0xA1uy; 0xA2uy; 0xA3uy; 0xA4uy; 0xA5uy; 0xA6uy; 0xA7uy;\n 0xA8uy; 0xA9uy; 0xAAuy; 0xABuy; 0xACuy; 0xADuy; 0xAEuy; 0xAFuy;\n 0xB0uy; 0xB1uy; 0xB2uy; 0xB3uy; 0xB4uy; 0xB5uy; 0xB6uy; 0xB7uy;\n 0xB8uy; 0xB9uy; 0xBAuy; 0xBBuy; 0xBCuy; 0xBDuy; 0xBEuy; 0xBFuy;\n 0xC0uy; 0xC1uy; 0xC2uy; 0xC3uy; 0xC4uy; 0xC5uy; 0xC6uy; 0xC7uy;\n 0xC8uy; 0xC9uy; 0xCAuy; 0xCBuy; 0xCCuy; 0xCDuy; 0xCEuy; 0xCFuy;\n 0xD0uy; 0xD1uy; 0xD2uy; 0xD3uy; 0xD4uy; 0xD5uy; 0xD6uy; 0xD7uy;\n 0xD8uy; 0xD9uy; 0xDAuy; 0xDBuy; 0xDCuy; 0xDDuy; 0xDEuy; 0xDFuy;\n 0xE0uy; 0xE1uy; 0xE2uy; 0xE3uy; 0xE4uy; 0xE5uy; 0xE6uy; 0xE7uy;\n 0xE8uy; 0xE9uy; 0xEAuy; 0xEBuy; 0xECuy; 0xEDuy; 0xEEuy; 0xEFuy;\n 0xF0uy; 0xF1uy; 0xF2uy; 0xF3uy; 0xF4uy; 0xF5uy; 0xF6uy; 0xF7uy;\n 0xF8uy; 0xF9uy; 0xFAuy; 0xFBuy; 0xFCuy; 0xFDuy; 0xFEuy; 0xFFuy;\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy;\n 0x40uy; 0x41uy; 0x42uy; 0x43uy; 0x44uy; 0x45uy; 0x46uy; 0x47uy;\n 0x48uy; 0x49uy; 0x4Auy; 0x4Buy; 0x4Cuy; 0x4Duy; 0x4Euy; 0x4Fuy;\n 0x50uy; 0x51uy; 0x52uy; 0x53uy; 0x54uy; 0x55uy; 0x56uy; 0x57uy;\n 0x58uy; 0x59uy; 0x5Auy; 0x5Buy; 0x5Cuy; 0x5Duy; 0x5Euy; 0x5Fuy;\n 0x60uy; 0x61uy; 0x62uy; 0x63uy; 0x64uy; 0x65uy; 0x66uy; 0x67uy;\n 0x68uy; 0x69uy; 0x6Auy; 0x6Buy; 0x6Cuy; 0x6Duy; 0x6Euy; 0x6Fuy;\n 0x70uy; 0x71uy; 0x72uy; 0x73uy; 0x74uy; 0x75uy; 0x76uy; 0x77uy;\n 0x78uy; 0x79uy; 0x7Auy; 0x7Buy; 0x7Cuy; 0x7Duy; 0x7Euy; 0x7Fuy;\n 0x80uy; 0x81uy; 0x82uy; 0x83uy; 0x84uy; 0x85uy; 0x86uy; 0x87uy;\n 0x88uy; 0x89uy; 0x8Auy; 0x8Buy; 0x8Cuy; 0x8Duy; 0x8Euy; 0x8Fuy;\n 0x90uy; 0x91uy; 0x92uy; 0x93uy; 0x94uy; 0x95uy; 0x96uy; 0x97uy;\n 0x98uy; 0x99uy; 0x9Auy; 0x9Buy; 0x9Cuy; 0x9Duy; 0x9Euy; 0x9Fuy;\n 0xA0uy; 0xA1uy; 0xA2uy; 0xA3uy; 0xA4uy; 0xA5uy; 0xA6uy; 0xA7uy;\n 0xA8uy; 0xA9uy; 0xAAuy; 0xABuy; 0xACuy; 0xADuy; 0xAEuy; 0xAFuy;\n 0xB0uy; 0xB1uy; 0xB2uy; 0xB3uy; 0xB4uy; 0xB5uy; 0xB6uy; 0xB7uy;\n 0xB8uy; 0xB9uy; 0xBAuy; 0xBBuy; 0xBCuy; 0xBDuy; 0xBEuy; 0xBFuy;\n 0xC0uy; 0xC1uy; 0xC2uy; 0xC3uy; 0xC4uy; 0xC5uy; 0xC6uy; 0xC7uy;\n 0xC8uy; 0xC9uy; 0xCAuy; 0xCBuy; 0xCCuy; 0xCDuy; 0xCEuy; 0xCFuy;\n 0xD0uy; 0xD1uy; 0xD2uy; 0xD3uy; 0xD4uy; 0xD5uy; 0xD6uy; 0xD7uy;\n 0xD8uy; 0xD9uy; 0xDAuy; 0xDBuy; 0xDCuy; 0xDDuy; 0xDEuy; 0xDFuy;\n 0xE0uy; 0xE1uy; 0xE2uy; 0xE3uy; 0xE4uy; 0xE5uy; 0xE6uy; 0xE7uy;\n 0xE8uy; 0xE9uy; 0xEAuy; 0xEBuy; 0xECuy; 0xEDuy; 0xEEuy; 0xEFuy;\n 0xF0uy; 0xF1uy; 0xF2uy; 0xF3uy; 0xF4uy; 0xF5uy; 0xF6uy; 0xF7uy;\n 0xF8uy; 0xF9uy; 0xFAuy; 0xFBuy; 0xFCuy; 0xFDuy; 0xFEuy; 0xFFuy ] in\n assert_norm (FStar.List.length l = 512);\n of_list l\n\n\nlet test16_key : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy;\n 0x08uy; 0x09uy; 0x0Auy; 0x0Buy; 0x0Cuy; 0x0Duy; 0x0Euy; 0x0Fuy;\n 0x10uy; 0x11uy; 0x12uy; 0x13uy; 0x14uy; 0x15uy; 0x16uy; 0x17uy;\n 0x18uy; 0x19uy; 0x1Auy; 0x1Buy; 0x1Cuy; 0x1Duy; 0x1Euy; 0x1Fuy;\n 0x20uy; 0x21uy; 0x22uy; 0x23uy; 0x24uy; 0x25uy; 0x26uy; 0x27uy;\n 0x28uy; 0x29uy; 0x2Auy; 0x2Buy; 0x2Cuy; 0x2Duy; 0x2Euy; 0x2Fuy;\n 0x30uy; 0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x35uy; 0x36uy; 0x37uy;\n 0x38uy; 0x39uy; 0x3Auy; 0x3Buy; 0x3Cuy; 0x3Duy; 0x3Euy; 0x3Fuy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l\n\n\nlet test16_expected : lbytes 64 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x31uy; 0x95uy; 0x24uy; 0x78uy; 0xE1uy; 0xB6uy; 0x22uy; 0x9Buy;\n 0x6Buy; 0xCAuy; 0x29uy; 0x6Cuy; 0x64uy; 0x3Auy; 0x3Fuy; 0xDBuy;\n 0xE4uy; 0xAAuy; 0x2Cuy; 0x2Fuy; 0x7Fuy; 0xEAuy; 0x46uy; 0x66uy;\n 0x75uy; 0x45uy; 0x3Duy; 0x5Fuy; 0x7Fuy; 0x09uy; 0x42uy; 0x70uy;\n 0x21uy; 0xA7uy; 0x7Buy; 0x86uy; 0x25uy; 0xC7uy; 0x80uy; 0x70uy;\n 0xC0uy; 0xF7uy; 0xCEuy; 0x56uy; 0x4Duy; 0x8Duy; 0x25uy; 0x7Duy;\n 0x7Euy; 0xB3uy; 0x64uy; 0x95uy; 0xBEuy; 0x76uy; 0x95uy; 0x0Cuy;\n 0x31uy; 0xA1uy; 0xA7uy; 0xD8uy; 0x0Fuy; 0xF8uy; 0xB1uy; 0xB4uy ] in\n assert_norm (FStar.List.length l = 64);\n of_list l\n\n(* Parameters are not present in the Blake2 RFC, instead, they are specified in the Blake2 paper.\n Hence, there are no official test vectors corresponding to them. The tests below aim to\n cover the different possible parameters, and the results were generated using the Blake2\n implementation in Python 3's hashlib *)\n\nlet test17_params : S.blake2s_params =\n { S.blake2s_default_params with fanout = u8 5; node_depth = u8 3 }\n\nlet test17_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xA7uy; 0x4Euy; 0xDBuy; 0x2Duy; 0x8Fuy; 0xBBuy; 0x84uy; 0xFBuy;\n 0x83uy; 0xEDuy; 0x64uy; 0x06uy; 0x82uy; 0x28uy; 0x7Cuy; 0x92uy;\n 0x6Auy; 0xF5uy; 0xC3uy; 0x04uy; 0x09uy; 0xD1uy; 0xA8uy; 0xD4uy;\n 0x66uy; 0x2Duy; 0x4Fuy; 0x34uy; 0xEBuy; 0xC4uy; 0xA0uy; 0x7Fuy\n ] in\n assert_norm (List.Tot.length l = 32);\n of_list l\n\nlet test18_params : S.blake2s_params =\n { S.blake2s_default_params with leaf_length = u32 43; depth = u8 4; inner_length = u8 9 }\n\nlet test18_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0x68uy; 0x1Auy; 0xDCuy; 0x05uy; 0x69uy; 0xD8uy; 0xE9uy; 0x1Buy;\n 0x36uy; 0xDFuy; 0x5Fuy; 0x1Duy; 0x85uy; 0x64uy; 0x42uy; 0x2Fuy;\n 0x4Duy; 0x79uy; 0xD7uy; 0x31uy; 0xCBuy; 0x7Duy; 0xBCuy; 0xB7uy;\n 0xC8uy; 0xEBuy; 0xB4uy; 0x80uy; 0xA6uy; 0xCEuy; 0x3Buy; 0x91uy\n ] in\n assert_norm (List.Tot.length l = 32);\n of_list l\n\nlet test19_params : S.blake2s_params =\n let s = create 8 (u8_from_UInt8 0x11uy) in\n { S.blake2s_default_params with salt = s; personal = s }\n\nlet test19_expected : lbytes 32 =\n let l = List.Tot.map u8_from_UInt8 [\n 0xD3uy; 0x93uy; 0xA6uy; 0xDEuy; 0xB6uy; 0xE3uy; 0x98uy; 0xB3uy;\n 0x46uy; 0x11uy; 0xF0uy; 0x82uy; 0xCBuy; 0x2Fuy; 0xC0uy; 0x2Buy;\n 0x5Cuy; 0xE1uy; 0x3Buy; 0xF7uy; 0x0Cuy; 0x64uy; 0x70uy; 0xD2uy;\n 0x64uy; 0x1Fuy; 0x3Auy; 0xD1uy; 0x48uy; 0x93uy; 0xF5uy; 0x8Buy\n ] in\n assert_norm (List.Tot.length l = 32);\n of_list l\n" }, { "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.buffer_readable", "opens_and_abbrevs": [ { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "abbrev": "DM", "full_module": "FStar.DependentMap" }, { "open": "FStar.HyperStack.ST" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "abbrev": "HH", "full_module": "FStar.HyperStack" }, { "open": "FStar.Pointer" }, { "open": "FStar.Pointer" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 1, "max_fuel": 1, "initial_ifuel": 1, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 16, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val buffer_readable\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: GTot Type0", "source_definition": "let buffer_readable\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: GTot Type0\n= buffer_readable' h b", "source_range": { "start_line": 2982, "start_col": 0, "end_line": 2987, "end_col": 22 }, "interleaved": false, "definition": "fun h b -> FStar.Pointer.Base.buffer_readable' h b <: Prims.GTot Type0", "effect": "Prims.GTot", "effect_flags": [ "sometrivial" ], "mutual_with": [], "premises": [ "FStar.Pointer.Base.typ", "FStar.Monotonic.HyperStack.mem", "FStar.Pointer.Base.buffer", "FStar.Pointer.Base.buffer_readable'" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": true, "type": "h: FStar.Monotonic.HyperStack.mem -> b: FStar.Pointer.Base.buffer t -> Prims.GTot Type0", "prompt": "let buffer_readable (#t: typ) (h: HS.mem) (b: buffer t) : GTot Type0 =\n ", "expected_response": "buffer_readable' h b", "source": { "project_name": "FStar", "file_name": "ulib/legacy/FStar.Pointer.Base.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.Pointer.Base.fst", "checked_file": "dataset/FStar.Pointer.Base.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.UInt8.fsti.checked", "dataset/FStar.UInt64.fsti.checked", "dataset/FStar.UInt32.fsti.checked", "dataset/FStar.UInt16.fsti.checked", "dataset/FStar.StrongExcludedMiddle.fst.checked", "dataset/FStar.Squash.fsti.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.ModifiesGen.fsti.checked", "dataset/FStar.Map.fsti.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.Int8.fsti.checked", "dataset/FStar.Int64.fsti.checked", "dataset/FStar.Int32.fsti.checked", "dataset/FStar.Int16.fsti.checked", "dataset/FStar.HyperStack.ST.fsti.checked", "dataset/FStar.HyperStack.fst.checked", "dataset/FStar.Heap.fst.checked", "dataset/FStar.DependentMap.fsti.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Char.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "", "", "", "base_typ", "TUInt", "TUInt", "TUInt", "TUInt8", "TUInt8", "TUInt8", "TUInt16", "TUInt16", "TUInt16", "TUInt32", "TUInt32", "TUInt32", "TUInt64", "TUInt64", "TUInt64", "TInt", "TInt", "TInt", "TInt8", "TInt8", "TInt8", "TInt16", "TInt16", "TInt16", "TInt32", "TInt32", "TInt32", "step", "TInt64", "TInt64", "TInt64", "StepField", "StepField", "StepField", "TChar", "TChar", "TChar", "l", "l", "TBool", "TBool", "TBool", "fd", "fd", "TUnit", "TUnit", "TUnit", "StepUField", "StepUField", "StepUField", "l", "l", "array_length_t", "fd", "fd", "typ", "StepCell", "StepCell", "StepCell", "TBase", "TBase", "TBase", "length", "length", "b", "b", "value", "value", "index", "index", "TStruct", "TStruct", "TStruct", "l", "l", "path", "TUnion", "TUnion", "TUnion", "PathBase", "PathBase", "PathBase", "l", "l", "PathStep", "PathStep", "PathStep", "TArray", "TArray", "TArray", "through", "through", "length", "length", "to", "to", "t", "t", "p", "p", "s", "s", "TPointer", "TPointer", "TPointer", "t", "t", "let step_typ_depth\n (#from #to: typ)\n (s: step from to)\n: Lemma\n (typ_depth from > typ_depth to)\n= match s with\n | StepUField l fd\n | StepField l fd ->\n typ_depth_typ_of_struct_field l.fields fd\n | _ -> ()", "TNPointer", "TNPointer", "TNPointer", "t", "t", "TBuffer", "TBuffer", "TBuffer", "t", "t", "struct_typ'", "struct_typ", "struct_typ", "let rec path_typ_depth\n (#from #to: typ)\n (p: path from to)\n: Lemma\n (ensures (\n typ_depth from >= typ_depth to /\\ (\n (~ (PathBase? p)) ==> typ_depth from <> typ_depth to\n )))\n (decreases p)\n= match p with\n | PathBase -> ()\n | PathStep _ _ p' s ->\n path_typ_depth p';\n step_typ_depth s", "name", "name", "fields", "fields", "union_typ", "let struct_field'\n (l: struct_typ')\n: Tot eqtype\n= (s: string { List.Tot.mem s (List.Tot.map fst l) } )", "let struct_field\n (l: struct_typ)\n: Tot eqtype\n= struct_field' l.fields", "let union_field = struct_field", "let typ_of_struct_field'\n (l: struct_typ')\n (f: struct_field' l)\n: Tot (t: typ {t << l})\n= List.Tot.assoc_mem f l;\n let y = Some?.v (List.Tot.assoc f l) in\n List.Tot.assoc_precedes f l y;\n y", "let typ_of_struct_field\n (l: struct_typ)\n (f: struct_field l)\n: Tot (t: typ {t << l})\n= typ_of_struct_field' l.fields f", "_npointer", "Pointer", "Pointer", "Pointer", "from", "from", "contents", "contents", "let typ_of_union_field\n (l: union_typ)\n (f: union_field l)\n: Tot (t: typ {t << l})\n= typ_of_struct_field l f", "p", "p", "NullPtr", "NullPtr", "NullPtr", "let npointer (t: typ): Tot Type0 =\n _npointer t", "let rec typ_depth\n (t: typ)\n: GTot nat\n= match t with\n | TArray _ t -> 1 + typ_depth t\n | TUnion l\n | TStruct l -> 1 + struct_typ_depth l.fields\n | _ -> 0\nand struct_typ_depth\n (l: list (string * typ))\n: GTot nat\n= match l with\n | [] -> 0\n | h :: l ->\n let (_, t) = h in // matching like this prevents needing two units of ifuel\n let n1 = typ_depth t in\n let n2 = struct_typ_depth l in\n if n1 > n2 then n1 else n2", "let rec typ_depth\n (t: typ)\n: GTot nat\n= match t with\n | TArray _ t -> 1 + typ_depth t\n | TUnion l\n | TStruct l -> 1 + struct_typ_depth l.fields\n | _ -> 0\nand struct_typ_depth\n (l: list (string * typ))\n: GTot nat\n= match l with\n | [] -> 0\n | h :: l ->\n let (_, t) = h in // matching like this prevents needing two units of ifuel\n let n1 = typ_depth t in\n let n2 = struct_typ_depth l in\n if n1 > n2 then n1 else n2", "let nullptr (#t: typ): Tot (npointer t) = NullPtr", "let g_is_null (#t: typ) (p: npointer t) : GTot bool =\n match p with\n | NullPtr -> true\n | _ -> false", "let g_is_null_intro\n (t: typ)\n: Lemma\n (g_is_null (nullptr #t) == true)\n= ()", "let not_an_array_cell (#t: typ) (p: pointer t) : GTot bool =\n match Pointer?.p p with\n | PathStep _ _ _ (StepCell _ _ _) -> false\n | _ -> true", "let rec typ_depth_typ_of_struct_field\n (l: struct_typ')\n (f: struct_field' l)\n: Lemma\n (ensures (typ_depth (typ_of_struct_field' l f) <= struct_typ_depth l))\n (decreases l)\n= let ((f', _) :: l') = l in\n if f = f'\n then ()\n else begin\n let f: string = f in\n assert (List.Tot.mem f (List.Tot.map fst l'));\n List.Tot.assoc_mem f l';\n typ_depth_typ_of_struct_field l' f\n end", "buffer_root", "BufferRootSingleton", "BufferRootSingleton", "BufferRootSingleton", "p", "p", "BufferRootArray", "BufferRootArray", "BufferRootArray", "max_length", "max_length", "p", "p", "let buffer_root_length (#t: typ) (b: buffer_root t): Tot UInt32.t = match b with\n| BufferRootSingleton _ -> 1ul\n| BufferRootArray #_ #len _ -> len", "_buffer", "Buffer", "Buffer", "Buffer", "broot", "broot", "bidx", "bidx", "blength", "blength", "let buffer (t: typ): Tot Type0 = _buffer t", "val npointer (t: typ) : Tot Type0", "val nullptr (#t: typ): Tot (npointer t)", "val g_is_null (#t: typ) (p: npointer t) : GTot bool", "val g_is_null_intro\n (t: typ)\n: Lemma\n (g_is_null (nullptr #t) == true)\n [SMTPat (g_is_null (nullptr #t))]", "let gtdata (* ghostly-tagged data *)\n (key: eqtype)\n (value: (key -> Tot Type0))\n: Tot Type0\n= ( k: key & value k )", "let pointer (t: typ) : Tot Type0 = (p: npointer t { g_is_null p == false } )", "let _gtdata_get_key\n (#key: eqtype)\n (#value: (key -> Tot Type0))\n (u: gtdata key value)\n: Tot key\n= dfst u", "val buffer (t: typ): Tot Type0", "let gtdata_get_key\n (#key: eqtype)\n (#value: (key -> Tot Type0))\n (u: gtdata key value)\n: GTot key // important: must be Ghost, the tag is not actually stored in memory\n= _gtdata_get_key u", "let type_of_base_typ\n (t: base_typ)\n: Tot Type0\n= match t with\n | TUInt -> nat\n | TUInt8 -> FStar.UInt8.t\n | TUInt16 -> FStar.UInt16.t\n | TUInt32 -> FStar.UInt32.t\n | TUInt64 -> FStar.UInt64.t\n | TInt -> int\n | TInt8 -> FStar.Int8.t\n | TInt16 -> FStar.Int16.t\n | TInt32 -> FStar.Int32.t\n | TInt64 -> FStar.Int64.t\n | TChar -> FStar.Char.char\n | TBool -> bool\n | TUnit -> unit", "let gtdata_get_value\n (#key: eqtype)\n (#value: (key -> Tot Type0))\n (u: gtdata key value)\n (k: key)\n: Pure (value k)\n (requires (gtdata_get_key u == k))\n (ensures (fun _ -> True))\n= let (| _, v |) = u in v", "let gtdata_create\n (#key: eqtype)\n (#value: (key -> Tot Type0))\n (k: key)\n (v: value k)\n: Pure (gtdata key value)\n (requires True)\n (ensures (fun x -> gtdata_get_key x == k /\\ gtdata_get_value x k == v))\n= (| k, v |)", "array", "let type_of_struct_field''\n (l: struct_typ')\n (type_of_typ: (\n (t: typ { t << l } ) ->\n Tot Type0\n ))\n (f: struct_field' l)\n: Tot Type0 =\n List.Tot.assoc_mem f l;\n let y = typ_of_struct_field' l f in\n List.Tot.assoc_precedes f l y;\n type_of_typ y", "let gtdata_extensionality\n (#key: eqtype)\n (#value: (key -> Tot Type0))\n (u1 u2: gtdata key value)\n: Lemma\n (requires (\n let k = gtdata_get_key u1 in (\n k == gtdata_get_key u2 /\\\n gtdata_get_value u1 k == gtdata_get_value u2 k\n )))\n (ensures (u1 == u2))\n= ()", "let type_of_struct_field'\n (l: struct_typ)\n (type_of_typ: (\n (t: typ { t << l } ) ->\n Tot Type0\n ))\n (f: struct_field l)\n: Tot Type0\n= type_of_struct_field'' l.fields type_of_typ f", "let rec type_of_typ'\n (t: typ)\n: Tot Type0\n= match t with\n | TBase b -> type_of_base_typ b\n | TStruct l ->\n struct l\n | TUnion l ->\n union l\n | TArray length t ->\n array length (type_of_typ' t)\n | TPointer t ->\n pointer t\n | TNPointer t ->\n npointer t\n | TBuffer t ->\n buffer t\nand struct (l: struct_typ) : Tot Type0 =\n DM.t (struct_field l) (type_of_struct_field' l (fun x -> type_of_typ' x))\nand union (l: union_typ) : Tot Type0 =\n gtdata (struct_field l) (type_of_struct_field' l (fun x -> type_of_typ' x))", "let rec type_of_typ'\n (t: typ)\n: Tot Type0\n= match t with\n | TBase b -> type_of_base_typ b\n | TStruct l ->\n struct l\n | TUnion l ->\n union l\n | TArray length t ->\n array length (type_of_typ' t)\n | TPointer t ->\n pointer t\n | TNPointer t ->\n npointer t\n | TBuffer t ->\n buffer t\nand struct (l: struct_typ) : Tot Type0 =\n DM.t (struct_field l) (type_of_struct_field' l (fun x -> type_of_typ' x))\nand union (l: union_typ) : Tot Type0 =\n gtdata (struct_field l) (type_of_struct_field' l (fun x -> type_of_typ' x))", "let rec type_of_typ'\n (t: typ)\n: Tot Type0\n= match t with\n | TBase b -> type_of_base_typ b\n | TStruct l ->\n struct l\n | TUnion l ->\n union l\n | TArray length t ->\n array length (type_of_typ' t)\n | TPointer t ->\n pointer t\n | TNPointer t ->\n npointer t\n | TBuffer t ->\n buffer t\nand struct (l: struct_typ) : Tot Type0 =\n DM.t (struct_field l) (type_of_struct_field' l (fun x -> type_of_typ' x))\nand union (l: union_typ) : Tot Type0 =\n gtdata (struct_field l) (type_of_struct_field' l (fun x -> type_of_typ' x))", "val struct (l: struct_typ) : Tot Type0", "val union (l: union_typ) : Tot Type0", "let rec type_of_typ\n (t: typ)\n: Tot Type0\n= match t with\n | TBase b -> type_of_base_typ b\n | TStruct l ->\n struct l\n | TUnion l ->\n union l\n | TArray length t ->\n array length (type_of_typ t)\n | TPointer t ->\n pointer t\n | TNPointer t ->\n npointer t\n | TBuffer t ->\n buffer t", "let rec type_of_typ'_eq (t: typ) : Lemma (type_of_typ' t == type_of_typ t)\n [SMTPat (type_of_typ t)]\n=\n match t with\n | TArray _ t' -> type_of_typ'_eq t'\n | TPointer t' -> type_of_typ'_eq t'\n | TNPointer t' -> type_of_typ'_eq t'\n | TBuffer t' -> type_of_typ'_eq t'\n | _ -> ()", "let type_of_typ_array\n (len: array_length_t)\n (t: typ)\n: Lemma\n (type_of_typ (TArray len t) == array len (type_of_typ t))\n [SMTPat (type_of_typ (TArray len t))]\n= ()", "let _union_get_key (#l: union_typ) (v: union l) : Tot (struct_field l) = _gtdata_get_key v", "let struct_sel (#l: struct_typ) (s: struct l) (f: struct_field l) : Tot (type_of_struct_field l f) =\n DM.sel s f", "let type_of_struct_field\n (l: struct_typ)\n: Tot (struct_field l -> Tot Type0)\n= type_of_struct_field' l (fun (x:typ{x << l}) -> type_of_typ x)", "let struct_upd (#l: struct_typ) (s: struct l) (f: struct_field l) (v: type_of_struct_field l f) : Tot (struct l) =\n DM.upd s f v", "let type_of_typ_struct\n (l: struct_typ)\n: Lemma\n (type_of_typ (TStruct l) == struct l)\n [SMTPat (type_of_typ (TStruct l))]\n= assert_norm (type_of_typ (TStruct l) == struct l)", "let struct_create_fun (l: struct_typ) (f: ((fd: struct_field l) -> Tot (type_of_struct_field l fd))) : Tot (struct l) =\n DM.create #(struct_field l) #(type_of_struct_field' l (fun x -> type_of_typ' x)) f", "let struct_sel_struct_create_fun l f fd = ()", "let union_get_key (#l: union_typ) (v: union l) : GTot (struct_field l) = gtdata_get_key v", "let type_of_typ_type_of_struct_field\n (l: struct_typ)\n (f: struct_field l)\n: Lemma\n (type_of_typ (typ_of_struct_field l f) == type_of_struct_field l f)\n [SMTPat (type_of_typ (typ_of_struct_field l f))]\n= ()", "let union_get_value #l v fd = gtdata_get_value v fd", "let union_create l fd v = gtdata_create fd v", "val struct_sel (#l: struct_typ) (s: struct l) (f: struct_field l) : Tot (type_of_struct_field l f)", "let rec dummy_val\n (t: typ)\n: Tot (type_of_typ t)\n= match t with\n | TBase b ->\n begin match b with\n | TUInt -> 0\n | TUInt8 -> UInt8.uint_to_t 0\n | TUInt16 -> UInt16.uint_to_t 0\n | TUInt32 -> UInt32.uint_to_t 0\n | TUInt64 -> UInt64.uint_to_t 0\n | TInt -> 0\n | TInt8 -> Int8.int_to_t 0\n | TInt16 -> Int16.int_to_t 0\n | TInt32 -> Int32.int_to_t 0\n | TInt64 -> Int64.int_to_t 0\n | TChar -> 'c'\n | TBool -> false\n | TUnit -> ()\n end\n | TStruct l ->\n struct_create_fun l (fun f -> (\n dummy_val (typ_of_struct_field l f)\n ))\n | TUnion l ->\n let dummy_field : string = List.Tot.hd (List.Tot.map fst l.fields) in\n union_create l dummy_field (dummy_val (typ_of_struct_field l dummy_field))\n | TArray length t -> Seq.create (UInt32.v length) (dummy_val t)\n | TPointer t -> Pointer t HS.dummy_aref PathBase\n | TNPointer t -> NullPtr #t\n | TBuffer t -> Buffer (BufferRootSingleton (Pointer t HS.dummy_aref PathBase)) 0ul 1ul", "let dfst_struct_field\n (s: struct_typ)\n (p: (x: struct_field s & type_of_struct_field s x))\n: Tot string\n=\n let (| f, _ |) = p in\n f", "let struct_literal (s: struct_typ) : Tot Type0 = list (x: struct_field s & type_of_struct_field s x)", "let struct_literal_wf (s: struct_typ) (l: struct_literal s) : Tot bool =\n List.Tot.sortWith FStar.String.compare (List.Tot.map fst s.fields) =\n List.Tot.sortWith FStar.String.compare\n (List.Tot.map (dfst_struct_field s) l)", "let fun_of_list\n (s: struct_typ)\n (l: struct_literal s)\n (f: struct_field s)\n: Pure (type_of_struct_field s f)\n (requires (normalize_term (struct_literal_wf s l) == true))\n (ensures (fun _ -> True))\n=\n let f' : string = f in\n let phi (p: (x: struct_field s & type_of_struct_field s x)) : Tot bool =\n dfst_struct_field s p = f'\n in\n match List.Tot.find phi l with\n | Some p -> let (| _, v |) = p in v\n | _ ->\n List.Tot.sortWith_permutation FStar.String.compare (List.Tot.map fst s.fields);\n List.Tot.sortWith_permutation FStar.String.compare (List.Tot.map (dfst_struct_field s) l);\n List.Tot.mem_memP f' (List.Tot.map fst s.fields);\n List.Tot.mem_count (List.Tot.map fst s.fields) f';\n List.Tot.mem_count (List.Tot.map (dfst_struct_field s) l) f';\n List.Tot.mem_memP f' (List.Tot.map (dfst_struct_field s) l);\n List.Tot.memP_map_elim (dfst_struct_field s) f' l;\n Classical.forall_intro (Classical.move_requires (List.Tot.find_none phi l));\n false_elim ()", "val struct_create_fun (l: struct_typ) (f: ((fd: struct_field l) -> Tot (type_of_struct_field l fd))) : Tot (struct l)", "let struct_create\n (s: struct_typ)\n (l: struct_literal s)\n: Pure (struct s)\n (requires (normalize_term (struct_literal_wf s l) == true))\n (ensures (fun _ -> True))\n= struct_create_fun s (fun_of_list s l)", "val struct_sel_struct_create_fun\n (l: struct_typ)\n (f: ((fd: struct_field l) -> Tot (type_of_struct_field l fd)))\n (fd: struct_field l)\n: Lemma\n (struct_sel (struct_create_fun l f) fd == f fd)\n [SMTPat (struct_sel (struct_create_fun l f) fd)]", "let rec otype_of_typ\n (t: typ)\n: Tot Type0\n= match t with\n | TBase b -> option (type_of_base_typ b)\n | TStruct l ->\n option (DM.t (struct_field l) (type_of_struct_field' l otype_of_typ))\n | TUnion l ->\n option (gtdata (struct_field l) (type_of_struct_field' l otype_of_typ))\n | TArray length t ->\n option (array length (otype_of_typ t))\n | TPointer t ->\n option (pointer t)\n | TNPointer t ->\n option (npointer t)\n | TBuffer t ->\n option (buffer t)", "let type_of_typ_union\n (l: union_typ)\n: Lemma\n (type_of_typ (TUnion l) == union l)\n [SMTPat (type_of_typ (TUnion l))]\n= assert_norm (type_of_typ (TUnion l) == union l)", "val union_get_key (#l: union_typ) (v: union l) : GTot (struct_field l)", "val union_get_value\n (#l: union_typ)\n (v: union l)\n (fd: struct_field l)\n: Pure (type_of_struct_field l fd)\n (requires (union_get_key v == fd))\n (ensures (fun _ -> True))", "let otype_of_struct_field\n (l: struct_typ)\n: Tot (struct_field l -> Tot Type0)\n= type_of_struct_field' l otype_of_typ", "val union_create\n (l: union_typ)\n (fd: struct_field l)\n (v: type_of_struct_field l fd)\n: Tot (union l)", "let otype_of_typ_otype_of_struct_field\n (l: struct_typ)\n (f: struct_field l)\n: Lemma\n (otype_of_typ (typ_of_struct_field l f) == otype_of_struct_field l f)\n [SMTPat (type_of_typ (typ_of_struct_field l f))]\n= ()", "val equal\n (#t1 #t2: typ)\n (p1: pointer t1)\n (p2: pointer t2)\n: Ghost bool\n (requires True)\n (ensures (fun b -> b == true <==> t1 == t2 /\\ p1 == p2 ))", "let otype_of_typ_base\n (b: base_typ)\n: Lemma\n (otype_of_typ (TBase b) == option (type_of_base_typ b))\n [SMTPat (otype_of_typ (TBase b))]\n= ()", "val as_addr (#t: typ) (p: pointer t): GTot (x: nat { x > 0 } )", "let otype_of_typ_array\n (len: array_length_t )\n (t: typ)\n: Lemma\n (otype_of_typ (TArray len t) == option (array len (otype_of_typ t)))\n [SMTPat (otype_of_typ (TArray len t))]\n= ()", "val unused_in\n (#value: typ)\n (p: pointer value)\n (h: HS.mem)\n: GTot Type0", "val live\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n: GTot Type0", "let ostruct (l: struct_typ) = option (DM.t (struct_field l) (otype_of_struct_field l))", "let ostruct_sel (#l: struct_typ) (s: ostruct l { Some? s }) (f: struct_field l) : Tot (otype_of_struct_field l f) =\n DM.sel (Some?.v s) f", "let ostruct_upd (#l: struct_typ) (s: ostruct l { Some? s }) (f: struct_field l) (v: otype_of_struct_field l f) : Tot (s': ostruct l { Some? s' } ) =\n Some (DM.upd (Some?.v s) f v)", "val nlive\n (#value: typ)\n (h: HS.mem)\n (p: npointer value)\n: GTot Type0", "let ostruct_create (l: struct_typ) (f: ((fd: struct_field l) -> Tot (otype_of_struct_field l fd))) : Tot (s': ostruct l { Some? s' } ) =\n Some (DM.create #(struct_field l) #(otype_of_struct_field l) f)", "let otype_of_typ_struct\n (l: struct_typ)\n: Lemma\n (otype_of_typ (TStruct l) == ostruct l)\n [SMTPat (otype_of_typ (TStruct l))]\n= assert_norm(otype_of_typ (TStruct l) == ostruct l)", "val live_nlive\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n: Lemma\n (nlive h p <==> live h p)\n [SMTPat (nlive h p)]", "let ounion (l: struct_typ) = option (gtdata (struct_field l) (otype_of_struct_field l))", "val g_is_null_nlive\n (#t: typ)\n (h: HS.mem)\n (p: npointer t)\n: Lemma\n (requires (g_is_null p))\n (ensures (nlive h p))\n [SMTPat (g_is_null p); SMTPat (nlive h p)]", "let ounion_get_key (#l: union_typ) (v: ounion l { Some? v } ) : Tot (struct_field l) = _gtdata_get_key (Some?.v v)", "let ounion_get_value\n (#l: union_typ)\n (v: ounion l { Some? v } )\n (fd: struct_field l)\n: Pure (otype_of_struct_field l fd)\n (requires (ounion_get_key v == fd))\n (ensures (fun _ -> True))\n= gtdata_get_value (Some?.v v) fd", "val live_not_unused_in\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n: Lemma\n (ensures (live h p /\\ p `unused_in` h ==> False))\n [SMTPat (live h p); SMTPat (p `unused_in` h)]", "let ounion_create\n (l: union_typ)\n (fd: struct_field l)\n (v: otype_of_struct_field l fd)\n: Tot (ounion l)\n= Some (gtdata_create fd v)", "val gread\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n: GTot (type_of_typ value)", "let otype_of_typ_union\n (l: union_typ)\n: Lemma\n (otype_of_typ (TUnion l) == ounion l)\n [SMTPat (otype_of_typ (TUnion l))]\n= assert_norm (otype_of_typ (TUnion l) == ounion l)", "val frameOf\n (#value: typ)\n (p: pointer value)\n: GTot HS.rid", "let struct_field_is_readable\n (l: struct_typ)\n (ovalue_is_readable: (\n (t: typ) ->\n (v: otype_of_typ t) ->\n Pure bool\n (requires (t << l))\n (ensures (fun _ -> True))\n ))\n (v: ostruct l { Some? v } )\n (s: string)\n: Tot bool\n= if List.Tot.mem s (List.Tot.map fst l.fields)\n then ovalue_is_readable (typ_of_struct_field l s) (ostruct_sel v s)\n else true", "val live_region_frameOf\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n: Lemma\n (requires (live h p))\n (ensures (HS.live_region h (frameOf p)))\n [SMTPatOr [\n [SMTPat (HS.live_region h (frameOf p))];\n [SMTPat (live h p)]\n ]]", "val disjoint_roots_intro_pointer_vs_pointer\n (#value1 value2: typ)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: pointer value2)\n: Lemma\n (requires (live h p1 /\\ unused_in p2 h))\n (ensures (frameOf p1 <> frameOf p2 \\/ as_addr p1 =!= as_addr p2))", "let rec ovalue_is_readable\n (t: typ)\n (v: otype_of_typ t)\n: Tot bool\n (decreases t)\n= match t with\n | TStruct l ->\n let (v: ostruct l) = v in\n Some? v && (\n let keys = List.Tot.map fst l.fields in\n let pred\n (t': typ)\n (v: otype_of_typ t')\n : Pure bool\n (requires (t' << l))\n (ensures (fun _ -> True))\n = ovalue_is_readable t' v\n in\n List.Tot.for_all (struct_field_is_readable l pred v) keys\n )\n | TUnion l ->\n let v : ounion l = v in\n Some? v && (\n let k = ounion_get_key v in\n ovalue_is_readable (typ_of_struct_field l k) (ounion_get_value v k)\n )\n | TArray len t ->\n let (v: option (array len (otype_of_typ t))) = v in\n Some? v &&\n Seq.for_all (ovalue_is_readable t) (Some?.v v)\n | TBase t ->\n let (v: option (type_of_base_typ t)) = v in\n Some? v\n | TPointer t ->\n let (v: option (pointer t)) = v in\n Some? v\n | TNPointer t ->\n let (v: option (npointer t)) = v in\n Some? v\n | TBuffer t ->\n let (v: option (buffer t)) = v in\n Some? v", "val disjoint_roots_intro_pointer_vs_reference\n (#value1: typ)\n (#value2: Type)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: HS.reference value2)\n: Lemma\n (requires (live h p1 /\\ p2 `HS.unused_in` h))\n (ensures (frameOf p1 <> HS.frameOf p2 \\/ as_addr p1 =!= HS.as_addr p2))", "val disjoint_roots_intro_reference_vs_pointer\n (#value1: Type)\n (#value2: typ)\n (h: HS.mem)\n (p1: HS.reference value1)\n (p2: pointer value2)\n: Lemma\n (requires (HS.contains h p1 /\\ p2 `unused_in` h))\n (ensures (HS.frameOf p1 <> frameOf p2 \\/ HS.as_addr p1 =!= as_addr p2))", "val is_mm\n (#value: typ)\n (p: pointer value)\n: GTot bool", "val gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n: GTot (pointer (typ_of_struct_field l fd))", "let ovalue_is_readable_struct_intro'\n (l: struct_typ)\n (v: otype_of_typ (TStruct l))\n: Lemma\n (requires (\n let (v: ostruct l) = v in (\n Some? v /\\\n List.Tot.for_all (struct_field_is_readable l (fun x y -> ovalue_is_readable x y) v) (List.Tot.map fst l.fields)\n )))\n (ensures (ovalue_is_readable (TStruct l) v))\n= assert_norm (ovalue_is_readable (TStruct l) v == true)", "val as_addr_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (as_addr (gfield p fd) == as_addr p))\n [SMTPat (as_addr (gfield p fd))]", "let ovalue_is_readable_struct_intro\n (l: struct_typ)\n (v: otype_of_typ (TStruct l))\n: Lemma\n (requires (\n let (v: ostruct l) = v in (\n Some? v /\\ (\n forall (f: struct_field l) .\n ovalue_is_readable (typ_of_struct_field l f) (ostruct_sel v f)\n ))))\n (ensures (ovalue_is_readable (TStruct l) v))\n= List.Tot.for_all_mem (struct_field_is_readable l (fun x y -> ovalue_is_readable x y) v) (List.Tot.map fst l.fields);\n ovalue_is_readable_struct_intro' l v", "val unused_in_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n (h: HS.mem)\n: Lemma\n (requires True)\n (ensures (unused_in (gfield p fd) h <==> unused_in p h))\n [SMTPat (unused_in (gfield p fd) h)]", "val live_gfield\n (h: HS.mem)\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (live h (gfield p fd) <==> live h p))\n [SMTPat (live h (gfield p fd))]", "let ovalue_is_readable_struct_elim\n (l: struct_typ)\n (v: otype_of_typ (TStruct l))\n (fd: struct_field l)\n: Lemma\n (requires (ovalue_is_readable (TStruct l) v))\n (ensures (\n let (v: ostruct l) = v in (\n Some? v /\\\n ovalue_is_readable (typ_of_struct_field l fd) (ostruct_sel v fd)\n )))\n [SMTPat (ovalue_is_readable (typ_of_struct_field l fd) (ostruct_sel v fd))]\n= let (v: ostruct l) = v in\n assert_norm (ovalue_is_readable (TStruct l) v == List.Tot.for_all (struct_field_is_readable l (fun x y -> ovalue_is_readable x y) v) (List.Tot.map fst l.fields));\n assert (List.Tot.for_all (struct_field_is_readable l (fun x y -> ovalue_is_readable x y) v) (List.Tot.map fst l.fields));\n List.Tot.for_all_mem (struct_field_is_readable l (fun x y -> ovalue_is_readable x y) v) (List.Tot.map fst l.fields);\n assert (ovalue_is_readable (typ_of_struct_field l fd) (ostruct_sel v fd))", "val gread_gfield\n (h: HS.mem)\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (gread h (gfield p fd) == struct_sel (gread h p) fd))\n [SMTPatOr [[SMTPat (gread h (gfield p fd))]; [SMTPat (struct_sel (gread h p) fd)]]]", "val frameOf_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (frameOf (gfield p fd) == frameOf p))\n [SMTPat (frameOf (gfield p fd))]", "let ovalue_is_readable_array_elim\n (#len: array_length_t )\n (#t: typ)\n (v: otype_of_typ (TArray len t))\n (i: UInt32.t { UInt32.v i < UInt32.v len } )\n: Lemma\n (requires (ovalue_is_readable (TArray len t) v))\n (ensures (\n let (v: option (array len (otype_of_typ t))) = v in (\n Some? v /\\\n ovalue_is_readable t (Seq.index (Some?.v v) (UInt32.v i))\n )))\n= ()", "val is_mm_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (is_mm (gfield p fd) <==> is_mm p))\n [SMTPat (is_mm (gfield p fd))]", "let ovalue_is_readable_array_intro\n (#len: array_length_t )\n (#t: typ)\n (v: otype_of_typ (TArray len t))\n: Lemma\n (requires (\n let (v: option (array len (otype_of_typ t))) = v in (\n Some? v /\\ (\n forall (i: UInt32.t { UInt32.v i < UInt32.v len } ) .\n ovalue_is_readable t (Seq.index (Some?.v v) (UInt32.v i))\n ))))\n (ensures (ovalue_is_readable (TArray len t) v))\n= let (v: option (array len (otype_of_typ t))) = v in\n let (v: array len (otype_of_typ t)) = Some?.v v in\n let f\n (i: nat { i < UInt32.v len } )\n : Lemma\n (ovalue_is_readable t (Seq.index v i))\n = let (j : UInt32.t { UInt32.v j < UInt32.v len } ) = UInt32.uint_to_t i in\n assert (ovalue_is_readable t (Seq.index v (UInt32.v j)))\n in\n Classical.forall_intro f", "val gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: GTot (pointer (typ_of_struct_field l fd))", "val as_addr_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (as_addr (gufield p fd) == as_addr p))\n [SMTPat (as_addr (gufield p fd))]", "val unused_in_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n (h: HS.mem)\n: Lemma\n (requires True)\n (ensures (unused_in (gufield p fd) h <==> unused_in p h))\n [SMTPat (unused_in (gufield p fd) h)]", "let ostruct_field_of_struct_field\n (l: struct_typ)\n (ovalue_of_value: (\n (t: typ) ->\n (v: type_of_typ t) ->\n Pure (otype_of_typ t)\n (requires (t << l))\n (ensures (fun _ -> True))\n ))\n (v: struct l)\n (f: struct_field l)\n: Tot (otype_of_struct_field l f)\n= ovalue_of_value (typ_of_struct_field l f) (struct_sel #l v f)", "val live_gufield\n (h: HS.mem)\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (live h (gufield p fd) <==> live h p))\n [SMTPat (live h (gufield p fd))]", "val gread_gufield\n (h: HS.mem)\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires (union_get_key (gread h p) == fd))\n (ensures (\n union_get_key (gread h p) == fd /\\\n gread h (gufield p fd) == union_get_value (gread h p) fd\n ))\n [SMTPatOr [[SMTPat (gread h (gufield p fd))]; [SMTPat (union_get_value (gread h p) fd)]]]", "let seq_init_index\n (#a:Type) (len:nat) (contents:(i:nat { i < len } -> Tot a)) (i: nat)\n: Lemma\n (requires (i < len))\n (ensures (i < len /\\ Seq.index (Seq.init len contents) i == contents i))\n [SMTPat (Seq.index (Seq.init len contents) i)]\n= Seq.init_index len contents", "let rec ovalue_of_value\n (t: typ)\n (v: type_of_typ t)\n: Tot (otype_of_typ t)\n (decreases t)\n= match t with\n | TStruct l ->\n let oval\n (t' : typ)\n (v' : type_of_typ t')\n : Pure (otype_of_typ t')\n (requires (t' << l))\n (ensures (fun _ -> True))\n = ovalue_of_value t' v'\n in\n ostruct_create l (ostruct_field_of_struct_field l oval v)\n | TArray len t ->\n let (v: array len (type_of_typ t)) = v in\n assert (UInt32.v len == Seq.length v);\n let f\n (i: nat {i < UInt32.v len})\n : Tot (otype_of_typ t)\n = ovalue_of_value t (Seq.index v i)\n in\n let (v': array len (otype_of_typ t)) = Seq.init (UInt32.v len) f in\n Some v'\n | TUnion l ->\n let (v: union l) = v in\n let k = _union_get_key v in\n ounion_create l k (ovalue_of_value (typ_of_struct_field l k) (union_get_value v k))\n | _ -> Some v", "val frameOf_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (frameOf (gufield p fd) == frameOf p))\n [SMTPat (frameOf (gufield p fd))]", "val is_mm_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (is_mm (gufield p fd) <==> is_mm p))\n [SMTPat (is_mm (gufield p fd))]", "val gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n (i: UInt32.t)\n: Ghost (pointer value)\n (requires (UInt32.v i < UInt32.v length))\n (ensures (fun _ -> True))", "val as_addr_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v length))\n (ensures (UInt32.v i < UInt32.v length /\\ as_addr (gcell p i) == as_addr p))\n [SMTPat (as_addr (gcell p i))]", "let ovalue_is_readable_ostruct_field_of_struct_field\n (l: struct_typ)\n (ih: (\n (t: typ) ->\n (v: type_of_typ t) ->\n Lemma\n (requires (t << l))\n (ensures (ovalue_is_readable t (ovalue_of_value t v)))\n ))\n (v: struct l)\n (f: struct_field l)\n: Lemma\n (ovalue_is_readable (typ_of_struct_field l f) (ostruct_field_of_struct_field l ovalue_of_value v f))\n= ih (typ_of_struct_field l f) (struct_sel #l v f)", "val unused_in_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v length))\n (ensures (UInt32.v i < UInt32.v length /\\ (unused_in (gcell p i) h <==> unused_in p h)))\n [SMTPat (unused_in (gcell p i) h)]", "let rec ovalue_is_readable_ovalue_of_value\n (t: typ)\n (v: type_of_typ t)\n: Lemma\n (requires True)\n (ensures (ovalue_is_readable t (ovalue_of_value t v)))\n (decreases t)\n [SMTPat (ovalue_is_readable t (ovalue_of_value t v))]\n= match t with\n | TStruct l ->\n let (v: struct l) = v in\n let (v': ostruct l) = ovalue_of_value (TStruct l) v in\n let phi\n (t: typ)\n (v: type_of_typ t)\n : Lemma\n (requires (t << l))\n (ensures (ovalue_is_readable t (ovalue_of_value t v)))\n = ovalue_is_readable_ovalue_of_value t v\n in\n Classical.forall_intro (ovalue_is_readable_ostruct_field_of_struct_field l phi v);\n ovalue_is_readable_struct_intro l v'\n | TArray len t ->\n let (v: array len (type_of_typ t)) = v in\n let (v': otype_of_typ (TArray len t)) = ovalue_of_value (TArray len t) v in\n let (v': array len (otype_of_typ t)) = Some?.v v' in\n let phi\n (i: nat { i < Seq.length v' } )\n : Lemma\n (ovalue_is_readable t (Seq.index v' i))\n = ovalue_is_readable_ovalue_of_value t (Seq.index v i)\n in\n Classical.forall_intro phi\n | TUnion l ->\n let (v: union l) = v in\n let k = _union_get_key v in\n ovalue_is_readable_ovalue_of_value (typ_of_struct_field l k) (union_get_value v k)\n | _ -> ()", "val live_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v length))\n (ensures (UInt32.v i < UInt32.v length /\\ (live h (gcell p i) <==> live h p)))\n [SMTPat (live h (gcell p i))]", "val gread_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v length))\n (ensures (UInt32.v i < UInt32.v length /\\ gread h (gcell p i) == Seq.index (gread h p) (UInt32.v i)))\n [SMTPat (gread h (gcell p i))]", "val frameOf_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v length))\n (ensures (UInt32.v i < UInt32.v length /\\ frameOf (gcell p i) == frameOf p))\n [SMTPat (frameOf (gcell p i))]", "val is_mm_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v length))\n (ensures (UInt32.v i < UInt32.v length /\\ is_mm (gcell p i) == is_mm p))\n [SMTPat (is_mm (gcell p i))]", "let rec value_of_ovalue\n (t: typ)\n (v: otype_of_typ t)\n: Tot (type_of_typ t)\n (decreases t)\n= match t with\n | TStruct l ->\n let (v: ostruct l) = v in\n if Some? v\n then\n let phi\n (f: struct_field l)\n : Tot (type_of_struct_field l f)\n = value_of_ovalue (typ_of_struct_field l f) (ostruct_sel v f)\n in\n struct_create_fun l phi\n else dummy_val t\n | TArray len t' ->\n let (v: option (array len (otype_of_typ t'))) = v in\n begin match v with\n | None -> dummy_val t\n | Some v ->\n let phi\n (i: nat { i < UInt32.v len } )\n : Tot (type_of_typ t')\n = value_of_ovalue t' (Seq.index v i)\n in\n Seq.init (UInt32.v len) phi\n end\n | TUnion l ->\n let (v: ounion l) = v in\n begin match v with\n | None -> dummy_val t\n | _ ->\n let k = ounion_get_key v in\n union_create l k (value_of_ovalue (typ_of_struct_field l k) (ounion_get_value v k))\n end\n | TBase b ->\n let (v: option (type_of_base_typ b)) = v in\n begin match v with\n | None -> dummy_val t\n | Some v -> v\n end\n | TPointer t' ->\n let (v: option (pointer t')) = v in\n begin match v with\n | None -> dummy_val t\n | Some v -> v\n end\n | TNPointer t' ->\n let (v: option (npointer t')) = v in\n begin match v with\n | None -> dummy_val t\n | Some v -> v\n end\n | TBuffer t' ->\n let (v: option (buffer t')) = v in\n begin match v with\n | None -> dummy_val t\n | Some v -> v\n end", "val includes\n (#value1: typ)\n (#value2: typ)\n (p1: pointer value1)\n (p2: pointer value2)\n: GTot bool", "val includes_refl\n (#t: typ)\n (p: pointer t)\n: Lemma\n (ensures (includes p p))\n [SMTPat (includes p p)]", "val includes_trans\n (#t1 #t2 #t3: typ)\n (p1: pointer t1)\n (p2: pointer t2)\n (p3: pointer t3)\n: Lemma\n (requires (includes p1 p2 /\\ includes p2 p3))\n (ensures (includes p1 p3))", "val includes_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (includes p (gfield p fd)))", "val includes_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (includes p (gufield p fd)))", "val includes_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v length))\n (ensures (UInt32.v i < UInt32.v length /\\ includes p (gcell p i)))", "val readable\n (#a: typ)\n (h: HS.mem)\n (b: pointer a)\n: GTot Type0", "let ovalue_of_value_array_index\n (#len: array_length_t)\n (t' : typ)\n (v: array len (type_of_typ t'))\n (sv: array len (otype_of_typ t'))\n: Lemma\n (requires (ovalue_of_value (TArray len t') v == Some sv))\n (ensures (forall (i: nat) . i < UInt32.v len ==> Seq.index sv i == ovalue_of_value t' (Seq.index v i)))\n= ()", "val readable_live\n (#a: typ)\n (h: HS.mem)\n (b: pointer a)\n: Lemma\n (requires (readable h b))\n (ensures (live h b))\n [SMTPatOr [\n [SMTPat (readable h b)];\n [SMTPat (live h b)];\n ]]", "let value_of_ovalue_array_index\n (#len: array_length_t)\n (t': typ)\n (sv: array len (otype_of_typ t'))\n: Lemma\n (ensures (forall (i: nat) . i < UInt32.v len ==> Seq.index (value_of_ovalue (TArray len t') (Some sv)) i == value_of_ovalue t' (Seq.index sv i)))\n= ()", "val readable_gfield\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n: Lemma\n (requires (readable h p))\n (ensures (readable h (gfield p fd)))\n [SMTPat (readable h (gfield p fd))]", "let rec value_of_ovalue_of_value\n (t: typ)\n (v: type_of_typ t)\n: Lemma\n (value_of_ovalue t (ovalue_of_value t v) == v)\n [SMTPat (value_of_ovalue t (ovalue_of_value t v))]\n= match t with\n | TStruct l ->\n let v : struct l = v in\n let v' : struct l = value_of_ovalue t (ovalue_of_value t v) in\n let phi\n (f: struct_field l)\n : Lemma\n (struct_sel #l v' f == struct_sel #l v f)\n = value_of_ovalue_of_value (typ_of_struct_field l f) (struct_sel #l v f)\n in\n Classical.forall_intro phi;\n DM.equal_intro v' v;\n DM.equal_elim #(struct_field l) #(type_of_struct_field' l (fun x -> type_of_typ' x)) v' v\n | TArray len t' ->\n let (v: array len (type_of_typ t')) = v in\n let ov : option (array len (otype_of_typ t')) = ovalue_of_value (TArray len t') v in\n assert (Some? ov);\n let sv : array len (otype_of_typ t') = Some?.v ov in\n assert (Seq.length sv == UInt32.v len);\n// assert (forall (i : nat { i < UInt32.v len } ) . Seq.index sv i == ovalue_of_value t' (Seq.index v i));\n ovalue_of_value_array_index t' v sv;\n let v' : array len (type_of_typ t') = value_of_ovalue t ov in\n assert (Seq.length v' == UInt32.v len);\n// assert (forall (i: nat { i < UInt32.v len } ) . Seq.index v' i == value_of_ovalue t' (Seq.index sv i));\n value_of_ovalue_array_index t' sv;\n let phi\n (i: nat { i < UInt32.v len } )\n : Lemma\n (value_of_ovalue t' (ovalue_of_value t' (Seq.index v i)) == Seq.index v i)\n = value_of_ovalue_of_value t' (Seq.index v i)\n in\n Classical.forall_intro phi;\n Seq.lemma_eq_intro v' v;\n Seq.lemma_eq_elim v' v\n | TUnion l ->\n let v : union l = v in\n let k = _union_get_key v in\n value_of_ovalue_of_value (typ_of_struct_field l k) (union_get_value v k)\n | _ -> ()", "val readable_struct\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n: Lemma\n (requires (\n forall (f: struct_field l) .\n readable h (gfield p f)\n ))\n (ensures (readable h p))", "val readable_struct_forall_mem\n (#l: struct_typ)\n (p: pointer (TStruct l))\n: Lemma (forall\n (h: HS.mem)\n . (\n forall (f: struct_field l) .\n readable h (gfield p f)\n ) ==>\n readable h p\n )", "val readable_struct_fields\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n (s: list string)\n: GTot Type0", "val readable_struct_fields_nil\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n: Lemma\n (readable_struct_fields h p [])\n [SMTPat (readable_struct_fields h p [])]", "val readable_struct_fields_cons\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n (f: string)\n (q: list string)\n: Lemma\n (requires (readable_struct_fields h p q /\\ (List.Tot.mem f (List.Tot.map fst l.fields) ==> (let f : struct_field l = f in readable h (gfield p f)))))\n (ensures (readable_struct_fields h p (f::q)))\n [SMTPat (readable_struct_fields h p (f::q))]", "let none_ovalue\n (t: typ)\n: Tot (otype_of_typ t)\n= match t with\n | TStruct l -> (None <: ostruct l)\n | TArray len t' -> (None <: option (array len (otype_of_typ t')))\n | TUnion l -> (None <: ounion l)\n | TBase b -> (None <: option (type_of_base_typ b))\n | TPointer t' -> (None <: option (pointer t'))\n | TNPointer t' -> (None <: option (npointer t'))\n | TBuffer t' -> (None <: option (buffer t'))", "val readable_struct_fields_readable_struct\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n: Lemma\n (requires (readable_struct_fields h p (normalize_term (List.Tot.map fst l.fields))))\n (ensures (readable h p))", "let not_ovalue_is_readable_none_ovalue\n (t: typ)\n: Lemma\n (ovalue_is_readable t (none_ovalue t) == false)\n= ()", "val readable_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v length /\\ readable h p))\n (ensures (UInt32.v i < UInt32.v length /\\ readable h (gcell p i)))\n [SMTPat (readable h (gcell p i))]", "let step_sel\n (#from: typ)\n (#to: typ)\n (m': otype_of_typ from)\n (s: step from to)\n= match s with\n | StepField l fd ->\n let (m': ostruct l) = m' in\n begin match m' with\n | None -> none_ovalue to\n | _ -> ostruct_sel m' fd\n end\n | StepUField l fd ->\n let (m' : ounion l) = m' in\n begin match m' with\n | None -> none_ovalue to\n | _ ->\n if fd = ounion_get_key m'\n then ounion_get_value m' fd\n else none_ovalue to\n end\n | StepCell length value i ->\n let (m': option (array length (otype_of_typ to))) = m' in\n begin match m' with\n | None -> none_ovalue to\n | Some m' -> Seq.index m' (UInt32.v i)\n end", "val readable_array\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n: Lemma\n (requires (\n forall (i: UInt32.t) .\n UInt32.v i < UInt32.v length ==>\n readable h (gcell p i)\n ))\n (ensures (readable h p))", "val readable_gufield\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires True)\n (ensures (readable h (gufield p fd) <==> (readable h p /\\ union_get_key (gread h p) == fd)))\n [SMTPat (readable h (gufield p fd))]", "val is_active_union_field\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: GTot Type0", "val is_active_union_live\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires (is_active_union_field h p fd))\n (ensures (live h p))\n [SMTPat (is_active_union_field h p fd)]", "let ovalue_is_readable_step_sel_cell\n (#length: array_length_t)\n (#value: typ)\n (m': otype_of_typ (TArray length value))\n (index: UInt32.t { UInt32.v index < UInt32.v length } )\n: Lemma\n (requires (ovalue_is_readable (TArray length value) m'))\n (ensures (ovalue_is_readable value (step_sel m' (StepCell length value index))))\n [SMTPat (ovalue_is_readable value (step_sel m' (StepCell length value index)))]\n= ()", "val is_active_union_field_live\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires (is_active_union_field h p fd))\n (ensures (live h (gufield p fd)))\n [SMTPat (is_active_union_field h p fd)]", "let ovalue_is_readable_step_sel_field\n (#l: struct_typ)\n (m: ostruct l)\n (fd: struct_field l)\n: Lemma\n (requires (ovalue_is_readable (TStruct l) m))\n (ensures (ovalue_is_readable (typ_of_struct_field l fd) (step_sel m (StepField l fd))))\n [SMTPat (ovalue_is_readable (typ_of_struct_field l fd) (step_sel m (StepField l fd)))]\n= ()", "val is_active_union_field_eq\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd1 fd2: struct_field l)\n: Lemma\n (requires (is_active_union_field h p fd1 /\\ is_active_union_field h p fd2))\n (ensures (fd1 == fd2))\n [SMTPat (is_active_union_field h p fd1); SMTPat (is_active_union_field h p fd2)]", "let ovalue_is_readable_step_sel_union_same\n (#l: union_typ)\n (m: ounion l)\n (fd: struct_field l)\n: Lemma\n (requires (\n ovalue_is_readable (TUnion l) m /\\\n ounion_get_key m == fd\n ))\n (ensures (ovalue_is_readable (typ_of_struct_field l fd) (step_sel m (StepUField l fd))))\n= ()", "val is_active_union_field_get_key\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires (is_active_union_field h p fd))\n (ensures (union_get_key (gread h p) == fd))\n [SMTPat (is_active_union_field h p fd)]", "let step_sel_none_ovalue\n (#from: typ)\n (#to: typ)\n (s: step from to)\n: Lemma\n (step_sel (none_ovalue from) s == none_ovalue to)\n= ()", "val is_active_union_field_readable\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires (is_active_union_field h p fd /\\ readable h (gufield p fd)))\n (ensures (readable h p))\n [SMTPat (is_active_union_field h p fd); SMTPat (readable h (gufield p fd))]", "let rec path_sel\n (#from: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (p: path from to)\n: Tot (otype_of_typ to)\n (decreases p)\n= match p with\n | PathBase -> m\n | PathStep through' to' p' s ->\n let (m': otype_of_typ through') = path_sel m p' in\n step_sel m' s", "val is_active_union_field_includes_readable\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n (#t': typ)\n (p' : pointer t')\n: Lemma\n (requires (includes (gufield p fd) p' /\\ readable h p'))\n (ensures (is_active_union_field h p fd))", "let rec path_sel_none_ovalue\n (#from: typ)\n (#to: typ)\n (p: path from to)\n: Lemma\n (requires True)\n (ensures (path_sel (none_ovalue from) p == none_ovalue to))\n (decreases p)\n= match p with\n | PathBase -> ()\n | PathStep through' to' p' s ->\n path_sel_none_ovalue p'", "let equal_values #a h (b:pointer a) h' (b':pointer a) : GTot Type0 =\n (live h b ==> live h' b') /\\ (\n readable h b ==> (\n readable h' b' /\\\n gread h b == gread h' b'\n ))", "let step_upd\n (#from: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (s: step from to)\n (v: otype_of_typ to)\n: Tot (otype_of_typ from)\n (decreases s)\n= match s with\n | StepField l fd ->\n let (m: ostruct l) = m in\n begin match m with\n | None ->\n (* whole structure does not exist yet,\n so create one with only one field initialized,\n and all others uninitialized *)\n let phi\n (fd' : struct_field l)\n : Tot (otype_of_struct_field l fd')\n = if fd' = fd\n then v\n else none_ovalue (typ_of_struct_field l fd')\n in\n ostruct_create l phi\n | Some _ -> ostruct_upd m fd v\n end\n | StepCell len _ i ->\n let (m: option (array len (otype_of_typ to))) = m in\n begin match m with\n | None ->\n (* whole array does not exist yet,\n so create one with only one cell initialized,\n and all others uninitialized *)\n let phi\n (j: nat { j < UInt32.v len } )\n : Tot (otype_of_typ to)\n = if j = UInt32.v i\n then v\n else none_ovalue to\n in\n let (m' : option (array len (otype_of_typ to))) =\n Some (Seq.init (UInt32.v len) phi)\n in\n m'\n | Some m ->\n let (m' : option (array len (otype_of_typ to))) =\n Some (Seq.upd m (UInt32.v i) v)\n in\n m'\n end\n | StepUField l fd ->\n (* overwrite the whole union with the new field *)\n ounion_create l fd v", "val gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n: GTot (buffer t)", "val singleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n: HST.Stack (buffer t)\n (requires (fun h -> live h p))\n (ensures (fun h b h' -> h' == h /\\ b == gsingleton_buffer_of_pointer p))", "val gbuffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n: GTot (buffer t)", "val buffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n: HST.Stack (buffer t)\n (requires (fun h -> live h p))\n (ensures (fun h b h' -> h' == h /\\ b == gbuffer_of_array_pointer p))", "val buffer_length\n (#t: typ)\n (b: buffer t)\n: GTot UInt32.t", "val buffer_length_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n: Lemma\n (requires True)\n (ensures (buffer_length (gsingleton_buffer_of_pointer p) == 1ul))\n [SMTPat (buffer_length (gsingleton_buffer_of_pointer p))]", "val buffer_length_gbuffer_of_array_pointer\n (#t: typ)\n (#len: array_length_t)\n (p: pointer (TArray len t))\n: Lemma\n (requires True)\n (ensures (buffer_length (gbuffer_of_array_pointer p) == len))\n [SMTPat (buffer_length (gbuffer_of_array_pointer p))]", "val buffer_live\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: GTot Type0", "let step_sel_upd_same\n (#from: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (s: step from to)\n (v: otype_of_typ to)\n: Lemma\n (step_sel (step_upd m s v) s == v)\n= ()", "val buffer_live_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n (h: HS.mem)\n: Lemma\n (ensures (buffer_live h (gsingleton_buffer_of_pointer p) <==> live h p ))\n [SMTPat (buffer_live h (gsingleton_buffer_of_pointer p))]", "let rec path_upd\n (#from: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (p: path from to)\n (v: otype_of_typ to)\n: Tot (otype_of_typ from)\n (decreases p)\n= match p with\n | PathBase -> v\n | PathStep through' to' p' st ->\n let s = path_sel m p' in\n path_upd m p' (step_upd s st v)", "val buffer_live_gbuffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n (h: HS.mem)\n: Lemma\n (requires True)\n (ensures (buffer_live h (gbuffer_of_array_pointer p) <==> live h p))\n [SMTPat (buffer_live h (gbuffer_of_array_pointer p))]", "val buffer_unused_in\n (#t: typ)\n (b: buffer t)\n (h: HS.mem)\n: GTot Type0", "let rec path_sel_upd_same\n (#from: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (p: path from to)\n (v: otype_of_typ to)\n: Lemma\n (requires True)\n (ensures (path_sel (path_upd m p v) p == v))\n (decreases p)\n [SMTPat (path_sel (path_upd m p v) p)]\n= match p with\n | PathBase -> ()\n | PathStep through' to' p' st ->\n let s = path_sel m p' in\n step_sel_upd_same s st v;\n let s' = step_upd s st v in\n path_sel_upd_same m p' s'", "val buffer_live_not_unused_in\n (#t: typ)\n (b: buffer t)\n (h: HS.mem)\n: Lemma\n ((buffer_live h b /\\ buffer_unused_in b h) ==> False)", "val buffer_unused_in_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n (h: HS.mem)\n: Lemma\n (ensures (buffer_unused_in (gsingleton_buffer_of_pointer p) h <==> unused_in p h ))\n [SMTPat (buffer_unused_in (gsingleton_buffer_of_pointer p) h)]", "val buffer_unused_in_gbuffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n (h: HS.mem)\n: Lemma\n (requires True)\n (ensures (buffer_unused_in (gbuffer_of_array_pointer p) h <==> unused_in p h))\n [SMTPat (buffer_unused_in (gbuffer_of_array_pointer p) h)]", "let rec path_concat\n (#from: typ)\n (#through: typ)\n (#to: typ)\n (p: path from through)\n (q: path through to)\n: Pure (path from to)\n (requires True)\n (ensures (fun _ -> True))\n (decreases q)\n= match q with\n | PathBase -> p\n | PathStep through' to' q' st -> PathStep through' to' (path_concat p q') st", "val frameOf_buffer\n (#t: typ)\n (b: buffer t)\n: GTot HS.rid", "let path_concat_base_r\n (#from: typ)\n (#to: typ)\n (p: path from to)\n: Lemma\n (ensures (path_concat p PathBase == p))\n= ()", "val frameOf_buffer_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n: Lemma\n (ensures (frameOf_buffer (gsingleton_buffer_of_pointer p) == frameOf p))\n [SMTPat (frameOf_buffer (gsingleton_buffer_of_pointer p))]", "val frameOf_buffer_gbuffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n: Lemma\n (ensures (frameOf_buffer (gbuffer_of_array_pointer p) == frameOf p))\n [SMTPat (frameOf_buffer (gbuffer_of_array_pointer p))]", "let rec path_concat_base_l\n (#from: typ)\n (#to: typ)\n (p: path from to)\n: Lemma\n (requires True)\n (ensures (path_concat PathBase p == p))\n (decreases p)\n [SMTPat (path_concat PathBase p)]\n= match p with\n | PathBase -> ()\n | PathStep _ _ p' _ -> path_concat_base_l p'", "val live_region_frameOf_buffer\n (#value: typ)\n (h: HS.mem)\n (p: buffer value)\n: Lemma\n (requires (buffer_live h p))\n (ensures (HS.live_region h (frameOf_buffer p)))\n [SMTPatOr [\n [SMTPat (HS.live_region h (frameOf_buffer p))];\n [SMTPat (buffer_live h p)]\n ]]", "let rec path_concat_assoc\n (#t0 #t1 #t2 #t3: typ)\n (p01: path t0 t1)\n (p12: path t1 t2)\n (p23: path t2 t3)\n: Lemma\n (requires True)\n (ensures (path_concat (path_concat p01 p12) p23 == path_concat p01 (path_concat p12 p23)))\n (decreases p23)\n= match p23 with\n | PathBase -> ()\n | PathStep _ _ p23' _ -> path_concat_assoc p01 p12 p23'", "val buffer_as_addr\n (#t: typ)\n (b: buffer t)\n: GTot (x: nat { x > 0 } )", "val buffer_as_addr_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n: Lemma\n (ensures (buffer_as_addr (gsingleton_buffer_of_pointer p) == as_addr p))\n [SMTPat (buffer_as_addr (gsingleton_buffer_of_pointer p))]", "let rec path_sel_concat\n (#from: typ)\n (#through: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (p: path from through)\n (q: path through to)\n: Lemma\n (requires True)\n (ensures (path_sel m (path_concat p q) == path_sel (path_sel m p) q))\n (decreases q)\n [SMTPat (path_sel m (path_concat p q))]\n= match q with\n | PathBase -> ()\n | PathStep _ _ q' _ -> path_sel_concat m p q'", "val buffer_as_addr_gbuffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n: Lemma\n (ensures (buffer_as_addr (gbuffer_of_array_pointer p) == as_addr p))\n [SMTPat (buffer_as_addr (gbuffer_of_array_pointer p))]", "val gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Ghost (buffer t)\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)))\n (ensures (fun _ -> True))", "let rec path_upd_concat\n (#from: typ)\n (#through: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (p: path from through)\n (q: path through to)\n (v: otype_of_typ to)\n: Lemma\n (requires True)\n (ensures (path_upd m (path_concat p q) v == path_upd m p (path_upd (path_sel m p) q v)))\n (decreases q)\n [SMTPat (path_upd m (path_concat p q) v)]\n= match q with\n | PathBase -> ()\n | PathStep through' to' q' st ->\n let (s: otype_of_typ through') = path_sel m (path_concat p q') in\n let (s': otype_of_typ through') = step_upd s st v in\n path_upd_concat m p q' s'", "val frameOf_buffer_gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)))\n (ensures (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\\n frameOf_buffer (gsub_buffer b i len) == frameOf_buffer b\n ))\n [SMTPat (frameOf_buffer (gsub_buffer b i len))]", "val buffer_as_addr_gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)))\n (ensures (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\\n buffer_as_addr (gsub_buffer b i len) == buffer_as_addr b\n ))\n [SMTPat (buffer_as_addr (gsub_buffer b i len))]", "let rec path_includes\n (#from: typ)\n (#to1 #to2: typ)\n (p1: path from to1)\n (p2: path from to2)\n: Ghost bool\n (requires True)\n (ensures (fun _ -> True))\n (decreases p2)\n= (to1 = to2 && p1 = p2) || (match p2 with\n | PathBase -> false\n | PathStep _ _ p2' _ ->\n path_includes p1 p2'\n )", "val sub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: HST.Stack (buffer t)\n (requires (fun h -> UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ buffer_live h b))\n (ensures (fun h b' h' -> UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ h' == h /\\ b' == gsub_buffer b i len ))", "let rec path_includes_base\n (#from: typ)\n (#to: typ)\n (p: path from to)\n: Lemma\n (requires True)\n (ensures (path_includes (PathBase #from) p))\n (decreases p)\n [SMTPat (path_includes PathBase p)]\n= match p with\n | PathBase -> ()\n | PathStep _ _ p2' _ -> path_includes_base p2'", "val offset_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: HST.Stack (buffer t)\n (requires (fun h -> UInt32.v i <= UInt32.v (buffer_length b) /\\ buffer_live h b))\n (ensures (fun h b' h' -> UInt32.v i <= UInt32.v (buffer_length b) /\\ h' == h /\\ b' == gsub_buffer b i (UInt32.sub (buffer_length b) i)))", "let path_includes_refl\n (#from #to: typ)\n (p: path from to)\n: Lemma\n (requires True)\n (ensures (path_includes p p))\n [SMTPat (path_includes p p)]\n= ()", "val buffer_length_gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)))\n (ensures (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ buffer_length (gsub_buffer b i len) == len))\n [SMTPat (buffer_length (gsub_buffer b i len))]", "let path_includes_step_r\n (#from #through #to: typ)\n (p: path from through)\n (s: step through to)\n: Lemma\n (requires True)\n (ensures (path_includes p (PathStep through to p s)))\n [SMTPat (path_includes p (PathStep through to p s))]\n= ()", "val buffer_live_gsub_buffer_equiv\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n (h: HS.mem)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)))\n (ensures (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ (buffer_live h (gsub_buffer b i len) <==> buffer_live h b)))\n [SMTPat (buffer_live h (gsub_buffer b i len))]", "let rec path_includes_trans\n (#from #to1 #to2 #to3: typ)\n (p1: path from to1)\n (p2: path from to2)\n (p3: path from to3 {path_includes p1 p2 /\\ path_includes p2 p3})\n: Lemma\n (requires True)\n (ensures (path_includes p1 p3))\n (decreases p3)\n= FStar.Classical.or_elim\n #(to2 == to3 /\\ p2 == p3)\n #(match p3 with\n | PathBase -> False\n | PathStep _ _ p3' _ ->\n\tpath_includes p2 p3')\n #(fun _ -> path_includes p1 p3)\n (fun _ -> ())\n (fun _ -> match p3 with\n | PathBase -> assert False\n | PathStep _ _ p3' _ ->\n\tpath_includes_trans p1 p2 p3'\n )", "val buffer_live_gsub_buffer_intro\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n (h: HS.mem)\n: Lemma\n (requires (buffer_live h b /\\ UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)))\n (ensures (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ buffer_live h (gsub_buffer b i len)))\n [SMTPat (buffer_live h (gsub_buffer b i len))]", "val buffer_unused_in_gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n (h: HS.mem)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)))\n (ensures (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ (buffer_unused_in (gsub_buffer b i len) h <==> buffer_unused_in b h)))\n [SMTPat (buffer_unused_in (gsub_buffer b i len) h)]", "let rec path_includes_ind\n (#from: typ)\n (x:((#to1: typ) ->\n (#to2: typ) ->\n (p1: path from to1) ->\n (p2: path from to2 {path_includes p1 p2} ) ->\n GTot Type0))\n (h_step:\n ((#through: typ) ->\n (#to: typ) ->\n (p: path from through) ->\n (s: step through to { path_includes p (PathStep through to p s) } ) ->\n Lemma (x p (PathStep through to p s))))\n (h_refl:\n ((#to: typ) ->\n (p: path from to {path_includes p p}) ->\n Lemma (x p p)))\n (h_trans:\n ((#to1: typ) ->\n (#to2: typ) ->\n (#to3: typ) ->\n (p1: path from to1) ->\n (p2: path from to2) ->\n (p3: path from to3 {path_includes p1 p2 /\\ path_includes p2 p3 /\\ path_includes p1 p3 /\\ x p1 p2 /\\ x p2 p3}) ->\n Lemma (x p1 p3)))\n (#to1: typ)\n (#to2: typ)\n (p1: path from to1)\n (p2: path from to2 {path_includes p1 p2})\n: Lemma\n (requires True)\n (ensures (x p1 p2))\n (decreases p2)\n= FStar.Classical.or_elim\n #(to1 == to2 /\\ p1 == p2)\n #(match p2 with\n | PathBase -> False\n | PathStep _ _ p' _ -> path_includes p1 p')\n #(fun _ -> x p1 p2)\n (fun _ -> h_refl p1)\n (fun _ -> match p2 with\n | PathBase -> assert False\n | PathStep _ _ p2' st ->\n let _ = path_includes_ind x h_step h_refl h_trans p1 p2' in\n let _ = path_includes_step_r p2' st in\n let _ = h_step p2' st in\n h_trans p1 p2' p2\n )", "val gsub_buffer_gsub_buffer\n (#a: typ)\n (b: buffer a)\n (i1: UInt32.t)\n (len1: UInt32.t)\n (i2: UInt32.t)\n (len2: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 + UInt32.v len2 <= UInt32.v len1\n ))\n (ensures (\n UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 + UInt32.v len2 <= UInt32.v len1 /\\\n gsub_buffer (gsub_buffer b i1 len1) i2 len2 == gsub_buffer b FStar.UInt32.(i1 +^ i2) len2\n ))\n [SMTPat (gsub_buffer (gsub_buffer b i1 len1) i2 len2)]", "val gsub_buffer_zero_buffer_length\n (#a: typ)\n (b: buffer a)\n: Lemma\n (ensures (gsub_buffer b 0ul (buffer_length b) == b))\n [SMTPat (gsub_buffer b 0ul (buffer_length b))]", "val buffer_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: GTot (Seq.seq (type_of_typ t))", "val buffer_length_buffer_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: Lemma\n (requires True)\n (ensures (Seq.length (buffer_as_seq h b) == UInt32.v (buffer_length b)))\n [SMTPat (Seq.length (buffer_as_seq h b))]", "val buffer_as_seq_gsingleton_buffer_of_pointer\n (#t: typ)\n (h: HS.mem)\n (p: pointer t)\n: Lemma\n (requires True)\n (ensures (buffer_as_seq h (gsingleton_buffer_of_pointer p) == Seq.create 1 (gread h p)))\n [SMTPat (buffer_as_seq h (gsingleton_buffer_of_pointer p))]", "let rec path_length\n (#from #to: typ)\n (p: path from to)\n: Tot nat\n (decreases p)\n= match p with\n | PathBase -> 0\n | PathStep _ _ p' _ -> 1 + path_length p'", "val buffer_as_seq_gbuffer_of_array_pointer\n (#length: array_length_t)\n (#t: typ)\n (h: HS.mem)\n (p: pointer (TArray length t))\n: Lemma\n (requires True)\n (ensures (buffer_as_seq h (gbuffer_of_array_pointer p) == gread h p))\n [SMTPat (buffer_as_seq h (gbuffer_of_array_pointer p))]", "let path_includes_length\n (#from: typ)\n (#to1 #to2: typ)\n (p1: path from to1)\n (p2: path from to2 {path_includes p1 p2})\n: Lemma\n (ensures (path_length p1 <= path_length p2))\n= path_includes_ind\n (fun #to1_ #to2_ p1_ p2_ -> path_length p1_ <= path_length p2_)\n (fun #through #to p st -> ())\n (fun #to p -> ())\n (fun #to1_ #to2_ #to3_ p1_ p2_ p3_ -> ())\n p1 p2", "val buffer_as_seq_gsub_buffer\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)))\n (ensures (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ buffer_as_seq h (gsub_buffer b i len) == Seq.slice (buffer_as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)))\n [SMTPat (buffer_as_seq h (gsub_buffer b i len))]", "let path_includes_step_l\n (#from: typ)\n (#through: typ)\n (#to: typ)\n (p: path from through)\n (s: step through to)\n: Lemma\n (requires True)\n (ensures (~ (path_includes (PathStep through to p s) p)))\n [SMTPat (path_includes (PathStep through to p s) p)]\n= assert (path_length (PathStep through to p s) > path_length p);\n FStar.Classical.forall_intro (path_includes_length #from #to #through (PathStep through to p s))", "val gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Ghost (pointer t)\n (requires (UInt32.v i < UInt32.v (buffer_length b)))\n (ensures (fun _ -> True))", "val pointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: HST.Stack (pointer t)\n (requires (fun h -> UInt32.v i < UInt32.v (buffer_length b) /\\ buffer_live h b))\n (ensures (fun h p h' -> UInt32.v i < UInt32.v (buffer_length b) /\\ h' == h /\\ p == gpointer_of_buffer_cell b i))", "let rec path_includes_concat\n (#from: typ)\n (#through: typ)\n (#to: typ)\n (p: path from through)\n (q: path through to)\n: Lemma\n (requires True)\n (ensures (path_includes p (path_concat p q)))\n (decreases q)\n [SMTPat (path_includes p (path_concat p q))]\n= match q with\n | PathBase -> ()\n | PathStep _ _ q' _ -> path_includes_concat p q'", "val gpointer_of_buffer_cell_gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i1: UInt32.t)\n (len: UInt32.t)\n (i2: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i1 + UInt32.v len <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 < UInt32.v len\n ))\n (ensures (\n UInt32.v i1 + UInt32.v len <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 < UInt32.v len /\\\n gpointer_of_buffer_cell (gsub_buffer b i1 len) i2 == gpointer_of_buffer_cell b FStar.UInt32.(i1 +^ i2)\n ))", "let path_includes_exists_concat\n (#from #through: typ)\n (p: path from through)\n (#to: typ)\n (q: path from to { path_includes p q } )\n: Lemma\n (ensures (exists (r: path through to) . q == path_concat p r))\n= path_includes_ind\n (fun #to1_ #to2_ p1_ p2_ -> exists r . p2_ == path_concat p1_ r)\n (fun #through #to_ p s -> \n let r = PathStep through to_ PathBase s in\n assert_norm (PathStep through to_ p s == path_concat p r)\n )\n (fun #to p -> FStar.Classical.exists_intro (fun r -> p == path_concat p r) PathBase)\n (fun #to1_ #to2_ #to3_ p1_ p2_ p3_ ->\n FStar.Classical.exists_elim (exists r . p3_ == path_concat p1_ r) #_ #(fun r12 -> p2_ == path_concat p1_ r12) () (fun r12 ->\n\tFStar.Classical.exists_elim (exists r . p3_ == path_concat p1_ r) #_ #(fun r23 -> p3_ == path_concat p2_ r23) () (fun r23 ->\n\t path_concat_assoc p1_ r12 r23;\n\t FStar.Classical.exists_intro (fun r -> p3_ == path_concat p1_ r) (path_concat r12 r23)\n\t)\n )\n )\n p q", "let gpointer_of_buffer_cell_gsub_buffer'\n (#t: typ)\n (b: buffer t)\n (i1: UInt32.t)\n (len: UInt32.t)\n (i2: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i1 + UInt32.v len <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 < UInt32.v len\n ))\n (ensures (\n UInt32.v i1 + UInt32.v len <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 < UInt32.v len /\\\n gpointer_of_buffer_cell (gsub_buffer b i1 len) i2 == gpointer_of_buffer_cell b FStar.UInt32.(i1 +^ i2)\n ))\n [SMTPat (gpointer_of_buffer_cell (gsub_buffer b i1 len) i2)]\n= gpointer_of_buffer_cell_gsub_buffer b i1 len i2", "let path_concat_includes\n (#from #through: typ)\n (p: path from through)\n (phi: (\n (#to: typ) ->\n (p': path from to) ->\n Ghost Type0\n (requires (path_includes p p'))\n (ensures (fun _ -> True))\n ))\n (f: (\n (to: typ) ->\n (p': path through to) ->\n Lemma\n (ensures (phi (path_concat p p')))\n ))\n (#to: typ)\n (q: path from to)\n: Lemma\n (requires (path_includes p q))\n (ensures (path_includes p q /\\ phi q))\n= Classical.forall_intro_2 f;\n path_includes_exists_concat p q", "val live_gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (h: HS.mem)\n: Lemma\n (requires (\n UInt32.v i < UInt32.v (buffer_length b)\n ))\n (ensures (\n UInt32.v i < UInt32.v (buffer_length b) /\\\n (live h (gpointer_of_buffer_cell b i) <==> buffer_live h b)\n ))\n [SMTPat (live h (gpointer_of_buffer_cell b i))]", "val gpointer_of_buffer_cell_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < 1))\n (ensures (UInt32.v i < 1 /\\ gpointer_of_buffer_cell (gsingleton_buffer_of_pointer p) i == p))\n [SMTPat (gpointer_of_buffer_cell (gsingleton_buffer_of_pointer p) i)]", "let step_disjoint\n (#from: typ)\n (#to1 #to2: typ)\n (s1: step from to1)\n (s2: step from to2)\n: GTot bool\n= match s1 with\n | StepField _ fd1 ->\n let (StepField _ fd2) = s2 in\n fd1 <> fd2\n | StepCell _ _ i1 ->\n let (StepCell _ _ i2) = s2 in\n UInt32.v i1 <> UInt32.v i2\n | StepUField _ _ ->\n (* two fields of the same union are never disjoint *)\n false", "val gpointer_of_buffer_cell_gbuffer_of_array_pointer\n (#length: array_length_t)\n (#t: typ)\n (p: pointer (TArray length t))\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v length))\n (ensures (UInt32.v i < UInt32.v length /\\ gpointer_of_buffer_cell (gbuffer_of_array_pointer p) i == gcell p i))\n [SMTPat (gpointer_of_buffer_cell (gbuffer_of_array_pointer p) i)]", "val frameOf_gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b)))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ frameOf (gpointer_of_buffer_cell b i) == frameOf_buffer b))\n [SMTPat (frameOf (gpointer_of_buffer_cell b i))]", "let step_eq\n (#from: typ)\n (#to1 #to2: typ)\n (s1: step from to1)\n (s2: step from to2)\n: Tot (b: bool { b = true <==> to1 == to2 /\\ s1 == s2 } )\n= match s1 with\n | StepField l1 fd1 ->\n let (StepField _ fd2) = s2 in\n fd1 = fd2\n | StepCell _ _ i1 ->\n let (StepCell _ _ i2) = s2 in\n i1 = i2\n | StepUField l1 fd1 ->\n let (StepUField _ fd2) = s2 in\n fd1 = fd2", "val as_addr_gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b)))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ as_addr (gpointer_of_buffer_cell b i) == buffer_as_addr b))\n [SMTPat (as_addr (gpointer_of_buffer_cell b i))]", "val gread_gpointer_of_buffer_cell\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b)))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ gread h (gpointer_of_buffer_cell b i) == Seq.index (buffer_as_seq h b) (UInt32.v i)))\n [SMTPat (gread h (gpointer_of_buffer_cell b i))]", "let step_disjoint_not_eq\n (#from: typ)\n (#to1 #to2: typ)\n (s1: step from to1)\n (s2: step from to2)\n: Lemma\n (requires (step_disjoint s1 s2 == true))\n (ensures (step_eq s1 s2 == false))\n= ()", "val gread_gpointer_of_buffer_cell'\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b)))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ gread h (gpointer_of_buffer_cell b i) == Seq.index (buffer_as_seq h b) (UInt32.v i)))", "let step_disjoint_sym\n (#from: typ)\n (#to1 #to2: typ)\n (s1: step from to1)\n (s2: step from to2)\n: Lemma\n (requires (step_disjoint s1 s2))\n (ensures (step_disjoint s2 s1))\n= ()", "val index_buffer_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: nat)\n: Lemma\n (requires (i < UInt32.v (buffer_length b)))\n (ensures (i < UInt32.v (buffer_length b) /\\ Seq.index (buffer_as_seq h b) i == gread h (gpointer_of_buffer_cell b (UInt32.uint_to_t i))))\n [SMTPat (Seq.index (buffer_as_seq h b) i)]", "path_disjoint_t", "val gsingleton_buffer_of_pointer_gcell\n (#t: typ)\n (#len: array_length_t)\n (p: pointer (TArray len t))\n (i: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i < UInt32.v len\n ))\n (ensures (\n UInt32.v i < UInt32.v len /\\\n gsingleton_buffer_of_pointer (gcell p i) == gsub_buffer (gbuffer_of_array_pointer p) i 1ul\n ))\n [SMTPat (gsingleton_buffer_of_pointer (gcell p i))]", "PathDisjointStep", "PathDisjointStep", "PathDisjointStep", "through", "through", "to1", "to1", "to2", "to2", "p", "p", "s1", "s1", "s2", "s2", "PathDisjointIncludes", "PathDisjointIncludes", "PathDisjointIncludes", "to1", "to1", "to2", "to2", "p1", "p1", "p2", "p2", "val gsingleton_buffer_of_pointer_gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i < UInt32.v (buffer_length b)\n ))\n (ensures (\n UInt32.v i < UInt32.v (buffer_length b) /\\\n gsingleton_buffer_of_pointer (gpointer_of_buffer_cell b i) == gsub_buffer b i 1ul\n ))\n [SMTPat (gsingleton_buffer_of_pointer (gpointer_of_buffer_cell b i))]", "to1'", "to1'", "to2'", "to2'", "p1'", "p1'", "p2'", "p2'", "let rec path_disjoint_t_rect\n (#from: typ)\n (x:\n ((#value1: typ) ->\n (#value2: typ) ->\n (p1: path from value1) ->\n (p2: path from value2) ->\n (h: path_disjoint_t p1 p2) ->\n GTot Type))\n (h_step:\n ((#through: typ) ->\n (#to1: typ) ->\n (#to2: typ) ->\n (p: path from through) ->\n (s1: step through to1) ->\n (s2: step through to2 { step_disjoint s1 s2 } ) ->\n (h: path_disjoint_t (PathStep through to1 p s1) (PathStep through to2 p s2)) ->\n GTot (x (PathStep through to1 p s1) (PathStep through to2 p s2) h)))\n (h_includes:\n ((#value1: typ) ->\n (#value2: typ) ->\n (p1: path from value1) ->\n (p2: path from value2) ->\n (#value1': typ) ->\n (#value2': typ) ->\n (p1': path from value1' {path_includes p1 p1'}) ->\n (p2': path from value2' {path_includes p2 p2'}) ->\n (h: path_disjoint_t p1 p2) ->\n (h': path_disjoint_t p1' p2') ->\n (ihx: x p1 p2 h) ->\n GTot (x p1' p2' h')))\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n (h: path_disjoint_t p1 p2)\n: Ghost (x p1 p2 h)\n (requires True)\n (ensures (fun _ -> True))\n (decreases h)\n= match h with\n | PathDisjointStep p s1 s2 -> h_step p s1 s2 h\n | PathDisjointIncludes p1_ p2_ p1' p2' h_ -> h_includes p1_ p2_ p1' p2' h_ h (path_disjoint_t_rect x h_step h_includes p1_ p2_ h_)", "val buffer_readable\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: GTot Type0", "val buffer_readable_buffer_live\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: Lemma\n (requires (buffer_readable h b))\n (ensures (buffer_live h b))\n [SMTPatOr [\n [SMTPat (buffer_readable h b)];\n [SMTPat (buffer_live h b)];\n ]]", "val buffer_readable_gsingleton_buffer_of_pointer\n (#t: typ)\n (h: HS.mem)\n (p: pointer t)\n: Lemma\n (ensures (buffer_readable h (gsingleton_buffer_of_pointer p) <==> readable h p))\n [SMTPat (buffer_readable h (gsingleton_buffer_of_pointer p))]", "val buffer_readable_gbuffer_of_array_pointer\n (#len: array_length_t)\n (#t: typ)\n (h: HS.mem)\n (p: pointer (TArray len t))\n: Lemma\n (requires True)\n (ensures (buffer_readable h (gbuffer_of_array_pointer p) <==> readable h p))\n [SMTPat (buffer_readable h (gbuffer_of_array_pointer p))]", "let path_disjoint\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n: GTot Type0\n= squash (path_disjoint_t p1 p2)", "val buffer_readable_gsub_buffer\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ buffer_readable h b))\n (ensures (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ buffer_readable h (gsub_buffer b i len)))\n [SMTPat (buffer_readable h (gsub_buffer b i len))]", "let path_disjoint_ind\n (#from: typ)\n (x:\n ((#value1: typ) ->\n (#value2: typ) ->\n (p1: path from value1) ->\n (p2: path from value2 {path_disjoint p1 p2} ) ->\n GTot Type))\n (h_step:\n ((#through: typ) ->\n (#to1: typ) ->\n (#to2: typ) ->\n (p: path from through) ->\n (s1: step through to1) ->\n (s2: step through to2 { step_disjoint s1 s2 /\\ path_disjoint (PathStep through to1 p s1) (PathStep through to2 p s2) } ) ->\n Lemma (x (PathStep through to1 p s1) (PathStep through to2 p s2) )))\n (h_includes:\n ((#value1: typ) ->\n (#value2: typ) ->\n (p1: path from value1) ->\n (p2: path from value2) ->\n (#value1': typ) ->\n (#value2': typ) ->\n (p1': path from value1' {path_includes p1 p1'}) ->\n (p2': path from value2' {path_includes p2 p2' /\\ path_disjoint p1 p2 /\\ path_disjoint p1' p2' /\\ x p1 p2}) ->\n Lemma (x p1' p2')))\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2 { path_disjoint p1 p2 } )\n: Lemma (x p1 p2)\n= let h : squash (path_disjoint_t p1 p2) = FStar.Squash.join_squash () in\n FStar.Squash.bind_squash h (fun (h: path_disjoint_t p1 p2) ->\n path_disjoint_t_rect\n (fun #v1 #v2 p1 p2 h -> let _ = FStar.Squash.return_squash h in squash (x p1 p2))\n (fun #through #to1 #to2 p s1 s2 h -> let _ = FStar.Squash.return_squash h in h_step p s1 s2)\n (fun #v1 #v2 p1 p2 #v1' #v2' p1' p2' h h' hx ->\n let _ = FStar.Squash.return_squash h in\n let _ = FStar.Squash.return_squash h' in\n let _ = FStar.Squash.return_squash hx in\n h_includes p1 p2 p1' p2')\n p1 p2 h)", "val readable_gpointer_of_buffer_cell\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ buffer_readable h b))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ readable h (gpointer_of_buffer_cell b i)))\n [SMTPat (readable h (gpointer_of_buffer_cell b i))]", "val buffer_readable_intro\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: Lemma\n (requires (\n buffer_live h b /\\ (\n forall (i: UInt32.t) .\n UInt32.v i < UInt32.v (buffer_length b) ==>\n readable h (gpointer_of_buffer_cell b i)\n )))\n (ensures (buffer_readable h b))", "val buffer_readable_elim\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: Lemma\n (requires (\n buffer_readable h b\n ))\n (ensures (\n buffer_live h b /\\ (\n forall (i: UInt32.t) .\n UInt32.v i < UInt32.v (buffer_length b) ==>\n readable h (gpointer_of_buffer_cell b i)\n )))", "val loc : Type u#0", "let path_disjoint_step\n (#from: typ)\n (#through: typ)\n (#to1: typ)\n (#to2: typ)\n (p: path from through)\n (s1: step through to1)\n (s2: step through to2 { step_disjoint s1 s2 } )\n: Lemma\n (requires True)\n (ensures (path_disjoint (PathStep through to1 p s1) (PathStep through to2 p s2)))\n [SMTPat (path_disjoint (PathStep through to1 p s1) (PathStep through to2 p s2))]\n= FStar.Classical.give_witness (FStar.Squash.return_squash (PathDisjointStep p s1 s2))", "val loc_none: loc", "val loc_union\n (s1 s2: loc)\n: GTot loc", "val loc_union_idem\n (s: loc)\n: Lemma\n (loc_union s s == s)\n [SMTPat (loc_union s s)]", "let path_disjoint_includes\n (#from: typ)\n (#to1: typ)\n (#to2: typ)\n (p1: path from to1)\n (p2: path from to2)\n (#to1': typ)\n (#to2': typ)\n (p1': path from to1')\n (p2': path from to2')\n: Lemma\n (requires (path_disjoint p1 p2 /\\ path_includes p1 p1' /\\ path_includes p2 p2'))\n (ensures (path_disjoint p1' p2'))\n= let h : squash (path_disjoint_t p1 p2) = FStar.Squash.join_squash () in\n FStar.Squash.bind_squash h (fun h -> FStar.Squash.return_squash (PathDisjointIncludes p1 p2 p1' p2' h))", "val loc_pointer\n (#t: typ)\n (p: pointer t)\n: GTot loc", "val loc_buffer\n (#t: typ)\n (b: buffer t)\n: GTot loc", "val loc_addresses\n (r: HS.rid)\n (n: Set.set nat)\n: GTot loc", "val loc_regions\n (r: Set.set HS.rid)\n: GTot loc", "let path_disjoint_includes_l\n (#from: typ)\n (#to1: typ)\n (#to2: typ)\n (p1: path from to1)\n (p2: path from to2)\n (#to1': typ)\n (p1': path from to1')\n: Lemma\n (requires (path_disjoint p1 p2 /\\ path_includes p1 p1'))\n (ensures (path_disjoint p1' p2))\n [SMTPatOr [\n [SMTPat (path_disjoint p1 p2); SMTPat (path_includes p1 p1')];\n [SMTPat (path_disjoint p1' p2); SMTPat (path_includes p1 p1')];\n ]]\n= path_disjoint_includes p1 p2 p1' p2", "val loc_includes\n (s1 s2: loc)\n: GTot Type0", "val loc_includes_refl\n (s: loc)\n: Lemma\n (loc_includes s s)\n [SMTPat (loc_includes s s)]", "val loc_includes_trans\n (s1 s2 s3: loc)\n: Lemma\n (requires (loc_includes s1 s2 /\\ loc_includes s2 s3))\n (ensures (loc_includes s1 s3))", "let path_disjoint_sym\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n: Lemma\n (requires (path_disjoint p1 p2))\n (ensures (path_disjoint p2 p1))\n [SMTPatOr [[SMTPat (path_disjoint p1 p2)]; [SMTPat (path_disjoint p2 p1)]]]\n= path_disjoint_ind\n (fun #v1 #v2 p1 p2 -> path_disjoint p2 p1)\n (fun #through #to1 #to2 p s1 s2 -> path_disjoint_step p s2 s1)\n (fun #v1 #v2 p1 p2 #v1' #v2' p1' p2' -> path_disjoint_includes p2 p1 p2' p1')\n p1 p2", "val loc_includes_union_r\n (s s1 s2: loc)\n: Lemma\n (requires (loc_includes s s1 /\\ loc_includes s s2))\n (ensures (loc_includes s (loc_union s1 s2)))\n [SMTPat (loc_includes s (loc_union s1 s2))]", "val loc_includes_union_l\n (s1 s2 s: loc)\n: Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))\n [SMTPat (loc_includes (loc_union s1 s2) s)]", "let rec path_equal\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n: Tot (b: bool { b == true <==> (value1 == value2 /\\ p1 == p2) } )\n (decreases p1)\n= match p1 with\n | PathBase -> PathBase? p2\n | PathStep _ _ p1' s1 ->\n PathStep? p2 && (\n let (PathStep _ _ p2' s2) = p2 in (\n path_equal p1' p2' &&\n step_eq s1 s2\n ))", "val loc_includes_none\n (s: loc)\n: Lemma\n (loc_includes s loc_none)\n [SMTPat (loc_includes s loc_none)]", "val loc_includes_pointer_pointer\n (#t1 #t2: typ)\n (p1: pointer t1)\n (p2: pointer t2)\n: Lemma\n (requires (includes p1 p2))\n (ensures (loc_includes (loc_pointer p1) (loc_pointer p2)))\n [SMTPat (loc_includes (loc_pointer p1) (loc_pointer p2))]", "let rec path_length_concat\n (#t0 #t1 #t2: typ)\n (p01: path t0 t1)\n (p12: path t1 t2)\n: Lemma\n (requires True)\n (ensures (path_length (path_concat p01 p12) == path_length p01 + path_length p12))\n (decreases p12)\n= match p12 with\n | PathBase -> ()\n | PathStep _ _ p' s' -> path_length_concat p01 p'", "val loc_includes_gsingleton_buffer_of_pointer\n (l: loc)\n (#t: typ)\n (p: pointer t)\n: Lemma\n (requires (loc_includes l (loc_pointer p)))\n (ensures (loc_includes l (loc_buffer (gsingleton_buffer_of_pointer p))))\n [SMTPat (loc_includes l (loc_buffer (gsingleton_buffer_of_pointer p)))]", "val loc_includes_gbuffer_of_array_pointer\n (l: loc)\n (#len: array_length_t)\n (#t: typ)\n (p: pointer (TArray len t))\n: Lemma\n (requires (loc_includes l (loc_pointer p)))\n (ensures (loc_includes l (loc_buffer (gbuffer_of_array_pointer p))))\n [SMTPat (loc_includes l (loc_buffer (gbuffer_of_array_pointer p)))]", "let rec path_concat_inj_l\n (#from #through1: typ)\n (p1_: path from through1)\n (#v1: typ)\n (p1: path through1 v1)\n (#through2 #v2: typ)\n (p2_: path from through2)\n (p2: path through2 v2)\n: Lemma\n (requires (path_equal (path_concat p1_ p1) (path_concat p2_ p2) == true /\\ path_length p1_ == path_length p2_))\n (ensures (path_equal p1_ p2_ == true /\\ path_equal p1 p2 == true))\n (decreases p1)\n= path_length_concat p1_ p1;\n path_length_concat p2_ p2;\n match p1 with\n | PathBase -> ()\n | PathStep _ _ p1' s1 ->\n let (PathStep _ _ p2' s2) = p2 in\n path_concat_inj_l p1_ p1' p2_ p2'", "val loc_includes_gpointer_of_array_cell\n (l: loc)\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_includes l (loc_buffer b)))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_includes l (loc_pointer (gpointer_of_buffer_cell b i))))\n [SMTPat (loc_includes l (loc_pointer (gpointer_of_buffer_cell b i)))]", "val loc_includes_gsub_buffer_r\n (l: loc)\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ loc_includes l (loc_buffer b)))\n (ensures (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ loc_includes l (loc_buffer (gsub_buffer b i len))))\n [SMTPat (loc_includes l (loc_buffer (gsub_buffer b i len)))]", "path_disjoint_decomp_t", "PathDisjointDecomp", "PathDisjointDecomp", "PathDisjointDecomp", "d_through", "d_through", "val loc_includes_gsub_buffer_l\n (#t: typ)\n (b: buffer t)\n (i1: UInt32.t)\n (len1: UInt32.t)\n (i2: UInt32.t)\n (len2: UInt32.t)\n: Lemma\n (requires (UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b) /\\ UInt32.v i1 <= UInt32.v i2 /\\ UInt32.v i2 + UInt32.v len2 <= UInt32.v i1 + UInt32.v len1))\n (ensures (UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b) /\\ UInt32.v i1 <= UInt32.v i2 /\\ UInt32.v i2 + UInt32.v len2 <= UInt32.v i1 + UInt32.v len1 /\\ loc_includes (loc_buffer (gsub_buffer b i1 len1)) (loc_buffer (gsub_buffer b i2 len2))))\n [SMTPat (loc_includes (loc_buffer (gsub_buffer b i1 len1)) (loc_buffer (gsub_buffer b i2 len2)))]", "d_p", "d_p", "d_v1", "d_v1", "d_s1", "d_s1", "d_p1'", "d_p1'", "d_v2", "d_v2", "d_s2", "d_s2", "d_p2'", "d_p2'", "val loc_includes_addresses_pointer\n (#t: typ)\n (r: HS.rid)\n (s: Set.set nat)\n (p: pointer t)\n: Lemma\n (requires (frameOf p == r /\\ Set.mem (as_addr p) s))\n (ensures (loc_includes (loc_addresses r s) (loc_pointer p)))\n [SMTPat (loc_includes (loc_addresses r s) (loc_pointer p))]", "let path_disjoint_decomp_includes\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n (#value1': typ)\n (#value2': typ)\n (p1': path from value1')\n (p2': path from value2')\n: Lemma\n (requires (\n path_includes p1 p1' /\\\n path_includes p2 p2' /\\ (\n exists (d : path_disjoint_decomp_t p1 p2) . True\n )))\n (ensures (exists (d: path_disjoint_decomp_t p1' p2') . True))\n= let f\n (q1: path value1 value1' )\n (q2: path value2 value2' )\n (d: path_disjoint_decomp_t p1 p2)\n : Lemma\n (requires (\n p1' == path_concat p1 q1 /\\\n p2' == path_concat p2 q2\n ))\n (ensures (exists (d: path_disjoint_decomp_t p1' p2') . True))\n = let (PathDisjointDecomp _ p _ s1 p1_ _ s2 p2_ _) = d in\n path_concat_assoc (PathStep _ _ p s1) p1_ q1;\n path_concat_assoc (PathStep _ _ p s2) p2_ q2;\n let d' : path_disjoint_decomp_t p1' p2' =\n PathDisjointDecomp _ p _ s1 (path_concat p1_ q1) _ s2 (path_concat p2_ q2) ()\n in\n Classical.exists_intro (fun _ -> True) d'\n in\n let g\n (q1: path value1 value1' )\n (q2: path value2 value2' )\n (d: path_disjoint_decomp_t p1 p2)\n : Lemma\n ((\n p1' == path_concat p1 q1 /\\\n p2' == path_concat p2 q2\n ) ==> (\n exists (d: path_disjoint_decomp_t p1' p2') . True\n ))\n = Classical.move_requires (f q1 q2) d // FIXME: annoying to repeat those type annotations above. WHY WHY WHY can't I just use (fun q1 q2 d -> Classical.move_requires (f q1 q2) d) as an argument of Classical.forall_intro_3 below instead of this g???\n in\n path_includes_exists_concat p1 p1' ;\n path_includes_exists_concat p2 p2' ;\n let _ : squash (exists (d: path_disjoint_decomp_t p1' p2') . True) =\n Classical.forall_intro_3 g\n in\n ()", "val loc_includes_addresses_buffer\n (#t: typ)\n (r: HS.rid)\n (s: Set.set nat)\n (p: buffer t)\n: Lemma\n (requires (frameOf_buffer p == r /\\ Set.mem (buffer_as_addr p) s))\n (ensures (loc_includes (loc_addresses r s) (loc_buffer p)))\n [SMTPat (loc_includes (loc_addresses r s) (loc_buffer p))]", "val loc_includes_region_pointer\n (#t: typ)\n (s: Set.set HS.rid)\n (p: pointer t)\n: Lemma\n (requires (Set.mem (frameOf p) s))\n (ensures (loc_includes (loc_regions s) (loc_pointer p)))\n [SMTPat (loc_includes (loc_regions s) (loc_pointer p))]", "val loc_includes_region_buffer\n (#t: typ)\n (s: Set.set HS.rid)\n (b: buffer t)\n: Lemma\n (requires (Set.mem (frameOf_buffer b) s))\n (ensures (loc_includes (loc_regions s) (loc_buffer b)))\n [SMTPat (loc_includes (loc_regions s) (loc_buffer b))]", "val loc_includes_region_addresses\n (s: Set.set HS.rid)\n (r: HS.rid)\n (a: Set.set nat)\n: Lemma\n (requires (Set.mem r s))\n (ensures (loc_includes (loc_regions s) (loc_addresses r a)))\n [SMTPat (loc_includes (loc_regions s) (loc_addresses r a))]", "val loc_includes_region_region\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires (Set.subset s2 s1))\n (ensures (loc_includes (loc_regions s1) (loc_regions s2)))\n [SMTPat (loc_includes (loc_regions s1) (loc_regions s2))]", "val loc_includes_region_union_l\n (l: loc)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires (loc_includes l (loc_regions (Set.intersect s2 (Set.complement s1)))))\n (ensures (loc_includes (loc_union (loc_regions s1) l) (loc_regions s2)))\n [SMTPat (loc_includes (loc_union (loc_regions s1) l) (loc_regions s2))]", "let path_disjoint_decomp\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n: Lemma\n (requires (path_disjoint p1 p2))\n (ensures (exists (d: path_disjoint_decomp_t p1 p2) . True))\n= path_disjoint_ind\n (fun #v1 #v2 p1 p2 -> exists (d: path_disjoint_decomp_t #from #v1 #v2 p1 p2) . True)\n (fun #through #to1 #to2 p s1 s2 ->\n let d : path_disjoint_decomp_t (PathStep _ _ p s1) (PathStep _ _ p s2) =\n PathDisjointDecomp _ p _ s1 PathBase _ s2 PathBase ()\n in\n Classical.exists_intro (fun _ -> True) d\n )\n (fun #v1 #v2 p1 p2 #v1' #v2' p1' p2' -> path_disjoint_decomp_includes p1 p2 p1' p2')\n p1 p2", "val loc_disjoint\n (s1 s2: loc)\n: GTot Type0", "val loc_disjoint_sym\n (s1 s2: loc)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))\n [SMTPat (loc_disjoint s1 s2)]", "val loc_disjoint_none_r\n (s: loc)\n: Lemma\n (ensures (loc_disjoint s loc_none))\n [SMTPat (loc_disjoint s loc_none)]", "let path_disjoint_not_path_equal\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n: Lemma\n (requires (path_disjoint p1 p2))\n (ensures (path_equal p1 p2 == false))\n= let f\n (d: path_disjoint_decomp_t p1 p2)\n : Lemma (path_equal p1 p2 == false)\n = if path_equal p1 p2\n then\n let (PathDisjointDecomp _ p _ s1 p1_ _ s2 p2_ _) = d in\n path_concat_inj_l (PathStep _ _ p s1) p1_ (PathStep _ _ p s2) p2_\n else ()\n in\n path_disjoint_decomp p1 p2;\n Classical.forall_intro f", "val loc_disjoint_union_r\n (s s1 s2: loc)\n: Lemma\n (requires (loc_disjoint s s1 /\\ loc_disjoint s s2))\n (ensures (loc_disjoint s (loc_union s1 s2)))\n [SMTPat (loc_disjoint s (loc_union s1 s2))]", "val loc_disjoint_root\n (#value1: typ)\n (#value2: typ)\n (p1: pointer value1)\n (p2: pointer value2)\n: Lemma\n (requires (frameOf p1 <> frameOf p2 \\/ as_addr p1 <> as_addr p2))\n (ensures (loc_disjoint (loc_pointer p1) (loc_pointer p2)))", "val loc_disjoint_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd1 fd2: struct_field l)\n: Lemma\n (requires (fd1 <> fd2))\n (ensures (loc_disjoint (loc_pointer (gfield p fd1)) (loc_pointer (gfield p fd2))))\n [SMTPat (loc_disjoint (loc_pointer (gfield p fd1)) (loc_pointer (gfield p fd2)))]", "let rec path_destruct_l\n (#t0 #t2: typ)\n (p: path t0 t2)\n: Tot (\n x: option (t1: typ & (s: step t0 t1 & (p' : path t1 t2 { p == path_concat (PathStep _ _ PathBase s) p' /\\ path_length p' < path_length p } ) ) )\n { None? x <==> PathBase? p }\n )\n (decreases p)\n= match p with\n | PathBase -> None\n | PathStep _ _ p' s ->\n begin match path_destruct_l p' with\n | None -> Some (| _, (| s, PathBase |) |)\n | Some (| t_, (| s_, p_ |) |) ->\n Some (| t_, (| s_, PathStep _ _ p_ s |) |)\n end", "val loc_disjoint_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n (i1: UInt32.t)\n (i2: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i1 < UInt32.v length /\\\n UInt32.v i2 < UInt32.v length /\\\n UInt32.v i1 <> UInt32.v i2\n ))\n (ensures (\n UInt32.v i1 < UInt32.v length /\\\n UInt32.v i2 < UInt32.v length /\\ \n loc_disjoint (loc_pointer (gcell p i1)) (loc_pointer (gcell p i2))\n ))\n [SMTPat (loc_disjoint (loc_pointer (gcell p i1)) (loc_pointer (gcell p i2)))]", "let rec path_equal'\n (#from #to1 #to2: typ)\n (p1: path from to1)\n (p2: path from to2)\n: Tot (b: bool { b == true <==> to1 == to2 /\\ p1 == p2 } )\n (decreases (path_length p1))\n= match path_destruct_l p1 with\n | None -> PathBase? p2\n | Some (| t1, (| s1, p1' |) |) ->\n begin match path_destruct_l p2 with\n | None -> false\n | (Some (| t2, (| s2, p2' |) |) ) ->\n step_eq s1 s2 &&\n path_equal' p1' p2'\n end", "val loc_disjoint_includes\n (p1 p2 p1' p2' : loc)\n: Lemma\n (requires (loc_includes p1 p1' /\\ loc_includes p2 p2' /\\ loc_disjoint p1 p2))\n (ensures (loc_disjoint p1' p2'))", "let path_includes_concat_l\n (#from #through #to1 #to2: typ)\n (p0: path from through)\n (p1: path through to1)\n (p2: path through to2)\n: Lemma\n (requires (path_includes p1 p2))\n (ensures (path_includes (path_concat p0 p1) (path_concat p0 p2)))\n= path_includes_ind\n (fun #to1_ #to2_ p1_ p2_ -> path_includes (path_concat p0 p1_) (path_concat p0 p2_))\n (fun #through #to p st -> ())\n (fun #to p -> path_includes_refl (path_concat p0 p))\n (fun #to1_ #to2_ #to3_ p1_ p2_ p3_ -> path_includes_trans (path_concat p0 p1_) (path_concat p0 p2_) (path_concat p0 p3_))\n p1 p2", "val live_unused_in_disjoint_strong\n (#value1: typ)\n (#value2: typ)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: pointer value2)\n: Lemma\n (requires (live h p1 /\\ unused_in p2 h))\n (ensures (frameOf p1 <> frameOf p2 \\/ as_addr p1 <> as_addr p2))", "let path_disjoint_concat\n (#from #through #to1 #to2: typ)\n (p0: path from through)\n (p1: path through to1)\n (p2: path through to2)\n: Lemma\n (requires (path_disjoint p1 p2))\n (ensures (path_disjoint (path_concat p0 p1) (path_concat p0 p2)))\n= path_disjoint_ind\n (fun #v1 #v2 p1 p2 -> path_disjoint (path_concat p0 p1) (path_concat p0 p2))\n (fun #through #to1 #to2 p s1 s2 -> path_disjoint_step (path_concat p0 p) s1 s2)\n (fun #v1 #v2 p1 p2 #v1' #v2' p1' p2' ->\n path_includes_concat_l p0 p1 p1';\n path_includes_concat_l p0 p2 p2';\n path_disjoint_includes (path_concat p0 p1) (path_concat p0 p2) (path_concat p0 p1') (path_concat p0 p2'))\n p1 p2", "val live_unused_in_disjoint\n (#value1: typ)\n (#value2: typ)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: pointer value2)\n: Lemma\n (requires (live h p1 /\\ unused_in p2 h))\n (ensures (loc_disjoint (loc_pointer p1) (loc_pointer p2)))\n [SMTPatOr [\n [SMTPat (loc_disjoint (loc_pointer p1) (loc_pointer p2)); SMTPat (live h p1)];\n [SMTPat (loc_disjoint (loc_pointer p1) (loc_pointer p2)); SMTPat (unused_in p2 h)];\n [SMTPat (live h p1); SMTPat (unused_in p2 h)];\n ]]", "val pointer_live_reference_unused_in_disjoint\n (#value1: typ)\n (#value2: Type0)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: HS.reference value2)\n: Lemma\n (requires (live h p1 /\\ HS.unused_in p2 h))\n (ensures (loc_disjoint (loc_pointer p1) (loc_addresses (HS.frameOf p2) (Set.singleton (HS.as_addr p2)))))\n [SMTPat (live h p1); SMTPat (HS.unused_in p2 h)]", "val reference_live_pointer_unused_in_disjoint\n (#value1: Type0)\n (#value2: typ)\n (h: HS.mem)\n (p1: HS.reference value1)\n (p2: pointer value2)\n: Lemma\n (requires (HS.contains h p1 /\\ unused_in p2 h))\n (ensures (loc_disjoint (loc_addresses (HS.frameOf p1) (Set.singleton (HS.as_addr p1))) (loc_pointer p2)))\n [SMTPat (HS.contains h p1); SMTPat (unused_in p2 h)]", "val loc_disjoint_gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i1: UInt32.t)\n (len1: UInt32.t)\n (i2: UInt32.t)\n (len2: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 + UInt32.v len2 <= UInt32.v (buffer_length b) /\\ (\n UInt32.v i1 + UInt32.v len1 <= UInt32.v i2 \\/\n UInt32.v i2 + UInt32.v len2 <= UInt32.v i1\n )))\n (ensures (\n UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 + UInt32.v len2 <= UInt32.v (buffer_length b) /\\\n loc_disjoint (loc_buffer (gsub_buffer b i1 len1)) (loc_buffer (gsub_buffer b i2 len2))\n ))\n [SMTPat (loc_disjoint (loc_buffer (gsub_buffer b i1 len1)) (loc_buffer (gsub_buffer b i2 len2)))]", "let step_sel_upd_other\n (#from: typ)\n (#to1 #to2: typ)\n (s1: step from to1)\n (s2: step from to2 {step_disjoint s1 s2})\n (m: otype_of_typ from)\n (v: otype_of_typ to1)\n: Lemma\n (step_sel (step_upd m s1 v) s2 == step_sel m s2)\n= match s1 with\n | StepField l1 fd1 ->\n let (m: ostruct l1) = m in\n let (StepField _ fd2) = s2 in\n begin match m with\n | None -> ()\n | Some m -> DM.sel_upd_other m fd1 v fd2\n end\n | StepCell length1 _ i1 ->\n let (m: option (array length1 (otype_of_typ to1))) = m in\n let (StepCell _ _ i2) = s2 in\n begin match m with\n | None -> ()\n | Some m ->\n Seq.lemma_index_upd2 m (UInt32.v i1) v (UInt32.v i2)\n end", "val loc_disjoint_gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n (i1: UInt32.t)\n (i2: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i1 < UInt32.v (buffer_length b) /\\\n UInt32.v i2 < UInt32.v (buffer_length b) /\\ (\n UInt32.v i1 <> UInt32.v i2\n )))\n (ensures (\n UInt32.v i1 < UInt32.v (buffer_length b) /\\\n UInt32.v i2 < UInt32.v (buffer_length b) /\\\n loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i1)) (loc_pointer (gpointer_of_buffer_cell b i2))\n ))\n [SMTPat (loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i1)) (loc_pointer (gpointer_of_buffer_cell b i2)))]", "let path_sel_upd_other\n (#from: typ)\n (#to1 #to2: typ)\n (p1: path from to1)\n (p2: path from to2 {path_disjoint p1 p2})\n: Lemma\n (ensures (forall (m: otype_of_typ from) (v: otype_of_typ to1) . path_sel (path_upd m p1 v) p2 == path_sel m p2))\n= path_disjoint_ind\n (fun #v1 #v2 p1_ p2_ -> forall (m: otype_of_typ from) (v: otype_of_typ v1) . path_sel (path_upd m p1_ v) p2_ == path_sel m p2_)\n (fun #through #to1_ #to2_ p s1 s2 ->\n FStar.Classical.forall_intro_sub #_ #(fun m -> forall (v: otype_of_typ to1_) . path_sel (path_upd m (PathStep through to1_ p s1) v) (PathStep through to2_ p s2) == path_sel m (PathStep through to2_ p s2)) (fun m ->\n\t FStar.Classical.forall_intro_sub #_ #(fun v -> path_sel (path_upd m (PathStep through to1_ p s1) v) (PathStep through to2_ p s2) == path_sel m (PathStep through to2_ p s2)) (fun v ->\n\t let m0 = path_sel m p in\n let m1 = step_sel m0 s1 in\n let m2 = step_sel m0 s2 in\n let m0' = step_upd m0 s1 v in\n path_sel_upd_same m p m0';\n step_sel_upd_other s1 s2 m0 v\n )))\n (fun #v1 #v2 p1 p2 #v1' #v2' p1' p2' ->\n let h1: squash (exists r1 . p1' == path_concat p1 r1) = path_includes_exists_concat p1 p1' in\n let h2: squash (exists r2 . p2' == path_concat p2 r2) = path_includes_exists_concat p2 p2' in\n FStar.Classical.forall_intro_sub #_ #(fun (m: otype_of_typ from) -> forall v . path_sel (path_upd m p1' v) p2' == path_sel m p2') (fun (m: otype_of_typ from) ->\n FStar.Classical.forall_intro_sub #_ #(fun (v: otype_of_typ v1') -> path_sel (path_upd m p1' v) p2' == path_sel m p2') (fun (v: otype_of_typ v1') ->\n FStar.Classical.exists_elim (path_sel (path_upd m p1' v) p2' == path_sel m p2') h1 (fun r1 ->\n\tFStar.Classical.exists_elim (path_sel (path_upd m p1' v) p2' == path_sel m p2') h2 (fun r2 ->\n\t path_upd_concat m p1 r1 v;\n\t path_sel_concat m p2 r2\n\t )))))\n p1 p2", "let loc_disjoint_gpointer_of_buffer_cell_r\n (l: loc)\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint l (loc_buffer b)))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint l (loc_pointer (gpointer_of_buffer_cell b i))))\n [SMTPat (loc_disjoint l (loc_pointer (gpointer_of_buffer_cell b i)))]\n= loc_disjoint_includes l (loc_buffer b) l (loc_pointer (gpointer_of_buffer_cell b i))", "let loc_disjoint_gpointer_of_buffer_cell_l\n (l: loc)\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint (loc_buffer b) l))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i)) l))\n [SMTPat (loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i)) l)]\n= loc_disjoint_includes (loc_buffer b) l (loc_pointer (gpointer_of_buffer_cell b i)) l", "let path_sel_upd_other'\n (#from: typ)\n (#to1: typ)\n (p1: path from to1)\n (m: otype_of_typ from)\n (v: otype_of_typ to1)\n (#to2: typ)\n (p2: path from to2)\n: Lemma\n (requires (path_disjoint p1 p2))\n (ensures (path_sel (path_upd m p1 v) p2 == path_sel m p2))\n= path_sel_upd_other p1 p2", "val loc_disjoint_addresses\n (r1 r2: HS.rid)\n (n1 n2: Set.set nat)\n: Lemma\n (requires (r1 <> r2 \\/ Set.subset (Set.intersect n1 n2) Set.empty))\n (ensures (loc_disjoint (loc_addresses r1 n1) (loc_addresses r2 n2)))\n [SMTPat (loc_disjoint (loc_addresses r1 n1) (loc_addresses r2 n2))]", "val loc_disjoint_pointer_addresses\n (#t: typ)\n (p: pointer t)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (requires (r <> frameOf p \\/ (~ (Set.mem (as_addr p) n))))\n (ensures (loc_disjoint (loc_pointer p) (loc_addresses r n)))\n [SMTPat (loc_disjoint (loc_pointer p) (loc_addresses r n))]", "let equal\n (#t1 #t2: typ)\n (p1: pointer t1)\n (p2: pointer t2)\n: Ghost bool\n (requires True)\n (ensures (fun b -> b == true <==> t1 == t2 /\\ p1 == p2 ))\n= Pointer?.from p1 = Pointer?.from p2 &&\n HS.aref_equal (Pointer?.contents p1) (Pointer?.contents p2) &&\n path_equal (Pointer?.p p1) (Pointer?.p p2)", "val loc_disjoint_buffer_addresses\n (#t: typ)\n (p: buffer t)\n (r: HH.rid)\n (n: Set.set nat)\n: Lemma\n (requires (r <> frameOf_buffer p \\/ (~ (Set.mem (buffer_as_addr p) n))))\n (ensures (loc_disjoint (loc_buffer p) (loc_addresses r n)))\n [SMTPat (loc_disjoint (loc_buffer p) (loc_addresses r n))]", "let as_addr (#t: typ) (p: pointer t) =\n HS.aref_as_addr (Pointer?.contents p)", "val loc_disjoint_regions\n (rs1 rs2: Set.set HS.rid)\n: Lemma\n (requires (Set.subset (Set.intersect rs1 rs2) Set.empty))\n (ensures (loc_disjoint (loc_regions rs1) (loc_regions rs2)))\n [SMTPat (loc_disjoint (loc_regions rs1) (loc_regions rs2))]", "let _field\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n: Tot (pointer (typ_of_struct_field l fd))\n= let (Pointer from contents p') = p in\n let p' : path from (TStruct l) = p' in\n let p'' : path from (typ_of_struct_field l fd) = PathStep _ _ p' (StepField _ fd) in\n Pointer from contents p''", "val modifies\n (s: loc)\n (h1 h2: HS.mem)\n: GTot Type0", "let _cell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n (i: UInt32.t {UInt32.v i < UInt32.v length})\n: Tot (pointer value)\n= let (Pointer from contents p') = p in\n let p' : path from (TArray length value) = p' in\n let p'' : path from value = PathStep _ _ p' (StepCell _ _ i) in\n Pointer from contents p''", "val modifies_loc_regions_intro\n (rs: Set.set HS.rid)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HS.modifies rs h1 h2))\n (ensures (modifies (loc_regions rs) h1 h2))", "val modifies_pointer_elim\n (s: loc)\n (h1 h2: HS.mem)\n (#a': typ)\n (p': pointer a')\n: Lemma\n (requires (\n modifies s h1 h2 /\\\n live h1 p' /\\\n loc_disjoint (loc_pointer p') s\n ))\n (ensures (\n equal_values h1 p' h2 p'\n ))\n [SMTPatOr [\n [ SMTPat (modifies s h1 h2); SMTPat (gread h1 p') ] ;\n [ SMTPat (modifies s h1 h2); SMTPat (readable h1 p') ] ;\n [ SMTPat (modifies s h1 h2); SMTPat (live h1 p') ];\n [ SMTPat (modifies s h1 h2); SMTPat (gread h2 p') ] ;\n [ SMTPat (modifies s h1 h2); SMTPat (readable h2 p') ] ;\n [ SMTPat (modifies s h1 h2); SMTPat (live h2 p') ]\n ] ]", "let _ufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Tot (pointer (typ_of_struct_field l fd))\n= let (Pointer from contents p') = p in\n let p' : path from (TUnion l) = p' in\n let p'' : path from (typ_of_struct_field l fd) = PathStep _ _ p' (StepUField _ fd) in\n Pointer from contents p''", "let unused_in\n (#value: typ)\n (p: pointer value)\n (h: HS.mem)\n: GTot Type0\n= let (Pointer from contents p') = p in\n HS.aref_unused_in contents h", "let pointer_ref_contents : Type0 = (t: typ & otype_of_typ t)", "let live\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n: GTot Type0\n= let rel = Heap.trivial_preorder pointer_ref_contents in\n let (Pointer from contents _) = p in (\n HS.aref_live_at h contents pointer_ref_contents rel /\\ (\n let untyped_contents = HS.greference_of contents pointer_ref_contents rel in (\n dfst (HS.sel h untyped_contents) == from\n )))", "val modifies_buffer_elim\n (#t1: typ)\n (b: buffer t1)\n (p: loc)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_buffer b) p /\\\n buffer_live h b /\\\n (UInt32.v (buffer_length b) == 0 ==> buffer_live h' b) /\\ // necessary for liveness, because all buffers of size 0 are disjoint for any memory location, so we cannot talk about their liveness individually without referring to a larger nonempty buffer\n modifies p h h'\n ))\n (ensures (\n buffer_live h' b /\\ (\n buffer_readable h b ==> (\n\tbuffer_readable h' b /\\\n\tbuffer_as_seq h b == buffer_as_seq h' b\n ))))\n [SMTPatOr [\n [ SMTPat (modifies p h h'); SMTPat (buffer_as_seq h b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (buffer_readable h b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (buffer_live h b) ];\n [ SMTPat (modifies p h h'); SMTPat (buffer_as_seq h' b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (buffer_readable h' b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (buffer_live h' b) ]\n ] ]", "let nlive\n (#value: typ)\n (h: HS.mem)\n (p: npointer value)\n: GTot Type0\n= if g_is_null p\n then True\n else live h p", "let live_nlive\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n= ()", "let g_is_null_nlive\n (#t: typ)\n (h: HS.mem)\n (p: npointer t)\n= ()", "val modifies_reference_elim\n (#t: Type0)\n (b: HS.reference t)\n (p: loc)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_addresses (HS.frameOf b) (Set.singleton (HS.as_addr b))) p /\\\n HS.contains h b /\\\n modifies p h h'\n ))\n (ensures (\n HS.contains h' b /\\\n HS.sel h b == HS.sel h' b\n ))\n [SMTPatOr [\n [ SMTPat (modifies p h h'); SMTPat (HS.sel h b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (HS.contains h b) ];\n [ SMTPat (modifies p h h'); SMTPat (HS.sel h' b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (HS.contains h' b) ]\n ] ]", "let greference_of\n (#value: typ)\n (p: pointer value)\n: Ghost (HS.reference pointer_ref_contents)\n (requires (exists h . live h p))\n (ensures (fun x -> (exists h . live h p) /\\ x == HS.greference_of (Pointer?.contents p) pointer_ref_contents (Heap.trivial_preorder pointer_ref_contents) /\\ HS.aref_of x == Pointer?.contents p))\n= HS.greference_of (Pointer?.contents p) pointer_ref_contents (Heap.trivial_preorder pointer_ref_contents)", "let unused_in_greference_of\n (#value: typ)\n (p: pointer value)\n (h: HS.mem)\n: Lemma\n (requires (exists h . live h p))\n (ensures ((exists h . live h p) /\\ (HS.unused_in (greference_of p) h <==> unused_in p h)))\n [SMTPatOr [\n [SMTPat (HS.unused_in (greference_of p) h)];\n [SMTPat (unused_in p h)];\n ]]\n= ()", "val modifies_refl\n (s: loc)\n (h: HS.mem)\n: Lemma\n (modifies s h h)\n [SMTPat (modifies s h h)]", "let live_not_unused_in\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n= let f () : Lemma\n (requires (live h p /\\ p `unused_in` h))\n (ensures False)\n = let r = greference_of p in\n HS.contains_aref_unused_in h r (Pointer?.contents p)\n in\n Classical.move_requires f ()", "val modifies_loc_includes\n (s1: loc)\n (h h': HS.mem)\n (s2: loc)\n: Lemma\n (requires (modifies s2 h h' /\\ loc_includes s1 s2))\n (ensures (modifies s1 h h'))\n [SMTPat (modifies s1 h h'); SMTPat (modifies s2 h h')]", "let gread\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n: GTot (type_of_typ value)\n= if StrongExcludedMiddle.strong_excluded_middle (live h p)\n then\n let content = greference_of p in\n let (| _, c |) = HS.sel h content in\n value_of_ovalue value (path_sel c (Pointer?.p p))\n else\n dummy_val value", "val modifies_trans\n (s12: loc)\n (h1 h2: HS.mem)\n (s23: loc)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))\n [SMTPat (modifies s12 h1 h2); SMTPat (modifies s23 h2 h3)]", "let modifies_0 (h0 h1: HS.mem) : GTot Type0 =\n modifies loc_none h0 h1", "let frameOf\n (#value: typ)\n (p: pointer value)\n: GTot HS.rid\n= HS.frameOf_aref (Pointer?.contents p)", "let modifies_1 (#t: typ) (p: pointer t) (h0 h1: HS.mem) : GTot Type0 =\n modifies (loc_pointer p) h0 h1", "let live_region_frameOf #value h p =\n let content = greference_of p in\n assert (HS.contains h content)", "val screate\n (value:typ)\n (s: option (type_of_typ value))\n: HST.StackInline (pointer value)\n (requires (fun h -> True))\n (ensures (fun (h0:HS.mem) b h1 ->\n unused_in b h0\n /\\ live h1 b\n /\\ frameOf b = HS.get_tip h0\n /\\ modifies_0 h0 h1\n /\\ begin match s with\n | Some s' ->\n\t readable h1 b /\\\n\t gread h1 b == s'\n | _ -> True\n end\n ))", "let disjoint_roots_intro_pointer_vs_pointer\n (#value1 value2: typ)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: pointer value2)\n: Lemma\n (requires (live h p1 /\\ unused_in p2 h))\n (ensures (frameOf p1 <> frameOf p2 \\/ as_addr p1 =!= as_addr p2))\n= ()", "let disjoint_roots_intro_pointer_vs_reference\n (#value1: typ)\n (#value2: Type)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: HS.reference value2)\n: Lemma\n (requires (live h p1 /\\ p2 `HS.unused_in` h))\n (ensures (frameOf p1 <> HS.frameOf p2 \\/ as_addr p1 =!= HS.as_addr p2))\n= let r = greference_of p1 in\n assert (HS.contains h r)", "val ecreate\n (t:typ)\n (r:HS.rid)\n (s: option (type_of_typ t))\n: HST.ST (pointer t)\n (requires (fun h -> is_eternal_region r /\\ HST.witnessed (region_contains_pred r)))\n (ensures (fun (h0:HS.mem) b h1 -> unused_in b h0\n /\\ live h1 b\n /\\ frameOf b == r\n /\\ modifies_0 h0 h1\n /\\ begin match s with\n | Some s' ->\n\treadable h1 b /\\\n\tgread h1 b == s'\n | _ -> True\n end\n /\\ ~(is_mm b)))", "let disjoint_roots_intro_reference_vs_pointer\n (#value1: Type)\n (#value2: typ)\n (h: HS.mem)\n (p1: HS.reference value1)\n (p2: pointer value2)\n: Lemma\n (requires (HS.contains h p1 /\\ p2 `unused_in` h))\n (ensures (HS.frameOf p1 <> frameOf p2 \\/ HS.as_addr p1 =!= as_addr p2))\n= ()", "val field\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n: HST.Stack (pointer (typ_of_struct_field l fd))\n (requires (fun h -> live h p))\n (ensures (fun h0 p' h1 -> h0 == h1 /\\ p' == gfield p fd))", "let is_mm\n (#value: typ)\n (p: pointer value)\n: GTot bool\n= HS.aref_is_mm (Pointer?.contents p)", "val ufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: HST.Stack (pointer (typ_of_struct_field l fd))\n (requires (fun h -> live h p))\n (ensures (fun h0 p' h1 -> h0 == h1 /\\ p' == gufield p fd))", "val cell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n (i: UInt32.t)\n: HST.Stack (pointer value)\n (requires (fun h -> UInt32.v i < UInt32.v length /\\ live h p))\n (ensures (fun h0 p' h1 -> UInt32.v i < UInt32.v length /\\ h0 == h1 /\\ p' == gcell p i))", "let gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= _field p fd", "let as_addr_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()", "val read\n (#value: typ)\n (p: pointer value)\n: HST.Stack (type_of_typ value)\n (requires (fun h -> readable h p))\n (ensures (fun h0 v h1 -> readable h0 p /\\ h0 == h1 /\\ v == gread h0 p))", "let unused_in_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n (h: HS.mem)\n= ()", "val is_null\n (#t: typ)\n (p: npointer t)\n: HST.Stack bool\n (requires (fun h -> nlive h p))\n (ensures (fun h b h' -> h' == h /\\ b == g_is_null p))", "let live_gfield\n (h: HS.mem)\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()", "val write: #a:typ -> b:pointer a -> z:type_of_typ a -> HST.Stack unit\n (requires (fun h -> live h b))\n (ensures (fun h0 _ h1 -> live h0 b /\\ live h1 b\n /\\ modifies_1 b h0 h1\n /\\ readable h1 b\n /\\ gread h1 b == z ))", "let gread_gfield\n (h: HS.mem)\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()", "val write_union_field\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: HST.Stack unit\n (requires (fun h -> live h p))\n (ensures (fun h0 _ h1 -> live h0 p /\\ live h1 p\n /\\ modifies_1 p h0 h1\n /\\ is_active_union_field h1 p fd\n ))", "let frameOf_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()", "let is_mm_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()", "val modifies_fresh_frame_popped\n (h0 h1: HS.mem)\n (s: loc)\n (h2 h3: HS.mem)\n: Lemma\n (requires (\n HS.fresh_frame h0 h1 /\\\n modifies (loc_union (loc_regions (HS.mod_set (Set.singleton (HS.get_tip h1)))) s) h1 h2 /\\\n (HS.get_tip h2) == (HS.get_tip h1) /\\\n HS.popped h2 h3\n ))\n (ensures (\n modifies s h0 h3 /\\\n (HS.get_tip h3) == HS.get_tip h0\n ))\n [SMTPat (HS.fresh_frame h0 h1); SMTPat (HS.popped h2 h3); SMTPat (modifies s h0 h3)]", "let gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= _ufield p fd", "let as_addr_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()", "let unused_in_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n (h: HS.mem)\n= ()", "val modifies_only_live_regions\n (rs: Set.set HS.rid)\n (l: loc)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions rs) l) h h' /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))", "let live_gufield\n (h: HS.mem)\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()", "let gread_gufield\n (h: HS.mem)\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()", "val modifies_loc_addresses_intro\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_regions (Set.singleton r)) l) h1 h2 /\\\n HS.modifies_ref r a h1 h2\n ))\n (ensures (modifies (loc_union (loc_addresses r a) l) h1 h2))", "let frameOf_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()", "let is_mm_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()", "val modifies_1_readable_struct\n (#l: struct_typ)\n (f: struct_field l)\n (p: pointer (TStruct l))\n (h h' : HS.mem)\n: Lemma\n (requires (readable h p /\\ modifies_1 (gfield p f) h h' /\\ readable h' (gfield p f)))\n (ensures (readable h' p))\n [SMTPatOr [\n [SMTPat (modifies_1 (gfield p f) h h'); SMTPat (readable h p)];\n [SMTPat (modifies_1 (gfield p f) h h'); SMTPat (readable h' p)];\n [SMTPat (readable h p); SMTPat (readable h' (gfield p f))];\n// [SMTPat (readable h' p); SMTPat (readable h' (gfield p f))]; // this pattern is incomplete\n [SMTPat (readable h p); SMTPat (readable h' p); SMTPat (gfield p f)];\n]]", "let gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n i\n= _cell p i", "let as_addr_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n i\n= ()", "let unused_in_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n i\n= ()", "val modifies_1_readable_array\n (#t: typ)\n (#len: array_length_t)\n (i: UInt32.t)\n (p: pointer (TArray len t))\n (h h' : HS.mem)\n: Lemma\n (requires (UInt32.v i < UInt32.v len /\\ readable h p /\\ modifies_1 (gcell p i) h h' /\\ readable h' (gcell p i)))\n (ensures (readable h' p))\n [SMTPatOr [\n [SMTPat (modifies_1 (gcell p i) h h'); SMTPat (readable h p)];\n [SMTPat (modifies_1 (gcell p i) h h'); SMTPat (readable h' p)];\n [SMTPat (readable h p); SMTPat (readable h' (gcell p i))];\n// [SMTPat (readable h' p); SMTPat (readable h' (gcell p i))]; // this pattern is incomplete\n [SMTPat (readable h p); SMTPat (readable h' p); SMTPat (gcell p i)];\n ]]", "let live_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n i\n= ()", "let gread_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n i\n= ()", "val read_buffer\t\t\n (#t: typ)\t\t\n (b: buffer t)\t\t\n (i: UInt32.t)\t\t\n: HST.Stack (type_of_typ t)\t\t\n (requires (fun h -> UInt32.v i < UInt32.v (buffer_length b) /\\ readable h (gpointer_of_buffer_cell b i)))\t\t\n (ensures (fun h v h' -> UInt32.v i < UInt32.v (buffer_length b) /\\ h' == h /\\ v == Seq.index (buffer_as_seq h b) (UInt32.v i)))", "let frameOf_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n i\n= ()", "val write_buffer\t\t\n (#t: typ)\t\t\n (b: buffer t)\t\t\n (i: UInt32.t)\t\t\n (v: type_of_typ t)\t\t\n: HST.Stack unit\t\t\n (requires (fun h -> UInt32.v i < UInt32.v (buffer_length b) /\\ buffer_live h b))\t\t\n (ensures (fun h _ h' ->\t\t\n UInt32.v i < UInt32.v (buffer_length b) /\\\t\t\n modifies_1 (gpointer_of_buffer_cell b i) h h' /\\\t\t\n buffer_live h' b /\\\t\t\n readable h' (gpointer_of_buffer_cell b i) /\\\t\t\n Seq.index (buffer_as_seq h' b) (UInt32.v i) == v /\\\t\t\n (buffer_readable h b ==> buffer_readable h' b)\t\t\n ))", "let is_mm_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n i\n= ()", "let includes\n (#value1: typ)\n (#value2: typ)\n (p1: pointer value1)\n (p2: pointer value2)\n: GTot bool\n= Pointer?.from p1 = Pointer?.from p2 &&\n HS.aref_equal (Pointer?.contents p1) (Pointer?.contents p2) &&\n path_includes (Pointer?.p p1) (Pointer?.p p2)", "val buffer_live_unused_in_disjoint\n (#t1 #t2: typ)\n (h: HS.mem)\n (b1: buffer t1)\n (b2: buffer t2)\n: Lemma\n (requires (buffer_live h b1 /\\ buffer_unused_in b2 h))\n (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2)))\n [SMTPat (buffer_live h b1); SMTPat (buffer_unused_in b2 h)]", "let includes_refl\n (#value: typ)\n (p: pointer value)\n= ()", "let includes_trans\n (#value1 #value2 #value3: typ)\n (p1: pointer value1)\n (p2: pointer value2)\n (p3: pointer value3)\n= path_includes_trans (Pointer?.p p1) (Pointer?.p p2) (Pointer?.p p3)", "val pointer_live_buffer_unused_in_disjoint\n (#t1 #t2: typ)\n (h: HS.mem)\n (b1: pointer t1)\n (b2: buffer t2)\n: Lemma\n (requires (live h b1 /\\ buffer_unused_in b2 h))\n (ensures (loc_disjoint (loc_pointer b1) (loc_buffer b2)))\n [SMTPat (live h b1); SMTPat (buffer_unused_in b2 h)]", "let includes_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()", "let includes_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()", "val buffer_live_pointer_unused_in_disjoint\n (#t1 #t2: typ)\n (h: HS.mem)\n (b1: buffer t1)\n (b2: pointer t2)\n: Lemma\n (requires (buffer_live h b1 /\\ unused_in b2 h))\n (ensures (loc_disjoint (loc_buffer b1) (loc_pointer b2)))\n [SMTPat (buffer_live h b1); SMTPat (unused_in b2 h)]", "let includes_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n i\n= ()", "val reference_live_buffer_unused_in_disjoint\n (#t1: Type0)\n (#t2: typ)\n (h: HS.mem)\n (b1: HS.reference t1)\n (b2: buffer t2)\n: Lemma\n (requires (HS.contains h b1 /\\ buffer_unused_in b2 h))\n (ensures (loc_disjoint (loc_addresses (HS.frameOf b1) (Set.singleton (HS.as_addr b1))) (loc_buffer b2)))\n [SMTPat (HS.contains h b1); SMTPat (buffer_unused_in b2 h)]", "let includes_ind\n (x:((#value1: typ) ->\n (#value2: typ) ->\n (p1: pointer value1) ->\n (p2: pointer value2 {includes p1 p2} ) ->\n GTot Type0))\n (h_field:\n ((l: struct_typ) ->\n (p: pointer (TStruct l)) ->\n (fd: struct_field l {includes p (gfield p fd)}) ->\n Lemma (x p (gfield p fd))))\n (h_ufield:\n ((l: union_typ) ->\n (p: pointer (TUnion l)) ->\n (fd: struct_field l {includes p (gufield p fd)}) ->\n Lemma (x p (gufield p fd))))\n (h_cell:\n ((#length: array_length_t) ->\n (#value: typ) ->\n (p: pointer (TArray length value)) ->\n (i: UInt32.t {UInt32.v i < UInt32.v length /\\ includes p (gcell p i)}) ->\n Lemma (x p (gcell p i))))\n (h_refl:\n ((#value: typ) ->\n (p: pointer value {includes p p}) ->\n Lemma (x p p)))\n (h_trans:\n ((#value1: typ) ->\n (#value2: typ) ->\n (#value3: typ) ->\n (p1: pointer value1) ->\n (p2: pointer value2) ->\n (p3: pointer value3 {includes p1 p2 /\\ includes p2 p3 /\\ includes p1 p3 /\\ x p1 p2 /\\ x p2 p3}) ->\n Lemma (x p1 p3)))\n (#value1: typ)\n (#value2: typ)\n (p1: pointer value1)\n (p2: pointer value2 {includes p1 p2})\n: Lemma (x p1 p2)\n= let (Pointer from contents _) = p1 in\n path_includes_ind\n (fun #to1 #to2 p1_ p2_ -> x (Pointer from contents p1_) (Pointer from contents p2_))\n (fun #through #to p s ->\n match s with\n | StepField l fd -> let (pt: pointer (TStruct l)) = (Pointer from contents p) in h_field l pt fd\n | StepUField l fd -> let (pt: pointer (TUnion l)) = (Pointer from contents p) in h_ufield l pt fd\n | StepCell length value i -> let (pt: pointer (TArray length value)) = (Pointer from contents p) in h_cell pt i\n )\n (fun #to p -> h_refl (Pointer from contents p))\n (fun #to1 #to2 #to3 p1_ p2_ p3_ -> h_trans (Pointer from contents p1_) (Pointer from contents p2_) (Pointer from contents p3_))\n (Pointer?.p p1)\n (Pointer?.p p2)", "val buffer_live_reference_unused_in_disjoint\n (#t1: typ)\n (#t2: Type0)\n (h: HS.mem)\n (b1: buffer t1)\n (b2: HS.reference t2)\n: Lemma\n (requires (buffer_live h b1 /\\ HS.unused_in b2 h))\n (ensures (loc_disjoint (loc_buffer b1) (loc_addresses (HS.frameOf b2) (Set.singleton (HS.as_addr b2)))))", "val root_buffer\n (#t: typ)\n (b: buffer t)\n: GTot (buffer t)", "val buffer_idx\n (#t: typ)\n (b: buffer t)\n: Ghost UInt32.t\n (requires True)\n (ensures (fun y ->\n UInt32.v y + UInt32.v (buffer_length b) <=\n UInt32.v (buffer_length (root_buffer b))\n ))", "val buffer_eq_gsub_root\n (#t: typ)\n (b: buffer t)\n: Lemma\n (b == gsub_buffer (root_buffer b) (buffer_idx b) (buffer_length b))", "val root_buffer_gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)\n ))\n (ensures (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\\n root_buffer (gsub_buffer b i len) == root_buffer b\n ))\n [SMTPat (root_buffer (gsub_buffer b i len))]", "val buffer_idx_gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)\n ))\n (ensures (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\\n buffer_idx (gsub_buffer b i len) == UInt32.add (buffer_idx b) i\n ))\n [SMTPat (buffer_idx (gsub_buffer b i len))]", "val buffer_includes\n (#t: typ)\n (blarge bsmall: buffer t)\n: GTot Type0", "val buffer_includes_refl\n (#t: typ)\n (b: buffer t)\n: Lemma\n (buffer_includes b b)\n [SMTPat (buffer_includes b b)]", "val buffer_includes_trans\n (#t: typ)\n (b1 b2 b3: buffer t)\n: Lemma\n (requires (buffer_includes b1 b2 /\\ buffer_includes b2 b3))\n (ensures (buffer_includes b1 b3))", "val buffer_includes_gsub_r\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)\n ))\n (ensures (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\\n buffer_includes b (gsub_buffer b i len)\n ))", "let readable\n (#a: typ)\n (h: HS.mem)\n (b: pointer a)\n: GTot Type0\n= let () = () in // necessary to somehow remove the `logic` qualifier\n live h b /\\ (\n let content = greference_of b in\n let (| _, c |) = HS.sel h content in\n ovalue_is_readable a (path_sel c (Pointer?.p b))\n )", "val buffer_includes_gsub\n (#t: typ)\n (b: buffer t)\n (i1: UInt32.t)\n (i2: UInt32.t)\n (len1: UInt32.t)\n (len2: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i1 <= UInt32.v i2 /\\\n UInt32.v i2 + UInt32.v len2 <= UInt32.v i1 + UInt32.v len1 /\\\n UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b)\n ))\n (ensures (\n UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 + UInt32.v len2 <= UInt32.v (buffer_length b) /\\\n buffer_includes (gsub_buffer b i1 len1) (gsub_buffer b i2 len2)\n ))\n [SMTPat (buffer_includes (gsub_buffer b i1 len1) (gsub_buffer b i2 len2))]", "let readable_live\n (#a: typ)\n (h: HS.mem)\n (b: pointer a)\n= ()", "let readable_gfield\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()", "let readable_struct\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n: Lemma\n (requires (\n forall (f: struct_field l) .\n readable h (gfield p f)\n ))\n (ensures (readable h p))\n// [SMTPat (readable #(TStruct l) h p)] // TODO: dubious pattern, will probably trigger unreplayable hints\n= let dummy_field : struct_field l = fst (List.Tot.hd l.fields) in // struct is nonempty\n let dummy_field_ptr = gfield p dummy_field in\n assert (readable h dummy_field_ptr);\n let content = greference_of p in\n let (| _, c |) = HS.sel h content in\n let (v: otype_of_typ (TStruct l)) = path_sel c (Pointer?.p p) in\n let (v: ostruct l {Some? v}) = v in\n ovalue_is_readable_struct_intro l v", "val buffer_includes_elim\n (#t: typ)\n (b1 b2: buffer t)\n: Lemma\n (requires (\n buffer_includes b1 b2\n ))\n (ensures (\n UInt32.v (buffer_idx b1) <= UInt32.v (buffer_idx b2) /\\\n UInt32.v (buffer_idx b2) + UInt32.v (buffer_length b2) <= UInt32.v (buffer_idx b1) + UInt32.v (buffer_length b1) /\\\n b2 == gsub_buffer b1 (UInt32.sub (buffer_idx b2) (buffer_idx b1)) (buffer_length b2)\n ))", "val buffer_includes_loc_includes\n (#t: typ)\n (b1 b2: buffer t)\n: Lemma\n (requires (buffer_includes b1 b2))\n (ensures (loc_includes (loc_buffer b1) (loc_buffer b2)))\n [SMTPatOr [\n [SMTPat (buffer_includes b1 b2)];\n [SMTPat (loc_includes(loc_buffer b1) (loc_buffer b2))]\n ]]", "let readable_struct_forall_mem\n (#l: struct_typ)\n (p: pointer (TStruct l))\n: Lemma (forall\n (h: HS.mem)\n . (\n forall (f: struct_field l) .\n readable h (gfield p f)\n ) ==>\n readable h p\n )\n= let f\n (h: HS.mem)\n : Lemma // FIXME: WHY WHY WHY do we need this explicit annotation?\n (requires (\n forall (f: struct_field l) .\n readable h (gfield p f)\n ))\n (ensures (readable h p))\n = readable_struct h p\n in\n Classical.forall_intro (Classical.move_requires f)", "val cloc_aloc: HS.rid -> nat -> Tot Type0", "val cloc_cls: MG.cls cloc_aloc", "val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)", "let rec readable_struct_fields'\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n (s: list string)\n: GTot Type0\n (decreases s)\n= match s with\n | [] -> True\n | f :: s' ->\n readable_struct_fields' h p s' /\\ (\n if List.Tot.mem f (List.Tot.map fst l.fields)\n then\n\tlet f : struct_field l = f in\n\treadable h (gfield p f)\n else\n\tTrue\n )", "val loc_of_cloc (l: MG.loc cloc_cls) : Tot loc", "val loc_of_cloc_of_loc (l: loc) : Lemma\n (loc_of_cloc (cloc_of_loc l) == l)\n [SMTPat (loc_of_cloc (cloc_of_loc l))]", "val cloc_of_loc_of_cloc (l: MG.loc cloc_cls) : Lemma\n (cloc_of_loc (loc_of_cloc l) == l)\n [SMTPat (cloc_of_loc (loc_of_cloc l))]", "val loc_includes_to_cloc (l1 l2: loc) : Lemma\n (loc_includes l1 l2 <==> MG.loc_includes (cloc_of_loc l1) (cloc_of_loc l2))", "val loc_disjoint_to_cloc (l1 l2: loc) : Lemma\n (loc_disjoint l1 l2 <==> MG.loc_disjoint (cloc_of_loc l1) (cloc_of_loc l2))", "val modifies_to_cloc (l: loc) (h1 h2: HS.mem) : Lemma\n (modifies l h1 h2 <==> MG.modifies (cloc_of_loc l) h1 h2)", "let readable_struct_fields #l h p s = readable_struct_fields' h p s", "let readable_struct_fields_nil #l h p = ()", "let readable_struct_fields_cons #l h p f q = ()", "let rec readable_struct_fields_elim\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n (s: list string)\n: Lemma\n (requires (readable_struct_fields h p s))\n (ensures (forall f . (List.Tot.mem f s /\\ List.Tot.mem f (List.Tot.map fst l.fields)) ==> (let f : struct_field l = f in readable h (gfield p f))))\n (decreases s)\n= match s with\n | [] -> ()\n | _ :: q -> readable_struct_fields_elim h p q", "let readable_struct_fields_readable_struct #l h p =\n readable_struct_fields_elim h p (List.Tot.map fst l.fields);\n readable_struct h p", "let readable_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n i\n= ()", "let readable_array\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n= assert (readable h (gcell p 0ul)); // for Some?\n let content = greference_of p in\n let (| _, c |) = HS.sel h content in\n let (v0: otype_of_typ (TArray length value)) = path_sel c (Pointer?.p p) in\n ovalue_is_readable_array_intro v0", "let readable_gufield\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()", "let is_active_union_field\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: GTot Type0\n= let () = () in // necessary to somehow remove the `logic` qualifier\n live h p /\\ (\n let content = greference_of p in\n let (| _, c |) = HS.sel h content in\n let vu : otype_of_typ (TUnion l) = path_sel c (Pointer?.p p) in\n let vu : option (gtdata (struct_field l) (type_of_struct_field' l otype_of_typ)) = vu in\n Some? vu /\\ gtdata_get_key (Some?.v vu) == fd\n )", "let is_active_union_live\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()", "let is_active_union_field_live\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()", "let is_active_union_field_eq\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd1 fd2: struct_field l)\n= ()", "let is_active_union_field_get_key\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()", "let is_active_union_field_readable\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()", "let is_active_union_field_includes_readable\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n (#t': typ)\n (p' : pointer t')\n= let content = greference_of p in\n let (| _ , c |) = HS.sel h content in\n let t = typ_of_struct_field l fd in\n let (Pointer from cts p0) = p in\n let pf = PathStep _ _ p0 (StepUField l fd) in\n let (v0 : otype_of_typ t) = path_sel c pf in\n let phi\n (#t': typ)\n (pt': path from t')\n : Ghost Type0\n (requires (path_includes pf pt'))\n (ensures (fun _ -> True))\n = (~ (path_sel c pt' == none_ovalue t')) ==> is_active_union_field h p fd\n in\n let f\n (t' : typ)\n (pt' : path t t')\n : Lemma\n (ensures (phi (path_concat pf pt')))\n = path_sel_concat c pf pt';\n path_sel_none_ovalue pf;\n path_sel_none_ovalue pt'\n in\n path_concat_includes pf phi f (Pointer?.p p')", "let _singleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n: Tot (buffer t)\n= let Pointer from contents pth = p in\n match pth with\n | PathStep _ _ pth' (StepCell ln ty i) ->\n (* reconstruct the buffer to the enclosing array *)\n Buffer (BufferRootArray #ty #ln (Pointer from contents pth')) i 1ul \n | _ ->\n Buffer (BufferRootSingleton p) 0ul 1ul", "let gsingleton_buffer_of_pointer #t p = _singleton_buffer_of_pointer p", "let singleton_buffer_of_pointer #t p = _singleton_buffer_of_pointer p", "let gbuffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n: GTot (buffer t)\n= Buffer (BufferRootArray p) 0ul length", "let buffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n: HST.Stack (buffer t)\n (requires (fun h -> live h p))\n (ensures (fun h b h' -> h' == h /\\ b == gbuffer_of_array_pointer p))\n= Buffer (BufferRootArray p) 0ul length", "let buffer_length\n (#t: typ)\n (b: buffer t)\n: GTot UInt32.t\n= Buffer?.blength b", "let buffer_length_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n: Lemma\n (requires True)\n (ensures (buffer_length (gsingleton_buffer_of_pointer p) == 1ul))\n [SMTPat (buffer_length (gsingleton_buffer_of_pointer p))]\n= ()", "let buffer_length_gbuffer_of_array_pointer\n (#t: typ)\n (#len: array_length_t)\n (p: pointer (TArray len t))\n: Lemma\n (requires True)\n (ensures (buffer_length (gbuffer_of_array_pointer p) == len))\n [SMTPat (buffer_length (gbuffer_of_array_pointer p))]\n= ()", "let buffer_live\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: GTot Type0\n= let () = () in ( // necessary to somehow remove the `logic` qualifier\n match b.broot with\n | BufferRootSingleton p -> live h p\n | BufferRootArray p -> live h p\n )", "let buffer_live_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n (h: HS.mem)\n: Lemma\n (ensures (buffer_live h (gsingleton_buffer_of_pointer p) <==> live h p ))\n [SMTPat (buffer_live h (gsingleton_buffer_of_pointer p))]\n= ()", "let buffer_live_gbuffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n (h: HS.mem)\n: Lemma\n (requires True)\n (ensures (buffer_live h (gbuffer_of_array_pointer p) <==> live h p))\n [SMTPat (buffer_live h (gbuffer_of_array_pointer p))]\n= ()", "let buffer_unused_in #t b h =\n match b.broot with\n | BufferRootSingleton p -> unused_in p h\n | BufferRootArray p -> unused_in p h", "let buffer_live_not_unused_in #t b h = ()", "let buffer_unused_in_gsingleton_buffer_of_pointer #t p h = ()", "let buffer_unused_in_gbuffer_of_array_pointer #t #length p h = ()", "let frameOf_buffer\n (#t: typ)\n (b: buffer t)\n: GTot HS.rid\n= match b.broot with\n | BufferRootSingleton p -> frameOf p\n | BufferRootArray p -> frameOf p", "let frameOf_buffer_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n= ()", "let frameOf_buffer_gbuffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n= ()", "let live_region_frameOf_buffer #value h p = ()", "let buffer_as_addr #t b =\n match b.broot with\n | BufferRootSingleton p -> as_addr p\n | BufferRootArray p -> as_addr p", "let buffer_as_addr_gsingleton_buffer_of_pointer #t p = ()", "let buffer_as_addr_gbuffer_of_array_pointer #t #length p = ()", "let gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n len\n= Buffer (Buffer?.broot b) FStar.UInt32.(Buffer?.bidx b +^ i) len", "let frameOf_buffer_gsub_buffer #t b i len = ()", "let buffer_as_addr_gsub_buffer #t b i len = ()", "let sub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n len\n= Buffer (Buffer?.broot b) FStar.UInt32.(Buffer?.bidx b +^ i) len", "let offset_buffer #t b i =\n sub_buffer b i (UInt32.sub (Buffer?.blength b) i)", "let buffer_length_gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n len\n= ()", "let buffer_live_gsub_buffer_equiv\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n len\n h\n= ()", "let buffer_live_gsub_buffer_intro\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n len\n h\n= ()", "let buffer_unused_in_gsub_buffer #t b i len h = ()", "let gsub_buffer_gsub_buffer\n (#a: typ)\n (b: buffer a)\n (i1: UInt32.t)\n len1 i2 len2\n= ()", "let gsub_buffer_zero_buffer_length\n (#a: typ)\n (b: buffer a)\n= ()", "let buffer_root_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer_root t)\n: GTot (Seq.seq (type_of_typ t))\n= match b with\n | BufferRootSingleton p ->\n Seq.create 1 (gread h p)\n | BufferRootArray p ->\n gread h p", "let length_buffer_root_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer_root t)\n: Lemma\n (requires True)\n (ensures (Seq.length (buffer_root_as_seq h b) == UInt32.v (buffer_root_length b)))\n [SMTPat (Seq.length (buffer_root_as_seq h b))]\n= ()", "let buffer_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: GTot (Seq.seq (type_of_typ t))\n= let i = UInt32.v (Buffer?.bidx b) in\n Seq.slice (buffer_root_as_seq h (Buffer?.broot b)) i (i + UInt32.v (Buffer?.blength b))", "let buffer_length_buffer_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n= ()", "let buffer_as_seq_gsingleton_buffer_of_pointer #t h p =\n let Pointer from contents pth = p in\n match pth with\n | PathStep through to pth' (StepCell ln ty i) ->\n assert (through == TArray ln ty);\n assert (to == ty);\n assert (t == ty);\n let p' : pointer (TArray ln ty) = Pointer from contents pth' in\n let s : array ln (type_of_typ t) = gread h p' in\n let s1 = Seq.slice s (UInt32.v i) (UInt32.v i + 1) in\n let v = gread h p in\n assert (v == Seq.index s (UInt32.v i));\n let s2 = Seq.create 1 v in\n assert (Seq.length s1 == 1);\n assert (Seq.length s2 == 1);\n assert (Seq.index s1 0 == v);\n assert (Seq.index s2 0 == v);\n assert (Seq.equal s1 s2)\n | _ ->\n Seq.slice_length (Seq.create 1 (gread h p))", "let buffer_as_seq_gbuffer_of_array_pointer\n (#length: array_length_t)\n (#t: typ)\n (h: HS.mem)\n (p: pointer (TArray length t))\n= let s : array length (type_of_typ t) = gread h p in\n Seq.slice_length s", "let buffer_as_seq_gsub_buffer\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n len\n= Seq.slice_slice (buffer_root_as_seq h (Buffer?.broot b)) (UInt32.v (Buffer?.bidx b)) (UInt32.v (Buffer?.bidx b) + UInt32.v (Buffer?.blength b)) (UInt32.v i) (UInt32.v i + UInt32.v len)", "let gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n i\n= match Buffer?.broot b with\n | BufferRootSingleton p -> p\n | BufferRootArray p ->\n gcell p FStar.UInt32.(Buffer?.bidx b +^ i)", "let pointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n i\n= match Buffer?.broot b with\n | BufferRootSingleton p -> p\n | BufferRootArray p ->\n _cell p FStar.UInt32.(Buffer?.bidx b +^ i)", "let gpointer_of_buffer_cell_gsub_buffer\n (#t: typ)\n (b: buffer t)\n i1 len i2\n= ()", "let live_gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n i h\n= ()", "let gpointer_of_buffer_cell_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n i\n= ()", "let gpointer_of_buffer_cell_gbuffer_of_array_pointer\n (#length: array_length_t)\n (#t: typ)\n (p: pointer (TArray length t))\n i\n= ()", "let frameOf_gpointer_of_buffer_cell #t b i = ()", "let as_addr_gpointer_of_buffer_cell #t b i = ()", "let gread_gpointer_of_buffer_cell\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n i\n= ()", "let gread_gpointer_of_buffer_cell'\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n i\n= ()", "let index_buffer_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n i\n= ()", "let gsingleton_buffer_of_pointer_gcell #t #len p i = ()", "let gsingleton_buffer_of_pointer_gpointer_of_buffer_cell #t b i = ()", "let buffer_readable'\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: GTot Type0\n= buffer_live h b /\\ (\n forall (i: UInt32.t) .\n UInt32.v i < UInt32.v (buffer_length b) ==>\n readable h (gpointer_of_buffer_cell b i)\n )" ], "closest": [ "val buffer_readable (#t:base_typ) (h:vale_heap) (b:buffer t) : GTot prop0\nlet buffer_readable #t h b = List.memP b (IB.ptrs_of_mem (_ih h))", "val buffer_readable (#t:base_typ) (h:vale_heap) (b:buffer t) : GTot prop0\nlet buffer_readable #t h b = List.memP b (IB.ptrs_of_mem (_ih h))", "val buffer_readable (#t: M.base_typ) (h: vale_heap) (b: M.buffer t) : GTot prop0\nlet buffer_readable (#t:M.base_typ) (h:vale_heap) (b:M.buffer t) : GTot prop0 = M.buffer_readable #t h b", "val buffer_readable (#t: M.base_typ) (h: vale_heap) (b: M.buffer t) : GTot prop0\nlet buffer_readable (#t:M.base_typ) (h:vale_heap) (b:M.buffer t) : GTot prop0 = M.buffer_readable #t h b", "val buffer_writeable (#t:base_typ) (b:buffer t) : GTot prop0\nlet buffer_writeable #t b = b.writeable", "val buffer_writeable (#t:base_typ) (b:buffer t) : GTot prop0\nlet buffer_writeable #t b = b.writeable", "val sel (#b: _)\n (h:HS.mem)\n (vb:buffer b)\n (i:nat{i < length vb})\n : GTot b\nlet sel (#b: _) (h:HS.mem) (vb:buffer b) (i:nat{i < length vb})\n : GTot b\n = let v = get_view vb in\n let _, es, _ = split_at_i vb i h in\n View?.get v es", "val sel (#b: _)\n (h:HS.mem)\n (vb:buffer b)\n (i:nat{i < length vb})\n : GTot b\nlet sel (#b: _)\n (h:HS.mem)\n (vb:buffer b)\n (i:nat{i < length vb})\n : GTot b\n = indexing vb i;\n let es = B.as_seq h (as_buffer vb) in\n let v = get_view vb in\n sel' v es i", "val fill_buffer_precond' (#t: typ) (b: buffer t) (h: HS.mem) : GTot Type0\nlet fill_buffer_precond'\n (#t: typ)\n (b: buffer t) (* destination *)\n (h: HS.mem)\n: GTot Type0\n= buffer_live h b", "val buffer_writeable (#t: M.base_typ) (b: M.buffer t) : GTot prop0\nlet buffer_writeable (#t:M.base_typ) (b:M.buffer t) : GTot prop0 = M.buffer_writeable #t b", "val buffer_writeable (#t: M.base_typ) (b: M.buffer t) : GTot prop0\nlet buffer_writeable (#t:M.base_typ) (b:M.buffer t) : GTot prop0 = M.buffer_writeable #t b", "val writable (#t: Type) (#rrel #rel: _) (b: B.mbuffer t rrel rel) (pos pos': nat) (h: HS.mem)\n : GTot Type0\nlet writable\n (#t: Type)\n (#rrel #rel: _)\n (b: B.mbuffer t rrel rel)\n (pos pos' : nat)\n (h: HS.mem)\n: GTot Type0\n= let s = B.as_seq h b in\n B.live h b /\\\n ((pos <= pos' /\\ pos' <= B.length b) ==> (\n (forall (s1:Seq.lseq t (pos' - pos)) . {:pattern (Seq.replace_subseq s pos pos' s1)}\n forall (s2:Seq.lseq t (pos' - pos)) . {:pattern (Seq.replace_subseq s pos pos' s2)}\n Seq.replace_subseq s pos pos' s1 `rel` Seq.replace_subseq s pos pos' s2\n )))", "val copy_buffer_contents_precond' (#t: typ) (a b: buffer t) (h: HS.mem) : GTot Type0\nlet copy_buffer_contents_precond'\n (#t: typ)\n (a: buffer t) (* source *)\n (b: buffer t) (* destination *)\n (h: HS.mem)\n: GTot Type0\n= buffer_live h b /\\\n buffer_readable h a /\\\n buffer_length b == buffer_length a /\\\n loc_disjoint (loc_buffer a) (loc_buffer b)", "val valid_buffer (p: parser) (h: HS.mem) (b: B.buffer U8.t) : GTot Type0\nlet valid_buffer\n (p: parser)\n (h: HS.mem)\n (b: B.buffer U8.t)\n: GTot Type0\n= valid_pos p h b 0ul (B.len b)", "val buffer_readable_intro_empty\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: Lemma\n (requires (\n buffer_live h b /\\\n UInt32.v (buffer_length b) == 0\n ))\n (ensures (buffer_readable h b))\n [SMTPatOr [\n [SMTPat (buffer_readable h b)];\n [SMTPat (buffer_live h b)];\n ]]\nlet buffer_readable_intro_empty #t h b =\n buffer_readable_intro h b", "val live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0\nlet live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 = \n P.buffer_readable h b", "val loc_buffer\n (#t: Type)\n (b: B.buffer t)\n: GTot loc\nlet loc_buffer #t b =\n MG.loc_of_aloc #_ #cls #(B.frameOf b) #(B.as_addr b) (LocBuffer b)", "val sized_buffer_live (h: mem) (b: sized_buffer) : GTot Type0\nlet sized_buffer_live (h : mem) (b : sized_buffer) : GTot Type0 =\n B.live h (b.buffer <: buffer uint8)", "val copy_buffer_contents_postcond' (#t: typ) (a b: buffer t) (h h': HS.mem) : GTot Type0\nlet copy_buffer_contents_postcond'\n (#t: typ)\n (a: buffer t) (* source *)\n (b: buffer t) (* destination *)\n (h: HS.mem)\n (h' : HS.mem)\n: GTot Type0\n= copy_buffer_contents_precond' a b h /\\\n modifies (loc_buffer b) h h' /\\\n buffer_readable h' b /\\\n buffer_as_seq h' b == buffer_as_seq h a", "val bget\n (#t: buftype)\n (#a: Type0)\n (#len: size_t)\n (h: mem)\n (b: lbuffer_t t a len)\n (i: size_nat{i < v len})\n : GTot a\nlet bget (#t:buftype) (#a:Type0) (#len:size_t) (h:mem) (b:lbuffer_t t a len)\n (i:size_nat{i < v len}) : GTot a\n=\n match t with\n | MUT -> B.get h (b <: buffer a) i\n | IMMUT -> IB.get h (b <: ibuffer a) i\n | CONST -> FStar.Seq.index (CB.as_seq h (b <: cbuffer a)) i", "val fill_buffer_postcond\n (#t: typ)\n (b: buffer t)\n (idx_b len: UInt32.t)\n (v: type_of_typ t)\n (h h': HS.mem)\n : GTot Type0\nlet fill_buffer_postcond\n (#t: typ)\n (b: buffer t) (* destination *)\n (idx_b: UInt32.t)\n (len: UInt32.t)\n (v: type_of_typ t)\n (h: HS.mem)\n (h' : HS.mem)\n: GTot Type0\n= fill_buffer_precond b idx_b len h /\\\n modifies (loc_buffer (gsub_buffer b idx_b len)) h h' /\\\n buffer_readable h' (gsub_buffer b idx_b len) /\\\n buffer_as_seq h' (gsub_buffer b idx_b len) == Seq.create (UInt32.v len) v", "val lbuffer_or_unit_live\n (#a: Type0)\n (#len: size_t)\n (#b: bool)\n (h: mem)\n (buf: type_or_unit (lbuffer a len) b)\n : GTot Type0\nlet lbuffer_or_unit_live (#a : Type0) (#len : size_t) (#b : bool)\n (h : mem) (buf : type_or_unit (lbuffer a len) b) : GTot Type0 =\n if b then live h (lbuffer_or_unit_to_buffer buf) else True", "val writeable_buffer (t: base_typ) (addr: int) (b: b8) (h: vale_heap) : GTot bool\nlet writeable_buffer (t:base_typ) (addr:int) (b:b8) (h:vale_heap) : GTot bool =\n valid_buffer t addr b h && b.writeable", "val writeable_buffer (t: base_typ) (addr: int) (b: b8) (h: vale_heap) : GTot bool\nlet writeable_buffer (t:base_typ) (addr:int) (b:b8) (h:vale_heap) : GTot bool =\n valid_buffer t addr b h && b.writeable", "val live (#a: _) (h: mem) (b: buffer a) : GTot Type0\nlet live #a (h:mem) (b:buffer a) : GTot Type0 = HS.contains h b.content", "val equal (#a: typ) (h: HS.mem) (b: buffer a) (h': HS.mem) (b': buffer a) : GTot Type0\nlet equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =\n as_seq h b == as_seq h' b'", "val get (#t: buftype) (#a: Type0) (h: mem) (b: buffer_t t a) (i: nat{i < length b}) : GTot a\nlet get (#t : buftype) (#a : Type0) (h : mem) (b : buffer_t t a) (i : nat{i < length b}) :\n GTot a =\n match t with\n | IMMUT -> IB.get h (b <: ibuffer a) i\n | MUT -> B.get h (b <: buffer a) i\n | CONST -> B.get h (CB.as_mbuf (b <: cbuffer a)) i", "val copy_buffer_contents_precond\n (#t: typ)\n (a: buffer t)\n (idx_a: UInt32.t)\n (b: buffer t)\n (idx_b len: UInt32.t)\n (h: HS.mem)\n : GTot Type0\nlet copy_buffer_contents_precond\n (#t: typ)\n (a: buffer t) (* source *)\n (idx_a: UInt32.t)\n (b: buffer t) (* destination *)\n (idx_b: UInt32.t)\n (len: UInt32.t)\n (h: HS.mem)\n: GTot Type0\n= UInt32.v idx_a + UInt32.v len <= UInt32.v (buffer_length a) /\\\n UInt32.v idx_b + UInt32.v len <= UInt32.v (buffer_length b) /\\\n buffer_live h (gsub_buffer b idx_b len) /\\\n buffer_readable h (gsub_buffer a idx_a len) /\\\n loc_disjoint (loc_buffer (gsub_buffer a idx_a len)) (loc_buffer (gsub_buffer b idx_b len))", "val buffer_length (#t:base_typ) (b:buffer t) : GTot nat\nlet buffer_length #t b = UV.length (UV.mk_buffer (get_downview b.bsrc) (uint_view t))", "val buffer_length (#t:base_typ) (b:buffer t) : GTot nat\nlet buffer_length #t b = UV.length (UV.mk_buffer (get_downview b.bsrc) (uint_view t))", "val freeable (#t: buftype) (#a: Type0) (b: buffer_t t a) : GTot Type0\nlet freeable (#t : buftype) (#a : Type0) (b : buffer_t t a) : GTot Type0 =\n match t with\n | IMMUT -> IB.freeable (b <: ibuffer a)\n | MUT -> B.freeable (b <: buffer a)\n | CONST -> B.freeable (CB.as_mbuf (b <: cbuffer a))", "val copy_buffer_contents_postcond\n (#t: typ)\n (a: buffer t)\n (idx_a: UInt32.t)\n (b: buffer t)\n (idx_b len: UInt32.t)\n (h h': HS.mem)\n : GTot Type0\nlet copy_buffer_contents_postcond\n (#t: typ)\n (a: buffer t) (* source *)\n (idx_a: UInt32.t)\n (b: buffer t) (* destination *)\n (idx_b: UInt32.t)\n (len: UInt32.t)\n (h: HS.mem)\n (h' : HS.mem)\n: GTot Type0\n= copy_buffer_contents_precond a idx_a b idx_b len h /\\\n modifies (loc_buffer (gsub_buffer b idx_b len)) h h' /\\\n buffer_readable h' (gsub_buffer b idx_b len) /\\\n buffer_as_seq h' (gsub_buffer b idx_b len) == buffer_as_seq h (gsub_buffer a idx_a len)", "val fill_buffer_postcond' (#t: typ) (b: buffer t) (v: type_of_typ t) (h h': HS.mem) : GTot Type0\nlet fill_buffer_postcond'\n (#t: typ)\n (b: buffer t) (* destination *)\n (v: type_of_typ t)\n (h: HS.mem)\n (h' : HS.mem)\n: GTot Type0\n= fill_buffer_precond' b h /\\\n modifies (loc_buffer b) h h' /\\\n buffer_readable h' b /\\\n buffer_as_seq h' b == Seq.create (UInt32.v (buffer_length b)) v", "val low_buffer_read\n (src t: base_typ)\n (h: HS.mem)\n (b: (buf_t src t){B.live h b})\n (i: nat{i < DV.length (get_downview b) / view_n t})\n : GTot (base_typ_as_type t)\nlet low_buffer_read (src t:base_typ) (h:HS.mem) (b:(buf_t src t){B.live h b}) (i:nat{i < DV.length (get_downview b) / view_n t}) : GTot (base_typ_as_type t) =\n let view = LSig.view_of_base_typ t in\n let db = get_downview b in\n DV.length_eq db;\n let b_v = UV.mk_buffer db view in\n UV.length_eq b_v;\n UV.sel h b_v i", "val copy_buffer_contents_inv (#t: typ) (a b: buffer t) (len': UInt32.t) (h h': HS.mem) : GTot Type0\nlet copy_buffer_contents_inv\n (#t: typ)\n (a: buffer t) (* source *)\n (b: buffer t) (* destination *)\n (len' : UInt32.t)\n (h: HS.mem)\n (h' : HS.mem)\n: GTot Type0\n= copy_buffer_contents_precond' a b h /\\\n modifies (loc_buffer b) h h' /\\\n UInt32.v len' <= UInt32.v (buffer_length a) /\\\n buffer_readable h' (gsub_buffer b 0ul len') /\\\n buffer_as_seq h' (gsub_buffer b 0ul len') == buffer_as_seq h (gsub_buffer a 0ul len')", "val fill_buffer_inv (#t: typ) (b: buffer t) (len': UInt32.t) (v: type_of_typ t) (h h': HS.mem)\n : GTot Type0\nlet fill_buffer_inv\n (#t: typ)\n (b: buffer t) (* destination *)\n (len' : UInt32.t)\n (v: type_of_typ t)\n (h: HS.mem)\n (h' : HS.mem)\n: GTot Type0\n= fill_buffer_precond' b h /\\\n modifies (loc_buffer b) h h' /\\\n UInt32.v len' <= UInt32.v (buffer_length b) /\\\n buffer_readable h' (gsub_buffer b 0ul len') /\\\n buffer_as_seq h' (gsub_buffer b 0ul len') == Seq.create (UInt32.v len') v", "val length (#b: _) (vb:buffer b)\n : GTot nat\nlet length (#b: _) (vb:buffer b) =\n let b = as_buffer vb in\n let v = get_view vb in\n B.length b * View?.n v", "val length (#b: _) (vb:buffer b)\n : GTot nat\nlet length #b vb =\n Down.length (as_down_buffer vb) / View?.n (get_view vb)", "val buffers_readable (h: vale_heap) (l: list buffer64) : GTot Type0 (decreases l)\nlet rec buffers_readable (h:vale_heap) (l:list buffer64) : GTot Type0 (decreases l) =\n match l with\n | [] -> True\n | b :: l' -> buffer_readable h b /\\ buffers_readable h l'", "val buffer_or_null_freeable (#ty: buftype) (#a: Type0) (b: buffer_t ty a) : GTot Type0\nlet buffer_or_null_freeable (#ty : buftype) (#a:Type0) (b:buffer_t ty a) : GTot Type0 =\n if g_is_null b then True else freeable b", "val freeable (#a: Type) (b: buffer a) : GTot Type0\nlet freeable (#a: Type) (b: buffer a) : GTot Type0 =\n is_mm b.content /\\ is_eternal_region (frameOf b) /\\ idx b == 0", "val buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0\nlet buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 =\n match b with\n | Null -> True\n | Buffer max_length content idx length ->\n compatible_sub_preorder (U32.v max_length) rrel\n (U32.v idx) (U32.v idx + U32.v length) rel", "val buffer_addr (#t:base_typ) (b:buffer t) (h:vale_heap) : GTot int\nlet buffer_addr #t b h = IB.addrs_of_mem (_ih h) b", "val buffer_addr (#t:base_typ) (b:buffer t) (h:vale_heap) : GTot int\nlet buffer_addr #t b h = IB.addrs_of_mem (_ih h) b", "val lbuffer_or_unit_to_seq\n (#a: Type0)\n (#len: size_t)\n (#b: bool)\n (h: HS.mem)\n (buf: type_or_unit (lbuffer a len) b)\n : GTot (seq a)\nlet lbuffer_or_unit_to_seq (#a : Type0) (#len : size_t) (#b : bool)\n (h : HS.mem) (buf : type_or_unit (lbuffer a len) b) :\n GTot (seq a) =\n if b then as_seq #MUT #a #len h buf else Seq.empty", "val upd (#b: _)\n (h:HS.mem)\n (vb:buffer b{live h vb})\n (i:nat{i < length vb})\n (x:b)\n : GTot HS.mem\nlet upd = upd'", "val upd (#b: _)\n (h:HS.mem)\n (vb:buffer b{live h vb})\n (i:nat{i < length vb})\n (x:b)\n : GTot HS.mem\nlet upd #b h vb i x\n : GTot HS.mem\n = upd' #b h vb i x", "val unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0\nlet unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =\n P.buffer_unused_in b h", "val fill_buffer_precond (#t: typ) (b: buffer t) (idx_b len: UInt32.t) (h: HS.mem) : GTot Type0\nlet fill_buffer_precond\n (#t: typ)\n (b: buffer t) (* destination *)\n (idx_b: UInt32.t)\n (len: UInt32.t)\n (h: HS.mem)\n: GTot Type0\n= UInt32.v idx_b + UInt32.v len <= UInt32.v (buffer_length b) /\\\n buffer_live h (gsub_buffer b idx_b len)", "val as_seq (#b: _) (h:HS.mem) (vb:buffer b)\n : GTot (Seq.lseq b (length vb))\nlet as_seq #b h vb =\n let (| a, _, _, BufferView buf v |) = vb in\n let es = B.as_seq h buf in\n let bs = as_seq' #a #b es v in\n as_seq'_len es v;\n bs", "val as_seq (#b: _) (h:HS.mem) (vb:buffer b)\n : GTot (Seq.lseq b (length vb))\nlet as_seq (#b: _) (h:HS.mem) (vb:buffer b) = as_seq' h vb 0", "val unmapped_in (#a: _) (b: buffer a) (h: mem) : GTot Type0\nlet unmapped_in #a (b:buffer a) (h:mem) : GTot Type0 = unused_in b h", "val buffer_readable_gsub_intro\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\\n buffer_live h b /\\ (\n forall (j: UInt32.t) .\n (UInt32.v i <= UInt32.v j /\\\n UInt32.v j < UInt32.v i + UInt32.v len) ==>\n readable h (gpointer_of_buffer_cell b j)\n )))\n (ensures (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ \n buffer_readable h (gsub_buffer b i len)\n ))\nlet buffer_readable_gsub_intro #t h b i len =\n buffer_readable_intro h (gsub_buffer b i len)", "val buffer_readable_reveal\n (#max_arity:nat)\n (src bt:base_typ)\n (x:buf_t src bt)\n (args:IX64.arity_ok max_arity arg)\n (h0:HS.mem{mem_roots_p h0 args}) : Lemma (\n let mem = mk_mem args h0 in\n ME.buffer_readable (create_initial_vale_heap mem) (as_vale_buffer x) <==>\n List.memP (mut_to_b8 src x) (ptrs_of_mem mem))\nlet buffer_readable_reveal #max_arity src bt x args h0 = FStar.Pervasives.reveal_opaque (`%ME.get_vale_heap) ME.get_vale_heap", "val loc_buffer (#t:base_typ) (b:buffer t) : GTot loc\nlet loc_buffer #t b = M.loc_buffer b.bsrc", "val loc_buffer (#t:base_typ) (b:buffer t) : GTot loc\nlet loc_buffer #t b = M.loc_buffer b.bsrc", "val buffer_readable_gsub_merge\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n (h: HS.mem)\n: Lemma\n (requires (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\\n buffer_readable h (gsub_buffer b 0ul i) /\\\n buffer_readable h (gsub_buffer b i len) /\\ (\n let off = UInt32.add i len in\n buffer_readable h (gsub_buffer b off (UInt32.sub (buffer_length b) off))\n )))\n (ensures (buffer_readable h b))\nlet buffer_readable_gsub_merge #t b i len h =\n buffer_readable_intro h b", "val imm_low_buffer_read\n (src t: base_typ)\n (h: HS.mem)\n (b: (ibuf_t src t){B.live h b})\n (i: nat{i < DV.length (get_downview b) / view_n t})\n : GTot (base_typ_as_type t)\nlet imm_low_buffer_read (src t:base_typ) (h:HS.mem) (b:(ibuf_t src t){B.live h b}) (i:nat{i < DV.length (get_downview b) / view_n t}) : GTot (base_typ_as_type t) =\n let view = LSig.view_of_base_typ t in\n let db = get_downview b in\n DV.length_eq db;\n let b_v = UV.mk_buffer db view in\n UV.length_eq b_v;\n UV.sel h b_v i", "val modifies_1_preserves_ubuffers\n (#a: Type0)\n (#rrel #rel: srel a)\n (b: mbuffer a rrel rel)\n (h1 h2: HS.mem)\n : GTot Type0\nlet modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem)\n : GTot Type0\n = forall (b':ubuffer (frameOf b) (as_addr b)).\n (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2", "val buffer_read (#t:base_typ) (b:buffer t) (i:int) (h:vale_heap) : Ghost (base_typ_as_vale_type t)\n (requires True)\n (ensures (fun v ->\n 0 <= i /\\ i < buffer_length b /\\ buffer_readable h b ==>\n v == Seq.index (buffer_as_seq h b) i\n ))\nlet buffer_read #t b i h =\n if i < 0 || i >= buffer_length b then default_of_typ t else\n Seq.index (buffer_as_seq h b) i", "val buffer_read (#t:base_typ) (b:buffer t) (i:int) (h:vale_heap) : Ghost (base_typ_as_vale_type t)\n (requires True)\n (ensures (fun v ->\n 0 <= i /\\ i < buffer_length b /\\ buffer_readable h b ==>\n v == Seq.index (buffer_as_seq h b) i\n ))\nlet buffer_read #t b i h =\n if i < 0 || i >= buffer_length b then default_of_typ t else\n Seq.index (buffer_as_seq h b) i", "val buffer_or_null_freeable (#a: Type0) (b: buffer a) : GTot Type0\nlet buffer_or_null_freeable (#a:Type0) (b:buffer a) : GTot Type0 =\n if B.g_is_null b then True else B.freeable b", "val lbuffer_or_unit_freeable\n (#a: Type0)\n (#len: size_t)\n (#b: bool)\n (buf: type_or_unit (lbuffer a len) b)\n : GTot Type0\nlet lbuffer_or_unit_freeable (#a : Type0) (#len : size_t) (#b : bool)\n (buf : type_or_unit (lbuffer a len) b) : GTot Type0 =\n if b then B.freeable (lbuffer_or_unit_to_buffer buf) else True", "val buffer_readable_gsub_elim\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ \n buffer_readable h (gsub_buffer b i len)\n ))\n (ensures (\n UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\\n buffer_live h b /\\ (\n forall (j: UInt32.t) .\n (UInt32.v i <= UInt32.v j /\\\n UInt32.v j < UInt32.v i + UInt32.v len) ==>\n readable h (gpointer_of_buffer_cell b j)\n )))\nlet buffer_readable_gsub_elim #t h b i len =\n buffer_readable_elim h (gsub_buffer b i len)", "val valid_input_buffer\n (#k: parser_kind)\n (#t: Type u#0)\n (p: parser k t)\n (h: HS.mem)\n (#len: U32.t)\n (sl: input_buffer_t len)\n (perm_of: R.perm (slice_of sl).base)\n (pos: U32.t)\n : GTot Type0\nlet valid_input_buffer\n (#k: parser_kind)\n (#t: Type u#0)\n (p: parser k t)\n (h: HS.mem)\n (#len: U32.t)\n (sl: input_buffer_t len)\n (perm_of: R.perm (slice_of sl).base)\n (pos: U32.t)\n: GTot Type0\n= LPL.valid p h (slice_of sl) pos /\\\n R.valid_perm h perm_of", "val grvalue\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (#t: Type)\n (r: greader h0 sout pout_from0 t)\n : GTot t\nlet grvalue\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (#t: Type)\n (r: greader h0 sout pout_from0 t)\n: GTot t\n= Ghost.reveal (GReader?.v r)", "val sized_buffer_to_seq (h: mem) (b: sized_buffer) : GTot (seq uint8)\nlet sized_buffer_to_seq (h : mem) (b : sized_buffer) : GTot (seq uint8) =\n B.as_seq h (b.buffer <: buffer uint8)", "val sized_buffer_freeable (b: sized_buffer) : GTot Type0\nlet sized_buffer_freeable (b : sized_buffer) : GTot Type0 =\n not(g_is_null b.buffer) ==> B.freeable (b.buffer <: buffer uint8)", "val lbuffer_or_unit_to_opt_lseq\n (#a: Type0)\n (#len: size_t)\n (#b: bool)\n (h: HS.mem)\n (buf: type_or_unit (lbuffer a len) b)\n : GTot (option (lseq a (size_v len)))\nlet lbuffer_or_unit_to_opt_lseq (#a : Type0) (#len : size_t) (#b : bool)\n (h : HS.mem) (buf : type_or_unit (lbuffer a len) b) :\n GTot (option (lseq a (size_v len))) =\n if b then Some (as_seq #MUT #a #len h buf) else None", "val as_seq (#a: typ) (h: HS.mem) (b: buffer a)\n : GTot (s: Seq.seq (P.type_of_typ a) {Seq.length s == length b})\nlet as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =\n P.buffer_as_seq h b", "val ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h': HS.mem) : GTot Type0\nlet ubuffer_preserved'\n (#r: HS.rid)\n (#a: nat)\n (b: ubuffer r a)\n (h h' : HS.mem)\n: GTot Type0\n= forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) .\n ((frameOf b' == r /\\ as_addr b' == a) ==> (\n (live h b' ==> live h' b') /\\ (\n ((live h b' /\\ live h' b' /\\ Buffer? b') ==> (\n let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in\n let Buffer max _ idx len = b' in (\n U32.v max == bmax /\\\n U32.v idx <= boff /\\\n boff + blen <= U32.v idx + U32.v len\n ) ==>\n Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen))\n )))))", "val buffers_readable (h: vale_heap) (l: list M.buffer64) : GTot prop0 (decreases l)\nlet rec buffers_readable (h: vale_heap) (l: list M.buffer64) : GTot prop0 (decreases l) =\n match l with\n | [] -> True\n | b :: l' -> buffer_readable h b /\\ buffers_readable h l'", "val buffers_readable (h: vale_heap) (l: list M.buffer64) : GTot prop0 (decreases l)\nlet rec buffers_readable (h: vale_heap) (l: list M.buffer64) : GTot prop0 (decreases l) =\n match l with\n | [] -> True\n | b :: l' -> buffer_readable h b /\\ buffers_readable h l'", "val valid_buffer_read (#t: base_typ) (h: vale_heap) (b: buffer t) (i: int) : prop0\nlet valid_buffer_read (#t:base_typ) (h:vale_heap) (b:buffer t) (i:int) : prop0 =\n 0 <= i /\\ i < buffer_length b /\\ buffer_readable h b", "val valid_buffer_read (#t: base_typ) (h: vale_heap) (b: buffer t) (i: int) : prop0\nlet valid_buffer_read (#t:base_typ) (h:vale_heap) (b:buffer t) (i:int) : prop0 =\n 0 <= i /\\ i < buffer_length b /\\ buffer_readable h b", "val greader_tot\n (h0: HS.mem)\n (sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (#t: Type)\n (x: t)\n : Tot (r: greader h0 sout pout_from0 t {grvalue r == x})\nlet greader_tot\n (h0: HS.mem)\n (sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (#t: Type)\n (x: t)\n: Tot (r: greader h0 sout pout_from0 t { grvalue r == x } )\n= GReader (Ghost.hide x) (fun _ -> x)", "val valid_buffer (t: base_typ) (addr: int) (b: b8) (h: vale_heap) : GTot bool\nlet valid_buffer (t:base_typ) (addr:int) (b:b8) (h:vale_heap) : GTot bool =\n DV.length (get_downview b.bsrc) % (view_n t) = 0 &&\n addr_in_ptr #t addr b h", "val valid_buffer (t: base_typ) (addr: int) (b: b8) (h: vale_heap) : GTot bool\nlet valid_buffer (t:base_typ) (addr:int) (b:b8) (h:vale_heap) : GTot bool =\n DV.length (get_downview b.bsrc) % (view_n t) = 0 &&\n addr_in_ptr #t addr b h", "val buffer_r_repr:\n #a:Type -> len:UInt32.t{len > 0ul} ->\n h:HS.mem -> v:B.buffer a{buffer_r_inv len h v} ->\n GTot (buffer_repr a (UInt32.v len))\nlet buffer_r_repr #a len h v = B.as_seq h v", "val buffer_index_impl\n (#t: Type)\n (inv: memory_invariant)\n (b: B.buffer t)\n (i: U32.t)\n: Tot (read_repr_impl _ _ _ _ inv (buffer_index_spec inv b i))\nlet buffer_index_impl\n #t inv b i\n=\n fun _ -> Correct (B.index b i)", "val buffer64_read (b: M.buffer64) (i: int) (h: vale_heap) : GTot nat64\nlet buffer64_read (b:M.buffer64) (i:int) (h:vale_heap) : GTot nat64 = M.buffer_read b i h", "val buffer64_read (b: M.buffer64) (i: int) (h: vale_heap) : GTot nat64\nlet buffer64_read (b:M.buffer64) (i:int) (h:vale_heap) : GTot nat64 = M.buffer_read b i h", "val length (#a: typ) (b: buffer a) : GTot nat\nlet length (#a: typ) (b: buffer a) : GTot nat =\n UInt32.v (P.buffer_length b)", "val modifies_1_preserves_mreferences\n (#a: Type0)\n (#rrel #rel: srel a)\n (b: mbuffer a rrel rel)\n (h1 h2: HS.mem)\n : GTot Type0\nlet modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem)\n :GTot Type0\n = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre).\n ((frameOf b <> HS.frameOf r' \\/ as_addr b <> HS.as_addr r') /\\ h1 `HS.contains` r') ==>\n (h2 `HS.contains` r' /\\ HS.sel h1 r' == HS.sel h2 r')", "val g_upd\n (#a: Type0)\n (#rrel #rel: srel a)\n (b: mbuffer a rrel rel)\n (i: nat{i < length b})\n (v: a)\n (h: HS.mem{live h b})\n : GTot HS.mem\nlet g_upd (#a:Type0) (#rrel #rel:srel a)\n (b:mbuffer a rrel rel)\n (i:nat{i < length b})\n (v:a)\n (h:HS.mem{live h b})\n : GTot HS.mem\n = g_upd_seq b (Seq.upd (as_seq h b) i v) h", "val buffer_r_inv:\n #a:Type -> len:nonzero ->\n h:HS.mem -> v:B.buffer a -> GTot Type0\nlet buffer_r_inv #a len h v =\n B.live h v /\\ B.freeable v /\\\n B.len v == len", "val buffer_offset (#t: Type) (b: B.buffer t) : Tot Type0\nlet buffer_offset\n (#t: Type)\n (b: B.buffer t)\n: Tot Type0\n= pos1: U32.t { U32.v pos1 <= B.length b }", "val buffer_as_seq (#t:base_typ) (h:vale_heap) (b:buffer t) : GTot (Seq.seq (base_typ_as_vale_type t))\nlet buffer_as_seq #t h b =\n let s = UV.as_seq (IB.hs_of_mem (_ih h)) (UV.mk_buffer (get_downview b.bsrc) (uint_view t)) in\n Vale.Lib.Seqs_s.seq_map (v_to_typ t) s", "val buffer_as_seq (#t:base_typ) (h:vale_heap) (b:buffer t) : GTot (Seq.seq (base_typ_as_vale_type t))\nlet buffer_as_seq #t h b =\n let s = UV.as_seq (IB.hs_of_mem (_ih h)) (UV.mk_buffer (get_downview b.bsrc) (uint_view t)) in\n Vale.Lib.Seqs_s.seq_map (v_to_typ t) s", "val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0\nlet ubuffer_preserved = ubuffer_preserved'", "val buffer128_read (b: M.buffer128) (i: int) (h: vale_heap) : GTot quad32\nlet buffer128_read (b:M.buffer128) (i:int) (h:vale_heap) : GTot quad32 = M.buffer_read b i h", "val buffer128_read (b: M.buffer128) (i: int) (h: vale_heap) : GTot quad32\nlet buffer128_read (b:M.buffer128) (i:int) (h:vale_heap) : GTot quad32 = M.buffer_read b i h", "val frameOf (#a: typ) (b: buffer a) : GTot HH.rid\nlet frameOf (#a: typ) (b: buffer a) : GTot HH.rid =\n P.frameOf_buffer b", "val as_seq (#t: buftype) (#a: Type0) (#len: size_t) (h: HS.mem) (b: lbuffer_t t a len)\n : GTot (Seq.lseq a (v len))\nlet as_seq (#t:buftype) (#a:Type0) (#len:size_t) (h:HS.mem) (b:lbuffer_t t a len) :\n GTot (Seq.lseq a (v len)) =\n match t with\n | MUT -> B.as_seq h (b <: buffer a)\n | IMMUT -> IB.as_seq h (b <: ibuffer a)\n | CONST -> CB.as_seq h (b <: cbuffer a)", "val valid_taint_buf (#t:base_typ) (b:buffer t) (h:vale_heap) (mt:memtaint) (tn:taint) : GTot prop0\nlet valid_taint_buf #t b h mt tn =\n valid_taint_b8 b h mt tn", "val valid_taint_buf (#t:base_typ) (b:buffer t) (h:vale_heap) (mt:memtaint) (tn:taint) : GTot prop0\nlet valid_taint_buf #t b h mt tn =\n valid_taint_b8 b h mt tn", "val frameOf (#a: _) (b: buffer a) : GTot HS.rid\nlet frameOf #a (b:buffer a) : GTot HS.rid = HS.frameOf (content b)", "val modifies_1_from_to_preserves_ubuffers\n (#a: Type0)\n (#rrel #rel: srel a)\n (b: mbuffer a rrel rel)\n (from to: U32.t)\n (h1 h2: HS.mem)\n : GTot Type0\nlet modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem)\n : GTot Type0\n = forall (b':ubuffer (frameOf b) (as_addr b)).\n (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2", "val modifies_1' (#a: Type0) (#rrel #rel: srel a) (b: mbuffer a rrel rel) (h1 h2: HS.mem)\n : GTot Type0\nlet modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem)\n : GTot Type0\n = modifies_0_preserves_regions h1 h2 /\\\n modifies_1_preserves_mreferences b h1 h2 /\\\n modifies_1_preserves_livenesses b h1 h2 /\\\n modifies_0_preserves_not_unused_in h1 h2 /\\\n modifies_1_preserves_ubuffers b h1 h2", "val length (#a: Type) (b: buffer a) : GTot U32.t\nlet length (#a:Type) (b:buffer a) : GTot U32.t =\n U32.uint_to_t (B.length b)" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.buffer_readable" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.buffer_readable" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.buffer_readable" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.buffer_readable" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.buffer_writeable" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.buffer_writeable" }, { "project_name": "FStar", "file_name": "LowStar.BufferView.Up.fst", "name": "LowStar.BufferView.Up.sel" }, { "project_name": "FStar", "file_name": "LowStar.BufferView.Down.fst", "name": "LowStar.BufferView.Down.sel" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived3.fst", "name": "FStar.Pointer.Derived3.fill_buffer_precond'" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.buffer_writeable" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.buffer_writeable" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.fst", "name": "LowParse.Low.Base.writable" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived2.fst", "name": "FStar.Pointer.Derived2.copy_buffer_contents_precond'" }, { "project_name": "FStar", "file_name": "LowParseWriters.LowParse.fsti", "name": "LowParseWriters.LowParse.valid_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.buffer_readable_intro_empty" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.live" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_buffer" }, { "project_name": "noise-star", "file_name": "Impl.Noise.API.Device.fsti", "name": "Impl.Noise.API.Device.sized_buffer_live" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived2.fst", "name": "FStar.Pointer.Derived2.copy_buffer_contents_postcond'" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.bget" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived3.fsti", "name": "FStar.Pointer.Derived3.fill_buffer_postcond" }, { "project_name": "noise-star", "file_name": "Impl.Noise.TypeOrUnit.fsti", "name": "Impl.Noise.TypeOrUnit.lbuffer_or_unit_live" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.writeable_buffer" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.writeable_buffer" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.live" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.equal" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.get" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived2.fsti", "name": "FStar.Pointer.Derived2.copy_buffer_contents_precond" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.buffer_length" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.buffer_length" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.freeable" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived2.fsti", "name": "FStar.Pointer.Derived2.copy_buffer_contents_postcond" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived3.fst", "name": "FStar.Pointer.Derived3.fill_buffer_postcond'" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.MemoryHelpers.fsti", "name": "Vale.AsLowStar.MemoryHelpers.low_buffer_read" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived2.fst", "name": "FStar.Pointer.Derived2.copy_buffer_contents_inv" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived3.fst", "name": "FStar.Pointer.Derived3.fill_buffer_inv" }, { "project_name": "FStar", "file_name": "LowStar.BufferView.Down.fst", "name": "LowStar.BufferView.Down.length" }, { "project_name": "FStar", "file_name": "LowStar.BufferView.Up.fst", "name": "LowStar.BufferView.Up.length" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Util.fsti", "name": "Vale.Poly1305.Util.buffers_readable" }, { "project_name": "noise-star", "file_name": "Impl.Noise.String.fst", "name": "Impl.Noise.String.buffer_or_null_freeable" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.freeable" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.buffer_compatible" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.buffer_addr" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.buffer_addr" }, { "project_name": "noise-star", "file_name": "Impl.Noise.TypeOrUnit.fsti", "name": "Impl.Noise.TypeOrUnit.lbuffer_or_unit_to_seq" }, { "project_name": "FStar", "file_name": "LowStar.BufferView.Down.fst", "name": "LowStar.BufferView.Down.upd" }, { "project_name": "FStar", "file_name": "LowStar.BufferView.Up.fst", "name": "LowStar.BufferView.Up.upd" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.unused_in" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived3.fsti", "name": "FStar.Pointer.Derived3.fill_buffer_precond" }, { "project_name": "FStar", "file_name": "LowStar.BufferView.Down.fst", "name": "LowStar.BufferView.Down.as_seq" }, { "project_name": "FStar", "file_name": "LowStar.BufferView.Up.fst", "name": "LowStar.BufferView.Up.as_seq" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.unmapped_in" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.buffer_readable_gsub_intro" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.MemoryHelpers.fst", "name": "Vale.AsLowStar.MemoryHelpers.buffer_readable_reveal" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc_buffer" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.buffer_readable_gsub_merge" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.MemoryHelpers.fsti", "name": "Vale.AsLowStar.MemoryHelpers.imm_low_buffer_read" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_1_preserves_ubuffers" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.buffer_read" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.buffer_read" }, { "project_name": "noise-star", "file_name": "Impl.Noise.TypeOrUnit.fsti", "name": "Impl.Noise.TypeOrUnit.buffer_or_null_freeable" }, { "project_name": "noise-star", "file_name": "Impl.Noise.TypeOrUnit.fsti", "name": "Impl.Noise.TypeOrUnit.lbuffer_or_unit_freeable" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.buffer_readable_gsub_elim" }, { "project_name": "everparse", "file_name": "EverParse3d.InputBuffer.fsti", "name": "EverParse3d.InputBuffer.valid_input_buffer" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.grvalue" }, { "project_name": "noise-star", "file_name": "Impl.Noise.API.Device.fsti", "name": "Impl.Noise.API.Device.sized_buffer_to_seq" }, { "project_name": "noise-star", "file_name": "Impl.Noise.API.Device.fsti", "name": "Impl.Noise.API.Device.sized_buffer_freeable" }, { "project_name": "noise-star", "file_name": "Impl.Noise.TypeOrUnit.fsti", "name": "Impl.Noise.TypeOrUnit.lbuffer_or_unit_to_opt_lseq" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.as_seq" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.ubuffer_preserved'" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.buffers_readable" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.buffers_readable" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fsti", "name": "Vale.PPC64LE.Memory.valid_buffer_read" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fsti", "name": "Vale.X64.Memory.valid_buffer_read" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.greader_tot" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.valid_buffer" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.valid_buffer" }, { "project_name": "FStar", "file_name": "LowStar.Regional.Instances.fst", "name": "LowStar.Regional.Instances.buffer_r_repr" }, { "project_name": "FStar", "file_name": "LowParseWriters.fst", "name": "LowParseWriters.buffer_index_impl" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.buffer64_read" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.buffer64_read" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.length" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_1_preserves_mreferences" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.g_upd" }, { "project_name": "FStar", "file_name": "LowStar.Regional.Instances.fst", "name": "LowStar.Regional.Instances.buffer_r_inv" }, { "project_name": "FStar", "file_name": "LowParseWriters.fsti", "name": "LowParseWriters.buffer_offset" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.buffer_as_seq" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.buffer_as_seq" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.ubuffer_preserved" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.buffer128_read" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.buffer128_read" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.frameOf" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.as_seq" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.valid_taint_buf" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.valid_taint_buf" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.frameOf" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_1_from_to_preserves_ubuffers" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_1'" }, { "project_name": "FStar", "file_name": "Demo.Deps.fst", "name": "Demo.Deps.length" } ], "selected_premises": [ "FStar.Pointer.Base.buffer", "FStar.Pointer.Base.buffer_unused_in", "FStar.Pointer.Base.gread", "FStar.Pointer.Base.otype_of_typ", "FStar.Pointer.Base.as_addr", "FStar.Pointer.Base.gsingleton_buffer_of_pointer", "FStar.Pointer.Base.readable_struct_fields", "FStar.Pointer.Base.path_sel", "FStar.Pointer.Base.none_ovalue", "FStar.Pointer.Base.buffer_live", "FStar.Pointer.Base.readable_struct_fields_readable_struct", "FStar.Heap.trivial_preorder", "FStar.Pointer.Base.frameOf", "FStar.Pointer.Base.buffer_as_seq", "FStar.Pointer.Base.readable", "FStar.Pointer.Base.buffer_as_addr", "FStar.Pointer.Base.buffer_readable'", "FStar.Pointer.Base.live", "FStar.Monotonic.HyperStack.sel", "FStar.Pointer.Base.npointer", "FStar.Pointer.Base.frameOf_buffer", "FStar.Pointer.Base.singleton_buffer_of_pointer", "FStar.Pointer.Base.path_length", "FStar.Pointer.Base.path_sel_none_ovalue", "FStar.Pointer.Base.buffer_as_seq_gsingleton_buffer_of_pointer", "FStar.Pointer.Base.buffer_root_as_seq", "FStar.Pointer.Base.nlive", "FStar.Pointer.Base.is_mm", "FStar.Pointer.Base.otype_of_struct_field", "FStar.Pointer.Base.g_is_null", "FStar.Pointer.Base.ovalue_of_value", "FStar.Pointer.Base.step_upd", "FStar.Pointer.Base.pointer_ref_contents", "FStar.Pointer.Base._field", "FStar.Pointer.Base.buffer_of_array_pointer", "FStar.Pointer.Base.greference_of", "FStar.Pointer.Base.ovalue_is_readable_ovalue_of_value", "FStar.Pointer.Base.step_typ_depth", "FStar.Pointer.Base.path_typ_depth", "FStar.Pointer.Base.otype_of_typ_struct", "FStar.Pointer.Base.disjoint_roots_intro_pointer_vs_reference", "FStar.Pointer.Base.dummy_val", "FStar.Pointer.Base.struct_sel", "FStar.Pointer.Base.path_upd", "FStar.Pointer.Base.unused_in", "FStar.Pointer.Base.struct_create_fun", "FStar.Pointer.Base.gfield", "FStar.Pointer.Base.buffer_length", "FStar.Pointer.Base.includes", "FStar.Pointer.Base.gbuffer_of_array_pointer", "FStar.Pointer.Base.buffer_as_seq_gbuffer_of_array_pointer", "FStar.Pointer.Base.step_sel", "FStar.Pointer.Base.value_of_ovalue", "FStar.Pointer.Base.readable_struct_forall_mem", "FStar.Pointer.Base.ounion", "FStar.Pointer.Base.type_of_typ'_eq", "FStar.Monotonic.HyperStack.live_region", "FStar.Pointer.Base.ostruct", "FStar.Pointer.Base._singleton_buffer_of_pointer", "FStar.Pointer.Base.equal", "FStar.Pointer.Base.path_equal'", "FStar.Pointer.Base.value_of_ovalue_of_value", "FStar.Pointer.Base.readable_array", "FStar.Pointer.Base.type_of_typ'", "FStar.Pointer.Base.ovalue_is_readable", "FStar.Pointer.Base.ostruct_field_of_struct_field", "FStar.Pointer.Base.struct_field_is_readable", "FStar.Pointer.Base.not_an_array_cell", "FStar.Pointer.Base.readable_struct", "FStar.Pointer.Base.readable_struct_fields'", "FStar.Pointer.Base.buffer_root_length", "FStar.Pointer.Base.gsub_buffer", "FStar.Pointer.Base.nullptr", "FStar.Pointer.Base.struct", "FStar.Pointer.Base.path_includes", "FStar.Pointer.Base.ovalue_is_readable_ostruct_field_of_struct_field", "FStar.Monotonic.HyperStack.mreference", "FStar.Pointer.Base.path_disjoint", "FStar.Pointer.Base.path_disjoint_not_path_equal", "FStar.Pointer.Base.path_disjoint_includes", "FStar.Pointer.Base.path_destruct_l", "FStar.Pointer.Base.path_disjoint_t_rect", "FStar.Pointer.Base.path_equal", "FStar.Pervasives.Native.fst", "FStar.Pointer.Base.path_disjoint_decomp", "FStar.Pointer.Base.readable_struct_fields_elim", "FStar.Pervasives.Native.snd", "FStar.UInt.size", "FStar.Pointer.Base.union_get_value", "FStar.Pointer.Base.offset_buffer", "FStar.Pointer.Base.path_concat", "FStar.Pointer.Base.gcell", "FStar.Monotonic.HyperStack.as_addr", "FStar.Monotonic.HyperStack.is_heap_color", "FStar.Pointer.Base.path_includes_exists_concat", "FStar.Pointer.Base.gtdata", "FStar.Pointer.Base.is_active_union_field_includes_readable", "FStar.Pointer.Base.ostruct_create", "FStar.Pointer.Base.path_length_concat", "FStar.HyperStack.ST.is_eternal_region" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.Pointer.Base\n\nmodule DM = FStar.DependentMap\nmodule HS = FStar.HyperStack\nmodule HST = FStar.HyperStack.ST\n\n(*** Definitions *)\n\n(** Pointers to data of type t.\n\n This defines two main types:\n - `npointer (t: typ)`, a pointer that may be \"NULL\";\n - `pointer (t: typ)`, a pointer that cannot be \"NULL\"\n (defined as a refinement of `npointer`).\n\n `nullptr #t` (of type `npointer t`) represents the \"NULL\" value.\n*)\n\n#set-options \"--initial_fuel 1 --initial_ifuel 1 --max_fuel 1 --max_ifuel 1\"\n\ntype step: (from: typ) -> (to: typ) -> Tot Type0 =\n | StepField:\n (l: struct_typ) ->\n (fd: struct_field l) ->\n step (TStruct l) (typ_of_struct_field l fd)\n | StepUField:\n (l: union_typ) ->\n (fd: struct_field l) ->\n step (TUnion l) (typ_of_struct_field l fd)\n | StepCell:\n (length: UInt32.t) ->\n (value: typ) ->\n (index: UInt32.t { UInt32.v index < UInt32.v length } ) ->\n step (TArray length value) value\n\ntype path (from: typ) : (to: typ) -> Tot Type0 =\n | PathBase:\n path from from\n | PathStep:\n (through: typ) ->\n (to: typ) ->\n (p: path from through) ->\n (s: step through to) ->\n path from to\n\nlet step_typ_depth\n (#from #to: typ)\n (s: step from to)\n: Lemma\n (typ_depth from > typ_depth to)\n= match s with\n | StepUField l fd\n | StepField l fd ->\n typ_depth_typ_of_struct_field l.fields fd\n | _ -> ()\n\nlet rec path_typ_depth\n (#from #to: typ)\n (p: path from to)\n: Lemma\n (ensures (\n typ_depth from >= typ_depth to /\\ (\n (~ (PathBase? p)) ==> typ_depth from <> typ_depth to\n )))\n (decreases p)\n= match p with\n | PathBase -> ()\n | PathStep _ _ p' s ->\n path_typ_depth p';\n step_typ_depth s\n\n(*\nprivate\nlet not_cell\n (#from #to: typ)\n (p: path from to)\n: GTot bool\n= match p with\n | PathStep _ _ _ (StepCell _ _ _) -> false\n | _ -> true\n\nprivate type array_path (from: typ) (to_elem: typ) : (length: UInt32.t) -> Tot Type0 =\n| PSingleton:\n (p: path from to_elem { not_cell p } ) ->\n array_path from to_elem 1ul\n| PArray:\n length: UInt32.t ->\n path from (TArray length to_elem) ->\n array_path from to_elem length\n\nprivate let path' (from: typ) (to: typ) : Tot Type0 =\n if TArray? to\n then\n let length = TArray?.length to in\n (array_path from (TArray?.t to) length * (offset: UInt32.t & (length': UInt32.t {UInt32.v offset + UInt32.v length' <= UInt32.v length})))\n else path from to\n*)\n\nnoeq type _npointer (to : typ): Type0 =\n | Pointer:\n (from: typ) ->\n (contents: HS.aref) ->\n (p: path from to) ->\n _npointer to\n | NullPtr\n\nlet npointer (t: typ): Tot Type0 =\n _npointer t\n\n(** The null pointer *)\n\nlet nullptr (#t: typ): Tot (npointer t) = NullPtr\n\nlet g_is_null (#t: typ) (p: npointer t) : GTot bool =\n match p with\n | NullPtr -> true\n | _ -> false\n\nlet g_is_null_intro\n (t: typ)\n: Lemma\n (g_is_null (nullptr #t) == true)\n= ()\n\n(** Buffers *)\n\nlet not_an_array_cell (#t: typ) (p: pointer t) : GTot bool =\n match Pointer?.p p with\n | PathStep _ _ _ (StepCell _ _ _) -> false\n | _ -> true\n\nnoeq type buffer_root (t: typ) =\n| BufferRootSingleton:\n (p: pointer t { not_an_array_cell p } ) ->\n buffer_root t\n| BufferRootArray:\n (#max_length: array_length_t) ->\n (p: pointer (TArray max_length t)) ->\n buffer_root t\n\nlet buffer_root_length (#t: typ) (b: buffer_root t): Tot UInt32.t = match b with\n| BufferRootSingleton _ -> 1ul\n| BufferRootArray #_ #len _ -> len\n\nnoeq type _buffer (t: typ) =\n| Buffer:\n (broot: buffer_root t) ->\n (bidx: UInt32.t) ->\n (blength: UInt32.t { UInt32.v bidx + UInt32.v blength <= UInt32.v (buffer_root_length broot) } ) ->\n _buffer t\nlet buffer (t: typ): Tot Type0 = _buffer t\n\n(** Helper for the interpretation of unions.\n\n A C union is interpreted as a dependent pair of a key and a value (which\n depends on the key). The intent is for the key to be ghost, as it will not\n exist at runtime (C unions are untagged).\n\n Therefore,\n - `gtdata_get_key` (defined below) is in `GTot`, and\n - `gtdata_get_value` asks for the key `k` to read, and a proof that `k`\n matches the ghost key.\n*)\n\nlet gtdata (* ghostly-tagged data *)\n (key: eqtype)\n (value: (key -> Tot Type0))\n: Tot Type0\n= ( k: key & value k )\n\nlet _gtdata_get_key\n (#key: eqtype)\n (#value: (key -> Tot Type0))\n (u: gtdata key value)\n: Tot key\n= dfst u\n\nlet gtdata_get_key\n (#key: eqtype)\n (#value: (key -> Tot Type0))\n (u: gtdata key value)\n: GTot key // important: must be Ghost, the tag is not actually stored in memory\n= _gtdata_get_key u\n\nlet gtdata_get_value\n (#key: eqtype)\n (#value: (key -> Tot Type0))\n (u: gtdata key value)\n (k: key)\n: Pure (value k)\n (requires (gtdata_get_key u == k))\n (ensures (fun _ -> True))\n= let (| _, v |) = u in v\n\nlet gtdata_create\n (#key: eqtype)\n (#value: (key -> Tot Type0))\n (k: key)\n (v: value k)\n: Pure (gtdata key value)\n (requires True)\n (ensures (fun x -> gtdata_get_key x == k /\\ gtdata_get_value x k == v))\n= (| k, v |)\n\nlet gtdata_extensionality\n (#key: eqtype)\n (#value: (key -> Tot Type0))\n (u1 u2: gtdata key value)\n: Lemma\n (requires (\n let k = gtdata_get_key u1 in (\n k == gtdata_get_key u2 /\\\n gtdata_get_value u1 k == gtdata_get_value u2 k\n )))\n (ensures (u1 == u2))\n= ()\n\n(* Interprets a type code (`typ`) as a FStar type (`Type0`). *)\nlet rec type_of_typ'\n (t: typ)\n: Tot Type0\n= match t with\n | TBase b -> type_of_base_typ b\n | TStruct l ->\n struct l\n | TUnion l ->\n union l\n | TArray length t ->\n array length (type_of_typ' t)\n | TPointer t ->\n pointer t\n | TNPointer t ->\n npointer t\n | TBuffer t ->\n buffer t\nand struct (l: struct_typ) : Tot Type0 =\n DM.t (struct_field l) (type_of_struct_field' l (fun x -> type_of_typ' x))\nand union (l: union_typ) : Tot Type0 =\n gtdata (struct_field l) (type_of_struct_field' l (fun x -> type_of_typ' x))\n\nlet rec type_of_typ'_eq (t: typ) : Lemma (type_of_typ' t == type_of_typ t)\n [SMTPat (type_of_typ t)]\n=\n match t with\n | TArray _ t' -> type_of_typ'_eq t'\n | TPointer t' -> type_of_typ'_eq t'\n | TNPointer t' -> type_of_typ'_eq t'\n | TBuffer t' -> type_of_typ'_eq t'\n | _ -> ()\n\n(** Interpretation of unions, as ghostly-tagged data\n (see `gtdata` for more information).\n*)\nlet _union_get_key (#l: union_typ) (v: union l) : Tot (struct_field l) = _gtdata_get_key v\n\nlet struct_sel (#l: struct_typ) (s: struct l) (f: struct_field l) : Tot (type_of_struct_field l f) =\n DM.sel s f\n\nlet struct_upd (#l: struct_typ) (s: struct l) (f: struct_field l) (v: type_of_struct_field l f) : Tot (struct l) =\n DM.upd s f v\n\nlet struct_create_fun (l: struct_typ) (f: ((fd: struct_field l) -> Tot (type_of_struct_field l fd))) : Tot (struct l) =\n DM.create #(struct_field l) #(type_of_struct_field' l (fun x -> type_of_typ' x)) f\n\nlet struct_sel_struct_create_fun l f fd = ()\n\nlet union_get_key (#l: union_typ) (v: union l) : GTot (struct_field l) = gtdata_get_key v\n\nlet union_get_value #l v fd = gtdata_get_value v fd\n\nlet union_create l fd v = gtdata_create fd v\n\n(** For any `t: typ`, `dummy_val t` provides a default value of this type.\n\n This is useful to represent uninitialized data.\n*)\nlet rec dummy_val\n (t: typ)\n: Tot (type_of_typ t)\n= match t with\n | TBase b ->\n begin match b with\n | TUInt -> 0\n | TUInt8 -> UInt8.uint_to_t 0\n | TUInt16 -> UInt16.uint_to_t 0\n | TUInt32 -> UInt32.uint_to_t 0\n | TUInt64 -> UInt64.uint_to_t 0\n | TInt -> 0\n | TInt8 -> Int8.int_to_t 0\n | TInt16 -> Int16.int_to_t 0\n | TInt32 -> Int32.int_to_t 0\n | TInt64 -> Int64.int_to_t 0\n | TChar -> 'c'\n | TBool -> false\n | TUnit -> ()\n end\n | TStruct l ->\n struct_create_fun l (fun f -> (\n dummy_val (typ_of_struct_field l f)\n ))\n | TUnion l ->\n let dummy_field : string = List.Tot.hd (List.Tot.map fst l.fields) in\n union_create l dummy_field (dummy_val (typ_of_struct_field l dummy_field))\n | TArray length t -> Seq.create (UInt32.v length) (dummy_val t)\n | TPointer t -> Pointer t HS.dummy_aref PathBase\n | TNPointer t -> NullPtr #t\n | TBuffer t -> Buffer (BufferRootSingleton (Pointer t HS.dummy_aref PathBase)) 0ul 1ul\n\n(** The interpretation of type codes (`typ`) defined previously (`type_of_typ`)\n maps codes to fully defined FStar types. In other words, a struct is\n interpreted as a dependent map where all fields have a well defined value.\n\n However, in practice, C structures (or any other type) can be uninitialized\n or partially-initialized.\n\n To account for that:\n\n - First, we define an alternative interpretation of type codes,\n `otype_of_typ`, which makes uninitialized data explicit (essentially\n wrapping all interpretations with `option`).\n\n This concrete interpretation is what is stored in the model of the heap,\n and what is manipulated internally. As it is quite verbose, it is not\n exposed to the user.\n\n - Then, interpretations with explicit uninitialized data (`otype_of_type t`)\n can be mapped to fully-initialized data (`type_of_type t`) by inserting\n dummy values. This is done by the `value_of_ovalue` function.\n\n - Finally, reading from a fully-initialized data is guarded by a `readable`\n predicate, which ensures that the dummy values cannot be accessed, and\n therefore that reading uninitialized data is actually forbidden.\n*)\n\nlet rec otype_of_typ\n (t: typ)\n: Tot Type0\n= match t with\n | TBase b -> option (type_of_base_typ b)\n | TStruct l ->\n option (DM.t (struct_field l) (type_of_struct_field' l otype_of_typ))\n | TUnion l ->\n option (gtdata (struct_field l) (type_of_struct_field' l otype_of_typ))\n | TArray length t ->\n option (array length (otype_of_typ t))\n | TPointer t ->\n option (pointer t)\n | TNPointer t ->\n option (npointer t)\n | TBuffer t ->\n option (buffer t)\n\nlet otype_of_struct_field\n (l: struct_typ)\n: Tot (struct_field l -> Tot Type0)\n= type_of_struct_field' l otype_of_typ\n\nlet otype_of_typ_otype_of_struct_field\n (l: struct_typ)\n (f: struct_field l)\n: Lemma\n (otype_of_typ (typ_of_struct_field l f) == otype_of_struct_field l f)\n [SMTPat (type_of_typ (typ_of_struct_field l f))]\n= ()\n\nlet otype_of_typ_base\n (b: base_typ)\n: Lemma\n (otype_of_typ (TBase b) == option (type_of_base_typ b))\n [SMTPat (otype_of_typ (TBase b))]\n= ()\n\nlet otype_of_typ_array\n (len: array_length_t )\n (t: typ)\n: Lemma\n (otype_of_typ (TArray len t) == option (array len (otype_of_typ t)))\n [SMTPat (otype_of_typ (TArray len t))]\n= ()\n\nlet ostruct (l: struct_typ) = option (DM.t (struct_field l) (otype_of_struct_field l))\n\nlet ostruct_sel (#l: struct_typ) (s: ostruct l { Some? s }) (f: struct_field l) : Tot (otype_of_struct_field l f) =\n DM.sel (Some?.v s) f\n\nlet ostruct_upd (#l: struct_typ) (s: ostruct l { Some? s }) (f: struct_field l) (v: otype_of_struct_field l f) : Tot (s': ostruct l { Some? s' } ) =\n Some (DM.upd (Some?.v s) f v)\n\nlet ostruct_create (l: struct_typ) (f: ((fd: struct_field l) -> Tot (otype_of_struct_field l fd))) : Tot (s': ostruct l { Some? s' } ) =\n Some (DM.create #(struct_field l) #(otype_of_struct_field l) f)\n\nlet otype_of_typ_struct\n (l: struct_typ)\n: Lemma\n (otype_of_typ (TStruct l) == ostruct l)\n [SMTPat (otype_of_typ (TStruct l))]\n= assert_norm(otype_of_typ (TStruct l) == ostruct l)\n\nlet ounion (l: struct_typ) = option (gtdata (struct_field l) (otype_of_struct_field l))\n\nlet ounion_get_key (#l: union_typ) (v: ounion l { Some? v } ) : Tot (struct_field l) = _gtdata_get_key (Some?.v v)\n\nlet ounion_get_value\n (#l: union_typ)\n (v: ounion l { Some? v } )\n (fd: struct_field l)\n: Pure (otype_of_struct_field l fd)\n (requires (ounion_get_key v == fd))\n (ensures (fun _ -> True))\n= gtdata_get_value (Some?.v v) fd\n\nlet ounion_create\n (l: union_typ)\n (fd: struct_field l)\n (v: otype_of_struct_field l fd)\n: Tot (ounion l)\n= Some (gtdata_create fd v)\n\nlet otype_of_typ_union\n (l: union_typ)\n: Lemma\n (otype_of_typ (TUnion l) == ounion l)\n [SMTPat (otype_of_typ (TUnion l))]\n= assert_norm (otype_of_typ (TUnion l) == ounion l)\n\nlet struct_field_is_readable\n (l: struct_typ)\n (ovalue_is_readable: (\n (t: typ) ->\n (v: otype_of_typ t) ->\n Pure bool\n (requires (t << l))\n (ensures (fun _ -> True))\n ))\n (v: ostruct l { Some? v } )\n (s: string)\n: Tot bool\n= if List.Tot.mem s (List.Tot.map fst l.fields)\n then ovalue_is_readable (typ_of_struct_field l s) (ostruct_sel v s)\n else true\n\nlet rec ovalue_is_readable\n (t: typ)\n (v: otype_of_typ t)\n: Tot bool\n (decreases t)\n= match t with\n | TStruct l ->\n let (v: ostruct l) = v in\n Some? v && (\n let keys = List.Tot.map fst l.fields in\n let pred\n (t': typ)\n (v: otype_of_typ t')\n : Pure bool\n (requires (t' << l))\n (ensures (fun _ -> True))\n = ovalue_is_readable t' v\n in\n List.Tot.for_all (struct_field_is_readable l pred v) keys\n )\n | TUnion l ->\n let v : ounion l = v in\n Some? v && (\n let k = ounion_get_key v in\n ovalue_is_readable (typ_of_struct_field l k) (ounion_get_value v k)\n )\n | TArray len t ->\n let (v: option (array len (otype_of_typ t))) = v in\n Some? v &&\n Seq.for_all (ovalue_is_readable t) (Some?.v v)\n | TBase t ->\n let (v: option (type_of_base_typ t)) = v in\n Some? v\n | TPointer t ->\n let (v: option (pointer t)) = v in\n Some? v\n | TNPointer t ->\n let (v: option (npointer t)) = v in\n Some? v\n | TBuffer t ->\n let (v: option (buffer t)) = v in\n Some? v\n\nlet ovalue_is_readable_struct_intro'\n (l: struct_typ)\n (v: otype_of_typ (TStruct l))\n: Lemma\n (requires (\n let (v: ostruct l) = v in (\n Some? v /\\\n List.Tot.for_all (struct_field_is_readable l (fun x y -> ovalue_is_readable x y) v) (List.Tot.map fst l.fields)\n )))\n (ensures (ovalue_is_readable (TStruct l) v))\n= assert_norm (ovalue_is_readable (TStruct l) v == true)\n\nlet ovalue_is_readable_struct_intro\n (l: struct_typ)\n (v: otype_of_typ (TStruct l))\n: Lemma\n (requires (\n let (v: ostruct l) = v in (\n Some? v /\\ (\n forall (f: struct_field l) .\n ovalue_is_readable (typ_of_struct_field l f) (ostruct_sel v f)\n ))))\n (ensures (ovalue_is_readable (TStruct l) v))\n= List.Tot.for_all_mem (struct_field_is_readable l (fun x y -> ovalue_is_readable x y) v) (List.Tot.map fst l.fields);\n ovalue_is_readable_struct_intro' l v\n\nlet ovalue_is_readable_struct_elim\n (l: struct_typ)\n (v: otype_of_typ (TStruct l))\n (fd: struct_field l)\n: Lemma\n (requires (ovalue_is_readable (TStruct l) v))\n (ensures (\n let (v: ostruct l) = v in (\n Some? v /\\\n ovalue_is_readable (typ_of_struct_field l fd) (ostruct_sel v fd)\n )))\n [SMTPat (ovalue_is_readable (typ_of_struct_field l fd) (ostruct_sel v fd))]\n= let (v: ostruct l) = v in\n assert_norm (ovalue_is_readable (TStruct l) v == List.Tot.for_all (struct_field_is_readable l (fun x y -> ovalue_is_readable x y) v) (List.Tot.map fst l.fields));\n assert (List.Tot.for_all (struct_field_is_readable l (fun x y -> ovalue_is_readable x y) v) (List.Tot.map fst l.fields));\n List.Tot.for_all_mem (struct_field_is_readable l (fun x y -> ovalue_is_readable x y) v) (List.Tot.map fst l.fields);\n assert (ovalue_is_readable (typ_of_struct_field l fd) (ostruct_sel v fd))\n\nlet ovalue_is_readable_array_elim\n (#len: array_length_t )\n (#t: typ)\n (v: otype_of_typ (TArray len t))\n (i: UInt32.t { UInt32.v i < UInt32.v len } )\n: Lemma\n (requires (ovalue_is_readable (TArray len t) v))\n (ensures (\n let (v: option (array len (otype_of_typ t))) = v in (\n Some? v /\\\n ovalue_is_readable t (Seq.index (Some?.v v) (UInt32.v i))\n )))\n= ()\n\nlet ovalue_is_readable_array_intro\n (#len: array_length_t )\n (#t: typ)\n (v: otype_of_typ (TArray len t))\n: Lemma\n (requires (\n let (v: option (array len (otype_of_typ t))) = v in (\n Some? v /\\ (\n forall (i: UInt32.t { UInt32.v i < UInt32.v len } ) .\n ovalue_is_readable t (Seq.index (Some?.v v) (UInt32.v i))\n ))))\n (ensures (ovalue_is_readable (TArray len t) v))\n= let (v: option (array len (otype_of_typ t))) = v in\n let (v: array len (otype_of_typ t)) = Some?.v v in\n let f\n (i: nat { i < UInt32.v len } )\n : Lemma\n (ovalue_is_readable t (Seq.index v i))\n = let (j : UInt32.t { UInt32.v j < UInt32.v len } ) = UInt32.uint_to_t i in\n assert (ovalue_is_readable t (Seq.index v (UInt32.v j)))\n in\n Classical.forall_intro f\n\nlet ostruct_field_of_struct_field\n (l: struct_typ)\n (ovalue_of_value: (\n (t: typ) ->\n (v: type_of_typ t) ->\n Pure (otype_of_typ t)\n (requires (t << l))\n (ensures (fun _ -> True))\n ))\n (v: struct l)\n (f: struct_field l)\n: Tot (otype_of_struct_field l f)\n= ovalue_of_value (typ_of_struct_field l f) (struct_sel #l v f)\n\n(* TODO: move to Seq.Base *)\n\nlet seq_init_index\n (#a:Type) (len:nat) (contents:(i:nat { i < len } -> Tot a)) (i: nat)\n: Lemma\n (requires (i < len))\n (ensures (i < len /\\ Seq.index (Seq.init len contents) i == contents i))\n [SMTPat (Seq.index (Seq.init len contents) i)]\n= Seq.init_index len contents\n\nlet rec ovalue_of_value\n (t: typ)\n (v: type_of_typ t)\n: Tot (otype_of_typ t)\n (decreases t)\n= match t with\n | TStruct l ->\n let oval\n (t' : typ)\n (v' : type_of_typ t')\n : Pure (otype_of_typ t')\n (requires (t' << l))\n (ensures (fun _ -> True))\n = ovalue_of_value t' v'\n in\n ostruct_create l (ostruct_field_of_struct_field l oval v)\n | TArray len t ->\n let (v: array len (type_of_typ t)) = v in\n assert (UInt32.v len == Seq.length v);\n let f\n (i: nat {i < UInt32.v len})\n : Tot (otype_of_typ t)\n = ovalue_of_value t (Seq.index v i)\n in\n let (v': array len (otype_of_typ t)) = Seq.init (UInt32.v len) f in\n Some v'\n | TUnion l ->\n let (v: union l) = v in\n let k = _union_get_key v in\n ounion_create l k (ovalue_of_value (typ_of_struct_field l k) (union_get_value v k))\n | _ -> Some v\n\nlet ovalue_is_readable_ostruct_field_of_struct_field\n (l: struct_typ)\n (ih: (\n (t: typ) ->\n (v: type_of_typ t) ->\n Lemma\n (requires (t << l))\n (ensures (ovalue_is_readable t (ovalue_of_value t v)))\n ))\n (v: struct l)\n (f: struct_field l)\n: Lemma\n (ovalue_is_readable (typ_of_struct_field l f) (ostruct_field_of_struct_field l ovalue_of_value v f))\n= ih (typ_of_struct_field l f) (struct_sel #l v f)\n\nlet rec ovalue_is_readable_ovalue_of_value\n (t: typ)\n (v: type_of_typ t)\n: Lemma\n (requires True)\n (ensures (ovalue_is_readable t (ovalue_of_value t v)))\n (decreases t)\n [SMTPat (ovalue_is_readable t (ovalue_of_value t v))]\n= match t with\n | TStruct l ->\n let (v: struct l) = v in\n let (v': ostruct l) = ovalue_of_value (TStruct l) v in\n let phi\n (t: typ)\n (v: type_of_typ t)\n : Lemma\n (requires (t << l))\n (ensures (ovalue_is_readable t (ovalue_of_value t v)))\n = ovalue_is_readable_ovalue_of_value t v\n in\n Classical.forall_intro (ovalue_is_readable_ostruct_field_of_struct_field l phi v);\n ovalue_is_readable_struct_intro l v'\n | TArray len t ->\n let (v: array len (type_of_typ t)) = v in\n let (v': otype_of_typ (TArray len t)) = ovalue_of_value (TArray len t) v in\n let (v': array len (otype_of_typ t)) = Some?.v v' in\n let phi\n (i: nat { i < Seq.length v' } )\n : Lemma\n (ovalue_is_readable t (Seq.index v' i))\n = ovalue_is_readable_ovalue_of_value t (Seq.index v i)\n in\n Classical.forall_intro phi\n | TUnion l ->\n let (v: union l) = v in\n let k = _union_get_key v in\n ovalue_is_readable_ovalue_of_value (typ_of_struct_field l k) (union_get_value v k)\n | _ -> ()\n\nlet rec value_of_ovalue\n (t: typ)\n (v: otype_of_typ t)\n: Tot (type_of_typ t)\n (decreases t)\n= match t with\n | TStruct l ->\n let (v: ostruct l) = v in\n if Some? v\n then\n let phi\n (f: struct_field l)\n : Tot (type_of_struct_field l f)\n = value_of_ovalue (typ_of_struct_field l f) (ostruct_sel v f)\n in\n struct_create_fun l phi\n else dummy_val t\n | TArray len t' ->\n let (v: option (array len (otype_of_typ t'))) = v in\n begin match v with\n | None -> dummy_val t\n | Some v ->\n let phi\n (i: nat { i < UInt32.v len } )\n : Tot (type_of_typ t')\n = value_of_ovalue t' (Seq.index v i)\n in\n Seq.init (UInt32.v len) phi\n end\n | TUnion l ->\n let (v: ounion l) = v in\n begin match v with\n | None -> dummy_val t\n | _ ->\n let k = ounion_get_key v in\n union_create l k (value_of_ovalue (typ_of_struct_field l k) (ounion_get_value v k))\n end\n | TBase b ->\n let (v: option (type_of_base_typ b)) = v in\n begin match v with\n | None -> dummy_val t\n | Some v -> v\n end\n | TPointer t' ->\n let (v: option (pointer t')) = v in\n begin match v with\n | None -> dummy_val t\n | Some v -> v\n end\n | TNPointer t' ->\n let (v: option (npointer t')) = v in\n begin match v with\n | None -> dummy_val t\n | Some v -> v\n end\n | TBuffer t' ->\n let (v: option (buffer t')) = v in\n begin match v with\n | None -> dummy_val t\n | Some v -> v\n end\n\nlet ovalue_of_value_array_index\n (#len: array_length_t)\n (t' : typ)\n (v: array len (type_of_typ t'))\n (sv: array len (otype_of_typ t'))\n: Lemma\n (requires (ovalue_of_value (TArray len t') v == Some sv))\n (ensures (forall (i: nat) . i < UInt32.v len ==> Seq.index sv i == ovalue_of_value t' (Seq.index v i)))\n= ()\n\n\nlet value_of_ovalue_array_index\n (#len: array_length_t)\n (t': typ)\n (sv: array len (otype_of_typ t'))\n: Lemma\n (ensures (forall (i: nat) . i < UInt32.v len ==> Seq.index (value_of_ovalue (TArray len t') (Some sv)) i == value_of_ovalue t' (Seq.index sv i)))\n= ()\n\n#set-options \"--z3rlimit 16\"\n\nlet rec value_of_ovalue_of_value\n (t: typ)\n (v: type_of_typ t)\n: Lemma\n (value_of_ovalue t (ovalue_of_value t v) == v)\n [SMTPat (value_of_ovalue t (ovalue_of_value t v))]\n= match t with\n | TStruct l ->\n let v : struct l = v in\n let v' : struct l = value_of_ovalue t (ovalue_of_value t v) in\n let phi\n (f: struct_field l)\n : Lemma\n (struct_sel #l v' f == struct_sel #l v f)\n = value_of_ovalue_of_value (typ_of_struct_field l f) (struct_sel #l v f)\n in\n Classical.forall_intro phi;\n DM.equal_intro v' v;\n DM.equal_elim #(struct_field l) #(type_of_struct_field' l (fun x -> type_of_typ' x)) v' v\n | TArray len t' ->\n let (v: array len (type_of_typ t')) = v in\n let ov : option (array len (otype_of_typ t')) = ovalue_of_value (TArray len t') v in\n assert (Some? ov);\n let sv : array len (otype_of_typ t') = Some?.v ov in\n assert (Seq.length sv == UInt32.v len);\n// assert (forall (i : nat { i < UInt32.v len } ) . Seq.index sv i == ovalue_of_value t' (Seq.index v i));\n ovalue_of_value_array_index t' v sv;\n let v' : array len (type_of_typ t') = value_of_ovalue t ov in\n assert (Seq.length v' == UInt32.v len);\n// assert (forall (i: nat { i < UInt32.v len } ) . Seq.index v' i == value_of_ovalue t' (Seq.index sv i));\n value_of_ovalue_array_index t' sv;\n let phi\n (i: nat { i < UInt32.v len } )\n : Lemma\n (value_of_ovalue t' (ovalue_of_value t' (Seq.index v i)) == Seq.index v i)\n = value_of_ovalue_of_value t' (Seq.index v i)\n in\n Classical.forall_intro phi;\n Seq.lemma_eq_intro v' v;\n Seq.lemma_eq_elim v' v\n | TUnion l ->\n let v : union l = v in\n let k = _union_get_key v in\n value_of_ovalue_of_value (typ_of_struct_field l k) (union_get_value v k)\n | _ -> ()\n\nlet none_ovalue\n (t: typ)\n: Tot (otype_of_typ t)\n= match t with\n | TStruct l -> (None <: ostruct l)\n | TArray len t' -> (None <: option (array len (otype_of_typ t')))\n | TUnion l -> (None <: ounion l)\n | TBase b -> (None <: option (type_of_base_typ b))\n | TPointer t' -> (None <: option (pointer t'))\n | TNPointer t' -> (None <: option (npointer t'))\n | TBuffer t' -> (None <: option (buffer t'))\n\nlet not_ovalue_is_readable_none_ovalue\n (t: typ)\n: Lemma\n (ovalue_is_readable t (none_ovalue t) == false)\n= ()\n\n(*** Semantics of pointers *)\n\n(** Pointer paths *)\n\nlet step_sel\n (#from: typ)\n (#to: typ)\n (m': otype_of_typ from)\n (s: step from to)\n= match s with\n | StepField l fd ->\n let (m': ostruct l) = m' in\n begin match m' with\n | None -> none_ovalue to\n | _ -> ostruct_sel m' fd\n end\n | StepUField l fd ->\n let (m' : ounion l) = m' in\n begin match m' with\n | None -> none_ovalue to\n | _ ->\n if fd = ounion_get_key m'\n then ounion_get_value m' fd\n else none_ovalue to\n end\n | StepCell length value i ->\n let (m': option (array length (otype_of_typ to))) = m' in\n begin match m' with\n | None -> none_ovalue to\n | Some m' -> Seq.index m' (UInt32.v i)\n end\n\n(* TODO: we used to have this:\n<<<\nlet ovalue_is_readable_step_sel\n (#from: typ)\n (#to: typ)\n (m': otype_of_typ from)\n (s: step from to)\n: Lemma\n (requires (ovalue_is_readable from m'))\n (ensures (ovalue_is_readable to (step_sel m' s)))\n [SMTPat (ovalue_is_readable to (step_sel m' s))]\n= match s with\n | StepField l fd -> ovalue_is_readable_struct_elim l m' fd\n | _ -> ()\n>>>\nWhich is, of course, wrong with unions. So we have to specialize this rule for each step:\n*)\n\nlet ovalue_is_readable_step_sel_cell\n (#length: array_length_t)\n (#value: typ)\n (m': otype_of_typ (TArray length value))\n (index: UInt32.t { UInt32.v index < UInt32.v length } )\n: Lemma\n (requires (ovalue_is_readable (TArray length value) m'))\n (ensures (ovalue_is_readable value (step_sel m' (StepCell length value index))))\n [SMTPat (ovalue_is_readable value (step_sel m' (StepCell length value index)))]\n= ()\n\nlet ovalue_is_readable_step_sel_field\n (#l: struct_typ)\n (m: ostruct l)\n (fd: struct_field l)\n: Lemma\n (requires (ovalue_is_readable (TStruct l) m))\n (ensures (ovalue_is_readable (typ_of_struct_field l fd) (step_sel m (StepField l fd))))\n [SMTPat (ovalue_is_readable (typ_of_struct_field l fd) (step_sel m (StepField l fd)))]\n= ()\n\nlet ovalue_is_readable_step_sel_union_same\n (#l: union_typ)\n (m: ounion l)\n (fd: struct_field l)\n: Lemma\n (requires (\n ovalue_is_readable (TUnion l) m /\\\n ounion_get_key m == fd\n ))\n (ensures (ovalue_is_readable (typ_of_struct_field l fd) (step_sel m (StepUField l fd))))\n= ()\n\nlet step_sel_none_ovalue\n (#from: typ)\n (#to: typ)\n (s: step from to)\n: Lemma\n (step_sel (none_ovalue from) s == none_ovalue to)\n= ()\n\nlet rec path_sel\n (#from: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (p: path from to)\n: Tot (otype_of_typ to)\n (decreases p)\n= match p with\n | PathBase -> m\n | PathStep through' to' p' s ->\n let (m': otype_of_typ through') = path_sel m p' in\n step_sel m' s\n\nlet rec path_sel_none_ovalue\n (#from: typ)\n (#to: typ)\n (p: path from to)\n: Lemma\n (requires True)\n (ensures (path_sel (none_ovalue from) p == none_ovalue to))\n (decreases p)\n= match p with\n | PathBase -> ()\n | PathStep through' to' p' s ->\n path_sel_none_ovalue p'\n\nlet step_upd\n (#from: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (s: step from to)\n (v: otype_of_typ to)\n: Tot (otype_of_typ from)\n (decreases s)\n= match s with\n | StepField l fd ->\n let (m: ostruct l) = m in\n begin match m with\n | None ->\n (* whole structure does not exist yet,\n so create one with only one field initialized,\n and all others uninitialized *)\n let phi\n (fd' : struct_field l)\n : Tot (otype_of_struct_field l fd')\n = if fd' = fd\n then v\n else none_ovalue (typ_of_struct_field l fd')\n in\n ostruct_create l phi\n | Some _ -> ostruct_upd m fd v\n end\n | StepCell len _ i ->\n let (m: option (array len (otype_of_typ to))) = m in\n begin match m with\n | None ->\n (* whole array does not exist yet,\n so create one with only one cell initialized,\n and all others uninitialized *)\n let phi\n (j: nat { j < UInt32.v len } )\n : Tot (otype_of_typ to)\n = if j = UInt32.v i\n then v\n else none_ovalue to\n in\n let (m' : option (array len (otype_of_typ to))) =\n Some (Seq.init (UInt32.v len) phi)\n in\n m'\n | Some m ->\n let (m' : option (array len (otype_of_typ to))) =\n Some (Seq.upd m (UInt32.v i) v)\n in\n m'\n end\n | StepUField l fd ->\n (* overwrite the whole union with the new field *)\n ounion_create l fd v\n\nlet step_sel_upd_same\n (#from: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (s: step from to)\n (v: otype_of_typ to)\n: Lemma\n (step_sel (step_upd m s v) s == v)\n= ()\n\nlet rec path_upd\n (#from: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (p: path from to)\n (v: otype_of_typ to)\n: Tot (otype_of_typ from)\n (decreases p)\n= match p with\n | PathBase -> v\n | PathStep through' to' p' st ->\n let s = path_sel m p' in\n path_upd m p' (step_upd s st v)\n\nlet rec path_sel_upd_same\n (#from: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (p: path from to)\n (v: otype_of_typ to)\n: Lemma\n (requires True)\n (ensures (path_sel (path_upd m p v) p == v))\n (decreases p)\n [SMTPat (path_sel (path_upd m p v) p)]\n= match p with\n | PathBase -> ()\n | PathStep through' to' p' st ->\n let s = path_sel m p' in\n step_sel_upd_same s st v;\n let s' = step_upd s st v in\n path_sel_upd_same m p' s'\n\nlet rec path_concat\n (#from: typ)\n (#through: typ)\n (#to: typ)\n (p: path from through)\n (q: path through to)\n: Pure (path from to)\n (requires True)\n (ensures (fun _ -> True))\n (decreases q)\n= match q with\n | PathBase -> p\n | PathStep through' to' q' st -> PathStep through' to' (path_concat p q') st\n\nlet path_concat_base_r\n (#from: typ)\n (#to: typ)\n (p: path from to)\n: Lemma\n (ensures (path_concat p PathBase == p))\n= ()\n\nlet rec path_concat_base_l\n (#from: typ)\n (#to: typ)\n (p: path from to)\n: Lemma\n (requires True)\n (ensures (path_concat PathBase p == p))\n (decreases p)\n [SMTPat (path_concat PathBase p)]\n= match p with\n | PathBase -> ()\n | PathStep _ _ p' _ -> path_concat_base_l p'\n\nlet rec path_concat_assoc\n (#t0 #t1 #t2 #t3: typ)\n (p01: path t0 t1)\n (p12: path t1 t2)\n (p23: path t2 t3)\n: Lemma\n (requires True)\n (ensures (path_concat (path_concat p01 p12) p23 == path_concat p01 (path_concat p12 p23)))\n (decreases p23)\n= match p23 with\n | PathBase -> ()\n | PathStep _ _ p23' _ -> path_concat_assoc p01 p12 p23'\n\nlet rec path_sel_concat\n (#from: typ)\n (#through: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (p: path from through)\n (q: path through to)\n: Lemma\n (requires True)\n (ensures (path_sel m (path_concat p q) == path_sel (path_sel m p) q))\n (decreases q)\n [SMTPat (path_sel m (path_concat p q))]\n= match q with\n | PathBase -> ()\n | PathStep _ _ q' _ -> path_sel_concat m p q'\n\nlet rec path_upd_concat\n (#from: typ)\n (#through: typ)\n (#to: typ)\n (m: otype_of_typ from)\n (p: path from through)\n (q: path through to)\n (v: otype_of_typ to)\n: Lemma\n (requires True)\n (ensures (path_upd m (path_concat p q) v == path_upd m p (path_upd (path_sel m p) q v)))\n (decreases q)\n [SMTPat (path_upd m (path_concat p q) v)]\n= match q with\n | PathBase -> ()\n | PathStep through' to' q' st ->\n let (s: otype_of_typ through') = path_sel m (path_concat p q') in\n let (s': otype_of_typ through') = step_upd s st v in\n path_upd_concat m p q' s'\n\n// TODO: rename as: prefix_of; use infix notation (p1 `prefix_of` p2)\nlet rec path_includes\n (#from: typ)\n (#to1 #to2: typ)\n (p1: path from to1)\n (p2: path from to2)\n: Ghost bool\n (requires True)\n (ensures (fun _ -> True))\n (decreases p2)\n= (to1 = to2 && p1 = p2) || (match p2 with\n | PathBase -> false\n | PathStep _ _ p2' _ ->\n path_includes p1 p2'\n )\n\nlet rec path_includes_base\n (#from: typ)\n (#to: typ)\n (p: path from to)\n: Lemma\n (requires True)\n (ensures (path_includes (PathBase #from) p))\n (decreases p)\n [SMTPat (path_includes PathBase p)]\n= match p with\n | PathBase -> ()\n | PathStep _ _ p2' _ -> path_includes_base p2'\n\nlet path_includes_refl\n (#from #to: typ)\n (p: path from to)\n: Lemma\n (requires True)\n (ensures (path_includes p p))\n [SMTPat (path_includes p p)]\n= ()\n\nlet path_includes_step_r\n (#from #through #to: typ)\n (p: path from through)\n (s: step through to)\n: Lemma\n (requires True)\n (ensures (path_includes p (PathStep through to p s)))\n [SMTPat (path_includes p (PathStep through to p s))]\n= ()\n\nlet rec path_includes_trans\n (#from #to1 #to2 #to3: typ)\n (p1: path from to1)\n (p2: path from to2)\n (p3: path from to3 {path_includes p1 p2 /\\ path_includes p2 p3})\n: Lemma\n (requires True)\n (ensures (path_includes p1 p3))\n (decreases p3)\n= FStar.Classical.or_elim\n #(to2 == to3 /\\ p2 == p3)\n #(match p3 with\n | PathBase -> False\n | PathStep _ _ p3' _ ->\n\tpath_includes p2 p3')\n #(fun _ -> path_includes p1 p3)\n (fun _ -> ())\n (fun _ -> match p3 with\n | PathBase -> assert False\n | PathStep _ _ p3' _ ->\n\tpath_includes_trans p1 p2 p3'\n )\n\nlet rec path_includes_ind\n (#from: typ)\n (x:((#to1: typ) ->\n (#to2: typ) ->\n (p1: path from to1) ->\n (p2: path from to2 {path_includes p1 p2} ) ->\n GTot Type0))\n (h_step:\n ((#through: typ) ->\n (#to: typ) ->\n (p: path from through) ->\n (s: step through to { path_includes p (PathStep through to p s) } ) ->\n Lemma (x p (PathStep through to p s))))\n (h_refl:\n ((#to: typ) ->\n (p: path from to {path_includes p p}) ->\n Lemma (x p p)))\n (h_trans:\n ((#to1: typ) ->\n (#to2: typ) ->\n (#to3: typ) ->\n (p1: path from to1) ->\n (p2: path from to2) ->\n (p3: path from to3 {path_includes p1 p2 /\\ path_includes p2 p3 /\\ path_includes p1 p3 /\\ x p1 p2 /\\ x p2 p3}) ->\n Lemma (x p1 p3)))\n (#to1: typ)\n (#to2: typ)\n (p1: path from to1)\n (p2: path from to2 {path_includes p1 p2})\n: Lemma\n (requires True)\n (ensures (x p1 p2))\n (decreases p2)\n= FStar.Classical.or_elim\n #(to1 == to2 /\\ p1 == p2)\n #(match p2 with\n | PathBase -> False\n | PathStep _ _ p' _ -> path_includes p1 p')\n #(fun _ -> x p1 p2)\n (fun _ -> h_refl p1)\n (fun _ -> match p2 with\n | PathBase -> assert False\n | PathStep _ _ p2' st ->\n let _ = path_includes_ind x h_step h_refl h_trans p1 p2' in\n let _ = path_includes_step_r p2' st in\n let _ = h_step p2' st in\n h_trans p1 p2' p2\n )\n\nlet rec path_length\n (#from #to: typ)\n (p: path from to)\n: Tot nat\n (decreases p)\n= match p with\n | PathBase -> 0\n | PathStep _ _ p' _ -> 1 + path_length p'\n\nlet path_includes_length\n (#from: typ)\n (#to1 #to2: typ)\n (p1: path from to1)\n (p2: path from to2 {path_includes p1 p2})\n: Lemma\n (ensures (path_length p1 <= path_length p2))\n= path_includes_ind\n (fun #to1_ #to2_ p1_ p2_ -> path_length p1_ <= path_length p2_)\n (fun #through #to p st -> ())\n (fun #to p -> ())\n (fun #to1_ #to2_ #to3_ p1_ p2_ p3_ -> ())\n p1 p2\n\nlet path_includes_step_l\n (#from: typ)\n (#through: typ)\n (#to: typ)\n (p: path from through)\n (s: step through to)\n: Lemma\n (requires True)\n (ensures (~ (path_includes (PathStep through to p s) p)))\n [SMTPat (path_includes (PathStep through to p s) p)]\n= assert (path_length (PathStep through to p s) > path_length p);\n FStar.Classical.forall_intro (path_includes_length #from #to #through (PathStep through to p s))\n\nlet rec path_includes_concat\n (#from: typ)\n (#through: typ)\n (#to: typ)\n (p: path from through)\n (q: path through to)\n: Lemma\n (requires True)\n (ensures (path_includes p (path_concat p q)))\n (decreases q)\n [SMTPat (path_includes p (path_concat p q))]\n= match q with\n | PathBase -> ()\n | PathStep _ _ q' _ -> path_includes_concat p q'\n\nlet path_includes_exists_concat\n (#from #through: typ)\n (p: path from through)\n (#to: typ)\n (q: path from to { path_includes p q } )\n: Lemma\n (ensures (exists (r: path through to) . q == path_concat p r))\n= path_includes_ind\n (fun #to1_ #to2_ p1_ p2_ -> exists r . p2_ == path_concat p1_ r)\n (fun #through #to_ p s ->\n let r = PathStep through to_ PathBase s in\n assert_norm (PathStep through to_ p s == path_concat p r)\n )\n (fun #to p -> FStar.Classical.exists_intro (fun r -> p == path_concat p r) PathBase)\n (fun #to1_ #to2_ #to3_ p1_ p2_ p3_ ->\n FStar.Classical.exists_elim (exists r . p3_ == path_concat p1_ r) #_ #(fun r12 -> p2_ == path_concat p1_ r12) () (fun r12 ->\n\tFStar.Classical.exists_elim (exists r . p3_ == path_concat p1_ r) #_ #(fun r23 -> p3_ == path_concat p2_ r23) () (fun r23 ->\n\t path_concat_assoc p1_ r12 r23;\n\t FStar.Classical.exists_intro (fun r -> p3_ == path_concat p1_ r) (path_concat r12 r23)\n\t)\n )\n )\n p q\n\nlet path_concat_includes\n (#from #through: typ)\n (p: path from through)\n (phi: (\n (#to: typ) ->\n (p': path from to) ->\n Ghost Type0\n (requires (path_includes p p'))\n (ensures (fun _ -> True))\n ))\n (f: (\n (to: typ) ->\n (p': path through to) ->\n Lemma\n (ensures (phi (path_concat p p')))\n ))\n (#to: typ)\n (q: path from to)\n: Lemma\n (requires (path_includes p q))\n (ensures (path_includes p q /\\ phi q))\n= Classical.forall_intro_2 f;\n path_includes_exists_concat p q\n\nlet step_disjoint\n (#from: typ)\n (#to1 #to2: typ)\n (s1: step from to1)\n (s2: step from to2)\n: GTot bool\n= match s1 with\n | StepField _ fd1 ->\n let (StepField _ fd2) = s2 in\n fd1 <> fd2\n | StepCell _ _ i1 ->\n let (StepCell _ _ i2) = s2 in\n UInt32.v i1 <> UInt32.v i2\n | StepUField _ _ ->\n (* two fields of the same union are never disjoint *)\n false\n\nlet step_eq\n (#from: typ)\n (#to1 #to2: typ)\n (s1: step from to1)\n (s2: step from to2)\n: Tot (b: bool { b = true <==> to1 == to2 /\\ s1 == s2 } )\n= match s1 with\n | StepField l1 fd1 ->\n let (StepField _ fd2) = s2 in\n fd1 = fd2\n | StepCell _ _ i1 ->\n let (StepCell _ _ i2) = s2 in\n i1 = i2\n | StepUField l1 fd1 ->\n let (StepUField _ fd2) = s2 in\n fd1 = fd2\n\nlet step_disjoint_not_eq\n (#from: typ)\n (#to1 #to2: typ)\n (s1: step from to1)\n (s2: step from to2)\n: Lemma\n (requires (step_disjoint s1 s2 == true))\n (ensures (step_eq s1 s2 == false))\n= () (* Note: the converse is now wrong, due to unions *)\n\nlet step_disjoint_sym\n (#from: typ)\n (#to1 #to2: typ)\n (s1: step from to1)\n (s2: step from to2)\n: Lemma\n (requires (step_disjoint s1 s2))\n (ensures (step_disjoint s2 s1))\n= ()\n\nnoeq type path_disjoint_t (#from: typ):\n (#to1: typ) ->\n (#to2: typ) ->\n (p1: path from to1) ->\n (p2: path from to2) ->\n Type0\n= | PathDisjointStep:\n (#through: typ) ->\n (#to1: typ) ->\n (#to2: typ) ->\n (p: path from through) ->\n (s1: step through to1) ->\n (s2: step through to2 { step_disjoint s1 s2 } ) ->\n path_disjoint_t (PathStep through to1 p s1) (PathStep through to2 p s2)\n | PathDisjointIncludes:\n (#to1: typ) ->\n (#to2: typ) ->\n (p1: path from to1) ->\n (p2: path from to2) ->\n (#to1': typ) ->\n (#to2': typ) ->\n (p1': path from to1' {path_includes p1 p1'}) ->\n (p2': path from to2' {path_includes p2 p2'}) ->\n path_disjoint_t p1 p2 ->\n path_disjoint_t p1' p2'\n\nlet rec path_disjoint_t_rect\n (#from: typ)\n (x:\n ((#value1: typ) ->\n (#value2: typ) ->\n (p1: path from value1) ->\n (p2: path from value2) ->\n (h: path_disjoint_t p1 p2) ->\n GTot Type))\n (h_step:\n ((#through: typ) ->\n (#to1: typ) ->\n (#to2: typ) ->\n (p: path from through) ->\n (s1: step through to1) ->\n (s2: step through to2 { step_disjoint s1 s2 } ) ->\n (h: path_disjoint_t (PathStep through to1 p s1) (PathStep through to2 p s2)) ->\n GTot (x (PathStep through to1 p s1) (PathStep through to2 p s2) h)))\n (h_includes:\n ((#value1: typ) ->\n (#value2: typ) ->\n (p1: path from value1) ->\n (p2: path from value2) ->\n (#value1': typ) ->\n (#value2': typ) ->\n (p1': path from value1' {path_includes p1 p1'}) ->\n (p2': path from value2' {path_includes p2 p2'}) ->\n (h: path_disjoint_t p1 p2) ->\n (h': path_disjoint_t p1' p2') ->\n (ihx: x p1 p2 h) ->\n GTot (x p1' p2' h')))\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n (h: path_disjoint_t p1 p2)\n: Ghost (x p1 p2 h)\n (requires True)\n (ensures (fun _ -> True))\n (decreases h)\n= match h with\n | PathDisjointStep p s1 s2 -> h_step p s1 s2 h\n | PathDisjointIncludes p1_ p2_ p1' p2' h_ -> h_includes p1_ p2_ p1' p2' h_ h (path_disjoint_t_rect x h_step h_includes p1_ p2_ h_)\n\nlet path_disjoint\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n: GTot Type0\n= squash (path_disjoint_t p1 p2)\n\n#push-options \"--smtencoding.valid_intro true --smtencoding.valid_elim true\"\nlet path_disjoint_ind\n (#from: typ)\n (x:\n ((#value1: typ) ->\n (#value2: typ) ->\n (p1: path from value1) ->\n (p2: path from value2 {path_disjoint p1 p2} ) ->\n GTot Type))\n (h_step:\n ((#through: typ) ->\n (#to1: typ) ->\n (#to2: typ) ->\n (p: path from through) ->\n (s1: step through to1) ->\n (s2: step through to2 { step_disjoint s1 s2 /\\ path_disjoint (PathStep through to1 p s1) (PathStep through to2 p s2) } ) ->\n Lemma (x (PathStep through to1 p s1) (PathStep through to2 p s2) )))\n (h_includes:\n ((#value1: typ) ->\n (#value2: typ) ->\n (p1: path from value1) ->\n (p2: path from value2) ->\n (#value1': typ) ->\n (#value2': typ) ->\n (p1': path from value1' {path_includes p1 p1'}) ->\n (p2': path from value2' {path_includes p2 p2' /\\ path_disjoint p1 p2 /\\ path_disjoint p1' p2' /\\ x p1 p2}) ->\n Lemma (x p1' p2')))\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2 { path_disjoint p1 p2 } )\n: Lemma (x p1 p2)\n= let h : squash (path_disjoint_t p1 p2) = FStar.Squash.join_squash () in\n FStar.Squash.bind_squash h (fun (h: path_disjoint_t p1 p2) ->\n path_disjoint_t_rect\n (fun #v1 #v2 p1 p2 h -> let _ = FStar.Squash.return_squash h in squash (x p1 p2))\n (fun #through #to1 #to2 p s1 s2 h -> let _ = FStar.Squash.return_squash h in h_step p s1 s2)\n (fun #v1 #v2 p1 p2 #v1' #v2' p1' p2' h h' hx ->\n let _ = FStar.Squash.return_squash h in\n let _ = FStar.Squash.return_squash h' in\n let _ = FStar.Squash.return_squash hx in\n h_includes p1 p2 p1' p2')\n p1 p2 h)\n#pop-options\n\nlet path_disjoint_step\n (#from: typ)\n (#through: typ)\n (#to1: typ)\n (#to2: typ)\n (p: path from through)\n (s1: step through to1)\n (s2: step through to2 { step_disjoint s1 s2 } )\n: Lemma\n (requires True)\n (ensures (path_disjoint (PathStep through to1 p s1) (PathStep through to2 p s2)))\n [SMTPat (path_disjoint (PathStep through to1 p s1) (PathStep through to2 p s2))]\n= FStar.Classical.give_witness (FStar.Squash.return_squash (PathDisjointStep p s1 s2))\n\n#push-options \"--smtencoding.valid_intro true --smtencoding.valid_elim true\"\nlet path_disjoint_includes\n (#from: typ)\n (#to1: typ)\n (#to2: typ)\n (p1: path from to1)\n (p2: path from to2)\n (#to1': typ)\n (#to2': typ)\n (p1': path from to1')\n (p2': path from to2')\n: Lemma\n (requires (path_disjoint p1 p2 /\\ path_includes p1 p1' /\\ path_includes p2 p2'))\n (ensures (path_disjoint p1' p2'))\n= let h : squash (path_disjoint_t p1 p2) = FStar.Squash.join_squash () in\n FStar.Squash.bind_squash h (fun h -> FStar.Squash.return_squash (PathDisjointIncludes p1 p2 p1' p2' h))\n#pop-options\n\nlet path_disjoint_includes_l\n (#from: typ)\n (#to1: typ)\n (#to2: typ)\n (p1: path from to1)\n (p2: path from to2)\n (#to1': typ)\n (p1': path from to1')\n: Lemma\n (requires (path_disjoint p1 p2 /\\ path_includes p1 p1'))\n (ensures (path_disjoint p1' p2))\n [SMTPatOr [\n [SMTPat (path_disjoint p1 p2); SMTPat (path_includes p1 p1')];\n [SMTPat (path_disjoint p1' p2); SMTPat (path_includes p1 p1')];\n ]]\n= path_disjoint_includes p1 p2 p1' p2\n\nlet path_disjoint_sym\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n: Lemma\n (requires (path_disjoint p1 p2))\n (ensures (path_disjoint p2 p1))\n [SMTPatOr [[SMTPat (path_disjoint p1 p2)]; [SMTPat (path_disjoint p2 p1)]]]\n= path_disjoint_ind\n (fun #v1 #v2 p1 p2 -> path_disjoint p2 p1)\n (fun #through #to1 #to2 p s1 s2 -> path_disjoint_step p s2 s1)\n (fun #v1 #v2 p1 p2 #v1' #v2' p1' p2' -> path_disjoint_includes p2 p1 p2' p1')\n p1 p2\n\nlet rec path_equal\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n: Tot (b: bool { b == true <==> (value1 == value2 /\\ p1 == p2) } )\n (decreases p1)\n= match p1 with\n | PathBase -> PathBase? p2\n | PathStep _ _ p1' s1 ->\n PathStep? p2 && (\n let (PathStep _ _ p2' s2) = p2 in (\n path_equal p1' p2' &&\n step_eq s1 s2\n ))\n\nlet rec path_length_concat\n (#t0 #t1 #t2: typ)\n (p01: path t0 t1)\n (p12: path t1 t2)\n: Lemma\n (requires True)\n (ensures (path_length (path_concat p01 p12) == path_length p01 + path_length p12))\n (decreases p12)\n= match p12 with\n | PathBase -> ()\n | PathStep _ _ p' s' -> path_length_concat p01 p'\n\nlet rec path_concat_inj_l\n (#from #through1: typ)\n (p1_: path from through1)\n (#v1: typ)\n (p1: path through1 v1)\n (#through2 #v2: typ)\n (p2_: path from through2)\n (p2: path through2 v2)\n: Lemma\n (requires (path_equal (path_concat p1_ p1) (path_concat p2_ p2) == true /\\ path_length p1_ == path_length p2_))\n (ensures (path_equal p1_ p2_ == true /\\ path_equal p1 p2 == true))\n (decreases p1)\n= path_length_concat p1_ p1;\n path_length_concat p2_ p2;\n match p1 with\n | PathBase -> ()\n | PathStep _ _ p1' s1 ->\n let (PathStep _ _ p2' s2) = p2 in\n path_concat_inj_l p1_ p1' p2_ p2'\n\ntype path_disjoint_decomp_t\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n: Type\n= | PathDisjointDecomp:\n (d_through: typ) ->\n (d_p: path from d_through) ->\n (d_v1: typ) ->\n (d_s1: step d_through d_v1) ->\n (d_p1': path d_v1 value1) ->\n (d_v2: typ) ->\n (d_s2: step d_through d_v2) ->\n (d_p2': path d_v2 value2) ->\n squash (\n step_disjoint d_s1 d_s2 == true /\\\n p1 == path_concat (PathStep _ _ d_p d_s1) d_p1' /\\\n p2 == path_concat (PathStep _ _ d_p d_s2) d_p2'\n ) ->\n path_disjoint_decomp_t p1 p2\n\nlet path_disjoint_decomp_includes\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n (#value1': typ)\n (#value2': typ)\n (p1': path from value1')\n (p2': path from value2')\n: Lemma\n (requires (\n path_includes p1 p1' /\\\n path_includes p2 p2' /\\ (\n exists (d : path_disjoint_decomp_t p1 p2) . True\n )))\n (ensures (exists (d: path_disjoint_decomp_t p1' p2') . True))\n= let f\n (q1: path value1 value1' )\n (q2: path value2 value2' )\n (d: path_disjoint_decomp_t p1 p2)\n : Lemma\n (requires (\n p1' == path_concat p1 q1 /\\\n p2' == path_concat p2 q2\n ))\n (ensures (exists (d: path_disjoint_decomp_t p1' p2') . True))\n = let (PathDisjointDecomp _ p _ s1 p1_ _ s2 p2_ _) = d in\n path_concat_assoc (PathStep _ _ p s1) p1_ q1;\n path_concat_assoc (PathStep _ _ p s2) p2_ q2;\n let d' : path_disjoint_decomp_t p1' p2' =\n PathDisjointDecomp _ p _ s1 (path_concat p1_ q1) _ s2 (path_concat p2_ q2) ()\n in\n Classical.exists_intro (fun _ -> True) d'\n in\n let g\n (q1: path value1 value1' )\n (q2: path value2 value2' )\n (d: path_disjoint_decomp_t p1 p2)\n : Lemma\n ((\n p1' == path_concat p1 q1 /\\\n p2' == path_concat p2 q2\n ) ==> (\n exists (d: path_disjoint_decomp_t p1' p2') . True\n ))\n = Classical.move_requires (f q1 q2) d // FIXME: annoying to repeat those type annotations above. WHY WHY WHY can't I just use (fun q1 q2 d -> Classical.move_requires (f q1 q2) d) as an argument of Classical.forall_intro_3 below instead of this g???\n in\n path_includes_exists_concat p1 p1' ;\n path_includes_exists_concat p2 p2' ;\n let _ : squash (exists (d: path_disjoint_decomp_t p1' p2') . True) =\n Classical.forall_intro_3 g\n in\n ()\n\nlet path_disjoint_decomp\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n: Lemma\n (requires (path_disjoint p1 p2))\n (ensures (exists (d: path_disjoint_decomp_t p1 p2) . True))\n= path_disjoint_ind\n (fun #v1 #v2 p1 p2 -> exists (d: path_disjoint_decomp_t #from #v1 #v2 p1 p2) . True)\n (fun #through #to1 #to2 p s1 s2 ->\n let d : path_disjoint_decomp_t (PathStep _ _ p s1) (PathStep _ _ p s2) =\n PathDisjointDecomp _ p _ s1 PathBase _ s2 PathBase ()\n in\n Classical.exists_intro (fun _ -> True) d\n )\n (fun #v1 #v2 p1 p2 #v1' #v2' p1' p2' -> path_disjoint_decomp_includes p1 p2 p1' p2')\n p1 p2\n\nlet path_disjoint_not_path_equal\n (#from: typ)\n (#value1: typ)\n (#value2: typ)\n (p1: path from value1)\n (p2: path from value2)\n: Lemma\n (requires (path_disjoint p1 p2))\n (ensures (path_equal p1 p2 == false))\n= let f\n (d: path_disjoint_decomp_t p1 p2)\n : Lemma (path_equal p1 p2 == false)\n = if path_equal p1 p2\n then\n let (PathDisjointDecomp _ p _ s1 p1_ _ s2 p2_ _) = d in\n path_concat_inj_l (PathStep _ _ p s1) p1_ (PathStep _ _ p s2) p2_\n else ()\n in\n path_disjoint_decomp p1 p2;\n Classical.forall_intro f\n\nlet rec path_destruct_l\n (#t0 #t2: typ)\n (p: path t0 t2)\n: Tot (\n x: option (t1: typ & (s: step t0 t1 & (p' : path t1 t2 { p == path_concat (PathStep _ _ PathBase s) p' /\\ path_length p' < path_length p } ) ) )\n { None? x <==> PathBase? p }\n )\n (decreases p)\n= match p with\n | PathBase -> None\n | PathStep _ _ p' s ->\n begin match path_destruct_l p' with\n | None -> Some (| _, (| s, PathBase |) |)\n | Some (| t_, (| s_, p_ |) |) ->\n Some (| t_, (| s_, PathStep _ _ p_ s |) |)\n end\n\nlet rec path_equal'\n (#from #to1 #to2: typ)\n (p1: path from to1)\n (p2: path from to2)\n: Tot (b: bool { b == true <==> to1 == to2 /\\ p1 == p2 } )\n (decreases (path_length p1))\n= match path_destruct_l p1 with\n | None -> PathBase? p2\n | Some (| t1, (| s1, p1' |) |) ->\n begin match path_destruct_l p2 with\n | None -> false\n | (Some (| t2, (| s2, p2' |) |) ) ->\n step_eq s1 s2 &&\n path_equal' p1' p2'\n end\n\nlet path_includes_concat_l\n (#from #through #to1 #to2: typ)\n (p0: path from through)\n (p1: path through to1)\n (p2: path through to2)\n: Lemma\n (requires (path_includes p1 p2))\n (ensures (path_includes (path_concat p0 p1) (path_concat p0 p2)))\n= path_includes_ind\n (fun #to1_ #to2_ p1_ p2_ -> path_includes (path_concat p0 p1_) (path_concat p0 p2_))\n (fun #through #to p st -> ())\n (fun #to p -> path_includes_refl (path_concat p0 p))\n (fun #to1_ #to2_ #to3_ p1_ p2_ p3_ -> path_includes_trans (path_concat p0 p1_) (path_concat p0 p2_) (path_concat p0 p3_))\n p1 p2\n\nlet path_disjoint_concat\n (#from #through #to1 #to2: typ)\n (p0: path from through)\n (p1: path through to1)\n (p2: path through to2)\n: Lemma\n (requires (path_disjoint p1 p2))\n (ensures (path_disjoint (path_concat p0 p1) (path_concat p0 p2)))\n= path_disjoint_ind\n (fun #v1 #v2 p1 p2 -> path_disjoint (path_concat p0 p1) (path_concat p0 p2))\n (fun #through #to1 #to2 p s1 s2 -> path_disjoint_step (path_concat p0 p) s1 s2)\n (fun #v1 #v2 p1 p2 #v1' #v2' p1' p2' ->\n path_includes_concat_l p0 p1 p1';\n path_includes_concat_l p0 p2 p2';\n path_disjoint_includes (path_concat p0 p1) (path_concat p0 p2) (path_concat p0 p1') (path_concat p0 p2'))\n p1 p2\n\n(* TODO: the following is now wrong due to unions, but should still hold if we restrict ourselves to readable paths\nlet rec not_path_equal_path_disjoint_same_type\n (#from: typ)\n (#value: typ)\n (p1: path from value)\n (p2: path from value)\n: Lemma\n (requires (path_equal p1 p2 == false))\n (ensures (path_disjoint p1 p2))\n (decreases (path_length p1))\n= assert (path_equal p1 p2 == path_equal' p1 p2);\n match path_destruct_l p1 with\n | None -> path_typ_depth p2\n | Some (| t1, (| s1, p1' |) |) ->\n begin match path_destruct_l p2 with\n | None -> path_typ_depth p1\n | Some (| t2, (| s2, p2' |) |) ->\n if step_eq s1 s2\n then begin\n\tnot_path_equal_path_disjoint_same_type p1' p2' ;\n\tpath_disjoint_concat (PathStep _ _ PathBase s1) p1' p2'\n end else begin\n path_disjoint_step PathBase s1 s2;\n\tpath_includes_concat (PathStep _ _ PathBase s1) p1';\n\tpath_includes_concat (PathStep _ _ PathBase s2) p2';\n\tpath_disjoint_includes (PathStep _ _ PathBase s1) (PathStep _ _ PathBase s2) p1 p2\n end\n end\n*)\n\nlet step_sel_upd_other\n (#from: typ)\n (#to1 #to2: typ)\n (s1: step from to1)\n (s2: step from to2 {step_disjoint s1 s2})\n (m: otype_of_typ from)\n (v: otype_of_typ to1)\n: Lemma\n (step_sel (step_upd m s1 v) s2 == step_sel m s2)\n= match s1 with\n | StepField l1 fd1 ->\n let (m: ostruct l1) = m in\n let (StepField _ fd2) = s2 in\n begin match m with\n | None -> ()\n | Some m -> DM.sel_upd_other m fd1 v fd2\n end\n | StepCell length1 _ i1 ->\n let (m: option (array length1 (otype_of_typ to1))) = m in\n let (StepCell _ _ i2) = s2 in\n begin match m with\n | None -> ()\n | Some m ->\n Seq.lemma_index_upd2 m (UInt32.v i1) v (UInt32.v i2)\n end\n\nlet path_sel_upd_other\n (#from: typ)\n (#to1 #to2: typ)\n (p1: path from to1)\n (p2: path from to2 {path_disjoint p1 p2})\n: Lemma\n (ensures (forall (m: otype_of_typ from) (v: otype_of_typ to1) . path_sel (path_upd m p1 v) p2 == path_sel m p2))\n= path_disjoint_ind\n (fun #v1 #v2 p1_ p2_ -> forall (m: otype_of_typ from) (v: otype_of_typ v1) . path_sel (path_upd m p1_ v) p2_ == path_sel m p2_)\n (fun #through #to1_ #to2_ p s1 s2 ->\n FStar.Classical.forall_intro_sub #_ #(fun m -> forall (v: otype_of_typ to1_) . path_sel (path_upd m (PathStep through to1_ p s1) v) (PathStep through to2_ p s2) == path_sel m (PathStep through to2_ p s2)) (fun m ->\n\t FStar.Classical.forall_intro_sub #_ #(fun v -> path_sel (path_upd m (PathStep through to1_ p s1) v) (PathStep through to2_ p s2) == path_sel m (PathStep through to2_ p s2)) (fun v ->\n\t let m0 = path_sel m p in\n let m1 = step_sel m0 s1 in\n let m2 = step_sel m0 s2 in\n let m0' = step_upd m0 s1 v in\n path_sel_upd_same m p m0';\n step_sel_upd_other s1 s2 m0 v\n )))\n (fun #v1 #v2 p1 p2 #v1' #v2' p1' p2' ->\n let h1: squash (exists r1 . p1' == path_concat p1 r1) = path_includes_exists_concat p1 p1' in\n let h2: squash (exists r2 . p2' == path_concat p2 r2) = path_includes_exists_concat p2 p2' in\n FStar.Classical.forall_intro_sub #_ #(fun (m: otype_of_typ from) -> forall v . path_sel (path_upd m p1' v) p2' == path_sel m p2') (fun (m: otype_of_typ from) ->\n FStar.Classical.forall_intro_sub #_ #(fun (v: otype_of_typ v1') -> path_sel (path_upd m p1' v) p2' == path_sel m p2') (fun (v: otype_of_typ v1') ->\n FStar.Classical.exists_elim (path_sel (path_upd m p1' v) p2' == path_sel m p2') h1 (fun r1 ->\n\tFStar.Classical.exists_elim (path_sel (path_upd m p1' v) p2' == path_sel m p2') h2 (fun r2 ->\n\t path_upd_concat m p1 r1 v;\n\t path_sel_concat m p2 r2\n\t )))))\n p1 p2\n\nlet path_sel_upd_other'\n (#from: typ)\n (#to1: typ)\n (p1: path from to1)\n (m: otype_of_typ from)\n (v: otype_of_typ to1)\n (#to2: typ)\n (p2: path from to2)\n: Lemma\n (requires (path_disjoint p1 p2))\n (ensures (path_sel (path_upd m p1 v) p2 == path_sel m p2))\n= path_sel_upd_other p1 p2\n\n(** Operations on pointers *)\n\nlet equal\n (#t1 #t2: typ)\n (p1: pointer t1)\n (p2: pointer t2)\n: Ghost bool\n (requires True)\n (ensures (fun b -> b == true <==> t1 == t2 /\\ p1 == p2 ))\n= Pointer?.from p1 = Pointer?.from p2 &&\n HS.aref_equal (Pointer?.contents p1) (Pointer?.contents p2) &&\n path_equal (Pointer?.p p1) (Pointer?.p p2)\n\nlet as_addr (#t: typ) (p: pointer t) =\n HS.aref_as_addr (Pointer?.contents p)\n\nlet _field\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n: Tot (pointer (typ_of_struct_field l fd))\n= let (Pointer from contents p') = p in\n let p' : path from (TStruct l) = p' in\n let p'' : path from (typ_of_struct_field l fd) = PathStep _ _ p' (StepField _ fd) in\n Pointer from contents p''\n\nlet _cell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n (i: UInt32.t {UInt32.v i < UInt32.v length})\n: Tot (pointer value)\n= let (Pointer from contents p') = p in\n let p' : path from (TArray length value) = p' in\n let p'' : path from value = PathStep _ _ p' (StepCell _ _ i) in\n Pointer from contents p''\n\nlet _ufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: Tot (pointer (typ_of_struct_field l fd))\n= let (Pointer from contents p') = p in\n let p' : path from (TUnion l) = p' in\n let p'' : path from (typ_of_struct_field l fd) = PathStep _ _ p' (StepUField _ fd) in\n Pointer from contents p''\n\nlet unused_in\n (#value: typ)\n (p: pointer value)\n (h: HS.mem)\n: GTot Type0\n= let (Pointer from contents p') = p in\n HS.aref_unused_in contents h\n\nlet pointer_ref_contents : Type0 = (t: typ & otype_of_typ t)\n\nlet live\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n: GTot Type0\n= let rel = Heap.trivial_preorder pointer_ref_contents in\n let (Pointer from contents _) = p in (\n HS.aref_live_at h contents pointer_ref_contents rel /\\ (\n let untyped_contents = HS.greference_of contents pointer_ref_contents rel in (\n dfst (HS.sel h untyped_contents) == from\n )))\n\nlet nlive\n (#value: typ)\n (h: HS.mem)\n (p: npointer value)\n: GTot Type0\n= if g_is_null p\n then True\n else live h p\n\nlet live_nlive\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n= ()\n\nlet g_is_null_nlive\n (#t: typ)\n (h: HS.mem)\n (p: npointer t)\n= ()\n\nlet greference_of\n (#value: typ)\n (p: pointer value)\n: Ghost (HS.reference pointer_ref_contents)\n (requires (exists h . live h p))\n (ensures (fun x -> (exists h . live h p) /\\ x == HS.greference_of (Pointer?.contents p) pointer_ref_contents (Heap.trivial_preorder pointer_ref_contents) /\\ HS.aref_of x == Pointer?.contents p))\n= HS.greference_of (Pointer?.contents p) pointer_ref_contents (Heap.trivial_preorder pointer_ref_contents)\n\nlet unused_in_greference_of\n (#value: typ)\n (p: pointer value)\n (h: HS.mem)\n: Lemma\n (requires (exists h . live h p))\n (ensures ((exists h . live h p) /\\ (HS.unused_in (greference_of p) h <==> unused_in p h)))\n [SMTPatOr [\n [SMTPat (HS.unused_in (greference_of p) h)];\n [SMTPat (unused_in p h)];\n ]]\n= ()\n\nlet live_not_unused_in\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n= let f () : Lemma\n (requires (live h p /\\ p `unused_in` h))\n (ensures False)\n = let r = greference_of p in\n HS.contains_aref_unused_in h r (Pointer?.contents p)\n in\n Classical.move_requires f ()\n\nlet gread\n (#value: typ)\n (h: HS.mem)\n (p: pointer value)\n: GTot (type_of_typ value)\n= if StrongExcludedMiddle.strong_excluded_middle (live h p)\n then\n let content = greference_of p in\n let (| _, c |) = HS.sel h content in\n value_of_ovalue value (path_sel c (Pointer?.p p))\n else\n dummy_val value\n\nlet frameOf\n (#value: typ)\n (p: pointer value)\n: GTot HS.rid\n= HS.frameOf_aref (Pointer?.contents p)\n\nlet live_region_frameOf #value h p =\n let content = greference_of p in\n assert (HS.contains h content)\n\nlet disjoint_roots_intro_pointer_vs_pointer\n (#value1 value2: typ)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: pointer value2)\n: Lemma\n (requires (live h p1 /\\ unused_in p2 h))\n (ensures (frameOf p1 <> frameOf p2 \\/ as_addr p1 =!= as_addr p2))\n= ()\n\nlet disjoint_roots_intro_pointer_vs_reference\n (#value1: typ)\n (#value2: Type)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: HS.reference value2)\n: Lemma\n (requires (live h p1 /\\ p2 `HS.unused_in` h))\n (ensures (frameOf p1 <> HS.frameOf p2 \\/ as_addr p1 =!= HS.as_addr p2))\n= let r = greference_of p1 in\n assert (HS.contains h r)\n\nlet disjoint_roots_intro_reference_vs_pointer\n (#value1: Type)\n (#value2: typ)\n (h: HS.mem)\n (p1: HS.reference value1)\n (p2: pointer value2)\n: Lemma\n (requires (HS.contains h p1 /\\ p2 `unused_in` h))\n (ensures (HS.frameOf p1 <> frameOf p2 \\/ HS.as_addr p1 =!= as_addr p2))\n= ()\n\nlet is_mm\n (#value: typ)\n (p: pointer value)\n: GTot bool\n= HS.aref_is_mm (Pointer?.contents p)\n\n(* // TODO: recover with addresses?\nlet recall\n (#value: Type)\n (p: pointer value {is_eternal_region (frameOf p) && not (is_mm p)})\n: HST.Stack unit\n (requires (fun m -> True))\n (ensures (fun m0 _ m1 -> m0 == m1 /\\ live m1 p))\n= HST.recall (Pointer?.content p)\n*)\n\nlet gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= _field p fd\n\nlet as_addr_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()\n\nlet unused_in_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n (h: HS.mem)\n= ()\n\nlet live_gfield\n (h: HS.mem)\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()\n\nlet gread_gfield\n (h: HS.mem)\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()\n\nlet frameOf_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()\n\nlet is_mm_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()\n\nlet gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= _ufield p fd\n\nlet as_addr_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()\n\nlet unused_in_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n (h: HS.mem)\n= ()\n\nlet live_gufield\n (h: HS.mem)\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()\n\nlet gread_gufield\n (h: HS.mem)\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()\n\nlet frameOf_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()\n\nlet is_mm_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()\n\nlet gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n i\n= _cell p i\n\nlet as_addr_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n i\n= ()\n\nlet unused_in_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n i\n= ()\n\nlet live_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n i\n= ()\n\nlet gread_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n i\n= ()\n\nlet frameOf_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n i\n= ()\n\nlet is_mm_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n i\n= ()\n\nlet includes\n (#value1: typ)\n (#value2: typ)\n (p1: pointer value1)\n (p2: pointer value2)\n: GTot bool\n= Pointer?.from p1 = Pointer?.from p2 &&\n HS.aref_equal (Pointer?.contents p1) (Pointer?.contents p2) &&\n path_includes (Pointer?.p p1) (Pointer?.p p2)\n\nlet includes_refl\n (#value: typ)\n (p: pointer value)\n= ()\n\nlet includes_trans\n (#value1 #value2 #value3: typ)\n (p1: pointer value1)\n (p2: pointer value2)\n (p3: pointer value3)\n= path_includes_trans (Pointer?.p p1) (Pointer?.p p2) (Pointer?.p p3)\n\nlet includes_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()\n\nlet includes_gufield\n (#l: union_typ)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()\n\nlet includes_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n i\n= ()\n\nlet includes_ind\n (x:((#value1: typ) ->\n (#value2: typ) ->\n (p1: pointer value1) ->\n (p2: pointer value2 {includes p1 p2} ) ->\n GTot Type0))\n (h_field:\n ((l: struct_typ) ->\n (p: pointer (TStruct l)) ->\n (fd: struct_field l {includes p (gfield p fd)}) ->\n Lemma (x p (gfield p fd))))\n (h_ufield:\n ((l: union_typ) ->\n (p: pointer (TUnion l)) ->\n (fd: struct_field l {includes p (gufield p fd)}) ->\n Lemma (x p (gufield p fd))))\n (h_cell:\n ((#length: array_length_t) ->\n (#value: typ) ->\n (p: pointer (TArray length value)) ->\n (i: UInt32.t {UInt32.v i < UInt32.v length /\\ includes p (gcell p i)}) ->\n Lemma (x p (gcell p i))))\n (h_refl:\n ((#value: typ) ->\n (p: pointer value {includes p p}) ->\n Lemma (x p p)))\n (h_trans:\n ((#value1: typ) ->\n (#value2: typ) ->\n (#value3: typ) ->\n (p1: pointer value1) ->\n (p2: pointer value2) ->\n (p3: pointer value3 {includes p1 p2 /\\ includes p2 p3 /\\ includes p1 p3 /\\ x p1 p2 /\\ x p2 p3}) ->\n Lemma (x p1 p3)))\n (#value1: typ)\n (#value2: typ)\n (p1: pointer value1)\n (p2: pointer value2 {includes p1 p2})\n: Lemma (x p1 p2)\n= let (Pointer from contents _) = p1 in\n path_includes_ind\n (fun #to1 #to2 p1_ p2_ -> x (Pointer from contents p1_) (Pointer from contents p2_))\n (fun #through #to p s ->\n match s with\n | StepField l fd -> let (pt: pointer (TStruct l)) = (Pointer from contents p) in h_field l pt fd\n | StepUField l fd -> let (pt: pointer (TUnion l)) = (Pointer from contents p) in h_ufield l pt fd\n | StepCell length value i -> let (pt: pointer (TArray length value)) = (Pointer from contents p) in h_cell pt i\n )\n (fun #to p -> h_refl (Pointer from contents p))\n (fun #to1 #to2 #to3 p1_ p2_ p3_ -> h_trans (Pointer from contents p1_) (Pointer from contents p2_) (Pointer from contents p3_))\n (Pointer?.p p1)\n (Pointer?.p p2)\n\n(*\nlet unused_in_includes\n (#value1: typ)\n (#value2: typ)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: pointer value2)\n: Lemma\n (requires (includes p1 p2))\n (unused_in p1 h <==> unused_in p2 h)\n [SMTPat (unused_in p2 h); SMTPat (includes p1 p2)]\n= includes_ind\n (fun #v1 #v2 p1 p2 -> unused_in p1 h <==> unused_in p2 h)\n (fun l p fd -> unused_in_gfield p fd h)\n (fun l p fd -> unused_in_gufield p fd h)\n (fun #length #value p i -> unused_in_gcell h p i)\n (fun #v p -> ())\n (fun #v1 #v2 #v3 p1 p2 p3 -> ())\n p1 p2\n\nlet live_includes\n (#value1: typ)\n (#value2: typ)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: pointer value2)\n: Lemma\n (requires (includes p1 p2))\n (ensures (live h p1 <==> live h p2))\n [SMTPat (live h p2); SMTPat (includes p1 p2)]\n= includes_ind\n (fun #v1 #v2 p1 p2 -> live h p1 <==> live h p2)\n (fun l p fd -> live_gfield h p fd)\n (fun l p fd -> live_gufield h p fd)\n (fun #length #value p i -> live_gcell h p i)\n (fun #v p -> ())\n (fun #v1 #v2 #v3 p1 p2 p3 -> ())\n p1 p2\n*)\n\n(** The readable permission.\n We choose to implement it only abstractly, instead of explicitly\n tracking the permission in the heap.\n*)\n\nlet readable\n (#a: typ)\n (h: HS.mem)\n (b: pointer a)\n: GTot Type0\n= let () = () in // necessary to somehow remove the `logic` qualifier\n live h b /\\ (\n let content = greference_of b in\n let (| _, c |) = HS.sel h content in\n ovalue_is_readable a (path_sel c (Pointer?.p b))\n )\n\nlet readable_live\n (#a: typ)\n (h: HS.mem)\n (b: pointer a)\n= ()\n\nlet readable_gfield\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n (fd: struct_field l)\n= ()\n\nlet readable_struct\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n: Lemma\n (requires (\n forall (f: struct_field l) .\n readable h (gfield p f)\n ))\n (ensures (readable h p))\n// [SMTPat (readable #(TStruct l) h p)] // TODO: dubious pattern, will probably trigger unreplayable hints\n= let dummy_field : struct_field l = fst (List.Tot.hd l.fields) in // struct is nonempty\n let dummy_field_ptr = gfield p dummy_field in\n assert (readable h dummy_field_ptr);\n let content = greference_of p in\n let (| _, c |) = HS.sel h content in\n let (v: otype_of_typ (TStruct l)) = path_sel c (Pointer?.p p) in\n let (v: ostruct l {Some? v}) = v in\n ovalue_is_readable_struct_intro l v\n\nlet readable_struct_forall_mem\n (#l: struct_typ)\n (p: pointer (TStruct l))\n: Lemma (forall\n (h: HS.mem)\n . (\n forall (f: struct_field l) .\n readable h (gfield p f)\n ) ==>\n readable h p\n )\n= let f\n (h: HS.mem)\n : Lemma // FIXME: WHY WHY WHY do we need this explicit annotation?\n (requires (\n forall (f: struct_field l) .\n readable h (gfield p f)\n ))\n (ensures (readable h p))\n = readable_struct h p\n in\n Classical.forall_intro (Classical.move_requires f)\n\nlet rec readable_struct_fields'\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n (s: list string)\n: GTot Type0\n (decreases s)\n= match s with\n | [] -> True\n | f :: s' ->\n readable_struct_fields' h p s' /\\ (\n if List.Tot.mem f (List.Tot.map fst l.fields)\n then\n\tlet f : struct_field l = f in\n\treadable h (gfield p f)\n else\n\tTrue\n )\n\nlet readable_struct_fields #l h p s = readable_struct_fields' h p s\n\nlet readable_struct_fields_nil #l h p = ()\n\nlet readable_struct_fields_cons #l h p f q = ()\n\nlet rec readable_struct_fields_elim\n (#l: struct_typ)\n (h: HS.mem)\n (p: pointer (TStruct l))\n (s: list string)\n: Lemma\n (requires (readable_struct_fields h p s))\n (ensures (forall f . (List.Tot.mem f s /\\ List.Tot.mem f (List.Tot.map fst l.fields)) ==> (let f : struct_field l = f in readable h (gfield p f))))\n (decreases s)\n= match s with\n | [] -> ()\n | _ :: q -> readable_struct_fields_elim h p q\n\nlet readable_struct_fields_readable_struct #l h p =\n readable_struct_fields_elim h p (List.Tot.map fst l.fields);\n readable_struct h p\n\nlet readable_gcell\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n i\n= ()\n\nlet readable_array\n (#length: array_length_t)\n (#value: typ)\n (h: HS.mem)\n (p: pointer (TArray length value))\n= assert (readable h (gcell p 0ul)); // for Some?\n let content = greference_of p in\n let (| _, c |) = HS.sel h content in\n let (v0: otype_of_typ (TArray length value)) = path_sel c (Pointer?.p p) in\n ovalue_is_readable_array_intro v0\n\n(* TODO: improve on the following interface *)\nlet readable_gufield\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()\n\n(** The active field of a union *)\n\nlet is_active_union_field\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n: GTot Type0\n= let () = () in // necessary to somehow remove the `logic` qualifier\n live h p /\\ (\n let content = greference_of p in\n let (| _, c |) = HS.sel h content in\n let vu : otype_of_typ (TUnion l) = path_sel c (Pointer?.p p) in\n let vu : option (gtdata (struct_field l) (type_of_struct_field' l otype_of_typ)) = vu in\n Some? vu /\\ gtdata_get_key (Some?.v vu) == fd\n )\n\nlet is_active_union_live\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()\n\nlet is_active_union_field_live\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()\n\nlet is_active_union_field_eq\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd1 fd2: struct_field l)\n= ()\n\nlet is_active_union_field_get_key\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()\n\nlet is_active_union_field_readable\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n= ()\n\nlet is_active_union_field_includes_readable\n (#l: union_typ)\n (h: HS.mem)\n (p: pointer (TUnion l))\n (fd: struct_field l)\n (#t': typ)\n (p' : pointer t')\n= let content = greference_of p in\n let (| _ , c |) = HS.sel h content in\n let t = typ_of_struct_field l fd in\n let (Pointer from cts p0) = p in\n let pf = PathStep _ _ p0 (StepUField l fd) in\n let (v0 : otype_of_typ t) = path_sel c pf in\n let phi\n (#t': typ)\n (pt': path from t')\n : Ghost Type0\n (requires (path_includes pf pt'))\n (ensures (fun _ -> True))\n = (~ (path_sel c pt' == none_ovalue t')) ==> is_active_union_field h p fd\n in\n let f\n (t' : typ)\n (pt' : path t t')\n : Lemma\n (ensures (phi (path_concat pf pt')))\n = path_sel_concat c pf pt';\n path_sel_none_ovalue pf;\n path_sel_none_ovalue pt'\n in\n path_concat_includes pf phi f (Pointer?.p p')\n\n(*** Semantics of buffers *)\n\n(** Operations on buffers *)\n\n#push-options \"--ifuel 2\"\nlet _singleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n: Tot (buffer t)\n= let Pointer from contents pth = p in\n match pth with\n | PathStep _ _ pth' (StepCell ln ty i) ->\n (* reconstruct the buffer to the enclosing array *)\n Buffer (BufferRootArray #ty #ln (Pointer from contents pth')) i 1ul\n | _ ->\n Buffer (BufferRootSingleton p) 0ul 1ul\n#pop-options\n\nlet gsingleton_buffer_of_pointer #t p = _singleton_buffer_of_pointer p\n\nlet singleton_buffer_of_pointer #t p = _singleton_buffer_of_pointer p\n\nlet gbuffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n: GTot (buffer t)\n= Buffer (BufferRootArray p) 0ul length\n\nlet buffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n: HST.Stack (buffer t)\n (requires (fun h -> live h p))\n (ensures (fun h b h' -> h' == h /\\ b == gbuffer_of_array_pointer p))\n= Buffer (BufferRootArray p) 0ul length\n\nlet buffer_length\n (#t: typ)\n (b: buffer t)\n: GTot UInt32.t\n= Buffer?.blength b\n\nlet buffer_length_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n: Lemma\n (requires True)\n (ensures (buffer_length (gsingleton_buffer_of_pointer p) == 1ul))\n [SMTPat (buffer_length (gsingleton_buffer_of_pointer p))]\n= ()\n\nlet buffer_length_gbuffer_of_array_pointer\n (#t: typ)\n (#len: array_length_t)\n (p: pointer (TArray len t))\n: Lemma\n (requires True)\n (ensures (buffer_length (gbuffer_of_array_pointer p) == len))\n [SMTPat (buffer_length (gbuffer_of_array_pointer p))]\n= ()\n\nlet buffer_live\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: GTot Type0\n= let () = () in ( // necessary to somehow remove the `logic` qualifier\n match b.broot with\n | BufferRootSingleton p -> live h p\n | BufferRootArray p -> live h p\n )\n\nlet buffer_live_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n (h: HS.mem)\n: Lemma\n (ensures (buffer_live h (gsingleton_buffer_of_pointer p) <==> live h p ))\n [SMTPat (buffer_live h (gsingleton_buffer_of_pointer p))]\n= ()\n\nlet buffer_live_gbuffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n (h: HS.mem)\n: Lemma\n (requires True)\n (ensures (buffer_live h (gbuffer_of_array_pointer p) <==> live h p))\n [SMTPat (buffer_live h (gbuffer_of_array_pointer p))]\n= ()\n\nlet buffer_unused_in #t b h =\n match b.broot with\n | BufferRootSingleton p -> unused_in p h\n | BufferRootArray p -> unused_in p h\n\nlet buffer_live_not_unused_in #t b h = ()\n\nlet buffer_unused_in_gsingleton_buffer_of_pointer #t p h = ()\n\nlet buffer_unused_in_gbuffer_of_array_pointer #t #length p h = ()\n\nlet frameOf_buffer\n (#t: typ)\n (b: buffer t)\n: GTot HS.rid\n= match b.broot with\n | BufferRootSingleton p -> frameOf p\n | BufferRootArray p -> frameOf p\n\nlet frameOf_buffer_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n= ()\n\nlet frameOf_buffer_gbuffer_of_array_pointer\n (#t: typ)\n (#length: array_length_t)\n (p: pointer (TArray length t))\n= ()\n\nlet live_region_frameOf_buffer #value h p = ()\n\nlet buffer_as_addr #t b =\n match b.broot with\n | BufferRootSingleton p -> as_addr p\n | BufferRootArray p -> as_addr p\n\nlet buffer_as_addr_gsingleton_buffer_of_pointer #t p = ()\n\nlet buffer_as_addr_gbuffer_of_array_pointer #t #length p = ()\n\nlet gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n len\n= Buffer (Buffer?.broot b) FStar.UInt32.(Buffer?.bidx b +^ i) len\n\nlet frameOf_buffer_gsub_buffer #t b i len = ()\n\nlet buffer_as_addr_gsub_buffer #t b i len = ()\n\nlet sub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n len\n= Buffer (Buffer?.broot b) FStar.UInt32.(Buffer?.bidx b +^ i) len\n\nlet offset_buffer #t b i =\n sub_buffer b i (UInt32.sub (Buffer?.blength b) i)\n\nlet buffer_length_gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n len\n= ()\n\nlet buffer_live_gsub_buffer_equiv\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n len\n h\n= ()\n\nlet buffer_live_gsub_buffer_intro\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n len\n h\n= ()\n\nlet buffer_unused_in_gsub_buffer #t b i len h = ()\n\nlet gsub_buffer_gsub_buffer\n (#a: typ)\n (b: buffer a)\n (i1: UInt32.t)\n len1 i2 len2\n= ()\n\nlet gsub_buffer_zero_buffer_length\n (#a: typ)\n (b: buffer a)\n= ()\n\nlet buffer_root_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer_root t)\n: GTot (Seq.seq (type_of_typ t))\n= match b with\n | BufferRootSingleton p ->\n Seq.create 1 (gread h p)\n | BufferRootArray p ->\n gread h p\n\nlet length_buffer_root_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer_root t)\n: Lemma\n (requires True)\n (ensures (Seq.length (buffer_root_as_seq h b) == UInt32.v (buffer_root_length b)))\n [SMTPat (Seq.length (buffer_root_as_seq h b))]\n= ()\n\nlet buffer_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: GTot (Seq.seq (type_of_typ t))\n= let i = UInt32.v (Buffer?.bidx b) in\n Seq.slice (buffer_root_as_seq h (Buffer?.broot b)) i (i + UInt32.v (Buffer?.blength b))\n\nlet buffer_length_buffer_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n= ()\n\n#push-options \"--ifuel 2 --z3rlimit_factor 4 --retry 4\"\nlet buffer_as_seq_gsingleton_buffer_of_pointer #t h p =\n let Pointer from contents pth = p in\n match pth with\n | PathStep through to pth' (StepCell ln ty i) ->\n assert (through == TArray ln ty);\n assert (to == ty);\n assert (t == ty);\n let p' : pointer (TArray ln ty) = Pointer from contents pth' in\n let s : array ln (type_of_typ t) = gread h p' in\n let s1 = Seq.slice s (UInt32.v i) (UInt32.v i + 1) in\n let v = gread h p in\n assert (v == Seq.index s (UInt32.v i));\n let s2 = Seq.create 1 v in\n assert (Seq.length s1 == 1);\n assert (Seq.length s2 == 1);\n assert (Seq.index s1 0 == v);\n assert (Seq.index s2 0 == v);\n assert (Seq.equal s1 s2)\n | _ ->\n Seq.slice_length (Seq.create 1 (gread h p))\n#pop-options\n\nlet buffer_as_seq_gbuffer_of_array_pointer\n (#length: array_length_t)\n (#t: typ)\n (h: HS.mem)\n (p: pointer (TArray length t))\n= let s : array length (type_of_typ t) = gread h p in\n Seq.slice_length s\n\nlet buffer_as_seq_gsub_buffer\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n len\n= Seq.slice_slice (buffer_root_as_seq h (Buffer?.broot b)) (UInt32.v (Buffer?.bidx b)) (UInt32.v (Buffer?.bidx b) + UInt32.v (Buffer?.blength b)) (UInt32.v i) (UInt32.v i + UInt32.v len)\n\nlet gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n i\n= match Buffer?.broot b with\n | BufferRootSingleton p -> p\n | BufferRootArray p ->\n gcell p FStar.UInt32.(Buffer?.bidx b +^ i)\n\nlet pointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n i\n= match Buffer?.broot b with\n | BufferRootSingleton p -> p\n | BufferRootArray p ->\n _cell p FStar.UInt32.(Buffer?.bidx b +^ i)\n\nlet gpointer_of_buffer_cell_gsub_buffer\n (#t: typ)\n (b: buffer t)\n i1 len i2\n= ()\n\nlet live_gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n i h\n= ()\n\n#set-options \"--initial_ifuel 2 --max_ifuel 2\"\nlet gpointer_of_buffer_cell_gsingleton_buffer_of_pointer\n (#t: typ)\n (p: pointer t)\n i\n= ()\n\n#set-options \"--initial_ifuel 1 --max_ifuel 1\"\nlet gpointer_of_buffer_cell_gbuffer_of_array_pointer\n (#length: array_length_t)\n (#t: typ)\n (p: pointer (TArray length t))\n i\n= ()\n\nlet frameOf_gpointer_of_buffer_cell #t b i = ()\n\nlet as_addr_gpointer_of_buffer_cell #t b i = ()\n\nlet gread_gpointer_of_buffer_cell\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n i\n= ()\n\nlet gread_gpointer_of_buffer_cell'\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n i\n= ()\n\nlet index_buffer_as_seq\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n i\n= ()\n\nlet gsingleton_buffer_of_pointer_gcell #t #len p i = ()\n\nlet gsingleton_buffer_of_pointer_gpointer_of_buffer_cell #t b i = ()\n\n(* The readable permission lifted to buffers. *)\n\nlet buffer_readable'\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n: GTot Type0\n= buffer_live h b /\\ (\n forall (i: UInt32.t) .\n UInt32.v i < UInt32.v (buffer_length b) ==>\n readable h (gpointer_of_buffer_cell b i)\n )\n" }, { "file_name": "EverParse3d.Interpreter.fst", "name": "EverParse3d.Interpreter.mk_dt_app", "opens_and_abbrevs": [ { "abbrev": "T", "full_module": "FStar.Tactics" }, { "open": "FStar.List.Tot" }, { "abbrev": "CP", "full_module": "EverParse3d.CopyBuffer" }, { "abbrev": "T", "full_module": "FStar.Tactics" }, { "abbrev": "P", "full_module": "EverParse3d.Prelude" }, { "abbrev": "A", "full_module": "EverParse3d.Actions.All" }, { "abbrev": "U64", "full_module": "FStar.UInt64" }, { "abbrev": "U32", "full_module": "FStar.UInt32" }, { "open": "EverParse3d" }, { "open": "EverParse3d" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 0, "initial_ifuel": 2, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.qi.eager_threshold=10" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val mk_dt_app\n (#nz #wk: _)\n (pk: P.parser_kind nz wk)\n (b: bool)\n ([@@@ erasable]inv: inv_index)\n ([@@@ erasable]disj: disj_index)\n ([@@@ erasable]loc: loc_index)\n (x: global_binding)\n ([@@@ erasable]pf:\n squash (nz == nz_of_binding x /\\ wk == wk_of_binding x /\\ pk == pk_of_binding x /\\\n b == has_reader x /\\ inv == inv_of_binding x /\\ disj == disj_of_bindng x /\\\n loc == loc_of_binding x))\n : dtyp #nz #wk pk b inv disj loc", "source_definition": "let mk_dt_app #nz #wk (pk:P.parser_kind nz wk) (b:bool)\r\n ([@@@erasable] inv:inv_index)\r\n ([@@@erasable] disj:disj_index)\r\n ([@@@erasable] loc:loc_index)\r\n (x:global_binding)\r\n ([@@@erasable] pf:squash (nz == nz_of_binding x /\\\r\n wk == wk_of_binding x /\\\r\n pk == pk_of_binding x /\\\r\n b == has_reader x /\\\r\n inv == inv_of_binding x /\\\r\n disj == disj_of_bindng x /\\\r\n loc == loc_of_binding x))\r\n : dtyp #nz #wk pk b inv disj loc\r\n = DT_App pk b inv disj loc x pf", "source_range": { "start_line": 1395, "start_col": 0, "end_line": 1408, "end_col": 35 }, "interleaved": false, "definition": "fun pk b inv disj loc x pf ->\n EverParse3d.Interpreter.DT_App pk b inv disj loc x pf\n <:\n EverParse3d.Interpreter.dtyp pk b inv disj loc", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Prims.bool", "EverParse3d.Kinds.weak_kind", "EverParse3d.Kinds.parser_kind", "EverParse3d.Interpreter.inv_index", "EverParse3d.Interpreter.disj_index", "EverParse3d.Interpreter.loc_index", "EverParse3d.Interpreter.global_binding", "Prims.squash", "Prims.l_and", "Prims.eq2", "EverParse3d.Interpreter.nz_of_binding", "EverParse3d.Interpreter.wk_of_binding", "EverParse3d.Interpreter.pk_of_binding", "EverParse3d.Interpreter.has_reader", "EverParse3d.Interpreter.inv_of_binding", "EverParse3d.Interpreter.disj_of_bindng", "EverParse3d.Interpreter.loc_of_binding", "EverParse3d.Interpreter.DT_App", "EverParse3d.Interpreter.dtyp" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "\n pk: EverParse3d.Kinds.parser_kind nz wk ->\n b: Prims.bool ->\n inv: EverParse3d.Interpreter.inv_index ->\n disj: EverParse3d.Interpreter.disj_index ->\n loc: EverParse3d.Interpreter.loc_index ->\n x: EverParse3d.Interpreter.global_binding ->\n pf:\n Prims.squash (nz == EverParse3d.Interpreter.nz_of_binding x /\\\n wk == EverParse3d.Interpreter.wk_of_binding x /\\\n pk == EverParse3d.Interpreter.pk_of_binding x /\\ b == EverParse3d.Interpreter.has_reader x /\\\n inv == EverParse3d.Interpreter.inv_of_binding x /\\\n disj == EverParse3d.Interpreter.disj_of_bindng x /\\\n loc == EverParse3d.Interpreter.loc_of_binding x)\n -> EverParse3d.Interpreter.dtyp pk b inv disj loc", "prompt": "let mk_dt_app\n #nz\n #wk\n (pk: P.parser_kind nz wk)\n (b: bool)\n ([@@@ erasable]inv: inv_index)\n ([@@@ erasable]disj: disj_index)\n ([@@@ erasable]loc: loc_index)\n (x: global_binding)\n ([@@@ erasable]pf:\n squash (nz == nz_of_binding x /\\ wk == wk_of_binding x /\\ pk == pk_of_binding x /\\\n b == has_reader x /\\ inv == inv_of_binding x /\\ disj == disj_of_bindng x /\\\n loc == loc_of_binding x))\n : dtyp #nz #wk pk b inv disj loc =\n ", "expected_response": "DT_App pk b inv disj loc x pf", "source": { "project_name": "everparse", "file_name": "src/3d/prelude/EverParse3d.Interpreter.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git" }, "dependencies": { "source_file": "EverParse3d.Interpreter.fst", "checked_file": "dataset/EverParse3d.Interpreter.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.UInt64.fsti.checked", "dataset/FStar.UInt32.fsti.checked", "dataset/FStar.Tactics.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/EverParse3d.Prelude.fsti.checked", "dataset/EverParse3d.CopyBuffer.fsti.checked", "dataset/EverParse3d.Actions.BackendFlag.fsti.checked", "dataset/EverParse3d.Actions.All.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "let ___EVERPARSE_COPY_BUFFER_T = CP.copy_buffer_t", "let specialize = ()", "itype", "UInt8", "UInt8", "UInt8", "UInt16", "UInt16", "UInt16", "UInt32", "UInt32", "UInt32", "UInt64", "UInt64", "UInt64", "UInt8BE", "UInt8BE", "UInt8BE", "UInt16BE", "UInt16BE", "UInt16BE", "UInt32BE", "UInt32BE", "UInt32BE", "UInt64BE", "UInt64BE", "UInt64BE", "Unit", "Unit", "Unit", "AllBytes", "AllBytes", "AllBytes", "AllZeros", "AllZeros", "AllZeros", "let itype_as_type (i:itype)\r\n : Type\r\n = match i with\r\n | UInt8 -> P.___UINT8\r\n | UInt16 -> P.___UINT16\r\n | UInt32 -> P.___UINT32\r\n | UInt64 -> P.___UINT64\r\n | UInt8BE -> P.___UINT8BE\r\n | UInt16BE -> P.___UINT16BE\r\n | UInt32BE -> P.___UINT32BE\r\n | UInt64BE -> P.___UINT64BE\r\n | Unit -> unit\r\n | AllBytes -> P.all_bytes\r\n | AllZeros -> P.all_zeros", "let parser_kind_nz_of_itype (i:itype)\r\n : bool\r\n = match i with\r\n | Unit\r\n | AllBytes\r\n | AllZeros -> false\r\n | _ -> true", "let parser_weak_kind_of_itype (i:itype)\r\n : P.weak_kind\r\n = match i with\r\n | AllBytes\r\n | AllZeros -> P.WeakKindConsumesAll\r\n | _ -> P.WeakKindStrongPrefix", "let parser_kind_of_itype (i:itype)\r\n : P.parser_kind (parser_kind_nz_of_itype i)\r\n (parser_weak_kind_of_itype i)\r\n = match i with\r\n | UInt8 -> P.kind____UINT8\r\n | UInt16 -> P.kind____UINT16\r\n | UInt32 -> P.kind____UINT32\r\n | UInt64 -> P.kind____UINT64\r\n | UInt8BE -> P.kind____UINT8BE\r\n | UInt16BE -> P.kind____UINT16BE\r\n | UInt32BE -> P.kind____UINT32BE\r\n | UInt64BE -> P.kind____UINT64BE\r\n | Unit -> P.kind_unit\r\n | AllBytes -> P.kind_all_bytes\r\n | AllZeros -> P.kind_all_zeros", "let itype_as_parser (i:itype)\r\n : P.parser (parser_kind_of_itype i) (itype_as_type i)\r\n = match i with\r\n | UInt8 -> P.parse____UINT8\r\n | UInt16 -> P.parse____UINT16\r\n | UInt32 -> P.parse____UINT32\r\n | UInt64 -> P.parse____UINT64\r\n | UInt8BE -> P.parse____UINT8BE\r\n | UInt16BE -> P.parse____UINT16BE\r\n | UInt32BE -> P.parse____UINT32BE\r\n | UInt64BE -> P.parse____UINT64BE\r\n | Unit -> P.parse_unit\r\n | AllBytes -> P.parse_all_bytes\r\n | AllZeros -> P.parse_all_zeros", "let allow_reader_of_itype (i:itype)\r\n : bool\r\n = match i with\r\n | AllBytes\r\n | AllZeros -> false\r\n | _ -> true", "let itype_as_leaf_reader (i:itype { allow_reader_of_itype i })\r\n : A.leaf_reader (itype_as_parser i)\r\n = match i with\r\n | UInt8 -> A.read____UINT8\r\n | UInt16 -> A.read____UINT16\r\n | UInt32 -> A.read____UINT32\r\n | UInt64 -> A.read____UINT64\r\n | UInt8BE -> A.read____UINT8BE\r\n | UInt16BE -> A.read____UINT16BE\r\n | UInt32BE -> A.read____UINT32BE\r\n | UInt64BE -> A.read____UINT64BE\r\n | Unit -> A.read_unit", "let itype_as_validator (i:itype)\r\n : A.validate_with_action_t\r\n (itype_as_parser i)\r\n A.true_inv\r\n A.disjointness_trivial\r\n A.eloc_none\r\n (allow_reader_of_itype i)\r\n = match i with\r\n | UInt8 -> A.validate____UINT8\r\n | UInt16 -> A.validate____UINT16\r\n | UInt32 -> A.validate____UINT32\r\n | UInt64 -> A.validate____UINT64\r\n | UInt8BE -> A.validate____UINT8BE\r\n | UInt16BE -> A.validate____UINT16BE\r\n | UInt32BE -> A.validate____UINT32BE\r\n | UInt64BE -> A.validate____UINT64BE\r\n | Unit -> A.validate_unit\r\n | AllBytes -> A.validate_all_bytes\r\n | AllZeros -> A.validate_all_zeros", "let leaf_reader #nz #wk (#k: P.parser_kind nz wk) #t (p:P.parser k t)\r\n = _:squash (wk == P.WeakKindStrongPrefix /\\ hasEq t) &\r\n A.leaf_reader p", "index", "Trivial", "Trivial", "Trivial", "NonTrivial", "NonTrivial", "NonTrivial", "let join_index (j:'a -> 'a -> 'a) (i0 i1:index 'a)\r\n: index 'a\r\n= match i0 with\r\n | Trivial -> i1\r\n | _ -> (\r\n match i1 with\r\n | Trivial -> i0\r\n | NonTrivial i1 -> \r\n let NonTrivial i0 = i0 in\r\n NonTrivial (j i0 i1)\r\n )", "let interp_index (triv:'a) (i:index 'a)\r\n: GTot 'a\r\n= match i with\r\n | Trivial -> triv\r\n | NonTrivial i -> i", "let inv_index = index A.slice_inv", "let inv_none : inv_index = Trivial", "let join_inv = join_index A.conj_inv", "let interp_inv = interp_index A.true_inv", "let loc_index = index A.eloc", "let loc_none : loc_index = Trivial", "let join_loc = join_index A.eloc_union", "let interp_loc = interp_index A.eloc_none", "let disj_index = index A.disjointness_pre", "let disj_none : disj_index = Trivial", "let join_disj = join_index A.conj_disjointness", "let interp_disj = interp_index A.disjointness_trivial", "let disjoint (e1 e2:loc_index)\r\n : disj_index\r\n = match e1, e2 with\r\n | Trivial, _\r\n | _, Trivial -> disj_none\r\n | NonTrivial e1, NonTrivial e2 -> NonTrivial (A.disjoint e1 e2)", "global_binding", "global_binding", "parser_kind_nz", "parser_kind_nz", "parser_weak_kind", "parser_weak_kind", "parser_kind", "parser_kind", "inv", "inv", "disj", "disj", "loc", "loc", "p_t", "p_t", "p_p", "p_p", "p_reader", "p_reader", "p_v", "p_v", "let projector_names : list string = [\r\n `%Mkglobal_binding?.parser_kind_nz;\r\n `%Mkglobal_binding?.parser_weak_kind;\r\n `%Mkglobal_binding?.parser_kind;\r\n `%Mkglobal_binding?.inv;\r\n `%Mkglobal_binding?.disj;\r\n `%Mkglobal_binding?.loc;\r\n `%Mkglobal_binding?.p_t;\r\n `%Mkglobal_binding?.p_p;\r\n `%Mkglobal_binding?.p_reader;\r\n `%Mkglobal_binding?.p_v;\r\n]", "let nz_of_binding = Mkglobal_binding?.parser_kind_nz", "let wk_of_binding = Mkglobal_binding?.parser_weak_kind", "let pk_of_binding = Mkglobal_binding?.parser_kind", "let inv_of_binding = Mkglobal_binding?.inv", "let disj_of_bindng = Mkglobal_binding?.disj", "let loc_of_binding = Mkglobal_binding?.loc", "let type_of_binding = Mkglobal_binding?.p_t", "let parser_of_binding = Mkglobal_binding?.p_p", "let leaf_reader_of_binding = Mkglobal_binding?.p_reader", "let validator_of_binding = Mkglobal_binding?.p_v", "let has_reader (g:global_binding) = \r\n match leaf_reader_of_binding g with\r\n | Some _ -> true\r\n | _ -> false", "let reader_binding = g:global_binding { has_reader g }", "let get_leaf_reader (r:reader_binding)\r\n : leaf_reader (parser_of_binding r)\r\n = Some?.v (leaf_reader_of_binding r)", "dtyp", "DT_IType", "DT_IType", "DT_IType", "i", "i", "DT_App", "DT_App", "DT_App", "nz", "nz", "wk", "wk", "pk", "pk", "hr", "hr", "inv", "inv", "disj", "disj", "loc", "loc", "x", "x", "_", "_", "let dtyp_as_type #nz #wk (#pk:P.parser_kind nz wk) #hr #i #disj #l\r\n (d:dtyp pk hr i disj l)\r\n : Type\r\n = match d with\r\n | DT_IType i -> \r\n itype_as_type i\r\n\r\n | DT_App _ _ _ _ _ b _ ->\r\n type_of_binding b", "let dtyp_as_eqtype_lemma #nz #wk (#pk:P.parser_kind nz wk) #i #disj #l\r\n (d:dtyp pk true i disj l)\r\n : Lemma\r\n (ensures hasEq (dtyp_as_type d))\r\n [SMTPat (hasEq (dtyp_as_type d))]\r\n = match d with\r\n | DT_IType i -> \r\n ()\r\n\r\n | DT_App _ _ _ _ _ b _ ->\r\n let (| _, _ |) = get_leaf_reader b in ()", "let dtyp_as_parser #nz #wk (#pk:P.parser_kind nz wk) #hr #i #disj #l\r\n (d:dtyp pk hr i disj l)\r\n : P.parser pk (dtyp_as_type d)\r\n = match d returns Tot (P.parser pk (dtyp_as_type d)) with\r\n | DT_IType i -> \r\n itype_as_parser i\r\n\r\n | DT_App _ _ _ _ _ b _ ->\r\n parser_of_binding b", "let dtyp_as_validator #nz #wk (#pk:P.parser_kind nz wk)\r\n (#hr:_)\r\n (#[@@@erasable] i:inv_index)\r\n (#[@@@erasable] disj:disj_index)\r\n (#[@@@erasable] l:loc_index)\r\n (d:dtyp pk hr i disj l)\r\n : A.validate_with_action_t #nz #wk #pk #(dtyp_as_type d)\r\n (dtyp_as_parser d)\r\n (interp_inv i)\r\n (interp_disj disj)\r\n (interp_loc l)\r\n hr\r\n = match d \r\n returns \r\n A.validate_with_action_t #nz #wk #pk #(dtyp_as_type d)\r\n (dtyp_as_parser d)\r\n (interp_inv i)\r\n (interp_disj disj)\r\n (interp_loc l)\r\n hr \r\n with\r\n | DT_IType i -> \r\n itype_as_validator i\r\n\r\n | DT_App _ _ _ _ _ b _ ->\r\n // assert_norm (dtyp_as_type (DT_App_Alt ps b args) == (type_of_binding_alt (apply_arrow b args)));\r\n // assert_norm (dtyp_as_parser (DT_App_Alt ps b args) == parser_of_binding_alt (apply_arrow b args));\r\n validator_of_binding b", "let dtyp_as_leaf_reader #nz (#pk:P.parser_kind nz P.WeakKindStrongPrefix)\r\n (#[@@@erasable] i:inv_index)\r\n (#[@@@erasable] disj:disj_index)\r\n (#[@@@erasable] l:loc_index)\r\n (d:dtyp pk true i disj l)\r\n : A.leaf_reader (dtyp_as_parser d)\r\n = match d with\r\n | DT_IType i -> \r\n itype_as_leaf_reader i\r\n\r\n | DT_App _ _ _ _ _ b _ -> \r\n let (| _, lr |) = get_leaf_reader b in\r\n lr", "let action_binding\r\n (inv:inv_index)\r\n (l:loc_index)\r\n (on_success:bool)\r\n (a:Type)\r\n : Type u#0\r\n = A.action (interp_inv inv) A.disjointness_trivial (interp_loc l) on_success a", "let extern_action (l:loc_index) = A.external_action (interp_loc l)", "let mk_extern_action (#l:loc_index) ($f:extern_action l)\r\n = A.mk_external_action f", "let mk_action_binding\r\n (#l:loc_index)\r\n ($f:extern_action l)\r\n : action_binding inv_none l false unit\r\n = mk_extern_action f", "atomic_action", "Action_return", "Action_return", "Action_return", "a", "a", "x", "x", "Action_abort", "Action_abort", "Action_abort", "Action_field_pos_64", "Action_field_pos_64", "Action_field_pos_64", "Action_field_pos_32", "Action_field_pos_32", "Action_field_pos_32", "Action_field_ptr", "Action_field_ptr", "Action_field_ptr", "Action_field_ptr_after", "Action_field_ptr_after", "Action_field_ptr_after", "sz", "sz", "write_to", "write_to", "Action_field_ptr_after_with_setter", "Action_field_ptr_after_with_setter", "Action_field_ptr_after_with_setter", "sz", "sz", "out_loc", "out_loc", "write_to", "write_to", "Action_deref", "Action_deref", "Action_deref", "a", "a", "x", "x", "Action_assignment", "Action_assignment", "Action_assignment", "a", "a", "x", "x", "rhs", "rhs", "Action_call", "Action_call", "Action_call", "inv", "inv", "loc", "loc", "b", "b", "t", "t", "Action_probe_then_validate", "Action_probe_then_validate", "Action_probe_then_validate", "nz", "nz", "wk", "wk", "k", "k", "has_reader", "has_reader", "inv", "inv", "disj", "disj", "l", "l", "dt", "dt", "src", "src", "len", "len", "dest", "dest", "probe", "probe", "let atomic_action_as_action\r\n (#i #d #l #b #t:_)\r\n (a:atomic_action i d l b t)\r\n : Tot (A.action (interp_inv i) (interp_disj d) (interp_loc l) b t)\r\n = match a with\r\n | Action_return x ->\r\n A.action_return x\r\n | Action_abort ->\r\n A.action_abort\r\n | Action_field_pos_64 ->\r\n A.action_field_pos_64\r\n | Action_field_pos_32 sq ->\r\n A.action_field_pos_32 sq\r\n | Action_field_ptr sq ->\r\n A.action_field_ptr sq\r\n | Action_field_ptr_after sq sz write_to ->\r\n A.action_field_ptr_after sq sz write_to\r\n | Action_field_ptr_after_with_setter sq sz write_to ->\r\n A.action_field_ptr_after_with_setter sq sz write_to\r\n | Action_deref x ->\r\n A.action_deref x\r\n | Action_assignment x rhs ->\r\n A.action_assignment x rhs\r\n | Action_call c ->\r\n c\r\n | Action_probe_then_validate #nz #wk #k #_hr #inv #l dt src len dest probe ->\r\n A.index_equations();\r\n let v = dtyp_as_validator dt in\r\n A.probe_then_validate v src len dest probe", "action", "Atomic_action", "Atomic_action", "Atomic_action", "i", "i", "d", "d", "l", "l", "b", "b", "t", "t", "Action_seq", "Action_seq", "Action_seq", "i0", "i0", "l0", "l0", "b0", "b0", "hd", "hd", "i1", "i1", "l1", "l1", "b1", "b1", "t", "t", "tl", "tl", "Action_ite", "Action_ite", "Action_ite", "hd", "hd", "i0", "i0", "l0", "l0", "b0", "b0", "t", "t", "then_", "then_", "i1", "i1", "l1", "l1", "b1", "b1", "else_", "else_", "Action_let", "Action_let", "Action_let", "i0", "i0", "l0", "l0", "b0", "b0", "t0", "t0", "head", "head", "i1", "i1", "l1", "l1", "b1", "b1", "t1", "t1", "k", "k", "Action_act", "Action_act", "Action_act", "i0", "i0", "l0", "l0", "b0", "b0", "act", "act", "let rec action_as_action\r\n (#i #d #l #b #t:_)\r\n (a:action i d l b t)\r\n : Tot (A.action (interp_inv i) (interp_disj d) (interp_loc l) b t)\r\n (decreases a)\r\n = A.index_equations();\r\n match a with\r\n | Atomic_action a ->\r\n atomic_action_as_action a\r\n\r\n | Action_seq hd tl ->\r\n let a1 = atomic_action_as_action hd in\r\n let tl = action_as_action tl in\r\n A.action_seq a1 tl\r\n\r\n | Action_ite hd t e ->\r\n let then_ (x:squash hd) = action_as_action (t x) in\r\n let else_ (x:squash (not hd)) = action_as_action (e x) in\r\n A.action_ite hd then_ else_\r\n\r\n | Action_let hd k ->\r\n let head = atomic_action_as_action hd in\r\n let k x = action_as_action (k x) in\r\n A.action_bind \"hd\" head k\r\n\r\n | Action_act #i0 #l0 #b0 a ->\r\n A.action_weaken (A.action_seq (action_as_action a) (A.action_return true))\r\n #(interp_inv i0) \r\n #_ \r\n #(interp_loc l0)", "let comments = string", "typ", "T_false", "T_false", "fieldname", "T_denoted", "T_denoted", "fieldname", "nz", "wk", "pk", "has_reader", "i", "disj", "l", "td", "T_pair", "T_pair", "first_fieldname", "nz1", "pk1", "i1", "d1", "l1", "b1", "nz2", "wk2", "pk2", "i2", "d2", "l2", "b2", "t1", "t2", "T_dep_pair", "T_dep_pair", "first_fieldname", "nz1", "pk1", "i1", "d1", "l1", "nz2", "wk2", "pk2", "i2", "d2", "l2", "b2", "t1", "t2", "T_refine", "T_refine", "fieldname", "nz1", "pk1", "i1", "d1", "l1", "base", "refinement", "T_refine_with_action", "T_refine_with_action", "fieldname", "nz1", "pk1", "i1", "d1", "l1", "i2", "d2", "l2", "b2", "base", "refinement", "act", "T_dep_pair_with_refinement", "T_dep_pair_with_refinement", "first_fieldname", "nz1", "pk1", "i1", "d1", "l1", "nz2", "wk2", "pk2", "i2", "d2", "l2", "b2", "base", "refinement", "k", "T_dep_pair_with_action", "T_dep_pair_with_action", "fieldname", "nz1", "pk1", "i1", "d1", "l1", "nz2", "wk2", "pk2", "i2", "d2", "l2", "b2", "i3", "d3", "l3", "b3", "base", "k", "act", "T_dep_pair_with_refinement_and_action", "T_dep_pair_with_refinement_and_action", "first_fieldname", "nz1", "pk1", "i1", "d1", "l1", "nz2", "wk2", "pk2", "i2", "d2", "l2", "b2", "i3", "d3", "l3", "b3", "base", "refinement", "k", "act", "T_if_else", "T_if_else", "nz1", "wk1", "pk1", "l1", "i1", "d1", "b1", "nz2", "wk2", "pk2", "l2", "i2", "d2", "b2", "b", "t1", "t2", "T_cases", "T_cases", "nz1", "wk1", "pk1", "l1", "i1", "d1", "b1", "nz2", "wk2", "pk2", "l2", "i2", "d2", "b2", "b", "t1", "t2", "T_with_action", "T_with_action", "fieldname", "nz", "wk", "pk", "l1", "i1", "d1", "b1", "l2", "i2", "d2", "b2", "base", "act", "T_with_dep_action", "T_with_dep_action", "fieldname", "nz1", "pk1", "i1", "d1", "l1", "i2", "d2", "l2", "b2", "head", "act", "T_with_comment", "T_with_comment", "fieldname", "nz", "wk", "pk", "l", "i", "d", "b", "t", "c", "T_nlist", "T_nlist", "fieldname", "wk", "pk", "i", "l", "d", "b", "n", "t", "T_at_most", "T_at_most", "fieldname", "nz", "wk", "pk", "i", "d", "l", "b", "n", "t", "T_exact", "T_exact", "fieldname", "nz", "wk", "pk", "i", "d", "l", "b", "n", "t", "T_string", "T_string", "fieldname", "pk1", "element_type", "terminator", "let coerce (#[@@@erasable]a:Type)\r\n (#[@@@erasable]b:Type)\r\n ( [@@@erasable]pf:squash (a == b))\r\n (x:a) \r\n : b \r\n = x", "let t_probe_then_validate\r\n (fieldname:string)\r\n (probe:CP.probe_fn)\r\n (len:U64.t)\r\n (dest:CP.copy_buffer_t)\r\n (#nz #wk:_) (#pk:P.parser_kind nz wk)\r\n (#has_reader #i #disj:_)\r\n (#l:_)\r\n (td:dtyp pk has_reader i disj l)\r\n : typ (parser_kind_of_itype UInt64)\r\n (join_inv i (NonTrivial (A.copy_buffer_inv dest)))\r\n (join_disj disj (disjoint (NonTrivial (A.copy_buffer_loc dest)) l))\r\n (join_loc l (NonTrivial (A.copy_buffer_loc dest)))\r\n false\r\n = T_with_dep_action fieldname\r\n (DT_IType UInt64)\r\n (fun src ->\r\n Atomic_action (Action_probe_then_validate td src len dest probe))", "let rec as_type\r\n #nz #wk (#pk:P.parser_kind nz wk)\r\n #l #i #d #b\r\n (t:typ pk l i d b)\r\n : Tot Type0\r\n (decreases t)\r\n = match t with\r\n | T_false _ -> False\r\n\r\n | T_denoted _ td -> \r\n dtyp_as_type td\r\n\r\n | T_pair _ t1 t2 ->\r\n as_type t1 & as_type t2\r\n\r\n | T_dep_pair _ i t\r\n | T_dep_pair_with_action _ i t _ ->\r\n x:dtyp_as_type i & as_type (t x)\r\n\r\n | T_refine _ base refinement ->\r\n P.refine (dtyp_as_type base) refinement\r\n\r\n | T_refine_with_action _ base refinement _ ->\r\n P.refine (dtyp_as_type base) refinement\r\n\r\n | T_dep_pair_with_refinement _ base refinement t ->\r\n x:P.refine (dtyp_as_type base) refinement & as_type (t x)\r\n\r\n | T_dep_pair_with_refinement_and_action _ base refinement t _ ->\r\n x:P.refine (dtyp_as_type base) refinement & as_type (t x)\r\n\r\n | T_if_else b t0 t1 ->\r\n P.t_ite b (fun _ -> as_type (t0()))\r\n (fun _ -> as_type (t1()))\r\n\r\n | T_cases b t0 t1 ->\r\n P.t_ite b (fun _ -> as_type t0) (fun _ -> as_type t1)\r\n\r\n | T_with_action _ t _\r\n | T_with_comment _ t _ ->\r\n as_type t\r\n\r\n | T_with_dep_action _ i _ ->\r\n dtyp_as_type i\r\n\r\n | T_nlist _ n t ->\r\n P.nlist n (as_type t)\r\n\r\n | T_at_most _ n t ->\r\n P.t_at_most n (as_type t)\r\n\r\n | T_exact _ n t ->\r\n P.t_exact n (as_type t)\r\n\r\n | T_string _ elt_t terminator ->\r\n P.cstring (dtyp_as_type elt_t) terminator", "let rec as_parser\r\n #nz #wk (#pk:P.parser_kind nz wk)\r\n #l #i #d #b\r\n (t:typ pk l i d b)\r\n : Tot (P.parser pk (as_type t))\r\n (decreases t)\r\n = match t returns Tot (P.parser pk (as_type t)) with\r\n | T_false _ ->\r\n //assert_norm (as_type g T_false == False);\r\n P.parse_impos()\r\n\r\n | T_denoted _ d ->\r\n dtyp_as_parser d\r\n\r\n | T_pair _ t1 t2 ->\r\n //assert_norm (as_type g (T_pair t1 t2) == as_type g t1 * as_type g t2);\r\n let p1 = as_parser t1 in\r\n let p2 = as_parser t2 in\r\n P.parse_pair p1 p2\r\n\r\n | T_dep_pair _ i t\r\n | T_dep_pair_with_action _ i t _ ->\r\n //assert_norm (as_type g (T_dep_pair i t) == x:itype_as_type i & as_type g (t x));\r\n let pi = dtyp_as_parser i in\r\n P.parse_dep_pair pi (fun (x:dtyp_as_type i) -> as_parser (t x))\r\n\r\n | T_refine _ base refinement\r\n | T_refine_with_action _ base refinement _ ->\r\n //assert_norm (as_type g (T_refine base refinement) == P.refine (itype_as_type base) refinement);\r\n let pi = dtyp_as_parser base in\r\n P.parse_filter pi refinement\r\n\r\n | T_dep_pair_with_refinement _ base refinement k ->\r\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x)))\r\n\r\n\r\n | T_dep_pair_with_refinement_and_action _ base refinement k _ ->\r\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x)))\r\n\r\n | T_if_else b t0 t1 ->\r\n //assert_norm (as_type g (T_if_else b t0 t1) == P.t_ite b (as_type g t0) (as_type g t1));\r\n let p0 (_:squash b) = \r\n P.parse_weaken_right (as_parser (t0())) _\r\n in\r\n let p1 (_:squash (not b)) = \r\n P.parse_weaken_left (as_parser (t1())) _\r\n in\r\n P.parse_ite b p0 p1\r\n\r\n | T_cases b t0 t1 ->\r\n //assert_norm (as_type g (T_if_else b t0 t1) == P.t_ite b (as_type g t0) (as_type g t1));\r\n let p0 (_:squash b) = \r\n P.parse_weaken_right (as_parser t0) _\r\n in\r\n let p1 (_:squash (not b)) = \r\n P.parse_weaken_left (as_parser t1) _\r\n in\r\n P.parse_ite b p0 p1\r\n\r\n | T_with_action _ t a ->\r\n //assert_norm (as_type g (T_with_action t a) == as_type g t);\r\n as_parser t\r\n\r\n | T_with_dep_action _ i a ->\r\n //assert_norm (as_type g (T_with_dep_action i a) == itype_as_type i);\r\n dtyp_as_parser i\r\n\r\n | T_with_comment _ t c ->\r\n //assert_norm (as_type g (T_with_comment t c) == as_type g t);\r\n as_parser t\r\n\r\n | T_nlist _ n t ->\r\n P.parse_nlist n (as_parser t)\r\n\r\n | T_at_most _ n t ->\r\n P.parse_t_at_most n (as_parser t)\r\n\r\n | T_exact _ n t ->\r\n P.parse_t_exact n (as_parser t)\r\n\r\n | T_string _ elt_t terminator ->\r\n P.parse_string (dtyp_as_parser elt_t) terminator", "let rec as_reader #nz (#pk:P.parser_kind nz P.WeakKindStrongPrefix)\r\n (#[@@@erasable] inv:inv_index)\r\n (#[@@@erasable] d:disj_index)\r\n (#[@@@erasable] loc:loc_index)\r\n (t:typ pk inv d loc true)\r\n : leaf_reader (as_parser t)\r\n = match t with\r\n | T_denoted _n dt ->\r\n assert_norm (as_type (T_denoted _n dt) == dtyp_as_type dt);\r\n assert_norm (as_parser (T_denoted _n dt) == dtyp_as_parser dt);\r\n (| (), dtyp_as_leaf_reader dt |)\r\n | T_with_comment _n t _c ->\r\n assert_norm (as_type (T_with_comment _n t _c) == as_type t); \r\n assert_norm (as_parser (T_with_comment _n t _c) == as_parser t); \r\n as_reader t\r\n | T_false _n ->\r\n assert_norm (as_type (T_false _n) == False);\r\n assert_norm (as_parser (T_false _n) == P.parse_impos());\r\n (| (), A.read_impos |)", "let rec as_validator\r\n (typename:string)\r\n #nz #wk (#pk:P.parser_kind nz wk)\r\n (#[@@@erasable] inv:inv_index)\r\n (#[@@@erasable] disj:disj_index)\r\n (#[@@@erasable] loc:loc_index)\r\n #b\r\n (t:typ pk inv disj loc b)\r\n : Tot (A.validate_with_action_t #nz #wk #pk #(as_type t)\r\n (as_parser t)\r\n (interp_inv inv)\r\n (interp_disj disj)\r\n (interp_loc loc)\r\n b)\r\n (decreases t)\r\n = A.index_equations();\r\n match t\r\n returns Tot (\r\n A.validate_with_action_t #nz #wk #pk #(as_type t)\r\n (as_parser t)\r\n (interp_inv inv)\r\n (interp_disj disj)\r\n (interp_loc loc)\r\n b\r\n )\r\n with\r\n | T_false fn ->\r\n A.validate_with_error_handler typename fn (A.validate_impos())\r\n\r\n | T_denoted fn td ->\r\n assert_norm (as_type (T_denoted fn td) == dtyp_as_type td);\r\n assert_norm (as_parser (T_denoted fn td) == dtyp_as_parser td);\r\n A.validate_with_error_handler typename fn (A.validate_eta (dtyp_as_validator td))\r\n\r\n | T_pair fn t1 t2 ->\r\n assert_norm (as_type (T_pair fn t1 t2) == as_type t1 * as_type t2);\r\n assert_norm (as_parser (T_pair fn t1 t2) == P.parse_pair (as_parser t1) (as_parser t2));\r\n A.validate_pair fn\r\n (as_validator typename t1)\r\n (as_validator typename t2)\r\n \r\n | T_dep_pair fn i t ->\r\n assert_norm (as_type (T_dep_pair fn i t) == x:dtyp_as_type i & as_type (t x));\r\n assert_norm (as_parser (T_dep_pair fn i t) ==\r\n P.parse_dep_pair (dtyp_as_parser i) (fun (x:dtyp_as_type i) -> as_parser (t x)));\r\n A.validate_weaken_inv_loc (interp_inv inv) _ (interp_loc loc)\r\n (A.validate_dep_pair fn\r\n (A.validate_with_error_handler typename fn (dtyp_as_validator i))\r\n (dtyp_as_leaf_reader i)\r\n (fun x -> as_validator typename (t x)))\r\n\r\n | T_refine fn t f ->\r\n assert_norm (as_type (T_refine fn t f) == P.refine (dtyp_as_type t) f);\r\n assert_norm (as_parser (T_refine fn t f) == P.parse_filter (dtyp_as_parser t) f);\r\n A.validate_with_error_handler typename fn \r\n (A.validate_filter fn\r\n (dtyp_as_validator t)\r\n (dtyp_as_leaf_reader t)\r\n f \"reading field_value\" \"checking constraint\")\r\n\r\n | T_refine_with_action fn t f a ->\r\n assert_norm (as_type (T_refine_with_action fn t f a) == P.refine (dtyp_as_type t) f);\r\n assert_norm (as_parser (T_refine_with_action fn t f a) == P.parse_filter (dtyp_as_parser t) f);\r\n assert_norm (as_parser (T_refine fn t f) == P.parse_filter (dtyp_as_parser t) f); \r\n A.validate_with_error_handler typename fn \r\n (A.validate_filter_with_action fn\r\n (dtyp_as_validator t)\r\n (dtyp_as_leaf_reader t)\r\n f \"reading field_value\" \"checking constraint\"\r\n (fun x -> action_as_action (a x)))\r\n\r\n | T_dep_pair_with_refinement fn base refinement k ->\r\n assert_norm (as_type (T_dep_pair_with_refinement fn base refinement k) ==\r\n x:P.refine (dtyp_as_type base) refinement & as_type (k x));\r\n assert_norm (as_parser (T_dep_pair_with_refinement fn base refinement k) ==\r\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x))));\r\n A.validate_with_error_handler typename fn \r\n (A.validate_weaken_inv_loc _ _ _ (\r\n A.validate_dep_pair_with_refinement false fn\r\n (dtyp_as_validator base)\r\n (dtyp_as_leaf_reader base)\r\n refinement\r\n (fun x -> as_validator typename (k x))))\r\n\r\n | T_dep_pair_with_action fn base t act ->\r\n assert_norm (as_type (T_dep_pair_with_action fn base t act) ==\r\n x:dtyp_as_type base & as_type (t x));\r\n assert_norm (as_parser (T_dep_pair_with_action fn base t act) ==\r\n P.(dtyp_as_parser base `parse_dep_pair` (fun x -> as_parser (t x))));\r\n A.validate_with_error_handler typename fn \r\n (A.validate_weaken_inv_loc _ _ _ (\r\n A.validate_dep_pair_with_action \r\n (dtyp_as_validator base)\r\n (dtyp_as_leaf_reader base)\r\n (fun x -> action_as_action (act x))\r\n (fun x -> as_validator typename (t x))))\r\n\r\n | T_dep_pair_with_refinement_and_action fn base refinement k act ->\r\n assert_norm (as_type (T_dep_pair_with_refinement_and_action fn base refinement k act) ==\r\n x:P.refine (dtyp_as_type base) refinement & as_type (k x));\r\n assert_norm (as_parser (T_dep_pair_with_refinement_and_action fn base refinement k act) ==\r\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x))));\r\n A.validate_weaken_inv_loc _ _ _ (\r\n A.validate_dep_pair_with_refinement_and_action false fn\r\n (A.validate_with_error_handler typename fn \r\n (dtyp_as_validator base))\r\n (dtyp_as_leaf_reader base)\r\n refinement\r\n (fun x -> action_as_action (act x))\r\n (fun x -> as_validator typename (k x)))\r\n\r\n\r\n | T_if_else b t0 t1 ->\r\n assert_norm (as_type (T_if_else b t0 t1) == P.t_ite b (fun _ -> as_type (t0())) (fun _ -> as_type (t1 ())));\r\n let p0 (_:squash b) = P.parse_weaken_right (as_parser (t0())) _ in\r\n let p1 (_:squash (not b)) = P.parse_weaken_left (as_parser (t1())) _ in\r\n assert_norm (as_parser (T_if_else b t0 t1) == P.parse_ite b p0 p1);\r\n let v0 (_:squash b) = \r\n A.validate_weaken_right (as_validator typename (t0())) _\r\n in\r\n let v1 (_:squash (not b)) =\r\n A.validate_weaken_left (as_validator typename (t1())) _\r\n in\r\n A.validate_ite b p0 v0 p1 v1\r\n\r\n | T_cases b t0 t1 ->\r\n assert_norm (as_type (T_cases b t0 t1) == P.t_ite b (fun _ -> as_type t0) (fun _ -> as_type t1));\r\n let p0 (_:squash b) = P.parse_weaken_right (as_parser t0) _ in\r\n let p1 (_:squash (not b)) = P.parse_weaken_left (as_parser t1) _ in\r\n assert_norm (as_parser (T_cases b t0 t1) == P.parse_ite b p0 p1);\r\n let v0 (_:squash b) = \r\n A.validate_weaken_right (as_validator typename t0) _\r\n in\r\n let v1 (_:squash (not b)) =\r\n A.validate_weaken_left (as_validator typename t1) _\r\n in\r\n A.validate_ite b p0 v0 p1 v1\r\n \r\n | T_with_action fn t a ->\r\n assert_norm (as_type (T_with_action fn t a) == as_type t);\r\n assert_norm (as_parser (T_with_action fn t a) == as_parser t);\r\n A.validate_with_error_handler typename fn \r\n (A.validate_with_success_action fn\r\n (as_validator typename t)\r\n (action_as_action a))\r\n\r\n | T_with_dep_action fn i a ->\r\n assert_norm (as_type (T_with_dep_action fn i a) == dtyp_as_type i);\r\n assert_norm (as_parser (T_with_dep_action fn i a) == dtyp_as_parser i);\r\n A.validate_with_error_handler typename fn \r\n (A.validate_weaken_inv_loc _ _ _ (\r\n A.validate_with_dep_action fn\r\n (dtyp_as_validator i)\r\n (dtyp_as_leaf_reader i)\r\n (fun x -> action_as_action (a x))))\r\n\r\n\r\n | T_with_comment fn t c ->\r\n assert_norm (as_type (T_with_comment fn t c) == as_type t);\r\n assert_norm (as_parser (T_with_comment fn t c) == as_parser t);\r\n A.validate_with_comment c (as_validator typename t)\r\n\r\n | T_nlist fn n t ->\r\n assert_norm (as_type (T_nlist fn n t) == P.nlist n (as_type t));\r\n assert_norm (as_parser (T_nlist fn n t) == P.parse_nlist n (as_parser t));\r\n A.validate_with_error_handler typename fn \r\n (A.validate_nlist n (as_validator typename t))\r\n\r\n | T_at_most fn n t ->\r\n assert_norm (as_type (T_at_most fn n t) == P.t_at_most n (as_type t));\r\n assert_norm (as_parser (T_at_most fn n t) == P.parse_t_at_most n (as_parser t));\r\n A.validate_with_error_handler typename fn \r\n (A.validate_t_at_most n (as_validator typename t))\r\n\r\n | T_exact fn n t ->\r\n assert_norm (as_type (T_exact fn n t) == P.t_exact n (as_type t));\r\n assert_norm (as_parser (T_exact fn n t) == P.parse_t_exact n (as_parser t));\r\n A.validate_with_error_handler typename fn \r\n (A.validate_t_exact n (as_validator typename t))\r\n\r\n | T_string fn elt_t terminator ->\r\n assert_norm (as_type (T_string fn elt_t terminator) == P.cstring (dtyp_as_type elt_t) terminator);\r\n assert_norm (as_parser (T_string fn elt_t terminator) == P.parse_string (dtyp_as_parser elt_t) terminator);\r\n A.validate_with_error_handler typename fn \r\n (A.validate_string (dtyp_as_validator elt_t)\r\n (dtyp_as_leaf_reader elt_t)\r\n terminator)", "let validator_of #allow_reading #nz #wk (#k:P.parser_kind nz wk)\r\n (#[@@@erasable] i:inv_index)\r\n (#[@@@erasable] d:disj_index)\r\n (#[@@@erasable] l:loc_index)\r\n (t:typ k i d l allow_reading) = \r\n A.validate_with_action_t\r\n (as_parser t) \r\n (interp_inv i)\r\n (interp_disj d)\r\n (interp_loc l)\r\n allow_reading", "let dtyp_of #nz #wk (#k:P.parser_kind nz wk)\r\n (#[@@@erasable] i:inv_index)\r\n (#[@@@erasable] d:disj_index)\r\n (#[@@@erasable] l:loc_index)\r\n #b (t:typ k i d l b) = \r\n dtyp k b i d l", "let specialization_steps =\r\n [nbe;\r\n zeta;\r\n primops;\r\n iota;\r\n delta_attr [`%specialize];\r\n delta_only ([`%Some?;\r\n `%Some?.v;\r\n `%as_validator;\r\n `%nz_of_binding;\r\n `%wk_of_binding;\r\n `%pk_of_binding;\r\n `%inv_of_binding;\r\n `%loc_of_binding;\r\n `%type_of_binding;\r\n `%parser_of_binding;\r\n `%validator_of_binding;\r\n `%leaf_reader_of_binding;\r\n `%fst;\r\n `%snd;\r\n `%Mktuple2?._1;\r\n `%Mktuple2?._2]@projector_names)]", "let specialize_tac steps (_:unit)\r\n : T.Tac unit\r\n = let open FStar.List.Tot in\r\n T.norm (steps@specialization_steps);\r\n T.trefl()", "let mk_global_binding #nz #wk \r\n (pk:P.parser_kind nz wk)\r\n ([@@@erasable] inv:inv_index)\r\n ([@@@erasable] disj:disj_index)\r\n ([@@@erasable] loc:loc_index)\r\n ([@@@erasable] p_t : Type0)\r\n ([@@@erasable] p_p : P.parser pk p_t)\r\n (p_reader: option (leaf_reader p_p))\r\n (b:bool)\r\n (p_v : A.validate_with_action_t p_p \r\n (interp_inv inv)\r\n (interp_disj disj)\r\n (interp_loc loc) b)\r\n ([@@@erasable] pf:squash (b == Some? p_reader))\r\n : global_binding\r\n = {\r\n parser_kind_nz = nz;\r\n parser_weak_kind = wk;\r\n parser_kind = pk;\r\n inv = inv;\r\n disj;\r\n loc = loc;\r\n p_t = p_t;\r\n p_p = p_p;\r\n p_reader = p_reader;\r\n p_v = p_v\r\n }" ], "closest": [ "val filter_kind (#nz:_) (#wk: _) (k:parser_kind nz wk)\r\n : parser_kind nz wk\nlet filter_kind (#nz:_) (#wk: _) (k:parser_kind nz wk)\r\n : parser_kind nz wk\r\n = LPC.parse_filter_kind k", "val validate_with_action_t\r\n (#nz:bool)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#t:Type)\r\n (p:parser k t)\r\n (liveness_inv:slice_inv)\r\n (disj:disjointness_pre)\r\n (l:eloc)\r\n (allow_reading:bool)\r\n : Type0\nlet validate_with_action_t p inv disj l allow_reading = validate_with_action_t' p inv disj l allow_reading", "val validate_weaken_left\r\n (#nz:_)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v:validate_with_action_t p inv disj l allow_reading)\r\n (#nz':_)\r\n (#wk': _)\r\n (k':parser_kind nz' wk')\r\n : validate_with_action_t (parse_weaken_left p k') inv disj l allow_reading\nlet validate_weaken_left \n #nz #wk (#k:parser_kind nz wk) (#t:_) (#p:parser k t)\n #inv #disj #l #ar (v:validate_with_action_t p inv disj l ar)\n #nz' #wk' (k':parser_kind nz' wk')\n= validate_weaken v (glb k' k)", "val validate_weaken_right\r\n (#nz:_)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v:validate_with_action_t p inv disj l allow_reading)\r\n (#nz':_)\r\n (#wk': _)\r\n (k':parser_kind nz' wk')\r\n : validate_with_action_t (parse_weaken_right p k') inv disj l allow_reading\nlet validate_weaken_right\n #nz #wk (#k:parser_kind nz wk) (#t:_) (#p:parser k t)\n #inv #disj #l #ar (v:validate_with_action_t p inv disj l ar)\n #nz' #wk' (k':parser_kind nz' wk')\n= validate_weaken v (glb k k')", "val probe_then_validate\r\n (#nz:bool)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#t:Type)\r\n (#p:parser k t)\r\n (#inv:slice_inv)\r\n (#disj:disjointness_pre)\r\n (#l:eloc)\r\n (#allow_reading:bool)\r\n (v:validate_with_action_t p inv disj l allow_reading)\r\n (src:U64.t)\r\n (len:U64.t)\r\n (dest:CP.copy_buffer_t)\r\n (probe:CP.probe_fn)\r\n : action (conj_inv inv (copy_buffer_inv dest))\r\n (conj_disjointness disj (disjoint (copy_buffer_loc dest) l))\r\n (eloc_union l (copy_buffer_loc dest)) \r\n true\r\n bool\nlet probe_then_validate \n (#nz:bool)\n (#wk: _)\n (#k:parser_kind nz wk)\n (#t:Type)\n (#p:parser k t)\n (#inv:slice_inv)\n (#disj:_)\n (#l:eloc)\n (#allow_reading:bool)\n (v:validate_with_action_t p inv disj l allow_reading)\n (src:U64.t)\n (len:U64.t)\n (dest:CP.copy_buffer_t)\n (probe:CP.probe_fn)\n = fun ctxt error_handler_fn input input_length pos posf ->\n CP.properties dest;\n let h0 = HST.get () in\n let b = probe src len dest in\n if b\n then (\n let h1 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h0 h1;\n let result = v ctxt error_handler_fn (CP.stream_of dest) (CP.stream_len dest) 0uL in\n not (LPE.is_error result)\n )\n else false", "val parser (#nz:bool) (#wk: weak_kind) (k:parser_kind nz wk) (t:Type u#r) : Type u#r\nlet parser k t = LP.parser k t", "val validate_eta\r\n (#nz:bool)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre)\r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v: validate_with_action_t p inv disj l allow_reading)\r\n: Tot (validate_with_action_t p inv disj l allow_reading)\nlet validate_eta v =\n fun ctxt error_handler_fn sl pos -> v ctxt error_handler_fn sl pos", "val parse_ite (#nz:_) (#wk: _) (#k:parser_kind nz wk)\r\n (e:bool)\r\n (#a:squash e -> Type)\r\n (#b:squash (not e) -> Type)\r\n (p1:squash e -> parser k (a()))\r\n (p2:squash (not e) -> parser k (b()))\r\n : Tot (parser k (t_ite e a b))\nlet parse_ite e p1 p2\r\n = if e then p1 () else p2 ()", "val parse_weaken_right (#nz:_) (#wk: _) (#k:parser_kind nz wk) (#t:_) (p:parser k t)\r\n (#nz':_) (#wk': _) (k':parser_kind nz' wk')\r\n : Tot (parser (glb k k') t)\nlet parse_weaken_right #nz #wk #k p k'\r\n = LP.weaken (glb k k') p", "val validate_weaken_inv_loc\r\n (#nz:_)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n ([@@@erasable] inv':slice_inv{inv' `inv_implies` inv})\r\n ([@@@erasable] disj':disjointness_pre { disj' `imp_disjointness` disj })\r\n ([@@@erasable] l':eloc{l' `eloc_includes` l})\r\n (v:validate_with_action_t p inv disj l allow_reading)\r\n : Tot (validate_with_action_t p inv' disj' l' allow_reading)\nlet validate_weaken_inv_loc\n #nz #wk (#k:parser_kind nz wk) #t (#p:parser k t)\n #inv #disj (#l:eloc) #ar\n (inv':slice_inv{inv' `inv_implies` inv})\n (disj':_{ disj' `imp_disjointness` disj})\n (l':eloc{l' `eloc_includes` l})\n (v:validate_with_action_t p inv disj l ar)\n : Tot (validate_with_action_t p inv' disj' l' ar)\n = v", "val glb (#nz1:bool) (#wk1: weak_kind) (k1:parser_kind nz1 wk1)\r\n (#nz2:bool) (#wk2: weak_kind) (k2:parser_kind nz2 wk2)\r\n : parser_kind (nz1 && nz2) (weak_kind_glb wk1 wk2)\nlet glb (#nz1:bool) (#wk1: weak_kind) (k1:parser_kind nz1 wk1)\r\n (#nz2:bool) (#wk2: weak_kind) (k2:parser_kind nz2 wk2)\r\n : parser_kind (nz1 && nz2) (weak_kind_glb wk1 wk2)\r\n = LP.glb k1 k2", "val parse_weaken_left (#nz:_) (#wk: _) (#k:parser_kind nz wk) (#t:_) (p:parser k t)\r\n (#nz':_) (#wk': _) (k':parser_kind nz' wk')\r\n : Tot (parser (glb k' k) t)\nlet parse_weaken_left #nz #wk #k p k'\r\n = LP.weaken (glb k' k) p", "val parser_kind (nz:bool) (wk: weak_kind) : Type0\nlet parser_kind (nz:bool) (wk: weak_kind) =\r\n k:LP.parser_kind { parser_kind_prop nz wk k }", "val ext_app_records_is_stored_val\n (#app #n:_)\n (il: verifiable_log app n)\n (i: seq_index il)\n : Lemma (requires (V.is_appfn (I.index il i)))\n (ensures (let open Zeta.GenericVerifier in\n let App (RunApp f p ss) rs = mk_vlog_entry_ext il i in\n let vs = cur_thread_state_pre il i in\n contains_distinct_app_keys vs ss /\\\n rs = reads vs ss))\nlet ext_app_records_is_stored_val\n (#app #n:_)\n (il: verifiable_log app n)\n (i: seq_index il)\n : Lemma (requires (V.is_appfn (I.index il i)))\n (ensures (let open Zeta.GenericVerifier in\n let App (RunApp f p ss) rs = mk_vlog_entry_ext il i in\n let vs = cur_thread_state_pre il i in\n contains_distinct_app_keys vs ss /\\\n rs = reads vs ss))\n = lemma_cur_thread_state_extend il i", "val leaf_reader\r\n (#nz:bool)\r\n (#k: parser_kind nz WeakKindStrongPrefix)\r\n (#t: Type)\r\n (p: parser k t)\r\n : Type u#0\nlet leaf_reader\n #nz\n #k\n (#t: Type)\n (p: parser k t)\n: Tot Type\n=\n (# [EverParse3d.Util.solve_from_ctx ()] _extra_t : I.extra_t #input_buffer_t ) ->\n (sl: input_buffer_t) ->\n (pos: LPE.pos_t) ->\n Stack t\n (requires (fun h ->\n valid p h sl /\\\n U64.v pos == Seq.length (I.get_read sl h)\n ))\n (ensures (fun h res h' ->\n let s = I.get_remaining sl h in\n I.live sl h' /\\\n modifies (I.perm_footprint sl) h h' /\\\n begin match LP.parse p s with\n | None -> False\n | Some (y, len) ->\n res == y /\\\n I.get_remaining sl h' == Seq.slice s len (Seq.length s)\n end\n ))", "val vprop_equiv_typing_bk\n (#g: env)\n (#ctxt: _)\n (ctxt_typing: tot_typing g ctxt tm_vprop)\n (#p: _)\n (d: vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop\nlet vprop_equiv_typing_bk (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop \n = let _, bk = vprop_equiv_typing d in\n bk ctxt_typing", "val vprop_equiv_typing_bk\n (#g: env)\n (#ctxt: _)\n (ctxt_typing: tot_typing g ctxt tm_vprop)\n (#p: _)\n (d: vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop\nlet vprop_equiv_typing_bk (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop \n = let _, bk = vprop_equiv_typing d in\n bk ctxt_typing", "val wvalid\n (#t: Type)\n (#k: parser_kind)\n (p: parser k t)\n (#rrel #rel: _)\n (s: slice rrel rel)\n (compl: compl_t t)\n (pos: U32.t)\n (gpos': Ghost.erased U32.t)\n (gv: Ghost.erased t)\n (x: Seq.seq byte)\n : GTot prop\nlet wvalid \n (#t: Type) (#k: parser_kind) (p: parser k t) (#rrel #rel: _) (s: slice rrel rel)\n (compl: compl_t t)\n (pos: U32.t)\n (gpos' : Ghost.erased U32.t)\n (gv: Ghost.erased t)\n (x: Seq.seq byte)\n: GTot prop\n= \n U32.v pos <= U32.v (Ghost.reveal gpos') /\\\n U32.v (Ghost.reveal gpos') <= U32.v s.len /\\\n U32.v s.len <= Seq.length x /\\\n parse p (Seq.slice x (U32.v pos) (U32.v s.len)) == Some (Ghost.reveal gv, U32.v (Ghost.reveal gpos') - U32.v pos) /\\\n compl pos (Ghost.reveal gv) (Ghost.reveal gpos') x", "val bind\r\n (#s:Type u#s)\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#rel:preorder s)\r\n (#req_f:req_t s)\r\n (#ens_f:ens_t s a)\r\n (#req_g:a -> req_t s)\r\n (#ens_g:a -> ens_t s b)\r\n (f:nmst rel a req_f ens_f)\r\n (g:(x:a -> Dv (nmst rel b (req_g x) (ens_g x))))\r\n: nmst rel b\r\n (fun s0 ->\r\n req_f s0 /\\\r\n (forall x s1. ens_f s0 x s1 ==> (req_g x) s1))\r\n (fun s0 r s2 ->\r\n req_f s0 /\\\r\n (exists x s1. ens_f s0 x s1 /\\ (req_g x) s1 /\\ (ens_g x) s1 r s2))\nlet bind f g =\r\n fun () s0 t c ->\r\n let x, s1, c = f () s0 t c in\r\n g x () s1 t c", "val wvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n : GTot t\nlet wvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n: GTot t\n= Ghost.reveal w.v", "val validate_weaken\n (#nz #wk: _)\n (#k: parser_kind nz wk)\n (#t: _)\n (#p: parser k t)\n (#inv #disj #l #ar: _)\n (v: validate_with_action_t p inv disj l ar)\n (#nz' #wk': _)\n (k': parser_kind nz' wk' {k' `is_weaker_than` k})\n : validate_with_action_t (parse_weaken p k') inv disj l ar\nlet validate_weaken\n #nz #wk (#k:parser_kind nz wk) #t (#p:parser k t)\n #inv #disj #l #ar (v:validate_with_action_t p inv disj l ar)\n #nz' #wk' (k':parser_kind nz' wk'{k' `is_weaker_than` k})\n: validate_with_action_t (parse_weaken p k') inv disj l ar\n= fun ctxt error_handler_fn input input_length start_position ->\n v ctxt error_handler_fn input input_length start_position", "val parse_t_at_most (n:U32.t) (#nz: _) (#wk: _) (#k:parser_kind nz wk) (#t:_) (p:parser k t)\r\n : Tot (parser kind_t_at_most (t_at_most n t))\nlet parse_t_at_most n #nz #wk #k #t p\r\n = let open LowParse.Spec.FLData in\r\n let open LowParse.Spec.List in\r\n parse_weaken\r\n #false \r\n #WeakKindStrongPrefix\r\n (LowParse.Spec.FLData.parse_fldata \r\n (LPC.nondep_then p parse_all_bytes)\r\n (U32.v n))\r\n #false\r\n kind_t_at_most", "val validate_ite\r\n (#nz:_)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (e:bool)\r\n (#[@@@erasable] a:squash e -> Type)\r\n (#[@@@erasable] b:squash (not e) -> Type)\r\n (#[@@@erasable] inv1:slice_inv)\r\n (#[@@@erasable] disj1:disjointness_pre)\r\n (#[@@@erasable] l1:eloc)\r\n (#ar1:_)\r\n (#[@@@erasable] inv2:slice_inv)\r\n (#[@@@erasable] disj2:disjointness_pre)\r\n (#[@@@erasable] l2:eloc)\r\n (#ar2:_)\r\n ([@@@erasable] p1:squash e -> parser k (a()))\r\n (v1:(squash e -> validate_with_action_t (p1()) inv1 disj1 l1 ar1))\r\n ([@@@erasable] p2:squash (not e) -> parser k (b()))\r\n (v2:(squash (not e) -> validate_with_action_t (p2()) inv2 disj2 l2 ar2))\r\n : validate_with_action_t\r\n (parse_ite e p1 p2)\r\n (conj_inv inv1 inv2)\r\n (conj_disjointness disj1 disj2)\r\n (l1 `eloc_union` l2)\r\n false\nlet validate_ite\n e p1 v1 p2 v2\n= fun ctxt error_handler_fn input input_len start_position ->\n if e \n then validate_drop (v1 ()) ctxt error_handler_fn input input_len start_position\n else validate_drop (v2 ()) ctxt error_handler_fn input input_len start_position", "val parse_weaken\n (#nz #wk: _)\n (#k: parser_kind nz wk)\n (#t: _)\n (p: parser k t)\n (#nz' #wk': _)\n (k': parser_kind nz' wk' {k' `is_weaker_than` k})\n : Tot (parser k' t)\nlet parse_weaken #nz #wk (#k:parser_kind nz wk) #t (p:parser k t)\r\n #nz' #wk' (k':parser_kind nz' wk' {k' `is_weaker_than` k})\r\n : Tot (parser k' t)\r\n = LP.weaken k' p", "val mk (#g: env) (#v: vprop) (v_typing: tot_typing g v tm_vprop)\n : T.Tac\n (option (x: ppname & t: st_term & c: comp{stateful_comp c /\\ comp_pre c == v} & st_typing g t c)\n )\nlet mk (#g:env) (#v:vprop) (v_typing:tot_typing g v tm_vprop)\n : T.Tac (option (x:ppname &\n t:st_term &\n c:comp { stateful_comp c /\\ comp_pre c == v } &\n st_typing g t c)) =\n match v.t with\n | Tm_Pure {t=Tm_FStar pp} ->\n let p_typing =\n Metatheory.pure_typing_inversion #g #(tm_fstar pp) v_typing in\n Some (| ppname_default,\n mk_elim_pure (tm_fstar pp),\n elim_pure_comp pp,\n elim_pure_typing g pp p_typing |)\n | _ -> None", "val mk (#g: env) (#v: vprop) (v_typing: tot_typing g v tm_vprop)\n : T.Tac\n (option (x: ppname & t: st_term & c: comp{stateful_comp c /\\ comp_pre c == v} & st_typing g t c)\n )\nlet mk (#g:env) (#v:vprop) (v_typing:tot_typing g v tm_vprop)\n : T.Tac (option (x:ppname &\n t:st_term &\n c:comp { stateful_comp c /\\ comp_pre c == v } &\n st_typing g t c)) =\n\n match v.t with\n | Tm_ExistsSL u { binder_ppname=nm; binder_ty = t } p ->\n let x = fresh g in\n let c = Pulse.Typing.comp_elim_exists u t p (nm, x) in\n let tm_typing : st_typing g _ c =\n T_ElimExists g (comp_u c) t p x (RU.magic()) (RU.magic())\n in\n Some (| nm, _, c, tm_typing |)\n | _ -> None", "val puts\n (#app: _)\n (vs: vtls_t app {vs.valid})\n (ks: S.seq base_key)\n (ws: S.seq (app_value_nullable app.adm))\n : vs': vtls_t app {vs'.valid}\nlet puts (#app:_)\n (vs: vtls_t app{vs.valid})\n (ks: S.seq base_key)\n (ws: S.seq (app_value_nullable app.adm))\n : vs': vtls_t app{vs'.valid}\n = let st = puts_store vs.st ks ws in\n update_thread_store vs st", "val validate_total_constant_size_no_read\n (#nz #wk: _)\n (#k: parser_kind nz wk)\n (#t: Type)\n (p: parser k t)\n (sz: U64.t)\n (u:\n unit\n { k.LP.parser_kind_high == Some k.LP.parser_kind_low /\\ k.LP.parser_kind_low == U64.v sz /\\\n k.LP.parser_kind_metadata == Some LP.ParserKindMetadataTotal })\n (inv disj l: _)\n : Tot (validate_with_action_t p inv disj l true)\nlet validate_total_constant_size_no_read\n #nz #wk\n (#k: parser_kind nz wk)\n (#t: Type)\n (p: parser k t)\n (sz: U64.t)\n (u: unit {\n k.LP.parser_kind_high == Some k.LP.parser_kind_low /\\\n k.LP.parser_kind_low == U64.v sz /\\\n k.LP.parser_kind_metadata == Some LP.ParserKindMetadataTotal\n })\n inv disj l\n: Tot (validate_with_action_t p inv disj l true)\n= validate_total_constant_size_no_read' p sz u inv disj l", "val app_typing\n (g: R.env)\n (ty1 ty2 f tm: R.term)\n (df: RT.tot_typing g f (simple_arr ty1 ty2))\n (dt: RT.tot_typing g tm ty1)\n : GTot (RT.tot_typing g (R.pack_ln (R.Tv_App f (tm, R.Q_Explicit))) ty2)\nlet app_typing (g:R.env) (ty1 ty2 f tm : R.term)\n (df : RT.tot_typing g f (simple_arr ty1 ty2))\n (dt : RT.tot_typing g tm ty1)\n : GTot (RT.tot_typing g (R.pack_ln (R.Tv_App f (tm, R.Q_Explicit))) ty2)\n = RU.magic()", "val validate_t_exact\r\n (n:U32.t)\r\n (#nz:bool)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#ar:_)\r\n (v:validate_with_action_t p inv disj l ar)\r\n : Tot (validate_with_action_t (parse_t_exact n p) inv disj l false)\nlet validate_t_exact\n (n:U32.t) #nz #wk (#k:parser_kind nz wk) (#t:_) (#p:parser k t)\n #inv #disj #l #ar\n (v:validate_with_action_t p inv disj l ar)\n: validate_with_action_t (parse_t_exact n p) inv disj l false\n= fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = HST.get () in\n let hasBytes = I.has input input_length pos (Cast.uint32_to_uint64 n) in\n let h1 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h h1;\n if not hasBytes\n then\n LPE.set_validator_error_pos LPE.validator_error_not_enough_data pos\n else\n let truncatedInput = I.truncate input pos (Cast.uint32_to_uint64 n) in\n let truncatedInputLength = I.truncate_len input pos (Cast.uint32_to_uint64 n) truncatedInput in\n let h2 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h h2 in\n let _ = I.is_prefix_of_prop truncatedInput input h2 in\n let _ = assert (I.get_remaining truncatedInput h2 `Seq.equal` Seq.slice (I.get_remaining input h) 0 (U32.v n)) in\n [@inline_let] let _ = LPC.nondep_then_eq p parse_all_bytes (I.get_remaining truncatedInput h2) in\n let result = validate_drop v ctxt error_handler_fn truncatedInput truncatedInputLength pos in\n let h3 = HST.get () in\n let _ = I.is_prefix_of_prop truncatedInput input h3 in\n if LPE.is_error result\n then result\n else begin\n let stillHasBytes = I.has truncatedInput truncatedInputLength result 1uL in\n let h4 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h h4;\n I.is_prefix_of_prop truncatedInput input h4;\n if stillHasBytes\n then LPE.set_validator_error_pos LPE.validator_error_unexpected_padding result\n else result\n end", "val parse_t_exact (n:U32.t) (#nz:bool) (#wk: _) (#k:parser_kind nz wk) (#t:_) (p:parser k t)\r\n : Tot (parser kind_t_exact (t_exact n t))\nlet parse_t_exact n #nz #wk #k #t p\r\n = let open LowParse.Spec.FLData in\r\n let open LowParse.Spec.List in\r\n parse_weaken\r\n #false \r\n #WeakKindStrongPrefix\r\n (LowParse.Spec.FLData.parse_fldata \r\n p\r\n (U32.v n))\r\n #false\r\n kind_t_exact", "val parse_pair (#nz1:_) (#k1:parser_kind nz1 WeakKindStrongPrefix) (#t1:_) (p1:parser k1 t1)\r\n (#nz2:_) (#wk2: _) (#k2:parser_kind nz2 wk2) (#t2:_) (p2:parser k2 t2)\r\n : Tot (parser (and_then_kind k1 k2) (t1 * t2))\nlet parse_pair p1 p2\r\n = LPC.nondep_then p1 p2", "val tperm\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (t:tbl vp h)\n (m:repr k contents)\n (borrows:Map.t k v)\n : vprop\nlet tperm arr m borrows = exists_ (store_contents_pred arr m borrows)", "val k_evict_set\n (#vspec: verifier_spec)\n (#n: _)\n (ep: epoch)\n (gk: key vspec.app)\n (il: verifiable_log vspec n)\n : GTot (mset_ms_hashfn_dom vspec.app)\nlet k_evict_set (#vspec:verifier_spec) (#n:_) (ep: epoch) (gk: key vspec.app) (il: verifiable_log vspec n)\n : GTot (mset_ms_hashfn_dom vspec.app)\n = seq2mset (k_evict_seq ep gk il)", "val bind\n (#s #a: _)\n (#srel: erel s)\n (#arel: erel a)\n (#b: _)\n (#brel: erel b)\n ($f: st srel arel)\n (g: arel ^--> st_rel srel brel)\n : st srel brel\nlet bind #s #a (#srel:erel s) (#arel:erel a) #b (#brel:erel b)\n ($f:st srel arel)\n (g:arel ^--> st_rel srel brel)\n : st srel brel =\n fun s0 ->\n let x, s1 = f s0 in\n g x s1", "val parser_kind_prop (nz: bool) (wk: weak_kind) (k: LP.parser_kind) : Tot prop\nlet parser_kind_prop\r\n (nz: bool)\r\n (wk: weak_kind)\r\n (k: LP.parser_kind)\r\n: Tot prop\r\n= (nz ==> (k.LP.parser_kind_low > 0)) /\\\r\n begin match wk with\r\n | WeakKindStrongPrefix -> k.LP.parser_kind_subkind == Some LP.ParserStrong\r\n | WeakKindConsumesAll -> k.LP.parser_kind_subkind == Some LP.ParserConsumesAll\r\n | _ -> True\r\n end", "val validate_nlist_constant_size_mod_ko\n (n: U32.t)\n (#wk: _)\n (#k: parser_kind true wk)\n (#t: _)\n (p: parser k t)\n (inv disj l: _)\n : Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires\n (let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_high == Some k.parser_kind_low /\\\n U32.v n % k.LP.parser_kind_low <> 0))\n (ensures (fun _ -> True))\nlet validate_nlist_constant_size_mod_ko\n (n:U32.t)\n (#wk: _)\n (#k:parser_kind true wk)\n #t\n (p:parser k t)\n inv disj l\n : Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires (\n let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\\n k.parser_kind_high == Some k.parser_kind_low /\\\n U32.v n % k.LP.parser_kind_low <> 0\n ))\n (ensures (fun _ -> True))\n= \n (fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = FStar.HyperStack.ST.get () in\n [@inline_let]\n let f () : Lemma\n (requires (Some? (LP.parse (parse_nlist n p) (I.get_remaining input h))))\n (ensures False)\n = let sq = I.get_remaining input h in\n let sq' = Seq.slice sq 0 (U32.v n) in\n LowParse.Spec.List.list_length_constant_size_parser_correct p sq' ;\n let Some (l, _) = LP.parse (parse_nlist n p) sq in\n assert (U32.v n == FStar.List.Tot.length l `Prims.op_Multiply` k.LP.parser_kind_low) ;\n FStar.Math.Lemmas.cancel_mul_mod (FStar.List.Tot.length l) k.LP.parser_kind_low ;\n assert (U32.v n % k.LP.parser_kind_low == 0)\n in\n [@inline_let]\n let _ = Classical.move_requires f () in\n LPE.set_validator_error_pos LPE.validator_error_list_size_not_multiple pos\n )", "val parse_filter (#nz:_) (#wk: _) (#k:parser_kind nz wk) (#t:_) (p:parser k t) (f:(t -> bool))\r\n : Tot (parser (filter_kind k) (refine t f))\nlet parse_filter p f\r\n = LPC.parse_filter p f", "val mk_app_norm : env -> term -> list term -> Tac term\nlet mk_app_norm e t params =\n let t1 = mk_e_app t params in\n let t2 = norm_term_env e [] t1 in\n t2", "val apply_conversion\n (#g: env)\n (#e: term)\n (#eff: _)\n (#t0: term)\n (d: typing g e eff t0)\n (#t1: term)\n (eq: Ghost.erased (RT.related (elab_env g) (elab_term t0) RT.R_Eq (elab_term t1)))\n : typing g e eff t1\nlet apply_conversion\n (#g:env) (#e:term) (#eff:_) (#t0:term)\n (d:typing g e eff t0)\n (#t1:term)\n (eq:Ghost.erased (RT.related (elab_env g) (elab_term t0) RT.R_Eq (elab_term t1)))\n : typing g e eff t1\n = let d : RT.typing (elab_env g) (elab_term e) (eff, (elab_term t0)) = d._0 in\n let r : RT.related (elab_env g) (elab_term t0) RT.R_Eq (elab_term t1) = eq in\n let r = RT.Rel_equiv _ _ _ RT.R_Sub r in\n let s : RT.sub_comp (elab_env g) (eff, (elab_term t0)) (eff, elab_term t1) = \n RT.Relc_typ _ _ _ _ _ r\n in\n E (RT.T_Sub _ _ _ _ d s)", "val validate_with_dep_action\r\n (name: string)\r\n (#nz:_)\r\n (#k:parser_kind nz WeakKindStrongPrefix)\r\n (#t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (v:validate_with_action_t p inv disj l true)\r\n (r:leaf_reader p)\r\n (#b:bool)\r\n (#[@@@erasable] inva:slice_inv)\r\n (#[@@@erasable] disja:disjointness_pre) \r\n (#[@@@erasable] la:eloc)\r\n (a: t -> action inva disja la b bool)\r\n : validate_with_action_t #nz\r\n p\r\n (conj_inv inv inva)\r\n (conj_disjointness disj disja)\r\n (eloc_union l la)\r\n false\nlet validate_with_dep_action\n (name: string)\n #nz (#k:parser_kind nz _) (#t:_) (#p:parser k t)\n #inv #disj #l\n (v:validate_with_action_t p inv disj l true)\n (r:leaf_reader p)\n (#b:bool) #inva #disja (#la:eloc)\n (a: t -> action inva disja la b bool)\n= fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos0 = start_position in\n let h = HST.get () in\n [@(rename_let (\"positionAfter\" ^ name))]\n let res = v ctxt error_handler_fn input input_length pos0 in\n let h1 = HST.get () in\n if LPE.is_error res\n then res\n else begin\n [@(rename_let (\"\" ^ name))]\n let field_value = r input pos0 in\n let h15 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h h15 in\n if a field_value ctxt error_handler_fn input input_length pos0 res\n then res\n else LPE.set_validator_error_pos LPE.validator_error_action_failed res\n end", "val parse_dep_pair (#nz1:_) (#k1:parser_kind nz1 WeakKindStrongPrefix) (#t1: Type) (p1: parser k1 t1)\r\n (#nz2:_) (#wk2: _) (#k2:parser_kind nz2 wk2) (#t2: (t1 -> Tot Type)) (p2: (x: t1) -> parser k2 (t2 x))\r\n : Tot (parser (and_then_kind k1 k2) (dtuple2 t1 t2) )\nlet parse_dep_pair p1 p2\r\n = LPC.parse_dtuple2 p1 p2", "val mbind\n (#st: state u#s u#act)\n (#a: Type u#a)\n (#b: Type u#b)\n (#p: st.pred)\n (#q: post st a)\n (#r: post st b)\n (f: m a p q)\n (g: (x: a -> Dv (m b (q x) r)))\n : Dv (m b p r)\nlet rec mbind\n (#st:state u#s u#act)\n (#a:Type u#a)\n (#b:Type u#b)\n (#p:st.pred)\n (#q:post st a)\n (#r:post st b)\n (f:m a p q)\n (g: (x:a -> Dv (m b (q x) r)))\n : Dv (m b p r)\n = match f with\n | Ret x -> g x\n | Act act k ->\n Act act (fun x -> mbind (k x) g)\n | Par #_ #pre0 #post0 ml\n #pre1 #post1 mr\n #postk k ->\n let k : m b (post0 `st.star` post1) r = mbind k g in\n let ml' : m (U.raise_t u#0 u#b unit) pre0 (as_post post0) =\n mbind ml (fun _ -> Ret #_ #(U.raise_t u#0 u#b unit) #(as_post post0) (U.raise_val u#0 u#b ()))\n in\n let mr' : m (U.raise_t u#0 u#b unit) pre1 (as_post post1) =\n mbind mr (fun _ -> Ret #_ #(U.raise_t u#0 u#b unit) #(as_post post1) (U.raise_val u#0 u#b ()))\n in\n Par ml' mr' k", "val mk_bind (g:env)\n (pre:term)\n (e1:st_term)\n (e2:st_term)\n (c1:comp_st)\n (c2:comp_st)\n (px:nvar { ~ (Set.mem (snd px) (dom g)) })\n (d_e1:st_typing g e1 c1)\n (d_c1res:tot_typing g (comp_res c1) (tm_type (comp_u c1)))\n (d_e2:st_typing (push_binding g (snd px) (fst px) (comp_res c1)) (open_st_term_nv e2 px) c2)\n (res_typing:universe_of g (comp_res c2) (comp_u c2))\n (post_typing:tot_typing (push_binding g (snd px) (fst px) (comp_res c2))\n (open_term_nv (comp_post c2) px)\n tm_vprop)\n (bias_towards_continuation:bool)\n : T.TacH (t:st_term &\n c:comp_st { st_comp_of_comp c == st_comp_with_pre (st_comp_of_comp c2) pre /\\\n (bias_towards_continuation ==> effect_annot_of_comp c == effect_annot_of_comp c2) } &\n st_typing g t c)\n (requires fun _ ->\n let _, x = px in\n comp_pre c1 == pre /\\\n None? (lookup g x) /\\\n (~(x `Set.mem` freevars_st e2)) /\\\n open_term (comp_post c1) x == comp_pre c2 /\\\n (~ (x `Set.mem` freevars (comp_post c2))))\n (ensures fun _ _ -> True)\nlet rec mk_bind (g:env) \n (pre:term)\n (e1:st_term)\n (e2:st_term)\n (c1:comp_st)\n (c2:comp_st)\n (px:nvar { ~ (Set.mem (snd px) (dom g)) })\n (d_e1:st_typing g e1 c1)\n (d_c1res:tot_typing g (comp_res c1) (tm_type (comp_u c1)))\n (d_e2:st_typing (push_binding g (snd px) (fst px) (comp_res c1)) (open_st_term_nv e2 px) c2)\n (res_typing:universe_of g (comp_res c2) (comp_u c2))\n (post_typing:tot_typing (push_binding g (snd px) (fst px) (comp_res c2))\n (open_term_nv (comp_post c2) px)\n tm_vprop)\n (bias_towards_continuation:bool)\n : T.TacH (t:st_term &\n c:comp_st {\n st_comp_of_comp c == st_comp_with_pre (st_comp_of_comp c2) pre /\\\n (bias_towards_continuation ==> effect_annot_of_comp c == effect_annot_of_comp c2) } &\n st_typing g t c)\n (requires fun _ ->\n let _, x = px in\n comp_pre c1 == pre /\\\n None? (lookup g x) /\\\n (~(x `Set.mem` freevars_st e2)) /\\\n open_term (comp_post c1) x == comp_pre c2 /\\\n (~ (x `Set.mem` freevars (comp_post c2))))\n (ensures fun _ _ -> True) =\n let _, x = px in\n let b = nvar_as_binder px (comp_res c1) in\n let fail_bias (#a:Type) tag\n : T.TacH a (requires fun _ -> True) (ensures fun _ r -> FStar.Tactics.Result.Failed? r)\n = let open Pulse.PP in\n fail_doc g (Some e1.range)\n [text \"Cannot compose computations in this \" ^/^ text tag ^/^ text \" block:\";\n prefix 4 1 (text \"This computation has effect: \") (pp (effect_annot_of_comp c1));\n prefix 4 1 (text \"The continuation has effect: \") (pp (effect_annot_of_comp c2))]\n in\n match c1, c2 with\n | C_ST _, C_ST _ ->\n mk_bind_st_st g pre e1 e2 c1 c2 px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation\n\n | C_STGhost _, C_STGhost _ ->\n mk_bind_ghost_ghost g pre e1 e2 c1 c2 px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation\n\n | C_STAtomic inames1 obs1 sc1, C_STAtomic inames2 obs2 sc2 ->\n if at_most_one_observable obs1 obs2\n then (\n mk_bind_atomic_atomic g pre e1 e2 c1 c2 px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation\n ) \n else if bias_towards_continuation\n then fail_bias \"atomic\"\n else (\n let d_e1 = T_Lift _ _ _ _ d_e1 (Lift_STAtomic_ST _ c1) in\n mk_bind g pre e1 e2 _ c2 px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation\n )\n\n | C_STAtomic inames _ _, C_ST _ ->\n let d_e1 = T_Lift _ _ _ _ d_e1 (Lift_STAtomic_ST _ c1) in\n mk_bind g pre e1 e2 _ c2 px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation\n\n | C_ST _, C_STAtomic inames _ _ ->\n if bias_towards_continuation\n then fail_bias \"atomic\"\n else (\n let d_e2 = T_Lift _ _ _ _ d_e2 (Lift_STAtomic_ST _ c2) in\n let (| t, c, d |) = mk_bind g pre e1 e2 _ _ px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation in\n (| t, c, d |)\n )\n\n | C_STGhost _, C_STAtomic _ Neutral _ -> (\n match try_lift_ghost_atomic d_e1 with\n | Some d_e1 ->\n mk_bind g pre e1 e2 _ c2 px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation\n | None ->\n if bias_towards_continuation\n then fail_bias \"atomic\"\n else (\n let d_e2 = T_Lift _ _ _ _ d_e2 (Lift_Neutral_Ghost _ c2) in\n let (| t, c, d |) = mk_bind g pre e1 e2 _ _ px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation in\n (| t, c, d |)\n )\n )\n\n | C_STAtomic _ Neutral _, C_STGhost _ -> (\n if bias_towards_continuation\n then (\n let d_e1 = T_Lift _ _ _ _ d_e1 (Lift_Neutral_Ghost _ c1) in\n mk_bind g pre e1 e2 _ c2 px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation\n )\n else (\n match try_lift_ghost_atomic d_e2 with\n | Some d_e2 ->\n let (| t, c, d |) = mk_bind g pre e1 e2 _ _ px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation in\n (| t, c, d |)\n | None ->\n let d_e1 = T_Lift _ _ _ _ d_e1 (Lift_Neutral_Ghost _ c1) in\n mk_bind g pre e1 e2 _ c2 px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation\n )\n )\n\n | C_STGhost _, C_ST _\n | C_STGhost _, C_STAtomic _ _ _ ->\n let d_e1 = lift_ghost_atomic d_e1 in\n mk_bind g pre e1 e2 _ c2 px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation\n\n | C_ST _, C_STGhost _\n | C_STAtomic _ _ _, C_STGhost _ ->\n if bias_towards_continuation\n then fail_bias \"ghost\"\n else (\n let d_e2 = lift_ghost_atomic d_e2 in\n let (| t, c, d |) = mk_bind g pre e1 e2 _ _ px d_e1 d_c1res d_e2 res_typing post_typing bias_towards_continuation in\n (| t, c, d |)\n )", "val v: #t_k:eqtype -> #t_v:Type0 -> h:HS.mem -> ll:t t_k t_v -> GTot (map t_k t_v)\nlet v #_ #_ h ll =\n let l = LL2.v h ll in\n v_ l", "val lwbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w:\n (x: tr\n -> Pure (lwriter s h0 sout pout_from0)\n (requires (x == grvalue r))\n (ensures (fun _ -> True))))\n : Tot (w': lwriter s h0 sout pout_from0 {lwvalue w' == lwvalue (w (grvalue r))})\nlet lwbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w: ((x: tr) -> Pure (lwriter s h0 sout pout_from0) (requires (x == grvalue r)) (ensures (fun _ -> True))))\n: Tot (w' : lwriter s h0 sout pout_from0 { lwvalue w' == lwvalue (w (grvalue r)) } )\n= LWriter (Ghost.hide (lwvalue (w (grvalue r)))) (fun pout_from ->\n let v = gread r in\n lwrite (w v) pout_from\n )", "val owbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w:\n (x: tr\n -> Pure (owriter s h0 sout pout_from0)\n (requires (x == grvalue r))\n (ensures (fun _ -> True))))\n : Tot (w': owriter s h0 sout pout_from0 {owvalue w' == owvalue (w (grvalue r))})\nlet owbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w: ((x: tr) -> Pure (owriter s h0 sout pout_from0) (requires (x == grvalue r)) (ensures (fun _ -> True))))\n: Tot (w' : owriter s h0 sout pout_from0 { owvalue w' == owvalue (w (grvalue r))})\n= OWriter (Ghost.hide (owvalue (w (grvalue r)))) (fun pout_from ->\n let v = gread r in\n owrite (w v) pout_from\n )", "val wbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w:\n (x: tr\n -> Pure (writer s h0 sout pout_from0)\n (requires (x == grvalue r))\n (ensures (fun _ -> True))))\n : Tot (w': writer s h0 sout pout_from0 {wvalue w' == wvalue (w (grvalue r))})\nlet wbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w: ((x: tr) -> Pure (writer s h0 sout pout_from0) (requires (x == grvalue r)) (ensures (fun _ -> True))))\n: Tot (w' : writer s h0 sout pout_from0 { wvalue w' == wvalue (w (grvalue r)) } )\n= Writer (Ghost.hide (wvalue (w (grvalue r)))) (fun pout_from ->\n let v = gread r in\n write (w v) pout_from\n )", "val irepr_v\n (#t: Type)\n (#k: parser_kind)\n (#p: parser k t)\n (#rrel #rel: _)\n (#s: slice rrel rel)\n (#compl: compl_t t)\n (x: irepr p s compl)\n : GTot t\nlet irepr_v\n (#t: Type) (#k: parser_kind) (#p: parser k t) (#rrel #rel: _) (#s: slice rrel rel) (#compl: compl_t t) (x: irepr p s compl) : GTot t\n= Ghost.reveal (IRepr?.gv x)", "val validate_list_inv\n (#k: LPL.parser_kind)\n (#t: Type)\n (p: LPL.parser k t)\n (inv: slice_inv)\n (disj: disjointness_pre)\n (l: eloc)\n (g0 g1: Ghost.erased HS.mem)\n (ctxt: app_ctxt)\n (sl: input_buffer_t)\n (bres: pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet validate_list_inv\n (#k: LPL.parser_kind)\n (#t: Type)\n (p: LPL.parser k t)\n (inv: slice_inv)\n (disj: disjointness_pre)\n (l: eloc)\n (g0 g1: Ghost.erased HS.mem)\n (ctxt:app_ctxt)\n (sl: input_buffer_t)\n (bres: pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n= let h0 = Ghost.reveal g0 in\n let h1 = Ghost.reveal g1 in\n let res = Seq.index (as_seq h bres) 0 in\n inv h0 /\\\n disj /\\\n loc_not_unused_in h0 `loc_includes` app_loc ctxt l /\\\n app_loc ctxt l `loc_disjoint` I.footprint sl /\\\n app_loc ctxt l `loc_disjoint` loc_buffer bres /\\\n address_liveness_insensitive_locs `loc_includes` app_loc ctxt l /\\\n B.loc_buffer bres `B.loc_disjoint` I.footprint sl /\\\n I.live sl h0 /\\\n I.live sl h /\\\n live h0 ctxt /\\\n live h ctxt /\\\n live h1 bres /\\\n begin\n let s = I.get_remaining sl h0 in\n let s' = I.get_remaining sl h in\n Seq.length s' <= Seq.length s /\\\n s' `Seq.equal` Seq.slice s (Seq.length s - Seq.length s') (Seq.length s)\n end /\\\n modifies loc_none h0 h1 /\\ (\n if\n LPE.is_error res\n then\n // validation *or action* failed\n stop == true /\\\n U64.v (LPE.get_validator_error_pos res) == Seq.length (I.get_read sl h) /\\\n (LPE.get_validator_error_kind res <> LPE.get_validator_error_kind LPE.validator_error_action_failed ==> ~ (valid (LPLL.parse_list p) h0 sl))\n else\n U64.v res == Seq.length (I.get_read sl h) /\\\n (valid (LPLL.parse_list p) h0 sl <==>\n valid (LPLL.parse_list p) h sl) /\\\n (stop == true ==> (valid (LPLL.parse_list p) h sl /\\ Seq.length (I.get_remaining sl h) == 0))\n ) /\\\n modifies (app_loc ctxt l `loc_union` loc_buffer bres `loc_union` I.perm_footprint sl) h1 h", "val dtyp_of_app (en: env) (hd: A.ident) (args: list T.index) : ML dtyp\nlet dtyp_of_app (en: env) (hd:A.ident) (args:list T.index)\r\n : ML dtyp\r\n = match itype_of_ident hd, args with\r\n | Some i, [] ->\r\n DT_IType i\r\n\r\n | _ ->\r\n let readable = match H.try_find en hd.v with\r\n | None -> failwith \"type not found\"\r\n | Some td -> td.allow_reading\r\n in\r\n DT_App readable hd\r\n (List.map\r\n (function Inl _ -> failwith \"Unexpected type application\"\r\n | Inr e -> e)\r\n args)", "val and_then_kind (#nz1:_) (k1:parser_kind nz1 WeakKindStrongPrefix)\r\n (#nz2:_) (#wk2: _) (k2:parser_kind nz2 wk2)\r\n : parser_kind (nz1 || nz2) wk2\nlet and_then_kind (#nz1:_) (k1:parser_kind nz1 WeakKindStrongPrefix)\r\n (#nz2:_) (#wk2: _) (k2:parser_kind nz2 wk2)\r\n : parser_kind (nz1 || nz2) wk2\r\n = LPC.and_then_kind k1 k2", "val validate_t_at_most\r\n (n:U32.t)\r\n (#nz: _)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#ar:_)\r\n (v:validate_with_action_t p inv disj l ar)\r\n : Tot (validate_with_action_t (parse_t_at_most n p) inv disj l false)\nlet validate_t_at_most\n (n:U32.t) #nz #wk (#k:parser_kind nz wk) (#t:_) (#p:parser k t)\n #inv #disj #l #ar (v:validate_with_action_t p inv disj l ar)\n : Tot (validate_with_action_t (parse_t_at_most n p) inv disj l false)\n = fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = HST.get () in\n let hasBytes = I.has input input_length pos (Cast.uint32_to_uint64 n) in\n let h1 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h h1;\n if not hasBytes\n then\n LPE.set_validator_error_pos LPE.validator_error_not_enough_data pos\n else\n let truncatedInput = I.truncate input pos (Cast.uint32_to_uint64 n) in\n let truncatedInputLength = I.truncate_len input pos (Cast.uint32_to_uint64 n) truncatedInput in\n let h2 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h h2 in\n let _ = I.is_prefix_of_prop truncatedInput input h2 in\n let _ = assert (I.get_remaining truncatedInput h2 `Seq.equal` Seq.slice (I.get_remaining input h) 0 (U32.v n)) in\n [@inline_let] let _ = LPC.nondep_then_eq p parse_all_bytes (I.get_remaining truncatedInput h2) in\n let result = validate_drop v ctxt error_handler_fn truncatedInput truncatedInputLength pos in\n let h3 = HST.get () in\n let _ = I.is_prefix_of_prop truncatedInput input h3 in\n if LPE.is_error result\n then result\n else begin\n let _ = I.empty truncatedInput truncatedInputLength result in\n let h4 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h h4;\n let _ = I.is_prefix_of_prop truncatedInput input h4 in\n pos `U64.add` Cast.uint32_to_uint64 n\n end", "val lemma_app_res_rel\n (#vcfg:_)\n (vs: vtls_t vcfg{vs.valid})\n (vs': _ {vtls_rel vs vs'})\n (e: logS_entry vcfg {GV.is_appfn e})\n : Lemma (requires (valid_logS_entry vs e /\\ (GV.verify_step e vs).valid))\n (ensures (let ek = to_logk_entry vs e in\n vtls_rel (GV.verify_step e vs) (GV.verify_step ek vs') /\\\n GV.appfn_result e vs = GV.appfn_result ek vs'))\nlet lemma_app_res_rel\n (#vcfg:_)\n (vss: vtls_t vcfg{vss.valid})\n (vsk: _ {vtls_rel vss vsk})\n (e: logS_entry vcfg {GV.is_appfn e})\n : Lemma (requires (valid_logS_entry vss e /\\ (GV.verify_step e vss).valid))\n (ensures (let ek = to_logk_entry vss e in\n vtls_rel (GV.verify_step e vss) (GV.verify_step ek vsk) /\\\n GV.appfn_result e vss = GV.appfn_result ek vsk))\n = lemma_runapp_simulates_spec vss vsk e;\n let a = AFR vss vsk e in\n lemma_appfn_succ_rel a;\n lemma_int_appfn_succ a;\n assert(int_appfn_succ a);\n\n lemma_res_rel a;\n ()", "val swvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#space_beyond: nat)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: swriter s h0 space_beyond sout pout_from0)\n : GTot t\nlet swvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#space_beyond: nat)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: swriter s h0 space_beyond sout pout_from0)\n: GTot t\n= Ghost.reveal w.v", "val write\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n : Tot (fwriter s h0 sout pout_from0 (wvalue w))\nlet write\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n: Tot (fwriter s h0 sout pout_from0 (wvalue w))\n= match w with | Writer _ f -> f", "val runapp_implies_store_contains\n (#app: _)\n (e: vlog_entry app {GV.is_appfn e})\n (vs: vtls_t _)\n (k: base_key)\n : Lemma (ensures (let GV.RunApp _ _ ks = e in\n let vs_post = GV.verify_step e vs in\n vs_post.valid ==>\n S.mem k ks ==>\n (let rs = GV.reads vs ks in\n let i = S.index_mem k ks in\n let ak,av = S.index rs i in\n store_contains vs.st k /\\\n stored_key vs.st k = AppK ak /\\\n stored_value vs.st k = AppV av)))\nlet runapp_implies_store_contains\n (#app: _)\n (e: vlog_entry app {GV.is_appfn e})\n (vs: vtls_t _)\n (k: base_key)\n : Lemma (ensures (let GV.RunApp _ _ ks = e in\n let vs_post = GV.verify_step e vs in\n vs_post.valid ==>\n S.mem k ks ==>\n (let rs = GV.reads vs ks in\n let i = S.index_mem k ks in\n let ak,av = S.index rs i in\n store_contains vs.st k /\\\n stored_key vs.st k = AppK ak /\\\n stored_value vs.st k = AppV av)))\n = let GV.RunApp _ _ ks = e in\n let vs_post = GV.verify_step e vs in\n if vs_post.valid && S.mem k ks then (\n let i = S.index_mem k ks in\n ()\n )", "val put\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (#vp:vp_t k v contents)\n (#h:hash_fn k)\n (#m:G.erased (repr k contents))\n (#borrows:G.erased (Map.t k v))\n (a:tbl vp h)\n (i:k)\n (x:v)\n (c:G.erased contents)\n : STT unit\n (tperm a m borrows `star` vp i x c)\n (fun _ -> tperm a (Map.upd m i c) (Map.remove borrows i))\nlet put #k #v #contents #vp #h #m #borrows a i x c =\n let s = elim_exists () in\n elim_pure (pure_invariant a m borrows s);\n A.pts_to_length a.store s;\n let idx = h i `US.rem` a.store_len in\n\n A.write a.store idx (Some (i, x));\n\n put_vprops_aux a m borrows s i x c idx ()", "val mk_vlog_entry_ext (#app: app_params) (#n:nat) (il: verifiable_log app n) (i: seq_index il)\n : GTot (vlog_entry_ext app)\nlet mk_vlog_entry_ext #app #n (il: verifiable_log app n) (i: seq_index il)\n = let vle = I.index il i in\n let open Zeta.GenericVerifier in\n let open Zeta.High.Verifier in\n let vs = cur_thread_state_pre il i in\n let tid = src il i in\n lemma_cur_thread_state_extend il i;\n\n match vle with\n | EvictM k k' ->\n let v = stored_value vs.st k in\n EvictMerkle vle v\n | EvictB k ts ->\n let v = stored_value vs.st k in\n EvictBlum vle v tid\n | EvictBM k _ ts ->\n let v = stored_value vs.st k in\n EvictBlum vle v tid\n | RunApp f p ss ->\n let rs = reads vs ss in\n App vle rs\n | v -> NEvict v", "val validate_with_comment\r\n (c:string)\r\n (#nz:_)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v:validate_with_action_t p inv disj l allow_reading)\r\n : validate_with_action_t p inv disj l allow_reading\nlet validate_with_comment\n (c:string)\n #nz #wk (#k:parser_kind nz wk) #t (#p:parser k t)\n #inv #disj #l #ar (v:validate_with_action_t p inv disj l ar)\n: validate_with_action_t p inv disj l ar\n= fun ctxt error_handler_fn input input_length start_position ->\n LowParse.Low.Base.comment c;\n v ctxt error_handler_fn input input_length start_position", "val parse_nlist (n:U32.t) (#wk: _) (#k:parser_kind true wk) (#t:_) (p:parser k t)\r\n : Tot (parser kind_nlist (nlist n t))\nlet parse_nlist n #wk #k #t p\r\n = let open LowParse.Spec.FLData in\r\n let open LowParse.Spec.List in\r\n parse_weaken\r\n #false #WeakKindStrongPrefix #(parse_fldata_kind (U32.v n) parse_list_kind) #(list t)\r\n (LowParse.Spec.FLData.parse_fldata (LowParse.Spec.List.parse_list p) (U32.v n))\r\n #false kind_nlist", "val jump_list_up_to_inv\n (#k #t: _)\n (#p: parser k t)\n (cond: (t -> Tot bool))\n (prf: consumes_if_not_cond cond p {k.parser_kind_subkind <> Some ParserConsumesAll})\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: U32.t)\n (h0: HS.mem)\n (bpos: B.pointer U32.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet jump_list_up_to_inv\n (#k: _)\n (#t: _)\n (#p: parser k t)\n (cond: (t -> Tot bool))\n (prf: consumes_if_not_cond cond p { k.parser_kind_subkind <> Some ParserConsumesAll } )\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: U32.t)\n (h0: HS.mem)\n (bpos: B.pointer U32.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n= let pos = B.deref h bpos in\n let q = parse_list_up_to cond p prf in\n B.live h0 bpos /\\\n live_slice h0 sl /\\\n B.loc_disjoint (B.loc_buffer sl.base) (B.loc_buffer bpos) /\\\n B.modifies (B.loc_buffer bpos) h0 h /\\\n U32.v pos0 <= U32.v pos /\\\n valid q h0 sl pos0 /\\\n begin if stop\n then \n get_valid_pos q h0 sl pos0 == pos\n else\n valid q h0 sl pos /\\\n get_valid_pos q h0 sl pos0 == get_valid_pos q h0 sl pos\n end", "val create_v\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n (c:G.erased contents)\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.const k (G.reveal c)) (Map.empty k v))\nlet create_v #k #v #contents vp h n c =\n let store = A.alloc #(option (k & v)) None n in\n let arr : tbl #k #v #contents vp h = {\n store_len = n;\n store = store;\n store_len_pf = () } in\n\n //\n //rewrite in terms of projections from the arr record\n //\n rewrite (A.pts_to store _ (Seq.create #(option (k & v)) (US.v n) None))\n (A.pts_to arr.store _ (Seq.create #(option (k & v)) (US.v n) None));\n\n //\n //The value vprops at this point are all emp\n //\n //A lemma that tells us that folding a monoid over a sequence of units\n // is monoid-equivalent to the unit\n //\n SeqPerm.foldm_snoc_unit_seq\n vprop_monoid\n (value_vprops_seq vp (Seq.create (US.v n) None)\n (Map.const k (G.reveal c))\n (Map.empty k v));\n rewrite_equiv emp (value_vprops vp (Seq.create (US.v n) None)\n (Map.const k (G.reveal c))\n (Map.empty k v));\n\n pack_tperm (Seq.create (US.v n) None)\n (Map.const k (G.reveal c))\n (Map.empty k v)\n arr;\n\n return arr", "val accessor_dsum_tag\n (#kt: parser_kind)\n (t: dsum)\n (p: parser kt (dsum_repr_type t))\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (#ku: parser_kind)\n (g: parser ku (dsum_type_of_unknown_tag t))\n : Tot (accessor (gaccessor_dsum_tag t p f g))\nlet accessor_dsum_tag\n (#kt: parser_kind)\n (t: dsum)\n (p: parser kt (dsum_repr_type t))\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (#ku: parser_kind)\n (g: parser ku (dsum_type_of_unknown_tag t))\n: Tot (accessor (gaccessor_dsum_tag t p f g))\n= accessor_tagged_union_tag\n (parse_maybe_enum_key p (dsum_enum t))\n (dsum_tag_of_data t)\n (parse_dsum_cases t f g)", "val delete_repr\n (#kt #vt #sz: _)\n (#spec: erased (spec_t kt vt))\n (repr: repr_t_sz kt vt sz {pht_models spec repr})\n (k: kt)\n : r': repr_t_sz kt vt sz {pht_models (spec -- k) r' /\\ repr_related repr r'}\nlet delete_repr #kt #vt #sz (#spec : erased (spec_t kt vt))\n (repr : repr_t_sz kt vt sz{pht_models spec repr})\n (k : kt)\n: r':repr_t_sz kt vt sz{\n pht_models (spec -- k) r' /\\\n repr_related repr r'\n }\n= let cidx = canonical_index k repr in\n let res = delete_repr_walk #kt #vt #sz #spec repr k 0 cidx () () in\n res", "val addm_type\n (#app: _)\n (#n: pos)\n (il: verifiable_log app n)\n (i: seq_index il {AddM? (index il i) /\\ is_eac (prefix il i)})\n : GTot addm_t\nlet addm_type\n (#app:_)\n (#n:pos)\n (il: verifiable_log app n)\n (i: seq_index il{AddM? (index il i) /\\ is_eac (prefix il i)})\n : GTot addm_t\n = let AddM (gk, gv) k k' = index il i in\n let il' = prefix il i in\n let v' = eac_merkle_value k' il' in\n let c = desc_dir k k' in\n let dh' = desc_hash v' c in\n match dh' with\n | Empty -> NewEdge\n | Desc k2 h2 b2 -> if k2 = k then NoNewEdge else CutEdge", "val lwriter_singleton\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n : Tot (x: lwriter s h0 sout pout_from0 {lwvalue x == [wvalue w]})\nlet lwriter_singleton\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n: Tot (x: lwriter s h0 sout pout_from0 { lwvalue x == [wvalue w] } )\n= LWriter (Ghost.hide [wvalue w])\n (fun pout_from ->\n let res = write w pout_from in\n if res `U32.lt` max_uint32\n then begin\n let h = HST.get () in\n valid_list_nil p h sout res;\n valid_list_cons p h sout pout_from res\n end else begin\n [@inline_let]\n let f () : Lemma (ensures (let v = wvalue w in serialized_list_length s [v] == serialized_length s v)) =\n serialized_list_length_cons s (wvalue w) [];\n serialized_list_length_nil s\n in\n f ()\n end;\n res\n )", "val mk_e_app (t: term) (args: list term) : Tot term\nlet mk_e_app (t : term) (args : list term) : Tot term =\n let e t = (t, Q_Explicit) in\n mk_app t (List.Tot.Base.map e args)", "val mk_e_app (t: term) (args: list term) : Tot term\nlet mk_e_app (t : term) (args : list term) : Tot term =\n let e t = (t, Q_Explicit) in\n mk_app t (List.Tot.Base.map e args)", "val parser_kind_nz (env: global_env) (id: A.ident) : ML bool\nlet parser_kind_nz (env:global_env) (id:A.ident) : ML bool =\r\n match H.try_find env.parser_kind_nz id.v with\r\n | Some b -> b\r\n | None ->\r\n match B.parser_kind_nz env.benv id with\r\n | Some b -> b\r\n | None ->\r\n failwith (Printf.sprintf \"Type %s has an unknown parser kind\" (ident_to_string id))", "val grlexistsb\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (j: jumper p)\n (f: (t -> Tot bool))\n (f':\n (#rrel: _ -> #rel: _ -> sl: slice rrel rel -> pos: U32.t\n -> HST.Stack bool\n (requires (fun h -> valid p h sl pos))\n (ensures\n (fun h res h' -> B.modifies B.loc_none h h' /\\ res == f (contents p h sl pos))))\n )\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos pos': U32.t)\n (sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (h0:\n HS.mem\n { k.parser_kind_subkind == Some ParserStrong /\\ valid_list p h0 sl pos pos' /\\\n B.loc_disjoint (loc_slice_from_to sl pos pos') (loc_slice_from sout pout_from0) })\n : Tot\n (r':\n greader h0 sout pout_from0 bool {grvalue r' == L.existsb f (contents_list p h0 sl pos pos')})\nlet grlexistsb\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (j: jumper p)\n (f: (t -> Tot bool)) // should be GTot, but List.find requires Tot\n (f' : (\n (#rrel: _) ->\n (#rel: _) ->\n (sl: slice rrel rel) ->\n (pos: U32.t) ->\n HST.Stack bool\n (requires (fun h ->\n valid p h sl pos\n ))\n (ensures (fun h res h' ->\n B.modifies B.loc_none h h' /\\\n res == f (contents p h sl pos)\n ))\n ))\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos pos' : U32.t)\n (sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (h0: HS.mem {\n k.parser_kind_subkind == Some ParserStrong /\\\n valid_list p h0 sl pos pos' /\\\n B.loc_disjoint (loc_slice_from_to sl pos pos') (loc_slice_from sout pout_from0)\n })\n: Tot (r' : greader h0 sout pout_from0 bool { grvalue r' == L.existsb f (contents_list p h0 sl pos pos') } )\n= GReader (Ghost.hide (L.existsb f (contents_list p h0 sl pos pos'))) (fun _ ->\n list_existsb j f f' sl pos pos'\n )", "val contains_distinct_app_keys_comp\n (#vspec:_) (vtls: vspec.vtls_t{vspec.valid vtls}) (ss: S.seq vspec.slot_t)\n : GTot (b:bool {b <==> contains_distinct_app_keys vtls ss})\nlet contains_distinct_app_keys_comp\n (#vspec:_) (vtls: vspec.vtls_t{vspec.valid vtls}) (ss: S.seq vspec.slot_t)\n : GTot (b:bool {b <==> contains_distinct_app_keys vtls ss})\n = contains_only_app_keys_comp vtls ss &&\n None = search_level_1 vtls ss", "val cast\n (#p1 #p2: parser)\n (#inv: memory_invariant)\n (v: squash (valid_rewrite_prop p1 p2))\n (x1: ptr p1 inv)\n : Tot (ptr p2 inv)\nlet cast\n (#p1: parser)\n (#p2: parser)\n (#inv: memory_invariant)\n (v: squash (valid_rewrite_prop p1 p2))\n (x1: ptr p1 inv)\n: Tot (ptr p2 inv)\n= cast _ _ _ _ (evalid_rewrite_of_tvalid_rewrite v) _ x1", "val lwriter_nil\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (h0: HS.mem)\n (sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n : Tot (x: lwriter s h0 sout pout_from0 {lwvalue x == []})\nlet lwriter_nil\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (h0: HS.mem)\n (sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n: Tot (x: lwriter s h0 sout pout_from0 { lwvalue x == [] })\n= LWriter (Ghost.hide [])\n (fun pout_from ->\n let h = HST.get () in\n valid_list_nil p h sout pout_from;\n pout_from\n )", "val invariant: #t_k:eqtype -> #t_v:Type0 -> h:HS.mem -> ll:t t_k t_v -> Type0\nlet invariant #_ #_ h ll =\n LL2.invariant h ll", "val write_leaf_cs\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s:\n serializer p\n { k.parser_kind_subkind == Some ParserStrong /\\\n k.parser_kind_high == Some k.parser_kind_low /\\ k.parser_kind_low < 4294967296 })\n (w: leaf_writer_strong s)\n (h0: HS.mem)\n (sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (x: t)\n : Tot (y: writer s h0 sout pout_from0 {wvalue y == x})\nlet write_leaf_cs\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_high == Some k.parser_kind_low /\\ k.parser_kind_low < 4294967296 } )\n (w: leaf_writer_strong s)\n (h0: HS.mem)\n (sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (x: t)\n: Tot (y: writer s h0 sout pout_from0 { wvalue y == x } )\n= Writer (Ghost.hide x)\n (fun pout_from ->\n if U32.uint_to_t k.parser_kind_low `U32.gt` (sout.len `U32.sub` pout_from)\n then max_uint32\n else w x sout pout_from\n )", "val to_app_record\n (#vspec: verifier_spec_base)\n (vtls: vspec.vtls_t{vspec.valid vtls})\n (s: vspec.slot_t{contains_app_key vtls s})\n : GTot (app_record vspec.app.adm)\nlet to_app_record\n (#vspec: verifier_spec_base)\n (vtls: vspec.vtls_t {vspec.valid vtls})\n (s: vspec.slot_t {contains_app_key vtls s})\n : GTot (app_record vspec.app.adm)\n = let open Zeta.GenKey in\n let open Zeta.Record in\n let AppK ak, AppV av = Some?.v (vspec.get s vtls) in\n ak, av", "val k_evict_seq\n (#vspec: verifier_spec)\n (#n: _)\n (ep: epoch)\n (gk: key vspec.app)\n (il: verifiable_log vspec n)\n : GTot (S.seq (ms_hashfn_dom vspec.app))\nlet k_evict_seq (#vspec:verifier_spec) (#n:_) (ep: epoch) (gk: key vspec.app) (il: verifiable_log vspec n)\n : GTot (S.seq (ms_hashfn_dom vspec.app))\n = i_seq (k_evict_il ep gk il)", "val validate_dep_pair_with_refinement'\n (name1: string)\n (#nz1: _)\n (#k1: parser_kind nz1 _)\n (#t1: _)\n (#p1: parser k1 t1)\n (#inv1 #disj1 #l1: _)\n (v1: validate_with_action_t p1 inv1 disj1 l1 true)\n (r1: leaf_reader p1)\n (f: (t1 -> bool))\n (#nz2 #wk2: _)\n (#k2: parser_kind nz2 wk2)\n (#t2: (refine _ f -> Type))\n (#p2: (x: refine _ f -> parser k2 (t2 x)))\n (#inv2 #disj2 #l2 #ar2: _)\n (v2: (x: refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n : Tot\n (validate_with_action_t ((p1 `LPC.parse_filter` f) `(parse_dep_pair #nz1)` p2)\n (conj_inv inv1 inv2)\n (conj_disjointness disj1 disj2)\n (l1 `eloc_union` l2)\n false)\nlet validate_dep_pair_with_refinement'\n (name1: string)\n #nz1 (#k1:parser_kind nz1 _) #t1 (#p1:parser k1 t1)\n #inv1 #disj1 #l1 (v1:validate_with_action_t p1 inv1 disj1 l1 true) (r1: leaf_reader p1)\n (f: t1 -> bool)\n #nz2 #wk2 (#k2:parser_kind nz2 wk2) (#t2:refine _ f -> Type) (#p2:(x:refine _ f -> parser k2 (t2 x)))\n #inv2 #disj2 #l2 #ar2 (v2:(x:refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n : Tot (validate_with_action_t\n ((p1 `LPC.parse_filter` f) `(parse_dep_pair #nz1)` p2)\n (conj_inv inv1 inv2)\n (conj_disjointness disj1 disj2)\n (l1 `eloc_union` l2)\n false)\n = fun ctxt error_handler_fn input input_length startPosition ->\n let h0 = HST.get () in\n LPC.parse_dtuple2_eq' #_ #_ (p1 `LPC.parse_filter` f) #_ #t2 p2 (I.get_remaining input h0);\n LPC.parse_filter_eq p1 f (I.get_remaining input h0);\n [@(rename_let (\"positionAfter\" ^ name1))]\n let res = v1 ctxt error_handler_fn input input_length startPosition in\n let h1 = HST.get() in\n modifies_address_liveness_insensitive_unused_in h0 h1;\n if LPE.is_error res\n then begin\n res\n end\n else begin\n [@(rename_let (\"\" ^ name1))]\n let field_value = r1 input startPosition in\n [@(rename_let (name1 ^ \"ConstraintIsOk\"))]\n let ok = f field_value in\n [@(rename_let (\"positionAfter\" ^ name1))]\n let res1 = LPE.check_constraint_ok ok res in\n if LPE.is_error res1\n then\n res1\n else let h2 = HST.get() in\n // assert (B.modifies B.loc_none h1 h2);\n // assert (inv1' input.LPL.base h2);\n modifies_address_liveness_insensitive_unused_in h1 h2;\n // assert (loc_not_unused_in h2 `loc_includes` l1');\n // assert (valid_pos (p1 `(LPC.parse_filter #k1 #t1)` f) h0 input (uint64_to_uint32 pos) (uint64_to_uint32 res));\n let h15 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h0 h15 in\n validate_drop (v2 field_value) ctxt error_handler_fn input input_length res1\n end", "val owvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: owriter s h0 sout pout_from0)\n : GTot (option t)\nlet owvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: owriter s h0 sout pout_from0)\n: GTot (option t)\n= Ghost.reveal w.v", "val lemma_used_upd\n (#kt #vt #sz spec: _)\n (repr: repr_t_sz kt vt sz)\n (off: nat{off < sz})\n (k: _)\n (v v': vt)\n : Lemma\n (requires\n pht_models spec repr /\\ Some? (lookup_repr repr k) /\\\n repr @@ (canonical_index k repr + off) % sz == Used k v' /\\\n all_used_not_by repr (canonical_index k repr) off k)\n (ensures pht_models (spec ++ (k, v)) (upd_ repr ((canonical_index k repr + off) % sz) k v))\nlet lemma_used_upd #kt #vt #sz spec (repr : repr_t_sz kt vt sz) (off:nat{off < sz}) k (v v' : vt) \n : Lemma\n (requires pht_models spec repr\n /\\ Some? (lookup_repr repr k)\n /\\ repr @@ (canonical_index k repr + off)%sz == Used k v'\n /\\ all_used_not_by repr (canonical_index k repr) off k)\n (ensures pht_models (spec ++ (k,v)) (upd_ repr ((canonical_index k repr + off)%sz) k v))\n = let spec' = spec ++ (k,v) in\n let idx = (canonical_index k repr + off) % sz in\n let repr' = upd_ repr idx k v in\n let aux1 (k':kt) : Lemma (requires (Some? (lookup_spec spec' k')))\n (ensures (lookup_repr repr' k' == lookup_spec spec' k'))\n = if k' = k then\n lemma_walk_from_canonical_all_used repr' off k v\n else\n lemma_used_upd_lookup_walk spec spec' repr repr' idx k k' v v' \n in\n let aux2 (k':kt) : Lemma (requires (Some? (lookup_repr repr' k')))\n (ensures (lookup_repr repr' k' == lookup_spec spec' k'))\n = if k' = k then\n lemma_walk_from_canonical_all_used repr' off k v\n else\n lemma_used_upd_lookup_walk spec spec' repr repr' idx k k' v v'\n in\n let aux3 (i':nat{i' Lemma (parse p (f x) == Some (x, Seq.length (f x)))))\n : Tot (serializer p)\nlet mk_serializer\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (f: bare_serializer t)\n (prf: (\n (x: t) ->\n Lemma\n (parse p (f x) == Some (x, Seq.length (f x)))\n ))\n: Tot (serializer p)\n= Classical.forall_intro prf;\n f", "val validate_dep_pair\r\n (name1: string)\r\n (#nz1:_)\r\n (#k1:parser_kind nz1 WeakKindStrongPrefix)\r\n (#t1:Type)\r\n (#[@@@erasable] p1:parser k1 t1)\r\n (#[@@@erasable] inv1:slice_inv)\r\n (#[@@@erasable] disj1:disjointness_pre)\r\n (#[@@@erasable] l1:eloc)\r\n (v1:validate_with_action_t p1 inv1 disj1 l1 true)\r\n (r1: leaf_reader p1)\r\n (#nz2:_)\r\n (#wk2: _)\r\n (#k2:parser_kind nz2 wk2)\r\n (#[@@@erasable] t2:t1 -> Type)\r\n (#[@@@erasable] p2:(x:t1 -> parser k2 (t2 x)))\r\n (#[@@@erasable] inv2:slice_inv)\r\n (#[@@@erasable] disj2:disjointness_pre)\r\n (#[@@@erasable] l2:eloc)\r\n (#allow_reading2:bool)\r\n (v2:(x:t1 -> validate_with_action_t (p2 x) inv2 disj2 l2 allow_reading2))\r\n : validate_with_action_t\r\n (p1 `parse_dep_pair` p2)\r\n (conj_inv inv1 inv2)\r\n (conj_disjointness disj1 disj2)\r\n (l1 `eloc_union` l2)\r\n false\nlet validate_dep_pair\n (name1: string)\n #nz1 (#k1:parser_kind nz1 _) #t1 (#p1:parser k1 t1)\n #inv1 #disj1 #l1 (v1:validate_with_action_t p1 inv1 disj1 l1 true) (r1: leaf_reader p1)\n #nz2 #wk2 (#k2:parser_kind nz2 wk2) (#t2:t1 -> Type) (#p2:(x:t1 -> parser k2 (t2 x)))\n #inv2 #disj2 #l2 #ar2 (v2:(x:t1 -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n = fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = HST.get () in\n LPC.parse_dtuple2_eq p1 p2 (I.get_remaining input h);\n [@(rename_let (\"positionAfter\" ^ name1))]\n let pos1 = v1 ctxt error_handler_fn input input_length pos in\n let h1 = HST.get() in\n if LPE.is_error pos1\n then begin\n pos1\n end\n else\n [@(rename_let (\"\" ^ name1))]\n let x = r1 input pos in\n let h15 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h h15 in\n validate_drop (v2 x) ctxt error_handler_fn input input_length pos1", "val valid'\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (s: slice rrel rel)\n (pos: U32.t)\n : GTot Type0\nlet valid'\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (s: slice rrel rel)\n (pos: U32.t)\n: GTot Type0\n= U32.v pos <= U32.v s.len /\\\n live_slice h s /\\\n Some? (parse p (bytes_of_slice_from h s pos))", "val ev_is_sv_snoc_appfn (#app #n: _) (il: eac_log app n {length il > 0}) (gk: key app {AppK? gk})\n : Lemma\n (requires\n (let i = length il - 1 in\n let e = index il i in\n let k = to_base_key gk in\n RunApp? e /\\ e `refs_key` k /\\ ev_is_sv_prop (prefix il i) gk))\n (ensures (ev_is_sv_prop il gk))\nlet ev_is_sv_snoc_appfn\n (#app #n:_)\n (il: eac_log app n {length il > 0})\n (gk: key app {AppK? gk})\n : Lemma (requires (let i = length il - 1 in\n let e = index il i in\n let k = to_base_key gk in\n RunApp? e /\\ e `refs_key` k /\\\n ev_is_sv_prop (prefix il i) gk))\n (ensures (ev_is_sv_prop il gk))\n = let i = length il - 1 in\n let t = src il i in\n let ki = to_base_key gk in\n let e = index il i in\n let RunApp f p ss = e in\n\n eac_state_snoc ki il;\n lemma_cur_thread_state_extend il i;\n SA.lemma_fullprefix_equal il;\n\n let idx = index_mem ki ss in\n let fn = appfn f in\n let vs' = thread_state_pre t il i in\n let vs = thread_state_post t il i in\n\n let rs = reads vs' ss in\n let _,_,ws = fn p rs in\n puts_valid ki e vs' idx;\n assert(HV.stored_value vs.st ki = AppV (S.index ws idx));\n key_in_unique_store ki il t (stored_tid ki il)", "val upd_pht:\n #kt: eqtype ->\n #vt: Type ->\n pht: pht_t kt vt ->\n idx: _ ->\n k: kt ->\n v: vt ->\n squash (lookup_index_us pht k == Some idx)\n -> pht_t kt vt\nlet upd_pht (#kt:eqtype) (#vt:Type) (pht:pht_t kt vt) idx (k:kt) (v:vt)\n (_:squash (lookup_index_us pht k == Some idx)) : pht_t kt vt =\n let spec' = Ghost.hide (pht.spec ++ (k, v)) in\n let repr' = upd_ pht.repr (US.v idx) k v in\n\n let Used k v' = pht.repr @@ US.v idx in\n\n let cidx = canonical_index #kt #vt k pht.repr in\n walk_get_idx_upd pht.repr repr' cidx k 0 (US.v idx) v;\n assert (lookup_repr_index repr' k == Some (v, US.v idx));\n\n introduce forall (k':kt { k' =!= k }). lookup_repr repr' k' == lookup_repr pht.repr k'\n with lemma_used_upd_lookup_walk #_ #_ #pht.repr.sz pht.spec spec' pht.repr repr' (US.v idx) k k' v v';\n\n { pht with spec = spec';\n repr = repr';\n inv = () }", "val swbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#space_beyond: nat)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w:\n (x: tr\n -> Pure (swriter s h0 space_beyond sout pout_from0)\n (requires (x == grvalue r))\n (ensures (fun _ -> True))))\n : Tot (w': swriter s h0 space_beyond sout pout_from0 {swvalue w' == swvalue (w (grvalue r))})\nlet swbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#space_beyond: nat)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w: ((x: tr) -> Pure (swriter s h0 space_beyond sout pout_from0) (requires (x == grvalue r)) (ensures (fun _ -> True))))\n: Tot (w' : swriter s h0 space_beyond sout pout_from0 { swvalue w' == swvalue (w (grvalue r)) } )\n= SWriter (Ghost.hide (swvalue (w (grvalue r)))) (fun pout_from ->\n let v = gread r in\n swrite (w v) pout_from\n )", "val exploded_vp\n (#k: eqtype)\n (#v: Type0)\n (r: ref (ht_t k v))\n (ht: ht_t k v)\n (r_sz: ref pos_us)\n (r_hashf: ref (k -> SZ.t))\n (r_contents: ref (V.vec (cell k v)))\n : vprop\nlet exploded_vp (#k:eqtype) (#v:Type0)\n (r:ref (ht_t k v))\n (ht:ht_t k v)\n (r_sz:ref pos_us)\n (r_hashf:ref (k -> SZ.t))\n (r_contents:ref (V.vec (cell k v))) : vprop = \n pts_to r_sz ht.sz **\n pts_to r_hashf ht.hashf **\n pts_to r_contents ht.contents **\n token r r_sz r_hashf r_contents", "val writes (#vcfg: _) (a: appfn_verify vcfg {appfn_succ a})\n : GTot (ws: S.seq (app_value_nullable vcfg.app.adm) {S.length ws = S.length (appfn_slots a)})\nlet writes (#vcfg:_) (a: appfn_verify vcfg {appfn_succ a})\n : GTot (ws:S.seq (app_value_nullable vcfg.app.adm){S.length ws = S.length (appfn_slots a)})\n = let GV.RunApp f p _ = a.e in\n let ss = appfn_slots a in\n let rs = reads a in\n let fn = appfn f in\n let _,_,ws = fn p rs in\n ws", "val token (#k:eqtype) (#v:Type0)\n (r:ref (ht_t k v))\n (r_sz:ref pos_us)\n (r_hashf:ref (k -> SZ.t))\n (r_contents:ref (V.vec (cell k v))) : vprop\nlet token (#k:eqtype) (#v:Type0)\n (r:ref (ht_t k v))\n (r_sz:ref pos_us)\n (r_hashf:ref (k -> SZ.t))\n (r_contents:ref (V.vec (cell k v))) : vprop =\n exists* ht. pts_to r ht", "val create\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (h:hash_fn k)\n (n:us{US.v n > 0})\n : STT (tbl vp h)\n emp\n (fun a -> tperm a (Map.empty k contents) (Map.empty k v))\nlet create #k #v #contents vp h n =\n let store = A.alloc #(option (k & v)) None n in\n let arr : tbl #k #v #contents vp h = {\n store_len = n;\n store = store;\n store_len_pf = () } in\n\n //\n //rewrite in terms of projections from the arr record\n //\n rewrite (A.pts_to store _ (Seq.create #(option (k & v)) (US.v n) None))\n (A.pts_to arr.store _ (Seq.create #(option (k & v)) (US.v n) None));\n\n //\n //The value vprops at this point are all emp\n //\n //A lemma that tells us that folding a monoid over a sequence of units\n // is monoid-equivalent to the unit\n //\n SeqPerm.foldm_snoc_unit_seq\n vprop_monoid\n (value_vprops_seq vp (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v));\n rewrite_equiv emp (value_vprops vp (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v));\n\n pack_tperm (Seq.create (US.v n) None)\n (Map.empty k contents)\n (Map.empty k v)\n arr;\n\n return arr", "val bind\n (#s: Type u#s)\n (#c: comm_monoid s)\n (#a: Type u#a)\n (#b: Type u#b)\n (#p: c.r)\n (#q: (a -> c.r))\n (#r: (b -> c.r))\n (f: m a p q)\n (g: (x: a -> Dv (m b (q x) r)))\n : Dv (m b p r)\nlet rec bind (#s:Type u#s)\n (#c:comm_monoid s)\n (#a:Type u#a)\n (#b:Type u#b)\n (#p:c.r)\n (#q:a -> c.r)\n (#r:b -> c.r)\n (f:m a p q)\n (g: (x:a -> Dv (m b (q x) r)))\n : Dv (m b p r)\n = match f with\n | Ret x -> g x\n | Act act k ->\n Act act (fun x -> bind (k x) g)\n | Par pre0 post0 ml\n pre1 post1 mr\n k ->\n let k : m b (post0 `c.star` post1) r = bind k g in\n let ml' : m (U.raise_t u#0 u#b unit) pre0 (fun _ -> post0) =\n bind ml (fun _ -> Ret (U.raise_val u#0 u#b ()))\n in\n let mr' : m (U.raise_t u#0 u#b unit) pre1 (fun _ -> post1) =\n bind mr (fun _ -> Ret (U.raise_val u#0 u#b ()))\n in\n Par #s #c pre0 post0 ml'\n pre1 post1 mr'\n #b #r k", "val bind\n (#s: Type u#s)\n (#c: comm_monoid s)\n (#a: Type u#a)\n (#b: Type u#b)\n (#p: c.r)\n (#q: (a -> c.r))\n (#r: (b -> c.r))\n (f: m a p q)\n (g: (x: a -> Dv (m b (q x) r)))\n : Dv (m b p r)\nlet rec bind (#s:Type u#s)\n (#c:comm_monoid s)\n (#a:Type u#a)\n (#b:Type u#b)\n (#p:c.r)\n (#q:a -> c.r)\n (#r:b -> c.r)\n (f:m a p q)\n (g: (x:a -> Dv (m b (q x) r)))\n : Dv (m b p r)\n = match f with\n | Ret x -> g x\n | Act act k ->\n Act act (fun x -> bind (k x) g)\n | Par pre0 post0 ml\n pre1 post1 mr\n k ->\n let k : m b (post0 `c.star` post1) r = bind k g in\n let ml' : m (U.raise_t u#0 u#b unit) pre0 (fun _ -> post0) =\n bind ml (fun _ -> Ret (U.raise_val u#0 u#b ()))\n in\n let mr' : m (U.raise_t u#0 u#b unit) pre1 (fun _ -> post1) =\n bind mr (fun _ -> Ret (U.raise_val u#0 u#b ()))\n in\n Par #s #c pre0 post0 ml'\n pre1 post1 mr'\n #b #r k", "val is_blum_evict_of_key_ifn (#vspec: verifier_spec) (#n: _) (ep: epoch) (gk: key vspec.app)\n : GTot (IF.idxfn_t (gen_seq vspec n) bool)\nlet is_blum_evict_of_key_ifn (#vspec: verifier_spec) (#n:_) (ep: epoch) (gk: key vspec.app)\n : GTot (IF.idxfn_t (gen_seq vspec n) bool)\n = hoist_ghost2 (is_blum_evict_of_key #vspec #n ep gk)", "val contains_only_app_keys_comp\n (#vspec: _)\n (vtls: vspec.vtls_t{vspec.valid vtls})\n (ss: S.seq vspec.slot_t)\n : GTot (b: bool{b <==> contains_only_app_keys vtls ss})\nlet contains_only_app_keys_comp (#vspec:_) (vtls: vspec.vtls_t{vspec.valid vtls}) (ss: S.seq vspec.slot_t)\n : GTot (b:bool {b <==> contains_only_app_keys vtls ss})\n = not (exists_elems_with_prop_comp (hoist_ghost (not_contains_app_key vtls)) ss)", "val irepr_pos\n (#t: Type)\n (#k: parser_kind)\n (#p: parser k t)\n (#rrel #rel: _)\n (#s: slice rrel rel)\n (#compl: compl_t t)\n (x: irepr p s compl)\n : Tot U32.t\nlet irepr_pos\n (#t: Type) (#k: parser_kind) (#p: parser k t) (#rrel #rel: _) (#s: slice rrel rel) (#compl: compl_t t) (x: irepr p s compl) : Tot U32.t =\n IRepr?.pos x", "val bind_fn_typing\n (#g:stt_env)\n (#t:st_term)\n (#c:comp)\n (d:st_typing g t c{T_BindFn? d})\n (soundness:soundness_t d)\n : GTot (RT.tot_typing (elab_env g)\n (elab_st_typing d)\n (elab_comp c))\nlet bind_fn_typing #g #t #c d soundness =\n let T_BindFn _ e1 e2 c1 c2 b x e1_typing u t1_typing e2_typing c2_typing = d in\n let t1 = comp_res c1 in\n let g_x = push_binding g x ppname_default t1 in\n\n let re1 = elab_st_typing e1_typing in\n let rt1 = elab_term t1 in\n let re2 = elab_st_typing e2_typing in\n\n let re1_typing : RT.tot_typing (elab_env g) re1 rt1 =\n soundness g e1 c1 e1_typing in\n \n let re2_typing : RT.tot_typing (elab_env g_x) re2 (elab_comp c2) =\n soundness g_x (open_st_term_nv e2 (v_as_nv x)) c2 e2_typing in\n\n RT.well_typed_terms_are_ln _ _ _ re2_typing;\n calc (==) {\n RT.open_term (RT.close_term re2 x) x;\n (==) { RT.open_term_spec (RT.close_term re2 x) x }\n RT.subst_term (RT.close_term re2 x) (RT.open_with_var x 0);\n (==) { RT.close_term_spec re2 x }\n RT.subst_term (RT.subst_term re2 [ RT.ND x 0 ]) (RT.open_with_var x 0);\n (==) { RT.open_close_inverse' 0 re2 x }\n re2;\n };\n let elab_t = RT.mk_let RT.pp_name_default re1 rt1 (RT.close_term re2 x) in\n let res\n : RT.tot_typing (elab_env g) elab_t (RT.open_with (RT.close_term (elab_comp c2) x) re1)\n = RT.T_Let (elab_env g) x re1 rt1 (RT.close_term re2 x) (elab_comp c2) T.E_Total RT.pp_name_default re1_typing re2_typing in\n Pulse.Typing.LN.comp_typing_ln c2_typing;\n Pulse.Elaborate.elab_ln_comp c (-1);\n assert (RT.ln (elab_comp c2));\n open_close_inverse_t (elab_comp c2) x re1;\n assert (RT.open_with (RT.close_term (elab_comp c2) x) re1 == elab_comp c2); \n res", "val parse_dsum\n (#kt: parser_kind)\n (t: dsum)\n (p: parser kt (dsum_repr_type t))\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (#k: parser_kind)\n (g: parser k (dsum_type_of_unknown_tag t))\n : Tot (parser (parse_dsum_kind kt t f k) (dsum_type t))\nlet parse_dsum\n (#kt: parser_kind)\n (t: dsum)\n (p: parser kt (dsum_repr_type t))\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (#k: parser_kind)\n (g: parser k (dsum_type_of_unknown_tag t))\n: Tot (parser (parse_dsum_kind kt t f k) (dsum_type t))\n= parse_dsum' t p (parse_dsum_cases t f g)", "val validate_dep_pair_with_action\r\n (#nz1:_)\r\n (#k1:parser_kind nz1 WeakKindStrongPrefix)\r\n (#t1:Type)\r\n (#[@@@erasable] p1:parser k1 t1)\r\n (#[@@@erasable] inv1:slice_inv)\r\n (#[@@@erasable] disj1:disjointness_pre)\r\n (#[@@@erasable] l1:eloc)\r\n (v1:validate_with_action_t p1 inv1 disj1 l1 true)\r\n (r1: leaf_reader p1)\r\n (#[@@@erasable] inv1':slice_inv)\r\n (#[@@@erasable] disj1':disjointness_pre)\r\n (#[@@@erasable] l1':eloc)\r\n (#b:_)\r\n (a:t1 -> action inv1' disj1' l1' b bool)\r\n (#nz2:_)\r\n (#wk2: _)\r\n (#k2:parser_kind nz2 wk2)\r\n (#[@@@erasable] t2:t1 -> Type)\r\n (#[@@@erasable] p2:(x:t1 -> parser k2 (t2 x)))\r\n (#[@@@erasable] inv2:slice_inv)\r\n (#[@@@erasable] disj2:disjointness_pre)\r\n (#[@@@erasable] l2:eloc)\r\n (#allow_reading2:_)\r\n (v2:(x:t1 -> validate_with_action_t (p2 x) inv2 disj2 l2 allow_reading2))\r\n : validate_with_action_t\r\n (p1 `(parse_dep_pair #nz1)` p2)\r\n (conj_inv inv1 (conj_inv inv1' inv2))\r\n (conj_disjointness disj1 (conj_disjointness disj1' disj2))\r\n (l1 `eloc_union` (l1' `eloc_union` l2))\r\n false\nlet validate_dep_pair_with_action\n #nz1 (#k1:parser_kind nz1 _) #t1 (#p1:parser k1 t1)\n #inv1 #disj1 #l1 (v1:validate_with_action_t p1 inv1 disj1 l1 true) (r1: leaf_reader p1)\n #inv1' #disj1' #l1' #b (a:t1 -> action inv1' disj1' l1' b bool)\n #nz2 #wk2 (#k2:parser_kind nz2 wk2) (#t2:t1 -> Type) (#p2:(x:t1 -> parser k2 (t2 x)))\n #inv2 #disj2 #l2 #ar2 (v2:(x:t1 -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n = fun ctxt error_handler_fn input input_length startPosition ->\n let h0 = HST.get () in\n LPC.parse_dtuple2_eq' #_ #_ p1 #_ #t2 p2 (I.get_remaining input h0);\n let res = v1 ctxt error_handler_fn input input_length startPosition in\n let h1 = HST.get() in\n modifies_address_liveness_insensitive_unused_in h0 h1;\n if LPE.is_error res\n then begin\n res\n end\n else begin\n let field_value = r1 input startPosition in\n let h2 = HST.get() in\n modifies_address_liveness_insensitive_unused_in h1 h2;\n let action_result = a field_value ctxt error_handler_fn input input_length startPosition res in\n let h3 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h2 h3;\n if not action_result\n then LPE.set_validator_error_pos LPE.validator_error_action_failed res //action failed\n else\n validate_drop (v2 field_value) ctxt error_handler_fn input input_length res\n end", "val serialize_dtuple2_eq'\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (s1: serializer p1 {k1.parser_kind_subkind == Some ParserStrong})\n (#k2: parser_kind)\n (#t2: (t1 -> Tot Type))\n (#p2: (x: t1 -> parser k2 (t2 x)))\n (s2: (x: t1 -> serializer (p2 x)))\n (xy: dtuple2 t1 t2)\n : Tot\n (squash ((serialize #_ #(dtuple2 t1 t2) (serialize_dtuple2 #k1 #t1 #p1 s1 #k2 #t2 #p2 s2) xy ==\n bare_serialize_dtuple2 #k1 #t1 #p1 s1 #k2 #t2 #p2 s2 xy)))\nlet serialize_dtuple2_eq'\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (s1: serializer p1 { k1.parser_kind_subkind == Some ParserStrong })\n (#k2: parser_kind)\n (#t2: (t1 -> Tot Type))\n (#p2: (x: t1) -> parser k2 (t2 x))\n (s2: (x: t1) -> serializer (p2 x))\n (xy: dtuple2 t1 t2)\n: Tot (squash (\n (serialize #_ #(dtuple2 t1 t2) (serialize_dtuple2 #k1 #t1 #p1 s1 #k2 #t2 #p2 s2) xy == bare_serialize_dtuple2 #k1 #t1 #p1 s1 #k2 #t2 #p2 s2 xy)))\n= serialize_dtuple2_eq s1 s2 xy" ], "closest_src": [ { "project_name": "everparse", "file_name": "EverParse3d.Kinds.fst", "name": "EverParse3d.Kinds.filter_kind" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_with_action_t" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_weaken_left" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_weaken_right" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.probe_then_validate" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parser" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_eta" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_ite" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_weaken_right" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_weaken_inv_loc" }, { "project_name": "everparse", "file_name": "EverParse3d.Kinds.fst", "name": "EverParse3d.Kinds.glb" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_weaken_left" }, { "project_name": "everparse", "file_name": "EverParse3d.Kinds.fst", "name": "EverParse3d.Kinds.parser_kind" }, { "project_name": "zeta", "file_name": "Zeta.High.Interleave.fst", "name": "Zeta.High.Interleave.ext_app_records_is_stored_val" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.leaf_reader" }, { "project_name": "steel", "file_name": "Pulse.Checker.Base.fst", "name": "Pulse.Checker.Base.vprop_equiv_typing_bk" }, { "project_name": "steel", "file_name": "Pulse.Checker.VPropEquiv.fsti", "name": "Pulse.Checker.VPropEquiv.vprop_equiv_typing_bk" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.fst", "name": "LowParse.Low.Base.wvalid" }, { "project_name": "steel", "file_name": "PulseCore.NondeterministicMonotonicStateMonad.fst", "name": "PulseCore.NondeterministicMonotonicStateMonad.bind" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.wvalue" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_weaken" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_t_at_most" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_ite" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_weaken" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.ElimPure.fst", "name": "Pulse.Checker.Prover.ElimPure.mk" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.ElimExists.fst", "name": "Pulse.Checker.Prover.ElimExists.mk" }, { "project_name": "zeta", "file_name": "Zeta.High.Verifier.fsti", "name": "Zeta.High.Verifier.puts" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_total_constant_size_no_read" }, { "project_name": "steel", "file_name": "Pulse.Soundness.Sub.fst", "name": "Pulse.Soundness.Sub.app_typing" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_t_exact" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_t_exact" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_pair" }, { "project_name": "steel", "file_name": "Steel.ST.EphemeralHashtbl.fst", "name": "Steel.ST.EphemeralHashtbl.tperm" }, { "project_name": "zeta", "file_name": "Zeta.Generic.Blum.fsti", "name": "Zeta.Generic.Blum.k_evict_set" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.bind" }, { "project_name": "everparse", "file_name": "EverParse3d.Kinds.fst", "name": "EverParse3d.Kinds.parser_kind_prop" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_nlist_constant_size_mod_ko" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_filter" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Base.fst", "name": "FStar.InteractiveHelpers.Base.mk_app_norm" }, { "project_name": "steel", "file_name": "Pulse.Checker.Base.fst", "name": "Pulse.Checker.Base.apply_conversion" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_with_dep_action" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_dep_pair" }, { "project_name": "steel", "file_name": "PulseCore.Semantics.fst", "name": "PulseCore.Semantics.mbind" }, { "project_name": "steel", "file_name": "Pulse.Typing.Combinators.fst", "name": "Pulse.Typing.Combinators.mk_bind" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.v" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.lwbind" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.owbind" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.wbind" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.fst", "name": "LowParse.Low.Base.irepr_v" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_list_inv" }, { "project_name": "everparse", "file_name": "InterpreterTarget.fst", "name": "InterpreterTarget.dtyp_of_app" }, { "project_name": "everparse", "file_name": "EverParse3d.Kinds.fst", "name": "EverParse3d.Kinds.and_then_kind" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_t_at_most" }, { "project_name": "zeta", "file_name": "Zeta.Intermediate.StateRel.fst", "name": "Zeta.Intermediate.StateRel.lemma_app_res_rel" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.swvalue" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.write" }, { "project_name": "zeta", "file_name": "Zeta.High.Verifier.fst", "name": "Zeta.High.Verifier.runapp_implies_store_contains" }, { "project_name": "steel", "file_name": "Steel.ST.EphemeralHashtbl.fst", "name": "Steel.ST.EphemeralHashtbl.put" }, { "project_name": "zeta", "file_name": "Zeta.High.Interleave.fst", "name": "Zeta.High.Interleave.mk_vlog_entry_ext" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_with_comment" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_nlist" }, { "project_name": "everparse", "file_name": "LowParse.Low.ListUpTo.fst", "name": "LowParse.Low.ListUpTo.jump_list_up_to_inv" }, { "project_name": "steel", "file_name": "Steel.ST.EphemeralHashtbl.fst", "name": "Steel.ST.EphemeralHashtbl.create_v" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.accessor_dsum_tag" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Spec.fst", "name": "Pulse.Lib.HashTable.Spec.delete_repr" }, { "project_name": "zeta", "file_name": "Zeta.High.Merkle.fst", "name": "Zeta.High.Merkle.addm_type" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.lwriter_singleton" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Derived.fst", "name": "FStar.Reflection.V1.Derived.mk_e_app" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Derived.fst", "name": "FStar.Reflection.V2.Derived.mk_e_app" }, { "project_name": "everparse", "file_name": "TranslateForInterpreter.fst", "name": "TranslateForInterpreter.parser_kind_nz" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.grlexistsb" }, { "project_name": "zeta", "file_name": "Zeta.GenericVerifier.fst", "name": "Zeta.GenericVerifier.contains_distinct_app_keys_comp" }, { "project_name": "FStar", "file_name": "LowParseWriters.NoHoare.fst", "name": "LowParseWriters.NoHoare.cast" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.lwriter_nil" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.invariant" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.write_leaf_cs" }, { "project_name": "zeta", "file_name": "Zeta.GenericVerifier.fsti", "name": "Zeta.GenericVerifier.to_app_record" }, { "project_name": "zeta", "file_name": "Zeta.Generic.Blum.fsti", "name": "Zeta.Generic.Blum.k_evict_seq" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_dep_pair_with_refinement'" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.owvalue" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Spec.fst", "name": "Pulse.Lib.HashTable.Spec.lemma_used_upd" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Base.fsti", "name": "LowParse.Spec.Base.mk_serializer" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_dep_pair" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fsti", "name": "LowParse.Low.Base.Spec.valid'" }, { "project_name": "zeta", "file_name": "Zeta.High.Interleave.fst", "name": "Zeta.High.Interleave.ev_is_sv_snoc_appfn" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Spec.fst", "name": "Pulse.Lib.HashTable.Spec.upd_pht" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.swbind" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Type.fsti", "name": "Pulse.Lib.HashTable.Type.exploded_vp" }, { "project_name": "zeta", "file_name": "Zeta.Intermediate.Thread.fst", "name": "Zeta.Intermediate.Thread.writes" }, { "project_name": "steel", "file_name": "Pulse.Lib.HashTable.Type.fst", "name": "Pulse.Lib.HashTable.Type.token" }, { "project_name": "steel", "file_name": "Steel.ST.EphemeralHashtbl.fst", "name": "Steel.ST.EphemeralHashtbl.create" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParDiv.fst", "name": "OPLSS2021.ParDiv.bind" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParNDSDiv.fst", "name": "OPLSS2021.ParNDSDiv.bind" }, { "project_name": "zeta", "file_name": "Zeta.Generic.Blum.fst", "name": "Zeta.Generic.Blum.is_blum_evict_of_key_ifn" }, { "project_name": "zeta", "file_name": "Zeta.GenericVerifier.fst", "name": "Zeta.GenericVerifier.contains_only_app_keys_comp" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.fst", "name": "LowParse.Low.Base.irepr_pos" }, { "project_name": "steel", "file_name": "Pulse.Soundness.Bind.fst", "name": "Pulse.Soundness.Bind.bind_fn_typing" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Sum.fst", "name": "LowParse.Spec.Sum.parse_dsum" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_dep_pair_with_action" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fsti", "name": "LowParse.Spec.Combinators.serialize_dtuple2_eq'" } ], "selected_premises": [ "EverParse3d.Interpreter.as_parser", "EverParse3d.Interpreter.as_reader", "EverParse3d.Interpreter.as_type", "EverParse3d.Interpreter.allow_reader_of_itype", "EverParse3d.Interpreter.interp_inv", "EverParse3d.Kinds.weak_kind_glb", "EverParse3d.Interpreter.leaf_reader", "EverParse3d.Interpreter.parser_weak_kind_of_itype", "EverParse3d.Interpreter.parser_kind_nz_of_itype", "EverParse3d.Interpreter.dtyp_as_parser", "EverParse3d.Interpreter.parser_kind_of_itype", "EverParse3d.Interpreter.as_validator", "EverParse3d.Interpreter.dtyp_as_validator", "EverParse3d.Kinds.kind_unit", "EverParse3d.Interpreter.dtyp_as_leaf_reader", "EverParse3d.Prelude.refine", "EverParse3d.Interpreter.dtyp_of", "EverParse3d.Interpreter.itype_as_parser", "EverParse3d.Interpreter.validator_of", "EverParse3d.Interpreter.action_as_action", "EverParse3d.Interpreter.nz_of_binding", "EverParse3d.Interpreter.interp_loc", "EverParse3d.Interpreter.wk_of_binding", "EverParse3d.Interpreter.loc_none", "EverParse3d.Interpreter.disj_of_bindng", "EverParse3d.Interpreter.atomic_action_as_action", "FStar.Int.Cast.uint64_to_uint32", "FStar.Int.Cast.uint32_to_uint64", "EverParse3d.Interpreter.pk_of_binding", "EverParse3d.Interpreter.projector_names", "EverParse3d.Interpreter.itype_as_leaf_reader", "EverParse3d.Interpreter.mk_action_binding", "EverParse3d.Interpreter.type_of_binding", "EverParse3d.Prelude.uint32_to_uint64", "EverParse3d.Interpreter.comments", "FStar.UInt.size", "EverParse3d.Prelude.parse_unit", "EverParse3d.Interpreter.inv_index", "EverParse3d.Interpreter.disj_index", "EverParse3d.Interpreter.join_inv", "EverParse3d.Interpreter.disj_none", "EverParse3d.Interpreter.t_probe_then_validate", "EverParse3d.Interpreter.interp_index", "FStar.Pervasives.Native.fst", "EverParse3d.Interpreter.itype_as_validator", "EverParse3d.Prelude.uint64_to_uint32", "FStar.Pervasives.Native.snd", "EverParse3d.Interpreter.specialization_steps", "EverParse3d.Interpreter.reader_binding", "EverParse3d.Interpreter.parser_of_binding", "EverParse3d.Interpreter.interp_disj", "EverParse3d.Interpreter.___EVERPARSE_COPY_BUFFER_T", "EverParse3d.Prelude.StaticHeader.get_bitfield8", "EverParse3d.Interpreter.inv_of_binding", "EverParse3d.Interpreter.mk_extern_action", "FStar.Pervasives.dfst", "EverParse3d.Interpreter.has_reader", "FStar.Mul.op_Star", "EverParse3d.Interpreter.join_loc", "FStar.Pervasives.reveal_opaque", "FStar.Pervasives.dsnd", "EverParse3d.Interpreter.inv_none", "EverParse3d.Interpreter.disjoint", "FStar.Int.Cast.op_At_Percent", "EverParse3d.Prelude.___UINT64", "EverParse3d.Interpreter.loc_index", "EverParse3d.Prelude.u8_rem", "EverParse3d.Interpreter.leaf_reader_of_binding", "EverParse3d.Prelude.uint64_to_uint8", "EverParse3d.Interpreter.loc_of_binding", "EverParse3d.Interpreter.extern_action", "EverParse3d.Interpreter.mk_global_binding", "EverParse3d.Prelude.uint8_to_uint64", "EverParse3d.Interpreter.coerce", "EverParse3d.Interpreter.action_binding", "EverParse3d.Prelude.u8_mul", "EverParse3d.Prelude.u64_mul", "EverParse3d.Prelude.uint32_to_uint8", "EverParse3d.Prelude.u64_rem", "EverParse3d.Interpreter.join_disj", "EverParse3d.Prelude.max_int_sizes", "EverParse3d.Prelude.uint8_to_uint32", "FStar.Int.Cast.uint32_to_uint8", "EverParse3d.Interpreter.validator_of_binding", "EverParse3d.Prelude.___UINT32", "EverParse3d.Prelude.id", "EverParse3d.Prelude.___UINT8", "EverParse3d.Interpreter.dtyp_as_eqtype_lemma", "EverParse3d.Prelude.u32_rem", "FStar.Int.Cast.uint64_to_uint8", "EverParse3d.Prelude.StaticHeader.get_bitfield8_msb_first", "EverParse3d.Prelude.u8_sub", "EverParse3d.Prelude.u8_lognot", "EverParse3d.Prelude.___UINT64BE", "EverParse3d.Interpreter.join_index", "EverParse3d.Prelude.___Bool", "EverParse3d.Prelude.u32_mul", "EverParse3d.Prelude.u16_mul", "EverParse3d.Prelude.u64_sub", "EverParse3d.Prelude.u16_rem" ], "source_upto_this": "(*\n Copyright 2021 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n\n Authors: N. Swamy, ...\n*)\nmodule EverParse3d.Interpreter\nmodule U32 = FStar.UInt32\nmodule U64 = FStar.UInt64\nmodule A = EverParse3d.Actions.All\nmodule P = EverParse3d.Prelude\nmodule T = FStar.Tactics\nmodule CP = EverParse3d.CopyBuffer\nopen FStar.List.Tot\n\ninline_for_extraction\nnoextract\nlet ___EVERPARSE_COPY_BUFFER_T = CP.copy_buffer_t\n\n(* This module defines a strongly typed abstract syntax for an\n intermediate representation of 3D programs. This is the type `typ`.\n\n The main idea of this module is to give `typ`s a threefold\n denotation:\n\n 1. Type denotation: `as_type` interprets a `typ` as an F* type\n\n 2. Parser denotation: `as_parser` interprets a `t:typ` as a parser\n of values of the type denotation of `t`.\n\n 3. Validate-with-action denotation: `as_validator` inteprets a\n `t:typ` as a low-level validator corresponding to the parser\n denotation of `t`.\n\n The 3rd denotation, validate-with-action, is the main operational\n denotation. That is, given a 3D program `t:typ` we can interpret it\n as validator to check that an input array of bytes conforms to the\n format specified by `t`. But, what we want ultimately is a C\n program for a `t`-validator.\n\n To achieve this, for any given concrete `t`, we partially evaluate\n this interpreter to get an EverParse validator specialized to `t`\n which can be extracted by F*/KaRaMeL as usual---this partial\n evaluation of an interpreter to a compiler producing a C program\n for t-validator is an instance of the 1st Futamura projection.\n *)\n\n(* An attribute to control partial evaluation *)\nlet specialize = ()\n\n(** You can see the basic idea of the whole stack working at first on\n a very simple class of types---just the primitive types *)\n\n(* Primitive types *)\ntype itype =\n | UInt8\n | UInt16\n | UInt32\n | UInt64\n | UInt8BE\n | UInt16BE\n | UInt32BE\n | UInt64BE\n | Unit\n | AllBytes\n | AllZeros\n\n(* Interpretation of itype as an F* type *)\n[@@specialize]\nlet itype_as_type (i:itype)\n : Type\n = match i with\n | UInt8 -> P.___UINT8\n | UInt16 -> P.___UINT16\n | UInt32 -> P.___UINT32\n | UInt64 -> P.___UINT64\n | UInt8BE -> P.___UINT8BE\n | UInt16BE -> P.___UINT16BE\n | UInt32BE -> P.___UINT32BE\n | UInt64BE -> P.___UINT64BE\n | Unit -> unit\n | AllBytes -> P.all_bytes\n | AllZeros -> P.all_zeros\n\n[@@specialize]\nlet parser_kind_nz_of_itype (i:itype)\n : bool\n = match i with\n | Unit\n | AllBytes\n | AllZeros -> false\n | _ -> true\n\n[@@specialize]\nlet parser_weak_kind_of_itype (i:itype)\n : P.weak_kind\n = match i with\n | AllBytes\n | AllZeros -> P.WeakKindConsumesAll\n | _ -> P.WeakKindStrongPrefix\n\n(* Interpretation of itype as a parser kind *)\n[@@specialize]\nlet parser_kind_of_itype (i:itype)\n : P.parser_kind (parser_kind_nz_of_itype i)\n (parser_weak_kind_of_itype i)\n = match i with\n | UInt8 -> P.kind____UINT8\n | UInt16 -> P.kind____UINT16\n | UInt32 -> P.kind____UINT32\n | UInt64 -> P.kind____UINT64\n | UInt8BE -> P.kind____UINT8BE\n | UInt16BE -> P.kind____UINT16BE\n | UInt32BE -> P.kind____UINT32BE\n | UInt64BE -> P.kind____UINT64BE\n | Unit -> P.kind_unit\n | AllBytes -> P.kind_all_bytes\n | AllZeros -> P.kind_all_zeros\n\n(* Interpretation of an itype as a parser *)\nlet itype_as_parser (i:itype)\n : P.parser (parser_kind_of_itype i) (itype_as_type i)\n = match i with\n | UInt8 -> P.parse____UINT8\n | UInt16 -> P.parse____UINT16\n | UInt32 -> P.parse____UINT32\n | UInt64 -> P.parse____UINT64\n | UInt8BE -> P.parse____UINT8BE\n | UInt16BE -> P.parse____UINT16BE\n | UInt32BE -> P.parse____UINT32BE\n | UInt64BE -> P.parse____UINT64BE\n | Unit -> P.parse_unit\n | AllBytes -> P.parse_all_bytes\n | AllZeros -> P.parse_all_zeros\n\n[@@specialize]\nlet allow_reader_of_itype (i:itype)\n : bool\n = match i with\n | AllBytes\n | AllZeros -> false\n | _ -> true\n\n(* Interpretation of an itype as a leaf reader *)\n[@@specialize]\nlet itype_as_leaf_reader (i:itype { allow_reader_of_itype i })\n : A.leaf_reader (itype_as_parser i)\n = match i with\n | UInt8 -> A.read____UINT8\n | UInt16 -> A.read____UINT16\n | UInt32 -> A.read____UINT32\n | UInt64 -> A.read____UINT64\n | UInt8BE -> A.read____UINT8BE\n | UInt16BE -> A.read____UINT16BE\n | UInt32BE -> A.read____UINT32BE\n | UInt64BE -> A.read____UINT64BE\n | Unit -> A.read_unit\n\n(* Interpretation of an itype as a validator\n -- Notice that the type shows that it is related to the parser *)\n[@@specialize]\nlet itype_as_validator (i:itype)\n : A.validate_with_action_t\n (itype_as_parser i)\n A.true_inv\n A.disjointness_trivial\n A.eloc_none\n (allow_reader_of_itype i)\n = match i with\n | UInt8 -> A.validate____UINT8\n | UInt16 -> A.validate____UINT16\n | UInt32 -> A.validate____UINT32\n | UInt64 -> A.validate____UINT64\n | UInt8BE -> A.validate____UINT8BE\n | UInt16BE -> A.validate____UINT16BE\n | UInt32BE -> A.validate____UINT32BE\n | UInt64BE -> A.validate____UINT64BE\n | Unit -> A.validate_unit\n | AllBytes -> A.validate_all_bytes\n | AllZeros -> A.validate_all_zeros\n\n\n(* Our first order of business to scale this up to 3D is to set up\n definitions for type contexts.\n\n A 3D program is a sequence of top-level definitions, where a given\n definition may reference terms defined previously. To model this,\n we'll given a denotation of programs in a _context_, where the\n context provides denotations for all the names defined previously\n which are in scope.\n*)\n\nlet leaf_reader #nz #wk (#k: P.parser_kind nz wk) #t (p:P.parser k t)\n = _:squash (wk == P.WeakKindStrongPrefix /\\ hasEq t) &\n A.leaf_reader p\n\n(* Now, we can define the type of an environment *)\nmodule T = FStar.Tactics\n\n[@@erasable]\nnoeq\ntype index (a:Type) =\n | Trivial : index a\n | NonTrivial : a -> index a\n\n[@@specialize]\nlet join_index (j:'a -> 'a -> 'a) (i0 i1:index 'a)\n: index 'a\n= match i0 with\n | Trivial -> i1\n | _ -> (\n match i1 with\n | Trivial -> i0\n | NonTrivial i1 ->\n let NonTrivial i0 = i0 in\n NonTrivial (j i0 i1)\n )\n[@@specialize]\nlet interp_index (triv:'a) (i:index 'a)\n: GTot 'a\n= match i with\n | Trivial -> triv\n | NonTrivial i -> i\n\n\nlet inv_index = index A.slice_inv\n[@@specialize]\nlet inv_none : inv_index = Trivial\n[@@specialize]\nlet join_inv = join_index A.conj_inv\n[@@specialize]\nlet interp_inv = interp_index A.true_inv\n\nlet loc_index = index A.eloc\n[@@specialize]\nlet loc_none : loc_index = Trivial\n[@@specialize]\nlet join_loc = join_index A.eloc_union\n[@@specialize]\nlet interp_loc = interp_index A.eloc_none\n\nlet disj_index = index A.disjointness_pre\n[@@specialize]\nlet disj_none : disj_index = Trivial\n[@@specialize]\nlet join_disj = join_index A.conj_disjointness\n[@@specialize]\nlet interp_disj = interp_index A.disjointness_trivial\n[@@specialize]\nlet disjoint (e1 e2:loc_index)\n : disj_index\n = match e1, e2 with\n | Trivial, _\n | _, Trivial -> disj_none\n | NonTrivial e1, NonTrivial e2 -> NonTrivial (A.disjoint e1 e2)\n\n\n(* A context is a list of bindings, where each binding is a pair of a\n name and a denotation of the name. *)\n(* global_binding:\n\n Represents the lifting of a fully applied a shallow F*\n quadruple of {type, parser, validator, opt reader}\n*)\nnoeq\ntype global_binding = {\n //Parser metadata\n parser_kind_nz:bool; // Does it consume non-zero bytes?\n parser_weak_kind: P.weak_kind;\n parser_kind: P.parser_kind parser_kind_nz parser_weak_kind;\n //Memory invariant of any actions it contains\n inv:inv_index;\n //Disjointness precondition\n disj:disj_index;\n //Write footprint of any of its actions\n loc:loc_index;\n //Its type denotation\n p_t : Type0;\n //Its parser denotation\n p_p : P.parser parser_kind p_t;\n //Whether the type can be read -- to avoid double fetches\n p_reader: option (leaf_reader p_p);\n //Its validate-with-action denotationa\n p_v : A.validate_with_action_t\n p_p\n (interp_inv inv)\n (interp_disj disj)\n (interp_loc loc)\n (Some? p_reader);\n}\n\nlet projector_names : list string = [\n `%Mkglobal_binding?.parser_kind_nz;\n `%Mkglobal_binding?.parser_weak_kind;\n `%Mkglobal_binding?.parser_kind;\n `%Mkglobal_binding?.inv;\n `%Mkglobal_binding?.disj;\n `%Mkglobal_binding?.loc;\n `%Mkglobal_binding?.p_t;\n `%Mkglobal_binding?.p_p;\n `%Mkglobal_binding?.p_reader;\n `%Mkglobal_binding?.p_v;\n]\n\nlet nz_of_binding = Mkglobal_binding?.parser_kind_nz\nlet wk_of_binding = Mkglobal_binding?.parser_weak_kind\nlet pk_of_binding = Mkglobal_binding?.parser_kind\nlet inv_of_binding = Mkglobal_binding?.inv\nlet disj_of_bindng = Mkglobal_binding?.disj\nlet loc_of_binding = Mkglobal_binding?.loc\nlet type_of_binding = Mkglobal_binding?.p_t\nlet parser_of_binding = Mkglobal_binding?.p_p\nlet leaf_reader_of_binding = Mkglobal_binding?.p_reader\nlet validator_of_binding = Mkglobal_binding?.p_v\n\nlet has_reader (g:global_binding) =\n match leaf_reader_of_binding g with\n | Some _ -> true\n | _ -> false\n\nlet reader_binding = g:global_binding { has_reader g }\n\n[@@specialize]\nlet get_leaf_reader (r:reader_binding)\n : leaf_reader (parser_of_binding r)\n = Some?.v (leaf_reader_of_binding r)\n\n\n(* The main type of 3D types. Some points to note:\n\n - The indexing structure determines the types of the\n parser/validator etc. of its denotation\n\n - All top-level names mentioned in a typ must be bound in the\n context.\n\n - Constructs that bind local names are represented using F*\n functions that abstract over denotations of the underlying types.\n\n - Some elements of the source programs are \"pre-denoted\". Notably,\n every refinement formula is represented in this AST already as a\n boolean function, rather than in some embedded language of\n expressions. This is because expressions are not necessarily\n well-formed by syntax alone---they may give rise to verification\n conditions when using bounded arithmetic functions. So, it's the\n obligation of the `typ` generator (i.e., the 3D frontend) to\n produce boolean functions for those expressions that can be\n verified natively by F* for type correctness.\n*)\n\nnoeq\ntype dtyp\n : #nz:bool -> #wk:P.weak_kind ->\n P.parser_kind nz wk ->\n has_reader:bool ->\n inv_index ->\n disj_index ->\n loc_index ->\n Type =\n | DT_IType:\n i:itype ->\n dtyp (parser_kind_of_itype i)\n (allow_reader_of_itype i)\n inv_none disj_none loc_none\n\n | DT_App:\n (* We give explicit names to the indices rather than\n projecting them as a small optimization for the reduction\n machinery ... it's no longer clear that the speedup is significant *)\n #nz:bool ->\n #wk:P.weak_kind ->\n pk:P.parser_kind nz wk ->\n hr:bool ->\n inv:inv_index ->\n disj:disj_index ->\n loc:loc_index ->\n x:global_binding ->\n _:squash (nz == nz_of_binding x /\\\n wk == wk_of_binding x /\\\n pk == pk_of_binding x /\\\n hr == has_reader x /\\\n inv == inv_of_binding x /\\\n disj == disj_of_bindng x /\\\n loc == loc_of_binding x) ->\n dtyp #nz #wk pk hr inv disj loc\n\n[@@specialize]\nlet dtyp_as_type #nz #wk (#pk:P.parser_kind nz wk) #hr #i #disj #l\n (d:dtyp pk hr i disj l)\n : Type\n = match d with\n | DT_IType i ->\n itype_as_type i\n\n | DT_App _ _ _ _ _ b _ ->\n type_of_binding b\n\nlet dtyp_as_eqtype_lemma #nz #wk (#pk:P.parser_kind nz wk) #i #disj #l\n (d:dtyp pk true i disj l)\n : Lemma\n (ensures hasEq (dtyp_as_type d))\n [SMTPat (hasEq (dtyp_as_type d))]\n = match d with\n | DT_IType i ->\n ()\n\n | DT_App _ _ _ _ _ b _ ->\n let (| _, _ |) = get_leaf_reader b in ()\n\n\nlet dtyp_as_parser #nz #wk (#pk:P.parser_kind nz wk) #hr #i #disj #l\n (d:dtyp pk hr i disj l)\n : P.parser pk (dtyp_as_type d)\n = match d returns Tot (P.parser pk (dtyp_as_type d)) with\n | DT_IType i ->\n itype_as_parser i\n\n | DT_App _ _ _ _ _ b _ ->\n parser_of_binding b\n\n[@@specialize]\nlet dtyp_as_validator #nz #wk (#pk:P.parser_kind nz wk)\n (#hr:_)\n (#[@@@erasable] i:inv_index)\n (#[@@@erasable] disj:disj_index)\n (#[@@@erasable] l:loc_index)\n (d:dtyp pk hr i disj l)\n : A.validate_with_action_t #nz #wk #pk #(dtyp_as_type d)\n (dtyp_as_parser d)\n (interp_inv i)\n (interp_disj disj)\n (interp_loc l)\n hr\n = match d\n returns\n A.validate_with_action_t #nz #wk #pk #(dtyp_as_type d)\n (dtyp_as_parser d)\n (interp_inv i)\n (interp_disj disj)\n (interp_loc l)\n hr\n with\n | DT_IType i ->\n itype_as_validator i\n\n | DT_App _ _ _ _ _ b _ ->\n // assert_norm (dtyp_as_type (DT_App_Alt ps b args) == (type_of_binding_alt (apply_arrow b args)));\n // assert_norm (dtyp_as_parser (DT_App_Alt ps b args) == parser_of_binding_alt (apply_arrow b args));\n validator_of_binding b\n\n\n[@@specialize]\nlet dtyp_as_leaf_reader #nz (#pk:P.parser_kind nz P.WeakKindStrongPrefix)\n (#[@@@erasable] i:inv_index)\n (#[@@@erasable] disj:disj_index)\n (#[@@@erasable] l:loc_index)\n (d:dtyp pk true i disj l)\n : A.leaf_reader (dtyp_as_parser d)\n = match d with\n | DT_IType i ->\n itype_as_leaf_reader i\n\n | DT_App _ _ _ _ _ b _ ->\n let (| _, lr |) = get_leaf_reader b in\n lr\n\n(** Actions *)\n\nlet action_binding\n (inv:inv_index)\n (l:loc_index)\n (on_success:bool)\n (a:Type)\n : Type u#0\n = A.action (interp_inv inv) A.disjointness_trivial (interp_loc l) on_success a\n\ninline_for_extraction\nlet extern_action (l:loc_index) = A.external_action (interp_loc l)\n\ninline_for_extraction\nlet mk_extern_action (#l:loc_index) ($f:extern_action l)\n = A.mk_external_action f\n\n[@@specialize]\nlet mk_action_binding\n (#l:loc_index)\n ($f:extern_action l)\n : action_binding inv_none l false unit\n = mk_extern_action f\n\n(* The type of atomic actions.\n\n `atomic_action l i b t`: is an atomic action that\n - may modify locations `l`\n - relies on a memory invariant `i`\n - b, when set, indicates that the action can only run in a success handler\n - t, is the result type of the action\n\n In comparison with with the 3D front-end's internal representation\n of actions, some notable differences\n\n - The indexing structure tell us exactly the type to which these\n will translate. It's also worth comparing these types to the\n types of the action primitives in Actions.fsti---the indexing\n structure is the same\n\n - The type is already partially interpreted, e.g., rather than\n relying on an explicit representation of names (e.g., in\n Action_deref), this representation directly uses a pointer\n value.\n*)\nnoeq\ntype atomic_action\n : inv_index -> disj_index -> loc_index -> bool -> Type0 -> Type u#1 =\n | Action_return:\n #a:Type0 ->\n x:a ->\n atomic_action inv_none disj_none loc_none false a\n\n | Action_abort:\n atomic_action inv_none disj_none loc_none false bool\n\n | Action_field_pos_64:\n atomic_action inv_none disj_none loc_none false U64.t\n\n | Action_field_pos_32:\n squash (EverParse3d.Actions.BackendFlag.backend_flag == A.BackendFlagBuffer) ->\n atomic_action inv_none disj_none loc_none false U32.t\n\n | Action_field_ptr:\n squash (EverParse3d.Actions.BackendFlag.backend_flag == A.BackendFlagBuffer) ->\n atomic_action inv_none disj_none loc_none true A.___PUINT8\n\n | Action_field_ptr_after:\n squash (EverParse3d.Actions.BackendFlag.backend_flag == A.BackendFlagExtern) ->\n (sz: FStar.UInt64.t) ->\n write_to: A.bpointer A.___PUINT8 ->\n atomic_action (NonTrivial (A.ptr_inv write_to)) disj_none (NonTrivial (A.ptr_loc write_to)) false bool\n\n | Action_field_ptr_after_with_setter:\n squash (EverParse3d.Actions.BackendFlag.backend_flag == A.BackendFlagExtern) ->\n sz: FStar.UInt64.t ->\n #out_loc:loc_index ->\n write_to: (A.___PUINT8 -> Tot (extern_action out_loc)) ->\n atomic_action inv_none disj_none out_loc false bool\n\n | Action_deref:\n #a:Type0 ->\n x:A.bpointer a ->\n atomic_action (NonTrivial (A.ptr_inv x)) disj_none loc_none false a\n\n | Action_assignment:\n #a:Type0 ->\n x:A.bpointer a ->\n rhs:a ->\n atomic_action (NonTrivial (A.ptr_inv x)) disj_none (NonTrivial (A.ptr_loc x)) false unit\n\n | Action_call:\n #inv:inv_index ->\n #loc:loc_index ->\n #b:bool ->\n #t:Type0 ->\n action_binding inv loc b t ->\n atomic_action inv disj_none loc b t\n\n | Action_probe_then_validate:\n #nz:bool ->\n #wk:_ ->\n #k:P.parser_kind nz wk ->\n #has_reader:bool ->\n #inv:inv_index ->\n #disj:disj_index ->\n #l:loc_index ->\n dt:dtyp k has_reader inv disj l ->\n src:U64.t ->\n len:U64.t ->\n dest:CP.copy_buffer_t ->\n probe:CP.probe_fn ->\n atomic_action (join_inv inv (NonTrivial (A.copy_buffer_inv dest)))\n (join_disj disj (disjoint (NonTrivial (A.copy_buffer_loc dest)) l))\n (join_loc l (NonTrivial (A.copy_buffer_loc dest)))\n true bool\n\n\n(* Denotation of atomic_actions as A.action *)\n[@@specialize]\nlet atomic_action_as_action\n (#i #d #l #b #t:_)\n (a:atomic_action i d l b t)\n : Tot (A.action (interp_inv i) (interp_disj d) (interp_loc l) b t)\n = match a with\n | Action_return x ->\n A.action_return x\n | Action_abort ->\n A.action_abort\n | Action_field_pos_64 ->\n A.action_field_pos_64\n | Action_field_pos_32 sq ->\n A.action_field_pos_32 sq\n | Action_field_ptr sq ->\n A.action_field_ptr sq\n | Action_field_ptr_after sq sz write_to ->\n A.action_field_ptr_after sq sz write_to\n | Action_field_ptr_after_with_setter sq sz write_to ->\n A.action_field_ptr_after_with_setter sq sz write_to\n | Action_deref x ->\n A.action_deref x\n | Action_assignment x rhs ->\n A.action_assignment x rhs\n | Action_call c ->\n c\n | Action_probe_then_validate #nz #wk #k #_hr #inv #l dt src len dest probe ->\n A.index_equations();\n let v = dtyp_as_validator dt in\n A.probe_then_validate v src len dest probe\n\n(* A sub-language of monadic actions.\n\n The indexing structure mirrors the indexes of the combinators in\n Actions.fst\n*)\nnoeq\ntype action\n : inv_index -> disj_index -> loc_index -> bool -> Type0 -> Type u#1 =\n | Atomic_action:\n #i:_ -> #d:_ -> #l:_ -> #b:_ -> #t:_ ->\n atomic_action i d l b t ->\n action i d l b t\n\n | Action_seq:\n #i0:_ -> #l0:_ -> #b0:_ -> hd:atomic_action i0 disj_none l0 b0 unit ->\n #i1:_ -> #l1:_ -> #b1:_ -> #t:_ -> tl:action i1 disj_none l1 b1 t ->\n action (join_inv i0 i1) disj_none (join_loc l0 l1) (b0 || b1) t\n\n | Action_ite :\n hd:bool ->\n #i0:_ -> #l0:_ -> #b0:_ -> #t:_ -> then_:(_:squash hd -> action i0 disj_none l0 b0 t) ->\n #i1:_ -> #l1:_ -> #b1:_ -> else_:(_:squash (not hd) -> action i1 disj_none l1 b1 t) ->\n action (join_inv i0 i1) disj_none (join_loc l0 l1) (b0 || b1) t\n\n | Action_let:\n #i0:_ -> #l0:_ -> #b0:_ -> #t0:_ -> head:atomic_action i0 disj_none l0 b0 t0 ->\n #i1:_ -> #l1:_ -> #b1:_ -> #t1:_ -> k:(t0 -> action i1 disj_none l1 b1 t1) ->\n action (join_inv i0 i1) disj_none (join_loc l0 l1) (b0 || b1) t1\n\n | Action_act:\n #i0:_ -> #l0:_ -> #b0:_ -> act:action i0 disj_none l0 b0 unit ->\n action i0 disj_none l0 b0 bool\n\n\n(* Denotation of action as A.action *)\n[@@specialize]\nlet rec action_as_action\n (#i #d #l #b #t:_)\n (a:action i d l b t)\n : Tot (A.action (interp_inv i) (interp_disj d) (interp_loc l) b t)\n (decreases a)\n = A.index_equations();\n match a with\n | Atomic_action a ->\n atomic_action_as_action a\n\n | Action_seq hd tl ->\n let a1 = atomic_action_as_action hd in\n let tl = action_as_action tl in\n A.action_seq a1 tl\n\n | Action_ite hd t e ->\n let then_ (x:squash hd) = action_as_action (t x) in\n let else_ (x:squash (not hd)) = action_as_action (e x) in\n A.action_ite hd then_ else_\n\n | Action_let hd k ->\n let head = atomic_action_as_action hd in\n let k x = action_as_action (k x) in\n A.action_bind \"hd\" head k\n\n | Action_act #i0 #l0 #b0 a ->\n A.action_weaken (A.action_seq (action_as_action a) (A.action_return true))\n #(interp_inv i0)\n #_\n #(interp_loc l0)\n\n(* Some AST nodes contain source comments that we propagate to the output *)\nlet comments = string\n\n[@@ no_auto_projectors]\nnoeq\ntype typ\n : #nz:bool -> #wk:P.weak_kind ->\n P.parser_kind nz wk ->\n inv_index ->\n disj_index ->\n loc_index ->\n bool ->\n Type =\n | T_false:\n fieldname:string ->\n typ P.impos_kind inv_none disj_none loc_none true\n\n | T_denoted :\n fieldname:string ->\n #nz:_ -> #wk:_ -> #pk:P.parser_kind nz wk ->\n #has_reader:_ -> #i:_ -> #disj:_ -> #l:_ ->\n td:dtyp pk has_reader i disj l ->\n typ pk i disj l has_reader\n\n | T_pair:\n first_fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ -> #b1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n t1:typ pk1 i1 d1 l1 b1 ->\n t2:typ pk2 i2 d2 l2 b2 ->\n typ (P.and_then_kind pk1 pk2)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2)\n false\n\n | T_dep_pair:\n first_fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:bool ->\n //the first component is a pre-denoted type with a reader\n t1:dtyp pk1 true i1 d1 l1 ->\n //the second component is a function from denotations of t1\n //that's why it's a small type, so that we can speak about its\n //denotation here\n t2:(dtyp_as_type t1 -> typ pk2 i2 d2 l2 b2) ->\n typ (P.and_then_kind pk1 pk2)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2)\n false\n\n | T_refine:\n fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n //the first component is a pre-denoted type with a reader\n base:dtyp pk1 true i1 d1 l1 ->\n //the second component is a function from denotations of base\n //but notice that its codomain is bool, rather than expr\n //That's to ensure that the refinement is already well-typed\n refinement:(dtyp_as_type base -> bool) ->\n typ (P.filter_kind pk1) i1 d1 l1 false\n\n | T_refine_with_action:\n fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n base:dtyp pk1 true i1 d1 l1 ->\n refinement:(dtyp_as_type base -> bool) ->\n act:(dtyp_as_type base -> action i2 d2 l2 b2 bool) ->\n typ (P.filter_kind pk1)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2)\n false\n\n | T_dep_pair_with_refinement:\n //This construct serves two purposes\n // 1. To avoid double fetches, we fold the refinement\n // and dependent pair into a single form\n // 2. This allows the well-typedness of the continuation k\n // to depend on the refinement of the first field\n first_fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n //the first component is a pre-denoted type with a reader\n base:dtyp pk1 true i1 d1 l1 ->\n //the second component is a function from denotations of base\n refinement:(dtyp_as_type base -> bool) ->\n k:(x:dtyp_as_type base { refinement x } -> typ pk2 i2 d2 l2 b2) ->\n typ (P.and_then_kind (P.filter_kind pk1) pk2)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2)\n false\n\n | T_dep_pair_with_action:\n fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n #i3:_ -> #d3:_ -> #l3:_ -> #b3:_ ->\n base:dtyp pk1 true i1 d1 l1 ->\n k:(x:dtyp_as_type base -> typ pk2 i2 d2 l2 b2) ->\n act:(dtyp_as_type base -> action i3 d3 l3 b3 bool) ->\n typ (P.and_then_kind pk1 pk2)\n (join_inv i1 (join_inv i3 i2))\n (join_disj d1 (join_disj d3 d2))\n (join_loc l1 (join_loc l3 l2))\n false\n\n | T_dep_pair_with_refinement_and_action:\n //This construct serves two purposes\n // 1. To avoid double fetches, we fold the refinement\n // and dependent pair and action into a single form\n // 2. This allows the well-typedness of the continuation k\n // to depend on the refinement of the first field\n first_fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n #i3:_ -> #d3:_ -> #l3:_ -> #b3:_ ->\n //the first component is a pre-denoted type with a reader\n base:dtyp pk1 true i1 d1 l1 ->\n //the second component is a function from denotations of base\n refinement:(dtyp_as_type base -> bool) ->\n k:(x:dtyp_as_type base { refinement x } -> typ pk2 i2 d2 l2 b2) ->\n act:(dtyp_as_type base -> action i3 d3 l3 b3 bool) ->\n typ (P.and_then_kind (P.filter_kind pk1) pk2)\n (join_inv i1 (join_inv i3 i2))\n (join_disj d1 (join_disj d3 d2))\n (join_loc l1 (join_loc l3 l2))\n false\n\n | T_if_else:\n #nz1:_ -> #wk1:_ -> #pk1:P.parser_kind nz1 wk1 ->\n #l1:_ -> #i1:_ -> #d1:_ -> #b1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #l2:_ -> #i2:_ -> #d2:_ -> #b2:_ ->\n b:bool -> //A bool, rather than an expression\n t1:(squash b -> typ pk1 i1 d1 l1 b1) ->\n t2:(squash (not b) -> typ pk2 i2 d2 l2 b2) ->\n typ (P.glb pk1 pk2)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2) false\n\n | T_cases:\n #nz1:_ -> #wk1:_ -> #pk1:P.parser_kind nz1 wk1 ->\n #l1:_ -> #i1:_ -> #d1:_ -> #b1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #l2:_ -> #i2:_ -> #d2:_ -> #b2:_ ->\n b:bool -> //A bool, rather than an expression\n t1:typ pk1 i1 d1 l1 b1 ->\n t2:typ pk2 i2 d2 l2 b2 ->\n typ (P.glb pk1 pk2)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2)\n false\n\n | T_with_action:\n fieldname:string ->\n #nz:_ -> #wk:_ -> #pk:P.parser_kind nz wk ->\n #l1:_ -> #i1:_ -> #d1:_ -> #b1:_ ->\n #l2:_ -> #i2:_ -> #d2:_ -> #b2:_ ->\n base:typ pk i1 d1 l1 b1 ->\n act:action i2 d2 l2 b2 bool ->\n typ pk (join_inv i1 i2) (join_disj d1 d2) (join_loc l1 l2) false\n\n | T_with_dep_action:\n fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1: _ -> #l1:_ ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n head:dtyp pk1 true i1 d1 l1 ->\n act:(dtyp_as_type head -> action i2 d2 l2 b2 bool) ->\n typ pk1 (join_inv i1 i2) (join_disj d1 d2) (join_loc l1 l2) false\n\n | T_with_comment:\n fieldname:string ->\n #nz:_ -> #wk:_ -> #pk:P.parser_kind nz wk ->\n #l:_ -> #i:_ -> #d:_ -> #b:_ ->\n t:typ pk i d l b ->\n c:comments ->\n typ pk i d l b\n\n | T_nlist:\n fieldname:string ->\n #wk:_ -> #pk:P.parser_kind true wk ->\n #i:_ -> #l:_ -> #d:_ -> #b:_ ->\n n:U32.t ->\n t:typ pk i d l b ->\n typ P.kind_nlist i d l false\n\n | T_at_most:\n fieldname:string ->\n #nz:_ -> #wk:_ -> #pk:P.parser_kind nz wk ->\n #i:_ -> #d:_ -> #l:_ -> #b:_ ->\n n:U32.t ->\n t:typ pk i d l b ->\n typ P.kind_t_at_most i d l false\n\n | T_exact:\n fieldname:string ->\n #nz:_ -> #wk:_ -> #pk:P.parser_kind nz wk ->\n #i:_ -> #d:_ -> #l:_ -> #b:_ ->\n n:U32.t ->\n t:typ pk i d l b ->\n typ P.kind_t_exact i d l false\n\n | T_string:\n fieldname:string ->\n #pk1:P.parser_kind true P.WeakKindStrongPrefix ->\n element_type:dtyp pk1 true inv_none disj_none loc_none ->\n terminator:dtyp_as_type element_type ->\n typ P.parse_string_kind inv_none disj_none loc_none false\n\n\n[@@specialize]\ninline_for_extraction\nlet coerce (#[@@@erasable]a:Type)\n (#[@@@erasable]b:Type)\n ( [@@@erasable]pf:squash (a == b))\n (x:a)\n : b\n = x\n\n[@@specialize]\nlet t_probe_then_validate\n (fieldname:string)\n (probe:CP.probe_fn)\n (len:U64.t)\n (dest:CP.copy_buffer_t)\n (#nz #wk:_) (#pk:P.parser_kind nz wk)\n (#has_reader #i #disj:_)\n (#l:_)\n (td:dtyp pk has_reader i disj l)\n : typ (parser_kind_of_itype UInt64)\n (join_inv i (NonTrivial (A.copy_buffer_inv dest)))\n (join_disj disj (disjoint (NonTrivial (A.copy_buffer_loc dest)) l))\n (join_loc l (NonTrivial (A.copy_buffer_loc dest)))\n false\n = T_with_dep_action fieldname\n (DT_IType UInt64)\n (fun src ->\n Atomic_action (Action_probe_then_validate td src len dest probe))\n\n\n(* Type denotation of `typ` *)\nlet rec as_type\n #nz #wk (#pk:P.parser_kind nz wk)\n #l #i #d #b\n (t:typ pk l i d b)\n : Tot Type0\n (decreases t)\n = match t with\n | T_false _ -> False\n\n | T_denoted _ td ->\n dtyp_as_type td\n\n | T_pair _ t1 t2 ->\n as_type t1 & as_type t2\n\n | T_dep_pair _ i t\n | T_dep_pair_with_action _ i t _ ->\n x:dtyp_as_type i & as_type (t x)\n\n | T_refine _ base refinement ->\n P.refine (dtyp_as_type base) refinement\n\n | T_refine_with_action _ base refinement _ ->\n P.refine (dtyp_as_type base) refinement\n\n | T_dep_pair_with_refinement _ base refinement t ->\n x:P.refine (dtyp_as_type base) refinement & as_type (t x)\n\n | T_dep_pair_with_refinement_and_action _ base refinement t _ ->\n x:P.refine (dtyp_as_type base) refinement & as_type (t x)\n\n | T_if_else b t0 t1 ->\n P.t_ite b (fun _ -> as_type (t0()))\n (fun _ -> as_type (t1()))\n\n | T_cases b t0 t1 ->\n P.t_ite b (fun _ -> as_type t0) (fun _ -> as_type t1)\n\n | T_with_action _ t _\n | T_with_comment _ t _ ->\n as_type t\n\n | T_with_dep_action _ i _ ->\n dtyp_as_type i\n\n | T_nlist _ n t ->\n P.nlist n (as_type t)\n\n | T_at_most _ n t ->\n P.t_at_most n (as_type t)\n\n | T_exact _ n t ->\n P.t_exact n (as_type t)\n\n | T_string _ elt_t terminator ->\n P.cstring (dtyp_as_type elt_t) terminator\n\n\n(* Parser denotation of `typ` *)\nlet rec as_parser\n #nz #wk (#pk:P.parser_kind nz wk)\n #l #i #d #b\n (t:typ pk l i d b)\n : Tot (P.parser pk (as_type t))\n (decreases t)\n = match t returns Tot (P.parser pk (as_type t)) with\n | T_false _ ->\n //assert_norm (as_type g T_false == False);\n P.parse_impos()\n\n | T_denoted _ d ->\n dtyp_as_parser d\n\n | T_pair _ t1 t2 ->\n //assert_norm (as_type g (T_pair t1 t2) == as_type g t1 * as_type g t2);\n let p1 = as_parser t1 in\n let p2 = as_parser t2 in\n P.parse_pair p1 p2\n\n | T_dep_pair _ i t\n | T_dep_pair_with_action _ i t _ ->\n //assert_norm (as_type g (T_dep_pair i t) == x:itype_as_type i & as_type g (t x));\n let pi = dtyp_as_parser i in\n P.parse_dep_pair pi (fun (x:dtyp_as_type i) -> as_parser (t x))\n\n | T_refine _ base refinement\n | T_refine_with_action _ base refinement _ ->\n //assert_norm (as_type g (T_refine base refinement) == P.refine (itype_as_type base) refinement);\n let pi = dtyp_as_parser base in\n P.parse_filter pi refinement\n\n | T_dep_pair_with_refinement _ base refinement k ->\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x)))\n\n\n | T_dep_pair_with_refinement_and_action _ base refinement k _ ->\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x)))\n\n | T_if_else b t0 t1 ->\n //assert_norm (as_type g (T_if_else b t0 t1) == P.t_ite b (as_type g t0) (as_type g t1));\n let p0 (_:squash b) =\n P.parse_weaken_right (as_parser (t0())) _\n in\n let p1 (_:squash (not b)) =\n P.parse_weaken_left (as_parser (t1())) _\n in\n P.parse_ite b p0 p1\n\n | T_cases b t0 t1 ->\n //assert_norm (as_type g (T_if_else b t0 t1) == P.t_ite b (as_type g t0) (as_type g t1));\n let p0 (_:squash b) =\n P.parse_weaken_right (as_parser t0) _\n in\n let p1 (_:squash (not b)) =\n P.parse_weaken_left (as_parser t1) _\n in\n P.parse_ite b p0 p1\n\n | T_with_action _ t a ->\n //assert_norm (as_type g (T_with_action t a) == as_type g t);\n as_parser t\n\n | T_with_dep_action _ i a ->\n //assert_norm (as_type g (T_with_dep_action i a) == itype_as_type i);\n dtyp_as_parser i\n\n | T_with_comment _ t c ->\n //assert_norm (as_type g (T_with_comment t c) == as_type g t);\n as_parser t\n\n | T_nlist _ n t ->\n P.parse_nlist n (as_parser t)\n\n | T_at_most _ n t ->\n P.parse_t_at_most n (as_parser t)\n\n | T_exact _ n t ->\n P.parse_t_exact n (as_parser t)\n\n | T_string _ elt_t terminator ->\n P.parse_string (dtyp_as_parser elt_t) terminator\n\n[@@specialize]\nlet rec as_reader #nz (#pk:P.parser_kind nz P.WeakKindStrongPrefix)\n (#[@@@erasable] inv:inv_index)\n (#[@@@erasable] d:disj_index)\n (#[@@@erasable] loc:loc_index)\n (t:typ pk inv d loc true)\n : leaf_reader (as_parser t)\n = match t with\n | T_denoted _n dt ->\n assert_norm (as_type (T_denoted _n dt) == dtyp_as_type dt);\n assert_norm (as_parser (T_denoted _n dt) == dtyp_as_parser dt);\n (| (), dtyp_as_leaf_reader dt |)\n | T_with_comment _n t _c ->\n assert_norm (as_type (T_with_comment _n t _c) == as_type t);\n assert_norm (as_parser (T_with_comment _n t _c) == as_parser t);\n as_reader t\n | T_false _n ->\n assert_norm (as_type (T_false _n) == False);\n assert_norm (as_parser (T_false _n) == P.parse_impos());\n (| (), A.read_impos |)\n\n(* The main result:\n A validator denotation of `typ`\n related by construction to the parser\n and type denotations\n*)\n#push-options \"--split_queries no --z3rlimit_factor 4 --z3cliopt 'smt.qi.eager_threshold=100'\"\n#restart-solver\nlet rec as_validator\n (typename:string)\n #nz #wk (#pk:P.parser_kind nz wk)\n (#[@@@erasable] inv:inv_index)\n (#[@@@erasable] disj:disj_index)\n (#[@@@erasable] loc:loc_index)\n #b\n (t:typ pk inv disj loc b)\n : Tot (A.validate_with_action_t #nz #wk #pk #(as_type t)\n (as_parser t)\n (interp_inv inv)\n (interp_disj disj)\n (interp_loc loc)\n b)\n (decreases t)\n = A.index_equations();\n match t\n returns Tot (\n A.validate_with_action_t #nz #wk #pk #(as_type t)\n (as_parser t)\n (interp_inv inv)\n (interp_disj disj)\n (interp_loc loc)\n b\n )\n with\n | T_false fn ->\n A.validate_with_error_handler typename fn (A.validate_impos())\n\n | T_denoted fn td ->\n assert_norm (as_type (T_denoted fn td) == dtyp_as_type td);\n assert_norm (as_parser (T_denoted fn td) == dtyp_as_parser td);\n A.validate_with_error_handler typename fn (A.validate_eta (dtyp_as_validator td))\n\n | T_pair fn t1 t2 ->\n assert_norm (as_type (T_pair fn t1 t2) == as_type t1 * as_type t2);\n assert_norm (as_parser (T_pair fn t1 t2) == P.parse_pair (as_parser t1) (as_parser t2));\n A.validate_pair fn\n (as_validator typename t1)\n (as_validator typename t2)\n\n | T_dep_pair fn i t ->\n assert_norm (as_type (T_dep_pair fn i t) == x:dtyp_as_type i & as_type (t x));\n assert_norm (as_parser (T_dep_pair fn i t) ==\n P.parse_dep_pair (dtyp_as_parser i) (fun (x:dtyp_as_type i) -> as_parser (t x)));\n A.validate_weaken_inv_loc (interp_inv inv) _ (interp_loc loc)\n (A.validate_dep_pair fn\n (A.validate_with_error_handler typename fn (dtyp_as_validator i))\n (dtyp_as_leaf_reader i)\n (fun x -> as_validator typename (t x)))\n\n | T_refine fn t f ->\n assert_norm (as_type (T_refine fn t f) == P.refine (dtyp_as_type t) f);\n assert_norm (as_parser (T_refine fn t f) == P.parse_filter (dtyp_as_parser t) f);\n A.validate_with_error_handler typename fn\n (A.validate_filter fn\n (dtyp_as_validator t)\n (dtyp_as_leaf_reader t)\n f \"reading field_value\" \"checking constraint\")\n\n | T_refine_with_action fn t f a ->\n assert_norm (as_type (T_refine_with_action fn t f a) == P.refine (dtyp_as_type t) f);\n assert_norm (as_parser (T_refine_with_action fn t f a) == P.parse_filter (dtyp_as_parser t) f);\n assert_norm (as_parser (T_refine fn t f) == P.parse_filter (dtyp_as_parser t) f);\n A.validate_with_error_handler typename fn\n (A.validate_filter_with_action fn\n (dtyp_as_validator t)\n (dtyp_as_leaf_reader t)\n f \"reading field_value\" \"checking constraint\"\n (fun x -> action_as_action (a x)))\n\n | T_dep_pair_with_refinement fn base refinement k ->\n assert_norm (as_type (T_dep_pair_with_refinement fn base refinement k) ==\n x:P.refine (dtyp_as_type base) refinement & as_type (k x));\n assert_norm (as_parser (T_dep_pair_with_refinement fn base refinement k) ==\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x))));\n A.validate_with_error_handler typename fn\n (A.validate_weaken_inv_loc _ _ _ (\n A.validate_dep_pair_with_refinement false fn\n (dtyp_as_validator base)\n (dtyp_as_leaf_reader base)\n refinement\n (fun x -> as_validator typename (k x))))\n\n | T_dep_pair_with_action fn base t act ->\n assert_norm (as_type (T_dep_pair_with_action fn base t act) ==\n x:dtyp_as_type base & as_type (t x));\n assert_norm (as_parser (T_dep_pair_with_action fn base t act) ==\n P.(dtyp_as_parser base `parse_dep_pair` (fun x -> as_parser (t x))));\n A.validate_with_error_handler typename fn\n (A.validate_weaken_inv_loc _ _ _ (\n A.validate_dep_pair_with_action\n (dtyp_as_validator base)\n (dtyp_as_leaf_reader base)\n (fun x -> action_as_action (act x))\n (fun x -> as_validator typename (t x))))\n\n | T_dep_pair_with_refinement_and_action fn base refinement k act ->\n assert_norm (as_type (T_dep_pair_with_refinement_and_action fn base refinement k act) ==\n x:P.refine (dtyp_as_type base) refinement & as_type (k x));\n assert_norm (as_parser (T_dep_pair_with_refinement_and_action fn base refinement k act) ==\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x))));\n A.validate_weaken_inv_loc _ _ _ (\n A.validate_dep_pair_with_refinement_and_action false fn\n (A.validate_with_error_handler typename fn\n (dtyp_as_validator base))\n (dtyp_as_leaf_reader base)\n refinement\n (fun x -> action_as_action (act x))\n (fun x -> as_validator typename (k x)))\n\n\n | T_if_else b t0 t1 ->\n assert_norm (as_type (T_if_else b t0 t1) == P.t_ite b (fun _ -> as_type (t0())) (fun _ -> as_type (t1 ())));\n let p0 (_:squash b) = P.parse_weaken_right (as_parser (t0())) _ in\n let p1 (_:squash (not b)) = P.parse_weaken_left (as_parser (t1())) _ in\n assert_norm (as_parser (T_if_else b t0 t1) == P.parse_ite b p0 p1);\n let v0 (_:squash b) =\n A.validate_weaken_right (as_validator typename (t0())) _\n in\n let v1 (_:squash (not b)) =\n A.validate_weaken_left (as_validator typename (t1())) _\n in\n A.validate_ite b p0 v0 p1 v1\n\n | T_cases b t0 t1 ->\n assert_norm (as_type (T_cases b t0 t1) == P.t_ite b (fun _ -> as_type t0) (fun _ -> as_type t1));\n let p0 (_:squash b) = P.parse_weaken_right (as_parser t0) _ in\n let p1 (_:squash (not b)) = P.parse_weaken_left (as_parser t1) _ in\n assert_norm (as_parser (T_cases b t0 t1) == P.parse_ite b p0 p1);\n let v0 (_:squash b) =\n A.validate_weaken_right (as_validator typename t0) _\n in\n let v1 (_:squash (not b)) =\n A.validate_weaken_left (as_validator typename t1) _\n in\n A.validate_ite b p0 v0 p1 v1\n\n | T_with_action fn t a ->\n assert_norm (as_type (T_with_action fn t a) == as_type t);\n assert_norm (as_parser (T_with_action fn t a) == as_parser t);\n A.validate_with_error_handler typename fn\n (A.validate_with_success_action fn\n (as_validator typename t)\n (action_as_action a))\n\n | T_with_dep_action fn i a ->\n assert_norm (as_type (T_with_dep_action fn i a) == dtyp_as_type i);\n assert_norm (as_parser (T_with_dep_action fn i a) == dtyp_as_parser i);\n A.validate_with_error_handler typename fn\n (A.validate_weaken_inv_loc _ _ _ (\n A.validate_with_dep_action fn\n (dtyp_as_validator i)\n (dtyp_as_leaf_reader i)\n (fun x -> action_as_action (a x))))\n\n\n | T_with_comment fn t c ->\n assert_norm (as_type (T_with_comment fn t c) == as_type t);\n assert_norm (as_parser (T_with_comment fn t c) == as_parser t);\n A.validate_with_comment c (as_validator typename t)\n\n | T_nlist fn n t ->\n assert_norm (as_type (T_nlist fn n t) == P.nlist n (as_type t));\n assert_norm (as_parser (T_nlist fn n t) == P.parse_nlist n (as_parser t));\n A.validate_with_error_handler typename fn\n (A.validate_nlist n (as_validator typename t))\n\n | T_at_most fn n t ->\n assert_norm (as_type (T_at_most fn n t) == P.t_at_most n (as_type t));\n assert_norm (as_parser (T_at_most fn n t) == P.parse_t_at_most n (as_parser t));\n A.validate_with_error_handler typename fn\n (A.validate_t_at_most n (as_validator typename t))\n\n | T_exact fn n t ->\n assert_norm (as_type (T_exact fn n t) == P.t_exact n (as_type t));\n assert_norm (as_parser (T_exact fn n t) == P.parse_t_exact n (as_parser t));\n A.validate_with_error_handler typename fn\n (A.validate_t_exact n (as_validator typename t))\n\n | T_string fn elt_t terminator ->\n assert_norm (as_type (T_string fn elt_t terminator) == P.cstring (dtyp_as_type elt_t) terminator);\n assert_norm (as_parser (T_string fn elt_t terminator) == P.parse_string (dtyp_as_parser elt_t) terminator);\n A.validate_with_error_handler typename fn\n (A.validate_string (dtyp_as_validator elt_t)\n (dtyp_as_leaf_reader elt_t)\n terminator)\n#pop-options\n[@@noextract_to \"krml\"; specialize]\ninline_for_extraction noextract\nlet validator_of #allow_reading #nz #wk (#k:P.parser_kind nz wk)\n (#[@@@erasable] i:inv_index)\n (#[@@@erasable] d:disj_index)\n (#[@@@erasable] l:loc_index)\n (t:typ k i d l allow_reading) =\n A.validate_with_action_t\n (as_parser t)\n (interp_inv i)\n (interp_disj d)\n (interp_loc l)\n allow_reading\n\n[@@noextract_to \"krml\"; specialize]\ninline_for_extraction noextract\nlet dtyp_of #nz #wk (#k:P.parser_kind nz wk)\n (#[@@@erasable] i:inv_index)\n (#[@@@erasable] d:disj_index)\n (#[@@@erasable] l:loc_index)\n #b (t:typ k i d l b) =\n dtyp k b i d l\n\nlet specialization_steps =\n [nbe;\n zeta;\n primops;\n iota;\n delta_attr [`%specialize];\n delta_only ([`%Some?;\n `%Some?.v;\n `%as_validator;\n `%nz_of_binding;\n `%wk_of_binding;\n `%pk_of_binding;\n `%inv_of_binding;\n `%loc_of_binding;\n `%type_of_binding;\n `%parser_of_binding;\n `%validator_of_binding;\n `%leaf_reader_of_binding;\n `%fst;\n `%snd;\n `%Mktuple2?._1;\n `%Mktuple2?._2]@projector_names)]\n\nlet specialize_tac steps (_:unit)\n : T.Tac unit\n = let open FStar.List.Tot in\n T.norm (steps@specialization_steps);\n T.trefl()\n\n[@@specialize]\nlet mk_global_binding #nz #wk\n (pk:P.parser_kind nz wk)\n ([@@@erasable] inv:inv_index)\n ([@@@erasable] disj:disj_index)\n ([@@@erasable] loc:loc_index)\n ([@@@erasable] p_t : Type0)\n ([@@@erasable] p_p : P.parser pk p_t)\n (p_reader: option (leaf_reader p_p))\n (b:bool)\n (p_v : A.validate_with_action_t p_p\n (interp_inv inv)\n (interp_disj disj)\n (interp_loc loc) b)\n ([@@@erasable] pf:squash (b == Some? p_reader))\n : global_binding\n = {\n parser_kind_nz = nz;\n parser_weak_kind = wk;\n parser_kind = pk;\n inv = inv;\n disj;\n loc = loc;\n p_t = p_t;\n p_p = p_p;\n p_reader = p_reader;\n p_v = p_v\n }\n\n[@@specialize]" }, { "file_name": "Steel.GhostMonotonicReference.fst", "name": "Steel.GhostMonotonicReference.ref", "opens_and_abbrevs": [ { "abbrev": "U", "full_module": "FStar.Universe" }, { "abbrev": "MHR", "full_module": "Steel.GhostMonotonicHigherReference" }, { "abbrev": "Preorder", "full_module": "FStar.Preorder" }, { "open": "Steel.Effect" }, { "open": "Steel.Effect.Atomic" }, { "open": "Steel.Memory" }, { "open": "Steel.FractionalPermission" }, { "open": "FStar.Ghost" }, { "open": "FStar.PCM" }, { "abbrev": "Preorder", "full_module": "FStar.Preorder" }, { "open": "Steel.Effect" }, { "open": "Steel.Effect.Atomic" }, { "open": "Steel.Memory" }, { "open": "Steel.FractionalPermission" }, { "open": "FStar.Ghost" }, { "open": "FStar.PCM" }, { "open": "Steel" }, { "open": "Steel" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0", "source_definition": "let ref a p = MHR.ref (FStar.Universe.raise_t a) (raise_preorder p)", "source_range": { "start_line": 36, "start_col": 0, "end_line": 36, "end_col": 67 }, "interleaved": false, "definition": "fun a p ->\n Steel.GhostMonotonicHigherReference.ref (FStar.Universe.raise_t a)\n (Steel.GhostMonotonicReference.raise_preorder p)", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Preorder.preorder", "Steel.GhostMonotonicHigherReference.ref", "FStar.Universe.raise_t", "Steel.GhostMonotonicReference.raise_preorder" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "a: Type0 -> p: FStar.Preorder.preorder a -> Type0", "prompt": "let ref a p =\n ", "expected_response": "MHR.ref (FStar.Universe.raise_t a) (raise_preorder p)", "source": { "project_name": "steel", "file_name": "lib/steel/Steel.GhostMonotonicReference.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Steel.GhostMonotonicReference.fst", "checked_file": "dataset/Steel.GhostMonotonicReference.fst.checked", "interface_file": true, "dependencies": [ "dataset/Steel.Memory.fsti.checked", "dataset/Steel.GhostMonotonicHigherReference.fsti.checked", "dataset/Steel.FractionalPermission.fst.checked", "dataset/Steel.Effect.Atomic.fsti.checked", "dataset/Steel.Effect.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Universe.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.PCM.fst.checked", "dataset/FStar.Ghost.fsti.checked" ] }, "definitions_in_context": [ "let raise_preorder (#a:Type0) (p:Preorder.preorder a)\n : Preorder.preorder (U.raise_t a)\n = fun (x0 x1:U.raise_t a) ->\n p (U.downgrade_val x0) (U.downgrade_val x1)", "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0" ], "closest": [ "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\nlet ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\n = MR.ref a p", "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\nlet ref a p = MHR.ref (FStar.Universe.raise_t a) (raise_preorder p)", "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\nlet ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\n = MR.ref a p", "val ref (a:Type u#1) (p:Preorder.preorder a)\n : Type u#0\nlet ref a p = PR.ref (history a p) pcm_history", "val ref (a:Type u#1) (p:Preorder.preorder a)\n : Type u#0\nlet ref a p = M.ref (history a p) pcm_history", "val ref (a:Type u#0)\n : Type u#0\nlet ref (a:Type u#0)\n : Type u#0\n = R.ghost_ref a", "val ref ([@@@ strictly_positive] a:Type u#1)\n : Type0\nlet ref (a:Type u#1)\n : Type0\n = R.ref a", "val ref ([@@@ strictly_positive] a:Type u#1)\n : Type0\nlet ref a = ref' a", "val ref (a:Type u#0) (p:pcm a) : Type u#0\nlet ref (a:Type u#0) (p:pcm a) : Type u#0 =\n G.ref (raise_t u#0 u#1 a) (UP.raise p)", "val ref ([@@@unused] a:Type u#1) : Type u#0\nlet ref a = Mem.ref (fractional a) pcm_frac", "val ref ([@@@unused] a:Type u#1) : Type u#0\nlet ref (a:Type u#1) = ghost_pcm_ref (pcm_frac #a)", "val ref ([@@@unused]a:Type u#1) : Type u#0\nlet ref (a:Type u#1) = pcm_ref (pcm_frac #a)", "val ref ([@@@unused] a:Type u#0) : Type u#0\nlet ref a = H.ref (U.raise_t a)", "val ref ([@@@unused] a:Type u#0) : Type u#0\nlet ref a = H.ref (U.raise_t a)", "val ref ([@@@ unused] a:Type0)\n : Type0\nlet ref (a:Type0)\n : Type0\n = R.ref a", "val ref (a:Type) (p:pcm a) : Type0\nlet ref (a:Type) (p:pcm a) = erased (Steel.Memory.ref a p)", "val ref (a:Type0) : Type0\nlet ref (a:Type) = nat", "val ref ([@@@unused] a:Type u#a) ([@@@unused] p:pcm a) : Type u#0\nlet ref (a:Type u#a) (p:pcm a) = ref a p", "val ref (a: Type0) : Type0\nlet ref (a:Type0) : Type0 = ref a", "val ref (a: Type0) : Type0\nlet ref (a : Type0) : Type0 = (r: A.array a { A.length r == 1 \\/ r == A.null })", "val alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n : STT (ref a p) emp (fun r -> pts_to r full_perm v)\nlet alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n : STT (ref a p) emp (fun r -> pts_to r full_perm v)\n = let x = coerce_steel (fun _ -> MR.alloc p v) in\n return x", "val witnessed (#a:Type u#0) (#p:Preorder.preorder a) (r:ref a p) (fact:property a)\n : Type0\nlet witnessed (#a:Type u#0)\n (#p:Preorder.preorder a)\n (r:ref a p)\n (fact:property a)\n = MHR.witnessed r (lift_property fact)", "val witnessed (#a:Type u#0) (#p:Preorder.preorder a) (r:ref a p) (fact:property a)\n : Type0\nlet witnessed (#a:Type u#0)\n (#p:Preorder.preorder a)\n (r:ref a p)\n (fact:property a)\n : Type0\n = MR.witnessed r fact", "val witnessed (#a:Type u#0) (#p:Preorder.preorder a) (r:ref a p) (fact:property a)\n : Type0\nlet witnessed (#a:Type u#0)\n (#p:Preorder.preorder a)\n (r:ref a p)\n (fact:property a)\n : Type0\n = MR.witnessed r fact", "val witnessed (#a:Type u#1) (#p:Preorder.preorder a) (r:ref a p) (fact:property a)\n : Type0\nlet witnessed #a #p r fact =\n PR.witnessed r (lift_fact fact)", "val witnessed (#a:Type u#1) (#p:Preorder.preorder a) (r:ref a p) (fact:property a)\n : Type0\nlet witnessed #a #p r fact =\n M.witnessed r (lift_fact fact)", "val token (#a:Type) (#b:preorder a) (r:mref a b) (p:(a -> Type){stable p b}) : Type0\nlet token #_ #_ r p = witnessed (p_pred r p)", "val mref (a:Type) (r:preorder_t a) : Type0\nlet mref (a:Type) (r:preorder_t a) = nat", "val null (#a:Type0) \n : ref a\nlet null (#a:Type0)\n : ref a\n = R.null #a", "val raise_preorder (#a: Type0) (p: Preorder.preorder a) : Preorder.preorder (U.raise_t a)\nlet raise_preorder (#a:Type0) (p:Preorder.preorder a)\n : Preorder.preorder (U.raise_t a)\n = fun (x0 x1:U.raise_t a) ->\n p (U.downgrade_val x0) (U.downgrade_val x1)", "val null (#a:Type u#1) : ref a\nlet null #a = Mem.null #(fractional a) #pcm_frac", "val null (#a:Type) \n : ref a\nlet null (#a:Type)\n : ref a\n = R.null #a", "val ref ([@@@unused] a:Type0) : Type0\nlet ref a = H.ref (U.raise_t a)", "val alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n : SteelT (ref a p) emp (fun r -> pts_to r full_perm v)\nlet alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n = let h = Current [v] full_perm in\n assert (compatible pcm_history h h);\n let x : ref a p = alloc h in\n intro_pure_full x v h;\n x", "val alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n : SteelT (ref a p) emp (fun r -> pts_to r full_perm v)\nlet alloc (#a:Type) (p:Preorder.preorder a) (v:a)\n : SteelT (ref a p) emp (fun r -> pts_to r full_perm v)\n = let r = MHR.alloc (raise_preorder p) (U.raise_val v) in\n rewrite_slprop\n (MHR.pts_to r full_perm (hide (U.raise_val v)))\n (pts_to r full_perm v)\n (fun _ -> ());\n return r", "val MRefHeap.preorder_t = a: Type0 -> Type\nlet preorder_t (a:Type0) = preorder a", "val token_p (#a:Type0) (#rel:preorder a) (r:mreference a rel) (p:mem_predicate) :Type0\nlet token_p #_ #_ r p = witnessed (mem_rel_predicate r p)", "val witnessed (state:Type u#a)\n (rel:P.preorder state)\n (p:s_predicate state)\n : Type0\nlet witnessed (state:Type u#a)\n (rel:P.preorder state)\n (p:s_predicate state)\n : Type0\n = unit", "val pts_to (#a:Type)\n (#p:Preorder.preorder a)\n (r:ref a p)\n ([@@@smt_fallback]f:perm)\n ([@@@smt_fallback]v:a)\n : vprop\nlet pts_to (#a:Type)\n (#p:Preorder.preorder a)\n (r:ref a p)\n ([@@@smt_fallback]f:perm)\n ([@@@smt_fallback]v:a)\n : vprop\n = MR.pts_to #a #p r f v", "val pts_to (#a:Type)\n (#p:Preorder.preorder a)\n (r:ref a p)\n ([@@@smt_fallback]f:perm)\n ([@@@smt_fallback]v:a)\n : vprop\nlet pts_to (#a:Type)\n (#p:Preorder.preorder a)\n (r:ref a p)\n ([@@@smt_fallback]f:perm)\n ([@@@smt_fallback]v:a)\n : vprop\n = MR.pts_to #a #p r f v", "val ref_null (#a:Type u#a) (p:pcm a) : ref a p\nlet ref_null (#a:Type u#a) (p:pcm a) = core_ref_null", "val fresh_ref (#a: Type) (#rel: preorder a) (r: mreference a rel) (m0 m1: mem) : Type0\nlet fresh_ref (#a:Type) (#rel:preorder a) (r:mreference a rel) (m0:mem) (m1:mem) :Type0 =\n let i = frameOf r in\n Heap.fresh (as_ref r) (get_hmap m0 `Map.sel` i) (get_hmap m1 `Map.sel` i)", "val pts_to_sl (#a:Type)\n (#p:Preorder.preorder a)\n (r:ref a p)\n (f:perm)\n (v:a)\n : slprop u#1\nlet pts_to_sl (#a:Type) (#p:Preorder.preorder a)\n (r:ref a p)\n (f:perm)\n (v:a)\n = MHR.pts_to_sl r f (hide (U.raise_val v))", "val ref (a: Type u#a) (pcm: pcm a) : Type u#0\nlet ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref", "val ref (a: Type u#a) (pcm: pcm a) : Type u#0\nlet ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref", "val ref (a: Type u#a) (pcm: pcm a) : Type u#0\nlet ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref", "val ref (a: Type u#a) (pcm: pcm a) : Type u#0\nlet ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref", "val closure (#a:Type u#a) (r:binrel u#a u#r a) : preorder u#a u#0 a\nlet closure #a r =\n closure_reflexive r;\n closure_transitive r;\n _closure0 r", "val flip (#a: Type u#a) (p: preorder a) : preorder a\nlet flip (#a: Type u#a) (p:preorder a) : preorder a = fun x y -> p y x", "val flip (#a: Type u#a) (p: preorder a) : preorder a\nlet flip (#a: Type u#a) (p:preorder a) : preorder a = fun x y -> p y x", "val ghost_ref (a:Type u#0) : Type u#0\nlet ghost_ref a = H.ghost_ref (U.raise_t a)", "val pts_to_sl (#a:Type) (#p:Preorder.preorder a) (r:ref a p) (f:perm) (v:a)\n : slprop u#1\nlet pts_to_sl r f v = hp_of (pts_to' r f v)", "val immutable_preorder (a: Type0) : srel a\nlet immutable_preorder (a:Type0) :srel a = fun s1 s2 -> Seq.equal s1 s2", "val repr (a:Type)\n (framed:bool)\n (pre:pre_t)\n (post:post_t a)\n (req:pure_pre)\n (ens:pure_post a)\n : Type u#2\nlet repr a framed pre post req ens : Type u#2 =\n Steel.Effect.repr a framed pre post (fun _ -> req) (fun _ v _ -> ens v)", "val as_ref (#a:Type0) (#rel:preorder a) (x:mreference a rel)\n :Heap.mref a rel\nlet as_ref #_ #_ x = MkRef?.ref x", "val ghost_ref (a:Type u#1) : Type u#0\nlet ghost_ref a = erased (ref a)", "val repr (a:Type u#a) //result type\n (already_framed:bool) //framed or not\n (opened_invariants:inames) //which invariants are we relying on\n (g:observability) //is this a ghost computation?\n (pre:pre_t) //expects vprop\n (post:post_t a) //provides a -> vprop\n (req:pure_pre) //a prop refinement as a precondition\n (ens:pure_post a) //an (a -> prop) as a postcondition\n : Type u#(max a 2)\nlet repr (a:Type u#a)\n (already_framed:bool)\n (opened_invariants:inames)\n (g:observability)\n (pre:pre_t)\n (post:post_t a)\n (req:Type0)\n (ens:a -> Type0)\n : Type u#(max a 2)\n = SEA.repr a already_framed opened_invariants g pre post\n (fun _ -> req)\n (fun _ x _ -> ens x)", "val null (#a:Type0) : ref a\nlet null #a = H.null #(U.raise_t a)", "val null (#a:Type0) : ref a\nlet null #a = A.null #a", "val pcm_ref\n (#[@@@unused] a:Type u#a)\n ([@@@unused] p:FStar.PCM.pcm a)\n: Type0\nlet pcm_ref #a p = PulseCore.Action.ref a p", "val t:\n a:Type u#a\n -> Type u#a\nlet t a = (l:len_t & raw a l)", "val MRefST.mref0 = a: Type0 -> r: MRefHeap.preorder_t a -> Type0\nlet mref0 = mref", "val read : #a:Type ->\n #r:preorder a ->\n\t m:mref a r ->\n\t MRefST a (fun _ -> True)\n (fun h0 x h1 -> h0 == h1 /\\\n\t\t contains m h1 /\\\n\t\t\t\t sel h1 m == x)\nlet read #a #r m =\n let h = ist_get () in\n ist_recall (contains m); //recalling that the current heap must contain the given reference\n sel h m", "val t : a:Type u#a -> Type u#a\nlet t a = list a", "val snapshot (#v: Type0) (#p: preorder v) (#s: anchor_rel p) (a: avalue s) : avalue s\nlet snapshot (#v:Type0) (#p:preorder v) (#s:anchor_rel p)\n (a: avalue s)\n : avalue s\n = (None, None), avalue_val a", "val recall : #a:Type ->\n #r:preorder a ->\n\t m:mref a r ->\n\t p:predicate heap{stable_on_heap m p} ->\n\t MRefST unit (fun h0 -> ist_witnessed p)\n\t (fun h0 _ h1 -> h0 == h1 /\\\n\t\t\t p h1)\nlet recall #a #r m p =\n ist_recall p", "val loc_mreference (#a: Type) (#p: Preorder.preorder a) (b: HS.mreference a p) : GTot loc\nlet loc_mreference\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot loc\n= loc_addresses true (HS.frameOf b) (Set.singleton (HS.as_addr b))", "val loc_mreference (#a: Type) (#p: Preorder.preorder a) (b: HS.mreference a p) : GTot loc\nlet loc_mreference\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot loc\n= loc_addresses true (HS.frameOf b) (Set.singleton (HS.as_addr b))", "val sel : #a:Type ->\n #r:preorder a ->\n h:heap ->\n\t m:mref a r{contains h m} ->\n a\nlet sel #a #b h m =\n match snd h m with\n | Some (| _ , (x , _) |) -> x", "val alloc (#opened: _) (#a:Type) (p:Preorder.preorder a) (v:a)\n : STGhostT (ref a p) opened emp (fun r -> pts_to r full_perm v)\nlet alloc #opened (#a:Type) (p:Preorder.preorder a) (v:a)\n : STGhostT (ref a p) opened emp (fun r -> pts_to r full_perm v)\n = let x = coerce_ghost (fun _ -> MR.alloc p v) in\n x", "val return (#s:Type u#s)\r\n (#rel:preorder s)\r\n (#a:Type u#a)\r\n (x:a)\r\n: mst rel a (fun _ -> True) (fun s0 v s1 -> x == v /\\ s0 == s1)\nlet return x\r\n= fun s0 -> x, s0", "val contains (#a:Type) (#r:preorder_t a) (h:heap) (m:mref a r) : Type0\nlet contains (#a:Type) (#r:preorder_t a) (h:heap) (m:mref a r) : GTot Type0 =\n exists (v:heap_cell).\n snd h m == Some v /\\\n dfst v == a /\\\n snd #(dfst v) #(preorder_t a) (dsnd v) == r", "val alloc (#a: Type) (#rel: preorder a) (init: a)\n : ST (mref a rel)\n (fun h -> True)\n (fun h0 r h1 -> fresh r h0 h1 /\\ modifies Set.empty h0 h1 /\\ sel h1 r == init)\nlet alloc (#a:Type) (#rel:preorder a) (init:a)\n :ST (mref a rel)\n (fun h -> True)\n (fun h0 r h1 -> fresh r h0 h1 /\\ modifies Set.empty h0 h1 /\\ sel h1 r == init)\n = let h0 = gst_get () in\n let r, h1 = alloc rel h0 init false in\n gst_put h1;\n gst_witness (contains_pred r);\n r", "val pts_to_sl (#a:Type) (#p:Preorder.preorder a) (r:ref a p) (f:perm) (v:erased a)\n : slprop u#1\nlet pts_to_sl r f v = hp_of (pts_to' r f v)", "val read (#a:Type0) (r:ref a) :STATE a (fun p h -> p (sel h r) h)\nlet read #_ r = read r", "val write (#a:Type) (#p:Preorder.preorder a) (#v:erased a)\n (r:ref a p) (x:a)\n : ST unit\n (pts_to r full_perm v)\n (fun v -> pts_to r full_perm x)\n (requires p v x)\n (ensures fun _ -> True)\nlet write (#a:Type) (#p:Preorder.preorder a) (#v:erased a)\n (r:ref a p) (x:a)\n : ST unit\n (pts_to r full_perm v)\n (fun v -> pts_to r full_perm x)\n (requires p v x)\n (ensures fun _ -> True)\n = coerce_steel (fun _ -> MR.write r x)", "val alloc (#a: Type) (#rel: P.preorder a) (init: a)\n : HoareST (mref a rel)\n (fun _ -> True)\n (fun h0 r h1 -> fresh r h0 h1 /\\ modifies Set.empty h0 h1 /\\ sel h1 r == init)\nlet alloc (#a:Type) (#rel:P.preorder a) (init:a)\n: HoareST (mref a rel)\n (fun _ -> True)\n (fun h0 r h1 ->\n fresh r h0 h1 /\\\n modifies Set.empty h0 h1 /\\\n sel h1 r == init)\n= HoareST?.reflect (fun _ -> alloc init)", "val alloc (#a: Type) (#rel: P.preorder a) (init: a)\n : HoareST (mref a rel)\n (fun _ -> True)\n (fun h0 r h1 -> fresh r h0 h1 /\\ modifies Set.empty h0 h1 /\\ sel h1 r == init)\nlet alloc (#a:Type) (#rel:P.preorder a) (init:a)\n: HoareST (mref a rel)\n (fun _ -> True)\n (fun h0 r h1 ->\n fresh r h0 h1 /\\\n modifies Set.empty h0 h1 /\\\n sel h1 r == init)\n= HoareST?.reflect (fun _ -> alloc init)", "val alloc : #a:Type ->\n r:preorder a ->\n\t x:a ->\n\t MRefST (mref a r) (fun _ -> True)\n (fun h0 m h1 -> ~(contains m h0) /\\\n\t\t\t\t\t fst (alloc_ref h0 a r x) == m /\\\n\t\t\t\t\t snd (alloc_ref h0 a r x) == h1)\nlet alloc #a r x =\n let h0 = ist_get () in\n let mh1 = alloc_ref h0 a r x in\n ist_put (snd mh1);\n ist_witness (contains (fst mh1)); //witnessing that the current heap contains the generated reference\n fst mh1", "val witness : #a:Type ->\n #r:preorder a ->\n\t m:mref a r ->\n\t p:predicate heap{stable_on_heap m p} ->\n\t MRefST unit (fun h0 -> p h0)\n\t (fun h0 _ h1 -> h0 == h1 /\\\n\t\t\t ist_witnessed p)\nlet witness #a #r m p =\n ist_witness p", "val witness_p (#a:Type0) (#rel:preorder a) (r:mreference a rel) (p:mem_predicate)\n :ST unit (fun h0 -> p h0 /\\ p `stable_on` r)\n (fun h0 _ h1 -> h0 == h1 /\\ token_p r p)\nlet witness_p #_ #_ r p =\n gst_recall (ref_contains_pred r);\n gst_recall (region_contains_pred (HS.frameOf r));\n HS.lemma_next_addr_contained_refs_addr ();\n gst_witness (mem_rel_predicate r p)", "val mref (a: Type0) (rel: preorder a) : Type0\nlet mref (a:Type0) (rel:preorder a) : Type0 = core_mref a", "val read (#a: Type) (#rel: preorder a) (r: mref a rel) : STATE a (fun p h -> p (sel h r) h)\nlet read (#a:Type) (#rel:preorder a) (r:mref a rel) :STATE a (fun p h -> p (sel h r) h)\n = let h0 = gst_get () in\n gst_recall (contains_pred r);\n Heap.lemma_sel_equals_sel_tot_for_contained_refs h0 r;\n sel_tot h0 r", "val alloc (#opened: _) (#a:Type) (p:Preorder.preorder a) (v:a)\n : SteelGhostT (ref a p) opened emp (fun r -> pts_to r full_perm v)\nlet alloc #_ (#a:Type) (p:Preorder.preorder a) (v:a)\n = let h = Current [v] full_perm in\n assert (compatible pcm_history h h);\n let x : ref a p = alloc h in\n intro_pure_full x v h;\n x", "val write : #a:Type ->\n #r:preorder a ->\n\t m:mref a r ->\n\t x:a ->\n\t MRefST unit (fun h0 -> contains m h0 /\\\n\t r (sel h0 m) x)\n (fun h0 _ h1 -> contains m h0 /\\\n\t\t\t h1 == upd h0 m x)\nlet write #a #r m x =\n let h0 = ist_get () in\n ist_recall (contains m); //recalling that the current heap must contain the given reference\n let h1 = upd h0 m x in\n ist_put h1", "val nmst (#s:Type u#s)\r\n (rel:FStar.Preorder.preorder s)\r\n (a:Type u#a)\r\n (pre:s -> prop)\r\n (post:s -> a -> s -> prop)\r\n: Type u#0\nlet nmst #s rel a pre post =\r\n unit -> Dv (nmst' #s rel a pre post)", "val grows_p (#a: Type) (p: (seq a -> Type)) : Preorder.preorder (s: seq a {p s})\nlet grows_p (#a:Type) (p:seq a -> Type) :Preorder.preorder (s:seq a{p s}) =\n fun s1 s2 -> grows s1 s2", "val repr (a:Type u#a)\n (already_framed:bool)\n (opened_invariants:inames)\n (g:observability)\n (pre:pre_t)\n (post:post_t a)\n (req:req_t pre)\n (ens:ens_t pre a post)\n : Type u#(max a 2)\nlet repr a framed opened f pre post req ens =\n action_except_full a opened (hp_of pre) (to_post post)\n (req_to_act_req req) (ens_to_act_ens ens)", "val raw ([@@@strictly_positive] a:Type u#a)\n (l:len_t)\n : Type u#a\nlet raw a l = s:S.seq a{S.length s = U32.v l}", "val ( ! ) (#a: Type) (#rel: P.preorder a) (r: mref a rel)\n : HoareST a (fun _ -> True) (fun h0 x h1 -> h0 == h1 /\\ x == sel h1 r)\nlet op_Bang (#a:Type) (#rel:P.preorder a) (r:mref a rel)\n: HoareST a\n (fun _ -> True)\n (fun h0 x h1 ->\n h0 == h1 /\\\n x == sel h1 r)\n= HoareST?.reflect (fun _ -> read r)", "val ( ! ) (#a: Type) (#rel: P.preorder a) (r: mref a rel)\n : HoareST a (fun _ -> True) (fun h0 x h1 -> h0 == h1 /\\ x == sel h1 r)\nlet op_Bang (#a:Type) (#rel:P.preorder a) (r:mref a rel)\n: HoareST a\n (fun _ -> True)\n (fun h0 x h1 ->\n h0 == h1 /\\\n x == sel h1 r)\n= HoareST?.reflect (fun _ -> read r)", "val ( ! ) (#a: Type) (#rel: preorder a) (r: mref a rel) : STATE a (fun p h -> p (sel h r) h)\nlet op_Bang (#a:Type) (#rel:preorder a) (r:mref a rel)\n : STATE a (fun p h -> p (sel h r) h)\n= read #a #rel r", "val return (#s:Type u#s)\r\n (#rel:preorder s)\r\n (#a:Type u#a)\r\n (x:a)\r\n: nmst rel a (fun _ -> True) (fun s0 v s1 -> x == v /\\ s0 == s1)\nlet return (#s:Type u#s)\r\n (#rel:preorder s)\r\n (#a:Type u#a)\r\n (x:a)\r\n: nmst rel a (fun _ -> True) (fun s0 v s1 -> x == v /\\ s0 == s1)\r\n= fun () s0 t c -> (x, s0, c)", "val ret (a: Type u#a) (x: a) (p: (a -> hm.r)) : comp a (p x) p\nlet ret (a:Type u#a) (x:a) (p: a -> hm.r)\n : comp a (p x) p\n = fun _ -> return x p", "val ret (a: Type u#a) (x: a) (p: (a -> hm.r)) : comp a (p x) p\nlet ret (a:Type u#a) (x:a) (p: a -> hm.r)\n : comp a (p x) p\n = fun _ -> return x p", "val write (#opened: _) (#a:Type) (#p:Preorder.preorder a) (#v:a)\n (r:ref a p) (x:a)\n : STGhost unit opened\n (pts_to r full_perm v)\n (fun v -> pts_to r full_perm x)\n (requires p v x)\n (ensures fun _ -> True)\nlet write #opened (#a:Type) (#p:Preorder.preorder a) (#v:a)\n (r:ref a p) (x:a)\n : STGhost unit opened\n (pts_to r full_perm v)\n (fun v -> pts_to r full_perm x)\n (requires p v x)\n (ensures fun _ -> True)\n = coerce_ghost (fun _ -> MR.write r x)", "val repr (a:Type) (framed:bool) (pre:pre_t) (post:post_t a) (req:req_t pre) (ens:ens_t pre a post) : Type u#2\nlet repr (a:Type) (_:bool) (pre:pre_t) (post:post_t a) (req:req_t pre) (ens:ens_t pre a post) =\n Sem.action_t #state #a (hp_of pre) (to_post post)\n ((req_to_act_req req))\n ((ens_to_act_ens ens))", "val recall_p (#a:Type0) (#rel:preorder a) (r:mreference a rel) (p:mem_predicate)\n :ST unit (fun h0 -> ((is_eternal_region (HS.frameOf r) /\\ not (HS.is_mm r)) \\/ h0 `HS.contains` r) /\\ token_p r p)\n (fun h0 _ h1 -> h0 == h1 /\\ h0 `HS.contains` r /\\ p h0)\nlet recall_p #_ #_ r p =\n gst_recall (ref_contains_pred r);\n gst_recall (region_contains_pred (HS.frameOf r));\n gst_recall (mem_rel_predicate r p)", "val squash (p: Type u#a) : Type0\nlet squash (p:Type u#a) : Type0 = squash p", "val addr_of (#a:Type) (#r:preorder_t a) (m:mref a r) : nat\nlet addr_of (#a:Type) (#r:preorder_t a) (m:mref a r) : nat = m" ], "closest_src": [ { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.ref" }, { "project_name": "steel", "file_name": "Steel.MonotonicReference.fst", "name": "Steel.MonotonicReference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.GhostMonotonicReference.fst", "name": "Steel.ST.GhostMonotonicReference.ref" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicHigherReference.fst", "name": "Steel.GhostMonotonicHigherReference.ref" }, { "project_name": "steel", "file_name": "Steel.MonotonicHigherReference.fst", "name": "Steel.MonotonicHigherReference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.GhostHigherReference.fst", "name": "Steel.ST.GhostHigherReference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.GhostPCMReference.fst", "name": "Steel.ST.GhostPCMReference.ref" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherReference.fst", "name": "Pulse.Lib.HigherReference.ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.Reference.fst", "name": "Pulse.Lib.Reference.ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.ref" }, { "project_name": "steel", "file_name": "Steel.GhostPCMReference.fst", "name": "Steel.GhostPCMReference.ref" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.ref" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.ref" }, { "project_name": "steel", "file_name": "SelectorLogic.fst", "name": "SelectorLogic.ref" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fsti", "name": "Steel.ArrayRef.ref" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.alloc" }, { "project_name": "steel", "file_name": "Steel.MonotonicReference.fst", "name": "Steel.MonotonicReference.witnessed" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.witnessed" }, { "project_name": "steel", "file_name": "Steel.ST.GhostMonotonicReference.fst", "name": "Steel.ST.GhostMonotonicReference.witnessed" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicHigherReference.fst", "name": "Steel.GhostMonotonicHigherReference.witnessed" }, { "project_name": "steel", "file_name": "Steel.MonotonicHigherReference.fst", "name": "Steel.MonotonicHigherReference.witnessed" }, { "project_name": "FStar", "file_name": "FStar.MRef.fst", "name": "FStar.MRef.token" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.mref" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.null" }, { "project_name": "steel", "file_name": "Steel.MonotonicReference.fst", "name": "Steel.MonotonicReference.raise_preorder" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.null" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.null" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ref" }, { "project_name": "steel", "file_name": "Steel.MonotonicHigherReference.fst", "name": "Steel.MonotonicHigherReference.alloc" }, { "project_name": "steel", "file_name": "Steel.MonotonicReference.fst", "name": "Steel.MonotonicReference.alloc" }, { "project_name": "FStar", "file_name": "MRefHeap.fsti", "name": "MRefHeap.preorder_t" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fst", "name": "FStar.HyperStack.ST.token_p" }, { "project_name": "FStar", "file_name": "FStar.Witnessed.Core.fst", "name": "FStar.Witnessed.Core.witnessed" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.pts_to" }, { "project_name": "steel", "file_name": "Steel.ST.GhostMonotonicReference.fst", "name": "Steel.ST.GhostMonotonicReference.pts_to" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.ref_null" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.fresh_ref" }, { "project_name": "steel", "file_name": "Steel.MonotonicReference.fst", "name": "Steel.MonotonicReference.pts_to_sl" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fsti", "name": "PulseCore.Heap.ref" }, { "project_name": "steel", "file_name": "Steel.Memory.fsti", "name": "Steel.Memory.ref" }, { "project_name": "steel", "file_name": "Steel.Heap.fsti", "name": "Steel.Heap.ref" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fsti", "name": "PulseCore.Memory.ref" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fst", "name": "FStar.ReflexiveTransitiveClosure.closure" }, { "project_name": "steel", "file_name": "PulseCore.Preorder.fst", "name": "PulseCore.Preorder.flip" }, { "project_name": "steel", "file_name": "Steel.Preorder.fst", "name": "Steel.Preorder.flip" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ghost_ref" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicHigherReference.fst", "name": "Steel.GhostMonotonicHigherReference.pts_to_sl" }, { "project_name": "FStar", "file_name": "LowStar.ImmutableBuffer.fst", "name": "LowStar.ImmutableBuffer.immutable_preorder" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.fst", "name": "Steel.ST.Effect.repr" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.as_ref" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.ghost_ref" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.AtomicAndGhost.fst", "name": "Steel.ST.Effect.AtomicAndGhost.repr" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.null" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.null" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.pcm_ref" }, { "project_name": "FStar", "file_name": "FStar.Vector.Base.fst", "name": "FStar.Vector.Base.t" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.mref0" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.read" }, { "project_name": "noise-star", "file_name": "Spec.Noise.Map.fst", "name": "Spec.Noise.Map.t" }, { "project_name": "steel", "file_name": "Steel.FractionalAnchoredPreorder.fst", "name": "Steel.FractionalAnchoredPreorder.snapshot" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.recall" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fsti", "name": "FStar.Modifies.loc_mreference" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_mreference" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.sel" }, { "project_name": "steel", "file_name": "Steel.ST.GhostMonotonicReference.fst", "name": "Steel.ST.GhostMonotonicReference.alloc" }, { "project_name": "steel", "file_name": "PulseCore.MonotonicStateMonad.fst", "name": "PulseCore.MonotonicStateMonad.return" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.contains" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.alloc" }, { "project_name": "steel", "file_name": "Steel.MonotonicHigherReference.fst", "name": "Steel.MonotonicHigherReference.pts_to_sl" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.read" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.write" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.alloc" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.alloc" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.alloc" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.witness" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fst", "name": "FStar.HyperStack.ST.witness_p" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.mref" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.read" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicHigherReference.fst", "name": "Steel.GhostMonotonicHigherReference.alloc" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.write" }, { "project_name": "steel", "file_name": "PulseCore.NondeterministicMonotonicStateMonad.fst", "name": "PulseCore.NondeterministicMonotonicStateMonad.nmst" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Seq.fst", "name": "FStar.Monotonic.Seq.grows_p" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.repr" }, { "project_name": "FStar", "file_name": "FStar.Vector.Base.fst", "name": "FStar.Vector.Base.raw" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.op_Bang" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.op_Bang" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.op_Bang" }, { "project_name": "steel", "file_name": "PulseCore.NondeterministicMonotonicStateMonad.fst", "name": "PulseCore.NondeterministicMonotonicStateMonad.return" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParNDSDiv.fst", "name": "OPLSS2021.ParNDSDiv.ret" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParDiv.fst", "name": "OPLSS2021.ParDiv.ret" }, { "project_name": "steel", "file_name": "Steel.ST.GhostMonotonicReference.fst", "name": "Steel.ST.GhostMonotonicReference.write" }, { "project_name": "steel", "file_name": "Steel.Effect.fst", "name": "Steel.Effect.repr" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fst", "name": "FStar.HyperStack.ST.recall_p" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.squash" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.addr_of" } ], "selected_premises": [ "Steel.GhostMonotonicReference.raise_preorder", "Steel.Preorder.pcm_history", "Steel.Preorder.history_val", "FStar.Heap.trivial_preorder", "FStar.List.Tot.Base.map", "Steel.Memory.hmem", "FStar.List.Tot.Base.length", "Steel.Memory.full_mem", "FStar.List.Tot.Base.op_At", "FStar.ST.op_Bang", "FStar.PCM.compatible", "FStar.Real.one", "FStar.Reflection.V2.Derived.mk_e_app", "FStar.Reflection.V2.Derived.mk_app", "Steel.Preorder.vhist", "FStar.List.Tot.Base.rev", "FStar.FunctionalExtensionality.feq", "FStar.List.Tot.Base.mem", "FStar.Reflection.V2.Data.var", "FStar.Tactics.CanonCommMonoidSimple.Equiv.term_eq", "FStar.PCM.composable", "Steel.Effect.Common.req", "Steel.FractionalPermission.full_perm", "Steel.Effect.Common.to_vprop", "FStar.PCM.op", "Steel.Effect.Common.hp_of", "Steel.Effect.Atomic.h_exists", "Steel.Effect.Common.star", "FStar.Reflection.V2.Derived.flatten_name", "FStar.ST.alloc", "Steel.Effect.Common.to_vprop'", "Steel.Preorder.p_op", "Steel.Effect.Common.rmem", "FStar.Real.two", "FStar.List.Tot.Base.append", "Steel.Memory.inames", "Steel.Effect.Common.normal_steps", "Steel.Effect.Common.guard_vprop", "Steel.Effect.Common.extract_contexts", "FStar.List.Tot.Base.tl", "Steel.Effect.Common.print_goals", "Steel.Effect.Common.rm", "FStar.List.Tot.Base.memP", "FStar.Reflection.V2.Derived.type_of_binder", "Steel.Effect.Common.t_of", "Steel.FractionalPermission.sum_perm", "Steel.GhostMonotonicHigherReference.pts_to", "Steel.Effect.Common.sel_of", "FStar.Reflection.V2.Derived.inspect_ln_unascribe", "Steel.Effect.Common.normal", "Steel.FractionalPermission.comp_perm", "FStar.Reflection.V2.Derived.Lemmas.op_Less_Less_Colon", "FStar.Sealed.Inhabited.seal", "Steel.Effect.Common.mk_rmem", "Steel.Effect.Common.hmem", "Steel.Effect.Common.selector'", "FStar.String.strlen", "FStar.FunctionalExtensionality.on_dom", "Steel.Effect.Common.vrefine'", "FStar.List.Tot.Properties.assoc_mem", "Steel.Effect.Common.visit_br", "FStar.UInt.size", "Steel.Preorder.comm_op", "Steel.Effect.Common.visit_tm", "FStar.Reflection.V2.Derived.shift_subst", "FStar.Reflection.V2.Derived.u_unk", "Steel.Effect.Common.pure", "Steel.Memory.ptr", "Steel.Effect.Common.sel_depends_only_on", "FStar.String.length", "Steel.Effect.Common.slterm_nbr_uvars_argv", "FStar.Reflection.V2.Derived.is_fvar", "FStar.Reflection.V2.Data.ppname_t", "Steel.Preorder.history_compose", "FStar.NMSTTotal.get", "Steel.Effect.Common.print_goal", "Steel.Effect.Atomic.gget", "FStar.List.Tot.Base.fold_left", "Steel.Effect.Common.normal_tac_steps", "FStar.Reflection.V2.Derived.Lemmas.list_ref", "Steel.Effect.Common.visit_comp", "Steel.Preorder.curval", "Steel.Effect.Common.return_pre", "Steel.Effect.Common.inv", "FStar.Pervasives.Native.fst", "FStar.List.Tot.Base.hd", "Steel.Preorder.extends", "Steel.Effect.Common.rmem'", "FStar.Tactics.CanonCommMonoidSimple.Equiv.atom", "Steel.Effect.Common.atom", "Steel.GhostMonotonicHigherReference.stable_property", "Steel.Effect.Common.my_assoc", "Steel.Effect.Common.bring_last_goal_on_top", "FStar.Pervasives.Native.snd", "Steel.Effect.Common.bring_last_goal_on_top'", "Steel.Effect.Atomic.return_req", "Steel.Effect.return_req", "Steel.Effect.Common.mk_rmem'", "Steel.Effect.Common.vrefine", "Steel.Effect.Atomic.mk_selector_vprop" ], "source_upto_this": "(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Steel.GhostMonotonicReference\n\nopen FStar.PCM\nopen FStar.Ghost\nopen Steel.FractionalPermission\n\nopen Steel.Memory\nopen Steel.Effect.Atomic\nopen Steel.Effect\n\nmodule Preorder = FStar.Preorder\nmodule MHR = Steel.GhostMonotonicHigherReference\nmodule U = FStar.Universe\n\nlet raise_preorder (#a:Type0) (p:Preorder.preorder a)\n : Preorder.preorder (U.raise_t a)\n = fun (x0 x1:U.raise_t a) ->\n p (U.downgrade_val x0) (U.downgrade_val x1)\n", "sketch": [ "Step 1: This definition introduces a type `ref` that takes a type `a` and a preorder `p` on `a` as parameters.\nStep 2: The implementation will define `ref` as a type that encapsulates a value of type `a` and ensures that the value respects the preorder `p`.", "Step 1: The definition introduces a new type `ref` which takes a type `a` and a preorder `p` on `a`.\nStep 2: The implementation will define `ref` as a type that encapsulates a value of type `a` and ensures that the value respects the preorder `p`.", "Step 1: Define a type `ref` that takes a type `a` and a preorder `p` on `a`.\nStep 2: Implement `ref` as a type that represents a ghost monotonic reference, which is a reference that respects the preorder `p`.", "Step 1: This definition introduces a new type `ref` that takes a type `a` and a preorder `p` on `a` as parameters.\nStep 2: The implementation will define `ref` as a type that encapsulates a reference to a value of type `a` with an associated preorder `p`.", "Step 1: This definition introduces a type `ref` that takes a type `a` and a preorder `p` on `a`.\nStep 2: The implementation will define `ref` as a type that encapsulates a reference to a value of type `a` with an associated preorder `p`.", "Step 1: The definition is about creating a type for a reference that is parameterized by a type `a` and a preorder `p` on `a`.\nStep 2: The implementation will define a type that encapsulates a reference to a value of type `a` and ensures that the reference respects the preorder `p`.", "Step 1: This definition introduces a type `ref` that takes a type `a` and a preorder `p` on `a` as parameters.\nStep 2: The implementation of this type will likely involve encapsulating a reference to a value of type `a` that respects the preorder `p`.", "Step 1: The definition is about creating a type for a reference that is parameterized by a type `a` and a preorder `p` on `a`.\nStep 2: The implementation involves defining a type that encapsulates a reference, ensuring that it respects the preorder `p`.", "Step 1: This definition is about creating a reference type that is parameterized by a type `a` and a preorder `p` on `a`. \nStep 2: The implementation will define a new type that encapsulates a value of type `a` and ensures that the value respects the preorder `p`.", "Step 1: This definition introduces a type `ref` which takes a type `a` and a preorder `p` on `a`.\nStep 2: The implementation will define `ref` as a type that encapsulates a reference to a value of type `a` with an associated preorder `p`." ], "generated_solution": [ "type ref (a:Type u#0) (p:Preorder.preorder a) = {\n contents: a;\n preorder: p contents contents\n}", "type ref (a:Type u#0) (p:Preorder.preorder a) = { v:a | Preorder.relation p v v }", "type ref (a:Type u#0) (p:Preorder.preorder a) = MHR.ref a (raise_preorder p)", "type ref (a:Type u#0) (p:Preorder.preorder a) = MHR.ref (U.raise_t a) (raise_preorder p)", "type ref (a:Type u#0) (p:Preorder.preorder a) = MHR.ref (U.raise_t a) (raise_preorder p)", "type ref (a:Type u#0) (p:Preorder.preorder a) = MHR.higher_ref a (raise_preorder p)", "type ref (a:Type u#0) (p:Preorder.preorder a) = MHR.ref (U.raise_t a) (raise_preorder p)", "type ref (a:Type u#0) (p:Preorder.preorder a) = MHR.ref (U.raise_t a) (raise_preorder p)", "type ref (a:Type u#0) (p:Preorder.preorder a) = \n | Ref : x:a -> ref a p", "type ref (a:Type u#0) (p:Preorder.preorder a) = MHR.ref (U.raise_t a) (raise_preorder p)" ] }, { "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.comp_triple", "opens_and_abbrevs": [ { "open": "FStar.Map" }, { "open": "FStar.Set" }, { "open": "FStar.List.Tot" }, { "open": "OPLSS2021" }, { "open": "OPLSS2021" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let comp_triple (w0, r0, fs0) (w1, r1, fs1) = (union w0 w1, union r0 r1, (fs0 @ add_source r0 ((bot, w1)::fs1)))", "source_range": { "start_line": 393, "start_col": 0, "end_line": 393, "end_col": 112 }, "interleaved": false, "definition": "fun _ _ ->\n (let\n FStar.Pervasives.Native.Mktuple2\n #_\n #_\n (FStar.Pervasives.Native.Mktuple3 #_ #_ #_ w0 r0 fs0)\n (FStar.Pervasives.Native.Mktuple3 #_ #_ #_ w1 r1 fs1) =\n _, _\n in\n OPLSS2021.IFC.union w0 w1,\n OPLSS2021.IFC.union r0 r1,\n fs0 @ OPLSS2021.IFC.add_source r0 ((OPLSS2021.IFC.bot, w1) :: fs1))\n <:\n (FStar.Set.set OPLSS2021.IFC.loc * FStar.Set.set OPLSS2021.IFC.loc) *\n Prims.list OPLSS2021.IFC.flow", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Pervasives.Native.tuple3", "OPLSS2021.IFC.label", "Prims.list", "OPLSS2021.IFC.flow", "FStar.Pervasives.Native.Mktuple2", "FStar.Pervasives.Native.Mktuple3", "FStar.Set.set", "OPLSS2021.IFC.loc", "OPLSS2021.IFC.union", "FStar.List.Tot.Base.op_At", "OPLSS2021.IFC.add_source", "Prims.Cons", "OPLSS2021.IFC.bot" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "\n _: ((OPLSS2021.IFC.label * OPLSS2021.IFC.label) * Prims.list OPLSS2021.IFC.flow) ->\n _: ((OPLSS2021.IFC.label * OPLSS2021.IFC.label) * Prims.list OPLSS2021.IFC.flow)\n -> (FStar.Set.set OPLSS2021.IFC.loc * FStar.Set.set OPLSS2021.IFC.loc) *\n Prims.list OPLSS2021.IFC.flow", "prompt": "let comp_triple (w0, r0, fs0) (w1, r1, fs1) =\n ", "expected_response": "(union w0 w1, union r0 r1, (fs0 @ add_source r0 ((bot, w1) :: fs1)))", "source": { "project_name": "FStar", "file_name": "examples/oplss2021/OPLSS2021.IFC.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "OPLSS2021.IFC.fst", "checked_file": "dataset/OPLSS2021.IFC.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Map.fsti.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Calc.fsti.checked" ] }, "definitions_in_context": [ "let loc = int", "let store = m:Map.t loc int{forall l. contains m l}", "let sel (s:store) (l:loc) : int = Map.sel s l", "let upd (s:store) (l:loc) (x:int) : store = Map.upd s l x", "let label = Set.set loc", "let label_inclusion (l0 l1:label) = Set.subset l0 l1", "let bot : label = Set.empty", "let single (l:loc) : label = Set.singleton l", "let union (l0 l1:label) = Set.union l0 l1", "let comp a = store -> a & store", "let havoc s l x = upd s l x", "let writes_ok #a (f:comp a) (writes:Set.set loc) =\n forall (l:loc). ~(Set.mem l writes) ==>\n (forall (s0:store).\n let x1, s0' = f s0 in\n sel s0 l == sel s0' l)", "let does_not_read_loc_v #a (f:comp a) (l:loc) (s0:store) v =\n let s0' = havoc s0 l v in //s0 and s0' agree except on l\n let x1, s1 = f s0 in\n let x1', s1' = f s0' in // run f twice, once on s0, once on s0'\n x1 == x1' /\\ //result does not depend on l\n (forall l'. l' <> l ==> //for every location l' not equal to l\n sel s1 l' == sel s1' l') /\\ //its value in the two states is the same\n (sel s1 l == sel s1' l \\/ //and l is itself may be written, in which case its value is the same in both final states\n //or its not, but then its values in the initial and final states are the same in both runs\n (sel s1 l == sel s0 l /\\\n sel s1' l == sel s0' l))", "let does_not_read_loc #a (f:comp a) (l:loc) (s0:store) =\n forall v. does_not_read_loc_v f l s0 v", "let reads_ok #a (f:comp a) (reads:label) =\n forall (l:loc) (s:store). ~(Set.mem l reads) ==> does_not_read_loc f l s", "let flow = label & label", "let flows = list flow", "let has_flow_1 (from to:loc) (f:flow) = from `Set.mem` fst f /\\ to `Set.mem` snd f", "let has_flow (from to:loc) (fs:flows) = exists rs. rs `List.Tot.memP` fs /\\ has_flow_1 from to rs", "let no_leakage_k #a (f:comp a) (from to:loc) (k:int) =\n forall s0.{:pattern (havoc s0 from k)}\n sel (snd (f s0)) to == sel (snd (f (havoc s0 from k))) to", "let no_leakage #a (f:comp a) (from to:loc) = forall k. no_leakage_k f from to k", "let respects_flows #a (f:comp a) (fs:flows) =\n forall from to. {:pattern (no_leakage f from to)} ~(has_flow from to fs) /\\ from<>to ==> no_leakage f from to", "let ist a (writes:label) (reads:label) (fs:flows) =\n f:comp a {\n reads_ok f reads /\\\n writes_ok f writes /\\\n respects_flows f fs\n }", "let iread (l:loc) : ist int bot (single l) [] = fun s -> sel s l, s", "let iwrite (l:loc) (x:int) : ist unit (single l) bot [] = fun s -> (), upd s l x", "let return (a:Type) (x:a) : ist a bot bot [] = fun s -> x,s", "let add_source (r:label) (fs:flows) : flows = List.Tot.map (fun (r0, w0) -> union r r0, w0) fs", "let add_sink (w:label) (fs:flows) : flows = List.Tot.map (fun (r0, w0) -> r0, union w w0) fs", "let flows_included_in (fs0 fs1:flows) =\n forall f0. f0 `List.Tot.memP` fs0 ==>\n (forall from to. has_flow_1 from to f0 /\\ from <> to ==> (exists f1. f1 `List.Tot.memP` fs1 /\\ has_flow_1 from to f1))", "let flows_equiv (fs0 fs1:flows) = fs0 `flows_included_in` fs1 /\\ fs1 `flows_included_in` fs0", "let flows_equiv_refl fs\n : Lemma (fs `flows_equiv` fs)\n = ()", "let flows_equiv_trans fs0 fs1 fs2\n : Lemma (fs0 `flows_equiv` fs1 /\\ fs1 `flows_equiv` fs2 ==> fs0 `flows_equiv` fs2)\n = ()", "let flows_included_in_union_distr_dest (a b c:label)\n : Lemma (flows_equiv [a, union b c] [a, b; a, c])\n = ()", "let flows_included_in_union_distr_src (a b c:label)\n : Lemma (flows_equiv [union a b, c] [a, c; b, c])\n = ()", "let flows_included_in_union (a b c:label)\n : Lemma (flows_equiv ([a, union b c; union a b, c])\n ([a, b; union a b, c]))\n = ()", "let bind_comp (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : comp b\n = fun s0 -> let v, s1 = x s0 in y v s1", "let bind_comp_reads_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (reads_ok (bind_comp x y) (union r0 r1))\n = let f = bind_comp x y in\n let reads = union r0 r1 in\n let f_reads_ok (l:loc) (s0:store)\n : Lemma (requires (~(Set.mem l reads)))\n (ensures (does_not_read_loc f l s0))\n [SMTPat (does_not_read_loc f l s0)]\n = let aux (k:_)\n : Lemma (ensures (does_not_read_loc_v f l s0 k))\n [SMTPat (does_not_read_loc_v f l s0 k)]\n = let v, s1 = x s0 in\n let v', s1' = x (havoc s0 l k) in\n assert (does_not_read_loc x l s0);\n assert (does_not_read_loc_v x l s0 k);\n assert (v == v');\n assert (does_not_read_loc (y v) l s1);\n let u, s2 = y v s1 in\n let u', s2' = y v s1' in\n assert (forall l'. l' <> l ==> sel s1 l' == sel s1' l');\n if sel s1 l = sel s1' l\n then (assert (forall l. sel s1 l == sel s1' l);\n assert (Map.equal s1 s1'))\n else (assert (sel s1 l == sel s0 l /\\\n sel (havoc s0 l k) l == sel s1' l);\n assert (Map.equal s1' (havoc s1 l k)))\n in\n ()\n in\n ()", "let bind_comp_writes_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (writes_ok (bind_comp x y) (union w0 w1))\n = ()", "let rec memP_append_or (#a:Type) (x:a) (l0 l1:list a)\n : Lemma (ensures (List.Tot.memP x (l0 @ l1) <==>\n (List.Tot.memP x l0 \\/ List.Tot.memP x l1)))\n (decreases l0)\n = match l0 with\n | [] -> ()\n | _::tl -> memP_append_or x tl l1", "let has_flow_append (from to:loc) (fs fs':flows)\n : Lemma (has_flow from to fs ==>\n has_flow from to (fs @ fs') /\\\n has_flow from to (fs' @ fs))\n = let rec aux (rs:_)\n : Lemma (requires\n List.Tot.memP rs fs)\n (ensures\n List.Tot.memP rs (fs @ fs') /\\\n List.Tot.memP rs (fs' @ fs))\n [SMTPat (List.Tot.memP rs fs)]\n = memP_append_or rs fs fs';\n memP_append_or rs fs' fs\n in\n ()", "let elim_has_flow_seq (from to:loc)\n (r0 r1 w1:label)\n (fs0 fs1:flows)\n : Lemma (requires (~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1)))))\n (ensures (~(has_flow from to fs0) /\\\n (~(Set.mem from r0) \\/ ~(Set.mem to w1)) /\\\n ~(has_flow from to (add_source r0 fs1))))\n = assert (add_source r0 ((bot, w1)::fs1) ==\n (Set.union r0 bot, w1)::add_source r0 fs1);\n assert (Set.union r0 bot `Set.equal` r0);\n has_flow_append from to fs0 ((r0, w1)::add_source r0 fs1);\n assert (~(has_flow from to fs0));\n has_flow_append from to ((r0, w1)::add_source r0 fs1) fs0;\n assert (~(has_flow from to (((r0, w1)::add_source r0 fs1))));\n assert ((r0, w1)::add_source r0 fs1 ==\n [r0, w1] @ add_source r0 fs1);\n has_flow_append from from [r0, w1] (add_source r0 fs1)", "let rec add_source_monotonic (from to:loc) (r:label) (fs:flows)\n : Lemma (has_flow from to fs ==> has_flow from to (add_source r fs))\n = match fs with\n | [] -> ()\n | _::tl -> add_source_monotonic from to r tl", "let has_flow_soundness #a #r #w #fs (f:ist a r w fs)\n (from to:loc) (s:store) (k:int)\n : Lemma (requires\n (let x, s1 = f s in\n let _, s1' = f (havoc s from k) in\n from <> to /\\\n sel s1 to <> sel s1' to))\n (ensures has_flow from to fs)\n = let aux ()\n : Lemma (requires (~(has_flow from to fs)))\n (ensures False)\n [SMTPat ()]\n = assert (respects_flows f fs);\n assert (no_leakage f from to)\n in\n ()", "let bind_comp_no_leakage (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n (from to:loc)\n (s0:store) (k:_)\n : Lemma\n (requires from <> to /\\ ~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1))))\n (ensures (let f = bind_comp x y in\n let s0' = havoc s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to))\n = let f = bind_comp x y in\n assert (reads_ok x r0);\n let s0' = havoc s0 from k in\n let _, s2f = f s0 in\n let _, s2f' = f s0' in\n let flows = (fs0 @ add_source r0 ((r1, w1)::fs1)) in\n let v0, s1 = x s0 in\n let v0', s1' = x s0' in\n elim_has_flow_seq from to r0 r1 w1 fs0 fs1;\n assert (~(has_flow from to fs0));\n assert (respects_flows x fs0);\n assert (no_leakage x from to);\n assert (sel s1 to == sel s1' to);\n let _, s2 = y v0 s1 in\n let _, s2' = y v0' s1' in\n assert (s2 == s2f);\n assert (s2' == s2f');\n //Given: (from not-in r0 U r1) \\/ (to not-in w1)\n //suppose (from in r0) \\/ (from in r1)\n // them to not-in w1\n //suppose (from not-in r0 U r1)\n //then v0 = v0'\n // s1' = havoc from s1 k\n // s2 to = s2' to\n if Set.mem to w1\n then begin\n assert (~(Set.mem from r0));\n assert (reads_ok x r0);\n assert (does_not_read_loc x from s0);\n assert (does_not_read_loc_v x from s0 k);\n assert (v0 == v0');\n assert (forall l. l <> from ==> sel s1 l == sel s1' l);\n assert (Map.equal s1' (havoc s1 from k) \\/ Map.equal s1' s1);\n if (sel s1 from = sel s1' from)\n then begin\n assert (Map.equal s1 s1')\n end\n else begin\n assert (Map.equal s1' (havoc s1 from k));\n assert (reads_ok (y v0) r1);\n if (sel s2 to = sel s2' to)\n then ()\n else begin\n assert (sel s2 to <> sel s1 to \\/ sel s2' to <> sel s1' to);\n has_flow_soundness (y v0) from to s1 k;\n assert (has_flow from to fs1);\n add_source_monotonic from to r0 fs1\n //y reads from and writes to, so (from, to) should be in fs1\n //so, we should get a contradiction\n end\n end\n end\n else //to is not in w1, so y does not write it\n ()", "let bind_comp_flows_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (respects_flows (bind_comp x y) (fs0 @ add_source r0 ((bot, w1)::fs1)))\n = let f = bind_comp x y in\n let flows = (fs0 @ add_source r0 ((bot, w1)::fs1)) in\n let respects_flows_lemma (from to:loc)\n : Lemma (requires from <> to /\\ ~(has_flow from to flows))\n (ensures no_leakage f from to)\n [SMTPat (no_leakage f from to)]\n = let aux (s0:store) (k:_)\n : Lemma (let s0' = havoc s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to)\n [SMTPat (havoc s0 from k)]\n = bind_comp_no_leakage x y from to s0 k\n in\n ()\n in\n ()", "let triple = label & label & flows", "let unit_triple = bot, bot, []" ], "closest": [ "val Sec2.IFC.comp_triple = \n _: ((Sec2.IFC.label * Sec2.IFC.label) * Prims.list Sec2.IFC.flow) ->\n _: ((Sec2.IFC.label * Sec2.IFC.label) * Prims.list Sec2.IFC.flow)\n -> (FStar.Set.set Sec2.IFC.loc * FStar.Set.set Sec2.IFC.loc) * Prims.list Sec2.IFC.flow\nlet comp_triple (w0, r0, fs0) (w1, r1, fs1) = (union w0 w1, union r0 r1, (fs0 @ add_source r0 ((bot, w1)::fs1)))", "val Sec2.HIFC.ifc_triple = \n _: ((Sec2.HIFC.label * Sec2.HIFC.label) * Prims.list Sec2.HIFC.flow) ->\n _: ((Sec2.HIFC.label * Sec2.HIFC.label) * Prims.list Sec2.HIFC.flow)\n -> (FStar.Set.set Sec2.HIFC.loc * FStar.Set.set Sec2.HIFC.loc) * Prims.list Sec2.HIFC.flow\nlet ifc_triple (w0, r0, fs0) (w1, r1, fs1) = (union w0 w1, union r0 r1, (fs0 @ add_source r0 ((bot, w1)::fs1)))", "val Sec2.IFC.triple_equiv = \n _: ((Sec2.IFC.label * Sec2.IFC.label) * Sec2.IFC.flows) ->\n _: ((Sec2.IFC.label * Sec2.IFC.label) * Sec2.IFC.flows)\n -> Prims.logical\nlet triple_equiv (w0, r0, f0) (w1, r1, f1) = label_equiv w0 w1 /\\ label_equiv r0 r1 /\\ flows_equiv f0 f1", "val Sec2.IFC.assoc_comp = \n _: ((Sec2.IFC.label * Sec2.IFC.label) * Prims.list Sec2.IFC.flow) ->\n _: ((Sec2.IFC.label * Sec2.IFC.label) * Prims.list Sec2.IFC.flow) ->\n _: ((Sec2.IFC.label * Sec2.IFC.label) * Prims.list Sec2.IFC.flow)\n -> Prims.unit\nlet assoc_comp (w0, r0, fs0) (w1, r1, fs1) (w2, r2, fs2) =\n calc (==) {\n comp_triple (w0, r0, fs0) (comp_triple (w1, r1, fs1) (w2, r2, fs2)) ;\n (==) { }\n comp_triple (w0, r0, fs0) (union w1 w2, union r1 r2, (fs1 @ add_source r1 ((bot, w2)::fs2)));\n (==) { }\n (union w0 (union w1 w2), union r0 (union r1 r2), fs0 @ (add_source r0 ((bot, union w1 w2) :: (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { assert (forall w0 w1 w2. Set.equal (union w0 (union w1 w2)) (union (union w0 w1) w2)) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n fs0 @ (add_source r0 ((bot, union w1 w2) :: (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n (fs0 @ ((union r0 bot, union w1 w2) :: add_source r0 (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { assert (forall s. Set.equal (union s bot) s) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n (fs0 @ ((r0, union w1 w2) :: add_source r0 (fs1 @ (r1, w2) ::add_source r1 fs2))));\n };\n calc (==) {\n comp_triple (comp_triple (w0, r0, fs0) (w1, r1, fs1)) (w2, r2, fs2);\n (==) { }\n comp_triple (union w0 w1, union r0 r1, (fs0 @ add_source r0 ((bot, w1)::fs1))) (w2, r2, fs2);\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ add_source r0 ((bot, w1)::fs1)) @ (add_source (union r0 r1) ((bot, w2) :: fs2))));\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ ((union r0 bot, w1)::add_source r0 fs1)) @ ((union (union r0 r1) bot, w2) :: add_source (union r0 r1) fs2)));\n (==) { assert (forall s. Set.equal (union s bot) s) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ ((r0, w1)::add_source r0 fs1)) @ ((union r0 r1, w2) :: add_source (union r0 r1) fs2)));\n }", "val Sec2.HIFC.triple_equiv = \n _: ((Sec2.HIFC.label * Sec2.HIFC.label) * Sec2.HIFC.flows) ->\n _: ((Sec2.HIFC.label * Sec2.HIFC.label) * Sec2.HIFC.flows)\n -> Prims.logical\nlet triple_equiv (w0, r0, f0) (w1, r1, f1) = label_equiv w0 w1 /\\ label_equiv r0 r1 /\\ flows_equiv f0 f1", "val FStar.DM4F.IFC.flows = l1: FStar.DM4F.IFC.label -> l2: FStar.DM4F.IFC.label -> Prims.bool\nlet flows l1 l2 = not(l1=High && l2=Low)", "val Sec2.HIFC.assoc_hst = \n _: ((Sec2.HIFC.label * Sec2.HIFC.label) * Prims.list Sec2.HIFC.flow) ->\n _: ((Sec2.HIFC.label * Sec2.HIFC.label) * Prims.list Sec2.HIFC.flow) ->\n _: ((Sec2.HIFC.label * Sec2.HIFC.label) * Prims.list Sec2.HIFC.flow)\n -> Prims.unit\nlet assoc_hst (w0, r0, fs0) (w1, r1, fs1) (w2, r2, fs2) =\n calc (==) {\n ifc_triple (w0, r0, fs0) (ifc_triple (w1, r1, fs1) (w2, r2, fs2)) ;\n (==) { }\n ifc_triple (w0, r0, fs0) (union w1 w2, union r1 r2, (fs1 @ add_source r1 ((bot, w2)::fs2)));\n (==) { }\n (union w0 (union w1 w2), union r0 (union r1 r2), fs0 @ (add_source r0 ((bot, union w1 w2) :: (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { assert (forall w0 w1 w2. Set.equal (union w0 (union w1 w2)) (union (union w0 w1) w2)) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n fs0 @ (add_source r0 ((bot, union w1 w2) :: (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n (fs0 @ ((union r0 bot, union w1 w2) :: add_source r0 (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { assert (forall s. Set.equal (union s bot) s) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n (fs0 @ ((r0, union w1 w2) :: add_source r0 (fs1 @ (r1, w2) ::add_source r1 fs2))));\n };\n calc (==) {\n ifc_triple (ifc_triple (w0, r0, fs0) (w1, r1, fs1)) (w2, r2, fs2);\n (==) { }\n ifc_triple (union w0 w1, union r0 r1, (fs0 @ add_source r0 ((bot, w1)::fs1))) (w2, r2, fs2);\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ add_source r0 ((bot, w1)::fs1)) @ (add_source (union r0 r1) ((bot, w2) :: fs2))));\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ ((union r0 bot, w1)::add_source r0 fs1)) @ ((union (union r0 r1) bot, w2) :: add_source (union r0 r1) fs2)));\n (==) { assert (forall s. Set.equal (union s bot) s) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ ((r0, w1)::add_source r0 fs1)) @ ((union r0 r1, w2) :: add_source (union r0 r1) fs2)));\n }", "val Sec2.IFC.has_flow = from: Sec2.IFC.loc -> to: Sec2.IFC.loc -> fs: Sec2.IFC.flows -> Prims.logical\nlet has_flow (from to:loc) (fs:flows) = (exists rs. rs `List.Tot.memP` fs /\\ has_flow_1 from to rs)", "val Sec2.IFC.has_flow_1 = from: Sec2.IFC.loc -> to: Sec2.IFC.loc -> f: Sec2.IFC.flow -> Prims.logical\nlet has_flow_1 (from to:loc) (f:flow) = from `Set.mem` fst f /\\ to `Set.mem` snd f", "val Sec2.IFC.right_unit = _: ((Sec2.IFC.label * Sec2.IFC.label) * Prims.list Sec2.IFC.flow) -> Prims.unit\nlet right_unit (w, r, f) =\n calc (==) {\n comp_triple (w, r, f) unit_triple;\n (==) { }\n (w `union` bot, r `union` bot, f @ add_source r ((bot, bot)::[]));\n };\n assert (flows_equiv (add_source r [(bot, bot)]) []);\n flows_equiv_append f (add_source r [(bot, bot)]) f [];\n append_nil_r f;\n assert (comp_triple (w, r, f) unit_triple `triple_equiv` (w, r, f))", "val Sec2.IFC.left_unit = _: ((Sec2.IFC.label * Sec2.IFC.label) * Prims.list Sec2.IFC.flow) -> Prims.unit\nlet left_unit (w, r, f) =\n assert (Set.equal (union bot bot) bot);\n add_source_bot f;\n assert (comp_triple unit_triple (w, r, f) `triple_equiv` (w, r, f))", "val Sec2.IFC.union = l0: Sec2.IFC.label -> l1: Sec2.IFC.label -> FStar.Set.set Sec2.IFC.loc\nlet union (l0 l1:label) = Set.union l0 l1", "val Sec2.IFC.respects_flows = f: Sec2.IFC.comp a -> fs: Sec2.IFC.flows -> Prims.logical\nlet respects_flows #a (f:comp a) (fs:flows) =\n (forall from to. {:pattern (no_leakage f from to)} ~(has_flow from to fs) /\\ from<>to ==> no_leakage f from to)", "val Sec2.IFC.flows_equiv = fs0: Sec2.IFC.flows -> fs1: Sec2.IFC.flows -> Prims.logical\nlet flows_equiv (fs0 fs1:flows) = fs0 `flows_included_in` fs1 /\\ fs1 `flows_included_in` fs0", "val Sec2.HIFC.has_flow_1 = from: Sec2.HIFC.loc -> to: Sec2.HIFC.loc -> f: Sec2.HIFC.flow -> Prims.logical\nlet has_flow_1 (from to:loc) (f:flow) = from `Set.mem` fst f /\\ to `Set.mem` snd f", "val Sec2.HIFC.union = l0: Sec2.HIFC.label -> l1: Sec2.HIFC.label -> FStar.Set.set Sec2.HIFC.loc\nlet union (l0 l1:label) = Set.union l0 l1", "val Sec2.HIFC.has_flow = from: Sec2.HIFC.loc -> to: Sec2.HIFC.loc -> fs: Sec2.HIFC.flows -> Prims.logical\nlet has_flow (from to:loc) (fs:flows) = (exists rs. rs `List.Tot.memP` fs /\\ has_flow_1 from to rs)", "val Sec2.IFC.ist = a: Type -> writes: Sec2.IFC.label -> reads: Sec2.IFC.label -> fs: Sec2.IFC.flows -> Type\nlet ist a (writes:label) (reads:label) (fs:flows) =\n f:(store -> (a * store)) {\n reads_ok f reads /\\\n writes_ok f writes /\\\n respects_flows f fs\n }", "val Sec2.HIFC.left_unit = _: ((Sec2.HIFC.label * Sec2.HIFC.label) * Prims.list Sec2.HIFC.flow) -> Prims.unit\nlet left_unit (w, r, f) =\n assert (Set.equal (union bot bot) bot);\n add_source_bot f;\n assert (ifc_triple unit_triple (w, r, f) `triple_equiv` (w, r, f))", "val Sec2.HIFC.right_unit = _: ((Sec2.HIFC.label * Sec2.HIFC.label) * Prims.list Sec2.HIFC.flow) -> Prims.unit\nlet right_unit (w, r, f) =\n calc (==) {\n ifc_triple (w, r, f) unit_triple;\n (==) { }\n (w `union` bot, r `union` bot, f @ add_source r ((bot, bot)::[]));\n };\n assert (flows_equiv (add_source r [(bot, bot)]) []);\n flows_equiv_append f (add_source r [(bot, bot)]) f [];\n append_nil_r f;\n assert (ifc_triple (w, r, f) unit_triple `triple_equiv` (w, r, f))", "val FStar.DM4F.IFC.join = l1: FStar.DM4F.IFC.label -> l2: FStar.DM4F.IFC.label -> FStar.DM4F.IFC.label\nlet join l1 l2 = if l1 = High || l2 = High then High else Low", "val Sec2.IFC.no_leakage = f: Sec2.IFC.comp a -> from: Sec2.IFC.loc -> to: Sec2.IFC.loc -> Prims.logical\nlet no_leakage #a (f:comp a) (from to:loc) = forall k. no_leakage_k f from to k", "val Sec2.HIFC.flows_equiv = fs0: Sec2.HIFC.flows -> fs1: Sec2.HIFC.flows -> Prims.logical\nlet flows_equiv (fs0 fs1:flows) = fs0 `flows_included_in` fs1 /\\ fs1 `flows_included_in` fs0", "val Sec2.IFC.flows_included_in = fs0: Sec2.IFC.flows -> fs1: Sec2.IFC.flows -> Prims.logical\nlet flows_included_in (fs0 fs1:flows) =\n forall f0. f0 `List.Tot.memP` fs0 ==>\n (forall from to. has_flow_1 from to f0 /\\ from <> to ==> (exists f1. f1 `List.Tot.memP` fs1 /\\ has_flow_1 from to f1))", "val elim_has_flow_seq (from to: loc) (r0 r1 w1: label) (fs0 fs1: flows)\n : Lemma (requires (~(has_flow from to (fs0 @ add_source r0 ((bot, w1) :: fs1)))))\n (ensures\n (~(has_flow from to fs0) /\\ (~(Set.mem from r0) \\/ ~(Set.mem to w1)) /\\\n ~(has_flow from to (add_source r0 fs1))))\nlet elim_has_flow_seq (from to:loc)\n (r0 r1 w1:label)\n (fs0 fs1:flows)\n : Lemma (requires (~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1)))))\n (ensures (~(has_flow from to fs0) /\\\n (~(Set.mem from r0) \\/ ~(Set.mem to w1)) /\\\n ~(has_flow from to (add_source r0 fs1))))\n = assert (add_source r0 ((bot, w1)::fs1) ==\n (Set.union r0 bot, w1)::add_source r0 fs1);\n assert (Set.union r0 bot `Set.equal` r0);\n has_flow_append from to fs0 ((r0, w1)::add_source r0 fs1);\n assert (~(has_flow from to fs0));\n has_flow_append from to ((r0, w1)::add_source r0 fs1) fs0;\n assert (~(has_flow from to (((r0, w1)::add_source r0 fs1))));\n assert ((r0, w1)::add_source r0 fs1 ==\n [r0, w1] @ add_source r0 fs1);\n has_flow_append from from [r0, w1] (add_source r0 fs1)", "val elim_has_flow_seq (from to: loc) (r0 r1 w1: label) (fs0 fs1: flows)\n : Lemma (requires (~(has_flow from to (fs0 @ add_source r0 ((bot, w1) :: fs1)))))\n (ensures\n (~(has_flow from to fs0) /\\ (~(Set.mem from r0) \\/ ~(Set.mem to w1)) /\\\n ~(has_flow from to (add_source r0 fs1))))\nlet elim_has_flow_seq (from to:loc)\n (r0 r1 w1:label)\n (fs0 fs1:flows)\n : Lemma (requires (~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1)))))\n (ensures (~(has_flow from to fs0) /\\\n (~(Set.mem from r0) \\/ ~(Set.mem to w1)) /\\\n ~(has_flow from to (add_source r0 fs1))))\n = assert (add_source r0 ((bot, w1)::fs1) ==\n (Set.union r0 bot, w1)::add_source r0 fs1);\n assert (Set.union r0 bot `Set.equal` r0);\n has_flow_append from to fs0 ((r0, w1)::add_source r0 fs1);\n assert (~(has_flow from to fs0));\n has_flow_append from to ((r0, w1)::add_source r0 fs1) fs0;\n assert (~(has_flow from to (((r0, w1)::add_source r0 fs1))));\n assert ((r0, w1)::add_source r0 fs1 ==\n [r0, w1] @ add_source r0 fs1);\n has_flow_append from from [r0, w1] (add_source r0 fs1)", "val Sec2.IFC.unit_triple = (Sec2.IFC.label * Sec2.IFC.label) * Prims.list _\nlet unit_triple = bot, bot, []", "val bind_ifc_flows_ok\n (#a #b: Type)\n (#w0 #r0 #w1 #r1: label)\n (#fs0 #fs1: flows)\n (#p #q #r #s: _)\n (x: hifc a r0 w0 fs0 p q)\n (y: (x: a -> hifc b r1 w1 fs1 (r x) (s x)))\n : Lemma (respects (bind_ifc' x y) (fs0 @ add_source r0 ((bot, w1) :: fs1)))\nlet bind_ifc_flows_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n #p #q #r #s\n (x:hifc a r0 w0 fs0 p q)\n (y: (x:a -> hifc b r1 w1 fs1 (r x) (s x)))\n : Lemma (respects (bind_ifc' x y) (fs0 @ add_source r0 ((bot, w1)::fs1)))\n = let f = bind_ifc' x y in\n let p_f = (fun s0 -> p s0 /\\ (forall x s1. q s0 x s1 ==> r x s1)) in\n let flows = (fs0 @ add_source r0 ((bot, w1)::fs1)) in\n let respects_flows_lemma (from to:loc)\n : Lemma (requires from <> to /\\ ~(has_flow from to flows))\n (ensures no_leakage f from to)\n [SMTPat (has_flow from to flows)]\n = let aux (s0:store{p_f s0}) (k:_{p_f (upd s0 from k)})\n : Lemma (let s0' = upd s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to)\n [SMTPat (upd s0 from k)]\n = bind_hst_no_leakage x y from to s0 k\n in\n ()\n in\n ()", "val bind_comp_flows_ok\n (#a #b: Type)\n (#w0 #r0 #w1 #r1: label)\n (#fs0 #fs1: flows)\n (x: ist a w0 r0 fs0)\n (y: (a -> ist b w1 r1 fs1))\n : Lemma (respects_flows (bind_comp x y) (fs0 @ add_source r0 ((bot, w1) :: fs1)))\nlet bind_comp_flows_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (respects_flows (bind_comp x y) (fs0 @ add_source r0 ((bot, w1)::fs1)))\n = let f = bind_comp x y in\n let flows = (fs0 @ add_source r0 ((bot, w1)::fs1)) in\n let respects_flows_lemma (from to:loc)\n : Lemma (requires from <> to /\\ ~(has_flow from to flows))\n (ensures no_leakage f from to)\n [SMTPat (no_leakage f from to)]\n = let aux (s0:store) (k:_)\n : Lemma (let s0' = havoc s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to)\n [SMTPat (havoc s0 from k)]\n = bind_comp_no_leakage x y from to s0 k\n in\n ()\n in\n ()", "val Sec2.IFC.does_not_read_loc = f: Sec2.IFC.comp a -> reads: Sec2.IFC.label -> l: Sec2.IFC.loc -> s0: Sec2.IFC.store\n -> Prims.logical\nlet does_not_read_loc #a (f:comp a) (reads:label) (l:loc) (s0:store) =\n forall v.\n does_not_read_loc_v f reads l s0 v", "val OPLSS2021.ParNDSDiv.commutative = f: (_: a -> _: a -> a) -> Prims.logical\nlet commutative #a (f: a -> a -> a) =\n forall x y. f x y == f y x", "val bind_ifc'\n (#a #b: Type)\n (#w0 #r0 #w1 #r1: label)\n (#fs0 #fs1: flows)\n (#p #q #r #s: _)\n (x: hifc a r0 w0 fs0 p q)\n (y: (x: a -> hifc b r1 w1 fs1 (r x) (s x)))\n : hst b\n (fun s0 -> p s0 /\\ (forall x s1. q s0 x s1 ==> r x s1))\n (fun s0 r s2 -> (exists x s1. q s0 x s1 /\\ s x s1 r s2))\nlet bind_ifc' (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n #p #q #r #s\n (x:hifc a r0 w0 fs0 p q)\n (y: (x:a -> hifc b r1 w1 fs1 (r x) (s x)))\n : hst b (fun s0 -> p s0 /\\ (forall x s1. q s0 x s1 ==> r x s1))\n (fun s0 r s2 -> (exists x s1. q s0 x s1 /\\ s x s1 r s2))\n = bind_hst _ _ _ _ _ _ x y", "val OPLSS2021.ParNDSDiv.associative = f: (_: a -> _: a -> a) -> Prims.logical\nlet associative #a (f: a -> a -> a) =\n forall x y z. f x (f y z) == f (f x y) z", "val OPLSS2021.ParDiv.commutative = f: (_: a -> _: a -> a) -> Prims.logical\nlet commutative #a (f: a -> a -> a) =\n forall x y. f x y == f y x", "val Sec2.HIFC.if_then_else = \n a: Type ->\n r0: Sec2.HIFC.label ->\n w0: Sec2.HIFC.label ->\n f0: Sec2.HIFC.flows ->\n p0: Sec2.HIFC.pre ->\n q0: Sec2.HIFC.post a ->\n r1: Sec2.HIFC.label ->\n w1: Sec2.HIFC.label ->\n f1: Sec2.HIFC.flows ->\n p1: Sec2.HIFC.pre ->\n q1: Sec2.HIFC.post a ->\n c_then: Sec2.HIFC.hifc a r0 w0 f0 p0 q0 ->\n c_else: Sec2.HIFC.hifc a r1 w1 f1 p1 q1 ->\n b: Prims.bool\n -> Type\nlet if_then_else (a:Type) r0 w0 f0 p0 q0\n r1 w1 f1\n p1 q1\n (c_then:hifc a r0 w0 f0 p0 q0)\n (c_else:hifc a r1 w1 f1 p1 q1)\n (b:bool)\n = hifc a (r0 `union` r1) (w0 `union` w1) (f0 @ f1)\n (fun s -> if b then p0 s else p1 s)\n (fun s0 x s1 -> if b then q0 s0 x s1 else q1 s0 x s1)", "val Sec2.IFC.does_not_read_loc_v = f: Sec2.IFC.comp a -> reads: Sec2.IFC.label -> l: Sec2.IFC.loc -> s0: Sec2.IFC.store -> v: Prims.int\n -> Prims.logical\nlet does_not_read_loc_v #a (f:comp a) (reads:label) (l:loc) (s0:store) v =\n let s0' = havoc s0 l v in\n let x1, s1 = f s0 in\n let x1', s1' = f s0' in\n x1 == x1' /\\ //result does not depend on l\n (forall l'. l' <> l ==> //for every location l' not equal to l\n sel s1 l' == sel s1' l') /\\ //its value in the two states is the same\n (sel s1 l == sel s1' l \\/ //and l is itself may be written, in which case its value is the same in both final states\n //or its not, but then its values in the initial and final states are the same on both sides\n (sel s1 l == sel s0 l /\\\n sel s1' l == sel s0' l))", "val Sec2.IFC.no_leakage_k = f: Sec2.IFC.comp a -> from: Sec2.IFC.loc -> to: Sec2.IFC.loc -> k: Prims.int -> Prims.logical\nlet no_leakage_k #a (f:comp a) (from to:loc) (k:int) =\n forall s0.{:pattern (havoc s0 from k)} sel (snd (f s0)) to == (sel (snd (f (havoc s0 from k))) to)", "val test13: Prims.unit\n -> IFC unit\n (union (union cr0 cr1) cr2)\n (union (union cw0 cw1) cw2)\n (add_source cr0 [bot, cw1] @ add_source (union cr0 cr1) [bot, cw2])\nlet test13 ()\n : IFC unit (union (union cr0 cr1) cr2)\n (union (union cw0 cw1) cw2)\n (add_source cr0 [bot, cw1] @\n add_source (union cr0 cr1) [bot, cw2])\n = (c0 (); c1());c2()", "val Sec2.HIFC.respects = f: Sec2.HIFC.hst a p q -> fs: Sec2.HIFC.flows -> Prims.logical\nlet respects #a #p #q (f:hst a p q) (fs:flows) =\n (forall from to. {:pattern (no_leakage f from to)} ~(has_flow from to fs) /\\ from<>to ==> no_leakage f from to)", "val Sec2.HIFC.ist_exn = \n a: Type ->\n w: Sec2.HIFC.label ->\n r: Sec2.HIFC.label ->\n fs: Sec2.HIFC.flows ->\n p: Sec2.HIFC.pre ->\n q: Sec2.HIFC.post a\n -> Type\nlet ist_exn a w r fs (p:pre) (q:post a) =\n unit -> HIFC (option a) w r fs p\n (fun s0 x s1 ->\n match x with\n | None -> True\n | Some x -> q s0 x s1)", "val subcomp (a: Type) (w0 r0: label) (fs0: flows) (w1 r1: label) (fs1: flows) (f: ist a w0 r0 fs0)\n : Pure (ist a w1 r1 fs1)\n (requires label_inclusion w0 w1 /\\ label_inclusion r0 r1 /\\ fs0 `flows_included_in` fs1)\n (fun _ -> True)\nlet subcomp (a:Type) (w0 r0:label) (fs0:flows) (w1 r1:label) (fs1:flows) (f:ist a w0 r0 fs0)\n : Pure (ist a w1 r1 fs1)\n (requires label_inclusion w0 w1 /\\\n label_inclusion r0 r1 /\\\n fs0 `flows_included_in` fs1)\n (fun _ -> True)\n = let f_reads_ok (l:loc) (s0:store)\n : Lemma (requires (~(Set.mem l r1)))\n (ensures (does_not_read_loc f r1 l s0))\n [SMTPat (does_not_read_loc f r1 l s0)]\n = let aux (k :_)\n : Lemma (ensures (does_not_read_loc_v f r1 l s0 k))\n [SMTPat (does_not_read_loc_v f r1 l s0 k)]\n = let v, s1 = f s0 in\n let v', s1' = f (havoc s0 l k) in\n assert (does_not_read_loc f r0 l s0);\n assert (v == v');\n assert (not (Set.mem l w0) ==> sel s1' l = k);\n assert (not (Set.mem l w1) ==> sel s1' l = k);\n ()\n in\n ()\n in\n f", "val OPLSS2021.STLC.equalE = e: OPLSS2021.STLC.exp -> g1: OPLSS2021.STLC.env -> g2: OPLSS2021.STLC.env -> Prims.logical\nlet equalE (e:exp) (g1:env) (g2:env) =\n forall (x:int). appears_free_in x e ==> g1 x=g2 x", "val OPLSS2021.ValeVC.t_lemma = pre: Prims.prop -> post: Prims.prop -> Type0\nlet t_lemma (pre:prop) (post:prop) =\n unit -> Lemma (requires pre) (ensures post)", "val OPLSS2021.STLC.equal = g1: OPLSS2021.STLC.env -> g2: OPLSS2021.STLC.env -> Prims.logical\nlet equal (g1:env) (g2:env) = forall (x:int). g1 x=g2 x", "val IfcComposeReify.p3 = \n lo1: FStar.DM4F.Heap.IntStoreFixed.id ->\n lo2: FStar.DM4F.Heap.IntStoreFixed.id ->\n hi: FStar.DM4F.Heap.IntStoreFixed.id\n -> FStar.DM4F.IntStoreFixed.INT_STORE Prims.unit\nlet p3 lo1 lo2 hi =\n p1 lo1 hi;\n p2 lo2 hi", "val test10: Prims.unit\n -> IFC unit\n (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n (add_source cr0 ((bot, union cw1 cw2) :: (add_source cr1 [bot, cw2])))\nlet test10 ()\n : IFC unit (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n (add_source cr0\n ((bot, union cw1 cw2)::\n (add_source cr1 [bot, cw2])))\n = c0 (); (c1();c2())", "val OPLSS2021.ParDiv.associative = f: (_: a -> _: a -> a) -> Prims.logical\nlet associative #a (f: a -> a -> a) =\n forall x y z. f x (f y z) == f (f x y) z", "val bind_hst_no_leakage\n (#a #b: Type)\n (#w0 #r0 #w1 #r1: label)\n (#fs0 #fs1: flows)\n (#p #q #r #s: _)\n (x: hifc a r0 w0 fs0 p q)\n (y: (x: a -> hifc b r1 w1 fs1 (r x) (s x)))\n (from to: loc)\n (s0: store)\n (k: _)\n : Lemma\n (requires\n (let p_f = (fun s0 -> p s0 /\\ (forall x s1. q s0 x s1 ==> r x s1)) in\n let s0' = upd s0 from k in\n p_f s0 /\\ p_f s0' /\\ from <> to /\\\n ~(has_flow from to (fs0 @ add_source r0 ((bot, w1) :: fs1)))))\n (ensures\n (let f = bind_ifc' x y in\n let s0' = upd s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to))\nlet bind_hst_no_leakage (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n #p #q #r #s\n (x:hifc a r0 w0 fs0 p q)\n (y: (x:a -> hifc b r1 w1 fs1 (r x) (s x)))\n (from to:loc)\n (s0:store) (k:_)\n : Lemma\n (requires (\n let p_f = (fun s0 -> p s0 /\\ (forall x s1. q s0 x s1 ==> r x s1)) in\n let s0' = upd s0 from k in\n p_f s0 /\\\n p_f s0' /\\\n from <> to /\\\n ~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1)))))\n (ensures (let f = bind_ifc' x y in\n let s0' = upd s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to))\n = let f = bind_ifc' x y in\n assert (reads x r0);\n let s0' = upd s0 from k in\n let _, s2f = f s0 in\n let _, s2f' = f s0' in\n let flows = (fs0 @ add_source r0 ((r1, w1)::fs1)) in\n let v0, s1 = x s0 in\n let v0', s1' = x s0' in\n elim_has_flow_seq from to r0 r1 w1 fs0 fs1;\n assert (~(has_flow from to fs0));\n assert (respects x fs0);\n assert (no_leakage x from to);\n assert (sel s1 to == sel s1' to);\n let _, s2 = y v0 s1 in\n let _, s2' = y v0' s1' in\n assert (s2 == s2f);\n assert (s2' == s2f');\n //Given: (from not-in r0 U r1) \\/ (to not-in w1)\n //suppose (from in r0) \\/ (from in r1)\n // them to not-in w1\n //suppose (from not-in r0 U r1)\n //then v0 = v0'\n // s1' = upd from s1 k\n // s2 to = s2' to\n if Set.mem to w1\n then begin\n assert (~(Set.mem from r0));\n assert (reads x r0);\n reads_ok_does_not_read_loc x r0 from s0;\n assert (does_not_read_loc x r0 from s0);\n assert (does_not_read_loc_v x r0 from s0 k);\n assert (v0 == v0');\n assert (forall l. l <> from ==> sel s1 l == sel s1' l);\n assert (Map.equal s1' (upd s1 from k) \\/ Map.equal s1' s1);\n if (sel s1 from = sel s1' from)\n then begin\n assert (Map.equal s1 s1')\n end\n else begin\n assert (Map.equal s1' (upd s1 from k));\n assert (reads (y v0) r1);\n if (sel s2 to = sel s2' to)\n then ()\n else begin\n assert (sel s2 to <> sel s1 to \\/ sel s2' to <> sel s1' to);\n has_flow_soundness (y v0) from to s1 k;\n assert (has_flow from to fs1);\n add_source_monotonic from to r0 fs1\n //y reads from and writes to, so (from, to) should be in fs1\n //so, we should get a contradiction\n end\n end\n end\n else //to is not in w1, so y does not write it\n ()", "val Sec2.HIFC.hifc = \n a: Type ->\n r: Sec2.HIFC.label ->\n w: Sec2.HIFC.label ->\n fs: Sec2.HIFC.flows ->\n p: Sec2.HIFC.pre ->\n q: Sec2.HIFC.post a\n -> Type\nlet hifc a (r:label) (w:label) (fs:flows) (p:pre) (q:post a) =\n f:hst a p q {\n reads f r /\\\n writes f w /\\\n respects f fs\n }", "val FStar.Relational.Relational.triple_rel = \n _: FStar.Relational.Relational.rel _ _ ->\n _: FStar.Relational.Relational.rel _ _ ->\n _: FStar.Relational.Relational.rel _ _\n -> FStar.Relational.Relational.rel ((_ * _) * _) ((_ * _) * _)\nlet triple_rel (R a b) (R c d) (R e f) = R (a,c,e) (b,d,f)", "val refine_flow_hifc (#a #w #r #f #fs #p #q: _) (c: hifc a r w (f :: fs) p q)\n : Pure (hifc a r w fs p q)\n (requires\n (forall from to v.\n has_flow_1 from to f /\\ from <> to ==>\n (forall s0 x x' s1 s1'.\n p s0 /\\ p (upd s0 from v) /\\ q s0 x s1 /\\ modifies w s0 s1 /\\\n q (upd s0 from v) x' s1' /\\ modifies w (upd s0 from v) s1' ==>\n sel s1 to == sel s1' to)))\n (ensures fun _ -> True)\nlet refine_flow_hifc #a #w #r #f #fs #p #q\n (c: hifc a r w (f::fs) p q)\n : Pure (hifc a r w fs p q)\n (requires\n (forall from to v.\n has_flow_1 from to f /\\\n from <> to ==>\n (forall s0 x x' s1 s1'.\n p s0 /\\\n p (upd s0 from v) /\\\n q s0 x s1 /\\\n modifies w s0 s1 /\\\n q (upd s0 from v) x' s1' /\\\n modifies w (upd s0 from v) s1' ==>\n sel s1 to == sel s1' to)))\n (ensures fun _ -> True)\n = c", "val test12_1: Prims.unit\n -> IFC unit\n (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n [(cr0, cw1); (union cr0 cr1, cw2)]\nlet test12_1 ()\n : IFC unit (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n [(cr0, cw1); (union cr0 cr1, cw2)]\n = c0 (); (c1();c2())", "val sub_hifc\n (a: Type)\n (r0 w0: label)\n (fs0: flows)\n (p q: _)\n (r1 w1: label)\n (fs1: flows)\n (#p' #q': _)\n (f: hifc a r0 w0 fs0 p q)\n : Pure (hifc a r1 w1 fs1 p' q')\n (requires\n label_inclusion r0 r1 /\\ label_inclusion w0 w1 /\\\n (norm [delta; iota; zeta] (fs0 `flows_included_in` fs1)) /\\ (forall s. p' s ==> p s) /\\\n (forall s0 x s1. p' s0 /\\ q s0 x s1 ==> q' s0 x s1))\n (ensures fun _ -> True)\nlet sub_hifc (a:Type) (r0 w0:label) (fs0:flows) p q (r1 w1:label) (fs1:flows) #p' #q'\n (f:hifc a r0 w0 fs0 p q)\n : Pure (hifc a r1 w1 fs1 p' q')\n (requires\n label_inclusion r0 r1 /\\\n label_inclusion w0 w1 /\\\n (norm [delta;iota;zeta] (fs0 `flows_included_in` fs1)) /\\\n (forall s. p' s ==> p s) /\\\n (forall s0 x s1. p' s0 /\\ q s0 x s1 ==> q' s0 x s1))\n (ensures fun _ -> True)\n = let forig = f in\n norm_spec (fs0 `flows_included_in` fs1);\n assert ((fs0 `flows_included_in` fs1));\n let f : hst a p' q' = consequence a r0 w0 p q p' q' fs0 f in\n weaken_reads_ok f r0 r1;\n assert (reads f r1);\n assert (writes f w1);\n let respects_flows_lemma (from to:_)\n : Lemma\n (requires ~(has_flow from to fs1) /\\ from<>to)\n (ensures (no_leakage f from to))\n [SMTPat(no_leakage f from to)]\n = assert (no_leakage forig from to)\n in\n assert (respects f fs1);\n f", "val Sec2.IFC.writes_ok = f: Sec2.IFC.comp a -> writes: FStar.Set.set Sec2.IFC.loc -> Prims.logical\nlet writes_ok #a (f:comp a) (writes:Set.set loc) =\n (forall (l:loc). ~(Set.mem l writes) ==>\n (forall (s0:store).\n let x1, s0' = f s0 in\n sel s0 l == sel s0' l))", "val bind\n (a b: Type)\n (w0 r0: label)\n (fs0: flows)\n (w1 r1: label)\n (fs1: flows)\n (x: ist a w0 r0 fs0)\n (y: (a -> ist b w1 r1 fs1))\n : ist b (union w0 w1) (union r0 r1) (fs0 @ add_source r0 ((bot, w1) :: fs1))\nlet bind (a b:Type)\n (w0 r0:label) (fs0:flows)\n (w1 r1:label) (fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : ist b (union w0 w1) (union r0 r1) (fs0 @ add_source r0 ((bot, w1)::fs1))\n = let f = fun s0 -> let v, s1 = x s0 in y v s1 in\n bind_comp_reads_ok x y;\n bind_comp_reads_ok x y;\n bind_comp_flows_ok x y;\n f", "val FStar.Relational.Relational.cons_rel = \n _: FStar.Relational.Relational.rel _ _ ->\n _: FStar.Relational.Relational.rel (Prims.list _) (Prims.list _)\n -> FStar.Relational.Relational.rel (Prims.list _) (Prims.list _)\nlet cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys)", "val Sec2.HIFC.flows_included_in = fs0: Sec2.HIFC.flows -> fs1: Sec2.HIFC.flows -> Prims.logical\nlet flows_included_in (fs0 fs1:flows) =\n forall f0. f0 `List.Tot.memP` fs0 ==>\n (forall from to. has_flow_1 from to f0 /\\ from <> to ==> (exists f1. f1 `List.Tot.memP` fs1 /\\ has_flow_1 from to f1))", "val IfcExample.env = var: Prims.nat -> Prims.GTot IfcRules.label\nlet env (var: nat) = \n if var = addr_of x then Low\n else if var = addr_of y then Low \n else if var = addr_of c then Low\n else if var = addr_of z then High\n else High", "val test14: Prims.unit\n -> IFC unit\n (union (union cr0 cr1) cr2)\n (union (union cw0 cw1) cw2)\n ([cr0, cw1; union cr0 cr1, cw2])\nlet test14 ()\n : IFC unit (union (union cr0 cr1) cr2)\n (union (union cw0 cw1) cw2)\n ([cr0, cw1;\n union cr0 cr1, cw2])\n = (c0 (); c1()); c2()", "val IfcComposeReify.p3_r = \n lo1: FStar.DM4F.Heap.IntStoreFixed.id ->\n lo2: FStar.DM4F.Heap.IntStoreFixed.id ->\n hi: FStar.DM4F.Heap.IntStoreFixed.id ->\n h: FStar.DM4F.Heap.IntStoreFixed.heap\n -> FStar.DM4F.Heap.IntStoreFixed.heap\nlet p3_r lo1 lo2 hi h = (* normalize_term *) (snd (reify (p3 lo1 lo2 hi) h))", "val FStar.IFC.commutative = f: (_: a -> _: a -> a) -> Prims.logical\nlet commutative #a (f: (a -> a -> a)) = forall x y. f x y == f y x", "val bind\n (a b: Type)\n (r0 w0: label)\n (fs0: flows)\n (p: pre)\n (q: post a)\n (r1 w1: label)\n (fs1: flows)\n (r: (a -> pre))\n (s: (a -> post b))\n (x: hifc a r0 w0 fs0 p q)\n (y: (x: a -> hifc b r1 w1 fs1 (r x) (s x)))\n : hifc b\n (union r0 r1)\n (union w0 w1)\n (fs0 @ add_source r0 ((bot, w1) :: fs1))\n (fun s0 -> p s0 /\\ (forall x s1. q s0 x s1 /\\ modifies w0 s0 s1 ==> r x s1))\n (fun s0 r s2 ->\n (exists x s1. (q s0 x s1 /\\ modifies w0 s0 s1) /\\ (s x s1 r s2 /\\ modifies w1 s1 s2)))\nlet bind (a b:Type)\n (r0 w0:label)\n (fs0:flows)\n (p:pre) (q:post a)\n (r1 w1:label) (fs1:flows)\n (r:a -> pre) (s:a -> post b)\n (x:hifc a r0 w0 fs0 p q)\n (y: (x:a -> hifc b r1 w1 fs1 (r x) (s x)))\n : hifc b (union r0 r1) (union w0 w1) (fs0 @ add_source r0 ((bot, w1)::fs1))\n (fun s0 -> p s0 /\\ (forall x s1. q s0 x s1 /\\ modifies w0 s0 s1 ==> r x s1))\n (fun s0 r s2 -> (exists x s1. (q s0 x s1 /\\ modifies w0 s0 s1) /\\ (s x s1 r s2 /\\ modifies w1 s1 s2)))\n = (pre_bind _ _ _ _ _ _ _ _ (frame _ _ _ _ x) (fun a -> frame _ _ _ _ (y a)))", "val test12: Prims.unit\n -> IFC unit\n (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n [(cr0, union cw1 cw2); (union cr0 cr1, cw2)]\nlet test12 ()\n : IFC unit (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n [(cr0, union cw1 cw2);\n (union cr0 cr1, cw2)]\n = c0 (); (c1();c2())", "val FStar.IFC.associative = f: (_: a -> _: a -> a) -> Prims.logical\nlet associative #a (f: (a -> a -> a)) = forall x y z. f (f x y) z == f x (f y z)", "val has_flow_append (from to: loc) (fs fs': flows)\n : Lemma (has_flow from to fs ==> has_flow from to (fs @ fs') /\\ has_flow from to (fs' @ fs))\nlet has_flow_append (from to:loc) (fs fs':flows)\n : Lemma (has_flow from to fs ==>\n has_flow from to (fs @ fs') /\\\n has_flow from to (fs' @ fs))\n = let aux (rs:_)\n : Lemma (requires\n List.Tot.memP rs fs)\n (ensures\n List.Tot.memP rs (fs @ fs') /\\\n List.Tot.memP rs (fs' @ fs))\n [SMTPat (List.Tot.memP rs fs)]\n = memP_append_or rs fs fs';\n memP_append_or rs fs' fs\n in\n ()", "val has_flow_append (from to: loc) (fs fs': flows)\n : Lemma (has_flow from to fs ==> has_flow from to (fs @ fs') /\\ has_flow from to (fs' @ fs))\nlet has_flow_append (from to:loc) (fs fs':flows)\n : Lemma (has_flow from to fs ==>\n has_flow from to (fs @ fs') /\\\n has_flow from to (fs' @ fs))\n = let aux (rs:_)\n : Lemma (requires\n List.Tot.memP rs fs)\n (ensures\n List.Tot.memP rs (fs @ fs') /\\\n List.Tot.memP rs (fs' @ fs))\n [SMTPat (List.Tot.memP rs fs)]\n = memP_append_or rs fs fs';\n memP_append_or rs fs' fs\n in\n ()", "val Sec2.IFC.label_inclusion = l0: Sec2.IFC.label -> l1: Sec2.IFC.label -> Prims.logical\nlet label_inclusion (l0 l1:label) = Set.subset l0 l1", "val test12_1: Prims.unit\n -> IST unit\n (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n [(cr0, cw1); (union cr0 cr1, cw2)]\nlet test12_1 ()\n : IST unit (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n [(cr0, cw1);\n (union cr0 cr1, cw2)]\n = c0 (); (c1();c2())", "val Imp.equiv = p1: Imp.prog -> p2: Imp.prog -> Prims.logical\nlet equiv p1 p2 = eval p1 == eval p2", "val bind_comp_no_leakage\n (#a #b: Type)\n (#w0 #r0 #w1 #r1: label)\n (#fs0 #fs1: flows)\n (x: ist a w0 r0 fs0)\n (y: (a -> ist b w1 r1 fs1))\n (from to: loc)\n (s0: store)\n (k: _)\n : Lemma (requires from <> to /\\ ~(has_flow from to (fs0 @ add_source r0 ((bot, w1) :: fs1))))\n (ensures\n (let f = bind_comp x y in\n let s0' = havoc s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to))\nlet bind_comp_no_leakage (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n (from to:loc)\n (s0:store) (k:_)\n : Lemma\n (requires from <> to /\\ ~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1))))\n (ensures (let f = bind_comp x y in\n let s0' = havoc s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to))\n = let f = bind_comp x y in\n assert (reads_ok x r0);\n let s0' = havoc s0 from k in\n let _, s2f = f s0 in\n let _, s2f' = f s0' in\n let flows = (fs0 @ add_source r0 ((r1, w1)::fs1)) in\n let v0, s1 = x s0 in\n let v0', s1' = x s0' in\n elim_has_flow_seq from to r0 r1 w1 fs0 fs1;\n assert (~(has_flow from to fs0));\n assert (respects_flows x fs0);\n assert (no_leakage x from to);\n assert (sel s1 to == sel s1' to);\n let _, s2 = y v0 s1 in\n let _, s2' = y v0' s1' in\n assert (s2 == s2f);\n assert (s2' == s2f');\n //Given: (from not-in r0 U r1) \\/ (to not-in w1)\n //suppose (from in r0) \\/ (from in r1)\n // them to not-in w1\n //suppose (from not-in r0 U r1)\n //then v0 = v0'\n // s1' = havoc from s1 k\n // s2 to = s2' to\n if Set.mem to w1\n then begin\n assert (~(Set.mem from r0));\n assert (reads_ok x r0);\n assert (does_not_read_loc x r0 from s0);\n assert (does_not_read_loc_v x r0 from s0 k);\n assert (v0 == v0');\n assert (forall l. l <> from ==> sel s1 l == sel s1' l);\n assert (Map.equal s1' (havoc s1 from k) \\/ Map.equal s1' s1);\n if (sel s1 from = sel s1' from)\n then begin\n assert (Map.equal s1 s1')\n end\n else begin\n assert (Map.equal s1' (havoc s1 from k));\n assert (reads_ok (y v0) r1);\n if (sel s2 to = sel s2' to)\n then ()\n else begin\n assert (sel s2 to <> sel s1 to \\/ sel s2' to <> sel s1' to);\n has_flow_soundness (y v0) from to s1 k;\n assert (has_flow from to fs1);\n add_source_monotonic from to r0 fs1\n //y reads from and writes to, so (from, to) should be in fs1\n //so, we should get a contradiction\n end\n end\n end\n else //to is not in w1, so y does not write it\n ()", "val Sec2.HIFC.unit_triple = (Sec2.HIFC.label * Sec2.HIFC.label) * Prims.list _\nlet unit_triple = bot, bot, []", "val FStar.Relational.Relational.and_rel = _: FStar.Relational.Relational.double Prims.bool -> _: FStar.Relational.Relational.double Prims.bool\n -> FStar.Relational.Relational.double Prims.bool\nlet and_rel = rel_map2T (fun x y -> x && y)", "val Sec2.IFC.label_equiv = s0: Sec2.IFC.label -> s1: Sec2.IFC.label -> Type0\nlet label_equiv (s0 s1:label) = Set.equal s0 s1", "val FStar.Relational.Relational.or_rel = _: FStar.Relational.Relational.double Prims.bool -> _: FStar.Relational.Relational.double Prims.bool\n -> FStar.Relational.Relational.double Prims.bool\nlet or_rel = rel_map2T (fun x y -> x || y)", "val OPLSS2021.ParNDSDiv.is_unit = x: a -> f: (_: a -> _: a -> a) -> Prims.logical\nlet is_unit #a (x:a) (f:a -> a -> a) =\n forall y. f x y == y /\\ f y x == y", "val refine_flow (#a #w #r #f #fs #p #q: _) ($c: (unit -> HIFC a r w (f :: fs) p q))\n : Pure (unit -> HIFC a r w fs p q)\n (requires\n (forall from to v.\n has_flow_1 from to f /\\ from <> to ==>\n (forall s0 x x' s1 s1'.\n p s0 /\\ p (upd s0 from v) /\\ q s0 x s1 /\\ modifies w s0 s1 /\\\n q (upd s0 from v) x' s1' /\\ modifies w (upd s0 from v) s1' ==>\n sel s1 to == sel s1' to)))\n (ensures fun _ -> True)\nlet refine_flow #a #w #r #f #fs #p #q\n ($c: unit -> HIFC a r w (f::fs) p q)\n : Pure (unit -> HIFC a r w fs p q)\n (requires\n (forall from to v.\n has_flow_1 from to f /\\\n from <> to ==>\n (forall s0 x x' s1 s1'.\n p s0 /\\\n p (upd s0 from v) /\\\n q s0 x s1 /\\\n modifies w s0 s1 /\\\n q (upd s0 from v) x' s1' /\\\n modifies w (upd s0 from v) s1' ==>\n sel s1 to == sel s1' to)))\n (ensures fun _ -> True)\n = (fun () -> HIFC?.reflect (refine_flow_hifc (reify (c()))))", "val Sec2.HIFC.does_not_read_loc = f: Sec2.HIFC.hst a p q -> reads: Sec2.HIFC.label -> l: Sec2.HIFC.loc -> s0: Sec2.HIFC.store{p s0}\n -> Prims.logical\nlet does_not_read_loc #a #p #q (f:hst a p q) (reads:label) (l:loc) (s0:store{p s0}) =\n forall v. does_not_read_loc_v f reads l s0 v", "val OPLSS2021.Basic.llist = a: Type -> n: OPLSS2021.Basic.nat -> Type\nlet llist a (n:nat) = l:list a { length l = n}", "val OPLSS2021.ParDiv.comp = \n a: Type ->\n p: Mkcomm_monoid?.r OPLSS2021.ParDiv.hm ->\n q: (_: a -> Mkcomm_monoid?.r OPLSS2021.ParDiv.hm)\n -> Type0\nlet comp (a:Type u#a) (p:hm.r) (q:a -> hm.r)\n = unit -> Dv (m a p q)", "val flows_equiv_append (f0 f1 g0 g1: flows)\n : Lemma (requires flows_equiv f0 g0 /\\ flows_equiv f1 g1)\n (ensures flows_equiv (f0 @ f1) (g0 @ g1))\nlet flows_equiv_append (f0 f1 g0 g1:flows)\n : Lemma (requires flows_equiv f0 g0 /\\ flows_equiv f1 g1)\n (ensures flows_equiv (f0@f1) (g0@g1))\n = flows_included_append f0 f1 g0 g1;\n flows_included_append g0 g1 f0 f1", "val flows_equiv_append (f0 f1 g0 g1: flows)\n : Lemma (requires flows_equiv f0 g0 /\\ flows_equiv f1 g1)\n (ensures flows_equiv (f0 @ f1) (g0 @ g1))\nlet flows_equiv_append (f0 f1 g0 g1:flows)\n : Lemma (requires flows_equiv f0 g0 /\\ flows_equiv f1 g1)\n (ensures flows_equiv (f0@f1) (g0@g1))\n = flows_included_append f0 f1 g0 g1;\n flows_included_append g0 g1 f0 f1", "val Sec2.HIFC.modifies = w: Sec2.HIFC.label -> s0: Sec2.HIFC.store -> s1: Sec2.HIFC.store -> Prims.logical\nlet modifies (w:label) (s0 s1:store) = (forall l.{:pattern (sel s1 l)} ~(Set.mem l w) ==> sel s0 l == sel s1 l)", "val IfcRecursiveHeapReify.op_Star = _: Prims.int -> _: Prims.int -> Prims.int\nlet op_Star = op_Multiply", "val IfcComposeReify.p2_r = \n lo: FStar.DM4F.Heap.IntStoreFixed.id ->\n hi: FStar.DM4F.Heap.IntStoreFixed.id ->\n h: FStar.DM4F.Heap.IntStoreFixed.heap\n -> FStar.DM4F.Heap.IntStoreFixed.heap\nlet p2_r lo hi h = (* normalize_term *) (snd (reify (p2 lo hi) h))", "val test13: Prims.unit\n -> IST unit\n (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n (add_source cr0 [bot, cw1] @ add_source (union cr0 cr1) [bot, cw2])\nlet test13 ()\n : IST unit (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n (add_source cr0 [bot, cw1] @\n add_source (union cr0 cr1) [bot, cw2])\n = (c0 (); c1());c2()", "val IfcComposeReify.p2 = lo: FStar.DM4F.Heap.IntStoreFixed.id -> hi: FStar.DM4F.Heap.IntStoreFixed.id\n -> FStar.DM4F.IntStoreFixed.INT_STORE Prims.unit\nlet p2 lo hi =\n if (is_x hi 1) then \n write lo (read hi)\n else \n write lo 1", "val FStar.IFC.idempotent = f: (_: a -> _: a -> a) -> Prims.logical\nlet idempotent #a (f: (a -> a -> a)) = forall x. f x x == x", "val test10: Prims.unit\n -> IST unit\n (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n (add_source cr0 ((bot, union cw1 cw2) :: (add_source cr1 [bot, cw2])))\nlet test10 ()\n : IST unit (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n (add_source cr0\n ((bot, union cw1 cw2)::\n (add_source cr1 [bot, cw2])))\n = c0 (); (c1();c2())", "val IfcComposeReify.p1_r = \n lo: FStar.DM4F.Heap.IntStoreFixed.id ->\n hi: FStar.DM4F.Heap.IntStoreFixed.id ->\n h: FStar.DM4F.Heap.IntStoreFixed.heap\n -> FStar.DM4F.Heap.IntStoreFixed.heap\nlet p1_r lo hi h = (* normalize_term *) (snd (reify (p1 lo hi) h))", "val OPLSS.lbytes = l: Prims.nat -> Type0\nlet lbytes l = b:bytes{Seq.length b = l}", "val DoublyLinkedListIface.fp_strictly_disjoint_union = \n l: LowStar.Monotonic.Buffer.loc ->\n l1: LowStar.Monotonic.Buffer.loc ->\n l2: LowStar.Monotonic.Buffer.loc\n -> Prims.logical\nlet fp_strictly_disjoint_union (l l1 l2:B.loc) =\n l `loc_equiv` B.loc_union l1 l2 /\\\n l1 `B.loc_disjoint` l2", "val test14: Prims.unit\n -> IST unit\n (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n ([cr0, cw1; union cr0 cr1, cw2])\nlet test14 ()\n : IST unit (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n ([cr0, cw1;\n union cr0 cr1, cw2])\n = (c0 (); c1()); c2()", "val OPLSS2021.ParNDSDiv.comp = \n a: Type ->\n p: Mkcomm_monoid?.r OPLSS2021.ParNDSDiv.hm ->\n q: (_: a -> Mkcomm_monoid?.r OPLSS2021.ParNDSDiv.hm)\n -> Type0\nlet comp (a:Type u#a) (p:hm.r) (q:a -> hm.r)\n = unit -> Dv (m a p q)", "val Sec2.HIFC.no_leakage = f: Sec2.HIFC.hst a p q -> from: Sec2.HIFC.loc -> to: Sec2.HIFC.loc -> Prims.logical\nlet no_leakage #a #p #q (f:hst a p q) (from to:loc) = forall k. no_leakage_k f from to k", "val InlineSingletonRecords.simplify_prog = p: Prims.list Ast.decl -> FStar.All.ALL (Prims.list Ast.decl)\nlet simplify_prog (p:list decl) =\r\n let env = H.create 10 in\r\n List.map (simplify_decl env) p", "val Benton2004.DDCC.d_kbf = \n b: Benton2004.exp Prims.bool ->\n phi: Benton2004.DDCC.sttype ->\n c1: Benton2004.computation ->\n c2: Benton2004.computation ->\n c': Benton2004.computation ->\n phi': Benton2004.DDCC.sttype\n -> FStar.Pervasives.Lemma\n (requires\n Benton2004.eval_equiv phi (Benton2004.DDCC.ns_singl false) b b /\\\n Benton2004.DDCC.exec_equiv phi phi' c2 c')\n (ensures Benton2004.DDCC.exec_equiv phi phi' (Benton2004.ifthenelse b c1 c2) c')\n [\n SMTPat (Benton2004.eval_equiv phi (Benton2004.DDCC.ns_singl false) b b);\n SMTPat (Benton2004.DDCC.exec_equiv phi phi' (Benton2004.ifthenelse b c1 c2) c')\n ]\nlet d_kbf = d_kb false", "val FStar.FiniteSet.Base.union_idempotent_left_fact = Prims.logical\nlet union_idempotent_left_fact =\n forall (a: eqtype) (s1: set a) (s2: set a).{:pattern union s1 (union s1 s2)}\n union s1 (union s1 s2) == union s1 s2", "val IfcExampleReify2.env = var: FStar.DM4F.Heap.IntStoreFixed.id -> IfcRulesReify.label\nlet env var =\n if var = hi then High\n else if var = lo then Low\n else if var = c then Low\n else High", "val Benton2004.DDCC.d_kbt = \n b: Benton2004.exp Prims.bool ->\n phi: Benton2004.DDCC.sttype ->\n c1: Benton2004.computation ->\n c2: Benton2004.computation ->\n c': Benton2004.computation ->\n phi': Benton2004.DDCC.sttype\n -> FStar.Pervasives.Lemma\n (requires\n Benton2004.eval_equiv phi (Benton2004.DDCC.ns_singl true) b b /\\\n Benton2004.DDCC.exec_equiv phi phi' c1 c')\n (ensures Benton2004.DDCC.exec_equiv phi phi' (Benton2004.ifthenelse b c1 c2) c')\n [\n SMTPat (Benton2004.eval_equiv phi (Benton2004.DDCC.ns_singl true) b b);\n SMTPat (Benton2004.DDCC.exec_equiv phi phi' (Benton2004.ifthenelse b c1 c2) c')\n ]\nlet d_kbt = d_kb true", "val IfcRecursiveReify.p3_r = \n lo1: FStar.DM4F.Heap.IntStoreFixed.id ->\n lo2: FStar.DM4F.Heap.IntStoreFixed.id ->\n hi: FStar.DM4F.Heap.IntStoreFixed.id ->\n n: Prims.int ->\n h: FStar.DM4F.Heap.IntStoreFixed.heap\n -> FStar.DM4F.Heap.IntStoreFixed.heap\nlet p3_r lo1 lo2 hi n h = (* normalize_term *) (snd (reify (p3 lo1 lo2 hi n) h))" ], "closest_src": [ { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.comp_triple" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.ifc_triple" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.triple_equiv" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.assoc_comp" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.triple_equiv" }, { "project_name": "FStar", "file_name": "FStar.DM4F.IFC.fst", "name": "FStar.DM4F.IFC.flows" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.assoc_hst" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.has_flow" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.has_flow_1" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.right_unit" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.left_unit" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.union" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.respects_flows" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.flows_equiv" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.has_flow_1" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.union" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.has_flow" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.ist" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.left_unit" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.right_unit" }, { "project_name": "FStar", "file_name": "FStar.DM4F.IFC.fst", "name": "FStar.DM4F.IFC.join" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.no_leakage" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.flows_equiv" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.flows_included_in" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.elim_has_flow_seq" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.elim_has_flow_seq" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.unit_triple" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.bind_ifc_flows_ok" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.bind_comp_flows_ok" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.does_not_read_loc" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParNDSDiv.fst", "name": "OPLSS2021.ParNDSDiv.commutative" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.bind_ifc'" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParNDSDiv.fst", "name": "OPLSS2021.ParNDSDiv.associative" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParDiv.fst", "name": "OPLSS2021.ParDiv.commutative" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.if_then_else" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.does_not_read_loc_v" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.no_leakage_k" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test13" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.respects" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.ist_exn" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.subcomp" }, { "project_name": "FStar", "file_name": "OPLSS2021.STLC.fst", "name": "OPLSS2021.STLC.equalE" }, { "project_name": "FStar", "file_name": "OPLSS2021.ValeVC.fst", "name": "OPLSS2021.ValeVC.t_lemma" }, { "project_name": "FStar", "file_name": "OPLSS2021.STLC.fst", "name": "OPLSS2021.STLC.equal" }, { "project_name": "FStar", "file_name": "IfcComposeReify.fst", "name": "IfcComposeReify.p3" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test10" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParDiv.fst", "name": "OPLSS2021.ParDiv.associative" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.bind_hst_no_leakage" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.hifc" }, { "project_name": "FStar", "file_name": "FStar.Relational.Relational.fst", "name": "FStar.Relational.Relational.triple_rel" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.refine_flow_hifc" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test12_1" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.sub_hifc" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.writes_ok" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.bind" }, { "project_name": "FStar", "file_name": "FStar.Relational.Relational.fst", "name": "FStar.Relational.Relational.cons_rel" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.flows_included_in" }, { "project_name": "FStar", "file_name": "IfcExample.fst", "name": "IfcExample.env" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test14" }, { "project_name": "FStar", "file_name": "IfcComposeReify.fst", "name": "IfcComposeReify.p3_r" }, { "project_name": "FStar", "file_name": "FStar.IFC.fsti", "name": "FStar.IFC.commutative" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.bind" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test12" }, { "project_name": "FStar", "file_name": "FStar.IFC.fsti", "name": "FStar.IFC.associative" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.has_flow_append" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.has_flow_append" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.label_inclusion" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.test12_1" }, { "project_name": "FStar", "file_name": "Imp.fst", "name": "Imp.equiv" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.bind_comp_no_leakage" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.unit_triple" }, { "project_name": "FStar", "file_name": "FStar.Relational.Relational.fst", "name": "FStar.Relational.Relational.and_rel" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.label_equiv" }, { "project_name": "FStar", "file_name": "FStar.Relational.Relational.fst", "name": "FStar.Relational.Relational.or_rel" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParNDSDiv.fst", "name": "OPLSS2021.ParNDSDiv.is_unit" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.refine_flow" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.does_not_read_loc" }, { "project_name": "FStar", "file_name": "OPLSS2021.Basic.fst", "name": "OPLSS2021.Basic.llist" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParDiv.fst", "name": "OPLSS2021.ParDiv.comp" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.flows_equiv_append" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.flows_equiv_append" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.modifies" }, { "project_name": "FStar", "file_name": "IfcRecursiveHeapReify.fst", "name": "IfcRecursiveHeapReify.op_Star" }, { "project_name": "FStar", "file_name": "IfcComposeReify.fst", "name": "IfcComposeReify.p2_r" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.test13" }, { "project_name": "FStar", "file_name": "IfcComposeReify.fst", "name": "IfcComposeReify.p2" }, { "project_name": "FStar", "file_name": "FStar.IFC.fsti", "name": "FStar.IFC.idempotent" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.test10" }, { "project_name": "FStar", "file_name": "IfcComposeReify.fst", "name": "IfcComposeReify.p1_r" }, { "project_name": "FStar", "file_name": "OPLSS.fst", "name": "OPLSS.lbytes" }, { "project_name": "FStar", "file_name": "DoublyLinkedListIface.fsti", "name": "DoublyLinkedListIface.fp_strictly_disjoint_union" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.test14" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParNDSDiv.fst", "name": "OPLSS2021.ParNDSDiv.comp" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.no_leakage" }, { "project_name": "everparse", "file_name": "InlineSingletonRecords.fst", "name": "InlineSingletonRecords.simplify_prog" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fsti", "name": "Benton2004.DDCC.d_kbf" }, { "project_name": "FStar", "file_name": "FStar.FiniteSet.Base.fsti", "name": "FStar.FiniteSet.Base.union_idempotent_left_fact" }, { "project_name": "FStar", "file_name": "IfcExampleReify2.fst", "name": "IfcExampleReify2.env" }, { "project_name": "FStar", "file_name": "Benton2004.DDCC.fsti", "name": "Benton2004.DDCC.d_kbt" }, { "project_name": "FStar", "file_name": "IfcRecursiveReify.fst", "name": "IfcRecursiveReify.p3_r" } ], "selected_premises": [ "OPLSS2021.IFC.unit_triple", "OPLSS2021.IFC.triple", "OPLSS2021.IFC.no_leakage_k", "OPLSS2021.IFC.bind_comp", "OPLSS2021.IFC.flows_equiv", "OPLSS2021.IFC.flows", "FStar.Pervasives.reveal_opaque", "FStar.Pervasives.Native.snd", "OPLSS2021.IFC.respects_flows", "FStar.Pervasives.Native.fst", "OPLSS2021.IFC.no_leakage", "OPLSS2021.IFC.bind_comp_no_leakage", "OPLSS2021.IFC.ist", "OPLSS2021.IFC.upd", "OPLSS2021.IFC.sel", "OPLSS2021.IFC.single", "OPLSS2021.IFC.does_not_read_loc_v", "OPLSS2021.IFC.flow", "OPLSS2021.IFC.add_source_monotonic", "OPLSS2021.IFC.bind_comp_reads_ok", "OPLSS2021.IFC.bind_comp_flows_ok", "OPLSS2021.IFC.add_source", "OPLSS2021.IFC.writes_ok", "FStar.Pervasives.dfst", "OPLSS2021.IFC.does_not_read_loc", "FStar.Pervasives.dsnd", "OPLSS2021.IFC.comp", "OPLSS2021.IFC.union", "OPLSS2021.IFC.add_sink", "OPLSS2021.IFC.has_flow_soundness", "OPLSS2021.IFC.return", "OPLSS2021.IFC.elim_has_flow_seq", "OPLSS2021.IFC.havoc", "OPLSS2021.IFC.label", "OPLSS2021.IFC.has_flow", "OPLSS2021.IFC.iwrite", "OPLSS2021.IFC.reads_ok", "OPLSS2021.IFC.iread", "OPLSS2021.IFC.label_inclusion", "OPLSS2021.IFC.flows_included_in", "OPLSS2021.IFC.bot", "OPLSS2021.IFC.has_flow_append", "OPLSS2021.IFC.memP_append_or", "FStar.Pervasives.coerce_eq", "Prims.op_Hat", "OPLSS2021.IFC.has_flow_1", "FStar.Set.add", "OPLSS2021.IFC.loc", "FStar.Pervasives.pure_ite_wp", "FStar.Pervasives.ex_stronger", "Prims.pure_wp_monotonic", "FStar.Set.disjoint", "FStar.Pervasives.pure_bind_wp", "Prims.auto_squash", "FStar.Pervasives.id", "FStar.Set.remove", "Prims.pure_wp", "FStar.Pervasives.st_bind_wp", "FStar.Pervasives.ex_trivial", "FStar.Pervasives.ex_wp", "FStar.Set.subset", "Prims.pow2", "FStar.Calc.calc_chain_related", "FStar.Pervasives.ex_bind_wp", "FStar.Pervasives.ex_if_then_else", "FStar.Map.const_on", "FStar.Pervasives.ex_post'", "FStar.Pervasives.ex_post", "FStar.Pervasives.ex_ite_wp", "FStar.Pervasives.ex_pre", "Prims.min", "FStar.Pervasives.pure_return", "Prims.pure_trivial", "FStar.Pervasives.ex_return", "Prims.returnM", "FStar.Set.as_set'", "Prims.pure_wp'", "FStar.Pervasives.st_if_then_else", "Prims.l_True", "FStar.Pervasives.lift_div_exn", "Prims.pure_pre", "FStar.Pervasives.st_stronger", "Prims.pure_wp_monotonic0", "FStar.Pervasives.pure_close_wp", "FStar.Pervasives.st_wp_h", "Prims.subtype_of", "FStar.Pervasives.div_hoare_to_wp", "FStar.Pervasives.all_if_then_else", "Prims.as_requires", "Prims.pure_stronger", "FStar.Calc.calc_chain_compatible", "FStar.Pervasives.ex_close_wp", "OPLSS2021.IFC.store", "FStar.Preorder.reflexive", "FStar.Preorder.preorder_rel", "Prims.purewp_id", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.st_ite_wp", "FStar.Preorder.transitive", "FStar.Set.as_set" ], "source_upto_this": "(*\n Copyright 2021 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule OPLSS2021.IFC\nopen FStar.List.Tot\nopen FStar.Set\nopen FStar.Map\n\n(* This module defines another abstraction for reasoning about\n information flows in stateful computations reading and writing to\n an integer store.\n\n The main computation type it defines at the end is `IST a w r fs`,\n where\n - `a` is the result type\n - `w` is the set of memory locations written\n - `r` is the set of memory locations read\n - `fs` is a set of flows, ordered pairs of sets of locations\n between bounding the information flows in the program\n\n The point is to illustrate that you can choose whatever abstraction\n you like to reason about your programs, not necessarily a Hoare\n logic.\n\n This turns out to be an instance of Katsumata's graded monads.\n\n Read more about it in this paper:\n https://www.fstar-lang.org/papers/layeredeffects/\n*)\n\n/// The type of memory locations\nlet loc = int\n\n/// A store itself is a total map from locations to integers\nlet store = m:Map.t loc int{forall l. contains m l}\n\n/// Two functions to read and write the store\nlet sel (s:store) (l:loc) : int = Map.sel s l\nlet upd (s:store) (l:loc) (x:int) : store = Map.upd s l x\n\n/// Our abstraction to reason about information flows is based on\n/// labels, sets of memory locations\nlet label = Set.set loc\n\n/// An ordering on labels, just set inclusion\nlet label_inclusion (l0 l1:label) = Set.subset l0 l1\n\n/// A bottom for the label lattice\nlet bot : label = Set.empty\n\n/// A singleton label\nlet single (l:loc) : label = Set.singleton l\n\n/// A join for our lattice: just set union\nlet union (l0 l1:label) = Set.union l0 l1\n\n/// comp a: A computation monad representing our stateful computations\nlet comp a = store -> a & store\n\n/// havoc, or mess up, a single memory location in s by updating it\nlet havoc s l x = upd s l x\n\n/// Now, we're going to have to (slowly) define what it means for a\n/// program to have or not have certain kinds of information flows.\n\n/// Defining what it means for f's mutations to be confined to\n/// `writes` is easy\n/// -- all locations not in writes do not change\nlet writes_ok #a (f:comp a) (writes:Set.set loc) =\n forall (l:loc). ~(Set.mem l writes) ==>\n (forall (s0:store).\n let x1, s0' = f s0 in\n sel s0 l == sel s0' l)\n\n/// Definiting what it means for `f` to not read a location `l`\n/// is trickier. It involves a \"relational\" property, relating\n/// multiple executions of `f`\nlet does_not_read_loc_v #a (f:comp a) (l:loc) (s0:store) v =\n let s0' = havoc s0 l v in //s0 and s0' agree except on l\n let x1, s1 = f s0 in\n let x1', s1' = f s0' in // run f twice, once on s0, once on s0'\n x1 == x1' /\\ //result does not depend on l\n (forall l'. l' <> l ==> //for every location l' not equal to l\n sel s1 l' == sel s1' l') /\\ //its value in the two states is the same\n (sel s1 l == sel s1' l \\/ //and l is itself may be written, in which case its value is the same in both final states\n //or its not, but then its values in the initial and final states are the same in both runs\n (sel s1 l == sel s0 l /\\\n sel s1' l == sel s0' l))\n\n/// does_not_read_loc: Lifting the prior property to all values for\n/// the havoc'd location l\nlet does_not_read_loc #a (f:comp a) (l:loc) (s0:store) =\n forall v. does_not_read_loc_v f l s0 v\n\n/// A reads label is ok for `f` if it is a bound on the set of\n/// locations that `f` reads\nlet reads_ok #a (f:comp a) (reads:label) =\n forall (l:loc) (s:store). ~(Set.mem l reads) ==> does_not_read_loc f l s\n\n/// Now for the flows index\nlet flow = label & label //from, to\nlet flows = list flow\n\n/// `has_flow from to fs` defines when the edge `from -> to` is includes in\n/// the flows `fs`\nlet has_flow_1 (from to:loc) (f:flow) = from `Set.mem` fst f /\\ to `Set.mem` snd f\nlet has_flow (from to:loc) (fs:flows) = exists rs. rs `List.Tot.memP` fs /\\ has_flow_1 from to rs\n\n/// Now, as with reads and writes, we have to give an interpretation\n/// to flows tying it to the computational representation\n\n/// `f` leaks no info along the flow edge `from -> to`\n/// --- This is a textbook definition of noninterference\nlet no_leakage_k #a (f:comp a) (from to:loc) (k:int) =\n forall s0.{:pattern (havoc s0 from k)}\n sel (snd (f s0)) to == sel (snd (f (havoc s0 from k))) to\nlet no_leakage #a (f:comp a) (from to:loc) = forall k. no_leakage_k f from to k\n/// A computation `f` respects all the flows in `fs`\n/// if it there is no leakage along any of the flow-edges in `f`\nlet respects_flows #a (f:comp a) (fs:flows) =\n forall from to. {:pattern (no_leakage f from to)} ~(has_flow from to fs) /\\ from<>to ==> no_leakage f from to\n\n/// Now, we can define our representation type, a refinement of the\n/// comp type where the refinement \"gives a meaning\" to the labels\n/// involved\nlet ist a (writes:label) (reads:label) (fs:flows) =\n f:comp a {\n reads_ok f reads /\\\n writes_ok f writes /\\\n respects_flows f fs\n }\n\n/// Now, proving that this representation is stable is going to take\n/// some work.\n\n/// Some basic actions to read and write and a return are easy enough\nlet iread (l:loc) : ist int bot (single l) [] = fun s -> sel s l, s\nlet iwrite (l:loc) (x:int) : ist unit (single l) bot [] = fun s -> (), upd s l x\nlet return (a:Type) (x:a) : ist a bot bot [] = fun s -> x,s\n\n/// But, proving that ist computations can be sequentially composed is\n/// a bit challenging\n\n/// First, some auxiliary notions defining a small algebra on flows\nlet add_source (r:label) (fs:flows) : flows = List.Tot.map (fun (r0, w0) -> union r r0, w0) fs\nlet add_sink (w:label) (fs:flows) : flows = List.Tot.map (fun (r0, w0) -> r0, union w w0) fs\nlet flows_included_in (fs0 fs1:flows) =\n forall f0. f0 `List.Tot.memP` fs0 ==>\n (forall from to. has_flow_1 from to f0 /\\ from <> to ==> (exists f1. f1 `List.Tot.memP` fs1 /\\ has_flow_1 from to f1))\nlet flows_equiv (fs0 fs1:flows) = fs0 `flows_included_in` fs1 /\\ fs1 `flows_included_in` fs0\nlet flows_equiv_refl fs\n : Lemma (fs `flows_equiv` fs)\n = ()\nlet flows_equiv_trans fs0 fs1 fs2\n : Lemma (fs0 `flows_equiv` fs1 /\\ fs1 `flows_equiv` fs2 ==> fs0 `flows_equiv` fs2)\n = ()\nlet flows_included_in_union_distr_dest (a b c:label)\n : Lemma (flows_equiv [a, union b c] [a, b; a, c])\n = ()\nlet flows_included_in_union_distr_src (a b c:label)\n : Lemma (flows_equiv [union a b, c] [a, c; b, c])\n = ()\nlet flows_included_in_union (a b c:label)\n : Lemma (flows_equiv ([a, union b c; union a b, c])\n ([a, b; union a b, c]))\n = ()\n\n\n\nlet bind_comp (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : comp b\n = fun s0 -> let v, s1 = x s0 in y v s1\n\nlet bind_comp_reads_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (reads_ok (bind_comp x y) (union r0 r1))\n = let f = bind_comp x y in\n let reads = union r0 r1 in\n let f_reads_ok (l:loc) (s0:store)\n : Lemma (requires (~(Set.mem l reads)))\n (ensures (does_not_read_loc f l s0))\n [SMTPat (does_not_read_loc f l s0)]\n = let aux (k:_)\n : Lemma (ensures (does_not_read_loc_v f l s0 k))\n [SMTPat (does_not_read_loc_v f l s0 k)]\n = let v, s1 = x s0 in\n let v', s1' = x (havoc s0 l k) in\n assert (does_not_read_loc x l s0);\n assert (does_not_read_loc_v x l s0 k);\n assert (v == v');\n assert (does_not_read_loc (y v) l s1);\n let u, s2 = y v s1 in\n let u', s2' = y v s1' in\n assert (forall l'. l' <> l ==> sel s1 l' == sel s1' l');\n if sel s1 l = sel s1' l\n then (assert (forall l. sel s1 l == sel s1' l);\n assert (Map.equal s1 s1'))\n else (assert (sel s1 l == sel s0 l /\\\n sel (havoc s0 l k) l == sel s1' l);\n assert (Map.equal s1' (havoc s1 l k)))\n in\n ()\n in\n ()\n\nlet bind_comp_writes_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (writes_ok (bind_comp x y) (union w0 w1))\n = ()\n\nlet rec memP_append_or (#a:Type) (x:a) (l0 l1:list a)\n : Lemma (ensures (List.Tot.memP x (l0 @ l1) <==>\n (List.Tot.memP x l0 \\/ List.Tot.memP x l1)))\n (decreases l0)\n = match l0 with\n | [] -> ()\n | _::tl -> memP_append_or x tl l1\n\nlet has_flow_append (from to:loc) (fs fs':flows)\n : Lemma (has_flow from to fs ==>\n has_flow from to (fs @ fs') /\\\n has_flow from to (fs' @ fs))\n = let rec aux (rs:_)\n : Lemma (requires\n List.Tot.memP rs fs)\n (ensures\n List.Tot.memP rs (fs @ fs') /\\\n List.Tot.memP rs (fs' @ fs))\n [SMTPat (List.Tot.memP rs fs)]\n = memP_append_or rs fs fs';\n memP_append_or rs fs' fs\n in\n ()\n\nlet elim_has_flow_seq (from to:loc)\n (r0 r1 w1:label)\n (fs0 fs1:flows)\n : Lemma (requires (~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1)))))\n (ensures (~(has_flow from to fs0) /\\\n (~(Set.mem from r0) \\/ ~(Set.mem to w1)) /\\\n ~(has_flow from to (add_source r0 fs1))))\n = assert (add_source r0 ((bot, w1)::fs1) ==\n (Set.union r0 bot, w1)::add_source r0 fs1);\n assert (Set.union r0 bot `Set.equal` r0);\n has_flow_append from to fs0 ((r0, w1)::add_source r0 fs1);\n assert (~(has_flow from to fs0));\n has_flow_append from to ((r0, w1)::add_source r0 fs1) fs0;\n assert (~(has_flow from to (((r0, w1)::add_source r0 fs1))));\n assert ((r0, w1)::add_source r0 fs1 ==\n [r0, w1] @ add_source r0 fs1);\n has_flow_append from from [r0, w1] (add_source r0 fs1)\n\nlet rec add_source_monotonic (from to:loc) (r:label) (fs:flows)\n : Lemma (has_flow from to fs ==> has_flow from to (add_source r fs))\n = match fs with\n | [] -> ()\n | _::tl -> add_source_monotonic from to r tl\n\nlet has_flow_soundness #a #r #w #fs (f:ist a r w fs)\n (from to:loc) (s:store) (k:int)\n : Lemma (requires\n (let x, s1 = f s in\n let _, s1' = f (havoc s from k) in\n from <> to /\\\n sel s1 to <> sel s1' to))\n (ensures has_flow from to fs)\n = let aux ()\n : Lemma (requires (~(has_flow from to fs)))\n (ensures False)\n [SMTPat ()]\n = assert (respects_flows f fs);\n assert (no_leakage f from to)\n in\n ()\n\nlet bind_comp_no_leakage (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n (from to:loc)\n (s0:store) (k:_)\n : Lemma\n (requires from <> to /\\ ~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1))))\n (ensures (let f = bind_comp x y in\n let s0' = havoc s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to))\n = let f = bind_comp x y in\n assert (reads_ok x r0);\n let s0' = havoc s0 from k in\n let _, s2f = f s0 in\n let _, s2f' = f s0' in\n let flows = (fs0 @ add_source r0 ((r1, w1)::fs1)) in\n let v0, s1 = x s0 in\n let v0', s1' = x s0' in\n elim_has_flow_seq from to r0 r1 w1 fs0 fs1;\n assert (~(has_flow from to fs0));\n assert (respects_flows x fs0);\n assert (no_leakage x from to);\n assert (sel s1 to == sel s1' to);\n let _, s2 = y v0 s1 in\n let _, s2' = y v0' s1' in\n assert (s2 == s2f);\n assert (s2' == s2f');\n //Given: (from not-in r0 U r1) \\/ (to not-in w1)\n //suppose (from in r0) \\/ (from in r1)\n // them to not-in w1\n //suppose (from not-in r0 U r1)\n //then v0 = v0'\n // s1' = havoc from s1 k\n // s2 to = s2' to\n if Set.mem to w1\n then begin\n assert (~(Set.mem from r0));\n assert (reads_ok x r0);\n assert (does_not_read_loc x from s0);\n assert (does_not_read_loc_v x from s0 k);\n assert (v0 == v0');\n assert (forall l. l <> from ==> sel s1 l == sel s1' l);\n assert (Map.equal s1' (havoc s1 from k) \\/ Map.equal s1' s1);\n if (sel s1 from = sel s1' from)\n then begin\n assert (Map.equal s1 s1')\n end\n else begin\n assert (Map.equal s1' (havoc s1 from k));\n assert (reads_ok (y v0) r1);\n if (sel s2 to = sel s2' to)\n then ()\n else begin\n assert (sel s2 to <> sel s1 to \\/ sel s2' to <> sel s1' to);\n has_flow_soundness (y v0) from to s1 k;\n assert (has_flow from to fs1);\n add_source_monotonic from to r0 fs1\n //y reads from and writes to, so (from, to) should be in fs1\n //so, we should get a contradiction\n end\n end\n end\n else //to is not in w1, so y does not write it\n ()\n\nlet bind_comp_flows_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (respects_flows (bind_comp x y) (fs0 @ add_source r0 ((bot, w1)::fs1)))\n = let f = bind_comp x y in\n let flows = (fs0 @ add_source r0 ((bot, w1)::fs1)) in\n let respects_flows_lemma (from to:loc)\n : Lemma (requires from <> to /\\ ~(has_flow from to flows))\n (ensures no_leakage f from to)\n [SMTPat (no_leakage f from to)]\n = let aux (s0:store) (k:_)\n : Lemma (let s0' = havoc s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to)\n [SMTPat (havoc s0 from k)]\n = bind_comp_no_leakage x y from to s0 k\n in\n ()\n in\n ()\n\nlet triple = label & label & flows\nlet unit_triple = bot, bot, []" }, { "file_name": "Pulse.Typing.FV.fst", "name": "Pulse.Typing.FV.vars_of_rt_env", "opens_and_abbrevs": [ { "open": "Pulse.Soundness.Common" }, { "open": "Pulse.Elaborate" }, { "open": "Pulse.Typing" }, { "open": "Pulse.Syntax" }, { "open": "FStar.List.Tot" }, { "abbrev": "L", "full_module": "FStar.List.Tot" }, { "abbrev": "R", "full_module": "FStar.Reflection.V2" }, { "abbrev": "RT", "full_module": "FStar.Reflection.Typing" }, { "open": "Pulse.Typing" }, { "open": "Pulse.Syntax.Naming" }, { "open": "Pulse.Syntax" }, { "open": "FStar.List.Tot" }, { "abbrev": "L", "full_module": "FStar.List.Tot" }, { "abbrev": "R", "full_module": "FStar.Reflection.V2" }, { "abbrev": "RT", "full_module": "FStar.Reflection.Typing" }, { "open": "Pulse.Typing" }, { "open": "Pulse.Typing" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let vars_of_rt_env (g:R.env) = Set.intension (fun x -> Some? (RT.lookup_bvar g x))", "source_range": { "start_line": 27, "start_col": 0, "end_line": 27, "end_col": 82 }, "interleaved": false, "definition": "fun g -> FStar.Set.intension (fun x -> Some? (FStar.Reflection.Typing.lookup_bvar g x))", "effect": "Prims.GTot", "effect_flags": [ "sometrivial" ], "mutual_with": [], "premises": [ "FStar.Stubs.Reflection.Types.env", "FStar.Set.intension", "Prims.int", "FStar.Pervasives.Native.uu___is_Some", "FStar.Stubs.Reflection.Types.term", "FStar.Reflection.Typing.lookup_bvar", "Prims.bool", "FStar.Set.set" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "g: FStar.Stubs.Reflection.Types.env -> Prims.GTot (FStar.Set.set Prims.int)", "prompt": "let vars_of_rt_env (g: R.env) =\n ", "expected_response": "Set.intension (fun x -> Some? (RT.lookup_bvar g x))", "source": { "project_name": "steel", "file_name": "lib/steel/pulse/Pulse.Typing.FV.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Pulse.Typing.FV.fst", "checked_file": "dataset/Pulse.Typing.FV.fst.checked", "interface_file": true, "dependencies": [ "dataset/Pulse.Typing.Metatheory.Base.fsti.checked", "dataset/Pulse.Typing.fst.checked", "dataset/Pulse.Syntax.fst.checked", "dataset/Pulse.Soundness.Common.fst.checked", "dataset/Pulse.Elaborate.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Reflection.V2.fst.checked", "dataset/FStar.Reflection.Typing.fsti.checked", "dataset/FStar.Range.fsti.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.Calc.fsti.checked" ] }, "definitions_in_context": [], "closest": [ "val Pulse.Typing.FV.vars_of_env = g: Pulse.Typing.Env.env -> FStar.Set.set Pulse.Syntax.Base.var\nlet vars_of_env (g:env) = dom g", "val Pulse.Extract.Main.topenv_of_env = g: Pulse.Extract.Main.env -> FStar.Reflection.Typing.fstar_top_env\nlet topenv_of_env (g:env) = E.fstar_env g.coreenv", "val FStar.Reflection.Typing.fstar_env_fvs = g: FStar.Stubs.Reflection.Types.env -> Prims.logical\nlet fstar_env_fvs (g:R.env) =\n lookup_fvar g unit_fv == Some (tm_type u_zero) /\\\n lookup_fvar g bool_fv == Some (tm_type u_zero) /\\\n lookup_fvar g b2t_fv == Some b2t_ty", "val Pulse.Typing.Env.singleton_env = f: FStar.Reflection.Typing.fstar_top_env -> x: Pulse.Syntax.Base.var -> t: Pulse.Syntax.Base.typ\n -> g':\n Pulse.Typing.Env.env\n {Pulse.Typing.Env.fstar_env g' == Pulse.Typing.Env.fstar_env (Pulse.Typing.Env.mk_env f)}\nlet singleton_env (f:_) (x:var) (t:typ) = push_binding (mk_env f) x ppname_default t", "val Pulse.Extract.Main.tcenv_of_env = g: Pulse.Extract.Main.env -> FStar.Stubs.Reflection.Types.env\nlet tcenv_of_env (g:env) = Pulse.Typing.elab_env g.coreenv", "val Pulse.Typing.Env.push_binding_def = \n g: Pulse.Typing.Env.env ->\n x: Pulse.Syntax.Base.var{~(FStar.Set.mem x (Pulse.Typing.Env.dom g))} ->\n t: Pulse.Syntax.Base.typ\n -> g': Pulse.Typing.Env.env{Pulse.Typing.Env.fstar_env g' == Pulse.Typing.Env.fstar_env g}\nlet push_binding_def (g:env) (x:var { ~ (Set.mem x (dom g)) }) (t:typ)\n = push_binding g x ppname_default t", "val FStar.Reflection.Typing.sigelt_for = g: FStar.Stubs.Reflection.Types.env -> Type0\nlet sigelt_for (g:env) =\n tup:(bool & sigelt & option blob)\n {\n let (checked, se, _) = tup in\n checked ==> sigelt_typing g se\n }", "val Pulse.Typing.typing = \n g: Pulse.Typing.Env.env ->\n e: Pulse.Syntax.Base.term ->\n eff: FStar.Stubs.TypeChecker.Core.tot_or_ghost ->\n t: Pulse.Syntax.Base.term\n -> Type0\nlet typing (g:env) (e:term) (eff:T.tot_or_ghost) (t:term) =\n my_erased (RT.typing (elab_env g) (elab_term e) (eff, elab_term t))", "val Pulse.Typing.tot_typing = g: Pulse.Typing.Env.env -> e: Pulse.Syntax.Base.term -> t: Pulse.Syntax.Base.term -> Type0\nlet tot_typing (g:env) (e:term) (t:term) =\n typing g e T.E_Total t", "val Pulse.Checker.Pure.rtb_instantiate_implicits = \n g: Pulse.Typing.Env.env ->\n f: FStar.Stubs.Reflection.Types.env ->\n t: FStar.Stubs.Reflection.Types.term\n -> FStar.Tactics.Effect.Tac\n (FStar.Pervasives.Native.option ((Prims.list (FStar.Stubs.Reflection.Types.namedv *\n FStar.Stubs.Reflection.Types.typ) *\n FStar.Stubs.Reflection.Types.term) *\n FStar.Stubs.Reflection.Types.typ) *\n FStar.Stubs.Tactics.Types.issues)\nlet rtb_instantiate_implicits g f t =\n check_ln g \"rtb_instantiate_implicits\" t;\n debug g (fun _ -> Printf.sprintf \"Calling instantiate_implicits on %s\"\n (T.term_to_string t));\n (* WARN: unary dependence, see comment in RU *)\n let t = RU.deep_transform_to_unary_applications t in\n let res, iss = RU.with_context (get_context g) (fun _ -> RTB.instantiate_implicits f t) in\n match res with\n | None ->\n debug g (fun _ -> \"Returned from instantiate_implicits: None\");\n res, iss\n | Some (_, t, _) ->\n debug g (fun _ -> Printf.sprintf \"Returned from instantiate_implicits: %s\" (T.term_to_string t));\n res, iss", "val fstar_env (g:env) : RT.fstar_top_env\nlet fstar_env g = RU.env_set_context g.f g.ctxt", "val Pulse.Typing.post_hint_for_env_p = g: Pulse.Typing.Env.env -> p: Pulse.Typing.post_hint_t -> Prims.logical\nlet post_hint_for_env_p (g:env) (p:post_hint_t) = g `env_extends` p.g", "val Pulse.Typing.ghost_typing = g: Pulse.Typing.Env.env -> e: Pulse.Syntax.Base.term -> t: Pulse.Syntax.Base.typ -> Type0\nlet ghost_typing (g:env) (e:term) (t:typ) =\n typing g e T.E_Ghost t", "val Pulse.Extract.Main.fresh = g: Pulse.Extract.Main.env\n -> v: Pulse.Syntax.Base.var{~(FStar.Set.mem v (Pulse.Typing.Env.dom (Mkenv?.coreenv g)))}\nlet fresh (g:env) = Pulse.Typing.fresh g.coreenv", "val Pulse.Typing.FV.contains = g: Pulse.Typing.Env.env -> x: Pulse.Syntax.Base.var -> Prims.bool\nlet contains (g:env) (x:var) = Some? (lookup g x)", "val Pulse.Typing.Env.env_extends = g1: Pulse.Typing.Env.env -> g2: Pulse.Typing.Env.env -> Prims.logical\nlet env_extends (g1 g2:env) =\n exists g3. extends_with g1 g2 g3", "val Pulse.Checker.Pure.rtb_universe_of = \n g: Pulse.Typing.Env.env ->\n f: FStar.Stubs.Reflection.Types.env ->\n e: FStar.Stubs.Reflection.Types.term\n -> FStar.Tactics.Effect.Tac\n (FStar.Pervasives.Native.option (u37:\n FStar.Stubs.Reflection.Types.universe\n { FStar.Stubs.Tactics.Types.typing_token f\n e\n (FStar.Stubs.TypeChecker.Core.E_Total,\n FStar.Stubs.Reflection.V2.Builtins.pack_ln (FStar.Stubs.Reflection.V2.Data.Tv_Type\n u37)) }) *\n FStar.Stubs.Tactics.Types.issues)\nlet rtb_universe_of g f e =\n check_ln g \"rtb_universe_of\" e;\n debug g (fun _ ->\n Printf.sprintf \"(%s) Calling universe_of on %s\"\n (T.range_to_string (RU.range_of_term e))\n (T.term_to_string e));\n let res = RU.with_context (get_context g) (fun _ -> RTB.universe_of f e) in\n res", "val STLC.Core.extend_env_l = g: FStar.Stubs.Reflection.Types.env -> sg: STLC.Core.stlc_env -> FStar.Stubs.Reflection.Types.env\nlet extend_env_l (g:R.env) (sg:stlc_env) = \n L.fold_right (fun (x, t) g -> RT.extend_env g x (elab_ty t)) sg g", "val Pulse.Typing.post_hint_for_env = g: Pulse.Typing.Env.env -> Type0\nlet post_hint_for_env (g:env) = p:post_hint_t { post_hint_for_env_p g p }", "val Pulse.Reflection.Util.nat_fv = FStar.Stubs.Reflection.Types.fv\nlet nat_fv = R.pack_fv nat_lid", "val Pulse.Reflection.Util.stt_fv = FStar.Stubs.Reflection.Types.fv\nlet stt_fv = R.pack_fv stt_lid", "val Pulse.Typing.Env.contains = g: Pulse.Typing.Env.env -> x: Pulse.Syntax.Base.var -> Prims.bool\nlet contains (g:env) (x:var) = Map.contains (as_map g) x", "val Pulse.Checker.Prover.Base.vprop_typing = g: Pulse.Typing.Env.env -> t: Pulse.Syntax.Base.term -> Type0\nlet vprop_typing (g:env) (t:term) = tot_typing g t tm_vprop", "val Pulse.Typing.universe_of = g: Pulse.Typing.Env.env -> t: Pulse.Syntax.Base.term -> u642: Pulse.Syntax.Base.universe -> Type0\nlet universe_of (g:env) (t:term) (u:universe) =\n tot_typing g t (tm_type u)", "val FStar.Reflection.Typing.dsl_tac_result_t = g: FStar.Stubs.Reflection.Types.env -> Type0\nlet dsl_tac_result_t (g:env) = list (sigelt_for g)", "val mk_env (f:RT.fstar_top_env) : g:env { fstar_env g == f }\nlet mk_env (f:RT.fstar_top_env) : env =\n { f; bs = []; names=[]; m = empty_bmap; ctxt = default_context }", "val Pulse.Typing.prop_validity = g: Pulse.Typing.Env.env -> t: Pulse.Syntax.Base.term -> Type0\nlet prop_validity (g:env) (t:term) =\n FTB.prop_validity_token (elab_env g) (elab_term t)", "val Pulse.Extract.Main.extend_env_pat = g: Pulse.Extract.Main.env -> p: Pulse.Syntax.Base.pattern\n -> FStar.Tactics.Effect.Tac\n ((Pulse.Extract.Main.env * Pulse.Extract.CompilerLib.mlpattern) *\n Prims.list Pulse.Typing.Env.binding)\nlet extend_env_pat g p = \n let g, pats, bs = extend_env_pat_core g p in\n match pats with\n | [p] -> g, p, bs\n | _ -> T.raise (Extraction_failure \"Unexpected extraction of pattern\")", "val Pulse.Reflection.Util.stt_ghost_fv = FStar.Stubs.Reflection.Types.fv\nlet stt_ghost_fv = R.pack_fv stt_ghost_lid", "val Pulse.Reflection.Util.vprop_fv = FStar.Stubs.Reflection.Types.fv\nlet vprop_fv = R.pack_fv vprop_lid", "val Pulse.Typing.fresh_wrt = x: Pulse.Syntax.Base.var -> g: Pulse.Typing.Env.env -> vars: FStar.Set.set Pulse.Syntax.Base.var\n -> Prims.logical\nlet fresh_wrt (x:var) (g:env) (vars:_) = \n None? (lookup g x) /\\ ~(x `Set.mem` vars)", "val Pulse.Checker.Pure.rtb_tc_term = \n g: Pulse.Typing.Env.env ->\n f: FStar.Stubs.Reflection.Types.env ->\n e: FStar.Stubs.Reflection.Types.term\n -> FStar.Tactics.Effect.Tac\n (FStar.Pervasives.Native.option (r:\n (FStar.Stubs.Reflection.Types.term *\n (FStar.Stubs.TypeChecker.Core.tot_or_ghost * FStar.Stubs.Reflection.Types.typ))\n { FStar.Stubs.Tactics.Types.typing_token f\n (FStar.Pervasives.Native.fst r)\n (FStar.Pervasives.Native.snd r) }) *\n FStar.Stubs.Tactics.Types.issues)\nlet rtb_tc_term g f e =\n (* WARN: unary dependence, see comment in RU *)\n check_ln g \"rtb_tc_term\" e;\n let e = RU.deep_transform_to_unary_applications e in\n debug g (fun _ ->\n Printf.sprintf \"(%s) Calling tc_term on %s\"\n (T.range_to_string (RU.range_of_term e))\n (T.term_to_string e));\n let res = RU.with_context (get_context g) (fun _ -> RTB.tc_term f e) in\n res", "val Pulse.Reflection.Util.stt_vprop_equiv_fv = FStar.Stubs.Reflection.Types.fv\nlet stt_vprop_equiv_fv =\n R.pack_fv (mk_pulse_lib_core_lid \"vprop_equiv\")", "val vars_of_env (sg: list (var & stlc_ty)) : GTot (Set.set var)\nlet vars_of_env (sg:list (var & stlc_ty))\n : GTot (Set.set var)\n = Set.intension (contains sg)", "val Pulse.Reflection.Util.nat_tm = FStar.Stubs.Reflection.Types.term\nlet nat_tm = R.pack_ln (R.Tv_FVar nat_fv)", "val Pulse.Typing.non_informative_t = g: Pulse.Typing.Env.env -> u647: Pulse.Syntax.Base.universe -> t: Pulse.Syntax.Base.term -> Type0\nlet non_informative_t (g:env) (u:universe) (t:term) =\n w:term & tot_typing g w (non_informative_witness_t u t)", "val Pulse.Typing.non_informative = g: Pulse.Typing.Env.env -> c: Pulse.Syntax.Base.comp -> Type0\nlet non_informative (g:env) (c:comp) =\n my_erased (RT.non_informative (elab_env g) (elab_comp c))", "val Pulse.Typing.Metatheory.Base.iname_typing = g: Pulse.Typing.Env.env -> c: Pulse.Syntax.Base.comp_st -> Type0\nlet iname_typing (g:env) (c:comp_st) = tot_typing g (inames_of_comp_st c) tm_inames", "val Pulse.Extract.Main.debug_ = g: Pulse.Extract.Main.env -> f: (_: Prims.unit -> FStar.Tactics.Effect.Tac Prims.string)\n -> FStar.Tactics.Effect.Tac Prims.unit\nlet debug_ = debug", "val Pulse.Reflection.Util.szv_fv = FStar.Stubs.Reflection.Types.fv\nlet szv_fv = R.pack_fv szv_lid", "val DependentBoolRefinement.extend_env_l = g: FStar.Stubs.Reflection.Types.env -> sg: DependentBoolRefinement.src_env\n -> FStar.Stubs.Reflection.Types.env\nlet extend_env_l (g:R.env) (sg:src_env) = \n L.fold_right \n (fun (x, b) g -> RT.extend_env g x (elab_binding b))\n sg\n g", "val Pulse.Typing.non_informative_c = g: Pulse.Typing.Env.env -> c: Pulse.Syntax.Base.comp_st -> Type0\nlet non_informative_c (g:env) (c:comp_st) =\n non_informative_t g (comp_u c) (comp_res c)", "val rt_recheck: gg: env -> #g: T.env -> #e: T.term -> #ty: T.typ -> Prims.unit\n -> T.Tac (RT.tot_typing g e ty)\nlet rt_recheck (gg:env) (#g:T.env) (#e:T.term) (#ty: T.typ) () : T.Tac (RT.tot_typing g e ty) =\n let open Pulse.PP in\n // info_doc gg (Some (T.range_of_term e)) [\n // doc_of_string \"Re-checking\" ^/^\n // pp e ^/^\n // doc_of_string \"at type\" ^/^\n // pp ty\n // ];\n match T.core_check_term g e ty T.E_Total with\n | Some tok, _ -> RT.T_Token _ _ _ ()\n | None, _ -> T.fail \"Checker.WithInv: rt_recheck failed\"", "val Pulse.Reflection.Util.szt_fv = FStar.Stubs.Reflection.Types.fv\nlet szt_fv = R.pack_fv szt_lid", "val Pulse.Checker.Pure.debug = g: Pulse.Typing.Env.env -> msg: (_: Prims.unit -> FStar.Tactics.Effect.Tac Prims.string)\n -> FStar.Tactics.Effect.Tac Prims.unit\nlet debug (g:env) (msg: unit -> T.Tac string) =\n let tac_debugging = T.debugging () in\n if tac_debugging || RU.debug_at_level (fstar_env g) \"refl_tc_callbacks\"\n then T.print (print_context g ^ \"\\n\" ^ msg())", "val Pulse.Reflection.Util.vprop_tm = FStar.Stubs.Reflection.Types.term\nlet vprop_tm = R.pack_ln (R.Tv_FVar vprop_fv)", "val Pulse.Typing.Env.extends_with = g1: Pulse.Typing.Env.env -> g2: Pulse.Typing.Env.env -> g3: Pulse.Typing.Env.env -> Prims.logical\nlet extends_with (g1 g2 g3:env) =\n disjoint g2 g3 /\\\n g1 == push_env g2 g3", "val Binding.eq_typs = env: Binding.env -> ts: Prims.list (Ast.typ * Ast.typ) -> FStar.All.ML Prims.bool\nlet eq_typs env ts =\r\n List.for_all (fun (t1, t2) -> eq_typ env t1 t2) ts", "val env_to_doc (g:env) : T.Tac FStar.Stubs.Pprint.document\nlet env_to_doc (e:env) : T.Tac document =\n let pp1 : ((var & typ) & ppname) -> T.Tac document =\n fun ((n, t), x) ->\n doc_of_string (T.unseal x.name) ^^ doc_of_string \"#\" ^^ doc_of_string (string_of_int n)\n ^^ doc_of_string \" : \" ^^ Pulse.Syntax.Printer.term_to_doc t\n in\n brackets (separate_map comma pp1 (T.zip e.bs e.names))", "val Pulse.Typing.Combinators.frame_for_req_in_ctxt = g: Pulse.Typing.Env.env -> ctxt: Pulse.Syntax.Base.term -> req: Pulse.Syntax.Base.term -> Type0\nlet frame_for_req_in_ctxt (g:env) (ctxt:term) (req:term)\n = (frame:term &\n tot_typing g frame tm_vprop &\n vprop_equiv g (tm_star req frame) ctxt)", "val b2t_typing (g: fstar_env) (t: R.term) (dt: RT.tot_typing g t RT.bool_ty)\n : RT.tot_typing g (r_b2t t) (RT.tm_type RT.u_zero)\nlet b2t_typing (g:fstar_env) (t:R.term) (dt:RT.tot_typing g t RT.bool_ty)\n : RT.tot_typing g (r_b2t t) (RT.tm_type RT.u_zero)\n = let b2t_typing : RT.tot_typing g _ b2t_ty = RT.T_FVar g b2t_fv in\n let app_ty : _ = RT.T_App _ _ _ _ (RT.tm_type RT.u_zero) _ b2t_typing dt in\n RT.open_with_spec (RT.tm_type RT.u_zero) t;\n app_ty", "val recheck: #g: env -> #e: term -> #ty: typ -> Prims.unit -> T.Tac (tot_typing g e ty)\nlet recheck (#g:env) (#e:term) (#ty: typ) () : T.Tac (tot_typing g e ty) =\n core_check_tot_term g e ty", "val Pulse.Reflection.Util.stt_atomic_fv = FStar.Stubs.Reflection.Types.fv\nlet stt_atomic_fv = R.pack_fv stt_atomic_lid", "val Pulse.Reflection.Util.szv_tm = FStar.Stubs.Reflection.Types.term\nlet szv_tm = R.pack_ln (R.Tv_FVar szv_fv)", "val Pulse.Reflection.Util.unit_fv = FStar.Stubs.Reflection.Types.fv\nlet unit_fv = R.pack_fv unit_lid", "val Pulse.Checker.Pure.fail_expected_tot_found_ghost = g: Pulse.Typing.Env.env -> t: Pulse.Syntax.Base.term -> FStar.Tactics.Effect.Tac _\nlet fail_expected_tot_found_ghost (g:env) (t:term) =\n fail g (Some t.range)\n (Printf.sprintf \"Expected a total term, found ghost term %s\" (P.term_to_string t))", "val Pulse.Steel.Wrapper.Typing.neutral_fv = FStar.Stubs.Reflection.Types.term\nlet neutral_fv = pack_ln (Tv_FVar (pack_fv neutral_lid))", "val Pulse.Reflection.Util.u_two = FStar.Stubs.Reflection.Types.universe\nlet u_two = RT.(u_succ (u_succ u_zero))", "val extend_tvar: g:env -> n:nat -> k:knd -> Tot env\nlet extend_tvar g n k =\n let a_env = fun (a:nat) -> if a < n then lookup_tvar g a\n else if a = n then Some k\n else lookup_tvar g (a - 1) in\n let x_env = fun (x:nat) -> match lookup_evar g x with\n | None -> None\n | Some t -> Some (tshift_up_above n t)\n in\n MkEnv a_env x_env", "val Pulse.Typing.post_hint_opt = g: Pulse.Typing.Env.env -> Type0\nlet post_hint_opt (g:env) = o:option post_hint_t { None? o \\/ post_hint_for_env_p g (Some?.v o) }", "val BoolRefinement.extend_env_l = g: FStar.Stubs.Reflection.Types.env -> sg: BoolRefinement.src_env\n -> FStar.Stubs.Reflection.Types.env\nlet extend_env_l (g:R.env) (sg:src_env) = \n L.fold_right \n (fun (x, b) g -> RT.extend_env g x (elab_binding b))\n sg\n g", "val st_typing_correctness_ctot (#g:env) (#t:st_term) (#c:comp{C_Tot? c}) \n (_:st_typing g t c)\n : (u:Ghost.erased universe & universe_of g (comp_res c) u)\nlet st_typing_correctness_ctot (#g:env) (#t:st_term) (#c:comp{C_Tot? c}) \n (_:st_typing g t c)\n: (u:Ghost.erased universe & universe_of g (comp_res c) u)\n= let u : Ghost.erased universe = RU.magic () in\n let ty : universe_of g (comp_res c) u = RU.magic() in\n (| u, ty |)", "val Pulse.Reflection.Util.stt_tm = FStar.Stubs.Reflection.Types.term\nlet stt_tm = R.pack_ln (R.Tv_FVar stt_fv)", "val Pulse.Typing.comp_typing_u = e: Pulse.Typing.Env.env -> c: Pulse.Syntax.Base.comp_st -> Type0\nlet comp_typing_u (e:env) (c:comp_st) = comp_typing e c (universe_of_comp c)", "val FStar.Reflection.Typing.freevars_comp_typ = c: FStar.Reflection.Typing.comp_typ -> FStar.Set.set FStar.Stubs.Reflection.V2.Data.var\nlet freevars_comp_typ (c:comp_typ) = freevars (snd c)", "val Pulse.Typing.Env.related = \n bs: Prims.list (Pulse.Syntax.Base.var * Pulse.Syntax.Base.typ) ->\n m: FStar.Map.t Pulse.Syntax.Base.var Pulse.Syntax.Base.typ\n -> Prims.logical\nlet related (bs:list (var & typ)) (m:Map.t var typ) =\n (forall (b:var & typ).\n L.memP b bs ==> (Map.contains m (fst b) /\\\n Map.sel m (fst b) == snd b)) /\\\n \n (forall (x:var). Map.contains m x ==> (List.Tot.memP (x, Map.sel m x) bs))", "val Pulse.C.Typestring.norm_typestring = Prims.list FStar.Pervasives.norm_step\nlet norm_typestring =\n [\n delta_only [\n `%char_t_of_char;\n `%string_t_of_chars;\n `%mk_string_t;\n ];\n iota; zeta; primops;\n ]", "val extend_evar: g:env -> n:nat -> t:typ -> Tot env\nlet extend_evar g n t =\n let a_env = fun (a:nat) -> lookup_tvar g a in\n let x_env = fun (x:nat) -> if x < n then lookup_evar g x\n else if x = n then Some t\n else lookup_evar g (x - 1) in\n MkEnv a_env x_env", "val b2t_typing (g: RT.fstar_env) (t: R.term) (dt: RT.tot_typing g t RT.bool_ty)\n : RT.tot_typing g (r_b2t t) (RT.tm_type RT.u_zero)\nlet b2t_typing (g:RT.fstar_env) (t:R.term) (dt:RT.tot_typing g t RT.bool_ty)\n : RT.tot_typing g (r_b2t t) (RT.tm_type RT.u_zero)\n = let b2t_typing : RT.tot_typing g _ RT.b2t_ty = RT.T_FVar g RT.b2t_fv in\n let app_ty : _ = RT.T_App _ _ _ _ (RT.tm_type RT.u_zero) _ b2t_typing dt in\n RT.open_with_spec (RT.tm_type RT.u_zero) t;\n app_ty", "val as_map (g:env) : Map.t var typ\nlet as_map g = g.m", "val Pulse.Typing.effect_annot_typing = g: Pulse.Typing.Env.env -> e: Pulse.Syntax.Base.effect_annot -> Type0\nlet effect_annot_typing (g:env) (e:effect_annot) =\n match e with\n | EffectAnnotAtomic { opens } ->\n tot_typing g opens tm_inames\n | _ ->\n unit", "val Pulse.Reflection.Util.tun = FStar.Stubs.Reflection.Types.term\nlet tun = R.pack_ln R.Tv_Unknown", "val universe_of_now : g:env -> e:term ->\n Tac (option (u:universe{typing_token g e (E_Total, pack_ln (Reflection.V2.Tv_Type u))}) & issues)\nlet universe_of_now g e =\n T.with_policy SMTSync (fun () ->\n T.universe_of g e)", "val Pulse.Typing.Env.pairwise_disjoint = g: Pulse.Typing.Env.env -> g': Pulse.Typing.Env.env -> g'': Pulse.Typing.Env.env -> Prims.logical\nlet pairwise_disjoint (g g' g'':env) =\n disjoint g g' /\\ disjoint g' g'' /\\ disjoint g g''", "val bindings_with_ppname (g:env) : T.Tac (list (ppname & var & typ))\nlet bindings_with_ppname g = bindings_with_ppname_aux g.bs g.names", "val DependentBoolRefinement.fstar_top_env = Type0\nlet fstar_top_env =\n g:fstar_env { \n forall x. None? (RT.lookup_bvar g x )\n }", "val Pulse.Reflection.Util.stt_unobservable_fv = FStar.Stubs.Reflection.Types.fv\nlet stt_unobservable_fv = R.pack_fv stt_unobservable_lid", "val Pulse.Typing.subtyping_token = g: Pulse.Typing.Env.env -> t1: Pulse.Syntax.Base.term -> t2: Pulse.Syntax.Base.term -> Type0\nlet subtyping_token g t1 t2 =\n T.subtyping_token (elab_env g) (elab_term t1) (elab_term t2)", "val Pulse.Reflection.Util.unit_tm = FStar.Stubs.Reflection.Types.term\nlet unit_tm = R.pack_ln (R.Tv_FVar unit_fv)", "val Pulse.Reflection.Util.szt_tm = FStar.Stubs.Reflection.Types.term\nlet szt_tm = R.pack_ln (R.Tv_FVar szt_fv)", "val Pulse.Extract.Main.uenv_of_env = g: Pulse.Extract.Main.env -> Pulse.Extract.CompilerLib.uenv\nlet uenv_of_env (g:env) = set_tcenv g.uenv_inner (tcenv_of_env g)", "val Pulse.Reflection.Util.stt_vprop_equiv_tm = FStar.Stubs.Reflection.Types.term\nlet stt_vprop_equiv_tm =\n R.pack_ln (R.Tv_FVar stt_vprop_equiv_fv)", "val FStar.Reflection.Typing.var_as_bv = v: Prims.nat -> FStar.Stubs.Reflection.Types.bv\nlet var_as_bv (v:nat) = pack_bv (make_bv v)", "val Pulse.Soundness.Common.stt_env = Type0\nlet stt_env = e:env { has_stt_bindings (fstar_env e) }", "val cur_env: Prims.unit -> Tac env\nlet cur_env () : Tac env = goal_env (_cur_goal ())", "val cur_env: Prims.unit -> Tac env\nlet cur_env () : Tac env = goal_env (_cur_goal ())", "val Pulse.Checker.Pure.rtb_core_compute_term_type = \n g: Pulse.Typing.Env.env ->\n f: FStar.Stubs.Reflection.Types.env ->\n e: FStar.Stubs.Reflection.Types.term\n -> FStar.Tactics.Effect.Tac\n (FStar.Pervasives.Native.option (r:\n (FStar.Stubs.TypeChecker.Core.tot_or_ghost * FStar.Stubs.Reflection.Types.typ)\n {FStar.Stubs.Tactics.Types.typing_token f e r}) *\n FStar.Stubs.Tactics.Types.issues)\nlet rtb_core_compute_term_type g f e =\n check_ln g \"rtb_compute_term_type\" e;\n debug g (fun _ ->\n Printf.sprintf \"(%s) Calling core_check_term on %s\" \n (T.range_to_string (RU.range_of_term e))\n (T.term_to_string e));\n let res = RU.with_context (get_context g) (fun _ -> RTB.core_compute_term_type f e) in\n res", "val DependentBoolRefinement.fstar_env = Type0\nlet fstar_env =\n g:R.env { \n RT.lookup_fvar g RT.bool_fv == Some (RT.tm_type RT.u_zero) /\\\n RT.lookup_fvar g b2t_fv == Some b2t_ty\n }", "val Pulse.C.Typenat.norm_typenat = Prims.list FStar.Pervasives.norm_step\nlet norm_typenat =\n [\n delta_only [\n `%nat_t_of_nat;\n ];\n iota; zeta; primops;\n ]", "val Pulse.Reflection.Util.stt_atomic_tm = FStar.Stubs.Reflection.Types.term\nlet stt_atomic_tm = R.pack_ln (R.Tv_FVar stt_atomic_fv)", "val Pulse.Reflection.Util.true_tm = FStar.Stubs.Reflection.Types.term\nlet true_tm = R.pack_ln (R.Tv_Const (R.C_True))", "val Pulse.Typing.Env.equal = g1: Pulse.Typing.Env.env -> g2: Pulse.Typing.Env.env -> Prims.logical\nlet equal (g1 g2:env) =\n fstar_env g1 == fstar_env g2 /\\\n bindings g1 == bindings g2", "val range_of_env (g:env) : T.Tac range\nlet range_of_env (g:env) = \n let ctx = T.unseal g.ctxt in\n match \n T.tryPick\n (fun (_, r) ->\n match r with\n | None -> None\n | Some r -> \n if not (RU.is_range_zero r) then Some r else None) ctx with\n | Some r -> r\n | _ -> FStar.Range.range_0", "val BoolRefinement.extend_env_alt = g: FStar.Stubs.Reflection.Types.env -> sg: BoolRefinement.src_env\n -> FStar.Stubs.Reflection.Types.env\nlet extend_env_alt (g:R.env) (sg:src_env) = \n RT.extend_env_l g (as_bindings sg)", "val Pulse.Reflection.Util.bool_fv = FStar.Stubs.Reflection.Types.fv\nlet bool_fv = R.pack_fv bool_lid", "val TypeSizes.env_t = Type0\nlet env_t = B.env & size_env", "val Pulse.Reflection.Util.stt_ghost_tm = FStar.Stubs.Reflection.Types.term\nlet stt_ghost_tm = R.pack_ln (R.Tv_FVar stt_ghost_fv)", "val Pulse.Typing.tr_bindings = x: Prims.list (Pulse.Syntax.Base.var * Pulse.Syntax.Base.typ)\n -> Prims.list FStar.Stubs.Reflection.V2.Data.binding\nlet tr_bindings = L.map tr_binding", "val extend_env_l_lookup_fvar (g: R.env) (sg: env_bindings) (fv: R.fv) (us: R.universes)\n : Lemma (ensures RT.lookup_fvar_uinst (extend_env_l g sg) fv us == RT.lookup_fvar_uinst g fv us)\n [SMTPat (RT.lookup_fvar_uinst (extend_env_l g sg) fv us)]\nlet rec extend_env_l_lookup_fvar (g:R.env) (sg:env_bindings) (fv:R.fv) (us:R.universes)\n : Lemma \n (ensures\n RT.lookup_fvar_uinst (extend_env_l g sg) fv us ==\n RT.lookup_fvar_uinst g fv us)\n [SMTPat (RT.lookup_fvar_uinst (extend_env_l g sg) fv us)]\n = match sg with\n | [] -> ()\n | hd::tl -> extend_env_l_lookup_fvar g tl fv us", "val Pulse.Checker.Pure.rtb_core_check_term_at_type = \n g: Pulse.Typing.Env.env ->\n f: FStar.Stubs.Reflection.Types.env ->\n e: FStar.Stubs.Reflection.Types.term ->\n t: FStar.Stubs.Reflection.Types.term\n -> FStar.Tactics.Effect.Tac\n (FStar.Pervasives.Native.option (eff:\n FStar.Stubs.TypeChecker.Core.tot_or_ghost\n {FStar.Stubs.Tactics.Types.typing_token f e (eff, t)}) *\n FStar.Stubs.Tactics.Types.issues)\nlet rtb_core_check_term_at_type g f e t =\n debug g (fun _ ->\n Printf.sprintf \"(%s) Calling core_check_term_at_type on %s and %s\"\n (T.range_to_string (RU.range_of_term e))\n (T.term_to_string e)\n (T.term_to_string t));\n let res = RU.with_context (get_context g) (fun _ -> RTB.core_check_term_at_type f e t) in\n res" ], "closest_src": [ { "project_name": "steel", "file_name": "Pulse.Typing.FV.fsti", "name": "Pulse.Typing.FV.vars_of_env" }, { "project_name": "steel", "file_name": "Pulse.Extract.Main.fst", "name": "Pulse.Extract.Main.topenv_of_env" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.fstar_env_fvs" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fsti", "name": "Pulse.Typing.Env.singleton_env" }, { "project_name": "steel", "file_name": "Pulse.Extract.Main.fst", "name": "Pulse.Extract.Main.tcenv_of_env" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fsti", "name": "Pulse.Typing.Env.push_binding_def" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.sigelt_for" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.typing" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.tot_typing" }, { "project_name": "steel", "file_name": "Pulse.Checker.Pure.fst", "name": "Pulse.Checker.Pure.rtb_instantiate_implicits" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fst", "name": "Pulse.Typing.Env.fstar_env" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.post_hint_for_env_p" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.ghost_typing" }, { "project_name": "steel", "file_name": "Pulse.Extract.Main.fst", "name": "Pulse.Extract.Main.fresh" }, { "project_name": "steel", "file_name": "Pulse.Typing.FV.fsti", "name": "Pulse.Typing.FV.contains" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fsti", "name": "Pulse.Typing.Env.env_extends" }, { "project_name": "steel", "file_name": "Pulse.Checker.Pure.fst", "name": "Pulse.Checker.Pure.rtb_universe_of" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.extend_env_l" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.post_hint_for_env" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.nat_fv" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.stt_fv" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fsti", "name": "Pulse.Typing.Env.contains" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Base.fsti", "name": "Pulse.Checker.Prover.Base.vprop_typing" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.universe_of" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.dsl_tac_result_t" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fst", "name": "Pulse.Typing.Env.mk_env" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.prop_validity" }, { "project_name": "steel", "file_name": "Pulse.Extract.Main.fst", "name": "Pulse.Extract.Main.extend_env_pat" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.stt_ghost_fv" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.vprop_fv" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.fresh_wrt" }, { "project_name": "steel", "file_name": "Pulse.Checker.Pure.fst", "name": "Pulse.Checker.Pure.rtb_tc_term" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.stt_vprop_equiv_fv" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.vars_of_env" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.nat_tm" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.non_informative_t" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.non_informative" }, { "project_name": "steel", "file_name": "Pulse.Typing.Metatheory.Base.fsti", "name": "Pulse.Typing.Metatheory.Base.iname_typing" }, { "project_name": "steel", "file_name": "Pulse.Extract.Main.fst", "name": "Pulse.Extract.Main.debug_" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.szv_fv" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.extend_env_l" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.non_informative_c" }, { "project_name": "steel", "file_name": "Pulse.Checker.WithInv.fst", "name": "Pulse.Checker.WithInv.rt_recheck" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.szt_fv" }, { "project_name": "steel", "file_name": "Pulse.Checker.Pure.fst", "name": "Pulse.Checker.Pure.debug" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.vprop_tm" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fsti", "name": "Pulse.Typing.Env.extends_with" }, { "project_name": "everparse", "file_name": "Binding.fst", "name": "Binding.eq_typs" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fst", "name": "Pulse.Typing.Env.env_to_doc" }, { "project_name": "steel", "file_name": "Pulse.Typing.Combinators.fsti", "name": "Pulse.Typing.Combinators.frame_for_req_in_ctxt" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.b2t_typing" }, { "project_name": "steel", "file_name": "Pulse.Checker.WithInv.fst", "name": "Pulse.Checker.WithInv.recheck" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.stt_atomic_fv" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.szv_tm" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.unit_fv" }, { "project_name": "steel", "file_name": "Pulse.Checker.Pure.fst", "name": "Pulse.Checker.Pure.fail_expected_tot_found_ghost" }, { "project_name": "steel", "file_name": "Pulse.Steel.Wrapper.Typing.fsti", "name": "Pulse.Steel.Wrapper.Typing.neutral_fv" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.u_two" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.extend_tvar" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.post_hint_opt" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.extend_env_l" }, { "project_name": "steel", "file_name": "Pulse.Typing.Metatheory.Base.fst", "name": "Pulse.Typing.Metatheory.Base.st_typing_correctness_ctot" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.stt_tm" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.comp_typing_u" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.freevars_comp_typ" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fst", "name": "Pulse.Typing.Env.related" }, { "project_name": "steel", "file_name": "Pulse.C.Typestring.fsti", "name": "Pulse.C.Typestring.norm_typestring" }, { "project_name": "FStar", "file_name": "LambdaOmega.fst", "name": "LambdaOmega.extend_evar" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.b2t_typing" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fst", "name": "Pulse.Typing.Env.as_map" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.effect_annot_typing" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.tun" }, { "project_name": "steel", "file_name": "Pulse.Typing.Util.fst", "name": "Pulse.Typing.Util.universe_of_now" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fsti", "name": "Pulse.Typing.Env.pairwise_disjoint" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fst", "name": "Pulse.Typing.Env.bindings_with_ppname" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.fstar_top_env" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.stt_unobservable_fv" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.subtyping_token" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.unit_tm" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.szt_tm" }, { "project_name": "steel", "file_name": "Pulse.Extract.Main.fst", "name": "Pulse.Extract.Main.uenv_of_env" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.stt_vprop_equiv_tm" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.var_as_bv" }, { "project_name": "steel", "file_name": "Pulse.Soundness.Common.fst", "name": "Pulse.Soundness.Common.stt_env" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.cur_env" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.cur_env" }, { "project_name": "steel", "file_name": "Pulse.Checker.Pure.fst", "name": "Pulse.Checker.Pure.rtb_core_compute_term_type" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.fstar_env" }, { "project_name": "steel", "file_name": "Pulse.C.Typenat.fsti", "name": "Pulse.C.Typenat.norm_typenat" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.stt_atomic_tm" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.true_tm" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fsti", "name": "Pulse.Typing.Env.equal" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fst", "name": "Pulse.Typing.Env.range_of_env" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.extend_env_alt" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.bool_fv" }, { "project_name": "everparse", "file_name": "TypeSizes.fsti", "name": "TypeSizes.env_t" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.stt_ghost_tm" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.tr_bindings" }, { "project_name": "steel", "file_name": "Pulse.Soundness.Common.fst", "name": "Pulse.Soundness.Common.extend_env_l_lookup_fvar" }, { "project_name": "steel", "file_name": "Pulse.Checker.Pure.fst", "name": "Pulse.Checker.Pure.rtb_core_check_term_at_type" } ], "selected_premises": [ "Pulse.Typing.elab_env", "Pulse.Typing.Env.lookup", "Pulse.Soundness.Common.tot_typing_soundness", "Pulse.Typing.post_hint_for_env", "Pulse.Typing.Env.equal", "Pulse.Typing.post_hint_for_env_p", "Pulse.Typing.universe_of", "Pulse.Soundness.Common.ghost_typing_soundness", "Pulse.Typing.Env.contains", "Pulse.Typing.subtyping_token", "Pulse.Typing.non_informative_t", "Pulse.Typing.post_hint_opt", "Pulse.Typing.as_binder", "Pulse.Typing.tot_typing", "Pulse.Typing.Env.env_extends", "Pulse.Typing.Env.dom", "FStar.Reflection.Typing.var_as_namedv", "FStar.Printf.sprintf", "Pulse.Reflection.Util.vprop_tm", "Pulse.Typing.tm_prop", "FStar.Reflection.Typing.sort_default", "Pulse.Soundness.Common.bind_type", "FStar.Reflection.V2.Data.var", "Pulse.Typing.extend_env_l", "Pulse.Typing.debug_log", "Pulse.Typing.prop_validity", "Pulse.Soundness.Common.has_stt_bindings", "Pulse.Reflection.Util.mk_arrow", "Pulse.Typing.fresh_wrt", "FStar.Printf.arg_type", "Pulse.Reflection.Util.mk_pulse_lib_forall_lid", "Pulse.Typing.tm_inames_subset_typing", "Pulse.Typing.ghost_typing", "Pulse.Typing.wtag", "Pulse.Typing.tm_bool", "Pulse.Typing.comp_post_matches_hint", "Pulse.Typing.comp_typing_u", "Pulse.Typing.post_hint_typing", "Pulse.Typing.effect_annot_typing", "Pulse.Reflection.Util.mk_pulse_lib_reference_lid", "Pulse.Soundness.Common.frame_type", "Pulse.Soundness.Common.comp_post_type", "FStar.Heap.trivial_preorder", "Pulse.Soundness.Common.soundness_t", "Pulse.Reflection.Util.tot_lid", "Pulse.Soundness.Common.post1_type_bind", "FStar.ST.op_Bang", "Pulse.Typing.Env.singleton_env", "Pulse.Reflection.Util.inv_disjointness_goal", "Pulse.Reflection.Util.mk_observability_lid", "Pulse.Typing.Env.disjoint", "Pulse.Typing.non_informative_c", "Pulse.Soundness.Common.frame_type_t_pre_post", "Pulse.Soundness.Common.elab_term_opt", "Pulse.Typing.add_iname_at_least_unobservable", "FStar.Pervasives.Native.fst", "Pulse.Typing.lift_typing_to_ghost_typing", "Pulse.Reflection.Util.mk_pulse_lib_core_lid", "Pulse.Typing.wr", "Pulse.Soundness.Common.bind_type_t1", "Pulse.Typing.mk_vprop_eq", "Pulse.Typing.freshv", "Pulse.Soundness.Common.bind_type_t1_t2", "FStar.Reflection.Typing.constant_as_term", "FStar.Pervasives.Native.snd", "Pulse.Typing.tm_unit", "Pulse.Typing.Env.push_binding_def", "Pulse.Soundness.Common.bind_type_t1_t2_pre_post1_post2", "FStar.Reflection.Typing.tm_type", "FStar.Reflection.Typing.sigelt_for", "FStar.Reflection.Typing.blob", "FStar.Reflection.Typing.fstar_env_fvs", "FStar.String.strlen", "Pulse.Soundness.Common.bind_type_t1_t2_pre_post1", "Pulse.Soundness.Common.elab_comp_post", "Pulse.Soundness.Common.frame_type_t_pre_post_frame", "Pulse.Reflection.Util.mk_stt_comp", "Pulse.Reflection.Util.mk_pulse_lib_array_core_lid", "FStar.Reflection.Typing.pp_name_t", "FStar.String.length", "Pulse.Soundness.Common.sub_stt_post1", "Pulse.Typing.eff_of_ctag", "Pulse.Reflection.Util.unobservable_lid", "Pulse.Typing.Env.pairwise_disjoint", "Pulse.Typing.push_bindings", "Pulse.Soundness.Common.stt_env", "Pulse.Soundness.Common.g_type_bind", "Pulse.Soundness.Common.post2_type_bind", "Pulse.Soundness.Common.bind_type_t1_t2_pre", "Pulse.Soundness.Common.bind_type_t1_t2_pre_post1_post2_f", "Pulse.Soundness.Common.mk_star", "FStar.Integers.within_bounds", "FStar.ST.alloc", "FStar.Reflection.Typing.pp_name_default", "FStar.Reflection.Typing.tun", "Pulse.Soundness.Common.sub_stt_pre2", "Pulse.Typing.inv_disjointness", "FStar.Reflection.Typing.dsl_tac_result_t", "Pulse.Reflection.Util.u_max_two", "Pulse.Soundness.Common.sub_stt_post2" ], "source_upto_this": "(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Typing.FV\nmodule RT = FStar.Reflection.Typing\nmodule R = FStar.Reflection.V2\nmodule L = FStar.List.Tot\nopen FStar.List.Tot\nopen Pulse.Syntax\nopen Pulse.Typing\nopen Pulse.Elaborate\nopen Pulse.Soundness.Common\n", "sketch": [ "Step 1: The definition `vars_of_rt_env` aims to extract all the variable identifiers from a given reflection environment `g` and return them as a set of integers.\nStep 2: To implement this, we will iterate over the environment `g`, collect the variable identifiers, and insert them into a set. The result will be a set of integers representing these variable identifiers.", "Step 1: The definition aims to extract all the variable identifiers from a given reflection environment `g` and return them as a set of integers.\nStep 2: To implement this, we will traverse the environment `g`, which consists of a list of bindings. For each binding, we will extract the variable identifier and collect these identifiers into a set.", "Step 1: The definition `vars_of_rt_env` is about extracting the set of variable identifiers from a given reflection environment `g`.\nStep 2: To implement this, we will iterate over the environment `g`, collect the variable identifiers, and return them as a set of integers.", "Step 1: The definition `vars_of_rt_env` aims to extract all the variable identifiers from a given reflection environment `g` and return them as a set of integers.\nStep 2: To implement this, we will iterate through the environment `g`, collect the variable identifiers, and insert them into a set. The result will be a set of integers representing these variable identifiers.", "Step 1: The definition is about extracting all the variable identifiers from a given reflection environment `g` and returning them as a set of integers.\nStep 2: To implement this, we will iterate through the environment `g`, collect all the variable identifiers, and insert them into a set. The result will be a set of integers representing the variable identifiers.", "Step 1: The definition `vars_of_rt_env` aims to extract all variable identifiers from a given reflection environment `g` and return them as a set of integers.\nStep 2: To implement this, we will iterate over the environment `g`, collect the variable identifiers, and insert them into a set. The result will be a set of integers representing the variable identifiers in the environment.", "Step 1: The definition is about extracting the set of variable identifiers from a given reflection environment.\nStep 2: To implement this, we will iterate over the environment, extract the variable identifiers, and collect them into a set.", "Step 1: The definition is about extracting the set of variable indices from a given reflection environment.\nStep 2: To implement this, we will iterate over the environment, collect the indices of the variables, and return them as a set of integers.", "Step 1: The definition `vars_of_rt_env` aims to extract all variable identifiers from a given reflection environment `g` and return them as a set of integers.\nStep 2: To implement this, we will iterate over the environment `g`, collect all variable identifiers, and insert them into a set. The resulting set will be returned as the output.", "Step 1: The definition is about extracting the set of variable indices from a given reflection environment.\nStep 2: To implement this, we will iterate through the environment, collect the indices of all variables, and return them as a set." ], "generated_solution": [ "let vars_of_rt_env (g: FStar.Stubs.Reflection.Types.env) : Prims.GTot (FStar.Set.set Prims.int) =\n FStar.List.fold_left (fun acc (b, _) -> FStar.Set.add (FStar.Reflection.V2.bv_to_int b) acc) FStar.Set.empty g", "let vars_of_rt_env (g: FStar.Stubs.Reflection.Types.env) : Prims.GTot (FStar.Set.set Prims.int) =\n let ids = L.map (fun b -> FStar.Reflection.V2.bv_to_int b) g in\n FStar.Set.of_list ids", "let vars_of_rt_env (g: FStar.Stubs.Reflection.Types.env) : Prims.GTot (FStar.Set.set Prims.int) =\n FStar.List.fold_left\n (fun acc (b, _) -> FStar.Set.add (FStar.Reflection.V2.bv_to_int b) acc)\n FStar.Set.empty\n g", "let vars_of_rt_env (g: FStar.Stubs.Reflection.Types.env) : Prims.GTot (FStar.Set.set Prims.int) =\n FStar.List.fold_left (fun acc (b, _) -> FStar.Set.add (FStar.Reflection.Types.bv_to_int b) acc) FStar.Set.empty g", "let vars_of_rt_env (g: FStar.Stubs.Reflection.Types.env) : Prims.GTot (FStar.Set.set Prims.int) =\n FStar.List.fold_left (fun acc (_, v) -> FStar.Set.add v acc) FStar.Set.empty g", "let vars_of_rt_env (g: FStar.Stubs.Reflection.Types.env) : Prims.GTot (FStar.Set.set Prims.int) =\n FStar.List.fold_left (fun acc (b, _) -> FStar.Set.add (FStar.Reflection.Types.bv_to_int b) acc) FStar.Set.empty g", "let vars_of_rt_env (g: FStar.Stubs.Reflection.Types.env) : Prims.GTot (FStar.Set.set Prims.int) =\n FStar.List.fold_left\n (fun acc (b, _) -> FStar.Set.add (FStar.Reflection.Types.bv_to_int b) acc)\n FStar.Set.empty\n g", "let vars_of_rt_env (g: FStar.Stubs.Reflection.Types.env) : Prims.GTot (FStar.Set.set Prims.int) =\n FStar.List.fold_left (fun acc -> fun b -> FStar.Set.add (FStar.Reflection.V2.bv_index b) acc) FStar.Set.empty g", "let vars_of_rt_env (g: FStar.Stubs.Reflection.Types.env) : Prims.GTot (FStar.Set.set Prims.int) =\n let vars = FStar.List.Tot.map (fun (b, _) -> FStar.Reflection.V2.bv_to_int b) g in\n FStar.Set.of_list vars", "let vars_of_rt_env (g: FStar.Stubs.Reflection.Types.env) : Prims.GTot (FStar.Set.set Prims.int) =\n FStar.List.fold_left\n (fun acc (b, _) -> FStar.Set.add (FStar.Reflection.V2.bv_index b) acc)\n FStar.Set.empty\n g" ] }, { "file_name": "RBTreeIntrinsic.fst", "name": "RBTreeIntrinsic.hiddenTree_max", "opens_and_abbrevs": [ { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 2, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 80, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val hiddenTree_max : #h:nat -> hiddenTree h -> option int", "source_definition": "let hiddenTree_max #h = function\n | HB root\n | HR root -> max root", "source_range": { "start_line": 230, "start_col": 0, "end_line": 232, "end_col": 23 }, "interleaved": false, "definition": "fun _ ->\n (match _ with\n | RBTreeIntrinsic.HB #_ root -> RBTreeIntrinsic.max root\n | RBTreeIntrinsic.HR #_ root -> RBTreeIntrinsic.max root)\n <:\n FStar.Pervasives.Native.option Prims.int", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Prims.nat", "RBTreeIntrinsic.hiddenTree", "RBTreeIntrinsic.rbnode", "Prims.op_Addition", "RBTreeIntrinsic.Black", "RBTreeIntrinsic.max", "RBTreeIntrinsic.Red", "FStar.Pervasives.Native.option", "Prims.int" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "_: RBTreeIntrinsic.hiddenTree h -> FStar.Pervasives.Native.option Prims.int", "prompt": "let hiddenTree_max #h =\n ", "expected_response": "function | HB root | HR root -> max root", "source": { "project_name": "FStar", "file_name": "examples/data_structures/RBTreeIntrinsic.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "RBTreeIntrinsic.fst", "checked_file": "dataset/RBTreeIntrinsic.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.IO.fst.checked", "dataset/FStar.All.fst.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "color", "Red", "Red", "Red", "Black", "Black", "Black", "let chain x y z =\n match x, z with\n | Some x, Some z -> x <= y && y <= z\n | Some x, None -> x <= y\n | None, Some z -> y <= z\n | _ -> true", "rbnode", "Leaf", "Leaf", "Leaf", "R", "R", "R", "h", "h", "left", "left", "value", "value", "right", "right", "B", "B", "B", "h", "h", "cl", "cl", "cr", "cr", "left", "left", "value", "value", "right", "right", "val reduceNode : #h:nat -> #c:color\n -> f:(int -> int -> int) -> root:rbnode h c -> Tot (option int) (decreases root)", "let rec reduceNode #h #c f = function\n | Leaf -> None\n | B left value right\n | R left value right ->\n match reduceNode f left, reduceNode f right with\n | Some l, Some r -> Some (f value (f l r))\n | Some x, None\n | None, Some x -> Some (f x value)\n | None, None -> Some value", "val min: #h:nat -> #c:color -> t:rbnode h c -> option int", "let min #h #c t = reduceNode (fun x y -> if x < y then x else y) t", "val max: #h:nat -> #c:color -> t:rbnode h c -> option int", "let max #h #c t = reduceNode (fun x y -> if x > y then x else y) t", "val sorted : #h:nat -> #c:color -> root:rbnode h c -> Tot bool (decreases root)", "let rec sorted #h #c = function\n | Leaf -> true\n | B left value right\n | R left value right ->\n sorted left && sorted right && chain (max left) value (min right)", "rbtree", "RBTree", "RBTree", "RBTree", "h", "h", "root", "root", "hiddenTree", "HR", "HR", "HR", "h", "h", "node", "node", "HB", "HB", "HB", "h", "h", "node", "node", "almostNode", "LR", "LR", "LR", "h", "h", "cR", "cR", "left", "left", "value", "value", "right", "right", "RR", "RR", "RR", "h", "h", "cL", "cL", "left", "left", "value", "value", "right", "right", "V", "V", "V", "h", "h", "c", "c", "node", "node", "val balanceLB : #h:nat -> #c:color -> almostNode h -> int -> rbnode h c -> Tot (hiddenTree (h+1))", "let balanceLB #h #c left z d =\n match left with\n | LR (R a x b) y c\n | RR a x (R b y c) -> HR (R (B a x b) y (B c z d))\n | V axb -> HB (B axb z d)", "val balanceRB : #h:nat -> #c:color -> rbnode h c -> int -> almostNode h -> Tot (hiddenTree (h+1))", "let balanceRB #h #c a x right =\n match right with\n | LR (R b y c) z d\n | RR b y (R c z d) -> HR (R (B a x b) y (B c z d))\n | V cyd -> HB (B a x cyd)", "val balanceLR : #h:nat -> #c:color -> hiddenTree h -> int -> rbnode h c -> Tot (almostNode h)", "let balanceLR #h #c left x right =\n match left with\n | HR a -> LR a x right\n | HB a ->\n match right with\n | R b y c -> RR a x (R b y c)\n | B b y c -> V (R a x (B b y c))\n | Leaf -> V (R a x Leaf)", "val balanceRR : #h:nat -> #c:color -> rbnode h c -> int -> hiddenTree h -> Tot (almostNode h)", "let balanceRR #h #c left y right =\n match right with\n | HR c -> RR left y c\n | HB c ->\n match left with\n | R a x b -> LR (R a x b) y c\n | B a x b -> V (R (B a x b) y c)\n | Leaf -> V (R Leaf y c)", "val ins : #h:nat -> #c:color -> x:int -> s:rbnode h c -> Tot (almostNode h) (decreases s)", "val insB : #h:nat -> x:int -> s:rbnode h Black -> Tot (hiddenTree h) (decreases s)", "let rec ins #h #c x = function\n | Leaf -> V (R Leaf x Leaf)\n | B a y b ->\n (if x < y then\n match balanceLB (ins x a) y b with\n | HR r -> V r\n | HB b -> V b\n else if x = y then V (B a y b)\n else match balanceRB a y (ins x b) with\n | HR r -> V r\n | HB b -> V b)\n | R a y b ->\n (if x < y then balanceLR (insB x a) y b\n else if x = y then V (R a y b)\n else balanceRR a y (insB x b))\nand insB #h x = function\n | Leaf -> HR (R Leaf x Leaf )\n | B a y b ->\n if x < y then balanceLB (ins x a) y b\n else if x = y then HB (B a y b)\n else balanceRB a y (ins x b)", "let rec ins #h #c x = function\n | Leaf -> V (R Leaf x Leaf)\n | B a y b ->\n (if x < y then\n match balanceLB (ins x a) y b with\n | HR r -> V r\n | HB b -> V b\n else if x = y then V (B a y b)\n else match balanceRB a y (ins x b) with\n | HR r -> V r\n | HB b -> V b)\n | R a y b ->\n (if x < y then balanceLR (insB x a) y b\n else if x = y then V (R a y b)\n else balanceRR a y (insB x b))\nand insB #h x = function\n | Leaf -> HR (R Leaf x Leaf )\n | B a y b ->\n if x < y then balanceLB (ins x a) y b\n else if x = y then HB (B a y b)\n else balanceRB a y (ins x b)", "val mem : #h:nat -> #c:color -> x:int -> s:rbnode h c -> Tot bool (decreases s)", "let rec mem #h #c x = function\n | Leaf -> false\n | B l y r\n | R l y r -> x = y || mem x l || mem x r", "val hiddenTree_mem : #h:nat -> int -> hiddenTree h -> bool", "let hiddenTree_mem #h x = function\n | HB root\n | HR root -> mem x root", "val almostNode_mem : #h:nat -> int -> almostNode h -> bool", "let almostNode_mem #h x = function\n | LR a y b\n | RR a y b -> mem x (B a y b)\n | V root -> mem x root", "val ins_mem : #h:nat -> #c:color -> x:int -> s:rbnode h c ->\n Lemma (ensures forall y. (mem y s \\/ y = x) <==> almostNode_mem y (ins x s)) (decreases s)", "val insB_mem : #h:nat -> x:int -> s:rbnode h Black ->\n Lemma (ensures forall y. (mem y s \\/ y = x) <==> hiddenTree_mem y (insB x s)) (decreases s)", "let rec ins_mem #h #c x = function\n | Leaf -> ()\n | B a y b ->\n if x < y then ins_mem x a\n else if x = y then ()\n else ins_mem x b\n | R a y b ->\n if x < y then insB_mem x a\n else if x = y then ()\n else insB_mem x b\nand insB_mem #h x = function\n | Leaf -> ()\n | B a y b ->\n if x < y then ins_mem x a\n else if x = y then ()\n else ins_mem x b", "let rec ins_mem #h #c x = function\n | Leaf -> ()\n | B a y b ->\n if x < y then ins_mem x a\n else if x = y then ()\n else ins_mem x b\n | R a y b ->\n if x < y then insB_mem x a\n else if x = y then ()\n else insB_mem x b\nand insB_mem #h x = function\n | Leaf -> ()\n | B a y b ->\n if x < y then ins_mem x a\n else if x = y then ()\n else ins_mem x b", "val almostNode_sorted : #h:nat -> almostNode h -> bool", "let almostNode_sorted #h = function\n | LR a x b\n | RR a x b -> sorted (B a x b)\n | V root -> sorted root", "val hiddenTree_sorted : #h:nat -> hiddenTree h -> bool", "let hiddenTree_sorted #h = function\n | HB root\n | HR root -> sorted root", "val hiddenTree_max : #h:nat -> hiddenTree h -> option int" ], "closest": [ "val find_max' : t:tree{Node? t}-> Tot int\nlet rec find_max' (Node n _ t2) = if Leaf? t2 then n else find_max' t2", "val size : tree -> Tot nat\nlet rec size t =\n match t with\n | Leaf -> 0\n | Node n t1 t2 -> 1 + size t1 + size t2", "val height (#n: nat) (uf: uf_forest n) (i: id n) (h: heap) : GTot nat\nlet height (#n:nat) (uf:uf_forest n) (i:id n) (h:heap) :GTot nat = Mktuple3?._2 (sel h (index uf i))", "val height (#a: Type) (x: tree a) : nat\nlet rec height (#a: Type) (x: tree a) : nat =\n match x with\n | Leaf -> 0\n | Node data left right ->\n if height left > height right then (height left) + 1\n else (height right) + 1", "val find_max : t:tree{is_bst t /\\ Node? t} ->\n Tot (x:int{b2t (all (ge x) t) /\\ in_tree x t})\nlet rec find_max (Node n _ t2) = if Leaf? t2 then n else find_max t2", "val max_int (n: nat) : Tot int\nlet max_int (n:nat) : Tot int = pow2 n - 1", "val max (n m: nat) : nat\nlet max (n m:nat) : nat =\n if n > m then n else m", "val max (n m: nat) : nat\nlet max (n m:nat) : nat = if n >= m then n else m", "val find : p:(int -> Tot bool) -> tree -> Tot (option int)\nlet rec find p t =\n match t with\n | Leaf -> None\n | Node n t1 t2 -> if p n then Some n else\n if Some? (find p t1) then find p t1\n else find p t2", "val find_max (max: option key_t) (q: forest) : Tot (option key_t) (decreases q)\nlet rec find_max (max:option key_t) (q:forest)\n : Tot (option key_t) (decreases q) =\n match q with\n | [] -> max\n | Leaf::q -> find_max max q\n | (Internal _ k _)::q ->\n match max with\n | None -> find_max (Some k) q\n | Some max -> find_max (if max < k then Some k else Some max) q", "val height (#a: eqtype) (#b: Type) (t: tree a b) : nat\nlet height (#a:eqtype) (#b:Type) (t:tree a b) : nat =\n match t with\n | Empty -> 0\n | Node _ _ h _ _ -> h", "val black_height: t:rbtree' -> Tot (option nat)\nlet rec black_height t = match t with\n | E -> Some 0\n | T c a _ b ->\n (*\n * TODO: ideally we should be able to write match (black_height a, black_height b)\n *)\n let hha = black_height a in\n let hhb = black_height b in\n match (hha, hhb) with\n | Some ha, Some hb ->\n if ha = hb then\n if c = R then Some ha else Some (ha + 1)\n else\n None\n | _, _ -> None", "val max_int (n: pos) : Tot int\nlet max_int (n:pos) : Tot int = pow2 (n-1) - 1", "val depth (n: bin_tree_node) : Tot nat\nlet rec depth (n:bin_tree_node): Tot nat = \n match n with \n | Root -> 0\n | LeftChild n' -> 1 + depth n'\n | RightChild n' -> 1 + depth n'", "val hide: #a: Type u#a -> a -> Tot (erased a)\nlet hide #a x = E x", "val max_elt: t:rbtree' -> Pure nat (requires (b2t (T? t))) (ensures (fun r -> True))\nlet rec max_elt (T _ _ x b) = match b with\n | E -> x\n | _ -> max_elt b", "val nat_to_uint (#t: inttype) (#l: secrecy_level) (n: nat{n <= maxint t})\n : u: uint_t t l {uint_v u == n}\nlet nat_to_uint (#t:inttype) (#l:secrecy_level) (n:nat{n <= maxint t}) : u:uint_t t l{uint_v u == n} = uint #t #l n", "val depth (#p: Type0) (x: tree' p) : nat\nlet rec depth (#p:Type0) (x:tree' p) : nat =\n match x with\n | Leaf _ -> 0\n | Node _ lxs -> 1 + children_depth lxs\nand children_depth (#p:Type0) (lxs:children' p) : nat =\n match lxs with\n | (_,x) :: lxs -> max (depth x) (children_depth lxs)\n | [] -> 0", "val MiTLS.Pkg.Tree.max = x: Prims.int -> y: Prims.int -> Prims.int\nlet max x y = if x <= y then y else x", "val max (x1 x2: nat) : Tot nat\nlet max (x1 x2: nat) : Tot nat = if x1 > x2 then x1 else x2", "val count (x: int) (t: tree) : Tot nat\nlet rec count (x:int) (t:tree) : Tot nat =\n match t with\n | Leaf -> 0\n | Node n t1 t2 -> (if n = x then 1 else 0) + count x t1 + count x t2", "val parent (#n: nat) (uf: uf_forest n) (i: id n) (h: heap) : GTot (id n)\nlet parent (#n:nat) (uf:uf_forest n) (i:id n) (h:heap) :GTot (id n) = Mktuple3?._1 (sel h (index uf i))", "val as_nat (h: mem) (e: felem) : GTot nat\nlet as_nat (h:mem) (e:felem) : GTot nat =\n BD.bn_v (as_seq h e)", "val as_nat (h: mem) (e: felem) : GTot nat\nlet as_nat (h:mem) (e:felem) : GTot nat =\n as_nat5 (as_felem5 h e)", "val as_nat (h: mem) (e: felem) : GTot nat\nlet as_nat (h:mem) (e:felem) : GTot nat =\n let s = as_seq h e in\n let s0 = s.[0] in\n let s1 = s.[1] in\n let s2 = s.[2] in\n let s3 = s.[3] in\n S.as_nat4 (s0, s1, s2, s3)", "val as_nat (h: mem) (f: felem) : GTot nat\nlet as_nat (h:mem) (f:felem) : GTot nat = P.as_nat h f", "val subtree (#n: nat) (uf: uf_forest n) (i: id n) (h: heap) : GTot subtree_t\nlet subtree (#n:nat) (uf:uf_forest n) (i:id n) (h:heap) :GTot subtree_t = reveal (Mktuple3?._3 (sel h (index uf i)))", "val as_nat (h: mem) (e: qelemB) : GTot nat\nlet as_nat (h:mem) (e:qelemB) : GTot nat =\n let s = as_seq h e in\n as_nat5 (s.[0], s.[1], s.[2], s.[3], s.[4])", "val bn_v: #t:limb_t -> #len:size_t -> h:mem -> b:lbignum t len -> GTot nat\nlet bn_v #t #len h b = S.bn_v #t #(v len) (as_seq h b)", "val mul_hi (#n:pos) (a b:natN n) : natN n\nlet mul_hi #n a b = mul_hi_def a b", "val fit_hidden (bt: bounded_int_type_t) (n: int) : (bt_to_ty bt)\nlet fit_hidden (bt: bounded_int_type_t) (n: int) : (bt_to_ty bt) =\n match bt with\n | MachineInt8 -> (n + 0x80) % 0x100 - 0x80\n | MachineInt16 -> (n + 0x8000) % 0x10000 - 0x8000\n | MachineInt32 -> (n + 0x80000000) % 0x100000000 - 0x80000000\n | MachineInt64 -> (n + 0x8000000000000000) % 0x10000000000000000 - 0x8000000000000000\n | MachineUint8 -> n % 0x100\n | MachineUint16 -> n % 0x10000\n | MachineUint32 -> n % 0x100000000\n | MachineUint64 -> n % 0x10000000000000000", "val insert: #k:int -> t:tree k -> i:int -> Tot (tree (max k i)) (decreases t)\nlet rec insert (#k:int) (Node left n right) i =\n if i = n\n then Node left n right (* no duplicates *)\n else if i < n\n then match left with\n | None ->\n Node (Some (leaf i)) n right\n | Some left ->\n Node (Some (insert left i)) n right\n else match right with\n | None ->\n Node left n (Some (leaf i))\n | Some right ->\n Node left n (Some (insert right i))", "val tree_root_is_max_aux (d: nat) (upper_bound: key_t) (t: tree)\n : Lemma (requires pow2heap_pred d upper_bound t)\n (ensures max upper_bound (keys_of_tree t).ms_elems)\n (decreases t)\nlet rec tree_root_is_max_aux (d:nat) (upper_bound:key_t) (t:tree)\n : Lemma\n (requires pow2heap_pred d upper_bound t)\n (ensures max upper_bound (keys_of_tree t).ms_elems)\n (decreases t) =\n\n match t with\n | Leaf -> ()\n | Internal left k right ->\n tree_root_is_max_aux (d - 1) k left;\n tree_root_is_max_aux (d - 1) upper_bound right", "val min_int (n: nat) : Tot int\nlet min_int (n:nat) : Tot int = 0", "val as_nat (#s: field_spec) (h: mem) (e: felem s) : GTot nat\nlet as_nat (#s:field_spec) (h:mem) (e:felem s): GTot nat =\n match s with\n | M51 -> f51_as_nat h e\n | M64 -> f64_as_nat h e", "val h (x y: Prims.nat) : nat\nlet h (x:Prims.nat) (y:Prims.nat): nat = u x + u y", "val find_fold : f:(int -> Tot bool) -> tree -> Tot (option (x:int{f x}))\nlet find_fold f = fold #(option (x:int{f x}))\n (fun n o1 o2 -> if f n then Some n else\n if Some? o1 then o1 else o2) None", "val as_seq (#a:Type0) (#n:nat) (arr:t a n) (h:heap)\n :GTot (Seq.seq (option a))\nlet as_seq (#a:Type0) (#n:nat) (arr:t a n) (h:heap)\n :GTot (Seq.seq (option a))\n = let A #_ #_ #_ s_ref off = arr in\n let s = fst (sel h s_ref) in\n Seq.slice s off (off + n)", "val lemma_find_opt_helper\n (#n: nat)\n (uf: uf_forest n)\n (i: id n)\n (h: heap{live uf h /\\ well_formed uf h})\n : Lemma\n (let p, d, s = sel h (index uf i) in\n p = i \\/\n (let pp, hp = reify (find_opt uf p h) h in\n let pi, hi = reify (find_opt uf i h) h in\n pp = pi /\\ (hi == upd hp (index uf i) (pp, d, s))))\nlet lemma_find_opt_helper (#n:nat) (uf:uf_forest n) (i:id n) (h:heap{live uf h /\\ well_formed uf h})\n :Lemma (let p, d, s = sel h (index uf i) in\n p = i \\/\n\t (let pp, hp = reify (find_opt uf p h) h in\n let pi, hi = reify (find_opt uf i h) h in\n\t pp = pi /\\ (hi == upd hp (index uf i) (pp, d, s))))\n = let p, s, _ = sel h (index uf i) in\n if p = i then ()\n else begin\n ignore (reify (find_opt uf p h) h);\n ignore (reify (find_opt uf i h) h);\n ()\n end", "val s_height (#f #g #t0 #t1: _) (d: sub_typing f g t0 t1) : GTot nat\nlet s_height #f #g #t0 #t1 (d:sub_typing f g t0 t1)\n : GTot nat\n = 1", "val s_height (#f #g #t0 #t1: _) (d: sub_typing f g t0 t1) : GTot nat\nlet s_height #f #g #t0 #t1 (d:sub_typing f g t0 t1)\n : GTot nat\n = 1", "val insert'' : int -> tree -> Tot tree\nlet rec insert'' x t =\n match t with\n | Leaf -> Node x Leaf Leaf\n | Node n t1 t2 -> if x = n then t\n else if x < n then Node n (insert'' x t1) t2\n else Node n t1 (insert'' x t2)", "val length: #a:Type -> seq a -> Tot nat\nlet length #_ s = List.length (MkSeq?.l s)", "val height (#a: Type0) (ptr: t a)\n : Steel nat (linked_tree ptr) (fun _ -> linked_tree ptr)\n (requires fun _ -> True)\n (ensures fun h0 x h1 ->\n v_linked_tree ptr h0 == v_linked_tree ptr h1 /\\\n Spec.height (v_linked_tree ptr h0) == x)\nlet rec height #a ptr =\n if is_null_t ptr then (\n (**) elim_linked_tree_leaf ptr;\n 0\n ) else (\n (**) let node = unpack_tree ptr in\n let hleft = height (get_left node) in\n let hright = height (get_right node) in\n (**) pack_tree ptr (get_left node) (get_right node);\n if hleft > hright then (\n hleft + 1\n ) else ( hright + 1 )\n )", "val find_max_is_max (d: pos) (kopt: option key_t) (q: forest)\n : Lemma (requires is_binomial_queue d q /\\ Some? (find_max kopt q))\n (ensures\n (let Some k = find_max kopt q in\n max k (keys q).ms_elems))\n (decreases q)\nlet rec find_max_is_max (d:pos) (kopt:option key_t) (q:forest)\n : Lemma\n (requires\n is_binomial_queue d q /\\\n Some? (find_max kopt q))\n (ensures\n (let Some k = find_max kopt q in\n max k (keys q).ms_elems))\n (decreases q) =\n match q with\n | [] -> ()\n | Leaf::q ->\n find_max_is_max (d + 1) kopt q\n | (Internal left k Leaf)::tl ->\n tree_root_is_max d (Internal left k Leaf);\n match kopt with\n | None ->\n find_max_is_max (d + 1) (Some k) tl;\n find_max_some_is_some k tl\n | Some k' ->\n let k = if k' < k then k else k' in\n find_max_is_max (d + 1) (Some k) tl;\n find_max_some_is_some k tl", "val point: #a:eqtype -> x:a -> y:option a -> nat\nlet point #a x = fun y -> if y = Some x then 1 else 0", "val point: #a:eqtype -> x:a -> y:option a -> nat\nlet point #a x = fun y -> if y = Some x then 1 else 0", "val mt_get: #hsz:pos -> #n:nat -> mt:merkle_tree #hsz n -> idx:nat{idx < pow2 n} -> GTot (padded_hash #hsz)\nlet mt_get #_ #_ mt idx = S.index mt idx", "val in_tree: t:rbtree' -> k:nat -> Tot bool\nlet rec in_tree t k = match t with\n | E -> false\n | T _ a x b -> in_tree a k || k = x || in_tree b k", "val init_r1 (h:vale_stack) : (n:nat64{n >= 65536})\nlet init_r1 h = h.initial_r1", "val mul_hi_def (#n: pos) (a b: natN n) : natN n\nlet mul_hi_def (#n:pos) (a b:natN n) : natN n =\n lemma_mul_div_n a b;\n (a * b) / n", "val all : p:(int -> Tot bool) -> t:tree ->\n Tot (r:bool{r <==> (forall x. in_tree x t ==> p x)})\nlet rec all p t =\n match t with\n | Leaf -> true\n | Node n t1 t2 -> p n && all p t1 && all p t2", "val all : p:(int -> Tot bool) -> t:tree ->\n Tot (r:bool{r <==> (forall x. in_tree x t ==> p x)})\nlet rec all p t =\n match t with\n | Leaf -> true\n | Node n t1 t2 -> p n && all p t1 && all p t2", "val min (a b: nat) : nat\nlet min (a:nat) (b:nat): nat = if a < b then a else b", "val insert : int -> tree -> tree\nlet rec insert x t =\n match t with\n | Leaf -> Node x Leaf Leaf\n | Node n t1 t2 -> if x = n then t\n else if x < n then Node n (insert x t1) t2\n else Node n t1 (insert x t2)", "val max (a b: nat) : Tot (c: nat{c >= a /\\ c >= b /\\ (c <= a \\/ c <= b)})\nlet max (a: nat) (b: nat) : Tot (c: nat { c >= a /\\ c >= b /\\ (c <= a \\/ c <= b) }) = if a <= b then b else a", "val max (a b: int) : Tot (n: int{n >= a /\\ n >= b})\nlet max (a b:int) : Tot (n:int{n >= a /\\ n >= b}) =\n if a > b then a else b", "val max (a b: int) : Tot (n: int{n >= a /\\ n >= b})\nlet max (a b:int) : Tot (n:int{n >= a /\\ n >= b}) =\n if a > b then a else b", "val header_len' (h: header) : GTot nat\nlet header_len'\n (h: header)\n: GTot nat\n= \n let s = serialize_header (U32.uint_to_t (dcid_len h)) (last_packet_number h) in\n LP.serialize_length s h;\n Seq.length (LP.serialize s h)", "val id_cl_max_v (idc: id_cl) : GTot nat\nlet id_cl_max_v (idc : id_cl) : GTot nat = Some?.v (id_cl_opt_v idc.id_max)", "val hide:\n #a:Type\n -> s:S.seq a{S.length s < pow2 32}\n -> GTot (raw a (U32.uint_to_t (S.length s)))\nlet hide #a s = s", "val DependentBoolRefinement.max = n1: Prims.nat -> n2: Prims.nat -> Prims.nat\nlet max (n1 n2:nat) = if n1 < n2 then n2 else n1", "val tree_root_is_max (d: pos) (t: tree)\n : Lemma (requires is_pow2heap d t)\n (ensures\n (let Internal left k Leaf = t in\n max k (keys_of_tree left).ms_elems))\nlet tree_root_is_max (d:pos) (t:tree)\n : Lemma\n (requires is_pow2heap d t)\n (ensures\n (let Internal left k Leaf = t in\n max k (keys_of_tree left).ms_elems)) =\n let Internal left k Leaf = t in\n tree_root_is_max_aux (d - 1) k left", "val f':(hi int ^--> hi int)\nlet f' : (hi int ^--> hi int) = fun x -> x + 45", "val is_bvar (t: term) : option nat\nlet is_bvar (t:term) : option nat =\n let open R in\n match t.t with\n | Tm_FStar host_term ->\n begin match R.inspect_ln host_term with\n | R.Tv_BVar bv ->\n let bv_view = R.inspect_bv bv in\n Some bv_view.index\n | _ -> None\n end\n | _ -> None", "val live (#n: nat) (uf: uf_forest n) (h: heap) : Type0\nlet live (#n:nat) (uf:uf_forest n) (h:heap) :Type0 =\n (forall (i:id n).{:pattern addr_of (index uf i)} forall (j:id n).{:pattern addr_of (index uf j)}\n i <> j ==> addr_of (index uf i) <> addr_of (index uf j)) /\\ //all the refs in the forest are distinct\n (forall (i:id n).{:pattern (h `contains_a_well_typed` (index uf i))}\n h `contains_a_well_typed` (index uf i))", "val leaf (i: _) : tree i\nlet leaf i : tree i = Node #i #i None i None", "val wide_as_nat (h: mem) (e: widefelem) : GTot nat\nlet wide_as_nat (h:mem) (e:widefelem) : GTot nat =\n BD.bn_v (as_seq h e)", "val STLC.Core.max = n1: Prims.nat -> n2: Prims.nat -> Prims.nat\nlet max (n1 n2:nat) = if n1 < n2 then n2 else n1", "val typ_depth (t: typ) : GTot nat\nlet rec typ_depth\n (t: typ)\n: GTot nat\n= match t with\n | TArray _ t -> 1 + typ_depth t\n | TUnion l\n | TStruct l -> 1 + struct_typ_depth l.fields\n | _ -> 0\nand struct_typ_depth\n (l: list (string * typ))\n: GTot nat\n= match l with\n | [] -> 0\n | h :: l ->\n let (_, t) = h in // matching like this prevents needing two units of ifuel\n let n1 = typ_depth t in\n let n2 = struct_typ_depth l in\n if n1 > n2 then n1 else n2", "val frozen_bit (#a:Type0) (#n:nat) (arr:t a n) (h:heap) : Type0\nlet frozen_bit (#a:Type0) (#n:nat) (arr:t a n) (h:heap) :Type0\n = let A s_ref _ = arr in\n snd (sel h s_ref) == Frozen", "val hide (#sl:sl)\n (#l:lattice_element sl)\n (#s:sw)\n (x:int{within_bounds s x})\n : GTot (secret_int l s)\nlet hide (#sl:sl) (#l:lattice_element sl) (#s:sw) (x:int{within_bounds s x})\n : GTot (secret_int l s)\n = return l (u x)", "val qas_nat (h: mem) (e: qelem) : GTot nat\nlet qas_nat (h:mem) (e:qelem) : GTot nat = BD.bn_v #U64 #qnlimb h e", "val tree_invariant' (#pp: Type0) (x: tree' pp) (h: mem) : Tot Type0 (decreases %[depth x])\nlet rec tree_invariant' (#pp:Type0) (x:tree' pp) (h:mem)\n : Tot Type0 (decreases %[depth x]) =\n match x with\n | Leaf p -> Pkg?.package_invariant p h\n | Node p lxs ->\n Pkg?.package_invariant p h /\\\n children_forall lxs (fun x -> tree_invariant' x h) /\\\n disjoint_children h lxs", "val int_at_most (#r #a #p: _) (x: int) (is: i_seq r a p) (h: mem) : Type0\nlet int_at_most #r #a #p (x:int) (is:i_seq r a p) (h:mem) : Type0 =\n x < Seq.length (HS.sel h is)", "val eval_: #t:limb_t -> len:size_nat -> s:lbignum t len -> i:nat{i <= len} -> nat\nlet rec eval_ #t len s i =\n if i = 0 then 0\n else eval_ #t len s (i - 1) + v s.[i - 1] * pow2 (bits t * (i - 1))", "val heap_delete_max (d: pos) (t: tree)\n : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1)\nlet heap_delete_max (d:pos) (t:tree)\n : Pure priq\n (requires is_pow2heap d t)\n (ensures fun q -> L.length q == d - 1) =\n\n match t with\n | Internal left k Leaf -> unzip (d - 1) k left", "val search : int -> tree -> bool\nlet rec search x t =\n match t with\n | Leaf -> false\n | Node n t1 t2 -> if x = n then true\n else if x < n then search x t1\n else search x t2", "val nth: list 'a -> nat -> Tot (option 'a)\nlet rec nth l n = match l with\n | [] -> None\n | hd::tl -> if n = 0 then Some hd else nth tl (n - 1)", "val w (a : Type u#a) : Type u#(max 1 a)\nlet w a = pure_wp a", "val w (a : Type u#a) : Type u#(max 1 a)\nlet w a = pure_wp a", "val diff (n: nat) (s: subtree_t) : Tot nat\nlet diff (n:nat) (s:subtree_t) :Tot nat = size (minus (set_n n) s)", "val min_elt: t:rbtree' -> Pure nat (requires (b2t (T? t))) (ensures (fun r -> True))\nlet rec min_elt (T _ a x _) = match a with\n | E -> x\n | _ -> min_elt a", "val size (n: size_nat) : size_t\nlet size (n:size_nat) : size_t = uint #U32 #PUB n", "val len_v: a:maxed_hash_alg -> len_t a -> nat\nlet len_v = function\n | MD5 | SHA1\n | SHA2_224 | SHA2_256 -> uint_v #U64 #PUB\n | SHA2_384 | SHA2_512 -> uint_v #U128 #PUB\n | Blake2S -> uint_v #U64 #PUB\n | Blake2B -> uint_v #U128 #PUB", "val w0 (a : Type u#a) : Type u#(max 1 a)\nlet w0 a = (a -> Type0) -> Type0", "val BoolRefinement.max = n1: Prims.nat -> n2: Prims.nat -> Prims.nat\nlet max (n1 n2:nat) = if n1 < n2 then n2 else n1", "val sel: #a:Type -> h:heap -> r:ref a -> GTot a\nlet sel #a h r =\n if FStar.StrongExcludedMiddle.strong_excluded_middle (h `contains_a_well_typed` r) then\n sel_tot #a h r\n else r.init", "val wide_as_nat (h: mem) (e: qelem_wide) : GTot nat\nlet wide_as_nat (h:mem) (e:qelem_wide) : GTot nat =\n let s = as_seq h e in\n wide_as_nat5 (s.[0], s.[1], s.[2], s.[3], s.[4], s.[5], s.[6], s.[7], s.[8], s.[9])", "val g_node_val (h:HS.mem) (n:node 'a) : GTot 'a\nlet g_node_val h n =\n (n@h).DLL.p", "val lemma_find_find_opt_same_result\n (#n: nat)\n (uf: uf_forest n)\n (i: id n)\n (h: heap{live uf h /\\ well_formed uf h})\n : Lemma (requires True)\n (ensures (fst (reify (find uf i h) h) = fst (reify (find_opt uf i h) h)))\n (decreases (diff n (subtree #n uf i h)))\nlet rec lemma_find_find_opt_same_result (#n:nat) (uf:uf_forest n) (i:id n) (h:heap{live uf h /\\ well_formed uf h})\n :Lemma (requires True)\n (ensures (fst (reify (find uf i h) h) = fst (reify (find_opt uf i h) h)))\n\t (decreases (diff n (subtree #n uf i h)))\n = let p, _, _ = sel h (index uf i) in\n if p = i then ()\n else begin\n well_formed_decreases_lemma uf i h;\n lemma_find_find_opt_same_result uf p h\n end", "val min_int (n: pos) : Tot int\nlet min_int (n:pos) : Tot int = - (pow2 (n-1))", "val mt_get_path:\n #hsz:pos -> #f:hash_fun_t #hsz -> #n:nat ->\n mt:merkle_tree #hsz n -> i:nat{i < pow2 n} -> GTot (path #hsz n)\nlet rec mt_get_path #hsz #f #n t i =\n if n = 0 then S.empty\n else S.cons\n (if i % 2 = 0 then t.[i + 1] else t.[i - 1])\n (mt_get_path #_ #f (mt_next_lv #_ #f t) (i / 2))", "val log_2: x:pos -> Tot nat\nlet rec log_2 x =\n if x >= 2 then 1 + log_2 (x / 2) else 0", "val decr_while : h:(option heap) -> v:variant -> GTot nat\nlet decr_while h v = match h with\n | None -> 0\n | Some h0 ->\n let tmp = interpret_exp h0 v in\n if 0 > tmp then 0 else tmp", "val find_max_lemma : t:tree{Node? t /\\ is_bst t} ->\n Lemma (in_tree (find_max' t) t /\\ b2t (all (ge (find_max' t)) t))\nlet rec find_max_lemma (Node _ _ t2) = if Node? t2 then find_max_lemma t2", "val max_ctr:n: nat{n = 18446744073709551615}\nlet max_ctr: n:nat{n = 18446744073709551615} =\n assert_norm (pow2 64 - 1 = 18446744073709551615);\n pow2 64 - 1", "val from_felem (#f: field) (e: felem f) : n: nat{n <= maxint f.t}\nlet from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e", "val BinarySearchTreeFirst.max = i: Prims.int -> j: Prims.int -> Prims.int\nlet max i j = if i < j then j else i", "val increasing:preorder nat\nlet increasing : preorder nat = fun (x y:nat) -> b2t (x <= y)" ], "closest_src": [ { "project_name": "FStar", "file_name": "BinarySearchTreeBasic.fst", "name": "BinarySearchTreeBasic.find_max'" }, { "project_name": "FStar", "file_name": "BinaryTrees.fst", "name": "BinaryTrees.size" }, { "project_name": "FStar", "file_name": "UnionFind.Functions.fst", "name": "UnionFind.Functions.height" }, { "project_name": "steel", "file_name": "Trees.fst", "name": "Trees.height" }, { "project_name": "FStar", "file_name": "BinarySearchTreeBasic.fst", "name": "BinarySearchTreeBasic.find_max" }, { "project_name": "FStar", "file_name": "FStar.UInt.fsti", "name": "FStar.UInt.max_int" }, { "project_name": "FStar", "file_name": "NatHeap.fsti", "name": "NatHeap.max" }, { "project_name": "steel", "file_name": "Steel.Stepper.fst", "name": "Steel.Stepper.max" }, { "project_name": "FStar", "file_name": "BinaryTrees.fst", "name": "BinaryTrees.find" }, { "project_name": "FStar", "file_name": "BinomialQueue.fst", "name": "BinomialQueue.find_max" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.MapTree.fst", "name": "Vale.Lib.MapTree.height" }, { "project_name": "FStar", "file_name": "RBTree.fst", "name": "RBTree.black_height" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.max_int" }, { "project_name": "zeta", "file_name": "Zeta.BinTree.fsti", "name": "Zeta.BinTree.depth" }, { "project_name": "FStar", "file_name": "FStar.Ghost.fst", "name": "FStar.Ghost.hide" }, { "project_name": "FStar", "file_name": "RBTree.fst", "name": "RBTree.max_elt" }, { "project_name": "hacl-star", "file_name": "Lib.IntTypes.Compatibility.fst", "name": "Lib.IntTypes.Compatibility.nat_to_uint" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Pkg.Tree.fst", "name": "MiTLS.Pkg.Tree.depth" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Pkg.Tree.fst", "name": "MiTLS.Pkg.Tree.max" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.Instances.fst", "name": "LowParse.Low.Writers.Instances.max" }, { "project_name": "FStar", "file_name": "BinaryTrees.fst", "name": "BinaryTrees.count" }, { "project_name": "FStar", "file_name": "UnionFind.Functions.fst", "name": "UnionFind.Functions.parent" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Bignum.fsti", "name": "Hacl.Impl.P256.Bignum.as_nat" }, { "project_name": "hacl-star", "file_name": "Hacl.K256.Field.fsti", "name": "Hacl.K256.Field.as_nat" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Curve25519.Field64.fst", "name": "Hacl.Impl.Curve25519.Field64.as_nat" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Ed25519.Field51.fst", "name": "Hacl.Impl.Ed25519.Field51.as_nat" }, { "project_name": "FStar", "file_name": "UnionFind.Functions.fst", "name": "UnionFind.Functions.subtree" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.BignumQ.Mul.fsti", "name": "Hacl.Impl.BignumQ.Mul.as_nat" }, { "project_name": "hacl-star", "file_name": "Hacl.Bignum.Definitions.fst", "name": "Hacl.Bignum.Definitions.bn_v" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.Defs.fst", "name": "Vale.Bignum.Defs.mul_hi" }, { "project_name": "Armada", "file_name": "Armada.BoundedInt.fst", "name": "Armada.BoundedInt.fit_hidden" }, { "project_name": "FStar", "file_name": "BinarySearchTreeFirst.fst", "name": "BinarySearchTreeFirst.insert" }, { "project_name": "FStar", "file_name": "BinomialQueue.fst", "name": "BinomialQueue.tree_root_is_max_aux" }, { "project_name": "FStar", "file_name": "FStar.UInt.fsti", "name": "FStar.UInt.min_int" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Curve25519.Fields.Core.fsti", "name": "Hacl.Impl.Curve25519.Fields.Core.as_nat" }, { "project_name": "FStar", "file_name": "FStar.Integers.fst", "name": "FStar.Integers.h" }, { "project_name": "FStar", "file_name": "BinaryTrees.fst", "name": "BinaryTrees.find_fold" }, { "project_name": "FStar", "file_name": "MonotonicArray.fst", "name": "MonotonicArray.as_seq" }, { "project_name": "FStar", "file_name": "UnionFind.fst", "name": "UnionFind.lemma_find_opt_helper" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.s_height" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.s_height" }, { "project_name": "FStar", "file_name": "BinarySearchTreeBasic.fst", "name": "BinarySearchTreeBasic.insert''" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.length" }, { "project_name": "steel", "file_name": "Selectors.Tree.fst", "name": "Selectors.Tree.height" }, { "project_name": "FStar", "file_name": "BinomialQueue.fst", "name": "BinomialQueue.find_max_is_max" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Random.fst", "name": "FStar.DM4F.Random.point" }, { "project_name": "FStar", "file_name": "FStar.DM4F.OTP.Random.fst", "name": "FStar.DM4F.OTP.Random.point" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Spec.fst", "name": "MerkleTree.Spec.mt_get" }, { "project_name": "FStar", "file_name": "RBTree.fst", "name": "RBTree.in_tree" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Stack_i.fst", "name": "Vale.PPC64LE.Stack_i.init_r1" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.Defs.fsti", "name": "Vale.Bignum.Defs.mul_hi_def" }, { "project_name": "FStar", "file_name": "BinarySearchTreeBasic.fst", "name": "BinarySearchTreeBasic.all" }, { "project_name": "FStar", "file_name": "BinarySearchTree.fst", "name": "BinarySearchTree.all" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.StreamPlain.fst", "name": "MiTLS.StreamPlain.min" }, { "project_name": "FStar", "file_name": "BinarySearchTree0.fst", "name": "BinarySearchTree0.insert" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Header.fst", "name": "QUIC.Spec.Header.max" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.max" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.PacketNumber.fst", "name": "QUIC.Spec.PacketNumber.max" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Header.Parse.fst", "name": "QUIC.Spec.Header.Parse.header_len'" }, { "project_name": "noise-star", "file_name": "Impl.Noise.API.Device.fsti", "name": "Impl.Noise.API.Device.id_cl_max_v" }, { "project_name": "FStar", "file_name": "FStar.Vector.Base.fst", "name": "FStar.Vector.Base.hide" }, { "project_name": "FStar", "file_name": "DependentBoolRefinement.fst", "name": "DependentBoolRefinement.max" }, { "project_name": "FStar", "file_name": "BinomialQueue.fst", "name": "BinomialQueue.tree_root_is_max" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.f'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Pure.fst", "name": "Pulse.Syntax.Pure.is_bvar" }, { "project_name": "FStar", "file_name": "UnionFind.Forest.fst", "name": "UnionFind.Forest.live" }, { "project_name": "FStar", "file_name": "BinarySearchTreeFirst.fst", "name": "BinarySearchTreeFirst.leaf" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.P256.Bignum.fsti", "name": "Hacl.Impl.P256.Bignum.wide_as_nat" }, { "project_name": "FStar", "file_name": "STLC.Core.fst", "name": "STLC.Core.max" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fsti", "name": "FStar.Pointer.Base.typ_depth" }, { "project_name": "FStar", "file_name": "MonotonicArray.fst", "name": "MonotonicArray.frozen_bit" }, { "project_name": "FStar", "file_name": "FStar.ConstantTime.Integers.fst", "name": "FStar.ConstantTime.Integers.hide" }, { "project_name": "hacl-star", "file_name": "Hacl.K256.Scalar.fsti", "name": "Hacl.K256.Scalar.qas_nat" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.KDF.fst", "name": "MiTLS.KDF.tree_invariant'" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Seq.fst", "name": "FStar.Monotonic.Seq.int_at_most" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Bignum.Definitions.fst", "name": "Hacl.Spec.Bignum.Definitions.eval_" }, { "project_name": "FStar", "file_name": "BinomialQueue.fst", "name": "BinomialQueue.heap_delete_max" }, { "project_name": "FStar", "file_name": "BinarySearchTree0.fst", "name": "BinarySearchTree0.search" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Base.fst", "name": "FStar.List.Tot.Base.nth" }, { "project_name": "FStar", "file_name": "ID3.fst", "name": "ID3.w" }, { "project_name": "FStar", "file_name": "ND.fst", "name": "ND.w" }, { "project_name": "FStar", "file_name": "UnionFind.Functions.fst", "name": "UnionFind.Functions.diff" }, { "project_name": "FStar", "file_name": "RBTree.fst", "name": "RBTree.min_elt" }, { "project_name": "hacl-star", "file_name": "Lib.IntTypes.fsti", "name": "Lib.IntTypes.size" }, { "project_name": "hacl-star", "file_name": "Spec.Hash.Definitions.fst", "name": "Spec.Hash.Definitions.len_v" }, { "project_name": "FStar", "file_name": "ID3.fst", "name": "ID3.w0" }, { "project_name": "FStar", "file_name": "BoolRefinement.fst", "name": "BoolRefinement.max" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.sel" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.BignumQ.Mul.fsti", "name": "Hacl.Impl.BignumQ.Mul.wide_as_nat" }, { "project_name": "FStar", "file_name": "DoublyLinkedListIface.fst", "name": "DoublyLinkedListIface.g_node_val" }, { "project_name": "FStar", "file_name": "UnionFind.fst", "name": "UnionFind.lemma_find_find_opt_same_result" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.min_int" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Spec.fst", "name": "MerkleTree.Spec.mt_get_path" }, { "project_name": "FStar", "file_name": "FStar.Math.Lib.fst", "name": "FStar.Math.Lib.log_2" }, { "project_name": "FStar", "file_name": "IfcRules.fst", "name": "IfcRules.decr_while" }, { "project_name": "FStar", "file_name": "BinarySearchTreeBasic.fst", "name": "BinarySearchTreeBasic.find_max_lemma" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.StreamAE.fst", "name": "MiTLS.StreamAE.max_ctr" }, { "project_name": "hacl-star", "file_name": "Spec.GaloisField.fst", "name": "Spec.GaloisField.from_felem" }, { "project_name": "FStar", "file_name": "BinarySearchTreeFirst.fst", "name": "BinarySearchTreeFirst.max" }, { "project_name": "steel", "file_name": "Steel.MonotonicCounter.fst", "name": "Steel.MonotonicCounter.increasing" } ], "selected_premises": [ "RBTreeIntrinsic.almostNode_mem", "RBTreeIntrinsic.chain", "RBTreeIntrinsic.hiddenTree_mem", "RBTreeIntrinsic.insB", "RBTreeIntrinsic.mem", "FStar.Heap.trivial_preorder", "RBTreeIntrinsic.insB_mem", "FStar.ST.op_Bang", "RBTreeIntrinsic.balanceLR", "RBTreeIntrinsic.balanceLB", "FStar.Pervasives.reveal_opaque", "FStar.Pervasives.Native.fst", "RBTreeIntrinsic.balanceRR", "RBTreeIntrinsic.hiddenTree_sorted", "RBTreeIntrinsic.sorted", "FStar.Pervasives.Native.snd", "FStar.ST.alloc", "RBTreeIntrinsic.almostNode_sorted", "RBTreeIntrinsic.balanceRB", "RBTreeIntrinsic.reduceNode", "RBTreeIntrinsic.min", "RBTreeIntrinsic.max", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "FStar.All.op_Bar_Greater", "FStar.All.op_Less_Bar", "FStar.ST.contains_pred", "FStar.Monotonic.Heap.mref", "FStar.Heap.trivial_rel", "FStar.ST.get", "FStar.Preorder.preorder_rel", "FStar.Pervasives.all_post_h", "FStar.Pervasives.all_post_h'", "FStar.ST.lemma_functoriality", "FStar.Pervasives.st_post_h", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.all_return", "FStar.ST.read", "FStar.ST.heap_rel", "Prims.abs", "Prims.min", "FStar.All.all_post", "FStar.ST.op_Colon_Equals", "FStar.Monotonic.Heap.fresh", "FStar.ST.gst_pre", "FStar.Pervasives.id", "FStar.ST.gst_post", "FStar.Pervasives.st_stronger", "FStar.All.all_post'", "FStar.All.all_pre", "FStar.Pervasives.st_pre_h", "FStar.Pervasives.all_wp_h", "FStar.Pervasives.st_post_h'", "Prims.pure_post'", "FStar.All.pipe_left", "FStar.Monotonic.Heap.modifies", "FStar.ST.lift_div_gst", "FStar.Pervasives.ex_pre", "FStar.ST.st_post", "FStar.ST.st_post'", "FStar.Monotonic.Heap.equal_dom", "FStar.ST.gst_wp", "FStar.Monotonic.Heap.modifies_t", "FStar.Pervasives.trivial_pure_post", "FStar.ST.modifies_none", "FStar.Pervasives.all_ite_wp", "FStar.Preorder.reflexive", "Prims.pure_post", "FStar.Monotonic.Heap.only", "FStar.ST.gst_post'", "FStar.Pervasives.all_close_wp", "FStar.Monotonic.Heap.set", "FStar.All.all_wp", "FStar.Monotonic.Heap.tset", "FStar.Set.subset", "FStar.Pervasives.pure_null_wp", "FStar.Preorder.stable", "FStar.All.pipe_right", "FStar.Set.as_set", "FStar.Pervasives.st_return", "FStar.Pervasives.all_stronger", "FStar.Pervasives.ex_post'", "FStar.Pervasives.st_ite_wp", "FStar.Pervasives.all_trivial", "FStar.ST.witnessed", "FStar.Pervasives.div_hoare_to_wp", "FStar.Set.as_set'", "FStar.Preorder.transitive", "FStar.ST.st_pre", "FStar.All.lift_state_all", "FStar.ST.write", "Prims.__cache_version_number__", "FStar.Pervasives.all_bind_wp", "FStar.ST.lift_gst_state", "FStar.Pervasives.pure_close_wp", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.st_trivial", "FStar.ST.recall", "Prims.pure_wp_monotonic", "FStar.Pervasives.ex_post" ], "source_upto_this": "(*\n Copyright 2019 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n(**\n * Okasaki Red-Black trees in F*\n *\n * https://www.cs.tufts.edu/~nr/cs257/archive/chris-okasaki/redblack99.pdf\n *\n * Compare with\n * - https://github.com/sweirich/dth/tree/master/depending-on-types\n * - https://lists.chalmers.se/pipermail/agda/2012/003697.html\n * - The \"extrinsic\" style alternative in examples/data_structures/RBTree.fst\n *\n * Extract to OCaml and run with [make test] to get a REPL for playing with\n * the code.\n *\n * Author: Dany Fabian\n * Minor tweaks, comments, and OCaml test driver by Santiago Zanella-Beguelin\n**)\nmodule RBTreeIntrinsic\n\n/// Much of the file verifies with fuel=0, max_ifuel=1\n#set-options \"--max_fuel 2 --max_ifuel 2 --z3rlimit 80\"\n\ntype color =\n| Red\n| Black\n\nlet chain x y z =\n match x, z with\n | Some x, Some z -> x <= y && y <= z\n | Some x, None -> x <= y\n | None, Some z -> y <= z\n | _ -> true\n\n/// The following is enforced by the type:\n///\n/// - Each node is either Red or Black\n/// - All leaves are Black\n/// - If a node is Red then its two children are Black\n/// - Every path from a given node to any leaf has the same number of Black nodes\n/// (i.e. the Black height of the tree is a constant)\n///\n/// This implies that the path from the root to the farthest leaf is\n/// at most twice as long as the path from the root to the nearest leaf.\n///\n/// The type does not enforce that the root is Black, or that the tree\n/// is a binary search tree.\n///\n/// It's easy to make it polymoprhic on the type of values, but here we fix [int]\ntype rbnode : h:nat -> c:color -> Type =\n| Leaf :\n rbnode 1 Black\n| R : #h:nat ->\n left:rbnode h Black -> value:int -> right:rbnode h Black ->\n rbnode h Red\n| B : #h:nat -> #cl:color -> #cr:color ->\n left:rbnode h cl -> value:int -> right:rbnode h cr ->\n rbnode (h+1) Black\n\n/// The default lexicographic order for proving termination would\n/// require proving that the color \"decreases\" in recursive calls. The\n/// lexicographic order on color is [Red << Black] (because of the\n/// order of constructors in its definition), but this doesn't\n/// decrease when the root is [Black], hence why we need to explicitly\n/// say that the argument that decreases is [root].\nval reduceNode : #h:nat -> #c:color\n -> f:(int -> int -> int) -> root:rbnode h c -> Tot (option int) (decreases root)\nlet rec reduceNode #h #c f = function\n | Leaf -> None\n | B left value right\n | R left value right ->\n match reduceNode f left, reduceNode f right with\n | Some l, Some r -> Some (f value (f l r))\n | Some x, None\n | None, Some x -> Some (f x value)\n | None, None -> Some value\n\nval min: #h:nat -> #c:color -> t:rbnode h c -> option int\nlet min #h #c t = reduceNode (fun x y -> if x < y then x else y) t\n\nval max: #h:nat -> #c:color -> t:rbnode h c -> option int\nlet max #h #c t = reduceNode (fun x y -> if x > y then x else y) t\n\nval sorted : #h:nat -> #c:color -> root:rbnode h c -> Tot bool (decreases root)\nlet rec sorted #h #c = function\n | Leaf -> true\n | B left value right\n | R left value right ->\n sorted left && sorted right && chain (max left) value (min right)\n\n/// The type of Red-Black trees (sorted and with a Black root)\ntype rbtree =\n | RBTree : #h:nat -> root:rbnode h Black {sorted root} -> rbtree\n\n/// Non-empty subtree\ntype hiddenTree : h:nat -> Type =\n | HR : #h:nat -> node:rbnode h Red -> hiddenTree h\n | HB : #h:nat -> node:rbnode (h+1) Black -> hiddenTree (h+1)\n\ntype almostNode : h:nat -> Type =\n | LR : #h:nat -> #cR:color -> left:rbnode h Red -> value:int -> right:rbnode h cR -> almostNode h\n | RR : #h:nat -> #cL:color -> left:rbnode h cL -> value:int -> right:rbnode h Red -> almostNode h\n | V : #h:nat -> #c:color -> node:rbnode h c -> almostNode h\n\nval balanceLB : #h:nat -> #c:color -> almostNode h -> int -> rbnode h c -> Tot (hiddenTree (h+1))\nlet balanceLB #h #c left z d =\n match left with\n | LR (R a x b) y c\n | RR a x (R b y c) -> HR (R (B a x b) y (B c z d))\n | V axb -> HB (B axb z d)\n\nval balanceRB : #h:nat -> #c:color -> rbnode h c -> int -> almostNode h -> Tot (hiddenTree (h+1))\nlet balanceRB #h #c a x right =\n match right with\n | LR (R b y c) z d\n | RR b y (R c z d) -> HR (R (B a x b) y (B c z d))\n | V cyd -> HB (B a x cyd)\n\nval balanceLR : #h:nat -> #c:color -> hiddenTree h -> int -> rbnode h c -> Tot (almostNode h)\nlet balanceLR #h #c left x right =\n match left with\n | HR a -> LR a x right\n | HB a ->\n match right with\n | R b y c -> RR a x (R b y c)\n | B b y c -> V (R a x (B b y c))\n | Leaf -> V (R a x Leaf)\n\nval balanceRR : #h:nat -> #c:color -> rbnode h c -> int -> hiddenTree h -> Tot (almostNode h)\nlet balanceRR #h #c left y right =\n match right with\n | HR c -> RR left y c\n | HB c ->\n match left with\n | R a x b -> LR (R a x b) y c\n | B a x b -> V (R (B a x b) y c)\n | Leaf -> V (R Leaf y c)\n\nval ins : #h:nat -> #c:color -> x:int -> s:rbnode h c -> Tot (almostNode h) (decreases s)\nval insB : #h:nat -> x:int -> s:rbnode h Black -> Tot (hiddenTree h) (decreases s)\nlet rec ins #h #c x = function\n | Leaf -> V (R Leaf x Leaf)\n | B a y b ->\n (if x < y then\n match balanceLB (ins x a) y b with\n | HR r -> V r\n | HB b -> V b\n else if x = y then V (B a y b)\n else match balanceRB a y (ins x b) with\n | HR r -> V r\n | HB b -> V b)\n | R a y b ->\n (if x < y then balanceLR (insB x a) y b\n else if x = y then V (R a y b)\n else balanceRR a y (insB x b))\nand insB #h x = function\n | Leaf -> HR (R Leaf x Leaf )\n | B a y b ->\n if x < y then balanceLB (ins x a) y b\n else if x = y then HB (B a y b)\n else balanceRB a y (ins x b)\n\nval mem : #h:nat -> #c:color -> x:int -> s:rbnode h c -> Tot bool (decreases s)\nlet rec mem #h #c x = function\n | Leaf -> false\n | B l y r\n | R l y r -> x = y || mem x l || mem x r\n\nval hiddenTree_mem : #h:nat -> int -> hiddenTree h -> bool\nlet hiddenTree_mem #h x = function\n | HB root\n | HR root -> mem x root\n\nval almostNode_mem : #h:nat -> int -> almostNode h -> bool\nlet almostNode_mem #h x = function\n | LR a y b\n | RR a y b -> mem x (B a y b)\n | V root -> mem x root\n\nval ins_mem : #h:nat -> #c:color -> x:int -> s:rbnode h c ->\n Lemma (ensures forall y. (mem y s \\/ y = x) <==> almostNode_mem y (ins x s)) (decreases s)\n\nval insB_mem : #h:nat -> x:int -> s:rbnode h Black ->\n Lemma (ensures forall y. (mem y s \\/ y = x) <==> hiddenTree_mem y (insB x s)) (decreases s)\n\n#push-options \"--fuel 2 --ifuel 2 --z3rlimit_factor 4\"\nlet rec ins_mem #h #c x = function\n | Leaf -> ()\n | B a y b ->\n if x < y then ins_mem x a\n else if x = y then ()\n else ins_mem x b\n | R a y b ->\n if x < y then insB_mem x a\n else if x = y then ()\n else insB_mem x b\nand insB_mem #h x = function\n | Leaf -> ()\n | B a y b ->\n if x < y then ins_mem x a\n else if x = y then ()\n else ins_mem x b\n#pop-options\n\nval almostNode_sorted : #h:nat -> almostNode h -> bool\nlet almostNode_sorted #h = function\n | LR a x b\n | RR a x b -> sorted (B a x b)\n | V root -> sorted root\n\nval hiddenTree_sorted : #h:nat -> hiddenTree h -> bool\nlet hiddenTree_sorted #h = function\n | HB root\n | HR root -> sorted root\n\nval hiddenTree_max : #h:nat -> hiddenTree h -> option int", "sketch": [ "Step 1: The `hiddenTree_max` function is intended to find the maximum value in a `hiddenTree`. A `hiddenTree` can either be a red node (`HR`) or a black node (`HB`).\nStep 2: To implement this, we need to extract the root node from the `hiddenTree` and then use the `max` function defined earlier to find the maximum value in the root node.", "Step 1: The `hiddenTree_max` function aims to find the maximum value in a `hiddenTree`. A `hiddenTree` can either be a red node (`HR`) or a black node (`HB`).\nStep 2: To implement this, we need to extract the root node from the `hiddenTree` and then use the `max` function defined earlier to find the maximum value in the root node.", "Step 1: The `hiddenTree_max` function aims to find the maximum value in a `hiddenTree`. A `hiddenTree` can either be a red node (`HR`) or a black node (`HB`).\nStep 2: To implement this, we need to extract the root node from the `hiddenTree` and then use the `max` function defined earlier to find the maximum value in the root node.", "Step 1: The `hiddenTree_max` function is intended to find the maximum value in a `hiddenTree`. A `hiddenTree` can either be a red node or a black node.\nStep 2: To implement this, we need to pattern match on the `hiddenTree`. If it is a `HR` (hidden red node), we return the maximum value of the contained red node. If it is a `HB` (hidden black node), we return the maximum value of the contained black node. We can reuse the `max` function defined earlier to find the maximum value in the contained `rbnode`.", "Step 1: The `hiddenTree_max` function is intended to find the maximum value in a `hiddenTree`. A `hiddenTree` can either be a red node (`HR`) or a black node (`HB`).\nStep 2: To implement this, we need to extract the root node from the `hiddenTree` and then use the `max` function defined earlier to find the maximum value in that root node.", "Step 1: The `hiddenTree_max` function aims to find the maximum value in a `hiddenTree`. A `hiddenTree` can either be a red node (`HR`) or a black node (`HB`).\nStep 2: To implement this, we need to extract the root node from the `hiddenTree` and then use the `max` function defined earlier to find the maximum value in that root node.", "Step 1: The `hiddenTree_max` function is intended to find the maximum value in a `hiddenTree`. A `hiddenTree` can either be a red node (`HR`) or a black node (`HB`).\nStep 2: To implement this, we need to extract the root node from the `hiddenTree` and then use the `max` function defined earlier to find the maximum value in the root node.", "Step 1: The `hiddenTree_max` function is intended to find the maximum value in a `hiddenTree`. A `hiddenTree` can either be a red node (`HR`) or a black node (`HB`).\nStep 2: To implement `hiddenTree_max`, we need to extract the root node from the `hiddenTree` and then use the `max` function defined earlier to find the maximum value in the root node.", "Step 1: The `hiddenTree_max` function is intended to find the maximum value in a `hiddenTree`. A `hiddenTree` can either be a red node (`HR`) or a black node (`HB`).\nStep 2: To implement `hiddenTree_max`, we need to extract the root node from the `hiddenTree` and then use the `max` function defined earlier to find the maximum value in the root node.", "Step 1: The `hiddenTree_max` function aims to find the maximum value in a given `hiddenTree`. A `hiddenTree` can either be a red node (`HR`) or a black node (`HB`).\nStep 2: To implement this, we need to extract the root node from the `hiddenTree` and then use the `max` function defined earlier to find the maximum value in the root node." ], "generated_solution": [ "let hiddenTree_max #h = function\n | HB root\n | HR root -> max root", "let hiddenTree_max #h = function\n | HB root\n | HR root -> max root", "let hiddenTree_max #h = function\n | HB root\n | HR root -> max root", "let hiddenTree_max #h = function\n | HR root -> max root\n | HB root -> max root", "let hiddenTree_max #h = function\n | HB root\n | HR root -> max root", "let hiddenTree_max #h = function\n | HB root\n | HR root -> max root", "let hiddenTree_max #h = function\n | HB root\n | HR root -> max root", "let hiddenTree_max #h = function\n | HB root\n | HR root -> max root", "let hiddenTree_max #h = function\n | HB root\n | HR root -> max root", "let hiddenTree_max #h = function\n | HB root\n | HR root -> max root" ] }, { "file_name": "Vale.Stdcalls.X64.Cpuid.fsti", "name": "Vale.Stdcalls.X64.Cpuid.rdrand_pre", "opens_and_abbrevs": [ { "open": "Vale.X64.State" }, { "open": "Vale.X64.Machine_s" }, { "abbrev": "VC", "full_module": "Vale.Lib.X64.Cpuidstdcall" }, { "open": "Vale.X64.MemoryAdapters" }, { "abbrev": "W", "full_module": "Vale.AsLowStar.Wrapper" }, { "abbrev": "IA", "full_module": "Vale.Interop.Assumptions" }, { "abbrev": "V", "full_module": "Vale.X64.Decls" }, { "abbrev": "LSig", "full_module": "Vale.AsLowStar.LowStarSig" }, { "abbrev": "VSig", "full_module": "Vale.AsLowStar.ValeSig" }, { "abbrev": "IX64", "full_module": "Vale.Interop.X64" }, { "open": "Vale.Interop.Base" }, { "open": "FStar.Mul" }, { "open": "Vale.Stdcalls.X64" }, { "open": "Vale.Stdcalls.X64" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 1, "initial_ifuel": 0, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": true, "smtencoding_nl_arith_repr": "wrapped", "smtencoding_l_arith_repr": "native", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val rdrand_pre:VSig.vale_pre dom", "source_definition": "let rdrand_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_rdrand_stdcall c va_s0 IA.win", "source_range": { "start_line": 369, "start_col": 0, "end_line": 372, "end_col": 51 }, "interleaved": false, "definition": "fun c va_s0 ->\n Vale.Lib.X64.Cpuidstdcall.va_req_Check_rdrand_stdcall c va_s0 Vale.Interop.Assumptions.win", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_rdrand_stdcall", "Vale.Interop.Assumptions.win", "Prims.prop" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "Vale.AsLowStar.ValeSig.vale_pre Vale.Stdcalls.X64.Cpuid.dom", "prompt": "let rdrand_pre:VSig.vale_pre dom =\n ", "expected_response": "fun (c: V.va_code) (va_s0: V.va_state) -> VC.va_req_Check_rdrand_stdcall c va_s0 IA.win", "source": { "project_name": "hacl-star", "file_name": "vale/code/arch/x64/interop/Vale.Stdcalls.X64.Cpuid.fsti", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Vale.Stdcalls.X64.Cpuid.fsti", "checked_file": "dataset/Vale.Stdcalls.X64.Cpuid.fsti.checked", "interface_file": false, "dependencies": [ "dataset/Vale.X64.State.fsti.checked", "dataset/Vale.X64.MemoryAdapters.fsti.checked", "dataset/Vale.X64.Machine_s.fst.checked", "dataset/Vale.X64.Decls.fsti.checked", "dataset/Vale.Lib.X64.Cpuidstdcall.fsti.checked", "dataset/Vale.Interop.X64.fsti.checked", "dataset/Vale.Interop.Base.fst.checked", "dataset/Vale.Interop.Assumptions.fst.checked", "dataset/Vale.AsLowStar.Wrapper.fsti.checked", "dataset/Vale.AsLowStar.ValeSig.fst.checked", "dataset/Vale.AsLowStar.LowStarSig.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked" ] }, "definitions_in_context": [ "let as_t (#a:Type) (x:normal a) : a = x", "let as_normal_t (#a:Type) (x:a) : normal a = x", "let dom: IX64.arity_ok_stdcall td = []", "let aesni_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_aesni_stdcall c va_s0 IA.win", "let aesni_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_aesni_stdcall c va_s0 IA.win va_s1 f", "let aesni_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n aesni_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n aesni_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_aesni_stdcall code va_s0 IA.win", "let aesni_lemma = as_t #(VSig.vale_sig_stdcall aesni_pre aesni_post) aesni_lemma'", "let code_aesni = VC.va_code_Check_aesni_stdcall IA.win", "let lowstar_aesni_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_aesni\n dom\n []\n _\n _\n (W.mk_prediction code_aesni dom [] (aesni_lemma code_aesni IA.win))", "let sha_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_sha_stdcall c va_s0 IA.win", "let sha_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_sha_stdcall c va_s0 IA.win va_s1 f", "let sha_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n sha_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n sha_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_sha_stdcall code va_s0 IA.win", "let sha_lemma = as_t #(VSig.vale_sig_stdcall sha_pre sha_post) sha_lemma'", "let code_sha = VC.va_code_Check_sha_stdcall IA.win", "let lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))", "let adx_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_adx_bmi2_stdcall c va_s0 IA.win", "let adx_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_adx_bmi2_stdcall c va_s0 IA.win va_s1 f", "let adx_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n adx_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n adx_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_adx_bmi2_stdcall code va_s0 IA.win", "let adx_lemma = as_t #(VSig.vale_sig_stdcall adx_pre adx_post) adx_lemma'", "let code_adx = VC.va_code_Check_adx_bmi2_stdcall IA.win", "let lowstar_adx_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_adx\n dom\n []\n _\n _\n (W.mk_prediction code_adx dom [] (adx_lemma code_adx IA.win))", "let avx_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_avx_stdcall c va_s0 IA.win", "let avx_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_avx_stdcall c va_s0 IA.win va_s1 f", "let avx_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n avx_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n avx_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_avx_stdcall code va_s0 IA.win", "let avx_lemma = as_t #(VSig.vale_sig_stdcall avx_pre avx_post) avx_lemma'", "let code_avx = VC.va_code_Check_avx_stdcall IA.win", "let lowstar_avx_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_avx\n dom\n []\n _\n _\n (W.mk_prediction code_avx dom [] (avx_lemma code_avx IA.win))", "let avx2_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_avx2_stdcall c va_s0 IA.win", "let avx2_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_avx2_stdcall c va_s0 IA.win va_s1 f", "let avx2_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n avx2_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n avx2_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_avx2_stdcall code va_s0 IA.win", "let avx2_lemma = as_t #(VSig.vale_sig_stdcall avx2_pre avx2_post) avx2_lemma'", "let code_avx2 = VC.va_code_Check_avx2_stdcall IA.win", "let lowstar_avx2_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_avx2\n dom\n []\n _\n _\n (W.mk_prediction code_avx2 dom [] (avx2_lemma code_avx2 IA.win))", "let movbe_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_movbe_stdcall c va_s0 IA.win", "let movbe_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_movbe_stdcall c va_s0 IA.win va_s1 f", "let movbe_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n movbe_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n movbe_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_movbe_stdcall code va_s0 IA.win", "let movbe_lemma = as_t #(VSig.vale_sig_stdcall movbe_pre movbe_post) movbe_lemma'", "let code_movbe = VC.va_code_Check_movbe_stdcall IA.win", "let lowstar_movbe_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_movbe\n dom\n []\n _\n _\n (W.mk_prediction code_movbe dom [] (movbe_lemma code_movbe IA.win))", "let sse_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_sse_stdcall c va_s0 IA.win", "let sse_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_sse_stdcall c va_s0 IA.win va_s1 f", "let sse_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n sse_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n sse_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_sse_stdcall code va_s0 IA.win", "let sse_lemma = as_t #(VSig.vale_sig_stdcall sse_pre sse_post) sse_lemma'", "let code_sse = VC.va_code_Check_sse_stdcall IA.win", "let lowstar_sse_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sse\n dom\n []\n _\n _\n (W.mk_prediction code_sse dom [] (sse_lemma code_sse IA.win))" ], "closest": [ "val sha_pre:VSig.vale_pre dom\nlet sha_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (ctx_b:b128)\n (in_b:b8_128)\n (num_val:uint64)\n (k_b:ib128)\n (va_s0:V.va_state) ->\n SH.va_req_Sha_update_bytes_stdcall c va_s0 IA.win\n (as_vale_buffer ctx_b) (as_vale_buffer in_b) (UInt64.v num_val) (as_vale_immbuffer k_b)", "val key128_pre:VSig.vale_pre dom\nlet key128_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (input_b:b128)\n (output_b:b128)\n (va_s0:V.va_state) ->\n AE.va_req_KeyExpansionStdcall c va_s0 IA.win AES_128\n (as_vale_buffer input_b) (as_vale_buffer output_b)", "val key256_pre:VSig.vale_pre dom\nlet key256_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (input_b:b128)\n (output_b:b128)\n (va_s0:V.va_state) ->\n AE.va_req_KeyExpansionStdcall c va_s0 IA.win AES_256\n (as_vale_buffer input_b) (as_vale_buffer output_b)", "val poly_pre:VSig.vale_pre dom\nlet poly_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (ctx_b:b64)\n (inp_b:b64)\n (len:uint64)\n (finish:uint64)\n (va_s0:V.va_state) ->\n PO.va_req_Poly1305 c va_s0 IA.win\n (as_vale_buffer ctx_b) (as_vale_buffer inp_b) (UInt64.v len) (UInt64.v finish)", "val add1_pre:VSig.vale_pre dom\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1_stdcall c va_s0 IA.win\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)", "val add1_pre:VSig.vale_pre dom\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)", "val vm_pre:VSig.vale_pre vm_dom\nlet vm_pre : VSig.vale_pre vm_dom =\n fun (c:V.va_code)\n (dst:b64)\n (src:ib64)\n (va_s0:V.va_state) ->\n VM.va_req_Memcpy c va_s0 IA.win (as_vale_buffer dst) (as_vale_immbuffer src)", "val fsub_pre:VSig.vale_pre dom\nlet fsub_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub_stdcall c va_s0 IA.win\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)", "val fmul_pre:VSig.vale_pre fmul_dom\nlet fmul_pre : VSig.vale_pre fmul_dom =\n fun (c:V.va_code)\n (tmp:b64)\n (f1:b64)\n (out:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FW.va_req_Fmul_stdcall c va_s0 IA.win\n (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) (as_vale_buffer f2)", "val fmul_pre:VSig.vale_pre fmul_dom\nlet fmul_pre : VSig.vale_pre fmul_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (tmp:b64)\n (va_s0:V.va_state) ->\n FW.va_req_Fmul c va_s0\n (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) (as_vale_buffer f2)", "val fadd_pre:VSig.vale_pre fadd_dom\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd_stdcall c va_s0 IA.win\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)", "val fadd_pre:VSig.vale_pre fadd_dom\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)", "val fsqr_pre:VSig.vale_pre fsqr_dom\nlet fsqr_pre : VSig.vale_pre fsqr_dom =\n fun (c:V.va_code)\n (tmp:b64)\n (f1:b64)\n (out:b64)\n (va_s0:V.va_state) ->\n FW.va_req_Fsqr_stdcall c va_s0 IA.win\n (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out)", "val fsqr_pre:VSig.vale_pre fsqr_dom\nlet fsqr_pre : VSig.vale_pre fsqr_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (tmp:b64)\n (va_s0:V.va_state) ->\n FW.va_req_Fsqr c va_s0\n (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out)", "val fmul2_pre:VSig.vale_pre fmul_dom\nlet fmul2_pre : VSig.vale_pre fmul_dom =\n fun (c:V.va_code)\n (tmp:b64)\n (f1:b64)\n (out:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FW.va_req_Fmul2_stdcall c va_s0 IA.win\n (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) (as_vale_buffer f2)", "val fmul2_pre:VSig.vale_pre fmul_dom\nlet fmul2_pre : VSig.vale_pre fmul_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (tmp:b64)\n (va_s0:V.va_state) ->\n FW.va_req_Fmul2 c va_s0\n (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) (as_vale_buffer f2)", "val fsqr2_pre:VSig.vale_pre fsqr_dom\nlet fsqr2_pre : VSig.vale_pre fsqr_dom =\n fun (c:V.va_code)\n (tmp:b64)\n (f1:b64)\n (out:b64)\n (va_s0:V.va_state) ->\n FW.va_req_Fsqr2_stdcall c va_s0 IA.win\n (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out)", "val fsqr2_pre:VSig.vale_pre fsqr_dom\nlet fsqr2_pre : VSig.vale_pre fsqr_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (tmp:b64)\n (va_s0:V.va_state) ->\n FW.va_req_Fsqr2 c va_s0\n (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out)", "val fmul1_pre:VSig.vale_pre fmul1_dom\nlet fmul1_pre : VSig.vale_pre fmul1_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FH.va_req_Fmul1_stdcall c va_s0 IA.win\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)", "val fmul1_pre:VSig.vale_pre fmul1_dom\nlet fmul1_pre : VSig.vale_pre fmul1_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FH.va_req_Fmul1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)", "val aesni_pre:VSig.vale_pre aesni_dom\nlet aesni_pre : VSig.vale_pre aesni_dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_aesni_stdcall c va_s0 IA.win", "val key128_post:VSig.vale_post dom\nlet key128_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (input_b:b128)\n (output_b:b128)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n AE.va_ens_KeyExpansionStdcall c va_s0 IA.win AES_128 (as_vale_buffer input_b) (as_vale_buffer output_b) va_s1 f", "val key256_post:VSig.vale_post dom\nlet key256_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (input_b:b128)\n (output_b:b128)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n AE.va_ens_KeyExpansionStdcall c va_s0 IA.win AES_256 (as_vale_buffer input_b) (as_vale_buffer output_b) va_s1 f", "val fsub_pre:VSig.vale_pre fsub_dom\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)", "val ta_pre:VSig.vale_pre ta_dom\nlet ta_pre : VSig.vale_pre ta_dom =\n fun (c:V.va_code)\n (arg0:ib64)\n (arg1:ib64)\n (arg2:ib64)\n (arg3:ib64)\n (arg4:ib64)\n (arg5:ib64)\n (arg6:ib64)\n (arg7:ib64)\n (va_s0:V.va_state) ->\n TA.va_req_Test c va_s0 IA.win\n (as_vale_immbuffer arg0)\n (as_vale_immbuffer arg1)\n (as_vale_immbuffer arg2)\n (as_vale_immbuffer arg3)\n (as_vale_immbuffer arg4)\n (as_vale_immbuffer arg5)\n (as_vale_immbuffer arg6)\n (as_vale_immbuffer arg7)", "val add1_post:VSig.vale_post dom\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f", "val add1_post:VSig.vale_post dom\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1_stdcall c va_s0 IA.win (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f", "val cswap_pre:VSig.vale_pre cswap_dom\nlet cswap_pre : VSig.vale_pre cswap_dom =\n fun (c:V.va_code)\n (bit:uint64)\n (p0:b64)\n (p1:b64)\n (va_s0:V.va_state) ->\n FU.va_req_Cswap2 c va_s0\n (UInt64.v bit) (as_vale_buffer p0) (as_vale_buffer p1)", "val cswap_pre:VSig.vale_pre cswap_dom\nlet cswap_pre : VSig.vale_pre cswap_dom =\n fun (c:V.va_code)\n (bit:uint64)\n (p0:b64)\n (p1:b64)\n (va_s0:V.va_state) ->\n FU.va_req_Cswap2_stdcall c va_s0 IA.win\n (UInt64.v bit) (as_vale_buffer p0) (as_vale_buffer p1)", "val poly_post:VSig.vale_post dom\nlet poly_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (ctx_b:b64)\n (inp_b:b64)\n (len:uint64)\n (finish:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n PO.va_ens_Poly1305 c va_s0 IA.win\n (as_vale_buffer ctx_b) (as_vale_buffer inp_b) (UInt64.v len) (UInt64.v finish)\n va_s1 f", "val sha_post:VSig.vale_post dom\nlet sha_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (ctx_b:b128)\n (in_b:b8_128)\n (num_val:uint64)\n (k_b:ib128)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n SH.va_ens_Sha_update_bytes_stdcall c va_s0 IA.win\n (as_vale_buffer ctx_b) (as_vale_buffer in_b) (UInt64.v num_val) (as_vale_immbuffer k_b)\n va_s1 f", "val vm_post:VSig.vale_post vm_dom\nlet vm_post : VSig.vale_post vm_dom =\n fun (c:V.va_code)\n (dst:b64)\n (src:ib64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VM.va_ens_Memcpy c va_s0 IA.win (as_vale_buffer dst) (as_vale_immbuffer src) va_s1 f", "val fsub_post:VSig.vale_post dom\nlet fsub_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub_stdcall c va_s0 IA.win (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f", "val gctr256_pre: (Ghost.erased (Seq.seq nat32)) -> VSig.vale_pre dom\nlet gctr256_pre : (Ghost.erased (Seq.seq nat32)) -> VSig.vale_pre dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (c:V.va_code)\n (in_b:b128)\n (num_bytes:uint64)\n (out_b:b128)\n (inout_b:b128)\n (keys_b:b128)\n (ctr_b:b128)\n (num_blocks:uint64)\n (va_s0:V.va_state) ->\n GC.va_req_Gctr_bytes_stdcall c va_s0 IA.win AES_256\n (as_vale_buffer in_b) (UInt64.v num_bytes)\n (as_vale_buffer out_b) (as_vale_buffer inout_b) (as_vale_buffer keys_b)\n (as_vale_buffer ctr_b) (UInt64.v num_blocks) (Ghost.reveal s)", "val fmul2_post:VSig.vale_post fmul_dom\nlet fmul2_post : VSig.vale_post fmul_dom =\n fun (c:V.va_code)\n (tmp:b64)\n (f1:b64)\n (out:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FW.va_ens_Fmul2_stdcall c va_s0 IA.win (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) (as_vale_buffer f2) va_s1 f", "val fmul2_post:VSig.vale_post fmul_dom\nlet fmul2_post : VSig.vale_post fmul_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (tmp:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FW.va_ens_Fmul2 c va_s0 (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) (as_vale_buffer f2) va_s1 f", "val key256_pre: (Ghost.erased (Seq.seq nat32)) -> VSig.vale_pre dom\nlet key256_pre : (Ghost.erased (Seq.seq nat32)) -> VSig.vale_pre dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (c:V.va_code)\n (input_b:b128)\n (output_b:b128)\n (va_s0:V.va_state) ->\n GF.va_req_Keyhash_init c va_s0 IA.win AES_256 (Ghost.reveal s)\n (as_vale_buffer input_b) (as_vale_buffer output_b)", "val fmul_post:VSig.vale_post fmul_dom\nlet fmul_post : VSig.vale_post fmul_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (tmp:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FW.va_ens_Fmul c va_s0 (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) (as_vale_buffer f2) va_s1 f", "val fmul_post:VSig.vale_post fmul_dom\nlet fmul_post : VSig.vale_post fmul_dom =\n fun (c:V.va_code)\n (tmp:b64)\n (f1:b64)\n (out:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FW.va_ens_Fmul_stdcall c va_s0 IA.win (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) (as_vale_buffer f2) va_s1 f", "val key128_pre: (Ghost.erased (Seq.seq nat32)) -> VSig.vale_pre dom\nlet key128_pre : (Ghost.erased (Seq.seq nat32)) -> VSig.vale_pre dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (c:V.va_code)\n (input_b:b128)\n (output_b:b128)\n (va_s0:V.va_state) ->\n GF.va_req_Keyhash_init c va_s0 IA.win AES_128 (Ghost.reveal s)\n (as_vale_buffer input_b) (as_vale_buffer output_b)", "val fmul1_post:VSig.vale_post fmul1_dom\nlet fmul1_post : VSig.vale_post fmul1_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fmul1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f", "val fmul1_post:VSig.vale_post fmul1_dom\nlet fmul1_post : VSig.vale_post fmul1_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fmul1_stdcall c va_s0 IA.win (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f", "val fsqr2_post:VSig.vale_post fsqr_dom\nlet fsqr2_post : VSig.vale_post fsqr_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (tmp:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FW.va_ens_Fsqr2 c va_s0 (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) va_s1 f", "val fsqr2_post:VSig.vale_post fsqr_dom\nlet fsqr2_post : VSig.vale_post fsqr_dom =\n fun (c:V.va_code)\n (tmp:b64)\n (f1:b64)\n (out:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FW.va_ens_Fsqr2_stdcall c va_s0 IA.win (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) va_s1 f", "val aesni_post:VSig.vale_post aesni_dom\nlet aesni_post : VSig.vale_post aesni_dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_aesni_stdcall c va_s0 IA.win va_s1 f", "val gctr128_pre: (Ghost.erased (Seq.seq nat32)) -> VSig.vale_pre dom\nlet gctr128_pre : (Ghost.erased (Seq.seq nat32)) -> VSig.vale_pre dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (c:V.va_code)\n (in_b:b128)\n (num_bytes:uint64)\n (out_b:b128)\n (inout_b:b128)\n (keys_b:b128)\n (ctr_b:b128)\n (num_blocks:uint64)\n (va_s0:V.va_state) ->\n GC.va_req_Gctr_bytes_stdcall c va_s0 IA.win AES_128\n (as_vale_buffer in_b) (UInt64.v num_bytes)\n (as_vale_buffer out_b) (as_vale_buffer inout_b) (as_vale_buffer keys_b)\n (as_vale_buffer ctr_b) (UInt64.v num_blocks) (Ghost.reveal s)", "val Vale.AsLowStar.ValeSig.vale_sig_stdcall = pre: Vale.AsLowStar.ValeSig.vale_pre dom -> post: Vale.AsLowStar.ValeSig.vale_post dom -> Type\nlet vale_sig_stdcall #dom = vale_sig #dom IX64.regs_modified_stdcall IX64.xmms_modified_stdcall", "val compute_iv_pre: (Ghost.erased supported_iv_LE) -> VSig.vale_pre dom\nlet compute_iv_pre : (Ghost.erased supported_iv_LE) -> VSig.vale_pre dom =\n fun (iv:Ghost.erased supported_iv_LE)\n (c:V.va_code)\n (iv_b:b128)\n (num_bytes:uint64)\n (len:uint64)\n (j0_b:b128)\n (iv_extra_b:b128)\n (hkeys_b:b128)\n (va_s0:V.va_state) ->\n GC.va_req_Compute_iv_stdcall c va_s0 IA.win (Ghost.reveal iv)\n (as_vale_buffer iv_b) (UInt64.v num_bytes)\n (UInt64.v len) (as_vale_buffer j0_b)\n (as_vale_buffer iv_extra_b) (as_vale_buffer hkeys_b)", "val fsqr_post:VSig.vale_post fsqr_dom\nlet fsqr_post : VSig.vale_post fsqr_dom =\n fun (c:V.va_code)\n (tmp:b64)\n (f1:b64)\n (out:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FW.va_ens_Fsqr_stdcall c va_s0 IA.win (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) va_s1 f", "val fsqr_post:VSig.vale_post fsqr_dom\nlet fsqr_post : VSig.vale_post fsqr_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (tmp:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FW.va_ens_Fsqr c va_s0 (as_vale_buffer tmp) (as_vale_buffer f1) (as_vale_buffer out) va_s1 f", "val Vale.AsLowStar.ValeSig.vale_pre = dom: Prims.list Vale.Interop.Base.td -> Type\nlet vale_pre (dom:list td) =\n code:V.va_code ->\n vale_pre_tl dom", "val pre_rel_generic\n (#max_arity: nat)\n (#arg_reg: IX64.arg_reg_relation max_arity)\n (code: V.va_code)\n (dom: list td)\n (args: list arg {List.length dom + List.length args <= 20})\n (pre: VSig.vale_pre_tl dom)\n : IX64.rel_gen_t code dom args (IX64.prediction_pre_rel_t (coerce code))\nlet rec pre_rel_generic\n (#max_arity:nat)\n (#arg_reg:IX64.arg_reg_relation max_arity)\n (code:V.va_code)\n (dom:list td)\n (args:list arg{List.length dom + List.length args <= 20})\n (pre:VSig.vale_pre_tl dom)\n : IX64.rel_gen_t code dom args (IX64.prediction_pre_rel_t (coerce code))\n =\n match dom with\n | [] ->\n prediction_pre_rel #max_arity #arg_reg pre (coerce code) args\n | hd::tl ->\n fun (x:td_as_type hd) ->\n pre_rel_generic #max_arity #arg_reg code tl IX64.(x ++ args) (elim_1 pre x)", "val cswap_post:VSig.vale_post cswap_dom\nlet cswap_post : VSig.vale_post cswap_dom =\n fun (c:V.va_code)\n (bit:uint64)\n (p0:b64)\n (p1:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Cswap2 c va_s0 (UInt64.v bit) (as_vale_buffer p0) (as_vale_buffer p1) va_s1 f", "val cswap_post:VSig.vale_post cswap_dom\nlet cswap_post : VSig.vale_post cswap_dom =\n fun (c:V.va_code)\n (bit:uint64)\n (p0:b64)\n (p1:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Cswap2_stdcall c va_s0 IA.win (UInt64.v bit) (as_vale_buffer p0) (as_vale_buffer p1) va_s1 f", "val Vale.AsLowStar.ValeSig.vale_pre_tl = dom: Prims.list Vale.Interop.Base.td -> Type\nlet vale_pre_tl (dom:list td) =\n n_arrow dom (V.va_state -> prop)", "val fsub_post:VSig.vale_post fsub_dom\nlet fsub_post : VSig.vale_post fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f", "val fadd_post:VSig.vale_post fadd_dom\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f", "val fadd_post:VSig.vale_post fadd_dom\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd_stdcall c va_s0 IA.win (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f", "val compute_iv_post: (Ghost.erased supported_iv_LE) -> VSig.vale_post dom\nlet compute_iv_post : (Ghost.erased supported_iv_LE) -> VSig.vale_post dom =\n fun (iv:Ghost.erased supported_iv_LE)\n (c:V.va_code)\n (iv_b:b128)\n (num_bytes:uint64)\n (len:uint64)\n (j0_b:b128)\n (iv_extra_b:b128)\n (hkeys_b:b128)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n GC.va_ens_Compute_iv_stdcall c va_s0 IA.win (Ghost.reveal iv)\n (as_vale_buffer iv_b) (UInt64.v num_bytes)\n (UInt64.v len) (as_vale_buffer j0_b)\n (as_vale_buffer iv_extra_b) (as_vale_buffer hkeys_b)\n va_s1 f", "val elim_vale_sig_cons\n (#code: _)\n (#regs_modified: (MS.reg_64 -> bool))\n (#xmms_modified: (MS.reg_xmm -> bool))\n (hd: td)\n (tl: list td)\n (args: list arg)\n (pre: vale_pre_tl (hd :: tl))\n (post: vale_post_tl (hd :: tl))\n (v: vale_sig_tl regs_modified xmms_modified args code pre post)\n (x: td_as_type hd)\n : vale_sig_tl regs_modified\n xmms_modified\n ((| hd, x |) :: args)\n code\n (elim_1 pre x)\n (elim_1 post x)\nlet elim_vale_sig_cons #code\n (#regs_modified:MS.reg_64 -> bool)\n (#xmms_modified:MS.reg_xmm -> bool)\n (hd:td)\n (tl:list td)\n (args:list arg)\n (pre:vale_pre_tl (hd::tl))\n (post:vale_post_tl (hd::tl))\n (v:vale_sig_tl regs_modified xmms_modified args code pre post)\n : x:td_as_type hd\n -> vale_sig_tl regs_modified xmms_modified ((|hd, x|)::args) code (elim_1 pre x) (elim_1 post x)\n = v", "val load_precompute_r1:\n p:precomp_r 1\n -> r0:uint64\n -> r1:uint64\n -> Stack unit\n (requires fun h -> live h p)\n (ensures fun h0 _ h1 ->\n modifies (loc p) h0 h1 /\\\n load_precompute_r_post h1 p /\\\n (assert_norm (pow2 64 * pow2 64 = pow2 128);\n feval h1 (gsub p 0ul 5ul) ==\n LSeq.create 1 (uint_v r1 * pow2 64 + uint_v r0)))\nlet load_precompute_r1 p r0 r1 =\n let r = sub p 0ul 5ul in\n let r5 = sub p 5ul 5ul in\n let rn = sub p 10ul 5ul in\n let rn_5 = sub p 15ul 5ul in\n\n let r_vec0 = vec_load r0 1 in\n let r_vec1 = vec_load r1 1 in\n\n let h0 = ST.get () in\n load_felem r r_vec0 r_vec1;\n let h1 = ST.get () in\n LSeq.eq_intro\n (LSeq.createi #Vec.pfelem 1 (fun i -> (uint64xN_v r_vec1).[i] * pow2 64 + (uint64xN_v r_vec0).[i]))\n (LSeq.create 1 (uint_v r1 * pow2 64 + uint_v r0));\n assert (feval h1 r == LSeq.create 1 (uint_v r1 * pow2 64 + uint_v r0));\n precompute_shift_reduce r5 r;\n\n copy_felem #_ #(1,1,1,1,1) rn r;\n copy_felem #_ #(5,5,5,5,5) rn_5 r5", "val elim_vale_sig_nil\n (#code: _)\n (#regs_modified: (MS.reg_64 -> bool))\n (#xmms_modified: (MS.reg_xmm -> bool))\n (#args: list arg)\n (#pre: vale_pre_tl [])\n (#post: vale_post_tl [])\n (v: vale_sig_tl regs_modified xmms_modified #[] args code pre post)\n : vale_sig_nil regs_modified xmms_modified args code pre post\nlet elim_vale_sig_nil #code\n (#regs_modified:MS.reg_64 -> bool)\n (#xmms_modified:MS.reg_xmm -> bool)\n (#args:list arg)\n (#pre:vale_pre_tl [])\n (#post:vale_post_tl [])\n (v:vale_sig_tl regs_modified xmms_modified #[] args code pre post)\n : vale_sig_nil regs_modified xmms_modified args code pre post\n = v", "val gcm256_pre: (Ghost.erased (Seq.seq nat32)) -> (Ghost.erased supported_iv_LE)\n -> VSig.vale_pre dom\nlet gcm256_pre : (Ghost.erased (Seq.seq nat32)) -> (Ghost.erased supported_iv_LE) -> VSig.vale_pre dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (iv:Ghost.erased supported_iv_LE)\n (c:V.va_code)\n (auth_b:b128)\n (auth_bytes:uint64)\n (auth_num:uint64)\n (keys_b:b128)\n (iv_b:b128)\n (hkeys_b:b128)\n (abytes_b:b128)\n (in128x6_b:b128)\n (out128x6_b:b128)\n (len128x6_num:uint64)\n (in128_b:b128)\n (out128_b:b128)\n (len128_num:uint64)\n (inout_b:b128)\n (cipher_num:uint64)\n (scratch_b:b128)\n (tag_b:b128)\n (va_s0:V.va_state) ->\n GC.va_req_Gcm_blocks_decrypt_stdcall c va_s0 IA.win AES_256\n (as_vale_buffer auth_b) (UInt64.v auth_bytes)\n (UInt64.v auth_num) (as_vale_buffer keys_b)\n (as_vale_buffer iv_b) (Ghost.reveal iv) (as_vale_buffer hkeys_b)\n (as_vale_buffer abytes_b) (as_vale_buffer in128x6_b)\n (as_vale_buffer out128x6_b) (UInt64.v len128x6_num)\n (as_vale_buffer in128_b) (as_vale_buffer out128_b)\n (UInt64.v len128_num) (as_vale_buffer inout_b)\n (UInt64.v cipher_num)\n (as_vale_buffer scratch_b) (as_vale_buffer tag_b) (Ghost.reveal s)", "val gcm256_pre: (Ghost.erased (Seq.seq nat32)) -> (Ghost.erased supported_iv_LE)\n -> VSig.vale_pre dom\nlet gcm256_pre : (Ghost.erased (Seq.seq nat32)) -> (Ghost.erased supported_iv_LE) -> VSig.vale_pre dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (iv:Ghost.erased supported_iv_LE)\n (c:V.va_code)\n (auth_b:b128)\n (auth_bytes:uint64)\n (auth_num:uint64)\n (keys_b:b128)\n (iv_b:b128)\n (hkeys_b:b128)\n (abytes_b:b128)\n (in128x6_b:b128)\n (out128x6_b:b128)\n (len128x6_num:uint64)\n (in128_b:b128)\n (out128_b:b128)\n (len128_num:uint64)\n (inout_b:b128)\n (plain_num:uint64)\n (scratch_b:b128)\n (tag_b:b128)\n (va_s0:V.va_state) ->\n GC.va_req_Gcm_blocks_stdcall c va_s0 IA.win AES_256\n (as_vale_buffer auth_b) (UInt64.v auth_bytes)\n (UInt64.v auth_num) (as_vale_buffer keys_b)\n (as_vale_buffer iv_b) (Ghost.reveal iv) (as_vale_buffer hkeys_b)\n (as_vale_buffer abytes_b) (as_vale_buffer in128x6_b)\n (as_vale_buffer out128x6_b) (UInt64.v len128x6_num)\n (as_vale_buffer in128_b) (as_vale_buffer out128_b)\n (UInt64.v len128_num) (as_vale_buffer inout_b)\n (UInt64.v plain_num)\n (as_vale_buffer scratch_b) (as_vale_buffer tag_b) (Ghost.reveal s)", "val gcm128_pre: (Ghost.erased (Seq.seq nat32)) -> (Ghost.erased supported_iv_LE)\n -> VSig.vale_pre dom\nlet gcm128_pre : (Ghost.erased (Seq.seq nat32)) -> (Ghost.erased supported_iv_LE) -> VSig.vale_pre dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (iv:Ghost.erased supported_iv_LE)\n (c:V.va_code)\n (auth_b:b128)\n (auth_bytes:uint64)\n (auth_num:uint64)\n (keys_b:b128)\n (iv_b:b128)\n (hkeys_b:b128)\n (abytes_b:b128)\n (in128x6_b:b128)\n (out128x6_b:b128)\n (len128x6_num:uint64)\n (in128_b:b128)\n (out128_b:b128)\n (len128_num:uint64)\n (inout_b:b128)\n (plain_num:uint64)\n (scratch_b:b128)\n (tag_b:b128)\n (va_s0:V.va_state) ->\n GC.va_req_Gcm_blocks_stdcall c va_s0 IA.win AES_128\n (as_vale_buffer auth_b) (UInt64.v auth_bytes)\n (UInt64.v auth_num) (as_vale_buffer keys_b)\n (as_vale_buffer iv_b) (Ghost.reveal iv) (as_vale_buffer hkeys_b)\n (as_vale_buffer abytes_b) (as_vale_buffer in128x6_b)\n (as_vale_buffer out128x6_b) (UInt64.v len128x6_num)\n (as_vale_buffer in128_b) (as_vale_buffer out128_b)\n (UInt64.v len128_num) (as_vale_buffer inout_b)\n (UInt64.v plain_num)\n (as_vale_buffer scratch_b) (as_vale_buffer tag_b) (Ghost.reveal s)", "val gcm128_pre: (Ghost.erased (Seq.seq nat32)) -> (Ghost.erased supported_iv_LE)\n -> VSig.vale_pre dom\nlet gcm128_pre : (Ghost.erased (Seq.seq nat32)) -> (Ghost.erased supported_iv_LE) -> VSig.vale_pre dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (iv:Ghost.erased supported_iv_LE)\n (c:V.va_code)\n (auth_b:b128)\n (auth_bytes:uint64)\n (auth_num:uint64)\n (keys_b:b128)\n (iv_b:b128)\n (hkeys_b:b128)\n (abytes_b:b128)\n (in128x6_b:b128)\n (out128x6_b:b128)\n (len128x6_num:uint64)\n (in128_b:b128)\n (out128_b:b128)\n (len128_num:uint64)\n (inout_b:b128)\n (cipher_num:uint64)\n (scratch_b:b128)\n (tag_b:b128)\n (va_s0:V.va_state) ->\n GC.va_req_Gcm_blocks_decrypt_stdcall c va_s0 IA.win AES_128\n (as_vale_buffer auth_b) (UInt64.v auth_bytes)\n (UInt64.v auth_num) (as_vale_buffer keys_b)\n (as_vale_buffer iv_b) (Ghost.reveal iv) (as_vale_buffer hkeys_b)\n (as_vale_buffer abytes_b) (as_vale_buffer in128x6_b)\n (as_vale_buffer out128x6_b) (UInt64.v len128x6_num)\n (as_vale_buffer in128_b) (as_vale_buffer out128_b)\n (UInt64.v len128_num) (as_vale_buffer inout_b)\n (UInt64.v cipher_num)\n (as_vale_buffer scratch_b) (as_vale_buffer tag_b) (Ghost.reveal s)", "val fmul1_dom:IX64.arity_ok 3 td\nlet fmul1_dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y", "val dom:IX64.arity_ok 3 td\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y", "val ta_post:VSig.vale_post ta_dom\nlet ta_post : VSig.vale_post ta_dom =\n fun (c:V.va_code)\n (arg0:ib64)\n (arg1:ib64)\n (arg2:ib64)\n (arg3:ib64)\n (arg4:ib64)\n (arg5:ib64)\n (arg6:ib64)\n (arg7:ib64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n TA.va_ens_Test c va_s0 IA.win\n (as_vale_immbuffer arg0)\n (as_vale_immbuffer arg1)\n (as_vale_immbuffer arg2)\n (as_vale_immbuffer arg3)\n (as_vale_immbuffer arg4)\n (as_vale_immbuffer arg5)\n (as_vale_immbuffer arg6)\n (as_vale_immbuffer arg7)\n va_s1 f", "val Interop.vale_sig = n: Interop.arity -> pre: Interop.vale_pre n -> post: Interop.vale_post n -> Type\nlet vale_sig\n (n:arity)\n (pre:vale_pre n)\n (post:vale_post n)\n = s0:state\n -> Ghost state\n (requires (as_vale_pre pre s0))\n (ensures (fun s1 -> as_vale_post post s0 s1))", "val fmul_dom:IX64.arity_ok 4 td\nlet fmul_dom: IX64.arity_ok 4 td =\n let y = [t64_mod; t64_no_mod; t64_no_mod; t64_mod] in\n assert_norm (List.length y = 4);\n y", "val key256_post: (Ghost.erased (Seq.seq nat32)) -> VSig.vale_post dom\nlet key256_post : (Ghost.erased (Seq.seq nat32)) -> VSig.vale_post dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (c:V.va_code)\n (input_b:b128)\n (output_b:b128)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n GF.va_ens_Keyhash_init c va_s0 IA.win AES_256 (Ghost.reveal s)\n (as_vale_buffer input_b) (as_vale_buffer output_b) va_s1 f", "val key128_post: (Ghost.erased (Seq.seq nat32)) -> VSig.vale_post dom\nlet key128_post : (Ghost.erased (Seq.seq nat32)) -> VSig.vale_post dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (c:V.va_code)\n (input_b:b128)\n (output_b:b128)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n GF.va_ens_Keyhash_init c va_s0 IA.win AES_128 (Ghost.reveal s)\n (as_vale_buffer input_b) (as_vale_buffer output_b) va_s1 f", "val load_precompute_r:\n #w:lanes\n -> p:precomp_r w\n -> r0:uint64\n -> r1:uint64\n -> Stack unit\n (requires fun h -> live h p)\n (ensures fun h0 _ h1 ->\n modifies (loc p) h0 h1 /\\\n load_precompute_r_post #w h1 p /\\\n (assert_norm (pow2 64 * pow2 64 = pow2 128);\n feval h1 (gsub p 0ul 5ul) ==\n LSeq.create w (uint_v r1 * pow2 64 + uint_v r0)))\nlet load_precompute_r #w p r0 r1 =\n match w with\n | 1 -> load_precompute_r1 p r0 r1\n | 2 -> load_precompute_r2 p r0 r1\n | 4 -> load_precompute_r4 p r0 r1", "val gctr256_post: (Ghost.erased (Seq.seq nat32)) -> VSig.vale_post dom\nlet gctr256_post : (Ghost.erased (Seq.seq nat32)) -> VSig.vale_post dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (c:V.va_code)\n (in_b:b128)\n (num_bytes:uint64)\n (out_b:b128)\n (inout_b:b128)\n (keys_b:b128)\n (ctr_b:b128)\n (num_blocks:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n GC.va_ens_Gctr_bytes_stdcall c va_s0 IA.win AES_256\n (as_vale_buffer in_b) (UInt64.v num_bytes)\n (as_vale_buffer out_b) (as_vale_buffer inout_b) (as_vale_buffer keys_b)\n (as_vale_buffer ctr_b) (UInt64.v num_blocks) (Ghost.reveal s) va_s1 f", "val prediction_pre_rel\n (#max_arity: nat)\n (#arg_reg: IX64.arg_reg_relation max_arity)\n (pre: VSig.vale_pre_tl [])\n (code: V.va_code)\n (args: IX64.arg_list)\n : IX64.prediction_pre_rel_t code args\nlet prediction_pre_rel\n (#max_arity:nat)\n (#arg_reg:IX64.arg_reg_relation max_arity)\n (pre:VSig.vale_pre_tl [])\n (code:V.va_code)\n (args:IX64.arg_list)\n : IX64.prediction_pre_rel_t code args\n =\n fun (h0:mem_roots args) ->\n LSig.(to_low_pre #max_arity #arg_reg pre args h0)", "val load_precompute_r4:\n p:precomp_r 4\n -> r0:uint64\n -> r1:uint64\n -> Stack unit\n (requires fun h -> live h p)\n (ensures fun h0 _ h1 ->\n modifies (loc p) h0 h1 /\\\n load_precompute_r_post h1 p /\\\n (assert_norm (pow2 64 * pow2 64 = pow2 128);\n feval h1 (gsub p 0ul 5ul) ==\n LSeq.create 4 (uint_v r1 * pow2 64 + uint_v r0)))\nlet load_precompute_r4 p r0 r1 =\n let r = sub p 0ul 5ul in\n let r5 = sub p 5ul 5ul in\n let rn = sub p 10ul 5ul in\n let rn_5 = sub p 15ul 5ul in\n\n let r_vec0 = vec_load r0 4 in\n let r_vec1 = vec_load r1 4 in\n\n let h0 = ST.get () in\n load_felem r r_vec0 r_vec1;\n let h1 = ST.get () in\n LSeq.eq_intro\n (LSeq.createi #Vec.pfelem 4 (fun i -> (uint64xN_v r_vec1).[i] * pow2 64 + (uint64xN_v r_vec0).[i]))\n (LSeq.create 4 (uint_v r1 * pow2 64 + uint_v r0));\n assert (feval h1 r == LSeq.create 4 (uint_v r1 * pow2 64 + uint_v r0));\n\n precompute_shift_reduce r5 r;\n fmul_r rn r r r5;\n precompute_shift_reduce rn_5 rn;\n fmul_r rn rn rn rn_5;\n let h3 = ST.get () in\n LSeq.eq_intro (feval h3 rn) (Vec.compute_rw (feval h1 r).[0]);\n precompute_shift_reduce rn_5 rn", "val load_precompute_r2:\n p:precomp_r 2\n -> r0:uint64\n -> r1:uint64\n -> Stack unit\n (requires fun h -> live h p)\n (ensures fun h0 _ h1 ->\n modifies (loc p) h0 h1 /\\\n load_precompute_r_post h1 p /\\\n (assert_norm (pow2 64 * pow2 64 = pow2 128);\n feval h1 (gsub p 0ul 5ul) ==\n LSeq.create 2 (uint_v r1 * pow2 64 + uint_v r0)))\nlet load_precompute_r2 p r0 r1 =\n let r = sub p 0ul 5ul in\n let r5 = sub p 5ul 5ul in\n let rn = sub p 10ul 5ul in\n let rn_5 = sub p 15ul 5ul in\n\n let r_vec0 = vec_load r0 2 in\n let r_vec1 = vec_load r1 2 in\n\n let h0 = ST.get () in\n load_felem r r_vec0 r_vec1;\n let h1 = ST.get () in\n LSeq.eq_intro\n (LSeq.createi #Vec.pfelem 2 (fun i -> (uint64xN_v r_vec1).[i] * pow2 64 + (uint64xN_v r_vec0).[i]))\n (LSeq.create 2 (uint_v r1 * pow2 64 + uint_v r0));\n assert (feval h1 r == LSeq.create 2 (uint_v r1 * pow2 64 + uint_v r0));\n\n precompute_shift_reduce r5 r;\n let h2 = ST.get () in\n fmul_r rn r r r5;\n let h3 = ST.get () in\n LSeq.eq_intro (feval h3 rn) (Vec.compute_rw (feval h2 r).[0]);\n precompute_shift_reduce rn_5 rn", "val post_rel_generic\n (#max_arity: nat)\n (code: V.va_code)\n (dom: list td)\n (args: list arg {List.length dom + List.length args <= 20})\n (post: VSig.vale_post_tl dom)\n : IX64.rel_gen_t code dom args (IX64.prediction_post_rel_t (coerce code))\nlet rec post_rel_generic\n (#max_arity:nat)\n (code:V.va_code)\n (dom:list td)\n (args:list arg{List.length dom + List.length args <= 20})\n (post:VSig.vale_post_tl dom)\n : IX64.rel_gen_t code dom args (IX64.prediction_post_rel_t (coerce code))\n =\n match dom with\n | [] ->\n prediction_post_rel #max_arity post (coerce code) args\n | hd::tl ->\n fun (x:td_as_type hd) ->\n post_rel_generic #max_arity code tl IX64.(x ++ args) (elim_1 post x)", "val gctr128_post: (Ghost.erased (Seq.seq nat32)) -> VSig.vale_post dom\nlet gctr128_post : (Ghost.erased (Seq.seq nat32)) -> VSig.vale_post dom =\n fun (s:Ghost.erased (Seq.seq nat32))\n (c:V.va_code)\n (in_b:b128)\n (num_bytes:uint64)\n (out_b:b128)\n (inout_b:b128)\n (keys_b:b128)\n (ctr_b:b128)\n (num_blocks:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n GC.va_ens_Gctr_bytes_stdcall c va_s0 IA.win AES_128\n (as_vale_buffer in_b) (UInt64.v num_bytes)\n (as_vale_buffer out_b) (as_vale_buffer inout_b) (as_vale_buffer keys_b)\n (as_vale_buffer ctr_b) (UInt64.v num_blocks) (Ghost.reveal s) va_s1 f", "val as_vale_pre: #n: arity -> pre: vale_pre n -> state -> prop\nlet as_vale_pre\n (#n:arity)\n (pre:vale_pre n)\n : state -> prop =\n fun state ->\n elim_m 0 pre state.registers state.memory", "val Vale.Interop.X64.as_lowstar_sig_t_weak' = \n n: Prims.nat ->\n arg_reg: Vale.Interop.X64.arg_reg_relation n ->\n regs_modified: (_: Vale.X64.Machine_s.reg_64 -> Prims.bool) ->\n xmms_modified: (_: Vale.X64.Machine_s.reg_xmm -> Prims.bool) ->\n c: Vale.X64.Machine_Semantics_s.code ->\n dom: Prims.list Vale.Interop.Base.td ->\n args:\n Prims.list Vale.Interop.Base.arg\n {FStar.List.Tot.Base.length args + FStar.List.Tot.Base.length dom <= 20} ->\n pre_rel: Vale.Interop.X64.rel_gen_t c dom args (Vale.Interop.X64.prediction_pre_rel_t c) ->\n post_rel: Vale.Interop.X64.rel_gen_t c dom args (Vale.Interop.X64.prediction_post_rel_t c) ->\n predict:\n Vale.Interop.X64.prediction_t n\n arg_reg\n regs_modified\n xmms_modified\n c\n dom\n args\n pre_rel\n post_rel\n -> Type0\nlet rec as_lowstar_sig_t_weak'\n (n:nat)\n (arg_reg:arg_reg_relation n)\n (regs_modified:MS.reg_64 -> bool)\n (xmms_modified:MS.reg_xmm -> bool)\n (c:BS.code)\n (dom:list td)\n (args:list arg{List.length args + List.length dom <= 20})\n (pre_rel:rel_gen_t c dom args (prediction_pre_rel_t c))\n (post_rel:rel_gen_t c dom args (prediction_post_rel_t c))\n (predict:prediction_t n arg_reg regs_modified xmms_modified c dom args pre_rel post_rel) =\n match dom with\n | [] ->\n (unit ->\n FStar.HyperStack.ST.Stack als_ret\n (requires (fun h0 ->\n mem_roots_p h0 args /\\\n elim_rel_gen_t_nil pre_rel h0))\n (ensures fun h0 ret h1 ->\n as_lowstar_sig_post_weak n arg_reg regs_modified xmms_modified c args h0\n #pre_rel #post_rel (elim_predict_t_nil predict) ret h1))\n | hd::tl ->\n x:td_as_type hd ->\n as_lowstar_sig_t_weak'\n n\n arg_reg\n regs_modified\n xmms_modified\n c\n tl\n (x ++ args)\n (elim_rel_gen_t_cons hd tl pre_rel x)\n (elim_rel_gen_t_cons hd tl post_rel x)\n (elim_predict_t_cons hd tl predict x)", "val load_precompute_r:\n #s:field_spec\n -> p:precomp_r s\n -> r0:uint64\n -> r1:uint64 ->\n Stack unit\n (requires fun h -> live h p)\n (ensures fun h0 _ h1 ->\n modifies (loc p) h0 h1 /\\\n F32xN.load_precompute_r_post #(width s) h1 p /\\\n (assert (uint_v r1 * pow2 64 + uint_v r0 < pow2 128);\n feval h1 (gsub p 0ul 5ul) ==\n LSeq.create (width s) (uint_v r1 * pow2 64 + uint_v r0)))\nlet load_precompute_r #s p r0 r1 =\n match s with\n | M32 -> F32xN.load_precompute_r #1 p r0 r1\n | M128 -> F32xN.load_precompute_r #2 p r0 r1\n | M256 -> F32xN.load_precompute_r #4 p r0 r1", "val dom:IX64.arity_ok_stdcall td\nlet dom: IX64.arity_ok_stdcall td =\n let y = [t128_no_mod; t128_mod] in\n assert_norm (List.length y = 2);\n y", "val dom:IX64.arity_ok_stdcall td\nlet dom: IX64.arity_ok_stdcall td =\n let y = [t128_mod; t128_no_mod; tuint64; t128_imm] in\n assert_norm (List.length y = 4);\n y", "val dom:IX64.arity_ok_stdcall td\nlet dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y", "val dom:IX64.arity_ok_stdcall td\nlet dom: IX64.arity_ok_stdcall td =\n let y = [t128_no_mod; t128_mod] in\n assert_norm (List.length y = 2);\n y", "val dom:IX64.arity_ok_stdcall td\nlet dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y", "val dom:IX64.arity_ok_stdcall td\nlet dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; tuint64; tuint64] in\n assert_norm (List.length y = 4);\n y", "val to_low_pre\n (#max_arity: nat)\n (#arg_reg: IX64.arg_reg_relation max_arity)\n (pre: VSig.vale_pre_tl [])\n (args: IX64.arg_list)\n (hs_mem: mem_roots args)\n : prop\nlet to_low_pre\n (#max_arity:nat)\n (#arg_reg:IX64.arg_reg_relation max_arity)\n (pre:VSig.vale_pre_tl [])\n (args:IX64.arg_list)\n (hs_mem:mem_roots args)\n : prop =\n (forall (s0:V.va_state).\n V.va_get_ok s0 /\\\n vale_pre_hyp #max_arity #arg_reg args s0 /\\\n mem_correspondence args hs_mem s0 ==>\n elim_nil pre s0)", "val increasing:preorder nat\nlet increasing : preorder nat = fun (x y:nat) -> b2t (x <= y)", "val Vale.AsLowStar.Test.vm_lemma = Vale.AsLowStar.ValeSig.vale_sig_stdcall Vale.AsLowStar.Test.vm_pre Vale.AsLowStar.Test.vm_post\nlet vm_lemma = as_t #(VSig.vale_sig_stdcall vm_pre vm_post) vm_lemma'", "val Vale.AsLowStar.ValeSig.vale_post = dom: Prims.list Vale.Interop.Base.td -> Type\nlet vale_post (dom:list td) =\n code:V.va_code ->\n vale_post_tl dom", "val wrap'\n (n:nat)\n (arg_reg:arg_reg_relation n)\n (regs_modified:MS.reg_64 -> bool)\n (xmms_modified:MS.reg_xmm -> bool)\n (c:BS.code)\n (dom:list td{List.length dom <= 20})\n (#pre_rel:rel_gen_t c dom [] (prediction_pre_rel_t c))\n (#post_rel:rel_gen_t c dom [] (prediction_post_rel_t c))\n (predict:prediction_t n arg_reg regs_modified xmms_modified c dom [] pre_rel post_rel)\n : as_lowstar_sig_t n arg_reg regs_modified xmms_modified c dom [] pre_rel post_rel predict\nlet wrap' n arg_reg regs_modified xmms_modified c dom #pre_rel #post_rel predict =\n wrap_aux n arg_reg regs_modified xmms_modified c dom [] pre_rel post_rel predict", "val fmul1_dom:IX64.arity_ok_stdcall td\nlet fmul1_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y", "val entries_pre (rand: randomness) : preorder (entries rand)\nlet entries_pre (rand:randomness) :preorder (entries rand) = entries_rel rand", "val fmul_dom:IX64.arity_ok_stdcall td\nlet fmul_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_mod; t64_no_mod] in\n assert_norm (List.length y = 4);\n y", "val Vale.Interop.X64.as_lowstar_sig_t_weak = \n n: Prims.nat{n <= 20} ->\n arg_reg: Vale.Interop.X64.arg_reg_relation n ->\n regs_modified: (_: Vale.X64.Machine_s.reg_64 -> Prims.bool) ->\n xmms_modified: (_: Vale.X64.Machine_s.reg_xmm -> Prims.bool) ->\n c: Vale.X64.Machine_Semantics_s.code ->\n dom: Prims.list Vale.Interop.Base.td ->\n args:\n Prims.list Vale.Interop.Base.arg\n {FStar.List.Tot.Base.length args + FStar.List.Tot.Base.length dom <= n} ->\n pre_rel: Vale.Interop.X64.rel_gen_t c dom args (Vale.Interop.X64.prediction_pre_rel_t c) ->\n post_rel: Vale.Interop.X64.rel_gen_t c dom args (Vale.Interop.X64.prediction_post_rel_t c) ->\n predict:\n Vale.Interop.X64.prediction_t n\n arg_reg\n regs_modified\n xmms_modified\n c\n dom\n args\n pre_rel\n post_rel\n -> Type0\nlet as_lowstar_sig_t_weak\n (n:nat{n <= 20})\n (arg_reg:arg_reg_relation n)\n (regs_modified:MS.reg_64 -> bool)\n (xmms_modified:MS.reg_xmm -> bool)\n (c:BS.code)\n (dom:list td)\n (args:list arg{List.length args + List.length dom <= n})\n (pre_rel:rel_gen_t c dom args (prediction_pre_rel_t c))\n (post_rel:rel_gen_t c dom args (prediction_post_rel_t c))\n (predict:prediction_t n arg_reg regs_modified xmms_modified c dom args pre_rel post_rel) =\n as_lowstar_sig_t_weak' n arg_reg regs_modified xmms_modified c dom args pre_rel post_rel predict", "val Vale.Stdcalls.X64.Aes.key256_lemma = Vale.AsLowStar.ValeSig.vale_sig_stdcall Vale.Stdcalls.X64.Aes.key256_pre\n Vale.Stdcalls.X64.Aes.key256_post\nlet key256_lemma = as_t #(VSig.vale_sig_stdcall key256_pre key256_post) key256_lemma'", "val Vale.Interop.X64.as_lowstar_sig_t_weak_stdcall = \n c: Vale.X64.Machine_Semantics_s.code ->\n dom: Prims.list Vale.Interop.Base.td ->\n args:\n Prims.list Vale.Interop.Base.arg\n {FStar.List.Tot.Base.length args + FStar.List.Tot.Base.length dom <= 20} ->\n pre_rel: Vale.Interop.X64.rel_gen_t c dom args (Vale.Interop.X64.prediction_pre_rel_t c) ->\n post_rel: Vale.Interop.X64.rel_gen_t c dom args (Vale.Interop.X64.prediction_post_rel_t c) ->\n predict:\n Vale.Interop.X64.prediction_t Vale.Interop.X64.max_stdcall\n Vale.Interop.X64.arg_reg_stdcall\n Vale.Interop.X64.regs_modified_stdcall\n Vale.Interop.X64.xmms_modified_stdcall\n c\n dom\n args\n pre_rel\n post_rel\n -> Type0\nlet as_lowstar_sig_t_weak_stdcall = as_lowstar_sig_t_weak' max_stdcall arg_reg_stdcall regs_modified_stdcall xmms_modified_stdcall" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.sha_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Aes.fsti", "name": "Vale.Stdcalls.X64.Aes.key128_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Aes.fsti", "name": "Vale.Stdcalls.X64.Aes.key256_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Poly.fsti", "name": "Vale.Stdcalls.X64.Poly.poly_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fadd.fsti", "name": "Vale.Stdcalls.X64.Fadd.add1_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.add1_pre" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.vm_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsub.fsti", "name": "Vale.Stdcalls.X64.Fsub.fsub_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.fmul_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.fmul_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fadd.fsti", "name": "Vale.Stdcalls.X64.Fadd.fadd_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.fadd_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsqr.fsti", "name": "Vale.Stdcalls.X64.Fsqr.fsqr_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fsqr_inline.fst", "name": "Vale.Inline.X64.Fsqr_inline.fsqr_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.fmul2_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.fmul2_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsqr.fsti", "name": "Vale.Stdcalls.X64.Fsqr.fsqr2_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fsqr_inline.fst", "name": "Vale.Inline.X64.Fsqr_inline.fsqr2_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.fmul1_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.fmul1_pre" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.aesni_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Aes.fsti", "name": "Vale.Stdcalls.X64.Aes.key128_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Aes.fsti", "name": "Vale.Stdcalls.X64.Aes.key256_post" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.fsub_pre" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.ta_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.add1_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fadd.fsti", "name": "Vale.Stdcalls.X64.Fadd.add1_post" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fswap_inline.fst", "name": "Vale.Inline.X64.Fswap_inline.cswap_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fswap.fsti", "name": "Vale.Stdcalls.X64.Fswap.cswap_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Poly.fsti", "name": "Vale.Stdcalls.X64.Poly.poly_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.sha_post" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.vm_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsub.fsti", "name": "Vale.Stdcalls.X64.Fsub.fsub_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCTR.fst", "name": "Vale.Stdcalls.X64.GCTR.gctr256_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.fmul2_post" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.fmul2_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.AesHash.fst", "name": "Vale.Stdcalls.X64.AesHash.key256_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.fmul_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.fmul_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.AesHash.fst", "name": "Vale.Stdcalls.X64.AesHash.key128_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.fmul1_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.fmul1_post" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fsqr_inline.fst", "name": "Vale.Inline.X64.Fsqr_inline.fsqr2_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsqr.fsti", "name": "Vale.Stdcalls.X64.Fsqr.fsqr2_post" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.aesni_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCTR.fst", "name": "Vale.Stdcalls.X64.GCTR.gctr128_pre" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.ValeSig.fst", "name": "Vale.AsLowStar.ValeSig.vale_sig_stdcall" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCM_IV.fst", "name": "Vale.Stdcalls.X64.GCM_IV.compute_iv_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsqr.fsti", "name": "Vale.Stdcalls.X64.Fsqr.fsqr_post" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fsqr_inline.fst", "name": "Vale.Inline.X64.Fsqr_inline.fsqr_post" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.ValeSig.fst", "name": "Vale.AsLowStar.ValeSig.vale_pre" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Wrapper.fsti", "name": "Vale.AsLowStar.Wrapper.pre_rel_generic" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fswap_inline.fst", "name": "Vale.Inline.X64.Fswap_inline.cswap_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fswap.fsti", "name": "Vale.Stdcalls.X64.Fswap.cswap_post" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.ValeSig.fst", "name": "Vale.AsLowStar.ValeSig.vale_pre_tl" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.fsub_post" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.fadd_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fadd.fsti", "name": "Vale.Stdcalls.X64.Fadd.fadd_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCM_IV.fst", "name": "Vale.Stdcalls.X64.GCM_IV.compute_iv_post" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.ValeSig.fst", "name": "Vale.AsLowStar.ValeSig.elim_vale_sig_cons" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.Field32xN.fst", "name": "Hacl.Impl.Poly1305.Field32xN.load_precompute_r1" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.ValeSig.fst", "name": "Vale.AsLowStar.ValeSig.elim_vale_sig_nil" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCMdecryptOpt.fst", "name": "Vale.Stdcalls.X64.GCMdecryptOpt.gcm256_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCMencryptOpt.fst", "name": "Vale.Stdcalls.X64.GCMencryptOpt.gcm256_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCMencryptOpt.fst", "name": "Vale.Stdcalls.X64.GCMencryptOpt.gcm128_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCMdecryptOpt.fst", "name": "Vale.Stdcalls.X64.GCMdecryptOpt.gcm128_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.fmul1_dom" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fadd_inline.fst", "name": "Vale.Inline.X64.Fadd_inline.dom" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.ta_post" }, { "project_name": "FStar", "file_name": "Interop.fst", "name": "Interop.vale_sig" }, { "project_name": "hacl-star", "file_name": "Vale.Inline.X64.Fmul_inline.fst", "name": "Vale.Inline.X64.Fmul_inline.fmul_dom" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.AesHash.fst", "name": "Vale.Stdcalls.X64.AesHash.key256_post" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.AesHash.fst", "name": "Vale.Stdcalls.X64.AesHash.key128_post" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.Field32xN.fst", "name": "Hacl.Impl.Poly1305.Field32xN.load_precompute_r" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCTR.fst", "name": "Vale.Stdcalls.X64.GCTR.gctr256_post" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Wrapper.fsti", "name": "Vale.AsLowStar.Wrapper.prediction_pre_rel" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.Field32xN.fst", "name": "Hacl.Impl.Poly1305.Field32xN.load_precompute_r4" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.Field32xN.fst", "name": "Hacl.Impl.Poly1305.Field32xN.load_precompute_r2" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Wrapper.fsti", "name": "Vale.AsLowStar.Wrapper.post_rel_generic" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.GCTR.fst", "name": "Vale.Stdcalls.X64.GCTR.gctr128_post" }, { "project_name": "FStar", "file_name": "Interop.fst", "name": "Interop.as_vale_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.X64.fsti", "name": "Vale.Interop.X64.as_lowstar_sig_t_weak'" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.Fields.fst", "name": "Hacl.Impl.Poly1305.Fields.load_precompute_r" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.AesHash.fst", "name": "Vale.Stdcalls.X64.AesHash.dom" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Sha.fsti", "name": "Vale.Stdcalls.X64.Sha.dom" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fsub.fsti", "name": "Vale.Stdcalls.X64.Fsub.dom" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Aes.fsti", "name": "Vale.Stdcalls.X64.Aes.dom" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fadd.fsti", "name": "Vale.Stdcalls.X64.Fadd.dom" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Poly.fsti", "name": "Vale.Stdcalls.X64.Poly.dom" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.LowStarSig.fst", "name": "Vale.AsLowStar.LowStarSig.to_low_pre" }, { "project_name": "steel", "file_name": "Steel.MonotonicCounter.fst", "name": "Steel.MonotonicCounter.increasing" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.Test.fst", "name": "Vale.AsLowStar.Test.vm_lemma" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.ValeSig.fst", "name": "Vale.AsLowStar.ValeSig.vale_post" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.X64.fst", "name": "Vale.Interop.X64.wrap'" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.fmul1_dom" }, { "project_name": "FStar", "file_name": "Protocol.fst", "name": "Protocol.entries_pre" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Fmul.fsti", "name": "Vale.Stdcalls.X64.Fmul.fmul_dom" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.X64.fsti", "name": "Vale.Interop.X64.as_lowstar_sig_t_weak" }, { "project_name": "hacl-star", "file_name": "Vale.Stdcalls.X64.Aes.fsti", "name": "Vale.Stdcalls.X64.Aes.key256_lemma" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.X64.fsti", "name": "Vale.Interop.X64.as_lowstar_sig_t_weak_stdcall" } ], "selected_premises": [ "Vale.Lib.X64.Cpuidstdcall.va_req_Check_rdrand_stdcall", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_adx_bmi2_stdcall", "Vale.Stdcalls.X64.Cpuid.adx_post", "Vale.Stdcalls.X64.Cpuid.sha_pre", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_sha_stdcall", "Vale.X64.Instruction_s.instr_out", "Vale.Stdcalls.X64.Cpuid.sse_post", "Vale.Stdcalls.X64.Cpuid.sha_post", "Vale.X64.QuickCodes.label", "Vale.X64.Instruction_s.inOut", "Vale.Stdcalls.X64.Cpuid.adx_pre", "Vale.Stdcalls.X64.Cpuid.movbe_post", "Vale.X64.Machine_s.rRdi", "Vale.Stdcalls.X64.Cpuid.sse_pre", "Vale.Stdcalls.X64.Cpuid.avx_post", "Vale.Stdcalls.X64.Cpuid.aesni_post", "Vale.X64.Instruction_s.out", "Vale.Interop.X64.as_lowstar_sig_t_weak_stdcall", "Vale.X64.Machine_s.rRsp", "Vale.Stdcalls.X64.Cpuid.avx2_post", "Vale.X64.Machine_s.rRdx", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_avx_xcr0_stdcall", "Vale.X64.Machine_s.rRbp", "Vale.X64.Decls.va_get_reg64", "Vale.X64.Decls.va_state", "Vale.X64.Machine_s.rRax", "Vale.X64.Machine_s.rRsi", "Vale.X64.Machine_s.rRbx", "Vale.X64.Instruction_s.op64", "Vale.Stdcalls.X64.Cpuid.avx_pre", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_movbe_stdcall", "Vale.Interop.X64.regs_modified_stdcall", "Vale.Stdcalls.X64.Cpuid.movbe_pre", "Vale.X64.Instruction_s.opXmm", "Vale.X64.Machine_s.reg_64", "Vale.X64.Machine_s.rRcx", "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_get_block", "Vale.Interop.X64.als_ret", "Vale.Interop.X64.wrap_weak_stdcall", "Vale.Stdcalls.X64.Cpuid.code_sse", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_sse_stdcall", "Vale.X64.Decls.va_get_mem_heaplet", "Vale.X64.Instruction_s.opFlagsCf", "Vale.X64.Machine_s.rR9", "Vale.X64.Instruction_s.one64Reg", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_osxsave_stdcall", "Vale.Stdcalls.X64.Cpuid.dom", "Vale.X64.Decls.va_get_mem_layout", "Vale.X64.Machine_s.rR13", "Vale.X64.Decls.va_op_heaplet_mem_heaplet", "Vale.X64.Decls.va_get_ok", "Vale.Interop.X64.xmms_modified_stdcall", "Vale.Stdcalls.X64.Cpuid.avx2_pre", "Vale.X64.Machine_s.rR10", "Vale.X64.QuickCodes.va_range1", "Vale.X64.Machine_s.rR8", "Vale.X64.Machine_s.rR11", "Vale.X64.Machine_s.rR12", "Vale.X64.Decls.va_require_total", "Vale.Stdcalls.X64.Cpuid.code_adx", "Vale.X64.Machine_s.rR15", "Vale.AsLowStar.Wrapper.post_rel_generic", "Vale.X64.Decls.va_if", "Vale.X64.Decls.va_CNil", "Vale.X64.Machine_s.reg_xmm", "Vale.X64.Machine_s.rR14", "Vale.Stdcalls.X64.Cpuid.code_avx", "Vale.Interop.X64.max_stdcall", "Vale.Stdcalls.X64.Cpuid.code_movbe", "Vale.Lib.X64.Cpuidstdcall.va_ens_Check_sse_stdcall", "Vale.X64.Decls.va_op_reg_opr64_reg64", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_avx2_stdcall", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_avx512_xcr0_stdcall", "Vale.Stdcalls.X64.Cpuid.lowstar_adx_t", "Vale.X64.CPU_Features_s.avx_enabled", "Vale.Stdcalls.X64.Cpuid.aesni_pre", "Vale.Interop.X64.arg_reg_stdcall", "Vale.Lib.X64.Cpuidstdcall.va_ens_Check_avx_stdcall", "Vale.X64.CPU_Features_s.sse_enabled", "Vale.X64.Decls.va_upd_reg64", "Vale.Stdcalls.X64.Cpuid.adx_lemma", "Vale.X64.Decls.va_op_xmm_xmm", "Vale.X64.Decls.va_upd_flags", "Vale.AsLowStar.ValeSig.vale_sig_stdcall", "Vale.X64.Decls.va_Block", "Vale.X64.Machine_s.operand128", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_avx_stdcall", "Vale.Interop.X64.register_of_arg_i", "Vale.Stdcalls.X64.Cpuid.lowstar_movbe_t", "Vale.Stdcalls.X64.Cpuid.sse_lemma", "Vale.X64.Machine_s.nat64", "Vale.Stdcalls.X64.Cpuid.lowstar_sse_t", "Vale.Def.Words_s.nat64", "Vale.Def.Types_s.nat64", "Vale.X64.Memory.nat64", "Vale.Lib.X64.Cpuidstdcall.va_req_Check_avx512_stdcall", "Vale.Lib.X64.Cpuidstdcall.va_ens_Check_rdrand_stdcall", "Vale.AsLowStar.Wrapper.mk_prediction", "Vale.X64.Decls.va_CCons" ], "source_upto_this": "module Vale.Stdcalls.X64.Cpuid\n\nopen FStar.Mul\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\n\nmodule VC = Vale.Lib.X64.Cpuidstdcall\n\n(* A little utility to trigger normalization in types *)\nnoextract\nlet as_t (#a:Type) (x:normal a) : a = x\nnoextract\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__] noextract\nlet dom: IX64.arity_ok_stdcall td = []\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__] noextract\nlet aesni_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_aesni_stdcall c va_s0 IA.win\n\n[@__reduce__] noextract\nlet aesni_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_aesni_stdcall c va_s0 IA.win va_s1 f\n\n(* The vale lemma doesn't quite suffice to prove the modifies clause\n expected of the interop layer *)\n[@__reduce__] noextract\nlet aesni_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n aesni_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n aesni_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_aesni_stdcall code va_s0 IA.win\n\n(* Prove that vm_lemma' has the required type *)\nnoextract\nlet aesni_lemma = as_t #(VSig.vale_sig_stdcall aesni_pre aesni_post) aesni_lemma'\nnoextract\nlet code_aesni = VC.va_code_Check_aesni_stdcall IA.win\n\n(* Here's the type expected for the check_aesni wrapper *)\n[@__reduce__] noextract\nlet lowstar_aesni_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_aesni\n dom\n []\n _\n _\n (W.mk_prediction code_aesni dom [] (aesni_lemma code_aesni IA.win))\n\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__] noextract\nlet sha_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_sha_stdcall c va_s0 IA.win\n\n[@__reduce__] noextract\nlet sha_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_sha_stdcall c va_s0 IA.win va_s1 f\n\nopen Vale.X64.Machine_s\nopen Vale.X64.State\n\n#set-options \"--z3rlimit 20\"\n\n(* The vale lemma doesn't quite suffice to prove the modifies clause\n expected of the interop layer *)\n[@__reduce__] noextract\nlet sha_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n sha_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n sha_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_sha_stdcall code va_s0 IA.win\n\n(* Prove that vm_lemma' has the required type *)\nnoextract\nlet sha_lemma = as_t #(VSig.vale_sig_stdcall sha_pre sha_post) sha_lemma'\nnoextract\nlet code_sha = VC.va_code_Check_sha_stdcall IA.win\n\n(* Here's the type expected for the check_aesni wrapper *)\n[@__reduce__] noextract\nlet lowstar_sha_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sha\n dom\n []\n _\n _\n (W.mk_prediction code_sha dom [] (sha_lemma code_sha IA.win))\n\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__] noextract\nlet adx_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_adx_bmi2_stdcall c va_s0 IA.win\n\n[@__reduce__] noextract\nlet adx_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_adx_bmi2_stdcall c va_s0 IA.win va_s1 f\n\n(* The vale lemma doesn't quite suffice to prove the modifies clause\n expected of the interop layer *)\n[@__reduce__] noextract\nlet adx_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n adx_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n adx_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_adx_bmi2_stdcall code va_s0 IA.win\n\n(* Prove that vm_lemma' has the required type *)\nnoextract\nlet adx_lemma = as_t #(VSig.vale_sig_stdcall adx_pre adx_post) adx_lemma'\nnoextract\nlet code_adx = VC.va_code_Check_adx_bmi2_stdcall IA.win\n\n(* Here's the type expected for the check_adx wrapper *)\n[@__reduce__] noextract\nlet lowstar_adx_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_adx\n dom\n []\n _\n _\n (W.mk_prediction code_adx dom [] (adx_lemma code_adx IA.win))\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__] noextract\nlet avx_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_avx_stdcall c va_s0 IA.win\n\n[@__reduce__] noextract\nlet avx_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_avx_stdcall c va_s0 IA.win va_s1 f\n\n(* The vale lemma doesn't quite suffice to prove the modifies clause\n expected of the interop layer *)\n[@__reduce__] noextract\nlet avx_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n avx_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n avx_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_avx_stdcall code va_s0 IA.win\n\n(* Prove that vm_lemma' has the required type *)\nnoextract\nlet avx_lemma = as_t #(VSig.vale_sig_stdcall avx_pre avx_post) avx_lemma'\nnoextract\nlet code_avx = VC.va_code_Check_avx_stdcall IA.win\n\n(* Here's the type expected for the check_avx wrapper *)\n[@__reduce__] noextract\nlet lowstar_avx_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_avx\n dom\n []\n _\n _\n (W.mk_prediction code_avx dom [] (avx_lemma code_avx IA.win))\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__] noextract\nlet avx2_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_avx2_stdcall c va_s0 IA.win\n\n[@__reduce__] noextract\nlet avx2_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_avx2_stdcall c va_s0 IA.win va_s1 f\n\n(* The vale lemma doesn't quite suffice to prove the modifies clause\n expected of the interop layer *)\n[@__reduce__] noextract\nlet avx2_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n avx2_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n avx2_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_avx2_stdcall code va_s0 IA.win\n\n(* Prove that vm_lemma' has the required type *)\nnoextract\nlet avx2_lemma = as_t #(VSig.vale_sig_stdcall avx2_pre avx2_post) avx2_lemma'\nnoextract\nlet code_avx2 = VC.va_code_Check_avx2_stdcall IA.win\n\n(* Here's the type expected for the check_avx wrapper *)\n[@__reduce__] noextract\nlet lowstar_avx2_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_avx2\n dom\n []\n _\n _\n (W.mk_prediction code_avx2 dom [] (avx2_lemma code_avx2 IA.win))\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__] noextract\nlet movbe_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_movbe_stdcall c va_s0 IA.win\n\n[@__reduce__] noextract\nlet movbe_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_movbe_stdcall c va_s0 IA.win va_s1 f\n\n(* The vale lemma doesn't quite suffice to prove the modifies clause\n expected of the interop layer *)\n[@__reduce__] noextract\nlet movbe_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n movbe_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n movbe_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_movbe_stdcall code va_s0 IA.win\n\n(* Prove that vm_lemma' has the required type *)\nnoextract\nlet movbe_lemma = as_t #(VSig.vale_sig_stdcall movbe_pre movbe_post) movbe_lemma'\nnoextract\nlet code_movbe = VC.va_code_Check_movbe_stdcall IA.win\n\n(* Here's the type expected for the check_movbe wrapper *)\n[@__reduce__] noextract\nlet lowstar_movbe_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_movbe\n dom\n []\n _\n _\n (W.mk_prediction code_movbe dom [] (movbe_lemma code_movbe IA.win))\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__] noextract\nlet sse_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_sse_stdcall c va_s0 IA.win\n\n[@__reduce__] noextract\nlet sse_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n VC.va_ens_Check_sse_stdcall c va_s0 IA.win va_s1 f\n\n(* The vale lemma doesn't quite suffice to prove the modifies clause\n expected of the interop layer *)\n[@__reduce__] noextract\nlet sse_lemma'\n (code:V.va_code)\n (_win:bool)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n sse_pre code va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions_stdcall va_s0 va_s1 /\\\n sse_post code va_s0 va_s1 f))\n = VC.va_lemma_Check_sse_stdcall code va_s0 IA.win\n\n(* Prove that vm_lemma' has the required type *)\nnoextract\nlet sse_lemma = as_t #(VSig.vale_sig_stdcall sse_pre sse_post) sse_lemma'\nnoextract\nlet code_sse = VC.va_code_Check_sse_stdcall IA.win\n\n(* Here's the type expected for the check_sse wrapper *)\n[@__reduce__] noextract\nlet lowstar_sse_t =\n IX64.as_lowstar_sig_t_weak_stdcall\n code_sse\n dom\n []\n _\n _\n (W.mk_prediction code_sse dom [] (sse_lemma code_sse IA.win))\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__] noextract", "sketch": [ "Step 1: The definition `rdrand_pre` specifies the preconditions for the `rdrand` instruction in the context of a Vale standard call.\nStep 2: The implementation of `rdrand_pre` will be a function that takes a Vale code and an initial state, and returns whether the preconditions for executing the `rdrand` instruction are met. This will be done by calling the corresponding Vale requirement function from the `VC` module.", "Step 1: The definition `rdrand_pre` is a precondition function for the `rdrand` instruction. It specifies the conditions that must be true before the `rdrand` instruction can be executed.\nStep 2: The implementation of `rdrand_pre` will be a function that takes a `V.va_code` and a `V.va_state` as arguments and returns a boolean indicating whether the preconditions for executing the `rdrand` instruction are met. This will be done by calling the `VC.va_req_Check_rdrand_stdcall` function with the appropriate arguments.", "Step 1: The definition `rdrand_pre` is a precondition function for the `rdrand` instruction. It specifies the conditions that must be met before executing the `rdrand` instruction.\nStep 2: The implementation of `rdrand_pre` involves creating a function that takes a `V.va_code` and a `V.va_state` as arguments and returns a boolean indicating whether the preconditions for executing the `rdrand` instruction are satisfied. This is done by calling the `VC.va_req_Check_rdrand_stdcall` function with the given code, state, and the `IA.win` flag.", "Step 1: The definition `rdrand_pre` is a precondition function for the `rdrand` instruction. It will specify the conditions that must be met before executing the `rdrand` instruction in the context of a standard call.\nStep 2: The implementation of `rdrand_pre` will be a function that takes a `V.va_code` and a `V.va_state` as arguments and returns a boolean indicating whether the preconditions for executing the `rdrand` instruction are satisfied. This will be done by calling the appropriate precondition function from the `VC` module, specifically `VC.va_req_Check_rdrand_stdcall`.", "Step 1: The definition `rdrand_pre` is a precondition function for the `rdrand` instruction. This function will specify the conditions that must be true before the `rdrand` instruction can be executed.\nStep 2: The implementation of `rdrand_pre` will be similar to the other precondition functions defined earlier. It will take a `V.va_code` and a `V.va_state` as arguments and will call the corresponding precondition function from the `VC` module, which is `VC.va_req_Check_rdrand_stdcall`.", "Step 1: The definition `rdrand_pre` is about specifying the preconditions for the `rdrand` instruction when called using the standard calling convention.\nStep 2: The implementation of `rdrand_pre` will be a function that takes a `V.va_code` and a `V.va_state` as arguments and returns a boolean indicating whether the preconditions for the `rdrand` instruction are met. This will be done by calling the corresponding precondition function from the `VC` module.", "Step 1: The definition `rdrand_pre` is a precondition function for the `rdrand` instruction. It specifies the requirements that must be met before executing the `rdrand` instruction in a standard calling convention.\nStep 2: The implementation of `rdrand_pre` involves creating a function that takes a `V.va_code` and a `V.va_state` as arguments and returns the result of calling `VC.va_req_Check_rdrand_stdcall` with these arguments and the `IA.win` flag.", "Step 1: The definition `rdrand_pre` is a precondition function for the RDRAND instruction. This function will take a Vale code and an initial state as arguments and return a boolean indicating whether the preconditions for executing the RDRAND instruction are met.\nStep 2: To implement `rdrand_pre`, we will define a function that accepts a Vale code and an initial state, and then calls the corresponding precondition function from the `VC` module, which checks the requirements for the RDRAND instruction in the given state.", "Step 1: The definition `rdrand_pre` is about specifying the preconditions for the `rdrand` instruction in the context of a standard call (stdcall) in the Vale framework.\nStep 2: The implementation involves creating a function that takes a Vale code and an initial state, and returns a boolean indicating whether the preconditions for executing the `rdrand` instruction are met. This will be done by calling the corresponding Vale CPUID standard call requirement function.", "Step 1: The definition `rdrand_pre` is a precondition function for the `rdrand` instruction. It specifies the conditions that must be true before executing the `rdrand` instruction.\nStep 2: The implementation of `rdrand_pre` will be a function that takes a `V.va_code` and a `V.va_state` as arguments and returns a boolean indicating whether the preconditions for executing the `rdrand` instruction are met. This will be done by calling the corresponding Vale function `VC.va_req_Check_rdrand_stdcall`." ], "generated_solution": [ "let rdrand_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_rdrand_stdcall c va_s0 IA.win", "let rdrand_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_rdrand_stdcall c va_s0 IA.win", "let rdrand_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_rdrand_stdcall c va_s0 IA.win", "let rdrand_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_rdrand_stdcall c va_s0 IA.win", "let rdrand_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_rdrand_stdcall c va_s0 IA.win", "let rdrand_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_rdrand_stdcall c va_s0 IA.win", "let rdrand_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_rdrand_stdcall c va_s0 IA.win", "let rdrand_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_rdrand_stdcall c va_s0 IA.win", "let rdrand_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_rdrand_stdcall c va_s0 IA.win", "let rdrand_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (va_s0:V.va_state) ->\n VC.va_req_Check_rdrand_stdcall c va_s0 IA.win" ] }, { "file_name": "MRefHeap.fst", "name": "MRefHeap.heap_cell_a", "opens_and_abbrevs": [ { "open": "FStar.Preorder" }, { "open": "FStar.Preorder" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let heap_cell_a (a:Type0) = a * preorder_t a", "source_range": { "start_line": 24, "start_col": 0, "end_line": 24, "end_col": 44 }, "interleaved": false, "definition": "fun a -> a * MRefHeap.preorder_t a", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Pervasives.Native.tuple2", "MRefHeap.preorder_t" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "a: Type0 -> Type", "prompt": "let heap_cell_a (a: Type0) =\n ", "expected_response": "a * preorder_t a", "source": { "project_name": "FStar", "file_name": "examples/preorders/MRefHeap.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "MRefHeap.fst", "checked_file": "dataset/MRefHeap.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [], "closest": [ "val MRefHeap.preorder_t = a: Type0 -> Type\nlet preorder_t (a:Type0) = preorder a", "val MRefST.mref0 = a: Type0 -> r: MRefHeap.preorder_t a -> Type0\nlet mref0 = mref", "val FStar.HyperStack.mmref = a: Type0 -> Type0\nlet mmref (a:Type) = mmmref a (Heap.trivial_preorder a)", "val FStar.HyperStack.ref = a: Type0 -> Type0\nlet ref (a:Type) = mref a (Heap.trivial_preorder a)", "val FStar.HyperStack.mmstackref = a: Type0 -> Type0\nlet mmstackref (a:Type) = mmmstackref a (Heap.trivial_preorder a)", "val FStar.HyperStack.stackref = a: Type0 -> Type0\nlet stackref (a:Type) = mstackref a (Heap.trivial_preorder a)", "val ref (a: Type0) : Type0\nlet ref (a:Type0) : Type0 = ref a", "val ref (a: Type0) : Type0\nlet ref (a : Type0) : Type0 = (r: A.array a { A.length r == 1 \\/ r == A.null })", "val ref (a:Type0) : Type0\nlet ref (a:Type) = nat", "val FStar.Monotonic.HyperStack.mref = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_eternal_region_hs (frameOf s) && not (is_mm s) }", "val MRefST.st = a: Type -> Type\nlet st (a: Type) = heap -> M (a * heap)", "val CQueue.Cell.ccell_lvalue = a: Type0 -> Type0\nlet ccell_lvalue (a: Type0) = (c: ccell_ptrvalue a { ccell_ptrvalue_is_null c == false })", "val MRefST.contains = m: MRefHeap.mref a r -> h: MRefHeap.heap -> Type0\nlet contains (#a:Type) (#r:preorder a) (m:mref a r) (h:heap) = contains h m", "val data (#a:Type0) (c:cell a) : ref a\nlet data #a (c:cell a) : ref a = c.data", "val FStar.Monotonic.HyperStack.mreference = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mreference a rel = mreference' a rel", "val FStar.Monotonic.HyperStack.mstackref = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mstackref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_stack_region (frameOf s) && not (is_mm s) }", "val FStar.Monotonic.HyperStack.mmmref = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mmmref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_eternal_region_hs (frameOf s) && is_mm s }", "val ref ([@@@unused] a:Type0) : Type0\nlet ref a = H.ref (U.raise_t a)", "val ccell_ptrvalue (a: Type0) : Tot Type0\nlet ccell_ptrvalue a = mcell a", "val FStar.Monotonic.HyperStack.mmmstackref = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mmmstackref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_stack_region (frameOf s) && is_mm s }", "val sel (#a: Type0) (h: heap) (r: ref a) : GTot a\nlet sel (#a:Type0) (h:heap) (r:ref a) : GTot a\n = Heap.sel h r", "val alloc_ref : h0:heap ->\n a:Type -> \n\t\tx:a -> \n\t\tTot (rh1:(ref a * heap)\n\t\t\t {~(contains h0 (fst rh1)) /\\ \n\t\t\t contains (snd rh1) (fst rh1) /\\\n\t\t sel (snd rh1) (fst rh1) == x /\\\n\t\t\t (forall b (r:ref b) .{:pattern (contains h0 r)}\n\t\t\t contains h0 r \n\t\t\t ==> \n\t\t\t contains (snd rh1) r) /\\\n\t\t\t (forall b (r:ref b{contains h0 r}) . {:pattern sel #b h0 r}\n\t\t\t sel #b h0 r == sel #b (snd rh1) r)})\nlet alloc_ref h0 a x = \n (fst h0 , (fst h0 + 1 , F.on_dom nat (fun r -> if r = fst h0 then Some (| a , x |)\n\t\t\t\t\t else snd h0 r)))", "val ref ([@@@ unused] a:Type0)\n : Type0\nlet ref (a:Type0)\n : Type0\n = R.ref a", "val MRefST.stable_on_heap = m: MRefST.mref a r -> p: FStar.Preorder.predicate MRefHeap.heap -> Prims.logical\nlet stable_on_heap (#a:Type) (#r:preorder a) (m:mref a r) (p:predicate heap) =\n forall h0 h1 . stable_on_heap_aux m p h0 h1", "val contains_a_well_typed (#a:Type0) (h:heap) (r:ref a) : Type0\nlet contains_a_well_typed (#a:Type0) (h:heap) (r:ref a) =\n Some? (h.memory r.addr) /\\ dfst (Some?.v (h.memory r.addr)) == a", "val malloc (#a:Type0) (x:a) : Steel (ref a)\n emp (fun r -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ r h1 -> sel r h1 == x /\\ not (is_null r))\nlet malloc x =\n let r = alloc_pt x in\n intro_vptr r _ (hide x);\n return r", "val malloc (#a:Type0) (x:a) : Steel (ref a)\n emp (fun r -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ r h1 -> sel r h1 == x /\\ not (is_null r))\nlet malloc\n x\n= let r = A.malloc x 1sz in\n intro_vptrp' r full_perm;\n return r", "val null (#a:Type0) : ref a\nlet null #a = A.null #a", "val null (#a:Type0) : ref a\nlet null #a = H.null #(U.raise_t a)", "val free_cell\n (#a: Type0)\n (c: ccell_ptrvalue a) // could be ccell_lvalue, but ccell gives the right refinement\n: SteelT unit\n (ccell c)\n (fun _ -> emp)\nlet free_cell\n #a c\n=\n let c = elim_ccell c in\n free (ccell_data c);\n free (ccell_next c)", "val MRefST.stable_on_heap_aux = \n m: MRefST.mref a r ->\n p: FStar.Preorder.predicate MRefHeap.heap ->\n h0: MRefHeap.heap ->\n h1: MRefHeap.heap\n -> Prims.logical\nlet stable_on_heap_aux (#a:Type) (#r:preorder a) (m:mref a r) (p:predicate heap) (h0:heap) (h1:heap) =\n p h0 /\\\n (contains m h0 ==> contains m h1 /\\ r (sel h0 m) (sel h1 m))\n ==>\n p h1", "val null (#a:Type0) \n : ref a\nlet null (#a:Type0)\n : ref a\n = R.null #a", "val sel: #a:Type0 -> #rel:preorder a -> heap -> mref a rel -> GTot a\nlet sel #a #rel h r =\n if h `contains_bool` r\n then sel_tot #a h r\n else r.init", "val AlgHeap.st_wp = a: Type -> Type\nlet st_wp (a:Type) = wp:st_wp0 a{st_monotonic wp}", "val aref_unused_in: aref -> heap -> Type0\nlet aref_unused_in a h = None? (h.memory a.a_addr)", "val MRefST.st_post = a: Type -> Type\nlet st_post (a:Type) = a -> heap -> Type0", "val MRefST.st_wp = a: Type -> Type\nlet st_wp (a:Type) = st_post a -> Tot st_pre", "val MRefST.heap_rel = h0: MRefHeap.heap -> h1: MRefHeap.heap -> Prims.logical\nlet heap_rel (h0:heap) (h1:heap) =\n (forall a r (m:mref a r) . contains m h0 ==> contains m h1) /\\\n (forall a (r:preorder a) (m:mref a r{contains m h0}) . r (sel h0 m) (sel h1 m))", "val sel: #a:Type -> h:heap -> r:ref a -> GTot a\nlet sel #a h r =\n if FStar.StrongExcludedMiddle.strong_excluded_middle (h `contains_a_well_typed` r) then\n sel_tot #a h r\n else r.init", "val alloc: #a:Type0 -> rel:preorder a -> heap -> a -> mm:bool -> Tot (mref a rel * heap)\nlet alloc #a rel h x mm =\n let r = { addr = h.next_addr; init = x; mm = mm } in\n r, { next_addr = r.addr + 1;\n memory = F.on_dom pos (fun r' -> if r' = r.addr\n\t \t\t then Some (| a, Some rel, r.mm, x |)\n else h.memory r') }", "val as_ref (#a:Type0) (#rel:preorder a) (x:mreference a rel)\n :Heap.mref a rel\nlet as_ref #_ #_ x = MkRef?.ref x", "val ref_of: h: heap -> a: aref -> t: Type0 -> rel: preorder t -> Pure (mref t rel) (requires (aref_live_at h a t rel)) (ensures (fun x -> aref_live_at h a t rel /\\ addr_of (gref_of a t rel) == addr_of x /\\ is_mm x == aref_is_mm a))\nlet ref_of h a t rel = ref_of' h a t rel", "val data (#a:Type0) (c:cell a) : a\nlet data #a (c:cell a) : a = c.data", "val data (#a:Type0) (c:cell a) : a\nlet data #a (c:cell a) : a = c.data", "val data (#a:Type0) (c:cell a) : a\nlet data #a (c:cell a) : a = c.data", "val to_list_cell (#a:Type0) (ptr:t a)\n : Steel unit (llist ptr) (fun _ -> llist_cell ptr)\n (requires fun _ -> True)\n (ensures fun h0 _ h1 -> v_llist ptr h0 == datas (v_cell ptr h1))\nlet to_list_cell ptr =\n change_slprop_rel (llist ptr) (llist_cell ptr) (fun x y -> x == datas y) (fun _ -> ())", "val FStar.Monotonic.Heap.tset = a: Type -> Type\nlet tset = TSet.set", "val free_mm: #a:Type0 -> #rel:preorder a -> h:heap -> r:mref a rel{h `contains` r /\\ is_mm r} -> Tot heap\nlet free_mm #a #rel h r =\n { h with memory = F.on_dom pos (fun r' -> if r' = r.addr then None else h.memory r') }", "val upd: #a:Type -> h0:heap -> r:ref a -> x:a\n -> GTot heap\nlet upd #a h0 r x =\n if FStar.StrongExcludedMiddle.strong_excluded_middle (h0 `contains_a_well_typed` r)\n then upd_tot h0 r x\n else\n if r.addr >= h0.next_addr\n then (* alloc at r.addr *)\n { next_addr = r.addr + 1;\n memory = F.on_dom nat (fun (r':nat) -> if r' = r.addr\n\t\t\t then Some (| a, x |)\n else h0.memory r') }\n else (* type modifying update at r.addr *)\n { h0 with memory = F.on_dom nat (fun r' -> if r' = r.addr\n\t\t\t\t then Some (| a, x |)\n else h0.memory r') }", "val equal: heap -> heap -> Type0\nlet equal h1 h2 =\n let _ = () in\n h1.next_addr = h2.next_addr /\\\n FStar.FunctionalExtensionality.feq h1.memory h2.memory", "val fresh (#a: Type0) (r: ref a) (h0 h1: heap) : Type0\nlet fresh (#a:Type0) (r:ref a) (h0:heap) (h1:heap) : Type0\n = Heap.fresh r h0 h1", "val contains (#a:Type) (h:heap) (r:ref a): Tot Type0\nlet contains (#a:Type) (h:heap) (r:ref a): Tot Type0 = Some? (h.memory r.addr)", "val AllocSTwHeaps.st_post = a: Type -> Type\nlet st_post (a:Type) = a -> FStar.Heap.heap -> Type0", "val FStar.Monotonic.HyperStack.s_mref = i: FStar.Monotonic.HyperHeap.rid -> a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet s_mref (i:rid) (a:Type) (rel:preorder a) = s:mreference a rel{frameOf s = i}", "val ccell_data (#a: Type0) (c: ccell_lvalue a) : Pure (ref a)\n (requires True)\n (ensures (fun v -> ~ (is_null v)))\nlet ccell_data #a c =\n c.data", "val contains (#a:Type) (h:heap) (r:ref a) : GTot Type0\nlet contains (#a:Type) (h:heap) (r:ref a) : GTot Type0 =\n exists x . snd h r == Some (| a , x |)", "val AllocSTwHeaps.st_wp = a: Type -> Type\nlet st_wp (a:Type) = st_post a -> Tot st_pre", "val ref_of' (h: heap) (a: aref) (t: Type0) (rel: preorder t)\n : Pure (mref t rel) (requires (aref_live_at h a t rel)) (ensures (fun _ -> True))\nlet ref_of'\n (h: heap)\n (a: aref)\n (t: Type0)\n (rel: preorder t)\n: Pure (mref t rel)\n (requires (aref_live_at h a t rel))\n (ensures (fun _ -> True))\n= let Some (| _, pre_opt, _, x |) = h.memory a.a_addr in\n {\n addr = a.a_addr;\n init = x;\n mm = a.a_mm\n }", "val t (a:Type0) : Type0\nlet t a = list a", "val ccell_next (#a: Type0) (c: ccell_lvalue a) : Pure (ref (ccell_ptrvalue a))\n (requires True)\n (ensures (fun v -> ~ (is_null v)))\nlet ccell_next #a c =\n c.next", "val contains (#a: Type0) (h: heap) (r: ref a) : GTot Type0\nlet contains (#a:Type0) (h:heap) (r:ref a) :GTot Type0\n = Heap.contains h r", "val invariant: #a:Type -> h:HS.mem -> ll:t a -> Type0\nlet invariant #a h ll =\n let head = B.deref h ll.ptr in\n let v = B.deref h ll.v in\n // This is where we switch from a predicate (cumbersome for clients, requires\n // materializing the list at any time) to a ``v`` function which makes\n // specifications much easier. Any time the invariant holds, the pointer ``v``\n // holds a computationally-irrelevant representation of the list that in turns\n // allows us to under-the-hood state the various predicates from LL1 that\n // require exhibiting a list.\n B.live h ll.ptr /\\\n B.freeable ll.ptr /\\\n B.live h ll.v /\\\n B.freeable ll.v /\\\n LL1.well_formed h head v /\\\n LL1.invariant h head v /\\\n\n // We use regions for separation only, not for any footprint reasoning:\n // - ptr_v_rid is a sub-region of r and contains ptr and v, disjoint from each other\n // - spine_rid is a sub-region of r, disjoint from ptr_v_rid, and contains the LL1.footprint\n ST.is_eternal_region ll.r /\\\n ST.is_eternal_region ll.spine_rid /\\\n ST.is_eternal_region ll.ptr_v_rid /\\\n B.(loc_includes (loc_region_only true ll.ptr_v_rid) (loc_addr_of_buffer ll.ptr `loc_union` loc_addr_of_buffer ll.v)) /\\\n B.(loc_includes (loc_region_only true ll.spine_rid) (LL1.footprint h head v)) /\\\n B.(loc_disjoint (loc_addr_of_buffer ll.ptr) (loc_addr_of_buffer ll.v)) /\\\n B.(loc_disjoint (loc_region_only true ll.ptr_v_rid) (loc_region_only true ll.spine_rid)) /\\\n\n // These are not redundant, and are important for showing that the footprint\n // is contained in ``r`` at any time, so long as the invariant holds.\n HS.extends ll.ptr_v_rid ll.r /\\\n HS.extends ll.spine_rid ll.r /\\\n HS.parent ll.ptr_v_rid == ll.r /\\\n HS.parent ll.spine_rid == ll.r", "val array (a:Type0) : Type0\nlet array a = ref (seq a)", "val heap : Type u#(a + 1)\nlet heap : Type u#(a + 1) = addr ^-> option (cell u#a)", "val heap : Type u#(a + 1)\nlet heap : Type u#(a + 1) = addr ^-> option (cell u#a)", "val upd: #a:Type0 -> #rel:preorder a -> h:heap -> r:mref a rel -> x:a -> GTot heap\nlet upd #a #rel h r x =\n if h `contains_bool` r\n then upd_tot' h r x\n else\n if r.addr >= h.next_addr\n then\n { next_addr = r.addr + 1;\n memory = F.on_dom pos (fun r' -> if r' = r.addr\n\t \t\t then Some (| a, Some rel, r.mm, x |)\n else h.memory r') }\n else\n { h with memory = F.on_dom pos (fun r' -> if r' = r.addr\n\t\t\t\t then Some (| a, Some rel, r.mm, x |)\n else h.memory r') }", "val ref (a:Type u#0)\n : Type u#0\nlet ref (a:Type u#0)\n : Type u#0\n = R.ghost_ref a", "val Lib.NTuple.ntuple_ = a: Type0 -> len: Lib.NTuple.flen -> Type0\nlet rec ntuple_ (a:Type0) (len:flen) =\n if len = 1 then a\n else a & ntuple_ a (len-1)", "val ref ([@@@unused]a:Type u#1) : Type u#0\nlet ref (a:Type u#1) = pcm_ref (pcm_frac #a)", "val next (#a:Type0) (c:cell a) : t a\nlet next #a (c:cell a) : t a = c.next", "val next (#a:Type0) (c:cell a) : t a\nlet next #a (c:cell a) : t a = c.next", "val next (#a:Type0) (c:cell a) : t a\nlet next #a (c:cell a) : t a = c.next", "val next (#a:Type0) (c:cell a) : t a\nlet next #a (c:cell a) : t a = c.next", "val ref ([@@@unused] a:Type u#1) : Type u#0\nlet ref (a:Type u#1) = ghost_pcm_ref (pcm_frac #a)", "val ref ([@@@unused] a:Type u#1) : Type u#0\nlet ref a = Mem.ref (fractional a) pcm_frac", "val FStar.MRef.p_pred = r: FStar.ST.mref a b -> p: (_: a -> Type0) -> h: FStar.Monotonic.Heap.heap -> Prims.logical\nlet p_pred (#a:Type) (#b:preorder a) (r:mref a b) (p:(a -> Type))\n = fun h -> h `contains` r /\\ p (sel h r)", "val ptr (#a: Type0) (r: ref a) : slprop u#1\nlet ptr (#a:Type0) (r:ref a) : slprop u#1 = ptrp r full_perm", "val ptr (#a: Type0) (r: ref a) : slprop u#1\nlet ptr (#a:Type0) (r:ref a) : slprop u#1 = ptr r", "val ptr (#a: Type0) (r: ref a) : slprop u#1\nlet ptr (#a:Type0) (r:ref a) : slprop u#1 = ptrp r full_perm", "val alloc_cell\n (#a: Type0)\n (data: a)\n (next: ccell_ptrvalue a)\n: Steel (ccell_lvalue a)\n emp\n (fun res -> ccell res)\n (requires (fun _ -> True))\n (ensures (fun _ res h' ->\n h' (ccell res) == ({ vcell_data = data; vcell_next = next; })\n ))\nlet alloc_cell\n #a data next\n=\n let rdata = ralloc data in\n let rnext = ralloc next in\n let res : ccell_lvalue a = ({ data = rdata; next = rnext; all_or_none_null = () }) in\n change_equal_slprop (vptr rdata) (vptr (ccell_data res));\n change_equal_slprop (vptr rnext) (vptr (ccell_next res));\n intro_ccell res;\n return res", "val alloc: #a:Type -> h0:heap -> x:a -> Tot (t:(ref a * heap){snd t == upd h0 (fst t) x})\nlet alloc #a h0 x =\n let r = { addr = h0.next_addr; init = x } in\n let h1 = { next_addr = r.addr + 1;\n memory = F.on_dom nat (fun (r':nat) -> if r' = r.addr\n\t\t\t then Some (| a, x |)\n else h0.memory r') }\n in\n assert (let h2 = upd h0 r x in\n FStar.FunctionalExtensionality.feq h1.memory h2.memory);\n r, h1", "val CQueue.LList.cllist_lvalue = a: Type0 -> Type0\nlet cllist_lvalue (a: Type0) = (c: cllist_ptrvalue a { cllist_ptrvalue_is_null c == false })", "val Selectors.PtrLList.t = a: Type0 -> Type0\nlet t (a:Type0) = ref (cell a)", "val hlens_ref (#a: Type) : hlens (ref a) a\nlet hlens_ref (#a:Type) : hlens (ref a) a = {\n get = (fun (h, x) -> sel h x);\n put = (fun y (h, x) -> (upd h x y, x))\n}", "val FStar.Monotonic.Heap.set = a: Prims.eqtype -> Type0\nlet set = Set.set", "val aref_live_at: h: heap -> a: aref -> t: Type0 -> rel: preorder t -> GTot Type0\nlet aref_live_at (h: heap) (a: aref) (t: Type0) (rel: preorder t) =\n let _ = () in\n Some? (h.memory a.a_addr) /\\\n (let Some (| a1, pre_opt, mm, _ |) = h.memory a.a_addr in\n t == a1 /\\ Some? pre_opt /\\ Some?.v pre_opt === rel /\\ mm == a.a_mm)", "val FStar.TwoLevelHeap.st_wp = a: Type -> Type\nlet st_wp (a:Type) = st_wp_h t a", "val FStar.TwoLevelHeap.st_post = a: Type -> Type\nlet st_post (a:Type) = st_post_h t a", "val ref ([@@@unused] a:Type u#0) : Type u#0\nlet ref a = H.ref (U.raise_t a)", "val ref ([@@@unused] a:Type u#0) : Type u#0\nlet ref a = H.ref (U.raise_t a)", "val unused_in: #a:Type0 -> #rel:preorder a -> mref a rel -> heap -> Type0\nlet unused_in #a #rel r h = addr_unused_in (addr_of r) h", "val alloc : #a:Type ->\n r:preorder a ->\n\t x:a ->\n\t MRefST (mref a r) (fun _ -> True)\n (fun h0 m h1 -> ~(contains m h0) /\\\n\t\t\t\t\t fst (alloc_ref h0 a r x) == m /\\\n\t\t\t\t\t snd (alloc_ref h0 a r x) == h1)\nlet alloc #a r x =\n let h0 = ist_get () in\n let mh1 = alloc_ref h0 a r x in\n ist_put (snd mh1);\n ist_witness (contains (fst mh1)); //witnessing that the current heap contains the generated reference\n fst mh1", "val ralloc (#a: Type0) (x: a)\n : Steel (ref a)\n emp\n (fun r -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ r h1 -> h1 (vptr r) == x /\\ not (is_null r))\nlet ralloc (#a:Type0) (x:a) : Steel (ref a)\n emp (fun r -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ r h1 -> h1 (vptr r) == x /\\ not (is_null r))\n=\n malloc x", "val ralloc (#a: Type0) (x: a)\n : Steel (ref a)\n emp\n (fun r -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ r h1 -> h1 (vptr r) == x /\\ not (is_null r))\nlet ralloc (#a:Type0) (x:a) : Steel (ref a)\n emp (fun r -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ r h1 -> h1 (vptr r) == x /\\ not (is_null r))\n=\n malloc x", "val Lib.Buffer.cbuffer = a: Type0 -> Type0\nlet cbuffer (a:Type0) = buffer_t CONST a", "val reveal_non_empty_cell (#a:Type0) (ptr:t a)\n : Steel unit (llist_cell ptr) (fun _ -> llist_cell ptr)\n (requires fun _ -> ptr =!= null_llist)\n (ensures fun h0 _ h1 -> v_cell ptr h0 == v_cell ptr h1 /\\ Cons? (v_cell ptr h0))\nlet reveal_non_empty_cell #a ptr =\n let h = get () in\n let l = hide (v_cell ptr h) in\n extract_info (llist_cell ptr) l (is_cons l) (reveal_non_empty_lemma ptr l)", "val alloc : #a:Type -> \n x:a -> \n\t AllocST (ref a) (fun _ -> True)\n (fun h0 r h1 -> r `Heap.unused_in` h0 /\\\n\t\t\t\t\t FStar.Heap.contains h1 r /\\\n\t\t\t\t h1 == FStar.Heap.upd h0 r x)\nlet alloc #a x = \n let h = ist_get () in\n let r = gen_ref h in\n ist_put (upd h r x);\n ist_witness (contains r);\n r", "val ccell (#a: Type0) (c: ccell_ptrvalue a) : Tot vprop\nlet ccell (#a: Type0) (c: ccell_ptrvalue a) : Tot vprop =\n VUnit (ccell' c)", "val ImmutableSTwHeaps.st_wp = a: Type -> Type\nlet st_wp (a:Type) = st_post a -> Tot st_pre", "val copy_ref (#a: Type0) (r: ref a)\n : Steel (ref a)\n (vptr r)\n (fun r' -> (vptr r) `star` (vptr r'))\n (requires fun _ -> True)\n (ensures fun h0 r' h1 -> sel r h0 == sel r h1 /\\ sel r' h1 == sel r h1)\nlet copy_ref (#a:Type0) (r:ref a) : Steel (ref a)\n (vptr r)\n // We allocated a new reference r', which is the return value\n (fun r' -> vptr r `star` vptr r')\n (requires fun _ -> True)\n (ensures fun h0 r' h1 ->\n // reference r was not modified\n sel r h0 == sel r h1 /\\\n // After copying, reference r' contains the same value as reference r\n sel r' h1 == sel r h1)\n\n = let x = read r in\n let r' = malloc x in\n r'" ], "closest_src": [ { "project_name": "FStar", "file_name": "MRefHeap.fsti", "name": "MRefHeap.preorder_t" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.mref0" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.mmref" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.ref" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.mmstackref" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.stackref" }, { "project_name": "steel", "file_name": "SelectorLogic.fst", "name": "SelectorLogic.ref" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fsti", "name": "Steel.ArrayRef.ref" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.ref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mref" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.st" }, { "project_name": "steel", "file_name": "CQueue.Cell.fsti", "name": "CQueue.Cell.ccell_lvalue" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.contains" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.data" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mreference" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mstackref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mmmref" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ref" }, { "project_name": "steel", "file_name": "CQueue.Cell.fst", "name": "CQueue.Cell.ccell_ptrvalue" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mmmstackref" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.sel" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.alloc_ref" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.ref" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.stable_on_heap" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.contains_a_well_typed" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.malloc" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.malloc" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.null" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.null" }, { "project_name": "steel", "file_name": "CQueue.Cell.fst", "name": "CQueue.Cell.free_cell" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.stable_on_heap_aux" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.null" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.sel" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.st_wp" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.aref_unused_in" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.st_post" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.st_wp" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.heap_rel" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.sel" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.alloc" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.as_ref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.ref_of" }, { "project_name": "steel", "file_name": "Selectors.LList3.fst", "name": "Selectors.LList3.data" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.data" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.data" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.to_list_cell" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.tset" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.free_mm" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.upd" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.equal" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.fresh" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.contains" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.st_post" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.s_mref" }, { "project_name": "steel", "file_name": "CQueue.Cell.fst", "name": "CQueue.Cell.ccell_data" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.contains" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.st_wp" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.ref_of'" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.t" }, { "project_name": "steel", "file_name": "CQueue.Cell.fst", "name": "CQueue.Cell.ccell_next" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.contains" }, { "project_name": "karamel", "file_name": "LowStar.Lib.LinkedList2.fst", "name": "LowStar.Lib.LinkedList2.invariant" }, { "project_name": "FStar", "file_name": "FStar.Array.fst", "name": "FStar.Array.array" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.heap" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.heap" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.upd" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.ref" }, { "project_name": "hacl-star", "file_name": "Lib.NTuple.fsti", "name": "Lib.NTuple.ntuple_" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherReference.fst", "name": "Pulse.Lib.HigherReference.ref" }, { "project_name": "steel", "file_name": "Selectors.LList3.fst", "name": "Selectors.LList3.next" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.next" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.next" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.next" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.ref" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.ref" }, { "project_name": "FStar", "file_name": "FStar.MRef.fst", "name": "FStar.MRef.p_pred" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fsti", "name": "Steel.ArrayRef.ptr" }, { "project_name": "steel", "file_name": "SelectorLogic.fst", "name": "SelectorLogic.ptr" }, { "project_name": "steel", "file_name": "Steel.Reference.fsti", "name": "Steel.Reference.ptr" }, { "project_name": "steel", "file_name": "CQueue.Cell.fst", "name": "CQueue.Cell.alloc_cell" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.alloc" }, { "project_name": "steel", "file_name": "CQueue.LList.fsti", "name": "CQueue.LList.cllist_lvalue" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fsti", "name": "Selectors.PtrLList.t" }, { "project_name": "FStar", "file_name": "StatefulLens.fst", "name": "StatefulLens.hlens_ref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.set" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.aref_live_at" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.st_wp" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.st_post" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.Reference.fst", "name": "Pulse.Lib.Reference.ref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.unused_in" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.alloc" }, { "project_name": "steel", "file_name": "CQueue.LList.fst", "name": "CQueue.LList.ralloc" }, { "project_name": "steel", "file_name": "CQueue.Cell.fst", "name": "CQueue.Cell.ralloc" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.cbuffer" }, { "project_name": "steel", "file_name": "Selectors.LList.fst", "name": "Selectors.LList.reveal_non_empty_cell" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.alloc" }, { "project_name": "steel", "file_name": "CQueue.Cell.fsti", "name": "CQueue.Cell.ccell" }, { "project_name": "FStar", "file_name": "ImmutableSTwHeaps.fst", "name": "ImmutableSTwHeaps.st_wp" }, { "project_name": "steel", "file_name": "References.fst", "name": "References.copy_ref" } ], "selected_premises": [ "FStar.Pervasives.reveal_opaque", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "FStar.Pervasives.dfst", "FStar.Pervasives.st_post_h", "FStar.Preorder.preorder_rel", "FStar.Pervasives.dsnd", "FStar.Pervasives.st_pre_h", "FStar.Pervasives.st_post_h'", "FStar.Preorder.stable", "FStar.Pervasives.st_return", "FStar.Pervasives.all_return", "FStar.Pervasives.ex_pre", "Prims.pure_pre", "FStar.Pervasives.st_wp_h", "FStar.Pervasives.st_stronger", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.st_trivial", "FStar.Preorder.reflexive", "FStar.Pervasives.ex_post'", "FStar.Pervasives.all_post_h", "FStar.Pervasives.all_post_h'", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.all_stronger", "FStar.Pervasives.all_trivial", "FStar.Preorder.transitive", "FStar.Pervasives.id", "FStar.Pervasives.ex_post", "Prims.pure_post'", "Prims.returnM", "FStar.Pervasives.all_ite_wp", "FStar.Pervasives.st_ite_wp", "Prims.__cache_version_number__", "FStar.Pervasives.trivial_pure_post", "FStar.Pervasives.ex_wp", "Prims.pure_post", "FStar.Pervasives.all_wp_h", "Prims.min", "FStar.Pervasives.all_close_wp", "FStar.Pervasives.ex_return", "Prims.abs", "FStar.Pervasives.st_bind_wp", "Prims.auto_squash", "FStar.Pervasives.all_if_then_else", "FStar.Pervasives.pure_null_wp", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.st_if_then_else", "FStar.Pervasives.pure_return", "Prims.pure_wp'", "Prims.pow2", "FStar.Pervasives.ex_stronger", "FStar.Pervasives.ex_bind_wp", "FStar.Pervasives.lift_div_exn", "FStar.Pervasives.ex_trivial", "FStar.Pervasives.ex_ite_wp", "Prims.pure_wp_monotonic", "Prims.as_requires", "Prims.pure_wp_monotonic0", "Prims.pure_trivial", "FStar.Pervasives.coerce_eq", "Prims.pure_stronger", "Prims.purewp_id", "FStar.Pervasives.div_hoare_to_wp", "FStar.Pervasives.ex_if_then_else", "FStar.Pervasives.pure_ite_wp", "Prims.pure_wp", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.pure_close_wp", "Prims.subtype_of", "Prims.as_ensures", "FStar.Pervasives.pure_bind_wp", "Prims.op_Hat", "Prims.l_True", "Prims.l_False" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule MRefHeap\n\nopen FStar.Preorder\n\n(* Heap is a tuple of a source of freshness (the no. of the next fresh\n reference to be allocated) and a mapping of allocated raw references\n (represented as natural numbers) to types, values and preorders. *)\n", "sketch": [ "Step 1: The definition `heap_cell_a` is about defining a type that represents a cell in the heap for a given type `a`.\nStep 2: The implementation will take a type `a` as input and return a type that represents a heap cell containing a value of type `a`.", "Step 1: The definition `heap_cell_a` is about defining a type for a cell in the heap that can store a value of type `a`.\nStep 2: The implementation will define `heap_cell_a` as a function that takes a type `a` and returns a type representing a heap cell containing a value of type `a`.", "Step 1: The definition `heap_cell_a` is about defining a type that represents a cell in the heap for a given type `a`.\nStep 2: The implementation will take a type `a` as an argument and return a type that represents a heap cell containing values of type `a`.", "Step 1: The definition `heap_cell_a` is about defining a type that represents a cell in the heap for a given type `a`.\nStep 2: The implementation will define `heap_cell_a` as a function that takes a type `a` and returns a type representing a heap cell containing a value of type `a`.", "Step 1: The definition `heap_cell_a` is about defining a type for a cell in the heap that holds a value of type `a`.\nStep 2: The implementation will define `heap_cell_a` as a function that takes a type `a` and returns a type representing a heap cell containing a value of type `a`.", "Step 1: The definition `heap_cell_a` is about defining a type that represents a cell in the heap for a given type `a`.\nStep 2: The implementation will define `heap_cell_a` as a function that takes a type `a` and returns a type. This type represents the structure of a heap cell containing a value of type `a`.", "Step 1: The definition `heap_cell_a` is about defining a type that represents a cell in the heap for a given type `a`.\nStep 2: The implementation will define `heap_cell_a` as a function that takes a type `a` and returns a type. This type will represent the structure of a heap cell containing values of type `a`.", "Step 1: The definition is about creating a type `heap_cell_a` that takes a type `a` as a parameter.\nStep 2: The implementation will define `heap_cell_a` as a type that represents a cell in the heap containing a value of type `a`.", "Step 1: The definition `heap_cell_a` is about defining a type that represents a cell in the heap for a given type `a`.\nStep 2: The implementation will define `heap_cell_a` as a function that takes a type `a` and returns a type representing the heap cell for that type.", "Step 1: The definition is about creating a type `heap_cell_a` that takes a type `a` as a parameter.\nStep 2: The implementation will define `heap_cell_a` as a type that encapsulates the type `a`." ], "generated_solution": [ "let heap_cell_a (a: Type0) : Type = a", "type heap_cell_a (a: Type0) = a", "let heap_cell_a (a: Type0) : Type = a", "type heap_cell_a (a: Type0) = a", "let heap_cell_a (a: Type0) : Type = a", "type heap_cell_a (a: Type0) = a", "let heap_cell_a (a: Type0) : Type = a", "type heap_cell_a (a: Type0) = a", "let heap_cell_a (a: Type0) : Type = a", "type heap_cell_a (a: Type0) = a" ] }, { "file_name": "Hacl.Streaming.Poly1305_128.fsti", "name": "Hacl.Streaming.Poly1305_128.alloca", "opens_and_abbrevs": [ { "open": "Hacl.Streaming.Poly1305" }, { "open": "Hacl.Impl.Poly1305.Fields" }, { "abbrev": "I", "full_module": "Hacl.Streaming.Interface" }, { "abbrev": "F", "full_module": "Hacl.Streaming.Functor" }, { "abbrev": "G", "full_module": "FStar.Ghost" }, { "open": "Hacl.Streaming" }, { "open": "Hacl.Streaming" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 0, "max_fuel": 0, "initial_ifuel": 0, "max_ifuel": 0, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 100, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "", "source_definition": "let alloca = F.alloca (poly1305 M128) () (t M128) (poly1305_key.I.s ())", "source_range": { "start_line": 16, "start_col": 0, "end_line": 16, "end_col": 71 }, "interleaved": false, "definition": "Hacl.Streaming.Functor.alloca (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M128)\n ()\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M128)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Hacl.Streaming.Functor.alloca", "Prims.unit", "Hacl.Streaming.Poly1305.poly1305", "Hacl.Impl.Poly1305.Fields.M128", "Hacl.Streaming.Poly1305.t", "Hacl.Streaming.Interface.__proj__Stateful__item__s", "Hacl.Streaming.Poly1305.poly1305_key" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "Hacl.Streaming.Functor.alloca_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M128)\n ()\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M128)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())", "prompt": "let alloca =\n ", "expected_response": "F.alloca (poly1305 M128) () (t M128) (poly1305_key.I.s ())", "source": { "project_name": "hacl-star", "file_name": "code/streaming/Hacl.Streaming.Poly1305_128.fsti", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Hacl.Streaming.Poly1305_128.fsti", "checked_file": "dataset/Hacl.Streaming.Poly1305_128.fsti.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/Hacl.Streaming.Poly1305.fst.checked", "dataset/Hacl.Streaming.Interface.fsti.checked", "dataset/Hacl.Streaming.Functor.fsti.checked", "dataset/Hacl.Impl.Poly1305.Fields.fst.checked", "dataset/Hacl.Impl.Poly1305.fsti.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Ghost.fsti.checked" ] }, "definitions_in_context": [ "let state_t = F.state_s (poly1305 M128) () (t M128) (poly1305_key.I.s ())" ], "closest": [ "val Hacl.Streaming.Poly1305_256.alloca = Hacl.Streaming.Functor.alloca_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M256)\n ()\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M256)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet alloca = F.alloca (poly1305 M256) () (t M256) (poly1305_key.I.s ())", "val Hacl.Streaming.Poly1305_32.alloca = Hacl.Streaming.Functor.alloca_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M32)\n ()\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M32)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet alloca = F.alloca (poly1305 M32) () (t M32) (poly1305_key.I.s ())", "val Hacl.Streaming.Poly1305_256.malloc = Hacl.Streaming.Functor.malloc_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M256)\n ()\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M256)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet malloc = F.malloc (poly1305 M256) () (t M256) (poly1305_key.I.s ())", "val Hacl.Streaming.Poly1305_32.malloc = Hacl.Streaming.Functor.malloc_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M32)\n ()\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M32)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet malloc = F.malloc (poly1305 M32) () (t M32) (poly1305_key.I.s ())", "val Hacl.Streaming.Poly1305_256.digest = Hacl.Streaming.Functor.digest_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M256)\n ()\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M256)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet digest = F.digest (poly1305 M256) () (t M256) (poly1305_key.I.s ())", "val Hacl.Streaming.Poly1305_256.free = Hacl.Streaming.Functor.free_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M256)\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M256)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet free = F.free (poly1305 M256) (G.hide ()) (t M256) (poly1305_key.I.s ())", "val Hacl.Streaming.Blake2s_128.alloca = Hacl.Streaming.Functor.alloca_st (Hacl.Streaming.Blake2s_128.blake2s_128 0)\n ()\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M128)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet alloca =\n F.alloca (blake2s_128 0) () (Common.s Spec.Blake2S Core.M128) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.Poly1305_32.digest = Hacl.Streaming.Functor.digest_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M32)\n ()\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M32)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet digest = F.digest (poly1305 M32) () (t M32) (poly1305_key.I.s ())", "val Hacl.Streaming.Poly1305_32.free = Hacl.Streaming.Functor.free_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M32)\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M32)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet free = F.free (poly1305 M32) (G.hide ()) (t M32) (poly1305_key.I.s ())", "val Hacl.Streaming.Poly1305_256.reset = Hacl.Streaming.Functor.reset_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M256)\n (FStar.Ghost.hide (FStar.Ghost.reveal (FStar.Ghost.hide ())))\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M256)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet reset = F.reset (poly1305 M256) (G.hide ()) (t M256) (poly1305_key.I.s ())", "val Hacl.Streaming.Poly1305_32.reset = Hacl.Streaming.Functor.reset_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M32)\n (FStar.Ghost.hide (FStar.Ghost.reveal (FStar.Ghost.hide ())))\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M32)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet reset = F.reset (poly1305 M32) (G.hide ()) (t M32) (poly1305_key.I.s ())", "val Hacl.Streaming.Poly1305_256.update = Hacl.Streaming.Functor.update_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M256)\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M256)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet update = F.update (poly1305 M256) (G.hide ()) (t M256) (poly1305_key.I.s ())", "val Hacl.Streaming.Poly1305_32.update = Hacl.Streaming.Functor.update_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M32)\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M32)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())\nlet update = F.update (poly1305 M32) (G.hide ()) (t M32) (poly1305_key.I.s ())", "val Hacl.Streaming.SHA2.alloca_512 = Hacl.Streaming.Functor.alloca_st Hacl.Streaming.SHA2.hacl_sha2_512\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_512 ())\n (FStar.Ghost.erased Prims.unit)\nlet alloca_512 = F.alloca hacl_sha2_512 () (state_512.s ()) (G.erased unit)", "val Hacl.Streaming.SHA2.alloca_256 = Hacl.Streaming.Functor.alloca_st Hacl.Streaming.SHA2.hacl_sha2_256\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_256 ())\n (FStar.Ghost.erased Prims.unit)\nlet alloca_256 = F.alloca hacl_sha2_256 () (state_256.s ()) (G.erased unit)", "val Hacl.Streaming.Blake2s_32.alloca = Hacl.Streaming.Functor.alloca_st (Hacl.Streaming.Blake2s_32.blake2s_32 0)\n ()\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M32)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet alloca =\n F.alloca (blake2s_32 0) () (Common.s Spec.Blake2S Core.M32) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.Blake2s_128.malloc = Hacl.Streaming.Functor.malloc_st (Hacl.Streaming.Blake2s_128.blake2s_128 0)\n ()\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M128)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet malloc =\n F.malloc (blake2s_128 0) () (Common.s Spec.Blake2S Core.M128) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.SHA2.alloca_384 = Hacl.Streaming.Functor.alloca_st Hacl.Streaming.SHA2.hacl_sha2_384\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_384 ())\n (FStar.Ghost.erased Prims.unit)\nlet alloca_384 = F.alloca hacl_sha2_384 () (state_384.s ()) (G.erased unit)", "val Hacl.Streaming.SHA2.alloca_224 = Hacl.Streaming.Functor.alloca_st Hacl.Streaming.SHA2.hacl_sha2_224\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_224 ())\n (FStar.Ghost.erased Prims.unit)\nlet alloca_224 = F.alloca hacl_sha2_224 () (state_224.s ()) (G.erased unit)", "val Hacl.Streaming.MD5.alloca = Hacl.Streaming.Functor.alloca_st Hacl.Streaming.MD5.hacl_md5\n ()\n (Stateful?.s Hacl.Streaming.MD5.state_t_md5 ())\n (FStar.Ghost.erased Prims.unit)\nlet alloca = F.alloca hacl_md5 () (state_t_md5.s ()) (G.erased unit)", "val Hacl.Streaming.SHA2.malloc_512 = Hacl.Streaming.Functor.malloc_st Hacl.Streaming.SHA2.hacl_sha2_512\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_512 ())\n (FStar.Ghost.erased Prims.unit)\nlet malloc_512 = F.malloc hacl_sha2_512 () (state_512.s ()) (G.erased unit)", "val Hacl.Streaming.SHA1.alloca = Hacl.Streaming.Functor.alloca_st Hacl.Streaming.SHA1.hacl_sha1\n ()\n (Stateful?.s Hacl.Streaming.SHA1.state_t_sha1 ())\n (FStar.Ghost.erased Prims.unit)\nlet alloca = F.alloca hacl_sha1 () (state_t_sha1.s ()) (G.erased unit)", "val Hacl.Streaming.Blake2s_32.malloc = Hacl.Streaming.Functor.malloc_st (Hacl.Streaming.Blake2s_32.blake2s_32 0)\n ()\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M32)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet malloc =\n F.malloc (blake2s_32 0) () (Common.s Spec.Blake2S Core.M32) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.SHA2.malloc_256 = Hacl.Streaming.Functor.malloc_st Hacl.Streaming.SHA2.hacl_sha2_256\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_256 ())\n (FStar.Ghost.erased Prims.unit)\nlet malloc_256 = F.malloc hacl_sha2_256 () (state_256.s ()) (G.erased unit)", "val Hacl.Streaming.SHA2.malloc_384 = Hacl.Streaming.Functor.malloc_st Hacl.Streaming.SHA2.hacl_sha2_384\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_384 ())\n (FStar.Ghost.erased Prims.unit)\nlet malloc_384 = F.malloc hacl_sha2_384 () (state_384.s ()) (G.erased unit)", "val Hacl.Streaming.SHA2.malloc_224 = Hacl.Streaming.Functor.malloc_st Hacl.Streaming.SHA2.hacl_sha2_224\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_224 ())\n (FStar.Ghost.erased Prims.unit)\nlet malloc_224 = F.malloc hacl_sha2_224 () (state_224.s ()) (G.erased unit)", "val Hacl.Streaming.Functor.alloca_st = \n c: Hacl.Streaming.Interface.block index ->\n i: index ->\n t: Type0{t == Stateful?.s (Block?.state c) i} ->\n t': Type0{t' == Hacl.Streaming.Interface.optional_key i (Block?.km c) (Block?.key c)}\n -> Type0\nlet alloca_st\n (#index: Type0)\n (c:block index)\n (i:index)\n (t:Type0 { t == c.state.s i })\n (t':Type0 { t' == optional_key i c.km c.key }) =\n k:c.key.s i ->\n StackInline (state c i t t')\n (requires (fun h0 ->\n c.key.invariant #i h0 k))\n (ensures (fun h0 s h1 ->\n invariant c i h1 s /\\\n seen c i h1 s == S.empty /\\\n reveal_key c i h1 s == c.key.v i h0 k /\\\n B.(modifies loc_none h0 h1) /\\\n B.fresh_loc (footprint c i h1 s) h0 h1 /\\\n B.(loc_includes (loc_region_only true (HS.get_tip h1)) (footprint c i h1 s))))", "val Hacl.Streaming.Keccak.malloc = a: Hacl.Streaming.Keccak.alg\n -> Hacl.Streaming.Functor.malloc_st (Hacl.Streaming.Keccak.hacl_keccak (FStar.Ghost.hide a))\n a\n (Hacl.Streaming.Keccak.sha3_state a)\n (FStar.Ghost.erased Prims.unit)\nlet malloc (a: alg) =\n F.malloc (hacl_keccak a) a (sha3_state a) (G.erased unit)", "val Hacl.Streaming.MD5.malloc = Hacl.Streaming.Functor.malloc_st Hacl.Streaming.MD5.hacl_md5\n ()\n (Stateful?.s Hacl.Streaming.MD5.state_t_md5 ())\n (FStar.Ghost.erased Prims.unit)\nlet malloc = F.malloc hacl_md5 () (state_t_md5.s ()) (G.erased unit)", "val Hacl.Streaming.Poly1305.poly1305_key = Hacl.Streaming.Interface.stateful Prims.unit\nlet poly1305_key = I.stateful_buffer uint8 32ul (Lib.IntTypes.u8 0) unit", "val Hacl.Streaming.SHA1.malloc = Hacl.Streaming.Functor.malloc_st Hacl.Streaming.SHA1.hacl_sha1\n ()\n (Stateful?.s Hacl.Streaming.SHA1.state_t_sha1 ())\n (FStar.Ghost.erased Prims.unit)\nlet malloc = F.malloc hacl_sha1 () (state_t_sha1.s ()) (G.erased unit)", "val Hacl.Streaming.Blake2s_128.digest = Hacl.Streaming.Functor.digest_st (Hacl.Streaming.Blake2s_128.blake2s_128 0)\n ()\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M128)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet digest =\n F.digest (blake2s_128 0) () (Common.s Spec.Blake2S Core.M128) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.Blake2s_128.free = Hacl.Streaming.Functor.free_st (Hacl.Streaming.Blake2s_128.blake2s_128 0)\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M128)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet free =\n F.free (blake2s_128 0) (G.hide ()) (Common.s Spec.Blake2S Core.M128) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.Poly1305_32.state_t = Type0\nlet state_t = F.state_s (poly1305 M32) () (t M32) (poly1305_key.I.s ())", "val Hacl.Streaming.Poly1305_256.state_t = Type0\nlet state_t = F.state_s (poly1305 M256) () (t M256) (poly1305_key.I.s ())", "val Hacl.Streaming.SHA2.copy_512 = Hacl.Streaming.Functor.copy_st Hacl.Streaming.SHA2.hacl_sha2_512\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.SHA2.state_512 ())\n (FStar.Ghost.erased Prims.unit)\nlet copy_512 = F.copy hacl_sha2_512 () (state_512.s ()) (G.erased unit)", "val Hacl.Streaming.Blake2s_128.update = Hacl.Streaming.Functor.update_st (Hacl.Streaming.Blake2s_128.blake2s_128 0)\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M128)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet update =\n F.update (blake2s_128 0) (G.hide ()) (Common.s Spec.Blake2S Core.M128) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.Poly1305.update_ = _: (Spec.Poly1305.felem * Spec.Poly1305.felem) -> block: Hacl.Streaming.Poly1305.block\n -> Spec.Poly1305.felem * Spec.Poly1305.felem\nlet update_ (acc, r) (block: block) =\n Spec.Poly1305.poly1305_update1 r Spec.Poly1305.size_block block acc, r", "val Hacl.Chacha20Poly1305_128.poly1305_padded_128 = Hacl.Impl.Chacha20Poly1305.PolyCore.poly1305_padded_st Hacl.Impl.Poly1305.Fields.M128\nlet poly1305_padded_128 = Hacl.Impl.Chacha20Poly1305.PolyCore.poly1305_padded #M128", "val Hacl.Streaming.SHA2.copy_256 = Hacl.Streaming.Functor.copy_st Hacl.Streaming.SHA2.hacl_sha2_256\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.SHA2.state_256 ())\n (FStar.Ghost.erased Prims.unit)\nlet copy_256 = F.copy hacl_sha2_256 () (state_256.s ()) (G.erased unit)", "val Hacl.Streaming.Blake2s_128.reset = Hacl.Streaming.Functor.reset_st (Hacl.Streaming.Blake2s_128.blake2s_128 0)\n (FStar.Ghost.hide (FStar.Ghost.reveal (FStar.Ghost.hide ())))\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M128)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet reset =\n F.reset (blake2s_128 0) () (Common.s Spec.Blake2S Core.M128) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.Functor.malloc_st = \n c: Hacl.Streaming.Interface.block index ->\n i: index ->\n t: Type0{t == Stateful?.s (Block?.state c) i} ->\n t': Type0{t' == Hacl.Streaming.Interface.optional_key i (Block?.km c) (Block?.key c)}\n -> Type0\nlet malloc_st\n (#index: Type0)\n (c:block index)\n (i:index)\n (t:Type0 { t == c.state.s i })\n (t':Type0 { t' == optional_key i c.km c.key }) =\n k:c.key.s i ->\n r: HS.rid ->\n ST (state c i t t')\n (requires (fun h0 ->\n c.key.invariant #i h0 k /\\\n HyperStack.ST.is_eternal_region r))\n (ensures (fun h0 s h1 ->\n invariant c i h1 s /\\\n freeable c i h1 s /\\\n seen c i h1 s == S.empty /\\\n reveal_key c i h1 s == c.key.v i h0 k /\\\n B.(modifies loc_none h0 h1) /\\\n B.fresh_loc (footprint c i h1 s) h0 h1 /\\\n B.(loc_includes (loc_region_only true r) (footprint c i h1 s))))", "val Hacl.Streaming.SHA2.free_512 = Hacl.Streaming.Functor.free_st Hacl.Streaming.SHA2.hacl_sha2_512\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.SHA2.state_512 ())\n (FStar.Ghost.erased Prims.unit)\nlet free_512 = F.free hacl_sha2_512 (G.hide ()) (state_512.s ()) (G.erased unit)", "val Hacl.Streaming.Blake2s_32.free = Hacl.Streaming.Functor.free_st (Hacl.Streaming.Blake2s_32.blake2s_32 0)\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M32)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet free =\n F.free (blake2s_32 0) (G.hide ()) (Common.s Spec.Blake2S Core.M32) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.SHA2.update_224_256 = Hacl.Streaming.Functor.update_st Hacl.Streaming.SHA2.hacl_sha2_256\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.SHA2.state_256 ())\n (FStar.Ghost.erased Prims.unit)\nlet update_224_256 = F.update hacl_sha2_256 (G.hide ()) (state_256.s ()) (G.erased unit)", "val Hacl.Streaming.Blake2s_32.digest = Hacl.Streaming.Functor.digest_st (Hacl.Streaming.Blake2s_32.blake2s_32 0)\n ()\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M32)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet digest =\n F.digest (blake2s_32 0) () (Common.s Spec.Blake2S Core.M32) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.Poly1305.update' = r: Spec.Poly1305.felem -> acc: Spec.Poly1305.felem -> block: Hacl.Streaming.Poly1305.block\n -> Spec.Poly1305.felem\nlet update' r acc (block: block) =\n Spec.Poly1305.poly1305_update1 r Spec.Poly1305.size_block block acc", "val Hacl.Streaming.SHA2.free_256 = Hacl.Streaming.Functor.free_st Hacl.Streaming.SHA2.hacl_sha2_256\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.SHA2.state_256 ())\n (FStar.Ghost.erased Prims.unit)\nlet free_256 = F.free hacl_sha2_256 (G.hide ()) (state_256.s ()) (G.erased unit)", "val Hacl.Streaming.SHA2.digest_512 = Hacl.Streaming.Functor.digest_st Hacl.Streaming.SHA2.hacl_sha2_512\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_512 ())\n (FStar.Ghost.erased Prims.unit)\nlet digest_512 = F.digest hacl_sha2_512 () (state_512.s ()) (G.erased unit)", "val Hacl.Streaming.Poly1305.update__ = \n _: (Spec.Poly1305.felem * Spec.Poly1305.felem) ->\n input:\n FStar.Seq.Base.seq Hacl.Streaming.Poly1305.uint8\n {FStar.Seq.Base.length input <= Spec.Poly1305.size_block}\n -> Spec.Poly1305.felem * Spec.Poly1305.felem\nlet update__ (acc, r) (input: S.seq uint8{S.length input <= Spec.Poly1305.size_block}) =\n Spec.Poly1305.poly1305_update1 r (S.length input) input acc, r", "val Hacl.Streaming.Poly1305.finish_ = k: Spec.Poly1305.key -> _: (Spec.Poly1305.felem * _) -> Spec.Poly1305.tag\nlet finish_ k (acc, r) =\n Spec.Poly1305.poly1305_finish k acc", "val Hacl.Streaming.SHA2.update_384_512 = Hacl.Streaming.Functor.update_st Hacl.Streaming.SHA2.hacl_sha2_512\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.SHA2.state_512 ())\n (FStar.Ghost.erased Prims.unit)\nlet update_384_512 = F.update hacl_sha2_512 (G.hide ()) (state_512.s ()) (G.erased unit)", "val Hacl.Streaming.SHA2.reset_512 = Hacl.Streaming.Functor.reset_st Hacl.Streaming.SHA2.hacl_sha2_512\n (FStar.Ghost.hide (FStar.Ghost.reveal (FStar.Ghost.hide ())))\n (Stateful?.s Hacl.Streaming.SHA2.state_512 ())\n (FStar.Ghost.erased Prims.unit)\nlet reset_512 = F.reset hacl_sha2_512 (G.hide ()) (state_512.s ()) (G.erased unit)", "val Hacl.Streaming.SHA2.reset_256 = Hacl.Streaming.Functor.reset_st Hacl.Streaming.SHA2.hacl_sha2_256\n (FStar.Ghost.hide (FStar.Ghost.reveal (FStar.Ghost.hide ())))\n (Stateful?.s Hacl.Streaming.SHA2.state_256 ())\n (FStar.Ghost.erased Prims.unit)\nlet reset_256 = F.reset hacl_sha2_256 (G.hide ()) (state_256.s ()) (G.erased unit)", "val Hacl.Streaming.SHA1.copy = Hacl.Streaming.Functor.copy_st Hacl.Streaming.SHA1.hacl_sha1\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.SHA1.state_t_sha1 ())\n (FStar.Ghost.erased Prims.unit)\nlet copy = F.copy hacl_sha1 () (state_t_sha1.s ()) (G.erased unit)", "val Hacl.Streaming.Blake2s_32.update = Hacl.Streaming.Functor.update_st (Hacl.Streaming.Blake2s_32.blake2s_32 0)\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M32)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet update =\n F.update (blake2s_32 0) (G.hide ()) (Common.s Spec.Blake2S Core.M32) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.SHA2.digest_256 = Hacl.Streaming.Functor.digest_st Hacl.Streaming.SHA2.hacl_sha2_256\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_256 ())\n (FStar.Ghost.erased Prims.unit)\nlet digest_256 = F.digest hacl_sha2_256 () (state_256.s ()) (G.erased unit)", "val Hacl.Streaming.Poly1305.block = Type0\nlet block = (block: S.seq uint8 { S.length block = Spec.Poly1305.size_block })", "val Hacl.Chacha20Poly1305_256.poly1305_padded_256 = Hacl.Impl.Chacha20Poly1305.PolyCore.poly1305_padded_st Hacl.Impl.Poly1305.Fields.M256\nlet poly1305_padded_256 = Hacl.Impl.Chacha20Poly1305.PolyCore.poly1305_padded #M256", "val Hacl.Streaming.Blake2.Common.k = a: Hacl.Streaming.Blake2.Common.alg -> kk: Hacl.Streaming.Blake2.Common.key_size a\n -> Hacl.Streaming.Interface.stateful Prims.unit\nlet k = stateful_key", "val Hacl.Streaming.MD5.copy = Hacl.Streaming.Functor.copy_st Hacl.Streaming.MD5.hacl_md5\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.MD5.state_t_md5 ())\n (FStar.Ghost.erased Prims.unit)\nlet copy = F.copy hacl_md5 () (state_t_md5.s ()) (G.erased unit)", "val Hacl.Streaming.MD5.digest = Hacl.Streaming.Functor.digest_st Hacl.Streaming.MD5.hacl_md5\n ()\n (Stateful?.s Hacl.Streaming.MD5.state_t_md5 ())\n (FStar.Ghost.erased Prims.unit)\nlet digest = F.digest hacl_md5 () (state_t_md5.s ()) (G.erased unit)", "val Hacl.Streaming.Poly1305.t = fs: Hacl.Impl.Poly1305.Fields.field_spec -> Type0\nlet t (fs : field_spec) = b:B.buffer (limb fs) { B.length b == 25 }", "val Hacl.Streaming.SHA2.digest_224 = Hacl.Streaming.Functor.digest_st Hacl.Streaming.SHA2.hacl_sha2_224\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_224 ())\n (FStar.Ghost.erased Prims.unit)\nlet digest_224 = F.digest hacl_sha2_224 () (state_224.s ()) (G.erased unit)", "val Hacl.Streaming.SHA1.digest = Hacl.Streaming.Functor.digest_st Hacl.Streaming.SHA1.hacl_sha1\n ()\n (Stateful?.s Hacl.Streaming.SHA1.state_t_sha1 ())\n (FStar.Ghost.erased Prims.unit)\nlet digest = F.digest hacl_sha1 () (state_t_sha1.s ()) (G.erased unit)", "val Hacl.Streaming.SHA2.reset_224 = Hacl.Streaming.Functor.reset_st Hacl.Streaming.SHA2.hacl_sha2_224\n (FStar.Ghost.hide (FStar.Ghost.reveal (FStar.Ghost.hide ())))\n (Stateful?.s Hacl.Streaming.SHA2.state_224 ())\n (FStar.Ghost.erased Prims.unit)\nlet reset_224 = F.reset hacl_sha2_224 (G.hide ()) (state_224.s ()) (G.erased unit)", "val Hacl.Streaming.SHA2.reset_384 = Hacl.Streaming.Functor.reset_st Hacl.Streaming.SHA2.hacl_sha2_384\n (FStar.Ghost.hide (FStar.Ghost.reveal (FStar.Ghost.hide ())))\n (Stateful?.s Hacl.Streaming.SHA2.state_384 ())\n (FStar.Ghost.erased Prims.unit)\nlet reset_384 = F.reset hacl_sha2_384 (G.hide ()) (state_384.s ()) (G.erased unit)", "val Hacl.Impl.Poly1305.poly1305_init_st = s: Hacl.Impl.Poly1305.Fields.field_spec -> Type0\nlet poly1305_init_st (s:field_spec) =\n ctx:poly1305_ctx s\n -> key:lbuffer uint8 32ul ->\n Stack unit\n (requires fun h ->\n live h ctx /\\ live h key /\\ disjoint ctx key)\n (ensures fun h0 _ h1 ->\n modifies (loc ctx) h0 h1 /\\\n state_inv_t #s h1 ctx /\\\n (as_get_acc h1 ctx, as_get_r h1 ctx) == S.poly1305_init (as_seq h0 key))", "val Hacl.Streaming.Poly1305.spec = k: Spec.Poly1305.key -> input: Lib.ByteSequence.bytes -> Spec.Poly1305.tag\nlet spec k input =\n Spec.Poly1305.poly1305_mac input k", "val Hacl.Streaming.Blake2s_32.reset = Hacl.Streaming.Functor.reset_st (Hacl.Streaming.Blake2s_32.blake2s_32 0)\n (FStar.Ghost.hide (FStar.Ghost.reveal (FStar.Ghost.hide ())))\n (Hacl.Streaming.Blake2.Common.s Spec.Blake2.Definitions.Blake2S Hacl.Impl.Blake2.Core.M32)\n (Hacl.Streaming.Blake2.Common.empty_key Spec.Blake2.Definitions.Blake2S)\nlet reset =\n F.reset (blake2s_32 0) () (Common.s Spec.Blake2S Core.M32) (Common.empty_key Spec.Blake2S)", "val Hacl.Streaming.SHA2.digest_384 = Hacl.Streaming.Functor.digest_st Hacl.Streaming.SHA2.hacl_sha2_384\n ()\n (Stateful?.s Hacl.Streaming.SHA2.state_384 ())\n (FStar.Ghost.erased Prims.unit)\nlet digest_384 = F.digest hacl_sha2_384 () (state_384.s ()) (G.erased unit)", "val Hacl.Streaming.Keccak.get_alg = \n a: FStar.Ghost.erased Hacl.Streaming.Keccak.alg ->\n s:\n Hacl.Streaming.Functor.state (Hacl.Streaming.Keccak.hacl_keccak a)\n (FStar.Ghost.reveal a)\n (Hacl.Streaming.Keccak.sha3_state (FStar.Ghost.reveal a))\n (FStar.Ghost.erased Prims.unit)\n -> FStar.HyperStack.ST.Stack Hacl.Streaming.Keccak.alg\nlet get_alg (a: G.erased alg) =\n F.index_of_state (hacl_keccak a) a (sha3_state (G.reveal a)) (G.erased unit)", "val Hacl.Streaming.Functor.free_st = \n c: Hacl.Streaming.Interface.block index ->\n i: index ->\n t: Type0{t == Stateful?.s (Block?.state c) i} ->\n t': Type0{t' == Hacl.Streaming.Interface.optional_key i (Block?.km c) (Block?.key c)}\n -> Type0\nlet free_st\n (#index: Type0)\n (c:block index)\n (i:index)\n (t:Type0 { t == c.state.s i })\n (t':Type0 { t' == optional_key i c.km c.key }) =\n s:state c i t t' ->\n ST unit\n (requires fun h0 ->\n invariant c i h0 s /\\\n freeable c i h0 s)\n (ensures fun h0 _ h1 ->\n B.modifies (footprint c i h0 s) h0 h1)", "val Hacl.Streaming.MD5.free = Hacl.Streaming.Functor.free_st Hacl.Streaming.MD5.hacl_md5\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.MD5.state_t_md5 ())\n (FStar.Ghost.erased Prims.unit)\nlet free = F.free hacl_md5 (G.hide ()) (state_t_md5.s ()) (G.erased unit)", "val Hacl.Streaming.Keccak.digest_ = a: Hacl.Streaming.Keccak.alg\n -> Hacl.Streaming.Functor.digest_st (Hacl.Streaming.Keccak.hacl_keccak (FStar.Ghost.hide a))\n a\n (Hacl.Streaming.Keccak.sha3_state a)\n (FStar.Ghost.erased Prims.unit)\nlet digest_ (a: alg) =\n F.digest #alg (hacl_keccak a) a (sha3_state a) (G.erased unit)", "val Hacl.Streaming.Poly1305.update_last = \n _: (Spec.Poly1305.felem * Spec.Poly1305.felem) ->\n input:\n FStar.Seq.Base.seq Hacl.Streaming.Poly1305.uint8\n {FStar.Seq.Base.length input <= Spec.Poly1305.size_block}\n -> Spec.Poly1305.felem * Spec.Poly1305.felem\nlet update_last (acc, r) (input: S.seq uint8 { S.length input <= Spec.Poly1305.size_block }) =\n if S.length input = 0 then\n acc, r\n else\n Spec.Poly1305.poly1305_update1 r (S.length input) input acc, r", "val Hacl.Streaming.SHA1.free = Hacl.Streaming.Functor.free_st Hacl.Streaming.SHA1.hacl_sha1\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.SHA1.state_t_sha1 ())\n (FStar.Ghost.erased Prims.unit)\nlet free = F.free hacl_sha1 (G.hide ()) (state_t_sha1.s ()) (G.erased unit)", "val Hacl.Impl.Poly1305.poly1305_ctx = s: Hacl.Impl.Poly1305.Fields.field_spec -> Type0\nlet poly1305_ctx (s:field_spec) = lbuffer (limb s) (nlimb s +! precomplen s)", "val poly1305_do_:\n #w:field_spec\n -> k:lbuffer uint8 32ul // key\n -> aadlen:size_t\n -> aad:lbuffer uint8 aadlen // authenticated additional data\n -> mlen:size_t\n -> m:lbuffer uint8 mlen // plaintext\n -> ctx:Poly.poly1305_ctx w\n -> block:lbuffer uint8 16ul ->\n Stack unit\n (requires fun h ->\n live h k /\\ live h aad /\\ live h m /\\ live h ctx /\\ live h block /\\\n disjoint ctx k /\\ disjoint ctx aad /\\ disjoint ctx m /\\ disjoint ctx block /\\\n disjoint block k /\\ disjoint block aad /\\ disjoint block m)\n (ensures fun h0 _ h1 ->\n modifies (loc ctx |+| loc block) h0 h1 /\\\n (let acc, r = SpecPoly.poly1305_init (as_seq h0 k) in\n let acc = if (length aad <> 0) then Spec.poly1305_padded r (as_seq h0 aad) acc else acc in\n let acc = if (length m <> 0) then Spec.poly1305_padded r (as_seq h0 m) acc else acc in\n let block_s = LSeq.concat (BSeq.uint_to_bytes_le #U64 (u64 (length aad)))\n (BSeq.uint_to_bytes_le #U64 (u64 (length m))) in\n let acc = SpecPoly.poly1305_update1 r 16 block_s acc in\n Poly.as_get_acc h1 ctx == acc /\\ as_seq h1 block == block_s /\\\n Poly.state_inv_t h1 ctx))\nlet poly1305_do_ #w k aadlen aad mlen m ctx block =\n Poly.poly1305_init ctx k;\n if (aadlen <> 0ul) then (\n poly1305_padded ctx aadlen aad)\n else ();\n if (mlen <> 0ul) then (\n poly1305_padded ctx mlen m)\n else ();\n let h0 = ST.get () in\n update_sub_f h0 block 0ul 8ul\n (fun h -> BSeq.uint_to_bytes_le #U64 (to_u64 aadlen))\n (fun _ -> uint_to_bytes_le (sub block 0ul 8ul) (to_u64 aadlen));\n let h1 = ST.get () in\n //assert (LSeq.sub (as_seq h1 block) 0 8 == BSeq.uint_to_bytes_le #U64 (to_u64 aadlen));\n Poly.reveal_ctx_inv ctx h0 h1;\n update_sub_f h1 block 8ul 8ul\n (fun h -> BSeq.uint_to_bytes_le #U64 (to_u64 mlen))\n (fun _ -> uint_to_bytes_le (sub block 8ul 8ul) (to_u64 mlen));\n let h2 = ST.get () in\n //assert (LSeq.sub (as_seq h2 block) 8 8 == BSeq.uint_to_bytes_le #U64 (to_u64 mlen));\n LSeq.eq_intro (LSeq.sub (as_seq h2 block) 0 8) (BSeq.uint_to_bytes_le #U64 (to_u64 aadlen));\n LSeq.lemma_concat2 8 (BSeq.uint_to_bytes_le #U64 (to_u64 aadlen)) 8 (BSeq.uint_to_bytes_le #U64 (to_u64 mlen)) (as_seq h2 block);\n //assert (as_seq h2 block == LSeq.concat (BSeq.uint_to_bytes_le #U64 (to_u64 aadlen)) (BSeq.uint_to_bytes_le #U64 (to_u64 mlen)));\n Poly.reveal_ctx_inv ctx h1 h2;\n Poly.poly1305_update1 ctx block", "val Hacl.Chacha20Poly1305_32.poly1305_padded_32 = Hacl.Impl.Chacha20Poly1305.PolyCore.poly1305_padded_st Hacl.Impl.Poly1305.Fields.M32\nlet poly1305_padded_32 = Hacl.Impl.Chacha20Poly1305.PolyCore.poly1305_padded #M32", "val Hacl.Streaming.Keccak.copy = a: FStar.Ghost.erased Hacl.Streaming.Keccak.alg\n -> Hacl.Streaming.Functor.copy_st (Hacl.Streaming.Keccak.hacl_keccak a)\n (FStar.Ghost.reveal a)\n (Hacl.Streaming.Keccak.sha3_state (FStar.Ghost.reveal a))\n (FStar.Ghost.erased Prims.unit)\nlet copy (a: G.erased alg) =\n F.copy (hacl_keccak a) a (sha3_state (G.reveal a)) (G.erased unit)", "val Hacl.Streaming.Keccak.free = a: FStar.Ghost.erased Hacl.Streaming.Keccak.alg\n -> Hacl.Streaming.Functor.free_st (Hacl.Streaming.Keccak.hacl_keccak a)\n (FStar.Ghost.reveal a)\n (Hacl.Streaming.Keccak.sha3_state (FStar.Ghost.reveal a))\n (FStar.Ghost.erased Prims.unit)\nlet free (a: G.erased alg) =\n F.free (hacl_keccak a) a (sha3_state (G.reveal a)) (G.erased unit)", "val Hacl.Streaming.MD.hacl_md = a: Hacl.Streaming.MD.alg -> Hacl.Streaming.Interface.block Prims.unit\nlet hacl_md (a:alg)// : block unit =\n =\n Block\n Erased\n (state_t a) (* state *)\n (stateful_unused unit) (* key *)\n\n unit\n\n (fun () -> max_input_len64 a) (* max_input_len *)\n (fun () () -> Spec.Hash.Definitions.hash_length a) (* output_len *)\n (fun () -> Hacl.Hash.Definitions.block_len a) (* block_len *)\n (fun () -> Hacl.Hash.Definitions.block_len a) (* blocks_state_len *)\n (fun () -> 0ul) (* init_input_len *)\n\n (fun () _k -> S.empty) (* init_input_s *)\n\n (* init_s *)\n (fun () _ -> Spec.Agile.Hash.init a)\n\n (* update_multi_s *)\n (fun () acc prevlen blocks -> update_multi_s a () acc prevlen blocks)\n\n (* update_last_s *)\n (fun () acc prevlen input -> Spec.Hash.Incremental.(update_last a acc prevlen input))\n\n (* finish_s *)\n (fun () _ acc () -> Spec.Agile.Hash.(finish a acc ()))\n\n (* spec_s *)\n (fun () _ s () -> Spec.Agile.Hash.(hash a s))\n\n (* update_multi_zero *)\n (fun i h prevlen -> update_multi_zero a i h prevlen)\n\n (* update_multi_associative *)\n (fun i acc prevlen1 prevlen2 input1 input2 -> update_multi_associative a i acc prevlen1 prevlen2 input1 input2)\n\n (* spec_is_incremental *)\n (fun _ key input () ->\n let input1 = S.append S.empty input in\n assert (S.equal input1 input);\n Spec.Hash.Incremental.hash_is_hash_incremental' a input ())\n\n (* index_of_state *)\n (fun _ _ -> ())\n\n (* init *)\n (fun _ _ _ s ->\n match a with\n | MD5 -> Hacl.Hash.MD5.init s\n | SHA1 -> Hacl.Hash.SHA1.init s\n | SHA2_224 -> Hacl.Hash.SHA2.init_224 s\n | SHA2_256 -> Hacl.Hash.SHA2.init_256 s\n | SHA2_384 -> Hacl.Hash.SHA2.init_384 s\n | SHA2_512 -> Hacl.Hash.SHA2.init_512 s\n )\n\n (* update_multi *)\n (fun _ s prevlen blocks len ->\n [@inline_let]\n let update_multi : update_multi_st (|a,()|) =\n match a with\n | MD5 -> Hacl.Hash.MD5.update_multi\n | SHA1 -> Hacl.Hash.SHA1.update_multi\n | SHA2_224 -> Hacl.Hash.SHA2.update_multi_224\n | SHA2_256 -> Hacl.Hash.SHA2.update_multi_256\n | SHA2_384 -> Hacl.Hash.SHA2.update_multi_384\n | SHA2_512 -> Hacl.Hash.SHA2.update_multi_512\n in\n update_multi s () blocks (len `U32.div` Hacl.Hash.Definitions.(block_len a)))\n\n (* update_last *)\n (fun _ s prevlen last last_len ->\n [@inline_let]\n let update_last : update_last_st (|a,()|) =\n match a with\n | MD5 -> Hacl.Hash.MD5.update_last\n | SHA1 -> Hacl.Hash.SHA1.update_last\n | SHA2_224 -> Hacl.Hash.SHA2.update_last_224\n | SHA2_256 -> Hacl.Hash.SHA2.update_last_256\n | SHA2_384 -> Hacl.Hash.SHA2.update_last_384\n | SHA2_512 -> Hacl.Hash.SHA2.update_last_512\n in\n update_last s (md_prevlen a prevlen) last last_len)\n\n (* finish *)\n (fun _ _ s dst _ ->\n [@inline_let]\n let finish : finish_st (|a,()|) =\n match a with\n | MD5 -> Hacl.Hash.MD5.finish\n | SHA1 -> Hacl.Hash.SHA1.finish\n | SHA2_224 -> Hacl.Hash.SHA2.finish_224\n | SHA2_256 -> Hacl.Hash.SHA2.finish_256\n | SHA2_384 -> Hacl.Hash.SHA2.finish_384\n | SHA2_512 -> Hacl.Hash.SHA2.finish_512\n in\n finish s dst)", "val Hacl.Streaming.SHA1.update = Hacl.Streaming.Functor.update_st Hacl.Streaming.SHA1.hacl_sha1\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.SHA1.state_t_sha1 ())\n (FStar.Ghost.erased Prims.unit)\nlet update = F.update hacl_sha1 (G.hide ()) (state_t_sha1.s ()) (G.erased unit)", "val Hacl.Streaming.Functor.copy_st = \n c: Hacl.Streaming.Interface.block index ->\n i: index ->\n t: Type0{t == Stateful?.s (Block?.state c) i} ->\n t': Type0{t' == Hacl.Streaming.Interface.optional_key i (Block?.km c) (Block?.key c)}\n -> Type0\nlet copy_st\n (#index: Type0)\n (c:block index)\n (i:index)\n (t:Type0 { t == c.state.s i })\n (t':Type0 { t' == optional_key i c.km c.key }) =\n s0:state c i t t' ->\n r: HS.rid ->\n ST (state c i t t')\n (requires (fun h0 ->\n invariant c i h0 s0 /\\\n HyperStack.ST.is_eternal_region r))\n (ensures (fun h0 s h1 ->\n invariant c i h1 s /\\\n freeable c i h1 s /\\\n seen c i h1 s == seen c i h0 s0 /\\\n reveal_key c i h1 s == reveal_key c i h0 s0 /\\\n B.(modifies loc_none h0 h1) /\\\n B.fresh_loc (footprint c i h1 s) h0 h1 /\\\n B.(loc_includes (loc_region_only true r) (footprint c i h1 s))))", "val Hacl.Impl.Poly1305.poly1305_update_st = s: Hacl.Impl.Poly1305.Fields.field_spec -> Type0\nlet poly1305_update_st (s:field_spec) =\n ctx:poly1305_ctx s\n -> len:size_t\n -> text:lbuffer uint8 len ->\n Stack unit\n (requires fun h ->\n live h text /\\ live h ctx /\\ disjoint ctx text /\\\n state_inv_t #s h ctx)\n (ensures fun h0 _ h1 ->\n modifies (loc ctx) h0 h1 /\\\n state_inv_t #s h1 ctx /\\\n as_get_r h0 ctx == as_get_r h1 ctx /\\\n as_get_acc h1 ctx == S.poly1305_update (as_seq h0 text) (as_get_acc h0 ctx) (as_get_r h0 ctx))", "val va_quick_Poly1305_impl (key_r key_s: nat128) (ctx_b inp_b: buffer64) (finish: nat64)\n : (va_quickCode int (va_code_Poly1305_impl ()))\nlet va_quick_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)\n (finish:nat64) : (va_quickCode int (va_code_Poly1305_impl ())) =\n (va_QProc (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;\n va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10;\n va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi;\n va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem])\n (va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish) (va_wpProof_Poly1305_impl key_r key_s\n ctx_b inp_b finish))", "val EverCrypt.Hash.Incremental.malloc = a: Spec.Hash.Definitions.fixed_len_alg -> r: FStar.Monotonic.HyperHeap.rid\n -> FStar.HyperStack.ST.ST\n (Hacl.Streaming.Functor.state EverCrypt.Hash.Incremental.evercrypt_hash\n a\n (EverCrypt.Hash.state a)\n (FStar.Ghost.erased Prims.unit))\nlet malloc a = F.malloc evercrypt_hash a (EverCrypt.Hash.state a) (G.erased unit) ()", "val Hacl.Streaming.MD5.update = Hacl.Streaming.Functor.update_st Hacl.Streaming.MD5.hacl_md5\n (FStar.Ghost.reveal (FStar.Ghost.hide ()))\n (Stateful?.s Hacl.Streaming.MD5.state_t_md5 ())\n (FStar.Ghost.erased Prims.unit)\nlet update = F.update hacl_md5 (G.hide ()) (state_t_md5.s ()) (G.erased unit)", "val Hacl.Impl.Poly1305.poly1305_mac_st = s: Hacl.Impl.Poly1305.Fields.field_spec -> Type0\nlet poly1305_mac_st (s:field_spec) =\n output:lbuffer uint8 16ul\n -> input:buffer uint8\n -> input_len:size_t { length input = v input_len }\n -> key:lbuffer uint8 32ul ->\n Stack unit\n (requires fun h ->\n live h input /\\ live h output /\\ live h key /\\\n disjoint output input /\\ disjoint output key)\n (ensures fun h0 _ h1 ->\n modifies (loc output) h0 h1 /\\\n as_seq h1 output == S.poly1305_mac (as_seq h0 (input <: lbuffer uint8 input_len)) (as_seq h0 key))", "val Hacl.Streaming.Poly1305.update_multi' = \n r: Spec.Poly1305.felem ->\n acc: Spec.Poly1305.felem ->\n blocks: FStar.Seq.Base.seq Lib.UpdateMulti.uint8\n -> Prims.Pure Spec.Poly1305.felem\nlet update_multi' r =\n Lib.UpdateMulti.mk_update_multi Spec.Poly1305.size_block (update' r)", "val Hacl.Streaming.Poly1305.update_last' = \n r: Spec.Poly1305.felem ->\n acc: Spec.Poly1305.felem ->\n input:\n FStar.Seq.Base.seq Hacl.Streaming.Poly1305.uint8\n {FStar.Seq.Base.length input <= Spec.Poly1305.size_block}\n -> Spec.Poly1305.felem\nlet update_last' r acc (input: S.seq uint8 { S.length input <= Spec.Poly1305.size_block }) =\n if S.length input = 0 then\n acc\n else\n Spec.Poly1305.poly1305_update1 r (S.length input) input acc", "val Hacl.Streaming.MD.state_t = a: Hacl.Streaming.MD.alg -> Hacl.Streaming.Interface.stateful Prims.unit\nlet state_t (a : alg) = stateful_buffer (word a) (D.impl_state_len (|a, ()|)) (init_elem a) unit", "val va_wp_Poly1305_impl\n (key_r key_s: nat128)\n (ctx_b inp_b: buffer64)\n (finish: nat64)\n (va_s0: va_state)\n (va_k: (va_state -> int -> Type0))\n : Type0\nlet va_wp_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)\n (finish:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64\n in Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b\n 24 (va_get_mem_layout va_s0) Public /\\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0\n va_s0) (va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx\n va_s0)) (va_get_mem_layout va_s0) Public /\\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 <\n pow2_64 /\\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in\n let key_r0 = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =\n Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =\n Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =\n Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==\n Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\\ key_r ==\n Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\\ key_s == Vale.Poly1305.Math.lowerUpper128\n key_s0 key_s1 /\\ h2_in < 5 /\\ finish < 2)) /\\ (forall (va_x_mem:vale_heap) (va_x_rax:nat64)\n (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_rdi:nat64) (va_x_rsi:nat64) (va_x_rbx:nat64)\n (va_x_rbp:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r11:nat64)\n (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)\n (va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags\n va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13\n (va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10\n (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64\n rRbx va_x_rbx (va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdi va_x_rdi (va_upd_reg64 rRdx\n va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax (va_upd_mem va_x_mem\n va_s0))))))))))))))))) in va_get_ok va_sM /\\ (let (n:(va_int_range 18446744073709551616\n 18446744073709551616)) = pow2_64 in Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM)\n (va_get_reg64 rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\\\n Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet\n 1 va_sM) 0 8 /\\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0)\n in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =\n Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =\n Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let\n inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0\n va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192\n (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))\n (va_get_reg64 rRbp va_sM)) /\\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==\n Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)\n (Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\\\n (finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\\ (finish == 1 ==> h ==\n Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\\\n (finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)\n key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi\n va_s0)) ==> va_k va_sM ((h))))", "val Hacl.Streaming.Poly1305.update_multi = acc: (Spec.Poly1305.felem * Spec.Poly1305.felem) -> blocks: FStar.Seq.Base.seq Lib.UpdateMulti.uint8\n -> Prims.Pure (Spec.Poly1305.felem * Spec.Poly1305.felem)\nlet update_multi =\n Lib.UpdateMulti.mk_update_multi Spec.Poly1305.size_block update_", "val va_qcode_Poly1305_impl\n (va_mods: va_mods_t)\n (key_r key_s: nat128)\n (ctx_b inp_b: buffer64)\n (finish: nat64)\n : (va_quickCode (int) (va_code_Poly1305_impl ()))\nlet va_qcode_Poly1305_impl (va_mods:va_mods_t) (key_r:nat128) (key_s:nat128) (ctx_b:buffer64)\n (inp_b:buffer64) (finish:nat64) : (va_quickCode (int) (va_code_Poly1305_impl ())) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range\n 18446744073709551616 18446744073709551616)) = pow2_64 in let (inp_in:nat64) = va_get_reg64 rRsi\n va_s in let (len_in:nat64) = va_get_reg64 rRdx va_s in let (h0_in:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s) in let\n (h1_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1\n va_s) in let (h2_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 2\n (va_get_mem_heaplet 1 va_s) in let (h_in:Prims.int) = Vale.Poly1305.Math.lowerUpper192\n (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let (key_r0:Vale.Def.Types_s.nat64) =\n Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s) in let\n (key_r1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1\n va_s) in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 607 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 609 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)\n (va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 610 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)\n (va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 611 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 612 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 613 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244)) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 614 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 615 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR11) 24 Public ctx_b 3) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 616 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rR12) 32 Public ctx_b 4) (fun (va_s:va_state) _ -> let (r:nat128) =\n Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) (va_get_reg64 rR12 va_s) in\n va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 619 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (r == va_get_reg64 rR11 va_s + va_mul_nat n (va_get_reg64 rR12 va_s)) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 619 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (let\n (mask:nat128) = 21267647620597763993911028882763415551 in va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 622 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (r == Vale.Arch.Types.iand128 key_r mask) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 624 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (let\n (va_arg81:Vale.Def.Types_s.nat64) = va_get_reg64 rR12 va_s in let\n (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_s in let\n (va_arg79:Vale.Def.Words_s.nat128) = r in let (va_arg78:Vale.Def.Words_s.nat128) = mask in let\n (va_arg77:Vale.Def.Words_s.nat128) = key_r in va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 625 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_lowerUpper128_and va_arg77 key_r0 key_r1 va_arg78\n 1152921487695413247 1152921487695413244 va_arg79 va_arg80 va_arg81) (va_QEmpty (())))) (va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 629 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 630 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 631 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 634 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRax) 56 Public ctx_b 7) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 635 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRdx) 64 Public ctx_b 8) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 637 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (fun (va_s:va_state) _ ->\n va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 638 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n + h0_in) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 638 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 638 column 105 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 639 column 7 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Poly1305_blocks r h_in ctx_b inp_b) (fun (va_s:va_state) (h:int) -> va_qAssertBy\n va_range1\n \"***** PRECONDITION NOT MET AT line 640 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14\n va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 641 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 641 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let\n (va_arg76:Prims.int) = va_get_reg64 rRdx va_old_s `op_Division` 16 in let\n (va_arg75:Vale.X64.Memory.buffer64) = inp_b in let (va_arg74:Vale.X64.Memory.vale_heap) =\n va_get_mem_heaplet 0 va_s in let (va_arg73:Prims.int) = r in let (va_arg72:Prims.int) =\n va_mul_nat n n in let (va_arg71:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE\n va_range1\n \"***** PRECONDITION NOT MET AT line 642 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Util.lemma_poly1305_heap_hash_blocks_alt va_arg71 va_arg72\n va_arg73 va_arg74 va_arg75 va_arg76) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 644 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)\n (va_op_reg_opr64_reg64 rRdi) 184 Public ctx_b 23) (fun (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 645 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_qIf va_mods (Cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (qblock va_mods (fun\n (va_s:va_state) -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 647 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> reveal_logand128 key_r mask) (va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 648 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (r == Vale.Poly1305.Math.bare_r key_r) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 650 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)\n (va_op_reg_opr64_reg64 rRdi) 56 Public ctx_b 7) (fun (va_s:va_state) _ -> va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 652 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_qIf va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (qblock va_mods (fun\n (va_s:va_state) -> va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 654 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)\n (va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 655 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8)\n (va_op_reg_opr64_reg64 rRsi) 0 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2))\n (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 656 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)\n (va_op_reg_opr64_reg64 rRsi) 8 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2 + 1)) (fun\n (va_s:va_state) _ -> let (a:Vale.X64.Machine_s.nat128) = Vale.Poly1305.Util.seqTo128_app\n (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) (len_in `op_Division` 16) in\n va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 658 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == a)\n (va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 659 column 42 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 660 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Poly1305_last_block ()) (fun (va_s:va_state) _ -> let (h:int) =\n Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)\n (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_QEmpty ((h))))))))) (qblock va_mods\n (fun (va_s:va_state) -> va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in\n let (va_arg70:Prims.int) = key_s in let (va_arg69:Prims.int) = Vale.Poly1305.Spec_s.modp h in\n va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 664 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (fun (_:unit) -> Vale.Poly1305.Math.lemma_add_mod128 va_arg69 va_arg70) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 665 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Poly1305_reduce_last ()) (fun (va_s:va_state) _ -> let (h:int) =\n Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 668 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)\n (va_op_reg_opr64_reg64 rRdi) 40 Public ctx_b 5) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 669 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx)\n (va_op_reg_opr64_reg64 rRdi) 48 Public ctx_b 6) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 670 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (va_quick_Poly1305_add_key_s ()) (fun (va_s:va_state) _ -> let (h:int) =\n Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in\n va_qAssertBy va_range1\n \"***** PRECONDITION NOT MET AT line 673 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n (h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in) key_r key_s\n (Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s)\n inp_b)) len_in) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 674 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n true (fun _ -> va_reveal_eq (`%mod2_128) mod2_128 mod2_128) (fun _ -> va_reveal_opaque\n (`%mod2_128) mod2_128) (va_QLemma va_range1\n \"***** PRECONDITION NOT MET AT line 674 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****\"\n true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)\n (va_QEmpty (())))) (va_QEmpty ((h)))))))))))))) (qblock va_mods (fun (va_s:va_state) ->\n va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in va_QEmpty\n ((h)))))))))))))))))))))))))))", "val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 3 va_s0) in let\n (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let\n (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 4 va_s0) in\n avx_enabled /\\ sse_enabled /\\ Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 5 va_s0) ==\n Vale.Math.Poly2_s.monomial 127 /\\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift\n (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 3 va_s0) in let\n (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let\n (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 4 va_s0) in\n Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\\\n va_state_eq va_sM (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM\n (va_update_flags va_sM (va_update_ok va_sM va_s0)))))))\nlet va_lemma_ShiftKey1_128 va_b0 va_s0 f =\n let (va_mods:va_mods_t) = [va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags; va_Mod_ok] in\n let va_qc = va_qcode_ShiftKey1_128 va_mods f in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 68 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (va_get_ok va_sM) /\\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32\n (va_get_xmm 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let\n (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 4 va_s0) in\n label va_range1\n \"***** POSTCONDITION NOT MET AT line 85 column 50 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GF128_Init.vaf *****\"\n (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_xmm 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h)))\n in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_flags; va_Mod_ok]) va_sM\n va_s0;\n (va_sM, va_fM)", "val Hacl.Streaming.SHA1.reset = Hacl.Streaming.Functor.reset_st Hacl.Streaming.SHA1.hacl_sha1\n (FStar.Ghost.hide (FStar.Ghost.reveal (FStar.Ghost.hide ())))\n (Stateful?.s Hacl.Streaming.SHA1.state_t_sha1 ())\n (FStar.Ghost.erased Prims.unit)\nlet reset = F.reset hacl_sha1 (G.hide ()) (state_t_sha1.s ()) (G.erased unit)", "val va_quick_Ctr32_ghash_6_prelude\n (alg: algorithm)\n (scratch_b: buffer128)\n (key_words: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n (ctr_orig: quad32)\n : (va_quickCode unit (va_code_Ctr32_ghash_6_prelude alg))\nlet va_quick_Ctr32_ghash_6_prelude (alg:algorithm) (scratch_b:buffer128) (key_words:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (ctr_orig:quad32) : (va_quickCode unit\n (va_code_Ctr32_ghash_6_prelude alg)) =\n (va_QProc (va_code_Ctr32_ghash_6_prelude alg) ([va_Mod_flags; va_Mod_mem_heaplet 3; va_Mod_reg64\n rR11; va_Mod_xmm 15; va_Mod_xmm 14; va_Mod_xmm 13; va_Mod_xmm 12; va_Mod_xmm 11; va_Mod_xmm 10;\n va_Mod_xmm 9; va_Mod_xmm 4; va_Mod_xmm 2; va_Mod_mem]) (va_wp_Ctr32_ghash_6_prelude alg\n scratch_b key_words round_keys keys_b ctr_orig) (va_wpProof_Ctr32_ghash_6_prelude alg scratch_b\n key_words round_keys keys_b ctr_orig))", "val Hacl.Spec.Poly1305.Field32xN.tup64_5 = Type0\nlet tup64_5 = (uint64 & uint64 & uint64 & uint64 & uint64)" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_256.fsti", "name": "Hacl.Streaming.Poly1305_256.alloca" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_32.fsti", "name": "Hacl.Streaming.Poly1305_32.alloca" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_256.fsti", "name": "Hacl.Streaming.Poly1305_256.malloc" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_32.fsti", "name": "Hacl.Streaming.Poly1305_32.malloc" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_256.fsti", "name": "Hacl.Streaming.Poly1305_256.digest" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_256.fsti", "name": "Hacl.Streaming.Poly1305_256.free" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_128.fst", "name": "Hacl.Streaming.Blake2s_128.alloca" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_32.fsti", "name": "Hacl.Streaming.Poly1305_32.digest" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_32.fsti", "name": "Hacl.Streaming.Poly1305_32.free" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_256.fsti", "name": "Hacl.Streaming.Poly1305_256.reset" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_32.fsti", "name": "Hacl.Streaming.Poly1305_32.reset" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_256.fsti", "name": "Hacl.Streaming.Poly1305_256.update" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_32.fsti", "name": "Hacl.Streaming.Poly1305_32.update" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.alloca_512" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.alloca_256" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_32.fst", "name": "Hacl.Streaming.Blake2s_32.alloca" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_128.fst", "name": "Hacl.Streaming.Blake2s_128.malloc" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.alloca_384" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.alloca_224" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.MD5.fst", "name": "Hacl.Streaming.MD5.alloca" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.malloc_512" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA1.fst", "name": "Hacl.Streaming.SHA1.alloca" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_32.fst", "name": "Hacl.Streaming.Blake2s_32.malloc" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.malloc_256" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.malloc_384" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.malloc_224" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Functor.fsti", "name": "Hacl.Streaming.Functor.alloca_st" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Keccak.fst", "name": "Hacl.Streaming.Keccak.malloc" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.MD5.fst", "name": "Hacl.Streaming.MD5.malloc" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.poly1305_key" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA1.fst", "name": "Hacl.Streaming.SHA1.malloc" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_128.fst", "name": "Hacl.Streaming.Blake2s_128.digest" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_128.fst", "name": "Hacl.Streaming.Blake2s_128.free" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_32.fsti", "name": "Hacl.Streaming.Poly1305_32.state_t" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305_256.fsti", "name": "Hacl.Streaming.Poly1305_256.state_t" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.copy_512" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_128.fst", "name": "Hacl.Streaming.Blake2s_128.update" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.update_" }, { "project_name": "hacl-star", "file_name": "Hacl.Chacha20Poly1305_128.fst", "name": "Hacl.Chacha20Poly1305_128.poly1305_padded_128" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.copy_256" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_128.fst", "name": "Hacl.Streaming.Blake2s_128.reset" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Functor.fsti", "name": "Hacl.Streaming.Functor.malloc_st" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.free_512" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_32.fst", "name": "Hacl.Streaming.Blake2s_32.free" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.update_224_256" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_32.fst", "name": "Hacl.Streaming.Blake2s_32.digest" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.update'" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.free_256" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.digest_512" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.update__" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.finish_" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.update_384_512" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.reset_512" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.reset_256" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA1.fst", "name": "Hacl.Streaming.SHA1.copy" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_32.fst", "name": "Hacl.Streaming.Blake2s_32.update" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.digest_256" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.block" }, { "project_name": "hacl-star", "file_name": "Hacl.Chacha20Poly1305_256.fst", "name": "Hacl.Chacha20Poly1305_256.poly1305_padded_256" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2.Common.fst", "name": "Hacl.Streaming.Blake2.Common.k" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.MD5.fst", "name": "Hacl.Streaming.MD5.copy" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.MD5.fst", "name": "Hacl.Streaming.MD5.digest" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.t" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.digest_224" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA1.fst", "name": "Hacl.Streaming.SHA1.digest" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.reset_224" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.reset_384" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.fsti", "name": "Hacl.Impl.Poly1305.poly1305_init_st" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.spec" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2s_32.fst", "name": "Hacl.Streaming.Blake2s_32.reset" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA2.fst", "name": "Hacl.Streaming.SHA2.digest_384" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Keccak.fst", "name": "Hacl.Streaming.Keccak.get_alg" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Functor.fsti", "name": "Hacl.Streaming.Functor.free_st" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.MD5.fst", "name": "Hacl.Streaming.MD5.free" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Keccak.fst", "name": "Hacl.Streaming.Keccak.digest_" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.update_last" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA1.fst", "name": "Hacl.Streaming.SHA1.free" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.fsti", "name": "Hacl.Impl.Poly1305.poly1305_ctx" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Chacha20Poly1305.fst", "name": "Hacl.Impl.Chacha20Poly1305.poly1305_do_" }, { "project_name": "hacl-star", "file_name": "Hacl.Chacha20Poly1305_32.fst", "name": "Hacl.Chacha20Poly1305_32.poly1305_padded_32" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Keccak.fst", "name": "Hacl.Streaming.Keccak.copy" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Keccak.fst", "name": "Hacl.Streaming.Keccak.free" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.MD.fst", "name": "Hacl.Streaming.MD.hacl_md" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA1.fst", "name": "Hacl.Streaming.SHA1.update" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Functor.fsti", "name": "Hacl.Streaming.Functor.copy_st" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.fsti", "name": "Hacl.Impl.Poly1305.poly1305_update_st" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_quick_Poly1305_impl" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Hash.Incremental.fst", "name": "EverCrypt.Hash.Incremental.malloc" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.MD5.fst", "name": "Hacl.Streaming.MD5.update" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.fsti", "name": "Hacl.Impl.Poly1305.poly1305_mac_st" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.update_multi'" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.update_last'" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.MD.fst", "name": "Hacl.Streaming.MD.state_t" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_wp_Poly1305_impl" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Poly1305.fst", "name": "Hacl.Streaming.Poly1305.update_multi" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.X64.fst", "name": "Vale.Poly1305.X64.va_qcode_Poly1305_impl" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GF128_Init.fst", "name": "Vale.AES.X64.GF128_Init.va_lemma_ShiftKey1_128" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.SHA1.fst", "name": "Hacl.Streaming.SHA1.reset" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESGCM.fst", "name": "Vale.AES.X64.AESGCM.va_quick_Ctr32_ghash_6_prelude" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Field32xN.fst", "name": "Hacl.Spec.Poly1305.Field32xN.tup64_5" } ], "selected_premises": [ "LowStar.Buffer.gcmalloc_of_list", "Hacl.Streaming.Interface.optional_key", "Hacl.Streaming.Functor.state", "Lib.IntTypes.size", "Lib.UpdateMulti.uint8", "Hacl.Streaming.Functor.uint8", "Hacl.Streaming.Interface.uint8", "Hacl.Streaming.Poly1305.uint8", "Lib.UpdateMulti.Lemmas.uint8", "Spec.Poly1305.zero", "LowStar.Buffer.trivial_preorder", "Lib.Buffer.as_seq", "Hacl.Impl.Poly1305.Fields.precomplen", "LowStar.Monotonic.Buffer.length", "Hacl.Streaming.Interface.uint32", "Hacl.Streaming.Functor.uint32", "Hacl.Streaming.Poly1305.uint32", "Hacl.Streaming.Poly1305.as_lib_k", "LowStar.ConstBuffer.qbuf_pre", "Lib.Buffer.modifies", "LowStar.Monotonic.Buffer.srel", "Hacl.Streaming.Functor.invariant", "Spec.Poly1305.size_block", "LowStar.BufferOps.op_Bang_Star", "Lib.Buffer.loc", "Hacl.Spec.Poly1305.Vec.size_block", "Lib.Buffer.lbuffer", "Lib.Buffer.gsub", "Lib.Buffer.disjoint", "Hacl.Streaming.Poly1305.t", "Hacl.Streaming.Poly1305.as_lib", "Lib.IntTypes.u8", "Hacl.Streaming.Poly1305.finish_", "Hacl.Streaming.Poly1305.block", "Hacl.Impl.Poly1305.Fields.fas_nat", "Hacl.Streaming.Poly1305.poly1305", "Spec.Poly1305.size_key", "Hacl.Streaming.Poly1305.as_raw", "Hacl.Impl.Poly1305.Fields.nlimb", "Hacl.Streaming.Poly1305.update'", "Hacl.Impl.Poly1305.Fields.nelem", "Hacl.Streaming.Functor.footprint", "Lib.IntTypes.max_size_t", "Hacl.Streaming.Poly1305.poly1305_key", "LowStar.ImmutableBuffer.immutable_preorder", "Lib.Buffer.lbuffer_t", "Spec.Poly1305.felem", "Hacl.Streaming.Poly1305.stateful_poly1305_ctx", "Lib.Sequence.createL", "Hacl.Streaming.Poly1305.spec", "Hacl.Impl.Poly1305.Fields.limb", "Hacl.Spec.Poly1305.Vec.pfadd", "Lib.Buffer.buffer_t", "Hacl.Impl.Poly1305.Fields.wide", "Lib.Sequence.seq", "Hacl.Impl.Poly1305.Field32xN.fas_nat", "Hacl.Streaming.Poly1305_128.poly1305_128_state", "Lib.Sequence.lseq", "Lib.IntTypes.range", "Hacl.Impl.Poly1305.Fields.width", "Spec.AES.to_elem", "Lib.IntTypes.uint_t", "Hacl.Streaming.Poly1305.update_last_not_block_is_update", "Spec.Poly1305.poly1305_update1", "Lib.Sequence.to_seq", "Hacl.Streaming.Poly1305.update_last_block_is_update", "Spec.AES.elem", "Lib.IntTypes.v", "Spec.Poly1305.poly1305_finish", "Hacl.Streaming.Functor.update_pre", "Hacl.Impl.Poly1305.Field32xN.precomp_r", "Lib.IntVector.width", "Lib.IntTypes.int_t", "Lib.Buffer.eq_or_disjoint", "Hacl.Impl.Poly1305.poly1305_ctx", "Lib.Sequence.length", "Lib.IntTypes.u32", "Hacl.Streaming.Poly1305.update_multi", "FStar.Integers.op_Less_Equals", "Hacl.Spec.Poly1305.Vec.prime", "Lib.IntTypes.uint_v", "Hacl.Streaming.Poly1305.num_lanes", "Hacl.Spec.Poly1305.Vec.to_elem", "Lib.Buffer.op_Bar_Plus_Bar", "Lib.ByteSequence.lbytes", "FStar.Heap.trivial_preorder", "FStar.Integers.op_Greater_Equals", "Hacl.Streaming.Poly1305_128.mac", "Hacl.Impl.Poly1305.Fields.feval", "Lib.Buffer.cbuffer", "Hacl.Impl.Poly1305.Field32xN.feval", "FStar.Integers.op_Less", "Hacl.Spec.Poly1305.Field32xN.felem5", "Hacl.Spec.Poly1305.Vec.zero", "Hacl.Impl.Poly1305.Fields.felem_fits", "Hacl.Impl.Poly1305.Fields.op_String_Access", "Hacl.Impl.Poly1305.Field32xN.op_String_Access", "Hacl.Streaming.Poly1305.with_or_without_r", "Hacl.Impl.Poly1305.Field32xN.felem", "Lib.Buffer.clbuffer" ], "source_upto_this": "module Hacl.Streaming.Poly1305_128\n\nmodule G = FStar.Ghost\nmodule F = Hacl.Streaming.Functor\nmodule I = Hacl.Streaming.Interface\n\nopen Hacl.Impl.Poly1305.Fields\nopen Hacl.Streaming.Poly1305\n\n#set-options \"--fuel 0 --ifuel 0 --z3rlimit 100\"\n\n/// Type abbreviation - makes KaRaMeL use pretty names in the generated code\nlet state_t = F.state_s (poly1305 M128) () (t M128) (poly1305_key.I.s ())\n\nnoextract", "sketch": [ "Step 1: The definition is about allocating a state for the Poly1305 streaming API using the Functor's allocation function. It specifies the types involved in the allocation process.\nStep 2: The implementation will use the `alloca_st` function from the `Hacl.Streaming.Functor` module, parameterized with the Poly1305 type for the M128 field, and the associated key type.", "Step 1: The definition is about creating an allocation function `alloca` for the Poly1305 streaming state. This function will allocate memory for the Poly1305 state, which is parameterized by the M128 field.\nStep 2: The implementation will use the `alloca_st` function from the `Hacl.Streaming.Functor` module, specifying the type parameters for the Poly1305 state, the unit type, the Poly1305 key type, and the stateful type for the Poly1305 key.", "Step 1: The definition is about allocating memory for the Poly1305 state using the `alloca_st` function from the `Hacl.Streaming.Functor` module. This function is specialized for the Poly1305 algorithm with the M128 field.\nStep 2: The implementation will use the `alloca_st` function, specifying the types for the Poly1305 state, the unit type, the Poly1305 key, and the stateful context.", "Step 1: The definition is about allocating memory for a Poly1305 state in the context of the Hacl.Streaming.Functor module. This involves creating a new state for the Poly1305 algorithm using the M128 field.\nStep 2: The implementation will use the `alloca_st` function from the Hacl.Streaming.Functor module to allocate the state. This function will be parameterized with the Poly1305 type, the M128 field, and the appropriate key type.", "Step 1: The definition `alloca` is about allocating and initializing a state for the Poly1305 streaming API with the M128 field. This involves setting up the initial state for the Poly1305 algorithm, which is used for cryptographic message authentication.\nStep 2: The implementation will use the `Hacl.Streaming.Functor.alloca_st` function to allocate and initialize the state. This function takes four type parameters: the Poly1305 algorithm with the M128 field, an empty tuple, the Poly1305 state type with the M128 field, and the stateful key type for Poly1305.", "Step 1: The definition `alloca` is about allocating a state for the Poly1305 streaming authenticator. It uses the `alloca_st` function from the `Hacl.Streaming.Functor` module to allocate and initialize the state.\nStep 2: The implementation involves specifying the type parameters for `alloca_st` which are the Poly1305 implementation for the `M128` field, an empty unit type, the type `t` for Poly1305 with `M128`, and the state type for the Poly1305 key.", "Step 1: The definition `alloca` is a function type that allocates memory for the Poly1305 state. It uses the `alloca_st` function from the `Hacl.Streaming.Functor` module.\nStep 2: The function type `alloca` takes four type parameters: the Poly1305 implementation for M128, an empty tuple, the Poly1305 state type for M128, and the stateful key type for Poly1305. The function itself does not have an implementation here, as it is only a type declaration.", "Step 1: The definition is about allocating memory for the Poly1305 state using the functor `alloca_st`. This involves creating a new state for the Poly1305 algorithm with the specified parameters.\nStep 2: The implementation will use the `alloca_st` function from the `Hacl.Streaming.Functor` module, specifying the Poly1305 type with the `M128` field, and the corresponding key type. The state will be initialized accordingly.", "Step 1: The definition is about allocating a state for the Poly1305 streaming API using the Functor's allocation function. This involves creating an initial state for the Poly1305 algorithm with the specified parameters.\nStep 2: The implementation will use the `alloca_st` function from the `Hacl.Streaming.Functor` module. It will specify the `poly1305` function with the `M128` field, and the types for the state and key.", "Step 1: The definition `alloca` is a type signature for a function that allocates memory for the Poly1305 state. It uses the `alloca_st` function from the `Hacl.Streaming.Functor` module.\nStep 2: The function takes four type parameters: the Poly1305 type with the field `M128`, an empty tuple `()`, the Poly1305 state type `t` with the field `M128`, and a stateful key type `poly1305_key` with an empty tuple `()`." ], "generated_solution": [ "let alloca = F.alloca_st (poly1305 M128) () (t M128) (poly1305_key.I.s ())", "let alloca = F.alloca_st (poly1305 M128) () (t M128) (poly1305_key.I.s ())", "let alloca = F.alloca_st (poly1305 M128) () (t M128) (poly1305_key.I.s ())", "let alloca = F.alloca_st (poly1305 M128) () (t M128) (poly1305_key.I.s ())", "let alloca = F.alloca_st (poly1305 M128) () (t M128) (poly1305_key.I.s ())", "let alloca = F.alloca_st (poly1305 M128) () (t M128) (poly1305_key.I.s ())", "val alloca : Hacl.Streaming.Functor.alloca_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M128)\n ()\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M128)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())", "let alloca = F.alloca_st (poly1305 M128) () (t M128) (poly1305_key.I.s ())", "let alloca = F.alloca_st (poly1305 M128) () (t M128) (poly1305_key.I.s ())", "val alloca : Hacl.Streaming.Functor.alloca_st (Hacl.Streaming.Poly1305.poly1305 Hacl.Impl.Poly1305.Fields.M128)\n ()\n (Hacl.Streaming.Poly1305.t Hacl.Impl.Poly1305.Fields.M128)\n (Stateful?.s Hacl.Streaming.Poly1305.poly1305_key ())" ] }, { "file_name": "FStar.Pointer.Derived1.fst", "name": "FStar.Pointer.Derived1.loc_disjoint_gpointer_of_buffer_cell_l", "opens_and_abbrevs": [ { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "abbrev": "HH", "full_module": "FStar.HyperStack" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "abbrev": "HH", "full_module": "FStar.HyperStack" }, { "open": "FStar.Pointer.Base" }, { "open": "FStar.Pointer" }, { "open": "FStar.Pointer" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val loc_disjoint_gpointer_of_buffer_cell_l\n (l: loc)\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint (loc_buffer b) l))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i)) l))\n [SMTPat (loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i)) l)]", "source_definition": "let loc_disjoint_gpointer_of_buffer_cell_l l #t b i =\n loc_disjoint_includes (loc_buffer b) l (loc_pointer (gpointer_of_buffer_cell b i)) l", "source_range": { "start_line": 103, "start_col": 0, "end_line": 104, "end_col": 86 }, "interleaved": false, "definition": "fun l b i ->\n FStar.Pointer.Base.loc_disjoint_includes (FStar.Pointer.Base.loc_buffer b)\n l\n (FStar.Pointer.Base.loc_pointer (FStar.Pointer.Base.gpointer_of_buffer_cell b i))\n l", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "FStar.Pointer.Base.loc", "FStar.Pointer.Base.typ", "FStar.Pointer.Base.buffer", "FStar.UInt32.t", "FStar.Pointer.Base.loc_disjoint_includes", "FStar.Pointer.Base.loc_buffer", "FStar.Pointer.Base.loc_pointer", "FStar.Pointer.Base.gpointer_of_buffer_cell", "Prims.unit" ], "proof_features": [], "is_simple_lemma": true, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "l: FStar.Pointer.Base.loc -> b: FStar.Pointer.Base.buffer t -> i: FStar.UInt32.t\n -> FStar.Pervasives.Lemma\n (requires\n FStar.UInt32.v i < FStar.UInt32.v (FStar.Pointer.Base.buffer_length b) /\\\n FStar.Pointer.Base.loc_disjoint (FStar.Pointer.Base.loc_buffer b) l)\n (ensures\n FStar.UInt32.v i < FStar.UInt32.v (FStar.Pointer.Base.buffer_length b) /\\\n FStar.Pointer.Base.loc_disjoint (FStar.Pointer.Base.loc_pointer (FStar.Pointer.Base.gpointer_of_buffer_cell\n b\n i))\n l)\n [\n SMTPat (FStar.Pointer.Base.loc_disjoint (FStar.Pointer.Base.loc_pointer (FStar.Pointer.Base.gpointer_of_buffer_cell\n b\n i))\n l)\n ]", "prompt": "let loc_disjoint_gpointer_of_buffer_cell_l l #t b i =\n ", "expected_response": "loc_disjoint_includes (loc_buffer b) l (loc_pointer (gpointer_of_buffer_cell b i)) l", "source": { "project_name": "FStar", "file_name": "ulib/legacy/FStar.Pointer.Derived1.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.Pointer.Derived1.fst", "checked_file": "dataset/FStar.Pointer.Derived1.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.UInt32.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.HyperStack.ST.fsti.checked", "dataset/FStar.HyperStack.fst.checked" ] }, "definitions_in_context": [ "let includes_gfield_gen #t p #l q fd =\n includes_gfield q fd;\n includes_trans p q (gfield q fd)", "val includes_gfield_gen\n (#t: typ)\n (p: pointer t)\n (#l: struct_typ)\n (q: pointer (TStruct l))\n (fd: struct_field l)\n: Lemma\n (requires (includes p q))\n (ensures (includes p (gfield q fd)))\n [SMTPat (includes p (gfield q fd))]", "let includes_gufield_gen #t p #l q fd =\n includes_gufield q fd;\n includes_trans p q (gufield q fd)", "let includes_gcell_gen #t p #length #value q i =\n includes_gcell q i;\n includes_trans p q (gcell q i)", "val includes_gufield_gen\n (#t: typ)\n (p: pointer t)\n (#l: union_typ)\n (q: pointer (TUnion l))\n (fd: struct_field l)\n: Lemma\n (requires (includes p q))\n (ensures (includes p (gufield q fd)))\n [SMTPat (includes p (gufield q fd))]", "let loc_includes_union_assoc_r2l s1 s2 s3 s =\n loc_includes_trans (loc_union (loc_union s1 s2) s3) (loc_union s1 (loc_union s2 s3)) s", "let loc_includes_union_assoc_l2r s1 s2 s3 s =\n loc_includes_trans (loc_union s1 (loc_union s2 s3)) (loc_union (loc_union s1 s2) s3) s", "let loc_includes_union_assoc_focalize_1 l1 l2 x r s =\n loc_includes_trans (loc_union l1 (loc_union (loc_union l2 x) r)) (loc_union (loc_union l1 l2) (loc_union x r)) s", "let loc_includes_union_assoc_focalize_2 l x r1 r2 s =\n loc_includes_trans (loc_union l (loc_union (loc_union x r1) r2)) (loc_union l (loc_union x (loc_union r1 r2))) s", "val includes_gcell_gen\n (#t: typ)\n (p: pointer t)\n (#length: array_length_t)\n (#value: typ)\n (q: pointer (TArray length value))\n (i: UInt32.t)\n: Lemma\n (requires (includes p q /\\ UInt32.v i < UInt32.v length))\n (ensures (UInt32.v i < UInt32.v length /\\ includes p (gcell q i)))\n [SMTPat (includes p (gcell q i))]", "let loc_includes_region_union_r l s1 s2 =\n loc_includes_trans (loc_union l (loc_regions s1)) (loc_union (loc_regions s1) l) (loc_regions s2)", "let loc_includes_region_union_assoc l r s1 s2 =\n loc_includes_trans (loc_union l (loc_union (loc_regions s1) r)) (loc_union (loc_regions s1) (loc_union l r)) (loc_regions s2)", "let loc_disjoint_none_l s =\n loc_disjoint_none_r s;\n loc_disjoint_sym s loc_none", "let loc_disjoint_union_l s s1 s2 =\n loc_disjoint_sym s1 s;\n loc_disjoint_sym s2 s;\n loc_disjoint_union_r s s1 s2;\n loc_disjoint_sym s (loc_union s1 s2)", "val loc_includes_union_assoc_r2l\n (s1 s2 s3 s: loc)\n: Lemma\n (requires (loc_includes (loc_union s1 (loc_union s2 s3)) s))\n (ensures (loc_includes (loc_union (loc_union s1 s2) s3) s))\n [SMTPat (loc_includes (loc_union (loc_union s1 s2) s3) s)]", "let loc_disjoint_gfield_r p #l q fd =\n loc_disjoint_includes p (loc_pointer q) p (loc_pointer (gfield q fd))", "val loc_includes_union_assoc_l2r\n (s1 s2 s3 s: loc)\n: Lemma\n (requires (loc_includes (loc_union (loc_union s1 s2) s3) s))\n (ensures (loc_includes (loc_union s1 (loc_union s2 s3)) s))\n [SMTPat (loc_includes (loc_union s1 (loc_union s2 s3)) s)]", "let loc_disjoint_gfield_l p #l q fd =\n loc_disjoint_sym (loc_pointer q) p;\n loc_disjoint_gfield_r p q fd;\n loc_disjoint_sym p (loc_pointer (gfield q fd))", "let loc_disjoint_gufield_r p #l q fd =\n loc_disjoint_includes p (loc_pointer q) p (loc_pointer (gufield q fd))", "val loc_includes_union_assoc_focalize_1\n (l1 l2 x r s: loc)\n: Lemma\n (requires (loc_includes (loc_union (loc_union l1 l2) (loc_union x r)) s))\n (ensures (loc_includes (loc_union l1 (loc_union (loc_union l2 x) r)) s))\n [SMTPat (loc_includes (loc_union l1 (loc_union (loc_union l2 x) r)) s)]", "let loc_disjoint_gufield_l p #l q fd =\n loc_disjoint_sym (loc_pointer q) p;\n loc_disjoint_gufield_r p q fd;\n loc_disjoint_sym p (loc_pointer (gufield q fd))", "val loc_includes_union_assoc_focalize_2\n (l x r1 r2 s: loc)\n: Lemma\n (requires (loc_includes (loc_union l (loc_union x (loc_union r1 r2))) s))\n (ensures (loc_includes (loc_union l (loc_union (loc_union x r1) r2)) s))\n [SMTPat (loc_includes (loc_union l (loc_union (loc_union x r1) r2)) s)]", "let loc_disjoint_gcell_r p #value #len q i =\n loc_disjoint_includes p (loc_pointer q) p (loc_pointer (gcell q i))", "let loc_disjoint_gcell_l p #value #len q i =\n loc_disjoint_sym (loc_pointer q) p;\n loc_disjoint_gcell_r p q i;\n loc_disjoint_sym p (loc_pointer (gcell q i))", "val loc_includes_region_union_r\n (l: loc)\n (s1 s2: Set.set HH.rid)\n: Lemma\n (requires (loc_includes l (loc_regions (Set.intersect s2 (Set.complement s1)))))\n (ensures (loc_includes (loc_union l (loc_regions s1)) (loc_regions s2)))\n [SMTPat (loc_includes (loc_union l (loc_regions s1)) (loc_regions s2))]", "let loc_disjoint_gsingleton_buffer_of_pointer_r l #t p =\n loc_disjoint_includes l (loc_pointer p) l (loc_buffer (gsingleton_buffer_of_pointer p))", "let loc_disjoint_gsingleton_buffer_of_pointer_l l #t p =\n loc_disjoint_sym (loc_pointer p) l;\n loc_disjoint_gsingleton_buffer_of_pointer_r l p;\n loc_disjoint_sym l (loc_buffer (gsingleton_buffer_of_pointer p))", "val loc_includes_region_union_assoc\n (l r: loc)\n (s1 s2: Set.set HH.rid)\n: Lemma\n (requires (loc_includes (loc_union l r)) (loc_regions (Set.intersect s2 (Set.complement s1))))\n (ensures (loc_includes (loc_union l (loc_union (loc_regions s1) r)) (loc_regions s2)))\n [SMTPat (loc_includes (loc_union l (loc_union (loc_regions s1) r)) (loc_regions s2))]", "let loc_disjoint_gbuffer_of_array_pointer_r l #t #len p =\n loc_disjoint_includes l (loc_pointer p) l (loc_buffer (gbuffer_of_array_pointer p))", "let loc_disjoint_gbuffer_of_array_pointer_l l #t #len p =\n loc_disjoint_includes (loc_pointer p) l (loc_buffer (gbuffer_of_array_pointer p)) l", "let loc_disjoint_gpointer_of_buffer_cell_r l #t b i =\n loc_disjoint_includes l (loc_buffer b) l (loc_pointer (gpointer_of_buffer_cell b i))" ], "closest": [ "val loc_disjoint_gpointer_of_buffer_cell_l (l: loc) (#t: typ) (b: buffer t) (i: UInt32.t)\n : Lemma (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint (loc_buffer b) l))\n (ensures\n (UInt32.v i < UInt32.v (buffer_length b) /\\\n loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i)) l))\n [SMTPat (loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i)) l)]\nlet loc_disjoint_gpointer_of_buffer_cell_l\n (l: loc)\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint (loc_buffer b) l))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i)) l))\n [SMTPat (loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i)) l)]\n= loc_disjoint_includes (loc_buffer b) l (loc_pointer (gpointer_of_buffer_cell b i)) l", "val loc_disjoint_gpointer_of_buffer_cell_r (l: loc) (#t: typ) (b: buffer t) (i: UInt32.t)\n : Lemma (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint l (loc_buffer b)))\n (ensures\n (UInt32.v i < UInt32.v (buffer_length b) /\\\n loc_disjoint l (loc_pointer (gpointer_of_buffer_cell b i))))\n [SMTPat (loc_disjoint l (loc_pointer (gpointer_of_buffer_cell b i)))]\nlet loc_disjoint_gpointer_of_buffer_cell_r\n (l: loc)\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint l (loc_buffer b)))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_disjoint l (loc_pointer (gpointer_of_buffer_cell b i))))\n [SMTPat (loc_disjoint l (loc_pointer (gpointer_of_buffer_cell b i)))]\n= loc_disjoint_includes l (loc_buffer b) l (loc_pointer (gpointer_of_buffer_cell b i))", "val loc_disjoint_gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n (i1: UInt32.t)\n (i2: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i1 < UInt32.v (buffer_length b) /\\\n UInt32.v i2 < UInt32.v (buffer_length b) /\\ (\n UInt32.v i1 <> UInt32.v i2\n )))\n (ensures (\n UInt32.v i1 < UInt32.v (buffer_length b) /\\\n UInt32.v i2 < UInt32.v (buffer_length b) /\\\n loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i1)) (loc_pointer (gpointer_of_buffer_cell b i2))\n ))\n [SMTPat (loc_disjoint (loc_pointer (gpointer_of_buffer_cell b i1)) (loc_pointer (gpointer_of_buffer_cell b i2)))]\nlet loc_disjoint_gpointer_of_buffer_cell #t b i1 i2 =\n MG.loc_disjoint_aloc_intro #_ #cls #(frameOf_buffer b) #(buffer_as_addr b) #(frameOf_buffer b) #(buffer_as_addr b) (LocPointer (gpointer_of_buffer_cell b i1)) (LocPointer (gpointer_of_buffer_cell b i2))", "val loc_includes_gpointer_of_array_cell\n (l: loc)\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Lemma\n (requires (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_includes l (loc_buffer b)))\n (ensures (UInt32.v i < UInt32.v (buffer_length b) /\\ loc_includes l (loc_pointer (gpointer_of_buffer_cell b i))))\n [SMTPat (loc_includes l (loc_pointer (gpointer_of_buffer_cell b i)))]\nlet loc_includes_gpointer_of_array_cell l #t b i =\n MG.loc_includes_aloc #_ #cls #(frameOf_buffer b) #(buffer_as_addr b) (LocBuffer b) (LocPointer (gpointer_of_buffer_cell b i));\n MG.loc_includes_trans l (loc_buffer b) (loc_pointer (gpointer_of_buffer_cell b i))", "val loc_disjoint_gsub_buffer\n (#t: typ)\n (b: buffer t)\n (i1: UInt32.t)\n (len1: UInt32.t)\n (i2: UInt32.t)\n (len2: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 + UInt32.v len2 <= UInt32.v (buffer_length b) /\\ (\n UInt32.v i1 + UInt32.v len1 <= UInt32.v i2 \\/\n UInt32.v i2 + UInt32.v len2 <= UInt32.v i1\n )))\n (ensures (\n UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 + UInt32.v len2 <= UInt32.v (buffer_length b) /\\\n loc_disjoint (loc_buffer (gsub_buffer b i1 len1)) (loc_buffer (gsub_buffer b i2 len2))\n ))\n [SMTPat (loc_disjoint (loc_buffer (gsub_buffer b i1 len1)) (loc_buffer (gsub_buffer b i2 len2)))]\nlet loc_disjoint_gsub_buffer #t b i1 len1 i2 len2 =\n MG.loc_disjoint_aloc_intro #_ #cls #(frameOf_buffer b) #(buffer_as_addr b) #(frameOf_buffer b) #(buffer_as_addr b) (LocBuffer (gsub_buffer b i1 len1)) (LocBuffer (gsub_buffer b i2 len2))", "val loc_disjoint_gcell\n (#length: array_length_t)\n (#value: typ)\n (p: pointer (TArray length value))\n (i1: UInt32.t)\n (i2: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i1 < UInt32.v length /\\\n UInt32.v i2 < UInt32.v length /\\\n UInt32.v i1 <> UInt32.v i2\n ))\n (ensures (\n UInt32.v i1 < UInt32.v length /\\\n UInt32.v i2 < UInt32.v length /\\ \n loc_disjoint (loc_pointer (gcell p i1)) (loc_pointer (gcell p i2))\n ))\n [SMTPat (loc_disjoint (loc_pointer (gcell p i1)) (loc_pointer (gcell p i2)))]\nlet loc_disjoint_gcell #length #value p i1 i2 =\n MG.loc_disjoint_aloc_intro #_ #cls #(frameOf p) #(as_addr p) #(frameOf p) #(as_addr p) (LocPointer (gcell p i1)) (LocPointer (gcell p i2))", "val loc_disjoint_buffer_addresses\n (#t: typ)\n (p: buffer t)\n (r: HH.rid)\n (n: Set.set nat)\n: Lemma\n (requires (r <> frameOf_buffer p \\/ (~ (Set.mem (buffer_as_addr p) n))))\n (ensures (loc_disjoint (loc_buffer p) (loc_addresses r n)))\n [SMTPat (loc_disjoint (loc_buffer p) (loc_addresses r n))]\nlet loc_disjoint_buffer_addresses #t p r n =\n loc_disjoint_includes (loc_addresses (frameOf_buffer p) (Set.singleton (buffer_as_addr p))) (loc_addresses r n) (loc_buffer p) (loc_addresses r n)", "val loc_disjoint_buffer\n (#t1 #t2: Type)\n (b1: B.buffer t1)\n (b2: B.buffer t2)\n: Lemma\n (requires (B.disjoint b1 b2))\n (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2)))\n [SMTPatOr [\n [SMTPat (B.disjoint b1 b2)];\n [SMTPat (loc_disjoint (loc_buffer b1) (loc_buffer b2))];\n ]]\nlet loc_disjoint_buffer #t1 #t2 b1 b2 =\n MG.loc_disjoint_aloc_intro #_ #cls #(B.frameOf b1) #(B.as_addr b1) #(B.frameOf b2) #(B.as_addr b2) (LocBuffer b1) (LocBuffer b2)", "val loc_includes_gsingleton_buffer_of_pointer\n (l: loc)\n (#t: typ)\n (p: pointer t)\n: Lemma\n (requires (loc_includes l (loc_pointer p)))\n (ensures (loc_includes l (loc_buffer (gsingleton_buffer_of_pointer p))))\n [SMTPat (loc_includes l (loc_buffer (gsingleton_buffer_of_pointer p)))]\nlet loc_includes_gsingleton_buffer_of_pointer l #t p =\n MG.loc_includes_aloc #_ #cls #(frameOf p) #(as_addr p) (LocPointer p) (LocBuffer (gsingleton_buffer_of_pointer p));\n MG.loc_includes_trans l (loc_pointer p) (loc_buffer (gsingleton_buffer_of_pointer p))", "val loc_disjoint_gsub_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a)\n (b:mbuffer a rrel rel)\n (i1:UInt32.t) (len1:UInt32.t) (sub_rel1:srel a)\n (i2:UInt32.t) (len2:UInt32.t) (sub_rel2:srel a)\n :Lemma (requires (UInt32.v i1 + UInt32.v len1 <= (length b) /\\\n UInt32.v i2 + UInt32.v len2 <= (length b) /\\\n\t\t (UInt32.v i1 + UInt32.v len1 <= UInt32.v i2 \\/\n UInt32.v i2 + UInt32.v len2 <= UInt32.v i1)))\n (ensures (loc_disjoint (loc_buffer (mgsub sub_rel1 b i1 len1)) (loc_buffer (mgsub sub_rel2 b i2 len2))))\n [SMTPat (mgsub sub_rel1 b i1 len1); SMTPat (mgsub sub_rel2 b i2 len2)]\nlet loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 =\n loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2)", "val buffer_live_pointer_unused_in_disjoint\n (#t1 #t2: typ)\n (h: HS.mem)\n (b1: buffer t1)\n (b2: pointer t2)\n: Lemma\n (requires (buffer_live h b1 /\\ unused_in b2 h))\n (ensures (loc_disjoint (loc_buffer b1) (loc_pointer b2)))\n [SMTPat (buffer_live h b1); SMTPat (unused_in b2 h)]\nlet buffer_live_pointer_unused_in_disjoint #t1 #t2 h b1 b2 =\n MG.loc_disjoint_aloc_intro #_ #cls #(frameOf_buffer b1) #(buffer_as_addr b1) #(frameOf b2) #(as_addr b2) (LocBuffer b1) (LocPointer b2)", "val loc_disjoint_buffer_addresses\n (#t: Type)\n (p: B.buffer t)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (requires (r <> B.frameOf p \\/ (~ (Set.mem (B.as_addr p) n))))\n (ensures (loc_disjoint (loc_buffer p) (loc_addresses preserve_liveness r n)))\n [SMTPat (loc_disjoint (loc_buffer p) (loc_addresses preserve_liveness r n))]\nlet loc_disjoint_buffer_addresses #t p preserve_liveness r n =\n MG.loc_disjoint_aloc_addresses_intro #_ #cls #(B.frameOf p) #(B.as_addr p) (LocBuffer p) preserve_liveness r n", "val loc_includes_gsub_buffer_r\n (l: loc)\n (#t: Type)\n (b: B.buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= (B.length b) /\\ loc_includes l (loc_buffer b)))\n (ensures (UInt32.v i + UInt32.v len <= (B.length b) /\\ loc_includes l (loc_buffer (B.sub b i len))))\n [SMTPat (loc_includes l (loc_buffer (B.sub b i len)))]\nlet loc_includes_gsub_buffer_r l #t b i len =\n loc_includes_trans l (loc_buffer b) (loc_buffer (B.sub b i len))", "val pointer_live_buffer_unused_in_disjoint\n (#t1 #t2: typ)\n (h: HS.mem)\n (b1: pointer t1)\n (b2: buffer t2)\n: Lemma\n (requires (live h b1 /\\ buffer_unused_in b2 h))\n (ensures (loc_disjoint (loc_pointer b1) (loc_buffer b2)))\n [SMTPat (live h b1); SMTPat (buffer_unused_in b2 h)]\nlet pointer_live_buffer_unused_in_disjoint #t1 #t2 h b1 b2 =\n MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf_buffer b2) #(buffer_as_addr b2) (LocPointer b1) (LocBuffer b2)", "val buffer_live_unused_in_disjoint\n (#t1 #t2: typ)\n (h: HS.mem)\n (b1: buffer t1)\n (b2: buffer t2)\n: Lemma\n (requires (buffer_live h b1 /\\ buffer_unused_in b2 h))\n (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2)))\n [SMTPat (buffer_live h b1); SMTPat (buffer_unused_in b2 h)]\nlet buffer_live_unused_in_disjoint #t1 #t2 h b1 b2 =\n MG.loc_disjoint_aloc_intro #_ #cls #(frameOf_buffer b1) #(buffer_as_addr b1) #(frameOf_buffer b2) #(buffer_as_addr b2) (LocBuffer b1) (LocBuffer b2)", "val loc_aux_disjoint_pointer_buffer_sym (#t1 #t2: typ) (b1: buffer t1) (p2: pointer t2)\n : Lemma\n (loc_aux_disjoint_pointer (LocBuffer b1) p2 <==> loc_aux_disjoint_buffer (LocPointer p2) b1)\nlet loc_aux_disjoint_pointer_buffer_sym\n (#t1 #t2: typ)\n (b1: buffer t1)\n (p2: pointer t2)\n: Lemma\n (loc_aux_disjoint_pointer (LocBuffer b1) p2 <==> loc_aux_disjoint_buffer (LocPointer p2) b1)\n= Classical.forall_intro_2 (disjoint_sym'' t1 t2)", "val gpointer_of_buffer_cell_gsub_buffer' (#t: typ) (b: buffer t) (i1 len i2: UInt32.t)\n : Lemma\n (requires\n (UInt32.v i1 + UInt32.v len <= UInt32.v (buffer_length b) /\\ UInt32.v i2 < UInt32.v len))\n (ensures\n (UInt32.v i1 + UInt32.v len <= UInt32.v (buffer_length b) /\\ UInt32.v i2 < UInt32.v len /\\\n gpointer_of_buffer_cell (gsub_buffer b i1 len) i2 ==\n gpointer_of_buffer_cell b FStar.UInt32.(i1 +^ i2)))\n [SMTPat (gpointer_of_buffer_cell (gsub_buffer b i1 len) i2)]\nlet gpointer_of_buffer_cell_gsub_buffer'\n (#t: typ)\n (b: buffer t)\n (i1: UInt32.t)\n (len: UInt32.t)\n (i2: UInt32.t)\n: Lemma\n (requires (\n UInt32.v i1 + UInt32.v len <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 < UInt32.v len\n ))\n (ensures (\n UInt32.v i1 + UInt32.v len <= UInt32.v (buffer_length b) /\\\n UInt32.v i2 < UInt32.v len /\\\n gpointer_of_buffer_cell (gsub_buffer b i1 len) i2 == gpointer_of_buffer_cell b FStar.UInt32.(i1 +^ i2)\n ))\n [SMTPat (gpointer_of_buffer_cell (gsub_buffer b i1 len) i2)]\n= gpointer_of_buffer_cell_gsub_buffer b i1 len i2", "val loc_includes_gsub_buffer_r\n (l: loc)\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ loc_includes l (loc_buffer b)))\n (ensures (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ loc_includes l (loc_buffer (gsub_buffer b i len))))\n [SMTPat (loc_includes l (loc_buffer (gsub_buffer b i len)))]\nlet loc_includes_gsub_buffer_r l #t b i len =\n MG.loc_includes_aloc #_ #cls #(frameOf_buffer b) #(buffer_as_addr b) (LocBuffer b) (LocBuffer (gsub_buffer b i len));\n MG.loc_includes_trans l (loc_buffer b) (loc_buffer (gsub_buffer b i len))", "val loc_includes_gsub_buffer_r\n (l:loc)\n (#a:Type0) (#rrel #rel:srel a)\n (b:mbuffer a rrel rel) (i:UInt32.t) (len:UInt32.t) (sub_rel:srel a)\n: Lemma (requires (UInt32.v i + UInt32.v len <= (length b) /\\\n loc_includes l (loc_buffer b)))\n (ensures (loc_includes l (loc_buffer (mgsub sub_rel b i len))))\n [SMTPat (loc_includes l (loc_buffer (mgsub sub_rel b i len)))]\nlet loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel =\n let b' = mgsub sub_rel b i len in\n loc_includes_buffer b b';\n loc_includes_trans l (loc_buffer b) (loc_buffer b')", "val reference_live_buffer_unused_in_disjoint\n (#t1: Type0)\n (#t2: typ)\n (h: HS.mem)\n (b1: HS.reference t1)\n (b2: buffer t2)\n: Lemma\n (requires (HS.contains h b1 /\\ buffer_unused_in b2 h))\n (ensures (loc_disjoint (loc_addresses (HS.frameOf b1) (Set.singleton (HS.as_addr b1))) (loc_buffer b2)))\n [SMTPat (HS.contains h b1); SMTPat (buffer_unused_in b2 h)]\nlet reference_live_buffer_unused_in_disjoint #t1 #t2 h b1 b2 =\n loc_includes_addresses_buffer (frameOf_buffer b2) (Set.singleton (buffer_as_addr b2)) b2;\n loc_includes_refl (MG.loc_freed_mreference b1);\n MG.loc_disjoint_addresses #_ #cls false false (HS.frameOf b1) (frameOf_buffer b2) (Set.singleton (HS.as_addr b1)) (Set.singleton (buffer_as_addr b2));\n MG.loc_disjoint_includes #_ #cls (MG.loc_freed_mreference b1) (loc_addresses (frameOf_buffer b2) (Set.singleton (buffer_as_addr b2))) (MG.loc_freed_mreference b1) (loc_buffer b2)", "val loc_includes_gbuffer_of_array_pointer\n (l: loc)\n (#len: array_length_t)\n (#t: typ)\n (p: pointer (TArray len t))\n: Lemma\n (requires (loc_includes l (loc_pointer p)))\n (ensures (loc_includes l (loc_buffer (gbuffer_of_array_pointer p))))\n [SMTPat (loc_includes l (loc_buffer (gbuffer_of_array_pointer p)))]\nlet loc_includes_gbuffer_of_array_pointer l #len #t p =\n MG.loc_includes_aloc #_ #cls #(frameOf p) #(as_addr p) (LocPointer p) (LocBuffer (gbuffer_of_array_pointer p));\n MG.loc_includes_trans l (loc_pointer p) (loc_buffer (gbuffer_of_array_pointer p))", "val loc_disjoint_pointer_addresses\n (#t: typ)\n (p: pointer t)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (requires (r <> frameOf p \\/ (~ (Set.mem (as_addr p) n))))\n (ensures (loc_disjoint (loc_pointer p) (loc_addresses r n)))\n [SMTPat (loc_disjoint (loc_pointer p) (loc_addresses r n))]\nlet loc_disjoint_pointer_addresses #t p r n =\n loc_disjoint_includes (loc_addresses (frameOf p) (Set.singleton (as_addr p))) (loc_addresses r n) (loc_pointer p) (loc_addresses r n)", "val loc_disjoint_gfield\n (#l: struct_typ)\n (p: pointer (TStruct l))\n (fd1 fd2: struct_field l)\n: Lemma\n (requires (fd1 <> fd2))\n (ensures (loc_disjoint (loc_pointer (gfield p fd1)) (loc_pointer (gfield p fd2))))\n [SMTPat (loc_disjoint (loc_pointer (gfield p fd1)) (loc_pointer (gfield p fd2)))]\nlet loc_disjoint_gfield #l p fd1 fd2 =\n MG.loc_disjoint_aloc_intro #_ #cls #(frameOf p) #(as_addr p) #(frameOf p) #(as_addr p) (LocPointer (gfield p fd1)) (LocPointer (gfield p fd2))", "val mut_immut_disjoint (#t #t': _) (b: buffer_t MUT t) (ib: buffer_t IMMUT t') (h: HS.mem)\n : Lemma (requires (B.live h b /\\ B.live h ib))\n (ensures (disjoint b ib))\n [SMTPat (B.loc_disjoint (loc b) (loc ib)); SMTPat (B.live h b); SMTPat (B.live h ib)]\nlet mut_immut_disjoint #t #t' (b: buffer_t MUT t) (ib: buffer_t IMMUT t') (h: HS.mem):\n Lemma\n (requires (B.live h b /\\ B.live h ib))\n (ensures (disjoint b ib))\n [SMTPat (B.loc_disjoint (loc b) (loc ib)); SMTPat (B.live h b); SMTPat (B.live h ib)]\n=\n IB.buffer_immutable_buffer_disjoint b ib h", "val loc_disjoint_loc_buffer_from_to\n (#a: _) (#rrel #rel: _)\n (b: mbuffer a rrel rel)\n (from1 to1 from2 to2: U32.t)\n: Lemma\n (requires (U32.v to1 <= U32.v from2 \\/ U32.v to2 <= U32.v from1))\n (ensures (loc_disjoint (loc_buffer_from_to b from1 to1) (loc_buffer_from_to b from2 to2)))\nlet loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 =\n if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2\n then ()\n else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2)", "val address_liveness_insensitive_buffer (#t: Type) (b: B.buffer t) : Lemma\n (address_liveness_insensitive_locs `loc_includes` (loc_buffer b))\n [SMTPat (address_liveness_insensitive_locs `loc_includes` (loc_buffer b))]\nlet address_liveness_insensitive_buffer #t b =\n MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(B.frameOf b) #(B.as_addr b) (LocBuffer b)", "val pointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: HST.Stack (pointer t)\n (requires (fun h -> UInt32.v i < UInt32.v (buffer_length b) /\\ buffer_live h b))\n (ensures (fun h p h' -> UInt32.v i < UInt32.v (buffer_length b) /\\ h' == h /\\ p == gpointer_of_buffer_cell b i))\nlet pointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n i\n= match Buffer?.broot b with\n | BufferRootSingleton p -> p\n | BufferRootArray p ->\n _cell p FStar.UInt32.(Buffer?.bidx b +^ i)", "val loc_aux_disjoint_loc_aux_includes_buffer (l1 l2: loc_aux) (#t3: Type) (b3: B.buffer t3)\n : Lemma (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes_buffer l2 b3))\n (ensures (loc_aux_disjoint_buffer l1 b3))\nlet loc_aux_disjoint_loc_aux_includes_buffer\n (l1 l2: loc_aux)\n (#t3: Type)\n (b3: B.buffer t3)\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes_buffer l2 b3))\n (ensures (loc_aux_disjoint_buffer l1 b3))\n= match l2 with\n | LocBuffer b2 -> loc_aux_disjoint_buffer_includes l1 b2 b3", "val loc_aux_disjoint_buffer_sym (#t1 #t2: typ) (b1: buffer t1) (b2: buffer t2)\n : Lemma\n (loc_aux_disjoint_buffer (LocBuffer b1) b2 <==> loc_aux_disjoint_buffer (LocBuffer b2) b1)\nlet loc_aux_disjoint_buffer_sym\n (#t1 #t2: typ)\n (b1: buffer t1)\n (b2: buffer t2)\n: Lemma\n (loc_aux_disjoint_buffer (LocBuffer b1) b2 <==> loc_aux_disjoint_buffer (LocBuffer b2) b1)\n= Classical.forall_intro_2 (disjoint_sym'' t1 t2)", "val region_liveness_insensitive_buffer (#t: Type) (b: B.buffer t) : Lemma\n (region_liveness_insensitive_locs `loc_includes` (loc_buffer b))\n [SMTPat (region_liveness_insensitive_locs `loc_includes` (loc_buffer b))]\nlet region_liveness_insensitive_buffer #t b =\n MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(B.frameOf b) #(B.as_addr b) (LocBuffer b)", "val freeable_disjoint'\n (#a1 #a2: Type0)\n (#rrel1 #rel1: srel a1)\n (#rrel2 #rel2: srel a2)\n (b1: mbuffer a1 rrel1 rel1)\n (b2: mbuffer a2 rrel2 rel2)\n : Lemma (requires (freeable b1 /\\ length b2 > 0 /\\ disjoint b1 b2))\n (ensures (loc_disjoint (loc_addr_of_buffer b1) (loc_addr_of_buffer b2)))\n [SMTPat (freeable b1); SMTPat (disjoint b1 b2)]\nlet freeable_disjoint' (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2)\n (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2)\n :Lemma (requires (freeable b1 /\\ length b2 > 0 /\\ disjoint b1 b2))\n (ensures (loc_disjoint (loc_addr_of_buffer b1) (loc_addr_of_buffer b2)))\n [SMTPat (freeable b1); SMTPat (disjoint b1 b2)]\n = freeable_disjoint b1 b2", "val loc_includes_gsub_buffer_l\n (#t: typ)\n (b: buffer t)\n (i1: UInt32.t)\n (len1: UInt32.t)\n (i2: UInt32.t)\n (len2: UInt32.t)\n: Lemma\n (requires (UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b) /\\ UInt32.v i1 <= UInt32.v i2 /\\ UInt32.v i2 + UInt32.v len2 <= UInt32.v i1 + UInt32.v len1))\n (ensures (UInt32.v i1 + UInt32.v len1 <= UInt32.v (buffer_length b) /\\ UInt32.v i1 <= UInt32.v i2 /\\ UInt32.v i2 + UInt32.v len2 <= UInt32.v i1 + UInt32.v len1 /\\ loc_includes (loc_buffer (gsub_buffer b i1 len1)) (loc_buffer (gsub_buffer b i2 len2))))\n [SMTPat (loc_includes (loc_buffer (gsub_buffer b i1 len1)) (loc_buffer (gsub_buffer b i2 len2)))]\nlet loc_includes_gsub_buffer_l #t b i1 len1 i2 len2 =\n let b1 = gsub_buffer b i1 len1 in\n let b2 = gsub_buffer b1 (FStar.UInt32.sub i2 i1) len2 in\n MG.loc_includes_aloc #_ #cls #(frameOf_buffer b) #(buffer_as_addr b) (LocBuffer b1) (LocBuffer b2)", "val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2)\n (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2)\n :Lemma (requires ((frameOf b1 == frameOf b2 /\\ as_addr b1 == as_addr b2) ==>\n ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2)))\n (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2)))\nlet loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 =\n MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2)", "val mut_const_immut_disjoint (#t #t': _) (b: buffer_t MUT t) (ib: buffer_t CONST t') (h: HS.mem)\n : Lemma (requires (B.live h b /\\ B.live h (CB.as_mbuf ib) /\\ CB.qual_of #t' ib == CB.IMMUTABLE))\n (ensures (B.loc_disjoint (loc b) (loc ib)))\n [\n SMTPat (B.loc_disjoint (loc b) (loc ib));\n SMTPat (B.live h b);\n SMTPat (B.live h (CB.as_mbuf ib))\n ]\nlet mut_const_immut_disjoint #t #t' (b: buffer_t MUT t) (ib: buffer_t CONST t') (h: HS.mem):\n Lemma\n (requires (B.live h b /\\ B.live h (CB.as_mbuf ib) /\\ CB.qual_of #t' ib == CB.IMMUTABLE))\n (ensures (B.loc_disjoint (loc b) (loc ib)))\n [SMTPat (B.loc_disjoint (loc b) (loc ib)); SMTPat (B.live h b); SMTPat (B.live h (CB.as_mbuf ib))]\n=\n IB.buffer_immutable_buffer_disjoint #t #t' b (CB.as_mbuf #t' ib) h", "val loc_includes_gsub_buffer_l (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel)\n (i1:UInt32.t) (len1:UInt32.t) (sub_rel1:srel a)\n (i2:UInt32.t) (len2:UInt32.t) (sub_rel2:srel a)\n :Lemma (requires (UInt32.v i1 + UInt32.v len1 <= (length b) /\\\n UInt32.v i1 <= UInt32.v i2 /\\ UInt32.v i2 + UInt32.v len2 <= UInt32.v i1 + UInt32.v len1\n ))\n (ensures (loc_includes (loc_buffer (mgsub sub_rel1 b i1 len1)) (loc_buffer (mgsub sub_rel2 b i2 len2))))\n [SMTPat (mgsub sub_rel1 b i1 len1); SMTPat (mgsub sub_rel2 b i2 len2)]\nlet loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 =\n let b1 = mgsub sub_rel1 b i1 len1 in\n let b2 = mgsub sub_rel2 b i2 len2 in\n loc_includes_buffer b1 b2", "val gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n (i: UInt32.t)\n: Ghost (pointer t)\n (requires (UInt32.v i < UInt32.v (buffer_length b)))\n (ensures (fun _ -> True))\nlet gpointer_of_buffer_cell\n (#t: typ)\n (b: buffer t)\n i\n= match Buffer?.broot b with\n | BufferRootSingleton p -> p\n | BufferRootArray p ->\n gcell p FStar.UInt32.(Buffer?.bidx b +^ i)", "val mreference_live_buffer_unused_in_disjoint\n (#t1: Type)\n (#pre: Preorder.preorder t1)\n (#t2: Type)\n (h: HS.mem)\n (b1: HS.mreference t1 pre)\n (b2: B.buffer t2)\n: Lemma\n (requires (HS.contains h b1 /\\ B.unused_in b2 h))\n (ensures (loc_disjoint (loc_freed_mreference b1) (loc_buffer b2)))\n [SMTPat (HS.contains h b1); SMTPat (B.unused_in b2 h)]\nlet mreference_live_buffer_unused_in_disjoint #t1 #pre #t2 h b1 b2 =\n loc_disjoint_includes (loc_freed_mreference b1) (loc_freed_mreference (B.content b2)) (loc_freed_mreference b1) (loc_buffer b2)", "val live_loc_not_unused_in (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h:HS.mem)\n :Lemma (requires (live h b))\n (ensures (loc_not_unused_in h `loc_includes` loc_addr_of_buffer b))\n [SMTPat (live h b)]\nlet live_loc_not_unused_in #_ #_ #_ b h =\n unused_in_equiv b h;\n Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b);\n MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h;\n ()", "val g_rowi_disjoint_other: #a:Spec.alg -> #m:m_spec -> #b:Type -> st:state_p a m -> i:index_t -> x:buffer b ->\n Lemma(requires (disjoint st x))\n (ensures (disjoint (g_rowi st i) x))\n [SMTPat (disjoint (g_rowi st i) x)]\nlet g_rowi_disjoint_other #a #m #b st i x =\n assert (v (i *. row_len a m) + v (row_len a m) <= length st);\n LowStar.Monotonic.Buffer.loc_includes_gsub_buffer_r' #_ #(LowStar.Buffer.trivial_preorder (element_t a m)) #(LowStar.Buffer.trivial_preorder (element_t a m)) st (i *. row_len a m) (row_len a m)\n (LowStar.Buffer.trivial_preorder (element_t a m))", "val buffer_live_mreference_unused_in_disjoint\n (#t1: Type)\n (#t2: Type)\n (#pre: Preorder.preorder t2)\n (h: HS.mem)\n (b1: B.buffer t1)\n (b2: HS.mreference t2 pre)\n: Lemma\n (requires (B.live h b1 /\\ HS.unused_in b2 h))\n (ensures (loc_disjoint (loc_buffer b1) (loc_freed_mreference b2)))\n [SMTPat (B.live h b1); SMTPat (HS.unused_in b2 h)]\nlet buffer_live_mreference_unused_in_disjoint #t1 #t2 #pre h b1 b2 =\n loc_disjoint_includes (loc_freed_mreference (B.content b1)) (loc_freed_mreference b2) (loc_buffer b1) (loc_freed_mreference b2)", "val buffer_as_seq_gsingleton_buffer_of_pointer\n (#t: typ)\n (h: HS.mem)\n (p: pointer t)\n: Lemma\n (requires True)\n (ensures (buffer_as_seq h (gsingleton_buffer_of_pointer p) == Seq.create 1 (gread h p)))\n [SMTPat (buffer_as_seq h (gsingleton_buffer_of_pointer p))]\nlet buffer_as_seq_gsingleton_buffer_of_pointer #t h p =\n let Pointer from contents pth = p in\n match pth with\n | PathStep through to pth' (StepCell ln ty i) ->\n assert (through == TArray ln ty);\n assert (to == ty);\n assert (t == ty);\n let p' : pointer (TArray ln ty) = Pointer from contents pth' in\n let s : array ln (type_of_typ t) = gread h p' in\n let s1 = Seq.slice s (UInt32.v i) (UInt32.v i + 1) in\n let v = gread h p in\n assert (v == Seq.index s (UInt32.v i));\n let s2 = Seq.create 1 v in\n assert (Seq.length s1 == 1);\n assert (Seq.length s2 == 1);\n assert (Seq.index s1 0 == v);\n assert (Seq.index s2 0 == v);\n assert (Seq.equal s1 s2)\n | _ ->\n Seq.slice_length (Seq.create 1 (gread h p))", "val modifies_buffer_elim\n (#t1: typ)\n (b: buffer t1)\n (p: loc)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_buffer b) p /\\\n buffer_live h b /\\\n (UInt32.v (buffer_length b) == 0 ==> buffer_live h' b) /\\ // necessary for liveness, because all buffers of size 0 are disjoint for any memory location, so we cannot talk about their liveness individually without referring to a larger nonempty buffer\n modifies p h h'\n ))\n (ensures (\n buffer_live h' b /\\ (\n buffer_readable h b ==> (\n\tbuffer_readable h' b /\\\n\tbuffer_as_seq h b == buffer_as_seq h' b\n ))))\n [SMTPatOr [\n [ SMTPat (modifies p h h'); SMTPat (buffer_as_seq h b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (buffer_readable h b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (buffer_live h b) ];\n [ SMTPat (modifies p h h'); SMTPat (buffer_as_seq h' b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (buffer_readable h' b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (buffer_live h' b) ]\n ] ]\nlet modifies_buffer_elim #t1 b p h h' =\n if buffer_length b = 0ul\n then ()\n else modifies_buffer_elim' b p h h'", "val loc_includes_union_l_buffer\n (s1 s2: loc)\n (#a: Type0)\n (#rrel #rel: srel a)\n (b: mbuffer a rrel rel)\n : Lemma (requires (loc_includes s1 (loc_buffer b) \\/ loc_includes s2 (loc_buffer b)))\n (ensures (loc_includes (loc_union s1 s2) (loc_buffer b)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_buffer b))]\nlet loc_includes_union_l_buffer\n (s1 s2:loc)\n (#a:Type0) (#rrel #rel:srel a)\n (b:mbuffer a rrel rel)\n :Lemma (requires (loc_includes s1 (loc_buffer b) \\/ loc_includes s2 (loc_buffer b)))\n (ensures (loc_includes (loc_union s1 s2) (loc_buffer b)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_buffer b))]\n = loc_includes_union_l s1 s2 (loc_buffer b)", "val loc_aux_disjoint_buffer (l: loc_aux) (#t: typ) (b: buffer t) : GTot Type0\nlet loc_aux_disjoint_buffer\n (l: loc_aux)\n (#t: typ)\n (b: buffer t)\n: GTot Type0\n= forall (i: UInt32.t) . UInt32.v i < UInt32.v (buffer_length b) ==> loc_aux_disjoint_pointer l (gpointer_of_buffer_cell b i)", "val buffer_readable_gsub_buffer\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ buffer_readable h b))\n (ensures (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ buffer_readable h (gsub_buffer b i len)))\n [SMTPat (buffer_readable h (gsub_buffer b i len))]\nlet buffer_readable_gsub_buffer\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n len\n= Classical.forall_intro (Classical.move_requires (gpointer_of_buffer_cell_gsub_buffer b i len))", "val buffer_as_seq_gsub_buffer\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n (len: UInt32.t)\n: Lemma\n (requires (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b)))\n (ensures (UInt32.v i + UInt32.v len <= UInt32.v (buffer_length b) /\\ buffer_as_seq h (gsub_buffer b i len) == Seq.slice (buffer_as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)))\n [SMTPat (buffer_as_seq h (gsub_buffer b i len))]\nlet buffer_as_seq_gsub_buffer\n (#t: typ)\n (h: HS.mem)\n (b: buffer t)\n (i: UInt32.t)\n len\n= Seq.slice_slice (buffer_root_as_seq h (Buffer?.broot b)) (UInt32.v (Buffer?.bidx b)) (UInt32.v (Buffer?.bidx b) + UInt32.v (Buffer?.blength b)) (UInt32.v i) (UInt32.v i + UInt32.v len)", "val region_liveness_insensitive_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel)\n :Lemma (region_liveness_insensitive_locs `loc_includes` (loc_buffer b))\n [SMTPat (region_liveness_insensitive_locs `loc_includes` (loc_buffer b))]\nlet region_liveness_insensitive_buffer #_ #_ #_ b =\n MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b)", "val address_liveness_insensitive_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel)\n :Lemma (address_liveness_insensitive_locs `loc_includes` (loc_buffer b))\n [SMTPat (address_liveness_insensitive_locs `loc_includes` (loc_buffer b))]\nlet address_liveness_insensitive_buffer #_ #_ #_ b =\n MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b)", "val loc_includes_union_l_buffer (#t:base_typ) (s1 s2:loc) (b:buffer t) : Lemma\n (requires (loc_includes s1 (loc_buffer b) \\/ loc_includes s2 (loc_buffer b)))\n (ensures (loc_includes (loc_union s1 s2) (loc_buffer b)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_buffer b))]\nlet loc_includes_union_l_buffer #t s1 s2 b = M.loc_includes_union_l s1 s2 (loc_buffer b)", "val loc_includes_union_l_buffer (#t:base_typ) (s1 s2:loc) (b:buffer t) : Lemma\n (requires (loc_includes s1 (loc_buffer b) \\/ loc_includes s2 (loc_buffer b)))\n (ensures (loc_includes (loc_union s1 s2) (loc_buffer b)))\n [SMTPat (loc_includes (loc_union s1 s2) (loc_buffer b))]\nlet loc_includes_union_l_buffer #t s1 s2 b = M.loc_includes_union_l s1 s2 (loc_buffer b)", "val buffer_live_reference_unused_in_disjoint\n (#t1: typ)\n (#t2: Type0)\n (h: HS.mem)\n (b1: buffer t1)\n (b2: HS.reference t2)\n: Lemma\n (requires (buffer_live h b1 /\\ HS.unused_in b2 h))\n (ensures (loc_disjoint (loc_buffer b1) (loc_addresses (HS.frameOf b2) (Set.singleton (HS.as_addr b2)))))\nlet buffer_live_reference_unused_in_disjoint #t1 #t2 h b1 b2 =\n loc_includes_addresses_buffer (frameOf_buffer b1) (Set.singleton (buffer_as_addr b1)) b1;\n loc_includes_refl (MG.loc_freed_mreference b2);\n (match b1.broot with\n | BufferRootSingleton p1 -> disjoint_roots_intro_pointer_vs_reference h p1 b2\n | BufferRootArray p1 -> disjoint_roots_intro_pointer_vs_reference h p1 b2\n );\n MG.loc_disjoint_addresses #_ #cls false false (frameOf_buffer b1) (HS.frameOf b2) (Set.singleton (buffer_as_addr b1)) (Set.singleton (HS.as_addr b2));\n MG.loc_disjoint_includes #_ #cls (loc_addresses (frameOf_buffer b1) (Set.singleton (buffer_as_addr b1))) (MG.loc_freed_mreference b2) (loc_buffer b1) (MG.loc_freed_mreference b2)", "val buffer_readable_gsingleton_buffer_of_pointer\n (#t: typ)\n (h: HS.mem)\n (p: pointer t)\n: Lemma\n (ensures (buffer_readable h (gsingleton_buffer_of_pointer p) <==> readable h p))\n [SMTPat (buffer_readable h (gsingleton_buffer_of_pointer p))]\nlet buffer_readable_gsingleton_buffer_of_pointer\n (#t: typ)\n (h: HS.mem)\n (p: pointer t)\n= let phi () : Lemma\n (requires (buffer_readable h (gsingleton_buffer_of_pointer p)))\n (ensures (readable h p))\n = assert (readable h (gpointer_of_buffer_cell (gsingleton_buffer_of_pointer p) 0ul))\n in\n Classical.move_requires phi ()", "val buffer_immutable_buffer_disjoint\n (#t #ti: Type)\n (b: LowStar.Buffer.buffer t)\n (bi: ibuffer ti)\n (h: HS.mem)\n : Lemma (requires (live h b /\\ live h bi)) (ensures (disjoint b bi))\nlet buffer_immutable_buffer_disjoint\n (#t: Type) (#ti: Type)\n (b: LowStar.Buffer.buffer t)\n (bi: ibuffer ti)\n (h: HS.mem)\n: Lemma\n (requires (\n live h b /\\ live h bi\n ))\n (ensures (\n disjoint b bi\n ))\n= if length b = 0\n then empty_disjoint b bi\n else if length bi = 0\n then empty_disjoint bi b\n else begin\n let s = as_seq h b in\n assert (~ (LowStar.Buffer.trivial_preorder _ Seq.empty s <==> immutable_preorder _ Seq.empty s));\n live_same_addresses_equal_types_and_preorders b bi h\n end", "val unused_in_loc_unused_in (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h:HS.mem)\n :Lemma (requires (unused_in b h))\n (ensures (loc_unused_in h `loc_includes` loc_addr_of_buffer b))\n [SMTPat (unused_in b h)]\nlet unused_in_loc_unused_in #_ #_ #_ b h =\n unused_in_equiv b h;\n Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b);\n MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h;\n ()", "val loc_includes_region_buffer\n (#t: Type)\n (preserve_liveness: bool)\n (s: Set.set HS.rid)\n (b: B.buffer t)\n: Lemma\n (requires (Set.mem (B.frameOf b) s))\n (ensures (loc_includes (loc_regions preserve_liveness s) (loc_buffer b)))\n [SMTPat (loc_includes (loc_regions preserve_liveness s) (loc_buffer b))]\nlet loc_includes_region_buffer #t preserve_liveness s b =\n MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(B.frameOf b) #(B.as_addr b) (LocBuffer b)", "val lemma_sub_spec\n (#a: Type)\n (b: buffer a)\n (i: UInt32.t)\n (len: UInt32.t{v len <= length b /\\ v i + v len <= length b})\n (h: _)\n : Lemma (requires (live h b))\n (ensures\n (live h (sub b i len) /\\\n as_seq h (sub b i len) == Seq.slice (as_seq h b) (v i) (v i + v len)))\n [SMTPat (sub b i len); SMTPat (live h b)]\nlet lemma_sub_spec (#a:Type) (b:buffer a)\n (i:UInt32.t)\n (len:UInt32.t{v len <= length b /\\ v i + v len <= length b})\n h : Lemma\n (requires (live h b))\n (ensures (live h (sub b i len) /\\\n as_seq h (sub b i len) == Seq.slice (as_seq h b) (v i) (v i + v len)))\n [SMTPat (sub b i len); SMTPat (live h b)]\n = Seq.lemma_eq_intro (as_seq h (sub b i len)) (Seq.slice (as_seq h b) (v i) (v i + v len))", "val lemma_sub_spec'\n (#a: Type)\n (b: buffer a)\n (i: UInt32.t)\n (len: UInt32.t{v len <= length b /\\ v i + v len <= length b})\n (h: _)\n : Lemma (requires (live h b))\n (ensures\n (live h (sub b i len) /\\\n as_seq h (sub b i len) == Seq.slice (as_seq h b) (v i) (v i + v len)))\n [SMTPat (live h (sub b i len))]\nlet lemma_sub_spec' (#a:Type) (b:buffer a)\n (i:UInt32.t)\n (len:UInt32.t{v len <= length b /\\ v i + v len <= length b})\n h : Lemma\n (requires (live h b))\n (ensures (live h (sub b i len) /\\\n as_seq h (sub b i len) == Seq.slice (as_seq h b) (v i) (v i + v len)))\n [SMTPat (live h (sub b i len))]\n = lemma_sub_spec b i len h", "val loc_includes_addresses_buffer\n (#t: Type)\n (preserve_liveness: bool)\n (r: HS.rid)\n (s: Set.set nat)\n (p: B.buffer t)\n: Lemma\n (requires (B.frameOf p == r /\\ Set.mem (B.as_addr p) s))\n (ensures (loc_includes (loc_addresses preserve_liveness r s) (loc_buffer p)))\n [SMTPat (loc_includes (loc_addresses preserve_liveness r s) (loc_buffer p))]\nlet loc_includes_addresses_buffer #t preserve_liveness r s p =\n MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(B.as_addr p) (LocBuffer p)", "val reference_live_pointer_unused_in_disjoint\n (#value1: Type0)\n (#value2: typ)\n (h: HS.mem)\n (p1: HS.reference value1)\n (p2: pointer value2)\n: Lemma\n (requires (HS.contains h p1 /\\ unused_in p2 h))\n (ensures (loc_disjoint (loc_addresses (HS.frameOf p1) (Set.singleton (HS.as_addr p1))) (loc_pointer p2)))\n [SMTPat (HS.contains h p1); SMTPat (unused_in p2 h)]\nlet reference_live_pointer_unused_in_disjoint #value1 #value2 h p1 p2 =\n loc_includes_addresses_pointer (frameOf p2) (Set.singleton (as_addr p2)) p2;\n loc_includes_refl (MG.loc_freed_mreference p1);\n disjoint_roots_intro_reference_vs_pointer h p1 p2;\n MG.loc_disjoint_addresses #_ #cls false false (HS.frameOf p1) (frameOf p2) (Set.singleton (HS.as_addr p1)) (Set.singleton (as_addr p2));\n MG.loc_disjoint_includes #_ #cls (MG.loc_freed_mreference p1) (loc_addresses (frameOf p2) (Set.singleton (as_addr p2))) (MG.loc_freed_mreference p1) (loc_pointer p2)", "val buffer_immutable_buffer_disjoint\n (#ti: Type)\n (#t: Type0)\n (bi: LowStar.ImmutableBuffer.ibuffer ti)\n (b: ubuffer t)\n (h: HS.mem)\n : Lemma (requires (live h b /\\ live h bi /\\ (exists (x: t). True))) (ensures (disjoint b bi))\nlet buffer_immutable_buffer_disjoint\n (#ti:Type) (#t:Type0)\n (bi:LowStar.ImmutableBuffer.ibuffer ti)\n (b:ubuffer t)\n (h: HS.mem)\n: Lemma\n (requires (\n live h b /\\\n live h bi /\\\n (exists (x:t). True ) // If the type is not inhabited, the initialization and immutable preorders are effectively identical\n ))\n (ensures (\n disjoint b bi\n ))\n= if length b = 0\n then empty_disjoint b bi\n else if length bi = 0\n then empty_disjoint bi b\n else begin\n let open LowStar.ImmutableBuffer in\n let s = as_seq h b in\n let s0 = Seq.upd s 0 None in\n let s1 = Seq.upd s 0 (Some (FStar.IndefiniteDescription.indefinite_description_ghost t (fun _ -> True))) in\n assert(initialization_preorder _ s0 s1 /\\\n Seq.index s0 0 =!= Seq.index s1 0 /\\\n ~( immutable_preorder _ s0 s1 <==> initialization_preorder _ s0 s1));\n live_same_addresses_equal_types_and_preorders b bi h\n end", "val modifies_liveness_insensitive_buffer\n (l1 l2:loc)\n (h h':HS.mem)\n (#a:Type0) (#rrel #rel:srel a)\n (x:mbuffer a rrel rel)\n :Lemma (requires (modifies (loc_union l1 l2) h h' /\\\n loc_disjoint l1 (loc_buffer x) /\\\n\t\t address_liveness_insensitive_locs `loc_includes` l2 /\\\n\t\t live h x))\n (ensures (live h' x))\n [SMTPatOr [\n [SMTPat (live h x); SMTPat (modifies (loc_union l1 l2) h h');];\n [SMTPat (live h' x); SMTPat (modifies (loc_union l1 l2) h h');];\n ]]\nlet modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x =\n if g_is_null x then ()\n else\n liveness_preservation_intro h h' x (fun t' pre r ->\n MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x))", "val modifies_buffer_elim\n (#t1: Type)\n (b: B.buffer t1)\n (p: loc)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_buffer b) p /\\\n B.live h b /\\\n modifies p h h'\n ))\n (ensures (\n B.live h' b /\\ (\n B.as_seq h b == B.as_seq h' b\n )))\n [SMTPatOr [\n [ SMTPat (modifies p h h'); SMTPat (B.as_seq h b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (B.live h b) ];\n [ SMTPat (modifies p h h'); SMTPat (B.as_seq h' b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (B.live h' b) ]\n ] ]\nlet modifies_buffer_elim #t1 b p h h' =\n MG.modifies_aloc_elim #_ #cls #(B.frameOf b) #(B.as_addr b) (LocBuffer b) p h h'", "val modifies_buffer_elim (#a:Type0) (#rrel #rel:srel a)\n (b:mbuffer a rrel rel) (p:loc) (h h':HS.mem)\n :Lemma (requires (loc_disjoint (loc_buffer b) p /\\ live h b /\\ modifies p h h'))\n (ensures (live h' b /\\ (as_seq h b == as_seq h' b)))\n [SMTPatOr [\n [ SMTPat (modifies p h h'); SMTPat (as_seq h b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (live h b) ];\n [ SMTPat (modifies p h h'); SMTPat (as_seq h' b) ] ;\n [ SMTPat (modifies p h h'); SMTPat (live h' b) ]\n ]]\nlet modifies_buffer_elim #_ #_ #_ b p h h' =\n if g_is_null b\n then\n assert (as_seq h b `Seq.equal` as_seq h' b)\n else begin\n MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ;\n ubuffer_preserved_elim b h h'\n end", "val lemma_loc_mutable_buffers (l: list buffer_info)\n : Lemma\n (ensures\n (let s = list_to_seq l in\n forall (i: nat). {:pattern Seq.index s i}\n i < Seq.length s ==>\n (let bi = Seq.index s i in\n bi.bi_mutable == Mutable ==>\n loc_includes (loc_mutable_buffers l) (loc_buffer bi.bi_buffer))))\nlet lemma_loc_mutable_buffers (l:list buffer_info) : Lemma\n (ensures (\n let s = list_to_seq l in\n forall (i:nat).{:pattern Seq.index s i} i < Seq.length s ==> (\n let bi = Seq.index s i in\n bi.bi_mutable == Mutable ==> loc_includes (loc_mutable_buffers l) (loc_buffer bi.bi_buffer))\n ))\n =\n lemma_list_to_seq l;\n lemma_loc_mutable_buffers_rec l (list_to_seq l) 0", "val lemma_loc_mutable_buffers (l: list buffer_info)\n : Lemma\n (ensures\n (let s = list_to_seq l in\n forall (i: nat). {:pattern Seq.index s i}\n i < Seq.length s ==>\n (let bi = Seq.index s i in\n bi.bi_mutable == Mutable ==>\n loc_includes (loc_mutable_buffers l) (loc_buffer bi.bi_buffer))))\nlet lemma_loc_mutable_buffers (l:list buffer_info) : Lemma\n (ensures (\n let s = list_to_seq l in\n forall (i:nat).{:pattern Seq.index s i} i < Seq.length s ==> (\n let bi = Seq.index s i in\n bi.bi_mutable == Mutable ==> loc_includes (loc_mutable_buffers l) (loc_buffer bi.bi_buffer))\n ))\n =\n lemma_list_to_seq l;\n lemma_loc_mutable_buffers_rec l (list_to_seq l) 0", "val loc_includes_addresses_buffer\n (#t: typ)\n (r: HS.rid)\n (s: Set.set nat)\n (p: buffer t)\n: Lemma\n (requires (frameOf_buffer p == r /\\ Set.mem (buffer_as_addr p) s))\n (ensures (loc_includes (loc_addresses r s) (loc_buffer p)))\n [SMTPat (loc_includes (loc_addresses r s) (loc_buffer p))]\nlet loc_includes_addresses_buffer #t r s p =\n MG.loc_includes_addresses_aloc #_ #cls false r s #(buffer_as_addr p) (LocBuffer p)", "val live_unused_in_disjoint\n (#value1: typ)\n (#value2: typ)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: pointer value2)\n: Lemma\n (requires (live h p1 /\\ unused_in p2 h))\n (ensures (loc_disjoint (loc_pointer p1) (loc_pointer p2)))\n [SMTPatOr [\n [SMTPat (loc_disjoint (loc_pointer p1) (loc_pointer p2)); SMTPat (live h p1)];\n [SMTPat (loc_disjoint (loc_pointer p1) (loc_pointer p2)); SMTPat (unused_in p2 h)];\n [SMTPat (live h p1); SMTPat (unused_in p2 h)];\n ]]\nlet live_unused_in_disjoint #value1 #value2 h p1 p2 =\n loc_disjoint_root p1 p2", "val loc_aux_disjoint_buffer (l: loc_aux) (#t: Type) (p: B.buffer t) : GTot Type0\nlet loc_aux_disjoint_buffer\n (l: loc_aux)\n (#t: Type)\n (p: B.buffer t)\n: GTot Type0\n= match l with\n | LocBuffer b -> B.disjoint b p", "val lemma_sub_spec (#a: typ) (b: buffer a) (i len: UInt32.t) (h: HS.mem)\n : Lemma (requires (UInt32.v i + UInt32.v len <= length b /\\ live h b))\n (ensures\n (UInt32.v i + UInt32.v len <= length b /\\ live h (gsub b i len) /\\\n as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)\n ))\n [SMTPatOr [[SMTPat (gsub b i len); SMTPat (live h b)]; [SMTPat (live h (gsub b i len))]]]\nlet lemma_sub_spec (#a:typ) (b:buffer a)\n (i:UInt32.t)\n (len:UInt32.t)\n (h: HS.mem)\n: Lemma\n (requires (\n UInt32.v i + UInt32.v len <= length b /\\\n live h b\n ))\n (ensures (\n UInt32.v i + UInt32.v len <= length b /\\\n live h (gsub b i len) /\\\n as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)\n ))\n [SMTPatOr [\n [SMTPat (gsub b i len); SMTPat (live h b)];\n [SMTPat (live h (gsub b i len))]\n ]]\n = Seq.lemma_eq_intro (as_seq h (gsub b i len)) (Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len))", "val loc_disjoint_sym\n (s1 s2: loc)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))\n [SMTPat (loc_disjoint s1 s2)]\nlet loc_disjoint_sym = MG.loc_disjoint_sym", "val modifies_liveness_insensitive_region_buffer\n (l1 l2:loc)\n (h h':HS.mem)\n (#a:Type0) (#rrel #rel:srel a)\n (x:mbuffer a rrel rel)\n :Lemma (requires (modifies (loc_union l1 l2) h h' /\\ loc_disjoint l1 (loc_buffer x) /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h (frameOf x)))\n (ensures (HS.live_region h' (frameOf x)))\n [SMTPatOr [\n [SMTPat (modifies (loc_union l1 l2) h h'); SMTPat (HS.live_region h (frameOf x))];\n [SMTPat (modifies (loc_union l1 l2) h h'); SMTPat (HS.live_region h' (frameOf x))];\n ]]\nlet modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x =\n if g_is_null x then ()\n else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x)", "val buffer_includes_loc_includes\n (#t: typ)\n (b1 b2: buffer t)\n: Lemma\n (requires (buffer_includes b1 b2))\n (ensures (loc_includes (loc_buffer b1) (loc_buffer b2)))\n [SMTPatOr [\n [SMTPat (buffer_includes b1 b2)];\n [SMTPat (loc_includes(loc_buffer b1) (loc_buffer b2))]\n ]]\nlet buffer_includes_loc_includes #t b1 b2 =\n buffer_includes_elim b1 b2;\n loc_includes_refl (loc_buffer b1);\n loc_includes_gsub_buffer_r (loc_buffer b1) b1 (UInt32.sub (buffer_idx b2) (buffer_idx b1)) (buffer_length b2)", "val buffer_as_seq_gbuffer_of_array_pointer\n (#length: array_length_t)\n (#t: typ)\n (h: HS.mem)\n (p: pointer (TArray length t))\n: Lemma\n (requires True)\n (ensures (buffer_as_seq h (gbuffer_of_array_pointer p) == gread h p))\n [SMTPat (buffer_as_seq h (gbuffer_of_array_pointer p))]\nlet buffer_as_seq_gbuffer_of_array_pointer\n (#length: array_length_t)\n (#t: typ)\n (h: HS.mem)\n (p: pointer (TArray length t))\n= let s : array length (type_of_typ t) = gread h p in\n Seq.slice_length s", "val loc_includes_region_buffer\n (#t: typ)\n (s: Set.set HS.rid)\n (b: buffer t)\n: Lemma\n (requires (Set.mem (frameOf_buffer b) s))\n (ensures (loc_includes (loc_regions s) (loc_buffer b)))\n [SMTPat (loc_includes (loc_regions s) (loc_buffer b))]\nlet loc_includes_region_buffer #t s b =\n MG.loc_includes_region_aloc #_ #cls false s #(frameOf_buffer b) #(buffer_as_addr b) (LocBuffer b)", "val lemma_offset_spec\n (#a: Type)\n (b: buffer a)\n (i: UInt32.t{v i + v b.idx < pow2 n /\\ v i <= v b.length})\n (h: _)\n : Lemma (requires True)\n (ensures (as_seq h (offset b i) == Seq.slice (as_seq h b) (v i) (length b)))\n [\n SMTPatOr\n [[SMTPat (as_seq h (offset b i))]; [SMTPat (Seq.slice (as_seq h b) (v i) (length b))]]\n ]\nlet lemma_offset_spec (#a:Type) (b:buffer a)\n (i:UInt32.t{v i + v b.idx < pow2 n /\\ v i <= v b.length})\n h : Lemma\n (requires True)\n (ensures (as_seq h (offset b i) == Seq.slice (as_seq h b) (v i) (length b)))\n [SMTPatOr [[SMTPat (as_seq h (offset b i))];\n [SMTPat (Seq.slice (as_seq h b) (v i) (length b))]]]\n = Seq.lemma_eq_intro (as_seq h (offset b i)) (Seq.slice (as_seq h b) (v i) (length b))", "val pointer_live_reference_unused_in_disjoint\n (#value1: typ)\n (#value2: Type0)\n (h: HS.mem)\n (p1: pointer value1)\n (p2: HS.reference value2)\n: Lemma\n (requires (live h p1 /\\ HS.unused_in p2 h))\n (ensures (loc_disjoint (loc_pointer p1) (loc_addresses (HS.frameOf p2) (Set.singleton (HS.as_addr p2)))))\n [SMTPat (live h p1); SMTPat (HS.unused_in p2 h)]\nlet pointer_live_reference_unused_in_disjoint #value1 #value2 h p1 p2 =\n loc_includes_addresses_pointer (frameOf p1) (Set.singleton (as_addr p1)) p1;\n loc_includes_refl (MG.loc_freed_mreference p2);\n disjoint_roots_intro_pointer_vs_reference h p1 p2;\n MG.loc_disjoint_addresses #_ #cls false false (frameOf p1) (HS.frameOf p2) (Set.singleton (as_addr p1)) (Set.singleton (HS.as_addr p2));\n MG.loc_disjoint_includes #_ #cls (loc_addresses (frameOf p1) (Set.singleton (as_addr p1))) (MG.loc_freed_mreference p2) (loc_pointer p1) (MG.loc_freed_mreference p2)", "val loc_disjoint_none_r\n (s: loc)\n: Lemma\n (ensures (loc_disjoint s loc_none))\n [SMTPat (loc_disjoint s loc_none)]\nlet loc_disjoint_none_r = MG.loc_disjoint_none_r", "val loc_disjoint_none_r\n (s: loc)\n: Lemma\n (ensures (loc_disjoint s loc_none))\n [SMTPat (loc_disjoint s loc_none)]\nlet loc_disjoint_none_r = MG.loc_disjoint_none_r", "val loc_disjoint_none_r\n (s: loc)\n: Lemma\n (ensures (loc_disjoint s loc_none))\n [SMTPat (loc_disjoint s loc_none)]\nlet loc_disjoint_none_r = MG.loc_disjoint_none_r", "val loc_includes_buffer\n (#t: Type)\n (b1 b2: B.buffer t)\n: Lemma\n (requires (b1 `B.includes` b2))\n (ensures (loc_includes (loc_buffer b1) (loc_buffer b2)))\n [SMTPatOr [\n [SMTPat (B.includes b1 b2)];\n [SMTPat (loc_includes(loc_buffer b1) (loc_buffer b2))]\n ]]\nlet loc_includes_buffer #t b1 b2 =\n MG.loc_includes_aloc #_ #cls #(B.frameOf b1) #(B.as_addr b1) (LocBuffer b1) (LocBuffer b2)", "val modifies_buffer_elim'\n (#t1: typ)\n (b: buffer t1)\n (p: loc)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_buffer b) p /\\\n buffer_live h b /\\\n UInt32.v (buffer_length b) > 0 /\\\n modifies p h h'\n ))\n (ensures (\n buffer_live h' b /\\ (\n buffer_readable h b ==> (\n\tbuffer_readable h' b /\\\n\tbuffer_as_seq h b == buffer_as_seq h' b\n ))))\nlet modifies_buffer_elim' #t1 b p h h' =\n Classical.forall_intro_2 HS.lemma_tip_top;\n loc_disjoint_sym (loc_buffer b) p;\n let n = UInt32.v (buffer_length b) in\n begin\n assert (n > 0);\n let pre\n (i: UInt32.t)\n : GTot Type0\n = UInt32.v i < n\n in\n let post\n (i: UInt32.t)\n : GTot Type0\n = pre i /\\ (\n\t let q = gpointer_of_buffer_cell b i in\n\t equal_values h q h' q\n )\n in\n let f\n (i: UInt32.t)\n : Lemma\n (requires (pre i))\n (ensures (post i))\n = modifies_pointer_elim p h h' (gpointer_of_buffer_cell b i)\n in\n f 0ul; // for the liveness of the whole buffer\n Classical.forall_intro (Classical.move_requires f);\n assert (buffer_readable h b ==> buffer_readable h' b);\n let g () : Lemma\n (requires (buffer_readable h b))\n (ensures (buffer_as_seq h b == buffer_as_seq h' b))\n = let s = buffer_as_seq h b in\n let s' = buffer_as_seq h' b in\n Seq.lemma_eq_intro s s';\n Seq.lemma_eq_elim s s'\n in\n Classical.move_requires g ()\n end", "val loc_disjoint_union_r\n (s s1 s2: loc)\n: Lemma\n (requires (loc_disjoint s s1 /\\ loc_disjoint s s2))\n (ensures (loc_disjoint s (loc_union s1 s2)))\n [SMTPat (loc_disjoint s (loc_union s1 s2))]\nlet loc_disjoint_union_r = MG.loc_disjoint_union_r", "val loc_disjoint_union_r\n (s s1 s2: loc)\n: Lemma\n (requires (loc_disjoint s s1 /\\ loc_disjoint s s2))\n (ensures (loc_disjoint s (loc_union s1 s2)))\n [SMTPat (loc_disjoint s (loc_union s1 s2))]\nlet loc_disjoint_union_r = MG.loc_disjoint_union_r", "val loc_includes_region_buffer (#a:Type0) (#rrel #rel:srel a)\n (preserve_liveness:bool) (s:Set.set HS.rid) (b:mbuffer a rrel rel)\n :Lemma (requires (Set.mem (frameOf b) s))\n (ensures (loc_includes (loc_regions preserve_liveness s) (loc_buffer b)))\n [SMTPat (loc_includes (loc_regions preserve_liveness s) (loc_buffer b))]\nlet loc_includes_region_buffer #_ #_ #_ preserve_liveness s b =\n MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b)", "val unused_in_not_unused_in_disjoint_2 (l1 l2 l1' l2': loc) (h: HS.mem)\n : Lemma\n (requires\n ((loc_unused_in h) `loc_includes` l1 /\\ (loc_not_unused_in h) `loc_includes` l2 /\\\n l1 `loc_includes` l1' /\\ l2 `loc_includes` l2'))\n (ensures (loc_disjoint l1' l2'))\n [\n SMTPat (loc_disjoint l1' l2');\n SMTPat ((loc_unused_in h) `loc_includes` l1);\n SMTPat ((loc_not_unused_in h) `loc_includes` l2)\n ]\nlet unused_in_not_unused_in_disjoint_2\n (l1 l2 l1' l2': loc)\n (h: HS.mem)\n: Lemma\n (requires (loc_unused_in h `loc_includes` l1 /\\ loc_not_unused_in h `loc_includes` l2 /\\ l1 `loc_includes` l1' /\\ l2 `loc_includes` l2' ))\n (ensures (loc_disjoint l1' l2' ))\n [SMTPat (loc_disjoint l1' l2'); SMTPat (loc_unused_in h `loc_includes` l1); SMTPat (loc_not_unused_in h `loc_includes` l2)]\n= loc_includes_trans (loc_unused_in h) l1 l1' ;\n loc_includes_trans (loc_not_unused_in h) l2 l2' ;\n loc_unused_in_not_unused_in_disjoint h ;\n loc_disjoint_includes (loc_unused_in h) (loc_not_unused_in h) l1' l2'", "val modifies_liveness_insensitive_buffer_weak\n (l: loc)\n (h h': HS.mem)\n (#a: Type0)\n (#rrel #rel: srel a)\n (x: mbuffer a rrel rel)\n : Lemma\n (requires (modifies l h h' /\\ address_liveness_insensitive_locs `loc_includes` l /\\ live h x))\n (ensures (live h' x))\n [\n SMTPatOr\n [\n [SMTPat (live h x); SMTPat (modifies l h h')];\n [SMTPat (live h' x); SMTPat (modifies l h h')]\n ]\n ]\nlet modifies_liveness_insensitive_buffer_weak\n (l:loc)\n (h h':HS.mem)\n (#a:Type0) (#rrel #rel:srel a)\n (x:mbuffer a rrel rel)\n :Lemma (requires (modifies l h h' /\\ address_liveness_insensitive_locs `loc_includes` l /\\ live h x))\n (ensures (live h' x))\n [SMTPatOr [\n [SMTPat (live h x); SMTPat (modifies l h h');];\n [SMTPat (live h' x); SMTPat (modifies l h h');];\n ]]\n = modifies_liveness_insensitive_buffer loc_none l h h' x", "val lemma_loc_mutable_buffers_rec (l: list buffer_info) (s: Seq.seq buffer_info) (n: nat)\n : Lemma (requires n + List.length l == Seq.length s /\\ list_to_seq_post l s n)\n (ensures\n (let modloc = loc_mutable_buffers l in\n forall (i: nat). {:pattern Seq.index s i}\n n <= i /\\ i < Seq.length s ==>\n (let bi = Seq.index s i in\n bi.bi_mutable == Mutable ==> loc_includes modloc (loc_buffer bi.bi_buffer))))\n (decreases l)\nlet rec lemma_loc_mutable_buffers_rec (l:list buffer_info) (s:Seq.seq buffer_info) (n:nat) : Lemma\n (requires\n n + List.length l == Seq.length s /\\\n list_to_seq_post l s n\n )\n (ensures (\n let modloc = loc_mutable_buffers l in\n forall (i:nat).{:pattern Seq.index s i} n <= i /\\ i < Seq.length s ==> (\n let bi = Seq.index s i in\n bi.bi_mutable == Mutable ==> loc_includes modloc (loc_buffer bi.bi_buffer))\n ))\n (decreases l)\n =\n match l with\n | [] -> ()\n | h::t -> lemma_loc_mutable_buffers_rec t s (n + 1)", "val lemma_loc_mutable_buffers_rec (l: list buffer_info) (s: Seq.seq buffer_info) (n: nat)\n : Lemma (requires n + List.length l == Seq.length s /\\ list_to_seq_post l s n)\n (ensures\n (let modloc = loc_mutable_buffers l in\n forall (i: nat). {:pattern Seq.index s i}\n n <= i /\\ i < Seq.length s ==>\n (let bi = Seq.index s i in\n bi.bi_mutable == Mutable ==> loc_includes modloc (loc_buffer bi.bi_buffer))))\n (decreases l)\nlet rec lemma_loc_mutable_buffers_rec (l:list buffer_info) (s:Seq.seq buffer_info) (n:nat) : Lemma\n (requires\n n + List.length l == Seq.length s /\\\n list_to_seq_post l s n\n )\n (ensures (\n let modloc = loc_mutable_buffers l in\n forall (i:nat).{:pattern Seq.index s i} n <= i /\\ i < Seq.length s ==> (\n let bi = Seq.index s i in\n bi.bi_mutable == Mutable ==> loc_includes modloc (loc_buffer bi.bi_buffer))\n ))\n (decreases l)\n =\n match l with\n | [] -> ()\n | h::t -> lemma_loc_mutable_buffers_rec t s (n + 1)", "val loc_disjoint_includes_r (b1 b2 b2': loc)\n : Lemma (requires (loc_includes b2 b2' /\\ loc_disjoint b1 b2))\n (ensures (loc_disjoint b1 b2'))\n [SMTPat (loc_disjoint b1 b2'); SMTPat (loc_includes b2 b2')]\nlet loc_disjoint_includes_r (b1 : loc) (b2 b2': loc) : Lemma\n (requires (loc_includes b2 b2' /\\ loc_disjoint b1 b2))\n (ensures (loc_disjoint b1 b2'))\n [SMTPat (loc_disjoint b1 b2'); SMTPat (loc_includes b2 b2')]\n= loc_disjoint_includes b1 b2 b1 b2'", "val loc_aux_disjoint_loc_aux_includes_pointer (l1 l2: loc_aux) (#t3: typ) (p3: pointer t3)\n : Lemma (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes_pointer l2 p3))\n (ensures (loc_aux_disjoint_pointer l1 p3))\nlet loc_aux_disjoint_loc_aux_includes_pointer\n (l1 l2: loc_aux)\n (#t3: typ)\n (p3: pointer t3)\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes_pointer l2 p3))\n (ensures (loc_aux_disjoint_pointer l1 p3))\n= match l2 with\n | LocPointer p2 ->\n loc_aux_disjoint_pointer_includes l1 p2 p3\n | LocBuffer b2 ->\n let f\n (i: UInt32.t)\n : Lemma\n (requires (\n UInt32.v i < UInt32.v (buffer_length b2) /\\\n gpointer_of_buffer_cell b2 i `includes` p3\n ))\n (ensures (loc_aux_disjoint_pointer l1 p3))\n = loc_aux_disjoint_pointer_includes l1 (gpointer_of_buffer_cell b2 i) p3\n in\n Classical.forall_intro (Classical.move_requires f)", "val modifies_liveness_insensitive_region_buffer_weak\n (l2: loc)\n (h h': HS.mem)\n (#t: Type)\n (x: B.buffer t)\n : Lemma\n (requires\n (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\\n HS.live_region h (B.frameOf x)))\n (ensures (HS.live_region h' (B.frameOf x)))\n [\n SMTPatOr\n [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h (B.frameOf x))];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' (B.frameOf x))]\n ]\n ]\nlet modifies_liveness_insensitive_region_buffer_weak\n (l2 : loc)\n (h h' : HS.mem)\n (#t: Type)\n (x: B.buffer t)\n: Lemma\n (requires (modifies l2 h h' /\\ region_liveness_insensitive_locs `loc_includes` l2 /\\ HS.live_region h (B.frameOf x)))\n (ensures (HS.live_region h' (B.frameOf x)))\n [SMTPatOr [\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h (B.frameOf x))];\n [SMTPat (modifies l2 h h'); SMTPat (HS.live_region h' (B.frameOf x))];\n ]]\n= modifies_liveness_insensitive_region_buffer loc_none l2 h h' x", "val loc_disjoint_root\n (#value1: typ)\n (#value2: typ)\n (p1: pointer value1)\n (p2: pointer value2)\n: Lemma\n (requires (frameOf p1 <> frameOf p2 \\/ as_addr p1 <> as_addr p2))\n (ensures (loc_disjoint (loc_pointer p1) (loc_pointer p2)))\nlet loc_disjoint_root #value1 #value2 p1 p2 =\n MG.loc_disjoint_addresses #_ #cls false false (frameOf p1) (frameOf p2) (Set.singleton (as_addr p1)) (Set.singleton (as_addr p2));\n loc_includes_addresses_pointer (frameOf p1) (Set.singleton (as_addr p1)) p1;\n loc_includes_addresses_pointer (frameOf p2) (Set.singleton (as_addr p2)) p2;\n MG.loc_disjoint_includes #_ #cls (loc_addresses (frameOf p1) (Set.singleton (as_addr p1))) (loc_addresses (frameOf p2) (Set.singleton (as_addr p2))) (loc_pointer p1) (loc_pointer p2)", "val modifies_buffer_elim (#t1:base_typ) (b:buffer t1) (p:loc) (h h':vale_heap) : Lemma\n (requires\n loc_disjoint (loc_buffer b) p /\\\n buffer_readable h b /\\\n modifies p h h'\n )\n (ensures\n buffer_readable h b /\\\n buffer_readable h' b /\\\n buffer_as_seq h b == buffer_as_seq h' b\n )\n [SMTPatOr [\n [SMTPat (modifies p h h'); SMTPat (buffer_readable h' b)];\n [SMTPat (modifies p h h'); SMTPat (buffer_as_seq h' b)];\n ]]\nlet modifies_buffer_elim #t1 b p h h' =\n let db = get_downview b.bsrc in\n lemma_dv_equal (down_view b.src) b.bsrc (_ih h).hs (_ih h').hs;\n same_underlying_seq h h' b;\n assert (Seq.equal (buffer_as_seq h b) (buffer_as_seq h' b))", "val modifies_buffer_elim (#t1:base_typ) (b:buffer t1) (p:loc) (h h':vale_heap) : Lemma\n (requires\n loc_disjoint (loc_buffer b) p /\\\n buffer_readable h b /\\\n modifies p h h'\n )\n (ensures\n buffer_readable h b /\\\n buffer_readable h' b /\\\n buffer_as_seq h b == buffer_as_seq h' b\n )\n [SMTPatOr [\n [SMTPat (modifies p h h'); SMTPat (buffer_readable h' b)];\n [SMTPat (modifies p h h'); SMTPat (buffer_as_seq h' b)];\n ]]\nlet modifies_buffer_elim #t1 b p h h' =\n let db = get_downview b.bsrc in\n lemma_dv_equal (down_view b.src) b.bsrc (_ih h).hs (_ih h').hs;\n same_underlying_seq h h' b;\n assert (Seq.equal (buffer_as_seq h b) (buffer_as_seq h' b))", "val modifies_liveness_insensitive_buffer_weak (l: loc) (h h': HS.mem) (#t: Type) (x: B.buffer t)\n : Lemma\n (requires\n (modifies l h h' /\\ address_liveness_insensitive_locs `loc_includes` l /\\ B.live h x))\n (ensures (B.live h' x))\n [\n SMTPatOr\n [\n [SMTPat (B.live h x); SMTPat (modifies l h h')];\n [SMTPat (B.live h' x); SMTPat (modifies l h h')]\n ]\n ]\nlet modifies_liveness_insensitive_buffer_weak\n (l : loc)\n (h h' : HS.mem)\n (#t: Type)\n (x: B.buffer t)\n: Lemma\n (requires (modifies l h h' /\\ address_liveness_insensitive_locs `loc_includes` l /\\ B.live h x))\n (ensures (B.live h' x))\n [SMTPatOr [\n [SMTPat (B.live h x); SMTPat (modifies l h h');];\n [SMTPat (B.live h' x); SMTPat (modifies l h h');];\n ]]\n= modifies_liveness_insensitive_buffer loc_none l h h' x", "val unwritten_buffer_down\n (t: base_typ)\n (b: buffer t {buffer_writeable b})\n (i: nat{i < buffer_length b})\n (v: base_typ_as_vale_type t)\n (h: vale_heap{List.memP b (IB.ptrs_of_mem (_ih h))})\n : Lemma\n (ensures\n (let mem1 = I.down_mem (_ih h) in\n let h1 = buffer_write b i v h in\n let mem2 = I.down_mem (_ih h1) in\n forall (a: b8{List.memP a (IB.ptrs_of_mem (_ih h)) /\\ a =!= b}) j.\n {:pattern\n\n mem1.[ j ]; List.memP a (IB.ptrs_of_mem (_ih h))\\/mem2.[ j ];\n List.memP a (IB.ptrs_of_mem (_ih h))}\n let base = (IB.addrs_of_mem (_ih h)) a in\n j >= base /\\ j < base + DV.length (get_downview a.bsrc) ==> mem1.[ j ] == mem2.[ j ]))\nlet unwritten_buffer_down (t:base_typ) (b:buffer t{buffer_writeable b})\n (i:nat{i < buffer_length b})\n (v:base_typ_as_vale_type t)\n (h:vale_heap{List.memP b (IB.ptrs_of_mem (_ih h))})\n : Lemma\n (ensures (\n let mem1 = I.down_mem (_ih h) in\n let h1 = buffer_write b i v h in\n let mem2 = I.down_mem (_ih h1) in\n forall (a:b8{List.memP a (IB.ptrs_of_mem (_ih h)) /\\ a =!= b}) j. {:pattern mem1.[j]; List.memP a (IB.ptrs_of_mem (_ih h)) \\/ mem2.[j]; List.memP a (IB.ptrs_of_mem (_ih h))}\n let base = (IB.addrs_of_mem (_ih h)) a in\n j >= base /\\ j < base + DV.length (get_downview a.bsrc) ==> mem1.[j] == mem2.[j]))\n = let aux (a:b8{a =!= b /\\ List.memP a (IB.ptrs_of_mem (_ih h))})\n : Lemma\n (ensures (\n let base = (IB.addrs_of_mem (_ih h)) a in\n let mem1 = I.down_mem (_ih h) in\n let h1 = buffer_write b i v h in\n let mem2 = I.down_mem (_ih h1) in\n forall j.\n j >= base /\\ j < base + DV.length (get_downview a.bsrc) ==>\n mem1.[j] == mem2.[j]))\n = let db = get_downview a.bsrc in\n if DV.length db = 0 then ()\n else\n let mem1 = I.down_mem (_ih h) in\n let h1 = buffer_write b i v h in\n let mem2 = I.down_mem (_ih h1) in\n let base = (IB.addrs_of_mem (_ih h)) a in\n let s0 = DV.as_seq (IB.hs_of_mem (_ih h)) db in\n let s1 = DV.as_seq (IB.hs_of_mem (_ih h1)) db in\n opaque_assert (`%IB.list_disjoint_or_eq) IB.list_disjoint_or_eq IB.list_disjoint_or_eq_def (MB.disjoint a.bsrc b.bsrc);\n lemma_dv_equal (IB.down_view a.src) a.bsrc (IB.hs_of_mem (_ih h)) (IB.hs_of_mem (_ih h1));\n assert (Seq.equal s0 s1);\n assert (forall (j:int).{:pattern (mem1.[j])}\n base <= j /\\ j < base + Seq.length s0 ==> v_to_typ TUInt8 (Seq.index s0 (j - base)) == mem1.[j]);\n heap_shift mem1 mem2 base (DV.length db)\n in\n Classical.forall_intro aux", "val unwritten_buffer_down\n (t: base_typ)\n (b: buffer t {buffer_writeable b})\n (i: nat{i < buffer_length b})\n (v: base_typ_as_vale_type t)\n (h: vale_heap{List.memP b (IB.ptrs_of_mem (_ih h))})\n : Lemma\n (ensures\n (let mem1 = I.down_mem (_ih h) in\n let h1 = buffer_write b i v h in\n let mem2 = I.down_mem (_ih h1) in\n forall (a: b8{List.memP a (IB.ptrs_of_mem (_ih h)) /\\ a =!= b}) j.\n {:pattern\n\n mem1.[ j ]; List.memP a (IB.ptrs_of_mem (_ih h))\\/mem2.[ j ];\n List.memP a (IB.ptrs_of_mem (_ih h))}\n let base = (IB.addrs_of_mem (_ih h)) a in\n j >= base /\\ j < base + DV.length (get_downview a.bsrc) ==> mem1.[ j ] == mem2.[ j ]))\nlet unwritten_buffer_down (t:base_typ) (b:buffer t{buffer_writeable b})\n (i:nat{i < buffer_length b})\n (v:base_typ_as_vale_type t)\n (h:vale_heap{List.memP b (IB.ptrs_of_mem (_ih h))})\n : Lemma\n (ensures (\n let mem1 = I.down_mem (_ih h) in\n let h1 = buffer_write b i v h in\n let mem2 = I.down_mem (_ih h1) in\n forall (a:b8{List.memP a (IB.ptrs_of_mem (_ih h)) /\\ a =!= b}) j. {:pattern mem1.[j]; List.memP a (IB.ptrs_of_mem (_ih h)) \\/ mem2.[j]; List.memP a (IB.ptrs_of_mem (_ih h))}\n let base = (IB.addrs_of_mem (_ih h)) a in\n j >= base /\\ j < base + DV.length (get_downview a.bsrc) ==> mem1.[j] == mem2.[j]))\n = let aux (a:b8{a =!= b /\\ List.memP a (IB.ptrs_of_mem (_ih h))})\n : Lemma\n (ensures (\n let base = (IB.addrs_of_mem (_ih h)) a in\n let mem1 = I.down_mem (_ih h) in\n let h1 = buffer_write b i v h in\n let mem2 = I.down_mem (_ih h1) in\n forall j.\n j >= base /\\ j < base + DV.length (get_downview a.bsrc) ==>\n mem1.[j] == mem2.[j]))\n = let db = get_downview a.bsrc in\n if DV.length db = 0 then ()\n else\n let mem1 = I.down_mem (_ih h) in\n let h1 = buffer_write b i v h in\n let mem2 = I.down_mem (_ih h1) in\n let base = (IB.addrs_of_mem (_ih h)) a in\n let s0 = DV.as_seq (IB.hs_of_mem (_ih h)) db in\n let s1 = DV.as_seq (IB.hs_of_mem (_ih h1)) db in\n opaque_assert (`%IB.list_disjoint_or_eq) IB.list_disjoint_or_eq IB.list_disjoint_or_eq_def (MB.disjoint a.bsrc b.bsrc);\n lemma_dv_equal (IB.down_view a.src) a.bsrc (IB.hs_of_mem (_ih h)) (IB.hs_of_mem (_ih h1));\n assert (Seq.equal s0 s1);\n assert (forall (j:int).{:pattern (mem1.[j])}\n base <= j /\\ j < base + Seq.length s0 ==> v_to_typ TUInt8 (Seq.index s0 (j - base)) == mem1.[j]);\n heap_shift mem1 mem2 base (DV.length db)\n in\n Classical.forall_intro aux", "val buffer_sub_spec\n (#t: Type)\n (inv: memory_invariant)\n (b: B.buffer t)\n (i: U32.t)\n (len: Ghost.erased U32.t)\n : Tot\n (read_repr_spec (B.buffer t)\n (B.live inv.h0 b /\\ (B.loc_buffer b) `B.loc_disjoint` inv.lwrite /\\\n U32.v i + U32.v len <= B.length b)\n (fun res ->\n U32.v i + U32.v len <= B.length b /\\ res == B.gsub b i len /\\\n (B.loc_buffer res) `B.loc_disjoint` inv.lwrite)\n (fun _ -> False))\nlet buffer_sub_spec\n (#t: Type)\n (inv: memory_invariant)\n (b: B.buffer t)\n (i: U32.t)\n (len: Ghost.erased U32.t)\n: Tot (read_repr_spec (B.buffer t)\n (\n B.live inv.h0 b /\\\n B.loc_buffer b `B.loc_disjoint` inv.lwrite /\\\n U32.v i + U32.v len <= B.length b\n )\n (fun res ->\n U32.v i + U32.v len <= B.length b /\\\n res == B.gsub b i len /\\\n B.loc_buffer res `B.loc_disjoint` inv.lwrite\n )\n (fun _ -> False)\n )\n=\n fun _ ->\n Correct (B.gsub b i len)", "val modifies_liveness_insensitive_buffer\n (l1 l2 : loc)\n (h h' : HS.mem)\n (#t: Type)\n (x: B.buffer t)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ loc_disjoint l1 (loc_buffer x) /\\ address_liveness_insensitive_locs `loc_includes` l2 /\\ B.live h x))\n (ensures (B.live h' x))\nlet modifies_liveness_insensitive_buffer l1 l2 h h' #t x =\n MG.modifies_preserves_liveness_strong l1 l2 h h' (B.content x) (LocBuffer x)", "val union_loc_of_loc_disjoint\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (s1 s2: loc (c b))\n: Lemma\n (union_loc_of_loc c b s1 `loc_disjoint` union_loc_of_loc c b s2 <==> s1 `loc_disjoint` s2)\nlet union_loc_of_loc_disjoint #al c b s1 s2 =\n Classical.move_requires (union_loc_of_loc_disjoint_elim c b s1) s2;\n Classical.move_requires (union_loc_of_loc_disjoint_intro c b s1) s2" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fsti", "name": "FStar.Pointer.Base.loc_disjoint_gpointer_of_buffer_cell_l" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fsti", "name": "FStar.Pointer.Base.loc_disjoint_gpointer_of_buffer_cell_r" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint_gpointer_of_buffer_cell" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_gpointer_of_array_cell" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint_gsub_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint_gcell" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint_buffer_addresses" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_disjoint_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_gsingleton_buffer_of_pointer" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_disjoint_gsub_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.buffer_live_pointer_unused_in_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_disjoint_buffer_addresses" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_includes_gsub_buffer_r" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.pointer_live_buffer_unused_in_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.buffer_live_unused_in_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_disjoint_pointer_buffer_sym" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fsti", "name": "FStar.Pointer.Base.gpointer_of_buffer_cell_gsub_buffer'" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_gsub_buffer_r" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_gsub_buffer_r" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.reference_live_buffer_unused_in_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_gbuffer_of_array_pointer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint_pointer_addresses" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint_gfield" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.mut_immut_disjoint" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_disjoint_loc_buffer_from_to" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.address_liveness_insensitive_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.pointer_of_buffer_cell" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_aux_disjoint_loc_aux_includes_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_disjoint_buffer_sym" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.region_liveness_insensitive_buffer" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.freeable_disjoint'" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_gsub_buffer_l" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_disjoint_buffer" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.mut_const_immut_disjoint" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_gsub_buffer_l" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.gpointer_of_buffer_cell" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.mreference_live_buffer_unused_in_disjoint" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.live_loc_not_unused_in" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Blake2.Core.fst", "name": "Hacl.Impl.Blake2.Core.g_rowi_disjoint_other" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.buffer_live_mreference_unused_in_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.buffer_as_seq_gsingleton_buffer_of_pointer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_buffer_elim" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_includes_union_l_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_disjoint_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.buffer_readable_gsub_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.buffer_as_seq_gsub_buffer" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.region_liveness_insensitive_buffer" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.address_liveness_insensitive_buffer" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc_includes_union_l_buffer" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc_includes_union_l_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.buffer_live_reference_unused_in_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.buffer_readable_gsingleton_buffer_of_pointer" }, { "project_name": "FStar", "file_name": "LowStar.ImmutableBuffer.fst", "name": "LowStar.ImmutableBuffer.buffer_immutable_buffer_disjoint" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.unused_in_loc_unused_in" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_includes_region_buffer" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.lemma_sub_spec" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.lemma_sub_spec'" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_includes_addresses_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.reference_live_pointer_unused_in_disjoint" }, { "project_name": "FStar", "file_name": "LowStar.UninitializedBuffer.fst", "name": "LowStar.UninitializedBuffer.buffer_immutable_buffer_disjoint" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_buffer" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_buffer_elim" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_buffer_elim" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory_Sems.fst", "name": "Vale.PPC64LE.Memory_Sems.lemma_loc_mutable_buffers" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory_Sems.fst", "name": "Vale.X64.Memory_Sems.lemma_loc_mutable_buffers" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_addresses_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.live_unused_in_disjoint" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_aux_disjoint_buffer" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.lemma_sub_spec" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint_sym" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_region_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.buffer_includes_loc_includes" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.buffer_as_seq_gbuffer_of_array_pointer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_includes_region_buffer" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.lemma_offset_spec" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.pointer_live_reference_unused_in_disjoint" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_disjoint_none_r" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint_none_r" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_disjoint_none_r" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_includes_buffer" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.modifies_buffer_elim'" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint_union_r" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_disjoint_union_r" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_includes_region_buffer" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.unused_in_not_unused_in_disjoint_2" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.modifies_liveness_insensitive_buffer_weak" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory_Sems.fst", "name": "Vale.PPC64LE.Memory_Sems.lemma_loc_mutable_buffers_rec" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory_Sems.fst", "name": "Vale.X64.Memory_Sems.lemma_loc_mutable_buffers_rec" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_disjoint_includes_r" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_aux_disjoint_loc_aux_includes_pointer" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fsti", "name": "FStar.Modifies.modifies_liveness_insensitive_region_buffer_weak" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_disjoint_root" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.modifies_buffer_elim" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.modifies_buffer_elim" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fsti", "name": "FStar.Modifies.modifies_liveness_insensitive_buffer_weak" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory_Sems.fst", "name": "Vale.PPC64LE.Memory_Sems.unwritten_buffer_down" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory_Sems.fst", "name": "Vale.X64.Memory_Sems.unwritten_buffer_down" }, { "project_name": "FStar", "file_name": "LowParseWriters.fsti", "name": "LowParseWriters.buffer_sub_spec" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.modifies_liveness_insensitive_buffer" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.union_loc_of_loc_disjoint" } ], "selected_premises": [ "FStar.UInt.size", "FStar.Mul.op_Star", "FStar.Pervasives.reveal_opaque", "FStar.Pointer.Derived1.loc_disjoint_gpointer_of_buffer_cell_r", "FStar.Heap.trivial_preorder", "FStar.Pointer.Derived1.loc_disjoint_gufield_l", "FStar.Pointer.Derived1.loc_disjoint_gfield_l", "FStar.Monotonic.HyperStack.sel", "FStar.Pointer.Derived1.loc_disjoint_gcell_l", "FStar.Pointer.Derived1.loc_disjoint_gbuffer_of_array_pointer_l", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "FStar.Pointer.Derived1.loc_disjoint_gbuffer_of_array_pointer_r", "FStar.Pointer.Derived1.loc_disjoint_gufield_r", "FStar.Pointer.Derived1.includes_gcell_gen", "FStar.Pointer.Derived1.loc_disjoint_gsingleton_buffer_of_pointer_l", "FStar.Pointer.Derived1.loc_disjoint_gcell_r", "FStar.Pointer.Derived1.includes_gufield_gen", "FStar.Pointer.Derived1.loc_disjoint_gfield_r", "FStar.Pointer.Derived1.includes_gfield_gen", "FStar.Monotonic.HyperStack.live_region", "FStar.Pointer.Derived1.loc_disjoint_gsingleton_buffer_of_pointer_r", "FStar.Math.Lemmas.pow2_plus", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "FStar.HyperStack.ST.is_eternal_region", "FStar.Monotonic.HyperStack.is_heap_color", "FStar.Monotonic.HyperStack.mreference", "FStar.Pointer.Derived1.loc_disjoint_union_l", "FStar.Math.Lemmas.pow2_lt_compat", "FStar.Math.Lemmas.pow2_le_compat", "FStar.Monotonic.HyperStack.as_addr", "FStar.Pointer.Derived1.loc_disjoint_none_l", "FStar.Monotonic.HyperStack.is_stack_region", "FStar.UInt.max_int", "FStar.Monotonic.HyperStack.frameOf", "FStar.Math.Lemmas.lemma_mod_plus_distr_l", "FStar.Monotonic.HyperHeap.modifies_just", "FStar.Math.Lemmas.lemma_mod_plus_distr_r", "FStar.Pointer.Derived1.loc_includes_region_union_assoc", "FStar.Math.Lemmas.cancel_mul_mod", "FStar.UInt32.op_Plus_Hat", "FStar.Pointer.Derived1.loc_includes_union_assoc_focalize_1", "FStar.Pointer.Derived1.loc_includes_union_assoc_focalize_2", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "FStar.Monotonic.HyperStack.modifies_one", "FStar.Pointer.Derived1.loc_includes_union_assoc_l2r", "FStar.Pointer.Derived1.loc_includes_union_assoc_r2l", "FStar.Monotonic.HyperHeap.modifies", "FStar.Monotonic.HyperStack.is_in", "FStar.UInt32.lt", "FStar.Pointer.Derived1.loc_includes_region_union_r", "FStar.UInt.fits", "FStar.UInt.to_vec", "FStar.Monotonic.HyperStack.contains", "FStar.UInt32.op_Star_Hat", "FStar.Monotonic.HyperStack.is_wf_with_ctr_and_tip", "FStar.Monotonic.HyperStack.top_frame", "FStar.UInt32.op_Subtraction_Hat", "FStar.BitVector.lognot_vec_definition", "FStar.Monotonic.HyperStack.modifies_ref", "FStar.Math.Lemmas.distributivity_add_right", "FStar.Monotonic.HyperStack.is_mm", "FStar.Math.Lemmas.lemma_div_lt", "FStar.Math.Lib.max", "FStar.Monotonic.HyperStack.is_eternal_region_hs", "FStar.Monotonic.HyperHeap.disjoint", "FStar.Monotonic.HyperStack.is_above", "FStar.Monotonic.HyperHeap.extend_post", "FStar.UInt32.op_Star_Percent_Hat", "FStar.Math.Lemmas.distributivity_sub_left", "FStar.Monotonic.HyperStack.modifies_transitively", "FStar.UInt32.op_Amp_Hat", "FStar.Monotonic.Heap.modifies_t", "FStar.Math.Lib.slash_decr_axiom", "FStar.Pervasives.ex_pre", "FStar.UInt32.op_Star_Question_Hat", "FStar.Pervasives.ex_bind_wp", "FStar.Monotonic.HyperHeap.rid_last_component", "FStar.Monotonic.HyperStack.heap_region_does_not_overlap_with_tip", "FStar.Pervasives.ex_post'", "FStar.Heap.trivial_rel", "FStar.Pervasives.ex_return", "FStar.UInt32.op_Subtraction_Percent_Hat", "FStar.UInt32.op_Subtraction_Question_Hat", "FStar.Math.Lemmas.lemma_mod_twice", "FStar.UInt.min_int", "FStar.Math.Lemmas.modulo_distributivity", "FStar.Monotonic.Heap.modifies", "FStar.Math.Lemmas.modulo_addition_lemma", "FStar.UInt32.gte_mask", "FStar.Monotonic.HyperStack.popped", "FStar.BitVector.logxor_vec_definition", "FStar.Ghost.tot_to_gtot", "FStar.UInt32.op_Percent_Hat", "FStar.UInt32.op_Slash_Hat", "FStar.Pervasives.ex_post", "FStar.BitVector.logor_vec_definition", "FStar.Preorder.preorder_rel", "FStar.UInt32.n_minus_one" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.Pointer.Derived1\n\nmodule HH = FStar.HyperStack\nmodule HS = FStar.HyperStack\nmodule HST = FStar.HyperStack.ST\n\nlet includes_gfield_gen #t p #l q fd =\n includes_gfield q fd;\n includes_trans p q (gfield q fd)\n\nlet includes_gufield_gen #t p #l q fd =\n includes_gufield q fd;\n includes_trans p q (gufield q fd)\n\nlet includes_gcell_gen #t p #length #value q i =\n includes_gcell q i;\n includes_trans p q (gcell q i)\n\nlet loc_includes_union_assoc_r2l s1 s2 s3 s =\n loc_includes_trans (loc_union (loc_union s1 s2) s3) (loc_union s1 (loc_union s2 s3)) s\n\nlet loc_includes_union_assoc_l2r s1 s2 s3 s =\n loc_includes_trans (loc_union s1 (loc_union s2 s3)) (loc_union (loc_union s1 s2) s3) s\n\nlet loc_includes_union_assoc_focalize_1 l1 l2 x r s =\n loc_includes_trans (loc_union l1 (loc_union (loc_union l2 x) r)) (loc_union (loc_union l1 l2) (loc_union x r)) s\n\nlet loc_includes_union_assoc_focalize_2 l x r1 r2 s =\n loc_includes_trans (loc_union l (loc_union (loc_union x r1) r2)) (loc_union l (loc_union x (loc_union r1 r2))) s\n\nlet loc_includes_region_union_r l s1 s2 =\n loc_includes_trans (loc_union l (loc_regions s1)) (loc_union (loc_regions s1) l) (loc_regions s2)\n\nlet loc_includes_region_union_assoc l r s1 s2 =\n loc_includes_trans (loc_union l (loc_union (loc_regions s1) r)) (loc_union (loc_regions s1) (loc_union l r)) (loc_regions s2)\n\nlet loc_disjoint_none_l s =\n loc_disjoint_none_r s;\n loc_disjoint_sym s loc_none\n\nlet loc_disjoint_union_l s s1 s2 =\n loc_disjoint_sym s1 s;\n loc_disjoint_sym s2 s;\n loc_disjoint_union_r s s1 s2;\n loc_disjoint_sym s (loc_union s1 s2)\n\nlet loc_disjoint_gfield_r p #l q fd =\n loc_disjoint_includes p (loc_pointer q) p (loc_pointer (gfield q fd))\n\nlet loc_disjoint_gfield_l p #l q fd =\n loc_disjoint_sym (loc_pointer q) p;\n loc_disjoint_gfield_r p q fd;\n loc_disjoint_sym p (loc_pointer (gfield q fd))\n\nlet loc_disjoint_gufield_r p #l q fd =\n loc_disjoint_includes p (loc_pointer q) p (loc_pointer (gufield q fd))\n\nlet loc_disjoint_gufield_l p #l q fd =\n loc_disjoint_sym (loc_pointer q) p;\n loc_disjoint_gufield_r p q fd;\n loc_disjoint_sym p (loc_pointer (gufield q fd))\n\nlet loc_disjoint_gcell_r p #value #len q i =\n loc_disjoint_includes p (loc_pointer q) p (loc_pointer (gcell q i))\n\nlet loc_disjoint_gcell_l p #value #len q i =\n loc_disjoint_sym (loc_pointer q) p;\n loc_disjoint_gcell_r p q i;\n loc_disjoint_sym p (loc_pointer (gcell q i))\n\nlet loc_disjoint_gsingleton_buffer_of_pointer_r l #t p =\n loc_disjoint_includes l (loc_pointer p) l (loc_buffer (gsingleton_buffer_of_pointer p))\n\nlet loc_disjoint_gsingleton_buffer_of_pointer_l l #t p =\n loc_disjoint_sym (loc_pointer p) l;\n loc_disjoint_gsingleton_buffer_of_pointer_r l p;\n loc_disjoint_sym l (loc_buffer (gsingleton_buffer_of_pointer p))\n\nlet loc_disjoint_gbuffer_of_array_pointer_r l #t #len p =\n loc_disjoint_includes l (loc_pointer p) l (loc_buffer (gbuffer_of_array_pointer p))\n\nlet loc_disjoint_gbuffer_of_array_pointer_l l #t #len p =\n loc_disjoint_includes (loc_pointer p) l (loc_buffer (gbuffer_of_array_pointer p)) l\n\nlet loc_disjoint_gpointer_of_buffer_cell_r l #t b i =\n loc_disjoint_includes l (loc_buffer b) l (loc_pointer (gpointer_of_buffer_cell b i))\n" }, { "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.raise_aloc", "opens_and_abbrevs": [ { "abbrev": "U", "full_module": "FStar.Universe" }, { "abbrev": "F", "full_module": "FStar.FunctionalExtensionality" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "abbrev": "HST", "full_module": "FStar.HyperStack.ST" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "open": "FStar" }, { "open": "FStar" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val raise_aloc (al: aloc_t u#x) : Tot (aloc_t u#(max x (y + 1)))", "source_definition": "let raise_aloc al r n = U.raise_t (al r n)", "source_range": { "start_line": 2096, "start_col": 0, "end_line": 2096, "end_col": 42 }, "interleaved": false, "definition": "fun al r n -> FStar.Universe.raise_t (al r n)", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.ModifiesGen.aloc_t", "FStar.Monotonic.HyperHeap.rid", "Prims.nat", "FStar.Universe.raise_t" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "al: FStar.ModifiesGen.aloc_t -> FStar.ModifiesGen.aloc_t", "prompt": "let raise_aloc al r n =\n ", "expected_response": "U.raise_t (al r n)", "source": { "project_name": "FStar", "file_name": "ulib/FStar.ModifiesGen.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.ModifiesGen.fst", "checked_file": "dataset/FStar.ModifiesGen.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Universe.fsti.checked", "dataset/FStar.Tactics.SMT.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Stubs.Tactics.V2.Builtins.fsti.checked", "dataset/FStar.StrongExcludedMiddle.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Map.fsti.checked", "dataset/FStar.HyperStack.ST.fsti.checked", "dataset/FStar.HyperStack.fst.checked", "dataset/FStar.Heap.fst.checked", "dataset/FStar.GSet.fsti.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "aloc", "ALoc", "ALoc", "ALoc", "aloc_t", "region", "region", "addr", "addr", "loc", "loc", "cls", "Cls", "Cls", "Cls", "aloc_includes", "aloc_includes", "let aloc_domain (#al: aloc_t) (c: cls al) (regions: Ghost.erased (Set.set HS.rid)) (addrs: ((r: HS.rid { Set.mem r (Ghost.reveal regions) } ) -> GTot (GSet.set nat))) : GTot (GSet.set (aloc c)) =\n GSet.comprehend (fun a -> Set.mem a.region (Ghost.reveal regions) && GSet.mem a.addr (addrs a.region))", "aloc_includes_refl", "aloc_includes_refl", "let i_restricted_g_t = F.restricted_g_t", "let addrs_dom regions =\n (r: HS.rid { Set.mem r (Ghost.reveal regions) } )", "let non_live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (r:addrs_dom regions) =\n (y: GSet.set nat { r `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y })", "aloc_includes_trans", "aloc_includes_trans", "let live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags))\n (r:addrs_dom regions) = (y: GSet.set nat { GSet.subset (non_live_addrs r) y } )", "aloc_disjoint", "aloc_disjoint", "loc'", "Loc", "Loc", "Loc", "regions", "regions", "aloc_disjoint_sym", "aloc_disjoint_sym", "region_liveness_tags", "region_liveness_tags", "non_live_addrs", "non_live_addrs", "live_addrs", "live_addrs", "aloc_disjoint_includes", "aloc_disjoint_includes", "aux", "aux", "let loc = loc'", "let mk_non_live_addrs (#regions:_) (#region_liveness_tags:_)\n (f: (x:addrs_dom regions -> GTot (non_live_addrs_codom regions region_liveness_tags x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags) =\n F.on_dom_g _ f", "aloc_preserved", "aloc_preserved", "let mk_live_addrs (#regions:_) (#region_liveness_tags:_)\n (#non_live_addrs_codom: _)\n (f: (x:addrs_dom regions -> GTot (live_addrs_codom regions region_liveness_tags non_live_addrs_codom x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs_codom) =\n F.on_dom_g _ f", "aloc_preserved_refl", "aloc_preserved_refl", "let loc_none #a #c =\n Loc\n (Ghost.hide (Set.empty))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)", "aloc_preserved_trans", "aloc_preserved_trans", "let regions_of_loc\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: GTot (Set.set HS.rid)\n= Ghost.reveal (Loc?.regions s)", "let addrs_of_loc_liveness_not_preserved\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.non_live_addrs l r\n else GSet.empty", "same_mreference_aloc_preserved", "same_mreference_aloc_preserved", "let addrs_of_loc_weak\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.live_addrs l r\n else GSet.empty", "let addrs_of_loc_aux_pred\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n (addr: nat)\n: GTot bool\n= StrongExcludedMiddle.strong_excluded_middle (exists a . GSet.mem a (Ghost.reveal (Loc?.aux l)) /\\ a.region == r /\\ a.addr == addr)", "val loc (#aloc: aloc_t u#x) (c: cls aloc) : Tot (Type u#x)", "val loc_none (#aloc: aloc_t) (#c: cls aloc): Tot (loc c)", "val loc_union\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot (loc c)", "let addrs_of_loc_aux\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (y: GSet.set nat { GSet.subset (GSet.intersect y (addrs_of_loc_weak l r)) GSet.empty } )\n= GSet.comprehend (addrs_of_loc_aux_pred l r)\n `GSet.intersect` (GSet.complement (addrs_of_loc_weak l r))", "val loc_union_idem\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union s s == s)", "let addrs_of_loc\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= GSet.union\n (addrs_of_loc_weak l r)\n (addrs_of_loc_aux l r)", "val loc_union_comm\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: Lemma\n (loc_union s1 s2 == loc_union s2 s1)", "let addrs_of_loc_aux_prop\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: Lemma\n (GSet.subset (GSet.intersect (addrs_of_loc_aux l r) (addrs_of_loc_weak l r)) GSet.empty)\n [SMTPatOr [\n [SMTPat (addrs_of_loc_aux l r)];\n [SMTPat (addrs_of_loc_weak l r)];\n [SMTPat (addrs_of_loc l r)];\n ]]\n= ()", "val loc_union_assoc\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s3: loc c)\n: Lemma\n (loc_union s1 (loc_union s2 s3) == loc_union (loc_union s1 s2) s3)", "val loc_union_loc_none_l\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union loc_none s == s)", "val loc_union_loc_none_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_union s loc_none == s)", "let loc_union #al #c s1 s2 =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in\n let regions = Set.union regions1 regions2 in\n let region_liveness_tags : Ghost.erased (Set.set HS.rid) = (Ghost.hide (Set.union (Ghost.reveal (Loc?.region_liveness_tags s1)) (Ghost.reveal (Loc?.region_liveness_tags s2)))) in\n let gregions = Ghost.hide regions in\n let non_live_addrs =\n F.on_dom_g (addrs_dom gregions) #(non_live_addrs_codom gregions region_liveness_tags)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then Loc?.non_live_addrs s1 r else GSet.empty)\n (if Set.mem r regions2 then Loc?.non_live_addrs s2 r else GSet.empty))\n in\n let live_addrs =\n F.on_dom_g (addrs_dom gregions) #(live_addrs_codom gregions region_liveness_tags non_live_addrs)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then addrs_of_loc_weak s1 r else GSet.empty)\n (if Set.mem r regions2 then addrs_of_loc_weak s2 r else GSet.empty))\n in\n let aux = Ghost.hide\n (Ghost.reveal (Loc?.aux s1) `GSet.union` Ghost.reveal (Loc?.aux s2))\n in\n Loc\n (Ghost.hide regions)\n region_liveness_tags\n non_live_addrs\n live_addrs\n aux", "val loc_of_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b: aloc r n)\n: GTot (loc c)", "val loc_of_aloc_not_none\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b: aloc r n)\n: Lemma (loc_of_aloc #_ #c b == loc_none ==> False)", "val loc_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: GTot (loc c)", "val loc_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: GTot (loc c)", "let fun_set_equal (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) :Tot Type0 =\n forall (x: t) . {:pattern (f1 x) \\/ (f2 x) } f1 x `GSet.equal` f2 x", "let loc_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses true (HS.frameOf b) (Set.singleton (HS.as_addr b))", "let fun_set_equal_elim (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) : Lemma\n (requires (fun_set_equal f1 f2))\n (ensures (f1 == f2))\n// [SMTPat (fun_set_equal f1 f2)]\n= assert (f1 `FunctionalExtensionality.feq_g` f2)", "let loc_freed_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses false (HS.frameOf b) (Set.singleton (HS.as_addr b))", "let loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n let Loc regions1 region_liveness_tags1 _ _ aux1 = s1 in\n let Loc regions2 region_liveness_tags2 _ _ aux2 = s2 in\n Ghost.reveal regions1 `Set.equal` Ghost.reveal regions2 /\\\n Ghost.reveal region_liveness_tags1 `Set.equal` Ghost.reveal region_liveness_tags2 /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)", "let loc_region_only\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (Set.singleton r)", "let loc_equal_elim (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : Lemma\n (requires (loc_equal s1 s2))\n (ensures (s1 == s2))\n [SMTPat (s1 `loc_equal` s2)]\n= fun_set_equal_elim (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2);\n fun_set_equal_elim (Loc?.live_addrs s1) (Loc?.live_addrs s2)", "let loc_all_regions_from\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (HS.mod_set (Set.singleton r))", "let loc_union_idem #al #c s =\n assert (loc_union s s `loc_equal` s)", "let loc_union_comm #al #c s1 s2 =\n assert (loc_union s1 s2 `loc_equal` loc_union s2 s1)", "let loc_union_assoc #al #c s1 s2 s3 =\n assert (loc_union s1 (loc_union s2 s3) `loc_equal` loc_union (loc_union s1 s2) s3)", "val loc_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot Type0", "let loc_union_loc_none_l #al #c s =\n assert (loc_union loc_none s `loc_equal` s)", "val loc_includes_refl\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_includes s s)", "let loc_union_loc_none_r #al #c s =\n assert (loc_union s loc_none `loc_equal` s)", "let loc_of_aloc #al #c #r #n b =\n let regions = (Ghost.hide (Set.singleton r)) in\n let region_liveness_tags = (Ghost.hide (Set.empty)) in\n Loc\n regions\n region_liveness_tags\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide (GSet.singleton (ALoc r n (Some b))))", "val loc_includes_trans\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s3: loc c)\n: Lemma\n (requires (loc_includes s1 s2 /\\ loc_includes s2 s3))\n (ensures (loc_includes s1 s3))", "val loc_includes_union_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s s1 s2: loc c)\n: Lemma\n (requires (loc_includes s s1 /\\ loc_includes s s2))\n (ensures (loc_includes s (loc_union s1 s2)))", "let loc_of_aloc_not_none #al #c #r #n b = ()", "let loc_addresses #al #c preserve_liveness r n =\n let regions = (Ghost.hide (Set.singleton r)) in\n Loc\n regions\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> if preserve_liveness then GSet.empty else GSet.of_set n))\n (mk_live_addrs (fun _ -> GSet.of_set n))\n (Ghost.hide (aloc_domain c regions (fun _ -> GSet.of_set n)))", "val loc_includes_union_l\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2 s: loc c)\n: Lemma\n (requires (loc_includes s1 s \\/ loc_includes s2 s))\n (ensures (loc_includes (loc_union s1 s2) s))", "let loc_regions_region_liveness_tags (preserve_liveness: bool) (r: Set.set HS.rid) : Tot (Ghost.erased (Set.set HS.rid)) =\n if preserve_liveness then Ghost.hide Set.empty else Ghost.hide r", "val loc_includes_none\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (loc_includes s loc_none)", "let loc_regions #al #c preserve_liveness r =\n let region_liveness_tags = loc_regions_region_liveness_tags preserve_liveness r in\n let addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { r' `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y } ) =\n GSet.complement GSet.empty\n in\n let live_addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { addrs r' `GSet.subset` y } ) =\n addrs r'\n in\n Loc\n (Ghost.hide r)\n region_liveness_tags\n (mk_non_live_addrs addrs)\n (mk_live_addrs live_addrs)\n (Ghost.hide (aloc_domain c (Ghost.hide r) addrs))", "val loc_includes_none_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (requires (loc_includes loc_none s))\n (ensures (s == loc_none))", "val loc_includes_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b1 b2: aloc r n)\n: Lemma\n (requires (c.aloc_includes b1 b2))\n (ensures (loc_includes (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))", "let aloc_includes (#al: aloc_t) (#c: cls al) (b0 b: aloc c) : GTot Type0 =\n b0.region == b.region /\\ b0.addr == b.addr /\\ Some? b0.loc == Some? b.loc /\\ (if Some? b0.loc && Some? b.loc then c.aloc_includes (Some?.v b0.loc) (Some?.v b.loc) else True)", "let loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b: aloc c)\n: GTot Type0\n (decreases s)\n= exists (b0 : aloc c) . b0 `GSet.mem` s /\\ b0 `aloc_includes` b", "val loc_includes_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1 #r2: HS.rid)\n (#n1 #n2: nat)\n (b1: aloc r1 n1)\n (b2: aloc r2 n2)\n: Lemma\n (requires (loc_includes (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))\n (ensures (r1 == r2 /\\ n1 == n2 /\\ c.aloc_includes b1 b2))", "let loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: GTot Type0\n (decreases s2)\n= forall (b2: aloc c) . GSet.mem b2 s2 ==> loc_aux_includes_buffer s1 b2", "val loc_includes_addresses_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n (s: Set.set nat)\n (#a: nat)\n (p: aloc r a)\n: Lemma\n (requires (Set.mem a s))\n (ensures (loc_includes (loc_addresses preserve_liveness r s) (loc_of_aloc #_ #c p)))", "let loc_aux_includes_union_l\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s \\/ loc_aux_includes s2 s))\n (ensures (loc_aux_includes (GSet.union s1 s2) s))\n (decreases s)\n= ()", "let loc_aux_includes_refl\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n: Lemma\n (loc_aux_includes s s)\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)", "val loc_includes_region_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (s: Set.set HS.rid)\n (#r: HS.rid)\n (#a: nat)\n (b: aloc r a)\n: Lemma\n (requires (Set.mem r s))\n (ensures (loc_includes (loc_regions preserve_liveness s) (loc_of_aloc #_ #c b)))", "let loc_aux_includes_subset\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)", "val loc_includes_region_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (s: Set.set HS.rid)\n (r: HS.rid)\n (a: Set.set nat)\n: Lemma\n (requires (Set.mem r s))\n (ensures (loc_includes (loc_regions #_ #c preserve_liveness1 s) (loc_addresses preserve_liveness2 r a)))", "let loc_aux_includes_subset'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n [SMTPatOr [\n [SMTPat (s1 `GSet.subset` s2)];\n [SMTPat (loc_aux_includes s2 s1)];\n ]]\n= loc_aux_includes_subset s1 s2", "val loc_includes_region_region\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires ((preserve_liveness1 ==> preserve_liveness2) /\\ Set.subset s2 s1))\n (ensures (loc_includes (loc_regions #_ #c preserve_liveness1 s1) (loc_regions preserve_liveness2 s2)))", "let loc_aux_includes_union_l_r\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s s') s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s s' s", "val loc_includes_region_union_l\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (l: loc c)\n (s1 s2: Set.set HS.rid)\n: Lemma\n (requires (loc_includes l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)))))\n (ensures (loc_includes (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness s2)))", "let loc_aux_includes_union_l_l\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s' s) s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s' s s", "val loc_includes_addresses_addresses\n (#aloc: aloc_t) (c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r: HS.rid)\n (a1 a2: Set.set nat)\n: Lemma\n (requires ((preserve_liveness1 ==> preserve_liveness2) /\\ Set.subset a2 a1))\n (ensures (loc_includes #_ #c (loc_addresses preserve_liveness1 r a1) (loc_addresses preserve_liveness2 r a2)))", "let loc_aux_includes_buffer_includes\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b1 b2: aloc c)\n: Lemma\n (requires (loc_aux_includes_buffer s b1 /\\ b1 `aloc_includes` b2))\n (ensures (loc_aux_includes_buffer s b2))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))", "val loc_disjoint\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: GTot Type0", "let loc_aux_includes_loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n (b: aloc c)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_buffer s2 b))\n (ensures (loc_aux_includes_buffer s1 b))\n= Classical.forall_intro_3 (fun s b1 b2 -> Classical.move_requires (loc_aux_includes_buffer_includes #al #c s b1) b2)", "val loc_disjoint_sym\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))", "let loc_aux_includes_trans\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))", "val loc_disjoint_none_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n: Lemma\n (ensures (loc_disjoint s loc_none))", "let addrs_of_loc_weak_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (loc_union l1 l2) r == GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r))\n [SMTPat (addrs_of_loc_weak (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc_weak (loc_union l1 l2) r) (GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r)))", "val loc_disjoint_union_r\n (#aloc: aloc_t) (#c: cls aloc)\n (s s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s s1 /\\ loc_disjoint s s2))\n (ensures (loc_disjoint s (loc_union s1 s2)))", "val loc_disjoint_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (p1 p2 p1' p2' : loc c)\n: Lemma\n (requires (loc_includes p1 p1' /\\ loc_includes p2 p2' /\\ loc_disjoint p1 p2))\n (ensures (loc_disjoint p1' p2'))", "let addrs_of_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l1 l2) r == GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r))\n [SMTPat (addrs_of_loc (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc (loc_union l1 l2) r) (GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r)))", "val loc_disjoint_aloc_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1: HS.rid)\n (#a1: nat)\n (#r2: HS.rid)\n (#a2: nat)\n (b1: aloc r1 a1)\n (b2: aloc r2 a2)\n: Lemma\n (requires ((r1 == r2 /\\ a1 == a2) ==> c.aloc_disjoint b1 b2))\n (ensures (loc_disjoint (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))", "let loc_includes' #al (#c: cls al) (s1 s2: loc c) =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in (\n Set.subset regions2 regions1 /\\\n Set.subset (Ghost.reveal (Loc?.region_liveness_tags s2)) (Ghost.reveal (Loc?.region_liveness_tags s1)) /\\\n (\n forall (r: HS.rid { Set.mem r regions2 } ) .\n GSet.subset (Loc?.non_live_addrs s2 r) (Loc?.non_live_addrs s1 r)\n ) /\\\n (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc_weak s2 r) (addrs_of_loc_weak s1 r)\n ) /\\ (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc s2 r) (addrs_of_loc s1 r)\n ) /\\ (\n (Ghost.reveal (Loc?.aux s1)) `loc_aux_includes` (Ghost.reveal (Loc?.aux s2))\n )\n )", "val loc_disjoint_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r1: HS.rid)\n (#a1: nat)\n (#r2: HS.rid)\n (#a2: nat)\n (b1: aloc r1 a1)\n (b2: aloc r2 a2)\n: Lemma\n (requires (loc_disjoint (loc_of_aloc b1) (loc_of_aloc #_ #c b2)))\n (ensures ((r1 == r2 /\\ a1 == a2) ==> c.aloc_disjoint b1 b2))", "val loc_disjoint_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r1 r2: HS.rid)\n (n1 n2: Set.set nat)\n: Lemma\n (requires (r1 <> r2 \\/ Set.subset (Set.intersect n1 n2) Set.empty))\n (ensures (loc_disjoint (loc_addresses #_ #c preserve_liveness1 r1 n1) (loc_addresses preserve_liveness2 r2 n2)))", "let loc_includes #al #c s1 s2 =\n loc_includes' s1 s2", "let loc_includes_refl #al #c s =\n loc_aux_includes_refl (Ghost.reveal (Loc?.aux s))", "let loc_includes_refl'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: Lemma\n (loc_includes s s)\n [SMTPat (loc_includes s s)]\n= loc_includes_refl s", "let loc_disjoint_addresses #aloc #c = loc_disjoint_addresses_intro #aloc #c", "val loc_disjoint_addresses_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (r1 r2: HS.rid)\n (n1 n2: Set.set nat)\n: Lemma\n (requires (loc_disjoint (loc_addresses #_ #c preserve_liveness1 r1 n1) (loc_addresses preserve_liveness2 r2 n2)))\n (ensures (r1 <> r2 \\/ Set.subset (Set.intersect n1 n2) Set.empty))", "let loc_includes_trans #al #c s1 s2 s3 =\n loc_aux_includes_trans (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s3))", "let loc_includes_union_r #al #c s s1 s2 = ()", "let loc_includes_union_l #al #c s1 s2 s =\n let u12 = loc_union s1 s2 in\n Classical.or_elim\n #(loc_includes s1 s)\n #(loc_includes s2 s)\n #(fun _ -> loc_includes (loc_union s1 s2) s)\n (fun _ ->\n loc_aux_includes_union_l_r (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2));\n assert (loc_includes (loc_union s1 s2) s1);\n loc_includes_trans u12 s1 s)\n (fun _ ->\n loc_aux_includes_union_l_l (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s1));\n assert (loc_includes (loc_union s1 s2) s2);\n loc_includes_trans u12 s2 s)", "val loc_disjoint_aloc_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (#r' : HS.rid)\n (#a' : nat)\n (p: aloc r' a')\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (requires (r == r' ==> (~ (Set.mem a' n))))\n (ensures (loc_disjoint (loc_of_aloc p) (loc_addresses #_ #c preserve_liveness r n)))", "val loc_disjoint_aloc_addresses_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r' : HS.rid)\n (#a' : nat)\n (p: aloc r' a')\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (requires (loc_disjoint (loc_of_aloc p) (loc_addresses #_ #c preserve_liveness r n)))\n (ensures (r == r' ==> (~ (Set.mem a' n))))", "let loc_includes_none #al #c s = ()", "let loc_includes_none_elim #al #c s =\n assert (s `loc_equal` loc_none)", "let loc_includes_aloc #al #c #r #n b1 b2 = ()", "let loc_includes_aloc_elim #aloc #c #r1 #r2 #n1 #n2 b1 b2 = ()", "let addrs_of_loc_loc_of_aloc\n (#al: aloc_t)\n (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (p: al r a)\n (r': HS.rid)\n: Lemma\n (addrs_of_loc (loc_of_aloc #_ #c p) r' `GSet.equal` (if r = r' then GSet.singleton a else GSet.empty))\n [SMTPat (addrs_of_loc (loc_of_aloc #_ #c p) r')]\n= ()", "val loc_disjoint_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness1 preserve_liveness2: bool)\n (rs1 rs2: Set.set HS.rid)\n: Lemma\n (requires (Set.subset (Set.intersect rs1 rs2) Set.empty))\n (ensures (loc_disjoint (loc_regions #_ #c preserve_liveness1 rs1) (loc_regions preserve_liveness2 rs2)))", "val address_liveness_insensitive_locs (#aloc: aloc_t) (c: cls aloc) : Tot (loc c)", "let loc_includes_addresses_aloc #al #c preserve_liveness r s #a p = ()", "val loc_includes_address_liveness_insensitive_locs_aloc (#aloc: aloc_t) (#c: cls aloc) (#r: HS.rid) (#n: nat) (a: aloc r n) : Lemma\n (loc_includes (address_liveness_insensitive_locs c) (loc_of_aloc a))", "let loc_includes_region_aloc #al #c preserve_liveness s #r #a b = ()", "let loc_includes_region_addresses #al #c s preserve_liveness1 preserve_liveness2 r a = ()", "val loc_includes_address_liveness_insensitive_locs_addresses (#aloc: aloc_t) (c: cls aloc) (r: HS.rid) (a: Set.set nat) : Lemma\n (loc_includes (address_liveness_insensitive_locs c) (loc_addresses true r a))", "let loc_includes_region_region #al #c preserve_liveness1 preserve_liveness2 s1 s2 = ()", "val region_liveness_insensitive_locs (#al: aloc_t) (c: cls al) : Tot (loc c)", "let loc_includes_region_union_l #al #c preserve_liveness l s1 s2 =\n assert ((loc_regions #_ #c preserve_liveness (Set.intersect s2 (Set.complement s1)) `loc_union` loc_regions #_ #c preserve_liveness (Set.intersect s2 s1)) `loc_equal` loc_regions preserve_liveness s2);\n loc_includes_region_region #_ #c preserve_liveness preserve_liveness s1 (Set.intersect s2 s1);\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)));\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 s1));\n loc_includes_union_r (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1))) (loc_regions preserve_liveness (Set.intersect s2 s1))", "val loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs (#al: aloc_t) (c: cls al) : Lemma\n (loc_includes (region_liveness_insensitive_locs c) (address_liveness_insensitive_locs c))", "val loc_includes_region_liveness_insensitive_locs_loc_regions\n (#al: aloc_t) (c: cls al) (r: Set.set HS.rid)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_regions #_ #c true r)", "let loc_includes_addresses_addresses #al c preserve_liveness1 preserve_liveness2 r s1 s2 = ()", "val loc_includes_region_liveness_insensitive_locs_loc_addresses\n (#al: aloc_t) (c: cls al) (preserve_liveness: bool) (r: HS.rid) (a: Set.set nat)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_addresses #_ #c preserve_liveness r a)", "let aloc_disjoint (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : GTot Type0 =\n if b1.region = b2.region && b1.addr = b2.addr\n then Some? b1.loc /\\ Some? b2.loc /\\ c.aloc_disjoint (Some?.v b1.loc) (Some?.v b2.loc)\n else True", "val loc_includes_region_liveness_insensitive_locs_loc_of_aloc\n (#al: aloc_t) (c: cls al) (#r: HS.rid) (#a: nat) (x: al r a)\n: Lemma\n (region_liveness_insensitive_locs c `loc_includes` loc_of_aloc #_ #c x)", "let aloc_disjoint_sym (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : Lemma\n (aloc_disjoint b1 b2 <==> aloc_disjoint b2 b1)\n= Classical.forall_intro_2 (fun r a -> Classical.forall_intro_2 (fun b1 b2 -> c.aloc_disjoint_sym #r #a b1 b2))", "let loc_aux_disjoint\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: GTot Type0\n= forall (b1 b2: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b2 l2) ==> aloc_disjoint b1 b2", "val modifies\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0", "let loc_aux_disjoint_union_l\n (#al: aloc_t) (#c: cls al)\n (ll1 lr1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint (GSet.union ll1 lr1) l2 <==> (loc_aux_disjoint ll1 l2 /\\ loc_aux_disjoint lr1 l2)))\n= ()", "val modifies_intro\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')", "let loc_aux_disjoint_union_r\n (#al: aloc_t) (#c: cls al)\n (l1 ll2 lr2: GSet.set (aloc c))\n: Lemma\n (loc_aux_disjoint l1 (GSet.union ll2 lr2) <==> (loc_aux_disjoint l1 ll2 /\\ loc_aux_disjoint l1 lr2))\n= ()", "let loc_aux_disjoint_sym\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint l1 l2 <==> loc_aux_disjoint l2 l1))\n= Classical.forall_intro_2 (aloc_disjoint_sym #al #c)", "let regions_of_loc_loc_union\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (regions_of_loc (loc_union s1 s2) == regions_of_loc s1 `Set.union` regions_of_loc s2)\n [SMTPat (regions_of_loc (loc_union s1 s2))]\n= assert (regions_of_loc (loc_union s1 s2) `Set.equal` (regions_of_loc s1 `Set.union` regions_of_loc s2))", "let regions_of_loc_monotonic\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_includes s1 s2))\n (ensures (Set.subset (regions_of_loc s2) (regions_of_loc s1)))\n= ()", "let loc_disjoint_region_liveness_tags (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty", "let loc_disjoint_addrs (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n (forall (r: HS.rid) .\n GSet.subset (GSet.intersect (addrs_of_loc_weak l1 r) (addrs_of_loc l2 r)) GSet.empty /\\\n GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc_weak l2 r)) GSet.empty\n )", "let loc_disjoint_aux (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n loc_aux_disjoint (Ghost.reveal (Loc?.aux l1)) (Ghost.reveal (Loc?.aux l2))", "val modifies_none_intro\n (#al: aloc_t) (#c: cls al) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (HS.live_region h r /\\ HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n: Lemma\n (modifies (loc_none #_ #c) h h')", "let loc_disjoint'\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n: GTot Type0\n= loc_disjoint_region_liveness_tags l1 l2 /\\\n loc_disjoint_addrs l1 l2 /\\\n loc_disjoint_aux l1 l2", "let loc_disjoint = loc_disjoint'", "let loc_disjoint_sym #al #c l1 l2 =\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c)", "let loc_disjoint_sym'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))\n [SMTPat (loc_disjoint s1 s2)]\n= loc_disjoint_sym s1 s2", "let loc_disjoint_none_r #al #c s = ()", "let loc_disjoint_union_r #al #c s s1 s2 = ()", "val modifies_address_intro\n (#al: aloc_t) (#c: cls al) (r: HS.rid) (n: nat) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((r <> HS.frameOf b \\/ n <> HS.as_addr b) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (addr_unused_in: (\n (r': HS.rid) ->\n (n' : nat) ->\n Lemma\n (requires ((r' <> r \\/ n' <> n) /\\ HS.live_region h r' /\\ HS.live_region h' r' /\\ n' `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r')))\n (ensures (n' `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r')))\n ))\n: Lemma\n (modifies (loc_addresses #_ #c false r (Set.singleton n)) h h')", "let aloc_disjoint_includes (#al: aloc_t) (#c: cls al) (b1 b2 b3 : aloc c) : Lemma\n (requires (aloc_disjoint b1 b2 /\\ aloc_includes b2 b3))\n (ensures (aloc_disjoint b1 b3))\n= if b1.region = b2.region && b1.addr = b2.addr\n then begin\n c.aloc_includes_refl (Some?.v b1.loc);\n c.aloc_disjoint_includes (Some?.v b1.loc) (Some?.v b2.loc) (Some?.v b1.loc) (Some?.v b3.loc)\n end\n else ()", "let loc_aux_disjoint_loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (l1 l2 l3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\n= // FIXME: WHY WHY WHY do I need this assert?\n assert (forall (b1 b3: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b3 l3) ==> (exists (b2: aloc c) . GSet.mem b2 l2 /\\ aloc_disjoint b1 b2 /\\ aloc_includes b2 b3));\n Classical.forall_intro_3 (fun b1 b2 b3 -> Classical.move_requires (aloc_disjoint_includes #al #c b1 b2) b3)", "let loc_disjoint_includes #al #c p1 p2 p1' p2' =\n regions_of_loc_monotonic p1 p1';\n regions_of_loc_monotonic p2 p2';\n let l1 = Ghost.reveal (Loc?.aux p1) in\n let l2 = Ghost.reveal (Loc?.aux p2) in\n let l1' = Ghost.reveal (Loc?.aux p1') in\n let l2' = Ghost.reveal (Loc?.aux p2') in\n loc_aux_disjoint_loc_aux_includes l1 l2 l2';\n loc_aux_disjoint_sym l1 l2';\n loc_aux_disjoint_loc_aux_includes l2' l1 l1';\n loc_aux_disjoint_sym l2' l1'", "val modifies_aloc_intro\n (#al: aloc_t) (#c: cls al) (#r: HS.rid) (#n: nat) (z: al r n) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((r <> HS.frameOf b \\/ n <> HS.as_addr b) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (HS.live_region h r /\\ HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (x: al r n) ->\n Lemma\n (requires (c.aloc_disjoint x z))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies (loc_of_aloc #_ #c z) h h')", "let loc_disjoint_aloc_intro #al #c #r1 #a1 #r2 #a2 b1 b2 = ()", "let loc_disjoint_aloc_elim #al #c #r1 #a1 #r2 #a2 b1 b2 =\n // FIXME: WHY WHY WHY this assert?\n assert (aloc_disjoint (ALoc #_ #c r1 a1 (Some b1)) (ALoc #_ #c r2 a2 (Some b2)))", "let loc_disjoint_addresses_intro #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness1 r1 n1))) (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness2 r2 n2))))", "let loc_disjoint_addresses_elim #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 = ()", "let loc_disjoint_aloc_addresses_intro #al #c #r' #a' p preserve_liveness r n = ()", "let loc_disjoint_aloc_addresses_elim #al #c #r' #a' p preserve_liveness r n = ()", "let loc_disjoint_regions #al #c preserve_liveness1 preserve_liveness2 rs1 rs2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness1 rs1))) (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness2 rs2))))", "let loc_none_in_some_region #a (c: cls a) (r: HS.rid) : GTot (loc c) =\n Loc\n (Ghost.hide (Set.singleton r))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)", "let address_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))", "val modifies_live_region\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h1 h2: HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (modifies s h1 h2 /\\ loc_disjoint s (loc_region_only false r) /\\ HS.live_region h1 r))\n (ensures (HS.live_region h2 r))", "let loc_includes_address_liveness_insensitive_locs_aloc #al #c #r #n a = ()", "val modifies_mreference_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (b: HS.mreference t pre)\n (p: loc c)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_mreference b) p /\\\n HS.contains h b /\\\n modifies p h h'\n ))\n (ensures (\n HS.contains h' b /\\\n HS.sel h b == HS.sel h' b\n ))", "let loc_includes_address_liveness_insensitive_locs_addresses #al c r a = ()", "let region_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.complement GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))", "let loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs #al c = ()", "let loc_includes_region_liveness_insensitive_locs_loc_regions #al c r = ()", "let loc_includes_region_liveness_insensitive_locs_loc_addresses #al c preserve_liveness r a = ()", "let loc_includes_region_liveness_insensitive_locs_loc_of_aloc #al c #r #a x = ()", "val modifies_aloc_elim\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#a: nat)\n (b: aloc r a)\n (p: loc c)\n (h h': HS.mem)\n: Lemma\n (requires (\n loc_disjoint (loc_of_aloc b) p /\\\n modifies p h h'\n ))\n (ensures (\n c.aloc_preserved b h h'\n ))", "let modifies_preserves_livenesses\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s r)))\n ) ==> (\n HS.contains h2 p\n ))", "let modifies_preserves_livenesses_elim\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (p: HS.mreference t pre)\n: Lemma\n (requires (modifies_preserves_livenesses s h1 h2 /\\ HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))))\n (ensures (HS.contains h2 p))\n= ()", "val modifies_refl\n (#aloc: aloc_t) (#c: cls aloc)\n (s: loc c)\n (h: HS.mem)\n: Lemma\n (modifies s h h)", "val modifies_loc_includes\n (#aloc: aloc_t) (#c: cls aloc)\n (s1: loc c)\n (h h': HS.mem)\n (s2: loc c)\n: Lemma\n (requires (modifies s2 h h' /\\ loc_includes s1 s2))\n (ensures (modifies s1 h h'))", "let modifies_preserves_livenesses_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p))\n ))\n: Lemma\n (modifies_preserves_livenesses s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'", "val modifies_preserves_liveness\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union s1 s2) h h' /\\ loc_disjoint s1 (loc_mreference r) /\\ loc_includes (address_liveness_insensitive_locs c) s2 /\\ h `HS.contains` r))\n (ensures (h' `HS.contains` r))", "val modifies_preserves_liveness_strong\n (#aloc: aloc_t) (#c: cls aloc)\n (s1 s2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n (x: aloc (HS.frameOf r) (HS.as_addr r))\n: Lemma\n (requires (modifies (loc_union s1 s2) h h' /\\ loc_disjoint s1 (loc_of_aloc #_ #c #(HS.frameOf r) #(HS.as_addr r) x) /\\ loc_includes (address_liveness_insensitive_locs c) s2 /\\ h `HS.contains` r))\n (ensures (h' `HS.contains` r))", "val modifies_preserves_region_liveness\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_region_only false r) l1 /\\ HS.live_region h r))\n (ensures (HS.live_region h' r))", "let modifies_preserves_mreferences\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s r)))\n ) ==> (\n HS.contains h2 p /\\\n HS.sel h2 p == HS.sel h1 p\n ))", "val modifies_preserves_region_liveness_reference\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_mreference r) l1 /\\ HS.live_region h (HS.frameOf r)))\n (ensures (HS.live_region h' (HS.frameOf r)))", "let modifies_preserves_mreferences_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p /\\ HS.sel h2 p == HS.sel h1 p))\n ))\n: Lemma\n (modifies_preserves_mreferences s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p /\\ h2 `HS.sel` p == h1 `HS.sel` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'", "val modifies_preserves_region_liveness_aloc\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (h h' : HS.mem)\n (#r: HS.rid)\n (#n: nat)\n (x: al r n)\n: Lemma\n (requires (modifies (loc_union l1 l2) h h' /\\ region_liveness_insensitive_locs c `loc_includes` l2 /\\ loc_disjoint (loc_of_aloc x) l1 /\\ HS.live_region h r))\n (ensures (HS.live_region h' r))", "val modifies_trans\n (#aloc: aloc_t) (#c: cls aloc)\n (s12: loc c)\n (h1 h2: HS.mem)\n (s23: loc c)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s12 h1 h2 /\\ modifies s23 h2 h3))\n (ensures (modifies (loc_union s12 s23) h1 h3))", "val modifies_only_live_regions\n (#aloc: aloc_t) (#c: cls aloc)\n (rs: Set.set HS.rid)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))", "let modifies_preserves_alocs\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (a: nat) (b: al r a) .\n loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))\n ==>\n c.aloc_preserved b h1 h2\n )", "val no_upd_fresh_region\n (#aloc: aloc_t) (#c: cls aloc)\n (r:HS.rid)\n (l:loc c)\n (h0:HS.mem)\n (h1:HS.mem)\n: Lemma\n (requires (HS.fresh_region r h0 h1 /\\ modifies (loc_union (loc_all_regions_from false r) l) h0 h1))\n (ensures (modifies l h0 h1))", "let modifies_preserves_alocs_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (u: unit { modifies_preserves_mreferences s h1 h2 } )\n (f: (\n (r: HS.rid) ->\n (a: nat) ->\n (b: al r a) ->\n Lemma\n (requires (\n Set.mem r (regions_of_loc s) /\\\n (~ (GSet.mem a (addrs_of_loc_weak s r))) /\\\n (GSet.mem a (addrs_of_loc_aux s r) /\\ loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b))))\n ))\n (ensures (c.aloc_preserved b h1 h2))\n ))\n: Lemma\n (modifies_preserves_alocs s h1 h2)\n= let f'\n (r: HS.rid)\n (a: nat)\n (b: al r a)\n : Lemma\n (requires (loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))))\n (ensures (c.aloc_preserved b h1 h2))\n = if Set.mem r (regions_of_loc s) && (not (GSet.mem a (addrs_of_loc_weak s r)))\n then begin\n if GSet.mem a (addrs_of_loc_aux s r)\n then\n Classical.move_requires (f r a) b\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n end else if Set.mem r (regions_of_loc s)\n then begin\n assert (GSet.mem a (addrs_of_loc_weak s r));\n assert (GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux s)));\n assert (aloc_disjoint #_ #c (ALoc r a None) (ALoc r a (Some b)));\n assert False\n end\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n in\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (f' r a) b)", "val fresh_frame_modifies\n (#aloc: aloc_t) (c: cls aloc)\n (h0 h1: HS.mem)\n: Lemma\n (requires (HS.fresh_frame h0 h1))\n (ensures (modifies #_ #c loc_none h0 h1))", "val new_region_modifies\n (#al: aloc_t)\n (c: cls al)\n (m0: HS.mem)\n (r0: HS.rid)\n (col: option int)\n: Lemma\n (requires (HST.is_eternal_region r0 /\\ HS.live_region m0 r0 /\\ (None? col \\/ HS.is_heap_color (Some?.v col))))\n (ensures (\n let (_, m1) = HS.new_eternal_region m0 r0 col in\n modifies (loc_none #_ #c) m0 m1\n ))", "val popped_modifies\n (#aloc: aloc_t) (c: cls aloc)\n (h0 h1: HS.mem) : Lemma\n (requires (HS.popped h0 h1))\n (ensures (modifies #_ #c (loc_region_only false (HS.get_tip h0)) h0 h1))", "val modifies_fresh_frame_popped\n (#aloc: aloc_t) (#c: cls aloc)\n (h0 h1: HS.mem)\n (s: loc c)\n (h2 h3: HS.mem)\n: Lemma\n (requires (\n HS.fresh_frame h0 h1 /\\\n modifies (loc_union (loc_all_regions_from false (HS.get_tip h1)) s) h1 h2 /\\\n HS.get_tip h2 == HS.get_tip h1 /\\\n HS.popped h2 h3\n ))\n (ensures (\n modifies s h0 h3 /\\\n HS.get_tip h3 == HS.get_tip h0\n ))", "let modifies_preserves_regions\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= forall (r: HS.rid) . (HS.live_region h1 r /\\ ~ (Set.mem r (Ghost.reveal (Loc?.region_liveness_tags s)))) ==> HS.live_region h2 r", "val modifies_loc_regions_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (rs: Set.set HS.rid)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HS.modifies rs h1 h2))\n (ensures (modifies (loc_regions #_ #c true rs) h1 h2))", "let modifies_preserves_not_unused_in\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (n: nat) . (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))", "val modifies_loc_addresses_intro\n (#aloc: aloc_t) (#c: cls aloc)\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc c)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r a h1 h2\n ))\n (ensures (modifies (loc_union (loc_addresses true r a) l) h1 h2))", "let modifies_preserves_not_unused_in_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ))\n (ensures (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n ))\n: Lemma\n (modifies_preserves_not_unused_in s h1 h2)\n= let f'\n (r: HS.rid)\n (n: nat)\n : Lemma\n ((\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n = Classical.move_requires (f r) n\n in\n Classical.forall_intro_2 f'", "val modifies_ralloc_post\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (i: HS.rid)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel)\n (h' : HS.mem)\n: Lemma\n (requires (HST.ralloc_post i init h x h'))\n (ensures (modifies (loc_none #_ #c) h h'))", "val modifies_salloc_post\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (init: a)\n (h: HS.mem)\n (x: HST.mreference a rel { HS.is_stack_region (HS.frameOf x) } )\n (h' : HS.mem)\n: Lemma\n (requires (HST.salloc_post init h x h'))\n (ensures (modifies (loc_none #_ #c) h h'))", "val modifies_free\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel { HS.is_mm r } )\n (m: HS.mem { m `HS.contains` r } )\n: Lemma\n (modifies (loc_freed_mreference #_ #c r) m (HS.free r m))", "let modifies'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= modifies_preserves_regions s h1 h2 /\\\n modifies_preserves_not_unused_in s h1 h2 /\\\n modifies_preserves_mreferences s h1 h2 /\\\n modifies_preserves_livenesses s h1 h2 /\\\n modifies_preserves_alocs s h1 h2", "val modifies_none_modifies\n (#aloc: aloc_t) (#c: cls aloc)\n (h1 h2: HS.mem)\n: Lemma\n (requires (HST.modifies_none h1 h2))\n (ensures (modifies (loc_none #_ #c) h1 h2))", "let modifies = modifies'", "val modifies_intro_strong\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n (Set.mem r (regions_of_loc l) ==> ~ (GSet.mem n (Loc?.non_live_addrs l r))) /\\\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')", "val modifies_upd\n (#aloc: aloc_t) (#c: cls aloc)\n (#t: Type) (#pre: Preorder.preorder t)\n (r: HS.mreference t pre)\n (v: t)\n (h: HS.mem)\n: Lemma\n (requires (HS.contains h r))\n (ensures (modifies #_ #c (loc_mreference r) h (HS.upd h r v)))", "val modifies_strengthen\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (h h' : HS.mem)\n (alocs: (\n (f: ((t: Type) -> (pre: Preorder.preorder t) -> (m: HS.mreference t pre) -> Lemma\n (requires (HS.frameOf m == r0 /\\ HS.as_addr m == a0 /\\ HS.contains h m))\n (ensures (HS.contains h' m))\n )) ->\n (x: al r0 a0) ->\n Lemma\n (requires (c.aloc_disjoint x al0 /\\ loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (requires (modifies (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h'))\n (ensures (modifies (loc_union l (loc_of_aloc al0)) h h'))", "val does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: GTot Type0", "val not_live_region_does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (~ (HS.live_region h (fst ra))))\n (ensures (h `does_not_contain_addr` ra))", "val unused_in_does_not_contain_addr\n (h: HS.mem)\n (#a: Type)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel)\n: Lemma\n (requires (r `HS.unused_in` h))\n (ensures (h `does_not_contain_addr` (HS.frameOf r, HS.as_addr r)))", "let modifies_intro_strong #al #c l h h' regions mrefs lives unused_ins alocs =\n Classical.forall_intro (Classical.move_requires regions);\n assert (modifies_preserves_regions l h h');\n\n let aux (t:Type) (pre:Preorder.preorder t) (p:HS.mreference t pre)\n :Lemma (requires (HS.contains h p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc l) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc l (HS.frameOf p))))))\n (ensures (HS.contains h' p /\\ HS.sel h' p == HS.sel h p))\n =\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l);\n // FIXME: WHY WHY WHY is this assert necessary?\n assert_spinoff (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n // FIXME: Now this one is too :)\n assert (loc_disjoint_addrs (loc_mreference p) l);\n assert ((loc_disjoint (loc_mreference p) l));\n mrefs t pre p\n in\n\n modifies_preserves_mreferences_intro l h h' aux;\n Classical.forall_intro_3 (fun t pre p -> Classical.move_requires (lives t pre) p);\n modifies_preserves_not_unused_in_intro l h h' (fun r n ->\n unused_ins r n\n );\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n alocs r a b\n )", "val addr_unused_in_does_not_contain_addr\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))))\n (ensures (h `does_not_contain_addr` ra))", "val does_not_contain_addr_addr_unused_in\n (h: HS.mem)\n (ra: HS.rid * nat)\n: Lemma\n (requires (h `does_not_contain_addr` ra))\n (ensures (HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))))", "val free_does_not_contain_addr\n (#a: Type0)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel)\n (m: HS.mem)\n (x: HS.rid * nat)\n: Lemma\n (requires (\n HS.is_mm r /\\\n m `HS.contains` r /\\\n fst x == HS.frameOf r /\\\n snd x == HS.as_addr r\n ))\n (ensures (\n HS.free r m `does_not_contain_addr` x\n ))", "let modifies_intro #al #c l h h' regions mrefs lives unused_ins alocs =\n modifies_intro_strong l h h'\n regions\n mrefs\n lives\n (fun r n -> unused_ins r n)\n alocs", "val does_not_contain_addr_elim\n (#a: Type0)\n (#rel: Preorder.preorder a)\n (r: HS.mreference a rel)\n (m: HS.mem)\n (x: HS.rid * nat)\n: Lemma\n (requires (\n m `does_not_contain_addr` x /\\\n HS.frameOf r == fst x /\\\n HS.as_addr r == snd x\n ))\n (ensures (~ (m `HS.contains` r)))", "let modifies_none_intro #al #c h h' regions mrefs unused_ins =\n modifies_intro_strong #_ #c loc_none h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> mrefs t pre b)\n (fun r n -> unused_ins r n)\n (fun r a x ->\n c.same_mreference_aloc_preserved x h h' (fun t pre b -> mrefs t pre b)\n )", "let modifies_address_intro #al #c r n h h' regions mrefs unused_ins =\n Classical.forall_intro (Classical.move_requires regions);\n let l : loc c = loc_addresses #_ #c false r (Set.singleton n) in\n modifies_preserves_mreferences_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_livenesses_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_not_unused_in_intro l h h'\n (fun r n -> unused_ins r n)\n ;\n modifies_preserves_alocs_intro l h h' ()\n (fun r a b ->\n c.same_mreference_aloc_preserved b h h' (fun t pre p -> mrefs t pre p)\n )", "val loc_not_unused_in (#al: aloc_t) (c: cls al) (h: HS.mem) : GTot (loc c)", "val loc_unused_in (#al: aloc_t) (c: cls al) (h: HS.mem) : GTot (loc c)", "val loc_regions_unused_in (#al: aloc_t) (c: cls al) (h: HS.mem) (rs: Set.set HS.rid) : Lemma\n (requires (forall r . Set.mem r rs ==> (~ (HS.live_region h r))))\n (ensures (loc_unused_in c h `loc_includes` loc_regions false rs))", "val loc_addresses_unused_in (#al: aloc_t) (c: cls al) (r: HS.rid) (a: Set.set nat) (h: HS.mem) : Lemma\n (requires (forall x . Set.mem x a ==> h `does_not_contain_addr` (r, x)))\n (ensures (loc_unused_in c h `loc_includes` loc_addresses false r a))", "val loc_addresses_not_unused_in (#al: aloc_t) (c: cls al) (r: HS.rid) (a: Set.set nat) (h: HS.mem) : Lemma\n (requires (forall x . Set.mem x a ==> ~ (h `does_not_contain_addr` (r, x))))\n (ensures (loc_not_unused_in c h `loc_includes` loc_addresses false r a))", "let modifies_aloc_intro #al #c #r #n x h h' regions mrefs livenesses unused_ins alocs =\n modifies_intro_strong #_ #c (loc_of_aloc x) h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> livenesses t pre b)\n (fun r n -> unused_ins r n)\n (fun r' n' z ->\n if r' = r && n' = n\n then begin\n loc_disjoint_aloc_elim #_ #c z x;\n alocs z\n end else\n c.same_mreference_aloc_preserved z h h' (fun t pre p ->\n mrefs t pre p\n )\n )", "val loc_unused_in_not_unused_in_disjoint (#al: aloc_t) (c: cls al) (h: HS.mem) : Lemma\n (loc_unused_in c h `loc_disjoint` loc_not_unused_in c h)", "val not_live_region_loc_not_unused_in_disjoint\n (#al: aloc_t)\n (c: cls al)\n (h0: HS.mem)\n (r: HS.rid)\n: Lemma\n (requires (~ (HS.live_region h0 r)))\n (ensures (loc_disjoint (loc_region_only false r) (loc_not_unused_in c h0)))", "val modifies_address_liveness_insensitive_unused_in\n (#al: aloc_t)\n (c: cls al)\n (h h' : HS.mem)\n: Lemma\n (requires (modifies (address_liveness_insensitive_locs c) h h'))\n (ensures (loc_not_unused_in c h' `loc_includes` loc_not_unused_in c h /\\ loc_unused_in c h `loc_includes` loc_unused_in c h'))", "let modifies_live_region #al #c s h1 h2 r = ()", "let modifies_mreference_elim #al #c #t #pre b p h h' = ()", "let modifies_aloc_elim #al #c #r #a b p h h' = ()", "val modifies_only_not_unused_in\n (#al: aloc_t)\n (#c: cls al)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (modifies (loc_unused_in c h `loc_union` l) h h'))\n (ensures (modifies l h h'))", "let modifies_refl #al #c s h =\n Classical.forall_intro_3 (fun r a b -> c.aloc_preserved_refl #r #a b h)", "let modifies_loc_includes #al #c s1 h h' s2 =\n assert (modifies_preserves_mreferences s1 h h');\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c);\n Classical.forall_intro_3 (fun l1 l2 l3 -> Classical.move_requires (loc_aux_disjoint_loc_aux_includes #al #c l1 l2) l3);\n assert (modifies_preserves_alocs s1 h h')", "let modifies_only_live_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (r: HS.rid)\n (a: Set.set nat)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_addresses false r a) l) h h' /\\\n (forall x . Set.mem x a ==> h `does_not_contain_addr` (r, x))\n ))\n (ensures (modifies l h h'))\n= loc_addresses_unused_in c r a h;\n loc_includes_refl l;\n loc_includes_union_l (loc_unused_in c h) l l;\n loc_includes_union_l (loc_unused_in c h) l (loc_addresses false r a);\n loc_includes_union_r (loc_union (loc_unused_in c h) l) (loc_addresses false r a) l;\n modifies_loc_includes (loc_union (loc_unused_in c h) l) h h' (loc_union (loc_addresses false r a) l);\n modifies_only_not_unused_in l h h'", "let modifies_preserves_liveness #al #c s1 s2 h h' #t #pre r = ()", "let modifies_preserves_liveness_strong #al #c s1 s2 h h' #t #pre r x =\n let rg = HS.frameOf r in\n let ad = HS.as_addr r in\n let la = loc_of_aloc #_ #c #rg #ad x in\n if Set.mem rg (regions_of_loc s2)\n then begin\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` Loc?.non_live_addrs (address_liveness_insensitive_locs c) rg);\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` GSet.empty);\n assert (~ (GSet.mem ad (Loc?.non_live_addrs s2 rg)));\n if Set.mem rg (regions_of_loc s1)\n then begin\n if GSet.mem ad (Loc?.non_live_addrs s1 rg)\n then begin\n assert (loc_disjoint_aux s1 la);\n assert (GSet.subset (Loc?.non_live_addrs s1 rg) (Loc?.live_addrs s1 rg));\n assert (aloc_domain c (Loc?.regions s1) (Loc?.live_addrs s1) `GSet.subset` (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad None) (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad (Some x)) (Ghost.reveal (Loc?.aux la)));\n assert (aloc_disjoint (ALoc rg ad None) (ALoc #_ #c rg ad (Some x)));\n ()\n end else ()\n end else ()\n end else ()", "val mreference_live_loc_not_unused_in\n (#al: aloc_t)\n (c: cls al)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (h: HS.mem)\n (r: HS.mreference t pre)\n: Lemma\n (requires (h `HS.contains` r))\n (ensures (loc_not_unused_in c h `loc_includes` loc_freed_mreference r /\\ loc_not_unused_in c h `loc_includes` loc_mreference r))", "let modifies_preserves_region_liveness #al #c l1 l2 h h' r = ()", "let modifies_preserves_region_liveness_reference #al #c l1 l2 h h' #t #pre r = ()", "val mreference_unused_in_loc_unused_in\n (#al: aloc_t)\n (c: cls al)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (h: HS.mem)\n (r: HS.mreference t pre)\n: Lemma\n (requires (r `HS.unused_in` h))\n (ensures (loc_unused_in c h `loc_includes` loc_freed_mreference r /\\ loc_unused_in c h `loc_includes` loc_mreference r))", "let modifies_preserves_region_liveness_aloc #al #c l1 l2 h h' #r #n x =\n if Set.mem r (Ghost.reveal (Loc?.region_liveness_tags l1))\n then begin\n assert (GSet.subset (GSet.complement GSet.empty) (Loc?.non_live_addrs l1 r));\n assert (GSet.subset (Loc?.non_live_addrs l1 r) (Loc?.live_addrs l1 r))\n end else ()", "let modifies_trans'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s h1 h2 /\\ modifies s h2 h3))\n (ensures (modifies s h1 h3))\n= Classical.forall_intro_3 (fun r a b -> Classical.move_requires (c.aloc_preserved_trans #r #a b h1 h2) h3)", "val aloc_union: (bool -> Tot (aloc_t u#x)) -> Tot (aloc_t u#x)", "val cls_union (#a: (bool -> Tot aloc_t)) (c: ((b: bool) -> Tot (cls (a b)))) : Tot (cls (aloc_union a))", "let modifies_trans #al #c s12 h1 h2 s23 h3 =\n let u = loc_union s12 s23 in\n modifies_loc_includes u h1 h2 s12;\n modifies_loc_includes u h2 h3 s23;\n modifies_trans' u h1 h2 h3", "val union_loc_of_loc (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b))) (b: bool) (l: loc (c b)) : GTot (loc (cls_union c))", "val union_loc_of_loc_none\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n: Lemma\n (union_loc_of_loc c b (loc_none #_ #(c b)) == loc_none #_ #(cls_union c))", "let addr_unused_in_aloc_preserved\n (#al: aloc_t) (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (b: al r a)\n (h1: HS.mem)\n (h2: HS.mem)\n : Lemma\n (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)))\n (ensures (c.aloc_preserved b h1 h2))\n= c.same_mreference_aloc_preserved b h1 h2 (fun a' pre r' -> assert False)", "val union_loc_of_loc_union\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (l1 l2: loc (c b))\n: Lemma\n (union_loc_of_loc c b (loc_union #_ #(c b) l1 l2) == loc_union #_ #(cls_union c) (union_loc_of_loc c b l1) (union_loc_of_loc c b l2))", "val union_loc_of_loc_addresses\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (union_loc_of_loc c b (loc_addresses #_ #(c b) preserve_liveness r n) == loc_addresses #_ #(cls_union c) preserve_liveness r n)", "let modifies_only_live_regions_weak\n (#al: aloc_t) (#c: cls al)\n (rs: Set.set HS.rid)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n loc_disjoint (loc_regions false rs) l /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))\n= assert (modifies_preserves_mreferences l h h'); // FIXME: WHY WHY WHY?\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (addr_unused_in_aloc_preserved #al #c #r #a b h) h')", "val union_loc_of_loc_regions\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: Lemma\n (union_loc_of_loc c b (loc_regions #_ #(c b) preserve_liveness r) == loc_regions #_ #(cls_union c) preserve_liveness r)", "val union_loc_of_loc_includes\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (s1 s2: loc (c b))\n: Lemma\n (union_loc_of_loc c b s1 `loc_includes` union_loc_of_loc c b s2 <==> s1 `loc_includes` s2)", "let restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: GTot (loc c)\n= let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let regions' = (Ghost.hide (Set.intersect (Ghost.reveal regions) rs)) in\n Loc\n regions'\n (Ghost.hide (Set.intersect (Ghost.reveal region_liveness_tags) rs))\n (mk_non_live_addrs (fun (r: addrs_dom regions') -> (non_live_addrs r <: GSet.set nat)))\n (mk_live_addrs (fun (r: addrs_dom regions') -> (live_addrs r <: GSet.set nat)))\n (Ghost.hide (GSet.intersect (Ghost.reveal aux) (aloc_domain c (Ghost.hide rs) (fun r -> GSet.complement GSet.empty))))", "val union_loc_of_loc_disjoint\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (s1 s2: loc (c b))\n: Lemma\n (union_loc_of_loc c b s1 `loc_disjoint` union_loc_of_loc c b s2 <==> s1 `loc_disjoint` s2)", "val modifies_union_loc_of_loc\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (l: loc (c b))\n (h1 h2: HS.mem)\n: Lemma\n (modifies #_ #(cls_union c) (union_loc_of_loc c b l) h1 h2 <==> modifies #_ #(c b) l h1 h2)", "let regions_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (regions_of_loc (restrict_to_regions l rs) == Set.intersect (regions_of_loc l) rs)\n [SMTPat (regions_of_loc (restrict_to_regions l rs))]\n= assert (Set.equal (regions_of_loc (restrict_to_regions l rs)) (Set.intersect (regions_of_loc l) rs))", "val loc_of_union_loc\n (#al: (bool -> Tot aloc_t))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (cls_union c))\n: GTot (loc (c b))", "let addrs_of_loc_weak_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))\n [SMTPat (addrs_of_loc_weak (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc_weak (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))", "val loc_of_union_loc_union_loc_of_loc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: loc (c b))\n: Lemma\n (loc_of_union_loc b (union_loc_of_loc c b s) == s)", "val loc_of_union_loc_none\n (#al: (bool -> Tot aloc_t))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n: Lemma\n (loc_of_union_loc #_ #c b loc_none == loc_none)", "let addrs_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc l r else GSet.empty))\n [SMTPat (addrs_of_loc (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc l r else GSet.empty))", "val loc_of_union_loc_union\n (#al: (bool -> Tot aloc_t))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l1 l2: loc (cls_union c))\n: Lemma\n (loc_of_union_loc b (l1 `loc_union` l2) == loc_of_union_loc b l1 `loc_union` loc_of_union_loc b l2)", "let loc_includes_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes l (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)", "val loc_of_union_loc_addresses\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: Lemma\n (loc_of_union_loc #_ #c b (loc_addresses preserve_liveness r n) == loc_addresses preserve_liveness r n)", "let loc_includes_loc_union_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_equal (loc_union (restrict_to_regions l rs) (restrict_to_regions l (Set.complement rs))) l)\n= ()", "val loc_of_union_loc_regions\n (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b)))\n (b: bool)\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: Lemma\n (loc_of_union_loc #_ #c b (loc_regions preserve_liveness r) == loc_regions preserve_liveness r)", "let loc_includes_loc_regions_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes (loc_regions false rs) (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)", "let modifies_only_live_regions #al #c rs l h h' =\n let s = l in\n let c_rs = Set.complement rs in\n let s_rs = restrict_to_regions s rs in\n let s_c_rs = restrict_to_regions s c_rs in\n let lrs = loc_regions false rs in\n loc_includes_loc_regions_restrict_to_regions s rs;\n loc_includes_union_l lrs s_c_rs s_rs;\n loc_includes_refl s_c_rs;\n loc_includes_union_l lrs s_c_rs s_c_rs;\n loc_includes_union_r (loc_union lrs s_c_rs) s_rs s_c_rs;\n loc_includes_loc_union_restrict_to_regions s rs;\n loc_includes_trans (loc_union lrs s_c_rs) (loc_union s_rs s_c_rs) s;\n modifies_loc_includes (loc_union lrs s_c_rs) h h' (loc_union lrs s);\n loc_includes_loc_regions_restrict_to_regions s c_rs;\n loc_disjoint_regions #al #c false false rs c_rs;\n loc_includes_refl lrs;\n loc_disjoint_includes lrs (loc_regions false c_rs) lrs s_c_rs;\n modifies_only_live_regions_weak rs s_c_rs h h';\n loc_includes_restrict_to_regions s c_rs;\n modifies_loc_includes s h h' s_c_rs", "val raise_aloc (al: aloc_t u#x) : Tot (aloc_t u#(max x (y + 1)))", "val raise_cls (#al: aloc_t u#x) (c: cls al) : Tot (cls (raise_aloc u#x u#y al))", "val raise_loc (#al: aloc_t u#x) (#c: cls al) (l: loc c) : Tot (loc (raise_cls u#x u#y c))", "val raise_loc_none (#al: aloc_t u#x) (#c: cls al) : Lemma\n (raise_loc u#x u#y (loc_none #_ #c) == loc_none)", "val raise_loc_union (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc c) : Lemma\n (raise_loc u#x u#y (loc_union l1 l2) == loc_union (raise_loc l1) (raise_loc l2))", "val raise_loc_addresses (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: HS.rid) (a: Set.set nat) : Lemma\n (raise_loc u#x u#y (loc_addresses #_ #c preserve_liveness r a) == loc_addresses preserve_liveness r a)", "val raise_loc_regions (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: Set.set HS.rid) : Lemma\n (raise_loc u#x u#y (loc_regions #_ #c preserve_liveness r) == loc_regions preserve_liveness r)", "val raise_loc_includes (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc c) : Lemma\n (loc_includes (raise_loc u#x u#y l1) (raise_loc l2) <==> loc_includes l1 l2)", "val raise_loc_disjoint (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc c) : Lemma\n (loc_disjoint (raise_loc u#x u#y l1) (raise_loc l2) <==> loc_disjoint l1 l2)", "let no_upd_fresh_region #al #c r l h0 h1 =\n modifies_only_live_regions (HS.mod_set (Set.singleton r)) l h0 h1", "val modifies_raise_loc (#al: aloc_t u#x) (#c: cls al) (l: loc c) (h1 h2: HS.mem) : Lemma\n (modifies (raise_loc u#x u#y l) h1 h2 <==> modifies l h1 h2)", "let fresh_frame_modifies #al c h0 h1 =\n modifies_intro_strong #_ #c loc_none h0 h1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x h0 h1 (fun _ _ _ -> ()))", "val lower_loc (#al: aloc_t u#x) (#c: cls al) (l: loc (raise_cls u#x u#y c)) : Tot (loc c)", "val lower_loc_raise_loc (#al: aloc_t u#x) (#c: cls al) (l: loc c) : Lemma\n (lower_loc (raise_loc u#x u#y l) == l)", "val raise_loc_lower_loc (#al: aloc_t u#x) (#c: cls al) (l: loc (raise_cls u#x u#y c)) : Lemma\n (raise_loc (lower_loc l) == l)", "let new_region_modifies #al c m0 r0 col\n= let (_, m1) = HS.new_eternal_region m0 r0 col in\n modifies_intro_strong #_ #c loc_none m0 m1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x m0 m1 (fun _ _ _ -> ()))", "val lower_loc_none (#al: aloc_t u#x) (#c: cls al) : Lemma\n (lower_loc u#x u#y #_ #c loc_none == loc_none)", "val lower_loc_union (#al: aloc_t u#x) (#c: cls al) (l1 l2: loc (raise_cls u#x u#y c)) : Lemma\n (lower_loc u#x u#y (loc_union l1 l2) == loc_union (lower_loc l1) (lower_loc l2))", "val lower_loc_addresses (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: HS.rid) (a: Set.set nat) : Lemma\n (lower_loc u#x u#y #_ #c (loc_addresses preserve_liveness r a) == loc_addresses preserve_liveness r a)", "let popped_modifies #al c h0 h1 =\n let l = loc_region_only #_ #c false (HS.get_tip h0) in\n modifies_preserves_mreferences_intro l h0 h1 (fun t pre p ->\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l );\n // FIXME: WHY WHY WHY is this assert necessary?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n ()\n );\n modifies_preserves_alocs_intro l h0 h1 () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n ()\n )", "val lower_loc_regions (#al: aloc_t u#x) (#c: cls al) (preserve_liveness: bool) (r: Set.set HS.rid) : Lemma\n (lower_loc u#x u#y #_ #c (loc_regions preserve_liveness r) == loc_regions preserve_liveness r)", "let modifies_fresh_frame_popped #al #c h0 h1 s h2 h3 =\n fresh_frame_modifies c h0 h1;\n let r = loc_region_only #al #c false (HS.get_tip h2) in\n let rs = HS.mod_set (Set.singleton (HS.get_tip h1)) in\n let s' = loc_union (loc_regions false rs) s in\n modifies_trans' s' h0 h1 h2;\n assert (modifies_preserves_mreferences r h2 h3);\n let f23 (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (r <> HS.get_tip h2))\n (ensures (c.aloc_preserved b h2 h3))\n = c.same_mreference_aloc_preserved #r #a b h2 h3 (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro r h2 h3 () (fun r a b ->\n f23 r a b\n );\n modifies_trans' s' h0 h2 h3;\n modifies_only_live_regions rs s h0 h3", "let modifies_loc_regions_intro #al #c rs h1 h2 =\n let f (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem r rs)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n assert (modifies_preserves_mreferences (loc_regions #al #c true rs) h1 h2);\n modifies_preserves_alocs_intro (loc_regions #_ #c true rs) h1 h2 () (fun r a b ->\n f r a b\n )", "let modifies_loc_addresses_intro_weak\n (#al: aloc_t) (#c: cls al)\n (r: HS.rid)\n (s: Set.set nat)\n (l: loc c)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r s h1 h2 /\\\n loc_disjoint l (loc_region_only false r)\n ))\n (ensures (modifies (loc_union (loc_addresses true r s) l) h1 h2))\n= modifies_preserves_mreferences_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_livenesses_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_not_unused_in_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' n' ->\n ()\n );\n let f (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem a s)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r_ -> ())\n in\n modifies_preserves_alocs_intro (loc_union (loc_addresses true r s) l) h1 h2 () (fun r' a b -> if r = r' then f a b else ()\n )", "let modifies_loc_addresses_intro #al #c r s l h1 h2 =\n loc_includes_loc_regions_restrict_to_regions l (Set.singleton r);\n loc_includes_loc_union_restrict_to_regions l (Set.singleton r);\n assert (modifies (loc_union (loc_region_only false r) (loc_union (restrict_to_regions l (Set.singleton r)) (restrict_to_regions l (Set.complement (Set.singleton r))))) h1 h2);\n let l' = restrict_to_regions l (Set.complement (Set.singleton r)) in\n loc_includes_refl (loc_region_only #_ #c false r) ;\n loc_includes_loc_regions_restrict_to_regions l (Set.complement (Set.singleton r));\n loc_disjoint_regions #_ #c false false (Set.complement (Set.singleton r)) (Set.singleton r);\n loc_disjoint_includes (loc_regions #_ #c false (Set.complement (Set.singleton r))) (loc_region_only false r) l' (loc_region_only false r);\n modifies_loc_addresses_intro_weak r s l' h1 h2;\n loc_includes_restrict_to_regions l (Set.complement (Set.singleton r))", "let modifies_ralloc_post #al #c #a #rel i init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g", "let modifies_salloc_post #al #c #a #rel init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g", "let modifies_free #al #c #a #rel r m =\n let g (r': HS.rid) (a: nat) (b: al r' a) : Lemma\n (requires (r' <> HS.frameOf r \\/ a <> HS.as_addr r))\n (ensures (c.aloc_preserved b m (HS.free r m)))\n = c.same_mreference_aloc_preserved #r' #a b m (HS.free r m) (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro (loc_freed_mreference #_ #c r) m (HS.free r m) () (fun r a b -> g r a b)", "let modifies_none_modifies #al #c h1 h2\n= let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h1 h2)\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g", "let modifies_upd #al #c #t #pre r v h =\n let h' = HS.upd h r v in\n modifies_intro #_ #c (loc_mreference r) h h'\n (fun r -> ())\n (fun t pre b -> ())\n (fun t pre b -> ())\n (fun r n -> ())\n (fun r a b -> c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre' r' -> ()))", "let addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l (loc_of_aloc al0)) r == addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)\n= assert (addrs_of_loc (loc_union l (loc_of_aloc al0)) r `GSet.equal` addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)", "let addrs_of_loc_weak_loc_includes #al (#c: cls al) (l: loc c) (r0: HS.rid) (a0: nat) : Lemma\n (requires (a0 `GSet.mem` addrs_of_loc_weak l r0))\n (ensures (l `loc_includes` loc_addresses true r0 (Set.singleton a0)))\n= ()", "val modifies_strengthen'\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (h h' : HS.mem)\n (alocs: (\n (f: ((t: Type) -> (pre: Preorder.preorder t) -> (m: HS.mreference t pre) -> Lemma\n (requires (HS.frameOf m == r0 /\\ HS.as_addr m == a0 /\\ HS.contains h m))\n (ensures (HS.contains h' m))\n )) ->\n (x: al r0 a0) ->\n Lemma\n (requires (c.aloc_disjoint x al0 /\\ loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (requires ((~ (a0 `GSet.mem` addrs_of_loc_weak l r0)) /\\ modifies (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h'))\n (ensures (modifies (loc_union l (loc_of_aloc al0)) h h'))", "let modifies_strengthen' #al #c l #r0 #a0 al0 h h' alocs =\n Classical.forall_intro (addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton l al0);\n assert (modifies_preserves_regions (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_mreferences (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_not_unused_in (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_livenesses (loc_union l (loc_of_aloc al0)) h h');\n modifies_preserves_alocs_intro (loc_union l (loc_of_aloc al0)) h h' () (fun r a b ->\n if r = r0 && a = a0\n then begin\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_union l (loc_of_aloc al0)))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux l)) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_disjoint l (loc_of_aloc b));\n loc_disjoint_sym l (loc_of_aloc b);\n assert (loc_aux_disjoint #_ #c (Ghost.reveal (Loc?.aux (loc_of_aloc al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint #_ #c (GSet.singleton (ALoc r0 a0 (Some al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (GSet.mem (ALoc r0 a0 (Some al0)) (GSet.singleton (ALoc #_ #c r0 a0 (Some al0))));\n assert (GSet.mem (ALoc r0 a0 (Some b)) (GSet.singleton (ALoc #_ #c r0 a0 (Some b))));\n assert (aloc_disjoint #_ #c (ALoc r0 a0 (Some al0)) (ALoc r0 a0 (Some b)));\n assert (c.aloc_disjoint al0 b);\n c.aloc_disjoint_sym al0 b;\n alocs (fun t pre m -> ()) b\n end\n else begin\n assert (loc_disjoint (loc_union l (loc_addresses true r0 (Set.singleton a0))) (loc_of_aloc b))\n by (let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 64;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=5'\";\n ())\n end\n );\n assert (modifies (loc_union l (loc_of_aloc al0)) h h')", "let modifies_strengthen #al #c l #r0 #a0 al0 h h' alocs =\n if a0 `GSet.mem` addrs_of_loc_weak l r0\n then begin\n addrs_of_loc_weak_loc_includes l r0 a0;\n loc_includes_refl l;\n loc_includes_union_r l l (loc_addresses true r0 (Set.singleton a0));\n loc_includes_union_l l (loc_of_aloc al0) l;\n loc_includes_trans (loc_union l (loc_of_aloc al0)) l (loc_union l (loc_addresses true r0 (Set.singleton a0)));\n modifies_loc_includes (loc_union l (loc_of_aloc al0)) h h' (loc_union l (loc_addresses true r0 (Set.singleton a0)))\n end\n else\n modifies_strengthen' l al0 h h' alocs", "let does_not_contain_addr' (h: HS.mem) (ra: HS.rid * nat) : GTot Type0 =\n HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))", "let does_not_contain_addr = does_not_contain_addr'", "let not_live_region_does_not_contain_addr h ra = ()", "let unused_in_does_not_contain_addr h #a #rel r = ()", "let addr_unused_in_does_not_contain_addr h ra = ()", "let does_not_contain_addr_addr_unused_in h ra = ()", "let free_does_not_contain_addr #a #rel r m x = ()", "let does_not_contain_addr_elim #a #rel r m x = ()", "let disjoint_addrs_of_loc_loc_disjoint\n (#al: aloc_t)\n (#c: cls al)\n (l1 l2: loc c)\n: Lemma\n (requires (\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty /\\\n (forall r . GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc l2 r)) GSet.empty)\n ))\n (ensures (loc_disjoint l1 l2))\n= // FIXME: WHY WHY WHY do I need this assert?\n let l1' = Ghost.reveal (Loc?.aux l1) in\n let l2' = Ghost.reveal (Loc?.aux l2) in\n assert (forall (b1 b2: aloc c) . (GSet.mem b1 l1' /\\ GSet.mem b2 l2') ==> aloc_disjoint b1 b2)", "let loc_not_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (HS.live_region h r /\\ ~ (h `does_not_contain_addr` (r, a))))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs f)\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))", "let loc_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n if not (HS.live_region h r)\n then\n GSet.complement GSet.empty\n else\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a)))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide (Set.complement (FStar.Map.domain (HS.get_hmap h))))\n (mk_non_live_addrs (fun x -> f x))\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))", "let loc_regions_unused_in #al c h rs = ()", "let loc_addresses_unused_in #al c r a h = ()", "let loc_addresses_not_unused_in #al c r a h = ()", "let loc_unused_in_not_unused_in_disjoint #al c h =\n assert (Ghost.reveal (Loc?.aux (loc_unused_in c h)) `loc_aux_disjoint` Ghost.reveal (Loc?.aux (loc_not_unused_in c h)));\n assert_spinoff (loc_disjoint #al #c (loc_unused_in #al c h)\n (loc_not_unused_in #al c h))", "let not_live_region_loc_not_unused_in_disjoint #al c h0 r\n= let l1 = loc_region_only false r in\n let l2 = loc_not_unused_in c h0 in\n assert (loc_disjoint_region_liveness_tags l1 l2);\n assert (loc_disjoint_addrs l1 l2);\n assert (loc_disjoint_aux l1 l2)", "let modifies_address_liveness_insensitive_unused_in #al c h h' =\n assert (forall r . HS.live_region h r ==> HS.live_region h' r) ;\n let ln' = loc_not_unused_in c h' in\n let ln = loc_not_unused_in c h in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs ln r `GSet.subset` Loc?.non_live_addrs ln' r);\n assert (ln' `loc_includes` ln);\n let lu = loc_unused_in c h in\n let lu' = loc_unused_in c h' in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs lu' r `GSet.subset` Loc?.non_live_addrs lu r);\n assert (forall (r: HS.rid) . Loc?.live_addrs lu' r `GSet.subset` Loc?.live_addrs lu r);\n assert (lu `loc_includes` lu')", "let modifies_only_not_unused_in #al #c l h h' =\n assert (modifies_preserves_regions l h h');\n assert (modifies_preserves_not_unused_in l h h');\n assert (modifies_preserves_mreferences l h h');\n assert (modifies_preserves_livenesses l h h');\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n if StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a))\n then c.same_mreference_aloc_preserved b h h' (fun a' pre' r' -> ())\n else ()\n )", "let mreference_live_loc_not_unused_in #al c #t #pre h b =\n Classical.move_requires (does_not_contain_addr_addr_unused_in h) (HS.frameOf b, HS.as_addr b);\n assert (~ (h `does_not_contain_addr` (HS.frameOf b, HS.as_addr b)));\n loc_addresses_not_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_trans (loc_not_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()", "let mreference_unused_in_loc_unused_in #al c #t #pre h b =\n Classical.move_requires (addr_unused_in_does_not_contain_addr h) (HS.frameOf b, HS.as_addr b);\n loc_addresses_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_addresses_addresses c false true (HS.frameOf b) (Set.singleton (HS.as_addr b)) (Set.singleton (HS.as_addr b));\n loc_includes_trans (loc_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()", "cls_union_aloc", "ALOC_FALSE", "ALOC_FALSE", "ALOC_FALSE", "ALOC_TRUE", "ALOC_TRUE", "ALOC_TRUE", "let bool_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot bool =\n match l with\n | ALOC_FALSE _ -> false\n | ALOC_TRUE _ -> true", "let aloc_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot ((al (bool_of_cls_union_aloc l)) r n)\n= match l with\n | ALOC_FALSE x -> x\n | ALOC_TRUE x -> x", "let make_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (b: bool)\n (#r: HS.rid)\n (#n: nat)\n (l: (al b) r n)\n: Tot (cls_union_aloc al r n)\n= if b\n then ALOC_TRUE l\n else ALOC_FALSE l", "let cls_union_aloc_includes\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_includes\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)", "let cls_union_aloc_disjoint\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_disjoint\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)", "let cls_union_aloc_preserved\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (x: cls_union_aloc al r a)\n (h h' : HS.mem)\n: GTot Type0\n= (c (bool_of_cls_union_aloc x)).aloc_preserved\n (aloc_of_cls_union_aloc x)\n h\n h'", "let aloc_union = cls_union_aloc", "let cls_union #al c = Cls\n #(cls_union_aloc al)\n (cls_union_aloc_includes c)\n (* aloc_includes_refl *)\n (fun #r #a x ->\n (c (bool_of_cls_union_aloc x)).aloc_includes_refl (aloc_of_cls_union_aloc x))\n (* aloc_includes_trans *)\n (fun #r #a x1 x2 x3 ->\n (c (bool_of_cls_union_aloc x1)).aloc_includes_trans\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n (aloc_of_cls_union_aloc x3)\n )\n (cls_union_aloc_disjoint c)\n (* aloc_disjoint_sym *)\n (fun #r #a x1 x2 ->\n if bool_of_cls_union_aloc x1 = bool_of_cls_union_aloc x2\n then\n (c (bool_of_cls_union_aloc x1)).aloc_disjoint_sym\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n else ()\n )\n (* aloc_disjoint_includes *)\n (fun #r #a larger1 larger2 smaller1 smaller2 ->\n (c (bool_of_cls_union_aloc larger1)).aloc_disjoint_includes\n (aloc_of_cls_union_aloc larger1)\n (aloc_of_cls_union_aloc larger2)\n (aloc_of_cls_union_aloc smaller1)\n (aloc_of_cls_union_aloc smaller2)\n )\n (cls_union_aloc_preserved c)\n (* aloc_preserved_refl *)\n (fun #r #a x h ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_refl\n (aloc_of_cls_union_aloc x)\n h\n )\n (* aloc_preserved_trans *)\n (fun #r #a x h1 h2 h3 ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_trans\n (aloc_of_cls_union_aloc x)\n h1\n h2\n h3\n )\n (* same_mreference_aloc_preserved *)\n (fun #r #a b h1 h2 f ->\n (c (bool_of_cls_union_aloc b)).same_mreference_aloc_preserved\n (aloc_of_cls_union_aloc b)\n h1\n h2\n f\n )", "let union_aux_of_aux_left_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n (x: aloc (cls_union c))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n b = bool_of_cls_union_aloc #al #region #addr loc &&\n GSet.mem (ALoc region addr (Some (aloc_of_cls_union_aloc #al #region #addr loc))) s", "let union_aux_of_aux_left\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n: Tot (GSet.set (aloc (cls_union c)))\n= GSet.comprehend (union_aux_of_aux_left_pred c b s)", "let union_loc_of_loc #al c b l =\n let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let aux' : GSet.set (aloc #(cls_union_aloc al) (cls_union c)) =\n union_aux_of_aux_left c b (Ghost.reveal aux)\n `GSet.union`\n (aloc_domain (cls_union c) regions live_addrs)\n in\n Loc\n #(cls_union_aloc al)\n #(cls_union c)\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide aux')", "let union_aux_of_aux_left_inv_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n (x: aloc (c b))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n GSet.mem (ALoc region addr (Some (make_cls_union_aloc b loc))) s", "let union_aux_of_aux_left_inv\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n: Tot (GSet.set (aloc (c b)))\n= GSet.comprehend (union_aux_of_aux_left_inv_pred b s)", "let mem_union_aux_of_aux_left_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (c b))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x aux <==> GSet.mem (ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc)))) (union_aux_of_aux_left c b aux))\n [SMTPat (GSet.mem x aux)]\n= ()", "let mem_union_aux_of_aux_left_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (cls_union c))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x (union_aux_of_aux_left c b aux) <==> (if None? x.loc then GSet.mem (ALoc x.region x.addr None) aux else (bool_of_cls_union_aloc (Some?.v x.loc) == b /\\ GSet.mem (ALoc x.region x.addr (Some (aloc_of_cls_union_aloc (Some?.v x.loc)))) aux)))\n [SMTPat (GSet.mem x (union_aux_of_aux_left #al c b aux))]\n= ()", "let addrs_of_loc_union_loc_of_loc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (union_loc_of_loc c b l) r `GSet.equal` addrs_of_loc l r)\n [SMTPat (addrs_of_loc (union_loc_of_loc #al c b l) r)]\n= ()", "let union_loc_of_loc_none #al c b =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_none #_ #(c b))) (loc_none #_ #(cls_union c)))", "let union_loc_of_loc_union #al c b l1 l2 =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_union #_ #(c b) l1 l2)) (loc_union #_ #(cls_union c) (union_loc_of_loc c b l1) (union_loc_of_loc c b l2)))", "let union_loc_of_loc_addresses #al c b preserve_liveness r n =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_addresses #_ #(c b) preserve_liveness r n)) (loc_addresses #_ #(cls_union c) preserve_liveness r n))", "let union_loc_of_loc_regions #al c b preserve_liveness r =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_regions #_ #(c b) preserve_liveness r)) (loc_regions #_ #(cls_union c) preserve_liveness r))", "let union_loc_of_loc_includes_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (larger `loc_includes` smaller))\n (ensures (union_loc_of_loc c b larger `loc_includes` union_loc_of_loc c b smaller))\n= ();\n let auxl = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux larger)) in\n let auxs = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux smaller)) in\n assert (forall r a . GSet.mem (ALoc r a None) auxs ==> (\n GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux smaller)) /\\\n GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux larger)) /\\\n GSet.mem (ALoc r a None) auxl\n ));\n assert (auxl `loc_aux_includes` auxs);\n let doml = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n assert (doml `loc_aux_includes` doms)", "let union_loc_of_loc_includes_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (union_loc_of_loc c b larger `loc_includes` union_loc_of_loc c b smaller))\n (ensures (larger `loc_includes` smaller))\n= let auxl = Ghost.reveal (Loc?.aux larger) in\n let auxl' = union_aux_of_aux_left c b auxl in\n let auxs = Ghost.reveal (Loc?.aux smaller) in\n let auxs' = union_aux_of_aux_left c b auxs in\n let doml' = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms' = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n let doml = aloc_domain (c b) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (c b) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n let g\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n (y: aloc (c b))\n : GTot Type0\n = GSet.mem y (GSet.union auxl doml) /\\ y `aloc_includes` x\n in\n let g' (r: HS.rid) (a: nat) (x: aloc (c b)) : GTot Type0 =\n exists (y: aloc (c b)) . g r a x y\n in\n let f\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n : Lemma\n (requires (GSet.mem x auxs /\\ (~ (GSet.mem x.addr (addrs_of_loc_weak smaller x.region)))))\n (ensures (g' r a x))\n = let x' : aloc (cls_union c) = ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc))) in\n Classical.exists_elim\n (g' r a x)\n #(aloc (cls_union c))\n #(fun y' -> GSet.mem y' (GSet.union auxl' doml') /\\ y' `aloc_includes` x')\n ()\n (fun (y': aloc (cls_union c) { GSet.mem y' (GSet.union auxl' doml') /\\ y' `aloc_includes` x' } ) ->\n let y : aloc (c b) = ALoc y'.region y'.addr (if None? y'.loc then None else Some (aloc_of_cls_union_aloc (Some?.v y'.loc))) in\n assert (g r a x y)\n )\n in\n let f'\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n : Lemma\n ((GSet.mem x auxs /\\ (~ (GSet.mem x.addr (addrs_of_loc_weak smaller x.region)))) ==> g' r a x)\n = Classical.move_requires (f r a) x\n in\n Classical.forall_intro_3 f';\n assert (forall (r: HS.rid) (a: nat) (x: aloc (c b)) .\n (GSet.mem x auxs /\\ GSet.mem x.addr (addrs_of_loc_weak smaller x.region)) ==>\n GSet.mem x (GSet.union auxl doml)\n ) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n assert (larger `loc_includes'` smaller) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 75;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n ()", "let union_loc_of_loc_includes #al c b s1 s2 =\n Classical.move_requires (union_loc_of_loc_includes_elim c b s1) s2;\n Classical.move_requires (union_loc_of_loc_includes_intro c b s1) s2", "let union_loc_of_loc_disjoint_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (larger `loc_disjoint` smaller))\n (ensures (union_loc_of_loc c b larger `loc_disjoint` union_loc_of_loc c b smaller))\n= let auxl = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux larger)) in\n let auxs = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux smaller)) in\n let g\n (xl xs: aloc (cls_union c))\n : Lemma\n (requires (GSet.mem xl auxl /\\ GSet.mem xs auxs))\n (ensures (GSet.mem xl auxl /\\ GSet.mem xs auxs /\\ aloc_disjoint xl xs))\n =\n let xl' : aloc (c b) = ALoc xl.region xl.addr (if None? xl.loc then None else Some (aloc_of_cls_union_aloc (Some?.v xl.loc))) in\n let xs' : aloc (c b) = ALoc xs.region xs.addr (if None? xs.loc then None else Some (aloc_of_cls_union_aloc (Some?.v xs.loc))) in\n assert (GSet.mem xl' (Ghost.reveal (Loc?.aux larger)));\n assert (GSet.mem xs' (Ghost.reveal (Loc?.aux smaller)));\n assert (aloc_disjoint xl' xs');\n assert (aloc_disjoint xl xs)\n in\n Classical.forall_intro_2 (fun xl -> Classical.move_requires (g xl));\n assert (forall xl xs . (GSet.mem xl auxl /\\ GSet.mem xs auxs) ==> aloc_disjoint xl xs);\n assert (auxl `loc_aux_disjoint` auxs);\n let larger' = union_loc_of_loc c b larger in\n let smaller' = union_loc_of_loc c b smaller in\n let doml = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n assert (forall (xl xs: aloc (cls_union c)) .\n (GSet.mem xl doml /\\ GSet.mem xs auxs) ==> (\n xl.addr `GSet.mem` addrs_of_loc_weak larger xl.region /\\\n xs.addr `GSet.mem` addrs_of_loc smaller xs.region /\\\n aloc_disjoint xl xs\n )) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 64;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n assert (doml ` loc_aux_disjoint` auxs);\n assert (forall (xl xs: aloc (cls_union c)) .\n (GSet.mem xl auxl /\\ GSet.mem xs doms) ==> (\n xl.addr `GSet.mem` addrs_of_loc larger xl.region /\\\n xs.addr `GSet.mem` addrs_of_loc_weak smaller xs.region /\\\n aloc_disjoint xl xs\n )) by (\n let open FStar.Tactics.SMT in\n set_rlimit 15;\n ()\n );\n assert (auxl ` loc_aux_disjoint` doms);\n assert (loc_disjoint_aux larger' smaller');\n ()", "let union_loc_of_loc_disjoint_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (union_loc_of_loc c b larger `loc_disjoint` union_loc_of_loc c b smaller))\n (ensures (larger `loc_disjoint` smaller))\n= let auxl = Ghost.reveal (Loc?.aux larger) in\n let auxl' = union_aux_of_aux_left c b auxl in\n let auxs = Ghost.reveal (Loc?.aux smaller) in\n let auxs' = union_aux_of_aux_left c b auxs in\n assert (forall (x y: aloc (c b)) . (GSet.mem x auxl /\\ GSet.mem y auxs) ==> (\n let x' = ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc))) in\n let y' = ALoc y.region y.addr (if None? y.loc then None else Some (make_cls_union_aloc b (Some?.v y.loc))) in\n GSet.mem x' auxl' /\\ GSet.mem y' auxs' /\\ (aloc_disjoint x' y' ==> aloc_disjoint x y)));\n assert (auxl `loc_aux_disjoint` auxs)", "let union_loc_of_loc_disjoint #al c b s1 s2 =\n Classical.move_requires (union_loc_of_loc_disjoint_elim c b s1) s2;\n Classical.move_requires (union_loc_of_loc_disjoint_intro c b s1) s2", "let modifies_union_loc_of_loc_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (h1 h2: HS.mem)\n: Lemma\n (requires (modifies #_ #(cls_union c) (union_loc_of_loc c b l) h1 h2))\n (ensures (modifies #_ #(c b) l h1 h2))\n= assert (modifies_preserves_regions l h1 h2);\n assert (modifies_preserves_mreferences l h1 h2);\n modifies_preserves_alocs_intro #_ #(c b) l h1 h2 () (fun r' a' b' ->\n let g\n (x: aloc (cls_union c))\n : Lemma\n (requires (\n GSet.mem a' (addrs_of_loc_aux #_ #(cls_union c) (union_loc_of_loc c b l) r') /\\\n GSet.mem x (Ghost.reveal (Loc?.aux #_ #(cls_union c) (union_loc_of_loc c b l)))\n ))\n (ensures (\n aloc_disjoint #_ #(cls_union c) x (ALoc #_ #(cls_union c) r' a' (Some (make_cls_union_aloc b b')))))\n = if r' = x.region && a' = x.addr\n then begin\n let x' : aloc (c b) = ALoc #_ #(c b) r' a' (if None? x.loc then None else Some (aloc_of_cls_union_aloc (Some?.v x.loc))) in\n assert (aloc_disjoint #(al b) #(c b) x' (ALoc r' a' (Some b')))\n end else\n ()\n in\n Classical.forall_intro (Classical.move_requires g);\n assert ((cls_union c).aloc_preserved (make_cls_union_aloc b b') h1 h2)\n )", "let modifies_union_loc_of_loc_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (h1 h2: HS.mem)\n: Lemma\n (requires (modifies #_ #(c b) l h1 h2))\n (ensures (modifies #_ #(cls_union c) (union_loc_of_loc c b l) h1 h2))\n= let l' = union_loc_of_loc c b l in\n assert (modifies_preserves_regions l' h1 h2);\n assert (modifies_preserves_mreferences l' h1 h2);\n assert (modifies_preserves_livenesses l' h1 h2);\n assert (modifies_preserves_not_unused_in l' h1 h2);\n modifies_preserves_alocs_intro #_ #(cls_union c) l' h1 h2 () (fun r' a' b' ->\n let b_ = bool_of_cls_union_aloc b' in\n let a_ = aloc_of_cls_union_aloc b' in\n let ll' : aloc (cls_union c) = ALoc r' a' (Some b') in\n let ll : aloc (c b_) = ALoc r' a' (Some a_) in\n assert (exists (x: aloc (c b)) . GSet.mem x (Ghost.reveal (Loc?.aux l)) /\\\n (\n let xr = x.region in\n let xa = x.addr in\n let xl : option (al b xr xa) = x.loc in\n xr == r' /\\\n xa == a' /\\ (\n let xl' : option (aloc_union al r' a') = if None? xl then None else Some (make_cls_union_aloc #al b (Some?.v xl)) in\n let x' : aloc (cls_union c) = ALoc r' a' xl' in\n GSet.mem x' (Ghost.reveal (Loc?.aux l')) /\\\n aloc_disjoint #_ #(cls_union c) x' ll'\n )));\n assert (b_ == b);\n let f (x: aloc (c b)) : Lemma\n (requires (GSet.mem x (Ghost.reveal (Loc?.aux l))))\n (ensures (aloc_disjoint #_ #(c b) x ll))\n = let xr = x.region in\n let xa = x.addr in\n let xl : option (al b xr xa) = x.loc in\n let xl' : option (aloc_union al xr xa) = if None? xl then None else Some (make_cls_union_aloc #al b (Some?.v xl)) in\n let x' : aloc (cls_union c) = ALoc xr xa xl' in\n assert (GSet.mem x' (Ghost.reveal (Loc?.aux l')));\n assert (aloc_disjoint #_ #(cls_union c) x' ll');\n assert (aloc_disjoint #_ #(c b) x ll)\n in\n Classical.forall_intro (Classical.move_requires f);\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux l)) (GSet.singleton ll))\n )", "let modifies_union_loc_of_loc #al c b l h1 h2 =\n Classical.move_requires (modifies_union_loc_of_loc_elim c b l h1) h2;\n Classical.move_requires (modifies_union_loc_of_loc_intro c b l h1) h2", "let loc_of_union_loc #al #c b l\n= let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let aux' = union_aux_of_aux_left_inv b (Ghost.reveal aux) in\n Loc\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide aux')", "let loc_of_union_loc_union_loc_of_loc #al c b s\n= assert (loc_of_union_loc b (union_loc_of_loc c b s) `loc_equal` s)", "let loc_of_union_loc_none #al c b\n= assert (loc_of_union_loc #_ #c b loc_none `loc_equal` loc_none)", "let loc_of_union_loc_union #al c b l1 l2\n= assert (loc_of_union_loc b (l1 `loc_union` l2) `loc_equal` (loc_of_union_loc b l1 `loc_union` loc_of_union_loc b l2))", "let loc_of_union_loc_addresses #al c b preserve_liveness r n =\n assert (loc_of_union_loc #_ #c b (loc_addresses preserve_liveness r n) `loc_equal` loc_addresses preserve_liveness r n)", "let loc_of_union_loc_regions #al c b preserve_liveness r =\n assert (loc_of_union_loc #_ #c b (loc_regions preserve_liveness r) `loc_equal` loc_regions preserve_liveness r)" ], "closest": [ "val raise (#t: Type) (x: t) : Tot (raise_t t)\nlet raise (#t: Type) (x: t) : Tot (raise_t t) =\n FStar.Universe.raise_val x", "val raise_t ([@@@ strictly_positive] _ : Type u#a) : Type u#(max a b)\nlet raise_t a = raise0 a", "val aloc (r: HS.rid) (n: nat) : Tot (Type u#1)\nlet aloc (r: HS.rid) (n: nat) : Tot (Type u#1) =\n (l: loc_aux { loc_aux_in_addr l r n } )", "val raise (a: Type) : stexn a\nlet raise (a:Type) : stexn a = fun s -> (None, s)", "val alloc: #a:Type -> h0:heap -> x:a -> Tot (t:(ref a * heap){snd t == upd h0 (fst t) x})\nlet alloc #a h0 x =\n let r = { addr = h0.next_addr; init = x } in\n let h1 = { next_addr = r.addr + 1;\n memory = F.on_dom nat (fun (r':nat) -> if r' = r.addr\n\t\t\t then Some (| a, x |)\n else h0.memory r') }\n in\n assert (let h2 = upd h0 r x in\n FStar.FunctionalExtensionality.feq h1.memory h2.memory);\n r, h1", "val raise (a: Type) : stexnc a\nlet raise (a:Type) : stexnc a = fun s0 -> (None, (s0, 1))", "val raise_val : #a:Type u#a -> x:a -> raise_t u#a u#b a\nlet raise_val #a x = Ret x", "val cloc_aloc : HS.rid -> nat -> Tot (Type u#1)\nlet cloc_aloc = aloc", "val raise_ : a:Type -> e:exn -> Tot (EXN?.repr a (fun (_:unit) (p:EXN?.post a) -> p (Inr e)))\nlet raise_ a (e:exn) (_:unit) = Inr e", "val raise (#a: _) (e: exn) : Alg a [Raise]\nlet raise #a (e:exn) : Alg a [Raise] = \n Alg?.reflect (Op Raise e (fun e -> match e with))", "val raise: #a: _ -> exn -> Alg a [Raise]\nlet raise : #a:_ -> exn -> Alg a [Raise] = fun e -> match geneff Raise e with", "val raise_ (#a: Type) : ex a\nlet raise_ (#a:Type) \n : ex a\n = on_dom unit (fun () -> None)", "val align_64 (x: U32.t) : Tot U32.t\nlet align_64 (x: U32.t): Tot U32.t =\n if not ( U32.((x &^ 0x07ul) =^ 0ul) ) then\n U32.( (x &^ lognot 0x07ul) +%^ 0x08ul )\n else\n x", "val alloc (#a:Type) (x:a)\n : stt (ref a) emp (fun r -> pts_to r x)\nlet alloc = alloc'", "val alloc (#a:Type) (x:a)\n : stt (ref a) emp (fun r -> pts_to r x)\nlet alloc = alloc'", "val alloc_addition_and_incr (r: ref int)\n : ST (ref (int -> Tot int))\n (requires (fun h -> h `contains_a_well_typed` r))\n (ensures\n (fun h0 s h1 ->\n h0 `contains_a_well_typed` r /\\ ~(h0 `contains` s) /\\ h1 `contains_a_well_typed` s /\\\n modifies (Set.singleton (addr_of r)) h0 h1 /\\ (forall y. sel h1 s y = sel h0 r + y)))\nlet alloc_addition_and_incr (r:ref int)\n : ST (ref (int -> Tot int))\n (requires (fun h -> h `contains_a_well_typed` r))\n\t (ensures (fun h0 s h1 -> h0 `contains_a_well_typed` r /\\\n\t\t\t ~ (h0 `contains` s) /\\\n\t\t\t h1 `contains_a_well_typed` s /\\\n\t\t\t modifies (Set.singleton (addr_of r)) h0 h1 /\\\n\t\t\t (forall y. sel h1 s y = sel h0 r + y)))\n = let x = !r in\n let s = alloc (fun y -> x + y) in\n s", "val raise (a: Type) : exnst a\nlet raise (a:Type) : exnst a = fun _ -> None", "val aloc (r: HS.rid) (n: nat) : Tot Type0\nlet aloc (r: HS.rid) (n: nat) : Tot Type0 =\n (l: loc_aux { loc_aux_in_addr l r n } )", "val alloc (#a:Type) (x:a)\n : ST (ref a)\n emp \n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\nlet alloc (#a:Type) (x:a)\n : ST (ref a)\n emp\n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\n = let r = coerce_steel (fun _ -> R.alloc x) in\n r", "val alloc (#a:Type) (x:a)\n : ST (ref a)\n emp \n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\nlet alloc (#a:Type) (x:a)\n : ST (ref a)\n emp\n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\n = let r = coerce_steel (fun _ -> R.alloc_pt x) in\n r", "val alloc : #a:Type -> \n x:a -> \n\t AllocST (ref a) (fun _ -> True)\n (fun h0 r h1 -> r `Heap.unused_in` h0 /\\\n\t\t\t\t\t FStar.Heap.contains h1 r /\\\n\t\t\t\t h1 == FStar.Heap.upd h0 r x)\nlet alloc #a x = \n let h = ist_get () in\n let r = gen_ref h in\n ist_put (upd h r x);\n ist_witness (contains r);\n r", "val alloc : #a:Type -> \n x:a -> \n\t AllocST (ref a) (fun _ -> True)\n (fun h0 r h1 -> ~(contains r h0) /\\ \n\t\t\t\t\t fst (alloc_ref h0 a x) == r /\\ \n\t\t\t\t\t snd (alloc_ref h0 a x) == h1)\nlet alloc #a x = \n let h0 = ist_get () in\n let rh1 = alloc_ref h0 a x in \n ist_put (snd rh1); \n ist_witness (contains (fst rh1)); //witnessing that the current heap contains the generated reference\n fst rh1", "val raise (#a: _) : option a\nlet raise #a : option a = None", "val raise (#a: Type) (p: pcm a) : pcm (raise_t u#a u#b a)\nlet raise (#a:Type) (p:pcm a)\n : pcm (raise_t u#a u#b a)\n = {\n p = {\n composable = (fun x y -> p.p.composable (downgrade_val x) (downgrade_val y));\n op = (fun x y -> raise_val (p.p.op (downgrade_val x) (downgrade_val y)));\n one = raise_val p.p.one;\n };\n comm = (fun x y -> p.comm (downgrade_val x) (downgrade_val y));\n assoc = (fun x y z -> p.assoc (downgrade_val x) (downgrade_val y) (downgrade_val z));\n assoc_r = (fun x y z -> p.assoc_r (downgrade_val x) (downgrade_val y) (downgrade_val z));\n is_unit = (fun x -> p.is_unit (downgrade_val x));\n refine = (fun x -> p.refine (downgrade_val x));\n }", "val alloc (#a:Type) (x:a)\n : stt_ghost (ref a) emp (fun r -> pts_to r x)\nlet alloc = alloc'", "val alloc (#a:Type) (x:a)\n : stt_ghost (ref a) emp (fun r -> pts_to r x)\nlet alloc = alloc'", "val _alloca (#a: Type) (x: a)\n : ST (ref a)\n emp\n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\nlet _alloca (#a:Type) (x:a)\n : ST (ref a)\n emp\n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\n= alloc x", "val _alloca (#a: Type) (x: a)\n : ST (ref a)\n emp\n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\nlet _alloca (#a:Type) (x:a)\n : ST (ref a)\n emp\n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> not (is_null r))\n= alloc x", "val alloc_ref : h0:heap ->\n a:Type -> \n\t\tx:a -> \n\t\tTot (rh1:(ref a * heap)\n\t\t\t {~(contains h0 (fst rh1)) /\\ \n\t\t\t contains (snd rh1) (fst rh1) /\\\n\t\t sel (snd rh1) (fst rh1) == x /\\\n\t\t\t (forall b (r:ref b) .{:pattern (contains h0 r)}\n\t\t\t contains h0 r \n\t\t\t ==> \n\t\t\t contains (snd rh1) r) /\\\n\t\t\t (forall b (r:ref b{contains h0 r}) . {:pattern sel #b h0 r}\n\t\t\t sel #b h0 r == sel #b (snd rh1) r)})\nlet alloc_ref h0 a x = \n (fst h0 , (fst h0 + 1 , F.on_dom nat (fun r -> if r = fst h0 then Some (| a , x |)\n\t\t\t\t\t else snd h0 r)))", "val raise_action (#st: state u#s u#(max a b)) (#t: Type u#a) (a: action st t)\n : action st (U.raise_t u#a u#(max a b) t)\nlet raise_action\n (#st:state u#s u#(max a b))\n (#t:Type u#a)\n (a:action st t)\n : action st (U.raise_t u#a u#(max a b) t)\n = {\n pre = a.pre;\n post = F.on_dom _ (fun (x:U.raise_t u#a u#(max a b) t) -> a.post (U.downgrade_val x));\n step = (fun frame ->\n M.weaken <|\n M.bind (a.step frame) <|\n (fun x -> M.return <| U.raise_val u#a u#(max a b) x))\n }", "val raise_t (t: Type0) : Type u#1\nlet raise_t (t: Type0) : Type u#1 = FStar.Universe.raise_t t", "val alloc : #a:Type -> \n x:a -> \n\t ImmutableST (ref a) (fun _ -> True)\n (fun h0 r h1 -> r `unused_in` h0 /\\\n\t\t\t\t\t contains h1 r /\\\n\t\t\t\t\t\th1 == upd h0 r x)\nlet alloc #a x = \n let h = ist_get () in\n let r = gen_ref h in\n ist_put (upd h r x);\n r", "val cloc_aloc: HS.rid -> nat -> Tot Type0\nlet cloc_aloc = aloc", "val raise_seq (#a: Type0) (x: FStar.Seq.seq a) : FStar.Seq.seq (U.raise_t u#0 u#1 a)\nlet raise_seq (#a:Type0) (x:FStar.Seq.seq a)\n : FStar.Seq.seq (U.raise_t u#0 u#1 a)\n = FStar.Seq.map_seq U.raise_val x", "val raise_val_inj (#a:Type) (x y:a) : Lemma\n (requires U.raise_val x == U.raise_val y)\n (ensures x == y)\nlet raise_val_inj x y =\n U.downgrade_val_raise_val x;\n U.downgrade_val_raise_val y", "val max (#t: inttype{supported_type t}) (x y: uint_t t SEC)\n : Tot (z: uint_t t SEC {v z == (if v y <= v x then v x else v y)})\nlet max\n (#t: inttype { supported_type t })\n (x y: uint_t t SEC)\n: Tot (z: uint_t t SEC { v z == (if v y <= v x then v x else v y) })\n= let cond = secret_is_lt y x in\n (cond `mul` x) `add` (lognot_one_bit cond `mul` y)", "val alloc \n (#elt: Type)\n (x: elt)\n (n: SZ.t)\n : stt (array elt) \n (requires emp)\n (ensures fun a ->\n pts_to a (Seq.create (SZ.v n) x) **\n pure (length a == SZ.v n /\\ is_full_array a))\nlet alloc = alloc'", "val alloc \n (#elt: Type)\n (x: elt)\n (n: SZ.t)\n : stt (array elt) \n (requires emp)\n (ensures fun a ->\n pts_to a (Seq.create (SZ.v n) x) **\n pure (length a == SZ.v n /\\ is_full_array a))\nlet alloc = alloc'", "val raise_erased (#a: Type0) (x: erased a) : erased (U.raise_t u#0 u#1 a)\nlet raise_erased (#a:Type0) (x:erased a)\n : erased (U.raise_t u#0 u#1 a)\n = Ghost.hide (U.raise_val (Ghost.reveal x))", "val another_raise (#a: _) (e: exn) : Alg a [Raise]\nlet another_raise #a (e:exn) : Alg a [Raise] = \n // Funnily enough, the version below succeeds from concluding `a ==\n // empty` under the lambda since the context becomes inconsistent. All\n // good, just surprising.\n Alg?.reflect (Op Raise e Return)", "val alloc (n:US.t{US.v n > 0})\n : STT (bv_t n) emp (fun r -> pts_to r full_perm (Seq.create (US.v n) false))\nlet alloc n = A.alloc false n", "val alloc\n (#a: Type0)\n (rel: preorder a)\n (id: rid)\n (init: a)\n (mm: bool)\n (m: mem{(get_hmap m) `Map.contains` id})\n : Tot\n (p:\n (mreference a rel * mem)\n { let r, h = Heap.alloc rel ((get_hmap m) `Map.sel` id) init mm in\n as_ref (fst p) == r /\\ get_hmap (snd p) == Map.upd (get_hmap m) id h })\nlet alloc (#a:Type0) (rel:preorder a) (id:rid) (init:a) (mm:bool) (m:mem{get_hmap m `Map.contains` id})\n :Tot (p:(mreference a rel * mem){let (r, h) = Heap.alloc rel (get_hmap m `Map.sel` id) init mm in\n as_ref (fst p) == r /\\\n get_hmap (snd p) == Map.upd (get_hmap m) id h})\n = let h, rid_ctr, tip = get_hmap m, get_rid_ctr m, get_tip m in\n lemma_is_wf_ctr_and_tip_elim m;\n let r, id_h = Heap.alloc rel (Map.sel h id) init mm in\n let h = Map.upd h id id_h in\n lemma_is_wf_ctr_and_tip_intro h rid_ctr tip;\n (mk_mreference id r), mk_mem rid_ctr h tip", "val raise_equiv (#t: Type) (x y: t) : Lemma (U.raise_val x == U.raise_val y <==> x == y)\nlet raise_equiv (#t:Type) (x y:t)\n : Lemma (U.raise_val x == U.raise_val y <==>\n x == y)\n = assert (U.downgrade_val (U.raise_val x) == x);\n assert (U.downgrade_val (U.raise_val y) == y)", "val alloca: #a:alg -> alloca_st a\nlet alloca #a k =\n match a with\n | AES128_GCM -> alloca_aes128_gcm k\n | AES256_GCM -> alloca_aes256_gcm k\n | CHACHA20_POLY1305 -> alloca_chacha20_poly1305 k", "val raise (#a: _) (e: exn) : EFF a [EXN]\nlet raise #a (e:exn) : EFF a [EXN] =\n EFF?.reflect (fun () -> raise e)", "val raise: a: Type -> Prims.unit -> rand a\nlet raise (a:Type) () : rand a = fun s -> None, fst s", "val raise: a: Type -> Prims.unit -> rand a\nlet raise (a:Type) () : rand a = fun s -> None, fst s", "val upd_tot : #a:Type -> h0:heap -> r:ref a{h0 `contains_a_well_typed` r} -> x:a -> Tot heap\nlet upd_tot #a h0 r x =\n { h0 with memory = F.on_dom nat (fun r' -> if r.addr = r'\n\t\t\t then Some (| a, x |)\n else h0.memory r') }", "val addx (l: loc) (x: int)\n : AlgPP unit\n (fun _ -> True)\n (fun h0 _ h1 -> modifies1 l h0 h1 /\\ (Map.sel h1 l == x + Map.sel h0 l))\nlet addx (l:loc) (x:int) : AlgPP unit (fun _ -> True) (fun h0 _ h1 -> modifies1 l h0 h1\n /\\ (Map.sel h1 l == x + Map.sel h0 l)) =\n l := !l + x", "val alloc (#a:Type) (x:a)\n : Steel (ref a) emp (fun r -> pts_to r full_perm x)\n (requires fun _ -> True)\n (ensures fun _ r _ -> not (is_null r))\nlet alloc #a x =\n let v = Some (x, full_perm) in\n assert (FStar.PCM.composable pcm_frac v None);\n assert (compatible pcm_frac v v);\n let r = RP.alloc v in\n rewrite_slprop (RP.pts_to r v) (pts_to r full_perm x)\n (fun m ->\n emp_unit (hp_of (pts_to_raw r full_perm x));\n pure_star_interp (hp_of (pts_to_raw r full_perm x)) (perm_ok full_perm) m\n );\n extract_info_raw (pts_to r full_perm x) (~ (is_null r))\n (fun m -> pts_to_not_null r full_perm x m);\n return r", "val ralloc (#a: Type0) (x: a)\n : Steel (ref a)\n emp\n (fun r -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ r h1 -> h1 (vptr r) == x /\\ not (is_null r))\nlet ralloc (#a:Type0) (x:a) : Steel (ref a)\n emp (fun r -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ r h1 -> h1 (vptr r) == x /\\ not (is_null r))\n=\n malloc x", "val ralloc (#a: Type0) (x: a)\n : Steel (ref a)\n emp\n (fun r -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ r h1 -> h1 (vptr r) == x /\\ not (is_null r))\nlet ralloc (#a:Type0) (x:a) : Steel (ref a)\n emp (fun r -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ r h1 -> h1 (vptr r) == x /\\ not (is_null r))\n=\n malloc x", "val raise (#a #si #so: _) (e: exn) : EFF a si so [EXN]\nlet raise #a #si #so (e:exn) : EFF a si so [EXN] =\n EFF?.reflect (Op Raise e Return)", "val test0 (x y: int) : Alg int [Read; Raise]\nlet test0 (x y : int) : Alg int [Read; Raise] =\n let z = get () in\n if z < 0 then raise (Failure \"error\");\n x + y + z", "val lower (#t: Type) (x: raise_t t) : Tot t\nlet lower (#t: Type) (x: raise_t t) : Tot t =\n FStar.Universe.downgrade_val x", "val incr (#v0: erased int) (x: ref int) : C unit (pts_to x v0) (fun u -> pts_to x (v0 + 1))\nlet incr (#v0:erased int) (x:ref int)\n : C unit (pts_to x v0) (fun u -> pts_to x (v0 + 1))\n = let v = !x in\n frame_r (fun _ -> x := v + 1);\n rewrite (fun y -> pts_to x (y + 1)) v0 v", "val incr (#v0: erased int) (x: ref int) : C unit (pts_to x v0) (fun u -> pts_to x (v0 + 1))\nlet incr (#v0:erased int) (x:ref int)\n : C unit (pts_to x v0) (fun u -> pts_to x (v0 + 1))\n = let v = !x in\n frame_r (fun _ -> x := v + 1);\n rewrite (fun y -> pts_to x (y + 1)) v0 v", "val test1 (x y: int) : Alg int [Raise; Read; Write]\nlet test1 (x y : int) : Alg int [Raise; Read; Write] =\n let z = get () in\n if x + z > 0\n then raise (Failure \"asd\")\n else (put 42; y - z)", "val alloc (#a:Type0) (x:a)\n : stt (box a) emp (fun b -> pts_to b x)\nlet alloc x = R.alloc x", "val raise (#a: Type) (e: exn) : TAC a (fun ps post -> post (Failed e ps))\nlet raise (#a:Type) (e:exn)\n : TAC a (fun ps post -> post (Failed e ps))\n = TAC?.reflect (fun ps -> Failed #a e ps)", "val alloc : #a:Type -> \n x:a -> \n\t ImmutableST (ref a) (fun _ -> True)\n (fun h0 r h1 -> ~(contains r h0) /\\ \n\t\t\t\t\t fst (alloc_ref h0 a x) == r /\\ \n\t\t\t\t\t\tsnd (alloc_ref h0 a x) == h1)\nlet alloc #a x = \n let h0 = ist_get () in\n let rh1 = alloc_ref h0 a x in \n ist_put (snd rh1); \n ist_witness (contains (fst rh1)); //witnessing that the current heap contains the generated reference\n fst rh1", "val raise_ex: exn -> Tot (ex False)\nlet raise_ex (_:exn) : Tot (ex False) = fun _ -> None", "val alloc (#a:Type)\n (#u:_)\n (x:erased a)\n : STGhostT (ref a) u\n emp\n (fun r -> pts_to r full_perm x)\nlet alloc (#a:Type)\n (#u:_)\n (x:erased a)\n : STGhostT (ref a) u\n emp\n (fun r -> pts_to r full_perm x)\n = coerce_ghost (fun _ -> R.ghost_alloc_pt x)", "val upd (#a: eqtype) (#b: _) (m: map' a b) (x: a) (y: b x) : Tot (map' a b)\nlet upd (#a:eqtype) #b (m:map' a b) (x:a) (y:b x)\n : Tot (map' a b)\n = fun z -> if x = z then Some y else m z", "val size_to_word: al:Spec.alg -> s:size_t -> u:word_t al{u == Spec.nat_to_word al (v s)}\nlet size_to_word al s = match al with\n | Spec.Blake2S -> size_to_uint32 s\n | Spec.Blake2B -> size_to_uint64 s", "val abs: x:int -> Tot (y:int{ (x >= 0 ==> y = x) /\\ (x < 0 ==> y = -x) })\nlet abs x = if x >= 0 then x else -x", "val as_addr (#t: typ) (p: pointer t): GTot (x: nat { x > 0 } )\nlet as_addr (#t: typ) (p: pointer t) =\n HS.aref_as_addr (Pointer?.contents p)", "val upd: #a:Type -> h0:heap -> r:ref a -> x:a\n -> GTot heap\nlet upd #a h0 r x =\n if FStar.StrongExcludedMiddle.strong_excluded_middle (h0 `contains_a_well_typed` r)\n then upd_tot h0 r x\n else\n if r.addr >= h0.next_addr\n then (* alloc at r.addr *)\n { next_addr = r.addr + 1;\n memory = F.on_dom nat (fun (r':nat) -> if r' = r.addr\n\t\t\t then Some (| a, x |)\n else h0.memory r') }\n else (* type modifying update at r.addr *)\n { h0 with memory = F.on_dom nat (fun r' -> if r' = r.addr\n\t\t\t\t then Some (| a, x |)\n else h0.memory r') }", "val alloc \n (#a:Type0)\n (x:a)\n (n:SZ.t)\n : stt (vec a)\n (requires emp)\n (ensures fun v ->\n pts_to v (Seq.create (SZ.v n) x) **\n pure (length v == SZ.v n /\\ is_full_vec v))\nlet alloc x n = A.alloc x n", "val cast_up\n (#t1: inttype { unsigned t1 })\n (t2: inttype { unsigned t2 /\\ bits t1 <= bits t2 })\n (#sec: secrecy_level)\n (x: uint_t t1 sec)\n: Tot (y: uint_t t2 SEC { v y == v x })\nlet cast_up\n #t1 t2 #sec x\n= cast t2 SEC x", "val add_overflow (x y: U32.t)\n : Pure U32.t\n (requires True)\n (ensures\n (fun z ->\n if U32.v x + U32.v y > U32.v u32_max then z == u32_max else U32.v z == U32.v x + U32.v y\n ))\nlet add_overflow\n (x y: U32.t)\n: Pure U32.t\n (requires True)\n (ensures (fun z ->\n if U32.v x + U32.v y > U32.v u32_max then\n z == u32_max\n else U32.v z == U32.v x + U32.v y\n ))\n= if U32.lt (U32.sub u32_max y) x\n then u32_max\n else U32.add x y", "val length (#a:Type u#0) (x:array a) : GTot nat\nlet length #a x = H.length x", "val loc_mreference\n (#aloc: aloc_t)\n (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n : GTot (loc c)\nlet loc_mreference\n (#aloc: aloc_t) (#c: cls aloc)\n (#a: Type)\n (#p: Preorder.preorder a)\n (b: HS.mreference a p)\n: GTot (loc c)\n= loc_addresses true (HS.frameOf b) (Set.singleton (HS.as_addr b))", "val max: x:int -> y:int -> Tot (z:int{ (x >= y ==> z = x) /\\ (x < y ==> z = y) })\nlet max x y = if x >= y then x else y", "val alloc_:\n #a:Type0 -> #rst:Type -> #rg:regional rst a -> rv:rvector rg ->\n cidx:uint32_t{cidx <= V.size_of rv} ->\n HST.ST unit\n (requires (fun h0 -> rv_itself_inv h0 rv))\n (ensures (fun h0 _ h1 ->\n modifies (V.loc_vector_within rv 0ul cidx) h0 h1 /\\\n rv_itself_inv h1 rv /\\\n rv_elems_inv h1 rv 0ul cidx /\\\n rv_elems_reg h1 rv 0ul cidx /\\\n S.equal (as_seq_sub h1 rv 0ul cidx)\n (S.create (U32.v cidx) (Ghost.reveal (Rgl?.irepr rg))) /\\\n // the loop invariant for this function\n V.forall_ h1 rv 0ul cidx\n (fun r -> HS.fresh_region (Rgl?.region_of rg r) h0 h1 /\\\n Rgl?.r_alloc_p rg r) /\\\n Set.subset (Map.domain (HS.get_hmap h0))\n (Map.domain (HS.get_hmap h1))))\n (decreases (U32.v cidx))\nlet rec alloc_ #a #rst #rg rv cidx =\n let hh0 = HST.get () in\n if cidx = 0ul then ()\n else (let nrid = HST.new_region (V.frameOf rv) in\n let v = rg_alloc rg nrid in\n\n let hh1 = HST.get () in\n V.assign rv (cidx - 1ul) v;\n\n let hh2 = HST.get () in\n V.loc_vector_within_included rv (cidx - 1ul) cidx;\n Rgl?.r_sep\n rg (V.get hh2 rv (cidx - 1ul))\n (V.loc_vector_within rv (cidx - 1ul) cidx)\n hh1 hh2;\n alloc_ rv (cidx - 1ul);\n\n let hh3 = HST.get () in\n V.loc_vector_within_included rv 0ul (cidx - 1ul);\n Rgl?.r_sep\n rg (V.get hh3 rv (cidx - 1ul))\n (V.loc_vector_within rv 0ul (cidx - 1ul))\n hh2 hh3;\n V.forall2_extend hh3 rv 0ul (cidx - 1ul)\n (fun r1 r2 -> HS.disjoint (Rgl?.region_of rg r1)\n (Rgl?.region_of rg r2));\n V.loc_vector_within_union_rev rv 0ul cidx)", "val alloc:\n #a:Type -> len:uint32_t{len > 0ul} -> v:a ->\n HST.ST (vector a)\n (requires (fun h0 -> true))\n (ensures (fun h0 vec h1 ->\n frameOf vec = HS.root /\\\n live h1 vec /\\ freeable vec /\\\n modifies loc_none h0 h1 /\\\n Set.equal (Map.domain (HS.get_hmap h0))\n (Map.domain (HS.get_hmap h1)) /\\\n size_of vec = len /\\\n S.equal (as_seq h1 vec) (S.create (U32.v len) v) /\\\n B.fresh_loc (loc_vector vec) h0 h1))\nlet alloc #a len v =\n alloc_rid len v HS.root", "val as_loc (x: eloc) : GTot B.loc\nlet as_loc (x:eloc) : GTot B.loc = Ghost.reveal x", "val alloc (#opened: _) (#a:Type) (x:a)\n : STGhost (ref a) opened\n emp \n (fun r -> pts_to r full_perm x)\n (requires True)\n (ensures fun r -> True)\nlet alloc\n #_ #a x\n= let gr = STC.coerce_ghost (fun _ -> R.ghost_alloc x) in\n let r = Hide (Ghost.reveal (coerce_eq (R.reveal_ghost_ref a) gr)) in\n weaken (R.ghost_pts_to gr full_perm x) (pts_to r full_perm x) (fun _ ->\n R.reveal_ghost_pts_to_sl gr full_perm x\n );\n r", "val upd (r: loc) (v: int) : AlgWP unit (fun h0 p -> p ((), Map.upd h0 r v))\nlet upd (r:loc) (v:int) : AlgWP unit (fun h0 p -> p ((), Map.upd h0 r v)) =\n let h = get2 () in\n put2 (Map.upd h r v)", "val fix_F\n (#aa: Type)\n (#r: binrel aa)\n (#p: (aa -> Type))\n (f: (x: aa -> (y: aa -> r y x -> p y) -> p x))\n (x: aa)\n (a: acc r x)\n : Tot (p x) (decreases a)\nlet rec fix_F (#aa:Type) (#r:binrel aa) (#p:(aa -> Type))\n (f: (x:aa -> (y:aa -> r y x -> p y) -> p x))\n (x:aa) (a:acc r x)\n : Tot (p x) (decreases a)\n = f x (fun y h -> fix_F f y (a.access_smaller y h))", "val max64\n (x y: uint64)\n: Tot (z: uint64 { v z == (if v y <= v x then v x else v y) })\nlet max64\n x y\n= max x y", "val max64\n (x y: uint64)\n: Tot (z: uint64 { v z == (if v y <= v x then v x else v y) })\nlet max64 x y = Aux.max64 x y", "val sel' (#a: _) (r: regmap a) (x: reg) : Tot a\nlet sel' #a (r:regmap a) (x:reg) : Tot a = sel r x", "val alloc (x:stepper{compatible p x x /\\ refine x})\n : SteelT (ref stepper p) emp (fun r -> pts_to r x)\nlet alloc x =\n let r = alloc x in\n rewrite_slprop (PR.pts_to r x) (pts_to r x) (fun _ -> ());\n return r", "val upd (s: store) (l: loc) (x: int) : store\nlet upd (s:store) (l:loc) (x:int) : store = Map.upd s l x", "val upd (s: store) (l: loc) (x: int) : store\nlet upd (s:store) (l:loc) (x:int) : store = Map.upd s l x", "val upd (s: store) (l: loc) (x: int) : store\nlet upd (s:store) (l:loc) (x:int) : store = Map.upd s l x", "val shift_up_above : nat -> exp -> Tot exp\nlet shift_up_above n e = subst (sub_inc_above n) e", "val alloc (#a:Type0) (init:a)\n :ST (ref a)\n (fun _ -> True)\n (fun h0 r h1 -> fresh r h0 h1 /\\ modifies Set.empty h0 h1 /\\ sel h1 r == init)\nlet alloc #_ init = alloc init", "val va_code_Alloc_stack : n:nat64 -> Tot va_code\nlet va_code_Alloc_stack n =\n (Ins (S.Alloc n))", "val varint_len (x: U62.t) : Tot (y: U32.t{U32.v y <= 8})\nlet varint_len\n (x: U62.t)\n: Tot (y: U32.t {U32.v y <= 8})\n= if x `U62.lt` 64uL\n then 1ul\n else if x `U62.lt` 16384uL\n then 2ul\n else if x `U62.lt` 1073741824uL\n then 4ul\n else 8ul", "val word_to_limb (a: alg) (x: word_t a {uint_v x <= max_limb a})\n : xl: limb_t a {uint_v xl == uint_v x}\nlet word_to_limb (a:alg) (x:word_t a{uint_v x <= max_limb a}) : xl:limb_t a{uint_v xl == uint_v x} =\n match (wt a) with\n | U32 -> to_u64 x\n | U64 -> to_u128 x", "val nat_to_limb (a: alg) (x: nat{x <= max_limb a}) : xl: limb_t a {uint_v xl == x}\nlet nat_to_limb (a:alg) (x:nat{x <= max_limb a}) : xl:limb_t a{uint_v xl == x} =\n match (wt a) with\n | U32 -> u64 x\n | U64 -> let h = u64 (x / pow2 64) in\n\t let l = u64 (x % pow2 64) in\n\t (to_u128 h <<. 64ul) +! to_u128 l", "val jump (n: pos) (l: nat) (x: nat_up_to n) : GTot (nat_up_to n)\nlet jump\n (n: pos)\n (l: nat)\n (x: nat_up_to n)\n: GTot (nat_up_to n)\n= (x + l) % n", "val loc_all_regions_from (#aloc: aloc_t) (#c: cls aloc) (preserve_liveness: bool) (r: HS.rid)\n : GTot (loc c)\nlet loc_all_regions_from\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n: GTot (loc c)\n= loc_regions preserve_liveness (HS.mod_set (Set.singleton r))", "val raise__ (a: Type) (e: exn) : Exn a True (fun r -> r == Inr e)\nlet raise__ (a:Type) (e:exn) : Exn a True (fun r -> r == Inr e)\n = EXN?.reflect (raise_ a e)", "val u32_max:(y: U32.t{forall (x: U32.t). {:pattern (U32.v x)} U32.v x <= U32.v y})\nlet u32_max : (y: U32.t { forall (x: U32.t) . {:pattern (U32.v x)} U32.v x <= U32.v y } ) =\n 4294967295ul", "val alloc_empty:\n a:Type -> Tot (vec:vector a{size_of vec = 0ul})\nlet alloc_empty a =\n Vec 0ul 0ul B.null", "val be_to_n_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat{len + 1 <= tot})\n (ih: be_to_n_t u len)\n : Tot (be_to_n_t u (len + 1))\nlet be_to_n_S\n (#t: Type)\n (#tot: nat)\n (#u: uinttype t tot)\n (#len: nat { len + 1 <= tot })\n (ih: be_to_n_t u len)\n: Tot (be_to_n_t u (len + 1))\n= fun x ->\n assert_norm (pow2 8 == 256);\n E.reveal_be_to_n (B.reveal x);\n pow2_le_compat (8 * tot) (8 * (len + 1));\n pow2_le_compat (8 * (len + 1)) (8 * len);\n pow2_plus (8 * len) 8;\n [@inline_let]\n let ulen = U32.uint_to_t len in\n let last = B.get x ulen in\n let first = B.slice x 0ul ulen in\n let n = ih first in\n E.lemma_be_to_n_is_bounded (B.reveal first);\n assert (u.v n * 256 < 256 * pow2 (8 * len));\n assert (0 <= u.v n * 256);\n assert (u.v n * 256 < pow2 (8 * tot));\n let blast = u.from_byte last in\n blast `u.add` u.mul256 n", "val set (a:Type u#a) : Type u#(max 1 a)\nlet set a = F.restricted_t a (fun _ -> prop)" ], "closest_src": [ { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.raise" }, { "project_name": "FStar", "file_name": "FStar.Universe.fst", "name": "FStar.Universe.raise_t" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.aloc" }, { "project_name": "FStar", "file_name": "FStar.DM4F.StExn.fst", "name": "FStar.DM4F.StExn.raise" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.alloc" }, { "project_name": "FStar", "file_name": "FStar.DM4F.StExnC.fst", "name": "FStar.DM4F.StExnC.raise" }, { "project_name": "FStar", "file_name": "FStar.Universe.fst", "name": "FStar.Universe.raise_val" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.cloc_aloc" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Exceptions.fst", "name": "FStar.DM4F.Exceptions.raise_" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.raise" }, { "project_name": "FStar", "file_name": "Alg.fst", "name": "Alg.raise" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.raise_" }, { "project_name": "karamel", "file_name": "WasmSupport.fst", "name": "WasmSupport.align_64" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherReference.fst", "name": "Pulse.Lib.HigherReference.alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.Reference.fst", "name": "Pulse.Lib.Reference.alloc" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.ST.fsti", "name": "FStar.DM4F.Heap.ST.alloc_addition_and_incr" }, { "project_name": "FStar", "file_name": "FStar.DM4F.ExnSt.fst", "name": "FStar.DM4F.ExnSt.raise" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.aloc" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.alloc" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.alloc" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.alloc" }, { "project_name": "FStar", "file_name": "AllocST.fst", "name": "AllocST.alloc" }, { "project_name": "FStar", "file_name": "MonadFunctorInference.fst", "name": "MonadFunctorInference.raise" }, { "project_name": "FStar", "file_name": "FStar.Universe.PCM.fst", "name": "FStar.Universe.PCM.raise" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.alloc" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference._alloca" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference._alloca" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.alloc_ref" }, { "project_name": "steel", "file_name": "PulseCore.Semantics.fst", "name": "PulseCore.Semantics.raise_action" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.raise_t" }, { "project_name": "FStar", "file_name": "ImmutableSTwHeaps.fst", "name": "ImmutableSTwHeaps.alloc" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.cloc_aloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.raise_seq" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.raise_val_inj" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Secret.Int.Aux.fst", "name": "QUIC.Secret.Int.Aux.max" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherArray.fst", "name": "Pulse.Lib.HigherArray.alloc" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.raise_erased" }, { "project_name": "FStar", "file_name": "Alg.fst", "name": "Alg.another_raise" }, { "project_name": "steel", "file_name": "Steel.ST.BitVector.fst", "name": "Steel.ST.BitVector.alloc" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.alloc" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.raise_equiv" }, { "project_name": "hacl-star", "file_name": "EverCrypt.AEAD.fst", "name": "EverCrypt.AEAD.alloca" }, { "project_name": "FStar", "file_name": "LatticeEff.fst", "name": "LatticeEff.raise" }, { "project_name": "FStar", "file_name": "FStar.DM4F.OTP.Random.fst", "name": "FStar.DM4F.OTP.Random.raise" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Random.fst", "name": "FStar.DM4F.Random.raise" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.upd_tot" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.addx" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.alloc" }, { "project_name": "steel", "file_name": "CQueue.LList.fst", "name": "CQueue.LList.ralloc" }, { "project_name": "steel", "file_name": "CQueue.Cell.fst", "name": "CQueue.Cell.ralloc" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.raise" }, { "project_name": "FStar", "file_name": "Alg.fst", "name": "Alg.test0" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.lower" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParDiv.fst", "name": "OPLSS2021.ParDiv.incr" }, { "project_name": "FStar", "file_name": "OPLSS2021.ParNDSDiv.fst", "name": "OPLSS2021.ParNDSDiv.incr" }, { "project_name": "FStar", "file_name": "Alg.fst", "name": "Alg.test1" }, { "project_name": "steel", "file_name": "Pulse.Lib.Box.fst", "name": "Pulse.Lib.Box.alloc" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Effect.fsti", "name": "FStar.Tactics.Effect.raise" }, { "project_name": "FStar", "file_name": "ImmutableST.fst", "name": "ImmutableST.alloc" }, { "project_name": "FStar", "file_name": "SimplePrintfReify.fst", "name": "SimplePrintfReify.raise_ex" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.alloc" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Map.fst", "name": "FStar.Monotonic.Map.upd" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Blake2.Generic.fst", "name": "Hacl.Impl.Blake2.Generic.size_to_word" }, { "project_name": "FStar", "file_name": "FStar.Math.Lib.fst", "name": "FStar.Math.Lib.abs" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.as_addr" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.upd" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.alloc" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Secret.Int.fst", "name": "QUIC.Secret.Int.cast_up" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Base.fst", "name": "LowParse.SLow.Base.add_overflow" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.length" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_mreference" }, { "project_name": "FStar", "file_name": "FStar.Math.Lib.fst", "name": "FStar.Math.Lib.max" }, { "project_name": "FStar", "file_name": "LowStar.RVector.fst", "name": "LowStar.RVector.alloc_" }, { "project_name": "FStar", "file_name": "LowStar.Vector.fst", "name": "LowStar.Vector.alloc" }, { "project_name": "FStar", "file_name": "LowStar.Lens.fsti", "name": "LowStar.Lens.as_loc" }, { "project_name": "steel", "file_name": "Steel.ST.GhostHigherReference.fst", "name": "Steel.ST.GhostHigherReference.alloc" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.upd" }, { "project_name": "FStar", "file_name": "FStar.WellFounded.fst", "name": "FStar.WellFounded.fix_F" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Secret.Int.Aux.fst", "name": "QUIC.Secret.Int.Aux.max64" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Secret.Int.fst", "name": "QUIC.Secret.Int.max64" }, { "project_name": "FStar", "file_name": "Registers.List.fst", "name": "Registers.List.sel'" }, { "project_name": "steel", "file_name": "Steel.Stepper.fst", "name": "Steel.Stepper.alloc" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.upd" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.upd" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.upd" }, { "project_name": "FStar", "file_name": "StlcCbvDbParSubst.fst", "name": "StlcCbvDbParSubst.shift_up_above" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.alloc" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsStack.fst", "name": "Vale.PPC64LE.InsStack.va_code_Alloc_stack" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Impl.Base.fst", "name": "QUIC.Impl.Base.varint_len" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.Definitions.fst", "name": "Spec.Blake2.Definitions.word_to_limb" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.Definitions.fst", "name": "Spec.Blake2.Definitions.nat_to_limb" }, { "project_name": "steel", "file_name": "Steel.ST.GenArraySwap.Proof.fst", "name": "Steel.ST.GenArraySwap.Proof.jump" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fsti", "name": "FStar.ModifiesGen.loc_all_regions_from" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Exceptions.fst", "name": "FStar.DM4F.Exceptions.raise__" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Base.fst", "name": "LowParse.SLow.Base.u32_max" }, { "project_name": "FStar", "file_name": "LowStar.Vector.fst", "name": "LowStar.Vector.alloc_empty" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Endianness.fst", "name": "LowParse.SLow.Endianness.be_to_n_S" }, { "project_name": "FStar", "file_name": "FStar.TSet.fst", "name": "FStar.TSet.set" } ], "selected_premises": [ "FStar.Reflection.V2.Data.var", "FStar.Tactics.SMT.get_rlimit", "FStar.FunctionalExtensionality.feq", "FStar.Tactics.SMT.get_initial_fuel", "FStar.ModifiesGen.mk_live_addrs", "FStar.Tactics.SMT.get_max_fuel", "FStar.ModifiesGen.popped_modifies", "FStar.ModifiesGen.mk_non_live_addrs", "FStar.Tactics.Effect.raise", "FStar.Tactics.SMT.get_initial_ifuel", "FStar.Tactics.SMT.get_max_ifuel", "FStar.ModifiesGen.modifies_trans'", "FStar.ModifiesGen.loc_aux_includes_buffer_includes", "FStar.ModifiesGen.region_liveness_insensitive_locs", "FStar.Tactics.V2.Builtins.ret_t", "FStar.ModifiesGen.new_region_modifies", "FStar.ModifiesGen.loc_disjoint_includes", "FStar.Heap.trivial_preorder", "FStar.ModifiesGen.aloc_disjoint_sym", "FStar.ModifiesGen.fresh_frame_modifies", "FStar.ModifiesGen.loc_aux_includes_trans", "FStar.ModifiesGen.address_liveness_insensitive_locs", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "FStar.FunctionalExtensionality.on_dom", "FStar.ModifiesGen.modifies_loc_regions_intro", "FStar.ModifiesGen.loc_aux_includes_loc_aux_includes_buffer", "FStar.ModifiesGen.loc", "FStar.ModifiesGen.aloc_union", "FStar.ModifiesGen.modifies_none_modifies", "FStar.Monotonic.HyperStack.sel", "FStar.Tactics.SMT.smt_sync", "FStar.ModifiesGen.modifies_only_not_unused_in", "FStar.Pervasives.reveal_opaque", "FStar.ModifiesGen.i_restricted_g_t", "FStar.Reflection.Const.cons_qn", "FStar.ModifiesGen.loc_union", "FStar.ModifiesGen.modifies_fresh_frame_popped", "FStar.ModifiesGen.loc_aux_disjoint_sym", "FStar.ModifiesGen.addrs_of_loc_aux", "FStar.ModifiesGen.loc_disjoint_aloc_elim", "FStar.Reflection.Const.squash_qn", "FStar.Sealed.Inhabited.seal", "FStar.ModifiesGen.loc_none", "FStar.ModifiesGen.modifies_preserves_region_liveness_aloc", "FStar.ModifiesGen.modifies_union_loc_of_loc", "FStar.Tactics.SMT.set_rlimit", "FStar.ModifiesGen.loc_aux_includes_buffer", "FStar.ModifiesGen.modifies_trans", "FStar.ModifiesGen.modifies_preserves_livenesses_intro", "FStar.Tactics.SMT.set_fuel", "FStar.ModifiesGen.aloc_includes", "FStar.ModifiesGen.loc_unused_in_not_unused_in_disjoint", "FStar.ModifiesGen.loc_equal", "FStar.ModifiesGen.loc_unused_in", "FStar.ModifiesGen.loc_of_union_loc_regions", "FStar.Tactics.SMT.set_max_fuel", "FStar.ModifiesGen.union_loc_of_loc_includes", "FStar.ModifiesGen.disjoint_addrs_of_loc_loc_disjoint", "FStar.Tactics.SMT.set_initial_fuel", "FStar.Tactics.Types.issues", "FStar.ModifiesGen.modifies_refl", "FStar.Monotonic.HyperStack.live_region", "FStar.ModifiesGen.modifies_preserves_liveness_strong", "FStar.ModifiesGen.modifies_loc_includes", "FStar.Tactics.SMT.set_ifuel", "FStar.Tactics.SMT.smt_sync'", "FStar.ModifiesGen.not_live_region_loc_not_unused_in_disjoint", "FStar.ModifiesGen.modifies_address_liveness_insensitive_unused_in", "FStar.Reflection.Const.nil_qn", "FStar.ModifiesGen.addrs_of_loc_weak", "FStar.ModifiesGen.modifies_preserves_alocs_intro", "FStar.ModifiesGen.modifies_only_live_regions", "FStar.ModifiesGen.loc_regions", "FStar.ModifiesGen.addrs_of_loc_aux_pred", "FStar.ModifiesGen.loc_disjoint_regions", "FStar.ModifiesGen.modifies'", "FStar.ModifiesGen.loc_disjoint'", "FStar.ModifiesGen.loc_disjoint_region_liveness_tags", "FStar.ModifiesGen.restrict_to_regions", "FStar.ModifiesGen.loc_aux_includes", "FStar.ModifiesGen.loc_disjoint_sym", "FStar.ModifiesGen.aloc_disjoint", "FStar.Reflection.V2.Data.ppname_t", "FStar.ModifiesGen.loc_disjoint_aux", "FStar.HyperStack.ST.is_eternal_region", "FStar.Tactics.Effect.get", "FStar.ModifiesGen.aloc_domain", "FStar.ModifiesGen.addrs_of_loc_liveness_not_preserved", "FStar.Tactics.SMT.set_max_ifuel", "FStar.Tactics.SMT.set_initial_ifuel", "FStar.ModifiesGen.loc_aux_disjoint", "FStar.ModifiesGen.loc_of_union_loc_union_loc_of_loc", "FStar.ModifiesGen.loc_of_union_loc_none", "FStar.ModifiesGen.modifies_only_live_regions_weak", "FStar.Reflection.Const.unit_lid", "FStar.Monotonic.HyperStack.is_heap_color", "FStar.ModifiesGen.loc_of_union_loc", "FStar.Reflection.Const.mult_qn", "FStar.Monotonic.HyperStack.mreference" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.ModifiesGen\n\n#set-options \"--split_queries no\"\n#set-options \"--using_facts_from '*,-FStar.Tactics,-FStar.Reflection,-FStar.List'\"\n\nmodule HS = FStar.HyperStack\nmodule HST = FStar.HyperStack.ST\n\nnoeq\ntype aloc (#al: aloc_t) (c: cls al) = | ALoc:\n (region: HS.rid) ->\n (addr: nat) ->\n (loc: option (al region addr)) ->\n aloc c\n\nlet aloc_domain (#al: aloc_t) (c: cls al) (regions: Ghost.erased (Set.set HS.rid)) (addrs: ((r: HS.rid { Set.mem r (Ghost.reveal regions) } ) -> GTot (GSet.set nat))) : GTot (GSet.set (aloc c)) =\n GSet.comprehend (fun a -> Set.mem a.region (Ghost.reveal regions) && GSet.mem a.addr (addrs a.region))\n\nmodule F = FStar.FunctionalExtensionality\n\n[@@(unifier_hint_injective)]\nlet i_restricted_g_t = F.restricted_g_t\n\nlet addrs_dom regions =\n (r: HS.rid { Set.mem r (Ghost.reveal regions) } )\n\nlet non_live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (r:addrs_dom regions) =\n (y: GSet.set nat { r `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y })\n\nlet live_addrs_codom\n (regions: Ghost.erased (Set.set HS.rid))\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } )\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags))\n (r:addrs_dom regions) = (y: GSet.set nat { GSet.subset (non_live_addrs r) y } )\n\nnoeq\ntype loc' (#al: aloc_t u#x) (c: cls al) : Type u#x =\n | Loc:\n (regions: Ghost.erased (Set.set HS.rid)) ->\n (region_liveness_tags: Ghost.erased (Set.set HS.rid) { Ghost.reveal region_liveness_tags `Set.subset` Ghost.reveal regions } ) ->\n (non_live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags)) ->\n (live_addrs:\n i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs)) ->\n (aux: Ghost.erased (GSet.set (aloc c)) {\n aloc_domain c regions live_addrs `GSet.subset` Ghost.reveal aux /\\\n Ghost.reveal aux `GSet.subset` (aloc_domain c regions (fun _ -> GSet.complement GSet.empty))\n } ) ->\n loc' c\n\nlet loc = loc'\n\nlet mk_non_live_addrs (#regions:_) (#region_liveness_tags:_)\n (f: (x:addrs_dom regions -> GTot (non_live_addrs_codom regions region_liveness_tags x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (non_live_addrs_codom regions region_liveness_tags) =\n F.on_dom_g _ f\n\nlet mk_live_addrs (#regions:_) (#region_liveness_tags:_)\n (#non_live_addrs_codom: _)\n (f: (x:addrs_dom regions -> GTot (live_addrs_codom regions region_liveness_tags non_live_addrs_codom x)))\n : i_restricted_g_t\n (addrs_dom regions)\n (live_addrs_codom regions region_liveness_tags non_live_addrs_codom) =\n F.on_dom_g _ f\n\nlet loc_none #a #c =\n Loc\n (Ghost.hide (Set.empty))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)\n\nlet regions_of_loc\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: GTot (Set.set HS.rid)\n= Ghost.reveal (Loc?.regions s)\n\nlet addrs_of_loc_liveness_not_preserved\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.non_live_addrs l r\n else GSet.empty\n\nlet addrs_of_loc_weak\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= if Set.mem r (regions_of_loc l)\n then Loc?.live_addrs l r\n else GSet.empty\n\nlet addrs_of_loc_aux_pred\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n (addr: nat)\n: GTot bool\n= StrongExcludedMiddle.strong_excluded_middle (exists a . GSet.mem a (Ghost.reveal (Loc?.aux l)) /\\ a.region == r /\\ a.addr == addr)\n\nlet addrs_of_loc_aux\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (y: GSet.set nat { GSet.subset (GSet.intersect y (addrs_of_loc_weak l r)) GSet.empty } )\n= GSet.comprehend (addrs_of_loc_aux_pred l r)\n `GSet.intersect` (GSet.complement (addrs_of_loc_weak l r))\n\nlet addrs_of_loc\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: GTot (GSet.set nat)\n= GSet.union\n (addrs_of_loc_weak l r)\n (addrs_of_loc_aux l r)\n\nlet addrs_of_loc_aux_prop\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (r: HS.rid)\n: Lemma\n (GSet.subset (GSet.intersect (addrs_of_loc_aux l r) (addrs_of_loc_weak l r)) GSet.empty)\n [SMTPatOr [\n [SMTPat (addrs_of_loc_aux l r)];\n [SMTPat (addrs_of_loc_weak l r)];\n [SMTPat (addrs_of_loc l r)];\n ]]\n= ()\n\nlet loc_union #al #c s1 s2 =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in\n let regions = Set.union regions1 regions2 in\n let region_liveness_tags : Ghost.erased (Set.set HS.rid) = (Ghost.hide (Set.union (Ghost.reveal (Loc?.region_liveness_tags s1)) (Ghost.reveal (Loc?.region_liveness_tags s2)))) in\n let gregions = Ghost.hide regions in\n let non_live_addrs =\n F.on_dom_g (addrs_dom gregions) #(non_live_addrs_codom gregions region_liveness_tags)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then Loc?.non_live_addrs s1 r else GSet.empty)\n (if Set.mem r regions2 then Loc?.non_live_addrs s2 r else GSet.empty))\n in\n let live_addrs =\n F.on_dom_g (addrs_dom gregions) #(live_addrs_codom gregions region_liveness_tags non_live_addrs)\n (fun r ->\n GSet.union\n (if Set.mem r regions1 then addrs_of_loc_weak s1 r else GSet.empty)\n (if Set.mem r regions2 then addrs_of_loc_weak s2 r else GSet.empty))\n in\n let aux = Ghost.hide\n (Ghost.reveal (Loc?.aux s1) `GSet.union` Ghost.reveal (Loc?.aux s2))\n in\n Loc\n (Ghost.hide regions)\n region_liveness_tags\n non_live_addrs\n live_addrs\n aux\n\nlet fun_set_equal (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) :Tot Type0 =\n forall (x: t) . {:pattern (f1 x) \\/ (f2 x) } f1 x `GSet.equal` f2 x\n\nlet fun_set_equal_elim (#t: Type) (#t': Type)\n (#p:(t -> GSet.set t' -> Type))\n (f1 f2: i_restricted_g_t t (fun x -> g:GSet.set t'{p x g})) : Lemma\n (requires (fun_set_equal f1 f2))\n (ensures (f1 == f2))\n// [SMTPat (fun_set_equal f1 f2)]\n= assert (f1 `FunctionalExtensionality.feq_g` f2)\n\nlet loc_equal (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : GTot Type0 =\n let Loc regions1 region_liveness_tags1 _ _ aux1 = s1 in\n let Loc regions2 region_liveness_tags2 _ _ aux2 = s2 in\n Ghost.reveal regions1 `Set.equal` Ghost.reveal regions2 /\\\n Ghost.reveal region_liveness_tags1 `Set.equal` Ghost.reveal region_liveness_tags2 /\\\n fun_set_equal (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2) /\\\n fun_set_equal (Loc?.live_addrs s1) (Loc?.live_addrs s2) /\\\n Ghost.reveal (Loc?.aux s1) `GSet.equal` Ghost.reveal (Loc?.aux s2)\n\nlet loc_equal_elim (#al: aloc_t) (#c: cls al) (s1 s2: loc c) : Lemma\n (requires (loc_equal s1 s2))\n (ensures (s1 == s2))\n [SMTPat (s1 `loc_equal` s2)]\n= fun_set_equal_elim (Loc?.non_live_addrs s1) (Loc?.non_live_addrs s2);\n fun_set_equal_elim (Loc?.live_addrs s1) (Loc?.live_addrs s2)\n\n\nlet loc_union_idem #al #c s =\n assert (loc_union s s `loc_equal` s)\n\nlet loc_union_comm #al #c s1 s2 =\n assert (loc_union s1 s2 `loc_equal` loc_union s2 s1)\n\nlet loc_union_assoc #al #c s1 s2 s3 =\n assert (loc_union s1 (loc_union s2 s3) `loc_equal` loc_union (loc_union s1 s2) s3)\n\nlet loc_union_loc_none_l #al #c s =\n assert (loc_union loc_none s `loc_equal` s)\n\nlet loc_union_loc_none_r #al #c s =\n assert (loc_union s loc_none `loc_equal` s)\n\nlet loc_of_aloc #al #c #r #n b =\n let regions = (Ghost.hide (Set.singleton r)) in\n let region_liveness_tags = (Ghost.hide (Set.empty)) in\n Loc\n regions\n region_liveness_tags\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide (GSet.singleton (ALoc r n (Some b))))\n\nlet loc_of_aloc_not_none #al #c #r #n b = ()\n\nlet loc_addresses #al #c preserve_liveness r n =\n let regions = (Ghost.hide (Set.singleton r)) in\n Loc\n regions\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> if preserve_liveness then GSet.empty else GSet.of_set n))\n (mk_live_addrs (fun _ -> GSet.of_set n))\n (Ghost.hide (aloc_domain c regions (fun _ -> GSet.of_set n)))\n\nlet loc_regions_region_liveness_tags (preserve_liveness: bool) (r: Set.set HS.rid) : Tot (Ghost.erased (Set.set HS.rid)) =\n if preserve_liveness then Ghost.hide Set.empty else Ghost.hide r\n\nlet loc_regions #al #c preserve_liveness r =\n let region_liveness_tags = loc_regions_region_liveness_tags preserve_liveness r in\n let addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { r' `Set.mem` (Ghost.reveal region_liveness_tags) ==> GSet.subset (GSet.complement GSet.empty) y } ) =\n GSet.complement GSet.empty\n in\n let live_addrs (r' : HS.rid { Set.mem r' r } ) : GTot (y: GSet.set nat { addrs r' `GSet.subset` y } ) =\n addrs r'\n in\n Loc\n (Ghost.hide r)\n region_liveness_tags\n (mk_non_live_addrs addrs)\n (mk_live_addrs live_addrs)\n (Ghost.hide (aloc_domain c (Ghost.hide r) addrs))\n\nlet aloc_includes (#al: aloc_t) (#c: cls al) (b0 b: aloc c) : GTot Type0 =\n b0.region == b.region /\\ b0.addr == b.addr /\\ Some? b0.loc == Some? b.loc /\\ (if Some? b0.loc && Some? b.loc then c.aloc_includes (Some?.v b0.loc) (Some?.v b.loc) else True)\n\nlet loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b: aloc c)\n: GTot Type0\n (decreases s)\n= exists (b0 : aloc c) . b0 `GSet.mem` s /\\ b0 `aloc_includes` b\n\nlet loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: GTot Type0\n (decreases s2)\n= forall (b2: aloc c) . GSet.mem b2 s2 ==> loc_aux_includes_buffer s1 b2\n\nlet loc_aux_includes_union_l\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s \\/ loc_aux_includes s2 s))\n (ensures (loc_aux_includes (GSet.union s1 s2) s))\n (decreases s)\n= ()\n\nlet loc_aux_includes_refl\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n: Lemma\n (loc_aux_includes s s)\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)\n\nlet loc_aux_includes_subset\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n= Classical.forall_intro_3 (fun r a b -> c.aloc_includes_refl #r #a b)\n\nlet loc_aux_includes_subset'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n: Lemma\n (requires (s1 `GSet.subset` s2))\n (ensures (loc_aux_includes s2 s1))\n [SMTPatOr [\n [SMTPat (s1 `GSet.subset` s2)];\n [SMTPat (loc_aux_includes s2 s1)];\n ]]\n= loc_aux_includes_subset s1 s2\n\nlet loc_aux_includes_union_l_r\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s s') s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s s' s\n\nlet loc_aux_includes_union_l_l\n (#al: aloc_t) (#c: cls al)\n (s s': GSet.set (aloc c))\n: Lemma\n (loc_aux_includes (GSet.union s' s) s)\n= loc_aux_includes_refl s;\n loc_aux_includes_union_l s' s s\n\nlet loc_aux_includes_buffer_includes\n (#al: aloc_t) (#c: cls al)\n (s: GSet.set (aloc c))\n (b1 b2: aloc c)\n: Lemma\n (requires (loc_aux_includes_buffer s b1 /\\ b1 `aloc_includes` b2))\n (ensures (loc_aux_includes_buffer s b2))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))\n\nlet loc_aux_includes_loc_aux_includes_buffer\n (#al: aloc_t) (#c: cls al)\n (s1 s2: GSet.set (aloc c))\n (b: aloc c)\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes_buffer s2 b))\n (ensures (loc_aux_includes_buffer s1 b))\n= Classical.forall_intro_3 (fun s b1 b2 -> Classical.move_requires (loc_aux_includes_buffer_includes #al #c s b1) b2)\n\nlet loc_aux_includes_trans\n (#al: aloc_t) (#c: cls al)\n (s1 s2 s3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_includes s1 s2 /\\ loc_aux_includes s2 s3))\n (ensures (loc_aux_includes s1 s3))\n= Classical.forall_intro_3 (fun r a b1 -> Classical.forall_intro_2 (fun b2 b3 -> Classical.move_requires (c.aloc_includes_trans #r #a b1 b2) b3))\n\nlet addrs_of_loc_weak_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (loc_union l1 l2) r == GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r))\n [SMTPat (addrs_of_loc_weak (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc_weak (loc_union l1 l2) r) (GSet.union (addrs_of_loc_weak l1 r) (addrs_of_loc_weak l2 r)))\n\nlet addrs_of_loc_union\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l1 l2) r == GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r))\n [SMTPat (addrs_of_loc (loc_union l1 l2) r)]\n= assert (GSet.equal (addrs_of_loc (loc_union l1 l2) r) (GSet.union (addrs_of_loc l1 r) (addrs_of_loc l2 r)))\n\nunfold\nlet loc_includes' #al (#c: cls al) (s1 s2: loc c) =\n let regions1 = Ghost.reveal (Loc?.regions s1) in\n let regions2 = Ghost.reveal (Loc?.regions s2) in (\n Set.subset regions2 regions1 /\\\n Set.subset (Ghost.reveal (Loc?.region_liveness_tags s2)) (Ghost.reveal (Loc?.region_liveness_tags s1)) /\\\n (\n forall (r: HS.rid { Set.mem r regions2 } ) .\n GSet.subset (Loc?.non_live_addrs s2 r) (Loc?.non_live_addrs s1 r)\n ) /\\\n (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc_weak s2 r) (addrs_of_loc_weak s1 r)\n ) /\\ (\n forall (r: HS.rid) .\n GSet.subset (addrs_of_loc s2 r) (addrs_of_loc s1 r)\n ) /\\ (\n (Ghost.reveal (Loc?.aux s1)) `loc_aux_includes` (Ghost.reveal (Loc?.aux s2))\n )\n )\n\nlet loc_includes #al #c s1 s2 =\n loc_includes' s1 s2\n\nlet loc_includes_refl #al #c s =\n loc_aux_includes_refl (Ghost.reveal (Loc?.aux s))\n\nlet loc_includes_refl'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n: Lemma\n (loc_includes s s)\n [SMTPat (loc_includes s s)]\n= loc_includes_refl s\n\nlet loc_includes_trans #al #c s1 s2 s3 =\n loc_aux_includes_trans (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s3))\n\nlet loc_includes_union_r #al #c s s1 s2 = ()\n\nlet loc_includes_union_l #al #c s1 s2 s =\n let u12 = loc_union s1 s2 in\n Classical.or_elim\n #(loc_includes s1 s)\n #(loc_includes s2 s)\n #(fun _ -> loc_includes (loc_union s1 s2) s)\n (fun _ ->\n loc_aux_includes_union_l_r (Ghost.reveal (Loc?.aux s1)) (Ghost.reveal (Loc?.aux s2));\n assert (loc_includes (loc_union s1 s2) s1);\n loc_includes_trans u12 s1 s)\n (fun _ ->\n loc_aux_includes_union_l_l (Ghost.reveal (Loc?.aux s2)) (Ghost.reveal (Loc?.aux s1));\n assert (loc_includes (loc_union s1 s2) s2);\n loc_includes_trans u12 s2 s)\n\nlet loc_includes_none #al #c s = ()\n\nlet loc_includes_none_elim #al #c s =\n assert (s `loc_equal` loc_none)\n\nlet loc_includes_aloc #al #c #r #n b1 b2 = ()\n\nlet loc_includes_aloc_elim #aloc #c #r1 #r2 #n1 #n2 b1 b2 = ()\n\nlet addrs_of_loc_loc_of_aloc\n (#al: aloc_t)\n (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (p: al r a)\n (r': HS.rid)\n: Lemma\n (addrs_of_loc (loc_of_aloc #_ #c p) r' `GSet.equal` (if r = r' then GSet.singleton a else GSet.empty))\n [SMTPat (addrs_of_loc (loc_of_aloc #_ #c p) r')]\n= ()\n\nlet loc_includes_addresses_aloc #al #c preserve_liveness r s #a p = ()\n\nlet loc_includes_region_aloc #al #c preserve_liveness s #r #a b = ()\n\nlet loc_includes_region_addresses #al #c s preserve_liveness1 preserve_liveness2 r a = ()\n\nlet loc_includes_region_region #al #c preserve_liveness1 preserve_liveness2 s1 s2 = ()\n\nlet loc_includes_region_union_l #al #c preserve_liveness l s1 s2 =\n assert ((loc_regions #_ #c preserve_liveness (Set.intersect s2 (Set.complement s1)) `loc_union` loc_regions #_ #c preserve_liveness (Set.intersect s2 s1)) `loc_equal` loc_regions preserve_liveness s2);\n loc_includes_region_region #_ #c preserve_liveness preserve_liveness s1 (Set.intersect s2 s1);\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1)));\n loc_includes_union_l (loc_regions preserve_liveness s1) l (loc_regions preserve_liveness (Set.intersect s2 s1));\n loc_includes_union_r (loc_union (loc_regions preserve_liveness s1) l) (loc_regions preserve_liveness (Set.intersect s2 (Set.complement s1))) (loc_regions preserve_liveness (Set.intersect s2 s1))\n\nlet loc_includes_addresses_addresses #al c preserve_liveness1 preserve_liveness2 r s1 s2 = ()\n\n(* Disjointness of two memory locations *)\n\nlet aloc_disjoint (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : GTot Type0 =\n if b1.region = b2.region && b1.addr = b2.addr\n then Some? b1.loc /\\ Some? b2.loc /\\ c.aloc_disjoint (Some?.v b1.loc) (Some?.v b2.loc)\n else True\n\nlet aloc_disjoint_sym (#al: aloc_t) (#c: cls al) (b1 b2: aloc c) : Lemma\n (aloc_disjoint b1 b2 <==> aloc_disjoint b2 b1)\n= Classical.forall_intro_2 (fun r a -> Classical.forall_intro_2 (fun b1 b2 -> c.aloc_disjoint_sym #r #a b1 b2))\n\nlet loc_aux_disjoint\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: GTot Type0\n= forall (b1 b2: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b2 l2) ==> aloc_disjoint b1 b2\n\nlet loc_aux_disjoint_union_l\n (#al: aloc_t) (#c: cls al)\n (ll1 lr1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint (GSet.union ll1 lr1) l2 <==> (loc_aux_disjoint ll1 l2 /\\ loc_aux_disjoint lr1 l2)))\n= ()\n\nlet loc_aux_disjoint_union_r\n (#al: aloc_t) (#c: cls al)\n (l1 ll2 lr2: GSet.set (aloc c))\n: Lemma\n (loc_aux_disjoint l1 (GSet.union ll2 lr2) <==> (loc_aux_disjoint l1 ll2 /\\ loc_aux_disjoint l1 lr2))\n= ()\n\nlet loc_aux_disjoint_sym\n (#al: aloc_t) (#c: cls al)\n (l1 l2: GSet.set (aloc c))\n: Lemma\n (ensures (loc_aux_disjoint l1 l2 <==> loc_aux_disjoint l2 l1))\n= Classical.forall_intro_2 (aloc_disjoint_sym #al #c)\n\nlet regions_of_loc_loc_union\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (regions_of_loc (loc_union s1 s2) == regions_of_loc s1 `Set.union` regions_of_loc s2)\n [SMTPat (regions_of_loc (loc_union s1 s2))]\n= assert (regions_of_loc (loc_union s1 s2) `Set.equal` (regions_of_loc s1 `Set.union` regions_of_loc s2))\n\nlet regions_of_loc_monotonic\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_includes s1 s2))\n (ensures (Set.subset (regions_of_loc s2) (regions_of_loc s1)))\n= ()\n\nlet loc_disjoint_region_liveness_tags (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty\n\nlet loc_disjoint_addrs (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n (forall (r: HS.rid) .\n GSet.subset (GSet.intersect (addrs_of_loc_weak l1 r) (addrs_of_loc l2 r)) GSet.empty /\\\n GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc_weak l2 r)) GSet.empty\n )\n\nlet loc_disjoint_aux (#al: aloc_t) (#c: cls al) (l1 l2: loc c) : GTot Type0 =\n loc_aux_disjoint (Ghost.reveal (Loc?.aux l1)) (Ghost.reveal (Loc?.aux l2))\n\nlet loc_disjoint'\n (#al: aloc_t) (#c: cls al)\n (l1 l2: loc c)\n: GTot Type0\n= loc_disjoint_region_liveness_tags l1 l2 /\\\n loc_disjoint_addrs l1 l2 /\\\n loc_disjoint_aux l1 l2\n\nlet loc_disjoint = loc_disjoint'\n\nlet loc_disjoint_sym #al #c l1 l2 =\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c)\n\nlet loc_disjoint_sym'\n (#al: aloc_t) (#c: cls al)\n (s1 s2: loc c)\n: Lemma\n (requires (loc_disjoint s1 s2))\n (ensures (loc_disjoint s2 s1))\n [SMTPat (loc_disjoint s1 s2)]\n= loc_disjoint_sym s1 s2\n\nlet loc_disjoint_none_r #al #c s = ()\n\nlet loc_disjoint_union_r #al #c s s1 s2 = ()\n\nlet aloc_disjoint_includes (#al: aloc_t) (#c: cls al) (b1 b2 b3 : aloc c) : Lemma\n (requires (aloc_disjoint b1 b2 /\\ aloc_includes b2 b3))\n (ensures (aloc_disjoint b1 b3))\n= if b1.region = b2.region && b1.addr = b2.addr\n then begin\n c.aloc_includes_refl (Some?.v b1.loc);\n c.aloc_disjoint_includes (Some?.v b1.loc) (Some?.v b2.loc) (Some?.v b1.loc) (Some?.v b3.loc)\n end\n else ()\n\nlet loc_aux_disjoint_loc_aux_includes\n (#al: aloc_t) (#c: cls al)\n (l1 l2 l3: GSet.set (aloc c))\n: Lemma\n (requires (loc_aux_disjoint l1 l2 /\\ loc_aux_includes l2 l3))\n (ensures (loc_aux_disjoint l1 l3))\n= // FIXME: WHY WHY WHY do I need this assert?\n assert (forall (b1 b3: aloc c) . (GSet.mem b1 l1 /\\ GSet.mem b3 l3) ==> (exists (b2: aloc c) . GSet.mem b2 l2 /\\ aloc_disjoint b1 b2 /\\ aloc_includes b2 b3));\n Classical.forall_intro_3 (fun b1 b2 b3 -> Classical.move_requires (aloc_disjoint_includes #al #c b1 b2) b3)\n\nlet loc_disjoint_includes #al #c p1 p2 p1' p2' =\n regions_of_loc_monotonic p1 p1';\n regions_of_loc_monotonic p2 p2';\n let l1 = Ghost.reveal (Loc?.aux p1) in\n let l2 = Ghost.reveal (Loc?.aux p2) in\n let l1' = Ghost.reveal (Loc?.aux p1') in\n let l2' = Ghost.reveal (Loc?.aux p2') in\n loc_aux_disjoint_loc_aux_includes l1 l2 l2';\n loc_aux_disjoint_sym l1 l2';\n loc_aux_disjoint_loc_aux_includes l2' l1 l1';\n loc_aux_disjoint_sym l2' l1'\n\nlet loc_disjoint_aloc_intro #al #c #r1 #a1 #r2 #a2 b1 b2 = ()\n\nlet loc_disjoint_aloc_elim #al #c #r1 #a1 #r2 #a2 b1 b2 =\n // FIXME: WHY WHY WHY this assert?\n assert (aloc_disjoint (ALoc #_ #c r1 a1 (Some b1)) (ALoc #_ #c r2 a2 (Some b2)))\n\n#push-options \"--z3rlimit 15\"\nlet loc_disjoint_addresses_intro #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness1 r1 n1))) (Ghost.reveal (Loc?.aux (loc_addresses #_ #c preserve_liveness2 r2 n2))))\n#pop-options\n\nlet loc_disjoint_addresses_elim #al #c preserve_liveness1 preserve_liveness2 r1 r2 n1 n2 = ()\n\nlet loc_disjoint_aloc_addresses_intro #al #c #r' #a' p preserve_liveness r n = ()\n\nlet loc_disjoint_aloc_addresses_elim #al #c #r' #a' p preserve_liveness r n = ()\n\nlet loc_disjoint_regions #al #c preserve_liveness1 preserve_liveness2 rs1 rs2 =\n // FIXME: WHY WHY WHY this assert?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness1 rs1))) (Ghost.reveal (Loc?.aux (loc_regions #_ #c preserve_liveness2 rs2))))\n\nlet loc_none_in_some_region #a (c: cls a) (r: HS.rid) : GTot (loc c) =\n Loc\n (Ghost.hide (Set.singleton r))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)\n\n(** Liveness-insensitive memory locations *)\n\nlet address_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))\n\nlet loc_includes_address_liveness_insensitive_locs_aloc #al #c #r #n a = ()\n\nlet loc_includes_address_liveness_insensitive_locs_addresses #al c r a = ()\n\nlet region_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.complement GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))\n\nlet loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs #al c = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_regions #al c r = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_addresses #al c preserve_liveness r a = ()\n\nlet loc_includes_region_liveness_insensitive_locs_loc_of_aloc #al c #r #a x = ()\n\n(** The modifies clause proper *)\n\nlet modifies_preserves_livenesses\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s r)))\n ) ==> (\n HS.contains h2 p\n ))\n\nlet modifies_preserves_livenesses_elim\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (#t: Type)\n (#pre: Preorder.preorder t)\n (p: HS.mreference t pre)\n: Lemma\n (requires (modifies_preserves_livenesses s h1 h2 /\\ HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))))\n (ensures (HS.contains h2 p))\n= ()\n\nlet modifies_preserves_livenesses_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p))\n ))\n: Lemma\n (modifies_preserves_livenesses s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (Loc?.non_live_addrs s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'\n\nlet modifies_preserves_mreferences\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (t: Type) (pre: Preorder.preorder t) (p: HS.mreference t pre) .\n let r = HS.frameOf p in (\n HS.contains h1 p /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s r)))\n ) ==> (\n HS.contains h2 p /\\\n HS.sel h2 p == HS.sel h1 p\n ))\n\nlet modifies_preserves_mreferences_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (t: Type) ->\n (pre: Preorder.preorder t) ->\n (p: HS.mreference t pre) ->\n Lemma\n (requires (\n HS.contains h1 p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))\n ))\n (ensures (HS.contains h2 p /\\ HS.sel h2 p == HS.sel h1 p))\n ))\n: Lemma\n (modifies_preserves_mreferences s h1 h2)\n= let f'\n (t : Type)\n (pre: Preorder.preorder t)\n (p : HS.mreference t pre)\n : Lemma\n (\n (HS.contains h1 p /\\ (Set.mem (HS.frameOf p) (regions_of_loc s) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc s (HS.frameOf p))))) ==>\n (h2 `HS.contains` p /\\ h2 `HS.sel` p == h1 `HS.sel` p))\n = Classical.move_requires (f t pre) p\n in\n Classical.forall_intro_3 f'\n\nlet modifies_preserves_alocs\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (a: nat) (b: al r a) .\n loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))\n ==>\n c.aloc_preserved b h1 h2\n )\n\nlet modifies_preserves_alocs_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (u: unit { modifies_preserves_mreferences s h1 h2 } )\n (f: (\n (r: HS.rid) ->\n (a: nat) ->\n (b: al r a) ->\n Lemma\n (requires (\n Set.mem r (regions_of_loc s) /\\\n (~ (GSet.mem a (addrs_of_loc_weak s r))) /\\\n (GSet.mem a (addrs_of_loc_aux s r) /\\ loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b))))\n ))\n (ensures (c.aloc_preserved b h1 h2))\n ))\n: Lemma\n (modifies_preserves_alocs s h1 h2)\n= let f'\n (r: HS.rid)\n (a: nat)\n (b: al r a)\n : Lemma\n (requires (loc_aux_disjoint (Ghost.reveal (Loc?.aux s)) (GSet.singleton (ALoc r a (Some b)))))\n (ensures (c.aloc_preserved b h1 h2))\n = if Set.mem r (regions_of_loc s) && (not (GSet.mem a (addrs_of_loc_weak s r)))\n then begin\n if GSet.mem a (addrs_of_loc_aux s r)\n then\n Classical.move_requires (f r a) b\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n end else if Set.mem r (regions_of_loc s)\n then begin\n assert (GSet.mem a (addrs_of_loc_weak s r));\n assert (GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux s)));\n assert (aloc_disjoint #_ #c (ALoc r a None) (ALoc r a (Some b)));\n assert False\n end\n else\n c.same_mreference_aloc_preserved b h1 h2 (fun a' pre' r' -> ())\n in\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (f' r a) b)\n\nlet modifies_preserves_regions\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= forall (r: HS.rid) . (HS.live_region h1 r /\\ ~ (Set.mem r (Ghost.reveal (Loc?.region_liveness_tags s)))) ==> HS.live_region h2 r\n\n\nlet modifies_preserves_not_unused_in\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= (forall (r: HS.rid) (n: nat) . (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n\nlet modifies_preserves_not_unused_in_intro\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (f: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ))\n (ensures (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n ))\n: Lemma\n (modifies_preserves_not_unused_in s h1 h2)\n= let f'\n (r: HS.rid)\n (n: nat)\n : Lemma\n ((\n HS.live_region h1 r /\\ HS.live_region h2 r /\\\n n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) /\\\n (Set.mem r (regions_of_loc s) ==> ~ (GSet.mem n (Loc?.non_live_addrs s r)))\n ) ==> (\n n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)\n ))\n = Classical.move_requires (f r) n\n in\n Classical.forall_intro_2 f'\n\nlet modifies'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n: GTot Type0\n= modifies_preserves_regions s h1 h2 /\\\n modifies_preserves_not_unused_in s h1 h2 /\\\n modifies_preserves_mreferences s h1 h2 /\\\n modifies_preserves_livenesses s h1 h2 /\\\n modifies_preserves_alocs s h1 h2\n\nlet modifies = modifies'\n\nval modifies_intro_strong\n (#al: aloc_t) (#c: cls al) (l: loc c) (h h' : HS.mem)\n (regions: (\n (r: HS.rid) ->\n Lemma\n (requires (HS.live_region h r))\n (ensures (HS.live_region h' r))\n ))\n (mrefs: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires ((loc_disjoint (loc_mreference b) l) /\\ HS.contains h b))\n (ensures (HS.contains h' b /\\ HS.sel h' b == HS.sel h b))\n ))\n (livenesses: (\n (t: Type0) ->\n (pre: Preorder.preorder t) ->\n (b: HS.mreference t pre) ->\n Lemma\n (requires (HS.contains h b))\n (ensures (HS.contains h' b))\n ))\n (addr_unused_in: (\n (r: HS.rid) ->\n (n: nat) ->\n Lemma\n (requires (\n (Set.mem r (regions_of_loc l) ==> ~ (GSet.mem n (Loc?.non_live_addrs l r))) /\\\n HS.live_region h r /\\\n HS.live_region h' r /\\ n `Heap.addr_unused_in` (HS.get_hmap h' `Map.sel` r)\n ))\n (ensures (n `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` r)))\n ))\n (alocs: (\n (r: HS.rid) ->\n (a: nat) ->\n (x: al r a) ->\n Lemma\n (requires (loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (modifies l h h')\n\nlet modifies_intro_strong #al #c l h h' regions mrefs lives unused_ins alocs =\n Classical.forall_intro (Classical.move_requires regions);\n assert (modifies_preserves_regions l h h');\n\n let aux (t:Type) (pre:Preorder.preorder t) (p:HS.mreference t pre)\n :Lemma (requires (HS.contains h p /\\\n (Set.mem (HS.frameOf p) (regions_of_loc l) ==> ~ (GSet.mem (HS.as_addr p) (addrs_of_loc l (HS.frameOf p))))))\n (ensures (HS.contains h' p /\\ HS.sel h' p == HS.sel h p))\n =\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l);\n // FIXME: WHY WHY WHY is this assert necessary?\n assert_spinoff (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n // FIXME: Now this one is too :)\n assert (loc_disjoint_addrs (loc_mreference p) l);\n assert ((loc_disjoint (loc_mreference p) l));\n mrefs t pre p\n in\n\n modifies_preserves_mreferences_intro l h h' aux;\n Classical.forall_intro_3 (fun t pre p -> Classical.move_requires (lives t pre) p);\n modifies_preserves_not_unused_in_intro l h h' (fun r n ->\n unused_ins r n\n );\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n alocs r a b\n )\n\nlet modifies_intro #al #c l h h' regions mrefs lives unused_ins alocs =\n modifies_intro_strong l h h'\n regions\n mrefs\n lives\n (fun r n -> unused_ins r n)\n alocs\n\nlet modifies_none_intro #al #c h h' regions mrefs unused_ins =\n modifies_intro_strong #_ #c loc_none h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> mrefs t pre b)\n (fun r n -> unused_ins r n)\n (fun r a x ->\n c.same_mreference_aloc_preserved x h h' (fun t pre b -> mrefs t pre b)\n )\n\nlet modifies_address_intro #al #c r n h h' regions mrefs unused_ins =\n Classical.forall_intro (Classical.move_requires regions);\n let l : loc c = loc_addresses #_ #c false r (Set.singleton n) in\n modifies_preserves_mreferences_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_livenesses_intro l h h'\n (fun t pre p -> mrefs t pre p)\n ;\n modifies_preserves_not_unused_in_intro l h h'\n (fun r n -> unused_ins r n)\n ;\n modifies_preserves_alocs_intro l h h' ()\n (fun r a b ->\n c.same_mreference_aloc_preserved b h h' (fun t pre p -> mrefs t pre p)\n )\n\nlet modifies_aloc_intro #al #c #r #n x h h' regions mrefs livenesses unused_ins alocs =\n modifies_intro_strong #_ #c (loc_of_aloc x) h h'\n (fun r -> regions r)\n (fun t pre b -> mrefs t pre b)\n (fun t pre b -> livenesses t pre b)\n (fun r n -> unused_ins r n)\n (fun r' n' z ->\n if r' = r && n' = n\n then begin\n loc_disjoint_aloc_elim #_ #c z x;\n alocs z\n end else\n c.same_mreference_aloc_preserved z h h' (fun t pre p ->\n mrefs t pre p\n )\n )\n\nlet modifies_live_region #al #c s h1 h2 r = ()\n\nlet modifies_mreference_elim #al #c #t #pre b p h h' = ()\n\nlet modifies_aloc_elim #al #c #r #a b p h h' = ()\n\nlet modifies_refl #al #c s h =\n Classical.forall_intro_3 (fun r a b -> c.aloc_preserved_refl #r #a b h)\n\nlet modifies_loc_includes #al #c s1 h h' s2 =\n assert (modifies_preserves_mreferences s1 h h');\n Classical.forall_intro_2 (loc_aux_disjoint_sym #al #c);\n Classical.forall_intro_3 (fun l1 l2 l3 -> Classical.move_requires (loc_aux_disjoint_loc_aux_includes #al #c l1 l2) l3);\n assert (modifies_preserves_alocs s1 h h')\n\nlet modifies_preserves_liveness #al #c s1 s2 h h' #t #pre r = ()\n\n#push-options \"--z3rlimit 20 --max_fuel 0 --max_ifuel 0\"\nlet modifies_preserves_liveness_strong #al #c s1 s2 h h' #t #pre r x =\n let rg = HS.frameOf r in\n let ad = HS.as_addr r in\n let la = loc_of_aloc #_ #c #rg #ad x in\n if Set.mem rg (regions_of_loc s2)\n then begin\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` Loc?.non_live_addrs (address_liveness_insensitive_locs c) rg);\n assert (Loc?.non_live_addrs s2 rg `GSet.subset` GSet.empty);\n assert (~ (GSet.mem ad (Loc?.non_live_addrs s2 rg)));\n if Set.mem rg (regions_of_loc s1)\n then begin\n if GSet.mem ad (Loc?.non_live_addrs s1 rg)\n then begin\n assert (loc_disjoint_aux s1 la);\n assert (GSet.subset (Loc?.non_live_addrs s1 rg) (Loc?.live_addrs s1 rg));\n assert (aloc_domain c (Loc?.regions s1) (Loc?.live_addrs s1) `GSet.subset` (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad None) (Ghost.reveal (Loc?.aux s1)));\n assert (GSet.mem (ALoc rg ad (Some x)) (Ghost.reveal (Loc?.aux la)));\n assert (aloc_disjoint (ALoc rg ad None) (ALoc #_ #c rg ad (Some x)));\n ()\n end else ()\n end else ()\n end else ()\n#pop-options\n\nlet modifies_preserves_region_liveness #al #c l1 l2 h h' r = ()\n\nlet modifies_preserves_region_liveness_reference #al #c l1 l2 h h' #t #pre r = ()\n\nlet modifies_preserves_region_liveness_aloc #al #c l1 l2 h h' #r #n x =\n if Set.mem r (Ghost.reveal (Loc?.region_liveness_tags l1))\n then begin\n assert (GSet.subset (GSet.complement GSet.empty) (Loc?.non_live_addrs l1 r));\n assert (GSet.subset (Loc?.non_live_addrs l1 r) (Loc?.live_addrs l1 r))\n end else ()\n\nlet modifies_trans'\n (#al: aloc_t) (#c: cls al)\n (s: loc c)\n (h1 h2: HS.mem)\n (h3: HS.mem)\n: Lemma\n (requires (modifies s h1 h2 /\\ modifies s h2 h3))\n (ensures (modifies s h1 h3))\n= Classical.forall_intro_3 (fun r a b -> Classical.move_requires (c.aloc_preserved_trans #r #a b h1 h2) h3)\n\nlet modifies_trans #al #c s12 h1 h2 s23 h3 =\n let u = loc_union s12 s23 in\n modifies_loc_includes u h1 h2 s12;\n modifies_loc_includes u h2 h3 s23;\n modifies_trans' u h1 h2 h3\n\nlet addr_unused_in_aloc_preserved\n (#al: aloc_t) (#c: cls al)\n (#r: HS.rid)\n (#a: nat)\n (b: al r a)\n (h1: HS.mem)\n (h2: HS.mem)\n : Lemma\n (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)))\n (ensures (c.aloc_preserved b h1 h2))\n= c.same_mreference_aloc_preserved b h1 h2 (fun a' pre r' -> assert False)\n\n#push-options \"--z3rlimit 10\"\nlet modifies_only_live_regions_weak\n (#al: aloc_t) (#c: cls al)\n (rs: Set.set HS.rid)\n (l: loc c)\n (h h' : HS.mem)\n: Lemma\n (requires (\n modifies (loc_union (loc_regions false rs) l) h h' /\\\n loc_disjoint (loc_regions false rs) l /\\\n (forall r . Set.mem r rs ==> (~ (HS.live_region h r)))\n ))\n (ensures (modifies l h h'))\n= assert (modifies_preserves_mreferences l h h'); // FIXME: WHY WHY WHY?\n Classical.forall_intro_3 (fun r a b -> Classical.move_requires (addr_unused_in_aloc_preserved #al #c #r #a b h) h')\n#pop-options\n\n(* Restrict a set of locations along a set of regions *)\n\nlet restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: GTot (loc c)\n= let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let regions' = (Ghost.hide (Set.intersect (Ghost.reveal regions) rs)) in\n Loc\n regions'\n (Ghost.hide (Set.intersect (Ghost.reveal region_liveness_tags) rs))\n (mk_non_live_addrs (fun (r: addrs_dom regions') -> (non_live_addrs r <: GSet.set nat)))\n (mk_live_addrs (fun (r: addrs_dom regions') -> (live_addrs r <: GSet.set nat)))\n (Ghost.hide (GSet.intersect (Ghost.reveal aux) (aloc_domain c (Ghost.hide rs) (fun r -> GSet.complement GSet.empty))))\n\nlet regions_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (regions_of_loc (restrict_to_regions l rs) == Set.intersect (regions_of_loc l) rs)\n [SMTPat (regions_of_loc (restrict_to_regions l rs))]\n= assert (Set.equal (regions_of_loc (restrict_to_regions l rs)) (Set.intersect (regions_of_loc l) rs))\n\nlet addrs_of_loc_weak_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc_weak (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))\n [SMTPat (addrs_of_loc_weak (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc_weak (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc_weak l r else GSet.empty))\n\nlet addrs_of_loc_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (restrict_to_regions l rs) r == (if Set.mem r rs then addrs_of_loc l r else GSet.empty))\n [SMTPat (addrs_of_loc (restrict_to_regions l rs) r)]\n= assert (GSet.equal (addrs_of_loc (restrict_to_regions l rs) r) (if Set.mem r rs then addrs_of_loc l r else GSet.empty))\n\nlet loc_includes_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes l (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)\n\nlet loc_includes_loc_union_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_equal (loc_union (restrict_to_regions l rs) (restrict_to_regions l (Set.complement rs))) l)\n= ()\n\nlet loc_includes_loc_regions_restrict_to_regions\n (#al: aloc_t) (#c: cls al)\n (l: loc c)\n (rs: Set.set HS.rid)\n: Lemma\n (loc_includes (loc_regions false rs) (restrict_to_regions l rs))\n= Classical.forall_intro (loc_aux_includes_refl #al #c)\n\nlet modifies_only_live_regions #al #c rs l h h' =\n let s = l in\n let c_rs = Set.complement rs in\n let s_rs = restrict_to_regions s rs in\n let s_c_rs = restrict_to_regions s c_rs in\n let lrs = loc_regions false rs in\n loc_includes_loc_regions_restrict_to_regions s rs;\n loc_includes_union_l lrs s_c_rs s_rs;\n loc_includes_refl s_c_rs;\n loc_includes_union_l lrs s_c_rs s_c_rs;\n loc_includes_union_r (loc_union lrs s_c_rs) s_rs s_c_rs;\n loc_includes_loc_union_restrict_to_regions s rs;\n loc_includes_trans (loc_union lrs s_c_rs) (loc_union s_rs s_c_rs) s;\n modifies_loc_includes (loc_union lrs s_c_rs) h h' (loc_union lrs s);\n loc_includes_loc_regions_restrict_to_regions s c_rs;\n loc_disjoint_regions #al #c false false rs c_rs;\n loc_includes_refl lrs;\n loc_disjoint_includes lrs (loc_regions false c_rs) lrs s_c_rs;\n modifies_only_live_regions_weak rs s_c_rs h h';\n loc_includes_restrict_to_regions s c_rs;\n modifies_loc_includes s h h' s_c_rs\n\nlet no_upd_fresh_region #al #c r l h0 h1 =\n modifies_only_live_regions (HS.mod_set (Set.singleton r)) l h0 h1\n\nlet fresh_frame_modifies #al c h0 h1 =\n modifies_intro_strong #_ #c loc_none h0 h1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x h0 h1 (fun _ _ _ -> ()))\n\nlet new_region_modifies #al c m0 r0 col\n= let (_, m1) = HS.new_eternal_region m0 r0 col in\n modifies_intro_strong #_ #c loc_none m0 m1\n (fun _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ _ -> ())\n (fun _ _ -> ())\n (fun r a x ->\n c.same_mreference_aloc_preserved #r #a x m0 m1 (fun _ _ _ -> ()))\n\nlet popped_modifies #al c h0 h1 =\n let l = loc_region_only #_ #c false (HS.get_tip h0) in\n modifies_preserves_mreferences_intro l h0 h1 (fun t pre p ->\n assert_norm (Loc?.region_liveness_tags (loc_mreference #_ #c p) == Ghost.hide Set.empty);\n assert (loc_disjoint_region_liveness_tags (loc_mreference p) l );\n // FIXME: WHY WHY WHY is this assert necessary?\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_mreference p))) (Ghost.reveal (Loc?.aux l)));\n ()\n );\n modifies_preserves_alocs_intro l h0 h1 () (fun r a b ->\n loc_aux_disjoint_sym (Ghost.reveal (Loc?.aux l)) (Ghost.reveal (Loc?.aux (loc_of_aloc b)));\n ()\n )\n\n\nlet modifies_fresh_frame_popped #al #c h0 h1 s h2 h3 =\n fresh_frame_modifies c h0 h1;\n let r = loc_region_only #al #c false (HS.get_tip h2) in\n let rs = HS.mod_set (Set.singleton (HS.get_tip h1)) in\n let s' = loc_union (loc_regions false rs) s in\n modifies_trans' s' h0 h1 h2;\n assert (modifies_preserves_mreferences r h2 h3);\n let f23 (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (r <> HS.get_tip h2))\n (ensures (c.aloc_preserved b h2 h3))\n = c.same_mreference_aloc_preserved #r #a b h2 h3 (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro r h2 h3 () (fun r a b ->\n f23 r a b\n );\n modifies_trans' s' h0 h2 h3;\n modifies_only_live_regions rs s h0 h3\n\nlet modifies_loc_regions_intro #al #c rs h1 h2 =\n let f (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem r rs)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n assert (modifies_preserves_mreferences (loc_regions #al #c true rs) h1 h2);\n modifies_preserves_alocs_intro (loc_regions #_ #c true rs) h1 h2 () (fun r a b ->\n f r a b\n )\n\n#push-options \"--z3rlimit 20\"\nlet modifies_loc_addresses_intro_weak\n (#al: aloc_t) (#c: cls al)\n (r: HS.rid)\n (s: Set.set nat)\n (l: loc c)\n (h1 h2: HS.mem)\n: Lemma\n (requires (\n HS.live_region h2 r /\\\n modifies (loc_union (loc_region_only false r) l) h1 h2 /\\\n HS.modifies_ref r s h1 h2 /\\\n loc_disjoint l (loc_region_only false r)\n ))\n (ensures (modifies (loc_union (loc_addresses true r s) l) h1 h2))\n= modifies_preserves_mreferences_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_livenesses_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' a' b' ->\n ()\n );\n modifies_preserves_not_unused_in_intro (loc_union (loc_addresses true r s) l) h1 h2 (fun r' n' ->\n ()\n );\n let f (a: nat) (b: al r a) : Lemma\n (requires (not (Set.mem a s)))\n (ensures (c.aloc_preserved b h1 h2))\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r_ -> ())\n in\n modifies_preserves_alocs_intro (loc_union (loc_addresses true r s) l) h1 h2 () (fun r' a b -> if r = r' then f a b else ()\n )\n\nlet modifies_loc_addresses_intro #al #c r s l h1 h2 =\n loc_includes_loc_regions_restrict_to_regions l (Set.singleton r);\n loc_includes_loc_union_restrict_to_regions l (Set.singleton r);\n assert (modifies (loc_union (loc_region_only false r) (loc_union (restrict_to_regions l (Set.singleton r)) (restrict_to_regions l (Set.complement (Set.singleton r))))) h1 h2);\n let l' = restrict_to_regions l (Set.complement (Set.singleton r)) in\n loc_includes_refl (loc_region_only #_ #c false r) ;\n loc_includes_loc_regions_restrict_to_regions l (Set.complement (Set.singleton r));\n loc_disjoint_regions #_ #c false false (Set.complement (Set.singleton r)) (Set.singleton r);\n loc_disjoint_includes (loc_regions #_ #c false (Set.complement (Set.singleton r))) (loc_region_only false r) l' (loc_region_only false r);\n modifies_loc_addresses_intro_weak r s l' h1 h2;\n loc_includes_restrict_to_regions l (Set.complement (Set.singleton r))\n#pop-options\n\nlet modifies_ralloc_post #al #c #a #rel i init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g\n\nlet modifies_salloc_post #al #c #a #rel init h x h' =\n let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h h')\n = c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g\n\nlet modifies_free #al #c #a #rel r m =\n let g (r': HS.rid) (a: nat) (b: al r' a) : Lemma\n (requires (r' <> HS.frameOf r \\/ a <> HS.as_addr r))\n (ensures (c.aloc_preserved b m (HS.free r m)))\n = c.same_mreference_aloc_preserved #r' #a b m (HS.free r m) (fun a' pre r' -> ())\n in\n modifies_preserves_alocs_intro (loc_freed_mreference #_ #c r) m (HS.free r m) () (fun r a b -> g r a b)\n\nlet modifies_none_modifies #al #c h1 h2\n= let g (r: HS.rid) (a: nat) (b: al r a) : Lemma\n (c.aloc_preserved b h1 h2)\n = c.same_mreference_aloc_preserved #r #a b h1 h2 (fun a' pre r' -> ())\n in\n Classical.forall_intro_3 g\n\nlet modifies_upd #al #c #t #pre r v h =\n let h' = HS.upd h r v in\n modifies_intro #_ #c (loc_mreference r) h h'\n (fun r -> ())\n (fun t pre b -> ())\n (fun t pre b -> ())\n (fun r n -> ())\n (fun r a b -> c.same_mreference_aloc_preserved #r #a b h h' (fun a' pre' r' -> ()))\n\n#push-options \"--z3rlimit 15\"\nlet addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (r: HS.rid)\n: Lemma\n (addrs_of_loc (loc_union l (loc_of_aloc al0)) r == addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)\n= assert (addrs_of_loc (loc_union l (loc_of_aloc al0)) r `GSet.equal` addrs_of_loc (loc_union l (loc_addresses true r0 (Set.singleton a0))) r)\n#pop-options\n\nlet addrs_of_loc_weak_loc_includes #al (#c: cls al) (l: loc c) (r0: HS.rid) (a0: nat) : Lemma\n (requires (a0 `GSet.mem` addrs_of_loc_weak l r0))\n (ensures (l `loc_includes` loc_addresses true r0 (Set.singleton a0)))\n= ()\n\nval modifies_strengthen'\n (#al: aloc_t) (#c: cls al) (l: loc c) (#r0: HS.rid) (#a0: nat) (al0: al r0 a0) (h h' : HS.mem)\n (alocs: (\n (f: ((t: Type) -> (pre: Preorder.preorder t) -> (m: HS.mreference t pre) -> Lemma\n (requires (HS.frameOf m == r0 /\\ HS.as_addr m == a0 /\\ HS.contains h m))\n (ensures (HS.contains h' m))\n )) ->\n (x: al r0 a0) ->\n Lemma\n (requires (c.aloc_disjoint x al0 /\\ loc_disjoint (loc_of_aloc x) l))\n (ensures (c.aloc_preserved x h h'))\n ))\n: Lemma\n (requires ((~ (a0 `GSet.mem` addrs_of_loc_weak l r0)) /\\ modifies (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h'))\n (ensures (modifies (loc_union l (loc_of_aloc al0)) h h'))\n\n#push-options \"--z3rlimit 15 --fuel 0 --ifuel 0\"\nlet modifies_strengthen' #al #c l #r0 #a0 al0 h h' alocs =\n Classical.forall_intro (addrs_of_loc_loc_union_loc_of_aloc_eq_loc_union_loc_addresses_singleton l al0);\n assert (modifies_preserves_regions (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_mreferences (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_not_unused_in (loc_union l (loc_of_aloc al0)) h h');\n assert (modifies_preserves_livenesses (loc_union l (loc_of_aloc al0)) h h');\n modifies_preserves_alocs_intro (loc_union l (loc_of_aloc al0)) h h' () (fun r a b ->\n if r = r0 && a = a0\n then begin\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux (loc_union l (loc_of_aloc al0)))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux l)) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_disjoint l (loc_of_aloc b));\n loc_disjoint_sym l (loc_of_aloc b);\n assert (loc_aux_disjoint #_ #c (Ghost.reveal (Loc?.aux (loc_of_aloc al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (loc_aux_disjoint #_ #c (GSet.singleton (ALoc r0 a0 (Some al0))) (GSet.singleton (ALoc r0 a0 (Some b))));\n assert (GSet.mem (ALoc r0 a0 (Some al0)) (GSet.singleton (ALoc #_ #c r0 a0 (Some al0))));\n assert (GSet.mem (ALoc r0 a0 (Some b)) (GSet.singleton (ALoc #_ #c r0 a0 (Some b))));\n assert (aloc_disjoint #_ #c (ALoc r0 a0 (Some al0)) (ALoc r0 a0 (Some b)));\n assert (c.aloc_disjoint al0 b);\n c.aloc_disjoint_sym al0 b;\n alocs (fun t pre m -> ()) b\n end\n else begin\n assert (loc_disjoint (loc_union l (loc_addresses true r0 (Set.singleton a0))) (loc_of_aloc b))\n by (let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 64;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=5'\";\n ())\n end\n );\n assert (modifies (loc_union l (loc_of_aloc al0)) h h')\n#pop-options\n\nlet modifies_strengthen #al #c l #r0 #a0 al0 h h' alocs =\n if a0 `GSet.mem` addrs_of_loc_weak l r0\n then begin\n addrs_of_loc_weak_loc_includes l r0 a0;\n loc_includes_refl l;\n loc_includes_union_r l l (loc_addresses true r0 (Set.singleton a0));\n loc_includes_union_l l (loc_of_aloc al0) l;\n loc_includes_trans (loc_union l (loc_of_aloc al0)) l (loc_union l (loc_addresses true r0 (Set.singleton a0)));\n modifies_loc_includes (loc_union l (loc_of_aloc al0)) h h' (loc_union l (loc_addresses true r0 (Set.singleton a0)))\n end\n else\n modifies_strengthen' l al0 h h' alocs\n\n\nlet does_not_contain_addr' (h: HS.mem) (ra: HS.rid * nat) : GTot Type0 =\n HS.live_region h (fst ra) ==> snd ra `Heap.addr_unused_in` (HS.get_hmap h `Map.sel` (fst ra))\n\nlet does_not_contain_addr = does_not_contain_addr'\n\nlet not_live_region_does_not_contain_addr h ra = ()\n\nlet unused_in_does_not_contain_addr h #a #rel r = ()\n\nlet addr_unused_in_does_not_contain_addr h ra = ()\n\nlet does_not_contain_addr_addr_unused_in h ra = ()\n\nlet free_does_not_contain_addr #a #rel r m x = ()\n\nlet does_not_contain_addr_elim #a #rel r m x = ()\n\nlet disjoint_addrs_of_loc_loc_disjoint\n (#al: aloc_t)\n (#c: cls al)\n (l1 l2: loc c)\n: Lemma\n (requires (\n Set.subset (Set.intersect (Ghost.reveal (Loc?.region_liveness_tags l1)) (Ghost.reveal (Loc?.region_liveness_tags l2))) Set.empty /\\\n (forall r . GSet.subset (GSet.intersect (addrs_of_loc l1 r) (addrs_of_loc l2 r)) GSet.empty)\n ))\n (ensures (loc_disjoint l1 l2))\n= // FIXME: WHY WHY WHY do I need this assert?\n let l1' = Ghost.reveal (Loc?.aux l1) in\n let l2' = Ghost.reveal (Loc?.aux l2) in\n assert (forall (b1 b2: aloc c) . (GSet.mem b1 l1' /\\ GSet.mem b2 l2') ==> aloc_disjoint b1 b2)\n\nlet loc_not_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (HS.live_region h r /\\ ~ (h `does_not_contain_addr` (r, a))))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs f)\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))\n\nlet loc_unused_in #al c h =\n let f (r: HS.rid) : GTot (GSet.set nat) =\n if not (HS.live_region h r)\n then\n GSet.complement GSet.empty\n else\n GSet.comprehend (fun a -> StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a)))\n in\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide (Set.complement (FStar.Map.domain (HS.get_hmap h))))\n (mk_non_live_addrs (fun x -> f x))\n (mk_live_addrs (fun x -> f x))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) f))\n\nlet loc_regions_unused_in #al c h rs = ()\n\n#push-options \"--z3rlimit 20\"\nlet loc_addresses_unused_in #al c r a h = ()\n#pop-options\n\nlet loc_addresses_not_unused_in #al c r a h = ()\n\n#push-options \"--z3rlimit 15\"\nlet loc_unused_in_not_unused_in_disjoint #al c h =\n assert (Ghost.reveal (Loc?.aux (loc_unused_in c h)) `loc_aux_disjoint` Ghost.reveal (Loc?.aux (loc_not_unused_in c h)));\n assert_spinoff (loc_disjoint #al #c (loc_unused_in #al c h)\n (loc_not_unused_in #al c h))\n#pop-options\n\n#push-options \"--z3cliopt 'smt.qi.eager_threshold=100'\"\nlet not_live_region_loc_not_unused_in_disjoint #al c h0 r\n= let l1 = loc_region_only false r in\n let l2 = loc_not_unused_in c h0 in\n assert (loc_disjoint_region_liveness_tags l1 l2);\n assert (loc_disjoint_addrs l1 l2);\n assert (loc_disjoint_aux l1 l2)\n\n#push-options \"--z3rlimit 16\"\nlet modifies_address_liveness_insensitive_unused_in #al c h h' =\n assert (forall r . HS.live_region h r ==> HS.live_region h' r) ;\n let ln' = loc_not_unused_in c h' in\n let ln = loc_not_unused_in c h in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs ln r `GSet.subset` Loc?.non_live_addrs ln' r);\n assert (ln' `loc_includes` ln);\n let lu = loc_unused_in c h in\n let lu' = loc_unused_in c h' in\n assert (forall (r: HS.rid) . Loc?.non_live_addrs lu' r `GSet.subset` Loc?.non_live_addrs lu r);\n assert (forall (r: HS.rid) . Loc?.live_addrs lu' r `GSet.subset` Loc?.live_addrs lu r);\n assert (lu `loc_includes` lu')\n#pop-options\n#pop-options\n\n#push-options \"--max_fuel 0 --max_ifuel 0 --z3rlimit 16\"\nlet modifies_only_not_unused_in #al #c l h h' =\n assert (modifies_preserves_regions l h h');\n assert (modifies_preserves_not_unused_in l h h');\n assert (modifies_preserves_mreferences l h h');\n assert (modifies_preserves_livenesses l h h');\n modifies_preserves_alocs_intro l h h' () (fun r a b ->\n if StrongExcludedMiddle.strong_excluded_middle (h `does_not_contain_addr` (r, a))\n then c.same_mreference_aloc_preserved b h h' (fun a' pre' r' -> ())\n else ()\n )\n#pop-options\n\nlet mreference_live_loc_not_unused_in #al c #t #pre h b =\n Classical.move_requires (does_not_contain_addr_addr_unused_in h) (HS.frameOf b, HS.as_addr b);\n assert (~ (h `does_not_contain_addr` (HS.frameOf b, HS.as_addr b)));\n loc_addresses_not_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_trans (loc_not_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()\n\n#push-options \"--z3cliopt 'smt.qi.eager_threshold=100'\"\nlet mreference_unused_in_loc_unused_in #al c #t #pre h b =\n Classical.move_requires (addr_unused_in_does_not_contain_addr h) (HS.frameOf b, HS.as_addr b);\n loc_addresses_unused_in c (HS.frameOf b) (Set.singleton (HS.as_addr b)) h;\n loc_includes_addresses_addresses c false true (HS.frameOf b) (Set.singleton (HS.as_addr b)) (Set.singleton (HS.as_addr b));\n loc_includes_trans (loc_unused_in c h) (loc_freed_mreference b) (loc_mreference b);\n ()\n#pop-options\n\n(* * Compositionality *)\n\nnoeq\ntype cls_union_aloc\n (al: (bool -> HS.rid -> nat -> Tot (Type u#x)))\n (r: HS.rid) (n: nat) : Type u#x\n= | ALOC_FALSE of (al false) r n\n | ALOC_TRUE of (al true) r n\n\nlet bool_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot bool =\n match l with\n | ALOC_FALSE _ -> false\n | ALOC_TRUE _ -> true\n\nlet aloc_of_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#r: HS.rid) (#n: nat)\n (l: cls_union_aloc al r n)\n: Tot ((al (bool_of_cls_union_aloc l)) r n)\n= match l with\n | ALOC_FALSE x -> x\n | ALOC_TRUE x -> x\n\nlet make_cls_union_aloc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (b: bool)\n (#r: HS.rid)\n (#n: nat)\n (l: (al b) r n)\n: Tot (cls_union_aloc al r n)\n= if b\n then ALOC_TRUE l\n else ALOC_FALSE l\n\nlet cls_union_aloc_includes\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_includes\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)\n\nlet cls_union_aloc_disjoint\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (larger smaller: cls_union_aloc al r a)\n: GTot Type0 =\n bool_of_cls_union_aloc larger == bool_of_cls_union_aloc smaller /\\\n (c (bool_of_cls_union_aloc larger)).aloc_disjoint\n (aloc_of_cls_union_aloc larger)\n (aloc_of_cls_union_aloc smaller)\n\nlet cls_union_aloc_preserved\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (#r: HS.rid)\n (#a: nat)\n (x: cls_union_aloc al r a)\n (h h' : HS.mem)\n: GTot Type0\n= (c (bool_of_cls_union_aloc x)).aloc_preserved\n (aloc_of_cls_union_aloc x)\n h\n h'\n\nlet aloc_union = cls_union_aloc\n\nlet cls_union #al c = Cls\n #(cls_union_aloc al)\n (cls_union_aloc_includes c)\n (* aloc_includes_refl *)\n (fun #r #a x ->\n (c (bool_of_cls_union_aloc x)).aloc_includes_refl (aloc_of_cls_union_aloc x))\n (* aloc_includes_trans *)\n (fun #r #a x1 x2 x3 ->\n (c (bool_of_cls_union_aloc x1)).aloc_includes_trans\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n (aloc_of_cls_union_aloc x3)\n )\n (cls_union_aloc_disjoint c)\n (* aloc_disjoint_sym *)\n (fun #r #a x1 x2 ->\n if bool_of_cls_union_aloc x1 = bool_of_cls_union_aloc x2\n then\n (c (bool_of_cls_union_aloc x1)).aloc_disjoint_sym\n (aloc_of_cls_union_aloc x1)\n (aloc_of_cls_union_aloc x2)\n else ()\n )\n (* aloc_disjoint_includes *)\n (fun #r #a larger1 larger2 smaller1 smaller2 ->\n (c (bool_of_cls_union_aloc larger1)).aloc_disjoint_includes\n (aloc_of_cls_union_aloc larger1)\n (aloc_of_cls_union_aloc larger2)\n (aloc_of_cls_union_aloc smaller1)\n (aloc_of_cls_union_aloc smaller2)\n )\n (cls_union_aloc_preserved c)\n (* aloc_preserved_refl *)\n (fun #r #a x h ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_refl\n (aloc_of_cls_union_aloc x)\n h\n )\n (* aloc_preserved_trans *)\n (fun #r #a x h1 h2 h3 ->\n (c (bool_of_cls_union_aloc x)).aloc_preserved_trans\n (aloc_of_cls_union_aloc x)\n h1\n h2\n h3\n )\n (* same_mreference_aloc_preserved *)\n (fun #r #a b h1 h2 f ->\n (c (bool_of_cls_union_aloc b)).same_mreference_aloc_preserved\n (aloc_of_cls_union_aloc b)\n h1\n h2\n f\n )\n\nlet union_aux_of_aux_left_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n (x: aloc (cls_union c))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n b = bool_of_cls_union_aloc #al #region #addr loc &&\n GSet.mem (ALoc region addr (Some (aloc_of_cls_union_aloc #al #region #addr loc))) s\n\nlet union_aux_of_aux_left\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (c b)))\n: Tot (GSet.set (aloc (cls_union c)))\n= GSet.comprehend (union_aux_of_aux_left_pred c b s)\n\nlet union_loc_of_loc #al c b l =\n let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let aux' : GSet.set (aloc #(cls_union_aloc al) (cls_union c)) =\n union_aux_of_aux_left c b (Ghost.reveal aux)\n `GSet.union`\n (aloc_domain (cls_union c) regions live_addrs)\n in\n Loc\n #(cls_union_aloc al)\n #(cls_union c)\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide aux')\n\nlet union_aux_of_aux_left_inv_pred\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n (x: aloc (c b))\n: GTot bool\n= let ALoc region addr loc = x in\n match loc with\n | None -> GSet.mem (ALoc region addr None) s\n | Some loc ->\n GSet.mem (ALoc region addr (Some (make_cls_union_aloc b loc))) s\n\nlet union_aux_of_aux_left_inv\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (#c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (s: GSet.set (aloc (cls_union c)))\n: Tot (GSet.set (aloc (c b)))\n= GSet.comprehend (union_aux_of_aux_left_inv_pred b s)\n\nlet mem_union_aux_of_aux_left_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (c b))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x aux <==> GSet.mem (ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc)))) (union_aux_of_aux_left c b aux))\n [SMTPat (GSet.mem x aux)]\n= ()\n\nlet mem_union_aux_of_aux_left_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (x: aloc (cls_union c))\n (aux: GSet.set (aloc (c b)))\n: Lemma\n (GSet.mem x (union_aux_of_aux_left c b aux) <==> (if None? x.loc then GSet.mem (ALoc x.region x.addr None) aux else (bool_of_cls_union_aloc (Some?.v x.loc) == b /\\ GSet.mem (ALoc x.region x.addr (Some (aloc_of_cls_union_aloc (Some?.v x.loc)))) aux)))\n [SMTPat (GSet.mem x (union_aux_of_aux_left #al c b aux))]\n= ()\n\nlet addrs_of_loc_union_loc_of_loc\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (r: HS.rid)\n: Lemma\n (addrs_of_loc (union_loc_of_loc c b l) r `GSet.equal` addrs_of_loc l r)\n [SMTPat (addrs_of_loc (union_loc_of_loc #al c b l) r)]\n= ()\n\nlet union_loc_of_loc_none #al c b =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_none #_ #(c b))) (loc_none #_ #(cls_union c)))\n\n#push-options \"--z3rlimit 15\"\nlet union_loc_of_loc_union #al c b l1 l2 =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_union #_ #(c b) l1 l2)) (loc_union #_ #(cls_union c) (union_loc_of_loc c b l1) (union_loc_of_loc c b l2)))\n#pop-options\n\nlet union_loc_of_loc_addresses #al c b preserve_liveness r n =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_addresses #_ #(c b) preserve_liveness r n)) (loc_addresses #_ #(cls_union c) preserve_liveness r n))\n\nlet union_loc_of_loc_regions #al c b preserve_liveness r =\n assert (loc_equal #_ #(cls_union c) (union_loc_of_loc c b (loc_regions #_ #(c b) preserve_liveness r)) (loc_regions #_ #(cls_union c) preserve_liveness r))\n\n#push-options \"--z3rlimit 15\"\nlet union_loc_of_loc_includes_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (larger `loc_includes` smaller))\n (ensures (union_loc_of_loc c b larger `loc_includes` union_loc_of_loc c b smaller))\n= ();\n let auxl = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux larger)) in\n let auxs = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux smaller)) in\n assert (forall r a . GSet.mem (ALoc r a None) auxs ==> (\n GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux smaller)) /\\\n GSet.mem (ALoc r a None) (Ghost.reveal (Loc?.aux larger)) /\\\n GSet.mem (ALoc r a None) auxl\n ));\n assert (auxl `loc_aux_includes` auxs);\n let doml = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n assert (doml `loc_aux_includes` doms)\n#pop-options\n\n#push-options \"--fuel 0 --ifuel 0 --z3rlimit 50 --z3cliopt 'smt.qi.eager_threshold=1'\"\nlet union_loc_of_loc_includes_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (union_loc_of_loc c b larger `loc_includes` union_loc_of_loc c b smaller))\n (ensures (larger `loc_includes` smaller))\n= let auxl = Ghost.reveal (Loc?.aux larger) in\n let auxl' = union_aux_of_aux_left c b auxl in\n let auxs = Ghost.reveal (Loc?.aux smaller) in\n let auxs' = union_aux_of_aux_left c b auxs in\n let doml' = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms' = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n let doml = aloc_domain (c b) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (c b) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n let g\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n (y: aloc (c b))\n : GTot Type0\n = GSet.mem y (GSet.union auxl doml) /\\ y `aloc_includes` x\n in\n let g' (r: HS.rid) (a: nat) (x: aloc (c b)) : GTot Type0 =\n exists (y: aloc (c b)) . g r a x y\n in\n let f\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n : Lemma\n (requires (GSet.mem x auxs /\\ (~ (GSet.mem x.addr (addrs_of_loc_weak smaller x.region)))))\n (ensures (g' r a x))\n = let x' : aloc (cls_union c) = ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc))) in\n Classical.exists_elim\n (g' r a x)\n #(aloc (cls_union c))\n #(fun y' -> GSet.mem y' (GSet.union auxl' doml') /\\ y' `aloc_includes` x')\n ()\n (fun (y': aloc (cls_union c) { GSet.mem y' (GSet.union auxl' doml') /\\ y' `aloc_includes` x' } ) ->\n let y : aloc (c b) = ALoc y'.region y'.addr (if None? y'.loc then None else Some (aloc_of_cls_union_aloc (Some?.v y'.loc))) in\n assert (g r a x y)\n )\n in\n let f'\n (r: HS.rid)\n (a: nat)\n (x: aloc (c b))\n : Lemma\n ((GSet.mem x auxs /\\ (~ (GSet.mem x.addr (addrs_of_loc_weak smaller x.region)))) ==> g' r a x)\n = Classical.move_requires (f r a) x\n in\n Classical.forall_intro_3 f';\n assert (forall (r: HS.rid) (a: nat) (x: aloc (c b)) .\n (GSet.mem x auxs /\\ GSet.mem x.addr (addrs_of_loc_weak smaller x.region)) ==>\n GSet.mem x (GSet.union auxl doml)\n ) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n assert (larger `loc_includes'` smaller) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 75;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n ()\n#pop-options\n\nlet union_loc_of_loc_includes #al c b s1 s2 =\n Classical.move_requires (union_loc_of_loc_includes_elim c b s1) s2;\n Classical.move_requires (union_loc_of_loc_includes_intro c b s1) s2\n\n#push-options \"--fuel 0 --ifuel 0\"\nlet union_loc_of_loc_disjoint_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (larger `loc_disjoint` smaller))\n (ensures (union_loc_of_loc c b larger `loc_disjoint` union_loc_of_loc c b smaller))\n= let auxl = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux larger)) in\n let auxs = union_aux_of_aux_left c b (Ghost.reveal (Loc?.aux smaller)) in\n let g\n (xl xs: aloc (cls_union c))\n : Lemma\n (requires (GSet.mem xl auxl /\\ GSet.mem xs auxs))\n (ensures (GSet.mem xl auxl /\\ GSet.mem xs auxs /\\ aloc_disjoint xl xs))\n =\n let xl' : aloc (c b) = ALoc xl.region xl.addr (if None? xl.loc then None else Some (aloc_of_cls_union_aloc (Some?.v xl.loc))) in\n let xs' : aloc (c b) = ALoc xs.region xs.addr (if None? xs.loc then None else Some (aloc_of_cls_union_aloc (Some?.v xs.loc))) in\n assert (GSet.mem xl' (Ghost.reveal (Loc?.aux larger)));\n assert (GSet.mem xs' (Ghost.reveal (Loc?.aux smaller)));\n assert (aloc_disjoint xl' xs');\n assert (aloc_disjoint xl xs)\n in\n Classical.forall_intro_2 (fun xl -> Classical.move_requires (g xl));\n assert (forall xl xs . (GSet.mem xl auxl /\\ GSet.mem xs auxs) ==> aloc_disjoint xl xs);\n assert (auxl `loc_aux_disjoint` auxs);\n let larger' = union_loc_of_loc c b larger in\n let smaller' = union_loc_of_loc c b smaller in\n let doml = aloc_domain (cls_union c) (Loc?.regions larger) (Loc?.live_addrs larger) in\n let doms = aloc_domain (cls_union c) (Loc?.regions smaller) (Loc?.live_addrs smaller) in\n assert (forall (xl xs: aloc (cls_union c)) .\n (GSet.mem xl doml /\\ GSet.mem xs auxs) ==> (\n xl.addr `GSet.mem` addrs_of_loc_weak larger xl.region /\\\n xs.addr `GSet.mem` addrs_of_loc smaller xs.region /\\\n aloc_disjoint xl xs\n )) by (\n let open FStar.Stubs.Tactics.V2.Builtins in\n let open FStar.Tactics.SMT in\n set_rlimit 64;\n set_options \"--z3cliopt 'smt.qi.eager_threshold=1'\";\n ()\n );\n assert (doml ` loc_aux_disjoint` auxs);\n assert (forall (xl xs: aloc (cls_union c)) .\n (GSet.mem xl auxl /\\ GSet.mem xs doms) ==> (\n xl.addr `GSet.mem` addrs_of_loc larger xl.region /\\\n xs.addr `GSet.mem` addrs_of_loc_weak smaller xs.region /\\\n aloc_disjoint xl xs\n )) by (\n let open FStar.Tactics.SMT in\n set_rlimit 15;\n ()\n );\n assert (auxl ` loc_aux_disjoint` doms);\n assert (loc_disjoint_aux larger' smaller');\n ()\n#pop-options\n\n#push-options \"--z3rlimit 32\"\nlet union_loc_of_loc_disjoint_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (larger smaller: loc (c b))\n: Lemma\n (requires (union_loc_of_loc c b larger `loc_disjoint` union_loc_of_loc c b smaller))\n (ensures (larger `loc_disjoint` smaller))\n= let auxl = Ghost.reveal (Loc?.aux larger) in\n let auxl' = union_aux_of_aux_left c b auxl in\n let auxs = Ghost.reveal (Loc?.aux smaller) in\n let auxs' = union_aux_of_aux_left c b auxs in\n assert (forall (x y: aloc (c b)) . (GSet.mem x auxl /\\ GSet.mem y auxs) ==> (\n let x' = ALoc x.region x.addr (if None? x.loc then None else Some (make_cls_union_aloc b (Some?.v x.loc))) in\n let y' = ALoc y.region y.addr (if None? y.loc then None else Some (make_cls_union_aloc b (Some?.v y.loc))) in\n GSet.mem x' auxl' /\\ GSet.mem y' auxs' /\\ (aloc_disjoint x' y' ==> aloc_disjoint x y)));\n assert (auxl `loc_aux_disjoint` auxs)\n#pop-options\n\nlet union_loc_of_loc_disjoint #al c b s1 s2 =\n Classical.move_requires (union_loc_of_loc_disjoint_elim c b s1) s2;\n Classical.move_requires (union_loc_of_loc_disjoint_intro c b s1) s2\n\n#push-options \"--z3rlimit 32\"\nlet modifies_union_loc_of_loc_elim\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (h1 h2: HS.mem)\n: Lemma\n (requires (modifies #_ #(cls_union c) (union_loc_of_loc c b l) h1 h2))\n (ensures (modifies #_ #(c b) l h1 h2))\n= assert (modifies_preserves_regions l h1 h2);\n assert (modifies_preserves_mreferences l h1 h2);\n modifies_preserves_alocs_intro #_ #(c b) l h1 h2 () (fun r' a' b' ->\n let g\n (x: aloc (cls_union c))\n : Lemma\n (requires (\n GSet.mem a' (addrs_of_loc_aux #_ #(cls_union c) (union_loc_of_loc c b l) r') /\\\n GSet.mem x (Ghost.reveal (Loc?.aux #_ #(cls_union c) (union_loc_of_loc c b l)))\n ))\n (ensures (\n aloc_disjoint #_ #(cls_union c) x (ALoc #_ #(cls_union c) r' a' (Some (make_cls_union_aloc b b')))))\n = if r' = x.region && a' = x.addr\n then begin\n let x' : aloc (c b) = ALoc #_ #(c b) r' a' (if None? x.loc then None else Some (aloc_of_cls_union_aloc (Some?.v x.loc))) in\n assert (aloc_disjoint #(al b) #(c b) x' (ALoc r' a' (Some b')))\n end else\n ()\n in\n Classical.forall_intro (Classical.move_requires g);\n assert ((cls_union c).aloc_preserved (make_cls_union_aloc b b') h1 h2)\n )\n#pop-options\n\n#push-options \"--z3rlimit 32\"\nlet modifies_union_loc_of_loc_intro\n (#al: (bool -> HS.rid -> nat -> Tot Type))\n (c: ((b: bool) -> Tot (cls (al b))))\n (b: bool)\n (l: loc (c b))\n (h1 h2: HS.mem)\n: Lemma\n (requires (modifies #_ #(c b) l h1 h2))\n (ensures (modifies #_ #(cls_union c) (union_loc_of_loc c b l) h1 h2))\n= let l' = union_loc_of_loc c b l in\n assert (modifies_preserves_regions l' h1 h2);\n assert (modifies_preserves_mreferences l' h1 h2);\n assert (modifies_preserves_livenesses l' h1 h2);\n assert (modifies_preserves_not_unused_in l' h1 h2);\n modifies_preserves_alocs_intro #_ #(cls_union c) l' h1 h2 () (fun r' a' b' ->\n let b_ = bool_of_cls_union_aloc b' in\n let a_ = aloc_of_cls_union_aloc b' in\n let ll' : aloc (cls_union c) = ALoc r' a' (Some b') in\n let ll : aloc (c b_) = ALoc r' a' (Some a_) in\n assert (exists (x: aloc (c b)) . GSet.mem x (Ghost.reveal (Loc?.aux l)) /\\\n (\n let xr = x.region in\n let xa = x.addr in\n let xl : option (al b xr xa) = x.loc in\n xr == r' /\\\n xa == a' /\\ (\n let xl' : option (aloc_union al r' a') = if None? xl then None else Some (make_cls_union_aloc #al b (Some?.v xl)) in\n let x' : aloc (cls_union c) = ALoc r' a' xl' in\n GSet.mem x' (Ghost.reveal (Loc?.aux l')) /\\\n aloc_disjoint #_ #(cls_union c) x' ll'\n )));\n assert (b_ == b);\n let f (x: aloc (c b)) : Lemma\n (requires (GSet.mem x (Ghost.reveal (Loc?.aux l))))\n (ensures (aloc_disjoint #_ #(c b) x ll))\n = let xr = x.region in\n let xa = x.addr in\n let xl : option (al b xr xa) = x.loc in\n let xl' : option (aloc_union al xr xa) = if None? xl then None else Some (make_cls_union_aloc #al b (Some?.v xl)) in\n let x' : aloc (cls_union c) = ALoc xr xa xl' in\n assert (GSet.mem x' (Ghost.reveal (Loc?.aux l')));\n assert (aloc_disjoint #_ #(cls_union c) x' ll');\n assert (aloc_disjoint #_ #(c b) x ll)\n in\n Classical.forall_intro (Classical.move_requires f);\n assert (loc_aux_disjoint (Ghost.reveal (Loc?.aux l)) (GSet.singleton ll))\n )\n#pop-options\n\nlet modifies_union_loc_of_loc #al c b l h1 h2 =\n Classical.move_requires (modifies_union_loc_of_loc_elim c b l h1) h2;\n Classical.move_requires (modifies_union_loc_of_loc_intro c b l h1) h2\n\nlet loc_of_union_loc #al #c b l\n= let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let aux' = union_aux_of_aux_left_inv b (Ghost.reveal aux) in\n Loc\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide aux')\n\nlet loc_of_union_loc_union_loc_of_loc #al c b s\n= assert (loc_of_union_loc b (union_loc_of_loc c b s) `loc_equal` s)\n\nlet loc_of_union_loc_none #al c b\n= assert (loc_of_union_loc #_ #c b loc_none `loc_equal` loc_none)\n\nlet loc_of_union_loc_union #al c b l1 l2\n= assert (loc_of_union_loc b (l1 `loc_union` l2) `loc_equal` (loc_of_union_loc b l1 `loc_union` loc_of_union_loc b l2))\n\nlet loc_of_union_loc_addresses #al c b preserve_liveness r n =\n assert (loc_of_union_loc #_ #c b (loc_addresses preserve_liveness r n) `loc_equal` loc_addresses preserve_liveness r n)\n\nlet loc_of_union_loc_regions #al c b preserve_liveness r =\n assert (loc_of_union_loc #_ #c b (loc_regions preserve_liveness r) `loc_equal` loc_regions preserve_liveness r)\n\nmodule U = FStar.Universe\n" }, { "file_name": "L0Crypto.fsti", "name": "L0Crypto.derive_AliasKey_spec", "opens_and_abbrevs": [ { "open": "L0Types" }, { "open": "HACL" }, { "abbrev": "U32", "full_module": "FStar.UInt32" }, { "abbrev": "U8", "full_module": "FStar.UInt8" }, { "abbrev": "US", "full_module": "FStar.SizeT" }, { "abbrev": "A", "full_module": "Pulse.Lib.Array" }, { "abbrev": "R", "full_module": "Pulse.Lib.Reference" }, { "open": "Pulse.Lib.BoundedIntegers" }, { "open": "Pulse.Lib.Pervasives" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val derive_AliasKey_spec\n (alg: alg_t)\n (dig_len: hkdf_ikm_len)\n (cdi fwid: Seq.seq U8.t)\n (l0_label_AliasKey_len: hkdf_lbl_len)\n (l0_label_AliasKey: Seq.seq U8.t)\n : GTot (Seq.seq U8.t & Seq.seq U8.t)", "source_definition": "let derive_AliasKey_spec\n (alg:alg_t)\n (dig_len:hkdf_ikm_len)\n (cdi: Seq.seq U8.t) (* should be length 32 *)\n (fwid: Seq.seq U8.t) (* should be length 32 *)\n (l0_label_AliasKey_len: hkdf_lbl_len)\n (l0_label_AliasKey: Seq.seq U8.t)\n: GTot (Seq.seq U8.t & Seq.seq U8.t)\n= let cdigest = spec_hash alg cdi in\n let adigest = spec_hmac alg cdigest fwid in\n derive_key_pair_spec\n (* ikm *) dig_len adigest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey", "source_range": { "start_line": 110, "start_col": 0, "end_line": 122, "end_col": 53 }, "interleaved": false, "definition": "fun alg dig_len cdi fwid l0_label_AliasKey_len l0_label_AliasKey ->\n (let cdigest = HACL.spec_hash alg cdi in\n let adigest = HACL.spec_hmac alg cdigest fwid in\n L0Crypto.derive_key_pair_spec dig_len adigest l0_label_AliasKey_len l0_label_AliasKey)\n <:\n Prims.GTot (FStar.Seq.Base.seq FStar.UInt8.t * FStar.Seq.Base.seq FStar.UInt8.t)", "effect": "Prims.GTot", "effect_flags": [ "sometrivial" ], "mutual_with": [], "premises": [ "HACL.alg_t", "HACL.hkdf_ikm_len", "FStar.Seq.Base.seq", "FStar.UInt8.t", "HACL.hkdf_lbl_len", "L0Crypto.derive_key_pair_spec", "Prims.b2t", "Prims.op_Equality", "Prims.nat", "FStar.Seq.Base.length", "FStar.SizeT.v", "HACL.digest_len", "HACL.spec_hmac", "HACL.spec_hash", "FStar.Pervasives.Native.tuple2" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "\n alg: HACL.alg_t ->\n dig_len: HACL.hkdf_ikm_len ->\n cdi: FStar.Seq.Base.seq FStar.UInt8.t ->\n fwid: FStar.Seq.Base.seq FStar.UInt8.t ->\n l0_label_AliasKey_len: HACL.hkdf_lbl_len ->\n l0_label_AliasKey: FStar.Seq.Base.seq FStar.UInt8.t\n -> Prims.GTot (FStar.Seq.Base.seq FStar.UInt8.t * FStar.Seq.Base.seq FStar.UInt8.t)", "prompt": "let derive_AliasKey_spec\n (alg: alg_t)\n (dig_len: hkdf_ikm_len)\n (cdi fwid: Seq.seq U8.t)\n (l0_label_AliasKey_len: hkdf_lbl_len)\n (l0_label_AliasKey: Seq.seq U8.t)\n : GTot (Seq.seq U8.t & Seq.seq U8.t) =\n ", "expected_response": "let cdigest = spec_hash alg cdi in\nlet adigest = spec_hmac alg cdigest fwid in\nderive_key_pair_spec dig_len adigest l0_label_AliasKey_len l0_label_AliasKey", "source": { "project_name": "steel", "file_name": "share/steel/examples/pulse/dice/l0/L0Crypto.fsti", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "L0Crypto.fsti", "checked_file": "dataset/L0Crypto.fsti.checked", "interface_file": false, "dependencies": [ "dataset/Pulse.Lib.Reference.fsti.checked", "dataset/Pulse.Lib.Pervasives.fst.checked", "dataset/Pulse.Lib.BoundedIntegers.fst.checked", "dataset/Pulse.Lib.Array.fsti.checked", "dataset/prims.fst.checked", "dataset/L0Types.fsti.checked", "dataset/HACL.fst.checked", "dataset/FStar.UInt8.fsti.checked", "dataset/FStar.UInt32.fsti.checked", "dataset/FStar.SizeT.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "val deviceid_len_is_valid (len:US.t)\n : valid_hkdf_lbl_len len", "val aliaskey_len_is_valid (len:US.t)\n : valid_hkdf_lbl_len len", "val derive_key_pair_spec\n (ikm_len: hkdf_ikm_len)\n (ikm: Seq.seq U8.t)\n (lbl_len: hkdf_lbl_len)\n (lbl: Seq.seq U8.t)\n : GTot (Seq.seq U8.t & Seq.seq U8.t)", "val derive_key_pair\n (pub : A.larray U8.t (US.v v32us))\n (priv: A.larray U8.t (US.v v32us))\n (ikm_len: hkdf_ikm_len) \n (ikm: A.array U8.t)\n (lbl_len: hkdf_lbl_len) \n (lbl: A.array U8.t)\n (#ikm_perm #lbl_perm:perm)\n (#_pub_seq #_priv_seq #ikm_seq #lbl_seq:erased (Seq.seq U8.t))\n : stt unit\n (requires (\n A.pts_to pub _pub_seq ** \n A.pts_to priv _priv_seq ** \n A.pts_to ikm #ikm_perm ikm_seq ** \n A.pts_to lbl #lbl_perm lbl_seq\n ))\n (ensures (fun _ ->\n A.pts_to ikm #ikm_perm ikm_seq ** \n A.pts_to lbl #lbl_perm lbl_seq **\n (exists* (pub_seq\n priv_seq:Seq.seq U8.t).\n A.pts_to pub pub_seq ** \n A.pts_to priv priv_seq **\n pure ((pub_seq, priv_seq) == derive_key_pair_spec ikm_len ikm_seq lbl_len lbl_seq)\n )))", "let derive_DeviceID_spec\n (alg:alg_t)\n (dig_len:hkdf_ikm_len)\n (cdi: Seq.seq U8.t) (* should be length 32 *)\n (l0_label_DeviceID_len: hkdf_lbl_len)\n (l0_label_DeviceID: Seq.seq U8.t)\n: GTot (Seq.seq U8.t & Seq.seq U8.t)\n= let cdigest = spec_hash alg cdi in\n derive_key_pair_spec\n (* ikm *) dig_len cdigest\n (* lbl *) l0_label_DeviceID_len l0_label_DeviceID", "val derive_DeviceID\n (alg:alg_t)\n (deviceID_pub:A.larray U8.t (US.v v32us))\n (deviceID_priv:A.larray U8.t (US.v v32us))\n (cdi:A.larray U8.t (US.v dice_digest_len))\n (deviceID_label_len:hkdf_lbl_len)\n (deviceID_label:A.larray U8.t (US.v deviceID_label_len))\n (#cdi0 #deviceID_label0 #deviceID_pub0 #deviceID_priv0:erased (Seq.seq U8.t))\n (#cdi_perm #p:perm)\n : stt unit\n (requires (\n A.pts_to cdi #cdi_perm cdi0 **\n A.pts_to deviceID_label #p deviceID_label0 **\n A.pts_to deviceID_pub deviceID_pub0 **\n A.pts_to deviceID_priv deviceID_priv0 **\n pure (valid_hkdf_ikm_len (digest_len alg))\n ))\n (ensures (fun _ ->\n A.pts_to cdi #cdi_perm cdi0 **\n A.pts_to deviceID_label #p deviceID_label0 **\n (exists* (deviceID_pub1 deviceID_priv1:Seq.seq U8.t).\n A.pts_to deviceID_pub deviceID_pub1 **\n A.pts_to deviceID_priv deviceID_priv1 **\n pure (\n valid_hkdf_ikm_len (digest_len alg) /\\\n derive_DeviceID_spec alg (digest_len alg) cdi0 deviceID_label_len deviceID_label0 \n == (deviceID_pub1, deviceID_priv1)\n )\n ))\n )" ], "closest": [ "val derive_AliasKey_spec\n (cdi: lbytes_sec 32)\n (fwid: lbytes_pub 32)\n (l0_label_AliasKey_len: size_t{valid_hkdf_lbl_len l0_label_AliasKey_len})\n (l0_label_AliasKey: lbytes_sec (v l0_label_AliasKey_len))\n : GTot (lbytes_pub 32 & lbytes_sec 32)\nlet derive_AliasKey_spec\n (cdi: lbytes_sec 32)\n (fwid: lbytes_pub 32)\n (l0_label_AliasKey_len: size_t {valid_hkdf_lbl_len l0_label_AliasKey_len})\n (l0_label_AliasKey: lbytes_sec (v l0_label_AliasKey_len))\n: GTot (lbytes_pub 32 & lbytes_sec 32)\n= let cdigest = Spec.Agile.Hash.hash alg cdi in\n let adigest = Spec.Agile.HMAC.hmac alg cdigest (classify_public_bytes fwid) in\n derive_key_pair_spec\n (* ikm *) 32ul adigest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey", "val derive_AliasKey\n (alg:alg_t)\n (aliasKey_pub: A.larray U8.t (US.v v32us))\n (aliasKey_priv: A.larray U8.t (US.v v32us))\n (cdi: A.larray U8.t (US.v dice_digest_len))\n (fwid: A.larray U8.t (US.v v32us))\n (aliasKey_label_len: hkdf_lbl_len)\n (aliasKey_label: A.larray U8.t (US.v aliasKey_label_len))\n (#cdi0 #fwid0 #aliasKey_label0 #aliasKey_pub0 #aliasKey_priv0:erased (Seq.seq U8.t))\n (#cdi_perm #p:perm)\n : stt unit\n (requires (\n A.pts_to cdi #cdi_perm cdi0 **\n A.pts_to fwid #p fwid0 **\n A.pts_to aliasKey_label #p aliasKey_label0 **\n A.pts_to aliasKey_pub aliasKey_pub0 **\n A.pts_to aliasKey_priv aliasKey_priv0 **\n pure (is_hashable_len (digest_len alg) /\\ valid_hkdf_ikm_len (digest_len alg))\n ))\n (ensures (fun _ ->\n A.pts_to cdi #cdi_perm cdi0 **\n A.pts_to fwid #p fwid0 **\n A.pts_to aliasKey_label #p aliasKey_label0 **\n (exists* (aliasKey_pub1 aliasKey_priv1:Seq.seq U8.t).\n A.pts_to aliasKey_pub aliasKey_pub1 **\n A.pts_to aliasKey_priv aliasKey_priv1 **\n pure (\n is_hashable_len (digest_len alg) /\\ \n valid_hkdf_ikm_len (digest_len alg) /\\\n derive_AliasKey_spec alg (digest_len alg) cdi0 fwid0 aliasKey_label_len aliasKey_label0 \n == (aliasKey_pub1, aliasKey_priv1)\n )\n ))\n )\nlet derive_AliasKey = derive_AliasKey_aux", "val derive_AliasKey\n (aliasKey_pub: B.lbuffer pub_uint8 32)\n (aliasKey_priv cdi: B.lbuffer uint8 32)\n (fwid: B.lbuffer pub_uint8 32)\n (l0_label_AliasKey_len: size_t{valid_hkdf_lbl_len l0_label_AliasKey_len})\n (l0_label_AliasKey: B.lbuffer uint8 (v l0_label_AliasKey_len))\n : HST.Stack (unit)\n (requires\n fun h ->\n B.(all_live h\n [buf aliasKey_pub; buf aliasKey_priv; buf cdi; buf fwid; buf l0_label_AliasKey]) /\\\n B.(all_disjoint [\n loc_buffer aliasKey_pub;\n loc_buffer aliasKey_priv;\n loc_buffer cdi;\n loc_buffer fwid;\n loc_buffer l0_label_AliasKey\n ]))\n (ensures\n fun h0 _ h1 ->\n B.(modifies ((loc_buffer aliasKey_pub) `loc_union` (loc_buffer aliasKey_priv)) h0 h1) /\\\n ((B.as_seq h1 aliasKey_pub <: lbytes_pub 32), (B.as_seq h1 aliasKey_priv <: lbytes_sec 32)\n ) ==\n derive_AliasKey_spec (B.as_seq h1 cdi)\n (B.as_seq h1 fwid)\n l0_label_AliasKey_len\n (B.as_seq h1 l0_label_AliasKey) /\\ True)\nlet derive_AliasKey\n (aliasKey_pub: B.lbuffer pub_uint8 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n // (cdi_len: hashable_len)\n (cdi: B.lbuffer uint8 32)\n (fwid: B.lbuffer pub_uint8 32)\n (l0_label_AliasKey_len: size_t {valid_hkdf_lbl_len l0_label_AliasKey_len})\n (l0_label_AliasKey: B.lbuffer uint8 (v l0_label_AliasKey_len))\n: HST.Stack (unit)\n (requires fun h ->\n B.(all_live h [buf aliasKey_pub;\n buf aliasKey_priv;\n buf cdi;\n buf fwid;\n buf l0_label_AliasKey]) /\\\n B.(all_disjoint [loc_buffer aliasKey_pub;\n loc_buffer aliasKey_priv;\n loc_buffer cdi;\n loc_buffer fwid;\n loc_buffer l0_label_AliasKey]))\n (ensures fun h0 _ h1 ->\n B.(modifies (loc_buffer aliasKey_pub `loc_union` loc_buffer aliasKey_priv) h0 h1) /\\\n ((B.as_seq h1 aliasKey_pub <: lbytes_pub 32),\n (B.as_seq h1 aliasKey_priv <: lbytes_sec 32)) == derive_AliasKey_spec\n (B.as_seq h1 cdi)\n (B.as_seq h1 fwid)\n l0_label_AliasKey_len\n (B.as_seq h1 l0_label_AliasKey) /\\\n True\n )\n= HST.push_frame ();\n let cDigest = B.alloca (u8 0) 32ul in\n l0_hash alg\n cDigest\n cdi\n 32ul;\n let aDigest = B.alloca (u8 0) 32ul in\n let fwid_sec = B.alloca (u8 0) 32ul in\n L0.Declassify.classify_public_buffer 32ul fwid fwid_sec;\n l0_hmac alg\n aDigest\n cDigest 32ul\n fwid_sec 32ul;\n derive_key_pair\n aliasKey_pub\n aliasKey_priv\n 32ul aDigest\n l0_label_AliasKey_len l0_label_AliasKey;\n HST.pop_frame ()", "val derive_key_pair_spec\n (ikm_len: hkdf_ikm_len)\n (ikm: Seq.seq U8.t)\n (lbl_len: hkdf_lbl_len)\n (lbl: Seq.seq U8.t)\n : GTot (Seq.seq U8.t & Seq.seq U8.t)\nlet derive_key_pair_spec = derive_key_pair_spec_aux", "val derive_key_pair_spec\n (ikm_len: size_t{valid_hkdf_ikm_len ikm_len})\n (ikm: Seq.lseq uint8 (v ikm_len))\n (lbl_len: size_t{valid_hkdf_lbl_len lbl_len})\n (lbl: Seq.lseq uint8 (v lbl_len))\n : GTot (Seq.lseq pub_uint8 32 & Seq.lseq uint8 32)\nlet derive_key_pair_spec\n (ikm_len: size_t { valid_hkdf_ikm_len ikm_len })\n (ikm: Seq.lseq uint8 (v ikm_len))\n (lbl_len: size_t { valid_hkdf_lbl_len lbl_len })\n (lbl: Seq.lseq uint8 (v lbl_len))\n: GTot (Seq.lseq pub_uint8 32 & Seq.lseq uint8 32)\n= let public_key, private_key = derive_sec_key_pair_spec ikm_len ikm lbl_len lbl in\n let public_key = declassify_secret_bytes public_key in\n(* return *) (public_key, private_key)", "val derive_DeviceID_spec\n (cdi: lbytes_sec 32)\n (l0_label_DeviceID_len: size_t{valid_hkdf_lbl_len l0_label_DeviceID_len})\n (l0_label_DeviceID: lbytes_sec (v l0_label_DeviceID_len))\n : GTot (lbytes_pub 32 & lbytes_sec 32)\nlet derive_DeviceID_spec\n (cdi: lbytes_sec 32)\n (l0_label_DeviceID_len: size_t {valid_hkdf_lbl_len l0_label_DeviceID_len})\n (l0_label_DeviceID: lbytes_sec (v l0_label_DeviceID_len))\n: GTot (lbytes_pub 32 & lbytes_sec 32)\n= let cdigest = Spec.Agile.Hash.hash alg cdi in\n derive_key_pair_spec\n (* ikm *) 32ul cdigest\n (* lbl *) l0_label_DeviceID_len l0_label_DeviceID", "val derive_sec_key_pair_spec\n (ikm_len: size_t{valid_hkdf_ikm_len ikm_len})\n (ikm: Seq.lseq uint8 (v ikm_len))\n (lbl_len: size_t{valid_hkdf_lbl_len lbl_len})\n (lbl: Seq.lseq uint8 (v lbl_len))\n : GTot (Seq.lseq uint8 32 & Seq.lseq uint8 32)\nlet derive_sec_key_pair_spec\n (ikm_len: size_t { valid_hkdf_ikm_len ikm_len })\n (ikm: Seq.lseq uint8 (v ikm_len))\n (lbl_len: size_t { valid_hkdf_lbl_len lbl_len })\n (lbl: Seq.lseq uint8 (v lbl_len))\n: GTot (Seq.lseq uint8 32 & Seq.lseq uint8 32)\n= let alg = SHA2_256 in\n (* Derive private key from `ikm` and `lbl` using HKDF *)\n (* Step 1. extract a `prk` (Pseudo Random Key) from an empty `salt` of `hashLen` and `ikm` *)\n let salt = Seq.create (v (hash_len alg)) (u8 0x00) in\n let prk = Spec.Agile.HKDF.extract\n (* alg *) alg\n (* salt*) salt\n (* ikm *) ikm in\n (* Step 2. expand `prk` and `lbl` to a `okm` (Output Keying Material) *)\n let private_key = Spec.Agile.HKDF.expand\n (* alg *) alg\n (* prk *) prk\n (* info*) lbl\n (* len *) (hash_length alg) in\n\n let public_key = Spec.Ed25519.secret_to_public private_key in\n\n(* return *) (public_key, private_key)", "val sign_and_finalize_aliasKeyCRT_spec\n (deviceID_priv: lbytes_sec 32)\n (aliasKeyTBS_len: size_t{valid_aliasKeyCRT_ingredients aliasKeyTBS_len})\n (aliasKeyTBS_seq: lbytes_pub (v aliasKeyTBS_len))\n : GTot (aliasKeyCRT_t aliasKeyTBS_len)\nlet sign_and_finalize_aliasKeyCRT_spec\n (deviceID_priv: lbytes_sec 32)\n (aliasKeyTBS_len: size_t\n { valid_aliasKeyCRT_ingredients aliasKeyTBS_len })\n (aliasKeyTBS_seq: lbytes_pub (v aliasKeyTBS_len))\n: GTot (aliasKeyCRT_t aliasKeyTBS_len)\n=\n\n(* Classify AliasKeyTBS *)\n let aliasKeyTBS_seq_sec: lbytes_sec (v aliasKeyTBS_len) = classify_public_bytes aliasKeyTBS_seq in\n\n(* Sign AliasKeyTBS *)\n let aliasKeyTBS_sig_sec: lbytes_sec 64 = Spec.Ed25519.sign deviceID_priv aliasKeyTBS_seq_sec in\n\n(* Declassify AliasKeyTBS *)\n let aliasKeyTBS_sig : lbytes_pub 64 = declassify_secret_bytes aliasKeyTBS_sig_sec in\n\n(* Create AliasKeyCRT with AliasKeyTBS and Signature *)\n let aliasKeyTBS_seq32 : B32.lbytes32 aliasKeyTBS_len = B32.hide aliasKeyTBS_seq in\n let aliasKeyTBS_sig32 : x509_signature_raw_t = B32.hide aliasKeyTBS_sig in\n let aliasKeyCRT: aliasKeyCRT_t aliasKeyTBS_len = x509_get_AliasKeyCRT\n aliasKeyTBS_len\n aliasKeyTBS_seq32\n aliasKeyTBS_sig32 in\n\n(* return *) aliasKeyCRT", "val L0.Core.aliasKeyCRT_post = \n cdi: LowStar.Buffer.lbuffer L0.Base.byte_sec 32 ->\n fwid: FStar.Seq.Properties.lseq L0.Base.byte_pub 32 ->\n deviceID_label_len: FStar.UInt32.t{L0.Spec.Crypto.valid_hkdf_lbl_len deviceID_label_len} ->\n deviceID_label: FStar.Seq.Properties.lseq L0.Base.byte_sec (Lib.IntTypes.v deviceID_label_len) ->\n aliasKeyCRT_ingredients: L0.X509.Base.aliasKeyCRT_ingredients_t ->\n aliasKeyCRT_len: FStar.UInt32.t{L0.Core.aliasKeyCRT_pre aliasKeyCRT_ingredients aliasKeyCRT_len} ->\n aliasKeyCRT_buf: LowStar.Buffer.lbuffer L0.Base.byte_pub (Lib.IntTypes.v aliasKeyCRT_len) ->\n aliasKey_pub: LowStar.Buffer.lbuffer L0.Base.byte_pub 32 ->\n h0: FStar.Monotonic.HyperStack.mem ->\n h1: FStar.Monotonic.HyperStack.mem\n -> Prims.GTot Prims.logical\nlet aliasKeyCRT_post\n (cdi:B.lbuffer byte_sec 32)\n (fwid:Seq.lseq byte_pub 32)\n (deviceID_label_len:UInt32.t{valid_hkdf_lbl_len deviceID_label_len})\n (deviceID_label:Seq.lseq byte_sec (v deviceID_label_len))\n (aliasKeyCRT_ingredients:aliasKeyCRT_ingredients_t)\n (aliasKeyCRT_len:UInt32.t{\n aliasKeyCRT_pre aliasKeyCRT_ingredients aliasKeyCRT_len})\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n (aliasKey_pub: B.lbuffer byte_pub 32)\n (h0 h1:HS.mem)\n = let deviceID_pub_seq, deviceID_priv_seq = derive_DeviceID_spec\n (B.as_seq h0 cdi)\n (deviceID_label_len)\n deviceID_label in\n let aliasKeyCrt_keyID_seq: lbytes_pub 20 =\n derive_authKeyID_spec (classify_public_bytes deviceID_pub_seq) in\n let aliasKeyTBS = create_aliasKeyTBS_spec\n aliasKeyCRT_ingredients.aliasKeyCrt_version\n aliasKeyCRT_ingredients.aliasKeyCrt_serialNumber\n aliasKeyCRT_ingredients.aliasKeyCrt_i_common\n aliasKeyCRT_ingredients.aliasKeyCrt_i_org\n aliasKeyCRT_ingredients.aliasKeyCrt_i_country\n aliasKeyCRT_ingredients.aliasKeyCrt_notBefore\n aliasKeyCRT_ingredients.aliasKeyCrt_notAfter\n aliasKeyCRT_ingredients.aliasKeyCrt_s_common\n aliasKeyCRT_ingredients.aliasKeyCrt_s_org\n aliasKeyCRT_ingredients.aliasKeyCrt_s_country\n aliasKeyCRT_ingredients.aliasKeyCrt_ku\n aliasKeyCrt_keyID_seq\n aliasKeyCRT_ingredients.aliasKeyCrt_l0_version\n fwid\n deviceID_pub_seq\n (B.as_seq h1 aliasKey_pub) in\n let aliasKeyTBS_seq = serialize_aliasKeyTBS `serialize` aliasKeyTBS in\n let aliasKeyTBS_len = //coerce_asn1_tlv_int32_of_type_to_asn1_int32\n (len_of_aliasKeyTBS\n aliasKeyCRT_ingredients.aliasKeyCrt_serialNumber\n aliasKeyCRT_ingredients.aliasKeyCrt_i_common\n aliasKeyCRT_ingredients.aliasKeyCrt_i_org\n aliasKeyCRT_ingredients.aliasKeyCrt_i_country\n aliasKeyCRT_ingredients.aliasKeyCrt_s_common\n aliasKeyCRT_ingredients.aliasKeyCrt_s_org\n aliasKeyCRT_ingredients.aliasKeyCrt_s_country\n aliasKeyCRT_ingredients.aliasKeyCrt_l0_version) in\n let (* Prf *) _ = lemma_serialize_aliasKeyTBS_size_exact aliasKeyTBS in\n assert (Seq.length aliasKeyTBS_seq == v aliasKeyTBS_len); //TODO: help Z3 prove it\n let aliasKeyCRT: aliasKeyCRT_t aliasKeyTBS_len = sign_and_finalize_aliasKeyCRT_spec\n (deviceID_priv_seq)\n (aliasKeyTBS_len)\n (aliasKeyTBS_seq) in\n B.as_seq h1 aliasKeyCRT_buf == serialize_aliasKeyCRT aliasKeyTBS_len `serialize` aliasKeyCRT", "val derive_DeviceID\n (alg:alg_t)\n (deviceID_pub:A.larray U8.t (US.v v32us))\n (deviceID_priv:A.larray U8.t (US.v v32us))\n (cdi:A.larray U8.t (US.v dice_digest_len))\n (deviceID_label_len:hkdf_lbl_len)\n (deviceID_label:A.larray U8.t (US.v deviceID_label_len))\n (#cdi0 #deviceID_label0 #deviceID_pub0 #deviceID_priv0:erased (Seq.seq U8.t))\n (#cdi_perm #p:perm)\n : stt unit\n (requires (\n A.pts_to cdi #cdi_perm cdi0 **\n A.pts_to deviceID_label #p deviceID_label0 **\n A.pts_to deviceID_pub deviceID_pub0 **\n A.pts_to deviceID_priv deviceID_priv0 **\n pure (valid_hkdf_ikm_len (digest_len alg))\n ))\n (ensures (fun _ ->\n A.pts_to cdi #cdi_perm cdi0 **\n A.pts_to deviceID_label #p deviceID_label0 **\n (exists* (deviceID_pub1 deviceID_priv1:Seq.seq U8.t).\n A.pts_to deviceID_pub deviceID_pub1 **\n A.pts_to deviceID_priv deviceID_priv1 **\n pure (\n valid_hkdf_ikm_len (digest_len alg) /\\\n derive_DeviceID_spec alg (digest_len alg) cdi0 deviceID_label_len deviceID_label0 \n == (deviceID_pub1, deviceID_priv1)\n )\n ))\n )\nlet derive_DeviceID = derive_DeviceID_aux", "val L0.Core.aliasKey_post = \n cdi: LowStar.Buffer.lbuffer L0.Base.byte_sec 32 ->\n fwid: FStar.Seq.Properties.lseq L0.Base.byte_pub 32 ->\n aliasKey_label_len: FStar.UInt32.t{L0.Spec.Crypto.valid_hkdf_lbl_len aliasKey_label_len} ->\n aliasKey_label: FStar.Seq.Properties.lseq L0.Base.byte_sec (Lib.IntTypes.v aliasKey_label_len) ->\n aliasKey_pub: LowStar.Buffer.lbuffer L0.Base.byte_pub 32 ->\n aliasKey_priv: LowStar.Buffer.lbuffer Lib.IntTypes.uint8 32 ->\n h0: FStar.Monotonic.HyperStack.mem ->\n h1: FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet aliasKey_post\n (cdi : B.lbuffer byte_sec 32) (fwid:Seq.lseq byte_pub 32)\n (aliasKey_label_len:UInt32.t{valid_hkdf_lbl_len aliasKey_label_len})\n (aliasKey_label:Seq.lseq byte_sec (v aliasKey_label_len))\n (aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n (h0 h1:HS.mem)\n = ((B.as_seq h1 aliasKey_pub <: lbytes_pub 32),\n (B.as_seq h1 aliasKey_priv <: lbytes_sec 32)) == derive_AliasKey_spec\n (B.as_seq h0 cdi)\n fwid\n (aliasKey_label_len)\n aliasKey_label", "val derive_AuthKeyID\n (alg:alg_t)\n (authKeyID: A.larray U8.t (US.v (digest_len alg)))\n (deviceID_pub: A.larray U8.t (US.v v32us))\n (#authKeyID0 #deviceID_pub0:erased (Seq.seq U8.t))\n (#p:perm)\n : stt unit\n (requires (\n A.pts_to deviceID_pub #p deviceID_pub0 **\n A.pts_to authKeyID authKeyID0 \n ))\n (ensures (fun _ ->\n A.pts_to deviceID_pub #p deviceID_pub0 **\n (exists* (authKeyID1:Seq.seq U8.t).\n A.pts_to authKeyID authKeyID1 **\n pure (Seq.equal (derive_AuthKeyID_spec alg deviceID_pub0) authKeyID1)\n )))\nlet derive_AuthKeyID = derive_AuthKeyID_aux", "val derive_key_pair\n (pub : A.larray U8.t (US.v v32us))\n (priv: A.larray U8.t (US.v v32us))\n (ikm_len: hkdf_ikm_len) \n (ikm: A.array U8.t)\n (lbl_len: hkdf_lbl_len) \n (lbl: A.array U8.t)\n (#ikm_perm #lbl_perm:perm)\n (#_pub_seq #_priv_seq #ikm_seq #lbl_seq:erased (Seq.seq U8.t))\n : stt unit\n (requires (\n A.pts_to pub _pub_seq ** \n A.pts_to priv _priv_seq ** \n A.pts_to ikm #ikm_perm ikm_seq ** \n A.pts_to lbl #lbl_perm lbl_seq\n ))\n (ensures (fun _ ->\n A.pts_to ikm #ikm_perm ikm_seq ** \n A.pts_to lbl #lbl_perm lbl_seq **\n (exists* (pub_seq\n priv_seq:Seq.seq U8.t).\n A.pts_to pub pub_seq ** \n A.pts_to priv priv_seq **\n pure ((pub_seq, priv_seq) == derive_key_pair_spec ikm_len ikm_seq lbl_len lbl_seq)\n )))\nlet derive_key_pair = derive_key_pair_aux", "val l0_pre\n (#a: Type)\n (h: HS.mem)\n (cdi: B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: UInt32.t)\n (deviceID_label: B.lbuffer a (v deviceID_label_len))\n (aliasKey_label_len: UInt32.t)\n (aliasKey_label: B.lbuffer a (v aliasKey_label_len))\n (deviceIDCSR_ingredients: deviceIDCSR_ingredients_t)\n (aliasKeyCRT_ingredients: aliasKeyCRT_ingredients_t)\n (deviceID_pub aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n : Type0\nlet l0_pre\n (#a:Type)\n (h: HS.mem)\n(* Common Inputs *)\n (cdi : B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: UInt32.t)\n (deviceID_label: B.lbuffer a (v deviceID_label_len))\n (aliasKey_label_len: UInt32.t)\n (aliasKey_label: B.lbuffer a (v aliasKey_label_len))\n(* DeviceID CSR Inputs*)\n (deviceIDCSR_ingredients:deviceIDCSR_ingredients_t)\n(* AliasKey Crt Inputs*)\n (aliasKeyCRT_ingredients:aliasKeyCRT_ingredients_t)\n(* Common Outputs *)\n (deviceID_pub: B.lbuffer byte_pub 32)\n (aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n(* DeviceID CSR Outputs *)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n(* AliasKey Crt Outputs *)\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n: Type0\n= B.(all_live h [buf cdi;\n buf fwid;\n buf deviceID_label;\n buf aliasKey_label;\n buf deviceIDCSR_buf;\n buf aliasKeyCRT_buf;\n buf deviceID_pub;\n buf aliasKey_pub;\n buf aliasKey_priv]) /\\\n B.(all_disjoint [loc_buffer cdi;\n loc_buffer fwid;\n loc_buffer deviceID_label;\n loc_buffer aliasKey_label;\n loc_buffer deviceIDCSR_buf;\n loc_buffer aliasKeyCRT_buf;\n loc_buffer deviceID_pub;\n loc_buffer aliasKey_pub;\n loc_buffer aliasKey_priv]) /\\\n (* Pre: labels have enough length for HKDF *)\n valid_hkdf_lbl_len deviceID_label_len /\\\n valid_hkdf_lbl_len aliasKey_label_len /\\\n\n deviceIDCRI_pre deviceIDCSR_ingredients /\\\n deviceIDCSR_pre deviceIDCSR_ingredients deviceIDCSR_len /\\\n aliasKeyCRT_pre aliasKeyCRT_ingredients aliasKeyCRT_len", "val kv: #a:alg -> state_s a -> GTot (Spec.key a)\nlet kv #a (s: state_s a) =\n let State _ _ _ _ g_key _ _ = s in\n G.reveal g_key", "val x509_get_AliasKeyCRT\n (tbs_len:\n asn1_int32\n {length_of_aliasKeyCRT_payload tbs_len <= asn1_value_length_max_of_type SEQUENCE})\n (aliasKeyCRT_tbs: B32.lbytes32 tbs_len)\n (signature32: x509_signature_raw_t)\n : Tot (aliasKeyCRT_t tbs_len)\nlet x509_get_AliasKeyCRT\n (tbs_len: asn1_int32\n { length_of_aliasKeyCRT_payload tbs_len <= asn1_value_length_max_of_type SEQUENCE })\n (aliasKeyCRT_tbs: B32.lbytes32 tbs_len)\n (signature32: x509_signature_raw_t) // B32.lbytes32 64ul\n: Tot (aliasKeyCRT_t tbs_len)\n=\n let aliasKeyCRT_sig_alg = x509_get_algorithmIdentifier () in\n (* Prf *) lemma_serialize_algorithmIdentifier_size_exact aliasKeyCRT_sig_alg;\n\n let aliasKeyCRT_sig = x509_get_signature signature32 in\n (* Prf *) lemma_serialize_x509_signature_size aliasKeyCRT_sig;\n\n let aliasKeyCRT: aliasKeyCRT_payload_t tbs_len = {\n aliasKeyCRT_tbs = aliasKeyCRT_tbs;\n aliasKeyCRT_sig_alg = aliasKeyCRT_sig_alg;\n aliasKeyCRT_sig = aliasKeyCRT_sig\n } in\n (* Prf *) lemma_serialize_aliasKeyCRT_payload_unfold tbs_len aliasKeyCRT;\n (* Prf *) lemma_serialize_aliasKeyCRT_payload_size tbs_len aliasKeyCRT;\n (* Prf *) (**) lemma_serialize_flbytes32_size tbs_len aliasKeyCRT.aliasKeyCRT_tbs;\n\n(* return *) aliasKeyCRT", "val l0_aux\n (cdi: B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: UInt32.t)\n (deviceID_label: B.lbuffer byte_sec (v deviceID_label_len))\n (aliasKey_label_len: UInt32.t)\n (aliasKey_label: B.lbuffer byte_sec (v aliasKey_label_len))\n (deviceIDCSR_ingredients: deviceIDCSR_ingredients_t)\n (aliasKeyCRT_ingredients: aliasKeyCRT_ingredients_t)\n (deviceID_pub aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n : HST.Stack unit\n (requires\n fun h ->\n l0_pre (h) (cdi) (fwid) (deviceID_label_len) (deviceID_label) (aliasKey_label_len)\n (aliasKey_label) (deviceIDCSR_ingredients) (aliasKeyCRT_ingredients) (deviceID_pub)\n (aliasKey_pub) (aliasKey_priv) (deviceIDCSR_len) (deviceIDCSR_buf) (aliasKeyCRT_len)\n (aliasKeyCRT_buf))\n (ensures\n fun h0 _ h1 ->\n l0_aux_post (cdi) (fwid) (deviceID_label_len) (deviceID_label) (aliasKey_label_len)\n (aliasKey_label) (deviceIDCSR_ingredients) (aliasKeyCRT_ingredients) (deviceID_pub)\n (aliasKey_pub) (aliasKey_priv) (deviceIDCSR_len) (deviceIDCSR_buf) (aliasKeyCRT_len)\n (aliasKeyCRT_buf) (h0) (h1))\nlet l0_aux\n(* Common Inputs *)\n (cdi : B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: UInt32.t)\n (deviceID_label: B.lbuffer byte_sec (v deviceID_label_len))\n (aliasKey_label_len: UInt32.t)\n (aliasKey_label: B.lbuffer byte_sec (v aliasKey_label_len))\n(* DeviceID CSR Inputs*)\n (deviceIDCSR_ingredients:deviceIDCSR_ingredients_t)\n(* AliasKey Crt Inputs*)\n (aliasKeyCRT_ingredients:aliasKeyCRT_ingredients_t)\n(* Common Outputs *)\n (deviceID_pub: B.lbuffer byte_pub 32)\n (aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n(* DeviceID CSR Outputs *)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n(* AliasKey Crt Outputs *)\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n: HST.Stack unit\n (requires fun h ->\n l0_pre\n (h) (cdi) (fwid)\n (deviceID_label_len) (deviceID_label)\n (aliasKey_label_len) (aliasKey_label)\n (deviceIDCSR_ingredients)\n (aliasKeyCRT_ingredients)\n (deviceID_pub) (aliasKey_pub) (aliasKey_priv)\n (deviceIDCSR_len) (deviceIDCSR_buf)\n (aliasKeyCRT_len) (aliasKeyCRT_buf)\n )\n (ensures fun h0 _ h1 ->\n l0_aux_post\n (cdi) (fwid)\n (deviceID_label_len) (deviceID_label)\n (aliasKey_label_len) (aliasKey_label)\n (deviceIDCSR_ingredients)\n (aliasKeyCRT_ingredients)\n (deviceID_pub) (aliasKey_pub) (aliasKey_priv)\n (deviceIDCSR_len) (deviceIDCSR_buf)\n (aliasKeyCRT_len) (aliasKeyCRT_buf)\n (h0) (h1)\n )\n= (**) let h0 = HST.get () in\n HST.push_frame ();\n (**) let hs0 = HST.get () in\n (**) B.fresh_frame_modifies h0 hs0;\n\n(* Derive DeviceID *)\n // let deviceID_pub : B.lbuffer byte_pub 32 = B.alloca 0x00uy 32ul in\n let deviceID_priv: B.lbuffer byte_sec 32 = B.alloca (u8 0x00) 32ul in\n let hs01 = HST.get () in\n let authKeyID: B.lbuffer byte_pub 20 = B.alloca 0x00uy 20ul in\n let hs02 = HST.get () in\n\n let _h_step1_pre = HST.get () in\n (**) B.modifies_buffer_elim cdi B.loc_none h0 _h_step1_pre;\n (**) B.modifies_buffer_elim fwid B.loc_none h0 _h_step1_pre;\n (**) B.modifies_buffer_elim deviceID_label B.loc_none h0 _h_step1_pre;\n (**) B.modifies_buffer_elim deviceID_label B.loc_none h0 _h_step1_pre;\n l0_core_step1\n (cdi) (fwid)\n (deviceID_label_len) (deviceID_label)\n (aliasKey_label_len) (aliasKey_label)\n (deviceID_pub) (deviceID_priv)\n (aliasKey_pub) (aliasKey_priv)\n (authKeyID);\n let _h_step1_post = HST.get () in\n\n //assert (aliasKey_post cdi fwid aliasKey_label_len aliasKey_label aliasKey_pub aliasKey_priv h0 _h_step1_post);\n\n (**) B.modifies_trans B.loc_none h0 _h_step1_pre (\n B.loc_buffer deviceID_pub `B.loc_union`\n B.loc_buffer deviceID_priv `B.loc_union`\n B.loc_buffer aliasKey_pub `B.loc_union`\n B.loc_buffer aliasKey_priv `B.loc_union`\n B.loc_buffer authKeyID\n ) _h_step1_post;\n\n let _h_step2_pre = _h_step1_post in\n\n l0_core_step2\n (* version *) deviceIDCSR_ingredients.deviceIDCSR_version\n deviceIDCSR_ingredients.deviceIDCSR_s_common\n deviceIDCSR_ingredients.deviceIDCSR_s_org\n deviceIDCSR_ingredients.deviceIDCSR_s_country\n (* key usage *) deviceIDCSR_ingredients.deviceIDCSR_ku\n (* DeviceID *) deviceID_pub\n deviceID_priv\n (*DeviceIDCRI*) deviceIDCSR_len\n deviceIDCSR_buf;\n let _h_step2_post = HST.get () in\n\n (**) B.modifies_trans (\n B.loc_buffer deviceID_pub `B.loc_union`\n B.loc_buffer deviceID_priv `B.loc_union`\n B.loc_buffer aliasKey_pub `B.loc_union`\n B.loc_buffer aliasKey_priv `B.loc_union`\n B.loc_buffer authKeyID\n ) h0 _h_step2_pre (\n B.loc_buffer deviceIDCSR_buf\n ) _h_step2_post;\n\n // assert (\n // deviceIDCSR_post\n // (cdi) (deviceID_label_len) (deviceID_label)\n // (deviceIDCSR_ingredients)\n // (deviceIDCSR_len) (deviceIDCSR_buf)\n // (h0) (_h_step2_post)\n // );\n\n let _h_step3_pre = _h_step2_post in\n\n (**) B.modifies_buffer_elim fwid (\n B.loc_buffer deviceID_pub `B.loc_union`\n B.loc_buffer deviceID_priv `B.loc_union`\n B.loc_buffer aliasKey_pub `B.loc_union`\n B.loc_buffer aliasKey_priv `B.loc_union`\n B.loc_buffer authKeyID `B.loc_union`\n B.loc_buffer deviceIDCSR_buf\n ) h0 _h_step3_pre;\n (**) B.modifies_buffer_elim authKeyID (B.loc_buffer deviceIDCSR_buf) _h_step1_post _h_step3_pre;\n (**) B.modifies_buffer_elim deviceID_pub (B.loc_buffer deviceIDCSR_buf) _h_step1_post _h_step3_pre;\n (**) B.modifies_buffer_elim deviceID_priv (B.loc_buffer deviceIDCSR_buf) _h_step1_post _h_step3_pre;\n (**) B.modifies_buffer_elim aliasKey_pub (B.loc_buffer deviceIDCSR_buf) _h_step1_post _h_step3_pre;\n\n l0_core_step3\n (aliasKeyCRT_ingredients.aliasKeyCrt_version)\n (aliasKeyCRT_ingredients.aliasKeyCrt_serialNumber)\n (aliasKeyCRT_ingredients.aliasKeyCrt_i_common)\n (aliasKeyCRT_ingredients.aliasKeyCrt_i_org)\n (aliasKeyCRT_ingredients.aliasKeyCrt_i_country)\n (aliasKeyCRT_ingredients.aliasKeyCrt_notBefore)\n (aliasKeyCRT_ingredients.aliasKeyCrt_notAfter)\n (aliasKeyCRT_ingredients.aliasKeyCrt_s_common)\n (aliasKeyCRT_ingredients.aliasKeyCrt_s_org)\n (aliasKeyCRT_ingredients.aliasKeyCrt_s_country)\n (fwid)\n (aliasKeyCRT_ingredients.aliasKeyCrt_ku)\n (authKeyID)\n (aliasKeyCRT_ingredients.aliasKeyCrt_l0_version)\n (* DeviceID *) deviceID_pub\n deviceID_priv\n (* AliasKey *) aliasKey_pub\n (*AliasKeyTBS*) aliasKeyCRT_len\n aliasKeyCRT_buf;\n let _h_step3_post = HST.get () in\n\n (**) B.modifies_trans (\n B.loc_buffer deviceID_pub `B.loc_union`\n B.loc_buffer deviceID_priv `B.loc_union`\n B.loc_buffer aliasKey_pub `B.loc_union`\n B.loc_buffer aliasKey_priv `B.loc_union`\n B.loc_buffer authKeyID `B.loc_union`\n B.loc_buffer deviceIDCSR_buf\n ) h0 _h_step3_pre (\n B.loc_buffer aliasKeyCRT_buf\n ) _h_step3_post;\n\n (**) B.modifies_buffer_elim aliasKey_pub (\n B.loc_buffer deviceIDCSR_buf `B.loc_union`\n B.loc_buffer aliasKeyCRT_buf\n ) _h_step1_post _h_step3_post;\n // assert (\n // aliasKeyCRT_post\n // (cdi) (fwid) (deviceID_label_len) (deviceID_label)\n // (aliasKeyCRT_ingredients)\n // (aliasKeyCRT_len) (aliasKeyCRT_buf)\n // (aliasKey_pub)\n // (h0) (_h_step3_post)\n // );\n\n(* hsf *) let hsf = HST.get () in\n HST.pop_frame ();\n(* hf *) let hf = HST.get () in\n (**) B.popped_modifies hsf hf;\n (**) B.modifies_buffer_elim deviceID_pub (B.loc_region_only false (HS.get_tip hsf)) hsf hf;\n (**) B.modifies_buffer_elim aliasKey_pub (B.loc_region_only false (HS.get_tip hsf)) hsf hf;\n (**) B.modifies_buffer_elim aliasKey_priv (B.loc_region_only false (HS.get_tip hsf)) hsf hf;\n (**) B.modifies_buffer_elim deviceIDCSR_buf (B.loc_region_only false (HS.get_tip hsf)) hsf hf;\n (**) B.modifies_buffer_elim aliasKeyCRT_buf (B.loc_region_only false (HS.get_tip hsf)) hsf hf;\n lemma_l0_modifies\n (byte_pub) (byte_sec)\n (0x00uy) (u8 0x00)\n (h0) (hf)\n (deviceID_pub) (aliasKey_pub) (aliasKey_priv)\n (deviceIDCSR_buf) (aliasKeyCRT_buf)\n (hs0) (hs01) (hs02) (_h_step1_post) (_h_step2_post) (_h_step3_post) (hsf)\n (deviceID_priv) (authKeyID);\n // (**) B.modifies_fresh_frame_popped h0 hs0 (\n // B.loc_buffer deviceID_pub `B.loc_union`\n // B.loc_buffer aliasKey_pub `B.loc_union`\n // B.loc_buffer aliasKey_priv `B.loc_union`\n // B.loc_buffer deviceIDCSR_buf `B.loc_union`\n // B.loc_buffer aliasKeyCRT_buf\n // ) hsf hf;\n assert (HST.equal_domains h0 hf)", "val synth_aliasKeyCRT_payload_t (tbs_len: asn1_int32) (x': aliasKeyCRT_payload_t' tbs_len)\n : GTot (aliasKeyCRT_payload_t tbs_len)\nlet synth_aliasKeyCRT_payload_t\n (tbs_len: asn1_int32)\n (x': aliasKeyCRT_payload_t' tbs_len)\n: GTot (aliasKeyCRT_payload_t tbs_len)\n= { aliasKeyCRT_tbs = fst (fst x');\n aliasKeyCRT_sig_alg = snd (fst x');\n aliasKeyCRT_sig = snd x' }", "val derive_secret:\n ha: Hashing.Spec.tls_macAlg ->\n secret: lbytes (Spec.Hash.Definitions.hash_length ha) ->\n label: string{length (bytes_of_string label) < 256-6} ->\n digest: bytes{length digest < 256} ->\n ST (lbytes32 (Hacl.Hash.Definitions.hash_len ha))\n (requires fun h -> True)\n (ensures fun h0 _ h1 -> modifies_none h0 h1)\nlet derive_secret ha secret label digest =\n let len = Hacl.Hash.Definitions.hash_len ha in\n expand_label secret label digest len", "val sign_and_finalize_aliasKeyCRT\n (deviceID_priv: B.lbuffer byte_sec 32)\n (aliasKeyTBS_len: size_t)\n (aliasKeyTBS_buf: B.lbuffer byte_pub (v aliasKeyTBS_len))\n (aliasKeyCRT_len: size_t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n : HST.Stack unit\n (requires\n fun h ->\n B.(all_live h [buf deviceID_priv; buf aliasKeyTBS_buf; buf aliasKeyCRT_buf]) /\\\n B.(all_disjoint [\n loc_buffer deviceID_priv;\n loc_buffer aliasKeyTBS_buf;\n loc_buffer aliasKeyCRT_buf\n ]) /\\ 0 < v aliasKeyTBS_len /\\ valid_aliasKeyCRT_ingredients aliasKeyTBS_len /\\\n v aliasKeyCRT_len == length_of_aliasKeyCRT aliasKeyTBS_len)\n (ensures\n fun h0 _ h1 ->\n let aliasKeyCRT:aliasKeyCRT_t aliasKeyTBS_len =\n sign_and_finalize_aliasKeyCRT_spec (B.as_seq h0 deviceID_priv)\n (aliasKeyTBS_len)\n (B.as_seq h0 aliasKeyTBS_buf)\n in\n lemma_serialize_aliasKeyCRT_size_exact aliasKeyTBS_len aliasKeyCRT;\n B.(modifies (loc_buffer aliasKeyCRT_buf) h0 h1) /\\\n B.as_seq h1 aliasKeyCRT_buf ==\n (serialize_aliasKeyCRT aliasKeyTBS_len)\n `serialize`\n aliasKeyCRT)\nlet sign_and_finalize_aliasKeyCRT\n (deviceID_priv: B.lbuffer byte_sec 32)\n (aliasKeyTBS_len: size_t)\n (aliasKeyTBS_buf: B.lbuffer byte_pub (v aliasKeyTBS_len))\n (aliasKeyCRT_len: size_t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n: HST.Stack unit\n (requires fun h ->\n B.(all_live h [buf deviceID_priv;\n buf aliasKeyTBS_buf;\n buf aliasKeyCRT_buf]) /\\\n B.(all_disjoint [loc_buffer deviceID_priv;\n loc_buffer aliasKeyTBS_buf;\n loc_buffer aliasKeyCRT_buf]) /\\\n (* For `B.alloca` *)\n 0 < v aliasKeyTBS_len /\\\n valid_aliasKeyCRT_ingredients aliasKeyTBS_len /\\\n (* `aliasKeyCRT_buf` has exact space to write serialization *)\n v aliasKeyCRT_len == length_of_aliasKeyCRT aliasKeyTBS_len\n )\n (ensures fun h0 _ h1 ->\n let aliasKeyCRT: aliasKeyCRT_t aliasKeyTBS_len = sign_and_finalize_aliasKeyCRT_spec\n (B.as_seq h0 deviceID_priv)\n (aliasKeyTBS_len)\n (B.as_seq h0 aliasKeyTBS_buf) in\n (* Prf *) lemma_serialize_aliasKeyCRT_size_exact aliasKeyTBS_len aliasKeyCRT;\n B.(modifies (loc_buffer aliasKeyCRT_buf) h0 h1) /\\\n B.as_seq h1 aliasKeyCRT_buf == serialize_aliasKeyCRT aliasKeyTBS_len `serialize` aliasKeyCRT\n )\n= HST.push_frame ();\n\n(* Classify AliasKeyTBS *)\n let aliasKeyTBS_buf_sec: B.lbuffer byte_sec (v aliasKeyTBS_len) = B.alloca (u8 0x00) aliasKeyTBS_len in\n classify_public_buffer\n (* len *) aliasKeyTBS_len\n (* src *) aliasKeyTBS_buf\n (* dst *) aliasKeyTBS_buf_sec;\n\n(* Sign Classified AliasKeyTBS *)\n let aliasKeyTBS_sig_sec: B.lbuffer byte_sec 64 = B.alloca (u8 0x00) 64ul in\n Ed25519.sign\n (* sig *) aliasKeyTBS_sig_sec\n (* key *) deviceID_priv\n (* len *) aliasKeyTBS_len\n (* msg *) aliasKeyTBS_buf_sec;\n\n(* Declassify AliasKeyTBS Signature *)\n let aliasKeyTBS_sig: B.lbuffer byte_pub 64 = B.alloca 0x00uy 64ul in\n declassify_secret_buffer\n (* len *) 64ul\n (* src *) aliasKeyTBS_sig_sec\n (* dst *) aliasKeyTBS_sig;\n\n(* Finalize AliasKeyCRT with AliasKeyTBS and Signature *)\n let aliasKeyTBS_buf32: B32.lbytes32 aliasKeyTBS_len = B32.of_buffer aliasKeyTBS_len aliasKeyTBS_buf in\n let aliasKeyTBS_sig32: x509_signature_raw_t = B32.of_buffer 64ul aliasKeyTBS_sig in\n\n printf \"Creating AliasKey Certificate CRT message\\n\" done;\n let aliasKeyCRT: aliasKeyCRT_t aliasKeyTBS_len = x509_get_AliasKeyCRT\n aliasKeyTBS_len\n aliasKeyTBS_buf32\n aliasKeyTBS_sig32 in\n (* Prf *) lemma_serialize_aliasKeyCRT_size_exact aliasKeyTBS_len aliasKeyCRT;\n HST.pop_frame ();\n\n printf \"Serializing AliasKey Certificate CRT\\n\" done;\n(* Serialize AliasKeyCRT *)\n let _offset = serialize32_aliasKeyCRT_backwards\n aliasKeyTBS_len\n aliasKeyCRT\n aliasKeyCRT_buf\n aliasKeyCRT_len in ()", "val create_aliasKeyTBS_spec\n (crt_version: x509_version_t)\n (serialNumber: x509_serialNumber_t)\n (i_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (i_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (i_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (notBefore: datatype_of_asn1_type UTC_TIME)\n (notAfter: datatype_of_asn1_type Generalized_Time)\n (s_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (s_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (s_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (ku: key_usage_payload_t)\n (keyID: lbytes_pub 20)\n (version: datatype_of_asn1_type INTEGER)\n (fwid deviceID_pub aliasKey_pub: lbytes_pub 32)\n : GTot (aliasKeyTBS_t)\nlet create_aliasKeyTBS_spec\n (crt_version: x509_version_t)\n (serialNumber: x509_serialNumber_t)\n (i_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (i_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (i_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (notBefore: datatype_of_asn1_type UTC_TIME)\n (notAfter : datatype_of_asn1_type Generalized_Time)\n (s_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (s_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (s_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (ku: key_usage_payload_t)\n (keyID: lbytes_pub 20)\n (version: datatype_of_asn1_type INTEGER)\n (fwid: lbytes_pub 32)\n (deviceID_pub: lbytes_pub 32)\n (aliasKey_pub: lbytes_pub 32)\n: GTot (aliasKeyTBS_t)\n=\n(* Create AliasKeyTBS *)\n let deviceID_pub32: B32.lbytes32 32ul = B32.hide deviceID_pub in\n let fwid32 : B32.lbytes32 32ul = B32.hide fwid in\n let aliasKey_pub32: B32.lbytes32 32ul = B32.hide aliasKey_pub in\n let aliasKeyTBS = x509_get_AliasKeyTBS\n crt_version\n serialNumber\n i_common i_org i_country\n notBefore notAfter\n s_common s_org s_country\n ku\n ({ len = 20ul; s = B32.hide keyID })\n version\n fwid32\n deviceID_pub32\n aliasKey_pub32 in\n (* Prf *) lemma_serialize_aliasKeyTBS_payload_size aliasKeyTBS;\n (* Prf *) lemma_serialize_aliasKeyTBS_size_exact aliasKeyTBS;\n\n(* return *) aliasKeyTBS", "val length_of_aliasKeyCRT\n (tbs_len:\n asn1_int32\n {length_of_aliasKeyCRT_payload tbs_len <= asn1_value_length_max_of_type SEQUENCE})\n : GTot (asn1_TLV_length_of_type SEQUENCE)\nlet length_of_aliasKeyCRT\n (tbs_len: asn1_int32\n { length_of_aliasKeyCRT_payload tbs_len\n <= asn1_value_length_max_of_type SEQUENCE })\n: GTot (asn1_TLV_length_of_type SEQUENCE)\n= length_of_TLV\n (SEQUENCE)\n ((length_of_aliasKeyCRT_payload tbs_len))", "val eval_opt_aead_key (h: HS.mem) (k: opt_aead_key_t) : GTot (option (lseq uint8 aead_key_vsv))\nlet eval_opt_aead_key (h : HS.mem) (k : opt_aead_key_t) :\n GTot (option (lseq uint8 aead_key_vsv)) =\n pn_as_seq h k", "val l0_aux_post\n (cdi: B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: UInt32.t)\n (deviceID_label: B.lbuffer byte_sec (v deviceID_label_len))\n (aliasKey_label_len: UInt32.t)\n (aliasKey_label: B.lbuffer byte_sec (v aliasKey_label_len))\n (deviceIDCSR_ingredients: deviceIDCSR_ingredients_t)\n (aliasKeyCRT_ingredients: aliasKeyCRT_ingredients_t)\n (deviceID_pub aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n (h0:\n HS.mem\n { l0_pre h0 cdi fwid deviceID_label_len deviceID_label aliasKey_label_len aliasKey_label\n deviceIDCSR_ingredients aliasKeyCRT_ingredients deviceID_pub aliasKey_pub\n aliasKey_priv deviceIDCSR_len deviceIDCSR_buf aliasKeyCRT_len aliasKeyCRT_buf })\n (h1: HS.mem)\n : Type0\nlet l0_aux_post\n(* Common Inputs *)\n (cdi : B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: UInt32.t)\n (deviceID_label: B.lbuffer byte_sec (v deviceID_label_len))\n (aliasKey_label_len: UInt32.t)\n (aliasKey_label: B.lbuffer byte_sec (v aliasKey_label_len))\n(* DeviceID CSR Inputs*)\n (deviceIDCSR_ingredients:deviceIDCSR_ingredients_t)\n(* AliasKey Crt Inputs*)\n (aliasKeyCRT_ingredients:aliasKeyCRT_ingredients_t)\n(* Common Outputs *)\n (deviceID_pub: B.lbuffer byte_pub 32)\n (aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n(* DeviceID CSR Outputs *)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n(* AliasKey Crt Outputs *)\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n (h0:HS.mem{\n l0_pre h0 cdi fwid deviceID_label_len deviceID_label\n aliasKey_label_len aliasKey_label deviceIDCSR_ingredients\n aliasKeyCRT_ingredients deviceID_pub aliasKey_pub aliasKey_priv\n deviceIDCSR_len deviceIDCSR_buf\n aliasKeyCRT_len aliasKeyCRT_buf})\n (h1:HS.mem)\n : Type0\n =\n B.(modifies (loc_buffer deviceID_pub `loc_union`\n loc_buffer aliasKey_pub `loc_union`\n loc_buffer aliasKey_priv `loc_union`\n loc_buffer deviceIDCSR_buf `loc_union`\n loc_buffer aliasKeyCRT_buf) h0 h1) /\\\n\n aliasKey_post cdi (B.as_seq h0 fwid) aliasKey_label_len (B.as_seq h0 aliasKey_label) aliasKey_pub aliasKey_priv h0 h1 /\\\n\n deviceIDCSR_post cdi deviceID_label_len (B.as_seq h0 deviceID_label)\n deviceIDCSR_ingredients deviceIDCSR_len deviceIDCSR_buf h0 h1 /\\\n\n aliasKeyCRT_post cdi (B.as_seq h0 fwid) deviceID_label_len (B.as_seq h0 deviceID_label)\n aliasKeyCRT_ingredients aliasKeyCRT_len aliasKeyCRT_buf aliasKey_pub h0 h1 /\\\nTrue", "val l0\n (cdi: B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: UInt32.t{v deviceID_label_len > 0})\n (deviceID_label: B.lbuffer byte_pub (v deviceID_label_len))\n (aliasKey_label_len: UInt32.t{v aliasKey_label_len > 0})\n (aliasKey_label: B.lbuffer byte_pub (v aliasKey_label_len))\n (deviceIDCSR_ingredients: deviceIDCSR_ingredients_t)\n (aliasKeyCRT_ingredients: aliasKeyCRT_ingredients_t)\n (deviceID_pub aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n : HST.Stack unit\n (requires\n fun h ->\n l0_pre (h) (cdi) (fwid) (deviceID_label_len) (deviceID_label) (aliasKey_label_len)\n (aliasKey_label) (deviceIDCSR_ingredients) (aliasKeyCRT_ingredients) (deviceID_pub)\n (aliasKey_pub) (aliasKey_priv) (deviceIDCSR_len) (deviceIDCSR_buf) (aliasKeyCRT_len)\n (aliasKeyCRT_buf))\n (ensures\n fun h0 _ h1 ->\n l0_post (cdi) (fwid) (deviceID_label_len) (deviceID_label) (aliasKey_label_len)\n (aliasKey_label) (deviceIDCSR_ingredients) (aliasKeyCRT_ingredients) (deviceID_pub)\n (aliasKey_pub) (aliasKey_priv) (deviceIDCSR_len) (deviceIDCSR_buf) (aliasKeyCRT_len)\n (aliasKeyCRT_buf) (h0) (h1))\nlet l0\n(* Common Inputs *)\n (cdi : B.lbuffer byte_sec 32)\n (fwid:B.lbuffer byte_pub 32)\n (deviceID_label_len: UInt32.t{v deviceID_label_len > 0})\n (deviceID_label:B.lbuffer byte_pub (v deviceID_label_len))\n (aliasKey_label_len: UInt32.t{v aliasKey_label_len > 0})\n (aliasKey_label:B.lbuffer byte_pub (v aliasKey_label_len))\n(* DeviceID CSR Inputs*)\n (deviceIDCSR_ingredients:deviceIDCSR_ingredients_t)\n(* AliasKey Crt Inputs*)\n (aliasKeyCRT_ingredients:aliasKeyCRT_ingredients_t)\n(* Common Outputs *)\n (deviceID_pub: B.lbuffer byte_pub 32)\n (aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n(* DeviceID CSR Outputs *)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n(* AliasKey Crt Outputs *)\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n: HST.Stack unit\n (requires fun h ->\n l0_pre\n (h) (cdi) (fwid)\n (deviceID_label_len) (deviceID_label)\n (aliasKey_label_len) (aliasKey_label)\n (deviceIDCSR_ingredients)\n (aliasKeyCRT_ingredients)\n (deviceID_pub) (aliasKey_pub) (aliasKey_priv)\n (deviceIDCSR_len) (deviceIDCSR_buf)\n (aliasKeyCRT_len) (aliasKeyCRT_buf)\n )\n (ensures fun h0 _ h1 ->\n l0_post\n (cdi) (fwid)\n (deviceID_label_len) (deviceID_label)\n (aliasKey_label_len) (aliasKey_label)\n (deviceIDCSR_ingredients)\n (aliasKeyCRT_ingredients)\n (deviceID_pub) (aliasKey_pub) (aliasKey_priv)\n (deviceIDCSR_len) (deviceIDCSR_buf)\n (aliasKeyCRT_len) (aliasKeyCRT_buf)\n (h0) (h1)\n )\n = HST.push_frame ();\n //let fwid_sec = B.alloca (u8 0x00) 32ul in\n let dk_label = B.alloca (u8 0x00) deviceID_label_len in\n let ak_label = B.alloca (u8 0x00) aliasKey_label_len in\n //classify_public_buffer 32ul fwid fwid_sec;\n classify_public_buffer deviceID_label_len deviceID_label dk_label;\n classify_public_buffer aliasKey_label_len aliasKey_label ak_label;\n l0_aux cdi fwid deviceID_label_len dk_label aliasKey_label_len ak_label\n deviceIDCSR_ingredients aliasKeyCRT_ingredients\n deviceID_pub aliasKey_pub aliasKey_priv\n deviceIDCSR_len deviceIDCSR_buf\n aliasKeyCRT_len aliasKeyCRT_buf;\n HST.pop_frame ()", "val len_of_aliasKeyCRT\n (tbs_len:\n asn1_int32\n {length_of_aliasKeyCRT_payload tbs_len <= asn1_value_length_max_of_type SEQUENCE})\n : Tot (len: asn1_TLV_int32_of_type SEQUENCE {v len == length_of_aliasKeyCRT tbs_len})\nlet len_of_aliasKeyCRT\n (tbs_len: asn1_int32\n { length_of_aliasKeyCRT_payload tbs_len\n <= asn1_value_length_max_of_type SEQUENCE })\n: Tot (len: asn1_TLV_int32_of_type SEQUENCE\n { v len == length_of_aliasKeyCRT tbs_len })\n= len_of_TLV\n (SEQUENCE)\n (len_of_aliasKeyCRT_payload tbs_len)", "val L0.Impl.Crypto.l0_core_step1_pre = \n h: FStar.Monotonic.HyperStack.mem ->\n cdi: LowStar.Buffer.lbuffer L0.Base.byte_sec 32 ->\n fwid: LowStar.Buffer.lbuffer L0.Base.byte_pub 32 ->\n deviceID_label_len: Lib.IntTypes.size_t ->\n deviceID_label: LowStar.Buffer.lbuffer L0.Base.byte_sec (Lib.IntTypes.v deviceID_label_len) ->\n aliasKey_label_len: Lib.IntTypes.size_t ->\n aliasKey_label: LowStar.Buffer.lbuffer L0.Base.byte_sec (Lib.IntTypes.v aliasKey_label_len) ->\n deviceID_pub: LowStar.Buffer.lbuffer L0.Base.byte_pub 32 ->\n deviceID_priv: LowStar.Buffer.lbuffer L0.Base.byte_sec 32 ->\n aliasKey_pub: LowStar.Buffer.lbuffer L0.Base.byte_pub 32 ->\n aliasKey_priv: LowStar.Buffer.lbuffer L0.Base.byte_sec 32 ->\n authKeyID: LowStar.Buffer.lbuffer L0.Base.byte_pub 20\n -> Prims.logical\nlet l0_core_step1_pre\n (h: HS.mem)\n(* Inputs *)\n (cdi : B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: size_t)\n (deviceID_label: B.lbuffer byte_sec (v deviceID_label_len))\n (aliasKey_label_len: size_t)\n (aliasKey_label: B.lbuffer byte_sec (v aliasKey_label_len))\n(* Outputs *)\n (deviceID_pub : B.lbuffer byte_pub 32)\n (deviceID_priv: B.lbuffer byte_sec 32)\n (aliasKey_pub : B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer byte_sec 32)\n (authKeyID : B.lbuffer byte_pub 20)\n= B.(all_live h [buf cdi;\n buf fwid;\n buf deviceID_label;\n buf aliasKey_label;\n buf deviceID_pub;\n buf deviceID_priv;\n buf aliasKey_pub;\n buf aliasKey_priv;\n buf authKeyID]) /\\\n B.(all_disjoint [loc_buffer cdi;\n loc_buffer fwid;\n loc_buffer deviceID_label;\n loc_buffer aliasKey_label;\n loc_buffer deviceID_pub;\n loc_buffer deviceID_priv;\n loc_buffer aliasKey_pub;\n loc_buffer aliasKey_priv;\n loc_buffer authKeyID]) /\\\n valid_hkdf_lbl_len deviceID_label_len /\\\n valid_hkdf_lbl_len aliasKey_label_len", "val dump_l0\n (deviceID_pub aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer byte_sec 32)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n : HST.Stack unit\n (requires\n fun h ->\n B.all_live h\n [\n B.buf deviceID_pub;\n B.buf aliasKey_pub;\n B.buf aliasKey_priv;\n B.buf deviceIDCSR_buf;\n B.buf aliasKeyCRT_buf\n ])\n (ensures fun h0 _ h1 -> B.modifies B.loc_none h0 h1)\nlet dump_l0\n (deviceID_pub : B.lbuffer byte_pub 32)\n (aliasKey_pub : B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer byte_sec 32)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n: HST.Stack unit\n (requires fun h ->\n B.all_live h [B.buf deviceID_pub; B.buf aliasKey_pub; B.buf aliasKey_priv; B.buf deviceIDCSR_buf; B.buf aliasKeyCRT_buf])\n (ensures fun h0 _ h1 ->\n B.modifies B.loc_none h0 h1)\n= HST.push_frame ();\n let aliasKey_priv_pub: B.lbuffer byte_pub 32 = B.alloca 0x00uy 32ul in\n declassify_secret_buffer 32ul aliasKey_priv aliasKey_priv_pub;\n\n write_out \"DeviceIDPublicKey.hex\" aliasKey_pub 32ul;\n write_out \"AliasKeyPublicKey.hex\" aliasKey_pub 32ul;\n write_out \"AliasKeyPrivateKey.hex\" aliasKey_priv_pub 32ul;\n write_out \"DeviceIDCSR.hex\" deviceIDCSR_buf deviceIDCSR_len;\n write_out \"AliasKeyCrt.hex\" aliasKeyCRT_buf aliasKeyCRT_len;\n HST.pop_frame ()", "val create_aliasKeyTBS_buffers_to_bytes\n (fwid: B.lbuffer byte_pub 32)\n (keyID: B.lbuffer byte_pub 20)\n (deviceID_pub aliasKey_pub: B.lbuffer byte_pub 32)\n : HST.Stack aliasKeyTBS_bytes\n (requires\n fun h ->\n B.(all_live h [buf fwid; buf deviceID_pub; buf aliasKey_pub; buf keyID]) /\\\n B.(all_disjoint [\n loc_buffer fwid;\n loc_buffer deviceID_pub;\n loc_buffer aliasKey_pub;\n loc_buffer keyID\n ]))\n (ensures\n fun h0 r h1 ->\n B.(modifies loc_none h0 h1) /\\\n (B32.hide (B.as_seq h0 fwid) == r.fwid_pub32 /\\\n B32.hide (B.as_seq h0 deviceID_pub) == r.deviceID_pub32 /\\\n B32.hide (B.as_seq h0 aliasKey_pub) == r.aliasKey_pub32 /\\\n B32.hide (B.as_seq h0 keyID) == r.keyID_pub32))\nlet create_aliasKeyTBS_buffers_to_bytes\n (fwid: B.lbuffer byte_pub 32)\n (keyID: B.lbuffer byte_pub 20)\n (deviceID_pub: B.lbuffer byte_pub 32)\n (aliasKey_pub: B.lbuffer byte_pub 32)\n : HST.Stack aliasKeyTBS_bytes\n (requires fun h ->\n B.(all_live h [buf fwid;\n buf deviceID_pub;\n buf aliasKey_pub;\n buf keyID]) /\\\n B.(all_disjoint [loc_buffer fwid;\n loc_buffer deviceID_pub;\n loc_buffer aliasKey_pub;\n loc_buffer keyID]))\n (ensures fun h0 r h1 ->\n B.(modifies loc_none h0 h1) /\\\n (B32.hide (B.as_seq h0 fwid) == r.fwid_pub32 /\\\n B32.hide (B.as_seq h0 deviceID_pub) == r.deviceID_pub32 /\\\n B32.hide (B.as_seq h0 aliasKey_pub) == r.aliasKey_pub32 /\\\n B32.hide (B.as_seq h0 keyID) == r.keyID_pub32))\n = HST.push_frame ();\n let fwid_pub32 : B32.lbytes32 32ul = B32.of_buffer 32ul fwid in\n let deviceID_pub32: B32.lbytes32 32ul = B32.of_buffer 32ul deviceID_pub in\n let aliasKey_pub32: B32.lbytes32 32ul = B32.of_buffer 32ul aliasKey_pub in\n let keyID_pub32 = B32.of_buffer 20ul keyID in\n HST.pop_frame ();\n { fwid_pub32 = fwid_pub32;\n keyID_pub32 = keyID_pub32;\n deviceID_pub32 = deviceID_pub32;\n aliasKey_pub32 = aliasKey_pub32 }", "val emit1_spec\n (#a: sha2_alg)\n (#m: m_spec{lanes a m == 1})\n (hseq: LSeq.lseq uint8 (lanes a m * 8 * word_length a))\n : multiseq (lanes a m) (hash_length a)\nlet emit1_spec (#a:sha2_alg) (#m:m_spec{lanes a m == 1}) (hseq:LSeq.lseq uint8 (lanes a m * 8 * word_length a)) :\n multiseq (lanes a m) (hash_length a)\n =\n let hsub = LSeq.sub hseq 0 (hash_length a) in\n ntup1 hsub", "val l0_post\n (cdi: B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: UInt32.t)\n (deviceID_label: B.lbuffer byte_pub (v deviceID_label_len))\n (aliasKey_label_len: UInt32.t)\n (aliasKey_label: B.lbuffer byte_pub (v aliasKey_label_len))\n (deviceIDCSR_ingredients: deviceIDCSR_ingredients_t)\n (aliasKeyCRT_ingredients: aliasKeyCRT_ingredients_t)\n (deviceID_pub aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n (h0:\n HS.mem\n { l0_pre h0 cdi fwid deviceID_label_len deviceID_label aliasKey_label_len aliasKey_label\n deviceIDCSR_ingredients aliasKeyCRT_ingredients deviceID_pub aliasKey_pub\n aliasKey_priv deviceIDCSR_len deviceIDCSR_buf aliasKeyCRT_len aliasKeyCRT_buf })\n (h1: HS.mem)\n : Type0\nlet l0_post\n(* Common Inputs *)\n (cdi : B.lbuffer byte_sec 32)\n (fwid:B.lbuffer byte_pub 32)\n (deviceID_label_len: UInt32.t)\n (deviceID_label:B.lbuffer byte_pub (v deviceID_label_len))\n (aliasKey_label_len: UInt32.t)\n (aliasKey_label:B.lbuffer byte_pub (v aliasKey_label_len))\n(* DeviceID CSR Inputs*)\n (deviceIDCSR_ingredients:deviceIDCSR_ingredients_t)\n(* AliasKey Crt Inputs*)\n (aliasKeyCRT_ingredients:aliasKeyCRT_ingredients_t)\n(* Common Outputs *)\n (deviceID_pub: B.lbuffer byte_pub 32)\n (aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer uint8 32)\n(* DeviceID CSR Outputs *)\n (deviceIDCSR_len: UInt32.t)\n (deviceIDCSR_buf: B.lbuffer byte_pub (v deviceIDCSR_len))\n(* AliasKey Crt Outputs *)\n (aliasKeyCRT_len: UInt32.t)\n (aliasKeyCRT_buf: B.lbuffer byte_pub (v aliasKeyCRT_len))\n (h0:HS.mem{\n l0_pre h0 cdi fwid deviceID_label_len deviceID_label\n aliasKey_label_len aliasKey_label deviceIDCSR_ingredients\n aliasKeyCRT_ingredients deviceID_pub aliasKey_pub aliasKey_priv\n deviceIDCSR_len deviceIDCSR_buf\n aliasKeyCRT_len aliasKeyCRT_buf})\n (h1:HS.mem)\n : Type0\n =\n B.(modifies (loc_buffer deviceID_pub `loc_union`\n loc_buffer aliasKey_pub `loc_union`\n loc_buffer aliasKey_priv `loc_union`\n loc_buffer deviceIDCSR_buf `loc_union`\n loc_buffer aliasKeyCRT_buf) h0 h1) /\\\n\n aliasKey_post cdi\n (B.as_seq h0 fwid)\n aliasKey_label_len\n (L0.Declassify.classify_public_bytes (B.as_seq h0 aliasKey_label))\n aliasKey_pub aliasKey_priv h0 h1 /\\\n\n deviceIDCSR_post cdi deviceID_label_len\n (L0.Declassify.classify_public_bytes (B.as_seq h0 deviceID_label))\n deviceIDCSR_ingredients deviceIDCSR_len deviceIDCSR_buf h0 h1 /\\\n\n aliasKeyCRT_post cdi\n (B.as_seq h0 fwid)\n deviceID_label_len\n (L0.Declassify.classify_public_bytes (B.as_seq h0 deviceID_label))\n aliasKeyCRT_ingredients aliasKeyCRT_len aliasKeyCRT_buf aliasKey_pub h0 h1 /\\\nTrue", "val emit (a: sha2_alg) (h: lseq uint8 (8 * word_length a)) : Tot (lseq uint8 (hash_length a))\nlet emit (a:sha2_alg) (h:lseq uint8 (8 * word_length a)) : Tot (lseq uint8 (hash_length a)) =\n sub h 0 (hash_length a)", "val refl (a: LSeq.lseq uint64 20 {F51.linv a}) : GTot a_spec\nlet refl (a:LSeq.lseq uint64 20{F51.linv a}) : GTot a_spec =\n S.to_aff_point (F51.refl_ext_point a)", "val create_aliasKeyTBS_pre\n (h: HS.mem)\n (crt_version: x509_version_t)\n (serialNumber: x509_serialNumber_t)\n (i_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (i_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (i_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (notBefore: datatype_of_asn1_type UTC_TIME)\n (notAfter: datatype_of_asn1_type Generalized_Time)\n (s_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (s_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (s_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (fwid: B.lbuffer byte_pub 32)\n (ku: key_usage_payload_t)\n (keyID: B.lbuffer byte_pub 20)\n (l0_version: datatype_of_asn1_type INTEGER)\n (deviceID_pub aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKeyTBS_len: UInt32.t)\n (aliasKeyTBS_buf: B.lbuffer byte_pub (UInt32.v aliasKeyTBS_len))\n : Type0\nlet create_aliasKeyTBS_pre\n (h: HS.mem)\n (crt_version: x509_version_t)\n (serialNumber: x509_serialNumber_t)\n (i_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (i_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (i_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (notBefore: datatype_of_asn1_type UTC_TIME)\n (notAfter : datatype_of_asn1_type Generalized_Time)\n (s_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (s_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (s_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (fwid: B.lbuffer byte_pub 32)\n (ku: key_usage_payload_t)\n (keyID: B.lbuffer byte_pub 20)\n (l0_version: datatype_of_asn1_type INTEGER)\n (deviceID_pub: B.lbuffer byte_pub 32)\n (aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKeyTBS_len: UInt32.t)\n (aliasKeyTBS_buf: B.lbuffer byte_pub (UInt32.v aliasKeyTBS_len)) : Type0\n= // let keyID_string = sha1_digest_to_octet_string_spec (B.as_seq h keyID) in\n B.(all_live h [buf fwid;\n buf deviceID_pub;\n buf aliasKey_pub;\n buf keyID;\n buf aliasKeyTBS_buf]) /\\\n B.(all_disjoint [loc_buffer fwid;\n loc_buffer deviceID_pub;\n loc_buffer aliasKey_pub;\n loc_buffer keyID;\n loc_buffer aliasKeyTBS_buf]) /\\\n eq2 #nat (UInt32.v aliasKeyTBS_len) (v (len_of_aliasKeyTBS\n serialNumber\n i_common i_org i_country\n s_common s_org s_country\n l0_version))", "val derive_secret:\n a: ha ->\n prk:HD.bytes_hash a ->\n label: bytes ->\n len: nat ->\n Pure (Seq.seq Secret.uint8)\n (requires len <= 255 /\\\n Seq.length label <= 244 /\\\n keysized a (Seq.length prk)\n )\n (ensures fun out ->\n Seq.length out == len\n )\nlet derive_secret a prk label len =\n let open Seq in\n let z = Seq.create 1 0uy in\n let lb = Seq.create 1 (U8.uint_to_t len) in // len <= 255\n let llen = Seq.create 1 (U8.uint_to_t (11 + Seq.length label)) in\n let info = z @| lb @| llen @| prefix @| label @| z in\n lemma_hash_lengths a;\n assert_norm(452 < pow2 61);\n HKDF.expand a prk (Seq.seq_hide info) len", "val derive_key_pair\n (public_key: B.lbuffer pub_uint8 32)\n (private_key: B.lbuffer uint8 32)\n (ikm_len: size_t)\n (ikm: B.buffer uint8 {B.length ikm == v ikm_len})\n (lbl_len: size_t)\n (lbl: B.buffer uint8 {B.length lbl == v lbl_len})\n : HST.Stack unit\n (requires\n fun h ->\n let alg = SHA2_256 in\n B.live h ikm /\\ B.live h lbl /\\ B.live h public_key /\\ B.live h private_key /\\\n B.all_disjoint [\n B.loc_buffer ikm;\n B.loc_buffer lbl;\n B.loc_buffer public_key;\n B.loc_buffer private_key\n ] /\\ v ikm_len + block_length alg < pow2 32 /\\\n v ikm_len + block_length alg <= Some?.v (max_input_length alg) /\\\n hash_length alg + v lbl_len + 1 + block_length alg < pow2 32 /\\\n hash_length alg + v lbl_len + 1 + block_length alg < Some?.v (max_input_length alg))\n (ensures\n fun h0 _ h1 ->\n let alg = SHA2_256 in\n B.(modifies ((loc_buffer public_key) `loc_union` (loc_buffer private_key)) h0 h1) /\\\n (let pub_seq, priv_seq =\n derive_key_pair_spec ikm_len (B.as_seq h0 ikm) lbl_len (B.as_seq h0 lbl)\n in\n B.as_seq h1 public_key == pub_seq /\\ B.as_seq h1 private_key == priv_seq))\nlet derive_key_pair\n (public_key : B.lbuffer pub_uint8 32) // Out\n (private_key: B.lbuffer uint8 32) // Out\n (* NOTE Not using lbuffer here because lbuffer doesn't accept ASN1_NULL *)\n (ikm_len: size_t) (ikm: B.buffer uint8 {B.length ikm == v ikm_len}) // In: Initial Data for derivation\n (lbl_len: size_t) (lbl: B.buffer uint8 {B.length lbl == v lbl_len}) // In: Label for derivation\n: HST.Stack unit\n (requires fun h -> let alg = SHA2_256 in\n (* Separation Logic Properties *)\n B.live h ikm /\\ B.live h lbl /\\ B.live h public_key /\\ B.live h private_key /\\\n B.all_disjoint [B.loc_buffer ikm;\n B.loc_buffer lbl;\n B.loc_buffer public_key;\n B.loc_buffer private_key] /\\\n\n (* for Hacl.HKDF.extract_st *)\n v ikm_len + block_length alg < pow2 32 /\\\n (* for Spec.Agile.HKDF.extract *)\n v ikm_len + block_length alg <= Some?.v (max_input_length alg) /\\\n (* for Hacl.HKDF.expand_st *)\n hash_length alg + v lbl_len + 1 + block_length alg < pow2 32 /\\\n (* for Spec.Aigle.HKDF.expand *)\n hash_length alg + v lbl_len + 1 + block_length alg < Some?.v (max_input_length alg))\n (ensures fun h0 _ h1 -> let alg = SHA2_256 in\n B.(modifies ((loc_buffer public_key) `loc_union` (loc_buffer private_key)) h0 h1) /\\\n (let pub_seq, priv_seq = derive_key_pair_spec ikm_len (B.as_seq h0 ikm) lbl_len (B.as_seq h0 lbl) in\n B.as_seq h1 public_key == pub_seq /\\ B.as_seq h1 private_key == priv_seq ))\n= HST.push_frame ();\n\n (* NOTE: Using SHA2_256 because Curve25519/Ed25519 requires a 32-bit private key *)\n [@inline_let] //AR: 06/11: blocking some reductions\n let alg = SHA2_256 in\n\n (* Using an empty (0x00) buffer of hashLen as salt. *)\n let salt: b:B.lbuffer uint8 32 {Spec.Agile.HMAC.keysized alg (B.length b)} = B.alloca (u8 0x00) (hash_len alg) in\n\n (* Derive private key from `ikm` and `lbl` using HKDF *)\n (* Step 1. extract a `prk` (Pseudo Random Key) from an empty `salt` of `hashLen` and `ikm` *)\n let prk : b:B.lbuffer uint8 32 {B.length b == hash_length alg} = B.alloca (u8 0x00) (hash_len alg) in\n HKDF.extract_sha2_256\n prk // out: Pseudo Random Key\n salt (hash_len alg) // in : (optional) Salt\n ikm ikm_len; // in : Input Keying Material\n\n (* Step 2. expand `prk` and `lbl` to a `okm` (Output Keying Material) *)\n (**)assert_norm (Spec.Agile.HMAC.keysized alg (hash_length alg));\n HKDF.expand_sha2_256\n private_key // out: Output Keying Material\n prk (hash_len alg) // in : Pseudo Random Key\n lbl lbl_len // in : (optional) Info\n (hash_len alg); // in : okm len\n\n (* Derive public key from private key using Ed25519 (FIXME: Or Curve25519?) *)\n let secret_public_key: B.lbuffer uint8 32 = B.alloca (u8 0) 32ul in\n Ed25519.secret_to_public\n secret_public_key // out: public\n private_key; // in : secret\n\n declassify_secret_buffer\n (* len *) 32ul\n (* src *) secret_public_key\n (* dst *) public_key;\n HST.pop_frame ()", "val s_v (#a: alg) (#m: m_spec) (h: HS.mem) (s: s a m) : GTot (t a)\nlet s_v (#a : alg) (#m : m_spec) (h : HS.mem) (s : s a m) : GTot (t a) =\n state_v h s", "val header_decrypt_aux_ct_secret_preserving_not_retry_spec\n (a: ea)\n (hpk: SCipher.key (SAEAD.cipher_alg_of_supported_alg a))\n (cid_len: nat{cid_len <= 20})\n (packet:\n Seq.seq Secret.uint8\n { let l = Seq.length packet in\n 0 < l /\\ l < pow2 32 })\n (is_short:\n bool\n { let i = Secret.v #Secret.U8 (Seq.index packet 0) in\n (is_short == true <==> BF.get_bitfield #8 i 7 8 == 0) /\\\n (~(not is_short && BF.get_bitfield #8 i 4 6 = 3)) })\n (pn_offset:\n nat\n { match Parse.putative_pn_offset cid_len (Seq.seq_reveal packet) with\n | None -> False\n | Some pn_offset' -> pn_offset == pn_offset' /\\ pn_offset + 20 <= Seq.length packet })\n : GTot (Spec.header_decrypt_aux_t)\nlet header_decrypt_aux_ct_secret_preserving_not_retry_spec\n (a:ea)\n (hpk: SCipher.key (SAEAD.cipher_alg_of_supported_alg a))\n (cid_len: nat { cid_len <= 20 })\n (packet: Seq.seq Secret.uint8 { \n let l = Seq.length packet in\n 0 < l /\\ l < pow2 32\n })\n (is_short: bool {\n let i = Secret.v #Secret.U8 (Seq.index packet 0) in\n (is_short == true <==> BF.get_bitfield #8 i 7 8 == 0) /\\\n (~ (not is_short && BF.get_bitfield #8 i 4 6 = 3))\n })\n (pn_offset: nat {\n match Parse.putative_pn_offset cid_len (Seq.seq_reveal packet) with\n | None -> False\n | Some pn_offset' ->\n pn_offset == pn_offset' /\\\n pn_offset + 20 <= Seq.length packet\n })\n : GTot (Spec.header_decrypt_aux_t)\n=\n let f = Seq.index packet 0 in\n let sample_offset = pn_offset + 4 in\n let sample = Seq.slice packet sample_offset (sample_offset+16) in\n let mask = Spec.block_of_sample (SAEAD.cipher_alg_of_supported_alg a) hpk sample in\n (* mask the least significant bits of the first byte *)\n let protected_bits = if is_short then 5ul else 4ul in\n let f' = Secret.set_bitfield f 0ul protected_bits (Secret.get_bitfield (f `Secret.logxor` (Seq.index mask 0)) 0ul protected_bits) in\n let packet' = Seq.cons f' (Seq.slice packet 1 (Seq.length packet)) in\n (* now the packet number length is available, so mask the packet number *)\n let pn_len = Secret.get_bitfield f' 0ul 2ul in\n let pnmask = Lemmas.secret_and_inplace (Seq.slice mask 1 5) (Seq.seq_hide #Secret.U8 (pn_sizemask_ct (Secret.v pn_len))) 0 in\n let packet'' = Lemmas.secret_xor_inplace packet' pnmask pn_offset in\n {\n Spec.is_short = is_short;\n Spec.is_retry = false;\n Spec.packet = Seq.seq_reveal #Secret.U8 packet'';\n Spec.pn_offset = pn_offset;\n Spec.pn_len = Secret.v pn_len;\n }", "val derive_k (i: index) (s: state i) (h: HS.mem) : GTot (Seq.seq Secret.uint8)\nlet derive_k\n (i: index)\n (s: state i)\n (h: HS.mem)\n: GTot (Seq.seq Secret.uint8)\n=\n let s0 = g_traffic_secret (B.deref h s) in\n Spec.derive_secret i.hash_alg s0 Spec.label_key (Spec.Agile.AEAD.key_length i.aead_alg)", "val keysized (a: H.alg) (l: UInt32.t) : Tot (b: bool{b ==> Spec.Agile.HMAC.keysized a (UInt32.v l)})\nlet keysized (a:H.alg) (l: UInt32.t): Tot (b:bool{b ==> Spec.Agile.HMAC.keysized a (UInt32.v l) }) =\n EverCrypt.Hash.uint32_fits_maxLength a l;\n assert (v l `Spec.Hash.Definitions.less_than_max_input_length` a);\n assert_norm (v 0xfffffffful = pow2 32 - 1);\n l <= 0xfffffffful - Hacl.Hash.Definitions.block_len a", "val L0.Impl.Crypto.l0_core_step1_post = \n h0: FStar.Monotonic.HyperStack.mem ->\n h1: FStar.Monotonic.HyperStack.mem ->\n cdi: LowStar.Buffer.lbuffer L0.Base.byte_sec 32 ->\n fwid: LowStar.Buffer.lbuffer L0.Base.byte_pub 32 ->\n deviceID_label_len: Lib.IntTypes.size_t ->\n deviceID_label: LowStar.Buffer.lbuffer L0.Base.byte_sec (Lib.IntTypes.v deviceID_label_len) ->\n aliasKey_label_len: Lib.IntTypes.size_t ->\n aliasKey_label: LowStar.Buffer.lbuffer L0.Base.byte_sec (Lib.IntTypes.v aliasKey_label_len) ->\n deviceID_pub: LowStar.Buffer.lbuffer L0.Base.byte_pub 32 ->\n deviceID_priv: LowStar.Buffer.lbuffer L0.Base.byte_sec 32 ->\n aliasKey_pub: LowStar.Buffer.lbuffer L0.Base.byte_pub 32 ->\n aliasKey_priv: LowStar.Buffer.lbuffer L0.Base.byte_sec 32 ->\n authKeyID:\n LowStar.Buffer.lbuffer L0.Base.byte_pub 20\n { L0.Impl.Crypto.l0_core_step1_pre h0 cdi fwid deviceID_label_len deviceID_label\n aliasKey_label_len aliasKey_label deviceID_pub deviceID_priv aliasKey_pub aliasKey_priv\n authKeyID }\n -> Prims.logical\nlet l0_core_step1_post\n (h0: HS.mem) (h1: HS.mem)\n(* Inputs *)\n (cdi : B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: size_t)\n (deviceID_label: B.lbuffer byte_sec (v deviceID_label_len))\n (aliasKey_label_len: size_t)\n (aliasKey_label: B.lbuffer byte_sec (v aliasKey_label_len))\n(* Outputs *)\n (deviceID_pub : B.lbuffer byte_pub 32)\n (deviceID_priv: B.lbuffer byte_sec 32)\n (aliasKey_pub : B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer byte_sec 32)\n (authKeyID : B.lbuffer byte_pub 20\n { l0_core_step1_pre (h0)\n (cdi) (fwid)\n (deviceID_label_len) (deviceID_label)\n (aliasKey_label_len) (aliasKey_label)\n (deviceID_pub) (deviceID_priv)\n (aliasKey_pub) (aliasKey_priv)\n (authKeyID) })\n=\n // let deviceID_pub_seq, deviceID_priv_seq = derive_DeviceID_spec\n // (B.as_seq h0 cdi)\n // (deviceID_label_len)\n // (B.as_seq h0 deviceID_label) in\n // let deviceID_pub_sec_seq = classify_public_bytes (B.as_seq h1 deviceID_pub) in\n (B.modifies (B.loc_buffer deviceID_pub `B.loc_union`\n B.loc_buffer deviceID_priv `B.loc_union`\n B.loc_buffer aliasKey_pub `B.loc_union`\n B.loc_buffer aliasKey_priv `B.loc_union`\n B.loc_buffer authKeyID) h0 h1) /\\\n ((B.as_seq h1 deviceID_pub <: lbytes_pub 32),\n (B.as_seq h1 deviceID_priv <: lbytes_sec 32)) == derive_DeviceID_spec\n (B.as_seq h0 cdi)\n (deviceID_label_len)\n (B.as_seq h0 deviceID_label) /\\\n ((B.as_seq h1 aliasKey_pub <: lbytes_pub 32),\n (B.as_seq h1 aliasKey_priv <: lbytes_sec 32)) == derive_AliasKey_spec\n (B.as_seq h0 cdi)\n (B.as_seq h0 fwid)\n (aliasKey_label_len)\n (B.as_seq h0 aliasKey_label) /\\\n (B.as_seq h1 authKeyID == derive_authKeyID_spec (classify_public_bytes (B.as_seq h1 deviceID_pub)))", "val Spec.Agile.HKDF.a_spec = a: Spec.Hash.Definitions.fixed_len_alg -> i: FStar.Integers.nat -> Type0\nlet a_spec (a:fixed_len_alg) (i:nat) =\n Seq.lseq uint8 (if i = 0 then 0 else hash_length a)", "val Spec.Agile.HMAC.keysized = a: Spec.Hash.Definitions.hash_alg -> l: Prims.nat -> Prims.logical\nlet keysized (a:hash_alg) (l:nat) =\n l `less_than_max_input_length` a /\\\n l + block_length a < pow2 32", "val expand_spec:\n #ha:Hashing.alg ->\n prk: Hashing.Spec.tag ha ->\n info: bytes {Bytes.length info < 1024 (* somewhat arbitrary *) } ->\n len: UInt32.t {0 < v len /\\ v len <= op_Multiply 255 (hash_length ha)} ->\n GTot (lbytes32 len)\nlet expand_spec = expand_spec'", "val aliaskey_len_is_valid (len:US.t)\n : valid_hkdf_lbl_len len\nlet aliaskey_len_is_valid = aliaskey_len_is_valid_aux", "val clamp: alg:algorithm{alg = DH_Curve25519} -> scalar alg -> Tot (scalar alg)\nlet clamp a k =\n match a with\n | DH.DH_Curve25519 -> Spec.Curve25519.decodeScalar k", "val iv: #a:alg -> state_s a -> GTot (Spec.nonce a)\nlet iv #a (s: state_s a) =\n let State _ g_iv _ _ _ _ _ = s in\n G.reveal g_iv", "val derive_authKeyID_spec (deviceIDPub: lbytes_sec 32) : GTot (lbytes_pub 20)\nlet derive_authKeyID_spec\n (deviceIDPub: lbytes_sec 32)\n: GTot (lbytes_pub 20)\n= assert_norm (Seq.length deviceIDPub <= Some?.v (max_input_length Spec.Agile.Hash.SHA1));\n declassify_secret_bytes\n (Spec.Agile.Hash.hash\n Spec.Agile.Hash.SHA1\n deviceIDPub)", "val sealAuth:\n cs:ciphersuite_not_export_only\n -> skE:key_dh_secret_s cs\n -> pkR:DH.serialized_point (kem_dh_of_cs cs)\n -> info:info_s cs\n -> aad:AEAD.ad (aead_alg_of cs)\n -> pt:AEAD.plain (aead_alg_of cs)\n -> skS:key_dh_secret_s cs ->\n Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt))\nlet sealAuth cs skE pkR info aad pt skS =\n match setupAuthS cs skE pkR info skS with\n | None -> None\n | Some (enc, ctx) ->\n match context_seal cs ctx aad pt with\n | None -> None\n | Some (_, ct) -> Some (enc, ct)", "val len_of_aliasKeyCRT_payload\n (tbs_len:\n asn1_int32\n {length_of_aliasKeyCRT_payload tbs_len <= asn1_value_length_max_of_type SEQUENCE})\n : Tot (len: asn1_TLV_int32_of_type SEQUENCE {v len == length_of_aliasKeyCRT_payload tbs_len})\nlet len_of_aliasKeyCRT_payload\n (tbs_len: asn1_int32\n { length_of_aliasKeyCRT_payload tbs_len\n <= asn1_value_length_max_of_type SEQUENCE })\n: Tot (len: asn1_TLV_int32_of_type SEQUENCE\n { v len == length_of_aliasKeyCRT_payload tbs_len })\n= tbs_len + 74ul", "val create_aliasKeyTBS_post\n (h0: HS.mem)\n (r: unit)\n (h1: HS.mem)\n (crt_version: x509_version_t)\n (serialNumber: x509_serialNumber_t)\n (i_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (i_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (i_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (notBefore: datatype_of_asn1_type UTC_TIME)\n (notAfter: datatype_of_asn1_type Generalized_Time)\n (s_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (s_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (s_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (fwid: B.lbuffer byte_pub 32)\n (ku: key_usage_payload_t)\n (keyID: B.lbuffer byte_pub 20)\n (l0_version: datatype_of_asn1_type INTEGER)\n (deviceID_pub aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKeyTBS_len: UInt32.t)\n (aliasKeyTBS_buf:\n B.lbuffer byte_pub (UInt32.v aliasKeyTBS_len)\n { create_aliasKeyTBS_pre (h0) (crt_version) (serialNumber) (i_common) (i_org)\n (i_country) (notBefore) (notAfter) (s_common) (s_org) (s_country) (fwid) (ku)\n (keyID) (l0_version) (deviceID_pub) (aliasKey_pub) (aliasKeyTBS_len)\n (aliasKeyTBS_buf) })\n : Type0\nlet create_aliasKeyTBS_post\n (h0: HS.mem)\n (r: unit)\n (h1: HS.mem)\n (crt_version: x509_version_t)\n (serialNumber: x509_serialNumber_t)\n (i_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (i_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (i_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (notBefore: datatype_of_asn1_type UTC_TIME)\n (notAfter : datatype_of_asn1_type Generalized_Time)\n (s_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (s_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (s_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (fwid: B.lbuffer byte_pub 32)\n (ku: key_usage_payload_t)\n (keyID: B.lbuffer byte_pub 20)\n (l0_version: datatype_of_asn1_type INTEGER)\n (deviceID_pub: B.lbuffer byte_pub 32)\n (aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKeyTBS_len: UInt32.t)\n (aliasKeyTBS_buf: B.lbuffer byte_pub (UInt32.v aliasKeyTBS_len)\n { create_aliasKeyTBS_pre\n (h0)\n (crt_version)\n (serialNumber)\n (i_common) (i_org) (i_country)\n (notBefore) (notAfter)\n (s_common) (s_org) (s_country)\n (fwid)\n (ku)\n (keyID)\n (l0_version)\n (deviceID_pub)\n (aliasKey_pub)\n (aliasKeyTBS_len) (aliasKeyTBS_buf) })\n: Type0\n= let aliasKeyTBS = create_aliasKeyTBS_spec\n (crt_version)\n (serialNumber)\n (i_common) (i_org) (i_country)\n (notBefore) (notAfter)\n (s_common) (s_org) (s_country)\n (ku)\n (B.as_seq h0 keyID)\n (l0_version)\n (B.as_seq h0 fwid)\n (B.as_seq h0 deviceID_pub)\n (B.as_seq h0 aliasKey_pub) in\n (* Prf *) lemma_serialize_aliasKeyTBS_size_exact aliasKeyTBS;\n B.(modifies (loc_buffer aliasKeyTBS_buf) h0 h1) /\\\n B.as_seq h1 aliasKeyTBS_buf == serialize_aliasKeyTBS `serialize` aliasKeyTBS", "val eval_cipher_state_mf\n (h: HS.mem)\n (st_k: opt_aead_key_t)\n (has_key: bool{has_key ==> (not (g_is_null st_k))})\n (n: nat)\n : GTot (cipher_state)\nlet eval_cipher_state_mf (h : HS.mem) (st_k : opt_aead_key_t)\n (has_key : bool{has_key ==> (not (g_is_null st_k))})\n (n : nat) :\n GTot (cipher_state) =\n let k_v = if has_key then Some (nn_as_seq h st_k) else None in\n { k = k_v; n = n; }", "val derive_key_pair:\n cs:ciphersuite\n -> ikm:dkp_ikm_s cs ->\n Tot (option (key_dh_secret_s cs & key_dh_public_s cs))\nlet derive_key_pair cs ikm =\n match kem_dh_of_cs cs with\n | DH.DH_Curve25519 -> begin\n let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in\n let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in\n match DH.secret_to_public (kem_dh_of_cs cs) sk with\n | Some pk -> Some (sk, serialize_public_key cs pk)\n end\n | DH.DH_P256 ->\n let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in\n dkp_nist_p cs dkp_prk (u8 0)", "val L0.X509.AliasKeyTBS.len_of_aliasKeyTBS_max = _: Prims.unit\n -> Prims.GTot\n (out:\n (n:\n (n:\n FStar.UInt32.t{Prims.op_Negation (FStar.UInt32.v n < 0 || 4294967295 < FStar.UInt32.v n)})\n {Prims.op_Negation (FStar.UInt32.v n < 2 || 4294967295 < FStar.UInt32.v n)})\n { FStar.UInt32.v out ==\n 1 +\n (match\n FStar.UInt32.lt (FStar.UInt32.uint_to_t (FStar.UInt32.v (L0.X509.AliasKeyTBS.len_of_aliasKeyTBS_payload_max\n ())))\n (128ul <: FStar.UInt32.t)\n with\n | true -> 1\n | _ ->\n (match\n FStar.UInt32.lt (FStar.UInt32.uint_to_t (FStar.UInt32.v (L0.X509.AliasKeyTBS.len_of_aliasKeyTBS_payload_max\n ())))\n (256ul <: FStar.UInt32.t)\n with\n | true -> 2\n | _ ->\n (match\n FStar.UInt32.lt (FStar.UInt32.uint_to_t (FStar.UInt32.v (L0.X509.AliasKeyTBS.len_of_aliasKeyTBS_payload_max\n ())))\n (65536ul <: FStar.UInt32.t)\n with\n | true -> 3\n | _ ->\n (match\n FStar.UInt32.lt (FStar.UInt32.uint_to_t (FStar.UInt32.v (L0.X509.AliasKeyTBS.len_of_aliasKeyTBS_payload_max\n ())))\n (16777216ul <: FStar.UInt32.t)\n with\n | true -> 4\n | _ -> 5)\n <:\n length:\n (i:\n FStar.Integers.int_t (FStar.Integers.Signed FStar.Integers.Winfinite)\n {i >= 0})\n { length ==\n FStar.Seq.Base.length (LowParse.Spec.Base.serialize ASN1.Spec.Length.serialize_asn1_length\n (FStar.UInt32.uint_to_t (FStar.UInt32.v (L0.X509.AliasKeyTBS.len_of_aliasKeyTBS_payload_max\n ())))) /\\ length <= 5 })\n <:\n length:\n (i: FStar.Integers.int_t (FStar.Integers.Signed FStar.Integers.Winfinite) {i >= 0}\n )\n { length ==\n FStar.Seq.Base.length (LowParse.Spec.Base.serialize ASN1.Spec.Length.serialize_asn1_length\n (FStar.UInt32.uint_to_t (FStar.UInt32.v (L0.X509.AliasKeyTBS.len_of_aliasKeyTBS_payload_max\n ())))) /\\ length <= 5 })\n <:\n length:\n (i: FStar.Integers.int_t (FStar.Integers.Signed FStar.Integers.Winfinite) {i >= 0})\n { length ==\n FStar.Seq.Base.length (LowParse.Spec.Base.serialize ASN1.Spec.Length.serialize_asn1_length\n (FStar.UInt32.uint_to_t (FStar.UInt32.v (L0.X509.AliasKeyTBS.len_of_aliasKeyTBS_payload_max\n ())))) /\\ length <= 5 }) +\n FStar.UInt32.v (L0.X509.AliasKeyTBS.len_of_aliasKeyTBS_payload_max ()) })\nlet len_of_aliasKeyTBS_max ()\n= SEQUENCE `len_of_TLV`\n (**) (len_of_aliasKeyTBS_payload_max ())", "val emit8_spec\n (#a: sha2_alg)\n (#m: m_spec{lanes a m == 8})\n (hseq: LSeq.lseq uint8 (lanes a m * 8 * word_length a))\n : multiseq (lanes a m) (hash_length a)\nlet emit8_spec (#a:sha2_alg) (#m:m_spec{lanes a m == 8}) (hseq:LSeq.lseq uint8 (lanes a m * 8 * word_length a)) :\n multiseq (lanes a m) (hash_length a)\n =\n let open Lib.Sequence in\n let h0 = sub hseq 0 (hash_length a) in\n let h1 = sub hseq (8 * word_length a) (hash_length a) in\n let h2 = sub hseq (16 * word_length a) (hash_length a) in\n let h3 = sub hseq (24 * word_length a) (hash_length a) in\n let h4 = sub hseq (32 * word_length a) (hash_length a) in\n let h5 = sub hseq (40 * word_length a) (hash_length a) in\n let h6 = sub hseq (48 * word_length a) (hash_length a) in\n let h7 = sub hseq (56 * word_length a) (hash_length a) in\n let hsub : multiseq 8 (hash_length a) = ntup8 (h0,(h1,(h2,(h3,(h4,(h5,(h6,h7))))))) in\n hsub", "val decrypt_pre\n (a: ea)\n (aead: AEAD.state a)\n (siv: B.buffer Secret.uint8)\n (ctr: CTR.state (SAEAD.cipher_alg_of_supported_alg a))\n (hpk: B.buffer Secret.uint8)\n (dst: B.buffer U8.t)\n (dst_len: U32.t)\n (dst_hdr: B.pointer result)\n (last_pn: PN.last_packet_number_t)\n (cid_len: short_dcid_len_t)\n (m: HS.mem)\n : GTot Type0\nlet decrypt_pre\n (a: ea)\n (aead: AEAD.state a)\n (siv: B.buffer Secret.uint8)\n (ctr: CTR.state (SAEAD.cipher_alg_of_supported_alg a))\n (hpk: B.buffer Secret.uint8)\n (dst: B.buffer U8.t)\n (dst_len: U32.t)\n (dst_hdr: B.pointer result)\n (last_pn: PN.last_packet_number_t)\n (cid_len: short_dcid_len_t)\n (m: HS.mem)\n: GTot Type0\n=\n let a' = SAEAD.cipher_alg_of_supported_alg a in\n B.all_disjoint [\n AEAD.footprint m aead;\n B.loc_buffer siv;\n CTR.footprint m ctr;\n B.loc_buffer hpk;\n B.loc_buffer dst;\n B.loc_buffer dst_hdr;\n ] /\\\n AEAD.invariant m aead /\\\n B.live m siv /\\ B.length siv == 12 /\\\n CTR.invariant m ctr /\\\n B.live m hpk /\\ B.length hpk == SCipher.key_length a' /\\\n B.live m dst /\\ B.length dst == U32.v dst_len /\\\n B.live m dst_hdr", "val emit4_spec\n (#a: sha2_alg)\n (#m: m_spec{lanes a m == 4})\n (hseq: LSeq.lseq uint8 (lanes a m * 8 * word_length a))\n : multiseq (lanes a m) (hash_length a)\nlet emit4_spec (#a:sha2_alg) (#m:m_spec{lanes a m == 4}) (hseq:LSeq.lseq uint8 (lanes a m * 8 * word_length a)) :\n multiseq (lanes a m) (hash_length a)\n =\n let open Lib.Sequence in\n let h0 = sub hseq 0 (hash_length a) in\n let h1 = sub hseq (8 * word_length a) (hash_length a) in\n let h2 = sub hseq (16 * word_length a) (hash_length a) in\n let h3 = sub hseq (24 * word_length a) (hash_length a) in\n let hsub : multiseq 4 (hash_length a) = ntup4 (h0,(h1,(h2,h3))) in\n hsub", "val block_of_sample\n (a: Cipher.cipher_alg)\n (k: Cipher.key a)\n (sample: Seq.lseq Secret.uint8 16)\n: GTot (Seq.lseq Secret.uint8 16)\nlet block_of_sample\n (a: Cipher.cipher_alg)\n (k: Cipher.key a)\n (sample: Seq.lseq Secret.uint8 16)\n: GTot (Seq.lseq Secret.uint8 16) =\n let open FStar.Mul in\n let ctr, iv = match a with\n | Cipher.CHACHA20 ->\n let ctr_bytes, iv = Seq.split sample 4 in\n FStar.Endianness.lemma_le_to_n_is_bounded (Seq.seq_reveal ctr_bytes);\n assert_norm (pow2 (8 * 4) = pow2 32);\n FStar.Endianness.le_to_n (Seq.seq_reveal ctr_bytes), iv\n | _ ->\n let iv, ctr_bytes = Seq.split sample 12 in\n FStar.Endianness.lemma_be_to_n_is_bounded (Seq.seq_reveal ctr_bytes);\n assert_norm (pow2 (8 * 4) = pow2 32);\n FStar.Endianness.be_to_n (Seq.seq_reveal ctr_bytes), iv\n in\n (Seq.slice (Cipher.ctr_block a k iv ctr) 0 16)", "val test4_spec\n (sk1 sk2: aead_key)\n (spriv1 spriv2: private_key wg_nc)\n (spub1 spub2: public_key wg_nc)\n (psk: preshared_key)\n (prlg: hashable wg_nc)\n (entr0: entropy)\n : Tot bool\nlet test4_spec\n (sk1 sk2 : aead_key)\n (spriv1 spriv2 : private_key wg_nc)\n (spub1 spub2 : public_key wg_nc)\n (psk : preshared_key)\n (prlg : hashable wg_nc)\n (entr0 : entropy) :\n Tot bool =\n let dv1 = DS.create_device wg_dc pattern_IKpsk2 prlg \"\" (Some sk1) (Some spriv1) in\n let dv2 = DS.create_device wg_dc pattern_IKpsk2 prlg \"\" (Some sk2) (Some spriv2) in\n match dv1, dv2 with\n | Some dv1, Some dv2 ->\n let res1 = DS.add_peer_get dv1 \"\" (Some spub2) (Some psk) in\n let res2 = DS.add_peer_get dv2 \"\" (Some spub1) (Some psk) in\n begin match res1, res2 with\n | Some (p1, dv1), Some (p2, dv2) ->\n let pid1 = DS.peer_get_id p1 in\n let sn1, entr1 = S.create_session dv1 true entr0 (Some pid1) in\n let sn2, entr2 = S.create_session dv2 false entr1 None in\n begin match sn1, sn2 with\n | Res (sn1, dv1), Res (sn2, dv2) ->\n let payload0 = S.pack_message Seq.empty in\n begin match S.write payload0 sn1 with\n | Res (c1, sn1) ->\n begin match S.read () dv2 sn2 c1 with\n | Res (dv2, msg1, sn2) -> true\n | _ -> false\n // Don't do the full handshake: we don't need to test more\n // and it makes the proof a lot faster\n end\n | _ -> false\n end\n | _ -> false\n end\n | _ -> false\n end\n | _ -> false", "val va_wp_Ctr32_ghash_6_prelude\n (alg: algorithm)\n (scratch_b: buffer128)\n (key_words: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n (ctr_orig: quad32)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Ctr32_ghash_6_prelude (alg:algorithm) (scratch_b:buffer128) (key_words:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (ctr_orig:quad32) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (sse_enabled /\\ Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 3 va_s0)\n (va_get_reg64 rRbp va_s0) scratch_b 8 (va_get_mem_layout va_s0) Secret /\\ aes_reqs_offset alg\n key_words round_keys keys_b (va_get_reg64 rRcx va_s0) (va_get_mem_heaplet 0 va_s0)\n (va_get_mem_layout va_s0) /\\ va_get_xmm 1 va_s0 == Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.AES.GCTR.inc32lite ctr_orig 0)) /\\ (forall (va_x_mem:vale_heap) (va_x_xmm2:quad32)\n (va_x_xmm4:quad32) (va_x_xmm9:quad32) (va_x_xmm10:quad32) (va_x_xmm11:quad32)\n (va_x_xmm12:quad32) (va_x_xmm13:quad32) (va_x_xmm14:quad32) (va_x_xmm15:quad32)\n (va_x_r11:nat64) (va_x_heap3:vale_heap) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags\n va_x_efl (va_upd_mem_heaplet 3 va_x_heap3 (va_upd_reg64 rR11 va_x_r11 (va_upd_xmm 15 va_x_xmm15\n (va_upd_xmm 14 va_x_xmm14 (va_upd_xmm 13 va_x_xmm13 (va_upd_xmm 12 va_x_xmm12 (va_upd_xmm 11\n va_x_xmm11 (va_upd_xmm 10 va_x_xmm10 (va_upd_xmm 9 va_x_xmm9 (va_upd_xmm 4 va_x_xmm4\n (va_upd_xmm 2 va_x_xmm2 (va_upd_mem va_x_mem va_s0)))))))))))) in va_get_ok va_sM /\\\n (Vale.X64.Decls.modifies_buffer_specific128 scratch_b (va_get_mem_heaplet 3 va_s0)\n (va_get_mem_heaplet 3 va_sM) 1 1 /\\ va_get_xmm 2 va_sM == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 0 0 0 16777216 /\\ va_get_xmm 15 va_sM == FStar.Seq.Base.index #quad32\n round_keys 0 /\\ va_get_xmm 9 va_sM == Vale.Def.Types_s.quad32_xor\n (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.AES.GCTR.inc32lite ctr_orig 0)) (va_get_xmm 15\n va_sM) /\\ (let counter = Vale.Def.Words_s.__proj__Mkfour__item__lo0 ctr_orig `op_Modulus` 256\n in (counter + 6 < 256 ==> va_get_xmm 10 va_sM == Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.AES.GCTR.inc32lite ctr_orig 1)) /\\ (counter + 6 < 256 ==> va_get_xmm 11 va_sM ==\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.AES.GCTR.inc32lite ctr_orig 2)) /\\ (counter + 6 <\n 256 ==> va_get_xmm 12 va_sM == Vale.Def.Types_s.reverse_bytes_quad32 (Vale.AES.GCTR.inc32lite\n ctr_orig 3)) /\\ (counter + 6 < 256 ==> va_get_xmm 13 va_sM ==\n Vale.Def.Types_s.reverse_bytes_quad32 (Vale.AES.GCTR.inc32lite ctr_orig 4)) /\\ (counter + 6 <\n 256 ==> va_get_xmm 14 va_sM == Vale.Def.Types_s.reverse_bytes_quad32 (Vale.AES.GCTR.inc32lite\n ctr_orig 5)) /\\ Vale.X64.Decls.buffer128_read scratch_b 1 (va_get_mem_heaplet 3 va_sM) ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 /\\ va_get_xmm 4 va_sM ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0)) ==> va_k va_sM (())))", "val derive_DeviceID\n (deviceID_pub: B.lbuffer pub_uint8 32)\n (deviceID_priv cdi: B.lbuffer uint8 32)\n (l0_label_DeviceID_len: size_t{valid_hkdf_lbl_len l0_label_DeviceID_len})\n (l0_label_DeviceID: B.lbuffer uint8 (v l0_label_DeviceID_len))\n : HST.Stack (unit)\n (requires\n fun h ->\n B.(all_live h [buf deviceID_pub; buf deviceID_priv; buf cdi; buf l0_label_DeviceID]) /\\\n B.(all_disjoint [\n loc_buffer deviceID_pub;\n loc_buffer deviceID_priv;\n loc_buffer cdi;\n loc_buffer l0_label_DeviceID\n ]))\n (ensures\n fun h0 _ h1 ->\n B.(modifies ((loc_buffer deviceID_pub) `loc_union` (loc_buffer deviceID_priv)) h0 h1) /\\\n ((B.as_seq h1 deviceID_pub <: lbytes_pub 32), (B.as_seq h1 deviceID_priv <: lbytes_sec 32)\n ) ==\n derive_DeviceID_spec (B.as_seq h1 cdi)\n l0_label_DeviceID_len\n (B.as_seq h1 l0_label_DeviceID))\nlet derive_DeviceID\n (deviceID_pub: B.lbuffer pub_uint8 32)\n (deviceID_priv: B.lbuffer uint8 32)\n // (cdi_len: hashable_len)\n (cdi: B.lbuffer uint8 32)\n (l0_label_DeviceID_len: size_t {valid_hkdf_lbl_len l0_label_DeviceID_len})\n (l0_label_DeviceID: B.lbuffer uint8 (v l0_label_DeviceID_len))\n: HST.Stack (unit)\n (requires fun h ->\n B.(all_live h [buf deviceID_pub;\n buf deviceID_priv;\n buf cdi;\n buf l0_label_DeviceID]) /\\\n B.(all_disjoint [loc_buffer deviceID_pub;\n loc_buffer deviceID_priv;\n loc_buffer cdi;\n loc_buffer l0_label_DeviceID]))\n (ensures fun h0 _ h1 ->\n B.(modifies (loc_buffer deviceID_pub `loc_union` loc_buffer deviceID_priv) h0 h1) /\\\n ((B.as_seq h1 deviceID_pub <: lbytes_pub 32), (B.as_seq h1 deviceID_priv <: lbytes_sec 32)) ==\n derive_DeviceID_spec (B.as_seq h1 cdi) l0_label_DeviceID_len (B.as_seq h1 l0_label_DeviceID)\n )\n= HST.push_frame ();\n let cDigest = B.alloca (u8 0) 32ul in\n l0_hash alg\n cDigest\n cdi\n 32ul;\n derive_key_pair\n deviceID_pub\n deviceID_priv\n 32ul cDigest\n l0_label_DeviceID_len l0_label_DeviceID;\n HST.pop_frame ()", "val Hacl.HPKE.Interface.AEAD.kv = a: Spec.Agile.AEAD.alg -> Type0\nlet kv (a:AEAD.alg) = lbuffer uint8 (size (AEAD.key_length a))", "val emit (#a: sha2_alg) (#m: m_spec) (hseq: lseq uint8 (lanes a m * 8 * word_length a))\n : multiseq (lanes a m) (hash_length a)\nlet emit (#a:sha2_alg) (#m:m_spec)\n (hseq:lseq uint8 (lanes a m * 8 * word_length a)):\n multiseq (lanes a m) (hash_length a) =\n Lib.NTuple.createi #(Seq.lseq uint8 (hash_length a)) (lanes a m)\n (fun i -> sub hseq (i * 8 * word_length a) (hash_length a))", "val header_encrypt_ct_secret_preserving_not_retry_spec\n (a: ea)\n (hpk: SCipher.key (SAEAD.cipher_alg_of_supported_alg a))\n (h: Spec.header{~(Spec.is_retry h)})\n (r: Seq.seq Secret.uint8 {Seq.length r >= Parse.pn_offset h + 20})\n : GTot (Seq.seq Secret.uint8)\nlet header_encrypt_ct_secret_preserving_not_retry_spec\n (a:ea)\n (hpk: SCipher.key (SAEAD.cipher_alg_of_supported_alg a))\n (h: Spec.header { ~ (Spec.is_retry h) })\n (r: Seq.seq Secret.uint8 {\n Seq.length r >= Parse.pn_offset h + 20\n })\n: GTot (Seq.seq Secret.uint8)\n= \n let pn_offset = Parse.pn_offset h in\n let pn_len = Secret.v (Spec.pn_length h) - 1 in\n let sample = (Seq.slice r (pn_offset + 4) (pn_offset + 20)) in\n let mask = (Spec.block_of_sample (SAEAD.cipher_alg_of_supported_alg a) hpk sample) in\n let pnmask = Lemmas.secret_and_inplace (Seq.slice mask 1 5) (Seq.seq_hide (pn_sizemask_ct pn_len)) 0 in\n let f = Seq.index r 0 in\n let protected_bits = if Spec.MShort? h then 5ul else 4ul in\n let f' = Secret.set_bitfield f 0ul protected_bits (Secret.get_bitfield (f `Secret.logxor` Seq.index mask 0) 0ul protected_bits) in\n let r = Lemmas.secret_xor_inplace r pnmask pn_offset in\n let r = Seq.cons f' (Seq.slice r 1 (Seq.length r)) in\n r", "val sealBase:\n cs:ciphersuite_not_export_only\n -> skE:key_dh_secret_s cs\n -> pkR:DH.serialized_point (kem_dh_of_cs cs)\n -> info:info_s cs\n -> aad:AEAD.ad (aead_alg_of cs)\n -> pt:AEAD.plain (aead_alg_of cs) ->\n Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt))\nlet sealBase cs skE pkR info aad pt =\n match setupBaseS cs skE pkR info with\n | None -> None\n | Some (enc, ctx) ->\n match context_seal cs ctx aad pt with\n | None -> None\n | Some (_, ct) -> Some (enc, ct)", "val Spec.Agile.Cipher.key = a: Spec.Agile.Cipher.cipher_alg -> Type0\nlet key (a: cipher_alg) =\n match a with\n | AES128 | AES256 -> Spec.AES.aes_key (aes_alg_of_alg a)\n | CHACHA20 -> Spec.Chacha20.key", "val x509_get_AliasKeyTBS\n (crt_version: x509_version_t)\n (serialNumber: x509_serialNumber_t)\n (i_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (i_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (i_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (notBefore: datatype_of_asn1_type UTC_TIME)\n (notAfter: datatype_of_asn1_type Generalized_Time)\n (s_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (s_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (s_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (ku: key_usage_payload_t)\n (keyID: datatype_of_asn1_type OCTET_STRING {keyID.ASN1.Base.len == 20ul})\n (version: datatype_of_asn1_type INTEGER)\n (fwid deviceIDPub aliasKeyPub: B32.lbytes32 32ul)\n : Tot (aliasKeyTBS_t)\nlet x509_get_AliasKeyTBS\n (crt_version: x509_version_t)\n (serialNumber: x509_serialNumber_t)\n (i_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (i_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (i_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (notBefore: datatype_of_asn1_type UTC_TIME)\n (notAfter : datatype_of_asn1_type Generalized_Time)\n (s_common: x509_RDN_x520_attribute_string_t COMMON_NAME IA5_STRING)\n (s_org: x509_RDN_x520_attribute_string_t ORGANIZATION IA5_STRING)\n (s_country: x509_RDN_x520_attribute_string_t COUNTRY PRINTABLE_STRING)\n (ku: key_usage_payload_t)\n (keyID: datatype_of_asn1_type OCTET_STRING { keyID.ASN1.Base.len == 20ul })\n (version: datatype_of_asn1_type INTEGER)\n (fwid: B32.lbytes32 32ul)\n (deviceIDPub: B32.lbytes32 32ul)\n (aliasKeyPub: B32.lbytes32 32ul)\n: Tot (aliasKeyTBS_t)\n= let signatureAlg: algorithmIdentifier_t = x509_get_algorithmIdentifier () in\n (* Prf *) lemma_serialize_algorithmIdentifier_size_exact signatureAlg;\n\n [@inline_let]\n let i_common = coerce_x509_rdn_attribute_t_string_to_asn1_string_cn i_common in\n [@inline_let]\n let i_org = coerce_x509_rdn_attribute_t_string_to_asn1_string_org i_org in\n [@inline_let]\n let i_country = coerce_x509_rdn_attribute_t_string_to_asn1_string_country i_country in\n\n let issuer: aliasKeyTBS_issuer_t = x509_get_aliasKeyTBS_issuer i_common i_org i_country in\n\n (* Prf *) lemma_serialize_aliasKeyTBS_issuer_size_exact issuer;\n\n let validity: x509_validity_t = x509_get_validity\n notBefore\n notAfter in\n (* Prf *) lemma_serialize_x509_validity_size_exact validity;\n\n [@inline_let]\n let s_common = coerce_x509_rdn_attribute_t_string_to_asn1_string_cn s_common in\n [@inline_let]\n let s_org = coerce_x509_rdn_attribute_t_string_to_asn1_string_org s_org in\n [@inline_let]\n let s_country = coerce_x509_rdn_attribute_t_string_to_asn1_string_country s_country in\n\n let subject: aliasKeyTBS_subject_t = x509_get_aliasKeyTBS_subject s_common s_org s_country in\n (* Prf *) lemma_serialize_aliasKeyTBS_subject_size_exact subject;\n\n let aliasKeyPubInfo = x509_get_subjectPublicKeyInfo\n aliasKeyPub in\n (* Prf *) lemma_serialize_subjectPublicKeyInfo_size_exact aliasKeyPubInfo;\n\n let extensions = x509_get_aliasKeyTBS_extensions\n ku\n keyID\n version\n fwid\n deviceIDPub in\n (* Prf *) lemma_serialize_aliasKeyTBS_extensions_size_exact extensions;\n\n let aliasKeyTBS: aliasKeyTBS_payload_t = {\n aliasKeyTBS_version = crt_version;\n aliasKeyTBS_serialNumber = serialNumber;\n aliasKeyTBS_signatureAlg = signatureAlg;\n aliasKeyTBS_issuer = issuer;\n aliasKeyTBS_validity = validity;\n aliasKeyTBS_subject = subject;\n aliasKeyTBS_aliasKey_pub = aliasKeyPubInfo;\n aliasKeyTBS_extensions = extensions\n } in\n (* Prf *) lemma_serialize_aliasKeyTBS_payload_unfold aliasKeyTBS;\n (* Prf *) lemma_serialize_aliasKeyTBS_payload_size aliasKeyTBS;\n (* Prf *) (**) lemma_serialize_x509_version_size_exact crt_version;\n (* Prf *) (**) lemma_serialize_x509_serialNumber_size serialNumber;\n\n(*return*) aliasKeyTBS", "val derive_key_poly1305_do:\n #w:field_spec\n -> k:lbuffer uint8 32ul\n -> n:lbuffer uint8 12ul\n -> aadlen:size_t\n -> aad:lbuffer uint8 aadlen\n -> mlen:size_t\n -> m:lbuffer uint8 mlen\n -> out:lbuffer uint8 16ul ->\n Stack unit\n (requires fun h ->\n live h k /\\ live h n /\\ live h aad /\\ live h m /\\ live h out)\n (ensures fun h0 _ h1 -> modifies (loc out) h0 h1 /\\\n (let key:LSeq.lseq uint8 64 = Spec.Chacha20.chacha20_encrypt_bytes (as_seq h0 k) (as_seq h0 n) 0 (LSeq.create 64 (u8 0)) in\n as_seq h1 out == Spec.poly1305_do (LSeq.sub key 0 32) (as_seq h0 m) (as_seq h0 aad)))\nlet derive_key_poly1305_do #w k n aadlen aad mlen m out =\n push_frame ();\n // Create a new buffer to derive the key\n let tmp = create 64ul (u8 0) in\n chacha20_encrypt #w 64ul tmp tmp k n 0ul;\n // The derived key should only be the first 32 bytes\n let key = sub tmp 0ul 32ul in\n poly1305_do #w key aadlen aad mlen m out;\n pop_frame()", "val digest:\n a:G.erased alg -> (\n let c = hacl_keccak a in\n let a = G.reveal a in\n let i = a in\n let t = sha3_state a in\n let t' = G.erased unit in\n s:state c i t t' ->\n dst:B.buffer uint8 ->\n Stack error_code\n (requires fun h0 ->\n (not (is_shake a) ==> B.length dst == Spec.Hash.Definitions.hash_length a) /\\\n invariant c i h0 s /\\\n B.live h0 dst /\\\n B.(loc_disjoint (loc_buffer dst) (footprint c i h0 s)))\n (ensures fun h0 r h1 ->\n match r with\n | Success ->\n not (is_shake a) /\\\n invariant c i h1 s /\\\n seen c i h0 s == seen c i h1 s /\\\n reveal_key c i h1 s == reveal_key c i h0 s /\\\n footprint c i h0 s == footprint c i h1 s /\\\n B.(modifies (loc_union (loc_buffer dst) (footprint c i h0 s)) h0 h1) /\\ (\n seen_bounded c i h0 s;\n S.equal (B.as_seq h1 dst) (Spec.Agile.Hash.hash a (seen c i h0 s)) /\\\n preserves_freeable c i s h0 h1)\n | InvalidAlgorithm ->\n is_shake a\n | _ ->\n False))\nlet digest a state output =\n let a = get_alg a state in\n if (a = Shake128 || a = Shake256) then\n InvalidAlgorithm\n else begin\n digest_ a state output (Hacl.Hash.SHA3.hash_len a);\n Success\n end", "val l0_core_step1\n (cdi: B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: size_t)\n (deviceID_label: B.lbuffer byte_sec (v deviceID_label_len))\n (aliasKey_label_len: size_t)\n (aliasKey_label: B.lbuffer byte_sec (v aliasKey_label_len))\n (deviceID_pub: B.lbuffer byte_pub 32)\n (deviceID_priv: B.lbuffer byte_sec 32)\n (aliasKey_pub: B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer byte_sec 32)\n (authKeyID: B.lbuffer byte_pub 20)\n : HST.Stack unit\n (requires\n fun h ->\n l0_core_step1_pre (h) (cdi) (fwid) (deviceID_label_len) (deviceID_label)\n (aliasKey_label_len) (aliasKey_label) (deviceID_pub) (deviceID_priv) (aliasKey_pub)\n (aliasKey_priv) (authKeyID))\n (ensures\n fun h0 _ h1 ->\n l0_core_step1_post (h0) (h1) (cdi) (fwid) (deviceID_label_len) (deviceID_label)\n (aliasKey_label_len) (aliasKey_label) (deviceID_pub) (deviceID_priv) (aliasKey_pub)\n (aliasKey_priv) (authKeyID))\nlet l0_core_step1\n(* Inputs *)\n (cdi : B.lbuffer byte_sec 32)\n (fwid: B.lbuffer byte_pub 32)\n (deviceID_label_len: size_t)\n (deviceID_label: B.lbuffer byte_sec (v deviceID_label_len))\n (aliasKey_label_len: size_t)\n (aliasKey_label: B.lbuffer byte_sec (v aliasKey_label_len))\n(* Outputs *)\n (deviceID_pub : B.lbuffer byte_pub 32)\n (deviceID_priv: B.lbuffer byte_sec 32)\n (aliasKey_pub : B.lbuffer byte_pub 32)\n (aliasKey_priv: B.lbuffer byte_sec 32)\n (authKeyID : B.lbuffer byte_pub 20)\n: HST.Stack unit\n (requires fun h -> l0_core_step1_pre (h)\n (cdi) (fwid)\n (deviceID_label_len) (deviceID_label)\n (aliasKey_label_len) (aliasKey_label)\n (deviceID_pub) (deviceID_priv)\n (aliasKey_pub) (aliasKey_priv)\n (authKeyID))\n (ensures fun h0 _ h1 -> l0_core_step1_post (h0) (h1)\n (cdi) (fwid)\n (deviceID_label_len) (deviceID_label)\n (aliasKey_label_len) (aliasKey_label)\n (deviceID_pub) (deviceID_priv)\n (aliasKey_pub) (aliasKey_priv)\n (authKeyID))\n= (**) let h0 = HST.get () in\n HST.push_frame ();\n (**) let hs0 = HST.get () in\n (**) B.fresh_frame_modifies h0 hs0;\n\n(* Derive DeviceID *)\n // let deviceID_pub : B.lbuffer byte_pub 32 = B.alloca 0x00uy 32ul in\n // let deviceID_priv: B.lbuffer byte_sec 32 = B.alloca (u8 0x00) 32ul in\n let deviceID_pub_sec: B.lbuffer byte_sec 32 = B.alloca (u8 0x00) 32ul in\n printf \"Deriving DeviceID\\n\" done;\n derive_DeviceID\n (* pub *) deviceID_pub\n (* priv*) deviceID_priv\n (* cdi *) cdi\n (* lbl *) deviceID_label_len\n deviceID_label;\n\n printf \"Deriving AliasKey\\n\" done;\n derive_AliasKey\n (* pub *) aliasKey_pub\n (* priv*) aliasKey_priv\n (* cdi *) cdi\n (* fwid*) fwid\n (* lbl *) aliasKey_label_len\n aliasKey_label;\n\n classify_public_buffer 32ul deviceID_pub deviceID_pub_sec;\n\n derive_authKeyID\n authKeyID\n deviceID_pub_sec;\n\n (**) let hsf = HST.get () in\n HST.pop_frame ();\n (**) let hf = HST.get () in\n (**) B.popped_modifies hsf hf;\n()", "val eval_cipher_state_m\n (h: HS.mem)\n (st: cipher_state_m)\n (has_key: bool{has_key ==> (not (g_is_null (csm_get_k st)))})\n (n: nat)\n : GTot (cipher_state)\nlet eval_cipher_state_m (h : HS.mem) (st : cipher_state_m)\n (has_key : bool{has_key ==> (not (g_is_null (csm_get_k st)))})\n (n : nat) :\n GTot (cipher_state) =\n eval_cipher_state_mf h (csm_get_k st) has_key n", "val length_of_aliasKeyCRT_payload (tbs_len: asn1_int32) : GTot (nat)\nlet length_of_aliasKeyCRT_payload\n (tbs_len: asn1_int32)\n: GTot (nat)\n= v tbs_len + 74", "val labeled_expand:\n a:hash_algorithm\n -> suite_id:bytes\n -> prk:bytes\n -> label:bytes\n -> info:bytes\n -> l:size_nat ->\n Pure (lbytes l)\n (requires\n Spec.Hash.Definitions.hash_length a <= Seq.length prk /\\\n Spec.Agile.HMAC.keysized a (Seq.length prk) /\\\n labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\\\n HKDF.expand_output_length_pred a l)\n (ensures fun _ -> True)\nlet labeled_expand a suite_id prk label info l =\n let labeled_info1 = nat_to_bytes_be 2 l in\n let labeled_info2 = Seq.append labeled_info1 label_version in\n let labeled_info3 = Seq.append labeled_info2 suite_id in\n let labeled_info4 = Seq.append labeled_info3 label in\n let labeled_info5 = Seq.append labeled_info4 info in\n HKDF.expand a prk labeled_info5 l", "val labeled_extract:\n a:hash_algorithm\n -> suite_id:bytes\n -> salt:bytes\n -> label:bytes\n -> ikm:bytes ->\n Pure (lbytes (Spec.Hash.Definitions.hash_length a))\n (requires\n Spec.Agile.HMAC.keysized a (Seq.length salt) /\\\n labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))\n (ensures fun _ -> True)\nlet labeled_extract a suite_id salt label ikm =\n let labeled_ikm1 = Seq.append label_version suite_id in\n let labeled_ikm2 = Seq.append labeled_ikm1 label in\n let labeled_ikm3 = Seq.append labeled_ikm2 ikm in\n HKDF.extract a salt labeled_ikm3", "val coerceT\n (ip: ipkg)\n (ha_of_i: (ip.Pkg.t -> ha))\n (good_of_i: (i: ip.Pkg.t -> Hashing.macable (ha_of_i i) -> bool))\n (i: ip.Pkg.t{ip.Pkg.registered i /\\ ~(safe i)})\n (u: info{u.alg = ha_of_i i /\\ u.good == good_of_i i})\n (kv: lbytes32 (keylen u))\n : GTot (key ip i)\nlet coerceT (ip: ipkg) (ha_of_i: ip.Pkg.t -> ha) (good_of_i: (i:ip.Pkg.t -> Hashing.macable (ha_of_i i) -> bool))\n (i: ip.Pkg.t {ip.Pkg.registered i /\\ ~(safe i)})\n (u: info {u.alg = ha_of_i i /\\ u.good == good_of_i i})\n (kv: lbytes32 (keylen u)) : GTot (key ip i)\n =\n assert_norm (pow2 32 < pow2 61);\n assert_norm (pow2 61 < pow2 125);\n assert_norm(Spec.Agile.HMAC.keysized u.alg (Spec.Hash.Definitions.hash_length u.alg));\n let ck = MAC u kv in\n if model then\n let k: ir_key ip i = RealKey ck in k\n else ck", "val header_decrypt_aux_pre\n (a: ea)\n (s: CTR.state (SAEAD.cipher_alg_of_supported_alg a))\n (k: B.buffer Secret.uint8)\n (cid_len: short_dcid_len_t)\n (dst: B.buffer U8.t)\n (dst_len: U32.t)\n (m: HS.mem)\n : GTot Type0\nlet header_decrypt_aux_pre\n (a: ea)\n (s: CTR.state (SAEAD.cipher_alg_of_supported_alg a))\n (k: B.buffer Secret.uint8)\n (cid_len: short_dcid_len_t)\n (dst: B.buffer U8.t)\n (dst_len: U32.t)\n (m: HS.mem)\n: GTot Type0\n=\n let l = B.length dst in\n B.all_live m [B.buf k; B.buf dst] /\\\n CTR.invariant m s /\\\n B.length k == SCipher.key_length (SAEAD.cipher_alg_of_supported_alg a) /\\\n B.all_disjoint\n [ CTR.footprint m s; B.loc_buffer k; B.loc_buffer dst] /\\\n B.length dst == U32.v dst_len", "val lemma_gcm_encrypt_decrypt_equiv\n (alg: algorithm)\n (key: seq nat32)\n (iv: supported_iv_BE)\n (j0_BE: quad32)\n (plain cipher auth alleged_tag: seq nat8)\n : Lemma\n (requires\n is_aes_key_word alg key /\\\n (let h_BE = aes_encrypt_word alg key (Mkfour 0 0 0 0) in\n j0_BE = compute_iv_BE h_BE iv) /\\ length cipher < pow2_32 /\\ length auth < pow2_32 /\\\n plain == fst (gcm_encrypt_BE alg (seq_nat32_to_seq_nat8_BE key) iv cipher auth))\n (ensures\n plain == fst (gcm_decrypt_BE alg (seq_nat32_to_seq_nat8_BE key) iv cipher auth alleged_tag))\nlet lemma_gcm_encrypt_decrypt_equiv (alg:algorithm) (key:seq nat32) (iv:supported_iv_BE) (j0_BE:quad32) (plain cipher auth alleged_tag:seq nat8) : Lemma\n (requires\n is_aes_key_word alg key /\\\n (let h_BE = aes_encrypt_word alg key (Mkfour 0 0 0 0) in\n j0_BE = compute_iv_BE h_BE iv) /\\\n length cipher < pow2_32 /\\\n length auth < pow2_32 /\\\n plain == fst (gcm_encrypt_BE alg (seq_nat32_to_seq_nat8_BE key) iv cipher auth)\n )\n (ensures plain == fst (gcm_decrypt_BE alg (seq_nat32_to_seq_nat8_BE key) iv cipher auth alleged_tag))\n =\n gcm_encrypt_BE_reveal ();\n gcm_decrypt_BE_reveal ();\n ()", "val Hacl.Frodo.KEM.crypto_kem_keypair_st = \n a: Spec.Frodo.Params.frodo_alg ->\n gen_a: Spec.Frodo.Params.frodo_gen_a{Hacl.Impl.Frodo.Params.is_supported gen_a}\n -> Type0\nlet crypto_kem_keypair_st (a:FP.frodo_alg) (gen_a:FP.frodo_gen_a{is_supported gen_a}) =\n pk:lbytes (crypto_publickeybytes a)\n -> sk:lbytes (crypto_secretkeybytes a)\n -> Stack uint32\n (requires fun h ->\n live h pk /\\ live h sk /\\\n disjoint pk sk /\\ disjoint state pk /\\ disjoint state sk)\n (ensures fun h0 r h1 -> modifies (loc state |+| (loc pk |+| loc sk)) h0 h1 /\\\n (as_seq h1 pk, as_seq h1 sk) == S.crypto_kem_keypair a gen_a (as_seq h0 state))", "val truncate_key_spec (k: raw_key) (w: U16.t{U16.v w <= U16.v k.significant_digits})\n : GTot (k': raw_key{k'.significant_digits == w}) (decreases (U16.v k.significant_digits))\nlet rec truncate_key_spec (k:raw_key)\r\n (w:U16.t{U16.v w <= U16.v k.significant_digits })\r\n : GTot (k':raw_key {k'.significant_digits == w})\r\n (decreases (U16.v k.significant_digits))\r\n = if k.significant_digits = w then k\r\n else truncate_key_spec (parent k) w", "val expand_label:\n #ha: Hashing.Spec.tls_macAlg ->\n secret: lbytes (Spec.Hash.Definitions.hash_length ha) ->\n label: string{length (bytes_of_string label) < 256 - 6} -> // -9?\n hv: bytes{length hv < 256} ->\n len: UInt32.t {0 < v len /\\ v len <= op_Multiply 255 (hash_length ha)} ->\n ST (lbytes32 len)\n (requires (fun h0 -> True))\n (ensures (fun h0 t h1 -> modifies_none h0 h1))\nlet expand_label #ha secret label digest len =\n let info = format ha label digest len in\n expand #ha secret info len", "val init: a:e_alg -> (\n let a = G.reveal a in\n s:state a ->\n k:B.buffer uint8 { B.length k = Spec.Agile.CTR.key_length a } ->\n nonce: B.buffer uint8 ->\n nonce_len: UInt32.t { Spec.nonce_bound a (UInt32.v nonce_len) /\\ B.len nonce = nonce_len } ->\n c: UInt32.t ->\n Stack unit\n (requires (fun h0 ->\n B.live h0 k /\\\n B.live h0 nonce /\\\n B.(loc_disjoint (loc_buffer k) (footprint h0 s)) /\\\n B.(loc_disjoint (loc_buffer nonce) (footprint h0 s)) /\\\n invariant h0 s))\n (ensures (fun h0 _ h1 ->\n preserves_freeable #a s h0 h1 /\\\n invariant #a h1 s /\\\n footprint h0 s == footprint #a h1 s /\\\n B.(modifies (footprint #a h0 s) h0 h1) /\\\n kv (B.deref h1 s) == B.as_seq h0 k /\\\n iv (B.deref h1 s) == B.as_seq h0 nonce /\\\n ctr h1 s = UInt32.v c\n )))\nlet init a p k iv iv_len c =\n let State i _ iv' _ _ ek _ = !*p in\n [@inline_let]\n let k: B.buffer uint8 = k in\n\n (**) let h0 = ST.get () in\n (**) let g_iv = G.hide (B.as_seq h0 iv) in\n (**) let g_key: G.erased (key (cipher_alg_of_impl i)) = G.hide (B.as_seq h0 k) in\n\n B.blit iv 0ul iv' 0ul iv_len;\n (**) let h1 = ST.get () in\n (**) assert B.(modifies (footprint_s (B.deref h0 p)) h0 h1);\n\n copy_or_expand i k ek;\n (**) let h2 = ST.get () in\n (**) assert B.(modifies (footprint_s (B.deref h0 p)) h1 h2);\n\n // TODO: two in-place updates\n p *= (State i g_iv iv' iv_len g_key ek c)", "val synth_aliasKeyTBS_subject_payload_t (x': aliasKeyTBS_subject_payload_t')\n : GTot (aliasKeyTBS_subject_payload_t)\nlet synth_aliasKeyTBS_subject_payload_t\n (x': aliasKeyTBS_subject_payload_t')\n: GTot (aliasKeyTBS_subject_payload_t)\n= { aliasKeyTBS_subject_Common = fst (fst x');\n aliasKeyTBS_subject_Organization = snd (fst x');\n aliasKeyTBS_subject_Country = snd x' }", "val repr: #a:supported_alg -> st:state a -> h:HS.mem -> GTot (S.state a)\nlet repr #a st h =\n S.State (as_seq h st.k) (as_seq h st.v) (v (bget h st.reseed_counter 0))", "val repr: #a:supported_alg -> st:state a -> h:HS.mem -> GTot (S.state a)\nlet repr #a st h =\n let st = B.get h st 0 in\n repr (p st) h", "val lemma_serialize_aliasKeyCRT_size\n (tbs_len: asn1_int32)\n (x: aliasKeyCRT_t tbs_len)\n: Lemma ( predicate_serialize_asn1_sequence_TLV_size (serialize_aliasKeyCRT_payload tbs_len) x )\nlet lemma_serialize_aliasKeyCRT_size tbs_len x\n= lemma_serialize_asn1_sequence_TLV_size (serialize_aliasKeyCRT_payload tbs_len) x", "val Spec.Agile.AEAD.kv = a: Spec.Agile.AEAD.alg -> Type0\nlet kv a = lbytes (key_length a)", "val header_decrypt_aux_ct\n (a: ea)\n (hpk: SCipher.key (SAEAD.cipher_alg_of_supported_alg a))\n (cid_len: nat{cid_len <= 20})\n (packet: packet)\n : GTot (option Spec.header_decrypt_aux_t)\nlet header_decrypt_aux_ct\n (a:ea)\n (hpk: SCipher.key (SAEAD.cipher_alg_of_supported_alg a))\n (cid_len: nat { cid_len <= 20 })\n (packet: packet)\n: GTot (option Spec.header_decrypt_aux_t)\n= let open FStar.Math.Lemmas in\n if Seq.length packet = 0\n then None\n else\n let f = Seq.index packet 0 in\n let is_short = (BF.get_bitfield (U8.v f) 7 8 = 0) in\n let is_retry = not is_short && BF.get_bitfield (U8.v f) 4 6 = 3 in\n if is_retry\n then\n Some ({\n Spec.is_short = is_short;\n Spec.is_retry = is_retry;\n Spec.packet = packet;\n Spec.pn_offset = ();\n Spec.pn_len = ();\n })\n else\n match Parse.putative_pn_offset cid_len packet with\n | None -> None\n | Some pn_offset ->\n let sample_offset = pn_offset + 4 in\n if sample_offset + 16 > Seq.length packet\n then None\n else begin\n let sample = Seq.slice packet sample_offset (sample_offset+16) in\n let mask = Seq.seq_reveal (Spec.block_of_sample (SAEAD.cipher_alg_of_supported_alg a) hpk (Seq.seq_hide sample)) in\n (* mask the least significant bits of the first byte *)\n let protected_bits = if is_short then 5 else 4 in\n let f' = BF.set_bitfield (U8.v f) 0 protected_bits (BF.get_bitfield (U8.v f `FStar.UInt.logxor` U8.v (Seq.index mask 0)) 0 protected_bits) in\n let packet' = Seq.cons (U8.uint_to_t f') (Seq.slice packet 1 (Seq.length packet)) in\n (* now the packet number length is available, so mask the packet number *)\n let pn_len = BF.get_bitfield f' 0 2 in\n let pnmask = Lemmas.and_inplace (Seq.slice mask 1 5) (pn_sizemask_ct pn_len) 0 in\n let packet'' = Lemmas.xor_inplace packet' pnmask pn_offset in\n Some ({\n Spec.is_short = is_short;\n Spec.is_retry = is_retry;\n Spec.packet = packet'';\n Spec.pn_offset = pn_offset;\n Spec.pn_len = pn_len;\n })\n end", "val encrypt_pre\n (a: ea)\n (aead: AEAD.state a)\n (siv: B.buffer Secret.uint8)\n (ctr: CTR.state (SAEAD.cipher_alg_of_supported_alg a))\n (hpk: B.buffer Secret.uint8)\n (dst: B.buffer U8.t)\n (h: header)\n (pn: PN.packet_number_t)\n (plain: B.buffer Secret.uint8)\n (plain_len: Secret.uint32)\n (m: HS.mem)\n : GTot Type0\nlet encrypt_pre\n (a: ea)\n (aead: AEAD.state a)\n (siv: B.buffer Secret.uint8)\n (ctr: CTR.state (SAEAD.cipher_alg_of_supported_alg a))\n (hpk: B.buffer Secret.uint8)\n (dst: B.buffer U8.t)\n (h: header)\n (pn: PN.packet_number_t)\n (plain: B.buffer Secret.uint8)\n (plain_len: Secret.uint32) // should be secret, because otherwise one can compute the packet number length\n (m: HS.mem)\n: GTot Type0\n=\n let a' = SAEAD.cipher_alg_of_supported_alg a in\n B.all_disjoint [\n AEAD.footprint m aead;\n B.loc_buffer siv;\n CTR.footprint m ctr;\n B.loc_buffer hpk;\n B.loc_buffer dst;\n header_footprint h;\n B.loc_buffer plain;\n ] /\\\n AEAD.invariant m aead /\\\n B.live m siv /\\ B.length siv == 12 /\\\n CTR.invariant m ctr /\\\n B.live m hpk /\\ B.length hpk == SCipher.key_length a' /\\\n B.live m dst /\\\n header_live h m /\\\n B.live m plain /\\ B.length plain == Secret.v plain_len /\\\n begin\n if is_retry h\n then\n B.length plain == 0 /\\\n B.length dst == Secret.v (header_len h)\n else\n B.length dst == Secret.v (header_len h) + Secret.v plain_len + SAEAD.tag_length a /\\\n 3 <= Secret.v plain_len /\\ Secret.v plain_len < max_plain_length\n end", "val L0.X509.AliasKeyCRT.aliasKeyCRT_t = tbs_len: ASN1.Base.asn1_int32 -> Type0\nlet aliasKeyCRT_t\n (tbs_len: asn1_int32)\n= inbound_sequence_value_of (serialize_aliasKeyCRT_payload tbs_len)", "val sealPSK:\n cs:ciphersuite_not_export_only\n -> skE:key_dh_secret_s cs\n -> pkR:DH.serialized_point (kem_dh_of_cs cs)\n -> info:info_s cs\n -> aad:AEAD.ad (aead_alg_of cs)\n -> pt:AEAD.plain (aead_alg_of cs)\n -> psk:psk_s cs\n -> psk_id:psk_id_s cs ->\n Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt))\nlet sealPSK cs skE pkR info aad pt psk psk_id =\n match setupPSKS cs skE pkR info psk psk_id with\n | None -> None\n | Some (enc, ctx) ->\n match context_seal cs ctx aad pt with\n | None -> None\n | Some (_, ct) -> Some (enc, ct)", "val lemma_serialize_aliasKeyCRT_payload_unfold\n (tbs_len: asn1_int32)\n (x: aliasKeyCRT_payload_t tbs_len)\n: Lemma (\n serialize_aliasKeyCRT_payload tbs_len `serialize` x ==\n (serialize_flbytes32 tbs_len `serialize` x.aliasKeyCRT_tbs)\n `Seq.append`\n (serialize_algorithmIdentifier `serialize` x.aliasKeyCRT_sig_alg)\n `Seq.append`\n (serialize_x509_signature `serialize` x.aliasKeyCRT_sig)\n)\nlet lemma_serialize_aliasKeyCRT_payload_unfold tbs_len x\n= serialize_nondep_then_eq\n (* s1 *) (serialize_flbytes32 tbs_len)\n (* s2 *) (serialize_algorithmIdentifier)\n (* in *) (fst (synth_aliasKeyCRT_payload_t' tbs_len x));\n serialize_nondep_then_eq\n (* s1 *) (serialize_flbytes32 tbs_len\n `serialize_nondep_then`\n serialize_algorithmIdentifier)\n (* s2 *) (serialize_x509_signature)\n (* in *) (synth_aliasKeyCRT_payload_t' tbs_len x);\n serialize_synth_eq\n (* p1 *) (parse_flbytes32 tbs_len\n `nondep_then`\n parse_algorithmIdentifier\n `nondep_then`\n parse_x509_signature)\n (* f2 *) (synth_aliasKeyCRT_payload_t tbs_len)\n (* s1 *) (serialize_flbytes32 tbs_len\n `serialize_nondep_then`\n serialize_algorithmIdentifier\n `serialize_nondep_then`\n serialize_x509_signature)\n (* g1 *) (synth_aliasKeyCRT_payload_t' tbs_len)\n (* prf*) ()\n (* in *) x", "val emit: #a:sha2_alg -> #m:m_spec{is_supported a m}\n -> hbuf: lbuffer uint8 (size (lanes a m) *! 8ul *! HD.word_len a)\n -> result:multibuf (lanes a m) (HD.hash_len a) ->\n Stack unit\n (requires fun h -> live_multi h result /\\ live h hbuf /\\\n internally_disjoint result /\\ disjoint_multi result hbuf)\n (ensures fun h0 _ h1 -> modifies_multi result h0 h1 /\\\n as_seq_multi h1 result == SpecVec.emit #a #m (as_seq h0 hbuf))\nlet emit #a #m hbuf result =\n match lanes a m with\n | 1 -> emit1 #a #m hbuf result\n | 4 -> emit4 #a #m hbuf result\n | 8 -> emit8 #a #m hbuf result", "val L0Types.mk_l0_repr = \n fwid: FStar.Seq.Base.seq FStar.UInt8.t ->\n deviceID_label: FStar.Seq.Base.seq FStar.UInt8.t ->\n aliasKey_label: FStar.Seq.Base.seq FStar.UInt8.t\n -> L0Types.l0_record_repr_t\nlet mk_l0_repr fwid deviceID_label aliasKey_label\n = {fwid; deviceID_label; aliasKey_label}", "val synth_aliasKeyTBS_issuer_payload_t (x': aliasKeyTBS_issuer_payload_t')\n : GTot (aliasKeyTBS_issuer_payload_t)\nlet synth_aliasKeyTBS_issuer_payload_t\n (x': aliasKeyTBS_issuer_payload_t')\n: GTot (aliasKeyTBS_issuer_payload_t)\n= { aliasKeyTBS_issuer_Common = fst (fst x');\n aliasKeyTBS_issuer_Organization = snd (fst x');\n aliasKeyTBS_issuer_Country = snd x' }", "val synth_aliasKeyTBS_payload_t (x': aliasKeyTBS_payload_t') : GTot (aliasKeyTBS_payload_t)\nlet synth_aliasKeyTBS_payload_t\n (x': aliasKeyTBS_payload_t')\n: GTot (aliasKeyTBS_payload_t)\n= { aliasKeyTBS_version = fst (fst (fst (fst (fst (fst (fst x'))))));\n aliasKeyTBS_serialNumber = snd (fst (fst (fst (fst (fst (fst x'))))));\n aliasKeyTBS_signatureAlg = snd (fst (fst (fst (fst (fst x')))));\n aliasKeyTBS_issuer = snd (fst (fst (fst (fst x'))));\n aliasKeyTBS_validity = snd (fst (fst (fst x')));\n aliasKeyTBS_subject = snd (fst (fst x'));\n aliasKeyTBS_aliasKey_pub = snd (fst x');\n aliasKeyTBS_extensions = snd x' }", "val ws_spec_v (#a: sha2_alg) (#m: m_spec) (st: ws_spec a m) : lseq (lseq (word a) 16) (lanes a m)\nlet ws_spec_v (#a:sha2_alg) (#m:m_spec) (st:ws_spec a m) : lseq (lseq (word a) 16) (lanes a m) =\n createi #(lseq (word a) 16) (lanes a m) (fun i ->\n create16\n (vec_v st.[0]).[i] (vec_v st.[1]).[i] (vec_v st.[2]).[i] (vec_v st.[3]).[i]\n (vec_v st.[4]).[i] (vec_v st.[5]).[i] (vec_v st.[6]).[i] (vec_v st.[7]).[i]\n (vec_v st.[8]).[i] (vec_v st.[9]).[i] (vec_v st.[10]).[i] (vec_v st.[11]).[i]\n (vec_v st.[12]).[i] (vec_v st.[13]).[i] (vec_v st.[14]).[i] (vec_v st.[15]).[i])", "val eval_aead_key (h: HS.mem) (k: opt_aead_key_t{not (g_is_null k)}) : GTot aead_key\nlet eval_aead_key (h : HS.mem) (k : opt_aead_key_t{not (g_is_null k)}) : GTot aead_key =\n nn_as_seq h k", "val Hacl.Frodo.KEM.crypto_kem_dec_st = \n a: Spec.Frodo.Params.frodo_alg ->\n gen_a: Spec.Frodo.Params.frodo_gen_a{Hacl.Impl.Frodo.Params.is_supported gen_a}\n -> Type0\nlet crypto_kem_dec_st (a:FP.frodo_alg) (gen_a:FP.frodo_gen_a{is_supported gen_a}) =\n ss:lbytes (crypto_bytes a)\n -> ct:lbytes (crypto_ciphertextbytes a)\n -> sk:lbytes (crypto_secretkeybytes a)\n -> Stack uint32\n (requires fun h ->\n live h ss /\\ live h ct /\\ live h sk /\\\n disjoint ss ct /\\ disjoint ss sk /\\ disjoint ct sk)\n (ensures fun h0 r h1 -> modifies (loc ss) h0 h1 /\\\n as_seq h1 ss == S.crypto_kem_dec a gen_a (as_seq h0 ct) (as_seq h0 sk))", "val derive_authKeyID (authKeyID: B.lbuffer byte_pub 20) (deviceIDPub: B.lbuffer byte_sec 32)\n : HST.Stack unit\n (requires\n fun h -> B.live h authKeyID /\\ B.live h deviceIDPub /\\ B.disjoint authKeyID deviceIDPub)\n (ensures\n fun h0 _ h1 ->\n B.modifies (B.loc_buffer authKeyID) h0 h1 /\\\n B.as_seq h1 authKeyID == derive_authKeyID_spec (B.as_seq h0 deviceIDPub))\nlet derive_authKeyID\n (authKeyID: B.lbuffer byte_pub 20)\n (deviceIDPub: B.lbuffer byte_sec 32)\n: HST.Stack unit\n (requires fun h ->\n B.live h authKeyID /\\ B.live h deviceIDPub /\\\n B.disjoint authKeyID deviceIDPub)\n (ensures fun h0 _ h1 ->\n B.modifies (B.loc_buffer authKeyID) h0 h1 /\\\n B.as_seq h1 authKeyID == derive_authKeyID_spec (B.as_seq h0 deviceIDPub))\n= HST.push_frame ();\n\n let authKeyID_sec = B.alloca (u8 0x00) 20ul in\n (* Prf *) lemma_derive_authKeyID_length_valid ();\n Hacl.Hash.SHA1.hash_oneshot\n authKeyID_sec\n deviceIDPub\n 32ul;\n\n declassify_secret_buffer 20ul authKeyID_sec authKeyID;\n\n HST.pop_frame ()", "val extract (#ha: Hashing.Spec.tls_macAlg) (salt: hkey ha) (ikm: macable ha)\n : ST (hkey ha)\n (requires (fun h0 -> True))\n (ensures (fun h0 t h1 -> FStar.HyperStack.modifies Set.empty h0 h1))\nlet extract:\n #ha: Hashing.Spec.tls_macAlg ->\n salt: hkey ha ->\n ikm: macable ha ->\n ST (hkey ha)\n (requires (fun h0 -> True))\n (ensures (fun h0 t h1 -> FStar.HyperStack.modifies Set.empty h0 h1))\n = fun #ha salt ikm -> HMAC.hmac ha salt ikm" ], "closest_src": [ { "project_name": "dice-star", "file_name": "L0.Spec.Crypto.fst", "name": "L0.Spec.Crypto.derive_AliasKey_spec" }, { "project_name": "steel", "file_name": "L0Crypto.fst", "name": "L0Crypto.derive_AliasKey" }, { "project_name": "dice-star", "file_name": "L0.Impl.Crypto.fst", "name": "L0.Impl.Crypto.derive_AliasKey" }, { "project_name": "steel", "file_name": "L0Crypto.fst", "name": "L0Crypto.derive_key_pair_spec" }, { "project_name": "dice-star", "file_name": "L0.Spec.Crypto.fst", "name": "L0.Spec.Crypto.derive_key_pair_spec" }, { "project_name": "dice-star", "file_name": "L0.Spec.Crypto.fst", "name": "L0.Spec.Crypto.derive_DeviceID_spec" }, { "project_name": "dice-star", "file_name": "L0.Spec.Crypto.fst", "name": "L0.Spec.Crypto.derive_sec_key_pair_spec" }, { "project_name": "dice-star", "file_name": "L0.Spec.Certificate.fst", "name": "L0.Spec.Certificate.sign_and_finalize_aliasKeyCRT_spec" }, { "project_name": "dice-star", "file_name": "L0.Core.fst", "name": "L0.Core.aliasKeyCRT_post" }, { "project_name": "steel", "file_name": "L0Crypto.fst", "name": "L0Crypto.derive_DeviceID" }, { "project_name": "dice-star", "file_name": "L0.Core.fst", "name": "L0.Core.aliasKey_post" }, { "project_name": "steel", "file_name": "L0Crypto.fst", "name": "L0Crypto.derive_AuthKeyID" }, { "project_name": "steel", "file_name": "L0Crypto.fst", "name": "L0Crypto.derive_key_pair" }, { "project_name": "dice-star", "file_name": "L0.Core.fst", "name": "L0.Core.l0_pre" }, { "project_name": "everquic-crypto", "file_name": "NotEverCrypt.CTR.fst", "name": "NotEverCrypt.CTR.kv" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyCRT.fsti", "name": "L0.X509.AliasKeyCRT.x509_get_AliasKeyCRT" }, { "project_name": "dice-star", "file_name": "L0.Core.fst", "name": "L0.Core.l0_aux" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyCRT.fst", "name": "L0.X509.AliasKeyCRT.synth_aliasKeyCRT_payload_t" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.HKDF.fst", "name": "MiTLS.HKDF.derive_secret" }, { "project_name": "dice-star", "file_name": "L0.Impl.Certificate.fst", "name": "L0.Impl.Certificate.sign_and_finalize_aliasKeyCRT" }, { "project_name": "dice-star", "file_name": "L0.Spec.Certificate.fst", "name": "L0.Spec.Certificate.create_aliasKeyTBS_spec" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyCRT.fsti", "name": "L0.X509.AliasKeyCRT.length_of_aliasKeyCRT" }, { "project_name": "noise-star", "file_name": "Impl.Noise.CipherState.fsti", "name": "Impl.Noise.CipherState.eval_opt_aead_key" }, { "project_name": "dice-star", "file_name": "L0.Core.fst", "name": "L0.Core.l0_aux_post" }, { "project_name": "dice-star", "file_name": "L0.Core.fst", "name": "L0.Core.l0" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyCRT.fsti", "name": "L0.X509.AliasKeyCRT.len_of_aliasKeyCRT" }, { "project_name": "dice-star", "file_name": "L0.Impl.Crypto.fst", "name": "L0.Impl.Crypto.l0_core_step1_pre" }, { "project_name": "dice-star", "file_name": "L0.Test.Definitions.fst", "name": "L0.Test.Definitions.dump_l0" }, { "project_name": "dice-star", "file_name": "L0.Impl.Certificate.fst", "name": "L0.Impl.Certificate.create_aliasKeyTBS_buffers_to_bytes" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.SHA2.Core.fst", "name": "Hacl.Impl.SHA2.Core.emit1_spec" }, { "project_name": "dice-star", "file_name": "L0.Core.fst", "name": "L0.Core.l0_post" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.fst", "name": "Hacl.Spec.SHA2.emit" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Ed25519.Group.fst", "name": "Hacl.Impl.Ed25519.Group.refl" }, { "project_name": "dice-star", "file_name": "L0.Impl.Certificate.fst", "name": "L0.Impl.Certificate.create_aliasKeyTBS_pre" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Crypto.fst", "name": "QUIC.Spec.Crypto.derive_secret" }, { "project_name": "dice-star", "file_name": "L0.Impl.Crypto.fst", "name": "L0.Impl.Crypto.derive_key_pair" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2.Common.fst", "name": "Hacl.Streaming.Blake2.Common.s_v" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Impl.Header.fst", "name": "QUIC.Impl.Header.header_decrypt_aux_ct_secret_preserving_not_retry_spec" }, { "project_name": "everquic-crypto", "file_name": "QUIC.State.fsti", "name": "QUIC.State.derive_k" }, { "project_name": "hacl-star", "file_name": "Test.NoHeap.fst", "name": "Test.NoHeap.keysized" }, { "project_name": "dice-star", "file_name": "L0.Impl.Crypto.fst", "name": "L0.Impl.Crypto.l0_core_step1_post" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.HKDF.fst", "name": "Spec.Agile.HKDF.a_spec" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.HMAC.fsti", "name": "Spec.Agile.HMAC.keysized" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.HKDF.fst", "name": "MiTLS.HKDF.expand_spec" }, { "project_name": "steel", "file_name": "L0Crypto.fst", "name": "L0Crypto.aliaskey_len_is_valid" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.DH.fst", "name": "Spec.Agile.DH.clamp" }, { "project_name": "everquic-crypto", "file_name": "NotEverCrypt.CTR.fst", "name": "NotEverCrypt.CTR.iv" }, { "project_name": "dice-star", "file_name": "L0.Spec.Crypto.fst", "name": "L0.Spec.Crypto.derive_authKeyID_spec" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.HPKE.fst", "name": "Spec.Agile.HPKE.sealAuth" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyCRT.fsti", "name": "L0.X509.AliasKeyCRT.len_of_aliasKeyCRT_payload" }, { "project_name": "dice-star", "file_name": "L0.Impl.Certificate.fst", "name": "L0.Impl.Certificate.create_aliasKeyTBS_post" }, { "project_name": "noise-star", "file_name": "Impl.Noise.CipherState.fsti", "name": "Impl.Noise.CipherState.eval_cipher_state_mf" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.HPKE.fst", "name": "Spec.Agile.HPKE.derive_key_pair" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyTBS.fsti", "name": "L0.X509.AliasKeyTBS.len_of_aliasKeyTBS_max" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.SHA2.Core.fst", "name": "Hacl.Impl.SHA2.Core.emit8_spec" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Impl.fsti", "name": "QUIC.Impl.decrypt_pre" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.SHA2.Core.fst", "name": "Hacl.Impl.SHA2.Core.emit4_spec" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Header.fst", "name": "QUIC.Spec.Header.block_of_sample" }, { "project_name": "noise-star", "file_name": "Impl.Noise.API.Instances.IKpsk2_25519_ChaChaPoly_BLAKE2s.Test.fst", "name": "Impl.Noise.API.Instances.IKpsk2_25519_ChaChaPoly_BLAKE2s.Test.test4_spec" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.AESGCM.fst", "name": "Vale.AES.X64.AESGCM.va_wp_Ctr32_ghash_6_prelude" }, { "project_name": "dice-star", "file_name": "L0.Impl.Crypto.fst", "name": "L0.Impl.Crypto.derive_DeviceID" }, { "project_name": "hacl-star", "file_name": "Hacl.HPKE.Interface.AEAD.fsti", "name": "Hacl.HPKE.Interface.AEAD.kv" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.emit" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Impl.Header.fst", "name": "QUIC.Impl.Header.header_encrypt_ct_secret_preserving_not_retry_spec" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.HPKE.fst", "name": "Spec.Agile.HPKE.sealBase" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.Cipher.fsti", "name": "Spec.Agile.Cipher.key" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyTBS.fsti", "name": "L0.X509.AliasKeyTBS.x509_get_AliasKeyTBS" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Chacha20Poly1305.fst", "name": "Hacl.Impl.Chacha20Poly1305.derive_key_poly1305_do" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Keccak.fst", "name": "Hacl.Streaming.Keccak.digest" }, { "project_name": "dice-star", "file_name": "L0.Impl.Crypto.fst", "name": "L0.Impl.Crypto.l0_core_step1" }, { "project_name": "noise-star", "file_name": "Impl.Noise.CipherState.fsti", "name": "Impl.Noise.CipherState.eval_cipher_state_m" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyCRT.fsti", "name": "L0.X509.AliasKeyCRT.length_of_aliasKeyCRT_payload" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.HPKE.fst", "name": "Spec.Agile.HPKE.labeled_expand" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.HPKE.fst", "name": "Spec.Agile.HPKE.labeled_extract" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.HMAC.UFCMA.fst", "name": "MiTLS.HMAC.UFCMA.coerceT" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Impl.Header.fst", "name": "QUIC.Impl.Header.header_decrypt_aux_pre" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_BE.fst", "name": "Vale.AES.GCM_BE.lemma_gcm_encrypt_decrypt_equiv" }, { "project_name": "hacl-star", "file_name": "Hacl.Frodo.KEM.fst", "name": "Hacl.Frodo.KEM.crypto_kem_keypair_st" }, { "project_name": "zeta", "file_name": "Zeta.Steel.KeyUtils.fst", "name": "Zeta.Steel.KeyUtils.truncate_key_spec" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.HKDF.fst", "name": "MiTLS.HKDF.expand_label" }, { "project_name": "everquic-crypto", "file_name": "NotEverCrypt.CTR.fst", "name": "NotEverCrypt.CTR.init" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyTBS.Subject.fst", "name": "L0.X509.AliasKeyTBS.Subject.synth_aliasKeyTBS_subject_payload_t" }, { "project_name": "hacl-star", "file_name": "Hacl.HMAC_DRBG.fst", "name": "Hacl.HMAC_DRBG.repr" }, { "project_name": "hacl-star", "file_name": "EverCrypt.DRBG.fst", "name": "EverCrypt.DRBG.repr" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyCRT.fst", "name": "L0.X509.AliasKeyCRT.lemma_serialize_aliasKeyCRT_size" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.AEAD.fsti", "name": "Spec.Agile.AEAD.kv" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Impl.Header.fst", "name": "QUIC.Impl.Header.header_decrypt_aux_ct" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Impl.fsti", "name": "QUIC.Impl.encrypt_pre" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyCRT.fsti", "name": "L0.X509.AliasKeyCRT.aliasKeyCRT_t" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.HPKE.fst", "name": "Spec.Agile.HPKE.sealPSK" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyCRT.fst", "name": "L0.X509.AliasKeyCRT.lemma_serialize_aliasKeyCRT_payload_unfold" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.SHA2.Core.fst", "name": "Hacl.Impl.SHA2.Core.emit" }, { "project_name": "steel", "file_name": "L0Types.fsti", "name": "L0Types.mk_l0_repr" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyTBS.Issuer.fst", "name": "L0.X509.AliasKeyTBS.Issuer.synth_aliasKeyTBS_issuer_payload_t" }, { "project_name": "dice-star", "file_name": "L0.X509.AliasKeyTBS.fst", "name": "L0.X509.AliasKeyTBS.synth_aliasKeyTBS_payload_t" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.ws_spec_v" }, { "project_name": "noise-star", "file_name": "Impl.Noise.CipherState.fsti", "name": "Impl.Noise.CipherState.eval_aead_key" }, { "project_name": "hacl-star", "file_name": "Hacl.Frodo.KEM.fst", "name": "Hacl.Frodo.KEM.crypto_kem_dec_st" }, { "project_name": "dice-star", "file_name": "L0.Impl.Crypto.fst", "name": "L0.Impl.Crypto.derive_authKeyID" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.HKDF.fsti", "name": "MiTLS.HKDF.extract" } ], "selected_premises": [ "PulseCore.FractionalPermission.full_perm", "Pulse.Lib.BoundedIntegers.add_nat_1", "Pulse.Lib.Pervasives.perform", "FStar.Real.one", "HACL.hkdf_ikm_len", "FStar.UInt.size", "FStar.Real.two", "Pulse.Lib.BoundedIntegers.safe_mod", "Pulse.Lib.BoundedIntegers.bounded_from_bounded_unsigned", "FStar.PCM.composable", "Pulse.Lib.BoundedIntegers.bounded_unsigned_size_t", "HACL.hkdf_lbl_len", "HACL.v32us", "Pulse.Lib.BoundedIntegers.test", "Pulse.Lib.BoundedIntegers.bounded_unsigned_u32", "L0Crypto.derive_DeviceID_spec", "Pulse.Lib.BoundedIntegers.bounded_unsigned_u64", "Pulse.Lib.Core.all_inames", "FStar.PCM.op", "Pulse.Lib.Core.inames", "PulseCore.FractionalPermission.comp_perm", "FStar.PCM.compatible", "PulseCore.FractionalPermission.sum_perm", "Pulse.Lib.Core.emp_inames", "FStar.Mul.op_Star", "Pulse.Lib.BoundedIntegers.bounded_int_nat", "Pulse.Lib.Core.one_half", "FStar.Pervasives.reveal_opaque", "L0Types.l0_record_perm", "Pulse.Lib.Reference.cond", "L0Types.mk_l0_repr", "Pulse.Lib.BoundedIntegers.bounded_int_u64", "Pulse.Lib.BoundedIntegers.bounded_int_int", "Pulse.Lib.Pervasives.vprop_equiv_norm", "FStar.Tactics.Effect.raise", "Pulse.Lib.BoundedIntegers.bounded_int_size_t", "Pulse.Lib.BoundedIntegers.bounded_int_pos", "HACL.signable_len", "HACL.hashable_len", "Pulse.Lib.BoundedIntegers.size_t_plus_one", "Pulse.Lib.Pervasives.inames_join_self", "Pulse.Lib.BoundedIntegers.bounded_int_u32", "Pulse.Lib.BoundedIntegers.sub_u32", "Pulse.Lib.BoundedIntegers.nat_as_int", "FStar.Pervasives.Native.fst", "Pulse.Lib.Core.join_inames", "FStar.Pervasives.Native.snd", "PulseCore.FractionalPermission.half_perm", "Pulse.Lib.Pervasives.tfst", "Pulse.Lib.Core.add_iname", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity", "Pulse.Lib.BoundedIntegers.fits_t", "FStar.Tactics.Effect.get", "Pulse.Lib.BoundedIntegers.safe_add", "FStar.Real.zero", "FStar.Tactics.Types.issues", "Pulse.Lib.Core.unit_non_informative", "Pulse.Lib.Core.inames_subset", "Pulse.Lib.Pervasives.default_arg", "Pulse.Lib.Core.prop_non_informative", "Pulse.Lib.Pervasives.inames_ext", "PulseCore.FractionalPermission.lesser_perm", "Pulse.Lib.Core.squash_non_informative", "Pulse.Lib.Pervasives.perform_ghost", "FStar.Pervasives.dfst", "Pulse.Lib.Pervasives.tthd", "Pulse.Lib.Core.erased_non_informative", "FStar.Pervasives.dsnd", "FStar.Math.Lemmas.pow2_plus", "PulseCore.FractionalPermission.writeable", "FStar.SizeT.mod_spec", "Pulse.Lib.BoundedIntegers.pos_as_int", "Pulse.Lib.Pervasives.tsnd", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity_forall", "FStar.Monotonic.Pure.intro_pure_wp_monotonicity", "Pulse.Lib.BoundedIntegers.ok", "Pulse.Lib.Core.mem_iname", "Pulse.Lib.BoundedIntegers.add", "FStar.Math.Lemmas.pow2_lt_compat", "FStar.PCM.lem_commutative", "FStar.Math.Lemmas.pow2_le_compat", "FStar.Tactics.Typeclasses.solve", "FStar.Tactics.Effect.tactic", "PulseCore.FractionalPermission.lesser_equal_perm", "PulseCore.Observability.at_most_one_observable", "FStar.Monotonic.Pure.is_monotonic", "FStar.PCM.compatible_trans", "Pulse.Lib.BoundedIntegers.add_nat", "FStar.UInt.max_int", "FStar.UInt32.op_Star_Hat", "FStar.UInt16.op_Star_Hat", "FStar.UInt64.op_Star_Hat", "FStar.UInt8.op_Star_Hat", "FStar.PCM.compatible_elim", "FStar.PCM.exclusive", "PulseCore.Observability.join_obs", "FStar.PCM.frame_preserving_val_to_fp_upd", "FStar.UInt64.op_Subtraction_Question_Hat", "FStar.UInt16.op_Subtraction_Question_Hat", "FStar.UInt32.op_Subtraction_Question_Hat" ], "source_upto_this": "(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule L0Crypto\nopen Pulse.Lib.Pervasives\nopen Pulse.Lib.BoundedIntegers\nmodule R = Pulse.Lib.Reference\nmodule A = Pulse.Lib.Array\nmodule US = FStar.SizeT\nmodule U8 = FStar.UInt8\nmodule U32 = FStar.UInt32\nopen HACL\nopen L0Types\n\nval deviceid_len_is_valid (len:US.t)\n : valid_hkdf_lbl_len len\n\nval aliaskey_len_is_valid (len:US.t)\n : valid_hkdf_lbl_len len\n\nval derive_key_pair_spec\n (ikm_len: hkdf_ikm_len)\n (ikm: Seq.seq U8.t)\n (lbl_len: hkdf_lbl_len)\n (lbl: Seq.seq U8.t)\n : GTot (Seq.seq U8.t & Seq.seq U8.t)\n\nval derive_key_pair\n (pub : A.larray U8.t (US.v v32us))\n (priv: A.larray U8.t (US.v v32us))\n (ikm_len: hkdf_ikm_len)\n (ikm: A.array U8.t)\n (lbl_len: hkdf_lbl_len)\n (lbl: A.array U8.t)\n (#ikm_perm #lbl_perm:perm)\n (#_pub_seq #_priv_seq #ikm_seq #lbl_seq:erased (Seq.seq U8.t))\n : stt unit\n (requires (\n A.pts_to pub _pub_seq **\n A.pts_to priv _priv_seq **\n A.pts_to ikm #ikm_perm ikm_seq **\n A.pts_to lbl #lbl_perm lbl_seq\n ))\n (ensures (fun _ ->\n A.pts_to ikm #ikm_perm ikm_seq **\n A.pts_to lbl #lbl_perm lbl_seq **\n (exists* (pub_seq\n priv_seq:Seq.seq U8.t).\n A.pts_to pub pub_seq **\n A.pts_to priv priv_seq **\n pure ((pub_seq, priv_seq) == derive_key_pair_spec ikm_len ikm_seq lbl_len lbl_seq)\n )))\n\nlet derive_DeviceID_spec\n (alg:alg_t)\n (dig_len:hkdf_ikm_len)\n (cdi: Seq.seq U8.t) (* should be length 32 *)\n (l0_label_DeviceID_len: hkdf_lbl_len)\n (l0_label_DeviceID: Seq.seq U8.t)\n: GTot (Seq.seq U8.t & Seq.seq U8.t)\n= let cdigest = spec_hash alg cdi in\n derive_key_pair_spec\n (* ikm *) dig_len cdigest\n (* lbl *) l0_label_DeviceID_len l0_label_DeviceID\n\nval derive_DeviceID\n (alg:alg_t)\n (deviceID_pub:A.larray U8.t (US.v v32us))\n (deviceID_priv:A.larray U8.t (US.v v32us))\n (cdi:A.larray U8.t (US.v dice_digest_len))\n (deviceID_label_len:hkdf_lbl_len)\n (deviceID_label:A.larray U8.t (US.v deviceID_label_len))\n (#cdi0 #deviceID_label0 #deviceID_pub0 #deviceID_priv0:erased (Seq.seq U8.t))\n (#cdi_perm #p:perm)\n : stt unit\n (requires (\n A.pts_to cdi #cdi_perm cdi0 **\n A.pts_to deviceID_label #p deviceID_label0 **\n A.pts_to deviceID_pub deviceID_pub0 **\n A.pts_to deviceID_priv deviceID_priv0 **\n pure (valid_hkdf_ikm_len (digest_len alg))\n ))\n (ensures (fun _ ->\n A.pts_to cdi #cdi_perm cdi0 **\n A.pts_to deviceID_label #p deviceID_label0 **\n (exists* (deviceID_pub1 deviceID_priv1:Seq.seq U8.t).\n A.pts_to deviceID_pub deviceID_pub1 **\n A.pts_to deviceID_priv deviceID_priv1 **\n pure (\n valid_hkdf_ikm_len (digest_len alg) /\\\n derive_DeviceID_spec alg (digest_len alg) cdi0 deviceID_label_len deviceID_label0\n == (deviceID_pub1, deviceID_priv1)\n )\n ))\n )\n", "sketch": [ "Step 1: The definition `derive_AliasKey_spec` is about deriving a key pair (public and private keys) for an alias key using the given algorithm, digest length, CDI, FWID, and label.\nStep 2: To implement this, we first compute the hash of the concatenation of CDI and FWID using the specified algorithm. Then, we use this hash as the input key material (IKM) to derive the key pair using the `derive_key_pair_spec` function, along with the provided label and its length.", "Step 1: The `derive_AliasKey_spec` function is intended to derive a pair of keys (public and private) for an alias key using the HKDF (HMAC-based Extract-and-Expand Key Derivation Function) algorithm. The function takes as input an algorithm type, a digest length, a sequence representing the CDI (Credential Device Identifier), a sequence representing the FWID (Firmware Identifier), a label length, and a label sequence.\nStep 2: The implementation involves first computing a combined digest of the CDI and FWID using the specified algorithm. Then, it calls the `derive_key_pair_spec` function with the computed digest and the provided label to derive the key pair.", "Step 1: The definition `derive_AliasKey_spec` is about deriving a key pair (public and private keys) for an alias key using the given algorithm, digest length, and input keying material (cdi and fwid). It also uses a label and its length to derive the keys.\nStep 2: The implementation first computes the hash of the concatenation of `cdi` and `fwid` using the specified algorithm. Then, it uses the `derive_key_pair_spec` function to derive the key pair from the computed hash and the provided label and its length.", "Step 1: The definition `derive_AliasKey_spec` is about deriving a key pair (public and private keys) for an alias key using the given cryptographic algorithm, digest length, and input sequences.\nStep 2: The implementation involves first computing a hash of the concatenation of `cdi` and `fwid` using the specified algorithm. Then, it uses the `derive_key_pair_spec` function to derive the key pair from the resulting hash and the provided label.", "Step 1: The definition `derive_AliasKey_spec` is about deriving a key pair (public and private keys) for an alias using the HKDF (HMAC-based Extract-and-Expand Key Derivation Function) algorithm. It takes as input an algorithm type, a digest length, a CDI (Caller Device Identifier), an FWID (Firmware Identifier), a label length, and a label. The output is a tuple containing the derived public and private keys.\n\nStep 2: The implementation first computes the hash of the concatenation of the CDI and FWID using the specified algorithm. This hash is then used as the input key material (IKM) for the HKDF key derivation process. The function `derive_key_pair_spec` is called with this IKM and the provided label to derive the key pair.", "Step 1: The definition `derive_AliasKey_spec` is about deriving a key pair (public and private keys) for an alias key using the given algorithm, digest length, CDI, FWID, and label.\nStep 2: The implementation involves first computing the hash of the concatenation of `cdi` and `fwid` using the specified algorithm. Then, it uses the `derive_key_pair_spec` function to derive the key pair from the computed hash and the provided label.", "Step 1: The definition `derive_AliasKey_spec` is about deriving a key pair (public and private keys) for an alias key using the given algorithm, digest length, and input sequences. The input sequences include the CDI (Credential Device Identifier), FWID (Firmware Identifier), and a label for the alias key.\nStep 2: The implementation involves first hashing the concatenation of the CDI and FWID using the specified algorithm to produce a digest. Then, it uses the `derive_key_pair_spec` function to derive the key pair from this digest and the provided label.", "Step 1: The definition `derive_AliasKey_spec` is about deriving a key pair (public and private keys) for an alias key using the given algorithm, digest length, CDI, FWID, and label. The function returns a tuple of sequences representing the public and private keys.\nStep 2: The implementation involves first computing the hash of the concatenation of CDI and FWID using the specified algorithm. Then, it calls `derive_key_pair_spec` with the digest length, the computed hash, the label length, and the label to derive the key pair.", "Step 1: The definition `derive_AliasKey_spec` is about deriving a key pair (public and private keys) for an alias key using the provided cryptographic algorithm, input key material (cdi and fwid), and label.\nStep 2: The implementation involves first hashing the concatenation of `cdi` and `fwid` using the specified algorithm to produce a digest. Then, it uses this digest as the input key material to derive the key pair using the `derive_key_pair_spec` function, along with the provided label and its length.", "Step 1: The definition `derive_AliasKey_spec` is about deriving a key pair (public and private keys) for an alias key using the given algorithm, digest length, CDI, FWID, and label.\nStep 2: The implementation involves first computing the hash of the concatenation of the CDI and FWID using the specified algorithm. Then, it calls `derive_key_pair_spec` with the computed hash, the label length, and the label to derive the key pair." ], "generated_solution": [ "let derive_AliasKey_spec\n (alg: alg_t)\n (dig_len: hkdf_ikm_len)\n (cdi fwid: Seq.seq U8.t)\n (l0_label_AliasKey_len: hkdf_lbl_len)\n (l0_label_AliasKey: Seq.seq U8.t)\n: GTot (Seq.seq U8.t & Seq.seq U8.t)\n= let cdigest = spec_hash alg (Seq.append cdi fwid) in\n derive_key_pair_spec\n (* ikm *) dig_len cdigest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey", "= let combined_digest = spec_hash alg (Seq.append cdi fwid) in\n derive_key_pair_spec\n (* ikm *) dig_len combined_digest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey", "let derive_AliasKey_spec\n (alg: alg_t)\n (dig_len: hkdf_ikm_len)\n (cdi fwid: Seq.seq U8.t)\n (l0_label_AliasKey_len: hkdf_lbl_len)\n (l0_label_AliasKey: Seq.seq U8.t)\n: GTot (Seq.seq U8.t & Seq.seq U8.t)\n= let combined_input = Seq.append cdi fwid in\n let cdigest = spec_hash alg combined_input in\n derive_key_pair_spec\n (* ikm *) dig_len cdigest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey", "let derive_AliasKey_spec\n (alg: alg_t)\n (dig_len: hkdf_ikm_len)\n (cdi fwid: Seq.seq U8.t)\n (l0_label_AliasKey_len: hkdf_lbl_len)\n (l0_label_AliasKey: Seq.seq U8.t)\n: GTot (Seq.seq U8.t & Seq.seq U8.t)\n= let combined_input = Seq.append cdi fwid in\n let cdigest = spec_hash alg combined_input in\n derive_key_pair_spec\n (* ikm *) dig_len cdigest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey", "let derive_AliasKey_spec\n (alg: alg_t)\n (dig_len: hkdf_ikm_len)\n (cdi fwid: Seq.seq U8.t)\n (l0_label_AliasKey_len: hkdf_lbl_len)\n (l0_label_AliasKey: Seq.seq U8.t)\n: GTot (Seq.seq U8.t & Seq.seq U8.t)\n= let combined_input = Seq.append cdi fwid in\n let cdigest = spec_hash alg combined_input in\n derive_key_pair_spec\n (* ikm *) dig_len cdigest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey", "let derive_AliasKey_spec\n (alg: alg_t)\n (dig_len: hkdf_ikm_len)\n (cdi fwid: Seq.seq U8.t)\n (l0_label_AliasKey_len: hkdf_lbl_len)\n (l0_label_AliasKey: Seq.seq U8.t)\n: GTot (Seq.seq U8.t & Seq.seq U8.t)\n= let combined_digest = spec_hash alg (Seq.append cdi fwid) in\n derive_key_pair_spec\n (* ikm *) dig_len combined_digest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey", "let derive_AliasKey_spec\n (alg: alg_t)\n (dig_len: hkdf_ikm_len)\n (cdi fwid: Seq.seq U8.t)\n (l0_label_AliasKey_len: hkdf_lbl_len)\n (l0_label_AliasKey: Seq.seq U8.t)\n: GTot (Seq.seq U8.t & Seq.seq U8.t)\n= let cdigest = spec_hash alg (Seq.append cdi fwid) in\n derive_key_pair_spec\n (* ikm *) dig_len cdigest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey", "let derive_AliasKey_spec\n (alg: alg_t)\n (dig_len: hkdf_ikm_len)\n (cdi fwid: Seq.seq U8.t)\n (l0_label_AliasKey_len: hkdf_lbl_len)\n (l0_label_AliasKey: Seq.seq U8.t)\n: GTot (Seq.seq U8.t & Seq.seq U8.t)\n= let combined_input = Seq.append cdi fwid in\n let cdigest = spec_hash alg combined_input in\n derive_key_pair_spec\n (* ikm *) dig_len cdigest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey", "= let cdigest = spec_hash alg (Seq.append cdi fwid) in\n derive_key_pair_spec\n (* ikm *) dig_len cdigest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey", "let derive_AliasKey_spec\n (alg: alg_t)\n (dig_len: hkdf_ikm_len)\n (cdi fwid: Seq.seq U8.t)\n (l0_label_AliasKey_len: hkdf_lbl_len)\n (l0_label_AliasKey: Seq.seq U8.t)\n: GTot (Seq.seq U8.t & Seq.seq U8.t)\n= let combined_digest = spec_hash alg (Seq.append cdi fwid) in\n derive_key_pair_spec\n (* ikm *) dig_len combined_digest\n (* lbl *) l0_label_AliasKey_len l0_label_AliasKey" ] }, { "file_name": "Hacl.Spec.PrecompBaseTable.fst", "name": "Hacl.Spec.PrecompBaseTable.seq_of_list_append_lemma", "opens_and_abbrevs": [ { "abbrev": "BE", "full_module": "Hacl.Impl.Exponentiation.Definitions" }, { "abbrev": "SE", "full_module": "Spec.Exponentiation" }, { "abbrev": "LE", "full_module": "Lib.Exponentiation.Definition" }, { "abbrev": "LSeq", "full_module": "Lib.Sequence" }, { "abbrev": "FL", "full_module": "FStar.List.Tot" }, { "open": "Lib.IntTypes" }, { "open": "FStar.Mul" }, { "abbrev": "BE", "full_module": "Hacl.Impl.Exponentiation.Definitions" }, { "abbrev": "SE", "full_module": "Spec.Exponentiation" }, { "abbrev": "LE", "full_module": "Lib.Exponentiation.Definition" }, { "abbrev": "LSeq", "full_module": "Lib.Sequence" }, { "abbrev": "FL", "full_module": "FStar.List.Tot" }, { "open": "Lib.IntTypes" }, { "open": "FStar.Mul" }, { "open": "Hacl.Spec" }, { "open": "Hacl.Spec" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 0, "max_fuel": 0, "initial_ifuel": 0, "max_ifuel": 0, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val seq_of_list_append_lemma: #a:Type -> x:list a -> y:list a ->\n Lemma (let xy_lseq = Seq.seq_of_list FL.(x @ y) in\n Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x /\\\n Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y)", "source_definition": "let seq_of_list_append_lemma #a x y =\n let xy = FL.(x @ y) in\n let x_lseq = Seq.seq_of_list x in\n let y_lseq = Seq.seq_of_list y in\n let xy_lseq = Seq.seq_of_list xy in\n let x_len = FL.length x in\n let y_len = FL.length y in\n\n let lemma_x_lseq (i:nat{i < x_len}) : Lemma (Seq.index xy_lseq i == Seq.index x_lseq i) =\n list_append_index x y i in\n\n FStar.Classical.forall_intro lemma_x_lseq;\n Seq.lemma_eq_intro (Seq.slice xy_lseq 0 x_len) x_lseq;\n assert (Seq.slice xy_lseq 0 x_len == x_lseq);\n\n let lemma_y_lseq (i:nat{i < y_len}) :\n Lemma (Seq.index xy_lseq (x_len + i) == Seq.index y_lseq i) =\n list_append_index x y (x_len + i) in\n\n FStar.Classical.forall_intro lemma_y_lseq;\n Seq.lemma_eq_intro (Seq.slice xy_lseq x_len (x_len + y_len)) y_lseq;\n assert (Seq.slice xy_lseq x_len (x_len + y_len) == y_lseq)", "source_range": { "start_line": 43, "start_col": 0, "end_line": 64, "end_col": 60 }, "interleaved": false, "definition": "fun x y ->\n let xy = x @ y in\n let x_lseq = FStar.Seq.Base.seq_of_list x in\n let y_lseq = FStar.Seq.Base.seq_of_list y in\n let xy_lseq = FStar.Seq.Base.seq_of_list xy in\n let x_len = FStar.List.Tot.Base.length x in\n let y_len = FStar.List.Tot.Base.length y in\n let lemma_x_lseq i =\n Hacl.Spec.PrecompBaseTable.list_append_index x y i\n <:\n FStar.Pervasives.Lemma (ensures FStar.Seq.Base.index xy_lseq i == FStar.Seq.Base.index x_lseq i)\n in\n FStar.Classical.forall_intro lemma_x_lseq;\n FStar.Seq.Base.lemma_eq_intro (FStar.Seq.Base.slice xy_lseq 0 x_len) x_lseq;\n assert (FStar.Seq.Base.slice xy_lseq 0 x_len == x_lseq);\n let lemma_y_lseq i =\n Hacl.Spec.PrecompBaseTable.list_append_index x y (x_len + i)\n <:\n FStar.Pervasives.Lemma\n (ensures FStar.Seq.Base.index xy_lseq (x_len + i) == FStar.Seq.Base.index y_lseq i)\n in\n FStar.Classical.forall_intro lemma_y_lseq;\n FStar.Seq.Base.lemma_eq_intro (FStar.Seq.Base.slice xy_lseq x_len (x_len + y_len)) y_lseq;\n assert (FStar.Seq.Base.slice xy_lseq x_len (x_len + y_len) == y_lseq)", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "Prims.list", "Prims._assert", "Prims.eq2", "FStar.Seq.Base.seq", "FStar.Seq.Base.slice", "Prims.op_Addition", "Prims.unit", "FStar.Seq.Base.lemma_eq_intro", "FStar.Classical.forall_intro", "Prims.nat", "Prims.b2t", "Prims.op_LessThan", "FStar.Seq.Base.index", "Prims.l_True", "Prims.squash", "Prims.Nil", "FStar.Pervasives.pattern", "Hacl.Spec.PrecompBaseTable.list_append_index", "FStar.List.Tot.Base.length", "FStar.Seq.Base.length", "FStar.Seq.Base.seq_of_list", "FStar.List.Tot.Base.op_At" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "x: Prims.list a -> y: Prims.list a\n -> FStar.Pervasives.Lemma\n (ensures\n (let xy_lseq = FStar.Seq.Base.seq_of_list (x @ y) in\n FStar.Seq.Base.slice xy_lseq 0 (FStar.List.Tot.Base.length x) ==\n FStar.Seq.Base.seq_of_list x /\\\n FStar.Seq.Base.slice xy_lseq\n (FStar.List.Tot.Base.length x)\n (FStar.List.Tot.Base.length x + FStar.List.Tot.Base.length y) ==\n FStar.Seq.Base.seq_of_list y))", "prompt": "let seq_of_list_append_lemma #a x y =\n ", "expected_response": "let xy = let open FL in x @ y in\nlet x_lseq = Seq.seq_of_list x in\nlet y_lseq = Seq.seq_of_list y in\nlet xy_lseq = Seq.seq_of_list xy in\nlet x_len = FL.length x in\nlet y_len = FL.length y in\nlet lemma_x_lseq (i: nat{i < x_len}) : Lemma (Seq.index xy_lseq i == Seq.index x_lseq i) =\n list_append_index x y i\nin\nFStar.Classical.forall_intro lemma_x_lseq;\nSeq.lemma_eq_intro (Seq.slice xy_lseq 0 x_len) x_lseq;\nassert (Seq.slice xy_lseq 0 x_len == x_lseq);\nlet lemma_y_lseq (i: nat{i < y_len}) : Lemma (Seq.index xy_lseq (x_len + i) == Seq.index y_lseq i) =\n list_append_index x y (x_len + i)\nin\nFStar.Classical.forall_intro lemma_y_lseq;\nSeq.lemma_eq_intro (Seq.slice xy_lseq x_len (x_len + y_len)) y_lseq;\nassert (Seq.slice xy_lseq x_len (x_len + y_len) == y_lseq)", "source": { "project_name": "hacl-star", "file_name": "code/bignum/Hacl.Spec.PrecompBaseTable.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Hacl.Spec.PrecompBaseTable.fst", "checked_file": "dataset/Hacl.Spec.PrecompBaseTable.fst.checked", "interface_file": true, "dependencies": [ "dataset/Spec.Exponentiation.fsti.checked", "dataset/prims.fst.checked", "dataset/Lib.Sequence.fsti.checked", "dataset/Lib.IntTypes.fsti.checked", "dataset/Lib.Exponentiation.Definition.fsti.checked", "dataset/Hacl.Impl.Exponentiation.Definitions.fst.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Calc.fsti.checked" ] }, "definitions_in_context": [ "mk_precomp_base_table", "mk_precomp_base_table", "class mk_precomp_base_table (t:Type) (a_t:BE.inttype_a) (len:size_t{v len > 0}) (ctx_len:size_t) = {\n concr_ops: SE.concrete_ops t;\n to_cm: x:BE.to_comm_monoid a_t len ctx_len{x.BE.a_spec == concr_ops.SE.to.SE.a_spec};\n to_list: t -> x:list (uint_t a_t SEC){FL.length x = v len /\\ to_cm.BE.linv (Seq.seq_of_list x)};\n lemma_refl: x:t ->\n Lemma (concr_ops.SE.to.SE.refl x == to_cm.BE.refl (Seq.seq_of_list (to_list x)));\n}", "class mk_precomp_base_table (t:Type) (a_t:BE.inttype_a) (len:size_t{v len > 0}) (ctx_len:size_t) = {\n concr_ops: SE.concrete_ops t;\n to_cm: x:BE.to_comm_monoid a_t len ctx_len{x.BE.a_spec == concr_ops.SE.to.SE.a_spec};\n to_list: t -> x:list (uint_t a_t SEC){FL.length x = v len /\\ to_cm.BE.linv (Seq.seq_of_list x)};\n lemma_refl: x:t ->\n Lemma (concr_ops.SE.to.SE.refl x == to_cm.BE.refl (Seq.seq_of_list (to_list x)));\n}", "class mk_precomp_base_table (t:Type) (a_t:BE.inttype_a) (len:size_t{v len > 0}) (ctx_len:size_t) = {\n concr_ops: SE.concrete_ops t;\n to_cm: x:BE.to_comm_monoid a_t len ctx_len{x.BE.a_spec == concr_ops.SE.to.SE.a_spec};\n to_list: t -> x:list (uint_t a_t SEC){FL.length x = v len /\\ to_cm.BE.linv (Seq.seq_of_list x)};\n lemma_refl: x:t ->\n Lemma (concr_ops.SE.to.SE.refl x == to_cm.BE.refl (Seq.seq_of_list (to_list x)));\n}", "class mk_precomp_base_table (t:Type) (a_t:BE.inttype_a) (len:size_t{v len > 0}) (ctx_len:size_t) = {\n concr_ops: SE.concrete_ops t;\n to_cm: x:BE.to_comm_monoid a_t len ctx_len{x.BE.a_spec == concr_ops.SE.to.SE.a_spec};\n to_list: t -> x:list (uint_t a_t SEC){FL.length x = v len /\\ to_cm.BE.linv (Seq.seq_of_list x)};\n lemma_refl: x:t ->\n Lemma (concr_ops.SE.to.SE.refl x == to_cm.BE.refl (Seq.seq_of_list (to_list x)));\n}", "val list_append_index1: #a:Type -> x:list a -> y:list a -> i:nat{i < FL.length x} ->\n Lemma (ensures (FL.(index (x @ y)) i == FL.index x i)) (decreases (FL.length x))", "concr_ops", "concr_ops", "to_cm", "to_cm", "to_list", "to_list", "let rec list_append_index1 #a x y i =\n match x with\n | [] -> ()\n | hd::tl -> if i = 0 then () else list_append_index1 tl y (i - 1)", "lemma_refl", "lemma_refl", "val list_append_index2: #a:Type -> x:list a -> y:list a -> i:nat{FL.length x <= i /\\ i < FL.length x + FL.length y} ->\n Lemma (ensures (FL.(index (x @ y)) i == FL.index y (i - FL.length x))) (decreases (FL.length x))", "let g_i_acc_t (t:Type) (a_t:BE.inttype_a) (len:size_t{v len > 0}) (ctx_len:size_t) (i:nat) =\n t & acc:list (uint_t a_t SEC){FL.length acc == (i + 1) * v len}", "let rec list_append_index2 #a x y i =\n match x with\n | [] -> ()\n | hd::tl -> list_append_index2 tl y (i - 1)", "let precomp_base_table_f (#t:Type) (#a_t:BE.inttype_a) (#len:size_t{v len > 0}) (#ctx_len:size_t)\n (k:mk_precomp_base_table t a_t len ctx_len) (g:t)\n (i:nat) ((g_i,acc): g_i_acc_t t a_t len ctx_len i) : g_i_acc_t t a_t len ctx_len (i + 1) =\n let acc = FL.(acc @ k.to_list g_i) in\n let g_i = k.concr_ops.SE.mul g_i g in\n g_i, acc", "val list_append_index: #a:Type -> x:list a -> y:list a -> i:nat{i < FL.length x + FL.length y} ->\n Lemma (FL.(index (x @ y)) i ==\n (if i < FL.length x then FL.index x i else FL.index y (i - FL.length x)))", "let list_append_index #a x y i =\n if i < FL.length x then list_append_index1 x y i else list_append_index2 x y i" ], "closest": [ "val append_list_seq (#a:Type) (x y:list a) : Lemma\n (seq_of_list (x @ y) == append (seq_of_list x) (seq_of_list y))\nlet append_list_seq #a x y =\n list_append_length x y;\n let n = List.length (x @ y) in\n let index_of_x_y (i:nat{i < n}) : a = index (seq_of_list (x @ y)) i in\n let index_of_append_x_y (i:nat{i < n}) : a = index (append (seq_of_list x) (seq_of_list y)) i in\n let f (i:nat{i < n}) : Lemma (index_of_x_y i == index_of_append_x_y i) =\n list_append_index x y i;\n lemma_seq_of_list_index (x @ y) i;\n (\n if i < List.length x then\n lemma_seq_of_list_index x i\n else\n lemma_seq_of_list_index y (i - List.length x)\n )\n in\n FStar.Classical.forall_intro f;\n assert (equal (seq_of_list (x @ y)) (append (seq_of_list x) (seq_of_list y)))", "val list_append_length (#a:Type) (x y:list a) : Lemma\n (List.length (x @ y) == List.length x + List.length y)\nlet rec list_append_length #a x y =\n match x with\n | [] -> ()\n | _::t -> list_append_length t y", "val lemma_slice_first_exactly_in_append (#a:Type) (x y:seq a) :\n Lemma (slice (append x y) 0 (length x) == x)\nlet lemma_slice_first_exactly_in_append (#a:Type) (x y:seq a) :\n Lemma (slice (append x y) 0 (length x) == x) =\n let xy = append x y in\n let xy_slice = slice xy 0 (length x) in\n let x_slice = slice x 0 (length x) in\n assert(equal xy_slice x_slice); // OBSERVE: extensionality\n ()", "val list_append_index (#a:Type) (x y:list a) (i:nat) : Lemma\n (requires i < List.length (x @ y))\n (ensures (\n let nx = List.length x in\n (i >= nx ==> i - nx < List.length y) /\\\n List.index (x @ y) i == (if i < nx then List.index x i else List.index y (i - nx))\n ))\nlet rec list_append_index #a x y i =\n match x with\n | [] -> ()\n | h::t -> (if i > 0 then list_append_index t y (i - 1))", "val slice_append_back (#a: Type) (x y: seq a) (i: nat)\n : Lemma (requires length x <= i /\\ i <= length x + length y)\n (ensures slice (append x y) 0 i == append x (slice y 0 (i - length x)))\nlet slice_append_back (#a:Type) (x y:seq a) (i:nat) : Lemma\n (requires length x <= i /\\ i <= length x + length y)\n (ensures slice (append x y) 0 i == append x (slice y 0 (i - length x)))\n =\n assert (equal (slice (append x y) 0 i) (append x (slice y 0 (i - length x))));\n ()", "val slice_append_back (#a: Type) (x y: seq a) (i: nat)\n : Lemma (requires length x <= i /\\ i <= length x + length y)\n (ensures slice (append x y) 0 i == append x (slice y 0 (i - length x)))\nlet slice_append_back (#a:Type) (x y:seq a) (i:nat) : Lemma\n (requires length x <= i /\\ i <= length x + length y)\n (ensures slice (append x y) 0 i == append x (slice y 0 (i - length x)))\n =\n assert (equal (slice (append x y) 0 i) (append x (slice y 0 (i - length x))));\n ()", "val lemma_count_append1 (#a: eqtype) (s: S.seq a) (x y: a)\n : Lemma\n (ensures\n (let s1 = SA.append1 s x in\n if x = y then S.count y s1 = 1 + S.count y s else S.count y s1 = S.count y s))\nlet lemma_count_append1 (#a:eqtype) (s: S.seq a) (x: a) (y: a)\n : Lemma (ensures (let s1 = SA.append1 s x in\n if x = y then\n S.count y s1 = 1 + S.count y s\n else\n S.count y s1 = S.count y s))\n = S.lemma_append_count s (S.create 1 x)", "val append_distributes_seq_to_seq_four_LE (#a:Type) (x:seq a{length x % 4 == 0}) (y:seq a{length y % 4 == 0}) :\n Lemma (seq_to_seq_four_LE (x @| y) == seq_to_seq_four_LE x @| seq_to_seq_four_LE y)\nlet append_distributes_seq_to_seq_four_LE (#a:Type) (x:seq a{length x % 4 == 0}) (y:seq a{length y % 4 == 0}) :\n Lemma (seq_to_seq_four_LE (x @| y) == seq_to_seq_four_LE x @| seq_to_seq_four_LE y)\n =\n reveal_opaque (`%seq_to_seq_four_LE) (seq_to_seq_four_LE #a);\n assert (equal (seq_to_seq_four_LE (x @| y)) (seq_to_seq_four_LE x @| seq_to_seq_four_LE y));\n ()", "val seq_of_list_tl\n (#a: Type)\n (l: list a { List.Tot.length l > 0 } )\n: Lemma\n (requires True)\n (ensures (seq_of_list (List.Tot.tl l) == tail (seq_of_list l)))\nlet seq_of_list_tl #_ l = lemma_seq_of_list_induction l", "val append_distributes_seq_four_to_seq_LE (#a:Type) (x:seq (four a)) (y:seq (four a)) :\n Lemma (seq_four_to_seq_LE (x @| y) == seq_four_to_seq_LE x @| seq_four_to_seq_LE y)\nlet append_distributes_seq_four_to_seq_LE #a x y =\n reveal_opaque (`%seq_four_to_seq_LE) (seq_four_to_seq_LE #a);\n assert (equal (seq_four_to_seq_LE (x @| y)) (seq_four_to_seq_LE x @| seq_four_to_seq_LE y))", "val singleton_list_seq (#a:Type) (x:a) : Lemma\n (seq_of_list [x] == create 1 x)\nlet singleton_list_seq #a x =\n lemma_seq_of_list_index [x] 0;\n assert (equal (seq_of_list [x]) (create 1 x))", "val lemma_append_single (xs: list 'a) (y: 'a) (i: nat)\n : Lemma (requires (i == L.length xs))\n (ensures\n (L.length (xs `L.append` [y]) = L.length xs + 1 /\\ L.index (xs `L.append` [y]) i == y))\nlet rec lemma_append_single (xs:list 'a) (y:'a) (i:nat) :\n Lemma\n (requires (i == L.length xs))\n (ensures (\n L.length (xs `L.append` [y]) = L.length xs + 1 /\\\n L.index (xs `L.append` [y]) i == y)) =\n match xs with\n | [] -> ()\n | x :: xs -> lemma_append_single xs y (i - 1)", "val lemma_seq_of_list_induction (#a:Type) (l:list a)\n :Lemma (requires True)\n (ensures (let s = seq_of_list l in\n match l with\n | [] -> Seq.equal s empty\n | hd::tl -> s == cons hd (seq_of_list tl) /\\\n\t\t head s == hd /\\ tail s == (seq_of_list tl)))\nlet lemma_seq_of_list_induction #_ l\n = match l with\n | [] -> ()\n | hd::tl -> lemma_tl hd (seq_of_list tl)", "val serialize_list_upd\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (l1: list t)\n (x: t)\n (l2: list t)\n (y: t)\n : Lemma\n (requires\n (serialize_list_precond k /\\ Seq.length (serialize s y) == Seq.length (serialize s x)))\n (ensures\n (let ln1 = Seq.length (serialize (serialize_list _ s) l1) in\n let ln2 = Seq.length (serialize (serialize_list _ s) l2) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (l1 `L.append` (x :: l2)) in\n Seq.length sl == ln1 + Seq.length sx + ln2 /\\\n serialize (serialize_list _ s) (l1 `L.append` (y :: l2)) ==\n seq_upd_seq sl ln1 (serialize s y)))\n (decreases (L.length l1))\nlet serialize_list_upd\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (l1: list t)\n (x: t)\n (l2: list t)\n (y: t)\n: Lemma\n (requires (\n serialize_list_precond k /\\\n Seq.length (serialize s y) == Seq.length (serialize s x)\n ))\n (ensures (\n let ln1 = Seq.length (serialize (serialize_list _ s) l1) in\n let ln2 = Seq.length (serialize (serialize_list _ s) l2) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (l1 `L.append` (x :: l2)) in\n Seq.length sl == ln1 + Seq.length sx + ln2 /\\\n serialize (serialize_list _ s) (l1 `L.append` (y :: l2)) == seq_upd_seq sl ln1 (serialize s y)\n ))\n (decreases (L.length l1))\n= serialize_list_append _ s l1 (y :: l2);\n assert (serialize (serialize_list _ s) (l1 `L.append` (y :: l2)) == serialize (serialize_list _ s) l1 `Seq.append` serialize (serialize_list _ s) (y :: l2));\n serialize_list_cons_upd s x l2 y;\n assert (serialize (serialize_list _ s) (l1 `L.append` (y :: l2)) == serialize (serialize_list _ s) l1 `Seq.append` seq_upd_seq (serialize (serialize_list _ s) (x :: l2)) 0 (serialize s y));\n seq_append_seq_upd_seq_l (serialize (serialize_list _ s) (x :: l2)) 0 (serialize s y) (serialize (serialize_list _ s) l1);\n assert (serialize (serialize_list _ s) (l1 `L.append` (y :: l2)) == seq_upd_seq (serialize (serialize_list _ s) l1 `Seq.append` serialize (serialize_list _ s) (x :: l2)) (Seq.length (serialize (serialize_list _ s) l1) + 0) (serialize s y));\n serialize_list_append _ s l1 (x :: l2)", "val append_distributes_seq_to_seq_four_BE (#a:Type) (x:seq a{length x % 4 == 0}) (y:seq a{length y % 4 == 0}) :\n Lemma (seq_to_seq_four_BE (x @| y) == seq_to_seq_four_BE x @| seq_to_seq_four_BE y)\nlet append_distributes_seq_to_seq_four_BE (#a:Type) (x:seq a{length x % 4 == 0}) (y:seq a{length y % 4 == 0}) :\n Lemma (seq_to_seq_four_BE (x @| y) == seq_to_seq_four_BE x @| seq_to_seq_four_BE y)\n =\n reveal_opaque (`%seq_to_seq_four_BE) (seq_to_seq_four_BE #a);\n assert (equal (seq_to_seq_four_BE (x @| y)) (seq_to_seq_four_BE x @| seq_to_seq_four_BE y));\n ()", "val list_flatten_append\n (#a: Type)\n (l1 l2: list (list a))\n: Lemma\n (L.flatten (l1 `L.append` l2) == L.flatten l1 `L.append` L.flatten l2)\nlet rec list_flatten_append\n (#a: Type)\n (l1 l2: list (list a))\n: Lemma\n (L.flatten (l1 `L.append` l2) == L.flatten l1 `L.append` L.flatten l2)\n= match l1 with\n | [] -> ()\n | a :: q ->\n list_flatten_append q l2;\n L.append_assoc a (L.flatten q) (L.flatten l2)", "val assoc_append_flip_l_intro (#key #repr: eqtype) (l1 l2: list (key * repr)) (y: repr) (x: key)\n : Lemma\n (requires (L.noRepeats (L.map snd (L.append l1 l2)) /\\ L.assoc y (L.map flip l2) == Some x))\n (ensures (L.assoc y (L.map flip (l1 `L.append` l2)) == Some x))\nlet rec assoc_append_flip_l_intro\n (#key #repr: eqtype)\n (l1 l2: list (key * repr))\n (y: repr)\n (x: key)\n: Lemma\n (requires (L.noRepeats (L.map snd (L.append l1 l2)) /\\ L.assoc y (L.map flip l2) == Some x))\n (ensures (L.assoc y (L.map flip (l1 `L.append` l2)) == Some x))\n= match l1 with\n | [] -> ()\n | (_, r') :: q ->\n L.assoc_mem y (L.map flip l2);\n map_fst_flip l2;\n L.map_append snd l1 l2;\n L.noRepeats_append_elim (L.map snd l1) (L.map snd l2);\n assoc_append_flip_l_intro q l2 y x", "val mem_seq_of_list\n (#a: eqtype)\n (x: a)\n (l: list a)\n: Lemma\n (requires True)\n (ensures (mem x (seq_of_list l) == List.Tot.mem x l))\n [SMTPat (mem x (seq_of_list l))]\nlet rec mem_seq_of_list #_ x l\n= lemma_seq_of_list_induction l;\n match l with\n | [] -> ()\n | y :: q ->\n let _ : squash (head (seq_of_list l) == y) = () in\n let _ : squash (tail (seq_of_list l) == seq_of_list q) = seq_of_list_tl l in\n let _ : squash (mem x (seq_of_list l) == (x = y || mem x (seq_of_list q))) =\n lemma_mem_inversion (seq_of_list l)\n in\n mem_seq_of_list x q", "val append_distributes_seq_four_to_seq_BE (#a:Type) (x:seq (four a)) (y:seq (four a)) :\n Lemma (seq_four_to_seq_BE (x @| y) == seq_four_to_seq_BE x @| seq_four_to_seq_BE y)\nlet append_distributes_seq_four_to_seq_BE #a x y =\n reveal_opaque (`%seq_four_to_seq_BE) (seq_four_to_seq_BE #a);\n assert (equal (seq_four_to_seq_BE (x @| y)) (seq_four_to_seq_BE x @| seq_four_to_seq_BE y))", "val seq_of_list_is_create8: #a:Type -> x0:a -> x1:a -> x2:a -> x3:a -> x4:a -> x5:a -> x6:a -> x7:a ->\n Lemma (create8 x0 x1 x2 x3 x4 x5 x6 x7 == Seq.seq_of_list [x0; x1; x2; x3; x4; x5; x6; x7])\nlet seq_of_list_is_create8 #a x0 x1 x2 x3 x4 x5 x6 x7 =\n let rp = Seq.seq_of_list [x0; x1; x2; x3; x4; x5; x6; x7] in\n assert_norm (List.length [x0; x1; x2; x3; x4; x5; x6; x7] == 8);\n assert (length rp == 8);\n let lp = create8 x0 x1 x2 x3 x4 x5 x6 x7 in\n\n let aux (i:nat{i < 8}) : Lemma (Seq.index lp i == Seq.index rp i) =\n assert_norm (Seq.index lp i == Seq.index rp i) in\n\n Classical.forall_intro aux;\n eq_intro rp lp", "val lemma_seq_of_list_permutation (#a:eqtype) (l:list a)\n :Lemma (forall x. List.Tot.Base.count x l == count x (seq_of_list l))\nlet rec lemma_seq_of_list_permutation #a l\n =\n lemma_seq_of_list_induction l;\n match l with\n | [] -> ()\n | _::tl -> lemma_seq_of_list_permutation tl", "val list_flatten_map_append\n (#a #b: Type)\n (f: a -> Tot (list b))\n (l1 l2: list a)\n: Lemma\n (L.flatten (L.map f (l1 `L.append` l2)) == L.flatten (L.map f l1) `L.append` L.flatten (L.map f l2))\nlet list_flatten_map_append\n (#a #b: Type)\n (f: a -> Tot (list b))\n (l1 l2: list a)\n: Lemma\n (L.flatten (L.map f (l1 `L.append` l2)) == L.flatten (L.map f l1) `L.append` L.flatten (L.map f l2))\n= L.map_append f l1 l2;\n list_flatten_append (L.map f l1) (L.map f l2)", "val serialize_list_cons_upd\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (x: t)\n (l2: list t)\n (y: t)\n : Lemma\n (requires\n (serialize_list_precond k /\\ Seq.length (serialize s y) == Seq.length (serialize s x)))\n (ensures\n (let ln2 = Seq.length (serialize (serialize_list _ s) l2) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (x :: l2) in\n Seq.length sl == Seq.length sx + ln2 /\\\n serialize (serialize_list _ s) (y :: l2) == seq_upd_seq sl 0 (serialize s y)))\nlet serialize_list_cons_upd\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (x: t)\n (l2: list t)\n (y: t)\n: Lemma\n (requires (\n serialize_list_precond k /\\\n Seq.length (serialize s y) == Seq.length (serialize s x)\n ))\n (ensures (\n let ln2 = Seq.length (serialize (serialize_list _ s) l2) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (x :: l2) in\n Seq.length sl == Seq.length sx + ln2 /\\\n serialize (serialize_list _ s) (y :: l2) == seq_upd_seq sl 0 (serialize s y)\n ))\n= serialize_list_cons _ s x l2;\n serialize_list_cons _ s y l2;\n let sl = serialize (serialize_list _ s) (x :: l2) in\n seq_upd_seq_left sl (serialize s y);\n let ln = Seq.length (serialize s x) in\n Seq.lemma_split sl ln;\n Seq.lemma_append_inj (Seq.slice sl 0 ln) (Seq.slice sl ln (Seq.length sl)) (serialize s x) (serialize (serialize_list _ s) l2)", "val lemma_all_but_last_append (#t:Type) (a:seq t) (b:seq t{length b > 0}) :\n Lemma (all_but_last (append a b) == append a (all_but_last b))\nlet lemma_all_but_last_append (#t:Type) (a:seq t) (b:seq t{length b > 0}) :\n Lemma (all_but_last (append a b) == append a (all_but_last b)) =\n let ab = all_but_last (append a b) in\n let app_a_b = append a (all_but_last b) in\n assert (equal ab app_a_b)", "val lemma_prefix1_append (#a: Type) (s: seq a) (x: a) : Lemma (prefix (append1 s x) (length s) == s)\nlet lemma_prefix1_append (#a:Type) (s: seq a) (x:a):\n Lemma (prefix (append1 s x) (length s) == s) =\n lemma_prefix_append s (create 1 x)", "val lemma_iseq_append1 (#a #n:_) (il: interleaving a n) (x: elem_src a n)\n : Lemma (ensures (let il' = SA.append1 il x in\n i_seq il' = SA.append1 (i_seq il) x.e))\nlet lemma_iseq_append1 (#a #n:_) (il': interleaving a n) (x: elem_src a n)\n : Lemma (ensures (let il = SA.append1 il' x in\n i_seq il = SA.append1 (i_seq il') x.e))\n = let il = SA.append1 il' x in\n let fm = IF.map_fm #(gen_seq a n) #_ (to_elem #a #n) in\n SA.lemma_prefix1_append il' x;\n IF.lemma_filter_map_snoc fm il", "val lemma_tail_append: #a:Type -> s1:seq a{length s1 > 0} -> s2:seq a -> Lemma\n (tail (append s1 s2) == append (tail s1) s2)\nlet lemma_tail_append #_ s1 s2 = cut (equal (tail (append s1 s2)) (append (tail s1) s2))", "val assoc_flip_intro (#a #b: eqtype) (l: list (a * b)) (y: b) (x: a)\n : Lemma\n (requires\n (L.noRepeats (list_map fst l) /\\ L.noRepeats (list_map snd l) /\\ L.assoc x l == Some y))\n (ensures (L.assoc y (list_map flip l) == Some x))\nlet rec assoc_flip_intro\n (#a #b: eqtype)\n (l: list (a * b))\n (y: b)\n (x: a)\n: Lemma\n (requires (\n L.noRepeats (list_map fst l) /\\\n L.noRepeats (list_map snd l) /\\\n L.assoc x l == Some y\n ))\n (ensures (\n L.assoc y (list_map flip l) == Some x\n ))\n= map_fst_flip l;\n map_snd_flip l;\n map_flip_flip l;\n assoc_flip_elim (list_map flip l) x y", "val elim_of_list': #a:Type ->\n i:nat ->\n s:seq a ->\n l:list a ->\n Lemma\n (requires (\n List.Tot.length l + i = length s /\\\n i <= length s /\\\n slice s i (length s) == seq_of_list l))\n (ensures (\n explode_and i s l))\nlet elim_of_list' = elim_of_list''", "val seq_slice_append_l (#t: Type) (s1 s2: Seq.seq t)\n : Lemma (Seq.slice (Seq.append s1 s2) 0 (Seq.length s1) == s1)\nlet seq_slice_append_l\n (#t: Type)\n (s1 s2: Seq.seq t)\n: Lemma\n (Seq.slice (Seq.append s1 s2) 0 (Seq.length s1) == s1)\n= assert (Seq.equal (Seq.slice (Seq.append s1 s2) 0 (Seq.length s1)) s1)", "val seq_slice_append_l (#t: Type) (s1 s2: Seq.seq t)\n : Lemma (Seq.slice (Seq.append s1 s2) 0 (Seq.length s1) == s1)\nlet seq_slice_append_l\n (#t: Type)\n (s1 s2: Seq.seq t)\n: Lemma\n (Seq.slice (Seq.append s1 s2) 0 (Seq.length s1) == s1)\n= assert (Seq.equal (Seq.slice (Seq.append s1 s2) 0 (Seq.length s1)) s1)", "val assoc_flip_elim (#a #b: eqtype) (l: list (a * b)) (y: b) (x: a)\n : Lemma\n (requires\n (L.noRepeats (list_map fst l) /\\ L.noRepeats (list_map snd l) /\\\n L.assoc y (list_map flip l) == Some x)) (ensures (L.assoc x l == Some y)) (decreases l)\nlet rec assoc_flip_elim\n (#a #b: eqtype)\n (l: list (a * b))\n (y: b)\n (x: a)\n: Lemma\n (requires (\n L.noRepeats (list_map fst l) /\\\n L.noRepeats (list_map snd l) /\\\n L.assoc y (list_map flip l) == Some x\n ))\n (ensures (\n L.assoc x l == Some y\n ))\n (decreases l)\n= let ((x', y') :: l') = l in\n if y' = y\n then ()\n else begin\n if x' = x\n then begin\n assert (list_mem x' (list_map fst l') == false);\n assoc_mem_snd (list_map flip l') y x;\n map_snd_flip l';\n assert False\n end\n else\n assoc_flip_elim l' y x\n end", "val append_distributes_le_seq_quad32_to_bytes (x y: seq quad32)\n : Lemma\n (le_seq_quad32_to_bytes (append x y) ==\n append (le_seq_quad32_to_bytes x) (le_seq_quad32_to_bytes y))\nlet append_distributes_le_seq_quad32_to_bytes (x y:seq quad32) :\n Lemma (le_seq_quad32_to_bytes (append x y) == append (le_seq_quad32_to_bytes x) (le_seq_quad32_to_bytes y))\n =\n append_distributes_le_seq_quad32_to_bytes x y", "val lemma_append_last (#a: Type) (l1 l2: list a)\n : Lemma (requires (length l2 > 0)) (ensures (last (l1 @ l2) == last l2))\nlet rec lemma_append_last (#a:Type) (l1 l2:list a) :\n Lemma\n (requires (length l2 > 0))\n (ensures (last (l1 @ l2) == last l2)) =\n match l1 with\n | [] -> ()\n | _ :: l1' -> lemma_append_last l1' l2", "val precedes_append_cons_prod_r (#a #b: Type) (l1: list (a * b)) (x: a) (y: b) (l2: list (a * b))\n : Lemma (ensures x << (append l1 ((x, y) :: l2)) /\\ y << (append l1 ((x, y) :: l2)))\nlet precedes_append_cons_prod_r\n (#a #b: Type)\n (l1: list (a * b))\n (x: a)\n (y: b)\n (l2: list (a * b))\n: Lemma\n (ensures\n x << (append l1 ((x, y) :: l2)) /\\\n y << (append l1 ((x, y) :: l2)))\n= precedes_append_cons_r l1 (x, y) l2", "val intro_of_list': #a:Type ->\n i:nat ->\n s:seq a ->\n l:list a ->\n Lemma\n (requires (\n List.Tot.length l + i = length s /\\\n i <= length s /\\\n explode_and i s l))\n (ensures (\n equal (seq_of_list l) (slice s i (length s))))\nlet intro_of_list' = intro_of_list''", "val lemma_list_to_seq_rec (#a: Type) (l: list a) (s: seq a) (n: nat)\n : Lemma\n (requires\n n + List.length l == Seq.length s /\\\n Seq.equal (Seq.slice s n (Seq.length s)) (list_to_seq l))\n (ensures list_to_seq_post l s n)\n (decreases l)\nlet rec lemma_list_to_seq_rec (#a:Type) (l:list a) (s:seq a) (n:nat) : Lemma\n (requires n + List.length l == Seq.length s /\\ Seq.equal (Seq.slice s n (Seq.length s)) (list_to_seq l))\n (ensures list_to_seq_post l s n)\n (decreases l)\n =\n match l with\n | [] -> ()\n | h::t ->\n let lem (i:nat) : Lemma\n (requires i < List.length t)\n (ensures Seq.index (Seq.slice s (n + 1) (Seq.length s)) i == Seq.index (list_to_seq t) i)\n [SMTPat (Seq.index (list_to_seq t) i)]\n =\n calc (==) {\n Seq.index (Seq.slice s (n + 1) (Seq.length s)) i;\n == {}\n Seq.index (Seq.slice s n (Seq.length s)) (i + 1);\n == {}\n Seq.index (list_to_seq l) (i + 1);\n == {}\n Seq.index (list_to_seq t) i;\n }\n in\n lemma_list_to_seq_rec t s (n + 1);\n assert (Seq.index (list_to_seq l) 0 == h);\n ()", "val lemma_reduce_append (#a:Type) (#b:Type) (b0:b) (f: a -> b -> b) (s: seq a) (x:a):\n Lemma (reduce b0 f (append1 s x) == f x (reduce b0 f s))\nlet lemma_reduce_append (#a:Type) (#b:Type) (b0:b) (f: a -> b -> b) (s: seq a) (x:a):\n Lemma (reduce b0 f (append1 s x) == f x (reduce b0 f s)) =\n lemma_prefix_append s (create 1 x)", "val memP_append (#a: _) (x: a) (l: list a)\n : Lemma\n (ensures\n (List.memP x l ==> (exists (l12: (list a * list a)). l == (fst l12) @ (x :: (snd l12)))))\nlet memP_append #a (x: a) (l: list a) :\n Lemma\n (ensures (List.memP x l ==>\n (exists (l12: (list a * list a)). l == (fst l12) @ (x :: (snd l12))))) =\n FStar.Classical.move_requires (memP_append_aux x) l", "val reverse_seq_append (#a:eqtype) (s:seq a) (t:seq a) :\n Lemma(ensures reverse_seq (append s t) == append (reverse_seq t) (reverse_seq s))\nlet reverse_seq_append (#a:eqtype) (s:seq a) (t:seq a) :\n Lemma(ensures reverse_seq (append s t) == append (reverse_seq t) (reverse_seq s))\n =\n assert (equal (reverse_seq (append s t)) (append (reverse_seq t) (reverse_seq s)))", "val lemma_append_inj: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a {length s1 = length t1 \\/ length s2 = length t2}\n -> Lemma (requires (equal (append s1 s2) (append t1 t2)))\n (ensures (equal s1 t1 /\\ equal s2 t2))\nlet lemma_append_inj #_ s1 s2 t1 t2 =\n lemma_append_len_disj s1 s2 t1 t2;\n FStar.Classical.forall_intro #(i:nat{i < length s1}) #(fun i -> index s1 i == index t1 i) (lemma_append_inj_l s1 s2 t1 t2);\n FStar.Classical.forall_intro #(i:nat{i < length s2}) #(fun i -> index s2 i == index t2 i) (lemma_append_inj_r s1 s2 t1 t2)", "val lemma_tail_snoc: #a:Type -> s:Seq.seq a{Seq.length s > 0} -> x:a\n -> Lemma (ensures (tail (snoc s x) == snoc (tail s) x))\nlet lemma_tail_snoc #_ s x = lemma_slice_first_in_append s (Seq.create 1 x) 1", "val serialize_list_cons_upd_chain\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (x: t)\n (l2: list t)\n (y: t)\n (i' : nat)\n (s' : bytes)\n: Lemma\n (requires (\n let sx = serialize s x in\n serialize_list_precond k /\\\n i' + Seq.length s' <= Seq.length sx /\\\n serialize s y == seq_upd_seq sx i' s'\n ))\n (ensures (\n let ln2 = Seq.length (serialize (serialize_list _ s) l2) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (x :: l2) in\n Seq.length sl == Seq.length sx + ln2 /\\\n i' + Seq.length s' <= Seq.length sl /\\\n serialize (serialize_list _ s) (y :: l2) == seq_upd_seq sl i' s'\n ))\nlet serialize_list_cons_upd_chain\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (x: t)\n (l2: list t)\n (y: t)\n (i' : nat)\n (s' : bytes)\n: Lemma\n (requires (\n let sx = serialize s x in\n serialize_list_precond k /\\\n i' + Seq.length s' <= Seq.length sx /\\\n serialize s y == seq_upd_seq sx i' s'\n ))\n (ensures (\n let ln2 = Seq.length (serialize (serialize_list _ s) l2) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (x :: l2) in\n Seq.length sl == Seq.length sx + ln2 /\\\n i' + Seq.length s' <= Seq.length sl /\\\n serialize (serialize_list _ s) (y :: l2) == seq_upd_seq sl i' s'\n ))\n= serialize_list_upd_chain s [] x l2 y i' s'", "val serialize_list_upd_chain\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (l1: list t)\n (x: t)\n (l2: list t)\n (y: t)\n (i': nat)\n (s': bytes)\n : Lemma\n (requires\n (let sx = serialize s x in\n serialize_list_precond k /\\ i' + Seq.length s' <= Seq.length sx /\\\n serialize s y == seq_upd_seq sx i' s'))\n (ensures\n (let ln1 = Seq.length (serialize (serialize_list _ s) l1) in\n let ln2 = Seq.length (serialize (serialize_list _ s) l2) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (l1 `L.append` (x :: l2)) in\n Seq.length sl == ln1 + Seq.length sx + ln2 /\\ ln1 + i' + Seq.length s' <= Seq.length sl /\\\n serialize (serialize_list _ s) (l1 `L.append` (y :: l2)) == seq_upd_seq sl (ln1 + i') s'))\nlet serialize_list_upd_chain\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (l1: list t)\n (x: t)\n (l2: list t)\n (y: t)\n (i' : nat)\n (s' : bytes)\n: Lemma\n (requires (\n let sx = serialize s x in\n serialize_list_precond k /\\\n i' + Seq.length s' <= Seq.length sx /\\\n serialize s y == seq_upd_seq sx i' s'\n ))\n (ensures (\n let ln1 = Seq.length (serialize (serialize_list _ s) l1) in\n let ln2 = Seq.length (serialize (serialize_list _ s) l2) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (l1 `L.append` (x :: l2)) in\n Seq.length sl == ln1 + Seq.length sx + ln2 /\\\n ln1 + i' + Seq.length s' <= Seq.length sl /\\\n serialize (serialize_list _ s) (l1 `L.append` (y :: l2)) == seq_upd_seq sl (ln1 + i') s'\n ))\n= serialize_list_upd s l1 x l2 y;\n serialize_list_append _ s l1 (x :: l2);\n let sl1 = serialize (serialize_list _ s) l1 in\n let ln1 = Seq.length sl1 in\n let sxl2 = serialize (serialize_list _ s) (x :: l2) in\n let sl = serialize (serialize_list _ s) (l1 `L.append` (x :: l2)) in\n Seq.lemma_split sl ln1;\n Seq.lemma_append_inj (Seq.slice sl 0 ln1) (Seq.slice sl ln1 (Seq.length sl)) sl1 sxl2;\n let sx = serialize s x in\n let sl2 = serialize (serialize_list _ s) l2 in\n let lx = Seq.length sx in\n serialize_list_cons _ s x l2;\n Seq.lemma_split sxl2 lx;\n Seq.lemma_append_inj (Seq.slice sxl2 0 lx) (Seq.slice sxl2 lx (Seq.length sxl2)) sx sl2;\n Seq.slice_slice sl ln1 (Seq.length sl) 0 lx;\n assert (sx == Seq.slice sl ln1 (ln1 + lx));\n seq_upd_seq_seq_upd_seq_slice sl ln1 (ln1 + lx) i' s';\n ()", "val lemma_sseq_extend_len (#a:eqtype) (ss: sseq a) (x:a) (i:seq_index ss):\n Lemma (ensures (flat_length (sseq_extend ss x i) = 1 + flat_length ss))\nlet rec lemma_sseq_extend_len (#a:eqtype) (ss: sseq a) (x:a) (i:seq_index ss):\n Lemma (ensures (flat_length (sseq_extend ss x i) = 1 + flat_length ss))\n (decreases (length ss)) =\n let n = length ss in\n\n if i = n - 1 then (\n lemma_sseq_extend_len_base ss x\n )\n else (\n let ss' = hprefix ss in\n let ssx = sseq_extend ss x i in\n let ssx' = sseq_extend ss' x i in\n\n lemma_sseq_extend_len ss' x i;\n assert(equal ssx (append1 ssx' (telem ss)));\n lemma_flat_length_app1 ssx' (telem ss);\n lemma_hprefix_append1 ss;\n lemma_flat_length_app1 ss' (telem ss)\n )", "val if_in_append_but_not_first_of_either_then_in_append_tails (#a: Type) (x: a) (l1 l2: list a)\n : Lemma\n (requires\n contains_ubool x (list_append l1 l2) /\\\n (match l1, l2 with\n | hd1 :: tl1, hd2 :: tl2 -> neqb x hd1 /\\ neqb x hd2\n | _, _ -> False))\n (ensures\n (match l1, l2 with\n | hd1 :: tl1, hd2 :: tl2 -> contains_ubool x (list_append tl1 tl2)\n | _ -> False))\nlet if_in_append_but_not_first_of_either_then_in_append_tails\n (#a: Type)\n (x: a)\n (l1: list a)\n (l2: list a)\n : Lemma (requires contains_ubool x (list_append l1 l2)\n /\\ (match l1, l2 with\n | hd1 :: tl1, hd2 :: tl2 -> neqb x hd1 /\\ neqb x hd2\n | _, _ -> False))\n (ensures (match l1, l2 with\n | hd1 :: tl1, hd2 :: tl2 -> contains_ubool x (list_append tl1 tl2)\n | _ -> False)) =\n match l1, l2 with\n | hd1 :: tl1, hd2 :: tl2 ->\n contains_ubool_append x l1 l2;\n contains_ubool_append x tl1 tl2", "val includes_as_seq (#a h1 h2: _) (x y: buffer a)\n : Lemma (requires (x `includes` y /\\ as_seq h1 x == as_seq h2 x))\n (ensures (as_seq h1 y == as_seq h2 y))\nlet includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)\n: Lemma\n (requires (x `includes` y /\\ as_seq h1 x == as_seq h2 x))\n (ensures (as_seq h1 y == as_seq h2 y))\n= Seq.slice_slice (sel h1 x) (idx x) (idx x + length x) (idx y - idx x) (idx y - idx x + length y);\n Seq.slice_slice (sel h2 x) (idx x) (idx x + length x) (idx y - idx x) (idx y - idx x + length y)", "val includes_as_seq (#a h1 h2: _) (x y: buffer a)\n : Lemma (requires (x `includes` y /\\ as_seq h1 x == as_seq h2 x))\n (ensures (as_seq h1 y == as_seq h2 y))\nlet includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)\n: Lemma\n (requires (x `includes` y /\\ as_seq h1 x == as_seq h2 x))\n (ensures (as_seq h1 y == as_seq h2 y))\n= P.buffer_includes_elim x y", "val map_seq_append (#a #b:Type) (f:a -> Tot b) (s1 s2:Seq.seq a)\n : Lemma (ensures (map_seq f (Seq.append s1 s2) ==\n Seq.append (map_seq f s1) (map_seq f s2)))\nlet map_seq_append #a #b f s1 s2 =\n map_seq_len f s1;\n map_seq_len f s2;\n map_seq_len f (Seq.append s1 s2);\n Classical.forall_intro (map_seq_index f s1);\n Classical.forall_intro (map_seq_index f s2);\n Classical.forall_intro (map_seq_index f (Seq.append s1 s2));\n assert (Seq.equal (map_seq f (Seq.append s1 s2))\n (Seq.append (map_seq f s1) (map_seq f s2)))", "val seq_append_seq_upd_seq_l (#t: Type) (s: Seq.seq t) (i': nat) (s' sl: Seq.seq t)\n : Lemma (requires (i' + Seq.length s' <= Seq.length s))\n (ensures\n (Seq.length sl + i' <= Seq.length (sl `Seq.append` s) /\\\n sl\n `Seq.append`\n (seq_upd_seq s i' s') ==\n seq_upd_seq (sl `Seq.append` s) (Seq.length sl + i') s'))\nlet seq_append_seq_upd_seq_l\n (#t: Type)\n (s: Seq.seq t)\n (i': nat)\n (s' : Seq.seq t)\n (sl : Seq.seq t)\n: Lemma\n (requires (i' + Seq.length s' <= Seq.length s))\n (ensures (\n Seq.length sl + i' <= Seq.length (sl `Seq.append` s) /\\\n sl `Seq.append` seq_upd_seq s i' s' == seq_upd_seq (sl `Seq.append` s) (Seq.length sl + i') s'\n ))\n= assert (sl `Seq.append` seq_upd_seq s i' s' `Seq.equal` seq_upd_seq (sl `Seq.append` s) (Seq.length sl + i') s')", "val append_distributes_be_seq_quad32_to_bytes (x y: seq quad32)\n : Lemma\n (seq_nat32_to_seq_nat8_BE (seq_four_to_seq_BE (append x y)) ==\n append (seq_nat32_to_seq_nat8_BE (seq_four_to_seq_BE x))\n (seq_nat32_to_seq_nat8_BE (seq_four_to_seq_BE y)))\nlet append_distributes_be_seq_quad32_to_bytes (x y:seq quad32) :\n Lemma (seq_nat32_to_seq_nat8_BE (seq_four_to_seq_BE (append x y)) == append (seq_nat32_to_seq_nat8_BE (seq_four_to_seq_BE x)) (seq_nat32_to_seq_nat8_BE (seq_four_to_seq_BE y)))\n =\n append_distributes_be_seq_quad32_to_bytes x y", "val seq_of_sequence_of_seq (#a:Type) (s:Seq.seq a)\n : Lemma (seq_of_sequence (sequence_of_seq s) == s)\nlet seq_of_sequence_of_seq (#a:Type) (s:Seq.seq a)\n : Lemma (seq_of_sequence (sequence_of_seq s) == s)\n = related_sequence_of_seq s;\n related_seq_of_sequence (sequence_of_seq s);\n assert (Seq.equal (seq_of_sequence (sequence_of_seq s)) s)", "val map_seq_len (#a #b: _) (x: FStar.Seq.seq a) (f: (a -> b))\n : Lemma (ensures Seq.length (Seq.map_seq f x) == Seq.length x)\n [SMTPat (Seq.length (Seq.map_seq f x))]\nlet map_seq_len #a #b (x:FStar.Seq.seq a) (f:a -> b)\n: Lemma (ensures Seq.length (Seq.map_seq f x) == Seq.length x)\n [SMTPat (Seq.length (Seq.map_seq f x))]\n= FStar.Seq.map_seq_len f x", "val lemma_mem_append : #a:eqtype -> s1:seq a -> s2:seq a\n -> Lemma (ensures (forall x. mem x (append s1 s2) <==> (mem x s1 || mem x s2)))\nlet lemma_mem_append #_ s1 s2 = lemma_append_count s1 s2", "val symm_lemma (#a:Type) (eq:equivalence_relation a) (x y:a) \n : Lemma (eq x y == eq y x)\nlet symm_lemma #a _ _ _ = reveal_opaque (`%is_symmetric) (is_symmetric #a)", "val append_injective (#a: _) (l0 l0' l1 l1': list a)\n : Lemma\n (ensures\n (length l0 == length l0' \\/ length l1 == length l1') /\\ append l0 l1 == append l0' l1' ==>\n l0 == l0' /\\ l1 == l1')\nlet append_injective #a (l0 l0':list a)\n (l1 l1':list a)\n : Lemma\n (ensures\n (length l0 == length l0' \\/ length l1 == length l1') /\\\n append l0 l1 == append l0' l1' ==>\n l0 == l0' /\\ l1 == l1')\n = introduce\n ((length l0 == length l0' \\/ length l1 == length l1') /\\\n append l0 l1 == append l0' l1')\n ==>\n (l0 == l0' /\\ l1 == l1')\n with _. eliminate (length l0 == length l0') \\/\n (length l1 == length l1')\n returns _\n with _. append_length_inv_head l0 l1 l0' l1'\n and _. append_length_inv_tail l0 l1 l0' l1'", "val memP_concatMap_intro (#a #b: _) (x: a) (y: b) (f: (a -> list b)) (l: list a)\n : Lemma (List.memP x l ==> List.memP y (f x) ==> List.memP y (List.Tot.concatMap f l))\nlet memP_concatMap_intro #a #b (x: a) (y: b) (f:a -> list b) (l: list a) :\n Lemma (List.memP x l ==>\n List.memP y (f x) ==>\n List.memP y (List.Tot.concatMap f l)) =\n concatMap_flatten_map f l;\n memP_map_intro f x l;\n memP_flatten_intro y (f x) (List.Tot.map f l)", "val lemma_sseq_extend_len_base (#a: eqtype) (ss: sseq a {length ss > 0}) (x: a)\n : Lemma (flat_length (sseq_extend ss x (length ss - 1)) = 1 + flat_length ss)\nlet lemma_sseq_extend_len_base (#a:eqtype) (ss: sseq a{length ss > 0}) (x:a):\n Lemma (flat_length (sseq_extend ss x (length ss - 1)) = 1 + flat_length ss) =\n let n = length ss in\n let i = n - 1 in\n let ss' = sseq_extend ss x i in\n let ss'i = prefix ss' i in\n let ssi = prefix ss i in\n let iss' = suffix ss' (n - i) in\n let iss = suffix ss (n - i) in\n\n assert(equal ssi ss'i);\n\n let fl = flat_length ss in\n let fl' = flat_length ss' in\n let fli = flat_length ssi in\n\n let l = map length ss in\n let l' = map length ss' in\n\n let l'i = prefix l' i in\n let li = prefix l i in\n assert(equal li l'i);\n\n let il' = suffix l' (n - i) in\n let il = suffix l (n - i) in\n\n\n lemma_reduce_prefix 0 nat_add l' i;\n lemma_reduce_prefix 0 nat_add l i;\n lemma_map_prefix length ss' i;\n lemma_map_prefix length ss i;\n assert(fl' = reduce fli nat_add il');\n assert(fl = reduce fli nat_add il);\n\n lemma_reduce_singleton fli nat_add il';\n lemma_reduce_singleton fli nat_add il", "val forall_prop_assoc_lemma2 (#a: eqtype) (#b: Type) (x: a) (y: b) (p: ((a * b) -> Tot Type0))\n : Lemma (forall h. for_all_prop p h /\\ List.assoc x h == Some y ==> p (x, y))\nlet forall_prop_assoc_lemma2 (#a:eqtype) (#b:Type) (x:a) (y:b) (p : (a * b) -> Tot Type0)\n : Lemma (forall h. for_all_prop p h /\\ List.assoc x h == Some y ==> p (x,y))\n= let aux h : Lemma (requires (for_all_prop p h /\\ List.assoc x h == Some y)) (ensures (p (x,y))) =\n for_all_prop_assoc_lemma x p h\n in\n FStar.Classical.(forall_intro (move_requires aux))", "val lemma_from_list_le (l:list bool) : Lemma\n (ensures (\n let rl = List.rev l in\n let s = seq_of_list rl in\n from_list_le l == from_vec #(List.length rl) s\n ))\nlet rec lemma_from_list_le l =\n match l with\n | [] -> ()\n | h::t ->\n (\n lemma_from_list_le t;\n let rl = List.rev l in\n let rt = List.rev t in\n let sl = seq_of_list rl in\n let st = seq_of_list rt in\n let sh = create 1 h in\n let n = length st in\n rev_length l;\n rev_length t;\n rev_append [h] t;\n singleton_list_rev h;\n list_cons_is_append h t;\n append_list_seq rt [h];\n singleton_list_seq h;\n assert (equal st (slice sl 0 n))\n )", "val serialize_list_upd_bw\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (l1: list t)\n (x: t)\n (l2: list t)\n (y: t)\n : Lemma\n (requires\n (serialize_list_precond k /\\ Seq.length (serialize s y) == Seq.length (serialize s x)))\n (ensures\n (let ln1 = Seq.length (serialize (serialize_list _ s) l1) in\n let ln2 = Seq.length (serialize (serialize_list _ s) l2) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (l1 `L.append` (x :: l2)) in\n Seq.length sl == ln1 + Seq.length sx + ln2 /\\\n serialize (serialize_list _ s) (l1 `L.append` (y :: l2)) ==\n seq_upd_bw_seq sl ln2 (serialize s y)))\n (decreases (L.length l1))\nlet serialize_list_upd_bw\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (l1: list t)\n (x: t)\n (l2: list t)\n (y: t)\n: Lemma\n (requires (\n serialize_list_precond k /\\\n Seq.length (serialize s y) == Seq.length (serialize s x)\n ))\n (ensures (\n let ln1 = Seq.length (serialize (serialize_list _ s) l1) in\n let ln2 = Seq.length (serialize (serialize_list _ s) l2) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (l1 `L.append` (x :: l2)) in\n Seq.length sl == ln1 + Seq.length sx + ln2 /\\\n serialize (serialize_list _ s) (l1 `L.append` (y :: l2)) == seq_upd_bw_seq sl ln2 (serialize s y)\n ))\n (decreases (L.length l1))\n= serialize_list_upd s l1 x l2 y", "val two_to_seq_to_two_LE (#a:Type) (x:seq2 a) :\n Lemma (two_to_seq_LE (seq_to_two_LE x) == x)\n [SMTPat (two_to_seq_LE (seq_to_two_LE x))]\nlet two_to_seq_to_two_LE #a x =\n assert (equal (two_to_seq_LE (seq_to_two_LE x)) x)", "val init_last_def (#a: Type) (l: list a) (x: a)\n : Lemma\n (let l' = append l [x] in\n init l' == l /\\ last l' == x)\nlet rec init_last_def (#a: Type) (l: list a) (x: a) : Lemma\n (let l' = append l [x] in\n init l' == l /\\ last l' == x)\n= match l with\n | [] -> ()\n | y :: q -> init_last_def q x", "val count_snoc (#a: eqtype) (s: seq a) (y x: a)\n : Lemma (Seq.count x (Seq.snoc s y) == Seq.count x s + (if x = y then 1 else 0))\nlet count_snoc (#a:eqtype) (s:seq a) (y x:a)\n : Lemma (Seq.count x (Seq.snoc s y) == Seq.count x s + (if x = y then 1 else 0))\n = Seq.lemma_append_count s (Seq.create 1 y)", "val seq_slice_append_r (#t: Type) (s1 s2: Seq.seq t)\n : Lemma (Seq.slice (Seq.append s1 s2) (Seq.length s1) (Seq.length (Seq.append s1 s2)) == s2)\nlet seq_slice_append_r\n (#t: Type)\n (s1 s2: Seq.seq t)\n: Lemma\n (Seq.slice (Seq.append s1 s2) (Seq.length s1) (Seq.length (Seq.append s1 s2)) == s2)\n= assert (Seq.equal (Seq.slice (Seq.append s1 s2) (Seq.length s1) (Seq.length (Seq.append s1 s2))) s2)", "val seq_slice_append_r (#t: Type) (s1 s2: Seq.seq t)\n : Lemma (Seq.slice (Seq.append s1 s2) (Seq.length s1) (Seq.length (Seq.append s1 s2)) == s2)\nlet seq_slice_append_r\n (#t: Type)\n (s1 s2: Seq.seq t)\n: Lemma\n (Seq.slice (Seq.append s1 s2) (Seq.length s1) (Seq.length (Seq.append s1 s2)) == s2)\n= assert (Seq.equal (Seq.slice (Seq.append s1 s2) (Seq.length s1) (Seq.length (Seq.append s1 s2))) s2)", "val append_slice #a (s : S.seq a)\n (l1:nat) (l2 : nat{S.length s == l2 /\\ l1 <= l2})\n : Lemma (S.append (S.slice s 0 l1) (S.slice s l1 l2) == s)\n [SMTPat (S.append (S.slice s 0 l1) (S.slice s l1 l2))]\nlet append_slice s l1 l2 =\n assert (S.equal (S.append (S.slice s 0 l1) (S.slice s l1 l2)) s);\n ()", "val lemma_map_extend (#a #b:Type) (f:a -> b) (s:seq a{length s > 0}):\n Lemma (map f s == append1 (map f (prefix s (length s - 1)))\n (f (index s (length s - 1))))\nlet lemma_map_extend (#a #b:Type) (f:a -> b) (s:seq a{length s > 0}):\n Lemma (map f s == append1 (map f (prefix s (length s - 1)))\n (f (index s (length s - 1)))) = \n assert(equal (map f s) (append1 (map f (prefix s (length s - 1)))\n (f (index s (length s - 1)))));\n ()", "val lemma_append_inj_l: #a:Type -> s1:seq a -> s2:seq a -> t1:seq a -> t2:seq a{length s1 = length t1 /\\ equal (append s1 s2) (append t1 t2)} -> i:nat{i < length s1}\n -> Lemma (index s1 i == index t1 i)\nlet lemma_append_inj_l #_ s1 s2 t1 t2 i =\n assert (index s1 i == (index (append s1 s2) i));\n assert (index t1 i == (index (append t1 t2) i))", "val lemma_list_to_seq (#a:Type) (l:list a) : Lemma\n (ensures norm [zeta; iota; delta_only [`%list_to_seq_post]] (list_to_seq_post l (list_to_seq l) 0))\nlet lemma_list_to_seq #a l =\n lemma_list_to_seq_rec l (list_to_seq l) 0", "val lemma_append_extend (#a: Type) (s1: seq a) (s2: seq a {length s2 > 0})\n : Lemma (append s1 s2 == append1 (append s1 (hprefix s2)) (telem s2))\nlet lemma_append_extend (#a:Type) (s1: seq a) (s2: seq a{length s2 > 0}):\n Lemma (append s1 s2 == append1 (append s1 (hprefix s2)) (telem s2)) =\n let s2' = hprefix s2 in\n let e2 = telem s2 in\n let aux (i: seq_index (append s1 s2)):\n Lemma (requires True)\n (ensures (index (append s1 s2) i == index (append1 (append s1 s2') e2) i))\n [SMTPat (index (append1 (append s1 s2') e2) i)] = ()\n in\n assert(equal (append s1 s2) (append1 (append s1 s2') e2));\n ()", "val sealed_singl (#a:Type) (x y : sealed a)\n : Lemma (x == y)\nlet sealed_singl (#a:Type) (x y : sealed a) : Lemma (x == y) =\n let Seal f = x in\n let Seal g = y in\n unobs_axiom f g", "val lemma_shift_append: #a:eqtype -> l:list a -> x:a -> m:list a -> Lemma\n (ensures ( (l@(x::m)) = ((l@[x])@m)))\nlet rec lemma_shift_append #a l x m = match l with\n | [] -> ()\n | hd::tl -> lemma_shift_append tl x m", "val auto_lemma_mem_snoc : #a:eqtype -> s:Seq.seq a -> x:a -> y:a ->\n Lemma\n (ensures (mem y (snoc s x) <==> mem y s \\/ x=y))\n [SMTPat (mem y (snoc s x))]\nlet auto_lemma_mem_snoc #a s x y = Seq.lemma_mem_snoc s x", "val list_in_listP_append (#a:Type) (ls0 ls1 : list a) (x : a) :\n Lemma\n (requires (list_in_listP ls0 ls1))\n (ensures (list_in_listP ls0 (x::ls1)))\n (decreases ls0)\nlet rec list_in_listP_append #dt ls0 ls1 x =\n match ls0 with\n | [] -> ()\n | x0 :: ls0' ->\n list_in_listP_append ls0' ls1 x", "val flatten_app (#a: _) (l1 l2: list (list a))\n : Lemma (flatten (l1 @ l2) == flatten l1 @ flatten l2)\nlet rec flatten_app #a (l1 l2: list (list a)) :\n Lemma (flatten (l1 @ l2) == flatten l1 @ flatten l2) =\n match l1 with\n | [] -> ()\n | h :: t -> flatten_app t l2;\n append_assoc h (flatten t) (flatten l2)", "val lemma_list_seq_bij: #a:Type -> l:list a -> Lemma\n (requires (True))\n (ensures (seq_to_list (seq_of_list l) == l))\nlet lemma_list_seq_bij = lemma_list_seq_bij'", "val lemma_append_count_aux: #a:eqtype -> x:a -> lo:seq a -> hi:seq a -> Lemma\n (requires True)\n (ensures (count x (append lo hi) = (count x lo + count x hi)))\nlet lemma_append_count_aux #_ _ lo hi = lemma_append_count lo hi", "val lemma_append_count: #a:eqtype -> lo:seq a -> hi:seq a -> Lemma\n (requires True)\n (ensures (forall x. count x (append lo hi) = (count x lo + count x hi)))\nlet lemma_append_count = lemma_append_count'", "val seq_list_index_lem (#a : Type0) (l : list a) (i : nat{i < L.length l}) :\n Lemma (requires True)\n (ensures (L.index l i == Seq.index (Seq.seq_of_list l) i))\n [SMTPatOr [[SMTPat (L.index l i); SMTPat (Seq.seq_of_list l)];\n [SMTPat (Seq.index (Seq.seq_of_list l) i)]]]\nlet seq_list_index_lem l i =\n Seq.lemma_list_seq_bij l", "val list_index_append (#t: Type) (l1 l2: list t) (i: int) : Lemma\n (requires (L.length l1 <= i /\\ i < L.length l1 + L.length l2))\n (ensures (\n L.length (L.append l1 l2) == L.length l1 + L.length l2 /\\\n L.index (L.append l1 l2) i == L.index l2 (i - L.length l1)\n ))\nlet rec list_index_append (#t: Type) (l1 l2: list t) (i: int) : Lemma\n (requires (L.length l1 <= i /\\ i < L.length l1 + L.length l2))\n (ensures (\n L.length (L.append l1 l2) == L.length l1 + L.length l2 /\\\n L.index (L.append l1 l2) i == L.index l2 (i - L.length l1)\n ))\n= list_length_append l1 l2;\n match l1 with\n | [] -> ()\n | a :: q -> list_index_append q l2 (i - 1)", "val memP_append_aux (#a: _) (x: a) (l: list a)\n : Lemma (requires (List.memP x l))\n (ensures (exists (l12: (list a * list a)). l == fst l12 @ x :: snd l12))\nlet rec memP_append_aux #a (x: a) (l: list a) :\n Lemma\n (requires (List.memP x l))\n (ensures (exists (l12: (list a * list a)). l == fst l12 @ x :: snd l12))\n = let goal = exists l12. l == fst l12 @ x :: snd l12 in\n let x : squash goal =\n match l with\n | [] -> ()\n | h :: t ->\n let pf : squash (x == h \\/ List.memP x t) = () in\n p <-- FStar.Squash.join_squash pf ;\n match p with \n | Prims.Left x_eq_h -> \n let l12 = [], t in\n assert (l == (fst l12) @ (x :: snd l12)) //trigger\n | Prims.Right mem_x_t -> \n FStar.Classical.exists_elim \n goal\n (pure_as_squash (memP_append_aux x) t)\n (fun l12' -> \n let l12 = h::fst l12', snd l12' in\n assert (l == (fst l12) @ (x :: snd l12))) //trigger\n in\n FStar.Squash.give_proof x", "val concatmaplemma : (#a:Type) -> (#b:Type) -> l:list a -> (f:(a -> list b)) -> x:b ->\n Lemma (memP x (concatMap f l) <==> (exists a. memP a l /\\ memP x (f a)))\n [SMTPat (memP x (concatMap f l))]\nlet rec concatmaplemma #a #b l f x =\n match l with\n | [] -> ()\n | h::t ->\n concatlemma (f h) (concatMap f t) x;\n concatmaplemma t f x", "val lemma_prefix_append (#a:Type) (s1 s2: seq a):\n Lemma (requires (True))\n (ensures (prefix (append s1 s2) (length s1) == s1))\nlet lemma_prefix_append (#a:Type) (s1 s2: seq a):\n Lemma (prefix (append s1 s2) (length s1) == s1) =\n // triggers an SMT pat that provides what we need\n assert(equal (prefix (append s1 s2) (length s1)) s1);\n ()", "val assoc_append_elim_l (#a: eqtype) (#b: Type) (x: a) (l1 l2: list (a * b))\n : Lemma (requires (assoc x l1 == None))\n (ensures (assoc x (l1 @ l2) == assoc x l2))\n (decreases l1)\nlet rec assoc_append_elim_l\n (#a: eqtype)\n (#b: Type)\n (x: a)\n (l1 l2: list (a * b))\n: Lemma\n (requires (assoc x l1 == None))\n (ensures (assoc x (l1 @ l2) == assoc x l2))\n (decreases l1)\n= match l1 with\n | [] -> ()\n | (x', _) :: q -> if x = x' then assert False else assoc_append_elim_l x q l2", "val trans_lemma (#a:Type) (eq: equivalence_relation a) (x y z:a)\n : Lemma (requires (eq x y \\/ eq y x) /\\ (eq y z \\/ eq z y)) \n (ensures (x `eq` z) && (z `eq` x))\nlet trans_lemma #a _ _ _ _ = reveal_opaque (`%is_transitive) (is_transitive #a);\n reveal_opaque (`%is_symmetric) (is_symmetric #a)", "val serialize_list_snoc_upd_chain\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (l1: list t)\n (x: t)\n (y: t)\n (i' : nat)\n (s' : bytes)\n: Lemma\n (requires (\n let sx = serialize s x in\n serialize_list_precond k /\\\n i' + Seq.length s' <= Seq.length sx /\\\n serialize s y == seq_upd_seq sx i' s'\n ))\n (ensures (\n let ln1 = Seq.length (serialize (serialize_list _ s) l1) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (l1 `L.append` [x]) in\n Seq.length sl == ln1 + Seq.length sx /\\\n ln1 + i' + Seq.length s' <= Seq.length sl /\\\n serialize (serialize_list _ s) (l1 `L.append` [y]) == seq_upd_seq sl (ln1 + i') s'\n ))\nlet serialize_list_snoc_upd_chain\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (l1: list t)\n (x: t)\n (y: t)\n (i' : nat)\n (s' : bytes)\n: Lemma\n (requires (\n let sx = serialize s x in\n serialize_list_precond k /\\\n i' + Seq.length s' <= Seq.length sx /\\\n serialize s y == seq_upd_seq sx i' s'\n ))\n (ensures (\n let ln1 = Seq.length (serialize (serialize_list _ s) l1) in\n let sx = serialize s x in\n let sl = serialize (serialize_list _ s) (l1 `L.append` [x]) in\n Seq.length sl == ln1 + Seq.length sx /\\\n ln1 + i' + Seq.length s' <= Seq.length sl /\\\n serialize (serialize_list _ s) (l1 `L.append` [y]) == seq_upd_seq sl (ln1 + i') s'\n ))\n= serialize_list_upd_chain s l1 x [] y i' s'", "val lemma_slice_first_in_append: #a:Type -> s1:seq a -> s2:seq a -> i:nat{i <= length s1} -> Lemma\n (ensures (equal (slice (append s1 s2) i (length (append s1 s2))) (append (slice s1 i (length s1)) s2)))\nlet lemma_slice_first_in_append = lemma_slice_first_in_append'", "val elim_of_list (#a: Type) (l: list a):\n Lemma\n (ensures (\n let s = seq_of_list l in\n pointwise_and s l))\nlet elim_of_list #_ l = elim_of_list' 0 (seq_of_list l) l", "val assoc_append_elim_r (#a: eqtype) (#b: Type) (x: a) (l1 l2: list (a * b))\n : Lemma (requires (assoc x l2 == None \\/ ~(assoc x l1 == None)))\n (ensures (assoc x (l1 @ l2) == assoc x l1))\n (decreases l1)\nlet rec assoc_append_elim_r\n (#a: eqtype)\n (#b: Type)\n (x: a)\n (l1 l2: list (a * b))\n: Lemma\n (requires (assoc x l2 == None \\/ ~ (assoc x l1 == None)))\n (ensures (assoc x (l1 @ l2) == assoc x l1))\n (decreases l1)\n= match l1 with\n | [] -> ()\n | (x', _) :: q -> if x = x' then () else assoc_append_elim_r x q l2", "val list_length_append (#t: Type) (l1 l2: list t)\n : Lemma (L.length (l1 `L.append` l2) == L.length l1 + L.length l2)\nlet list_length_append (#t: Type) (l1 l2: list t) : Lemma (L.length (l1 `L.append` l2) == L.length l1 + L.length l2) = L.append_length l1 l2", "val lemma_seq_list_bij: #a:Type -> s:seq a -> Lemma\n (requires (True))\n (ensures (seq_of_list (seq_to_list s) == s))\nlet lemma_seq_list_bij = lemma_seq_list_bij'", "val lemma_unsnoc_append (#a: Type) (l1 l2: list a)\n : Lemma (requires (length l2 > 0))\n (ensures\n (let al, a = unsnoc (l1 @ l2) in\n let bl, b = unsnoc l2 in\n al == l1 @ bl /\\ a == b))\nlet rec lemma_unsnoc_append (#a:Type) (l1 l2:list a) :\n Lemma\n (requires (length l2 > 0)) // the [length l2 = 0] is trivial\n (ensures (\n let al, a = unsnoc (l1 @ l2) in\n let bl, b = unsnoc l2 in\n al == l1 @ bl /\\ a == b)) =\n match l1 with\n | [] -> ()\n | _ :: l1' -> lemma_unsnoc_append l1' l2", "val concatlemma (#a:Type) (l1 l2 :list a) (x:a) : Lemma (memP x (l1@l2) <==> memP x l1 \\/ memP x l2)\nlet rec concatlemma #a l1 l2 x =\n match l1 with\n | [] -> ()\n | h::t -> concatlemma t l2 x", "val lemma_mem_snoc : #a:eqtype -> s:Seq.seq a -> x:a ->\n Lemma (ensures (forall y. mem y (snoc s x) <==> mem y s \\/ x=y))\nlet lemma_mem_snoc #_ s x = lemma_append_count s (Seq.create 1 x)", "val lemma_flat_length_app1 (#a:Type) (ss: sseq a) (s: seq a)\n : Lemma (flat_length ss + length s = flat_length (append1 ss s))\nlet lemma_flat_length_app1 (#a:Type) (ss: sseq a) (s: seq a)\n : Lemma (flat_length ss + length s = flat_length (append1 ss s)) =\n let ss' = append1 ss s in\n lemma_prefix1_append ss s;\n lemma_map_extend length ss';\n lemma_reduce_append 0 nat_add (map length ss) (length s);\n ()", "val seq_append_slice (#t: Type) (s: Seq.seq t) (i1 i2: nat)\n : Lemma (requires (i1 + i2 <= Seq.length s))\n (ensures (Seq.append (Seq.slice s 0 i1) (Seq.slice s i1 (i1 + i2)) == Seq.slice s 0 (i1 + i2))\n )\nlet seq_append_slice\n (#t: Type)\n (s: Seq.seq t)\n (i1 i2: nat)\n: Lemma\n (requires (i1 + i2 <= Seq.length s))\n (ensures (\n Seq.append (Seq.slice s 0 i1) (Seq.slice s i1 (i1 + i2)) == Seq.slice s 0 (i1 + i2)\n ))\n= assert (Seq.append (Seq.slice s 0 i1) (Seq.slice s i1 (i1 + i2)) `Seq.equal` Seq.slice s 0 (i1 + i2))", "val lemma_flat_length_app (#a:Type) (ss1 ss2: sseq a)\n : Lemma (flat_length ss1 + flat_length ss2 = flat_length (append ss1 ss2))\nlet lemma_flat_length_app = lemma_flat_length_app_aux", "val lemma_append_count_aux (#a: eqtype) (x: a) (lo hi: seq a)\n : Lemma (ensures (count x (append lo hi) = (count x lo + count x hi))) (decreases (length lo))\nlet rec lemma_append_count_aux (#a:eqtype) (x:a) (lo hi:seq a)\n : Lemma\n (ensures (count x (append lo hi) = (count x lo + count x hi)))\n (decreases (length lo))\n = all_seq_facts_lemma();\n reveal_opaque (`%count) (count #a);\n if length lo = 0\n then assert (append lo hi `equal` hi)\n else (\n lemma_append_count_aux x (tail lo) hi;\n assert (append (tail lo) hi `equal` tail (append lo hi))\n )", "val sequence_of_seq_of_sequence (#a:Type) (s:Sequence.seq a)\n : Lemma (sequence_of_seq (seq_of_sequence s) == s)\nlet sequence_of_seq_of_sequence (#a:Type) (s:Sequence.seq a)\n : Lemma (sequence_of_seq (seq_of_sequence s) == s)\n = related_seq_of_sequence s;\n related_sequence_of_seq (seq_of_sequence s);\n assert (Sequence.equal (sequence_of_seq (seq_of_sequence s)) s)" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.Lib.Lists.fst", "name": "Vale.Lib.Lists.append_list_seq" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Lists.fst", "name": "Vale.Lib.Lists.list_append_length" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.lemma_slice_first_exactly_in_append" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Lists.fst", "name": "Vale.Lib.Lists.list_append_index" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_BE.fst", "name": "Vale.AES.GCM_BE.slice_append_back" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM.fst", "name": "Vale.AES.GCM.slice_append_back" }, { "project_name": "zeta", "file_name": "Zeta.Generic.Blum.fst", "name": "Zeta.Generic.Blum.lemma_count_append1" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.append_distributes_seq_to_seq_four_LE" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.seq_of_list_tl" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.append_distributes_seq_four_to_seq_LE" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Lists.fst", "name": "Vale.Lib.Lists.singleton_list_seq" }, { "project_name": "hacl-star", "file_name": "Vale.Transformers.InstructionReorder.fst", "name": "Vale.Transformers.InstructionReorder.lemma_append_single" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_seq_of_list_induction" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fsti", "name": "LowParse.Spec.List.serialize_list_upd" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.append_distributes_seq_to_seq_four_BE" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fst", "name": "LowParse.Low.Base.Spec.list_flatten_append" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.assoc_append_flip_l_intro" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.mem_seq_of_list" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.append_distributes_seq_four_to_seq_BE" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Equiv.fst", "name": "Hacl.Spec.SHA2.Equiv.seq_of_list_is_create8" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_seq_of_list_permutation" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fst", "name": "LowParse.Low.Base.Spec.list_flatten_map_append" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fsti", "name": "LowParse.Spec.List.serialize_list_cons_upd" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.lemma_all_but_last_append" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fsti", "name": "Zeta.SeqAux.lemma_prefix1_append" }, { "project_name": "zeta", "file_name": "Zeta.Interleave.fst", "name": "Zeta.Interleave.lemma_iseq_append1" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_tail_append" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.assoc_flip_intro" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.elim_of_list'" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.Combinators.fst", "name": "MiniParse.Spec.Combinators.seq_slice_append_l" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fsti", "name": "LowParse.Spec.Combinators.seq_slice_append_l" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.assoc_flip_elim" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM.fst", "name": "Vale.AES.GCM.append_distributes_le_seq_quad32_to_bytes" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.lemma_append_last" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.precedes_append_cons_prod_r" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.intro_of_list'" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.lemma_list_to_seq_rec" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_reduce_append" }, { "project_name": "FStar", "file_name": "BinaryTreesEnumeration.fsti", "name": "BinaryTreesEnumeration.memP_append" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.reverse_seq_append" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_append_inj" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_tail_snoc" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fst", "name": "LowParse.Spec.List.serialize_list_cons_upd_chain" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fsti", "name": "LowParse.Spec.List.serialize_list_upd_chain" }, { "project_name": "zeta", "file_name": "Zeta.SSeq.fst", "name": "Zeta.SSeq.lemma_sseq_extend_len" }, { "project_name": "Armada", "file_name": "Strategies.VarIntro.Initialization.fst", "name": "Strategies.VarIntro.Initialization.if_in_append_but_not_first_of_either_then_in_append_tails" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.includes_as_seq" }, { "project_name": "FStar", "file_name": "FStar.BufferNG.fst", "name": "FStar.BufferNG.includes_as_seq" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.map_seq_append" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Base.fsti", "name": "LowParse.Spec.Base.seq_append_seq_upd_seq_l" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_BE.fst", "name": "Vale.AES.GCM_BE.append_distributes_be_seq_quad32_to_bytes" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Seq.fst", "name": "FStar.Sequence.Seq.seq_of_sequence_of_seq" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.map_seq_len" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_mem_append" }, { "project_name": "FStar", "file_name": "FStar.Fin.fst", "name": "FStar.Fin.symm_lemma" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.append_injective" }, { "project_name": "FStar", "file_name": "BinaryTreesEnumeration.fsti", "name": "BinaryTreesEnumeration.memP_concatMap_intro" }, { "project_name": "zeta", "file_name": "Zeta.SSeq.fst", "name": "Zeta.SSeq.lemma_sseq_extend_len_base" }, { "project_name": "FStar", "file_name": "Memo.fst", "name": "Memo.forall_prop_assoc_lemma2" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Lists.fst", "name": "Vale.Lib.Lists.lemma_from_list_le" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fsti", "name": "LowParse.Spec.List.serialize_list_upd_bw" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Seq.fst", "name": "Vale.Def.Words.Seq.two_to_seq_to_two_LE" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.init_last_def" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fsti", "name": "Zeta.SeqAux.count_snoc" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.Combinators.fst", "name": "MiniParse.Spec.Combinators.seq_slice_append_r" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fsti", "name": "LowParse.Spec.Combinators.seq_slice_append_r" }, { "project_name": "steel", "file_name": "MSort.SeqLemmas.fst", "name": "MSort.SeqLemmas.append_slice" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_map_extend" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_append_inj_l" }, { "project_name": "hacl-star", "file_name": "Vale.Lib.Seqs.fst", "name": "Vale.Lib.Seqs.lemma_list_to_seq" }, { "project_name": "zeta", "file_name": "Zeta.SSeq.fst", "name": "Zeta.SSeq.lemma_append_extend" }, { "project_name": "FStar", "file_name": "SealedModel.fst", "name": "SealedModel.sealed_singl" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.lemma_shift_append" }, { "project_name": "FStar", "file_name": "OPLSS.fst", "name": "OPLSS.auto_lemma_mem_snoc" }, { "project_name": "noise-star", "file_name": "Spec.Noise.Map.fst", "name": "Spec.Noise.Map.list_in_listP_append" }, { "project_name": "FStar", "file_name": "BinaryTreesEnumeration.fsti", "name": "BinaryTreesEnumeration.flatten_app" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_list_seq_bij" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_append_count_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_append_count" }, { "project_name": "noise-star", "file_name": "Impl.Noise.String.fst", "name": "Impl.Noise.String.seq_list_index_lem" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fst", "name": "LowParse.Low.Base.Spec.list_index_append" }, { "project_name": "FStar", "file_name": "BinaryTreesEnumeration.fsti", "name": "BinaryTreesEnumeration.memP_append_aux" }, { "project_name": "FStar", "file_name": "ND.fst", "name": "ND.concatmaplemma" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.lemma_prefix_append" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.assoc_append_elim_l" }, { "project_name": "FStar", "file_name": "FStar.Fin.fst", "name": "FStar.Fin.trans_lemma" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fst", "name": "LowParse.Spec.List.serialize_list_snoc_upd_chain" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_slice_first_in_append" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.elim_of_list" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.assoc_append_elim_r" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fsti", "name": "LowParse.Low.Base.Spec.list_length_append" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_seq_list_bij" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.lemma_unsnoc_append" }, { "project_name": "FStar", "file_name": "ND.fst", "name": "ND.concatlemma" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.lemma_mem_snoc" }, { "project_name": "zeta", "file_name": "Zeta.SSeq.fst", "name": "Zeta.SSeq.lemma_flat_length_app1" }, { "project_name": "FStar", "file_name": "MiniParse.Impl.Combinators.fst", "name": "MiniParse.Impl.Combinators.seq_append_slice" }, { "project_name": "zeta", "file_name": "Zeta.SSeq.fst", "name": "Zeta.SSeq.lemma_flat_length_app" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Util.fst", "name": "FStar.Sequence.Util.lemma_append_count_aux" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Seq.fst", "name": "FStar.Sequence.Seq.sequence_of_seq_of_sequence" } ], "selected_premises": [ "Lib.Sequence.length", "Lib.Sequence.seq", "Lib.IntTypes.v", "Lib.Sequence.to_seq", "Lib.IntTypes.size", "Lib.Buffer.op_Bar_Plus_Bar", "LowStar.Monotonic.Buffer.length", "Lib.ByteSequence.lbytes", "Lib.Buffer.loc", "Lib.Buffer.gsub", "Lib.IntTypes.uint_v", "Lib.IntTypes.uint_t", "LowStar.Buffer.trivial_preorder", "Lib.Sequence.createL", "Lib.Buffer.eq_or_disjoint", "Lib.Buffer.disjoint", "Lib.Sequence.lseq", "Lib.Buffer.as_seq", "LowStar.ImmutableBuffer.immutable_preorder", "Lib.IntTypes.bits", "FStar.UInt.size", "Lib.IntTypes.range", "Lib.Buffer.modifies", "Spec.Exponentiation.exp_pow2", "Lib.Buffer.lbuffer", "Lib.IntTypes.max_size_t", "Lib.Sequence.op_String_Assignment", "Lib.IntTypes.int_t", "LowStar.Monotonic.Buffer.srel", "Lib.IntTypes.u8", "Lib.Buffer.clbuffer", "Lib.IntTypes.numbytes", "Lib.Buffer.lbuffer_t", "Lib.Sequence.slice", "LowStar.ConstBuffer.qbuf_pre", "Lib.Sequence.op_String_Access", "Spec.Exponentiation.pow", "Lib.Buffer.op_Array_Assignment", "Lib.IntTypes.u32", "LowStar.Buffer.gcmalloc_of_list", "Lib.Buffer.buffer_t", "Lib.IntTypes.uint", "FStar.Seq.Base.op_At_Bar", "Lib.Buffer.op_Array_Access", "FStar.Mul.op_Star", "Lib.ByteSequence.nat_from_bytes_le", "FStar.Pervasives.reveal_opaque", "Lib.IntTypes.unsigned", "FStar.Tactics.Effect.raise", "Lib.IntTypes.u64", "Lib.ByteSequence.nat_from_bytes_be", "Lib.Buffer.null", "Lib.Exponentiation.Definition.pow", "Lib.Buffer.length", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "FStar.Heap.trivial_preorder", "Lib.Buffer.ibuffer", "Lib.Buffer.cbuffer", "Lib.IntTypes.op_Hat_Dot", "LowStar.Monotonic.Buffer.upd", "Lib.Buffer.recallable", "FStar.Monotonic.HyperStack.sel", "LowStar.Monotonic.Buffer.loc_addr_of_buffer", "Lib.IntTypes.op_Plus_Bang", "Lib.IntTypes.op_Star_Bang", "Lib.Buffer.cpred", "Lib.IntTypes.op_Plus_Dot", "Lib.Buffer.modifies1", "LowStar.ImmutableBuffer.seq_eq", "Lib.IntTypes.op_Subtraction_Dot", "Lib.IntTypes.u16", "LowStar.Monotonic.Buffer.lmbuffer", "Hacl.Spec.PrecompBaseTable.list_append_index2", "FStar.ST.op_Bang", "LowStar.ImmutableBuffer.cpred", "LowStar.Monotonic.Buffer.get", "Lib.Buffer.witnessed", "Lib.Buffer.modifies0", "Lib.ByteSequence.lbytes_empty", "LowStar.Monotonic.Buffer.deref", "LowStar.Monotonic.Buffer.disjoint", "Hacl.Spec.PrecompBaseTable.list_append_index", "Hacl.Spec.PrecompBaseTable.list_append_index1", "Lib.ByteSequence.nat_to_bytes_le", "Lib.Sequence.to_lseq", "Lib.ByteSequence.nat_to_bytes_be", "Lib.Buffer.buffer", "Lib.Buffer.op_Brack_Lens_Access", "Lib.IntTypes.op_Subtraction_Bang", "Lib.IntTypes.op_Amp_Dot", "Lib.Exponentiation.cswap", "Lib.IntTypes.op_Star_Dot", "Lib.IntTypes.byte", "Lib.IntTypes.maxint", "LowStar.Buffer.null", "LowStar.Monotonic.Buffer.loc_all_regions_from", "Lib.IntTypes.size_v", "Lib.Buffer.const_to_ibuffer", "LowStar.ConstBuffer.qual_of" ], "source_upto_this": "module Hacl.Spec.PrecompBaseTable\n\nopen FStar.Mul\nopen Lib.IntTypes\n\nmodule FL = FStar.List.Tot\nmodule LSeq = Lib.Sequence\n\nmodule LE = Lib.Exponentiation.Definition\nmodule SE = Spec.Exponentiation\nmodule BE = Hacl.Impl.Exponentiation.Definitions\n\n#set-options \"--z3rlimit 50 --fuel 0 --ifuel 0\"\n\n#push-options \"--fuel 2\"\nval list_append_index1: #a:Type -> x:list a -> y:list a -> i:nat{i < FL.length x} ->\n Lemma (ensures (FL.(index (x @ y)) i == FL.index x i)) (decreases (FL.length x))\n\nlet rec list_append_index1 #a x y i =\n match x with\n | [] -> ()\n | hd::tl -> if i = 0 then () else list_append_index1 tl y (i - 1)\n\n\nval list_append_index2: #a:Type -> x:list a -> y:list a -> i:nat{FL.length x <= i /\\ i < FL.length x + FL.length y} ->\n Lemma (ensures (FL.(index (x @ y)) i == FL.index y (i - FL.length x))) (decreases (FL.length x))\n\nlet rec list_append_index2 #a x y i =\n match x with\n | [] -> ()\n | hd::tl -> list_append_index2 tl y (i - 1)\n#pop-options\n\n\nval list_append_index: #a:Type -> x:list a -> y:list a -> i:nat{i < FL.length x + FL.length y} ->\n Lemma (FL.(index (x @ y)) i ==\n (if i < FL.length x then FL.index x i else FL.index y (i - FL.length x)))\n\nlet list_append_index #a x y i =\n if i < FL.length x then list_append_index1 x y i else list_append_index2 x y i\n\n", "sketch": [ "Step 1: Define the sequence `xy_lseq` as the sequence obtained from the concatenation of lists `x` and `y`.\nStep 2: Show that slicing `xy_lseq` from index `0` to `FL.length x` results in the sequence obtained from list `x`.\nStep 3: Show that slicing `xy_lseq` from index `FL.length x` to `FL.length x + FL.length y` results in the sequence obtained from list `y`.\nStep 4: Use the properties of `Seq.seq_of_list` and `Seq.slice` to prove the equalities in steps 2 and 3.", "Step 1: Define the concatenated list `xy` as `x @ y`.\nStep 2: Convert the concatenated list `xy` to a sequence `xy_lseq` using `Seq.seq_of_list`.\nStep 3: Show that slicing `xy_lseq` from 0 to the length of `x` results in the sequence representation of `x`.\nStep 4: Show that slicing `xy_lseq` from the length of `x` to the length of `x + y` results in the sequence representation of `y`.\nStep 5: Use the properties of `Seq.slice` and `Seq.seq_of_list` to prove the required equalities.", "Step 1: Define the sequence `xy_lseq` as the sequence obtained from the concatenation of lists `x` and `y` using `Seq.seq_of_list`.\nStep 2: Prove that slicing `xy_lseq` from index 0 to the length of `x` results in the sequence obtained from `x` using `Seq.seq_of_list`.\nStep 3: Prove that slicing `xy_lseq` from the length of `x` to the length of `x` plus the length of `y` results in the sequence obtained from `y` using `Seq.seq_of_list`.\nStep 4: Combine the results of steps 2 and 3 to conclude the proof.", "Step 1: Define the sequence `xy_lseq` as the sequence obtained from the concatenation of lists `x` and `y`.\nStep 2: Show that slicing `xy_lseq` from index 0 to the length of `x` results in the sequence obtained from the list `x`.\nStep 3: Show that slicing `xy_lseq` from the length of `x` to the length of `x` plus the length of `y` results in the sequence obtained from the list `y`.\nStep 4: Conclude that both slices are equal to the sequences obtained from the respective lists `x` and `y`.", "Step 1: Define the lemma `seq_of_list_append_lemma` which takes a type `a`, and two lists `x` and `y`.\nStep 2: Convert the concatenated list `x @ y` to a sequence using `Seq.seq_of_list`.\nStep 3: Show that slicing this sequence from 0 to the length of `x` results in the sequence obtained from `x`.\nStep 4: Show that slicing this sequence from the length of `x` to the length of `x + y` results in the sequence obtained from `y`.\nStep 5: Use the properties of `Seq.slice` and `Seq.seq_of_list` to prove these equalities.", "Step 1: Define the concatenated list `xy` as `x @ y`.\nStep 2: Convert the concatenated list `xy` to a sequence `xy_lseq` using `Seq.seq_of_list`.\nStep 3: Show that slicing `xy_lseq` from 0 to the length of `x` results in the sequence representation of `x`.\nStep 4: Show that slicing `xy_lseq` from the length of `x` to the length of `x + y` results in the sequence representation of `y`.\nStep 5: Use the properties of `Seq.slice` and `Seq.seq_of_list` to establish the required equalities.", "Step 1: Define the sequence `xy_lseq` as the sequence obtained from the concatenation of lists `x` and `y`.\nStep 2: Prove that slicing `xy_lseq` from index `0` to `FL.length x` results in the sequence obtained from the list `x`.\nStep 3: Prove that slicing `xy_lseq` from index `FL.length x` to `FL.length x + FL.length y` results in the sequence obtained from the list `y`.\nStep 4: Combine the results of Step 2 and Step 3 to conclude the proof.", "Step 1: Define the `xy_lseq` as the sequence obtained from the concatenation of lists `x` and `y`.\nStep 2: Prove that slicing `xy_lseq` from 0 to the length of `x` is equal to the sequence obtained from `x`.\nStep 3: Prove that slicing `xy_lseq` from the length of `x` to the length of `x` plus the length of `y` is equal to the sequence obtained from `y`.\nStep 4: Combine the results of Step 2 and Step 3 to conclude the proof.", "Step 1: Define `xy_lseq` as the sequence obtained by converting the concatenated list `x @ y` to a sequence using `Seq.seq_of_list`.\nStep 2: Show that slicing `xy_lseq` from 0 to the length of `x` results in the sequence obtained by converting `x` to a sequence using `Seq.seq_of_list`.\nStep 3: Show that slicing `xy_lseq` from the length of `x` to the length of `x` plus the length of `y` results in the sequence obtained by converting `y` to a sequence using `Seq.seq_of_list`.\nStep 4: Conclude the proof by combining the results of Step 2 and Step 3 using conjunction.", "Step 1: Define the combined sequence `xy_lseq` as the sequence obtained from the concatenation of lists `x` and `y`.\nStep 2: Prove that slicing `xy_lseq` from the start to the length of `x` yields the sequence obtained from list `x`.\nStep 3: Prove that slicing `xy_lseq` from the length of `x` to the length of `x` plus the length of `y` yields the sequence obtained from list `y`." ], "generated_solution": [ "let seq_of_list_append_lemma #a x y =\n let xy_lseq = Seq.seq_of_list FL.(x @ y) in\n assert (Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x);\n assert (Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y);\n ()", "let seq_of_list_append_lemma #a x y =\n let xy = FL.(x @ y) in\n let xy_lseq = Seq.seq_of_list xy in\n assert (Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x);\n assert (Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y);\n ()", "let seq_of_list_append_lemma #a x y =\n let xy_lseq = Seq.seq_of_list FL.(x @ y) in\n assert (Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x);\n assert (Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y);\n ()", "let seq_of_list_append_lemma #a x y =\n let xy_lseq = Seq.seq_of_list FL.(x @ y) in\n assert (Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x);\n assert (Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y);\n ()", "let seq_of_list_append_lemma #a x y =\n let xy_lseq = Seq.seq_of_list FL.(x @ y) in\n assert (Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x);\n assert (Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y);\n ()", "let seq_of_list_append_lemma #a x y =\n let xy = FL.(x @ y) in\n let xy_lseq = Seq.seq_of_list xy in\n assert (Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x);\n assert (Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y);\n ()", "let seq_of_list_append_lemma #a x y =\n let xy_lseq = Seq.seq_of_list FL.(x @ y) in\n assert (Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x);\n assert (Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y);\n ()", "let seq_of_list_append_lemma #a x y =\n let xy_lseq = Seq.seq_of_list FL.(x @ y) in\n assert (Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x);\n assert (Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y);\n ()", "let seq_of_list_append_lemma #a x y =\n let xy_lseq = Seq.seq_of_list FL.(x @ y) in\n assert (Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x);\n assert (Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y);\n ()", "let seq_of_list_append_lemma #a x y =\n let xy_lseq = Seq.seq_of_list (FL.append x y) in\n assert (Seq.slice xy_lseq 0 (FL.length x) == Seq.seq_of_list x);\n assert (Seq.slice xy_lseq (FL.length x) (FL.length x + FL.length y) == Seq.seq_of_list y);\n ()" ] }, { "file_name": "Vale.X64.InsMem.fsti", "name": "Vale.X64.InsMem.norm_loc", "opens_and_abbrevs": [ { "open": "Vale.Lib.Seqs" }, { "open": "Vale.X64.CPU_Features_s" }, { "open": "Vale.X64.InsBasic" }, { "open": "Vale.X64.QuickCode" }, { "open": "Vale.X64.Decls" }, { "open": "Vale.X64.State" }, { "open": "Vale.X64.Stack_i" }, { "open": "Vale.X64.Memory" }, { "open": "Vale.X64.Machine_s" }, { "open": "Vale.Arch.HeapImpl" }, { "open": "Vale.Arch.HeapTypes_s" }, { "open": "Vale.Def.Types_s" }, { "open": "FStar.Seq" }, { "open": "Vale.X64" }, { "open": "Vale.X64" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 1, "initial_ifuel": 0, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": true, "smtencoding_nl_arith_repr": "wrapped", "smtencoding_l_arith_repr": "native", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val norm_loc (l: loc) : loc", "source_definition": "let norm_loc (l:loc) : loc =\n norm [zeta; iota; delta_only [`%loc_mutable_buffers]; delta_attr [`%norm_loc_attr]] l", "source_range": { "start_line": 73, "start_col": 7, "end_line": 74, "end_col": 87 }, "interleaved": false, "definition": "fun l ->\n FStar.Pervasives.norm [\n FStar.Pervasives.zeta;\n FStar.Pervasives.iota;\n FStar.Pervasives.delta_only [\"Vale.X64.Memory.loc_mutable_buffers\"];\n FStar.Pervasives.delta_attr [\"Vale.X64.InsMem.norm_loc_attr\"]\n ]\n l\n <:\n Vale.X64.Memory.loc", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Vale.X64.Memory.loc", "FStar.Pervasives.norm", "Prims.Cons", "FStar.Pervasives.norm_step", "FStar.Pervasives.zeta", "FStar.Pervasives.iota", "FStar.Pervasives.delta_only", "Prims.string", "Prims.Nil", "FStar.Pervasives.delta_attr" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "l: Vale.X64.Memory.loc -> Vale.X64.Memory.loc", "prompt": "let norm_loc (l: loc) : loc =\n ", "expected_response": "norm [zeta; iota; delta_only [`%loc_mutable_buffers]; delta_attr [`%norm_loc_attr]] l", "source": { "project_name": "hacl-star", "file_name": "obj/Vale.X64.InsMem.fsti", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Vale.X64.InsMem.fsti", "checked_file": "dataset/Vale.X64.InsMem.fsti.checked", "interface_file": false, "dependencies": [ "dataset/Vale.X64.State.fsti.checked", "dataset/Vale.X64.Stack_i.fsti.checked", "dataset/Vale.X64.QuickCode.fst.checked", "dataset/Vale.X64.Memory.fsti.checked", "dataset/Vale.X64.Machine_s.fst.checked", "dataset/Vale.X64.InsBasic.fsti.checked", "dataset/Vale.X64.Decls.fsti.checked", "dataset/Vale.X64.CPU_Features_s.fst.checked", "dataset/Vale.Lib.Seqs.fsti.checked", "dataset/Vale.Def.Types_s.fst.checked", "dataset/Vale.Arch.HeapTypes_s.fst.checked", "dataset/Vale.Arch.HeapImpl.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Seq.Base.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "val va_code_Mem64_lemma : va_dummy:unit -> Tot va_code", "val va_codegen_success_Mem64_lemma : va_dummy:unit -> Tot va_pbool", "val va_lemma_Mem64_lemma : va_b0:va_code -> va_s0:va_state -> h:heaplet_id -> base:operand64 ->\n offset:int -> b:buffer64 -> index:int -> t:taint\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Mem64_lemma ()) va_s0 /\\ va_get_ok va_s0 /\\ (let\n heap_h = va_get_mem_heaplet h va_s0 in (OReg? base) /\\ valid_src_addr heap_h b index /\\\n valid_layout_buffer b (va_get_mem_layout va_s0) heap_h false /\\ valid_taint_buf64 b heap_h\n ((va_get_mem_layout va_s0).vl_taint) t /\\ eval_operand base va_s0 + offset == buffer_addr b\n heap_h + 8 `op_Multiply` index)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let heap_h = va_get_mem_heaplet h va_s0 in valid_operand (va_opr_code_Mem64 h base offset t)\n va_sM /\\ load_mem64 (buffer_addr b heap_h + 8 `op_Multiply` index) (va_get_mem va_sM) ==\n buffer_read b index heap_h) /\\ va_state_eq va_sM (va_update_ok va_sM va_s0)))", "let va_wp_Mem64_lemma (h:heaplet_id) (base:operand64) (offset:int) (b:buffer64) (index:int)\n (t:taint) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (let heap_h = va_get_mem_heaplet h va_s0 in (OReg? base) /\\ valid_src_addr\n heap_h b index /\\ valid_layout_buffer b (va_get_mem_layout va_s0) heap_h false /\\\n valid_taint_buf64 b heap_h ((va_get_mem_layout va_s0).vl_taint) t /\\ eval_operand base va_s0 +\n offset == buffer_addr b heap_h + 8 `op_Multiply` index) /\\ (let va_sM = va_s0 in va_get_ok\n va_sM /\\ (let heap_h = va_get_mem_heaplet h va_s0 in valid_operand (va_opr_code_Mem64 h base\n offset t) va_sM /\\ load_mem64 (buffer_addr b heap_h + 8 `op_Multiply` index) (va_get_mem va_sM)\n == buffer_read b index heap_h) ==> va_k va_sM (())))", "val va_wpProof_Mem64_lemma : h:heaplet_id -> base:operand64 -> offset:int -> b:buffer64 ->\n index:int -> t:taint -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Mem64_lemma h base offset b index t va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Mem64_lemma ()) ([]) va_s0 va_k\n ((va_sM, va_f0, va_g))))", "let va_quick_Mem64_lemma (h:heaplet_id) (base:operand64) (offset:int) (b:buffer64) (index:int)\n (t:taint) : (va_quickCode unit (va_code_Mem64_lemma ())) =\n (va_QProc (va_code_Mem64_lemma ()) ([]) (va_wp_Mem64_lemma h base offset b index t)\n (va_wpProof_Mem64_lemma h base offset b index t))", "let buffer64_write (b:buffer64) (i:int) (v:nat64) (h:vale_heap) : Ghost vale_heap\n (requires buffer_readable h b /\\ buffer_writeable b)\n (ensures fun _ -> True)\n =\n buffer_write b i v h", "let heaplet_id_is_none (h:vale_heap) =\n get_heaplet_id h == None", "let heaplet_id_is_some (h:vale_heap) (i:heaplet_id) =\n get_heaplet_id h == Some i", "let norm_list (p:prop) : prop =\n norm [zeta; iota; delta_only [`%list_to_seq_post]] p", "let norm_loc_attr = ()" ], "closest": [ "val norm_loc (l: loc) : loc\nlet norm_loc (l:loc) : loc =\n norm [zeta; iota; delta_only [`%loc_mutable_buffers]; delta_attr [`%norm_loc_attr]] l", "val loc_none : loc\nlet loc_none = M.loc_none", "val loc_none : loc\nlet loc_none = M.loc_none", "val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)\nlet cloc_of_loc l =\n assert_norm (MG.cls abuffer == MG.cls ubuffer);\n coerce (MG.loc cloc_cls) l", "val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)\nlet cloc_of_loc l = l", "val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)\nlet cloc_of_loc l = l", "val as_loc (x: eloc) : GTot B.loc\nlet as_loc (x:eloc) : GTot B.loc = Ghost.reveal x", "val loc_none: loc\nlet loc_none = MG.loc_none", "val loc_none: loc\nlet loc_none = MG.loc_none", "val loc_none: loc\nlet loc_none = MG.loc_none", "val single (l: loc) : label\nlet single (l:loc) : label = Set.singleton l", "val single (l: loc) : label\nlet single (l:loc) : label = Set.singleton l", "val single (l: loc) : label\nlet single (l:loc) : label = Set.singleton l", "val app_loc (x: AppCtxt.app_ctxt) (l: eloc) : eloc\nlet app_loc (x:AppCtxt.app_ctxt) (l:eloc) : eloc = \n AppCtxt.properties x;\n AppCtxt.loc_of x `loc_union` l", "val arg_loc (x: arg) : GTot B.loc\nlet arg_loc (x:arg) : GTot B.loc =\n match x with\n | (|TD_Buffer _ _ _, x|) -> B.loc_buffer x\n | (|TD_ImmBuffer _ _ _, x|) -> B.loc_buffer x\n | (|TD_Base _, _|) -> B.loc_none", "val modified_arg_loc (x: arg) : GTot B.loc\nlet modified_arg_loc (x:arg) : GTot B.loc =\n match x with\n | (|TD_Buffer _ _ {modified=true}, x|) -> B.loc_buffer x\n | _ -> B.loc_none", "val union (l1 l2: B.loc) : GTot B.loc\nlet union (l1:B.loc) (l2:B.loc) : GTot B.loc = B.loc_union l1 l2", "val sel (s: store) (l: loc) : int\nlet sel (s:store) (l:loc) : int = Map.sel s l", "val sel (s: store) (l: loc) : int\nlet sel (s:store) (l:loc) : int = Map.sel s l", "val sel (s: store) (l: loc) : int\nlet sel (s:store) (l:loc) : int = Map.sel s l", "val read (l: loc) : IST int bot (single l) []\nlet read (l:loc) : IST int bot (single l) [] = IST?.reflect (iread l)", "val read (l: loc) : IST int bot (single l) []\nlet read (l:loc) : IST int bot (single l) [] = IST?.reflect (iread l)", "val layout_modifies_loc (layout:vale_heap_layout_inner) : loc\nlet layout_modifies_loc layout = layout.vl_mod_loc", "val layout_modifies_loc (layout:vale_heap_layout_inner) : loc\nlet layout_modifies_loc layout = layout.vl_mod_loc", "val loc_of_cloc (l: MG.loc cloc_cls) : Tot loc\nlet loc_of_cloc l = l", "val loc_of_cloc (l: MG.loc cloc_cls) : Tot loc\nlet loc_of_cloc l = l", "val loc_of_cloc (l: MG.loc cloc_cls) : Tot loc\nlet loc_of_cloc l =\n assert_norm (MG.cls abuffer == MG.cls ubuffer);\n coerce loc l", "val norm_list (p: prop) : prop\nlet norm_list (p:prop) : prop =\n norm [zeta; iota; delta_only [`%list_to_seq_post]] p", "val fresh_loc (l: loc) (h h': HS.mem) : GTot Type0\nlet fresh_loc (l: loc) (h h' : HS.mem) : GTot Type0 =\n loc_unused_in h `loc_includes` l /\\\n loc_not_unused_in h' `loc_includes` l", "val loc : Type u#0\nlet loc = M.loc", "val loc : Type u#0\nlet loc = M.loc", "val loc : Type u#0\nlet loc = MG.loc cls", "val loc : Type u#1\nlet loc = MG.loc cls", "val path_loc: path_p -> GTot loc\nlet path_loc p = B.loc_all_regions_from false (B.frameOf p)", "val loc_regions\n (r: Set.set HS.rid)\n: GTot loc\nlet loc_regions = MG.loc_regions false", "val loc : Type0\nlet loc = MG.loc cls", "val lower_loc (#al: aloc_t u#x) (#c: cls al) (l: loc (raise_cls u#x u#y c)) : Tot (loc c)\nlet lower_loc #al #c l =\n let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n Loc\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide (GSet.comprehend (lower_loc_aux_pred c aux)))", "val write (l: loc) (x: int) : IST unit (single l) bot []\nlet write (l:loc) (x:int) : IST unit (single l) bot [] = IST?.reflect (iwrite l x)", "val write (l: loc) (x: int) : IST unit (single l) bot []\nlet write (l:loc) (x:int) : IST unit (single l) bot [] = IST?.reflect (iwrite l x)", "val value_of_const_loc\n (lv: locations_with_values)\n (l: location_eq{L.mem l (locations_of_locations_with_values lv)})\n : location_val_eqt l\nlet rec value_of_const_loc (lv:locations_with_values) (l:location_eq{\n L.mem l (locations_of_locations_with_values lv)\n }) : location_val_eqt l =\n let x :: xs = lv in\n if dfst x = l then dsnd x else value_of_const_loc xs l", "val address_liveness_insensitive_locs: loc\nlet address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _", "val address_liveness_insensitive_locs: loc\nlet address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _", "val modified_arg_mloc (x: arg) : GTot ME.loc\nlet modified_arg_mloc (x:arg) : GTot ME.loc =\n match x with\n | (|TD_Buffer src t {modified=true}, x|) -> ME.loc_buffer (as_vale_buffer #src #t x)\n | _ -> ME.loc_none", "val location_val_t : location -> Type u#1\nlet location_val_t a =\n match a with\n | ALocMem -> heap_impl\n | ALocStack -> FStar.Universe.raise_t (machine_stack & memTaint_t)\n | ALocReg r -> FStar.Universe.raise_t (t_reg r)\n | ALocCf -> FStar.Universe.raise_t flag_val_t\n | ALocOf -> FStar.Universe.raise_t flag_val_t", "val loc_all_args (args: list arg) : GTot B.loc\nlet loc_all_args (args:list arg) : GTot B.loc =\n let l = List.Tot.map_gtot arg_loc args in\n List.Tot.fold_right_gtot l B.loc_union B.loc_none", "val loc_vector: #a:Type -> vector a -> GTot loc\nlet loc_vector #a vec =\n B.loc_buffer (Vec?.vs vec)", "val reify_ : norm_step\nlet reify_ = Reify", "val loc (#t: buftype) (#a: Type0) (b: buffer_t t a) : GTot B.loc\nlet loc (#t:buftype) (#a:Type0) (b:buffer_t t a) : GTot B.loc =\n match t with\n | MUT -> B.loc_buffer (b <: buffer a)\n | IMMUT -> B.loc_buffer (b <: ibuffer a)\n | CONST -> CB.loc_buffer (b <: cbuffer a)", "val loc_regions\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: GTot loc\nlet loc_regions = MG.loc_regions", "val loc_regions\n (preserve_liveness: bool)\n (r: Set.set HS.rid)\n: GTot loc\nlet loc_regions = MG.loc_regions", "val raise_loc (#al: aloc_t u#x) (#c: cls al) (l: loc c) : Tot (loc (raise_cls u#x u#y c))\nlet raise_loc #al #c l =\n let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n Loc\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide (GSet.comprehend (raise_loc_aux_pred c aux)))", "val loc_none:loc_index\nlet loc_none : loc_index = Trivial", "val raise_location_val_eqt (#l: location_eq) (v: location_val_eqt l) : location_val_t l\nlet raise_location_val_eqt (#l:location_eq) (v:location_val_eqt l) : location_val_t l =\n coerce (FStar.Universe.raise_val v)", "val loc_addresses\n (r: HS.rid)\n (n: Set.set nat)\n: GTot loc\nlet loc_addresses = MG.loc_addresses #_ #cls false", "val norm (s: list norm_step) (#a: Type) (x: a) : Tot a\nlet norm _ #_ x = x", "val loc_union\n (s1 s2: loc)\n: GTot loc\nlet loc_union = MG.loc_union", "val loc_union\n (s1 s2: loc)\n: GTot loc\nlet loc_union = MG.loc_union", "val loc_union\n (s1 s2: loc)\n: GTot loc\nlet loc_union = MG.loc_union", "val iread (l: loc) : ist int bot (single l) []\nlet iread (l:loc) : ist int bot (single l) [] = fun s -> sel s l, s", "val iread (l: loc) : ist int bot (single l) []\nlet iread (l:loc) : ist int bot (single l) [] = fun s -> sel s l, s", "val size_l: prog -> pos\nlet rec size : inst -> pos = function\n | Add _ _ _\n | Sub _ _ _\n | Mul _ _ _\n | Const _ _ -> 1\n //| If0 _ i j -> 1 + size_l i + size_l j\n //| Seq i -> 1 + size_l i\n\nand size_l : prog -> pos = function\n | [] -> 1\n | hd::tl -> size hd + size_l tl", "val union_loc_of_loc (#al: (bool -> Tot aloc_t)) (c: (b: bool) -> Tot (cls (al b))) (b: bool) (l: loc (c b)) : GTot (loc (cls_union c))\nlet union_loc_of_loc #al c b l =\n let (Loc regions region_liveness_tags non_live_addrs live_addrs aux) = l in\n let aux' : GSet.set (aloc #(cls_union_aloc al) (cls_union c)) =\n union_aux_of_aux_left c b (Ghost.reveal aux)\n `GSet.union`\n (aloc_domain (cls_union c) regions live_addrs)\n in\n Loc\n #(cls_union_aloc al)\n #(cls_union c)\n regions\n region_liveness_tags\n non_live_addrs\n live_addrs\n (Ghost.hide aux')", "val loc_none (#aloc: aloc_t) (#c: cls aloc): Tot (loc c)\nlet loc_none #a #c =\n Loc\n (Ghost.hide (Set.empty))\n (Ghost.hide (Set.empty))\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide GSet.empty)", "val loc_pne_region: unit -> GTot loc\nlet loc_pne_region _ = loc_region_only true q_pne_region", "val norm_term (s: list norm_step) (t: term) : Tac term\nlet norm_term (s : list norm_step) (t : term) : Tac term =\n let e =\n try cur_env ()\n with | _ -> top_env ()\n in\n norm_term_env e s t", "val norm_term (s: list norm_step) (t: term) : Tac term\nlet norm_term (s : list norm_step) (t : term) : Tac term =\n let e =\n try cur_env ()\n with | _ -> top_env ()\n in\n norm_term_env e s t", "val union_loc_to_new (l: M.loc old_and_new_cl_union) : GTot NewM.loc\nlet union_loc_to_new (l: M.loc old_and_new_cl_union) : GTot NewM.loc =\n NewM.loc_of_cloc (M.lower_loc (M.loc_of_union_loc true l))", "val loc_union (s1 s2:loc) : GTot loc\nlet loc_union = M.loc_union", "val loc_union (s1 s2:loc) : GTot loc\nlet loc_union = M.loc_union", "val read (l: loc)\n : HIFC int (single l) bot [] (requires fun _ -> True) (ensures fun s0 x s1 -> x == sel s0 l)\nlet read (l:loc)\n : HIFC int (single l) bot []\n (requires fun _ -> True)\n (ensures fun s0 x s1 -> x == sel s0 l)\n = HIFC?.reflect (iread l)", "val mt_loc: mt_p -> GTot loc\nlet mt_loc mt = B.loc_all_regions_from false (B.frameOf mt)", "val iwrite (l: loc) (x: int) : ist unit (single l) bot []\nlet iwrite (l:loc) (x:int) : ist unit (single l) bot [] = fun s -> (), upd s l x", "val iwrite (l: loc) (x: int) : ist unit (single l) bot []\nlet iwrite (l:loc) (x:int) : ist unit (single l) bot [] = fun s -> (), upd s l x", "val lemma_value_of_const_loc_mem (c: locations_with_values) (l: location_eq) (v: location_val_eqt l)\n : Lemma\n (requires (L.mem l (locations_of_locations_with_values c) /\\ value_of_const_loc c l = v))\n (ensures (L.mem (| l, v |) c))\nlet rec lemma_value_of_const_loc_mem (c:locations_with_values) (l:location_eq) (v:location_val_eqt l) :\n Lemma\n (requires (\n L.mem l (locations_of_locations_with_values c) /\\\n value_of_const_loc c l = v))\n (ensures (L.mem (|l,v|) c)) =\n let x :: xs = c in\n if dfst x = l then () else lemma_value_of_const_loc_mem xs l v", "val norm_tac: unit -> T.Tac unit\nlet norm_tac (_:unit) : T.Tac unit =\n T.mapply (`vprop_equiv_refl)", "val modifies1 (l: loc) (h0 h1: state) : Type0\nlet modifies1 (l:loc) (h0 h1 : state) : Type0 =\n forall y. y <> l ==> Map.sel h0 y == Map.sel h1 y", "val loc_addresses\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: GTot loc\nlet loc_addresses = MG.loc_addresses", "val loc_addresses\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: GTot loc\nlet loc_addresses = MG.loc_addresses", "val loc (#aloc: aloc_t u#x) (c: cls aloc) : Tot (Type u#x)\nlet loc = loc'", "val region_liveness_insensitive_locs (#al: aloc_t) (c: cls al) : Tot (loc c)\nlet region_liveness_insensitive_locs #al c =\n Loc\n (Ghost.hide (Set.complement Set.empty))\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> GSet.complement GSet.empty))\n (mk_live_addrs (fun _ -> GSet.complement GSet.empty))\n (Ghost.hide (aloc_domain c (Ghost.hide (Set.complement Set.empty)) (fun _ -> GSet.complement GSet.empty)))", "val region_liveness_insensitive_locs: loc\nlet region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _", "val region_liveness_insensitive_locs: loc\nlet region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _", "val v (#t #l: _) (u: int_t t l) : range_t t\nlet v #t #l (u:int_t t l) : range_t t =\n match l with\n | PUB -> pub_int_v #t u\n | SEC -> sec_int_v #t u", "val loc_idx_region: unit -> GTot loc\nlet loc_idx_region _ = loc_region_only true q_idx_region", "val LowStar.Monotonic.Buffer.loc_union_l = l: Prims.list LowStar.Monotonic.Buffer.loc -> Prims.GTot LowStar.Monotonic.Buffer.loc\nlet loc_union_l (l:list loc) =\n BigOps.normal (List.Tot.fold_right_gtot l loc_union loc_none)", "val swap (l1 l2: loc)\n : AlgPP unit\n (fun _ -> l1 <> l2)\n (fun h0 _ h1 ->\n modifies [l1; l2] h0 h1 /\\ Map.sel h1 l1 == Map.sel h0 l2 /\\\n Map.sel h1 l2 == Map.sel h0 l1)\nlet swap (l1 l2 : loc) : AlgPP unit (fun _ -> l1 <> l2)\n (fun h0 _ h1 -> \n modifies [l1;l2] h0 h1 /\\\n Map.sel h1 l1 == Map.sel h0 l2 /\\\n Map.sel h1 l2 == Map.sel h0 l1)\n =\n let r = !l2 in\n l2 := !l1;\n l1 := r", "val raise_loc_lower_loc (#al: aloc_t u#x) (#c: cls al) (l: loc (raise_cls u#x u#y c)) : Lemma\n (raise_loc (lower_loc l) == l)\nlet raise_loc_lower_loc #al #c l =\n assert (raise_loc (lower_loc l) `loc_equal` l)", "val old_to_union_loc (l: OldM.loc) : GTot (M.loc old_and_new_cl_union)\nlet old_to_union_loc (l: OldM.loc) : GTot (M.loc old_and_new_cl_union) =\n M.union_loc_of_loc old_and_new_cl false (OldM.cloc_of_loc l)", "val sel (r: loc) : AlgWP int (fun h0 p -> p (Map.sel h0 r, h0))\nlet sel (r:loc) : AlgWP int (fun h0 p -> p (Map.sel h0 r, h0)) =\n let h = get2 () in\n Map.sel h r", "val normalize_n (#w: lanes) (r: pfelem) (acc: elem w) : pfelem\nlet normalize_n (#w:lanes) (r:pfelem) (acc:elem w) : pfelem =\n match w with\n | 1 -> normalize_1 r acc\n | 2 -> normalize_2 r acc\n | 4 -> normalize_4 r acc", "val f:(lo int ^--> lo int)\nlet f : (lo int ^--> lo int) = fun x -> x + 45", "val view_n (t: base_typ) : pos\nlet view_n (t:base_typ) : pos = view_n_unfold t", "val loc_of_aloc\n (#aloc: aloc_t) (#c: cls aloc)\n (#r: HS.rid)\n (#n: nat)\n (b: aloc r n)\n: GTot (loc c)\nlet loc_of_aloc #al #c #r #n b =\n let regions = (Ghost.hide (Set.singleton r)) in\n let region_liveness_tags = (Ghost.hide (Set.empty)) in\n Loc\n regions\n region_liveness_tags\n (mk_non_live_addrs (fun _ -> GSet.empty))\n (mk_live_addrs (fun _ -> GSet.empty))\n (Ghost.hide (GSet.singleton (ALoc r n (Some b))))", "val upd (s: store) (l: loc) (x: int) : store\nlet upd (s:store) (l:loc) (x:int) : store = Map.upd s l x", "val upd (s: store) (l: loc) (x: int) : store\nlet upd (s:store) (l:loc) (x:int) : store = Map.upd s l x", "val upd (s: store) (l: loc) (x: int) : store\nlet upd (s:store) (l:loc) (x:int) : store = Map.upd s l x", "val normalize_1 (r: pfelem) (acc: elem 1) : pfelem\nlet normalize_1 (r:pfelem) (acc:elem 1) : pfelem =\n pfmul acc.[0] r", "val write (l: loc) (x: int)\n : HIFC unit bot (single l) [] (requires fun _ -> True) (ensures fun _ _ s1 -> sel s1 l == x)\nlet write (l:loc) (x:int)\n : HIFC unit bot (single l) []\n (requires fun _ -> True)\n (ensures fun _ _ s1 -> sel s1 l == x)\n = HIFC?.reflect (iwrite l x)", "val loc_addresses\n (#aloc: aloc_t) (#c: cls aloc)\n (preserve_liveness: bool)\n (r: HS.rid)\n (n: Set.set nat)\n: GTot (loc c)\nlet loc_addresses #al #c preserve_liveness r n =\n let regions = (Ghost.hide (Set.singleton r)) in\n Loc\n regions\n (Ghost.hide Set.empty)\n (mk_non_live_addrs (fun _ -> if preserve_liveness then GSet.empty else GSet.of_set n))\n (mk_live_addrs (fun _ -> GSet.of_set n))\n (Ghost.hide (aloc_domain c regions (fun _ -> GSet.of_set n)))", "val normalize (x: term) : ML term\nlet normalize (x:term) : ML term = readback (translate [] x)" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsMem.fsti", "name": "Vale.PPC64LE.InsMem.norm_loc" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc_none" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc_none" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.cloc_of_loc" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.cloc_of_loc" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.cloc_of_loc" }, { "project_name": "FStar", "file_name": "LowStar.Lens.fsti", "name": "LowStar.Lens.as_loc" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_none" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_none" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_none" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.single" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.single" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.single" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.app_loc" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Base.fst", "name": "Vale.Interop.Base.arg_loc" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Base.fst", "name": "Vale.Interop.Base.modified_arg_loc" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.union" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.sel" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.sel" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.sel" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.read" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.read" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.layout_modifies_loc" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.layout_modifies_loc" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_of_cloc" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_of_cloc" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_of_cloc" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.InsMem.fsti", "name": "Vale.PPC64LE.InsMem.norm_list" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.fresh_loc" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.fst", "name": "MerkleTree.Low.path_loc" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_regions" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.lower_loc" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.write" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.write" }, { "project_name": "hacl-star", "file_name": "Vale.Transformers.InstructionReorder.fst", "name": "Vale.Transformers.InstructionReorder.value_of_const_loc" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.address_liveness_insensitive_locs" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.address_liveness_insensitive_locs" }, { "project_name": "hacl-star", "file_name": "Vale.AsLowStar.ValeSig.fst", "name": "Vale.AsLowStar.ValeSig.modified_arg_mloc" }, { "project_name": "hacl-star", "file_name": "Vale.Transformers.Locations.fst", "name": "Vale.Transformers.Locations.location_val_t" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Base.fst", "name": "Vale.Interop.Base.loc_all_args" }, { "project_name": "FStar", "file_name": "LowStar.Vector.fst", "name": "LowStar.Vector.loc_vector" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fst", "name": "FStar.Pervasives.reify_" }, { "project_name": "hacl-star", "file_name": "Lib.Buffer.fsti", "name": "Lib.Buffer.loc" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_regions" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_regions" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.raise_loc" }, { "project_name": "everparse", "file_name": "EverParse3d.Interpreter.fst", "name": "EverParse3d.Interpreter.loc_none" }, { "project_name": "hacl-star", "file_name": "Vale.Transformers.Locations.fsti", "name": "Vale.Transformers.Locations.raise_location_val_eqt" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_addresses" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fst", "name": "FStar.Pervasives.norm" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_union" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_union" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc_union" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.iread" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.iread" }, { "project_name": "FStar", "file_name": "Imp.fst", "name": "Imp.size_l" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.union_loc_of_loc" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.loc_none" }, { "project_name": "everquic-crypto", "file_name": "Mem.fst", "name": "Mem.loc_pne_region" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.norm_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.norm_term" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.union_loc_to_new" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc_union" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc_union" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.read" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Low.fst", "name": "MerkleTree.Low.mt_loc" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.iwrite" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.iwrite" }, { "project_name": "hacl-star", "file_name": "Vale.Transformers.InstructionReorder.fst", "name": "Vale.Transformers.InstructionReorder.lemma_value_of_const_loc_mem" }, { "project_name": "steel", "file_name": "Pulse.Lib.LinkedList.fst", "name": "Pulse.Lib.LinkedList.norm_tac" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.modifies1" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc_addresses" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.loc_addresses" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.loc" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.region_liveness_insensitive_locs" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.region_liveness_insensitive_locs" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.region_liveness_insensitive_locs" }, { "project_name": "hacl-star", "file_name": "Lib.IntTypes.fsti", "name": "Lib.IntTypes.v" }, { "project_name": "everquic-crypto", "file_name": "Mem.fst", "name": "Mem.loc_idx_region" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.loc_union_l" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.swap" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.raise_loc_lower_loc" }, { "project_name": "FStar", "file_name": "LowStar.ToFStarBuffer.fst", "name": "LowStar.ToFStarBuffer.old_to_union_loc" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.sel" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Vec.fst", "name": "Hacl.Spec.Poly1305.Vec.normalize_n" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.f" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Types.fst", "name": "Vale.Interop.Types.view_n" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.loc_of_aloc" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.upd" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.upd" }, { "project_name": "FStar", "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.upd" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Vec.fst", "name": "Hacl.Spec.Poly1305.Vec.normalize_1" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.write" }, { "project_name": "FStar", "file_name": "FStar.ModifiesGen.fst", "name": "FStar.ModifiesGen.loc_addresses" }, { "project_name": "FStar", "file_name": "FullReductionInterpreter.fst", "name": "FullReductionInterpreter.normalize" } ], "selected_premises": [ "FStar.UInt.size", "Vale.Def.Types_s.nat8", "Vale.X64.Memory.nat8", "Vale.X64.InsBasic.vale_heap", "Vale.X64.InsBasic.vale_stack", "Vale.Def.Types_s.nat64", "Vale.X64.Memory.nat64", "Vale.X64.Machine_s.reg_xmm", "FStar.Mul.op_Star", "Vale.X64.CPU_Features_s.avx_enabled", "Vale.X64.Decls.quad32", "Vale.Lib.Map16.sel", "Vale.X64.Decls.va_int_range", "Vale.X64.Machine_s.quad32", "Vale.X64.Memory.quad32", "Vale.Def.Prop_s.prop0", "Vale.Def.Words_s.nat32", "Vale.X64.Memory.base_typ_as_vale_type", "Vale.Def.Words_s.natN", "Vale.X64.CPU_Features_s.sse_enabled", "Vale.X64.Memory.get_vale_heap", "Vale.X64.Decls.va_upd_mem", "Vale.X64.Machine_s.operand64", "Vale.X64.Decls.va_upd_mem_heaplet", "Vale.X64.Machine_s.nat64", "Vale.X64.Decls.va_if", "Vale.X64.Memory.vuint128", "Vale.X64.Decls.buffer128_read", "Vale.X64.Memory.nat32", "Vale.Def.Types_s.nat32", "Vale.X64.Machine_s.operand128", "Vale.X64.Decls.va_value_xmm", "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_upd_mem_layout", "Vale.X64.Decls.va_upd_xmm", "Vale.X64.Decls.va_state", "Vale.X64.Machine_s.reg_64", "FStar.FunctionalExtensionality.feq", "Vale.Def.Words_s.nat8", "Vale.X64.Decls.va_get_mem_heaplet", "Vale.Def.Words_s.nat64", "Vale.X64.Decls.va_upd_flags", "Vale.X64.Decls.va_get_mem_layout", "Vale.X64.Decls.get_reg", "Vale.Def.Words_s.pow2_32", "Vale.X64.Decls.va_get_ok", "Vale.X64.Decls.va_upd_ok", "Vale.X64.CPU_Features_s.avx2_enabled", "Vale.X64.Decls.va_get_mem", "Vale.X64.Decls.validSrcAddrs128", "Vale.Lib.Seqs_s.seq_map", "Vale.X64.Decls.va_upd_reg64", "Vale.X64.QuickCode.mods_t", "Vale.X64.Decls.vale_heap", "Vale.X64.Decls.buffer_length", "Vale.X64.Decls.va_upd_stack", "Vale.X64.Decls.validDstAddrs128", "FStar.Pervasives.reveal_opaque", "Vale.X64.Decls.va_mul_nat", "Vale.X64.QuickCode.quickProc_wp", "Vale.X64.Decls.va_reveal_eq", "Vale.X64.Decls.heaplet_id", "Vale.X64.InsMem.heaplet_id_is_some", "Vale.X64.Decls.buffer128_as_seq", "Vale.X64.State.eval_maddr", "Vale.X64.QuickCode.mod_eq", "Vale.X64.Decls.memTaint_type", "Vale.X64.Flags.flag_val_t", "Vale.X64.Decls.va_is_src_xmm", "Vale.X64.QuickCode.k_true", "Vale.X64.Decls.va_get_xmm", "Vale.X64.Decls.s128", "Vale.X64.Machine_s.pow2_64", "Vale.X64.Decls.va_get_reg64", "Vale.X64.Decls.validSrcAddrsOffset128", "Vale.X64.Decls.validDstAddrsOffset128", "Vale.X64.Memory.heaplet_id", "Vale.X64.Decls.va_upd_operand_xmm", "Vale.X64.Memory.scale_by", "Vale.X64.Decls.va_get_stack", "Vale.X64.Memory.vale_heap", "Vale.X64.Memory.vuint64", "Vale.Def.Words_s.pow2_64", "Vale.X64.Decls.va_upd_stackTaint", "Vale.Def.Words.Four_s.nat_to_four", "Vale.Arch.HeapImpl.heaplet_id", "Vale.X64.Decls.state_inv", "Vale.X64.Decls.va_get_block", "Vale.X64.Machine_s.t_reg", "FStar.Heap.trivial_preorder", "Vale.X64.Decls.validDstAddrs", "Vale.X64.Regs.sel", "Vale.X64.State.eval_reg_64", "Vale.X64.State.eval_reg_int", "Vale.X64.Regs.eta_sel", "Vale.X64.Machine_s.rRdi", "Vale.X64.Decls.va_is_dst_xmm", "Vale.X64.Decls.validSrcAddrs64", "Vale.X64.Decls.va_require_total", "Vale.X64.CPU_Features_s.avx_xcr0" ], "source_upto_this": "module Vale.X64.InsMem\nopen FStar.Seq\nopen Vale.Def.Types_s\nopen Vale.Arch.HeapTypes_s\nopen Vale.Arch.HeapImpl\nopen Vale.X64.Machine_s\nopen Vale.X64.Memory\nopen Vale.X64.Stack_i\nopen Vale.X64.State\nopen Vale.X64.Decls\nopen Vale.X64.QuickCode\nopen Vale.X64.InsBasic\nopen Vale.X64.CPU_Features_s\nopen Vale.Lib.Seqs\n//-- Mem64_lemma\n\nval va_code_Mem64_lemma : va_dummy:unit -> Tot va_code\n\nval va_codegen_success_Mem64_lemma : va_dummy:unit -> Tot va_pbool\n\nval va_lemma_Mem64_lemma : va_b0:va_code -> va_s0:va_state -> h:heaplet_id -> base:operand64 ->\n offset:int -> b:buffer64 -> index:int -> t:taint\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Mem64_lemma ()) va_s0 /\\ va_get_ok va_s0 /\\ (let\n heap_h = va_get_mem_heaplet h va_s0 in (OReg? base) /\\ valid_src_addr heap_h b index /\\\n valid_layout_buffer b (va_get_mem_layout va_s0) heap_h false /\\ valid_taint_buf64 b heap_h\n ((va_get_mem_layout va_s0).vl_taint) t /\\ eval_operand base va_s0 + offset == buffer_addr b\n heap_h + 8 `op_Multiply` index)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let heap_h = va_get_mem_heaplet h va_s0 in valid_operand (va_opr_code_Mem64 h base offset t)\n va_sM /\\ load_mem64 (buffer_addr b heap_h + 8 `op_Multiply` index) (va_get_mem va_sM) ==\n buffer_read b index heap_h) /\\ va_state_eq va_sM (va_update_ok va_sM va_s0)))\n[@ va_qattr]\nlet va_wp_Mem64_lemma (h:heaplet_id) (base:operand64) (offset:int) (b:buffer64) (index:int)\n (t:taint) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (let heap_h = va_get_mem_heaplet h va_s0 in (OReg? base) /\\ valid_src_addr\n heap_h b index /\\ valid_layout_buffer b (va_get_mem_layout va_s0) heap_h false /\\\n valid_taint_buf64 b heap_h ((va_get_mem_layout va_s0).vl_taint) t /\\ eval_operand base va_s0 +\n offset == buffer_addr b heap_h + 8 `op_Multiply` index) /\\ (let va_sM = va_s0 in va_get_ok\n va_sM /\\ (let heap_h = va_get_mem_heaplet h va_s0 in valid_operand (va_opr_code_Mem64 h base\n offset t) va_sM /\\ load_mem64 (buffer_addr b heap_h + 8 `op_Multiply` index) (va_get_mem va_sM)\n == buffer_read b index heap_h) ==> va_k va_sM (())))\n\nval va_wpProof_Mem64_lemma : h:heaplet_id -> base:operand64 -> offset:int -> b:buffer64 ->\n index:int -> t:taint -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Mem64_lemma h base offset b index t va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Mem64_lemma ()) ([]) va_s0 va_k\n ((va_sM, va_f0, va_g))))\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Mem64_lemma (h:heaplet_id) (base:operand64) (offset:int) (b:buffer64) (index:int)\n (t:taint) : (va_quickCode unit (va_code_Mem64_lemma ())) =\n (va_QProc (va_code_Mem64_lemma ()) ([]) (va_wp_Mem64_lemma h base offset b index t)\n (va_wpProof_Mem64_lemma h base offset b index t))\n//--\nlet buffer64_write (b:buffer64) (i:int) (v:nat64) (h:vale_heap) : Ghost vale_heap\n (requires buffer_readable h b /\\ buffer_writeable b)\n (ensures fun _ -> True)\n =\n buffer_write b i v h\n\nlet heaplet_id_is_none (h:vale_heap) =\n get_heaplet_id h == None\n\nlet heaplet_id_is_some (h:vale_heap) (i:heaplet_id) =\n get_heaplet_id h == Some i\n\nunfold let norm_list (p:prop) : prop =\n norm [zeta; iota; delta_only [`%list_to_seq_post]] p\n\nirreducible let norm_loc_attr = ()\n", "sketch": [ "Step 1: The `norm_loc` function is intended to normalize a location (`loc`). This means it will take a location and return a normalized version of it.\nStep 2: The implementation will likely involve applying some normalization rules or transformations to the input location to produce the normalized location. This could involve simplifying or standardizing the representation of the location.", "Step 1: The `norm_loc` function is intended to normalize a location (`loc`). This typically involves transforming the location into a canonical form or ensuring it adheres to certain constraints or properties.\nStep 2: The implementation will likely involve pattern matching on the `loc` type to handle different cases and applying transformations or checks to return a normalized location.", "Step 1: The definition `norm_loc` is about normalizing a location (`loc`). This involves transforming or simplifying the location in some way to a standard or canonical form.\nStep 2: The implementation of `norm_loc` will likely involve applying some normalization rules or transformations to the input location `l`. This could involve operations like simplifying expressions, resolving references, or applying specific rules defined for locations.", "Step 1: The function `norm_loc` is intended to normalize a location (`loc`). This typically means transforming the location into a canonical form or a simplified version that is easier to work with in subsequent computations.\nStep 2: The implementation of `norm_loc` will likely involve applying some normalization rules or transformations to the input location. This could involve simplifying expressions, resolving symbolic references, or other similar operations to produce a normalized location.", "Step 1: The `norm_loc` function is intended to normalize a given location (`loc`). This means it will transform the location into a canonical form, which is useful for ensuring consistency when comparing locations.\nStep 2: The implementation will likely involve applying certain normalization rules or transformations to the input location. This could involve simplifying expressions, resolving symbolic references, or other similar operations to ensure the location is in its simplest and most consistent form.", "Step 1: The `norm_loc` function is intended to normalize a given location (`loc`). This means transforming the location into a canonical or standard form.\nStep 2: The implementation will likely involve some form of simplification or transformation of the input location to ensure it adheres to a specific format or set of rules.", "Step 1: The definition `norm_loc` is about normalizing a location (`loc`). A location in this context is likely an address or a pointer in memory.\nStep 2: To implement `norm_loc`, we need to define a function that takes a location and returns a normalized version of it. The normalization process will depend on the specific rules or transformations that are considered \"normal\" for a location in this context. This might involve simplifying the address, resolving symbolic references, or applying certain canonical forms.", "Step 1: The function `norm_loc` is intended to normalize a location (`loc`). This typically involves simplifying or transforming the location to a canonical form.\nStep 2: The implementation will likely involve applying some normalization rules or transformations to the input location. This could involve reducing expressions, simplifying paths, or other location-specific transformations.", "Step 1: The definition `norm_loc` is about normalizing a location (`loc`). This typically involves simplifying or transforming the location to a standard form.\nStep 2: The implementation will likely involve using normalization tactics or functions provided by F* to transform the given location into its normalized form.", "Step 1: The `norm_loc` function is intended to normalize a given location (`loc`). This typically involves simplifying or standardizing the representation of the location.\nStep 2: The implementation will likely involve applying certain normalization rules or transformations to the input location. This could include operations like reducing expressions, simplifying paths, or applying specific normalization functions." ], "generated_solution": [ "let norm_loc (l: loc) : loc =\n // Apply normalization rules to the location `l`\n // For example, this could involve simplifying the representation of `l`\n // or applying some standard transformation to it.\n // The exact rules depend on the definition of `loc` and what \"normalization\" means in this context.\n l", "let norm_loc (l: loc) : loc =\n match l with\n | Loc1 x -> Loc1 (normalize x)\n | Loc2 (x, y) -> Loc2 (normalize x, normalize y)\n | _ -> l", "let norm_loc (l: loc) : loc =\n // Apply normalization rules to the location `l`\n // This is a placeholder implementation; actual rules would depend on the specifics of `loc`\n l", "let norm_loc (l: loc) : loc =\n // Apply normalization rules to the location `l`\n // This is a placeholder implementation; actual rules will depend on the definition of `loc`\n l", "let norm_loc (l: loc) : loc =\n // Apply normalization rules to the location `l`\n // This is a placeholder for the actual normalization logic\n l", "let norm_loc (l: loc) : loc =\n // Assuming `loc` has a structure that can be normalized\n // Here, we just return the input as a placeholder\n l", "let norm_loc (l: loc) : loc =\n // Assuming normalization involves some canonical form or simplification\n // This is a placeholder implementation; actual logic depends on the definition of `loc`\n l", "let norm_loc (l: loc) : loc =\n // Apply normalization rules to the location `l`\n // This is a placeholder implementation; actual rules depend on the definition of `loc`\n l", "let norm_loc (l: loc) : loc =\n norm [zeta; iota; delta_only [`%loc]] l", "let norm_loc (l: loc) : loc =\n norm [zeta; iota; delta_only [`%loc_to_seq_post]] l" ] }, { "file_name": "Pulse.Lib.Priv.Trade0.fst", "name": "Pulse.Lib.Priv.Trade0.frame_stick", "opens_and_abbrevs": [ { "abbrev": "GW", "full_module": "Pulse.Lib.GhostWitness" }, { "open": "Pulse.Lib.Pervasives" }, { "open": "PulseCore.Observability" }, { "open": "Pulse.Lib.Core" }, { "open": "Pulse.Lib.Priv" }, { "open": "Pulse.Lib.Priv" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val frame_stick\n (hyp concl: vprop)\n (f: vprop)\n: stt_ghost unit\n (stick hyp concl)\n (fun _ -> stick (hyp ** f) (concl ** f))", "source_definition": "let frame_stick = __frame_stick", "source_range": { "start_line": 111, "start_col": 0, "end_line": 111, "end_col": 31 }, "interleaved": false, "definition": "Pulse.Lib.Priv.Trade0.__frame_stick", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Pulse.Lib.Priv.Trade0.__frame_stick" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "hyp: Pulse.Lib.Core.vprop -> concl: Pulse.Lib.Core.vprop -> f: Pulse.Lib.Core.vprop\n -> Pulse.Lib.Core.stt_ghost Prims.unit\n (Pulse.Lib.Priv.Trade0.stick hyp concl)\n (fun _ -> Pulse.Lib.Priv.Trade0.stick (hyp ** f) (concl ** f))", "prompt": "let frame_stick =\n ", "expected_response": "__frame_stick", "source": { "project_name": "steel", "file_name": "share/steel/examples/pulse/lib/pledge/Pulse.Lib.Priv.Trade0.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Pulse.Lib.Priv.Trade0.fst", "checked_file": "dataset/Pulse.Lib.Priv.Trade0.fst.checked", "interface_file": true, "dependencies": [ "dataset/PulseCore.Observability.fst.checked", "dataset/Pulse.Lib.Pervasives.fst.checked", "dataset/Pulse.Lib.GhostWitness.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "val stick :\n (hyp : vprop) ->\n (concl : vprop) ->\n vprop", "let implication p q : Type u#2 =\n unit -> stt_ghost unit p (fun _ -> q)", "val elim_stick\n (hyp concl: vprop)\n: stt_ghost unit\n ((stick hyp concl) ** hyp)\n (fun _ -> concl)", "let exists_implication p q : Type u#0 =\n squash (implication p q)", "let ctx (v:vprop) : vprop = v", "val intro_stick\n (hyp concl: vprop)\n (v: vprop)\n (f_elim: unit -> (\n stt_ghost unit\n (v ** hyp)\n (fun _ -> concl)\n ))\n: stt_ghost unit\n v\n (fun _ -> stick hyp concl)", "let stick (p q:vprop)\n: vprop\n= exists* (v:vprop). ctx v ** pure (exists_implication (v ** p) q)", "```pulse\nunobservable\nfn return (#a:Type u#2) (x:a)\nrequires emp\nreturns v:a\nensures pure (v == x)\n{\n x\n}\n```", "val frame_stick\n (hyp concl: vprop)\n (f: vprop)\n: stt_ghost unit\n (stick hyp concl)\n (fun _ -> stick (hyp ** f) (concl ** f))", "let psquash (a:Type u#a) : prop = squash a", "```pulse\nghost\nfn __elim_stick (hyp concl: vprop)\nrequires stick hyp concl ** hyp\nensures concl\n{\n unfold (stick hyp concl);\n with v. assert ctx v;\n let u : squash (psquash (implication (v ** hyp) concl)) =\n elim_pure_explicit (psquash (implication (v ** hyp) concl));\n let u : squash (implication (v ** hyp) concl) =\n FStar.Squash.join_squash u;\n let f = GW.ghost_witness2 (implication (reveal v ** hyp) concl) u;\n unfold ctx;\n f ();\n}\n```", "let elim_stick = __elim_stick", "```pulse\nghost\nfn __intro_stick\n (hyp concl: vprop)\n (v: vprop)\n (f_elim: unit -> (\n stt_ghost unit\n (v ** hyp)\n (fun _ -> concl)\n ))\nrequires v\nensures stick hyp concl\n{\n let f = FStar.Squash.return_squash #(implication (v ** hyp) concl) f_elim;\n fold (ctx v);\n fold (stick hyp concl);\n}\n```", "let intro_stick = __intro_stick", "```pulse\nghost\nfn __frame_stick\n (hyp concl: vprop)\n (f: vprop)\nrequires stick hyp concl\nensures stick (hyp ** f) (concl ** f)\n{\n ghost\n fn aux (_:unit)\n requires stick hyp concl ** (hyp ** f)\n ensures concl ** f\n {\n elim_stick hyp concl;\n };\n intro_stick (hyp ** f) (concl ** f) (stick hyp concl) aux;\n}\n```" ], "closest": [ "val elim_stick\n (hyp concl: vprop)\n: stt_ghost unit\n ((stick hyp concl) ** hyp)\n (fun _ -> concl)\nlet elim_stick p q =\n T.elim_trade_ghost p q", "val intro_stick\n (hyp concl: vprop)\n (v: vprop)\n (f_elim: unit -> (\n stt_ghost unit\n (v ** hyp)\n (fun _ -> concl)\n ))\n: stt_ghost unit\n v\n (fun _ -> stick hyp concl)\nlet intro_stick p q v f =\n T.intro_trade p q v f", "val frame_ghost\n (#a:Type u#a)\n (#pre:vprop) (#post:a -> vprop)\n (frame:vprop)\n (e:stt_ghost a pre post)\n: stt_ghost a (pre ** frame) (fun x -> post x ** frame)\nlet frame_ghost = A.frame_ghost", "val stick :\n (hyp : vprop) ->\n (concl : vprop) ->\n vprop\nlet stick (p q : vprop) =\n T.trade p q", "val frame_ghost\r\n (#a:Type u#a)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt_ghost a pre post)\r\n: stt_ghost a (pre ** frame) (fun x -> post x ** frame)\nlet frame_ghost\r\n (#a:Type u#a)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt_ghost a pre post)\r\n: stt_ghost a (pre ** frame) (fun x -> post x ** frame)\r\n= Ghost.hide (A.frame (Ghost.reveal e))", "val return_pledge (f:vprop) (v:vprop)\n : stt_ghost unit v (fun _ -> pledge f v)\nlet return_pledge = __return_pledge", "val intro_implies\n (#opened: _)\n (hyp concl v: vprop)\n (f_elim: (opened': inames -> STGhostT unit opened' (v `star` hyp) (fun _ -> concl)))\n : STGhostT unit opened v (fun _ -> ( @==> ) hyp concl)\nlet intro_implies\n (#opened: _)\n (hyp concl: vprop)\n (v: vprop)\n (f_elim: (\n (opened': inames) ->\n STGhostT unit opened'\n (v `star` hyp)\n (fun _ -> concl)\n ))\n: STGhostT unit opened\n v\n (fun _ -> (@==>) hyp concl)\n= intro_implies_gen hyp concl v f_elim", "val elim_trade_ghost\n (#[T.exact (`invlist_empty)] is : invlist)\n (hyp concl: vprop)\n: stt_ghost unit\n (invlist_v is ** (trade #is hyp concl) ** hyp)\n (fun _ -> invlist_v is ** concl)\nlet elim_trade_ghost #is = __elim_trade_ghost #is", "val frame_stt\n (#a:Type u#a)\n (#pre:vprop) (#post:a -> vprop)\n (frame:vprop)\n (e:stt a pre post)\n: stt a (pre ** frame) (fun x -> post x ** frame)\nlet frame_stt = I.frame", "val intro_implies_gen\n (#opened: _)\n (#[T.exact (`(hide Set.empty))] is : inames)\n (hyp concl: vprop)\n (v: vprop)\n (f_elim: (\n (opened': inames {opened' /! is}) ->\n STGhostT unit opened'\n (v `star` hyp)\n (fun _ -> concl)\n ))\n: STGhostT unit opened\n v\n (fun _ -> (@==>) #is hyp concl)\nlet intro_implies_gen #opened #is = implies_fold #opened #is", "val intro_trade\n (#[T.exact (`invlist_empty)] is : invlist)\n (hyp concl: vprop)\n (extra: vprop)\n (f_elim: unit -> (\n stt_ghost unit\n (invlist_v is ** extra ** hyp)\n (fun _ -> invlist_v is ** concl)\n ))\n: stt_ghost unit\n extra\n (fun _ -> trade #is hyp concl)\nlet intro_trade #is = __intro_trade #is", "val noop (p:slprop)\r\n: stt_ghost unit p (fun _ -> p)\nlet noop (p:slprop)\r\n: stt_ghost unit p (fun _ -> p)\r\n= Ghost.hide (A.return #_ #(fun _ -> p) ())", "val implies_fold\n (#opened: _)\n (#is: inames)\n (hyp concl v: vprop)\n (f_elim: elim_implies_t is hyp concl v)\n : STGhostT unit opened v (fun _ -> ( @==> ) #is hyp concl)\nlet implies_fold\n (#opened: _)\n (#is : inames)\n (hyp concl: vprop)\n (v: vprop)\n (f_elim: elim_implies_t is hyp concl v)\n: STGhostT unit opened\n v\n (fun _ -> (@==>) #is hyp concl)\n= intro_pure (squash (elim_implies_t is hyp concl v));\n intro_exists v (fun v -> v `star` pure (squash (elim_implies_t is hyp concl v)))", "val drop_ (p:vprop)\n: stt_ghost unit p (fun _ -> emp)\nlet drop_ (p:vprop) = A.drop p", "val assert_ (p:vprop)\n: stt_ghost unit p (fun _ -> p)\nlet assert_ (p:vprop) = A.noop p", "val drop (p:slprop)\r\n: stt_ghost unit p (fun _ -> emp)\nlet drop p = Ghost.hide (A.drop p)", "val return_pledge (is:invlist) (f:vprop) (v:vprop)\n : stt_ghost unit v (fun _ -> pledge is f v)\nlet return_pledge = __return_pledge", "val frame\r\n (#a:Type u#a)\r\n (#pre:slprop) (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt a pre post)\r\n: stt a (pre ** frame) (fun x -> post x ** frame)\nlet frame\r\n (#a:Type u#a)\r\n (#pre:slprop) (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt a pre post)\r\n: stt a (pre `star` frame) (fun x -> post x `star` frame)\r\n= fun _ -> Sem.frame frame (e())", "val elim_implies (#opened: _) (hyp concl: vprop)\n : STGhostT unit opened ((implies_ hyp concl) `star` hyp) (fun _ -> concl)\nlet elim_implies\n (#opened: _)\n (hyp concl: vprop)\n: STGhostT unit opened\n ((implies_ hyp concl) `star` hyp)\n (fun _ -> concl)\n= elim_implies_gen hyp concl", "val squash_pledge (is:invlist) (f:vprop) (v1:vprop)\n : stt_ghost unit (pledge is f (pledge is f v1)) (fun () -> pledge is f v1)\nlet squash_pledge = __squash_pledge", "val bind_pledge (#is:invlist) (#f:vprop) (#v1:vprop) (#v2:vprop)\n (extra : vprop)\n (k : ustep is (f ** extra ** v1) (f ** pledge is f v2))\n : stt_ghost unit (pledge is f v1 ** extra) (fun () -> pledge is f v2)\nlet bind_pledge #os #f #v1 #v2 extra k = __bind_pledge #os #f #v1 #v2 extra k", "val bind_pledge (#is:invlist) (#f:vprop) (#v1:vprop) (#v2:vprop)\n (extra : vprop)\n (k : ustep is (f ** extra ** v1) (f ** pledge f v2))\n : stt_ghost unit (pledge f v1 ** extra) (fun () -> pledge f v2)\nlet bind_pledge #os #f #v1 #v2 extra k = __bind_pledge #os #f #v1 #v2 extra k", "val bind_pledge' (#is:invlist) (#f:vprop) (#v1:vprop) (#v2:vprop)\n (extra : vprop)\n (k : ustep is (extra ** v1) (pledge f v2))\n : stt_ghost unit (pledge f v1 ** extra) (fun () -> pledge f v2)\nlet bind_pledge' = __bind_pledge'", "val redeem_pledge_ghost (is:invlist) (f:vprop) (v:vprop)\n : stt_ghost unit (invlist_v is ** f ** pledge is f v) (fun () -> invlist_v is ** f ** v)\nlet redeem_pledge_ghost = __redeem_pledge_ghost", "val par_stt\n (#preL:vprop)\n (#postL:vprop) \n (#preR:vprop)\n (#postR:vprop)\n (f:stt unit preL (fun _ -> postL))\n (g:stt unit preR (fun _ -> postR))\n: stt unit\n (preL ** preR)\n (fun _ -> postL ** postR)\nlet par_stt = I.par", "val implies_apply (#opened: _) (#is: inames{opened /! is}) (v hyp concl: vprop)\n : STGhost unit\n opened\n (v `star` hyp)\n (fun _ -> concl)\n (is_implies is hyp concl v)\n (fun _ -> True)\nlet implies_apply\n (#opened: _)\n (#is : inames{opened /! is})\n (v hyp concl: vprop)\n: STGhost unit opened\n (v `star` hyp)\n (fun _ -> concl)\n (is_implies is hyp concl v)\n (fun _ -> True)\n= let sq : squash (is_implies is hyp concl v) = () in\n let _ : squash (elim_implies_t is hyp concl v) = FStar.Squash.join_squash sq in\n let f : Ghost.erased (elim_implies_t is hyp concl v) = FStar.IndefiniteDescription.elim_squash #(elim_implies_t is hyp concl v) () in\n Ghost.reveal f _", "val sub_ghost\n (#a:Type u#a)\n (#pre1:vprop)\n (pre2:vprop)\n (#post1:a -> vprop)\n (post2:a -> vprop)\n (pf1 : vprop_equiv pre1 pre2)\n (pf2 : vprop_post_equiv post1 post2)\n (e:stt_ghost a pre1 post1)\n: stt_ghost a pre2 post2\nlet sub_ghost = A.sub_ghost", "val bind_pledge' (#is:invlist) (#f:vprop) (#v1:vprop) (#v2:vprop)\n (extra : vprop)\n (k : ustep is (extra ** v1) (pledge is f v2))\n : stt_ghost unit (pledge is f v1 ** extra) (fun () -> pledge is f v2)\nlet bind_pledge' = __bind_pledge'", "val elim_implies_gen\n (#opened: _)\n (#[T.exact (`(hide Set.empty))] is : inames{opened /! is})\n (hyp concl: vprop)\n: STGhostT unit opened\n ((implies_ #is hyp concl) `star` hyp)\n (fun _ -> concl)\nlet elim_implies_gen\n (#opened: _)\n (#is : inames{opened /! is})\n (hyp concl: vprop)\n: STGhostT unit opened\n (((@==>) #is hyp concl) `star` hyp)\n (fun _ -> concl)\n= let v = implies_unfold hyp concl in\n implies_apply #opened #is v hyp concl", "val intro_pure (p:prop) (_:squash p)\n: stt_ghost unit emp (fun _ -> pure p)\nlet intro_pure p _ = A.intro_pure p ()", "val perform_ghost\n (#a #pre #post : _)\n (f : unit -> stt_ghost a pre post)\n : stt_ghost a pre post\nlet perform_ghost f = f ()", "val join_pledge (#f:vprop) (v1:vprop) (v2:vprop)\n : stt_ghost unit\n (pledge f v1 ** pledge f v2)\n (fun () -> pledge f (v1 ** v2))\nlet join_pledge = __join_pledge", "val frame_lpost\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post: post_t st a)\n (lpre: l_pre pre)\n (lpost: l_post pre post)\n (#frame: st.hprop)\n (f_frame: fp_prop frame)\n : l_post (pre `st.star` frame) (fun x -> (post x) `st.star` frame)\nlet frame_lpost\n (#st:st)\n (#a:Type)\n (#pre:st.hprop)\n (#post:post_t st a)\n (lpre:l_pre pre)\n (lpost:l_post pre post)\n (#frame:st.hprop)\n (f_frame:fp_prop frame)\n : l_post (pre `st.star` frame) (fun x -> post x `st.star` frame)\n =\n fun h0 x h1 -> lpre h0 /\\ lpost h0 x h1 /\\ f_frame h1", "val return_ghost\r\n (#a:Type u#a)\r\n (x:a)\r\n (p:a -> slprop)\r\n: stt_ghost a (p x) (fun r -> p r ** pure (r == x))\nlet return_ghost #a x p = Ghost.hide (return_atomic #a x p)", "val exists_cong (#a:_)\n (#u:_)\n (p:a -> vprop)\n (q:a -> vprop {forall x. equiv (p x) (q x) })\n : STGhostT unit u\n (exists_ p)\n (fun _ -> exists_ q)\nlet exists_cong #a #u p q\n = coerce_ghost (fun _ -> SEA.exists_cong #a #u p q)", "val intro_pure (p:prop) (pf:squash p)\r\n: stt_ghost unit emp (fun _ -> pure p)\nlet intro_pure (p:prop) (pf:squash p)\r\n: stt_ghost unit emp (fun _ -> pure p)\r\n= Ghost.hide (A.intro_pure p pf)", "val rewrite (p:vprop) (q:vprop) (_:vprop_equiv p q)\n: stt_ghost unit p (fun _ -> q)\nlet rewrite p q (pf:vprop_equiv p q)\n : stt_ghost unit p (fun _ -> q)\n = slprop_equiv_elim p q;\n A.noop q", "val trade_sub_inv\n (#os1 : invlist)\n (#os2 : invlist{invlist_sub os1 os2})\n (hyp concl: vprop)\n: stt_ghost unit\n (trade #os1 hyp concl)\n (fun _ -> trade #os2 hyp concl)\nlet trade_sub_inv = __trade_sub_inv", "val sub_ghost\r\n (#a:Type u#a)\r\n (#pre1:slprop)\r\n (pre2:slprop)\r\n (#post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1 : slprop_equiv pre1 pre2)\r\n (pf2 : slprop_post_equiv post1 post2)\r\n (e:stt_ghost a pre1 post1)\r\n: stt_ghost a pre2 post2\nlet sub_ghost pre2 post2 pf1 pf2 e\r\n= Ghost.hide (A.sub pre2 post2 e)", "val coerce_ghostF (#a:Type)\n (#o:inames)\n (#p:vprop)\n (#q:a -> vprop)\n (#pre:Type0)\n (#post: a -> Type0)\n ($f:unit -> SA.SteelGhostBase a true o Unobservable p q\n (fun _ -> pre)\n (fun _ x _ -> post x))\n : STG.STGhostBase a true o Unobservable p q pre post\nlet coerce_ghostF #a #o #p #q #pre #post f\n = STGhostBase?.reflect (SA.reify_steel_ghost_comp f)", "val squash_pledge' (is1 is2 is : invlist) (f:vprop) (v1:vprop)\n : stt_ghost unit\n (pure (invlist_sub is1 is) **\n pure (invlist_sub is2 is) **\n pledge is1 f (pledge is2 f v1))\n (fun () -> pledge is f v1)\nlet squash_pledge' = __squash_pledge'", "val fix_stt_ghost_1 (#a : Type) (#b : a -> Type) (#pre : a -> vprop) (#post : (x:a -> b x -> vprop))\n (ff : (x:a -> (y:a{y << x} -> stt_ghost (b y) (pre y) (post y)) -> stt_ghost (b x) (pre x) (post x)))\n : x:a -> stt_ghost (b x) (pre x) (post x)\nlet fix_stt_ghost_1 (#a : Type) (#b : a -> Type) (#pre : a -> vprop) (#post : (x:a -> b x -> vprop))\n (ff : (x:a -> (y:a{y << x} -> stt_ghost (b y) (pre y) (post y)) -> stt_ghost (b x) (pre x) (post x)))\n : x:a -> stt_ghost (b x) (pre x) (post x)\n = fix_1 #a #(fun x -> stt_ghost (b x) (pre x) (post x)) ff", "val make_pledge (is:invlist) (f:vprop) (v:vprop) (extra:vprop)\n ($k : ustep is (f ** extra) (f ** v))\n : stt_ghost unit extra (fun _ -> pledge is f v)\nlet make_pledge os f v extra k = __make_pledge os f v extra k", "val coerce_ghost (#a:Type)\n (#o:inames)\n (#p:vprop)\n (#q:a -> vprop)\n (#pre:Type0)\n (#post: a -> Type0)\n ($f:unit -> SA.SteelGhostBase a false o Unobservable p q\n (fun _ -> pre)\n (fun _ x _ -> post x))\n : STG.STGhostBase a false o Unobservable p q pre post\nlet coerce_ghost (#a:Type)\n (#o:inames)\n (#p:vprop)\n (#q:a -> vprop)\n (#pre:Type0)\n (#post: a -> Type0)\n ($f:unit -> SA.SteelGhostBase a false o Unobservable p q\n (fun _ -> pre)\n (fun _ x _ -> post x))\n : STG.STGhostBase a false o Unobservable p q pre post\n = STG.STGhostBase?.reflect (SA.reify_steel_ghost_comp f)", "val recall\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (#fact:property a)\r\n (r:erased (ref a pcm))\r\n (v:Ghost.erased a)\r\n (w:witnessed r fact)\r\n: stt_ghost (v1:Ghost.erased a{compatible pcm v v1})\r\n (pts_to r v)\r\n (fun v1 -> pts_to r v ** pure (fact v1))\nlet recall #a #pcm #fact r v w = Ghost.hide (A.recall r v w)", "val share (#p:vprop) (#f:perm) (#u:_) (i:inv p)\n : SteelGhostT unit u\n (active f i)\n (fun _ -> active (half_perm f) i `star` active (half_perm f) i)\nlet share #p #f #u i = ghost_share_pt #_ #_ #_ #(hide true) (gref i)", "val stt_ghost\n (a:Type u#a)\n (pre:vprop)\n (post:a -> vprop)\n: Type u#(max 2 a)\nlet stt_ghost = A.stt_ghost", "val bind_ghost\n (#a:Type u#a)\n (#b:Type u#b)\n (#pre1:vprop)\n (#post1:a -> vprop)\n (#post2:b -> vprop)\n (e1:stt_ghost a pre1 post1)\n (e2:(x:a -> stt_ghost b (post1 x) post2))\n: stt_ghost b pre1 post2\nlet bind_ghost = A.bind_ghost", "val assert_ (#opened_invariants:_)\n (p:vprop)\n : STGhostT unit opened_invariants p (fun _ -> p)\nlet assert_ #o p = coerce_ghost (fun _ -> slassert0 p)", "val implies_unfold (#opened: _) (#is: inames) (hyp concl: vprop)\n : STGhost vprop\n opened\n (( @==> ) #is hyp concl)\n (fun v -> v)\n True\n (fun v -> is_implies is hyp concl v)\nlet implies_unfold\n (#opened: _)\n (#is : inames)\n (hyp concl: vprop)\n: STGhost vprop opened\n ((@==>) #is hyp concl)\n (fun v -> v)\n True\n (fun v -> is_implies is hyp concl v)\n= let v = elim_exists () in\n let _ = elim_pure _ in\n v", "val intro_forall\n (#a:Type)\n (#p:a->vprop)\n (v:vprop)\n (f_elim : (x:a -> stt_ghost unit v (fun _ -> p x)))\n: stt_ghost unit\n v\n (fun _ -> forall* x. p x)\nlet intro_forall\n (#a:Type)\n (#p:a->vprop)\n (v:vprop)\n (f_elim : (x:a -> stt_ghost unit v (fun _ -> p x)))\n: stt_ghost unit\n v\n (fun _ -> forall* x. p x)\n= let _ : squash (universal_quantifier v p) = FStar.Squash.return_squash f_elim in\n let m1\n : stt_ghost unit (emp ** v) (fun _ -> pure (is_forall v p) ** v) \n = frame_ghost v (intro_pure (is_forall v p) ()) in\n let m2 ()\n : stt_ghost unit\n (pure (is_forall v p) ** token v) \n (fun _ -> forall* x. p x)\n = intro_exists (fun (v:vprop) -> pure (is_forall v p) ** token v) v\n in\n let m = bind_ghost m1 m2 in\n sub_ghost v _\n (vprop_equiv_unit _)\n (intro_vprop_post_equiv _ _ (fun _ -> vprop_equiv_refl _))\n m", "val frame_lpre\n (#st: st)\n (#pre: st.hprop)\n (lpre: l_pre pre)\n (#frame: st.hprop)\n (f_frame: fp_prop frame)\n : l_pre (pre `st.star` frame)\nlet frame_lpre (#st:st) (#pre:st.hprop) (lpre:l_pre pre) (#frame:st.hprop) (f_frame:fp_prop frame)\n : l_pre (pre `st.star` frame)\n =\n fun h -> lpre h /\\ f_frame h", "val ghost_recall\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (#fact:property a)\r\n (r:ghost_ref pcm)\r\n (v:Ghost.erased a)\r\n (w:ghost_witnessed r fact)\r\n: stt_ghost (v1:Ghost.erased a{compatible pcm v v1})\r\n (ghost_pts_to r v)\r\n (fun v1 -> ghost_pts_to r v ** pure (fact v1))\nlet ghost_recall\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (#fact:property a)\r\n (r:ghost_ref pcm)\r\n (v:Ghost.erased a)\r\n (w:ghost_witnessed r fact)\r\n= Ghost.hide (A.recall r v w)", "val bind_ghost\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#pre1:slprop)\r\n (#post1:a -> slprop)\r\n (#post2:b -> slprop)\r\n (e1:stt_ghost a pre1 post1)\r\n (e2:(x:a -> stt_ghost b (post1 x) post2))\r\n: stt_ghost b pre1 post2\nlet bind_ghost\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#pre1:slprop)\r\n (#post1:a -> slprop)\r\n (#post2:b -> slprop)\r\n (e1:stt_ghost a pre1 post1)\r\n (e2:(x:a -> stt_ghost b (post1 x) post2))\r\n: stt_ghost b pre1 post2\r\n= let e1 = Ghost.reveal e1 in\r\n let e2 = FStar.Ghost.Pull.pull (fun (x:a) -> Ghost.reveal (e2 x)) in\r\n Ghost.hide (A.bind e1 e2)", "val get (#p:vprop) (#opened:inames) (_:unit) : SteelGhostF (erased (rmem p))\n opened\n p (fun _ -> p)\n (requires fun _ -> True)\n (ensures fun h0 r h1 -> frame_equalities p h0 h1 /\\ frame_equalities p r h1)\nlet get () = SteelGhost?.reflect (get0 ())", "val implies_concl_r (#opened: _) (q r p: vprop)\n : STGhostT unit opened (p `star` (q @==> r)) (fun _ -> q @==> (r `star` p))\nlet implies_concl_r\n (#opened: _)\n (q r p: vprop)\n: STGhostT unit opened\n (p `star` (q @==> r))\n (fun _ -> q @==> (r `star` p))\n= implies_concl_l p q r;\n implies_with_tactic (p `star` r) (r `star` p);\n implies_trans q (p `star` r) (r `star` p)", "val make_pledge (#is:invlist) (f:vprop) (v:vprop) (extra:vprop)\n ($k : ustep is (f ** extra) (f ** v))\n : stt_ghost unit extra (fun _ -> pledge f v)\nlet make_pledge #is f v extra k = __make_pledge #is f v extra k", "val ffold\n (p fp: (nat -> vprop))\n (ss: (i: nat -> stt_ghost unit (p i ** fp i) (fun () -> fp (i + 1))))\n (n i: nat)\n : stt unit ((pure (i <= n) ** fp i) ** range p i n) (fun _ -> fp n)\nlet ffold\n (p : (nat -> vprop))\n (fp : (nat -> vprop))\n (ss : (i:nat -> stt_ghost unit (p i ** fp i) (fun () -> fp (i+1))))\n (n:nat)\n : (i:nat) -> stt unit (pure (i <= n) ** fp i ** range p i n) (fun _ -> fp n)\n = fix_stt_1 (__ffold p fp ss n)", "val intro_vbind (#opened: _) (a b': vprop) (t: Type0) (b: (t_of a -> Tot vprop))\n : SteelGhost unit\n opened\n (a `star` b')\n (fun _ -> vbind a t b)\n (fun h -> t_of b' == t /\\ b' == b (h a))\n (fun h _ h' -> t_of b' == t /\\ b' == b (h a) /\\ h' (vbind a t b) == h b')\nlet intro_vbind\n (#opened: _)\n (a: vprop)\n (b' : vprop)\n (t: Type0)\n (b: (t_of a -> Tot vprop))\n: SteelGhost unit opened\n (a `star` b')\n (fun _ -> vbind a t b)\n (fun h -> t_of b' == t /\\ b' == b (h a))\n (fun h _ h' ->\n t_of b' == t /\\\n b' == b (h a) /\\\n h' (vbind a t b) == h b'\n )\n=\n intro_vpure (t == t_of b');\n intro_vdep\n a\n (vpure (t == t_of b') `star` b')\n (vbind0_payload a t b);\n intro_vrewrite\n (a `vdep` vbind0_payload a t b)\n (vbind0_rewrite a t b);\n change_slprop_rel\n (vbind0 a t b)\n (vbind a t b)\n (fun x y -> x == y)\n (fun _ -> ())", "val rewrite_with_squash (#o: _) (p q: vprop) (f: (unit -> squash (p == q)))\n : STGhostT unit o p (fun _ -> q)\nlet rewrite_with_squash #o (p q:vprop)\r\n (f:unit -> squash (p == q))\r\n : STGhostT unit o p (fun _ -> q)\r\n = f();\r\n rewrite p q", "val elim_trade\n (#[T.exact (`invlist_empty)] is : invlist)\n (hyp concl: vprop)\n: stt_atomic unit #Unobservable (invlist_names is)\n ((trade #is hyp concl) ** hyp)\n (fun _ -> concl)\nlet elim_trade #is = __elim_trade #is", "val lift_exists (#a:_)\n (#u:_)\n (p:a -> vprop)\n : STGhostT unit u\n (exists_ p)\n (fun _a -> exists_ #(U.raise_t a) (U.lift_dom p))\nlet lift_exists (#a:_) (#u:_) (p:a -> vprop)\n = coerce_ghost (fun _ -> SEA.lift_exists #a #u p)", "val rewrite_pledge0 (#is:invlist) (#f:vprop) (v1 : vprop) (v2 : vprop)\n (k : ustep0 v1 v2)\n : stt_ghost unit\n (pledge is f v1)\n (fun _ -> pledge is f v2)\nlet rewrite_pledge0 = __rewrite_pledge0", "val join_pledge (#is:invlist) (#f:vprop) (v1:vprop) (v2:vprop)\n : stt_ghost unit \n (pledge is f v1 ** pledge is f v2)\n (fun () -> pledge is f (v1 ** v2))\nlet join_pledge = __join_pledge", "val ghost_write\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ghost_ref p)\r\n (x y:Ghost.erased a)\r\n (f:FStar.PCM.frame_preserving_upd p x y)\r\n: stt_ghost unit\r\n (ghost_pts_to r x)\r\n (fun _ -> ghost_pts_to r y)\nlet ghost_write r x y f = Ghost.hide (A.write r x y f)", "val elim_pure (p:prop)\r\n: stt_ghost (squash p) (pure p) (fun _ -> emp)\nlet elim_pure (p:prop)\r\n: stt_ghost (squash p) (pure p) (fun _ -> emp)\r\n= Ghost.hide (A.elim_pure p)", "val stt_ghost\r\n (a:Type u#a)\r\n (pre:slprop)\r\n (post:a -> slprop)\r\n: Type u#(max 2 a)\nlet stt_ghost a pre post = Ghost.erased (act a emp_inames pre post)", "val redeem_pledge (f:vprop) (v:vprop)\n : stt unit (f ** pledge f v) (fun () -> f ** v)\nlet redeem_pledge = __redeem_pledge", "val share\n (#a:Type)\n (v:vec a)\n (#s:Ghost.erased (Seq.seq a))\n (#p:perm)\n : stt_ghost unit\n (requires pts_to v #p s)\n (ensures fun _ -> pts_to v #(half_perm p) s ** pts_to v #(half_perm p) s)\nlet share v = A.share v", "val elim_forall\n (#a:Type)\n (#p:a->vprop)\n (x:a)\n: stt_ghost unit\n (forall* x. p x)\n (fun _ -> p x)\nlet elim_forall\n (#a:Type u#a)\n (#p:a->vprop)\n (x:a)\n: stt_ghost unit\n (forall* (x:a). p x)\n (fun _ -> p x)\n= let m1 = elim_exists #vprop (fun (v:vprop) -> pure (is_forall v p) ** token v) in\n let m2 (v:Ghost.erased vprop)\n : stt_ghost unit \n (pure (is_forall v p) ** token v)\n (fun _ -> p x)\n = bind_ghost\n (frame_ghost \n (token v)\n (elim_pure_explicit (is_forall v p)))\n (fun (pf:squash (is_forall v p)) ->\n let f = extract_q v p pf in\n sub_ghost (emp ** Ghost.reveal v)\n (fun _ -> p x)\n (vprop_equiv_sym _ _ (vprop_equiv_unit _))\n (intro_vprop_post_equiv \n (fun _ -> p x)\n (fun _ -> p x)\n (fun _ -> vprop_equiv_refl (p x)))\n (f x))\n in\n bind_ghost m1 m2", "val funfold\n (p fp: (nat -> vprop))\n (ss: (i: nat -> stt_ghost unit (fp (i + 1)) (fun () -> p i ** fp i)))\n (n: nat)\n : stt unit (fp n) (fun _ -> fp 0 ** range p 0 n)\nlet funfold\n (p : (nat -> vprop))\n (fp : (nat -> vprop))\n (ss : (i:nat -> stt_ghost unit (fp (i+1)) (fun () -> p i ** fp i)))\n : (n:nat) -> stt unit (fp n) (fun _ -> fp 0 ** range p 0 n)\n = fix_stt_1 (__funfold p fp ss)", "val intro_vrewrite (#opened:inames)\n (v: vprop) (#t: Type) (f: (normal (t_of v) -> GTot t))\n: SteelGhost unit opened v (fun _ -> vrewrite v f)\n (fun _ -> True) (fun h _ h' -> h' (vrewrite v f) == f (h v))\nlet intro_vrewrite\n v #t f\n= let x : Ghost.erased (t_of v) = gget v in\n let x' : Ghost.erased t = Ghost.hide (f (Ghost.reveal x)) in\n change_slprop\n v\n (vrewrite v f)\n x\n x'\n (fun m ->\n vrewrite_sel_eq v f m\n )", "val pack_value_vprops\n (#opened: _)\n (#k: eqtype)\n (#v: Type0)\n (#contents: Type)\n (vp: vp_t k v contents)\n (s: Seq.seq (option (k & v)))\n (m: Map.t k contents)\n (borrows: Map.t k v)\n (idx: US.t{US.v idx < Seq.length s})\n (p: vprop)\n : STGhost unit\n opened\n (((value_vprops vp (seq_until s (US.v idx)) m borrows) `star` p)\n `star`\n (value_vprops vp (seq_from s (US.v idx)) m borrows))\n (fun _ -> value_vprops vp s m borrows)\n (requires Seq.index (value_vprops_seq vp s m borrows) (US.v idx) == p)\n (ensures fun _ -> True)\nlet pack_value_vprops (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s:Seq.seq (option (k & v)))\n (m:Map.t k contents)\n (borrows:Map.t k v)\n (idx:US.t{US.v idx < Seq.length s})\n (p:vprop)\n : STGhost unit opened\n (value_vprops vp (seq_until s (US.v idx)) m borrows\n `star`\n p\n `star`\n value_vprops vp (seq_from s (US.v idx)) m borrows)\n (fun _ -> value_vprops vp s m borrows)\n (requires Seq.index (value_vprops_seq vp s m borrows) (US.v idx) == p)\n (ensures fun _ -> True)\n = SeqPerm.foldm_snoc_singleton vprop_monoid p;\n assert (Seq.equal (value_vprops_seq vp (Seq.create 1 (Seq.index s (US.v idx))) m borrows)\n (Seq.create 1 p));\n rewrite_equiv p (value_vprops vp (seq_at s (US.v idx)) m borrows);\n value_vprops_split3 vp s m borrows (US.v idx);\n rewrite_equiv\n (value_vprops vp (seq_until s (US.v idx)) m borrows\n `star`\n value_vprops vp (seq_at s (US.v idx)) m borrows\n `star`\n value_vprops vp (seq_from s (US.v idx)) m borrows)\n (value_vprops vp s m borrows)", "val elim_pure () (#p:prop)\n: stt_ghost (squash p) (pure p) (fun _ -> emp)\nlet elim_pure _ #p = A.elim_pure p", "val rewrite_pledge (#is:invlist) (#f:vprop) (v1 : vprop) (v2 : vprop)\n (k : ustep is v1 v2)\n : stt_ghost unit\n (pledge f v1)\n (fun _ -> pledge f v2)\nlet rewrite_pledge = __rewrite_pledge", "val gen_elim\n (#opened: _)\n (#[@@@ framing_implicit] p: vprop)\n (#[@@@ framing_implicit] a: Type0)\n (#[@@@ framing_implicit] q: Ghost.erased a -> Tot vprop)\n (#[@@@ framing_implicit] post: Ghost.erased a -> Tot prop)\n (#[@@@ framing_implicit] sq: squash (gen_elim_prop_placeholder true p a q post))\n (_: unit)\n: STGhostF (Ghost.erased a) opened p (fun x -> guard_vprop (q x)) ( (T.with_tactic solve_gen_elim_prop) (squash (gen_elim_prop true p a q post))) post\nlet gen_elim\n #opened #p #a #q #post #sq _\n= gen_elim' #opened _ p a q post sq ()", "val adjoint_intro_implies\n (#opened: _)\n (#[T.exact (`(hide Set.empty))] is: inames)\n (p q r: vprop)\n (f: (opened: inames{opened /! is} -> STGhostT unit opened (p `star` q) (fun _ -> r)))\n : STGhostT unit opened p (fun _ -> ( @==> ) #is q r)\nlet adjoint_intro_implies\n (#opened: _)\n (#[T.exact (`(hide Set.empty))] is : inames)\n (p q r: vprop)\n (f: (\n (opened: inames{opened /! is}) ->\n STGhostT unit opened\n (p `star` q) (fun _ -> r)\n ))\n: STGhostT unit opened\n p\n (fun _ -> (@==>) #is q r)\n= intro_implies_gen q r p (fun _ ->\n f _\n )", "val with_invlist_ghost (#pre : vprop) (#post : vprop)\n (is : invlist)\n (f : unit -> stt_ghost unit (invlist_v is ** pre) (fun _ -> invlist_v is ** post))\n : stt_atomic unit #Unobservable (invlist_names is) pre (fun _ -> post)\nlet with_invlist_ghost = __with_invlist_ghost", "val gen_elim\n (#opened: _)\n (#[@@@ framing_implicit] p: vprop)\n (#[@@@ framing_implicit] a: Type)\n (#[@@@ framing_implicit] q: Ghost.erased a -> Tot vprop)\n (#[@@@ framing_implicit] post: Ghost.erased a -> Tot prop)\n (#[@@@ framing_implicit] sq: squash (gen_elim_prop_placeholder true p a q post))\n (_: unit)\n: STGhostF (Ghost.erased a) opened p (fun x -> guard_vprop (q x)) ( (T.with_tactic solve_gen_elim_prop) (squash (gen_elim_prop true p a q post))) post\nlet gen_elim\n #opened #p #a #q #post #sq _\n= gen_elim' #opened _ p a q post sq ()", "val intro_vdep2 (#opened:inames)\n (v: vprop)\n (q: vprop)\n (x: t_of v)\n (p: (t_of v -> Tot vprop))\n: SteelGhost unit opened\n (v `star` q)\n (fun _ -> vdep v p)\n (requires (fun h ->\n q == p x /\\\n x == h v\n ))\n (ensures (fun h _ h' ->\n let x2 = h' (vdep v p) in\n q == p (h v) /\\\n dfst x2 == (h v) /\\\n dsnd x2 == (h q)\n ))\nlet intro_vdep2\n v q x p\n=\n intro_vdep v q p", "val frame_flip (#pre #a #post: _) (frame: slprop) (e: stt a pre post)\n : stt a (pre ** frame) (fun x -> frame ** post x)\nlet frame_flip (#pre #a #post:_) (frame:slprop) (e:stt a pre post)\n: stt a (pre ** frame) (fun x -> frame ** post x)\n= let i\n : vprop_post_equiv (fun x -> post x ** frame) (fun x -> frame ** post x)\n = intro_vprop_post_equiv _ _ (fun x -> vprop_equiv_comm (post x) frame)\n in\n sub_stt _ _ (vprop_equiv_refl _) i (frame_stt frame e)", "val ghost_share\n (#a:Type)\n (#pcm:pcm a)\n (r:ghost_pcm_ref pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n: stt_ghost unit\n (ghost_pcm_pts_to r (v0 `op pcm` v1))\n (fun _ -> ghost_pcm_pts_to r v0 ** ghost_pcm_pts_to r v1)\nlet ghost_share = A.ghost_share", "val frame_atomic\n (#a:Type u#a)\n (#obs:_)\n (#opens:inames)\n (#pre:vprop) (#post:a -> vprop)\n (frame:vprop)\n (e:stt_atomic a #obs opens pre post)\n: stt_atomic a #obs opens (pre ** frame) (fun x -> post x ** frame)\nlet frame_atomic = A.frame_atomic", "val elim_pure_explicit (p:prop)\n: stt_ghost (squash p) (pure p) (fun _ -> emp)\nlet elim_pure_explicit p = A.elim_pure p", "val rewrite_pledge (#is:invlist) (#f:vprop) (v1 : vprop) (v2 : vprop)\n (k : ustep is v1 v2)\n : stt_ghost unit\n (pledge is f v1)\n (fun _ -> pledge is f v2)\nlet rewrite_pledge = __rewrite_pledge", "val implies_uncurry (#opened: _) (h1 h2 c: vprop)\n : STGhostT unit opened (( @==> ) h1 (( @==> ) h2 c)) (fun _ -> ( @==> ) (h1 `star` h2) c)\nlet implies_uncurry\n (#opened: _)\n (h1 h2 c: vprop)\n: STGhostT unit opened\n ((@==>) h1 ((@==>) h2 c))\n (fun _ -> (@==>) (h1 `star` h2) c)\n= implies_uncurry_gen #_ #(Set.empty) #(Set.empty) h1 h2 c;\n assert (Set.union Set.empty Set.empty `Set.equal` (Set.empty #iname));\n noop ();\n rewrite (implies_ #(Set.union Set.empty Set.empty) (h1 `star` h2) c) (implies_ #(Set.empty) (h1 `star` h2) c)", "val ghost_write\n (#a:Type)\n (#p:pcm a)\n (r:ghost_pcm_ref p)\n (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n: stt_ghost unit\n (ghost_pcm_pts_to r x)\n (fun _ -> ghost_pcm_pts_to r y)\nlet ghost_write = A.ghost_write", "val implies_emp_l (#opened: _) (p: vprop) : STGhostT unit opened p (fun _ -> emp @==> p)\nlet implies_emp_l\n (#opened: _)\n (p: vprop)\n: STGhostT unit opened\n p\n (fun _ -> emp @==> p)\n= intro_implies emp p p (fun _ -> noop ())", "val share2 (#a:Type) (r:ref a) (#v:erased a)\n : stt_ghost unit\n (pts_to r v)\n (fun _ -> pts_to r #one_half v ** pts_to r #one_half v)\nlet share2 (#a:Type) (r:ref a) (#v:erased a) = share r #v #full_perm", "val share2 (#a:Type) (r:ref a) (#v:erased a)\n : stt_ghost unit\n (pts_to r v)\n (fun _ -> pts_to r #one_half v ** pts_to r #one_half v)\nlet share2 (#a:Type) (r:ref a) (#v:erased a) = share #a r #v", "val share2 (#a:Type) (r:ref a) (#v:erased a)\n : stt_ghost unit\n (pts_to r v)\n (fun _ -> pts_to r #one_half v ** pts_to r #one_half v)\nlet share2 (#a:Type) (r:ref a) (#v:erased a) = share r #v #full_perm", "val share2 (#a:Type) (r:ref a) (#v:erased a)\n : stt_ghost unit\n (pts_to r v)\n (fun _ -> pts_to r #one_half v ** pts_to r #one_half v)\nlet share2 (#a:Type) (r:ref a) (#v:erased a)\n: stt_ghost unit\n (pts_to r v)\n (fun _ -> pts_to r #one_half v ** pts_to r #one_half v)\n= share #a r #v", "val implies_join (#opened: _) (h1 c1 h2 c2: vprop)\n : STGhostT unit\n opened\n ((( @==> ) h1 c1) `star` (( @==> ) h2 c2))\n (fun _ -> ( @==> ) (h1 `star` h2) (c1 `star` c2))\nlet implies_join\n (#opened: _)\n (h1 c1 h2 c2: vprop)\n: STGhostT unit opened\n (((@==>) h1 c1) `star` ((@==>) h2 c2))\n (fun _ -> (@==>) (h1 `star` h2) (c1 `star` c2))\n= implies_join_gen h1 c1 h2 c2;\n assert (Set.union Set.empty Set.empty `Set.equal` (Set.empty #iname));\n noop ();\n rewrite (implies_ #(Set.union Set.empty Set.empty) (h1 `star` h2) (c1 `star` c2)) (implies_ #(Set.empty) (h1 `star` h2) (c1 `star` c2))", "val implies_concl_l (#opened: _) (p q r: vprop)\n : STGhostT unit opened (p `star` (q @==> r)) (fun _ -> q @==> (p `star` r))\nlet implies_concl_l\n (#opened: _)\n (p q r: vprop)\n: STGhostT unit opened\n (p `star` (q @==> r))\n (fun _ -> q @==> (p `star` r))\n= implies_with_tactic q (emp `star` q);\n implies_emp_l p;\n implies_join emp p q r;\n implies_trans q (emp `star` q) (p `star` r)", "val share\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\r\n: stt_ghost unit\r\n (pts_to r (v0 `op pcm` v1))\r\n (fun _ -> pts_to r v0 ** pts_to r v1)\nlet share #a #pcm r v0 v1 = Ghost.hide (A.share r v0 v1)", "val intro_vdep (#opened:inames)\n (v: vprop)\n (q: vprop)\n (p: (t_of v -> Tot vprop))\n: SteelGhost unit opened\n (v `star` q)\n (fun _ -> vdep v p)\n (requires (fun h -> q == p (h v)))\n (ensures (fun h _ h' ->\n let x2 = h' (vdep v p) in\n q == p (h v) /\\\n dfst x2 == (h v) /\\\n dsnd x2 == (h q)\n ))\nlet intro_vdep\n v q p\n=\n reveal_star v q;\n change_slprop_rel_with_cond\n (v `star` q)\n (vdep v p)\n (vdep_cond v q p)\n (vdep_rel v q p)\n (fun m -> intro_vdep_lemma v q p m)", "val frame'\n (a: Type)\n (fr p: parser)\n (l: memory_invariant)\n (f: (unit -> EWrite a parse_empty p (fun _ -> True) (fun _ _ _ -> True) (fun _ -> True) l))\n : EWrite a\n fr\n (fr `parse_pair` p)\n (fun _ -> True)\n (fun vin v (vin', vout) ->\n vin' == vin /\\ destr_repr_spec _ _ _ _ _ _ _ f () == Correct (v, vout))\n (fun vin -> Error? (destr_repr_spec _ _ _ _ _ _ _ f ()))\n l\nlet frame'\n (a: Type)\n (fr: parser)\n (p: parser)\n (l: memory_invariant)\n (f: unit ->\n EWrite a parse_empty p (fun _ -> True) (fun _ _ _ -> True) (fun _ -> True) l\n )\n: EWrite a fr (fr `parse_pair` p)\n (fun _ -> True)\n (fun vin v (vin', vout) ->\n vin' == vin /\\\n destr_repr_spec _ _ _ _ _ _ _ f () == Correct (v, vout)\n )\n (fun vin ->\n Error? (destr_repr_spec _ _ _ _ _ _ _ f ())\n )\n l\n=\n frame _ _ _ _ _ _ _ (fun _ -> recast_writer _ _ _ _ _ _ _ f)", "val share2 (#a:Type) (r:box a) (#v:erased a)\n : stt_ghost unit\n (pts_to r v)\n (fun _ -> pts_to r #one_half v ** pts_to r #one_half v)\nlet share2 b = R.share2 b", "val mk_selector_vprop_intro\n (#opened: _) (#t: Type0) (#x: t)\n (p: t -> vprop) (p_inj: interp_hp_of_injective p)\n: SteelGhost unit opened\n (p x)\n (fun _ -> mk_selector_vprop p p_inj)\n (fun _ -> True)\n (fun _ _ h' -> h' (mk_selector_vprop p p_inj) == x)\nlet mk_selector_vprop_intro\n #_ #_ #x p p_inj\n= change_slprop_rel\n (p _)\n (mk_selector_vprop p p_inj)\n (fun _ x' -> x == x')\n (fun m ->\n intro_h_exists x (hp_of_pointwise p) m;\n let x' = mk_selector_vprop_sel' p p_inj m in\n p_inj x x' m\n )", "val ghost_witness\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ghost_ref pcm)\r\n (fact:stable_property pcm)\r\n (v:Ghost.erased a)\r\n (pf:squash (forall z. compatible pcm v z ==> fact z))\r\n: stt_ghost\r\n (ghost_witnessed r fact)\r\n (ghost_pts_to r v)\r\n (fun _ -> ghost_pts_to r v)\nlet ghost_witness\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ghost_ref pcm)\r\n (fact:stable_property pcm)\r\n (v:Ghost.erased a)\r\n (pf:squash (forall z. compatible pcm v z ==> fact z))\r\n= Ghost.hide (A.witness r fact v pf)" ], "closest_src": [ { "project_name": "steel", "file_name": "Pulse.Lib.Stick.fst", "name": "Pulse.Lib.Stick.elim_stick" }, { "project_name": "steel", "file_name": "Pulse.Lib.Stick.fst", "name": "Pulse.Lib.Stick.intro_stick" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.frame_ghost" }, { "project_name": "steel", "file_name": "Pulse.Lib.Stick.fst", "name": "Pulse.Lib.Stick.stick" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.frame_ghost" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.Simple.fst", "name": "Pulse.Lib.Par.Pledge.Simple.return_pledge" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.intro_implies" }, { "project_name": "steel", "file_name": "Pulse.Lib.Trade.fst", "name": "Pulse.Lib.Trade.elim_trade_ghost" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.frame_stt" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.intro_implies_gen" }, { "project_name": "steel", "file_name": "Pulse.Lib.Trade.fst", "name": "Pulse.Lib.Trade.intro_trade" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.noop" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.implies_fold" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.drop_" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.assert_" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.drop" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.fst", "name": "Pulse.Lib.Par.Pledge.return_pledge" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.frame" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.elim_implies" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.fst", "name": "Pulse.Lib.Par.Pledge.squash_pledge" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.fst", "name": "Pulse.Lib.Par.Pledge.bind_pledge" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.Simple.fst", "name": "Pulse.Lib.Par.Pledge.Simple.bind_pledge" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.Simple.fst", "name": "Pulse.Lib.Par.Pledge.Simple.bind_pledge'" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.fst", "name": "Pulse.Lib.Par.Pledge.redeem_pledge_ghost" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.par_stt" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.implies_apply" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.sub_ghost" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.fst", "name": "Pulse.Lib.Par.Pledge.bind_pledge'" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.elim_implies_gen" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.intro_pure" }, { "project_name": "steel", "file_name": "Pulse.Lib.Pervasives.fst", "name": "Pulse.Lib.Pervasives.perform_ghost" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.Simple.fst", "name": "Pulse.Lib.Par.Pledge.Simple.join_pledge" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.frame_lpost" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.return_ghost" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.exists_cong" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.intro_pure" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.rewrite" }, { "project_name": "steel", "file_name": "Pulse.Lib.Trade.fst", "name": "Pulse.Lib.Trade.trade_sub_inv" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.sub_ghost" }, { "project_name": "steel", "file_name": "Steel.ST.Coercions.fst", "name": "Steel.ST.Coercions.coerce_ghostF" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.fst", "name": "Pulse.Lib.Par.Pledge.squash_pledge'" }, { "project_name": "steel", "file_name": "Pulse.Lib.Fixpoints.fst", "name": "Pulse.Lib.Fixpoints.fix_stt_ghost_1" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.fst", "name": "Pulse.Lib.Par.Pledge.make_pledge" }, { "project_name": "steel", "file_name": "Steel.ST.Coercions.fst", "name": "Steel.ST.Coercions.coerce_ghost" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.recall" }, { "project_name": "steel", "file_name": "Steel.DisposableInvariant.fst", "name": "Steel.DisposableInvariant.share" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.stt_ghost" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.bind_ghost" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.assert_" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.implies_unfold" }, { "project_name": "steel", "file_name": "Pulse.Lib.Forall.fst", "name": "Pulse.Lib.Forall.intro_forall" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.frame_lpre" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.ghost_recall" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.bind_ghost" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.get" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_concl_r" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.Simple.fst", "name": "Pulse.Lib.Par.Pledge.Simple.make_pledge" }, { "project_name": "steel", "file_name": "ParallelFor.fst", "name": "ParallelFor.ffold" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.intro_vbind" }, { "project_name": "zeta", "file_name": "Zeta.Steel.VerifierSteps.fst", "name": "Zeta.Steel.VerifierSteps.rewrite_with_squash" }, { "project_name": "steel", "file_name": "Pulse.Lib.Trade.fst", "name": "Pulse.Lib.Trade.elim_trade" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.lift_exists" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.fst", "name": "Pulse.Lib.Par.Pledge.rewrite_pledge0" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.fst", "name": "Pulse.Lib.Par.Pledge.join_pledge" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.ghost_write" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.elim_pure" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.stt_ghost" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.Simple.fst", "name": "Pulse.Lib.Par.Pledge.Simple.redeem_pledge" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.share" }, { "project_name": "steel", "file_name": "Pulse.Lib.Forall.fst", "name": "Pulse.Lib.Forall.elim_forall" }, { "project_name": "steel", "file_name": "ParallelFor.fst", "name": "ParallelFor.funfold" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.intro_vrewrite" }, { "project_name": "steel", "file_name": "Steel.ST.EphemeralHashtbl.fst", "name": "Steel.ST.EphemeralHashtbl.pack_value_vprops" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.elim_pure" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.Simple.fst", "name": "Pulse.Lib.Par.Pledge.Simple.rewrite_pledge" }, { "project_name": "steel", "file_name": "Steel.ST.GenElim.fst", "name": "Steel.ST.GenElim.gen_elim" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.adjoint_intro_implies" }, { "project_name": "steel", "file_name": "Pulse.Lib.InvList.fst", "name": "Pulse.Lib.InvList.with_invlist_ghost" }, { "project_name": "steel", "file_name": "Steel.ST.GenElim1.fst", "name": "Steel.ST.GenElim1.gen_elim" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.intro_vdep2" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.frame_flip" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.ghost_share" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.frame_atomic" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.elim_pure_explicit" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.fst", "name": "Pulse.Lib.Par.Pledge.rewrite_pledge" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_uncurry" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.ghost_write" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_emp_l" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.share2" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.share2" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherReference.fst", "name": "Pulse.Lib.HigherReference.share2" }, { "project_name": "steel", "file_name": "Pulse.Lib.Reference.fst", "name": "Pulse.Lib.Reference.share2" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_join" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_concl_l" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.share" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.intro_vdep" }, { "project_name": "FStar", "file_name": "LowParseWriters.fsti", "name": "LowParseWriters.frame'" }, { "project_name": "steel", "file_name": "Pulse.Lib.Box.fst", "name": "Pulse.Lib.Box.share2" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.mk_selector_vprop_intro" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.ghost_witness" } ], "selected_premises": [ "PulseCore.FractionalPermission.full_perm", "Pulse.Lib.Core.emp_inames", "Pulse.Lib.Pervasives.perform", "Pulse.Lib.Priv.Trade0.stick", "Pulse.Lib.Priv.Trade0.ctx", "Pulse.Lib.Core.all_inames", "Pulse.Lib.Reference.cond", "FStar.PCM.composable", "FStar.Real.one", "FStar.UInt.size", "FStar.Real.two", "Pulse.Lib.Core.inames", "Pulse.Lib.Priv.Trade0.elim_stick", "Pulse.Lib.Pervasives.vprop_equiv_norm", "PulseCore.FractionalPermission.comp_perm", "FStar.PCM.op", "FStar.PCM.compatible", "FStar.Mul.op_Star", "PulseCore.FractionalPermission.sum_perm", "Pulse.Lib.Priv.Trade0.intro_stick", "Pulse.Lib.Core.one_half", "Pulse.Lib.Priv.Trade0.psquash", "FStar.Pervasives.reveal_opaque", "Pulse.Lib.Pervasives.inames_join_self", "Pulse.Lib.Core.unit_non_informative", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "Pulse.Lib.Core.join_inames", "Pulse.Lib.Pervasives.tfst", "Pulse.Lib.Pervasives.perform_ghost", "PulseCore.FractionalPermission.half_perm", "Pulse.Lib.Core.add_iname", "Pulse.Lib.Pervasives.default_arg", "FStar.Real.zero", "Pulse.Lib.Core.prop_non_informative", "Pulse.Lib.Pervasives.inames_ext", "Pulse.Lib.Core.erased_non_informative", "FStar.Math.Lemmas.pow2_plus", "Pulse.Lib.Pervasives.tthd", "PulseCore.FractionalPermission.lesser_perm", "FStar.Pervasives.dfst", "PulseCore.FractionalPermission.writeable", "Pulse.Lib.Core.inames_subset", "FStar.Pervasives.dsnd", "Pulse.Lib.Core.squash_non_informative", "Pulse.Lib.Pervasives.tsnd", "Pulse.Lib.Core.mem_iname", "FStar.Math.Lemmas.pow2_lt_compat", "FStar.Math.Lemmas.pow2_le_compat", "Pulse.Lib.Core.add_inv", "Pulse.Lib.Core.mem_inv", "FStar.Math.Lemmas.lemma_mod_plus_distr_l", "FStar.UInt32.lt", "PulseCore.FractionalPermission.lesser_equal_perm", "FStar.PCM.lem_commutative", "FStar.PCM.compatible_elim", "FStar.Real.test_le3", "PulseCore.Observability.at_most_one_observable", "FStar.Math.Lemmas.lemma_mod_plus_distr_r", "FStar.Math.Lib.slash_decr_axiom", "FStar.Math.Lib.max", "FStar.PCM.frame_compatible", "FStar.PCM.frame_preserving_val_to_fp_upd", "FStar.Real.test_div_lt", "FStar.Real.test_le2", "FStar.UInt.shift_left", "FStar.UInt.div", "FStar.UInt.to_vec", "FStar.UInt.shift_right", "FStar.UInt.udiv", "FStar.Real.test_le1", "FStar.UInt.msb", "FStar.PCM.compatible_trans", "FStar.UInt.one_extend", "FStar.Pervasives.id", "FStar.UInt.one", "FStar.UInt.max_int", "Pulse.Lib.Core.remove_inv", "FStar.Math.Lib.div_non_eucl_decr_lemma", "FStar.Real.test", "FStar.UInt.lte", "FStar.UInt32.gt", "FStar.Real.test_lt3", "FStar.UInt32.op_Equals_Hat", "FStar.UInt32.lte", "FStar.UInt.lt", "FStar.Pervasives.coerce_eq", "FStar.Math.Lib.slash_star_axiom", "FStar.Real.test_sqrt_2_scale", "FStar.UInt.incr", "FStar.UInt32.op_Greater_Equals_Hat", "FStar.Real.test_lt2", "FStar.Math.Lib.powx", "FStar.Math.Lib.div", "FStar.Math.Lib.min", "FStar.Real.test_div_eq", "FStar.Real.test_ge1", "Prims.pure_post", "FStar.Math.Lib.div_non_eucl", "FStar.UInt.ones" ], "source_upto_this": "(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Lib.Priv.Trade0\nopen PulseCore.Observability\nopen Pulse.Lib.Pervasives\n\nmodule GW = Pulse.Lib.GhostWitness\n\n#set-options \"--print_universes\"\n\n(* Do NOT use this module. Use a simple Trade instead. This is only here\nto be able to define subtyping of invariants for InvList, which cannot use trades. *)\n\nlet implication p q : Type u#2 =\n unit -> stt_ghost unit p (fun _ -> q)\n\nlet exists_implication p q : Type u#0 =\n squash (implication p q)\n\nlet ctx (v:vprop) : vprop = v\n\nlet stick (p q:vprop)\n: vprop\n= exists* (v:vprop). ctx v ** pure (exists_implication (v ** p) q)\n\n```pulse\nunobservable\nfn return (#a:Type u#2) (x:a)\nrequires emp\nreturns v:a\nensures pure (v == x)\n{\n x\n}\n```\n\n(* Fake squash *)\nlet psquash (a:Type u#a) : prop = squash a\n\n```pulse\nghost\nfn __elim_stick (hyp concl: vprop)\nrequires stick hyp concl ** hyp\nensures concl\n{\n unfold (stick hyp concl);\n with v. assert ctx v;\n let u : squash (psquash (implication (v ** hyp) concl)) =\n elim_pure_explicit (psquash (implication (v ** hyp) concl));\n let u : squash (implication (v ** hyp) concl) =\n FStar.Squash.join_squash u;\n let f = GW.ghost_witness2 (implication (reveal v ** hyp) concl) u;\n unfold ctx;\n f ();\n}\n```\nlet elim_stick = __elim_stick\n\n```pulse\nghost\nfn __intro_stick\n (hyp concl: vprop)\n (v: vprop)\n (f_elim: unit -> (\n stt_ghost unit\n (v ** hyp)\n (fun _ -> concl)\n ))\nrequires v\nensures stick hyp concl\n{\n let f = FStar.Squash.return_squash #(implication (v ** hyp) concl) f_elim;\n fold (ctx v);\n fold (stick hyp concl);\n}\n```\nlet intro_stick = __intro_stick\n\n```pulse\nghost\nfn __frame_stick\n (hyp concl: vprop)\n (f: vprop)\nrequires stick hyp concl\nensures stick (hyp ** f) (concl ** f)\n{\n ghost\n fn aux (_:unit)\n requires stick hyp concl ** (hyp ** f)\n ensures concl ** f\n {\n elim_stick hyp concl;\n };\n intro_stick (hyp ** f) (concl ** f) (stick hyp concl) aux;\n}\n```", "sketch": [ "Step 1: The `frame_stick` function aims to extend the context of a given `stick` hypothesis and conclusion by adding an additional frame `f` to both the hypothesis and the conclusion.\nStep 2: The implementation involves using the `__frame_stick` function to achieve this. The `__frame_stick` function takes the original hypothesis and conclusion, along with the additional frame, and ensures that the new `stick` property holds for the extended hypothesis and conclusion.", "Step 1: The definition `frame_stick` is about framing a `stick` property. Given a hypothesis `hyp`, a conclusion `concl`, and an additional frame `f`, it ensures that if `stick hyp concl` holds, then `stick (hyp ** f) (concl ** f)` also holds.\nStep 2: The implementation uses the `__frame_stick` function to achieve this. It calls `__frame_stick` with the given `hyp`, `concl`, and `f` to frame the `stick` property accordingly.", "Step 1: The definition `frame_stick` aims to extend the context of a given hypothesis (`hyp`) and conclusion (`concl`) with an additional frame (`f`). This is useful in modular reasoning where we want to maintain certain properties while adding new conditions.\nStep 2: The implementation uses the `__frame_stick` function to achieve this. It takes the hypothesis, conclusion, and the frame as inputs and ensures that the new context is correctly framed.", "Step 1: The definition `frame_stick` is about extending the context of a given logical implication. Specifically, if we have a proof that `hyp` implies `concl` under some context, we want to extend this proof to show that `hyp` combined with an additional context `f` implies `concl` combined with the same additional context `f`.\nStep 2: The implementation uses the `__frame_stick` function to achieve this. It takes `hyp`, `concl`, and `f` as arguments and constructs a ghost computation that ensures the extended implication holds.", "Step 1: The `frame_stick` function is designed to extend the context of a given hypothesis and conclusion by an additional frame `f`. This means that if we have a proof of `stick hyp concl`, we can derive a proof of `stick (hyp ** f) (concl ** f)`.\n\nStep 2: The implementation of `frame_stick` uses the `__frame_stick` function defined earlier. This function internally uses `elim_stick` to eliminate the original `stick hyp concl` and then introduces the new `stick (hyp ** f) (concl ** f)` using `intro_stick`.", "Step 1: The definition `frame_stick` is about framing the `stick` predicate. Given a hypothesis `hyp`, a conclusion `concl`, and an additional frame `f`, it shows that if `stick hyp concl` holds, then `stick (hyp ** f) (concl ** f)` also holds.\nStep 2: The implementation uses the `__frame_stick` function to achieve this. It calls `__frame_stick` with the given `hyp`, `concl`, and `f`, ensuring that the required preconditions and postconditions are met.", "Step 1: The definition `frame_stick` is about framing a given hypothesis and conclusion with an additional vprop `f`. This means that if we have a proof that `hyp` implies `concl`, we want to extend this proof to show that `hyp ** f` implies `concl ** f`.\nStep 2: The implementation uses the `__frame_stick` function to achieve this. It calls `__frame_stick` with the given `hyp`, `concl`, and `f`, which internally uses `elim_stick` and `intro_stick` to frame the hypothesis and conclusion.", "Step 1: The definition `frame_stick` is about framing a given hypothesis (`hyp`) and conclusion (`concl`) with an additional proposition (`f`). This means that if we have a proof of `stick hyp concl`, we want to derive a proof of `stick (hyp ** f) (concl ** f)`.\n\nStep 2: The implementation uses the `__frame_stick` function to achieve this. The `__frame_stick` function internally uses the `aux` function to handle the framing by eliminating the original `stick hyp concl` and then introducing the new framed version `stick (hyp ** f) (concl ** f)`.", "Step 1: The definition `frame_stick` is about framing a stick property. Given a hypothesis `hyp`, a conclusion `concl`, and an additional frame `f`, it shows that if `stick hyp concl` holds, then `stick (hyp ** f) (concl ** f)` also holds.\nStep 2: The implementation uses the `__frame_stick` function to achieve this. It calls `__frame_stick` with the given `hyp`, `concl`, and `f`, which internally uses `elim_stick` and `intro_stick` to manipulate the stick properties accordingly.", "Step 1: The definition `frame_stick` is about framing a stick property. Given a hypothesis `hyp`, a conclusion `concl`, and an additional frame `f`, it ensures that if `stick hyp concl` holds, then `stick (hyp ** f) (concl ** f)` also holds.\nStep 2: The implementation uses the `__frame_stick` function to achieve this. It calls `__frame_stick` with the given `hyp`, `concl`, and `f` to frame the stick property accordingly." ], "generated_solution": [ "let frame_stick hyp concl f =\n __frame_stick hyp concl f", "let frame_stick (hyp concl: vprop) (f: vprop) : stt_ghost unit (stick hyp concl) (fun _ -> stick (hyp ** f) (concl ** f)) =\n __frame_stick hyp concl f", "let frame_stick (hyp concl: vprop) (f: vprop) : stt_ghost unit (stick hyp concl) (fun _ -> stick (hyp ** f) (concl ** f)) =\n __frame_stick hyp concl f", "let frame_stick hyp concl f =\n __frame_stick hyp concl f", "let frame_stick (hyp concl: vprop) (f: vprop) : stt_ghost unit (stick hyp concl) (fun _ -> stick (hyp ** f) (concl ** f)) =\n __frame_stick hyp concl f", "let frame_stick (hyp concl: vprop) (f: vprop) : stt_ghost unit (stick hyp concl) (fun _ -> stick (hyp ** f) (concl ** f)) =\n __frame_stick hyp concl f", "let frame_stick (hyp concl: vprop) (f: vprop) : stt_ghost unit (stick hyp concl) (fun _ -> stick (hyp ** f) (concl ** f)) =\n __frame_stick hyp concl f", "let frame_stick (hyp concl: vprop) (f: vprop) : stt_ghost unit (stick hyp concl) (fun _ -> stick (hyp ** f) (concl ** f)) =\n __frame_stick hyp concl f", "let frame_stick hyp concl f =\n __frame_stick hyp concl f", "let frame_stick (hyp concl: vprop) (f: vprop) : stt_ghost unit (stick hyp concl) (fun _ -> stick (hyp ** f) (concl ** f)) =\n __frame_stick hyp concl f" ] }, { "file_name": "Steel.Heap.fst", "name": "Steel.Heap.sel_action'", "opens_and_abbrevs": [ { "abbrev": "PP", "full_module": "Steel.Preorder" }, { "abbrev": "W", "full_module": "FStar.WellFounded" }, { "abbrev": "Frac", "full_module": "Steel.FractionalPermission" }, { "open": "FStar.PCM" }, { "open": "FStar.FunctionalExtensionality" }, { "abbrev": "F", "full_module": "FStar.FunctionalExtensionality" }, { "open": "FStar.PCM" }, { "open": "FStar.Ghost" }, { "open": "Steel" }, { "open": "Steel" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 2, "initial_ifuel": 2, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 4, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val sel_action' (#a #pcm: _) (r: ref a pcm) (v0: erased a) (h: full_hheap (pts_to r v0))\n : v:\n a\n { compatible pcm v0 v /\\\n (forall frame.\n composable pcm frame v0 /\\ interp (pts_to r frame) h ==> compatible pcm frame v) }", "source_definition": "let sel_action' (#a:_) (#pcm:_) (r:ref a pcm) (v0:erased a) (h:full_hheap (pts_to r v0))\n : v:a{compatible pcm v0 v /\\\n (forall frame. composable pcm frame v0 /\\\n interp (pts_to r frame) h ==>\n compatible pcm frame v)}\n = sel_v r v0 h", "source_range": { "start_line": 768, "start_col": 0, "end_line": 773, "end_col": 16 }, "interleaved": false, "definition": "fun r v0 h ->\n Steel.Heap.sel_v r v0 h\n <:\n v:\n a\n { FStar.PCM.compatible pcm (FStar.Ghost.reveal v0) v /\\\n (forall (frame: a).\n FStar.PCM.composable pcm frame (FStar.Ghost.reveal v0) /\\\n Steel.Heap.interp (Steel.Heap.pts_to r frame) h ==>\n FStar.PCM.compatible pcm frame v) }", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.PCM.pcm", "Steel.Heap.ref", "FStar.Ghost.erased", "Steel.Heap.full_hheap", "Steel.Heap.pts_to", "FStar.Ghost.reveal", "Steel.Heap.sel_v", "Prims.l_and", "FStar.PCM.compatible", "Prims.l_Forall", "Prims.l_imp", "FStar.PCM.composable", "Steel.Heap.interp" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "\n r: Steel.Heap.ref a pcm ->\n v0: FStar.Ghost.erased a ->\n h: Steel.Heap.full_hheap (Steel.Heap.pts_to r (FStar.Ghost.reveal v0))\n -> v:\n a\n { FStar.PCM.compatible pcm (FStar.Ghost.reveal v0) v /\\\n (forall (frame: a).\n FStar.PCM.composable pcm frame (FStar.Ghost.reveal v0) /\\\n Steel.Heap.interp (Steel.Heap.pts_to r frame) h ==>\n FStar.PCM.compatible pcm frame v) }", "prompt": "let sel_action' (#a #pcm: _) (r: ref a pcm) (v0: erased a) (h: full_hheap (pts_to r v0))\n : v:\n a\n { compatible pcm v0 v /\\\n (forall frame.\n composable pcm frame v0 /\\ interp (pts_to r frame) h ==> compatible pcm frame v) } =\n ", "expected_response": "sel_v r v0 h", "source": { "project_name": "steel", "file_name": "lib/steel/Steel.Heap.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Steel.Heap.fst", "checked_file": "dataset/Steel.Heap.fst.checked", "interface_file": true, "dependencies": [ "dataset/Steel.Preorder.fst.checked", "dataset/Steel.FractionalPermission.fst.checked", "dataset/prims.fst.checked", "dataset/FStar.WellFounded.fst.checked", "dataset/FStar.PropositionalExtensionality.fst.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.PredicateExtensionality.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.PCM.fst.checked", "dataset/FStar.IndefiniteDescription.fsti.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Calc.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "cell", "Ref", "Ref", "Ref", "a", "a", "p", "p", "frac", "frac", "v", "v", "let addr = nat", "let heap : Type u#(a + 1) = addr ^-> option (cell u#a)", "val heap : Type u#(a + 1)", "let empty_heap : heap = F.on _ (fun _ -> None)", "let contains_addr (m:heap) (a:addr)\n : bool\n = Some? (m a)", "val core_ref : Type u#0", "let select_addr (m:heap) (a:addr{contains_addr m a})\n : cell\n = Some?.v (m a)", "let ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref", "val core_ref_null : core_ref", "let update_addr' (m:heap) (a:addr) (c:option cell)\n : heap\n = F.on _ (fun a' -> if a = a' then c else m a')", "let null (#a:Type u#a) (#pcm:pcm a) : ref a pcm = core_ref_null", "let update_addr (m:heap) (a:addr) (c:cell)\n : heap\n = update_addr' m a (Some c)", "val core_ref_is_null (r:core_ref) : b:bool { b <==> r == core_ref_null }", "let disjoint_cells (c0 c1:cell u#h) : prop =\n let Ref t0 p0 f0 v0 = c0 in\n let Ref t1 p1 f1 v1 = c1 in\n t0 == t1 /\\\n p0 == p1 /\\\n composable p0 v0 v1 /\\\n (Frac.sum_perm f0 f1 `Frac.lesser_equal_perm` Frac.full_perm) /\\\n (Frac.sum_perm f0 f1 == Frac.full_perm ==> p0.refine (op p0 v0 v1))", "let is_null (#a:Type u#a) (#pcm:pcm a) (r:ref a pcm) : (b:bool{b <==> r == null}) = core_ref_is_null r", "val disjoint (h0 h1:heap u#h) : prop", "val disjoint_sym (h0 h1:heap u#h)\n : Lemma (disjoint h0 h1 <==> disjoint h1 h0)\n [SMTPat (disjoint h0 h1)]", "let disjoint_cells_sym (c0 c1:cell u#h)\n : Lemma (requires disjoint_cells c0 c1)\n (ensures disjoint_cells c1 c0)\n = let Ref t0 p0 f0 v0 = c0 in\n let Ref t1 p1 f0 v1 = c1 in\n p0.comm v0 v1;\n ()", "val join (h0:heap u#h) (h1:heap u#h{disjoint h0 h1}) : heap u#h", "val join_commutative (h0 h1:heap)\n : Lemma\n (requires\n disjoint h0 h1)\n (ensures\n (disjoint h1 h0 /\\\n join h0 h1 == join h1 h0))", "let disjoint_addr (m0 m1:heap u#h) (a:addr)\n : prop\n = match m0 a, m1 a with\n | Some c0, Some c1 ->\n disjoint_cells c0 c1\n | Some _, None\n | None, Some _\n | None, None ->\n True", "val disjoint_join (h0 h1 h2:heap)\n : Lemma (disjoint h1 h2 /\\\n disjoint h0 (join h1 h2) ==>\n disjoint h0 h1 /\\\n disjoint h0 h2 /\\\n disjoint (join h0 h1) h2 /\\\n disjoint (join h0 h2) h1)", "core_ref", "Null", "Null", "Null", "Addr", "Addr", "Addr", "let core_ref_null = Null", "let core_ref_is_null (r:core_ref) = Null? r", "val join_associative (h0 h1 h2:heap)\n : Lemma\n (requires\n disjoint h1 h2 /\\\n disjoint h0 (join h1 h2))\n (ensures\n (disjoint h0 h1 /\\\n disjoint (join h0 h1) h2 /\\\n join h0 (join h1 h2) == join (join h0 h1) h2))", "let disjoint (m0 m1:heap u#h)\n : prop\n = forall a. disjoint_addr m0 m1 a", "let disjoint_sym (m0 m1:heap u#h)\n = let aux (m0 m1:heap u#h) (a:addr)\n : Lemma (requires disjoint_addr m0 m1 a)\n (ensures disjoint_addr m1 m0 a)\n [SMTPat (disjoint_addr m1 m0 a)]\n = match m0 a, m1 a with\n | Some c0, Some c1 -> disjoint_cells_sym c0 c1\n | _ -> ()\n in\n ()", "let join_cells (c0:cell u#h) (c1:cell u#h{disjoint_cells c0 c1}) =\n let Ref a0 p0 f0 v0 = c0 in\n let Ref a1 p1 f1 v1 = c1 in\n Ref a0 p0 (Frac.sum_perm f0 f1) (op p0 v0 v1)", "let heap_prop_is_affine (p:heap u#a -> prop) : prop =\n forall (h0 h1: heap u#a). p h0 /\\ disjoint h0 h1 ==> p (join h0 h1)", "let join (m0:heap) (m1:heap{disjoint m0 m1})\n : heap\n = F.on _ (fun a ->\n match m0 a, m1 a with\n | None, None -> None\n | None, Some x -> Some x\n | Some x, None -> Some x\n | Some c0, Some c1 ->\n Some (join_cells c0 c1))", "let a_heap_prop = p:(heap -> prop) { heap_prop_is_affine p }", "let disjoint_join_cells_assoc (c0 c1 c2:cell u#h)\n : Lemma\n (requires disjoint_cells c1 c2 /\\\n disjoint_cells c0 (join_cells c1 c2))\n (ensures disjoint_cells c0 c1 /\\\n disjoint_cells (join_cells c0 c1) c2 /\\\n join_cells (join_cells c0 c1) c2 == join_cells c0 (join_cells c1 c2))\n = let Ref a0 p0 f0 v0 = c0 in\n let Ref a1 p1 f1 v1 = c1 in\n let Ref a2 p2 f2 v2 = c2 in\n p0.assoc v0 v1 v2", "val slprop : Type u#(a + 1)", "val interp (p:slprop u#a) (m:heap u#a) : prop", "val as_slprop (f:a_heap_prop) : p:slprop{forall h.interp p h <==> f h}", "let disjoint_join' (m0 m1 m2:heap u#h)\n : Lemma (requires disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures disjoint m0 m1 /\\ disjoint (join m0 m1) m2)\n [SMTPat (disjoint (join m0 m1) m2)]\n = let aux (a:addr)\n : Lemma (disjoint_addr m0 m1 a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n assert (disjoint m0 m1);\n let aux (a:addr)\n : Lemma (disjoint_addr (join m0 m1) m2 a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n ()", "let hprop (fp:slprop u#a) =\n q:(heap u#a -> prop){\n forall (h0:heap{interp fp h0}) (h1:heap{disjoint h0 h1}).\n q h0 <==> q (join h0 h1)\n }", "let hheap (p:slprop u#a) = m:heap u#a {interp p m}", "let equiv (p1 p2:slprop) =\n forall m. interp p1 m <==> interp p2 m", "let mem_equiv (m0 m1:heap) =\n forall a. m0 a == m1 a", "val slprop_extensionality (p q:slprop)\n : Lemma\n (requires p `equiv` q)\n (ensures p == q)", "let mem_equiv_eq (m0 m1:heap)\n : Lemma\n (requires\n m0 `mem_equiv` m1)\n (ensures\n m0 == m1)\n [SMTPat (m0 `mem_equiv` m1)]\n = F.extensionality _ _ m0 m1", "val emp : slprop u#a", "val pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a", "let join_cells_commutative (c0:cell u#h) (c1:cell u#h{disjoint_cells c0 c1})\n : Lemma (disjoint_cells_sym c0 c1; join_cells c0 c1 == join_cells c1 c0)\n [SMTPat (join_cells c0 c1)]\n = let Ref a0 p0 _ v0 = c0 in\n let Ref a1 p1 _ v1 = c1 in\n p0.comm v0 v1", "val h_and (p1 p2:slprop u#a) : slprop u#a", "val h_or (p1 p2:slprop u#a) : slprop u#a", "val star (p1 p2:slprop u#a) : slprop u#a", "val wand (p1 p2:slprop u#a) : slprop u#a", "val h_exists (#[@@@strictly_positive] a:Type u#b)\n ([@@@strictly_positive] f: (a -> slprop u#a))\n : slprop u#a", "let join_commutative' (m0 m1:heap)\n : Lemma\n (requires\n disjoint m0 m1)\n (ensures\n join m0 m1 `mem_equiv` join m1 m0)\n [SMTPat (join m0 m1)]\n = ()", "val h_forall (#a:Type u#b) (f: (a -> slprop u#a)) : slprop u#a", "val h_refine (p:slprop u#a) (r:a_heap_prop u#a) : slprop u#a", "let join_commutative m0 m1 = ()", "val affine_star (p q:slprop) (h:heap)\n : Lemma ((interp (p `star` q) h ==> interp p h /\\ interp q h))", "let disjoint_join (m0 m1 m2:heap)\n : Lemma (disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) ==>\n disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\n [SMTPat (disjoint m0 (join m1 m2))]\n = let aux ()\n : Lemma\n (requires disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\n [SMTPat ()]\n = disjoint_join' m0 m1 m2;\n join_commutative m0 m1;\n disjoint_join' m0 m2 m1\n in\n ()", "val equiv_symmetric (p1 p2:slprop)\n : squash (p1 `equiv` p2 ==> p2 `equiv` p1)", "val equiv_extensional_on_star (p1 p2 p3:slprop)\n : squash (p1 `equiv` p2 ==> (p1 `star` p3) `equiv` (p2 `star` p3))", "val emp_unit (p:slprop)\n : Lemma (p `equiv` (p `star` emp))", "val intro_emp (h:heap)\n : Lemma (interp emp h)", "val h_exists_cong (#a:Type) (p q : a -> slprop)\n : Lemma\n (requires (forall x. p x `equiv` q x))\n (ensures (h_exists p `equiv` h_exists q))", "let join_associative' (m0 m1 m2:heap)\n : Lemma\n (requires\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures\n (disjoint_join m0 m1 m2;\n join m0 (join m1 m2) `mem_equiv` join (join m0 m1) m2))\n [SMTPatOr\n [[SMTPat (join m0 (join m1 m2))];\n [SMTPat (join (join m0 m1) m2)]]]\n = disjoint_join m0 m1 m2;\n let l = join m0 (join m1 m2) in\n let r = join (join m0 m1) m2 in\n let aux (a:addr)\n : Lemma (l a == r a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n ()", "val intro_h_exists (#a:_) (x:a) (p:a -> slprop) (h:heap)\n : Lemma (interp (p x) h ==> interp (h_exists p) h)", "val elim_h_exists (#a:_) (p:a -> slprop) (h:heap)\n : Lemma (interp (h_exists p) h ==> (exists x. interp (p x) h))", "val intro_h_forall (#a:_) (p:a -> slprop) (h:heap)\n : Lemma ((forall x. interp (p x) h) ==> interp (h_forall p) h)", "val elim_h_forall (#a:_) (p:a -> slprop) (h:heap) (x:a)\n : Lemma (interp (h_forall p) h ==> interp (p x) h)", "val intro_h_and (p q: slprop) (h:heap)\n : Lemma (interp p h /\\ interp q h ==> interp (h_and p q) h)", "val elim_h_and (p q: slprop) (h:heap)\n : Lemma (interp (h_and p q) h ==> (interp p h /\\ interp q h))", "let join_associative (m0 m1 m2:heap) = join_associative' m0 m1 m2", "val intro_h_or_left (p q: slprop) (h:heap)\n : Lemma (interp p h ==> interp (h_or p q) h)", "let join_associative2 (m0 m1 m2:heap)\n : Lemma\n (requires\n disjoint m0 m1 /\\\n disjoint (join m0 m1) m2)\n (ensures\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) /\\\n join m0 (join m1 m2) `mem_equiv` join (join m0 m1) m2)\n [SMTPat (join (join m0 m1) m2)]\n = disjoint_join m2 m0 m1;\n join_commutative (join m0 m1) m2;\n join_associative m2 m0 m1", "val intro_h_or_right (p q: slprop) (h:heap)\n : Lemma (interp q h ==> interp (h_or p q) h)", "val elim_h_or (p q: slprop) (h:heap)\n : Lemma (interp (h_or p q) h ==> (interp p h \\/ interp q h))", "val intro_wand (p1 p2: slprop u#a) (h:heap)\n : Lemma ((forall h1. h `disjoint` h1 /\\ interp p1 h1 ==> interp p2 (join h h1))\n ==> interp (wand p1 p2) h)", "val elim_wand (p1 p2: slprop u#a) (h:heap) (h1:heap)\n : Lemma ((interp (wand p1 p2) h /\\ h `disjoint` h1 /\\ interp p1 h1)\n ==> interp p2 (join h h1))", "let slprop = p:(heap ^-> prop) { heap_prop_is_affine p }", "let interp (p:slprop u#a) (m:heap u#a)\n : Tot prop\n = p m", "let as_slprop p = FStar.FunctionalExtensionality.on _ p", "val interp_depends_only_on (hp:slprop u#a)\n : Lemma\n (forall (h0:hheap hp) (h1:heap u#a{disjoint h0 h1}).\n interp hp h0 <==> interp hp (join h0 h1))", "let slprop_extensionality (p q:slprop)\n : Lemma\n (requires p `equiv` q)\n (ensures p == q)\n = FStar.PredicateExtensionality.predicateExtensionality _ p q", "let emp : slprop u#a = as_slprop (fun h -> True)", "let affine_hprop_intro\n (p:heap u#a -> prop)\n (lemma: (h0 : heap u#a) -> (h1: heap u#a) -> Lemma\n (requires (p h0 /\\ disjoint h0 h1))\n (ensures (p (join h0 h1)))\n )\n : Lemma (heap_prop_is_affine p)\n =\n let aux (h0 h1: heap u#a) : Lemma (p h0 /\\ disjoint h0 h1 ==> p (join h0 h1)) =\n let aux (_ : squash (p h0 /\\ disjoint h0 h1)) : Lemma (disjoint h0 h1 /\\ p (join h0 h1)) =\n lemma h0 h1\n in\n Classical.impl_intro aux\n in\n Classical.forall_intro_2 aux", "let ptr (#a: Type u#a) (#pcm: pcm a) (r:ref a pcm) =\n h_exists (pts_to r)", "val pts_to_compatible\n (#a:Type u#a)\n (#pcm: pcm a)\n (x:ref a pcm)\n (v0 v1:a)\n (h:heap u#a)\n : Lemma\n (interp (pts_to x v0 `star` pts_to x v1) h\n <==>\n (composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) h))", "let pts_to_cell (#a:Type u#a) (pcm:pcm a) (v:a) (c:cell u#a) =\n let Ref a' pcm' _ v' = c in\n a == a' /\\\n pcm == pcm' /\\\n compatible pcm v v'", "let pts_to_cell_join (#a:Type u#a) (pcm:pcm a) (v1 v2:a) (c:cell u#a)\n : Lemma (requires (pts_to_cell pcm v1 c /\\ pts_to_cell pcm v2 c))\n (ensures joinable pcm v1 v2)\n = ()", "let pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a =\n let hprop (h: heap) : Tot prop =\n Addr? r /\\\n h `contains_addr` (Addr?._0 r) /\\\n pts_to_cell pcm v (select_addr h (Addr?._0 r))\n in\n affine_hprop_intro hprop (fun h0 h1 ->\n match r with | Null -> () | Addr r -> (\n match h0 r, h1 r, (join h0 h1) r with\n | Some (Ref a0 pcm0 _ v0), Some (Ref a1 pcm1 _ v1), Some (Ref a01 pcm01 _ v01) ->\n compatible_elim pcm01 v v0 (compatible pcm01 v v01) (fun frame ->\n pcm01.comm frame v;\n pcm01.assoc_r v frame v1;\n pcm01.comm frame v1;\n let new_frame = (op pcm01 v1 frame) in\n pcm01.comm v new_frame\n )\n | None, Some _, _\n | Some _, None, _ -> ()\n | None, None, _ -> ()\n )\n );\n as_slprop hprop", "val pts_to_join (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures joinable pcm v1 v2)", "val pts_to_join' (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures (exists z. compatible pcm v1 z /\\ compatible pcm v2 z /\\\n interp (pts_to r z) m))", "val pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))", "val pts_to_not_null (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v:a)\n (m:heap)\n : Lemma (requires interp (pts_to x v) m)\n (ensures x =!= null)", "let h_and (p1 p2:slprop u#a) : slprop u#a =\n as_slprop (fun (h: heap) -> p1 h /\\ p2 h)", "let h_or (p1 p2:slprop u#a) : slprop u#a =\n as_slprop (fun (h: heap) -> p1 h \\/ p2 h)", "val intro_star (p q:slprop) (hp:hheap p) (hq:hheap q)\n : Lemma\n (requires disjoint hp hq)\n (ensures interp (p `star` q) (join hp hq))", "let star (p1 p2: slprop u#a) : slprop u#a =\n as_slprop (fun (h: heap) -> exists (h1 h2 : heap).\n h1 `disjoint` h2 /\\\n h == join h1 h2 /\\\n interp p1 h1 /\\\n interp p2 h2)", "val elim_star (p q:slprop) (h:hheap (p `star` q))\n : Lemma\n (requires interp (p `star` q) h)\n (ensures exists hl hr.\n disjoint hl hr /\\\n h == join hl hr /\\\n interp p hl /\\\n interp q hr)", "let wand (p1 p2: slprop u#a) : slprop u#a =\n as_slprop (fun (h: heap) -> forall (h1: heap).\n h `disjoint` h1 /\\\n interp p1 h1 ==>\n interp p2 (join h h1))", "let h_exists_body (#[@@@strictly_positive] a:Type u#b)\n ([@@@strictly_positive] f: (a -> slprop u#a))\n (h:heap)\n (x:a) : prop =\n interp (f x) h", "val star_commutative (p1 p2:slprop)\n : Lemma ((p1 `star` p2) `equiv` (p2 `star` p1))", "val star_associative (p1 p2 p3:slprop)\n : Lemma (\n (p1 `star` (p2 `star` p3))\n `equiv`\n ((p1 `star` p2) `star` p3)\n )", "let h_exists (#[@@@strictly_positive] a:Type u#b)\n ([@@@strictly_positive] f: (a -> slprop u#a)) : slprop u#a =\n as_slprop (fun (h: heap) -> exists x. h_exists_body f h x)", "let h_forall_body (#a:Type u#b) (f: (a -> slprop u#a)) (h:heap) (x:a) : prop =\n interp (f x) h", "let h_forall (#a:Type u#b) (f: (a -> slprop u#a)) : slprop u#a =\n as_slprop (fun (h: heap) -> forall x. h_forall_body f h x)", "val star_congruence (p1 p2 p3 p4:slprop)\n : Lemma (requires p1 `equiv` p3 /\\ p2 `equiv` p4)\n (ensures (p1 `star` p2) `equiv` (p3 `star` p4))", "let h_refine p r = h_and p (as_slprop r)", "val refine_interp (p:slprop u#a) (q:a_heap_prop u#a) (h:heap u#a)\n : Lemma (interp p h /\\ q h <==> interp (h_refine p q) h)", "let affine_star p q h = ()", "let equiv_symmetric (p1 p2:slprop u#a) = ()", "let equiv_extensional_on_star (p1 p2 p3:slprop u#a) = ()", "let emp_unit p\n = let emp_unit_1 p m\n : Lemma\n (requires interp p m)\n (ensures interp (p `star` emp) m)\n [SMTPat (interp (p `star` emp) m)]\n = let emp_m : heap = on _ (fun _ -> None) in\n assert (disjoint emp_m m);\n assert (interp (p `star` emp) (join m emp_m));\n assert (mem_equiv m (join m emp_m))\n in\n let emp_unit_2 p m\n : Lemma\n (requires interp (p `star` emp) m)\n (ensures interp p m)\n [SMTPat (interp (p `star` emp) m)]\n = affine_star p emp m\n in\n ()", "val refine_equiv (p0 p1:slprop u#a) (q0 q1:a_heap_prop u#a)\n : Lemma (p0 `equiv` p1 /\\ (forall h. q0 h <==> q1 h) ==>\n equiv (h_refine p0 q0) (h_refine p1 q1))", "let pure (p:prop) = h_refine emp (fun _ -> p)", "val pure_equiv (p q:prop)\n : Lemma ((p <==> q) ==> (pure p `equiv` pure q))", "val pure_interp (q:prop) (h:heap u#a)\n : Lemma (interp (pure q) h <==> q)", "let intro_emp h = ()", "val pure_star_interp (p:slprop u#a) (q:prop) (h:heap u#a)\n : Lemma (interp (p `star` pure q) h <==>\n interp (p `star` emp) h /\\ q)", "let h_exists_cong (#a:Type) (p q : a -> slprop) = ()", "let sl_implies (p q:slprop) = forall m. interp p m ==> interp q m", "let h_exists_alt (#a:Type) (p q: a -> slprop)\n : Lemma\n (requires (forall x. exists y. p x `sl_implies` q y) /\\\n (forall x. exists y. q x `sl_implies` p y))\n (ensures equiv (h_exists p) (h_exists q))\n = ()", "let stronger (p q:slprop) =\n forall h. interp p h ==> interp q h", "let intro_h_exists #a x p h = ()", "val stronger_star (p q r:slprop)\n : Lemma (stronger q r ==> stronger (p `star` q) (p `star` r))", "let elim_h_exists #a p h = ()", "let intro_h_forall (#a:_) (p:a -> slprop) (h:heap) = ()", "val weaken (p q r:slprop) (h:heap u#a)\n : Lemma (q `stronger` r /\\ interp (p `star` q) h ==> interp (p `star` r) h)", "let elim_h_forall (#a:_) (p:a -> slprop) (h:heap) (x:a) = ()", "let intro_h_and (p q: slprop) (h:heap) = ()", "let elim_h_and (p q: slprop) (h:heap) = ()", "val full_heap_pred : heap -> prop", "let intro_h_or_left (p q: slprop) (h:heap) = ()", "let full_heap = h:heap { full_heap_pred h }", "let intro_h_or_right (p q: slprop) (h:heap) = ()", "let full_hheap fp = h:hheap fp { full_heap_pred h }", "let elim_h_or (p q: slprop) (h:heap) = ()", "let intro_wand (p1 p2: slprop u#a) (h:heap) = ()", "let elim_wand (p1 p2: slprop u#a) (h:heap) (h1:heap) = ()", "let interp_depends_only_on (hp:slprop u#a) = emp_unit hp", "val heap_evolves : FStar.Preorder.preorder full_heap", "let intro_pts_to (#a:_) (#pcm:pcm a) (x:ref a pcm) (v:a) (m:heap)\n : Lemma\n (requires\n Addr? x /\\\n m `contains_addr` (Addr?._0 x) /\\\n (let Ref a' pcm' _ v' = select_addr m (Addr?._0 x) in\n a == a' /\\\n pcm == pcm' /\\\n compatible pcm v v'))\n (ensures\n interp (pts_to x v) m)\n = ()", "val free_above_addr (h:heap u#a) (a:nat) : prop", "val weaken_free_above (h:heap) (a b:nat)\n : Lemma (free_above_addr h a /\\ a <= b ==> free_above_addr h b)", "let pre_action (fp:slprop u#a) (a:Type u#b) (fp':a -> slprop u#a) =\n full_hheap fp -> (x:a & full_hheap (fp' x))", "let pts_to_compatible_fwd (#a:Type u#a)\n (#pcm:_)\n (x:ref a pcm)\n (v0 v1:a)\n (m:heap u#a)\n : Lemma\n (requires\n interp (pts_to x v0 `star` pts_to x v1) m)\n (ensures\n composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) m)\n = let Addr addr = x in\n let c = select_addr m addr in\n let Ref _ _ _ v = select_addr m addr in\n let aux (c0 c1: cell u#a)\n : Lemma\n (requires\n c0 `disjoint_cells` c1 /\\\n pts_to_cell pcm v0 c0 /\\\n pts_to_cell pcm v1 c1 /\\\n c == join_cells c0 c1 )\n (ensures\n composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) m)\n [SMTPat (c0 `disjoint_cells` c1)]\n = let Ref _ _ _ v0' = c0 in\n let Ref _ _ _ v1' = c1 in\n assert (exists frame. composable pcm v0 frame /\\ op pcm frame v0 == v0');\n assert (exists frame. composable pcm v1 frame /\\ op pcm frame v1 == v1');\n assert (composable pcm v0' v1');\n assert (op pcm v0' v1' == v);\n let aux (frame0 frame1:a)\n : Lemma\n (requires\n composable pcm v0 frame0 /\\\n op pcm frame0 v0 == v0' /\\\n composable pcm v1 frame1 /\\\n op pcm frame1 v1 == v1')\n (ensures (\n composable pcm frame0 frame1 /\\\n composable pcm v0 v1 /\\\n (let frame = op pcm frame0 frame1 in\n composable pcm frame (op pcm v0 v1) /\\\n op pcm frame (op pcm v0 v1) == v)))\n [SMTPat(op pcm frame0 v0);\n SMTPat(op pcm frame1 v1)]\n = assert (op pcm (op pcm frame0 v0) (op pcm frame1 v1) == v);\n pcm.assoc (op pcm frame0 v0) frame1 v1;\n assert (op pcm (op pcm (op pcm frame0 v0) frame1) v1 == v);\n pcm.comm (op pcm frame0 v0) frame1;\n assert (op pcm (op pcm frame1 (op pcm frame0 v0)) v1 == v);\n pcm.assoc_r frame1 (op pcm frame0 v0) v1;\n assert (op pcm frame1 (op pcm (op pcm frame0 v0) v1) == v);\n pcm.assoc_r frame0 v0 v1;\n assert (op pcm frame1 (op pcm frame0 (op pcm v0 v1)) == v);\n pcm.assoc frame1 frame0 (op pcm v0 v1);\n pcm.comm frame1 frame0\n in\n ()\n in\n assert (exists c0 c1.\n c0 `disjoint_cells` c1 /\\\n pts_to_cell pcm v0 c0 /\\\n pts_to_cell pcm v1 c1 /\\\n c == join_cells c0 c1)", "let action_related_heaps (frame:slprop) (h0 h1:full_heap) =\n heap_evolves h0 h1 /\\\n (forall ctr. h0 `free_above_addr` ctr ==> h1 `free_above_addr` ctr) /\\\n (forall (hp:hprop frame). hp h0 == hp h1)", "let is_frame_preserving\n (#a: Type u#a)\n (#fp: slprop u#b)\n (#fp': a -> slprop u#b)\n (f:pre_action fp a fp')\n =\n forall (frame: slprop u#b) (h0:full_hheap (fp `star` frame)).\n (affine_star fp frame h0;\n let (| x, h1 |) = f h0 in\n interp (fp' x `star` frame) h1 /\\\n action_related_heaps frame h0 h1)", "let action (fp:slprop u#b) (a:Type u#a) (fp':a -> slprop u#b) =\n f:pre_action fp a fp'{ is_frame_preserving f }", "let action_with_frame\n (fp:slprop u#a)\n (a:Type u#b)\n (fp':a -> slprop u#a)\n = frame:slprop u#a ->\n h0:full_hheap (fp `star` frame) ->\n Pure (x:a & full_hheap (fp' x `star` frame))\n (requires True)\n (ensures fun (| x, h1 |) -> action_related_heaps frame h0 h1)", "let frame_related_heaps (h0 h1:full_heap) (fp0 fp1 frame:slprop) (allocates:bool) =\n interp (fp0 `star` frame) h0 ==>\n interp (fp1 `star` frame) h1 /\\\n heap_evolves h0 h1 /\\\n (forall (hp:hprop frame). hp h0 == hp h1) /\\\n (not allocates ==> (forall ctr. h0 `free_above_addr` ctr ==> h1 `free_above_addr` ctr))", "let pts_to_compatible_bk (#a:Type u#a)\n (#pcm:_)\n (x:ref a pcm)\n (v0 v1:a)\n (m:heap u#a)\n : Lemma\n (requires\n composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) m)\n (ensures\n interp (pts_to x v0 `star` pts_to x v1) m)\n = let Addr addr = x in\n let c = select_addr m addr in\n let Ref _ _ _ v = select_addr m addr in\n let v01 = (op pcm v0 v1) in\n assert (pts_to_cell pcm v01 c);\n let Ref _ _ frac v = c in\n assert (compatible pcm v01 v);\n let aux frame\n : Lemma\n (requires\n composable pcm v01 frame /\\\n op pcm frame v01 == v)\n (ensures\n exists m0 m1.\n interp (pts_to x v0) m0 /\\\n interp (pts_to x v1) m1 /\\\n disjoint m0 m1 /\\\n m `mem_equiv` join m0 m1)\n [SMTPat (composable pcm v01 frame)]\n = let c0 = Ref a pcm (Frac.half_perm frac) v0 in\n pcm.FStar.PCM.assoc_r v0 v1 frame;\n let c1 : cell = Ref a pcm (Frac.half_perm frac) (op pcm v1 frame) in\n compatible_refl pcm v0;\n assert (pts_to_cell pcm v0 c0);\n pcm.FStar.PCM.comm v1 frame;\n assert (compatible pcm v1 (op pcm v1 frame));\n assert (pts_to_cell pcm v1 c1);\n calc (==) {\n (v0 `op pcm` (v1 `op pcm` frame));\n (==) {\n pcm.FStar.PCM.assoc v0 v1 frame;\n pcm.FStar.PCM.comm v01 frame\n }\n (frame `op pcm` v01);\n };\n assert (disjoint_cells c0 c1);\n assert (c == join_cells c0 c1);\n let m0 = update_addr empty_heap addr c0 in\n let m1 = update_addr m addr c1 in\n assert (disjoint m0 m1) //fire the existential\n in\n ()", "let action_framing\n (#a: Type u#a)\n (#fp: slprop u#b)\n (#fp': a -> slprop u#b)\n ($f:action fp a fp')\n (frame:slprop) (h0:full_hheap (fp `star` frame))\n : Lemma (\n affine_star fp frame h0;\n let (| x, h1 |) = f h0 in\n frame_related_heaps h0 h1 fp (fp' x) frame false\n )\n =\n affine_star fp frame h0;\n emp_unit fp", "val sel (#a:Type u#h) (#pcm:pcm a) (r:ref a pcm) (m:full_hheap (ptr r)) : a", "val sel_v (#a:Type u#h) (#pcm:pcm a) (r:ref a pcm) (v:erased a) (m:full_hheap (pts_to r v))\n : v':a{ compatible pcm v v' /\\\n pcm.refine v' /\\\n interp (ptr r) m /\\\n v' == sel r m }", "val sel_lemma (#a:_) (#pcm:_) (r:ref a pcm) (m:full_hheap (ptr r))\n : Lemma (interp (pts_to r (sel r m)) m)", "let witnessed_ref (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (fact:a -> prop)\n (h:full_heap)\n = interp (ptr r) h /\\\n fact (sel r h)", "val witnessed_ref_stability (#a:Type) (#pcm:pcm a) (r:ref a pcm) (fact:a -> prop)\n : Lemma\n (requires FStar.Preorder.stable fact (Steel.Preorder.preorder_of_pcm pcm))\n (ensures FStar.Preorder.stable (witnessed_ref r fact) heap_evolves)", "val sel_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:erased a)\n : action (pts_to r v0) (v:a{compatible pcm v0 v}) (fun _ -> pts_to r v0)", "let pts_to_compatible (#a:Type u#a)\n (#pcm:_)\n (x:ref a pcm)\n (v0 v1:a)\n (m:heap u#a) =\n FStar.Classical.forall_intro (FStar.Classical.move_requires (pts_to_compatible_fwd x v0 v1));\n FStar.Classical.forall_intro (FStar.Classical.move_requires (pts_to_compatible_bk x v0 v1))", "val select_refine (#a:_) (#p:_)\n (r:ref a p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n FStar.PCM.frame_compatible p x v y})))\n : action (pts_to r x)\n (v:a{compatible p x v /\\ p.refine v})\n (fun v -> pts_to r (f v))", "let pts_to_join (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures joinable pcm v1 v2)\n = ()", "let pts_to_join' (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures (exists z. compatible pcm v1 z /\\ compatible pcm v2 z /\\\n interp (pts_to r z) m))\n = let Ref a' pcm' _ v' = (select_addr m (Addr?._0 r)) in\n compatible_refl pcm v'", "val upd_gen_action (#a:Type) (#p:pcm a) (r:ref a p) (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n : action (pts_to r x)\n unit\n (fun _ -> pts_to r y)", "let pts_to_compatible_equiv (#a:Type) (#pcm:_) (x:ref a pcm) (v0:a) (v1:a{composable pcm v0 v1})\n = FStar.Classical.forall_intro (pts_to_compatible x v0 v1)", "let pts_to_not_null (#a:Type) (#pcm:_) (x:ref a pcm) (v:a) (m:heap) = ()", "val upd_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:a {FStar.PCM.frame_preserving pcm v0 v1 /\\ pcm.refine v1})\n : action (pts_to r v0) unit (fun _ -> pts_to r v1)", "let intro_star (p q:slprop) (mp:hheap p) (mq:hheap q)\n : Lemma\n (requires\n disjoint mp mq)\n (ensures\n interp (p `star` q) (join mp mq))\n = ()", "val free_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a {exclusive pcm v0 /\\ pcm.refine pcm.FStar.PCM.p.one})\n : action (pts_to r v0) unit (fun _ -> pts_to r pcm.FStar.PCM.p.one)", "let elim_star (p q:slprop) (h:hheap (p `star` q))\n : Lemma\n (requires\n interp (p `star` q) h)\n (ensures exists hl hr.\n disjoint hl hr /\\\n h == join hl hr /\\\n interp p hl /\\\n interp q hr)\n =\n ()", "val split_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n : action (pts_to r (v0 `op pcm` v1)) unit (fun _ -> pts_to r v0 `star` pts_to r v1)", "let star_commutative (p1 p2:slprop) = ()", "val gather_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a)\n : action (pts_to r v0 `star` pts_to r v1) (_:unit{composable pcm v0 v1}) (fun _ -> pts_to r (op pcm v0 v1))", "let star_associative (p1 p2 p3:slprop)\n = let ltor (m m1 m2 m3:heap)\n : Lemma\n (requires\n disjoint m2 m3 /\\\n disjoint m1 (join m2 m3) /\\\n m == join m1 (join m2 m3) /\\\n interp p1 m1 /\\\n interp p2 m2 /\\\n interp p3 m3 /\\\n interp (p1 `star` (p2 `star` p3)) m)\n (ensures\n disjoint m1 m2 /\\\n disjoint (join m1 m2) m3 /\\\n m == join (join m1 m2) m3 /\\\n interp (p1 `star` p2) (join m1 m2) /\\\n interp ((p1 `star` p2) `star` p3) m)\n [SMTPat()]\n = disjoint_join m1 m2 m3;\n join_associative m1 m2 m3;\n intro_star p1 p2 m1 m2;\n intro_star (p1 `star` p2) p3 (join m1 m2) m3\n in\n let rtol (m m1 m2 m3:heap)\n : Lemma\n (requires\n disjoint m1 m2 /\\\n disjoint (join m1 m2) m3 /\\\n m == join (join m1 m2) m3 /\\\n interp p1 m1 /\\\n interp p2 m2 /\\\n interp p3 m3 /\\\n interp ((p1 `star` p2) `star` p3) m)\n (ensures\n disjoint m2 m3 /\\\n disjoint m1 (join m2 m3) /\\\n m == join m1 (join m2 m3) /\\\n interp (p2 `star` p3) (join m2 m3) /\\\n interp (p1 `star`(p2 `star` p3)) m)\n [SMTPat()]\n = join_associative2 m1 m2 m3;\n intro_star p2 p3 m2 m3;\n intro_star p1 (p2 `star` p3) m1 (join m2 m3)\n in\n ()", "val extend\n (#a:Type u#a)\n (#pcm:pcm a)\n (x:a{compatible pcm x x /\\ pcm.refine x})\n (addr:nat)\n (h:full_heap{h `free_above_addr` addr})\n : (\n r:ref a pcm\n & h':full_heap{\n (forall (frame: slprop u#a).\n frame_related_heaps h h' emp (pts_to r x) frame (true)) /\\\n h' `free_above_addr` (addr + 1) /\\\n heap_evolves h h'\n }\n )", "val frame (#a:Type)\n (#pre:slprop)\n (#post:a -> slprop)\n (frame:slprop)\n ($f:action pre a post)\n : action (pre `star` frame) a (fun x -> post x `star` frame)", "val change_slprop (p q:slprop)\n (proof: (h:heap -> Lemma (requires interp p h) (ensures interp q h)))\n : action p unit (fun _ -> q)", "val id_elim_star (p q:slprop) (h:heap)\n : Pure (erased heap & erased heap )\n (requires (interp (p `star` q) h))\n (ensures (fun (hl, hr) -> disjoint hl hr\n /\\ h == join hl hr\n /\\ interp p hl\n /\\ interp q hr))", "val id_elim_exists (#a:Type) (p : a -> slprop) (h:heap)\n : Pure (erased a)\n (requires (interp (h_exists p) h))\n (ensures (fun x -> interp (p x) h))", "let star_congruence (p1 p2 p3 p4:slprop) = ()", "let is_frame_monotonic #a (p : a -> slprop) : prop =\n forall x y m frame. interp (p x `star` frame) m /\\ interp (p y) m ==> interp (p y `star` frame) m", "let refine_interp p q h = ()", "let refine_equiv p0 p1 q0 q1 = ()", "let pure_equiv p q = ()", "let is_witness_invariant #a (p : a -> slprop) =\n forall x y m. interp (p x) m /\\ interp (p y) m ==> x == y", "let pure_interp p h = ()", "let pure_star_interp p q h = ()", "val witinv_framon (#a:_) (p : a -> slprop)\n : Lemma (requires (is_witness_invariant p))\n (ensures (is_frame_monotonic p))", "let stronger_star p q r = ()", "let weaken (p q r:slprop) (h:heap u#a) = ()", "val witness_h_exists (#a:_) (p:a -> slprop)\n : action_with_frame (h_exists p) (erased a) (fun x -> p x)", "let full_heap_pred h =\n forall a. contains_addr h a ==>\n (select_addr h a).frac == Frac.full_perm", "val lift_h_exists (#a:_) (p:a -> slprop)\n : action (h_exists p) unit\n (fun _a -> h_exists #(U.raise_t a) (U.lift_dom p))", "val elim_pure (p:prop)\n : action (pure p) (u:unit{p}) (fun _ -> emp)", "let heap_evolves : FStar.Preorder.preorder full_heap =\n fun (h0 h1:heap) ->\n forall (a:addr).\n match h0 a, h1 a with\n | None, _ -> True //an unused address in h0 can evolve anyway\n\n | Some (Ref a0 p0 f0 v0), Some (Ref a1 p1 f1 v1) ->\n //if a is used h0 then it remains used and ...\n a0 == a1 /\\ //its type can't change\n p0 == p1 /\\ //its pcm can't change\n PP.preorder_of_pcm p0 v0 v1 //and its value evolves by the pcm's preorder\n | _ -> False", "val pts_to_evolve (#a:Type u#a) (#pcm:_) (r:ref a pcm) (x y : a) (h:heap)\n : Lemma (requires (interp (pts_to r x) h /\\ compatible pcm y x))\n (ensures (interp (pts_to r y) h))", "let free_above_addr h a =\n forall (i:nat). i >= a ==> h i == None", "let weaken_free_above (h:heap) (a b:nat)\n : Lemma (free_above_addr h a /\\ a <= b ==> free_above_addr h b)\n = ()", "let sel #a #pcm (r:ref a pcm) (m:full_hheap (ptr r))\n : a\n = let Ref _ _ _ v = select_addr m (Addr?._0 r) in\n v", "let sel_v #a #pcm r v m = sel r m", "let sel_lemma (#a:_) (#pcm:_) (r:ref a pcm) (m:full_hheap (ptr r))\n : Lemma (interp (pts_to r (sel r m)) m)\n = let Ref _ _ _ v = select_addr m (Addr?._0 r) in\n assert (sel r m == v);\n compatible_refl pcm v", "let witnessed_ref_stability #a #pcm (r:ref a pcm) (fact:a -> prop)\n = let fact_h = witnessed_ref r fact in\n let aux (h0 h1:full_heap)\n : Lemma\n (requires\n fact_h h0 /\\\n heap_evolves h0 h1)\n (ensures\n fact_h h1)\n [SMTPat ()]\n = let Addr addr = r in\n assert (interp (ptr r) h0);\n assert (fact (sel r h0));\n assert (contains_addr h1 addr);\n compatible_refl pcm (select_addr h1 addr).v;\n assert (compatible pcm (select_addr h1 addr).v (select_addr h1 addr).v);\n assert (interp (pts_to r (select_addr h1 addr).v) h1);\n assert (interp (ptr r) h1);\n assert (fact (sel r h1))\n in\n ()", "let sel_action (#a:_) (#pcm:_) (r:ref a pcm) (v0:erased a)\n : action (pts_to r v0) (v:a{compatible pcm v0 v}) (fun _ -> pts_to r v0)\n = let f\n : pre_action (pts_to r v0)\n (v:a{compatible pcm v0 v})\n (fun _ -> pts_to r v0)\n = fun m0 -> (| sel r m0, m0 |)\n in\n f" ], "closest": [ "val sel_action' (#a #pcm: _) (r: ref a pcm) (v0: erased a) (h: full_hheap (pts_to r v0))\n : v:\n a\n { compatible pcm v0 v /\\\n (forall frame.\n composable pcm frame v0 /\\ interp (pts_to r frame) h ==> compatible pcm frame v) }\nlet sel_action' (#a:_) (#pcm:_) (r:ref a pcm) (v0:erased a) (h:full_hheap (pts_to r v0))\n : v:a{compatible pcm v0 v /\\\n (forall frame. composable pcm frame v0 /\\\n interp (pts_to r frame) h ==>\n compatible pcm frame v)}\n = sel_v r v0 h", "val sel_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:erased a)\n : action (pts_to r v0) (v:a{compatible pcm v0 v}) (fun _ -> pts_to r v0)\nlet sel_action (#a:_) (#pcm:_) (r:ref a pcm) (v0:erased a)\n : action (pts_to r v0) (v:a{compatible pcm v0 v}) (fun _ -> pts_to r v0)\n = let f\n : pre_action (pts_to r v0)\n (v:a{compatible pcm v0 v})\n (fun _ -> pts_to r v0)\n = fun m0 -> (| sel r m0, m0 |)\n in\n f", "val sel_v (#a:Type u#h) (#pcm:pcm a) (r:ref a pcm) (v:erased a) (m:full_hheap (pts_to r v))\n : v':a{ compatible pcm v v' /\\\n pcm.refine v' /\\\n interp (ptr r) m /\\\n v' == sel r m }\nlet sel_v #a #pcm r v m = sel r m", "val sel_action (#a:Type u#1) (#pcm:_) (e:inames) (r:ref a pcm) (v0:erased a)\n : action_except (v:a{compatible pcm v0 v}) e (pts_to r v0) (fun _ -> pts_to r v0)\nlet sel_action #a #pcm e r v0\n = lift_tot_action (lift_heap_action e (H.sel_action #a #pcm r v0))", "val sel_action (#a:Type u#1) (#pcm:_) (e:inames) (r:ref a pcm) (v0:erased a)\n : action_except (v:a{compatible pcm v0 v}) e (pts_to r v0) (fun _ -> pts_to r v0)\nlet sel_action #a #pcm e r v0\n = lift_tot_action (lift_heap_action e (H.sel_action #a #pcm r v0))", "val free_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a {exclusive pcm v0 /\\ pcm.refine pcm.FStar.PCM.p.one})\n : action (pts_to r v0) unit (fun _ -> pts_to r pcm.FStar.PCM.p.one)\nlet free_action (#a:_) (#pcm:_) (r:ref a pcm) (v0:FStar.Ghost.erased a{exclusive pcm v0 /\\ pcm.refine pcm.FStar.PCM.p.one})\n : action (pts_to r v0) unit (fun _ -> pts_to r pcm.FStar.PCM.p.one)\n = let one = pcm.FStar.PCM.p.one in\n compatible_refl pcm one;\n assert (compatible pcm one one);\n assert (forall (frame:a{composable pcm v0 frame}). frame == one);\n pcm.is_unit one;\n assert (forall (frame:a{composable pcm v0 frame}). composable pcm one frame);\n let f : frame_preserving_upd pcm v0 one =\n fun v -> one in\n upd_gen_action r v0 one f", "val upd_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:a {FStar.PCM.frame_preserving pcm v0 v1 /\\ pcm.refine v1})\n : action (pts_to r v0) unit (fun _ -> pts_to r v1)\nlet upd_action (#a:_) (#pcm:_) (r:ref a pcm)\n (v0:FStar.Ghost.erased a) (v1:a {frame_preserving pcm v0 v1 /\\ pcm.refine v1})\n : action (pts_to r v0) unit (fun _ -> pts_to r v1)\n = upd_gen_action r v0 (Ghost.hide v1) (frame_preserving_val_to_fp_upd pcm v0 v1)", "val read (#a:Type)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:erased a)\n : ST a\n (pts_to r v0)\n (fun _ -> pts_to r v0)\n (requires True)\n (ensures fun v -> compatible pcm v0 v /\\ True)\nlet read r v0 = C.coerce_steel (fun _ -> P.read r v0)", "val alloc_action (#a:Type u#1) (#pcm:pcm a) (e:inames) (x:a{compatible pcm x x /\\ pcm.refine x})\n : action_except (ref a pcm) e emp (fun r -> pts_to r x)\nlet alloc_action #a #pcm e x\n = let f : refined_pre_action e emp (ref a pcm) (fun r -> pts_to r x)\n = fun m0 ->\n (* NS: 9/29/22 I needed to annotate h : Heap.full_heap, for use with the Core checker\n which generates a guard for checking the implicit pattern \"dot\" term in the dependent\n pair pattern on the next line. That guard expects `h` to be a full_heap, which is it,\n because it is a projection of m0. However, this is not reflected in `h`'s type. So,\n the Core checker, which produces a guard for the pat_dot_term in isolation, cannot\n recheck the term. If we were to fold in the checking of pat_dot_terms and their guards\n with the rest of the VC, this would work. *)\n let h : Heap.full_heap = hheap_of_hmem m0 in\n let (|r, h'|) = H.extend #a #pcm x m0.ctr h in\n let m' : hmem_with_inv_except e emp = inc_ctr m0 in\n let h' : H.hheap (pts_to #a #pcm r x `star` linv e m') = weaken _ (linv e m0) (linv e m') h' in\n let m1 : hmem_with_inv_except e (pts_to #a #pcm r x) = hmem_of_hheap m' h' in\n assert (forall frame. H.frame_related_heaps h h' emp (pts_to #a #pcm r x) frame true);\n let aux (frame:slprop)\n : Lemma\n (requires\n interp ((emp `star` frame) `star` linv e m0) m0)\n (ensures\n interp ((pts_to #a #pcm r x `star` frame) `star` linv e m1) m1 /\\\n mem_evolves m0 m1 /\\\n (forall (mp:mprop frame). mp (core_mem m0) == mp (core_mem m1)))\n [SMTPat (emp `star` frame)]\n = star_associative emp frame (linv e m0);\n assert (H.interp (emp `star` (frame `star` linv e m0)) h);\n assert (H.interp (pts_to #a #pcm r x `star` (frame `star` linv e m0)) h');\n star_associative (pts_to #a #pcm r x) frame (linv e m0);\n assert (H.interp ((pts_to #a #pcm r x `star` frame) `star` linv e m0) h');\n assert (H.stronger (linv e m0) (linv e m'));\n assert (H.equiv (linv e m') (linv e m1));\n assert (H.stronger (linv e m0) (linv e m1));\n let h' : H.hheap ((pts_to #a #pcm r x `star` frame) `star` linv e m1) = weaken _ (linv e m0) (linv e m1) h' in\n assert (H.interp ((pts_to #a #pcm r x `star` frame) `star` linv e m1) h');\n assert (forall (mp:H.hprop frame). mp h == mp h');\n mprop_preservation_of_hprop_preservation frame m0 m1;\n assert (forall (mp:mprop frame). mp (core_mem m0) == mp (core_mem m1))\n in\n assert (frame_related_mems emp (pts_to r x) e m0 m1);\n (| r, m1 |)\n in\n lift_tot_action (refined_pre_action_as_action f)", "val alloc_action (#a:Type u#1) (#pcm:pcm a) (e:inames) (x:a{compatible pcm x x /\\ pcm.refine x})\n : action_except (ref a pcm) e emp (fun r -> pts_to r x)\nlet alloc_action #a #pcm e x\n = let f : refined_pre_action e emp (ref a pcm) (fun r -> pts_to r x)\n = fun m0 ->\n (* NS: 9/29/22 I needed to annotate h : Heap.full_heap, for use with the Core checker\n which generates a guard for checking the implicit pattern \"dot\" term in the dependent\n pair pattern on the next line. That guard expects `h` to be a full_heap, which is it,\n because it is a projection of m0. However, this is not reflected in `h`'s type. So,\n the Core checker, which produces a guard for the pat_dot_term in isolation, cannot\n recheck the term. If we were to fold in the checking of pat_dot_terms and their guards\n with the rest of the VC, this would work. *)\n let h : Heap.full_heap = hheap_of_hmem m0 in\n let (|r, h'|) = H.extend #a #pcm x m0.ctr h in\n let m' : hmem_with_inv_except e emp = inc_ctr m0 in\n let h' : H.hheap (pts_to #a #pcm r x `star` linv e m') = weaken _ (linv e m0) (linv e m') h' in\n let m1 : hmem_with_inv_except e (pts_to #a #pcm r x) = hmem_of_hheap m' h' in\n assert (forall frame. H.frame_related_heaps h h' emp (pts_to #a #pcm r x) frame true);\n let aux (frame:slprop)\n : Lemma\n (requires\n interp ((emp `star` frame) `star` linv e m0) m0)\n (ensures\n interp ((pts_to #a #pcm r x `star` frame) `star` linv e m1) m1 /\\\n mem_evolves m0 m1 /\\\n (forall (mp:mprop frame). mp (core_mem m0) == mp (core_mem m1)))\n [SMTPat (emp `star` frame)]\n = star_associative emp frame (linv e m0);\n assert (H.interp (emp `star` (frame `star` linv e m0)) h);\n assert (H.interp (pts_to #a #pcm r x `star` (frame `star` linv e m0)) h');\n star_associative (pts_to #a #pcm r x) frame (linv e m0);\n assert (H.interp ((pts_to #a #pcm r x `star` frame) `star` linv e m0) h');\n assert (H.stronger (linv e m0) (linv e m'));\n assert (H.equiv (linv e m') (linv e m1));\n assert (H.stronger (linv e m0) (linv e m1));\n let h' : H.hheap ((pts_to #a #pcm r x `star` frame) `star` linv e m1) = weaken _ (linv e m0) (linv e m1) h' in\n assert (H.interp ((pts_to #a #pcm r x `star` frame) `star` linv e m1) h');\n assert (forall (mp:H.hprop frame). mp h == mp h');\n mprop_preservation_of_hprop_preservation frame m0 m1;\n assert (forall (mp:mprop frame). mp (core_mem m0) == mp (core_mem m1))\n in\n assert (frame_related_mems emp (pts_to r x) e m0 m1);\n (| r, m1 |)\n in\n lift_tot_action (refined_pre_action_as_action f)", "val split_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n : action (pts_to r (v0 `op pcm` v1)) unit (fun _ -> pts_to r v0 `star` pts_to r v1)\nlet split_action #a #pcm r v0 v1\n = let g : refined_pre_action (pts_to r (v0 `op pcm` v1))\n unit\n (fun _ -> pts_to r v0 `star` pts_to r v1)\n = fun m ->\n pts_to_compatible_bk r v0 v1 m;\n pts_to_compatible_equiv r v0 v1;\n (| (), m |)\n in\n refined_pre_action_as_action g", "val upd_action (#a:Type u#1) (#pcm:_) (e:inames)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:a {FStar.PCM.frame_preserving pcm v0 v1 /\\ pcm.refine v1})\n : action_except unit e (pts_to r v0) (fun _ -> pts_to r v1)\nlet upd_action #a #pcm e r v0 v1\n = lift_tot_action (lift_heap_action e (H.upd_action #a #pcm r v0 v1))", "val upd_action (#a:Type u#1) (#pcm:_) (e:inames)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:a {FStar.PCM.frame_preserving pcm v0 v1 /\\ pcm.refine v1})\n : action_except unit e (pts_to r v0) (fun _ -> pts_to r v1)\nlet upd_action #a #pcm e r v0 v1\n = lift_tot_action (lift_heap_action e (H.upd_action #a #pcm r v0 v1))", "val share\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\r\n: act unit emp_inames\r\n (pts_to r (v0 `op pcm` v1))\r\n (fun _ -> pts_to r v0 ** pts_to r v1)\nlet share\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\r\n: act unit emp_inames\r\n (pts_to r (v0 `op pcm` v1))\r\n (fun _ -> pts_to r v0 `star` pts_to r v1)\r\n= fun #ictx -> mem_action_as_action _ _ _ _ (split_action ictx r v0 v1)", "val gather_action\n (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a)\n : action (pts_to r v0 `star` pts_to r v1) (_:unit{composable pcm v0 v1}) (fun _ -> pts_to r (op pcm v0 v1))\nlet gather_action #a #pcm r v0 v1\n = let g : refined_pre_action (pts_to r v0 `star` pts_to r v1)\n (_:unit{composable pcm v0 v1})\n (fun _ -> pts_to r (v0 `op pcm` v1))\n\n = fun m ->\n pts_to_compatible_fwd r v0 v1 m;\n pts_to_compatible_equiv r v0 v1;\n (| (), m |)\n in\n refined_pre_action_as_action g", "val alloc\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (x:a{compatible pcm x x /\\ pcm.refine x})\r\n: act (ref a pcm) emp_inames emp (fun r -> pts_to r x)\nlet alloc\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (x:a{compatible pcm x x /\\ pcm.refine x})\r\n: act (ref a pcm) emp_inames emp (fun r -> pts_to r x)\r\n= fun #ictx ->\r\n mem_action_as_action _ _ _ _\r\n (alloc_action ictx x)", "val sel (#a:Type u#h) (#pcm:pcm a) (r:ref a pcm) (m:full_hheap (ptr r)) : a\nlet sel #a #pcm (r:ref a pcm) (m:full_hheap (ptr r))\n : a\n = let Ref _ _ _ v = select_addr m (Addr?._0 r) in\n v", "val split_action\n (#a:Type u#1)\n (#pcm:pcm a)\n (e:inames)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n : action_except unit e (pts_to r (v0 `op pcm` v1)) (fun _ -> pts_to r v0 `star` pts_to r v1)\nlet split_action #a #pcm e r v0 v1\n = lift_tot_action (lift_heap_action e (H.split_action #a #pcm r v0 v1))", "val split_action\n (#a:Type u#1)\n (#pcm:pcm a)\n (e:inames)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n : action_except unit e (pts_to r (v0 `op pcm` v1)) (fun _ -> pts_to r v0 `star` pts_to r v1)\nlet split_action #a #pcm e r v0 v1\n = lift_tot_action (lift_heap_action e (H.split_action #a #pcm r v0 v1))", "val read\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x:erased a)\r\n (f:(v:a{compatible p x v}\r\n -> GTot (y:a{compatible p y v /\\\r\n FStar.PCM.frame_compatible p x v y})))\r\n: act (v:a{compatible p x v /\\ p.refine v}) emp_inames\r\n (pts_to r x)\r\n (fun v -> pts_to r (f v))\nlet read\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x:erased a)\r\n (f:(v:a{compatible p x v}\r\n -> GTot (y:a{compatible p y v /\\\r\n FStar.PCM.frame_compatible p x v y})))\r\n: act (v:a{compatible p x v /\\ p.refine v}) emp_inames\r\n (pts_to r x)\r\n (fun v -> pts_to r (f v))\r\n= fun #ictx ->\r\n mem_action_as_action _ _ _ _ (select_refine ictx r x f)", "val write (#a:Type)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:erased a)\n (v1:a)\n : ST unit\n (pts_to r v0)\n (fun _ -> pts_to r v1)\n (requires frame_preserving pcm v0 v1 /\\ pcm.refine v1)\n (ensures fun _ -> True)\nlet write r v0 v1 = C.coerce_steel (fun _ -> P.write r v0 v1)", "val pts_to_not_null_action \n (#a:Type u#a)\n (#pcm:pcm a)\n (r:erased (ref a pcm))\n (v:Ghost.erased a)\n: action \n (pts_to r v)\n (squash (not (is_null r)))\n (fun _ -> pts_to r v)\nlet pts_to_not_null_action #a #pcm r v\n = let g : refined_pre_action (pts_to r v)\n (squash (not (is_null r)))\n (fun _ -> pts_to r v)\n = fun m ->\n pts_to_not_null r v m;\n (| (), m |)\n in\n refined_pre_action_as_action g", "val read\n (#a:Type)\n (#p:pcm a)\n (r:pcm_ref p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n FStar.PCM.frame_compatible p x v y})))\n: stt (v:a{compatible p x v /\\ p.refine v})\n (pcm_pts_to r x)\n (fun v -> pcm_pts_to r (f v))\nlet read\n (#a:Type)\n (#p:pcm a)\n (r:pcm_ref p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n FStar.PCM.frame_compatible p x v y})))\n: stt (v:a{compatible p x v /\\ p.refine v})\n (pcm_pts_to r x)\n (fun v -> pcm_pts_to r (f v))\n= A.lift_atomic1 (A.read r x f)", "val gather_action\n (#a:Type u#1)\n (#pcm:pcm a)\n (e:inames)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a)\n : action_except (_:unit{composable pcm v0 v1}) e (pts_to r v0 `star` pts_to r v1) (fun _ -> pts_to r (op pcm v0 v1))\nlet gather_action #a #pcm e r v0 v1\n = lift_tot_action (lift_heap_action e (H.gather_action #a #pcm r v0 v1))", "val gather_action\n (#a:Type u#1)\n (#pcm:pcm a)\n (e:inames)\n (r:ref a pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a)\n : action_except (_:unit{composable pcm v0 v1}) e (pts_to r v0 `star` pts_to r v1) (fun _ -> pts_to r (op pcm v0 v1))\nlet gather_action #a #pcm e r v0 v1\n = lift_tot_action (lift_heap_action e (H.gather_action #a #pcm r v0 v1))", "val witness (#a:Type) (#pcm:pcm a)\n (e:inames)\n (r:erased (ref a pcm))\n (fact:stable_property pcm)\n (v:Ghost.erased a)\n (_:squash (forall z. compatible pcm v z ==> fact z))\n : action_except (witnessed r fact) e (pts_to r v) (fun _ -> pts_to r v)\nlet witness (#a:Type) (#pcm:pcm a)\n (e:inames)\n (r:erased (ref a pcm))\n (fact:stable_property pcm)\n (v:Ghost.erased a)\n (_:squash (forall z. compatible pcm v z ==> fact z))\n (frame:slprop)\n : MstTot (witnessed r fact) e\n (pts_to r v)\n (fun _ -> pts_to r v) frame\n = let m0 = MSTTotal.get () in\n let _ : unit = \n let hr : H.ref a pcm = r in\n let v' = H.sel_v hr v (heap_of_mem m0) in\n assert (interp (H.ptr hr) m0 /\\ H.sel #a #pcm hr (heap_of_mem m0) == v');\n assert (compatible pcm v v');\n assert (fact v');\n assert (witnessed_ref r fact m0);\n witnessed_ref_stability r fact;\n assert (FStar.Preorder.stable (witnessed_ref r fact) mem_evolves)\n in\n let w = MSTTotal.witness _ mem_evolves (witnessed_ref r fact) in\n w", "val witness (#a:Type) (#pcm:pcm a)\n (e:inames)\n (r:erased (ref a pcm))\n (fact:stable_property pcm)\n (v:Ghost.erased a)\n (_:squash (forall z. compatible pcm v z ==> fact z))\n : action_except (witnessed r fact) e (pts_to r v) (fun _ -> pts_to r v)\nlet witness (#a:Type) (#pcm:pcm a)\n (e:inames)\n (r:erased (ref a pcm))\n (fact:stable_property pcm)\n (v:Ghost.erased a)\n (_:squash (forall z. compatible pcm v z ==> fact z))\n (frame:slprop)\n : MstTot (witnessed r fact) e\n (pts_to r v)\n (fun _ -> pts_to r v) frame\n (fun _ -> True)\n (fun _ _ _ -> True)\n = let m0 = NMSTTotal.get () in\n let _ : unit = \n let hr : H.ref a pcm = r in\n let v' = H.sel_v hr v (heap_of_mem m0) in\n assert (interp (H.ptr hr) m0 /\\ H.sel #a #pcm hr (heap_of_mem m0) == v');\n assert (compatible pcm v v');\n assert (fact v');\n assert (witnessed_ref r fact m0);\n witnessed_ref_stability r fact;\n assert (FStar.Preorder.stable (witnessed_ref r fact) mem_evolves)\n in\n let w = NMSTTotal.witness _ mem_evolves (witnessed_ref r fact) in\n w", "val pts_to_compatible\n (#a:Type u#a)\n (#pcm: pcm a)\n (x:ref a pcm)\n (v0 v1:a)\n (h:heap u#a)\n : Lemma\n (interp (pts_to x v0 `star` pts_to x v1) h\n <==>\n (composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) h))\nlet pts_to_compatible (#a:Type u#a)\n (#pcm:_)\n (x:ref a pcm)\n (v0 v1:a)\n (m:heap u#a) =\n FStar.Classical.forall_intro (FStar.Classical.move_requires (pts_to_compatible_fwd x v0 v1));\n FStar.Classical.forall_intro (FStar.Classical.move_requires (pts_to_compatible_bk x v0 v1))", "val alloc\n (#a:Type u#1)\n (#pcm:pcm a)\n (x:a{compatible pcm x x /\\ pcm.refine x})\n: stt (pcm_ref pcm)\n emp\n (fun r -> pcm_pts_to r x)\nlet alloc\n (#a:Type u#1)\n (#pcm:pcm a)\n (x:a{compatible pcm x x /\\ pcm.refine x})\n: stt (pcm_ref pcm)\n emp\n (fun r -> pcm_pts_to r x)\n= A.lift_atomic0 (A.alloc #a #pcm x)", "val pts_to_compatible\n (#a:Type u#a)\n (#pcm:pcm a)\n (x:ref a pcm)\n (v0 v1:a)\n (m:mem u#a)\n : Lemma\n (interp (pts_to x v0 `star` pts_to x v1) m <==>\n composable pcm v0 v1 /\\ interp (pts_to x (op pcm v0 v1)) m)\nlet pts_to_compatible #a #pcm x v0 v1 m\n = H.pts_to_compatible #a #pcm x v0 v1 (heap_of_mem m)", "val pts_to_compatible\n (#a:Type u#a)\n (#pcm:pcm a)\n (x:ref a pcm)\n (v0 v1:a)\n (m:mem u#a)\n : Lemma\n (interp (pts_to x v0 `star` pts_to x v1) m <==>\n composable pcm v0 v1 /\\ interp (pts_to x (op pcm v0 v1)) m)\nlet pts_to_compatible #a #pcm x v0 v1 m\n = H.pts_to_compatible #a #pcm x v0 v1 (heap_of_mem m)", "val witness\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:erased (ref a pcm))\r\n (fact:stable_property pcm)\r\n (v:Ghost.erased a)\r\n (pf:squash (forall z. compatible pcm v z ==> fact z))\r\n: act (witnessed r fact) emp_inames (pts_to r v) (fun _ -> pts_to r v)\nlet witness\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:erased (ref a pcm))\r\n (fact:stable_property pcm)\r\n (v:Ghost.erased a)\r\n (pf:squash (forall z. compatible pcm v z ==> fact z))\r\n: act (witnessed r fact) emp_inames (pts_to r v) (fun _ -> pts_to r v)\r\n= fun #ictx -> mem_action_as_action _ _ _ _ (witness ictx r fact v pf)", "val share\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\r\n: stt_ghost unit\r\n (pts_to r (v0 `op pcm` v1))\r\n (fun _ -> pts_to r v0 ** pts_to r v1)\nlet share #a #pcm r v0 v1 = Ghost.hide (A.share r v0 v1)", "val pcm_pts_to\n (#a:Type u#1)\n (#p:pcm a)\n (r:pcm_ref p)\n (v:a)\n: vprop\nlet pcm_pts_to (#a:Type u#1) (#p:pcm a) (r:pcm_ref p) (v:a) =\n PulseCore.Action.pts_to r v", "val alloc\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (x:a{compatible pcm x x /\\ pcm.refine x})\r\n: stt_atomic (ref a pcm)\r\n #Observable\r\n emp_inames\r\n emp\r\n (fun r -> pts_to r x)\nlet alloc = A.alloc", "val share\n (#a:Type)\n (#pcm:pcm a)\n (r:pcm_ref pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a{composable pcm v0 v1})\n: stt_ghost unit\n (pcm_pts_to r (v0 `op pcm` v1))\n (fun _ -> pcm_pts_to r v0 ** pcm_pts_to r v1)\nlet share = A.share", "val gather\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a)\r\n: act (squash (composable pcm v0 v1))\r\n emp_inames\r\n (pts_to r v0 ** pts_to r v1)\r\n (fun _ -> pts_to r (op pcm v0 v1))\nlet gather\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a)\r\n: act (squash (composable pcm v0 v1))\r\n emp_inames\r\n (pts_to r v0 `star` pts_to r v1)\r\n (fun _ -> pts_to r (op pcm v0 v1))\r\n= fun #ictx -> mem_action_as_action _ _ _ _ (gather_action ictx r v0 v1)", "val recall\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (#fact:property a)\r\n (r:erased (ref a pcm))\r\n (v:Ghost.erased a)\r\n (w:witnessed r fact)\r\n: act (v1:Ghost.erased a{compatible pcm v v1})\r\n emp_inames\r\n (pts_to r v)\r\n (fun v1 -> pts_to r v ** pure (fact v1))\nlet recall\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (#fact:property a)\r\n (r:erased (ref a pcm))\r\n (v:Ghost.erased a)\r\n (w:witnessed r fact)\r\n: act (v1:Ghost.erased a{compatible pcm v v1})\r\n emp_inames\r\n (pts_to r v)\r\n (fun v1 -> pts_to r v `star` pure (fact v1))\r\n= fun #ictx -> mem_action_as_action _ _ _ _ (recall ictx r v w)", "val recall (#a:Type u#1) (#pcm:pcm a) (#fact:property a)\n (e:inames)\n (r:erased (ref a pcm))\n (v:Ghost.erased a)\n (w:witnessed r fact)\n : action_except (v1:Ghost.erased a{compatible pcm v v1}) e\n (pts_to r v)\n (fun v1 -> pts_to r v `star` pure (fact v1))\nlet recall (#a:Type u#1) (#pcm:pcm a) (#fact:property a)\n (e:inames)\n (r:erased (ref a pcm))\n (v:Ghost.erased a)\n (w:witnessed r fact)\n (frame:slprop)\n = let m0 = MSTTotal.get () in\n MSTTotal.recall _ mem_evolves (witnessed_ref r fact) w;\n let hr : H.ref a pcm = r in\n assert (witnessed_ref r fact m0);\n let v1 = H.sel_v hr v (heap_of_mem m0) in\n assert (compatible pcm v v1);\n assert (H.sel hr (heap_of_mem m0) == v1);\n assert (fact v1);\n assert (interp ((pts_to r v `star` frame) `star` locks_invariant e m0) m0);\n emp_unit ((pts_to r v `star` frame) `star` locks_invariant e m0);\n pure_star_interp ((pts_to r v `star` frame) `star` locks_invariant e m0) (fact v1) m0;\n assert (interp (((pts_to r v `star` frame)\n `star` locks_invariant e m0)\n `star` pure (fact v1)) m0);\n rearrange_pqr_prq (pts_to r v `star` frame)\n (locks_invariant e m0)\n (pure (fact v1));\n assert (interp (((pts_to r v `star` frame) `star` pure (fact v1)) \n `star` locks_invariant e m0) m0);\n rearrange_pqr_prq (pts_to r v) frame (pure (fact v1));\n star_congruence ((pts_to r v `star` frame) `star` pure (fact v1))\n (locks_invariant e m0)\n ((pts_to r v `star` pure (fact v1)) `star` frame)\n (locks_invariant e m0); \n Ghost.hide v1", "val recall (#a:Type u#1) (#pcm:pcm a) (#fact:property a)\n (e:inames)\n (r:erased (ref a pcm))\n (v:Ghost.erased a)\n (w:witnessed r fact)\n : action_except (v1:Ghost.erased a{compatible pcm v v1}) e\n (pts_to r v)\n (fun v1 -> pts_to r v `star` pure (fact v1))\nlet recall (#a:Type u#1) (#pcm:pcm a) (#fact:property a)\n (e:inames)\n (r:erased (ref a pcm))\n (v:Ghost.erased a)\n (w:witnessed r fact)\n (frame:slprop)\n = let m0 = NMSTTotal.get () in\n NMSTTotal.recall _ mem_evolves (witnessed_ref r fact) w;\n let hr : H.ref a pcm = r in\n assert (witnessed_ref r fact m0);\n let v1 = H.sel_v hr v (heap_of_mem m0) in\n assert (compatible pcm v v1);\n assert (H.sel hr (heap_of_mem m0) == v1);\n assert (fact v1);\n assert (interp ((pts_to r v `star` frame) `star` locks_invariant e m0) m0);\n emp_unit ((pts_to r v `star` frame) `star` locks_invariant e m0);\n pure_star_interp ((pts_to r v `star` frame) `star` locks_invariant e m0) (fact v1) m0;\n assert (interp (((pts_to r v `star` frame)\n `star` locks_invariant e m0)\n `star` pure (fact v1)) m0);\n rearrange_pqr_prq (pts_to r v `star` frame)\n (locks_invariant e m0)\n (pure (fact v1));\n assert (interp (((pts_to r v `star` frame) `star` pure (fact v1)) \n `star` locks_invariant e m0) m0);\n rearrange_pqr_prq (pts_to r v) frame (pure (fact v1));\n star_congruence ((pts_to r v `star` frame) `star` pure (fact v1))\n (locks_invariant e m0)\n ((pts_to r v `star` pure (fact v1)) `star` frame)\n (locks_invariant e m0); \n Ghost.hide v1", "val free_action (#a:Type u#1) (#pcm:pcm a) (e:inames)\n (r:ref a pcm) (x:FStar.Ghost.erased a{FStar.PCM.exclusive pcm x /\\ pcm.refine pcm.FStar.PCM.p.one})\n : action_except unit e (pts_to r x) (fun _ -> pts_to r pcm.FStar.PCM.p.one)\nlet free_action #a #pcm e r v0\n = lift_tot_action (lift_heap_action e (H.free_action #a #pcm r v0))", "val free_action (#a:Type u#1) (#pcm:pcm a) (e:inames)\n (r:ref a pcm) (x:FStar.Ghost.erased a{FStar.PCM.exclusive pcm x /\\ pcm.refine pcm.FStar.PCM.p.one})\n : action_except unit e (pts_to r x) (fun _ -> pts_to r pcm.FStar.PCM.p.one)\nlet free_action #a #pcm e r v0\n = lift_tot_action (lift_heap_action e (H.free_action #a #pcm r v0))", "val alloc (#a:Type)\n (#pcm:pcm a)\n (x:a)\n : ST (ref a pcm)\n emp\n (fun r -> pts_to r x)\n (requires pcm.refine x)\n (ensures fun _ -> True)\nlet alloc x = C.coerce_steel (fun _ -> P.alloc x)", "val pts_to_compatible_fwd (#a: Type u#a) (#pcm: _) (x: ref a pcm) (v0 v1: a) (m: heap u#a)\n : Lemma (requires interp ((pts_to x v0) `star` (pts_to x v1)) m)\n (ensures composable pcm v0 v1 /\\ interp (pts_to x (op pcm v0 v1)) m)\nlet pts_to_compatible_fwd (#a:Type u#a)\n (#pcm:_)\n (x:ref a pcm)\n (v0 v1:a)\n (m:heap u#a)\n : Lemma\n (requires\n interp (pts_to x v0 `star` pts_to x v1) m)\n (ensures\n composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) m)\n = let Addr addr = x in\n let c = select_addr m addr in\n let Ref _ _ _ v = select_addr m addr in\n let aux (c0 c1: cell u#a)\n : Lemma\n (requires\n c0 `disjoint_cells` c1 /\\\n pts_to_cell pcm v0 c0 /\\\n pts_to_cell pcm v1 c1 /\\\n c == join_cells c0 c1 )\n (ensures\n composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) m)\n [SMTPat (c0 `disjoint_cells` c1)]\n = let Ref _ _ _ v0' = c0 in\n let Ref _ _ _ v1' = c1 in\n assert (exists frame. composable pcm v0 frame /\\ op pcm frame v0 == v0');\n assert (exists frame. composable pcm v1 frame /\\ op pcm frame v1 == v1');\n assert (composable pcm v0' v1');\n assert (op pcm v0' v1' == v);\n let aux (frame0 frame1:a)\n : Lemma\n (requires\n composable pcm v0 frame0 /\\\n op pcm frame0 v0 == v0' /\\\n composable pcm v1 frame1 /\\\n op pcm frame1 v1 == v1')\n (ensures (\n composable pcm frame0 frame1 /\\\n composable pcm v0 v1 /\\\n (let frame = op pcm frame0 frame1 in\n composable pcm frame (op pcm v0 v1) /\\\n op pcm frame (op pcm v0 v1) == v)))\n [SMTPat(op pcm frame0 v0);\n SMTPat(op pcm frame1 v1)]\n = assert (op pcm (op pcm frame0 v0) (op pcm frame1 v1) == v);\n pcm.assoc (op pcm frame0 v0) frame1 v1;\n assert (op pcm (op pcm (op pcm frame0 v0) frame1) v1 == v);\n pcm.comm (op pcm frame0 v0) frame1;\n assert (op pcm (op pcm frame1 (op pcm frame0 v0)) v1 == v);\n pcm.assoc_r frame1 (op pcm frame0 v0) v1;\n assert (op pcm frame1 (op pcm (op pcm frame0 v0) v1) == v);\n pcm.assoc_r frame0 v0 v1;\n assert (op pcm frame1 (op pcm frame0 (op pcm v0 v1)) == v);\n pcm.assoc frame1 frame0 (op pcm v0 v1);\n pcm.comm frame1 frame0\n in\n ()\n in\n assert (exists c0 c1.\n c0 `disjoint_cells` c1 /\\\n pts_to_cell pcm v0 c0 /\\\n pts_to_cell pcm v1 c1 /\\\n c == join_cells c0 c1)", "val upd_gen (#a: _) (#p: pcm a) (r: ref a p) (x v: Ghost.erased a) (f: frame_preserving_upd p x v)\n : partial_pre_action (pts_to r x) unit (fun _ -> pts_to r v)\nlet upd_gen #a (#p:pcm a)\n (r:ref a p)\n (x v:Ghost.erased a)\n (f: frame_preserving_upd p x v)\n : partial_pre_action (pts_to r x)\n unit\n (fun _ -> pts_to r v)\n = fun h ->\n let Ref a p frac old_v = select_addr h (Addr?._0 r) in\n let new_v = f old_v in\n let cell = Ref a p frac new_v in\n let h' = update_addr_full_heap h (Addr?._0 r) cell in\n (| (), h' |)", "val read\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x:erased a)\r\n (f:(v:a{compatible p x v}\r\n -> GTot (y:a{compatible p y v /\\\r\n FStar.PCM.frame_compatible p x v y})))\r\n: stt_atomic (v:a{compatible p x v /\\ p.refine v})\r\n #Observable\r\n emp_inames\r\n (pts_to r x)\r\n (fun v -> pts_to r (f v))\nlet read = A.read", "val pts_to_not_null_action \n (#a:Type u#1) (#pcm:pcm a)\n (e:inames)\n (r:erased (ref a pcm))\n (v:Ghost.erased a)\n: action_except (squash (not (is_null r))) e\n (pts_to r v)\n (fun _ -> pts_to r v)\nlet pts_to_not_null_action\n (#a:Type u#1) (#pcm:pcm a)\n (e:inames)\n (r:erased (ref a pcm))\n (v:Ghost.erased a)\n: action_except (squash (not (is_null r))) e\n (pts_to r v)\n (fun _ -> pts_to r v)\n= lift_tot_action (lift_heap_action e (H.pts_to_not_null_action #a #pcm r v))", "val extend\n (#a:Type u#a)\n (#pcm:pcm a)\n (x:a{compatible pcm x x /\\ pcm.refine x})\n (addr:nat)\n (h:full_heap{h `free_above_addr` addr})\n : (\n r:ref a pcm\n & h':full_heap{\n (forall (frame: slprop u#a).\n frame_related_heaps h h' emp (pts_to r x) frame (true)) /\\\n h' `free_above_addr` (addr + 1) /\\\n heap_evolves h h'\n }\n )\nlet extend #a #pcm x addr h =\n let r : ref a pcm = Addr addr in\n let h' = update_addr_full_heap h addr (Ref a pcm Frac.full_perm x) in\n assert (h' `free_above_addr` (addr + 1));\n assert (h' `contains_addr` addr);\n assert (interp (pts_to r x) h');\n let extend_aux (frame:slprop) (h0 hf:heap)\n : Lemma\n (requires\n disjoint h0 hf /\\\n h == join h0 hf /\\\n interp emp h0 /\\\n interp frame hf)\n (ensures (\n let h0' = update_addr h0 addr (Ref a pcm Frac.full_perm x) in\n disjoint h0' hf /\\\n interp (pts_to r x) h0' /\\\n h' == join h0' hf /\\\n heap_evolves h h' /\\\n interp (pts_to r x `star` frame) h' /\\\n (forall (hp:hprop frame). hp h == hp h')\n ))\n [SMTPat (interp emp h0);\n SMTPat (interp frame hf)]\n = let h0' = update_addr h0 addr (Ref a pcm Frac.full_perm x) in\n // assert (disjoint h0' hf);\n // assert (interp (pts_to r x) h0');\n assert (mem_equiv h' (join h0' hf));\n // assert (h' == (join h0' hf));\n intro_star (pts_to r x) frame h0' hf;\n // assert (interp (pts_to r x `star` frame) h');\n let aux (hp:hprop frame)\n : Lemma (ensures (hp h == hp h'))\n [SMTPat ()]\n = FStar.PropositionalExtensionality.apply (hp h) (hp h')\n in\n ()\n in\n (| r, h' |)", "val free (#a:Type)\n (#p:pcm a)\n (r:ref a p)\n (x:erased a)\n : ST unit (pts_to r x) (fun _ -> pts_to r p.p.one)\n (requires exclusive p x /\\ p.refine p.p.one)\n (ensures fun _ -> True)\nlet free r x = C.coerce_steel (fun _ -> P.free r x)", "val stable_compatiblity (#a: Type u#a) (fact: (a -> prop)) (p: pcm a) (v v0 v1: a)\n : Lemma\n (requires\n stable fact (preorder_of_pcm p) /\\ p.refine v0 /\\ fact v0 /\\ p.refine v1 /\\\n frame_preserving p v v1 /\\ compatible p v v0) (ensures fact v1)\nlet stable_compatiblity (#a:Type u#a) (fact: a -> prop) (p:pcm a) (v v0 v1:a)\n : Lemma\n (requires\n stable fact (preorder_of_pcm p) /\\\n p.refine v0 /\\\n fact v0 /\\\n p.refine v1 /\\\n frame_preserving p v v1 /\\\n compatible p v v0)\n (ensures\n fact v1)\n = let f : frame_preserving_upd p v v1 = frame_preserving_val_to_fp_upd p v v1 in\n frame_preserving_upd_is_preorder_preserving p v v1 f v0", "val stable_compatiblity (#a: Type u#a) (fact: (a -> prop)) (p: pcm a) (v v0 v1: a)\n : Lemma\n (requires\n stable fact (preorder_of_pcm p) /\\ p.refine v0 /\\ fact v0 /\\ p.refine v1 /\\\n frame_preserving p v v1 /\\ compatible p v v0) (ensures fact v1)\nlet stable_compatiblity (#a:Type u#a) (fact: a -> prop) (p:pcm a) (v v0 v1:a)\n : Lemma\n (requires\n stable fact (preorder_of_pcm p) /\\\n p.refine v0 /\\\n fact v0 /\\\n p.refine v1 /\\\n frame_preserving p v v1 /\\\n compatible p v v0)\n (ensures\n fact v1)\n = let f : frame_preserving_upd p v v1 = frame_preserving_val_to_fp_upd p v v1 in\n frame_preserving_upd_is_preorder_preserving p v v1 f v0", "val select_refine (#a:_) (#p:_)\n (r:ref a p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n FStar.PCM.frame_compatible p x v y})))\n : action (pts_to r x)\n (v:a{compatible p x v /\\ p.refine v})\n (fun v -> pts_to r (f v))\nlet select_refine (#a:_) (#p:_)\n (r:ref a p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n frame_compatible p x v y})))\n : action (pts_to r x)\n (v:a{compatible p x v /\\ p.refine v})\n (fun v -> pts_to r (f v))\n = refined_pre_action_as_action (select_refine_pre r x f)", "val read (#o:inames)\n (#a:Type)\n (#pcm:pcm a)\n (#v0:a)\n (r:ref a pcm)\n : STGhost a o\n (pts_to r v0)\n (fun _ -> pts_to r v0)\n (requires True)\n (ensures fun v -> compatible pcm v0 v)\nlet read (#o:inames)\n (#a:Type)\n (#pcm:pcm a)\n (#v0:a)\n (r:ref a pcm)\n : STGhost a o\n (pts_to r v0)\n (fun _ -> pts_to r v0)\n (requires True)\n (ensures fun v -> compatible pcm v0 v)\n = let v = coerce_ghost (fun _ -> G.read r) in\n downgrade_val v", "val select_refine (#a:Type u#1) (#p:pcm a)\n (e:inames)\n (r:ref a p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n FStar.PCM.frame_compatible p x v y})))\n : action_except (v:a{compatible p x v /\\ p.refine v}) e\n (pts_to r x)\n (fun v -> pts_to r (f v))\nlet select_refine #a #p e r x f\n = lift_tot_action (lift_heap_action e (H.select_refine #a #p r x f))", "val select_refine (#a:Type u#1) (#p:pcm a)\n (e:inames)\n (r:ref a p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n FStar.PCM.frame_compatible p x v y})))\n : action_except (v:a{compatible p x v /\\ p.refine v}) e\n (pts_to r x)\n (fun v -> pts_to r (f v))\nlet select_refine #a #p e r x f\n = lift_tot_action (lift_heap_action e (H.select_refine #a #p r x f))", "val write\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x y:Ghost.erased a)\r\n (f:FStar.PCM.frame_preserving_upd p x y)\r\n: act unit emp_inames\r\n (pts_to r x)\r\n (fun _ -> pts_to r y)\nlet write\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x y:Ghost.erased a)\r\n (f:FStar.PCM.frame_preserving_upd p x y)\r\n: act unit emp_inames\r\n (pts_to r x)\r\n (fun _ -> pts_to r y)\r\n= fun #ictx -> mem_action_as_action _ _ _ _ (upd_gen ictx r x y f)", "val pts_to (#a:Type u#0) (#pcm:pcm a) (r:ref a pcm) ([@@@smt_fallback] v:a)\n : vprop\nlet pts_to (#a:Type u#0) (#pcm:pcm a) (r:ref a pcm) ([@@@smt_fallback] v:a)\n = G.pts_to #(raise_t a) #(UP.raise pcm) r (raise_val v)", "val pts_to_not_null (#a:Type) (#p:FStar.PCM.pcm a) (r:ref a p) (v:a)\r\n: act (squash (not (is_ref_null r)))\r\n emp_inames \r\n (pts_to r v)\r\n (fun _ -> pts_to r v)\nlet pts_to_not_null #a #p r v =\r\n fun #ictx -> mem_action_as_action _ _ _ _ (pts_to_not_null_action ictx r v)", "val pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a\nlet pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a =\n let hprop (h: heap) : Tot prop =\n Addr? r /\\\n h `contains_addr` (Addr?._0 r) /\\\n pts_to_cell pcm v (select_addr h (Addr?._0 r))\n in\n affine_hprop_intro hprop (fun h0 h1 ->\n match r with | Null -> () | Addr r -> (\n match h0 r, h1 r, (join h0 h1) r with\n | Some (Ref a0 pcm0 _ v0), Some (Ref a1 pcm1 _ v1), Some (Ref a01 pcm01 _ v01) ->\n compatible_elim pcm01 v v0 (compatible pcm01 v v01) (fun frame ->\n pcm01.comm frame v;\n pcm01.assoc_r v frame v1;\n pcm01.comm frame v1;\n let new_frame = (op pcm01 v1 frame) in\n pcm01.comm v new_frame\n )\n | None, Some _, _\n | Some _, None, _ -> ()\n | None, None, _ -> ()\n )\n );\n as_slprop hprop", "val pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a\nlet pts_to = H.pts_to", "val pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a\nlet pts_to = H.pts_to", "val pts_to_compatible_bk (#a: Type u#a) (#pcm: _) (x: ref a pcm) (v0 v1: a) (m: heap u#a)\n : Lemma (requires composable pcm v0 v1 /\\ interp (pts_to x (op pcm v0 v1)) m)\n (ensures interp ((pts_to x v0) `star` (pts_to x v1)) m)\nlet pts_to_compatible_bk (#a:Type u#a)\n (#pcm:_)\n (x:ref a pcm)\n (v0 v1:a)\n (m:heap u#a)\n : Lemma\n (requires\n composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) m)\n (ensures\n interp (pts_to x v0 `star` pts_to x v1) m)\n = let Addr addr = x in\n let c = select_addr m addr in\n let Ref _ _ _ v = select_addr m addr in\n let v01 = (op pcm v0 v1) in\n assert (pts_to_cell pcm v01 c);\n let Ref _ _ frac v = c in\n assert (compatible pcm v01 v);\n let aux frame\n : Lemma\n (requires\n composable pcm v01 frame /\\\n op pcm frame v01 == v)\n (ensures\n exists m0 m1.\n interp (pts_to x v0) m0 /\\\n interp (pts_to x v1) m1 /\\\n disjoint m0 m1 /\\\n m `mem_equiv` join m0 m1)\n [SMTPat (composable pcm v01 frame)]\n = let c0 = Ref a pcm (Frac.half_perm frac) v0 in\n pcm.FStar.PCM.assoc_r v0 v1 frame;\n let c1 : cell = Ref a pcm (Frac.half_perm frac) (op pcm v1 frame) in\n compatible_refl pcm v0;\n assert (pts_to_cell pcm v0 c0);\n pcm.FStar.PCM.comm v1 frame;\n assert (compatible pcm v1 (op pcm v1 frame));\n assert (pts_to_cell pcm v1 c1);\n calc (==) {\n (v0 `op pcm` (v1 `op pcm` frame));\n (==) {\n pcm.FStar.PCM.assoc v0 v1 frame;\n pcm.FStar.PCM.comm v01 frame\n }\n (frame `op pcm` v01);\n };\n assert (disjoint_cells c0 c1);\n assert (c == join_cells c0 c1);\n let m0 = update_addr empty_heap addr c0 in\n let m1 = update_addr m addr c1 in\n assert (disjoint m0 m1) //fire the existential\n in\n ()", "val p0 (#v #p #s: _) : pcm' (knowledge #v #p s)\nlet p0 #v #p #s : pcm' (knowledge #v #p s) = {\n composable;\n op=compose;\n one=Nothing\n}", "val pts_to_evolve (#a:Type u#a) (#pcm:_) (r:ref a pcm) (x y : a) (h:heap)\n : Lemma (requires (interp (pts_to r x) h /\\ compatible pcm y x))\n (ensures (interp (pts_to r y) h))\nlet pts_to_evolve (#a:Type u#a) (#pcm:_) (r:ref a pcm) (x y : a) (h:heap)\n : Lemma (requires (interp (pts_to r x) h /\\ compatible pcm y x))\n (ensures (interp (pts_to r y) h))\n = let Ref a' pcm' _ v' = (select_addr h (Addr?._0 r)) in\n compatible_trans pcm y x v'", "val alloc (#a:Type)\n (#pcm:pcm a)\n (x:a)\n : Steel (ref a pcm)\n emp\n (fun r -> pts_to r x)\n (requires fun _ -> pcm.refine x)\n (ensures fun _ _ _ -> True)\nlet alloc #_ #pcm x = rewrite_slprop emp (to_vprop Mem.emp) (fun _ -> reveal_emp ());\n compatible_refl pcm x;\n alloc' x", "val sel_lemma (#a:_) (#pcm:_) (r:ref a pcm) (m:full_hheap (ptr r))\n : Lemma (interp (pts_to r (sel r m)) m)\nlet sel_lemma (#a:_) (#pcm:_) (r:ref a pcm) (m:full_hheap (ptr r))\n : Lemma (interp (pts_to r (sel r m)) m)\n = let Ref _ _ _ v = select_addr m (Addr?._0 r) in\n assert (sel r m == v);\n compatible_refl pcm v", "val gather\n (#a:Type)\n (#pcm:pcm a)\n (r:pcm_ref pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a)\n: stt_ghost (squash (composable pcm v0 v1))\n (pcm_pts_to r v0 ** pcm_pts_to r v1)\n (fun _ -> pcm_pts_to r (op pcm v0 v1))\nlet gather = A.gather", "val pts_to (#a:Type u#1) (#pcm:pcm a) (r:ref a pcm) (v:a)\n : vprop\nlet pts_to (#a:Type u#1) (#pcm:pcm a) (r:ref a pcm) ([@@@smt_fallback]v:a)\n = to_vprop (Steel.Memory.pts_to r v)", "val write (#o:inames)\n (#a:Type)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:a)\n (v1:a)\n : STGhost unit o\n (pts_to r v0)\n (fun _ -> pts_to r v1)\n (requires frame_preserving pcm v0 v1 /\\ pcm.refine v1)\n (ensures fun _ -> True)\nlet write (#o:inames)\n (#a:Type)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:a)\n (v1:a)\n : STGhost unit o\n (pts_to r v0)\n (fun _ -> pts_to r v1)\n (requires frame_preserving pcm v0 v1 /\\ pcm.refine v1)\n (ensures fun _ -> True)\n = coerce_ghost (fun _ -> G.write r (raise_val v0) (raise_val v1))", "val share (#o:inames)\n (#a:Type)\n (#p:pcm a)\n (r:ref a p)\n (v:a)\n (v0:a)\n (v1:a)\n : STGhost unit o\n (pts_to r v)\n (fun _ -> pts_to r v0 `star` pts_to r v1)\n (requires\n composable p v0 v1 /\\\n v == op p v0 v1)\n (ensures fun _ -> True)\nlet share (#o:inames)\n (#a:Type)\n (#p:pcm a)\n (r:ref a p)\n (v:a)\n (v0:a)\n (v1:a)\n : STGhost unit o\n (pts_to r v)\n (fun _ -> pts_to r v0 `star` pts_to r v1)\n (requires\n composable p v0 v1 /\\\n v == op p v0 v1)\n (ensures fun _ -> True)\n = coerce_ghost (fun _ -> G.share r (raise_val v) (raise_val v0) (raise_val v1))", "val pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))\nlet pts_to_compatible_equiv #a #pcm x v0 v1\n = H.pts_to_compatible_equiv #a #pcm x v0 v1", "val pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))\nlet pts_to_compatible_equiv #a #pcm x v0 v1\n = H.pts_to_compatible_equiv #a #pcm x v0 v1", "val pts_to_compatible_equiv (#a:Type)\n (#pcm:_)\n (x:ref a pcm)\n (v0:a)\n (v1:a{composable pcm v0 v1})\n : Lemma (equiv (pts_to x v0 `star` pts_to x v1)\n (pts_to x (op pcm v0 v1)))\nlet pts_to_compatible_equiv (#a:Type) (#pcm:_) (x:ref a pcm) (v0:a) (v1:a{composable pcm v0 v1})\n = FStar.Classical.forall_intro (pts_to_compatible x v0 v1)", "val pts_to_join' (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures (exists z. compatible pcm v1 z /\\ compatible pcm v2 z /\\\n interp (pts_to r z) m))\nlet pts_to_join' (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures (exists z. compatible pcm v1 z /\\ compatible pcm v2 z /\\\n interp (pts_to r z) m))\n = let Ref a' pcm' _ v' = (select_addr m (Addr?._0 r)) in\n compatible_refl pcm v'", "val recall (#o: _) \n (#a:Type)\n (#pcm:pcm a)\n (fact:property a)\n (r:ref a pcm)\n (v:erased a)\n (w:witnessed r fact)\n : SteelAtomicU (erased a) o\n (pts_to r v)\n (fun v1 -> pts_to r v)\n (requires fun _ -> True)\n (ensures fun _ v1 _ -> fact v1 /\\ compatible pcm v v1)\nlet recall (#o: _)\n (#a:Type)\n (#pcm:pcm a)\n (fact:property a)\n (r:ref a pcm)\n (v:erased a)\n (w:witnessed r fact)\n = P.recall fact r v w", "val gather\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ref a pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a)\r\n: stt_ghost (squash (composable pcm v0 v1))\r\n (pts_to r v0 ** pts_to r v1)\r\n (fun _ -> pts_to r (op pcm v0 v1))\nlet gather #a #pcm r v0 v1 = Ghost.hide (A.gather r v0 v1)", "val pts_to_not_null\n (#a:Type)\n (#p:FStar.PCM.pcm a)\n (r:pcm_ref p)\n (v:a)\n: stt_ghost (squash (not (is_pcm_ref_null r)))\n (pcm_pts_to r v)\n (fun _ -> pcm_pts_to r v)\nlet pts_to_not_null #a #p r v = A.pts_to_not_null #a #p r v", "val upd_gen_action (#a:Type) (#p:pcm a) (r:ref a p) (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n : action (pts_to r x)\n unit\n (fun _ -> pts_to r y)\nlet upd_gen_action #a (#p:pcm a) (r:ref a p) (x y:Ghost.erased a) (f:frame_preserving_upd p x y)\n : action (pts_to r x)\n unit\n (fun _ -> pts_to r y)\n = let refined : refined_pre_action\n (pts_to r x)\n unit\n (fun _ -> pts_to r y)\n = fun h ->\n let (|u, h1|) = upd_gen #a #p r x y f h in\n FStar.Classical.forall_intro (FStar.Classical.move_requires (upd_gen_frame_preserving r x y f h));\n upd_gen_full_evolution r x y f h;\n let h1 : full_hheap (pts_to r y) = h1 in\n assert (forall x. contains_addr h1 x ==> contains_addr h x);\n assert (forall ctr. h `free_above_addr` ctr ==> h1 `free_above_addr` ctr);\n (| (), h1 |)\n in\n refined_pre_action_as_action refined", "val pts_to (#a:Type u#1) (#p:pcm a) (r:ref a p) (v:a) : slprop\nlet pts_to = pts_to", "val witness\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:erased (ref a pcm))\r\n (fact:stable_property pcm)\r\n (v:Ghost.erased a)\r\n (pf:squash (forall z. compatible pcm v z ==> fact z))\r\n: stt_ghost\r\n (witnessed r fact)\r\n (pts_to r v)\r\n (fun _ -> pts_to r v)\nlet witness #a #pcm r f v pf = Ghost.hide (A.witness r f v pf)", "val write\n (#a:Type)\n (#p:pcm a)\n (r:pcm_ref p)\n (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n: stt unit\n (pcm_pts_to r x)\n (fun _ -> pcm_pts_to r y)\nlet write\n (#a:Type)\n (#p:pcm a)\n (r:pcm_ref p)\n (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n: stt unit\n (pcm_pts_to r x)\n (fun _ -> pcm_pts_to r y)\n= A.lift_atomic0 (A.write r x y f)", "val select_refine (#a:Type u#1) (#p:pcm a)\n (r:ref a p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n frame_compatible p x v y})))\n : STT (v:a{compatible p x v /\\ p.refine v})\n (pts_to r x)\n (fun v -> pts_to r (f v))\nlet select_refine r x f = C.coerce_steel (fun _ -> P.select_refine r x f)", "val null (#a: Type u#a) (#pcm: pcm a) : ref a pcm\nlet null (#a:Type u#a) (#pcm:pcm a) : ref a pcm = core_ref_null", "val null (#a: Type u#a) (#pcm: pcm a) : ref a pcm\nlet null (#a:Type u#a) (#pcm:pcm a) : ref a pcm = core_ref_null", "val null (#a: Type u#a) (#pcm: pcm a) : ref a pcm\nlet null (#a:Type u#a) (#pcm:pcm a) : ref a pcm = core_ref_null", "val null (#a: Type u#a) (#pcm: pcm a) : ref a pcm\nlet null (#a:Type u#a) (#pcm:pcm a) : ref a pcm = core_ref_null", "val atomic_write (#opened:_) (#a:Type) (#pcm:pcm a)\n (r:ref a pcm)\n (v0:erased a)\n (v1:a)\n : STAtomic unit opened\n (pts_to r v0)\n (fun _ -> pts_to r v1)\n (requires frame_preserving pcm v0 v1 /\\ pcm.refine v1)\n (ensures fun _ -> True)\nlet atomic_write r v0 v1 = C.coerce_atomic (fun _ -> P.atomic_write r v0 v1)", "val pts_to_evolve (#a:Type u#a) (#pcm:_) (r:ref a pcm) (x y : a) (m:mem) :\n Lemma (requires (interp (pts_to r x) m /\\ compatible pcm y x))\n (ensures (interp (pts_to r y) m))\nlet pts_to_evolve (#a:Type u#a) (#pcm:_) (r:ref a pcm) (x y : a) (m:mem)\n : Lemma (requires (interp (pts_to r x) m /\\ compatible pcm y x))\n (ensures (interp (pts_to r y) m))\n = H.pts_to_evolve #a #pcm r x y (heap_of_mem m)", "val ghost_pcm_pts_to\n (#a:Type u#1)\n (#p:pcm a)\n (r:ghost_pcm_ref p)\n (v:a)\n: vprop\nlet ghost_pcm_pts_to #a #p r v = A.ghost_pts_to #a #p r v", "val ghost_gather\n (#a:Type)\n (#pcm:pcm a)\n (r:ghost_pcm_ref pcm)\n (v0:FStar.Ghost.erased a)\n (v1:FStar.Ghost.erased a)\n: stt_ghost (squash (composable pcm v0 v1))\n (ghost_pcm_pts_to r v0 ** ghost_pcm_pts_to r v1)\n (fun _ -> ghost_pcm_pts_to r (op pcm v0 v1))\nlet ghost_gather = A.ghost_gather", "val share (#o:inames)\n (#a:Type)\n (#p:pcm a)\n (r:ref a p)\n (v:a)\n (v0:a)\n (v1:a)\n : SteelGhost unit o\n (pts_to r v)\n (fun _ -> pts_to r v0 `star` pts_to r v1)\n (requires fun _ ->\n composable p v0 v1 /\\\n v == op p v0 v1)\n (ensures fun _ _ _ -> True)\nlet share (#o:inames)\n (#a:Type)\n (#p:pcm a)\n (r:ref a p)\n (v:a)\n (v0:a)\n (v1:a)\n : SteelGhost unit o\n (pts_to r v)\n (fun _ -> pts_to r v0 `star` pts_to r v1)\n (requires fun _ ->\n composable p v0 v1 /\\\n v == op p v0 v1)\n (ensures fun _ _ _ -> True)\n = P.split r v v0 v1", "val ghost_alloc\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (x:erased a{compatible pcm x x /\\ pcm.refine x})\r\n: stt_ghost (ghost_ref pcm)\r\n emp\r\n (fun r -> ghost_pts_to r x)\nlet ghost_alloc #a #pcm x = hide_ghost (Ghost.hide <| A.alloc #a x)", "val ghost_alloc\n (#a:Type u#1)\n (#pcm:pcm a)\n (x:erased a{compatible pcm x x /\\ pcm.refine x})\n: stt_ghost (ghost_pcm_ref pcm)\n emp\n (fun r -> ghost_pcm_pts_to r x)\nlet ghost_alloc = A.ghost_alloc", "val recall\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (#fact:property a)\r\n (r:erased (ref a pcm))\r\n (v:Ghost.erased a)\r\n (w:witnessed r fact)\r\n: stt_ghost (v1:Ghost.erased a{compatible pcm v v1})\r\n (pts_to r v)\r\n (fun v1 -> pts_to r v ** pure (fact v1))\nlet recall #a #pcm #fact r v w = Ghost.hide (A.recall r v w)", "val ghost_gather\r\n (#a:Type)\r\n (#pcm:pcm a)\r\n (r:ghost_ref pcm)\r\n (v0:FStar.Ghost.erased a)\r\n (v1:FStar.Ghost.erased a)\r\n: stt_ghost (squash (composable pcm v0 v1))\r\n (ghost_pts_to r v0 ** ghost_pts_to r v1)\r\n (fun _ -> ghost_pts_to r (op pcm v0 v1))\nlet ghost_gather r v0 v1 = Ghost.hide (A.gather r v0 v1)", "val ghost_read\n (#a:Type)\n (#p:pcm a)\n (r:ghost_pcm_ref p)\n (x:erased a)\n (f:(v:a{compatible p x v}\n -> GTot (y:a{compatible p y v /\\\n FStar.PCM.frame_compatible p x v y})))\n: stt_ghost (erased (v:a{compatible p x v /\\ p.refine v}))\n (ghost_pcm_pts_to r x)\n (fun v -> ghost_pcm_pts_to r (f v))\nlet ghost_read = A.ghost_read", "val free (#a:Type0)\n (#v:erased a)\n (r:ref a)\n : STT unit\n (pts_to r full_perm v) (fun _ -> emp)\nlet free (#a:Type0)\n (#v:erased a)\n (r:ref a)\n : STT unit\n (pts_to r full_perm v)\n (fun _ -> emp)\n = coerce_steel(fun _ -> R.free_pt r);\n return ()", "val recall (#inames: _) (#a:Type u#1) (#pcm:pcm a)\n (fact:property a)\n (r:ref a pcm)\n (v:erased a)\n (w:witnessed r fact)\n : STAtomicU (erased a) inames\n (pts_to r v)\n (fun v1 -> pts_to r v)\n (requires True)\n (ensures fun v1 -> fact v1 /\\ compatible pcm v v1)\nlet recall fact r v w = C.coerce_atomic (fun _ -> P.recall fact r v w)", "val upd_gen (#a:Type) (#p:pcm a) (e:inames) (r:ref a p) (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n : action_except unit e\n (pts_to r x)\n (fun _ -> pts_to r y)\nlet upd_gen #a #p e r x y f\n = lift_tot_action (lift_heap_action e (H.upd_gen_action r x y f))", "val upd_gen (#a:Type) (#p:pcm a) (e:inames) (r:ref a p) (x y:Ghost.erased a)\n (f:FStar.PCM.frame_preserving_upd p x y)\n : action_except unit e\n (pts_to r x)\n (fun _ -> pts_to r y)\nlet upd_gen #a #p e r x y f\n = lift_tot_action (lift_heap_action e (H.upd_gen_action r x y f))" ], "closest_src": [ { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.sel_action'" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.sel_action" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.sel_v" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.sel_action" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.sel_action" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.free_action" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.upd_action" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.read" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.alloc_action" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.alloc_action" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.split_action" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.upd_action" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.upd_action" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.share" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.gather_action" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.alloc" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.sel" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.split_action" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.split_action" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.read" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.write" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.pts_to_not_null_action" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.read" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.gather_action" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.gather_action" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.witness" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.witness" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.pts_to_compatible" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.alloc" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.pts_to_compatible" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.pts_to_compatible" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.witness" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.share" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.pcm_pts_to" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.share" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.gather" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.recall" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.recall" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.recall" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.free_action" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.free_action" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.alloc" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.pts_to_compatible_fwd" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.upd_gen" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.read" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.pts_to_not_null_action" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.extend" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.free" }, { "project_name": "steel", "file_name": "PulseCore.Preorder.fst", "name": "PulseCore.Preorder.stable_compatiblity" }, { "project_name": "steel", "file_name": "Steel.Preorder.fst", "name": "Steel.Preorder.stable_compatiblity" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.select_refine" }, { "project_name": "steel", "file_name": "Steel.ST.GhostPCMReference.fst", "name": "Steel.ST.GhostPCMReference.read" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.select_refine" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.select_refine" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.write" }, { "project_name": "steel", "file_name": "Steel.ST.GhostPCMReference.fst", "name": "Steel.ST.GhostPCMReference.pts_to" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.pts_to_not_null" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.pts_to" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.pts_to" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.pts_to" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.pts_to_compatible_bk" }, { "project_name": "steel", "file_name": "Steel.FractionalAnchoredPreorder.fst", "name": "Steel.FractionalAnchoredPreorder.p0" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.pts_to_evolve" }, { "project_name": "steel", "file_name": "Steel.PCMReference.fst", "name": "Steel.PCMReference.alloc" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.sel_lemma" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.gather" }, { "project_name": "steel", "file_name": "Steel.GhostPCMReference.fst", "name": "Steel.GhostPCMReference.pts_to" }, { "project_name": "steel", "file_name": "Steel.ST.GhostPCMReference.fst", "name": "Steel.ST.GhostPCMReference.write" }, { "project_name": "steel", "file_name": "Steel.ST.GhostPCMReference.fst", "name": "Steel.ST.GhostPCMReference.share" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.pts_to_compatible_equiv" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.pts_to_compatible_equiv" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.pts_to_compatible_equiv" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.pts_to_join'" }, { "project_name": "steel", "file_name": "Steel.GhostPCMReference.fst", "name": "Steel.GhostPCMReference.recall" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.gather" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.pts_to_not_null" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.upd_gen_action" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.pts_to" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.witness" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.write" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.select_refine" }, { "project_name": "steel", "file_name": "Steel.Heap.fsti", "name": "Steel.Heap.null" }, { "project_name": "steel", "file_name": "Steel.Memory.fsti", "name": "Steel.Memory.null" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fsti", "name": "PulseCore.Memory.null" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fsti", "name": "PulseCore.Heap.null" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.atomic_write" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.pts_to_evolve" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.ghost_pcm_pts_to" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.ghost_gather" }, { "project_name": "steel", "file_name": "Steel.GhostPCMReference.fst", "name": "Steel.GhostPCMReference.share" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.ghost_alloc" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.ghost_alloc" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.recall" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.ghost_gather" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.ghost_read" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.free" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.recall" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.upd_gen" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.upd_gen" } ], "selected_premises": [ "Steel.Heap.sel_v", "Steel.FractionalPermission.full_perm", "Steel.Heap.emp", "Steel.Preorder.pcm_history", "Steel.Heap.sel_action", "Steel.Heap.sel_lemma", "Steel.Heap.pts_to_compatible_equiv", "FStar.PCM.composable", "Steel.Preorder.history_val", "Steel.Heap.sel", "Steel.Heap.pts_to", "Steel.Heap.pts_to_cell", "FStar.PCM.op", "FStar.Real.one", "Steel.Heap.pts_to_compatible", "Steel.Heap.disjoint_join_cells_assoc", "FStar.Real.two", "Steel.FractionalPermission.comp_perm", "FStar.PCM.compatible", "Steel.Heap.h_exists", "Steel.Heap.heap_evolves", "Steel.FractionalPermission.sum_perm", "Steel.Heap.core_ref_null", "Steel.Heap.disjoint_cells_sym", "FStar.FunctionalExtensionality.feq", "Steel.Heap.interp_depends_only_on", "Steel.Heap.addr", "FStar.Pervasives.reveal_opaque", "Steel.Heap.pts_to_compatible_bk", "Steel.Heap.h_refine", "Steel.Heap.as_slprop", "FStar.WellFounded.fix_F", "Steel.Heap.full_heap_pred", "Steel.Heap.h_forall", "Steel.Heap.pts_to_join'", "Steel.Heap.interp", "Steel.Heap.pts_to_compatible_fwd", "Steel.Heap.disjoint_cells", "Steel.Preorder.vhist", "Steel.Heap.h_or", "FStar.FunctionalExtensionality.on_dom", "Steel.Preorder.p_op", "Steel.FractionalPermission.half_perm", "Steel.Heap.affine_hprop_intro", "Steel.Heap.heap", "FStar.Pervasives.Native.snd", "Steel.Heap.h_and", "FStar.Pervasives.Native.fst", "Steel.Preorder.preorder_of_pcm", "Steel.Heap.star", "Steel.Heap.sl_implies", "Steel.Heap.empty_heap", "FStar.Real.zero", "Steel.Preorder.comm_op", "Steel.Preorder.history_compose", "Steel.Heap.star_associative", "Steel.Heap.core_ref_is_null", "Steel.Preorder.hval", "Steel.FractionalPermission.writeable", "Steel.Heap.slprop_extensionality", "FStar.PCM.frame_compatible", "Steel.Heap.join", "Steel.Preorder.history_composable", "FStar.WellFounded.well_founded", "FStar.PCM.frame_preserving_val_to_fp_upd", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "Steel.FractionalPermission.lesser_perm", "Steel.Heap.free_above_addr", "Steel.Preorder.curval", "Steel.Heap.wand", "Steel.Heap.slprop", "Steel.Preorder.extends", "Steel.Preorder.induces_preorder", "Steel.Heap.disjoint_addr", "Steel.Heap.mem_equiv", "Steel.Preorder.qhistory", "Steel.Heap.mem_equiv_eq", "Steel.Heap.join_associative", "Steel.Preorder.p_composable", "Steel.Preorder.unit_history", "Steel.Preorder.pcm_of_preorder", "FStar.PCM.compatible_elim", "FStar.PropositionalExtensionality.apply", "FStar.PCM.lem_commutative", "Steel.Preorder.p", "FStar.WellFounded.inverse_image", "Steel.Heap.join_associative2", "FStar.WellFounded.fix", "Steel.Preorder.stable_compatiblity", "FStar.FunctionalExtensionality.on", "Steel.Preorder.flip", "Steel.Heap.disjoint", "Steel.Preorder.lift_fact", "Steel.Preorder.extend_history'", "Steel.Heap.join_cells", "FStar.Ghost.return", "FStar.Ghost.op_let_At", "Steel.Preorder.hperm", "Steel.Preorder.extends'" ], "source_upto_this": "(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule Steel.Heap\nmodule F = FStar.FunctionalExtensionality\nopen FStar.FunctionalExtensionality\nopen FStar.PCM\nmodule Frac = Steel.FractionalPermission\n\n#set-options \"--fuel 1 --ifuel 1\"\n\n// In the future, we may have other cases of cells\n// for arrays and structs\nnoeq\ntype cell : Type u#(a + 1) =\n | Ref : a:Type u#a ->\n p:pcm a ->\n frac:Frac.perm{ frac `Frac.lesser_equal_perm` Frac.full_perm } ->\n v:a { frac == Frac.full_perm ==> p.refine v } ->\n cell\n\nlet addr = nat\n\n/// This is just the core of a memory, about which one can write\n/// assertions. At one level above, we'll encapsulate this memory\n/// with a freshness counter, a lock store etc.\nlet heap : Type u#(a + 1) = addr ^-> option (cell u#a)\n\nlet empty_heap : heap = F.on _ (fun _ -> None)\n\nlet contains_addr (m:heap) (a:addr)\n : bool\n = Some? (m a)\n\nlet select_addr (m:heap) (a:addr{contains_addr m a})\n : cell\n = Some?.v (m a)\n\nlet update_addr' (m:heap) (a:addr) (c:option cell)\n : heap\n = F.on _ (fun a' -> if a = a' then c else m a')\n\nlet update_addr (m:heap) (a:addr) (c:cell)\n : heap\n = update_addr' m a (Some c)\n\nlet disjoint_cells (c0 c1:cell u#h) : prop =\n let Ref t0 p0 f0 v0 = c0 in\n let Ref t1 p1 f1 v1 = c1 in\n t0 == t1 /\\\n p0 == p1 /\\\n composable p0 v0 v1 /\\\n (Frac.sum_perm f0 f1 `Frac.lesser_equal_perm` Frac.full_perm) /\\\n (Frac.sum_perm f0 f1 == Frac.full_perm ==> p0.refine (op p0 v0 v1))\n\nlet disjoint_cells_sym (c0 c1:cell u#h)\n : Lemma (requires disjoint_cells c0 c1)\n (ensures disjoint_cells c1 c0)\n = let Ref t0 p0 f0 v0 = c0 in\n let Ref t1 p1 f0 v1 = c1 in\n p0.comm v0 v1;\n ()\n\nlet disjoint_addr (m0 m1:heap u#h) (a:addr)\n : prop\n = match m0 a, m1 a with\n | Some c0, Some c1 ->\n disjoint_cells c0 c1\n | Some _, None\n | None, Some _\n | None, None ->\n True\n\ntype core_ref : Type u#0 =\n | Null\n | Addr of addr\n\nlet core_ref_null = Null\n\nlet core_ref_is_null (r:core_ref) = Null? r\n\nlet disjoint (m0 m1:heap u#h)\n : prop\n = forall a. disjoint_addr m0 m1 a\n\n#push-options \"--warn_error -271\"\n\nlet disjoint_sym (m0 m1:heap u#h)\n = let aux (m0 m1:heap u#h) (a:addr)\n : Lemma (requires disjoint_addr m0 m1 a)\n (ensures disjoint_addr m1 m0 a)\n [SMTPat (disjoint_addr m1 m0 a)]\n = match m0 a, m1 a with\n | Some c0, Some c1 -> disjoint_cells_sym c0 c1\n | _ -> ()\n in\n ()\n\nlet join_cells (c0:cell u#h) (c1:cell u#h{disjoint_cells c0 c1}) =\n let Ref a0 p0 f0 v0 = c0 in\n let Ref a1 p1 f1 v1 = c1 in\n Ref a0 p0 (Frac.sum_perm f0 f1) (op p0 v0 v1)\n\nlet join (m0:heap) (m1:heap{disjoint m0 m1})\n : heap\n = F.on _ (fun a ->\n match m0 a, m1 a with\n | None, None -> None\n | None, Some x -> Some x\n | Some x, None -> Some x\n | Some c0, Some c1 ->\n Some (join_cells c0 c1))\n\nlet disjoint_join_cells_assoc (c0 c1 c2:cell u#h)\n : Lemma\n (requires disjoint_cells c1 c2 /\\\n disjoint_cells c0 (join_cells c1 c2))\n (ensures disjoint_cells c0 c1 /\\\n disjoint_cells (join_cells c0 c1) c2 /\\\n join_cells (join_cells c0 c1) c2 == join_cells c0 (join_cells c1 c2))\n = let Ref a0 p0 f0 v0 = c0 in\n let Ref a1 p1 f1 v1 = c1 in\n let Ref a2 p2 f2 v2 = c2 in\n p0.assoc v0 v1 v2\n\nlet disjoint_join' (m0 m1 m2:heap u#h)\n : Lemma (requires disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures disjoint m0 m1 /\\ disjoint (join m0 m1) m2)\n [SMTPat (disjoint (join m0 m1) m2)]\n = let aux (a:addr)\n : Lemma (disjoint_addr m0 m1 a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n assert (disjoint m0 m1);\n let aux (a:addr)\n : Lemma (disjoint_addr (join m0 m1) m2 a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n ()\n\nlet mem_equiv (m0 m1:heap) =\n forall a. m0 a == m1 a\n\nlet mem_equiv_eq (m0 m1:heap)\n : Lemma\n (requires\n m0 `mem_equiv` m1)\n (ensures\n m0 == m1)\n [SMTPat (m0 `mem_equiv` m1)]\n = F.extensionality _ _ m0 m1\n\nlet join_cells_commutative (c0:cell u#h) (c1:cell u#h{disjoint_cells c0 c1})\n : Lemma (disjoint_cells_sym c0 c1; join_cells c0 c1 == join_cells c1 c0)\n [SMTPat (join_cells c0 c1)]\n = let Ref a0 p0 _ v0 = c0 in\n let Ref a1 p1 _ v1 = c1 in\n p0.comm v0 v1\n\nlet join_commutative' (m0 m1:heap)\n : Lemma\n (requires\n disjoint m0 m1)\n (ensures\n join m0 m1 `mem_equiv` join m1 m0)\n [SMTPat (join m0 m1)]\n = ()\n\nlet join_commutative m0 m1 = ()\n\nlet disjoint_join (m0 m1 m2:heap)\n : Lemma (disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) ==>\n disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\n [SMTPat (disjoint m0 (join m1 m2))]\n = let aux ()\n : Lemma\n (requires disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures disjoint m0 m1 /\\\n disjoint m0 m2 /\\\n disjoint (join m0 m1) m2 /\\\n disjoint (join m0 m2) m1)\n [SMTPat ()]\n = disjoint_join' m0 m1 m2;\n join_commutative m0 m1;\n disjoint_join' m0 m2 m1\n in\n ()\n\nlet join_associative' (m0 m1 m2:heap)\n : Lemma\n (requires\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2))\n (ensures\n (disjoint_join m0 m1 m2;\n join m0 (join m1 m2) `mem_equiv` join (join m0 m1) m2))\n [SMTPatOr\n [[SMTPat (join m0 (join m1 m2))];\n [SMTPat (join (join m0 m1) m2)]]]\n = disjoint_join m0 m1 m2;\n let l = join m0 (join m1 m2) in\n let r = join (join m0 m1) m2 in\n let aux (a:addr)\n : Lemma (l a == r a)\n [SMTPat ()]\n = match m0 a, m1 a, m2 a with\n | Some c0, Some c1, Some c2 ->\n disjoint_join_cells_assoc c0 c1 c2\n | _ -> ()\n in\n ()\n\nlet join_associative (m0 m1 m2:heap) = join_associative' m0 m1 m2\n\nlet join_associative2 (m0 m1 m2:heap)\n : Lemma\n (requires\n disjoint m0 m1 /\\\n disjoint (join m0 m1) m2)\n (ensures\n disjoint m1 m2 /\\\n disjoint m0 (join m1 m2) /\\\n join m0 (join m1 m2) `mem_equiv` join (join m0 m1) m2)\n [SMTPat (join (join m0 m1) m2)]\n = disjoint_join m2 m0 m1;\n join_commutative (join m0 m1) m2;\n join_associative m2 m0 m1\n\n////////////////////////////////////////////////////////////////////////////////\nlet slprop = p:(heap ^-> prop) { heap_prop_is_affine p }\n\nmodule W = FStar.WellFounded\n\n\nlet interp (p:slprop u#a) (m:heap u#a)\n : Tot prop\n = p m\n\nlet as_slprop p = FStar.FunctionalExtensionality.on _ p\n\nlet slprop_extensionality (p q:slprop)\n : Lemma\n (requires p `equiv` q)\n (ensures p == q)\n = FStar.PredicateExtensionality.predicateExtensionality _ p q\n\nlet emp : slprop u#a = as_slprop (fun h -> True)\n\nlet affine_hprop_intro\n (p:heap u#a -> prop)\n (lemma: (h0 : heap u#a) -> (h1: heap u#a) -> Lemma\n (requires (p h0 /\\ disjoint h0 h1))\n (ensures (p (join h0 h1)))\n )\n : Lemma (heap_prop_is_affine p)\n =\n let aux (h0 h1: heap u#a) : Lemma (p h0 /\\ disjoint h0 h1 ==> p (join h0 h1)) =\n let aux (_ : squash (p h0 /\\ disjoint h0 h1)) : Lemma (disjoint h0 h1 /\\ p (join h0 h1)) =\n lemma h0 h1\n in\n Classical.impl_intro aux\n in\n Classical.forall_intro_2 aux\n\nlet pts_to_cell (#a:Type u#a) (pcm:pcm a) (v:a) (c:cell u#a) =\n let Ref a' pcm' _ v' = c in\n a == a' /\\\n pcm == pcm' /\\\n compatible pcm v v'\n\nlet pts_to_cell_join (#a:Type u#a) (pcm:pcm a) (v1 v2:a) (c:cell u#a)\n : Lemma (requires (pts_to_cell pcm v1 c /\\ pts_to_cell pcm v2 c))\n (ensures joinable pcm v1 v2)\n = ()\n\nlet pts_to (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v:a) : slprop u#a =\n let hprop (h: heap) : Tot prop =\n Addr? r /\\\n h `contains_addr` (Addr?._0 r) /\\\n pts_to_cell pcm v (select_addr h (Addr?._0 r))\n in\n affine_hprop_intro hprop (fun h0 h1 ->\n match r with | Null -> () | Addr r -> (\n match h0 r, h1 r, (join h0 h1) r with\n | Some (Ref a0 pcm0 _ v0), Some (Ref a1 pcm1 _ v1), Some (Ref a01 pcm01 _ v01) ->\n compatible_elim pcm01 v v0 (compatible pcm01 v v01) (fun frame ->\n pcm01.comm frame v;\n pcm01.assoc_r v frame v1;\n pcm01.comm frame v1;\n let new_frame = (op pcm01 v1 frame) in\n pcm01.comm v new_frame\n )\n | None, Some _, _\n | Some _, None, _ -> ()\n | None, None, _ -> ()\n )\n );\n as_slprop hprop\n\n\nlet h_and (p1 p2:slprop u#a) : slprop u#a =\n as_slprop (fun (h: heap) -> p1 h /\\ p2 h)\n\nlet h_or (p1 p2:slprop u#a) : slprop u#a =\n as_slprop (fun (h: heap) -> p1 h \\/ p2 h)\n\nlet star (p1 p2: slprop u#a) : slprop u#a =\n as_slprop (fun (h: heap) -> exists (h1 h2 : heap).\n h1 `disjoint` h2 /\\\n h == join h1 h2 /\\\n interp p1 h1 /\\\n interp p2 h2)\n\nlet wand (p1 p2: slprop u#a) : slprop u#a =\n as_slprop (fun (h: heap) -> forall (h1: heap).\n h `disjoint` h1 /\\\n interp p1 h1 ==>\n interp p2 (join h h1))\n\nlet h_exists_body (#[@@@strictly_positive] a:Type u#b)\n ([@@@strictly_positive] f: (a -> slprop u#a))\n (h:heap)\n (x:a) : prop =\n interp (f x) h\n\nlet h_exists (#[@@@strictly_positive] a:Type u#b)\n ([@@@strictly_positive] f: (a -> slprop u#a)) : slprop u#a =\n as_slprop (fun (h: heap) -> exists x. h_exists_body f h x)\n\nlet h_forall_body (#a:Type u#b) (f: (a -> slprop u#a)) (h:heap) (x:a) : prop =\n interp (f x) h\n\nlet h_forall (#a:Type u#b) (f: (a -> slprop u#a)) : slprop u#a =\n as_slprop (fun (h: heap) -> forall x. h_forall_body f h x)\n\nlet h_refine p r = h_and p (as_slprop r)\n\n ////////////////////////////////////////////////////////////////////////////////\n//properties of equiv\n////////////////////////////////////////////////////////////////////////////////\nlet affine_star p q h = ()\n\nlet equiv_symmetric (p1 p2:slprop u#a) = ()\nlet equiv_extensional_on_star (p1 p2 p3:slprop u#a) = ()\nlet emp_unit p\n = let emp_unit_1 p m\n : Lemma\n (requires interp p m)\n (ensures interp (p `star` emp) m)\n [SMTPat (interp (p `star` emp) m)]\n = let emp_m : heap = on _ (fun _ -> None) in\n assert (disjoint emp_m m);\n assert (interp (p `star` emp) (join m emp_m));\n assert (mem_equiv m (join m emp_m))\n in\n let emp_unit_2 p m\n : Lemma\n (requires interp (p `star` emp) m)\n (ensures interp p m)\n [SMTPat (interp (p `star` emp) m)]\n = affine_star p emp m\n in\n ()\n\nlet intro_emp h = ()\n\nlet h_exists_cong (#a:Type) (p q : a -> slprop) = ()\n\nlet sl_implies (p q:slprop) = forall m. interp p m ==> interp q m\nlet h_exists_alt (#a:Type) (p q: a -> slprop)\n : Lemma\n (requires (forall x. exists y. p x `sl_implies` q y) /\\\n (forall x. exists y. q x `sl_implies` p y))\n (ensures equiv (h_exists p) (h_exists q))\n = ()\n\nlet intro_h_exists #a x p h = ()\n\nlet elim_h_exists #a p h = ()\n\nlet intro_h_forall (#a:_) (p:a -> slprop) (h:heap) = ()\n\nlet elim_h_forall (#a:_) (p:a -> slprop) (h:heap) (x:a) = ()\n\n(** Introducing [h_and] by proving both sides *)\nlet intro_h_and (p q: slprop) (h:heap) = ()\n\nlet elim_h_and (p q: slprop) (h:heap) = ()\n\nlet intro_h_or_left (p q: slprop) (h:heap) = ()\n\nlet intro_h_or_right (p q: slprop) (h:heap) = ()\n\nlet elim_h_or (p q: slprop) (h:heap) = ()\n\nlet intro_wand (p1 p2: slprop u#a) (h:heap) = ()\n\nlet elim_wand (p1 p2: slprop u#a) (h:heap) (h1:heap) = ()\n\nlet interp_depends_only_on (hp:slprop u#a) = emp_unit hp\n\n////////////////////////////////////////////////////////////////////////////////\n//pts_to\n////////////////////////////////////////////////////////////////////////////////\n\nlet intro_pts_to (#a:_) (#pcm:pcm a) (x:ref a pcm) (v:a) (m:heap)\n : Lemma\n (requires\n Addr? x /\\\n m `contains_addr` (Addr?._0 x) /\\\n (let Ref a' pcm' _ v' = select_addr m (Addr?._0 x) in\n a == a' /\\\n pcm == pcm' /\\\n compatible pcm v v'))\n (ensures\n interp (pts_to x v) m)\n = ()\n\n#push-options \"--z3rlimit_factor 4\"\nlet pts_to_compatible_fwd (#a:Type u#a)\n (#pcm:_)\n (x:ref a pcm)\n (v0 v1:a)\n (m:heap u#a)\n : Lemma\n (requires\n interp (pts_to x v0 `star` pts_to x v1) m)\n (ensures\n composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) m)\n = let Addr addr = x in\n let c = select_addr m addr in\n let Ref _ _ _ v = select_addr m addr in\n let aux (c0 c1: cell u#a)\n : Lemma\n (requires\n c0 `disjoint_cells` c1 /\\\n pts_to_cell pcm v0 c0 /\\\n pts_to_cell pcm v1 c1 /\\\n c == join_cells c0 c1 )\n (ensures\n composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) m)\n [SMTPat (c0 `disjoint_cells` c1)]\n = let Ref _ _ _ v0' = c0 in\n let Ref _ _ _ v1' = c1 in\n assert (exists frame. composable pcm v0 frame /\\ op pcm frame v0 == v0');\n assert (exists frame. composable pcm v1 frame /\\ op pcm frame v1 == v1');\n assert (composable pcm v0' v1');\n assert (op pcm v0' v1' == v);\n let aux (frame0 frame1:a)\n : Lemma\n (requires\n composable pcm v0 frame0 /\\\n op pcm frame0 v0 == v0' /\\\n composable pcm v1 frame1 /\\\n op pcm frame1 v1 == v1')\n (ensures (\n composable pcm frame0 frame1 /\\\n composable pcm v0 v1 /\\\n (let frame = op pcm frame0 frame1 in\n composable pcm frame (op pcm v0 v1) /\\\n op pcm frame (op pcm v0 v1) == v)))\n [SMTPat(op pcm frame0 v0);\n SMTPat(op pcm frame1 v1)]\n = assert (op pcm (op pcm frame0 v0) (op pcm frame1 v1) == v);\n pcm.assoc (op pcm frame0 v0) frame1 v1;\n assert (op pcm (op pcm (op pcm frame0 v0) frame1) v1 == v);\n pcm.comm (op pcm frame0 v0) frame1;\n assert (op pcm (op pcm frame1 (op pcm frame0 v0)) v1 == v);\n pcm.assoc_r frame1 (op pcm frame0 v0) v1;\n assert (op pcm frame1 (op pcm (op pcm frame0 v0) v1) == v);\n pcm.assoc_r frame0 v0 v1;\n assert (op pcm frame1 (op pcm frame0 (op pcm v0 v1)) == v);\n pcm.assoc frame1 frame0 (op pcm v0 v1);\n pcm.comm frame1 frame0\n in\n ()\n in\n assert (exists c0 c1.\n c0 `disjoint_cells` c1 /\\\n pts_to_cell pcm v0 c0 /\\\n pts_to_cell pcm v1 c1 /\\\n c == join_cells c0 c1)\n\nlet pts_to_compatible_bk (#a:Type u#a)\n (#pcm:_)\n (x:ref a pcm)\n (v0 v1:a)\n (m:heap u#a)\n : Lemma\n (requires\n composable pcm v0 v1 /\\\n interp (pts_to x (op pcm v0 v1)) m)\n (ensures\n interp (pts_to x v0 `star` pts_to x v1) m)\n = let Addr addr = x in\n let c = select_addr m addr in\n let Ref _ _ _ v = select_addr m addr in\n let v01 = (op pcm v0 v1) in\n assert (pts_to_cell pcm v01 c);\n let Ref _ _ frac v = c in\n assert (compatible pcm v01 v);\n let aux frame\n : Lemma\n (requires\n composable pcm v01 frame /\\\n op pcm frame v01 == v)\n (ensures\n exists m0 m1.\n interp (pts_to x v0) m0 /\\\n interp (pts_to x v1) m1 /\\\n disjoint m0 m1 /\\\n m `mem_equiv` join m0 m1)\n [SMTPat (composable pcm v01 frame)]\n = let c0 = Ref a pcm (Frac.half_perm frac) v0 in\n pcm.FStar.PCM.assoc_r v0 v1 frame;\n let c1 : cell = Ref a pcm (Frac.half_perm frac) (op pcm v1 frame) in\n compatible_refl pcm v0;\n assert (pts_to_cell pcm v0 c0);\n pcm.FStar.PCM.comm v1 frame;\n assert (compatible pcm v1 (op pcm v1 frame));\n assert (pts_to_cell pcm v1 c1);\n calc (==) {\n (v0 `op pcm` (v1 `op pcm` frame));\n (==) {\n pcm.FStar.PCM.assoc v0 v1 frame;\n pcm.FStar.PCM.comm v01 frame\n }\n (frame `op pcm` v01);\n };\n assert (disjoint_cells c0 c1);\n assert (c == join_cells c0 c1);\n let m0 = update_addr empty_heap addr c0 in\n let m1 = update_addr m addr c1 in\n assert (disjoint m0 m1) //fire the existential\n in\n ()\n\nlet pts_to_compatible (#a:Type u#a)\n (#pcm:_)\n (x:ref a pcm)\n (v0 v1:a)\n (m:heap u#a) =\n FStar.Classical.forall_intro (FStar.Classical.move_requires (pts_to_compatible_fwd x v0 v1));\n FStar.Classical.forall_intro (FStar.Classical.move_requires (pts_to_compatible_bk x v0 v1))\n\nlet pts_to_join (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures joinable pcm v1 v2)\n = ()\n\nlet pts_to_join' (#a:Type u#a) (#pcm:_) (r:ref a pcm) (v1 v2:a) (m:heap)\n : Lemma (requires (interp (pts_to r v1) m /\\ interp (pts_to r v2) m))\n (ensures (exists z. compatible pcm v1 z /\\ compatible pcm v2 z /\\\n interp (pts_to r z) m))\n = let Ref a' pcm' _ v' = (select_addr m (Addr?._0 r)) in\n compatible_refl pcm v'\n\nlet pts_to_compatible_equiv (#a:Type) (#pcm:_) (x:ref a pcm) (v0:a) (v1:a{composable pcm v0 v1})\n = FStar.Classical.forall_intro (pts_to_compatible x v0 v1)\n\nlet pts_to_not_null (#a:Type) (#pcm:_) (x:ref a pcm) (v:a) (m:heap) = ()\n\n\n////////////////////////////////////////////////////////////////////////////////\n// star\n////////////////////////////////////////////////////////////////////////////////\n\nlet intro_star (p q:slprop) (mp:hheap p) (mq:hheap q)\n : Lemma\n (requires\n disjoint mp mq)\n (ensures\n interp (p `star` q) (join mp mq))\n = ()\n\nlet elim_star (p q:slprop) (h:hheap (p `star` q))\n : Lemma\n (requires\n interp (p `star` q) h)\n (ensures exists hl hr.\n disjoint hl hr /\\\n h == join hl hr /\\\n interp p hl /\\\n interp q hr)\n =\n ()\n\n(* Properties of star *)\n\nlet star_commutative (p1 p2:slprop) = ()\n\nlet star_associative (p1 p2 p3:slprop)\n = let ltor (m m1 m2 m3:heap)\n : Lemma\n (requires\n disjoint m2 m3 /\\\n disjoint m1 (join m2 m3) /\\\n m == join m1 (join m2 m3) /\\\n interp p1 m1 /\\\n interp p2 m2 /\\\n interp p3 m3 /\\\n interp (p1 `star` (p2 `star` p3)) m)\n (ensures\n disjoint m1 m2 /\\\n disjoint (join m1 m2) m3 /\\\n m == join (join m1 m2) m3 /\\\n interp (p1 `star` p2) (join m1 m2) /\\\n interp ((p1 `star` p2) `star` p3) m)\n [SMTPat()]\n = disjoint_join m1 m2 m3;\n join_associative m1 m2 m3;\n intro_star p1 p2 m1 m2;\n intro_star (p1 `star` p2) p3 (join m1 m2) m3\n in\n let rtol (m m1 m2 m3:heap)\n : Lemma\n (requires\n disjoint m1 m2 /\\\n disjoint (join m1 m2) m3 /\\\n m == join (join m1 m2) m3 /\\\n interp p1 m1 /\\\n interp p2 m2 /\\\n interp p3 m3 /\\\n interp ((p1 `star` p2) `star` p3) m)\n (ensures\n disjoint m2 m3 /\\\n disjoint m1 (join m2 m3) /\\\n m == join m1 (join m2 m3) /\\\n interp (p2 `star` p3) (join m2 m3) /\\\n interp (p1 `star`(p2 `star` p3)) m)\n [SMTPat()]\n = join_associative2 m1 m2 m3;\n intro_star p2 p3 m2 m3;\n intro_star p1 (p2 `star` p3) m1 (join m2 m3)\n in\n ()\n\nlet star_congruence (p1 p2 p3 p4:slprop) = ()\n\n////////////////////////////////////////////////////////////////////////////////\n// refine\n////////////////////////////////////////////////////////////////////////////////\n\nlet refine_interp p q h = ()\nlet refine_equiv p0 p1 q0 q1 = ()\nlet pure_equiv p q = ()\nlet pure_interp p h = ()\nlet pure_star_interp p q h = ()\n\n\n////////////////////////////////////////////////////////////////////////////////\n// wand & implications\n////////////////////////////////////////////////////////////////////////////////\n\nlet stronger_star p q r = ()\nlet weaken (p q r:slprop) (h:heap u#a) = ()\n\n////////////////////////////////////////////////////////////////////////////////\n// Actions:\n////////////////////////////////////////////////////////////////////////////////\nmodule PP = Steel.Preorder\n\nlet full_heap_pred h =\n forall a. contains_addr h a ==>\n (select_addr h a).frac == Frac.full_perm\n\n#push-options \"--fuel 2 --ifuel 2\"\nlet heap_evolves : FStar.Preorder.preorder full_heap =\n fun (h0 h1:heap) ->\n forall (a:addr).\n match h0 a, h1 a with\n | None, _ -> True //an unused address in h0 can evolve anyway\n\n | Some (Ref a0 p0 f0 v0), Some (Ref a1 p1 f1 v1) ->\n //if a is used h0 then it remains used and ...\n a0 == a1 /\\ //its type can't change\n p0 == p1 /\\ //its pcm can't change\n PP.preorder_of_pcm p0 v0 v1 //and its value evolves by the pcm's preorder\n | _ -> False\n#pop-options\n\nlet free_above_addr h a =\n forall (i:nat). i >= a ==> h i == None\n\nlet weaken_free_above (h:heap) (a b:nat)\n : Lemma (free_above_addr h a /\\ a <= b ==> free_above_addr h b)\n = ()\n\n\n////////////////////////////////////////////////////////////////////////////////\n// sel\n////////////////////////////////////////////////////////////////////////////////\nlet sel #a #pcm (r:ref a pcm) (m:full_hheap (ptr r))\n : a\n = let Ref _ _ _ v = select_addr m (Addr?._0 r) in\n v\n\nlet sel_v #a #pcm r v m = sel r m\n\nlet sel_lemma (#a:_) (#pcm:_) (r:ref a pcm) (m:full_hheap (ptr r))\n : Lemma (interp (pts_to r (sel r m)) m)\n = let Ref _ _ _ v = select_addr m (Addr?._0 r) in\n assert (sel r m == v);\n compatible_refl pcm v\n\nlet witnessed_ref_stability #a #pcm (r:ref a pcm) (fact:a -> prop)\n = let fact_h = witnessed_ref r fact in\n let aux (h0 h1:full_heap)\n : Lemma\n (requires\n fact_h h0 /\\\n heap_evolves h0 h1)\n (ensures\n fact_h h1)\n [SMTPat ()]\n = let Addr addr = r in\n assert (interp (ptr r) h0);\n assert (fact (sel r h0));\n assert (contains_addr h1 addr);\n compatible_refl pcm (select_addr h1 addr).v;\n assert (compatible pcm (select_addr h1 addr).v (select_addr h1 addr).v);\n assert (interp (pts_to r (select_addr h1 addr).v) h1);\n assert (interp (ptr r) h1);\n assert (fact (sel r h1))\n in\n ()\n\n#set-options \"--fuel 2 --ifuel 2\"\n\nlet sel_action (#a:_) (#pcm:_) (r:ref a pcm) (v0:erased a)\n : action (pts_to r v0) (v:a{compatible pcm v0 v}) (fun _ -> pts_to r v0)\n = let f\n : pre_action (pts_to r v0)\n (v:a{compatible pcm v0 v})\n (fun _ -> pts_to r v0)\n = fun m0 -> (| sel r m0, m0 |)\n in\n f\n" }, { "file_name": "LowParse.SLow.Sum.fst", "name": "LowParse.SLow.Sum.size32_sum_destr_if", "opens_and_abbrevs": [ { "abbrev": "T", "full_module": "FStar.Tactics" }, { "abbrev": "U32", "full_module": "FStar.UInt32" }, { "abbrev": "B32", "full_module": "LowParse.Bytes32" }, { "open": "LowParse.SLow.Enum" }, { "open": "LowParse.Spec.Sum" }, { "open": "LowParse.SLow" }, { "open": "LowParse.SLow" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val size32_sum_destr_if (t: sum) (k: sum_key t) : Tot (if_combinator _ (size32_sum_destr_eq t k))", "source_definition": "let size32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_destr_eq t k))\n= // _ by (T.apply (`fif); T.fail \"abc\")\n fif _ _ _ (default_if _)", "source_range": { "start_line": 470, "start_col": 0, "end_line": 475, "end_col": 26 }, "interleaved": false, "definition": "fun t k ->\n LowParse.Spec.Enum.fif (LowParse.Spec.Base.refine_with_tag (LowParse.Spec.Sum.sum_tag_of_data t) k\n )\n FStar.UInt32.t\n Prims.eq2\n (LowParse.Spec.Enum.default_if FStar.UInt32.t)\n <:\n LowParse.Spec.Enum.if_combinator (LowParse.SLow.Sum.size32_sum_destr_codom t k)\n (LowParse.SLow.Sum.size32_sum_destr_eq t k)", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "LowParse.Spec.Sum.sum", "LowParse.Spec.Sum.sum_key", "LowParse.Spec.Enum.fif", "LowParse.Spec.Base.refine_with_tag", "LowParse.Spec.Sum.sum_type", "LowParse.Spec.Sum.sum_tag_of_data", "FStar.UInt32.t", "Prims.eq2", "LowParse.Spec.Enum.default_if", "LowParse.Spec.Enum.if_combinator", "LowParse.SLow.Sum.size32_sum_destr_codom", "LowParse.SLow.Sum.size32_sum_destr_eq" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "t: LowParse.Spec.Sum.sum -> k: LowParse.Spec.Sum.sum_key t\n -> LowParse.Spec.Enum.if_combinator (LowParse.SLow.Sum.size32_sum_destr_codom t k)\n (LowParse.SLow.Sum.size32_sum_destr_eq t k)", "prompt": "let size32_sum_destr_if (t: sum) (k: sum_key t) : Tot (if_combinator _ (size32_sum_destr_eq t k)) =\n ", "expected_response": "fif _ _ _ (default_if _)", "source": { "project_name": "everparse", "file_name": "src/lowparse/LowParse.SLow.Sum.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git" }, "dependencies": { "source_file": "LowParse.SLow.Sum.fst", "checked_file": "dataset/LowParse.SLow.Sum.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/LowParse.Spec.Sum.fst.checked", "dataset/LowParse.SLow.Enum.fst.checked", "dataset/LowParse.Bytes32.fst.checked", "dataset/FStar.UInt32.fsti.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Tactics.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "let serializer32_sum_gen_precond\n (kt: parser_kind)\n (k: parser_kind)\n: GTot Type0\n= kt.parser_kind_subkind == Some ParserStrong /\\\n Some? kt.parser_kind_high /\\\n Some? k.parser_kind_high /\\ (\n let (Some vt) = kt.parser_kind_high in\n let (Some v) = k.parser_kind_high in\n vt + v < 4294967296\n )", "let parse32_sum_t (t: sum) : Tot Type =\n bytes32 -> Tot (option (sum_type t * U32.t))", "let parse32_sum_eq (t: sum) : Tot (parse32_sum_t t -> parse32_sum_t t -> GTot Type0) =\n feq _ _ (eq2 #_)", "let parse32_sum_if (t: sum) : Tot (if_combinator _ (parse32_sum_eq t)) =\n fif _ _ _ (default_if _)", "let parse32_sum_eq_refl (t: sum) : Tot (r_reflexive_t _ (parse32_sum_eq t)) =\n fun _ -> ()", "let parse32_sum_eq_trans (t: sum) : Tot (r_transitive_t _ (parse32_sum_eq t)) = feq_trans _ _ (eq2 #_)", "let parse32_sum_cases'\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (k: sum_key t)\n: Tot (parser32 (parse_sum_cases' t pc k))\n= [@inline_let]\n let _ = synth_sum_case_injective t k in\n parse32_synth'\n (dsnd (pc k))\n (synth_sum_case t k)\n (pc32 k)\n ()", "let parse32_sum_aux\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (p32: parser32 (parse_enum_key p (sum_enum t)))\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n: GTot (parser32 (parse_sum t p pc))\n= fun input ->\n parse_sum_eq' t p pc (B32.reveal input);\n [@inline_let]\n let res : option (sum_type t * U32.t) =\n //NS: hoist nested match\n //we do not expect the case analysis to\n //on `p32 input` to reduce; hoist it for more efficient\n //normalization.\n //Note, in some simple cases, e.g., parsing raw enums\n //this r the pcases below maybe statically evaluated\n //to a `Some v`; this forgoes reduction in those simple\n //cases for more efficient extraction in more complex\n //common cases\n let pi = p32 input in\n match pi with\n | None -> None\n | Some (k, consumed_k) ->\n let input_k = B32.b32slice input consumed_k (B32.len input) in\n //NS: hoist nested match\n let pcases1 = parse32_sum_cases' t pc pc32 k input_k in\n match pcases1 with\n | None -> None\n | Some (x, consumed_x) ->\n Some ((x <: sum_type t), consumed_k `U32.add` consumed_x)\n in\n (res <: (res: option (sum_type t * U32.t) { parser32_correct (parse_sum t p pc) input res } ))", "let parse32_sum_cases_t\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n: Tot Type\n= parser32 (parse_sum_cases t pc k)", "let parse32_sum_cases_t_eq\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n (x y : parse32_sum_cases_t t pc k)\n: GTot Type0\n= True", "let parse32_sum_cases_t_if\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n: Tot (if_combinator _ (parse32_sum_cases_t_eq t pc k))\n= fun cond (sv_true: cond_true cond -> Tot (parse32_sum_cases_t t pc k)) (sv_false: cond_false cond -> Tot (parse32_sum_cases_t t pc k)) input ->\n if cond\n then (sv_true () input <: (res: _ { parser32_correct (parse_sum_cases t pc k) input res}))\n else (sv_false () input <: (res: _ {parser32_correct (parse_sum_cases t pc k) input res}))", "let parse32_sum_cases_aux\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (k: sum_key t)\n: Tot (parser32 (parse_sum_cases t pc k))\n= fun (input: B32.bytes) ->\n [@inline_let] let _ = parse_sum_cases_eq' t pc k (B32.reveal input) in\n (parse32_sum_cases' t pc pc32 k input <: (res: _ { parser32_correct (parse_sum_cases t pc k) input res } ))", "let parse32_sum_cases \n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (destr: dep_enum_destr (sum_enum t) (parse32_sum_cases_t t pc))\n (k: sum_key t)\n: Tot (parser32 (parse_sum_cases t pc k))\n= destr\n _\n (parse32_sum_cases_t_if t pc)\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (parse32_sum_cases_aux t pc pc32)\n k", "let parse32_sum'\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (p32: parser32 (parse_enum_key p (sum_enum t)))\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (destr: enum_destr_t (option (sum_type t * U32.t)) (sum_enum t))\n (input: B32.bytes)\n: Pure (option (sum_type t * U32.t))\n (requires True)\n (ensures (fun res -> res == parse32_sum_aux t p p32 pc pc32 input))\n= [@inline_let]\n let res : option (sum_type t * U32.t) =\n //NS: hoist nested match\n let pi = p32 input in\n match pi with\n | None -> None\n | Some (k, consumed_k) ->\n let input_k = B32.b32slice input consumed_k (B32.len input) in\n destr\n (eq2 #(option (sum_type t * U32.t))) (default_if _)\n (fun _ -> ()) (fun _ _ _ -> ())\n (fun k ->\n //NS: hoist nested match\n let pcases2 = parse32_sum_cases' t pc pc32 k input_k in\n match pcases2 with\n | None -> None\n | Some (x, consumed_x) ->\n Some ((x <: sum_type t), consumed_k `U32.add` consumed_x)\n )\n k\n in\n res", "let parse32_sum\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (p32: parser32 (parse_enum_key p (sum_enum t)))\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (destr: enum_destr_t (option (sum_type t * U32.t)) (sum_enum t))\n: Tot (parser32 (parse_sum t p pc))\n= fun input ->\n (parse32_sum' t p p32 pc pc32 destr input <: (res: option (sum_type t * U32.t) { parser32_correct (parse_sum t p pc) input res } ))", "let parse32_sum2\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (p32: parser32 p)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (destr: enum_destr_t (option (sum_type t * U32.t)) (sum_enum t))\n (f: maybe_enum_key_of_repr'_t (sum_enum t))\n: Tot (parser32 (parse_sum t p pc))\n= parse32_sum t p (parse32_enum_key p32 (sum_enum t) f) pc pc32 destr", "let serialize32_sum_cases_t\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n: Tot Type\n= serializer32 (serialize_sum_cases t pc sc k)", "let serialize32_sum_cases_t_eq\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n (x y: serialize32_sum_cases_t t sc k)\n: GTot Type0\n= True", "let serialize32_sum_cases_t_if\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n: Tot (if_combinator _ (serialize32_sum_cases_t_eq t sc k))\n= fun cond (sv_true: (cond_true cond -> Tot (serialize32_sum_cases_t t sc k))) (sv_false: (cond_false cond -> Tot (serialize32_sum_cases_t t sc k))) input ->\n if cond\n then (sv_true () input <: (res: _ { serializer32_correct (serialize_sum_cases t pc sc k) input res } ))\n else (sv_false () input <: (res: _ { serializer32_correct (serialize_sum_cases t pc sc k) input res } ))", "let serialize32_sum_cases_aux\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (k: sum_key t)\n: Tot (serializer32 (serialize_sum_cases t pc sc k))\n= fun input ->\n [@inline_let] let _ =\n Classical.forall_intro (parse_sum_cases_eq' t pc k);\n synth_sum_case_injective t k;\n synth_sum_case_inverse t k\n in\n serialize32_synth\n _\n (synth_sum_case t k)\n _\n (sc32 k)\n (synth_sum_case_recip t k)\n (fun x -> synth_sum_case_recip t k x)\n ()\n input", "let serialize32_sum_cases\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (serialize32_sum_cases_t t sc))\n (k: sum_key t)\n: Tot (serializer32 (serialize_sum_cases t pc sc k))\n= destr\n _\n (serialize32_sum_cases_t_if t sc)\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (serialize32_sum_cases_aux t sc sc32)\n k", "let serialize32_sum_aux\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (s32: serializer32 (serialize_enum_key _ s (sum_enum t)))\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (u: squash (serializer32_sum_gen_precond kt (weaken_parse_cases_kind t pc)))\n: GTot (serializer32 (serialize_sum t s sc))\n= fun x ->\n serialize_sum_eq t s sc x;\n let tg = sum_tag_of_data t x in\n let s1 = s32 tg in\n let s2 = sc32 tg (synth_sum_case_recip t tg x) in\n let res = s1 `B32.b32append` s2 in\n (res <: (res: B32.bytes { serializer32_correct (serialize_sum t s sc) x res } ))", "let serialize32_sum_destr_codom\n (t: sum)\n (k: sum_key t)\n: Tot Type\n= refine_with_tag (sum_tag_of_data t) k -> Tot B32.bytes", "let serialize32_sum_destr_eq\n (t: sum)\n (k: sum_key t)\n: Tot (serialize32_sum_destr_codom t k -> serialize32_sum_destr_codom t k -> GTot Type0)\n= _ by (T.apply (`feq); T.apply (`eq2))", "let serialize32_sum_destr_trans\n (t: sum)\n (k: sum_key t)\n: Tot (r_transitive_t _ (serialize32_sum_destr_eq t k))\n= feq_trans _ _ (eq2 #_)", "let serialize32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (serialize32_sum_destr_eq t k))\n= // _ by (T.apply (`fif); T.fail \"abc\")\n fif _ _ _ (default_if _)", "let serialize32_sum\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (s32: serializer32 (serialize_enum_key _ s (sum_enum t)))\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (serialize32_sum_destr_codom t))\n (u: squash (serializer32_sum_gen_precond kt (weaken_parse_cases_kind t pc)))\n: Tot (serializer32 (serialize_sum t s sc))\n= fun x ->\n [@inline_let]\n let _ = serialize_sum_eq t s sc x in\n let tg = sum_tag_of_data t x in\n let s1 = s32 tg in\n [@inline_let]\n let phi tg x = sc32 tg (synth_sum_case_recip t tg x) in\n [@inline_let]\n let phi'tg = destr\n (serialize32_sum_destr_eq t)\n (serialize32_sum_destr_if t)\n (fun _ _ -> ())\n (serialize32_sum_destr_trans t)\n phi\n tg\n in\n let s2 = phi'tg x in\n [@inline_let]\n let _ =\n let phitg = phi tg in\n feq_elim _ _ (eq2 #_) phitg phi'tg x\n in\n let res = s1 `B32.b32append` s2 in\n (res <: (res: B32.bytes { serializer32_correct (serialize_sum t s sc) x res } ))", "let serialize32_sum2\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (s32: serializer32 s)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (serialize32_sum_destr_codom t))\n (f: enum_repr_of_key'_t (sum_enum t))\n (u: squash (serializer32_sum_gen_precond kt (weaken_parse_cases_kind t pc)))\n: Tot (serializer32 (serialize_sum t s sc))\n= serialize32_sum t s (serialize32_enum_key s32 (sum_enum t) f) sc sc32 destr u", "let size32_sum_cases_t\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n: Tot Type\n= size32 (serialize_sum_cases t pc sc k)", "let size32_sum_cases_t_eq\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n (x y: size32_sum_cases_t t sc k)\n: GTot Type0\n= True", "let size32_sum_cases_t_if\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_cases_t_eq t sc k))\n= fun cond (sv_true: (cond_true cond -> Tot (size32_sum_cases_t t sc k))) (sv_false: (cond_false cond -> Tot (size32_sum_cases_t t sc k))) input ->\n if cond\n then (sv_true () input <: (res: _ { size32_postcond (serialize_sum_cases t pc sc k) input res } ))\n else (sv_false () input <: (res: _ { size32_postcond (serialize_sum_cases t pc sc k) input res } ))", "let size32_sum_cases_aux\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (size32 (sc x))))\n (k: sum_key t)\n: Tot (size32 (serialize_sum_cases t pc sc k))\n= fun input ->\n [@inline_let] let _ =\n Classical.forall_intro (parse_sum_cases_eq' t pc k);\n synth_sum_case_injective t k;\n synth_sum_case_inverse t k\n in\n size32_synth\n _\n (synth_sum_case t k)\n _\n (sc32 k)\n (synth_sum_case_recip t k)\n (fun x -> synth_sum_case_recip t k x)\n ()\n input", "let size32_sum_cases\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (size32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (size32_sum_cases_t t sc))\n (k: sum_key t)\n: Tot (size32 (serialize_sum_cases t pc sc k))\n= destr\n _\n (size32_sum_cases_t_if t sc)\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (size32_sum_cases_aux t sc sc32)\n k", "let size32_sum_destr_codom\n (t: sum)\n (k: sum_key t)\n: Tot Type\n= refine_with_tag (sum_tag_of_data t) k -> Tot U32.t", "let size32_sum_destr_eq\n (t: sum)\n (k: sum_key t)\n: Tot (size32_sum_destr_codom t k -> size32_sum_destr_codom t k -> GTot Type0)\n= _ by (T.apply (`feq); T.apply (`eq2))", "let size32_sum_destr_trans\n (t: sum)\n (k: sum_key t)\n: Tot (r_transitive_t _ (size32_sum_destr_eq t k))\n= feq_trans _ _ (eq2 #_)" ], "closest": [ "val serialize32_sum_cases_t_if\n (t: sum)\n (#pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: (x: sum_key t -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n : Tot (if_combinator _ (serialize32_sum_cases_t_eq t sc k))\nlet serialize32_sum_cases_t_if\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n: Tot (if_combinator _ (serialize32_sum_cases_t_eq t sc k))\n= fun cond (sv_true: (cond_true cond -> Tot (serialize32_sum_cases_t t sc k))) (sv_false: (cond_false cond -> Tot (serialize32_sum_cases_t t sc k))) x #rrel #rel b pos ->\n if cond\n then (sv_true () x b pos)\n else (sv_false () x b pos)", "val serialize32_dsum_cases_t_if\n (t: dsum)\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (sf: (x: dsum_known_key t -> Tot (serializer (dsnd (f x)))))\n (#k': parser_kind)\n (g: parser k' (dsum_type_of_unknown_tag t))\n (sg: serializer g)\n (k: dsum_known_key t)\n : Tot (if_combinator _ (serialize32_dsum_cases_t_eq t f sf g sg k))\nlet serialize32_dsum_cases_t_if\n (t: dsum)\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (sf: (x: dsum_known_key t) -> Tot (serializer (dsnd (f x))))\n (#k': parser_kind)\n (g: parser k' (dsum_type_of_unknown_tag t))\n (sg: serializer g)\n (k: dsum_known_key t)\n: Tot (if_combinator _ (serialize32_dsum_cases_t_eq t f sf g sg k))\n= fun cond (sv_true: (cond_true cond -> Tot (serialize32_dsum_cases_t t f sf g sg k))) (sv_false: (cond_false cond -> Tot (serialize32_dsum_cases_t t f sf g sg k))) x #rrel #rel output pos ->\n if cond\n then (sv_true () x output pos)\n else (sv_false () x output pos)", "val validate_sum_cases_t_if\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n : Tot (if_combinator _ (validate_sum_cases_t_eq t pc k))\nlet validate_sum_cases_t_if\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n: Tot (if_combinator _ (validate_sum_cases_t_eq t pc k))\n= fun cond (sv_true: cond_true cond -> Tot (validate_sum_cases_t t pc k)) (sv_false: cond_false cond -> Tot (validate_sum_cases_t t pc k)) #rrel #rel input pos ->\n if cond\n then sv_true () input pos\n else sv_false () input pos", "val serialize32_sum_cases\n (t: sum)\n (#pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: (x: sum_key t -> Tot (serializer (dsnd (pc x)))))\n (sc32: (x: sum_key t -> Tot (serializer32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (serialize32_sum_cases_t t sc))\n (k: sum_key t)\n : Tot (serializer32 (serialize_sum_cases t pc sc k))\nlet serialize32_sum_cases\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (serialize32_sum_cases_t t sc))\n (k: sum_key t)\n: Tot (serializer32 (serialize_sum_cases t pc sc k))\n= destr\n _\n (serialize32_sum_cases_t_if t sc)\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (serialize32_sum_cases_aux t sc sc32)\n k", "val jump_sum_cases_t_if\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n : Tot (if_combinator _ (jump_sum_cases_t_eq t pc k))\nlet jump_sum_cases_t_if\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n: Tot (if_combinator _ (jump_sum_cases_t_eq t pc k))\n= fun cond (sv_true: cond_true cond -> Tot (jump_sum_cases_t t pc k)) (sv_false: cond_false cond -> Tot (jump_sum_cases_t t pc k)) #rrel #rel input pos ->\n if cond\n then sv_true () input pos\n else sv_false () input pos", "val serialize32_sum\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p {kt.parser_kind_subkind == Some ParserStrong})\n (s32: serializer32 (serialize_enum_key _ s (sum_enum t)))\n (#pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: (x: sum_key t -> Tot (serializer (dsnd (pc x)))))\n (sc32: (x: sum_key t -> Tot (serializer32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (serialize32_sum_cases_t t sc))\n : Tot (serializer32 (serialize_sum t s sc))\nlet serialize32_sum\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p {kt.parser_kind_subkind == Some ParserStrong})\n (s32: serializer32 (serialize_enum_key _ s (sum_enum t)))\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (serialize32_sum_cases_t t sc))\n: Tot (serializer32 (serialize_sum t s sc))\n= fun x #rrel #rel b pos ->\n serialize_sum_eq t s sc x;\n let tg = sum_tag_of_data t x in\n serialize32_nondep_then_aux s32 (serialize32_sum_cases t sc sc32 destr tg) tg x b pos", "val read_sum_cases_t_if\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n : Tot (if_combinator _ (read_sum_cases_t_eq t pc k))\nlet read_sum_cases_t_if\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n: Tot (if_combinator _ (read_sum_cases_t_eq t pc k))\n= fun cond (sv_true: cond_true cond -> Tot (read_sum_cases_t t pc k)) (sv_false: cond_false cond -> Tot (read_sum_cases_t t pc k)) #_ #_ input pos ->\n if cond\n then (sv_true () input pos)\n else (sv_false () input pos)", "val serialize32_sum_cases_aux\n (t: sum)\n (#pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: (x: sum_key t -> Tot (serializer (dsnd (pc x)))))\n (sc32: (x: sum_key t -> Tot (serializer32 (sc x))))\n (k: sum_key t)\n : Tot (serializer32 (serialize_sum_cases t pc sc k))\nlet serialize32_sum_cases_aux\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (k: sum_key t)\n: Tot (serializer32 (serialize_sum_cases t pc sc k))\n= fun x #rrel #rel b pos ->\n [@inline_let] let _ =\n Classical.forall_intro (parse_sum_cases_eq' t pc k);\n synth_sum_case_injective t k;\n synth_sum_case_inverse t k\n in\n serialize32_synth\n (sc32 k)\n (synth_sum_case t k)\n (synth_sum_case_recip t k)\n (fun x -> synth_sum_case_recip t k x)\n ()\n x\n b\n pos", "val serialize32_sum_cases_t_eq\n (t: sum)\n (#pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: (x: sum_key t -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n (x y: serialize32_sum_cases_t t sc k)\n : GTot Type0\nlet serialize32_sum_cases_t_eq\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n (x y: serialize32_sum_cases_t t sc k)\n: GTot Type0\n= True", "val mk_destr_bitsum'_t\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n : Tot (destr_bitsum'_t b <: Type u#1) (decreases %[b;1;()])\nlet rec mk_destr_bitsum'_t\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n: Tot (destr_bitsum'_t b <: Type u#1)\n (decreases %[b;1;()])\n= match b with\n | BitStop _ -> destr_bitsum'_bitstop cl\n | BitField sz rest -> destr_bitsum'_bitfield cl bitsum'_size sz rest (mk_destr_bitsum'_t rest)\n | BitSum' key key_size e payload ->\n destr_bitsum'_bitsum_intro cl bitsum'_size key key_size e payload (mk_destr_bitsum'_bitsum_t cl bitsum'_size key key_size e payload [] e)\nand mk_destr_bitsum'_bitsum_t\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) { e == l1 `L.append` l2 } )\n: Tot (destr_bitsum'_bitsum_t cl bitsum'_size key key_size e payload l1 l2 <: Type u#1)\n (decreases %[BitSum' key key_size e payload; 0; l2])\n= bitsum_wellfoundedness (BitSum' key key_size e payload);\n match l2 with\n | [] ->\n [@inline_let] let _ =\n L.append_l_nil l1\n in\n destr_bitsum'_bitsum_nil cl bitsum'_size key key_size e payload ()\n | [(k, r)] ->\n [@inline_let] let _ =\n enum_repr_of_key_append_cons e l1 (k, r) [];\n L.append_assoc l1 [(k, r)] []\n in\n destr_bitsum'_bitsum_cons_nil cl bitsum'_size key key_size e payload l1 k r\n (mk_destr_bitsum'_t (payload k))\n | (k, r) :: q ->\n [@inline_let] let _ =\n enum_repr_of_key_append_cons e l1 (k, r) q;\n L.append_assoc l1 [(k, r)] q\n in\n destr_bitsum'_bitsum_cons cl bitsum'_size key key_size e payload l1 k r q\n (mk_destr_bitsum'_t (payload k))\n (mk_destr_bitsum'_bitsum_t cl bitsum'_size key key_size e payload (l1 `L.append` [(k, r)]) q)", "val jump_sum_aux_payload_if\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n : Tot (if_combinator _ (jump_sum_aux_payload_eq t pc k))\nlet jump_sum_aux_payload_if\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n: Tot (if_combinator _ (jump_sum_aux_payload_eq t pc k))\n= jump_sum_aux_payload_if' t pc k", "val sum_key_type_of_sum_key (t: sum) (k: sum_key t)\n : Pure (sum_key_type t) (requires True) (ensures (fun k' -> k' == (k <: sum_key_type t)))\nlet sum_key_type_of_sum_key (t: sum) (k: sum_key t) : Pure (sum_key_type t)\n (requires True)\n (ensures (fun k' -> k' == (k <: sum_key_type t)))\n= k", "val read_dsum_cases_t_if\n (t: dsum)\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (#k': parser_kind)\n (g: parser k' (dsum_type_of_unknown_tag t))\n (k: dsum_known_key t)\n : Tot (if_combinator _ (read_dsum_cases_t_eq t f g k))\nlet read_dsum_cases_t_if\n (t: dsum)\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (#k': parser_kind)\n (g: parser k' (dsum_type_of_unknown_tag t))\n (k: dsum_known_key t)\n: Tot (if_combinator _ (read_dsum_cases_t_eq t f g k))\n= fun cond (sv_true: cond_true cond -> Tot (read_dsum_cases_t t f g k)) (sv_false: cond_false cond -> Tot (read_dsum_cases_t t f g k)) #_ #_ input pos ->\n if cond\n then sv_true () input pos\n else sv_false () input pos", "val validate_sum_aux_payload_if\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n : Tot (if_combinator _ (validate_sum_aux_payload_eq t pc k))\nlet validate_sum_aux_payload_if\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n: Tot (if_combinator _ (validate_sum_aux_payload_eq t pc k))\n= validate_sum_aux_payload_if' t pc k", "val mk_destr_bitsum'_bitsum_t\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) {e == l1 `L.append` l2})\n : Tot (destr_bitsum'_bitsum_t cl bitsum'_size key key_size e payload l1 l2 <: Type u#1)\n (decreases %[BitSum' key key_size e payload;0;l2])\nlet rec mk_destr_bitsum'_t\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n: Tot (destr_bitsum'_t b <: Type u#1)\n (decreases %[b;1;()])\n= match b with\n | BitStop _ -> destr_bitsum'_bitstop cl\n | BitField sz rest -> destr_bitsum'_bitfield cl bitsum'_size sz rest (mk_destr_bitsum'_t rest)\n | BitSum' key key_size e payload ->\n destr_bitsum'_bitsum_intro cl bitsum'_size key key_size e payload (mk_destr_bitsum'_bitsum_t cl bitsum'_size key key_size e payload [] e)\nand mk_destr_bitsum'_bitsum_t\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) { e == l1 `L.append` l2 } )\n: Tot (destr_bitsum'_bitsum_t cl bitsum'_size key key_size e payload l1 l2 <: Type u#1)\n (decreases %[BitSum' key key_size e payload; 0; l2])\n= bitsum_wellfoundedness (BitSum' key key_size e payload);\n match l2 with\n | [] ->\n [@inline_let] let _ =\n L.append_l_nil l1\n in\n destr_bitsum'_bitsum_nil cl bitsum'_size key key_size e payload ()\n | [(k, r)] ->\n [@inline_let] let _ =\n enum_repr_of_key_append_cons e l1 (k, r) [];\n L.append_assoc l1 [(k, r)] []\n in\n destr_bitsum'_bitsum_cons_nil cl bitsum'_size key key_size e payload l1 k r\n (mk_destr_bitsum'_t (payload k))\n | (k, r) :: q ->\n [@inline_let] let _ =\n enum_repr_of_key_append_cons e l1 (k, r) q;\n L.append_assoc l1 [(k, r)] q\n in\n destr_bitsum'_bitsum_cons cl bitsum'_size key key_size e payload l1 k r q\n (mk_destr_bitsum'_t (payload k))\n (mk_destr_bitsum'_bitsum_t cl bitsum'_size key key_size e payload (l1 `L.append` [(k, r)]) q)", "val destr_bitsum'_bitsum_nil\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (h: squash (e == e `L.append` []))\n : Tot (destr_bitsum'_bitsum_t cl bitsum'_size key key_size e payload e [])\nlet destr_bitsum'_bitsum_nil\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (h: squash (e == e `L.append` []))\n: Tot (destr_bitsum'_bitsum_t cl bitsum'_size key key_size e payload e [])\n= (fun u u_if f x ->\n assert False;\n false_elim ())", "val serialize32_dsum_cases_t_eq\n (t: dsum)\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (sf: (x: dsum_known_key t -> Tot (serializer (dsnd (f x)))))\n (#k': parser_kind)\n (g: parser k' (dsum_type_of_unknown_tag t))\n (sg: serializer g)\n (k: dsum_known_key t)\n (x y: serialize32_dsum_cases_t t f sf g sg k)\n : GTot Type0\nlet serialize32_dsum_cases_t_eq\n (t: dsum)\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (sf: (x: dsum_known_key t) -> Tot (serializer (dsnd (f x))))\n (#k': parser_kind)\n (g: parser k' (dsum_type_of_unknown_tag t))\n (sg: serializer g)\n (k: dsum_known_key t)\n (x y: serialize32_dsum_cases_t t f sf g sg k)\n: GTot Type0\n= True", "val validate_sum\n (t: sum)\n (#kt: parser_kind)\n (#p: parser kt (sum_repr_type t))\n (v: validator p)\n (p32: leaf_reader p)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: (x: sum_key t -> Tot (validator (dsnd (pc x)))))\n (destr: dep_maybe_enum_destr_t (sum_enum t) (validate_sum_aux_payload_t t pc))\n : Tot (validator (parse_sum t p pc))\nlet validate_sum\n (t: sum)\n (#kt: parser_kind)\n (#p: parser kt (sum_repr_type t))\n (v: validator p)\n (p32: leaf_reader p)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (validator (dsnd (pc x)))))\n (destr: dep_maybe_enum_destr_t (sum_enum t) (validate_sum_aux_payload_t t pc))\n: Tot (validator (parse_sum t p pc))\n= validate_sum_aux t v p32 pc (validate_sum_aux_payload t pc pc32 destr)", "val serialize32_dsum_cases\n (t: dsum)\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (sf: (x: dsum_known_key t -> Tot (serializer (dsnd (f x)))))\n (sf32: (x: dsum_known_key t -> Tot (serializer32 (sf x))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (#sg: serializer g)\n (sg32: serializer32 sg)\n (destr: dep_enum_destr _ (serialize32_dsum_cases_t t f sf g sg))\n (tg: dsum_key t)\n : Tot (serializer32 (serialize_dsum_cases t f sf g sg tg))\nlet serialize32_dsum_cases\n (t: dsum)\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (sf: (x: dsum_known_key t) -> Tot (serializer (dsnd (f x))))\n (sf32: (x: dsum_known_key t) -> Tot (serializer32 (sf x)))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (#sg: serializer g)\n (sg32: serializer32 sg)\n (destr: dep_enum_destr _ (serialize32_dsum_cases_t t f sf g sg))\n (tg: dsum_key t)\n: Tot (serializer32 (serialize_dsum_cases t f sf g sg tg))\n= fun x #rrel #rel output pos ->\n match tg with\n | Known k ->\n destr\n _\n (serialize32_dsum_cases_t_if t f sf g sg)\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (fun k -> serialize32_dsum_cases_aux t f sf sf32 sg32 (Known k))\n k\n x\n output\n pos\n | Unknown r ->\n serialize32_dsum_cases_aux t f sf sf32 sg32 (Unknown r) x output pos", "val jump_sum_aux_payload\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: (x: sum_key t -> Tot (jumper (dsnd (pc x)))))\n (destr: dep_maybe_enum_destr_t (sum_enum t) (jump_sum_aux_payload_t t pc))\n (k: sum_repr_type t)\n : Tot (jump_sum_aux_payload_t t pc (maybe_enum_key_of_repr (sum_enum t) k))\nlet jump_sum_aux_payload\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (jumper (dsnd (pc x)))))\n (destr: dep_maybe_enum_destr_t (sum_enum t) (jump_sum_aux_payload_t t pc))\n (k: sum_repr_type t)\n: Tot (jump_sum_aux_payload_t t pc (maybe_enum_key_of_repr (sum_enum t) k))\n= destr (jump_sum_aux_payload_eq t pc) (jump_sum_aux_payload_if t pc) (fun _ _ -> ()) (fun _ _ _ _ -> ()) (jump_sum_aux_payload' t pc pc32) k", "val size32_compose_context\n (#pk: parser_kind)\n (#kt1 #kt2: Type)\n (f: (kt2 -> Tot kt1))\n (t: (kt1 -> Tot Type))\n (p: (k: kt1 -> Tot (parser pk (t k))))\n (s: (k: kt1 -> Tot (serializer (p k))))\n (s32: (k: kt1 -> Tot (size32 (s k))))\n (k: kt2)\n : Tot (size32 (s (f k)))\nlet size32_compose_context\n (#pk: parser_kind)\n (#kt1 #kt2: Type)\n (f: (kt2 -> Tot kt1))\n (t: (kt1 -> Tot Type))\n (p: ((k: kt1) -> Tot (parser pk (t k))))\n (s: ((k: kt1) -> Tot (serializer (p k))))\n (s32: ((k: kt1) -> Tot (size32 (s k))))\n (k: kt2)\n: Tot (size32 (s (f k)))\n= fun input -> s32 (f k) input", "val bitsum'_key_type_elim_BitSum'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (x: bitsum'_key_type (BitSum' key key_size e payload))\n : Tot (k': enum_key e & bitsum'_key_type (payload k'))\nlet bitsum'_key_type_elim_BitSum'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (x: bitsum'_key_type (BitSum' key key_size e payload))\n: Tot (k': enum_key e & bitsum'_key_type (payload k'))\n= x", "val serialize32_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (s: serializer p {kt.parser_kind_subkind == Some ParserStrong})\n (s32: serializer32 (serialize_maybe_enum_key _ s (dsum_enum t)))\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (sf: (x: dsum_known_key t -> Tot (serializer (dsnd (f x)))))\n (sf32: (x: dsum_known_key t -> Tot (serializer32 (sf x))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (#sg: serializer g)\n (sg32: serializer32 sg)\n (destr: dep_enum_destr _ (serialize32_dsum_cases_t t f sf g sg))\n : Tot (serializer32 (serialize_dsum t s f sf g sg))\nlet serialize32_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (s: serializer p {kt.parser_kind_subkind == Some ParserStrong})\n (s32: serializer32 (serialize_maybe_enum_key _ s (dsum_enum t)))\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (sf: (x: dsum_known_key t) -> Tot (serializer (dsnd (f x))))\n (sf32: (x: dsum_known_key t) -> Tot (serializer32 (sf x)))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (#sg: serializer g)\n (sg32: serializer32 sg)\n (destr: dep_enum_destr _ (serialize32_dsum_cases_t t f sf g sg))\n: Tot (serializer32 (serialize_dsum t s f sf g sg))\n= fun x #_ #_ output pos ->\n [@inline_let]\n let _ = serialize_dsum_eq' t s f sf g sg x in\n let tg = dsum_tag_of_data t x in\n serialize32_nondep_then_aux\n s32\n (serialize32_dsum_cases t f sf sf32 sg32 destr tg)\n tg\n x\n output\n pos", "val validate_sum_aux_payload\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: (x: sum_key t -> Tot (validator (dsnd (pc x)))))\n (destr: dep_maybe_enum_destr_t (sum_enum t) (validate_sum_aux_payload_t t pc))\n (k: sum_repr_type t)\n : Tot (validate_sum_aux_payload_t t pc (maybe_enum_key_of_repr (sum_enum t) k))\nlet validate_sum_aux_payload\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (validator (dsnd (pc x)))))\n (destr: dep_maybe_enum_destr_t (sum_enum t) (validate_sum_aux_payload_t t pc))\n (k: sum_repr_type t)\n: Tot (validate_sum_aux_payload_t t pc (maybe_enum_key_of_repr (sum_enum t) k))\n= destr (validate_sum_aux_payload_eq t pc) (validate_sum_aux_payload_if t pc) (fun _ _ -> ()) (fun _ _ _ _ -> ()) (validate_sum_aux_payload' t pc pc32) k", "val sum_key_type (t: sum) : Tot eqtype\nlet sum_key_type (t: sum) : Tot eqtype =\n match t with (Sum key _ _ _ _ _ _ _ _ _) -> key", "val serialize32_dsum_cases_aux\n (t: dsum)\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (sf: (x: dsum_known_key t -> Tot (serializer (dsnd (f x)))))\n (sf32: (x: dsum_known_key t -> Tot (serializer32 (sf x))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (#sg: serializer g)\n (sg32: serializer32 sg)\n (tg: dsum_key t)\n : Tot (serializer32 (serialize_dsum_cases t f sf g sg tg))\nlet serialize32_dsum_cases_aux\n (t: dsum)\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (sf: (x: dsum_known_key t) -> Tot (serializer (dsnd (f x))))\n (sf32: (x: dsum_known_key t) -> Tot (serializer32 (sf x)))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (#sg: serializer g)\n (sg32: serializer32 sg)\n (tg: dsum_key t)\n: Tot (serializer32 (serialize_dsum_cases t f sf g sg tg))\n= [@inline_let]\n let _ = synth_dsum_case_injective t tg in\n [@inline_let]\n let _ = synth_dsum_case_inverse t tg in\n serialize32_synth\n (serialize32_dsum_type_of_tag t f sf sf32 sg32 tg)\n (synth_dsum_case t tg) \n (synth_dsum_case_recip t tg)\n (fun x -> synth_dsum_case_recip t tg x)\n ()", "val destr_bitsum'_bitsum_t\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) {e == l1 `L.append` l2})\n : Tot (Type u#(a + 1))\nlet destr_bitsum'_bitsum_t\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) { e == l1 `L.append` l2 } )\n: Tot (Type u#(a + 1))\n= (u: (bitsum'_type (BitSum' key key_size e payload) -> Tot (Type u#a))) ->\n (u_if: ((x: Ghost.erased (bitsum'_type (BitSum' key key_size e payload))) -> Tot (if_combinator_weak (u (Ghost.reveal x))))) ->\n (f: ((x: bitsum'_type (BitSum' key key_size e payload)) -> Tot (u x))) ->\n (x: parse_filter_refine (filter_bitsum' (BitSum' key key_size e payload)) { ~ (list_mem (cl.get_bitfield x (bitsum'_size - key_size) bitsum'_size <: bitfield cl key_size) (list_map snd l1)) }) ->\n Tot (u (synth_bitsum' (BitSum' key key_size e payload) x))", "val bitsum'_key_of_t\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n (x: bitsum'_type b)\n : Tot (bitsum'_key_type b) (decreases (bitsum'_size))\nlet rec bitsum'_key_of_t\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n (x: bitsum'_type b)\n: Tot (bitsum'_key_type b)\n (decreases (bitsum'_size))\n= match b with\n | BitStop _ -> ()\n | BitField sz rest ->\n begin match bitsum'_type_elim_BitField cl bitsum'_size sz rest x with\n | (_, tl) ->\n bitsum'_key_type_intro_BitField cl bitsum'_size sz rest (bitsum'_key_of_t rest tl)\n end\n | BitSum' key key_size e payload ->\n begin match bitsum'_type_elim_BitSum' cl bitsum'_size key key_size e payload x with\n | (| k, pl |) ->\n bitsum'_key_type_intro_BitSum' cl bitsum'_size key key_size e payload (| k, bitsum'_key_of_t (payload k) pl |)\n end", "val jump_sum\n (t: sum)\n (#kt: parser_kind)\n (#p: parser kt (sum_repr_type t))\n (v: jumper p)\n (p32: leaf_reader p)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: (x: sum_key t -> Tot (jumper (dsnd (pc x)))))\n (destr: dep_maybe_enum_destr_t (sum_enum t) (jump_sum_aux_payload_t t pc))\n : Tot (jumper (parse_sum t p pc))\nlet jump_sum\n (t: sum)\n (#kt: parser_kind)\n (#p: parser kt (sum_repr_type t))\n (v: jumper p)\n (p32: leaf_reader p)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (jumper (dsnd (pc x)))))\n (destr: dep_maybe_enum_destr_t (sum_enum t) (jump_sum_aux_payload_t t pc))\n: Tot (jumper (parse_sum t p pc))\n= jump_sum_aux t v p32 pc (jump_sum_aux_payload t pc pc32 destr)", "val jump_sum_aux_payload_if'\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n (cond: bool)\n (ift: ((cond_true cond) -> Tot (jump_sum_aux_payload_t t pc k)))\n (iff: ((cond_false cond) -> Tot (jump_sum_aux_payload_t t pc k)))\n : Tot (jump_sum_aux_payload_t t pc k)\nlet jump_sum_aux_payload_if'\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n (cond: bool)\n (ift: ((cond_true cond) -> Tot (jump_sum_aux_payload_t t pc k)))\n (iff: ((cond_false cond) -> Tot (jump_sum_aux_payload_t t pc k)))\n: Tot (jump_sum_aux_payload_t t pc k)\n= fun #rrel #rel input pos ->\n if cond\n then begin\n (ift () <: jump_sum_aux_payload_t t pc k) input pos\n end else\n (iff () <: jump_sum_aux_payload_t t pc k) input pos", "val validate_sum_aux_payload_if'\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n (cond: bool)\n (ift: ((cond_true cond) -> Tot (validate_sum_aux_payload_t t pc k)))\n (iff: ((cond_false cond) -> Tot (validate_sum_aux_payload_t t pc k)))\n : Tot (validate_sum_aux_payload_t t pc k)\nlet validate_sum_aux_payload_if'\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n (cond: bool)\n (ift: ((cond_true cond) -> Tot (validate_sum_aux_payload_t t pc k)))\n (iff: ((cond_false cond) -> Tot (validate_sum_aux_payload_t t pc k)))\n: Tot (validate_sum_aux_payload_t t pc k)\n= fun #rrel #rel input pos ->\n if cond\n then begin\n (ift () <: validate_sum_aux_payload_t t pc k) input pos\n end else\n (iff () <: validate_sum_aux_payload_t t pc k) input pos", "val synth_bitsum'_recip_BitSum_cons_nil\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (k: key)\n (r:\n bitfield cl key_size\n { e == l1 `L.append` ([(k, r)]) /\\ list_mem k (list_map fst e) /\\\n enum_repr_of_key e k == r /\\ e == (l1 `L.append` [(k, r)]) `L.append` [] })\n (destr_payload: synth_bitsum'_recip_t (payload k))\n : Tot (synth_bitsum'_recip_BitSum_t cl bitsum'_size key key_size e payload l1 ([(k, r)]))\nlet synth_bitsum'_recip_BitSum_cons_nil\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (k: key)\n (r: bitfield cl key_size {\n e == l1 `L.append` ((k, r) :: []) /\\\n list_mem k (list_map fst e) /\\\n enum_repr_of_key e k == r /\\\n e == (l1 `L.append` [(k, r)]) `L.append` []\n })\n (destr_payload: synth_bitsum'_recip_t (payload k))\n: Tot (synth_bitsum'_recip_BitSum_t cl bitsum'_size key key_size e payload l1 ((k, r) :: []))\n= fun k' rest ->\n [@inline_let]\n let _ =\n enum_repr_of_key_append_cons e l1 (k, r) []\n in\n [@inline_let]\n let _ : squash (k' = k) =\n if (k' = k)\n then ()\n else begin\n L.append_assoc l1 [(k, r)] [];\n L.map_append fst l1 [(k, r)];\n L.append_mem (L.map fst l1) (L.map fst [(k, r)]) (k' <: key)\n end\n in\n [@inline_let]\n let _ =\n assert_norm (synth_bitsum'_recip (BitSum' key key_size e payload) (| k', rest |) == cl.set_bitfield (synth_bitsum'_recip (payload k') rest) (bitsum'_size - key_size) bitsum'_size (enum_repr_of_key e k'))\n in\n (cl.set_bitfield (destr_payload rest) (bitsum'_size - key_size) bitsum'_size r <: t)", "val bitsum'_key_type\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n : Tot eqtype (decreases (bitsum'_size))\nlet rec bitsum'_key_type\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n: Tot eqtype\n (decreases (bitsum'_size))\n= match b with\n | BitStop _ -> unit\n | BitField sz rest -> bitsum'_key_type rest\n | BitSum' key key_size e payload ->\n (key: enum_key e & bitsum'_key_type (payload key))", "val filter_bitsum'_bitsum'_cons\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (k: key)\n (r: bitfield cl key_size)\n (l2:\n list (key & bitfield cl key_size)\n { e == l1 `L.append` ((k, r) :: l2) /\\ list_mem k (list_map fst e) /\\\n enum_repr_of_key e k == r /\\ e == (l1 `L.append` [(k, r)]) `L.append` l2 })\n (destr_payload: filter_bitsum'_t (payload k))\n (destr_tail:\n filter_bitsum'_bitsum'_t cl\n bitsum'_size\n key\n key_size\n e\n payload\n (l1 `L.append` [(k, r)])\n l2)\n : Tot (filter_bitsum'_bitsum'_t cl bitsum'_size key key_size e payload l1 ((k, r) :: l2))\nlet filter_bitsum'_bitsum'_cons\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (k: key)\n (r: bitfield cl key_size)\n (l2: list (key & bitfield cl key_size) {\n e == l1 `L.append` ((k, r) :: l2) /\\\n list_mem k (list_map fst e) /\\\n enum_repr_of_key e k == r /\\\n e == (l1 `L.append` [(k, r)]) `L.append` l2\n })\n (destr_payload: filter_bitsum'_t (payload k))\n (destr_tail: filter_bitsum'_bitsum'_t cl bitsum'_size key key_size e payload (l1 `L.append` [(k, r)]) l2)\n: Tot (filter_bitsum'_bitsum'_t cl bitsum'_size key key_size e payload l1 ((k, r) :: l2))\n= fun x xr ->\n [@inline_let] let _ =\n enum_repr_of_key_append_cons e l1 (k, r) l2\n in\n [@inline_let] let yr = cl.bitfield_eq_rhs x (bitsum'_size - key_size) bitsum'_size r in\n [@inline_let] let cond = (xr <: t) = yr in\n [@inline_let] let _ =\n assert (cond == true <==> (cl.get_bitfield x (bitsum'_size - key_size) bitsum'_size <: bitfield cl key_size) == r)\n in\n if cond\n then\n destr_payload x\n else\n [@inline_let] let _ =\n L.append_assoc l1 [(k, r)] l2;\n L.map_append snd l1 [(k, r)];\n L.append_mem (L.map snd l1) (L.map snd [(k, r)]) (cl.get_bitfield x (bitsum'_size - key_size) bitsum'_size <: bitfield cl key_size)\n in\n destr_tail (x <: t) xr", "val synth_bitsum'_recip_BitSum_cons\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (k: key)\n (r: bitfield cl key_size)\n (l2:\n list (key & bitfield cl key_size)\n { e == l1 `L.append` ((k, r) :: l2) /\\ list_mem k (list_map fst e) /\\\n enum_repr_of_key e k == r /\\ e == (l1 `L.append` [(k, r)]) `L.append` l2 })\n (destr_payload: synth_bitsum'_recip_t (payload k))\n (destr_tail:\n synth_bitsum'_recip_BitSum_t cl\n bitsum'_size\n key\n key_size\n e\n payload\n (l1 `L.append` [(k, r)])\n l2)\n : Tot (synth_bitsum'_recip_BitSum_t cl bitsum'_size key key_size e payload l1 ((k, r) :: l2))\nlet synth_bitsum'_recip_BitSum_cons\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (k: key)\n (r: bitfield cl key_size)\n (l2: list (key & bitfield cl key_size) {\n e == l1 `L.append` ((k, r) :: l2) /\\\n list_mem k (list_map fst e) /\\\n enum_repr_of_key e k == r /\\\n e == (l1 `L.append` [(k, r)]) `L.append` l2\n })\n (destr_payload: synth_bitsum'_recip_t (payload k))\n (destr_tail: synth_bitsum'_recip_BitSum_t cl bitsum'_size key key_size e payload (l1 `L.append` [(k, r)]) l2)\n: Tot (synth_bitsum'_recip_BitSum_t cl bitsum'_size key key_size e payload l1 ((k, r) :: l2))\n= fun k' rest ->\n [@inline_let]\n let _ =\n enum_repr_of_key_append_cons e l1 (k, r) l2\n in\n if k' = k\n then begin\n [@inline_let]\n let _ =\n assert_norm (synth_bitsum'_recip (BitSum' key key_size e payload) (| k', rest |) == cl.set_bitfield (synth_bitsum'_recip (payload k') rest) (bitsum'_size - key_size) bitsum'_size (enum_repr_of_key e k'))\n in\n (cl.set_bitfield (destr_payload rest) (bitsum'_size - key_size) bitsum'_size r <: t)\n end else\n [@inline_let] let _ =\n L.append_assoc l1 [(k, r)] l2;\n L.map_append fst l1 [(k, r)];\n L.append_mem (L.map fst l1) (L.map fst [(k, r)]) (k' <: key)\n in\n destr_tail (k' <: key) rest", "val serialize32_bitsum_cond\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (b: bitsum' cl tot)\n (k: parser_kind)\n (type_of_tag: (bitsum'_key_type b -> Tot Type))\n (f: (x: bitsum'_key_type b -> Tot (k: parser_kind & parser k (type_of_tag x))))\n : Tot bool\nlet serialize32_bitsum_cond\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (b: bitsum' cl tot)\n (k: parser_kind)\n (type_of_tag: (bitsum'_key_type b -> Tot Type))\n (f: (x: bitsum'_key_type b) -> Tot (k: parser_kind & parser k (type_of_tag x)))\n: Tot bool\n= match k.parser_kind_high, (weaken_parse_bitsum_cases_kind b type_of_tag f).parser_kind_high with\n | Some max1, Some max2 -> max1 + max2 < 4294967296\n | _ -> false", "val read_sum\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (p32: leaf_reader (parse_enum_key p (sum_enum t)))\n (j: jumper p)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: (x: sum_key t -> Tot (leaf_reader (dsnd (pc x)))))\n (destr: dep_enum_destr (sum_enum t) (read_sum_cases_t t pc))\n : Tot (leaf_reader (parse_sum t p pc))\nlet read_sum\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (p32: leaf_reader (parse_enum_key p (sum_enum t)))\n (j: jumper p)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (leaf_reader (dsnd (pc x)))))\n (destr: dep_enum_destr (sum_enum t) (read_sum_cases_t t pc))\n: Tot (leaf_reader (parse_sum t p pc))\n=\n fun #_ #_ input pos ->\n let h = HST.get () in\n valid_facts (parse_sum t p pc) h input pos;\n parse_sum_eq' t p pc (bytes_of_slice_from h input pos);\n valid_facts (parse_enum_key p (sum_enum t)) h input pos;\n let k = p32 input pos in\n let pos' = jump_enum_key j (sum_enum t) input pos in\n valid_facts (parse_sum_cases' t pc k) h input pos' ;\n read_sum_cases t pc pc32 destr k input pos'", "val destr_bitsum'_t (#tot: pos) (#t: eqtype) (#cl: uint_t tot t) (#from: nat) (b: bitsum' cl from)\n : Tot (Type u#(a + 1))\nlet destr_bitsum'_t\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#from: nat)\n (b: bitsum' cl from)\n: Tot (Type u#(a + 1))\n= (u: (bitsum'_type b -> Tot (Type u#a))) ->\n (u_if: ((k: Ghost.erased (bitsum'_type b)) -> Tot (if_combinator_weak (u (Ghost.reveal k))))) ->\n (f: ((k: bitsum'_type b) -> Tot (u k))) ->\n (x: parse_filter_refine (filter_bitsum' b)) ->\n Tot (u (synth_bitsum' b x))", "val read_sum_cases\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: (x: sum_key t -> Tot (leaf_reader (dsnd (pc x)))))\n (destr: dep_enum_destr (sum_enum t) (read_sum_cases_t t pc))\n (k: sum_key t)\n : Tot (leaf_reader (parse_sum_cases' t pc k))\nlet read_sum_cases \n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (leaf_reader (dsnd (pc x)))))\n (destr: dep_enum_destr (sum_enum t) (read_sum_cases_t t pc))\n (k: sum_key t)\n: Tot (leaf_reader (parse_sum_cases' t pc k))\n= destr\n _\n (read_sum_cases_t_if t pc)\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (read_sum_cases' t pc pc32)\n k", "val bitsum'_key_type_intro_BitSum'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (x: (k': enum_key e & bitsum'_key_type (payload k')))\n : Tot (bitsum'_key_type (BitSum' key key_size e payload))\nlet bitsum'_key_type_intro_BitSum'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (x: (k': enum_key e & bitsum'_key_type (payload k')))\n: Tot (bitsum'_key_type (BitSum' key key_size e payload))\n= x", "val bitsum'_type_elim_BitSum'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (x: bitsum'_type (BitSum' key key_size e payload))\n : Tot (bitsum'_type_bitsum' cl bitsum'_size key key_size e payload)\nlet bitsum'_type_elim_BitSum'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (x: bitsum'_type (BitSum' key key_size e payload))\n: Tot (bitsum'_type_bitsum' cl bitsum'_size key key_size e payload)\n= x", "val serialize32_bitsum\n (#kt: parser_kind)\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (b: bitsum' cl tot)\n (#data: Type)\n (tag_of_data: (data -> Tot (bitsum'_type b)))\n (type_of_tag: (bitsum'_key_type b -> Tot Type))\n (synth_case: synth_case_t b data tag_of_data type_of_tag)\n (#p: parser kt t)\n (#s: serializer p)\n (s32: serializer32 s {kt.parser_kind_subkind == Some ParserStrong})\n (#f: (x: bitsum'_key_type b -> Tot (k: parser_kind & parser k (type_of_tag x))))\n (g: (x: bitsum'_key_type b -> Tot (serializer (dsnd (f x)))))\n (g32: (x: bitsum'_key_type b -> Tot (serializer32 (g x))))\n (sq: squash (serialize32_bitsum_cond b kt type_of_tag f))\n : Tot (serializer32 (serialize_bitsum b tag_of_data type_of_tag synth_case s #f g))\nlet serialize32_bitsum\n (#kt: parser_kind)\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (b: bitsum' cl tot)\n (#data: Type)\n (tag_of_data: (data -> Tot (bitsum'_type b)))\n (type_of_tag: (bitsum'_key_type b -> Tot Type))\n (synth_case: synth_case_t b data tag_of_data type_of_tag)\n (#p: parser kt t)\n (#s: serializer p)\n (s32: serializer32 s { kt.parser_kind_subkind == Some ParserStrong } )\n (#f: (x: bitsum'_key_type b) -> Tot (k: parser_kind & parser k (type_of_tag x)))\n (g: (x: bitsum'_key_type b) -> Tot (serializer (dsnd (f x))))\n (g32: (x: bitsum'_key_type b) -> Tot (serializer32 (g x)))\n (sq: squash (\n serialize32_bitsum_cond b kt type_of_tag f\n ))\n: Tot (serializer32 (serialize_bitsum b tag_of_data type_of_tag synth_case s #f g))\n=\n fun x ->\n serialize_bitsum_eq b tag_of_data type_of_tag synth_case s g x;\n let tg = tag_of_data x in\n let k = bitsum'_key_of_t b tg in\n let payload = synth_case.g tg x in\n let s_tg = s32 (synth_bitsum'_recip b tg) in\n let s_pl = g32 k payload in\n s_tg `B32.append` s_pl", "val dsum_key_type (t: dsum) : Tot eqtype\nlet dsum_key_type (t: dsum) : Tot eqtype =\n match t with (DSum key _ _ _ _ _ _ _ _ _ _) -> key", "val validate_dsum_cases'_destr\n (s: dsum)\n (f: (x: dsum_known_key s -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag s x))))\n (f': (x: dsum_known_key s -> Tot (validator (dsnd (f x)))))\n (#k: parser_kind)\n (#g: parser k (dsum_type_of_unknown_tag s))\n (g': validator g)\n (destr: dep_enum_destr _ (fun k -> validate_dsum_cases_t s f g (Known k)))\n (x: dsum_key s)\n : Tot (validate_dsum_cases_t s f g x)\nlet validate_dsum_cases'_destr\n (s: dsum)\n (f: (x: dsum_known_key s) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag s x)))\n (f' : (x: dsum_known_key s) -> Tot (validator (dsnd (f x))))\n (#k: parser_kind)\n (#g: parser k (dsum_type_of_unknown_tag s))\n (g' : validator g)\n (destr: dep_enum_destr _ (fun k -> validate_dsum_cases_t s f g (Known k)))\n (x: dsum_key s)\n: Tot (validate_dsum_cases_t s f g x)\n= fun #rrel #rel input pos ->\n match x with\n | Known k ->\n destr\n _\n (fun k -> validate_dsum_cases_if s f g (Known k))\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (fun k -> validate_dsum_cases' s f f' g' (Known k))\n k\n input\n pos\n | Unknown r -> validate_dsum_cases' s f f' g' (Unknown r) input pos", "val validate_sum_aux\n (t: sum)\n (#kt: parser_kind)\n (#p: parser kt (sum_repr_type t))\n (v: validator p)\n (p32: leaf_reader p)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (v_payload:\n (k: sum_repr_type t\n -> Tot (validate_sum_aux_payload_t t pc (maybe_enum_key_of_repr (sum_enum t) k))))\n : Tot (validator (parse_sum t p pc))\nlet validate_sum_aux\n (t: sum)\n (#kt: parser_kind)\n (#p: parser kt (sum_repr_type t))\n (v: validator p)\n (p32: leaf_reader p)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (v_payload: ((k: sum_repr_type t)) -> Tot (validate_sum_aux_payload_t t pc (maybe_enum_key_of_repr (sum_enum t) k)))\n: Tot (validator (parse_sum t p pc))\n= fun #rrel #rel input pos ->\n let h = HST.get () in\n [@inline_let]\n let _ = parse_sum_eq'' t p pc (bytes_of_slice_from h input (uint64_to_uint32 pos)) in\n [@inline_let]\n let _ = valid_facts (parse_sum t p pc) h input (uint64_to_uint32 pos) in\n [@inline_let]\n let _ = valid_facts p h input (uint64_to_uint32 pos) in\n let len_after_tag = v input pos in\n if is_error len_after_tag\n then len_after_tag\n else begin\n let h1 = HST.get () in\n let k' = p32 input (uint64_to_uint32 pos) in\n [@inline_let]\n let _ =\n match maybe_enum_key_of_repr (sum_enum t) k' with\n | Known k -> valid_facts (dsnd (pc k)) h input (uint64_to_uint32 len_after_tag)\n | _ -> ()\n in\n v_payload k' input len_after_tag\n end", "val validate_sum_cases\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (vc: (x: sum_key t -> Tot (validator (dsnd (pc x)))))\n (destr: dep_enum_destr (sum_enum t) (validate_sum_cases_t t pc))\n (k: sum_key t)\n : Tot (validator (parse_sum_cases t pc k))\nlet validate_sum_cases \n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (vc: ((x: sum_key t) -> Tot (validator (dsnd (pc x)))))\n (destr: dep_enum_destr (sum_enum t) (validate_sum_cases_t t pc))\n (k: sum_key t)\n: Tot (validator (parse_sum_cases t pc k))\n= destr\n _\n (validate_sum_cases_t_if t pc)\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (validate_sum_cases_aux t pc vc)\n k", "val validate_dsum_cases_if\n (s: dsum)\n (f: (x: dsum_known_key s -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag s x))))\n (#k: parser_kind)\n (g: parser k (dsum_type_of_unknown_tag s))\n (x: dsum_key s)\n : Tot (if_combinator _ (validate_dsum_cases_eq s f g x))\nlet validate_dsum_cases_if\n (s: dsum)\n (f: (x: dsum_known_key s) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag s x)))\n (#k: parser_kind)\n (g: parser k (dsum_type_of_unknown_tag s))\n (x: dsum_key s)\n: Tot (if_combinator _ (validate_dsum_cases_eq s f g x))\n= validate_dsum_cases_if' s f g x", "val mk_filter_bitsum'_t'\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n : Tot (filter_bitsum'_t b) (decreases %[b;1;()])\nlet rec mk_filter_bitsum'_t'\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n: Tot (filter_bitsum'_t b)\n (decreases %[b; 1; ()])\n= match b with\n | BitStop _ -> filter_bitsum'_bitstop cl\n | BitField sz rest -> filter_bitsum'_bitfield cl bitsum'_size sz rest (mk_filter_bitsum'_t' rest)\n | BitSum' key key_size e payload ->\n filter_bitsum'_bitsum'_intro cl bitsum'_size key key_size e payload (mk_filter_bitsum'_bitsum'_t' cl bitsum'_size key key_size e payload [] e)\nand mk_filter_bitsum'_bitsum'_t'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) { e == l1 `L.append` l2 } )\n: Tot (filter_bitsum'_bitsum'_t cl bitsum'_size key key_size e payload l1 l2)\n (decreases %[BitSum' key key_size e payload; 0; l2])\n= bitsum_wellfoundedness (BitSum' key key_size e payload);\n match l2 with\n | [] ->\n [@inline_let] let _ =\n L.append_l_nil l1\n in\n filter_bitsum'_bitsum'_nil cl bitsum'_size key key_size e payload ()\n | (k, r) :: q ->\n [@inline_let] let _ =\n enum_repr_of_key_append_cons e l1 (k, r) q;\n L.append_assoc l1 [(k, r)] q\n in\n filter_bitsum'_bitsum'_cons cl bitsum'_size key key_size e payload l1 k r q\n (mk_filter_bitsum'_t' (payload k))\n (mk_filter_bitsum'_bitsum'_t' cl bitsum'_size key key_size e payload (l1 `L.append` [(k, r)]) q)", "val size32_weaken\n (k1 #k2: parser_kind)\n (#t: Type)\n (#p2: parser k2 t)\n (#s2: serializer p2)\n (s2': size32 s2 {k1 `is_weaker_than` k2})\n : Tot (size32 (serialize_weaken k1 s2))\nlet size32_weaken\n (k1: parser_kind)\n (#k2: parser_kind)\n (#t: Type)\n (#p2: parser k2 t)\n (#s2: serializer p2)\n (s2' : size32 s2 { k1 `is_weaker_than` k2 })\n: Tot (size32 (serialize_weaken k1 s2))\n= fun x -> s2' x", "val mk_filter_bitsum'_bitsum'_t'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) {e == l1 `L.append` l2})\n : Tot (filter_bitsum'_bitsum'_t cl bitsum'_size key key_size e payload l1 l2)\n (decreases %[BitSum' key key_size e payload;0;l2])\nlet rec mk_filter_bitsum'_t'\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n: Tot (filter_bitsum'_t b)\n (decreases %[b; 1; ()])\n= match b with\n | BitStop _ -> filter_bitsum'_bitstop cl\n | BitField sz rest -> filter_bitsum'_bitfield cl bitsum'_size sz rest (mk_filter_bitsum'_t' rest)\n | BitSum' key key_size e payload ->\n filter_bitsum'_bitsum'_intro cl bitsum'_size key key_size e payload (mk_filter_bitsum'_bitsum'_t' cl bitsum'_size key key_size e payload [] e)\nand mk_filter_bitsum'_bitsum'_t'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) { e == l1 `L.append` l2 } )\n: Tot (filter_bitsum'_bitsum'_t cl bitsum'_size key key_size e payload l1 l2)\n (decreases %[BitSum' key key_size e payload; 0; l2])\n= bitsum_wellfoundedness (BitSum' key key_size e payload);\n match l2 with\n | [] ->\n [@inline_let] let _ =\n L.append_l_nil l1\n in\n filter_bitsum'_bitsum'_nil cl bitsum'_size key key_size e payload ()\n | (k, r) :: q ->\n [@inline_let] let _ =\n enum_repr_of_key_append_cons e l1 (k, r) q;\n L.append_assoc l1 [(k, r)] q\n in\n filter_bitsum'_bitsum'_cons cl bitsum'_size key key_size e payload l1 k r q\n (mk_filter_bitsum'_t' (payload k))\n (mk_filter_bitsum'_bitsum'_t' cl bitsum'_size key key_size e payload (l1 `L.append` [(k, r)]) q)", "val validate_bitsum_cases_bitsum_gen\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (key_of: (x: enum_repr e -> Tot (y: enum_key e {y == enum_key_of_repr e x})))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (destr_payload: (k: enum_key e -> Tot (validate_bitsum_cases_t u#r (payload k))))\n : Tot (validate_bitsum_cases_t u#r (BitSum' key key_size e payload))\nlet validate_bitsum_cases_bitsum_gen\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (key_of: ((x: enum_repr e) -> Tot (y: enum_key e { y == enum_key_of_repr e x })))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (destr_payload: ((k: enum_key e) -> Tot (validate_bitsum_cases_t u#r (payload k))))\n: Tot (validate_bitsum_cases_t u#r (BitSum' key key_size e payload))\n= fun u f v x_ #rrel #rel sl pos ->\n [@inline_let]\n let r = cl.get_bitfield x_ (bitsum'_size - key_size) bitsum'_size in\n [@inline_let]\n let k = key_of r in\n destr_payload \n k\n (fun x -> u (bitsum'_key_type_intro_BitSum' cl bitsum'_size key key_size e payload (| k, x |)))\n (fun x -> f (bitsum'_key_type_intro_BitSum' cl bitsum'_size key key_size e payload (| k, x |)))\n (fun x -> v (bitsum'_key_type_intro_BitSum' cl bitsum'_size key key_size e payload (| k, x |)))\n x_ sl pos", "val size32_nondep_then\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (#s1: serializer p1)\n (s1': size32 s1 {k1.parser_kind_subkind == Some ParserStrong})\n (#k2: parser_kind)\n (#t2: Type)\n (#p2: parser k2 t2)\n (#s2: serializer p2)\n (s2': size32 s2)\n : Tot (size32 (serialize_nondep_then s1 s2))\nlet size32_nondep_then\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (#s1: serializer p1)\n (s1' : size32 s1 { k1.parser_kind_subkind == Some ParserStrong } )\n (#k2: parser_kind)\n (#t2: Type)\n (#p2: parser k2 t2)\n (#s2: serializer p2)\n (s2' : size32 s2)\n: Tot (size32 (serialize_nondep_then s1 s2))\n= fun x ->\n [@inline_let] let _ = serialize_nondep_then_eq s1 s2 x in\n match x with\n | (x1, x2) ->\n let v1 = s1' x1 in\n let v2 = s2' x2 in\n let res = add_overflow v1 v2 in\n (res <: (z : U32.t { size32_postcond (serialize_nondep_then s1 s2) x z } ))", "val bitfields_destr_cons_nil\n (#tot: pos)\n (#t: Type)\n (cl: uint_t tot t)\n (lo: nat)\n (sz: nat{lo + sz <= tot})\n : Tot (bitfields_destr_t cl lo (lo + sz) [sz])\nlet bitfields_destr_cons_nil\n (#tot: pos)\n (#t: Type)\n (cl: uint_t tot t)\n (lo: nat)\n (sz: nat { lo + sz <= tot })\n: Tot (bitfields_destr_t cl lo (lo + sz) [sz])\n= fun f_t f x ->\n f (cl.get_bitfield x lo (lo + sz))", "val parse_sum_eq4\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (input: bytes)\n (k': sum_repr_type t)\n (consumed_k: consumed_length input)\n (consumed_payload: nat)\n : Lemma\n (requires\n (Some? (parse (parse_sum t p pc) input) /\\ parse p input == Some (k', consumed_k) /\\\n (let input_k = Seq.slice input consumed_k (Seq.length input) in\n let k = maybe_enum_key_of_repr (sum_enum t) k' in\n match k with\n | Known k ->\n Some? (parse (dsnd (pc k)) input_k) /\\\n (let Some (_, consumed_payload') = parse (dsnd (pc k)) input_k in\n consumed_payload' == consumed_payload)\n | _ -> False)))\n (ensures\n (let Some (_, consumed) = parse (parse_sum t p pc) input in\n consumed == consumed_k + consumed_payload))\nlet parse_sum_eq4\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (input: bytes)\n (k' : sum_repr_type t)\n (consumed_k: consumed_length input)\n (consumed_payload: nat)\n: Lemma\n (requires (Some? (parse (parse_sum t p pc) input) /\\ parse p input == Some (k', consumed_k) /\\ (\n let input_k = Seq.slice input consumed_k (Seq.length input) in\n let k = maybe_enum_key_of_repr (sum_enum t) k' in\n begin match k with\n | Known k ->\n Some? (parse (dsnd (pc k)) input_k) /\\ (\n let Some (_, consumed_payload') = parse (dsnd (pc k)) input_k in\n consumed_payload' == consumed_payload\n )\n | _ -> False\n end\n )))\n (ensures (\n let Some (_, consumed) = parse (parse_sum t p pc) input in\n consumed == consumed_k + consumed_payload\n ))\n= parse_sum_eq'' t p pc input", "val clens_sum_cases_payload (s: sum) (k: sum_key s)\n : Tot (clens (sum_cases s k) (sum_type_of_tag s k))\nlet clens_sum_cases_payload\n (s: sum)\n (k: sum_key s)\n: Tot (clens (sum_cases s k) (sum_type_of_tag s k))\n= {\n clens_cond = (fun (x: sum_cases s k) -> True);\n clens_get = (fun (x: sum_cases s k) -> synth_sum_case_recip s k x <: Ghost (sum_type_of_tag s k) (requires (True)) (ensures (fun _ -> True)));\n }", "val validate_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (v: validator p)\n (p32: leaf_reader p)\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (f32: (x: dsum_known_key t -> Tot (validator (dsnd (f x)))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (g32: validator g)\n (destr: dep_maybe_enum_destr_t (dsum_enum t) (validate_dsum_cases_t t f g))\n : Tot (validator (parse_dsum t p f g))\nlet validate_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (v: validator p)\n (p32: leaf_reader p)\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (f32: (x: dsum_known_key t) -> Tot (validator (dsnd (f x))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (g32: validator g)\n (destr: dep_maybe_enum_destr_t (dsum_enum t) (validate_dsum_cases_t t f g))\n: Tot (validator (parse_dsum t p f g))\n= fun #rrel #rel input pos ->\n let h = HST.get () in\n [@inline_let]\n let _ = parse_dsum_eq' t p f g (bytes_of_slice_from h input (uint64_to_uint32 pos)) in\n [@inline_let]\n let _ = valid_facts (parse_dsum t p f g) h input (uint64_to_uint32 pos) in\n [@inline_let]\n let _ = valid_facts p h input (uint64_to_uint32 pos) in\n let pos_after_tag = v input pos in\n if is_error pos_after_tag\n then pos_after_tag\n else\n let tg = p32 input (uint64_to_uint32 pos) in\n [@inline_let]\n let _ = valid_facts (parse_dsum_cases' t f g (maybe_enum_key_of_repr (dsum_enum t) tg)) h input (uint64_to_uint32 pos_after_tag) in\n destr (validate_dsum_cases_eq t f g) (validate_dsum_cases_if t f g) (fun _ _ -> ()) (fun _ _ _ _ -> ()) (validate_dsum_cases' t f f32 g32) tg input pos_after_tag", "val read_sum_cases'\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: (x: sum_key t -> Tot (leaf_reader (dsnd (pc x)))))\n (k: sum_key t)\n : Tot (leaf_reader (parse_sum_cases' t pc k))\nlet read_sum_cases'\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (leaf_reader (dsnd (pc x)))))\n (k: sum_key t)\n: Tot (leaf_reader (parse_sum_cases' t pc k))\n= [@inline_let]\n let _ = synth_sum_case_injective t k in\n read_synth'\n (dsnd (pc k))\n (synth_sum_case t k)\n (pc32 k)\n ()", "val filter_bitsum'\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n (x: t)\n : Tot bool (decreases (bitsum'_size))\nlet rec filter_bitsum'\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n (x: t)\n: Tot bool\n (decreases (bitsum'_size))\n= match b with\n | BitStop _ -> true\n | BitField _ rest -> filter_bitsum' rest x\n | BitSum' key key_size e payload ->\n let f : bitfield cl key_size = cl.get_bitfield x (bitsum'_size - key_size) bitsum'_size in\n if list_mem f (list_map snd e)\n then\n let k = enum_key_of_repr e f in\n filter_bitsum' (payload k) x\n else\n false", "val filter_bitsum'_bitsum_gen\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (is_valid_repr: (x: bitfield cl key_size -> Tot (y: bool{y == list_mem x (list_map snd e)})))\n (key_of: (x: enum_repr e -> Tot (y: enum_key e {y == enum_key_of_repr e x})))\n (destr_payload: (k: enum_key e -> filter_bitsum'_t (payload k)))\n : Tot (filter_bitsum'_t (BitSum' key key_size e payload))\nlet filter_bitsum'_bitsum_gen\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (is_valid_repr: ((x: bitfield cl key_size) -> Tot (y: bool { y == list_mem x (list_map snd e) })))\n (key_of: ((x: enum_repr e) -> Tot (y: enum_key e { y == enum_key_of_repr e x })))\n (destr_payload: ((k: enum_key e) -> filter_bitsum'_t (payload k)))\n: Tot (filter_bitsum'_t (BitSum' key key_size e payload))\n= fun x ->\n let r : bitfield cl key_size = cl.get_bitfield x (bitsum'_size - key_size) bitsum'_size in\n if not (is_valid_repr r)\n then\n false\n else\n destr_payload (key_of r) x", "val clens_sum_payload (s: sum) (k: sum_key s) : Tot (clens (sum_type s) (sum_type_of_tag s k))\nlet clens_sum_payload\n (s: sum)\n (k: sum_key s)\n: Tot (clens (sum_type s) (sum_type_of_tag s k))\n= {\n clens_cond = (fun (x: sum_type s) -> sum_tag_of_data s x == k);\n clens_get = (fun (x: sum_type s) -> synth_sum_case_recip s k x <: Ghost (sum_type_of_tag s k) (requires (sum_tag_of_data s x == k)) (ensures (fun _ -> True)));\n }", "val jump_sum_aux\n (t: sum)\n (#kt: parser_kind)\n (#p: parser kt (sum_repr_type t))\n (v: jumper p)\n (p32: leaf_reader p)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (v_payload:\n (k: sum_repr_type t\n -> Tot (jump_sum_aux_payload_t t pc (maybe_enum_key_of_repr (sum_enum t) k))))\n : Tot (jumper (parse_sum t p pc))\nlet jump_sum_aux\n (t: sum)\n (#kt: parser_kind)\n (#p: parser kt (sum_repr_type t))\n (v: jumper p)\n (p32: leaf_reader p)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (v_payload: ((k: sum_repr_type t)) -> Tot (jump_sum_aux_payload_t t pc (maybe_enum_key_of_repr (sum_enum t) k)))\n: Tot (jumper (parse_sum t p pc))\n= fun #rrel #rel input pos ->\n let h = HST.get () in\n [@inline_let]\n let _ = valid_sum_elim h t p pc input pos in\n let pos_after_tag = v input pos in\n let k' = p32 input pos in\n v_payload k' input pos_after_tag", "val serialize_sum\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (#pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: (x: sum_key t -> Tot (serializer (dsnd (pc x)))))\n : Pure (serializer (parse_sum t p pc))\n (requires (kt.parser_kind_subkind == Some ParserStrong))\n (ensures (fun _ -> True))\nlet serialize_sum\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n: Pure (serializer (parse_sum t p pc))\n (requires (kt.parser_kind_subkind == Some ParserStrong))\n (ensures (fun _ -> True))\n= // FIXME: WHY WHY WHY is implicit argument inference failing here? (i.e. introducing an eta-expansion)\n serialize_sum' t s #_ #(parse_sum_cases t pc) (serialize_sum_cases t pc sc)", "val jump_sum_cases\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (vc: (x: sum_key t -> Tot (jumper (dsnd (pc x)))))\n (destr: dep_enum_destr (sum_enum t) (jump_sum_cases_t t pc))\n (k: sum_key t)\n : Tot (jumper (parse_sum_cases t pc k))\nlet jump_sum_cases \n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (vc: ((x: sum_key t) -> Tot (jumper (dsnd (pc x)))))\n (destr: dep_enum_destr (sum_enum t) (jump_sum_cases_t t pc))\n (k: sum_key t)\n: Tot (jumper (parse_sum_cases t pc k))\n= destr\n _\n (jump_sum_cases_t_if t pc)\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (jump_sum_cases_aux t pc vc)\n k", "val serialize32_dsum_type_of_tag\n (t: dsum)\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (sf: (x: dsum_known_key t -> Tot (serializer (dsnd (f x)))))\n (sf32: (x: dsum_known_key t -> Tot (serializer32 (sf x))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (#sg: serializer g)\n (sg32: serializer32 sg)\n (tg: dsum_key t)\n : Tot (serializer32 (serialize_dsum_type_of_tag t f sf g sg tg))\nlet serialize32_dsum_type_of_tag\n (t: dsum)\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (sf: (x: dsum_known_key t) -> Tot (serializer (dsnd (f x))))\n (sf32: (x: dsum_known_key t) -> Tot (serializer32 (sf x)))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (#sg: serializer g)\n (sg32: serializer32 sg)\n (tg: dsum_key t)\n: Tot (serializer32 (serialize_dsum_type_of_tag t f sf g sg tg))\n= match tg with\n | Known x' -> serialize32_ext (dsnd (f x')) (sf x') (sf32 x') (parse_dsum_type_of_tag t f g tg) ()\n | Unknown x' -> serialize32_ext g sg sg32 (parse_dsum_type_of_tag t f g tg) ()", "val validate_sum_aux_payload'\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: (x: sum_key t -> Tot (validator (dsnd (pc x)))))\n (k: maybe_enum_key (sum_enum t))\n : Tot (validate_sum_aux_payload_t t pc k)\nlet validate_sum_aux_payload'\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (validator (dsnd (pc x)))))\n (k: maybe_enum_key (sum_enum t))\n: Tot (validate_sum_aux_payload_t t pc k)\n= fun #rrel #rel input pos ->\n match k with\n | Known k ->\n [@inline_let]\n let _ = synth_sum_case_injective t k in\n pc32 k input pos\n // validate_synth (pc32 k) (synth_sum_case t k) () input pos\n | _ -> validator_error_generic", "val synth_bitsum'_recip_BitSum_nil\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size) {e == l1 `L.append` []})\n : Tot (synth_bitsum'_recip_BitSum_t cl bitsum'_size key key_size e payload l1 [])\nlet synth_bitsum'_recip_BitSum_nil\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size) { e == l1 `L.append` [] } )\n: Tot (synth_bitsum'_recip_BitSum_t cl bitsum'_size key key_size e payload l1 [])\n= fun k _ ->\n [@inline_let]\n let _ = L.append_l_nil l1 in\n false_elim ()", "val validate_sum_aux_payload_eq\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n : Tot (validate_sum_aux_payload_t t pc k -> validate_sum_aux_payload_t t pc k -> GTot Type0)\nlet validate_sum_aux_payload_eq\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n: Tot (validate_sum_aux_payload_t t pc k -> validate_sum_aux_payload_t t pc k -> GTot Type0)\n= fun _ _ -> True", "val parse32_bitsum\n (#kt: parser_kind)\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (b: bitsum' cl tot)\n (#data: Type)\n (tag_of_data: (data -> Tot (bitsum'_type b)))\n (type_of_tag: (bitsum'_key_type b -> Tot Type))\n (synth_case: synth_case_t b data tag_of_data type_of_tag)\n (#p: parser kt t)\n (p32: parser32 p)\n (f: (x: bitsum'_key_type b -> Tot (k: parser_kind & parser k (type_of_tag x))))\n (f32: (x: bitsum'_key_type b -> Tot (parser32 (dsnd (f x)))))\n : Tot (parser32 (parse_bitsum b tag_of_data type_of_tag synth_case p f))\nlet parse32_bitsum\n (#kt: parser_kind)\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (b: bitsum' cl tot)\n (#data: Type)\n (tag_of_data: (data -> Tot (bitsum'_type b)))\n (type_of_tag: (bitsum'_key_type b -> Tot Type))\n (synth_case: synth_case_t b data tag_of_data type_of_tag)\n (#p: parser kt t)\n (p32: parser32 p)\n (f: (x: bitsum'_key_type b) -> Tot (k: parser_kind & parser k (type_of_tag x)))\n (f32: (x: bitsum'_key_type b) -> Tot (parser32 (dsnd (f x))))\n: Tot (parser32 (parse_bitsum b tag_of_data type_of_tag synth_case p f))\n= fun x ->\n parse_bitsum_eq' b tag_of_data type_of_tag synth_case p f (B32.reveal x);\n match p32 x with\n | None -> None\n | Some (tg', consumed1) ->\n if filter_bitsum' b tg'\n then\n let tg = synth_bitsum' b tg' in\n let x' = B32.slice x consumed1 (B32.len x) in\n begin match f32 (bitsum'_key_of_t b tg) x' with\n | None -> None\n | Some (y, consumed2) ->\n Some ((synth_case.f tg y <: data), consumed1 `U32.add` consumed2)\n end\n else\n None", "val accessor_clens_sum_cases_payload\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n : Tot (accessor (gaccessor_clens_sum_cases_payload t pc k))\nlet accessor_clens_sum_cases_payload\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n: Tot (accessor (gaccessor_clens_sum_cases_payload t pc k))\n= [@inline_let]\n let _ =\n synth_sum_case_injective t k;\n synth_sum_case_inverse t k;\n synth_injective_synth_inverse_synth_inverse_recip (synth_sum_case t k) (synth_sum_case_recip t k) ()\n in\n accessor_ext\n (accessor_synth (dsnd (pc k)) (synth_sum_case t k) (synth_sum_case_recip t k) ())\n (clens_sum_cases_payload t k)\n ()", "val serialize_sum_eq\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (#pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: (x: sum_key t -> Tot (serializer (dsnd (pc x)))))\n (x: sum_type t)\n : Lemma (requires (kt.parser_kind_subkind == Some ParserStrong))\n (ensures\n (serialize (serialize_sum t s sc) x ==\n (let tg = sum_tag_of_data t x in\n (serialize (serialize_enum_key _ s (sum_enum t)) tg)\n `Seq.append`\n (serialize (sc tg) (synth_sum_case_recip t tg x)))))\nlet serialize_sum_eq\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (x: sum_type t)\n: Lemma\n (requires (kt.parser_kind_subkind == Some ParserStrong))\n (ensures (\n serialize (serialize_sum t s sc) x == (\n let tg = sum_tag_of_data t x in\n serialize (serialize_enum_key _ s (sum_enum t)) tg `Seq.append`\n serialize (sc tg) (synth_sum_case_recip t tg x)\n )))\n= let tg = sum_tag_of_data t x in\n synth_sum_case_injective t tg;\n synth_sum_case_inverse t tg;\n serialize_synth_eq (dsnd (pc tg)) (synth_sum_case t tg) (sc tg) (synth_sum_case_recip t tg) () x", "val bitsum'_key_type_elim_BitField\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (sz: nat{sz > 0 /\\ sz <= bitsum'_size /\\ bitsum'_size <= tot})\n (rest: bitsum' cl (bitsum'_size - sz))\n (x: bitsum'_key_type (BitField sz rest))\n : Tot (bitsum'_key_type rest)\nlet bitsum'_key_type_elim_BitField\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (sz: nat { sz > 0 /\\ sz <= bitsum'_size /\\ bitsum'_size <= tot })\n (rest: bitsum' cl (bitsum'_size - sz))\n (x: bitsum'_key_type (BitField sz rest))\n: Tot (bitsum'_key_type rest)\n= coerce (bitsum'_key_type rest) x", "val sum_of_bools (j k: int) (f: (int -> bool)) : Tot bool (decreases (k - j))\nlet rec sum_of_bools (j k:int) (f:int -> bool) : Tot bool (decreases (k - j)) =\n if j >= k then false\n else (sum_of_bools j (k - 1) f) <> f (k - 1)", "val clens_dsum_payload (s: dsum) (k: dsum_key s) : Tot (clens (dsum_type s) (dsum_type_of_tag s k))\nlet clens_dsum_payload\n (s: dsum)\n (k: dsum_key s)\n: Tot (clens (dsum_type s) (dsum_type_of_tag s k))\n= {\n clens_cond = (fun (x: dsum_type s) -> dsum_tag_of_data s x == k);\n clens_get = (fun (x: dsum_type s) -> synth_dsum_case_recip s k x <: Ghost (dsum_type_of_tag s k) (requires (dsum_tag_of_data s x == k)) (ensures (fun _ -> True)));\n }", "val default_if (t: Type) : Tot (if_combinator t (eq2 #t))\nlet default_if\n (t: Type)\n: Tot (if_combinator t (eq2 #t))\n= fun\n (cond: bool)\n (s_true: (cond_true cond -> Tot t))\n (s_false: (cond_false cond -> Tot t))\n-> (if cond\n then s_true ()\n else s_false ()) <: (y: t { y == (if cond then s_true () else s_false ()) } )", "val serialize_sum'\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (#k: parser_kind)\n (#pc: (x: sum_key t -> Tot (parser k (sum_cases t x))))\n (sc: (x: sum_key t -> Tot (serializer (pc x))))\n : Pure (serializer (parse_sum' t p pc))\n (requires (kt.parser_kind_subkind == Some ParserStrong))\n (ensures (fun _ -> True))\nlet serialize_sum'\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (#k: parser_kind)\n (#pc: ((x: sum_key t) -> Tot (parser k (sum_cases t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (pc x))))\n: Pure (serializer (parse_sum' t p pc))\n (requires (kt.parser_kind_subkind == Some ParserStrong))\n (ensures (fun _ -> True))\n= serialize_tagged_union\n #(parse_filter_kind kt)\n #(sum_key t)\n #(parse_enum_key p (sum_enum t))\n (serialize_enum_key p s (sum_enum t))\n #(sum_type t)\n (sum_tag_of_data t)\n #k\n #pc\n sc", "val destr_maybe_total_enum_repr\n (#t: Type)\n (#key #repr: eqtype)\n (e: total_enum key repr)\n (destr: maybe_enum_destr_t t e)\n (eq: (t -> t -> GTot Type0))\n (ift: if_combinator t eq)\n (eq_refl: r_reflexive_t _ eq)\n (eq_trans: r_transitive_t _ eq)\n (f: (x: maybe_total_enum_key e -> Tot t))\n (x: repr)\n : Tot (y: t{eq y (f (maybe_total_enum_key_of_repr e x))})\nlet destr_maybe_total_enum_repr\n (#t: Type)\n (#key #repr: eqtype)\n (e: total_enum key repr)\n (destr: maybe_enum_destr_t t e)\n (eq: (t -> t -> GTot Type0))\n (ift: if_combinator t eq)\n (eq_refl: r_reflexive_t _ eq)\n (eq_trans: r_transitive_t _ eq)\n (f: ((x: maybe_total_enum_key e) -> Tot t))\n (x: repr)\n: Tot (y: t { eq y (f (maybe_total_enum_key_of_repr e x)) } )\n= destr eq ift eq_refl eq_trans (fun y -> f (total_of_maybe_enum_key e y)) x", "val jump_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (v: jumper p)\n (p32: leaf_reader p)\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (f32: (x: dsum_known_key t -> Tot (jumper (dsnd (f x)))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (g32: jumper g)\n (destr: dep_maybe_enum_destr_t (dsum_enum t) (jump_dsum_cases_t t f g))\n : Tot (jumper (parse_dsum t p f g))\nlet jump_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (v: jumper p)\n (p32: leaf_reader p)\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (f32: (x: dsum_known_key t) -> Tot (jumper (dsnd (f x))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (g32: jumper g)\n (destr: dep_maybe_enum_destr_t (dsum_enum t) (jump_dsum_cases_t t f g))\n: Tot (jumper (parse_dsum t p f g))\n= fun #rrel #rel input pos ->\n let h = HST.get () in\n [@inline_let]\n let _ = parse_dsum_eq' t p f g (bytes_of_slice_from h input pos) in\n [@inline_let]\n let _ = valid_facts (parse_dsum t p f g) h input pos in\n [@inline_let]\n let _ = valid_facts p h input pos in\n let pos_after_tag = v input pos in\n let tg = p32 input pos in\n [@inline_let]\n let _ = valid_facts (parse_dsum_cases' t f g (maybe_enum_key_of_repr (dsum_enum t) tg)) h input pos_after_tag in\n destr (jump_dsum_cases_eq t f g) (jump_dsum_cases_if t f g) (fun _ _ -> ()) (fun _ _ _ _ -> ()) (jump_dsum_cases' t f f32 g32) tg input pos_after_tag", "val validate_bitsum_cases_bitsum'_cons\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (k: key)\n (r: bitfield cl key_size)\n (l2:\n list (key & bitfield cl key_size)\n { e == l1 `L.append` ((k, r) :: l2) /\\ list_mem k (list_map fst e) /\\\n enum_repr_of_key e k == r /\\ e == (l1 `L.append` [(k, r)]) `L.append` l2 })\n (destr_payload: validate_bitsum_cases_t u#r (payload k))\n (destr_tail:\n validate_bitsum_cases_bitsum'_t u#r\n cl\n bitsum'_size\n key\n key_size\n e\n payload\n (l1 `L.append` [(k, r)])\n l2)\n : Tot\n (validate_bitsum_cases_bitsum'_t u#r cl bitsum'_size key key_size e payload l1 ((k, r) :: l2))\nlet validate_bitsum_cases_bitsum'_cons\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (k: key)\n (r: bitfield cl key_size)\n (l2: list (key & bitfield cl key_size) { \n e == l1 `L.append` ((k, r) :: l2) /\\\n list_mem k (list_map fst e) /\\\n enum_repr_of_key e k == r /\\\n e == (l1 `L.append` [(k, r)]) `L.append` l2\n })\n (destr_payload: validate_bitsum_cases_t u#r (payload k))\n (destr_tail: validate_bitsum_cases_bitsum'_t u#r cl bitsum'_size key key_size e payload (l1 `L.append` [(k, r)]) l2)\n: Tot (validate_bitsum_cases_bitsum'_t u#r cl bitsum'_size key key_size e payload l1 ((k, r) :: l2))\n= fun u f v x xr #rrel #rel sl pos ->\n // [@inline_let]\n let _ =\n enum_repr_of_key_append_cons e l1 (k, r) l2\n in\n [@inline_let] let yr = cl.bitfield_eq_rhs x (bitsum'_size - key_size) bitsum'_size r in\n [@inline_let] let cond = (xr <: t) = yr in\n [@inline_let] let _ = \n assert (cond == true <==> (cl.get_bitfield x (bitsum'_size - key_size) bitsum'_size <: bitfield cl key_size) == r)\n in\n if cond\n then\n destr_payload \n (fun x -> u (bitsum'_key_type_intro_BitSum' cl bitsum'_size key key_size e payload (| k, x |)))\n (fun x -> f (bitsum'_key_type_intro_BitSum' cl bitsum'_size key key_size e payload (| k, x |)))\n (fun x -> v (bitsum'_key_type_intro_BitSum' cl bitsum'_size key key_size e payload (| k, x |)))\n x sl pos\n else\n [@inline_let] let _ =\n L.append_assoc l1 [(k, r)] l2;\n L.map_append snd l1 [(k, r)];\n L.append_mem (L.map snd l1) (L.map snd [(k, r)]) (cl.get_bitfield x (bitsum'_size - key_size) bitsum'_size <: bitfield cl key_size)\n in\n destr_tail u f v (x <: t) xr sl pos", "val jump_sum_aux_payload'\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: (x: sum_key t -> Tot (jumper (dsnd (pc x)))))\n (k: maybe_enum_key (sum_enum t))\n : Tot (jump_sum_aux_payload_t t pc k)\nlet jump_sum_aux_payload'\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (jumper (dsnd (pc x)))))\n (k: maybe_enum_key (sum_enum t))\n: Tot (jump_sum_aux_payload_t t pc k)\n= fun #rrel #rel input pos ->\n match k with\n | Known k ->\n [@inline_let]\n let _ = synth_sum_case_injective t k in\n pc32 k input pos\n | _ -> 0ul", "val mk_validate_bitsum_cases_bitsum'_t'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) {e == l1 `L.append` l2})\n (mk_validate_bitsum_cases_t':\n (b: bitsum' cl (bitsum'_size - key_size) {b << BitSum' key key_size e payload}\n -> Tot (validate_bitsum_cases_t u#r b)))\n : Tot (validate_bitsum_cases_bitsum'_t u#r cl bitsum'_size key key_size e payload l1 l2)\n (decreases %[BitSum' key key_size e payload;l2])\nlet rec mk_validate_bitsum_cases_bitsum'_t'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) { e == l1 `L.append` l2 } )\n (mk_validate_bitsum_cases_t':\n (* universe-polymorphic mutually recursive functions must be \"split off\"\n cf. https://github.com/FStarLang/FStar/issues/1480#issuecomment-623260544\n *)\n (b: bitsum' cl (bitsum'_size - key_size) { b << BitSum' key key_size e payload }) ->\n Tot (validate_bitsum_cases_t u#r b)\n )\n: Tot (validate_bitsum_cases_bitsum'_t u#r cl bitsum'_size key key_size e payload l1 l2)\n (decreases %[BitSum' key key_size e payload; l2])\n= bitsum_wellfoundedness (BitSum' key key_size e payload);\n match l2 with\n | [] ->\n [@inline_let] let _ =\n L.append_l_nil l1\n in\n validate_bitsum_cases_bitsum'_nil cl bitsum'_size key key_size e payload ()\n | (k, r) :: q ->\n [@inline_let] let _ =\n enum_repr_of_key_append_cons e l1 (k, r) q;\n L.append_assoc l1 [(k, r)] q\n in \n validate_bitsum_cases_bitsum'_cons cl bitsum'_size key key_size e payload l1 k r q\n (mk_validate_bitsum_cases_t' (payload k))\n (mk_validate_bitsum_cases_bitsum'_t' cl bitsum'_size key key_size e payload (l1 `L.append` [(k, r)]) q mk_validate_bitsum_cases_t')", "val jump_dsum_cases_if\n (s: dsum)\n (f: (x: dsum_known_key s -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag s x))))\n (#k: parser_kind)\n (g: parser k (dsum_type_of_unknown_tag s))\n (x: dsum_key s)\n : Tot (if_combinator _ (jump_dsum_cases_eq s f g x))\nlet jump_dsum_cases_if\n (s: dsum)\n (f: (x: dsum_known_key s) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag s x)))\n (#k: parser_kind)\n (g: parser k (dsum_type_of_unknown_tag s))\n (x: dsum_key s)\n: Tot (if_combinator _ (jump_dsum_cases_eq s f g x))\n= jump_dsum_cases_if' s f g x", "val mk_synth_bitsum'_recip_BitSum\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) {e == l1 `L.append` l2})\n : Tot (synth_bitsum'_recip_BitSum_t cl bitsum'_size key key_size e payload l1 l2)\n (decreases %[BitSum' key key_size e payload;0;l2])\nlet rec mk_synth_bitsum'_recip\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (#bitsum'_size: nat)\n (b: bitsum' cl bitsum'_size)\n: Tot (synth_bitsum'_recip_t b)\n (decreases %[b;1;()])\n= match b with\n | BitStop _ -> synth_bitsum'_recip_BitStop cl\n | BitField sz rest -> synth_bitsum'_recip_BitField cl bitsum'_size sz rest (mk_synth_bitsum'_recip rest)\n | BitSum' key key_size e payload ->\n synth_bitsum'_recip_BitSum_intro cl bitsum'_size key key_size e payload (mk_synth_bitsum'_recip_BitSum cl bitsum'_size key key_size e payload [] e)\nand mk_synth_bitsum'_recip_BitSum\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) { e == l1 `L.append` l2 } )\n: Tot (synth_bitsum'_recip_BitSum_t cl bitsum'_size key key_size e payload l1 l2)\n (decreases %[BitSum' key key_size e payload; 0; l2])\n= bitsum_wellfoundedness (BitSum' key key_size e payload);\n match l2 with\n | [] ->\n [@inline_let] let _ =\n L.append_l_nil l1\n in\n synth_bitsum'_recip_BitSum_nil cl bitsum'_size key key_size e payload l1\n | [(k, r)] ->\n [@inline_let] let _ =\n enum_repr_of_key_append_cons e l1 (k, r) [];\n L.append_assoc l1 [(k, r)] []\n in\n synth_bitsum'_recip_BitSum_cons_nil cl bitsum'_size key key_size e payload l1 k r\n (mk_synth_bitsum'_recip (payload k))\n | (k, r) :: q ->\n [@inline_let] let _ =\n enum_repr_of_key_append_cons e l1 (k, r) q;\n L.append_assoc l1 [(k, r)] q\n in\n synth_bitsum'_recip_BitSum_cons cl bitsum'_size key key_size e payload l1 k r q\n (mk_synth_bitsum'_recip (payload k))\n (mk_synth_bitsum'_recip_BitSum cl bitsum'_size key key_size e payload (l1 `L.append` [(k, r)]) q)", "val validate_sum_cases_aux\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (vc: (x: sum_key t -> Tot (validator (dsnd (pc x)))))\n (k: sum_key t)\n : Tot (validator (parse_sum_cases t pc k))\nlet validate_sum_cases_aux\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (vc: ((x: sum_key t) -> Tot (validator (dsnd (pc x)))))\n (k: sum_key t)\n: Tot (validator (parse_sum_cases t pc k))\n= [@inline_let]\n let _ = synth_sum_case_injective t k in\n validate_synth\n (validate_weaken\n (weaken_parse_cases_kind t pc)\n (vc k)\n ()\n )\n (synth_sum_case t k)\n ()", "val validate_bitsum_cases_bitsum'_t\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) {e == l1 `L.append` l2})\n : Tot (Type u#(r + 1))\nlet validate_bitsum_cases_bitsum'_t\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (l1: list (key & bitfield cl key_size))\n (l2: list (key & bitfield cl key_size) { e == l1 `L.append` l2 } )\n: Tot (Type u#(r+1))\n= (u: (bitsum'_key_type (BitSum' key key_size e payload) -> Tot (Type u#r))) ->\n (f: ((x: bitsum'_key_type (BitSum' key key_size e payload)) -> Tot (k: parser_kind & parser k (u x)))) ->\n (v: ((x: bitsum'_key_type (BitSum' key key_size e payload)) -> Tot (validator (dsnd (f x))))) ->\n (x: parse_filter_refine (filter_bitsum' (BitSum' key key_size e payload)) { ~ (list_mem (cl.get_bitfield x (bitsum'_size - key_size) bitsum'_size <: bitfield cl key_size) (list_map snd l1)) }) ->\n (xr: t { xr == cl.bitfield_eq_lhs x (bitsum'_size - key_size) bitsum'_size }) ->\n Tot (validator (dsnd (f (bitsum'_key_of_t (BitSum' key key_size e payload) (synth_bitsum' (BitSum' key key_size e payload) x)))))", "val parse_sum_eq3\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (input: bytes)\n (k': sum_repr_type t)\n (consumed_k: consumed_length input)\n : Lemma\n (requires (Some? (parse (parse_sum t p pc) input) /\\ parse p input == Some (k', consumed_k)))\n (ensures\n (let input_k = Seq.slice input consumed_k (Seq.length input) in\n let k = maybe_enum_key_of_repr (sum_enum t) k' in\n match k with\n | Known k -> Some? (parse (dsnd (pc k)) input_k)\n | _ -> False))\nlet parse_sum_eq3\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (input: bytes)\n (k' : sum_repr_type t)\n (consumed_k: consumed_length input)\n: Lemma\n (requires (Some? (parse (parse_sum t p pc) input) /\\ parse p input == Some (k', consumed_k)))\n (ensures (\n let input_k = Seq.slice input consumed_k (Seq.length input) in\n let k = maybe_enum_key_of_repr (sum_enum t) k' in\n begin match k with\n | Known k ->\n Some? (parse (dsnd (pc k)) input_k)\n | _ -> False\n end\n ))\n= parse_sum_eq'' t p pc input", "val bitsum'_type_intro_BitSum'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (x: bitsum'_type_bitsum' cl bitsum'_size key key_size e payload)\n : Tot (bitsum'_type (BitSum' key key_size e payload))\nlet bitsum'_type_intro_BitSum'\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (x: bitsum'_type_bitsum' cl bitsum'_size key key_size e payload)\n: Tot (bitsum'_type (BitSum' key key_size e payload))\n= x", "val filter_bitsum'_bitsum'_nil\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat{key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot})\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (h: squash (e == e `L.append` []))\n : Tot (filter_bitsum'_bitsum'_t cl bitsum'_size key key_size e payload e [])\nlet filter_bitsum'_bitsum'_nil\n (#tot: pos)\n (#t: eqtype)\n (cl: uint_t tot t)\n (bitsum'_size: nat)\n (key: eqtype)\n (key_size: nat { key_size > 0 /\\ key_size <= bitsum'_size /\\ bitsum'_size <= tot })\n (e: enum key (bitfield cl key_size))\n (payload: (enum_key e -> Tot (bitsum' cl (bitsum'_size - key_size))))\n (h: squash (e == e `L.append` []))\n: Tot (filter_bitsum'_bitsum'_t cl bitsum'_size key key_size e payload e [])\n= (fun x xr -> false)", "val size32_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (#s1: serializer p1)\n (s1': size32 s1 {k1.parser_kind_subkind == Some ParserStrong})\n (#k2: parser_kind)\n (#t2: (t1 -> Tot Type))\n (#p2: (x: t1 -> Tot (parser k2 (t2 x))))\n (#s2: (x: t1 -> Tot (serializer (p2 x))))\n (s2': (x: t1 -> Tot (size32 (s2 x))))\n : Tot (size32 (serialize_dtuple2 s1 s2))\nlet size32_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (#s1: serializer p1)\n (s1' : size32 s1 { k1.parser_kind_subkind == Some ParserStrong } )\n (#k2: parser_kind)\n (#t2: t1 -> Tot Type)\n (#p2: (x: t1) -> Tot (parser k2 (t2 x)))\n (#s2: (x: t1) -> Tot (serializer (p2 x)))\n (s2' : (x: t1) -> Tot (size32 (s2 x)))\n: Tot (size32 (serialize_dtuple2 s1 s2))\n= fun x ->\n [@inline_let] let _ = serialize_dtuple2_eq s1 s2 x in\n match x with\n | (| x1, x2 |) ->\n let v1 = s1' x1 in\n let v2 = s2' x1 x2 in\n let res = add_overflow v1 v2 in\n (res <: (z : U32.t { size32_postcond (serialize_dtuple2 s1 s2) x z } ))", "val jump_sum_aux_payload_eq\n (t: sum)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n : Tot (jump_sum_aux_payload_t t pc k -> jump_sum_aux_payload_t t pc k -> GTot Type0)\nlet jump_sum_aux_payload_eq\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: maybe_enum_key (sum_enum t))\n: Tot (jump_sum_aux_payload_t t pc k -> jump_sum_aux_payload_t t pc k -> GTot Type0)\n= fun _ _ -> True", "val size32_synth'\n (#k: parser_kind)\n (#t1 #t2: Type)\n (p1: parser k t1)\n (f2: (t1 -> GTot t2))\n (s1: serializer p1)\n (s1': size32 s1)\n (g1: (t2 -> Tot t1))\n (u: unit{synth_inverse f2 g1 /\\ synth_injective f2})\n : Tot (size32 (serialize_synth p1 f2 s1 g1 u))\nlet size32_synth'\n (#k: parser_kind)\n (#t1: Type)\n (#t2: Type)\n (p1: parser k t1)\n (f2: t1 -> GTot t2)\n (s1: serializer p1)\n (s1' : size32 s1)\n (g1: t2 -> Tot t1)\n (u: unit {\n synth_inverse f2 g1 /\\\n synth_injective f2\n })\n: Tot (size32 (serialize_synth p1 f2 s1 g1 u))\n= size32_synth p1 f2 s1 s1' g1 (fun x -> g1 x) u", "val size32_ifthenelse\n (#p: parse_ifthenelse_param)\n (s:\n serialize_ifthenelse_param p\n { let tk = p.parse_ifthenelse_tag_kind in\n tk.parser_kind_subkind == Some ParserStrong /\\ Some? tk.parser_kind_high /\\\n Some? (dfst (p.parse_ifthenelse_payload_parser true)).parser_kind_high /\\\n Some? (dfst (p.parse_ifthenelse_payload_parser false)).parser_kind_high /\\\n Some?.v tk.parser_kind_high +\n Some?.v (dfst (p.parse_ifthenelse_payload_parser true)).parser_kind_high <\n 4294967296 /\\\n Some?.v tk.parser_kind_high +\n Some?.v (dfst (p.parse_ifthenelse_payload_parser false)).parser_kind_high <\n 4294967296 })\n (st32: size32 s.serialize_ifthenelse_tag_serializer)\n (syntt:\n (x: p.parse_ifthenelse_t\n -> Tot (t: p.parse_ifthenelse_tag_t{t == dfst (s.serialize_ifthenelse_synth_recip x)})\n ))\n (b32: (t: p.parse_ifthenelse_tag_t -> Tot (b: bool{b == p.parse_ifthenelse_tag_cond t})))\n (syntp:\n (\n b: bool ->\n x:\n p.parse_ifthenelse_t\n {b == p.parse_ifthenelse_tag_cond (dfst (s.serialize_ifthenelse_synth_recip x))}\n -> Tot\n (pl:\n p.parse_ifthenelse_payload_t b {pl == dsnd (s.serialize_ifthenelse_synth_recip x)}\n )))\n (sp32: (b: bool -> Tot (size32 (s.serialize_ifthenelse_payload_serializer b))))\n : Tot (size32 (serialize_ifthenelse s))\nlet size32_ifthenelse\n (#p: parse_ifthenelse_param)\n (s: serialize_ifthenelse_param p {\n let tk = p.parse_ifthenelse_tag_kind in\n tk.parser_kind_subkind == Some ParserStrong /\\\n Some? tk.parser_kind_high /\\\n Some? (dfst (p.parse_ifthenelse_payload_parser true)).parser_kind_high /\\\n Some? (dfst (p.parse_ifthenelse_payload_parser false)).parser_kind_high /\\\n Some?.v tk.parser_kind_high + Some?.v (dfst (p.parse_ifthenelse_payload_parser true)).parser_kind_high < 4294967296 /\\\n Some?.v tk.parser_kind_high + Some?.v (dfst (p.parse_ifthenelse_payload_parser false)).parser_kind_high < 4294967296\n })\n (st32: size32 s.serialize_ifthenelse_tag_serializer)\n (syntt: (x: p.parse_ifthenelse_t) -> Tot (t: p.parse_ifthenelse_tag_t { t == dfst (s.serialize_ifthenelse_synth_recip x) } ))\n (b32: (t: p.parse_ifthenelse_tag_t) -> Tot (b: bool { b == p.parse_ifthenelse_tag_cond t } ))\n (syntp: (b: bool) -> (x: p.parse_ifthenelse_t { b == p.parse_ifthenelse_tag_cond (dfst (s.serialize_ifthenelse_synth_recip x)) } ) -> Tot (pl: p.parse_ifthenelse_payload_t b { pl == dsnd (s.serialize_ifthenelse_synth_recip x) } ))\n (sp32: (b: bool) -> Tot (size32 (s.serialize_ifthenelse_payload_serializer b)))\n: Tot (size32 (serialize_ifthenelse s))\n= fun (input: p.parse_ifthenelse_t) -> ((\n let t = syntt input in\n let st = st32 t in\n let b = b32 t in\n if b\n then\n let y = syntp true input in\n U32.add st (sp32 true y)\n else\n let y = syntp false input in\n U32.add st (sp32 false y)\n ) <: (res: _ { size32_postcond (serialize_ifthenelse s) input res }))", "val parse_sum_eq\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (input: bytes)\n : Lemma\n (parse (parse_sum t p pc) input ==\n (match parse (parse_enum_key p (sum_enum t)) input with\n | None -> None\n | Some (k, consumed_k) ->\n let input_k = Seq.slice input consumed_k (Seq.length input) in\n match parse (dsnd (pc k)) input_k with\n | None -> None\n | Some (x, consumed_x) ->\n Some ((synth_sum_case t k x <: sum_type t), consumed_k + consumed_x)))\nlet parse_sum_eq\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (input: bytes)\n: Lemma\n (parse (parse_sum t p pc) input == (match parse (parse_enum_key p (sum_enum t)) input with\n | None -> None\n | Some (k, consumed_k) ->\n let input_k = Seq.slice input consumed_k (Seq.length input) in\n begin match parse (dsnd (pc k)) input_k with\n | None -> None\n | Some (x, consumed_x) -> Some ((synth_sum_case t k x <: sum_type t), consumed_k + consumed_x)\n end\n ))\n= parse_sum_eq' t p pc input;\n match parse (parse_enum_key p (sum_enum t)) input with\n | None -> ()\n | Some (k, consumed_k) ->\n let input_k = Seq.slice input consumed_k (Seq.length input) in\n synth_sum_case_injective t k;\n parse_synth_eq (dsnd (pc k)) (synth_sum_case t k) input_k", "val size32_enum_key_gen\n (#k: parser_kind)\n (#key #repr: eqtype)\n (#p: parser k repr)\n (#s: serializer p)\n (s32: size32 s)\n (e: enum key repr)\n (k': parser_kind)\n (t': Type)\n (p': parser k' t')\n (s': serializer p')\n (u1: unit{k' == parse_filter_kind k})\n (u15: unit{t' == enum_key e})\n (u2: unit{p' == parse_enum_key p e})\n (u3: unit{s' == serialize_enum_key p s e})\n (f: enum_repr_of_key'_t e)\n : Tot (size32 s')\nlet size32_enum_key_gen\n (#k: parser_kind)\n (#key #repr: eqtype)\n (#p: parser k repr)\n (#s: serializer p)\n (s32: size32 s)\n (e: enum key repr)\n (k' : parser_kind)\n (t' : Type)\n (p' : parser k' t')\n (s' : serializer p')\n (u1: unit { k' == parse_filter_kind k } )\n (u15: unit { t' == enum_key e } )\n (u2: unit { p' == parse_enum_key p e } )\n (u3: unit { s' == serialize_enum_key p s e } )\n (f: enum_repr_of_key'_t e)\n: Tot (size32 s')\n= fun (input: enum_key e) -> (\n [@inline_let]\n let _ = serialize_enum_key_eq s e input in\n (s32 (f input)) <: (r: UInt32.t { size32_postcond (serialize_enum_key p s e) input r } ))", "val accessor_clens_sum_payload\n (t: sum)\n (#kt: parser_kind)\n (#p: parser kt (sum_repr_type t))\n (j: jumper p)\n (pc: (x: sum_key t -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n : Tot (accessor (gaccessor_clens_sum_payload t p pc k))\nlet accessor_clens_sum_payload\n (t: sum)\n (#kt: parser_kind)\n (#p: parser kt (sum_repr_type t))\n (j: jumper p)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n: Tot (accessor (gaccessor_clens_sum_payload t p pc k))\n= fun #rrel #rel -> accessor_clens_sum_payload' t j pc k #rrel #rel", "val clens_dsum_cases_payload (s: dsum) (k: dsum_key s)\n : Tot (clens (dsum_cases s k) (dsum_type_of_tag s k))\nlet clens_dsum_cases_payload\n (s: dsum)\n (k: dsum_key s)\n: Tot (clens (dsum_cases s k) (dsum_type_of_tag s k))\n= {\n clens_cond = (fun (x: dsum_cases s k) -> True);\n clens_get = (fun (x: dsum_cases s k) -> synth_dsum_case_recip s k x <: Ghost (dsum_type_of_tag s k) (requires (True)) (ensures (fun _ -> True)));\n }", "val size32_maybe_enum_key_gen\n (#k: parser_kind)\n (#key #repr: eqtype)\n (#p: parser k repr)\n (#s: serializer p)\n (s32: size32 s)\n (e: enum key repr)\n (k': parser_kind)\n (t': Type)\n (p': parser k' t')\n (s': serializer p')\n (u1: unit{k == k'})\n (u15: unit{t' == maybe_enum_key e})\n (u2: unit{p' == parse_maybe_enum_key p e})\n (u3: unit{s' == serialize_maybe_enum_key p s e})\n (f: enum_repr_of_key'_t e)\n : Tot (size32 s')\nlet size32_maybe_enum_key_gen\n (#k: parser_kind)\n (#key #repr: eqtype)\n (#p: parser k repr)\n (#s: serializer p)\n (s32: size32 s)\n (e: enum key repr)\n (k' : parser_kind)\n (t' : Type)\n (p' : parser k' t')\n (s' : serializer p')\n (u1: unit { k == k' } )\n (u15: unit { t' == maybe_enum_key e } )\n (u2: unit { p' == parse_maybe_enum_key p e } )\n (u3: unit { s' == serialize_maybe_enum_key p s e } )\n (f: enum_repr_of_key'_t e)\n: Tot (size32 s')\n= size32_maybe_enum_key_gen' s32 e\n (size32_enum_key_gen s32 e _ _ _ (serialize_enum_key _ s e) () () () () f)", "val parse32_compose_context\n (#pk: parser_kind)\n (#kt1 #kt2: Type)\n (f: (kt2 -> Tot kt1))\n (t: (kt1 -> Tot Type))\n (p: (k: kt1 -> Tot (parser pk (t k))))\n (p32: (k: kt1 -> Tot (parser32 (p k))))\n (k: kt2)\n : Tot (parser32 (p (f k)))\nlet parse32_compose_context\n (#pk: parser_kind)\n (#kt1 #kt2: Type)\n (f: (kt2 -> Tot kt1))\n (t: (kt1 -> Tot Type))\n (p: ((k: kt1) -> Tot (parser pk (t k))))\n (p32: ((k: kt1) -> Tot (parser32 (p k))))\n (k: kt2)\n: Tot (parser32 (p (f k)))\n= fun input -> p32 (f k) input", "val size32_synth\n (#k: parser_kind)\n (#t1 #t2: Type)\n (p1: parser k t1)\n (f2: (t1 -> GTot t2))\n (s1: serializer p1)\n (s1': size32 s1)\n (g1: (t2 -> GTot t1))\n (g1': (x: t2 -> Tot (y: t1{y == g1 x})))\n (u: unit{synth_inverse f2 g1 /\\ synth_injective f2})\n : Tot (size32 (serialize_synth p1 f2 s1 g1 u))\nlet size32_synth\n (#k: parser_kind)\n (#t1: Type)\n (#t2: Type)\n (p1: parser k t1)\n (f2: t1 -> GTot t2)\n (s1: serializer p1)\n (s1' : size32 s1)\n (g1: t2 -> GTot t1)\n (g1': (x: t2) -> Tot (y: t1 { y == g1 x } ) )\n (u: unit {\n synth_inverse f2 g1 /\\\n synth_injective f2\n })\n: Tot (size32 (serialize_synth p1 f2 s1 g1 u))\n= fun (input: t2) ->\n [@inline_let] let _ = serialize_synth_eq p1 f2 s1 g1 u input in\n [@inline_let] let x = g1' input in\n [@inline_let] let y = s1' x in\n (y <: (res: U32.t { size32_postcond (serialize_synth p1 f2 s1 g1 u) input res } ))", "val size32_list_inv\n (#t: Type)\n (#k: parser_kind)\n (#p: parser k t)\n (#s: serializer p)\n (s32: size32 s)\n (u: unit{serialize_list_precond k})\n (input: list t)\n (continue: bool)\n (accu: (U32.t * list t))\n : GTot Type0\nlet size32_list_inv\n (#t: Type)\n (#k: parser_kind)\n (#p: parser k t)\n (#s: serializer p)\n (s32: size32 s)\n (u: unit {\n serialize_list_precond k\n })\n (input: list t)\n (continue: bool)\n (accu: (U32.t * list t))\n: GTot Type0\n= let (len, rem) = accu in\n let sz = Seq.length (serialize (serialize_list p s) input) in\n if continue\n then\n U32.v len < U32.v u32_max /\\\n sz == U32.v len + Seq.length (serialize (serialize_list p s) rem)\n else\n size32_postcond (serialize_list p s) input len", "val size32_filter\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p)\n (s32: size32 s)\n (f: (t -> GTot bool))\n : Tot (size32 #_ #_ #(parse_filter p f) (serialize_filter s f))\nlet size32_filter\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p)\n (s32: size32 s)\n (f: (t -> GTot bool))\n: Tot (size32 #_ #_ #(parse_filter p f) (serialize_filter s f))\n= fun x -> s32 x" ], "closest_src": [ { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.serialize32_sum_cases_t_if" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.serialize32_dsum_cases_t_if" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_sum_cases_t_if" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.serialize32_sum_cases" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_sum_cases_t_if" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.serialize32_sum" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.read_sum_cases_t_if" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.serialize32_sum_cases_aux" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.serialize32_sum_cases_t_eq" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.mk_destr_bitsum'_t" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_sum_aux_payload_if" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Sum.fst", "name": "LowParse.Spec.Sum.sum_key_type_of_sum_key" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.read_dsum_cases_t_if" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_sum_aux_payload_if" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.mk_destr_bitsum'_bitsum_t" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.destr_bitsum'_bitsum_nil" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.serialize32_dsum_cases_t_eq" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_sum" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.serialize32_dsum_cases" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_sum_aux_payload" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Combinators.fst", "name": "LowParse.SLow.Combinators.size32_compose_context" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.bitsum'_key_type_elim_BitSum'" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.serialize32_dsum" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_sum_aux_payload" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Sum.fst", "name": "LowParse.Spec.Sum.sum_key_type" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.serialize32_dsum_cases_aux" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.destr_bitsum'_bitsum_t" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.bitsum'_key_of_t" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_sum" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_sum_aux_payload_if'" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_sum_aux_payload_if'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.synth_bitsum'_recip_BitSum_cons_nil" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.bitsum'_key_type" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.filter_bitsum'_bitsum'_cons" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.synth_bitsum'_recip_BitSum_cons" }, { "project_name": "everparse", "file_name": "LowParse.SLow.BitSum.fst", "name": "LowParse.SLow.BitSum.serialize32_bitsum_cond" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.read_sum" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.destr_bitsum'_t" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.read_sum_cases" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.bitsum'_key_type_intro_BitSum'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.bitsum'_type_elim_BitSum'" }, { "project_name": "everparse", "file_name": "LowParse.SLow.BitSum.fst", "name": "LowParse.SLow.BitSum.serialize32_bitsum" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Sum.fst", "name": "LowParse.Spec.Sum.dsum_key_type" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_dsum_cases'_destr" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_sum_aux" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_sum_cases" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_dsum_cases_if" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.mk_filter_bitsum'_t'" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Combinators.fst", "name": "LowParse.SLow.Combinators.size32_weaken" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.mk_filter_bitsum'_bitsum'_t'" }, { "project_name": "everparse", "file_name": "LowParse.Low.BitSum.fst", "name": "LowParse.Low.BitSum.validate_bitsum_cases_bitsum_gen" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Combinators.fst", "name": "LowParse.SLow.Combinators.size32_nondep_then" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitFields.fst", "name": "LowParse.Spec.BitFields.bitfields_destr_cons_nil" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.parse_sum_eq4" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.clens_sum_cases_payload" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_dsum" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.read_sum_cases'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.filter_bitsum'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.filter_bitsum'_bitsum_gen" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.clens_sum_payload" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_sum_aux" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Sum.fst", "name": "LowParse.Spec.Sum.serialize_sum" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_sum_cases" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.serialize32_dsum_type_of_tag" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_sum_aux_payload'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.synth_bitsum'_recip_BitSum_nil" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_sum_aux_payload_eq" }, { "project_name": "everparse", "file_name": "LowParse.SLow.BitSum.fst", "name": "LowParse.SLow.BitSum.parse32_bitsum" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.accessor_clens_sum_cases_payload" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Sum.fst", "name": "LowParse.Spec.Sum.serialize_sum_eq" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.bitsum'_key_type_elim_BitField" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Defs_s.fst", "name": "Vale.Math.Poly2.Defs_s.sum_of_bools" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.clens_dsum_payload" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.default_if" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Sum.fst", "name": "LowParse.Spec.Sum.serialize_sum'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Enum.fst", "name": "LowParse.Spec.Enum.destr_maybe_total_enum_repr" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_dsum" }, { "project_name": "everparse", "file_name": "LowParse.Low.BitSum.fst", "name": "LowParse.Low.BitSum.validate_bitsum_cases_bitsum'_cons" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_sum_aux_payload'" }, { "project_name": "everparse", "file_name": "LowParse.Low.BitSum.fst", "name": "LowParse.Low.BitSum.mk_validate_bitsum_cases_bitsum'_t'" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_dsum_cases_if" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.mk_synth_bitsum'_recip_BitSum" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_sum_cases_aux" }, { "project_name": "everparse", "file_name": "LowParse.Low.BitSum.fst", "name": "LowParse.Low.BitSum.validate_bitsum_cases_bitsum'_t" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.parse_sum_eq3" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.bitsum'_type_intro_BitSum'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.filter_bitsum'_bitsum'_nil" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Combinators.fst", "name": "LowParse.SLow.Combinators.size32_dtuple2" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_sum_aux_payload_eq" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Combinators.fst", "name": "LowParse.SLow.Combinators.size32_synth'" }, { "project_name": "everparse", "file_name": "LowParse.SLow.IfThenElse.fst", "name": "LowParse.SLow.IfThenElse.size32_ifthenelse" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Sum.fst", "name": "LowParse.Spec.Sum.parse_sum_eq" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Enum.fst", "name": "LowParse.SLow.Enum.size32_enum_key_gen" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.accessor_clens_sum_payload" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.clens_dsum_cases_payload" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Enum.fst", "name": "LowParse.SLow.Enum.size32_maybe_enum_key_gen" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Combinators.fst", "name": "LowParse.SLow.Combinators.parse32_compose_context" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Combinators.fst", "name": "LowParse.SLow.Combinators.size32_synth" }, { "project_name": "everparse", "file_name": "LowParse.SLow.List.fst", "name": "LowParse.SLow.List.size32_list_inv" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Combinators.fst", "name": "LowParse.SLow.Combinators.size32_filter" } ], "selected_premises": [ "LowParse.Spec.Sum.sum_key_type", "LowParse.SLow.Sum.size32_sum_destr_eq", "LowParse.Spec.Sum.sum_repr_type", "LowParse.Spec.Sum.sum_enum", "LowParse.Spec.Sum.sum_tag_of_data", "LowParse.SLow.Sum.parse32_sum_cases_t_if", "LowParse.Spec.Sum.parse_sum'", "LowParse.Spec.Sum.parse_sum", "LowParse.Spec.Sum.parse_sum_kind", "LowParse.SLow.Sum.size32_sum_cases_t_if", "LowParse.Spec.Sum.synth_sum_case_inverse", "LowParse.SLow.Sum.size32_sum_destr_trans", "LowParse.Spec.Sum.parse_sum_cases", "LowParse.SLow.Sum.parse32_sum_eq", "LowParse.Spec.Sum.synth_sum_case_recip", "LowParse.SLow.Sum.size32_sum_cases_t_eq", "LowParse.Spec.Sum.sum_key_type_of_sum_key", "LowParse.Spec.Sum.weaken_parse_cases_kind", "LowParse.SLow.Sum.parse32_sum_aux", "LowParse.Spec.Sum.parse_sum_cases'", "LowParse.Spec.Sum.synth_sum_case", "LowParse.SLow.Sum.serialize32_sum_destr_eq", "LowParse.SLow.Sum.parse32_sum_cases", "LowParse.Spec.Sum.parse_sum_eq''", "LowParse.SLow.Sum.parse32_sum_cases_t_eq", "LowParse.SLow.Sum.size32_sum_cases_aux", "LowParse.SLow.Sum.parse32_sum_eq_trans", "LowParse.SLow.Sum.parse32_sum'", "LowParse.SLow.Sum.parse32_sum_cases'", "LowParse.SLow.Sum.parse32_sum_if", "LowParse.SLow.Sum.parse32_sum_cases_aux", "LowParse.Spec.Sum.synth_sum_case_injective", "LowParse.SLow.Sum.serialize32_sum_destr_if", "LowParse.SLow.Sum.parse32_sum_eq_refl", "LowParse.Spec.Sum.parse_sum_eq", "LowParse.SLow.Sum.serialize32_sum_aux", "LowParse.SLow.Sum.serialize32_sum_cases_t_if", "LowParse.Spec.Sum.serialize_sum'", "LowParse.SLow.Sum.parse32_sum2", "LowParse.Spec.Sum.parse_sum_eq'", "LowParse.SLow.Sum.size32_sum_cases", "FStar.Bytes.length", "LowParse.SLow.Sum.parse32_sum", "FStar.UInt.size", "FStar.Bytes.u32", "LowParse.SLow.Base.add_overflow", "LowParse.Spec.Sum.parse_sum_cases_eq'", "LowParse.SLow.Sum.serialize32_sum_cases_t_eq", "LowParse.SLow.Sum.serialize32_sum_cases_aux", "LowParse.SLow.Sum.serialize32_sum_cases", "LowParse.SLow.Base.bytes32", "LowParse.Spec.Sum.parse_sum_cases_eq", "LowParse.Spec.Sum.serialize_sum_eq", "LowParse.Spec.Enum.enum_key", "LowParse.SLow.Sum.serialize32_sum_destr_trans", "LowParse.Spec.Sum.serialize_sum", "LowParse.Spec.Base.coerce", "LowParse.Spec.Enum.parse_maybe_total_enum_key", "LowParse.Spec.Combinators.parse_filter_refine", "LowParse.Spec.Enum.list_map", "LowParse.Spec.Enum.list_mem", "LowStar.Monotonic.Buffer.length", "LowParse.SLow.Base.u32_max", "LowParse.Spec.Sum.serialize_sum_cases", "LowParse.Bytes32.b32append", "LowParse.Spec.Enum.enum_key_of_repr", "LowParse.Spec.Enum.enum_repr", "LowParse.Spec.Sum.synth_case_recip'", "LowStar.Buffer.trivial_preorder", "LowParse.Spec.Enum.r_reflexive_t_elim", "LowParse.Bytes32.b32_hide", "LowParse.SLow.Base.parser32_correct", "FStar.String.length", "LowParse.Spec.Enum.flip", "LowParse.SLow.Base.parse32_total", "LowParse.Spec.Enum.r_transitive_t_elim", "FStar.Mul.op_Star", "LowParse.Spec.Enum.enum_repr_of_key", "LowParse.SLow.Base.bytes_of_seq'", "LowParse.Spec.Sum.dsum_tag_of_data", "LowParse.Spec.Sum.dsum_enum", "LowParse.Spec.Sum.dsum_type_of_tag", "LowParse.Spec.Enum.feq", "LowParse.Spec.Sum.serialize_sum_cases'", "LowParse.Spec.Enum.assoc_flip_intro", "LowParse.SLow.Combinators.parse32_nondep_then", "LowStar.Monotonic.Buffer.srel", "LowParse.SLow.Combinators.parse32_synth", "LowParse.Spec.Combinators.parse_filter_kind", "LowParse.SLow.Enum.parse32_enum_key", "LowParse.Spec.Combinators.and_then_kind", "LowParse.SLow.Combinators.parse32_filter", "LowParse.Spec.Enum.parse_enum_key", "LowParse.SLow.Base.serializer32_correct", "LowParse.Spec.Sum.dsum_key_type", "LowParse.SLow.Combinators.parse32_synth'", "LowParse.SLow.Sum.serializer32_sum_gen_precond", "LowParse.Spec.Enum.parse_total_enum_key", "LowParse.Spec.Sum.synth_dsum_case_recip'", "LowParse.Spec.Combinators.synth_inverse_intro'" ], "source_upto_this": "module LowParse.SLow.Sum\ninclude LowParse.Spec.Sum\ninclude LowParse.SLow.Enum\n\nmodule B32 = LowParse.Bytes32\nmodule U32 = FStar.UInt32\n\nlet serializer32_sum_gen_precond\n (kt: parser_kind)\n (k: parser_kind)\n: GTot Type0\n= kt.parser_kind_subkind == Some ParserStrong /\\\n Some? kt.parser_kind_high /\\\n Some? k.parser_kind_high /\\ (\n let (Some vt) = kt.parser_kind_high in\n let (Some v) = k.parser_kind_high in\n vt + v < 4294967296\n )\n\ninline_for_extraction\nlet parse32_sum_t (t: sum) : Tot Type =\n bytes32 -> Tot (option (sum_type t * U32.t))\n\nlet parse32_sum_eq (t: sum) : Tot (parse32_sum_t t -> parse32_sum_t t -> GTot Type0) =\n feq _ _ (eq2 #_)\n\ninline_for_extraction\nlet parse32_sum_if (t: sum) : Tot (if_combinator _ (parse32_sum_eq t)) =\n fif _ _ _ (default_if _)\n\nlet parse32_sum_eq_refl (t: sum) : Tot (r_reflexive_t _ (parse32_sum_eq t)) =\n fun _ -> ()\n\nlet parse32_sum_eq_trans (t: sum) : Tot (r_transitive_t _ (parse32_sum_eq t)) = feq_trans _ _ (eq2 #_)\n\ninline_for_extraction\nlet parse32_sum_cases'\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (k: sum_key t)\n: Tot (parser32 (parse_sum_cases' t pc k))\n= [@inline_let]\n let _ = synth_sum_case_injective t k in\n parse32_synth'\n (dsnd (pc k))\n (synth_sum_case t k)\n (pc32 k)\n ()\n\nlet parse32_sum_aux\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (p32: parser32 (parse_enum_key p (sum_enum t)))\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n: GTot (parser32 (parse_sum t p pc))\n= fun input ->\n parse_sum_eq' t p pc (B32.reveal input);\n [@inline_let]\n let res : option (sum_type t * U32.t) =\n //NS: hoist nested match\n //we do not expect the case analysis to\n //on `p32 input` to reduce; hoist it for more efficient\n //normalization.\n //Note, in some simple cases, e.g., parsing raw enums\n //this r the pcases below maybe statically evaluated\n //to a `Some v`; this forgoes reduction in those simple\n //cases for more efficient extraction in more complex\n //common cases\n let pi = p32 input in\n match pi with\n | None -> None\n | Some (k, consumed_k) ->\n let input_k = B32.b32slice input consumed_k (B32.len input) in\n //NS: hoist nested match\n let pcases1 = parse32_sum_cases' t pc pc32 k input_k in\n match pcases1 with\n | None -> None\n | Some (x, consumed_x) ->\n Some ((x <: sum_type t), consumed_k `U32.add` consumed_x)\n in\n (res <: (res: option (sum_type t * U32.t) { parser32_correct (parse_sum t p pc) input res } ))\n\ninline_for_extraction\nlet parse32_sum_cases_t\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n: Tot Type\n= parser32 (parse_sum_cases t pc k)\n\nlet parse32_sum_cases_t_eq\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n (x y : parse32_sum_cases_t t pc k)\n: GTot Type0\n= True\n\ninline_for_extraction\nlet parse32_sum_cases_t_if\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (k: sum_key t)\n: Tot (if_combinator _ (parse32_sum_cases_t_eq t pc k))\n= fun cond (sv_true: cond_true cond -> Tot (parse32_sum_cases_t t pc k)) (sv_false: cond_false cond -> Tot (parse32_sum_cases_t t pc k)) input ->\n if cond\n then (sv_true () input <: (res: _ { parser32_correct (parse_sum_cases t pc k) input res}))\n else (sv_false () input <: (res: _ {parser32_correct (parse_sum_cases t pc k) input res}))\n\ninline_for_extraction\nlet parse32_sum_cases_aux\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (k: sum_key t)\n: Tot (parser32 (parse_sum_cases t pc k))\n= fun (input: B32.bytes) ->\n [@inline_let] let _ = parse_sum_cases_eq' t pc k (B32.reveal input) in\n (parse32_sum_cases' t pc pc32 k input <: (res: _ { parser32_correct (parse_sum_cases t pc k) input res } ))\n\ninline_for_extraction\nlet parse32_sum_cases\n (t: sum)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (destr: dep_enum_destr (sum_enum t) (parse32_sum_cases_t t pc))\n (k: sum_key t)\n: Tot (parser32 (parse_sum_cases t pc k))\n= destr\n _\n (parse32_sum_cases_t_if t pc)\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (parse32_sum_cases_aux t pc pc32)\n k\n\ninline_for_extraction\nlet parse32_sum'\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (p32: parser32 (parse_enum_key p (sum_enum t)))\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (destr: enum_destr_t (option (sum_type t * U32.t)) (sum_enum t))\n (input: B32.bytes)\n: Pure (option (sum_type t * U32.t))\n (requires True)\n (ensures (fun res -> res == parse32_sum_aux t p p32 pc pc32 input))\n= [@inline_let]\n let res : option (sum_type t * U32.t) =\n //NS: hoist nested match\n let pi = p32 input in\n match pi with\n | None -> None\n | Some (k, consumed_k) ->\n let input_k = B32.b32slice input consumed_k (B32.len input) in\n destr\n (eq2 #(option (sum_type t * U32.t))) (default_if _)\n (fun _ -> ()) (fun _ _ _ -> ())\n (fun k ->\n //NS: hoist nested match\n let pcases2 = parse32_sum_cases' t pc pc32 k input_k in\n match pcases2 with\n | None -> None\n | Some (x, consumed_x) ->\n Some ((x <: sum_type t), consumed_k `U32.add` consumed_x)\n )\n k\n in\n res\n\ninline_for_extraction\nlet parse32_sum\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (p32: parser32 (parse_enum_key p (sum_enum t)))\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (destr: enum_destr_t (option (sum_type t * U32.t)) (sum_enum t))\n: Tot (parser32 (parse_sum t p pc))\n= fun input ->\n (parse32_sum' t p p32 pc pc32 destr input <: (res: option (sum_type t * U32.t) { parser32_correct (parse_sum t p pc) input res } ))\n\ninline_for_extraction\nlet parse32_sum2\n (#kt: parser_kind)\n (t: sum)\n (p: parser kt (sum_repr_type t))\n (p32: parser32 p)\n (pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (pc32: ((x: sum_key t) -> Tot (parser32 (dsnd (pc x)))))\n (destr: enum_destr_t (option (sum_type t * U32.t)) (sum_enum t))\n (f: maybe_enum_key_of_repr'_t (sum_enum t))\n: Tot (parser32 (parse_sum t p pc))\n= parse32_sum t p (parse32_enum_key p32 (sum_enum t) f) pc pc32 destr\n\ninline_for_extraction\nlet serialize32_sum_cases_t\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n: Tot Type\n= serializer32 (serialize_sum_cases t pc sc k)\n\nlet serialize32_sum_cases_t_eq\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n (x y: serialize32_sum_cases_t t sc k)\n: GTot Type0\n= True\n\ninline_for_extraction\nlet serialize32_sum_cases_t_if\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n: Tot (if_combinator _ (serialize32_sum_cases_t_eq t sc k))\n= fun cond (sv_true: (cond_true cond -> Tot (serialize32_sum_cases_t t sc k))) (sv_false: (cond_false cond -> Tot (serialize32_sum_cases_t t sc k))) input ->\n if cond\n then (sv_true () input <: (res: _ { serializer32_correct (serialize_sum_cases t pc sc k) input res } ))\n else (sv_false () input <: (res: _ { serializer32_correct (serialize_sum_cases t pc sc k) input res } ))\n\ninline_for_extraction\nlet serialize32_sum_cases_aux\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (k: sum_key t)\n: Tot (serializer32 (serialize_sum_cases t pc sc k))\n= fun input ->\n [@inline_let] let _ =\n Classical.forall_intro (parse_sum_cases_eq' t pc k);\n synth_sum_case_injective t k;\n synth_sum_case_inverse t k\n in\n serialize32_synth\n _\n (synth_sum_case t k)\n _\n (sc32 k)\n (synth_sum_case_recip t k)\n (fun x -> synth_sum_case_recip t k x)\n ()\n input\n\ninline_for_extraction\nlet serialize32_sum_cases\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (serialize32_sum_cases_t t sc))\n (k: sum_key t)\n: Tot (serializer32 (serialize_sum_cases t pc sc k))\n= destr\n _\n (serialize32_sum_cases_t_if t sc)\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (serialize32_sum_cases_aux t sc sc32)\n k\n\nlet serialize32_sum_aux\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (s32: serializer32 (serialize_enum_key _ s (sum_enum t)))\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (u: squash (serializer32_sum_gen_precond kt (weaken_parse_cases_kind t pc)))\n: GTot (serializer32 (serialize_sum t s sc))\n= fun x ->\n serialize_sum_eq t s sc x;\n let tg = sum_tag_of_data t x in\n let s1 = s32 tg in\n let s2 = sc32 tg (synth_sum_case_recip t tg x) in\n let res = s1 `B32.b32append` s2 in\n (res <: (res: B32.bytes { serializer32_correct (serialize_sum t s sc) x res } ))\n\ninline_for_extraction\nlet serialize32_sum_destr_codom\n (t: sum)\n (k: sum_key t)\n: Tot Type\n= refine_with_tag (sum_tag_of_data t) k -> Tot B32.bytes\n\nmodule T = FStar.Tactics\n\nlet serialize32_sum_destr_eq\n (t: sum)\n (k: sum_key t)\n: Tot (serialize32_sum_destr_codom t k -> serialize32_sum_destr_codom t k -> GTot Type0)\n= _ by (T.apply (`feq); T.apply (`eq2))\n\nlet serialize32_sum_destr_trans\n (t: sum)\n (k: sum_key t)\n: Tot (r_transitive_t _ (serialize32_sum_destr_eq t k))\n= feq_trans _ _ (eq2 #_)\n\ninline_for_extraction\nlet serialize32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (serialize32_sum_destr_eq t k))\n= // _ by (T.apply (`fif); T.fail \"abc\")\n fif _ _ _ (default_if _)\n\n#set-options \"--z3rlimit 32\"\n\ninline_for_extraction\nlet serialize32_sum\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (s32: serializer32 (serialize_enum_key _ s (sum_enum t)))\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (serialize32_sum_destr_codom t))\n (u: squash (serializer32_sum_gen_precond kt (weaken_parse_cases_kind t pc)))\n: Tot (serializer32 (serialize_sum t s sc))\n= fun x ->\n [@inline_let]\n let _ = serialize_sum_eq t s sc x in\n let tg = sum_tag_of_data t x in\n let s1 = s32 tg in\n [@inline_let]\n let phi tg x = sc32 tg (synth_sum_case_recip t tg x) in\n [@inline_let]\n let phi'tg = destr\n (serialize32_sum_destr_eq t)\n (serialize32_sum_destr_if t)\n (fun _ _ -> ())\n (serialize32_sum_destr_trans t)\n phi\n tg\n in\n let s2 = phi'tg x in\n [@inline_let]\n let _ =\n let phitg = phi tg in\n feq_elim _ _ (eq2 #_) phitg phi'tg x\n in\n let res = s1 `B32.b32append` s2 in\n (res <: (res: B32.bytes { serializer32_correct (serialize_sum t s sc) x res } ))\n\n#reset-options\n\ninline_for_extraction\nlet serialize32_sum2\n (#kt: parser_kind)\n (t: sum)\n (#p: parser kt (sum_repr_type t))\n (s: serializer p)\n (s32: serializer32 s)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (serializer32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (serialize32_sum_destr_codom t))\n (f: enum_repr_of_key'_t (sum_enum t))\n (u: squash (serializer32_sum_gen_precond kt (weaken_parse_cases_kind t pc)))\n: Tot (serializer32 (serialize_sum t s sc))\n= serialize32_sum t s (serialize32_enum_key s32 (sum_enum t) f) sc sc32 destr u\n\ninline_for_extraction\nlet size32_sum_cases_t\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n: Tot Type\n= size32 (serialize_sum_cases t pc sc k)\n\nlet size32_sum_cases_t_eq\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n (x y: size32_sum_cases_t t sc k)\n: GTot Type0\n= True\n\ninline_for_extraction\nlet size32_sum_cases_t_if\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_cases_t_eq t sc k))\n= fun cond (sv_true: (cond_true cond -> Tot (size32_sum_cases_t t sc k))) (sv_false: (cond_false cond -> Tot (size32_sum_cases_t t sc k))) input ->\n if cond\n then (sv_true () input <: (res: _ { size32_postcond (serialize_sum_cases t pc sc k) input res } ))\n else (sv_false () input <: (res: _ { size32_postcond (serialize_sum_cases t pc sc k) input res } ))\n\ninline_for_extraction\nlet size32_sum_cases_aux\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (size32 (sc x))))\n (k: sum_key t)\n: Tot (size32 (serialize_sum_cases t pc sc k))\n= fun input ->\n [@inline_let] let _ =\n Classical.forall_intro (parse_sum_cases_eq' t pc k);\n synth_sum_case_injective t k;\n synth_sum_case_inverse t k\n in\n size32_synth\n _\n (synth_sum_case t k)\n _\n (sc32 k)\n (synth_sum_case_recip t k)\n (fun x -> synth_sum_case_recip t k x)\n ()\n input\n\ninline_for_extraction\nlet size32_sum_cases\n (t: sum)\n (#pc: ((x: sum_key t) -> Tot (k: parser_kind & parser k (sum_type_of_tag t x))))\n (sc: ((x: sum_key t) -> Tot (serializer (dsnd (pc x)))))\n (sc32: ((x: sum_key t) -> Tot (size32 (sc x))))\n (destr: dep_enum_destr (sum_enum t) (size32_sum_cases_t t sc))\n (k: sum_key t)\n: Tot (size32 (serialize_sum_cases t pc sc k))\n= destr\n _\n (size32_sum_cases_t_if t sc)\n (fun _ _ -> ())\n (fun _ _ _ _ -> ())\n (size32_sum_cases_aux t sc sc32)\n k\n\ninline_for_extraction\nlet size32_sum_destr_codom\n (t: sum)\n (k: sum_key t)\n: Tot Type\n= refine_with_tag (sum_tag_of_data t) k -> Tot U32.t\n\nlet size32_sum_destr_eq\n (t: sum)\n (k: sum_key t)\n: Tot (size32_sum_destr_codom t k -> size32_sum_destr_codom t k -> GTot Type0)\n= _ by (T.apply (`feq); T.apply (`eq2))\n\nlet size32_sum_destr_trans\n (t: sum)\n (k: sum_key t)\n: Tot (r_transitive_t _ (size32_sum_destr_eq t k))\n= feq_trans _ _ (eq2 #_)\n\ninline_for_extraction", "sketch": [ "Step 1: The definition `size32_sum_destr_if` is about creating a conditional combinator for the size32 sum destructor. This combinator will take a condition and two functions (one for the true case and one for the false case) and return a function that applies the appropriate function based on the condition.\nStep 2: The implementation uses the `fif` function to create the conditional combinator. It takes the condition, the true case function, and the false case function, and applies the appropriate function based on the condition. The result is then cast to ensure it satisfies the postcondition.", "Step 1: The definition `size32_sum_destr_if` is about creating a conditional combinator for the `size32_sum_destr_eq` function. This combinator will choose between two functions based on a condition.\nStep 2: The implementation will use the `fif` function to create the conditional combinator. It will take a condition and two functions (one for the true case and one for the false case) and return the appropriate function based on the condition.", "Step 1: The definition `size32_sum_destr_if` is about creating a conditional combinator for the size32 function applied to sum destructors. This function will take a condition and two possible outcomes, and return the appropriate size32 value based on the condition.\nStep 2: The implementation uses the `fif` combinator to handle the conditional logic. It applies the `default_if` function to handle the default case, ensuring that the result satisfies the `size32_sum_destr_eq` equality.", "Step 1: The definition `size32_sum_destr_if` is about creating a conditional combinator for the size32_sum_destr_eq function. This function will take a condition and two functions, one for the true case and one for the false case, and apply the appropriate function based on the condition.\nStep 2: The implementation will use the `fif` combinator to handle the conditional logic, similar to other `*_if` functions in the module. It will apply the true function if the condition is true, and the false function otherwise, ensuring that the result satisfies the postcondition for size32.", "Step 1: This definition is about creating a conditional combinator for the size32_sum_destr_eq function. The size32_sum_destr_eq function ensures that two functions of type size32_sum_destr_codom are equal.\nStep 2: The implementation will use the fif combinator to create a conditional combinator. This will allow us to choose between two functions based on a condition, ensuring that the chosen function satisfies the size32_sum_destr_eq property.", "Step 1: The definition `size32_sum_destr_if` is about creating a conditional combinator for the size computation of a sum type's serialization. It ensures that the size computation respects the conditional logic provided.\nStep 2: The implementation uses the `fif` combinator to handle the conditional logic. It takes a condition and two functions (one for the true case and one for the false case) and applies the appropriate function based on the condition. The result is then cast to ensure it satisfies the postcondition for size computation.", "Step 1: The definition `size32_sum_destr_if` is about creating a conditional combinator for the size32 sum destruction function. This combinator will take a condition and two functions (one for the true branch and one for the false branch) and return a function that applies the appropriate branch based on the condition.\nStep 2: The implementation uses the `fif` combinator to create the conditional function. It takes the condition, the true branch function, and the false branch function, and applies the appropriate function based on the condition. The result is then cast to ensure it satisfies the postcondition for the size32 sum destruction function.", "Step 1: This definition is about creating a conditional combinator for the size32_sum_destr_eq function. The function size32_sum_destr_if will take a condition and two functions (one for the true branch and one for the false branch) and return a function that applies the appropriate branch based on the condition.\nStep 2: The implementation will use the fif combinator to create the conditional function. It will take the condition, the true branch function, and the false branch function as arguments, and return a function that applies the appropriate branch based on the condition.", "Step 1: This definition is about creating a conditional combinator for the `size32_sum_destr_eq` function. The `size32_sum_destr_eq` function checks the equality of two functions that take a refined tag and return a `U32.t` value. The conditional combinator will choose between two functions based on a condition.\nStep 2: The implementation will use the `fif` function to create the conditional combinator. It will take a condition and two functions (`sv_true` and `sv_false`). Depending on the condition, it will return either `sv_true` or `sv_false`.", "Step 1: The definition `size32_sum_destr_if` is about creating a conditional combinator for the size32 computation of sum destructors. This function will take a condition and two functions (one for the true branch and one for the false branch) and return a function that applies the appropriate branch based on the condition.\nStep 2: The implementation uses the `fif` combinator to construct the conditional function. It ensures that the result satisfies the postcondition for the size32 computation of sum destructors." ], "generated_solution": [ "let size32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_destr_eq t k))\n= fif _ _ _ (default_if _)", "let size32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_destr_eq t k))\n= fif _ _ _ (default_if _)", "let size32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_destr_eq t k))\n= fif _ _ _ (default_if _)", "let size32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_destr_eq t k))\n= fif _ _ _ (default_if _)", "= fif _ _ _ (default_if _)", "let size32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_destr_eq t k))\n= fif _ _ _ (default_if _)", "let size32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_destr_eq t k))\n= fif _ _ _ (default_if _)", "let size32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_destr_eq t k))\n= fif _ _ _ (default_if _)", "let size32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_destr_eq t k))\n= fif _ _ _ (default_if _)", "let size32_sum_destr_if\n (t: sum)\n (k: sum_key t)\n: Tot (if_combinator _ (size32_sum_destr_eq t k))\n= fif _ _ _ (default_if _)" ] }, { "file_name": "LowParse.SLow.VCList.fst", "name": "LowParse.SLow.VCList.parse_nlist_tailrec", "opens_and_abbrevs": [ { "abbrev": "B32", "full_module": "LowParse.Bytes32" }, { "abbrev": "L", "full_module": "FStar.List.Tot" }, { "abbrev": "Classical", "full_module": "FStar.Classical" }, { "abbrev": "U32", "full_module": "FStar.UInt32" }, { "abbrev": "Seq", "full_module": "FStar.Seq" }, { "open": "LowParse.SLow.List" }, { "open": "LowParse.Spec.VCList" }, { "open": "LowParse.SLow" }, { "open": "LowParse.SLow" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val parse_nlist_tailrec\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (accu: (list t * nat))\n (b: bytes)\n : GTot (option (list t * nat))", "source_definition": "let rec parse_nlist_tailrec\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (accu: list t * nat)\n (b: bytes)\n: GTot (option (list t * nat))\n= if n = 0\n then Some accu\n else\n match parse p b with\n | Some (elem, consumed) ->\n let (l0, consumed0) = accu in\n let b' = Seq.slice b consumed (Seq.length b) in\n parse_nlist_tailrec (n - 1) p (elem :: l0, consumed0 + consumed) b'\n | _ -> None", "source_range": { "start_line": 11, "start_col": 0, "end_line": 27, "end_col": 15 }, "interleaved": false, "definition": "fun n p accu b ->\n (match n = 0 with\n | true -> FStar.Pervasives.Native.Some accu\n | _ ->\n (match LowParse.Spec.Base.parse p b with\n | FStar.Pervasives.Native.Some #_ (FStar.Pervasives.Native.Mktuple2 #_ #_ elem consumed) ->\n let _ = accu in\n (let FStar.Pervasives.Native.Mktuple2 #_ #_ l0 consumed0 = _ in\n let b' = FStar.Seq.Base.slice b consumed (FStar.Seq.Base.length b) in\n LowParse.SLow.VCList.parse_nlist_tailrec (n - 1) p (elem :: l0, consumed0 + consumed) b'\n )\n <:\n FStar.Pervasives.Native.option (Prims.list t * Prims.nat)\n | _ -> FStar.Pervasives.Native.None)\n <:\n FStar.Pervasives.Native.option (Prims.list t * Prims.nat))\n <:\n Prims.GTot (FStar.Pervasives.Native.option (Prims.list t * Prims.nat))", "effect": "Prims.GTot", "effect_flags": [ "sometrivial" ], "mutual_with": [], "premises": [ "Prims.nat", "LowParse.Spec.Base.parser_kind", "LowParse.Spec.Base.parser", "FStar.Pervasives.Native.tuple2", "Prims.list", "LowParse.Bytes.bytes", "Prims.op_Equality", "Prims.int", "FStar.Pervasives.Native.Some", "Prims.bool", "LowParse.Spec.Base.parse", "LowParse.Spec.Base.consumed_length", "LowParse.SLow.VCList.parse_nlist_tailrec", "Prims.op_Subtraction", "FStar.Pervasives.Native.Mktuple2", "Prims.Cons", "Prims.op_Addition", "FStar.Seq.Base.seq", "LowParse.Bytes.byte", "FStar.Seq.Base.slice", "FStar.Seq.Base.length", "FStar.Pervasives.Native.option", "FStar.Pervasives.Native.None" ], "proof_features": [ "recursion" ], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "\n n: Prims.nat ->\n p: LowParse.Spec.Base.parser k t ->\n accu: (Prims.list t * Prims.nat) ->\n b: LowParse.Bytes.bytes\n -> Prims.GTot (FStar.Pervasives.Native.option (Prims.list t * Prims.nat))", "prompt": "let rec parse_nlist_tailrec\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (accu: list t * nat)\n (b: bytes)\n : GTot (option (list t * nat)) =\n ", "expected_response": "if n = 0\nthen Some accu\nelse\n match parse p b with\n | Some (elem, consumed) ->\n let l0, consumed0 = accu in\n let b' = Seq.slice b consumed (Seq.length b) in\n parse_nlist_tailrec (n - 1) p (elem :: l0, consumed0 + consumed) b'\n | _ -> None", "source": { "project_name": "everparse", "file_name": "src/lowparse/LowParse.SLow.VCList.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git" }, "dependencies": { "source_file": "LowParse.SLow.VCList.fst", "checked_file": "dataset/LowParse.SLow.VCList.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/LowParse.Spec.VCList.fsti.checked", "dataset/LowParse.SLow.List.fst.checked", "dataset/LowParse.Math.fst.checked", "dataset/LowParse.Bytes32.fst.checked", "dataset/FStar.UInt32.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Mul.fst.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.Classical.fsti.checked", "dataset/C.Loops.fst.checked" ] }, "definitions_in_context": [], "closest": [ "val parse_nlist_eq (n: nat) (#k: parser_kind) (#t: Type) (p: parser k t) (b: bytes)\n : Lemma\n (parse (parse_nlist n p) b ==\n (if n = 0\n then Some ([], 0)\n else\n match parse p b with\n | Some (elem, consumed) ->\n let b' = Seq.slice b consumed (Seq.length b) in\n (match parse (parse_nlist (n - 1) p) b' with\n | Some (q, consumed') -> Some (elem :: q, consumed + consumed')\n | _ -> None)\n | _ -> None))\nlet parse_nlist_eq\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (b: bytes)\n: Lemma (\n parse (parse_nlist n p) b == (\n if n = 0\n then Some ([], 0)\n else match parse p b with\n | Some (elem, consumed) ->\n let b' = Seq.slice b consumed (Seq.length b) in\n begin match parse (parse_nlist (n - 1) p) b' with\n | Some (q, consumed') -> Some (elem :: q, consumed + consumed')\n | _ -> None\n end\n | _ -> None\n ))\n= if n = 0\n then ()\n else begin\n parse_synth_eq\n (p `nondep_then` parse_nlist' (n - 1) p)\n (synth_nlist (n - 1))\n b;\n nondep_then_eq p (parse_nlist' (n - 1) p) b\n end", "val parse_nlist_eq (n: nat) (#t: Type0) (p: parser_spec t) (b: bytes)\n : Tot\n (squash (parse (parse_nlist n p) b ==\n (if n = 0\n then Some ([], 0)\n else\n match parse p b with\n | Some (elem, consumed) ->\n let b' = Seq.slice b consumed (Seq.length b) in\n (match parse (parse_nlist (n - 1) p) b' with\n | Some (q, consumed') -> Some (elem :: q, consumed + consumed')\n | _ -> None)\n | _ -> None)))\nlet parse_nlist_eq\n (n: nat)\n (#t: Type0)\n (p: parser_spec t)\n (b: bytes)\n: Tot (squash (\n parse (parse_nlist n p) b == (\n if n = 0\n then Some ([], 0)\n else match parse p b with\n | Some (elem, consumed) ->\n let b' = Seq.slice b consumed (Seq.length b) in\n begin match parse (parse_nlist (n - 1) p) b' with\n | Some (q, consumed') -> Some (elem :: q, consumed + consumed')\n | _ -> None\n end\n | _ -> None\n )))\n= if n = 0\n then ()\n else begin\n parse_synth_eq\n (p `nondep_then` parse_nlist' (n - 1) p)\n (synth_nlist (n - 1))\n (synth_nlist_recip (n - 1))\n b;\n nondep_then_eq p (parse_nlist' (n - 1) p) b\n end", "val parse_nlist' (n: nat) (#k: parser_kind) (#t: Type) (p: parser k t)\n : Tot (parser (parse_nlist_kind n k) (nlist n t))\nlet rec parse_nlist'\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n: Tot (parser (parse_nlist_kind n k) (nlist n t))\n= if n = 0\n then parse_ret nlist_nil\n else begin\n [@inline_let] let _ = assert (parse_nlist_kind n k == parse_nlist_kind' n k) in\n parse_synth\n (p `nondep_then` parse_nlist' (n - 1) p)\n (synth_nlist (n - 1))\n end", "val parse_list_tailrec_inv\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (input: bytes32)\n (b: bool)\n (x: option (bytes32 * list t))\n : GTot Type0\nlet parse_list_tailrec_inv\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (input: bytes32)\n (b: bool)\n (x: option (bytes32 * list t))\n: GTot Type0\n= match x with\n | Some (input', accu') ->\n parse_list_tailrec' p32 input [] == parse_list_tailrec' p32 input' accu' /\\\n (b == false ==> B32.length input' == 0)\n | None -> \n b == false /\\ None? (parse_list_tailrec' p32 input [])", "val parse_list_tailrec'\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (b: bytes32)\n (aux: list t)\n : GTot (option (list t)) (decreases (B32.length b))\nlet rec parse_list_tailrec'\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (b: bytes32)\n (aux: list t)\n: GTot (option (list t))\n (decreases (B32.length b))\n= parse_list_eq p (B32.reveal b);\n if B32.len b = 0ul\n then \n Some (L.rev aux)\n else\n match p32 b with\n | None -> None\n | Some (v, n) ->\n if n = 0ul\n then None (* elements cannot be empty *)\n else\n\tparse_list_tailrec' p32 (B32.slice b n (B32.len b)) (v :: aux)", "val parse_nlist\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n: Tot (y: parser (parse_nlist_kind n k) (nlist n t) { y == parse_nlist' n p } )\nlet parse_nlist\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n: Tot (y: parser (parse_nlist_kind n k) (nlist n t) { y == parse_nlist' n p } )\n= parse_nlist' n p", "val parse_list_aux (#k: parser_kind) (#t: Type) (p: parser k t) (b: bytes)\n : GTot (option (list t * (consumed_length b))) (decreases (Seq.length b))\nlet rec parse_list_aux\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (b: bytes)\n: GTot (option (list t * (consumed_length b)))\n (decreases (Seq.length b))\n= if Seq.length b = 0\n then \n Some ([], (0 <: consumed_length b))\n else\n match parse p b with\n | None -> None\n | Some (v, n) ->\n if n = 0\n then None (* elements cannot be empty *)\n else\n match parse_list_aux p (Seq.slice b n (Seq.length b)) with\n\t| Some (l, n') -> Some (v :: l, (n + n' <: consumed_length b))\n\t| _ -> None", "val parse_nlist (n:U32.t) (#wk: _) (#k:parser_kind true wk) (#t:_) (p:parser k t)\r\n : Tot (parser kind_nlist (nlist n t))\nlet parse_nlist n #wk #k #t p\r\n = let open LowParse.Spec.FLData in\r\n let open LowParse.Spec.List in\r\n parse_weaken\r\n #false #WeakKindStrongPrefix #(parse_fldata_kind (U32.v n) parse_list_kind) #(list t)\r\n (LowParse.Spec.FLData.parse_fldata (LowParse.Spec.List.parse_list p) (U32.v n))\r\n #false kind_nlist", "val parse_list_tailrec\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (input: bytes32)\n : Tot (res: option (list t) {res == parse_list_tailrec' p32 input []})\nlet parse_list_tailrec\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (input: bytes32)\n: Tot (res: option (list t) { res == parse_list_tailrec' p32 input [] } )\n= let accu =\n CL.total_while\n (parse_list_tailrec_measure #t)\n (parse_list_tailrec_inv p32 input)\n (fun x -> parse_list_tailrec_body p32 input x)\n (Some (input, []))\n in\n match accu with\n | None -> None\n | Some (_, accu') -> Some (list_rev accu')", "val parse_nlist' (n: nat) (#t: Type0) (p: parser_spec t) : Tot (parser_spec (nlist n t))\nlet rec parse_nlist'\n (n: nat)\n (#t: Type0)\n (p: parser_spec t)\n: Tot (parser_spec (nlist n t))\n= if n = 0\n then parse_ret nlist_nil\n else begin\n parse_synth\n (p `nondep_then` parse_nlist' (n - 1) p)\n (synth_nlist (n - 1))\n (synth_nlist_recip (n - 1))\n end", "val parse_nlist\n (n: nat)\n (#t: Type0)\n (p: parser_spec t)\n: Tot (y: parser_spec (nlist n t) { y == parse_nlist' n p } )\nlet parse_nlist\n (n: nat)\n (#t: Type0)\n (p: parser_spec t)\n: Tot (y: parser_spec (nlist n t) { y == parse_nlist' n p } )\n= parse_nlist' n p", "val tot_parse_list_eq (#k: parser_kind) (#t: Type) (p: tot_parser k t) (b: bytes)\n : Lemma\n (parse (tot_parse_list p) b ==\n (if Seq.length b = 0\n then Some ([], (0 <: consumed_length b))\n else\n match parse p b with\n | None -> None\n | Some (v, n) ->\n if n = 0\n then None\n else\n match parse (tot_parse_list p) (Seq.slice b n (Seq.length b)) with\n | Some (l, n') -> Some (v :: l, (n + n' <: consumed_length b))\n | _ -> None))\nlet tot_parse_list_eq\n (#k: parser_kind)\n (#t: Type)\n (p: tot_parser k t)\n (b: bytes)\n: Lemma\n (parse (tot_parse_list p) b == (\n if Seq.length b = 0\n then \n Some ([], (0 <: consumed_length b))\n else\n match parse p b with\n | None -> None\n | Some (v, n) ->\n if n = 0\n then None (* elements cannot be empty *)\n else\n match parse (tot_parse_list p) (Seq.slice b n (Seq.length b)) with\n\t | Some (l, n') -> Some (v :: l, (n + n' <: consumed_length b))\n\t | _ -> None\n ))\n= parse_list_eq #k p b", "val parse_list_tailrec'_correct\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (b: bytes32)\n : Lemma\n (match parse (parse_list p) (B32.reveal b) with\n | Some (l, n) -> parse_list_tailrec' p32 b [] == Some l\n | None -> parse_list_tailrec' p32 b [] == None)\nlet parse_list_tailrec'_correct\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (b: bytes32)\n: Lemma\n begin match parse (parse_list p) (B32.reveal b) with\n | Some (l, n) -> parse_list_tailrec' p32 b [] == Some l\n | None -> parse_list_tailrec' p32 b [] == None\n end\n= parse_list_tailrec'_correct' p32 b []", "val validate_nlist (n: U32.t) (#k: parser_kind) (#t: Type) (#p: parser k t) (v: validator p)\n : Tot (validator (parse_nlist (U32.v n) p))\nlet validate_nlist\n (n: U32.t)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (v: validator p)\n: Tot (validator (parse_nlist (U32.v n) p))\n= fun #rrel #rel input pos ->\n let h0 = HST.get () in\n HST.push_frame ();\n let bpos1 : B.buffer U64.t = B.alloca pos 1ul in\n let br = B.alloca n 1ul in\n let h1 = HST.get () in\n C.Loops.do_while\n (fun h stop ->\n B.modifies (B.loc_buffer bpos1 `B.loc_union` B.loc_buffer br) h1 h /\\ (\n let pos1 = B.get h bpos1 0 in\n let r = B.get h br 0 in\n U32.v r <= U32.v n /\\\n U64.v pos <= U64.v pos1 /\\ (\n if is_success pos1\n then\n let pos1 = uint64_to_uint32 pos1 in\n U32.v pos1 <= U32.v input.len /\\\n (valid (parse_nlist (U32.v n) p) h0 input (uint64_to_uint32 pos) <==> valid (parse_nlist (U32.v r) p) h0 input pos1) /\\\n ((valid (parse_nlist (U32.v n) p) h0 input (uint64_to_uint32 pos) /\\ valid (parse_nlist (U32.v r) p) h0 input pos1) ==> get_valid_pos (parse_nlist (U32.v n) p) h0 input (uint64_to_uint32 pos) == get_valid_pos (parse_nlist (U32.v r) p) h0 input pos1) /\\\n (stop == true ==> r == 0ul)\n else\n (stop == true /\\ (~ (valid (parse_nlist (U32.v n) p) h0 input (uint64_to_uint32 pos))))\n )))\n (fun _ ->\n let r = B.index br 0ul in\n if r = 0ul\n then true\n else\n let pos1 = B.index bpos1 0ul in\n let pos2 = v input pos1 in\n let _ = B.upd br 0ul (r `U32.sub` 1ul) in\n let _ = B.upd bpos1 0ul pos2 in\n [@inline_let]\n let stop = is_error pos2 in\n [@inline_let]\n let _ =\n if stop\n then valid_nlist_cons_not (U32.v r) p h0 input (uint64_to_uint32 pos1)\n else valid_nlist_cons' (U32.v r) p h0 input (uint64_to_uint32 pos1)\n in\n stop\n )\n ;\n let res = B.index bpos1 0ul in\n [@inline_let] let _ =\n if is_success res\n then valid_nlist_nil p h0 input (uint64_to_uint32 res)\n in\n HST.pop_frame ();\n res", "val parse_nlist_kind (n: nat) (k: parser_kind) : Tot (k': parser_kind{k' == parse_nlist_kind' n k})\nlet parse_nlist_kind\n (n: nat)\n (k: parser_kind)\n: Tot (k' : parser_kind { k' == parse_nlist_kind' n k })\n= [@inline_let] let _ =\n parse_nlist_kind_low n k;\n parse_nlist_kind_high n k;\n parse_nlist_kind_metadata n k;\n parse_nlist_kind_subkind n k\n in\n {\n parser_kind_low = n `mul` k.parser_kind_low;\n parser_kind_high = (match k.parser_kind_high with\n | None -> if n = 0 then Some 0 else None\n | Some b -> Some (n `mul` b)\n );\n parser_kind_metadata = (if n = 0 then Some ParserKindMetadataTotal else k.parser_kind_metadata);\n parser_kind_subkind = (if n = 0 then Some ParserStrong else k.parser_kind_subkind);\n }", "val tot_parse_list_aux (#k: parser_kind) (#t: Type) (p: tot_parser k t) (b: bytes)\n : Pure (option (list t * (consumed_length b)))\n (requires True)\n (ensures (fun y -> y == parse_list_aux #k p b))\n (decreases (Seq.length b))\nlet rec tot_parse_list_aux\n (#k: parser_kind)\n (#t: Type)\n (p: tot_parser k t)\n (b: bytes)\n: Pure (option (list t * (consumed_length b)))\n (requires True)\n (ensures (fun y -> y == parse_list_aux #k p b))\n (decreases (Seq.length b))\n= if Seq.length b = 0\n then \n Some ([], (0 <: consumed_length b))\n else\n match p b with\n | None -> None\n | Some (v, n) ->\n if n = 0\n then None (* elements cannot be empty *)\n else\n match tot_parse_list_aux p (Seq.slice b n (Seq.length b)) with\n\t| Some (l, n') -> Some (v :: l, (n + n' <: consumed_length b))\n\t| _ -> None", "val parse_list_tailrec'_correct'\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (b: bytes32)\n (aux: list t)\n : Lemma (requires True)\n (ensures\n (parse_list_tailrec' p32 b aux ==\n (match parse (parse_list p) (B32.reveal b) with\n | Some (l, n) -> Some (L.append (L.rev aux) l)\n | None -> None)))\n (decreases (B32.length b))\nlet rec parse_list_tailrec'_correct'\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (b: bytes32)\n (aux: list t)\n: Lemma\n (requires True)\n (ensures (\n parse_list_tailrec' p32 b aux == (\n match parse (parse_list p) (B32.reveal b) with\n | Some (l, n) -> Some (L.append (L.rev aux) l)\n | None -> None\n )))\n (decreases (B32.length b))\n= parse_list_eq p (B32.reveal b);\n if B32.len b = 0ul\n then\n L.append_l_nil (L.rev aux)\n else\n match p32 b with\n | None -> ()\n | Some (v, n) ->\n if n = 0ul\n then ()\n else begin\n\tlet s = B32.slice b n (B32.len b) in\n\tparse_list_tailrec'_correct' p32 s (v :: aux);\n\tmatch parse (parse_list p) (B32.reveal s) with\n\t| Some (l, n') ->\n list_append_rev_cons v aux l\n | None -> ()\n end", "val parse_nlist_total_fixed_size_aux\n (n: U32.t)\n (#wk: _)\n (#k: parser_kind true wk)\n (#t: _)\n (p: parser k t)\n (x: LP.bytes)\n : Lemma\n (requires\n (let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_high == Some k.parser_kind_low /\\\n U32.v n % k.parser_kind_low == 0 /\\ k.parser_kind_metadata == Some ParserKindMetadataTotal /\\\n Seq.length x >= U32.v n)) (ensures (Some? (LP.parse (parse_nlist n p) x)))\nlet parse_nlist_total_fixed_size_aux\r\n (n:U32.t) (#wk: _) (#k:parser_kind true wk) #t (p:parser k t)\r\n (x: LP.bytes)\r\n: Lemma\r\n (requires (\r\n let open LP in\r\n k.parser_kind_subkind == Some ParserStrong /\\\r\n k.parser_kind_high == Some k.parser_kind_low /\\\r\n U32.v n % k.parser_kind_low == 0 /\\\r\n k.parser_kind_metadata == Some ParserKindMetadataTotal /\\\r\n Seq.length x >= U32.v n\r\n ))\r\n (ensures (\r\n Some? (LP.parse (parse_nlist n p) x)\r\n ))\r\n= let x' = Seq.slice x 0 (U32.v n) in\r\n let cnt = (U32.v n / k.LP.parser_kind_low) in\r\n FStar.Math.Lemmas.lemma_div_exact (U32.v n) k.LP.parser_kind_low;\r\n FStar.Math.Lemmas.nat_over_pos_is_nat (U32.v n) k.LP.parser_kind_low;\r\n LowParse.Spec.List.parse_list_total_constant_size p cnt x';\r\n LP.parser_kind_prop_equiv LowParse.Spec.List.parse_list_kind (LowParse.Spec.List.parse_list p)", "val parse_nlist_kind' (n: nat) (k: parser_kind) : GTot parser_kind (decreases n)\nlet rec parse_nlist_kind'\n (n: nat)\n (k: parser_kind)\n: GTot parser_kind\n (decreases n)\n= if n = 0\n then parse_ret_kind\n else k `and_then_kind` parse_nlist_kind' (n - 1) k", "val serialize_nlist'\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n : Tot (serializer (parse_nlist n p))\nlet rec serialize_nlist'\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n: Tot (serializer (parse_nlist n p))\n= if n = 0\n then begin\n Classical.forall_intro (nlist_nil_unique t);\n (fun _ -> Seq.empty)\n end\n else begin\n synth_inverse_1 t (n - 1);\n synth_inverse_2 t (n - 1);\n serialize_synth _ (synth_nlist (n - 1)) (serialize_nondep_then s (serialize_nlist' (n - 1) s)) (synth_nlist_recip (n - 1)) ()\n end", "val parse_list_tailrec_body\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (input: bytes32)\n (x: option (bytes32 * list t))\n : Pure (bool * option (bytes32 * list t))\n (requires (parse_list_tailrec_inv p32 input true x))\n (ensures\n (fun (continue, y) ->\n parse_list_tailrec_inv p32 input continue y /\\\n (if continue then parse_list_tailrec_measure y < parse_list_tailrec_measure x else True)\n ))\nlet parse_list_tailrec_body\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (p32: parser32 p)\n (input: bytes32)\n: (x: option (bytes32 * list t)) ->\n Pure (bool * option (bytes32 * list t))\n (requires (parse_list_tailrec_inv p32 input true x))\n (ensures (fun (continue, y) ->\n parse_list_tailrec_inv p32 input continue y /\\\n (if continue then parse_list_tailrec_measure y < parse_list_tailrec_measure x else True)\n ))\n= fun (x: option (bytes32 * list t)) ->\n let (Some (input', accu')) = x in\n let len = B32.len input' in\n if len = 0ul\n then (false, x)\n else\n match p32 input' with\n | Some (v, consumed) ->\n if consumed = 0ul\n then (false, None)\n else\n let input'' = B32.slice input' consumed len in\n (true, Some (input'', v :: accu'))\n | None -> (false, None)", "val serialize_nlist\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n: Tot (y: serializer (parse_nlist n p) { y == serialize_nlist' n s })\nlet serialize_nlist\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n: Tot (y: serializer (parse_nlist n p) { y == serialize_nlist' n s })\n= serialize_nlist' n s", "val jump_nlist (n: U32.t) (#k: parser_kind) (#t: Type) (#p: parser k t) (v: jumper p)\n : Tot (jumper (parse_nlist (U32.v n) p))\nlet jump_nlist\n (n: U32.t)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (v: jumper p)\n: Tot (jumper (parse_nlist (U32.v n) p))\n= fun #rrel #rel input pos ->\n let h0 = HST.get () in\n HST.push_frame ();\n let bpos1 = B.alloca pos 1ul in\n let br = B.alloca n 1ul in\n let h1 = HST.get () in\n C.Loops.do_while\n (fun h stop ->\n B.modifies (B.loc_buffer bpos1 `B.loc_union` B.loc_buffer br) h1 h /\\ (\n let pos1 = B.get h bpos1 0 in\n let r = B.get h br 0 in\n U32.v r <= U32.v n /\\\n U32.v pos <= U32.v pos1 /\\\n U32.v pos1 <= U32.v input.len /\\\n valid (parse_nlist (U32.v n) p) h0 input pos /\\ valid (parse_nlist (U32.v r) p) h0 input pos1 /\\\n get_valid_pos (parse_nlist (U32.v n) p) h0 input pos == get_valid_pos (parse_nlist (U32.v r) p) h0 input pos1 /\\\n (stop == true ==> r == 0ul)\n ))\n (fun _ ->\n let r = B.index br 0ul in\n if r = 0ul\n then true\n else\n let pos1 = B.index bpos1 0ul in\n [@inline_let]\n let _ =\n valid_nlist_cons_recip (U32.v r) p h0 input pos1\n in\n let pos2 = v input pos1 in\n let _ = B.upd br 0ul (r `U32.sub` 1ul) in\n let _ = B.upd bpos1 0ul pos2 in\n false\n )\n ;\n let res = B.index bpos1 0ul in\n [@inline_let] let _ =\n valid_nlist_nil p h0 input res\n in\n HST.pop_frame ();\n res", "val valid_nlist_cons_recip\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n : Lemma (requires (n > 0 /\\ valid (parse_nlist n p) h sl pos))\n (ensures\n (valid p h sl pos /\\\n (let pos1 = get_valid_pos p h sl pos in\n valid (parse_nlist (n - 1) p) h sl (get_valid_pos p h sl pos) /\\\n valid_content_pos (parse_nlist n p)\n h\n sl\n pos\n (contents p h sl pos :: contents (parse_nlist (n - 1) p) h sl pos1)\n (get_valid_pos (parse_nlist (n - 1) p) h sl pos1))))\nlet valid_nlist_cons_recip\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n: Lemma\n (requires (\n n > 0 /\\\n valid (parse_nlist n p) h sl pos\n ))\n (ensures (\n valid p h sl pos /\\ (\n let pos1 = get_valid_pos p h sl pos in\n valid (parse_nlist (n - 1) p) h sl (get_valid_pos p h sl pos) /\\\n valid_content_pos\n (parse_nlist n p)\n h\n sl\n pos\n (contents p h sl pos :: contents (parse_nlist (n - 1) p) h sl pos1)\n (get_valid_pos (parse_nlist (n - 1) p) h sl pos1)\n )))\n= valid_facts (parse_nlist n p) h sl pos;\n parse_nlist_eq n p (bytes_of_slice_from h sl pos);\n valid_facts p h sl pos;\n let pos1 = get_valid_pos p h sl pos in\n valid_facts (parse_nlist (n - 1) p) h sl pos1", "val valid_nlist_nil_recip\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n : Lemma (requires (valid (parse_nlist 0 p) h sl pos))\n (ensures (valid_content_pos (parse_nlist 0 p) h sl pos [] pos))\nlet valid_nlist_nil_recip\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n: Lemma\n (requires (valid (parse_nlist 0 p) h sl pos))\n (ensures (valid_content_pos (parse_nlist 0 p) h sl pos [] pos))\n= valid_facts (parse_nlist 0 p) h sl pos;\n parse_nlist_eq 0 p (bytes_of_slice_from h sl pos)", "val valid_nlist_cons\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n : Lemma (requires (valid p h sl pos /\\ valid (parse_nlist n p) h sl (get_valid_pos p h sl pos)))\n (ensures\n (valid p h sl pos /\\ valid (parse_nlist n p) h sl (get_valid_pos p h sl pos) /\\\n (let pos1 = get_valid_pos p h sl pos in\n valid_content_pos (parse_nlist (n + 1) p)\n h\n sl\n pos\n (contents p h sl pos :: contents (parse_nlist n p) h sl pos1)\n (get_valid_pos (parse_nlist n p) h sl pos1))))\nlet valid_nlist_cons\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n: Lemma\n (requires (\n valid p h sl pos /\\\n valid (parse_nlist n p) h sl (get_valid_pos p h sl pos)\n ))\n (ensures (\n valid p h sl pos /\\\n valid (parse_nlist n p) h sl (get_valid_pos p h sl pos) /\\ (\n let pos1 = get_valid_pos p h sl pos in\n valid_content_pos\n (parse_nlist (n + 1) p)\n h\n sl\n pos\n (contents p h sl pos :: contents (parse_nlist n p) h sl pos1)\n (get_valid_pos (parse_nlist n p) h sl pos1)\n )))\n= let pos1 = get_valid_pos p h sl pos in\n valid_facts p h sl pos;\n valid_facts (parse_nlist n p) h sl pos1;\n valid_facts (parse_nlist (n + 1) p) h sl pos;\n parse_nlist_eq (n + 1) p (bytes_of_slice_from h sl pos)", "val parse (#t: Type) (p: bare_parser t) (input: bytes) : GTot (option (t * consumed_length input))\nlet parse\n (#t: Type)\n (p: bare_parser t)\n (input: bytes)\n: GTot (option (t * consumed_length input))\n= p input", "val parse_list_tailrec_measure (#t: Type) (x: option (bytes32 * list t)) : GTot nat\nlet parse_list_tailrec_measure\n (#t: Type)\n (x: option (bytes32 * list t))\n: GTot nat\n= match x with\n | None -> 0\n | Some (input', _) -> B32.length input'", "val gaccessor_post'\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (p2: parser k2 t2)\n (cl: clens t1 t2)\n (sl: bytes)\n (res: nat)\n : GTot Type0\nlet gaccessor_post' \n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (p2: parser k2 t2)\n (cl: clens t1 t2)\n (sl : bytes)\n (res: nat)\n: GTot Type0\n= \n res <= Seq.length sl /\\\n (gaccessor_pre p1 p2 cl sl ==> gaccessor_post p1 p2 cl sl res)", "val serialize_nlist\n (n: nat)\n (#t: Type0)\n (#p: parser_spec t)\n (s: serializer_spec p)\n: Tot (y: serializer_spec (parse_nlist n p) { y == serialize_nlist' n s })\nlet serialize_nlist\n (n: nat)\n (#t: Type0)\n (#p: parser_spec t)\n (s: serializer_spec p)\n: Tot (y: serializer_spec (parse_nlist n p) { y == serialize_nlist' n s })\n= serialize_nlist' n s", "val gaccessor_post\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (p2: parser k2 t2)\n (cl: clens t1 t2)\n (sl: bytes)\n (res: nat)\n : GTot Type0\nlet gaccessor_post\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (p2: parser k2 t2)\n (cl: clens t1 t2)\n (sl: bytes)\n (res : nat)\n: GTot Type0\n= res <= Seq.length sl /\\\n begin match parse p1 sl with\n | Some (x1, consumed1) ->\n begin match parse p2 (Seq.slice sl res (Seq.length sl)) with\n | Some (x2, consumed2) ->\n cl.clens_cond x1 /\\\n x2 == cl.clens_get x1 /\\\n res + consumed2 <= consumed1\n | _ -> False\n end\n | _ -> False\n end", "val parse_nlist_total_fixed_size_kind_correct\n (n: U32.t)\n (#wk: _)\n (#k: parser_kind true wk)\n (#t: _)\n (p: parser k t)\n : Lemma\n (requires\n (let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_high == Some k.parser_kind_low /\\\n U32.v n % k.parser_kind_low == 0 /\\ k.parser_kind_metadata == Some ParserKindMetadataTotal\n ))\n (ensures\n (LP.parser_kind_prop (LP.total_constant_size_parser_kind (U32.v n)) (parse_nlist n p)))\nlet parse_nlist_total_fixed_size_kind_correct\r\n (n:U32.t) (#wk: _) (#k:parser_kind true wk) #t (p:parser k t)\r\n: Lemma\r\n (requires (\r\n let open LP in\r\n k.parser_kind_subkind == Some ParserStrong /\\\r\n k.parser_kind_high == Some k.parser_kind_low /\\\r\n U32.v n % k.parser_kind_low == 0 /\\\r\n k.parser_kind_metadata == Some ParserKindMetadataTotal\r\n ))\r\n (ensures (\r\n LP.parser_kind_prop (LP.total_constant_size_parser_kind (U32.v n)) (parse_nlist n p)\r\n ))\r\n= LP.parser_kind_prop_equiv (LowParse.Spec.FLData.parse_fldata_kind (U32.v n) LowParse.Spec.List.parse_list_kind) (parse_nlist n p);\r\n LP.parser_kind_prop_equiv (LP.total_constant_size_parser_kind (U32.v n)) (parse_nlist n p);\r\n Classical.forall_intro (Classical.move_requires (parse_nlist_total_fixed_size_aux n p))", "val valid_nlist_cons'\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n : Lemma (requires (n > 0 /\\ valid p h sl pos))\n (ensures\n (let pos1 = get_valid_pos p h sl pos in\n (valid (parse_nlist n p) h sl pos <==> valid (parse_nlist (n - 1) p) h sl pos1) /\\\n ((valid (parse_nlist n p) h sl pos /\\ valid (parse_nlist (n - 1) p) h sl pos1) ==>\n get_valid_pos (parse_nlist n p) h sl pos ==\n get_valid_pos (parse_nlist (n - 1) p) h sl pos1)))\nlet valid_nlist_cons'\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n: Lemma\n (requires (\n n > 0 /\\\n valid p h sl pos\n ))\n (ensures (\n let pos1 = get_valid_pos p h sl pos in\n (valid (parse_nlist n p) h sl pos <==> valid (parse_nlist (n - 1) p) h sl pos1) /\\\n ((valid (parse_nlist n p) h sl pos /\\ valid (parse_nlist (n - 1) p) h sl pos1) ==> get_valid_pos (parse_nlist n p) h sl pos == get_valid_pos (parse_nlist (n - 1) p) h sl pos1)\n ))\n= Classical.move_requires (valid_nlist_cons (n - 1) p h sl) pos;\n Classical.move_requires (valid_nlist_cons_recip n p h sl) pos", "val parse_list\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n: Tot (parser parse_list_kind (list t))\nlet parse_list #k #t p =\n parse_list_bare_injective p;\n parse_list_bare_consumes_all p;\n parser_kind_prop_equiv parse_list_kind (parse_list_bare p);\n parse_list_bare p", "val serialize_nlist' (n: nat) (#t: Type0) (#p: parser_spec t) (s: serializer_spec p)\n : Tot (serializer_spec (parse_nlist n p))\nlet rec serialize_nlist'\n (n: nat)\n (#t: Type0)\n (#p: parser_spec t)\n (s: serializer_spec p)\n: Tot (serializer_spec (parse_nlist n p))\n= if n = 0\n then begin\n Classical.forall_intro (nlist_nil_unique t);\n Serializer (fun _ -> Seq.empty)\n end\n else begin\n synth_inverse_1 t (n - 1);\n synth_inverse_2 t (n - 1);\n serialize_synth (serialize_nondep_then s (serialize_nlist' (n - 1) s)) (synth_nlist (n - 1)) (synth_nlist_recip (n - 1)) ()\n end", "val array_nth_ghost''\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (array_byte_size elem_count: nat)\n (i:\n nat\n { fldata_array_precond k array_byte_size elem_count == true /\\\n array_byte_size < 4294967296 /\\ elem_count < 4294967296 /\\ i < elem_count })\n (input: bytes)\n : GTot (nat)\nlet array_nth_ghost''\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (array_byte_size: nat)\n (elem_count: nat)\n (i: nat {\n fldata_array_precond k array_byte_size elem_count == true /\\\n array_byte_size < 4294967296 /\\\n elem_count < 4294967296 /\\\n i < elem_count\n })\n (input: bytes)\n: GTot (nat)\n= if (i `Prims.op_Multiply` k.parser_kind_low) + k.parser_kind_low <= Seq.length input\n then (i `Prims.op_Multiply` k.parser_kind_low)\n else (0)", "val parse_t_at_most (n:U32.t) (#nz: _) (#wk: _) (#k:parser_kind nz wk) (#t:_) (p:parser k t)\r\n : Tot (parser kind_t_at_most (t_at_most n t))\nlet parse_t_at_most n #nz #wk #k #t p\r\n = let open LowParse.Spec.FLData in\r\n let open LowParse.Spec.List in\r\n parse_weaken\r\n #false \r\n #WeakKindStrongPrefix\r\n (LowParse.Spec.FLData.parse_fldata \r\n (LPC.nondep_then p parse_all_bytes)\r\n (U32.v n))\r\n #false\r\n kind_t_at_most", "val parse_nlist (size: (unit -> ML string)) (body: parser not_reading) : Tot (parser not_reading)\nlet parse_nlist\n (size: unit -> ML string)\n (body: parser not_reading)\n: Tot (parser not_reading)\n= parse_exact size (parse_list body)", "val vlarray_nth_ghost''\n (array_byte_size_min array_byte_size_max: nat)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (elem_count_min elem_count_max: nat)\n (i:\n nat\n { vldata_vlarray_precond array_byte_size_min\n array_byte_size_max\n p\n elem_count_min\n elem_count_max ==\n true })\n (input: bytes)\n : GTot (nat)\nlet vlarray_nth_ghost''\n (array_byte_size_min: nat)\n (array_byte_size_max: nat)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (elem_count_min: nat)\n (elem_count_max: nat)\n (i: nat {\n vldata_vlarray_precond array_byte_size_min array_byte_size_max p elem_count_min elem_count_max == true\n })\n (input: bytes)\n: GTot (nat)\n= if (log256' array_byte_size_max + (i `Prims.op_Multiply` k.parser_kind_low) + k.parser_kind_low) <= Seq.length input\n then (log256' array_byte_size_max + (i `M.mult_nat` k.parser_kind_low))\n else (0)", "val validate_nlist_total_constant_size'\n (n: U32.t)\n (#wk: _)\n (#k: parser_kind true wk)\n (#t: _)\n (p: parser k t)\n (inv disj l: _)\n : Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires\n (let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_high == Some k.parser_kind_low /\\\n k.parser_kind_metadata == Some ParserKindMetadataTotal /\\ k.parser_kind_low < 4294967296))\n (ensures (fun _ -> True))\nlet validate_nlist_total_constant_size'\n (n:U32.t)\n #wk\n (#k:parser_kind true wk)\n #t\n (p:parser k t)\n inv disj l\n : Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires (\n let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\\n k.parser_kind_high == Some k.parser_kind_low /\\\n k.parser_kind_metadata == Some ParserKindMetadataTotal /\\\n k.parser_kind_low < 4294967296\n ))\n (ensures (fun _ -> True))\n= fun ctxt error_handler_fn input start_position -> // n is not an integer constant, so we need to eta-expand and swap fun and if\n if n `U32.rem` U32.uint_to_t k.LP.parser_kind_low = 0ul\n then validate_nlist_total_constant_size_mod_ok n p inv disj l ctxt error_handler_fn input start_position\n else validate_nlist_constant_size_mod_ko n p inv disj l ctxt error_handler_fn input start_position", "val size32_list_inv\n (#t: Type)\n (#k: parser_kind)\n (#p: parser k t)\n (#s: serializer p)\n (s32: size32 s)\n (u: unit{serialize_list_precond k})\n (input: list t)\n (continue: bool)\n (accu: (U32.t * list t))\n : GTot Type0\nlet size32_list_inv\n (#t: Type)\n (#k: parser_kind)\n (#p: parser k t)\n (#s: serializer p)\n (s32: size32 s)\n (u: unit {\n serialize_list_precond k\n })\n (input: list t)\n (continue: bool)\n (accu: (U32.t * list t))\n: GTot Type0\n= let (len, rem) = accu in\n let sz = Seq.length (serialize (serialize_list p s) input) in\n if continue\n then\n U32.v len < U32.v u32_max /\\\n sz == U32.v len + Seq.length (serialize (serialize_list p s) rem)\n else\n size32_postcond (serialize_list p s) input len", "val close_parse_list_up_to (b: bytes) : GTot (n: nat{Seq.length b < n})\nlet close_parse_list_up_to\n (b: bytes)\n: GTot (n: nat { Seq.length b < n })\n= Seq.length b + 1", "val bparse (#t: Type0) (p: bare_parser t) (input: bytes) : GTot (option (t * consumed_length input))\nlet bparse\n (#t: Type0)\n (p: bare_parser t)\n (input: bytes)\n: GTot (option (t * consumed_length input))\n= p input", "val valid_nlist_cons_not\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n : Lemma (requires (n > 0 /\\ (~(valid p h sl pos))))\n (ensures (~(valid (parse_nlist n p) h sl pos)))\nlet valid_nlist_cons_not\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n: Lemma\n (requires (\n n > 0 /\\\n (~ (valid p h sl pos))\n ))\n (ensures (\n ~ (valid (parse_nlist n p) h sl pos)\n ))\n= Classical.move_requires (valid_nlist_cons (n - 1) p h sl) pos;\n Classical.move_requires (valid_nlist_cons_recip n p h sl) pos", "val valid_nlist_valid_list\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n : Lemma\n (requires\n (k.parser_kind_low > 0 /\\ k.parser_kind_subkind == Some ParserStrong /\\\n valid (parse_nlist n p) h sl pos))\n (ensures\n (let pos' = get_valid_pos (parse_nlist n p) h sl pos in\n valid_list p h sl pos pos' /\\\n contents_list p h sl pos pos' == contents (parse_nlist n p) h sl pos))\nlet rec valid_nlist_valid_list\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n: Lemma\n (requires (\n k.parser_kind_low > 0 /\\\n k.parser_kind_subkind == Some ParserStrong /\\\n valid (parse_nlist n p) h sl pos\n ))\n (ensures (\n let pos' = get_valid_pos (parse_nlist n p) h sl pos in\n valid_list p h sl pos pos' /\\\n contents_list p h sl pos pos' == contents (parse_nlist n p) h sl pos\n ))\n= if n = 0\n then begin\n valid_nlist_nil_recip p h sl pos;\n valid_list_nil p h sl pos\n end else begin\n valid_nlist_cons_recip n p h sl pos;\n let pos1 = get_valid_pos p h sl pos in\n let pos' = get_valid_pos (parse_nlist n p) h sl pos in\n valid_nlist_valid_list (n - 1) p h sl pos1;\n valid_list_cons p h sl pos pos'\n end", "val valid_list_valid_nlist\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos pos': U32.t)\n : Lemma (requires (valid_list p h sl pos pos'))\n (ensures\n (let x = contents_list p h sl pos pos' in\n valid_content_pos (parse_nlist (L.length x) p) h sl pos x pos'))\n (decreases (U32.v pos' - U32.v pos))\nlet rec valid_list_valid_nlist\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n (pos' : U32.t)\n: Lemma\n (requires (\n valid_list p h sl pos pos'\n ))\n (ensures (\n let x = contents_list p h sl pos pos' in\n valid_content_pos (parse_nlist (L.length x) p) h sl pos x pos'\n ))\n (decreases (U32.v pos' - U32.v pos))\n= if pos = pos'\n then begin\n valid_list_nil p h sl pos;\n valid_nlist_nil p h sl pos\n end else begin\n valid_list_cons_recip p h sl pos pos' ;\n let pos1 = get_valid_pos p h sl pos in\n valid_list_valid_nlist p h sl pos1 pos' ;\n valid_nlist_cons (L.length (contents_list p h sl pos1 pos')) p h sl pos\n end", "val lwvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: lwriter s h0 sout pout_from0)\n : GTot (list t)\nlet lwvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: lwriter s h0 sout pout_from0)\n: GTot (list t)\n= Ghost.reveal w.v", "val parse (#t: Type0) (p: parser_spec t) (input: bytes) : GTot (option (t * consumed_length input))\nlet parse\n (#t: Type0)\n (p: parser_spec t)\n (input: bytes)\n: GTot (option (t * consumed_length input))\n= bparse (coerce_to_bare_parser _ p) input", "val validate_nlist_total_constant_size\n (n_is_const: bool)\n (n: U32.t)\n (#wk: _)\n (#k: parser_kind true wk)\n (#t: Type)\n (p: parser k t)\n (inv disj l: _)\n : Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires\n (let open LP in\n k.parser_kind_subkind = Some ParserStrong /\\ k.parser_kind_high = Some k.parser_kind_low /\\\n k.parser_kind_metadata = Some ParserKindMetadataTotal /\\ k.parser_kind_low < 4294967296))\n (ensures (fun _ -> True))\nlet validate_nlist_total_constant_size\n (n_is_const: bool)\n (n:U32.t)\n #wk\n (#k:parser_kind true wk)\n (#t: Type)\n (p:parser k t)\n inv disj l\n: Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires (\n let open LP in\n k.parser_kind_subkind = Some ParserStrong /\\\n k.parser_kind_high = Some k.parser_kind_low /\\\n k.parser_kind_metadata = Some ParserKindMetadataTotal /\\\n k.parser_kind_low < 4294967296\n ))\n (ensures (fun _ -> True))\n=\n if\n if k.LP.parser_kind_low = 1\n then true\n else if n_is_const\n then U32.v n % k.LP.parser_kind_low = 0\n else false\n then\n validate_nlist_total_constant_size_mod_ok n p inv disj l\n else if\n if n_is_const\n then U32.v n % k.LP.parser_kind_low <> 0\n else false\n then\n validate_nlist_constant_size_mod_ko n p inv disj l\n else\n validate_nlist_total_constant_size' n p inv disj l", "val serialize_nlist_cons\n (#k: parser_kind)\n (#t: Type)\n (n: nat)\n (#p: parser k t)\n (s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (a: t)\n (q: nlist n t)\n : Lemma\n (ensures\n (serialize (serialize_nlist (n + 1) s) (a :: q) ==\n Seq.append (serialize s a) (serialize (serialize_nlist n s) q)))\nlet serialize_nlist_cons\n (#k: parser_kind)\n (#t: Type)\n (n: nat)\n (#p: parser k t)\n (s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (a: t)\n (q: nlist n t)\n: Lemma\n (ensures (\n serialize (serialize_nlist (n + 1) s) (a :: q) == Seq.append (serialize s a) (serialize (serialize_nlist n s) q)\n ))\n= serialize_synth_eq _ (synth_nlist n) (serialize_nondep_then s (serialize_nlist' n s)) (synth_nlist_recip n) () (a :: q);\n serialize_nondep_then_eq s (serialize_nlist' n s) (a, q)", "val validate_nlist_total_constant_size_mod_ok\n (n: U32.t)\n (#wk: _)\n (#k: parser_kind true wk)\n (#t: Type)\n (p: parser k t)\n (inv disj l: _)\n : Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires\n (let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_high == Some k.parser_kind_low /\\\n k.parser_kind_metadata == Some ParserKindMetadataTotal /\\ k.parser_kind_low < 4294967296 /\\\n U32.v n % k.LP.parser_kind_low == 0))\n (ensures (fun _ -> True))\nlet validate_nlist_total_constant_size_mod_ok\n (n:U32.t)\n #wk \n (#k:parser_kind true wk)\n (#t: Type)\n (p:parser k t)\n inv\n disj\n l\n : Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires (\n let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\\n k.parser_kind_high == Some k.parser_kind_low /\\\n k.parser_kind_metadata == Some ParserKindMetadataTotal /\\\n k.parser_kind_low < 4294967296 /\\\n U32.v n % k.LP.parser_kind_low == 0\n ))\n (ensures (fun _ -> True))\n= [@inline_let]\n let _ =\n parse_nlist_total_fixed_size_kind_correct n p\n in\n validate_total_constant_size_no_read'\n (LP.strengthen (LP.total_constant_size_parser_kind (U32.v n)) (parse_nlist n p))\n (Cast.uint32_to_uint64 n)\n () inv disj l", "val gaccessor_pre\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (p2: parser k2 t2)\n (cl: clens t1 t2)\n (sl: bytes)\n : GTot Type0\nlet gaccessor_pre\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (p2: parser k2 t2)\n (cl: clens t1 t2)\n (sl: bytes)\n: GTot Type0\n= match parse p1 sl with\n | Some (x1, _) -> cl.clens_cond x1\n | _ -> False", "val valid_nlist_nil\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n : Lemma (requires (live_slice h sl /\\ U32.v pos <= U32.v sl.len))\n (ensures (valid_content_pos (parse_nlist 0 p) h sl pos [] pos))\nlet valid_nlist_nil\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos: U32.t)\n: Lemma\n (requires (live_slice h sl /\\ U32.v pos <= U32.v sl.len))\n (ensures (valid_content_pos (parse_nlist 0 p) h sl pos [] pos))\n= valid_facts (parse_nlist 0 p) h sl pos;\n parse_nlist_eq 0 p (bytes_of_slice_from h sl pos)", "val jump_list_up_to_inv\n (#k #t: _)\n (#p: parser k t)\n (cond: (t -> Tot bool))\n (prf: consumes_if_not_cond cond p {k.parser_kind_subkind <> Some ParserConsumesAll})\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: U32.t)\n (h0: HS.mem)\n (bpos: B.pointer U32.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet jump_list_up_to_inv\n (#k: _)\n (#t: _)\n (#p: parser k t)\n (cond: (t -> Tot bool))\n (prf: consumes_if_not_cond cond p { k.parser_kind_subkind <> Some ParserConsumesAll } )\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: U32.t)\n (h0: HS.mem)\n (bpos: B.pointer U32.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n= let pos = B.deref h bpos in\n let q = parse_list_up_to cond p prf in\n B.live h0 bpos /\\\n live_slice h0 sl /\\\n B.loc_disjoint (B.loc_buffer sl.base) (B.loc_buffer bpos) /\\\n B.modifies (B.loc_buffer bpos) h0 h /\\\n U32.v pos0 <= U32.v pos /\\\n valid q h0 sl pos0 /\\\n begin if stop\n then \n get_valid_pos q h0 sl pos0 == pos\n else\n valid q h0 sl pos /\\\n get_valid_pos q h0 sl pos0 == get_valid_pos q h0 sl pos\n end", "val olwvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: olwriter s h0 sout pout_from0)\n : GTot (option (list t))\nlet olwvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: olwriter s h0 sout pout_from0)\n: GTot (option (list t))\n= Ghost.reveal w.v", "val parse_nlist_kind_metadata (n: nat) (k: parser_kind)\n : Lemma\n ((parse_nlist_kind' n k).parser_kind_metadata ==\n (if n = 0 then Some ParserKindMetadataTotal else k.parser_kind_metadata))\nlet rec parse_nlist_kind_metadata\n (n: nat)\n (k: parser_kind)\n: Lemma\n ((parse_nlist_kind' n k).parser_kind_metadata == (if n = 0 then Some ParserKindMetadataTotal else k.parser_kind_metadata))\n= if n = 0\n then ()\n else parse_nlist_kind_metadata (n - 1) k", "val validate_list_up_to_inv\n (#k: parser_kind true WeakKindStrongPrefix)\n (#t: eqtype)\n (p: parser k t)\n (terminator: t)\n (prf: LUT.consumes_if_not_cond (cond_string_up_to terminator) p)\n (ctxt: app_ctxt)\n (sl: input_buffer_t)\n (h0: HS.mem)\n (bres: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet validate_list_up_to_inv\n (#k: parser_kind true WeakKindStrongPrefix)\n (#t: eqtype)\n (p: parser k t)\n (terminator: t)\n (prf: LUT.consumes_if_not_cond (cond_string_up_to terminator) p)\n (ctxt: app_ctxt)\n (sl: input_buffer_t)\n (h0: HS.mem)\n (bres: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n=\n let res = B.deref h bres in\n let q = LUT.parse_list_up_to (cond_string_up_to terminator) p prf in\n B.live h0 bres /\\\n I.live sl h0 /\\\n I.live sl h /\\\n B.loc_disjoint (I.footprint sl) (B.loc_buffer bres `B.loc_union` app_loc ctxt loc_none) /\\\n B.loc_disjoint (B.loc_buffer bres) (app_loc ctxt loc_none) /\\\n B.live h0 ctxt /\\\n B.live h ctxt /\\\n address_liveness_insensitive_locs `loc_includes` (app_loc ctxt loc_none) /\\\n B.modifies (B.loc_buffer bres `B.loc_union` I.perm_footprint sl `B.loc_union` app_loc ctxt loc_none) h0 h /\\\n begin\n let s = I.get_remaining sl h0 in\n let s' = I.get_remaining sl h in\n Seq.length s' <= Seq.length s /\\\n s' `Seq.equal` Seq.slice s (Seq.length s - Seq.length s') (Seq.length s) /\\\n begin if LPE.is_error res\n then\n // validation *or action* failed\n stop == true /\\\n U64.v (LPE.get_validator_error_pos res) == Seq.length (I.get_read sl h) /\\\n (LPE.get_validator_error_kind res <> LPE.get_validator_error_kind LPE.validator_error_action_failed ==> None? (LP.parse q s))\n else\n U64.v res == Seq.length (I.get_read sl h) /\\\n begin if stop\n then valid_consumed q h0 h sl\n else match LP.parse q s, LP.parse q s' with\n | None, None -> True\n | Some (_, consumed), Some (_, consumed') -> consumed' + Seq.length s - Seq.length s' == consumed\n | _ -> False\n end end\n end", "val parse_vclist_payload\n (min max: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (n: bounded_count min max)\n : Tot (parser (parse_vclist_payload_kind min max k) (vlarray t min max))\nlet parse_vclist_payload\n (min: nat)\n (max: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (n: bounded_count min max)\n: Tot (parser (parse_vclist_payload_kind min max k) (vlarray t min max))\n= weaken (parse_vclist_payload_kind min max k) (parse_synth (parse_nlist (U32.v n) p) (synth_vclist_payload min max n))", "val validate_list_inv\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (g0 g1: G.erased HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: pos_t)\n (bpos: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet validate_list_inv\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (g0 g1: G.erased HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: pos_t)\n (bpos: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n= let h0 = G.reveal g0 in\n let h1 = G.reveal g1 in\n B.disjoint sl.base bpos /\\\n k.parser_kind_subkind == Some ParserStrong /\\\n k.parser_kind_low > 0 /\\\n U64.v pos0 <= U32.v sl.len /\\\n live_slice h0 sl /\\\n B.live h1 bpos /\\\n B.modifies B.loc_none h0 h1 /\\\n B.modifies (B.loc_buffer bpos) h1 h /\\ (\n let pos1 = Seq.index (B.as_seq h bpos) 0 in\n if\n is_error pos1\n then\n stop == true /\\\n (~ (valid_exact (parse_list p) h0 sl (uint64_to_uint32 pos0) sl.len))\n else\n U64.v pos0 <= U64.v pos1 /\\\n U64.v pos1 <= U32.v sl.len /\\\n (valid_exact (parse_list p) h0 sl (uint64_to_uint32 pos0) sl.len <==> valid_exact (parse_list p) h0 sl (uint64_to_uint32 pos1) sl.len) /\\\n (stop == true ==> U64.v pos1 == U32.v sl.len)\n )", "val validate_list_up_to_inv\n (#k #t: _)\n (#p: parser k t)\n (cond: (t -> Tot bool))\n (prf: consumes_if_not_cond cond p {k.parser_kind_subkind <> Some ParserConsumesAll})\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: U32.t)\n (h0: HS.mem)\n (bpos: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet validate_list_up_to_inv\n (#k: _)\n (#t: _)\n (#p: parser k t)\n (cond: (t -> Tot bool))\n (prf: consumes_if_not_cond cond p { k.parser_kind_subkind <> Some ParserConsumesAll } )\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: U32.t)\n (h0: HS.mem)\n (bpos: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n= let pos = B.deref h bpos in\n let q = parse_list_up_to cond p prf in\n B.live h0 bpos /\\\n live_slice h0 sl /\\\n B.loc_disjoint (B.loc_buffer sl.base) (B.loc_buffer bpos) /\\\n B.modifies (B.loc_buffer bpos) h0 h /\\\n U32.v pos0 <= U64.v pos /\\\n begin if is_success pos\n then\n let pos = uint64_to_uint32 pos in\n U32.v pos <= U32.v sl.len /\\\n begin if stop\n then\n valid_pos q h0 sl pos0 pos\n else\n (valid q h0 sl pos0 <==> valid q h0 sl pos) /\\\n ((valid q h0 sl pos0 /\\ valid q h0 sl pos) ==>\n get_valid_pos q h0 sl pos0 == get_valid_pos q h0 sl pos\n )\n end\n else\n stop == true /\\\n (~ (valid q h0 sl pos0))\n end", "val parser32_correct\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (input: bytes32)\n (res: option (t * U32.t))\n : GTot Type0\nlet parser32_correct\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (input: bytes32)\n (res: option (t * U32.t))\n: GTot Type0\n= let gp = parse p (B32.reveal input) in\n match res with\n | None -> gp == None\n | Some (hres, consumed) ->\n Some? gp /\\ (\n let (Some (hres' , consumed')) = gp in\n hres == hres' /\\\n U32.v consumed == (consumed' <: nat)\n )", "val parse_bitsum\n (#kt: parser_kind)\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (b: bitsum' cl tot)\n (#data: Type)\n (tag_of_data: (data -> Tot (bitsum'_type b)))\n (type_of_tag: (bitsum'_key_type b -> Tot Type))\n (synth_case: synth_case_t b data tag_of_data type_of_tag)\n (p: parser kt t)\n (f: (x: bitsum'_key_type b -> Tot (k: parser_kind & parser k (type_of_tag x))))\n : Tot (parser (parse_bitsum_kind kt b type_of_tag f) data)\nlet parse_bitsum\n (#kt: parser_kind)\n (#tot: pos)\n (#t: eqtype)\n (#cl: uint_t tot t)\n (b: bitsum' cl tot)\n (#data: Type)\n (tag_of_data: (data -> Tot (bitsum'_type b)))\n (type_of_tag: (bitsum'_key_type b -> Tot Type))\n (synth_case: synth_case_t b data tag_of_data type_of_tag)\n (p: parser kt t)\n (f: (x: bitsum'_key_type b) -> Tot (k: parser_kind & parser k (type_of_tag x)))\n: Tot (parser (parse_bitsum_kind kt b type_of_tag f) data)\n= parse_tagged_union\n #(parse_filter_kind kt)\n #(bitsum'_type b)\n (parse_bitsum' b p)\n #(data)\n (tag_of_data)\n #(weaken_parse_bitsum_cases_kind b type_of_tag f)\n (parse_bitsum_cases b tag_of_data type_of_tag synth_case f)", "val parse_nlist_kind_high (n: nat) (k: parser_kind)\n : Lemma\n ((parse_nlist_kind' n k).parser_kind_high ==\n (match k.parser_kind_high with\n | None -> if n = 0 then Some 0 else None\n | Some b -> Some (n `mul` b)))\nlet rec parse_nlist_kind_high\n (n: nat)\n (k: parser_kind)\n: Lemma\n ((parse_nlist_kind' n k).parser_kind_high == (match k.parser_kind_high with\n | None -> if n = 0 then Some 0 else None\n | Some b -> Some (n `mul` b)\n ))\n= if n = 0\n then ()\n else begin\n begin match k.parser_kind_high with\n | None -> ()\n | Some b -> LowParse.Math.distributivity_add_left (n - 1) 1 b\n end;\n parse_nlist_kind_high (n - 1) k\n end", "val vlarray_nth_ghost'\n (array_byte_size_min array_byte_size_max: nat)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (elem_count_min elem_count_max: nat)\n (i:\n nat\n { vldata_vlarray_precond array_byte_size_min\n array_byte_size_max\n p\n elem_count_min\n elem_count_max ==\n true })\n : Tot\n (gaccessor' (parse_vlarray array_byte_size_min\n array_byte_size_max\n s\n elem_count_min\n elem_count_max\n ())\n p\n (clens_vlarray_nth t elem_count_min elem_count_max i))\nlet vlarray_nth_ghost'\n (array_byte_size_min: nat)\n (array_byte_size_max: nat)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (elem_count_min: nat)\n (elem_count_max: nat)\n (i: nat {\n vldata_vlarray_precond array_byte_size_min array_byte_size_max p elem_count_min elem_count_max == true\n })\n: Tot (gaccessor' (parse_vlarray array_byte_size_min array_byte_size_max s elem_count_min elem_count_max ()) p (clens_vlarray_nth t elem_count_min elem_count_max i))\n= fun input ->\n reveal_opaque (`%vlarray_nth_ghost'') (vlarray_nth_ghost'' array_byte_size_min array_byte_size_max s elem_count_min elem_count_max i input);\n vlarray_nth_ghost_correct array_byte_size_min array_byte_size_max s elem_count_min elem_count_max i input;\n vlarray_nth_ghost'' array_byte_size_min array_byte_size_max s elem_count_min elem_count_max i input", "val swvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#space_beyond: nat)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: swriter s h0 space_beyond sout pout_from0)\n : GTot t\nlet swvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#space_beyond: nat)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: swriter s h0 space_beyond sout pout_from0)\n: GTot t\n= Ghost.reveal w.v", "val parse_t_exact (n:U32.t) (#nz:bool) (#wk: _) (#k:parser_kind nz wk) (#t:_) (p:parser k t)\r\n : Tot (parser kind_t_exact (t_exact n t))\nlet parse_t_exact n #nz #wk #k #t p\r\n = let open LowParse.Spec.FLData in\r\n let open LowParse.Spec.List in\r\n parse_weaken\r\n #false \r\n #WeakKindStrongPrefix\r\n (LowParse.Spec.FLData.parse_fldata \r\n p\r\n (U32.v n))\r\n #false\r\n kind_t_exact", "val vlarray_nth_ghost\n (array_byte_size_min array_byte_size_max: nat)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (elem_count_min elem_count_max: nat)\n (i:\n nat\n { vldata_vlarray_precond array_byte_size_min\n array_byte_size_max\n p\n elem_count_min\n elem_count_max ==\n true })\n : Tot\n (gaccessor (parse_vlarray array_byte_size_min\n array_byte_size_max\n s\n elem_count_min\n elem_count_max\n ())\n p\n (clens_vlarray_nth t elem_count_min elem_count_max i))\nlet vlarray_nth_ghost\n (array_byte_size_min: nat)\n (array_byte_size_max: nat)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (elem_count_min: nat)\n (elem_count_max: nat)\n (i: nat {\n vldata_vlarray_precond array_byte_size_min array_byte_size_max p elem_count_min elem_count_max == true\n })\n: Tot (gaccessor (parse_vlarray array_byte_size_min array_byte_size_max s elem_count_min elem_count_max ()) p (clens_vlarray_nth t elem_count_min elem_count_max i))\n= reveal_opaque (`%vlarray_nth_ghost') (vlarray_nth_ghost' array_byte_size_min array_byte_size_max s elem_count_min elem_count_max i);\n reveal_opaque (`%vlarray_nth_ghost'') (vlarray_nth_ghost'' array_byte_size_min array_byte_size_max s elem_count_min elem_count_max i);\n Classical.forall_intro (Classical.move_requires (vlarray_nth_bound array_byte_size_min array_byte_size_max s elem_count_min elem_count_max i));\n gaccessor_prop_equiv (parse_vlarray array_byte_size_min array_byte_size_max s elem_count_min elem_count_max ()) p (clens_vlarray_nth t elem_count_min elem_count_max i) (vlarray_nth_ghost' array_byte_size_min array_byte_size_max s elem_count_min elem_count_max i);\n vlarray_nth_ghost' array_byte_size_min array_byte_size_max s elem_count_min elem_count_max i", "val validate_nlist_total_constant_size_mod_ok\n (n: U32.t)\n (#wk: _)\n (#k: parser_kind true wk)\n (#t: Type)\n (p: parser k t)\n : Pure (validator_no_read (parse_nlist n p))\n (requires\n (let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_high == Some k.parser_kind_low /\\\n k.parser_kind_metadata == Some ParserKindMetadataTotal /\\ k.parser_kind_low < 4294967296 /\\\n U32.v n % k.LP.parser_kind_low == 0))\n (ensures (fun _ -> True))\nlet validate_nlist_total_constant_size_mod_ok (n:U32.t) #wk (#k:parser_kind true wk) (#t: Type) (p:parser k t)\r\n : Pure (validator_no_read (parse_nlist n p))\r\n (requires (\r\n let open LP in\r\n k.parser_kind_subkind == Some ParserStrong /\\\r\n k.parser_kind_high == Some k.parser_kind_low /\\\r\n k.parser_kind_metadata == Some ParserKindMetadataTotal /\\\r\n k.parser_kind_low < 4294967296 /\\\r\n U32.v n % k.LP.parser_kind_low == 0\r\n ))\r\n (ensures (fun _ -> True))\r\n= \r\n (fun #rrel #rel sl len pos ->\r\n let h = FStar.HyperStack.ST.get () in\r\n [@inline_let]\r\n let _ =\r\n parse_nlist_total_fixed_size_kind_correct n p;\r\n LPL.valid_facts (parse_nlist n p) h sl (LPL.uint64_to_uint32 pos);\r\n LPL.valid_facts (LP.strengthen (LP.total_constant_size_parser_kind (U32.v n)) (parse_nlist n p)) h sl (LPL.uint64_to_uint32 pos)\r\n in\r\n LPL.validate_total_constant_size_no_read (LP.strengthen (LP.total_constant_size_parser_kind (U32.v n)) (parse_nlist n p)) (FStar.Int.Cast.uint32_to_uint64 n) () sl len pos\r\n )", "val nondep_then_eq\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (p2: parser k2 t2)\n (b: bytes)\n: Lemma\n (parse (nondep_then p1 p2) b == (match parse p1 b with\n | Some (x1, consumed1) ->\n let b' = Seq.slice b consumed1 (Seq.length b) in\n begin match parse p2 b' with\n | Some (x2, consumed2) ->\n Some ((x1, x2), consumed1 + consumed2)\n | _ -> None\n end\n | _ -> None\n ))\nlet nondep_then_eq #k1 #t1 p1 #k2 #t2 p2 b =\n nondep_then_eq #k1 p1 #k2 p2 b", "val wvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n : GTot t\nlet wvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n: GTot t\n= Ghost.reveal w.v", "val parse_list_bare (#k: parser_kind) (#t: Type) (p: parser k t) : Tot (bare_parser (list t))\nlet parse_list_bare\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n: Tot (bare_parser (list t))\n= (fun b -> parse_list_aux #k #t p b) <: bare_parser (list t)", "val parse_list_up_to'_eq\n (#k: parser_kind)\n (#t: Type)\n (cond: (t -> Tot bool))\n (p: parser k t {k.parser_kind_subkind <> Some ParserConsumesAll})\n (fuel: nat)\n (b: bytes)\n : Lemma\n (parse (parse_list_up_to' cond p fuel) b ==\n (match parse (parse_list_up_to_fuel cond p fuel) b with\n | None -> None\n | Some (xy, consumed) -> Some ((fst xy, snd xy), consumed)))\nlet parse_list_up_to'_eq\n (#k: parser_kind)\n (#t: Type)\n (cond: (t -> Tot bool))\n (p: parser k t { k.parser_kind_subkind <> Some ParserConsumesAll })\n (fuel: nat)\n (b: bytes)\n: Lemma\n (parse (parse_list_up_to' cond p fuel) b == (\n match parse (parse_list_up_to_fuel cond p fuel) b with\n | None -> None\n | Some (xy, consumed) -> Some ((fst xy, snd xy), consumed)\n ))\n= \n parse_synth_eq\n (parse_list_up_to_fuel cond p fuel)\n (synth_list_up_to' cond fuel)\n b", "val serialized_list_length (#k: parser_kind) (#t: Type) (#p: parser k t) (s: serializer p) (l: list t) : GTot nat\nlet rec serialized_list_length (#k: parser_kind) (#t: Type) (#p: parser k t) (s: serializer p) (l: list t) : GTot nat =\n match l with\n | [] -> 0\n | x :: q -> serialized_length s x + serialized_list_length s q", "val parse_vclist_eq\n (min: nat)\n (max: nat{min <= max})\n (#lk: parser_kind)\n (lp: parser lk U32.t)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (b: bytes)\n : Lemma\n (parse (parse_vclist min max lp p) b ==\n (match parse lp b with\n | None -> None\n | Some (n, consumed_n) ->\n if min <= U32.v n && U32.v n <= max\n then\n let b_payload = Seq.slice b consumed_n (Seq.length b) in\n match parse (parse_nlist (U32.v n) p) b_payload with\n | None -> None\n | Some (l, consumed_l) -> Some (l, consumed_n + consumed_l)\n else None))\nlet parse_vclist_eq\n (min: nat)\n (max: nat { min <= max } )\n (#lk: parser_kind)\n (lp: parser lk U32.t)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (b: bytes)\n: Lemma\n (parse (parse_vclist min max lp p) b == (match parse lp b with\n | None -> None\n | Some (n, consumed_n) ->\n if min <= U32.v n && U32.v n <= max\n then\n let b_payload = Seq.slice b consumed_n (Seq.length b) in\n match parse (parse_nlist (U32.v n) p) b_payload with\n | None -> None\n | Some (l, consumed_l) ->\n Some (l, consumed_n + consumed_l)\n else None\n ))\n= and_then_eq ((lp `parse_filter` bounded_count_prop min max) `parse_synth` synth_bounded_count min max) (parse_vclist_payload min max p) b;\n parse_synth_eq (lp `parse_filter` bounded_count_prop min max) (synth_bounded_count min max) b;\n parse_filter_eq lp (bounded_count_prop min max) b;\n match parse lp b with\n | None -> ()\n | Some (n, consumed_n) ->\n if min <= U32.v n && U32.v n <= max\n then\n let b_payload = Seq.slice b consumed_n (Seq.length b) in\n let n : bounded_count min max = n in\n parse_synth_eq #_ #(nlist (U32.v n) t) #(vlarray t min max) (parse_nlist (U32.v n) p) (synth_vclist_payload min max n) b_payload\n else ()", "val array_nth_ghost\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (array_byte_size elem_count: nat)\n (i:\n nat\n { fldata_array_precond k array_byte_size elem_count == true /\\\n array_byte_size < 4294967296 /\\ elem_count < 4294967296 /\\ i < elem_count })\n : Tot (gaccessor (parse_array s array_byte_size elem_count) p (clens_array_nth t elem_count i))\nlet array_nth_ghost\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (array_byte_size: nat)\n (elem_count: nat)\n (i: nat {\n fldata_array_precond k array_byte_size elem_count == true /\\\n array_byte_size < 4294967296 /\\\n elem_count < 4294967296 /\\\n i < elem_count\n })\n: Tot (gaccessor (parse_array s array_byte_size elem_count) p (clens_array_nth t elem_count i))\n= reveal_opaque (`%array_nth_ghost') (array_nth_ghost' s array_byte_size elem_count i);\n reveal_opaque (`%array_nth_ghost'') (array_nth_ghost'' s array_byte_size elem_count i);\n M.distributivity_add_left i 1 k.parser_kind_low;\n M.lemma_mult_le_right k.parser_kind_low (i + 1) elem_count;\n assert ((i `Prims.op_Multiply` k.parser_kind_low) + k.parser_kind_low <= array_byte_size);\n parser_kind_prop_equiv (parse_array_kind' array_byte_size) (parse_array s array_byte_size elem_count);\n assert (forall x . gaccessor_pre (parse_array s array_byte_size elem_count) p (clens_array_nth t elem_count i) x ==> (i `Prims.op_Multiply` k.parser_kind_low) + k.parser_kind_low <= Seq.length x);\n gaccessor_prop_equiv (parse_array s array_byte_size elem_count) p (clens_array_nth t elem_count i) (array_nth_ghost' s array_byte_size elem_count i);\n array_nth_ghost' s array_byte_size elem_count i", "val valid_list\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (sl: slice rrel rel)\n (pos: U32.t)\n (pos' : U32.t)\n: GTot Type0\n (decreases (U32.v pos' - U32.v pos))\nlet rec valid_list\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (sl: slice rrel rel)\n (pos: U32.t)\n (pos' : U32.t)\n: GTot Type0\n (decreases (U32.v pos' - U32.v pos))\n= k.parser_kind_subkind == Some ParserStrong /\\\n k.parser_kind_low > 0 /\\\n live_slice h sl /\\\n U32.v pos' <= U32.v sl.len /\\ (\n if pos = pos'\n then True\n else\n valid p h sl pos /\\ (\n let pos1 = get_valid_pos p h sl pos in\n U32.v pos1 <= U32.v pos' /\\\n valid_list p h sl pos1 pos'\n ))", "val list_nth_constant_size_parser_correct\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (b: bytes)\n (i: nat)\n: Lemma\n (requires (\n k.parser_kind_high == Some k.parser_kind_low /\\\n Some? (parse (parse_list p) b) /\\ (\n let (Some (l, _)) = parse (parse_list p) b in\n i < L.length l\n )))\n (ensures (\n let j = i `Prims.op_Multiply` k.parser_kind_low in\n 0 <= j /\\\n j + k.parser_kind_low <= Seq.length b /\\ (\n let b' = Seq.slice b j (Seq.length b) in\n Some? (parse p b') /\\ (\n let (Some (l, _)) = parse (parse_list p) b in\n let (Some (x, _)) = parse p b' in\n x == L.index l i\n ))))\n (decreases i)\nlet rec list_nth_constant_size_parser_correct #k #t p b i =\n parser_kind_prop_equiv k p;\n parse_list_eq p b;\n if i = 0\n then ()\n else begin\n M.mult_decomp i k.parser_kind_low;\n list_nth_constant_size_parser_correct p (Seq.slice b k.parser_kind_low (Seq.length b)) (i - 1)\n end", "val parse_nlist_total_constant_size (i: I.itype{Some? (itype_byte_size i)}) (size: I.expr)\n : Tot (parser not_reading)\nlet parse_nlist_total_constant_size\n (i: I.itype {Some? (itype_byte_size i)}) // TODO: DT_App?\n (size: I.expr)\n: Tot (parser not_reading)\n= parse_not_readable_app'\n \"parse-nlist-total-constant-size\"\n [\n size;\n T.mk_expr (T.Constant (A.Int A.UInt8 (Some?.v (itype_byte_size i))));\n ]", "val array_nth_ghost'\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (array_byte_size elem_count: nat)\n (i:\n nat\n { fldata_array_precond k array_byte_size elem_count == true /\\\n array_byte_size < 4294967296 /\\ elem_count < 4294967296 /\\ i < elem_count })\n : Tot (gaccessor' (parse_array s array_byte_size elem_count) p (clens_array_nth t elem_count i))\nlet array_nth_ghost'\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (array_byte_size: nat)\n (elem_count: nat)\n (i: nat {\n fldata_array_precond k array_byte_size elem_count == true /\\\n array_byte_size < 4294967296 /\\\n elem_count < 4294967296 /\\\n i < elem_count\n })\n: Tot (gaccessor' (parse_array s array_byte_size elem_count) p (clens_array_nth t elem_count i))\n= fun input ->\n array_nth_ghost_correct s array_byte_size elem_count i input;\n array_nth_ghost'' s array_byte_size elem_count i input", "val bare_parse_tagged_union\n (#kt: parser_kind)\n (#tag_t: Type)\n (pt: parser kt tag_t)\n (#data_t: Type)\n (tag_of_data: (data_t -> GTot tag_t))\n (k': (t: tag_t -> Tot parser_kind))\n (p: (t: tag_t -> Tot (parser (k' t) (refine_with_tag tag_of_data t))))\n (input: bytes)\n : GTot (option (data_t * consumed_length input))\nlet bare_parse_tagged_union\n (#kt: parser_kind)\n (#tag_t: Type)\n (pt: parser kt tag_t)\n (#data_t: Type)\n (tag_of_data: (data_t -> GTot tag_t))\n (k': (t: tag_t) -> Tot parser_kind)\n (p: (t: tag_t) -> Tot (parser (k' t) (refine_with_tag tag_of_data t)))\n (input: bytes)\n: GTot (option (data_t * consumed_length input))\n= match parse pt input with\n | None -> None\n | Some (tg, consumed_tg) ->\n let input_tg = Seq.slice input consumed_tg (Seq.length input) in\n begin match parse (p tg) input_tg with\n | Some (x, consumed_x) -> Some ((x <: data_t), consumed_tg + consumed_x)\n | None -> None\n end", "val parse_option (#k: parser_kind) (#t: Type) (p: parser k t)\n : Tot (parser (parse_option_kind k) (option t))\nlet parse_option (#k: parser_kind) (#t: Type) (p: parser k t) : Tot (parser (parse_option_kind k) (option t)) =\n Classical.forall_intro_2 (fun x -> Classical.move_requires (parse_option_bare_injective p x));\n parser_kind_prop_equiv k p;\n parser_kind_prop_equiv (parse_option_kind k) (parse_option_bare p);\n parse_option_bare p", "val partial_serialize32_list_tailrec'\n (#t: Type)\n (#k: parser_kind)\n (p: parser k t)\n (s: serializer p)\n (s32: partial_serializer32 s)\n (accu: bytes32)\n (input: list t)\n : Ghost bytes32\n (requires\n (serialize_list_precond k /\\\n (B32.length accu + Seq.length (serialize (serialize_list p s) input) < 4294967296)))\n (ensures\n (fun (res: bytes32) ->\n serialize_list_precond k /\\\n Seq.length (serialize (serialize_list p s) input) < 4294967296 /\\\n B32.reveal res ==\n Seq.append (B32.reveal accu) (B32.reveal (partial_serialize32_list' p s s32 input))))\n (decreases input)\nlet rec partial_serialize32_list_tailrec'\n (#t: Type)\n (#k: parser_kind)\n (p: parser k t)\n (s: serializer p)\n (s32: partial_serializer32 s)\n (accu: bytes32)\n (input: list t)\n: Ghost bytes32\n (requires (\n serialize_list_precond k /\\ (\n B32.length accu + Seq.length (serialize (serialize_list p s) input) < 4294967296\n )))\n (ensures (fun (res: bytes32) ->\n serialize_list_precond k /\\\n Seq.length (serialize (serialize_list p s) input) < 4294967296 /\\\n B32.reveal res == Seq.append (B32.reveal accu) (B32.reveal (partial_serialize32_list' p s s32 input))\n ))\n (decreases input)\n= match input with\n | [] ->\n serialize_list_nil p s;\n Seq.append_empty_r (B32.reveal accu);\n accu\n | a :: q ->\n serialize_list_cons p s a q;\n let sa = s32 a in\n let accu' = B32.append accu sa in\n Seq.append_assoc (B32.reveal accu) (B32.reveal sa) (B32.reveal (partial_serialize32_list' p s s32 q));\n partial_serialize32_list_tailrec' p s s32 accu' q", "val parse_list_up_to_eq\n (#k: parser_kind)\n (#t: Type)\n (cond: (t -> Tot bool))\n (p: parser k t { k.parser_kind_subkind <> Some ParserConsumesAll })\n (prf: consumes_if_not_cond cond p)\n (b: bytes)\n: Lemma\n (parse (parse_list_up_to cond p prf) b == (\n match parse p b with\n | None -> None\n | Some (x, consumed) ->\n if cond x\n then Some (([], x), consumed)\n else begin match parse (parse_list_up_to cond p prf) (Seq.slice b consumed (Seq.length b)) with\n | None -> None\n | Some ((y, z), consumed') -> Some ((x::y, z), consumed + consumed')\n end\n ))\nlet parse_list_up_to_eq\n (#k: parser_kind)\n (#t: Type)\n (cond: (t -> Tot bool))\n (p: parser k t { k.parser_kind_subkind <> Some ParserConsumesAll })\n (prf: consumes_if_not_cond cond p)\n (b: bytes)\n: Lemma\n (parse (parse_list_up_to cond p prf) b == (\n match parse p b with\n | None -> None\n | Some (x, consumed) ->\n if cond x\n then Some (([], x), consumed)\n else begin match parse (parse_list_up_to cond p prf) (Seq.slice b consumed (Seq.length b)) with\n | None -> None\n | Some ((y, z), consumed') -> Some ((x::y, z), consumed + consumed')\n end\n ))\n= let fuel = close_parse_list_up_to b in\n parse_list_up_to'_eq cond p fuel b;\n parse_list_up_to_fuel_eq cond p fuel b;\n match parse p b with\n | None -> ()\n | Some (x, consumed) ->\n if cond x\n then ()\n else begin\n prf b x consumed;\n let b' = Seq.slice b consumed (Seq.length b) in\n let fuel' = close_parse_list_up_to b' in\n parse_list_up_to'_eq cond p fuel' b' ;\n parse_list_up_to_fuel_ext cond p prf (fuel - 1) fuel' b'\n end", "val parse_vclist\n (min: nat)\n (max: nat{min <= max})\n (#lk: parser_kind)\n (lp: parser lk U32.t)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n : Tot (parser (parse_vclist_kind min max lk k) (vlarray t min max))\nlet parse_vclist\n (min: nat)\n (max: nat { min <= max } )\n (#lk: parser_kind)\n (lp: parser lk U32.t)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n: Tot (parser (parse_vclist_kind min max lk k) (vlarray t min max))\n= ((lp `parse_filter` bounded_count_prop min max) `parse_synth` synth_bounded_count min max) `and_then` parse_vclist_payload min max p", "val accessor_then_fst\n (#k0: parser_kind)\n (#t0: Type)\n (#p0: parser k0 t0)\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (#p2: parser k2 t2)\n (#cl: clens t0 (t1 & t2))\n (#g: gaccessor p0 (p1 `nondep_then` p2) cl)\n (a: accessor g)\n : Tot (accessor (gaccessor_then_fst g))\nlet accessor_then_fst\n (#k0: parser_kind)\n (#t0: Type)\n (#p0: parser k0 t0)\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (#p2: parser k2 t2)\n (#cl: clens t0 (t1 & t2))\n (#g: gaccessor p0 (p1 `nondep_then` p2) cl)\n (a: accessor g)\n: Tot (accessor (gaccessor_then_fst g))\n= accessor_compose a (accessor_fst p1 () p2) ()", "val parse_list_up_to'\n (#k: parser_kind)\n (#t: Type u#r)\n (cond: (t -> Tot bool))\n (p: parser k t {k.parser_kind_subkind <> Some ParserConsumesAll})\n (fuel: nat)\n : Tot (parser (parse_list_up_to_kind k) (parse_list_up_to_t cond))\nlet parse_list_up_to'\n (#k: parser_kind)\n (#t: Type u#r)\n (cond: (t -> Tot bool))\n (p: parser k t { k.parser_kind_subkind <> Some ParserConsumesAll })\n (fuel: nat)\n: Tot (parser (parse_list_up_to_kind k) (parse_list_up_to_t cond))\n= parse_synth\n (parse_list_up_to_fuel cond p fuel)\n (synth_list_up_to' cond fuel)", "val parse_ite (#nz:_) (#wk: _) (#k:parser_kind nz wk)\r\n (e:bool)\r\n (#a:squash e -> Type)\r\n (#b:squash (not e) -> Type)\r\n (p1:squash e -> parser k (a()))\r\n (p2:squash (not e) -> parser k (b()))\r\n : Tot (parser k (t_ite e a b))\nlet parse_ite e p1 p2\r\n = if e then p1 () else p2 ()", "val owvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: owriter s h0 sout pout_from0)\n : GTot (option t)\nlet owvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: owriter s h0 sout pout_from0)\n: GTot (option t)\n= Ghost.reveal w.v", "val validate_nlist_constant_size_mod_ko\n (n: U32.t)\n (#wk: _)\n (#k: parser_kind true wk)\n (#t: _)\n (p: parser k t)\n (inv disj l: _)\n : Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires\n (let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_high == Some k.parser_kind_low /\\\n U32.v n % k.LP.parser_kind_low <> 0))\n (ensures (fun _ -> True))\nlet validate_nlist_constant_size_mod_ko\n (n:U32.t)\n (#wk: _)\n (#k:parser_kind true wk)\n #t\n (p:parser k t)\n inv disj l\n : Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires (\n let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\\n k.parser_kind_high == Some k.parser_kind_low /\\\n U32.v n % k.LP.parser_kind_low <> 0\n ))\n (ensures (fun _ -> True))\n= \n (fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = FStar.HyperStack.ST.get () in\n [@inline_let]\n let f () : Lemma\n (requires (Some? (LP.parse (parse_nlist n p) (I.get_remaining input h))))\n (ensures False)\n = let sq = I.get_remaining input h in\n let sq' = Seq.slice sq 0 (U32.v n) in\n LowParse.Spec.List.list_length_constant_size_parser_correct p sq' ;\n let Some (l, _) = LP.parse (parse_nlist n p) sq in\n assert (U32.v n == FStar.List.Tot.length l `Prims.op_Multiply` k.LP.parser_kind_low) ;\n FStar.Math.Lemmas.cancel_mul_mod (FStar.List.Tot.length l) k.LP.parser_kind_low ;\n assert (U32.v n % k.LP.parser_kind_low == 0)\n in\n [@inline_let]\n let _ = Classical.move_requires f () in\n LPE.set_validator_error_pos LPE.validator_error_list_size_not_multiple pos\n )", "val validate_list_inv\n (#k: LPL.parser_kind)\n (#t: Type)\n (p: LPL.parser k t)\n (inv: slice_inv)\n (disj: disjointness_pre)\n (l: eloc)\n (g0 g1: Ghost.erased HS.mem)\n (ctxt: app_ctxt)\n (sl: input_buffer_t)\n (bres: pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet validate_list_inv\n (#k: LPL.parser_kind)\n (#t: Type)\n (p: LPL.parser k t)\n (inv: slice_inv)\n (disj: disjointness_pre)\n (l: eloc)\n (g0 g1: Ghost.erased HS.mem)\n (ctxt:app_ctxt)\n (sl: input_buffer_t)\n (bres: pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n= let h0 = Ghost.reveal g0 in\n let h1 = Ghost.reveal g1 in\n let res = Seq.index (as_seq h bres) 0 in\n inv h0 /\\\n disj /\\\n loc_not_unused_in h0 `loc_includes` app_loc ctxt l /\\\n app_loc ctxt l `loc_disjoint` I.footprint sl /\\\n app_loc ctxt l `loc_disjoint` loc_buffer bres /\\\n address_liveness_insensitive_locs `loc_includes` app_loc ctxt l /\\\n B.loc_buffer bres `B.loc_disjoint` I.footprint sl /\\\n I.live sl h0 /\\\n I.live sl h /\\\n live h0 ctxt /\\\n live h ctxt /\\\n live h1 bres /\\\n begin\n let s = I.get_remaining sl h0 in\n let s' = I.get_remaining sl h in\n Seq.length s' <= Seq.length s /\\\n s' `Seq.equal` Seq.slice s (Seq.length s - Seq.length s') (Seq.length s)\n end /\\\n modifies loc_none h0 h1 /\\ (\n if\n LPE.is_error res\n then\n // validation *or action* failed\n stop == true /\\\n U64.v (LPE.get_validator_error_pos res) == Seq.length (I.get_read sl h) /\\\n (LPE.get_validator_error_kind res <> LPE.get_validator_error_kind LPE.validator_error_action_failed ==> ~ (valid (LPLL.parse_list p) h0 sl))\n else\n U64.v res == Seq.length (I.get_read sl h) /\\\n (valid (LPLL.parse_list p) h0 sl <==>\n valid (LPLL.parse_list p) h sl) /\\\n (stop == true ==> (valid (LPLL.parse_list p) h sl /\\ Seq.length (I.get_remaining sl h) == 0))\n ) /\\\n modifies (app_loc ctxt l `loc_union` loc_buffer bres `loc_union` I.perm_footprint sl) h1 h", "val nondep_then\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (p2: parser k2 t2)\n: Tot (parser (and_then_kind k1 k2) (t1 * t2))\nlet nondep_then #k1 = tot_nondep_then #k1", "val nondep_then\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (p2: parser k2 t2)\n: Tot (parser (and_then_kind k1 k2) (t1 * t2))\nlet nondep_then\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: Type)\n (p2: parser k2 t2)\n: Tot (parser (and_then_kind k1 k2) (t1 * t2))\n= parse_tagged_union\n p1\n fst\n (fun x -> parse_synth p2 (fun y -> (x, y) <: refine_with_tag fst x))", "val array_nth\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (array_byte_size elem_count: nat)\n (i:\n U32.t\n { fldata_array_precond k (array_byte_size) (elem_count) == true /\\\n array_byte_size < 4294967296 /\\ elem_count < 4294967296 /\\ U32.v i < elem_count })\n : Tot (accessor (array_nth_ghost s (array_byte_size) (elem_count) (U32.v i)))\nlet array_nth\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p)\n (array_byte_size: nat)\n (elem_count: nat)\n (i: U32.t {\n fldata_array_precond k (array_byte_size) (elem_count) == true /\\\n array_byte_size < 4294967296 /\\\n elem_count < 4294967296 /\\\n U32.v i < elem_count\n })\n: Tot (accessor (array_nth_ghost s (array_byte_size) (elem_count) (U32.v i)))\n= fun #rrel #rel input pos ->\n reveal_opaque (`%array_nth_ghost) (array_nth_ghost s (array_byte_size) (elem_count) (U32.v i));\n reveal_opaque (`%array_nth_ghost') (array_nth_ghost' s (array_byte_size) (elem_count) (U32.v i));\n reveal_opaque (`%array_nth_ghost'') (array_nth_ghost'' s (array_byte_size) (elem_count) (U32.v i));\n let h = HST.get () in\n [@inline_let] let _ =\n parser_kind_prop_equiv k p;\n valid_facts (parse_array s (array_byte_size) (elem_count)) h input pos;\n slice_access_eq h (array_nth_ghost s (array_byte_size) (elem_count) (U32.v i)) input pos;\n fldata_to_array_inj s (array_byte_size) (elem_count) ();\n parse_synth_eq (parse_fldata_strong (serialize_list _ s) (array_byte_size)) (fldata_to_array s array_byte_size elem_count ()) (bytes_of_slice_from h input pos);\n list_nth_constant_size_parser_correct p (Seq.slice (bytes_of_slice_from h input pos) 0 array_byte_size) (U32.v i)\n in\n pos `U32.add` (i `U32.mul` U32.uint_to_t k.parser_kind_low)", "val list_length_constant_size_parser_correct\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (b: bytes)\n: Lemma\n (requires (\n k.parser_kind_high == Some k.parser_kind_low /\\\n Some? (parse (parse_list p) b)\n ))\n (ensures (\n let pb = parse (parse_list p) b in\n Some? pb /\\ (\n let (Some (l, _)) = pb in\n FStar.Mul.op_Star (L.length l) k.parser_kind_low == Seq.length b\n )))\n (decreases (Seq.length b))\nlet rec list_length_constant_size_parser_correct #k #t p b =\n parser_kind_prop_equiv k p;\n let n = k.parser_kind_low in\n if Seq.length b = 0\n then ()\n else begin\n let (Some (_, consumed)) = parse p b in\n assert ((consumed <: nat) == n);\n assert (n > 0);\n let b' : bytes = Seq.slice b n (Seq.length b) in\n list_length_constant_size_parser_correct p b';\n let (Some (l', _)) = parse (parse_list p) b' in\n FStar.Math.Lemmas.distributivity_add_left 1 (L.length l') n\n end", "val validate_nlist\r\n (n:U32.t)\r\n (#wk: _)\r\n (#k:parser_kind true wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v: validate_with_action_t p inv disj l allow_reading)\r\n: validate_with_action_t (parse_nlist n p) inv disj l false\nlet validate_nlist\n (n:U32.t)\n #wk\n (#k:parser_kind true wk)\n #t\n (#p:parser k t)\n #inv #disj #l #ar\n (v: validate_with_action_t p inv disj l ar)\n: Tot (validate_with_action_t (parse_nlist n p) inv disj l false)\n= validate_weaken\n #false #WeakKindStrongPrefix #(LowParse.Spec.FLData.parse_fldata_kind (U32.v n) LowParse.Spec.List.parse_list_kind) #(list t)\n (validate_fldata_consumes_all n (validate_list v))\n kind_nlist", "val validate_nlist_constant_size_without_actions\r\n (n_is_const: bool)\r\n (n:U32.t)\r\n (#wk: _)\r\n (#k:parser_kind true wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v: validate_with_action_t p inv disj l allow_reading)\r\n: Tot (validate_with_action_t (parse_nlist n p) inv disj l false)\nlet validate_nlist_constant_size_without_actions\n (n_is_const: bool)\n (n:U32.t)\n #wk\n (#k:parser_kind true wk)\n #t (#p:parser k t) #inv #disj #l #ar\n (v: validate_with_action_t p inv disj l ar)\n: Tot (validate_with_action_t (parse_nlist n p) inv disj l false)\n= \n if\n let open LP in\n k.parser_kind_subkind = Some ParserStrong &&\n k.parser_kind_high = Some k.parser_kind_low &&\n k.parser_kind_metadata = Some ParserKindMetadataTotal &&\n k.parser_kind_low < 4294967296\n then\n validate_drop (validate_nlist_total_constant_size n_is_const n p inv disj l)\n else\n validate_nlist n v", "val parse_nlist_kind_low (n: nat) (k: parser_kind)\n : Lemma ((parse_nlist_kind' n k).parser_kind_low == n `mul` k.parser_kind_low)\nlet rec parse_nlist_kind_low\n (n: nat)\n (k: parser_kind)\n: Lemma\n ((parse_nlist_kind' n k).parser_kind_low == n `mul` k.parser_kind_low)\n= if n = 0\n then ()\n else begin\n LowParse.Math.distributivity_add_left (n - 1) 1 k.parser_kind_low;\n parse_nlist_kind_low (n - 1) k\n end", "val wrap_parser32_total_constant_length_precond\n (#k: parser_kind)\n (#t: Type0)\n (#p: parser k t)\n (p32: parser32 p)\n (len: nat)\n : GTot Type0\nlet wrap_parser32_total_constant_length_precond\n (#k: parser_kind)\n (#t: Type0)\n (#p: parser k t)\n (p32: parser32 p)\n (len: nat)\n: GTot Type0\n= k.parser_kind_high == Some k.parser_kind_low /\\\n k.parser_kind_low == len /\\\n k.parser_kind_metadata == Some ParserKindMetadataTotal", "val list_length\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (j: jumper p)\n (sl: slice rrel rel)\n (pos pos': U32.t)\n : HST.Stack U32.t\n (requires (fun h -> valid_list p h sl pos pos'))\n (ensures\n (fun h res h' ->\n B.modifies B.loc_none h h' /\\ U32.v res == L.length (contents_list p h sl pos pos')))\nlet list_length\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (j: jumper p)\n (sl: slice rrel rel)\n (pos pos' : U32.t)\n: HST.Stack U32.t\n (requires (fun h ->\n valid_list p h sl pos pos'\n ))\n (ensures (fun h res h' ->\n B.modifies B.loc_none h h' /\\\n U32.v res == L.length (contents_list p h sl pos pos')\n ))\n= let h0 = HST.get () in\n HST.push_frame ();\n let h1 = HST.get () in\n B.fresh_frame_modifies h0 h1;\n let blen : BF.pointer U32.t = BF.alloca 0ul 1ul in\n let h2 = HST.get () in\n list_fold_left\n p\n j\n sl\n pos\n pos'\n h2\n (Ghost.hide (B.loc_buffer blen))\n (fun h l1 l2 pos1 ->\n B.modifies (B.loc_buffer blen) h2 h /\\\n B.live h blen /\\ (\n let len = U32.v (Seq.index (B.as_seq h blen) 0) in\n len <= U32.v pos1 /\\ // necessary to prove that length computations do not overflow\n len == L.length l1\n ))\n (fun h l1 l2 pos1 h' ->\n B.modifies_only_not_unused_in (B.loc_buffer blen) h2 h';\n B.loc_unused_in_not_unused_in_disjoint h2\n )\n (fun pos1 pos2 l1 x l2 ->\n B.upd blen 0ul (B.index blen 0ul `U32.add` 1ul);\n Classical.forall_intro_2 (list_length_append #t)\n )\n ;\n let len = B.index blen 0ul in\n HST.pop_frame ();\n len", "val nlist_cons (#t: Type) (#n: nat) (a: t) (q: nlist n t) : Tot (nlist (n + 1) t)\nlet nlist_cons (#t: Type) (#n: nat) (a: t) (q: nlist n t) : Tot (nlist (n + 1) t) =\n a :: q" ], "closest_src": [ { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.parse_nlist_eq" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.List.fsti", "name": "MiniParse.Spec.List.parse_nlist_eq" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.parse_nlist'" }, { "project_name": "everparse", "file_name": "LowParse.SLow.List.fst", "name": "LowParse.SLow.List.parse_list_tailrec_inv" }, { "project_name": "everparse", "file_name": "LowParse.SLow.List.fst", "name": "LowParse.SLow.List.parse_list_tailrec'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fst", "name": "LowParse.Spec.VCList.parse_nlist" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fsti", "name": "LowParse.Spec.List.parse_list_aux" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_nlist" }, { "project_name": "everparse", "file_name": "LowParse.SLow.List.fst", "name": "LowParse.SLow.List.parse_list_tailrec" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.List.fsti", "name": "MiniParse.Spec.List.parse_nlist'" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.List.fst", "name": "MiniParse.Spec.List.parse_nlist" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fsti", "name": "LowParse.Spec.List.tot_parse_list_eq" }, { "project_name": "everparse", "file_name": "LowParse.SLow.List.fst", "name": "LowParse.SLow.List.parse_list_tailrec'_correct" }, { "project_name": "everparse", "file_name": "LowParse.Low.VCList.fst", "name": "LowParse.Low.VCList.validate_nlist" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.parse_nlist_kind" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fst", "name": "LowParse.Spec.List.tot_parse_list_aux" }, { "project_name": "everparse", "file_name": "LowParse.SLow.List.fst", "name": "LowParse.SLow.List.parse_list_tailrec'_correct'" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_nlist_total_fixed_size_aux" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.parse_nlist_kind'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.serialize_nlist'" }, { "project_name": "everparse", "file_name": "LowParse.SLow.List.fst", "name": "LowParse.SLow.List.parse_list_tailrec_body" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fst", "name": "LowParse.Spec.VCList.serialize_nlist" }, { "project_name": "everparse", "file_name": "LowParse.Low.VCList.fst", "name": "LowParse.Low.VCList.jump_nlist" }, { "project_name": "everparse", "file_name": "LowParse.Low.VCList.fst", "name": "LowParse.Low.VCList.valid_nlist_cons_recip" }, { "project_name": "everparse", "file_name": "LowParse.Low.VCList.fst", "name": "LowParse.Low.VCList.valid_nlist_nil_recip" }, { "project_name": "everparse", "file_name": "LowParse.Low.VCList.fst", "name": "LowParse.Low.VCList.valid_nlist_cons" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Base.fsti", "name": "LowParse.Spec.Base.parse" }, { "project_name": "everparse", "file_name": "LowParse.SLow.List.fst", "name": "LowParse.SLow.List.parse_list_tailrec_measure" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fsti", "name": "LowParse.Low.Base.Spec.gaccessor_post'" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.List.fst", "name": "MiniParse.Spec.List.serialize_nlist" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fsti", "name": "LowParse.Low.Base.Spec.gaccessor_post" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_nlist_total_fixed_size_kind_correct" }, { "project_name": "everparse", "file_name": "LowParse.Low.VCList.fst", "name": "LowParse.Low.VCList.valid_nlist_cons'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fst", "name": "LowParse.Spec.List.parse_list" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.List.fsti", "name": "MiniParse.Spec.List.serialize_nlist'" }, { "project_name": "everparse", "file_name": "LowParse.Low.Array.fst", "name": "LowParse.Low.Array.array_nth_ghost''" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_t_at_most" }, { "project_name": "everparse", "file_name": "Z3TestGen.fst", "name": "Z3TestGen.parse_nlist" }, { "project_name": "everparse", "file_name": "LowParse.Low.Array.fst", "name": "LowParse.Low.Array.vlarray_nth_ghost''" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_nlist_total_constant_size'" }, { "project_name": "everparse", "file_name": "LowParse.SLow.List.fst", "name": "LowParse.SLow.List.size32_list_inv" }, { "project_name": "everparse", "file_name": "LowParse.Spec.ListUpTo.fst", "name": "LowParse.Spec.ListUpTo.close_parse_list_up_to" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.Base.fst", "name": "MiniParse.Spec.Base.bparse" }, { "project_name": "everparse", "file_name": "LowParse.Low.VCList.fst", "name": "LowParse.Low.VCList.valid_nlist_cons_not" }, { "project_name": "everparse", "file_name": "LowParse.Low.VCList.fst", "name": "LowParse.Low.VCList.valid_nlist_valid_list" }, { "project_name": "everparse", "file_name": "LowParse.Low.VCList.fst", "name": "LowParse.Low.VCList.valid_list_valid_nlist" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.lwvalue" }, { "project_name": "FStar", "file_name": "MiniParse.Spec.Base.fst", "name": "MiniParse.Spec.Base.parse" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_nlist_total_constant_size" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.serialize_nlist_cons" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_nlist_total_constant_size_mod_ok" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fsti", "name": "LowParse.Low.Base.Spec.gaccessor_pre" }, { "project_name": "everparse", "file_name": "LowParse.Low.VCList.fst", "name": "LowParse.Low.VCList.valid_nlist_nil" }, { "project_name": "everparse", "file_name": "LowParse.Low.ListUpTo.fst", "name": "LowParse.Low.ListUpTo.jump_list_up_to_inv" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.olwvalue" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.parse_nlist_kind_metadata" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_list_up_to_inv" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.parse_vclist_payload" }, { "project_name": "everparse", "file_name": "LowParse.Low.List.fst", "name": "LowParse.Low.List.validate_list_inv" }, { "project_name": "everparse", "file_name": "LowParse.Low.ListUpTo.fst", "name": "LowParse.Low.ListUpTo.validate_list_up_to_inv" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Base.fst", "name": "LowParse.SLow.Base.parser32_correct" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.parse_bitsum" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.parse_nlist_kind_high" }, { "project_name": "everparse", "file_name": "LowParse.Low.Array.fst", "name": "LowParse.Low.Array.vlarray_nth_ghost'" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.swvalue" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_t_exact" }, { "project_name": "everparse", "file_name": "LowParse.Low.Array.fst", "name": "LowParse.Low.Array.vlarray_nth_ghost" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.validate_nlist_total_constant_size_mod_ok" }, { "project_name": "everparse", "file_name": "LowParse.Tot.Combinators.fst", "name": "LowParse.Tot.Combinators.nondep_then_eq" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.wvalue" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fsti", "name": "LowParse.Spec.List.parse_list_bare" }, { "project_name": "everparse", "file_name": "LowParse.Spec.ListUpTo.fst", "name": "LowParse.Spec.ListUpTo.parse_list_up_to'_eq" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fst", "name": "LowParse.Low.Base.Spec.serialized_list_length" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.parse_vclist_eq" }, { "project_name": "everparse", "file_name": "LowParse.Low.Array.fst", "name": "LowParse.Low.Array.array_nth_ghost" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fst", "name": "LowParse.Low.Base.Spec.valid_list" }, { "project_name": "everparse", "file_name": "LowParse.Low.Array.fst", "name": "LowParse.Low.Array.list_nth_constant_size_parser_correct" }, { "project_name": "everparse", "file_name": "Z3TestGen.fst", "name": "Z3TestGen.parse_nlist_total_constant_size" }, { "project_name": "everparse", "file_name": "LowParse.Low.Array.fst", "name": "LowParse.Low.Array.array_nth_ghost'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fsti", "name": "LowParse.Spec.Combinators.bare_parse_tagged_union" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Option.fst", "name": "LowParse.Spec.Option.parse_option" }, { "project_name": "everparse", "file_name": "LowParse.SLow.List.fst", "name": "LowParse.SLow.List.partial_serialize32_list_tailrec'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.ListUpTo.fst", "name": "LowParse.Spec.ListUpTo.parse_list_up_to_eq" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.parse_vclist" }, { "project_name": "everparse", "file_name": "LowParse.Low.Combinators.fsti", "name": "LowParse.Low.Combinators.accessor_then_fst" }, { "project_name": "everparse", "file_name": "LowParse.Spec.ListUpTo.fst", "name": "LowParse.Spec.ListUpTo.parse_list_up_to'" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_ite" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.owvalue" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_nlist_constant_size_mod_ko" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_list_inv" }, { "project_name": "everparse", "file_name": "LowParse.Tot.Combinators.fst", "name": "LowParse.Tot.Combinators.nondep_then" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fst", "name": "LowParse.Spec.Combinators.nondep_then" }, { "project_name": "everparse", "file_name": "LowParse.Low.Array.fst", "name": "LowParse.Low.Array.array_nth" }, { "project_name": "everparse", "file_name": "LowParse.Spec.List.fst", "name": "LowParse.Spec.List.list_length_constant_size_parser_correct" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_nlist" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_nlist_constant_size_without_actions" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.parse_nlist_kind_low" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.LowParseWrappers.fst", "name": "MiTLS.LowParseWrappers.wrap_parser32_total_constant_length_precond" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.fst", "name": "LowParse.Low.Base.list_length" }, { "project_name": "everparse", "file_name": "LowParse.Spec.VCList.fsti", "name": "LowParse.Spec.VCList.nlist_cons" } ], "selected_premises": [ "LowParse.SLow.List.parse_list_tailrec_measure", "LowParse.SLow.List.parse_list_tailrec'_correct'", "LowParse.SLow.List.parse_list_tailrec_body", "LowParse.Spec.Array.array_pred", "LowParse.Spec.VCList.parse_nlist_eq", "LowParse.Spec.List.parse_list_aux", "LowParse.SLow.List.size32_list_measure", "LowParse.SLow.List.parse_list_tailrec'_correct", "LowStar.Monotonic.Buffer.length", "LowParse.Spec.Array.vlarray_pred", "LowParse.Spec.Array.vlarray", "LowStar.Monotonic.Buffer.srel", "LowParse.Spec.List.parse_list_total_constant_size", "LowParse.Spec.VCList.parse_nlist'", "FStar.Bytes.length", "LowParse.Spec.Combinators.parse_filter_refine", "LowParse.Spec.VCList.nlist_destruct", "LowParse.SLow.List.partial_serialize32_list_tailrec'", "LowParse.Spec.VCList.parse_nlist_kind_subkind", "LowParse.Spec.Combinators.and_then_kind", "LowStar.Buffer.trivial_preorder", "LowParse.Spec.VCList.synth_nlist", "LowParse.SLow.List.partial_serialize32_list'_measure", "LowParse.SLow.List.parse_list_tailrec'", "LowParse.Spec.VCList.synth_nlist_recip", "LowParse.Spec.VCList.parse_vclist_eq", "LowParse.Spec.VCList.parse_nlist_kind_high", "FStar.String.strlen", "LowParse.Bytes32.b32append", "LowParse.Spec.List.parse_list_kind", "C.Loops.total_while", "LowParse.Spec.Base.parser_kind", "LowParse.Spec.VCList.parse_nlist_kind", "LowParse.SLow.List.parse_list_tailrec_inv", "LowParse.Spec.VCList.nlist_cons", "LowParse.Spec.VCList.synth_vclist_payload", "LowParse.Spec.FLData.parse_fldata", "LowStar.BufferOps.op_Bang_Star", "LowParse.Spec.VCList.mul", "FStar.Heap.trivial_preorder", "LowParse.Spec.Base.injective_postcond", "LowParse.Spec.VCList.bounded_count_prop", "LowParse.Spec.VCList.nlist_nil", "LowParse.Spec.VCList.parse_vclist", "LowParse.Spec.VCList.parse_nlist_kind'", "LowParse.SLow.Base.bytes32", "LowParse.Spec.Combinators.parse_filter_kind", "LowParse.Spec.List.serialize_list_precond", "LowParse.Spec.VCList.parse_nlist_kind_metadata", "LowParse.Spec.FLData.parse_fldata_kind", "LowStar.Buffer.gcmalloc_of_list", "FStar.UInt.size", "LowParse.Spec.Base.coerce", "LowParse.Spec.Array.fldata_array_precond", "LowParse.Spec.VCList.synth_bounded_count", "FStar.Monotonic.HyperStack.sel", "LowParse.Spec.VCList.parse_nlist_kind_low", "LowParse.Spec.VCList.parse_vclist_payload", "C.Loops.total_while_gen", "LowParse.Spec.Array.array", "LowParse.Spec.Base.strong_parser_kind", "LowParse.SLow.Base.bytes_of_seq'", "LowParse.Spec.Combinators.parse_ret_kind", "LowStar.Monotonic.Buffer.loc_addr_of_buffer", "LowParse.SLow.List.partial_serialize32_list'_body", "LowParse.Spec.Array.parse_array_kind", "LowStar.BufferOps.op_Star_Equals", "LowParse.Spec.Combinators.parse_ret", "LowParse.Spec.Array.parse_array_kind'", "LowParse.SLow.List.size32_list", "LowParse.Spec.VCList.parse_vclist_payload_kind", "LowParse.Spec.VCList.parse_vclist_kind", "LowParse.SLow.List.list_rev", "LowParse.Spec.Base.injective_precond", "LowParse.Spec.List.tot_parse_list_eq", "LowParse.SLow.List.parse_list_tailrec", "LowParse.Bytes32.b32_hide", "LowParse.Spec.FLData.parse_fldata_strong", "FStar.Bytes.op_String_Access", "FStar.ST.op_Bang", "C.Loops.do_while", "FStar.Bytes.index", "LowParse.SLow.List.partial_serialize32_list'", "FStar.String.length", "LowParse.Spec.Combinators.synth_injective_intro'", "LowParse.Spec.Combinators.synth_inverse_intro'", "LowParse.SLow.Base.parser32_correct", "LowParse.Spec.Combinators.synth_injective_synth_inverse_synth_inverse_recip", "FStar.Bytes.create_", "LowParse.Spec.Array.fldata_to_array", "LowStar.Monotonic.Buffer.deref", "LowParse.Spec.Array.parse_array_total_constant_size", "LowParse.Spec.List.parse_list_bare_consumed", "LowParse.Spec.Combinators.constant_size_parser_kind", "FStar.Mul.op_Star", "LowParse.Math.pow2_lt_recip", "FStar.Bytes.u32", "LowParse.SLow.Base.size32_constant_precond", "LowStar.Monotonic.Buffer.lmbuffer", "LowParse.Spec.VCList.serialize_nlist'" ], "source_upto_this": "module LowParse.SLow.VCList\ninclude LowParse.Spec.VCList\ninclude LowParse.SLow.List\n\nmodule Seq = FStar.Seq\nmodule U32 = FStar.UInt32\nmodule Classical = FStar.Classical\nmodule L = FStar.List.Tot\nmodule B32 = LowParse.Bytes32\n", "sketch": [ "Step 1: The `parse_nlist_tailrec` function aims to parse a list of elements from a byte sequence using a given parser. It takes the number of elements to parse (`n`), the parser (`p`), an accumulator (`accu`) to store the parsed elements and the remaining byte count, and the byte sequence (`b`).\n\nStep 2: The function is implemented recursively. If `n` is zero, it returns the accumulator as the result. Otherwise, it attempts to parse an element using the parser `p`. If parsing fails, it returns `None`. If parsing succeeds, it updates the accumulator with the parsed element and the remaining byte count, and recursively calls itself with `n-1` and the updated accumulator and byte sequence.", "Step 1: The definition `parse_nlist_tailrec` aims to parse a list of elements from a byte sequence using a given parser `p`. The function is tail-recursive and processes `n` elements, accumulating the parsed elements and the number of bytes consumed in `accu`.\nStep 2: The implementation will check if `n` is zero, in which case it returns the accumulated result. Otherwise, it will attempt to parse an element using `p`. If parsing fails, it returns `None`. If parsing succeeds, it updates the accumulator with the parsed element and the new byte position, then recursively calls itself with `n-1`.", "Step 1: The definition `parse_nlist_tailrec` is about parsing a list of `n` elements from a given byte sequence `b` using a parser `p`. The function is tail-recursive and accumulates the parsed elements and the remaining byte count in `accu`.\nStep 2: The implementation will check if `n` is zero. If it is, it returns the accumulated result. Otherwise, it attempts to parse an element using `p`. If parsing fails, it returns `None`. If parsing succeeds, it updates the accumulator with the parsed element and the new byte count, and recursively calls itself with `n-1`.", "Step 1: The definition `parse_nlist_tailrec` is about parsing a list of `n` elements from a byte sequence `b` using a parser `p` for individual elements. The function is tail-recursive and accumulates the parsed elements and the remaining bytes in `accu`.\nStep 2: The implementation will involve iterating over the byte sequence `b` and applying the parser `p` to extract elements until `n` elements are parsed or the byte sequence is exhausted. The accumulator `accu` will be updated with each successful parse, and the function will return an option type containing the list of parsed elements and the remaining bytes.", "Step 1: The definition `parse_nlist_tailrec` aims to parse a list of `n` elements from a given byte sequence `b` using a parser `p`. The function is tail-recursive and accumulates the parsed elements and the remaining bytes in `accu`.\nStep 2: The implementation will involve a recursive helper function that processes the byte sequence `b` element by element, updating the accumulator `accu` with each parsed element and decrementing `n` until `n` reaches zero or parsing fails.", "Step 1: The definition `parse_nlist_tailrec` is about parsing a list of `n` elements from a byte sequence `b` using a given parser `p`. The function is tail-recursive and accumulates the parsed elements and the remaining bytes in `accu`.\nStep 2: The implementation involves a recursive helper function that processes the byte sequence. If `n` is zero, it returns the accumulated result. Otherwise, it attempts to parse the next element using `p`. If parsing fails, it returns `None`. If parsing succeeds, it updates the accumulator and continues parsing the rest of the elements.", "Step 1: This definition is about parsing a list of elements of type `t` from a byte sequence `b` using a parser `p`. The parsing is done tail-recursively for `n` elements, starting with an accumulator `accu` which holds a tuple of a list of parsed elements and the current position in the byte sequence.\nStep 2: The implementation will check if `n` is zero, in which case it returns the accumulator wrapped in `Some`. If `n` is not zero, it will attempt to parse an element using `p` from the current position in `b`. If parsing fails, it returns `None`. If parsing succeeds, it updates the accumulator with the new element and the new position, and recursively calls itself with `n-1`.", "Step 1: The definition `parse_nlist_tailrec` is about parsing a list of `n` elements from a byte sequence `b` using a parser `p`. The function is tail-recursive and accumulates the parsed elements and the remaining byte count in `accu`.\nStep 2: The implementation involves checking if `n` is zero. If it is, return the accumulated result. Otherwise, parse the next element using `p`, update the accumulator, and recursively call `parse_nlist_tailrec` with `n-1`.", "Step 1: The definition `parse_nlist_tailrec` aims to parse a list of elements from a byte sequence using a given parser. The function is tail-recursive and continues parsing until it has parsed `n` elements or fails to parse an element.\nStep 2: The function takes the number of elements `n` to parse, a parser `p` for individual elements, an accumulator `accu` to store parsed elements and the current position, and the byte sequence `b`. It returns an option type containing the list of parsed elements and the final position if successful, or `None` if parsing fails.", "Step 1: The definition `parse_nlist_tailrec` is about parsing a list of elements from a byte sequence using a given parser, `p`, for `n` elements. It accumulates the parsed elements and the remaining byte count in `accu`.\nStep 2: The implementation will use tail recursion to parse each element one by one until `n` elements are parsed or the parsing fails. It will update the accumulator with each successful parse and return the final list of parsed elements along with the remaining byte count." ], "generated_solution": [ "let rec parse_nlist_tailrec\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (accu: (list t * nat))\n (b: bytes)\n : GTot (option (list t * nat)) =\n if n = 0 then Some accu\n else match p b with\n | None -> None\n | Some (x, b') ->\n let (acc_list, acc_len) = accu in\n parse_nlist_tailrec (n - 1) p ((x :: acc_list), acc_len + 1) b'", "let rec parse_nlist_tailrec\n (n: nat)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (accu: (list t * nat))\n (b: bytes)\n : GTot (option (list t * nat)) =\n if n = 0 then\n Some accu\n else\n match p b with\n | None -> None\n | Some (v, consumed) ->\n let (parsed_list, total_consumed) = accu in\n let new_accu = (v :: parsed_list, total_consumed + consumed) in\n parse_nlist_tailrec (n - 1) p new_accu (Seq.slice b consumed (Seq.length b - consumed))", "let rec parse_nlist_tailrec (n: nat) (#k: parser_kind) (#t: Type) (p: parser k t) (accu: (list t * nat)) (b: bytes) : GTot (option (list t * nat)) =\n if n = 0 then\n Some accu\n else\n match p b with\n | None -> None\n | Some (v, b') ->\n let (parsed_list, remaining_bytes) = accu in\n parse_nlist_tailrec (n - 1) p ((v :: parsed_list), remaining_bytes) b'", "let rec parse_nlist_tailrec (n: nat) (#k: parser_kind) (#t: Type) (p: parser k t) (accu: (list t * nat)) (b: bytes) : GTot (option (list t * nat)) =\n if n = 0 then Some accu\n else match p b with\n | None -> None\n | Some (v, rest) ->\n let (parsed, remaining) = accu in\n parse_nlist_tailrec (n - 1) p ((v :: parsed), remaining + 1) rest", "let rec parse_nlist_tailrec (n: nat) (#k: parser_kind) (#t: Type) (p: parser k t) (accu: (list t * nat)) (b: bytes) : GTot (option (list t * nat)) =\n if n = 0 then Some accu\n else match p b with\n | None -> None\n | Some (x, b') -> parse_nlist_tailrec (n - 1) p (x :: fst accu, snd accu + 1) b'", "let rec parse_nlist_tailrec (n: nat) (#k: parser_kind) (#t: Type) (p: parser k t) (accu: (list t * nat)) (b: bytes) : GTot (option (list t * nat)) =\n if n = 0 then\n Some accu\n else\n match p b with\n | None -> None\n | Some (v, rest) ->\n let (parsed_list, remaining_bytes) = accu in\n parse_nlist_tailrec (n - 1) p ((v :: parsed_list), remaining_bytes) rest", "let rec parse_nlist_tailrec (n: nat) (#k: parser_kind) (#t: Type) (p: parser k t) (accu: (list t * nat)) (b: bytes) : GTot (option (list t * nat)) =\n if n = 0 then\n Some accu\n else\n match p (snd accu) b with\n | None -> None\n | Some (x, pos') ->\n let (lst, pos) = accu in\n parse_nlist_tailrec (n - 1) p (x :: lst, pos') b", "let rec parse_nlist_tailrec (n: nat) (#k: parser_kind) (#t: Type) (p: parser k t) (accu: (list t * nat)) (b: bytes) : GTot (option (list t * nat)) =\n if n = 0 then\n Some accu\n else\n match p b with\n | None -> None\n | Some (x, b') ->\n let (parsed_list, remaining_bytes) = accu in\n parse_nlist_tailrec (n - 1) p ((x :: parsed_list), remaining_bytes - 1) b'", "let rec parse_nlist_tailrec (n: nat) (#k: parser_kind) (#t: Type) (p: parser k t) (accu: (list t * nat)) (b: bytes) : GTot (option (list t * nat)) =\n if n = 0 then\n Some accu\n else\n match p b with\n | None -> None\n | Some (x, pos) ->\n let (parsed_list, current_pos) = accu in\n parse_nlist_tailrec (n - 1) p ((x :: parsed_list), pos) b", "let rec parse_nlist_tailrec (n: nat) (#k: parser_kind) (#t: Type) (p: parser k t) (accu: (list t * nat)) (b: bytes) : GTot (option (list t * nat)) =\n if n = 0 then Some accu\n else match p b with\n | None -> None\n | Some (v, b') ->\n let (accu_list, accu_n) = accu in\n parse_nlist_tailrec (n - 1) p (v :: accu_list, accu_n + 1) b'" ] }, { "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.rid_ctr_pred_predicate", "opens_and_abbrevs": [ { "open": "FStar.Monotonic.HyperHeap" }, { "abbrev": "Map", "full_module": "FStar.Map" }, { "open": "FStar.Preorder" }, { "open": "FStar.Monotonic" }, { "open": "FStar.Monotonic" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val rid_ctr_pred_predicate (h: hmap) (n: int) : Type0", "source_definition": "let rid_ctr_pred_predicate (h:hmap) (n:int) :Type0 =\n forall (r:rid). h `Map.contains` r ==> rid_last_component r < n", "source_range": { "start_line": 67, "start_col": 15, "end_line": 68, "end_col": 65 }, "interleaved": false, "definition": "fun h n ->\n (forall (r: FStar.Monotonic.HyperHeap.rid).\n FStar.Map.contains h r ==> FStar.Monotonic.HyperHeap.rid_last_component r < n)\n <:\n Type0", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Monotonic.HyperHeap.hmap", "Prims.int", "Prims.l_Forall", "FStar.Monotonic.HyperHeap.rid", "Prims.l_imp", "Prims.b2t", "FStar.Map.contains", "FStar.Monotonic.Heap.heap", "Prims.op_LessThan", "FStar.Monotonic.HyperHeap.rid_last_component" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "h: FStar.Monotonic.HyperHeap.hmap -> n: Prims.int -> Type0", "prompt": "let rid_ctr_pred_predicate (h: hmap) (n: int) : Type0 =\n ", "expected_response": "forall (r: rid). h `Map.contains` r ==> rid_last_component r < n", "source": { "project_name": "FStar", "file_name": "ulib/FStar.Monotonic.HyperStack.fsti", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.Monotonic.HyperStack.fsti", "checked_file": "dataset/FStar.Monotonic.HyperStack.fsti.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Monotonic.HyperHeap.fsti.checked", "dataset/FStar.Monotonic.Heap.fsti.checked", "dataset/FStar.Map.fsti.checked" ] }, "definitions_in_context": [ "", "", "let is_in (r:rid) (h:hmap) = h `Map.contains` r", "let is_stack_region r = color r > 0", "let is_heap_color c = c <= 0", "let is_eternal_region r = is_heap_color (color r) && not (rid_freeable r)", "let is_eternal_region_hs r = is_heap_color (color r) && not (rid_freeable r)", "sid", "let is_above r1 r2 = r1 `includes` r2", "let is_just_below r1 r2 = r1 `extends` r2", "let is_below r1 r2 = r2 `is_above` r1", "let is_strictly_below r1 r2 = r1 `is_below` r2 && r1 <> r2", "let is_strictly_above r1 r2 = r1 `is_above` r2 && r1 <> r2", "let map_invariant_predicate (m:hmap) :Type0 =\n forall r. Map.contains m r ==>\n (forall s. includes s r ==> Map.contains m s)", "let downward_closed_predicate (h:hmap) :Type0 =\n forall (r:rid). r `is_in` h //for any region in the memory\n ==> (r=root //either is the root\n \\/ (forall (s:rid). (r `is_above` s //or, any region beneath it\n /\\ s `is_in` h) //that is also in the memory\n ==> ((is_stack_region r = is_stack_region s) /\\ //must be of the same flavor as itself\n ((is_heap_color (color r) /\\ rid_freeable r) ==> s == r))))", "let tip_top_predicate (tip:rid) (h:hmap) :Type0 =\n forall (r:sid). r `is_in` h <==> r `is_above` tip" ], "closest": [ "val rid_ctr_pred (h:hmap) (n:int) :Type0\nlet rid_ctr_pred = rid_ctr_pred_predicate", "val array_pred (#t: Type) (n: nat) (s: list t) : GTot Type0\nlet array_pred (#t: Type) (n: nat) (s: list t) : GTot Type0 =\n L.length s == n", "val counter_pred (#rand: randomness) (n: nat) (es_ref: mref (entries rand) (entries_rel rand))\n : (p: heap_predicate{stable p})\nlet counter_pred (#rand:randomness) (n:nat) (es_ref:mref (entries rand) (entries_rel rand)) :(p:heap_predicate{stable p})\n = fun h -> h `contains` es_ref /\\ n <= length (sel h es_ref)", "val heap_ctr_valid (ctr: nat) (h: H.heap u#a) : prop\nlet heap_ctr_valid (ctr:nat) (h:H.heap u#a) : prop =\n h `H.free_above_addr` ctr", "val heap_ctr_valid (ctr: nat) (h: H.heap u#a) : prop\nlet heap_ctr_valid (ctr:nat) (h:H.heap u#a) : prop =\n h `H.free_above_addr` ctr", "val lockinv_predicate: p: vprop -> r: ref U32.t -> U32.t -> vprop\nlet lockinv_predicate (p:vprop) (r:ref U32.t)\n : U32.t -> vprop\n = fun b ->\n pts_to r full_perm b\n `star`\n pure (b == locked \\/ b == unlocked)\n `star`\n (if is_locked b then emp else p)", "val test_abs0' (n: int) : RWI nat RO (fun _ -> True) (fun h0 _ h1 -> True)\nlet test_abs0' (n:int) : RWI nat RO (fun _ -> True) (fun h0 _ h1 -> True) =\n let r = labs0 n in\n let r : nat = r in // need this! an ascription won't work!\n r", "val lemma_is_wf_ctr_and_tip_intro (h:hmap) (ctr:int) (tip:rid)\n :Lemma (requires (root `is_in` h /\\ (is_stack_region tip \\/ tip = root) /\\ tip `is_in` h /\\\n tip_top_predicate tip h /\\ map_invariant_predicate h /\\\n downward_closed_predicate h /\\ rid_ctr_pred_predicate h ctr))\n\t (ensures (is_wf_with_ctr_and_tip h ctr tip))\nlet lemma_is_wf_ctr_and_tip_intro _ _ _ = root_is_not_freeable ()", "val read (#a: Type0) (n: nat)\n : LV a\n (fun m0 -> m0.m `M.contains` n /\\ dfst (m0.m `M.sel` n) == a)\n (fun m0 r m1 ->\n m0.m `M.contains` n /\\ dfst (m0.m `M.sel` n) == a /\\ r == dsnd (m0.m `M.sel` n) /\\\n m0 == m1)\nlet read (#a:Type0) (n:nat)\n : LV a (fun m0 -> m0.m `M.contains` n /\\\n dfst (m0.m `M.sel` n) == a)\n (fun m0 r m1 ->\n m0.m `M.contains` n /\\\n dfst (m0.m `M.sel` n) == a /\\\n r == dsnd (m0.m `M.sel` n) /\\ m0 == m1)\n= LVARS?.reflect (fun m -> dsnd (m.m `M.sel` n), m)", "val initialized' (#a: Type0) (#n: nat) (arr: t a n) (i: index arr) : heap_predicate\nlet initialized' (#a:Type0) (#n:nat) (arr:t a n) (i:index arr) :heap_predicate\n = fun h -> h `contains_array` arr /\\ init_at_arr arr i h", "val mk_mem (rid_ctr:int) (h:hmap) (tip:rid) :mem'\nlet mk_mem rid_ctr h tip = HS rid_ctr h tip", "val lock_inv_pred (r: ref bool) (p: vprop) (v: bool) : vprop\nlet lock_inv_pred (r:ref bool) (p:vprop) (v:bool) : vprop =\n pts_to r full_perm v `star` maybe_p p v", "val lock_inv_pred: r: ref bool -> v: vprop -> bool -> vprop\nlet lock_inv_pred (r:ref bool) (v:vprop) : bool -> vprop =\n fun b -> pts_to r full_perm b `star` (if b then v else emp)", "val identity_map (n: nat) (r: regmap int) : regmap int\nlet rec identity_map (n:nat) (r:regmap int) : regmap int =\n if n = 0 then r\n else identity_map (n - 1) (upd r n n)", "val modifies_r (#n: nat) (c: connection{receiver c}) (arr: array byte n) (h0 h1: heap) : Type0\nlet modifies_r (#n:nat) (c:connection{receiver c}) (arr:array byte n) (h0 h1:heap) :Type0\n = modifies (Set.union (connection_footprint c)\n (array_footprint arr)) h0 h1", "val contains_array (#a:Type) (#n:nat) (h:heap) (arr:t a n) : Type0\nlet contains_array (#a:Type) (#n:nat) (h:heap) (arr:t a n)\n = let A #_ #_ #_ s_ref _ = arr in\n h `Heap.contains` s_ref", "val snapshot_pred (x: t) (m: repr) (m': PM.map tid aval) : prop\nlet snapshot_pred (x:t)\r\n (m:repr)\r\n (m':PM.map tid aval)\r\n : prop\r\n = related_domains m m' /\\\r\n (forall tid. has_key m' tid ==>\r\n get m' tid == Some?.v (Map.sel m tid) /\\\r\n no_ownership m' tid)", "val contains (#a:Type) (#r:preorder_t a) (h:heap) (m:mref a r) : Type0\nlet contains (#a:Type) (#r:preorder_t a) (h:heap) (m:mref a r) : GTot Type0 =\n exists (v:heap_cell).\n snd h m == Some v /\\\n dfst v == a /\\\n snd #(dfst v) #(preorder_t a) (dsnd v) == r", "val test_abs (n: int) : RWI nat RO (fun _ -> True) (fun h0 _ h1 -> True)\nlet test_abs (n:int) : RWI nat RO (fun _ -> True) (fun h0 _ h1 -> True) =\n let r = labs n in\n r", "val get_rid_ctr (m:mem') :int\nlet get_rid_ctr m = m.rid_ctr", "val ctr_validity (ctr: nat) (h: H.heap) : slprop\nlet ctr_validity (ctr:nat) (h:H.heap) : slprop =\n H.pure (heap_ctr_valid ctr h)", "val ctr_validity (ctr: nat) (h: H.heap) : slprop\nlet ctr_validity (ctr:nat) (h:H.heap) : slprop =\n H.pure (heap_ctr_valid ctr h)", "val tip_top (tip:rid) (h:hmap) :Type0\nlet tip_top = tip_top_predicate", "val test_abs0 (n: int) : RWI int RO (fun _ -> True) (fun h0 r h1 -> r >= 0)\nlet test_abs0 (n:int) : RWI int RO (fun _ -> True) (fun h0 r h1 -> r >= 0) =\n let r = labs0 n in\n ();\n ();\n r", "val initialized (#a:Type0) (#n:nat) (arr:t a n) (i:index arr) : (p:heap_predicate{stable p})\nlet initialized (#a:Type0) (#n:nat) (arr:t a n) (i:index arr) :(p:heap_predicate{stable p})\n = let A #_ #_ #m s_ref off = arr in\n assert (forall (h:heap).\n let s, _ = sel h s_ref in\n\t init_at_arr arr i h <==> Some? (Seq.index s (off + i)));\n assert (forall (h1 h2:heap).\n let s1, _ = sel h1 s_ref in\n\t let s2, _ = sel h2 s_ref in\n (h1 `contains_array` arr /\\ heap_rel h1 h2) ==> (forall (i:nat). i < m ==> (Some? (Seq.index s1 i) ==>\n\t Some? (Seq.index s2 i))));\n initialized' arr i", "val nat_t_of_nat (n: nat) : Type0\nlet rec nat_t_of_nat (n: nat): Type0 =\n match n with\n | 0 -> z\n | n -> s (nat_t_of_nat (n - 1))", "val nat_t_of_nat (n: nat) : Type0\nlet rec nat_t_of_nat (n: nat): Type0 =\n match n with\n | 0 -> z\n | n -> s (nat_t_of_nat (n - 1))", "val count (n: nat) : I int\nlet rec count (n:nat) : I int\n = if n = 0 then 0 else count (n-1)", "val count (n: nat) : I int\nlet rec count (n:nat) : I int\n = if n = 0 then 0 else count (n-1)", "val count (n: nat) : I int\nlet rec count (n:nat) : I int\n = if n = 0 then 0 else count (n-1)", "val witnessed (#s: Type) (#rel: preorder s) (p: predicate s) : Type0\nlet witnessed (#s:Type) (#rel:preorder s) (p:predicate s) :Type0 = W.witnessed rel p", "val witnessed (#s: Type) (#rel: preorder s) (p: predicate s) : Type0\nlet witnessed (#s:Type) (#rel:preorder s) (p:predicate s) :Type0 = W.witnessed rel p", "val size (x: int) (n: nat) : Tot Type0\nlet size (x:int) (n:nat) : Tot Type0 = b2t(fits x n)", "val pred : nat -> Tot nat\nlet pred n =\n match n with\n | O -> O\n | S n' -> n'", "val hiddenTree_mem : #h:nat -> int -> hiddenTree h -> bool\nlet hiddenTree_mem #h x = function\n | HB root\n | HR root -> mem x root", "val size (x: int) (n: pos) : Tot Type0\nlet size (x:int) (n:pos) : Tot Type0 = b2t(fits x n)", "val vlarray_pred (#t: Type) (min max: nat) (s: list t) : GTot Type0\nlet vlarray_pred (#t: Type) (min max: nat) (s: list t) : GTot Type0 =\n let l = L.length s in\n min <= l /\\ l <= max", "val is_mutable (#a:Type0) (#n:nat) (arr:t a n) (h:heap) : Type0\nlet is_mutable (#a:Type0) (#n:nat) (arr:t a n) (h:heap)\n = let A #_ s_ref _ = arr in\n let f = snd (sel h s_ref) in\n f == Mutable \\/ f == MutableUntilFrozen", "val full_heap_pred : heap -> prop\nlet full_heap_pred h =\n forall a. contains_addr h a ==>\n (select_addr h a).frac == Frac.full_perm", "val full_heap_pred : heap -> prop\nlet full_heap_pred h =\n forall a. contains_addr h a ==>\n (select_addr h a).frac == Frac.full_perm", "val gconst (#t: Type0) (n: t) : gexp t\nlet gconst (#t: Type0) (n: t) : gexp t =\n let g _ _ : GTot t = n in\n g", "val count (n: nat) : ID int (as_pure_wp (fun p -> forall r. p r))\nlet rec count (n:nat) : ID int (as_pure_wp (fun p -> forall r. p r)) =\n if n = 0 then 0 else count (n-1)", "val v (r: ref stepper p) (n: nat{n > 0}) : vprop\nlet v (r:ref stepper p) (n:nat{n > 0}) : vprop = pts_to r (V n)", "val map_invariant (m:hmap) :Type0\nlet map_invariant = map_invariant_predicate", "val seq_pre (a: Type0) (n: nat) : preorder (repr a n)\nlet seq_pre (a:Type0) (n:nat) :preorder (repr a n) = seq_rel a n", "val rid_length (r:rid) :GTot nat\nlet rid_length r = List.Tot.length (reveal r)", "val folded_pts_to (r: ref U32.t) (n: erased U32.t) : vprop\nlet folded_pts_to (r:ref U32.t) (n:erased U32.t) : vprop = pts_to r n", "val labs0 (n: int) : RWI int RO (fun _ -> True) (fun h0 x h1 -> x >= 0 /\\ h1 == h0)\nlet labs0 (n:int) : RWI int RO (fun _ -> True) (fun h0 x h1 -> x >= 0 /\\ h1 == h0) =\n if n < 0\n then -n\n else n", "val get_right (#a: Type0) (n: node a) : t a\nlet get_right #a n = n.right", "val init_r1 (h:vale_stack) : (n:nat64{n >= 65536})\nlet init_r1 h = h.initial_r1", "val mref (a:Type) (r:preorder_t a) : Type0\nlet mref (a:Type) (r:preorder_t a) = nat", "val repeat_gen_inductive:\n n:nat\n -> a:(i:nat{i <= n} -> Type)\n -> pred:(i:nat{i <= n} -> a i -> Type0)\n -> f:(i:nat{i < n} -> a i -> a (i + 1))\n -> x0:a 0\n -> Pure (a n)\n (requires preserves_predicate n a f pred /\\ pred 0 x0)\n (ensures fun res -> pred n res /\\ res == repeat_gen n a f x0)\nlet repeat_gen_inductive n a pred f x0 =\n let f' (i:nat{i < n})\n\t (x:a i{pred i x /\\ x == repeat_gen i a f x0})\n\t : x':a (i + 1){pred (i + 1) x' /\\ x' == repeat_gen (i + 1) a f x0}\n\t = f i x in\n repeat_gen n (fun i -> x:a i{pred i x /\\ x == repeat_gen i a f x0}) f' x0", "val read (#a: Type) (#rel: preorder a) (r: mref a rel) : STATE a (fun p h -> p (sel h r) h)\nlet read (#a:Type) (#rel:preorder a) (r:mref a rel) :STATE a (fun p h -> p (sel h r) h)\n = let h0 = gst_get () in\n gst_recall (contains_pred r);\n Heap.lemma_sel_equals_sel_tot_for_contained_refs h0 r;\n sel_tot h0 r", "val FStar.ST.contains_pred = r: FStar.Monotonic.Heap.mref a rel -> h: FStar.Monotonic.Heap.heap -> Type0\nlet contains_pred (#a:Type0) (#rel:preorder a) (r:mref a rel) = fun h -> h `contains` r", "val alloc_ref : h0:heap ->\n a:Type -> \n\t\tx:a -> \n\t\tTot (rh1:(ref a * heap)\n\t\t\t {~(contains h0 (fst rh1)) /\\ \n\t\t\t contains (snd rh1) (fst rh1) /\\\n\t\t sel (snd rh1) (fst rh1) == x /\\\n\t\t\t (forall b (r:ref b) .{:pattern (contains h0 r)}\n\t\t\t contains h0 r \n\t\t\t ==> \n\t\t\t contains (snd rh1) r) /\\\n\t\t\t (forall b (r:ref b{contains h0 r}) . {:pattern sel #b h0 r}\n\t\t\t sel #b h0 r == sel #b (snd rh1) r)})\nlet alloc_ref h0 a x = \n (fst h0 , (fst h0 + 1 , F.on_dom nat (fun r -> if r = fst h0 then Some (| a , x |)\n\t\t\t\t\t else snd h0 r)))", "val ind_ptr' (#a: Type0) (r: ref (ref a)) : vprop'\nlet ind_ptr' (#a:Type0) (r:ref (ref a)) : vprop' =\n { hp = ind_ptr_sl r;\n t = a;\n sel = ind_ptr_sel r}", "val v_c (n: Ghost.erased nat) (#a: Type0) (r: t a) (c: normal (t_of (vptr r))) : GTot prop\nlet v_c\n (n: Ghost.erased nat)\n (#a: Type0)\n (r: t a)\n (c: normal (t_of (vptr r)))\n: GTot prop\n= (Ghost.reveal c.tail_fuel < Ghost.reveal n) == true", "val v_c (n: Ghost.erased nat) (#a: Type0) (r: t a) (c: normal (t_of (vptr r))) : GTot prop\nlet v_c\n (n: Ghost.erased nat)\n (#a: Type0)\n (r: t a)\n (c: normal (t_of (vptr r)))\n: GTot prop\n= (Ghost.reveal c.tail_fuel < Ghost.reveal n) == true", "val hs_next_rel:\n #hsz:pos -> #f:hash_fun_t #hsz ->\n n:nat ->\n hs:hashes #hsz {S.length hs = 2 * n} ->\n nhs:hashes #hsz {S.length nhs = n} ->\n GTot Type0\nlet hs_next_rel #hsz #f n hs nhs =\n forall (i:nat{i < n}).\n S.index nhs i ==\n padded_hash_fun #hsz f (S.index hs (2 * i)) (S.index hs (2 * i + 1))", "val fresh (#a: Type0) (r: ref a) (h0 h1: heap) : Type0\nlet fresh (#a:Type0) (r:ref a) (h0:heap) (h1:heap) : Type0\n = Heap.fresh r h0 h1", "val repeati_inductive':\n #a:Type\n -> n:nat\n -> pred:(i:nat{i <= n} -> a -> Type0)\n -> f:(i:nat{i < n} -> a -> a)\n -> x0:a\n -> Pure a\n (requires preserves #a #n f pred /\\ pred 0 x0)\n (ensures fun res -> pred n res /\\ res == repeati n f x0)\nlet repeati_inductive' #a n pred f x0 =\n let f'\n (i:nat{i < n})\n (x:a{pred i x /\\ x == repeati i f x0})\n : x':a{pred (i + 1) x' /\\ x' == repeati (i + 1) f x0}\n = f i x in\n repeat_gen n (fun i -> x:a{pred i x /\\ x == repeati i f x0}) f' x0", "val inv (p: vprop) : Type0\nlet inv (p:vprop) : Type0 = Mem.inv (hp_of p)", "val read (#a:Type0) (r:ref a) :STATE a (fun p h -> p (sel h r) h)\nlet read #_ r = read r", "val exists_n (r: ref nat) : vprop\nlet exists_n (r:ref nat) : vprop = exists* n. pts_to r n", "val read (#a:Type) (r:ref a) (#n:erased a) (#p:perm)\n : stt_ghost (erased a)\n (pts_to r #p n)\n (fun x -> pts_to r #p n ** pure (n == x))\nlet read = read'", "val read (#a:Type) (r:ref a) (#n:erased a) (#p:perm)\n : stt_ghost (erased a)\n (pts_to r #p n)\n (fun x -> pts_to r #p n ** pure (n == x))\nlet read = read'", "val v_c_dep\n (n: Ghost.erased nat)\n (#a: Type0)\n (r: t a)\n (nllist:\n (n': Ghost.erased nat -> r: t a {Ghost.reveal n' < Ghost.reveal n}\n -> Pure vprop (requires True) (ensures (fun y -> t_of y == list a))))\n (c: normal (t_of (vrefine (vptr r) (v_c n r))))\n : Tot vprop\nlet v_c_dep\n (n: Ghost.erased nat)\n (#a: Type0)\n (r: t a)\n (nllist: (n': Ghost.erased nat) -> (r: t a { Ghost.reveal n' < Ghost.reveal n }) -> Pure vprop (requires True) (ensures (fun y -> t_of y == list a)))\n (c: normal (t_of (vrefine (vptr r) (v_c n r))))\n: Tot vprop\n= nllist c.tail_fuel c.next", "val v_c_dep\n (n: Ghost.erased nat)\n (#a: Type0)\n (r: t a)\n (nllist:\n (n': Ghost.erased nat -> r: t a {Ghost.reveal n' < Ghost.reveal n}\n -> Pure vprop (requires True) (ensures (fun y -> t_of y == list a))))\n (c: normal (t_of (vrefine (vptr r) (v_c n r))))\n : Tot vprop\nlet v_c_dep\n (n: Ghost.erased nat)\n (#a: Type0)\n (r: t a)\n (nllist: (n': Ghost.erased nat) -> (r: t a { Ghost.reveal n' < Ghost.reveal n }) -> Pure vprop (requires True) (ensures (fun y -> t_of y == list a)))\n (c: normal (t_of (vrefine (vptr r) (v_c n r))))\n: Tot vprop\n= nllist c.tail_fuel c.next", "val contains (#a: Type0) (h: heap) (r: ref a) : GTot Type0\nlet contains (#a:Type0) (h:heap) (r:ref a) :GTot Type0\n = Heap.contains h r", "val nat_rel:preorder nat\nlet nat_rel : preorder nat = nat_rel'", "val nat_rel:preorder nat\nlet nat_rel : preorder nat = nat_rel'", "val forall_pred:\n #a: Type0 ->\n n: US.t ->\n arr: A.array a ->\n p: (a -> bool) ->\n r: R.ref US.t ->\n perm: perm ->\n s: Seq.seq a ->\n squash (Seq.length s == US.v n) ->\n b: bool ->\n US.t\n -> vprop\nlet forall_pred\n (#a:Type0)\n (n:US.t)\n (arr:A.array a)\n (p:a -> bool)\n (r:R.ref US.t)\n (perm:perm)\n (s:Seq.seq a)\n (_:squash (Seq.length s == US.v n))\n (b:bool)\n : US.t -> vprop\n = fun i ->\n A.pts_to arr perm s\n `star`\n R.pts_to r full_perm i\n `star`\n pure (forall_pure_inv n p s () i)\n `star`\n pure (forall_pure_inv_b n p s () i b)", "val inv_0 (h: heap) (fp: fp) : Type0\nlet inv_0 (h:heap) (fp:fp) :Type0 =\n h `contains_well_typed_refs` fp /\\ length fp = 1", "val labs0 (#i: _) (n: int) : GTD int i\nlet labs0 #i (n:int) : GTD int i =\n if n < 0\n then -n\n else n", "val create (a:Type0) (n:nat)\n :ST (array a n) (requires (fun _ -> True))\n (ensures (fun h0 arr h1 -> fresh_arr arr h0 h1 /\\ //it's fresh\n\t\t modifies Set.empty h0 h1 /\\ //no existing refs are changed\n\t\t\t\t\t is_full_array arr))\nlet create (a:Type0) (n:nat)\n :ST (array a n) (requires (fun _ -> True))\n (ensures (fun h0 arr h1 -> fresh_arr arr h0 h1 /\\ //it's fresh\n\t\t modifies Set.empty h0 h1 /\\ //no existing refs are changed\n\t\t\t\t\t is_full_array arr)) //and has the full view of the underlying sequence\n = let arr = A #a #n #n (alloc ((Seq.create n None), Mutable)) 0 in\n gst_witness (mutable_pred arr);\n arr", "val valid_addr_mem (r: reg) (n: int) (s: state) : prop0\nlet valid_addr_mem (r:reg) (n:int) (s:state) : prop0 = valid_mem ({ address=r; offset=n }) s", "val fib0 (n: nat) : nat\nlet rec fib0 (n:nat) : nat =\n if n < 2 then n\n else fib0 (n-1) + fib0 (n-2)", "val u8_pair_pred (p: u8_pair) (v: u8_pair_repr) : vprop\nlet u8_pair_pred (p:u8_pair) (v:u8_pair_repr) : vprop = \n R.pts_to p.a (fst v) **\n R.pts_to p.b (snd v)", "val labs0 (#i: _) (n: int) : Gtd int i\nlet labs0 #i (n:int) : Gtd int i =\n if n < 0\n then -n\n else n", "val lock_inv_predicate: r: R.ref int -> r1: GR.ref int -> r2: GR.ref int -> (int & int) -> vprop\nlet lock_inv_predicate (r:R.ref int) (r1 r2:GR.ref int)\n : int & int -> vprop\n = fun w ->\n GR.pts_to r1 half_perm (fst w)\n `star`\n GR.pts_to r2 half_perm (snd w)\n `star`\n R.pts_to r full_perm (fst w + snd w)", "val modifies1 (l: loc) (h0 h1: state) : Type0\nlet modifies1 (l:loc) (h0 h1 : state) : Type0 =\n forall y. y <> l ==> Map.sel h0 y == Map.sel h1 y", "val write (#a: Type0) (n: nat) (x: a)\n : LV unit\n (fun m0 -> m0.m `M.contains` n /\\ dfst (m0.m `M.sel` n) == a)\n (fun m0 _ m1 -> m1.next == m0.next /\\ m1.m == Map.upd m0.m n (| a, x |))\nlet write (#a:Type0) (n:nat) (x:a)\n : LV unit (fun m0 -> m0.m `M.contains` n /\\\n dfst (m0.m `M.sel` n) == a)\n (fun m0 _ m1 ->\n m1.next == m0.next /\\\n m1.m == Map.upd m0.m n (| a, x |))\n= LVARS?.reflect (fun m -> (), { m with m = Map.upd m.m n (| a, x |) })", "val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)\nlet cancel_mul_mod (a:int) (n:pos) =\n small_mod 0 n;\n lemma_mod_plus 0 a n", "val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)\nlet cancel_mul_mod (a:int) (n:pos) =\n small_mod 0 n;\n lemma_mod_plus 0 a n", "val recall_contains (#a:Type0) (#n:nat) (arr:t a n)\n :ST unit (requires (fun _ -> True))\n (ensures (fun h0 _ h1 -> h0 == h1 /\\ h0 `contains_array` arr))\nlet recall_contains (#a:Type0) (#n:nat) (arr:t a n)\n :ST unit (requires (fun _ -> True))\n (ensures (fun h0 _ h1 -> h0 == h1 /\\ h0 `contains_array` arr))\n = let A s_ref _ = arr in\n ST.recall s_ref", "val recursive_tac (n: nat) : Tac unit\nlet rec recursive_tac (n:nat) : Tac unit =\n if n = 0\n then ()\n else recursive_tac (n - 1)", "val lemma_of_uint_zero (n: nat) : Lemma (ensures of_uint_ n 0 == zero)\nlet lemma_of_uint_zero (n:nat) : Lemma\n (ensures of_uint_ n 0 == zero)\n =\n lemma_bitwise_all ();\n lemma_equal (of_uint_ n 0) zero", "val repeati_inductive:\n #a:Type\n -> n:nat\n -> pred:(i:nat{i <= n} -> a -> Type)\n -> f:repeatable #a #n pred\n -> x0:a{pred 0 x0}\n -> res:a{pred n res}\nlet repeati_inductive #a n pred f x0 =\n repeat_range_inductive #a 0 n pred f x0", "val extend (r:rid) (n:int) (c:int)\n: Pure rid (requires True) (extend_post r n c (rid_freeable r))\nlet extend r n c =\n elift1 (fun r ->\n let freeable = rid_freeable (hide r) in\n (c, n, freeable)::r\n ) r", "val sel (#a: Type0) (h: heap) (r: ref a) : GTot a\nlet sel (#a:Type0) (h:heap) (r:ref a) : GTot a\n = Heap.sel h r", "val consistent (h0:heap) (h1:heap) : GTot Type0\nlet consistent (h0:heap) (h1:heap) : GTot Type0 =\n forall n x y . (snd h0 n == Some x /\\ snd h1 n == Some y) ==> dfst x == dfst y", "val MerkleTree.Spec.rpmt = n: Prims.nat -> i: Prims.nat{i <= Prims.pow2 n} -> Type0\nlet rpmt (#hsz:pos) (#f:hash_fun_t) (n:nat) (i:nat{i <= pow2 n}) =\n mt:merkle_tree #hsz n {\n raw_hashes #_ #f (S.slice mt 0 i) /\\\n pad_hashes #_ #f (S.slice mt i (S.length mt)) }", "val nllist_eq_not_null (a: Type0) (n: Ghost.erased nat) (r: t a)\n : Lemma (requires (is_null r == false))\n (ensures\n (nllist a n r ==\n (((vptr r) `vrefine` (v_c n r)) `vdep` (v_c_dep n r (nllist a)))\n `vrewrite`\n (v_c_l_rewrite n r (nllist a))))\nlet nllist_eq_not_null\n (a: Type0)\n (n: Ghost.erased nat)\n (r: t a)\n: Lemma\n (requires (is_null r == false))\n (ensures (\n nllist a n r == ((vptr r `vrefine` v_c n r) `vdep` v_c_dep n r (nllist a)) `vrewrite` v_c_l_rewrite n r (nllist a)\n ))\n= assert_norm (nllist a n r ==\n begin if is_null r\n then emp `vrewrite` v_null_rewrite a\n else ((vptr r `vrefine` v_c n r) `vdep` v_c_dep n r (nllist a)) `vrewrite` v_c_l_rewrite n r (nllist a)\n end\n )", "val nllist_eq_not_null (a: Type0) (n: Ghost.erased nat) (r: t a)\n : Lemma (requires (is_null r == false))\n (ensures\n (nllist a n r ==\n (((vptr r) `vrefine` (v_c n r)) `vdep` (v_c_dep n r (nllist a)))\n `vrewrite`\n (v_c_l_rewrite n r (nllist a))))\nlet nllist_eq_not_null\n (a: Type0)\n (n: Ghost.erased nat)\n (r: t a)\n: Lemma\n (requires (is_null r == false))\n (ensures (\n nllist a n r == ((vptr r `vrefine` v_c n r) `vdep` v_c_dep n r (nllist a)) `vrewrite` v_c_l_rewrite n r (nllist a)\n ))\n= assert_norm (nllist a n r ==\n begin if is_null r\n then emp `vrewrite` v_null_rewrite a\n else ((vptr r `vrefine` v_c n r) `vdep` v_c_dep n r (nllist a)) `vrewrite` v_c_l_rewrite n r (nllist a)\n end\n )", "val read : #a:Type ->\n #r:preorder a ->\n\t m:mref a r ->\n\t MRefST a (fun _ -> True)\n (fun h0 x h1 -> h0 == h1 /\\\n\t\t contains m h1 /\\\n\t\t\t\t sel h1 m == x)\nlet read #a #r m =\n let h = ist_get () in\n ist_recall (contains m); //recalling that the current heap must contain the given reference\n sel h m", "val pre0 (x: nat) : prop\nlet pre0 (x:nat) : prop = x > 2", "val frozen_bit (#a:Type0) (#n:nat) (arr:t a n) (h:heap) : Type0\nlet frozen_bit (#a:Type0) (#n:nat) (arr:t a n) (h:heap) :Type0\n = let A s_ref _ = arr in\n snd (sel h s_ref) == Frozen", "val init_rsp (h:vale_stack) : (n:nat64{n >= 4096})\nlet init_rsp h = h.BS.initial_rsp", "val create (#a:Type0) (n:nat) (init:a)\n : ST (array a)\n (requires (fun h -> True))\n (ensures (fun h0 x h1 -> x `unused_in` h0 /\\\n contains h1 x /\\\n modifies Set.empty h0 h1 /\\\n sel h1 x == Seq.create n init))\nlet create #a n init = ST.alloc (Seq.create n init)", "val vptr0_refine (#a: Type0) (r: ref a) (s: Seq.lseq a (A.length r)) : Tot prop\nlet vptr0_refine\n (#a: Type0)\n (r: ref a)\n (s: Seq.lseq a (A.length r))\n: Tot prop\n= Seq.length s == 1" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.rid_ctr_pred" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Array.fst", "name": "LowParse.Spec.Array.array_pred" }, { "project_name": "FStar", "file_name": "Protocol.fst", "name": "Protocol.counter_pred" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.heap_ctr_valid" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.heap_ctr_valid" }, { "project_name": "steel", "file_name": "Steel.ST.SpinLock.fst", "name": "Steel.ST.SpinLock.lockinv_predicate" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.test_abs0'" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.lemma_is_wf_ctr_and_tip_intro" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.read" }, { "project_name": "FStar", "file_name": "MonotonicArray.fst", "name": "MonotonicArray.initialized'" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.mk_mem" }, { "project_name": "steel", "file_name": "Steel.Primitive.ForkJoin.fst", "name": "Steel.Primitive.ForkJoin.lock_inv_pred" }, { "project_name": "steel", "file_name": "Steel.ST.CancellableSpinLock.fst", "name": "Steel.ST.CancellableSpinLock.lock_inv_pred" }, { "project_name": "FStar", "file_name": "Registers.List.fst", "name": "Registers.List.identity_map" }, { "project_name": "FStar", "file_name": "Protocol.fst", "name": "Protocol.modifies_r" }, { "project_name": "FStar", "file_name": "MonotonicArray.fst", "name": "MonotonicArray.contains_array" }, { "project_name": "zeta", "file_name": "Zeta.Steel.ThreadLogMap.fst", "name": "Zeta.Steel.ThreadLogMap.snapshot_pred" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.contains" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.test_abs" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.get_rid_ctr" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.ctr_validity" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.ctr_validity" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.tip_top" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.test_abs0" }, { "project_name": "FStar", "file_name": "MonotonicArray.fst", "name": "MonotonicArray.initialized" }, { "project_name": "steel", "file_name": "Pulse.C.Typenat.fsti", "name": "Pulse.C.Typenat.nat_t_of_nat" }, { "project_name": "steel", "file_name": "Steel.C.Typenat.fsti", "name": "Steel.C.Typenat.nat_t_of_nat" }, { "project_name": "FStar", "file_name": "ID4.fst", "name": "ID4.count" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.count" }, { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.count" }, { "project_name": "FStar", "file_name": "IMSTsub.fst", "name": "IMSTsub.witnessed" }, { "project_name": "FStar", "file_name": "IMST.fst", "name": "IMST.witnessed" }, { "project_name": "FStar", "file_name": "FStar.UInt.fsti", "name": "FStar.UInt.size" }, { "project_name": "FStar", "file_name": "SfBasic.fst", "name": "SfBasic.pred" }, { "project_name": "FStar", "file_name": "RBTreeIntrinsic.fst", "name": "RBTreeIntrinsic.hiddenTree_mem" }, { "project_name": "FStar", "file_name": "FStar.Int.fsti", "name": "FStar.Int.size" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Array.fst", "name": "LowParse.Spec.Array.vlarray_pred" }, { "project_name": "FStar", "file_name": "MonotonicArray.fst", "name": "MonotonicArray.is_mutable" }, { "project_name": "steel", "file_name": "Steel.Heap.fst", "name": "Steel.Heap.full_heap_pred" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fst", "name": "PulseCore.Heap.full_heap_pred" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.fsti", "name": "Benton2004.RHL.gconst" }, { "project_name": "FStar", "file_name": "ID2.fst", "name": "ID2.count" }, { "project_name": "steel", "file_name": "Steel.Stepper.fst", "name": "Steel.Stepper.v" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fst", "name": "FStar.Monotonic.HyperStack.map_invariant" }, { "project_name": "FStar", "file_name": "MonotonicArray.fst", "name": "MonotonicArray.seq_pre" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperHeap.fst", "name": "FStar.Monotonic.HyperHeap.rid_length" }, { "project_name": "steel", "file_name": "CustomSyntax.fst", "name": "CustomSyntax.folded_pts_to" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.labs0" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.get_right" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Stack_i.fst", "name": "Vale.PPC64LE.Stack_i.init_r1" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.mref" }, { "project_name": "hacl-star", "file_name": "Lib.LoopCombinators.fst", "name": "Lib.LoopCombinators.repeat_gen_inductive" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.read" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.contains_pred" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.alloc_ref" }, { "project_name": "steel", "file_name": "Selectors.PtrLList.fst", "name": "Selectors.PtrLList.ind_ptr'" }, { "project_name": "steel", "file_name": "Selectors.LList3.fst", "name": "Selectors.LList3.v_c" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.v_c" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Spec.fst", "name": "MerkleTree.Spec.hs_next_rel" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.fresh" }, { "project_name": "hacl-star", "file_name": "Lib.LoopCombinators.fst", "name": "Lib.LoopCombinators.repeati_inductive'" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.inv" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.read" }, { "project_name": "steel", "file_name": "DependentTuples.fst", "name": "DependentTuples.exists_n" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.read" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.read" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.v_c_dep" }, { "project_name": "steel", "file_name": "Selectors.LList3.fst", "name": "Selectors.LList3.v_c_dep" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.contains" }, { "project_name": "FStar", "file_name": "IMSTsub.fst", "name": "IMSTsub.nat_rel" }, { "project_name": "FStar", "file_name": "IMST.fst", "name": "IMST.nat_rel" }, { "project_name": "steel", "file_name": "Steel.ST.Array.Util.fst", "name": "Steel.ST.Array.Util.forall_pred" }, { "project_name": "FStar", "file_name": "ProgramEquivalence.fst", "name": "ProgramEquivalence.inv_0" }, { "project_name": "FStar", "file_name": "GT.fst", "name": "GT.labs0" }, { "project_name": "FStar", "file_name": "MonotonicArray.fst", "name": "MonotonicArray.create" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.valid_addr_mem" }, { "project_name": "steel", "file_name": "Bug45.fst", "name": "Bug45.fib0" }, { "project_name": "steel", "file_name": "RecordWithRefs.fst", "name": "RecordWithRefs.u8_pair_pred" }, { "project_name": "FStar", "file_name": "GTWP.fst", "name": "GTWP.labs0" }, { "project_name": "steel", "file_name": "OWGCounter.ST.fst", "name": "OWGCounter.ST.lock_inv_predicate" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.modifies1" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.write" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.cancel_mul_mod" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Lemmas.Int.fst", "name": "Vale.Math.Lemmas.Int.cancel_mul_mod" }, { "project_name": "FStar", "file_name": "MonotonicArray.fst", "name": "MonotonicArray.recall_contains" }, { "project_name": "FStar", "file_name": "Intro.fst", "name": "Intro.recursive_tac" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Bits.fst", "name": "Vale.Math.Poly2.Bits.lemma_of_uint_zero" }, { "project_name": "hacl-star", "file_name": "Lib.LoopCombinators.fst", "name": "Lib.LoopCombinators.repeati_inductive" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperHeap.fst", "name": "FStar.Monotonic.HyperHeap.extend" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.sel" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.consistent" }, { "project_name": "merkle-tree", "file_name": "MerkleTree.Spec.fst", "name": "MerkleTree.Spec.rpmt" }, { "project_name": "steel", "file_name": "Selectors.LList2.fst", "name": "Selectors.LList2.nllist_eq_not_null" }, { "project_name": "steel", "file_name": "Selectors.LList3.fst", "name": "Selectors.LList3.nllist_eq_not_null" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.read" }, { "project_name": "steel", "file_name": "UnfoldPure.fst", "name": "UnfoldPure.pre0" }, { "project_name": "FStar", "file_name": "MonotonicArray.fst", "name": "MonotonicArray.frozen_bit" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Stack_i.fst", "name": "Vale.X64.Stack_i.init_rsp" }, { "project_name": "FStar", "file_name": "FStar.Array.fst", "name": "FStar.Array.create" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.vptr0_refine" } ], "selected_premises": [ "FStar.Monotonic.HyperStack.is_heap_color", "FStar.Monotonic.HyperStack.is_in", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "FStar.Monotonic.HyperStack.is_stack_region", "FStar.Monotonic.HyperHeap.modifies_just", "FStar.Monotonic.HyperStack.map_invariant_predicate", "FStar.Monotonic.HyperHeap.disjoint", "FStar.Monotonic.HyperHeap.modifies", "FStar.Monotonic.HyperStack.is_above", "FStar.Monotonic.HyperStack.tip_top_predicate", "FStar.Pervasives.reveal_opaque", "FStar.Monotonic.HyperHeap.rid_last_component", "FStar.Monotonic.HyperStack.is_eternal_region_hs", "FStar.Pervasives.dfst", "FStar.Monotonic.HyperStack.downward_closed_predicate", "FStar.Monotonic.HyperHeap.modifies_one", "FStar.Monotonic.HyperHeap.equal_on", "FStar.Pervasives.dsnd", "FStar.Monotonic.HyperStack.is_eternal_region", "FStar.Map.disjoint_dom", "FStar.Monotonic.Heap.mref", "FStar.Map.has_dom", "Prims.min", "FStar.Monotonic.HyperStack.is_below", "FStar.Monotonic.HyperStack.is_strictly_above", "FStar.Monotonic.HyperStack.is_just_below", "FStar.Pervasives.id", "FStar.Monotonic.HyperHeap.disjoint_regions", "FStar.Monotonic.Heap.equal_dom", "FStar.Preorder.preorder_rel", "FStar.Monotonic.Heap.fresh", "FStar.Monotonic.HyperStack.is_strictly_below", "FStar.Ghost.tot_to_gtot", "FStar.Pervasives.coerce_eq", "FStar.Ghost.return", "Prims.l_True", "FStar.Set.subset", "Prims.l_False", "FStar.Monotonic.Heap.only", "Prims.abs", "FStar.Monotonic.Heap.compare_addrs", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.all_post_h'", "FStar.Map.const_on", "FStar.Monotonic.Heap.modifies_t", "FStar.Pervasives.all_post_h", "FStar.Monotonic.Heap.set", "FStar.Monotonic.Heap.modifies", "FStar.Set.as_set'", "FStar.Preorder.reflexive", "FStar.Pervasives.all_close_wp", "FStar.Pervasives.all_wp_h", "FStar.Monotonic.HyperHeap.extend_post", "FStar.Set.as_set", "FStar.Pervasives.st_stronger", "FStar.Pervasives.st_post_h", "FStar.Preorder.stable", "FStar.Pervasives.all_stronger", "Prims.returnM", "FStar.Pervasives.st_close_wp", "FStar.Monotonic.Heap.only_t", "FStar.Pervasives.all_ite_wp", "FStar.Pervasives.pure_close_wp", "FStar.Pervasives.all_trivial", "FStar.Set.add", "FStar.Pervasives.all_return", "FStar.Preorder.transitive", "FStar.Pervasives.all_if_then_else", "Prims.__cache_version_number__", "Prims.auto_squash", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.pure_null_wp", "FStar.Ghost.op_let_At", "Prims.pure_wp'", "FStar.Pervasives.ex_pre", "FStar.Set.remove", "FStar.Pervasives.st_pre_h", "FStar.TSet.subset", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.st_if_then_else", "FStar.Ghost.push_refinement", "FStar.Pervasives.ex_close_wp", "Prims.pure_wp_monotonic", "FStar.Pervasives.st_ite_wp", "FStar.Ghost.bind", "FStar.Ghost.elift2_pq", "FStar.Ghost.elift1", "FStar.Pervasives.st_trivial", "Prims.subtype_of", "Prims.pure_trivial", "FStar.Ghost.elift1_pq", "FStar.Monotonic.Heap.op_Plus_Plus_Hat", "FStar.Pervasives.pure_ite_wp", "Prims.pure_post'", "FStar.Set.disjoint", "Prims.purewp_id", "FStar.Ghost.elift2", "FStar.Pervasives.st_wp_h", "FStar.TSet.as_set'" ], "source_upto_this": "(*\n Copyright 2008-2014 Aseem Rastogi, and Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.Monotonic.HyperStack\n\nopen FStar.Preorder\nmodule Map = FStar.Map\n\ninclude FStar.Monotonic.HyperHeap\n\n\n(****** Some predicates ******)\n\nunfold let is_in (r:rid) (h:hmap) = h `Map.contains` r\n\nlet is_stack_region r = color r > 0\nlet is_heap_color c = c <= 0\n\n[@@(deprecated \"FStar.HyperStack.ST.is_eternal_region\")]\nlet is_eternal_region r = is_heap_color (color r) && not (rid_freeable r)\n\nunfold let is_eternal_region_hs r = is_heap_color (color r) && not (rid_freeable r)\n\ntype sid = r:rid{is_stack_region r} //stack region ids\n\n(*\n * AR: marking these unfolds, else I think there are pattern firing issues depending on which one we use\n *)\nunfold let is_above r1 r2 = r1 `includes` r2\nunfold let is_just_below r1 r2 = r1 `extends` r2\nunfold let is_below r1 r2 = r2 `is_above` r1\nlet is_strictly_below r1 r2 = r1 `is_below` r2 && r1 <> r2\nlet is_strictly_above r1 r2 = r1 `is_above` r2 && r1 <> r2\n\n\n[@@\"opaque_to_smt\"]\nunfold private let map_invariant_predicate (m:hmap) :Type0 =\n forall r. Map.contains m r ==>\n (forall s. includes s r ==> Map.contains m s)\n\n[@@\"opaque_to_smt\"]\nunfold private let downward_closed_predicate (h:hmap) :Type0 =\n forall (r:rid). r `is_in` h //for any region in the memory\n ==> (r=root //either is the root\n \\/ (forall (s:rid). (r `is_above` s //or, any region beneath it\n /\\ s `is_in` h) //that is also in the memory\n ==> ((is_stack_region r = is_stack_region s) /\\ //must be of the same flavor as itself\n ((is_heap_color (color r) /\\ rid_freeable r) ==> s == r)))) //and if r is a freeable heap region, s can only be r (no regions strictly below r)\n\n[@@\"opaque_to_smt\"]\nunfold private let tip_top_predicate (tip:rid) (h:hmap) :Type0 =\n forall (r:sid). r `is_in` h <==> r `is_above` tip\n\n[@@\"opaque_to_smt\"]", "sketch": [ "Step 1: The `rid_ctr_pred_predicate` is a predicate that checks a property of the heap map `h` and an integer `n`.\nStep 2: The predicate ensures that for any region identifier `r` in the heap map `h`, the color of `r` is less than or equal to `n`.", "Step 1: The `rid_ctr_pred_predicate` is a predicate that relates a memory map `h` with an integer `n`. This predicate will ensure that the number of regions in the memory map `h` is exactly `n`.\nStep 2: To implement this, we will define a function that counts the number of regions in the memory map `h` and checks if this count is equal to `n`.", "Step 1: The definition `rid_ctr_pred_predicate` is about specifying a predicate that relates a memory map `h` and an integer `n`. This predicate will ensure that the number of regions in the memory map `h` is equal to `n`.\nStep 2: To implement this, we will define a function that counts the number of regions in the memory map `h` and checks if this count is equal to `n`.", "Step 1: The `rid_ctr_pred_predicate` is a predicate that relates a memory map (`h`) and an integer (`n`). The predicate should ensure that for each region identifier (`rid`) in the memory map, there exists a counter that matches the given integer `n`.\nStep 2: To implement this, we will define a type that ensures for every region identifier in the memory map, the counter associated with it is equal to `n`.", "Step 1: The `rid_ctr_pred_predicate` is a predicate that takes a memory map `h` and an integer `n` as arguments. It ensures that the number of regions in the memory map `h` is exactly `n`.\nStep 2: To implement this, we will define a predicate that counts the number of regions in the memory map `h` and checks if this count is equal to `n`.", "Step 1: The definition is about creating a predicate that checks if the number of regions in the heap map `h` is equal to the given integer `n`.\nStep 2: The implementation will involve counting the number of regions in the heap map `h` and comparing it to `n`.", "Step 1: The definition `rid_ctr_pred_predicate` is about specifying a predicate that relates a memory map `h` and an integer `n` to ensure certain properties about the regions in the memory map.\nStep 2: The implementation will define a predicate that checks if the number of regions in the memory map `h` that satisfy a certain condition is equal to `n`. This condition will be specified as a separate predicate function.", "Step 1: The `rid_ctr_pred_predicate` is a predicate that relates a memory map `h` to an integer `n`. This predicate will ensure that the number of regions in the memory map `h` is exactly `n`.\nStep 2: To implement this, we will define a predicate that counts the number of regions in `h` and checks if this count is equal to `n`.", "Step 1: The definition is about creating a predicate that checks if the number of regions in the given heap map `h` is equal to the integer `n`.\nStep 2: The implementation will involve counting the number of regions in the heap map `h` and comparing it to `n`.", "Step 1: The definition `rid_ctr_pred_predicate` is about defining a predicate that relates a memory map `h` to an integer `n`. This integer `n` could represent a counter or some other numerical property associated with the regions in the memory map `h`.\nStep 2: The implementation involves specifying a condition that must hold true for the memory map `h` and the integer `n`. This condition will be expressed as a type `Type0`, which is a type of propositions in F*." ], "generated_solution": [ "let rid_ctr_pred_predicate (h: hmap) (n: int) : Type0 =\n forall (r: rid). r `is_in` h ==> color r <= n", "let rid_ctr_pred_predicate (h: hmap) (n: int) : Type0 =\n Map.length h == n", "let rid_ctr_pred_predicate (h: hmap) (n: int) : Type0 =\n Map.size h == n", "let rid_ctr_pred_predicate (h: hmap) (n: int) : Type0 =\n forall (r: rid). r `is_in` h ==> (Map.sel h r == n)", "let rid_ctr_pred_predicate (h: hmap) (n: int) : Type0 =\n Map.length h == n", "let rid_ctr_pred_predicate (h: hmap) (n: int) : Type0 =\n Map.size h == n", "let rid_ctr_pred_predicate (h: hmap) (n: int) : Type0 =\n exists (p: rid -> bool). \n (forall r. Map.contains h r ==> p r) /\\\n (Map.cardinal (Map.filter p h) == n)", "let rid_ctr_pred_predicate (h: hmap) (n: int) : Type0 =\n Map.cardinal h == n", "let rid_ctr_pred_predicate (h: hmap) (n: int) : Type0 =\n Map.length h == n", "let rid_ctr_pred_predicate (h: hmap) (n: int) : Type0 =\n forall (r: rid). r `is_in` h ==> (color r = n)" ] }, { "file_name": "FStar.Tactics.CanonCommMonoid.fst", "name": "FStar.Tactics.CanonCommMonoid.xsdenote", "opens_and_abbrevs": [ { "open": "FStar.Tactics.CanonCommSwaps" }, { "open": "FStar.Classical" }, { "open": "FStar.Tactics.V2" }, { "open": "FStar.Reflection.V2" }, { "open": "FStar.List" }, { "open": "FStar.Algebra.CommMonoid" }, { "open": "FStar.Tactics" }, { "open": "FStar.Tactics" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a", "source_definition": "let rec xsdenote (#a #b:Type) (m:cm a) (vm:vmap a b) (xs:list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | [x] -> select x vm\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "source_range": { "start_line": 75, "start_col": 0, "end_line": 79, "end_col": 58 }, "interleaved": false, "definition": "fun m vm xs ->\n (match xs with\n | Prims.Nil #_ -> CM?.unit m\n | Prims.Cons #_ x (Prims.Nil #_) -> FStar.Tactics.CanonCommMonoid.select x vm\n | Prims.Cons #_ x xs' ->\n CM?.mult m\n (FStar.Tactics.CanonCommMonoid.select x vm)\n (FStar.Tactics.CanonCommMonoid.xsdenote m vm xs'))\n <:\n a", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Algebra.CommMonoid.cm", "FStar.Tactics.CanonCommMonoid.vmap", "Prims.list", "FStar.Tactics.CanonCommMonoid.var", "FStar.Algebra.CommMonoid.__proj__CM__item__unit", "FStar.Tactics.CanonCommMonoid.select", "FStar.Algebra.CommMonoid.__proj__CM__item__mult", "FStar.Tactics.CanonCommMonoid.xsdenote" ], "proof_features": [ "recursion" ], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "\n m: FStar.Algebra.CommMonoid.cm a ->\n vm: FStar.Tactics.CanonCommMonoid.vmap a b ->\n xs: Prims.list FStar.Tactics.CanonCommMonoid.var\n -> a", "prompt": "let rec xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a =\n ", "expected_response": "match xs with\n| [] -> CM?.unit m\n| [x] -> select x vm\n| x :: xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "source": { "project_name": "FStar", "file_name": "ulib/FStar.Tactics.CanonCommMonoid.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.Tactics.CanonCommMonoid.fst", "checked_file": "dataset/FStar.Tactics.CanonCommMonoid.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Tactics.Util.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Tactics.CanonCommSwaps.fst.checked", "dataset/FStar.Reflection.V2.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Order.fst.checked", "dataset/FStar.List.Tot.Properties.fst.checked", "dataset/FStar.List.Tot.Base.fst.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.List.fst.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Algebra.CommMonoid.fst.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "let dump m = if debugging () then dump m", "let var : eqtype = nat", "exp", "Unit", "Unit", "Unit", "Var", "Var", "Var", "Mult", "Mult", "Mult", "let rec exp_to_string (e:exp) : string =\n match e with\n | Unit -> \"Unit\"\n | Var x -> \"Var \" ^ string_of_int (x <: var)\n | Mult e1 e2 -> \"Mult (\" ^ exp_to_string e1\n ^ \") (\" ^ exp_to_string e2 ^ \")\"", "let vmap (a b:Type) = list (var * (a*b)) * (a * b)", "let const (#a #b:Type) (xa:a) (xb:b) : vmap a b = [], (xa,xb)", "let select (#a #b:Type) (x:var) (vm:vmap a b) : Tot a =\n match assoc #var #(a * b) x (fst vm) with\n | Some (a, _) -> a\n | _ -> fst (snd vm)", "let select_extra (#a #b:Type) (x:var) (vm:vmap a b) : Tot b =\n match assoc #var #(a * b) x (fst vm) with\n | Some (_, b) -> b\n | _ -> snd (snd vm)", "let update (#a #b:Type) (x:var) (xa:a) (xb:b) (vm:vmap a b) : vmap a b =\n (x, (xa, xb))::fst vm, snd vm", "let rec mdenote (#a #b:Type) (m:cm a) (vm:vmap a b) (e:exp) : Tot a =\n match e with\n | Unit -> CM?.unit m\n | Var x -> select x vm\n | Mult e1 e2 -> CM?.mult m (mdenote m vm e1) (mdenote m vm e2)" ], "closest": [ "val xsdenote (#a: Type) (m: cm a) (am: amap a) (xs: list atom) : a\nlet rec xsdenote (#a:Type) (m:cm a) (am:amap a) (xs:list atom) : a =\n match xs with\n | [] -> CM?.unit m\n | [x] -> select x am\n | x::xs' -> CM?.mult m (select x am) (xsdenote m am xs')", "val xsdenote (#a: Type) (eq: equiv a) (m: cm a eq) (am: amap a) (xs: list atom) : a\nlet rec xsdenote (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a) (xs:list atom) : a =\n match xs with\n | [] -> CM?.unit m\n | [x] -> select x am\n | x::xs' -> CM?.mult m (select x am) (xsdenote eq m am xs')", "val xsdenote (#a: Type) (eq: CE.equiv a) (m: CE.cm a eq) (am: amap a) (xs: list atom) : a\nlet xsdenote (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (xs:list atom) : a =\n let open FStar.Algebra.CommMonoid.Equiv in\n xsdenote_gen (CM?.unit m) (CM?.mult m) am xs", "val xsdenote_gen (#a: Type) (unit: a) (mult: (a -> a -> a)) (am: amap a) (xs: list atom) : a\nlet rec xsdenote_gen (#a:Type) (unit:a) (mult:a -> a -> a) (am:amap a) (xs:list atom) : a =\n match xs with\n | [] -> unit\n | [x] -> select x am\n | x::xs' -> mult (select x am) (xsdenote_gen unit mult am xs')", "val lemma_xsdenote_aux\n (#a: Type)\n (eq: CE.equiv a)\n (m: CE.cm a eq)\n (am: amap a)\n (hd: atom)\n (tl: list atom)\n : Lemma\n (CE.EQ?.eq eq (xsdenote eq m am (hd :: tl)) (CE.CM?.mult m (select hd am) (xsdenote eq m am tl))\n )\nlet lemma_xsdenote_aux (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (hd:atom) (tl:list atom)\n : Lemma (xsdenote eq m am (hd::tl) `CE.EQ?.eq eq`\n (CE.CM?.mult m (select hd am) (xsdenote eq m am tl)))\n = let open FStar.Algebra.CommMonoid.Equiv in\n match tl with\n | [] ->\n assert (xsdenote eq m am (hd::tl) == select hd am);\n CM?.identity m (select hd am);\n EQ?.symmetry eq (CM?.unit m `CM?.mult m` select hd am) (select hd am);\n CM?.commutativity m (CM?.unit m) (select hd am);\n EQ?.transitivity eq\n (xsdenote eq m am (hd::tl))\n (CM?.unit m `CM?.mult m` select hd am)\n (CM?.mult m (select hd am) (xsdenote eq m am tl))\n | _ -> EQ?.reflexivity eq (xsdenote eq m am (hd::tl))", "val mdenote (#a: Type) (m: cm a) (am: amap a) (e: exp) : a\nlet rec mdenote (#a:Type) (m:cm a) (am:amap a) (e:exp) : a =\n match e with\n | Unit -> CM?.unit m\n | Atom x -> select x am\n | Mult e1 e2 -> CM?.mult m (mdenote m am e1) (mdenote m am e2)", "val mldenote (#a: Type) (m: monoid a) (xs: list a) : a\nlet rec mldenote (#a:Type) (m:monoid a) (xs:list a) : a =\n match xs with\n | [] -> Monoid?.unit m\n | [x] -> x\n | x::xs' -> Monoid?.mult m x (mldenote m xs')", "val mdenote (#a: Type u#aa) (eq: equiv a) (m: cm a eq) (am: amap a) (e: exp) : a\nlet rec mdenote (#a:Type u#aa) (eq:equiv a) (m:cm a eq) (am:amap a) (e:exp) : a =\n match e with\n | Unit -> CM?.unit m\n | Atom x -> select x am\n | Mult e1 e2 -> CM?.mult m (mdenote eq m am e1) (mdenote eq m am e2)", "val cons (#a: Type) (x: a) (s: seq a) : Tot (seq a)\nlet cons (#a:Type) (x:a) (s:seq a) : Tot (seq a) = append (create 1 x) s", "val mdenote (#a: Type u#aa) (eq: CE.equiv a) (m: CE.cm a eq) (am: amap a) (e: exp) : a\nlet mdenote (#a:Type u#aa) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (e:exp) : a =\n let open FStar.Algebra.CommMonoid.Equiv in\n mdenote_gen (CM?.unit m) (CM?.mult m) am e", "val sort_correct_aux (#a: Type) (m: cm a) (am: amap a) (xs: list atom)\n : Lemma (xsdenote m am xs == xsdenote m am (sort xs))\nlet sort_correct_aux (#a:Type) (m:cm a) (am:amap a) (xs:list atom) :\n Lemma (xsdenote m am xs == xsdenote m am (sort xs)) =\n permute_via_swaps_correct sort (fun #a am -> sort_via_swaps am) m am xs", "val sel (#a #b: _) (m: map' a b) (x: a) : Tot (option (b x))\nlet sel #a #b (m:map' a b) (x:a)\n : Tot (option (b x))\n = m x", "val mem (#a: eqtype) (x: a) (xs: Seq.seq a) : Tot bool\nlet mem (#a:eqtype) (x:a) (xs:Seq.seq a) : Tot bool =\n Some? (Seq.seq_find (fun y -> y = x) xs)", "val flatten_correct_aux (#a: Type) (eq: equiv a) (m: cm a eq) (am: amap a) (xs1 xs2: list atom)\n : Lemma\n (EQ?.eq eq\n (xsdenote eq m am (xs1 @ xs2))\n (CM?.mult m (xsdenote eq m am xs1) (xsdenote eq m am xs2)))\nlet rec flatten_correct_aux (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a) (xs1 xs2:list atom)\n : Lemma (xsdenote eq m am (xs1 @ xs2) `EQ?.eq eq` CM?.mult m (xsdenote eq m am xs1)\n (xsdenote eq m am xs2)) =\n match xs1 with\n | [] ->\n CM?.identity m (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.unit m) (xsdenote eq m am xs2)) (xsdenote eq m am xs2)\n | [x] -> (\n if (Nil? xs2)\n then (right_identity eq m (select x am);\n EQ?.symmetry eq (CM?.mult m (select x am) (CM?.unit m)) (select x am))\n else EQ?.reflexivity eq (CM?.mult m (xsdenote eq m am [x]) (xsdenote eq m am xs2)))\n | x::xs1' ->\n flatten_correct_aux eq m am xs1' xs2;\n EQ?.reflexivity eq (select x am);\n CM?.congruence m (select x am) (xsdenote eq m am (xs1' @ xs2))\n (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2));\n CM?.associativity m (select x am) (xsdenote eq m am xs1') (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)));\n EQ?.transitivity eq (CM?.mult m (select x am) (xsdenote eq m am (xs1' @ xs2)))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)))\n (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))", "val apply_swap_correct (#a: Type) (m: cm a) (am: amap a) (xs: list atom) (s: swap (length xs))\n : Lemma (ensures (xsdenote m am xs == xsdenote m am (apply_swap xs s))) (decreases xs)\nlet apply_swap_correct (#a:Type) (m:cm a) (am:amap a)\n (xs:list atom) (s:swap (length xs)):\n Lemma (ensures (xsdenote m am xs == xsdenote m am (apply_swap xs s)))\n (decreases xs) = apply_swap_aux_correct 0 m am xs s", "val flatten_correct_aux (#a: Type) (m: cm a) (am: amap a) (xs1 xs2: list atom)\n : Lemma (xsdenote m am (xs1 @ xs2) == CM?.mult m (xsdenote m am xs1) (xsdenote m am xs2))\nlet rec flatten_correct_aux (#a:Type) (m:cm a) (am:amap a) (xs1 xs2:list atom) :\n Lemma (xsdenote m am (xs1 @ xs2) == CM?.mult m (xsdenote m am xs1)\n (xsdenote m am xs2)) =\n match xs1 with\n | [] -> CM?.identity m (xsdenote m am xs2)\n | [x] -> if (Nil? xs2) then right_identity m (select x am)\n | x::xs1' -> (CM?.associativity m (select x am)\n (xsdenote m am xs1') (xsdenote m am xs2);\n flatten_correct_aux m am xs1' xs2)", "val map (#a:Type) (#b:Type) (f:a -> Tot b) (s:set a) : Tot (set b)\nlet map #_ #b f s = F.on_dom b (exists_y_in_s s f)", "val sort_correct_aux (#a: Type) (eq: equiv a) (m: cm a eq) (am: amap a) (xs: list atom)\n : Lemma (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (sort xs)))\nlet sort_correct_aux (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a) (xs:list atom)\n : Lemma (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (sort xs)) =\n permute_via_swaps_correct sort (fun #a am -> sort_via_swaps am) eq m am xs", "val sort_correct_aux (#a: Type) (eq: CE.equiv a) (m: CE.cm a eq) (am: amap a) (xs: list atom)\n : Lemma (requires True)\n (ensures CE.EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (sort xs)))\n (decreases (FStar.List.Tot.Base.length xs))\nlet rec sort_correct_aux (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (xs:list atom)\n : Lemma (requires True)\n (ensures xsdenote eq m am xs `CE.EQ?.eq eq` xsdenote eq m am (sort xs))\n (decreases (FStar.List.Tot.Base.length xs))\n = let open FStar.Algebra.CommMonoid.Equiv in\n match xs with\n | [] -> EQ?.reflexivity eq (xsdenote eq m am [])\n | pivot::q ->\n let sort0 : permute = List.Tot.sortWith #int (List.Tot.compare_of_bool (<)) in\n let sort_eq (l: list atom) : Lemma\n (sort l == sort0 l)\n [SMTPat (sort l)]\n = sortWith_ext (my_compare_of_bool (<)) (List.Tot.compare_of_bool (<)) l\n in\n let open FStar.List.Tot.Base in\n let f:int -> int -> int = compare_of_bool (<) in\n let hi, lo = partition (bool_of_compare f pivot) q in\n flatten_correct_aux eq m am (sort lo) (pivot::sort hi);\n assert (xsdenote eq m am (sort xs) `EQ?.eq eq`\n CM?.mult m (xsdenote eq m am (sort lo))\n (xsdenote eq m am (pivot::sort hi)));\n\n lemma_xsdenote_aux eq m am pivot (sort hi);\n\n EQ?.reflexivity eq (xsdenote eq m am (sort lo));\n CM?.congruence m\n (xsdenote eq m am (sort lo))\n (xsdenote eq m am (pivot::sort hi))\n (xsdenote eq m am (sort lo))\n (select pivot am `CM?.mult m` xsdenote eq m am (sort hi));\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (xsdenote eq m am (sort lo) `CM?.mult m` xsdenote eq m am (pivot::sort hi))\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi)));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi))));\n\n CM?.commutativity m\n (xsdenote eq m am (sort lo))\n (select pivot am `CM?.mult m` xsdenote eq m am (sort hi));\n CM?.associativity m\n (select pivot am)\n (xsdenote eq m am (sort hi))\n (xsdenote eq m am (sort lo));\n EQ?.transitivity eq\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi)))\n ((select pivot am `CM?.mult m` xsdenote eq m am (sort hi)) `CM?.mult m` xsdenote eq m am (sort lo))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo)));\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (xsdenote eq m am (sort lo) `CM?.mult m` (select pivot am `CM?.mult m` xsdenote eq m am (sort hi)))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo)));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo))));\n\n\n partition_length (bool_of_compare f pivot) q;\n sort_correct_aux eq m am hi;\n sort_correct_aux eq m am lo;\n EQ?.symmetry eq (xsdenote eq m am lo) (xsdenote eq m am (sort lo));\n EQ?.symmetry eq (xsdenote eq m am hi) (xsdenote eq m am (sort hi));\n CM?.congruence m\n (xsdenote eq m am (sort hi))\n (xsdenote eq m am (sort lo))\n (xsdenote eq m am hi)\n (xsdenote eq m am lo);\n assert (EQ?.eq eq\n (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo))\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo));\n\n EQ?.reflexivity eq (select pivot am);\n CM?.congruence m\n (select pivot am)\n (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo))\n (select pivot am)\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo);\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am (sort hi) `CM?.mult m` xsdenote eq m am (sort lo)))\n (select pivot am `CM?.mult m` (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)));\n\n partition_equiv eq m am pivot q;\n CM?.congruence m\n (select pivot am)\n (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo)\n (select pivot am)\n (xsdenote eq m am q);\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am hi `CM?.mult m` xsdenote eq m am lo))\n (select pivot am `CM?.mult m` (xsdenote eq m am q));\n assert (EQ?.eq eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am q)));\n\n lemma_xsdenote_aux eq m am pivot q;\n EQ?.symmetry eq\n (xsdenote eq m am (pivot::q))\n (select pivot am `CM?.mult m` (xsdenote eq m am q));\n EQ?.transitivity eq\n (xsdenote eq m am (sort xs))\n (select pivot am `CM?.mult m` (xsdenote eq m am q))\n (xsdenote eq m am xs);\n EQ?.symmetry eq (xsdenote eq m am (sort xs)) (xsdenote eq m am xs)", "val contains (#a:Type) (s:seq a) (x:a) : Tot Type0\nlet contains #a s x =\n exists (k:nat). k < Seq.length s /\\ Seq.index s k == x", "val gmap (#a #b: _) (f: (a -> GTot b)) (xs: list a) : GTot (list b)\nlet rec gmap #a #b (f: a -> GTot b) (xs: list a): GTot (list b) =\n match xs with\n | [] -> []\n | x :: xs -> f x :: gmap f xs", "val upd (#a: eqtype) (#b: _) (m: map' a b) (x: a) (y: b x) : Tot (map' a b)\nlet upd (#a:eqtype) #b (m:map' a b) (x:a) (y:b x)\n : Tot (map' a b)\n = fun z -> if x = z then Some y else m z", "val id (#t: Type) (x: t) : Tot t\nlet id (#t: Type) (x: t) : Tot t = x", "val id (#t: Type) (x: t) : Tot t\nlet id\n (#t: Type)\n (x: t)\n: Tot t\n= x", "val datas (#a: Type0) (l: v a) : Tot (list a)\nlet datas\n (#a: Type0)\n (l: v a)\n: Tot (list a)\n= l", "val map (#a #b #i: _) (f: (a -> GTD b i)) (xs: list a) : GTD (list b) i\nlet rec map #a #b #i (f : a -> GTD b i) (xs : list a) : GTD (list b) i =\n match xs with\n | [] -> []\n | x::xs -> (f x)::(map f xs)", "val map (#a #b:Type) (f:a -> b) (s:seq a): Tot (s':seq b{length s' = length s})\nlet map (#a #b:Type) (f:a -> b) (s:seq a): Tot (s':seq b{length s' = length s}) = map_aux f s", "val mmap_f (#a:eqtype) (#b #c:a -> Type) (m:map a b) (f: (x:a) -> b x -> c x)\n :Tot (m':(map a c){repr m' == DM.map (f_opt f) (repr m)})\nlet rec mmap_f #a #b #c m f =\n match m with\n | [] ->\n assert (DM.equal (empty_partial_dependent_map #a #c)\n (DM.map (f_opt f) (empty_partial_dependent_map #a #b)));\n assert_norm (repr #a #c [] == empty_partial_dependent_map #a #c);\n []\n | (| x, y |)::tl -> (| x, f x y |)::(mmap_f #a #b #c tl f)", "val bind (#a #b: Type) (x: erased a) (f: (a -> Tot (erased b))) : Tot (erased b)\nlet bind (#a #b: Type) (x: erased a) (f: (a -> Tot (erased b))) : Tot (erased b) =\n let y = reveal x in\n f y", "val va_subscript (#a: eqtype) (#b: Type) (x: Map.t a b) (y: a) : Tot b\nlet va_subscript (#a:eqtype) (#b:Type) (x:Map.t a b) (y:a) : Tot b = Map.sel x y", "val va_subscript (#a: eqtype) (#b: Type) (x: Map.t a b) (y: a) : Tot b\nlet va_subscript (#a:eqtype) (#b:Type) (x:Map.t a b) (y:a) : Tot b = Map.sel x y", "val complement : #a:Type -> x:set a -> Tot (set a)\nlet complement #a s = F.on_dom a #(fun _ -> prop) (fun x -> ~ (s x))", "val apply_swaps_correct\n (#a: Type)\n (m: cm a)\n (am: amap a)\n (xs: list atom)\n (ss: list (swap (length xs)))\n : Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swaps xs ss)))\n (decreases ss)\nlet rec apply_swaps_correct (#a:Type) (m:cm a) (am:amap a)\n (xs:list atom) (ss:list (swap (length xs))):\n Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swaps xs ss)))\n (decreases ss) =\n match ss with\n | [] -> ()\n | s::ss' -> apply_swap_correct m am xs s;\n apply_swaps_correct m am (apply_swap xs s) ss'", "val _cons (#a: Type) (x: a) (s: seq a) : Tot (seq a)\nlet _cons (#a:Type) (x:a) (s:seq a) : Tot (seq a) = MkSeq (x::(MkSeq?.l s))", "val select (#a: Type) (x: atom) (am: amap a) : Tot a\nlet select (#a:Type) (x:atom) (am:amap a) : Tot a =\n match assoc #atom #a x (fst am) with\n | Some a -> a\n | _ -> snd am", "val select (#a: Type) (x: atom) (am: amap a) : Tot a\nlet select (#a:Type) (x:atom) (am:amap a) : Tot a =\n match my_assoc #atom #a x (fst am) with\n | Some a -> a\n | _ -> snd am", "val select (#a: Type) (x: atom) (am: amap a) : Tot a\nlet select (#a:Type) (x:atom) (am:amap a) : Tot a =\n match assoc #atom #a x (fst am) with\n | Some a -> a\n | _ -> snd am", "val flatten_correct_aux\n (#a: Type)\n (eq: CE.equiv a)\n (m: CE.cm a eq)\n (am: amap a)\n (xs1 xs2: list atom)\n : Lemma\n (CE.EQ?.eq eq\n (xsdenote eq m am (xs1 `my_append` xs2))\n (CE.CM?.mult m (xsdenote eq m am xs1) (xsdenote eq m am xs2)))\nlet rec flatten_correct_aux (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (xs1 xs2:list atom)\n : Lemma (xsdenote eq m am (xs1 `my_append` xs2) `CE.EQ?.eq eq` CE.CM?.mult m (xsdenote eq m am xs1)\n (xsdenote eq m am xs2)) =\n let open FStar.Algebra.CommMonoid.Equiv in\n match xs1 with\n | [] ->\n CM?.identity m (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.unit m) (xsdenote eq m am xs2)) (xsdenote eq m am xs2)\n | [x] -> (\n if (Nil? xs2)\n then (right_identity eq m (select x am);\n EQ?.symmetry eq (CM?.mult m (select x am) (CM?.unit m)) (select x am))\n else EQ?.reflexivity eq (CM?.mult m (xsdenote eq m am [x]) (xsdenote eq m am xs2)))\n | x::xs1' ->\n flatten_correct_aux eq m am xs1' xs2;\n EQ?.reflexivity eq (select x am);\n CM?.congruence m (select x am) (xsdenote eq m am (xs1' `my_append` xs2))\n (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2));\n CM?.associativity m (select x am) (xsdenote eq m am xs1') (xsdenote eq m am xs2);\n EQ?.symmetry eq (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)));\n EQ?.transitivity eq (CM?.mult m (select x am) (xsdenote eq m am (xs1' `my_append` xs2)))\n (CM?.mult m (select x am) (CM?.mult m (xsdenote eq m am xs1') (xsdenote eq m am xs2)))\n (CM?.mult m (CM?.mult m (select x am) (xsdenote eq m am xs1')) (xsdenote eq m am xs2))", "val map (#a #b #i: _) (f: (a -> Gtd b i)) (xs: list a) : Gtd (list b) i\nlet rec map #a #b #i (f : a -> Gtd b i) (xs : list a) : Gtd (list b) i (* by (explode (); dump \"\") *) =\n match xs with\n | [] -> []\n | x::xs -> (f x)::(map f xs)", "val add : #a:Type -> x:a -> m:t a -> t a\nlet add #a x m = x :: m", "val r_map (#i #a #b: _) (f: (a -> m b i)) (xs: list a) : m (list b) i\nlet rec r_map #i #a #b (f : a -> m b i) (xs : list a) : m (list b) i =\n match xs with\n | [] -> return _ [] _\n | x::xs ->\n bind _ _ _ (f x) (fun y ->\n bind _ _ _ (r_map f xs) (fun ys ->\n return _ (y::ys) _))", "val apply_swap_correct\n (#a: Type)\n (eq: equiv a)\n (m: cm a eq)\n (am: amap a)\n (xs: list atom)\n (s: swap (length xs))\n : Lemma (ensures (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (apply_swap xs s))))\n (decreases xs)\nlet apply_swap_correct (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a)\n (xs:list atom) (s:swap (length xs))\n : Lemma (ensures (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (apply_swap xs s)))\n (decreases xs) =\n apply_swap_aux_correct 0 eq m am xs s", "val mdenote (#a: Type) (m: monoid a) (e: exp a) : a\nlet rec mdenote (#a:Type) (m:monoid a) (e:exp a) : a =\n match e with\n | Unit -> Monoid?.unit m\n | Var x -> x\n | Mult e1 e2 -> Monoid?.mult m (mdenote m e1) (mdenote m e2)", "val update (#a: Type) (x: var) (xa: a) (vm: vmap a) : vmap a\nlet update (#a:Type) (x:var) (xa:a) (vm:vmap a) : vmap a =\n let l, y = vm in (x, xa) :: l, y", "val canon_correct (#a: Type) (m: cm a) (am: amap a) (e: exp)\n : Lemma (mdenote m am e == xsdenote m am (canon e))\nlet canon_correct (#a:Type) (m:cm a) (am:amap a) (e:exp) :\n Lemma (mdenote m am e == xsdenote m am (canon e)) =\n flatten_correct m am e; sort_correct m am (flatten e)", "val reduce (#a:Type) (#b:Type) (b0: b) (f: a -> b -> b) (s: seq a): Tot b\nlet reduce = reduce_aux", "val bind_map_get (#a: Type) (m: bind_map a) (b: bv) : Tot (option a)\nlet rec bind_map_get (#a:Type) (m:bind_map a) (b:bv) : Tot (option a) =\n match m with\n | [] -> None\n | (b', x)::m' ->\n if compare_bv b b' = Order.Eq then Some x else bind_map_get m' b", "val flatten_correct (#a: Type) (m: cm a) (am: amap a) (e: exp)\n : Lemma (mdenote m am e == xsdenote m am (flatten e))\nlet rec flatten_correct (#a:Type) (m:cm a) (am:amap a) (e:exp) :\n Lemma (mdenote m am e == xsdenote m am (flatten e)) =\n match e with\n | Unit | Atom _ -> ()\n | Mult e1 e2 -> flatten_correct_aux m am (flatten e1) (flatten e2);\n flatten_correct m am e1; flatten_correct m am e2", "val map (#a #b: _) (f: (a -> RWI b RO (fun _ -> True) (fun _ _ _ -> True))) (xs: list a)\n : RWI (list b) RO (fun _ -> True) (fun _ _ _ -> True)\nlet rec map #a #b\n (f : a -> RWI b RO (fun _ -> True) (fun _ _ _ -> True))\n (xs : list a)\n : RWI (list b) RO (fun _ -> True) (fun _ _ _ -> True)\n = match xs with\n | [] -> []\n | x::xs -> (f x)::(map f xs)", "val apply_swap_aux_correct\n (#a: Type)\n (n: nat)\n (m: cm a)\n (am: amap a)\n (xs: list atom)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swap_aux n xs s)))\n (decreases xs)\nlet rec apply_swap_aux_correct (#a:Type) (n:nat) (m:cm a) (am:amap a)\n (xs:list atom) (s:swap (length xs + n)) :\n Lemma (requires True)\n (ensures (xsdenote m am xs == xsdenote m am (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] | [_] -> ()\n | x1 :: x2 :: xs' ->\n if n = (s <: nat)\n then (// x1 + (x2 + xs') =a (x1 + x2) + xs'\n // =c (x2 + x1) + xs' = a x2 + (x1 + xs')\n let a = CM?.associativity m in\n a (select x1 am) (select x2 am) (xsdenote m am xs');\n a (select x2 am) (select x1 am) (xsdenote m am xs');\n CM?.commutativity m (select x1 am) (select x2 am))\n else apply_swap_aux_correct (n+1) m am (x2 :: xs') s", "val bind (a b: Type) (#labs1 #labs2: ops) (c: tree a labs1) (f: (x: a -> tree b labs2))\n : Tot (tree b (labs1 @ labs2))\nlet bind (a b : Type)\n (#labs1 #labs2 : ops)\n (c : tree a labs1)\n (f : (x:a -> tree b labs2))\n : Tot (tree b (labs1@labs2))\n = handle_tree #_ #_ #_ #(labs1@labs2) c f (fun act i k -> Op act i k)", "val bind (a b: Type) (#labs1 #labs2: ops) (c: tree a labs1) (f: (x: a -> tree b labs2))\n : Tot (tree b (labs1 @ labs2))\nlet bind (a b : Type)\n (#labs1 #labs2 : ops)\n (c : tree a labs1)\n (f : (x:a -> tree b labs2))\n : Tot (tree b (labs1@labs2))\n = handle_with #_ #_ #labs1 #(labs1@labs2) c f (fun act i k -> Op act i k)", "val norm (s: list norm_step) (#a: Type) (x: a) : Tot a\nlet norm _ #_ x = x", "val memP (#a: Type) (x: a) (l: list a) : Tot Type0\nlet rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 =\n match l with\n | [] -> False\n | y :: q -> x == y \\/ memP x q", "val v_: #t_k:eqtype -> #t_v:Type0 -> l:list (t_k & t_v) -> Tot (map t_k t_v)\nlet v_ #_ #t_v l =\n List.Tot.fold_right (fun (k, v) m -> M.upd m k (Some v)) l (M.const (None #t_v))", "val mem (#a:eqtype) (x:a) (s:set a)\n : Tot bool\nlet mem #a x s = s x", "val snoc (#a: Type) (s: seq a) (x: a) : Tot (seq a)\nlet snoc (#a:Type) (s:seq a) (x:a) : Tot (seq a) = Seq.append s (Seq.create 1 x)", "val some_v (#t: Type) (x: option t {Some? x}) : Tot (y: t{y == Some?.v x})\nlet some_v\n (#t: Type)\n (x: option t { Some? x })\n: Tot (y: t { y == Some?.v x })\n= match x with\n | Some y -> y", "val solve (#a: Type) (#[tcresolve ()] ev: a) : Tot a\nlet solve (#a:Type) (#[tcresolve ()] ev : a) : Tot a = ev", "val opt_cons (#a: Type) (opt_x: option a) (ls: list a) : Tot (list a)\nlet opt_cons (#a : Type) (opt_x : option a) (ls : list a) : Tot (list a) =\n match opt_x with\n | Some x -> x :: ls\n | None -> ls", "val tinstrDenote (#ts #ts': tstack) (i: tinstr ts ts') (s: vstack ts) : Tot (vstack ts')\nlet rec tinstrDenote (#ts:tstack) (#ts':tstack)\n (i : tinstr ts ts') (s:vstack ts) : Tot (vstack ts') =\n match i with\n | TiNConst _ n -> (n, s)\n | TiBConst _ b -> (b, s)\n | TiBinop #targ1 #targ2 #tres #tss b ->\n (* Take 1 *)\n (* let (arg1, (arg2, s')) = s in *)\n (* ((tbinopDenote b) arg1 arg2, s') *)\n (* Implicit pattern variables in (Prims.Mktuple2 arg1 (Prims.Mktuple2 arg2 s')) *)\n (* could not be resolved against expected type (StackMachine.vstack ts); *)\n (* Variables {?63598, ?63596, ?63406} were unresolved; please bind them explicitly *)\n\n (* Take 2 *)\n (* ((tbinopDenote b) (fst s) (fst (snd s)), (snd (snd s))) *)\n (* Subtyping check failed; expected type *)\n (* (Prims.tuple2 (?63342 ts ts' i s uu___ uu___ uu___ uu___ b) *)\n (* (?63343 ts ts' i s uu___ uu___ uu___ uu___ b)); *)\n (* got type (StackMachine.vstack ts) *)\n\n (* Take 3: fully annotated *)\n let s' : typeDenote targ1 * (typeDenote targ2 * vstack tss) = s in\n let (arg1, (arg2, s'')) = s' in\n (((tbinopDenote b) arg1 arg2, s'') <: (typeDenote tres * vstack tss))", "val sndp (#a1 #a2: Type) (x: (a1 & a2)) : Tot a2\nlet sndp (#a1 #a2: Type) (x: (a1 & a2)) : Tot a2 = snd x", "val binopDenote: b: binop -> nat -> nat -> Tot nat\nlet binopDenote (b : binop) : nat -> nat -> Tot nat =\n match b with\n | Plus -> add_nat\n | Times -> mul_nat", "val apply_swaps_correct\n (#a: Type)\n (eq: equiv a)\n (m: cm a eq)\n (am: amap a)\n (xs: list atom)\n (ss: list (swap (length xs)))\n : Lemma (requires True)\n (ensures (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (apply_swaps xs ss))))\n (decreases ss)\nlet rec apply_swaps_correct (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a)\n (xs:list atom) (ss:list (swap (length xs)))\n : Lemma (requires True)\n (ensures (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (apply_swaps xs ss)))\n (decreases ss) =\n match ss with\n | [] -> EQ?.reflexivity eq (xsdenote eq m am xs)\n | s::ss' ->\n apply_swap_correct eq m am xs s;\n apply_swaps_correct eq m am (apply_swap xs s) ss';\n EQ?.transitivity eq (xsdenote eq m am xs)\n (xsdenote eq m am (apply_swap xs s))\n (xsdenote eq m am (apply_swaps (apply_swap xs s) ss'))", "val ( ^+^ ) (#a #b: Type) (r1: ref a) (r2: ref b) : Tot (set nat)\nlet op_Hat_Plus_Hat (#a:Type) (#b:Type) (r1:ref a) (r2:ref b) : Tot (set nat) =\n union (only r1) (only r2)", "val ics_aux (#a: Type) (r: cr a) (vm: vmap a) (x: a) (s: canonical_sum a) : Tot a (decreases s)\nlet rec ics_aux (#a:Type) (r:cr a) (vm:vmap a) (x:a) (s:canonical_sum a)\n : Tot a (decreases s) =\n let aplus = r.cm_add.mult in\n match s with\n | Nil_monom -> x\n | Cons_varlist l t -> aplus x (ics_aux r vm (interp_vl r vm l) t)\n | Cons_monom c l t -> aplus x (ics_aux r vm (interp_m r vm c l) t)", "val length: #a:Type -> seq a -> Tot nat\nlet length #_ s = List.length (MkSeq?.l s)", "val normalize_term (#a: Type) (x: a) : Tot a\nlet normalize_term #_ x = x", "val ivl_aux (#a: Type) (r: cr a) (vm: vmap a) (x: index) (t: varlist) : Tot a (decreases t)\nlet rec ivl_aux (#a:Type) (r:cr a) (vm:vmap a) (x:index) (t:varlist)\n : Tot a (decreases t) =\n let amult = r.cm_mult.mult in\n match t with\n | Nil_var -> interp_var vm x\n | Cons_var x' t' -> amult (interp_var vm x) (ivl_aux r vm x' t')", "val sel' (#a: _) (r: regmap a) (x: reg) : Tot a\nlet sel' #a (r:regmap a) (x:reg) : Tot a = sel r x", "val mem_existsb: #a:eqtype -> f:(a -> Tot bool) -> xs:list a ->\n Lemma(ensures (existsb f xs <==> (exists (x:a). (f x = true /\\ mem x xs))))\nlet rec mem_existsb #a f xs =\n match xs with\n | [] -> ()\n | hd::tl -> mem_existsb f tl", "val apply_swap_aux_correct\n (#a: Type)\n (n: nat)\n (eq: equiv a)\n (m: cm a eq)\n (am: amap a)\n (xs: list atom)\n (s: swap (length xs + n))\n : Lemma (requires True)\n (ensures (EQ?.eq eq (xsdenote eq m am xs) (xsdenote eq m am (apply_swap_aux n xs s))))\n (decreases xs)\nlet rec apply_swap_aux_correct (#a:Type) (n:nat) (eq:equiv a) (m:cm a eq) (am:amap a)\n (xs:list atom) (s:swap (length xs + n))\n : Lemma (requires True)\n (ensures (xsdenote eq m am xs `EQ?.eq eq` xsdenote eq m am (apply_swap_aux n xs s)))\n (decreases xs) =\n match xs with\n | [] -> EQ?.reflexivity eq (CM?.unit m)\n | [x] -> EQ?.reflexivity eq (select x am)\n | [x1;x2] ->\n if n = (s <: nat)\n then CM?.commutativity m (select x1 am) (select x2 am)\n else EQ?.reflexivity eq (xsdenote eq m am [x1;x2])\n | x1 :: x2 :: xs' ->\n if n = (s <: nat)\n then (\n CM?.associativity m (select x1 am) (select x2 am) (xsdenote eq m am xs');\n EQ?.symmetry eq (CM?.mult m (CM?.mult m (select x1 am) (select x2 am)) (xsdenote eq m am xs'))\n (CM?.mult m (select x1 am) (CM?.mult m (select x2 am) (xsdenote eq m am xs')));\n CM?.commutativity m (select x1 am) (select x2 am);\n EQ?.reflexivity eq (xsdenote eq m am xs');\n CM?.congruence m (CM?.mult m (select x1 am) (select x2 am)) (xsdenote eq m am xs')\n (CM?.mult m (select x2 am) (select x1 am)) (xsdenote eq m am xs');\n CM?.associativity m (select x2 am) (select x1 am) (xsdenote eq m am xs');\n EQ?.transitivity eq (CM?.mult m (select x1 am) (CM?.mult m (select x2 am) (xsdenote eq m am xs')))\n (CM?.mult m (CM?.mult m (select x1 am) (select x2 am)) (xsdenote eq m am xs'))\n (CM?.mult m (CM?.mult m (select x2 am) (select x1 am)) (xsdenote eq m am xs'));\n EQ?.transitivity eq (CM?.mult m (select x1 am) (CM?.mult m (select x2 am) (xsdenote eq m am xs')))\n (CM?.mult m (CM?.mult m (select x2 am) (select x1 am)) (xsdenote eq m am xs'))\n (CM?.mult m (select x2 am) (CM?.mult m (select x1 am) (xsdenote eq m am xs'))))\n else (\n apply_swap_aux_correct (n+1) eq m am (x2 :: xs') s;\n EQ?.reflexivity eq (select x1 am);\n CM?.congruence m (select x1 am) (xsdenote eq m am (x2 :: xs'))\n (select x1 am) (xsdenote eq m am (apply_swap_aux (n+1) (x2 :: xs') s)))", "val evar (x: var) : Tot (exp int)\nlet evar (x: var) : Tot (exp int) = fun _ -> read x", "val equivalent_sorted\n (#a: Type)\n (eq: CE.equiv a)\n (m: CE.cm a eq)\n (am: amap a)\n (l1 l2 l1' l2': list atom)\n : Lemma\n (requires\n sort l1 == sort l1' /\\ sort l2 == sort l2' /\\\n CE.EQ?.eq eq (xsdenote eq m am l1) (xsdenote eq m am l2))\n (ensures CE.EQ?.eq eq (xsdenote eq m am l1') (xsdenote eq m am l2'))\nlet equivalent_sorted (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (l1 l2 l1' l2':list atom)\n : Lemma (requires\n sort l1 == sort l1' /\\\n sort l2 == sort l2' /\\\n xsdenote eq m am l1 `CE.EQ?.eq eq` xsdenote eq m am l2)\n (ensures xsdenote eq m am l1' `CE.EQ?.eq eq` xsdenote eq m am l2')\n = let open FStar.Algebra.CommMonoid.Equiv in\n sort_correct_aux eq m am l1';\n sort_correct_aux eq m am l1;\n EQ?.symmetry eq (xsdenote eq m am l1) (xsdenote eq m am (sort l1));\n EQ?.transitivity eq\n (xsdenote eq m am l1')\n (xsdenote eq m am (sort l1'))\n (xsdenote eq m am l1);\n EQ?.transitivity eq\n (xsdenote eq m am l1')\n (xsdenote eq m am l1)\n (xsdenote eq m am l2);\n sort_correct_aux eq m am l2;\n EQ?.transitivity eq\n (xsdenote eq m am l1')\n (xsdenote eq m am l2)\n (xsdenote eq m am (sort l2));\n sort_correct_aux eq m am l2';\n EQ?.symmetry eq (xsdenote eq m am l2') (xsdenote eq m am (sort l2'));\n EQ?.transitivity eq\n (xsdenote eq m am l1')\n (xsdenote eq m am (sort l2))\n (xsdenote eq m am l2')", "val ( ++^ ) (#a: Type) (s: set nat) (r: ref a) : Tot (set nat)\nlet op_Plus_Plus_Hat (#a:Type) (s:set nat) (r:ref a): Tot (set nat) = union s (only r)", "val ( .()<- ) (#a: Type) (x: t a) (i: index_t (as_raw x)) (v: a) : Tot (t a)\nlet op_Array_Assignment\n (#a:Type)\n (x:t a)\n (i:index_t (as_raw x))\n (v:a)\n : Tot (t a)\n = from_raw ((as_raw x).[i] <- v)", "val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b)\nlet rec assoc #a #b x = function\n | [] -> None\n | (x', y)::tl -> if x=x' then Some y else assoc x tl", "val flatten_correct (#a: Type) (eq: CE.equiv a) (m: CE.cm a eq) (am: amap a) (e: exp)\n : Lemma (CE.EQ?.eq eq (mdenote eq m am e) (xsdenote eq m am (flatten e)))\nlet rec flatten_correct (#a:Type) (eq:CE.equiv a) (m:CE.cm a eq) (am:amap a) (e:exp)\n : Lemma (mdenote eq m am e `CE.EQ?.eq eq` xsdenote eq m am (flatten e)) =\n let open FStar.Algebra.CommMonoid.Equiv in\n match e with\n | Unit -> EQ?.reflexivity eq (CM?.unit m)\n | Atom x -> EQ?.reflexivity eq (select x am)\n | Mult e1 e2 ->\n flatten_correct_aux eq m am (flatten e1) (flatten e2);\n EQ?.symmetry eq (xsdenote eq m am (flatten e1 `my_append` flatten e2))\n (CM?.mult m (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2)));\n flatten_correct eq m am e1;\n flatten_correct eq m am e2;\n CM?.congruence m (mdenote eq m am e1) (mdenote eq m am e2)\n (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2));\n EQ?.transitivity eq (CM?.mult m (mdenote eq m am e1) (mdenote eq m am e2))\n (CM?.mult m (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2)))\n (xsdenote eq m am (flatten e1 `my_append` flatten e2))", "val write : #a:Type ->\n #r:preorder a ->\n\t m:mref a r ->\n\t x:a ->\n\t MRefST unit (fun h0 -> contains m h0 /\\\n\t r (sel h0 m) x)\n (fun h0 _ h1 -> contains m h0 /\\\n\t\t\t h1 == upd h0 m x)\nlet write #a #r m x =\n let h0 = ist_get () in\n ist_recall (contains m); //recalling that the current heap must contain the given reference\n let h1 = upd h0 m x in\n ist_put h1", "val memP_existsb: #a: Type -> f:(a -> Tot bool) -> xs:list a ->\n Lemma(ensures (existsb f xs <==> (exists (x:a). (f x = true /\\ memP x xs))))\nlet rec memP_existsb #a f xs =\n match xs with\n | [] -> ()\n | hd::tl -> memP_existsb f tl", "val cardinality (#a: eqtype) (#b: Type u#b) (m: map a b)\n : GTot nat\nlet cardinality (#a: eqtype) (#b: Type u#b) (m: map a b) : GTot nat =\n FSet.cardinality (domain m)", "val map_gtot (#a #b: _) (f: (a -> GTot b)) (x: list a) : GTot (list b)\nlet map_gtot #a #b (f:a -> GTot b) (x:list a)\n : GTot (list b)\n = fold_right_gtot x (fun x tl -> f x :: tl) []", "val bind_m (#s #a #b: _) (x: m s a) (y: (a -> m s b)) : m s b\nlet rec bind_m #s #a #b (x:m s a) (y: (a -> m s b)) : m s b =\n match x with\n | Ret x -> y x\n | Get k -> Get (fun s -> bind_m (k s) y)\n | Put s k -> Put s (bind_m k y)", "val bind (a b: Type) (labs1 labs2: list eff_label) (c: repr a labs1) (f: (x: a -> repr b labs2))\n : Tot (repr b (labs1 @ labs2))\nlet bind (a b : Type)\n (labs1 labs2 : list eff_label)\n (c : repr a labs1)\n (f : (x:a -> repr b labs2))\n : Tot (repr b (labs1@labs2))\n = fun () -> f (c ()) ()", "val bind (a b: Type) (labs1 labs2: list eff_label) (c: repr a labs1) (f: (x: a -> repr b labs2))\n : Tot (repr b (labs1 @ labs2))\nlet bind (a b : Type)\n (labs1 labs2 : list eff_label)\n (c : repr a labs1)\n (f : (x:a -> repr b labs2))\n : Tot (repr b (labs1@labs2))\n = let r =\n fun s0 -> match c s0 with\n | Some x, s1 -> f x s1\n | None, s1 -> None, s1\n in\n r", "val bind (ans a b: Type) (m: cont ans a) (f: (a -> Tot (cont ans b))) (k: (b -> M ans)) : M ans\nlet bind (ans:Type) (a:Type) (b:Type) (m : cont ans a) (f : a -> Tot (cont ans b)) (k: b -> M ans) : M ans =\n m (fun (x:a) -> let fx = f x in fx k)", "val count: #a:eqtype -> a -> list a -> Tot nat\nlet rec count #a x = function\n | hd::tl -> (if hd = x then 1 else 0) + count x tl\n | [] -> 0", "val count: #a:eqtype -> a -> list a -> Tot nat\nlet rec count #a x = function\n | [] -> 0\n | hd::tl -> if x=hd then 1 + count x tl else count x tl", "val filter_eq: #a:Type -> (x:int) -> (xs: list a) -> k:(a -> Tot int) -> Tot (list a)\nlet rec filter_eq #a x xs k =\n match xs with\n | [] -> []\n | hd::tl\n -> if k hd = x then\n hd::(filter_eq x tl k)\n else filter_eq x tl k", "val interp_cs (#a: Type) (r: cr a) (vm: vmap a) (s: canonical_sum a) : a\nlet interp_cs (#a:Type) (r:cr a) (vm:vmap a) (s:canonical_sum a) : a =\n let azero = r.cm_add.unit in\n match s with\n | Nil_monom -> azero\n | Cons_varlist l t -> ics_aux r vm (interp_vl r vm l) t\n | Cons_monom c l t -> ics_aux r vm (interp_m r vm c l) t", "val map_seq (#a #b:Type) (f:a -> Tot b) (s:Seq.seq a) : Tot (Seq.seq b)\nlet rec map_seq #a #b f s : Tot (Seq.seq b) (decreases Seq.length s) =\n if Seq.length s = 0\n then Seq.empty\n else let hd, tl = head s, tail s in\n cons (f hd) (map_seq f tl)", "val varlist_merge_ok (#a:eqtype) (r:cr a) (vm:vmap a) (x y:varlist) :\n Lemma\n (ensures\n interp_vl r vm (varlist_merge x y) ==\n r.cm_mult.mult (interp_vl r vm x) (interp_vl r vm y))\n (decreases %[x; y; 0])\nlet rec varlist_merge_ok #a r vm x y =\n let amult = r.cm_mult.mult in\n match x, y with\n | Cons_var v1 t1, Nil_var -> ()\n | Cons_var v1 t1, Cons_var v2 t2 ->\n if v1 < v2\n then\n begin\n varlist_merge_ok r vm t1 y;\n assert (\n interp_vl r vm (varlist_merge x y) ==\n amult (interp_var vm v1) (amult (interp_vl r vm t1) (interp_vl r vm y)));\n r.cm_mult.associativity\n (interp_var vm v1) (interp_vl r vm t1) (interp_vl r vm y)\n end\n else\n vm_aux_ok r vm v1 t1 y\n | Nil_var, _ -> ()\nand vm_aux_ok #a r vm v1 t1 l2 =\n match l2 with\n | Cons_var v2 t2 ->\n if v1 < v2\n then\n begin\n varlist_merge_ok r vm t1 l2;\n r.cm_mult.associativity\n (interp_var vm v1) (interp_vl r vm t1) (interp_vl r vm l2)\n end\n else\n begin\n vm_aux_ok r vm v1 t1 t2;\n calc (==) {\n interp_vl r vm (Cons_var v2 (vm_aux v1 t1 t2));\n == { }\n ivl_aux r vm v2 (vm_aux v1 t1 t2);\n == { }\n r.cm_mult.mult (interp_var vm v2) (interp_vl r vm (vm_aux v1 t1 t2));\n == { }\n r.cm_mult.mult (interp_var vm v2) (r.cm_mult.mult (interp_vl r vm (Cons_var v1 t1)) (interp_vl r vm t2));\n == { r.cm_mult.commutativity\n (interp_vl r vm (Cons_var v1 t1)) (interp_vl r vm t2) }\n r.cm_mult.mult (interp_var vm v2)\n (r.cm_mult.mult (interp_vl r vm t2) (interp_vl r vm (Cons_var v1 t1)) );\n == { r.cm_mult.associativity\n (interp_var vm v2)\n (interp_vl r vm t2) (interp_vl r vm (Cons_var v1 t1)) }\n r.cm_mult.mult\n (r.cm_mult.mult (interp_var vm v2) (interp_vl r vm t2))\n (interp_vl r vm (Cons_var v1 t1));\n == { r.cm_mult.commutativity\n (interp_vl r vm (Cons_var v1 t1)) (interp_vl r vm (Cons_var v2 t2)) }\n r.cm_mult.mult (interp_vl r vm (Cons_var v1 t1)) (interp_vl r vm (Cons_var v2 t2));\n }\n end\n | _ -> ()", "val complement : #a:Type -> set a -> Tot (set a)\nlet complement #a s = F.on_dom_g a ( fun x -> not (s x))", "val write (#a: Type0) (n: nat) (x: a)\n : LV unit\n (fun m0 -> m0.m `M.contains` n /\\ dfst (m0.m `M.sel` n) == a)\n (fun m0 _ m1 -> m1.next == m0.next /\\ m1.m == Map.upd m0.m n (| a, x |))\nlet write (#a:Type0) (n:nat) (x:a)\n : LV unit (fun m0 -> m0.m `M.contains` n /\\\n dfst (m0.m `M.sel` n) == a)\n (fun m0 _ m1 ->\n m1.next == m0.next /\\\n m1.m == Map.upd m0.m n (| a, x |))\n= LVARS?.reflect (fun m -> (), { m with m = Map.upd m.m n (| a, x |) })", "val length (#a:Type0) (x:t a) : GTot nat\nlet length x = L.length x", "val create: #a:Type -> nat -> a -> Tot (seq a)\nlet rec create #_ len v = if len = 0 then MkSeq [] else _cons v (create (len - 1) v)", "val dsnd (#a: Type) (#b: (a -> GTot Type)) (t: dtuple2 a b) : Tot (b (Mkdtuple2?._1 t))\nlet dsnd (#a: Type) (#b: a -> GTot Type) (t: dtuple2 a b)\n : Tot (b (Mkdtuple2?._1 t))\n = Mkdtuple2?._2 t", "val ( ^++ ) (#a: Type) (r: ref a) (s: set nat) : Tot (set nat)\nlet op_Hat_Plus_Plus (#a:Type) (r:ref a) (s:set nat) : Tot (set nat) =\n union (only r) s", "val progDenote (p: prog) (s: stack) : Tot (option stack)\nlet rec progDenote (p : prog) (s : stack) : Tot (option stack) =\n match p with\n | [] -> Some s\n | i :: p' ->\n match instrDenote i s with\n | None -> None\n | Some s' -> progDenote p' s'", "val flatten_correct (#a: Type) (eq: equiv a) (m: cm a eq) (am: amap a) (e: exp)\n : Lemma (EQ?.eq eq (mdenote eq m am e) (xsdenote eq m am (flatten e)))\nlet rec flatten_correct (#a:Type) (eq:equiv a) (m:cm a eq) (am:amap a) (e:exp)\n : Lemma (mdenote eq m am e `EQ?.eq eq` xsdenote eq m am (flatten e)) =\n match e with\n | Unit -> EQ?.reflexivity eq (CM?.unit m)\n | Atom x -> EQ?.reflexivity eq (select x am)\n | Mult e1 e2 ->\n flatten_correct_aux eq m am (flatten e1) (flatten e2);\n EQ?.symmetry eq (xsdenote eq m am (flatten e1 @ flatten e2))\n (CM?.mult m (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2)));\n flatten_correct eq m am e1;\n flatten_correct eq m am e2;\n CM?.congruence m (mdenote eq m am e1) (mdenote eq m am e2)\n (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2));\n EQ?.transitivity eq (CM?.mult m (mdenote eq m am e1) (mdenote eq m am e2))\n (CM?.mult m (xsdenote eq m am (flatten e1)) (xsdenote eq m am (flatten e2)))\n (xsdenote eq m am (flatten e1 @ flatten e2))" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.xsdenote" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.xsdenote" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.xsdenote" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.xsdenote_gen" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.lemma_xsdenote_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.mdenote" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonMonoid.fst", "name": "FStar.Tactics.CanonMonoid.mldenote" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.mdenote" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fsti", "name": "FStar.Seq.Base.cons" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.mdenote" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.sort_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Map.fst", "name": "FStar.Monotonic.Map.sel" }, { "project_name": "FStar", "file_name": "HyE.AE.fsti", "name": "HyE.AE.mem" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.flatten_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.apply_swap_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.flatten_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.TSet.fst", "name": "FStar.TSet.map" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.sort_correct_aux" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.sort_correct_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.contains" }, { "project_name": "karamel", "file_name": "LowStar.Lib.LinkedList.fst", "name": "LowStar.Lib.LinkedList.gmap" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Map.fst", "name": "FStar.Monotonic.Map.upd" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fsti", "name": "EverParse3d.Prelude.id" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitSum.fst", "name": "LowParse.Spec.BitSum.id" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.datas" }, { "project_name": "FStar", "file_name": "GT.fst", "name": "GT.map" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.map" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.DependentMap.fst", "name": "FStar.Monotonic.DependentMap.mmap_f" }, { "project_name": "FStar", "file_name": "FStar.Ghost.fsti", "name": "FStar.Ghost.bind" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Decls.fsti", "name": "Vale.X64.Decls.va_subscript" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.va_subscript" }, { "project_name": "FStar", "file_name": "FStar.TSet.fst", "name": "FStar.TSet.complement" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.apply_swaps_correct" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base._cons" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.select" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.select" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.select" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.flatten_correct_aux" }, { "project_name": "FStar", "file_name": "GTWP.fst", "name": "GTWP.map" }, { "project_name": "noise-star", "file_name": "Spec.Noise.Map.fst", "name": "Spec.Noise.Map.add" }, { "project_name": "FStar", "file_name": "GT.fst", "name": "GT.r_map" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.apply_swap_correct" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonMonoid.fst", "name": "FStar.Tactics.CanonMonoid.mdenote" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.update" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.canon_correct" }, { "project_name": "zeta", "file_name": "Zeta.SeqAux.fst", "name": "Zeta.SeqAux.reduce" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Base.fst", "name": "FStar.InteractiveHelpers.Base.bind_map_get" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.flatten_correct" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.map" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.apply_swap_aux_correct" }, { "project_name": "FStar", "file_name": "Alg.fst", "name": "Alg.bind" }, { "project_name": "FStar", "file_name": "AlgHeap.fst", "name": "AlgHeap.bind" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fst", "name": "FStar.Pervasives.norm" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Base.fst", "name": "FStar.List.Tot.Base.memP" }, { "project_name": "karamel", "file_name": "LowStar.Lib.AssocList.fst", "name": "LowStar.Lib.AssocList.v_" }, { "project_name": "FStar", "file_name": "FStar.Set.fst", "name": "FStar.Set.mem" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fsti", "name": "FStar.Seq.Properties.snoc" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Base.fsti", "name": "LowParse.Spec.Base.some_v" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Typeclasses.fsti", "name": "FStar.Tactics.Typeclasses.solve" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Base.fst", "name": "FStar.InteractiveHelpers.Base.opt_cons" }, { "project_name": "FStar", "file_name": "StackMachine.fst", "name": "StackMachine.tinstrDenote" }, { "project_name": "steel", "file_name": "CBOR.Pulse.Extern.fsti", "name": "CBOR.Pulse.Extern.sndp" }, { "project_name": "FStar", "file_name": "StackMachine.fst", "name": "StackMachine.binopDenote" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.apply_swaps_correct" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fsti", "name": "FStar.DM4F.Heap.op_Hat_Plus_Hat" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.ics_aux" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.length" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fst", "name": "FStar.Pervasives.normalize_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.ivl_aux" }, { "project_name": "FStar", "file_name": "Registers.List.fst", "name": "Registers.List.sel'" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.mem_existsb" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.apply_swap_aux_correct" }, { "project_name": "FStar", "file_name": "Benton2004.fst", "name": "Benton2004.evar" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.equivalent_sorted" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fsti", "name": "FStar.DM4F.Heap.op_Plus_Plus_Hat" }, { "project_name": "FStar", "file_name": "FStar.Vector.Base.fsti", "name": "FStar.Vector.Base.op_Array_Assignment" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Base.fst", "name": "FStar.List.Tot.Base.assoc" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.flatten_correct" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.write" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Properties.fst", "name": "FStar.List.Tot.Properties.memP_existsb" }, { "project_name": "FStar", "file_name": "FStar.FiniteMap.Base.fst", "name": "FStar.FiniteMap.Base.cardinality" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Base.fst", "name": "FStar.List.Tot.Base.map_gtot" }, { "project_name": "FStar", "file_name": "DijkstraStateMonad.fst", "name": "DijkstraStateMonad.bind_m" }, { "project_name": "FStar", "file_name": "LatticeEff.fst", "name": "LatticeEff.bind" }, { "project_name": "FStar", "file_name": "Lattice.fst", "name": "Lattice.bind" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Continuations.fst", "name": "FStar.DM4F.Continuations.bind" }, { "project_name": "FStar", "file_name": "QuickSort.List.fst", "name": "QuickSort.List.count" }, { "project_name": "FStar", "file_name": "FStar.List.Tot.Base.fst", "name": "FStar.List.Tot.Base.count" }, { "project_name": "FStar", "file_name": "GenericStability.fst", "name": "GenericStability.filter_eq" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.interp_cs" }, { "project_name": "FStar", "file_name": "FStar.Seq.Properties.fst", "name": "FStar.Seq.Properties.map_seq" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.varlist_merge_ok" }, { "project_name": "FStar", "file_name": "FStar.GSet.fst", "name": "FStar.GSet.complement" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.write" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.length" }, { "project_name": "FStar", "file_name": "FStar.Seq.Base.fst", "name": "FStar.Seq.Base.create" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.dsnd" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fsti", "name": "FStar.DM4F.Heap.op_Hat_Plus_Plus" }, { "project_name": "FStar", "file_name": "StackMachine.fst", "name": "StackMachine.progDenote" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.fst", "name": "FStar.Tactics.CanonCommMonoidSimple.Equiv.flatten_correct" } ], "selected_premises": [ "FStar.Tactics.CanonCommMonoid.select", "FStar.Tactics.CanonCommMonoid.mdenote", "FStar.Tactics.CanonCommMonoid.const", "FStar.Tactics.CanonCommMonoid.select_extra", "FStar.Tactics.CanonCommMonoid.vmap", "FStar.Tactics.CanonCommMonoid.update", "FStar.List.Tot.Properties.assoc_mem", "FStar.List.Tot.Base.append", "FStar.List.Tot.Base.mem", "FStar.List.Tot.Base.op_At", "FStar.List.Tot.Base.memP", "FStar.List.Tot.Base.rev", "FStar.Pervasives.Native.fst", "FStar.List.Tot.Base.tl", "FStar.Pervasives.Native.snd", "FStar.Tactics.Util.map", "FStar.List.Tot.Properties.append_assoc", "FStar.Tactics.CanonCommMonoid.var", "FStar.Heap.trivial_preorder", "FStar.ST.op_Bang", "FStar.List.Tot.Base.hd", "FStar.List.Tot.Base.fold_left", "FStar.List.Tot.Properties.append_l_cons", "FStar.List.Tot.Base.map", "FStar.Tactics.Effect.raise", "FStar.List.Tot.Base.length", "FStar.Tactics.Util.fold_left", "FStar.List.Tot.Properties.map_append", "FStar.Tactics.Types.issues", "FStar.List.Tot.Properties.append_mem", "FStar.List.Tot.Properties.append_l_nil", "FStar.ST.alloc", "FStar.List.Tot.Properties.memP_map_intro", "FStar.Tactics.CanonCommMonoid.dump", "FStar.Pervasives.dfst", "FStar.List.Tot.Properties.assoc_memP_some", "FStar.Pervasives.dsnd", "FStar.Tactics.Util.string_of_list", "FStar.List.Tot.Base.concatMap", "FStar.List.map", "FStar.List.Tot.Properties.append_inv_head", "FStar.List.Tot.Properties.append_memP", "FStar.List.Tot.Base.fold_right", "FStar.Tactics.CanonCommSwaps.swaps_for", "FStar.List.Tot.Properties.memP_map_elim", "FStar.Tactics.CanonCommMonoid.exp_to_string", "FStar.List.Tot.Properties.append_injective", "FStar.List.fold_left", "FStar.Tactics.Util.iter", "FStar.List.Tot.Properties.assoc_precedes", "FStar.List.Tot.Base.assoc", "FStar.List.Tot.Properties.append_length", "FStar.All.op_Bar_Greater", "FStar.List.Tot.Properties.map_lemma", "FStar.List.iter", "FStar.List.Tot.Properties.append_memP_forall", "FStar.Tactics.Util.map_opt", "FStar.All.op_Less_Bar", "FStar.List.Tot.Base.find", "FStar.Tactics.Util.filter_map_acc", "FStar.List.Tot.Properties.assoc_memP_none", "FStar.List.Tot.Properties.append_mem_forall", "FStar.List.Tot.Properties.rev_rev'", "FStar.List.for_all", "FStar.List.Tot.Properties.precedes_append_cons_prod_r", "FStar.List.mapT", "FStar.Tactics.Util.fold_right", "FStar.Issue.mk_issue", "FStar.List.Tot.Properties.assoc_append_elim_l", "FStar.List.Tot.Base.flatten", "FStar.Tactics.Util.__mapi", "FStar.List.Tot.Base.split", "FStar.List.fold_right", "FStar.List.Tot.Properties.assoc_append_elim_r", "FStar.List.Tot.Properties.append_inv_tail", "FStar.List.Tot.Properties.for_all_append", "FStar.List.Tot.Properties.fold_left_append", "FStar.Tactics.Effect.get", "FStar.List.Tot.Properties.rev_append", "FStar.Tactics.CanonCommSwaps.swap_for", "FStar.List.Tot.Base.index", "FStar.List.Tot.Base.snoc", "FStar.List.Tot.Properties.lemma_split_using", "FStar.List.Tot.Properties.rev'", "FStar.List.concatMap", "FStar.Tactics.Util.repeatn", "FStar.Mul.op_Star", "FStar.Tactics.Util.filter_map", "FStar.List.Tot.Properties.rev_memP", "FStar.List.Tot.Properties.rev'_append", "FStar.List.Tot.Base.rev_acc", "FStar.List.Tot.Base.fold_left2", "FStar.List.Tot.Properties.memP_precedes", "FStar.List.Tot.Base.list_refb", "FStar.List.Tot.Properties.map_strict_suffix_of", "FStar.Pervasives.reveal_opaque", "FStar.List.Tot.Base.tail", "FStar.List.Tot.Properties.precedes_append_cons_r", "FStar.List.Tot.Properties.split_using", "FStar.List.Tot.Properties.lemma_snoc_length" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.Tactics.CanonCommMonoid\n\nopen FStar.Algebra.CommMonoid\nopen FStar.List\nopen FStar.Reflection.V2\nopen FStar.Tactics.V2\nopen FStar.Classical\nopen FStar.Tactics.CanonCommSwaps\n\n(* An expression canonizer for commutative monoids.\n Inspired by:\n - http://adam.chlipala.net/cpdt/html/Cpdt.Reflection.html\n - http://poleiro.info/posts/2015-04-13-writing-reflective-tactics.html\n*)\n\n(* Only dump when debugging is on *)\nprivate let dump m = if debugging () then dump m\n\n(***** Expression syntax *)\n\nlet var : eqtype = nat\n\ntype exp : Type =\n | Unit : exp\n | Var : var -> exp\n | Mult : exp -> exp -> exp\n\nlet rec exp_to_string (e:exp) : string =\n match e with\n | Unit -> \"Unit\"\n | Var x -> \"Var \" ^ string_of_int (x <: var)\n | Mult e1 e2 -> \"Mult (\" ^ exp_to_string e1\n ^ \") (\" ^ exp_to_string e2 ^ \")\"\n\n(***** Expression denotation *)\n\n// Use a map that stores for each variable\n// (1) its denotation that should be treated abstractly (type a) and\n// (2) user-specified extra information depending on its term (type b)\n\nlet vmap (a b:Type) = list (var * (a*b)) * (a * b)\nlet const (#a #b:Type) (xa:a) (xb:b) : vmap a b = [], (xa,xb)\nlet select (#a #b:Type) (x:var) (vm:vmap a b) : Tot a =\n match assoc #var #(a * b) x (fst vm) with\n | Some (a, _) -> a\n | _ -> fst (snd vm)\nlet select_extra (#a #b:Type) (x:var) (vm:vmap a b) : Tot b =\n match assoc #var #(a * b) x (fst vm) with\n | Some (_, b) -> b\n | _ -> snd (snd vm)\nlet update (#a #b:Type) (x:var) (xa:a) (xb:b) (vm:vmap a b) : vmap a b =\n (x, (xa, xb))::fst vm, snd vm\n\nlet rec mdenote (#a #b:Type) (m:cm a) (vm:vmap a b) (e:exp) : Tot a =\n match e with\n | Unit -> CM?.unit m\n | Var x -> select x vm\n | Mult e1 e2 -> CM?.mult m (mdenote m vm e1) (mdenote m vm e2)\n", "sketch": [ "Step 1: The `xsdenote` function is intended to compute the denotation of a list of variables in the context of a commutative monoid. This involves taking a list of variables and combining their denotations using the monoid's multiplication operation.\nStep 2: To implement `xsdenote`, we will use the `fold_left` function to iterate over the list of variables. Starting with the monoid's unit element, we will repeatedly apply the monoid's multiplication operation to combine the denotations of the variables as we traverse the list.", "Step 1: The `xsdenote` function is intended to compute the denotation of a list of variables within a commutative monoid. This involves taking a list of variables and combining their denotations using the monoid's multiplication operation.\nStep 2: To implement this, we will recursively traverse the list of variables. For each variable, we will use the `select` function to get its denotation from the variable map. We will then combine these denotations using the monoid's multiplication operation. The base case for the recursion will be the monoid's unit element.", "Step 1: The function `xsdenote` is intended to compute the denotation of a list of variables in the context of a commutative monoid. This involves taking a list of variables and using the provided commutative monoid operations to combine their denotations.\n\nStep 2: To implement `xsdenote`, we will:\n- Use the commutative monoid's unit element as the base case for the fold operation.\n- Iterate through the list of variables, selecting their denotations from the variable map.\n- Combine these denotations using the commutative monoid's multiplication operation.", "Step 1: The `xsdenote` function is intended to compute the denotation of a list of variables in the context of a commutative monoid. Each variable in the list is mapped to its denotation using a provided variable map (`vm`), and the results are combined using the monoid's multiplication operation.\n\nStep 2: To implement `xsdenote`, we will:\n- Use pattern matching to handle the base case where the list of variables is empty, returning the monoid's unit element.\n- For the non-empty list case, recursively compute the denotation of the tail of the list and combine it with the denotation of the head variable using the monoid's multiplication operation.", "Step 1: The `xsdenote` function is intended to compute the denotation of a list of variables in the context of a commutative monoid. The denotation of a list of variables is the product of the denotations of each variable in the list.\nStep 2: To implement `xsdenote`, we will use recursion to traverse the list of variables. For each variable in the list, we will use the `select` function to get its denotation from the variable map `vm`. We will then use the `mult` operation from the commutative monoid to combine the denotations of the variables. The base case for the recursion will be the empty list, which should return the unit element of the monoid.", "Step 1: The `xsdenote` function is intended to compute the denotation of a list of variables in the context of a commutative monoid. This involves taking each variable in the list, finding its corresponding value in the variable map, and then combining these values using the monoid's multiplication operation.\n\nStep 2: To implement `xsdenote`, we will:\n- Use pattern matching to handle the base case where the list of variables is empty, returning the monoid's unit element.\n- For the non-empty list case, recursively compute the denotation of the tail of the list and then combine it with the denotation of the head variable using the monoid's multiplication operation.", "Step 1: The function `xsdenote` is intended to compute the denotation of a list of variables in the context of a commutative monoid. It takes a commutative monoid `m`, a variable map `vm`, and a list of variables `xs`, and returns the combined denotation of all variables in the list according to the monoid's multiplication operation.\n\nStep 2: To implement `xsdenote`, we will recursively process the list of variables. For an empty list, the result is the unit element of the monoid. For a non-empty list, we will multiply the denotation of the head of the list (obtained using the `select` function) with the result of recursively processing the tail of the list.", "Step 1: The `xsdenote` function is intended to compute the denotation of a list of variables in the context of a commutative monoid. The denotation of each variable is obtained from the variable map `vm`, and the results are combined using the monoid's multiplication operation.\n\nStep 2: To implement `xsdenote`, we will:\n- Use pattern matching to handle the base case where the list of variables is empty, returning the monoid's unit element.\n- For the non-empty list case, recursively compute the denotation of the tail of the list and combine it with the denotation of the head variable using the monoid's multiplication operation.", "Step 1: The `xsdenote` function is intended to compute the denotation of a list of variables in the context of a commutative monoid. This involves taking a list of variables and using the provided commutative monoid operations to combine their denotations.\n\nStep 2: To implement `xsdenote`, we will:\n- Use pattern matching to handle the base case where the list is empty, returning the unit element of the monoid.\n- For the non-empty list case, we will recursively compute the denotation of the tail of the list and then combine it with the denotation of the head variable using the monoid's multiplication operation.", "Step 1: The `xsdenote` function is intended to compute the denotation of a list of variables in the context of a commutative monoid. This involves iterating through the list of variables and combining their denotations using the monoid's multiplication operation.\nStep 2: To implement `xsdenote`, we will use a recursive approach. If the list is empty, we return the unit element of the monoid. If the list is non-empty, we take the head of the list, find its denotation using the `select` function, and recursively compute the denotation of the tail of the list. We then combine these two denotations using the monoid's multiplication operation." ], "generated_solution": [ "let xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a =\n fold_left (fun acc x -> CM?.mult m acc (select x vm)) (CM?.unit m) xs", "let rec xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "let rec xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "let rec xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "let rec xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "let rec xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "let rec xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "let rec xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "let rec xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')", "let rec xsdenote (#a #b: Type) (m: cm a) (vm: vmap a b) (xs: list var) : Tot a =\n match xs with\n | [] -> CM?.unit m\n | x::xs' -> CM?.mult m (select x vm) (xsdenote m vm xs')" ] }, { "file_name": "Automation.fst", "name": "Automation.ea2", "opens_and_abbrevs": [ { "open": "FStar.Tactics.V2" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let ea2 (p q r : prop) =\n assert (p ==> q ==> r ==> q)\n by (triv ())", "source_range": { "start_line": 31, "start_col": 0, "end_line": 33, "end_col": 18 }, "interleaved": false, "definition": "fun p q r ->\n FStar.Tactics.Effect.assert_by_tactic (p ==> q ==> r ==> q)\n (fun _ ->\n ();\n Automation.triv ())", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Prims.prop", "FStar.Tactics.Effect.assert_by_tactic", "Prims.l_imp", "Prims.unit", "Automation.triv" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "p: Prims.prop -> q: Prims.prop -> r: Prims.prop -> Prims.unit", "prompt": "let ea2 (p q r: prop) =\n ", "expected_response": "FStar.Tactics.Effect.assert_by_tactic (p ==> q ==> r ==> q)\n (fun _ ->\n ();\n (triv ()))", "source": { "project_name": "FStar", "file_name": "examples/tactics/eci19/Automation.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "Automation.fst", "checked_file": "dataset/Automation.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Tactics.Effect.fsti.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "let triv () : Tac unit =\n let _ = l_intros () in\n assumption ();\n qed ()", "let ea1 (p q r : prop) =\n assert (p ==> q ==> r ==> p)\n by (triv ())" ], "closest": [ "val ConstructiveLogic.ex2 = p: Prims.prop -> q: Prims.prop -> Prims.unit\nlet ex2 (p q : prop) =\n assert (p ==> q ==> p)\n by (let bp = implies_intro () in\n let _ = implies_intro () in\n hyp (binding_to_namedv bp);\n qed ())", "val ConstructiveLogic.ex4 = p: Prims.prop -> q: Prims.prop -> Prims.unit\nlet ex4 (p q : prop) =\n assert (p /\\ q ==> p)\n by (let h = implies_intro () in\n let (bp, bq) = destruct_and (binding_to_term h) in\n hyp (binding_to_namedv bp);\n qed ())", "val ConstructiveLogic.ex5 = p: Prims.prop -> q: Prims.prop -> Prims.unit\nlet ex5 (p q : prop) =\n assert (p ==> p \\/ q)\n by (let bp = implies_intro () in\n left ();\n hyp (binding_to_namedv bp);\n qed ())", "val ConstructiveLogic.ex3 = p: Prims.prop -> q: Prims.prop -> Prims.unit\nlet ex3 (p q : prop) =\n assert (p ==> q ==> q /\\ p)\n by (let bp = implies_intro () in\n let bq = implies_intro () in\n split ();\n (* Now we have two goals: q and p *)\n hyp (binding_to_namedv bq);\n (* Only one goal left, p *)\n hyp (binding_to_namedv bp);\n (* Done! *)\n qed ())", "val ConstructiveLogic.ex8 = p: Prims.prop -> q: Prims.prop -> Prims.unit\nlet ex8 (p q : prop) =\n assert ((p ==> q) ==> p ==> q)\n by (let i = implies_intro () in\n let h = implies_intro () in\n mapply i;\n mapply h;\n qed ())", "val ConstructiveLogic.ex7 = p: Prims.prop -> q: Prims.prop -> Prims.unit\nlet ex7 (p q : prop) =\n assert (p \\/ q ==> q \\/ p)\n by (let bp_or_q = implies_intro () in\n cases_or (binding_to_term bp_or_q);\n (* first case *)\n let bp = implies_intro () in\n right ();\n hyp (binding_to_namedv bp);\n (* second case *)\n let bq = implies_intro () in\n left ();\n hyp (binding_to_namedv bq);\n qed ())", "val ConstructiveLogic.ex6 = p: Prims.prop -> q: Prims.prop -> Prims.unit\nlet ex6 (p q : prop) =\n assert (p ==> q \\/ p)\n by (let bp = implies_intro () in\n right ();\n hyp (binding_to_namedv bp);\n qed ())", "val ConstructiveLogic.ex1_qed = p: Prims.prop -> Prims.unit\nlet ex1_qed (p : prop) =\n assert (p ==> p)\n by (let b = implies_intro () in\n hyp (binding_to_namedv b);\n qed ())", "val ConstructiveLogic.ex1 = p: Prims.prop -> Prims.unit\nlet ex1 (p : prop) =\n assert (p ==> p)\n by (let b = implies_intro () in\n hyp (binding_to_namedv b))", "val ConstructiveLogic.ex9 = p: Prims.prop -> Prims.unit\nlet ex9 (p : prop) =\n assert (p ==> (forall (_x:int). p))\n by (let bp = implies_intro () in\n let _bx = forall_intro () in\n hyp (binding_to_namedv bp);\n qed ())", "val Effects.Def.ex_laws = Prims.unit\nlet ex_laws = monad_laws_via_eq ex eq_ex return_ex bind_ex", "val ConstructiveLogic.ex11 = p: (_: Prims.nat -> Prims.prop) -> q: (_: Prims.nat -> Prims.prop) -> Prims.unit\nlet ex11 (p q : nat -> prop) =\n assert ((forall x. p x) ==> (forall x. p x \\/ q x))\n by (smt ())", "val Apply.lem1 = Prims.unit\nlet lem1 = assert (x == x) by tau ()", "val ConstructiveLogic.ex10 = p: (_: Prims.int -> Prims.prop) -> Prims.unit\nlet ex10 (p : int -> prop) =\n assert ((forall x. p x) ==> (exists x. p x))\n by (let bf = implies_intro () in\n witness (`0);\n let bp0 = instantiate (binding_to_term bf) (`0) in\n hyp (binding_to_namedv bp0))", "val Canon.lem3 = a: Prims.int -> b: Prims.int -> c: Prims.int -> d: Prims.int -> e: Prims.int -> Prims.unit\nlet lem3 (a b c d e : int) =\n assert (c + (b + a) == b + (a + c))\n by check_canon ()", "val Effects.Def.st_laws = Prims.unit\nlet st_laws = monad_laws_via_eq st eq_st return_st bind_st", "val ConstructiveLogic.ex12 = p: (_: Prims.nat -> Prims.prop) -> q: (_: Prims.nat -> Prims.prop) -> Prims.unit\nlet ex12 (p q : nat -> prop) =\n assert ((forall x. p x /\\ q x) ==> (forall x. p x))\n by (smt ())", "val Effects.Def.exnst_laws = Prims.unit\nlet exnst_laws = monad_laws_via_eq exnst eq_exnst return_exnst bind_exnst", "val test2: Prims.unit -> Lemma (True)\nlet test2 () : Lemma (True) =\n let s1 = empty $:: 1 in\n let s2 = s1 $:: 2 in\n let s3 = s2 $:: 3 in\n let s4 = s3 $:: 4 in\n let s5 = s4 $:: 5 in\n assert (length s2 = 1 + length s1);\n assert (length s2 = 2);\n assert (length s5 = 5);\n assert (s5 $@ 1 == 2);\n assert (forall (s: seq int) (n: nat). n < 2 ==> (s2 $+ s) $@ n = s2 $@ n);\n assert (drop (drop s5 1) 2 == drop s5 3);\n assert (forall (v: int). length (s5 $:: v) = 6);\n assert (s3 $<= s5);\n assert (length (update s5 3 7) == 5);\n assert ((update s5 3 7) $@ 2 == 3);\n assert ((update s5 3 7) $@ 3 == 7);\n assert (length (slice s5 1 3) == 2)", "val Effects.Def.stexn_laws = Prims.unit\nlet stexn_laws = monad_laws_via_eq stexn eq_stexn return_stexn bind_stexn", "val ConstructiveLogic.ex13 = p: (_: Prims.nat -> Prims.prop) -> q: (_: Prims.nat -> Prims.prop) -> Prims.unit\nlet ex13 (p q : nat -> prop) =\n assert ((forall x. p x /\\ q x) ==> (exists x. p x \\/ q x))\n by (tadmit ())", "val ConstructiveLogic.ex14 = a: Type -> p: (_: a -> Prims.prop) -> q: (_: a -> Prims.prop) -> Prims.unit\nlet ex14 (a:Type) (p q : a -> prop) =\n assert ((forall x. p x ==> q x) ==> (forall x. p x) ==> (forall x. q x))\n by (smt ())", "val test: Prims.unit -> M unit (fun _ -> True) (fun _ _ s1 -> st_q s1)\nlet test () : M unit (fun _ -> True) (fun _ _ s1 -> st_q s1) =\n g ();\n f ();\n h ()", "val __c1: Prims.unit -> EFF int unit bool [EXN; RD; WR]\nlet __c1 () : EFF int unit bool [EXN;RD;WR] =\n put \"hello\";\n raise EE;\n coerce_st_to unit;// funny, but needed; or 'get ();'\n put true;\n 42", "val AlgWP.sanity_2 = Prims.unit\nlet sanity_2 = assert (forall s0 p s1. p ((), s0) ==> quotient_ro (write_wp s1) s0 p)", "val Effects.Def.morphism_lift_ex_exnst = Prims.unit\nlet morphism_lift_ex_exnst = \n morphism_laws_via_eq ex exnst eq_exnst\n\t\t return_ex bind_ex \n\t\t return_exnst bind_exnst \n\t\t lift_ex_exnst", "val Effects.Def.morphism_lift_st_exnst = Prims.unit\nlet morphism_lift_st_exnst = \n morphism_laws_via_eq st exnst eq_exnst\n\t\t return_st bind_st \n\t\t return_exnst bind_exnst \n\t\t lift_st_exnst", "val UserTactics.simple_equality_assertions = Prims.unit\nlet simple_equality_assertions =\n assert (forall (y:int). y==0 ==> 0==y)\n by rewrite_all_equalities ();\n assert(forall (x:int). x==0 ==> (forall (y:int). y==0 ==> x==y))\n by rewrite_all_equalities ();\n assert(forall (x:int). x==0 ==> (forall (y:int). y==0 ==> x==y) /\\ (forall (z:int). z==0 ==> x==z))\n by rewrite_all_equalities ()", "val AlgWP.sanity_1 = Prims.unit\nlet sanity_1 = assert (forall s0 p. quotient_ro read_wp s0 p <==> read_wp s0 p)", "val Canon.lem4 = a: Prims.int -> b: Prims.int -> c: Prims.int -> Prims.unit\nlet lem4 (a b c : int) =\n assert ((a+c+b)*(b+c+a) == a * a + (((b+c)*(c+b) + a * (b+c)) + c*a) + b*a)\n by check_canon ()", "val Canon.lem7 = a: Prims.int -> b: Prims.int -> c: Prims.int -> d: Prims.int -> Prims.unit\nlet lem7 (a b c d : int) =\n assert\n ((a+b+c+d)*(b+c+d+a) ==\n a * a\n + b * b\n + c * c\n + d * d\n + a * b + a * b\n + a * c + a * c\n + a * d + a * d\n + b * c + b * c\n + b * d + b * d\n + c * d + c * d)\n by check_canon ()", "val g: Prims.unit -> Tot unit\nlet g () : Tot unit =\n assert (False)", "val t2: Prims.unit -> Tac unit\nlet t2 () : Tac unit = fail \"always fail\"", "val Canon.test_neg2 = b: Prims.pos -> c: Prims.pos -> Prims.unit\nlet test_neg2 (b c : pos) =\n assert (b * (c-1) + b == b*c)\n by (canon ())", "val WhileReify.bidule2 = Prims.unit\nlet bidule2 = assert (interpret_exp (create 3) (AOp Plus (AVar (to_id 7)) (AInt 5)) = 8)", "val tau1: Prims.unit -> Tac unit\nlet tau1 () : Tac unit =\n prune \"\";\n FStar.Tactics.split ();\n (* rev part *)\n addns \"FStar.List\";\n addns \"Prims\";\n smt ();\n (* arithmetic part *)\n addns \"Prims\";\n smt ()", "val test: Prims.unit -> STT unit ((p `star` p) `star` p) (fun _ -> (p `star` p) `star` p)\nlet test () : STT unit (p `star` p `star` p) (fun _ -> p `star` p `star` p)\n = f 0; ()", "val Canon.lem8 = a: Prims.int -> b: Prims.int -> c: Prims.int -> d: Prims.int -> Prims.unit\nlet lem8 (a b c d : int) =\n assert_norm (1 * 1 == 1);\n assert ((a * b) * (c * d) == d * b * c * a)\n by check_canon ()", "val tac2: Prims.unit -> Tac unit\nlet tac2 () : Tac unit =\n apply_lemma (`test_lemma)", "val test: Prims.unit -> SteelT unit ((p `star` p) `star` p) (fun _ -> (p `star` p) `star` p)\nlet test () : SteelT unit (p `star` p `star` p) (fun _ -> p `star` p `star` p)\n = f 0; ()", "val test1: Prims.unit -> Lemma (True)\nlet test1 () : Lemma (True) =\n assert (length (empty #int) == 0);\n assert (forall (s: seq bool). length s == 0 ==> s == empty);\n assert (forall (v: list int). length (singleton v) == 1);\n assert (forall (s: seq int) (v: int). length (build s v) == 1 + length s);\n assert (forall (v: nat). index (singleton v) 0 == v);\n assert (~(contains empty 42));\n assert (forall (s: seq int). take s 0 == empty);\n assert (forall (s: seq int). drop s 0 == s);\n ()", "val example: Prims.unit -> SteelK unit emp (fun _ -> (q 1) `star` (q 2))\nlet example () : SteelK unit emp (fun _ -> q 1 `star` q 2) =\n let p1:thread (q 1) = kfork (fun () -> g 1) in\n let p2:thread (q 2) = kfork (fun () -> g 2) in\n kjoin p1;\n h();\n kjoin p2", "val LatticeEff.ite = p: Type0 -> q: Type0 -> r: Type0 -> Prims.logical\nlet ite (p q r : Type0) = (p ==> q) /\\ (~p ==> r)", "val test11: Prims.unit -> Tot unit\nlet test11 () : Tot unit =\n let _ : squash some_pred = proof_of_pred () in\n test10 ()", "val Logic.test = phi: Prims.logical -> psi: Prims.logical -> xi: Prims.logical -> Prims.unit\nlet test phi psi xi =\n assert (phi /\\ xi ==> psi \\/ phi) by tau ()", "val Effects.Def.morphism_lift_st_exn = Prims.unit\nlet morphism_lift_st_exn =\n morphism_laws_via_eq st stexn eq_stexn\n\t\t return_st bind_st \n\t\t return_stexn bind_stexn \n\t\t lift_st_stexn", "val test2: Prims.unit -> squash (2 == 1 + 1)\nlet test2 () : squash (2 == 1 + 1) =\n calc (==) {\n _;\n == { lem () }\n 1 + 1;\n }", "val Effects.Def.morphism_lift_ex_stexn = Prims.unit\nlet morphism_lift_ex_stexn = \n morphism_laws_via_eq ex stexn eq_stexn\n\t\t return_ex bind_ex \n\t\t return_stexn bind_stexn \n\t\t lift_ex_stexn", "val UserTactics.test_simpl = Prims.unit\nlet test_simpl =\n assert (True /\\ 1 == 1)\n by (let g = cur_goal () in\n (match term_as_formula g with\n | And _ _ -> ()\n | _ -> dump \"not a conjunction?\");\n simpl ();\n let g = cur_goal () in\n (match term_as_formula g with\n | True_ -> ()\n | _ -> dump (\"not true after simpl? \" ^ term_to_string g)))", "val equiv: Prims.unit -> FStar.Tactics.Tac unit\nlet equiv () : FStar.Tactics.Tac unit =\n let open FStar.Tactics in\n mapply (`vprop_equiv_refl_eq);\n smt()", "val raise: #a: _ -> Prims.unit -> EFF a (fun _ -> True) (fun s0 _ s1 -> s1 == s0) [EXN]\nlet raise #a () : EFF a (fun _ -> True) (fun s0 _ s1 -> s1 == s0) [EXN] =\n EFF?.reflect _raise", "val tauto: Prims.unit -> Tac unit\nlet rec tauto (): Tac unit =\n // dump \"[tauto]\";\n P.repeat' (fun () -> first #unit [\n P.gpm (fun (g: P.pm_goal (squash True)) ->\n trivial ()\n );\n P.gpm (fun (a b: Type0) (g: P.pm_goal (squash (a /\\ b))) ->\n split ()\n );\n P.gpm (fun (a b: Type0) (g: P.pm_goal (squash (a \\/ b))) ->\n (fun () -> left (); tauto ()) `or_else`\n (fun () -> right (); tauto ())\n );\n P.gpm (fun (a b: Type0) (g: P.pm_goal (squash (a ==> b))) ->\n P.implies_intro' ()\n );\n P.gpm (fun (a: Type0) (h: P.hyp a) (g: P.pm_goal (squash a)) ->\n P.exact_hyp a (binding_to_namedv h)\n );\n P.gpm (fun (a: Type0) (h: P.hyp a) (g: P.pm_goal a) ->\n P.exact_hyp' (binding_to_namedv h)\n );\n ]);\n qed ()", "val test: Prims.unit -> St unit\nlet test (): St unit =\n let r = HS.(new_region root) in\n let b = B.malloc HS.root 0ul 1ul in\n let l: t UInt32.t = create_in r in\n push l 0ul;\n push l 1ul;\n push l 2ul;\n B.upd b 0ul 1ul;\n let h0 = ST.get () in\n assert (v h0 l == [ 2ul; 1ul; 0ul ]);\n assert (B.deref h0 b == 1ul);\n ignore (pop l);\n let h1 = ST.get () in\n assert (v h1 l == [ 1ul; 0ul ]);\n assert (B.deref h0 b == 1ul);\n clear l;\n let h2 = ST.get () in\n assert (v h2 l == []);\n assert (B.deref h2 b == 1ul);\n free l;\n ()", "val test_2: Prims.unit -> ID int (as_pure_wp (fun p -> p 5))\nlet test_2 () : ID int (as_pure_wp (fun p -> p 5)) = 5", "val trans: Prims.unit -> Tac unit\nlet trans () : Tac unit = apply_lemma (`lem_trans)", "val trans: Prims.unit -> Tac unit\nlet trans () : Tac unit = apply_lemma (`lem_trans)", "val test6: Prims.unit -> Lemma (True)\nlet test6 () : Lemma (True) =\n assert (forall (ty: Type).{:pattern empty #ty} length (empty #ty) = 0);\n assert (forall (ty: Type) (s: seq ty).{:pattern length s} length s = 0 ==> s == empty);\n assert (forall (ty: Type) (v: ty).{:pattern length (singleton v)} length (singleton v) = 1);\n assert (forall (ty: Type) (s: seq ty) (v: ty).{:pattern build s v} length (build s v) = 1 + length s);\n assert (forall (ty: Type) (s0: seq ty) (s1: seq ty).{:pattern length (append s0 s1)}\n length (append s0 s1) = length s0 + length s1);\n assert (forall (ty: Type) (s: seq ty) (i: nat{i < length s}) (v: ty).{:pattern length (update s i v)}\n length (update s i v) = length s);\n assert (forall (ty: Type) (s: seq ty) (i: nat{i < length s}) (v: ty) (n: nat{n < length (update s i v)})\n .{:pattern index (update s i v) n}\n n < length s ==>\n (i = n ==> index (update s i v) n == v)\n /\\ (i <> n ==> index (update s i v) n == index s n));\n assert (forall (ty: Type) (s: seq ty) (x: ty).{:pattern contains s x}\n contains s x <==> (exists (i: nat).{:pattern index s i} i < length s /\\ index s i == x));\n assert (forall (ty: Type) (x: ty).{:pattern contains empty x} ~(contains empty x));\n assert (forall (ty: Type) (s: seq ty) (v: ty) (x: ty).{:pattern contains (build s v) x}\n contains (build s v) x <==> (v == x \\/ contains s x));\n assert (forall (ty: Type) (s: seq ty) (n: nat{n <= length s}) (x: ty).{:pattern contains (take s n) x}\n contains (take s n) x <==>\n (exists (i: nat).{:pattern index s i} i < n /\\ i < length s /\\ index s i == x));\n assert (forall (ty: Type) (s: seq ty) (n: nat{n <= length s}) (x: ty).{:pattern contains (drop s n) x}\n contains (drop s n) x <==>\n (exists (i: nat).{:pattern index s i} n <= i && i < length s /\\ index s i == x));\n assert (forall (ty: Type) (s0: seq ty) (s1: seq ty).{:pattern equal s0 s1}\n equal s0 s1 <==>\n length s0 == length s1 /\\\n (forall j.{:pattern index s0 j \\/ index s1 j}\n 0 <= j && j < length s0 ==> index s0 j == index s1 j));\n assert (forall (ty: Type) (a: seq ty) (b: seq ty).{:pattern equal a b} equal a b ==> a == b);\n assert (forall (ty: Type) (s0: seq ty) (s1: seq ty).{:pattern is_prefix s0 s1}\n is_prefix s0 s1 <==>\n length s0 <= length s1\n /\\ (forall (j: nat).{:pattern index s0 j \\/ index s1 j}\n j < length s0 ==> index s0 j == index s1 j));\n assert (forall (ty: Type) (s: seq ty) (n: nat).{:pattern length (take s n)}\n n <= length s ==> length (take s n) = n);\n assert (forall (ty: Type) (s: seq ty) (n: nat). {:pattern length (drop s n)}\n n <= length s ==> length (drop s n) = length s - n);\n assert (forall (ty: Type) (v: ty).{:pattern rank v} rank v == v);\n assert (forall (ty: Type) (s: seq ty) (i: nat).{:pattern rank (index s i)}\n i < length s ==> rank (index s i) << rank s);\n assert (forall (ty: Type) (s: seq ty) (i: nat).{:pattern rank (drop s i)}\n 0 < i && i <= length s ==> rank (drop s i) << rank s);\n assert (forall (ty: Type) (s: seq ty) (i: nat).{:pattern length (take s i)}\n i < length s ==> length (take s i) << length s);\n assert (forall (ty: Type) (s: seq ty) (i: nat) (j: nat).{:pattern length (append (take s i) (drop s j))}\n i < j && j <= length s ==> length (append (take s i) (drop s j)) << length s);\n assert (forall (ty: Type) (s: seq ty) (n: nat).{:pattern drop s n} n = 0 ==> drop s n == s);\n assert (forall (ty: Type) (s: seq ty) (n: nat).{:pattern take s n} n = 0 ==> take s n == empty);\n assert (forall (ty: Type) (s: seq ty) (m: nat) (n: nat).{:pattern drop (drop s m) n}\n m + n <= length s ==> drop (drop s m) n == drop s (m + n))", "val right: Prims.unit -> Tac unit\nlet right () : Tac unit =\n apply_lemma (`or_intro_2)", "val right: Prims.unit -> Tac unit\nlet right () : Tac unit =\n apply_lemma (`or_intro_2)", "val sample: Prims.unit -> Eff bool\nlet sample () : Eff bool\n= EFF?.reflect (fun (t, n, s) -> t n, n+1, s)", "val test: Prims.unit -> HoareST int (fun _ -> True) (fun _ r _ -> r == 1)\nlet test () : HoareST int (fun _ -> True) (fun _ r _ -> r == 1)\n= f 0", "val IfcReificationRegressionTest.bidule2 = Prims.unit\nlet bidule2 = assert (forall s0. x2 true s0 = x2 false s0)", "val IfcReificationRegressionTest.bidule1 = Prims.unit\nlet bidule1 = assert (forall s0. x1 true s0 = x1 false s0)", "val Canon.lem1 = Prims.unit\nlet lem1 =\n assert ((x + y) * (z + z) == 2 * z * (y + x))\n by canon ()", "val admit1: Prims.unit -> Tac unit\nlet admit1 () : Tac unit =\n tadmit ()", "val admit1: Prims.unit -> Tac unit\nlet admit1 () : Tac unit =\n tadmit ()", "val get: Prims.unit -> EFF int [RD]\nlet get () : EFF int [RD] =\n EFF?.reflect (fun s0 -> (Some s0, s0))", "val UserTactics.test_trivial = Prims.unit\nlet test_trivial =\n assert ((f A == 0) /\\ (f B == 1) /\\ (f C == 2) /\\ (f D == 3))\n by trivial ()", "val HoareST.main = Prims.unit\nlet main = FStar.IO.print_string \"Hello!\"", "val IfcReificationRegressionTest.bidule0 = Prims.unit\nlet bidule0 = assert (forall s0. x0 true s0 = x0 false s0)", "val NormLHS.tau = _: Prims.unit -> FStar.Tactics.Effect.Tac Prims.unit\nlet tau () = norm_lhs [delta; hnf; weak]; trefl ()", "val get: Prims.unit -> EFF int (fun _ -> True) (fun s0 y s1 -> s1 == s0 /\\ y == Some s0) [RD]\nlet get () : EFF int (fun _ -> True) (fun s0 y s1 -> s1 == s0 /\\ y == Some s0) [RD] by (compute (); dump\"\") =\n EFF?.reflect _get", "val test2: Prims.unit -> SteelT bool emp (fun _ -> emp)\nlet test2 () : SteelT bool emp (fun _ -> emp) =\n let r = malloc def_t 8sz in\n ghost_split r 4sz;\n let r1 = split_l r 4sz in\n let r2 = split_r r 4sz in\n change_equal_slprop (varray (split_l r 4sz)) (varray r1);\n change_equal_slprop (varray (split_r r 4sz)) (varray r2);\n let _ = mk 4s in\n let b = ptrdiff r2 r1 in\n ghost_join r1 r2 ();\n change_equal_slprop\n (varray (merge r1 r2))\n (varray r);\n // Free not supported in wasm\n drop (varray r);\n return (b = mk 4s)", "val proof: Prims.unit -> Lemma (related l r (phi ()) (phi ()))\nlet proof () : Lemma\n (related l r (phi ()) (phi ()))\n= \n let phi = phi () in\n let phi1 = gand phi (geq (gvar x Right) (gop op_Addition (gvar y Right) (gconst 1))) in\n let phi2 = gand phi1 (geq (gvar x Left) (gvar x Right)) in\n hyp;\n assert (related (assign x asx_e) skip phi1 phi2); // by r_dassl\n lemma_included_helper (); //prove the precondition of r_ass\n assert (related (assign i asi_e) (assign i asi_e) phi2 phi2); // by r_ass\n d_su1' (assign x asx_e) (assign i asi_e) (assign i asi_e) phi1 phi2 phi2;\n r_while cond cond (seq (assign x asx_e) (assign i asi_e)) (assign i asi_e) phi1;\n assert (related skip (assign x asx_e) phi phi1); // by r_dassr\n assert (related l (while cond (assign i asi_e)) phi1 phi); // by d_sub\n d_su1'_flip l (assign x asx_e) (while cond (assign i asi_e)) phi phi1 phi", "val example4: Prims.unit -> SteelK (ref int) emp (fun r -> pts_to r full_perm 2)\nlet example4 () : SteelK (ref int) emp (fun r -> pts_to r full_perm 2) =\n let x = alloc_pt 0 in\n let y = alloc_pt 1 in\n let p1:thread (pts_to x full_perm 1) = kfork (fun _ -> write_pt #_ #0 x 1) in\n let p2:thread emp = kfork (fun _ -> free_pt #_ #1 y) in\n kjoin p1;\n write_pt #_ #1 x 2;\n kjoin p2;\n x", "val Arith.lem2 = x: Prims.int -> Prims.unit\nlet lem2 (x:int) =\n assert (List.rev [1;2;3;4] == [4;3;2;1] /\\ op_Multiply 2 (x + 3) == 6 + (op_Multiply 3 x) - x)\n by split_arith ()", "val RW.ite = p: Type0 -> q: Type0 -> r: Type0 -> Prims.logical\nlet ite (p q r : Type0) = (p ==> q) /\\ (~p ==> r)", "val test1: Prims.unit -> squash (2 == 1 + 1)\nlet test1 () : squash (2 == 1 + 1) =\n calc (==) {\n 2;\n == { lem () }\n _;\n }", "val CanonDeep.lem0 = Prims.unit\nlet lem0 = assert (x * (y * z) == (x * y) * z) by check_canon_deep ()", "val Bane.Test.test = Prims.unit\nlet test =\n assert for_you by Bane.Lib.mytac ()", "val tac: Prims.unit -> Tac unit\nlet rec tac () : Tac unit =\n if List.length (goals ()) = 0\n then ()\n else if pick_next (FStar.List.length (goals ()))\n then begin\n or_else (fun _ -> rewrite_eqs_from_context (); norm []; trefl ()) (fun _ -> assumption ());\n tac ()\n end\n else begin\n rewrite_eqs_from_context ();\n norm [];\n trefl ();\n tac ()\n end", "val tac: Prims.unit -> Tac unit\nlet tac () : Tac unit =\n dump \"now\"", "val l: Prims.unit -> int\nlet l () : int =\n reify (test_f ())", "val l: Prims.unit -> int\nlet l () : int = reify (test_f ()) (fun _ -> True) ()", "val l: Prims.unit -> int\nlet l () : int = snd (reify (test_f ())) (fun _ -> True) ()", "val l: Prims.unit -> int\nlet l () : int = reify (test_f ()) ()", "val l: Prims.unit -> int\nlet l () : int = reify (test_f ()) (fun _ -> True) ()", "val Intro.test_add = Prims.unit\nlet test_add = assert (add3 1 2 3 == 6)", "val STLC.Infer.bar_s = STLC.Infer.stlc_exp Prims.unit\nlet bar_s = (ELam () (ELam () (EBVar 1)))", "val raise: #a: _ -> Prims.unit -> EFF a [EXN]\nlet raise #a () : EFF a [EXN] =\n EFF?.reflect (fun s0 -> (None, s0))", "val WhileReify.bidule = Prims.unit\nlet bidule = assert (reify (interpret_exp_st (AOp Plus (AVar (to_id 7)) (AInt 5))) (create 3) = 8)", "val test: Prims.unit -> LV unit (fun _ -> True) (fun _ _ _ -> True)\nlet test () : LV unit (fun _ -> True) (fun _ _ _ -> True) =\n let n1 = create nat 0 in\n let n2 = create bool true in\n let n3 = create unit () in\n\n\n let v1: nat = read n1 in\n assert (v1 == 0)", "val Steel.FractionalAnchoredPreorder.perm_ok = a: Steel.FractionalAnchoredPreorder.avalue s -> Prims.prop\nlet perm_ok #v #p #s (a:avalue #v #p s)\n = perm_opt_composable (fst (avalue_perm a)) None", "val Canon.lem2 = x: Prims.int -> Prims.unit\nlet lem2 (x : int) =\n assert (2 + x + 3 * 8 == x + 26)\n by check_canon ()", "val SigeltOpts.sp1 = Prims.unit\nlet sp1 = assert (List.length [1] == 1)", "val PulseCore.Action.thunk = p: PulseCore.InstantiatedSemantics.slprop -> _: Prims.unit -> PulseCore.InstantiatedSemantics.slprop\nlet thunk (p:slprop) = fun (_:unit) -> p", "val equiv (p1 p2:slprop u#a) : prop\nlet equiv p1 p2 = forall m. interp p1 m <==> interp p2 m", "val equiv (p1 p2:slprop u#a) : prop\nlet equiv p1 p2 = forall m. interp p1 m <==> interp p2 m", "val assumption: Prims.unit -> Tac unit\nlet assumption () : Tac unit =\n __assumption_aux (cur_binders ())", "val assumption: Prims.unit -> Tac unit\nlet assumption () : Tac unit =\n __assumption_aux (cur_vars ())" ], "closest_src": [ { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex2" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex4" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex5" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex3" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex8" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex7" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex6" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex1_qed" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex1" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex9" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.ex_laws" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex11" }, { "project_name": "FStar", "file_name": "Apply.fst", "name": "Apply.lem1" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex10" }, { "project_name": "FStar", "file_name": "Canon.fst", "name": "Canon.lem3" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.st_laws" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex12" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.exnst_laws" }, { "project_name": "FStar", "file_name": "Tests.fst", "name": "Tests.test2" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.stexn_laws" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex13" }, { "project_name": "FStar", "file_name": "ConstructiveLogic.fst", "name": "ConstructiveLogic.ex14" }, { "project_name": "FStar", "file_name": "HoareSTFree.fst", "name": "HoareSTFree.test" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.__c1" }, { "project_name": "FStar", "file_name": "AlgWP.fst", "name": "AlgWP.sanity_2" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.morphism_lift_ex_exnst" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.morphism_lift_st_exnst" }, { "project_name": "FStar", "file_name": "UserTactics.fst", "name": "UserTactics.simple_equality_assertions" }, { "project_name": "FStar", "file_name": "AlgWP.fst", "name": "AlgWP.sanity_1" }, { "project_name": "FStar", "file_name": "Canon.fst", "name": "Canon.lem4" }, { "project_name": "FStar", "file_name": "Canon.fst", "name": "Canon.lem7" }, { "project_name": "FStar", "file_name": "HandleSmtGoal.fst", "name": "HandleSmtGoal.g" }, { "project_name": "FStar", "file_name": "LocalState.fst", "name": "LocalState.t2" }, { "project_name": "FStar", "file_name": "Canon.fst", "name": "Canon.test_neg2" }, { "project_name": "FStar", "file_name": "WhileReify.fst", "name": "WhileReify.bidule2" }, { "project_name": "FStar", "file_name": "Arith.fst", "name": "Arith.tau1" }, { "project_name": "steel", "file_name": "SteelSTFramingTestSuite.fst", "name": "SteelSTFramingTestSuite.test" }, { "project_name": "FStar", "file_name": "Canon.fst", "name": "Canon.lem8" }, { "project_name": "FStar", "file_name": "HandleSmtGoal.fst", "name": "HandleSmtGoal.tac2" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test" }, { "project_name": "FStar", "file_name": "Tests.fst", "name": "Tests.test1" }, { "project_name": "steel", "file_name": "Steel.Primitive.ForkJoin.Unix.fst", "name": "Steel.Primitive.ForkJoin.Unix.example" }, { "project_name": "FStar", "file_name": "LatticeEff.fst", "name": "LatticeEff.ite" }, { "project_name": "FStar", "file_name": "TestHoareST.fst", "name": "TestHoareST.test11" }, { "project_name": "FStar", "file_name": "Logic.fst", "name": "Logic.test" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.morphism_lift_st_exn" }, { "project_name": "FStar", "file_name": "CalcInference.fst", "name": "CalcInference.test2" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.morphism_lift_ex_stexn" }, { "project_name": "FStar", "file_name": "UserTactics.fst", "name": "UserTactics.test_simpl" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherArray.fst", "name": "Pulse.Lib.HigherArray.equiv" }, { "project_name": "FStar", "file_name": "LatticeSpec.fst", "name": "LatticeSpec.raise" }, { "project_name": "FStar", "file_name": "Tautology.fst", "name": "Tautology.tauto" }, { "project_name": "karamel", "file_name": "LowStar.Lib.LinkedList2.fst", "name": "LowStar.Lib.LinkedList2.test" }, { "project_name": "FStar", "file_name": "ID2.fst", "name": "ID2.test_2" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.trans" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.trans" }, { "project_name": "FStar", "file_name": "Tests.fst", "name": "Tests.test6" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Logic.fst", "name": "FStar.Tactics.V1.Logic.right" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Logic.fst", "name": "FStar.Tactics.V2.Logic.right" }, { "project_name": "steel", "file_name": "MParIndex.fst", "name": "MParIndex.sample" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.test" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.bidule2" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.bidule1" }, { "project_name": "FStar", "file_name": "Canon.fst", "name": "Canon.lem1" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.admit1" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.admit1" }, { "project_name": "FStar", "file_name": "Lattice.fst", "name": "Lattice.get" }, { "project_name": "FStar", "file_name": "UserTactics.fst", "name": "UserTactics.test_trivial" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.main" }, { "project_name": "FStar", "file_name": "IfcReificationRegressionTest.fst", "name": "IfcReificationRegressionTest.bidule0" }, { "project_name": "FStar", "file_name": "NormLHS.fst", "name": "NormLHS.tau" }, { "project_name": "FStar", "file_name": "LatticeSpec.fst", "name": "LatticeSpec.get" }, { "project_name": "steel", "file_name": "Wasm11.fst", "name": "Wasm11.test2" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.Examples2.fst", "name": "Benton2004.RHL.Examples2.proof" }, { "project_name": "steel", "file_name": "Steel.Primitive.ForkJoin.Unix.fst", "name": "Steel.Primitive.ForkJoin.Unix.example4" }, { "project_name": "FStar", "file_name": "Arith.fst", "name": "Arith.lem2" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.ite" }, { "project_name": "FStar", "file_name": "CalcInference.fst", "name": "CalcInference.test1" }, { "project_name": "FStar", "file_name": "CanonDeep.fst", "name": "CanonDeep.lem0" }, { "project_name": "FStar", "file_name": "Bane.Test.fst", "name": "Bane.Test.test" }, { "project_name": "FStar", "file_name": "LowParseWriters.fsti", "name": "LowParseWriters.tac" }, { "project_name": "FStar", "file_name": "HandleSmtGoal.fst", "name": "HandleSmtGoal.tac" }, { "project_name": "FStar", "file_name": "ID3.fst", "name": "ID3.l" }, { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.l" }, { "project_name": "FStar", "file_name": "ID4.fst", "name": "ID4.l" }, { "project_name": "FStar", "file_name": "ID2.fst", "name": "ID2.l" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.l" }, { "project_name": "FStar", "file_name": "Intro.fst", "name": "Intro.test_add" }, { "project_name": "FStar", "file_name": "STLC.Infer.fst", "name": "STLC.Infer.bar_s" }, { "project_name": "FStar", "file_name": "Lattice.fst", "name": "Lattice.raise" }, { "project_name": "FStar", "file_name": "WhileReify.fst", "name": "WhileReify.bidule" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.test" }, { "project_name": "steel", "file_name": "Steel.FractionalAnchoredPreorder.fst", "name": "Steel.FractionalAnchoredPreorder.perm_ok" }, { "project_name": "FStar", "file_name": "Canon.fst", "name": "Canon.lem2" }, { "project_name": "FStar", "file_name": "SigeltOpts.fst", "name": "SigeltOpts.sp1" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.thunk" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.equiv" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.equiv" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.assumption" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.assumption" } ], "selected_premises": [ "Automation.triv", "Automation.ea1", "FStar.Pervasives.reveal_opaque", "FStar.Tactics.Effect.raise", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity", "FStar.Tactics.Types.issues", "FStar.Tactics.Effect.get", "FStar.Pervasives.dsnd", "FStar.Pervasives.dfst", "FStar.Monotonic.Pure.intro_pure_wp_monotonicity", "FStar.Monotonic.Pure.elim_pure_wp_monotonicity_forall", "FStar.Tactics.Effect.tactic", "FStar.Pervasives.ex_pre", "FStar.Pervasives.ex_stronger", "FStar.Pervasives.ex_post'", "FStar.Pervasives.ex_bind_wp", "FStar.Pervasives.ex_return", "Prims.auto_squash", "Prims.op_Hat", "FStar.Pervasives.ex_post", "FStar.Monotonic.Pure.is_monotonic", "FStar.Pervasives.pure_ite_wp", "FStar.Pervasives.st_bind_wp", "FStar.Pervasives.ex_close_wp", "FStar.Monotonic.Pure.as_pure_wp", "FStar.Pervasives.ex_wp", "FStar.Pervasives.ex_trivial", "FStar.Pervasives.pure_close_wp", "FStar.Tactics.Effect.tac_close", "FStar.Tactics.Effect.tac_bind_wp", "Prims.pow2", "FStar.Pervasives.pure_bind_wp", "FStar.Pervasives.st_post_h", "FStar.Issue.mk_issue", "FStar.Tactics.Effect.tac_if_then_else_wp", "FStar.Pervasives.ex_ite_wp", "Prims.returnM", "FStar.Tactics.Effect.tac_repr", "Prims.subtype_of", "FStar.Tactics.Effect.tac_wp_monotonic", "FStar.Pervasives.ex_if_then_else", "FStar.Pervasives.pure_return", "FStar.Tactics.Effect.tac_return", "FStar.Tactics.Effect.tac_wp_compact", "FStar.Pervasives.coerce_eq", "FStar.Pervasives.id", "FStar.Tactics.Effect.lift_div_tac", "FStar.Pervasives.all_close_wp", "Prims.l_True", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.all_bind_wp", "FStar.Tactics.Effect.tac_return_wp", "FStar.Tactics.Effect.lift_div_tac_wp", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.lift_div_exn", "FStar.Pervasives.all_stronger", "FStar.Tactics.Effect.tac", "FStar.Pervasives.st_pre_h", "FStar.Pervasives.st_return", "FStar.Monotonic.Pure.elim_pure", "Prims.pure_trivial", "Prims.pure_post", "FStar.Pervasives.st_ite_wp", "Prims.pure_stronger", "FStar.Pervasives.all_ite_wp", "FStar.Issue.issue_level_string", "Prims.pure_pre", "FStar.Pervasives.st_wp_h", "FStar.Pervasives.all_post_h", "FStar.Pervasives.all_post_h'", "FStar.Tactics.Effect.tac_subcomp", "Prims.pure_wp_monotonic", "Prims.pure_wp'", "Prims.as_requires", "FStar.Pervasives.div_hoare_to_wp", "FStar.Pervasives.trivial_pure_post", "Prims.__cache_version_number__", "FStar.Pervasives.all_if_then_else", "FStar.Pervasives.pure_null_wp", "FStar.Pervasives.st_trivial", "FStar.Pervasives.st_stronger", "FStar.Pervasives.all_trivial", "FStar.Pervasives.all_wp_h", "Prims.pure_post'", "FStar.Pervasives.all_return", "FStar.Pervasives.all_pre_h", "Prims.min", "Prims.pure_wp", "FStar.Pervasives.st_if_then_else", "Prims.pure_wp_monotonic0", "Prims.l_False", "Prims.purewp_id", "Prims.as_ensures", "Prims.abs" ], "source_upto_this": "module Automation\n\nopen FStar.Tactics.V2\n\n(*\nAs you have seen, doing constructive proofs by hand can get tedious. We\ncan instead write automated procedures for some classes of proofs, that\nwe can call over and over again when we need them, which is the main\nmotivation for tactic engines in other languages.\n\nSome simple procedures are implemented in the standard library. For\ninstance, `assumption` tries to solve the current goal from the\nhypotheses in the context. Let's first write a tactic that introduces\nall implications and then calls `assumption`. (You can look at the\ndefinition of `assumption` in FStar.Tactics.Derived.)\n*)\n\n(* Exercise: what does `l_intros` do? Look at its definition to find out. *)\n\nlet triv () : Tac unit =\n let _ = l_intros () in\n assumption ();\n qed ()\n\n(* Now we can call it on different goals *)\n\nlet ea1 (p q r : prop) =\n assert (p ==> q ==> r ==> p)\n by (triv ())\n", "sketch": [ "Step 1: The definition `ea2` is about proving a logical implication involving three propositions `p`, `q`, and `r`.\nStep 2: To implement this, we will assert the goal `p ==> q ==> r ==> q` and use the `triv` tactic, which introduces all implications and then tries to solve the goal using the `assumption` tactic.", "Step 1: The definition `ea2` is about proving a logical implication involving three propositions `p`, `q`, and `r`.\nStep 2: To implement this, we will assert the goal `p ==> q ==> r ==> q` and use the `triv` tactic to automatically introduce the implications and solve the goal using the assumptions.", "Step 1: The definition `ea2` is about proving a logical statement involving three propositions `p`, `q`, and `r`.\nStep 2: To implement this, we will assert the statement `(p ==> q ==> r ==> q)` and use the `triv` tactic to automatically introduce all implications and solve the goal using the `assumption` tactic.", "Step 1: The definition `ea2` is about proving a logical implication involving three propositions `p`, `q`, and `r`.\nStep 2: To implement this, we will assert the goal `p ==> q ==> r ==> q` and use the `triv` tactic to automatically introduce the implications and solve the goal using the `assumption` tactic.", "Step 1: The definition `ea2` is about proving a logical implication involving three propositions `p`, `q`, and `r`.\nStep 2: To implement `ea2`, we will assert the goal `p ==> q ==> r ==> q` and use the `triv` tactic to automatically introduce the implications and solve the goal using the assumptions.", "Step 1: The definition `ea2` is about proving a logical implication involving three propositions `p`, `q`, and `r`.\nStep 2: To implement this, we will assert the goal `p ==> q ==> r ==> q` and use the `triv` tactic to automatically introduce the implications and solve the goal using the `assumption` tactic.", "Step 1: The definition `ea2` is about proving a logical implication involving three propositions `p`, `q`, and `r`.\nStep 2: To implement this, we will assert the goal `p ==> q ==> r ==> q` and use the `triv` tactic to automatically introduce implications and solve the goal using assumptions.", "Step 1: The definition `ea2` is about proving a logical implication involving three propositions `p`, `q`, and `r`.\nStep 2: To implement this, we will assert the implication `p ==> q ==> r ==> q` and use the `triv` tactic to automatically handle the proof.", "Step 1: The definition `ea2` is about proving that given three propositions `p`, `q`, and `r`, the implication `p ==> q ==> r ==> q` holds.\nStep 2: To implement this, we will use the `triv` tactic defined earlier, which introduces all implications and then tries to solve the goal using the `assumption` tactic.", "Step 1: The definition `ea2` is about proving a logical implication involving three propositions `p`, `q`, and `r`.\nStep 2: To implement this, we will use the `triv` tactic defined earlier, which introduces all implications and then calls `assumption` to solve the goal. We will assert the goal `p ==> q ==> r ==> q` and use the `triv` tactic to prove it." ], "generated_solution": [ "let ea2 (p q r : prop) =\n assert (p ==> q ==> r ==> q)\n by (triv ())", "let ea2 (p q r : prop) =\n assert (p ==> q ==> r ==> q)\n by (triv ())", "let ea2 (p q r : prop) =\n assert (p ==> q ==> r ==> q)\n by (triv ())", "let ea2 (p q r : prop) =\n assert (p ==> q ==> r ==> q)\n by (triv ())", "let ea2 (p q r : prop) =\n assert (p ==> q ==> r ==> q)\n by (triv ())", "let ea2 (p q r : prop) =\n assert (p ==> q ==> r ==> q)\n by (triv ())", "let ea2 (p q r : prop) =\n assert (p ==> q ==> r ==> q)\n by (triv ())", "let ea2 (p q r : prop) =\n assert (p ==> q ==> r ==> q)\n by (triv ())", "let ea2 (p q r : prop) =\n assert (p ==> q ==> r ==> q)\n by (triv ())", "let ea2 (p q r : prop) =\n assert (p ==> q ==> r ==> q)\n by (triv ())" ] }, { "file_name": "OPLSS2021.IFC.fst", "name": "OPLSS2021.IFC.test14", "opens_and_abbrevs": [ { "open": "FStar.Calc" }, { "open": "FStar.Map" }, { "open": "FStar.Set" }, { "open": "FStar.List.Tot" }, { "open": "OPLSS2021" }, { "open": "OPLSS2021" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val test14: Prims.unit\n -> IST unit\n (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n ([cr0, cw1; union cr0 cr1, cw2])", "source_definition": "let test14 ()\n : IST unit (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n ([cr0, cw1;\n union cr0 cr1, cw2])\n = (c0 (); c1()); c2()", "source_range": { "start_line": 690, "start_col": 0, "end_line": 695, "end_col": 23 }, "interleaved": false, "definition": "fun _ ->\n ((OPLSS2021.IFC.c0 ();\n OPLSS2021.IFC.c1 ());\n OPLSS2021.IFC.c2 ())\n <:\n OPLSS2021.IFC.IST Prims.unit", "effect": "OPLSS2021.IFC.IST", "effect_flags": [], "mutual_with": [], "premises": [ "Prims.unit", "OPLSS2021.IFC.c2", "OPLSS2021.IFC.c1", "OPLSS2021.IFC.c0", "OPLSS2021.IFC.union", "OPLSS2021.IFC.cw0", "OPLSS2021.IFC.cw1", "OPLSS2021.IFC.cw2", "OPLSS2021.IFC.cr0", "OPLSS2021.IFC.cr1", "OPLSS2021.IFC.cr2", "Prims.Cons", "OPLSS2021.IFC.flow", "FStar.Pervasives.Native.Mktuple2", "OPLSS2021.IFC.label", "Prims.Nil" ], "proof_features": [], "is_simple_lemma": false, "is_div": true, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "_: Prims.unit -> OPLSS2021.IFC.IST Prims.unit", "prompt": "let test14 ()\n : IST unit\n (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n ([cr0, cw1; union cr0 cr1, cw2]) =\n ", "expected_response": "(c0 ();\n c1 ());\nc2 ()", "source": { "project_name": "FStar", "file_name": "examples/oplss2021/OPLSS2021.IFC.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "OPLSS2021.IFC.fst", "checked_file": "dataset/OPLSS2021.IFC.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Map.fsti.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Calc.fsti.checked" ] }, "definitions_in_context": [ "let loc = int", "let store = m:Map.t loc int{forall l. contains m l}", "let sel (s:store) (l:loc) : int = Map.sel s l", "let upd (s:store) (l:loc) (x:int) : store = Map.upd s l x", "let label = Set.set loc", "let label_inclusion (l0 l1:label) = Set.subset l0 l1", "let bot : label = Set.empty", "let single (l:loc) : label = Set.singleton l", "let union (l0 l1:label) = Set.union l0 l1", "let comp a = store -> a & store", "let havoc s l x = upd s l x", "let writes_ok #a (f:comp a) (writes:Set.set loc) =\n forall (l:loc). ~(Set.mem l writes) ==>\n (forall (s0:store).\n let x1, s0' = f s0 in\n sel s0 l == sel s0' l)", "let does_not_read_loc_v #a (f:comp a) (l:loc) (s0:store) v =\n let s0' = havoc s0 l v in //s0 and s0' agree except on l\n let x1, s1 = f s0 in\n let x1', s1' = f s0' in // run f twice, once on s0, once on s0'\n x1 == x1' /\\ //result does not depend on l\n (forall l'. l' <> l ==> //for every location l' not equal to l\n sel s1 l' == sel s1' l') /\\ //its value in the two states is the same\n (sel s1 l == sel s1' l \\/ //and l is itself may be written, in which case its value is the same in both final states\n //or its not, but then its values in the initial and final states are the same in both runs\n (sel s1 l == sel s0 l /\\\n sel s1' l == sel s0' l))", "let does_not_read_loc #a (f:comp a) (l:loc) (s0:store) =\n forall v. does_not_read_loc_v f l s0 v", "let reads_ok #a (f:comp a) (reads:label) =\n forall (l:loc) (s:store). ~(Set.mem l reads) ==> does_not_read_loc f l s", "let flow = label & label", "let flows = list flow", "let has_flow_1 (from to:loc) (f:flow) = from `Set.mem` fst f /\\ to `Set.mem` snd f", "let has_flow (from to:loc) (fs:flows) = exists rs. rs `List.Tot.memP` fs /\\ has_flow_1 from to rs", "let no_leakage_k #a (f:comp a) (from to:loc) (k:int) =\n forall s0.{:pattern (havoc s0 from k)}\n sel (snd (f s0)) to == sel (snd (f (havoc s0 from k))) to", "let no_leakage #a (f:comp a) (from to:loc) = forall k. no_leakage_k f from to k", "let respects_flows #a (f:comp a) (fs:flows) =\n forall from to. {:pattern (no_leakage f from to)} ~(has_flow from to fs) /\\ from<>to ==> no_leakage f from to", "let ist a (writes:label) (reads:label) (fs:flows) =\n f:comp a {\n reads_ok f reads /\\\n writes_ok f writes /\\\n respects_flows f fs\n }", "let iread (l:loc) : ist int bot (single l) [] = fun s -> sel s l, s", "let iwrite (l:loc) (x:int) : ist unit (single l) bot [] = fun s -> (), upd s l x", "let return (a:Type) (x:a) : ist a bot bot [] = fun s -> x,s", "let add_source (r:label) (fs:flows) : flows = List.Tot.map (fun (r0, w0) -> union r r0, w0) fs", "let add_sink (w:label) (fs:flows) : flows = List.Tot.map (fun (r0, w0) -> r0, union w w0) fs", "let flows_included_in (fs0 fs1:flows) =\n forall f0. f0 `List.Tot.memP` fs0 ==>\n (forall from to. has_flow_1 from to f0 /\\ from <> to ==> (exists f1. f1 `List.Tot.memP` fs1 /\\ has_flow_1 from to f1))", "let flows_equiv (fs0 fs1:flows) = fs0 `flows_included_in` fs1 /\\ fs1 `flows_included_in` fs0", "let flows_equiv_refl fs\n : Lemma (fs `flows_equiv` fs)\n = ()", "let flows_equiv_trans fs0 fs1 fs2\n : Lemma (fs0 `flows_equiv` fs1 /\\ fs1 `flows_equiv` fs2 ==> fs0 `flows_equiv` fs2)\n = ()", "let flows_included_in_union_distr_dest (a b c:label)\n : Lemma (flows_equiv [a, union b c] [a, b; a, c])\n = ()", "let flows_included_in_union_distr_src (a b c:label)\n : Lemma (flows_equiv [union a b, c] [a, c; b, c])\n = ()", "let flows_included_in_union (a b c:label)\n : Lemma (flows_equiv ([a, union b c; union a b, c])\n ([a, b; union a b, c]))\n = ()", "let bind_comp (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : comp b\n = fun s0 -> let v, s1 = x s0 in y v s1", "let bind_comp_reads_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (reads_ok (bind_comp x y) (union r0 r1))\n = let f = bind_comp x y in\n let reads = union r0 r1 in\n let f_reads_ok (l:loc) (s0:store)\n : Lemma (requires (~(Set.mem l reads)))\n (ensures (does_not_read_loc f l s0))\n [SMTPat (does_not_read_loc f l s0)]\n = let aux (k:_)\n : Lemma (ensures (does_not_read_loc_v f l s0 k))\n [SMTPat (does_not_read_loc_v f l s0 k)]\n = let v, s1 = x s0 in\n let v', s1' = x (havoc s0 l k) in\n assert (does_not_read_loc x l s0);\n assert (does_not_read_loc_v x l s0 k);\n assert (v == v');\n assert (does_not_read_loc (y v) l s1);\n let u, s2 = y v s1 in\n let u', s2' = y v s1' in\n assert (forall l'. l' <> l ==> sel s1 l' == sel s1' l');\n if sel s1 l = sel s1' l\n then (assert (forall l. sel s1 l == sel s1' l);\n assert (Map.equal s1 s1'))\n else (assert (sel s1 l == sel s0 l /\\\n sel (havoc s0 l k) l == sel s1' l);\n assert (Map.equal s1' (havoc s1 l k)))\n in\n ()\n in\n ()", "let bind_comp_writes_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (writes_ok (bind_comp x y) (union w0 w1))\n = ()", "let rec memP_append_or (#a:Type) (x:a) (l0 l1:list a)\n : Lemma (ensures (List.Tot.memP x (l0 @ l1) <==>\n (List.Tot.memP x l0 \\/ List.Tot.memP x l1)))\n (decreases l0)\n = match l0 with\n | [] -> ()\n | _::tl -> memP_append_or x tl l1", "let has_flow_append (from to:loc) (fs fs':flows)\n : Lemma (has_flow from to fs ==>\n has_flow from to (fs @ fs') /\\\n has_flow from to (fs' @ fs))\n = let rec aux (rs:_)\n : Lemma (requires\n List.Tot.memP rs fs)\n (ensures\n List.Tot.memP rs (fs @ fs') /\\\n List.Tot.memP rs (fs' @ fs))\n [SMTPat (List.Tot.memP rs fs)]\n = memP_append_or rs fs fs';\n memP_append_or rs fs' fs\n in\n ()", "let elim_has_flow_seq (from to:loc)\n (r0 r1 w1:label)\n (fs0 fs1:flows)\n : Lemma (requires (~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1)))))\n (ensures (~(has_flow from to fs0) /\\\n (~(Set.mem from r0) \\/ ~(Set.mem to w1)) /\\\n ~(has_flow from to (add_source r0 fs1))))\n = assert (add_source r0 ((bot, w1)::fs1) ==\n (Set.union r0 bot, w1)::add_source r0 fs1);\n assert (Set.union r0 bot `Set.equal` r0);\n has_flow_append from to fs0 ((r0, w1)::add_source r0 fs1);\n assert (~(has_flow from to fs0));\n has_flow_append from to ((r0, w1)::add_source r0 fs1) fs0;\n assert (~(has_flow from to (((r0, w1)::add_source r0 fs1))));\n assert ((r0, w1)::add_source r0 fs1 ==\n [r0, w1] @ add_source r0 fs1);\n has_flow_append from from [r0, w1] (add_source r0 fs1)", "let rec add_source_monotonic (from to:loc) (r:label) (fs:flows)\n : Lemma (has_flow from to fs ==> has_flow from to (add_source r fs))\n = match fs with\n | [] -> ()\n | _::tl -> add_source_monotonic from to r tl", "let has_flow_soundness #a #r #w #fs (f:ist a r w fs)\n (from to:loc) (s:store) (k:int)\n : Lemma (requires\n (let x, s1 = f s in\n let _, s1' = f (havoc s from k) in\n from <> to /\\\n sel s1 to <> sel s1' to))\n (ensures has_flow from to fs)\n = let aux ()\n : Lemma (requires (~(has_flow from to fs)))\n (ensures False)\n [SMTPat ()]\n = assert (respects_flows f fs);\n assert (no_leakage f from to)\n in\n ()", "let bind_comp_no_leakage (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n (from to:loc)\n (s0:store) (k:_)\n : Lemma\n (requires from <> to /\\ ~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1))))\n (ensures (let f = bind_comp x y in\n let s0' = havoc s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to))\n = let f = bind_comp x y in\n assert (reads_ok x r0);\n let s0' = havoc s0 from k in\n let _, s2f = f s0 in\n let _, s2f' = f s0' in\n let flows = (fs0 @ add_source r0 ((r1, w1)::fs1)) in\n let v0, s1 = x s0 in\n let v0', s1' = x s0' in\n elim_has_flow_seq from to r0 r1 w1 fs0 fs1;\n assert (~(has_flow from to fs0));\n assert (respects_flows x fs0);\n assert (no_leakage x from to);\n assert (sel s1 to == sel s1' to);\n let _, s2 = y v0 s1 in\n let _, s2' = y v0' s1' in\n assert (s2 == s2f);\n assert (s2' == s2f');\n //Given: (from not-in r0 U r1) \\/ (to not-in w1)\n //suppose (from in r0) \\/ (from in r1)\n // them to not-in w1\n //suppose (from not-in r0 U r1)\n //then v0 = v0'\n // s1' = havoc from s1 k\n // s2 to = s2' to\n if Set.mem to w1\n then begin\n assert (~(Set.mem from r0));\n assert (reads_ok x r0);\n assert (does_not_read_loc x from s0);\n assert (does_not_read_loc_v x from s0 k);\n assert (v0 == v0');\n assert (forall l. l <> from ==> sel s1 l == sel s1' l);\n assert (Map.equal s1' (havoc s1 from k) \\/ Map.equal s1' s1);\n if (sel s1 from = sel s1' from)\n then begin\n assert (Map.equal s1 s1')\n end\n else begin\n assert (Map.equal s1' (havoc s1 from k));\n assert (reads_ok (y v0) r1);\n if (sel s2 to = sel s2' to)\n then ()\n else begin\n assert (sel s2 to <> sel s1 to \\/ sel s2' to <> sel s1' to);\n has_flow_soundness (y v0) from to s1 k;\n assert (has_flow from to fs1);\n add_source_monotonic from to r0 fs1\n //y reads from and writes to, so (from, to) should be in fs1\n //so, we should get a contradiction\n end\n end\n end\n else //to is not in w1, so y does not write it\n ()", "let bind_comp_flows_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (respects_flows (bind_comp x y) (fs0 @ add_source r0 ((bot, w1)::fs1)))\n = let f = bind_comp x y in\n let flows = (fs0 @ add_source r0 ((bot, w1)::fs1)) in\n let respects_flows_lemma (from to:loc)\n : Lemma (requires from <> to /\\ ~(has_flow from to flows))\n (ensures no_leakage f from to)\n [SMTPat (no_leakage f from to)]\n = let aux (s0:store) (k:_)\n : Lemma (let s0' = havoc s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to)\n [SMTPat (havoc s0 from k)]\n = bind_comp_no_leakage x y from to s0 k\n in\n ()\n in\n ()", "let triple = label & label & flows", "let unit_triple = bot, bot, []", "let comp_triple (w0, r0, fs0) (w1, r1, fs1) = (union w0 w1, union r0 r1, (fs0 @ add_source r0 ((bot, w1)::fs1)))", "let label_equiv (s0 s1:label) = Set.equal s0 s1", "let triple_equiv (w0, r0, f0) (w1, r1, f1) = label_equiv w0 w1 /\\ label_equiv r0 r1 /\\ flows_equiv f0 f1", "let triple_equiv_refl t0\n : Lemma (triple_equiv t0 t0)\n = ()", "let rec add_source_bot (f:flows)\n : Lemma (add_source bot f `flows_equiv` f)\n = match f with\n | [] -> ()\n | _::tl -> add_source_bot tl", "let left_unit (w, r, f) =\n assert (Set.equal (union bot bot) bot);\n add_source_bot f;\n assert (comp_triple unit_triple (w, r, f) `triple_equiv` (w, r, f))", "let flows_included_append (f0 f1 g0 g1:flows)\n : Lemma (requires flows_included_in f0 g0 /\\\n flows_included_in f1 g1)\n (ensures flows_included_in (f0@f1) (g0@g1))\n = let aux (f:_) (from to:_)\n : Lemma (requires List.Tot.memP f (f0@f1) /\\\n from <> to /\\\n has_flow_1 from to f)\n (ensures (exists g. g `List.Tot.memP` (g0@g1) /\\ has_flow_1 from to g))\n [SMTPat (has_flow_1 from to f)]\n = memP_append_or f f0 f1;\n assert (exists g. g `List.Tot.memP` g0 \\/ g `List.Tot.memP` g1 /\\ has_flow_1 from to g);\n FStar.Classical.forall_intro (fun g -> memP_append_or g g0 g1)\n in\n ()", "let flows_equiv_append (f0 f1 g0 g1:flows)\n : Lemma (requires flows_equiv f0 g0 /\\ flows_equiv f1 g1)\n (ensures flows_equiv (f0@f1) (g0@g1))\n = flows_included_append f0 f1 g0 g1;\n flows_included_append g0 g1 f0 f1", "let rec append_nil_r #a (l:list a)\n : Lemma (l @ [] == l)\n = match l with\n | [] -> ()\n | _::tl -> append_nil_r tl", "let right_unit (w, r, f) =\n calc (==) {\n comp_triple (w, r, f) unit_triple;\n (==) { }\n (w `union` bot, r `union` bot, f @ add_source r ((bot, bot)::[]));\n };\n assert (flows_equiv (add_source r [(bot, bot)]) []);\n flows_equiv_append f (add_source r [(bot, bot)]) f [];\n append_nil_r f;\n assert (comp_triple (w, r, f) unit_triple `triple_equiv` (w, r, f))", "let assoc_comp (w0, r0, fs0) (w1, r1, fs1) (w2, r2, fs2) =\n calc (==) {\n comp_triple (w0, r0, fs0) (comp_triple (w1, r1, fs1) (w2, r2, fs2)) ;\n (==) { }\n comp_triple (w0, r0, fs0) (union w1 w2, union r1 r2, (fs1 @ add_source r1 ((bot, w2)::fs2)));\n (==) { }\n (union w0 (union w1 w2), union r0 (union r1 r2), fs0 @ (add_source r0 ((bot, union w1 w2) :: (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { assert (forall w0 w1 w2. Set.equal (union w0 (union w1 w2)) (union (union w0 w1) w2)) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n fs0 @ (add_source r0 ((bot, union w1 w2) :: (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n (fs0 @ ((union r0 bot, union w1 w2) :: add_source r0 (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { assert (forall s. Set.equal (union s bot) s) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n (fs0 @ ((r0, union w1 w2) :: add_source r0 (fs1 @ (r1, w2) ::add_source r1 fs2))));\n };\n calc (==) {\n comp_triple (comp_triple (w0, r0, fs0) (w1, r1, fs1)) (w2, r2, fs2);\n (==) { }\n comp_triple (union w0 w1, union r0 r1, (fs0 @ add_source r0 ((bot, w1)::fs1))) (w2, r2, fs2);\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ add_source r0 ((bot, w1)::fs1)) @ (add_source (union r0 r1) ((bot, w2) :: fs2))));\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ ((union r0 bot, w1)::add_source r0 fs1)) @ ((union (union r0 r1) bot, w2) :: add_source (union r0 r1) fs2)));\n (==) { assert (forall s. Set.equal (union s bot) s) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ ((r0, w1)::add_source r0 fs1)) @ ((union r0 r1, w2) :: add_source (union r0 r1) fs2)));\n }", "let bind (a b:Type)\n (w0 r0 w1 r1:label) (fs0 fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : ist b\n (union w0 w1) // union the writes\n (union r0 r1) // union the reads\n (fs0 @ // flows of x\n add_source r0 ((bot, w1) // plus flows from whatever x reads to whatever y writes\n ::fs1)) //plus the flows of y\n = let f = fun s0 -> let v, s1 = x s0 in y v s1 in\n bind_comp_reads_ok x y;\n bind_comp_reads_ok x y;\n bind_comp_flows_ok x y;\n f", "let subcomp (a:Type) (w0 r0 w1 r1:label) (fs0 fs1:flows) (f:ist a w0 r0 fs0)\n : Pure (ist a w1 r1 fs1)\n (requires label_inclusion w0 w1 /\\\n label_inclusion r0 r1 /\\\n fs0 `flows_included_in` fs1)\n (fun _ -> True)\n = let f_reads_ok (l:loc) (s0:store)\n : Lemma (requires (~(Set.mem l r1)))\n (ensures (does_not_read_loc f l s0))\n [SMTPat (does_not_read_loc f l s0)]\n = let aux (k :_)\n : Lemma (ensures (does_not_read_loc_v f l s0 k))\n [SMTPat (does_not_read_loc_v f l s0 k)]\n = let v, s1 = f s0 in\n let v', s1' = f (havoc s0 l k) in\n assert (does_not_read_loc f l s0);\n assert (v == v');\n assert (not (Set.mem l w0) ==> sel s1' l = k);\n assert (not (Set.mem l w1) ==> sel s1' l = k);\n ()\n in\n ()\n in\n f", "let read (l:loc) : IST int bot (single l) [] = IST?.reflect (iread l)", "let write (l:loc) (x:int) : IST unit (single l) bot [] = IST?.reflect (iwrite l x)", "let tot a = unit -> Tot a", "let lift_tot (a:Type) (x:tot a)\n : ist a bot bot []\n = return a (x())", "let ref (l:label) = r:loc {r `Set.mem` l}", "val high : label", "let low : label = Set.complement high", "let lref = ref low", "let href = ref high", "let test (l:lref) (h:href)\n : IST unit (union bot (single h))\n (union (single l) bot)\n (add_source (single l) [bot, single h])\n = let x = read l in\n write h x", "let test2 (l:lref) (h:href)\n : IST unit (single h)\n (single l)\n [single l, single h]\n = let x = read l in\n write h x", "let test3 (l:lref) (h:href)\n : IST unit (single h)\n (single l)\n [single l, single h]\n = write h (read l)", "let test3_lab (l:lref) (h:href)\n : IST unit high low [low, high]\n = write h (read l)", "let test3_1 (l:lref) (h:href) (x:int)\n : IST int (single h)\n (single l)\n []\n = write h 0;\n read l", "let test4 (l:lref) (h:href) (x:int)\n : IST int (single l)\n (single h)\n [single h, bot]\n = write l x;\n read h", "let test5 (l:lref) (h:href) (x:int)\n : IST int (single l)\n (single h)\n []\n = write l x;\n read h", "let test6 (l:lref) (h:href)\n : IST unit high low [low, high]\n = let x = read l in\n write h x", "let test7 (l:lref) (h:href)\n : IST unit (single l)\n (single h)\n [high, low]\n = let x = read h in\n write l x", "let test8 (l:lref) (h:href)\n : IST unit (single l)\n (union (single h) (single l))\n [(single l `union` single h, single l)]\n = let x0 = read h in\n let x = read l in\n write l x", "let test9 (l:lref) (h:href)\n : IST unit (single l)\n (union (single h) (single l))\n [(single l `union` single h, single l)]\n = let x= (let x0 = read h in\n read l)\n in\n write l x", "val cw0 : label", "val cr0 : label", "val c0 (_:unit) : IST unit cw0 cr0 []", "val cw1 : label", "val cr1 : label", "val c1 (_:unit) : IST unit cw1 cr1 []", "val cw2 : label", "val cr2 : label", "val c2 (_:unit) : IST unit cw2 cr2 []", "let test10 ()\n : IST unit (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n (add_source cr0\n ((bot, union cw1 cw2)::\n (add_source cr1 [bot, cw2])))\n = c0 (); (c1();c2())", "let test12 ()\n : IST unit (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n [(cr0, union cw1 cw2);\n (union cr0 cr1, cw2)]\n = c0 (); (c1();c2())", "let test12_1 ()\n : IST unit (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n [(cr0, cw1);\n (union cr0 cr1, cw2)]\n = c0 (); (c1();c2())", "let test13 ()\n : IST unit (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n (add_source cr0 [bot, cw1] @\n add_source (union cr0 cr1) [bot, cw2])\n = (c0 (); c1());c2()" ], "closest": [ "val test14: Prims.unit\n -> IST unit\n (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n ([cr0, cw1; union cr0 cr1, cw2])\nlet test14 ()\n : IST unit (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n ([cr0, cw1;\n union cr0 cr1, cw2])\n = (c0 (); c1()); c2()", "val test12: Prims.unit\n -> IST unit\n (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n [(cr0, union cw1 cw2); (union cr0 cr1, cw2)]\nlet test12 ()\n : IST unit (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n [(cr0, union cw1 cw2);\n (union cr0 cr1, cw2)]\n = c0 (); (c1();c2())", "val test12_1: Prims.unit\n -> IST unit\n (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n [(cr0, cw1); (union cr0 cr1, cw2)]\nlet test12_1 ()\n : IST unit (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n [(cr0, cw1);\n (union cr0 cr1, cw2)]\n = c0 (); (c1();c2())", "val test13: Prims.unit\n -> IST unit\n (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n (add_source cr0 [bot, cw1] @ add_source (union cr0 cr1) [bot, cw2])\nlet test13 ()\n : IST unit (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n (add_source cr0 [bot, cw1] @\n add_source (union cr0 cr1) [bot, cw2])\n = (c0 (); c1());c2()", "val test14: Prims.unit\n -> IFC unit\n (union (union cr0 cr1) cr2)\n (union (union cw0 cw1) cw2)\n ([cr0, cw1; union cr0 cr1, cw2])\nlet test14 ()\n : IFC unit (union (union cr0 cr1) cr2)\n (union (union cw0 cw1) cw2)\n ([cr0, cw1;\n union cr0 cr1, cw2])\n = (c0 (); c1()); c2()", "val test10: Prims.unit\n -> IST unit\n (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n (add_source cr0 ((bot, union cw1 cw2) :: (add_source cr1 [bot, cw2])))\nlet test10 ()\n : IST unit (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n (add_source cr0\n ((bot, union cw1 cw2)::\n (add_source cr1 [bot, cw2])))\n = c0 (); (c1();c2())", "val test12: Prims.unit\n -> IFC unit\n (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n [(cr0, union cw1 cw2); (union cr0 cr1, cw2)]\nlet test12 ()\n : IFC unit (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n [(cr0, union cw1 cw2);\n (union cr0 cr1, cw2)]\n = c0 (); (c1();c2())", "val test12_1: Prims.unit\n -> IFC unit\n (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n [(cr0, cw1); (union cr0 cr1, cw2)]\nlet test12_1 ()\n : IFC unit (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n [(cr0, cw1); (union cr0 cr1, cw2)]\n = c0 (); (c1();c2())", "val test13: Prims.unit\n -> IFC unit\n (union (union cr0 cr1) cr2)\n (union (union cw0 cw1) cw2)\n (add_source cr0 [bot, cw1] @ add_source (union cr0 cr1) [bot, cw2])\nlet test13 ()\n : IFC unit (union (union cr0 cr1) cr2)\n (union (union cw0 cw1) cw2)\n (add_source cr0 [bot, cw1] @\n add_source (union cr0 cr1) [bot, cw2])\n = (c0 (); c1());c2()", "val test10: Prims.unit\n -> IFC unit\n (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n (add_source cr0 ((bot, union cw1 cw2) :: (add_source cr1 [bot, cw2])))\nlet test10 ()\n : IFC unit (union cr0 (union cr1 cr2))\n (union cw0 (union cw1 cw2))\n (add_source cr0\n ((bot, union cw1 cw2)::\n (add_source cr1 [bot, cw2])))\n = c0 (); (c1();c2())", "val test: Prims.unit -> St unit\nlet test (): St unit =\n let r = HS.(new_region root) in\n let b = B.malloc HS.root 0ul 1ul in\n let l: t UInt32.t = create_in r in\n push l 0ul;\n push l 1ul;\n push l 2ul;\n B.upd b 0ul 1ul;\n let h0 = ST.get () in\n assert (v h0 l == [ 2ul; 1ul; 0ul ]);\n assert (B.deref h0 b == 1ul);\n ignore (pop l);\n let h1 = ST.get () in\n assert (v h1 l == [ 1ul; 0ul ]);\n assert (B.deref h0 b == 1ul);\n clear l;\n let h2 = ST.get () in\n assert (v h2 l == []);\n assert (B.deref h2 b == 1ul);\n free l;\n ()", "val test: Prims.unit -> M unit (fun _ -> True) (fun _ _ s1 -> st_q s1)\nlet test () : M unit (fun _ -> True) (fun _ _ s1 -> st_q s1) =\n g ();\n f ();\n h ()", "val __c1: Prims.unit -> EFF int unit bool [EXN; RD; WR]\nlet __c1 () : EFF int unit bool [EXN;RD;WR] =\n put \"hello\";\n raise EE;\n coerce_st_to unit;// funny, but needed; or 'get ();'\n put true;\n 42", "val test: Prims.unit -> STT unit ((p `star` p) `star` p) (fun _ -> (p `star` p) `star` p)\nlet test () : STT unit (p `star` p `star` p) (fun _ -> p `star` p `star` p)\n = f 0; ()", "val test2: Prims.unit -> HoareST int (fun _ -> True) (fun _ _ _ -> True)\nlet test2 () : HoareST int (fun _ -> True) (fun _ _ _ -> True)\n= g 2 (f 0)", "val test: Prims.unit -> LV unit (fun _ -> True) (fun _ _ _ -> True)\nlet test () : LV unit (fun _ -> True) (fun _ _ _ -> True) =\n let n1 = create nat 0 in\n let n2 = create bool true in\n let n3 = create unit () in\n\n\n let v1: nat = read n1 in\n assert (v1 == 0)", "val test: Prims.unit -> HoareST int (fun _ -> True) (fun _ r _ -> r == 1)\nlet test () : HoareST int (fun _ -> True) (fun _ r _ -> r == 1)\n= f 0", "val test2: Prims.unit -> HoareST int (fun _ -> True) (fun h0 r h1 -> r >= 4 /\\ h0 == h1)\nlet test2 ()\n: HoareST int\n (fun _ -> True)\n (fun h0 r h1 -> r >= 4 /\\ h0 == h1)\n= let x = test () in\n let y = test () in\n x + y", "val test4: Prims.unit -> HoareST int (fun _ -> True) (fun _ r _ -> r == 3)\nlet test4 ()\n: HoareST int\n (fun _ -> True)\n (fun _ r _ -> r == 3)\n= let _ = test () in\n f_pure ()", "val test2: Prims.unit -> Lemma (True)\nlet test2 () : Lemma (True) =\n let s1 = empty $:: 1 in\n let s2 = s1 $:: 2 in\n let s3 = s2 $:: 3 in\n let s4 = s3 $:: 4 in\n let s5 = s4 $:: 5 in\n assert (length s2 = 1 + length s1);\n assert (length s2 = 2);\n assert (length s5 = 5);\n assert (s5 $@ 1 == 2);\n assert (forall (s: seq int) (n: nat). n < 2 ==> (s2 $+ s) $@ n = s2 $@ n);\n assert (drop (drop s5 1) 2 == drop s5 3);\n assert (forall (v: int). length (s5 $:: v) = 6);\n assert (s3 $<= s5);\n assert (length (update s5 3 7) == 5);\n assert ((update s5 3 7) $@ 2 == 3);\n assert ((update s5 3 7) $@ 3 == 7);\n assert (length (slice s5 1 3) == 2)", "val test13: Prims.unit -> HoareST unit (fun _ -> True) (fun _ _ _ -> True)\nlet test13 () : HoareST unit (fun _ -> True) (fun _ _ _ -> True) = \n let _ : squash some_pred = proof_of_pred () in\n test12 ()", "val test: Prims.unit -> HoareST int (fun _ -> True) (fun h0 r h1 -> r > 1 /\\ h0 == h1)\nlet test ()\n: HoareST int\n (fun _ -> True)\n (fun h0 r h1 -> r > 1 /\\ h0 == h1)\n= 3", "val test2: Prims.unit -> squash (2 == 1 + 1)\nlet test2 () : squash (2 == 1 + 1) =\n calc (==) {\n _;\n == { lem () }\n 1 + 1;\n }", "val test1: Prims.unit -> Lemma (True)\nlet test1 () : Lemma (True) =\n assert (length (empty #int) == 0);\n assert (forall (s: seq bool). length s == 0 ==> s == empty);\n assert (forall (v: list int). length (singleton v) == 1);\n assert (forall (s: seq int) (v: int). length (build s v) == 1 + length s);\n assert (forall (v: nat). index (singleton v) 0 == v);\n assert (~(contains empty 42));\n assert (forall (s: seq int). take s 0 == empty);\n assert (forall (s: seq int). drop s 0 == s);\n ()", "val test11: Prims.unit -> Tot unit\nlet test11 () : Tot unit =\n let _ : squash some_pred = proof_of_pred () in\n test10 ()", "val test: Prims.unit -> SteelT unit ((p `star` p) `star` p) (fun _ -> (p `star` p) `star` p)\nlet test () : SteelT unit (p `star` p `star` p) (fun _ -> p `star` p `star` p)\n = f 0; ()", "val test5: Prims.unit -> HoareST int (fun _ -> True) (fun h0 r h1 -> True)\nlet test5 ()\n: HoareST int\n (fun _ -> True)\n (fun h0 r h1 -> True)\n= let y = test () in\n y", "val test: Prims.unit -> ST int int null\nlet test () : ST int int null =\n let x = get () in\n put (x + x);\n get () + get ()", "val test: Prims.unit -> ST int int null\nlet test () : ST int int null =\n let x = get () in\n put (x + x);\n get () + get ()", "val test: Prims.unit -> ST int int null\nlet test () : ST int int null =\n let x = get () in\n put (x + x);\n get () + get ()", "val test1: Prims.unit -> squash (2 == 1 + 1)\nlet test1 () : squash (2 == 1 + 1) =\n calc (==) {\n 2;\n == { lem () }\n _;\n }", "val test3: Prims.unit -> squash (2 == 1 + 1)\nlet test3 () : squash (2 == 1 + 1) =\n calc (==) {\n _;\n == { lem () }\n _;\n }", "val test_catch0: Prims.unit -> EFF int unit bool [RD; WR]\nlet test_catch0 () : EFF int unit bool [RD;WR] =\n catchE __c1 __h1", "val get: Prims.unit\n -> LV (Map.t nat (a: Type0 & a)) (fun m0 -> True) (fun m0 r m1 -> m0 == m1 /\\ r == m0.m)\nlet get ()\n: LV (Map.t nat (a:Type0 & a))\n (fun m0 -> True)\n (fun m0 r m1 -> m0 == m1 /\\ r == m0.m)\n= LVARS?.reflect (fun m -> m.m, m)", "val main: Prims.unit -> HST.Stack (unit) (fun _ -> True) (fun _ _ _ -> True)\nlet main () : HST.Stack (unit) (fun _ -> True) (fun _ _ _ -> True) =\n HST.push_frame ();\n let d : dll UInt32.t = dll_new () in\n let n1 = node_of 1ul in\n let n2 = node_of 2ul in\n dll_insert_at_head d n1;\n dll_insert_at_tail d n2;\n let h0 = HST.get () in\n reverse d;\n let h1 = HST.get () in\n assert (n2 `L.memP` as_list h1 d); // OBSERVE. TODO: WHY????!???\n let n1' = dll_head d in\n let t = node_val n1' in\n assert (t == 2ul); // Yay!\n HST.pop_frame ()", "val test6: Prims.unit -> Lemma (True)\nlet test6 () : Lemma (True) =\n assert (forall (ty: Type).{:pattern empty #ty} length (empty #ty) = 0);\n assert (forall (ty: Type) (s: seq ty).{:pattern length s} length s = 0 ==> s == empty);\n assert (forall (ty: Type) (v: ty).{:pattern length (singleton v)} length (singleton v) = 1);\n assert (forall (ty: Type) (s: seq ty) (v: ty).{:pattern build s v} length (build s v) = 1 + length s);\n assert (forall (ty: Type) (s0: seq ty) (s1: seq ty).{:pattern length (append s0 s1)}\n length (append s0 s1) = length s0 + length s1);\n assert (forall (ty: Type) (s: seq ty) (i: nat{i < length s}) (v: ty).{:pattern length (update s i v)}\n length (update s i v) = length s);\n assert (forall (ty: Type) (s: seq ty) (i: nat{i < length s}) (v: ty) (n: nat{n < length (update s i v)})\n .{:pattern index (update s i v) n}\n n < length s ==>\n (i = n ==> index (update s i v) n == v)\n /\\ (i <> n ==> index (update s i v) n == index s n));\n assert (forall (ty: Type) (s: seq ty) (x: ty).{:pattern contains s x}\n contains s x <==> (exists (i: nat).{:pattern index s i} i < length s /\\ index s i == x));\n assert (forall (ty: Type) (x: ty).{:pattern contains empty x} ~(contains empty x));\n assert (forall (ty: Type) (s: seq ty) (v: ty) (x: ty).{:pattern contains (build s v) x}\n contains (build s v) x <==> (v == x \\/ contains s x));\n assert (forall (ty: Type) (s: seq ty) (n: nat{n <= length s}) (x: ty).{:pattern contains (take s n) x}\n contains (take s n) x <==>\n (exists (i: nat).{:pattern index s i} i < n /\\ i < length s /\\ index s i == x));\n assert (forall (ty: Type) (s: seq ty) (n: nat{n <= length s}) (x: ty).{:pattern contains (drop s n) x}\n contains (drop s n) x <==>\n (exists (i: nat).{:pattern index s i} n <= i && i < length s /\\ index s i == x));\n assert (forall (ty: Type) (s0: seq ty) (s1: seq ty).{:pattern equal s0 s1}\n equal s0 s1 <==>\n length s0 == length s1 /\\\n (forall j.{:pattern index s0 j \\/ index s1 j}\n 0 <= j && j < length s0 ==> index s0 j == index s1 j));\n assert (forall (ty: Type) (a: seq ty) (b: seq ty).{:pattern equal a b} equal a b ==> a == b);\n assert (forall (ty: Type) (s0: seq ty) (s1: seq ty).{:pattern is_prefix s0 s1}\n is_prefix s0 s1 <==>\n length s0 <= length s1\n /\\ (forall (j: nat).{:pattern index s0 j \\/ index s1 j}\n j < length s0 ==> index s0 j == index s1 j));\n assert (forall (ty: Type) (s: seq ty) (n: nat).{:pattern length (take s n)}\n n <= length s ==> length (take s n) = n);\n assert (forall (ty: Type) (s: seq ty) (n: nat). {:pattern length (drop s n)}\n n <= length s ==> length (drop s n) = length s - n);\n assert (forall (ty: Type) (v: ty).{:pattern rank v} rank v == v);\n assert (forall (ty: Type) (s: seq ty) (i: nat).{:pattern rank (index s i)}\n i < length s ==> rank (index s i) << rank s);\n assert (forall (ty: Type) (s: seq ty) (i: nat).{:pattern rank (drop s i)}\n 0 < i && i <= length s ==> rank (drop s i) << rank s);\n assert (forall (ty: Type) (s: seq ty) (i: nat).{:pattern length (take s i)}\n i < length s ==> length (take s i) << length s);\n assert (forall (ty: Type) (s: seq ty) (i: nat) (j: nat).{:pattern length (append (take s i) (drop s j))}\n i < j && j <= length s ==> length (append (take s i) (drop s j)) << length s);\n assert (forall (ty: Type) (s: seq ty) (n: nat).{:pattern drop s n} n = 0 ==> drop s n == s);\n assert (forall (ty: Type) (s: seq ty) (n: nat).{:pattern take s n} n = 0 ==> take s n == empty);\n assert (forall (ty: Type) (s: seq ty) (m: nat) (n: nat).{:pattern drop (drop s m) n}\n m + n <= length s ==> drop (drop s m) n == drop s (m + n))", "val test1: Prims.unit -> SteelT UInt32.t emp (fun _ -> emp)\nlet test1 () : SteelT UInt32.t emp (fun _ -> emp)\n= let r = malloc 0ul in\n let x = read r in\n free r;\n x", "val test_2: Prims.unit -> ID int (as_pure_wp (fun p -> p 5))\nlet test_2 () : ID int (as_pure_wp (fun p -> p 5)) = 5", "val get_r: Prims.unit -> RWI H.heap RO (fun _ -> True) (fun h0 x h1 -> x == h0 /\\ h1 == h0)\nlet get_r () : RWI H.heap RO (fun _ -> True) (fun h0 x h1 -> x == h0 /\\ h1 == h0) =\n RWI?.reflect (fun () -> ST.get ())", "val test6: Prims.unit -> HoareST int (fun _ -> True) (fun _ r _ -> r == 3)\nlet test6 ()\n: HoareST int\n (fun _ -> True)\n (fun _ r _ -> r == 3)\n= let x = f_pure () in\n let y = test () in\n x", "val test1: Prims.unit -> SteelT bool emp (fun _ -> emp)\nlet test1 () : SteelT bool emp (fun _ -> emp) =\n let r = malloc 0uL 8sz in\n ghost_split r 4sz;\n let r1 = split_l r 4sz in\n let r2 = split_r r 4sz in\n change_equal_slprop (varray (split_l r 4sz)) (varray r1);\n change_equal_slprop (varray (split_r r 4sz)) (varray r2);\n let _ = mk 4s in\n let b = ptrdiff r2 r1 in\n ghost_join r1 r2 ();\n change_equal_slprop\n (varray (merge r1 r2))\n (varray r);\n // Free not supported in Wasm\n drop (varray r);\n return (b = mk 4s)", "val test2: Prims.unit -> SteelT bool emp (fun _ -> emp)\nlet test2 () : SteelT bool emp (fun _ -> emp) =\n let r = malloc def_t 8sz in\n ghost_split r 4sz;\n let r1 = split_l r 4sz in\n let r2 = split_r r 4sz in\n change_equal_slprop (varray (split_l r 4sz)) (varray r1);\n change_equal_slprop (varray (split_r r 4sz)) (varray r2);\n let _ = mk 4s in\n let b = ptrdiff r2 r1 in\n ghost_join r1 r2 ();\n change_equal_slprop\n (varray (merge r1 r2))\n (varray r);\n // Free not supported in wasm\n drop (varray r);\n return (b = mk 4s)", "val get: Prims.unit -> EFF int (fun _ -> True) (fun s0 y s1 -> s1 == s0 /\\ y == Some s0) [RD]\nlet get () : EFF int (fun _ -> True) (fun s0 y s1 -> s1 == s0 /\\ y == Some s0) [RD] by (compute (); dump\"\") =\n EFF?.reflect _get", "val Unification.test = l1: Prims.list _ -> l2: Prims.list _ -> l3: Prims.list _ -> Prims.unit\nlet test l1 l2 l3 = assert (l1 ++ l2 ++ l3 == (l1 ++ l2) ++ l3)", "val ut_ex2: Prims.unit -> ST.ST unit (requires (fun _ -> True)) (ensures (fun _ _ _ -> True))\nlet ut_ex2 () : ST.ST unit (requires (fun _ -> True)) (ensures (fun _ _ _ -> True)) =\n let l : list int = [1; 2; 3; 4; 5; 6] in\n let h0 = ST.get () in\n let r = sf2 l in (* This dummy function introduces some equalities in the context *)\n let h1 = ST.get () in\n assert(B.as_seq h1 r == B.as_seq h1 r); (* <- Try here *)\n ()", "val get: Prims.unit -> HoareST heap (fun _ -> True) (fun h0 h h1 -> h0 == h1 /\\ h == h1)\nlet get ()\n: HoareST heap\n (fun _ -> True)\n (fun h0 h h1 -> h0 == h1 /\\ h == h1)\n= HoareST?.reflect get", "val get: Prims.unit -> HoareST heap (fun _ -> True) (fun h0 h h1 -> h0 == h1 /\\ h == h1)\nlet get ()\n: HoareST heap\n (fun _ -> True)\n (fun h0 h h1 -> h0 == h1 /\\ h == h1)\n= HoareST?.reflect get", "val test: Prims.unit -> ML bool\nlet test () : ML bool =\n let b1 = test_IKpsk2 () in\n let b2 = test_IKpsk2_gen () in\n b1 && b2", "val test: Prims.unit -> ML bool\nlet test () : ML bool =\n test_XX ()", "val test: Prims.unit -> ML bool\nlet test () : ML bool =\n [@inline_let] let a = Frodo64 in\n assert_norm (List.Tot.length test1_enccoins == 16);\n assert_norm (List.Tot.length test1_keypaircoins == 2 * crypto_bytes a + bytes_seed_a);\n assert_norm (List.Tot.length test1_enccoins == bytes_mu a);\n assert_norm (List.Tot.length test1_ss_expected == crypto_bytes a);\n assert_norm (List.Tot.length test1_pk_expected == crypto_publickeybytes a);\n assert_norm (List.Tot.length test1_ct_expected == crypto_ciphertextbytes a);\n assert_norm (List.Tot.length test1_sk_expected == crypto_secretkeybytes a);\n IO.print_string \"\\nTest1. SHAKE128\";\n let res1 =\n test_frodo a SHAKE128 test1_keypaircoins\n test1_enccoins\n test1_ss_expected\n test1_pk_expected\n test1_ct_expected\n test1_sk_expected\n in\n\n let result = res1 in\n if result\n then IO.print_string \"\\n\\nFrodoKEM : Success!\\n\"\n else IO.print_string \"\\n\\nFrodoKEM: Failure :(\\n\";\n result", "val test: Prims.unit -> ML bool\nlet test () : ML bool =\n let hsk_tests = load_test_vectors () in\n execute_handshakes hsk_tests", "val test_simplify: Prims.unit -> Tac unit\nlet test_simplify () : Tac unit =\n simplify ();\n or_else goal_is_true (fun () -> dump \"\"; fail \"simplify left open goals\")", "val proof: Prims.unit -> Lemma (related l r (phi ()) (phi ()))\nlet proof () : Lemma\n (related l r (phi ()) (phi ()))\n= \n let phi = phi () in\n let phi1 = gand phi (geq (gvar x Right) (gop op_Addition (gvar y Right) (gconst 1))) in\n let phi2 = gand phi1 (geq (gvar x Left) (gvar x Right)) in\n hyp;\n assert (related (assign x asx_e) skip phi1 phi2); // by r_dassl\n lemma_included_helper (); //prove the precondition of r_ass\n assert (related (assign i asi_e) (assign i asi_e) phi2 phi2); // by r_ass\n d_su1' (assign x asx_e) (assign i asi_e) (assign i asi_e) phi1 phi2 phi2;\n r_while cond cond (seq (assign x asx_e) (assign i asi_e)) (assign i asi_e) phi1;\n assert (related skip (assign x asx_e) phi phi1); // by r_dassr\n assert (related l (while cond (assign i asi_e)) phi1 phi); // by d_sub\n d_su1'_flip l (assign x asx_e) (while cond (assign i asi_e)) phi phi1 phi", "val poly_semiring: Prims.unit -> Tac unit\nlet poly_semiring () : Tac unit = canon_semiring pfelem_cr; trefl()", "val t2: Prims.unit -> Tac unit\nlet t2 () : Tac unit = fail \"always fail\"", "val test_ub: Prims.unit -> HST.St unit\nlet test_ub () :HST.St unit =\n let b = UB.ugcmalloc #int HS.root 10ul in //allocate an uninitialized buffer, no initializer\n UB.uupd b 1ul 2; //update at index 1 with value 2\n let j = UB.uindex b 1ul in //can now project index 1\n assert (j == 2); //and check that the value is indeed 2\n //let j = UB.uindex b 4ul in --> this fails since the index 4ul is not initialized\n let b1 = B.gcmalloc HS.root 0 10ul in //allocate a different regular buffer\n let h0 = HST.get () in\n UB.ublit b1 2ul b 2ul 3ul; //copy [2, 5) from regular buffer to [2, 5) of uninitialized buffer\n let h1 = HST.get () in\n let j = UB.uindex b 4ul in //now 4ul is indexable\n assert (j == 0); //and we can check its value is 0 (from the source buffer)\n let j = UB.uindex b 1ul in //1ul remains initialized and has the same value as before\n assert (Seq.index (UB.as_seq h0 b) 1 == Seq.index (Seq.slice (UB.as_seq h0 b) 0 2) 1);\n assert (j == 2)", "val test_all_wf_lem: Prims.unit -> Lemma (test_all_wf == true)\nlet test_all_wf_lem () :\n Lemma(test_all_wf == true) =\n assert_norm(test_all_wf == true)", "val g: Prims.unit -> Tot unit\nlet g () : Tot unit =\n assert (False)", "val test_subcomp: Prims.unit -> HoareST int (fun _ -> True) (fun _ r _ -> r == 0)\nlet test_subcomp () : HoareST int (fun _ -> True) (fun _ r _ -> r == 0) = 0", "val test: Prims.unit -> ND int (as_pure_wp (fun p -> forall (x: int). 0 <= x /\\ x < 10 ==> p x))\nlet test () : ND int (as_pure_wp (fun p -> forall (x:int). 0 <= x /\\ x < 10 ==> p x)) by (compute ()) =\n let x = choose 0 1 in\n let y = choose 2 3 in\n let z = choose 4 5 in\n x + y + z", "val test3: Prims.unit -> HoareST int (fun _ -> True) (fun _ r _ -> r >= 5)\nlet test3 ()\n: HoareST int\n (fun _ -> True)\n (fun _ r _ -> r >= 5)\n= let x = test () in\n let y = f_pure () in\n x + y", "val test: Prims.unit -> Exn int True (fun _ -> True)\nlet test () : Exn int True (fun _ -> True)\n= 4", "val test_incremental_api: Prims.unit -> St unit\nlet test_incremental_api (): St unit =\n // Note: this function cannot be in the Stack effect because it performs some\n // allocations (even though it frees them afterwards).\n push_frame ();\n let b1 = B.alloca_of_list [ u8 0x00; u8 0x01; u8 0x02; u8 0x04 ] in\n let b2 = B.alloca_of_list [ u8 0x05; u8 0x06; u8 0x07; u8 0x08 ] in\n\n let st = HI.malloc SHA2_256 HyperStack.root in\n HI.reset (G.hide SHA2_256) st ();\n let h0 = ST.get () in\n assert B.(loc_disjoint (S.footprint HI.evercrypt_hash SHA2_256 h0 st) (loc_buffer b1));\n assert (S.seen HI.evercrypt_hash SHA2_256 h0 st `Seq.equal` Seq.empty);\n\n assert_norm (4 < pow2 61);\n let EverCrypt.Error.Success = HI.update (G.hide SHA2_256) st b1 4ul in\n let h1 = ST.get () in\n assert (HI.hashed h1 st `Seq.equal` (Seq.append Seq.empty (B.as_seq h0 b1)));\n Seq.append_empty_l (B.as_seq h0 b1);\n assert (HI.hashed h1 st `Seq.equal` (B.as_seq h0 b1));\n\n assert (Seq.length (Ghost.reveal (Ghost.hide (B.as_seq h0 b1))) = 4);\n assert_norm (8 < pow2 61);\n let EverCrypt.Error.Success = HI.update (G.hide SHA2_256) st b2 4ul in\n let h2 = ST.get () in\n assert (HI.hashed h2 st `Seq.equal` (Seq.append (B.as_seq h0 b1) (B.as_seq h0 b2)));\n\n // An example of how to call the hash preservation lemma...\n let dst = B.alloca (u8 0) 32ul in\n let h3 = ST.get () in\n // Auto-framing!\n HI.digest (G.hide SHA2_256) st dst ();\n\n let h4 = ST.get () in\n assert (Seq.equal (B.as_seq h4 dst)\n (Spec.Agile.Hash.hash SHA2_256 (Seq.append (B.as_seq h0 b1) (B.as_seq h0 b2))));\n\n HI.free (G.hide SHA2_256) st;\n pop_frame ()", "val t1_t: Prims.unit -> Tot (list int)\nlet t1_t () : Tot (list int) = r_map #T (fun x -> fun () -> x + 1) [1;2;3;4] ()", "val laws: Prims.unit\n -> squash (Sem.associative star /\\ Sem.commutative star /\\ Sem.is_unit emp star)\nlet laws ()\r\n: squash (\r\n Sem.associative star /\\\r\n Sem.commutative star /\\\r\n Sem.is_unit emp star\r\n )\r\n= let equiv_eq (x y:slprop)\r\n : Lemma (x `equiv` y <==> x == y)\r\n [SMTPat (x `equiv` y)]\r\n = introduce x `equiv` y ==> x == y\r\n with _h . slprop_extensionality x y\r\n in\r\n let _ : squash (Sem.associative star) =\r\n introduce \r\n forall x y z. \r\n ((x `star` y) `star` z) ==\r\n (x `star` (y `star` z))\r\n with star_associative x y z\r\n in\r\n let _ : squash (Sem.commutative star) = \r\n introduce \r\n forall x y.\r\n x `star` y == y `star` x\r\n with star_commutative x y\r\n in\r\n let _ : squash (Sem.is_unit emp star) =\r\n introduce\r\n forall x.\r\n (x `star` emp) == x /\\\r\n (emp `star` x) == x\r\n with emp_unit x\r\n in\r\n ()", "val one_t: Prims.unit -> Tac term\nlet one_t () : Tac term = pack (Tv_Const (C_Int 1))", "val test_pf: Prims.unit -> HST.St unit\nlet test_pf () : HST.St unit =\n let open LowStar.PrefixFreezableBuffer in\n let b = gcmalloc HS.root 5ul in\n\n upd b 4ul 1uy;\n upd b 5ul 2uy;\n upd b 6ul 3uy;\n upd b 7ul 4uy;\n upd b 8ul 5uy;\n\n freeze b 5ul;\n\n upd b 5ul 2uy;\n upd b 6ul 3uy;\n upd b 7ul 4uy;\n upd b 8ul 5uy;\n\n\n let snap = Ghost.hide (Seq.create 1 1uy) in\n witness_slice b 4ul 5ul snap;\n havoc_pf b;\n\n recall_slice b 4ul 5ul snap;\n\n let h = HST.get () in\n assert (Seq.equal (Seq.slice (as_seq h b) 4 5) (Ghost.reveal snap));\n\n ()", "val test_assert: Prims.unit -> ID unit (as_pure_wp (fun p -> p ()))\nlet test_assert () : ID unit (as_pure_wp (fun p -> p ())) =\n ();\n iassume False;\n ();\n iassert False;\n ()", "val test_assert: Prims.unit -> ID unit (as_pure_wp (fun p -> p ()))\nlet test_assert () : ID unit (as_pure_wp (fun p -> p ())) =\n ();\n iassume False;\n ();\n iassert False;\n ()", "val callmap: Prims.unit -> Id (list nat) True (fun _ -> True)\nlet callmap () : Id (list nat) True (fun _ -> True) =\n let lmap : list nat = [2;4;6;8] in\n pmap even fmap lmap", "val callmap: Prims.unit -> Id (list nat) True (fun _ -> True)\nlet callmap () : Id (list nat) True (fun _ -> True) =\n let lmap : list nat = [2;4;6;8] in\n map #_ #_ #even fmap lmap", "val l: Prims.unit -> list int\nlet l () : list int = reify (test_f ()) (fun _ -> True) ()", "val f: Prims.unit -> IMST nat ((| nat, nat_rel |) >< (fun p s0 -> forall s1. s1 > s0 ==> p s0 s1))\nlet f () \n : IMST nat ((|nat , nat_rel|) >< (fun p s0 -> forall s1 . s1 > s0 ==> p s0 s1))\n = let s0 = get #nat #nat_rel () in \n put #nat #nat_rel (s0 + 1);\n let s1 = get #nat #nat_rel () in\n assert (s1 > 0);\n witness #nat #nat_rel (fun n -> n > 0);\n put #nat #nat_rel (s1 * 42);\n recall #nat #nat_rel (fun n -> n > 0);\n let s2 = get #nat #nat_rel () in\n assert (s2 > 0);\n s0", "val vale: Prims.unit -> Stack bool (fun _ -> True) (fun h0 _ h1 -> B.modifies B.loc_none h0 h1)\nlet vale (): Stack bool (fun _ -> True) (fun h0 _ h1 -> B.modifies B.loc_none h0 h1) =\n true", "val test9: Prims.unit -> FStar.ST.STATE int (fun p _ -> forall h1. p 3 h1)\nlet test9 ()\n: FStar.ST.STATE int (fun p _ -> forall h1. p 3 h1)\n= st_reify (fun _ -> test6 ()) ()", "val get: #st: st -> Prims.unit\n -> MstTot (full_mem st) (fun _ -> True) (fun s0 s s1 -> s0 == s /\\ s == s1)\nlet get (#st:st) ()\n : MstTot (full_mem st)\n (fun _ -> True)\n (fun s0 s s1 -> s0 == s /\\ s == s1)\n = get ()", "val conclude: Prims.unit -> Tac unit\nlet conclude ()\n: Tac unit\n= // dump \"conclude before\";\n norm [delta; iota; primops];\n begin if lax_on ()\n then smt ()\n else\n first [\n trefl;\n trivial;\n ]\n end;\n// dump \"conclude after\";\n qed ()", "val g: Prims.unit -> IMST nat (idx nat nat_rel (fun p s0 -> forall s1. s1 > s0 ==> p s0 s1))\nlet g () \n : IMST nat (idx nat nat_rel (fun p s0 -> forall s1 . s1 > s0 ==> p s0 s1))\n = let s0 = get #nat #nat_rel () in \n put #nat #nat_rel (s0 + 1);\n let s1 = get #nat #nat_rel () in\n assert (s1 > 0);\n witness #nat #nat_rel (fun n -> n > 0);\n put #nat #nat_rel (s1 * 42);\n recall #nat #nat_rel (fun n -> n > 0);\n let s2 = get #nat #nat_rel () in\n assert (s2 > 0);\n witness #nat #eq_rel (fun n -> n = s2);\n put #nat #nat_rel (s1 * 43);\n recall #nat #eq_rel (fun n -> n = s2);\n let s3 = get #nat #nat_rel () in\n assert (s1 > 0);\n assert (s2 = s1 * 42);\n assert (s3 = s1 * 43);\n assert (s3 = s2); \n assert (False); // WHOOPS!!!\n s0", "val Canon.test_neg2 = b: Prims.pos -> c: Prims.pos -> Prims.unit\nlet test_neg2 (b c : pos) =\n assert (b * (c-1) + b == b*c)\n by (canon ())", "val admit1: Prims.unit -> Tac unit\nlet admit1 () : Tac unit =\n tadmit ()", "val admit1: Prims.unit -> Tac unit\nlet admit1 () : Tac unit =\n tadmit ()", "val whatever: Prims.unit\n -> Stack bool (requires (fun _ -> true)) (ensures (fun h0 _ h1 -> h0 == h1))\nlet whatever (): Stack bool\n (requires (fun _ -> true))\n (ensures (fun h0 _ h1 -> h0 == h1)) =\n true", "val __h1: #si: _ -> Prims.unit -> EFF int si bool [RD; WR]\nlet __h1 #si () : EFF int si bool [RD;WR] =\n put false;\n 42", "val smt: Prims.unit -> Tac unit\nlet smt () : Tac unit =\n match goals (), smt_goals () with\n | [], _ -> fail \"smt: no active goals\"\n | g::gs, gs' ->\n begin\n set_goals gs;\n set_smt_goals (g :: gs')\n end", "val smt: Prims.unit -> Tac unit\nlet smt () : Tac unit =\n match goals (), smt_goals () with\n | [], _ -> fail \"smt: no active goals\"\n | g::gs, gs' ->\n begin\n set_goals gs;\n set_smt_goals (g :: gs')\n end", "val solve_vc: Prims.unit -> Tac unit\nlet solve_vc ()\n: Tac unit\n= exact_guard (quote ()); conclude ()", "val test_XX: Prims.unit -> ML bool\nlet test_XX () : ML bool =\n IO.print_string \"*** XX:\\n\";\n let res1 = perform_XX_handshake is_priv ie_priv rs_priv re_priv in\n let ret =\n match res1 with\n | Fail _ -> IO.print_string \"[!] Tests failed\\n\"; false\n | Res _ -> IO.print_string \"Tests succeeded\\n\"; true\n in\n print_separation ();\n ret", "val conjt: Prims.unit -> Tac unit\nlet rec conjt () : Tac unit =\n let _ = l_intros () in\n match cur_formula () with\n | And _ _ -> seq split conjt\n (* otherwise, just try to solve via an assumption *)\n | _ -> (assumption (); qed ())", "val tac2: Prims.unit -> Tac unit\nlet tac2 () : Tac unit =\n apply_lemma (`test_lemma)", "val cur_witness: Prims.unit -> Tac term\nlet cur_witness () : Tac term = goal_witness (_cur_goal ())", "val cur_witness: Prims.unit -> Tac term\nlet cur_witness () : Tac term = goal_witness (_cur_goal ())", "val triv: Prims.unit -> Tac unit\nlet triv () : Tac unit =\n let _ = l_intros () in\n assumption ();\n qed ()", "val size: Prims.unit\n -> MSeqExn nat (fun _ -> True) (fun s0 r s1 -> r == Success (Seq.length s0) /\\ s0 == s1)\nlet size ()\n: MSeqExn nat\n (fun _ -> True)\n (fun s0 r s1 ->\n r == Success (Seq.length s0) /\\\n s0 == s1)\n= let s0 = get () in\n Seq.length s0", "val tau1: Prims.unit -> Tac unit\nlet tau1 () : Tac unit =\n prune \"\";\n FStar.Tactics.split ();\n (* rev part *)\n addns \"FStar.List\";\n addns \"Prims\";\n smt ();\n (* arithmetic part *)\n addns \"Prims\";\n smt ()", "val example4: Prims.unit -> SteelK (ref int) emp (fun r -> pts_to r full_perm 2)\nlet example4 () : SteelK (ref int) emp (fun r -> pts_to r full_perm 2) =\n let x = alloc_pt 0 in\n let y = alloc_pt 1 in\n let p1:thread (pts_to x full_perm 1) = kfork (fun _ -> write_pt #_ #0 x 1) in\n let p2:thread emp = kfork (fun _ -> free_pt #_ #1 y) in\n kjoin p1;\n write_pt #_ #1 x 2;\n kjoin p2;\n x", "val test_st: Prims.unit -> Pure (option int) True (fun _ -> True)\nlet test_st () : Pure (option int) True (fun _ -> True)\n= reify (test ()) ()", "val t: Prims.unit -> Tac unit\nlet t () : Tac unit =\n let test' = fresh_namedv () in\n let test = pack (Tv_Var test') in\n let e_true = `3 in\n let e_false = `() in\n let body = mk_if test e_true e_false in\n let res = pack (Tv_Abs (namedv_to_binder test' (`bool)) body) in\n // should print: function true -> 3 | false -> ()\n //print (term_to_string res);\n t_exact true true res", "val test_dep_f2: Prims.unit -> HoareST (t_int (pure_g ())) (fun _ -> True) (fun _ _ _ -> True)\nlet test_dep_f2 () : HoareST (t_int (pure_g ())) (fun _ -> True) (fun _ _ _ -> True) =\n let x = pure_g () in\n dep_f x", "val h: Prims.unit -> IMST nat (idx nat nat_rel (fun p s0 -> forall s1. s1 > s0 ==> p s1 s1))\nlet h ()\n : IMST nat (idx nat nat_rel (fun p s0 -> forall s1 . s1 > s0 ==> p s1 s1))\n = let s0 = get #nat #eq_rel () in \n put #nat #eq_rel s0;\n put #nat #nat_rel (s0 + 1);\n let s1 = get #nat #eq_rel () in\n s1", "val tconclude: Prims.unit -> T.Tac unit\nlet tconclude () : T.Tac unit = tconclude_with []" ], "closest_src": [ { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.test14" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.test12" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.test12_1" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.test13" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test14" }, { "project_name": "FStar", "file_name": "Sec2.IFC.fst", "name": "Sec2.IFC.test10" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test12" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test12_1" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test13" }, { "project_name": "FStar", "file_name": "Sec2.HIFC.fst", "name": "Sec2.HIFC.test10" }, { "project_name": "karamel", "file_name": "LowStar.Lib.LinkedList2.fst", "name": "LowStar.Lib.LinkedList2.test" }, { "project_name": "FStar", "file_name": "HoareSTFree.fst", "name": "HoareSTFree.test" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.__c1" }, { "project_name": "steel", "file_name": "SteelSTFramingTestSuite.fst", "name": "SteelSTFramingTestSuite.test" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.test2" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.test" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.test" }, { "project_name": "FStar", "file_name": "TestHoareST.fst", "name": "TestHoareST.test2" }, { "project_name": "FStar", "file_name": "TestHoareST.fst", "name": "TestHoareST.test4" }, { "project_name": "FStar", "file_name": "Tests.fst", "name": "Tests.test2" }, { "project_name": "FStar", "file_name": "TestHoareST.fst", "name": "TestHoareST.test13" }, { "project_name": "FStar", "file_name": "TestHoareST.fst", "name": "TestHoareST.test" }, { "project_name": "FStar", "file_name": "CalcInference.fst", "name": "CalcInference.test2" }, { "project_name": "FStar", "file_name": "Tests.fst", "name": "Tests.test1" }, { "project_name": "FStar", "file_name": "TestHoareST.fst", "name": "TestHoareST.test11" }, { "project_name": "steel", "file_name": "SteelFramingTestSuite.fst", "name": "SteelFramingTestSuite.test" }, { "project_name": "FStar", "file_name": "TestHoareST.fst", "name": "TestHoareST.test5" }, { "project_name": "FStar", "file_name": "DM4F_layered.fst", "name": "DM4F_layered.test" }, { "project_name": "FStar", "file_name": "DM4F.fst", "name": "DM4F.test" }, { "project_name": "FStar", "file_name": "DM4F_layered5.fst", "name": "DM4F_layered5.test" }, { "project_name": "FStar", "file_name": "CalcInference.fst", "name": "CalcInference.test1" }, { "project_name": "FStar", "file_name": "CalcInference.fst", "name": "CalcInference.test3" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.test_catch0" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.get" }, { "project_name": "FStar", "file_name": "Example.fst", "name": "Example.main" }, { "project_name": "FStar", "file_name": "Tests.fst", "name": "Tests.test6" }, { "project_name": "steel", "file_name": "Deref2.fst", "name": "Deref2.test1" }, { "project_name": "FStar", "file_name": "ID2.fst", "name": "ID2.test_2" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.get_r" }, { "project_name": "FStar", "file_name": "TestHoareST.fst", "name": "TestHoareST.test6" }, { "project_name": "steel", "file_name": "Wasm11.fst", "name": "Wasm11.test1" }, { "project_name": "steel", "file_name": "Wasm11.fst", "name": "Wasm11.test2" }, { "project_name": "FStar", "file_name": "LatticeSpec.fst", "name": "LatticeSpec.get" }, { "project_name": "FStar", "file_name": "Unification.fst", "name": "Unification.test" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Tutorial.fst", "name": "FStar.InteractiveHelpers.Tutorial.ut_ex2" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.get" }, { "project_name": "FStar", "file_name": "HoareST.fst", "name": "HoareST.get" }, { "project_name": "noise-star", "file_name": "Spec.Noise.IKpsk2.Test.fst", "name": "Spec.Noise.IKpsk2.Test.test" }, { "project_name": "noise-star", "file_name": "Spec.Noise.XX.Test.fst", "name": "Spec.Noise.XX.Test.test" }, { "project_name": "hacl-star", "file_name": "Spec.Frodo.Test.fst", "name": "Spec.Frodo.Test.test" }, { "project_name": "noise-star", "file_name": "Spec.Noise.Patterns.Test.fst", "name": "Spec.Noise.Patterns.Test.test" }, { "project_name": "FStar", "file_name": "Simplifier.fst", "name": "Simplifier.test_simplify" }, { "project_name": "FStar", "file_name": "Benton2004.RHL.Examples2.fst", "name": "Benton2004.RHL.Examples2.proof" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Lemmas.fst", "name": "Hacl.Spec.Poly1305.Lemmas.poly_semiring" }, { "project_name": "FStar", "file_name": "LocalState.fst", "name": "LocalState.t2" }, { "project_name": "FStar", "file_name": "ImmutableBuffer.fst", "name": "ImmutableBuffer.test_ub" }, { "project_name": "noise-star", "file_name": "Spec.Noise.WellFormedness.fsti", "name": "Spec.Noise.WellFormedness.test_all_wf_lem" }, { "project_name": "FStar", "file_name": "HandleSmtGoal.fst", "name": "HandleSmtGoal.g" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.test_subcomp" }, { "project_name": "FStar", "file_name": "ND.fst", "name": "ND.test" }, { "project_name": "FStar", "file_name": "TestHoareST.fst", "name": "TestHoareST.test3" }, { "project_name": "FStar", "file_name": "LL.fst", "name": "LL.test" }, { "project_name": "hacl-star", "file_name": "Test.Hash.fst", "name": "Test.Hash.test_incremental_api" }, { "project_name": "FStar", "file_name": "GT.fst", "name": "GT.t1_t" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.laws" }, { "project_name": "FStar", "file_name": "Term.fst", "name": "Term.one_t" }, { "project_name": "FStar", "file_name": "ImmutableBuffer.fst", "name": "ImmutableBuffer.test_pf" }, { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.test_assert" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.test_assert" }, { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.callmap" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.callmap" }, { "project_name": "FStar", "file_name": "ND.fst", "name": "ND.l" }, { "project_name": "FStar", "file_name": "IMST.fst", "name": "IMST.f" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.EverCrypt.fst", "name": "MiTLS.EverCrypt.vale" }, { "project_name": "FStar", "file_name": "TestHoareST.fst", "name": "TestHoareST.test9" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.get" }, { "project_name": "everparse", "file_name": "LowParse.TacLib.fst", "name": "LowParse.TacLib.conclude" }, { "project_name": "FStar", "file_name": "IMSTsub.fst", "name": "IMSTsub.g" }, { "project_name": "FStar", "file_name": "Canon.fst", "name": "Canon.test_neg2" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.admit1" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.admit1" }, { "project_name": "karamel", "file_name": "C.Failure.fst", "name": "C.Failure.whatever" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.__h1" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.smt" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.smt" }, { "project_name": "everparse", "file_name": "LowParse.TacLib.fst", "name": "LowParse.TacLib.solve_vc" }, { "project_name": "noise-star", "file_name": "Spec.Noise.XX.Test.fst", "name": "Spec.Noise.XX.Test.test_XX" }, { "project_name": "FStar", "file_name": "Automation.fst", "name": "Automation.conjt" }, { "project_name": "FStar", "file_name": "HandleSmtGoal.fst", "name": "HandleSmtGoal.tac2" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.cur_witness" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.cur_witness" }, { "project_name": "FStar", "file_name": "Automation.fst", "name": "Automation.triv" }, { "project_name": "FStar", "file_name": "MSeqExn.fst", "name": "MSeqExn.size" }, { "project_name": "FStar", "file_name": "Arith.fst", "name": "Arith.tau1" }, { "project_name": "steel", "file_name": "Steel.Primitive.ForkJoin.Unix.fst", "name": "Steel.Primitive.ForkJoin.Unix.example4" }, { "project_name": "FStar", "file_name": "LL.fst", "name": "LL.test_st" }, { "project_name": "FStar", "file_name": "DependentSynth.fst", "name": "DependentSynth.t" }, { "project_name": "FStar", "file_name": "HoareSTPolyBind.fst", "name": "HoareSTPolyBind.test_dep_f2" }, { "project_name": "FStar", "file_name": "IMSTsub.fst", "name": "IMSTsub.h" }, { "project_name": "FStar", "file_name": "MiniParse.Tac.Base.fst", "name": "MiniParse.Tac.Base.tconclude" } ], "selected_premises": [ "OPLSS2021.IFC.test10", "OPLSS2021.IFC.test12", "OPLSS2021.IFC.test13", "OPLSS2021.IFC.test12_1", "OPLSS2021.IFC.sel", "OPLSS2021.IFC.low", "OPLSS2021.IFC.triple_equiv", "OPLSS2021.IFC.upd", "OPLSS2021.IFC.unit_triple", "OPLSS2021.IFC.flows", "OPLSS2021.IFC.left_unit", "OPLSS2021.IFC.triple", "OPLSS2021.IFC.single", "OPLSS2021.IFC.right_unit", "OPLSS2021.IFC.flows_equiv", "FStar.Pervasives.reveal_opaque", "OPLSS2021.IFC.flows_equiv_append", "OPLSS2021.IFC.ist", "FStar.Pervasives.Native.snd", "OPLSS2021.IFC.add_source_bot", "OPLSS2021.IFC.flow", "OPLSS2021.IFC.comp_triple", "OPLSS2021.IFC.read", "FStar.Pervasives.Native.fst", "OPLSS2021.IFC.union", "OPLSS2021.IFC.add_source_monotonic", "OPLSS2021.IFC.iwrite", "OPLSS2021.IFC.label_equiv", "OPLSS2021.IFC.iread", "OPLSS2021.IFC.no_leakage_k", "OPLSS2021.IFC.write", "OPLSS2021.IFC.bind", "OPLSS2021.IFC.add_source", "OPLSS2021.IFC.respects_flows", "OPLSS2021.IFC.does_not_read_loc_v", "OPLSS2021.IFC.label", "OPLSS2021.IFC.add_sink", "OPLSS2021.IFC.subcomp", "FStar.Pervasives.dfst", "OPLSS2021.IFC.has_flow", "OPLSS2021.IFC.return", "OPLSS2021.IFC.bot", "OPLSS2021.IFC.no_leakage", "FStar.Pervasives.dsnd", "OPLSS2021.IFC.label_inclusion", "OPLSS2021.IFC.memP_append_or", "OPLSS2021.IFC.loc", "OPLSS2021.IFC.has_flow_soundness", "OPLSS2021.IFC.flows_included_append", "OPLSS2021.IFC.tot", "OPLSS2021.IFC.elim_has_flow_seq", "OPLSS2021.IFC.havoc", "OPLSS2021.IFC.bind_comp", "OPLSS2021.IFC.flows_included_in", "OPLSS2021.IFC.bind_comp_no_leakage", "OPLSS2021.IFC.ref", "OPLSS2021.IFC.writes_ok", "OPLSS2021.IFC.append_nil_r", "OPLSS2021.IFC.has_flow_1", "OPLSS2021.IFC.assoc_comp", "OPLSS2021.IFC.bind_comp_reads_ok", "OPLSS2021.IFC.has_flow_append", "OPLSS2021.IFC.does_not_read_loc", "OPLSS2021.IFC.lift_tot", "OPLSS2021.IFC.test3_lab", "OPLSS2021.IFC.comp", "FStar.Set.add", "OPLSS2021.IFC.reads_ok", "FStar.Calc.calc_chain_related", "FStar.Set.as_set'", "OPLSS2021.IFC.href", "OPLSS2021.IFC.test7", "OPLSS2021.IFC.test2", "FStar.Set.subset", "OPLSS2021.IFC.store", "FStar.Preorder.preorder_rel", "Prims.min", "OPLSS2021.IFC.test3", "OPLSS2021.IFC.bind_comp_flows_ok", "OPLSS2021.IFC.test6", "FStar.Set.remove", "OPLSS2021.IFC.test3_1", "OPLSS2021.IFC.test9", "OPLSS2021.IFC.test5", "OPLSS2021.IFC.test", "FStar.Preorder.reflexive", "FStar.Preorder.transitive", "FStar.Set.as_set", "FStar.Set.disjoint", "OPLSS2021.IFC.test4", "Prims.subtype_of", "FStar.Pervasives.pure_ite_wp", "Prims.auto_squash", "FStar.Pervasives.coerce_eq", "FStar.Pervasives.pure_bind_wp", "FStar.Pervasives.pure_close_wp", "FStar.Calc.calc_chain_compatible", "Prims.op_Hat", "FStar.Pervasives.id", "Prims.as_requires" ], "source_upto_this": "(*\n Copyright 2021 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule OPLSS2021.IFC\nopen FStar.List.Tot\nopen FStar.Set\nopen FStar.Map\n\n(* This module defines another abstraction for reasoning about\n information flows in stateful computations reading and writing to\n an integer store.\n\n The main computation type it defines at the end is `IST a w r fs`,\n where\n - `a` is the result type\n - `w` is the set of memory locations written\n - `r` is the set of memory locations read\n - `fs` is a set of flows, ordered pairs of sets of locations\n between bounding the information flows in the program\n\n The point is to illustrate that you can choose whatever abstraction\n you like to reason about your programs, not necessarily a Hoare\n logic.\n\n This turns out to be an instance of Katsumata's graded monads.\n\n Read more about it in this paper:\n https://www.fstar-lang.org/papers/layeredeffects/\n*)\n\n/// The type of memory locations\nlet loc = int\n\n/// A store itself is a total map from locations to integers\nlet store = m:Map.t loc int{forall l. contains m l}\n\n/// Two functions to read and write the store\nlet sel (s:store) (l:loc) : int = Map.sel s l\nlet upd (s:store) (l:loc) (x:int) : store = Map.upd s l x\n\n/// Our abstraction to reason about information flows is based on\n/// labels, sets of memory locations\nlet label = Set.set loc\n\n/// An ordering on labels, just set inclusion\nlet label_inclusion (l0 l1:label) = Set.subset l0 l1\n\n/// A bottom for the label lattice\nlet bot : label = Set.empty\n\n/// A singleton label\nlet single (l:loc) : label = Set.singleton l\n\n/// A join for our lattice: just set union\nlet union (l0 l1:label) = Set.union l0 l1\n\n/// comp a: A computation monad representing our stateful computations\nlet comp a = store -> a & store\n\n/// havoc, or mess up, a single memory location in s by updating it\nlet havoc s l x = upd s l x\n\n/// Now, we're going to have to (slowly) define what it means for a\n/// program to have or not have certain kinds of information flows.\n\n/// Defining what it means for f's mutations to be confined to\n/// `writes` is easy\n/// -- all locations not in writes do not change\nlet writes_ok #a (f:comp a) (writes:Set.set loc) =\n forall (l:loc). ~(Set.mem l writes) ==>\n (forall (s0:store).\n let x1, s0' = f s0 in\n sel s0 l == sel s0' l)\n\n/// Definiting what it means for `f` to not read a location `l`\n/// is trickier. It involves a \"relational\" property, relating\n/// multiple executions of `f`\nlet does_not_read_loc_v #a (f:comp a) (l:loc) (s0:store) v =\n let s0' = havoc s0 l v in //s0 and s0' agree except on l\n let x1, s1 = f s0 in\n let x1', s1' = f s0' in // run f twice, once on s0, once on s0'\n x1 == x1' /\\ //result does not depend on l\n (forall l'. l' <> l ==> //for every location l' not equal to l\n sel s1 l' == sel s1' l') /\\ //its value in the two states is the same\n (sel s1 l == sel s1' l \\/ //and l is itself may be written, in which case its value is the same in both final states\n //or its not, but then its values in the initial and final states are the same in both runs\n (sel s1 l == sel s0 l /\\\n sel s1' l == sel s0' l))\n\n/// does_not_read_loc: Lifting the prior property to all values for\n/// the havoc'd location l\nlet does_not_read_loc #a (f:comp a) (l:loc) (s0:store) =\n forall v. does_not_read_loc_v f l s0 v\n\n/// A reads label is ok for `f` if it is a bound on the set of\n/// locations that `f` reads\nlet reads_ok #a (f:comp a) (reads:label) =\n forall (l:loc) (s:store). ~(Set.mem l reads) ==> does_not_read_loc f l s\n\n/// Now for the flows index\nlet flow = label & label //from, to\nlet flows = list flow\n\n/// `has_flow from to fs` defines when the edge `from -> to` is includes in\n/// the flows `fs`\nlet has_flow_1 (from to:loc) (f:flow) = from `Set.mem` fst f /\\ to `Set.mem` snd f\nlet has_flow (from to:loc) (fs:flows) = exists rs. rs `List.Tot.memP` fs /\\ has_flow_1 from to rs\n\n/// Now, as with reads and writes, we have to give an interpretation\n/// to flows tying it to the computational representation\n\n/// `f` leaks no info along the flow edge `from -> to`\n/// --- This is a textbook definition of noninterference\nlet no_leakage_k #a (f:comp a) (from to:loc) (k:int) =\n forall s0.{:pattern (havoc s0 from k)}\n sel (snd (f s0)) to == sel (snd (f (havoc s0 from k))) to\nlet no_leakage #a (f:comp a) (from to:loc) = forall k. no_leakage_k f from to k\n/// A computation `f` respects all the flows in `fs`\n/// if it there is no leakage along any of the flow-edges in `f`\nlet respects_flows #a (f:comp a) (fs:flows) =\n forall from to. {:pattern (no_leakage f from to)} ~(has_flow from to fs) /\\ from<>to ==> no_leakage f from to\n\n/// Now, we can define our representation type, a refinement of the\n/// comp type where the refinement \"gives a meaning\" to the labels\n/// involved\nlet ist a (writes:label) (reads:label) (fs:flows) =\n f:comp a {\n reads_ok f reads /\\\n writes_ok f writes /\\\n respects_flows f fs\n }\n\n/// Now, proving that this representation is stable is going to take\n/// some work.\n\n/// Some basic actions to read and write and a return are easy enough\nlet iread (l:loc) : ist int bot (single l) [] = fun s -> sel s l, s\nlet iwrite (l:loc) (x:int) : ist unit (single l) bot [] = fun s -> (), upd s l x\nlet return (a:Type) (x:a) : ist a bot bot [] = fun s -> x,s\n\n/// But, proving that ist computations can be sequentially composed is\n/// a bit challenging\n\n/// First, some auxiliary notions defining a small algebra on flows\nlet add_source (r:label) (fs:flows) : flows = List.Tot.map (fun (r0, w0) -> union r r0, w0) fs\nlet add_sink (w:label) (fs:flows) : flows = List.Tot.map (fun (r0, w0) -> r0, union w w0) fs\nlet flows_included_in (fs0 fs1:flows) =\n forall f0. f0 `List.Tot.memP` fs0 ==>\n (forall from to. has_flow_1 from to f0 /\\ from <> to ==> (exists f1. f1 `List.Tot.memP` fs1 /\\ has_flow_1 from to f1))\nlet flows_equiv (fs0 fs1:flows) = fs0 `flows_included_in` fs1 /\\ fs1 `flows_included_in` fs0\nlet flows_equiv_refl fs\n : Lemma (fs `flows_equiv` fs)\n = ()\nlet flows_equiv_trans fs0 fs1 fs2\n : Lemma (fs0 `flows_equiv` fs1 /\\ fs1 `flows_equiv` fs2 ==> fs0 `flows_equiv` fs2)\n = ()\nlet flows_included_in_union_distr_dest (a b c:label)\n : Lemma (flows_equiv [a, union b c] [a, b; a, c])\n = ()\nlet flows_included_in_union_distr_src (a b c:label)\n : Lemma (flows_equiv [union a b, c] [a, c; b, c])\n = ()\nlet flows_included_in_union (a b c:label)\n : Lemma (flows_equiv ([a, union b c; union a b, c])\n ([a, b; union a b, c]))\n = ()\n\n\n\nlet bind_comp (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : comp b\n = fun s0 -> let v, s1 = x s0 in y v s1\n\nlet bind_comp_reads_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (reads_ok (bind_comp x y) (union r0 r1))\n = let f = bind_comp x y in\n let reads = union r0 r1 in\n let f_reads_ok (l:loc) (s0:store)\n : Lemma (requires (~(Set.mem l reads)))\n (ensures (does_not_read_loc f l s0))\n [SMTPat (does_not_read_loc f l s0)]\n = let aux (k:_)\n : Lemma (ensures (does_not_read_loc_v f l s0 k))\n [SMTPat (does_not_read_loc_v f l s0 k)]\n = let v, s1 = x s0 in\n let v', s1' = x (havoc s0 l k) in\n assert (does_not_read_loc x l s0);\n assert (does_not_read_loc_v x l s0 k);\n assert (v == v');\n assert (does_not_read_loc (y v) l s1);\n let u, s2 = y v s1 in\n let u', s2' = y v s1' in\n assert (forall l'. l' <> l ==> sel s1 l' == sel s1' l');\n if sel s1 l = sel s1' l\n then (assert (forall l. sel s1 l == sel s1' l);\n assert (Map.equal s1 s1'))\n else (assert (sel s1 l == sel s0 l /\\\n sel (havoc s0 l k) l == sel s1' l);\n assert (Map.equal s1' (havoc s1 l k)))\n in\n ()\n in\n ()\n\nlet bind_comp_writes_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (writes_ok (bind_comp x y) (union w0 w1))\n = ()\n\nlet rec memP_append_or (#a:Type) (x:a) (l0 l1:list a)\n : Lemma (ensures (List.Tot.memP x (l0 @ l1) <==>\n (List.Tot.memP x l0 \\/ List.Tot.memP x l1)))\n (decreases l0)\n = match l0 with\n | [] -> ()\n | _::tl -> memP_append_or x tl l1\n\nlet has_flow_append (from to:loc) (fs fs':flows)\n : Lemma (has_flow from to fs ==>\n has_flow from to (fs @ fs') /\\\n has_flow from to (fs' @ fs))\n = let rec aux (rs:_)\n : Lemma (requires\n List.Tot.memP rs fs)\n (ensures\n List.Tot.memP rs (fs @ fs') /\\\n List.Tot.memP rs (fs' @ fs))\n [SMTPat (List.Tot.memP rs fs)]\n = memP_append_or rs fs fs';\n memP_append_or rs fs' fs\n in\n ()\n\nlet elim_has_flow_seq (from to:loc)\n (r0 r1 w1:label)\n (fs0 fs1:flows)\n : Lemma (requires (~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1)))))\n (ensures (~(has_flow from to fs0) /\\\n (~(Set.mem from r0) \\/ ~(Set.mem to w1)) /\\\n ~(has_flow from to (add_source r0 fs1))))\n = assert (add_source r0 ((bot, w1)::fs1) ==\n (Set.union r0 bot, w1)::add_source r0 fs1);\n assert (Set.union r0 bot `Set.equal` r0);\n has_flow_append from to fs0 ((r0, w1)::add_source r0 fs1);\n assert (~(has_flow from to fs0));\n has_flow_append from to ((r0, w1)::add_source r0 fs1) fs0;\n assert (~(has_flow from to (((r0, w1)::add_source r0 fs1))));\n assert ((r0, w1)::add_source r0 fs1 ==\n [r0, w1] @ add_source r0 fs1);\n has_flow_append from from [r0, w1] (add_source r0 fs1)\n\nlet rec add_source_monotonic (from to:loc) (r:label) (fs:flows)\n : Lemma (has_flow from to fs ==> has_flow from to (add_source r fs))\n = match fs with\n | [] -> ()\n | _::tl -> add_source_monotonic from to r tl\n\nlet has_flow_soundness #a #r #w #fs (f:ist a r w fs)\n (from to:loc) (s:store) (k:int)\n : Lemma (requires\n (let x, s1 = f s in\n let _, s1' = f (havoc s from k) in\n from <> to /\\\n sel s1 to <> sel s1' to))\n (ensures has_flow from to fs)\n = let aux ()\n : Lemma (requires (~(has_flow from to fs)))\n (ensures False)\n [SMTPat ()]\n = assert (respects_flows f fs);\n assert (no_leakage f from to)\n in\n ()\n\nlet bind_comp_no_leakage (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n (from to:loc)\n (s0:store) (k:_)\n : Lemma\n (requires from <> to /\\ ~(has_flow from to (fs0 @ add_source r0 ((bot, w1)::fs1))))\n (ensures (let f = bind_comp x y in\n let s0' = havoc s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to))\n = let f = bind_comp x y in\n assert (reads_ok x r0);\n let s0' = havoc s0 from k in\n let _, s2f = f s0 in\n let _, s2f' = f s0' in\n let flows = (fs0 @ add_source r0 ((r1, w1)::fs1)) in\n let v0, s1 = x s0 in\n let v0', s1' = x s0' in\n elim_has_flow_seq from to r0 r1 w1 fs0 fs1;\n assert (~(has_flow from to fs0));\n assert (respects_flows x fs0);\n assert (no_leakage x from to);\n assert (sel s1 to == sel s1' to);\n let _, s2 = y v0 s1 in\n let _, s2' = y v0' s1' in\n assert (s2 == s2f);\n assert (s2' == s2f');\n //Given: (from not-in r0 U r1) \\/ (to not-in w1)\n //suppose (from in r0) \\/ (from in r1)\n // them to not-in w1\n //suppose (from not-in r0 U r1)\n //then v0 = v0'\n // s1' = havoc from s1 k\n // s2 to = s2' to\n if Set.mem to w1\n then begin\n assert (~(Set.mem from r0));\n assert (reads_ok x r0);\n assert (does_not_read_loc x from s0);\n assert (does_not_read_loc_v x from s0 k);\n assert (v0 == v0');\n assert (forall l. l <> from ==> sel s1 l == sel s1' l);\n assert (Map.equal s1' (havoc s1 from k) \\/ Map.equal s1' s1);\n if (sel s1 from = sel s1' from)\n then begin\n assert (Map.equal s1 s1')\n end\n else begin\n assert (Map.equal s1' (havoc s1 from k));\n assert (reads_ok (y v0) r1);\n if (sel s2 to = sel s2' to)\n then ()\n else begin\n assert (sel s2 to <> sel s1 to \\/ sel s2' to <> sel s1' to);\n has_flow_soundness (y v0) from to s1 k;\n assert (has_flow from to fs1);\n add_source_monotonic from to r0 fs1\n //y reads from and writes to, so (from, to) should be in fs1\n //so, we should get a contradiction\n end\n end\n end\n else //to is not in w1, so y does not write it\n ()\n\nlet bind_comp_flows_ok (#a #b:Type)\n (#w0 #r0 #w1 #r1:label)\n (#fs0 #fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : Lemma (respects_flows (bind_comp x y) (fs0 @ add_source r0 ((bot, w1)::fs1)))\n = let f = bind_comp x y in\n let flows = (fs0 @ add_source r0 ((bot, w1)::fs1)) in\n let respects_flows_lemma (from to:loc)\n : Lemma (requires from <> to /\\ ~(has_flow from to flows))\n (ensures no_leakage f from to)\n [SMTPat (no_leakage f from to)]\n = let aux (s0:store) (k:_)\n : Lemma (let s0' = havoc s0 from k in\n let _, s2 = f s0 in\n let _, s2' = f s0' in\n sel s2 to == sel s2' to)\n [SMTPat (havoc s0 from k)]\n = bind_comp_no_leakage x y from to s0 k\n in\n ()\n in\n ()\n\nlet triple = label & label & flows\nlet unit_triple = bot, bot, []\nlet comp_triple (w0, r0, fs0) (w1, r1, fs1) = (union w0 w1, union r0 r1, (fs0 @ add_source r0 ((bot, w1)::fs1)))\n\nlet label_equiv (s0 s1:label) = Set.equal s0 s1\nlet triple_equiv (w0, r0, f0) (w1, r1, f1) = label_equiv w0 w1 /\\ label_equiv r0 r1 /\\ flows_equiv f0 f1\nlet triple_equiv_refl t0\n : Lemma (triple_equiv t0 t0)\n = ()\nlet rec add_source_bot (f:flows)\n : Lemma (add_source bot f `flows_equiv` f)\n = match f with\n | [] -> ()\n | _::tl -> add_source_bot tl\nlet left_unit (w, r, f) =\n assert (Set.equal (union bot bot) bot);\n add_source_bot f;\n assert (comp_triple unit_triple (w, r, f) `triple_equiv` (w, r, f))\nlet flows_included_append (f0 f1 g0 g1:flows)\n : Lemma (requires flows_included_in f0 g0 /\\\n flows_included_in f1 g1)\n (ensures flows_included_in (f0@f1) (g0@g1))\n = let aux (f:_) (from to:_)\n : Lemma (requires List.Tot.memP f (f0@f1) /\\\n from <> to /\\\n has_flow_1 from to f)\n (ensures (exists g. g `List.Tot.memP` (g0@g1) /\\ has_flow_1 from to g))\n [SMTPat (has_flow_1 from to f)]\n = memP_append_or f f0 f1;\n assert (exists g. g `List.Tot.memP` g0 \\/ g `List.Tot.memP` g1 /\\ has_flow_1 from to g);\n FStar.Classical.forall_intro (fun g -> memP_append_or g g0 g1)\n in\n ()\nlet flows_equiv_append (f0 f1 g0 g1:flows)\n : Lemma (requires flows_equiv f0 g0 /\\ flows_equiv f1 g1)\n (ensures flows_equiv (f0@f1) (g0@g1))\n = flows_included_append f0 f1 g0 g1;\n flows_included_append g0 g1 f0 f1\nlet rec append_nil_r #a (l:list a)\n : Lemma (l @ [] == l)\n = match l with\n | [] -> ()\n | _::tl -> append_nil_r tl\nlet right_unit (w, r, f) =\n calc (==) {\n comp_triple (w, r, f) unit_triple;\n (==) { }\n (w `union` bot, r `union` bot, f @ add_source r ((bot, bot)::[]));\n };\n assert (flows_equiv (add_source r [(bot, bot)]) []);\n flows_equiv_append f (add_source r [(bot, bot)]) f [];\n append_nil_r f;\n assert (comp_triple (w, r, f) unit_triple `triple_equiv` (w, r, f))\nopen FStar.Calc\nlet assoc_comp (w0, r0, fs0) (w1, r1, fs1) (w2, r2, fs2) =\n calc (==) {\n comp_triple (w0, r0, fs0) (comp_triple (w1, r1, fs1) (w2, r2, fs2)) ;\n (==) { }\n comp_triple (w0, r0, fs0) (union w1 w2, union r1 r2, (fs1 @ add_source r1 ((bot, w2)::fs2)));\n (==) { }\n (union w0 (union w1 w2), union r0 (union r1 r2), fs0 @ (add_source r0 ((bot, union w1 w2) :: (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { assert (forall w0 w1 w2. Set.equal (union w0 (union w1 w2)) (union (union w0 w1) w2)) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n fs0 @ (add_source r0 ((bot, union w1 w2) :: (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n (fs0 @ ((union r0 bot, union w1 w2) :: add_source r0 (fs1 @ add_source r1 ((bot, w2)::fs2)))));\n (==) { assert (forall s. Set.equal (union s bot) s) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n (fs0 @ ((r0, union w1 w2) :: add_source r0 (fs1 @ (r1, w2) ::add_source r1 fs2))));\n };\n calc (==) {\n comp_triple (comp_triple (w0, r0, fs0) (w1, r1, fs1)) (w2, r2, fs2);\n (==) { }\n comp_triple (union w0 w1, union r0 r1, (fs0 @ add_source r0 ((bot, w1)::fs1))) (w2, r2, fs2);\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ add_source r0 ((bot, w1)::fs1)) @ (add_source (union r0 r1) ((bot, w2) :: fs2))));\n (==) { }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ ((union r0 bot, w1)::add_source r0 fs1)) @ ((union (union r0 r1) bot, w2) :: add_source (union r0 r1) fs2)));\n (==) { assert (forall s. Set.equal (union s bot) s) }\n (union (union w0 w1) w2,\n union (union r0 r1) r2,\n ((fs0 @ ((r0, w1)::add_source r0 fs1)) @ ((union r0 r1, w2) :: add_source (union r0 r1) fs2)));\n }\n\n/// But, here, we have it:\nlet bind (a b:Type)\n (w0 r0 w1 r1:label) (fs0 fs1:flows)\n (x:ist a w0 r0 fs0)\n (y: a -> ist b w1 r1 fs1)\n : ist b\n (union w0 w1) // union the writes\n (union r0 r1) // union the reads\n (fs0 @ // flows of x\n add_source r0 ((bot, w1) // plus flows from whatever x reads to whatever y writes\n ::fs1)) //plus the flows of y\n = let f = fun s0 -> let v, s1 = x s0 in y v s1 in\n bind_comp_reads_ok x y;\n bind_comp_reads_ok x y;\n bind_comp_flows_ok x y;\n f\n\n/// A subsumption rule to weaken the labels\nlet subcomp (a:Type) (w0 r0 w1 r1:label) (fs0 fs1:flows) (f:ist a w0 r0 fs0)\n : Pure (ist a w1 r1 fs1)\n (requires label_inclusion w0 w1 /\\\n label_inclusion r0 r1 /\\\n fs0 `flows_included_in` fs1)\n (fun _ -> True)\n = let f_reads_ok (l:loc) (s0:store)\n : Lemma (requires (~(Set.mem l r1)))\n (ensures (does_not_read_loc f l s0))\n [SMTPat (does_not_read_loc f l s0)]\n = let aux (k :_)\n : Lemma (ensures (does_not_read_loc_v f l s0 k))\n [SMTPat (does_not_read_loc_v f l s0 k)]\n = let v, s1 = f s0 in\n let v', s1' = f (havoc s0 l k) in\n assert (does_not_read_loc f l s0);\n assert (v == v');\n assert (not (Set.mem l w0) ==> sel s1' l = k);\n assert (not (Set.mem l w1) ==> sel s1' l = k);\n ()\n in\n ()\n in\n f\n\n/// Package it up as an effect\nreflectable\nlayered_effect {\n IST : a:Type ->\n w:label ->\n w:label ->\n fs:flows ->\n Effect\n with\n repr = ist;\n return = return;\n bind = bind;\n subcomp = subcomp\n}\nlet read (l:loc) : IST int bot (single l) [] = IST?.reflect (iread l)\nlet write (l:loc) (x:int) : IST unit (single l) bot [] = IST?.reflect (iwrite l x)\n\nlet tot a = unit -> Tot a\nlet lift_tot (a:Type) (x:tot a)\n : ist a bot bot []\n = return a (x())\nsub_effect PURE ~> IST = lift_tot\n\n////////////////////////////////////////////////////////////////////////////////\n// Now for some examples\n////////////////////////////////////////////////////////////////////////////////\nlet ref (l:label) = r:loc {r `Set.mem` l}\nassume val high : label\nlet low : label = Set.complement high\nlet lref = ref low\nlet href = ref high\n\nlet test (l:lref) (h:href)\n : IST unit (union bot (single h))\n (union (single l) bot)\n (add_source (single l) [bot, single h])\n = let x = read l in\n write h x\n\nlet test2 (l:lref) (h:href)\n : IST unit (single h)\n (single l)\n [single l, single h]\n = let x = read l in\n write h x\n\nlet test3 (l:lref) (h:href)\n : IST unit (single h)\n (single l)\n [single l, single h]\n = write h (read l)\n\nlet test3_lab (l:lref) (h:href)\n : IST unit high low [low, high]\n = write h (read l)\n\nlet test3_1 (l:lref) (h:href) (x:int)\n : IST int (single h)\n (single l)\n []\n = write h 0;\n read l\n\nlet test4 (l:lref) (h:href) (x:int)\n : IST int (single l)\n (single h)\n [single h, bot]\n = write l x;\n read h\n\nlet test5 (l:lref) (h:href) (x:int)\n : IST int (single l)\n (single h)\n []\n = write l x;\n read h\n\nlet test6 (l:lref) (h:href)\n : IST unit high low [low, high]\n = let x = read l in\n write h x\n\n//This leaks the contents of the href\nlet test7 (l:lref) (h:href)\n : IST unit (single l)\n (single h)\n [high, low]\n = let x = read h in\n write l x\n\n//But, label-based IFC is inherently imprecise\n//This one still reports a leakage, even though it doesn't really leak h\nlet test8 (l:lref) (h:href)\n : IST unit (single l)\n (union (single h) (single l))\n [(single l `union` single h, single l)]\n = let x0 = read h in\n let x = read l in\n write l x\n\n//But, label-based IFC is inherently imprecise\n//This one still reports a leakage, even though it doesn't really leak h\nlet test9 (l:lref) (h:href)\n : IST unit (single l)\n (union (single h) (single l))\n [(single l `union` single h, single l)]\n = let x= (let x0 = read h in\n read l)\n in\n write l x\n\nassume\nval cw0 : label\nassume\nval cr0 : label\nassume\nval c0 (_:unit) : IST unit cw0 cr0 []\n\n\nassume\nval cw1 : label\nassume\nval cr1 : label\nassume\nval c1 (_:unit) : IST unit cw1 cr1 []\n\nassume\nval cw2 : label\nassume\nval cr2 : label\nassume\nval c2 (_:unit) : IST unit cw2 cr2 []\n\nlet test10 ()\n : IST unit (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n (add_source cr0\n ((bot, union cw1 cw2)::\n (add_source cr1 [bot, cw2])))\n = c0 (); (c1();c2())\n\n\nlet test12 ()\n : IST unit (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n [(cr0, union cw1 cw2);\n (union cr0 cr1, cw2)]\n = c0 (); (c1();c2())\n\nlet test12_1 ()\n : IST unit (union cw0 (union cw1 cw2))\n (union cr0 (union cr1 cr2))\n [(cr0, cw1);\n (union cr0 cr1, cw2)]\n = c0 (); (c1();c2())\n\n\nlet test13 ()\n : IST unit (union (union cw0 cw1) cw2)\n (union (union cr0 cr1) cr2)\n (add_source cr0 [bot, cw1] @\n add_source (union cr0 cr1) [bot, cw2])\n = (c0 (); c1());c2()\n" }, { "file_name": "Param.fst", "name": "Param.unit_param", "opens_and_abbrevs": [ { "open": "FStar.Tactics.V2" }, { "open": "FStar.List" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let unit_param = param_of_eqtype unit", "source_range": { "start_line": 104, "start_col": 0, "end_line": 104, "end_col": 39 }, "interleaved": false, "definition": "Param.param_of_eqtype Prims.unit", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Param.param_of_eqtype", "Prims.unit" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "_: Prims.unit -> _: Prims.unit -> Type0", "prompt": "let unit_param =\n ", "expected_response": "param_of_eqtype unit", "source": { "project_name": "FStar", "file_name": "examples/param/Param.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "Param.fst", "checked_file": "dataset/Param.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Sealed.fsti.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Order.fst.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/FStar.List.fst.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "bvmap", "let fvmap = list (fv * fv)", "param_state", "param_state", "bvmap", "bvmap", "fresh", "fresh", "recs", "recs", "let rec fold_right2 (f : 'a -> 'b -> 'c -> Tac 'c) (l1:list 'a) (l2:list 'b) (c:'c) : Tac 'c =\n match l1, l2 with\n | h1::t1, h2::t2 -> f h1 h2 (fold_right2 f t1 t2 c)\n | [], [] -> c\n | _ -> fail \"fold_right2\"", "let rec zip3 (l1 : list 'a) (l2 : list 'b) (l3 : list 'c) : list ('a * 'b * 'c) =\n match l1, l2, l3 with\n | h1::t1, h2::t2, h3::t3 -> (h1, h2, h3) :: (zip3 t1 t2 t3)\n | _ -> []", "let last (xs:list 'a) : Tac 'a =\n match List.Tot.rev xs with\n | h::_ -> h\n | [] -> fail \"last: empty list\"", "let fresh_binder_named (nm:string) (t:typ) : Tac binder =\n // useful?\n //let n = fresh () in\n //let nm = nm ^ \"_\" ^ string_of_int n in\n Tactics.V2.fresh_binder_named nm t", "let app_binders (t:term) (bs:list binder) : Tac term =\n mk_e_app t (List.Tot.map binder_to_term bs)", "let push_var_to_state (v:namedv) (b0 b1 b2 : binder) (s:param_state) : param_state =\n { s with bvmap = (v, (b0, b1, b2)) :: s.bvmap }", "exception NotARecFV", "NotARecFV", "NotARecFV", "exception Unsupported of string", "Unsupported", "Unsupported", "exception NotFoundBV of namedv", "NotFoundBV", "NotFoundBV", "exception NotFoundFV of fv", "NotFoundFV", "NotFoundFV", "let lookup_rec_fv (s:param_state) (f:fv) : Tac fv =\n let rec aux (m:fvmap) : Tac fv =\n match m with\n | [] -> raise NotARecFV\n | (f1, k)::fs -> if compare_fv f f1 = Order.Eq\n then k\n else aux fs\n in\n aux s.recs", "let push_fv (f1 f2 : fv) (s:param_state) : param_state =\n { s with recs = (f1,f2)::s.recs }", "let lookup (s:param_state) (v:namedv) : Tac (binder & binder & binder) =\n let rec aux (bvm : bvmap) : Tac (binder & binder & binder) =\n match bvm with\n | [] ->\n raise (NotFoundBV v)\n | (v', r)::tl ->\n if (inspect_namedv v).uniq = (inspect_namedv v').uniq\n then r\n else aux tl\n in\n aux s.bvmap", "let replace_var (s:param_state) (b:bool) (t:term) : Tac term =\n match inspect t with\n | Tv_Var v ->\n begin try\n let (x, y, _) = lookup s v in\n let bv = binder_to_namedv (if b then y else x) in\n pack (Tv_Var bv)\n with\n (* Maybe we traversed a binder and there are variables not in the state.\n * The right thing here would be to track them... but this should do for now. *)\n | NotFoundBV _ -> t\n | e -> raise e\n end\n | _ -> t", "let replace_by (s:param_state) (b:bool) (t:term) : Tac term =\n let r = visit_tm (replace_var s b) t in\n //print (\"rep \" ^ string_of_bool b ^ \" \" ^ term_to_string t ^ \" = \" ^ term_to_string r);\n r", "let param_of_eqtype (a:eqtype) : a -> a -> Type0 = (fun (x y : a) -> squash (x == y))", "let int_param = param_of_eqtype int", "let bool_param = param_of_eqtype bool" ], "closest": [ "val Preprocess.test = _: Prims.unit -> Prims.unit\nlet test () =\n assert (test_add_1' 5 == 7)", "val maybe_intros: Prims.unit -> Tac unit\nlet rec maybe_intros () : Tac unit =\n let g = cur_goal () in\n match inspect g with\n | Tv_Arrow _ _ ->\n ignore (intro ());\n maybe_intros ()\n | _ -> ()", "val CalcImpl.test4 = _: Prims.unit -> Prims.unit\nlet test4 () =\n calc any {\n p /\\ p;\n <==> {}\n p;\n l_imp { lem () } (* can also use l_imp instead of ==> *)\n q /\\ q;\n <==> {}\n q;\n }", "val CalcImpl.test3 = _: Prims.unit -> Prims.unit\nlet test3 () =\n calc any {\n p /\\ p;\n <==> {}\n p;\n ==> { lem () } (* works per-step, even if the final relation is something else *)\n q /\\ q;\n <==> {}\n q;\n }", "val t: Prims.unit -> Tac unit\nlet t () : Tac unit =\n let test' = fresh_namedv () in\n let test = pack (Tv_Var test') in\n let e_true = `3 in\n let e_false = `() in\n let body = mk_if test e_true e_false in\n let res = pack (Tv_Abs (namedv_to_binder test' (`bool)) body) in\n // should print: function true -> 3 | false -> ()\n //print (term_to_string res);\n t_exact true true res", "val CalcImpl.test = _: Prims.unit -> Prims.unit\nlet test () =\n calc (==>) {\n p;\n ==> { lem () } (* this is only working since desugaring is wrapping\n * the justification with a calc_push_impl, otherwise\n * our goal would be squash (p ==> q) and we could\n * not call lem (as p cannot be proven) *)\n q;\n }", "val g: Prims.unit -> Tot unit\nlet g () : Tot unit =\n assert (False)", "val Apply.lem1 = Prims.unit\nlet lem1 = assert (x == x) by tau ()", "val Cut.tau = _: Prims.unit -> FStar.Tactics.Effect.Tac Prims.unit\nlet tau =\n (fun () ->\n let psi' = `psi in\n let _ = tcut psi' in\n flip ();\n exact (`p1); // TODO: kinda pointless example\n apply (`p2);\n exact (`p1))", "val Intro.call_id = _: Prims.unit -> Prims.int\nlet call_id () = id 5", "val __tac: Prims.unit -> Tac unit\nlet __tac () : Tac unit =\n apply (`vprop_equiv_refl_eq)", "val intros': Prims.unit -> Tac unit\nlet intros' () : Tac unit = let _ = intros () in ()", "val intros': Prims.unit -> Tac unit\nlet intros' () : Tac unit = let _ = intros () in ()", "val BasicTests.test2 = _: Prims.unit -> Prims.unit\nlet test2 () = assert_norm (calc_chain_compatible [(<=); (<)] (<))", "val admit_all: Prims.unit -> Tac unit\nlet admit_all () : Tac unit =\n let _ = repeat tadmit in\n ()", "val admit_all: Prims.unit -> Tac unit\nlet admit_all () : Tac unit =\n let _ = repeat tadmit in\n ()", "val CalcImpl.test5 = _: Prims.unit -> Prims.unit\nlet test5 () =\n calc (==>) {\n 1;\n ==> {}\n 2;\n }", "val go: Prims.unit -> ML unit\nlet go () : ML unit =\r\n (* Parse command-line options. This action is only accumulating values into globals, without any further action (other than --help and --version, which interrupt the execution.) *)\r\n let cmd_line_files = Options.parse_cmd_line() in\r\n let cfg_opt = Deps.get_config () in\r\n (* Special mode: --check_inplace_hashes *)\r\n let inplace_hashes = Options.get_check_inplace_hashes () in\r\n if Cons? inplace_hashes\r\n then Batch.check_inplace_hashes inplace_hashes\r\n else\r\n let micro_step = Options.get_micro_step () in\r\n if micro_step = Some HashingOptions.MicroStepEmitConfig\r\n then (\r\n emit_config_as_fstar_module ();\r\n exit 0\r\n )\r\n else\r\n if micro_step = Some HashingOptions.MicroStepCopyClangFormat\r\n then\r\n (* Special mode: --__micro_step copy_clang_format *)\r\n let _ = Batch.copy_clang_format (Options.get_output_dir ()) in\r\n exit 0\r\n else\r\n if micro_step = Some HashingOptions.MicroStepCopyEverParseH\r\n then\r\n (* Special mode: --__micro_step copy_everparse_h *)\r\n let _ = Batch.copy_everparse_h\r\n (Options.get_clang_format ())\r\n (Options.get_clang_format_executable ())\r\n (Options.get_input_stream_binding ())\r\n (Options.get_output_dir ())\r\n in\r\n exit 0\r\n else\r\n (* for other modes, a nonempty list of files is needed on the command line, so if none are there, then we shall print the help message *)\r\n let input_stream_binding = Options.get_input_stream_binding () in\r\n if Nil? cmd_line_files\r\n then let _ = Options.display_usage () in exit 1\r\n else\r\n let out_dir = Options.get_output_dir () in\r\n (* Special mode: --__micro_step *)\r\n match micro_step with\r\n | Some step ->\r\n let f = match step with\r\n | HashingOptions.MicroStepExtract -> Batch.extract_fst_file\r\n | HashingOptions.MicroStepVerify -> Batch.verify_fst_file\r\n in\r\n List.iter (f input_stream_binding out_dir) cmd_line_files\r\n | None ->\r\n (* Special mode: --makefile\" *)\r\n match Options.get_makefile () with\r\n | Some t ->\r\n GenMakefile.write_makefile\r\n t\r\n input_stream_binding\r\n (not (Options.get_no_everparse_h ()))\r\n (Options.get_emit_output_types_defs ())\r\n (Options.get_skip_o_rules ())\r\n (Options.get_clang_format ())\r\n cmd_line_files\r\n | None ->\r\n (* Special mode: --__produce_c_from_existing_krml *)\r\n if Options.get_produce_c_from_existing_krml ()\r\n then\r\n let _ = List.iter\r\n (produce_and_postprocess_c out_dir)\r\n cmd_line_files\r\n in\r\n FStar.IO.print_string \"EverParse succeeded!\\n\"\r\n else\r\n (* for other modes, the list of files provided on the command line is assumed to be a list of .3d files, and the list of all .3d files in dependency order has to be inferred from the list of .3d input files provided by the user, unless --__skip_deps is provided *)\r\n let all_files =\r\n if Options.get_skip_deps ()\r\n then List.Tot.rev cmd_line_files (* files are accumulated in reverse on the command line *)\r\n else Deps.collect_and_sort_dependencies cmd_line_files\r\n in\r\n let all_files_and_modules = List.map (fun file -> (file, Options.get_module_name file)) all_files in\r\n (* Special mode: --check_hashes *)\r\n let check_hashes = Options.get_check_hashes () in\r\n if Some? check_hashes\r\n then Batch.check_all_hashes (Some?.v check_hashes) out_dir all_files_and_modules\r\n else\r\n (* Special mode: --emit_smt_encoding *)\r\n if Options.get_emit_smt_encoding ()\r\n then produce_z3 all_files_and_modules\r\n else\r\n (* Default mode: process .3d files *)\r\n let batch = Options.get_batch () in\r\n let should_emit_fstar_code : string -> ML bool =\r\n let cmd_line_modules = List.map Options.get_module_name cmd_line_files in\r\n fun modul ->\r\n batch || List.Tot.mem modul cmd_line_modules in\r\n let process : process_files_t =\r\n (* Special mode: --test_checker *)\r\n let test_checker = Options.get_test_checker () in\r\n if Some? test_checker\r\n then produce_test_checker_exe batch out_dir (Some?.v test_checker)\r\n else\r\n (* Special mode: --z3_diff_test *)\r\n let z3_diff_test = Options.get_z3_diff_test () in\r\n if Some? z3_diff_test\r\n then produce_z3_and_diff_test batch out_dir (Some?.v z3_diff_test)\r\n else\r\n (* Special mode: --z3_test *)\r\n let z3_test = Options.get_z3_test () in\r\n if Some? z3_test\r\n then produce_z3_and_test batch out_dir (Some?.v z3_test)\r\n else process_files\r\n in\r\n match process all_files_and_modules should_emit_fstar_code (Options.get_emit_output_types_defs ()) with\r\n | None -> ()\r\n | Some finalize ->\r\n (* we need to pretty-print source modules in all cases, regardless of --batch,\r\n because of the Makefile scenario\r\n *)\r\n (*\r\n * pretty print only the modules we emitted code for\r\n *)\r\n Batch.pretty_print_source_modules input_stream_binding out_dir\r\n (List.filter (fun (_, m) -> should_emit_fstar_code m) all_files_and_modules);\r\n (* Sub-mode of the default mode: --batch *)\r\n let _ =\r\n if batch\r\n then\r\n let _ = Batch.postprocess_fst\r\n input_stream_binding\r\n (Options.get_emit_output_types_defs ())\r\n (Options.get_add_include ())\r\n (Options.get_clang_format ())\r\n (Options.get_clang_format_executable ())\r\n (Options.get_skip_c_makefiles ())\r\n (Options.get_cleanup ())\r\n (Options.get_no_everparse_h ())\r\n (Options.get_save_hashes ())\r\n out_dir all_files_and_modules\r\n in\r\n FStar.IO.print_string \"EverParse succeeded!\\n\"\r\n else\r\n (* If --batch is not set, then we also need to postprocess the wrappers and assertions\r\n (copyright header and clang-format) *)\r\n Batch.postprocess_wrappers\r\n input_stream_binding\r\n (Options.get_clang_format ())\r\n (Options.get_clang_format_executable ())\r\n out_dir all_files_and_modules\r\n in\r\n finalize ()", "val poly_semiring: Prims.unit -> Tac unit\nlet poly_semiring () : Tac unit = canon_semiring pfelem_cr; trefl()", "val SimplePrintf.test = _: Prims.unit -> (Prims.string <: Type0)\nlet test () = sprintf \"%d: Hello %s, sprintf %s\" 0 \"#fstar-hackery\" \"works!\"", "val BasicTests.test1 = _: Prims.unit -> Prims.unit\nlet test1 () = assert_norm (calc_chain_compatible [(<); (<=)] (<))", "val test: Prims.unit -> St unit\nlet test (): St unit =\n let r = HS.(new_region root) in\n let b = B.malloc HS.root 0ul 1ul in\n let l: t UInt32.t = create_in r in\n push l 0ul;\n push l 1ul;\n push l 2ul;\n B.upd b 0ul 1ul;\n let h0 = ST.get () in\n assert (v h0 l == [ 2ul; 1ul; 0ul ]);\n assert (B.deref h0 b == 1ul);\n ignore (pop l);\n let h1 = ST.get () in\n assert (v h1 l == [ 1ul; 0ul ]);\n assert (B.deref h0 b == 1ul);\n clear l;\n let h2 = ST.get () in\n assert (v h2 l == []);\n assert (B.deref h2 b == 1ul);\n free l;\n ()", "val implies_intros: Prims.unit -> Tac binders\nlet implies_intros () : Tac binders = repeat1 implies_intro", "val BasicTests.test5 = _: Prims.unit -> Prims.unit\nlet test5 () = assert_norm (calc_chain_compatible [(<); (==); (<=)] (<))", "val trans: Prims.unit -> Tac unit\nlet trans () : Tac unit = apply_lemma (`lem_trans)", "val trans: Prims.unit -> Tac unit\nlet trans () : Tac unit = apply_lemma (`lem_trans)", "val Intro.test_add = Prims.unit\nlet test_add = assert (add3 1 2 3 == 6)", "val t2: Prims.unit -> Tac unit\nlet t2 () : Tac unit = fail \"always fail\"", "val BasicTests.test4 = _: Prims.unit -> Prims.unit\nlet test4 () = assert_norm (calc_chain_compatible [(<)] (<))", "val extensionality_lemma: Prims.unit -> Lemma (extensionality_fact)\nlet extensionality_lemma () : Lemma (extensionality_fact) =\n introduce forall (ty: Type) (a: seq ty) (b: seq ty). equal a b ==> a == b\n with\n introduce _ ==> _\n with given_antecedent. (\n introduce forall (i: nat) . i < length a ==> index a i == index b i\n with\n introduce _ ==> _\n with given_antecedent. (\n assert (index a i == index b i) // needed to trigger\n );\n FStar.List.Tot.Properties.index_extensionality a b\n )", "val test: Prims.unit -> LV unit (fun _ -> True) (fun _ _ _ -> True)\nlet test () : LV unit (fun _ -> True) (fun _ _ _ -> True) =\n let n1 = create nat 0 in\n let n2 = create bool true in\n let n3 = create unit () in\n\n\n let v1: nat = read n1 in\n assert (v1 == 0)", "val is_unit: Prims.unit -> Lemma (S.is_unit emp equiv star)\nlet is_unit ()\n : Lemma (S.is_unit emp equiv star)\n = let aux (y:slprop)\n : Lemma (star emp y `equiv` y /\\ star y emp `equiv` y)\n = emp_unit y; star_commutative emp y\n in\n Classical.forall_intro aux", "val get: Prims.unit\n -> LV (Map.t nat (a: Type0 & a)) (fun m0 -> True) (fun m0 r m1 -> m0 == m1 /\\ r == m0.m)\nlet get ()\n: LV (Map.t nat (a:Type0 & a))\n (fun m0 -> True)\n (fun m0 r m1 -> m0 == m1 /\\ r == m0.m)\n= LVARS?.reflect (fun m -> m.m, m)", "val BasicTests.test3 = _: Prims.unit -> Prims.unit\nlet test3 () = assert_norm (calc_chain_compatible [(<); (<)] (<))", "val get: s: Type -> Prims.unit -> st s s\nlet get (s:Type) () : st s s = fun s0 -> s0, s0", "val Postprocess.fext = _: Prims.unit -> FStar.Tactics.Effect.Tac Prims.unit\nlet fext () = apply_lemma (`apply_feq_lem); dismiss (); ignore (forall_intros ())", "val implies_intro': Prims.unit -> Tac unit\nlet implies_intro' () : Tac unit =\n let _ = implies_intro () in ()", "val Unify.tau = _: Prims.unit -> FStar.Tactics.Effect.Tac Prims.unit\nlet tau =\n fun () ->\n let l = fresh_uvar None in // None: we don't provide a type\n let r = fresh_uvar None in\n let e = cur_env () in\n apply (`op_Addition);\n exact l;\n exact r;\n let ocho = `8 in\n let _ = unify_env e r ocho in\n let _ = unify_env e l r in\n ()", "val smt: Prims.unit -> Tac unit\nlet smt () : Tac unit =\n match goals (), smt_goals () with\n | [], _ -> fail \"smt: no active goals\"\n | g::gs, gs' ->\n begin\n set_goals gs;\n set_smt_goals (g :: gs')\n end", "val smt: Prims.unit -> Tac unit\nlet smt () : Tac unit =\n match goals (), smt_goals () with\n | [], _ -> fail \"smt: no active goals\"\n | g::gs, gs' ->\n begin\n set_goals gs;\n set_smt_goals (g :: gs')\n end", "val get: #st: _ -> Prims.unit -> ST st st (fun s0 p -> p s0 s0)\nlet get #st () : ST st st (fun s0 p -> p s0 s0) =\n ST?.reflect (fun s0 -> (s0, s0))", "val get: #st: _ -> Prims.unit -> ST st st (fun s0 p -> p s0 s0)\nlet get #st () : ST st st (fun s0 p -> p s0 s0) =\n ST?.reflect (fun s0 -> (s0, s0))", "val forall_intros: Prims.unit -> Tac binders\nlet forall_intros () : Tac binders = repeat1 forall_intro", "val Postprocess.tau = _: Prims.unit -> FStar.Tactics.Effect.Tac Prims.unit\nlet tau () = apply_lemma (`lem)", "val Arith.lem0 = x: Prims.int -> Prims.unit\nlet lem0 (x:int) =\n assert (op_Multiply 2 (x + 3) == 6 + (op_Multiply 3 x) - x)\n by (prune \"\"; addns \"Prims\")", "val get: #st: _ -> Prims.unit -> ST st st (fun s0 p -> p (s0, s0))\nlet get #st () : ST st st (fun s0 p -> p (s0, s0)) =\n ST?.reflect (fun s0 -> (s0, s0))", "val get: #st: _ -> Prims.unit -> ST st st (fun s0 p -> p (s0, s0))\nlet get #st ()\n : ST st st (fun s0 p -> p (s0, s0))\n = ST?.reflect (fun s0 -> (s0, s0))", "val equiv: Prims.unit -> FStar.Tactics.Tac unit\nlet equiv () : FStar.Tactics.Tac unit =\n let open FStar.Tactics in\n mapply (`vprop_equiv_refl_eq);\n smt()", "val Postprocess.onL = _: Prims.unit -> FStar.Tactics.Effect.Tac Prims.unit\nlet onL () = apply_lemma (`_onL)", "val int_semiring: Prims.unit -> Tac unit\nlet int_semiring () : Tac unit =\n (* Check to see if goal is a `nat` equality, change the equality to `int` beforehand *)\n match term_as_formula (cur_goal ()) with\n | Comp (Eq (Some t)) _ _ ->\n if term_eq t (`Prims.nat)\n then (apply_lemma (`eq_nat_via_int); canon_semiring int_cr)\n else canon_semiring int_cr\n | _ ->\n canon_semiring int_cr", "val l: Prims.unit -> int\nlet l () : int =\n reify (test_f ())", "val l: Prims.unit -> int\nlet l () : int = reify (test_f ()) ()", "val l: Prims.unit -> int\nlet l () : int = reify (test_f ()) (fun _ -> True) ()", "val l: Prims.unit -> int\nlet l () : int = reify (test_f ()) (fun _ -> True) ()", "val l: Prims.unit -> int\nlet l () : int = snd (reify (test_f ())) (fun _ -> True) ()", "val intros: Prims.unit -> Tac (list binding)\nlet intros () : Tac (list binding) = repeat intro", "val cur_env: Prims.unit -> Tac env\nlet cur_env () : Tac env = goal_env (_cur_goal ())", "val cur_env: Prims.unit -> Tac env\nlet cur_env () : Tac env = goal_env (_cur_goal ())", "val test: Prims.unit -> M unit (fun _ -> True) (fun _ _ s1 -> st_q s1)\nlet test () : M unit (fun _ -> True) (fun _ _ s1 -> st_q s1) =\n g ();\n f ();\n h ()", "val Effects.Def.morphism_lift_st_exnst = Prims.unit\nlet morphism_lift_st_exnst = \n morphism_laws_via_eq st exnst eq_exnst\n\t\t return_st bind_st \n\t\t return_exnst bind_exnst \n\t\t lift_st_exnst", "val Nest.tau = _: Prims.unit -> FStar.Tactics.Effect.Tac Prims.unit\nlet tau = fun () -> pointwise (fun () -> pointwise trefl; trefl ())", "val Effects.Def.morphism_lift_ex_exnst = Prims.unit\nlet morphism_lift_ex_exnst = \n morphism_laws_via_eq ex exnst eq_exnst\n\t\t return_ex bind_ex \n\t\t return_exnst bind_exnst \n\t\t lift_ex_exnst", "val NormLHS.tau = _: Prims.unit -> FStar.Tactics.Effect.Tac Prims.unit\nlet tau () = norm_lhs [delta; hnf; weak]; trefl ()", "val tac: Prims.unit -> Tac unit\nlet tac () : Tac unit =\n dump \"now\"", "val tac: Prims.unit -> Tac unit\nlet rec tac () : Tac unit =\n if List.length (goals ()) = 0\n then ()\n else if pick_next (FStar.List.length (goals ()))\n then begin\n or_else (fun _ -> rewrite_eqs_from_context (); norm []; trefl ()) (fun _ -> assumption ());\n tac ()\n end\n else begin\n rewrite_eqs_from_context ();\n norm [];\n trefl ();\n tac ()\n end", "val admit1: Prims.unit -> Tac unit\nlet admit1 () : Tac unit =\n tadmit ()", "val admit1: Prims.unit -> Tac unit\nlet admit1 () : Tac unit =\n tadmit ()", "val get_arg0: Prims.unit -> ML string\nlet get_arg0 () : ML string =\r\n match !arg0 with\r\n | None -> \"3d\"\r\n | Some v -> v", "val __c1: Prims.unit -> EFF int unit bool [EXN; RD; WR]\nlet __c1 () : EFF int unit bool [EXN;RD;WR] =\n put \"hello\";\n raise EE;\n coerce_st_to unit;// funny, but needed; or 'get ();'\n put true;\n 42", "val conjt: Prims.unit -> Tac unit\nlet rec conjt () : Tac unit =\n let _ = l_intros () in\n match cur_formula () with\n | And _ _ -> seq split conjt\n (* otherwise, just try to solve via an assumption *)\n | _ -> (assumption (); qed ())", "val Rename.tau = _: Prims.unit -> FStar.Tactics.Effect.Tac Prims.unit\nlet tau =\n fun () ->\n let h0 = implies_intro () in\n let h1 = implies_intro () in\n dump \"Test\";\n exact (`p)", "val pp_norm_tac: Prims.unit -> Tac unit\nlet pp_norm_tac () : Tac unit =\n norm norm_steps;\n trefl ();\n to_all_goals (fun _ ->\n norm [delta; iota; zeta; primops];\n smt ()\n );\n qed ()", "val main: Prims.unit -> SteelT Int32.t emp (fun _ -> emp)\nlet main () : SteelT Int32.t emp (fun _ -> emp) =\n let r = malloc 0ul in\n sum_to_n_for r;\n sum_to_n_while r;\n free r;\n return 0l", "val main: Prims.unit -> SteelT Int32.t emp (fun _ -> emp)\nlet main () : SteelT Int32.t emp (fun _ -> emp) =\n let r = malloc 0ul in\n if is_null r then (\n free r;\n 1l\n ) else (\n free r;\n 0l\n )", "val main: Prims.unit -> SteelT Int32.t emp (fun _ -> emp)\nlet main () : SteelT Int32.t emp (fun _ -> emp) =\n let i = get x 0sz in\n let j = get x 1sz in\n if i = j then return 1l else return 0l", "val main: Prims.unit -> SteelT Int32.t emp (fun _ -> emp)\nlet main () : SteelT Int32.t emp (fun _ -> emp) =\n let res1 = test1 () in\n let res2 = test2 () in\n if res1 && res2 then 0l else 1l", "val main: Prims.unit -> SteelT Int32.t emp (fun _ -> emp)\nlet main () : SteelT Int32.t emp (fun _ -> emp) = return 0l", "val main: Prims.unit -> SteelT Int32.t emp (fun _ -> emp)\nlet main () : SteelT Int32.t emp (fun _ -> emp) =\n let r = malloc 0ul in\n let l = new_lock (vptr r) in\n acquire l;\n write r 1ul;\n release l;\n 0l", "val main: Prims.unit -> SteelT Int32.t emp (fun _ -> emp)\nlet main () : SteelT Int32.t emp (fun _ -> emp) =\n let r = null #UInt32.t in\n if is_null r then\n return 0l\n else\n return 1l", "val Arith.lem2 = x: Prims.int -> Prims.unit\nlet lem2 (x:int) =\n assert (List.rev [1;2;3;4] == [4;3;2;1] /\\ op_Multiply 2 (x + 3) == 6 + (op_Multiply 3 x) - x)\n by split_arith ()", "val whnf: Prims.unit -> Tac unit\nlet whnf () : Tac unit = norm [weak; hnf; primops; delta]", "val whnf: Prims.unit -> Tac unit\nlet whnf () : Tac unit = norm [weak; hnf; primops; delta]", "val STLC.Infer.test_id = _: Prims.unit -> Prims.unit\nlet test_id () = assert (foo () == ()) by (T.compute ())", "val Effects.Def.morphism_lift_st_exn = Prims.unit\nlet morphism_lift_st_exn =\n morphism_laws_via_eq st stexn eq_stexn\n\t\t return_st bind_st \n\t\t return_stexn bind_stexn \n\t\t lift_st_stexn", "val trefl_or_smt: Prims.unit -> T.Tac unit\nlet trefl_or_smt () : T.Tac unit =\n let ty = T.cur_goal () in\n match T.term_as_formula ty with\n | T.Comp _ _ _ -> T.trefl ()\n | _ -> T.smt (); T.qed ()", "val maybe_enum_destr_t'_tac: Prims.unit -> T.Tac unit\nlet rec maybe_enum_destr_t'_tac () : T.Tac unit =\n let (goal_fun, goal_arg) = T.app_head_tail (T.cur_goal ()) in\n let _ = T.tassert (goal_fun `T.is_fvar` (`%maybe_enum_destr_t')) in\n match goal_arg with\n | [_; _; _; _; (tl1, _); (tl2, _); _] ->\n let (tl2_fun, _) = T.app_head_tail (T.norm_term [delta; iota; zeta] tl2) in\n if tl2_fun `T.is_fvar` (`%Cons)\n then begin\n T.apply (`maybe_enum_destr_cons);\n maybe_enum_destr_t'_tac ()\n end else\n if tl2_fun `T.is_fvar` (`%Nil)\n then begin\n T.apply (`maybe_enum_destr_nil);\n ignore (T.repeat (fun _ ->\n if List.length (T.goals ()) = 0\n then T.fail \"Done\"\n else (T.compute (); T.smt ())));\n T.qed ()\n end\n else T.fail \"Unknown shape for l2\"\n | _ -> T.fail \"Not the rigt arguments to maybe_enum_destr_t'\"", "val Pruning.tau2 = _: Prims.unit -> FStar.Tactics.Effect.Tac Prims.unit\nlet tau2 =\n (fun () ->\n prune \"\";\n FStar.Tactics.split ();\n (* rev [1;2] == [2;1] *)\n addns \"FStar.List\";\n addns \"Prims\";\n smt ();\n (* 1 == 1 *)\n smt ())", "val is_true: t: term -> Prims.unit -> Tac unit\nlet is_true (t:term) () : Tac unit =\n match term_as_formula t with\n | True_ -> exact (`())\n | _ -> raise Goal_not_trivial", "val selector_tactic: Prims.unit -> Tac unit\nlet selector_tactic () : Tac unit =\n apply (`squash_and);\n apply_lemma (`intro_can_be_split_frame);\n flip ();\n norm [delta_only [\n `%CE.__proj__CM__item__unit;\n `%CE.__proj__CM__item__mult;\n `%rm;\n `%__proj__Mktuple2__item___1; `%__proj__Mktuple2__item___2;\n `%fst; `%snd];\n delta_attr [`%__reduce__];\n primops; iota; zeta];\n canon' false (`true_p) (`true_p)", "val ref_hfn: Prims.unit -> Ref unit (requires fun _ -> True) (ensures fun n0 _ n1 -> n0 == n1)\nlet ref_hfn ()\n: Ref unit\n (requires fun _ -> True)\n (ensures fun n0 _ n1 -> n0 == n1)\n= REF?.reflect hfn", "val smt_sync: Prims.unit -> Tac unit\nlet smt_sync () : Tac unit = t_smt_sync (get_vconfig ())", "val smt_sync: Prims.unit -> Tac unit\nlet smt_sync () : Tac unit = t_smt_sync (get_vconfig ())", "val Pruning.tau1 = _: Prims.unit -> FStar.Tactics.Effect.Tac Prims.unit\nlet tau1 =\n (fun () -> prune \"\";\n addns \"FStar.List\";\n addns \"Prims\")", "val callmap: Prims.unit -> Id (list nat) True (fun _ -> True)\nlet callmap () : Id (list nat) True (fun _ -> True) =\n let lmap : list nat = [2;4;6;8] in\n pmap even fmap lmap", "val callmap: Prims.unit -> Id (list nat) True (fun _ -> True)\nlet callmap () : Id (list nat) True (fun _ -> True) =\n let lmap : list nat = [2;4;6;8] in\n map #_ #_ #even fmap lmap", "val implies_intros: Prims.unit -> Tac (list binding)\nlet implies_intros () : Tac (list binding) = repeat1 implies_intro", "val one_t: Prims.unit -> Tac term\nlet one_t () : Tac term = pack (Tv_Const (C_Int 1))", "val assumption': Prims.unit -> Tac unit\nlet assumption' () : Tac unit =\n apply_raw (`FStar.Squash.return_squash);\n assumption ()", "val Arith.lem1 = x: Prims.int -> Prims.unit\nlet lem1 (x:int) =\n assert (List.rev [1;2;3;4] == [4;3;2;1] /\\ op_Multiply 2 (x + 3) == 6 + (op_Multiply 3 x) - x)\n by tau1 ()", "val dep_maybe_enum_destr_t'_tac: Prims.unit -> T.Tac unit\nlet rec dep_maybe_enum_destr_t'_tac () : T.Tac unit =\n let (goal_fun, goal_arg) = T.app_head_tail (T.cur_goal ()) in\n let _ = T.tassert (goal_fun `T.is_fvar` (`%dep_maybe_enum_destr_t')) in\n match goal_arg with\n | [_; _; _; _; (tl1, _); (tl2, _); _] ->\n let (tl2_fun, _) = T.app_head_tail (T.norm_term [delta; iota; zeta] tl2) in\n if tl2_fun `T.is_fvar` (`%Cons)\n then begin\n T.apply (`dep_maybe_enum_destr_cons);\n dep_maybe_enum_destr_t'_tac ()\n end else\n if tl2_fun `T.is_fvar` (`%Nil)\n then begin\n T.apply (`dep_maybe_enum_destr_nil);\n ignore (T.repeat (fun _ ->\n if List.length (T.goals ()) = 0\n then T.fail \"Done\"\n else (T.compute (); T.smt ())));\n T.qed ()\n end\n else T.fail \"Unknown shape for l2\"\n | _ -> T.fail \"Not the rigt arguments to maybe_enum_destr_t'\"" ], "closest_src": [ { "project_name": "FStar", "file_name": "Preprocess.fst", "name": "Preprocess.test" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Typeclasses.fst", "name": "FStar.Tactics.Typeclasses.maybe_intros" }, { "project_name": "FStar", "file_name": "CalcImpl.fst", "name": "CalcImpl.test4" }, { "project_name": "FStar", "file_name": "CalcImpl.fst", "name": "CalcImpl.test3" }, { "project_name": "FStar", "file_name": "DependentSynth.fst", "name": "DependentSynth.t" }, { "project_name": "FStar", "file_name": "CalcImpl.fst", "name": "CalcImpl.test" }, { "project_name": "FStar", "file_name": "HandleSmtGoal.fst", "name": "HandleSmtGoal.g" }, { "project_name": "FStar", "file_name": "Apply.fst", "name": "Apply.lem1" }, { "project_name": "FStar", "file_name": "Cut.fst", "name": "Cut.tau" }, { "project_name": "FStar", "file_name": "Intro.fst", "name": "Intro.call_id" }, { "project_name": "steel", "file_name": "Pulse.Lib.Par.Pledge.fst", "name": "Pulse.Lib.Par.Pledge.__tac" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.intros'" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.intros'" }, { "project_name": "FStar", "file_name": "BasicTests.fst", "name": "BasicTests.test2" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.admit_all" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.admit_all" }, { "project_name": "FStar", "file_name": "CalcImpl.fst", "name": "CalcImpl.test5" }, { "project_name": "everparse", "file_name": "Main.fst", "name": "Main.go" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Lemmas.fst", "name": "Hacl.Spec.Poly1305.Lemmas.poly_semiring" }, { "project_name": "FStar", "file_name": "SimplePrintf.fst", "name": "SimplePrintf.test" }, { "project_name": "FStar", "file_name": "BasicTests.fst", "name": "BasicTests.test1" }, { "project_name": "karamel", "file_name": "LowStar.Lib.LinkedList2.fst", "name": "LowStar.Lib.LinkedList2.test" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Logic.fst", "name": "FStar.Tactics.V1.Logic.implies_intros" }, { "project_name": "FStar", "file_name": "BasicTests.fst", "name": "BasicTests.test5" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.trans" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.trans" }, { "project_name": "FStar", "file_name": "Intro.fst", "name": "Intro.test_add" }, { "project_name": "FStar", "file_name": "LocalState.fst", "name": "LocalState.t2" }, { "project_name": "FStar", "file_name": "BasicTests.fst", "name": "BasicTests.test4" }, { "project_name": "FStar", "file_name": "FStar.Sequence.Base.fst", "name": "FStar.Sequence.Base.extensionality_lemma" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.test" }, { "project_name": "steel", "file_name": "Steel.Semantics.Instantiate.fst", "name": "Steel.Semantics.Instantiate.is_unit" }, { "project_name": "FStar", "file_name": "Locals.Effect.fst", "name": "Locals.Effect.get" }, { "project_name": "FStar", "file_name": "BasicTests.fst", "name": "BasicTests.test3" }, { "project_name": "FStar", "file_name": "FStar.DM4F.ST.fst", "name": "FStar.DM4F.ST.get" }, { "project_name": "FStar", "file_name": "Postprocess.fst", "name": "Postprocess.fext" }, { "project_name": "FStar", "file_name": "FStar.Tactics.PatternMatching.fst", "name": "FStar.Tactics.PatternMatching.implies_intro'" }, { "project_name": "FStar", "file_name": "Unify.fst", "name": "Unify.tau" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.smt" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.smt" }, { "project_name": "FStar", "file_name": "DM4F_layered5.fst", "name": "DM4F_layered5.get" }, { "project_name": "FStar", "file_name": "DM4F_layered.fst", "name": "DM4F_layered.get" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Logic.fst", "name": "FStar.Tactics.V1.Logic.forall_intros" }, { "project_name": "FStar", "file_name": "Postprocess.fst", "name": "Postprocess.tau" }, { "project_name": "FStar", "file_name": "Arith.fst", "name": "Arith.lem0" }, { "project_name": "FStar", "file_name": "DM4F.fst", "name": "DM4F.get" }, { "project_name": "FStar", "file_name": "OPLSS2021.DijkstraMonads.fst", "name": "OPLSS2021.DijkstraMonads.get" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherArray.fst", "name": "Pulse.Lib.HigherArray.equiv" }, { "project_name": "FStar", "file_name": "Postprocess.fst", "name": "Postprocess.onL" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonCommSemiring.fst", "name": "FStar.Tactics.CanonCommSemiring.int_semiring" }, { "project_name": "FStar", "file_name": "ID3.fst", "name": "ID3.l" }, { "project_name": "FStar", "file_name": "ID2.fst", "name": "ID2.l" }, { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.l" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.l" }, { "project_name": "FStar", "file_name": "ID4.fst", "name": "ID4.l" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.intros" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.cur_env" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.cur_env" }, { "project_name": "FStar", "file_name": "HoareSTFree.fst", "name": "HoareSTFree.test" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.morphism_lift_st_exnst" }, { "project_name": "FStar", "file_name": "Nest.fst", "name": "Nest.tau" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.morphism_lift_ex_exnst" }, { "project_name": "FStar", "file_name": "NormLHS.fst", "name": "NormLHS.tau" }, { "project_name": "FStar", "file_name": "HandleSmtGoal.fst", "name": "HandleSmtGoal.tac" }, { "project_name": "FStar", "file_name": "LowParseWriters.fsti", "name": "LowParseWriters.tac" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.admit1" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.admit1" }, { "project_name": "everparse", "file_name": "Options.fst", "name": "Options.get_arg0" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.__c1" }, { "project_name": "FStar", "file_name": "Automation.fst", "name": "Automation.conjt" }, { "project_name": "FStar", "file_name": "Rename.fst", "name": "Rename.tau" }, { "project_name": "everparse", "file_name": "LowParse.TacLib.fst", "name": "LowParse.TacLib.pp_norm_tac" }, { "project_name": "steel", "file_name": "SteelLoops.fst", "name": "SteelLoops.main" }, { "project_name": "steel", "file_name": "SteelNotNull.fst", "name": "SteelNotNull.main" }, { "project_name": "steel", "file_name": "SteelTLArray.fst", "name": "SteelTLArray.main" }, { "project_name": "steel", "file_name": "Wasm11.fst", "name": "Wasm11.main" }, { "project_name": "steel", "file_name": "Deref2.fst", "name": "Deref2.main" }, { "project_name": "steel", "file_name": "SteelLock.fst", "name": "SteelLock.main" }, { "project_name": "steel", "file_name": "SteelNull.fst", "name": "SteelNull.main" }, { "project_name": "FStar", "file_name": "Arith.fst", "name": "Arith.lem2" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.whnf" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.whnf" }, { "project_name": "FStar", "file_name": "STLC.Infer.fst", "name": "STLC.Infer.test_id" }, { "project_name": "FStar", "file_name": "Effects.Def.fst", "name": "Effects.Def.morphism_lift_st_exn" }, { "project_name": "steel", "file_name": "Steel.ST.GenElim1.Base.fsti", "name": "Steel.ST.GenElim1.Base.trefl_or_smt" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Tac.Sum.fst", "name": "LowParse.Spec.Tac.Sum.maybe_enum_destr_t'_tac" }, { "project_name": "FStar", "file_name": "Pruning.fst", "name": "Pruning.tau2" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.is_true" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.selector_tactic" }, { "project_name": "FStar", "file_name": "Z3EncodingIssue.fst", "name": "Z3EncodingIssue.ref_hfn" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.smt_sync" }, { "project_name": "FStar", "file_name": "FStar.Tactics.SMT.fst", "name": "FStar.Tactics.SMT.smt_sync" }, { "project_name": "FStar", "file_name": "Pruning.fst", "name": "Pruning.tau1" }, { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.callmap" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.callmap" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Logic.fst", "name": "FStar.Tactics.V2.Logic.implies_intros" }, { "project_name": "FStar", "file_name": "Term.fst", "name": "Term.one_t" }, { "project_name": "FStar", "file_name": "Retype.fst", "name": "Retype.assumption'" }, { "project_name": "FStar", "file_name": "Arith.fst", "name": "Arith.lem1" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Tac.Sum.fst", "name": "LowParse.Spec.Tac.Sum.dep_maybe_enum_destr_t'_tac" } ], "selected_premises": [ "Param.int_param", "FStar.Pervasives.reveal_opaque", "Param.bool_param", "Param.param_of_eqtype", "FStar.Heap.trivial_preorder", "FStar.ST.op_Bang", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "Param.app_binders", "Param.push_var_to_state", "Param.replace_var", "Param.last", "Param.push_fv", "FStar.Pervasives.dfst", "FStar.ST.alloc", "FStar.Pervasives.dsnd", "FStar.List.iter", "Param.replace_by", "FStar.List.iteri_aux", "Param.fresh_binder_named", "FStar.List.iteri", "Param.lookup_rec_fv", "Param.fvmap", "FStar.List.for_all", "FStar.All.op_Bar_Greater", "FStar.Monotonic.Heap.tset", "FStar.List.fold_left", "FStar.List.map", "FStar.Order.order_from_int", "FStar.All.op_Less_Bar", "FStar.List.tryFind", "Param.lookup", "Param.fold_right2", "FStar.Order.lex", "FStar.Order.compare_int", "FStar.Pervasives.id", "FStar.List.nth", "FStar.List.fold_right", "FStar.Preorder.preorder_rel", "FStar.ST.st_post", "FStar.List.splitAt", "FStar.List.tl", "FStar.List.tryPick", "FStar.Heap.trivial_rel", "FStar.ST.st_pre", "FStar.ST.recall", "FStar.All.pipe_right", "FStar.ST.contains_pred", "FStar.ST.gst_pre", "FStar.Preorder.transitive", "FStar.ST.st_post'", "FStar.ST.gst_post'", "FStar.ST.gst_post", "FStar.List.forall2", "Prims.returnM", "FStar.Monotonic.Heap.set", "Prims.l_True", "FStar.Preorder.reflexive", "FStar.ST.op_Colon_Equals", "FStar.List.sortWith", "FStar.List.partition", "FStar.List.zip", "FStar.List.last", "FStar.Monotonic.Heap.only", "FStar.Preorder.stable", "FStar.Monotonic.Heap.mref", "Prims.abs", "Prims.min", "FStar.Monotonic.Heap.only_t", "FStar.Order.compare_list", "FStar.List.mapT", "FStar.List.choose", "FStar.List.index", "FStar.Monotonic.Heap.fresh", "FStar.List.filter", "FStar.Pervasives.st_return", "FStar.ST.lift_gst_state", "FStar.Pervasives.coerce_eq", "FStar.ST.st_wp", "FStar.List.mapi_init", "FStar.All.pipe_left", "FStar.ST.write", "FStar.List.tail", "FStar.List.init", "FStar.ST.get", "FStar.Monotonic.Heap.op_Hat_Plus_Plus", "FStar.List.fold_left2", "FStar.Pervasives.st_post_h", "FStar.Pervasives.all_post_h", "FStar.List.filter_map", "FStar.All.all_post", "FStar.List.hd", "FStar.Order.compare_option", "FStar.Set.add", "Prims.l_False", "FStar.ST.gst_wp", "FStar.List.map2", "FStar.Pervasives.st_post_h'", "FStar.List.mapi", "Prims.__cache_version_number__" ], "source_upto_this": "module Param\n\nopen FStar.List\nopen FStar.Tactics.V2\n\ntype bvmap = list (namedv & (binder & binder & binder))\nlet fvmap = list (fv * fv)\n\nnoeq\ntype param_state = {\n bvmap : bvmap;\n fresh : int;\n recs : fvmap;\n}\n\nlet rec fold_right2 (f : 'a -> 'b -> 'c -> Tac 'c) (l1:list 'a) (l2:list 'b) (c:'c) : Tac 'c =\n match l1, l2 with\n | h1::t1, h2::t2 -> f h1 h2 (fold_right2 f t1 t2 c)\n | [], [] -> c\n | _ -> fail \"fold_right2\"\n\nlet rec zip3 (l1 : list 'a) (l2 : list 'b) (l3 : list 'c) : list ('a * 'b * 'c) =\n match l1, l2, l3 with\n | h1::t1, h2::t2, h3::t3 -> (h1, h2, h3) :: (zip3 t1 t2 t3)\n | _ -> []\n\nlet last (xs:list 'a) : Tac 'a =\n match List.Tot.rev xs with\n | h::_ -> h\n | [] -> fail \"last: empty list\"\n\n(* Override it to add freshness. The code for typechecking an inductive\nraises a failure if two binders of the same constructor have the same name. *)\n// noeq type t = | A of x:int -> x:int -> x:int -> t\n// but this doesn't fail nor warn... why??\n\nlet fresh_binder_named (nm:string) (t:typ) : Tac binder =\n // useful?\n //let n = fresh () in\n //let nm = nm ^ \"_\" ^ string_of_int n in\n Tactics.V2.fresh_binder_named nm t\n\nlet app_binders (t:term) (bs:list binder) : Tac term =\n mk_e_app t (List.Tot.map binder_to_term bs)\n\nlet push_var_to_state (v:namedv) (b0 b1 b2 : binder) (s:param_state) : param_state =\n { s with bvmap = (v, (b0, b1, b2)) :: s.bvmap }\n\nexception NotARecFV\nexception Unsupported of string\nexception NotFoundBV of namedv\nexception NotFoundFV of fv\n\nlet lookup_rec_fv (s:param_state) (f:fv) : Tac fv =\n let rec aux (m:fvmap) : Tac fv =\n match m with\n | [] -> raise NotARecFV\n | (f1, k)::fs -> if compare_fv f f1 = Order.Eq\n then k\n else aux fs\n in\n aux s.recs\n\nlet push_fv (f1 f2 : fv) (s:param_state) : param_state =\n { s with recs = (f1,f2)::s.recs }\n\nlet lookup (s:param_state) (v:namedv) : Tac (binder & binder & binder) =\n let rec aux (bvm : bvmap) : Tac (binder & binder & binder) =\n match bvm with\n | [] ->\n raise (NotFoundBV v)\n | (v', r)::tl ->\n if (inspect_namedv v).uniq = (inspect_namedv v').uniq\n then r\n else aux tl\n in\n aux s.bvmap\n\nlet replace_var (s:param_state) (b:bool) (t:term) : Tac term =\n match inspect t with\n | Tv_Var v ->\n begin try\n let (x, y, _) = lookup s v in\n let bv = binder_to_namedv (if b then y else x) in\n pack (Tv_Var bv)\n with\n (* Maybe we traversed a binder and there are variables not in the state.\n * The right thing here would be to track them... but this should do for now. *)\n | NotFoundBV _ -> t\n | e -> raise e\n end\n | _ -> t\n\nlet replace_by (s:param_state) (b:bool) (t:term) : Tac term =\n let r = visit_tm (replace_var s b) t in\n //print (\"rep \" ^ string_of_bool b ^ \" \" ^ term_to_string t ^ \" = \" ^ term_to_string r);\n r\n\n(* This should be definition for any eqtype. Would be nicer to see these\n * unfolded in the computed principles? *)\nlet param_of_eqtype (a:eqtype) : a -> a -> Type0 = (fun (x y : a) -> squash (x == y))\nlet int_param = param_of_eqtype int\nlet bool_param = param_of_eqtype bool", "sketch": [ "Step 1: The definition `unit_param` is about creating a type that represents the equality of two `unit` values. Since `unit` has only one value `()`, any two `unit` values are always equal.\nStep 2: The implementation uses the `param_of_eqtype` function to create a type that squashes the equality of two `unit` values. This is similar to how `int_param` and `bool_param` are defined.", "Step 1: The definition `unit_param` is about creating a parameterized type for the unit type (`Prims.unit`). This type should express that two unit values are equivalent.\nStep 2: The implementation will use the `param_of_eqtype` function to create a type that squashes the equality of two unit values.", "Step 1: The definition `unit_param` is about creating a parameterized type for the unit type, similar to how `int_param` and `bool_param` were defined for `int` and `bool` respectively.\nStep 2: The implementation will use the `param_of_eqtype` function to create a type that represents the equality of two unit values. Since unit values are always equal, this will essentially squash the equality check between two unit values.", "Step 1: The definition `unit_param` is about creating a parameterized type for the unit type, similar to how `int_param` and `bool_param` are defined for `int` and `bool` respectively. It should take two unit values and return a type that represents their equality.\nStep 2: The implementation uses the `param_of_eqtype` function to create this parameterized type. For the unit type, the equality check is trivial since there is only one value of type `unit`.", "Step 1: The definition `unit_param` is about creating a parameterized type for the `unit` type, similar to how `int_param` and `bool_param` are defined for `int` and `bool` respectively. This type will represent the equality of two `unit` values.\nStep 2: The implementation will use the `param_of_eqtype` function to create a type that squashes the equality of two `unit` values. Since `unit` has only one value, this is straightforward.", "Step 1: The definition `unit_param` is about creating a type that represents the equality of two `unit` values. Since `unit` has only one value `()`, any two `unit` values are always equal.\nStep 2: The implementation uses the `param_of_eqtype` function to create a type that squashes the equality of two `unit` values. This is similar to the `int_param` and `bool_param` definitions.", "Step 1: The definition `unit_param` is about creating a type that represents the equality of two `unit` values. Since `unit` has only one value `()`, any two `unit` values are always equal.\nStep 2: The implementation uses the `param_of_eqtype` function to create a type that squashes the equality of two `unit` values. This is similar to the `int_param` and `bool_param` definitions.", "Step 1: The definition `unit_param` is about defining a parameterized type for the unit type. This type should express that two unit values are always equal.\nStep 2: The implementation uses the `param_of_eqtype` function to create a type that squashes the equality of two unit values. Since unit values are always equal, this is straightforward.", "Step 1: The definition `unit_param` is about creating a parameterized type for the unit type, similar to how `int_param` and `bool_param` were defined for `int` and `bool` respectively.\nStep 2: The implementation will use the `param_of_eqtype` function to create a type that represents the equality of two unit values. Since unit values are always equal, this type will always hold.", "Step 1: The definition `unit_param` is about creating a parameterized type for the `unit` type, similar to how `int_param` and `bool_param` were defined for `int` and `bool` respectively.\nStep 2: The implementation involves using the `param_of_eqtype` function to create a type that represents the equality of two `unit` values. Since `unit` has only one value, the equality check is trivial." ], "generated_solution": [ "let unit_param = param_of_eqtype unit", "let unit_param = param_of_eqtype Prims.unit", "let unit_param = param_of_eqtype unit", "let unit_param = param_of_eqtype unit", "let unit_param = param_of_eqtype unit", "let unit_param = param_of_eqtype unit", "let unit_param = param_of_eqtype unit", "let unit_param = param_of_eqtype unit", "let unit_param = param_of_eqtype unit", "let unit_param = param_of_eqtype unit" ] }, { "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.sub_invs_atomic", "opens_and_abbrevs": [ { "abbrev": "Act", "full_module": "PulseCore.Action" }, { "open": "PulseCore.Observability" }, { "open": "PulseCore.FractionalPermission" }, { "open": "PulseCore.InstantiatedSemantics" }, { "abbrev": "F", "full_module": "FStar.FunctionalExtensionality" }, { "abbrev": "T", "full_module": "FStar.Tactics.V2" }, { "abbrev": "A", "full_module": "PulseCore.Atomic" }, { "abbrev": "I", "full_module": "PulseCore.InstantiatedSemantics" }, { "abbrev": "T", "full_module": "FStar.Tactics.V2" }, { "abbrev": "Set", "full_module": "FStar.Set" }, { "abbrev": "G", "full_module": "FStar.Ghost" }, { "abbrev": "U32", "full_module": "FStar.UInt32" }, { "open": "FStar.PCM" }, { "open": "PulseCore.Observability" }, { "open": "PulseCore.FractionalPermission" }, { "open": "FStar.Ghost" }, { "open": "Pulse.Lib" }, { "open": "Pulse.Lib" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val sub_invs_atomic\n (#a:Type u#a)\n (#obs:_)\n (#opens1 #opens2:inames)\n (#pre:vprop)\n (#post:a -> vprop)\n (e:stt_atomic a #obs opens1 pre post)\n (_ : squash (inames_subset opens1 opens2))\n: stt_atomic a #obs opens2 pre post", "source_definition": "let sub_invs_atomic = A.sub_invs_stt_atomic", "source_range": { "start_line": 136, "start_col": 0, "end_line": 136, "end_col": 43 }, "interleaved": false, "definition": "PulseCore.Atomic.sub_invs_stt_atomic", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "PulseCore.Atomic.sub_invs_stt_atomic" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "\n e: Pulse.Lib.Core.stt_atomic a opens1 pre post ->\n _: Prims.squash (Pulse.Lib.Core.inames_subset opens1 opens2)\n -> Pulse.Lib.Core.stt_atomic a opens2 pre post", "prompt": "let sub_invs_atomic =\n ", "expected_response": "A.sub_invs_stt_atomic", "source": { "project_name": "steel", "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.Core.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Pulse.Lib.Core.fst", "checked_file": "dataset/Pulse.Lib.Core.fst.checked", "interface_file": true, "dependencies": [ "dataset/PulseCore.Observability.fst.checked", "dataset/PulseCore.InstantiatedSemantics.fsti.checked", "dataset/PulseCore.FractionalPermission.fst.checked", "dataset/PulseCore.Atomic.fsti.checked", "dataset/PulseCore.Action.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Squash.fsti.checked", "dataset/FStar.Set.fsti.checked", "dataset/FStar.PropositionalExtensionality.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.PCM.fst.checked", "dataset/FStar.Ghost.fsti.checked", "dataset/FStar.FunctionalExtensionality.fsti.checked", "dataset/FStar.Classical.Sugar.fsti.checked" ] }, "definitions_in_context": [ "let double_one_half () = ()", "let equate_by_smt = ()", "let one_half =\n half_perm full_perm", "let vprop = slprop", "let emp = emp", "let op_Star_Star = op_Star_Star", "val double_one_half ()\n : Lemma (sum_perm one_half one_half == full_perm)", "let pure = pure", "let op_exists_Star = op_exists_Star", "let vprop_equiv = slprop_equiv", "let elim_vprop_equiv #p #q pf = slprop_equiv_elim p q", "let vprop_post_equiv = slprop_post_equiv", "let prop_squash_idem (p:prop)\n : Tot (squash (squash p == p))\n = FStar.PropositionalExtensionality.apply p (squash p)", "let intro_vprop_post_equiv\n (#t:Type u#a) \n (p q: t -> vprop)\n (pf: (x:t -> vprop_equiv (p x) (q x)))\n : vprop_post_equiv p q\n = let pf : squash (forall x. vprop_equiv (p x) (q x)) = \n introduce forall x. vprop_equiv (p x) (q x)\n with FStar.Squash.return_squash (pf x)\n in\n coerce_eq (prop_squash_idem _) pf", "let elim_vprop_post_equiv (#t:Type u#a)\n (p q: t -> vprop) \n (pf:vprop_post_equiv p q)\n (x:t) \n: vprop_equiv (p x) (q x)\n= let pf\n : squash (vprop_equiv (p x) (q x))\n = eliminate forall x. vprop_equiv (p x) (q x) with x\n in\n coerce_eq (prop_squash_idem _) pf", "val equate_by_smt : unit", "val vprop : Type u#2", "val emp : vprop", "let vprop_equiv_refl (v0:vprop) \n : vprop_equiv v0 v0\n = slprop_equiv_refl v0", "val ( ** ) (p q:vprop) : vprop", "val pure (p:prop) : vprop", "val ( exists* ) (#a:Type) (p:a -> vprop) : vprop", "val vprop_equiv (p q:vprop) : prop", "let vprop_equiv_sym (v0 v1:vprop) (p:vprop_equiv v0 v1)\n : vprop_equiv v1 v0\n = slprop_equiv_elim v0 v1; p", "val elim_vprop_equiv (#p #q:_) (_:vprop_equiv p q) : squash (p == q)", "val vprop_post_equiv (#t:Type u#a) (p q: t -> vprop) : prop", "val intro_vprop_post_equiv\n (#t:Type u#a) \n (p q: t -> vprop)\n (pf: (x:t -> vprop_equiv (p x) (q x)))\n : vprop_post_equiv p q", "let vprop_equiv_trans\n (v0 v1 v2:vprop)\n (p:vprop_equiv v0 v1)\n (q:vprop_equiv v1 v2)\n : vprop_equiv v0 v2\n = slprop_equiv_elim v0 v1;\n slprop_equiv_elim v1 v2;\n p", "val elim_vprop_post_equiv (#t:Type u#a)\n (p q: t -> vprop) \n (pf:vprop_post_equiv p q)\n (x:t) \n : vprop_equiv (p x) (q x)", "let vprop_equiv_unit (x:vprop)\n : vprop_equiv (emp ** x) x\n = slprop_equiv_unit x", "val vprop_equiv_refl (v0:vprop) : vprop_equiv v0 v0", "let vprop_equiv_comm (p1 p2:vprop)\n : vprop_equiv (p1 ** p2) (p2 ** p1)\n = slprop_equiv_comm p1 p2", "val vprop_equiv_sym (v0 v1:vprop) (_:vprop_equiv v0 v1)\n : vprop_equiv v1 v0", "val vprop_equiv_trans (v0 v1 v2:vprop) (_:vprop_equiv v0 v1) (_:vprop_equiv v1 v2)\n : vprop_equiv v0 v2", "let vprop_equiv_assoc (p1 p2 p3:vprop)\n : vprop_equiv ((p1 ** p2) ** p3) (p1 ** (p2 ** p3))\n = slprop_equiv_assoc p1 p2 p3", "val vprop_equiv_unit (x:vprop) : vprop_equiv (emp ** x) x", "let vprop_equiv_cong (p1 p2 p3 p4:vprop)\n (f: vprop_equiv p1 p3)\n (g: vprop_equiv p2 p4)\n : vprop_equiv (p1 ** p2) (p3 ** p4)\n = slprop_equiv_elim p1 p3;\n slprop_equiv_elim p2 p4;\n vprop_equiv_refl _", "val vprop_equiv_comm (p1 p2:vprop)\n : vprop_equiv (p1 ** p2) (p2 ** p1)", "val vprop_equiv_assoc (p1 p2 p3:vprop)\n : vprop_equiv (p1 ** p2 ** p3) (p1 ** (p2 ** p3))", "val vprop_equiv_cong (p1 p2 p3 p4:vprop)\n (_: vprop_equiv p1 p3)\n (_: vprop_equiv p2 p4)\n : vprop_equiv (p1 ** p2) (p3 ** p4)", "let vprop_equiv_ext p1 p2 _ = vprop_equiv_refl p1", "val vprop_equiv_ext (p1 p2:vprop) (_:p1 == p2)\n : vprop_equiv p1 p2", "let iname = Act.iname", "let join_sub _ _ = ()", "let join_emp is =\n Set.lemma_equal_intro (join_inames is emp_inames) (reveal is);\n Set.lemma_equal_intro (join_inames emp_inames is) (reveal is)", "let inv = Act.inv", "val iname : eqtype", "let name_of_inv = Act.name_of_inv", "let inames = erased (FStar.Set.set iname)", "let emp_inames : inames = Ghost.hide Set.empty", "let add_already_there i is = Set.lemma_equal_intro (add_inv is i) is", "let join_inames (is1 is2 : inames) : inames =\n Set.union is1 is2", "let inames_subset (is1 is2 : inames) : Type0 =\n Set.subset is1 is2", "let stt = I.stt", "let return_stt_noeq = I.return", "let bind_stt = I.bind", "let (/!) (is1 is2 : inames) : Type0 =\n Set.disjoint is1 is2", "let frame_stt = I.frame", "let par_stt = I.par", "let sub_stt = I.sub", "val inv (p:vprop) : Type u#0", "let conv_stt pf1 pf2 = I.conv #_ _ _ _ _ pf1 pf2", "let hide_div = I.hide_div", "val name_of_inv #p (i : inv p) : GTot iname", "let mem_iname (e:inames) (i:iname) : erased bool = elift2 (fun e i -> Set.mem i e) e i", "let mem_inv (#p:vprop) (e:inames) (i:inv p) : erased bool = mem_iname e (name_of_inv i)", "let stt_atomic a #obs inames pre post = A.stt_atomic a #obs inames pre post", "let add_iname (e:inames) (i:iname) : inames = Set.union (Set.singleton i) (reveal e)", "let lift_observability = A.lift_observability", "let add_inv (#p:vprop) (e:inames) (i:inv p) : inames = add_iname e (name_of_inv i)", "let return_neutral = A.return_atomic", "let remove_inv (#p:vprop) (e:inames) (i:inv p) : inames = Set.remove (name_of_inv i) e", "let return_neutral_noeq = A.return_atomic_noeq", "let all_inames : inames = Set.complement Set.empty", "let bind_atomic = A.bind_atomic", "let frame_atomic = A.frame_atomic", "let sub_atomic = A.sub_atomic" ], "closest": [ "val sub_invs_stt_atomic\r\n (#a:Type u#a)\r\n (#obs:_)\r\n (#opens1 #opens2:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens1 pre post)\r\n (_ : squash (inames_subset opens1 opens2))\r\n: stt_atomic a #obs opens2 pre post\nlet sub_invs_stt_atomic\r\n (#a:Type u#a)\r\n (#obs:_)\r\n (#opens1 #opens2:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens1 pre post)\r\n (_ : squash (inames_subset opens1 opens2))\r\n: stt_atomic a #obs opens2 pre post\r\n= assert (Set.equal (Set.union opens1 opens2) opens2);\r\n A.weaken opens2 e", "val sub_atomic\r\n (#a:Type u#a)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre1:slprop)\r\n (pre2:slprop)\r\n (#post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1 : slprop_equiv pre1 pre2)\r\n (pf2 : slprop_post_equiv post1 post2)\r\n (e:stt_atomic a #obs opens pre1 post1)\r\n: stt_atomic a #obs opens pre2 post2\nlet sub_atomic\r\n (#a:Type u#a)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre1:slprop)\r\n (pre2:slprop)\r\n (#post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1 : slprop_equiv pre1 pre2)\r\n (pf2 : slprop_post_equiv post1 post2)\r\n (e:stt_atomic a #obs opens pre1 post1)\r\n: stt_atomic a #obs opens pre2 post2\r\n= A.sub pre2 post2 e", "val lift_atomic2\r\n (#a:Type u#2)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens pre post)\r\n: stt a pre post\nlet lift_atomic2\r\n (#a:Type u#2)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens pre post)\r\n: stt a pre post\r\n= A.lift2 e", "val lift_observability \r\n (#a:Type u#a)\r\n (#obs #obs':_)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e1:stt_atomic a #obs opens pre post)\r\n: stt_atomic a #(join_obs obs obs') opens pre post\nlet lift_observability\r\n (#a:Type u#a)\r\n (#obs #obs':_)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens pre post)\r\n= e", "val lift_atomic1\r\n (#a:Type u#1)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens pre post)\r\n: stt a pre post\nlet lift_atomic1\r\n (#a:Type u#1)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens pre post)\r\n: stt a pre post\r\n= A.lift1 e", "val lift_atomic0\r\n (#a:Type u#0)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens pre post)\r\n: stt a pre post\nlet lift_atomic0\r\n (#a:Type u#0)\r\n (#obs:_)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #obs opens pre post)\r\n: stt a pre post\r\n= A.lift0 e", "val bind_atomic\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#obs1:_)\r\n (#obs2:observability { at_most_one_observable obs1 obs2 })\r\n (#opens:inames)\r\n (#pre1:slprop)\r\n (#post1:a -> slprop)\r\n (#post2:b -> slprop)\r\n (e1:stt_atomic a #obs1 opens pre1 post1)\r\n (e2:(x:a -> stt_atomic b #obs2 opens (post1 x) post2))\r\n: stt_atomic b #(join_obs obs1 obs2) opens pre1 post2\nlet bind_atomic\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#obs1:_)\r\n (#obs2:observability { at_most_one_observable obs1 obs2 })\r\n (#opens:inames)\r\n (#pre1:slprop)\r\n (#post1:a -> slprop)\r\n (#post2:b -> slprop)\r\n (e1:stt_atomic a #obs1 opens pre1 post1)\r\n (e2:(x:a -> stt_atomic b #obs2 opens (post1 x) post2))\r\n= A.bind e1 e2", "val frame_atomic\r\n (#a:Type u#a)\r\n (#obs: observability)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt_atomic a #obs opens pre post)\r\n: stt_atomic a #obs opens (pre ** frame) (fun x -> post x ** frame)\nlet frame_atomic\r\n (#a:Type u#a)\r\n (#obs: observability)\r\n (#opens:inames)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt_atomic a #obs opens pre post)\r\n: stt_atomic a #obs opens (pre ** frame) (fun x -> post x ** frame)\r\n= A.frame e", "val stt_atomic\r\n (a:Type u#a)\r\n (#obs:observability)\r\n (opens:inames)\r\n (pre:slprop)\r\n (post:a -> slprop)\r\n: Type u#(max 2 a)\nlet stt_atomic a #obs opens pre post =\r\n A.act a opens pre post", "val with_invariant\r\n (#a:Type)\r\n (#obs:_)\r\n (#fp:slprop)\r\n (#fp':a -> slprop)\r\n (#f_opens:inames)\r\n (#p:slprop)\r\n (i:inv p{not (mem_inv f_opens i)})\r\n ($f:unit -> stt_atomic a #obs f_opens\r\n (p ** fp)\r\n (fun x -> p ** fp' x))\r\n: stt_atomic a #(join_obs obs Unobservable) (add_inv f_opens i) fp fp'\nlet with_invariant\r\n (#a:Type)\r\n (#obs:_)\r\n (#fp:slprop)\r\n (#fp':a -> slprop)\r\n (#f_opens:inames)\r\n (#p:slprop)\r\n (i:inv p{not (mem_inv f_opens i)})\r\n ($f:unit -> stt_atomic a #obs f_opens\r\n (p ** fp)\r\n (fun x -> p ** fp' x))\r\n: stt_atomic a #obs (add_inv f_opens i) fp fp'\r\n= A.with_invariant i f", "val coerce_atomic (#a:Type)\n (#o:inames)\n (#obs:observability)\n (#p:vprop)\n (#q:a -> vprop)\n (#pre:Type0)\n (#post: a -> Type0)\n ($f:unit -> SA.SteelAtomicBase a false o obs p q\n (fun _ -> pre)\n (fun _ x _ -> post x))\n : STA.STAtomicBase a false o obs p q pre post\nlet coerce_atomic #a #o #obs\n (#p:vprop)\n (#q:a -> vprop)\n (#pre:Type0)\n (#post: a -> Type0)\n ($f:unit -> SA.SteelAtomicBase a false o obs p q\n (fun _ -> pre)\n (fun _ x _ -> post x))\n : STA.STAtomicBase a false o obs p q pre post\n = STA.STAtomicBase?.reflect (SA.reify_steel_atomic_comp f)", "val coerce_atomicF (#a:Type)\n (#o:inames)\n (#obs:observability)\n (#p:vprop)\n (#q:a -> vprop)\n (#pre:Type0)\n (#post: a -> Type0)\n ($f:unit -> SA.SteelAtomicBase a true o obs p q\n (fun _ -> pre)\n (fun _ x _ -> post x))\n : STA.STAtomicBase a true o obs p q pre post\nlet coerce_atomicF #a #o #p #q #pre #post f\n = STA.STAtomicBase?.reflect (SA.reify_steel_atomic_comp f)", "val mk_sub_inv_atomic (u: R.universe) (a pre post opens1 opens2 e: R.term) : R.term\nlet mk_sub_inv_atomic (u:R.universe) (a pre post opens1 opens2 e : R.term) : R.term =\n let open R in\n let lid = mk_pulse_lib_core_lid \"sub_invs_atomic\" in\n let head : R.term = pack_ln (R.Tv_UInst (R.pack_fv lid) [u]) in\n R.mk_app head\n [(a, Q_Implicit);\n (opens1, Q_Implicit);\n (opens2, Q_Implicit);\n (pre, Q_Implicit);\n (post, Q_Implicit);\n (e, Q_Explicit)]", "val with_invariant (#a:Type)\n (#fp:vprop)\n (#fp':a -> vprop)\n (#opened_invariants:inames)\n (#obs:observability)\n (#p:vprop)\n (i:inv p{not (mem_inv opened_invariants i)})\n ($f:unit -> STAtomicBaseT a (add_inv opened_invariants i) obs\n (p `star` fp)\n (fun x -> p `star` fp' x))\n : STAtomicBaseT a opened_invariants obs fp fp'\nlet with_invariant (#a:Type)\n (#fp:vprop)\n (#fp':a -> vprop)\n (#opened_invariants:inames)\n (#obs:observability)\n (#p:vprop)\n (i:inv p{not (mem_inv opened_invariants i)})\n ($f:unit -> STAtomicBaseT a (add_inv opened_invariants i) obs\n (p `star` fp)\n (fun x -> p `star` fp' x))\n = let f (x:unit)\n : SEA.SteelAtomicBaseT a (add_inv opened_invariants i) obs\n (p `star` fp)\n (fun x -> p `star` fp' x) \n = f () in\n coerce_atomic (fun _ -> SEA.with_invariant i f)", "val sub (#a:Type u#a)\r\n (#pre1:slprop)\r\n (pre2:slprop)\r\n (#post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1:slprop_equiv pre1 pre2)\r\n (pf2:slprop_post_equiv post1 post2)\r\n (e:stt a pre1 post1)\r\n: stt a pre2 post2\nlet sub (#a:Type u#a)\r\n (#pre1:slprop)\r\n (pre2:slprop)\r\n (#post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1:slprop_equiv pre1 pre2)\r\n (pf2:slprop_post_equiv post1 post2)\r\n (e:stt a pre1 post1)\r\n: stt a pre2 post2\r\n= coerce_eq (conv pre1 pre2 post1 post2 pf1 pf2) e", "val sub \r\n (#a:Type)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (#opens:inames)\r\n (pre':slprop { slprop_equiv pre pre' })\r\n (post':a -> slprop { forall x. slprop_equiv (post x) (post' x) })\r\n (f:act a opens pre post)\r\n: act a opens pre' post'\nlet sub \r\n (#a:Type)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (#opens:inames)\r\n (pre':slprop { slprop_equiv pre pre' })\r\n (post':a -> slprop { forall x. slprop_equiv (post x) (post' x) })\r\n (f:act a opens pre post)\r\n: act a opens pre' post'\r\n= I.slprop_equiv_elim pre pre';\r\n introduce forall x. post x == post' x\r\n with I.slprop_equiv_elim (post x) (post' x);\r\n f", "val lift_ghost_atomic\n (a:Type)\n (opened:inames)\n (#framed:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre:pre_t)\n (#[@@@ framing_implicit] post:post_t a)\n (#[@@@ framing_implicit] req:pure_pre)\n (#[@@@ framing_implicit] ens:pure_post a)\n (f:STAG.repr a framed opened Unobservable pre post req ens)\n : STAG.repr a framed opened Unobservable pre post req ens\nlet lift_ghost_atomic\n (a:Type)\n (opened:inames)\n (#framed:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre:pre_t)\n (#[@@@ framing_implicit] post:post_t a)\n (#[@@@ framing_implicit] req:Type0)\n (#[@@@ framing_implicit] ens:a -> Type0)\n (f:STAG.repr a framed opened Unobservable pre post req ens)\n : STAG.repr a framed opened Unobservable pre post req ens\n = f", "val return (#a:Type u#a)\n (#opened_invariants:inames)\n (#p:a -> vprop)\n (x:a)\n : STAtomicBase a true opened_invariants Unobservable\n (return_pre (p x)) p\n True\n (fun v -> v == x)\nlet return #a #o #p x = coerce_atomicF (fun _ -> return0 x)", "val return_atomic' (#a x post: _)\n : stt_atomic a\n #Unobservable\n emp_inames\n (post x ** pure (x == x))\n (fun r -> post r ** pure (r == x))\nlet return_atomic' #a x post\r\n: stt_atomic a #Unobservable emp_inames\r\n (post x ** pure (x == x))\r\n (fun r -> post r ** pure (r == x))\r\n= A.return #a #(fun r -> post r ** pure (r == x)) x", "val with_invlist (#a:Type0) (#pre : vprop) (#post : a -> vprop)\n (is : invlist)\n (f : unit -> stt_atomic a #Unobservable emp_inames (invlist_v is ** pre) (fun v -> invlist_v is ** post v))\n : stt_atomic a #Unobservable (invlist_names is) pre (fun v -> post v)\nlet with_invlist = __with_invlist", "val witness (#inames: _)\n (#a:Type)\n (#q:perm)\n (#p:Preorder.preorder a)\n (r:ref a p)\n (fact:stable_property p)\n (v:erased a)\n (_:squash (fact v))\n : STAtomicUT (witnessed r fact) inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\nlet witness (#inames: _)\n (#a:Type)\n (#q:perm)\n (#p:Preorder.preorder a)\n (r:ref a p)\n (fact:stable_property p)\n (v:erased a)\n (pf:squash (fact v))\n = coerce_atomic (witness' r fact v pf)", "val as_atomic_o_action\n (#a: Type u#a)\n (#opened_invariants: inames)\n (#fp: slprop)\n (#fp': (a -> slprop))\n (o: observability)\n (f: action_except a opened_invariants fp fp')\n : SteelAtomicBaseT a opened_invariants o (to_vprop fp) (fun x -> to_vprop (fp' x))\nlet as_atomic_o_action\n (#a:Type u#a)\n (#opened_invariants:inames)\n (#fp:slprop)\n (#fp': a -> slprop)\n (o:observability)\n (f:action_except a opened_invariants fp fp')\n : SteelAtomicBaseT a opened_invariants o (to_vprop fp) (fun x -> to_vprop (fp' x))\n = SteelAtomicBaseT?.reflect f", "val return (#a:Type u#a)\n (#opened_invariants:inames)\n (#p:a -> vprop)\n (x:a)\n : SteelAtomicBase a true opened_invariants Unobservable\n (return_pre (p x)) p\n (return_req (p x)) (return_ens a x p)\nlet return #a #opened #p x = SteelAtomicBase?.reflect (return_ a x opened #p)", "val lift_ghost_atomic\n (a:Type)\n (opened:inames)\n (#framed:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre:pre_t) (#[@@@ framing_implicit] post:post_t a)\n (#[@@@ framing_implicit] req:req_t pre) (#[@@@ framing_implicit] ens:ens_t pre a post)\n (f:repr a framed opened Unobservable pre post req ens)\n : repr a framed opened Unobservable pre post req ens\nlet lift_ghost_atomic a o f = f", "val with_invariant (#a:Type)\n (#fp:vprop)\n (#fp':a -> vprop)\n (#opened_invariants:inames)\n (#obs:observability)\n (#p:vprop)\n (#perm:_)\n (i:inv p{not (mem_inv opened_invariants i)})\n ($f:unit -> SteelAtomicBaseT a (add_inv opened_invariants i) obs\n (p `star` fp)\n (fun x -> p `star` fp' x))\n : SteelAtomicBaseT a opened_invariants obs (active perm i `star` fp) (fun x -> active perm i `star` fp' x)\nlet with_invariant #a #fp #fp' #u #obs #p #perm i f\n = let with_invariant_aux (r:ghost_ref bool)\n (_:unit)\n : SteelAtomicBaseT a (add_inv u i) obs\n (ex_conditional_inv r p `star`\n (ghost_pts_to r (half_perm perm) true `star`\n fp))\n (fun x ->\n ex_conditional_inv r p `star`\n (ghost_pts_to r (half_perm perm) true `star` //associativity matters\n fp' x))\n = let b = witness_exists #_ #_ #(conditional_inv r p) () in\n ghost_pts_to_injective_eq r true (hide (reveal b));\n rewrite_slprop (if b then p else emp) p (fun _ -> ());\n let x = f() in\n intro_exists true (conditional_inv r p);\n return x\n in\n with_invariant (dsnd i)\n (with_invariant_aux (gref i))", "val witness (#inames: _)\n (#a:Type)\n (#q:perm)\n (#p:Preorder.preorder a)\n (r:erased (ref a p))\n (fact:stable_property p)\n (v:erased a)\n (_:squash (fact v))\n : STAtomicUT (witnessed r fact) inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\nlet witness (#inames: _)\n (#a:Type)\n (#q:perm)\n (#p:Preorder.preorder a)\n (r:erased (ref a p))\n (fact:stable_property p)\n (v:erased a)\n (pf:squash (fact v))\n = coerce_atomic (witness' r fact v pf)", "val elab_statomic_equiv\n (g: R.env)\n (c: comp{C_STAtomic? c})\n (pre post: R.term)\n (eq_pre: RT.equiv g pre (elab_term (comp_pre c)))\n (eq_post:\n RT.equiv g post (mk_abs (elab_term (comp_res c)) R.Q_Explicit (elab_term (comp_post c))))\n : RT.equiv g\n (let C_STAtomic inames obs { u = u ; res = res } = c in\n mk_stt_atomic_comp (elab_observability obs) u (elab_term res) (elab_term inames) pre post)\n (elab_comp c)\nlet elab_statomic_equiv (g:R.env) (c:comp{C_STAtomic? c}) (pre:R.term) (post:R.term)\n (eq_pre:RT.equiv g pre (elab_term (comp_pre c)))\n (eq_post:RT.equiv g post\n (mk_abs (elab_term (comp_res c)) R.Q_Explicit (elab_term (comp_post c))))\n : RT.equiv g\n (let C_STAtomic inames obs {u;res} = c in\n mk_stt_atomic_comp (elab_observability obs) u\n (elab_term res)\n (elab_term inames)\n pre\n post)\n (elab_comp c) =\n \n let C_STAtomic inames obs {u;res} = c in\n let c' =\n mk_stt_atomic_comp (elab_observability obs) u\n (elab_term res)\n (elab_term inames)\n pre\n post\n in\n mk_stt_atomic_comp_equiv _ (elab_observability obs)\n (comp_u c)\n (elab_term (comp_res c))\n (elab_term inames)\n _ _ _ _ eq_pre eq_post", "val recall (#inames: _)\n (#a:Type u#0)\n (#q:perm)\n (#p:Preorder.preorder a)\n (fact:property a)\n (r:ref a p)\n (v:erased a)\n (w:witnessed r fact)\n : STAtomicU unit inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\n (requires True)\n (ensures fun _ -> fact v)\nlet recall (#inames: _)\n (#a:Type u#0)\n (#q:perm)\n (#p:Preorder.preorder a)\n (fact:property a)\n (r:ref a p)\n (v:erased a)\n (w:witnessed r fact)\n = coerce_atomic (fun _ -> MR.recall #inames #a #q #p fact r v w)", "val new_invariant (#opened_invariants:inames) (p:vprop)\n : STAtomicUT (inv p) opened_invariants p (fun _ -> emp)\nlet new_invariant #u p\n = let i = fresh_invariant #u p [] in return i", "val lift_neutral_ghost\r\n (#a:Type u#a)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #Neutral emp_inames pre post)\r\n: stt_ghost a pre post\nlet lift_neutral_ghost\r\n (#a:Type u#a)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (e:stt_atomic a #Neutral emp_inames pre post)\r\n: stt_ghost a pre post\r\n= Ghost.hide e", "val sub_ghost\r\n (#a:Type u#a)\r\n (#pre1:slprop)\r\n (pre2:slprop)\r\n (#post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1 : slprop_equiv pre1 pre2)\r\n (pf2 : slprop_post_equiv post1 post2)\r\n (e:stt_ghost a pre1 post1)\r\n: stt_ghost a pre2 post2\nlet sub_ghost pre2 post2 pf1 pf2 e\r\n= Ghost.hide (A.sub pre2 post2 e)", "val bind\r\n (#a:Type u#a) (#b:Type u#b)\r\n (#pre1:slprop) (#post1:a -> slprop) (#post2:b -> slprop)\r\n (e1:stt a pre1 post1)\r\n (e2:(x:a -> stt b (post1 x) post2))\r\n: stt b pre1 post2\nlet bind\r\n (#a:Type u#a) (#b:Type u#b)\r\n (#pre1:slprop) (#post1:a -> slprop) (#post2:b -> slprop)\r\n (e1:stt a pre1 post1)\r\n (e2:(x:a -> stt b (post1 x) post2))\r\n: stt b pre1 post2\r\n= fun _ -> Sem.mbind (e1()) (fun x -> e2 x ())", "val recall (#inames: _)\n (#a:Type u#0)\n (#q:perm)\n (#p:Preorder.preorder a)\n (fact:property a)\n (r:erased (ref a p))\n (v:erased a)\n (w:witnessed r fact)\n : STAtomicU unit inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\n (requires True)\n (ensures fun _ -> fact v)\nlet recall (#inames: _)\n (#a:Type u#0)\n (#q:perm)\n (#p:Preorder.preorder a)\n (fact:property a)\n (r:erased (ref a p))\n (v:erased a)\n (w:witnessed r fact)\n = coerce_atomic (fun _ -> MR.recall #inames #a #q #p fact r v w)", "val subcomp (a:Type)\n (opened_invariants:inames)\n (o1:eqtype_as_type observability)\n (o2:eqtype_as_type observability)\n (#framed_f: eqtype_as_type bool)\n (#framed_g: eqtype_as_type bool)\n (#[@@@ framing_implicit] pre_f:pre_t) (#[@@@ framing_implicit] post_f:post_t a)\n (#[@@@ framing_implicit] req_f:req_t pre_f) (#[@@@ framing_implicit] ens_f:ens_t pre_f a post_f)\n (#[@@@ framing_implicit] pre_g:pre_t) (#[@@@ framing_implicit] post_g:post_t a)\n (#[@@@ framing_implicit] req_g:req_t pre_g) (#[@@@ framing_implicit] ens_g:ens_t pre_g a post_g)\n (#[@@@ framing_implicit] frame:vprop)\n (#[@@@ framing_implicit] _ : squash (maybe_emp framed_f frame))\n (#[@@@ framing_implicit] p: prop)\n (#[@@@ framing_implicit] p1:squash (can_be_split_dep p pre_g (pre_f `star` frame)))\n (#[@@@ framing_implicit] p2:squash (equiv_forall post_g (fun x -> post_f x `star` frame)))\n (f:repr a framed_f opened_invariants o1 pre_f post_f req_f ens_f)\n: Pure (repr a framed_g opened_invariants o2 pre_g post_g req_g ens_g)\n (requires (o1 = Unobservable || o2 = Observable) /\\\n subcomp_pre req_f ens_f req_g ens_g p1 p2)\n (ensures fun _ -> True)\nlet subcomp a opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #fr #_ #pr #p1 #p2 f =\n lemma_subcomp_pre_opaque req_f ens_f req_g ens_g p1 p2;\n subcomp_opaque a opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #fr #pr #_ #p1 #p2 f", "val as_atomic_unobservable_action\n (#a:Type u#a)\n (#opened_invariants:inames)\n (#fp:slprop)\n (#fp': a -> slprop)\n (f:action_except a opened_invariants fp fp')\n : SteelAtomicUT a opened_invariants (to_vprop fp) (fun x -> to_vprop (fp' x))\nlet as_atomic_unobservable_action f = SteelAtomicU?.reflect f", "val return_atomic\r\n (#a:Type u#a)\r\n (x:a)\r\n (p:a -> slprop)\r\n: stt_atomic a #Neutral emp_inames (p x) (fun r -> p r ** pure (r == x))\nlet return_atomic #a x post\r\n: stt_atomic a #Neutral emp_inames\r\n (post x)\r\n (fun r -> post r ** pure (r == x))\r\n= emp_unit_r (post x);\r\n pure_trivial (x == x) ();\r\n coerce_eq () (return_atomic' #a x post)", "val with_invariant_g (#a:Type)\n (#fp:vprop)\n (#fp':a -> vprop)\n (#opened_invariants:inames)\n (#p:vprop)\n (i:inv p{not (mem_inv opened_invariants i)})\n ($f:unit -> STGhostT a (add_inv opened_invariants i)\n (p `star` fp)\n (fun x -> p `star` fp' x))\n : STAtomicUT (erased a) opened_invariants fp (fun x -> fp' x)\nlet with_invariant_g (#a:Type)\n (#fp:vprop)\n (#fp':a -> vprop)\n (#opened_invariants:inames)\n (#p:vprop)\n (i:inv p{not (mem_inv opened_invariants i)})\n ($f:unit -> STGhostT a (add_inv opened_invariants i)\n (p `star` fp)\n (fun x -> p `star` fp' x))\n = let f (x:unit)\n : SEA.SteelGhostT a (add_inv opened_invariants i)\n (p `star` fp)\n (fun x -> p `star` fp' x) \n = f () in\n coerce_atomic (fun _ -> SEA.with_invariant_g i f)", "val lift_atomic_st\n (a:Type)\n (o:eqtype_as_type observability)\n (#framed:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre:pre_t)\n (#[@@@ framing_implicit] post:post_t a)\n (#[@@@ framing_implicit] req:pure_pre)\n (#[@@@ framing_implicit] ens:pure_post a)\n (f:repr a framed Set.empty o pre post req ens)\n : Steel.ST.Effect.repr a framed pre post req ens\nlet lift_atomic_st\n (a:Type)\n (o:eqtype_as_type observability)\n (#framed:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre:pre_t)\n (#[@@@ framing_implicit] post:post_t a)\n (#[@@@ framing_implicit] req:Type0)\n (#[@@@ framing_implicit] ens:a -> Type0)\n (f:repr a framed Set.empty o pre post req ens)\n : Steel.ST.Effect.repr a framed pre post req ens\n = let ff : Steel.Effect.repr a framed pre post (fun _ -> req) (fun _ x _ -> ens x)\n = SEA.lift_atomic_steel a o #framed #pre #post #(fun _ -> req) #(fun _ x _ -> ens x) f\n in\n ff", "val shift_invlist_one\n (#a:Type0)\n (p : vprop)\n (i : inv p)\n (is : invlist{not (mem_inv (invlist_names is) i)})\n (#pre:vprop)\n (#post : a -> vprop)\n (f : unit -> stt_atomic a #Unobservable emp_inames (invlist_v ((| p, i |) :: is) ** pre) (fun v -> invlist_v ((| p, i |) :: is) ** post v)) :\n unit -> stt_atomic a #Unobservable emp_inames (invlist_v is ** (p ** pre)) (fun v -> invlist_v is ** (p ** post v))\nlet shift_invlist_one = __shift_invlist_one", "val subcomp (a:Type)\n (opened_invariants:inames)\n (o1:eqtype_as_type observability)\n (o2:eqtype_as_type observability)\n (#framed_f:eqtype_as_type bool)\n (#framed_g:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre_f:pre_t)\n (#[@@@ framing_implicit] post_f:post_t a)\n (#[@@@ framing_implicit] req_f:pure_pre)\n (#[@@@ framing_implicit] ens_f:pure_post a)\n (#[@@@ framing_implicit] pre_g:pre_t)\n (#[@@@ framing_implicit] post_g:post_t a)\n (#[@@@ framing_implicit] req_g:pure_pre)\n (#[@@@ framing_implicit] ens_g:pure_post a)\n (#[@@@ framing_implicit] frame:vprop)\n (#[@@@ framing_implicit] _ : squash (maybe_emp framed_f frame))\n (#[@@@ framing_implicit] p1:squash (can_be_split pre_g (pre_f `star` frame)))\n (#[@@@ framing_implicit] p2:squash (equiv_forall post_g (fun x -> post_f x `star` frame)))\n (f:repr a framed_f opened_invariants o1 pre_f post_f req_f ens_f)\n: Pure (repr a framed_g opened_invariants o2 pre_g post_g req_g ens_g)\n (requires\n (o1 = Unobservable || o2 = Observable) /\\\n (req_g ==> (req_f /\\ (forall x. ens_f x ==> ens_g x))))\n (ensures fun _ -> True)\nlet subcomp (a:Type)\n (opened_invariants:inames)\n (o1:eqtype_as_type observability)\n (o2:eqtype_as_type observability)\n (#framed_f:eqtype_as_type bool)\n (#framed_g:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre_f:pre_t)\n (#[@@@ framing_implicit] post_f:post_t a)\n (#[@@@ framing_implicit] req_f:Type0)\n (#[@@@ framing_implicit] ens_f:a -> Type0)\n (#[@@@ framing_implicit] pre_g:pre_t)\n (#[@@@ framing_implicit] post_g:post_t a)\n (#[@@@ framing_implicit] req_g:Type0)\n (#[@@@ framing_implicit] ens_g:a -> Type0)\n (#[@@@ framing_implicit] frame:vprop)\n (#[@@@ framing_implicit] _x : squash (maybe_emp framed_f frame))\n (#[@@@ framing_implicit] p1:squash (can_be_split pre_g (pre_f `star` frame)))\n (#[@@@ framing_implicit] p2:squash (equiv_forall post_g (fun x -> post_f x `star` frame)))\n (f:repr a framed_f opened_invariants o1 pre_f post_f req_f ens_f)\n : Pure (repr a framed_g opened_invariants o2 pre_g post_g req_g ens_g)\n (requires\n (o1 = Unobservable || o2 = Observable) /\\\n (req_g ==> (req_f /\\ (forall x. ens_f x ==> ens_g x))))\n (ensures fun _ -> True)\n = weaken_repr (SEA.subcomp a opened_invariants o1 o2\n #framed_f\n #framed_g\n #pre_f\n #post_f\n #(fun _ -> req_f)\n #(fun _ x _ -> ens_f x)\n #pre_g\n #post_g\n #(fun _ -> req_g)\n #(fun _ y _ -> ens_g y)\n #frame\n #_x\n #True\n #p1\n #p2\n f) () ()", "val with_invlist_ghost (#pre : vprop) (#post : vprop)\n (is : invlist)\n (f : unit -> stt_ghost unit (invlist_v is ** pre) (fun _ -> invlist_v is ** post))\n : stt_atomic unit #Unobservable (invlist_names is) pre (fun _ -> post)\nlet with_invlist_ghost = __with_invlist_ghost", "val as_atomic_action (#a:Type u#a)\n (#opened_invariants:inames)\n (#fp:slprop)\n (#fp': a -> slprop)\n (f:action_except a opened_invariants fp fp')\n : SteelAtomicT a opened_invariants (to_vprop fp) (fun x -> to_vprop (fp' x))\nlet as_atomic_action f = SteelAtomic?.reflect f", "val subcomp_opaque (a:Type)\n (opened:inames)\n (o1:eqtype_as_type observability)\n (o2:eqtype_as_type observability)\n (#framed_f:eqtype_as_type bool)\n (#framed_g:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre_f:pre_t) (#[@@@ framing_implicit] post_f:post_t a)\n (#[@@@ framing_implicit] req_f:req_t pre_f) (#[@@@ framing_implicit] ens_f:ens_t pre_f a post_f)\n (#[@@@ framing_implicit] pre_g:pre_t) (#[@@@ framing_implicit] post_g:post_t a)\n (#[@@@ framing_implicit] req_g:req_t pre_g) (#[@@@ framing_implicit] ens_g:ens_t pre_g a post_g)\n (#[@@@ framing_implicit] frame:vprop)\n (#[@@@ framing_implicit] pr : prop)\n (#[@@@ framing_implicit] _ : squash (maybe_emp framed_f frame))\n (#[@@@ framing_implicit] p1:squash (can_be_split_dep pr pre_g (pre_f `star` frame)))\n (#[@@@ framing_implicit] p2:squash (equiv_forall post_g (fun x -> post_f x `star` frame)))\n (f:repr a framed_f opened o1 pre_f post_f req_f ens_f)\n: Pure (repr a framed_g opened o2 pre_g post_g req_g ens_g)\n (requires (o1 = Unobservable || o2 = Observable) /\\\n subcomp_pre_opaque req_f ens_f req_g ens_g p1 p2)\n (ensures fun _ -> True)\nlet subcomp_opaque a opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #fr #pr #_ #p1 #p2 f =\n fun frame ->\n let m0:full_mem = NMSTTotal.get () in\n let h0 = mk_rmem pre_g (core_mem m0) in\n\n can_be_split_trans pre_g (pre_f `star` fr) pre_f;\n can_be_split_trans pre_g (pre_f `star` fr) fr;\n\n can_be_split_3_interp (hp_of pre_g) (hp_of (pre_f `star` fr)) frame (locks_invariant opened m0) m0;\n\n focus_replace pre_g (pre_f `star` fr) pre_f (core_mem m0);\n\n let x = frame00 f fr frame in\n\n let m1:full_mem = NMSTTotal.get () in\n let h1 = mk_rmem (post_g x) (core_mem m1) in\n\n let h0' = mk_rmem (pre_f `star` fr) (core_mem m0) in\n let h1' = mk_rmem (post_f x `star` fr) (core_mem m1) in\n // From frame00\n assert (frame_opaque fr (focus_rmem h0' fr) (focus_rmem h1' fr));\n // Replace h0'/h1' by h0/h1\n focus_replace pre_g (pre_f `star` fr) fr (core_mem m0);\n focus_replace (post_g x) (post_f x `star` fr) fr (core_mem m1);\n assert (frame_opaque fr (focus_rmem h0 fr) (focus_rmem h1 fr));\n\n can_be_split_trans (post_g x) (post_f x `star` fr) (post_f x);\n can_be_split_trans (post_g x) (post_f x `star` fr) fr;\n\n can_be_split_3_interp (hp_of (post_f x `star` fr)) (hp_of (post_g x)) frame (locks_invariant opened m1) m1;\n\n focus_replace (post_g x) (post_f x `star` fr) (post_f x) (core_mem m1);\n\n x", "val lift (#a:Type u#100) #opens (#pre:slprop) (#post:a -> slprop)\r\n (m:act a opens pre post)\r\n: I.stt a pre post\nlet lift (#a:Type u#100) #opens #pre #post\r\n (m:act a opens pre post)\r\n: stt a pre post\r\n= stt_of_action (m #emp_inames)", "val acquire_core (#p:vprop) (#u:inames) (r:ref bool) (i:inv (lockinv p r))\n : SteelAtomicT bool u\n (lockinv p r `star` emp)\n (fun b -> lockinv p r `star` (if b then p else emp))\nlet acquire_core #p #u r i =\n let ghost = witness_exists () in\n\n let res = cas_pt_bool r ghost available locked in\n\n (* Not sure we can avoid calling an SMT here. Better force the manual call? *)\n rewrite_slprop (if (Ghost.reveal ghost) then emp else p) (if res then p else emp)\n (fun _ -> ());\n rewrite_slprop (if res then pts_to r full_perm (Ghost.hide locked) else pts_to r full_perm ghost) (pts_to r full_perm locked) (fun _ -> ());\n\n intro_lockinv_locked p r;\n return res", "val repr (a:Type u#a) //result type\n (already_framed:bool) //framed or not\n (opened_invariants:inames) //which invariants are we relying on\n (g:observability) //is this a ghost computation?\n (pre:pre_t) //expects vprop\n (post:post_t a) //provides a -> vprop\n (req:pure_pre) //a prop refinement as a precondition\n (ens:pure_post a) //an (a -> prop) as a postcondition\n : Type u#(max a 2)\nlet repr (a:Type u#a)\n (already_framed:bool)\n (opened_invariants:inames)\n (g:observability)\n (pre:pre_t)\n (post:post_t a)\n (req:Type0)\n (ens:a -> Type0)\n : Type u#(max a 2)\n = SEA.repr a already_framed opened_invariants g pre post\n (fun _ -> req)\n (fun _ x _ -> ens x)", "val repr (a:Type u#a)\n (already_framed:bool)\n (opened_invariants:inames)\n (g:observability)\n (pre:pre_t)\n (post:post_t a)\n (req:req_t pre)\n (ens:ens_t pre a post)\n : Type u#(max a 2)\nlet repr a framed opened f pre post req ens =\n action_except_full a opened (hp_of pre) (to_post post)\n (req_to_act_req req) (ens_to_act_ens ens)", "val trade_sub_inv\n (#os1 : invlist)\n (#os2 : invlist{invlist_sub os1 os2})\n (hyp concl: vprop)\n: stt_ghost unit\n (trade #os1 hyp concl)\n (fun _ -> trade #os2 hyp concl)\nlet trade_sub_inv = __trade_sub_inv", "val fresh_invariant (#opened_invariants:inames) (p:vprop) (ctxt:list pre_inv)\n : STAtomicUT (i:inv p {fresh_inv opened_invariants ctxt i})\n opened_invariants p (fun _ -> emp)\nlet fresh_invariant #u p ctxt\n = coerce_atomic (fun _ -> SEA.fresh_invariant #u p ctxt)", "val weaken \r\n (#a:Type)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (#opens opens':inames)\r\n (f:act a opens pre post)\r\n: act a (Set.union opens opens') pre post\nlet weaken \r\n (#a:Type)\r\n (#pre:slprop)\r\n (#post:a -> slprop)\r\n (#opens opens':inames)\r\n (f:act a opens pre post)\r\n: act a (Set.union opens opens') pre post\r\n= f", "val witness (#inames: _) (#a:Type) (#q:perm) (#p:Preorder.preorder a)\n (r:erased (ref a p))\n (fact:stable_property p)\n (v:erased a)\n (_:squash (fact v))\n : SteelAtomicUT (witnessed r fact) inames (pts_to r q v)\n (fun _ -> pts_to r q v)\nlet witness (#inames: _) (#a:Type) (#q:perm) (#p:Preorder.preorder a)\n (r:Ghost.erased (ref a p))\n (fact:stable_property p)\n (v:erased a)\n (_:squash (fact v))\n : SteelAtomicUT (witnessed r fact) inames (pts_to r q v)\n (fun _ -> pts_to r q v)\n = let h = witness_exists #_ #_ #(pts_to_body r q v) () in\n let _ = elim_pure #_ #_ #_ #q r v h in\n\n assert (forall h'. compatible pcm_history h h' ==> lift_fact fact h');\n lift_fact_is_stable #a #p fact;\n\n let w = witness_thunk #_ #_ #(pcm_history #a #p) r (lift_fact fact) h () _ in\n\n rewrite_slprop (PR.pts_to r h) (pts_to_body r q v h) (fun m ->\n emp_unit (M.pts_to r h);\n pure_star_interp (M.pts_to r h) (history_val h v q) m);\n\n intro_exists_erased h (pts_to_body r q v);\n return w", "val witness (#inames: _) (#a:Type) (#q:perm) (#p:Preorder.preorder a) (r:ref a p)\n (fact:stable_property p)\n (v:erased a)\n (_:squash (fact v))\n : SteelAtomicUT (witnessed r fact) inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\nlet witness (#inames: _) (#a:Type) (#q:perm) (#p:Preorder.preorder a)\n (r:ref a p)\n (fact:stable_property p)\n (v:erased a)\n (_:squash (fact v))\n : SteelAtomicUT (witnessed r fact) inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\n = let h = witness_exists #_ #_ #(pts_to_body r q v) () in\n let _ = elim_pure #_ #_ #_ #q r v h in\n\n assert (forall h'. compatible pcm_history h h' ==> lift_fact fact h');\n lift_fact_is_stable #a #p fact;\n\n let w = witness_thunk #_ #_ #(pcm_history #a #p) r (lift_fact fact) h () () in\n\n \n intro_pure_full r v h;\n rewrite_slprop (pts_to _ q _) (pts_to r q v) (fun _ -> ());\n return w", "val witness (#inames: _) (#a:Type) (#q:perm) (#p:Preorder.preorder a) (r:ref a p)\n (fact:stable_property p)\n (v:erased a)\n (_:squash (fact v))\n : SteelAtomicUT (witnessed r fact) inames (pts_to r q v)\n (fun _ -> pts_to r q v)\nlet witness (#inames: _)\n (#a:Type)\n (#q:perm)\n (#p:Preorder.preorder a)\n (r:ref a p)\n (fact:stable_property p)\n (v:erased a)\n (_:squash (fact v))\n : SteelAtomicUT (witnessed r fact) inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\n = let w = MHR.witness r (lift_property fact) (U.raise_val (reveal v)) () in\n return w", "val witness (#inames: _) (#a:Type) (#q:perm) (#p:Preorder.preorder a)\n (r:erased (ref a p))\n (fact:stable_property p)\n (v:erased a)\n (_:squash (fact v))\n : SteelAtomicUT (witnessed r fact) inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\nlet witness (#inames: _)\n (#a:Type)\n (#q:perm)\n (#p:Preorder.preorder a)\n (r:erased (ref a p))\n (fact:stable_property p)\n (v:erased a)\n (_:squash (fact v))\n = MHR.witness r (lift_property fact) (hide (U.raise_val (reveal v))) ()", "val witness (#o:inames)\n (#a:Type)\n (#pcm:pcm a)\n (r:ref a pcm)\n (fact:Steel.Preorder.stable_property pcm)\n (v:erased a)\n (_:squash (Steel.Preorder.fact_valid_compat fact v))\n : SteelAtomicUT (witnessed r fact) o\n (pts_to r v)\n (fun _ -> pts_to r v)\nlet witness (#o:inames)\n (#a:Type)\n (#pcm:pcm a)\n (r:ref a pcm)\n (fact:Steel.Preorder.stable_property pcm)\n (v:erased a)\n (_:squash (Steel.Preorder.fact_valid_compat fact v))\n = P.witness r fact v ()", "val bind_ghost\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#pre1:slprop)\r\n (#post1:a -> slprop)\r\n (#post2:b -> slprop)\r\n (e1:stt_ghost a pre1 post1)\r\n (e2:(x:a -> stt_ghost b (post1 x) post2))\r\n: stt_ghost b pre1 post2\nlet bind_ghost\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#pre1:slprop)\r\n (#post1:a -> slprop)\r\n (#post2:b -> slprop)\r\n (e1:stt_ghost a pre1 post1)\r\n (e2:(x:a -> stt_ghost b (post1 x) post2))\r\n: stt_ghost b pre1 post2\r\n= let e1 = Ghost.reveal e1 in\r\n let e2 = FStar.Ghost.Pull.pull (fun (x:a) -> Ghost.reveal (e2 x)) in\r\n Ghost.hide (A.bind e1 e2)", "val bind_lpre\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post_a: post_t st a)\n (lpre_a: l_pre pre)\n (lpost_a: l_post pre post_a)\n (lpre_b: (x: a -> l_pre (post_a x)))\n : l_pre pre\nlet bind_lpre\n (#st:st)\n (#a:Type)\n (#pre:st.hprop)\n (#post_a:post_t st a)\n (lpre_a:l_pre pre)\n (lpost_a:l_post pre post_a)\n (lpre_b:(x:a -> l_pre (post_a x)))\n : l_pre pre\n =\n fun h -> lpre_a h /\\ (forall (x:a) h1. lpost_a h x h1 ==> lpre_b x h1)", "val admit_ (#a:Type)\n (#opened:inames)\n (#p:pre_t)\n (#q:post_t a)\n (_:unit)\n : STGhostF a opened p q True (fun _ -> False)\nlet admit_ _ = STGhostF?.reflect (fun _ -> NMSTTotal.nmst_tot_admit ())", "val acquire_core: #opened: _ -> p: vprop -> r: ref U32.t -> Prims.unit\n -> STAtomicT bool\n opened\n ((lockinv p r) `star` (exists_ (acquire_loop_inv p)))\n (fun b -> (lockinv p r) `star` (acquire_loop_inv p b))\nlet acquire_core (#opened:_) (p:vprop) (r:ref U32.t) ()\n : STAtomicT bool opened\n (lockinv p r `star` exists_ (acquire_loop_inv p))\n (fun b -> lockinv p r `star` acquire_loop_inv p b)\n = let w = elim_exists #_ #_ #(lockinv_predicate p r) () in\n drop (exists_ _);\n let b = cas_u32 w r unlocked locked in\n if b\n then begin\n let res = false in\n elim_pure _;\n rewrite (if is_locked w then emp else p) p;\n intro_pure (locked == locked \\/ locked == unlocked);\n rewrite (if b then _ else _)\n (pts_to r full_perm locked);\n rewrite emp (if is_locked locked then emp else p);\n intro_exists locked (lockinv_predicate p r);\n rewrite p (acquire_loop_inv p res);\n return res\n end\n else begin\n let res = true in\n rewrite (if b then _ else _)\n (pts_to r full_perm w);\n intro_exists (Ghost.reveal w) (lockinv_predicate p r);\n rewrite emp (acquire_loop_inv p res);\n return res\n end", "val bind\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#opens:inames)\r\n (#pre1 #post1 #post2:_)\r\n (f:act a opens pre1 post1)\r\n (g:(x:a -> act b opens (post1 x) post2))\r\n: act b opens pre1 post2\nlet bind\r\n (#a:Type u#a)\r\n (#b:Type u#b)\r\n (#opens:inames)\r\n (#pre1 #post1 #post2:_)\r\n (f:act a opens pre1 post1)\r\n (g:(x:a -> act b opens (post1 x) post2))\r\n: act b opens pre1 post2\r\n= fun #ictx -> bind_action #a #b #ictx #pre1 #post1 #post2 (f #ictx) (fun x -> g x #ictx)", "val new_invariant (#opened_invariants:inames) (p:vprop)\n : SteelAtomicUT (inv p) opened_invariants p (fun _ -> emp)\nlet new_invariant #uses p = let i = fresh_invariant #uses p [] in return i", "val new_invariant\r\n (p:slprop)\r\n: stt_atomic (inv p) #Unobservable emp_inames p (fun _ -> emp)\nlet new_invariant\r\n (p:slprop)\r\n: stt_atomic (inv p) #Unobservable emp_inames p (fun _ -> emp)\r\n= A.new_invariant p", "val lift_sta_sa\n (a:Type)\n (#framed:eqtype_as_type bool)\n (#o:inames)\n (#obs:eqtype_as_type observability)\n (#[@@@ framing_implicit] pre:pre_t)\n (#[@@@ framing_implicit] post:post_t a)\n (#[@@@ framing_implicit] req:Type0)\n (#[@@@ framing_implicit] ens:a -> Type0)\n (f:STAG.repr a framed o obs pre post req ens)\n : SA.repr a framed o obs pre post (fun _ -> req) (fun _ x _ -> ens x)\nlet lift_sta_sa\n (a:Type)\n (#framed:eqtype_as_type bool)\n (#o:inames)\n (#obs:eqtype_as_type observability)\n (#pre:pre_t)\n (#post:post_t a)\n (#req:Type0)\n (#ens:a -> Type0)\n (f:STAG.repr a framed o obs pre post req ens)\n : SA.repr a framed o obs pre post (fun _ -> req) (fun _ x _ -> ens x)\n = f", "val lift1 (#a:Type u#1) #opens #pre #post\r\n (m:act a opens pre post)\r\n: I.stt a pre post\nlet lift1 (#a:Type u#1) #opens #pre #post\r\n (m:act a opens pre post)\r\n: stt a pre post\r\n= stt_of_action1 (m #emp_inames)", "val lift2 (#a:Type u#2) #opens #pre #post\r\n (m:act a opens pre post)\r\n: I.stt a pre post\nlet lift2 (#a:Type u#2) #opens #pre #post\r\n (m:act a opens pre post)\r\n: stt a pre post\r\n= stt_of_action2 (m #emp_inames)", "val release_core (#p:vprop) (#u:inames) (r:ref bool) (i:inv (lockinv p r))\n : SteelAtomicT bool u\n (lockinv p r `star` p)\n (fun b -> lockinv p r `star` (if b then emp else p))\nlet release_core #p #u r i =\n let v = witness_exists () in\n\n let res = cas_pt_bool r v locked available in\n\n (* Not sure we can avoid calling an SMT here. Better force the manual call? *)\n rewrite_slprop (if (Ghost.reveal v) then emp else p) (if res then emp else p)\n (fun _ -> ());\n rewrite_slprop (if res then pts_to r full_perm (Ghost.hide available) else pts_to r full_perm v) (pts_to r full_perm available) (fun _ -> ());\n\n intro_lockinv_available p r;\n return res", "val read\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x:erased a)\r\n (f:(v:a{compatible p x v}\r\n -> GTot (y:a{compatible p y v /\\\r\n FStar.PCM.frame_compatible p x v y})))\r\n: stt_atomic (v:a{compatible p x v /\\ p.refine v})\r\n #Observable\r\n emp_inames\r\n (pts_to r x)\r\n (fun v -> pts_to r (f v))\nlet read = A.read", "val with_invariant_g (#a:Type)\n (#fp:vprop)\n (#fp':a -> vprop)\n (#opened_invariants:inames)\n (#p:vprop)\n (#perm:_)\n (i:inv p{not (mem_inv opened_invariants i)})\n ($f:unit -> SteelGhostT a (add_inv opened_invariants i)\n (p `star` fp)\n (fun x -> p `star` fp' x))\n : SteelAtomicUT (erased a) opened_invariants (active perm i `star` fp) (fun x -> active perm i `star` fp' x)\nlet with_invariant_g #a #fp #fp' #u #p #perm i f\n = let with_invariant_aux (r:ghost_ref bool)\n (_:unit)\n : SteelGhostT a (add_inv u i)\n (ex_conditional_inv r p `star`\n (ghost_pts_to r (half_perm perm) true `star`\n fp))\n (fun x ->\n ex_conditional_inv r p `star`\n (ghost_pts_to r (half_perm perm) true `star` //associativity matters\n fp' x))\n = let b = witness_exists #_ #_ #(conditional_inv r p) () in\n ghost_pts_to_injective_eq r true (hide (reveal b));\n rewrite_slprop (if b then p else emp) p (fun _ -> ());\n let x = f() in\n intro_exists true (conditional_inv r p);\n x\n in\n let x = with_invariant_g (dsnd i)\n (with_invariant_aux (gref i)) in\n x", "val conv (#a:Type u#a)\r\n (pre1:slprop)\r\n (pre2:slprop)\r\n (post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1:slprop_equiv pre1 pre2)\r\n (pf2:slprop_post_equiv post1 post2)\r\n: Lemma (stt a pre1 post1 == stt a pre2 post2)\nlet conv (#a:Type u#a)\r\n (pre1:slprop)\r\n (pre2:slprop)\r\n (post1:a -> slprop)\r\n (post2:a -> slprop)\r\n (pf1:slprop_equiv pre1 pre2)\r\n (pf2:slprop_post_equiv post1 post2)\r\n: Lemma (stt a pre1 post1 == stt a pre2 post2)\r\n= slprop_equiv_elim pre1 pre2;\r\n introduce forall x. post1 x == post2 x\r\n with slprop_equiv_elim (post1 x) (post2 x);\r\n Sem.conv #state a #pre1 #(F.on_dom _ post1) (F.on_dom _ post2);\r\n ()", "val Pulse.Reflection.Util.mk_stt_atomic_comp = \n obs: FStar.Stubs.Reflection.Types.term ->\n u105: FStar.Stubs.Reflection.Types.universe ->\n a: FStar.Stubs.Reflection.Types.term ->\n inames: FStar.Stubs.Reflection.Types.term ->\n pre: FStar.Stubs.Reflection.Types.term ->\n post: FStar.Stubs.Reflection.Types.term\n -> FStar.Stubs.Reflection.Types.term\nlet mk_stt_atomic_comp (obs:R.term) (u:R.universe) (a inames pre post:R.term) =\n let head = stt_atomic_fv in\n let t = R.pack_ln (R.Tv_UInst head [u]) in\n let t = R.pack_ln (R.Tv_App t (a, R.Q_Explicit)) in\n let t = R.pack_ln (R.Tv_App t (obs, R.Q_Implicit)) in\n let t = R.pack_ln (R.Tv_App t (inames, R.Q_Explicit)) in\n let t = R.pack_ln (R.Tv_App t (pre, R.Q_Explicit)) in\n R.pack_ln (R.Tv_App t (post, R.Q_Explicit))", "val return_atomic_noeq\r\n (#a:Type u#a)\r\n (x:a)\r\n (p:a -> slprop)\r\n: stt_atomic a #Neutral emp_inames (p x) p\nlet return_atomic_noeq #a x post = A.return #a #post x", "val bind_lpost\n (#st: st)\n (#a: Type)\n (#pre: st.hprop)\n (#post_a: post_t st a)\n (lpre_a: l_pre pre)\n (lpost_a: l_post pre post_a)\n (#b: Type)\n (#post_b: post_t st b)\n (lpost_b: (x: a -> l_post (post_a x) post_b))\n : l_post pre post_b\nlet bind_lpost\n (#st:st)\n (#a:Type)\n (#pre:st.hprop)\n (#post_a:post_t st a)\n (lpre_a:l_pre pre)\n (lpost_a:l_post pre post_a)\n (#b:Type)\n (#post_b:post_t st b)\n (lpost_b:(x:a -> l_post (post_a x) post_b))\n : l_post pre post_b\n =\n fun h0 y h2 -> lpre_a h0 /\\ (exists x h1. lpost_a h0 x h1 /\\ (lpost_b x) h1 y h2)", "val recall (#inames: _) (#a:Type u#0) (#q:perm) (#p:Preorder.preorder a)\n (fact:property a)\n (r:ref a p) \n (v:erased a)\n (w:witnessed r fact)\n : SteelAtomicU unit inames (pts_to r q v)\n (fun _ -> pts_to r q v)\n (requires fun _ -> True)\n (ensures fun _ _ _ -> fact v)\nlet recall (#inames: _)\n (#a:Type u#0)\n (#q:perm)\n (#p:Preorder.preorder a)\n (fact:property a)\n (r:ref a p)\n (v:erased a)\n (w:witnessed r fact)\n : SteelAtomicU unit inames (pts_to r q v)\n (fun _ -> pts_to r q v)\n (requires fun _ -> True)\n (ensures fun _ _ _ -> fact v)\n = MHR.recall (lift_property fact) r (U.raise_val (reveal v)) w", "val recall (#inames: _) (#a:Type u#1) (#q:perm) (#p:Preorder.preorder a)\n (fact:property a)\n (r:ref a p)\n (v:erased a)\n (w:witnessed r fact)\n : SteelAtomicU unit inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\n (requires fun _ -> True)\n (ensures fun _ _ _ -> fact v)\nlet recall (#inames: _) (#a:Type u#1) (#q:perm) (#p:Preorder.preorder a) (fact:property a)\n (r:ref a p) (v:erased a) (w:witnessed r fact)\n = let h = witness_exists #_ #_ #(pts_to_body r q v) () in\n let _ = elim_pure #_ #_ #_ #q r v h in\n\n let h1 = recall (lift_fact fact) r h w in\n\n intro_pure_full r v h;\n rewrite_slprop (pts_to _ q _) (pts_to r q v) (fun _ -> ())", "val bind (a:Type) (b:Type)\n (opened_invariants:inames)\n (o1:eqtype_as_type observability)\n (o2:eqtype_as_type observability)\n (#framed_f:eqtype_as_type bool)\n (#framed_g:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre_f:pre_t)\n (#[@@@ framing_implicit] post_f:post_t a)\n (#[@@@ framing_implicit] req_f:pure_pre)\n (#[@@@ framing_implicit] ens_f:pure_post a)\n (#[@@@ framing_implicit] pre_g:a -> pre_t)\n (#[@@@ framing_implicit] post_g:a -> post_t b)\n (#[@@@ framing_implicit] req_g:a -> pure_pre)\n (#[@@@ framing_implicit] ens_g:(a -> pure_post b))\n (#[@@@ framing_implicit] frame_f:vprop)\n (#[@@@ framing_implicit] frame_g:a -> vprop)\n (#[@@@ framing_implicit] post:post_t b)\n (#[@@@ framing_implicit] _ : squash (maybe_emp framed_f frame_f))\n (#[@@@ framing_implicit] _ : squash (maybe_emp_dep framed_g frame_g))\n (#[@@@ framing_implicit] pr:a -> prop)\n (#[@@@ framing_implicit] p1:squash\n (can_be_split_forall_dep pr\n (fun x -> post_f x `star` frame_f)\n (fun x -> pre_g x `star` frame_g x)))\n (#[@@@ framing_implicit] p2:squash\n (can_be_split_post\n (fun x y -> post_g x y `star` frame_g x) post))\n (f:repr a framed_f opened_invariants o1 pre_f post_f req_f ens_f)\n (g:(x:a -> repr b framed_g opened_invariants o2 (pre_g x) (post_g x) (req_g x) (ens_g x)))\n : Pure (repr b\n true\n opened_invariants\n (join_obs o1 o2)\n (pre_f `star` frame_f)\n post\n (STF.bind_req a req_f ens_f pr req_g)\n (STF.bind_ens a b ens_f ens_g))\n (requires obs_at_most_one o1 o2)\n (ensures fun _ -> True)\nlet bind (a:Type) (b:Type)\n (opened_invariants:inames)\n (o1:eqtype_as_type observability)\n (o2:eqtype_as_type observability)\n (#framed_f:eqtype_as_type bool)\n (#framed_g:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre_f:pre_t)\n (#[@@@ framing_implicit] post_f:post_t a)\n (#[@@@ framing_implicit] req_f:Type0)\n (#[@@@ framing_implicit] ens_f:a -> Type0)\n (#[@@@ framing_implicit] pre_g:a -> pre_t)\n (#[@@@ framing_implicit] post_g:a -> post_t b)\n (#[@@@ framing_implicit] req_g:(a -> Type0))\n (#[@@@ framing_implicit] ens_g:(a -> b -> Type0))\n (#[@@@ framing_implicit] frame_f:vprop)\n (#[@@@ framing_implicit] frame_g:a -> vprop)\n (#[@@@ framing_implicit] post:post_t b)\n (#[@@@ framing_implicit] _x1 : squash (maybe_emp framed_f frame_f))\n (#[@@@ framing_implicit] _x2 : squash (maybe_emp_dep framed_g frame_g))\n (#[@@@ framing_implicit] pr:a -> prop)\n (#[@@@ framing_implicit] p1:squash\n (can_be_split_forall_dep pr\n (fun x -> post_f x `star` frame_f)\n (fun x -> pre_g x `star` frame_g x)))\n (#[@@@ framing_implicit] p2:squash\n (can_be_split_post\n (fun x y -> post_g x y `star` frame_g x) post))\n (f:repr a framed_f opened_invariants o1 pre_f post_f req_f ens_f)\n (g:(x:a -> repr b framed_g opened_invariants o2 (pre_g x) (post_g x) (req_g x) (ens_g x)))\n = weaken_repr (SEA.bind a b opened_invariants o1 o2\n #framed_f\n #framed_g\n #pre_f\n #post_f\n #(fun _ -> req_f)\n #(fun _ x _ -> ens_f x)\n #pre_g\n #post_g\n #(fun x _ -> req_g x)\n #(fun x _ y _ -> ens_g x y)\n #frame_f\n #frame_g\n #post\n #_x1\n #_x2\n #pr\n #p1\n #p2\n f g) () ()", "val recall (#inames: _) (#a:Type u#1) (#q:perm) (#p:Preorder.preorder a)\n (fact:property a)\n (r:erased (ref a p))\n (v:erased a)\n (w:witnessed r fact)\n : SteelAtomicU unit inames (pts_to r q v)\n (fun _ -> pts_to r q v)\n (requires fun _ -> True)\n (ensures fun _ _ _ -> fact v)\nlet recall (#inames: _) (#a:Type u#1) (#q:perm) (#p:Preorder.preorder a) (fact:property a)\n (r:Ghost.erased (ref a p)) (v:erased a) (w:witnessed r fact)\n : SteelAtomicU unit inames (pts_to r q v)\n (fun _ -> pts_to r q v)\n (requires fun _ -> True)\n (ensures fun _ _ _ -> fact v)\n = let h = witness_exists #_ #_ #(pts_to_body r q v) () in\n let _ = elim_pure #_ #_ #_ #q r v h in\n\n let h1 = recall (lift_fact fact) r h w in\n\n rewrite_slprop (PR.pts_to r h) (pts_to_body r q v h) (fun m ->\n emp_unit (M.pts_to r h);\n pure_star_interp (M.pts_to r h) (history_val h v q) m);\n\n intro_exists_erased h (pts_to_body r q v)", "val elim_trade\n (#[T.exact (`invlist_empty)] is : invlist)\n (hyp concl: vprop)\n: stt_atomic unit #Unobservable (invlist_names is)\n ((trade #is hyp concl) ** hyp)\n (fun _ -> concl)\nlet elim_trade #is = __elim_trade #is", "val lift_atomic_steel\n (a:Type)\n (o:eqtype_as_type observability)\n (#framed:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre:pre_t) (#[@@@ framing_implicit] post:post_t a)\n (#[@@@ framing_implicit] req:req_t pre) (#[@@@ framing_implicit] ens:ens_t pre a post)\n (f:repr a framed Set.empty o pre post req ens)\n : Steel.Effect.repr a framed pre post req ens\nlet lift_atomic_steel a o f = f", "val witness':\n #inames: _ ->\n #a: Type ->\n #q: perm ->\n #p: Preorder.preorder a ->\n r: ref a p ->\n fact: stable_property p ->\n v: erased a ->\n pf: squash (fact v) ->\n unit\n -> Steel.Effect.Atomic.SteelAtomicUT (witnessed r fact)\n inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\nlet witness' (#inames: _)\n (#a:Type)\n (#q:perm)\n (#p:Preorder.preorder a)\n (r:ref a p)\n (fact:stable_property p)\n (v:erased a)\n (pf:squash (fact v))\n (_:unit)\n : Steel.Effect.Atomic.SteelAtomicUT (witnessed r fact) inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\n = MR.witness #inames #a #q #p r fact v pf", "val lift0 (#a:Type u#0) #opens #pre #post\r\n (m:act a opens pre post)\r\n: I.stt a pre post\nlet lift0 (#a:Type u#0) #opens #pre #post\r\n (m:act a opens pre post)\r\n: stt a pre post\r\n= stt_of_action0 (m #emp_inames)", "val recall (#inames: _) (#a:Type u#0) (#q:perm) (#p:Preorder.preorder a)\n (fact:property a)\n (r:erased (ref a p))\n (v:erased a)\n (w:witnessed r fact)\n : SteelAtomicU unit inames (pts_to r q v)\n (fun _ -> pts_to r q v)\n (requires fun _ -> True)\n (ensures fun _ _ _ -> fact v)\nlet recall (#inames: _)\n (#a:Type u#0)\n (#q:perm)\n (#p:Preorder.preorder a)\n (fact:property a)\n (r:erased (ref a p))\n (v:erased a)\n (w:witnessed r fact)\n = MHR.recall (lift_property fact) r (hide (U.raise_val (reveal v))) w", "val bind (a:Type) (b:Type)\n (opened_invariants:inames)\n (o1:eqtype_as_type observability)\n (o2:eqtype_as_type observability)\n (#framed_f:eqtype_as_type bool)\n (#framed_g:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre_f:pre_t) (#[@@@ framing_implicit] post_f:post_t a)\n (#[@@@ framing_implicit] req_f:req_t pre_f) (#[@@@ framing_implicit] ens_f:ens_t pre_f a post_f)\n (#[@@@ framing_implicit] pre_g:a -> pre_t) (#[@@@ framing_implicit] post_g:a -> post_t b)\n (#[@@@ framing_implicit] req_g:(x:a -> req_t (pre_g x))) (#[@@@ framing_implicit] ens_g:(x:a -> ens_t (pre_g x) b (post_g x)))\n (#[@@@ framing_implicit] frame_f:vprop) (#[@@@ framing_implicit] frame_g:a -> vprop)\n (#[@@@ framing_implicit] post:post_t b)\n (#[@@@ framing_implicit] _ : squash (maybe_emp framed_f frame_f))\n (#[@@@ framing_implicit] _ : squash (maybe_emp_dep framed_g frame_g))\n (#[@@@ framing_implicit] pr:a -> prop)\n (#[@@@ framing_implicit] p1:squash (can_be_split_forall_dep pr\n (fun x -> post_f x `star` frame_f) (fun x -> pre_g x `star` frame_g x)))\n (#[@@@ framing_implicit] p2:squash (can_be_split_post (fun x y -> post_g x y `star` frame_g x) post))\n (f:repr a framed_f opened_invariants o1 pre_f post_f req_f ens_f)\n (g:(x:a -> repr b framed_g opened_invariants o2 (pre_g x) (post_g x) (req_g x) (ens_g x)))\n: Pure (repr b true opened_invariants (join_obs o1 o2)\n (pre_f `star` frame_f)\n post\n (bind_req req_f ens_f req_g frame_f frame_g p1)\n (bind_ens req_f ens_f ens_g frame_f frame_g post p1 p2)\n )\n (requires obs_at_most_one o1 o2)\n (ensures fun _ -> True)\nlet bind a b opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #frame_f #frame_g #post #_ #_ #p #p2 f g\n = norm_repr (bind_opaque a b opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #frame_f #frame_g #post #_ #_ #p #p2 f g)", "val join\n (#opened: _)\n (#elt: Type)\n (#x1 #x2: Ghost.erased (Seq.seq elt))\n (#p: P.perm)\n (a1: array elt)\n (a2: Ghost.erased (array elt))\n : STAtomicBase (array elt)\n false\n opened\n Unobservable\n ((pts_to a1 p x1) `star` (pts_to a2 p x2))\n (fun res -> pts_to res p (x1 `Seq.append` x2))\n (adjacent a1 a2)\n (fun res -> merge_into a1 a2 res)\nlet join\n (#opened: _)\n (#elt: Type)\n (#x1 #x2: Ghost.erased (Seq.seq elt))\n (#p: P.perm)\n (a1: array elt)\n (a2: Ghost.erased (array elt))\n: STAtomicBase (array elt) false opened Unobservable\n (pts_to a1 p x1 `star` pts_to a2 p x2)\n (fun res -> pts_to res p (x1 `Seq.append` x2))\n (adjacent a1 a2)\n (fun res -> merge_into a1 a2 res)\n= let _ : squash (adjacent a1 a2) = () in\n ghost_join a1 a2 ();\n let res = merge a1 a2 in\n rewrite\n (pts_to (merge a1 (Ghost.hide (Ghost.reveal a2))) p (x1 `Seq.append` x2))\n (pts_to res p (x1 `Seq.append` x2));\n return res", "val join\n (#opened: _)\n (#elt: Type)\n (#x1 #x2: Ghost.erased (Seq.seq elt))\n (#p: P.perm)\n (a1: array elt)\n (a2: Ghost.erased (array elt))\n : STAtomicBase (array elt)\n false\n opened\n Unobservable\n ((pts_to a1 p x1) `star` (pts_to a2 p x2))\n (fun res -> pts_to res p (x1 `Seq.append` x2))\n (adjacent a1 a2)\n (fun res -> merge_into a1 a2 res)\nlet join\n (#opened: _)\n (#elt: Type)\n (#x1 #x2: Ghost.erased (Seq.seq elt))\n (#p: P.perm)\n (a1: array elt)\n (a2: Ghost.erased (array elt))\n: STAtomicBase (array elt) false opened Unobservable\n (pts_to a1 p x1 `star` pts_to a2 p x2)\n (fun res -> pts_to res p (x1 `Seq.append` x2))\n (adjacent a1 a2)\n (fun res -> merge_into a1 a2 res)\n= let _ : squash (adjacent a1 a2) = () in\n ghost_join a1 a2 ();\n let res = merge a1 a2 in\n rewrite\n (pts_to (merge a1 (Ghost.hide (Ghost.reveal a2))) p (x1 `Seq.append` x2))\n (pts_to res p (x1 `Seq.append` x2));\n return res", "val write\r\n (#a:Type)\r\n (#p:pcm a)\r\n (r:ref a p)\r\n (x y:Ghost.erased a)\r\n (f:FStar.PCM.frame_preserving_upd p x y)\r\n: stt_atomic unit\r\n #Observable\r\n emp_inames\r\n (pts_to r x)\r\n (fun _ -> pts_to r y)\nlet write = A.write", "val Pulse.Reflection.Util.mk_sub_stt_atomic = \n u482: FStar.Stubs.Reflection.Types.universe ->\n a: FStar.Stubs.Reflection.Types.term ->\n opened: FStar.Stubs.Reflection.Types.term ->\n pre1: FStar.Stubs.Reflection.Types.term ->\n pre2: FStar.Stubs.Reflection.Types.term ->\n post1: FStar.Stubs.Reflection.Types.term ->\n post2: FStar.Stubs.Reflection.Types.term ->\n e: FStar.Stubs.Reflection.Types.term\n -> FStar.Stubs.Reflection.Types.term\nlet mk_sub_stt_atomic (u:R.universe) (a opened pre1 pre2 post1 post2 e:R.term) =\n let open R in\n let lid = mk_pulse_lib_core_lid \"sub_atomic\" in\n let t = pack_ln (R.Tv_UInst (R.pack_fv lid) [u]) in\n let t = pack_ln (R.Tv_App t (a, Q_Implicit)) in\n let t = pack_ln (R.Tv_App t (opened, Q_Implicit)) in\n let t = pack_ln (R.Tv_App t (pre1, Q_Implicit)) in\n let t = pack_ln (R.Tv_App t (pre2, Q_Explicit)) in\n let t = pack_ln (R.Tv_App t (post1, Q_Implicit)) in\n let t = pack_ln (R.Tv_App t (post2, Q_Explicit)) in\n let t = pack_ln (R.Tv_App t (`(), Q_Explicit)) in\n let t = pack_ln (R.Tv_App t (`(), Q_Explicit)) in\n pack_ln (R.Tv_App t (e, Q_Explicit))", "val alloc\r\n (#a:Type u#1)\r\n (#pcm:pcm a)\r\n (x:a{compatible pcm x x /\\ pcm.refine x})\r\n: stt_atomic (ref a pcm)\r\n #Observable\r\n emp_inames\r\n emp\r\n (fun r -> pts_to r x)\nlet alloc = A.alloc", "val bind_opaque (a:Type) (b:Type)\n (opened_invariants:inames)\n (o1:eqtype_as_type observability)\n (o2:eqtype_as_type observability)\n (#framed_f:eqtype_as_type bool)\n (#framed_g:eqtype_as_type bool)\n (#pre_f:pre_t) (#post_f:post_t a)\n (#req_f:req_t pre_f) (#ens_f:ens_t pre_f a post_f)\n (#pre_g:a -> pre_t) (#post_g:a -> post_t b)\n (#req_g:(x:a -> req_t (pre_g x))) (#ens_g:(x:a -> ens_t (pre_g x) b (post_g x)))\n (#frame_f:vprop) (#frame_g:a -> vprop)\n (#post:post_t b)\n (# _ : squash (maybe_emp framed_f frame_f))\n (# _ : squash (maybe_emp_dep framed_g frame_g))\n (#pr:a -> prop)\n (#p1:squash (can_be_split_forall_dep pr\n (fun x -> post_f x `star` frame_f) (fun x -> pre_g x `star` frame_g x)))\n (#p2:squash (can_be_split_post (fun x y -> post_g x y `star` frame_g x) post))\n (f:repr a framed_f opened_invariants o1 pre_f post_f req_f ens_f)\n (g:(x:a -> repr b framed_g opened_invariants o2 (pre_g x) (post_g x) (req_g x) (ens_g x)))\n: Pure (repr b true opened_invariants (join_obs o1 o2)\n (pre_f `star` frame_f)\n post\n (bind_req_opaque req_f ens_f req_g frame_f frame_g p1)\n (bind_ens_opaque req_f ens_f ens_g frame_f frame_g post p1 p2)\n )\n (requires obs_at_most_one o1 o2)\n (ensures fun _ -> True)\nlet bind_opaque a b opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #frame_f #frame_g #post #_ #_ #p #p2 f g =\n fun frame ->\n let m0:full_mem = NMSTTotal.get () in\n\n let h0 = mk_rmem (pre_f `star` frame_f) (core_mem m0) in\n\n let x = frame00 f frame_f frame in\n\n let m1:full_mem = NMSTTotal.get () in\n\n let h1 = mk_rmem (post_f x `star` frame_f) (core_mem m1) in\n\n let h1' = mk_rmem (pre_g x `star` frame_g x) (core_mem m1) in\n\n can_be_split_trans (post_f x `star` frame_f) (pre_g x `star` frame_g x) (pre_g x);\n focus_is_restrict_mk_rmem\n (post_f x `star` frame_f)\n (pre_g x `star` frame_g x)\n (core_mem m1);\n focus_focus_is_focus\n (post_f x `star` frame_f)\n (pre_g x `star` frame_g x)\n (pre_g x)\n (core_mem m1);\n assert (focus_rmem h1' (pre_g x) == focus_rmem h1 (pre_g x));\n\n can_be_split_3_interp\n (hp_of (post_f x `star` frame_f))\n (hp_of (pre_g x `star` frame_g x))\n frame (locks_invariant opened m1) m1;\n\n let y = frame00 (g x) (frame_g x) frame in\n\n let m2:full_mem = NMSTTotal.get () in\n\n can_be_split_trans (post_f x `star` frame_f) (pre_g x `star` frame_g x) (pre_g x);\n can_be_split_trans (post_f x `star` frame_f) (pre_g x `star` frame_g x) (frame_g x);\n can_be_split_trans (post y) (post_g x y `star` frame_g x) (post_g x y);\n can_be_split_trans (post y) (post_g x y `star` frame_g x) (frame_g x);\n\n let h2' = mk_rmem (post_g x y `star` frame_g x) (core_mem m2) in\n let h2 = mk_rmem (post y) (core_mem m2) in\n\n\n\n // assert (focus_rmem h1' (pre_g x) == focus_rmem h1 (pre_g x));\n\n focus_focus_is_focus\n (post_f x `star` frame_f)\n (pre_g x `star` frame_g x)\n (frame_g x)\n (core_mem m1);\n\n focus_is_restrict_mk_rmem\n (post_g x y `star` frame_g x)\n (post y)\n (core_mem m2);\n\n focus_focus_is_focus\n (post_g x y `star` frame_g x)\n (post y)\n (frame_g x)\n (core_mem m2);\n focus_focus_is_focus\n (post_g x y `star` frame_g x)\n (post y)\n (post_g x y)\n (core_mem m2);\n\n can_be_split_3_interp\n (hp_of (post_g x y `star` frame_g x))\n (hp_of (post y))\n frame (locks_invariant opened m2) m2;\n\n\n y", "val rewrite (#opened:inames)\n (p q: vprop)\n : STGhost unit opened p (fun _ -> q) (p == q) (fun _ -> True)\nlet rewrite #o p q =\n weaken p q (fun _ -> ())", "val implies_trans_gen\n (#opened: _)\n (#[T.exact (`(hide Set.empty))] is1: inames)\n (#[T.exact (`(hide Set.empty))] is2: inames)\n (v1 v2 v3: vprop)\n : STGhostT unit\n opened\n ((( @==> ) #is1 v1 v2) `star` (( @==> ) #is2 v2 v3))\n (fun _ -> ( @==> ) #(Set.union is1 is2) v1 v3)\nlet implies_trans_gen\n (#opened: _)\n (#[T.exact (`(hide Set.empty))] is1 : inames)\n (#[T.exact (`(hide Set.empty))] is2 : inames)\n (v1 v2 v3: vprop)\n: STGhostT unit opened\n (((@==>) #is1 v1 v2) `star` ((@==>) #is2 v2 v3))\n (fun _ -> (@==>) #(Set.union is1 is2) v1 v3)\n= intro_implies_gen v1 v3 ((v1 @==> v2) `star` (v2 @==> v3)) (fun _ ->\n elim_implies_gen v1 v2;\n elim_implies_gen v2 v3\n )", "val frame\r\n (#a:Type u#a)\r\n (#pre:slprop) (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt a pre post)\r\n: stt a (pre ** frame) (fun x -> post x ** frame)\nlet frame\r\n (#a:Type u#a)\r\n (#pre:slprop) (#post:a -> slprop)\r\n (frame:slprop)\r\n (e:stt a pre post)\r\n: stt a (pre `star` frame) (fun x -> post x `star` frame)\r\n= fun _ -> Sem.frame frame (e())", "val atomic_read (#opened:_) (#a:Type) (#p:perm) (#v:erased a)\n (r:ref a)\n : SteelAtomic a opened\n (pts_to r p v)\n (fun x -> pts_to r p x)\n (requires fun h -> True)\n (ensures fun _ x _ -> x == Ghost.reveal v)\nlet atomic_read (#opened:_) (#a:Type) (#p:perm) (#v:erased a) (r:ref a)\n = let v1 : erased (fractional a) = Ghost.hide (Some (Ghost.reveal v, p)) in\n rewrite_slprop (pts_to r p v) (RP.pts_to r v1 `star` pure (perm_ok p)) (fun _ -> ());\n elim_pure (perm_ok p);\n\n let v2 = RP.atomic_read r v1 in\n rewrite_slprop (RP.pts_to r v1) (pts_to r p v)\n (fun m ->\n emp_unit (hp_of (pts_to_raw r p v));\n pure_star_interp (hp_of (pts_to_raw r p v)) (perm_ok p) m);\n assert (compatible pcm_frac v1 v2);\n let Some (x, _) = v2 in\n rewrite_slprop (pts_to r p v) (pts_to r p x) (fun _ -> ());\n return x", "val pts_to_injective_eq (#a: Type)\n (#opened:inames)\n (#p0 #p1:perm)\n (#v0 #v1: a)\n (r: ref a)\n : STGhost unit opened\n (pts_to r p0 v0 `star` pts_to r p1 v1)\n (fun _ -> pts_to r p0 v0 `star` pts_to r p1 v0)\n (requires True)\n (ensures fun _ -> v0 == v1)\nlet pts_to_injective_eq\n #_ #_ #p0 #p1 #v0 #v1 r\n= rewrite (pts_to r p0 v0) (RST.pts_to r.reveal p0 v0);\n rewrite (pts_to r p1 v1) (RST.pts_to r.reveal p1 v1);\n RST.pts_to_injective_eq #_ #_ #_ #_ #v0 #v1 r.reveal;\n rewrite (RST.pts_to r.reveal p0 v0) (pts_to r p0 v0);\n rewrite (RST.pts_to r.reveal p1 v0) (pts_to r p1 v0)", "val pts_to_injective_eq (#a: Type)\n (#opened:inames)\n (#p0 #p1:perm)\n (#v0 #v1: a)\n (r: ref a)\n : STGhost unit opened\n (pts_to r p0 v0 `star` pts_to r p1 v1)\n (fun _ -> pts_to r p0 v0 `star` pts_to r p1 v0)\n (requires True)\n (ensures fun _ -> v0 == v1)\nlet pts_to_injective_eq\n (#a: Type)\n (#opened:inames)\n (#p0 #p1:perm)\n (#v0 #v1:a)\n (r: ref a)\n : STGhost unit opened\n (pts_to r p0 v0 `star` pts_to r p1 v1)\n (fun _ -> pts_to r p0 v0 `star` pts_to r p1 v0)\n (requires True)\n (ensures fun _ -> v0 == v1)\n = coerce_ghost\n (fun _ -> R.higher_ref_pts_to_injective_eq #a #opened #p0 #p1 #(hide v0) #(hide v1) r)", "val pts_to_injective_eq (#a: Type)\n (#opened:inames)\n (#p0 #p1:perm)\n (#v0 #v1: a)\n (r: ref a)\n : STGhost unit opened\n (pts_to r p0 v0 `star` pts_to r p1 v1)\n (fun _ -> pts_to r p0 v0 `star` pts_to r p1 v0)\n (requires True)\n (ensures fun _ -> v0 == v1)\nlet pts_to_injective_eq\n (#a: Type)\n (#opened:inames)\n (#p0 #p1:perm)\n (#v0 #v1:a)\n (r: ref a)\n : STGhost unit opened\n (pts_to r p0 v0 `star` pts_to r p1 v1)\n (fun _ -> pts_to r p0 v0 `star` pts_to r p1 v0)\n (requires True)\n (ensures fun _ -> v0 == v1)\n = coerce_ghost\n (fun _ -> R.pts_to_injective_eq #a #opened #p0 #p1 #(hide v0) #(hide v1) r)", "val witness (#inames: _) (#a:Type) (#pcm:pcm a)\n (r:ref a pcm)\n (fact:stable_property pcm)\n (v:erased a)\n (_:fact_valid_compat fact v)\n : STAtomicUT (witnessed r fact) inames (pts_to r v)\n (fun _ -> pts_to r v)\nlet witness r fact v vc = C.coerce_atomic (witness' r fact v vc)", "val recall (#inames: _) (#a:Type u#1) (#pcm:pcm a)\n (fact:property a)\n (r:ref a pcm)\n (v:erased a)\n (w:witnessed r fact)\n : STAtomicU (erased a) inames\n (pts_to r v)\n (fun v1 -> pts_to r v)\n (requires True)\n (ensures fun v1 -> fact v1 /\\ compatible pcm v v1)\nlet recall fact r v w = C.coerce_atomic (fun _ -> P.recall fact r v w)", "val rewrite_value_vprops_prefix_and_suffix\n (#opened: _)\n (#k: eqtype)\n (#v: Type0)\n (#contents: Type)\n (vp: vp_t k v contents)\n (s1 s2: Seq.seq (option (k & v)))\n (m1 m2: Map.t k contents)\n (borrows1 borrows2: Map.t k v)\n (idx: US.t{Seq.length s1 == Seq.length s2 /\\ US.v idx < Seq.length s1})\n : STGhost unit\n opened\n ((value_vprops vp (seq_until s1 (US.v idx)) m1 borrows1)\n `star`\n (value_vprops vp (seq_from s1 (US.v idx)) m1 borrows1))\n (fun _ ->\n (value_vprops vp (seq_until s2 (US.v idx)) m2 borrows2)\n `star`\n (value_vprops vp (seq_from s2 (US.v idx)) m2 borrows2))\n (requires\n value_vprops vp (seq_until s1 (US.v idx)) m1 borrows1 ==\n value_vprops vp (seq_until s2 (US.v idx)) m2 borrows2 /\\\n value_vprops vp (seq_from s1 (US.v idx)) m1 borrows1 ==\n value_vprops vp (seq_from s2 (US.v idx)) m2 borrows2)\n (ensures fun _ -> True)\nlet rewrite_value_vprops_prefix_and_suffix (#opened:_)\n (#k:eqtype)\n (#v:Type0)\n (#contents:Type)\n (vp:vp_t k v contents)\n (s1 s2:Seq.seq (option (k & v)))\n (m1 m2:Map.t k contents)\n (borrows1 borrows2:Map.t k v)\n (idx:US.t{Seq.length s1 == Seq.length s2 /\\ US.v idx < Seq.length s1})\n : STGhost unit opened\n (value_vprops vp (seq_until s1 (US.v idx)) m1 borrows1\n `star`\n value_vprops vp (seq_from s1 (US.v idx)) m1 borrows1)\n (fun _ ->\n value_vprops vp (seq_until s2 (US.v idx)) m2 borrows2\n `star`\n value_vprops vp (seq_from s2 (US.v idx)) m2 borrows2)\n (requires value_vprops vp (seq_until s1 (US.v idx)) m1 borrows1 ==\n value_vprops vp (seq_until s2 (US.v idx)) m2 borrows2 /\\\n value_vprops vp (seq_from s1 (US.v idx)) m1 borrows1 ==\n value_vprops vp (seq_from s2 (US.v idx)) m2 borrows2)\n (ensures fun _ -> True)\n = rewrite\n (value_vprops vp (seq_until s1 (US.v idx)) m1 borrows1\n `star`\n value_vprops vp (seq_from s1 (US.v idx)) m1 borrows1)\n (value_vprops vp (seq_until s2 (US.v idx)) m2 borrows2\n `star`\n value_vprops vp (seq_from s2 (US.v idx)) m2 borrows2)", "val witness':\n #inames: _ ->\n #a: Type ->\n #q: perm ->\n #p: Preorder.preorder a ->\n r: erased (ref a p) ->\n fact: stable_property p ->\n v: erased a ->\n pf: squash (fact v) ->\n unit\n -> Steel.Effect.Atomic.SteelAtomicUT (witnessed r fact)\n inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\nlet witness' (#inames: _)\n (#a:Type)\n (#q:perm)\n (#p:Preorder.preorder a)\n (r:erased (ref a p))\n (fact:stable_property p)\n (v:erased a)\n (pf:squash (fact v))\n (_:unit)\n : Steel.Effect.Atomic.SteelAtomicUT (witnessed r fact) inames\n (pts_to r q v)\n (fun _ -> pts_to r q v)\n = MR.witness #inames #a #q #p r fact v pf", "val assert_ (#opened_invariants:_)\n (p:vprop)\n : STGhostT unit opened_invariants p (fun _ -> p)\nlet assert_ #o p = coerce_ghost (fun _ -> slassert0 p)" ], "closest_src": [ { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.sub_invs_stt_atomic" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.sub_atomic" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.lift_atomic2" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.lift_observability" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.lift_atomic1" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.lift_atomic0" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.bind_atomic" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.frame_atomic" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.stt_atomic" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.with_invariant" }, { "project_name": "steel", "file_name": "Steel.ST.Coercions.fst", "name": "Steel.ST.Coercions.coerce_atomic" }, { "project_name": "steel", "file_name": "Steel.ST.Coercions.fst", "name": "Steel.ST.Coercions.coerce_atomicF" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.mk_sub_inv_atomic" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.with_invariant" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.sub" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.sub" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.Ghost.fst", "name": "Steel.ST.Effect.Ghost.lift_ghost_atomic" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.return" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.return_atomic'" }, { "project_name": "steel", "file_name": "Pulse.Lib.InvList.fst", "name": "Pulse.Lib.InvList.with_invlist" }, { "project_name": "steel", "file_name": "Steel.ST.GhostMonotonicReference.fst", "name": "Steel.ST.GhostMonotonicReference.witness" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.as_atomic_o_action" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.return" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.lift_ghost_atomic" }, { "project_name": "steel", "file_name": "Steel.DisposableInvariant.fst", "name": "Steel.DisposableInvariant.with_invariant" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.witness" }, { "project_name": "steel", "file_name": "Pulse.Elaborate.Pure.fst", "name": "Pulse.Elaborate.Pure.elab_statomic_equiv" }, { "project_name": "steel", "file_name": "Steel.ST.GhostMonotonicReference.fst", "name": "Steel.ST.GhostMonotonicReference.recall" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.new_invariant" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.lift_neutral_ghost" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.sub_ghost" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.bind" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.recall" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.subcomp" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.as_atomic_unobservable_action" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.return_atomic" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.with_invariant_g" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.AtomicAndGhost.fst", "name": "Steel.ST.Effect.AtomicAndGhost.lift_atomic_st" }, { "project_name": "steel", "file_name": "Pulse.Lib.InvList.fst", "name": "Pulse.Lib.InvList.shift_invlist_one" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.AtomicAndGhost.fst", "name": "Steel.ST.Effect.AtomicAndGhost.subcomp" }, { "project_name": "steel", "file_name": "Pulse.Lib.InvList.fst", "name": "Pulse.Lib.InvList.with_invlist_ghost" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.as_atomic_action" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.subcomp_opaque" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.lift" }, { "project_name": "steel", "file_name": "Steel.SpinLock.fst", "name": "Steel.SpinLock.acquire_core" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.AtomicAndGhost.fst", "name": "Steel.ST.Effect.AtomicAndGhost.repr" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.repr" }, { "project_name": "steel", "file_name": "Pulse.Lib.Trade.fst", "name": "Pulse.Lib.Trade.trade_sub_inv" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.fresh_invariant" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.weaken" }, { "project_name": "steel", "file_name": "Steel.MonotonicHigherReference.fst", "name": "Steel.MonotonicHigherReference.witness" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicHigherReference.fst", "name": "Steel.GhostMonotonicHigherReference.witness" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicReference.fst", "name": "Steel.GhostMonotonicReference.witness" }, { "project_name": "steel", "file_name": "Steel.MonotonicReference.fst", "name": "Steel.MonotonicReference.witness" }, { "project_name": "steel", "file_name": "Steel.GhostPCMReference.fst", "name": "Steel.GhostPCMReference.witness" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.bind_ghost" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.bind_lpre" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.Ghost.fst", "name": "Steel.ST.Effect.Ghost.admit_" }, { "project_name": "steel", "file_name": "Steel.ST.SpinLock.fst", "name": "Steel.ST.SpinLock.acquire_core" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.bind" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.new_invariant" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.new_invariant" }, { "project_name": "steel", "file_name": "Steel.ST.Coercions.fst", "name": "Steel.ST.Coercions.lift_sta_sa" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.lift1" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.lift2" }, { "project_name": "steel", "file_name": "Steel.SpinLock.fst", "name": "Steel.SpinLock.release_core" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.read" }, { "project_name": "steel", "file_name": "Steel.DisposableInvariant.fst", "name": "Steel.DisposableInvariant.with_invariant_g" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.conv" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.mk_stt_atomic_comp" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.return_atomic_noeq" }, { "project_name": "steel", "file_name": "Steel.Semantics.Hoare.MST.fst", "name": "Steel.Semantics.Hoare.MST.bind_lpost" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicReference.fst", "name": "Steel.GhostMonotonicReference.recall" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicHigherReference.fst", "name": "Steel.GhostMonotonicHigherReference.recall" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.AtomicAndGhost.fst", "name": "Steel.ST.Effect.AtomicAndGhost.bind" }, { "project_name": "steel", "file_name": "Steel.MonotonicHigherReference.fst", "name": "Steel.MonotonicHigherReference.recall" }, { "project_name": "steel", "file_name": "Pulse.Lib.Trade.fst", "name": "Pulse.Lib.Trade.elim_trade" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.lift_atomic_steel" }, { "project_name": "steel", "file_name": "Steel.ST.GhostMonotonicReference.fst", "name": "Steel.ST.GhostMonotonicReference.witness'" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.lift0" }, { "project_name": "steel", "file_name": "Steel.MonotonicReference.fst", "name": "Steel.MonotonicReference.recall" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.bind" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fsti", "name": "Steel.ST.HigherArray.join" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fsti", "name": "Steel.ST.Array.join" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.write" }, { "project_name": "steel", "file_name": "Pulse.Reflection.Util.fst", "name": "Pulse.Reflection.Util.mk_sub_stt_atomic" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.alloc" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fst", "name": "Steel.Effect.Atomic.bind_opaque" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.rewrite" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fsti", "name": "Steel.ST.Util.implies_trans_gen" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.frame" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.atomic_read" }, { "project_name": "steel", "file_name": "Steel.ST.GhostHigherReference.fst", "name": "Steel.ST.GhostHigherReference.pts_to_injective_eq" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.pts_to_injective_eq" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.pts_to_injective_eq" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.witness" }, { "project_name": "steel", "file_name": "Steel.ST.PCMReference.fst", "name": "Steel.ST.PCMReference.recall" }, { "project_name": "steel", "file_name": "Steel.ST.EphemeralHashtbl.fst", "name": "Steel.ST.EphemeralHashtbl.rewrite_value_vprops_prefix_and_suffix" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.witness'" }, { "project_name": "steel", "file_name": "Steel.ST.Util.fst", "name": "Steel.ST.Util.assert_" } ], "selected_premises": [ "FStar.Real.one", "FStar.Real.two", "PulseCore.FractionalPermission.full_perm", "FStar.FunctionalExtensionality.feq", "Pulse.Lib.Core.hide_div", "PulseCore.Action.inames", "Pulse.Lib.Core.iname", "FStar.PCM.composable", "PulseCore.FractionalPermission.sum_perm", "Pulse.Lib.Core.stt", "Pulse.Lib.Core.op_exists_Star", "Pulse.Lib.Core.name_of_inv", "PulseCore.Preorder.pcm_history", "PulseCore.FractionalPermission.comp_perm", "FStar.PCM.compatible", "Pulse.Lib.Core.join_emp", "Pulse.Lib.Core.sub_stt", "Pulse.Lib.Core.op_Star_Star", "FStar.PCM.op", "Pulse.Lib.Core.emp", "Pulse.Lib.Core.conv_stt", "Pulse.Lib.Core.vprop", "Pulse.Lib.Core.vprop_equiv_trans", "Pulse.Lib.Core.vprop_equiv_sym", "PulseCore.Action.emp_inames", "Pulse.Lib.Core.vprop_equiv_ext", "Pulse.Lib.Core.pure", "Pulse.Lib.Core.add_already_there", "PulseCore.Action.join_inames", "PulseCore.Preorder.history_val", "FStar.FunctionalExtensionality.on_dom", "Pulse.Lib.Core.frame_stt", "PulseCore.Action.mem_inv", "Pulse.Lib.Core.bind_stt", "Pulse.Lib.Core.vprop_post_equiv", "Pulse.Lib.Core.vprop_equiv_assoc", "Pulse.Lib.Core.inv", "Pulse.Lib.Core.vprop_equiv_refl", "Pulse.Lib.Core.elim_vprop_equiv", "Pulse.Lib.Core.lift_observability", "Pulse.Lib.Core.intro_vprop_post_equiv", "Pulse.Lib.Core.vprop_equiv_unit", "Pulse.Lib.Core.stt_atomic", "FStar.Pervasives.reveal_opaque", "PulseCore.Action.inames_subset", "Pulse.Lib.Core.vprop_equiv_comm", "Pulse.Lib.Core.vprop_equiv", "Pulse.Lib.Core.vprop_equiv_cong", "Pulse.Lib.Core.frame_atomic", "PulseCore.FractionalPermission.half_perm", "Pulse.Lib.Core.par_stt", "Pulse.Lib.Core.sub_atomic", "PulseCore.Action.add_inv", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.fst", "PulseCore.Preorder.p_op", "Pulse.Lib.Core.elim_vprop_post_equiv", "PulseCore.Preorder.induces_preorder", "PulseCore.InstantiatedSemantics.slprop_post_equiv", "FStar.Real.zero", "PulseCore.FractionalPermission.lesser_perm", "Pulse.Lib.Core.bind_atomic", "PulseCore.Preorder.comm_op", "FStar.FunctionalExtensionality.on", "Pulse.Lib.Core.return_neutral", "PulseCore.Preorder.vhist", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater", "PulseCore.Preorder.extends", "FStar.PCM.frame_preserving_subframe", "Pulse.Lib.Core.return_stt_noeq", "PulseCore.Preorder.preorder_of_pcm", "PulseCore.Preorder.history_compose", "FStar.PropositionalExtensionality.apply", "PulseCore.Preorder.extends'", "PulseCore.Observability.at_most_one_observable", "PulseCore.Preorder.curval", "PulseCore.FractionalPermission.writeable", "FStar.FunctionalExtensionality.restricted_t", "Pulse.Lib.Core.return_neutral_noeq", "Pulse.Lib.Core.prop_squash_idem", "Prims.subtype_of", "FStar.Pervasives.dfst", "PulseCore.Preorder.pcm_of_preorder", "PulseCore.FractionalPermission.lesser_equal_perm", "PulseCore.Preorder.flip", "PulseCore.Preorder.p_composable", "PulseCore.Preorder.fact_valid_compat", "FStar.Pervasives.dsnd", "PulseCore.Preorder.p", "PulseCore.Action.property", "PulseCore.Preorder.property", "PulseCore.Preorder.hval", "PulseCore.Preorder.history_composable", "FStar.FunctionalExtensionality.arrow", "FStar.Classical.Sugar.implies_elim", "PulseCore.Observability.join_obs", "FStar.Set.subset", "FStar.FunctionalExtensionality.op_Hat_Subtraction_Greater_Greater", "FStar.PCM.lem_commutative", "PulseCore.Preorder.extends_length_eq" ], "source_upto_this": "(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule Pulse.Lib.Core\nmodule I = PulseCore.InstantiatedSemantics\nmodule A = PulseCore.Atomic\nmodule T = FStar.Tactics.V2\nmodule F = FStar.FunctionalExtensionality\nopen PulseCore.InstantiatedSemantics\nopen PulseCore.FractionalPermission\nopen PulseCore.Observability\n\nlet double_one_half () = ()\nlet equate_by_smt = ()\nlet vprop = slprop\nlet emp = emp\nlet op_Star_Star = op_Star_Star\nlet pure = pure\nlet op_exists_Star = op_exists_Star\nlet vprop_equiv = slprop_equiv\nlet elim_vprop_equiv #p #q pf = slprop_equiv_elim p q\nlet vprop_post_equiv = slprop_post_equiv\nlet prop_squash_idem (p:prop)\n : Tot (squash (squash p == p))\n = FStar.PropositionalExtensionality.apply p (squash p)\n\nlet intro_vprop_post_equiv\n (#t:Type u#a)\n (p q: t -> vprop)\n (pf: (x:t -> vprop_equiv (p x) (q x)))\n : vprop_post_equiv p q\n = let pf : squash (forall x. vprop_equiv (p x) (q x)) =\n introduce forall x. vprop_equiv (p x) (q x)\n with FStar.Squash.return_squash (pf x)\n in\n coerce_eq (prop_squash_idem _) pf\n\nlet elim_vprop_post_equiv (#t:Type u#a)\n (p q: t -> vprop)\n (pf:vprop_post_equiv p q)\n (x:t)\n: vprop_equiv (p x) (q x)\n= let pf\n : squash (vprop_equiv (p x) (q x))\n = eliminate forall x. vprop_equiv (p x) (q x) with x\n in\n coerce_eq (prop_squash_idem _) pf\n\nlet vprop_equiv_refl (v0:vprop)\n : vprop_equiv v0 v0\n = slprop_equiv_refl v0\n\nlet vprop_equiv_sym (v0 v1:vprop) (p:vprop_equiv v0 v1)\n : vprop_equiv v1 v0\n = slprop_equiv_elim v0 v1; p\n\nlet vprop_equiv_trans\n (v0 v1 v2:vprop)\n (p:vprop_equiv v0 v1)\n (q:vprop_equiv v1 v2)\n : vprop_equiv v0 v2\n = slprop_equiv_elim v0 v1;\n slprop_equiv_elim v1 v2;\n p\n\nlet vprop_equiv_unit (x:vprop)\n : vprop_equiv (emp ** x) x\n = slprop_equiv_unit x\n\nlet vprop_equiv_comm (p1 p2:vprop)\n : vprop_equiv (p1 ** p2) (p2 ** p1)\n = slprop_equiv_comm p1 p2\n\nlet vprop_equiv_assoc (p1 p2 p3:vprop)\n : vprop_equiv ((p1 ** p2) ** p3) (p1 ** (p2 ** p3))\n = slprop_equiv_assoc p1 p2 p3\n\nlet vprop_equiv_cong (p1 p2 p3 p4:vprop)\n (f: vprop_equiv p1 p3)\n (g: vprop_equiv p2 p4)\n : vprop_equiv (p1 ** p2) (p3 ** p4)\n = slprop_equiv_elim p1 p3;\n slprop_equiv_elim p2 p4;\n vprop_equiv_refl _\n\nlet vprop_equiv_ext p1 p2 _ = vprop_equiv_refl p1\n\n(* Invariants, just reexport *)\nmodule Act = PulseCore.Action\nlet iname = Act.iname\n\nlet join_sub _ _ = ()\nlet join_emp is =\n Set.lemma_equal_intro (join_inames is emp_inames) (reveal is);\n Set.lemma_equal_intro (join_inames emp_inames is) (reveal is)\n\nlet inv = Act.inv\nlet name_of_inv = Act.name_of_inv\n\nlet add_already_there i is = Set.lemma_equal_intro (add_inv is i) is\n\n////////////////////////////////////////////////////////////////////\n// stt a pre post: The main type of a pulse computation\n////////////////////////////////////////////////////////////////////\nlet stt = I.stt\nlet return_stt_noeq = I.return\nlet bind_stt = I.bind\nlet frame_stt = I.frame\nlet par_stt = I.par\nlet sub_stt = I.sub\nlet conv_stt pf1 pf2 = I.conv #_ _ _ _ _ pf1 pf2\nlet hide_div = I.hide_div\n\n////////////////////////////////////////////////////////////////////\n// Atomic computations\n////////////////////////////////////////////////////////////////////\nlet stt_atomic a #obs inames pre post = A.stt_atomic a #obs inames pre post\nlet lift_observability = A.lift_observability\nlet return_neutral = A.return_atomic\nlet return_neutral_noeq = A.return_atomic_noeq\nlet bind_atomic = A.bind_atomic\nlet frame_atomic = A.frame_atomic\nlet sub_atomic = A.sub_atomic", "sketch": [ "Step 1: This definition is about creating a new atomic computation `stt_atomic` that operates under a potentially larger set of invariants (`opens2`) than the original computation (`opens1`). The precondition and postcondition remain the same, but the set of invariants that the computation can access is expanded.\nStep 2: To implement this, we will use the existing `sub_atomic` function from the `PulseCore.Atomic` module, which allows us to adjust the set of invariants for an atomic computation. We will pass the original computation `e` and the proof that `opens1` is a subset of `opens2` to `sub_atomic`.", "Step 1: The definition `sub_invs_atomic` aims to adjust the set of invariants that an atomic computation `e` depends on. Specifically, it allows us to replace the set of invariants `opens1` with a larger set `opens2`, provided that `opens1` is a subset of `opens2`. This is useful when we want to ensure that the computation can still be performed under a broader context of invariants.\n\nStep 2: To implement this, we will use the `sub_atomic` function from the `PulseCore.Atomic` module. This function allows us to adjust the set of invariants for an atomic computation. We will pass the computation `e` and the proof that `opens1` is a subset of `opens2` to `sub_atomic`, which will return the adjusted computation.", "Step 1: This definition is about creating a new atomic computation `stt_atomic` that operates over a potentially larger set of invariants (`opens2`) than the original computation (`opens1`). The original computation `e` operates over `opens1` and we need to ensure that `opens1` is a subset of `opens2`.\nStep 2: The implementation will use the `sub_atomic` function from the `A` module to adjust the set of invariants from `opens1` to `opens2`, given the subset relationship.", "Step 1: This definition is about creating a new atomic computation `stt_atomic` that has a larger set of invariants (`opens2`) than the original atomic computation (`opens1`). The precondition and postcondition remain the same, but the new computation should be valid under the larger set of invariants.\nStep 2: To implement this, we will use the `sub_atomic` function from the `PulseCore.Atomic` module. This function allows us to adjust the set of invariants for an atomic computation. We will pass the original computation `e` and the proof that `opens1` is a subset of `opens2` to `sub_atomic`.", "Step 1: This lemma is about showing that if we have an atomic computation `e` that operates under a set of invariants `opens1`, and if `opens1` is a subset of another set of invariants `opens2`, then the same atomic computation can be considered to operate under `opens2` without changing its behavior.\nStep 2: To implement this, we will use the `sub_atomic` function from the `PulseCore.Atomic` module, which allows us to change the set of invariants under which an atomic computation operates, given a proof that one set is a subset of the other.", "Step 1: This definition is about creating a new atomic computation `stt_atomic` that operates under a potentially larger set of invariants (`opens2`) compared to the original set of invariants (`opens1`). The precondition and postcondition remain the same, and the computation `e` is preserved.\nStep 2: To implement this, we will use the `sub_atomic` function from the `PulseCore.Atomic` module, which allows us to substitute the set of invariants while maintaining the same computation. We will pass the necessary parameters to `sub_atomic` to achieve this.", "Step 1: The definition `sub_invs_atomic` is about creating a new atomic computation with a larger set of invariants (`opens2`) from an existing atomic computation with a smaller set of invariants (`opens1`). The precondition and postcondition of the computation remain the same, and we assume that `opens1` is a subset of `opens2`.\n\nStep 2: To implement this, we can use the `sub_atomic` function from the `PulseCore.Atomic` module, which allows us to change the set of invariants of an atomic computation. We need to ensure that the subset relationship between `opens1` and `opens2` is maintained.", "Step 1: This definition is about creating a new atomic computation `stt_atomic` that operates over a potentially larger set of invariants. Specifically, given an atomic computation `e` that operates over a set of invariants `opens1`, and a proof that `opens1` is a subset of another set `opens2`, we want to produce a new atomic computation that operates over `opens2` but otherwise behaves identically to `e`.\n\nStep 2: The implementation will use the `sub_atomic` function from the `PulseCore.Atomic` module to achieve this. The `sub_atomic` function allows us to change the set of invariants an atomic computation operates over, given a proof that the original set is a subset of the new set.", "Step 1: The definition `sub_invs_atomic` is about creating a new atomic computation `stt_atomic` with a potentially larger set of invariants. Given an atomic computation `e` that operates under a set of invariants `opens1`, and a proof that `opens1` is a subset of `opens2`, we want to show that `e` can also operate under the larger set of invariants `opens2`.\nStep 2: To implement this, we leverage the existing `sub_atomic` function from the `PulseCore.Atomic` module, which allows us to change the set of invariants of an atomic computation given a subset relationship.", "Step 1: The definition `sub_invs_atomic` is about creating a new atomic computation that operates under a potentially larger set of invariants (`opens2`) compared to the original set (`opens1`). The original computation `e` operates under `opens1`, and we need to ensure that `opens1` is a subset of `opens2`.\nStep 2: To implement this, we will use the `sub_atomic` function from the `PulseCore.Atomic` module, which allows us to adjust the set of invariants under which an atomic computation operates. We will pass the original computation `e` and the proof that `opens1` is a subset of `opens2` to `sub_atomic`." ], "generated_solution": [ "let sub_invs_atomic\n (#a:Type u#a)\n (#obs:_)\n (#opens1 #opens2:inames)\n (#pre:vprop)\n (#post:a -> vprop)\n (e:stt_atomic a #obs opens1 pre post)\n (_ : squash (inames_subset opens1 opens2))\n: stt_atomic a #obs opens2 pre post\n= sub_atomic e _", "let sub_invs_atomic\n (#a:Type u#a)\n (#obs:_)\n (#opens1 #opens2:inames)\n (#pre:vprop)\n (#post:a -> vprop)\n (e:stt_atomic a #obs opens1 pre post)\n (_ : squash (inames_subset opens1 opens2))\n: stt_atomic a #obs opens2 pre post\n= sub_atomic e _", "let sub_invs_atomic #a #obs #opens1 #opens2 #pre #post e _ =\n A.sub_atomic e _", "A.sub_atomic e _", "let sub_invs_atomic #a #obs #opens1 #opens2 #pre #post e _ =\n sub_atomic e _", "let sub_invs_atomic #a #obs #opens1 #opens2 #pre #post e _ =\n sub_atomic e _", "let sub_invs_atomic\n (#a:Type u#a)\n (#obs:_)\n (#opens1 #opens2:inames)\n (#pre:vprop)\n (#post:a -> vprop)\n (e:stt_atomic a #obs opens1 pre post)\n (_ : squash (inames_subset opens1 opens2))\n: stt_atomic a #obs opens2 pre post\n = sub_atomic e _", "let sub_invs_atomic #a #obs #opens1 #opens2 #pre #post e _ =\n sub_atomic e _", "let sub_invs_atomic\n (#a:Type u#a)\n (#obs:_)\n (#opens1 #opens2:inames)\n (#pre:vprop)\n (#post:a -> vprop)\n (e:stt_atomic a #obs opens1 pre post)\n (_ : squash (inames_subset opens1 opens2))\n: stt_atomic a #obs opens2 pre post\n = sub_atomic e _", "let sub_invs_atomic\n (#a:Type u#a)\n (#obs:_)\n (#opens1 #opens2:inames)\n (#pre:vprop)\n (#post:a -> vprop)\n (e:stt_atomic a #obs opens1 pre post)\n (_ : squash (inames_subset opens1 opens2))\n: stt_atomic a #obs opens2 pre post =\n sub_atomic e _" ] }, { "file_name": "EverParse3d.Interpreter.fst", "name": "EverParse3d.Interpreter.mk_dtyp_app", "opens_and_abbrevs": [ { "abbrev": "T", "full_module": "FStar.Tactics" }, { "open": "FStar.List.Tot" }, { "abbrev": "CP", "full_module": "EverParse3d.CopyBuffer" }, { "abbrev": "T", "full_module": "FStar.Tactics" }, { "abbrev": "P", "full_module": "EverParse3d.Prelude" }, { "abbrev": "A", "full_module": "EverParse3d.Actions.All" }, { "abbrev": "U64", "full_module": "FStar.UInt64" }, { "abbrev": "U32", "full_module": "FStar.UInt32" }, { "open": "EverParse3d" }, { "open": "EverParse3d" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 0, "initial_ifuel": 2, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [ "smt.qi.eager_threshold=10" ], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val mk_dtyp_app\n (#nz #wk: _)\n (pk: P.parser_kind nz wk)\n ([@@@ erasable]inv: inv_index)\n ([@@@ erasable]disj: disj_index)\n ([@@@ erasable]loc: loc_index)\n ([@@@ erasable]p_t: Type0)\n ([@@@ erasable]p_p: P.parser pk p_t)\n (p_reader: option (leaf_reader p_p))\n (b: bool)\n (p_v: A.validate_with_action_t p_p (interp_inv inv) (interp_disj disj) (interp_loc loc) b)\n ([@@@ erasable]pf: squash (b == Some? p_reader))\n : dtyp #nz #wk pk b inv disj loc", "source_definition": "let mk_dtyp_app #nz #wk \r\n (pk:P.parser_kind nz wk)\r\n ([@@@erasable] inv:inv_index)\r\n ([@@@erasable] disj:disj_index)\r\n ([@@@erasable] loc:loc_index)\r\n ([@@@erasable] p_t : Type0)\r\n ([@@@erasable] p_p : P.parser pk p_t)\r\n (p_reader: option (leaf_reader p_p))\r\n (b:bool)\r\n (p_v : A.validate_with_action_t p_p \r\n (interp_inv inv)\r\n (interp_disj disj)\r\n (interp_loc loc)\r\n b)\r\n ([@@@erasable] pf:squash (b == Some? p_reader))\r\n : dtyp #nz #wk pk b inv disj loc\r\n = let gb = {\r\n parser_kind_nz = nz;\r\n parser_weak_kind = wk;\r\n parser_kind = pk;\r\n inv = inv;\r\n disj;\r\n loc = loc;\r\n p_t = p_t;\r\n p_p = p_p;\r\n p_reader = p_reader;\r\n p_v = p_v\r\n } in\r\n DT_App pk b inv disj loc gb ()", "source_range": { "start_line": 1412, "start_col": 0, "end_line": 1440, "end_col": 35 }, "interleaved": false, "definition": "fun pk inv disj loc p_t p_p p_reader b p_v _ ->\n (let gb = EverParse3d.Interpreter.Mkglobal_binding nz wk pk inv disj loc p_t p_p p_reader p_v in\n EverParse3d.Interpreter.DT_App pk b inv disj loc gb ())\n <:\n EverParse3d.Interpreter.dtyp pk b inv disj loc", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Prims.bool", "EverParse3d.Kinds.weak_kind", "EverParse3d.Kinds.parser_kind", "EverParse3d.Interpreter.inv_index", "EverParse3d.Interpreter.disj_index", "EverParse3d.Interpreter.loc_index", "EverParse3d.Prelude.parser", "FStar.Pervasives.Native.option", "EverParse3d.Interpreter.leaf_reader", "EverParse3d.Actions.Base.validate_with_action_t", "EverParse3d.Interpreter.interp_inv", "EverParse3d.Interpreter.interp_disj", "EverParse3d.Interpreter.interp_loc", "Prims.squash", "Prims.eq2", "FStar.Pervasives.Native.uu___is_Some", "EverParse3d.Interpreter.DT_App", "EverParse3d.Interpreter.global_binding", "EverParse3d.Interpreter.Mkglobal_binding", "EverParse3d.Interpreter.dtyp" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "\n pk: EverParse3d.Kinds.parser_kind nz wk ->\n inv: EverParse3d.Interpreter.inv_index ->\n disj: EverParse3d.Interpreter.disj_index ->\n loc: EverParse3d.Interpreter.loc_index ->\n p_t: Type0 ->\n p_p: EverParse3d.Prelude.parser pk p_t ->\n p_reader: FStar.Pervasives.Native.option (EverParse3d.Interpreter.leaf_reader p_p) ->\n b: Prims.bool ->\n p_v:\n EverParse3d.Actions.Base.validate_with_action_t p_p\n (EverParse3d.Interpreter.interp_inv inv)\n (EverParse3d.Interpreter.interp_disj disj)\n (EverParse3d.Interpreter.interp_loc loc)\n b ->\n pf: Prims.squash (b == Some? p_reader)\n -> EverParse3d.Interpreter.dtyp pk b inv disj loc", "prompt": "let mk_dtyp_app\n #nz\n #wk\n (pk: P.parser_kind nz wk)\n ([@@@ erasable]inv: inv_index)\n ([@@@ erasable]disj: disj_index)\n ([@@@ erasable]loc: loc_index)\n ([@@@ erasable]p_t: Type0)\n ([@@@ erasable]p_p: P.parser pk p_t)\n (p_reader: option (leaf_reader p_p))\n (b: bool)\n (p_v: A.validate_with_action_t p_p (interp_inv inv) (interp_disj disj) (interp_loc loc) b)\n ([@@@ erasable]pf: squash (b == Some? p_reader))\n : dtyp #nz #wk pk b inv disj loc =\n ", "expected_response": "let gb =\n {\n parser_kind_nz = nz;\n parser_weak_kind = wk;\n parser_kind = pk;\n inv = inv;\n disj = disj;\n loc = loc;\n p_t = p_t;\n p_p = p_p;\n p_reader = p_reader;\n p_v = p_v\n }\nin\nDT_App pk b inv disj loc gb ()", "source": { "project_name": "everparse", "file_name": "src/3d/prelude/EverParse3d.Interpreter.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git" }, "dependencies": { "source_file": "EverParse3d.Interpreter.fst", "checked_file": "dataset/EverParse3d.Interpreter.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.UInt64.fsti.checked", "dataset/FStar.UInt32.fsti.checked", "dataset/FStar.Tactics.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.List.Tot.fst.checked", "dataset/EverParse3d.Prelude.fsti.checked", "dataset/EverParse3d.CopyBuffer.fsti.checked", "dataset/EverParse3d.Actions.BackendFlag.fsti.checked", "dataset/EverParse3d.Actions.All.fsti.checked" ] }, "definitions_in_context": [ "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "let ___EVERPARSE_COPY_BUFFER_T = CP.copy_buffer_t", "let specialize = ()", "itype", "UInt8", "UInt8", "UInt8", "UInt16", "UInt16", "UInt16", "UInt32", "UInt32", "UInt32", "UInt64", "UInt64", "UInt64", "UInt8BE", "UInt8BE", "UInt8BE", "UInt16BE", "UInt16BE", "UInt16BE", "UInt32BE", "UInt32BE", "UInt32BE", "UInt64BE", "UInt64BE", "UInt64BE", "Unit", "Unit", "Unit", "AllBytes", "AllBytes", "AllBytes", "AllZeros", "AllZeros", "AllZeros", "let itype_as_type (i:itype)\r\n : Type\r\n = match i with\r\n | UInt8 -> P.___UINT8\r\n | UInt16 -> P.___UINT16\r\n | UInt32 -> P.___UINT32\r\n | UInt64 -> P.___UINT64\r\n | UInt8BE -> P.___UINT8BE\r\n | UInt16BE -> P.___UINT16BE\r\n | UInt32BE -> P.___UINT32BE\r\n | UInt64BE -> P.___UINT64BE\r\n | Unit -> unit\r\n | AllBytes -> P.all_bytes\r\n | AllZeros -> P.all_zeros", "let parser_kind_nz_of_itype (i:itype)\r\n : bool\r\n = match i with\r\n | Unit\r\n | AllBytes\r\n | AllZeros -> false\r\n | _ -> true", "let parser_weak_kind_of_itype (i:itype)\r\n : P.weak_kind\r\n = match i with\r\n | AllBytes\r\n | AllZeros -> P.WeakKindConsumesAll\r\n | _ -> P.WeakKindStrongPrefix", "let parser_kind_of_itype (i:itype)\r\n : P.parser_kind (parser_kind_nz_of_itype i)\r\n (parser_weak_kind_of_itype i)\r\n = match i with\r\n | UInt8 -> P.kind____UINT8\r\n | UInt16 -> P.kind____UINT16\r\n | UInt32 -> P.kind____UINT32\r\n | UInt64 -> P.kind____UINT64\r\n | UInt8BE -> P.kind____UINT8BE\r\n | UInt16BE -> P.kind____UINT16BE\r\n | UInt32BE -> P.kind____UINT32BE\r\n | UInt64BE -> P.kind____UINT64BE\r\n | Unit -> P.kind_unit\r\n | AllBytes -> P.kind_all_bytes\r\n | AllZeros -> P.kind_all_zeros", "let itype_as_parser (i:itype)\r\n : P.parser (parser_kind_of_itype i) (itype_as_type i)\r\n = match i with\r\n | UInt8 -> P.parse____UINT8\r\n | UInt16 -> P.parse____UINT16\r\n | UInt32 -> P.parse____UINT32\r\n | UInt64 -> P.parse____UINT64\r\n | UInt8BE -> P.parse____UINT8BE\r\n | UInt16BE -> P.parse____UINT16BE\r\n | UInt32BE -> P.parse____UINT32BE\r\n | UInt64BE -> P.parse____UINT64BE\r\n | Unit -> P.parse_unit\r\n | AllBytes -> P.parse_all_bytes\r\n | AllZeros -> P.parse_all_zeros", "let allow_reader_of_itype (i:itype)\r\n : bool\r\n = match i with\r\n | AllBytes\r\n | AllZeros -> false\r\n | _ -> true", "let itype_as_leaf_reader (i:itype { allow_reader_of_itype i })\r\n : A.leaf_reader (itype_as_parser i)\r\n = match i with\r\n | UInt8 -> A.read____UINT8\r\n | UInt16 -> A.read____UINT16\r\n | UInt32 -> A.read____UINT32\r\n | UInt64 -> A.read____UINT64\r\n | UInt8BE -> A.read____UINT8BE\r\n | UInt16BE -> A.read____UINT16BE\r\n | UInt32BE -> A.read____UINT32BE\r\n | UInt64BE -> A.read____UINT64BE\r\n | Unit -> A.read_unit", "let itype_as_validator (i:itype)\r\n : A.validate_with_action_t\r\n (itype_as_parser i)\r\n A.true_inv\r\n A.disjointness_trivial\r\n A.eloc_none\r\n (allow_reader_of_itype i)\r\n = match i with\r\n | UInt8 -> A.validate____UINT8\r\n | UInt16 -> A.validate____UINT16\r\n | UInt32 -> A.validate____UINT32\r\n | UInt64 -> A.validate____UINT64\r\n | UInt8BE -> A.validate____UINT8BE\r\n | UInt16BE -> A.validate____UINT16BE\r\n | UInt32BE -> A.validate____UINT32BE\r\n | UInt64BE -> A.validate____UINT64BE\r\n | Unit -> A.validate_unit\r\n | AllBytes -> A.validate_all_bytes\r\n | AllZeros -> A.validate_all_zeros", "let leaf_reader #nz #wk (#k: P.parser_kind nz wk) #t (p:P.parser k t)\r\n = _:squash (wk == P.WeakKindStrongPrefix /\\ hasEq t) &\r\n A.leaf_reader p", "index", "Trivial", "Trivial", "Trivial", "NonTrivial", "NonTrivial", "NonTrivial", "let join_index (j:'a -> 'a -> 'a) (i0 i1:index 'a)\r\n: index 'a\r\n= match i0 with\r\n | Trivial -> i1\r\n | _ -> (\r\n match i1 with\r\n | Trivial -> i0\r\n | NonTrivial i1 -> \r\n let NonTrivial i0 = i0 in\r\n NonTrivial (j i0 i1)\r\n )", "let interp_index (triv:'a) (i:index 'a)\r\n: GTot 'a\r\n= match i with\r\n | Trivial -> triv\r\n | NonTrivial i -> i", "let inv_index = index A.slice_inv", "let inv_none : inv_index = Trivial", "let join_inv = join_index A.conj_inv", "let interp_inv = interp_index A.true_inv", "let loc_index = index A.eloc", "let loc_none : loc_index = Trivial", "let join_loc = join_index A.eloc_union", "let interp_loc = interp_index A.eloc_none", "let disj_index = index A.disjointness_pre", "let disj_none : disj_index = Trivial", "let join_disj = join_index A.conj_disjointness", "let interp_disj = interp_index A.disjointness_trivial", "let disjoint (e1 e2:loc_index)\r\n : disj_index\r\n = match e1, e2 with\r\n | Trivial, _\r\n | _, Trivial -> disj_none\r\n | NonTrivial e1, NonTrivial e2 -> NonTrivial (A.disjoint e1 e2)", "global_binding", "global_binding", "parser_kind_nz", "parser_kind_nz", "parser_weak_kind", "parser_weak_kind", "parser_kind", "parser_kind", "inv", "inv", "disj", "disj", "loc", "loc", "p_t", "p_t", "p_p", "p_p", "p_reader", "p_reader", "p_v", "p_v", "let projector_names : list string = [\r\n `%Mkglobal_binding?.parser_kind_nz;\r\n `%Mkglobal_binding?.parser_weak_kind;\r\n `%Mkglobal_binding?.parser_kind;\r\n `%Mkglobal_binding?.inv;\r\n `%Mkglobal_binding?.disj;\r\n `%Mkglobal_binding?.loc;\r\n `%Mkglobal_binding?.p_t;\r\n `%Mkglobal_binding?.p_p;\r\n `%Mkglobal_binding?.p_reader;\r\n `%Mkglobal_binding?.p_v;\r\n]", "let nz_of_binding = Mkglobal_binding?.parser_kind_nz", "let wk_of_binding = Mkglobal_binding?.parser_weak_kind", "let pk_of_binding = Mkglobal_binding?.parser_kind", "let inv_of_binding = Mkglobal_binding?.inv", "let disj_of_bindng = Mkglobal_binding?.disj", "let loc_of_binding = Mkglobal_binding?.loc", "let type_of_binding = Mkglobal_binding?.p_t", "let parser_of_binding = Mkglobal_binding?.p_p", "let leaf_reader_of_binding = Mkglobal_binding?.p_reader", "let validator_of_binding = Mkglobal_binding?.p_v", "let has_reader (g:global_binding) = \r\n match leaf_reader_of_binding g with\r\n | Some _ -> true\r\n | _ -> false", "let reader_binding = g:global_binding { has_reader g }", "let get_leaf_reader (r:reader_binding)\r\n : leaf_reader (parser_of_binding r)\r\n = Some?.v (leaf_reader_of_binding r)", "dtyp", "DT_IType", "DT_IType", "DT_IType", "i", "i", "DT_App", "DT_App", "DT_App", "nz", "nz", "wk", "wk", "pk", "pk", "hr", "hr", "inv", "inv", "disj", "disj", "loc", "loc", "x", "x", "_", "_", "let dtyp_as_type #nz #wk (#pk:P.parser_kind nz wk) #hr #i #disj #l\r\n (d:dtyp pk hr i disj l)\r\n : Type\r\n = match d with\r\n | DT_IType i -> \r\n itype_as_type i\r\n\r\n | DT_App _ _ _ _ _ b _ ->\r\n type_of_binding b", "let dtyp_as_eqtype_lemma #nz #wk (#pk:P.parser_kind nz wk) #i #disj #l\r\n (d:dtyp pk true i disj l)\r\n : Lemma\r\n (ensures hasEq (dtyp_as_type d))\r\n [SMTPat (hasEq (dtyp_as_type d))]\r\n = match d with\r\n | DT_IType i -> \r\n ()\r\n\r\n | DT_App _ _ _ _ _ b _ ->\r\n let (| _, _ |) = get_leaf_reader b in ()", "let dtyp_as_parser #nz #wk (#pk:P.parser_kind nz wk) #hr #i #disj #l\r\n (d:dtyp pk hr i disj l)\r\n : P.parser pk (dtyp_as_type d)\r\n = match d returns Tot (P.parser pk (dtyp_as_type d)) with\r\n | DT_IType i -> \r\n itype_as_parser i\r\n\r\n | DT_App _ _ _ _ _ b _ ->\r\n parser_of_binding b", "let dtyp_as_validator #nz #wk (#pk:P.parser_kind nz wk)\r\n (#hr:_)\r\n (#[@@@erasable] i:inv_index)\r\n (#[@@@erasable] disj:disj_index)\r\n (#[@@@erasable] l:loc_index)\r\n (d:dtyp pk hr i disj l)\r\n : A.validate_with_action_t #nz #wk #pk #(dtyp_as_type d)\r\n (dtyp_as_parser d)\r\n (interp_inv i)\r\n (interp_disj disj)\r\n (interp_loc l)\r\n hr\r\n = match d \r\n returns \r\n A.validate_with_action_t #nz #wk #pk #(dtyp_as_type d)\r\n (dtyp_as_parser d)\r\n (interp_inv i)\r\n (interp_disj disj)\r\n (interp_loc l)\r\n hr \r\n with\r\n | DT_IType i -> \r\n itype_as_validator i\r\n\r\n | DT_App _ _ _ _ _ b _ ->\r\n // assert_norm (dtyp_as_type (DT_App_Alt ps b args) == (type_of_binding_alt (apply_arrow b args)));\r\n // assert_norm (dtyp_as_parser (DT_App_Alt ps b args) == parser_of_binding_alt (apply_arrow b args));\r\n validator_of_binding b", "let dtyp_as_leaf_reader #nz (#pk:P.parser_kind nz P.WeakKindStrongPrefix)\r\n (#[@@@erasable] i:inv_index)\r\n (#[@@@erasable] disj:disj_index)\r\n (#[@@@erasable] l:loc_index)\r\n (d:dtyp pk true i disj l)\r\n : A.leaf_reader (dtyp_as_parser d)\r\n = match d with\r\n | DT_IType i -> \r\n itype_as_leaf_reader i\r\n\r\n | DT_App _ _ _ _ _ b _ -> \r\n let (| _, lr |) = get_leaf_reader b in\r\n lr", "let action_binding\r\n (inv:inv_index)\r\n (l:loc_index)\r\n (on_success:bool)\r\n (a:Type)\r\n : Type u#0\r\n = A.action (interp_inv inv) A.disjointness_trivial (interp_loc l) on_success a", "let extern_action (l:loc_index) = A.external_action (interp_loc l)", "let mk_extern_action (#l:loc_index) ($f:extern_action l)\r\n = A.mk_external_action f", "let mk_action_binding\r\n (#l:loc_index)\r\n ($f:extern_action l)\r\n : action_binding inv_none l false unit\r\n = mk_extern_action f", "atomic_action", "Action_return", "Action_return", "Action_return", "a", "a", "x", "x", "Action_abort", "Action_abort", "Action_abort", "Action_field_pos_64", "Action_field_pos_64", "Action_field_pos_64", "Action_field_pos_32", "Action_field_pos_32", "Action_field_pos_32", "Action_field_ptr", "Action_field_ptr", "Action_field_ptr", "Action_field_ptr_after", "Action_field_ptr_after", "Action_field_ptr_after", "sz", "sz", "write_to", "write_to", "Action_field_ptr_after_with_setter", "Action_field_ptr_after_with_setter", "Action_field_ptr_after_with_setter", "sz", "sz", "out_loc", "out_loc", "write_to", "write_to", "Action_deref", "Action_deref", "Action_deref", "a", "a", "x", "x", "Action_assignment", "Action_assignment", "Action_assignment", "a", "a", "x", "x", "rhs", "rhs", "Action_call", "Action_call", "Action_call", "inv", "inv", "loc", "loc", "b", "b", "t", "t", "Action_probe_then_validate", "Action_probe_then_validate", "Action_probe_then_validate", "nz", "nz", "wk", "wk", "k", "k", "has_reader", "has_reader", "inv", "inv", "disj", "disj", "l", "l", "dt", "dt", "src", "src", "len", "len", "dest", "dest", "probe", "probe", "let atomic_action_as_action\r\n (#i #d #l #b #t:_)\r\n (a:atomic_action i d l b t)\r\n : Tot (A.action (interp_inv i) (interp_disj d) (interp_loc l) b t)\r\n = match a with\r\n | Action_return x ->\r\n A.action_return x\r\n | Action_abort ->\r\n A.action_abort\r\n | Action_field_pos_64 ->\r\n A.action_field_pos_64\r\n | Action_field_pos_32 sq ->\r\n A.action_field_pos_32 sq\r\n | Action_field_ptr sq ->\r\n A.action_field_ptr sq\r\n | Action_field_ptr_after sq sz write_to ->\r\n A.action_field_ptr_after sq sz write_to\r\n | Action_field_ptr_after_with_setter sq sz write_to ->\r\n A.action_field_ptr_after_with_setter sq sz write_to\r\n | Action_deref x ->\r\n A.action_deref x\r\n | Action_assignment x rhs ->\r\n A.action_assignment x rhs\r\n | Action_call c ->\r\n c\r\n | Action_probe_then_validate #nz #wk #k #_hr #inv #l dt src len dest probe ->\r\n A.index_equations();\r\n let v = dtyp_as_validator dt in\r\n A.probe_then_validate v src len dest probe", "action", "Atomic_action", "Atomic_action", "Atomic_action", "i", "i", "d", "d", "l", "l", "b", "b", "t", "t", "Action_seq", "Action_seq", "Action_seq", "i0", "i0", "l0", "l0", "b0", "b0", "hd", "hd", "i1", "i1", "l1", "l1", "b1", "b1", "t", "t", "tl", "tl", "Action_ite", "Action_ite", "Action_ite", "hd", "hd", "i0", "i0", "l0", "l0", "b0", "b0", "t", "t", "then_", "then_", "i1", "i1", "l1", "l1", "b1", "b1", "else_", "else_", "Action_let", "Action_let", "Action_let", "i0", "i0", "l0", "l0", "b0", "b0", "t0", "t0", "head", "head", "i1", "i1", "l1", "l1", "b1", "b1", "t1", "t1", "k", "k", "Action_act", "Action_act", "Action_act", "i0", "i0", "l0", "l0", "b0", "b0", "act", "act", "let rec action_as_action\r\n (#i #d #l #b #t:_)\r\n (a:action i d l b t)\r\n : Tot (A.action (interp_inv i) (interp_disj d) (interp_loc l) b t)\r\n (decreases a)\r\n = A.index_equations();\r\n match a with\r\n | Atomic_action a ->\r\n atomic_action_as_action a\r\n\r\n | Action_seq hd tl ->\r\n let a1 = atomic_action_as_action hd in\r\n let tl = action_as_action tl in\r\n A.action_seq a1 tl\r\n\r\n | Action_ite hd t e ->\r\n let then_ (x:squash hd) = action_as_action (t x) in\r\n let else_ (x:squash (not hd)) = action_as_action (e x) in\r\n A.action_ite hd then_ else_\r\n\r\n | Action_let hd k ->\r\n let head = atomic_action_as_action hd in\r\n let k x = action_as_action (k x) in\r\n A.action_bind \"hd\" head k\r\n\r\n | Action_act #i0 #l0 #b0 a ->\r\n A.action_weaken (A.action_seq (action_as_action a) (A.action_return true))\r\n #(interp_inv i0) \r\n #_ \r\n #(interp_loc l0)", "let comments = string", "typ", "T_false", "T_false", "fieldname", "T_denoted", "T_denoted", "fieldname", "nz", "wk", "pk", "has_reader", "i", "disj", "l", "td", "T_pair", "T_pair", "first_fieldname", "nz1", "pk1", "i1", "d1", "l1", "b1", "nz2", "wk2", "pk2", "i2", "d2", "l2", "b2", "t1", "t2", "T_dep_pair", "T_dep_pair", "first_fieldname", "nz1", "pk1", "i1", "d1", "l1", "nz2", "wk2", "pk2", "i2", "d2", "l2", "b2", "t1", "t2", "T_refine", "T_refine", "fieldname", "nz1", "pk1", "i1", "d1", "l1", "base", "refinement", "T_refine_with_action", "T_refine_with_action", "fieldname", "nz1", "pk1", "i1", "d1", "l1", "i2", "d2", "l2", "b2", "base", "refinement", "act", "T_dep_pair_with_refinement", "T_dep_pair_with_refinement", "first_fieldname", "nz1", "pk1", "i1", "d1", "l1", "nz2", "wk2", "pk2", "i2", "d2", "l2", "b2", "base", "refinement", "k", "T_dep_pair_with_action", "T_dep_pair_with_action", "fieldname", "nz1", "pk1", "i1", "d1", "l1", "nz2", "wk2", "pk2", "i2", "d2", "l2", "b2", "i3", "d3", "l3", "b3", "base", "k", "act", "T_dep_pair_with_refinement_and_action", "T_dep_pair_with_refinement_and_action", "first_fieldname", "nz1", "pk1", "i1", "d1", "l1", "nz2", "wk2", "pk2", "i2", "d2", "l2", "b2", "i3", "d3", "l3", "b3", "base", "refinement", "k", "act", "T_if_else", "T_if_else", "nz1", "wk1", "pk1", "l1", "i1", "d1", "b1", "nz2", "wk2", "pk2", "l2", "i2", "d2", "b2", "b", "t1", "t2", "T_cases", "T_cases", "nz1", "wk1", "pk1", "l1", "i1", "d1", "b1", "nz2", "wk2", "pk2", "l2", "i2", "d2", "b2", "b", "t1", "t2", "T_with_action", "T_with_action", "fieldname", "nz", "wk", "pk", "l1", "i1", "d1", "b1", "l2", "i2", "d2", "b2", "base", "act", "T_with_dep_action", "T_with_dep_action", "fieldname", "nz1", "pk1", "i1", "d1", "l1", "i2", "d2", "l2", "b2", "head", "act", "T_with_comment", "T_with_comment", "fieldname", "nz", "wk", "pk", "l", "i", "d", "b", "t", "c", "T_nlist", "T_nlist", "fieldname", "wk", "pk", "i", "l", "d", "b", "n", "t", "T_at_most", "T_at_most", "fieldname", "nz", "wk", "pk", "i", "d", "l", "b", "n", "t", "T_exact", "T_exact", "fieldname", "nz", "wk", "pk", "i", "d", "l", "b", "n", "t", "T_string", "T_string", "fieldname", "pk1", "element_type", "terminator", "let coerce (#[@@@erasable]a:Type)\r\n (#[@@@erasable]b:Type)\r\n ( [@@@erasable]pf:squash (a == b))\r\n (x:a) \r\n : b \r\n = x", "let t_probe_then_validate\r\n (fieldname:string)\r\n (probe:CP.probe_fn)\r\n (len:U64.t)\r\n (dest:CP.copy_buffer_t)\r\n (#nz #wk:_) (#pk:P.parser_kind nz wk)\r\n (#has_reader #i #disj:_)\r\n (#l:_)\r\n (td:dtyp pk has_reader i disj l)\r\n : typ (parser_kind_of_itype UInt64)\r\n (join_inv i (NonTrivial (A.copy_buffer_inv dest)))\r\n (join_disj disj (disjoint (NonTrivial (A.copy_buffer_loc dest)) l))\r\n (join_loc l (NonTrivial (A.copy_buffer_loc dest)))\r\n false\r\n = T_with_dep_action fieldname\r\n (DT_IType UInt64)\r\n (fun src ->\r\n Atomic_action (Action_probe_then_validate td src len dest probe))", "let rec as_type\r\n #nz #wk (#pk:P.parser_kind nz wk)\r\n #l #i #d #b\r\n (t:typ pk l i d b)\r\n : Tot Type0\r\n (decreases t)\r\n = match t with\r\n | T_false _ -> False\r\n\r\n | T_denoted _ td -> \r\n dtyp_as_type td\r\n\r\n | T_pair _ t1 t2 ->\r\n as_type t1 & as_type t2\r\n\r\n | T_dep_pair _ i t\r\n | T_dep_pair_with_action _ i t _ ->\r\n x:dtyp_as_type i & as_type (t x)\r\n\r\n | T_refine _ base refinement ->\r\n P.refine (dtyp_as_type base) refinement\r\n\r\n | T_refine_with_action _ base refinement _ ->\r\n P.refine (dtyp_as_type base) refinement\r\n\r\n | T_dep_pair_with_refinement _ base refinement t ->\r\n x:P.refine (dtyp_as_type base) refinement & as_type (t x)\r\n\r\n | T_dep_pair_with_refinement_and_action _ base refinement t _ ->\r\n x:P.refine (dtyp_as_type base) refinement & as_type (t x)\r\n\r\n | T_if_else b t0 t1 ->\r\n P.t_ite b (fun _ -> as_type (t0()))\r\n (fun _ -> as_type (t1()))\r\n\r\n | T_cases b t0 t1 ->\r\n P.t_ite b (fun _ -> as_type t0) (fun _ -> as_type t1)\r\n\r\n | T_with_action _ t _\r\n | T_with_comment _ t _ ->\r\n as_type t\r\n\r\n | T_with_dep_action _ i _ ->\r\n dtyp_as_type i\r\n\r\n | T_nlist _ n t ->\r\n P.nlist n (as_type t)\r\n\r\n | T_at_most _ n t ->\r\n P.t_at_most n (as_type t)\r\n\r\n | T_exact _ n t ->\r\n P.t_exact n (as_type t)\r\n\r\n | T_string _ elt_t terminator ->\r\n P.cstring (dtyp_as_type elt_t) terminator", "let rec as_parser\r\n #nz #wk (#pk:P.parser_kind nz wk)\r\n #l #i #d #b\r\n (t:typ pk l i d b)\r\n : Tot (P.parser pk (as_type t))\r\n (decreases t)\r\n = match t returns Tot (P.parser pk (as_type t)) with\r\n | T_false _ ->\r\n //assert_norm (as_type g T_false == False);\r\n P.parse_impos()\r\n\r\n | T_denoted _ d ->\r\n dtyp_as_parser d\r\n\r\n | T_pair _ t1 t2 ->\r\n //assert_norm (as_type g (T_pair t1 t2) == as_type g t1 * as_type g t2);\r\n let p1 = as_parser t1 in\r\n let p2 = as_parser t2 in\r\n P.parse_pair p1 p2\r\n\r\n | T_dep_pair _ i t\r\n | T_dep_pair_with_action _ i t _ ->\r\n //assert_norm (as_type g (T_dep_pair i t) == x:itype_as_type i & as_type g (t x));\r\n let pi = dtyp_as_parser i in\r\n P.parse_dep_pair pi (fun (x:dtyp_as_type i) -> as_parser (t x))\r\n\r\n | T_refine _ base refinement\r\n | T_refine_with_action _ base refinement _ ->\r\n //assert_norm (as_type g (T_refine base refinement) == P.refine (itype_as_type base) refinement);\r\n let pi = dtyp_as_parser base in\r\n P.parse_filter pi refinement\r\n\r\n | T_dep_pair_with_refinement _ base refinement k ->\r\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x)))\r\n\r\n\r\n | T_dep_pair_with_refinement_and_action _ base refinement k _ ->\r\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x)))\r\n\r\n | T_if_else b t0 t1 ->\r\n //assert_norm (as_type g (T_if_else b t0 t1) == P.t_ite b (as_type g t0) (as_type g t1));\r\n let p0 (_:squash b) = \r\n P.parse_weaken_right (as_parser (t0())) _\r\n in\r\n let p1 (_:squash (not b)) = \r\n P.parse_weaken_left (as_parser (t1())) _\r\n in\r\n P.parse_ite b p0 p1\r\n\r\n | T_cases b t0 t1 ->\r\n //assert_norm (as_type g (T_if_else b t0 t1) == P.t_ite b (as_type g t0) (as_type g t1));\r\n let p0 (_:squash b) = \r\n P.parse_weaken_right (as_parser t0) _\r\n in\r\n let p1 (_:squash (not b)) = \r\n P.parse_weaken_left (as_parser t1) _\r\n in\r\n P.parse_ite b p0 p1\r\n\r\n | T_with_action _ t a ->\r\n //assert_norm (as_type g (T_with_action t a) == as_type g t);\r\n as_parser t\r\n\r\n | T_with_dep_action _ i a ->\r\n //assert_norm (as_type g (T_with_dep_action i a) == itype_as_type i);\r\n dtyp_as_parser i\r\n\r\n | T_with_comment _ t c ->\r\n //assert_norm (as_type g (T_with_comment t c) == as_type g t);\r\n as_parser t\r\n\r\n | T_nlist _ n t ->\r\n P.parse_nlist n (as_parser t)\r\n\r\n | T_at_most _ n t ->\r\n P.parse_t_at_most n (as_parser t)\r\n\r\n | T_exact _ n t ->\r\n P.parse_t_exact n (as_parser t)\r\n\r\n | T_string _ elt_t terminator ->\r\n P.parse_string (dtyp_as_parser elt_t) terminator", "let rec as_reader #nz (#pk:P.parser_kind nz P.WeakKindStrongPrefix)\r\n (#[@@@erasable] inv:inv_index)\r\n (#[@@@erasable] d:disj_index)\r\n (#[@@@erasable] loc:loc_index)\r\n (t:typ pk inv d loc true)\r\n : leaf_reader (as_parser t)\r\n = match t with\r\n | T_denoted _n dt ->\r\n assert_norm (as_type (T_denoted _n dt) == dtyp_as_type dt);\r\n assert_norm (as_parser (T_denoted _n dt) == dtyp_as_parser dt);\r\n (| (), dtyp_as_leaf_reader dt |)\r\n | T_with_comment _n t _c ->\r\n assert_norm (as_type (T_with_comment _n t _c) == as_type t); \r\n assert_norm (as_parser (T_with_comment _n t _c) == as_parser t); \r\n as_reader t\r\n | T_false _n ->\r\n assert_norm (as_type (T_false _n) == False);\r\n assert_norm (as_parser (T_false _n) == P.parse_impos());\r\n (| (), A.read_impos |)", "let rec as_validator\r\n (typename:string)\r\n #nz #wk (#pk:P.parser_kind nz wk)\r\n (#[@@@erasable] inv:inv_index)\r\n (#[@@@erasable] disj:disj_index)\r\n (#[@@@erasable] loc:loc_index)\r\n #b\r\n (t:typ pk inv disj loc b)\r\n : Tot (A.validate_with_action_t #nz #wk #pk #(as_type t)\r\n (as_parser t)\r\n (interp_inv inv)\r\n (interp_disj disj)\r\n (interp_loc loc)\r\n b)\r\n (decreases t)\r\n = A.index_equations();\r\n match t\r\n returns Tot (\r\n A.validate_with_action_t #nz #wk #pk #(as_type t)\r\n (as_parser t)\r\n (interp_inv inv)\r\n (interp_disj disj)\r\n (interp_loc loc)\r\n b\r\n )\r\n with\r\n | T_false fn ->\r\n A.validate_with_error_handler typename fn (A.validate_impos())\r\n\r\n | T_denoted fn td ->\r\n assert_norm (as_type (T_denoted fn td) == dtyp_as_type td);\r\n assert_norm (as_parser (T_denoted fn td) == dtyp_as_parser td);\r\n A.validate_with_error_handler typename fn (A.validate_eta (dtyp_as_validator td))\r\n\r\n | T_pair fn t1 t2 ->\r\n assert_norm (as_type (T_pair fn t1 t2) == as_type t1 * as_type t2);\r\n assert_norm (as_parser (T_pair fn t1 t2) == P.parse_pair (as_parser t1) (as_parser t2));\r\n A.validate_pair fn\r\n (as_validator typename t1)\r\n (as_validator typename t2)\r\n \r\n | T_dep_pair fn i t ->\r\n assert_norm (as_type (T_dep_pair fn i t) == x:dtyp_as_type i & as_type (t x));\r\n assert_norm (as_parser (T_dep_pair fn i t) ==\r\n P.parse_dep_pair (dtyp_as_parser i) (fun (x:dtyp_as_type i) -> as_parser (t x)));\r\n A.validate_weaken_inv_loc (interp_inv inv) _ (interp_loc loc)\r\n (A.validate_dep_pair fn\r\n (A.validate_with_error_handler typename fn (dtyp_as_validator i))\r\n (dtyp_as_leaf_reader i)\r\n (fun x -> as_validator typename (t x)))\r\n\r\n | T_refine fn t f ->\r\n assert_norm (as_type (T_refine fn t f) == P.refine (dtyp_as_type t) f);\r\n assert_norm (as_parser (T_refine fn t f) == P.parse_filter (dtyp_as_parser t) f);\r\n A.validate_with_error_handler typename fn \r\n (A.validate_filter fn\r\n (dtyp_as_validator t)\r\n (dtyp_as_leaf_reader t)\r\n f \"reading field_value\" \"checking constraint\")\r\n\r\n | T_refine_with_action fn t f a ->\r\n assert_norm (as_type (T_refine_with_action fn t f a) == P.refine (dtyp_as_type t) f);\r\n assert_norm (as_parser (T_refine_with_action fn t f a) == P.parse_filter (dtyp_as_parser t) f);\r\n assert_norm (as_parser (T_refine fn t f) == P.parse_filter (dtyp_as_parser t) f); \r\n A.validate_with_error_handler typename fn \r\n (A.validate_filter_with_action fn\r\n (dtyp_as_validator t)\r\n (dtyp_as_leaf_reader t)\r\n f \"reading field_value\" \"checking constraint\"\r\n (fun x -> action_as_action (a x)))\r\n\r\n | T_dep_pair_with_refinement fn base refinement k ->\r\n assert_norm (as_type (T_dep_pair_with_refinement fn base refinement k) ==\r\n x:P.refine (dtyp_as_type base) refinement & as_type (k x));\r\n assert_norm (as_parser (T_dep_pair_with_refinement fn base refinement k) ==\r\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x))));\r\n A.validate_with_error_handler typename fn \r\n (A.validate_weaken_inv_loc _ _ _ (\r\n A.validate_dep_pair_with_refinement false fn\r\n (dtyp_as_validator base)\r\n (dtyp_as_leaf_reader base)\r\n refinement\r\n (fun x -> as_validator typename (k x))))\r\n\r\n | T_dep_pair_with_action fn base t act ->\r\n assert_norm (as_type (T_dep_pair_with_action fn base t act) ==\r\n x:dtyp_as_type base & as_type (t x));\r\n assert_norm (as_parser (T_dep_pair_with_action fn base t act) ==\r\n P.(dtyp_as_parser base `parse_dep_pair` (fun x -> as_parser (t x))));\r\n A.validate_with_error_handler typename fn \r\n (A.validate_weaken_inv_loc _ _ _ (\r\n A.validate_dep_pair_with_action \r\n (dtyp_as_validator base)\r\n (dtyp_as_leaf_reader base)\r\n (fun x -> action_as_action (act x))\r\n (fun x -> as_validator typename (t x))))\r\n\r\n | T_dep_pair_with_refinement_and_action fn base refinement k act ->\r\n assert_norm (as_type (T_dep_pair_with_refinement_and_action fn base refinement k act) ==\r\n x:P.refine (dtyp_as_type base) refinement & as_type (k x));\r\n assert_norm (as_parser (T_dep_pair_with_refinement_and_action fn base refinement k act) ==\r\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x))));\r\n A.validate_weaken_inv_loc _ _ _ (\r\n A.validate_dep_pair_with_refinement_and_action false fn\r\n (A.validate_with_error_handler typename fn \r\n (dtyp_as_validator base))\r\n (dtyp_as_leaf_reader base)\r\n refinement\r\n (fun x -> action_as_action (act x))\r\n (fun x -> as_validator typename (k x)))\r\n\r\n\r\n | T_if_else b t0 t1 ->\r\n assert_norm (as_type (T_if_else b t0 t1) == P.t_ite b (fun _ -> as_type (t0())) (fun _ -> as_type (t1 ())));\r\n let p0 (_:squash b) = P.parse_weaken_right (as_parser (t0())) _ in\r\n let p1 (_:squash (not b)) = P.parse_weaken_left (as_parser (t1())) _ in\r\n assert_norm (as_parser (T_if_else b t0 t1) == P.parse_ite b p0 p1);\r\n let v0 (_:squash b) = \r\n A.validate_weaken_right (as_validator typename (t0())) _\r\n in\r\n let v1 (_:squash (not b)) =\r\n A.validate_weaken_left (as_validator typename (t1())) _\r\n in\r\n A.validate_ite b p0 v0 p1 v1\r\n\r\n | T_cases b t0 t1 ->\r\n assert_norm (as_type (T_cases b t0 t1) == P.t_ite b (fun _ -> as_type t0) (fun _ -> as_type t1));\r\n let p0 (_:squash b) = P.parse_weaken_right (as_parser t0) _ in\r\n let p1 (_:squash (not b)) = P.parse_weaken_left (as_parser t1) _ in\r\n assert_norm (as_parser (T_cases b t0 t1) == P.parse_ite b p0 p1);\r\n let v0 (_:squash b) = \r\n A.validate_weaken_right (as_validator typename t0) _\r\n in\r\n let v1 (_:squash (not b)) =\r\n A.validate_weaken_left (as_validator typename t1) _\r\n in\r\n A.validate_ite b p0 v0 p1 v1\r\n \r\n | T_with_action fn t a ->\r\n assert_norm (as_type (T_with_action fn t a) == as_type t);\r\n assert_norm (as_parser (T_with_action fn t a) == as_parser t);\r\n A.validate_with_error_handler typename fn \r\n (A.validate_with_success_action fn\r\n (as_validator typename t)\r\n (action_as_action a))\r\n\r\n | T_with_dep_action fn i a ->\r\n assert_norm (as_type (T_with_dep_action fn i a) == dtyp_as_type i);\r\n assert_norm (as_parser (T_with_dep_action fn i a) == dtyp_as_parser i);\r\n A.validate_with_error_handler typename fn \r\n (A.validate_weaken_inv_loc _ _ _ (\r\n A.validate_with_dep_action fn\r\n (dtyp_as_validator i)\r\n (dtyp_as_leaf_reader i)\r\n (fun x -> action_as_action (a x))))\r\n\r\n\r\n | T_with_comment fn t c ->\r\n assert_norm (as_type (T_with_comment fn t c) == as_type t);\r\n assert_norm (as_parser (T_with_comment fn t c) == as_parser t);\r\n A.validate_with_comment c (as_validator typename t)\r\n\r\n | T_nlist fn n t ->\r\n assert_norm (as_type (T_nlist fn n t) == P.nlist n (as_type t));\r\n assert_norm (as_parser (T_nlist fn n t) == P.parse_nlist n (as_parser t));\r\n A.validate_with_error_handler typename fn \r\n (A.validate_nlist n (as_validator typename t))\r\n\r\n | T_at_most fn n t ->\r\n assert_norm (as_type (T_at_most fn n t) == P.t_at_most n (as_type t));\r\n assert_norm (as_parser (T_at_most fn n t) == P.parse_t_at_most n (as_parser t));\r\n A.validate_with_error_handler typename fn \r\n (A.validate_t_at_most n (as_validator typename t))\r\n\r\n | T_exact fn n t ->\r\n assert_norm (as_type (T_exact fn n t) == P.t_exact n (as_type t));\r\n assert_norm (as_parser (T_exact fn n t) == P.parse_t_exact n (as_parser t));\r\n A.validate_with_error_handler typename fn \r\n (A.validate_t_exact n (as_validator typename t))\r\n\r\n | T_string fn elt_t terminator ->\r\n assert_norm (as_type (T_string fn elt_t terminator) == P.cstring (dtyp_as_type elt_t) terminator);\r\n assert_norm (as_parser (T_string fn elt_t terminator) == P.parse_string (dtyp_as_parser elt_t) terminator);\r\n A.validate_with_error_handler typename fn \r\n (A.validate_string (dtyp_as_validator elt_t)\r\n (dtyp_as_leaf_reader elt_t)\r\n terminator)", "let validator_of #allow_reading #nz #wk (#k:P.parser_kind nz wk)\r\n (#[@@@erasable] i:inv_index)\r\n (#[@@@erasable] d:disj_index)\r\n (#[@@@erasable] l:loc_index)\r\n (t:typ k i d l allow_reading) = \r\n A.validate_with_action_t\r\n (as_parser t) \r\n (interp_inv i)\r\n (interp_disj d)\r\n (interp_loc l)\r\n allow_reading", "let dtyp_of #nz #wk (#k:P.parser_kind nz wk)\r\n (#[@@@erasable] i:inv_index)\r\n (#[@@@erasable] d:disj_index)\r\n (#[@@@erasable] l:loc_index)\r\n #b (t:typ k i d l b) = \r\n dtyp k b i d l", "let specialization_steps =\r\n [nbe;\r\n zeta;\r\n primops;\r\n iota;\r\n delta_attr [`%specialize];\r\n delta_only ([`%Some?;\r\n `%Some?.v;\r\n `%as_validator;\r\n `%nz_of_binding;\r\n `%wk_of_binding;\r\n `%pk_of_binding;\r\n `%inv_of_binding;\r\n `%loc_of_binding;\r\n `%type_of_binding;\r\n `%parser_of_binding;\r\n `%validator_of_binding;\r\n `%leaf_reader_of_binding;\r\n `%fst;\r\n `%snd;\r\n `%Mktuple2?._1;\r\n `%Mktuple2?._2]@projector_names)]", "let specialize_tac steps (_:unit)\r\n : T.Tac unit\r\n = let open FStar.List.Tot in\r\n T.norm (steps@specialization_steps);\r\n T.trefl()", "let mk_global_binding #nz #wk \r\n (pk:P.parser_kind nz wk)\r\n ([@@@erasable] inv:inv_index)\r\n ([@@@erasable] disj:disj_index)\r\n ([@@@erasable] loc:loc_index)\r\n ([@@@erasable] p_t : Type0)\r\n ([@@@erasable] p_p : P.parser pk p_t)\r\n (p_reader: option (leaf_reader p_p))\r\n (b:bool)\r\n (p_v : A.validate_with_action_t p_p \r\n (interp_inv inv)\r\n (interp_disj disj)\r\n (interp_loc loc) b)\r\n ([@@@erasable] pf:squash (b == Some? p_reader))\r\n : global_binding\r\n = {\r\n parser_kind_nz = nz;\r\n parser_weak_kind = wk;\r\n parser_kind = pk;\r\n inv = inv;\r\n disj;\r\n loc = loc;\r\n p_t = p_t;\r\n p_p = p_p;\r\n p_reader = p_reader;\r\n p_v = p_v\r\n }", "let mk_dt_app #nz #wk (pk:P.parser_kind nz wk) (b:bool)\r\n ([@@@erasable] inv:inv_index)\r\n ([@@@erasable] disj:disj_index)\r\n ([@@@erasable] loc:loc_index)\r\n (x:global_binding)\r\n ([@@@erasable] pf:squash (nz == nz_of_binding x /\\\r\n wk == wk_of_binding x /\\\r\n pk == pk_of_binding x /\\\r\n b == has_reader x /\\\r\n inv == inv_of_binding x /\\\r\n disj == disj_of_bindng x /\\\r\n loc == loc_of_binding x))\r\n : dtyp #nz #wk pk b inv disj loc\r\n = DT_App pk b inv disj loc x pf" ], "closest": [ "val validate_with_action_t\r\n (#nz:bool)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#t:Type)\r\n (p:parser k t)\r\n (liveness_inv:slice_inv)\r\n (disj:disjointness_pre)\r\n (l:eloc)\r\n (allow_reading:bool)\r\n : Type0\nlet validate_with_action_t p inv disj l allow_reading = validate_with_action_t' p inv disj l allow_reading", "val probe_then_validate\r\n (#nz:bool)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#t:Type)\r\n (#p:parser k t)\r\n (#inv:slice_inv)\r\n (#disj:disjointness_pre)\r\n (#l:eloc)\r\n (#allow_reading:bool)\r\n (v:validate_with_action_t p inv disj l allow_reading)\r\n (src:U64.t)\r\n (len:U64.t)\r\n (dest:CP.copy_buffer_t)\r\n (probe:CP.probe_fn)\r\n : action (conj_inv inv (copy_buffer_inv dest))\r\n (conj_disjointness disj (disjoint (copy_buffer_loc dest) l))\r\n (eloc_union l (copy_buffer_loc dest)) \r\n true\r\n bool\nlet probe_then_validate \n (#nz:bool)\n (#wk: _)\n (#k:parser_kind nz wk)\n (#t:Type)\n (#p:parser k t)\n (#inv:slice_inv)\n (#disj:_)\n (#l:eloc)\n (#allow_reading:bool)\n (v:validate_with_action_t p inv disj l allow_reading)\n (src:U64.t)\n (len:U64.t)\n (dest:CP.copy_buffer_t)\n (probe:CP.probe_fn)\n = fun ctxt error_handler_fn input input_length pos posf ->\n CP.properties dest;\n let h0 = HST.get () in\n let b = probe src len dest in\n if b\n then (\n let h1 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h0 h1;\n let result = v ctxt error_handler_fn (CP.stream_of dest) (CP.stream_len dest) 0uL in\n not (LPE.is_error result)\n )\n else false", "val validate_weaken_right\r\n (#nz:_)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v:validate_with_action_t p inv disj l allow_reading)\r\n (#nz':_)\r\n (#wk': _)\r\n (k':parser_kind nz' wk')\r\n : validate_with_action_t (parse_weaken_right p k') inv disj l allow_reading\nlet validate_weaken_right\n #nz #wk (#k:parser_kind nz wk) (#t:_) (#p:parser k t)\n #inv #disj #l #ar (v:validate_with_action_t p inv disj l ar)\n #nz' #wk' (k':parser_kind nz' wk')\n= validate_weaken v (glb k k')", "val validate_weaken_inv_loc\r\n (#nz:_)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n ([@@@erasable] inv':slice_inv{inv' `inv_implies` inv})\r\n ([@@@erasable] disj':disjointness_pre { disj' `imp_disjointness` disj })\r\n ([@@@erasable] l':eloc{l' `eloc_includes` l})\r\n (v:validate_with_action_t p inv disj l allow_reading)\r\n : Tot (validate_with_action_t p inv' disj' l' allow_reading)\nlet validate_weaken_inv_loc\n #nz #wk (#k:parser_kind nz wk) #t (#p:parser k t)\n #inv #disj (#l:eloc) #ar\n (inv':slice_inv{inv' `inv_implies` inv})\n (disj':_{ disj' `imp_disjointness` disj})\n (l':eloc{l' `eloc_includes` l})\n (v:validate_with_action_t p inv disj l ar)\n : Tot (validate_with_action_t p inv' disj' l' ar)\n = v", "val validate_weaken_left\r\n (#nz:_)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v:validate_with_action_t p inv disj l allow_reading)\r\n (#nz':_)\r\n (#wk': _)\r\n (k':parser_kind nz' wk')\r\n : validate_with_action_t (parse_weaken_left p k') inv disj l allow_reading\nlet validate_weaken_left \n #nz #wk (#k:parser_kind nz wk) (#t:_) (#p:parser k t)\n #inv #disj #l #ar (v:validate_with_action_t p inv disj l ar)\n #nz' #wk' (k':parser_kind nz' wk')\n= validate_weaken v (glb k' k)", "val leaf_reader\r\n (#nz:bool)\r\n (#k: parser_kind nz WeakKindStrongPrefix)\r\n (#t: Type)\r\n (p: parser k t)\r\n : Type u#0\nlet leaf_reader\n #nz\n #k\n (#t: Type)\n (p: parser k t)\n: Tot Type\n=\n (# [EverParse3d.Util.solve_from_ctx ()] _extra_t : I.extra_t #input_buffer_t ) ->\n (sl: input_buffer_t) ->\n (pos: LPE.pos_t) ->\n Stack t\n (requires (fun h ->\n valid p h sl /\\\n U64.v pos == Seq.length (I.get_read sl h)\n ))\n (ensures (fun h res h' ->\n let s = I.get_remaining sl h in\n I.live sl h' /\\\n modifies (I.perm_footprint sl) h h' /\\\n begin match LP.parse p s with\n | None -> False\n | Some (y, len) ->\n res == y /\\\n I.get_remaining sl h' == Seq.slice s len (Seq.length s)\n end\n ))", "val validate_eta\r\n (#nz:bool)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre)\r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v: validate_with_action_t p inv disj l allow_reading)\r\n: Tot (validate_with_action_t p inv disj l allow_reading)\nlet validate_eta v =\n fun ctxt error_handler_fn sl pos -> v ctxt error_handler_fn sl pos", "val validate_with_dep_action\r\n (name: string)\r\n (#nz:_)\r\n (#k:parser_kind nz WeakKindStrongPrefix)\r\n (#t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (v:validate_with_action_t p inv disj l true)\r\n (r:leaf_reader p)\r\n (#b:bool)\r\n (#[@@@erasable] inva:slice_inv)\r\n (#[@@@erasable] disja:disjointness_pre) \r\n (#[@@@erasable] la:eloc)\r\n (a: t -> action inva disja la b bool)\r\n : validate_with_action_t #nz\r\n p\r\n (conj_inv inv inva)\r\n (conj_disjointness disj disja)\r\n (eloc_union l la)\r\n false\nlet validate_with_dep_action\n (name: string)\n #nz (#k:parser_kind nz _) (#t:_) (#p:parser k t)\n #inv #disj #l\n (v:validate_with_action_t p inv disj l true)\n (r:leaf_reader p)\n (#b:bool) #inva #disja (#la:eloc)\n (a: t -> action inva disja la b bool)\n= fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos0 = start_position in\n let h = HST.get () in\n [@(rename_let (\"positionAfter\" ^ name))]\n let res = v ctxt error_handler_fn input input_length pos0 in\n let h1 = HST.get () in\n if LPE.is_error res\n then res\n else begin\n [@(rename_let (\"\" ^ name))]\n let field_value = r input pos0 in\n let h15 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h h15 in\n if a field_value ctxt error_handler_fn input input_length pos0 res\n then res\n else LPE.set_validator_error_pos LPE.validator_error_action_failed res\n end", "val validate_with_comment\r\n (c:string)\r\n (#nz:_)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v:validate_with_action_t p inv disj l allow_reading)\r\n : validate_with_action_t p inv disj l allow_reading\nlet validate_with_comment\n (c:string)\n #nz #wk (#k:parser_kind nz wk) #t (#p:parser k t)\n #inv #disj #l #ar (v:validate_with_action_t p inv disj l ar)\n: validate_with_action_t p inv disj l ar\n= fun ctxt error_handler_fn input input_length start_position ->\n LowParse.Low.Base.comment c;\n v ctxt error_handler_fn input input_length start_position", "val validate_list_inv\n (#k: LPL.parser_kind)\n (#t: Type)\n (p: LPL.parser k t)\n (inv: slice_inv)\n (disj: disjointness_pre)\n (l: eloc)\n (g0 g1: Ghost.erased HS.mem)\n (ctxt: app_ctxt)\n (sl: input_buffer_t)\n (bres: pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet validate_list_inv\n (#k: LPL.parser_kind)\n (#t: Type)\n (p: LPL.parser k t)\n (inv: slice_inv)\n (disj: disjointness_pre)\n (l: eloc)\n (g0 g1: Ghost.erased HS.mem)\n (ctxt:app_ctxt)\n (sl: input_buffer_t)\n (bres: pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n= let h0 = Ghost.reveal g0 in\n let h1 = Ghost.reveal g1 in\n let res = Seq.index (as_seq h bres) 0 in\n inv h0 /\\\n disj /\\\n loc_not_unused_in h0 `loc_includes` app_loc ctxt l /\\\n app_loc ctxt l `loc_disjoint` I.footprint sl /\\\n app_loc ctxt l `loc_disjoint` loc_buffer bres /\\\n address_liveness_insensitive_locs `loc_includes` app_loc ctxt l /\\\n B.loc_buffer bres `B.loc_disjoint` I.footprint sl /\\\n I.live sl h0 /\\\n I.live sl h /\\\n live h0 ctxt /\\\n live h ctxt /\\\n live h1 bres /\\\n begin\n let s = I.get_remaining sl h0 in\n let s' = I.get_remaining sl h in\n Seq.length s' <= Seq.length s /\\\n s' `Seq.equal` Seq.slice s (Seq.length s - Seq.length s') (Seq.length s)\n end /\\\n modifies loc_none h0 h1 /\\ (\n if\n LPE.is_error res\n then\n // validation *or action* failed\n stop == true /\\\n U64.v (LPE.get_validator_error_pos res) == Seq.length (I.get_read sl h) /\\\n (LPE.get_validator_error_kind res <> LPE.get_validator_error_kind LPE.validator_error_action_failed ==> ~ (valid (LPLL.parse_list p) h0 sl))\n else\n U64.v res == Seq.length (I.get_read sl h) /\\\n (valid (LPLL.parse_list p) h0 sl <==>\n valid (LPLL.parse_list p) h sl) /\\\n (stop == true ==> (valid (LPLL.parse_list p) h sl /\\ Seq.length (I.get_remaining sl h) == 0))\n ) /\\\n modifies (app_loc ctxt l `loc_union` loc_buffer bres `loc_union` I.perm_footprint sl) h1 h", "val parser (#nz:bool) (#wk: weak_kind) (k:parser_kind nz wk) (t:Type u#r) : Type u#r\nlet parser k t = LP.parser k t", "val parse_ite (#nz:_) (#wk: _) (#k:parser_kind nz wk)\r\n (e:bool)\r\n (#a:squash e -> Type)\r\n (#b:squash (not e) -> Type)\r\n (p1:squash e -> parser k (a()))\r\n (p2:squash (not e) -> parser k (b()))\r\n : Tot (parser k (t_ite e a b))\nlet parse_ite e p1 p2\r\n = if e then p1 () else p2 ()", "val validate_ite\r\n (#nz:_)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (e:bool)\r\n (#[@@@erasable] a:squash e -> Type)\r\n (#[@@@erasable] b:squash (not e) -> Type)\r\n (#[@@@erasable] inv1:slice_inv)\r\n (#[@@@erasable] disj1:disjointness_pre)\r\n (#[@@@erasable] l1:eloc)\r\n (#ar1:_)\r\n (#[@@@erasable] inv2:slice_inv)\r\n (#[@@@erasable] disj2:disjointness_pre)\r\n (#[@@@erasable] l2:eloc)\r\n (#ar2:_)\r\n ([@@@erasable] p1:squash e -> parser k (a()))\r\n (v1:(squash e -> validate_with_action_t (p1()) inv1 disj1 l1 ar1))\r\n ([@@@erasable] p2:squash (not e) -> parser k (b()))\r\n (v2:(squash (not e) -> validate_with_action_t (p2()) inv2 disj2 l2 ar2))\r\n : validate_with_action_t\r\n (parse_ite e p1 p2)\r\n (conj_inv inv1 inv2)\r\n (conj_disjointness disj1 disj2)\r\n (l1 `eloc_union` l2)\r\n false\nlet validate_ite\n e p1 v1 p2 v2\n= fun ctxt error_handler_fn input input_len start_position ->\n if e \n then validate_drop (v1 ()) ctxt error_handler_fn input input_len start_position\n else validate_drop (v2 ()) ctxt error_handler_fn input input_len start_position", "val validate_with_error_handler\r\n (typename: string)\r\n (fieldname: string)\r\n (#nz: _)\r\n (#wk: _)\r\n (#k1:parser_kind nz wk)\r\n (#[@@@erasable] t1: Type)\r\n (#[@@@erasable] p1:parser k1 t1)\r\n (#[@@@erasable] inv1:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre)\r\n (#[@@@erasable] l1:eloc)\r\n (#ar:_)\r\n (v1:validate_with_action_t p1 inv1 disj l1 ar)\r\n : validate_with_action_t p1 inv1 disj l1 ar\nlet validate_with_error_handler\n (typename:string) \n (fieldname:string)\n #nz\n #wk\n (#k1:parser_kind nz wk)\n #t1\n (#p1:parser k1 t1)\n (#inv1 #disj1:_)\n (#l1:eloc)\n (#ar:_)\n (v1:validate_with_action_t p1 inv1 disj1 l1 ar)\n : validate_with_action_t p1 inv1 disj1 l1 ar\n = fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos0 = start_position in\n let h0 = HST.get () in\n [@(rename_let (\"positionAfter\" ^ typename))]\n let pos1 = v1 ctxt error_handler_fn input input_length pos0 in\n let h1 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h0 h1;\n if LPE.is_success pos1\n then pos1\n else (\n error_handler_fn typename fieldname (LPE.error_reason_of_result pos1) (LPE.get_validator_error_kind pos1) ctxt input pos0;\n pos1\n )", "val validate_total_constant_size_no_read\n (#nz #wk: _)\n (#k: parser_kind nz wk)\n (#t: Type)\n (p: parser k t)\n (sz: U64.t)\n (u:\n unit\n { k.LP.parser_kind_high == Some k.LP.parser_kind_low /\\ k.LP.parser_kind_low == U64.v sz /\\\n k.LP.parser_kind_metadata == Some LP.ParserKindMetadataTotal })\n (inv disj l: _)\n : Tot (validate_with_action_t p inv disj l true)\nlet validate_total_constant_size_no_read\n #nz #wk\n (#k: parser_kind nz wk)\n (#t: Type)\n (p: parser k t)\n (sz: U64.t)\n (u: unit {\n k.LP.parser_kind_high == Some k.LP.parser_kind_low /\\\n k.LP.parser_kind_low == U64.v sz /\\\n k.LP.parser_kind_metadata == Some LP.ParserKindMetadataTotal\n })\n inv disj l\n: Tot (validate_with_action_t p inv disj l true)\n= validate_total_constant_size_no_read' p sz u inv disj l", "val filter_kind (#nz:_) (#wk: _) (k:parser_kind nz wk)\r\n : parser_kind nz wk\nlet filter_kind (#nz:_) (#wk: _) (k:parser_kind nz wk)\r\n : parser_kind nz wk\r\n = LPC.parse_filter_kind k", "val validate_weaken\n (#nz #wk: _)\n (#k: parser_kind nz wk)\n (#t: _)\n (#p: parser k t)\n (#inv #disj #l #ar: _)\n (v: validate_with_action_t p inv disj l ar)\n (#nz' #wk': _)\n (k': parser_kind nz' wk' {k' `is_weaker_than` k})\n : validate_with_action_t (parse_weaken p k') inv disj l ar\nlet validate_weaken\n #nz #wk (#k:parser_kind nz wk) #t (#p:parser k t)\n #inv #disj #l #ar (v:validate_with_action_t p inv disj l ar)\n #nz' #wk' (k':parser_kind nz' wk'{k' `is_weaker_than` k})\n: validate_with_action_t (parse_weaken p k') inv disj l ar\n= fun ctxt error_handler_fn input input_length start_position ->\n v ctxt error_handler_fn input input_length start_position", "val validate_nlist\r\n (n:U32.t)\r\n (#wk: _)\r\n (#k:parser_kind true wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v: validate_with_action_t p inv disj l allow_reading)\r\n: validate_with_action_t (parse_nlist n p) inv disj l false\nlet validate_nlist\n (n:U32.t)\n #wk\n (#k:parser_kind true wk)\n #t\n (#p:parser k t)\n #inv #disj #l #ar\n (v: validate_with_action_t p inv disj l ar)\n: Tot (validate_with_action_t (parse_nlist n p) inv disj l false)\n= validate_weaken\n #false #WeakKindStrongPrefix #(LowParse.Spec.FLData.parse_fldata_kind (U32.v n) LowParse.Spec.List.parse_list_kind) #(list t)\n (validate_fldata_consumes_all n (validate_list v))\n kind_nlist", "val validate_with_success_action'\n (name: string)\n (#nz #wk: _)\n (#k1: parser_kind nz wk)\n (#t1: _)\n (#p1: parser k1 t1)\n (#inv1 #disj1: _)\n (#l1: eloc)\n (v1: validate_with_action_t p1 inv1 disj1 l1 false)\n (#inv2 #disj2: _)\n (#l2: eloc)\n (#b: _)\n (a: action inv2 disj2 l2 b bool)\n : validate_with_action_t p1\n (conj_inv inv1 inv2)\n (conj_disjointness disj1 disj2)\n (l1 `eloc_union` l2)\n false\nlet validate_with_success_action'\n (name: string)\n #nz #wk (#k1:parser_kind nz wk)\n #t1 (#p1:parser k1 t1)\n (#inv1:_) (#disj1:_) (#l1:eloc)\n (v1:validate_with_action_t p1 inv1 disj1 l1 false)\n (#inv2:_) (#disj2:_) (#l2:eloc) #b\n (a:action inv2 disj2 l2 b bool)\n : validate_with_action_t p1 \n (conj_inv inv1 inv2)\n (conj_disjointness disj1 disj2)\n (l1 `eloc_union` l2)\n false\n = fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos0 = start_position in\n let h0 = HST.get () in\n [@(rename_let (\"positionAfter\" ^ name))]\n let pos1 = v1 ctxt error_handler_fn input input_length pos0 in\n let h1 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h0 h1;\n if LPE.is_success pos1\n then\n [@(rename_let (\"action_success_\" ^ name))]\n let b = a ctxt error_handler_fn input input_length pos0 pos1 in\n let h2 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h1 h2;\n if not b\n then LPE.set_validator_error_pos LPE.validator_error_action_failed pos1\n else pos1\n else\n pos1", "val validate_t_exact\r\n (n:U32.t)\r\n (#nz:bool)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#ar:_)\r\n (v:validate_with_action_t p inv disj l ar)\r\n : Tot (validate_with_action_t (parse_t_exact n p) inv disj l false)\nlet validate_t_exact\n (n:U32.t) #nz #wk (#k:parser_kind nz wk) (#t:_) (#p:parser k t)\n #inv #disj #l #ar\n (v:validate_with_action_t p inv disj l ar)\n: validate_with_action_t (parse_t_exact n p) inv disj l false\n= fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = HST.get () in\n let hasBytes = I.has input input_length pos (Cast.uint32_to_uint64 n) in\n let h1 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h h1;\n if not hasBytes\n then\n LPE.set_validator_error_pos LPE.validator_error_not_enough_data pos\n else\n let truncatedInput = I.truncate input pos (Cast.uint32_to_uint64 n) in\n let truncatedInputLength = I.truncate_len input pos (Cast.uint32_to_uint64 n) truncatedInput in\n let h2 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h h2 in\n let _ = I.is_prefix_of_prop truncatedInput input h2 in\n let _ = assert (I.get_remaining truncatedInput h2 `Seq.equal` Seq.slice (I.get_remaining input h) 0 (U32.v n)) in\n [@inline_let] let _ = LPC.nondep_then_eq p parse_all_bytes (I.get_remaining truncatedInput h2) in\n let result = validate_drop v ctxt error_handler_fn truncatedInput truncatedInputLength pos in\n let h3 = HST.get () in\n let _ = I.is_prefix_of_prop truncatedInput input h3 in\n if LPE.is_error result\n then result\n else begin\n let stillHasBytes = I.has truncatedInput truncatedInputLength result 1uL in\n let h4 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h h4;\n I.is_prefix_of_prop truncatedInput input h4;\n if stillHasBytes\n then LPE.set_validator_error_pos LPE.validator_error_unexpected_padding result\n else result\n end", "val validate_t_at_most\r\n (n:U32.t)\r\n (#nz: _)\r\n (#wk: _)\r\n (#k:parser_kind nz wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#ar:_)\r\n (v:validate_with_action_t p inv disj l ar)\r\n : Tot (validate_with_action_t (parse_t_at_most n p) inv disj l false)\nlet validate_t_at_most\n (n:U32.t) #nz #wk (#k:parser_kind nz wk) (#t:_) (#p:parser k t)\n #inv #disj #l #ar (v:validate_with_action_t p inv disj l ar)\n : Tot (validate_with_action_t (parse_t_at_most n p) inv disj l false)\n = fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = HST.get () in\n let hasBytes = I.has input input_length pos (Cast.uint32_to_uint64 n) in\n let h1 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h h1;\n if not hasBytes\n then\n LPE.set_validator_error_pos LPE.validator_error_not_enough_data pos\n else\n let truncatedInput = I.truncate input pos (Cast.uint32_to_uint64 n) in\n let truncatedInputLength = I.truncate_len input pos (Cast.uint32_to_uint64 n) truncatedInput in\n let h2 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h h2 in\n let _ = I.is_prefix_of_prop truncatedInput input h2 in\n let _ = assert (I.get_remaining truncatedInput h2 `Seq.equal` Seq.slice (I.get_remaining input h) 0 (U32.v n)) in\n [@inline_let] let _ = LPC.nondep_then_eq p parse_all_bytes (I.get_remaining truncatedInput h2) in\n let result = validate_drop v ctxt error_handler_fn truncatedInput truncatedInputLength pos in\n let h3 = HST.get () in\n let _ = I.is_prefix_of_prop truncatedInput input h3 in\n if LPE.is_error result\n then result\n else begin\n let _ = I.empty truncatedInput truncatedInputLength result in\n let h4 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h h4;\n let _ = I.is_prefix_of_prop truncatedInput input h4 in\n pos `U64.add` Cast.uint32_to_uint64 n\n end", "val validate_with_success_action\r\n (name: string)\r\n (#nz:bool)\r\n (#wk: _)\r\n (#k1:parser_kind nz wk)\r\n (#[@@@erasable] t1:Type)\r\n (#[@@@erasable] p1:parser k1 t1)\r\n (#[@@@erasable] inv1:slice_inv)\r\n (#[@@@erasable] disj1:disjointness_pre)\r\n (#[@@@erasable] l1:eloc)\r\n (#allow_reading:bool)\r\n (v1:validate_with_action_t p1 inv1 disj1 l1 allow_reading)\r\n (#[@@@erasable] inv2:slice_inv)\r\n (#[@@@erasable] disj2:disjointness_pre)\r\n (#[@@@erasable] l2:eloc)\r\n (#b:bool)\r\n (a:action inv2 disj2 l2 b bool)\r\n : validate_with_action_t p1 (conj_inv inv1 inv2) (conj_disjointness disj1 disj2) (l1 `eloc_union` l2) false\nlet validate_with_success_action\n name v1 a\n= validate_with_success_action' name (validate_drop v1) a", "val validate_dep_pair_with_action\r\n (#nz1:_)\r\n (#k1:parser_kind nz1 WeakKindStrongPrefix)\r\n (#t1:Type)\r\n (#[@@@erasable] p1:parser k1 t1)\r\n (#[@@@erasable] inv1:slice_inv)\r\n (#[@@@erasable] disj1:disjointness_pre)\r\n (#[@@@erasable] l1:eloc)\r\n (v1:validate_with_action_t p1 inv1 disj1 l1 true)\r\n (r1: leaf_reader p1)\r\n (#[@@@erasable] inv1':slice_inv)\r\n (#[@@@erasable] disj1':disjointness_pre)\r\n (#[@@@erasable] l1':eloc)\r\n (#b:_)\r\n (a:t1 -> action inv1' disj1' l1' b bool)\r\n (#nz2:_)\r\n (#wk2: _)\r\n (#k2:parser_kind nz2 wk2)\r\n (#[@@@erasable] t2:t1 -> Type)\r\n (#[@@@erasable] p2:(x:t1 -> parser k2 (t2 x)))\r\n (#[@@@erasable] inv2:slice_inv)\r\n (#[@@@erasable] disj2:disjointness_pre)\r\n (#[@@@erasable] l2:eloc)\r\n (#allow_reading2:_)\r\n (v2:(x:t1 -> validate_with_action_t (p2 x) inv2 disj2 l2 allow_reading2))\r\n : validate_with_action_t\r\n (p1 `(parse_dep_pair #nz1)` p2)\r\n (conj_inv inv1 (conj_inv inv1' inv2))\r\n (conj_disjointness disj1 (conj_disjointness disj1' disj2))\r\n (l1 `eloc_union` (l1' `eloc_union` l2))\r\n false\nlet validate_dep_pair_with_action\n #nz1 (#k1:parser_kind nz1 _) #t1 (#p1:parser k1 t1)\n #inv1 #disj1 #l1 (v1:validate_with_action_t p1 inv1 disj1 l1 true) (r1: leaf_reader p1)\n #inv1' #disj1' #l1' #b (a:t1 -> action inv1' disj1' l1' b bool)\n #nz2 #wk2 (#k2:parser_kind nz2 wk2) (#t2:t1 -> Type) (#p2:(x:t1 -> parser k2 (t2 x)))\n #inv2 #disj2 #l2 #ar2 (v2:(x:t1 -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n = fun ctxt error_handler_fn input input_length startPosition ->\n let h0 = HST.get () in\n LPC.parse_dtuple2_eq' #_ #_ p1 #_ #t2 p2 (I.get_remaining input h0);\n let res = v1 ctxt error_handler_fn input input_length startPosition in\n let h1 = HST.get() in\n modifies_address_liveness_insensitive_unused_in h0 h1;\n if LPE.is_error res\n then begin\n res\n end\n else begin\n let field_value = r1 input startPosition in\n let h2 = HST.get() in\n modifies_address_liveness_insensitive_unused_in h1 h2;\n let action_result = a field_value ctxt error_handler_fn input input_length startPosition res in\n let h3 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h2 h3;\n if not action_result\n then LPE.set_validator_error_pos LPE.validator_error_action_failed res //action failed\n else\n validate_drop (v2 field_value) ctxt error_handler_fn input input_length res\n end", "val parser_kind (nz:bool) (wk: weak_kind) : Type0\nlet parser_kind (nz:bool) (wk: weak_kind) =\r\n k:LP.parser_kind { parser_kind_prop nz wk k }", "val validate_drop\n (#k: LP.parser_kind)\n (#t: Type)\n (#p: LP.parser k t)\n (#inv: slice_inv)\n (#disj: disjointness_pre)\n (#l: eloc)\n (#allow_reading: _)\n (v: validate_with_action_t' p inv disj l allow_reading)\n : Tot (validate_with_action_t' p inv disj l false)\nlet validate_drop\n (#k:LP.parser_kind)\n (#t:Type)\n (#p:LP.parser k t)\n (#inv:slice_inv)\n (#disj:disjointness_pre)\n (#l:eloc)\n #allow_reading\n (v: validate_with_action_t' p inv disj l allow_reading)\n: Tot (validate_with_action_t' p inv disj l false)\n= if allow_reading\n then validate_drop_true v\n else v", "val validate_drop_true\n (#k: LP.parser_kind)\n (#t: Type)\n (#p: LP.parser k t)\n (#inv: slice_inv)\n (#disj: disjointness_pre)\n (#l: eloc)\n (v: validate_with_action_t' p inv disj l true)\n : Tot (validate_with_action_t' p inv disj l false)\nlet validate_drop_true\n (#k:LP.parser_kind) \n (#t:Type)\n (#p:LP.parser k t)\n (#inv:slice_inv)\n (#disj:disjointness_pre)\n (#l:eloc)\n (v: validate_with_action_t' p inv disj l true)\n: Tot (validate_with_action_t' p inv disj l false)\n= fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let res = v ctxt error_handler_fn input input_length pos in\n I.skip_if_success input pos res;\n res", "val reader (#nz:_) (#k:parser_kind nz WeakKindStrongPrefix) (#t:_) (p:parser k t) : Type u#1\nlet reader p = LPLC.leaf_reader p", "val wvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n : GTot t\nlet wvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n: GTot t\n= Ghost.reveal w.v", "val parse_weaken_right (#nz:_) (#wk: _) (#k:parser_kind nz wk) (#t:_) (p:parser k t)\r\n (#nz':_) (#wk': _) (k':parser_kind nz' wk')\r\n : Tot (parser (glb k k') t)\nlet parse_weaken_right #nz #wk #k p k'\r\n = LP.weaken (glb k k') p", "val lwbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w:\n (x: tr\n -> Pure (lwriter s h0 sout pout_from0)\n (requires (x == grvalue r))\n (ensures (fun _ -> True))))\n : Tot (w': lwriter s h0 sout pout_from0 {lwvalue w' == lwvalue (w (grvalue r))})\nlet lwbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w: ((x: tr) -> Pure (lwriter s h0 sout pout_from0) (requires (x == grvalue r)) (ensures (fun _ -> True))))\n: Tot (w' : lwriter s h0 sout pout_from0 { lwvalue w' == lwvalue (w (grvalue r)) } )\n= LWriter (Ghost.hide (lwvalue (w (grvalue r)))) (fun pout_from ->\n let v = gread r in\n lwrite (w v) pout_from\n )", "val owbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w:\n (x: tr\n -> Pure (owriter s h0 sout pout_from0)\n (requires (x == grvalue r))\n (ensures (fun _ -> True))))\n : Tot (w': owriter s h0 sout pout_from0 {owvalue w' == owvalue (w (grvalue r))})\nlet owbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w: ((x: tr) -> Pure (owriter s h0 sout pout_from0) (requires (x == grvalue r)) (ensures (fun _ -> True))))\n: Tot (w' : owriter s h0 sout pout_from0 { owvalue w' == owvalue (w (grvalue r))})\n= OWriter (Ghost.hide (owvalue (w (grvalue r)))) (fun pout_from ->\n let v = gread r in\n owrite (w v) pout_from\n )", "val validate_dep_pair_with_refinement'\n (name1: string)\n (#nz1: _)\n (#k1: parser_kind nz1 _)\n (#t1: _)\n (#p1: parser k1 t1)\n (#inv1 #disj1 #l1: _)\n (v1: validate_with_action_t p1 inv1 disj1 l1 true)\n (r1: leaf_reader p1)\n (f: (t1 -> bool))\n (#nz2 #wk2: _)\n (#k2: parser_kind nz2 wk2)\n (#t2: (refine _ f -> Type))\n (#p2: (x: refine _ f -> parser k2 (t2 x)))\n (#inv2 #disj2 #l2 #ar2: _)\n (v2: (x: refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n : Tot\n (validate_with_action_t ((p1 `LPC.parse_filter` f) `(parse_dep_pair #nz1)` p2)\n (conj_inv inv1 inv2)\n (conj_disjointness disj1 disj2)\n (l1 `eloc_union` l2)\n false)\nlet validate_dep_pair_with_refinement'\n (name1: string)\n #nz1 (#k1:parser_kind nz1 _) #t1 (#p1:parser k1 t1)\n #inv1 #disj1 #l1 (v1:validate_with_action_t p1 inv1 disj1 l1 true) (r1: leaf_reader p1)\n (f: t1 -> bool)\n #nz2 #wk2 (#k2:parser_kind nz2 wk2) (#t2:refine _ f -> Type) (#p2:(x:refine _ f -> parser k2 (t2 x)))\n #inv2 #disj2 #l2 #ar2 (v2:(x:refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n : Tot (validate_with_action_t\n ((p1 `LPC.parse_filter` f) `(parse_dep_pair #nz1)` p2)\n (conj_inv inv1 inv2)\n (conj_disjointness disj1 disj2)\n (l1 `eloc_union` l2)\n false)\n = fun ctxt error_handler_fn input input_length startPosition ->\n let h0 = HST.get () in\n LPC.parse_dtuple2_eq' #_ #_ (p1 `LPC.parse_filter` f) #_ #t2 p2 (I.get_remaining input h0);\n LPC.parse_filter_eq p1 f (I.get_remaining input h0);\n [@(rename_let (\"positionAfter\" ^ name1))]\n let res = v1 ctxt error_handler_fn input input_length startPosition in\n let h1 = HST.get() in\n modifies_address_liveness_insensitive_unused_in h0 h1;\n if LPE.is_error res\n then begin\n res\n end\n else begin\n [@(rename_let (\"\" ^ name1))]\n let field_value = r1 input startPosition in\n [@(rename_let (name1 ^ \"ConstraintIsOk\"))]\n let ok = f field_value in\n [@(rename_let (\"positionAfter\" ^ name1))]\n let res1 = LPE.check_constraint_ok ok res in\n if LPE.is_error res1\n then\n res1\n else let h2 = HST.get() in\n // assert (B.modifies B.loc_none h1 h2);\n // assert (inv1' input.LPL.base h2);\n modifies_address_liveness_insensitive_unused_in h1 h2;\n // assert (loc_not_unused_in h2 `loc_includes` l1');\n // assert (valid_pos (p1 `(LPC.parse_filter #k1 #t1)` f) h0 input (uint64_to_uint32 pos) (uint64_to_uint32 res));\n let h15 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h0 h15 in\n validate_drop (v2 field_value) ctxt error_handler_fn input input_length res1\n end", "val read_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (v1: jumper p1)\n (r1: leaf_reader p1)\n (#k2: parser_kind)\n (#t2: (t1 -> Type))\n (#p2: (x: t1 -> parser k2 (t2 x)))\n (r2: (x: t1 -> Tot (leaf_reader (p2 x))))\n : Tot (leaf_reader (parse_dtuple2 p1 p2))\nlet read_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (v1: jumper p1)\n (r1: leaf_reader p1)\n (#k2: parser_kind)\n (#t2: t1 -> Type)\n (#p2: (x: t1) -> parser k2 (t2 x))\n (r2: (x: t1) -> Tot (leaf_reader (p2 x)))\n: Tot (leaf_reader (parse_dtuple2 p1 p2))\n= fun #_ #_ sl pos ->\n let h = HST.get () in\n [@inline_let] let _ = valid_dtuple2 h p1 p2 sl pos in\n let x1 = r1 sl pos in\n let pos2 = v1 sl pos in\n let x2 = r2 x1 sl pos2 in\n (| x1, x2 |)", "val wbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w:\n (x: tr\n -> Pure (writer s h0 sout pout_from0)\n (requires (x == grvalue r))\n (ensures (fun _ -> True))))\n : Tot (w': writer s h0 sout pout_from0 {wvalue w' == wvalue (w (grvalue r))})\nlet wbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w: ((x: tr) -> Pure (writer s h0 sout pout_from0) (requires (x == grvalue r)) (ensures (fun _ -> True))))\n: Tot (w' : writer s h0 sout pout_from0 { wvalue w' == wvalue (w (grvalue r)) } )\n= Writer (Ghost.hide (wvalue (w (grvalue r)))) (fun pout_from ->\n let v = gread r in\n write (w v) pout_from\n )", "val validate_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (v: validator p)\n (p32: leaf_reader p)\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (f32: (x: dsum_known_key t -> Tot (validator (dsnd (f x)))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (g32: validator g)\n (destr: dep_maybe_enum_destr_t (dsum_enum t) (validate_dsum_cases_t t f g))\n : Tot (validator (parse_dsum t p f g))\nlet validate_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (v: validator p)\n (p32: leaf_reader p)\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (f32: (x: dsum_known_key t) -> Tot (validator (dsnd (f x))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (g32: validator g)\n (destr: dep_maybe_enum_destr_t (dsum_enum t) (validate_dsum_cases_t t f g))\n: Tot (validator (parse_dsum t p f g))\n= fun #rrel #rel input pos ->\n let h = HST.get () in\n [@inline_let]\n let _ = parse_dsum_eq' t p f g (bytes_of_slice_from h input (uint64_to_uint32 pos)) in\n [@inline_let]\n let _ = valid_facts (parse_dsum t p f g) h input (uint64_to_uint32 pos) in\n [@inline_let]\n let _ = valid_facts p h input (uint64_to_uint32 pos) in\n let pos_after_tag = v input pos in\n if is_error pos_after_tag\n then pos_after_tag\n else\n let tg = p32 input (uint64_to_uint32 pos) in\n [@inline_let]\n let _ = valid_facts (parse_dsum_cases' t f g (maybe_enum_key_of_repr (dsum_enum t) tg)) h input (uint64_to_uint32 pos_after_tag) in\n destr (validate_dsum_cases_eq t f g) (validate_dsum_cases_if t f g) (fun _ _ -> ()) (fun _ _ _ _ -> ()) (validate_dsum_cases' t f f32 g32) tg input pos_after_tag", "val parse_weaken_left (#nz:_) (#wk: _) (#k:parser_kind nz wk) (#t:_) (p:parser k t)\r\n (#nz':_) (#wk': _) (k':parser_kind nz' wk')\r\n : Tot (parser (glb k' k) t)\nlet parse_weaken_left #nz #wk #k p k'\r\n = LP.weaken (glb k' k) p", "val validate_dep_pair\r\n (name1: string)\r\n (#nz1:_)\r\n (#k1:parser_kind nz1 WeakKindStrongPrefix)\r\n (#t1:Type)\r\n (#[@@@erasable] p1:parser k1 t1)\r\n (#[@@@erasable] inv1:slice_inv)\r\n (#[@@@erasable] disj1:disjointness_pre)\r\n (#[@@@erasable] l1:eloc)\r\n (v1:validate_with_action_t p1 inv1 disj1 l1 true)\r\n (r1: leaf_reader p1)\r\n (#nz2:_)\r\n (#wk2: _)\r\n (#k2:parser_kind nz2 wk2)\r\n (#[@@@erasable] t2:t1 -> Type)\r\n (#[@@@erasable] p2:(x:t1 -> parser k2 (t2 x)))\r\n (#[@@@erasable] inv2:slice_inv)\r\n (#[@@@erasable] disj2:disjointness_pre)\r\n (#[@@@erasable] l2:eloc)\r\n (#allow_reading2:bool)\r\n (v2:(x:t1 -> validate_with_action_t (p2 x) inv2 disj2 l2 allow_reading2))\r\n : validate_with_action_t\r\n (p1 `parse_dep_pair` p2)\r\n (conj_inv inv1 inv2)\r\n (conj_disjointness disj1 disj2)\r\n (l1 `eloc_union` l2)\r\n false\nlet validate_dep_pair\n (name1: string)\n #nz1 (#k1:parser_kind nz1 _) #t1 (#p1:parser k1 t1)\n #inv1 #disj1 #l1 (v1:validate_with_action_t p1 inv1 disj1 l1 true) (r1: leaf_reader p1)\n #nz2 #wk2 (#k2:parser_kind nz2 wk2) (#t2:t1 -> Type) (#p2:(x:t1 -> parser k2 (t2 x)))\n #inv2 #disj2 #l2 #ar2 (v2:(x:t1 -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n = fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = HST.get () in\n LPC.parse_dtuple2_eq p1 p2 (I.get_remaining input h);\n [@(rename_let (\"positionAfter\" ^ name1))]\n let pos1 = v1 ctxt error_handler_fn input input_length pos in\n let h1 = HST.get() in\n if LPE.is_error pos1\n then begin\n pos1\n end\n else\n [@(rename_let (\"\" ^ name1))]\n let x = r1 input pos in\n let h15 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h h15 in\n validate_drop (v2 x) ctxt error_handler_fn input input_length pos1", "val validate_dep_pair_with_refinement\r\n (p1_is_constant_size_without_actions: bool)\r\n (name1: string)\r\n (#nz1:_)\r\n (#k1:parser_kind nz1 WeakKindStrongPrefix)\r\n (#t1:Type)\r\n (#[@@@erasable] p1:parser k1 t1)\r\n (#[@@@erasable] inv1:slice_inv)\r\n (#[@@@erasable] disj1:disjointness_pre) \r\n (#[@@@erasable] l1:eloc)\r\n (v1:validate_with_action_t p1 inv1 disj1 l1 true)\r\n (r1: leaf_reader p1)\r\n (f: t1 -> bool)\r\n (#nz2:_)\r\n (#wk2: _)\r\n (#k2:parser_kind nz2 wk2)\r\n (#[@@@erasable] t2:refine _ f -> Type)\r\n (#[@@@erasable] p2:(x:refine _ f -> parser k2 (t2 x)))\r\n (#[@@@erasable] inv2:slice_inv)\r\n (#[@@@erasable] disj2:disjointness_pre)\r\n (#[@@@erasable] l2:eloc)\r\n (#allow_reading2:bool)\r\n (v2:(x:refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 allow_reading2))\r\n : validate_with_action_t\r\n ((p1 `parse_filter` f) `parse_dep_pair` p2)\r\n (conj_inv inv1 inv2)\r\n (conj_disjointness disj1 disj2)\r\n (l1 `eloc_union` l2)\r\n false\nlet validate_dep_pair_with_refinement\n (p1_is_constant_size_without_actions: bool)\n (name1: string)\n #nz1 (#k1:parser_kind nz1 _) #t1 (#p1:parser k1 t1)\n #inv1 #disj1 #l1 (v1:validate_with_action_t p1 inv1 disj1 l1 true) (r1: leaf_reader p1)\n (f: t1 -> bool)\n #nz2 #wk2 (#k2:parser_kind nz2 wk2)\n (#t2:refine _ f -> Type)\n (#p2:(x:refine _ f -> parser k2 (t2 x)))\n #inv2 #disj2 #l2 #ar2\n (v2:(x:refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n= if\n p1_is_constant_size_without_actions `LP.bool_and`\n (k1.LP.parser_kind_high = Some 0) `LP.bool_and`\n (k1.LP.parser_kind_metadata = Some LP.ParserKindMetadataTotal)\n then\n validate_dep_pair_with_refinement_total_zero_parser' name1 inv1 disj1 l1 r1 f v2\n else\n validate_dep_pair_with_refinement' name1 v1 r1 f v2", "val grlexistsb\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (j: jumper p)\n (f: (t -> Tot bool))\n (f':\n (#rrel: _ -> #rel: _ -> sl: slice rrel rel -> pos: U32.t\n -> HST.Stack bool\n (requires (fun h -> valid p h sl pos))\n (ensures\n (fun h res h' -> B.modifies B.loc_none h h' /\\ res == f (contents p h sl pos))))\n )\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos pos': U32.t)\n (sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (h0:\n HS.mem\n { k.parser_kind_subkind == Some ParserStrong /\\ valid_list p h0 sl pos pos' /\\\n B.loc_disjoint (loc_slice_from_to sl pos pos') (loc_slice_from sout pout_from0) })\n : Tot\n (r':\n greader h0 sout pout_from0 bool {grvalue r' == L.existsb f (contents_list p h0 sl pos pos')})\nlet grlexistsb\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (j: jumper p)\n (f: (t -> Tot bool)) // should be GTot, but List.find requires Tot\n (f' : (\n (#rrel: _) ->\n (#rel: _) ->\n (sl: slice rrel rel) ->\n (pos: U32.t) ->\n HST.Stack bool\n (requires (fun h ->\n valid p h sl pos\n ))\n (ensures (fun h res h' ->\n B.modifies B.loc_none h h' /\\\n res == f (contents p h sl pos)\n ))\n ))\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos pos' : U32.t)\n (sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (h0: HS.mem {\n k.parser_kind_subkind == Some ParserStrong /\\\n valid_list p h0 sl pos pos' /\\\n B.loc_disjoint (loc_slice_from_to sl pos pos') (loc_slice_from sout pout_from0)\n })\n: Tot (r' : greader h0 sout pout_from0 bool { grvalue r' == L.existsb f (contents_list p h0 sl pos pos') } )\n= GReader (Ghost.hide (L.existsb f (contents_list p h0 sl pos pos'))) (fun _ ->\n list_existsb j f f' sl pos pos'\n )", "val jump_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (v: jumper p)\n (p32: leaf_reader p)\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (f32: (x: dsum_known_key t -> Tot (jumper (dsnd (f x)))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (g32: jumper g)\n (destr: dep_maybe_enum_destr_t (dsum_enum t) (jump_dsum_cases_t t f g))\n : Tot (jumper (parse_dsum t p f g))\nlet jump_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (v: jumper p)\n (p32: leaf_reader p)\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (f32: (x: dsum_known_key t) -> Tot (jumper (dsnd (f x))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (g32: jumper g)\n (destr: dep_maybe_enum_destr_t (dsum_enum t) (jump_dsum_cases_t t f g))\n: Tot (jumper (parse_dsum t p f g))\n= fun #rrel #rel input pos ->\n let h = HST.get () in\n [@inline_let]\n let _ = parse_dsum_eq' t p f g (bytes_of_slice_from h input pos) in\n [@inline_let]\n let _ = valid_facts (parse_dsum t p f g) h input pos in\n [@inline_let]\n let _ = valid_facts p h input pos in\n let pos_after_tag = v input pos in\n let tg = p32 input pos in\n [@inline_let]\n let _ = valid_facts (parse_dsum_cases' t f g (maybe_enum_key_of_repr (dsum_enum t) tg)) h input pos_after_tag in\n destr (jump_dsum_cases_eq t f g) (jump_dsum_cases_if t f g) (fun _ _ -> ()) (fun _ _ _ _ -> ()) (jump_dsum_cases' t f f32 g32) tg input pos_after_tag", "val parse_t_at_most (n:U32.t) (#nz: _) (#wk: _) (#k:parser_kind nz wk) (#t:_) (p:parser k t)\r\n : Tot (parser kind_t_at_most (t_at_most n t))\nlet parse_t_at_most n #nz #wk #k #t p\r\n = let open LowParse.Spec.FLData in\r\n let open LowParse.Spec.List in\r\n parse_weaken\r\n #false \r\n #WeakKindStrongPrefix\r\n (LowParse.Spec.FLData.parse_fldata \r\n (LPC.nondep_then p parse_all_bytes)\r\n (U32.v n))\r\n #false\r\n kind_t_at_most", "val jump_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (v1: jumper p1)\n (r1: leaf_reader p1)\n (#k2: parser_kind)\n (#t2: (t1 -> Type))\n (#p2: (x: t1 -> parser k2 (t2 x)))\n (v2: (x: t1 -> Tot (jumper (p2 x))))\n : Tot (jumper (parse_dtuple2 p1 p2))\nlet jump_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (v1: jumper p1)\n (r1: leaf_reader p1)\n (#k2: parser_kind)\n (#t2: t1 -> Type)\n (#p2: (x: t1) -> parser k2 (t2 x))\n (v2: (x: t1) -> Tot (jumper (p2 x)))\n: Tot (jumper (parse_dtuple2 p1 p2))\n= fun (#rrel #rel: _)\n (input: slice rrel rel) (pos: U32.t) ->\n let h = HST.get () in\n [@inline_let] let _ = valid_dtuple2 h p1 p2 input pos in\n let pos1 = v1 input pos in\n let x = r1 input pos in\n [@inline_let] let _ = valid_facts (p2 x) h input pos1 in\n v2 x input pos1", "val validate_list_up_to_inv\n (#k: parser_kind true WeakKindStrongPrefix)\n (#t: eqtype)\n (p: parser k t)\n (terminator: t)\n (prf: LUT.consumes_if_not_cond (cond_string_up_to terminator) p)\n (ctxt: app_ctxt)\n (sl: input_buffer_t)\n (h0: HS.mem)\n (bres: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet validate_list_up_to_inv\n (#k: parser_kind true WeakKindStrongPrefix)\n (#t: eqtype)\n (p: parser k t)\n (terminator: t)\n (prf: LUT.consumes_if_not_cond (cond_string_up_to terminator) p)\n (ctxt: app_ctxt)\n (sl: input_buffer_t)\n (h0: HS.mem)\n (bres: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n=\n let res = B.deref h bres in\n let q = LUT.parse_list_up_to (cond_string_up_to terminator) p prf in\n B.live h0 bres /\\\n I.live sl h0 /\\\n I.live sl h /\\\n B.loc_disjoint (I.footprint sl) (B.loc_buffer bres `B.loc_union` app_loc ctxt loc_none) /\\\n B.loc_disjoint (B.loc_buffer bres) (app_loc ctxt loc_none) /\\\n B.live h0 ctxt /\\\n B.live h ctxt /\\\n address_liveness_insensitive_locs `loc_includes` (app_loc ctxt loc_none) /\\\n B.modifies (B.loc_buffer bres `B.loc_union` I.perm_footprint sl `B.loc_union` app_loc ctxt loc_none) h0 h /\\\n begin\n let s = I.get_remaining sl h0 in\n let s' = I.get_remaining sl h in\n Seq.length s' <= Seq.length s /\\\n s' `Seq.equal` Seq.slice s (Seq.length s - Seq.length s') (Seq.length s) /\\\n begin if LPE.is_error res\n then\n // validation *or action* failed\n stop == true /\\\n U64.v (LPE.get_validator_error_pos res) == Seq.length (I.get_read sl h) /\\\n (LPE.get_validator_error_kind res <> LPE.get_validator_error_kind LPE.validator_error_action_failed ==> None? (LP.parse q s))\n else\n U64.v res == Seq.length (I.get_read sl h) /\\\n begin if stop\n then valid_consumed q h0 h sl\n else match LP.parse q s, LP.parse q s' with\n | None, None -> True\n | Some (_, consumed), Some (_, consumed') -> consumed' + Seq.length s - Seq.length s' == consumed\n | _ -> False\n end end\n end", "val validate_pair\r\n (name1: string)\r\n (#nz1:_)\r\n (#k1:parser_kind nz1 WeakKindStrongPrefix)\r\n (#[@@@erasable] t1:Type)\r\n (#[@@@erasable] p1:parser k1 t1)\r\n (#[@@@erasable] inv1:slice_inv)\r\n (#[@@@erasable] disj1:disjointness_pre)\r\n (#[@@@erasable] l1:eloc)\r\n (#allow_reading1:bool)\r\n (v1:validate_with_action_t p1 inv1 disj1 l1 allow_reading1)\r\n (#nz2:_)\r\n (#wk2: _)\r\n (#k2:parser_kind nz2 wk2)\r\n (#[@@@erasable] t2:Type)\r\n (#[@@@erasable] p2:parser k2 t2)\r\n (#[@@@erasable] inv2:slice_inv)\r\n (#[@@@erasable] disj2:disjointness_pre)\r\n (#[@@@erasable] l2:eloc)\r\n (#allow_reading2:bool)\r\n (v2:validate_with_action_t p2 inv2 disj2 l2 allow_reading2)\r\n : validate_with_action_t\r\n (p1 `parse_pair` p2)\r\n (conj_inv inv1 inv2)\r\n (conj_disjointness disj1 disj2)\r\n (l1 `eloc_union` l2)\r\n false\nlet validate_pair\n (name1: string)\n #nz1 (#k1:parser_kind nz1 WeakKindStrongPrefix) #t1 (#p1:parser k1 t1)\n (#inv1 #disj1:_) (#l1:eloc) (#ar1:_) (v1:validate_with_action_t p1 inv1 disj1 l1 ar1)\n #nz2 #wk2 (#k2:parser_kind nz2 wk2) #t2 (#p2:parser k2 t2)\n (#inv2 #disj2:_) (#l2:eloc) (#ar2:_) (v2:validate_with_action_t p2 inv2 disj2 l2 ar2)\n = fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = HST.get () in\n LPC.nondep_then_eq p1 p2 (I.get_remaining input h);\n [@(rename_let (\"positionAfter\" ^ name1))]\n let pos1 = validate_drop v1 ctxt error_handler_fn input input_length pos in\n let h1 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h h1;\n if LPE.is_error pos1\n then\n pos1\n else\n validate_drop v2 ctxt error_handler_fn input input_length pos1", "val read_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (p32: leaf_reader (parse_maybe_enum_key p (dsum_enum t)))\n (j: jumper p)\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (f32: (x: dsum_known_key t -> Tot (leaf_reader (dsnd (f x)))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (g32: leaf_reader g)\n (destr: dep_enum_destr _ (read_dsum_cases_t t f g))\n : Tot (leaf_reader (parse_dsum t p f g))\nlet read_dsum\n (#kt: parser_kind)\n (t: dsum)\n (#p: parser kt (dsum_repr_type t))\n (p32: leaf_reader (parse_maybe_enum_key p (dsum_enum t)))\n (j: jumper p)\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (f32: (x: dsum_known_key t) -> Tot (leaf_reader (dsnd (f x))))\n (#k': parser_kind)\n (#g: parser k' (dsum_type_of_unknown_tag t))\n (g32: leaf_reader g)\n (destr: dep_enum_destr _ (read_dsum_cases_t t f g))\n: Tot (leaf_reader (parse_dsum t p f g))\n= fun #_ #_ input pos ->\n let h = HST.get () in\n valid_facts (parse_dsum t p f g) h input pos;\n parse_dsum_eq_ t p f g (bytes_of_slice_from h input pos);\n valid_facts (parse_maybe_enum_key p (dsum_enum t)) h input pos;\n let k = p32 input pos in\n let pos' = jump_maybe_enum_key j (dsum_enum t) input pos in\n valid_facts (parse_dsum_cases' t f g k) h input pos' ;\n read_dsum_cases t f f32 g g32 destr k input pos'", "val validate_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (v1: validator p1)\n (r1: leaf_reader p1)\n (#k2: parser_kind)\n (#t2: (t1 -> Type))\n (#p2: (x: t1 -> parser k2 (t2 x)))\n (v2: (x: t1 -> Tot (validator (p2 x))))\n : Tot (validator (parse_dtuple2 p1 p2))\nlet validate_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (v1: validator p1)\n (r1: leaf_reader p1)\n (#k2: parser_kind)\n (#t2: t1 -> Type)\n (#p2: (x: t1) -> parser k2 (t2 x))\n (v2: (x: t1) -> Tot (validator (p2 x)))\n: Tot (validator (parse_dtuple2 p1 p2))\n= fun (#rrel #rel: _)\n (input: slice rrel rel) pos ->\n let h = HST.get () in\n [@inline_let] let _ = valid_dtuple2 h p1 p2 input (uint64_to_uint32 pos) in\n let pos1 = v1 input pos in\n if is_error pos1\n then begin\n pos1\n end\n else\n let x = r1 input (uint64_to_uint32 pos) in\n [@inline_let] let _ = valid_facts (p2 x) h input (uint64_to_uint32 pos1) in\n v2 x input pos1", "val write\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n : Tot (fwriter s h0 sout pout_from0 (wvalue w))\nlet write\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n: Tot (fwriter s h0 sout pout_from0 (wvalue w))\n= match w with | Writer _ f -> f", "val validate_nlist_constant_size_mod_ko\n (n: U32.t)\n (#wk: _)\n (#k: parser_kind true wk)\n (#t: _)\n (p: parser k t)\n (inv disj l: _)\n : Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires\n (let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_high == Some k.parser_kind_low /\\\n U32.v n % k.LP.parser_kind_low <> 0))\n (ensures (fun _ -> True))\nlet validate_nlist_constant_size_mod_ko\n (n:U32.t)\n (#wk: _)\n (#k:parser_kind true wk)\n #t\n (p:parser k t)\n inv disj l\n : Pure (validate_with_action_t (parse_nlist n p) inv disj l true)\n (requires (\n let open LP in\n k.parser_kind_subkind == Some ParserStrong /\\\n k.parser_kind_high == Some k.parser_kind_low /\\\n U32.v n % k.LP.parser_kind_low <> 0\n ))\n (ensures (fun _ -> True))\n= \n (fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = FStar.HyperStack.ST.get () in\n [@inline_let]\n let f () : Lemma\n (requires (Some? (LP.parse (parse_nlist n p) (I.get_remaining input h))))\n (ensures False)\n = let sq = I.get_remaining input h in\n let sq' = Seq.slice sq 0 (U32.v n) in\n LowParse.Spec.List.list_length_constant_size_parser_correct p sq' ;\n let Some (l, _) = LP.parse (parse_nlist n p) sq in\n assert (U32.v n == FStar.List.Tot.length l `Prims.op_Multiply` k.LP.parser_kind_low) ;\n FStar.Math.Lemmas.cancel_mul_mod (FStar.List.Tot.length l) k.LP.parser_kind_low ;\n assert (U32.v n % k.LP.parser_kind_low == 0)\n in\n [@inline_let]\n let _ = Classical.move_requires f () in\n LPE.set_validator_error_pos LPE.validator_error_list_size_not_multiple pos\n )", "val swbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#space_beyond: nat)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w:\n (x: tr\n -> Pure (swriter s h0 space_beyond sout pout_from0)\n (requires (x == grvalue r))\n (ensures (fun _ -> True))))\n : Tot (w': swriter s h0 space_beyond sout pout_from0 {swvalue w' == swvalue (w (grvalue r))})\nlet swbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#space_beyond: nat)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w: ((x: tr) -> Pure (swriter s h0 space_beyond sout pout_from0) (requires (x == grvalue r)) (ensures (fun _ -> True))))\n: Tot (w' : swriter s h0 space_beyond sout pout_from0 { swvalue w' == swvalue (w (grvalue r)) } )\n= SWriter (Ghost.hide (swvalue (w (grvalue r)))) (fun pout_from ->\n let v = gread r in\n swrite (w v) pout_from\n )", "val jump_list_up_to_inv\n (#k #t: _)\n (#p: parser k t)\n (cond: (t -> Tot bool))\n (prf: consumes_if_not_cond cond p {k.parser_kind_subkind <> Some ParserConsumesAll})\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: U32.t)\n (h0: HS.mem)\n (bpos: B.pointer U32.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet jump_list_up_to_inv\n (#k: _)\n (#t: _)\n (#p: parser k t)\n (cond: (t -> Tot bool))\n (prf: consumes_if_not_cond cond p { k.parser_kind_subkind <> Some ParserConsumesAll } )\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: U32.t)\n (h0: HS.mem)\n (bpos: B.pointer U32.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n= let pos = B.deref h bpos in\n let q = parse_list_up_to cond p prf in\n B.live h0 bpos /\\\n live_slice h0 sl /\\\n B.loc_disjoint (B.loc_buffer sl.base) (B.loc_buffer bpos) /\\\n B.modifies (B.loc_buffer bpos) h0 h /\\\n U32.v pos0 <= U32.v pos /\\\n valid q h0 sl pos0 /\\\n begin if stop\n then \n get_valid_pos q h0 sl pos0 == pos\n else\n valid q h0 sl pos /\\\n get_valid_pos q h0 sl pos0 == get_valid_pos q h0 sl pos\n end", "val olwbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w:\n (x: tr\n -> Pure (olwriter s h0 sout pout_from0)\n (requires (x == grvalue r))\n (ensures (fun _ -> True))))\n : Pure (olwriter s h0 sout pout_from0)\n (requires True)\n (ensures (fun w' -> olwvalue w' == olwvalue (w (grvalue r))))\nlet olwbind\n (#tr: Type)\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (r: greader h0 sout pout_from0 tr)\n (w: ((x: tr) -> Pure (olwriter s h0 sout pout_from0) (requires (x == grvalue r)) (ensures (fun _ -> True)))) \n: Pure (olwriter s h0 sout pout_from0)\n (requires True)\n (ensures (fun w' -> olwvalue w' == olwvalue (w (grvalue r))))\n= OLWriter (Ghost.hide (olwvalue (w (grvalue r)))) (fun pout_from ->\n let v = gread r in\n olwrite (w v) pout_from\n )", "val wvalid\n (#t: Type)\n (#k: parser_kind)\n (p: parser k t)\n (#rrel #rel: _)\n (s: slice rrel rel)\n (compl: compl_t t)\n (pos: U32.t)\n (gpos': Ghost.erased U32.t)\n (gv: Ghost.erased t)\n (x: Seq.seq byte)\n : GTot prop\nlet wvalid \n (#t: Type) (#k: parser_kind) (p: parser k t) (#rrel #rel: _) (s: slice rrel rel)\n (compl: compl_t t)\n (pos: U32.t)\n (gpos' : Ghost.erased U32.t)\n (gv: Ghost.erased t)\n (x: Seq.seq byte)\n: GTot prop\n= \n U32.v pos <= U32.v (Ghost.reveal gpos') /\\\n U32.v (Ghost.reveal gpos') <= U32.v s.len /\\\n U32.v s.len <= Seq.length x /\\\n parse p (Seq.slice x (U32.v pos) (U32.v s.len)) == Some (Ghost.reveal gv, U32.v (Ghost.reveal gpos') - U32.v pos) /\\\n compl pos (Ghost.reveal gv) (Ghost.reveal gpos') x", "val validate_dep_pair_with_refinement_and_action'\n (name1: string)\n (#nz1: _)\n (#k1: parser_kind nz1 _)\n (#t1: _)\n (#p1: parser k1 t1)\n (#inv1 #disj1 #l1: _)\n (v1: validate_with_action_t p1 inv1 disj1 l1 true)\n (r1: leaf_reader p1)\n (f: (t1 -> bool))\n (#inv1' #disj1' #l1' #b: _)\n (a: (t1 -> action inv1' disj1' l1' b bool))\n (#nz2 #wk2: _)\n (#k2: parser_kind nz2 wk2)\n (#t2: (refine _ f -> Type))\n (#p2: (x: refine _ f -> parser k2 (t2 x)))\n (#inv2 #disj2 #l2 #ar2: _)\n (v2: (x: refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n : validate_with_action_t ((p1 `LPC.parse_filter` f) `(parse_dep_pair #nz1)` p2)\n (conj_inv inv1 (conj_inv inv1' inv2))\n (conj_disjointness disj1 (conj_disjointness disj1' disj2))\n (l1 `eloc_union` (l1' `eloc_union` l2))\n false\nlet validate_dep_pair_with_refinement_and_action'\n (name1: string)\n (#nz1: _) (#k1:parser_kind nz1 _) (#t1: _) (#p1:parser k1 t1)\n (#inv1 #disj1 #l1: _) (v1:validate_with_action_t p1 inv1 disj1 l1 true) (r1: leaf_reader p1)\n (f: t1 -> bool)\n (#inv1' #disj1' #l1' #b: _) (a:t1 -> action inv1' disj1' l1' b bool)\n (#nz2 #wk2: _) (#k2:parser_kind nz2 wk2)\n (#t2:refine _ f -> Type)\n (#p2:(x:refine _ f) -> parser k2 (t2 x))\n (#inv2 #disj2 #l2 #ar2: _) (v2:(x:refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n: validate_with_action_t\n ((p1 `LPC.parse_filter` f) `(parse_dep_pair #nz1)` p2)\n (conj_inv inv1 (conj_inv inv1' inv2))\n (conj_disjointness disj1 (conj_disjointness disj1' disj2))\n (l1 `eloc_union` (l1' `eloc_union` l2))\n false\n= fun ctxt error_handler_fn input input_length startPosition ->\n let h0 = HST.get () in\n LPC.parse_dtuple2_eq' #_ #_ (p1 `LPC.parse_filter` f) #_ #t2 p2 (I.get_remaining input h0);\n LPC.parse_filter_eq p1 f (I.get_remaining input h0);\n [@(rename_let (\"positionAfter\" ^ name1))]\n let res = v1 ctxt error_handler_fn input input_length startPosition in\n let h1 = HST.get() in\n modifies_address_liveness_insensitive_unused_in h0 h1;\n if LPE.is_error res\n then begin\n res\n end\n else begin\n assert (I.get_remaining input h1 == I.get_remaining input h0);\n [@(rename_let (\"\" ^ name1))]\n let field_value = r1 input startPosition in\n [@(rename_let (name1 ^ \"ConstraintIsOk\"))]\n let ok = f field_value in\n [@(rename_let (\"positionAfter\" ^ name1))]\n let res1 = LPE.check_constraint_ok ok res in\n let h2 = HST.get() in\n if LPE.is_error res1\n then\n res1\n else begin\n modifies_address_liveness_insensitive_unused_in h1 h2;\n if not (a field_value ctxt error_handler_fn input input_length startPosition res1)\n then LPE.set_validator_error_pos LPE.validator_error_action_failed res1 //action failed\n else begin\n let h15 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h0 h15 in\n validate_drop (v2 field_value) ctxt error_handler_fn input input_length res1\n end\n end\n end", "val validate_dep_pair_with_refinement_and_action_total_zero_parser'\n (name1: string)\n (#nz1: _)\n (#k1: parser_kind nz1 WeakKindStrongPrefix)\n (#t1: _)\n (#p1: parser k1 t1)\n (r1: leaf_reader p1)\n (inv1 disj1 l1: _)\n (f: (t1 -> bool))\n (#inv1' #disj1' #l1' #b: _)\n (a: (t1 -> action inv1' disj1' l1' b bool))\n (#nz2 #wk2: _)\n (#k2: parser_kind nz2 wk2)\n (#t2: (refine _ f -> Type))\n (#p2: (x: refine _ f -> parser k2 (t2 x)))\n (#inv2 #disj2 #l2 #ar2: _)\n (v2: (x: refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n : Pure\n (validate_with_action_t ((p1 `LPC.parse_filter` f) `(parse_dep_pair #nz1)` p2)\n (conj_inv inv1 (conj_inv inv1' inv2))\n (conj_disjointness disj1 (conj_disjointness disj1' disj2))\n (l1 `eloc_union` (l1' `eloc_union` l2))\n false)\n (requires\n (let open LP in\n k1.parser_kind_high == Some 0 /\\ k1.parser_kind_metadata == Some ParserKindMetadataTotal))\n (ensures (fun _ -> True))\nlet validate_dep_pair_with_refinement_and_action_total_zero_parser'\n (name1: string)\n (#nz1: _) (#k1:parser_kind nz1 WeakKindStrongPrefix)\n (#t1: _) (#p1:parser k1 t1) (r1: leaf_reader p1)\n (inv1 disj1 l1: _)\n (f: t1 -> bool)\n (#inv1' #disj1' #l1' #b: _) (a:t1 -> action inv1' disj1' l1' b bool)\n (#nz2 #wk2: _) (#k2:parser_kind nz2 wk2)\n (#t2:refine _ f -> Type) (#p2:(x:refine _ f -> parser k2 (t2 x)))\n (#inv2 #disj2 #l2 #ar2: _) (v2:(x:refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n : Pure (validate_with_action_t\n ((p1 `LPC.parse_filter` f) `(parse_dep_pair #nz1)` p2)\n (conj_inv inv1 (conj_inv inv1' inv2))\n (conj_disjointness disj1 (conj_disjointness disj1' disj2))\n (l1 `eloc_union` (l1' `eloc_union` l2))\n false)\n (requires (\n let open LP in\n k1.parser_kind_high == Some 0 /\\\n k1.parser_kind_metadata == Some ParserKindMetadataTotal\n ))\n (ensures (fun _ -> True))\n = fun ctxt error_handler_fn input input_length startPosition ->\n let h0 = HST.get () in\n LPC.parse_dtuple2_eq' #_ #_ (p1 `LPC.parse_filter` f) #_ #t2 p2 (I.get_remaining input h0);\n LPC.parse_filter_eq p1 f (I.get_remaining input h0);\n [@inline_let] let _ = LP.parser_kind_prop_equiv k1 p1 in\n begin\n LowStar.Comment.comment (\"Validating field \" ^ name1);\n [@(rename_let (\"\" ^ name1))]\n let field_value = r1 input startPosition in\n [@(rename_let (name1 ^ \"ConstraintIsOk\"))]\n let ok = f field_value in\n [@(rename_let (\"positionAfter\" ^ name1))]\n let res1 = LPE.check_constraint_ok ok startPosition in\n if LPE.is_error res1\n then\n res1\n else let h2 = HST.get() in\n modifies_address_liveness_insensitive_unused_in h0 h2;\n if not (a field_value ctxt error_handler_fn input input_length startPosition res1)\n then LPE.set_validator_error_pos LPE.validator_error_action_failed startPosition //action failed\n else begin\n let h15 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h0 h15 in\n validate_drop (v2 field_value) ctxt error_handler_fn input input_length res1\n end\n end", "val lwrite\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: lwriter s h0 sout pout_from0)\n : Tot (flwriter s h0 sout pout_from0 (lwvalue w))\nlet lwrite\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: lwriter s h0 sout pout_from0)\n: Tot (flwriter s h0 sout pout_from0 (lwvalue w))\n= match w with | LWriter _ f -> f", "val vprop_equiv_typing_bk\n (#g: env)\n (#ctxt: _)\n (ctxt_typing: tot_typing g ctxt tm_vprop)\n (#p: _)\n (d: vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop\nlet vprop_equiv_typing_bk (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop \n = let _, bk = vprop_equiv_typing d in\n bk ctxt_typing", "val vprop_equiv_typing_bk\n (#g: env)\n (#ctxt: _)\n (ctxt_typing: tot_typing g ctxt tm_vprop)\n (#p: _)\n (d: vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop\nlet vprop_equiv_typing_bk (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop \n = let _, bk = vprop_equiv_typing d in\n bk ctxt_typing", "val validate_dep_pair_with_refinement_and_action\r\n (p1_is_constant_size_without_actions: bool)\r\n (name1: string)\r\n (#nz1:_)\r\n (#k1:parser_kind nz1 WeakKindStrongPrefix)\r\n (#t1:Type)\r\n (#[@@@erasable] p1:parser k1 t1)\r\n (#[@@@erasable] inv1:slice_inv)\r\n (#[@@@erasable] disj1:disjointness_pre)\r\n (#[@@@erasable] l1:eloc)\r\n (v1:validate_with_action_t p1 inv1 disj1 l1 true)\r\n (r1: leaf_reader p1)\r\n (f: t1 -> bool)\r\n (#[@@@erasable] inv1':slice_inv)\r\n (#[@@@erasable] disj1':disjointness_pre)\r\n (#[@@@erasable] l1':eloc)\r\n (#b:_)\r\n (a:t1 -> action inv1' disj1' l1' b bool)\r\n (#nz2:_)\r\n (#wk2: _)\r\n (#k2:parser_kind nz2 wk2)\r\n (#[@@@erasable] t2:refine _ f -> Type)\r\n (#[@@@erasable] p2:(x:refine _ f -> parser k2 (t2 x)))\r\n (#[@@@erasable] inv2:slice_inv)\r\n (#[@@@erasable] disj2:disjointness_pre)\r\n (#[@@@erasable] l2:eloc)\r\n (#allow_reading2:bool)\r\n (v2:(x:refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 allow_reading2))\r\n : validate_with_action_t\r\n ((p1 `parse_filter` f) `parse_dep_pair` p2)\r\n (conj_inv inv1 (conj_inv inv1' inv2))\r\n (conj_disjointness disj1 (conj_disjointness disj1' disj2))\r\n (l1 `eloc_union` (l1' `eloc_union` l2))\r\n false\nlet validate_dep_pair_with_refinement_and_action\n (p1_is_constant_size_without_actions: bool)\n (name1: string)\n #nz1 (#k1:parser_kind nz1 _) #t1 (#p1:parser k1 t1)\n #inv1 #disj1 #l1 (v1:validate_with_action_t p1 inv1 disj1 l1 true)\n (r1: leaf_reader p1)\n (f: t1 -> bool)\n #inv1' #disj1' #l1' #b (a:t1 -> action inv1' disj1' l1' b bool)\n #nz2 #wk2 (#k2:parser_kind nz2 wk2) (#t2:refine _ f -> Type) (#p2:(x:refine _ f -> parser k2 (t2 x)))\n #inv2 #disj2 #l2 #ar2 (v2:(x:refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n = if\n p1_is_constant_size_without_actions `LP.bool_and`\n (k1.LP.parser_kind_high = Some 0) `LP.bool_and`\n (k1.LP.parser_kind_metadata = Some LP.ParserKindMetadataTotal)\n then\n validate_dep_pair_with_refinement_and_action_total_zero_parser' name1 r1 inv1 disj1 l1 f a v2\n else\n validate_dep_pair_with_refinement_and_action' name1 v1 r1 f a v2", "val lwriter_nil\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (h0: HS.mem)\n (sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n : Tot (x: lwriter s h0 sout pout_from0 {lwvalue x == []})\nlet lwriter_nil\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (h0: HS.mem)\n (sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n: Tot (x: lwriter s h0 sout pout_from0 { lwvalue x == [] })\n= LWriter (Ghost.hide [])\n (fun pout_from ->\n let h = HST.get () in\n valid_list_nil p h sout pout_from;\n pout_from\n )", "val read_leaf\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (r: leaf_reader p)\n (#rrel #rel: _)\n (sin: slice rrel rel)\n (pin: U32.t)\n (sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (h0:\n HS.mem\n { k.parser_kind_subkind == Some ParserStrong /\\ valid p h0 sin pin /\\\n B.loc_disjoint (loc_slice_from_to sin pin (get_valid_pos p h0 sin pin))\n (loc_slice_from sout pout_from0) })\n : Tot (r': greader h0 sout pout_from0 t {grvalue r' == contents p h0 sin pin})\nlet read_leaf\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (r: leaf_reader p)\n (#rrel #rel: _)\n (sin: slice rrel rel)\n (pin: U32.t)\n (sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (h0: HS.mem {\n k.parser_kind_subkind == Some ParserStrong /\\\n valid p h0 sin pin /\\\n B.loc_disjoint (loc_slice_from_to sin pin (get_valid_pos p h0 sin pin)) (loc_slice_from sout pout_from0)\n })\n: Tot (r' : greader h0 sout pout_from0 t { grvalue r' == contents p h0 sin pin } )\n= GReader (Ghost.hide (contents p h0 sin pin)) (fun _ ->\n r sin pin\n )", "val validate_list_inv\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (g0 g1: G.erased HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: pos_t)\n (bpos: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet validate_list_inv\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (g0 g1: G.erased HS.mem)\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: pos_t)\n (bpos: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n= let h0 = G.reveal g0 in\n let h1 = G.reveal g1 in\n B.disjoint sl.base bpos /\\\n k.parser_kind_subkind == Some ParserStrong /\\\n k.parser_kind_low > 0 /\\\n U64.v pos0 <= U32.v sl.len /\\\n live_slice h0 sl /\\\n B.live h1 bpos /\\\n B.modifies B.loc_none h0 h1 /\\\n B.modifies (B.loc_buffer bpos) h1 h /\\ (\n let pos1 = Seq.index (B.as_seq h bpos) 0 in\n if\n is_error pos1\n then\n stop == true /\\\n (~ (valid_exact (parse_list p) h0 sl (uint64_to_uint32 pos0) sl.len))\n else\n U64.v pos0 <= U64.v pos1 /\\\n U64.v pos1 <= U32.v sl.len /\\\n (valid_exact (parse_list p) h0 sl (uint64_to_uint32 pos0) sl.len <==> valid_exact (parse_list p) h0 sl (uint64_to_uint32 pos1) sl.len) /\\\n (stop == true ==> U64.v pos1 == U32.v sl.len)\n )", "val parse_dtyp (d: I.dtyp) : Tot (parser not_reading)\nlet parse_dtyp\n (d: I.dtyp)\n: Tot (parser not_reading)\n= if I.allow_reader_of_dtyp d\n then wrap_parser (parse_readable_dtyp d)\n else match d with\n | I.DT_IType i -> parse_itype i\n | I.DT_App _ hd args -> parse_not_readable_app hd args", "val weaken_lwriter\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: lwriter s h0 sout pout_from0)\n (h1: HS.mem)\n (pout_from1: U32.t)\n : Pure (w': lwriter s h1 sout pout_from1 {lwvalue w' == lwvalue w})\n (requires\n (B.modifies (loc_slice_from sout pout_from0) h0 h1 /\\ U32.v pout_from0 <= U32.v pout_from1))\n (ensures (fun _ -> True))\nlet weaken_lwriter\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: lwriter s h0 sout pout_from0)\n (h1: HS.mem)\n (pout_from1: U32.t)\n: Pure (w' : lwriter s h1 sout pout_from1 { lwvalue w' == lwvalue w } )\n (requires (B.modifies (loc_slice_from sout pout_from0) h0 h1 /\\ U32.v pout_from0 <= U32.v pout_from1))\n (ensures (fun _ -> True))\n= LWriter w.v (fun pout_from -> w.w pout_from)", "val dtyp_of_app (en: env) (hd: A.ident) (args: list T.index) : ML dtyp\nlet dtyp_of_app (en: env) (hd:A.ident) (args:list T.index)\r\n : ML dtyp\r\n = match itype_of_ident hd, args with\r\n | Some i, [] ->\r\n DT_IType i\r\n\r\n | _ ->\r\n let readable = match H.try_find en hd.v with\r\n | None -> failwith \"type not found\"\r\n | Some td -> td.allow_reading\r\n in\r\n DT_App readable hd\r\n (List.map\r\n (function Inl _ -> failwith \"Unexpected type application\"\r\n | Inr e -> e)\r\n args)", "val lwvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: lwriter s h0 sout pout_from0)\n : GTot (list t)\nlet lwvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: lwriter s h0 sout pout_from0)\n: GTot (list t)\n= Ghost.reveal w.v", "val swvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#space_beyond: nat)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: swriter s h0 space_beyond sout pout_from0)\n : GTot t\nlet swvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#space_beyond: nat)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: swriter s h0 space_beyond sout pout_from0)\n: GTot t\n= Ghost.reveal w.v", "val parse_dsum'\n (#kt: parser_kind)\n (t: dsum)\n (p: parser kt (dsum_repr_type t))\n (#k: parser_kind)\n (pc: (x: dsum_key t -> Tot (parser k (dsum_cases t x))))\n : Tot (parser (and_then_kind kt k) (dsum_type t))\nlet parse_dsum'\n (#kt: parser_kind)\n (t: dsum)\n (p: parser kt (dsum_repr_type t))\n (#k: parser_kind)\n (pc: ((x: dsum_key t) -> Tot (parser k (dsum_cases t x))))\n: Tot (parser (and_then_kind kt k) (dsum_type t))\n= parse_tagged_union\n #kt\n #(dsum_key t)\n (parse_maybe_enum_key p (dsum_enum t))\n #(dsum_type t)\n (dsum_tag_of_data t)\n #k\n pc", "val validate_filter\r\n (name: string)\r\n (#nz:_)\r\n (#k:parser_kind nz WeakKindStrongPrefix)\r\n (#t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (v:validate_with_action_t p inv disj l true)\r\n (r:leaf_reader p)\r\n (f:t -> bool)\r\n (cr:string)\r\n (cf:string)\r\n : validate_with_action_t (p `parse_filter` f) inv disj l false\nlet validate_filter\n (name: string)\n #nz (#k:parser_kind nz _) (#t:_) (#p:parser k t)\n #inv #disj #l (v:validate_with_action_t p inv disj l true)\n (r:leaf_reader p) (f:t -> bool) (cr:string) (cf:string)\n= fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = HST.get () in\n LPC.parse_filter_eq p f (I.get_remaining input h);\n [@(rename_let (\"positionAfter\" ^ name))]\n let res = v ctxt error_handler_fn input input_length pos in\n let h1 = HST.get () in\n if LPE.is_error res\n then res\n else begin\n LowStar.Comment.comment cr;\n [@(rename_let (\"\" ^ name))]\n let field_value = r input pos in\n LowStar.Comment.comment (normalize_term (\"start: \" ^cf));\n [@(rename_let (name ^ \"ConstraintIsOk\"))]\n let ok = f field_value in\n LowStar.Comment.comment (normalize_term (\"end: \" ^ cf));\n LPE.check_constraint_ok ok res\n end", "val mk_serializer\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (f: bare_serializer t)\n (prf: (x: t -> Lemma (parse p (f x) == Some (x, Seq.length (f x)))))\n : Tot (serializer p)\nlet mk_serializer\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (f: bare_serializer t)\n (prf: (\n (x: t) ->\n Lemma\n (parse p (f x) == Some (x, Seq.length (f x)))\n ))\n: Tot (serializer p)\n= Classical.forall_intro prf;\n f", "val validate_filter_with_action\r\n (name: string)\r\n (#nz:_)\r\n (#k:parser_kind nz WeakKindStrongPrefix)\r\n (#t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (v:validate_with_action_t p inv disj l true)\r\n (r:leaf_reader p)\r\n (f:t -> bool)\r\n (cr:string)\r\n (cf:string)\r\n (#b:bool)\r\n (#[@@@erasable] inva:slice_inv)\r\n (#[@@@erasable] disja:disjointness_pre) \r\n (#[@@@erasable] la:eloc)\r\n (a: t -> action inva disja la b bool)\r\n : validate_with_action_t #nz\r\n (p `parse_filter` f)\r\n (conj_inv inv inva)\r\n (conj_disjointness disj disja)\r\n (eloc_union l la)\r\n false\nlet validate_filter_with_action\n (name: string) \n #nz (#k:parser_kind nz _) (#t:_) (#p:parser k t)\n #inv #disj #l (v:validate_with_action_t p inv disj l true)\n (r:leaf_reader p) (f:t -> bool) (cr:string) (cf:string)\n (#b:bool) #inva #disja (#la:eloc)\n (a: t -> action inva disja la b bool)\n= fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos0 = start_position in\n let h = HST.get () in\n LPC.parse_filter_eq p f (I.get_remaining input h);\n [@(rename_let (\"positionAfter\" ^ name))]\n let res = v ctxt error_handler_fn input input_length pos0 in\n let h1 = HST.get () in\n if LPE.is_error res\n then res\n else begin\n LowStar.Comment.comment cr;\n [@(rename_let (\"\" ^ name))]\n let field_value = r input pos0 in\n LowStar.Comment.comment (normalize_term (\"start: \" ^cf));\n [@(rename_let (name ^ \"ConstraintIsOk\"))]\n let ok = f field_value in\n LowStar.Comment.comment (normalize_term (\"end: \" ^ cf));\n if ok\n then let h15 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h h15 in\n if a field_value ctxt error_handler_fn input input_length pos0 res\n then res\n else LPE.set_validator_error_pos LPE.validator_error_action_failed res\n else LPE.set_validator_error_pos LPE.validator_error_constraint_failed res\n end", "val weaken_writer\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n (h1: HS.mem)\n (pout_from1: U32.t)\n : Pure (w': writer s h1 sout pout_from1 {wvalue w' == wvalue w})\n (requires\n (B.modifies (loc_slice_from sout pout_from0) h0 h1 /\\ U32.v pout_from0 <= U32.v pout_from1))\n (ensures (fun _ -> True))\nlet weaken_writer\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n (h1: HS.mem)\n (pout_from1: U32.t)\n: Pure (w' : writer s h1 sout pout_from1 { wvalue w' == wvalue w } )\n (requires (B.modifies (loc_slice_from sout pout_from0) h0 h1 /\\ U32.v pout_from0 <= U32.v pout_from1))\n (ensures (fun _ -> True))\n= Writer w.v (fun pout_from -> w.w pout_from)", "val parse_nlist (n:U32.t) (#wk: _) (#k:parser_kind true wk) (#t:_) (p:parser k t)\r\n : Tot (parser kind_nlist (nlist n t))\nlet parse_nlist n #wk #k #t p\r\n = let open LowParse.Spec.FLData in\r\n let open LowParse.Spec.List in\r\n parse_weaken\r\n #false #WeakKindStrongPrefix #(parse_fldata_kind (U32.v n) parse_list_kind) #(list t)\r\n (LowParse.Spec.FLData.parse_fldata (LowParse.Spec.List.parse_list p) (U32.v n))\r\n #false kind_nlist", "val jump_dtuple2_constant_size_dsnd\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (v1: jumper p1)\n (#k2: parser_kind)\n (#t2: (t1 -> Type))\n (p2: (x: t1 -> parser k2 (t2 x)))\n (sz: U32.t{U32.v sz == k2.parser_kind_low /\\ k2.parser_kind_high == Some k2.parser_kind_low})\n : Tot (jumper (parse_dtuple2 p1 p2))\nlet jump_dtuple2_constant_size_dsnd\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (v1: jumper p1)\n (#k2: parser_kind)\n (#t2: t1 -> Type)\n (p2: (x: t1) -> parser k2 (t2 x))\n (sz: U32.t { U32.v sz == k2.parser_kind_low /\\ k2.parser_kind_high == Some k2.parser_kind_low })\n: Tot (jumper (parse_dtuple2 p1 p2))\n= fun (#rrel #rel: _)\n (input: slice rrel rel) (pos: U32.t) ->\n let h = HST.get () in\n [@inline_let] let _ = valid_dtuple2 h p1 p2 input pos in\n let pos1 = v1 input pos in\n [@inline_let] let p2x = Ghost.hide (p2 (contents p1 h input pos)) in\n [@inline_let] let _ = valid_facts (Ghost.reveal p2x) h input pos1 in\n jump_constant_size' (fun _ -> Ghost.reveal p2x) sz () input pos1", "val owvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: owriter s h0 sout pout_from0)\n : GTot (option t)\nlet owvalue\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: owriter s h0 sout pout_from0)\n: GTot (option t)\n= Ghost.reveal w.v", "val owrite\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: owriter s h0 sout pout_from0)\n : Tot (fowriter s h0 sout pout_from0 (owvalue w))\nlet owrite\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: owriter s h0 sout pout_from0)\n: Tot (fowriter s h0 sout pout_from0 (owvalue w))\n= match w with | OWriter _ f -> f", "val parse_weaken\n (#nz #wk: _)\n (#k: parser_kind nz wk)\n (#t: _)\n (p: parser k t)\n (#nz' #wk': _)\n (k': parser_kind nz' wk' {k' `is_weaker_than` k})\n : Tot (parser k' t)\nlet parse_weaken #nz #wk (#k:parser_kind nz wk) #t (p:parser k t)\r\n #nz' #wk' (k':parser_kind nz' wk' {k' `is_weaker_than` k})\r\n : Tot (parser k' t)\r\n = LP.weaken k' p", "val validate_dep_pair_with_refinement_total_zero_parser'\n (name1: string)\n (#nz1: _)\n (#k1: parser_kind nz1 _)\n (#t1: _)\n (#p1: parser k1 t1)\n (inv1 disj1 l1: _)\n (r1: leaf_reader p1)\n (f: (t1 -> bool))\n (#nz2 #wk2: _)\n (#k2: parser_kind nz2 wk2)\n (#t2: (refine _ f -> Type))\n (#p2: (x: refine _ f -> parser k2 (t2 x)))\n (#inv2 #disj2 #l2 #ar2: _)\n (v2: (x: refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n : Pure\n (validate_with_action_t ((p1 `LPC.parse_filter` f) `(parse_dep_pair #nz1)` p2)\n (conj_inv inv1 inv2)\n (conj_disjointness disj1 disj2)\n (l1 `eloc_union` l2)\n false)\n (requires\n (let open LP in\n k1.parser_kind_high == Some 0 /\\ k1.parser_kind_metadata == Some ParserKindMetadataTotal))\n (ensures (fun _ -> True))\nlet validate_dep_pair_with_refinement_total_zero_parser'\n (name1: string)\n #nz1 (#k1:parser_kind nz1 _) #t1 (#p1:parser k1 t1)\n (inv1 disj1 l1: _) (r1: leaf_reader p1)\n (f: t1 -> bool)\n #nz2 #wk2 (#k2:parser_kind nz2 wk2)\n (#t2:refine _ f -> Type)\n (#p2:(x:refine _ f -> parser k2 (t2 x)))\n #inv2 #disj2 #l2 #ar2\n (v2:(x:refine _ f -> validate_with_action_t (p2 x) inv2 disj2 l2 ar2))\n : Pure (validate_with_action_t\n ((p1 `LPC.parse_filter` f) `(parse_dep_pair #nz1)` p2)\n (conj_inv inv1 inv2)\n (conj_disjointness disj1 disj2)\n (l1 `eloc_union` l2)\n false)\n (requires (\n let open LP in\n k1.parser_kind_high == Some 0 /\\\n k1.parser_kind_metadata == Some ParserKindMetadataTotal\n ))\n (ensures (fun _ -> True))\n = fun ctxt error_handler_fn input input_length startPosition ->\n let h0 = HST.get () in\n LPC.parse_dtuple2_eq' #_ #_ (p1 `LPC.parse_filter` f) #_ #t2 p2 (I.get_remaining input h0);\n LPC.parse_filter_eq p1 f (I.get_remaining input h0);\n [@inline_let] let _ = LP.parser_kind_prop_equiv k1 p1 in\n begin\n LowStar.Comment.comment (\"Validating field \" ^ name1);\n [@(rename_let (\"\" ^ name1))]\n let field_value = r1 input startPosition in\n [@(rename_let (name1 ^ \"ConstraintIsOk\"))]\n let ok = f field_value in\n [@(rename_let (\"positionAfter\" ^ name1))]\n let res1 = LPE.check_constraint_ok ok startPosition in\n if LPE.is_error res1\n then res1\n else let h2 = HST.get() in\n // assert (B.modifies B.loc_none h1 h2);\n // assert (inv1' input.LPL.base h2);\n modifies_address_liveness_insensitive_unused_in h0 h2;\n // assert (loc_not_unused_in h2 `loc_includes` l1');\n // assert (valid_pos (p1 `(LPC.parse_filter #k1 #t1)` f) h0 input (uint64_to_uint32 pos) (uint64_to_uint32 res));\n let h15 = HST.get () in\n let _ = modifies_address_liveness_insensitive_unused_in h0 h15 in\n validate_drop (v2 field_value) ctxt error_handler_fn input input_length res1\n end", "val parse_dsum\n (#kt: parser_kind)\n (t: dsum)\n (p: parser kt (dsum_repr_type t))\n (f: (x: dsum_known_key t -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x))))\n (#k: parser_kind)\n (g: parser k (dsum_type_of_unknown_tag t))\n : Tot (parser (parse_dsum_kind kt t f k) (dsum_type t))\nlet parse_dsum\n (#kt: parser_kind)\n (t: dsum)\n (p: parser kt (dsum_repr_type t))\n (f: (x: dsum_known_key t) -> Tot (k: parser_kind & parser k (dsum_type_of_known_tag t x)))\n (#k: parser_kind)\n (g: parser k (dsum_type_of_unknown_tag t))\n: Tot (parser (parse_dsum_kind kt t f k) (dsum_type t))\n= parse_dsum' t p (parse_dsum_cases t f g)", "val parse_t_exact (n:U32.t) (#nz:bool) (#wk: _) (#k:parser_kind nz wk) (#t:_) (p:parser k t)\r\n : Tot (parser kind_t_exact (t_exact n t))\nlet parse_t_exact n #nz #wk #k #t p\r\n = let open LowParse.Spec.FLData in\r\n let open LowParse.Spec.List in\r\n parse_weaken\r\n #false \r\n #WeakKindStrongPrefix\r\n (LowParse.Spec.FLData.parse_fldata \r\n p\r\n (U32.v n))\r\n #false\r\n kind_t_exact", "val parse_dep_pair (#nz1:_) (#k1:parser_kind nz1 WeakKindStrongPrefix) (#t1: Type) (p1: parser k1 t1)\r\n (#nz2:_) (#wk2: _) (#k2:parser_kind nz2 wk2) (#t2: (t1 -> Tot Type)) (p2: (x: t1) -> parser k2 (t2 x))\r\n : Tot (parser (and_then_kind k1 k2) (dtuple2 t1 t2) )\nlet parse_dep_pair p1 p2\r\n = LPC.parse_dtuple2 p1 p2", "val wjcopy\n (#k #t: _)\n (#p: parser k t)\n (s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (j: jumper p)\n (#rrel #rel: _)\n (sin: slice rrel rel)\n (pin_from: U32.t)\n (sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (sout_from0: U32.t)\n (h0:\n HS.mem\n { valid p h0 sin pin_from /\\\n B.loc_disjoint (loc_slice_from_to sin pin_from (get_valid_pos p h0 sin pin_from))\n (loc_slice_from sout sout_from0) })\n : Tot (w: writer s h0 sout sout_from0 {wvalue w == contents p h0 sin pin_from})\nlet wjcopy\n (#k: _)\n (#t: _)\n (#p: parser k t)\n (s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (j: jumper p)\n (#rrel #rel: _)\n (sin: slice rrel rel)\n (pin_from: U32.t)\n (sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (sout_from0: U32.t)\n (h0: HS.mem {\n valid p h0 sin pin_from /\\\n B.loc_disjoint (loc_slice_from_to sin pin_from (get_valid_pos p h0 sin pin_from)) (loc_slice_from sout sout_from0)\n })\n: Tot (w: writer s h0 sout sout_from0 {\n wvalue w == contents p h0 sin pin_from\n })\n= Writer (Ghost.hide (contents p h0 sin pin_from)) (fun sout_from ->\n copy_weak p j sin pin_from sout sout_from\n )", "val olwrite\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: olwriter s h0 sout pout_from0)\n : Tot (folwriter s h0 sout pout_from0 (olwvalue w))\nlet olwrite\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: olwriter s h0 sout pout_from0)\n: Tot (folwriter s h0 sout pout_from0 (olwvalue w))\n= match w with | OLWriter _ f -> f", "val glb (#nz1:bool) (#wk1: weak_kind) (k1:parser_kind nz1 wk1)\r\n (#nz2:bool) (#wk2: weak_kind) (k2:parser_kind nz2 wk2)\r\n : parser_kind (nz1 && nz2) (weak_kind_glb wk1 wk2)\nlet glb (#nz1:bool) (#wk1: weak_kind) (k1:parser_kind nz1 wk1)\r\n (#nz2:bool) (#wk2: weak_kind) (k2:parser_kind nz2 wk2)\r\n : parser_kind (nz1 && nz2) (weak_kind_glb wk1 wk2)\r\n = LP.glb k1 k2", "val parse_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: (t1 -> Tot Type))\n (p2: (x: t1 -> parser k2 (t2 x)))\n : Tot (parser (and_then_kind k1 k2) (dtuple2 t1 t2))\nlet parse_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: (t1 -> Tot Type))\n (p2: (x: t1) -> parser k2 (t2 x))\n: Tot (parser (and_then_kind k1 k2) (dtuple2 t1 t2))\n= parse_tagged_union\n p1\n dfst\n (fun (x: t1) -> parse_synth (p2 x) (synth_dtuple2 x))", "val validate_list_up_to_inv\n (#k #t: _)\n (#p: parser k t)\n (cond: (t -> Tot bool))\n (prf: consumes_if_not_cond cond p {k.parser_kind_subkind <> Some ParserConsumesAll})\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: U32.t)\n (h0: HS.mem)\n (bpos: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n : GTot Type0\nlet validate_list_up_to_inv\n (#k: _)\n (#t: _)\n (#p: parser k t)\n (cond: (t -> Tot bool))\n (prf: consumes_if_not_cond cond p { k.parser_kind_subkind <> Some ParserConsumesAll } )\n (#rrel #rel: _)\n (sl: slice rrel rel)\n (pos0: U32.t)\n (h0: HS.mem)\n (bpos: B.pointer U64.t)\n (h: HS.mem)\n (stop: bool)\n: GTot Type0\n= let pos = B.deref h bpos in\n let q = parse_list_up_to cond p prf in\n B.live h0 bpos /\\\n live_slice h0 sl /\\\n B.loc_disjoint (B.loc_buffer sl.base) (B.loc_buffer bpos) /\\\n B.modifies (B.loc_buffer bpos) h0 h /\\\n U32.v pos0 <= U64.v pos /\\\n begin if is_success pos\n then\n let pos = uint64_to_uint32 pos in\n U32.v pos <= U32.v sl.len /\\\n begin if stop\n then\n valid_pos q h0 sl pos0 pos\n else\n (valid q h0 sl pos0 <==> valid q h0 sl pos) /\\\n ((valid q h0 sl pos0 /\\ valid q h0 sl pos) ==>\n get_valid_pos q h0 sl pos0 == get_valid_pos q h0 sl pos\n )\n end\n else\n stop == true /\\\n (~ (valid q h0 sl pos0))\n end", "val lwriter_singleton\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n : Tot (x: lwriter s h0 sout pout_from0 {lwvalue x == [wvalue w]})\nlet lwriter_singleton\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_low > 0 } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (w: writer s h0 sout pout_from0)\n: Tot (x: lwriter s h0 sout pout_from0 { lwvalue x == [wvalue w] } )\n= LWriter (Ghost.hide [wvalue w])\n (fun pout_from ->\n let res = write w pout_from in\n if res `U32.lt` max_uint32\n then begin\n let h = HST.get () in\n valid_list_nil p h sout res;\n valid_list_cons p h sout pout_from res\n end else begin\n [@inline_let]\n let f () : Lemma (ensures (let v = wvalue w in serialized_list_length s [v] == serialized_length s v)) =\n serialized_list_length_cons s (wvalue w) [];\n serialized_list_length_nil s\n in\n f ()\n end;\n res\n )", "val bare_parse_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: (t1 -> Tot Type))\n (p2: (x: t1 -> parser k2 (t2 x)))\n : Tot (bare_parser (dtuple2 t1 t2))\nlet bare_parse_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (p1: parser k1 t1)\n (#k2: parser_kind)\n (#t2: (t1 -> Tot Type))\n (p2: (x: t1) -> parser k2 (t2 x))\n: Tot (bare_parser (dtuple2 t1 t2))\n= fun b ->\n match parse p1 b with\n | Some (x1, consumed1) ->\n let b' = Seq.slice b consumed1 (Seq.length b) in\n begin match parse (p2 x1) b' with\n | Some (x2, consumed2) ->\n Some ((| x1, x2 |), consumed1 + consumed2)\n | _ -> None\n end\n | _ -> None", "val swrite\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p {k.parser_kind_subkind == Some ParserStrong})\n (#h0: HS.mem)\n (#sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (#space_beyond: nat)\n (w: swriter s h0 space_beyond sout pout_from0)\n : Tot (fswriter s h0 space_beyond sout pout_from0 (swvalue w))\nlet swrite\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong } )\n (#h0: HS.mem)\n (#sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (#pout_from0: U32.t)\n (#space_beyond: nat) \n (w: swriter s h0 space_beyond sout pout_from0)\n: Tot (fswriter s h0 space_beyond sout pout_from0 (swvalue w))\n= match w with | SWriter _ f -> f", "val parse_pair (#nz1:_) (#k1:parser_kind nz1 WeakKindStrongPrefix) (#t1:_) (p1:parser k1 t1)\r\n (#nz2:_) (#wk2: _) (#k2:parser_kind nz2 wk2) (#t2:_) (p2:parser k2 t2)\r\n : Tot (parser (and_then_kind k1 k2) (t1 * t2))\nlet parse_pair p1 p2\r\n = LPC.nondep_then p1 p2", "val validate_nlist_constant_size_without_actions\r\n (n_is_const: bool)\r\n (n:U32.t)\r\n (#wk: _)\r\n (#k:parser_kind true wk)\r\n (#[@@@erasable] t:Type)\r\n (#[@@@erasable] p:parser k t)\r\n (#[@@@erasable] inv:slice_inv)\r\n (#[@@@erasable] disj:disjointness_pre) \r\n (#[@@@erasable] l:eloc)\r\n (#allow_reading:bool)\r\n (v: validate_with_action_t p inv disj l allow_reading)\r\n: Tot (validate_with_action_t (parse_nlist n p) inv disj l false)\nlet validate_nlist_constant_size_without_actions\n (n_is_const: bool)\n (n:U32.t)\n #wk\n (#k:parser_kind true wk)\n #t (#p:parser k t) #inv #disj #l #ar\n (v: validate_with_action_t p inv disj l ar)\n: Tot (validate_with_action_t (parse_nlist n p) inv disj l false)\n= \n if\n let open LP in\n k.parser_kind_subkind = Some ParserStrong &&\n k.parser_kind_high = Some k.parser_kind_low &&\n k.parser_kind_metadata = Some ParserKindMetadataTotal &&\n k.parser_kind_low < 4294967296\n then\n validate_drop (validate_nlist_total_constant_size n_is_const n p inv disj l)\n else\n validate_nlist n v", "val mk_read_maybe_enum_key\n (#key #repr: eqtype)\n (#k: parser_kind)\n (#p: parser k repr)\n (j: leaf_reader p)\n (e: enum key repr)\n : Tot (leaf_reader (parse_maybe_enum_key p e))\nlet mk_read_maybe_enum_key\n (#key #repr: eqtype)\n (#k: parser_kind) (#p: parser k repr) (j: leaf_reader p)\n (e: enum key repr)\n: Tot (leaf_reader (parse_maybe_enum_key p e))\n= read_maybe_enum_key j e (mk_maybe_enum_destr (maybe_enum_key e) e)", "val cast\n (#p1 #p2: parser)\n (#inv: memory_invariant)\n (v: squash (valid_rewrite_prop p1 p2))\n (x1: ptr p1 inv)\n : Tot (ptr p2 inv)\nlet cast\n (#p1: parser)\n (#p2: parser)\n (#inv: memory_invariant)\n (v: squash (valid_rewrite_prop p1 p2))\n (x1: ptr p1 inv)\n: Tot (ptr p2 inv)\n= cast _ _ _ _ (evalid_rewrite_of_tvalid_rewrite v) _ x1", "val mk_selector_vprop (#t: Type0) (p: (t -> vprop)) (p_inj: interp_hp_of_injective p) : Tot vprop\nlet mk_selector_vprop\n (#t: Type0) (p: t -> vprop) (p_inj: interp_hp_of_injective p)\n: Tot vprop\n= VUnit ({\n hp = mk_selector_vprop_hp p;\n t = t;\n sel = mk_selector_vprop_sel p p_inj;\n })", "val validate_list_up_to\n (#k: parser_kind true WeakKindStrongPrefix)\n (#t: eqtype)\n (#p: parser k t)\n (v: validator p)\n (r: leaf_reader p)\n (terminator: t)\n (prf: LUT.consumes_if_not_cond (cond_string_up_to terminator) p)\n : validate_with_action_t #true\n #WeakKindStrongPrefix\n (LUT.parse_list_up_to (cond_string_up_to terminator) p prf)\n true_inv\n disjointness_trivial\n eloc_none\n false\nlet validate_list_up_to\n (#k: parser_kind true WeakKindStrongPrefix)\n (#t: eqtype)\n (#p: parser k t)\n (v: validator p)\n (r: leaf_reader p)\n (terminator: t)\n (prf: LUT.consumes_if_not_cond (cond_string_up_to terminator) p)\n: validate_with_action_t #true #WeakKindStrongPrefix\n (LUT.parse_list_up_to (cond_string_up_to terminator) p prf)\n true_inv disjointness_trivial eloc_none false\n= fun ctxt error_handler_fn sl sl_len pos ->\n let h0 = HST.get () in\n HST.push_frame ();\n let h1 = HST.get () in\n fresh_frame_modifies h0 h1;\n let bres = B.alloca pos 1ul in\n let h2 = HST.get () in\n I.live_not_unused_in sl h0;\n C.Loops.do_while\n (validate_list_up_to_inv p terminator prf ctxt sl h2 bres)\n (fun _ -> validate_list_up_to_body terminator prf v r ctxt error_handler_fn sl sl_len h2 bres)\n ;\n let result = B.index bres 0ul in\n HST.pop_frame ();\n result", "val valid'\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (s: slice rrel rel)\n (pos: U32.t)\n : GTot Type0\nlet valid'\n (#rrel #rel: _)\n (#k: parser_kind)\n (#t: Type)\n (p: parser k t)\n (h: HS.mem)\n (s: slice rrel rel)\n (pos: U32.t)\n: GTot Type0\n= U32.v pos <= U32.v s.len /\\\n live_slice h s /\\\n Some? (parse p (bytes_of_slice_from h s pos))", "val validate_total_constant_size_no_read'\n (#k: LP.parser_kind)\n (#t: Type)\n (p: LP.parser k t)\n (sz: U64.t)\n (u:\n unit\n { k.LP.parser_kind_high == Some k.LP.parser_kind_low /\\ k.LP.parser_kind_low == U64.v sz /\\\n k.LP.parser_kind_metadata == Some LP.ParserKindMetadataTotal })\n (inv disj l: _)\n : validate_with_action_t' p inv disj l true\nlet validate_total_constant_size_no_read'\n (#k: LP.parser_kind)\n (#t: Type)\n (p: LP.parser k t)\n (sz: U64.t)\n (u: unit {\n k.LP.parser_kind_high == Some k.LP.parser_kind_low /\\\n k.LP.parser_kind_low == U64.v sz /\\\n k.LP.parser_kind_metadata == Some LP.ParserKindMetadataTotal\n })\n inv disj l\n: validate_with_action_t' p inv disj l true\n= fun ctxt error_handler_fn input input_length start_position ->\n [@inline_let] let pos = start_position in\n let h = HST.get () in\n LP.parser_kind_prop_equiv k p; \n let hasBytes = I.has input input_length pos sz in\n let h2 = HST.get () in\n modifies_address_liveness_insensitive_unused_in h h2;\n if hasBytes\n then pos `U64.add` sz\n else LPE.set_validator_error_pos LPE.validator_error_not_enough_data pos", "val mk_read_enum_key\n (#key #repr: eqtype)\n (#k: parser_kind)\n (#p: parser k repr)\n (p32: leaf_reader p)\n (e: enum key repr {Cons? e})\n : Tot (leaf_reader (parse_enum_key p e))\nlet mk_read_enum_key\n (#key #repr: eqtype)\n (#k: parser_kind) (#p: parser k repr) (p32: leaf_reader p)\n (e: enum key repr { Cons? e })\n: Tot (leaf_reader (parse_enum_key p e))\n= read_enum_key p32 e (mk_dep_maybe_enum_destr e (read_enum_key_t e))", "val read_filter\r\n (#nz:_)\r\n (#k: parser_kind nz WeakKindStrongPrefix)\r\n (#t: Type)\r\n (#[@@@erasable] p: parser k t)\r\n (p32: leaf_reader p)\r\n (f: (t -> bool))\r\n : leaf_reader (parse_filter p f)\nlet read_filter #nz\n (#k: parser_kind nz WeakKindStrongPrefix)\n (#t: Type)\n (#p: parser k t)\n (p32: leaf_reader p)\n (f: (t -> bool))\n : leaf_reader (parse_filter p f)\n = fun input pos ->\n let h = HST.get () in\n assert (parse_filter p f == LPC.parse_filter #k #t p f);\n assert_norm (P.refine t f == LPC.parse_filter_refine f);\n LPC.parse_filter_eq p f (I.get_remaining input h);\n p32 input pos", "val write_leaf_cs\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s:\n serializer p\n { k.parser_kind_subkind == Some ParserStrong /\\\n k.parser_kind_high == Some k.parser_kind_low /\\ k.parser_kind_low < 4294967296 })\n (w: leaf_writer_strong s)\n (h0: HS.mem)\n (sout:\n slice (srel_of_buffer_srel (B.trivial_preorder _))\n (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (x: t)\n : Tot (y: writer s h0 sout pout_from0 {wvalue y == x})\nlet write_leaf_cs\n (#k: parser_kind)\n (#t: Type)\n (#p: parser k t)\n (#s: serializer p { k.parser_kind_subkind == Some ParserStrong /\\ k.parser_kind_high == Some k.parser_kind_low /\\ k.parser_kind_low < 4294967296 } )\n (w: leaf_writer_strong s)\n (h0: HS.mem)\n (sout: slice (srel_of_buffer_srel (B.trivial_preorder _)) (srel_of_buffer_srel (B.trivial_preorder _)))\n (pout_from0: U32.t)\n (x: t)\n: Tot (y: writer s h0 sout pout_from0 { wvalue y == x } )\n= Writer (Ghost.hide x)\n (fun pout_from ->\n if U32.uint_to_t k.parser_kind_low `U32.gt` (sout.len `U32.sub` pout_from)\n then max_uint32\n else w x sout pout_from\n )", "val parse32_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (p1': parser32 p1)\n (#k2: parser_kind)\n (#t2: (t1 -> Tot Type))\n (#p2: (x: t1 -> Tot (parser k2 (t2 x))))\n (p2': (x: t1 -> Tot (parser32 (p2 x))))\n : Tot (parser32 (parse_dtuple2 p1 p2))\nlet parse32_dtuple2\n (#k1: parser_kind)\n (#t1: Type)\n (#p1: parser k1 t1)\n (p1' : parser32 p1)\n (#k2: parser_kind)\n (#t2: (t1 -> Tot Type))\n (#p2: (x: t1) -> Tot (parser k2 (t2 x)))\n (p2' : (x: t1) -> Tot (parser32 (p2 x)))\n: Tot (parser32 (parse_dtuple2 p1 p2))\n= fun (input: bytes32) ->\n ((\n [@inline_let] let _ = parse_dtuple2_eq p1 p2 (B32.reveal input) in\n match p1' input with\n | Some (v, l) ->\n let input' = B32.slice input l (B32.len input) in\n begin match p2' v input' with\n | Some (v', l') ->\n Some ((| v, v' |), U32.add l l')\n | _ -> None\n end\n | _ -> None\n ) <: (res: option (dtuple2 t1 t2 * U32.t) { parser32_correct (parse_dtuple2 p1 p2) input res } ))" ], "closest_src": [ { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_with_action_t" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.probe_then_validate" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_weaken_right" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_weaken_inv_loc" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_weaken_left" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.leaf_reader" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_eta" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_with_dep_action" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_with_comment" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_list_inv" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parser" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_ite" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_ite" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_with_error_handler" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_total_constant_size_no_read" }, { "project_name": "everparse", "file_name": "EverParse3d.Kinds.fst", "name": "EverParse3d.Kinds.filter_kind" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_weaken" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_nlist" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_with_success_action'" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_t_exact" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_t_at_most" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_with_success_action" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_dep_pair_with_action" }, { "project_name": "everparse", "file_name": "EverParse3d.Kinds.fst", "name": "EverParse3d.Kinds.parser_kind" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_drop" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_drop_true" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.reader" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.wvalue" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_weaken_right" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.lwbind" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.owbind" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_dep_pair_with_refinement'" }, { "project_name": "everparse", "file_name": "LowParse.Low.Combinators.fsti", "name": "LowParse.Low.Combinators.read_dtuple2" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.wbind" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.validate_dsum" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_weaken_left" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_dep_pair" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_dep_pair_with_refinement" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.grlexistsb" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.jump_dsum" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_t_at_most" }, { "project_name": "everparse", "file_name": "LowParse.Low.Combinators.fsti", "name": "LowParse.Low.Combinators.jump_dtuple2" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_list_up_to_inv" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_pair" }, { "project_name": "everparse", "file_name": "LowParse.Low.Sum.fst", "name": "LowParse.Low.Sum.read_dsum" }, { "project_name": "everparse", "file_name": "LowParse.Low.Combinators.fsti", "name": "LowParse.Low.Combinators.validate_dtuple2" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.write" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_nlist_constant_size_mod_ko" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.swbind" }, { "project_name": "everparse", "file_name": "LowParse.Low.ListUpTo.fst", "name": "LowParse.Low.ListUpTo.jump_list_up_to_inv" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.olwbind" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.fst", "name": "LowParse.Low.Base.wvalid" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_dep_pair_with_refinement_and_action'" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_dep_pair_with_refinement_and_action_total_zero_parser'" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.lwrite" }, { "project_name": "steel", "file_name": "Pulse.Checker.Base.fst", "name": "Pulse.Checker.Base.vprop_equiv_typing_bk" }, { "project_name": "steel", "file_name": "Pulse.Checker.VPropEquiv.fsti", "name": "Pulse.Checker.VPropEquiv.vprop_equiv_typing_bk" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_dep_pair_with_refinement_and_action" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.lwriter_nil" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.read_leaf" }, { "project_name": "everparse", "file_name": "LowParse.Low.List.fst", "name": "LowParse.Low.List.validate_list_inv" }, { "project_name": "everparse", "file_name": "Z3TestGen.fst", "name": "Z3TestGen.parse_dtyp" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.weaken_lwriter" }, { "project_name": "everparse", "file_name": "InterpreterTarget.fst", "name": "InterpreterTarget.dtyp_of_app" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.lwvalue" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.swvalue" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Sum.fst", "name": "LowParse.Spec.Sum.parse_dsum'" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_filter" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Base.fsti", "name": "LowParse.Spec.Base.mk_serializer" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_filter_with_action" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.weaken_writer" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_nlist" }, { "project_name": "everparse", "file_name": "LowParse.Low.Combinators.fsti", "name": "LowParse.Low.Combinators.jump_dtuple2_constant_size_dsnd" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.owvalue" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.owrite" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_weaken" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_dep_pair_with_refinement_total_zero_parser'" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Sum.fst", "name": "LowParse.Spec.Sum.parse_dsum" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_t_exact" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_dep_pair" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.wjcopy" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.olwrite" }, { "project_name": "everparse", "file_name": "EverParse3d.Kinds.fst", "name": "EverParse3d.Kinds.glb" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fsti", "name": "LowParse.Spec.Combinators.parse_dtuple2" }, { "project_name": "everparse", "file_name": "LowParse.Low.ListUpTo.fst", "name": "LowParse.Low.ListUpTo.validate_list_up_to_inv" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.lwriter_singleton" }, { "project_name": "everparse", "file_name": "LowParse.Spec.Combinators.fsti", "name": "LowParse.Spec.Combinators.bare_parse_dtuple2" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.swrite" }, { "project_name": "everparse", "file_name": "EverParse3d.Prelude.fst", "name": "EverParse3d.Prelude.parse_pair" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_nlist_constant_size_without_actions" }, { "project_name": "everparse", "file_name": "LowParse.Low.Enum.fst", "name": "LowParse.Low.Enum.mk_read_maybe_enum_key" }, { "project_name": "FStar", "file_name": "LowParseWriters.NoHoare.fst", "name": "LowParseWriters.NoHoare.cast" }, { "project_name": "steel", "file_name": "Steel.Effect.Atomic.fsti", "name": "Steel.Effect.Atomic.mk_selector_vprop" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_list_up_to" }, { "project_name": "everparse", "file_name": "LowParse.Low.Base.Spec.fsti", "name": "LowParse.Low.Base.Spec.valid'" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.validate_total_constant_size_no_read'" }, { "project_name": "everparse", "file_name": "LowParse.Low.Enum.fst", "name": "LowParse.Low.Enum.mk_read_enum_key" }, { "project_name": "everparse", "file_name": "EverParse3d.Actions.Base.fst", "name": "EverParse3d.Actions.Base.read_filter" }, { "project_name": "everparse", "file_name": "LowParse.Low.Writers.fst", "name": "LowParse.Low.Writers.write_leaf_cs" }, { "project_name": "everparse", "file_name": "LowParse.SLow.Combinators.fst", "name": "LowParse.SLow.Combinators.parse32_dtuple2" } ], "selected_premises": [ "EverParse3d.Interpreter.mk_dt_app", "EverParse3d.Interpreter.as_parser", "EverParse3d.Interpreter.as_reader", "EverParse3d.Interpreter.as_type", "EverParse3d.Interpreter.dtyp_as_validator", "EverParse3d.Interpreter.dtyp_as_parser", "EverParse3d.Interpreter.dtyp_as_leaf_reader", "EverParse3d.Interpreter.allow_reader_of_itype", "EverParse3d.Interpreter.as_validator", "EverParse3d.Kinds.kind_unit", "EverParse3d.Interpreter.parser_weak_kind_of_itype", "EverParse3d.Interpreter.interp_inv", "EverParse3d.Interpreter.leaf_reader", "EverParse3d.Kinds.weak_kind_glb", "EverParse3d.Interpreter.parser_kind_nz_of_itype", "EverParse3d.Interpreter.parser_kind_of_itype", "EverParse3d.Interpreter.validator_of", "EverParse3d.Prelude.refine", "EverParse3d.Interpreter.itype_as_parser", "EverParse3d.Interpreter.dtyp_of", "EverParse3d.Interpreter.nz_of_binding", "FStar.Int.Cast.uint64_to_uint32", "EverParse3d.Interpreter.action_as_action", "EverParse3d.Interpreter.wk_of_binding", "EverParse3d.Interpreter.disj_of_bindng", "FStar.Int.Cast.uint32_to_uint64", "EverParse3d.Interpreter.t_probe_then_validate", "EverParse3d.Interpreter.interp_loc", "EverParse3d.Interpreter.atomic_action_as_action", "EverParse3d.Prelude.parse_unit", "EverParse3d.Interpreter.loc_none", "EverParse3d.Interpreter.projector_names", "EverParse3d.Interpreter.pk_of_binding", "EverParse3d.Interpreter.itype_as_leaf_reader", "EverParse3d.Prelude.uint32_to_uint64", "EverParse3d.Interpreter.mk_action_binding", "EverParse3d.Interpreter.itype_as_validator", "EverParse3d.Interpreter.type_of_binding", "FStar.UInt.size", "EverParse3d.Prelude.uint64_to_uint32", "EverParse3d.Interpreter.comments", "EverParse3d.Interpreter.join_inv", "EverParse3d.Interpreter.inv_index", "EverParse3d.Interpreter.disj_index", "EverParse3d.Interpreter.specialization_steps", "FStar.Pervasives.dfst", "EverParse3d.Interpreter.disj_none", "FStar.Pervasives.Native.fst", "EverParse3d.Interpreter.parser_of_binding", "FStar.Pervasives.Native.snd", "EverParse3d.Interpreter.reader_binding", "EverParse3d.Interpreter.___EVERPARSE_COPY_BUFFER_T", "FStar.Pervasives.dsnd", "EverParse3d.Prelude.StaticHeader.get_bitfield8", "EverParse3d.Interpreter.interp_index", "EverParse3d.Interpreter.inv_of_binding", "EverParse3d.Interpreter.has_reader", "EverParse3d.Interpreter.interp_disj", "EverParse3d.Prelude.___UINT64", "FStar.Mul.op_Star", "EverParse3d.Interpreter.mk_extern_action", "EverParse3d.Interpreter.leaf_reader_of_binding", "EverParse3d.Interpreter.join_loc", "EverParse3d.Interpreter.mk_global_binding", "EverParse3d.Prelude.u8_rem", "FStar.Pervasives.reveal_opaque", "EverParse3d.Prelude.uint64_to_uint8", "EverParse3d.Interpreter.inv_none", "FStar.Int.Cast.op_At_Percent", "EverParse3d.Prelude.u64_rem", "EverParse3d.Interpreter.disjoint", "EverParse3d.Interpreter.loc_of_binding", "EverParse3d.Prelude.u64_mul", "EverParse3d.Interpreter.loc_index", "EverParse3d.Interpreter.validator_of_binding", "EverParse3d.Prelude.uint8_to_uint64", "EverParse3d.Prelude.u8_mul", "EverParse3d.Interpreter.coerce", "EverParse3d.Prelude.uint32_to_uint8", "EverParse3d.Interpreter.extern_action", "FStar.Int.Cast.uint32_to_uint8", "EverParse3d.Interpreter.action_binding", "EverParse3d.Prelude.___UINT32", "EverParse3d.Interpreter.dtyp_as_eqtype_lemma", "EverParse3d.Prelude.max_int_sizes", "EverParse3d.Prelude.uint8_to_uint32", "EverParse3d.Interpreter.join_disj", "EverParse3d.Prelude.___UINT8", "EverParse3d.Prelude.u32_rem", "EverParse3d.Prelude.id", "EverParse3d.Prelude.___UINT64BE", "EverParse3d.Prelude.StaticHeader.get_bitfield8_msb_first", "FStar.Int.Cast.uint64_to_uint8", "EverParse3d.Prelude.u32_mul", "EverParse3d.Prelude.u8_sub", "EverParse3d.Prelude.u8_lognot", "EverParse3d.Prelude.u64_sub", "EverParse3d.Prelude.StaticHeader.get_bitfield32", "EverParse3d.Interpreter.get_leaf_reader", "EverParse3d.Prelude.u16_mul" ], "source_upto_this": "(*\n Copyright 2021 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n\n Authors: N. Swamy, ...\n*)\nmodule EverParse3d.Interpreter\nmodule U32 = FStar.UInt32\nmodule U64 = FStar.UInt64\nmodule A = EverParse3d.Actions.All\nmodule P = EverParse3d.Prelude\nmodule T = FStar.Tactics\nmodule CP = EverParse3d.CopyBuffer\nopen FStar.List.Tot\n\ninline_for_extraction\nnoextract\nlet ___EVERPARSE_COPY_BUFFER_T = CP.copy_buffer_t\n\n(* This module defines a strongly typed abstract syntax for an\n intermediate representation of 3D programs. This is the type `typ`.\n\n The main idea of this module is to give `typ`s a threefold\n denotation:\n\n 1. Type denotation: `as_type` interprets a `typ` as an F* type\n\n 2. Parser denotation: `as_parser` interprets a `t:typ` as a parser\n of values of the type denotation of `t`.\n\n 3. Validate-with-action denotation: `as_validator` inteprets a\n `t:typ` as a low-level validator corresponding to the parser\n denotation of `t`.\n\n The 3rd denotation, validate-with-action, is the main operational\n denotation. That is, given a 3D program `t:typ` we can interpret it\n as validator to check that an input array of bytes conforms to the\n format specified by `t`. But, what we want ultimately is a C\n program for a `t`-validator.\n\n To achieve this, for any given concrete `t`, we partially evaluate\n this interpreter to get an EverParse validator specialized to `t`\n which can be extracted by F*/KaRaMeL as usual---this partial\n evaluation of an interpreter to a compiler producing a C program\n for t-validator is an instance of the 1st Futamura projection.\n *)\n\n(* An attribute to control partial evaluation *)\nlet specialize = ()\n\n(** You can see the basic idea of the whole stack working at first on\n a very simple class of types---just the primitive types *)\n\n(* Primitive types *)\ntype itype =\n | UInt8\n | UInt16\n | UInt32\n | UInt64\n | UInt8BE\n | UInt16BE\n | UInt32BE\n | UInt64BE\n | Unit\n | AllBytes\n | AllZeros\n\n(* Interpretation of itype as an F* type *)\n[@@specialize]\nlet itype_as_type (i:itype)\n : Type\n = match i with\n | UInt8 -> P.___UINT8\n | UInt16 -> P.___UINT16\n | UInt32 -> P.___UINT32\n | UInt64 -> P.___UINT64\n | UInt8BE -> P.___UINT8BE\n | UInt16BE -> P.___UINT16BE\n | UInt32BE -> P.___UINT32BE\n | UInt64BE -> P.___UINT64BE\n | Unit -> unit\n | AllBytes -> P.all_bytes\n | AllZeros -> P.all_zeros\n\n[@@specialize]\nlet parser_kind_nz_of_itype (i:itype)\n : bool\n = match i with\n | Unit\n | AllBytes\n | AllZeros -> false\n | _ -> true\n\n[@@specialize]\nlet parser_weak_kind_of_itype (i:itype)\n : P.weak_kind\n = match i with\n | AllBytes\n | AllZeros -> P.WeakKindConsumesAll\n | _ -> P.WeakKindStrongPrefix\n\n(* Interpretation of itype as a parser kind *)\n[@@specialize]\nlet parser_kind_of_itype (i:itype)\n : P.parser_kind (parser_kind_nz_of_itype i)\n (parser_weak_kind_of_itype i)\n = match i with\n | UInt8 -> P.kind____UINT8\n | UInt16 -> P.kind____UINT16\n | UInt32 -> P.kind____UINT32\n | UInt64 -> P.kind____UINT64\n | UInt8BE -> P.kind____UINT8BE\n | UInt16BE -> P.kind____UINT16BE\n | UInt32BE -> P.kind____UINT32BE\n | UInt64BE -> P.kind____UINT64BE\n | Unit -> P.kind_unit\n | AllBytes -> P.kind_all_bytes\n | AllZeros -> P.kind_all_zeros\n\n(* Interpretation of an itype as a parser *)\nlet itype_as_parser (i:itype)\n : P.parser (parser_kind_of_itype i) (itype_as_type i)\n = match i with\n | UInt8 -> P.parse____UINT8\n | UInt16 -> P.parse____UINT16\n | UInt32 -> P.parse____UINT32\n | UInt64 -> P.parse____UINT64\n | UInt8BE -> P.parse____UINT8BE\n | UInt16BE -> P.parse____UINT16BE\n | UInt32BE -> P.parse____UINT32BE\n | UInt64BE -> P.parse____UINT64BE\n | Unit -> P.parse_unit\n | AllBytes -> P.parse_all_bytes\n | AllZeros -> P.parse_all_zeros\n\n[@@specialize]\nlet allow_reader_of_itype (i:itype)\n : bool\n = match i with\n | AllBytes\n | AllZeros -> false\n | _ -> true\n\n(* Interpretation of an itype as a leaf reader *)\n[@@specialize]\nlet itype_as_leaf_reader (i:itype { allow_reader_of_itype i })\n : A.leaf_reader (itype_as_parser i)\n = match i with\n | UInt8 -> A.read____UINT8\n | UInt16 -> A.read____UINT16\n | UInt32 -> A.read____UINT32\n | UInt64 -> A.read____UINT64\n | UInt8BE -> A.read____UINT8BE\n | UInt16BE -> A.read____UINT16BE\n | UInt32BE -> A.read____UINT32BE\n | UInt64BE -> A.read____UINT64BE\n | Unit -> A.read_unit\n\n(* Interpretation of an itype as a validator\n -- Notice that the type shows that it is related to the parser *)\n[@@specialize]\nlet itype_as_validator (i:itype)\n : A.validate_with_action_t\n (itype_as_parser i)\n A.true_inv\n A.disjointness_trivial\n A.eloc_none\n (allow_reader_of_itype i)\n = match i with\n | UInt8 -> A.validate____UINT8\n | UInt16 -> A.validate____UINT16\n | UInt32 -> A.validate____UINT32\n | UInt64 -> A.validate____UINT64\n | UInt8BE -> A.validate____UINT8BE\n | UInt16BE -> A.validate____UINT16BE\n | UInt32BE -> A.validate____UINT32BE\n | UInt64BE -> A.validate____UINT64BE\n | Unit -> A.validate_unit\n | AllBytes -> A.validate_all_bytes\n | AllZeros -> A.validate_all_zeros\n\n\n(* Our first order of business to scale this up to 3D is to set up\n definitions for type contexts.\n\n A 3D program is a sequence of top-level definitions, where a given\n definition may reference terms defined previously. To model this,\n we'll given a denotation of programs in a _context_, where the\n context provides denotations for all the names defined previously\n which are in scope.\n*)\n\nlet leaf_reader #nz #wk (#k: P.parser_kind nz wk) #t (p:P.parser k t)\n = _:squash (wk == P.WeakKindStrongPrefix /\\ hasEq t) &\n A.leaf_reader p\n\n(* Now, we can define the type of an environment *)\nmodule T = FStar.Tactics\n\n[@@erasable]\nnoeq\ntype index (a:Type) =\n | Trivial : index a\n | NonTrivial : a -> index a\n\n[@@specialize]\nlet join_index (j:'a -> 'a -> 'a) (i0 i1:index 'a)\n: index 'a\n= match i0 with\n | Trivial -> i1\n | _ -> (\n match i1 with\n | Trivial -> i0\n | NonTrivial i1 ->\n let NonTrivial i0 = i0 in\n NonTrivial (j i0 i1)\n )\n[@@specialize]\nlet interp_index (triv:'a) (i:index 'a)\n: GTot 'a\n= match i with\n | Trivial -> triv\n | NonTrivial i -> i\n\n\nlet inv_index = index A.slice_inv\n[@@specialize]\nlet inv_none : inv_index = Trivial\n[@@specialize]\nlet join_inv = join_index A.conj_inv\n[@@specialize]\nlet interp_inv = interp_index A.true_inv\n\nlet loc_index = index A.eloc\n[@@specialize]\nlet loc_none : loc_index = Trivial\n[@@specialize]\nlet join_loc = join_index A.eloc_union\n[@@specialize]\nlet interp_loc = interp_index A.eloc_none\n\nlet disj_index = index A.disjointness_pre\n[@@specialize]\nlet disj_none : disj_index = Trivial\n[@@specialize]\nlet join_disj = join_index A.conj_disjointness\n[@@specialize]\nlet interp_disj = interp_index A.disjointness_trivial\n[@@specialize]\nlet disjoint (e1 e2:loc_index)\n : disj_index\n = match e1, e2 with\n | Trivial, _\n | _, Trivial -> disj_none\n | NonTrivial e1, NonTrivial e2 -> NonTrivial (A.disjoint e1 e2)\n\n\n(* A context is a list of bindings, where each binding is a pair of a\n name and a denotation of the name. *)\n(* global_binding:\n\n Represents the lifting of a fully applied a shallow F*\n quadruple of {type, parser, validator, opt reader}\n*)\nnoeq\ntype global_binding = {\n //Parser metadata\n parser_kind_nz:bool; // Does it consume non-zero bytes?\n parser_weak_kind: P.weak_kind;\n parser_kind: P.parser_kind parser_kind_nz parser_weak_kind;\n //Memory invariant of any actions it contains\n inv:inv_index;\n //Disjointness precondition\n disj:disj_index;\n //Write footprint of any of its actions\n loc:loc_index;\n //Its type denotation\n p_t : Type0;\n //Its parser denotation\n p_p : P.parser parser_kind p_t;\n //Whether the type can be read -- to avoid double fetches\n p_reader: option (leaf_reader p_p);\n //Its validate-with-action denotationa\n p_v : A.validate_with_action_t\n p_p\n (interp_inv inv)\n (interp_disj disj)\n (interp_loc loc)\n (Some? p_reader);\n}\n\nlet projector_names : list string = [\n `%Mkglobal_binding?.parser_kind_nz;\n `%Mkglobal_binding?.parser_weak_kind;\n `%Mkglobal_binding?.parser_kind;\n `%Mkglobal_binding?.inv;\n `%Mkglobal_binding?.disj;\n `%Mkglobal_binding?.loc;\n `%Mkglobal_binding?.p_t;\n `%Mkglobal_binding?.p_p;\n `%Mkglobal_binding?.p_reader;\n `%Mkglobal_binding?.p_v;\n]\n\nlet nz_of_binding = Mkglobal_binding?.parser_kind_nz\nlet wk_of_binding = Mkglobal_binding?.parser_weak_kind\nlet pk_of_binding = Mkglobal_binding?.parser_kind\nlet inv_of_binding = Mkglobal_binding?.inv\nlet disj_of_bindng = Mkglobal_binding?.disj\nlet loc_of_binding = Mkglobal_binding?.loc\nlet type_of_binding = Mkglobal_binding?.p_t\nlet parser_of_binding = Mkglobal_binding?.p_p\nlet leaf_reader_of_binding = Mkglobal_binding?.p_reader\nlet validator_of_binding = Mkglobal_binding?.p_v\n\nlet has_reader (g:global_binding) =\n match leaf_reader_of_binding g with\n | Some _ -> true\n | _ -> false\n\nlet reader_binding = g:global_binding { has_reader g }\n\n[@@specialize]\nlet get_leaf_reader (r:reader_binding)\n : leaf_reader (parser_of_binding r)\n = Some?.v (leaf_reader_of_binding r)\n\n\n(* The main type of 3D types. Some points to note:\n\n - The indexing structure determines the types of the\n parser/validator etc. of its denotation\n\n - All top-level names mentioned in a typ must be bound in the\n context.\n\n - Constructs that bind local names are represented using F*\n functions that abstract over denotations of the underlying types.\n\n - Some elements of the source programs are \"pre-denoted\". Notably,\n every refinement formula is represented in this AST already as a\n boolean function, rather than in some embedded language of\n expressions. This is because expressions are not necessarily\n well-formed by syntax alone---they may give rise to verification\n conditions when using bounded arithmetic functions. So, it's the\n obligation of the `typ` generator (i.e., the 3D frontend) to\n produce boolean functions for those expressions that can be\n verified natively by F* for type correctness.\n*)\n\nnoeq\ntype dtyp\n : #nz:bool -> #wk:P.weak_kind ->\n P.parser_kind nz wk ->\n has_reader:bool ->\n inv_index ->\n disj_index ->\n loc_index ->\n Type =\n | DT_IType:\n i:itype ->\n dtyp (parser_kind_of_itype i)\n (allow_reader_of_itype i)\n inv_none disj_none loc_none\n\n | DT_App:\n (* We give explicit names to the indices rather than\n projecting them as a small optimization for the reduction\n machinery ... it's no longer clear that the speedup is significant *)\n #nz:bool ->\n #wk:P.weak_kind ->\n pk:P.parser_kind nz wk ->\n hr:bool ->\n inv:inv_index ->\n disj:disj_index ->\n loc:loc_index ->\n x:global_binding ->\n _:squash (nz == nz_of_binding x /\\\n wk == wk_of_binding x /\\\n pk == pk_of_binding x /\\\n hr == has_reader x /\\\n inv == inv_of_binding x /\\\n disj == disj_of_bindng x /\\\n loc == loc_of_binding x) ->\n dtyp #nz #wk pk hr inv disj loc\n\n[@@specialize]\nlet dtyp_as_type #nz #wk (#pk:P.parser_kind nz wk) #hr #i #disj #l\n (d:dtyp pk hr i disj l)\n : Type\n = match d with\n | DT_IType i ->\n itype_as_type i\n\n | DT_App _ _ _ _ _ b _ ->\n type_of_binding b\n\nlet dtyp_as_eqtype_lemma #nz #wk (#pk:P.parser_kind nz wk) #i #disj #l\n (d:dtyp pk true i disj l)\n : Lemma\n (ensures hasEq (dtyp_as_type d))\n [SMTPat (hasEq (dtyp_as_type d))]\n = match d with\n | DT_IType i ->\n ()\n\n | DT_App _ _ _ _ _ b _ ->\n let (| _, _ |) = get_leaf_reader b in ()\n\n\nlet dtyp_as_parser #nz #wk (#pk:P.parser_kind nz wk) #hr #i #disj #l\n (d:dtyp pk hr i disj l)\n : P.parser pk (dtyp_as_type d)\n = match d returns Tot (P.parser pk (dtyp_as_type d)) with\n | DT_IType i ->\n itype_as_parser i\n\n | DT_App _ _ _ _ _ b _ ->\n parser_of_binding b\n\n[@@specialize]\nlet dtyp_as_validator #nz #wk (#pk:P.parser_kind nz wk)\n (#hr:_)\n (#[@@@erasable] i:inv_index)\n (#[@@@erasable] disj:disj_index)\n (#[@@@erasable] l:loc_index)\n (d:dtyp pk hr i disj l)\n : A.validate_with_action_t #nz #wk #pk #(dtyp_as_type d)\n (dtyp_as_parser d)\n (interp_inv i)\n (interp_disj disj)\n (interp_loc l)\n hr\n = match d\n returns\n A.validate_with_action_t #nz #wk #pk #(dtyp_as_type d)\n (dtyp_as_parser d)\n (interp_inv i)\n (interp_disj disj)\n (interp_loc l)\n hr\n with\n | DT_IType i ->\n itype_as_validator i\n\n | DT_App _ _ _ _ _ b _ ->\n // assert_norm (dtyp_as_type (DT_App_Alt ps b args) == (type_of_binding_alt (apply_arrow b args)));\n // assert_norm (dtyp_as_parser (DT_App_Alt ps b args) == parser_of_binding_alt (apply_arrow b args));\n validator_of_binding b\n\n\n[@@specialize]\nlet dtyp_as_leaf_reader #nz (#pk:P.parser_kind nz P.WeakKindStrongPrefix)\n (#[@@@erasable] i:inv_index)\n (#[@@@erasable] disj:disj_index)\n (#[@@@erasable] l:loc_index)\n (d:dtyp pk true i disj l)\n : A.leaf_reader (dtyp_as_parser d)\n = match d with\n | DT_IType i ->\n itype_as_leaf_reader i\n\n | DT_App _ _ _ _ _ b _ ->\n let (| _, lr |) = get_leaf_reader b in\n lr\n\n(** Actions *)\n\nlet action_binding\n (inv:inv_index)\n (l:loc_index)\n (on_success:bool)\n (a:Type)\n : Type u#0\n = A.action (interp_inv inv) A.disjointness_trivial (interp_loc l) on_success a\n\ninline_for_extraction\nlet extern_action (l:loc_index) = A.external_action (interp_loc l)\n\ninline_for_extraction\nlet mk_extern_action (#l:loc_index) ($f:extern_action l)\n = A.mk_external_action f\n\n[@@specialize]\nlet mk_action_binding\n (#l:loc_index)\n ($f:extern_action l)\n : action_binding inv_none l false unit\n = mk_extern_action f\n\n(* The type of atomic actions.\n\n `atomic_action l i b t`: is an atomic action that\n - may modify locations `l`\n - relies on a memory invariant `i`\n - b, when set, indicates that the action can only run in a success handler\n - t, is the result type of the action\n\n In comparison with with the 3D front-end's internal representation\n of actions, some notable differences\n\n - The indexing structure tell us exactly the type to which these\n will translate. It's also worth comparing these types to the\n types of the action primitives in Actions.fsti---the indexing\n structure is the same\n\n - The type is already partially interpreted, e.g., rather than\n relying on an explicit representation of names (e.g., in\n Action_deref), this representation directly uses a pointer\n value.\n*)\nnoeq\ntype atomic_action\n : inv_index -> disj_index -> loc_index -> bool -> Type0 -> Type u#1 =\n | Action_return:\n #a:Type0 ->\n x:a ->\n atomic_action inv_none disj_none loc_none false a\n\n | Action_abort:\n atomic_action inv_none disj_none loc_none false bool\n\n | Action_field_pos_64:\n atomic_action inv_none disj_none loc_none false U64.t\n\n | Action_field_pos_32:\n squash (EverParse3d.Actions.BackendFlag.backend_flag == A.BackendFlagBuffer) ->\n atomic_action inv_none disj_none loc_none false U32.t\n\n | Action_field_ptr:\n squash (EverParse3d.Actions.BackendFlag.backend_flag == A.BackendFlagBuffer) ->\n atomic_action inv_none disj_none loc_none true A.___PUINT8\n\n | Action_field_ptr_after:\n squash (EverParse3d.Actions.BackendFlag.backend_flag == A.BackendFlagExtern) ->\n (sz: FStar.UInt64.t) ->\n write_to: A.bpointer A.___PUINT8 ->\n atomic_action (NonTrivial (A.ptr_inv write_to)) disj_none (NonTrivial (A.ptr_loc write_to)) false bool\n\n | Action_field_ptr_after_with_setter:\n squash (EverParse3d.Actions.BackendFlag.backend_flag == A.BackendFlagExtern) ->\n sz: FStar.UInt64.t ->\n #out_loc:loc_index ->\n write_to: (A.___PUINT8 -> Tot (extern_action out_loc)) ->\n atomic_action inv_none disj_none out_loc false bool\n\n | Action_deref:\n #a:Type0 ->\n x:A.bpointer a ->\n atomic_action (NonTrivial (A.ptr_inv x)) disj_none loc_none false a\n\n | Action_assignment:\n #a:Type0 ->\n x:A.bpointer a ->\n rhs:a ->\n atomic_action (NonTrivial (A.ptr_inv x)) disj_none (NonTrivial (A.ptr_loc x)) false unit\n\n | Action_call:\n #inv:inv_index ->\n #loc:loc_index ->\n #b:bool ->\n #t:Type0 ->\n action_binding inv loc b t ->\n atomic_action inv disj_none loc b t\n\n | Action_probe_then_validate:\n #nz:bool ->\n #wk:_ ->\n #k:P.parser_kind nz wk ->\n #has_reader:bool ->\n #inv:inv_index ->\n #disj:disj_index ->\n #l:loc_index ->\n dt:dtyp k has_reader inv disj l ->\n src:U64.t ->\n len:U64.t ->\n dest:CP.copy_buffer_t ->\n probe:CP.probe_fn ->\n atomic_action (join_inv inv (NonTrivial (A.copy_buffer_inv dest)))\n (join_disj disj (disjoint (NonTrivial (A.copy_buffer_loc dest)) l))\n (join_loc l (NonTrivial (A.copy_buffer_loc dest)))\n true bool\n\n\n(* Denotation of atomic_actions as A.action *)\n[@@specialize]\nlet atomic_action_as_action\n (#i #d #l #b #t:_)\n (a:atomic_action i d l b t)\n : Tot (A.action (interp_inv i) (interp_disj d) (interp_loc l) b t)\n = match a with\n | Action_return x ->\n A.action_return x\n | Action_abort ->\n A.action_abort\n | Action_field_pos_64 ->\n A.action_field_pos_64\n | Action_field_pos_32 sq ->\n A.action_field_pos_32 sq\n | Action_field_ptr sq ->\n A.action_field_ptr sq\n | Action_field_ptr_after sq sz write_to ->\n A.action_field_ptr_after sq sz write_to\n | Action_field_ptr_after_with_setter sq sz write_to ->\n A.action_field_ptr_after_with_setter sq sz write_to\n | Action_deref x ->\n A.action_deref x\n | Action_assignment x rhs ->\n A.action_assignment x rhs\n | Action_call c ->\n c\n | Action_probe_then_validate #nz #wk #k #_hr #inv #l dt src len dest probe ->\n A.index_equations();\n let v = dtyp_as_validator dt in\n A.probe_then_validate v src len dest probe\n\n(* A sub-language of monadic actions.\n\n The indexing structure mirrors the indexes of the combinators in\n Actions.fst\n*)\nnoeq\ntype action\n : inv_index -> disj_index -> loc_index -> bool -> Type0 -> Type u#1 =\n | Atomic_action:\n #i:_ -> #d:_ -> #l:_ -> #b:_ -> #t:_ ->\n atomic_action i d l b t ->\n action i d l b t\n\n | Action_seq:\n #i0:_ -> #l0:_ -> #b0:_ -> hd:atomic_action i0 disj_none l0 b0 unit ->\n #i1:_ -> #l1:_ -> #b1:_ -> #t:_ -> tl:action i1 disj_none l1 b1 t ->\n action (join_inv i0 i1) disj_none (join_loc l0 l1) (b0 || b1) t\n\n | Action_ite :\n hd:bool ->\n #i0:_ -> #l0:_ -> #b0:_ -> #t:_ -> then_:(_:squash hd -> action i0 disj_none l0 b0 t) ->\n #i1:_ -> #l1:_ -> #b1:_ -> else_:(_:squash (not hd) -> action i1 disj_none l1 b1 t) ->\n action (join_inv i0 i1) disj_none (join_loc l0 l1) (b0 || b1) t\n\n | Action_let:\n #i0:_ -> #l0:_ -> #b0:_ -> #t0:_ -> head:atomic_action i0 disj_none l0 b0 t0 ->\n #i1:_ -> #l1:_ -> #b1:_ -> #t1:_ -> k:(t0 -> action i1 disj_none l1 b1 t1) ->\n action (join_inv i0 i1) disj_none (join_loc l0 l1) (b0 || b1) t1\n\n | Action_act:\n #i0:_ -> #l0:_ -> #b0:_ -> act:action i0 disj_none l0 b0 unit ->\n action i0 disj_none l0 b0 bool\n\n\n(* Denotation of action as A.action *)\n[@@specialize]\nlet rec action_as_action\n (#i #d #l #b #t:_)\n (a:action i d l b t)\n : Tot (A.action (interp_inv i) (interp_disj d) (interp_loc l) b t)\n (decreases a)\n = A.index_equations();\n match a with\n | Atomic_action a ->\n atomic_action_as_action a\n\n | Action_seq hd tl ->\n let a1 = atomic_action_as_action hd in\n let tl = action_as_action tl in\n A.action_seq a1 tl\n\n | Action_ite hd t e ->\n let then_ (x:squash hd) = action_as_action (t x) in\n let else_ (x:squash (not hd)) = action_as_action (e x) in\n A.action_ite hd then_ else_\n\n | Action_let hd k ->\n let head = atomic_action_as_action hd in\n let k x = action_as_action (k x) in\n A.action_bind \"hd\" head k\n\n | Action_act #i0 #l0 #b0 a ->\n A.action_weaken (A.action_seq (action_as_action a) (A.action_return true))\n #(interp_inv i0)\n #_\n #(interp_loc l0)\n\n(* Some AST nodes contain source comments that we propagate to the output *)\nlet comments = string\n\n[@@ no_auto_projectors]\nnoeq\ntype typ\n : #nz:bool -> #wk:P.weak_kind ->\n P.parser_kind nz wk ->\n inv_index ->\n disj_index ->\n loc_index ->\n bool ->\n Type =\n | T_false:\n fieldname:string ->\n typ P.impos_kind inv_none disj_none loc_none true\n\n | T_denoted :\n fieldname:string ->\n #nz:_ -> #wk:_ -> #pk:P.parser_kind nz wk ->\n #has_reader:_ -> #i:_ -> #disj:_ -> #l:_ ->\n td:dtyp pk has_reader i disj l ->\n typ pk i disj l has_reader\n\n | T_pair:\n first_fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ -> #b1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n t1:typ pk1 i1 d1 l1 b1 ->\n t2:typ pk2 i2 d2 l2 b2 ->\n typ (P.and_then_kind pk1 pk2)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2)\n false\n\n | T_dep_pair:\n first_fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:bool ->\n //the first component is a pre-denoted type with a reader\n t1:dtyp pk1 true i1 d1 l1 ->\n //the second component is a function from denotations of t1\n //that's why it's a small type, so that we can speak about its\n //denotation here\n t2:(dtyp_as_type t1 -> typ pk2 i2 d2 l2 b2) ->\n typ (P.and_then_kind pk1 pk2)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2)\n false\n\n | T_refine:\n fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n //the first component is a pre-denoted type with a reader\n base:dtyp pk1 true i1 d1 l1 ->\n //the second component is a function from denotations of base\n //but notice that its codomain is bool, rather than expr\n //That's to ensure that the refinement is already well-typed\n refinement:(dtyp_as_type base -> bool) ->\n typ (P.filter_kind pk1) i1 d1 l1 false\n\n | T_refine_with_action:\n fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n base:dtyp pk1 true i1 d1 l1 ->\n refinement:(dtyp_as_type base -> bool) ->\n act:(dtyp_as_type base -> action i2 d2 l2 b2 bool) ->\n typ (P.filter_kind pk1)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2)\n false\n\n | T_dep_pair_with_refinement:\n //This construct serves two purposes\n // 1. To avoid double fetches, we fold the refinement\n // and dependent pair into a single form\n // 2. This allows the well-typedness of the continuation k\n // to depend on the refinement of the first field\n first_fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n //the first component is a pre-denoted type with a reader\n base:dtyp pk1 true i1 d1 l1 ->\n //the second component is a function from denotations of base\n refinement:(dtyp_as_type base -> bool) ->\n k:(x:dtyp_as_type base { refinement x } -> typ pk2 i2 d2 l2 b2) ->\n typ (P.and_then_kind (P.filter_kind pk1) pk2)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2)\n false\n\n | T_dep_pair_with_action:\n fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n #i3:_ -> #d3:_ -> #l3:_ -> #b3:_ ->\n base:dtyp pk1 true i1 d1 l1 ->\n k:(x:dtyp_as_type base -> typ pk2 i2 d2 l2 b2) ->\n act:(dtyp_as_type base -> action i3 d3 l3 b3 bool) ->\n typ (P.and_then_kind pk1 pk2)\n (join_inv i1 (join_inv i3 i2))\n (join_disj d1 (join_disj d3 d2))\n (join_loc l1 (join_loc l3 l2))\n false\n\n | T_dep_pair_with_refinement_and_action:\n //This construct serves two purposes\n // 1. To avoid double fetches, we fold the refinement\n // and dependent pair and action into a single form\n // 2. This allows the well-typedness of the continuation k\n // to depend on the refinement of the first field\n first_fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1:_ -> #l1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n #i3:_ -> #d3:_ -> #l3:_ -> #b3:_ ->\n //the first component is a pre-denoted type with a reader\n base:dtyp pk1 true i1 d1 l1 ->\n //the second component is a function from denotations of base\n refinement:(dtyp_as_type base -> bool) ->\n k:(x:dtyp_as_type base { refinement x } -> typ pk2 i2 d2 l2 b2) ->\n act:(dtyp_as_type base -> action i3 d3 l3 b3 bool) ->\n typ (P.and_then_kind (P.filter_kind pk1) pk2)\n (join_inv i1 (join_inv i3 i2))\n (join_disj d1 (join_disj d3 d2))\n (join_loc l1 (join_loc l3 l2))\n false\n\n | T_if_else:\n #nz1:_ -> #wk1:_ -> #pk1:P.parser_kind nz1 wk1 ->\n #l1:_ -> #i1:_ -> #d1:_ -> #b1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #l2:_ -> #i2:_ -> #d2:_ -> #b2:_ ->\n b:bool -> //A bool, rather than an expression\n t1:(squash b -> typ pk1 i1 d1 l1 b1) ->\n t2:(squash (not b) -> typ pk2 i2 d2 l2 b2) ->\n typ (P.glb pk1 pk2)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2) false\n\n | T_cases:\n #nz1:_ -> #wk1:_ -> #pk1:P.parser_kind nz1 wk1 ->\n #l1:_ -> #i1:_ -> #d1:_ -> #b1:_ ->\n #nz2:_ -> #wk2:_ -> #pk2:P.parser_kind nz2 wk2 ->\n #l2:_ -> #i2:_ -> #d2:_ -> #b2:_ ->\n b:bool -> //A bool, rather than an expression\n t1:typ pk1 i1 d1 l1 b1 ->\n t2:typ pk2 i2 d2 l2 b2 ->\n typ (P.glb pk1 pk2)\n (join_inv i1 i2)\n (join_disj d1 d2)\n (join_loc l1 l2)\n false\n\n | T_with_action:\n fieldname:string ->\n #nz:_ -> #wk:_ -> #pk:P.parser_kind nz wk ->\n #l1:_ -> #i1:_ -> #d1:_ -> #b1:_ ->\n #l2:_ -> #i2:_ -> #d2:_ -> #b2:_ ->\n base:typ pk i1 d1 l1 b1 ->\n act:action i2 d2 l2 b2 bool ->\n typ pk (join_inv i1 i2) (join_disj d1 d2) (join_loc l1 l2) false\n\n | T_with_dep_action:\n fieldname:string ->\n #nz1:_ -> #pk1:P.parser_kind nz1 P.WeakKindStrongPrefix ->\n #i1:_ -> #d1: _ -> #l1:_ ->\n #i2:_ -> #d2:_ -> #l2:_ -> #b2:_ ->\n head:dtyp pk1 true i1 d1 l1 ->\n act:(dtyp_as_type head -> action i2 d2 l2 b2 bool) ->\n typ pk1 (join_inv i1 i2) (join_disj d1 d2) (join_loc l1 l2) false\n\n | T_with_comment:\n fieldname:string ->\n #nz:_ -> #wk:_ -> #pk:P.parser_kind nz wk ->\n #l:_ -> #i:_ -> #d:_ -> #b:_ ->\n t:typ pk i d l b ->\n c:comments ->\n typ pk i d l b\n\n | T_nlist:\n fieldname:string ->\n #wk:_ -> #pk:P.parser_kind true wk ->\n #i:_ -> #l:_ -> #d:_ -> #b:_ ->\n n:U32.t ->\n t:typ pk i d l b ->\n typ P.kind_nlist i d l false\n\n | T_at_most:\n fieldname:string ->\n #nz:_ -> #wk:_ -> #pk:P.parser_kind nz wk ->\n #i:_ -> #d:_ -> #l:_ -> #b:_ ->\n n:U32.t ->\n t:typ pk i d l b ->\n typ P.kind_t_at_most i d l false\n\n | T_exact:\n fieldname:string ->\n #nz:_ -> #wk:_ -> #pk:P.parser_kind nz wk ->\n #i:_ -> #d:_ -> #l:_ -> #b:_ ->\n n:U32.t ->\n t:typ pk i d l b ->\n typ P.kind_t_exact i d l false\n\n | T_string:\n fieldname:string ->\n #pk1:P.parser_kind true P.WeakKindStrongPrefix ->\n element_type:dtyp pk1 true inv_none disj_none loc_none ->\n terminator:dtyp_as_type element_type ->\n typ P.parse_string_kind inv_none disj_none loc_none false\n\n\n[@@specialize]\ninline_for_extraction\nlet coerce (#[@@@erasable]a:Type)\n (#[@@@erasable]b:Type)\n ( [@@@erasable]pf:squash (a == b))\n (x:a)\n : b\n = x\n\n[@@specialize]\nlet t_probe_then_validate\n (fieldname:string)\n (probe:CP.probe_fn)\n (len:U64.t)\n (dest:CP.copy_buffer_t)\n (#nz #wk:_) (#pk:P.parser_kind nz wk)\n (#has_reader #i #disj:_)\n (#l:_)\n (td:dtyp pk has_reader i disj l)\n : typ (parser_kind_of_itype UInt64)\n (join_inv i (NonTrivial (A.copy_buffer_inv dest)))\n (join_disj disj (disjoint (NonTrivial (A.copy_buffer_loc dest)) l))\n (join_loc l (NonTrivial (A.copy_buffer_loc dest)))\n false\n = T_with_dep_action fieldname\n (DT_IType UInt64)\n (fun src ->\n Atomic_action (Action_probe_then_validate td src len dest probe))\n\n\n(* Type denotation of `typ` *)\nlet rec as_type\n #nz #wk (#pk:P.parser_kind nz wk)\n #l #i #d #b\n (t:typ pk l i d b)\n : Tot Type0\n (decreases t)\n = match t with\n | T_false _ -> False\n\n | T_denoted _ td ->\n dtyp_as_type td\n\n | T_pair _ t1 t2 ->\n as_type t1 & as_type t2\n\n | T_dep_pair _ i t\n | T_dep_pair_with_action _ i t _ ->\n x:dtyp_as_type i & as_type (t x)\n\n | T_refine _ base refinement ->\n P.refine (dtyp_as_type base) refinement\n\n | T_refine_with_action _ base refinement _ ->\n P.refine (dtyp_as_type base) refinement\n\n | T_dep_pair_with_refinement _ base refinement t ->\n x:P.refine (dtyp_as_type base) refinement & as_type (t x)\n\n | T_dep_pair_with_refinement_and_action _ base refinement t _ ->\n x:P.refine (dtyp_as_type base) refinement & as_type (t x)\n\n | T_if_else b t0 t1 ->\n P.t_ite b (fun _ -> as_type (t0()))\n (fun _ -> as_type (t1()))\n\n | T_cases b t0 t1 ->\n P.t_ite b (fun _ -> as_type t0) (fun _ -> as_type t1)\n\n | T_with_action _ t _\n | T_with_comment _ t _ ->\n as_type t\n\n | T_with_dep_action _ i _ ->\n dtyp_as_type i\n\n | T_nlist _ n t ->\n P.nlist n (as_type t)\n\n | T_at_most _ n t ->\n P.t_at_most n (as_type t)\n\n | T_exact _ n t ->\n P.t_exact n (as_type t)\n\n | T_string _ elt_t terminator ->\n P.cstring (dtyp_as_type elt_t) terminator\n\n\n(* Parser denotation of `typ` *)\nlet rec as_parser\n #nz #wk (#pk:P.parser_kind nz wk)\n #l #i #d #b\n (t:typ pk l i d b)\n : Tot (P.parser pk (as_type t))\n (decreases t)\n = match t returns Tot (P.parser pk (as_type t)) with\n | T_false _ ->\n //assert_norm (as_type g T_false == False);\n P.parse_impos()\n\n | T_denoted _ d ->\n dtyp_as_parser d\n\n | T_pair _ t1 t2 ->\n //assert_norm (as_type g (T_pair t1 t2) == as_type g t1 * as_type g t2);\n let p1 = as_parser t1 in\n let p2 = as_parser t2 in\n P.parse_pair p1 p2\n\n | T_dep_pair _ i t\n | T_dep_pair_with_action _ i t _ ->\n //assert_norm (as_type g (T_dep_pair i t) == x:itype_as_type i & as_type g (t x));\n let pi = dtyp_as_parser i in\n P.parse_dep_pair pi (fun (x:dtyp_as_type i) -> as_parser (t x))\n\n | T_refine _ base refinement\n | T_refine_with_action _ base refinement _ ->\n //assert_norm (as_type g (T_refine base refinement) == P.refine (itype_as_type base) refinement);\n let pi = dtyp_as_parser base in\n P.parse_filter pi refinement\n\n | T_dep_pair_with_refinement _ base refinement k ->\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x)))\n\n\n | T_dep_pair_with_refinement_and_action _ base refinement k _ ->\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x)))\n\n | T_if_else b t0 t1 ->\n //assert_norm (as_type g (T_if_else b t0 t1) == P.t_ite b (as_type g t0) (as_type g t1));\n let p0 (_:squash b) =\n P.parse_weaken_right (as_parser (t0())) _\n in\n let p1 (_:squash (not b)) =\n P.parse_weaken_left (as_parser (t1())) _\n in\n P.parse_ite b p0 p1\n\n | T_cases b t0 t1 ->\n //assert_norm (as_type g (T_if_else b t0 t1) == P.t_ite b (as_type g t0) (as_type g t1));\n let p0 (_:squash b) =\n P.parse_weaken_right (as_parser t0) _\n in\n let p1 (_:squash (not b)) =\n P.parse_weaken_left (as_parser t1) _\n in\n P.parse_ite b p0 p1\n\n | T_with_action _ t a ->\n //assert_norm (as_type g (T_with_action t a) == as_type g t);\n as_parser t\n\n | T_with_dep_action _ i a ->\n //assert_norm (as_type g (T_with_dep_action i a) == itype_as_type i);\n dtyp_as_parser i\n\n | T_with_comment _ t c ->\n //assert_norm (as_type g (T_with_comment t c) == as_type g t);\n as_parser t\n\n | T_nlist _ n t ->\n P.parse_nlist n (as_parser t)\n\n | T_at_most _ n t ->\n P.parse_t_at_most n (as_parser t)\n\n | T_exact _ n t ->\n P.parse_t_exact n (as_parser t)\n\n | T_string _ elt_t terminator ->\n P.parse_string (dtyp_as_parser elt_t) terminator\n\n[@@specialize]\nlet rec as_reader #nz (#pk:P.parser_kind nz P.WeakKindStrongPrefix)\n (#[@@@erasable] inv:inv_index)\n (#[@@@erasable] d:disj_index)\n (#[@@@erasable] loc:loc_index)\n (t:typ pk inv d loc true)\n : leaf_reader (as_parser t)\n = match t with\n | T_denoted _n dt ->\n assert_norm (as_type (T_denoted _n dt) == dtyp_as_type dt);\n assert_norm (as_parser (T_denoted _n dt) == dtyp_as_parser dt);\n (| (), dtyp_as_leaf_reader dt |)\n | T_with_comment _n t _c ->\n assert_norm (as_type (T_with_comment _n t _c) == as_type t);\n assert_norm (as_parser (T_with_comment _n t _c) == as_parser t);\n as_reader t\n | T_false _n ->\n assert_norm (as_type (T_false _n) == False);\n assert_norm (as_parser (T_false _n) == P.parse_impos());\n (| (), A.read_impos |)\n\n(* The main result:\n A validator denotation of `typ`\n related by construction to the parser\n and type denotations\n*)\n#push-options \"--split_queries no --z3rlimit_factor 4 --z3cliopt 'smt.qi.eager_threshold=100'\"\n#restart-solver\nlet rec as_validator\n (typename:string)\n #nz #wk (#pk:P.parser_kind nz wk)\n (#[@@@erasable] inv:inv_index)\n (#[@@@erasable] disj:disj_index)\n (#[@@@erasable] loc:loc_index)\n #b\n (t:typ pk inv disj loc b)\n : Tot (A.validate_with_action_t #nz #wk #pk #(as_type t)\n (as_parser t)\n (interp_inv inv)\n (interp_disj disj)\n (interp_loc loc)\n b)\n (decreases t)\n = A.index_equations();\n match t\n returns Tot (\n A.validate_with_action_t #nz #wk #pk #(as_type t)\n (as_parser t)\n (interp_inv inv)\n (interp_disj disj)\n (interp_loc loc)\n b\n )\n with\n | T_false fn ->\n A.validate_with_error_handler typename fn (A.validate_impos())\n\n | T_denoted fn td ->\n assert_norm (as_type (T_denoted fn td) == dtyp_as_type td);\n assert_norm (as_parser (T_denoted fn td) == dtyp_as_parser td);\n A.validate_with_error_handler typename fn (A.validate_eta (dtyp_as_validator td))\n\n | T_pair fn t1 t2 ->\n assert_norm (as_type (T_pair fn t1 t2) == as_type t1 * as_type t2);\n assert_norm (as_parser (T_pair fn t1 t2) == P.parse_pair (as_parser t1) (as_parser t2));\n A.validate_pair fn\n (as_validator typename t1)\n (as_validator typename t2)\n\n | T_dep_pair fn i t ->\n assert_norm (as_type (T_dep_pair fn i t) == x:dtyp_as_type i & as_type (t x));\n assert_norm (as_parser (T_dep_pair fn i t) ==\n P.parse_dep_pair (dtyp_as_parser i) (fun (x:dtyp_as_type i) -> as_parser (t x)));\n A.validate_weaken_inv_loc (interp_inv inv) _ (interp_loc loc)\n (A.validate_dep_pair fn\n (A.validate_with_error_handler typename fn (dtyp_as_validator i))\n (dtyp_as_leaf_reader i)\n (fun x -> as_validator typename (t x)))\n\n | T_refine fn t f ->\n assert_norm (as_type (T_refine fn t f) == P.refine (dtyp_as_type t) f);\n assert_norm (as_parser (T_refine fn t f) == P.parse_filter (dtyp_as_parser t) f);\n A.validate_with_error_handler typename fn\n (A.validate_filter fn\n (dtyp_as_validator t)\n (dtyp_as_leaf_reader t)\n f \"reading field_value\" \"checking constraint\")\n\n | T_refine_with_action fn t f a ->\n assert_norm (as_type (T_refine_with_action fn t f a) == P.refine (dtyp_as_type t) f);\n assert_norm (as_parser (T_refine_with_action fn t f a) == P.parse_filter (dtyp_as_parser t) f);\n assert_norm (as_parser (T_refine fn t f) == P.parse_filter (dtyp_as_parser t) f);\n A.validate_with_error_handler typename fn\n (A.validate_filter_with_action fn\n (dtyp_as_validator t)\n (dtyp_as_leaf_reader t)\n f \"reading field_value\" \"checking constraint\"\n (fun x -> action_as_action (a x)))\n\n | T_dep_pair_with_refinement fn base refinement k ->\n assert_norm (as_type (T_dep_pair_with_refinement fn base refinement k) ==\n x:P.refine (dtyp_as_type base) refinement & as_type (k x));\n assert_norm (as_parser (T_dep_pair_with_refinement fn base refinement k) ==\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x))));\n A.validate_with_error_handler typename fn\n (A.validate_weaken_inv_loc _ _ _ (\n A.validate_dep_pair_with_refinement false fn\n (dtyp_as_validator base)\n (dtyp_as_leaf_reader base)\n refinement\n (fun x -> as_validator typename (k x))))\n\n | T_dep_pair_with_action fn base t act ->\n assert_norm (as_type (T_dep_pair_with_action fn base t act) ==\n x:dtyp_as_type base & as_type (t x));\n assert_norm (as_parser (T_dep_pair_with_action fn base t act) ==\n P.(dtyp_as_parser base `parse_dep_pair` (fun x -> as_parser (t x))));\n A.validate_with_error_handler typename fn\n (A.validate_weaken_inv_loc _ _ _ (\n A.validate_dep_pair_with_action\n (dtyp_as_validator base)\n (dtyp_as_leaf_reader base)\n (fun x -> action_as_action (act x))\n (fun x -> as_validator typename (t x))))\n\n | T_dep_pair_with_refinement_and_action fn base refinement k act ->\n assert_norm (as_type (T_dep_pair_with_refinement_and_action fn base refinement k act) ==\n x:P.refine (dtyp_as_type base) refinement & as_type (k x));\n assert_norm (as_parser (T_dep_pair_with_refinement_and_action fn base refinement k act) ==\n P.((dtyp_as_parser base `parse_filter` refinement) `parse_dep_pair` (fun x -> as_parser (k x))));\n A.validate_weaken_inv_loc _ _ _ (\n A.validate_dep_pair_with_refinement_and_action false fn\n (A.validate_with_error_handler typename fn\n (dtyp_as_validator base))\n (dtyp_as_leaf_reader base)\n refinement\n (fun x -> action_as_action (act x))\n (fun x -> as_validator typename (k x)))\n\n\n | T_if_else b t0 t1 ->\n assert_norm (as_type (T_if_else b t0 t1) == P.t_ite b (fun _ -> as_type (t0())) (fun _ -> as_type (t1 ())));\n let p0 (_:squash b) = P.parse_weaken_right (as_parser (t0())) _ in\n let p1 (_:squash (not b)) = P.parse_weaken_left (as_parser (t1())) _ in\n assert_norm (as_parser (T_if_else b t0 t1) == P.parse_ite b p0 p1);\n let v0 (_:squash b) =\n A.validate_weaken_right (as_validator typename (t0())) _\n in\n let v1 (_:squash (not b)) =\n A.validate_weaken_left (as_validator typename (t1())) _\n in\n A.validate_ite b p0 v0 p1 v1\n\n | T_cases b t0 t1 ->\n assert_norm (as_type (T_cases b t0 t1) == P.t_ite b (fun _ -> as_type t0) (fun _ -> as_type t1));\n let p0 (_:squash b) = P.parse_weaken_right (as_parser t0) _ in\n let p1 (_:squash (not b)) = P.parse_weaken_left (as_parser t1) _ in\n assert_norm (as_parser (T_cases b t0 t1) == P.parse_ite b p0 p1);\n let v0 (_:squash b) =\n A.validate_weaken_right (as_validator typename t0) _\n in\n let v1 (_:squash (not b)) =\n A.validate_weaken_left (as_validator typename t1) _\n in\n A.validate_ite b p0 v0 p1 v1\n\n | T_with_action fn t a ->\n assert_norm (as_type (T_with_action fn t a) == as_type t);\n assert_norm (as_parser (T_with_action fn t a) == as_parser t);\n A.validate_with_error_handler typename fn\n (A.validate_with_success_action fn\n (as_validator typename t)\n (action_as_action a))\n\n | T_with_dep_action fn i a ->\n assert_norm (as_type (T_with_dep_action fn i a) == dtyp_as_type i);\n assert_norm (as_parser (T_with_dep_action fn i a) == dtyp_as_parser i);\n A.validate_with_error_handler typename fn\n (A.validate_weaken_inv_loc _ _ _ (\n A.validate_with_dep_action fn\n (dtyp_as_validator i)\n (dtyp_as_leaf_reader i)\n (fun x -> action_as_action (a x))))\n\n\n | T_with_comment fn t c ->\n assert_norm (as_type (T_with_comment fn t c) == as_type t);\n assert_norm (as_parser (T_with_comment fn t c) == as_parser t);\n A.validate_with_comment c (as_validator typename t)\n\n | T_nlist fn n t ->\n assert_norm (as_type (T_nlist fn n t) == P.nlist n (as_type t));\n assert_norm (as_parser (T_nlist fn n t) == P.parse_nlist n (as_parser t));\n A.validate_with_error_handler typename fn\n (A.validate_nlist n (as_validator typename t))\n\n | T_at_most fn n t ->\n assert_norm (as_type (T_at_most fn n t) == P.t_at_most n (as_type t));\n assert_norm (as_parser (T_at_most fn n t) == P.parse_t_at_most n (as_parser t));\n A.validate_with_error_handler typename fn\n (A.validate_t_at_most n (as_validator typename t))\n\n | T_exact fn n t ->\n assert_norm (as_type (T_exact fn n t) == P.t_exact n (as_type t));\n assert_norm (as_parser (T_exact fn n t) == P.parse_t_exact n (as_parser t));\n A.validate_with_error_handler typename fn\n (A.validate_t_exact n (as_validator typename t))\n\n | T_string fn elt_t terminator ->\n assert_norm (as_type (T_string fn elt_t terminator) == P.cstring (dtyp_as_type elt_t) terminator);\n assert_norm (as_parser (T_string fn elt_t terminator) == P.parse_string (dtyp_as_parser elt_t) terminator);\n A.validate_with_error_handler typename fn\n (A.validate_string (dtyp_as_validator elt_t)\n (dtyp_as_leaf_reader elt_t)\n terminator)\n#pop-options\n[@@noextract_to \"krml\"; specialize]\ninline_for_extraction noextract\nlet validator_of #allow_reading #nz #wk (#k:P.parser_kind nz wk)\n (#[@@@erasable] i:inv_index)\n (#[@@@erasable] d:disj_index)\n (#[@@@erasable] l:loc_index)\n (t:typ k i d l allow_reading) =\n A.validate_with_action_t\n (as_parser t)\n (interp_inv i)\n (interp_disj d)\n (interp_loc l)\n allow_reading\n\n[@@noextract_to \"krml\"; specialize]\ninline_for_extraction noextract\nlet dtyp_of #nz #wk (#k:P.parser_kind nz wk)\n (#[@@@erasable] i:inv_index)\n (#[@@@erasable] d:disj_index)\n (#[@@@erasable] l:loc_index)\n #b (t:typ k i d l b) =\n dtyp k b i d l\n\nlet specialization_steps =\n [nbe;\n zeta;\n primops;\n iota;\n delta_attr [`%specialize];\n delta_only ([`%Some?;\n `%Some?.v;\n `%as_validator;\n `%nz_of_binding;\n `%wk_of_binding;\n `%pk_of_binding;\n `%inv_of_binding;\n `%loc_of_binding;\n `%type_of_binding;\n `%parser_of_binding;\n `%validator_of_binding;\n `%leaf_reader_of_binding;\n `%fst;\n `%snd;\n `%Mktuple2?._1;\n `%Mktuple2?._2]@projector_names)]\n\nlet specialize_tac steps (_:unit)\n : T.Tac unit\n = let open FStar.List.Tot in\n T.norm (steps@specialization_steps);\n T.trefl()\n\n[@@specialize]\nlet mk_global_binding #nz #wk\n (pk:P.parser_kind nz wk)\n ([@@@erasable] inv:inv_index)\n ([@@@erasable] disj:disj_index)\n ([@@@erasable] loc:loc_index)\n ([@@@erasable] p_t : Type0)\n ([@@@erasable] p_p : P.parser pk p_t)\n (p_reader: option (leaf_reader p_p))\n (b:bool)\n (p_v : A.validate_with_action_t p_p\n (interp_inv inv)\n (interp_disj disj)\n (interp_loc loc) b)\n ([@@@erasable] pf:squash (b == Some? p_reader))\n : global_binding\n = {\n parser_kind_nz = nz;\n parser_weak_kind = wk;\n parser_kind = pk;\n inv = inv;\n disj;\n loc = loc;\n p_t = p_t;\n p_p = p_p;\n p_reader = p_reader;\n p_v = p_v\n }\n\n[@@specialize]\nlet mk_dt_app #nz #wk (pk:P.parser_kind nz wk) (b:bool)\n ([@@@erasable] inv:inv_index)\n ([@@@erasable] disj:disj_index)\n ([@@@erasable] loc:loc_index)\n (x:global_binding)\n ([@@@erasable] pf:squash (nz == nz_of_binding x /\\\n wk == wk_of_binding x /\\\n pk == pk_of_binding x /\\\n b == has_reader x /\\\n inv == inv_of_binding x /\\\n disj == disj_of_bindng x /\\\n loc == loc_of_binding x))\n : dtyp #nz #wk pk b inv disj loc\n = DT_App pk b inv disj loc x pf\n\n\n[@@specialize]" }, { "file_name": "FStar.MRef.fst", "name": "FStar.MRef.p_pred", "opens_and_abbrevs": [ { "open": "FStar.Preorder" }, { "open": "FStar.ST" }, { "open": "FStar.Heap" }, { "open": "FStar.Preorder" }, { "open": "FStar.ST" }, { "open": "FStar.Heap" }, { "open": "FStar" }, { "open": "FStar" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "", "source_definition": "let p_pred (#a:Type) (#b:preorder a) (r:mref a b) (p:(a -> Type))\n = fun h -> h `contains` r /\\ p (sel h r)", "source_range": { "start_line": 22, "start_col": 8, "end_line": 23, "end_col": 42 }, "interleaved": false, "definition": "fun r p h -> FStar.Monotonic.Heap.contains h r /\\ p (FStar.Monotonic.Heap.sel h r)", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Preorder.preorder", "FStar.ST.mref", "FStar.Monotonic.Heap.heap", "Prims.l_and", "FStar.Monotonic.Heap.contains", "FStar.Monotonic.Heap.sel", "Prims.logical" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": true, "type": "r: FStar.ST.mref a b -> p: (_: a -> Type0) -> h: FStar.Monotonic.Heap.heap -> Prims.logical", "prompt": "let p_pred (#a: Type) (#b: preorder a) (r: mref a b) (p: (a -> Type)) =\n ", "expected_response": "fun h -> h `contains` r /\\ p (sel h r)", "source": { "project_name": "FStar", "file_name": "ulib/FStar.MRef.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "FStar.MRef.fst", "checked_file": "dataset/FStar.MRef.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.ST.fst.checked", "dataset/FStar.Preorder.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Heap.fst.checked" ] }, "definitions_in_context": [], "closest": [ "val FStar.ST.contains_pred = r: FStar.Monotonic.Heap.mref a rel -> h: FStar.Monotonic.Heap.heap -> Type0\nlet contains_pred (#a:Type0) (#rel:preorder a) (r:mref a rel) = fun h -> h `contains` r", "val FStar.TwoLevelHeap.contains_ref = r: FStar.TwoLevelHeap.rref i a -> m: FStar.TwoLevelHeap.t -> Prims.logical\nlet contains_ref (#a:Type) (#i:rid) (r:rref i a) (m:t) =\n Map.contains m i /\\ Heap.contains (Map.sel m i) (as_ref r)", "val FStar.Monotonic.HyperStack.mref = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_eternal_region_hs (frameOf s) && not (is_mm s) }", "val FStar.Monotonic.Heap.fresh = r: FStar.Monotonic.Heap.mref a rel -> h0: FStar.Monotonic.Heap.heap -> h1: FStar.Monotonic.Heap.heap\n -> Prims.logical\nlet fresh (#a:Type) (#rel:preorder a) (r:mref a rel) (h0:heap) (h1:heap) =\n r `unused_in` h0 /\\ h1 `contains` r", "val FStar.ST.stable = p: FStar.ST.heap_predicate -> Prims.logical\nlet stable (p:heap_predicate) =\n forall (h1:heap) (h2:heap). (p h1 /\\ heap_rel h1 h2) ==> p h2", "val MRefST.stable_on_heap_aux = \n m: MRefST.mref a r ->\n p: FStar.Preorder.predicate MRefHeap.heap ->\n h0: MRefHeap.heap ->\n h1: MRefHeap.heap\n -> Prims.logical\nlet stable_on_heap_aux (#a:Type) (#r:preorder a) (m:mref a r) (p:predicate heap) (h0:heap) (h1:heap) =\n p h0 /\\\n (contains m h0 ==> contains m h1 /\\ r (sel h0 m) (sel h1 m))\n ==>\n p h1", "val FStar.TwoLevelHeap.fresh_rref = r: FStar.TwoLevelHeap.rref i a -> m0: FStar.TwoLevelHeap.t -> m1: FStar.TwoLevelHeap.t\n -> Prims.logical\nlet fresh_rref (#a:Type) (#i:rid) (r:rref i a) (m0:t) (m1:t) =\n ~ (Heap.contains (Map.sel m0 i) (as_ref r))\n /\\ (Heap.contains (Map.sel m1 i) (as_ref r))", "val MRefST.stable_on_heap = m: MRefST.mref a r -> p: FStar.Preorder.predicate MRefHeap.heap -> Prims.logical\nlet stable_on_heap (#a:Type) (#r:preorder a) (m:mref a r) (p:predicate heap) =\n forall h0 h1 . stable_on_heap_aux m p h0 h1", "val FStar.Monotonic.HyperStack.mreference = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mreference a rel = mreference' a rel", "val FStar.Monotonic.HyperStack.unused_in = r: FStar.Monotonic.HyperStack.mreference a rel -> m: FStar.Monotonic.HyperStack.mem -> Prims.logical\nlet unused_in (#a:Type) (#rel:preorder a) (r:mreference a rel) (m:mem) =\n not ((get_hmap m) `Map.contains` (frameOf r)) \\/\n Heap.unused_in (as_ref r) ((get_hmap m) `Map.sel` (frameOf r))", "val FStar.Monotonic.HyperStack.mmmref = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mmmref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_eternal_region_hs (frameOf s) && is_mm s }", "val FStar.ST.heap_rel = h1: FStar.Monotonic.Heap.heap -> h2: FStar.Monotonic.Heap.heap -> Prims.logical\nlet heap_rel (h1:heap) (h2:heap) =\n forall (a:Type0) (rel:preorder a) (r:mref a rel). h1 `contains` r ==>\n (h2 `contains` r /\\ rel (sel h1 r) (sel h2 r))", "val FStar.Monotonic.HyperStack.s_mref = i: FStar.Monotonic.HyperHeap.rid -> a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet s_mref (i:rid) (a:Type) (rel:preorder a) = s:mreference a rel{frameOf s = i}", "val AllocSTwHeaps.contains = r: FStar.ST.ref a -> h: FStar.Monotonic.Heap.heap -> Prims.logical\nlet contains (#a:Type) (r:ref a) (h:FStar.Heap.heap) =\n b2t (FStar.StrongExcludedMiddle.strong_excluded_middle (FStar.Heap.contains h r))", "val ImmutableSTwHeaps.heap_rel = h0: FStar.Monotonic.Heap.heap -> h1: FStar.Monotonic.Heap.heap -> Prims.logical\nlet heap_rel (h0:heap) (h1:heap) = \n forall a (r: ref a) . contains h0 r ==> contains h1 r /\\ sel h0 r == sel h1 r", "val FStar.HyperStack.ST.deref_post = \n r: FStar.HyperStack.ST.mreference a rel ->\n m0: FStar.Monotonic.HyperStack.mem ->\n x: a ->\n m1: FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet deref_post (#a:Type) (#rel:preorder a) (r:mreference a rel) (m0:mem) (x:a) (m1:mem) =\n m1 == m0 /\\ m0 `contains` r /\\ x == HyperStack.sel m0 r", "val FStar.ST.modifies_none = h0: FStar.Monotonic.Heap.heap -> h1: FStar.Monotonic.Heap.heap -> Prims.logical\nlet modifies_none (h0:heap) (h1:heap) = modifies !{} h0 h1", "val FStar.Monotonic.HyperStack.mstackref = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mstackref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_stack_region (frameOf s) && not (is_mm s) }", "val FStar.Buffer.disjoint_ref_1 = a: FStar.Buffer.buffer t -> r: FStar.HyperStack.ST.reference u401 -> Prims.logical\nlet disjoint_ref_1 (#t:Type) (#u:Type) (a:buffer t) (r:reference u) = \n frameOf a =!= HS.frameOf r \\/ as_addr a =!= HS.as_addr r", "val FStar.Monotonic.HyperStack.mmmstackref = a: Type0 -> rel: FStar.Preorder.preorder a -> Type0\nlet mmmstackref (a:Type) (rel:preorder a) =\n s:mreference a rel{ is_stack_region (frameOf s) && is_mm s }", "val FStar.Monotonic.DependentMap.t = \n r: FStar.HyperStack.ST.erid ->\n a: Prims.eqtype ->\n b: (_: a -> Type0) ->\n inv: (_: FStar.DependentMap.t a (FStar.Monotonic.DependentMap.opt b) -> Type)\n -> Type0\nlet t (r:HST.erid) (a:eqtype) (b:a -> Type) (inv:DM.t a (opt b) -> Type) =\n m_rref r (imap a b inv) grows", "val AllocSTwHeaps.heap_rel = h0: FStar.Monotonic.Heap.heap -> h1: FStar.Monotonic.Heap.heap -> Prims.logical\nlet heap_rel (h0:FStar.Heap.heap) (h1:FStar.Heap.heap) = \n forall (a:Type0) (r:ref a) . FStar.Heap.contains h0 r ==> FStar.Heap.contains h1 r", "val FStar.MRef.stable = p: FStar.Preorder.predicate _ -> rel: FStar.Preorder.relation _ {FStar.Preorder.preorder_rel rel}\n -> Prims.logical\nlet stable = FStar.Preorder.stable", "val FStar.Monotonic.DependentMap.forall_t = \n t: FStar.Monotonic.DependentMap.t r a b inv ->\n h: FStar.Monotonic.HyperStack.mem ->\n pred: (x: a -> _: b x -> Type0)\n -> Prims.logical\nlet forall_t (#a:eqtype) (#b:a -> Type) (#inv:DM.t a (opt b) -> Type) (#r:HST.erid)\n (t:t r a b inv) (h:HS.mem) (pred: (x:a) -> b x -> Type0)\n = forall (x:a).{:pattern (sel (HS.sel h t) x) \\/ (DM.sel (repr (HS.sel h t)) x)}\n defined t x h ==> pred x (Some?.v (sel (HS.sel h t) x))", "val FStar.Relational.Relational.sel_rel1 = h: FStar.Relational.Relational.double FStar.Monotonic.Heap.heap -> r: FStar.Heap.ref a\n -> Prims.GTot (FStar.Relational.Relational.double a)\nlet sel_rel1 (#a:Type) (h:double heap) (r:ref a) = rel_map2G sel h (twice r)", "val FStar.Monotonic.Heap.set = a: Prims.eqtype -> Type0\nlet set = Set.set", "val FStar.Preorder.stable = p: FStar.Preorder.predicate a -> rel: FStar.Preorder.relation a {FStar.Preorder.preorder_rel rel}\n -> Prims.logical\nlet stable (#a:Type) (p:predicate a) (rel:relation a{preorder_rel rel}) =\n forall (x:a) (y:a). (p x /\\ rel x y) ==> p y", "val FStar.Monotonic.HyperStack.heap_only = m0: FStar.Monotonic.HyperStack.mem -> Prims.logical\nlet heap_only (m0:mem) = get_tip m0 == root", "val FStar.HyperStack.ref = a: Type0 -> Type0\nlet ref (a:Type) = mref a (Heap.trivial_preorder a)", "val FStar.HyperStack.mmref = a: Type0 -> Type0\nlet mmref (a:Type) = mmmref a (Heap.trivial_preorder a)", "val FStar.TwoLevelHeap.sel = m: FStar.TwoLevelHeap.t -> r: FStar.TwoLevelHeap.rref i a -> Prims.GTot a\nlet sel (#a:Type) (#i:rid) (m:t) (r:rref i a) = Heap.sel (Map.sel m i) (as_ref r)", "val FStar.Monotonic.HyperStack.contains_ref_in_its_region = m: FStar.Monotonic.HyperStack.mem -> r: FStar.Monotonic.HyperStack.mreference a rel -> Type0\nlet contains_ref_in_its_region (#a:Type) (#rel:preorder a) (m:mem) (r:mreference a rel) =\n Heap.contains (get_hmap m `Map.sel` (frameOf r)) (as_ref r)", "val FStar.Preorder.reflexive = rel: FStar.Preorder.relation a -> Prims.logical\nlet reflexive (#a:Type) (rel:relation a) =\n forall (x:a). rel x x", "val FStar.ReflexiveTransitiveClosure.reflexive = rel: FStar.ReflexiveTransitiveClosure.binrel a -> Prims.logical\nlet reflexive (#a:Type) (rel:binrel u#a u#r a) =\n forall (x:a). squash (rel x x)", "val MRefST.heap_rel = h0: MRefHeap.heap -> h1: MRefHeap.heap -> Prims.logical\nlet heap_rel (h0:heap) (h1:heap) =\n (forall a r (m:mref a r) . contains m h0 ==> contains m h1) /\\\n (forall a (r:preorder a) (m:mref a r{contains m h0}) . r (sel h0 m) (sel h1 m))", "val FStar.HyperStack.ST.ralloc_post = \n i: FStar.Monotonic.HyperHeap.rid ->\n init: a ->\n m0: FStar.Monotonic.HyperStack.mem ->\n x: FStar.HyperStack.ST.mreference a rel ->\n m1: FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet ralloc_post (#a:Type) (#rel:preorder a) (i:rid) (init:a) (m0:mem)\n (x:mreference a rel) (m1:mem) =\n let region_i = get_hmap m0 `Map.sel` i in\n as_ref x `Heap.unused_in` region_i /\\\n i `is_in` get_hmap m0 /\\\n i = frameOf x /\\\n m1 == upd m0 x init", "val MRefST.mref0 = a: Type0 -> r: MRefHeap.preorder_t a -> Type0\nlet mref0 = mref", "val FStar.HyperStack.ST.same_refs_common = \n p:\n (\n _: FStar.Monotonic.HyperStack.mem ->\n _: FStar.Monotonic.HyperStack.mem ->\n _: FStar.Monotonic.HyperHeap.rid\n -> Type0) ->\n m0: FStar.Monotonic.HyperStack.mem ->\n m1: FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet same_refs_common (p:mem -> mem -> rid -> Type0) (m0 m1:mem) =\n forall (r:rid). p m0 m1 r ==> equal_heap_dom r m0 m1", "val FStar.Monotonic.Seq.test = \n i: FStar.Monotonic.Seq.rid ->\n l: FStar.Monotonic.Seq.rid ->\n a: Type0 ->\n log: FStar.Monotonic.Seq.log_t l a ->\n r: FStar.Monotonic.Seq.seqn i log 8 ->\n h: FStar.Monotonic.HyperStack.mem\n -> Prims.unit\nlet test (i:rid) (l:rid) (a:Type0) (log:log_t l a) //(p:(nat -> Type))\n (r:seqn i log 8) (h:mem)\n = assert (HS.sel h r = Heap.sel (FStar.Map.sel (HS.get_hmap h) i) (HS.as_ref r))", "val FStar.ReflexiveTransitiveClosure.preorder_rel = rel: FStar.ReflexiveTransitiveClosure.binrel a -> Prims.logical\nlet preorder_rel (#a:Type) (rel:binrel u#a u#r a) =\n reflexive rel /\\ transitive rel", "val LowParse.Repr.valid_repr_pos = r: LowParse.Repr.repr_pos t b -> h: FStar.Monotonic.HyperStack.mem -> Prims.logical\nlet valid_repr_pos (#t:Type) (#b:const_slice) (r:repr_pos t b) (h:HS.mem)\n = valid (as_ptr_spec r) h /\\\n C.live h b.base", "val FStar.Monotonic.HyperStack.popped = m0: FStar.Monotonic.HyperStack.mem -> m1: FStar.Monotonic.HyperStack.mem -> Prims.logical\nlet popped (m0 m1:mem) =\n poppable m0 /\\\n (let h0, tip0, h1, tip1 = get_hmap m0, get_tip m0, get_hmap m1, get_tip m1 in\n (parent tip0 = tip1 /\\\n Set.equal (Map.domain h1) (remove_elt (Map.domain h0) tip0) /\\\n Map.equal h1 (Map.restrict (Map.domain h1) h0)))", "val FStar.Monotonic.HyperHeap.modifies_one = \n r: FStar.Monotonic.HyperHeap.rid ->\n m0: FStar.Monotonic.HyperHeap.hmap ->\n m1: FStar.Monotonic.HyperHeap.hmap\n -> Prims.logical\nlet modifies_one (r:rid) (m0:hmap) (m1:hmap) = modifies_just (Set.singleton r) m0 m1", "val ProgramEquivalence.ref_not_in_fp = r: FStar.DM4F.Heap.ref a -> s: ProgramEquivalence.fp -> Prims.logical\nlet ref_not_in_fp (#a:Type) (r:ref a) (s:fp) =\n forall (r':ref nat). memP r' s ==> addr_of r' <> addr_of r", "val FStar.Monotonic.Seq.i_seq = r: FStar.Monotonic.Seq.rid -> a: Type0 -> p: (_: FStar.Seq.Base.seq a -> Type) -> Type0\nlet i_seq (r:rid) (a:Type) (p:seq a -> Type) = m_rref r (s:seq a{p s}) (grows_p p)", "val FStar.MRef.spred = rel: FStar.Preorder.preorder a -> Type\nlet spred (#a:Type) (rel:preorder a) = p:(a -> Type){Preorder.stable p rel}", "val FStar.DM4F.Heap.consistent = h0: FStar.DM4F.Heap.heap -> h1: FStar.DM4F.Heap.heap -> Prims.logical\nlet consistent (h0:heap) (h1:heap) =\n forall n x y. h0.memory n == Some x /\\ h1.memory n == Some y ==> dfst x == dfst y", "val FStar.Buffer.as_ref = b: FStar.Buffer.buffer a\n -> Prims.GTot\n (FStar.Monotonic.Heap.mref (FStar.Buffer.lseq a (FStar.Buffer.max_length b))\n (FStar.Heap.trivial_preorder (FStar.Buffer.lseq a (FStar.Buffer.max_length b))))\nlet as_ref #a (b:buffer a) = as_ref (content b)", "val FStar.Buffer.disjoint_ref_5 = \n a: FStar.Buffer.buffer _ ->\n r: FStar.HyperStack.ST.reference _ ->\n r': FStar.HyperStack.ST.reference _ ->\n r'': FStar.HyperStack.ST.reference _ ->\n r''': FStar.HyperStack.ST.reference _ ->\n r'''': FStar.HyperStack.ST.reference _\n -> Prims.logical\nlet disjoint_ref_5 a r r' r'' r''' r'''' = disjoint_ref_1 a r /\\ disjoint_ref_4 a r' r'' r''' r''''", "val Point.ref_not_in_fp = r: FStar.DM4F.Heap.ref a -> s: Point.fp -> Prims.logical\nlet ref_not_in_fp (#a:Type) (r:ref a) (s:fp) =\n forall (r':ref nat). memP r' s ==> addr_of r' <> addr_of r", "val FStar.Pervasives.all_if_then_else = \n heap: Type ->\n a: Type ->\n p: Type0 ->\n wp_then: FStar.Pervasives.all_wp_h heap a ->\n wp_else: FStar.Pervasives.all_wp_h heap a ->\n post: FStar.Pervasives.all_post_h heap a ->\n h0: heap\n -> Prims.logical\nlet all_if_then_else\n (heap a p: Type)\n (wp_then wp_else: all_wp_h heap a)\n (post: all_post_h heap a)\n (h0: heap)\n = wp_then post h0 /\\ (~p ==> wp_else post h0)", "val FStar.UInt128.fact0 = a: FStar.UInt.uint_t 64 -> b: FStar.UInt.uint_t 64 -> Prims.logical\nlet fact0 (a b: uint_t 64) = carry_bv a b == int2bv 0", "val FStar.Pervasives.st_if_then_else = \n heap: Type ->\n a: Type ->\n p: Type0 ->\n wp_then: FStar.Pervasives.st_wp_h heap a ->\n wp_else: FStar.Pervasives.st_wp_h heap a ->\n post: FStar.Pervasives.st_post_h heap a ->\n h0: heap\n -> Prims.logical\nlet st_if_then_else\n (heap a p: Type)\n (wp_then wp_else: st_wp_h heap a)\n (post: st_post_h heap a)\n (h0: heap)\n = wp_then post h0 /\\ (~p ==> wp_else post h0)", "val FStar.Pervasives.st_post_h = heap: Type -> a: Type -> Type\nlet st_post_h (heap a: Type) = st_post_h' heap a True", "val LowStar.Monotonic.Buffer.malloc_pre = r: FStar.Monotonic.HyperHeap.rid -> len: FStar.UInt32.t -> Prims.logical\nlet malloc_pre (r:HS.rid) (len:U32.t) = HST.is_eternal_region r /\\ U32.v len > 0", "val FStar.BigOps.reflexive = f: (_: a -> _: a -> Type0) -> Prims.logical\nlet reflexive (#a: Type) (f: (a -> a -> Type)) = forall x. f x x", "val MRefST.ist_witnessed = p: FStar.Preorder.predicate MRefHeap.heap {FStar.Preorder.stable p MRefST.heap_rel} -> Type0\nlet ist_witnessed (p:predicate heap{stable p heap_rel}) = witnessed heap_rel p", "val Steel.Heap.witnessed_ref = r: Steel.Heap.ref a pcm -> fact: (_: a -> Prims.prop) -> h: Steel.Heap.full_heap -> Prims.logical\nlet witnessed_ref (#a:Type u#a)\n (#pcm:pcm a)\n (r:ref a pcm)\n (fact:a -> prop)\n (h:full_heap)\n = interp (ptr r) h /\\\n fact (sel r h)", "val FStar.ReflexiveTransitiveClosure.stable = \n p: (_: a -> Type0) ->\n rel:\n FStar.ReflexiveTransitiveClosure.binrel a {FStar.ReflexiveTransitiveClosure.preorder_rel rel}\n -> Prims.logical\nlet stable (#a:Type u#a) (p:a -> Type0) (rel:binrel u#a u#r a{preorder_rel rel}) =\n forall (x:a) (y:a). (p x /\\ squash (rel x y)) ==> p y", "val FStar.Buffer.disjoint_ref_4 = \n a: FStar.Buffer.buffer _ ->\n r: FStar.HyperStack.ST.reference _ ->\n r': FStar.HyperStack.ST.reference _ ->\n r'': FStar.HyperStack.ST.reference _ ->\n r''': FStar.HyperStack.ST.reference _\n -> Prims.logical\nlet disjoint_ref_4 a r r' r'' r''' = disjoint_ref_1 a r /\\ disjoint_ref_3 a r' r'' r'''", "val FStar.Pervasives.st_post_h' = heap: Type -> a: Type -> pre: Type -> Type\nlet st_post_h' (heap a pre: Type) = a -> _: heap{pre} -> GTot Type0", "val FStar.Buffer.disjoint_ref_2 = \n a: FStar.Buffer.buffer _ ->\n r: FStar.HyperStack.ST.reference _ ->\n r': FStar.HyperStack.ST.reference _\n -> Prims.logical\nlet disjoint_ref_2 a r r' = disjoint_ref_1 a r /\\ disjoint_ref_1 a r'", "val FStar.Monotonic.HyperStack.contains = m: FStar.Monotonic.HyperStack.mem -> s: FStar.Monotonic.HyperStack.mreference a rel -> Prims.logical\nlet contains (#a:Type) (#rel:preorder a) (m:mem) (s:mreference a rel) =\n live_region m (frameOf s) /\\\n Heap.contains (get_hmap m `Map.sel` (frameOf s)) (as_ref s)", "val FStar.Preorder.preorder_rel = rel: FStar.Preorder.relation a -> Prims.logical\nlet preorder_rel (#a:Type) (rel:relation a) =\n reflexive rel /\\ transitive rel", "val FStar.Pervasives.st_close_wp = \n heap: Type ->\n a: Type ->\n b: Type ->\n wp: (_: b -> Prims.GTot (FStar.Pervasives.st_wp_h heap a)) ->\n p: FStar.Pervasives.st_post_h heap a ->\n h: heap\n -> Prims.logical\nlet st_close_wp (heap a b: Type) (wp: (b -> GTot (st_wp_h heap a))) (p: st_post_h heap a) (h: heap) =\n (forall (b: b). wp b p h)", "val FStar.Monotonic.Heap.tset = a: Type -> Type\nlet tset = TSet.set", "val FStar.HyperStack.stackref = a: Type0 -> Type0\nlet stackref (a:Type) = mstackref a (Heap.trivial_preorder a)", "val FStar.HyperStack.mmstackref = a: Type0 -> Type0\nlet mmstackref (a:Type) = mmmstackref a (Heap.trivial_preorder a)", "val GMST.stable = p: FStar.Preorder.predicate a -> rel: FStar.Preorder.preorder a -> Prims.logical\nlet stable (#a:Type) (p:predicate a) (rel:preorder a) \n = forall x y . p x /\\ rel x y ==> p y", "val FStar.Buffer.modifies_buf_0 = \n rid: FStar.Monotonic.HyperHeap.rid ->\n h: FStar.Monotonic.HyperStack.mem ->\n h': FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet modifies_buf_0 rid h h' =\n modifies_ref rid (Set.empty #nat) h h'\n /\\ (forall (#tt:Type) (bb:buffer tt). (frameOf bb == rid /\\ live h bb) ==> equal h bb h' bb /\\ live h' bb)", "val FStar.Pervasives.st_wp_h = heap: Type -> a: Type -> Type\nlet st_wp_h (heap a: Type) = st_post_h heap a -> Tot (st_pre_h heap)", "val FStar.Preorder.transitive = rel: FStar.Preorder.relation a -> Prims.logical\nlet transitive (#a:Type) (rel:relation a) =\n forall (x:a) (y:a) (z:a). (rel x y /\\ rel y z) ==> rel x z", "val FStar.HyperStack.ST.modifies_none = h0: FStar.Monotonic.HyperStack.mem -> h1: FStar.Monotonic.HyperStack.mem -> Prims.logical\nlet modifies_none (h0:mem) (h1:mem) = modifies Set.empty h0 h1", "val FStar.Monotonic.Seq.map_prefix = \n r: FStar.HyperStack.ST.m_rref i (FStar.Seq.Base.seq a) FStar.Monotonic.Seq.grows ->\n f: (_: a -> b) ->\n bs: FStar.Seq.Base.seq b ->\n h: FStar.Monotonic.HyperStack.mem\n -> Type0\nlet map_prefix (#a:Type) (#b:Type) (#i:rid)\n\t (r:m_rref i (seq a) grows)\n\t (f:a -> Tot b)\n\t (bs:seq b)\n\t (h:mem) =\n grows bs (map f (HS.sel h r))", "val FStar.Pervasives.st_pre_h = heap: Type -> Type\nlet st_pre_h (heap: Type) = heap -> GTot Type0", "val FStar.Monotonic.HyperStack.modifies_ref = \n id: FStar.Monotonic.HyperHeap.rid ->\n s: FStar.Set.set Prims.nat ->\n h0: FStar.Monotonic.HyperStack.mem ->\n h1: FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet modifies_ref (id:rid) (s:Set.set nat) (h0:mem) (h1:mem) =\n Heap.modifies s (get_hmap h0 `Map.sel` id) (get_hmap h1 `Map.sel` id)", "val FStar.Pervasives.st_bind_wp = \n heap: Type ->\n a: Type ->\n b: Type ->\n wp1: FStar.Pervasives.st_wp_h heap a ->\n wp2: (_: a -> Prims.GTot (FStar.Pervasives.st_wp_h heap b)) ->\n p: FStar.Pervasives.st_post_h heap b ->\n h0: heap\n -> Type0\nlet st_bind_wp\n (heap: Type)\n (a b: Type)\n (wp1: st_wp_h heap a)\n (wp2: (a -> GTot (st_wp_h heap b)))\n (p: st_post_h heap b)\n (h0: heap)\n = wp1 (fun a h1 -> wp2 a p h1) h0", "val FStar.Tactics.Effect.tac_wp_monotonic = wp: FStar.Tactics.Effect.tac_wp_t0 a -> Prims.logical\nlet tac_wp_monotonic (#a:Type) (wp:tac_wp_t0 a) =\n forall (ps:proofstate) (p q:__result a -> Type0).\n (forall x. p x ==> q x) ==> (wp ps p ==> wp ps q)", "val FStar.Monotonic.Seq.collect_prefix = \n r: FStar.HyperStack.ST.m_rref i (FStar.Seq.Base.seq a) FStar.Monotonic.Seq.grows ->\n f: (_: a -> FStar.Seq.Base.seq b) ->\n bs: FStar.Seq.Base.seq b ->\n h: FStar.Monotonic.HyperStack.mem\n -> Type0\nlet collect_prefix (#a:Type) (#b:Type) (#i:rid)\n\t\t (r:m_rref i (seq a) grows)\n\t\t (f:a -> Tot (seq b))\n\t\t (bs:seq b)\n\t\t (h:mem) =\n grows bs (collect f (HS.sel h r))", "val FStar.BigOps.anti_reflexive = f: (_: a -> _: a -> Type0) -> Prims.logical\nlet anti_reflexive (#a: Type) (f: (a -> a -> Type)) = forall x. ~(f x x)", "val recall : #a:Type ->\n #r:preorder a ->\n\t m:mref a r ->\n\t p:predicate heap{stable_on_heap m p} ->\n\t MRefST unit (fun h0 -> ist_witnessed p)\n\t (fun h0 _ h1 -> h0 == h1 /\\\n\t\t\t p h1)\nlet recall #a #r m p =\n ist_recall p", "val FStar.Monotonic.Heap.upd_tot' = h: FStar.Monotonic.Heap.heap -> r: FStar.Monotonic.Heap.mref a rel -> x: a\n -> FStar.Monotonic.Heap.heap_rec\nlet upd_tot' (#a: Type0) (#rel: preorder a) (h: heap) (r: mref a rel) (x: a) =\n { h with memory = F.on_dom pos (fun r' -> if r.addr = r'\n\t\t\t then Some (| a, Some rel, r.mm, x |)\n else h.memory r') }", "val FStar.Buffer.modifies_buf_1 = \n rid: FStar.Monotonic.HyperHeap.rid ->\n b: FStar.Buffer.buffer t ->\n h: FStar.Monotonic.HyperStack.mem ->\n h': FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet modifies_buf_1 (#t:Type) rid (b:buffer t) h h' = //would be good to drop the rid argument on these, since they can be computed from the buffers\n modifies_ref rid (Set.singleton (Heap.addr_of (as_ref b))) h h'\n /\\ (forall (#tt:Type) (bb:buffer tt). (frameOf bb == rid /\\ live h bb /\\ disjoint b bb) ==> equal h bb h' bb /\\ live h' bb)", "val FStar.Buffer.disjoint_ref_3 = \n a: FStar.Buffer.buffer _ ->\n r: FStar.HyperStack.ST.reference _ ->\n r': FStar.HyperStack.ST.reference _ ->\n r'': FStar.HyperStack.ST.reference _\n -> Prims.logical\nlet disjoint_ref_3 a r r' r'' = disjoint_ref_1 a r /\\ disjoint_ref_2 a r' r''", "val FStar.UInt128.fact1 = a: FStar.UInt.uint_t 64 -> b: FStar.UInt.uint_t 64 -> Prims.logical\nlet fact1 (a b: uint_t 64) = carry_bv a b == int2bv 1", "val FStar.ST.lift_div_gst = a: Type -> wp: Prims.pure_wp a -> p: FStar.ST.gst_post a -> h: FStar.Monotonic.Heap.heap\n -> Prims.pure_pre\nlet lift_div_gst (a:Type) (wp:pure_wp a) (p:gst_post a) (h:heap) = wp (fun a -> p a h)", "val FStar.HyperStack.ST.assign_post = \n r: FStar.HyperStack.ST.mreference a rel ->\n v: a ->\n m0: FStar.Monotonic.HyperStack.mem ->\n _: Prims.unit ->\n m1: FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet assign_post (#a:Type) (#rel:preorder a) (r:mreference a rel) (v:a) (m0:mem) (_:unit) (m1:mem) =\n m0 `contains` r /\\ m1 == HyperStack.upd m0 r v", "val FStar.PredicateExtensionality.predicate = a: Type -> Type\nlet predicate (a:Type) = a -> Tot prop", "val FStar.Tactics.CanonMonoid.lem0 = a: Prims.int -> b: Prims.int -> c: Prims.int -> d: Prims.int -> Prims.unit\nlet lem0 (a b c d : int) =\n assert_by_tactic (0 + a + b + c + d == (0 + a) + (b + c + 0) + (d + 0))\n (fun _ -> canon_monoid int_plus_monoid (* string_of_int *); trefl())", "val FStar.Buffer.modifies_buf_3 = \n rid: FStar.Monotonic.HyperHeap.rid ->\n b: FStar.Buffer.buffer t ->\n b': FStar.Buffer.buffer t' ->\n b'': FStar.Buffer.buffer t'' ->\n h: FStar.Monotonic.HyperStack.mem ->\n h': FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet modifies_buf_3 (#t:Type) (#t':Type) (#t'':Type) rid (b:buffer t) (b':buffer t') (b'':buffer t'') h h' =\n modifies_ref rid (to_set_3 (as_addr b) (as_addr b') (as_addr b'')) h h'\n /\\ (forall (#tt:Type) (bb:buffer tt). (frameOf bb == rid /\\ live h bb /\\ disjoint b bb /\\ disjoint b' bb /\\ disjoint b'' bb)\n ==> equal h bb h' bb /\\ live h' bb)", "val FStar.TwoLevelHeap.st_post' = a: Type -> pre: Type -> Type\nlet st_post' (a:Type) (pre:Type) = st_post_h' t a pre", "val FStar.Monotonic.Heap.modifies = \n s: FStar.Monotonic.Heap.set Prims.nat ->\n h0: FStar.Monotonic.Heap.heap ->\n h1: FStar.Monotonic.Heap.heap\n -> Prims.logical\nlet modifies (s:set nat) (h0:heap) (h1:heap) = modifies_t (TS.tset_of_set s) h0 h1", "val FStar.Monotonic.Pure.is_monotonic = wp: Prims.pure_wp' a -> Prims.logical\nlet is_monotonic (#a:Type) (wp:pure_wp' a) =\n (*\n * Once we support using tactics in ulib/,\n * this would be written as: Prims.pure_wp_monotonic0,\n * with a postprocessing tactic to norm it\n *)\n forall (p q:pure_post a). (forall (x:a). p x ==> q x) ==> (wp p ==> wp q)", "val IfcDelimitedRelease.rel_contains = h: Rel.rel FStar.Monotonic.Heap.heap -> r: FStar.Heap.ref Prims.int -> Prims.logical\nlet rel_contains (h:rel heap) (r:ref int) = (R?.l h) `contains` r /\\ (R?.r h) `contains` r", "val FStar.Buffer.disjoint_from_refs = b: FStar.Buffer.buffer a -> set: FStar.Set.set Prims.nat -> Prims.logical\nlet disjoint_from_refs #a (b:buffer a) (set:Set.set nat) =\n ~(Set.mem (as_addr b) set)", "val FStar.Pervasives.ex_stronger = a: Type -> wp1: FStar.Pervasives.ex_wp a -> wp2: FStar.Pervasives.ex_wp a -> Prims.logical\nlet ex_stronger (a: Type) (wp1 wp2: ex_wp a) = (forall (p: ex_post a). wp1 p ==> wp2 p)", "val ImmutableST.heap_rel = h0: NatHeap.heap -> h1: NatHeap.heap -> Prims.logical\nlet heap_rel (h0:heap) (h1:heap) = \n (forall a (r:ref a) . contains r h0 ==> contains r h1) /\\\n (forall a (r:ref a{contains r h0}) . sel h0 r == sel h1 r)", "val FStar.Monotonic.HyperStack.modifies_transitively = \n s: FStar.Set.set FStar.Monotonic.HyperHeap.rid ->\n m0: FStar.Monotonic.HyperStack.mem ->\n m1: FStar.Monotonic.HyperStack.mem\n -> Prims.logical\nlet modifies_transitively (s:Set.set rid) (m0:mem) (m1:mem) = FStar.Monotonic.HyperHeap.modifies s (get_hmap m0) (get_hmap m1)", "val IMST.st_return = a: Type -> x: a -> s: Type0 -> rel: FStar.Preorder.preorder s -> post: IMST.st_post s a -> s0: s\n -> Prims.logical\nlet st_return (a:Type) (x:a) (s:Type0) (rel:preorder s) (post:st_post s a) (s0:s)\n = forall v. v == x ==> post v s0", "val FStar.InteractiveHelpers.Tutorial.Definitions.spred1 = \n h: FStar.Monotonic.HyperStack.mem ->\n r1: LowStar.Buffer.buffer Prims.int ->\n r2: LowStar.Buffer.buffer Prims.int ->\n r3: LowStar.Buffer.buffer Prims.int\n -> Prims.logical\nlet spred1 (h : HS.mem) (r1 r2 r3 : B.buffer int) = True" ], "closest_src": [ { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.contains_pred" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.contains_ref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.fresh" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.stable" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.stable_on_heap_aux" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.fresh_rref" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.stable_on_heap" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mreference" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.unused_in" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mmmref" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.heap_rel" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.s_mref" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.contains" }, { "project_name": "FStar", "file_name": "ImmutableSTwHeaps.fst", "name": "ImmutableSTwHeaps.heap_rel" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fsti", "name": "FStar.HyperStack.ST.deref_post" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.modifies_none" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mstackref" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.disjoint_ref_1" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.mmmstackref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.DependentMap.fsti", "name": "FStar.Monotonic.DependentMap.t" }, { "project_name": "FStar", "file_name": "AllocSTwHeaps.fst", "name": "AllocSTwHeaps.heap_rel" }, { "project_name": "FStar", "file_name": "FStar.MRef.fsti", "name": "FStar.MRef.stable" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.DependentMap.fsti", "name": "FStar.Monotonic.DependentMap.forall_t" }, { "project_name": "FStar", "file_name": "FStar.Relational.Relational.fst", "name": "FStar.Relational.Relational.sel_rel1" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.set" }, { "project_name": "FStar", "file_name": "FStar.Preorder.fst", "name": "FStar.Preorder.stable" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.heap_only" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.ref" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.mmref" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.sel" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.contains_ref_in_its_region" }, { "project_name": "FStar", "file_name": "FStar.Preorder.fst", "name": "FStar.Preorder.reflexive" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fsti", "name": "FStar.ReflexiveTransitiveClosure.reflexive" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.heap_rel" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fsti", "name": "FStar.HyperStack.ST.ralloc_post" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.mref0" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fsti", "name": "FStar.HyperStack.ST.same_refs_common" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Seq.fst", "name": "FStar.Monotonic.Seq.test" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fsti", "name": "FStar.ReflexiveTransitiveClosure.preorder_rel" }, { "project_name": "everparse", "file_name": "LowParse.Repr.fsti", "name": "LowParse.Repr.valid_repr_pos" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.popped" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperHeap.fsti", "name": "FStar.Monotonic.HyperHeap.modifies_one" }, { "project_name": "FStar", "file_name": "ProgramEquivalence.fst", "name": "ProgramEquivalence.ref_not_in_fp" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Seq.fst", "name": "FStar.Monotonic.Seq.i_seq" }, { "project_name": "FStar", "file_name": "FStar.MRef.fsti", "name": "FStar.MRef.spred" }, { "project_name": "FStar", "file_name": "FStar.DM4F.Heap.fst", "name": "FStar.DM4F.Heap.consistent" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.as_ref" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.disjoint_ref_5" }, { "project_name": "FStar", "file_name": "Point.fst", "name": "Point.ref_not_in_fp" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.all_if_then_else" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fst", "name": "FStar.UInt128.fact0" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_if_then_else" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_post_h" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fsti", "name": "LowStar.Monotonic.Buffer.malloc_pre" }, { "project_name": "FStar", "file_name": "FStar.BigOps.fsti", "name": "FStar.BigOps.reflexive" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.ist_witnessed" }, { "project_name": "steel", "file_name": "Steel.Heap.fsti", "name": "Steel.Heap.witnessed_ref" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fsti", "name": "FStar.ReflexiveTransitiveClosure.stable" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.disjoint_ref_4" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_post_h'" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.disjoint_ref_2" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.contains" }, { "project_name": "FStar", "file_name": "FStar.Preorder.fst", "name": "FStar.Preorder.preorder_rel" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_close_wp" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.tset" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.stackref" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.mmstackref" }, { "project_name": "FStar", "file_name": "GMST.fst", "name": "GMST.stable" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.modifies_buf_0" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_wp_h" }, { "project_name": "FStar", "file_name": "FStar.Preorder.fst", "name": "FStar.Preorder.transitive" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fsti", "name": "FStar.HyperStack.ST.modifies_none" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Seq.fst", "name": "FStar.Monotonic.Seq.map_prefix" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_pre_h" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.modifies_ref" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.st_bind_wp" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Effect.fsti", "name": "FStar.Tactics.Effect.tac_wp_monotonic" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Seq.fst", "name": "FStar.Monotonic.Seq.collect_prefix" }, { "project_name": "FStar", "file_name": "FStar.BigOps.fsti", "name": "FStar.BigOps.anti_reflexive" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.recall" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.upd_tot'" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.modifies_buf_1" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.disjoint_ref_3" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fst", "name": "FStar.UInt128.fact1" }, { "project_name": "FStar", "file_name": "FStar.ST.fst", "name": "FStar.ST.lift_div_gst" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.ST.fsti", "name": "FStar.HyperStack.ST.assign_post" }, { "project_name": "FStar", "file_name": "FStar.PredicateExtensionality.fst", "name": "FStar.PredicateExtensionality.predicate" }, { "project_name": "FStar", "file_name": "FStar.Tactics.CanonMonoid.fst", "name": "FStar.Tactics.CanonMonoid.lem0" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.modifies_buf_3" }, { "project_name": "FStar", "file_name": "FStar.TwoLevelHeap.fst", "name": "FStar.TwoLevelHeap.st_post'" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fsti", "name": "FStar.Monotonic.Heap.modifies" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Pure.fst", "name": "FStar.Monotonic.Pure.is_monotonic" }, { "project_name": "FStar", "file_name": "IfcDelimitedRelease.fst", "name": "IfcDelimitedRelease.rel_contains" }, { "project_name": "FStar", "file_name": "FStar.Buffer.fst", "name": "FStar.Buffer.disjoint_from_refs" }, { "project_name": "FStar", "file_name": "FStar.Pervasives.fsti", "name": "FStar.Pervasives.ex_stronger" }, { "project_name": "FStar", "file_name": "ImmutableST.fst", "name": "ImmutableST.heap_rel" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.modifies_transitively" }, { "project_name": "FStar", "file_name": "IMST.fst", "name": "IMST.st_return" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Tutorial.Definitions.fst", "name": "FStar.InteractiveHelpers.Tutorial.Definitions.spred1" } ], "selected_premises": [ "FStar.ST.contains_pred", "FStar.ST.op_Bang", "FStar.ST.read", "FStar.Monotonic.Heap.only", "FStar.Monotonic.Heap.mref", "FStar.ST.alloc", "FStar.ST.op_Colon_Equals", "FStar.Heap.trivial_preorder", "FStar.Monotonic.Heap.only_t", "FStar.ST.write", "FStar.Monotonic.Heap.compare_addrs", "FStar.ST.recall", "FStar.Monotonic.Heap.fresh", "FStar.Heap.trivial_rel", "FStar.Monotonic.Heap.equal_dom", "FStar.Preorder.preorder_rel", "FStar.ST.heap_rel", "FStar.Monotonic.Heap.op_Hat_Plus_Plus", "FStar.Monotonic.Heap.op_Hat_Plus_Hat", "FStar.Monotonic.Heap.op_Plus_Plus_Hat", "FStar.ST.get", "FStar.Monotonic.Heap.modifies_t", "FStar.Pervasives.st_post_h", "FStar.Monotonic.Heap.modifies", "FStar.Preorder.stable", "FStar.ST.witnessed", "FStar.Pervasives.Native.fst", "FStar.ST.lemma_functoriality", "FStar.Pervasives.Native.snd", "FStar.Pervasives.id", "FStar.ST.modifies_none", "FStar.Pervasives.st_pre_h", "FStar.Preorder.reflexive", "FStar.ST.stable", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.dfst", "FStar.ST.gst_pre", "FStar.Preorder.transitive", "FStar.Pervasives.st_return", "Prims.pure_pre", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.dsnd", "FStar.Pervasives.st_stronger", "FStar.Pervasives.ex_pre", "Prims.returnM", "FStar.ST.st_pre", "FStar.Pervasives.all_return", "FStar.Pervasives.all_post_h", "FStar.Pervasives.st_wp_h", "FStar.ST.gst_post", "FStar.Pervasives.all_post_h'", "FStar.Monotonic.Heap.set", "FStar.Set.subset", "Prims.__cache_version_number__", "Prims.min", "FStar.ST.gst_post'", "FStar.Pervasives.st_trivial", "FStar.Set.as_set'", "Prims.abs", "FStar.Set.as_set", "Prims.subtype_of", "Prims.pow2", "FStar.Monotonic.Heap.tset", "FStar.Pervasives.ex_post'", "FStar.TSet.as_set'", "Prims.pure_post'", "FStar.Pervasives.all_stronger", "FStar.ST.st_post'", "FStar.ST.gst_wp", "FStar.Pervasives.ex_post", "FStar.ST.st_post", "FStar.Pervasives.coerce_eq", "Prims.op_Hat", "Prims.auto_squash", "FStar.Pervasives.all_trivial", "FStar.Pervasives.pure_return", "FStar.Pervasives.st_ite_wp", "FStar.Pervasives.st_close_wp", "FStar.Pervasives.reveal_opaque", "FStar.Pervasives.st_if_then_else", "FStar.Pervasives.all_wp_h", "FStar.TSet.subset", "FStar.Pervasives.all_bind_wp", "FStar.ST.lift_div_gst", "FStar.Pervasives.all_close_wp", "FStar.Set.add", "FStar.Pervasives.trivial_pure_post", "FStar.Pervasives.ex_wp", "FStar.Pervasives.all_ite_wp", "FStar.ST.st_wp", "FStar.Pervasives.all_if_then_else", "Prims.l_False", "Prims.pure_post", "FStar.ST.lift_gst_state", "FStar.Pervasives.pure_close_wp", "FStar.Pervasives.st_bind_wp", "FStar.Pervasives.pure_null_wp", "FStar.Pervasives.ex_stronger", "Prims.l_True", "Prims.as_requires" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule FStar.MRef\nopen FStar.Heap\nopen FStar.ST\n\nopen FStar.Preorder\n", "sketch": [ "Step 1: The definition `p_pred` is about defining a predicate that takes a mutable reference `r` of type `FStar.ST.mref a b`, a predicate `p` of type `a -> Type0`, and a heap `h` of type `FStar.Monotonic.Heap.heap`. The result is a logical proposition (`Prims.logical`).\nStep 2: The implementation will involve checking if the value stored in the mutable reference `r` satisfies the predicate `p` in the context of the heap `h`.", "Step 1: The definition `p_pred` is about creating a predicate that takes a mutable reference `r`, a predicate `p` on the type `a`, and a heap `h`. It returns a logical proposition indicating whether the predicate `p` holds for the value stored in the reference `r` within the heap `h`.\nStep 2: To implement this, we need to access the value stored in the reference `r` within the heap `h` and then check if the predicate `p` holds for this value.", "Step 1: The definition `p_pred` is about creating a predicate that takes a mutable reference `r`, a predicate `p` on the type `a`, and a heap `h`, and returns a logical proposition.\nStep 2: The implementation involves specifying that `p_pred` is a function that takes three arguments: a mutable reference `r` of type `FStar.ST.mref a b`, a predicate `p` which is a function from `a` to `Type0`, and a heap `h` of type `FStar.Monotonic.Heap.heap`. The return type is a logical proposition `Prims.logical`.", "Step 1: The definition `p_pred` is about defining a predicate that takes a mutable reference `r`, a predicate `p` on the type `a`, and a heap `h`. It returns a logical proposition.\nStep 2: The implementation involves specifying the types of the inputs and ensuring that the predicate `p` holds for the value stored in the reference `r` within the heap `h`.", "Step 1: The definition `p_pred` is about specifying a logical predicate on a mutable reference `r` in the heap. The predicate `p` is a function that takes an argument of type `a` and returns a type `Type0`. The heap `h` represents the current state of the memory.\nStep 2: The implementation of `p_pred` will involve checking that the predicate `p` holds for the value stored in the mutable reference `r` within the heap `h`.", "Step 1: The definition `p_pred` is about defining a predicate that takes a mutable reference `r` of type `FStar.ST.mref a b`, a predicate `p` of type `a -> Type0`, and a heap `h` of type `FStar.Monotonic.Heap.heap`. The purpose of this predicate is to assert some logical condition involving these parameters.\nStep 2: The implementation will involve specifying the types of the parameters and the return type, which is `Prims.logical`. This indicates that the function returns a logical proposition.", "Step 1: The definition `p_pred` is about creating a predicate that checks a property `p` on the value stored in a mutable reference `r` within a given heap `h`.\nStep 2: The implementation will take a mutable reference `r`, a predicate `p` on the type `a`, and a heap `h`. It will return a logical proposition indicating whether the value stored in the reference `r` in the heap `h` satisfies the predicate `p`.", "Step 1: The definition `p_pred` is about specifying a logical predicate on a mutable reference `r` in the heap `h`. The predicate `p` is a function that takes a value of type `a` and returns a type `Type0`.\nStep 2: The implementation involves defining a logical predicate that ensures the value stored in the mutable reference `r` satisfies the predicate `p` in the given heap `h`.", "Step 1: The definition `p_pred` is a predicate that takes three arguments: a mutable reference `r` of type `FStar.ST.mref a b`, a predicate `p` which is a function from type `a` to `Type0`, and a heap `h` of type `FStar.Monotonic.Heap.heap`.\nStep 2: The implementation of `p_pred` should return a logical value indicating whether the predicate `p` holds for the value stored in the mutable reference `r` in the heap `h`.", "Step 1: The definition `p_pred` is about specifying a predicate on a mutable reference (`mref`) in the context of a heap. It takes three arguments: a mutable reference `r` of type `FStar.ST.mref a b`, a predicate `p` which is a function from type `a` to `Type0`, and a heap `h` of type `FStar.Monotonic.Heap.heap`.\nStep 2: The implementation of `p_pred` will return a logical proposition (`Prims.logical`) that asserts the predicate `p` holds for the value stored in the mutable reference `r` within the heap `h`." ], "generated_solution": [ "let p_pred (r: FStar.ST.mref a b) (p: a -> Type0) (h: FStar.Monotonic.Heap.heap) : Prims.logical =\n p (FStar.Heap.read r h)", "let p_pred (r: FStar.ST.mref a b) (p: a -> Type0) (h: FStar.Monotonic.Heap.heap) : Prims.logical =\n let v = FStar.Heap.read r h in\n p v", "let p_pred (r: FStar.ST.mref a b) (p: a -> Type0) (h: FStar.Monotonic.Heap.heap) : Prims.logical =\n (* Implementation goes here *)\n true", "let p_pred (r: FStar.ST.mref a b) (p: a -> Type0) (h: FStar.Monotonic.Heap.heap) : Prims.logical =\n p (FStar.ST.read r h)", "let p_pred (r: FStar.ST.mref a b) (p: a -> Type0) (h: FStar.Monotonic.Heap.heap) : Prims.logical =\n p (FStar.ST.read r h)", "val p_pred : r: FStar.ST.mref a b -> p: (_: a -> Type0) -> h: FStar.Monotonic.Heap.heap -> Prims.logical", "let p_pred (r: FStar.ST.mref a b) (p: a -> Type0) (h: FStar.Monotonic.Heap.heap) : Prims.logical =\n p (FStar.ST.read r h)", "let p_pred (r: FStar.ST.mref a b) (p: a -> Type0) (h: FStar.Monotonic.Heap.heap) : Prims.logical =\n p (FStar.ST.read r h)", "let p_pred (r: FStar.ST.mref a b) (p: a -> Type0) (h: FStar.Monotonic.Heap.heap) : Prims.logical =\n p (FStar.ST.read r h)", "let p_pred (r: FStar.ST.mref a b) (p: a -> Type0) (h: FStar.Monotonic.Heap.heap) : Prims.logical =\n p (FStar.ST.read r h)" ] }, { "file_name": "Pulse.Lib.HigherReference.fst", "name": "Pulse.Lib.HigherReference.ref", "opens_and_abbrevs": [ { "open": "Pulse.Lib.PCM.Fraction" }, { "open": "FStar.PCM" }, { "open": "Pulse.Main" }, { "open": "Pulse.Lib.Core" }, { "abbrev": "T", "full_module": "FStar.Tactics" }, { "abbrev": "U32", "full_module": "FStar.UInt32" }, { "open": "FStar.Ghost" }, { "open": "PulseCore.FractionalPermission" }, { "open": "Pulse.Lib.Core" }, { "open": "Pulse.Lib" }, { "open": "Pulse.Lib" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val ref ([@@@unused]a:Type u#1) : Type u#0", "source_definition": "let ref (a:Type u#1) = pcm_ref (pcm_frac #a)", "source_range": { "start_line": 23, "start_col": 0, "end_line": 23, "end_col": 44 }, "interleaved": false, "definition": "fun a -> Pulse.Lib.Core.pcm_ref Pulse.Lib.PCM.Fraction.pcm_frac", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Pulse.Lib.Core.pcm_ref", "Pulse.Lib.PCM.Fraction.fractional", "Pulse.Lib.PCM.Fraction.pcm_frac" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": true, "type": "a: Type -> Type0", "prompt": "let ref (a: Type u#1) =\n ", "expected_response": "pcm_ref (pcm_frac #a)", "source": { "project_name": "steel", "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.HigherReference.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git" }, "dependencies": { "source_file": "Pulse.Lib.HigherReference.fst", "checked_file": "dataset/Pulse.Lib.HigherReference.fst.checked", "interface_file": true, "dependencies": [ "dataset/Pulse.Main.fsti.checked", "dataset/Pulse.Lib.PCM.Fraction.fst.checked", "dataset/Pulse.Lib.Core.fsti.checked", "dataset/prims.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.PCM.fst.checked" ] }, "definitions_in_context": [], "closest": [ "val ref ([@@@unused] a:Type u#1) : Type u#0\nlet ref a = Mem.ref (fractional a) pcm_frac", "val ref ([@@@unused] a:Type u#1) : Type u#0\nlet ref (a:Type u#1) = ghost_pcm_ref (pcm_frac #a)", "val ref ([@@@unused] a:Type u#0) : Type u#0\nlet ref a = H.ref (U.raise_t a)", "val ref ([@@@unused] a:Type u#0) : Type u#0\nlet ref a = H.ref (U.raise_t a)", "val ref ([@@@unused] a:Type0) : Type0\nlet ref a = H.ref (U.raise_t a)", "val ref (a:Type u#0)\n : Type u#0\nlet ref (a:Type u#0)\n : Type u#0\n = R.ghost_ref a", "val ref ([@@@ strictly_positive] a:Type u#1)\n : Type0\nlet ref (a:Type u#1)\n : Type0\n = R.ref a", "val ref ([@@@ strictly_positive] a:Type u#1)\n : Type0\nlet ref a = ref' a", "val ref ([@@@ unused] a:Type0)\n : Type0\nlet ref (a:Type0)\n : Type0\n = R.ref a", "val ref ([@@@unused] a:Type u#a) ([@@@unused] p:pcm a) : Type u#0\nlet ref (a:Type u#a) (p:pcm a) = ref a p", "val ref (a:Type0) : Type0\nlet ref (a:Type) = nat", "val ref (a: Type0) : Type0\nlet ref (a : Type0) : Type0 = (r: A.array a { A.length r == 1 \\/ r == A.null })", "val ref (a: Type0) : Type0\nlet ref (a:Type0) : Type0 = ref a", "val null (#a:Type u#1) : ref a\nlet null #a = Mem.null #(fractional a) #pcm_frac", "val ref (a:Type u#1) (p:Preorder.preorder a)\n : Type u#0\nlet ref a p = M.ref (history a p) pcm_history", "val ref (a:Type u#1) (p:Preorder.preorder a)\n : Type u#0\nlet ref a p = PR.ref (history a p) pcm_history", "val ghost_ref (a:Type u#1) : Type u#0\nlet ghost_ref a = erased (ref a)", "val ghost_ref (a:Type u#0) : Type u#0\nlet ghost_ref a = H.ghost_ref (U.raise_t a)", "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\nlet ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\n = MR.ref a p", "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\nlet ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\n = MR.ref a p", "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\nlet ref a p = MHR.ref (FStar.Universe.raise_t a) (raise_preorder p)", "val ref (a:Type u#0) (p:Preorder.preorder a)\n : Type u#0\nlet ref a p = MHR.ref (FStar.Universe.raise_t a) (raise_preorder p)", "val array ([@@@strictly_positive] a:Type u#0) : Type u#0\nlet array a = H.array (U.raise_t a)", "val ref (a:Type u#0) (p:pcm a) : Type u#0\nlet ref (a:Type u#0) (p:pcm a) : Type u#0 =\n G.ref (raise_t u#0 u#1 a) (UP.raise p)", "val null (#a:Type0) : ref a\nlet null #a = H.null #(U.raise_t a)", "val null (#a:Type0) : ref a\nlet null #a = A.null #a", "val null (#a:Type0) \n : ref a\nlet null (#a:Type0)\n : ref a\n = R.null #a", "val t : a:Type u#a -> Type u#a\nlet t a = list a", "val ghost_ref (#[@@@unused] a:Type u#a) ([@@@unused]p:pcm a) : Type0\nlet ghost_ref #a p = Ghost.erased (ref a p)", "val null (#a:Type) \n : ref a\nlet null (#a:Type)\n : ref a\n = R.null #a", "val core_ref : Type u#0\nlet core_ref = H.core_ref", "val core_ref : Type u#0\nlet core_ref = H.core_ref", "val ref (a: Type u#a) (pcm: pcm a) : Type u#0\nlet ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref", "val ref (a: Type u#a) (pcm: pcm a) : Type u#0\nlet ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref", "val ref (a: Type u#a) (pcm: pcm a) : Type u#0\nlet ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref", "val ref (a: Type u#a) (pcm: pcm a) : Type u#0\nlet ref (a:Type u#a) (pcm:pcm a) : Type u#0 = core_ref", "val arg_t (a: arg) : Type u#1\nlet rec arg_t (a:arg) : Type u#1 =\n match a with\n | Base t -> lift (base_typ_as_type t)\n | Array t -> (l:UInt32.t & r:_ & s:_ & lmbuffer (base_typ_as_type t) r s l)\n | Any -> (a:Type0 & (a -> StTrivial unit) & a)", "val arg_t (a: arg) : Type u#1\nlet rec arg_t (a:arg) : Type u#1 =\n match a with\n | Base t -> lift (base_typ_as_type t)\n | Array t -> lift ((l:UInt32.t & lmbuffer (base_typ_as_type t) l) & perm & Ghost.erased (Seq.seq (base_typ_as_type t)))\n | Any -> (a:Type0 & (a -> StTrivial unit) & a)", "val t:\n a:Type u#a\n -> Type u#a\nlet t a = (l:len_t & raw a l)", "val ref (a:Type) (p:pcm a) : Type0\nlet ref (a:Type) (p:pcm a) = erased (Steel.Memory.ref a p)", "val loc : Type u#0\nlet loc = M.loc", "val loc : Type u#0\nlet loc = MG.loc cls", "val loc : Type u#0\nlet loc = M.loc", "val pcm_ref\n (#[@@@unused] a:Type u#a)\n ([@@@unused] p:FStar.PCM.pcm a)\n: Type0\nlet pcm_ref #a p = PulseCore.Action.ref a p", "val null (#a: Type u#1) : array a\nlet null (#a: Type u#1) : array a\n= { p = null_ptr a; length =Ghost.hide 0 }", "val raw ([@@@strictly_positive] a:Type u#a)\n (l:len_t)\n : Type u#a\nlet raw a l = s:S.seq a{S.length s = U32.v l}", "val null (#a: Type u#a) : array a\nlet null (#a: Type u#a) : array a\n= (| null_ptr a, Ghost.hide 0 |)", "val ref (#t: Type) (td: typedef t) : Tot Type0\nlet ref (#t: Type) (td: typedef t) : Tot Type0 = (p: ptr td { ~ (p == null td) })", "val ref (#t: Type) (td: typedef t) : Tot Type0\nlet ref (#t: Type) (td: typedef t) : Tot Type0 = (p: ptr td { ~ (p == null td) })", "val ptr (#a: Type0) (r: ref a) : slprop u#1\nlet ptr (#a:Type0) (r:ref a) : slprop u#1 = ptrp r full_perm", "val ptr (#a: Type0) (r: ref a) : slprop u#1\nlet ptr (#a:Type0) (r:ref a) : slprop u#1 = ptr r", "val ptr (#a: Type0) (r: ref a) : slprop u#1\nlet ptr (#a:Type0) (r:ref a) : slprop u#1 = ptrp r full_perm", "val const_buffer (a:Type u#0) : Type u#0\nlet const_buffer a = qbuf a", "val t (a:Type0) : Type0\nlet t a = list a", "val lower (t: Type u#a) : Type0\nlet lower (t:Type u#a) : Type0 = unit -> Dv t", "val loc : Type u#1\nlet loc = MG.loc cls", "val m (a : Type u#a) : Type u#a\nlet m a = list a", "val lock_store:Type u#(a + 1)\nlet lock_store : Type u#(a+1) = list (lock_state u#a)", "val lock_store:Type u#(a + 1)\nlet lock_store : Type u#(a+1) = list (lock_state u#a)", "val null_ptr (a: Type u#a) : ptr a\nlet null_ptr (a:Type u#a)\n: ptr a\n= { base_len = 0sz; base = pcm_ref_null (PA.pcm a 0) ; offset = 0 }", "val closure_reflexive: #a:Type u#a -> r:binrel u#a u#r a -> Lemma (reflexive (_closure0 r))\nlet closure_reflexive #a r =\n assert (forall x. _closure0 r x x) by\n (let x = forall_intro () in\n mapply (`FStar.Squash.return_squash);\n mapply (`Refl))", "val ref_null (#a:Type u#a) (p:pcm a) : ref a p\nlet ref_null (#a:Type u#a) (p:pcm a) = core_ref_null", "val p (x: Type u#1) : Type u#0\nlet p (x : Type u#1) : Type u#0 =\n exists a. i a == x /\\ ~(a x)", "val p (x: Type u#1) : Type u#0\nlet p (x : Type u#1) : Type u#0 =\n exists a. pa x a", "val read (#a:Type0) (r:ref a) :STATE a (fun p h -> p (sel h r) h)\nlet read #_ r = read r", "val ch : Type u#1\nlet ch : Type u#1 = (p:dprot & channel p)", "val squash (p: Type u#a) : Type0\nlet squash (p:Type u#a) : Type0 = squash p", "val FStar.HyperStack.ref = a: Type0 -> Type0\nlet ref (a:Type) = mref a (Heap.trivial_preorder a)", "val hlens_ref (#a: Type) : hlens (ref a) a\nlet hlens_ref (#a:Type) : hlens (ref a) a = {\n get = (fun (h, x) -> sel h x);\n put = (fun y (h, x) -> (upd h x y, x))\n}", "val null_t (#a: Type0) : t a\nlet null_t #a = null", "val is_null (#a:Type u#1) (r:ref a) : (b:bool{b <==> r == null})\nlet is_null #a r = Mem.is_null #(fractional a) #pcm_frac r", "val repr (a: Type u#aa) (i: int) : Type u#aa\nlet repr (a:Type u#aa) (i:int) : Type u#aa =\n raise_t (x:int{x==i})", "val copy_ref (#a: Type0) (r: ref a)\n : Steel (ref a)\n (vptr r)\n (fun r' -> (vptr r) `star` (vptr r'))\n (requires fun _ -> True)\n (ensures fun h0 r' h1 -> sel r h0 == sel r h1 /\\ sel r' h1 == sel r h1)\nlet copy_ref (#a:Type0) (r:ref a) : Steel (ref a)\n (vptr r)\n // We allocated a new reference r', which is the return value\n (fun r' -> vptr r `star` vptr r')\n (requires fun _ -> True)\n (ensures fun h0 r' h1 ->\n // reference r was not modified\n sel r h0 == sel r h1 /\\\n // After copying, reference r' contains the same value as reference r\n sel r' h1 == sel r h1)\n\n = let x = read r in\n let r' = malloc x in\n r'", "val null (#a: Type0) : array a\nlet null (#a: Type0) : array a\n= (| null_ptr a, Ghost.hide 0 |)", "val dummy_ref (a: Type) : Tot (ref a)\nlet dummy_ref a = R.dummy_ghost_ref a", "val ghost_pcm_ref\n (#[@@@unused] a:Type u#a)\n ([@@@unused] p:FStar.PCM.pcm a)\n: Type0\nlet ghost_pcm_ref #a p = A.ghost_ref #a p", "val return (a: Type u#aa) (x: a) : repr a 0\nlet return (a:Type u#aa) (x:a) : repr a 0 =\n raise_val 0", "val heap: Type u#1\nlet heap = h:(nat * (F.restricted_t nat (fun _ -> (option (dtuple2 Type0 (fun a -> a))))))\n\t\t {(forall (n:nat) . n < fst h ==> (exists v . snd h n == Some v)) /\\ \n\t\t\t(forall (n:nat) . n >= fst h ==> snd h n == None)}", "val array ([@@@ strictly_positive]elt: Type u#a) : Tot Type0\nlet array ([@@@strictly_positive] elt: Type u#a) : Tot Type0 =\n (p: ptr elt & (length: Ghost.erased nat {offset p + length <= base_len (base p)}))", "val node (a:Type0) : Type0\nlet node a = B.pointer (DLL.node a)", "val test1:Type u#2\nlet test1 : Type u#2 = Type u#1", "val repr (a:Type u#a) //result type\n (already_framed:bool) //framed or not\n (opened_invariants:inames) //which invariants are we relying on\n (g:observability) //is this a ghost computation?\n (pre:pre_t) //expects vprop\n (post:post_t a) //provides a -> vprop\n (req:pure_pre) //a prop refinement as a precondition\n (ens:pure_post a) //an (a -> prop) as a postcondition\n : Type u#(max a 2)\nlet repr (a:Type u#a)\n (already_framed:bool)\n (opened_invariants:inames)\n (g:observability)\n (pre:pre_t)\n (post:post_t a)\n (req:Type0)\n (ens:a -> Type0)\n : Type u#(max a 2)\n = SEA.repr a already_framed opened_invariants g pre post\n (fun _ -> req)\n (fun _ x _ -> ens x)", "val heap :Type u#1\nlet heap = h:heap_rec{(forall (n:nat). n >= h.next_addr ==> None? (h.memory n))}", "val buffer (dest: Type u#a) : Type u#(max a 1)\nlet buffer (dest:Type u#a) : Type u#(max a 1) = (src:Type0 & rrel:B.srel src & rel:B.srel src & buffer_view src rrel rel dest)", "val closure (#a:Type u#a) (r:binrel u#a u#r a) : preorder u#a u#0 a\nlet closure #a r =\n closure_reflexive r;\n closure_transitive r;\n _closure0 r", "val MRefST.st = a: Type -> Type\nlet st (a: Type) = heap -> M (a * heap)", "val unused_in: #a:Type0 -> #rel:preorder a -> mref a rel -> heap -> Type0\nlet unused_in #a #rel r h = addr_unused_in (addr_of r) h", "val no_tree:Type u#1\nlet no_tree : Type u#1 = a:Type u#0 -> GTot unit", "val write_ref (#a:Type0) (r:R.ref (vec a))\n (i:SZ.t)\n (x:a)\n (#v:erased (vec a))\n (#s:erased (Seq.seq a) { SZ.v i < Seq.length s})\n : stt unit\n (requires R.pts_to r v ** pts_to v s)\n (ensures fun _ -> R.pts_to r v ** pts_to v (Seq.upd s (SZ.v i) x))\nlet write_ref = write_ref'", "val fresh_ref (#a: Type) (#rel: preorder a) (r: mreference a rel) (m0 m1: mem) : Type0\nlet fresh_ref (#a:Type) (#rel:preorder a) (r:mreference a rel) (m0:mem) (m1:mem) :Type0 =\n let i = frameOf r in\n Heap.fresh (as_ref r) (get_hmap m0 `Map.sel` i) (get_hmap m1 `Map.sel` i)", "val buffer (dest: Type u#a) : Type u#(max 1 a)\nlet buffer (dest:Type u#a) : Type u#(max 1 a) = (src:Type0 & rrel:B.srel src & rel:B.srel src & buffer_view src rrel rel dest)", "val array (a:Type0) : Type0\nlet array a = ref (seq a)", "val heap : Type u#1\nlet heap = h:(nat * (nat -> Tot (option heap_cell)))\n\t\t {(forall (n:nat) . n < fst h ==> (exists v . snd h n == Some v)) /\\\n\t\t\t(forall (n:nat) . n >= fst h ==> snd h n == None)}", "val alloc (#a:Type)\n (#u:_)\n (x:erased a)\n : STGhostT (ref a) u\n emp\n (fun r -> pts_to r full_perm x)\nlet alloc (#a:Type)\n (#u:_)\n (x:erased a)\n : STGhostT (ref a) u\n emp\n (fun r -> pts_to r full_perm x)\n = coerce_ghost (fun _ -> R.ghost_alloc_pt x)", "val read (#a: Type0) (r: ref a)\n : Steel a\n (vptr r)\n (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun h0 x h1 -> sel r h0 == sel r h1 /\\ x == sel r h1)\nlet read (#a:Type0) (r:ref a) : Steel a\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun h0 x h1 -> sel r h0 == sel r h1 /\\ x == sel r h1)\n= readp r full_perm", "val read (#a: Type0) (r: ref a)\n : Steel a\n (vptr r)\n (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun h0 x h1 -> sel r h0 == sel r h1 /\\ x == sel r h1)\nlet read (#a:Type0) (r:ref a) : Steel a\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun h0 x h1 -> sel r h0 == sel r h1 /\\ x == sel r h1)\n= readp r full_perm", "val write (#a:Type0) (r:ref a) (x:a) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> x == sel r h1)\nlet write\n r x\n= elim_vptrp r full_perm;\n A.upd r 0sz x;\n intro_vptrp' r full_perm", "val write (#a:Type0) (r:ref a) (x:a) : Steel unit\n (vptr r) (fun _ -> vptr r)\n (requires fun _ -> True)\n (ensures fun _ _ h1 -> x == sel r h1)\nlet write r x =\n let _ = elim_vptr r _ in\n write_pt r x;\n intro_vptr r _ x", "val repr (a: Type u#aa) (w: wp0 a) : Type u#(max 1 aa)\nlet repr (a : Type u#aa) (w : wp0 a) : Type u#(max 1 aa) =\n // Hmmm, the explicit post bumps the universe level\n ( squash (monotonic w) & (p:erased (a -> Type0) -> squash (w p) -> v:a{reveal p v}))", "val ptr ([@@@unused] elt: Type0) : Type0\nlet ptr elt = H.ptr (raise_t elt)" ], "closest_src": [ { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherGhostReference.fst", "name": "Pulse.Lib.HigherGhostReference.ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.GhostReference.fst", "name": "Pulse.Lib.GhostReference.ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.Reference.fst", "name": "Pulse.Lib.Reference.ref" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.GhostHigherReference.fst", "name": "Steel.ST.GhostHigherReference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.ref" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.ref" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.ref" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fsti", "name": "Steel.ArrayRef.ref" }, { "project_name": "steel", "file_name": "SelectorLogic.fst", "name": "SelectorLogic.ref" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.null" }, { "project_name": "steel", "file_name": "Steel.MonotonicHigherReference.fst", "name": "Steel.MonotonicHigherReference.ref" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicHigherReference.fst", "name": "Steel.GhostMonotonicHigherReference.ref" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.ghost_ref" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.ghost_ref" }, { "project_name": "steel", "file_name": "Steel.ST.GhostMonotonicReference.fst", "name": "Steel.ST.GhostMonotonicReference.ref" }, { "project_name": "steel", "file_name": "Steel.ST.MonotonicReference.fst", "name": "Steel.ST.MonotonicReference.ref" }, { "project_name": "steel", "file_name": "Steel.MonotonicReference.fst", "name": "Steel.MonotonicReference.ref" }, { "project_name": "steel", "file_name": "Steel.GhostMonotonicReference.fst", "name": "Steel.GhostMonotonicReference.ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.Array.Core.fst", "name": "Pulse.Lib.Array.Core.array" }, { "project_name": "steel", "file_name": "Steel.ST.GhostPCMReference.fst", "name": "Steel.ST.GhostPCMReference.ref" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.null" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.null" }, { "project_name": "steel", "file_name": "Steel.ST.Reference.fst", "name": "Steel.ST.Reference.null" }, { "project_name": "noise-star", "file_name": "Spec.Noise.Map.fst", "name": "Spec.Noise.Map.t" }, { "project_name": "steel", "file_name": "PulseCore.Atomic.fst", "name": "PulseCore.Atomic.ghost_ref" }, { "project_name": "steel", "file_name": "Steel.ST.HigherReference.fst", "name": "Steel.ST.HigherReference.null" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.core_ref" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.core_ref" }, { "project_name": "steel", "file_name": "Steel.Heap.fsti", "name": "Steel.Heap.ref" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fsti", "name": "PulseCore.Memory.ref" }, { "project_name": "steel", "file_name": "Steel.Memory.fsti", "name": "Steel.Memory.ref" }, { "project_name": "steel", "file_name": "PulseCore.Heap.fsti", "name": "PulseCore.Heap.ref" }, { "project_name": "FStar", "file_name": "LowStar.Printf.fst", "name": "LowStar.Printf.arg_t" }, { "project_name": "steel", "file_name": "Steel.ST.Printf.fst", "name": "Steel.ST.Printf.arg_t" }, { "project_name": "FStar", "file_name": "FStar.Vector.Base.fst", "name": "FStar.Vector.Base.t" }, { "project_name": "steel", "file_name": "Steel.GhostPCMReference.fst", "name": "Steel.GhostPCMReference.ref" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory.fst", "name": "Vale.PPC64LE.Memory.loc" }, { "project_name": "FStar", "file_name": "FStar.Pointer.Base.fst", "name": "FStar.Pointer.Base.loc" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory.fst", "name": "Vale.X64.Memory.loc" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.pcm_ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherArray.fst", "name": "Pulse.Lib.HigherArray.null" }, { "project_name": "FStar", "file_name": "FStar.Vector.Base.fst", "name": "FStar.Vector.Base.raw" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fsti", "name": "Steel.ST.HigherArray.null" }, { "project_name": "steel", "file_name": "Steel.ST.C.Types.Base.fsti", "name": "Steel.ST.C.Types.Base.ref" }, { "project_name": "steel", "file_name": "Pulse.C.Types.Base.fsti", "name": "Pulse.C.Types.Base.ref" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fsti", "name": "Steel.ArrayRef.ptr" }, { "project_name": "steel", "file_name": "SelectorLogic.fst", "name": "SelectorLogic.ptr" }, { "project_name": "steel", "file_name": "Steel.Reference.fsti", "name": "Steel.Reference.ptr" }, { "project_name": "FStar", "file_name": "LowStar.ConstBuffer.fst", "name": "LowStar.ConstBuffer.const_buffer" }, { "project_name": "steel", "file_name": "Steel.TLArray.fst", "name": "Steel.TLArray.t" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.lower" }, { "project_name": "FStar", "file_name": "FStar.Modifies.fst", "name": "FStar.Modifies.loc" }, { "project_name": "FStar", "file_name": "ND.fst", "name": "ND.m" }, { "project_name": "steel", "file_name": "PulseCore.Memory.fst", "name": "PulseCore.Memory.lock_store" }, { "project_name": "steel", "file_name": "Steel.Memory.fst", "name": "Steel.Memory.lock_store" }, { "project_name": "steel", "file_name": "Pulse.Lib.HigherArray.fst", "name": "Pulse.Lib.HigherArray.null_ptr" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fst", "name": "FStar.ReflexiveTransitiveClosure.closure_reflexive" }, { "project_name": "steel", "file_name": "PulseCore.Action.fst", "name": "PulseCore.Action.ref_null" }, { "project_name": "FStar", "file_name": "InjectiveTypeFormers.SMT.fst", "name": "InjectiveTypeFormers.SMT.p" }, { "project_name": "FStar", "file_name": "InjectiveTypeFormers.Explicit.fst", "name": "InjectiveTypeFormers.Explicit.p" }, { "project_name": "FStar", "file_name": "FStar.Ref.fst", "name": "FStar.Ref.read" }, { "project_name": "steel", "file_name": "Duplex.PCM.fst", "name": "Duplex.PCM.ch" }, { "project_name": "steel", "file_name": "CQueue.fst", "name": "CQueue.squash" }, { "project_name": "FStar", "file_name": "FStar.HyperStack.fst", "name": "FStar.HyperStack.ref" }, { "project_name": "FStar", "file_name": "StatefulLens.fst", "name": "StatefulLens.hlens_ref" }, { "project_name": "steel", "file_name": "Selectors.Tree.Core.fst", "name": "Selectors.Tree.Core.null_t" }, { "project_name": "steel", "file_name": "Steel.HigherReference.fst", "name": "Steel.HigherReference.is_null" }, { "project_name": "FStar", "file_name": "Degenerate.fst", "name": "Degenerate.repr" }, { "project_name": "steel", "file_name": "References.fst", "name": "References.copy_ref" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fsti", "name": "Steel.ST.Array.null" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.dummy_ref" }, { "project_name": "steel", "file_name": "Pulse.Lib.Core.fst", "name": "Pulse.Lib.Core.ghost_pcm_ref" }, { "project_name": "FStar", "file_name": "Degenerate.fst", "name": "Degenerate.return" }, { "project_name": "FStar", "file_name": "NatHeap.fst", "name": "NatHeap.heap" }, { "project_name": "steel", "file_name": "Steel.ST.HigherArray.fsti", "name": "Steel.ST.HigherArray.array" }, { "project_name": "FStar", "file_name": "DoublyLinkedListIface.fst", "name": "DoublyLinkedListIface.node" }, { "project_name": "FStar", "file_name": "Param.fst", "name": "Param.test1" }, { "project_name": "steel", "file_name": "Steel.ST.Effect.AtomicAndGhost.fst", "name": "Steel.ST.Effect.AtomicAndGhost.repr" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.heap" }, { "project_name": "FStar", "file_name": "LowStar.BufferView.fsti", "name": "LowStar.BufferView.buffer" }, { "project_name": "FStar", "file_name": "FStar.ReflexiveTransitiveClosure.fst", "name": "FStar.ReflexiveTransitiveClosure.closure" }, { "project_name": "FStar", "file_name": "MRefST.fst", "name": "MRefST.st" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.Heap.fst", "name": "FStar.Monotonic.Heap.unused_in" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Pkg.Tree.fst", "name": "MiTLS.Pkg.Tree.no_tree" }, { "project_name": "steel", "file_name": "Pulse.Lib.Vec.fst", "name": "Pulse.Lib.Vec.write_ref" }, { "project_name": "FStar", "file_name": "FStar.Monotonic.HyperStack.fsti", "name": "FStar.Monotonic.HyperStack.fresh_ref" }, { "project_name": "FStar", "file_name": "LowStar.BufferView.Down.fsti", "name": "LowStar.BufferView.Down.buffer" }, { "project_name": "FStar", "file_name": "FStar.Array.fst", "name": "FStar.Array.array" }, { "project_name": "FStar", "file_name": "MRefHeap.fst", "name": "MRefHeap.heap" }, { "project_name": "steel", "file_name": "Steel.ST.GhostReference.fst", "name": "Steel.ST.GhostReference.alloc" }, { "project_name": "steel", "file_name": "Steel.Reference.fsti", "name": "Steel.Reference.read" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fsti", "name": "Steel.ArrayRef.read" }, { "project_name": "steel", "file_name": "Steel.ArrayRef.fst", "name": "Steel.ArrayRef.write" }, { "project_name": "steel", "file_name": "Steel.Reference.fst", "name": "Steel.Reference.write" }, { "project_name": "FStar", "file_name": "ID4.fst", "name": "ID4.repr" }, { "project_name": "steel", "file_name": "Steel.ST.Array.fst", "name": "Steel.ST.Array.ptr" } ], "selected_premises": [ "FStar.Real.one", "FStar.PCM.compatible", "Pulse.Lib.Core.all_inames", "Pulse.Lib.Core.inames", "FStar.PCM.composable", "PulseCore.FractionalPermission.full_perm", "FStar.PCM.op", "Pulse.Lib.PCM.Fraction.compose", "FStar.Real.two", "Pulse.Lib.PCM.Fraction.composable", "Pulse.Lib.Core.emp_inames", "Pulse.Lib.PCM.Fraction.pcm_frac", "Pulse.Lib.PCM.Fraction.fractional", "PulseCore.FractionalPermission.sum_perm", "Pulse.Lib.Core.one_half", "PulseCore.FractionalPermission.comp_perm", "Pulse.Lib.PCM.Fraction.mk_frame_preserving_upd_none", "FStar.UInt.size", "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "Pulse.Lib.PCM.Fraction.full_values_compatible", "Pulse.Lib.PCM.Fraction.mk_frame_preserving_upd", "FStar.Mul.op_Star", "Pulse.Lib.Core.prop_non_informative", "PulseCore.FractionalPermission.writeable", "FStar.Pervasives.reveal_opaque", "Pulse.Lib.Core.unit_non_informative", "Pulse.Lib.Core.squash_non_informative", "PulseCore.FractionalPermission.lesser_perm", "Pulse.Lib.Core.join_inames", "Pulse.Lib.Core.erased_non_informative", "Pulse.Lib.Core.mem_iname", "FStar.Real.zero", "Pulse.Lib.Core.add_iname", "Pulse.Lib.Core.inames_subset", "PulseCore.FractionalPermission.half_perm", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "PulseCore.Observability.at_most_one_observable", "FStar.Preorder.preorder_rel", "PulseCore.FractionalPermission.lesser_equal_perm", "Pulse.Lib.Core.mem_inv", "FStar.PCM.lem_commutative", "FStar.Pervasives.st_post_h", "FStar.PCM.frame_compatible", "FStar.PCM.lem_assoc_l", "FStar.PCM.compatible_trans", "FStar.Pervasives.id", "FStar.PCM.frame_preserving_val_to_fp_upd", "FStar.PCM.compatible_elim", "Pulse.Lib.Core.add_inv", "FStar.PCM.exclusive", "FStar.PCM.lem_assoc_r", "FStar.Pervasives.st_pre_h", "PulseCore.Observability.join_obs", "FStar.Pervasives.ex_pre", "FStar.Ghost.return", "FStar.Math.Lemmas.pow2_plus", "FStar.Pervasives.st_post_h'", "FStar.BitVector.logor_vec", "FStar.Pervasives.all_post_h", "FStar.Pervasives.all_pre_h", "Pulse.Lib.Core.remove_inv", "FStar.Preorder.reflexive", "FStar.UInt32.n", "FStar.UInt.to_vec", "FStar.UInt32.lt", "FStar.Preorder.stable", "FStar.PCM.lem_is_unit", "FStar.PCM.compose_frame_preserving_updates", "FStar.Ghost.tot_to_gtot", "FStar.BitVector.logand_vec", "FStar.Math.Lib.slash_decr_axiom", "FStar.Real.test", "FStar.BitVector.logxor_vec", "FStar.Pervasives.all_post_h'", "FStar.UInt.msb", "FStar.Math.Lib.max", "FStar.Preorder.transitive", "FStar.Pervasives.ex_post'", "FStar.Calc.calc_chain_related", "FStar.Real.mul_nil_r", "FStar.BitVector.lognot_vec", "FStar.UInt.max_int", "FStar.UInt32.gt", "FStar.UInt.shift_right", "FStar.UInt.shift_left", "Prims.__cache_version_number__", "FStar.UInt.logor", "FStar.Pervasives.st_stronger", "FStar.Pervasives.st_wp_h", "FStar.UInt.udiv", "FStar.Pervasives.ex_post", "FStar.UInt.xor", "FStar.Pervasives.st_return", "FStar.UInt.one_extend", "FStar.Pervasives.coerce_eq", "FStar.UInt.from_vec", "FStar.Pervasives.st_trivial", "FStar.Math.Lib.powx" ], "source_upto_this": "(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Lib.HigherReference\nopen Pulse.Lib.Core\nopen Pulse.Main\nopen FStar.PCM\nopen Pulse.Lib.PCM.Fraction\n", "sketch": [ "Step 1: The definition introduces a type `ref` that takes a type parameter `a` of universe level `u#1`.\nStep 2: The `ref` type is defined to be of universe level `u#0`.", "Step 1: The definition introduces a type `ref` that takes a type `a` as a parameter. The `[@@@unused]` attribute indicates that the parameter `a` is not used within the definition.\nStep 2: The type `ref` is defined as a type at universe level `u#0`, which is a lower universe level compared to the universe level of the type parameter `a` (`u#1`).", "Step 1: The definition is about creating a type `ref` that takes a type `a` as a parameter. This type `a` is annotated with the `[@@@unused]` attribute, indicating that it might not be used directly in the definition.\nStep 2: The implementation of the definition will declare `ref` as a type that takes a type `a` of universe level `u#1` and returns a type of universe level `u#0`.", "Step 1: The definition is about creating a type alias `ref` that represents a reference to a value of type `a`.\nStep 2: The implementation uses the `Type` keyword to define a new type, and the `[@@@unused]` attribute to indicate that the type parameter `a` is intentionally unused.", "Step 1: The definition introduces a type `ref` that takes a type parameter `a` of universe level `u#1`.\nStep 2: The type `ref` is defined to be of universe level `u#0`.", "Step 1: The definition is about creating a type `ref` that takes a type `a` as a parameter. This type `a` is marked as unused with the `[@@@unused]` attribute.\nStep 2: The implementation involves defining `ref` as a type that takes a type `a` of universe level `u#1` and returns a type of universe level `u#0`.", "Step 1: The definition introduces a type `ref` that takes a type parameter `a` of universe level `u#1`.\nStep 2: The implementation of `ref` is a type that resides in universe level `u#0`.", "Step 1: The definition introduces a type `ref` that takes a type parameter `a` of universe level `u#1`.\nStep 2: The implementation of `ref` is a type of universe level `u#0`.", "Step 1: The definition introduces a type `ref` that takes a type parameter `a` of universe level `u#1`.\nStep 2: The `ref` type is defined to be of universe level `u#0`.", "Step 1: The definition is about creating a type `ref` that takes a type `a` as a parameter. This type `a` is annotated with a universe level `u#1`.\nStep 2: The implementation of the definition specifies that `ref` is a type that exists at universe level `u#0`." ], "generated_solution": [ "type ref ([@@@unused]a:Type u#1) : Type u#0", "type ref ([@@@unused]a:Type u#1) : Type u#0", "ref ([@@@unused]a:Type u#1) : Type u#0", "Type u#0", "type ref ([@@@unused]a:Type u#1) : Type u#0", "let ref ([@@@unused]a:Type u#1) : Type u#0 = unit", "Type u#0", "Type u#0", "type ref ([@@@unused]a:Type u#1) : Type u#0", "type ref ([@@@unused]a:Type u#1) : Type u#0" ] }, { "file_name": "LowParse.Endianness.fst", "name": "LowParse.Endianness.n_to_le_eq_rev_n_to_be", "opens_and_abbrevs": [ { "open": "FStar.Math.Lemmas" }, { "abbrev": "U8", "full_module": "FStar.UInt8" }, { "abbrev": "S", "full_module": "FStar.Seq" }, { "open": "FStar.Mul" }, { "open": "FStar.Endianness" }, { "open": "LowParse" }, { "open": "LowParse" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val n_to_le_eq_rev_n_to_be (len n: nat)\n : Lemma (requires (n < pow2 (8 * len))) (ensures (n_to_le len n == seq_rev (n_to_be len n)))", "source_definition": "let n_to_le_eq_rev_n_to_be\n (len: nat)\n (n: nat)\n: Lemma\n (requires (n < pow2 (8 * len)))\n (ensures (n_to_le len n == seq_rev (n_to_be len n)))\n= le_to_n_eq_be_to_n_rev (n_to_le len n);\n be_to_n_inj (seq_rev (n_to_le len n)) (n_to_be len n);\n seq_rev_involutive (n_to_le len n)", "source_range": { "start_line": 257, "start_col": 0, "end_line": 265, "end_col": 36 }, "interleaved": false, "definition": "fun len n ->\n (LowParse.Endianness.le_to_n_eq_be_to_n_rev (FStar.Endianness.n_to_le len n);\n FStar.Endianness.be_to_n_inj (LowParse.Endianness.seq_rev (FStar.Endianness.n_to_le len n))\n (FStar.Endianness.n_to_be len n);\n LowParse.Endianness.seq_rev_involutive (FStar.Endianness.n_to_le len n))\n <:\n FStar.Pervasives.Lemma (requires n < Prims.pow2 (8 * len))\n (ensures\n FStar.Endianness.n_to_le len n == LowParse.Endianness.seq_rev (FStar.Endianness.n_to_be len n)\n )", "effect": "FStar.Pervasives.Lemma", "effect_flags": [ "lemma" ], "mutual_with": [], "premises": [ "Prims.nat", "LowParse.Endianness.seq_rev_involutive", "FStar.UInt8.t", "FStar.Endianness.n_to_le", "Prims.unit", "FStar.Endianness.be_to_n_inj", "LowParse.Endianness.seq_rev", "FStar.Endianness.n_to_be", "LowParse.Endianness.le_to_n_eq_be_to_n_rev", "Prims.b2t", "Prims.op_LessThan", "Prims.pow2", "FStar.Mul.op_Star", "Prims.squash", "Prims.eq2", "FStar.Seq.Base.seq", "Prims.l_or", "Prims.l_and", "FStar.Seq.Base.length", "FStar.Endianness.le_to_n", "Prims.Nil", "FStar.Pervasives.pattern" ], "proof_features": [], "is_simple_lemma": true, "is_div": false, "is_proof": true, "is_simply_typed": false, "is_type": false, "type": "len: Prims.nat -> n: Prims.nat\n -> FStar.Pervasives.Lemma (requires n < Prims.pow2 (8 * len))\n (ensures\n FStar.Endianness.n_to_le len n ==\n LowParse.Endianness.seq_rev (FStar.Endianness.n_to_be len n))", "prompt": "let n_to_le_eq_rev_n_to_be (len n: nat)\n : Lemma (requires (n < pow2 (8 * len))) (ensures (n_to_le len n == seq_rev (n_to_be len n))) =\n ", "expected_response": "le_to_n_eq_be_to_n_rev (n_to_le len n);\nbe_to_n_inj (seq_rev (n_to_le len n)) (n_to_be len n);\nseq_rev_involutive (n_to_le len n)", "source": { "project_name": "everparse", "file_name": "src/lowparse/LowParse.Endianness.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git" }, "dependencies": { "source_file": "LowParse.Endianness.fst", "checked_file": "dataset/LowParse.Endianness.fst.checked", "interface_file": true, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Math.Lemmas.fst.checked", "dataset/FStar.Classical.fsti.checked" ] }, "definitions_in_context": [ "let rec index_be_to_n'\n (b: bytes)\n (i: nat)\n: Lemma\n (requires (\n i < S.length b\n ))\n (ensures (\n U8.v (S.index b i) == (be_to_n b / pow2 (8 * (S.length b - 1 - i))) % pow2 8\n ))\n (decreases (S.length b))\n= reveal_be_to_n b;\n if i = S.length b - 1\n then ()\n else begin\n let l = S.length b in\n let l' = l - 1 in\n let b' = S.slice b 0 l' in\n index_be_to_n' b' i;\n assert (S.index b i == S.index b' i);\n let open FStar.Math.Lemmas in\n let x = be_to_n b in\n let x' = be_to_n b' in\n assert (U8.v (S.index b i) == x' / pow2 (8 * (l' - 1 - i)) % pow2 8);\n let y = (U8.v (S.last b) + pow2 8 * x') / pow2 (8 * (l - 1 - i)) % pow2 8 in\n pow2_plus 8 (8 * (l' - 1 - i));\n division_multiplication_lemma (U8.v (S.last b) + pow2 8 * x') (pow2 8) (pow2 (8 * (l' - 1 - i)));\n assert (pow2 8 * x' == x' * pow2 8);\n division_addition_lemma (U8.v (S.last b)) (pow2 8) x';\n small_division_lemma_1 (U8.v (S.last b)) (pow2 8);\n assert (y == x' / pow2 (8 * (l' - 1 - i)) % pow2 8)\n end", "val index_be_to_n\n (b: bytes)\n (i: nat)\n: Lemma\n (requires (\n i < S.length b\n ))\n (ensures (\n U8.v (S.index b i) == (be_to_n b / pow2 (8 * (S.length b - 1 - i))) % pow2 8\n ))", "val index_n_to_be\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i)) == (n / pow2 (8 * (len - 1 - i)) % pow2 8\n ))", "val index_n_to_be_zero_left\n (len: nat)\n (n: nat)\n (j: nat)\n (i: nat)\n: Lemma\n (requires (\n i < j /\\\n j <= len /\\\n n < pow2 (8 * (len - j))\n ))\n (ensures (\n pow2 (8 * (len - j)) <= pow2 (8 * len) /\\\n U8.v (S.index (n_to_be len n) i) == 0\n ))", "let index_be_to_n = index_be_to_n'", "let index_n_to_be\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i)) == (n / pow2 (8 * (len - 1 - i)) % pow2 8\n ))\n= index_be_to_n (n_to_be len n) i", "val index_n_to_be_zero_right\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len) /\\\n n % pow2 (8 * (len - i)) == 0\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i) == 0\n ))", "let index_n_to_be_zero_left\n (len: nat)\n (n: nat)\n (j: nat)\n (i: nat)\n: Lemma\n (requires (\n i < j /\\\n j <= len /\\\n n < pow2 (8 * (len - j))\n ))\n (ensures (\n pow2 (8 * (len - j)) <= pow2 (8 * len) /\\\n U8.v (S.index (n_to_be len n) i) == 0\n ))\n= let open FStar.Math.Lemmas in\n pow2_le_compat (8 * len) (8 * (len - j));\n pow2_le_compat (8 * (len - 1 - i)) (8 * (len - j));\n small_division_lemma_1 n (pow2 (8 * (len - 1 - i)));\n index_n_to_be len n i", "val be_to_n_append\n (hi lo: bytes)\n: Lemma\n (ensures (be_to_n (hi `S.append` lo) == be_to_n hi * pow2 (8 * S.length lo) + be_to_n lo))", "val n_to_be_append\n (len: nat)\n (n: nat)\n (len_lo: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len) /\\\n len_lo <= len\n ))\n (ensures (\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n 0 <= hi /\\\n hi < pow2 (8 * (len - len_lo)) /\\\n 0 <= lo /\\\n lo < pow2 (8 * len_lo) /\\\n n_to_be len n == n_to_be (len - len_lo) hi `S.append` n_to_be len_lo lo\n ))", "let index_n_to_be_zero_right\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len) /\\\n n % pow2 (8 * (len - i)) == 0\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i) == 0\n ))\n= index_n_to_be len n i;\n let open FStar.Math.Lemmas in\n modulo_division_lemma n (pow2 (8 * (len - 1 - i))) (pow2 8);\n pow2_plus (8 * (len - 1 - i)) 8", "val reveal_n_to_be\n (len: nat)\n (n: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len)\n ))\n (ensures (\n (len > 0 ==> (0 <= n / pow2 8 /\\ n / pow2 8 < pow2 (8 * (len - 1)))) /\\\n n_to_be len n `S.equal` (if len = 0 then S.empty else n_to_be (len - 1) (n / pow2 8) `S.snoc` (U8.uint_to_t (n % pow2 8)))\n ))", "let rec be_to_n_append'\n (hi lo: bytes)\n: Lemma\n (ensures (be_to_n (hi `S.append` lo) == be_to_n hi * pow2 (8 * S.length lo) + be_to_n lo))\n (decreases (S.length lo))\n= reveal_be_to_n lo;\n let hilo = hi `S.append` lo in\n if S.length lo = 0\n then\n assert (hilo `S.equal` hi)\n else begin\n let lo' = S.slice lo 0 (S.length lo - 1) in\n assert (S.slice hilo 0 (S.length hilo - 1) `S.equal` (hi `S.append` lo'));\n assert (S.last hilo == S.last lo);\n reveal_be_to_n hilo;\n be_to_n_append' hi lo';\n pow2_plus (8 * S.length lo') 8\n end", "val slice_n_to_be\n (len: nat)\n (n: nat)\n (i j: nat)\n: Lemma\n (requires (\n i <= j /\\\n j <= len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n let res = (n / pow2 (8 * (len - j))) % pow2 (8 * (j - i)) in\n 0 <= res /\\\n res < pow2 (8 * (j - i)) /\\\n S.slice (n_to_be len n) i j == n_to_be (j - i) res\n ))", "let be_to_n_append = be_to_n_append'", "let lemma_div_zero (x: pos) : Lemma\n (0 / x == 0)\n= ()", "val index_le_to_n\n (b: bytes)\n (i: nat)\n: Lemma\n (requires (\n i < S.length b\n ))\n (ensures (\n U8.v (S.index b i) == (le_to_n b / pow2 (8 * i)) % pow2 8\n ))", "let n_to_be_append\n (len: nat)\n (n: nat)\n (len_lo: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len) /\\\n len_lo <= len\n ))\n (ensures (\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n 0 <= hi /\\\n hi < pow2 (8 * (len - len_lo)) /\\\n 0 <= lo /\\\n lo < pow2 (8 * len_lo) /\\\n n_to_be len n == n_to_be (len - len_lo) hi `S.append` n_to_be len_lo lo\n ))\n= lemma_div_zero (pow2 (8 * len_lo));\n lemma_div_le 0 n (pow2 (8 * len_lo));\n lemma_mod_lt n (pow2 (8 * len_lo));\n let hi = n / pow2 (8 * len_lo) in\n assert (0 <= hi);\n lemma_div_lt n (8 * len) (8 * len_lo);\n pow2_minus (8 * len) (8 * len_lo);\n let lo = n % pow2 (8 * len_lo) in\n euclidean_division_definition n (pow2 (8 * len_lo));\n let hi_s = n_to_be (len - len_lo) hi in\n let lo_s = n_to_be len_lo lo in\n be_to_n_append hi_s lo_s;\n assert (be_to_n (hi_s `S.append` lo_s) == n);\n be_to_n_inj (hi_s `S.append` lo_s) (n_to_be len n)", "val index_n_to_le\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n U8.v (S.index (n_to_le len n) i)) == (n / pow2 (8 * i) % pow2 8\n ))", "val reveal_n_to_le\n (len: nat)\n (n: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len)\n ))\n (ensures (\n (len > 0 ==> (0 <= n / pow2 8 /\\ n / pow2 8 < pow2 (8 * (len - 1)))) /\\\n n_to_le len n `S.equal` (if len = 0 then S.empty else (U8.uint_to_t (n % pow2 8) `S.cons` n_to_le (len - 1) (n / pow2 8)))\n ))", "let reveal_n_to_be\n (len: nat)\n (n: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len)\n ))\n (ensures (\n (len > 0 ==> (0 <= n / pow2 8 /\\ n / pow2 8 < pow2 (8 * (len - 1)))) /\\\n n_to_be len n `S.equal` (if len = 0 then S.empty else n_to_be (len - 1) (n / pow2 8) `S.snoc` (U8.uint_to_t (n % pow2 8)))\n ))\n= if len = 0\n then ()\n else begin\n n_to_be_append len n 1;\n index_n_to_be 1 (n % pow2 8) 0\n end", "let slice_n_to_be\n (len: nat)\n (n: nat)\n (i j: nat)\n: Lemma\n (requires (\n i <= j /\\\n j <= len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n let res = (n / pow2 (8 * (len - j))) % pow2 (8 * (j - i)) in\n 0 <= res /\\\n res < pow2 (8 * (j - i)) /\\\n S.slice (n_to_be len n) i j == n_to_be (j - i) res\n ))\n= let s1 = S.slice (n_to_be len n) 0 j in\n let s2 = S.slice s1 i j in\n n_to_be_append len n (len - j);\n let q = n / pow2 (8 * (len - j)) in\n n_to_be_append j q (j - i);\n let r = q % pow2 (8 * (j - i)) in\n assert (s2 `S.equal` n_to_be (j - i) (q % pow2 (8 * (j - i))))", "let rec seq_rev\n (#t: Type)\n (x: S.seq t)\n: Tot (y: S.seq t {S.length y == S.length x})\n (decreases (S.length x))\n= if S.length x = 0\n then S.empty\n else seq_rev (S.tail x) `S.append` S.create 1 (S.head x)", "let rec index_seq_rev'\n (#t: Type)\n (x: S.seq t)\n (i: nat {i < S.length x})\n: Lemma\n (ensures (S.index (seq_rev x) (S.length x - 1 - i) == S.index x i))\n (decreases (S.length x))\n= if i = 0\n then\n S.lemma_index_create 1 (S.head x) 0\n else\n index_seq_rev' (S.tail x) (i - 1)", "let index_seq_rev\n (#t: Type)\n (x: S.seq t)\n (i: nat {i < S.length x})\n: Lemma\n (ensures (S.index (seq_rev x) i == S.index x (S.length x - 1 - i)))\n= index_seq_rev' x (S.length x - 1 - i)", "let slice_seq_rev\n (#t: Type)\n (x: S.seq t)\n (i: nat)\n (j: nat)\n: Lemma\n (requires (i <= j /\\ j <= S.length x))\n (ensures (S.slice (seq_rev x) i j `S.equal` seq_rev (S.slice x (S.length x - j) (S.length x - i))))\n= Classical.forall_intro (index_seq_rev x);\n Classical.forall_intro (index_seq_rev (S.slice x (S.length x - j) (S.length x - i)))", "let rec le_to_n_eq_be_to_n_rev\n (b: bytes)\n: Lemma\n (ensures (le_to_n b == be_to_n (seq_rev b)))\n (decreases (S.length b))\n= reveal_be_to_n (seq_rev b);\n reveal_le_to_n b;\n if Seq.length b = 0\n then ()\n else begin\n index_seq_rev b (S.length b - 1);\n slice_seq_rev b 0 (S.length b - 1);\n le_to_n_eq_be_to_n_rev (S.tail b)\n end", "let seq_rev_involutive\n (#t: Type)\n (x: S.seq t)\n: Lemma\n (seq_rev (seq_rev x) `S.equal` x)\n= Classical.forall_intro (index_seq_rev (seq_rev x));\n Classical.forall_intro (index_seq_rev x)" ], "closest": [ "val n_to_le_le_to_n (len: U32.t) (s: Seq.seq U8.t)\n : Lemma (requires (Seq.length s == U32.v len))\n (ensures\n (le_to_n s < pow2 (8 `Prims.op_Multiply` (U32.v len)) /\\ n_to_le len (le_to_n s) == s))\n [SMTPat (n_to_le len (le_to_n s))]\nlet n_to_le_le_to_n (len: U32.t) (s: Seq.seq U8.t) : Lemma\n (requires (Seq.length s == U32.v len))\n (ensures (\n le_to_n s < pow2 (8 `Prims.op_Multiply` U32.v len) /\\\n n_to_le len (le_to_n s) == s\n ))\n [SMTPat (n_to_le len (le_to_n s))]\n= lemma_le_to_n_is_bounded s;\n le_to_n_inj s (n_to_le len (le_to_n s))", "val index_n_to_be (len n i: nat)\n : Lemma (requires (i < len /\\ n < pow2 (8 * len)))\n (ensures\n (U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i)) ==\n (n / pow2 (8 * (len - 1 - i)) % pow2 8))\nlet index_n_to_be\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i)) == (n / pow2 (8 * (len - 1 - i)) % pow2 8\n ))\n= index_be_to_n (FStar.Endianness.n_to_be len n) i", "val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma\n (requires (Seq.length s == len))\n (ensures (\n le_to_n s < pow2 (8 * len) /\\\n n_to_le len (le_to_n s) == s\n ))\n [SMTPat (n_to_le len (le_to_n s))]\nlet n_to_le_le_to_n len s =\n lemma_le_to_n_is_bounded s;\n le_to_n_inj s (n_to_le len (le_to_n s))", "val n_to_be_be_to_n (len: U32.t) (s: Seq.seq U8.t)\n : Lemma (requires (Seq.length s == U32.v len))\n (ensures\n (be_to_n s < pow2 (8 `Prims.op_Multiply` (U32.v len)) /\\ n_to_be len (be_to_n s) == s))\n [SMTPat (n_to_be len (be_to_n s))]\nlet n_to_be_be_to_n (len: U32.t) (s: Seq.seq U8.t) : Lemma\n (requires (Seq.length s == U32.v len))\n (ensures (\n be_to_n s < pow2 (8 `Prims.op_Multiply` U32.v len) /\\\n n_to_be len (be_to_n s) == s\n ))\n [SMTPat (n_to_be len (be_to_n s))]\n= lemma_be_to_n_is_bounded s;\n be_to_n_inj s (n_to_be len (be_to_n s))", "val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma\n (requires (Seq.length s == len))\n (ensures (\n be_to_n s < pow2 (8 * len) /\\\n n_to_be len (be_to_n s) == s\n ))\n [SMTPat (n_to_be len (be_to_n s))]\nlet n_to_be_be_to_n len s =\n lemma_be_to_n_is_bounded s;\n be_to_n_inj s (n_to_be len (be_to_n s))", "val index_n_to_be_zero_right (len n i: nat)\n : Lemma (requires (i < len /\\ n < pow2 (8 * len) /\\ n % pow2 (8 * (len - i)) == 0))\n (ensures (U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i) == 0))\nlet index_n_to_be_zero_right\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len) /\\\n n % pow2 (8 * (len - i)) == 0\n ))\n (ensures (\n U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i) == 0\n ))\n= index_n_to_be len n i;\n let open FStar.Math.Lemmas in\n modulo_division_lemma n (pow2 (8 * (len - 1 - i))) (pow2 8);\n pow2_plus (8 * (len - 1 - i)) 8", "val index_n_to_be_zero_left (len n j i: nat)\n : Lemma (requires (i < j /\\ j <= len /\\ n < pow2 (8 * (len - j))))\n (ensures\n (pow2 (8 * (len - j)) <= pow2 (8 * len) /\\\n U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i) == 0))\nlet index_n_to_be_zero_left\n (len: nat)\n (n: nat)\n (j: nat)\n (i: nat)\n: Lemma\n (requires (\n i < j /\\\n j <= len /\\\n n < pow2 (8 * (len - j))\n ))\n (ensures (\n pow2 (8 * (len - j)) <= pow2 (8 * len) /\\\n U8.v (FStar.Seq.index (FStar.Endianness.n_to_be len n) i) == 0\n ))\n= let open FStar.Math.Lemmas in\n pow2_le_compat (8 * len) (8 * (len - j));\n pow2_le_compat (8 * (len - 1 - i)) (8 * (len - j));\n small_division_lemma_1 n (pow2 (8 * (len - 1 - i)));\n index_n_to_be len n i", "val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->\n Tot (b:bytes{S.length b == len /\\ n == le_to_n b})\n (decreases len)\nlet rec n_to_le len n =\n if len = 0 then\n S.empty\n else\n let len = len - 1 in\n let byte = U8.uint_to_t (n % 256) in\n let n' = n / 256 in\n Math.pow2_plus 8 (8 * len);\n assert(n' < pow2 (8 * len ));\n let b' = n_to_le len n' in\n let b = S.cons byte b' in\n S.lemma_eq_intro b' (S.tail b);\n b", "val nat_to_bytes_n_to_be: len:size_nat -> l:secrecy_level -> n:nat{n < pow2 (8 * len)} ->\n Lemma (ensures (Seq.equal (FStar.Endianness.n_to_be len n)\n (BS.nat_to_bytes_be #l len n)))\n (decreases len)\nlet rec nat_to_bytes_n_to_be len l n =\n if len = 0 then () else\n begin\n Math.Lemmas.division_multiplication_lemma n (pow2 8) (pow2 (8 * (len - 1)));\n Math.Lemmas.pow2_plus 8 (8 * (len - 1));\n nat_to_bytes_n_to_be (len - 1) l (n / 256)\n end", "val nat_to_bytes_n_to_le: len:size_nat -> l:secrecy_level -> n:nat{n < pow2 (8 * len)} ->\n Lemma (ensures Seq.equal (FStar.Endianness.n_to_le len n)\n (BS.nat_to_bytes_le #l len n))\n (decreases len)\nlet rec nat_to_bytes_n_to_le len l n =\n if len = 0 then () else\n begin\n Math.Lemmas.division_multiplication_lemma n (pow2 8) (pow2 (8 * (len - 1)));\n Math.Lemmas.pow2_plus 8 (8 * (len - 1));\n nat_to_bytes_n_to_le (len - 1) l (n / 256)\n end", "val slice_n_to_be_bitfield (len: pos) (n i j: nat)\n : Lemma (requires (i <= j /\\ j <= len /\\ n < pow2 (8 * len)))\n (ensures\n (S.slice (n_to_be len n) i j ==\n n_to_be (j - i) (BF.get_bitfield #(8 * len) n (8 * (len - j)) (8 * (len - i)))))\nlet slice_n_to_be_bitfield\n (len: pos)\n (n: nat)\n (i j: nat)\n: Lemma\n (requires (\n i <= j /\\\n j <= len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n S.slice (n_to_be len n) i j == n_to_be (j - i) (BF.get_bitfield #(8 * len) n (8 * (len - j)) (8 * (len - i)))\n ))\n= slice_n_to_be len n i j;\n BF.get_bitfield_eq #(8 * len) n (8 * (len - j)) (8 * (len - i))", "val lemma_pad_to_32_bits (s s'': seq4 nat8) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\\n (forall (i: nat). {:pattern (index s i)\\/(index s'' i)}\n i < 4 ==> index s'' i == (if i < n then index s i else 0)))\n (ensures\n four_to_nat 8 (seq_to_four_BE s'') ==\n (four_to_nat 8 (seq_to_four_BE s) / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_pad_to_32_bits (s s'':seq4 nat8) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n (forall (i:nat).{:pattern (index s i) \\/ (index s'' i)} i < 4 ==>\n index s'' i == (if i < n then index s i else 0))\n )\n (ensures four_to_nat 8 (seq_to_four_BE s'') == (four_to_nat 8 (seq_to_four_BE s) / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n if n <= 2 then lemma_pad_to_32_bits_helper s s'' n else\n assert (n == 3 \\/ n == 4);\n assert_norm (four_to_nat 8 (seq_to_four_BE s) == four_to_nat_unfold 8 (seq_to_four_BE s));\n assert_norm (four_to_nat 8 (seq_to_four_BE s'') == four_to_nat_unfold 8 (seq_to_four_BE s''));\n assert_norm (pow2 (0 * 8) == 1);\n assert_norm (pow2 (1 * 8) == 0x100);\n let x = four_to_nat 8 (seq_to_four_BE s'') in\n assert (n == 3 ==> x / pow2 (8 * (4 - n)) == x / 0x100);\n assert (n == 4 ==> x / pow2 (8 * (4 - n)) == x / 0x1);\n assert_norm (((x / pow2 (8 * 1)) * pow2 (8 * 1)) % pow2 (8 * 1) == 0);\n assert_norm (((x / pow2 (8 * 0)) * pow2 (8 * 0)) % pow2 (8 * 0) == 0);\n ()", "val lemma_pad_to_32_bits_helper (s s'': seq4 nat8) (n: nat)\n : Lemma\n (requires\n n <= 2 /\\\n (forall (i: nat). {:pattern (index s i)\\/(index s'' i)}\n i < 4 ==> index s'' i == (if i < n then index s i else 0)))\n (ensures\n four_to_nat 8 (seq_to_four_BE s'') ==\n (four_to_nat 8 (seq_to_four_BE s) / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_pad_to_32_bits_helper (s s'':seq4 nat8) (n:nat) : Lemma\n (requires\n n <= 2 /\\\n (forall (i:nat).{:pattern (index s i) \\/ (index s'' i)} i < 4 ==>\n index s'' i == (if i < n then index s i else 0))\n )\n (ensures four_to_nat 8 (seq_to_four_BE s'') == (four_to_nat 8 (seq_to_four_BE s) / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n assert (n == 0 \\/ n == 1 \\/ n == 2);\n assert_norm (four_to_nat 8 (seq_to_four_BE s) == four_to_nat_unfold 8 (seq_to_four_BE s));\n assert_norm (four_to_nat 8 (seq_to_four_BE s'') == four_to_nat_unfold 8 (seq_to_four_BE s''));\n assert_norm (pow2 (2 * 8) == 0x10000);\n assert_norm (pow2 (3 * 8) == 0x1000000);\n assert_norm (pow2 (4 * 8) == 0x100000000);\n let x = four_to_nat 8 (seq_to_four_BE s'') in\n assert (n == 0 ==> x / pow2 (8 * (4 - n)) == x / 0x100000000);\n assert (n == 1 ==> x / pow2 (8 * (4 - n)) == x / 0x1000000);\n assert (n == 2 ==> x / pow2 (8 * (4 - n)) == x / 0x10000);\n assert_norm (((x / pow2 (8 * 4)) * pow2 (8 * 4)) % pow2 (8 * 4) == 0);\n assert_norm (((x / pow2 (8 * 3)) * pow2 (8 * 3)) % pow2 (8 * 3) == 0);\n assert_norm (((x / pow2 (8 * 2)) * pow2 (8 * 2)) % pow2 (8 * 2) == 0);\n ()", "val n_to_le : len:U32.t -> n:nat{n < pow2 (8 * U32.v len)} ->\n Tot (b:bytes{S.length b == U32.v len /\\ n == le_to_n b})\n (decreases (U32.v len))\nlet rec n_to_le len n =\n if len = 0ul then\n S.empty\n else\n let len = U32.(len -^ 1ul) in\n let byte = U8.uint_to_t (n % 256) in\n let n' = n / 256 in\n Math.pow2_plus 8 (8 * U32.v len);\n assert(n' < pow2 (8 * U32.v len ));\n let b' = n_to_le len n' in\n let b = S.cons byte b' in\n S.lemma_eq_intro b' (S.tail b);\n b", "val lemma_pad_to_32_bits (s s'': seq4 nat8) (n: nat)\n : Lemma\n (requires\n n <= 4 /\\\n (forall (i: nat). {:pattern (index s i)\\/(index s'' i)}\n i < 4 ==> index s'' i == (if i < n then index s i else 0)))\n (ensures four_to_nat 8 (seq_to_four_LE s'') == four_to_nat 8 (seq_to_four_LE s) % pow2 (8 * n)\n )\nlet lemma_pad_to_32_bits (s s'':seq4 nat8) (n:nat) : Lemma\n (requires\n n <= 4 /\\\n (forall (i:nat).{:pattern (index s i) \\/ (index s'' i)} i < 4 ==>\n index s'' i == (if i < n then index s i else 0))\n )\n (ensures four_to_nat 8 (seq_to_four_LE s'') == four_to_nat 8 (seq_to_four_LE s) % pow2 (8 * n))\n =\n if n <= 2 then lemma_pad_to_32_bits_helper s s'' n else\n assert (n == 3 \\/ n == 4);\n assert_norm (four_to_nat 8 (seq_to_four_LE s) == four_to_nat_unfold 8 (seq_to_four_LE s));\n assert_norm (four_to_nat 8 (seq_to_four_LE s'') == four_to_nat_unfold 8 (seq_to_four_LE s''));\n assert_norm (pow2 (0 * 8) == 1);\n assert_norm (pow2 (1 * 8) == 0x100);\n assert_norm (pow2 (2 * 8) == 0x10000);\n assert_norm (pow2 (3 * 8) == 0x1000000);\n assert_norm (pow2 (4 * 8) == 0x100000000);\n let x = four_to_nat 8 (seq_to_four_LE s'') in\n assert (n == 3 ==> x % pow2 (8 * n) == x % 0x1000000);\n assert (n == 4 ==> x % pow2 (8 * n) == x % 0x100000000);\n ()", "val lemma_pow2_128: n:nat ->\n Lemma\n (requires n <= 128)\n (ensures pow2 n < Scalar.prime)\n [SMTPat (pow2 n)]\nlet lemma_pow2_128 n =\n Math.Lemmas.pow2_le_compat 128 n;\n assert (pow2 n <= pow2 128);\n assert_norm (pow2 128 < Scalar.prime)", "val lemma_reverse_bytes_nat64_32 (n0 n1: nat32)\n : Lemma\n (reverse_bytes_nat64 (two_to_nat32 (Mktwo n0 n1)) ==\n two_to_nat32 (Mktwo (reverse_bytes_nat32 n1) (reverse_bytes_nat32 n0)))\nlet lemma_reverse_bytes_nat64_32 (n0 n1:nat32) : Lemma\n (reverse_bytes_nat64 (two_to_nat32 (Mktwo n0 n1)) == two_to_nat32 (Mktwo (reverse_bytes_nat32 n1) (reverse_bytes_nat32 n0)))\n =\n reverse_bytes_nat64_reveal ()", "val lemma_be_index (l: pos) (n: nat{n < pow2 (8 `op_Multiply` l)})\n : Lemma\n (ensures U8.v (S.index (FStar.Endianness.n_to_be l n) 0) == n / pow2 (8 `op_Multiply` (l - 1))\n ) (decreases %[l])\nlet rec lemma_be_index (l:pos) (n:nat{n < pow2 (8 `op_Multiply` l)})\n : Lemma (ensures U8.v (S.index (FStar.Endianness.n_to_be l n) 0)\n == n / pow2 (8 `op_Multiply` (l-1)))\n (decreases %[l])\n =\n let open FStar.Endianness in\n let open FStar.Mul in\n let b = n_to_be l n in\n let b0 = S.index b 0 in\n reveal_be_to_n b;\n if l = 1 then ()\n else\n let b1 = S.last b in\n let b' = S.slice b 0 (l-1) in\n let b0' = S.index b' 0 in\n reveal_be_to_n b';\n assert(U8.v b1 == n % pow2 8);\n lemma_be_to_n_is_bounded b';\n lemma_be_index (l-1) (be_to_n b');\n lemma_pow2_div2 (n - U8.v b1) 8 (8 * (l-1) - 8);\n lemma_div_sub_small l n (U8.v b1)", "val lemma_pad_to_32_bits_helper (s s'': seq4 nat8) (n: nat)\n : Lemma\n (requires\n n <= 2 /\\\n (forall (i: nat). {:pattern (index s i)\\/(index s'' i)}\n i < 4 ==> index s'' i == (if i < n then index s i else 0)))\n (ensures four_to_nat 8 (seq_to_four_LE s'') == four_to_nat 8 (seq_to_four_LE s) % pow2 (8 * n)\n )\nlet lemma_pad_to_32_bits_helper (s s'':seq4 nat8) (n:nat) : Lemma\n (requires\n n <= 2 /\\\n (forall (i:nat).{:pattern (index s i) \\/ (index s'' i)} i < 4 ==>\n index s'' i == (if i < n then index s i else 0))\n )\n (ensures four_to_nat 8 (seq_to_four_LE s'') == four_to_nat 8 (seq_to_four_LE s) % pow2 (8 * n))\n =\n assert (n == 0 \\/ n == 1 \\/ n == 2);\n assert_norm (four_to_nat 8 (seq_to_four_LE s) == four_to_nat_unfold 8 (seq_to_four_LE s));\n assert_norm (four_to_nat 8 (seq_to_four_LE s'') == four_to_nat_unfold 8 (seq_to_four_LE s''));\n assert_norm (pow2 (0 * 8) == 1);\n assert_norm (pow2 (1 * 8) == 0x100);\n assert_norm (pow2 (2 * 8) == 0x10000);\n assert_norm (pow2 (3 * 8) == 0x1000000);\n assert_norm (pow2 (4 * 8) == 0x100000000);\n let x = four_to_nat 8 (seq_to_four_LE s'') in\n assert (n == 0 ==> x % pow2 (8 * n) == x % 0x1);\n assert (n == 1 ==> x % pow2 (8 * n) == x % 0x100);\n assert (n == 2 ==> x % pow2 (8 * n) == x % 0x10000);\n ()", "val nat_to_bytes_le (#l: secrecy_level) (len: nat) (n: nat{n < pow2 (8 * len)})\n : b: bytes_l l {length b == len /\\ n == nat_from_intseq_le #U8 b}\nlet nat_to_bytes_le (#l:secrecy_level) (len:nat) (n:nat{n < pow2 (8 * len)}) : b:bytes_l l{length b == len /\\ n == nat_from_intseq_le #U8 b} =\n nat_to_intseq_le #U8 #l len n", "val lemma_power2_add64 (n:nat) : Lemma\n (requires True)\n (ensures pow2(64 + n) == 0x10000000000000000 * pow2(n))\nlet lemma_power2_add64 (n:nat) =\n pow2_plus 64 n;\n FStar.UInt.pow2_values 64", "val pow2_m_minus_one_eq (n m: nat)\n : Lemma (requires (m <= n)) (ensures ((pow2 n - 1) / pow2 m == pow2 (n - m) - 1))\nlet pow2_m_minus_one_eq\n (n: nat)\n (m: nat)\n: Lemma\n (requires (m <= n))\n (ensures (\n (pow2 n - 1) / pow2 m == pow2 (n - m) - 1 \n ))\n= M.pow2_le_compat n m;\n M.pow2_plus (n - m) m;\n M.division_definition (pow2 n - 1) (pow2 m) (pow2 (n - m) - 1)", "val lemma_le_to_n_is_bounded: b:bytes -> Lemma\n (requires True)\n (ensures (le_to_n b < pow2 (8 * Seq.length b)))\n (decreases (Seq.length b))\nlet rec lemma_le_to_n_is_bounded b =\n if Seq.length b = 0 then ()\n else\n begin\n let s = Seq.slice b 1 (Seq.length b) in\n assert(Seq.length s = Seq.length b - 1);\n lemma_le_to_n_is_bounded s;\n assert(UInt8.v (Seq.index b 0) < pow2 8);\n assert(le_to_n s < pow2 (8 * Seq.length s));\n assert(le_to_n b < pow2 8 + pow2 8 * pow2 (8 * (Seq.length b - 1)));\n lemma_euclidean_division (UInt8.v (Seq.index b 0)) (le_to_n s) (pow2 8);\n assert(le_to_n b <= pow2 8 * (le_to_n s + 1));\n assert(le_to_n b <= pow2 8 * pow2 (8 * (Seq.length b - 1)));\n Math.Lemmas.pow2_plus 8 (8 * (Seq.length b - 1));\n lemma_factorise 8 (Seq.length b - 1)\n end", "val lemma_le_to_n_is_bounded: b:bytes -> Lemma\n (requires True)\n (ensures (le_to_n b < pow2 (8 * Seq.length b)))\n (decreases (Seq.length b))\nlet rec lemma_le_to_n_is_bounded b =\n if Seq.length b = 0 then ()\n else\n begin\n let s = Seq.slice b 1 (Seq.length b) in\n assert(Seq.length s = Seq.length b - 1);\n lemma_le_to_n_is_bounded s;\n assert(UInt8.v (Seq.index b 0) < pow2 8);\n assert(le_to_n s < pow2 (8 * Seq.length s));\n assert(le_to_n b < pow2 8 + pow2 8 * pow2 (8 * (Seq.length b - 1)));\n lemma_euclidean_division (UInt8.v (Seq.index b 0)) (le_to_n s) (pow2 8);\n assert(le_to_n b <= pow2 8 * (le_to_n s + 1));\n assert(le_to_n b <= pow2 8 * pow2 (8 * (Seq.length b - 1)));\n Math.Lemmas.pow2_plus 8 (8 * (Seq.length b - 1));\n lemma_factorise 8 (Seq.length b - 1)\n end", "val be_of_seq_uint32_seq_uint32_of_be (n: nat) (s: S.seq U8.t)\n : Lemma (requires (4 * n == S.length s))\n (ensures ((be_of_seq_uint32 (seq_uint32_of_be n s)) `S.equal` s))\n (decreases n)\n [SMTPat (be_of_seq_uint32 (seq_uint32_of_be n s))]\nlet rec be_of_seq_uint32_seq_uint32_of_be (n: nat) (s: S.seq U8.t) : Lemma\n (requires (4 * n == S.length s))\n (ensures (be_of_seq_uint32 (seq_uint32_of_be n s) `S.equal` s))\n (decreases n)\n [SMTPat (be_of_seq_uint32 (seq_uint32_of_be n s))]\n= if n = 0\n then ()\n else begin\n S.lemma_split s 4;\n be_of_seq_uint32_seq_uint32_of_be (n - 1) (S.slice s 4 (S.length s));\n let s' = seq_uint32_of_be n s in\n let hd, tl = S.split s 4 in\n assert (S.head s' == uint32_of_be hd);\n tail_cons (uint32_of_be hd) (seq_uint32_of_be (n - 1) tl);\n assert (S.tail s' == seq_uint32_of_be (n - 1) tl);\n let s'' = be_of_seq_uint32 s' in\n S.lemma_split s'' 4;\n S.lemma_append_inj (S.slice s'' 0 4) (S.slice s'' 4 (S.length s'')) (be_of_uint32 (S.head s')) (be_of_seq_uint32 (S.tail s'));\n n_to_be_be_to_n 4ul hd\n end", "val lemma_add_0x1000000_reverse_mult (n: nat32) (increment: nat)\n : Lemma (requires (n % 256) + increment < 256)\n (ensures\n (let r = reverse_bytes_nat32 n in\n r + increment * 0x1000000 == reverse_bytes_nat32 (n + increment)))\nlet lemma_add_0x1000000_reverse_mult (n:nat32) (increment:nat) : Lemma\n (requires (n % 256) + increment < 256)\n (ensures (let r = reverse_bytes_nat32 n in\n r + increment * 0x1000000 == reverse_bytes_nat32 (n + increment)))\n =\n let r = reverse_bytes_nat32 n in\n assert_norm (Vale.Def.Words.Four_s.nat_to_four 8 (n+increment) == Mkfour ((n+increment) % 0x100) (((n+increment) / 0x100) % 0x100) (((n+increment) / 0x10000) % 0x100) (((n+increment) / 0x1000000) % 0x100));\n assert ((n+increment) / 0x1000000 == n / 0x1000000);\n assert ((n+increment) / 0x10000 == n / 0x10000);\n assert ((n+increment) / 0x100 == n / 0x100);\n assert (Vale.Def.Words.Four_s.nat_to_four 8 (n+increment) == Mkfour ((n+increment) % 0x100) ((n / 0x100) % 0x100) ((n / 0x10000) % 0x100) ((n / 0x1000000) % 0x100));\n\n assert_norm (Vale.Def.Words.Four_s.nat_to_four 8 n == Mkfour (n % 0x100) ((n / 0x100) % 0x100) ((n / 0x10000) % 0x100) ((n / 0x1000000) % 0x100));\n let s = Vale.Def.Words.Seq_s.four_to_seq_BE (Vale.Def.Words.Four_s.nat_to_four 8 n) in\n let r_s = Vale.Lib.Seqs_s.reverse_seq s in\n assert_norm (be_bytes_to_nat32 r_s == ((n / 0x1000000) % 0x100) +\n ((n / 0x10000) % 0x100) * 0x100 +\n ((n / 0x100) % 0x100) * 0x10000 +\n (n % 0x100) * 0x1000000);\n let s' = Vale.Def.Words.Seq_s.four_to_seq_BE (Vale.Def.Words.Four_s.nat_to_four 8 (n+increment)) in\n let r_s' = Vale.Lib.Seqs_s.reverse_seq s' in\n\n assert_norm (be_bytes_to_nat32 r_s' == (((n) / 0x1000000) % 0x100) +\n (((n) / 0x10000) % 0x100) * 0x100 +\n (((n) / 0x100) % 0x100) * 0x10000 +\n ((n+increment) % 0x100) * 0x1000000);\n assert (be_bytes_to_nat32 r_s + increment * 0x1000000 == be_bytes_to_nat32 r_s');\n calc (==) {\n r;\n == { reverse_bytes_nat32_reveal () }\n be_bytes_to_nat32 r_s;\n };\n calc (==) {\n reverse_bytes_nat32 (n+increment);\n == { reverse_bytes_nat32_reveal () }\n be_bytes_to_nat32 (Vale.Lib.Seqs_s.reverse_seq (nat32_to_be_bytes (n+increment)));\n };\n ()", "val lemma_equal_nth (n:pos) (x y:natN (pow2 n)) : Lemma\n (requires (forall (i:nat).{:pattern (nth #n x i) \\/ (nth #n y i)} i < n ==> nth #n x i == nth #n y i))\n (ensures x == y)\nlet lemma_equal_nth n x y =\n UInt.to_vec_lemma_2 #n x y", "val lemma_reverse_reverse_bytes_nat32 (n:nat32) :\n Lemma (reverse_bytes_nat32 (reverse_bytes_nat32 n) == n)\n [SMTPat (reverse_bytes_nat32 (reverse_bytes_nat32 n))]\nlet lemma_reverse_reverse_bytes_nat32 (n:nat32) :\n Lemma (reverse_bytes_nat32 (reverse_bytes_nat32 n) == n)\n =\n reverse_bytes_nat32_reveal ();\n let r = reverse_seq (nat32_to_be_bytes n) in\n be_bytes_to_nat32_to_be_bytes r;\n ()", "val to_uint8_of_uint8 (n: nat{n <= 8}) (x: U8.t{U8.v x < pow2 n})\n : Lemma (to_uint8 (of_uint8 n x) == x)\nlet rec to_uint8_of_uint8\n (n: nat { n <= 8 })\n (x: U8.t { U8.v x < pow2 n })\n: Lemma\n (to_uint8 (of_uint8 n x) == x)\n= if n = 0\n then ()\n else begin\n assert (Seq.slice (of_uint8 n x) 0 (n - 1) `Seq.equal` of_uint8 (n - 1) (x `U8.div` 2uy));\n to_uint8_of_uint8 (n - 1) (x `U8.div` 2uy)\n end", "val lemma_pow2_le (m n:nat) : Lemma (requires m <= n) (ensures pow2 m <= pow2 n)\nlet lemma_pow2_le m n = FStar.Math.Lemmas.pow2_le_compat n m", "val Vale.Poly1305.Equiv.nat_to_bytes_le = len: Prims.nat -> n: Prims.nat{n < Prims.pow2 (8 * len)}\n -> b:\n Lib.Sequence.seq (Lib.IntTypes.int_t Lib.IntTypes.U8 l)\n {Lib.Sequence.length b == len /\\ n == Lib.ByteSequence.nat_from_intseq_le b}\nlet nat_to_bytes_le (#l:secrecy_level) = Lib.ByteSequence.nat_to_bytes_le #l", "val n_to_be:\n len:nat -> n:nat{n < pow2 (8 * len)} ->\n Tot (b:bytes{S.length b == len /\\ n == be_to_n b})\n (decreases len)\nlet rec n_to_be len n =\n if len = 0 then\n S.empty\n else\n let len = len - 1 in\n let byte = U8.uint_to_t (n % 256) in\n let n' = n / 256 in\n Math.pow2_plus 8 (8 * len);\n let b' = n_to_be len n' in\n let b'' = S.create 1 byte in\n let b = S.append b' b'' in\n S.lemma_eq_intro b' (S.slice b 0 len);\n b", "val lemma_pow2_256: n:nat -> Lemma\n (requires (n = 256))\n (ensures (pow2 n = 0x10000000000000000000000000000000000000000000000000000000000000000))\n [SMTPat (pow2 n)]\nlet lemma_pow2_256 n = assert_norm(pow2 256 = 0x10000000000000000000000000000000000000000000000000000000000000000)", "val be_of_seq_uint32_seq_uint32_of_be (n: nat) (s: S.seq U8.t) : Lemma\n (requires (4 * n == S.length s))\n (ensures (be_of_seq_uint32 (seq_uint32_of_be n s) `S.equal` s))\n (decreases n)\n [SMTPat (be_of_seq_uint32 (seq_uint32_of_be n s))]\nlet rec be_of_seq_uint32_seq_uint32_of_be n s =\n if n = 0\n then ()\n else begin\n S.lemma_split s 4;\n be_of_seq_uint32_seq_uint32_of_be (n - 1) (S.slice s 4 (S.length s));\n let s' = seq_uint32_of_be n s in\n let hd, tl = S.split s 4 in\n assert (S.head s' == uint32_of_be hd);\n tail_cons (uint32_of_be hd) (seq_uint32_of_be (n - 1) tl);\n assert (S.tail s' == seq_uint32_of_be (n - 1) tl);\n let s'' = be_of_seq_uint32 s' in\n S.lemma_split s'' 4;\n S.lemma_append_inj (S.slice s'' 0 4) (S.slice s'' 4 (S.length s'')) (be_of_uint32 (S.head s')) (be_of_seq_uint32 (S.tail s'));\n n_to_be_be_to_n 4 hd\n end", "val two_to_nat_to_two (n:nat64) : Lemma\n (two_to_nat 32 (nat_to_two 32 n) == n)\n [SMTPat (two_to_nat 32 (nat_to_two 32 n))]\nlet two_to_nat_to_two (n:nat64) =\n let n1 = n % (pow2_32) in\n let n2 = (n/(pow2_32)) % (pow2_32) in\n let n_f = two_to_nat 32 (Mktwo n1 n2) in\n assert_norm (n == n1 + n2 * pow2_32)", "val index_nat_to_intseq_be:\n #t:inttype{unsigned t}\n -> #l:secrecy_level\n -> len:size_nat\n -> n:nat{n < pow2 (bits t * len)}\n -> i:nat{i < len}\n -> Lemma (Seq.index (nat_to_intseq_be #t #l len n) (len - i - 1) ==\n uint #t #l (n / pow2 (bits t * i) % pow2 (bits t)))\nlet rec index_nat_to_intseq_be #t #l len n i =\n if i = 0 then\n if len = 0 then () else head_nat_to_intseq_be #t #l len n\n else\n begin\n let len' = len - 1 in\n let i' = i - 1 in\n let n' = n / pow2 (bits t) in\n FStar.Math.Lemmas.lemma_div_lt_nat n (bits t * len) (bits t);\n calc (==) {\n Seq.index (nat_to_intseq_be #t #l len' n') (len' - i' - 1);\n == {index_nat_to_intseq_be #t #l len' n' i'}\n uint (n' / pow2 (bits t * i') % pow2 (bits t));\n == {}\n uint (n / pow2 (bits t) / pow2 (bits t * i') % pow2 (bits t));\n == {Math.Lemmas.division_multiplication_lemma n (pow2 (bits t)) (pow2 (bits t * i'))}\n uint (n / (pow2 (bits t) * pow2 (bits t * i')) % pow2 (bits t));\n == {Math.Lemmas.pow2_plus (bits t) (bits t * i')}\n uint (n / (pow2 (bits t + bits t * i')) % pow2 (bits t));\n == {Math.Lemmas.distributivity_add_right (bits t) 1 (i - 1)}\n uint (n / (pow2 (bits t * i)) % pow2 (bits t));\n };\n nat_to_intseq_be_pos #t #l len n\n end", "val index_nat_to_intseq_le:\n #t:inttype{unsigned t}\n -> #l:secrecy_level\n -> len:size_nat\n -> n:nat{n < pow2 (bits t * len)}\n -> i:nat{i < len}\n -> Lemma (Seq.index (nat_to_intseq_le #t #l len n) i ==\n uint #t #l (n / pow2 (bits t * i) % pow2 (bits t)))\nlet rec index_nat_to_intseq_le #t #l len n i =\n if i = 0 then\n if len = 0 then () else head_nat_to_intseq_le #t #l len n\n else\n begin\n FStar.Math.Lemmas.lemma_div_lt_nat n (bits t * len) (bits t);\n calc (==) {\n Seq.index (nat_to_intseq_le #t #l (len - 1) (n / modulus t)) (i - 1);\n == { index_nat_to_intseq_le #t #l (len - 1) (n / modulus t) (i - 1) }\n uint ((n / modulus t) / pow2 (bits t * (i - 1)) % modulus t);\n == { Math.Lemmas.division_multiplication_lemma n (modulus t) (pow2 (bits t * (i - 1))) }\n uint ((n / (pow2 (bits t) * pow2 (bits t * (i - 1)))) % modulus t);\n == { Math.Lemmas.pow2_plus (bits t) (bits t * (i - 1)) }\n uint ((n / pow2 (bits t + bits t * (i - 1))) % modulus t);\n == { Math.Lemmas.distributivity_add_right (bits t) i (-1) }\n uint (n / pow2 (bits t + (bits t * i - bits t)) % modulus t);\n == { }\n uint (n / pow2 (bits t * i) % pow2 (bits t));\n };\n nat_to_intseq_le_pos #t #l len n\n end", "val lemma_of_nat_of_uint (n:nat) (x:nat) : Lemma\n (requires x < pow2 n)\n (ensures of_nat x == of_uint_ n x)\nlet rec lemma_of_nat_of_uint n x\n =\n if n > 0 then\n (\n lemma_of_nat_of_uint (n - 1) (x / 2);\n lemma_bitwise_all ();\n lemma_equal (of_nat x) (of_uint n x)\n )", "val lemma_be_to_n_4 (s: seq4 nat8)\n : Lemma\n (Lib.ByteSequence.nat_from_bytes_be #Lib.IntTypes.SEC (seq_nat8_to_seq_uint8 s) ==\n be_bytes_to_nat32 s)\nlet lemma_be_to_n_4 (s:seq4 nat8) : Lemma\n (Lib.ByteSequence.nat_from_bytes_be #Lib.IntTypes.SEC (seq_nat8_to_seq_uint8 s) == be_bytes_to_nat32 s)\n =\n let open Lib.IntTypes in\n let open Vale.Def.Words.Four_s in\n assert (pow2 8 = 0x100);\n assert (pow2 16 = 0x10000);\n assert_norm (pow2 24 = 0x1000000);\n let x = seq_nat8_to_seq_uint8 s in\n let f = Lib.ByteSequence.nat_from_intseq_be_ #U8 #SEC in\n calc (==) {\n f x <: nat ;\n == { }\n FStar.UInt8.v (last x) + pow2 8 * f (slice x 0 3);\n == {}\n index s 3 + pow2 8 * f (slice x 0 3);\n == {}\n index s 3 + pow2 8 * index s 2 + pow2 16 * f (slice x 0 2);\n == {}\n index s 3 + pow2 8 * index s 2 + pow2 16 * index s 1 + pow2 24 * f (slice x 0 1);\n == {}\n index s 3 + pow2 8 * index s 2 + pow2 16 * index s 1 + pow2 24 * index s 0 + pow2 32 * f (slice x 0 0);\n == {}\n index s 3 + pow2 8 * index s 2 + pow2 16 * index s 1 + pow2 24 * index s 0;\n == {}\n four_to_nat_unfold 8 (seq_to_four_BE s);\n == {reveal_opaque (`%four_to_nat) four_to_nat}\n be_bytes_to_nat32 s;\n }", "val lemma_be_to_n_4 (s: seq4 nat8)\n : Lemma\n (Lib.ByteSequence.nat_from_bytes_be #Lib.IntTypes.SEC (seq_nat8_to_seq_uint8 s) ==\n be_bytes_to_nat32 s)\nlet lemma_be_to_n_4 (s:seq4 nat8) : Lemma\n (Lib.ByteSequence.nat_from_bytes_be #Lib.IntTypes.SEC (seq_nat8_to_seq_uint8 s) == be_bytes_to_nat32 s)\n =\n let open Lib.IntTypes in\n let open Vale.Def.Words.Four_s in\n assert (pow2 8 = 0x100);\n assert (pow2 16 = 0x10000);\n assert_norm (pow2 24 = 0x1000000);\n let x = seq_nat8_to_seq_uint8 s in\n let f = Lib.ByteSequence.nat_from_intseq_be_ #U8 #SEC in\n calc (==) {\n f x <: nat ;\n == { }\n FStar.UInt8.v (last x) + pow2 8 * f (slice x 0 3);\n == {}\n index s 3 + pow2 8 * f (slice x 0 3);\n == {}\n index s 3 + pow2 8 * index s 2 + pow2 16 * f (slice x 0 2);\n == {}\n index s 3 + pow2 8 * index s 2 + pow2 16 * index s 1 + pow2 24 * f (slice x 0 1);\n == {}\n index s 3 + pow2 8 * index s 2 + pow2 16 * index s 1 + pow2 24 * index s 0 + pow2 32 * f (slice x 0 0);\n == {}\n index s 3 + pow2 8 * index s 2 + pow2 16 * index s 1 + pow2 24 * index s 0;\n == {}\n four_to_nat_unfold 8 (seq_to_four_BE s);\n == {reveal_opaque (`%four_to_nat) four_to_nat}\n be_bytes_to_nat32 s;\n }", "val lemma_be_to_n_is_bounded: b:bytes -> Lemma\n (requires True)\n (ensures (be_to_n b < pow2 (8 * Seq.length b)))\n (decreases (Seq.length b))\nlet rec lemma_be_to_n_is_bounded b =\n if Seq.length b = 0 then ()\n else\n begin\n let s = Seq.slice b 0 (Seq.length b - 1) in\n assert(Seq.length s = Seq.length b - 1);\n lemma_be_to_n_is_bounded s;\n assert(UInt8.v (Seq.last b) < pow2 8);\n assert(be_to_n s < pow2 (8 * Seq.length s));\n assert(be_to_n b < pow2 8 + pow2 8 * pow2 (8 * (Seq.length b - 1)));\n lemma_euclidean_division (UInt8.v (Seq.last b)) (be_to_n s) (pow2 8);\n assert(be_to_n b <= pow2 8 * (be_to_n s + 1));\n assert(be_to_n b <= pow2 8 * pow2 (8 * (Seq.length b - 1)));\n Math.Lemmas.pow2_plus 8 (8 * (Seq.length b - 1));\n lemma_factorise 8 (Seq.length b - 1)\n end", "val lemma_be_to_n_is_bounded: b:bytes -> Lemma\n (requires True)\n (ensures (be_to_n b < pow2 (8 * Seq.length b)))\n (decreases (Seq.length b))\nlet rec lemma_be_to_n_is_bounded b =\n if Seq.length b = 0 then ()\n else\n begin\n let s = Seq.slice b 0 (Seq.length b - 1) in\n assert(Seq.length s = Seq.length b - 1);\n lemma_be_to_n_is_bounded s;\n assert(UInt8.v (Seq.last b) < pow2 8);\n assert(be_to_n s < pow2 (8 * Seq.length s));\n assert(be_to_n b < pow2 8 + pow2 8 * pow2 (8 * (Seq.length b - 1)));\n lemma_euclidean_division (UInt8.v (Seq.last b)) (be_to_n s) (pow2 8);\n assert(be_to_n b <= pow2 8 * (be_to_n s + 1));\n assert(be_to_n b <= pow2 8 * pow2 (8 * (Seq.length b - 1)));\n Math.Lemmas.pow2_plus 8 (8 * (Seq.length b - 1));\n lemma_factorise 8 (Seq.length b - 1)\n end", "val mod_then_mul_64 (n: nat) : Lemma ((n % pow2 64) * pow2 64 == n * pow2 64 % pow2 128)\nlet mod_then_mul_64 (n:nat) : Lemma (n % pow2 64 * pow2 64 == n * pow2 64 % pow2 128) =\n Math.pow2_plus 64 64;\n mod_mul n (pow2 64) (pow2 64)", "val nat_from_bytes_le_eq_lemma_: len:size_nat{len < 16} -> b:lseq uint8 len -> Lemma\n (let tmp = create 16 (u8 0) in\n nat_from_intseq_le b == nat_from_intseq_le (update_sub tmp 0 len b))\nlet nat_from_bytes_le_eq_lemma_ len b =\n let tmp = create 16 (u8 0) in\n let r = update_sub tmp 0 len b in\n assert (Seq.slice r 0 len == b);\n assert (forall (i:nat). len <= i /\\ i < 16 ==> r.[i] == u8 0);\n assert (forall (i:nat). i < 16 - len ==> Seq.index (Seq.slice r len 16) i == u8 0);\n nat_from_intseq_le_slice_lemma #U8 #SEC #16 r len;\n assert (nat_from_intseq_le r == nat_from_intseq_le (Seq.slice r 0 len) + pow2 (len * 8) * nat_from_intseq_le (Seq.slice r len 16));\n assert (nat_from_intseq_le r == nat_from_intseq_le b + pow2 (len * 8) * nat_from_intseq_le (Seq.slice r len 16));\n lemma_nat_from_bytes_le_zeroes (16 - len) (Seq.slice r len 16)", "val seq_uint32_of_be_be_of_seq_uint32 (n: nat) (s: S.seq U32.t)\n : Lemma (requires (n == S.length s))\n (ensures ((seq_uint32_of_be n (be_of_seq_uint32 s)) `S.equal` s))\n (decreases n)\n [SMTPat (seq_uint32_of_be n (be_of_seq_uint32 s))]\nlet rec seq_uint32_of_be_be_of_seq_uint32 (n: nat) (s: S.seq U32.t) : Lemma\n (requires (n == S.length s))\n (ensures (seq_uint32_of_be n (be_of_seq_uint32 s) `S.equal` s))\n (decreases n)\n [SMTPat (seq_uint32_of_be n (be_of_seq_uint32 s))]\n= if n = 0\n then ()\n else begin\n assert (s `S.equal` S.cons (S.head s) (S.tail s));\n seq_uint32_of_be_be_of_seq_uint32 (n - 1) (S.tail s);\n let s' = be_of_seq_uint32 s in\n S.lemma_split s' 4;\n S.lemma_append_inj (S.slice s' 0 4) (S.slice s' 4 (S.length s')) (be_of_uint32 (S.head s)) (be_of_seq_uint32 (S.tail s))\n end", "val lemma_to_nat_rec (len: nat) (p: poly) (c n i: nat)\n : Lemma (requires degree p < len /\\ normalize (poly_nat_eq_rec len p c n))\n (ensures p.[ len - n + i ] == (of_nat c).[ i ])\nlet rec lemma_to_nat_rec (len:nat) (p:poly) (c:nat) (n:nat) (i:nat) : Lemma\n (requires degree p < len /\\ normalize (poly_nat_eq_rec len p c n))\n (ensures p.[len - n + i] == (of_nat c).[i])\n =\n lemma_bitwise_all ();\n if (i > 0 && n > 0) then lemma_to_nat_rec len p (c / 2) (n - 1) (i - 1)", "val uints_to_bytes_le_nat_lemma: #t:inttype{unsigned t /\\ ~(U1? t)} -> #l:secrecy_level\n -> len:nat{len * numbytes t < pow2 32}\n -> n:nat{n < pow2 (bits t * len)}\n -> Lemma\n (uints_to_bytes_le #t #l #len (nat_to_intseq_le #t #l len n) ==\n nat_to_bytes_le (len * numbytes t) n)\nlet uints_to_bytes_le_nat_lemma #t #l len n =\n Classical.forall_intro (uints_to_bytes_le_nat_lemma_ #t #l len n);\n eq_intro (uints_to_bytes_le #t #l #len (nat_to_intseq_le #t #l len n))\n (nat_to_bytes_le (len * numbytes t) n)", "val pow2_lt_len: len:size_pos -> Lemma (pow2 (8 * len - 1) < pow2 (8 * (len - 1)) * (pow2 8 - 1))\nlet pow2_lt_len len =\n let a = pow2 (8 * len - 1) in\n let b = pow2 (8 * (len - 1)) * (pow2 8 - 1) in\n calc (==) {\n b / a;\n (==) { Math.Lemmas.pow2_plus (8 * len - 8) 7 }\n b / (pow2 (8 * len - 8) * pow2 7);\n (==) { Math.Lemmas.division_multiplication_lemma b (pow2 (8 * len - 8)) (pow2 7) }\n b / pow2 (8 * len - 8) / pow2 7;\n (==) { Math.Lemmas.cancel_mul_div (pow2 8 - 1) (pow2 (8 * len - 8)) }\n (pow2 8 - 1) / pow2 7;\n (==) { Math.Lemmas.pow2_plus 7 1 }\n (pow2 7 * 2 - 1) / pow2 7;\n (==) { }\n 1;\n };\n // assert (b / a * a <= b);\n // assert (a <= b)\n\n calc (>) {\n pow2 (8 * len - 8) * (pow2 8 - 1) % pow2 (8 * len - 1);\n (==) { Math.Lemmas.pow2_plus (8 * len - 8) 8 }\n (pow2 (8 * len) - pow2 (8 * len - 8)) % pow2 (8 * len - 1);\n (==) { Math.Lemmas.lemma_mod_plus_distr_l (pow2 (8 * len)) (- pow2 (8 * len - 8)) (pow2 (8 * len - 1)) }\n (pow2 (8 * len) % pow2 (8 * len - 1) - pow2 (8 * len - 8)) % pow2 (8 * len - 1);\n (==) { Math.Lemmas.pow2_multiplication_modulo_lemma_1 1 (8 * len - 1) (8 * len) }\n (0 - pow2 (8 * len - 8)) % pow2 (8 * len - 1);\n //(==) { Math.Lemmas.pow2_lt_compat (8 * len - 1) (8 * len - 8) }\n //pow2 (8 * len - 1) - pow2 (8 * len - 8);\n (>) { Math.Lemmas.pow2_lt_compat (8 * len - 1) (8 * len - 8) }\n 0;\n };\n\n assert (a < b)", "val lemma_inot_nth_all (n:pos) : Lemma\n (forall (m:_{m==pow2_norm n}) (x:natN (pow2 n)).{:pattern (inot #m x)}\n (forall (i:nat{i < n}).{:pattern (nth #n (inot #m x) i)}\n nth #n (inot #m x) i == not (nth #n x i)))\nlet lemma_inot_nth_all n =\n FStar.Classical.forall_intro (lemma_inot_nth n)", "val uints_to_bytes_le_nat_lemma_: #t:inttype{unsigned t /\\ ~(U1? t)} -> #l:secrecy_level\n -> len:nat{len * numbytes t < pow2 32}\n -> n:nat{n < pow2 (bits t * len)}\n -> i:nat{i < len * numbytes t}\n -> Lemma\n (Seq.index (uints_to_bytes_le #t #l #len (nat_to_intseq_le #t #l len n)) i ==\n Seq.index (nat_to_bytes_le (len * numbytes t) n) i)\nlet uints_to_bytes_le_nat_lemma_ #t #l len n i =\n let s:lseq (uint_t t l) len = nat_to_intseq_le #t #l len n in\n calc (==) {\n Seq.index (uints_to_bytes_le #t #l #len (nat_to_intseq_le #t #l len n)) i;\n == { index_uints_to_bytes_le_aux #t #l len n i }\n Seq.index (nat_to_bytes_le #l (numbytes t) (v s.[i / numbytes t])) (i % numbytes t);\n == { index_nat_to_intseq_to_bytes_le #t #l len n i}\n Seq.index (nat_to_bytes_le (len * numbytes t) n) i;\n }", "val nat_from_bytes_le_eq_lemma: len0:size_nat -> len:size_nat{len0 <= len} -> b:lseq uint8 len0 -> Lemma\n (let tmp = create len (u8 0) in\n nat_from_intseq_le b == nat_from_intseq_le (update_sub tmp 0 len0 b))\nlet nat_from_bytes_le_eq_lemma len0 len b =\n let tmp = create len (u8 0) in\n let r = update_sub tmp 0 len0 b in\n assert (slice r 0 len0 == b);\n assert (forall (i:nat). i < len - len0 ==> r.[len0 + i] == u8 0);\n nat_from_intseq_le_slice_lemma #U8 #SEC #len r len0;\n assert (nat_from_intseq_le r == nat_from_intseq_le (slice r 0 len0) + pow2 (len0 * 8) * nat_from_intseq_le (Seq.slice r len0 len));\n assert (nat_from_intseq_le r == nat_from_intseq_le b + pow2 (len0 * 8) * nat_from_intseq_le (Seq.slice r len0 len));\n lemma_nat_from_bytes_le_zeroes (len - len0) (Seq.slice r len0 len)", "val n_to_be:\n len:U32.t -> n:nat{n < pow2 (8 * U32.v len)} ->\n Tot (b:bytes{S.length b == U32.v len /\\ n == be_to_n b})\n (decreases (U32.v len))\nlet rec n_to_be len n =\n if len = 0ul then\n S.empty\n else\n let len = U32.(len -^ 1ul) in\n let byte = U8.uint_to_t (n % 256) in\n let n' = n / 256 in\n Math.pow2_plus 8 (8 * U32.v len);\n assert(n' < pow2 (8 * U32.v len ));\n let b' = n_to_be len n' in\n let b'' = S.create 1 byte in\n let b = S.append b' b'' in\n S.lemma_eq_intro b' (S.slice b 0 (U32.v len));\n b", "val lemma_div_pow2_le (a: int) (n m: nat)\n : Lemma (requires (m <= n /\\ a <= pow2 n))\n (ensures (m <= n /\\ a <= pow2 n /\\ a / pow2 m <= pow2 (n - m)))\nlet lemma_div_pow2_le (a: int) (n m: nat) : Lemma\n (requires (m <= n /\\ a <= pow2 n))\n (ensures (m <= n /\\ a <= pow2 n /\\ a / pow2 m <= pow2 (n - m)))\n= if a = pow2 n\n then pow2_multiplication_division_lemma_1 1 m n\n else lemma_div_lt a n m", "val nat_from_bytes_be_eq_lemma: len0:size_nat -> len:size_nat{len0 <= len} -> b:lseq uint8 len0 ->\n Lemma (let tmp = create len (u8 0) in\n nat_from_intseq_be b == nat_from_intseq_be (update_sub tmp (len - len0) len0 b))\nlet nat_from_bytes_be_eq_lemma len0 len b =\n let tmp = create len (u8 0) in\n let r = update_sub tmp (len - len0) len0 b in\n assert (slice r (len - len0) len == b);\n assert (forall (i:nat). i < len - len0 ==> r.[i] == u8 0);\n nat_from_intseq_be_slice_lemma #U8 #SEC #len r (len - len0);\n assert (nat_from_intseq_be r == nat_from_intseq_be (slice r (len - len0) len) + pow2 (len0 * 8) * nat_from_intseq_be (Seq.slice r 0 (len - len0)));\n assert (nat_from_intseq_be r == nat_from_intseq_be b + pow2 (len0 * 8) * nat_from_intseq_be (Seq.slice r 0 (len - len0)));\n lemma_nat_from_bytes_be_zeroes (len - len0) (Seq.slice r 0 (len - len0))", "val uints_to_bytes_be_nat_lemma_: #t:inttype{unsigned t /\\ ~(U1? t)} -> #l:secrecy_level\n -> len:nat{len * numbytes t < pow2 32}\n -> n:nat{n < pow2 (bits t * len)}\n -> i:nat{i < len * numbytes t}\n -> Lemma\n (Seq.index (uints_to_bytes_be #t #l #len (nat_to_intseq_be #t #l len n)) i ==\n Seq.index (nat_to_bytes_be (len * numbytes t) n) i)\nlet uints_to_bytes_be_nat_lemma_ #t #l len n i =\n let s:lseq (uint_t t l) len = nat_to_intseq_be #t #l len n in\n calc (==) {\n Seq.index (uints_to_bytes_be #t #l #len (nat_to_intseq_be #t #l len n)) i;\n == { index_uints_to_bytes_be_aux #t #l len n i }\n Seq.index (nat_to_bytes_be #l (numbytes t) (v s.[i / numbytes t])) (i % numbytes t);\n == { index_nat_to_intseq_to_bytes_be #t #l len n (len * numbytes t - 1 - i)}\n Seq.index (nat_to_bytes_be (len * numbytes t) n) i;\n }", "val lemma_div_n_8_upper2 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures\n (hi64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) ==\n 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_div_n_8_upper2 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures (hi64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) == 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n hi64_reveal ();\n if n <= 2 then lemma_div_n_8_upper2_helper q n else\n let Mkfour _ _ _ _ = q in // avoid ifuel\n let f (n:nat{n <= 4}) = (hi64_def q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) == 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) in\n assert_norm (f 4);\n assert_norm (f 3);\n ()", "val nat_from_bytes_le_eq_lemma: len:size_nat{len < 16} -> b:lseq uint8 len -> Lemma\n (let tmp = create 16 (u8 0) in\n nat_from_bytes_le b == nat_from_bytes_le (update_sub tmp 0 len b))\nlet nat_from_bytes_le_eq_lemma len b = nat_from_bytes_le_eq_lemma_ len b", "val uints_to_bytes_be_nat_lemma: #t:inttype{unsigned t /\\ ~(U1? t)} -> #l:secrecy_level\n -> len:nat{len * numbytes t < pow2 32}\n -> n:nat{n < pow2 (bits t * len)}\n -> Lemma\n (uints_to_bytes_be #t #l #len (nat_to_intseq_be #t #l len n) ==\n nat_to_bytes_be (len * numbytes t) n)\nlet uints_to_bytes_be_nat_lemma #t #l len n =\n Classical.forall_intro (uints_to_bytes_be_nat_lemma_ #t #l len n);\n eq_intro (uints_to_bytes_be #t #l #len (nat_to_intseq_be #t #l len n))\n (nat_to_bytes_be (len * numbytes t) n)", "val seq_uint32_of_be_be_of_seq_uint32 (n: nat) (s: S.seq U32.t) : Lemma\n (requires (n == S.length s))\n (ensures (seq_uint32_of_be n (be_of_seq_uint32 s) `S.equal` s))\n (decreases n)\n [SMTPat (seq_uint32_of_be n (be_of_seq_uint32 s))]\nlet rec seq_uint32_of_be_be_of_seq_uint32 n s =\n if n = 0\n then ()\n else begin\n assert (s `S.equal` S.cons (S.head s) (S.tail s));\n seq_uint32_of_be_be_of_seq_uint32 (n - 1) (S.tail s);\n let s' = be_of_seq_uint32 s in\n S.lemma_split s' 4;\n S.lemma_append_inj (S.slice s' 0 4) (S.slice s' 4 (S.length s')) (be_of_uint32 (S.head s)) (be_of_seq_uint32 (S.tail s))\n end", "val lemma_aux_0 (a b n: nat)\n : Lemma\n (pow2 n * a + pow2 (n + 56) * b = pow2 n * (a % pow2 56) + pow2 (n + 56) * (b + a / pow2 56))\nlet lemma_aux_0 (a:nat) (b:nat) (n:nat) : Lemma\n (pow2 n * a + pow2 (n+56) * b = pow2 n * (a % pow2 56) + pow2 (n+56) * (b + a / pow2 56))\n = Math.Lemmas.lemma_div_mod a (pow2 56);\n Math.Lemmas.pow2_plus n 56;\n assert(a = pow2 56 * (a / pow2 56) + (a % pow2 56));\n Math.Lemmas.distributivity_add_right (pow2 n) (pow2 56 * (a / pow2 56)) (a % pow2 56);\n Math.Lemmas.paren_mul_right (pow2 n) (pow2 56) (a / pow2 56);\n Math.Lemmas.distributivity_add_right (pow2 (n+56)) b (a / pow2 56)", "val lemma_div_n_8_lower2 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures\n (lo64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) ==\n 0x100000000 * q.lo1 + (q.lo0 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_div_n_8_lower2 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures (lo64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) == 0x100000000 * q.lo1 + (q.lo0 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n hi64_reveal ();\n lo64_reveal ();\n let Mkfour q0 q1 _ _ = q in\n lemma_div_n_8_upper2 (Mkfour 0 0 q0 q1) n", "val int2bv_nat_lemma (#n: pos) (num: uint_t n)\n : Lemma (ensures (int2bv_nat #n num == int2bv #n num))\nlet int2bv_nat_lemma (#n: pos) (num: uint_t n)\n : Lemma\n (ensures (int2bv_nat #n num == int2bv #n num)) =\n assert (num < pow2 n);\n FStar.Math.Lemmas.modulo_lemma num (pow2 n);\n assert (num % pow2 n = num)", "val lemma_div_n_8_upper1 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures\n ((hi64 q / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32 ==\n (q.hi3 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_div_n_8_upper1 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures ((hi64 q / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32 == (q.hi3 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n hi64_reveal ();\n let Mkfour _ _ _ _ = q in // avoid ifuel\n let f (n:nat{n <= 4}) = ((hi64_def q / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32 == (q.hi3 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) in\n assert_norm (f 0);\n assert_norm (f 1);\n assert_norm (f 2);\n assert_norm (f 3);\n assert_norm (f 4);\n ()", "val lemma_le_bytes_to_seq_quad32_length (b: seq nat8)\n : Lemma (requires length b % 16 == 0)\n (ensures length (le_bytes_to_seq_quad32 b) == length b / 16)\nlet lemma_le_bytes_to_seq_quad32_length (b:seq nat8) : Lemma\n (requires length b % 16 == 0)\n (ensures length (le_bytes_to_seq_quad32 b) == length b / 16)\n =\n reveal_opaque (`%le_bytes_to_seq_quad32) le_bytes_to_seq_quad32;\n ()", "val lemma_div_n_8_lower1 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures\n ((lo64 q / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32 ==\n (q.lo1 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_div_n_8_lower1 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures ((lo64 q / pow2 (8 * (8 - n))) * pow2 (8 * (8 - n))) / pow2_32 == (q.lo1 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n hi64_reveal ();\n lo64_reveal ();\n let Mkfour q0 q1 _ _ = q in\n lemma_div_n_8_upper1 (Mkfour 0 0 q0 q1) n", "val lemma_div_sub_small (l n x: nat)\n : Lemma (requires l > 1)\n (ensures\n (n - n % pow2 8) / pow2 (8 `op_Multiply` (l - 1)) == n / pow2 (8 `op_Multiply` (l - 1)))\nlet lemma_div_sub_small (l:nat) (n:nat) (x:nat)\n : Lemma (requires l > 1)\n (ensures (n - n % pow2 8) / pow2 (8 `op_Multiply` (l-1)) == n / pow2 (8 `op_Multiply` (l-1)))\n =\n let open FStar.Math.Lemmas in\n let open FStar.Mul in\n lemma_mod_spec n (pow2 8);\n lemma_pow2_div2 n 8 (8*(l-2));\n lemma_pow2_div2 (n - n % pow2 8) 8 (8*(l-2))", "val lemma_iand_nth_all (n:pos) : Lemma\n (forall (m:_{m==pow2_norm n}) (x y:natN (pow2 n)).{:pattern (iand #m x y)}\n (forall (i:nat{i < n}).{:pattern (nth #n (iand #m x y) i)}\n nth #n (iand #m x y) i == (nth #n x i && nth #n y i)))\nlet lemma_iand_nth_all n =\n FStar.Classical.forall_intro_2 (lemma_iand_nth n)", "val nat_to_bytes_be (#l: secrecy_level) (len: nat) (n: nat{n < pow2 (8 * len)})\n : b: bytes_l l {length b == len /\\ n == nat_from_intseq_be #U8 b}\nlet nat_to_bytes_be (#l:secrecy_level) (len:nat) (n:nat{n < pow2 (8 * len)}) : b:bytes_l l{length b == len /\\ n == nat_from_intseq_be #U8 b} =\n nat_to_intseq_be #U8 #l len n", "val lemma_reverse_define (a:poly) (n:nat) : Lemma\n (forall (i:int).{:pattern (reverse a n).[i]} (reverse a n).[i] == (a.[n - i] && i >= 0))\nlet lemma_reverse_define p n =\n FStar.Classical.forall_intro (lemma_reverse_define_i p n)", "val lemma_msb_pow2: #n:pos -> a:uint_t n ->\n Lemma (msb a <==> a >= pow2 (n-1))\nlet lemma_msb_pow2 #n a = if n = 1 then () else from_vec_propriety (to_vec a) 1", "val lemma_prime_value: n:nat -> Lemma\n (requires (n = 255))\n (ensures (pow2 n - 19 = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed))\n [SMTPat (pow2 n - 19)]\nlet lemma_prime_value n = assert_norm(pow2 255 - 19 = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed)", "val index_be_to_n (b: bytes) (i: nat)\n : Lemma (requires (i < S.length b))\n (ensures\n (U8.v (FStar.Seq.index b i) ==\n (FStar.Endianness.be_to_n b / pow2 (8 * (S.length b - 1 - i))) % pow2 8))\n (decreases (S.length b))\nlet rec index_be_to_n\n (b: bytes)\n (i: nat)\n: Lemma\n (requires (\n i < S.length b\n ))\n (ensures (\n U8.v (FStar.Seq.index b i) == (FStar.Endianness.be_to_n b / pow2 (8 * (S.length b - 1 - i))) % pow2 8\n ))\n (decreases (S.length b))\n= let open FStar.Endianness in\n reveal_be_to_n b;\n if i = S.length b - 1\n then ()\n else begin\n let l = S.length b in\n let l' = l - 1 in\n let b' = S.slice b 0 l' in\n index_be_to_n b' i;\n assert (FStar.Seq.index b i == FStar.Seq.index b' i);\n let open FStar.Math.Lemmas in\n let x = be_to_n b in\n let x' = be_to_n b' in\n assert (U8.v (FStar.Seq.index b i) == x' / pow2 (8 * (l' - 1 - i)) % pow2 8);\n let y = (U8.v (S.last b) + pow2 8 * x') / pow2 (8 * (l - 1 - i)) % pow2 8 in\n pow2_plus 8 (8 * (l' - 1 - i));\n division_multiplication_lemma (U8.v (S.last b) + pow2 8 * x') (pow2 8) (pow2 (8 * (l' - 1 - i)));\n assert (pow2 8 * x' == x' * pow2 8);\n division_addition_lemma (U8.v (S.last b)) (pow2 8) x';\n small_division_lemma_1 (U8.v (S.last b)) (pow2 8);\n assert (y == x' / pow2 (8 * (l' - 1 - i)) % pow2 8)\n end", "val lemma_sum_pow_seq_bound (#n:nat) (s:seq (natN n)) : Lemma\n (ensures 0 <= sum_pow_seq s /\\ sum_pow_seq s < pow_int n (length s))\nlet lemma_sum_pow_seq_bound #n s =\n lemma_sum_pow_seq_bound_rec s (length s)", "val lemma_sum_pow_seq_bound_rec (#n: nat) (s: seq (natN n)) (i: nat{i <= length s})\n : Lemma (ensures 0 <= sum_pow_seq_left s i /\\ sum_pow_seq_left s i < pow_int n i)\nlet rec lemma_sum_pow_seq_bound_rec (#n:nat) (s:seq (natN n)) (i:nat{i <= length s}) : Lemma\n (ensures 0 <= sum_pow_seq_left s i /\\ sum_pow_seq_left s i < pow_int n i)\n =\n let open FStar.Math.Lemmas in\n if i > 0 then (\n calc (<=) {\n 0;\n <= {lemma_sum_pow_seq_bound_rec s (i - 1)}\n sum_pow_seq_left s (i - 1);\n <= {lemma_pow_nat n (i - 1); nat_times_nat_is_nat s.[i - 1] (pow_int n (i - 1))}\n s.[i - 1] * pow_int n (i - 1) + sum_seq_left (pow_seq s) 0 (i - 1);\n == {}\n sum_pow_seq_left s i;\n };\n calc (<=) {\n sum_pow_seq_left s i + 1;\n == {}\n s.[i - 1] * pow_int n (i - 1) + sum_seq_left (pow_seq s) 0 (i - 1) + 1;\n <= {lemma_sum_pow_seq_bound_rec s (i - 1)}\n s.[i - 1] * pow_int n (i - 1) + pow_int n (i - 1);\n <= {lemma_pow_nat n (i - 1); lemma_mult_le_right (pow_int n (i - 1)) s.[i - 1] (n - 1)}\n (n - 1) * pow_int n (i - 1) + pow_int n (i - 1);\n == {}\n pow_int n i;\n }\n )", "val nth_size (n1: nat) (n2: nat{n1 <= n2}) (x: U.uint_t n1) (i: nat{i < n2})\n : Lemma (x < pow2 n2 /\\ nth #n2 x i == (i < n1 && nth #n1 x i))\nlet rec nth_size (n1: nat) (n2: nat { n1 <= n2 }) (x: U.uint_t n1) (i: nat { i < n2 }) : Lemma\n (x < pow2 n2 /\\ nth #n2 x i == (i < n1 && nth #n1 x i))\n= M.pow2_le_compat n2 n1;\n if i < n1\n then begin\n if i = 0\n then ()\n else nth_size (n1 - 1) (n2 - 1) (x / 2) (i - 1)\n end else nth_le_pow2_m #n2 x n1 i", "val lemma_iand_pow2 (n:pos) (x:natN (pow2 n)) (i:nat{i < n}) : Lemma\n (pow2 i < pow2 n /\\ (iand x (pow2 i) == 0 \\/ iand x (pow2 i) == pow2 i))\nlet lemma_iand_pow2 (n:pos) (x:natN (pow2 n)) (i:nat{i < n}) : Lemma\n (pow2 i < pow2 n /\\ (iand x (pow2 i) == 0 \\/ iand x (pow2 i) == pow2 i))\n =\n let open FStar.UInt in\n FStar.Math.Lemmas.pow2_lt_compat n i;\n assert (pow2 i < pow2 n);\n let result = iand x (pow2 i) in\n\n if nth #n x (n - i - 1) then (\n let helper (j:nat{j < n}) : Lemma (nth #n result j = nth #n (pow2 i) j)\n =\n pow2_nth_lemma #n i j;\n lemma_iand_nth_i n x (pow2 i) j;\n assert (nth #n result j = (nth #n x j && nth #n (pow2 i) j));\n ()\n in\n FStar.Classical.forall_intro helper;\n nth_lemma #n result (pow2 i);\n assert(iand x (pow2 i) == pow2 i);\n ()\n ) else (\n let helper (j:nat{j < n}) : Lemma (nth #n result j = false)\n =\n pow2_nth_lemma #n i j;\n lemma_iand_nth_i n x (pow2 i) j;\n assert (nth #n result j = (nth #n x j && nth #n (pow2 i) j));\n ()\n in\n FStar.Classical.forall_intro helper;\n nth_lemma #n (zero n) result;\n assert(iand x (pow2 i) == 0);\n ()\n );\n ()", "val lemma_ixor_nth_all (n:pos) : Lemma\n (forall (m:_{m==pow2_norm n}) (x y:natN (pow2 n)).{:pattern (ixor #m x y)}\n (forall (i:nat{i < n}).{:pattern (nth #n (ixor #m x y) i)}\n nth #n (ixor #m x y) i == (nth #n x i <> nth #n y i)))\nlet lemma_ixor_nth_all n =\n FStar.Classical.forall_intro_2 (lemma_ixor_nth n)", "val lemma_ishl_nth_all (n:pos) : Lemma\n (forall (m:_{m==pow2_norm n}) (x:natN (pow2 n)) (y:nat).{:pattern (ishl #m x y)}\n (forall (i:nat{i < n}).{:pattern (nth #n (ishl #m x y) i)}\n nth #n (ishl #m x y) i == (i + y < n && nth #n x (i + y))))\nlet lemma_ishl_nth_all n =\n FStar.Classical.forall_intro_2 (lemma_ishl_nth n)", "val index_nat_to_intseq_to_bytes_le:\n #t:inttype{unsigned t /\\ ~(U1? t)}\n -> #l:secrecy_level\n -> len:nat{len * numbytes t < pow2 32}\n -> n:nat{n < pow2 (bits t * len)}\n -> i:nat{i < len * numbytes t}\n -> Lemma (let s:lseq (int_t t l) len = nat_to_intseq_le #t #l len n in\n Seq.index (nat_to_bytes_le #l (numbytes t) (v s.[i / numbytes t])) (i % numbytes t) ==\n Seq.index (nat_to_bytes_le #l (len * numbytes t) n) i)\nlet index_nat_to_intseq_to_bytes_le #t #l len n i =\n let s:lseq (int_t t l) len = nat_to_intseq_le #t #l len n in\n let m = numbytes t in\n index_nat_to_intseq_le #U8 #l (len * m) n i;\n assert (Seq.index (nat_to_bytes_le #l (len * m) n) i ==\n uint (n / pow2 (8 * i) % pow2 8));\n index_nat_to_intseq_le #U8 #l m (v s.[i / m]) (i % m);\n assert (Seq.index (nat_to_bytes_le #l m (v s.[i / m])) (i % m) ==\n uint (v s.[i / m] / pow2 (8 * (i % m)) % pow2 8));\n index_nat_to_intseq_le #t #l len n (i / m);\n some_arithmetic t n i", "val lemma_div_pow2_ge (a: int) (n m: nat)\n : Lemma (requires (m <= n /\\ pow2 n <= a)) (ensures (pow2 (n - m) <= a / pow2 m))\nlet lemma_div_pow2_ge (a: int) (n m: nat) : Lemma\n (requires (m <= n /\\ pow2 n <= a))\n (ensures (pow2 (n - m) <= a / pow2 m))\n= pow2_multiplication_division_lemma_1 1 m n;\n lemma_div_le (pow2 n) a (pow2 m)", "val lemma_ishr_nth_all (n:pos) : Lemma\n (forall (m:_{m==pow2_norm n}) (x:natN (pow2 n)) (y:nat).{:pattern (ishr #m x y)}\n (forall (i:nat{i < n}).{:pattern (nth #n (ishr #m x y) i)}\n nth #n (ishr #m x y) i == (i - y >= 0 && nth #n x (i - y))))\nlet lemma_ishr_nth_all n =\n FStar.Classical.forall_intro_2 (lemma_ishr_nth n)", "val le_to_n_inj\n (b1 b2: Seq.seq U8.t)\n: Lemma\n (requires (Seq.length b1 == Seq.length b2 /\\ le_to_n b1 == le_to_n b2))\n (ensures (Seq.equal b1 b2))\n (decreases (Seq.length b1))\nlet rec le_to_n_inj b1 b2 =\n if Seq.length b1 = 0\n then ()\n else begin\n le_to_n_inj (Seq.slice b1 1 (Seq.length b1)) (Seq.slice b2 1 (Seq.length b2));\n Seq.lemma_split b1 1;\n Seq.lemma_split b2 1\n end", "val lemma_inot_nth_i (n:pos) (x:natN (pow2 n)) (i:nat{i < n}) : Lemma\n (nth #n (inot x) i == not (nth #n x i))\nlet lemma_inot_nth_i n x i =\n reveal_inot n x", "val reveal_iand_all (n:pos) : Lemma\n (forall (m:_{m==pow2_norm n}) (x y:natN (pow2 n)).{:pattern (iand #m x y)}\n iand #m x y == UInt.logand #n x y)\nlet reveal_iand_all n =\n FStar.Classical.forall_intro_2 (reveal_iand n)", "val lemma_mod_n_8_lower1 (q: quad32) (n: nat)\n : Lemma (requires n <= 4) (ensures lo64 q % pow2 (8 * n) == q.lo0 % pow2 (8 * n))\nlet lemma_mod_n_8_lower1 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures lo64 q % pow2 (8 * n) == q.lo0 % pow2 (8 * n))\n =\n lo64_reveal ();\n let Mkfour _ _ _ _ = q in // avoid ifuel\n let f (n:nat{n <= 4}) = lo64_def q % pow2 (8 * n) == q.lo0 % pow2 (8 * n) in\n assert_norm (f 0);\n assert_norm (f 1);\n assert_norm (f 2);\n assert_norm (f 3);\n assert_norm (f 4);\n ()", "val pow2_le_compat: n:nat -> m:nat -> Lemma\n (requires (m <= n))\n (ensures (pow2 m <= pow2 n))\nlet pow2_le_compat n m =\n if m < n then pow2_lt_compat n m", "val reveal_be_to_n_slice (b: bytes) (i j: nat)\n : Lemma (requires i < j /\\ j <= S.length b)\n (ensures\n (let open FStar.Mul in\n let open FStar.Endianness in\n let h = U8.v (S.index b (j - 1)) in\n be_to_n (S.slice b i j) = h + pow2 8 * be_to_n (S.slice b i (j - 1))))\nlet rec reveal_be_to_n_slice (b:bytes) (i j:nat) : Lemma\n (requires i < j /\\ j <= S.length b)\n (ensures (\n let open FStar.Mul in\n let open FStar.Endianness in\n let h = U8.v (S.index b (j-1)) in\n be_to_n (S.slice b i j) = h + pow2 8 * be_to_n (S.slice b i (j - 1)))) =\n FStar.Endianness.reveal_be_to_n (S.slice b i j)", "val le_to_n_inj (b1 b2: Seq.seq U8.t)\n : Lemma (requires (Seq.length b1 == Seq.length b2 /\\ le_to_n b1 == le_to_n b2))\n (ensures (Seq.equal b1 b2))\n (decreases (Seq.length b1))\nlet rec le_to_n_inj\n (b1 b2: Seq.seq U8.t)\n: Lemma\n (requires (Seq.length b1 == Seq.length b2 /\\ le_to_n b1 == le_to_n b2))\n (ensures (Seq.equal b1 b2))\n (decreases (Seq.length b1))\n= if Seq.length b1 = 0\n then ()\n else begin\n le_to_n_inj (Seq.slice b1 1 (Seq.length b1)) (Seq.slice b2 1 (Seq.length b2));\n Seq.lemma_split b1 1;\n Seq.lemma_split b2 1\n end", "val lemma_correctness_slice_be_to_n (b: bytes) (i: nat)\n : Lemma (requires i <= S.length b)\n (ensures\n (let open FStar.Endianness in\n let open FStar.Mul in\n be_to_n b % pow2 (8 * i) = be_to_n (S.slice b (S.length b - i) (S.length b))))\n (decreases i)\nlet rec lemma_correctness_slice_be_to_n (b:bytes) (i:nat) : Lemma\n (requires i <= S.length b)\n (ensures (\n let open FStar.Endianness in\n let open FStar.Mul in\n be_to_n b % pow2 (8 * i) =\n be_to_n (S.slice b (S.length b - i) (S.length b))))\n (decreases i) =\n let open FStar.Endianness in\n let open FStar.Math.Lemmas in\n let open FStar.Mul in\n if i = 0 then reveal_be_to_n S.empty\n else begin\n reveal_be_to_n b;\n let h = U8.v (S.index b (S.length b - 1)) in\n let l = S.slice b 0 (S.length b - 1) in\n let pow = pow2 (8*i) in\n //assert (be_to_n b = h + pow2 8 * be_to_n l);\n modulo_distributivity h (pow2 8 * be_to_n l) pow;\n pow2_le_compat (8*i) 8;\n small_mod h pow;\n //assert (be_to_n b % pow = (h + (pow2 8 * be_to_n l)%pow) % pow);\n lemma_modulo_shift_byte (be_to_n l) i;\n lemma_correctness_slice_be_to_n l (i-1);\n //assert (be_to_n b % pow = (h + pow2 8 * be_to_n (S.slice b (S.length b - i) (S.length b - 1))) % pow);\n reveal_be_to_n_slice b (S.length b - i) (S.length b);\n //assert (be_to_n b % pow = be_to_n (S.slice b (S.length b - i) (S.length b)) % pow);\n lemma_be_to_n_is_bounded (S.slice b (S.length b - i) (S.length b));\n FStar.Math.Lemmas.small_mod (be_to_n (S.slice b (S.length b - i) (S.length b))) pow\n end", "val lemma_div_n_8_upper2_helper (q: quad32) (n: nat)\n : Lemma (requires n <= 2)\n (ensures\n (hi64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) ==\n 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\nlet lemma_div_n_8_upper2_helper (q:quad32) (n:nat) : Lemma\n (requires n <= 2)\n (ensures (hi64 q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) == 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)))\n =\n hi64_reveal ();\n let Mkfour _ _ _ _ = q in // avoid ifuel\n let f (n:nat{n <= 4}) = (hi64_def q / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) == 0x100000000 * q.hi3 + (q.hi2 / pow2 (8 * (4 - n))) * pow2 (8 * (4 - n)) in\n assert_norm (f 2);\n assert_norm (f 1);\n assert_norm (f 0);\n ()", "val lemma_mod_n_8_lower2 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures lo64 q % pow2 (8 * (4 + n)) == q.lo0 + 0x100000000 * (q.lo1 % pow2 (8 * n)))\nlet lemma_mod_n_8_lower2 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures lo64 q % pow2 (8 * (4 + n)) == q.lo0 + 0x100000000 * (q.lo1 % pow2 (8 * n)))\n =\n lo64_reveal ();\n if n <= 2 then lemma_mod_n_8_lower2_helper q n else\n let Mkfour _ _ _ _ = q in // avoid ifuel\n let f (n:nat{n <= 4}) = lo64_def q % pow2 (8 * (4 + n)) == q.lo0 + 0x100000000 * (q.lo1 % pow2 (8 * n)) in\n assert_norm (f 4);\n assert_norm (f 3);\n ()", "val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->\n Lemma (requires (a < pow2 n))\n (ensures (a / pow2 m < pow2 (n-m)))\nlet lemma_div_lt_nat a n m =\n lemma_div_mod a (pow2 m);\n assert(a = pow2 m * (a / pow2 m) + a % pow2 m);\n pow2_plus m (n-m);\n assert(pow2 n = pow2 m * pow2 (n - m))", "val reveal_inot_all (n:pos) : Lemma\n (forall (m:_{m==pow2_norm n}) (x:natN (pow2 n)).{:pattern (inot #m x)}\n inot #m x == UInt.lognot #n x)\nlet reveal_inot_all n =\n FStar.Classical.forall_intro (reveal_inot n)", "val lemma_reverse_reverse (a:poly) (n:nat) : Lemma\n (requires degree a <= n)\n (ensures reverse (reverse a n) n == a)\n [SMTPat (reverse (reverse a n) n)]\nlet lemma_reverse_reverse a n =\n lemma_reverse_define_all ();\n lemma_index_all ();\n lemma_equal a (reverse (reverse a n) n)", "val reveal_ishl_all (n:pos) : Lemma\n (forall (m:_{m==pow2_norm n}) (x:natN (pow2 n)) (y:nat).{:pattern (ishl #m x y)}\n ishl #m x y == UInt.shift_left #n x y)\nlet reveal_ishl_all n =\n FStar.Classical.forall_intro_2 (reveal_ishl n)", "val bitfield_be_to_n_slice (s: S.seq U8.t) (i j: nat)\n : Lemma (requires (Seq.length s > 0 /\\ i <= j /\\ j <= S.length s))\n (ensures\n (let len = S.length s in\n be_to_n s < pow2 (8 * len) /\\\n be_to_n (S.slice s i j) ==\n BF.get_bitfield #(8 * len) (be_to_n s) (8 * (len - j)) (8 * (len - i))))\nlet bitfield_be_to_n_slice\n (s: S.seq U8.t)\n (i: nat)\n (j: nat)\n: Lemma\n (requires (\n Seq.length s > 0 /\\\n i <= j /\\ j <= S.length s\n ))\n (ensures (\n let len = S.length s in\n be_to_n s < pow2 (8 * len) /\\\n be_to_n (S.slice s i j) == BF.get_bitfield #(8 * len) (be_to_n s) (8 * (len - j)) (8 * (len - i))\n ))\n= let len = S.length s in\n lemma_be_to_n_is_bounded s;\n slice_n_to_be_bitfield len (be_to_n s) i j", "val lemma_mod_n_8_upper2 (q: quad32) (n: nat)\n : Lemma (requires n <= 4)\n (ensures hi64 q % pow2 (8 * (4 + n)) == q.hi2 + 0x100000000 * (q.hi3 % pow2 (8 * n)))\nlet lemma_mod_n_8_upper2 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures hi64 q % pow2 (8 * (4 + n)) == q.hi2 + 0x100000000 * (q.hi3 % pow2 (8 * n)))\n =\n hi64_reveal ();\n lo64_reveal ();\n let Mkfour _ _ q2 q3 = q in\n lemma_mod_n_8_lower2 (Mkfour q2 q3 0 0) n", "val slice_commutes_le_seq_quad32_to_bytes (s:seq quad32) (n:nat{n <= length s}) (n':nat{ n <= n' /\\ n' <= length s}) :\n Lemma(slice (le_seq_quad32_to_bytes s) (n * 16) (n' * 16) ==\n le_seq_quad32_to_bytes (slice s n n'))\nlet slice_commutes_le_seq_quad32_to_bytes (s:seq quad32) (n:nat{n <= length s}) (n':nat{ n <= n' /\\ n' <= length s}) :\n Lemma(slice (le_seq_quad32_to_bytes s) (n * 16) (n' * 16) ==\n le_seq_quad32_to_bytes (slice s n n'))\n =\n le_seq_quad32_to_bytes_reveal ();\n slice_commutes_seq_four_to_seq_LE s n n';\n assert (slice (seq_four_to_seq_LE s) (n * 4) (n' * 4) == seq_four_to_seq_LE (slice s n n'));\n(*\n le_seq_quad32_to_bytes (slice s n n') == seq_four_to_seq_LE (seq_map (nat_to_four 8) (seq_four_to_seq_LE (slice s n n')));\n == seq_four_to_seq_LE (seq_map (nat_to_four 8) (slice (seq_four_to_seq_LE s) (n * 4) (n' * 4))\n slice (le_seq_quad32_to_bytes s) (n * 16) (n' * 16)\n == slice (seq_four_to_seq_LE (seq_map (nat_to_four 8) (seq_four_to_seq_LE s))) (n * 16) (n' * 16)\n == seq_four_to_seq_LE (slice (seq_map (nat_to_four 8) (seq_four_to_seq_LE s)) (n * 4) (n' * 4))\n*)\n slice_seq_map_commute (nat_to_four 8) (seq_four_to_seq_LE s) (n*4) (n'*4);\n\n let s_inner = (seq_map (nat_to_four 8) (seq_four_to_seq_LE s)) in\n slice_commutes_seq_four_to_seq_LE s_inner (n * 4) (n' * 4);\n ()", "val lemma_mod_n_8_upper1 (q: quad32) (n: nat)\n : Lemma (requires n <= 4) (ensures hi64 q % pow2 (8 * n) == q.hi2 % pow2 (8 * n))\nlet lemma_mod_n_8_upper1 (q:quad32) (n:nat) : Lemma\n (requires n <= 4)\n (ensures hi64 q % pow2 (8 * n) == q.hi2 % pow2 (8 * n))\n =\n hi64_reveal ();\n lo64_reveal ();\n let Mkfour _ _ q2 q3 = q in\n lemma_mod_n_8_lower1 (Mkfour q2 q3 0 0) n", "val lemma_inot_nth (n:pos) (x:natN (pow2 n)) : Lemma\n (forall (m:_{m==pow2_norm n}) (i:nat{i < n}).{:pattern (nth #n (inot #m x) i)}\n nth #n (inot #m x) i == not (nth #n x i))\nlet lemma_inot_nth n x =\n FStar.Classical.forall_intro (lemma_inot_nth_i n x)" ], "closest_src": [ { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.n_to_le_le_to_n" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.index_n_to_be" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.n_to_le_le_to_n" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.n_to_be_be_to_n" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.n_to_be_be_to_n" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.index_n_to_be_zero_right" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.index_n_to_be_zero_left" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.n_to_le" }, { "project_name": "hacl-star", "file_name": "Lib.ByteBuffer.fst", "name": "Lib.ByteBuffer.nat_to_bytes_n_to_be" }, { "project_name": "hacl-star", "file_name": "Lib.ByteBuffer.fst", "name": "Lib.ByteBuffer.nat_to_bytes_n_to_le" }, { "project_name": "everparse", "file_name": "LowParse.Endianness.BitFields.fst", "name": "LowParse.Endianness.BitFields.slice_n_to_be_bitfield" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_pad_to_32_bits" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_pad_to_32_bits_helper" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.n_to_le" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_pad_to_32_bits" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Poly1305.Vec.fst", "name": "Hacl.Spec.Poly1305.Vec.lemma_pow2_128" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.Types.fst", "name": "Vale.Arch.Types.lemma_reverse_bytes_nat64_32" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.lemma_be_index" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_pad_to_32_bits_helper" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fsti", "name": "Lib.ByteSequence.nat_to_bytes_le" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Math.fst", "name": "Vale.Poly1305.Math.lemma_power2_add64" }, { "project_name": "everparse", "file_name": "LowParse.BitFields.fst", "name": "LowParse.BitFields.pow2_m_minus_one_eq" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.lemma_le_to_n_is_bounded" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.lemma_le_to_n_is_bounded" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.be_of_seq_uint32_seq_uint32_of_be" }, { "project_name": "hacl-star", "file_name": "Vale.AES.AES_helpers.fst", "name": "Vale.AES.AES_helpers.lemma_add_0x1000000_reverse_mult" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_equal_nth" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.Types.fst", "name": "Vale.Arch.Types.lemma_reverse_reverse_bytes_nat32" }, { "project_name": "everparse", "file_name": "LowParse.Spec.BitVector.fst", "name": "LowParse.Spec.BitVector.to_uint8_of_uint8" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Bits.fst", "name": "Vale.Math.Bits.lemma_pow2_le" }, { "project_name": "hacl-star", "file_name": "Vale.Poly1305.Equiv.fsti", "name": "Vale.Poly1305.Equiv.nat_to_bytes_le" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.n_to_be" }, { "project_name": "hacl-star", "file_name": "Spec.Curve25519.Lemmas.fst", "name": "Spec.Curve25519.Lemmas.lemma_pow2_256" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.be_of_seq_uint32_seq_uint32_of_be" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Words.Two.fst", "name": "Vale.Def.Words.Two.two_to_nat_to_two" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.index_nat_to_intseq_be" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.index_nat_to_intseq_le" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Bits.fst", "name": "Vale.Math.Poly2.Bits.lemma_of_nat_of_uint" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.SHA_helpers.fst", "name": "Vale.SHA.PPC64LE.SHA_helpers.lemma_be_to_n_4" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.SHA_helpers.fst", "name": "Vale.SHA.SHA_helpers.lemma_be_to_n_4" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.lemma_be_to_n_is_bounded" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.lemma_be_to_n_is_bounded" }, { "project_name": "FStar", "file_name": "FStar.UInt128.fst", "name": "FStar.UInt128.mod_then_mul_64" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.Lemmas.fst", "name": "Hacl.Impl.Poly1305.Lemmas.nat_from_bytes_le_eq_lemma_" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.seq_uint32_of_be_be_of_seq_uint32" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Bits.fst", "name": "Vale.Math.Poly2.Bits.lemma_to_nat_rec" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.uints_to_bytes_le_nat_lemma" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.FFDHE.Lemmas.fst", "name": "Hacl.Spec.FFDHE.Lemmas.pow2_lt_len" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_inot_nth_all" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.uints_to_bytes_le_nat_lemma_" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Bignum.Convert.fst", "name": "Hacl.Spec.Bignum.Convert.nat_from_bytes_le_eq_lemma" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.n_to_be" }, { "project_name": "everparse", "file_name": "LowParse.Math.fst", "name": "LowParse.Math.lemma_div_pow2_le" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.Bignum.Convert.fst", "name": "Hacl.Spec.Bignum.Convert.nat_from_bytes_be_eq_lemma" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.uints_to_bytes_be_nat_lemma_" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_div_n_8_upper2" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Poly1305.Lemmas.fst", "name": "Hacl.Impl.Poly1305.Lemmas.nat_from_bytes_le_eq_lemma" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.uints_to_bytes_be_nat_lemma" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.seq_uint32_of_be_be_of_seq_uint32" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.BignumQ.Lemmas.fst", "name": "Hacl.Spec.BignumQ.Lemmas.lemma_aux_0" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_div_n_8_lower2" }, { "project_name": "FStar", "file_name": "FStar.BV.fst", "name": "FStar.BV.int2bv_nat_lemma" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_div_n_8_upper1" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.SHA_helpers.fst", "name": "Vale.SHA.SHA_helpers.lemma_le_bytes_to_seq_quad32_length" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_div_n_8_lower1" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.lemma_div_sub_small" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_iand_nth_all" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fsti", "name": "Lib.ByteSequence.nat_to_bytes_be" }, { "project_name": "hacl-star", "file_name": "Vale.Math.Poly2.Lemmas.fst", "name": "Vale.Math.Poly2.Lemmas.lemma_reverse_define" }, { "project_name": "FStar", "file_name": "FStar.UInt.fst", "name": "FStar.UInt.lemma_msb_pow2" }, { "project_name": "hacl-star", "file_name": "Spec.Curve25519.Lemmas.fst", "name": "Spec.Curve25519.Lemmas.lemma_prime_value" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.index_be_to_n" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.Lemmas.fst", "name": "Vale.Bignum.Lemmas.lemma_sum_pow_seq_bound" }, { "project_name": "hacl-star", "file_name": "Vale.Bignum.Lemmas.fst", "name": "Vale.Bignum.Lemmas.lemma_sum_pow_seq_bound_rec" }, { "project_name": "everparse", "file_name": "LowParse.BitFields.fst", "name": "LowParse.BitFields.nth_size" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_iand_pow2" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_ixor_nth_all" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_ishl_nth_all" }, { "project_name": "hacl-star", "file_name": "Lib.ByteSequence.fst", "name": "Lib.ByteSequence.index_nat_to_intseq_to_bytes_le" }, { "project_name": "everparse", "file_name": "LowParse.Math.fst", "name": "LowParse.Math.lemma_div_pow2_ge" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_ishr_nth_all" }, { "project_name": "FStar", "file_name": "FStar.Endianness.fst", "name": "FStar.Endianness.le_to_n_inj" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_inot_nth_i" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.reveal_iand_all" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_mod_n_8_lower1" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.pow2_le_compat" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.reveal_be_to_n_slice" }, { "project_name": "karamel", "file_name": "FStar.Krml.Endianness.fst", "name": "FStar.Krml.Endianness.le_to_n_inj" }, { "project_name": "everquic-crypto", "file_name": "QUIC.Spec.Lemmas.fst", "name": "QUIC.Spec.Lemmas.lemma_correctness_slice_be_to_n" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers_BE.fst", "name": "Vale.AES.GCM_helpers_BE.lemma_div_n_8_upper2_helper" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_mod_n_8_lower2" }, { "project_name": "FStar", "file_name": "FStar.Math.Lemmas.fst", "name": "FStar.Math.Lemmas.lemma_div_lt_nat" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.reveal_inot_all" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GF128.fst", "name": "Vale.AES.GF128.lemma_reverse_reverse" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.reveal_ishl_all" }, { "project_name": "everparse", "file_name": "LowParse.Endianness.BitFields.fst", "name": "LowParse.Endianness.BitFields.bitfield_be_to_n_slice" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_mod_n_8_upper2" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.Types.fst", "name": "Vale.Arch.Types.slice_commutes_le_seq_quad32_to_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.AES.GCM_helpers.fst", "name": "Vale.AES.GCM_helpers.lemma_mod_n_8_upper1" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.TypesNative.fst", "name": "Vale.Arch.TypesNative.lemma_inot_nth" } ], "selected_premises": [ "LowParse.Endianness.index_n_to_be", "FStar.Mul.op_Star", "LowParse.Endianness.index_n_to_be_zero_right", "LowParse.Endianness.index_be_to_n'", "LowParse.Endianness.index_n_to_be_zero_left", "LowParse.Endianness.reveal_n_to_be", "LowParse.Endianness.slice_seq_rev", "LowParse.Endianness.index_be_to_n", "LowParse.Endianness.n_to_be_append", "LowParse.Endianness.slice_n_to_be", "LowParse.Endianness.index_seq_rev'", "LowParse.Endianness.be_to_n_append", "FStar.Pervasives.reveal_opaque", "FStar.Math.Lemmas.pow2_plus", "LowParse.Endianness.seq_rev_involutive", "LowParse.Endianness.le_to_n_eq_be_to_n_rev", "FStar.Math.Lemmas.pow2_le_compat", "FStar.Math.Lemmas.pow2_lt_compat", "LowParse.Endianness.index_seq_rev", "LowParse.Endianness.seq_rev", "LowParse.Endianness.be_to_n_append'", "FStar.Math.Lemmas.lemma_div_lt", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "FStar.Math.Lemmas.cancel_mul_mod", "FStar.Math.Lemmas.lemma_mod_plus_distr_l", "FStar.Math.Lemmas.lemma_div_lt_nat", "FStar.Math.Lemmas.lemma_mod_plus_distr_r", "FStar.Math.Lemmas.lemma_mult_lt_sqr", "FStar.Math.Lemmas.lemma_mod_mul_distr_l", "FStar.Math.Lemmas.distributivity_sub_left", "FStar.Math.Lemmas.distributivity_add_right", "FStar.Math.Lemmas.lemma_mod_plus", "FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1", "FStar.Math.Lemmas.distributivity_sub_right", "FStar.Math.Lemmas.lemma_mod_sub", "FStar.Math.Lemmas.pow2_modulo_modulo_lemma_2", "FStar.Math.Lemmas.lemma_div_le", "FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1", "FStar.Math.Lemmas.division_multiplication_lemma", "FStar.Math.Lemmas.lemma_mod_spec2", "FStar.Math.Lemmas.multiple_modulo_lemma", "FStar.Math.Lemmas.pow2_modulo_division_lemma_1", "FStar.Math.Lemmas.modulo_distributivity", "FStar.Math.Lemmas.pow2_minus", "FStar.Math.Lemmas.lemma_div_plus", "FStar.Math.Lemmas.modulo_addition_lemma", "FStar.Pervasives.Native.snd", "FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2", "FStar.Math.Lemmas.pow2_modulo_division_lemma_2", "FStar.Math.Lemmas.pow2_double_mult", "FStar.Math.Lemmas.lemma_mod_twice", "FStar.Pervasives.Native.fst", "FStar.Math.Lemmas.division_addition_lemma", "FStar.Math.Lemmas.lemma_mul_sub_distr", "FStar.Math.Lemmas.div_exact_r", "FStar.Math.Lemmas.multiple_division_lemma", "FStar.Math.Lemmas.mul_ineq1", "FStar.Math.Lemmas.pow2_multiplication_division_lemma_1", "FStar.Math.Lib.log_2", "FStar.Math.Lemmas.sub_div_mod_1", "FStar.Math.Lemmas.lemma_mod_sub_distr", "FStar.Math.Lemmas.lemma_mod_mod", "FStar.Math.Lib.slash_decr_axiom", "FStar.Math.Lib.powx_lemma2", "FStar.Math.Lemmas.lemma_mod_add_distr", "FStar.Math.Lemmas.mod_mul_div_exact", "FStar.Pervasives.pure_return", "FStar.Math.Lemmas.pow2_multiplication_division_lemma_2", "FStar.Math.Lemmas.lemma_mod_plus_mul_distr", "FStar.Math.Lemmas.mod_pow2_div2", "FStar.Math.Lemmas.modulo_sub_lemma", "FStar.Math.Lemmas.modulo_modulo_lemma", "FStar.Math.Lemmas.lemma_div_lt_cancel", "FStar.Math.Lemmas.lemma_mod_sub_1", "FStar.Math.Lemmas.lemma_mod_mult_zero", "Prims.pure_pre", "FStar.Pervasives.st_return", "FStar.Math.Lemmas.lemma_mod_plus_injective", "FStar.Math.Lemmas.mod_mult_exact", "FStar.Math.Lib.powx", "FStar.Pervasives.ex_return", "FStar.Pervasives.ex_wp", "FStar.Math.Lemmas.modulo_scale_lemma", "Prims.pow2", "FStar.Pervasives.all_return", "FStar.Pervasives.all_if_then_else", "FStar.Pervasives.all_ite_wp", "FStar.Math.Lemmas.add_div_mod_1", "FStar.Preorder.stable", "FStar.Calc.calc_chain_compatible", "FStar.Pervasives.all_trivial", "FStar.Math.Lemmas.lemma_mod_spec", "Prims.pure_wp_monotonic", "FStar.Math.Lib.slash_star_axiom", "FStar.Pervasives.all_wp_h", "FStar.Preorder.transitive", "FStar.Math.Lib.max", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.ex_bind_wp", "FStar.Math.Lemmas.division_definition" ], "source_upto_this": "module LowParse.Endianness\n\nlet rec index_be_to_n'\n (b: bytes)\n (i: nat)\n: Lemma\n (requires (\n i < S.length b\n ))\n (ensures (\n U8.v (S.index b i) == (be_to_n b / pow2 (8 * (S.length b - 1 - i))) % pow2 8\n ))\n (decreases (S.length b))\n= reveal_be_to_n b;\n if i = S.length b - 1\n then ()\n else begin\n let l = S.length b in\n let l' = l - 1 in\n let b' = S.slice b 0 l' in\n index_be_to_n' b' i;\n assert (S.index b i == S.index b' i);\n let open FStar.Math.Lemmas in\n let x = be_to_n b in\n let x' = be_to_n b' in\n assert (U8.v (S.index b i) == x' / pow2 (8 * (l' - 1 - i)) % pow2 8);\n let y = (U8.v (S.last b) + pow2 8 * x') / pow2 (8 * (l - 1 - i)) % pow2 8 in\n pow2_plus 8 (8 * (l' - 1 - i));\n division_multiplication_lemma (U8.v (S.last b) + pow2 8 * x') (pow2 8) (pow2 (8 * (l' - 1 - i)));\n assert (pow2 8 * x' == x' * pow2 8);\n division_addition_lemma (U8.v (S.last b)) (pow2 8) x';\n small_division_lemma_1 (U8.v (S.last b)) (pow2 8);\n assert (y == x' / pow2 (8 * (l' - 1 - i)) % pow2 8)\n end\n\nlet index_be_to_n = index_be_to_n'\n\nlet index_n_to_be\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i)) == (n / pow2 (8 * (len - 1 - i)) % pow2 8\n ))\n= index_be_to_n (n_to_be len n) i\n\nlet index_n_to_be_zero_left\n (len: nat)\n (n: nat)\n (j: nat)\n (i: nat)\n: Lemma\n (requires (\n i < j /\\\n j <= len /\\\n n < pow2 (8 * (len - j))\n ))\n (ensures (\n pow2 (8 * (len - j)) <= pow2 (8 * len) /\\\n U8.v (S.index (n_to_be len n) i) == 0\n ))\n= let open FStar.Math.Lemmas in\n pow2_le_compat (8 * len) (8 * (len - j));\n pow2_le_compat (8 * (len - 1 - i)) (8 * (len - j));\n small_division_lemma_1 n (pow2 (8 * (len - 1 - i)));\n index_n_to_be len n i\n\nlet index_n_to_be_zero_right\n (len: nat)\n (n: nat)\n (i: nat)\n: Lemma\n (requires (\n i < len /\\\n n < pow2 (8 * len) /\\\n n % pow2 (8 * (len - i)) == 0\n ))\n (ensures (\n U8.v (S.index (n_to_be len n) i) == 0\n ))\n= index_n_to_be len n i;\n let open FStar.Math.Lemmas in\n modulo_division_lemma n (pow2 (8 * (len - 1 - i))) (pow2 8);\n pow2_plus (8 * (len - 1 - i)) 8\n\nopen FStar.Math.Lemmas\n\nlet rec be_to_n_append'\n (hi lo: bytes)\n: Lemma\n (ensures (be_to_n (hi `S.append` lo) == be_to_n hi * pow2 (8 * S.length lo) + be_to_n lo))\n (decreases (S.length lo))\n= reveal_be_to_n lo;\n let hilo = hi `S.append` lo in\n if S.length lo = 0\n then\n assert (hilo `S.equal` hi)\n else begin\n let lo' = S.slice lo 0 (S.length lo - 1) in\n assert (S.slice hilo 0 (S.length hilo - 1) `S.equal` (hi `S.append` lo'));\n assert (S.last hilo == S.last lo);\n reveal_be_to_n hilo;\n be_to_n_append' hi lo';\n pow2_plus (8 * S.length lo') 8\n end\n\nlet be_to_n_append = be_to_n_append'\n\nlet lemma_div_zero (x: pos) : Lemma\n (0 / x == 0)\n= ()\n\nlet n_to_be_append\n (len: nat)\n (n: nat)\n (len_lo: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len) /\\\n len_lo <= len\n ))\n (ensures (\n let hi = n / pow2 (8 * len_lo) in\n let lo = n % pow2 (8 * len_lo) in\n 0 <= hi /\\\n hi < pow2 (8 * (len - len_lo)) /\\\n 0 <= lo /\\\n lo < pow2 (8 * len_lo) /\\\n n_to_be len n == n_to_be (len - len_lo) hi `S.append` n_to_be len_lo lo\n ))\n= lemma_div_zero (pow2 (8 * len_lo));\n lemma_div_le 0 n (pow2 (8 * len_lo));\n lemma_mod_lt n (pow2 (8 * len_lo));\n let hi = n / pow2 (8 * len_lo) in\n assert (0 <= hi);\n lemma_div_lt n (8 * len) (8 * len_lo);\n pow2_minus (8 * len) (8 * len_lo);\n let lo = n % pow2 (8 * len_lo) in\n euclidean_division_definition n (pow2 (8 * len_lo));\n let hi_s = n_to_be (len - len_lo) hi in\n let lo_s = n_to_be len_lo lo in\n be_to_n_append hi_s lo_s;\n assert (be_to_n (hi_s `S.append` lo_s) == n);\n be_to_n_inj (hi_s `S.append` lo_s) (n_to_be len n)\n\nlet reveal_n_to_be\n (len: nat)\n (n: nat)\n: Lemma\n (requires (\n n < pow2 (8 * len)\n ))\n (ensures (\n (len > 0 ==> (0 <= n / pow2 8 /\\ n / pow2 8 < pow2 (8 * (len - 1)))) /\\\n n_to_be len n `S.equal` (if len = 0 then S.empty else n_to_be (len - 1) (n / pow2 8) `S.snoc` (U8.uint_to_t (n % pow2 8)))\n ))\n= if len = 0\n then ()\n else begin\n n_to_be_append len n 1;\n index_n_to_be 1 (n % pow2 8) 0\n end\n\nlet slice_n_to_be\n (len: nat)\n (n: nat)\n (i j: nat)\n: Lemma\n (requires (\n i <= j /\\\n j <= len /\\\n n < pow2 (8 * len)\n ))\n (ensures (\n let res = (n / pow2 (8 * (len - j))) % pow2 (8 * (j - i)) in\n 0 <= res /\\\n res < pow2 (8 * (j - i)) /\\\n S.slice (n_to_be len n) i j == n_to_be (j - i) res\n ))\n= let s1 = S.slice (n_to_be len n) 0 j in\n let s2 = S.slice s1 i j in\n n_to_be_append len n (len - j);\n let q = n / pow2 (8 * (len - j)) in\n n_to_be_append j q (j - i);\n let r = q % pow2 (8 * (j - i)) in\n assert (s2 `S.equal` n_to_be (j - i) (q % pow2 (8 * (j - i))))\n\nlet rec seq_rev\n (#t: Type)\n (x: S.seq t)\n: Tot (y: S.seq t {S.length y == S.length x})\n (decreases (S.length x))\n= if S.length x = 0\n then S.empty\n else seq_rev (S.tail x) `S.append` S.create 1 (S.head x)\n\nlet rec index_seq_rev'\n (#t: Type)\n (x: S.seq t)\n (i: nat {i < S.length x})\n: Lemma\n (ensures (S.index (seq_rev x) (S.length x - 1 - i) == S.index x i))\n (decreases (S.length x))\n= if i = 0\n then\n S.lemma_index_create 1 (S.head x) 0\n else\n index_seq_rev' (S.tail x) (i - 1)\n\nlet index_seq_rev\n (#t: Type)\n (x: S.seq t)\n (i: nat {i < S.length x})\n: Lemma\n (ensures (S.index (seq_rev x) i == S.index x (S.length x - 1 - i)))\n= index_seq_rev' x (S.length x - 1 - i)\n\nlet slice_seq_rev\n (#t: Type)\n (x: S.seq t)\n (i: nat)\n (j: nat)\n: Lemma\n (requires (i <= j /\\ j <= S.length x))\n (ensures (S.slice (seq_rev x) i j `S.equal` seq_rev (S.slice x (S.length x - j) (S.length x - i))))\n= Classical.forall_intro (index_seq_rev x);\n Classical.forall_intro (index_seq_rev (S.slice x (S.length x - j) (S.length x - i)))\n\nlet rec le_to_n_eq_be_to_n_rev\n (b: bytes)\n: Lemma\n (ensures (le_to_n b == be_to_n (seq_rev b)))\n (decreases (S.length b))\n= reveal_be_to_n (seq_rev b);\n reveal_le_to_n b;\n if Seq.length b = 0\n then ()\n else begin\n index_seq_rev b (S.length b - 1);\n slice_seq_rev b 0 (S.length b - 1);\n le_to_n_eq_be_to_n_rev (S.tail b)\n end\n\nlet seq_rev_involutive\n (#t: Type)\n (x: S.seq t)\n: Lemma\n (seq_rev (seq_rev x) `S.equal` x)\n= Classical.forall_intro (index_seq_rev (seq_rev x));\n Classical.forall_intro (index_seq_rev x)\n", "sketch": [ "Step 1: Reveal the definitions of `n_to_le` and `n_to_be` to make their internal structures accessible.\nStep 2: Use induction on the length `len` to handle the base case and the inductive step.\nStep 3: For the base case where `len = 0`, show that both `n_to_le` and `n_to_be` produce an empty sequence, and thus their reverse is also empty.\nStep 4: For the inductive step, assume the lemma holds for `len - 1` and prove it for `len`.\nStep 5: Decompose `n` into its high and low parts for the current length and use the inductive hypothesis.\nStep 6: Show that reversing the concatenation of the high and low parts of `n_to_be` results in the same sequence as `n_to_le` for the current length.", "Step 1: We need to reveal the definitions of `n_to_le` and `n_to_be` to understand their structure.\nStep 2: If `len` is 0, both `n_to_le` and `n_to_be` will be empty sequences, and their reverse will also be empty, so the lemma holds trivially.\nStep 3: For `len > 0`, use the `reveal_n_to_be` lemma to express `n_to_be len n` in terms of `n_to_be (len - 1) (n / pow2 8)` and the last byte.\nStep 4: Similarly, express `n_to_le len n` in terms of `n_to_le (len - 1) (n / pow2 8)` and the first byte.\nStep 5: Use the `seq_rev` function to reverse the sequence and show that reversing the sequence of `n_to_be` results in the sequence of `n_to_le`.\nStep 6: Use induction on `len` to complete the proof.", "Step 1: Use the `reveal_n_to_be` lemma to reveal the structure of `n_to_be len n`.\nStep 2: Use the `reveal_n_to_le` lemma to reveal the structure of `n_to_le len n`.\nStep 3: Use induction on `len` to handle the base case and the inductive step.\nStep 4: For the base case where `len = 0`, show that both `n_to_le` and `n_to_be` are empty sequences.\nStep 5: For the inductive step, assume the lemma holds for `len - 1` and prove it for `len`.\nStep 6: Use the properties of `seq_rev` and the structure of `n_to_be` and `n_to_le` to show that reversing `n_to_be` gives `n_to_le`.", "Step 1: Use the `reveal_n_to_be` lemma to reveal the structure of `n_to_be len n`.\nStep 2: Use the `reveal_le_to_n` lemma to reveal the structure of `n_to_le len n`.\nStep 3: Use induction on `len` to handle the base case where `len = 0` and the inductive case where `len > 0`.\nStep 4: For the base case, show that both `n_to_le 0 n` and `seq_rev (n_to_be 0 n)` are empty sequences.\nStep 5: For the inductive case, use the structure revealed in Step 1 and Step 2 to show that `n_to_le len n` is equal to the reverse of `n_to_be len n`.\nStep 6: Use the `seq_rev_involutive` lemma to handle the reverse operation on sequences.\nStep 7: Conclude the proof by showing that the inductive hypothesis holds for `len - 1`.", "Step 1: Use the `reveal_n_to_be` lemma to reveal the structure of `n_to_be len n`.\nStep 2: Use the `reveal_le_to_n` lemma to reveal the structure of `n_to_le len n`.\nStep 3: Perform a case analysis on whether `len` is zero.\nStep 4: If `len` is zero, both `n_to_le len n` and `n_to_be len n` are empty sequences, and their equality is trivial.\nStep 5: If `len` is non-zero, use the `n_to_be_append` lemma to decompose `n_to_be len n` into its high and low parts.\nStep 6: Use the `seq_rev` function to reverse the sequence and apply the `seq_rev_involutive` lemma to simplify the expression.\nStep 7: Use the `le_to_n_eq_be_to_n_rev` lemma to relate the little-endian and big-endian representations.\nStep 8: Conclude that `n_to_le len n` is equal to the reverse of `n_to_be len n`.", "Step 1: Use the `reveal_n_to_be` lemma to reveal the structure of `n_to_be len n`.\nStep 2: Use the `reveal_le_to_n` lemma to reveal the structure of `n_to_le len n`.\nStep 3: Use induction on the length `len` to handle the base case and the inductive step.\nStep 4: For the base case where `len = 0`, show that both `n_to_le` and `n_to_be` produce empty sequences.\nStep 5: For the inductive step, assume the lemma holds for `len - 1` and prove it for `len`.\nStep 6: Use the `seq_rev` function properties, particularly `seq_rev_involutive`, to relate the sequences.\nStep 7: Use the `le_to_n_eq_be_to_n_rev` lemma to connect little-endian and big-endian representations via sequence reversal.\nStep 8: Conclude that `n_to_le len n` is equal to `seq_rev (n_to_be len n)`.", "Step 1: We need to show that converting a number `n` to little-endian format and then reversing it is equivalent to converting `n` to big-endian format.\nStep 2: Use the previously proven lemma `le_to_n_eq_be_to_n_rev` which states that converting a byte sequence to a number in little-endian format is the same as converting the reversed byte sequence to a number in big-endian format.\nStep 3: Apply the `reveal_n_to_be` lemma to understand the structure of `n_to_be`.\nStep 4: Use the `seq_rev_involutive` lemma to show that reversing the sequence twice yields the original sequence.\nStep 5: Combine these results to conclude the proof.", "Step 1: Use the `reveal_n_to_be` lemma to reveal the structure of `n_to_be len n`.\nStep 2: Use the `reveal_n_to_le` lemma to reveal the structure of `n_to_le len n`.\nStep 3: Use induction on `len` to prove the lemma.\nStep 4: For the base case where `len = 0`, show that both `n_to_le 0 n` and `seq_rev (n_to_be 0 n)` are empty sequences.\nStep 5: For the inductive step, assume the lemma holds for `len - 1` and prove it for `len`.\nStep 6: Use the structure of `n_to_be` and `n_to_le` to relate them through `seq_rev`.\nStep 7: Conclude the proof by showing that `n_to_le len n` is equal to `seq_rev (n_to_be len n)`.", "Step 1: Use the `reveal_n_to_be` lemma to reveal the structure of `n_to_be len n`.\nStep 2: Use the `reveal_n_to_le` lemma to reveal the structure of `n_to_le len n`.\nStep 3: Apply induction on the length `len` to handle the base case where `len = 0` and the inductive case where `len > 0`.\nStep 4: For the base case, show that both `n_to_le 0 n` and `seq_rev (n_to_be 0 n)` are equal to `S.empty`.\nStep 5: For the inductive case, assume the lemma holds for `len - 1` and show it holds for `len`.\nStep 6: Use the inductive hypothesis to relate `n_to_le (len - 1) (n / pow2 8)` and `seq_rev (n_to_be (len - 1) (n / pow2 8))`.\nStep 7: Show that appending the last byte of `n_to_le len n` to the reversed sequence of `n_to_be (len - 1) (n / pow2 8)` results in `seq_rev (n_to_be len n)`.", "Step 1: Reveal the definitions of `n_to_le` and `n_to_be` to make their internal structure accessible.\nStep 2: Use induction on the length `len` to handle the base case and the inductive step.\nStep 3: For the base case where `len = 0`, show that both `n_to_le` and `n_to_be` produce an empty sequence, and thus their reverse is also empty.\nStep 4: For the inductive step, assume the lemma holds for `len - 1` and prove it for `len`.\nStep 5: Use the `n_to_be_append` lemma to decompose `n_to_be len n` into the concatenation of `n_to_be (len - 1) (n / pow2 8)` and the last byte.\nStep 6: Show that reversing this concatenation results in the sequence formed by reversing the last byte and then reversing the rest.\nStep 7: Use the inductive hypothesis to show that reversing `n_to_be (len - 1) (n / pow2 8)` gives `n_to_le (len - 1) (n / pow2 8)`.\nStep 8: Combine the results to show that `n_to_le len n` is equal to the reverse of `n_to_be len n`." ], "generated_solution": [ "= reveal_n_to_be len n;\n reveal_n_to_le len n;\n if len = 0\n then ()\n else begin\n let hi = n / pow2 8 in\n let lo = n % pow2 8 in\n n_to_le_eq_rev_n_to_be (len - 1) hi;\n seq_rev_involutive (n_to_be (len - 1) hi `S.snoc` U8.uint_to_t lo);\n assert (seq_rev (n_to_be len n) `S.equal` (seq_rev (n_to_be (len - 1) hi) `S.snoc` U8.uint_to_t lo));\n assert (n_to_le len n `S.equal` (n_to_le (len - 1) hi `S.snoc` U8.uint_to_t lo));\n assert (seq_rev (n_to_be (len - 1) hi) `S.equal` n_to_le (len - 1) hi);\n assert (seq_rev (n_to_be len n) `S.equal` (n_to_le (len - 1) hi `S.snoc` U8.uint_to_t lo));\n assert (n_to_le len n `S.equal` seq_rev (n_to_be len n))\n end", "= reveal_n_to_be len n;\n reveal_n_to_le len n;\n if len = 0\n then ()\n else begin\n let hi = n / pow2 8 in\n let lo = n % pow2 8 in\n assert (n_to_be len n `S.equal` (n_to_be (len - 1) hi `S.snoc` (U8.uint_to_t lo)));\n assert (n_to_le len n `S.equal` (U8.uint_to_t lo `S.cons` n_to_le (len - 1) hi));\n seq_rev_involutive (n_to_be (len - 1) hi);\n seq_rev_involutive (n_to_le (len - 1) hi);\n assert (seq_rev (n_to_be (len - 1) hi `S.snoc` (U8.uint_to_t lo)) `S.equal` (seq_rev (n_to_be (len - 1) hi) `S.cons` (U8.uint_to_t lo)));\n assert (seq_rev (n_to_le (len - 1) hi `S.cons` (U8.uint_to_t lo)) `S.equal` (seq_rev (n_to_le (len - 1) hi) `S.snoc` (U8.uint_to_t lo)));\n n_to_le_eq_rev_n_to_be (len - 1) hi\n end", "let rec n_to_le_eq_rev_n_to_be (len n: nat) : Lemma (requires (n < pow2 (8 * len))) (ensures (n_to_le len n == seq_rev (n_to_be len n))) =\n reveal_n_to_be len n;\n reveal_n_to_le len n;\n if len = 0 then\n assert (n_to_le 0 n `S.equal` S.empty);\n assert (n_to_be 0 n `S.equal` S.empty);\n assert (seq_rev (n_to_be 0 n) `S.equal` S.empty)\n else\n n_to_le_eq_rev_n_to_be (len - 1) (n / pow2 8);\n seq_rev_involutive (n_to_be (len - 1) (n / pow2 8));\n assert (n_to_le len n `S.equal` (n_to_le (len - 1) (n / pow2 8) `S.snoc` (U8.uint_to_t (n % pow2 8))));\n assert (seq_rev (n_to_be len n) `S.equal` (seq_rev (n_to_be (len - 1) (n / pow2 8)) `S.snoc` (U8.uint_to_t (n % pow2 8))));\n assert (n_to_le (len - 1) (n / pow2 8) `S.equal` seq_rev (n_to_be (len - 1) (n / pow2 8)));\n assert (n_to_le len n `S.equal` (seq_rev (n_to_be (len - 1) (n / pow2 8)) `S.snoc` (U8.uint_to_t (n % pow2 8))));\n assert (n_to_le len n `S.equal` seq_rev (n_to_be len n))", "let rec n_to_le_eq_rev_n_to_be (len: nat) (n: nat) : Lemma\n (requires (n < pow2 (8 * len)))\n (ensures (n_to_le len n == seq_rev (n_to_be len n)))\n (decreases len)\n= reveal_n_to_be len n;\n reveal_le_to_n len n;\n if len = 0 then\n assert (n_to_le 0 n == S.empty);\n assert (seq_rev (n_to_be 0 n) == S.empty)\n else\n let hi = n / pow2 8 in\n let lo = n % pow2 8 in\n n_to_le_eq_rev_n_to_be (len - 1) hi;\n assert (n_to_le len n == n_to_le (len - 1) hi `S.snoc` (U8.uint_to_t lo));\n assert (seq_rev (n_to_be len n) == seq_rev (n_to_be (len - 1) hi `S.snoc` (U8.uint_to_t lo)));\n seq_rev_involutive (n_to_be (len - 1) hi);\n assert (seq_rev (n_to_be (len - 1) hi `S.snoc` (U8.uint_to_t lo)) == (U8.uint_to_t lo) `S.append` seq_rev (n_to_be (len - 1) hi));\n assert (n_to_le (len - 1) hi == seq_rev (n_to_be (len - 1) hi));\n assert (n_to_le len n == (U8.uint_to_t lo) `S.append` seq_rev (n_to_be (len - 1) hi))", "= reveal_n_to_be len n;\n reveal_le_to_n n;\n if len = 0\n then ()\n else begin\n n_to_be_append len n 1;\n let hi = n / pow2 8 in\n let lo = n % pow2 8 in\n assert (n_to_be len n == n_to_be (len - 1) hi `S.snoc` (U8.uint_to_t lo));\n seq_rev (n_to_be len n);\n seq_rev_involutive (n_to_be len n);\n le_to_n_eq_be_to_n_rev (n_to_be len n)\n end", "= reveal_n_to_be len n;\n reveal_le_to_n n;\n if len = 0\n then assert (n_to_le 0 n == S.empty /\\ seq_rev (n_to_be 0 n) == S.empty)\n else begin\n n_to_le_eq_rev_n_to_be (len - 1) (n / pow2 8);\n seq_rev_involutive (n_to_be (len - 1) (n / pow2 8));\n assert (n_to_le len n == n_to_le (len - 1) (n / pow2 8) `S.snoc` (U8.uint_to_t (n % pow2 8)));\n assert (seq_rev (n_to_be len n) == seq_rev (n_to_be (len - 1) (n / pow2 8) `S.snoc` (U8.uint_to_t (n % pow2 8))));\n assert (seq_rev (n_to_be (len - 1) (n / pow2 8) `S.snoc` (U8.uint_to_t (n % pow2 8))) == S.create 1 (U8.uint_to_t (n % pow2 8)) `S.append` seq_rev (n_to_be (len - 1) (n / pow2 8)));\n assert (n_to_le (len - 1) (n / pow2 8) == seq_rev (n_to_be (len - 1) (n / pow2 8)));\n assert (n_to_le len n == S.create 1 (U8.uint_to_t (n % pow2 8)) `S.append` seq_rev (n_to_be (len - 1) (n / pow2 8)));\n assert (n_to_le len n == seq_rev (n_to_be len n))\n end", "= reveal_n_to_be len n;\n reveal_n_to_le len n;\n le_to_n_eq_be_to_n_rev (n_to_be len n);\n seq_rev_involutive (n_to_be len n)", "= reveal_n_to_be len n;\n reveal_n_to_le len n;\n if len = 0\n then assert (n_to_le 0 n `S.equal` S.empty);\n assert (seq_rev (n_to_be 0 n) `S.equal` S.empty)\n else begin\n let hi = n / pow2 8 in\n let lo = n % pow2 8 in\n assert (n_to_le len n `S.equal` n_to_le (len - 1) hi `S.snoc` (U8.uint_to_t lo));\n assert (n_to_be len n `S.equal` n_to_be (len - 1) hi `S.snoc` (U8.uint_to_t lo));\n seq_rev_involutive (n_to_be (len - 1) hi);\n assert (seq_rev (n_to_be len n) `S.equal` (seq_rev (n_to_be (len - 1) hi) `S.append` S.create 1 (U8.uint_to_t lo)));\n seq_rev_append (n_to_be (len - 1) hi) (S.create 1 (U8.uint_to_t lo));\n assert (seq_rev (S.create 1 (U8.uint_to_t lo)) `S.equal` S.create 1 (U8.uint_to_t lo));\n assert (seq_rev (n_to_be len n) `S.equal` (S.create 1 (U8.uint_to_t lo) `S.append` seq_rev (n_to_be (len - 1) hi)));\n n_to_le_eq_rev_n_to_be (len - 1) hi;\n assert (n_to_le (len - 1) hi `S.equal` seq_rev (n_to_be (len - 1) hi));\n assert (n_to_le len n `S.equal` (seq_rev (n_to_be (len - 1) hi) `S.snoc` (U8.uint_to_t lo)));\n assert (n_to_le len n `S.equal` seq_rev (n_to_be len n))\n end", "= reveal_n_to_be len n;\n reveal_n_to_le len n;\n if len = 0\n then\n assert (n_to_le 0 n `S.equal` S.empty);\n assert (seq_rev (n_to_be 0 n) `S.equal` S.empty)\n else\n let hi = n / pow2 8 in\n let lo = n % pow2 8 in\n assert (n_to_le len n == n_to_le (len - 1) hi `S.snoc` (U8.uint_to_t lo));\n assert (n_to_be len n == n_to_be (len - 1) hi `S.snoc` (U8.uint_to_t lo));\n seq_rev_involutive (n_to_be (len - 1) hi);\n le_to_n_eq_be_to_n_rev (n_to_be (len - 1) hi);\n assert (seq_rev (n_to_be len n) == (U8.uint_to_t lo) `S.append` seq_rev (n_to_be (len - 1) hi));\n assert (n_to_le len n == seq_rev (n_to_be len n))", "= reveal_n_to_be len n;\n reveal_n_to_le len n;\n if len = 0\n then ()\n else begin\n n_to_be_append len n 1;\n n_to_le_append len n 1;\n seq_rev_involutive (n_to_be (len - 1) (n / pow2 8));\n le_to_n_eq_be_to_n_rev (n_to_be (len - 1) (n / pow2 8));\n assert (n_to_le (len - 1) (n / pow2 8) == seq_rev (n_to_be (len - 1) (n / pow2 8)));\n assert (n_to_le len n == seq_rev (n_to_be len n))\n end" ] }, { "file_name": "Hacl.Hash.SHA2.fst", "name": "Hacl.Hash.SHA2.coerce_to_mb_state", "opens_and_abbrevs": [ { "abbrev": "Vec", "full_module": "Hacl.Spec.SHA2.Vec" }, { "open": "Lib.NTuple" }, { "open": "Lib.MultiBuffer" }, { "open": "Spec.Hash.Definitions" }, { "open": "Hacl.Hash.Definitions" }, { "abbrev": "B", "full_module": "LowStar.Buffer" }, { "abbrev": "HS", "full_module": "FStar.HyperStack" }, { "abbrev": "ST", "full_module": "FStar.HyperStack.ST" }, { "open": "Spec.Hash.Definitions" }, { "open": "Hacl.Hash.Definitions" }, { "open": "Hacl.Hash" }, { "open": "Hacl.Hash" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 0, "max_fuel": 0, "initial_ifuel": 1, "max_ifuel": 1, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 100, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": false, "reuse_hint_for": null }, "source_type": "val coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a", "source_definition": "let coerce_to_mb_state (a:sha2_alg) (b:state (| a, () |)) : mb_state_32 a\n = Lib.IntVector.reveal_vec_1 (word_t a);\n b", "source_range": { "start_line": 36, "start_col": 0, "end_line": 38, "end_col": 5 }, "interleaved": false, "definition": "fun a b ->\n (Lib.IntVector.reveal_vec_1 (Spec.Hash.Definitions.word_t a);\n b)\n <:\n Hacl.Hash.SHA2.mb_state_32 a", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "Spec.Hash.Definitions.sha2_alg", "Hacl.Hash.Definitions.state", "Prims.Mkdtuple2", "Spec.Hash.Definitions.hash_alg", "Hacl.Hash.Definitions.m_spec", "Prims.unit", "Lib.IntVector.reveal_vec_1", "Spec.Hash.Definitions.word_t", "Hacl.Hash.SHA2.mb_state_32" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": false, "is_type": false, "type": "a: Spec.Hash.Definitions.sha2_alg -> b: Hacl.Hash.Definitions.state (| a, () |)\n -> Hacl.Hash.SHA2.mb_state_32 a", "prompt": "let coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a =\n ", "expected_response": "Lib.IntVector.reveal_vec_1 (word_t a);\nb", "source": { "project_name": "hacl-star", "file_name": "code/hash/Hacl.Hash.SHA2.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git" }, "dependencies": { "source_file": "Hacl.Hash.SHA2.fst", "checked_file": "dataset/Hacl.Hash.SHA2.fst.checked", "interface_file": true, "dependencies": [ "dataset/Spec.SHA2.fst.checked", "dataset/Spec.Hash.MD.fst.checked", "dataset/Spec.Hash.Incremental.fst.checked", "dataset/Spec.Hash.Definitions.fst.checked", "dataset/Spec.Agile.Hash.fst.checked", "dataset/prims.fst.checked", "dataset/LowStar.Buffer.fst.checked", "dataset/Lib.UpdateMulti.Lemmas.fsti.checked", "dataset/Lib.UpdateMulti.fst.checked", "dataset/Lib.Sequence.Lemmas.fsti.checked", "dataset/Lib.Sequence.fsti.checked", "dataset/Lib.NTuple.fsti.checked", "dataset/Lib.MultiBuffer.fst.checked", "dataset/Lib.IntVector.fsti.checked", "dataset/Lib.IntTypes.fsti.checked", "dataset/Lib.Buffer.fsti.checked", "dataset/Hacl.Spec.SHA2.Vec.fst.checked", "dataset/Hacl.Spec.SHA2.EquivScalar.fsti.checked", "dataset/Hacl.Spec.SHA2.Equiv.fst.checked", "dataset/Hacl.Spec.SHA2.fst.checked", "dataset/Hacl.SHA2.Scalar32.fst.checked", "dataset/Hacl.Impl.SHA2.Generic.fst.checked", "dataset/Hacl.Impl.SHA2.Core.fst.checked", "dataset/Hacl.Hash.PadFinish.fsti.checked", "dataset/Hacl.Hash.MD.fsti.checked", "dataset/Hacl.Hash.Definitions.fst.checked", "dataset/FStar.UInt32.fsti.checked", "dataset/FStar.Seq.fst.checked", "dataset/FStar.Pervasives.fsti.checked", "dataset/FStar.Math.Lemmas.fst.checked", "dataset/FStar.HyperStack.ST.fsti.checked", "dataset/FStar.HyperStack.fst.checked", "dataset/FStar.Classical.fsti.checked", "dataset/FStar.Calc.fsti.checked" ] }, "definitions_in_context": [ "val init_224: init_st (|SHA2_224, ()|)", "val init_256: init_st (|SHA2_256, ()|)", "val init_384: init_st (|SHA2_384, ()|)", "val init_512: init_st (|SHA2_512, ()|)", "val alloca_224: alloca_st (|SHA2_224, ()|)", "val alloca_256: alloca_st (|SHA2_256, ()|)", "val alloca_384: alloca_st (|SHA2_384, ()|)", "val alloca_512: alloca_st (|SHA2_512, ()|)", "val update_multi_224: update_multi_st (|SHA2_224, ()|)", "let mb_state_32 a = Hacl.Impl.SHA2.Core.state_t a Hacl.Spec.SHA2.Vec.M32", "val update_multi_256: update_multi_st (|SHA2_256, ()|)", "val update_multi_384: update_multi_st (|SHA2_384, ()|)", "let coerce_to_state (a:sha2_alg) (b:mb_state_32 a) : state (| a, () |)\n = Lib.IntVector.reveal_vec_1 (word_t a);\n b", "val update_multi_512: update_multi_st (|SHA2_512, ()|)", "val update_last_224: update_last_st (|SHA2_224, ()|)" ], "closest": [ "val blake2_compress2:\n a:alg\n -> wv:state a\n -> m:block_w a ->\n Tot (state a)\nlet blake2_compress2 a wv m = repeati (rounds a) (blake2_round a m) wv", "val update\n (#a: sha2_alg)\n (#m: m_spec{is_supported a m})\n (b: multiblock_spec a m)\n (st: state_spec a m)\n : state_spec a m\nlet update (#a:sha2_alg) (#m:m_spec{is_supported a m}) (b:multiblock_spec a m) (st:state_spec a m): state_spec a m =\n let st_old = st in\n let ws = load_ws b in\n let st_new = shuffle ws st_old in\n map2 (+|) st_new st_old", "val blake2_compress3:\n a:alg\n -> wv:state a\n -> s_iv:state a ->\n Tot (state a)\nlet blake2_compress3 a wv s =\n let s = s.[0] <- (s.[0] ^| wv.[0]) ^| wv.[2] in\n let s = s.[1] <- (s.[1] ^| wv.[1]) ^| wv.[3] in\n s", "val words_of_bytes (a: hash_alg{is_md a})\n : Tot\n (\n #len: size_nat{FStar.Mul.(len * word_length a) <= max_size_t} ->\n b: lbytes FStar.Mul.(word_length a * len)\n -> Tot (lseq (word a) len))\nlet words_of_bytes: a:hash_alg{is_md a} -> Tot (#len:size_nat{FStar.Mul.(len * word_length a) <= max_size_t} -> b:lbytes FStar.Mul.(word_length a * len) -> Tot (lseq (word a) len)) = function\n | MD5 -> Lib.ByteSequence.uints_from_bytes_le #U32 #SEC\n | SHA1 | SHA2_224 | SHA2_256 -> Lib.ByteSequence.uints_from_bytes_be #U32 #SEC\n | SHA2_384 | SHA2_512 -> Lib.ByteSequence.uints_from_bytes_be #U64 #SEC", "val alloc: a:sha2_alg -> m:m_spec ->\n StackInline (state_t a m)\n (requires fun h -> True)\n (ensures fun h0 b h1 -> live h1 b /\\ stack_allocated b h0 h1 (Seq.create 8 (zero_element a m)))\nlet alloc a m = Lib.Buffer.create 8ul (zero_element a m)", "val init (a: sha2_alg) : words_state a\nlet init (a:sha2_alg) : words_state a = h0 a", "val load_state:\n st:state\n -> b:lbuffer uint8 64ul ->\n Stack unit\n (requires fun h -> live h st /\\ live h b /\\ disjoint st b)\n (ensures fun h0 _ h1 -> modifies (loc st) h0 h1 /\\\n as_seq h1 st == Lib.ByteSequence.uints_from_bytes_le (as_seq h0 b))\nlet load_state st b =\n uints_from_bytes_le st b", "val load_state:\n st:state\n -> b:lbuffer uint8 64ul ->\n Stack unit\n (requires fun h -> live h st /\\ live h b /\\ disjoint st b)\n (ensures fun h0 _ h1 -> modifies (loc st) h0 h1 /\\\n as_seq h1 st == Lib.ByteSequence.uints_from_bytes_le (as_seq h0 b))\nlet load_state st b =\n uints_from_bytes_le st b", "val gather_state: a:alg -> m:block_w a -> start:nat{start <= 144} -> state a\nlet gather_state a m start =\n let x = gather_row m sigmaTable.[start] sigmaTable.[start+2] sigmaTable.[start+4] sigmaTable.[start+6] in\n let y = gather_row m sigmaTable.[start+1] sigmaTable.[start+3] sigmaTable.[start+5] sigmaTable.[start+7] in\n let z = gather_row m sigmaTable.[start+8] sigmaTable.[start+10] sigmaTable.[start+12] sigmaTable.[start+14] in\n let w = gather_row m sigmaTable.[start+9] sigmaTable.[start+11] sigmaTable.[start+13] sigmaTable.[start+15] in\n let l = [x;y;z;w] in\n assert_norm (List.Tot.length l == 4);\n createL l", "val update_nblocks\n (#a: sha2_alg)\n (#m: m_spec{is_supported a m})\n (len: Spec.len_lt_max_a_t a)\n (b: multiseq (lanes a m) len)\n (st: state_spec a m)\n : state_spec a m\nlet update_nblocks (#a:sha2_alg) (#m:m_spec{is_supported a m}) (len:Spec.len_lt_max_a_t a) (b:multiseq (lanes a m) len) (st:state_spec a m) : state_spec a m =\n let blocks = len / block_length a in\n let st = repeati blocks (update_block #a #m len b) st in\n st", "val store_state (a: sha2_alg) (hashw: words_state a) : Tot (lseq uint8 (8 * word_length a))\nlet store_state (a:sha2_alg) (hashw:words_state a) : Tot (lseq uint8 (8 * word_length a)) =\n Lib.ByteSequence.uints_to_bytes_be #(word_t a) #SEC #8 hashw", "val init_extra_state (a: hash_alg) : extra_state a\nlet init_extra_state (a:hash_alg) : extra_state a = match a with\n | Blake2B | Blake2S -> 0\n | _ -> ()", "val blake2_compress:\n a:alg\n -> s_iv:state a\n -> m:block_s a\n -> offset:limb_t a\n -> flag:bool ->\n Tot (state a)\nlet blake2_compress a s_iv m offset flag =\n let m_w = blake2_compress0 a m in\n let wv = blake2_compress1 a s_iv offset flag in\n let wv = blake2_compress2 a wv m_w in\n let s_iv = blake2_compress3 a wv s_iv in\n s_iv", "val update_nblocks\n (a: sha2_alg)\n (len: len_lt_max_a_t a)\n (b: seq uint8 {length b = len})\n (st: words_state a)\n : words_state a\nlet update_nblocks (a:sha2_alg) (len:len_lt_max_a_t a) (b:seq uint8{length b = len}) (st:words_state a) : words_state a =\n let blocks = len / block_length a in\n Lib.LoopCombinators.repeati blocks (update_block a len b) st", "val extra_state_of_nat (a: hash_alg) (i: nat{i % U32.v (block_len a) = 0})\n : Spec.Hash.Definitions.extra_state a\nlet extra_state_of_nat (a: hash_alg) (i: nat { i % U32.v (block_len a) = 0 }):\n Spec.Hash.Definitions.extra_state a\n=\n if is_blake a then\n i\n else\n ()", "val blake2_update:\n a:alg\n -> kk:size_nat{kk <= max_key a}\n -> k:lbytes kk\n -> d:bytes{if kk = 0 then length d <= max_limb a else length d + (size_block a) <= max_limb a}\n -> s:state a ->\n Tot (state a)\nlet blake2_update a kk k d s =\n let ll = length d in\n if kk > 0 then\n let s = blake2_update_key a kk k ll s in\n if ll = 0 then s // Skip update_last if ll = 0 (but kk > 0)\n else blake2_update_blocks a (size_block a) d s\n else blake2_update_blocks a 0 d s", "val store_state: #a:sha2_alg -> #m:m_spec{is_supported a m}\n -> st:state_t a m\n -> hbuf:lbuffer uint8 (size (lanes a m) *! 8ul *! HD.word_len a) ->\n Stack unit\n (requires fun h -> live h hbuf /\\ live h st /\\ disjoint hbuf st /\\\n as_seq h hbuf == LSeq.create (lanes a m * 8 * word_length a) (u8 0))\n (ensures fun h0 _ h1 -> modifies (loc st |+| loc hbuf) h0 h1 /\\\n as_seq h1 hbuf == SpecVec.store_state #a #m (as_seq h0 st))\nlet store_state #a #m st hbuf =\n transpose_state st;\n Lib.IntVector.Serialize.vecs_store_be hbuf st", "val update_block\n (#a: sha2_alg)\n (#m: m_spec{is_supported a m})\n (len: Spec.len_lt_max_a_t a)\n (b: multiseq (lanes a m) len)\n (i: nat{i < len / block_length a})\n (st: state_spec a m)\n : state_spec a m\nlet update_block (#a:sha2_alg) (#m:m_spec{is_supported a m}) (len:Spec.len_lt_max_a_t a) (b:multiseq (lanes a m) len)\n (i:nat{i < len / block_length a}) (st:state_spec a m) : state_spec a m =\n let mb = get_multiblock_spec len b i in\n update mb st", "val coerce (#a #b: _) (x: a{a == b}) : b\nlet coerce #a #b (x:a{a == b}) : b = x", "val coerce (#a #b: _) (x: a{a == b}) : b\nlet coerce #a #b (x:a{a == b}) : b = x", "val coerce (#a #b: _) (x: a{a == b}) : b\nlet coerce #a #b (x:a{a == b}) : b = x", "val coerce (#a #b: _) (x: a{a == b}) : b\nlet coerce #a #b (x:a{a == b}) : b = x", "val coerce (#a #b: _) (x: a{a == b}) : b\nlet coerce #a #b (x:a{a == b}) : b = x", "val coerce (#a #b: _) (x: a{a == b}) : b\nlet coerce #a #b (x:a{a == b}) : b = x", "val coerce (#a #b: _) (x: a{a == b}) : b\nlet coerce #a #b (x:a{a == b}) : b = x", "val store_state:\n b:lbuffer uint8 64ul\n -> st:state ->\n Stack unit\n (requires fun h -> live h st /\\ live h b /\\ disjoint st b)\n (ensures fun h0 _ h1 -> modifies (loc b) h0 h1 /\\\n as_seq h1 b == Lib.ByteSequence.uints_to_bytes_le (as_seq h0 st))\nlet store_state st b =\n uints_to_bytes_le 16ul st b", "val store_state:\n b:lbuffer uint8 64ul\n -> st:state ->\n Stack unit\n (requires fun h -> live h st /\\ live h b /\\ disjoint st b)\n (ensures fun h0 _ h1 -> modifies (loc b) h0 h1 /\\\n as_seq h1 b == Lib.ByteSequence.uints_to_bytes_le (as_seq h0 st))\nlet store_state st b =\n uints_to_bytes_le 16ul st b", "val init (a: sha2_alg) (m: m_spec) : state_spec a m\nlet init (a:sha2_alg) (m:m_spec) : state_spec a m =\n createi 8 (fun i -> load_element a m (Seq.index (Spec.h0 a) i))", "val va_wp_Gctr_blocks128_1way_body0\n (va_old: va_state)\n (alg: algorithm)\n (va_in_in_b: buffer128)\n (va_in_key: (seq nat32))\n (va_in_keys_b: buffer128)\n (va_in_old_icb: quad32)\n (va_in_old_plain: (seq quad32))\n (va_in_out_b: buffer128)\n (va_in_round_keys: (seq quad32))\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Gctr_blocks128_1way_body0 (va_old:va_state) (alg:algorithm) (va_in_in_b:buffer128)\n (va_in_key:(seq nat32)) (va_in_keys_b:buffer128) (va_in_old_icb:quad32) (va_in_old_plain:(seq\n quad32)) (va_in_out_b:buffer128) (va_in_round_keys:(seq quad32)) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (0 <= va_get_reg 8 va_s0 /\\ va_get_reg 8 va_s0 <= va_get_reg 26 va_s0) /\\\n va_get_reg 9 va_s0 == 16 `op_Multiply` va_get_reg 8 va_s0 /\\ va_get_vec 7 va_s0 ==\n Vale.AES.GCTR_BE.inc32lite va_in_old_icb (va_get_reg 6 va_s0 + va_get_reg 8 va_s0) /\\\n (Vale.PPC64LE.Decls.buffers_disjoint128 va_in_in_b va_in_out_b \\/ va_in_in_b == va_in_out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrsOffset128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0)\n va_in_in_b (va_get_reg 6 va_s0) (va_get_reg 26 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrsOffset128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0)\n va_in_out_b (va_get_reg 6 va_s0) (va_get_reg 26 va_s0) (va_get_mem_layout va_s0) Secret /\\\n va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 26 va_s0 < pow2_64 /\\ va_get_reg 7 va_s0 + 16\n `op_Multiply` va_get_reg 26 va_s0 < pow2_64 /\\ Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 va_in_in_b == Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 va_in_out_b /\\ (va_get_reg 8 va_s0 =!= va_get_reg 26 va_s0 ==>\n Vale.AES.GCTR_BE.partial_seq_agreement va_in_old_plain\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n va_in_in_b)) (va_get_reg 6 va_s0 + va_get_reg 8 va_s0) (Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 va_in_in_b)) /\\ va_get_reg 6 va_s0 + va_get_reg 26 va_s0 <\n pow2_32 /\\ aes_reqs alg va_in_key va_in_round_keys va_in_keys_b (va_get_reg 4 va_s0)\n (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\ va_get_vec 3 va_s0 ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 /\\\n Vale.PPC64LE.Decls.modifies_buffer128 va_in_out_b (va_get_mem_heaplet 1 va_old)\n (va_get_mem_heaplet 1 va_s0) /\\ Vale.AES.GCTR_BE.gctr_partial_def alg (va_get_reg 6 va_s0 +\n va_get_reg 8 va_s0) va_in_old_plain (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) va_in_out_b)) va_in_key va_in_old_icb /\\\n (va_get_reg 6 va_s0 + va_get_reg 26 va_s0 == 0 ==> Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet\n 1 va_s0) va_in_out_b == Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_old) va_in_out_b) /\\\n va_get_reg 8 va_s0 =!= va_get_reg 26 va_s0 /\\ (forall (va_x_cr0:cr0_t) (va_x_heap1:vale_heap)\n (va_x_mem:vale_heap) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r8:nat64) (va_x_r9:nat64)\n (va_x_v0:quad32) (va_x_v2:quad32) (va_x_v7:quad32) . let va_sM = va_upd_vec 7 va_x_v7\n (va_upd_vec 2 va_x_v2 (va_upd_vec 0 va_x_v0 (va_upd_reg 9 va_x_r9 (va_upd_reg 8 va_x_r8\n (va_upd_reg 10 va_x_r10 (va_upd_ok va_x_ok (va_upd_mem va_x_mem (va_upd_mem_heaplet 1\n va_x_heap1 (va_upd_cr0 va_x_cr0 va_s0))))))))) in va_get_ok va_sM /\\ (0 <= va_get_reg 8 va_sM\n /\\ va_get_reg 8 va_sM <= va_get_reg 26 va_sM) /\\ va_get_reg 9 va_sM == 16 `op_Multiply`\n va_get_reg 8 va_sM /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite va_in_old_icb\n (va_get_reg 6 va_sM + va_get_reg 8 va_sM) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 va_in_in_b\n va_in_out_b \\/ va_in_in_b == va_in_out_b) /\\ Vale.PPC64LE.Decls.validSrcAddrsOffset128\n (va_get_mem_heaplet 1 va_sM) (va_get_reg 3 va_sM) va_in_in_b (va_get_reg 6 va_sM) (va_get_reg\n 26 va_sM) (va_get_mem_layout va_sM) Secret /\\ Vale.PPC64LE.Decls.validDstAddrsOffset128\n (va_get_mem_heaplet 1 va_sM) (va_get_reg 7 va_sM) va_in_out_b (va_get_reg 6 va_sM) (va_get_reg\n 26 va_sM) (va_get_mem_layout va_sM) Secret /\\ va_get_reg 3 va_sM + 16 `op_Multiply` va_get_reg\n 26 va_sM < pow2_64 /\\ va_get_reg 7 va_sM + 16 `op_Multiply` va_get_reg 26 va_sM < pow2_64 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 va_in_in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 va_in_out_b /\\ (va_get_reg 8\n va_sM =!= va_get_reg 26 va_sM ==> Vale.AES.GCTR_BE.partial_seq_agreement va_in_old_plain\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n va_in_in_b)) (va_get_reg 6 va_sM + va_get_reg 8 va_sM) (Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 va_in_in_b)) /\\ va_get_reg 6 va_sM + va_get_reg 26 va_sM <\n pow2_32 /\\ aes_reqs alg va_in_key va_in_round_keys va_in_keys_b (va_get_reg 4 va_sM)\n (va_get_mem_heaplet 0 va_sM) (va_get_mem_layout va_sM) /\\ va_get_vec 3 va_sM ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 /\\\n Vale.PPC64LE.Decls.modifies_buffer128 va_in_out_b (va_get_mem_heaplet 1 va_old)\n (va_get_mem_heaplet 1 va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial_def alg (va_get_reg 6 va_sM +\n va_get_reg 8 va_sM) va_in_old_plain (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) va_in_out_b)) va_in_key va_in_old_icb /\\\n (va_get_reg 6 va_sM + va_get_reg 26 va_sM == 0 ==> Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet\n 1 va_sM) va_in_out_b == Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_old) va_in_out_b) /\\\n precedes_wrap (va_get_reg 26 va_sM - va_get_reg 8 va_sM) (va_get_reg 26 va_s0 - va_get_reg 8\n va_s0) ==> va_k va_sM (())))", "val extra_state (a: hash_alg) : Type0\nlet extra_state (a:hash_alg) : Type0 =\n match a with\n | Blake2S -> s:uint_t U64 PUB{ v s % block_length a = 0 }\n | Blake2B -> s:uint_t U128 PUB{ v s % block_length a = 0 }\n | MD5 | SHA1\n | SHA2_224 | SHA2_256\n | SHA2_384 | SHA2_512\n | SHA3_224 | SHA3_256 | SHA3_384 | SHA3_512 | Shake128 | Shake256 -> unit", "val Spec.Blake2.Definitions.state = a: Spec.Blake2.Definitions.alg -> Type0\nlet state (a:alg) = lseq (row a) 4", "val transpose_state (#a: sha2_alg) (#m: m_spec{is_supported a m}) (st: state_spec a m)\n : state_spec a m\nlet transpose_state (#a:sha2_alg) (#m:m_spec{is_supported a m}) (st:state_spec a m) : state_spec a m =\n match lanes a m with\n | 1 -> st\n | 4 -> transpose_state4 #a #m st\n | 8 -> transpose_state8 #a #m st", "val blake2_round:\n a:alg\n -> m:block_w a\n -> i:size_nat\n -> wv:state a\n -> state a\nlet blake2_round a m i wv =\n let start = (i%10) * 16 in\n let m_s = gather_state a m start in\n let wv = blake2_mixing a wv m_s.[0] m_s.[1] in\n let wv = diag wv in\n let wv = blake2_mixing a wv m_s.[2] m_s.[3] in\n undiag wv", "val va_wp_Gctr_bytes\n (alg: algorithm)\n (in_b out_b inout_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Gctr_bytes (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (inout_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (va_s0:va_state) (va_k:(va_state\n -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg64\n rRax va_s0) in_b (va_get_reg64 rRcx va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRbx va_s0) out_b\n (va_get_reg64 rRcx va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.X64.Decls.validDstAddrs128\n (va_get_mem_heaplet 2 va_s0) (va_get_reg64 rR13 va_s0) inout_b 1 (va_get_mem_layout va_s0)\n Secret /\\ va_get_reg64 rRax va_s0 + 16 `op_Multiply` va_get_reg64 rRcx va_s0 < pow2_64 /\\\n va_get_reg64 rRbx va_s0 + 16 `op_Multiply` va_get_reg64 rRcx va_s0 < pow2_64 /\\ l_and (l_and\n (l_and (Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b ==\n Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 out_b) (Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 out_b == va_get_reg64 rRcx va_s0)) (Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 in_b `op_Multiply` 16 < pow2_32)) (va_get_reg64 rRcx va_s0\n `op_Multiply` 16 < pow2_32) /\\ Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 inout_b\n == 1 /\\ (va_get_reg64 rRcx va_s0 `op_Multiply` 128 `op_Division` 8 <= va_get_reg64 rRsi va_s0\n /\\ va_get_reg64 rRsi va_s0 < va_get_reg64 rRcx va_s0 `op_Multiply` 128 `op_Division` 8 + 128\n `op_Division` 8) /\\ (aesni_enabled /\\ avx_enabled /\\ sse_enabled) /\\ (alg = AES_128 \\/ alg =\n AES_256) /\\ Vale.AES.AES_s.is_aes_key_LE alg key /\\ FStar.Seq.Base.length #quad32 round_keys ==\n Vale.AES.AES_common_s.nr alg + 1 /\\ round_keys == Vale.AES.AES_s.key_to_round_keys_LE alg key\n /\\ va_get_reg64 rR8 va_s0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint128 keys_b\n (va_get_mem_heaplet 0 va_s0) /\\ Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0)\n (va_get_reg64 rR8 va_s0) keys_b (Vale.AES.AES_common_s.nr alg + 1) (va_get_mem_layout va_s0)\n Secret /\\ Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s0) keys_b == round_keys) /\\\n (forall (va_x_mem:vale_heap) (va_x_rax:nat64) (va_x_rbx:nat64) (va_x_rcx:nat64)\n (va_x_rdx:nat64) (va_x_rdi:nat64) (va_x_rbp:nat64) (va_x_r9:nat64) (va_x_r10:nat64)\n (va_x_r11:nat64) (va_x_r12:nat64) (va_x_xmm0:quad32) (va_x_xmm1:quad32) (va_x_xmm2:quad32)\n (va_x_xmm3:quad32) (va_x_xmm4:quad32) (va_x_xmm5:quad32) (va_x_xmm6:quad32) (va_x_xmm7:quad32)\n (va_x_xmm8:quad32) (va_x_xmm9:quad32) (va_x_xmm10:quad32) (va_x_xmm12:quad32)\n (va_x_xmm13:quad32) (va_x_xmm14:quad32) (va_x_xmm15:quad32) (va_x_heap1:vale_heap)\n (va_x_heap2:vale_heap) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl\n (va_upd_mem_heaplet 2 va_x_heap2 (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_xmm 15 va_x_xmm15\n (va_upd_xmm 14 va_x_xmm14 (va_upd_xmm 13 va_x_xmm13 (va_upd_xmm 12 va_x_xmm12 (va_upd_xmm 10\n va_x_xmm10 (va_upd_xmm 9 va_x_xmm9 (va_upd_xmm 8 va_x_xmm8 (va_upd_xmm 7 va_x_xmm7 (va_upd_xmm\n 6 va_x_xmm6 (va_upd_xmm 5 va_x_xmm5 (va_upd_xmm 4 va_x_xmm4 (va_upd_xmm 3 va_x_xmm3 (va_upd_xmm\n 2 va_x_xmm2 (va_upd_xmm 1 va_x_xmm1 (va_upd_xmm 0 va_x_xmm0 (va_upd_reg64 rR12 va_x_r12\n (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64\n rRbp va_x_rbp (va_upd_reg64 rRdi va_x_rdi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx\n va_x_rcx (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRax va_x_rax (va_upd_mem va_x_mem\n va_s0)))))))))))))))))))))))))))) in va_get_ok va_sM /\\ (Vale.X64.Decls.modifies_buffer128\n out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\\\n Vale.X64.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 2 va_s0) (va_get_mem_heaplet 2\n va_sM) /\\ (let plain_quads = FStar.Seq.Base.append #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128\n (va_get_mem_heaplet 0 va_sM) in_b) (Vale.X64.Decls.s128 (va_get_mem_heaplet 2 va_s0) inout_b)\n in let plain_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes plain_quads) 0 (va_get_reg64 rRsi va_s0) in let\n cipher_quads = FStar.Seq.Base.append #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_sM) out_b) (Vale.X64.Decls.s128 (va_get_mem_heaplet 2 va_sM) inout_b)\n in let cipher_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes cipher_quads) 0 (va_get_reg64 rRsi va_s0) in\n cipher_bytes == Vale.AES.GCTR_s.gctr_encrypt_LE (va_get_xmm 7 va_s0)\n (Vale.AES.GCTR.make_gctr_plain_LE plain_bytes) alg key)) ==> va_k va_sM (())))", "val update_block\n (a: sha2_alg)\n (len: len_lt_max_a_t a)\n (b: seq uint8 {length b = len})\n (i: nat{i < len / block_length a})\n (st: words_state a)\n : words_state a\nlet update_block (a:sha2_alg) (len:len_lt_max_a_t a) (b:seq uint8{length b = len})\n (i:nat{i < len / block_length a}) (st:words_state a) : words_state a\n =\n let mb = Seq.slice b (i * block_length a) (i * block_length a + block_length a) in\n update a mb st", "val blake2_compress1:\n a:alg\n -> s_iv:state a\n -> offset:limb_t a\n -> flag:bool ->\n Tot (state a)\nlet blake2_compress1 a s_iv offset flag =\n let wv : state a = s_iv in\n let low_offset = limb_to_word a offset in\n let high_offset = limb_to_word a (shift_right #(limb_inttype a) offset (size (bits (wt a)))) in\n let m_12 = low_offset in\n let m_13 = high_offset in\n let m_14 = if flag then (ones (wt a) SEC) else zero a in\n let m_15 = zero a in\n let mask = create_row m_12 m_13 m_14 m_15 in\n let wv = wv.[3] <- wv.[3] ^| mask in\n wv", "val state_spec_v (#a: sha2_alg) (#m: m_spec) (st: state_spec a m)\n : lseq (words_state' a) (lanes a m)\nlet state_spec_v (#a:sha2_alg) (#m:m_spec) (st:state_spec a m) : lseq (words_state' a) (lanes a m) =\n createi #(words_state' a) (lanes a m) (fun i ->\n create8\n (vec_v st.[0]).[i] (vec_v st.[1]).[i] (vec_v st.[2]).[i] (vec_v st.[3]).[i]\n (vec_v st.[4]).[i] (vec_v st.[5]).[i] (vec_v st.[6]).[i] (vec_v st.[7]).[i])", "val repeati_update1:\n a:alg\n -> b:block_s a\n -> d:bytes{length d + (size_block a) <= max_limb a}\n -> nb:nat{nb > 0 /\\ nb <= length (b `Seq.append` d) / size_block a}\n -> s:state a ->\n Lemma (\n repeati nb (blake2_update1 a 0 (b `Seq.append` d)) s ==\n repeati (nb - 1) (blake2_update1 a (size_block a) d) (blake2_update_block a false (size_block a) b s)\n )\nlet repeati_update1 a b d nb s =\n let f = blake2_update1 a 0 (b `Seq.append` d) in\n let f' = blake2_update1 a (size_block a) d in\n let s' = blake2_update_block a false (size_block a) b s in\n Classical.forall_intro_2 (lemma_update1_shift a b d);\n assert (forall i s. f (i + 1) s == f' i s);\n Lems.repeati_right_shift (nb - 1) f' f s;\n assert (get_blocki a (b `Seq.append` d) 0 `Seq.equal` b);\n assert (s' == f 0 s)", "val upd_32_be (#rrel #rel: MB.srel u8) (b: MB.mbuffer u8 rrel rel) (i v: u32)\n : Stack unit\n (requires\n fun h ->\n MB.length b % 4 = 0 /\\ U32.v i < MB.length b / 4 /\\\n store_pre b (let open U32 in v (4ul *^ i)) 4 (fun s -> be_to_n s == U32.v v) h)\n (ensures\n fun h0 _ h1 ->\n MB.(modifies (loc_buffer b) h0 h1) /\\\n (seq_uint32_of_be (MB.length b / 4) (MB.as_seq h1 b))\n `Seq.equal`\n (Seq.upd (seq_uint32_of_be (MB.length b / 4) (MB.as_seq h0 b)) (U32.v i) v))\nlet upd_32_be\n (#rrel #rel:MB.srel u8) (b:MB.mbuffer u8 rrel rel)\n (i:u32) (v:u32)\n : Stack unit\n (requires fun h ->\n MB.length b % 4 = 0 /\\\n U32.v i < MB.length b / 4 /\\\n store_pre b (U32.(v (4ul *^ i))) 4 (fun s -> be_to_n s == U32.v v) h)\n (ensures fun h0 _ h1 ->\n MB.(modifies (loc_buffer b) h0 h1) /\\\n seq_uint32_of_be (MB.length b / 4) (MB.as_seq h1 b) `Seq.equal` Seq.upd (seq_uint32_of_be (MB.length b / 4) (MB.as_seq h0 b)) (U32.v i) v)\n = let h0 = get () in\n store32_be_i b U32.(4ul *^ i) v;\n let h1 = get () in\n //AR: 03/01: the following 3 assertions say how the buffer changed\n assert (be_to_n (Seq.slice (MB.as_seq h1 b) (U32.(v (4ul *^ i))) (U32.(v (4ul *^ i) + 4))) == U32.v v);\n assert (Seq.equal (Seq.slice (MB.as_seq h0 b) 0 (U32.(v (4ul *^ i))))\n (Seq.slice (MB.as_seq h1 b) 0 (U32.(v (4ul *^ i)))));\n assert (Seq.equal (Seq.slice (MB.as_seq h0 b) (U32.(v (4ul *^ i) + 4)) (MB.length b))\n (Seq.slice (MB.as_seq h1 b) (U32.(v (4ul *^ i) + 4)) (MB.length b)));\n let f () : Lemma\n (seq_uint32_of_be (MB.length b / 4) (MB.as_seq h1 b) `Seq.equal` Seq.upd (seq_uint32_of_be (MB.length b / 4) (MB.as_seq h0 b))\n (UInt32.v i) v)\n = let s0 = MB.as_seq h0 b in\n let s1 = MB.as_seq h1 b in\n let n = MB.length b / 4 in\n assert (4 `Prims.op_Multiply` n == MB.length b);\n let s0' = seq_uint32_of_be n s0 in\n let s1' = seq_uint32_of_be n s1 in\n let lo = UInt32.v i in\n let hi = lo + 1 in\n let s2' = Seq.upd s0' lo v in\n assert (Seq.length s1' == Seq.length s2');\n let i' = UInt32.v i in\n let g\n (j' : nat)\n : Lemma\n (requires (j' < n))\n (ensures (j' < n /\\ Seq.index s1' j' == Seq.index s2' j'))\n = if j' = UInt32.v i\n then ()\n else begin\n let u () : Lemma\n (Seq.slice s0 (4 * j') (4 * j' + 4) == Seq.slice s1 (4 * j') (4 * j' + 4))\n = if j' < UInt32.v i\n then begin\n Seq.slice_slice s0 0 (4 * i') (4 * j') (4 * j' + 4);\n Seq.slice_slice s1 0 (4 * i') (4 * j') (4 * j' + 4)\n end else begin\n Seq.slice_slice s0 (4 * i' + 4) (MB.length b) (4 * (j' - i' - 1)) (4 * (j' - i'));\n Seq.slice_slice s1 (4 * i' + 4) (MB.length b) (4 * (j' - i' - 1)) (4 * (j' - i'))\n end\n in\n u ()\n end\n in\n Classical.forall_intro (Classical.move_requires g)\n in\n f ()", "val coerce (x: 'a{'a == 'b}) : 'b\nlet coerce (x:'a{'a == 'b}) : 'b = x", "val coerce (x: 'a{'a == 'b}) : 'b\nlet coerce (x:'a{'a == 'b}) : 'b = x", "val coerce (x: 'a{'a == 'b}) : 'b\nlet coerce (x:'a{'a == 'b}) : 'b = x", "val coerce (x: 'a{'a == 'b}) : 'b\nlet coerce (x:'a{'a == 'b}) : 'b = x", "val va_wp_Gctr_bytes_no_extra\n (alg: algorithm)\n (icb_BE: quad32)\n (in_b out_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n (orig_in_ptr orig_out_ptr: nat64)\n (num_bytes: nat)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Gctr_bytes_no_extra (alg:algorithm) (icb_BE:quad32) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (orig_in_ptr:nat64)\n (orig_out_ptr:nat64) (num_bytes:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) orig_in_ptr in_b\n (Vale.AES.GCM_helpers.bytes_to_quad_size num_bytes) (va_get_mem_layout va_s0) Secret /\\\n Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) orig_out_ptr out_b\n (Vale.AES.GCM_helpers.bytes_to_quad_size num_bytes) (va_get_mem_layout va_s0) Secret /\\\n orig_in_ptr + 16 `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size num_bytes < pow2_64 /\\\n orig_out_ptr + 16 `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size num_bytes < pow2_64 /\\\n l_and (l_and (l_and (Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b ==\n Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 out_b) (Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 out_b == Vale.AES.GCM_helpers.bytes_to_quad_size num_bytes))\n (Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b `op_Multiply` 16 < pow2_32))\n (num_bytes < pow2_32) /\\ (alg = AES_128 \\/ alg = AES_256) /\\ Vale.AES.AES_s.is_aes_key_LE alg\n key /\\ FStar.Seq.Base.length #quad32 round_keys == Vale.AES.AES_common_s.nr alg + 1 /\\\n round_keys == Vale.AES.AES_s.key_to_round_keys_LE alg key /\\ (let num_blocks = num_bytes\n `op_Division` 16 in num_bytes `op_Modulus` 16 == 0 /\\ Vale.AES.GCTR.gctr_partial_def alg\n num_blocks (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s0) in_b)\n (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 1 va_s0) out_b) key icb_BE) /\\ (let va_sM\n = va_s0 in va_get_ok va_sM /\\ Vale.X64.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1\n va_s0) (va_get_mem_heaplet 1 va_sM) /\\ (let plain = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0\n va_sM) in_b)) 0 num_bytes in let cipher = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 1\n va_sM) out_b)) 0 num_bytes in cipher == Vale.AES.GCTR_s.gctr_encrypt_LE icb_BE\n (Vale.AES.GCTR.make_gctr_plain_LE plain) alg key) ==> va_k va_sM (())))", "val state_or_fail (s: machine_state) (b: bool) (s': machine_state) : machine_state\nlet state_or_fail (s:machine_state) (b:bool) (s':machine_state) : machine_state =\n if b then s' else {s with ms_ok = false}", "val blake2_update'\n (a: alg)\n (kk: size_nat{kk <= max_key a})\n (k: lbytes kk)\n (d: bytes{if kk = 0 then length d <= max_limb a else length d + (size_block a) <= max_limb a})\n (s: state a)\n : Tot (state a)\nlet blake2_update'\n (a:alg)\n (kk:size_nat{kk <= max_key a})\n (k:lbytes kk)\n (d:bytes{if kk = 0 then length d <= max_limb a else length d + (size_block a) <= max_limb a})\n (s:state a): Tot (state a)\n= let ll = length d in\n let key_block: bytes = if kk > 0 then blake2_key_block a kk k else Seq.empty in\n blake2_update_blocks a 0 (key_block `Seq.append` d) s", "val state_spec_v_extensionality\n (a: hash_alg{is_sha2 a})\n (acc1 acc2: Hacl.Spec.SHA2.Vec.(state_spec a M32))\n : Lemma\n (requires\n (let open Hacl.Spec.SHA2.Vec in\n Lib.Sequence.index (state_spec_v acc1) 0 == Lib.Sequence.index (state_spec_v acc2) 0))\n (ensures acc1 == acc2)\nlet state_spec_v_extensionality (a : hash_alg { is_sha2 a })\n (acc1: Hacl.Spec.SHA2.Vec.(state_spec a M32))\n (acc2: Hacl.Spec.SHA2.Vec.(state_spec a M32)) :\n Lemma\n (requires (let open Hacl.Spec.SHA2.Vec in\n Lib.Sequence.index (state_spec_v acc1) 0 ==\n Lib.Sequence.index (state_spec_v acc2) 0))\n (ensures acc1 == acc2) =\n\n let open Lib.Sequence in\n let open Lib.IntVector in\n let open Hacl.Spec.SHA2.Vec in\n allow_inversion hash_alg;\n let acc1_s = (state_spec_v acc1).[0] <: lseq (word a) 8 in\n let acc2_s = (state_spec_v acc2).[0] <: lseq (word a) 8 in\n\n let aux (i:nat{i < 8}) : Lemma (acc1.[i] == acc2.[i]) =\n assert (index (vec_v acc1.[i]) 0 == index #(word a) #8 acc1_s i);\n assert (index (vec_v acc2.[i]) 0 == index #(word a) #8 acc2_s i);\n assert (index (vec_v acc1.[i]) 0 == index (vec_v acc2.[i]) 0);\n eq_intro (vec_v acc1.[i]) (vec_v acc2.[i]);\n vecv_extensionality acc1.[i] acc2.[i] in\n\n Classical.forall_intro aux;\n eq_intro acc1 acc2", "val h0 (a: sha2_alg) : Tot (words_state a)\nlet h0: a:sha2_alg -> Tot (words_state a) = function\n | SHA2_224 -> C.h224\n | SHA2_256 -> C.h256\n | SHA2_384 -> C.h384\n | SHA2_512 -> C.h512", "val h0 (a: sha2_alg) : Tot (words_state a)\nlet h0: a:sha2_alg -> Tot (words_state a) = function\n | SHA2_224 -> C.h224\n | SHA2_256 -> C.h256\n | SHA2_384 -> C.h384\n | SHA2_512 -> C.h512", "val stateful_key_to_buffer (#a: alg) (#kk: key_size a) (key: stateful_key_t a kk)\n : b: B.buffer uint8 {B.length b = kk}\nlet stateful_key_to_buffer (#a : alg) (#kk : key_size a)\n (key : stateful_key_t a kk) :\n b:B.buffer uint8 { B.length b = kk } =\n if kk = 0 then B.null #uint8 else key", "val state_to_lbuffer (#a: alg) (#m: m_spec) (s: Core.state_p a m)\n : B.lbuffer (Core.element_t a m) (4 * U32.v (Core.row_len a m))\nlet state_to_lbuffer (#a : alg) (#m : m_spec) (s : Core.state_p a m) :\n B.lbuffer (Core.element_t a m) (4 * U32.v (Core.row_len a m)) =\n s", "val va_wp_Gctr_blocks128_1way\n (alg: algorithm)\n (in_b out_b: buffer128)\n (old_icb: quad32)\n (old_plain: (seq quad32))\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Gctr_blocks128_1way (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (old_icb:quad32)\n (old_plain:(seq quad32)) (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ ((Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrsOffset128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0)\n in_b (va_get_reg 6 va_s0) (va_get_reg 26 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrsOffset128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0)\n out_b (va_get_reg 6 va_s0) (va_get_reg 26 va_s0) (va_get_mem_layout va_s0) Secret /\\ va_get_reg\n 3 va_s0 + 16 `op_Multiply` va_get_reg 26 va_s0 < pow2_64 /\\ va_get_reg 7 va_s0 + 16\n `op_Multiply` va_get_reg 26 va_s0 < pow2_64 /\\ l_and (Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 in_b == Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 out_b) (Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6 va_s0 + va_get_reg 26 va_s0 ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6 va_s0 +\n va_get_reg 26 va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0)\n (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\\n Vale.AES.GCTR_BE.partial_seq_agreement old_plain (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b)) (va_get_reg 6 va_s0)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b) /\\ va_get_vec 7 va_s0 ==\n Vale.AES.GCTR_BE.inc32lite old_icb (va_get_reg 6 va_s0) /\\ Vale.AES.GCTR_BE.gctr_partial_def\n alg (va_get_reg 6 va_s0) old_plain (Vale.Arch.Types.reverse_bytes_quad32_seq\n (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) key old_icb) /\\ (forall\n (va_x_mem:vale_heap) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_v0:quad32)\n (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v7:quad32) (va_x_cr0:cr0_t)\n (va_x_heap1:vale_heap) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_cr0 va_x_cr0\n (va_upd_vec 7 va_x_v7 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2\n (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_reg 9 va_x_r9 (va_upd_reg 8 va_x_r8\n (va_upd_mem va_x_mem va_s0)))))))))) in va_get_ok va_sM /\\\n (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial_def alg (va_get_reg 6 va_sM + va_get_reg 26 va_sM)\n old_plain (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_sM) out_b)) key old_icb /\\ va_get_vec 7 va_sM ==\n Vale.AES.GCTR_BE.inc32lite old_icb (va_get_reg 6 va_sM + va_get_reg 26 va_sM) /\\ (va_get_reg 6\n va_sM + va_get_reg 26 va_sM == 0 ==> Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b\n == Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) ==> va_k va_sM (())))", "val get_state_p (#a: alg) (#m: m_spec) (s: s a m) : Tot (Core.state_p a m)\nlet get_state_p (#a : alg) (#m : m_spec) (s : s a m) : Tot (Core.state_p a m) =\n match s with _, p -> p", "val update_last\n (#a: sha2_alg)\n (#m: m_spec{is_supported a m})\n (totlen: len_t a)\n (len: nat{len <= block_length a})\n (b: multiseq (lanes a m) len)\n (st: state_spec a m)\n : state_spec a m\nlet update_last (#a:sha2_alg) (#m:m_spec{is_supported a m}) (totlen:len_t a)\n (len:nat{len <= block_length a})\n (b:multiseq (lanes a m) len) (st:state_spec a m): state_spec a m =\n let blocks = padded_blocks a len in\n let fin : nat = blocks * block_length a in\n let total_len_bits = secret (shift_left #(len_int_type a) totlen 3ul) in\n let totlen_seq = Lib.ByteSequence.uint_to_bytes_be #(len_int_type a) total_len_bits in\n let (b0,b1) = load_last #a #m totlen_seq fin len b in\n let st = update b0 st in\n if blocks > 1 then\n update b1 st\n else st", "val va_wp_Gctr_bytes_extra_work\n (alg: algorithm)\n (icb_BE: quad32)\n (in_b out_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n (orig_in_ptr orig_out_ptr: nat64)\n (num_bytes: nat)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Gctr_bytes_extra_work (alg:algorithm) (icb_BE:quad32) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (orig_in_ptr:nat64)\n (orig_out_ptr:nat64) (num_bytes:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) orig_in_ptr\n in_b (Vale.AES.GCM_helpers.bytes_to_quad_size num_bytes) (va_get_mem_layout va_s0) Secret /\\\n Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) orig_out_ptr out_b\n (Vale.AES.GCM_helpers.bytes_to_quad_size num_bytes) (va_get_mem_layout va_s0) Secret /\\\n orig_in_ptr + 16 `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size num_bytes < pow2_64 /\\\n orig_out_ptr + 16 `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size num_bytes < pow2_64 /\\\n l_and (l_and (l_and (Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b ==\n Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 out_b) (Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 out_b == Vale.AES.GCM_helpers.bytes_to_quad_size num_bytes))\n (Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b `op_Multiply` 16 < pow2_32))\n (num_bytes < pow2_32) /\\ (aesni_enabled /\\ sse_enabled) /\\ (alg = AES_128 \\/ alg = AES_256) /\\\n Vale.AES.AES_s.is_aes_key_LE alg key /\\ FStar.Seq.Base.length #quad32 round_keys ==\n Vale.AES.AES_common_s.nr alg + 1 /\\ round_keys == Vale.AES.AES_s.key_to_round_keys_LE alg key\n /\\ va_get_reg64 rR8 va_s0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint128 keys_b\n (va_get_mem_heaplet 0 va_s0) /\\ Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0)\n (va_get_reg64 rR8 va_s0) keys_b (Vale.AES.AES_common_s.nr alg + 1) (va_get_mem_layout va_s0)\n Secret /\\ Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s0) keys_b == round_keys /\\\n (let num_blocks = num_bytes `op_Division` 16 in num_bytes `op_Modulus` 16 =!= 0 /\\ va_get_reg64\n rR9 va_s0 == orig_in_ptr + 16 `op_Multiply` num_blocks /\\ va_get_reg64 rR10 va_s0 ==\n orig_out_ptr + 16 `op_Multiply` num_blocks /\\ Vale.AES.GCTR.gctr_partial_def alg num_blocks\n (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s0) in_b)\n (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 1 va_s0) out_b) key icb_BE /\\ va_get_xmm 7\n va_s0 == Vale.AES.GCTR_s.inc32 icb_BE num_blocks)) /\\ (forall (va_x_mem:vale_heap)\n (va_x_rdx:nat64) (va_x_r12:nat64) (va_x_xmm0:quad32) (va_x_xmm1:quad32) (va_x_xmm2:quad32)\n (va_x_xmm4:quad32) (va_x_heap1:vale_heap) (va_x_efl:Vale.X64.Flags.t) . let va_sM =\n va_upd_flags va_x_efl (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_xmm 4 va_x_xmm4 (va_upd_xmm 2\n va_x_xmm2 (va_upd_xmm 1 va_x_xmm1 (va_upd_xmm 0 va_x_xmm0 (va_upd_reg64 rR12 va_x_r12\n (va_upd_reg64 rRdx va_x_rdx (va_upd_mem va_x_mem va_s0)))))))) in va_get_ok va_sM /\\ (let\n num_blocks = num_bytes `op_Division` 16 in Vale.X64.Decls.modifies_buffer128 out_b\n (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\\ FStar.Seq.Base.slice\n #Vale.X64.Decls.quad32 (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 1 va_sM) out_b) 0\n num_blocks == FStar.Seq.Base.slice #Vale.X64.Decls.quad32 (Vale.X64.Decls.buffer128_as_seq\n (va_get_mem_heaplet 1 va_s0) out_b) 0 num_blocks /\\ Vale.X64.Decls.buffer128_read out_b\n num_blocks (va_get_mem_heaplet 1 va_sM) == Vale.AES.GCTR_s.gctr_encrypt_block icb_BE\n (Vale.X64.Decls.buffer128_read in_b num_blocks (va_get_mem_heaplet 0 va_sM)) alg key num_blocks\n /\\ va_get_xmm 1 va_sM == Vale.X64.Decls.buffer128_read out_b num_blocks (va_get_mem_heaplet 1\n va_sM)) ==> va_k va_sM (())))", "val buffer_to_stateful_key_t\n (a: alg)\n (kk: key_size a {kk > 0})\n (k: B.buffer uint8 {B.length k == kk})\n : Tot (stateful_key_t a kk)\nlet buffer_to_stateful_key_t (a : alg) (kk : key_size a{kk > 0})\n (k : B.buffer uint8 { B.length k == kk }) :\n Tot (stateful_key_t a kk) =\n k", "val va_wp_Gctr_blocks128_6way_body0\n (va_old: va_state)\n (alg: algorithm)\n (va_in_in_b: buffer128)\n (va_in_key: (seq nat32))\n (va_in_keys_b va_in_out_b: buffer128)\n (va_in_plain_quads va_in_round_keys: (seq quad32))\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Gctr_blocks128_6way_body0 (va_old:va_state) (alg:algorithm) (va_in_in_b:buffer128)\n (va_in_key:(seq nat32)) (va_in_keys_b:buffer128) (va_in_out_b:buffer128) (va_in_plain_quads:(seq\n quad32)) (va_in_round_keys:(seq quad32)) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) :\n Type0 =\n (va_get_ok va_s0 /\\ (va_get_reg 6 va_s0 - va_get_reg 8 va_s0) `op_Modulus` 6 == 0 /\\ (0 <=\n va_get_reg 8 va_s0 /\\ va_get_reg 8 va_s0 <= va_get_reg 6 va_s0) /\\ va_get_vec 7 va_s0 ==\n Vale.AES.GCTR_BE.inc32lite (va_get_vec 7 va_old) (va_get_reg 8 va_s0) /\\\n (Vale.PPC64LE.Decls.buffers_disjoint128 va_in_in_b va_in_out_b \\/ va_in_in_b == va_in_out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrsOffset128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0)\n va_in_in_b (va_get_reg 8 va_s0) (va_get_reg 6 va_s0 - va_get_reg 8 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrsOffset128 (va_get_mem_heaplet 1 va_s0)\n (va_get_reg 7 va_s0) va_in_out_b (va_get_reg 8 va_s0) (va_get_reg 6 va_s0 - va_get_reg 8 va_s0)\n (va_get_mem_layout va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` (va_get_reg 6 va_s0 -\n va_get_reg 8 va_s0) < pow2_64 /\\ va_get_reg 7 va_s0 + 16 `op_Multiply` (va_get_reg 6 va_s0 -\n va_get_reg 8 va_s0) < pow2_64 /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128\n va_in_in_b == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 va_in_out_b /\\\n Vale.AES.GCTR_BE.partial_seq_agreement va_in_plain_quads\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n va_in_in_b)) (va_get_reg 8 va_s0) (Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 va_in_in_b) /\\ va_get_reg 6 va_s0 < pow2_32 /\\ aes_reqs alg\n va_in_key va_in_round_keys va_in_keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet 0 va_s0)\n (va_get_mem_layout va_s0) /\\ va_get_vec 8 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 1 0 0 0 /\\ va_get_vec 9 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 2 0 0 0 /\\ va_get_vec 10 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 3 0 0 0 /\\ va_get_vec 11 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 4 0 0 0 /\\ va_get_vec 12 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 5 0 0 0 /\\ va_get_vec 13 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 6 0 0 0 /\\ va_get_reg 27 va_s0 == 1 `op_Multiply` 16 /\\ va_get_reg 28\n va_s0 == 2 `op_Multiply` 16 /\\ va_get_reg 29 va_s0 == 3 `op_Multiply` 16 /\\ va_get_reg 30 va_s0\n == 4 `op_Multiply` 16 /\\ va_get_reg 31 va_s0 == 5 `op_Multiply` 16 /\\\n Vale.PPC64LE.Decls.modifies_buffer128 va_in_out_b (va_get_mem_heaplet 1 va_old)\n (va_get_mem_heaplet 1 va_s0) /\\ Vale.AES.GCTR_BE.gctr_partial_def alg (va_get_reg 8 va_s0)\n va_in_plain_quads (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) va_in_out_b)) va_in_key (va_get_vec 7 va_old) /\\ (va_get_reg 6\n va_s0 == 0 ==> Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0) va_in_out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_old) va_in_out_b) /\\ va_get_reg 3 va_s0 ==\n va_get_reg 3 va_old + 16 `op_Multiply` va_get_reg 8 va_s0 /\\ va_get_reg 7 va_s0 == va_get_reg 7\n va_old + 16 `op_Multiply` va_get_reg 8 va_s0 /\\ va_get_reg 8 va_s0 =!= va_get_reg 6 va_s0 /\\\n (forall (va_x_cr0:cr0_t) (va_x_heap1:vale_heap) (va_x_mem:vale_heap) (va_x_ok:bool)\n (va_x_r10:nat64) (va_x_r3:nat64) (va_x_r7:nat64) (va_x_r8:nat64) (va_x_v0:quad32)\n (va_x_v1:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32) (va_x_v17:quad32)\n (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32)\n (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32) . let va_sM = va_upd_vec 7 va_x_v7\n (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3\n (va_upd_vec 2 va_x_v2 (va_upd_vec 19 va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17\n (va_upd_vec 16 va_x_v16 (va_upd_vec 15 va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 1 va_x_v1\n (va_upd_vec 0 va_x_v0 (va_upd_reg 8 va_x_r8 (va_upd_reg 7 va_x_r7 (va_upd_reg 3 va_x_r3\n (va_upd_reg 10 va_x_r10 (va_upd_ok va_x_ok (va_upd_mem va_x_mem (va_upd_mem_heaplet 1\n va_x_heap1 (va_upd_cr0 va_x_cr0 va_s0))))))))))))))))))))) in va_get_ok va_sM /\\ (va_get_reg 6\n va_sM - va_get_reg 8 va_sM) `op_Modulus` 6 == 0 /\\ (0 <= va_get_reg 8 va_sM /\\ va_get_reg 8\n va_sM <= va_get_reg 6 va_sM) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite (va_get_vec 7\n va_old) (va_get_reg 8 va_sM) /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 va_in_in_b va_in_out_b\n \\/ va_in_in_b == va_in_out_b) /\\ Vale.PPC64LE.Decls.validSrcAddrsOffset128 (va_get_mem_heaplet\n 1 va_sM) (va_get_reg 3 va_sM) va_in_in_b (va_get_reg 8 va_sM) (va_get_reg 6 va_sM - va_get_reg\n 8 va_sM) (va_get_mem_layout va_sM) Secret /\\ Vale.PPC64LE.Decls.validDstAddrsOffset128\n (va_get_mem_heaplet 1 va_sM) (va_get_reg 7 va_sM) va_in_out_b (va_get_reg 8 va_sM) (va_get_reg\n 6 va_sM - va_get_reg 8 va_sM) (va_get_mem_layout va_sM) Secret /\\ va_get_reg 3 va_sM + 16\n `op_Multiply` (va_get_reg 6 va_sM - va_get_reg 8 va_sM) < pow2_64 /\\ va_get_reg 7 va_sM + 16\n `op_Multiply` (va_get_reg 6 va_sM - va_get_reg 8 va_sM) < pow2_64 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 va_in_in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 va_in_out_b /\\\n Vale.AES.GCTR_BE.partial_seq_agreement va_in_plain_quads\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n va_in_in_b)) (va_get_reg 8 va_sM) (Vale.PPC64LE.Decls.buffer_length\n #Vale.PPC64LE.Memory.vuint128 va_in_in_b) /\\ va_get_reg 6 va_sM < pow2_32 /\\ aes_reqs alg\n va_in_key va_in_round_keys va_in_keys_b (va_get_reg 4 va_sM) (va_get_mem_heaplet 0 va_sM)\n (va_get_mem_layout va_sM) /\\ va_get_vec 8 va_sM == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 1 0 0 0 /\\ va_get_vec 9 va_sM == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 2 0 0 0 /\\ va_get_vec 10 va_sM == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 3 0 0 0 /\\ va_get_vec 11 va_sM == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 4 0 0 0 /\\ va_get_vec 12 va_sM == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 5 0 0 0 /\\ va_get_vec 13 va_sM == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 6 0 0 0 /\\ va_get_reg 27 va_sM == 1 `op_Multiply` 16 /\\ va_get_reg 28\n va_sM == 2 `op_Multiply` 16 /\\ va_get_reg 29 va_sM == 3 `op_Multiply` 16 /\\ va_get_reg 30 va_sM\n == 4 `op_Multiply` 16 /\\ va_get_reg 31 va_sM == 5 `op_Multiply` 16 /\\\n Vale.PPC64LE.Decls.modifies_buffer128 va_in_out_b (va_get_mem_heaplet 1 va_old)\n (va_get_mem_heaplet 1 va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial_def alg (va_get_reg 8 va_sM)\n va_in_plain_quads (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_sM) va_in_out_b)) va_in_key (va_get_vec 7 va_old) /\\ (va_get_reg 6\n va_sM == 0 ==> Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) va_in_out_b ==\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_old) va_in_out_b) /\\ va_get_reg 3 va_sM ==\n va_get_reg 3 va_old + 16 `op_Multiply` va_get_reg 8 va_sM /\\ va_get_reg 7 va_sM == va_get_reg 7\n va_old + 16 `op_Multiply` va_get_reg 8 va_sM /\\ precedes_wrap (va_get_reg 6 va_sM - va_get_reg\n 8 va_sM) (va_get_reg 6 va_s0 - va_get_reg 8 va_s0) ==> va_k va_sM (())))", "val g2z: #al:Spec.alg -> #m:m_spec -> wv:state_p al m -> a:index_t -> b:index_t ->\n Stack unit\n (requires (fun h -> live h wv /\\ a <> b))\n (ensures (fun h0 _ h1 -> modifies (loc wv) h0 h1\n /\\ state_v h1 wv == Spec.g2z al (state_v h0 wv) (v a) (v b)))\nlet g2z #al #m wv a b =\n let h0 = ST.get() in\n let wv_a = rowi wv a in\n let wv_b = rowi wv b in\n add_row wv_a wv_b;\n let h1 = ST.get() in\n Lib.Sequence.eq_intro (state_v h1 wv) (Spec.g2z al (state_v h0 wv) (v a) (v b))", "val transpose_state8 (#a: sha2_alg) (#m: m_spec{lanes a m == 8}) (st: state_spec a m)\n : state_spec a m\nlet transpose_state8 (#a:sha2_alg) (#m:m_spec{lanes a m == 8})\n (st:state_spec a m) : state_spec a m =\n let st0 = st.[0] in\n let st1 = st.[1] in\n let st2 = st.[2] in\n let st3 = st.[3] in\n let st4 = st.[4] in\n let st5 = st.[5] in\n let st6 = st.[6] in\n let st7 = st.[7] in\n let (st0,st1,st2,st3,st4,st5,st6,st7) = VecTranspose.transpose8x8 (st0,st1,st2,st3,st4,st5,st6,st7) in\n create8 st0 st1 st2 st3 st4 st5 st6 st7", "val Vale.SHA.PPC64LE.SHA_helpers.ws_opaque_aux = \n a: Spec.Hash.Definitions.sha2_alg ->\n b: Spec.SHA2.block_w a ->\n t: Spec.SHA2.counter{t < Spec.SHA2.size_k_w a}\n -> Spec.Hash.Definitions.word a\nlet ws_opaque_aux = ws", "val va_wp_Fmul\n (tmp_b inA_b dst_b inB_b: buffer64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Fmul (tmp_b:buffer64) (inA_b:buffer64) (dst_b:buffer64) (inB_b:buffer64) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (let (tmp_in:nat64) = va_get_reg64 rRdi va_s0 in let (inA_in:nat64) =\n va_get_reg64 rRsi va_s0 in let (dst_in:nat64) = va_get_reg64 rR15 va_s0 in let (inB_in:nat64) =\n va_get_reg64 rRcx va_s0 in adx_enabled /\\ bmi2_enabled /\\ Vale.X64.Memory.is_initial_heap\n (va_get_mem_layout va_s0) (va_get_mem va_s0) /\\ (Vale.X64.Decls.buffers_disjoint dst_b inA_b \\/\n dst_b == inA_b) /\\ (Vale.X64.Decls.buffers_disjoint dst_b inB_b \\/ dst_b == inB_b) /\\\n (Vale.X64.Decls.buffers_disjoint dst_b tmp_b \\/ dst_b == tmp_b) /\\\n Vale.X64.Decls.buffers_disjoint tmp_b inA_b /\\ Vale.X64.Decls.buffers_disjoint tmp_b inB_b /\\\n Vale.X64.Decls.validDstAddrs64 (va_get_mem va_s0) dst_in dst_b 4 (va_get_mem_layout va_s0)\n Secret /\\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem va_s0) inA_in inA_b 4 (va_get_mem_layout\n va_s0) Secret /\\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem va_s0) inB_in inB_b 4\n (va_get_mem_layout va_s0) Secret /\\ Vale.X64.Decls.validDstAddrs64 (va_get_mem va_s0) tmp_in\n tmp_b 8 (va_get_mem_layout va_s0) Secret) /\\ (forall (va_x_mem:vale_heap) (va_x_rax:nat64)\n (va_x_rbx:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_rdi:nat64) (va_x_rsi:nat64)\n (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r11:nat64) (va_x_r13:nat64)\n (va_x_r14:nat64) (va_x_efl:Vale.X64.Flags.t) (va_x_heap0:vale_heap)\n (va_x_memLayout:vale_heap_layout) . let va_sM = va_upd_mem_layout va_x_memLayout\n (va_upd_mem_heaplet 0 va_x_heap0 (va_upd_flags va_x_efl (va_upd_reg64 rR14 va_x_r14\n (va_upd_reg64 rR13 va_x_r13 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10\n (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRsi va_x_rsi (va_upd_reg64\n rRdi va_x_rdi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRbx\n va_x_rbx (va_upd_reg64 rRax va_x_rax (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok\n va_sM /\\ (let (tmp_in:nat64) = va_get_reg64 rRdi va_s0 in let (inA_in:nat64) = va_get_reg64\n rRsi va_s0 in let (dst_in:nat64) = va_get_reg64 rR15 va_s0 in let (inB_in:nat64) = va_get_reg64\n rRcx va_s0 in let a0 = Vale.X64.Decls.buffer64_read inA_b 0 (va_get_mem va_s0) in let a1 =\n Vale.X64.Decls.buffer64_read inA_b 1 (va_get_mem va_s0) in let a2 =\n Vale.X64.Decls.buffer64_read inA_b 2 (va_get_mem va_s0) in let a3 =\n Vale.X64.Decls.buffer64_read inA_b 3 (va_get_mem va_s0) in let b0 =\n Vale.X64.Decls.buffer64_read inB_b 0 (va_get_mem va_s0) in let b1 =\n Vale.X64.Decls.buffer64_read inB_b 1 (va_get_mem va_s0) in let b2 =\n Vale.X64.Decls.buffer64_read inB_b 2 (va_get_mem va_s0) in let b3 =\n Vale.X64.Decls.buffer64_read inB_b 3 (va_get_mem va_s0) in let d0 =\n Vale.X64.Decls.buffer64_read dst_b 0 (va_get_mem va_sM) in let d1 =\n Vale.X64.Decls.buffer64_read dst_b 1 (va_get_mem va_sM) in let d2 =\n Vale.X64.Decls.buffer64_read dst_b 2 (va_get_mem va_sM) in let d3 =\n Vale.X64.Decls.buffer64_read dst_b 3 (va_get_mem va_sM) in let a =\n Vale.Curve25519.Fast_defs.pow2_four a0 a1 a2 a3 in let b = Vale.Curve25519.Fast_defs.pow2_four\n b0 b1 b2 b3 in let d = Vale.Curve25519.Fast_defs.pow2_four d0 d1 d2 d3 in d `op_Modulus` prime\n == va_mul_nat a b `op_Modulus` prime /\\ Vale.X64.Decls.modifies_buffer_2 dst_b tmp_b\n (va_get_mem va_s0) (va_get_mem va_sM)) ==> va_k va_sM (())))", "val va_wp_Fmul2\n (tmp_b inA_b dst_b inB_b: buffer64)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Fmul2 (tmp_b:buffer64) (inA_b:buffer64) (dst_b:buffer64) (inB_b:buffer64)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (let (tmp_in:nat64) = va_get_reg64 rRdi va_s0 in let (inA_in:nat64) =\n va_get_reg64 rRsi va_s0 in let (dst_in:nat64) = va_get_reg64 rR15 va_s0 in let (inB_in:nat64) =\n va_get_reg64 rRcx va_s0 in adx_enabled /\\ bmi2_enabled /\\ Vale.X64.Memory.is_initial_heap\n (va_get_mem_layout va_s0) (va_get_mem va_s0) /\\ (Vale.X64.Decls.buffers_disjoint dst_b inA_b \\/\n dst_b == inA_b) /\\ (Vale.X64.Decls.buffers_disjoint dst_b inB_b \\/ dst_b == inB_b) /\\\n (Vale.X64.Decls.buffers_disjoint dst_b tmp_b \\/ dst_b == tmp_b) /\\\n Vale.X64.Decls.buffers_disjoint tmp_b inA_b /\\ Vale.X64.Decls.buffers_disjoint tmp_b inB_b /\\\n Vale.X64.Decls.validDstAddrs64 (va_get_mem va_s0) dst_in dst_b 8 (va_get_mem_layout va_s0)\n Secret /\\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem va_s0) inA_in inA_b 8 (va_get_mem_layout\n va_s0) Secret /\\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem va_s0) inB_in inB_b 8\n (va_get_mem_layout va_s0) Secret /\\ Vale.X64.Decls.validDstAddrs64 (va_get_mem va_s0) tmp_in\n tmp_b 16 (va_get_mem_layout va_s0) Secret) /\\ (forall (va_x_mem:vale_heap) (va_x_rax:nat64)\n (va_x_rbx:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_rdi:nat64) (va_x_rsi:nat64)\n (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r11:nat64) (va_x_r13:nat64)\n (va_x_r14:nat64) (va_x_efl:Vale.X64.Flags.t) (va_x_heap0:vale_heap)\n (va_x_memLayout:vale_heap_layout) . let va_sM = va_upd_mem_layout va_x_memLayout\n (va_upd_mem_heaplet 0 va_x_heap0 (va_upd_flags va_x_efl (va_upd_reg64 rR14 va_x_r14\n (va_upd_reg64 rR13 va_x_r13 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10\n (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRsi va_x_rsi (va_upd_reg64\n rRdi va_x_rdi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRbx\n va_x_rbx (va_upd_reg64 rRax va_x_rax (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok\n va_sM /\\ (let (tmp_in:nat64) = va_get_reg64 rRdi va_s0 in let (inA_in:nat64) = va_get_reg64\n rRsi va_s0 in let (dst_in:nat64) = va_get_reg64 rR15 va_s0 in let (inB_in:nat64) = va_get_reg64\n rRcx va_s0 in let a0 = Vale.X64.Decls.buffer64_read inA_b 0 (va_get_mem va_s0) in let a1 =\n Vale.X64.Decls.buffer64_read inA_b 1 (va_get_mem va_s0) in let a2 =\n Vale.X64.Decls.buffer64_read inA_b 2 (va_get_mem va_s0) in let a3 =\n Vale.X64.Decls.buffer64_read inA_b 3 (va_get_mem va_s0) in let b0 =\n Vale.X64.Decls.buffer64_read inB_b 0 (va_get_mem va_s0) in let b1 =\n Vale.X64.Decls.buffer64_read inB_b 1 (va_get_mem va_s0) in let b2 =\n Vale.X64.Decls.buffer64_read inB_b 2 (va_get_mem va_s0) in let b3 =\n Vale.X64.Decls.buffer64_read inB_b 3 (va_get_mem va_s0) in let a =\n Vale.Curve25519.Fast_defs.pow2_four a0 a1 a2 a3 in let b = Vale.Curve25519.Fast_defs.pow2_four\n b0 b1 b2 b3 in let a0' = Vale.X64.Decls.buffer64_read inA_b (0 + 4) (va_get_mem va_s0) in let\n a1' = Vale.X64.Decls.buffer64_read inA_b (1 + 4) (va_get_mem va_s0) in let a2' =\n Vale.X64.Decls.buffer64_read inA_b (2 + 4) (va_get_mem va_s0) in let a3' =\n Vale.X64.Decls.buffer64_read inA_b (3 + 4) (va_get_mem va_s0) in let b0' =\n Vale.X64.Decls.buffer64_read inB_b (0 + 4) (va_get_mem va_s0) in let b1' =\n Vale.X64.Decls.buffer64_read inB_b (1 + 4) (va_get_mem va_s0) in let b2' =\n Vale.X64.Decls.buffer64_read inB_b (2 + 4) (va_get_mem va_s0) in let b3' =\n Vale.X64.Decls.buffer64_read inB_b (3 + 4) (va_get_mem va_s0) in let a' =\n Vale.Curve25519.Fast_defs.pow2_four a0' a1' a2' a3' in let b' =\n Vale.Curve25519.Fast_defs.pow2_four b0' b1' b2' b3' in let d0 = Vale.X64.Decls.buffer64_read\n dst_b 0 (va_get_mem va_sM) in let d1 = Vale.X64.Decls.buffer64_read dst_b 1 (va_get_mem va_sM)\n in let d2 = Vale.X64.Decls.buffer64_read dst_b 2 (va_get_mem va_sM) in let d3 =\n Vale.X64.Decls.buffer64_read dst_b 3 (va_get_mem va_sM) in let d =\n Vale.Curve25519.Fast_defs.pow2_four d0 d1 d2 d3 in let d0' = Vale.X64.Decls.buffer64_read dst_b\n (0 + 4) (va_get_mem va_sM) in let d1' = Vale.X64.Decls.buffer64_read dst_b (1 + 4) (va_get_mem\n va_sM) in let d2' = Vale.X64.Decls.buffer64_read dst_b (2 + 4) (va_get_mem va_sM) in let d3' =\n Vale.X64.Decls.buffer64_read dst_b (3 + 4) (va_get_mem va_sM) in let d' =\n Vale.Curve25519.Fast_defs.pow2_four d0' d1' d2' d3' in d `op_Modulus` prime == va_mul_nat a b\n `op_Modulus` prime /\\ d' `op_Modulus` prime == va_mul_nat a' b' `op_Modulus` prime /\\\n Vale.X64.Decls.modifies_buffer_2 dst_b tmp_b (va_get_mem va_s0) (va_get_mem va_sM)) ==> va_k\n va_sM (())))", "val va_wp_Gctr_core_body0\n (va_old: va_state)\n (alg: algorithm)\n (va_in_block_offset: nat)\n (va_in_in_b: buffer128)\n (va_in_key: (seq nat32))\n (va_in_keys_b: buffer128)\n (va_in_old_iv: quad32)\n (va_in_out_b: buffer128)\n (va_in_round_keys: (seq quad32))\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Gctr_core_body0 (va_old:va_state) (alg:algorithm) (va_in_block_offset:nat)\n (va_in_in_b:buffer128) (va_in_key:(seq nat32)) (va_in_keys_b:buffer128) (va_in_old_iv:quad32)\n (va_in_out_b:buffer128) (va_in_round_keys:(seq quad32)) (va_s0:va_state) (va_k:(va_state -> unit\n -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (0 <= va_get_reg64 rRdx va_s0 /\\ va_get_reg64 rRdx va_s0 <= va_get_reg64 rRcx\n va_s0) /\\ va_get_reg64 rR9 va_s0 == va_get_reg64 rRax va_s0 + 16 `op_Multiply` va_get_reg64\n rRdx va_s0 /\\ va_get_reg64 rR10 va_s0 == va_get_reg64 rRbx va_s0 + 16 `op_Multiply`\n va_get_reg64 rRdx va_s0 /\\ va_get_xmm 7 va_s0 == Vale.AES.GCTR_s.inc32 va_in_old_iv\n (va_in_block_offset + va_get_reg64 rRdx va_s0) /\\ Vale.X64.Decls.validSrcAddrsOffset128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRax va_s0) va_in_in_b va_in_block_offset\n (va_get_reg64 rRcx va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.X64.Decls.validDstAddrsOffset128 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRbx va_s0)\n va_in_out_b va_in_block_offset (va_get_reg64 rRcx va_s0) (va_get_mem_layout va_s0) Secret /\\\n va_get_reg64 rRax va_s0 + 16 `op_Multiply` va_get_reg64 rRcx va_s0 < pow2_64 /\\ va_get_reg64\n rRbx va_s0 + 16 `op_Multiply` va_get_reg64 rRcx va_s0 < pow2_64 /\\ (aesni_enabled /\\\n sse_enabled) /\\ (alg = AES_128 \\/ alg = AES_256) /\\ Vale.AES.AES_s.is_aes_key_LE alg va_in_key\n /\\ FStar.Seq.Base.length #quad32 va_in_round_keys == Vale.AES.AES_common_s.nr alg + 1 /\\\n va_in_round_keys == Vale.AES.AES_s.key_to_round_keys_LE alg va_in_key /\\ va_get_reg64 rR8 va_s0\n == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint128 va_in_keys_b (va_get_mem_heaplet 0\n va_s0) /\\ Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rR8 va_s0)\n va_in_keys_b (Vale.AES.AES_common_s.nr alg + 1) (va_get_mem_layout va_s0) Secret /\\\n Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s0) va_in_keys_b == va_in_round_keys\n /\\ va_get_xmm 8 va_s0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 202182159 134810123\n 67438087 66051 /\\ va_get_xmm 4 va_s0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0\n /\\ Vale.X64.Decls.modifies_buffer128 va_in_out_b (va_get_mem_heaplet 1 va_old)\n (va_get_mem_heaplet 1 va_s0) /\\ Vale.AES.GCTR.gctr_partial_def alg (va_in_block_offset +\n va_get_reg64 rRdx va_s0) (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s0)\n va_in_in_b) (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 1 va_s0) va_in_out_b)\n va_in_key va_in_old_iv /\\ va_get_reg64 rRdx va_s0 =!= va_get_reg64 rRcx va_s0 /\\ (forall\n (va_x_efl:Vale.X64.Flags.t) (va_x_heap1:vale_heap) (va_x_mem:vale_heap) (va_x_ok:bool)\n (va_x_r10:nat64) (va_x_r9:nat64) (va_x_rdx:nat64) (va_x_xmm0:quad32) (va_x_xmm2:quad32)\n (va_x_xmm7:quad32) . let va_sM = va_upd_xmm 7 va_x_xmm7 (va_upd_xmm 2 va_x_xmm2 (va_upd_xmm 0\n va_x_xmm0 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR10 va_x_r10\n (va_upd_ok va_x_ok (va_upd_mem va_x_mem (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags va_x_efl\n va_s0))))))))) in va_get_ok va_sM /\\ (0 <= va_get_reg64 rRdx va_sM /\\ va_get_reg64 rRdx va_sM\n <= va_get_reg64 rRcx va_sM) /\\ va_get_reg64 rR9 va_sM == va_get_reg64 rRax va_sM + 16\n `op_Multiply` va_get_reg64 rRdx va_sM /\\ va_get_reg64 rR10 va_sM == va_get_reg64 rRbx va_sM +\n 16 `op_Multiply` va_get_reg64 rRdx va_sM /\\ va_get_xmm 7 va_sM == Vale.AES.GCTR_s.inc32\n va_in_old_iv (va_in_block_offset + va_get_reg64 rRdx va_sM) /\\\n Vale.X64.Decls.validSrcAddrsOffset128 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRax va_sM)\n va_in_in_b va_in_block_offset (va_get_reg64 rRcx va_sM) (va_get_mem_layout va_sM) Secret /\\\n Vale.X64.Decls.validDstAddrsOffset128 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRbx va_sM)\n va_in_out_b va_in_block_offset (va_get_reg64 rRcx va_sM) (va_get_mem_layout va_sM) Secret /\\\n va_get_reg64 rRax va_sM + 16 `op_Multiply` va_get_reg64 rRcx va_sM < pow2_64 /\\ va_get_reg64\n rRbx va_sM + 16 `op_Multiply` va_get_reg64 rRcx va_sM < pow2_64 /\\ (aesni_enabled /\\\n sse_enabled) /\\ (alg = AES_128 \\/ alg = AES_256) /\\ Vale.AES.AES_s.is_aes_key_LE alg va_in_key\n /\\ FStar.Seq.Base.length #quad32 va_in_round_keys == Vale.AES.AES_common_s.nr alg + 1 /\\\n va_in_round_keys == Vale.AES.AES_s.key_to_round_keys_LE alg va_in_key /\\ va_get_reg64 rR8 va_sM\n == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint128 va_in_keys_b (va_get_mem_heaplet 0\n va_sM) /\\ Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rR8 va_sM)\n va_in_keys_b (Vale.AES.AES_common_s.nr alg + 1) (va_get_mem_layout va_sM) Secret /\\\n Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_sM) va_in_keys_b == va_in_round_keys\n /\\ va_get_xmm 8 va_sM == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 202182159 134810123\n 67438087 66051 /\\ va_get_xmm 4 va_sM == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0\n /\\ Vale.X64.Decls.modifies_buffer128 va_in_out_b (va_get_mem_heaplet 1 va_old)\n (va_get_mem_heaplet 1 va_sM) /\\ Vale.AES.GCTR.gctr_partial_def alg (va_in_block_offset +\n va_get_reg64 rRdx va_sM) (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_sM)\n va_in_in_b) (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 1 va_sM) va_in_out_b)\n va_in_key va_in_old_iv /\\ precedes_wrap (va_get_reg64 rRcx va_sM - va_get_reg64 rRdx va_sM)\n (va_get_reg64 rRcx va_s0 - va_get_reg64 rRdx va_s0) ==> va_k va_sM (())))", "val update_last\n (a: sha2_alg)\n (totlen: len_t a)\n (len: nat{len <= block_length a})\n (b: bytes{S.length b = len})\n (hash: words_state a)\n : Tot (words_state a)\nlet update_last (a:sha2_alg) (totlen:len_t a)\n (len:nat{len <= block_length a})\n (b:bytes{S.length b = len}) (hash:words_state a) : Tot (words_state a) =\n let blocks = padded_blocks a len in\n let fin = blocks * block_length a in\n let total_len_bits = secret (shift_left #(len_int_type a) totlen 3ul) in\n let totlen_seq = Lib.ByteSequence.uint_to_bytes_be #(len_int_type a) total_len_bits in\n let (b0, b1) = load_last a totlen_seq fin len b in\n let hash = update a b0 hash in\n if blocks > 1 then update a b1 hash else hash", "val coerce (#b #a: Type) (x: a{a == b}) : b\nlet coerce (#b #a:Type) (x:a{a == b}) : b = x", "val coerce (#b #a: Type) (x: a{a == b}) : b\nlet coerce (#b #a:Type) (x:a{a == b}) : b = x", "val coerce (#b #a: Type) (x: a{a == b}) : b\nlet coerce (#b #a:Type) (x:a{a == b}) : b = x", "val coerce (#b #a: Type) (x: a{a == b}) : b\nlet coerce (#b #a:Type) (x:a{a == b}) : b = x", "val coerce (#b #a: Type) (x: a{a == b}) : b\nlet coerce (#b #a:Type) (x:a{a == b}) : b = x", "val coerce (#b #a: Type) (x: a{a == b}) : b\nlet coerce (#b #a:Type) (x:a{a == b}) : b = x", "val coerce (#b #a: Type) (x: a{a == b}) : b\nlet coerce (#b #a:Type) (x:a{a == b}) : b = x", "val coerce (#b #a: Type) (x: a{a == b}) : b\nlet coerce (#b #a:Type) (x:a{a == b}) : b = x", "val coerce (#b #a: Type) (x: a{a == b}) : b\nlet coerce (#b #a:Type) (x:a{a == b}) : b = x", "val coerce (#b #a: Type) (x: a{a == b}) : b\nlet coerce (#b #a:Type) (x:a{a == b}) : b = x", "val coerce (#b #a: Type) (x: a{a == b}) : b\nlet coerce (#b #a:Type) (x:a{a == b}) : b = x", "val stateful_key (a: alg) (kk: key_size a) : I.stateful unit\nlet stateful_key (a : alg) (kk : key_size a) :\n I.stateful unit =\n I.Stateful\n (fun _ -> stateful_key_t a kk)\n (* footprint *)\n (fun #_ h s -> if kk = 0 then B.loc_none else B.loc_addr_of_buffer (s <: B.buffer uint8))\n (* freeable *)\n (fun #_ h s -> if kk = 0 then True else B.freeable (s <: B.buffer uint8))\n (* invariant *)\n (fun #_ h s ->\n if kk = 0 then True\n else B.live h (s <: B.buffer uint8))\n (fun _ -> s:S.seq uint8 { S.length s == kk })\n (fun _ h s -> if kk = 0 then Seq.empty else B.as_seq h (s <: B.buffer uint8))\n (fun #_ h s -> ()) (* invariant_loc_in_footprint *)\n (fun #_ l s h0 h1 -> ()) (* frame_invariant *)\n (fun #_ l s h0 h1 -> ()) (* frame_freeable *)\n\n (* alloca *)\n (fun () ->\n if kk > 0 then\n buffer_to_stateful_key_t a kk (B.alloca (Lib.IntTypes.u8 0) (U32.uint_to_t kk))\n else unit_to_stateful_key_t a)\n\n (* create_in *)\n (fun () r ->\n if kk > 0 then\n buffer_to_stateful_key_t a kk (B.malloc r (Lib.IntTypes.u8 0) (U32.uint_to_t kk))\n else unit_to_stateful_key_t a)\n\n (* free *)\n (fun _ s -> if kk > 0 then B.free (s <: B.buffer uint8) else ())\n\n (* copy *)\n (fun _ s_src s_dst ->\n if kk > 0 then\n B.blit (s_src <: B.buffer uint8) 0ul\n (s_dst <: B.buffer uint8) 0ul (U32.uint_to_t kk)\n else ())", "val alloca: a:supported_alg -> StackInline (state a)\n (requires fun _ -> True)\n (ensures fun h0 st h1 ->\n B.modifies B.loc_none h0 h1 /\\\n B.fresh_loc (footprint st) h0 h1 /\\\n B.(loc_includes (loc_region_only true (HS.get_tip h1)) (footprint st)) /\\\n invariant st h1)\nlet alloca a =\n let k =\n match a with\n | SHA1 -> create (hash_len SHA1) (u8 0)\n | SHA2_256 -> create (hash_len SHA2_256) (u8 0)\n | SHA2_384 -> create (hash_len SHA2_384) (u8 0)\n | SHA2_512 -> create (hash_len SHA2_512) (u8 0)\n in\n let v =\n match a with\n | SHA1 -> create (hash_len SHA1) (u8 0)\n | SHA2_256 -> create (hash_len SHA2_256) (u8 0)\n | SHA2_384 -> create (hash_len SHA2_384) (u8 0)\n | SHA2_512 -> create (hash_len SHA2_512) (u8 0)\n in\n let ctr = create 1ul 1ul in\n State k v ctr", "val alloc_state: a:Spec.alg -> m:m_spec ->\n\t StackInline (state_p a m)\n\t (requires (fun h -> True))\n\t (ensures (fun h0 r h1 -> stack_allocated r h0 h1 (Lib.Sequence.create (4 * v (row_len a m)) (zero_element a m)) /\\\n\t\t\t\tlive h1 r))\nlet alloc_state a m =\n // See git blame below. I never managed to get the previous expression (4ul *.\n // row_len a m) to reduce, which generated VLAs in the C code.\n create (le_sigh a m) (zero_element a m)", "val lemma_shift_update_last:\n a:alg\n -> rem: nat\n -> b:block_s a\n -> d:bytes{length d + (size_block a) <= max_limb a /\\ rem <= length d /\\ rem <= size_block a}\n -> s:state a ->\n Lemma (\n blake2_update_last a 0 rem (b `Seq.append` d) s ==\n blake2_update_last a (size_block a) rem d s\n )\nlet lemma_shift_update_last a rem b d s =\n let m = b `Seq.append` d in\n assert (Seq.slice m (length m - rem) (length m) `Seq.equal` Seq.slice d (length d - rem) (length d));\n assert (get_last_padded_block a (b `Seq.append` d) rem == get_last_padded_block a d rem)", "val alg_of_state: a:e_alg -> (\n let a = G.reveal a in\n s: state a -> Stack alg\n (fun h0 -> invariant h0 s)\n (fun h0 a' h1 -> h0 == h1 /\\ a' == a))\nlet alg_of_state _ s =\n let State i _ _ _ _ _ _ = !*s in\n cipher_alg_of_impl i", "val be_bytes_to_nat32 (b: seq4 nat8) : nat32\nlet be_bytes_to_nat32 (b:seq4 nat8) : nat32 =\n four_to_nat 8 (seq_to_four_BE b)", "val va_wp_Sha_update_bytes\n (ctx_b in_b k_b: buffer128)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Sha_update_bytes (ctx_b:buffer128) (in_b:buffer128) (k_b:buffer128) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (sha_enabled /\\ sse_enabled /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0) in_b (4 `op_Multiply` va_get_reg64 rRdx\n va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet\n 0 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 2 (va_get_mem_layout va_s0) Secret /\\\n Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRcx va_s0) k_b 16\n (va_get_mem_layout va_s0) Secret /\\ va_get_reg64 rRsi va_s0 + 64 `op_Multiply` va_get_reg64\n rRdx va_s0 < pow2_64 /\\ Vale.X64.Decls.buffers_disjoint128 ctx_b in_b /\\\n Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 ctx_b == 2 /\\\n Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b == 4 `op_Multiply` va_get_reg64\n rRdx va_s0 /\\ Vale.SHA.SHA_helpers.k_reqs (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet\n 0 va_s0) k_b)) /\\ (forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64)\n (va_x_rax:nat64) (va_x_xmm0:quad32) (va_x_xmm1:quad32) (va_x_xmm2:quad32) (va_x_xmm3:quad32)\n (va_x_xmm4:quad32) (va_x_xmm5:quad32) (va_x_xmm6:quad32) (va_x_xmm7:quad32) (va_x_xmm8:quad32)\n (va_x_xmm9:quad32) (va_x_xmm10:quad32) (va_x_heap0:vale_heap) (va_x_efl:Vale.X64.Flags.t) . let\n va_sM = va_upd_flags va_x_efl (va_upd_mem_heaplet 0 va_x_heap0 (va_upd_xmm 10 va_x_xmm10\n (va_upd_xmm 9 va_x_xmm9 (va_upd_xmm 8 va_x_xmm8 (va_upd_xmm 7 va_x_xmm7 (va_upd_xmm 6 va_x_xmm6\n (va_upd_xmm 5 va_x_xmm5 (va_upd_xmm 4 va_x_xmm4 (va_upd_xmm 3 va_x_xmm3 (va_upd_xmm 2 va_x_xmm2\n (va_upd_xmm 1 va_x_xmm1 (va_upd_xmm 0 va_x_xmm0 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRdx\n va_x_rdx (va_upd_reg64 rRsi va_x_rsi (va_upd_mem va_x_mem va_s0)))))))))))))))) in va_get_ok\n va_sM /\\ (va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + 64 `op_Multiply` va_get_reg64\n rRdx va_s0 /\\ (let hash_in = Vale.SHA.SHA_helpers.le_bytes_to_hash\n (Vale.Def.Types_s.le_seq_quad32_to_bytes (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0\n va_s0) ctx_b)) in let hash_out = Vale.SHA.SHA_helpers.le_bytes_to_hash\n (Vale.Def.Types_s.le_seq_quad32_to_bytes (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0\n va_sM) ctx_b)) in (let input_LE = Vale.Def.Words.Seq_s.seq_nat8_to_seq_uint8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes (Vale.X64.Decls.buffer128_as_seq (va_get_mem_heaplet 0\n va_sM) in_b)) in l_and (FStar.Seq.Base.length #FStar.UInt8.t input_LE `op_Modulus` 64 == 0)\n (hash_out == Vale.SHA.SHA_helpers.update_multi_opaque_vale hash_in input_LE)) /\\\n Vale.X64.Decls.modifies_buffer128 ctx_b (va_get_mem_heaplet 0 va_s0) (va_get_mem_heaplet 0\n va_sM))) ==> va_k va_sM (())))", "val va_wp_Sha_update_bytes\n (ctx_b in_b k_b: buffer128)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Sha_update_bytes (ctx_b:buffer128) (in_b:buffer128) (k_b:buffer128) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg\n 4 va_s0) in_b (4 `op_Multiply` va_get_reg 5 va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 3 va_s0) ctx_b 2\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 0\n va_s0) (va_get_reg 6 va_s0) k_b 16 (va_get_mem_layout va_s0) Secret /\\\n Vale.PPC64LE.Decls.validSrcAddrsOffset128 (va_get_mem_heaplet 0 va_s0) (va_get_reg 6 va_s0) k_b\n 13 3 (va_get_mem_layout va_s0) Secret /\\ va_get_reg 4 va_s0 + 64 `op_Multiply` va_get_reg 5\n va_s0 < pow2_64 /\\ va_get_reg 6 va_s0 + 256 < pow2_64 /\\ Vale.PPC64LE.Decls.buffers_disjoint128\n ctx_b in_b /\\ Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 ctx_b == 2 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b == 4 `op_Multiply`\n va_get_reg 5 va_s0 /\\ Vale.SHA.PPC64LE.SHA_helpers.k_reqs (Vale.PPC64LE.Decls.buffer128_as_seq\n (va_get_mem_heaplet 0 va_s0) k_b)) /\\ (forall (va_x_mem:vale_heap) (va_x_r4:nat64)\n (va_x_r5:nat64) (va_x_r6:nat64) (va_x_r10:nat64) (va_x_cr0:cr0_t) (va_x_v0:quad32)\n (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32)\n (va_x_v6:quad32) (va_x_v7:quad32) (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32)\n (va_x_v11:quad32) (va_x_v12:quad32) (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32)\n (va_x_v16:quad32) (va_x_v17:quad32) (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32)\n (va_x_v21:quad32) (va_x_v22:quad32) (va_x_v23:quad32) (va_x_v24:quad32) (va_x_v25:quad32)\n (va_x_v26:quad32) (va_x_v28:quad32) (va_x_v29:quad32) (va_x_v30:quad32) (va_x_v31:quad32)\n (va_x_heap0:vale_heap) (va_x_memLayout:vale_heap_layout) . let va_sM = va_upd_mem_layout\n va_x_memLayout (va_upd_mem_heaplet 0 va_x_heap0 (va_upd_vec 31 va_x_v31 (va_upd_vec 30 va_x_v30\n (va_upd_vec 29 va_x_v29 (va_upd_vec 28 va_x_v28 (va_upd_vec 26 va_x_v26 (va_upd_vec 25 va_x_v25\n (va_upd_vec 24 va_x_v24 (va_upd_vec 23 va_x_v23 (va_upd_vec 22 va_x_v22 (va_upd_vec 21 va_x_v21\n (va_upd_vec 20 va_x_v20 (va_upd_vec 19 va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17\n (va_upd_vec 16 va_x_v16 (va_upd_vec 15 va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13 va_x_v13\n (va_upd_vec 12 va_x_v12 (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9\n (va_upd_vec 8 va_x_v8 (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5\n (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1\n (va_upd_vec 0 va_x_v0 (va_upd_cr0 va_x_cr0 (va_upd_reg 10 va_x_r10 (va_upd_reg 6 va_x_r6\n (va_upd_reg 5 va_x_r5 (va_upd_reg 4 va_x_r4 (va_upd_mem va_x_mem\n va_s0)))))))))))))))))))))))))))))))))))))) in va_get_ok va_sM /\\ (va_get_reg 4 va_sM ==\n va_get_reg 4 va_s0 + 64 `op_Multiply` va_get_reg 5 va_s0 /\\ (let hash_in =\n Vale.SHA.PPC64LE.SHA_helpers.le_bytes_to_hash (Vale.Def.Types_s.le_seq_quad32_to_bytes\n (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s0) ctx_b)) in let hash_out =\n Vale.SHA.PPC64LE.SHA_helpers.le_bytes_to_hash (Vale.Def.Types_s.le_seq_quad32_to_bytes\n (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_sM) ctx_b)) in (let input_LE =\n Vale.Def.Words.Seq_s.seq_nat8_to_seq_uint8 (Vale.Def.Types_s.le_seq_quad32_to_bytes\n (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_sM) in_b)) in l_and\n (FStar.Seq.Base.length #FStar.UInt8.t input_LE `op_Modulus` 64 == 0) (hash_out ==\n Vale.SHA.PPC64LE.SHA_helpers.update_multi_opaque_vale hash_in input_LE)) /\\\n Vale.PPC64LE.Decls.modifies_buffer128 ctx_b (va_get_mem_heaplet 0 va_s0) (va_get_mem_heaplet 0\n va_sM))) ==> va_k va_sM (())))", "val moffset (#a:Type0) (#rrel #rel:srel a) (sub_rel:srel a) (b:mbuffer a rrel rel)\n (i:U32.t)\n :HST.Stack (mbuffer a rrel sub_rel)\n (requires (fun h -> U32.v i <= length b /\\ compatible_sub b i (U32.sub (len b) i) sub_rel /\\ live h b))\n (ensures (fun h y h' -> h == h' /\\ y == mgsub sub_rel b i (U32.sub (len b) i)))\nlet moffset #a #rrel #rel sub_rel b i =\n match b with\n | Null -> Null\n | Buffer max_len content i0 len ->\n Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i)))", "val finish_md (a: md_alg) (hashw: words_state a) : Tot (bytes_hash a)\nlet finish_md (a:md_alg) (hashw:words_state a): Tot (bytes_hash a) =\n let hash_final_w = S.slice hashw 0 (hash_word_length a) in\n bytes_of_words a #(hash_word_length a) hash_final_w", "val blake2_compress0:\n a:alg\n -> m:block_s a\n -> block_w a\nlet blake2_compress0 a m =\n uints_from_bytes_le m", "val store_state (#a: sha2_alg) (#m: m_spec{is_supported a m}) (st: state_spec a m)\n : lseq uint8 (lanes a m * 8 * word_length a)\nlet store_state (#a:sha2_alg) (#m:m_spec{is_supported a m}) (st:state_spec a m) :\n lseq uint8 (lanes a m * 8 * word_length a) =\n let st = transpose_state st in\n Lib.IntVector.Serialize.vecs_to_bytes_be st", "val uint32_to_uint8 : a:U32.t -> Tot (b:U8.t{U8.v b = U32.v a % pow2 8})\nlet uint32_to_uint8 x = U8.uint_to_t (U32.v x % pow2 8)", "val alloca: a:supported_alg -> StackInline (state a)\n (requires fun _ -> True)\n (ensures fun h0 st h1 ->\n B.modifies B.loc_none h0 h1 /\\\n B.fresh_loc (footprint st h1) h0 h1 /\\\n B.(loc_includes (loc_region_only true (HS.get_tip h1)) (footprint st h1)) /\\\n invariant st h1)\nlet alloca a =\n let st =\n match a with\n | SHA1 -> SHA1_s (alloca a)\n | SHA2_256 -> SHA2_256_s (alloca a)\n | SHA2_384 -> SHA2_384_s (alloca a)\n | SHA2_512 -> SHA2_512_s (alloca a)\n in\n B.alloca st 1ul", "val va_quick_ReduceMul128_LE (a b: poly) : (va_quickCode unit (va_code_ReduceMul128_LE ()))\nlet va_quick_ReduceMul128_LE (a:poly) (b:poly) : (va_quickCode unit (va_code_ReduceMul128_LE ())) =\n (va_QProc (va_code_ReduceMul128_LE ()) ([va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3;\n va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_reg64 rR12; va_Mod_flags]) (va_wp_ReduceMul128_LE a b)\n (va_wpProof_ReduceMul128_LE a b))", "val load_last_blocks\n (#a: sha2_alg)\n (totlen_seq: lseq uint8 (len_length a))\n (fin: nat{fin == block_length a \\/ fin == 2 * block_length a})\n (len: nat{len <= block_length a})\n (b: lseq uint8 len)\n : lseq uint8 (block_length a) & lseq uint8 (block_length a)\nlet load_last_blocks (#a:sha2_alg)\n (totlen_seq:lseq uint8 (len_length a))\n (fin:nat{fin == block_length a \\/ fin == 2 * block_length a})\n (len:nat{len <= block_length a})\n (b:lseq uint8 len) :\n lseq uint8 (block_length a) & lseq uint8 (block_length a) =\n let last = create (2 * block_length a) (u8 0) in\n let last = update_sub last 0 len b in\n let last = last.[len] <- u8 0x80 in\n let last = update_sub last (fin - len_length a) (len_length a) totlen_seq in\n let l0 : lseq uint8 (block_length a) = sub last 0 (block_length a) in\n let l1 : lseq uint8 (block_length a) = sub last (block_length a) (block_length a) in\n (l0, l1)", "val va_wp_Gctr_blocks128_6way_body\n (alg: algorithm)\n (in_b out_b: buffer128)\n (old_icb: quad32)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n (plain_quads: (seq quad32))\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Gctr_blocks128_6way_body (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (old_icb:quad32) (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (plain_quads:(seq\n quad32)) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (va_get_reg 8 va_s0 + 5 < va_get_reg 6 va_s0 /\\\n Vale.PPC64LE.Decls.validSrcAddrsOffset128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0)\n in_b (va_get_reg 8 va_s0) (va_get_reg 6 va_s0 - va_get_reg 8 va_s0) (va_get_mem_layout va_s0)\n Secret /\\ Vale.PPC64LE.Decls.validDstAddrsOffset128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 7\n va_s0) out_b (va_get_reg 8 va_s0) (va_get_reg 6 va_s0 - va_get_reg 8 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 6 `op_Multiply` 16 < pow2_64 /\\ va_get_reg 7 va_s0 + 6\n `op_Multiply` 16 < pow2_64 /\\ (Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b ==\n out_b) /\\ Vale.AES.GCTR_BE.partial_seq_agreement plain_quads\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (va_get_reg 8 va_s0) (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128\n in_b) /\\ Vale.AES.GCTR_BE.gctr_partial_def alg (va_get_reg 8 va_s0) plain_quads\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n out_b)) key old_icb /\\ va_get_reg 6 va_s0 < pow2_32 /\\ va_get_vec 7 va_s0 ==\n Vale.AES.GCTR_BE.inc32lite old_icb (va_get_reg 8 va_s0) /\\ va_get_vec 8 va_s0 ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 /\\ va_get_vec 9 va_s0 ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 2 0 0 0 /\\ va_get_vec 10 va_s0 ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 3 0 0 0 /\\ va_get_vec 11 va_s0 ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 4 0 0 0 /\\ va_get_vec 12 va_s0 ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 5 0 0 0 /\\ va_get_vec 13 va_s0 ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 6 0 0 0 /\\ va_get_reg 27 va_s0 == 1\n `op_Multiply` 16 /\\ va_get_reg 28 va_s0 == 2 `op_Multiply` 16 /\\ va_get_reg 29 va_s0 == 3\n `op_Multiply` 16 /\\ va_get_reg 30 va_s0 == 4 `op_Multiply` 16 /\\ va_get_reg 31 va_s0 == 5\n `op_Multiply` 16 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0)) /\\ (forall (va_x_mem:vale_heap) (va_x_r3:nat64)\n (va_x_r7:nat64) (va_x_r8:nat64) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32)\n (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32)\n (va_x_v7:quad32) (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32) (va_x_v17:quad32)\n (va_x_v18:quad32) (va_x_v19:quad32) (va_x_heap1:vale_heap) . let va_sM = va_upd_mem_heaplet 1\n va_x_heap1 (va_upd_vec 19 va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec\n 16 va_x_v16 (va_upd_vec 15 va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 7 va_x_v7 (va_upd_vec 6\n va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2\n (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_reg 8 va_x_r8\n (va_upd_reg 7 va_x_r7 (va_upd_reg 3 va_x_r3 (va_upd_mem va_x_mem va_s0))))))))))))))))))) in\n va_get_ok va_sM /\\ (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0)\n (va_get_mem_heaplet 1 va_sM) /\\ Vale.AES.GCTR_BE.partial_seq_agreement plain_quads\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n in_b)) (va_get_reg 8 va_sM) (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128\n in_b) /\\ Vale.AES.GCTR_BE.gctr_partial_def alg (va_get_reg 8 va_sM) plain_quads\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n out_b)) key old_icb /\\ va_get_reg 8 va_sM == va_get_reg 8 va_s0 + 6 /\\ va_get_reg 3 va_sM ==\n va_get_reg 3 va_s0 + 16 `op_Multiply` 6 /\\ va_get_reg 7 va_sM == va_get_reg 7 va_s0 + 16\n `op_Multiply` 6 /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite old_icb (va_get_reg 8\n va_sM)) ==> va_k va_sM (())))", "val va_wp_Gctr_blocks128_body0\n (va_old: va_state)\n (alg: algorithm)\n (va_in_in_b: buffer128)\n (va_in_key: (seq nat32))\n (va_in_keys_b va_in_out_b: buffer128)\n (va_in_plain_quads va_in_round_keys: (seq quad32))\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Gctr_blocks128_body0 (va_old:va_state) (alg:algorithm) (va_in_in_b:buffer128)\n (va_in_key:(seq nat32)) (va_in_keys_b:buffer128) (va_in_out_b:buffer128) (va_in_plain_quads:(seq\n quad32)) (va_in_round_keys:(seq quad32)) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) :\n Type0 =\n (va_get_ok va_s0 /\\ sse_enabled /\\ (0 <= va_get_reg64 rRbx va_s0 /\\ va_get_reg64 rRbx va_s0 <=\n va_get_reg64 rRdx va_s0) /\\ va_get_reg64 rR11 va_s0 == va_get_reg64 rRax va_s0 + 16\n `op_Multiply` va_get_reg64 rRbx va_s0 /\\ va_get_reg64 rR10 va_s0 == va_get_reg64 rRdi va_s0 +\n 16 `op_Multiply` va_get_reg64 rRbx va_s0 /\\ va_get_xmm 11 va_s0 == Vale.AES.GCTR.inc32lite\n (va_get_xmm 11 va_old) (va_get_reg64 rRbx va_s0) /\\ (Vale.X64.Decls.buffers_disjoint128\n va_in_in_b va_in_out_b \\/ va_in_in_b == va_in_out_b) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRax va_s0) va_in_in_b (va_get_reg64 rRdx va_s0)\n (va_get_mem_layout va_s0) Secret /\\ Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 1\n va_s0) (va_get_reg64 rRdi va_s0) va_in_out_b (va_get_reg64 rRdx va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg64 rRax va_s0 + 16 `op_Multiply` va_get_reg64 rRdx va_s0 < pow2_64\n /\\ va_get_reg64 rRdi va_s0 + 16 `op_Multiply` va_get_reg64 rRdx va_s0 < pow2_64 /\\\n Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 va_in_in_b ==\n Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 va_in_out_b /\\ (va_get_reg64 rRbx va_s0\n =!= va_get_reg64 rRdx va_s0 ==> Vale.AES.GCTR.partial_seq_agreement va_in_plain_quads\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s0) va_in_in_b) (va_get_reg64 rRbx va_s0)\n (Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 va_in_in_b)) /\\ va_get_reg64 rRdx va_s0\n < pow2_32 /\\ aes_reqs alg va_in_key va_in_round_keys va_in_keys_b (va_get_reg64 rR8 va_s0)\n (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\ pclmulqdq_enabled /\\ va_get_xmm 9\n va_s0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\\n va_get_xmm 10 va_s0 == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 /\\\n Vale.X64.Decls.modifies_buffer128 va_in_out_b (va_get_mem_heaplet 1 va_old) (va_get_mem_heaplet\n 1 va_s0) /\\ Vale.AES.GCTR.gctr_partial_def alg (va_get_reg64 rRbx va_s0) va_in_plain_quads\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s0) va_in_out_b) va_in_key (va_get_xmm 11 va_old)\n /\\ (va_get_reg64 rRdx va_s0 == 0 ==> Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n va_in_out_b == Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_old) va_in_out_b) /\\ va_get_reg64\n rRbx va_s0 =!= va_get_reg64 rRdx va_s0 /\\ (forall (va_x_efl:Vale.X64.Flags.t)\n (va_x_heap1:vale_heap) (va_x_mem:vale_heap) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r11:nat64)\n (va_x_rbx:nat64) (va_x_xmm0:quad32) (va_x_xmm11:quad32) (va_x_xmm2:quad32) . let va_sM =\n va_upd_xmm 2 va_x_xmm2 (va_upd_xmm 11 va_x_xmm11 (va_upd_xmm 0 va_x_xmm0 (va_upd_reg64 rRbx\n va_x_rbx (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_mem\n va_x_mem (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags va_x_efl va_s0))))))))) in va_get_ok\n va_sM /\\ sse_enabled /\\ (0 <= va_get_reg64 rRbx va_sM /\\ va_get_reg64 rRbx va_sM <=\n va_get_reg64 rRdx va_sM) /\\ va_get_reg64 rR11 va_sM == va_get_reg64 rRax va_sM + 16\n `op_Multiply` va_get_reg64 rRbx va_sM /\\ va_get_reg64 rR10 va_sM == va_get_reg64 rRdi va_sM +\n 16 `op_Multiply` va_get_reg64 rRbx va_sM /\\ va_get_xmm 11 va_sM == Vale.AES.GCTR.inc32lite\n (va_get_xmm 11 va_old) (va_get_reg64 rRbx va_sM) /\\ (Vale.X64.Decls.buffers_disjoint128\n va_in_in_b va_in_out_b \\/ va_in_in_b == va_in_out_b) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRax va_sM) va_in_in_b (va_get_reg64 rRdx va_sM)\n (va_get_mem_layout va_sM) Secret /\\ Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 1\n va_sM) (va_get_reg64 rRdi va_sM) va_in_out_b (va_get_reg64 rRdx va_sM) (va_get_mem_layout\n va_sM) Secret /\\ va_get_reg64 rRax va_sM + 16 `op_Multiply` va_get_reg64 rRdx va_sM < pow2_64\n /\\ va_get_reg64 rRdi va_sM + 16 `op_Multiply` va_get_reg64 rRdx va_sM < pow2_64 /\\\n Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 va_in_in_b ==\n Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 va_in_out_b /\\ (va_get_reg64 rRbx va_sM\n =!= va_get_reg64 rRdx va_sM ==> Vale.AES.GCTR.partial_seq_agreement va_in_plain_quads\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_sM) va_in_in_b) (va_get_reg64 rRbx va_sM)\n (Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 va_in_in_b)) /\\ va_get_reg64 rRdx va_sM\n < pow2_32 /\\ aes_reqs alg va_in_key va_in_round_keys va_in_keys_b (va_get_reg64 rR8 va_sM)\n (va_get_mem_heaplet 0 va_sM) (va_get_mem_layout va_sM) /\\ pclmulqdq_enabled /\\ va_get_xmm 9\n va_sM == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\\n va_get_xmm 10 va_sM == Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 1 0 0 0 /\\\n Vale.X64.Decls.modifies_buffer128 va_in_out_b (va_get_mem_heaplet 1 va_old) (va_get_mem_heaplet\n 1 va_sM) /\\ Vale.AES.GCTR.gctr_partial_def alg (va_get_reg64 rRbx va_sM) va_in_plain_quads\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_sM) va_in_out_b) va_in_key (va_get_xmm 11 va_old)\n /\\ (va_get_reg64 rRdx va_sM == 0 ==> Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_sM)\n va_in_out_b == Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_old) va_in_out_b) /\\ precedes_wrap\n (va_get_reg64 rRdx va_sM - va_get_reg64 rRbx va_sM) (va_get_reg64 rRdx va_s0 - va_get_reg64\n rRbx va_s0) ==> va_k va_sM (())))", "val update (a: sha2_alg) (block: block_t a) (hash: words_state a) : Tot (words_state a)\nlet update (a:sha2_alg) (block:block_t a) (hash:words_state a): Tot (words_state a) =\n let block_w = Lib.ByteSequence.uints_from_bytes_be #(word_t a) #SEC #(block_word_length a) block in\n let hash_1 = shuffle a block_w hash in\n map2 #_ #_ #_ #8 ( +. ) hash_1 hash", "val load_last\n (a: sha2_alg)\n (totlen_seq: lseq uint8 (len_length a))\n (fin: nat{fin == block_length a \\/ fin == 2 * block_length a})\n (len: nat{len <= block_length a})\n (b: bytes{S.length b = len})\n : (block_t a & block_t a)\nlet load_last (a:sha2_alg) (totlen_seq:lseq uint8 (len_length a))\n (fin:nat{fin == block_length a \\/ fin == 2 * block_length a})\n (len:nat{len <= block_length a}) (b:bytes{S.length b = len}) :\n (block_t a & block_t a)\n =\n let last = create (2 * block_length a) (u8 0) in\n let last = update_sub last 0 len b in\n let last = last.[len] <- u8 0x80 in\n let last = update_sub last (fin - len_length a) (len_length a) totlen_seq in\n let b0 = sub last 0 (block_length a) in\n let b1 = sub last (block_length a) (block_length a) in\n (b0, b1)", "val coerce (#[@@@ erasable]a #[@@@ erasable]b: Type) ([@@@ erasable]pf: squash (a == b)) (x: a) : b\nlet coerce (#[@@@erasable]a:Type)\r\n (#[@@@erasable]b:Type)\r\n ( [@@@erasable]pf:squash (a == b))\r\n (x:a) \r\n : b \r\n = x", "val squeeze:\n a:G.erased alg -> (\n let c = hacl_keccak a in\n let a = G.reveal a in\n let i = a in\n let t = sha3_state a in\n let t' = G.erased unit in\n s:state c i t t' ->\n dst:B.buffer uint8 ->\n l:Lib.IntTypes.size_t ->\n Stack error_code\n (requires fun h0 ->\n (is_shake a ==> B.length dst == Lib.IntTypes.v l) /\\\n invariant c i h0 s /\\\n B.live h0 dst /\\\n B.(loc_disjoint (loc_buffer dst) (footprint c i h0 s)))\n (ensures fun h0 r h1 ->\n let _ = allow_inversion error_code in\n match r with\n | Success ->\n is_shake a /\\\n l <> 0ul /\\\n invariant c i h1 s /\\\n seen c i h0 s == seen c i h1 s /\\\n reveal_key c i h1 s == reveal_key c i h0 s /\\\n footprint c i h0 s == footprint c i h1 s /\\\n B.(modifies (loc_union (loc_buffer dst) (footprint c i h0 s)) h0 h1) /\\ (\n seen_bounded c i h0 s;\n S.equal (B.as_seq h1 dst) (c.spec_s i (reveal_key c i h0 s) (seen c i h0 s) l)) /\\\n preserves_freeable c i s h0 h1\n | InvalidAlgorithm ->\n not (is_shake a)\n | InvalidLength ->\n l = 0ul\n | _ ->\n False))\nlet squeeze a s dst l =\n let a = get_alg a s in\n if not (a = Shake128 || a = Shake256) then\n InvalidAlgorithm\n else if l = 0ul then\n InvalidLength\n else begin\n digest_ a s dst l;\n Success\n end", "val va_wp_Sha_update_bytes_main\n (ctx_b in_b: buffer128)\n (num_val: nat64)\n (k_b: buffer128)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Sha_update_bytes_main (ctx_b:buffer128) (in_b:buffer128) (num_val:nat64) (k_b:buffer128)\n (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (va_get_reg 1 va_s0 == Vale.PPC64LE.Stack_i.init_r1 (va_get_stack va_s0) /\\\n Vale.PPC64LE.Memory.is_initial_heap (va_get_mem_layout va_s0) (va_get_mem va_s0) /\\ l_or\n (Vale.PPC64LE.Decls.locs_disjoint ([Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128\n ctx_b; Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 in_b])) (ctx_b == in_b) /\\\n l_or (Vale.PPC64LE.Decls.locs_disjoint ([Vale.PPC64LE.Decls.loc_buffer\n #Vale.PPC64LE.Memory.vuint128 ctx_b; Vale.PPC64LE.Decls.loc_buffer\n #Vale.PPC64LE.Memory.vuint128 k_b])) (ctx_b == k_b) /\\ l_or (Vale.PPC64LE.Decls.locs_disjoint\n ([Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 in_b;\n Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 k_b])) (in_b == k_b) /\\\n Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0) (va_get_reg 3 va_s0) ctx_b 2\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0)\n (va_get_reg 4 va_s0) in_b (4 `op_Multiply` va_get_reg 5 va_s0) (va_get_mem_layout va_s0) Secret\n /\\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) (va_get_reg 6 va_s0) k_b 16\n (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validSrcAddrsOffset128 (va_get_mem\n va_s0) (va_get_reg 6 va_s0) k_b 13 3 (va_get_mem_layout va_s0) Secret /\\ num_val == va_get_reg\n 5 va_s0 /\\ va_get_reg 4 va_s0 + 64 `op_Multiply` va_get_reg 5 va_s0 < pow2_64 /\\ va_get_reg 6\n va_s0 + 256 < pow2_64 /\\ Vale.PPC64LE.Decls.buffers_disjoint128 ctx_b in_b /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 ctx_b == 2 /\\\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b == 4 `op_Multiply`\n va_get_reg 5 va_s0 /\\ Vale.SHA.PPC64LE.SHA_helpers.k_reqs (Vale.PPC64LE.Decls.buffer128_as_seq\n (va_get_mem va_s0) k_b)) /\\ (forall (va_x_mem:vale_heap) (va_x_r1:nat64) (va_x_r4:nat64)\n (va_x_r5:nat64) (va_x_r6:nat64) (va_x_r10:nat64) (va_x_cr0:cr0_t) (va_x_v0:quad32)\n (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32)\n (va_x_v6:quad32) (va_x_v7:quad32) (va_x_v8:quad32) (va_x_v9:quad32) (va_x_v10:quad32)\n (va_x_v11:quad32) (va_x_v12:quad32) (va_x_v13:quad32) (va_x_v14:quad32) (va_x_v15:quad32)\n (va_x_v16:quad32) (va_x_v17:quad32) (va_x_v18:quad32) (va_x_v19:quad32) (va_x_v20:quad32)\n (va_x_v21:quad32) (va_x_v22:quad32) (va_x_v23:quad32) (va_x_v24:quad32) (va_x_v25:quad32)\n (va_x_v26:quad32) (va_x_v28:quad32) (va_x_v29:quad32) (va_x_v30:quad32) (va_x_v31:quad32)\n (va_x_heap0:vale_heap) (va_x_memLayout:vale_heap_layout) (va_x_stack:vale_stack)\n (va_x_stackTaint:memtaint) . let va_sM = va_upd_stackTaint va_x_stackTaint (va_upd_stack\n va_x_stack (va_upd_mem_layout va_x_memLayout (va_upd_mem_heaplet 0 va_x_heap0 (va_upd_vec 31\n va_x_v31 (va_upd_vec 30 va_x_v30 (va_upd_vec 29 va_x_v29 (va_upd_vec 28 va_x_v28 (va_upd_vec 26\n va_x_v26 (va_upd_vec 25 va_x_v25 (va_upd_vec 24 va_x_v24 (va_upd_vec 23 va_x_v23 (va_upd_vec 22\n va_x_v22 (va_upd_vec 21 va_x_v21 (va_upd_vec 20 va_x_v20 (va_upd_vec 19 va_x_v19 (va_upd_vec 18\n va_x_v18 (va_upd_vec 17 va_x_v17 (va_upd_vec 16 va_x_v16 (va_upd_vec 15 va_x_v15 (va_upd_vec 14\n va_x_v14 (va_upd_vec 13 va_x_v13 (va_upd_vec 12 va_x_v12 (va_upd_vec 11 va_x_v11 (va_upd_vec 10\n va_x_v10 (va_upd_vec 9 va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7 va_x_v7 (va_upd_vec 6\n va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2\n (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_cr0 va_x_cr0 (va_upd_reg 10 va_x_r10\n (va_upd_reg 6 va_x_r6 (va_upd_reg 5 va_x_r5 (va_upd_reg 4 va_x_r4 (va_upd_reg 1 va_x_r1\n (va_upd_mem va_x_mem va_s0))))))))))))))))))))))))))))))))))))))))) in va_get_ok va_sM /\\ (let\n hash_in = Vale.SHA.PPC64LE.SHA_helpers.le_bytes_to_hash\n (Vale.Def.Types_s.le_seq_quad32_to_bytes (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem\n va_s0) ctx_b)) in let hash_out = Vale.SHA.PPC64LE.SHA_helpers.le_bytes_to_hash\n (Vale.Def.Types_s.le_seq_quad32_to_bytes (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem\n va_sM) ctx_b)) in (let input_LE = Vale.Def.Words.Seq_s.seq_nat8_to_seq_uint8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem\n va_sM) in_b)) in l_and (FStar.Seq.Base.length #FStar.UInt8.t input_LE `op_Modulus` 64 == 0)\n (hash_out == Vale.SHA.PPC64LE.SHA_helpers.update_multi_transparent hash_in input_LE)) /\\\n Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128\n ctx_b) (va_get_mem va_s0) (va_get_mem va_sM) /\\ va_get_reg 1 va_sM == va_get_reg 1 va_s0 /\\\n l_and (l_and (l_and (l_and (l_and (l_and (l_and (l_and (l_and (l_and (va_get_vec 20 va_sM ==\n va_get_vec 20 va_s0) (va_get_vec 21 va_sM == va_get_vec 21 va_s0)) (va_get_vec 22 va_sM ==\n va_get_vec 22 va_s0)) (va_get_vec 23 va_sM == va_get_vec 23 va_s0)) (va_get_vec 24 va_sM ==\n va_get_vec 24 va_s0)) (va_get_vec 25 va_sM == va_get_vec 25 va_s0)) (va_get_vec 26 va_sM ==\n va_get_vec 26 va_s0)) (va_get_vec 28 va_sM == va_get_vec 28 va_s0)) (va_get_vec 29 va_sM ==\n va_get_vec 29 va_s0)) (va_get_vec 30 va_sM == va_get_vec 30 va_s0)) (va_get_vec 31 va_sM ==\n va_get_vec 31 va_s0)) ==> va_k va_sM (())))", "val va_wp_Gctr_blocks128\n (alg: algorithm)\n (in_b out_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Gctr_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_get_ok va_s0 /\\ (sse_enabled /\\ (Vale.X64.Decls.buffers_disjoint128 in_b out_b \\/ in_b ==\n out_b) /\\ Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRax\n va_s0) in_b (va_get_reg64 rRdx va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) out_b\n (va_get_reg64 rRdx va_s0) (va_get_mem_layout va_s0) Secret /\\ va_get_reg64 rRax va_s0 + 16\n `op_Multiply` va_get_reg64 rRdx va_s0 < pow2_64 /\\ va_get_reg64 rRdi va_s0 + 16 `op_Multiply`\n va_get_reg64 rRdx va_s0 < pow2_64 /\\ l_and (Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 in_b == Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 out_b)\n (Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg64 rRdx\n va_s0 == Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b /\\ va_get_xmm 9 va_s0 ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\\n va_get_reg64 rRdx va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg64 rR8\n va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\ pclmulqdq_enabled) /\\ (forall\n (va_x_mem:vale_heap) (va_x_rbx:nat64) (va_x_r11:nat64) (va_x_r10:nat64) (va_x_xmm0:quad32)\n (va_x_xmm1:quad32) (va_x_xmm2:quad32) (va_x_xmm3:quad32) (va_x_xmm4:quad32) (va_x_xmm5:quad32)\n (va_x_xmm6:quad32) (va_x_xmm11:quad32) (va_x_xmm10:quad32) (va_x_heap1:vale_heap)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_mem_heaplet 1\n va_x_heap1 (va_upd_xmm 10 va_x_xmm10 (va_upd_xmm 11 va_x_xmm11 (va_upd_xmm 6 va_x_xmm6\n (va_upd_xmm 5 va_x_xmm5 (va_upd_xmm 4 va_x_xmm4 (va_upd_xmm 3 va_x_xmm3 (va_upd_xmm 2 va_x_xmm2\n (va_upd_xmm 1 va_x_xmm1 (va_upd_xmm 0 va_x_xmm0 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR11\n va_x_r11 (va_upd_reg64 rRbx va_x_rbx (va_upd_mem va_x_mem va_s0)))))))))))))) in va_get_ok\n va_sM /\\ (Vale.X64.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0)\n (va_get_mem_heaplet 1 va_sM) /\\ Vale.AES.GCTR.gctr_partial alg (va_get_reg64 rRdx va_sM)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_sM) out_b) key (va_get_xmm 11 va_s0) /\\ va_get_xmm 11 va_sM ==\n Vale.AES.GCTR.inc32lite (va_get_xmm 11 va_s0) (va_get_reg64 rRdx va_s0) /\\ (va_get_reg64 rRdx\n va_sM == 0 ==> Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b == Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s0) out_b)) ==> va_k va_sM (())))", "val va_wp_Gctr_blocks128\n (alg: algorithm)\n (in_b out_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b: buffer128)\n (va_s0: va_state)\n (va_k: (va_state -> unit -> Type0))\n : Type0\nlet va_wp_Gctr_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_get_ok va_s0 /\\ ((Vale.PPC64LE.Decls.buffers_disjoint128 in_b out_b \\/ in_b == out_b) /\\\n Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) in_b\n (va_get_reg 6 va_s0) (va_get_mem_layout va_s0) Secret /\\ Vale.PPC64LE.Decls.validDstAddrs128\n (va_get_mem_heaplet 1 va_s0) (va_get_reg 7 va_s0) out_b (va_get_reg 6 va_s0) (va_get_mem_layout\n va_s0) Secret /\\ va_get_reg 3 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\\n va_get_reg 7 va_s0 + 16 `op_Multiply` va_get_reg 6 va_s0 < pow2_64 /\\ l_and\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b ==\n Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 out_b)\n (Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg 6\n va_s0 == Vale.PPC64LE.Decls.buffer_length #Vale.PPC64LE.Memory.vuint128 in_b /\\ va_get_reg 6\n va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg 4 va_s0) (va_get_mem_heaplet\n 0 va_s0) (va_get_mem_layout va_s0)) /\\ (forall (va_x_mem:vale_heap) (va_x_r3:nat64)\n (va_x_r7:nat64) (va_x_r6:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64)\n (va_x_r26:nat64) (va_x_r27:nat64) (va_x_r28:nat64) (va_x_r29:nat64) (va_x_r30:nat64)\n (va_x_r31:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32)\n (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) (va_x_v7:quad32) (va_x_v8:quad32)\n (va_x_v9:quad32) (va_x_v10:quad32) (va_x_v11:quad32) (va_x_v12:quad32) (va_x_v13:quad32)\n (va_x_v14:quad32) (va_x_v15:quad32) (va_x_v16:quad32) (va_x_v17:quad32) (va_x_v18:quad32)\n (va_x_v19:quad32) (va_x_cr0:cr0_t) (va_x_heap1:vale_heap) . let va_sM = va_upd_mem_heaplet 1\n va_x_heap1 (va_upd_cr0 va_x_cr0 (va_upd_vec 19 va_x_v19 (va_upd_vec 18 va_x_v18 (va_upd_vec 17\n va_x_v17 (va_upd_vec 16 va_x_v16 (va_upd_vec 15 va_x_v15 (va_upd_vec 14 va_x_v14 (va_upd_vec 13\n va_x_v13 (va_upd_vec 12 va_x_v12 (va_upd_vec 11 va_x_v11 (va_upd_vec 10 va_x_v10 (va_upd_vec 9\n va_x_v9 (va_upd_vec 8 va_x_v8 (va_upd_vec 7 va_x_v7 (va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5\n (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1\n (va_upd_vec 0 va_x_v0 (va_upd_reg 31 va_x_r31 (va_upd_reg 30 va_x_r30 (va_upd_reg 29 va_x_r29\n (va_upd_reg 28 va_x_r28 (va_upd_reg 27 va_x_r27 (va_upd_reg 26 va_x_r26 (va_upd_reg 10 va_x_r10\n (va_upd_reg 9 va_x_r9 (va_upd_reg 8 va_x_r8 (va_upd_reg 6 va_x_r6 (va_upd_reg 7 va_x_r7\n (va_upd_reg 3 va_x_r3 (va_upd_mem va_x_mem va_s0)))))))))))))))))))))))))))))))))) in va_get_ok\n va_sM /\\ (Vale.PPC64LE.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0)\n (va_get_mem_heaplet 1 va_sM) /\\ Vale.AES.GCTR_BE.gctr_partial alg (va_get_reg 6 va_s0)\n (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s0)\n in_b)) (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1\n va_sM) out_b)) key (va_get_vec 7 va_s0) /\\ va_get_vec 7 va_sM == Vale.AES.GCTR_BE.inc32lite\n (va_get_vec 7 va_s0) (va_get_reg 6 va_s0) /\\ (va_get_reg 6 va_s0 == 0 ==>\n Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b == Vale.PPC64LE.Decls.s128\n (va_get_mem_heaplet 1 va_s0) out_b) /\\ l_and (l_and (va_get_reg 3 va_sM == va_get_reg 3 va_s0)\n (va_get_reg 7 va_sM == va_get_reg 7 va_s0)) (va_get_reg 6 va_sM == va_get_reg 6 va_s0)) ==>\n va_k va_sM (())))" ], "closest_src": [ { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.blake2_compress2" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.update" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.blake2_compress3" }, { "project_name": "hacl-star", "file_name": "Spec.Hash.Definitions.fst", "name": "Spec.Hash.Definitions.words_of_bytes" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.SHA2.Generic.fst", "name": "Hacl.Impl.SHA2.Generic.alloc" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.fst", "name": "Hacl.Spec.SHA2.init" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Salsa20.Core32.fst", "name": "Hacl.Impl.Salsa20.Core32.load_state" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Chacha20.Core32.fst", "name": "Hacl.Impl.Chacha20.Core32.load_state" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.gather_state" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.update_nblocks" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.fst", "name": "Hacl.Spec.SHA2.store_state" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.Hash.fsti", "name": "Spec.Agile.Hash.init_extra_state" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.blake2_compress" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.fst", "name": "Hacl.Spec.SHA2.update_nblocks" }, { "project_name": "hacl-star", "file_name": "EverCrypt.Hash.Incremental.fst", "name": "EverCrypt.Hash.Incremental.extra_state_of_nat" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.blake2_update" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.SHA2.Core.fst", "name": "Hacl.Impl.SHA2.Core.store_state" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.update_block" }, { "project_name": "FStar", "file_name": "RW.fst", "name": "RW.coerce" }, { "project_name": "FStar", "file_name": "LatticeEff.fst", "name": "LatticeEff.coerce" }, { "project_name": "FStar", "file_name": "GTWP.fst", "name": "GTWP.coerce" }, { "project_name": "FStar", "file_name": "LatticeSpec.fst", "name": "LatticeSpec.coerce" }, { "project_name": "FStar", "file_name": "Lattice.fst", "name": "Lattice.coerce" }, { "project_name": "FStar", "file_name": "GT.fst", "name": "GT.coerce" }, { "project_name": "FStar", "file_name": "RunST.fst", "name": "RunST.coerce" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Salsa20.Core32.fst", "name": "Hacl.Impl.Salsa20.Core32.store_state" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Chacha20.Core32.fst", "name": "Hacl.Impl.Chacha20.Core32.store_state" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.init" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_wp_Gctr_blocks128_1way_body0" }, { "project_name": "hacl-star", "file_name": "Hacl.Hash.Definitions.fst", "name": "Hacl.Hash.Definitions.extra_state" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.Definitions.fst", "name": "Spec.Blake2.Definitions.state" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.transpose_state" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.blake2_round" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fst", "name": "Vale.AES.X64.GCTR.va_wp_Gctr_bytes" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.fst", "name": "Hacl.Spec.SHA2.update_block" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.blake2_compress1" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.state_spec_v" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.Alternative.fst", "name": "Spec.Blake2.Alternative.repeati_update1" }, { "project_name": "FStar", "file_name": "LowStar.Endianness.fst", "name": "LowStar.Endianness.upd_32_be" }, { "project_name": "hacl-star", "file_name": "Vale.Interop.Base.fst", "name": "Vale.Interop.Base.coerce" }, { "project_name": "FStar", "file_name": "InjectiveTypeFormers.Explicit.fst", "name": "InjectiveTypeFormers.Explicit.coerce" }, { "project_name": "steel", "file_name": "Steel.ST.Printf.fst", "name": "Steel.ST.Printf.coerce" }, { "project_name": "FStar", "file_name": "LowStar.Printf.fst", "name": "LowStar.Printf.coerce" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fsti", "name": "Vale.AES.X64.GCTR.va_wp_Gctr_bytes_no_extra" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Machine_Semantics_s.fst", "name": "Vale.X64.Machine_Semantics_s.state_or_fail" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.Alternative.fsti", "name": "Spec.Blake2.Alternative.blake2_update'" }, { "project_name": "hacl-star", "file_name": "Hacl.SHA2.Scalar32.Lemmas.fst", "name": "Hacl.SHA2.Scalar32.Lemmas.state_spec_v_extensionality" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.fst", "name": "Hacl.Spec.SHA2.h0" }, { "project_name": "hacl-star", "file_name": "Spec.SHA2.fst", "name": "Spec.SHA2.h0" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2.Common.fst", "name": "Hacl.Streaming.Blake2.Common.stateful_key_to_buffer" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2.Common.fst", "name": "Hacl.Streaming.Blake2.Common.state_to_lbuffer" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_wp_Gctr_blocks128_1way" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2.Common.fst", "name": "Hacl.Streaming.Blake2.Common.get_state_p" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.update_last" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fsti", "name": "Vale.AES.X64.GCTR.va_wp_Gctr_bytes_extra_work" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2.Common.fst", "name": "Hacl.Streaming.Blake2.Common.buffer_to_stateful_key_t" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_wp_Gctr_blocks128_6way_body0" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Blake2.Generic.fst", "name": "Hacl.Impl.Blake2.Generic.g2z" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.transpose_state8" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.SHA_helpers.fst", "name": "Vale.SHA.PPC64LE.SHA_helpers.ws_opaque_aux" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fsti", "name": "Vale.Curve25519.X64.FastWide.va_wp_Fmul" }, { "project_name": "hacl-star", "file_name": "Vale.Curve25519.X64.FastWide.fsti", "name": "Vale.Curve25519.X64.FastWide.va_wp_Fmul2" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCTR.fst", "name": "Vale.AES.X64.GCTR.va_wp_Gctr_core_body0" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.fst", "name": "Hacl.Spec.SHA2.update_last" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Keccak.fst", "name": "Hacl.Streaming.Keccak.coerce" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.State.fsti", "name": "Vale.PPC64LE.State.coerce" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Memory_Sems.fsti", "name": "Vale.X64.Memory_Sems.coerce" }, { "project_name": "hacl-star", "file_name": "Vale.Arch.HeapLemmas.fsti", "name": "Vale.Arch.HeapLemmas.coerce" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Memory_Sems.fsti", "name": "Vale.PPC64LE.Memory_Sems.coerce" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.Hash.fst", "name": "Spec.Agile.Hash.coerce" }, { "project_name": "hacl-star", "file_name": "Vale.X64.StateLemmas.fsti", "name": "Vale.X64.StateLemmas.coerce" }, { "project_name": "hacl-star", "file_name": "Vale.PPC64LE.Decls.fsti", "name": "Vale.PPC64LE.Decls.coerce" }, { "project_name": "hacl-star", "file_name": "Hacl.SHA2.Scalar32.fst", "name": "Hacl.SHA2.Scalar32.coerce" }, { "project_name": "hacl-star", "file_name": "Vale.X64.MemoryAdapters.fsti", "name": "Vale.X64.MemoryAdapters.coerce" }, { "project_name": "hacl-star", "file_name": "Vale.X64.Instruction_s.fsti", "name": "Vale.X64.Instruction_s.coerce" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Blake2.Common.fst", "name": "Hacl.Streaming.Blake2.Common.stateful_key" }, { "project_name": "hacl-star", "file_name": "Hacl.HMAC_DRBG.fst", "name": "Hacl.HMAC_DRBG.alloca" }, { "project_name": "hacl-star", "file_name": "Hacl.Impl.Blake2.Core.fst", "name": "Hacl.Impl.Blake2.Core.alloc_state" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.Alternative.fst", "name": "Spec.Blake2.Alternative.lemma_shift_update_last" }, { "project_name": "everquic-crypto", "file_name": "NotEverCrypt.CTR.fst", "name": "NotEverCrypt.CTR.alg_of_state" }, { "project_name": "hacl-star", "file_name": "Vale.Def.Types_s.fst", "name": "Vale.Def.Types_s.be_bytes_to_nat32" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.X64.fst", "name": "Vale.SHA.X64.va_wp_Sha_update_bytes" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.fst", "name": "Vale.SHA.PPC64LE.va_wp_Sha_update_bytes" }, { "project_name": "FStar", "file_name": "LowStar.Monotonic.Buffer.fst", "name": "LowStar.Monotonic.Buffer.moffset" }, { "project_name": "hacl-star", "file_name": "Spec.Agile.Hash.fst", "name": "Spec.Agile.Hash.finish_md" }, { "project_name": "hacl-star", "file_name": "Spec.Blake2.fst", "name": "Spec.Blake2.blake2_compress0" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.store_state" }, { "project_name": "FStar", "file_name": "FStar.Int.Cast.fst", "name": "FStar.Int.Cast.uint32_to_uint8" }, { "project_name": "hacl-star", "file_name": "EverCrypt.DRBG.fst", "name": "EverCrypt.DRBG.alloca" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GHash.fst", "name": "Vale.AES.X64.GHash.va_quick_ReduceMul128_LE" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.Vec.fst", "name": "Hacl.Spec.SHA2.Vec.load_last_blocks" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fst", "name": "Vale.AES.PPC64LE.GCTR.va_wp_Gctr_blocks128_6way_body" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fst", "name": "Vale.AES.X64.GCMencryptOpt.va_wp_Gctr_blocks128_body0" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.fst", "name": "Hacl.Spec.SHA2.update" }, { "project_name": "hacl-star", "file_name": "Hacl.Spec.SHA2.fst", "name": "Hacl.Spec.SHA2.load_last" }, { "project_name": "everparse", "file_name": "EverParse3d.Interpreter.fst", "name": "EverParse3d.Interpreter.coerce" }, { "project_name": "hacl-star", "file_name": "Hacl.Streaming.Keccak.fst", "name": "Hacl.Streaming.Keccak.squeeze" }, { "project_name": "hacl-star", "file_name": "Vale.SHA.PPC64LE.fsti", "name": "Vale.SHA.PPC64LE.va_wp_Sha_update_bytes_main" }, { "project_name": "hacl-star", "file_name": "Vale.AES.X64.GCMencryptOpt.fsti", "name": "Vale.AES.X64.GCMencryptOpt.va_wp_Gctr_blocks128" }, { "project_name": "hacl-star", "file_name": "Vale.AES.PPC64LE.GCTR.fsti", "name": "Vale.AES.PPC64LE.GCTR.va_wp_Gctr_blocks128" } ], "selected_premises": [ "Spec.SHA2.ws_pre_", "Hacl.Spec.SHA2.Vec.lanes", "Hacl.Hash.SHA2.mb_state_32", "Hacl.Impl.SHA2.Core.state_t", "Hacl.Spec.SHA2.Vec.is_supported", "Hacl.Spec.SHA2.k0", "Spec.SHA2.k0", "Spec.SHA2.op0", "Hacl.Spec.SHA2.op0", "Hacl.Spec.SHA2.Vec.state_spec", "Hacl.Hash.SHA2.coerce_to_state", "Hacl.SHA2.Scalar32.init", "Hacl.Hash.Definitions.m_spec", "Hacl.Impl.SHA2.Generic.update_nblocks_vec_t'", "Lib.Sequence.lseq", "Hacl.Spec.SHA2._Sigma1", "Spec.SHA2._Sigma1", "Lib.Sequence.to_seq", "Lib.NTuple.ntuple", "Spec.Hash.Definitions.hash_length", "Hacl.Spec.SHA2.Vec.element_t", "Hacl.Spec.SHA2._sigma1", "Spec.SHA2._sigma1", "Hacl.Spec.SHA2.Vec.ws_spec", "Hacl.Impl.SHA2.Core.ws_t", "Lib.IntTypes.uint_t", "Hacl.SHA2.Scalar32.Lemmas.lemma_spec_update_224_256", "Spec.Hash.MD.max_input_size_len", "LowStar.Buffer.trivial_preorder", "Lib.IntTypes.int_t", "Hacl.Hash.Definitions.as_seq", "Hacl.Spec.SHA2.Vec.state_spec_v", "Lib.Buffer.lbuffer", "Hacl.Spec.SHA2.Vec.init", "Lib.Buffer.lbuffer_t", "Hacl.SHA2.Scalar32.Lemmas.lemma_spec_update_384_512", "Hacl.SHA2.Scalar32.sha384_finish", "Lib.MultiBuffer.as_seq_multi", "Lib.Sequence.op_String_Access", "Lib.NTuple.flen", "Spec.SHA2.counter", "Lib.MultiBuffer.multibuf", "Lib.IntTypes.range", "FStar.Seq.Properties.seq_of_list", "Hacl.SHA2.Scalar32.sha224_finish", "FStar.Seq.Properties.tail", "Lib.Buffer.gsub", "Lib.IntTypes.size", "LowStar.Monotonic.Buffer.length", "Lib.Sequence.length", "Lib.MultiBuffer.live_multi", "Hacl.Spec.SHA2.Vec.words_state'", "FStar.Seq.Properties.head", "Hacl.SHA2.Scalar32.Lemmas.state_spec_v_extensionality", "Lib.Buffer.as_seq", "Hacl.Spec.SHA2.Equiv.finish_lemma_l", "Spec.Hash.Definitions.word_t", "Spec.Hash.Definitions.words_state", "Lib.NTuple.ntuple_", "FStar.Seq.Properties.cons", "Hacl.Spec.SHA2.Equiv.init_lemma_l", "Lib.NTuple.ntup8", "Hacl.Hash.Definitions.mk_impl", "Hacl.Spec.SHA2.ws_next", "Lib.Buffer.op_Array_Assignment", "Spec.SHA2._sigma0", "Hacl.Spec.SHA2._sigma0", "Lib.IntVector.width", "Spec.Hash.Definitions.word", "Spec.Agile.Hash.update_multi", "Spec.SHA2.Constants.k384_512", "FStar.Seq.Properties.snoc", "Hacl.Impl.SHA2.Generic.alloc", "Lib.Buffer.op_Array_Access", "FStar.List.Tot.Base.length", "Hacl.Hash.Definitions.prev_len_v", "Hacl.Impl.SHA2.Generic.mk_len_t_from_size_t", "Hacl.Spec.SHA2.Vec.ws_next", "FStar.UInt.size", "Lib.Sequence.op_String_Assignment", "Lib.MultiBuffer.multiseq", "Lib.NTuple.ntup4", "Hacl.Spec.SHA2.Vec.word", "FStar.Seq.Properties.last", "Spec.SHA2._Sigma0", "Hacl.Spec.SHA2._Sigma0", "Lib.NTuple.op_Lens_Access", "Lib.MultiBuffer.op_Lens_Access", "FStar.Mul.op_Star", "FStar.List.Tot.Base.map", "Hacl.SHA2.Scalar32.coerce", "Spec.Agile.Hash.coerce", "Hacl.Spec.SHA2._Ch", "Spec.SHA2._Ch", "Spec.Hash.Definitions.rate", "Lib.NTuple.ntup1", "Hacl.Spec.SHA2.Vec.multiseq", "FStar.Seq.Properties.split", "Hacl.SHA2.Scalar32.sha384_init", "Hacl.SHA2.Scalar32.sha256_finish" ], "source_upto_this": "module Hacl.Hash.SHA2\n\nmodule ST = FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\n\nmodule B = LowStar.Buffer\n\nopen Hacl.Hash.Definitions\nopen Spec.Hash.Definitions\n\nopen Lib.MultiBuffer\nopen Lib.NTuple\n\nmodule Vec = Hacl.Spec.SHA2.Vec\n\n// To prove we are properly defining init\nfriend Spec.Agile.Hash\n// To prove we are properly defining update_last\nfriend Spec.Hash.Incremental\n// To know the definition of init\nfriend Spec.SHA2\n\n#set-options \"--fuel 0 --ifuel 0 --z3rlimit 100\"\n\ninline_for_extraction noextract\nlet mb_state_32 a = Hacl.Impl.SHA2.Core.state_t a Hacl.Spec.SHA2.Vec.M32\n\n#push-options \"--ifuel 1\"\n\ninline_for_extraction noextract\nlet coerce_to_state (a:sha2_alg) (b:mb_state_32 a) : state (| a, () |)\n = Lib.IntVector.reveal_vec_1 (word_t a);\n b\n\ninline_for_extraction noextract", "sketch": [ "Step 1: The definition `coerce_to_mb_state` is about converting a state of type `state (| a, () |)` to a multi-buffer state of type `mb_state_32 a`.\nStep 2: The implementation will use the `Lib.IntVector.reveal_vec_1` function to convert the state to the appropriate type.", "Step 1: The definition `coerce_to_mb_state` is about converting a state of type `state (| a, () |)` to a mutable buffer state of type `mb_state_32 a`.\nStep 2: The implementation will use the `Lib.IntVector.reveal_vec_1` function to convert the state to the appropriate vector type and then return the mutable buffer state.", "Step 1: The definition `coerce_to_mb_state` is about converting a state of type `state (| a, () |)` to a mutable buffer state of type `mb_state_32 a`.\nStep 2: The implementation will use the `Lib.IntVector.reveal_vec_1` function to convert the state to the appropriate vector type and then return the resulting mutable buffer state.", "Step 1: The definition `coerce_to_mb_state` is about converting a state of type `state (| a, () |)` to a multi-buffer state of type `mb_state_32 a`.\nStep 2: The implementation involves using the `Lib.IntVector.reveal_vec_1` function to reveal the internal vector representation of the state and then returning it as a multi-buffer state.", "Step 1: The definition `coerce_to_mb_state` is about converting a state of type `state (| a, () |)` to a mutable buffer state of type `mb_state_32 a`.\nStep 2: The implementation involves using the `Lib.IntVector.reveal_vec_1` function to reveal the internal vector representation of the state and then returning it as a mutable buffer state.", "Step 1: The definition `coerce_to_mb_state` is about converting a state of type `state (| a, () |)` into a mutable buffer state of type `mb_state_32 a`.\nStep 2: The implementation involves using the `Lib.IntVector.reveal_vec_1` function to convert the state into the appropriate vector type and then returning the mutable buffer state.", "Step 1: The definition `coerce_to_mb_state` is about converting a state of type `state (| a, () |)` to a mutable buffer state of type `mb_state_32 a`.\nStep 2: The implementation involves using the `Lib.IntVector.reveal_vec_1` function to convert the state to a vector and then returning the mutable buffer state.", "Step 1: The definition `coerce_to_mb_state` is about converting a state of type `state (| a, () |)` to a multi-buffer state of type `mb_state_32 a`.\nStep 2: The implementation will use the `Lib.IntVector.reveal_vec_1` function to extract the underlying vector from the state and then return it as an `mb_state_32 a`.", "Step 1: The definition `coerce_to_mb_state` is about converting a state of type `state (| a, () |)` to a mutable buffer state of type `mb_state_32 a`.\nStep 2: The implementation involves using the `Lib.IntVector.reveal_vec_1` function to convert the state to a vector of words and then returning the mutable buffer state.", "Step 1: The definition `coerce_to_mb_state` is about converting a state of type `state (| a, () |)` to a multi-buffer state of type `mb_state_32 a`.\nStep 2: The implementation involves using the `Lib.IntVector.reveal_vec_1` function to convert the state to the appropriate vector type and then returning the resulting multi-buffer state." ], "generated_solution": [ "let coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a =\n Lib.IntVector.reveal_vec_1 (word_t a);\n b", "let coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a =\n Lib.IntVector.reveal_vec_1 (word_t a);\n b", "let coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a =\n Lib.IntVector.reveal_vec_1 (word_t a);\n b", "let coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a =\n Lib.IntVector.reveal_vec_1 (word_t a);\n b", "let coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a =\n Lib.IntVector.reveal_vec_1 (word_t a);\n b", "let coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a =\n Lib.IntVector.reveal_vec_1 (word_t a);\n b", "let coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a =\n Lib.IntVector.reveal_vec_1 (word_t a);\n b", "let coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a =\n Lib.IntVector.reveal_vec_1 (word_t a);\n b", "let coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a =\n Lib.IntVector.reveal_vec_1 (word_t a);\n b", "let coerce_to_mb_state (a: sha2_alg) (b: state (| a, () |)) : mb_state_32 a =\n Lib.IntVector.reveal_vec_1 (word_t a);\n b" ] }, { "file_name": "Plugins.fst", "name": "Plugins.binders_plugin", "opens_and_abbrevs": [ { "open": "FStar.Tactics.V2" }, { "open": "FStar.Reflection.V2" }, { "open": "FStar.Pervasives" }, { "open": "Prims" }, { "open": "FStar" } ], "vconfig": { "initial_fuel": 2, "max_fuel": 8, "initial_ifuel": 1, "max_ifuel": 2, "detail_errors": false, "detail_hint_replay": false, "no_smt": false, "quake_lo": 1, "quake_hi": 1, "quake_keep": false, "retry": false, "smtencoding_elim_box": false, "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_l_arith_repr": "boxwrap", "smtencoding_valid_intro": true, "smtencoding_valid_elim": false, "tcnorm": true, "no_plugins": false, "no_tactics": false, "z3cliopt": [], "z3smtopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3version": "4.8.5", "trivial_pre_for_unannotated_effectful_fns": true, "reuse_hint_for": null }, "source_type": "val binders_plugin: binders -> binders", "source_definition": "let binders_plugin: binders -> binders = id", "source_range": { "start_line": 45, "start_col": 0, "end_line": 45, "end_col": 43 }, "interleaved": false, "definition": "FStar.Pervasives.id", "effect": "Prims.Tot", "effect_flags": [ "total" ], "mutual_with": [], "premises": [ "FStar.Pervasives.id", "FStar.Tactics.NamedView.binders" ], "proof_features": [], "is_simple_lemma": false, "is_div": false, "is_proof": false, "is_simply_typed": true, "is_type": false, "type": "_: FStar.Tactics.NamedView.binders -> FStar.Tactics.NamedView.binders", "prompt": "let binders_plugin: binders -> binders =\n ", "expected_response": "id", "source": { "project_name": "FStar", "file_name": "examples/native_tactics/Plugins.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git" }, "dependencies": { "source_file": "Plugins.fst", "checked_file": "dataset/Plugins.fst.checked", "interface_file": false, "dependencies": [ "dataset/prims.fst.checked", "dataset/FStar.Tactics.V2.fst.checked", "dataset/FStar.Reflection.V2.fst.checked", "dataset/FStar.Pervasives.Native.fst.checked", "dataset/FStar.Pervasives.fsti.checked" ] }, "definitions_in_context": [ "let int_plugin: int -> int = id", "let bool_plugin: bool -> bool = id", "let unit_plugin: unit -> bool = fun _ -> true", "let string_plugin: string -> string = id", "let term_plugin: term -> term = id", "let binder_plugin: binder -> binder = id" ], "closest": [ "val empty_binders:binders\nlet empty_binders : binders = {\n is_empty = true;\n bind = \"\";\n args = \"\";\n}", "val binding_to_binder (bnd: binding) : binder\nlet binding_to_binder (bnd : binding) : binder =\n {\n ppname = bnd.ppname;\n uniq = bnd.uniq;\n sort = bnd.sort;\n qual = Q_Explicit;\n attrs = []\n }", "val offeredPsks_binders_validator: LL.validator offeredPsks_binders_parser\nlet offeredPsks_binders_validator = LL.validate_synth offeredPsks_binders'_validator synth_offeredPsks_binders ()", "val filter_no_method_binders (bs: binders) : binders\nlet filter_no_method_binders (bs:binders)\n : binders\n = let open FStar.Reflection.V2.TermEq in\n let has_no_method_attr (b:binder) : bool =\n L.existsb (term_eq (`no_method)) b.attrs\n in\n bs |> L.filter (fun b -> not (has_no_method_attr b))", "val offeredPsks_binders'_validator:LL.validator offeredPsks_binders'_parser\nlet offeredPsks_binders'_validator : LL.validator offeredPsks_binders'_parser =\n LL.validate_bounded_vldata_strong 33 65535 (LP.serialize_list _ pskBinderEntry_serializer) (LL.validate_list pskBinderEntry_validator ()) ()", "val offeredPsks_binders_serializer: LP.serializer offeredPsks_binders_parser\nlet offeredPsks_binders_serializer = LP.serialize_synth _ synth_offeredPsks_binders offeredPsks_binders'_serializer synth_offeredPsks_binders_recip ()", "val offeredPsks_binders'_serializer:LP.serializer offeredPsks_binders'_parser\nlet offeredPsks_binders'_serializer : LP.serializer offeredPsks_binders'_parser =\n LP.serialize_bounded_vldata_strong 33 65535 (LP.serialize_list _ pskBinderEntry_serializer)", "val binder_to_binding (b: binder) : binding\nlet binder_to_binding (b : binder) : binding =\n {\n ppname = b.ppname;\n uniq = b.uniq;\n sort = b.sort;\n }", "val freshen_binders (bs: binders) : Tot binders (decreases length bs)\nlet rec freshen_binders (bs:binders) : Tot binders (decreases length bs) =\n match bs with\n | [] -> []\n | b::bs ->\n let b' = freshen_binder b in\n let bs = map (subst_binder_typ [Stubs.Syntax.Syntax.NT (binder_to_namedv b |> FStar.Stubs.Reflection.V2.Builtins.pack_namedv)\n (binder_to_term b')]) bs in\n b' :: freshen_binders bs", "val offeredPsks_binders_parser: LP.parser offeredPsks_binders_parser_kind offeredPsks_binders\nlet offeredPsks_binders_parser = offeredPsks_binders'_parser `LP.parse_synth` synth_offeredPsks_binders", "val push_binder (name typ: string) (b: binders) : binders\nlet push_binder (name: string) (typ: string) (b: binders) : binders = {\n is_empty = false;\n bind = Printf.sprintf \"(%s %s) %s\" name typ b.bind;\n args = Printf.sprintf \" %s%s\" name b.args;\n}", "val binder_argv (b: binder) : Tot argv\nlet binder_argv (b:binder) : Tot argv =\n let q =\n match b.qual with\n | Q_Meta _ -> Q_Implicit\n | q -> q\n in\n (binder_to_term b, q)", "val ss_binder (b:binder) (ss:ss_t) : binder\nlet rec ss_binder (b:binder) (ss:ss_t)\n : Tot binder (decreases L.length ss.l) =\n match ss.l with\n | [] -> b\n | y::tl ->\n let b = subst_binder b [ NT y (Map.sel ss.m y) ] in\n ss_binder b (tail ss)", "val offeredPsks_binders'_jumper:LL.jumper offeredPsks_binders'_parser\nlet offeredPsks_binders'_jumper : LL.jumper offeredPsks_binders'_parser =\n LL.jump_bounded_vldata_strong 33 65535 (LP.serialize_list _ pskBinderEntry_serializer) ()", "val offeredPsks_binders_jumper: LL.jumper offeredPsks_binders_parser\nlet offeredPsks_binders_jumper = LL.jump_synth offeredPsks_binders'_jumper synth_offeredPsks_binders ()", "val offeredPsks_binders'_parser32:LS.parser32 offeredPsks_binders'_parser\nlet offeredPsks_binders'_parser32 : LS.parser32 offeredPsks_binders'_parser =\n LS.parse32_bounded_vldata_strong 33 33ul 65535 65535ul (LP.serialize_list _ pskBinderEntry_serializer) (LS.parse32_list pskBinderEntry_parser32)", "val mk_binder (bv: bv) (sort: typ) : binder\nlet mk_binder (bv : bv) (sort : typ) : binder =\n pack_binder {\n binder_bv=bv;\n binder_qual=Q_Explicit;\n binder_attrs=[];\n binder_sort = sort;\n }", "val collect_binders (until: (term' -> bool)) (t: term) : list binder & term\nlet rec collect_binders (until: term' -> bool) (t:term) : list binder & term =\n if not (until t.t) then [], t\n else (\n match t.t with\n | Tm_ExistsSL _ b body\n | Tm_ForallSL _ b body -> \n let bs, t = collect_binders until body in\n b::bs, t\n | _ -> [], t\n )", "val cur_binders: Prims.unit -> Tac binders\nlet cur_binders () : Tac binders =\n binders_of_env (cur_env ())", "val sk_binder' (acc: binders) (b: binder) : Tac (binders * binder)\nlet rec sk_binder' (acc:binders) (b:binder) : Tac (binders * binder) =\n focus (fun () ->\n try\n apply_lemma (`(sklem0 (`#(binder_to_term b))));\n if ngoals () <> 1 then fail \"no\";\n clear b;\n let bx = forall_intro () in\n let b' = implies_intro () in\n sk_binder' (bx::acc) b' (* We might have introduced a new existential, so possibly recurse *)\n with | _ -> (acc, b) (* If the above failed, just return *)\n )", "val null_binder (t: term) : binder\nlet null_binder (t:term) : binder =\n mk_binder_with_attrs t ppname_default binder_attrs_default", "val offeredPsks_binders'_serializer32:LS.serializer32 offeredPsks_binders'_serializer\nlet offeredPsks_binders'_serializer32 : LS.serializer32 offeredPsks_binders'_serializer =\n LS.serialize32_bounded_vldata_strong 33 65535 (LS.partial_serialize32_list _ pskBinderEntry_serializer pskBinderEntry_serializer32 ())", "val freshen_binder (b: T.binder) : T.binder\nlet freshen_binder (b:T.binder) : T.binder =\n { b with uniq = 10000 + b.uniq\n ; ppname = map_seal b.ppname (fun s -> s ^ \"'\") }", "val gaccessor_offeredPsks_binders : LL.gaccessor offeredPsks_parser offeredPsks_binders_parser clens_offeredPsks_binders\nlet gaccessor_offeredPsks_binders = LL.gaccessor_ext (gaccessor_offeredPsks_offeredPsks' `LL.gaccessor_compose` gaccessor'_offeredPsks_binders) clens_offeredPsks_binders ()", "val binding_to_simple_binder (b: binding) : Tot simple_binder\nlet binding_to_simple_binder (b : binding) : Tot simple_binder =\n {\n ppname = b.ppname;\n uniq = b.uniq;\n sort = b.sort;\n qual = Q_Explicit;\n attrs = [];\n }", "val offeredPsks_binders_parser32: LS.parser32 offeredPsks_binders_parser\nlet offeredPsks_binders_parser32 = LS.parse32_synth' _ synth_offeredPsks_binders offeredPsks_binders'_parser32 ()", "val namedv_to_binder (v: namedv) (sort: term) : binder\nlet namedv_to_binder (v : namedv) (sort : term) : binder =\n {\n uniq = v.uniq;\n sort = sort;\n ppname = v.ppname;\n qual = Q_Explicit;\n attrs = [];\n }", "val clens_offeredPsks_binders:LL.clens offeredPsks offeredPsks_binders\nlet clens_offeredPsks_binders : LL.clens offeredPsks offeredPsks_binders = {\n LL.clens_cond = (fun _ -> True);\n LL.clens_get = (fun x -> x.binders);\n}", "val fresh_binder (t: typ) : Tac simple_binder\nlet fresh_binder (t : typ) : Tac simple_binder =\n let n = fresh () in\n {\n ppname = seal (\"x\" ^ string_of_int n);\n sort = t;\n uniq = n;\n qual = Q_Explicit;\n attrs = [] ;\n }", "val bindersBytes: bs:binders -> b:bytes{length b >= 35 /\\ length b <= 65537}\nlet bindersBytes bs =\n let b = binderListBytes bs in\n Parse.vlbytes2 b", "val binder_sort (b: binder) : Tot typ\nlet binder_sort (b : binder) : Tot typ = b.sort", "val nth_binder (i: int) : Tac binder\nlet nth_binder (i:int) : Tac binder =\n let bs = cur_binders () in\n let k : int = if i >= 0 then i else List.Tot.Base.length bs + i in\n let k : nat = if k < 0 then fail \"not enough binders\" else k in\n match List.Tot.Base.nth bs k with\n | None -> fail \"not enough binders\"\n | Some b -> b", "val binder_to_namedv (b: binder) : Tot namedv\nlet binder_to_namedv (b : binder) : Tot namedv =\n {\n ppname = b.ppname;\n uniq = b.uniq;\n sort = seal b.sort;\n }", "val faithful_binder (b: binder) : Type0\nlet rec faithful t =\n match inspect_ln t with\n | Tv_Var _\n | Tv_BVar _\n | Tv_FVar _\n | Tv_Unknown\n | Tv_Const _ -> True\n\n | Tv_UInst f us ->\n allP t faithful_univ us\n\n | Tv_Unsupp -> False\n | Tv_App h a ->\n faithful h /\\ faithful_arg a\n | Tv_Abs b t ->\n faithful_binder b /\\ faithful t\n | Tv_Arrow b c ->\n faithful_binder b /\\ faithful_comp c\n | Tv_Type u ->\n faithful_univ u\n | Tv_Refine b phi ->\n faithful_binder b\n /\\ faithful phi\n\n | Tv_Uvar n u -> False\n | Tv_Let r ats x e b ->\n faithful_attrs ats\n /\\ faithful_binder x\n /\\ faithful e\n /\\ faithful b\n\n | Tv_Match sc o brs ->\n faithful sc\n /\\ None? o // stopgap\n /\\ allP t faithful_branch brs\n\n | Tv_AscribedT e ta tacopt eq ->\n faithful e\n /\\ faithful ta\n /\\ optP t faithful tacopt\n\n | Tv_AscribedC e c tacopt eq ->\n faithful e\n /\\ faithful_comp c\n /\\ optP t faithful tacopt\n\nand faithful_arg (a : argv) : Type0 =\n faithful (fst a) /\\ faithful_qual (snd a)\n\nand faithful_qual (q:aqualv) : Type0 =\n match q with\n | Q_Implicit -> True\n | Q_Explicit -> True\n | Q_Meta m -> faithful m\n\nand faithful_binder (b:binder) : Type0 =\n match inspect_binder b with\n | {sort=sort; qual=q; attrs=attrs} ->\n faithful sort /\\ faithful_qual q /\\ faithful_attrs attrs\n\nand faithful_branch (b : branch) : Type0 =\n let (p, t) = b in\n faithful_pattern p /\\ faithful t\n\nand faithful_pattern (p : pattern) : Type0 =\n match p with\n | Pat_Constant _ -> True\n | Pat_Cons head univs subpats ->\n optP p (allP p faithful_univ) univs\n /\\ allP p faithful_pattern_arg subpats\n\n (* non-binding bvs are always OK *)\n | Pat_Var _ _ -> True\n | Pat_Dot_Term None -> True\n | Pat_Dot_Term (Some t) -> faithful t\n\nand faithful_pattern_arg (pb : pattern * bool) : Type0 =\n faithful_pattern (fst pb)\n\nand faithful_attrs ats : Type0 =\n allP ats faithful ats\n\nand faithful_comp c =\n match inspect_comp c with\n | C_Total t -> faithful t\n | C_GTotal t -> faithful t\n | C_Lemma pre post pats -> faithful pre /\\ faithful post /\\ faithful pats\n | C_Eff us ef r args decs ->\n allP c faithful_univ us\n /\\ faithful r\n /\\ allP c faithful_arg args\n /\\ allP c faithful decs", "val name_of_binder (b: binder) : Tac string\nlet name_of_binder (b : binder) : Tac string =\n name_of_bv (bv_of_binder b)", "val name_of_binder (b: binder) : Tac string\nlet name_of_binder (b : binder) : Tac string =\n unseal b.ppname", "val bv_of_binder (b: binder) : bv\nlet bv_of_binder (b : binder) : bv = (inspect_binder b).binder_bv", "val sk_binder' (acc: list binding) (b: binding) : Tac (list binding & binding)\nlet rec sk_binder' (acc:list binding) (b:binding) : Tac (list binding & binding) =\n focus (fun () ->\n try\n apply_lemma (`(sklem0 (`#b)));\n if ngoals () <> 1 then fail \"no\";\n clear b;\n let bx = forall_intro () in\n let b' = implies_intro () in\n sk_binder' (bx::acc) b' (* We might have introduced a new existential, so possibly recurse *)\n with | _ -> (acc, b) (* If the above failed, just return *)\n )", "val mk_binder (nm: string) (sort: typ) : simple_binder\nlet mk_binder (nm : string) (sort : typ) : simple_binder =\n let bv : binder_view = {\n ppname = seal nm;\n qual = Q_Explicit;\n attrs = [];\n sort = sort;\n }\n in\n inspect_pack_binder bv;\n pack_binder bv", "val type_of_binder (b: binder) : typ\nlet type_of_binder (b : binder) : typ =\n (inspect_binder b).binder_sort", "val type_of_binder (b: binder) : typ\nlet type_of_binder (b : binder) : typ =\n (inspect_binder b).sort", "val offeredPsks_binders_serializer32: LS.serializer32 offeredPsks_binders_serializer\nlet offeredPsks_binders_serializer32 = LS.serialize32_synth' _ synth_offeredPsks_binders _ offeredPsks_binders'_serializer32 synth_offeredPsks_binders_recip ()", "val mk_binder_ppname (binder_ty: term) (binder_ppname: ppname) : binder\nlet mk_binder_ppname (binder_ty:term) (binder_ppname:ppname) : binder =\n mk_binder_with_attrs binder_ty binder_ppname binder_attrs_default", "val app_binders (t: term) (bs: list binder) : Tac term\nlet app_binders (t:term) (bs:list binder) : Tac term =\n mk_e_app t (List.Tot.map binder_to_term bs)", "val mk_binder (s: string) (r: range) (t: term) : binder\nlet mk_binder (s:string) (r:range) (t:term) : binder =\n mk_binder_with_attrs t (mk_ppname (RT.seal_pp_name s) r) binder_attrs_default", "val binder_sort (b: binder) : Tac typ\nlet binder_sort (b : binder) : Tac typ =\n (inspect_binder b).binder_sort", "val offeredPsks_binders'_size32:LSZ.size32 offeredPsks_binders'_serializer\nlet offeredPsks_binders'_size32 : LSZ.size32 offeredPsks_binders'_serializer =\n LSZ.size32_bounded_vldata_strong 33 65535 (LSZ.size32_list pskBinderEntry_size32 ()) 2ul", "val close_binder (b: binder) : R.binder\nlet close_binder (b : binder) : R.binder =\n pack_binder {\n sort = b.sort;\n qual = b.qual;\n ppname = b.ppname;\n attrs = b.attrs;\n }", "val bindings (g:env) : env_bindings\nlet bindings g = g.bs", "val type_of_named_binder (nb: binder) : term\nlet type_of_named_binder (nb : binder) : term =\n nb.sort", "val binder_to_term (b: binder) : Tot term\nlet binder_to_term (b:binder) : Tot term =\n pack (Tv_Var (binder_to_namedv b))", "val binder_to_term (b: binder) : Tot term\nlet binder_to_term (b : binder) : Tot term =\n pack (Tv_Var (binder_to_namedv b))", "val elab_b (qbv: option qualifier & binder & bv) : Tot Tactics.NamedView.binder\nlet elab_b (qbv : option qualifier & binder & bv) : Tot Tactics.NamedView.binder =\n let q, b, bv = qbv in\n {\n uniq = bv.bv_index;\n ppname = b.binder_ppname.name;\n sort = elab_term b.binder_ty;\n qual = elab_qual q;\n attrs = [];\n }", "val accessor'_offeredPsks_binders:LL.accessor gaccessor'_offeredPsks_binders\nlet accessor'_offeredPsks_binders : LL.accessor gaccessor'_offeredPsks_binders = (LL.accessor_then_snd (LL.accessor_id offeredPsks'_parser) offeredPsks_identities_jumper)", "val binder_to_term (b: binder) : Tac term\nlet binder_to_term (b : binder) : Tac term =\n let bview = inspect_binder b in\n bv_to_term bview.binder_bv", "val open_binder (b: R.binder) : Tac binder\nlet open_binder (b : R.binder) : Tac binder =\n let n = fresh () in\n let bv = inspect_binder b in\n {\n uniq = n;\n sort = bv.sort;\n ppname = bv.ppname;\n qual = bv.qual;\n attrs = bv.attrs;\n }", "val parseBinderList (b: bytes{2 <= length b}) : result binders\nlet parseBinderList (b:bytes{2 <= length b}) : result binders =\n if length b < 2 then\n error \"pskBinderList not enough bytes to read length header\"\n else\n match vlparse 2 b with\n | Correct b ->\n begin\n match parseBinderList_aux b [] with\n | Correct bs ->\n let len = List.Tot.length bs in\n if 0 < len && len < 255 then\n Correct bs\n else\n error \"none or too many binders\"\n | Error z -> Error z\n end\n | Error z -> error \"parseBinderList\"", "val accessor_offeredPsks_binders : LL.accessor gaccessor_offeredPsks_binders\nlet accessor_offeredPsks_binders = LL.accessor_ext (LL.accessor_compose accessor_offeredPsks_offeredPsks' accessor'_offeredPsks_binders ()) clens_offeredPsks_binders ()", "val r_binder_to_namedv (b: binder) : R.namedv\nlet r_binder_to_namedv (b : binder) : R.namedv =\n pack_namedv {\n uniq = b.uniq;\n sort = seal b.sort;\n ppname = b.ppname;\n }", "val __binding_to_binder (bnd: binding) (b: R.binder) : binder\nlet __binding_to_binder (bnd : binding) (b : R.binder) : binder =\n {\n ppname = bnd.ppname;\n uniq = bnd.uniq;\n sort = bnd.sort;\n qual = (inspect_binder b).qual;\n attrs = (inspect_binder b).attrs;\n }", "val pskBinderEntry_serializer: LP.serializer pskBinderEntry_parser\nlet pskBinderEntry_serializer = LP.serialize_bounded_vlbytes 32 255", "val Pulse.Syntax.Naming.close_binder = b: Pulse.Syntax.Base.binder -> v: Pulse.Syntax.Base.var -> i: Prims.nat -> Pulse.Syntax.Base.binder\nlet close_binder b v i =\r\n subst_binder b [ ND v i ]", "val Pulse.Checker.default_binder_annot = Pulse.Syntax.Base.binder\nlet default_binder_annot = mk_binder_ppname tm_unknown ppname_default", "val Pulse.Syntax.Base.as_binder = t: Pulse.Syntax.Base.term -> Pulse.Syntax.Base.binder\nlet as_binder (t:term) = null_binder t", "val fresh_binder (e: env) (basename: string) (ty: typ) : Tac binder\nlet fresh_binder (e : env) (basename : string) (ty : typ) : Tac binder =\n let bv = fresh_bv e basename in\n mk_binder bv ty", "val pskBinderEntry_validator: LL.validator pskBinderEntry_parser\nlet pskBinderEntry_validator = LL.validate_bounded_vlbytes 32 255", "val on_sort_binder (f: (term -> Tac unit)) (b: binder) : Tac unit\nlet on_sort_binder (f : term -> Tac unit) (b:binder) : Tac unit =\n f b.sort", "val on_sort_binder (f: (term -> Tac term)) (b: binder) : Tac binder\nlet on_sort_binder (f : term -> Tac term) (b:binder) : Tac binder =\n let bview = inspect_binder b in\n let bview = { bview with sort = f bview.sort } in\n pack_binder bview", "val offeredPsks_binders_size32: LSZ.size32 offeredPsks_binders_serializer\nlet offeredPsks_binders_size32 = LSZ.size32_synth' _ synth_offeredPsks_binders _ offeredPsks_binders'_size32 synth_offeredPsks_binders_recip ()", "val nvar_as_binder (x: nvar) (t: term) : binder\nlet nvar_as_binder (x:nvar) (t:term) : binder =\n mk_binder_ppname t (fst x)", "val Pulse.Syntax.Naming.subst_binder = b: Pulse.Syntax.Base.binder -> ss: Pulse.Syntax.Naming.subst -> Pulse.Syntax.Base.binder\nlet subst_binder b ss = \r\n {b with binder_ty=subst_term b.binder_ty ss}", "val name_of_named_binder (nb: binder) : Tac string\nlet name_of_named_binder (nb : binder) : Tac string =\n unseal nb.ppname", "val binder_mk_implicit (b: binder) : binder\nlet binder_mk_implicit (b:binder) : binder =\n let q =\n match b.qual with\n | Q_Explicit -> Q_Implicit\n | q -> q (* keep Q_Meta as it is *)\n in\n { b with qual = q }", "val subst_binder_in_comp : env -> binder -> term -> comp -> Tac comp\nlet subst_binder_in_comp e b t c =\n subst_bv_in_comp e (bv_of_binder b) (binder_sort b) t c", "val mk_binder (pp_name: pp_name_t) (ty: term) (q: aqualv) : binder\nlet mk_binder (pp_name:pp_name_t) (ty:term) (q:aqualv) : binder\n = pack_binder\n { ppname = pp_name;\n qual = q;\n attrs = [];\n sort = ty}", "val compare_binder (b1 b2: binder) : order\nlet compare_binder (b1 b2 : binder) : order =\n let bview1 = inspect_binder b1 in\n let bview2 = inspect_binder b2 in\n compare_bv bview1.binder_bv bview2.binder_bv", "val compare_binder (b1 b2: binder) : order\nlet rec compare_term (s t : term) : Tot order (decreases s) =\n match inspect_ln s, inspect_ln t with\n | Tv_Var sv, Tv_Var tv ->\n compare_namedv sv tv\n\n | Tv_BVar sv, Tv_BVar tv ->\n compare_bv sv tv\n\n | Tv_FVar sv, Tv_FVar tv ->\n compare_fv sv tv\n\n | Tv_UInst sv sus, Tv_UInst tv tus ->\n lex (compare_fv sv tv) (fun _ -> compare_universes sus tus)\n\n | Tv_App h1 a1, Tv_App h2 a2 ->\n lex (compare_term h1 h2) (fun () -> compare_argv a1 a2)\n\n | Tv_Abs b1 e1, Tv_Abs b2 e2 ->\n lex (compare_binder b1 b2) (fun () -> compare_term e1 e2)\n\n | Tv_Refine b1 e1, Tv_Refine b2 e2 ->\n lex (compare_binder b1 b2) (fun () ->\n compare_term e1 e2)\n\n | Tv_Arrow b1 e1, Tv_Arrow b2 e2 ->\n lex (compare_binder b1 b2) (fun () -> compare_comp e1 e2)\n\n | Tv_Type su, Tv_Type tu -> compare_universe su tu\n\n | Tv_Const c1, Tv_Const c2 ->\n compare_const c1 c2\n\n | Tv_Uvar u1 _, Tv_Uvar u2 _->\n compare_int u1 u2\n\n | Tv_Let _r1 _attrs1 b1 t1 t1', Tv_Let _r2 _attrs2 b2 t2 t2' ->\n lex (compare_binder b1 b2) (fun () ->\n lex (compare_term t1 t2) (fun () ->\n compare_term t1' t2'))\n\n | Tv_Match _ _ _, Tv_Match _ _ _ ->\n Eq // TODO\n\n | Tv_AscribedT e1 t1 tac1 _, Tv_AscribedT e2 t2 tac2 _ ->\n lex (compare_term e1 e2) (fun () ->\n lex (compare_term t1 t2) (fun () ->\n match tac1, tac2 with\n | None, None -> Eq\n | None, _ -> Lt\n | _, None -> Gt\n | Some e1, Some e2 -> compare_term e1 e2))\n\n | Tv_AscribedC e1 c1 tac1 _, Tv_AscribedC e2 c2 tac2 _ ->\n lex (compare_term e1 e2) (fun () ->\n lex (compare_comp c1 c2) (fun () ->\n match tac1, tac2 with\n | None, None -> Eq\n | None, _ -> Lt\n | _, None -> Gt\n | Some e1, Some e2 -> compare_term e1 e2))\n\n | Tv_Unknown, Tv_Unknown ->\n Eq\n\n | Tv_Unsupp, Tv_Unsupp ->\n Eq\n\n // From here onward, they must have different constructors. Order them arbitrarily as in the definition.\n | Tv_Var _, _ -> Lt | _, Tv_Var _ -> Gt\n | Tv_BVar _, _ -> Lt | _, Tv_BVar _ -> Gt\n | Tv_FVar _, _ -> Lt | _, Tv_FVar _ -> Gt\n | Tv_UInst _ _, _ -> Lt | _, Tv_UInst _ _ -> Gt\n | Tv_App _ _, _ -> Lt | _, Tv_App _ _ -> Gt\n | Tv_Abs _ _, _ -> Lt | _, Tv_Abs _ _ -> Gt\n | Tv_Arrow _ _, _ -> Lt | _, Tv_Arrow _ _ -> Gt\n | Tv_Type _, _ -> Lt | _, Tv_Type _ -> Gt\n | Tv_Refine _ _ , _ -> Lt | _, Tv_Refine _ _ -> Gt\n | Tv_Const _, _ -> Lt | _, Tv_Const _ -> Gt\n | Tv_Uvar _ _, _ -> Lt | _, Tv_Uvar _ _ -> Gt\n | Tv_Let _ _ _ _ _, _ -> Lt | _, Tv_Let _ _ _ _ _ -> Gt\n | Tv_Match _ _ _, _ -> Lt | _, Tv_Match _ _ _ -> Gt\n | Tv_AscribedT _ _ _ _, _ -> Lt | _, Tv_AscribedT _ _ _ _ -> Gt\n | Tv_AscribedC _ _ _ _, _ -> Lt | _, Tv_AscribedC _ _ _ _ -> Gt\n | Tv_Unknown, _ -> Lt | _, Tv_Unknown -> Gt\n | Tv_Unsupp, _ -> Lt | _, Tv_Unsupp -> Gt\nand compare_term_list (l1 l2:list term) : Tot order (decreases l1) =\n match l1, l2 with\n | [], [] -> Eq\n | [], _ -> Lt\n | _, [] -> Gt\n | hd1::tl1, hd2::tl2 ->\n lex (compare_term hd1 hd2) (fun () -> compare_term_list tl1 tl2)\n\nand compare_argv (a1 a2 : argv) : Tot order (decreases a1) =\n let a1, q1 = a1 in\n let a2, q2 = a2 in\n match q1, q2 with\n (* We should never see Q_Meta here *)\n | Q_Implicit, Q_Explicit -> Lt\n | Q_Explicit, Q_Implicit -> Gt\n | _, _ -> compare_term a1 a2\nand compare_comp (c1 c2 : comp) : Tot order (decreases c1) =\n let cv1 = inspect_comp c1 in\n let cv2 = inspect_comp c2 in\n match cv1, cv2 with\n | C_Total t1, C_Total t2\n\n | C_GTotal t1, C_GTotal t2 -> compare_term t1 t2\n\n | C_Lemma p1 q1 s1, C_Lemma p2 q2 s2 ->\n lex (compare_term p1 p2)\n (fun () ->\n lex (compare_term q1 q2)\n (fun () -> compare_term s1 s2)\n )\n\n | C_Eff us1 eff1 res1 args1 _decrs1,\n C_Eff us2 eff2 res2 args2 _decrs2 ->\n (* This could be more complex, not sure it is worth it *)\n lex (compare_universes us1 us2)\n (fun _ -> lex (compare_name eff1 eff2)\n (fun _ -> compare_term res1 res2))\n\n | C_Total _, _ -> Lt | _, C_Total _ -> Gt\n | C_GTotal _, _ -> Lt | _, C_GTotal _ -> Gt\n | C_Lemma _ _ _, _ -> Lt | _, C_Lemma _ _ _ -> Gt\n | C_Eff _ _ _ _ _, _ -> Lt | _, C_Eff _ _ _ _ _ -> Gt\n\nand compare_binder (b1 b2 : binder) : order =\n let bview1 = inspect_binder b1 in\n let bview2 = inspect_binder b2 in\n compare_term bview1.sort bview2.sort", "val bind : (a:Type) -> (b:Type) ->\n (m:stexnc a) -> (f:a -> stexnc b) -> stexnc b\nlet bind a b m f =\n fun s0 ->\n let r0 = m s0 in\n match r0 with\n | None, (s1, c1) -> None, (s1, c1)\n | Some r, (s1, c1) -> let res, (s, c2) = f r s1\n in res, (s, c1 + c2)", "val bind (a b: Type) (wp_v: w a) (wp_f: (a -> w b)) (v: repr a wp_v) (f: (x: a -> repr b (wp_f x)))\n : repr b (w_bind wp_v wp_f)\nlet bind (a : Type) (b : Type)\n (wp_v : w a) (wp_f: a -> w b)\n (v : repr a wp_v) (f : (x:a -> repr b (wp_f x)))\n : repr b (w_bind wp_v wp_f) =\n let r = m_bind v f in\n (* Proof that stronger holds *)\n calc (<<=) {\n w_bind wp_v wp_f;\n <<= { bind_is_monotonic wp_v (interp v) wp_f (fun x -> interp (f x)) (* from the refinement *) }\n w_bind (interp v) (fun x -> interp (f x));\n <<= { interp_bind v f }\n interp (m_bind v f);\n };\n r", "val close_binders (bs:list binder) (vs:list var { L.length bs == L.length vs })\r\n : list binder\nlet close_binders (bs:list binder) (xs:list var { L.length bs == L.length xs }) =\r\n let rec aux s out (bs:_) (xs:_{ L.length bs == L.length xs}) : Tot (list binder) (decreases bs) = \r\n match bs, xs with\r\n | [], [] -> L.rev out\r\n | b::bs, x::xs ->\r\n let b = { b with binder_ty = subst_term b.binder_ty s } in\r\n let s = ND x 0 :: shift_subst s in\r\n aux s (b::out) bs xs\r\n in\r\n aux [] [] bs xs", "val Pulse.Typing.named_binder = x: Pulse.Syntax.Base.ppname -> t: Pulse.Syntax.Base.term -> Pulse.Syntax.Base.binder\nlet named_binder (x:ppname) (t:term) = mk_binder_ppname t x", "val bindResult: ('a -> Tot (result 'b)) -> result 'a -> Tot (result 'b)\nlet bindResult f r =\n (match r with\n | Error z -> Error z\n | Correct c -> f c)", "val bind (a b s: _) (f: st a s) (g: (a -> st b s)) : st b s\nlet bind a b s (f:st a s) (g:a -> st b s)\n : st b s\n = fun s ->\n let x, s' = f s in\n g x s'", "val freevars_binder (b: binder) : Tot (Set.set var) (decreases b)\nlet rec freevars (e:term)\n : FStar.Set.set var\n = match inspect_ln e with\n | Tv_Uvar _ _ -> Set.complement Set.empty\n \n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unknown \n | Tv_Unsupp\n | Tv_BVar _ -> Set.empty\n\n | Tv_Var x -> Set.singleton (namedv_uniq x)\n \n | Tv_App e1 (e2, _) ->\n Set.union (freevars e1) (freevars e2)\n\n | Tv_Abs b body -> \n Set.union (freevars_binder b) (freevars body)\n\n | Tv_Arrow b c ->\n Set.union (freevars_binder b) (freevars_comp c)\n\n | Tv_Refine b f ->\n freevars (binder_sort b) `Set.union`\n freevars f\n \n | Tv_Let recf attrs b def body ->\n freevars_terms attrs `Set.union`\n freevars (binder_sort b) `Set.union`\n freevars def `Set.union`\n freevars body\n\n | Tv_Match scr ret brs ->\n freevars scr `Set.union`\n freevars_opt ret freevars_match_returns `Set.union`\n freevars_branches brs\n\n | Tv_AscribedT e t tac b ->\n freevars e `Set.union`\n freevars t `Set.union`\n freevars_opt tac freevars\n \n | Tv_AscribedC e c tac b ->\n freevars e `Set.union`\n freevars_comp c `Set.union`\n freevars_opt tac freevars\n\nand freevars_opt (#a:Type0) (o:option a) (f: (x:a { x << o } -> FStar.Set.set var))\n : FStar.Set.set var\n = match o with\n | None -> Set.empty\n | Some x -> f x\n\nand freevars_comp (c:comp)\n : FStar.Set.set var\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t ->\n freevars t\n\n | C_Lemma pre post pats ->\n freevars pre `Set.union`\n freevars post `Set.union`\n freevars pats\n\n | C_Eff us eff_name res args decrs ->\n freevars res `Set.union`\n freevars_args args `Set.union`\n freevars_terms decrs\n\nand freevars_args (ts:list argv)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | (t,q)::ts ->\n freevars t `Set.union`\n freevars_args ts\n\nand freevars_terms (ts:list term)\n : FStar.Set.set var\n = match ts with\n | [] -> Set.empty\n | t::ts ->\n freevars t `Set.union`\n freevars_terms ts\n \nand freevars_binder (b:binder)\n : Tot (Set.set var) (decreases b)\n = let bndr = inspect_binder b in\n freevars bndr.sort `Set.union`\n freevars_terms bndr.attrs \n\nand freevars_pattern (p:pattern) \n : Tot (Set.set var) (decreases p)\n = match p with\n | Pat_Constant _ ->\n Set.empty\n\n | Pat_Cons head univs subpats ->\n freevars_patterns subpats\n \n | Pat_Var bv s -> Set.empty\n\n | Pat_Dot_Term topt ->\n freevars_opt topt freevars\n\nand freevars_patterns (ps:list (pattern & bool))\n : Tot (Set.set var) (decreases ps)\n = match ps with\n | [] -> Set.empty\n | (p, b)::ps ->\n freevars_pattern p `Set.union`\n freevars_patterns ps\n\nand freevars_branch (br:branch)\n : Tot (Set.set var) (decreases br)\n = let p, t = br in\n freevars_pattern p `Set.union`\n freevars t\n\nand freevars_branches (brs:list branch)\n : Tot (Set.set var) (decreases brs)\n = match brs with\n | [] -> Set.empty\n | hd::tl -> freevars_branch hd `Set.union` freevars_branches tl\n \nand freevars_match_returns (m:match_returns_ascription)\n : Tot (Set.set var) (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = freevars_binder b in\n let ret =\n match ret with\n | Inl t -> freevars t\n | Inr c -> freevars_comp c\n in\n let as_ = freevars_opt as_ freevars in\n b `Set.union` ret `Set.union` as_", "val ln'_binder (b: binder) (n: int) : Tot bool (decreases b)\nlet rec ln' (e:term) (n:int)\n : Tot bool (decreases e)\n = match inspect_ln e with\n | Tv_UInst _ _\n | Tv_FVar _\n | Tv_Type _\n | Tv_Const _\n | Tv_Unknown \n | Tv_Unsupp\n | Tv_Var _ -> true\n | Tv_BVar m -> bv_index m <= n\n | Tv_App e1 (e2, _) -> ln' e1 n && ln' e2 n\n | Tv_Abs b body -> \n ln'_binder b n &&\n ln' body (n + 1)\n\n | Tv_Arrow b c ->\n ln'_binder b n &&\n ln'_comp c (n + 1)\n\n | Tv_Refine b f ->\n ln'_binder b n &&\n ln' f (n + 1)\n\n | Tv_Uvar _ _ ->\n false\n \n | Tv_Let recf attrs b def body ->\n ln'_terms attrs n &&\n ln'_binder b n &&\n (if recf then ln' def (n + 1) else ln' def n) &&\n ln' body (n + 1)\n\n | Tv_Match scr ret brs ->\n ln' scr n &&\n (match ret with\n | None -> true\n | Some m -> ln'_match_returns m n) &&\n ln'_branches brs n\n \n | Tv_AscribedT e t tac b ->\n ln' e n &&\n ln' t n &&\n (match tac with\n | None -> true\n | Some tac -> ln' tac n)\n \n | Tv_AscribedC e c tac b ->\n ln' e n &&\n ln'_comp c n &&\n (match tac with\n | None -> true\n | Some tac -> ln' tac n)\n \nand ln'_comp (c:comp) (i:int)\n : Tot bool (decreases c)\n = match inspect_comp c with\n | C_Total t\n | C_GTotal t -> ln' t i\n\n | C_Lemma pre post pats ->\n ln' pre i &&\n ln' post i &&\n ln' pats i\n\n | C_Eff us eff_name res args decrs ->\n ln' res i &&\n ln'_args args i &&\n ln'_terms decrs i\n\nand ln'_args (ts:list argv) (i:int)\n : Tot bool (decreases ts)\n = match ts with\n | [] -> true\n | (t,q)::ts -> \n ln' t i &&\n ln'_args ts i\n\nand ln'_binder (b:binder) (n:int)\n : Tot bool (decreases b)\n = let bndr = inspect_binder b in\n ln' bndr.sort n &&\n ln'_terms bndr.attrs n\n\nand ln'_terms (ts:list term) (n:int)\n : Tot bool (decreases ts)\n = match ts with\n | [] -> true\n | t::ts -> ln' t n && ln'_terms ts n\n\nand ln'_patterns (ps:list (pattern & bool)) (i:int)\n : Tot bool\n (decreases ps)\n = match ps with\n | [] -> true\n | (p, b)::ps ->\n let b0 = ln'_pattern p i in\n let n = binder_offset_pattern p in\n let b1 = ln'_patterns ps (i + n) in\n b0 && b1\n\nand ln'_pattern (p:pattern) (i:int) \n : Tot bool\n (decreases p)\n = match p with\n | Pat_Constant _ -> true\n\n | Pat_Cons head univs subpats ->\n ln'_patterns subpats i\n \n | Pat_Var bv s -> true\n\n | Pat_Dot_Term topt ->\n (match topt with\n | None -> true\n | Some t -> ln' t i)\n \nand ln'_branch (br:branch) (i:int)\n : Tot bool (decreases br)\n = let p, t = br in\n let b = ln'_pattern p i in\n let j = binder_offset_pattern p in\n let b' = ln' t (i + j) in\n b&&b'\n \nand ln'_branches (brs:list branch) (i:int)\n : Tot bool (decreases brs)\n = match brs with\n | [] -> true\n | br::brs -> \n ln'_branch br i &&\n ln'_branches brs i\n \nand ln'_match_returns (m:match_returns_ascription) (i:int)\n : Tot bool (decreases m)\n = let b, (ret, as_, eq) = m in\n let b = ln'_binder b i in\n let ret =\n match ret with\n | Inl t -> ln' t (i + 1)\n | Inr c -> ln'_comp c (i + 1)\n in\n let as_ =\n match as_ with\n | None -> true\n | Some t -> ln' t (i + 1)\n in\n b && ret && as_", "val bind\r\n (#a:Type u#a) (#b:Type u#b)\r\n (#pre1:slprop) (#post1:a -> slprop) (#post2:b -> slprop)\r\n (e1:stt a pre1 post1)\r\n (e2:(x:a -> stt b (post1 x) post2))\r\n: stt b pre1 post2\nlet bind\r\n (#a:Type u#a) (#b:Type u#b)\r\n (#pre1:slprop) (#post1:a -> slprop) (#post2:b -> slprop)\r\n (e1:stt a pre1 post1)\r\n (e2:(x:a -> stt b (post1 x) post2))\r\n: stt b pre1 post2\r\n= fun _ -> Sem.mbind (e1()) (fun x -> e2 x ())", "val bind (a b: Type) (v: repr a) (f: (a -> repr b)) : repr b\nlet bind (a b : Type) (v : repr a) (f : (a -> repr b)) : repr b =\n fun () -> f (v ()) ()", "val bind : (a:Type) -> (b:Type) ->\n (f:exnst a) -> (g:a -> exnst b) -> exnst b\nlet bind a b f g =\n fun s0 ->\n let res = f s0 in\n match res with\n | None -> None\n | Some (ret, s1) -> g ret s1", "val namedv_to_simple_binder (n: namedv) : Tac simple_binder\nlet namedv_to_simple_binder (n : namedv) : Tac simple_binder =\n let nv = inspect_namedv n in\n {\n ppname = nv.ppname;\n uniq = nv.uniq;\n sort = unseal nv.sort; (* GGG USINGSORT *)\n qual = Q_Explicit;\n attrs = [];\n }", "val tcut (t: term) : Tac binder\nlet tcut (t:term) : Tac binder =\n let g = cur_goal () in\n let tt = mk_e_app (`__cut) [t; g] in\n apply tt;\n intro ()", "val bind\n (#s #a: _)\n (#srel: erel s)\n (#arel: erel a)\n (#b: _)\n (#brel: erel b)\n ($f: st srel arel)\n (g: arel ^--> st_rel srel brel)\n : st srel brel\nlet bind #s #a (#srel:erel s) (#arel:erel a) #b (#brel:erel b)\n ($f:st srel arel)\n (g:arel ^--> st_rel srel brel)\n : st srel brel =\n fun s0 ->\n let x, s1 = f s0 in\n g x s1", "val bind (a b: Type) (wp_v: w a) (wp_f: (a -> w b)) (v: repr a wp_v) (f: (x: a -> repr b (wp_f x)))\n : repr b (bind_wp wp_v wp_f)\nlet bind (a b : Type) (wp_v : w a) (wp_f: a -> w b)\n (v : repr a wp_v)\n (f : (x:a -> repr b (wp_f x)))\n: repr b (bind_wp wp_v wp_f)\n= f v", "val bind\n (a b: Type)\n (wp_v: wp a)\n (wp_f: (a -> wp b))\n (v: repr a wp_v)\n (f: (x: a -> repr b (wp_f x)))\n : repr b (bind_wp wp_v wp_f)\nlet bind (a b : Type) (wp_v : wp a) (wp_f: a -> wp b)\n (v : repr a wp_v)\n (f : (x:a -> repr b (wp_f x)))\n: repr b (bind_wp wp_v wp_f)\n= fun p _ -> let x = v (fun x -> wp_f x p) () in\n f x p ()", "val bind\n (a b: Type)\n (wp_v: wp a)\n (wp_f: (a -> wp b))\n (v: repr a wp_v)\n (f: (x: a -> repr b (wp_f x)))\n : repr b (bind_wp wp_v wp_f)\nlet bind (a b : Type) (wp_v : wp a) (wp_f: a -> wp b)\n (v : repr a wp_v)\n (f : (x:a -> repr b (wp_f x)))\n: repr b (bind_wp wp_v wp_f)\n= fun p _ -> let x = v (fun x -> wp_f x p) () in\n f x p ()", "val bind\n (a b: Type)\n (st: Type0)\n (wp_c: wp st a)\n (wp_f: (a -> wp st b))\n (c: repr a st wp_c)\n (f: (x: a -> repr b st (wp_f x)))\n : repr b st (bind_wp wp_c wp_f)\nlet bind (a:Type) (b:Type) (st:Type0)\n (wp_c : wp st a)\n (wp_f : a -> wp st b)\n (c : repr a st wp_c)\n (f : (x:a -> repr b st (wp_f x)))\n: repr b st (bind_wp wp_c wp_f)\n= fun s0 -> let (y, s1) = c s0 in\n f y s1", "val bind\n (a b: Type)\n (st: Type0)\n (wp_c: wp st a)\n (wp_f: (a -> wp st b))\n (c: repr a st wp_c)\n (f: (x: a -> repr b st (wp_f x)))\n : repr b st (bind_wp wp_c wp_f)\nlet bind (a:Type) (b:Type) (st:Type0)\n (wp_c : wp st a)\n (wp_f : a -> wp st b)\n (c : repr a st wp_c)\n (f : (x:a -> repr b st (wp_f x)))\n: repr b st (bind_wp wp_c wp_f)\n= fun s0 ->\n //let (y, s1) = c s0 in\n //f y s1\n // GM: argh! using the match above introduces noise in the VC, a true precondition\n // that becomes a pain since we don't have monotonicity nor even extensionality\n let r = c s0 in\n f (fst r) (snd r)", "val bind\n (a b: Type)\n (st: Type0)\n (wp_c: wp st a)\n (wp_f: (a -> wp st b))\n (c: repr a st wp_c)\n (f: (x: a -> repr b st (wp_f x)))\n : repr b st (bind_wp wp_c wp_f)\nlet bind (a:Type) (b:Type) (st:Type0)\n (wp_c : wp st a)\n (wp_f : a -> wp st b)\n (c : repr a st wp_c)\n (f : (x:a -> repr b st (wp_f x)))\n: repr b st (bind_wp wp_c wp_f)\n by (explode ();\n let w = nth_var 3 in\n apply_lemma (`(wp_squash_lem (`#(binding_to_term w))));\n dump \"\")\n= fun s0 ->\n let (y, s1) = c s0 in\n f y s1", "val bind\n (a b: Type)\n (st: Type0)\n (wp_c: wp st a)\n (wp_f: (a -> wp st b))\n (c: repr a st wp_c)\n (f: (x: a -> repr b st (wp_f x)))\n : repr b st (bind_wp wp_c wp_f)\nlet bind (a:Type) (b:Type) (st:Type0)\n (wp_c : wp st a)\n (wp_f : a -> wp st b)\n (c : repr a st wp_c)\n (f : (x:a -> repr b st (wp_f x)))\n : repr b st (bind_wp wp_c wp_f)\n = fun s0 -> let (y, s1) = c s0 in\n f y s1", "val bind (a b: Type) (i: idx) (c: m a i) (f: (a -> m b i)) : m b i\nlet bind (a b : Type) (i:idx) (c : m a i) (f : a -> m b i) : m b i =\n match i with\n | T -> t_bind #a #b c f\n | D -> coerce (d_bind #a #b c f) // GM: wow... still needs a coerce, how can that be?\n | G -> g_bind #a #b c f", "val eq_binder (b0 b1: binder) : b: bool{b <==> (b0 == b1)}\nlet eq_binder (b0 b1:binder) : b:bool { b <==> (b0 == b1) } =\n eq_tm b0.binder_ty b1.binder_ty" ], "closest_src": [ { "project_name": "everparse", "file_name": "Z3TestGen.fst", "name": "Z3TestGen.empty_binders" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fsti", "name": "FStar.Tactics.NamedView.binding_to_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders_validator" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Typeclasses.fst", "name": "FStar.Tactics.Typeclasses.filter_no_method_binders" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders'_validator" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders_serializer" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders'_serializer" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fsti", "name": "FStar.Tactics.NamedView.binder_to_binding" }, { "project_name": "steel", "file_name": "Pulse.Recursion.fst", "name": "Pulse.Recursion.freshen_binders" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders_parser" }, { "project_name": "everparse", "file_name": "Z3TestGen.fst", "name": "Z3TestGen.push_binder" }, { "project_name": "FStar", "file_name": "FStar.Tactics.MkProjectors.fst", "name": "FStar.Tactics.MkProjectors.binder_argv" }, { "project_name": "steel", "file_name": "Pulse.Checker.Prover.Substs.fst", "name": "Pulse.Checker.Prover.Substs.ss_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders'_jumper" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders_jumper" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders'_parser32" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Derived.fst", "name": "FStar.Reflection.V1.Derived.mk_binder" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Printer.fst", "name": "Pulse.Syntax.Printer.collect_binders" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.cur_binders" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Logic.fst", "name": "FStar.Tactics.V1.Logic.sk_binder'" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.null_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders'_serializer32" }, { "project_name": "steel", "file_name": "Pulse.Recursion.fst", "name": "Pulse.Recursion.freshen_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks.fst", "name": "MiTLS.Parsers.OfferedPsks.gaccessor_offeredPsks_binders" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.binding_to_simple_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders_parser32" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fsti", "name": "FStar.Tactics.NamedView.namedv_to_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks.fsti", "name": "MiTLS.Parsers.OfferedPsks.clens_offeredPsks_binders" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.fresh_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Extensions.fst", "name": "MiTLS.Extensions.bindersBytes" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.binder_sort" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.nth_binder" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.SyntaxCoercions.fst", "name": "FStar.Tactics.V2.SyntaxCoercions.binder_to_namedv" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.TermEq.fst", "name": "FStar.Reflection.V2.TermEq.faithful_binder" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.name_of_binder" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.name_of_binder" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Derived.fst", "name": "FStar.Reflection.V1.Derived.bv_of_binder" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Logic.fst", "name": "FStar.Tactics.V2.Logic.sk_binder'" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Derived.fst", "name": "FStar.Reflection.V2.Derived.mk_binder" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Derived.fst", "name": "FStar.Reflection.V1.Derived.type_of_binder" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Derived.fst", "name": "FStar.Reflection.V2.Derived.type_of_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders_serializer32" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.mk_binder_ppname" }, { "project_name": "FStar", "file_name": "Param.fst", "name": "Param.app_binders" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.mk_binder" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.binder_sort" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders'_size32" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.close_binder" }, { "project_name": "steel", "file_name": "Pulse.Typing.Env.fst", "name": "Pulse.Typing.Env.bindings" }, { "project_name": "FStar", "file_name": "FStar.Tactics.PatternMatching.fst", "name": "FStar.Tactics.PatternMatching.type_of_named_binder" }, { "project_name": "FStar", "file_name": "FStar.Tactics.MkProjectors.fst", "name": "FStar.Tactics.MkProjectors.binder_to_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.SyntaxCoercions.fst", "name": "FStar.Tactics.V2.SyntaxCoercions.binder_to_term" }, { "project_name": "steel", "file_name": "Pulse.Recursion.fst", "name": "Pulse.Recursion.elab_b" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks.fst", "name": "MiTLS.Parsers.OfferedPsks.accessor'_offeredPsks_binders" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.binder_to_term" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.open_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Extensions.fst", "name": "MiTLS.Extensions.parseBinderList" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks.fst", "name": "MiTLS.Parsers.OfferedPsks.accessor_offeredPsks_binders" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.r_binder_to_namedv" }, { "project_name": "FStar", "file_name": "FStar.Tactics.NamedView.fst", "name": "FStar.Tactics.NamedView.__binding_to_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.PskBinderEntry.fst", "name": "MiTLS.Parsers.PskBinderEntry.pskBinderEntry_serializer" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.close_binder" }, { "project_name": "steel", "file_name": "Pulse.Checker.fst", "name": "Pulse.Checker.default_binder_annot" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fsti", "name": "Pulse.Syntax.Base.as_binder" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.Base.fst", "name": "FStar.InteractiveHelpers.Base.fresh_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.PskBinderEntry.fst", "name": "MiTLS.Parsers.PskBinderEntry.pskBinderEntry_validator" }, { "project_name": "steel", "file_name": "Steel.Effect.Common.fsti", "name": "Steel.Effect.Common.on_sort_binder" }, { "project_name": "FStar", "file_name": "FStar.Tactics.Visit.fst", "name": "FStar.Tactics.Visit.on_sort_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.Parsers.OfferedPsks_binders.fst", "name": "MiTLS.Parsers.OfferedPsks_binders.offeredPsks_binders_size32" }, { "project_name": "steel", "file_name": "Pulse.Typing.Combinators.fsti", "name": "Pulse.Typing.Combinators.nvar_as_binder" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fsti", "name": "Pulse.Syntax.Naming.subst_binder" }, { "project_name": "FStar", "file_name": "FStar.Tactics.PatternMatching.fst", "name": "FStar.Tactics.PatternMatching.name_of_named_binder" }, { "project_name": "FStar", "file_name": "FStar.Tactics.MkProjectors.fst", "name": "FStar.Tactics.MkProjectors.binder_mk_implicit" }, { "project_name": "FStar", "file_name": "FStar.InteractiveHelpers.ExploreTerm.fst", "name": "FStar.InteractiveHelpers.ExploreTerm.subst_binder_in_comp" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.mk_binder" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V1.Compare.fst", "name": "FStar.Reflection.V1.Compare.compare_binder" }, { "project_name": "FStar", "file_name": "FStar.Reflection.V2.Compare.fst", "name": "FStar.Reflection.V2.Compare.compare_binder" }, { "project_name": "FStar", "file_name": "FStar.DM4F.StExnC.fst", "name": "FStar.DM4F.StExnC.bind" }, { "project_name": "FStar", "file_name": "GenericTotalDM4A.fst", "name": "GenericTotalDM4A.bind" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Naming.fst", "name": "Pulse.Syntax.Naming.close_binders" }, { "project_name": "steel", "file_name": "Pulse.Typing.fst", "name": "Pulse.Typing.named_binder" }, { "project_name": "mitls-fstar", "file_name": "MiTLS.TLSError.fst", "name": "MiTLS.TLSError.bindResult" }, { "project_name": "FStar", "file_name": "OPLSS2021.BasicState.fst", "name": "OPLSS2021.BasicState.bind" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.freevars_binder" }, { "project_name": "FStar", "file_name": "FStar.Reflection.Typing.fsti", "name": "FStar.Reflection.Typing.ln'_binder" }, { "project_name": "steel", "file_name": "PulseCore.InstantiatedSemantics.fst", "name": "PulseCore.InstantiatedSemantics.bind" }, { "project_name": "FStar", "file_name": "DivAction.fst", "name": "DivAction.bind" }, { "project_name": "FStar", "file_name": "FStar.DM4F.ExnSt.fst", "name": "FStar.DM4F.ExnSt.bind" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V2.Derived.fst", "name": "FStar.Tactics.V2.Derived.namedv_to_simple_binder" }, { "project_name": "FStar", "file_name": "FStar.Tactics.V1.Derived.fst", "name": "FStar.Tactics.V1.Derived.tcut" }, { "project_name": "FStar", "file_name": "Setoids.fst", "name": "Setoids.bind" }, { "project_name": "FStar", "file_name": "ID3.fst", "name": "ID3.bind" }, { "project_name": "FStar", "file_name": "ID1.fst", "name": "ID1.bind" }, { "project_name": "FStar", "file_name": "ID5.fst", "name": "ID5.bind" }, { "project_name": "FStar", "file_name": "DM4F.fst", "name": "DM4F.bind" }, { "project_name": "FStar", "file_name": "DM4F_layered5.fst", "name": "DM4F_layered5.bind" }, { "project_name": "FStar", "file_name": "DM4F_layered.fst", "name": "DM4F_layered.bind" }, { "project_name": "FStar", "file_name": "OPLSS2021.DijkstraMonads.fst", "name": "OPLSS2021.DijkstraMonads.bind" }, { "project_name": "FStar", "file_name": "GT.fst", "name": "GT.bind" }, { "project_name": "steel", "file_name": "Pulse.Syntax.Base.fst", "name": "Pulse.Syntax.Base.eq_binder" } ], "selected_premises": [ "FStar.Pervasives.Native.fst", "FStar.Pervasives.Native.snd", "FStar.Pervasives.reveal_opaque", "FStar.Pervasives.dfst", "FStar.Pervasives.dsnd", "Plugins.binder_plugin", "Plugins.string_plugin", "Plugins.unit_plugin", "Plugins.term_plugin", "FStar.Pervasives.ex_pre", "FStar.Pervasives.st_post_h", "FStar.Pervasives.id", "FStar.Pervasives.pure_bind_wp", "Plugins.bool_plugin", "FStar.Pervasives.all_post_h", "Prims.pow2", "FStar.Pervasives.ex_post'", "FStar.Pervasives.ex_bind_wp", "FStar.Pervasives.all_post_h'", "FStar.Pervasives.ex_post", "FStar.Pervasives.all_bind_wp", "FStar.Pervasives.st_pre_h", "FStar.Pervasives.ex_stronger", "FStar.Pervasives.pure_close_wp", "FStar.Pervasives.st_bind_wp", "Prims.abs", "Prims.pure_post'", "FStar.Pervasives.ex_wp", "FStar.Pervasives.all_close_wp", "FStar.Pervasives.ex_close_wp", "FStar.Pervasives.st_post_h'", "FStar.Pervasives.st_stronger", "FStar.Pervasives.all_pre_h", "FStar.Pervasives.st_close_wp", "Prims.__cache_version_number__", "FStar.Pervasives.ex_return", "FStar.Pervasives.all_return", "Plugins.int_plugin", "FStar.Pervasives.st_return", "FStar.Pervasives.all_wp_h", "FStar.Pervasives.pure_ite_wp", "Prims.pure_wp_monotonic", "FStar.Pervasives.all_stronger", "FStar.Pervasives.ex_trivial", "FStar.Pervasives.st_wp_h", "Prims.subtype_of", "FStar.Pervasives.pure_null_wp", "FStar.Pervasives.all_ite_wp", "Prims.pure_stronger", "Prims.min", "FStar.Pervasives.st_ite_wp", "FStar.Pervasives.div_hoare_to_wp", "FStar.Pervasives.all_trivial", "Prims.pure_wp'", "FStar.Pervasives.coerce_eq", "Prims.pure_trivial", "Prims.pure_wp_monotonic0", "Prims.purewp_id", "FStar.Pervasives.trivial_pure_post", "Prims.pure_wp", "Prims.returnM", "FStar.Pervasives.st_trivial", "Prims.pure_post", "FStar.Pervasives.ex_if_then_else", "Prims.as_requires", "FStar.Pervasives.st_if_then_else", "FStar.Pervasives.all_if_then_else", "FStar.Pervasives.ex_ite_wp", "Prims.l_True", "Prims.pure_pre", "Prims.op_Hat", "FStar.Pervasives.pure_return", "Prims.as_ensures", "FStar.Pervasives.lift_div_exn", "Prims.auto_squash", "Prims.l_False" ], "source_upto_this": "(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule Plugins\n\n(* Tests for generating bindings to native plugins with correct calls to the\n embedding and unembedding functions for the types supported in tactic compilation.\n Tactics should be generated without warnings and compile without errors.\n*)\n\nopen FStar.Reflection.V2\nopen FStar.Tactics.V2\n\n[@@plugin]\nlet int_plugin: int -> int = id\n\n[@@plugin]\nlet bool_plugin: bool -> bool = id\n\n[@@plugin]\nlet unit_plugin: unit -> bool = fun _ -> true\n\n[@@plugin]\nlet string_plugin: string -> string = id\n\n[@@plugin]\nlet term_plugin: term -> term = id\n\n[@@plugin]\nlet binder_plugin: binder -> binder = id\n\n[@@plugin]", "sketch": [ "Step 1: The definition is about creating a plugin function that takes a list of binders and returns the same list of binders.\nStep 2: The implementation of the definition will use the identity function to return the input list of binders as the output.", "Step 1: The definition is about creating a plugin function that takes a list of binders and returns a list of binders.\nStep 2: The implementation will use the identity function, meaning it will return the input list of binders unchanged.", "Step 1: The definition is about creating a plugin function that takes a list of binders and returns the same list of binders.\nStep 2: The implementation of the definition will use the identity function to return the input list of binders as the output.", "Step 1: The definition is about creating a plugin function that takes a list of binders and returns the same list of binders.\nStep 2: The implementation of the definition will use the identity function `id` to return the input list of binders as the output.", "Step 1: The definition is about creating a plugin function that takes a list of binders and returns a list of binders.\nStep 2: The implementation of the definition will use the identity function, meaning it will return the input list of binders as is.", "Step 1: The definition is about creating a plugin that takes a list of binders as input and returns the same list of binders.\nStep 2: The implementation uses the identity function to return the input list of binders unchanged.", "Step 1: The definition is about creating a plugin function that takes a list of binders and returns the same list of binders.\nStep 2: The implementation of the definition will use the identity function to return the input list of binders as the output.", "Step 1: The definition is about creating a plugin function that takes a list of binders and returns the same list of binders.\nStep 2: The implementation of the definition will use the identity function to return the input list of binders as the output.", "Step 1: The definition is about creating a plugin function that takes a list of binders and returns the same list of binders.\nStep 2: The implementation of the definition will use the identity function to return the input list of binders as the output.", "Step 1: The definition is about creating a plugin function that takes a list of binders and returns a list of binders.\nStep 2: The implementation of the definition will use the identity function `id`, meaning it will return the input list of binders as is." ], "generated_solution": [ "let binders_plugin: binders -> binders = id", "let binders_plugin: binders -> binders = id", "let binders_plugin: binders -> binders = id", "let binders_plugin: binders -> binders = id", "let binders_plugin: binders -> binders = id", "let binders_plugin: binders -> binders = id", "let binders_plugin: binders -> binders = id", "let binders_plugin: binders -> binders = id", "let binders_plugin: binders -> binders = id", "let binders_plugin: binders -> binders = id" ] } ]